1,1,1,0,0.0000911,"\int 0 \, dx","Int[0,x]","0","0",1,"0","A",1,1,1,1.000,1,"{8}"
2,1,1,0,0.0000688,"\int 1 \, dx","Int[1,x]","x","x",1,"x","A",1,1,1,1.000,1,"{8}"
3,1,3,0,0.0002996,"\int 5 \, dx","Int[5,x]","5 x","5 x",1,"5*x","A",1,1,1,1.000,1,"{8}"
4,1,3,0,0.0002742,"\int -2 \, dx","Int[-2,x]","-2 x","-2 x",1,"-2*x","A",1,1,1,1.000,1,"{8}"
5,1,5,0,0.0002704,"\int -\frac{3}{2} \, dx","Int[-3/2,x]","-\frac{3 x}{2}","-\frac{3 x}{2}",1,"(-3*x)/2","A",1,1,3,0.3333,1,"{8}"
6,1,3,0,0.0005006,"\int \pi  \, dx","Int[Pi,x]","\pi  x","\pi  x",1,"Pi*x","A",1,1,1,1.000,1,"{8}"
7,1,3,0,0.0003791,"\int a \, dx","Int[a,x]","a x","a x",1,"a*x","A",1,1,1,1.000,1,"{8}"
8,1,4,0,0.0004491,"\int 3 a \, dx","Int[3*a,x]","3 a x","3 a x",1,"3*a*x","A",1,1,3,0.3333,1,"{8}"
9,1,14,0,0.0077652,"\int \frac{\pi }{\sqrt{16-e^2}} \, dx","Int[Pi/Sqrt[16 - E^2],x]","\frac{\pi  x}{\sqrt{16-e^2}}","\frac{\pi  x}{\sqrt{16-e^2}}",1,"(Pi*x)/Sqrt[16 - E^2]","A",1,1,13,0.07692,1,"{8}"
10,1,7,0,0.0004215,"\int x^{100} \, dx","Int[x^100,x]","\frac{x^{101}}{101}","\frac{x^{101}}{101}",1,"x^101/101","A",1,1,3,0.3333,1,"{30}"
11,1,7,0,0.0003908,"\int x^3 \, dx","Int[x^3,x]","\frac{x^4}{4}","\frac{x^4}{4}",1,"x^4/4","A",1,1,3,0.3333,1,"{30}"
12,1,7,0,0.0004105,"\int x^2 \, dx","Int[x^2,x]","\frac{x^3}{3}","\frac{x^3}{3}",1,"x^3/3","A",1,1,3,0.3333,1,"{30}"
13,1,7,0,0.0004007,"\int x \, dx","Int[x,x]","\frac{x^2}{2}","\frac{x^2}{2}",1,"x^2/2","A",1,1,1,1.000,1,"{30}"
14,1,1,0,0.0000875,"\int 1 \, dx","Int[1,x]","x","x",1,"x","A",1,1,1,1.000,1,"{8}"
15,1,2,0,0.0001859,"\int \frac{1}{x} \, dx","Int[x^(-1),x]","\log (x)","\log (x)",1,"Log[x]","A",1,1,3,0.3333,1,"{29}"
16,1,5,0,0.0005682,"\int \frac{1}{x^2} \, dx","Int[x^(-2),x]","-\frac{1}{x}","-\frac{1}{x}",1,"-x^(-1)","A",1,1,3,0.3333,1,"{30}"
17,1,7,0,0.0004021,"\int \frac{1}{x^3} \, dx","Int[x^(-3),x]","-\frac{1}{2 x^2}","-\frac{1}{2 x^2}",1,"-1/(2*x^2)","A",1,1,3,0.3333,1,"{30}"
18,1,7,0,0.0004275,"\int \frac{1}{x^4} \, dx","Int[x^(-4),x]","-\frac{1}{3 x^3}","-\frac{1}{3 x^3}",1,"-1/(3*x^3)","A",1,1,3,0.3333,1,"{30}"
19,1,7,0,0.0004328,"\int \frac{1}{x^{100}} \, dx","Int[x^(-100),x]","-\frac{1}{99 x^{99}}","-\frac{1}{99 x^{99}}",1,"-1/(99*x^99)","A",1,1,3,0.3333,1,"{30}"
20,1,9,0,0.000528,"\int x^{5/2} \, dx","Int[x^(5/2),x]","\frac{2 x^{7/2}}{7}","\frac{2 x^{7/2}}{7}",1,"(2*x^(7/2))/7","A",1,1,5,0.2000,1,"{30}"
21,1,9,0,0.0004273,"\int x^{3/2} \, dx","Int[x^(3/2),x]","\frac{2 x^{5/2}}{5}","\frac{2 x^{5/2}}{5}",1,"(2*x^(5/2))/5","A",1,1,5,0.2000,1,"{30}"
22,1,9,0,0.000424,"\int \sqrt{x} \, dx","Int[Sqrt[x],x]","\frac{2 x^{3/2}}{3}","\frac{2 x^{3/2}}{3}",1,"(2*x^(3/2))/3","A",1,1,5,0.2000,1,"{30}"
23,1,7,0,0.0004059,"\int \frac{1}{\sqrt{x}} \, dx","Int[1/Sqrt[x],x]","2 \sqrt{x}","2 \sqrt{x}",1,"2*Sqrt[x]","A",1,1,5,0.2000,1,"{30}"
24,1,7,0,0.0003881,"\int \frac{1}{x^{3/2}} \, dx","Int[x^(-3/2),x]","-\frac{2}{\sqrt{x}}","-\frac{2}{\sqrt{x}}",1,"-2/Sqrt[x]","A",1,1,5,0.2000,1,"{30}"
25,1,9,0,0.0003914,"\int \frac{1}{x^{5/2}} \, dx","Int[x^(-5/2),x]","-\frac{2}{3 x^{3/2}}","-\frac{2}{3 x^{3/2}}",1,"-2/(3*x^(3/2))","A",1,1,5,0.2000,1,"{30}"
26,1,9,0,0.0006694,"\int x^{5/3} \, dx","Int[x^(5/3),x]","\frac{3 x^{8/3}}{8}","\frac{3 x^{8/3}}{8}",1,"(3*x^(8/3))/8","A",1,1,5,0.2000,1,"{30}"
27,1,9,0,0.0004124,"\int x^{4/3} \, dx","Int[x^(4/3),x]","\frac{3 x^{7/3}}{7}","\frac{3 x^{7/3}}{7}",1,"(3*x^(7/3))/7","A",1,1,5,0.2000,1,"{30}"
28,1,9,0,0.0004024,"\int x^{2/3} \, dx","Int[x^(2/3),x]","\frac{3 x^{5/3}}{5}","\frac{3 x^{5/3}}{5}",1,"(3*x^(5/3))/5","A",1,1,5,0.2000,1,"{30}"
29,1,9,0,0.0004372,"\int \sqrt[3]{x} \, dx","Int[x^(1/3),x]","\frac{3 x^{4/3}}{4}","\frac{3 x^{4/3}}{4}",1,"(3*x^(4/3))/4","A",1,1,5,0.2000,1,"{30}"
30,1,9,0,0.0004063,"\int \frac{1}{\sqrt[3]{x}} \, dx","Int[x^(-1/3),x]","\frac{3 x^{2/3}}{2}","\frac{3 x^{2/3}}{2}",1,"(3*x^(2/3))/2","A",1,1,5,0.2000,1,"{30}"
31,1,7,0,0.0004344,"\int \frac{1}{x^{2/3}} \, dx","Int[x^(-2/3),x]","3 \sqrt[3]{x}","3 \sqrt[3]{x}",1,"3*x^(1/3)","A",1,1,5,0.2000,1,"{30}"
32,1,7,0,0.0004932,"\int \frac{1}{x^{4/3}} \, dx","Int[x^(-4/3),x]","-\frac{3}{\sqrt[3]{x}}","-\frac{3}{\sqrt[3]{x}}",1,"-3/x^(1/3)","A",1,1,5,0.2000,1,"{30}"
33,1,9,0,0.0004151,"\int \frac{1}{x^{5/3}} \, dx","Int[x^(-5/3),x]","-\frac{3}{2 x^{2/3}}","-\frac{3}{2 x^{2/3}}",1,"-3/(2*x^(2/3))","A",1,1,5,0.2000,1,"{30}"
34,1,11,0,0.0020883,"\int x^n \, dx","Int[x^n,x]","\frac{x^{n+1}}{n+1}","\frac{x^{n+1}}{n+1}",1,"x^(1 + n)/(1 + n)","A",1,1,3,0.3333,1,"{30}"
35,1,16,0,0.00327,"\int (b x)^n \, dx","Int[(b*x)^n,x]","\frac{(b x)^{n+1}}{b (n+1)}","\frac{(b x)^{n+1}}{b (n+1)}",1,"(b*x)^(1 + n)/(b*(1 + n))","A",1,1,5,0.2000,1,"{32}"
36,1,23,0,0.0140041,"\int \frac{1}{\sqrt{-a}+e (c+d x)} \, dx","Int[(Sqrt[-a] + e*(c + d*x))^(-1),x]","\frac{\log \left(\sqrt{-a}+c e+d e x\right)}{d e}","\frac{\log \left(\sqrt{-a}+c e+d e x\right)}{d e}",1,"Log[Sqrt[-a] + c*e + d*e*x]/(d*e)","A",2,2,17,0.1176,1,"{33, 31}"
37,1,23,0,0.0118938,"\int (c+d (a+b x))^{5/2} \, dx","Int[(c + d*(a + b*x))^(5/2),x]","\frac{2 (d (a+b x)+c)^{7/2}}{7 b d}","\frac{2 (d (a+b x)+c)^{7/2}}{7 b d}",1,"(2*(c + d*(a + b*x))^(7/2))/(7*b*d)","A",2,2,13,0.1538,1,"{33, 32}"
38,1,23,0,0.0109621,"\int (c+d (a+b x))^{3/2} \, dx","Int[(c + d*(a + b*x))^(3/2),x]","\frac{2 (d (a+b x)+c)^{5/2}}{5 b d}","\frac{2 (d (a+b x)+c)^{5/2}}{5 b d}",1,"(2*(c + d*(a + b*x))^(5/2))/(5*b*d)","A",2,2,13,0.1538,1,"{33, 32}"
39,1,23,0,0.0108698,"\int \sqrt{c+d (a+b x)} \, dx","Int[Sqrt[c + d*(a + b*x)],x]","\frac{2 (d (a+b x)+c)^{3/2}}{3 b d}","\frac{2 (d (a+b x)+c)^{3/2}}{3 b d}",1,"(2*(c + d*(a + b*x))^(3/2))/(3*b*d)","A",2,2,13,0.1538,1,"{33, 32}"
40,1,21,0,0.0103886,"\int \frac{1}{\sqrt{c+d (a+b x)}} \, dx","Int[1/Sqrt[c + d*(a + b*x)],x]","\frac{2 \sqrt{d (a+b x)+c}}{b d}","\frac{2 \sqrt{d (a+b x)+c}}{b d}",1,"(2*Sqrt[c + d*(a + b*x)])/(b*d)","A",2,2,13,0.1538,1,"{33, 32}"
41,1,21,0,0.0105183,"\int \frac{1}{(c+d (a+b x))^{3/2}} \, dx","Int[(c + d*(a + b*x))^(-3/2),x]","-\frac{2}{b d \sqrt{d (a+b x)+c}}","-\frac{2}{b d \sqrt{d (a+b x)+c}}",1,"-2/(b*d*Sqrt[c + d*(a + b*x)])","A",2,2,13,0.1538,1,"{33, 32}"
42,1,23,0,0.0108823,"\int \frac{1}{(c+d (a+b x))^{5/2}} \, dx","Int[(c + d*(a + b*x))^(-5/2),x]","-\frac{2}{3 b d (d (a+b x)+c)^{3/2}}","-\frac{2}{3 b d (d (a+b x)+c)^{3/2}}",1,"-2/(3*b*d*(c + d*(a + b*x))^(3/2))","A",2,2,13,0.1538,1,"{33, 32}"
43,1,17,0,0.0081869,"\int x^3 (a+b x) \, dx","Int[x^3*(a + b*x),x]","\frac{a x^4}{4}+\frac{b x^5}{5}","\frac{a x^4}{4}+\frac{b x^5}{5}",1,"(a*x^4)/4 + (b*x^5)/5","A",2,1,9,0.1111,1,"{43}"
44,1,17,0,0.0067273,"\int x^2 (a+b x) \, dx","Int[x^2*(a + b*x),x]","\frac{a x^3}{3}+\frac{b x^4}{4}","\frac{a x^3}{3}+\frac{b x^4}{4}",1,"(a*x^3)/3 + (b*x^4)/4","A",2,1,9,0.1111,1,"{43}"
45,1,17,0,0.0060435,"\int x (a+b x) \, dx","Int[x*(a + b*x),x]","\frac{a x^2}{2}+\frac{b x^3}{3}","\frac{a x^2}{2}+\frac{b x^3}{3}",1,"(a*x^2)/2 + (b*x^3)/3","A",2,1,7,0.1429,1,"{43}"
46,1,12,0,0.0022218,"\int (a+b x) \, dx","Int[a + b*x,x]","a x+\frac{b x^2}{2}","a x+\frac{b x^2}{2}",1,"a*x + (b*x^2)/2","A",1,0,5,0,1,"{}"
47,1,8,0,0.0030192,"\int \frac{a+b x}{x} \, dx","Int[(a + b*x)/x,x]","a \log (x)+b x","a \log (x)+b x",1,"b*x + a*Log[x]","A",2,1,9,0.1111,1,"{43}"
48,1,11,0,0.0043358,"\int \frac{a+b x}{x^2} \, dx","Int[(a + b*x)/x^2,x]","b \log (x)-\frac{a}{x}","b \log (x)-\frac{a}{x}",1,"-(a/x) + b*Log[x]","A",2,1,9,0.1111,1,"{43}"
49,1,17,0,0.0017435,"\int \frac{a+b x}{x^3} \, dx","Int[(a + b*x)/x^3,x]","-\frac{(a+b x)^2}{2 a x^2}","-\frac{(a+b x)^2}{2 a x^2}",1,"-(a + b*x)^2/(2*a*x^2)","A",1,1,9,0.1111,1,"{37}"
50,1,17,0,0.0047191,"\int \frac{a+b x}{x^4} \, dx","Int[(a + b*x)/x^4,x]","-\frac{a}{3 x^3}-\frac{b}{2 x^2}","-\frac{a}{3 x^3}-\frac{b}{2 x^2}",1,"-a/(3*x^3) - b/(2*x^2)","A",2,1,9,0.1111,1,"{43}"
51,1,17,0,0.0047952,"\int \frac{a+b x}{x^5} \, dx","Int[(a + b*x)/x^5,x]","-\frac{a}{4 x^4}-\frac{b}{3 x^3}","-\frac{a}{4 x^4}-\frac{b}{3 x^3}",1,"-a/(4*x^4) - b/(3*x^3)","A",2,1,9,0.1111,1,"{43}"
52,1,30,0,0.011715,"\int x^3 (a+b x)^2 \, dx","Int[x^3*(a + b*x)^2,x]","\frac{a^2 x^4}{4}+\frac{2}{5} a b x^5+\frac{b^2 x^6}{6}","\frac{a^2 x^4}{4}+\frac{2}{5} a b x^5+\frac{b^2 x^6}{6}",1,"(a^2*x^4)/4 + (2*a*b*x^5)/5 + (b^2*x^6)/6","A",2,1,11,0.09091,1,"{43}"
53,1,30,0,0.0099083,"\int x^2 (a+b x)^2 \, dx","Int[x^2*(a + b*x)^2,x]","\frac{a^2 x^3}{3}+\frac{1}{2} a b x^4+\frac{b^2 x^5}{5}","\frac{a^2 x^3}{3}+\frac{1}{2} a b x^4+\frac{b^2 x^5}{5}",1,"(a^2*x^3)/3 + (a*b*x^4)/2 + (b^2*x^5)/5","A",2,1,11,0.09091,1,"{43}"
54,1,30,0,0.0094348,"\int x (a+b x)^2 \, dx","Int[x*(a + b*x)^2,x]","\frac{a^2 x^2}{2}+\frac{2}{3} a b x^3+\frac{b^2 x^4}{4}","\frac{a^2 x^2}{2}+\frac{2}{3} a b x^3+\frac{b^2 x^4}{4}",1,"(a^2*x^2)/2 + (2*a*b*x^3)/3 + (b^2*x^4)/4","A",2,1,9,0.1111,1,"{43}"
55,1,14,0,0.0014801,"\int (a+b x)^2 \, dx","Int[(a + b*x)^2,x]","\frac{(a+b x)^3}{3 b}","\frac{(a+b x)^3}{3 b}",1,"(a + b*x)^3/(3*b)","A",1,1,7,0.1429,1,"{32}"
56,1,22,0,0.006339,"\int \frac{(a+b x)^2}{x} \, dx","Int[(a + b*x)^2/x,x]","a^2 \log (x)+2 a b x+\frac{b^2 x^2}{2}","a^2 \log (x)+2 a b x+\frac{b^2 x^2}{2}",1,"2*a*b*x + (b^2*x^2)/2 + a^2*Log[x]","A",2,1,11,0.09091,1,"{43}"
57,1,20,0,0.0081317,"\int \frac{(a+b x)^2}{x^2} \, dx","Int[(a + b*x)^2/x^2,x]","-\frac{a^2}{x}+2 a b \log (x)+b^2 x","-\frac{a^2}{x}+2 a b \log (x)+b^2 x",1,"-(a^2/x) + b^2*x + 2*a*b*Log[x]","A",2,1,11,0.09091,1,"{43}"
58,1,24,0,0.0081578,"\int \frac{(a+b x)^2}{x^3} \, dx","Int[(a + b*x)^2/x^3,x]","-\frac{a^2}{2 x^2}-\frac{2 a b}{x}+b^2 \log (x)","-\frac{a^2}{2 x^2}-\frac{2 a b}{x}+b^2 \log (x)",1,"-a^2/(2*x^2) - (2*a*b)/x + b^2*Log[x]","A",2,1,11,0.09091,1,"{43}"
59,1,17,0,0.0015496,"\int \frac{(a+b x)^2}{x^4} \, dx","Int[(a + b*x)^2/x^4,x]","-\frac{(a+b x)^3}{3 a x^3}","-\frac{(a+b x)^3}{3 a x^3}",1,"-(a + b*x)^3/(3*a*x^3)","A",1,1,11,0.09091,1,"{37}"
60,1,30,0,0.0078972,"\int \frac{(a+b x)^2}{x^5} \, dx","Int[(a + b*x)^2/x^5,x]","-\frac{a^2}{4 x^4}-\frac{2 a b}{3 x^3}-\frac{b^2}{2 x^2}","-\frac{a^2}{4 x^4}-\frac{2 a b}{3 x^3}-\frac{b^2}{2 x^2}",1,"-a^2/(4*x^4) - (2*a*b)/(3*x^3) - b^2/(2*x^2)","A",2,1,11,0.09091,1,"{43}"
61,1,30,0,0.0080537,"\int \frac{(a+b x)^2}{x^6} \, dx","Int[(a + b*x)^2/x^6,x]","-\frac{a^2}{5 x^5}-\frac{a b}{2 x^4}-\frac{b^2}{3 x^3}","-\frac{a^2}{5 x^5}-\frac{a b}{2 x^4}-\frac{b^2}{3 x^3}",1,"-a^2/(5*x^5) - (a*b)/(2*x^4) - b^2/(3*x^3)","A",2,1,11,0.09091,1,"{43}"
62,1,30,0,0.0080024,"\int \frac{(a+b x)^2}{x^7} \, dx","Int[(a + b*x)^2/x^7,x]","-\frac{a^2}{6 x^6}-\frac{2 a b}{5 x^5}-\frac{b^2}{4 x^4}","-\frac{a^2}{6 x^6}-\frac{2 a b}{5 x^5}-\frac{b^2}{4 x^4}",1,"-a^2/(6*x^6) - (2*a*b)/(5*x^5) - b^2/(4*x^4)","A",2,1,11,0.09091,1,"{43}"
63,1,30,0,0.0081628,"\int \frac{(a+b x)^2}{x^8} \, dx","Int[(a + b*x)^2/x^8,x]","-\frac{a^2}{7 x^7}-\frac{a b}{3 x^6}-\frac{b^2}{5 x^5}","-\frac{a^2}{7 x^7}-\frac{a b}{3 x^6}-\frac{b^2}{5 x^5}",1,"-a^2/(7*x^7) - (a*b)/(3*x^6) - b^2/(5*x^5)","A",2,1,11,0.09091,1,"{43}"
64,1,43,0,0.0181752,"\int x^4 (a+b x)^3 \, dx","Int[x^4*(a + b*x)^3,x]","\frac{1}{2} a^2 b x^6+\frac{a^3 x^5}{5}+\frac{3}{7} a b^2 x^7+\frac{b^3 x^8}{8}","\frac{1}{2} a^2 b x^6+\frac{a^3 x^5}{5}+\frac{3}{7} a b^2 x^7+\frac{b^3 x^8}{8}",1,"(a^3*x^5)/5 + (a^2*b*x^6)/2 + (3*a*b^2*x^7)/7 + (b^3*x^8)/8","A",2,1,11,0.09091,1,"{43}"
65,1,43,0,0.0161845,"\int x^3 (a+b x)^3 \, dx","Int[x^3*(a + b*x)^3,x]","\frac{3}{5} a^2 b x^5+\frac{a^3 x^4}{4}+\frac{1}{2} a b^2 x^6+\frac{b^3 x^7}{7}","\frac{3}{5} a^2 b x^5+\frac{a^3 x^4}{4}+\frac{1}{2} a b^2 x^6+\frac{b^3 x^7}{7}",1,"(a^3*x^4)/4 + (3*a^2*b*x^5)/5 + (a*b^2*x^6)/2 + (b^3*x^7)/7","A",2,1,11,0.09091,1,"{43}"
66,1,43,0,0.0146646,"\int x^2 (a+b x)^3 \, dx","Int[x^2*(a + b*x)^3,x]","\frac{3}{4} a^2 b x^4+\frac{a^3 x^3}{3}+\frac{3}{5} a b^2 x^5+\frac{b^3 x^6}{6}","\frac{3}{4} a^2 b x^4+\frac{a^3 x^3}{3}+\frac{3}{5} a b^2 x^5+\frac{b^3 x^6}{6}",1,"(a^3*x^3)/3 + (3*a^2*b*x^4)/4 + (3*a*b^2*x^5)/5 + (b^3*x^6)/6","A",2,1,11,0.09091,1,"{43}"
67,1,30,0,0.008693,"\int x (a+b x)^3 \, dx","Int[x*(a + b*x)^3,x]","\frac{(a+b x)^5}{5 b^2}-\frac{a (a+b x)^4}{4 b^2}","\frac{(a+b x)^5}{5 b^2}-\frac{a (a+b x)^4}{4 b^2}",1,"-(a*(a + b*x)^4)/(4*b^2) + (a + b*x)^5/(5*b^2)","A",2,1,9,0.1111,1,"{43}"
68,1,14,0,0.0016024,"\int (a+b x)^3 \, dx","Int[(a + b*x)^3,x]","\frac{(a+b x)^4}{4 b}","\frac{(a+b x)^4}{4 b}",1,"(a + b*x)^4/(4*b)","A",1,1,7,0.1429,1,"{32}"
69,1,35,0,0.0105865,"\int \frac{(a+b x)^3}{x} \, dx","Int[(a + b*x)^3/x,x]","3 a^2 b x+a^3 \log (x)+\frac{3}{2} a b^2 x^2+\frac{b^3 x^3}{3}","3 a^2 b x+a^3 \log (x)+\frac{3}{2} a b^2 x^2+\frac{b^3 x^3}{3}",1,"3*a^2*b*x + (3*a*b^2*x^2)/2 + (b^3*x^3)/3 + a^3*Log[x]","A",2,1,11,0.09091,1,"{43}"
70,1,34,0,0.0132317,"\int \frac{(a+b x)^3}{x^2} \, dx","Int[(a + b*x)^3/x^2,x]","3 a^2 b \log (x)-\frac{a^3}{x}+3 a b^2 x+\frac{b^3 x^2}{2}","3 a^2 b \log (x)-\frac{a^3}{x}+3 a b^2 x+\frac{b^3 x^2}{2}",1,"-(a^3/x) + 3*a*b^2*x + (b^3*x^2)/2 + 3*a^2*b*Log[x]","A",2,1,11,0.09091,1,"{43}"
71,1,33,0,0.0126738,"\int \frac{(a+b x)^3}{x^3} \, dx","Int[(a + b*x)^3/x^3,x]","-\frac{3 a^2 b}{x}-\frac{a^3}{2 x^2}+3 a b^2 \log (x)+b^3 x","-\frac{3 a^2 b}{x}-\frac{a^3}{2 x^2}+3 a b^2 \log (x)+b^3 x",1,"-a^3/(2*x^2) - (3*a^2*b)/x + b^3*x + 3*a*b^2*Log[x]","A",2,1,11,0.09091,1,"{43}"
72,1,37,0,0.0122868,"\int \frac{(a+b x)^3}{x^4} \, dx","Int[(a + b*x)^3/x^4,x]","-\frac{3 a^2 b}{2 x^2}-\frac{a^3}{3 x^3}-\frac{3 a b^2}{x}+b^3 \log (x)","-\frac{3 a^2 b}{2 x^2}-\frac{a^3}{3 x^3}-\frac{3 a b^2}{x}+b^3 \log (x)",1,"-a^3/(3*x^3) - (3*a^2*b)/(2*x^2) - (3*a*b^2)/x + b^3*Log[x]","A",2,1,11,0.09091,1,"{43}"
73,1,17,0,0.0016722,"\int \frac{(a+b x)^3}{x^5} \, dx","Int[(a + b*x)^3/x^5,x]","-\frac{(a+b x)^4}{4 a x^4}","-\frac{(a+b x)^4}{4 a x^4}",1,"-(a + b*x)^4/(4*a*x^4)","A",1,1,11,0.09091,1,"{37}"
74,1,36,0,0.005332,"\int \frac{(a+b x)^3}{x^6} \, dx","Int[(a + b*x)^3/x^6,x]","\frac{b (a+b x)^4}{20 a^2 x^4}-\frac{(a+b x)^4}{5 a x^5}","\frac{b (a+b x)^4}{20 a^2 x^4}-\frac{(a+b x)^4}{5 a x^5}",1,"-(a + b*x)^4/(5*a*x^5) + (b*(a + b*x)^4)/(20*a^2*x^4)","A",2,2,11,0.1818,1,"{45, 37}"
75,1,43,0,0.0126824,"\int \frac{(a+b x)^3}{x^7} \, dx","Int[(a + b*x)^3/x^7,x]","-\frac{3 a^2 b}{5 x^5}-\frac{a^3}{6 x^6}-\frac{3 a b^2}{4 x^4}-\frac{b^3}{3 x^3}","-\frac{3 a^2 b}{5 x^5}-\frac{a^3}{6 x^6}-\frac{3 a b^2}{4 x^4}-\frac{b^3}{3 x^3}",1,"-a^3/(6*x^6) - (3*a^2*b)/(5*x^5) - (3*a*b^2)/(4*x^4) - b^3/(3*x^3)","A",2,1,11,0.09091,1,"{43}"
76,1,43,0,0.0129022,"\int \frac{(a+b x)^3}{x^8} \, dx","Int[(a + b*x)^3/x^8,x]","-\frac{a^2 b}{2 x^6}-\frac{a^3}{7 x^7}-\frac{3 a b^2}{5 x^5}-\frac{b^3}{4 x^4}","-\frac{a^2 b}{2 x^6}-\frac{a^3}{7 x^7}-\frac{3 a b^2}{5 x^5}-\frac{b^3}{4 x^4}",1,"-a^3/(7*x^7) - (a^2*b)/(2*x^6) - (3*a*b^2)/(5*x^5) - b^3/(4*x^4)","A",2,1,11,0.09091,1,"{43}"
77,1,66,0,0.031675,"\int x^6 (a+b x)^5 \, dx","Int[x^6*(a + b*x)^5,x]","a^2 b^3 x^{10}+\frac{10}{9} a^3 b^2 x^9+\frac{5}{8} a^4 b x^8+\frac{a^5 x^7}{7}+\frac{5}{11} a b^4 x^{11}+\frac{b^5 x^{12}}{12}","a^2 b^3 x^{10}+\frac{10}{9} a^3 b^2 x^9+\frac{5}{8} a^4 b x^8+\frac{a^5 x^7}{7}+\frac{5}{11} a b^4 x^{11}+\frac{b^5 x^{12}}{12}",1,"(a^5*x^7)/7 + (5*a^4*b*x^8)/8 + (10*a^3*b^2*x^9)/9 + a^2*b^3*x^10 + (5*a*b^4*x^11)/11 + (b^5*x^12)/12","A",2,1,11,0.09091,1,"{43}"
78,1,69,0,0.0276943,"\int x^5 (a+b x)^5 \, dx","Int[x^5*(a + b*x)^5,x]","\frac{10}{9} a^2 b^3 x^9+\frac{5}{4} a^3 b^2 x^8+\frac{5}{7} a^4 b x^7+\frac{a^5 x^6}{6}+\frac{1}{2} a b^4 x^{10}+\frac{b^5 x^{11}}{11}","\frac{10}{9} a^2 b^3 x^9+\frac{5}{4} a^3 b^2 x^8+\frac{5}{7} a^4 b x^7+\frac{a^5 x^6}{6}+\frac{1}{2} a b^4 x^{10}+\frac{b^5 x^{11}}{11}",1,"(a^5*x^6)/6 + (5*a^4*b*x^7)/7 + (5*a^3*b^2*x^8)/4 + (10*a^2*b^3*x^9)/9 + (a*b^4*x^10)/2 + (b^5*x^11)/11","A",2,1,11,0.09091,1,"{43}"
79,1,69,0,0.0250605,"\int x^4 (a+b x)^5 \, dx","Int[x^4*(a + b*x)^5,x]","\frac{5}{4} a^2 b^3 x^8+\frac{10}{7} a^3 b^2 x^7+\frac{5}{6} a^4 b x^6+\frac{a^5 x^5}{5}+\frac{5}{9} a b^4 x^9+\frac{b^5 x^{10}}{10}","\frac{5}{4} a^2 b^3 x^8+\frac{10}{7} a^3 b^2 x^7+\frac{5}{6} a^4 b x^6+\frac{a^5 x^5}{5}+\frac{5}{9} a b^4 x^9+\frac{b^5 x^{10}}{10}",1,"(a^5*x^5)/5 + (5*a^4*b*x^6)/6 + (10*a^3*b^2*x^7)/7 + (5*a^2*b^3*x^8)/4 + (5*a*b^4*x^9)/9 + (b^5*x^10)/10","A",2,1,11,0.09091,1,"{43}"
80,1,64,0,0.0264511,"\int x^3 (a+b x)^5 \, dx","Int[x^3*(a + b*x)^5,x]","\frac{3 a^2 (a+b x)^7}{7 b^4}-\frac{a^3 (a+b x)^6}{6 b^4}+\frac{(a+b x)^9}{9 b^4}-\frac{3 a (a+b x)^8}{8 b^4}","\frac{3 a^2 (a+b x)^7}{7 b^4}-\frac{a^3 (a+b x)^6}{6 b^4}+\frac{(a+b x)^9}{9 b^4}-\frac{3 a (a+b x)^8}{8 b^4}",1,"-(a^3*(a + b*x)^6)/(6*b^4) + (3*a^2*(a + b*x)^7)/(7*b^4) - (3*a*(a + b*x)^8)/(8*b^4) + (a + b*x)^9/(9*b^4)","A",2,1,11,0.09091,1,"{43}"
81,1,47,0,0.0205076,"\int x^2 (a+b x)^5 \, dx","Int[x^2*(a + b*x)^5,x]","\frac{a^2 (a+b x)^6}{6 b^3}+\frac{(a+b x)^8}{8 b^3}-\frac{2 a (a+b x)^7}{7 b^3}","\frac{a^2 (a+b x)^6}{6 b^3}+\frac{(a+b x)^8}{8 b^3}-\frac{2 a (a+b x)^7}{7 b^3}",1,"(a^2*(a + b*x)^6)/(6*b^3) - (2*a*(a + b*x)^7)/(7*b^3) + (a + b*x)^8/(8*b^3)","A",2,1,11,0.09091,1,"{43}"
82,1,30,0,0.0079793,"\int x (a+b x)^5 \, dx","Int[x*(a + b*x)^5,x]","\frac{(a+b x)^7}{7 b^2}-\frac{a (a+b x)^6}{6 b^2}","\frac{(a+b x)^7}{7 b^2}-\frac{a (a+b x)^6}{6 b^2}",1,"-(a*(a + b*x)^6)/(6*b^2) + (a + b*x)^7/(7*b^2)","A",2,1,9,0.1111,1,"{43}"
83,1,14,0,0.0017074,"\int (a+b x)^5 \, dx","Int[(a + b*x)^5,x]","\frac{(a+b x)^6}{6 b}","\frac{(a+b x)^6}{6 b}",1,"(a + b*x)^6/(6*b)","A",1,1,7,0.1429,1,"{32}"
84,1,59,0,0.0175937,"\int \frac{(a+b x)^5}{x} \, dx","Int[(a + b*x)^5/x,x]","5 a^3 b^2 x^2+\frac{10}{3} a^2 b^3 x^3+5 a^4 b x+a^5 \log (x)+\frac{5}{4} a b^4 x^4+\frac{b^5 x^5}{5}","5 a^3 b^2 x^2+\frac{10}{3} a^2 b^3 x^3+5 a^4 b x+a^5 \log (x)+\frac{5}{4} a b^4 x^4+\frac{b^5 x^5}{5}",1,"5*a^4*b*x + 5*a^3*b^2*x^2 + (10*a^2*b^3*x^3)/3 + (5*a*b^4*x^4)/4 + (b^5*x^5)/5 + a^5*Log[x]","A",2,1,11,0.09091,1,"{43}"
85,1,58,0,0.0207801,"\int \frac{(a+b x)^5}{x^2} \, dx","Int[(a + b*x)^5/x^2,x]","5 a^2 b^3 x^2+10 a^3 b^2 x+5 a^4 b \log (x)-\frac{a^5}{x}+\frac{5}{3} a b^4 x^3+\frac{b^5 x^4}{4}","5 a^2 b^3 x^2+10 a^3 b^2 x+5 a^4 b \log (x)-\frac{a^5}{x}+\frac{5}{3} a b^4 x^3+\frac{b^5 x^4}{4}",1,"-(a^5/x) + 10*a^3*b^2*x + 5*a^2*b^3*x^2 + (5*a*b^4*x^3)/3 + (b^5*x^4)/4 + 5*a^4*b*Log[x]","A",2,1,11,0.09091,1,"{43}"
86,1,60,0,0.0216892,"\int \frac{(a+b x)^5}{x^3} \, dx","Int[(a + b*x)^5/x^3,x]","10 a^2 b^3 x+10 a^3 b^2 \log (x)-\frac{5 a^4 b}{x}-\frac{a^5}{2 x^2}+\frac{5}{2} a b^4 x^2+\frac{b^5 x^3}{3}","10 a^2 b^3 x+10 a^3 b^2 \log (x)-\frac{5 a^4 b}{x}-\frac{a^5}{2 x^2}+\frac{5}{2} a b^4 x^2+\frac{b^5 x^3}{3}",1,"-a^5/(2*x^2) - (5*a^4*b)/x + 10*a^2*b^3*x + (5*a*b^4*x^2)/2 + (b^5*x^3)/3 + 10*a^3*b^2*Log[x]","A",2,1,11,0.09091,1,"{43}"
87,1,60,0,0.0216694,"\int \frac{(a+b x)^5}{x^4} \, dx","Int[(a + b*x)^5/x^4,x]","-\frac{10 a^3 b^2}{x}+10 a^2 b^3 \log (x)-\frac{5 a^4 b}{2 x^2}-\frac{a^5}{3 x^3}+5 a b^4 x+\frac{b^5 x^2}{2}","-\frac{10 a^3 b^2}{x}+10 a^2 b^3 \log (x)-\frac{5 a^4 b}{2 x^2}-\frac{a^5}{3 x^3}+5 a b^4 x+\frac{b^5 x^2}{2}",1,"-a^5/(3*x^3) - (5*a^4*b)/(2*x^2) - (10*a^3*b^2)/x + 5*a*b^4*x + (b^5*x^2)/2 + 10*a^2*b^3*Log[x]","A",2,1,11,0.09091,1,"{43}"
88,1,57,0,0.0201166,"\int \frac{(a+b x)^5}{x^5} \, dx","Int[(a + b*x)^5/x^5,x]","-\frac{5 a^3 b^2}{x^2}-\frac{10 a^2 b^3}{x}-\frac{5 a^4 b}{3 x^3}-\frac{a^5}{4 x^4}+5 a b^4 \log (x)+b^5 x","-\frac{5 a^3 b^2}{x^2}-\frac{10 a^2 b^3}{x}-\frac{5 a^4 b}{3 x^3}-\frac{a^5}{4 x^4}+5 a b^4 \log (x)+b^5 x",1,"-a^5/(4*x^4) - (5*a^4*b)/(3*x^3) - (5*a^3*b^2)/x^2 - (10*a^2*b^3)/x + b^5*x + 5*a*b^4*Log[x]","A",2,1,11,0.09091,1,"{43}"
89,1,61,0,0.0209423,"\int \frac{(a+b x)^5}{x^6} \, dx","Int[(a + b*x)^5/x^6,x]","-\frac{10 a^3 b^2}{3 x^3}-\frac{5 a^2 b^3}{x^2}-\frac{5 a^4 b}{4 x^4}-\frac{a^5}{5 x^5}-\frac{5 a b^4}{x}+b^5 \log (x)","-\frac{10 a^3 b^2}{3 x^3}-\frac{5 a^2 b^3}{x^2}-\frac{5 a^4 b}{4 x^4}-\frac{a^5}{5 x^5}-\frac{5 a b^4}{x}+b^5 \log (x)",1,"-a^5/(5*x^5) - (5*a^4*b)/(4*x^4) - (10*a^3*b^2)/(3*x^3) - (5*a^2*b^3)/x^2 - (5*a*b^4)/x + b^5*Log[x]","A",2,1,11,0.09091,1,"{43}"
90,1,17,0,0.0016275,"\int \frac{(a+b x)^5}{x^7} \, dx","Int[(a + b*x)^5/x^7,x]","-\frac{(a+b x)^6}{6 a x^6}","-\frac{(a+b x)^6}{6 a x^6}",1,"-(a + b*x)^6/(6*a*x^6)","A",1,1,11,0.09091,1,"{37}"
91,1,36,0,0.0045536,"\int \frac{(a+b x)^5}{x^8} \, dx","Int[(a + b*x)^5/x^8,x]","\frac{b (a+b x)^6}{42 a^2 x^6}-\frac{(a+b x)^6}{7 a x^7}","\frac{b (a+b x)^6}{42 a^2 x^6}-\frac{(a+b x)^6}{7 a x^7}",1,"-(a + b*x)^6/(7*a*x^7) + (b*(a + b*x)^6)/(42*a^2*x^6)","A",2,2,11,0.1818,1,"{45, 37}"
92,1,56,0,0.0096565,"\int \frac{(a+b x)^5}{x^9} \, dx","Int[(a + b*x)^5/x^9,x]","-\frac{b^2 (a+b x)^6}{168 a^3 x^6}+\frac{b (a+b x)^6}{28 a^2 x^7}-\frac{(a+b x)^6}{8 a x^8}","-\frac{b^2 (a+b x)^6}{168 a^3 x^6}+\frac{b (a+b x)^6}{28 a^2 x^7}-\frac{(a+b x)^6}{8 a x^8}",1,"-(a + b*x)^6/(8*a*x^8) + (b*(a + b*x)^6)/(28*a^2*x^7) - (b^2*(a + b*x)^6)/(168*a^3*x^6)","A",3,2,11,0.1818,1,"{45, 37}"
93,1,67,0,0.022074,"\int \frac{(a+b x)^5}{x^{10}} \, dx","Int[(a + b*x)^5/x^10,x]","-\frac{10 a^3 b^2}{7 x^7}-\frac{5 a^2 b^3}{3 x^6}-\frac{5 a^4 b}{8 x^8}-\frac{a^5}{9 x^9}-\frac{a b^4}{x^5}-\frac{b^5}{4 x^4}","-\frac{10 a^3 b^2}{7 x^7}-\frac{5 a^2 b^3}{3 x^6}-\frac{5 a^4 b}{8 x^8}-\frac{a^5}{9 x^9}-\frac{a b^4}{x^5}-\frac{b^5}{4 x^4}",1,"-a^5/(9*x^9) - (5*a^4*b)/(8*x^8) - (10*a^3*b^2)/(7*x^7) - (5*a^2*b^3)/(3*x^6) - (a*b^4)/x^5 - b^5/(4*x^4)","A",2,1,11,0.09091,1,"{43}"
94,1,69,0,0.0205153,"\int \frac{(a+b x)^5}{x^{11}} \, dx","Int[(a + b*x)^5/x^11,x]","-\frac{5 a^3 b^2}{4 x^8}-\frac{10 a^2 b^3}{7 x^7}-\frac{5 a^4 b}{9 x^9}-\frac{a^5}{10 x^{10}}-\frac{5 a b^4}{6 x^6}-\frac{b^5}{5 x^5}","-\frac{5 a^3 b^2}{4 x^8}-\frac{10 a^2 b^3}{7 x^7}-\frac{5 a^4 b}{9 x^9}-\frac{a^5}{10 x^{10}}-\frac{5 a b^4}{6 x^6}-\frac{b^5}{5 x^5}",1,"-a^5/(10*x^10) - (5*a^4*b)/(9*x^9) - (5*a^3*b^2)/(4*x^8) - (10*a^2*b^3)/(7*x^7) - (5*a*b^4)/(6*x^6) - b^5/(5*x^5)","A",2,1,11,0.09091,1,"{43}"
95,1,69,0,0.020542,"\int \frac{(a+b x)^5}{x^{12}} \, dx","Int[(a + b*x)^5/x^12,x]","-\frac{10 a^3 b^2}{9 x^9}-\frac{5 a^2 b^3}{4 x^8}-\frac{a^4 b}{2 x^{10}}-\frac{a^5}{11 x^{11}}-\frac{5 a b^4}{7 x^7}-\frac{b^5}{6 x^6}","-\frac{10 a^3 b^2}{9 x^9}-\frac{5 a^2 b^3}{4 x^8}-\frac{a^4 b}{2 x^{10}}-\frac{a^5}{11 x^{11}}-\frac{5 a b^4}{7 x^7}-\frac{b^5}{6 x^6}",1,"-a^5/(11*x^11) - (a^4*b)/(2*x^10) - (10*a^3*b^2)/(9*x^9) - (5*a^2*b^3)/(4*x^8) - (5*a*b^4)/(7*x^7) - b^5/(6*x^6)","A",2,1,11,0.09091,1,"{43}"
96,1,67,0,0.0207173,"\int \frac{(a+b x)^5}{x^{13}} \, dx","Int[(a + b*x)^5/x^13,x]","-\frac{a^3 b^2}{x^{10}}-\frac{10 a^2 b^3}{9 x^9}-\frac{5 a^4 b}{11 x^{11}}-\frac{a^5}{12 x^{12}}-\frac{5 a b^4}{8 x^8}-\frac{b^5}{7 x^7}","-\frac{a^3 b^2}{x^{10}}-\frac{10 a^2 b^3}{9 x^9}-\frac{5 a^4 b}{11 x^{11}}-\frac{a^5}{12 x^{12}}-\frac{5 a b^4}{8 x^8}-\frac{b^5}{7 x^7}",1,"-a^5/(12*x^12) - (5*a^4*b)/(11*x^11) - (a^3*b^2)/x^10 - (10*a^2*b^3)/(9*x^9) - (5*a*b^4)/(8*x^8) - b^5/(7*x^7)","A",2,1,11,0.09091,1,"{43}"
97,1,67,0,0.0215932,"\int \frac{(a+b x)^5}{x^{14}} \, dx","Int[(a + b*x)^5/x^14,x]","-\frac{10 a^3 b^2}{11 x^{11}}-\frac{a^2 b^3}{x^{10}}-\frac{5 a^4 b}{12 x^{12}}-\frac{a^5}{13 x^{13}}-\frac{5 a b^4}{9 x^9}-\frac{b^5}{8 x^8}","-\frac{10 a^3 b^2}{11 x^{11}}-\frac{a^2 b^3}{x^{10}}-\frac{5 a^4 b}{12 x^{12}}-\frac{a^5}{13 x^{13}}-\frac{5 a b^4}{9 x^9}-\frac{b^5}{8 x^8}",1,"-a^5/(13*x^13) - (5*a^4*b)/(12*x^12) - (10*a^3*b^2)/(11*x^11) - (a^2*b^3)/x^10 - (5*a*b^4)/(9*x^9) - b^5/(8*x^8)","A",2,1,11,0.09091,1,"{43}"
98,1,95,0,0.0480825,"\int x^8 (a+b x)^7 \, dx","Int[x^8*(a + b*x)^7,x]","\frac{3}{2} a^2 b^5 x^{14}+\frac{35}{13} a^3 b^4 x^{13}+\frac{35}{12} a^4 b^3 x^{12}+\frac{21}{11} a^5 b^2 x^{11}+\frac{7}{10} a^6 b x^{10}+\frac{a^7 x^9}{9}+\frac{7}{15} a b^6 x^{15}+\frac{b^7 x^{16}}{16}","\frac{3}{2} a^2 b^5 x^{14}+\frac{35}{13} a^3 b^4 x^{13}+\frac{35}{12} a^4 b^3 x^{12}+\frac{21}{11} a^5 b^2 x^{11}+\frac{7}{10} a^6 b x^{10}+\frac{a^7 x^9}{9}+\frac{7}{15} a b^6 x^{15}+\frac{b^7 x^{16}}{16}",1,"(a^7*x^9)/9 + (7*a^6*b*x^10)/10 + (21*a^5*b^2*x^11)/11 + (35*a^4*b^3*x^12)/12 + (35*a^3*b^4*x^13)/13 + (3*a^2*b^5*x^14)/2 + (7*a*b^6*x^15)/15 + (b^7*x^16)/16","A",2,1,11,0.09091,1,"{43}"
99,1,95,0,0.0396834,"\int x^7 (a+b x)^7 \, dx","Int[x^7*(a + b*x)^7,x]","\frac{21}{13} a^2 b^5 x^{13}+\frac{35}{12} a^3 b^4 x^{12}+\frac{35}{11} a^4 b^3 x^{11}+\frac{21}{10} a^5 b^2 x^{10}+\frac{7}{9} a^6 b x^9+\frac{a^7 x^8}{8}+\frac{1}{2} a b^6 x^{14}+\frac{b^7 x^{15}}{15}","\frac{21}{13} a^2 b^5 x^{13}+\frac{35}{12} a^3 b^4 x^{12}+\frac{35}{11} a^4 b^3 x^{11}+\frac{21}{10} a^5 b^2 x^{10}+\frac{7}{9} a^6 b x^9+\frac{a^7 x^8}{8}+\frac{1}{2} a b^6 x^{14}+\frac{b^7 x^{15}}{15}",1,"(a^7*x^8)/8 + (7*a^6*b*x^9)/9 + (21*a^5*b^2*x^10)/10 + (35*a^4*b^3*x^11)/11 + (35*a^3*b^4*x^12)/12 + (21*a^2*b^5*x^13)/13 + (a*b^6*x^14)/2 + (b^7*x^15)/15","A",2,1,11,0.09091,1,"{43}"
100,1,95,0,0.0385288,"\int x^6 (a+b x)^7 \, dx","Int[x^6*(a + b*x)^7,x]","\frac{7}{4} a^2 b^5 x^{12}+\frac{35}{11} a^3 b^4 x^{11}+\frac{7}{2} a^4 b^3 x^{10}+\frac{7}{3} a^5 b^2 x^9+\frac{7}{8} a^6 b x^8+\frac{a^7 x^7}{7}+\frac{7}{13} a b^6 x^{13}+\frac{b^7 x^{14}}{14}","\frac{7}{4} a^2 b^5 x^{12}+\frac{35}{11} a^3 b^4 x^{11}+\frac{7}{2} a^4 b^3 x^{10}+\frac{7}{3} a^5 b^2 x^9+\frac{7}{8} a^6 b x^8+\frac{a^7 x^7}{7}+\frac{7}{13} a b^6 x^{13}+\frac{b^7 x^{14}}{14}",1,"(a^7*x^7)/7 + (7*a^6*b*x^8)/8 + (7*a^5*b^2*x^9)/3 + (7*a^4*b^3*x^10)/2 + (35*a^3*b^4*x^11)/11 + (7*a^2*b^5*x^12)/4 + (7*a*b^6*x^13)/13 + (b^7*x^14)/14","A",2,1,11,0.09091,1,"{43}"
101,1,96,0,0.0402941,"\int x^5 (a+b x)^7 \, dx","Int[x^5*(a + b*x)^7,x]","\frac{10 a^2 (a+b x)^{11}}{11 b^6}-\frac{a^3 (a+b x)^{10}}{b^6}+\frac{5 a^4 (a+b x)^9}{9 b^6}-\frac{a^5 (a+b x)^8}{8 b^6}+\frac{(a+b x)^{13}}{13 b^6}-\frac{5 a (a+b x)^{12}}{12 b^6}","\frac{10 a^2 (a+b x)^{11}}{11 b^6}-\frac{a^3 (a+b x)^{10}}{b^6}+\frac{5 a^4 (a+b x)^9}{9 b^6}-\frac{a^5 (a+b x)^8}{8 b^6}+\frac{(a+b x)^{13}}{13 b^6}-\frac{5 a (a+b x)^{12}}{12 b^6}",1,"-(a^5*(a + b*x)^8)/(8*b^6) + (5*a^4*(a + b*x)^9)/(9*b^6) - (a^3*(a + b*x)^10)/b^6 + (10*a^2*(a + b*x)^11)/(11*b^6) - (5*a*(a + b*x)^12)/(12*b^6) + (a + b*x)^13/(13*b^6)","A",2,1,11,0.09091,1,"{43}"
102,1,81,0,0.0364159,"\int x^4 (a+b x)^7 \, dx","Int[x^4*(a + b*x)^7,x]","\frac{3 a^2 (a+b x)^{10}}{5 b^5}-\frac{4 a^3 (a+b x)^9}{9 b^5}+\frac{a^4 (a+b x)^8}{8 b^5}+\frac{(a+b x)^{12}}{12 b^5}-\frac{4 a (a+b x)^{11}}{11 b^5}","\frac{3 a^2 (a+b x)^{10}}{5 b^5}-\frac{4 a^3 (a+b x)^9}{9 b^5}+\frac{a^4 (a+b x)^8}{8 b^5}+\frac{(a+b x)^{12}}{12 b^5}-\frac{4 a (a+b x)^{11}}{11 b^5}",1,"(a^4*(a + b*x)^8)/(8*b^5) - (4*a^3*(a + b*x)^9)/(9*b^5) + (3*a^2*(a + b*x)^10)/(5*b^5) - (4*a*(a + b*x)^11)/(11*b^5) + (a + b*x)^12/(12*b^5)","A",2,1,11,0.09091,1,"{43}"
103,1,64,0,0.0299538,"\int x^3 (a+b x)^7 \, dx","Int[x^3*(a + b*x)^7,x]","\frac{a^2 (a+b x)^9}{3 b^4}-\frac{a^3 (a+b x)^8}{8 b^4}+\frac{(a+b x)^{11}}{11 b^4}-\frac{3 a (a+b x)^{10}}{10 b^4}","\frac{a^2 (a+b x)^9}{3 b^4}-\frac{a^3 (a+b x)^8}{8 b^4}+\frac{(a+b x)^{11}}{11 b^4}-\frac{3 a (a+b x)^{10}}{10 b^4}",1,"-(a^3*(a + b*x)^8)/(8*b^4) + (a^2*(a + b*x)^9)/(3*b^4) - (3*a*(a + b*x)^10)/(10*b^4) + (a + b*x)^11/(11*b^4)","A",2,1,11,0.09091,1,"{43}"
104,1,47,0,0.0236088,"\int x^2 (a+b x)^7 \, dx","Int[x^2*(a + b*x)^7,x]","\frac{a^2 (a+b x)^8}{8 b^3}+\frac{(a+b x)^{10}}{10 b^3}-\frac{2 a (a+b x)^9}{9 b^3}","\frac{a^2 (a+b x)^8}{8 b^3}+\frac{(a+b x)^{10}}{10 b^3}-\frac{2 a (a+b x)^9}{9 b^3}",1,"(a^2*(a + b*x)^8)/(8*b^3) - (2*a*(a + b*x)^9)/(9*b^3) + (a + b*x)^10/(10*b^3)","A",2,1,11,0.09091,1,"{43}"
105,1,30,0,0.0081933,"\int x (a+b x)^7 \, dx","Int[x*(a + b*x)^7,x]","\frac{(a+b x)^9}{9 b^2}-\frac{a (a+b x)^8}{8 b^2}","\frac{(a+b x)^9}{9 b^2}-\frac{a (a+b x)^8}{8 b^2}",1,"-(a*(a + b*x)^8)/(8*b^2) + (a + b*x)^9/(9*b^2)","A",2,1,9,0.1111,1,"{43}"
106,1,14,0,0.0017025,"\int (a+b x)^7 \, dx","Int[(a + b*x)^7,x]","\frac{(a+b x)^8}{8 b}","\frac{(a+b x)^8}{8 b}",1,"(a + b*x)^8/(8*b)","A",1,1,7,0.1429,1,"{32}"
107,1,87,0,0.0273506,"\int \frac{(a+b x)^7}{x} \, dx","Int[(a + b*x)^7/x,x]","\frac{21}{2} a^5 b^2 x^2+\frac{35}{3} a^4 b^3 x^3+\frac{35}{4} a^3 b^4 x^4+\frac{21}{5} a^2 b^5 x^5+7 a^6 b x+a^7 \log (x)+\frac{7}{6} a b^6 x^6+\frac{b^7 x^7}{7}","\frac{21}{2} a^5 b^2 x^2+\frac{35}{3} a^4 b^3 x^3+\frac{35}{4} a^3 b^4 x^4+\frac{21}{5} a^2 b^5 x^5+7 a^6 b x+a^7 \log (x)+\frac{7}{6} a b^6 x^6+\frac{b^7 x^7}{7}",1,"7*a^6*b*x + (21*a^5*b^2*x^2)/2 + (35*a^4*b^3*x^3)/3 + (35*a^3*b^4*x^4)/4 + (21*a^2*b^5*x^5)/5 + (7*a*b^6*x^6)/6 + (b^7*x^7)/7 + a^7*Log[x]","A",2,1,11,0.09091,1,"{43}"
108,1,86,0,0.0321975,"\int \frac{(a+b x)^7}{x^2} \, dx","Int[(a + b*x)^7/x^2,x]","\frac{35}{2} a^4 b^3 x^2+\frac{35}{3} a^3 b^4 x^3+\frac{21}{4} a^2 b^5 x^4+21 a^5 b^2 x+7 a^6 b \log (x)-\frac{a^7}{x}+\frac{7}{5} a b^6 x^5+\frac{b^7 x^6}{6}","\frac{35}{2} a^4 b^3 x^2+\frac{35}{3} a^3 b^4 x^3+\frac{21}{4} a^2 b^5 x^4+21 a^5 b^2 x+7 a^6 b \log (x)-\frac{a^7}{x}+\frac{7}{5} a b^6 x^5+\frac{b^7 x^6}{6}",1,"-(a^7/x) + 21*a^5*b^2*x + (35*a^4*b^3*x^2)/2 + (35*a^3*b^4*x^3)/3 + (21*a^2*b^5*x^4)/4 + (7*a*b^6*x^5)/5 + (b^7*x^6)/6 + 7*a^6*b*Log[x]","A",2,1,11,0.09091,1,"{43}"
109,1,84,0,0.0327259,"\int \frac{(a+b x)^7}{x^3} \, dx","Int[(a + b*x)^7/x^3,x]","\frac{35}{2} a^3 b^4 x^2+7 a^2 b^5 x^3+35 a^4 b^3 x+21 a^5 b^2 \log (x)-\frac{7 a^6 b}{x}-\frac{a^7}{2 x^2}+\frac{7}{4} a b^6 x^4+\frac{b^7 x^5}{5}","\frac{35}{2} a^3 b^4 x^2+7 a^2 b^5 x^3+35 a^4 b^3 x+21 a^5 b^2 \log (x)-\frac{7 a^6 b}{x}-\frac{a^7}{2 x^2}+\frac{7}{4} a b^6 x^4+\frac{b^7 x^5}{5}",1,"-a^7/(2*x^2) - (7*a^6*b)/x + 35*a^4*b^3*x + (35*a^3*b^4*x^2)/2 + 7*a^2*b^5*x^3 + (7*a*b^6*x^4)/4 + (b^7*x^5)/5 + 21*a^5*b^2*Log[x]","A",2,1,11,0.09091,1,"{43}"
110,1,86,0,0.0316721,"\int \frac{(a+b x)^7}{x^4} \, dx","Int[(a + b*x)^7/x^4,x]","\frac{21}{2} a^2 b^5 x^2-\frac{21 a^5 b^2}{x}+35 a^3 b^4 x+35 a^4 b^3 \log (x)-\frac{7 a^6 b}{2 x^2}-\frac{a^7}{3 x^3}+\frac{7}{3} a b^6 x^3+\frac{b^7 x^4}{4}","\frac{21}{2} a^2 b^5 x^2-\frac{21 a^5 b^2}{x}+35 a^3 b^4 x+35 a^4 b^3 \log (x)-\frac{7 a^6 b}{2 x^2}-\frac{a^7}{3 x^3}+\frac{7}{3} a b^6 x^3+\frac{b^7 x^4}{4}",1,"-a^7/(3*x^3) - (7*a^6*b)/(2*x^2) - (21*a^5*b^2)/x + 35*a^3*b^4*x + (21*a^2*b^5*x^2)/2 + (7*a*b^6*x^3)/3 + (b^7*x^4)/4 + 35*a^4*b^3*Log[x]","A",2,1,11,0.09091,1,"{43}"
111,1,86,0,0.0320514,"\int \frac{(a+b x)^7}{x^5} \, dx","Int[(a + b*x)^7/x^5,x]","-\frac{21 a^5 b^2}{2 x^2}-\frac{35 a^4 b^3}{x}+21 a^2 b^5 x+35 a^3 b^4 \log (x)-\frac{7 a^6 b}{3 x^3}-\frac{a^7}{4 x^4}+\frac{7}{2} a b^6 x^2+\frac{b^7 x^3}{3}","-\frac{21 a^5 b^2}{2 x^2}-\frac{35 a^4 b^3}{x}+21 a^2 b^5 x+35 a^3 b^4 \log (x)-\frac{7 a^6 b}{3 x^3}-\frac{a^7}{4 x^4}+\frac{7}{2} a b^6 x^2+\frac{b^7 x^3}{3}",1,"-a^7/(4*x^4) - (7*a^6*b)/(3*x^3) - (21*a^5*b^2)/(2*x^2) - (35*a^4*b^3)/x + 21*a^2*b^5*x + (7*a*b^6*x^2)/2 + (b^7*x^3)/3 + 35*a^3*b^4*Log[x]","A",2,1,11,0.09091,1,"{43}"
112,1,84,0,0.0321007,"\int \frac{(a+b x)^7}{x^6} \, dx","Int[(a + b*x)^7/x^6,x]","-\frac{7 a^5 b^2}{x^3}-\frac{35 a^4 b^3}{2 x^2}-\frac{35 a^3 b^4}{x}+21 a^2 b^5 \log (x)-\frac{7 a^6 b}{4 x^4}-\frac{a^7}{5 x^5}+7 a b^6 x+\frac{b^7 x^2}{2}","-\frac{7 a^5 b^2}{x^3}-\frac{35 a^4 b^3}{2 x^2}-\frac{35 a^3 b^4}{x}+21 a^2 b^5 \log (x)-\frac{7 a^6 b}{4 x^4}-\frac{a^7}{5 x^5}+7 a b^6 x+\frac{b^7 x^2}{2}",1,"-a^7/(5*x^5) - (7*a^6*b)/(4*x^4) - (7*a^5*b^2)/x^3 - (35*a^4*b^3)/(2*x^2) - (35*a^3*b^4)/x + 7*a*b^6*x + (b^7*x^2)/2 + 21*a^2*b^5*Log[x]","A",2,1,11,0.09091,1,"{43}"
113,1,85,0,0.0313059,"\int \frac{(a+b x)^7}{x^7} \, dx","Int[(a + b*x)^7/x^7,x]","-\frac{21 a^5 b^2}{4 x^4}-\frac{35 a^4 b^3}{3 x^3}-\frac{35 a^3 b^4}{2 x^2}-\frac{21 a^2 b^5}{x}-\frac{7 a^6 b}{5 x^5}-\frac{a^7}{6 x^6}+7 a b^6 \log (x)+b^7 x","-\frac{21 a^5 b^2}{4 x^4}-\frac{35 a^4 b^3}{3 x^3}-\frac{35 a^3 b^4}{2 x^2}-\frac{21 a^2 b^5}{x}-\frac{7 a^6 b}{5 x^5}-\frac{a^7}{6 x^6}+7 a b^6 \log (x)+b^7 x",1,"-a^7/(6*x^6) - (7*a^6*b)/(5*x^5) - (21*a^5*b^2)/(4*x^4) - (35*a^4*b^3)/(3*x^3) - (35*a^3*b^4)/(2*x^2) - (21*a^2*b^5)/x + b^7*x + 7*a*b^6*Log[x]","A",2,1,11,0.09091,1,"{43}"
114,1,89,0,0.0332283,"\int \frac{(a+b x)^7}{x^8} \, dx","Int[(a + b*x)^7/x^8,x]","-\frac{21 a^5 b^2}{5 x^5}-\frac{35 a^4 b^3}{4 x^4}-\frac{35 a^3 b^4}{3 x^3}-\frac{21 a^2 b^5}{2 x^2}-\frac{7 a^6 b}{6 x^6}-\frac{a^7}{7 x^7}-\frac{7 a b^6}{x}+b^7 \log (x)","-\frac{21 a^5 b^2}{5 x^5}-\frac{35 a^4 b^3}{4 x^4}-\frac{35 a^3 b^4}{3 x^3}-\frac{21 a^2 b^5}{2 x^2}-\frac{7 a^6 b}{6 x^6}-\frac{a^7}{7 x^7}-\frac{7 a b^6}{x}+b^7 \log (x)",1,"-a^7/(7*x^7) - (7*a^6*b)/(6*x^6) - (21*a^5*b^2)/(5*x^5) - (35*a^4*b^3)/(4*x^4) - (35*a^3*b^4)/(3*x^3) - (21*a^2*b^5)/(2*x^2) - (7*a*b^6)/x + b^7*Log[x]","A",2,1,11,0.09091,1,"{43}"
115,1,17,0,0.0016742,"\int \frac{(a+b x)^7}{x^9} \, dx","Int[(a + b*x)^7/x^9,x]","-\frac{(a+b x)^8}{8 a x^8}","-\frac{(a+b x)^8}{8 a x^8}",1,"-(a + b*x)^8/(8*a*x^8)","A",1,1,11,0.09091,1,"{37}"
116,1,36,0,0.0048768,"\int \frac{(a+b x)^7}{x^{10}} \, dx","Int[(a + b*x)^7/x^10,x]","\frac{b (a+b x)^8}{72 a^2 x^8}-\frac{(a+b x)^8}{9 a x^9}","\frac{b (a+b x)^8}{72 a^2 x^8}-\frac{(a+b x)^8}{9 a x^9}",1,"-(a + b*x)^8/(9*a*x^9) + (b*(a + b*x)^8)/(72*a^2*x^8)","A",2,2,11,0.1818,1,"{45, 37}"
117,1,56,0,0.0098383,"\int \frac{(a+b x)^7}{x^{11}} \, dx","Int[(a + b*x)^7/x^11,x]","-\frac{b^2 (a+b x)^8}{360 a^3 x^8}+\frac{b (a+b x)^8}{45 a^2 x^9}-\frac{(a+b x)^8}{10 a x^{10}}","-\frac{b^2 (a+b x)^8}{360 a^3 x^8}+\frac{b (a+b x)^8}{45 a^2 x^9}-\frac{(a+b x)^8}{10 a x^{10}}",1,"-(a + b*x)^8/(10*a*x^10) + (b*(a + b*x)^8)/(45*a^2*x^9) - (b^2*(a + b*x)^8)/(360*a^3*x^8)","A",3,2,11,0.1818,1,"{45, 37}"
118,1,76,0,0.0163322,"\int \frac{(a+b x)^7}{x^{12}} \, dx","Int[(a + b*x)^7/x^12,x]","\frac{b^3 (a+b x)^8}{1320 a^4 x^8}-\frac{b^2 (a+b x)^8}{165 a^3 x^9}+\frac{3 b (a+b x)^8}{110 a^2 x^{10}}-\frac{(a+b x)^8}{11 a x^{11}}","\frac{b^3 (a+b x)^8}{1320 a^4 x^8}-\frac{b^2 (a+b x)^8}{165 a^3 x^9}+\frac{3 b (a+b x)^8}{110 a^2 x^{10}}-\frac{(a+b x)^8}{11 a x^{11}}",1,"-(a + b*x)^8/(11*a*x^11) + (3*b*(a + b*x)^8)/(110*a^2*x^10) - (b^2*(a + b*x)^8)/(165*a^3*x^9) + (b^3*(a + b*x)^8)/(1320*a^4*x^8)","A",4,2,11,0.1818,1,"{45, 37}"
119,1,96,0,0.0255781,"\int \frac{(a+b x)^7}{x^{13}} \, dx","Int[(a + b*x)^7/x^13,x]","-\frac{b^4 (a+b x)^8}{3960 a^5 x^8}+\frac{b^3 (a+b x)^8}{495 a^4 x^9}-\frac{b^2 (a+b x)^8}{110 a^3 x^{10}}+\frac{b (a+b x)^8}{33 a^2 x^{11}}-\frac{(a+b x)^8}{12 a x^{12}}","-\frac{b^4 (a+b x)^8}{3960 a^5 x^8}+\frac{b^3 (a+b x)^8}{495 a^4 x^9}-\frac{b^2 (a+b x)^8}{110 a^3 x^{10}}+\frac{b (a+b x)^8}{33 a^2 x^{11}}-\frac{(a+b x)^8}{12 a x^{12}}",1,"-(a + b*x)^8/(12*a*x^12) + (b*(a + b*x)^8)/(33*a^2*x^11) - (b^2*(a + b*x)^8)/(110*a^3*x^10) + (b^3*(a + b*x)^8)/(495*a^4*x^9) - (b^4*(a + b*x)^8)/(3960*a^5*x^8)","A",5,2,11,0.1818,1,"{45, 37}"
120,1,93,0,0.0328734,"\int \frac{(a+b x)^7}{x^{14}} \, dx","Int[(a + b*x)^7/x^14,x]","-\frac{21 a^5 b^2}{11 x^{11}}-\frac{7 a^4 b^3}{2 x^{10}}-\frac{35 a^3 b^4}{9 x^9}-\frac{21 a^2 b^5}{8 x^8}-\frac{7 a^6 b}{12 x^{12}}-\frac{a^7}{13 x^{13}}-\frac{a b^6}{x^7}-\frac{b^7}{6 x^6}","-\frac{21 a^5 b^2}{11 x^{11}}-\frac{7 a^4 b^3}{2 x^{10}}-\frac{35 a^3 b^4}{9 x^9}-\frac{21 a^2 b^5}{8 x^8}-\frac{7 a^6 b}{12 x^{12}}-\frac{a^7}{13 x^{13}}-\frac{a b^6}{x^7}-\frac{b^7}{6 x^6}",1,"-a^7/(13*x^13) - (7*a^6*b)/(12*x^12) - (21*a^5*b^2)/(11*x^11) - (7*a^4*b^3)/(2*x^10) - (35*a^3*b^4)/(9*x^9) - (21*a^2*b^5)/(8*x^8) - (a*b^6)/x^7 - b^7/(6*x^6)","A",2,1,11,0.09091,1,"{43}"
121,1,95,0,0.0302973,"\int \frac{(a+b x)^7}{x^{15}} \, dx","Int[(a + b*x)^7/x^15,x]","-\frac{7 a^5 b^2}{4 x^{12}}-\frac{35 a^4 b^3}{11 x^{11}}-\frac{7 a^3 b^4}{2 x^{10}}-\frac{7 a^2 b^5}{3 x^9}-\frac{7 a^6 b}{13 x^{13}}-\frac{a^7}{14 x^{14}}-\frac{7 a b^6}{8 x^8}-\frac{b^7}{7 x^7}","-\frac{7 a^5 b^2}{4 x^{12}}-\frac{35 a^4 b^3}{11 x^{11}}-\frac{7 a^3 b^4}{2 x^{10}}-\frac{7 a^2 b^5}{3 x^9}-\frac{7 a^6 b}{13 x^{13}}-\frac{a^7}{14 x^{14}}-\frac{7 a b^6}{8 x^8}-\frac{b^7}{7 x^7}",1,"-a^7/(14*x^14) - (7*a^6*b)/(13*x^13) - (7*a^5*b^2)/(4*x^12) - (35*a^4*b^3)/(11*x^11) - (7*a^3*b^4)/(2*x^10) - (7*a^2*b^5)/(3*x^9) - (7*a*b^6)/(8*x^8) - b^7/(7*x^7)","A",2,1,11,0.09091,1,"{43}"
122,1,95,0,0.0304734,"\int \frac{(a+b x)^7}{x^{16}} \, dx","Int[(a + b*x)^7/x^16,x]","-\frac{21 a^5 b^2}{13 x^{13}}-\frac{35 a^4 b^3}{12 x^{12}}-\frac{35 a^3 b^4}{11 x^{11}}-\frac{21 a^2 b^5}{10 x^{10}}-\frac{a^6 b}{2 x^{14}}-\frac{a^7}{15 x^{15}}-\frac{7 a b^6}{9 x^9}-\frac{b^7}{8 x^8}","-\frac{21 a^5 b^2}{13 x^{13}}-\frac{35 a^4 b^3}{12 x^{12}}-\frac{35 a^3 b^4}{11 x^{11}}-\frac{21 a^2 b^5}{10 x^{10}}-\frac{a^6 b}{2 x^{14}}-\frac{a^7}{15 x^{15}}-\frac{7 a b^6}{9 x^9}-\frac{b^7}{8 x^8}",1,"-a^7/(15*x^15) - (a^6*b)/(2*x^14) - (21*a^5*b^2)/(13*x^13) - (35*a^4*b^3)/(12*x^12) - (35*a^3*b^4)/(11*x^11) - (21*a^2*b^5)/(10*x^10) - (7*a*b^6)/(9*x^9) - b^7/(8*x^8)","A",2,1,11,0.09091,1,"{43}"
123,1,132,0,0.0759259,"\int x^{11} (a+b x)^{10} \, dx","Int[x^11*(a + b*x)^10,x]","\frac{9}{4} a^2 b^8 x^{20}+\frac{120}{19} a^3 b^7 x^{19}+\frac{35}{3} a^4 b^6 x^{18}+\frac{252}{17} a^5 b^5 x^{17}+\frac{105}{8} a^6 b^4 x^{16}+8 a^7 b^3 x^{15}+\frac{45}{14} a^8 b^2 x^{14}+\frac{10}{13} a^9 b x^{13}+\frac{a^{10} x^{12}}{12}+\frac{10}{21} a b^9 x^{21}+\frac{b^{10} x^{22}}{22}","\frac{9}{4} a^2 b^8 x^{20}+\frac{120}{19} a^3 b^7 x^{19}+\frac{35}{3} a^4 b^6 x^{18}+\frac{252}{17} a^5 b^5 x^{17}+\frac{105}{8} a^6 b^4 x^{16}+8 a^7 b^3 x^{15}+\frac{45}{14} a^8 b^2 x^{14}+\frac{10}{13} a^9 b x^{13}+\frac{a^{10} x^{12}}{12}+\frac{10}{21} a b^9 x^{21}+\frac{b^{10} x^{22}}{22}",1,"(a^10*x^12)/12 + (10*a^9*b*x^13)/13 + (45*a^8*b^2*x^14)/14 + 8*a^7*b^3*x^15 + (105*a^6*b^4*x^16)/8 + (252*a^5*b^5*x^17)/17 + (35*a^4*b^6*x^18)/3 + (120*a^3*b^7*x^19)/19 + (9*a^2*b^8*x^20)/4 + (10*a*b^9*x^21)/21 + (b^10*x^22)/22","A",2,1,11,0.09091,1,"{43}"
124,1,132,0,0.0592057,"\int x^{10} (a+b x)^{10} \, dx","Int[x^10*(a + b*x)^10,x]","\frac{45}{19} a^2 b^8 x^{19}+\frac{20}{3} a^3 b^7 x^{18}+\frac{210}{17} a^4 b^6 x^{17}+\frac{63}{4} a^5 b^5 x^{16}+14 a^6 b^4 x^{15}+\frac{60}{7} a^7 b^3 x^{14}+\frac{45}{13} a^8 b^2 x^{13}+\frac{5}{6} a^9 b x^{12}+\frac{a^{10} x^{11}}{11}+\frac{1}{2} a b^9 x^{20}+\frac{b^{10} x^{21}}{21}","\frac{45}{19} a^2 b^8 x^{19}+\frac{20}{3} a^3 b^7 x^{18}+\frac{210}{17} a^4 b^6 x^{17}+\frac{63}{4} a^5 b^5 x^{16}+14 a^6 b^4 x^{15}+\frac{60}{7} a^7 b^3 x^{14}+\frac{45}{13} a^8 b^2 x^{13}+\frac{5}{6} a^9 b x^{12}+\frac{a^{10} x^{11}}{11}+\frac{1}{2} a b^9 x^{20}+\frac{b^{10} x^{21}}{21}",1,"(a^10*x^11)/11 + (5*a^9*b*x^12)/6 + (45*a^8*b^2*x^13)/13 + (60*a^7*b^3*x^14)/7 + 14*a^6*b^4*x^15 + (63*a^5*b^5*x^16)/4 + (210*a^4*b^6*x^17)/17 + (20*a^3*b^7*x^18)/3 + (45*a^2*b^8*x^19)/19 + (a*b^9*x^20)/2 + (b^10*x^21)/21","A",2,1,11,0.09091,1,"{43}"
125,1,132,0,0.0595646,"\int x^9 (a+b x)^{10} \, dx","Int[x^9*(a + b*x)^10,x]","\frac{5}{2} a^2 b^8 x^{18}+\frac{120}{17} a^3 b^7 x^{17}+\frac{105}{8} a^4 b^6 x^{16}+\frac{84}{5} a^5 b^5 x^{15}+15 a^6 b^4 x^{14}+\frac{120}{13} a^7 b^3 x^{13}+\frac{15}{4} a^8 b^2 x^{12}+\frac{10}{11} a^9 b x^{11}+\frac{a^{10} x^{10}}{10}+\frac{10}{19} a b^9 x^{19}+\frac{b^{10} x^{20}}{20}","\frac{5}{2} a^2 b^8 x^{18}+\frac{120}{17} a^3 b^7 x^{17}+\frac{105}{8} a^4 b^6 x^{16}+\frac{84}{5} a^5 b^5 x^{15}+15 a^6 b^4 x^{14}+\frac{120}{13} a^7 b^3 x^{13}+\frac{15}{4} a^8 b^2 x^{12}+\frac{10}{11} a^9 b x^{11}+\frac{a^{10} x^{10}}{10}+\frac{10}{19} a b^9 x^{19}+\frac{b^{10} x^{20}}{20}",1,"(a^10*x^10)/10 + (10*a^9*b*x^11)/11 + (15*a^8*b^2*x^12)/4 + (120*a^7*b^3*x^13)/13 + 15*a^6*b^4*x^14 + (84*a^5*b^5*x^15)/5 + (105*a^4*b^6*x^16)/8 + (120*a^3*b^7*x^17)/17 + (5*a^2*b^8*x^18)/2 + (10*a*b^9*x^19)/19 + (b^10*x^20)/20","A",2,1,11,0.09091,1,"{43}"
126,1,147,0,0.0642461,"\int x^8 (a+b x)^{10} \, dx","Int[x^8*(a + b*x)^10,x]","\frac{28 a^2 (a+b x)^{17}}{17 b^9}-\frac{7 a^3 (a+b x)^{16}}{2 b^9}+\frac{14 a^4 (a+b x)^{15}}{3 b^9}-\frac{4 a^5 (a+b x)^{14}}{b^9}+\frac{28 a^6 (a+b x)^{13}}{13 b^9}-\frac{2 a^7 (a+b x)^{12}}{3 b^9}+\frac{a^8 (a+b x)^{11}}{11 b^9}+\frac{(a+b x)^{19}}{19 b^9}-\frac{4 a (a+b x)^{18}}{9 b^9}","\frac{28 a^2 (a+b x)^{17}}{17 b^9}-\frac{7 a^3 (a+b x)^{16}}{2 b^9}+\frac{14 a^4 (a+b x)^{15}}{3 b^9}-\frac{4 a^5 (a+b x)^{14}}{b^9}+\frac{28 a^6 (a+b x)^{13}}{13 b^9}-\frac{2 a^7 (a+b x)^{12}}{3 b^9}+\frac{a^8 (a+b x)^{11}}{11 b^9}+\frac{(a+b x)^{19}}{19 b^9}-\frac{4 a (a+b x)^{18}}{9 b^9}",1,"(a^8*(a + b*x)^11)/(11*b^9) - (2*a^7*(a + b*x)^12)/(3*b^9) + (28*a^6*(a + b*x)^13)/(13*b^9) - (4*a^5*(a + b*x)^14)/b^9 + (14*a^4*(a + b*x)^15)/(3*b^9) - (7*a^3*(a + b*x)^16)/(2*b^9) + (28*a^2*(a + b*x)^17)/(17*b^9) - (4*a*(a + b*x)^18)/(9*b^9) + (a + b*x)^19/(19*b^9)","A",2,1,11,0.09091,1,"{43}"
127,1,132,0,0.0566174,"\int x^7 (a+b x)^{10} \, dx","Int[x^7*(a + b*x)^10,x]","\frac{21 a^2 (a+b x)^{16}}{16 b^8}-\frac{7 a^3 (a+b x)^{15}}{3 b^8}+\frac{5 a^4 (a+b x)^{14}}{2 b^8}-\frac{21 a^5 (a+b x)^{13}}{13 b^8}+\frac{7 a^6 (a+b x)^{12}}{12 b^8}-\frac{a^7 (a+b x)^{11}}{11 b^8}+\frac{(a+b x)^{18}}{18 b^8}-\frac{7 a (a+b x)^{17}}{17 b^8}","\frac{21 a^2 (a+b x)^{16}}{16 b^8}-\frac{7 a^3 (a+b x)^{15}}{3 b^8}+\frac{5 a^4 (a+b x)^{14}}{2 b^8}-\frac{21 a^5 (a+b x)^{13}}{13 b^8}+\frac{7 a^6 (a+b x)^{12}}{12 b^8}-\frac{a^7 (a+b x)^{11}}{11 b^8}+\frac{(a+b x)^{18}}{18 b^8}-\frac{7 a (a+b x)^{17}}{17 b^8}",1,"-(a^7*(a + b*x)^11)/(11*b^8) + (7*a^6*(a + b*x)^12)/(12*b^8) - (21*a^5*(a + b*x)^13)/(13*b^8) + (5*a^4*(a + b*x)^14)/(2*b^8) - (7*a^3*(a + b*x)^15)/(3*b^8) + (21*a^2*(a + b*x)^16)/(16*b^8) - (7*a*(a + b*x)^17)/(17*b^8) + (a + b*x)^18/(18*b^8)","A",2,1,11,0.09091,1,"{43}"
128,1,112,0,0.0524065,"\int x^6 (a+b x)^{10} \, dx","Int[x^6*(a + b*x)^10,x]","\frac{a^2 (a+b x)^{15}}{b^7}-\frac{10 a^3 (a+b x)^{14}}{7 b^7}+\frac{15 a^4 (a+b x)^{13}}{13 b^7}-\frac{a^5 (a+b x)^{12}}{2 b^7}+\frac{a^6 (a+b x)^{11}}{11 b^7}+\frac{(a+b x)^{17}}{17 b^7}-\frac{3 a (a+b x)^{16}}{8 b^7}","\frac{a^2 (a+b x)^{15}}{b^7}-\frac{10 a^3 (a+b x)^{14}}{7 b^7}+\frac{15 a^4 (a+b x)^{13}}{13 b^7}-\frac{a^5 (a+b x)^{12}}{2 b^7}+\frac{a^6 (a+b x)^{11}}{11 b^7}+\frac{(a+b x)^{17}}{17 b^7}-\frac{3 a (a+b x)^{16}}{8 b^7}",1,"(a^6*(a + b*x)^11)/(11*b^7) - (a^5*(a + b*x)^12)/(2*b^7) + (15*a^4*(a + b*x)^13)/(13*b^7) - (10*a^3*(a + b*x)^14)/(7*b^7) + (a^2*(a + b*x)^15)/b^7 - (3*a*(a + b*x)^16)/(8*b^7) + (a + b*x)^17/(17*b^7)","A",2,1,11,0.09091,1,"{43}"
129,1,98,0,0.0452189,"\int x^5 (a+b x)^{10} \, dx","Int[x^5*(a + b*x)^10,x]","\frac{5 a^2 (a+b x)^{14}}{7 b^6}-\frac{10 a^3 (a+b x)^{13}}{13 b^6}+\frac{5 a^4 (a+b x)^{12}}{12 b^6}-\frac{a^5 (a+b x)^{11}}{11 b^6}+\frac{(a+b x)^{16}}{16 b^6}-\frac{a (a+b x)^{15}}{3 b^6}","\frac{5 a^2 (a+b x)^{14}}{7 b^6}-\frac{10 a^3 (a+b x)^{13}}{13 b^6}+\frac{5 a^4 (a+b x)^{12}}{12 b^6}-\frac{a^5 (a+b x)^{11}}{11 b^6}+\frac{(a+b x)^{16}}{16 b^6}-\frac{a (a+b x)^{15}}{3 b^6}",1,"-(a^5*(a + b*x)^11)/(11*b^6) + (5*a^4*(a + b*x)^12)/(12*b^6) - (10*a^3*(a + b*x)^13)/(13*b^6) + (5*a^2*(a + b*x)^14)/(7*b^6) - (a*(a + b*x)^15)/(3*b^6) + (a + b*x)^16/(16*b^6)","A",2,1,11,0.09091,1,"{43}"
130,1,81,0,0.0390572,"\int x^4 (a+b x)^{10} \, dx","Int[x^4*(a + b*x)^10,x]","\frac{6 a^2 (a+b x)^{13}}{13 b^5}-\frac{a^3 (a+b x)^{12}}{3 b^5}+\frac{a^4 (a+b x)^{11}}{11 b^5}+\frac{(a+b x)^{15}}{15 b^5}-\frac{2 a (a+b x)^{14}}{7 b^5}","\frac{6 a^2 (a+b x)^{13}}{13 b^5}-\frac{a^3 (a+b x)^{12}}{3 b^5}+\frac{a^4 (a+b x)^{11}}{11 b^5}+\frac{(a+b x)^{15}}{15 b^5}-\frac{2 a (a+b x)^{14}}{7 b^5}",1,"(a^4*(a + b*x)^11)/(11*b^5) - (a^3*(a + b*x)^12)/(3*b^5) + (6*a^2*(a + b*x)^13)/(13*b^5) - (2*a*(a + b*x)^14)/(7*b^5) + (a + b*x)^15/(15*b^5)","A",2,1,11,0.09091,1,"{43}"
131,1,64,0,0.035897,"\int x^3 (a+b x)^{10} \, dx","Int[x^3*(a + b*x)^10,x]","\frac{a^2 (a+b x)^{12}}{4 b^4}-\frac{a^3 (a+b x)^{11}}{11 b^4}+\frac{(a+b x)^{14}}{14 b^4}-\frac{3 a (a+b x)^{13}}{13 b^4}","\frac{a^2 (a+b x)^{12}}{4 b^4}-\frac{a^3 (a+b x)^{11}}{11 b^4}+\frac{(a+b x)^{14}}{14 b^4}-\frac{3 a (a+b x)^{13}}{13 b^4}",1,"-(a^3*(a + b*x)^11)/(11*b^4) + (a^2*(a + b*x)^12)/(4*b^4) - (3*a*(a + b*x)^13)/(13*b^4) + (a + b*x)^14/(14*b^4)","A",2,1,11,0.09091,1,"{43}"
132,1,47,0,0.0296192,"\int x^2 (a+b x)^{10} \, dx","Int[x^2*(a + b*x)^10,x]","\frac{a^2 (a+b x)^{11}}{11 b^3}+\frac{(a+b x)^{13}}{13 b^3}-\frac{a (a+b x)^{12}}{6 b^3}","\frac{a^2 (a+b x)^{11}}{11 b^3}+\frac{(a+b x)^{13}}{13 b^3}-\frac{a (a+b x)^{12}}{6 b^3}",1,"(a^2*(a + b*x)^11)/(11*b^3) - (a*(a + b*x)^12)/(6*b^3) + (a + b*x)^13/(13*b^3)","A",2,1,11,0.09091,1,"{43}"
133,1,30,0,0.0082832,"\int x (a+b x)^{10} \, dx","Int[x*(a + b*x)^10,x]","\frac{(a+b x)^{12}}{12 b^2}-\frac{a (a+b x)^{11}}{11 b^2}","\frac{(a+b x)^{12}}{12 b^2}-\frac{a (a+b x)^{11}}{11 b^2}",1,"-(a*(a + b*x)^11)/(11*b^2) + (a + b*x)^12/(12*b^2)","A",2,1,9,0.1111,1,"{43}"
134,1,14,0,0.0015093,"\int (a+b x)^{10} \, dx","Int[(a + b*x)^10,x]","\frac{(a+b x)^{11}}{11 b}","\frac{(a+b x)^{11}}{11 b}",1,"(a + b*x)^11/(11*b)","A",1,1,7,0.1429,1,"{32}"
135,1,122,0,0.0433098,"\int \frac{(a+b x)^{10}}{x} \, dx","Int[(a + b*x)^10/x,x]","\frac{45}{2} a^8 b^2 x^2+40 a^7 b^3 x^3+\frac{105}{2} a^6 b^4 x^4+\frac{252}{5} a^5 b^5 x^5+35 a^4 b^6 x^6+\frac{120}{7} a^3 b^7 x^7+\frac{45}{8} a^2 b^8 x^8+10 a^9 b x+a^{10} \log (x)+\frac{10}{9} a b^9 x^9+\frac{b^{10} x^{10}}{10}","\frac{45}{2} a^8 b^2 x^2+40 a^7 b^3 x^3+\frac{105}{2} a^6 b^4 x^4+\frac{252}{5} a^5 b^5 x^5+35 a^4 b^6 x^6+\frac{120}{7} a^3 b^7 x^7+\frac{45}{8} a^2 b^8 x^8+10 a^9 b x+a^{10} \log (x)+\frac{10}{9} a b^9 x^9+\frac{b^{10} x^{10}}{10}",1,"10*a^9*b*x + (45*a^8*b^2*x^2)/2 + 40*a^7*b^3*x^3 + (105*a^6*b^4*x^4)/2 + (252*a^5*b^5*x^5)/5 + 35*a^4*b^6*x^6 + (120*a^3*b^7*x^7)/7 + (45*a^2*b^8*x^8)/8 + (10*a*b^9*x^9)/9 + (b^10*x^10)/10 + a^10*Log[x]","A",2,1,11,0.09091,1,"{43}"
136,1,115,0,0.0468345,"\int \frac{(a+b x)^{10}}{x^2} \, dx","Int[(a + b*x)^10/x^2,x]","60 a^7 b^3 x^2+70 a^6 b^4 x^3+63 a^5 b^5 x^4+42 a^4 b^6 x^5+20 a^3 b^7 x^6+\frac{45}{7} a^2 b^8 x^7+45 a^8 b^2 x+10 a^9 b \log (x)-\frac{a^{10}}{x}+\frac{5}{4} a b^9 x^8+\frac{b^{10} x^9}{9}","60 a^7 b^3 x^2+70 a^6 b^4 x^3+63 a^5 b^5 x^4+42 a^4 b^6 x^5+20 a^3 b^7 x^6+\frac{45}{7} a^2 b^8 x^7+45 a^8 b^2 x+10 a^9 b \log (x)-\frac{a^{10}}{x}+\frac{5}{4} a b^9 x^8+\frac{b^{10} x^9}{9}",1,"-(a^10/x) + 45*a^8*b^2*x + 60*a^7*b^3*x^2 + 70*a^6*b^4*x^3 + 63*a^5*b^5*x^4 + 42*a^4*b^6*x^5 + 20*a^3*b^7*x^6 + (45*a^2*b^8*x^7)/7 + (5*a*b^9*x^8)/4 + (b^10*x^9)/9 + 10*a^9*b*Log[x]","A",2,1,11,0.09091,1,"{43}"
137,1,119,0,0.0490299,"\int \frac{(a+b x)^{10}}{x^3} \, dx","Int[(a + b*x)^10/x^3,x]","105 a^6 b^4 x^2+84 a^5 b^5 x^3+\frac{105}{2} a^4 b^6 x^4+24 a^3 b^7 x^5+\frac{15}{2} a^2 b^8 x^6+120 a^7 b^3 x+45 a^8 b^2 \log (x)-\frac{10 a^9 b}{x}-\frac{a^{10}}{2 x^2}+\frac{10}{7} a b^9 x^7+\frac{b^{10} x^8}{8}","105 a^6 b^4 x^2+84 a^5 b^5 x^3+\frac{105}{2} a^4 b^6 x^4+24 a^3 b^7 x^5+\frac{15}{2} a^2 b^8 x^6+120 a^7 b^3 x+45 a^8 b^2 \log (x)-\frac{10 a^9 b}{x}-\frac{a^{10}}{2 x^2}+\frac{10}{7} a b^9 x^7+\frac{b^{10} x^8}{8}",1,"-a^10/(2*x^2) - (10*a^9*b)/x + 120*a^7*b^3*x + 105*a^6*b^4*x^2 + 84*a^5*b^5*x^3 + (105*a^4*b^6*x^4)/2 + 24*a^3*b^7*x^5 + (15*a^2*b^8*x^6)/2 + (10*a*b^9*x^7)/7 + (b^10*x^8)/8 + 45*a^8*b^2*Log[x]","A",2,1,11,0.09091,1,"{43}"
138,1,115,0,0.047252,"\int \frac{(a+b x)^{10}}{x^4} \, dx","Int[(a + b*x)^10/x^4,x]","126 a^5 b^5 x^2+70 a^4 b^6 x^3+30 a^3 b^7 x^4+9 a^2 b^8 x^5-\frac{45 a^8 b^2}{x}+210 a^6 b^4 x+120 a^7 b^3 \log (x)-\frac{5 a^9 b}{x^2}-\frac{a^{10}}{3 x^3}+\frac{5}{3} a b^9 x^6+\frac{b^{10} x^7}{7}","126 a^5 b^5 x^2+70 a^4 b^6 x^3+30 a^3 b^7 x^4+9 a^2 b^8 x^5-\frac{45 a^8 b^2}{x}+210 a^6 b^4 x+120 a^7 b^3 \log (x)-\frac{5 a^9 b}{x^2}-\frac{a^{10}}{3 x^3}+\frac{5}{3} a b^9 x^6+\frac{b^{10} x^7}{7}",1,"-a^10/(3*x^3) - (5*a^9*b)/x^2 - (45*a^8*b^2)/x + 210*a^6*b^4*x + 126*a^5*b^5*x^2 + 70*a^4*b^6*x^3 + 30*a^3*b^7*x^4 + 9*a^2*b^8*x^5 + (5*a*b^9*x^6)/3 + (b^10*x^7)/7 + 120*a^7*b^3*Log[x]","A",2,1,11,0.09091,1,"{43}"
139,1,119,0,0.0494338,"\int \frac{(a+b x)^{10}}{x^5} \, dx","Int[(a + b*x)^10/x^5,x]","-\frac{45 a^8 b^2}{2 x^2}+105 a^4 b^6 x^2+40 a^3 b^7 x^3+\frac{45}{4} a^2 b^8 x^4-\frac{120 a^7 b^3}{x}+252 a^5 b^5 x+210 a^6 b^4 \log (x)-\frac{10 a^9 b}{3 x^3}-\frac{a^{10}}{4 x^4}+2 a b^9 x^5+\frac{b^{10} x^6}{6}","-\frac{45 a^8 b^2}{2 x^2}+105 a^4 b^6 x^2+40 a^3 b^7 x^3+\frac{45}{4} a^2 b^8 x^4-\frac{120 a^7 b^3}{x}+252 a^5 b^5 x+210 a^6 b^4 \log (x)-\frac{10 a^9 b}{3 x^3}-\frac{a^{10}}{4 x^4}+2 a b^9 x^5+\frac{b^{10} x^6}{6}",1,"-a^10/(4*x^4) - (10*a^9*b)/(3*x^3) - (45*a^8*b^2)/(2*x^2) - (120*a^7*b^3)/x + 252*a^5*b^5*x + 105*a^4*b^6*x^2 + 40*a^3*b^7*x^3 + (45*a^2*b^8*x^4)/4 + 2*a*b^9*x^5 + (b^10*x^6)/6 + 210*a^6*b^4*Log[x]","A",2,1,11,0.09091,1,"{43}"
140,1,117,0,0.0518441,"\int \frac{(a+b x)^{10}}{x^6} \, dx","Int[(a + b*x)^10/x^6,x]","-\frac{15 a^8 b^2}{x^3}-\frac{60 a^7 b^3}{x^2}+60 a^3 b^7 x^2+15 a^2 b^8 x^3-\frac{210 a^6 b^4}{x}+210 a^4 b^6 x+252 a^5 b^5 \log (x)-\frac{5 a^9 b}{2 x^4}-\frac{a^{10}}{5 x^5}+\frac{5}{2} a b^9 x^4+\frac{b^{10} x^5}{5}","-\frac{15 a^8 b^2}{x^3}-\frac{60 a^7 b^3}{x^2}+60 a^3 b^7 x^2+15 a^2 b^8 x^3-\frac{210 a^6 b^4}{x}+210 a^4 b^6 x+252 a^5 b^5 \log (x)-\frac{5 a^9 b}{2 x^4}-\frac{a^{10}}{5 x^5}+\frac{5}{2} a b^9 x^4+\frac{b^{10} x^5}{5}",1,"-a^10/(5*x^5) - (5*a^9*b)/(2*x^4) - (15*a^8*b^2)/x^3 - (60*a^7*b^3)/x^2 - (210*a^6*b^4)/x + 210*a^4*b^6*x + 60*a^3*b^7*x^2 + 15*a^2*b^8*x^3 + (5*a*b^9*x^4)/2 + (b^10*x^5)/5 + 252*a^5*b^5*Log[x]","A",2,1,11,0.09091,1,"{43}"
141,1,119,0,0.0488931,"\int \frac{(a+b x)^{10}}{x^7} \, dx","Int[(a + b*x)^10/x^7,x]","-\frac{45 a^8 b^2}{4 x^4}-\frac{40 a^7 b^3}{x^3}-\frac{105 a^6 b^4}{x^2}+\frac{45}{2} a^2 b^8 x^2-\frac{252 a^5 b^5}{x}+120 a^3 b^7 x+210 a^4 b^6 \log (x)-\frac{2 a^9 b}{x^5}-\frac{a^{10}}{6 x^6}+\frac{10}{3} a b^9 x^3+\frac{b^{10} x^4}{4}","-\frac{45 a^8 b^2}{4 x^4}-\frac{40 a^7 b^3}{x^3}-\frac{105 a^6 b^4}{x^2}+\frac{45}{2} a^2 b^8 x^2-\frac{252 a^5 b^5}{x}+120 a^3 b^7 x+210 a^4 b^6 \log (x)-\frac{2 a^9 b}{x^5}-\frac{a^{10}}{6 x^6}+\frac{10}{3} a b^9 x^3+\frac{b^{10} x^4}{4}",1,"-a^10/(6*x^6) - (2*a^9*b)/x^5 - (45*a^8*b^2)/(4*x^4) - (40*a^7*b^3)/x^3 - (105*a^6*b^4)/x^2 - (252*a^5*b^5)/x + 120*a^3*b^7*x + (45*a^2*b^8*x^2)/2 + (10*a*b^9*x^3)/3 + (b^10*x^4)/4 + 210*a^4*b^6*Log[x]","A",2,1,11,0.09091,1,"{43}"
142,1,115,0,0.0496511,"\int \frac{(a+b x)^{10}}{x^8} \, dx","Int[(a + b*x)^10/x^8,x]","-\frac{9 a^8 b^2}{x^5}-\frac{30 a^7 b^3}{x^4}-\frac{70 a^6 b^4}{x^3}-\frac{126 a^5 b^5}{x^2}-\frac{210 a^4 b^6}{x}+45 a^2 b^8 x+120 a^3 b^7 \log (x)-\frac{5 a^9 b}{3 x^6}-\frac{a^{10}}{7 x^7}+5 a b^9 x^2+\frac{b^{10} x^3}{3}","-\frac{9 a^8 b^2}{x^5}-\frac{30 a^7 b^3}{x^4}-\frac{70 a^6 b^4}{x^3}-\frac{126 a^5 b^5}{x^2}-\frac{210 a^4 b^6}{x}+45 a^2 b^8 x+120 a^3 b^7 \log (x)-\frac{5 a^9 b}{3 x^6}-\frac{a^{10}}{7 x^7}+5 a b^9 x^2+\frac{b^{10} x^3}{3}",1,"-a^10/(7*x^7) - (5*a^9*b)/(3*x^6) - (9*a^8*b^2)/x^5 - (30*a^7*b^3)/x^4 - (70*a^6*b^4)/x^3 - (126*a^5*b^5)/x^2 - (210*a^4*b^6)/x + 45*a^2*b^8*x + 5*a*b^9*x^2 + (b^10*x^3)/3 + 120*a^3*b^7*Log[x]","A",2,1,11,0.09091,1,"{43}"
143,1,119,0,0.0489553,"\int \frac{(a+b x)^{10}}{x^9} \, dx","Int[(a + b*x)^10/x^9,x]","-\frac{15 a^8 b^2}{2 x^6}-\frac{24 a^7 b^3}{x^5}-\frac{105 a^6 b^4}{2 x^4}-\frac{84 a^5 b^5}{x^3}-\frac{105 a^4 b^6}{x^2}-\frac{120 a^3 b^7}{x}+45 a^2 b^8 \log (x)-\frac{10 a^9 b}{7 x^7}-\frac{a^{10}}{8 x^8}+10 a b^9 x+\frac{b^{10} x^2}{2}","-\frac{15 a^8 b^2}{2 x^6}-\frac{24 a^7 b^3}{x^5}-\frac{105 a^6 b^4}{2 x^4}-\frac{84 a^5 b^5}{x^3}-\frac{105 a^4 b^6}{x^2}-\frac{120 a^3 b^7}{x}+45 a^2 b^8 \log (x)-\frac{10 a^9 b}{7 x^7}-\frac{a^{10}}{8 x^8}+10 a b^9 x+\frac{b^{10} x^2}{2}",1,"-a^10/(8*x^8) - (10*a^9*b)/(7*x^7) - (15*a^8*b^2)/(2*x^6) - (24*a^7*b^3)/x^5 - (105*a^6*b^4)/(2*x^4) - (84*a^5*b^5)/x^3 - (105*a^4*b^6)/x^2 - (120*a^3*b^7)/x + 10*a*b^9*x + (b^10*x^2)/2 + 45*a^2*b^8*Log[x]","A",2,1,11,0.09091,1,"{43}"
144,1,114,0,0.0530741,"\int \frac{(a+b x)^{10}}{x^{10}} \, dx","Int[(a + b*x)^10/x^10,x]","-\frac{45 a^8 b^2}{7 x^7}-\frac{20 a^7 b^3}{x^6}-\frac{42 a^6 b^4}{x^5}-\frac{63 a^5 b^5}{x^4}-\frac{70 a^4 b^6}{x^3}-\frac{60 a^3 b^7}{x^2}-\frac{45 a^2 b^8}{x}-\frac{5 a^9 b}{4 x^8}-\frac{a^{10}}{9 x^9}+10 a b^9 \log (x)+b^{10} x","-\frac{45 a^8 b^2}{7 x^7}-\frac{20 a^7 b^3}{x^6}-\frac{42 a^6 b^4}{x^5}-\frac{63 a^5 b^5}{x^4}-\frac{70 a^4 b^6}{x^3}-\frac{60 a^3 b^7}{x^2}-\frac{45 a^2 b^8}{x}-\frac{5 a^9 b}{4 x^8}-\frac{a^{10}}{9 x^9}+10 a b^9 \log (x)+b^{10} x",1,"-a^10/(9*x^9) - (5*a^9*b)/(4*x^8) - (45*a^8*b^2)/(7*x^7) - (20*a^7*b^3)/x^6 - (42*a^6*b^4)/x^5 - (63*a^5*b^5)/x^4 - (70*a^4*b^6)/x^3 - (60*a^3*b^7)/x^2 - (45*a^2*b^8)/x + b^10*x + 10*a*b^9*Log[x]","A",2,1,11,0.09091,1,"{43}"
145,1,124,0,0.0484612,"\int \frac{(a+b x)^{10}}{x^{11}} \, dx","Int[(a + b*x)^10/x^11,x]","-\frac{45 a^8 b^2}{8 x^8}-\frac{120 a^7 b^3}{7 x^7}-\frac{35 a^6 b^4}{x^6}-\frac{252 a^5 b^5}{5 x^5}-\frac{105 a^4 b^6}{2 x^4}-\frac{40 a^3 b^7}{x^3}-\frac{45 a^2 b^8}{2 x^2}-\frac{10 a^9 b}{9 x^9}-\frac{a^{10}}{10 x^{10}}-\frac{10 a b^9}{x}+b^{10} \log (x)","-\frac{45 a^8 b^2}{8 x^8}-\frac{120 a^7 b^3}{7 x^7}-\frac{35 a^6 b^4}{x^6}-\frac{252 a^5 b^5}{5 x^5}-\frac{105 a^4 b^6}{2 x^4}-\frac{40 a^3 b^7}{x^3}-\frac{45 a^2 b^8}{2 x^2}-\frac{10 a^9 b}{9 x^9}-\frac{a^{10}}{10 x^{10}}-\frac{10 a b^9}{x}+b^{10} \log (x)",1,"-a^10/(10*x^10) - (10*a^9*b)/(9*x^9) - (45*a^8*b^2)/(8*x^8) - (120*a^7*b^3)/(7*x^7) - (35*a^6*b^4)/x^6 - (252*a^5*b^5)/(5*x^5) - (105*a^4*b^6)/(2*x^4) - (40*a^3*b^7)/x^3 - (45*a^2*b^8)/(2*x^2) - (10*a*b^9)/x + b^10*Log[x]","A",2,1,11,0.09091,1,"{43}"
146,1,17,0,0.0016535,"\int \frac{(a+b x)^{10}}{x^{12}} \, dx","Int[(a + b*x)^10/x^12,x]","-\frac{(a+b x)^{11}}{11 a x^{11}}","-\frac{(a+b x)^{11}}{11 a x^{11}}",1,"-(a + b*x)^11/(11*a*x^11)","A",1,1,11,0.09091,1,"{37}"
147,1,36,0,0.0048916,"\int \frac{(a+b x)^{10}}{x^{13}} \, dx","Int[(a + b*x)^10/x^13,x]","\frac{b (a+b x)^{11}}{132 a^2 x^{11}}-\frac{(a+b x)^{11}}{12 a x^{12}}","\frac{b (a+b x)^{11}}{132 a^2 x^{11}}-\frac{(a+b x)^{11}}{12 a x^{12}}",1,"-(a + b*x)^11/(12*a*x^12) + (b*(a + b*x)^11)/(132*a^2*x^11)","A",2,2,11,0.1818,1,"{45, 37}"
148,1,56,0,0.0099815,"\int \frac{(a+b x)^{10}}{x^{14}} \, dx","Int[(a + b*x)^10/x^14,x]","-\frac{b^2 (a+b x)^{11}}{858 a^3 x^{11}}+\frac{b (a+b x)^{11}}{78 a^2 x^{12}}-\frac{(a+b x)^{11}}{13 a x^{13}}","-\frac{b^2 (a+b x)^{11}}{858 a^3 x^{11}}+\frac{b (a+b x)^{11}}{78 a^2 x^{12}}-\frac{(a+b x)^{11}}{13 a x^{13}}",1,"-(a + b*x)^11/(13*a*x^13) + (b*(a + b*x)^11)/(78*a^2*x^12) - (b^2*(a + b*x)^11)/(858*a^3*x^11)","A",3,2,11,0.1818,1,"{45, 37}"
149,1,76,0,0.0170879,"\int \frac{(a+b x)^{10}}{x^{15}} \, dx","Int[(a + b*x)^10/x^15,x]","\frac{b^3 (a+b x)^{11}}{4004 a^4 x^{11}}-\frac{b^2 (a+b x)^{11}}{364 a^3 x^{12}}+\frac{3 b (a+b x)^{11}}{182 a^2 x^{13}}-\frac{(a+b x)^{11}}{14 a x^{14}}","\frac{b^3 (a+b x)^{11}}{4004 a^4 x^{11}}-\frac{b^2 (a+b x)^{11}}{364 a^3 x^{12}}+\frac{3 b (a+b x)^{11}}{182 a^2 x^{13}}-\frac{(a+b x)^{11}}{14 a x^{14}}",1,"-(a + b*x)^11/(14*a*x^14) + (3*b*(a + b*x)^11)/(182*a^2*x^13) - (b^2*(a + b*x)^11)/(364*a^3*x^12) + (b^3*(a + b*x)^11)/(4004*a^4*x^11)","A",4,2,11,0.1818,1,"{45, 37}"
150,1,96,0,0.0250919,"\int \frac{(a+b x)^{10}}{x^{16}} \, dx","Int[(a + b*x)^10/x^16,x]","-\frac{b^4 (a+b x)^{11}}{15015 a^5 x^{11}}+\frac{b^3 (a+b x)^{11}}{1365 a^4 x^{12}}-\frac{2 b^2 (a+b x)^{11}}{455 a^3 x^{13}}+\frac{2 b (a+b x)^{11}}{105 a^2 x^{14}}-\frac{(a+b x)^{11}}{15 a x^{15}}","-\frac{b^4 (a+b x)^{11}}{15015 a^5 x^{11}}+\frac{b^3 (a+b x)^{11}}{1365 a^4 x^{12}}-\frac{2 b^2 (a+b x)^{11}}{455 a^3 x^{13}}+\frac{2 b (a+b x)^{11}}{105 a^2 x^{14}}-\frac{(a+b x)^{11}}{15 a x^{15}}",1,"-(a + b*x)^11/(15*a*x^15) + (2*b*(a + b*x)^11)/(105*a^2*x^14) - (2*b^2*(a + b*x)^11)/(455*a^3*x^13) + (b^3*(a + b*x)^11)/(1365*a^4*x^12) - (b^4*(a + b*x)^11)/(15015*a^5*x^11)","A",5,2,11,0.1818,1,"{45, 37}"
151,1,116,0,0.0351052,"\int \frac{(a+b x)^{10}}{x^{17}} \, dx","Int[(a + b*x)^10/x^17,x]","\frac{b^5 (a+b x)^{11}}{48048 a^6 x^{11}}-\frac{b^4 (a+b x)^{11}}{4368 a^5 x^{12}}+\frac{b^3 (a+b x)^{11}}{728 a^4 x^{13}}-\frac{b^2 (a+b x)^{11}}{168 a^3 x^{14}}+\frac{b (a+b x)^{11}}{48 a^2 x^{15}}-\frac{(a+b x)^{11}}{16 a x^{16}}","\frac{b^5 (a+b x)^{11}}{48048 a^6 x^{11}}-\frac{b^4 (a+b x)^{11}}{4368 a^5 x^{12}}+\frac{b^3 (a+b x)^{11}}{728 a^4 x^{13}}-\frac{b^2 (a+b x)^{11}}{168 a^3 x^{14}}+\frac{b (a+b x)^{11}}{48 a^2 x^{15}}-\frac{(a+b x)^{11}}{16 a x^{16}}",1,"-(a + b*x)^11/(16*a*x^16) + (b*(a + b*x)^11)/(48*a^2*x^15) - (b^2*(a + b*x)^11)/(168*a^3*x^14) + (b^3*(a + b*x)^11)/(728*a^4*x^13) - (b^4*(a + b*x)^11)/(4368*a^5*x^12) + (b^5*(a + b*x)^11)/(48048*a^6*x^11)","A",6,2,11,0.1818,1,"{45, 37}"
152,1,136,0,0.0487079,"\int \frac{(a+b x)^{10}}{x^{18}} \, dx","Int[(a + b*x)^10/x^18,x]","-\frac{b^6 (a+b x)^{11}}{136136 a^7 x^{11}}+\frac{b^5 (a+b x)^{11}}{12376 a^6 x^{12}}-\frac{3 b^4 (a+b x)^{11}}{6188 a^5 x^{13}}+\frac{b^3 (a+b x)^{11}}{476 a^4 x^{14}}-\frac{b^2 (a+b x)^{11}}{136 a^3 x^{15}}+\frac{3 b (a+b x)^{11}}{136 a^2 x^{16}}-\frac{(a+b x)^{11}}{17 a x^{17}}","-\frac{b^6 (a+b x)^{11}}{136136 a^7 x^{11}}+\frac{b^5 (a+b x)^{11}}{12376 a^6 x^{12}}-\frac{3 b^4 (a+b x)^{11}}{6188 a^5 x^{13}}+\frac{b^3 (a+b x)^{11}}{476 a^4 x^{14}}-\frac{b^2 (a+b x)^{11}}{136 a^3 x^{15}}+\frac{3 b (a+b x)^{11}}{136 a^2 x^{16}}-\frac{(a+b x)^{11}}{17 a x^{17}}",1,"-(a + b*x)^11/(17*a*x^17) + (3*b*(a + b*x)^11)/(136*a^2*x^16) - (b^2*(a + b*x)^11)/(136*a^3*x^15) + (b^3*(a + b*x)^11)/(476*a^4*x^14) - (3*b^4*(a + b*x)^11)/(6188*a^5*x^13) + (b^5*(a + b*x)^11)/(12376*a^6*x^12) - (b^6*(a + b*x)^11)/(136136*a^7*x^11)","A",7,2,11,0.1818,1,"{45, 37}"
153,1,130,0,0.047175,"\int \frac{(a+b x)^{10}}{x^{19}} \, dx","Int[(a + b*x)^10/x^19,x]","-\frac{45 a^8 b^2}{16 x^{16}}-\frac{8 a^7 b^3}{x^{15}}-\frac{15 a^6 b^4}{x^{14}}-\frac{252 a^5 b^5}{13 x^{13}}-\frac{35 a^4 b^6}{2 x^{12}}-\frac{120 a^3 b^7}{11 x^{11}}-\frac{9 a^2 b^8}{2 x^{10}}-\frac{10 a^9 b}{17 x^{17}}-\frac{a^{10}}{18 x^{18}}-\frac{10 a b^9}{9 x^9}-\frac{b^{10}}{8 x^8}","-\frac{45 a^8 b^2}{16 x^{16}}-\frac{8 a^7 b^3}{x^{15}}-\frac{15 a^6 b^4}{x^{14}}-\frac{252 a^5 b^5}{13 x^{13}}-\frac{35 a^4 b^6}{2 x^{12}}-\frac{120 a^3 b^7}{11 x^{11}}-\frac{9 a^2 b^8}{2 x^{10}}-\frac{10 a^9 b}{17 x^{17}}-\frac{a^{10}}{18 x^{18}}-\frac{10 a b^9}{9 x^9}-\frac{b^{10}}{8 x^8}",1,"-a^10/(18*x^18) - (10*a^9*b)/(17*x^17) - (45*a^8*b^2)/(16*x^16) - (8*a^7*b^3)/x^15 - (15*a^6*b^4)/x^14 - (252*a^5*b^5)/(13*x^13) - (35*a^4*b^6)/(2*x^12) - (120*a^3*b^7)/(11*x^11) - (9*a^2*b^8)/(2*x^10) - (10*a*b^9)/(9*x^9) - b^10/(8*x^8)","A",2,1,11,0.09091,1,"{43}"
154,1,126,0,0.0493592,"\int \frac{(a+b x)^{10}}{x^{20}} \, dx","Int[(a + b*x)^10/x^20,x]","-\frac{45 a^8 b^2}{17 x^{17}}-\frac{15 a^7 b^3}{2 x^{16}}-\frac{14 a^6 b^4}{x^{15}}-\frac{18 a^5 b^5}{x^{14}}-\frac{210 a^4 b^6}{13 x^{13}}-\frac{10 a^3 b^7}{x^{12}}-\frac{45 a^2 b^8}{11 x^{11}}-\frac{5 a^9 b}{9 x^{18}}-\frac{a^{10}}{19 x^{19}}-\frac{a b^9}{x^{10}}-\frac{b^{10}}{9 x^9}","-\frac{45 a^8 b^2}{17 x^{17}}-\frac{15 a^7 b^3}{2 x^{16}}-\frac{14 a^6 b^4}{x^{15}}-\frac{18 a^5 b^5}{x^{14}}-\frac{210 a^4 b^6}{13 x^{13}}-\frac{10 a^3 b^7}{x^{12}}-\frac{45 a^2 b^8}{11 x^{11}}-\frac{5 a^9 b}{9 x^{18}}-\frac{a^{10}}{19 x^{19}}-\frac{a b^9}{x^{10}}-\frac{b^{10}}{9 x^9}",1,"-a^10/(19*x^19) - (5*a^9*b)/(9*x^18) - (45*a^8*b^2)/(17*x^17) - (15*a^7*b^3)/(2*x^16) - (14*a^6*b^4)/x^15 - (18*a^5*b^5)/x^14 - (210*a^4*b^6)/(13*x^13) - (10*a^3*b^7)/x^12 - (45*a^2*b^8)/(11*x^11) - (a*b^9)/x^10 - b^10/(9*x^9)","A",2,1,11,0.09091,1,"{43}"
155,1,15,0,0.0016425,"\int c (a+b x) \, dx","Int[c*(a + b*x),x]","\frac{c (a+b x)^2}{2 b}","\frac{c (a+b x)^2}{2 b}",1,"(c*(a + b*x)^2)/(2*b)","A",1,1,7,0.1429,1,"{9}"
156,1,20,0,0.0036228,"\int \frac{(c+d) (a+b x)}{e} \, dx","Int[((c + d)*(a + b*x))/e,x]","\frac{(c+d) (a+b x)^2}{2 b e}","\frac{(c+d) (a+b x)^2}{2 b e}",1,"((c + d)*(a + b*x)^2)/(2*b*e)","A",1,1,12,0.08333,1,"{9}"
157,1,70,0,0.0344801,"\int \frac{x^5}{a+b x} \, dx","Int[x^5/(a + b*x),x]","-\frac{a^3 x^2}{2 b^4}+\frac{a^2 x^3}{3 b^3}+\frac{a^4 x}{b^5}-\frac{a^5 \log (a+b x)}{b^6}-\frac{a x^4}{4 b^2}+\frac{x^5}{5 b}","-\frac{a^3 x^2}{2 b^4}+\frac{a^2 x^3}{3 b^3}+\frac{a^4 x}{b^5}-\frac{a^5 \log (a+b x)}{b^6}-\frac{a x^4}{4 b^2}+\frac{x^5}{5 b}",1,"(a^4*x)/b^5 - (a^3*x^2)/(2*b^4) + (a^2*x^3)/(3*b^3) - (a*x^4)/(4*b^2) + x^5/(5*b) - (a^5*Log[a + b*x])/b^6","A",2,1,11,0.09091,1,"{43}"
158,1,57,0,0.0231751,"\int \frac{x^4}{a+b x} \, dx","Int[x^4/(a + b*x),x]","\frac{a^2 x^2}{2 b^3}-\frac{a^3 x}{b^4}+\frac{a^4 \log (a+b x)}{b^5}-\frac{a x^3}{3 b^2}+\frac{x^4}{4 b}","\frac{a^2 x^2}{2 b^3}-\frac{a^3 x}{b^4}+\frac{a^4 \log (a+b x)}{b^5}-\frac{a x^3}{3 b^2}+\frac{x^4}{4 b}",1,"-((a^3*x)/b^4) + (a^2*x^2)/(2*b^3) - (a*x^3)/(3*b^2) + x^4/(4*b) + (a^4*Log[a + b*x])/b^5","A",2,1,11,0.09091,1,"{43}"
159,1,44,0,0.0196606,"\int \frac{x^3}{a+b x} \, dx","Int[x^3/(a + b*x),x]","\frac{a^2 x}{b^3}-\frac{a^3 \log (a+b x)}{b^4}-\frac{a x^2}{2 b^2}+\frac{x^3}{3 b}","\frac{a^2 x}{b^3}-\frac{a^3 \log (a+b x)}{b^4}-\frac{a x^2}{2 b^2}+\frac{x^3}{3 b}",1,"(a^2*x)/b^3 - (a*x^2)/(2*b^2) + x^3/(3*b) - (a^3*Log[a + b*x])/b^4","A",2,1,11,0.09091,1,"{43}"
160,1,31,0,0.013926,"\int \frac{x^2}{a+b x} \, dx","Int[x^2/(a + b*x),x]","\frac{a^2 \log (a+b x)}{b^3}-\frac{a x}{b^2}+\frac{x^2}{2 b}","\frac{a^2 \log (a+b x)}{b^3}-\frac{a x}{b^2}+\frac{x^2}{2 b}",1,"-((a*x)/b^2) + x^2/(2*b) + (a^2*Log[a + b*x])/b^3","A",2,1,11,0.09091,1,"{43}"
161,1,18,0,0.0092203,"\int \frac{x}{a+b x} \, dx","Int[x/(a + b*x),x]","\frac{x}{b}-\frac{a \log (a+b x)}{b^2}","\frac{x}{b}-\frac{a \log (a+b x)}{b^2}",1,"x/b - (a*Log[a + b*x])/b^2","A",2,1,9,0.1111,1,"{43}"
162,1,10,0,0.0016758,"\int \frac{1}{a+b x} \, dx","Int[(a + b*x)^(-1),x]","\frac{\log (a+b x)}{b}","\frac{\log (a+b x)}{b}",1,"Log[a + b*x]/b","A",1,1,7,0.1429,1,"{31}"
163,1,18,0,0.0038605,"\int \frac{1}{x (a+b x)} \, dx","Int[1/(x*(a + b*x)),x]","\frac{\log (x)}{a}-\frac{\log (a+b x)}{a}","\frac{\log (x)}{a}-\frac{\log (a+b x)}{a}",1,"Log[x]/a - Log[a + b*x]/a","A",3,3,11,0.2727,1,"{36, 29, 31}"
164,1,28,0,0.012679,"\int \frac{1}{x^2 (a+b x)} \, dx","Int[1/(x^2*(a + b*x)),x]","-\frac{b \log (x)}{a^2}+\frac{b \log (a+b x)}{a^2}-\frac{1}{a x}","-\frac{b \log (x)}{a^2}+\frac{b \log (a+b x)}{a^2}-\frac{1}{a x}",1,"-(1/(a*x)) - (b*Log[x])/a^2 + (b*Log[a + b*x])/a^2","A",2,1,11,0.09091,1,"{44}"
165,1,42,0,0.0175658,"\int \frac{1}{x^3 (a+b x)} \, dx","Int[1/(x^3*(a + b*x)),x]","\frac{b^2 \log (x)}{a^3}-\frac{b^2 \log (a+b x)}{a^3}+\frac{b}{a^2 x}-\frac{1}{2 a x^2}","\frac{b^2 \log (x)}{a^3}-\frac{b^2 \log (a+b x)}{a^3}+\frac{b}{a^2 x}-\frac{1}{2 a x^2}",1,"-1/(2*a*x^2) + b/(a^2*x) + (b^2*Log[x])/a^3 - (b^2*Log[a + b*x])/a^3","A",2,1,11,0.09091,1,"{44}"
166,1,56,0,0.0214565,"\int \frac{1}{x^4 (a+b x)} \, dx","Int[1/(x^4*(a + b*x)),x]","-\frac{b^2}{a^3 x}-\frac{b^3 \log (x)}{a^4}+\frac{b^3 \log (a+b x)}{a^4}+\frac{b}{2 a^2 x^2}-\frac{1}{3 a x^3}","-\frac{b^2}{a^3 x}-\frac{b^3 \log (x)}{a^4}+\frac{b^3 \log (a+b x)}{a^4}+\frac{b}{2 a^2 x^2}-\frac{1}{3 a x^3}",1,"-1/(3*a*x^3) + b/(2*a^2*x^2) - b^2/(a^3*x) - (b^3*Log[x])/a^4 + (b^3*Log[a + b*x])/a^4","A",2,1,11,0.09091,1,"{44}"
167,1,68,0,0.0354385,"\int \frac{1}{x^5 (a+b x)} \, dx","Int[1/(x^5*(a + b*x)),x]","-\frac{b^2}{2 a^3 x^2}+\frac{b^3}{a^4 x}+\frac{b^4 \log (x)}{a^5}-\frac{b^4 \log (a+b x)}{a^5}+\frac{b}{3 a^2 x^3}-\frac{1}{4 a x^4}","-\frac{b^2}{2 a^3 x^2}+\frac{b^3}{a^4 x}+\frac{b^4 \log (x)}{a^5}-\frac{b^4 \log (a+b x)}{a^5}+\frac{b}{3 a^2 x^3}-\frac{1}{4 a x^4}",1,"-1/(4*a*x^4) + b/(3*a^2*x^3) - b^2/(2*a^3*x^2) + b^3/(a^4*x) + (b^4*Log[x])/a^5 - (b^4*Log[a + b*x])/a^5","A",2,1,11,0.09091,1,"{44}"
168,1,81,0,0.0592848,"\int \frac{x^6}{(a+b x)^2} \, dx","Int[x^6/(a + b*x)^2,x]","-\frac{2 a^3 x^2}{b^5}+\frac{a^2 x^3}{b^4}-\frac{a^6}{b^7 (a+b x)}+\frac{5 a^4 x}{b^6}-\frac{6 a^5 \log (a+b x)}{b^7}-\frac{a x^4}{2 b^3}+\frac{x^5}{5 b^2}","-\frac{2 a^3 x^2}{b^5}+\frac{a^2 x^3}{b^4}-\frac{a^6}{b^7 (a+b x)}+\frac{5 a^4 x}{b^6}-\frac{6 a^5 \log (a+b x)}{b^7}-\frac{a x^4}{2 b^3}+\frac{x^5}{5 b^2}",1,"(5*a^4*x)/b^6 - (2*a^3*x^2)/b^5 + (a^2*x^3)/b^4 - (a*x^4)/(2*b^3) + x^5/(5*b^2) - a^6/(b^7*(a + b*x)) - (6*a^5*Log[a + b*x])/b^7","A",2,1,11,0.09091,1,"{43}"
169,1,72,0,0.0423157,"\int \frac{x^5}{(a+b x)^2} \, dx","Int[x^5/(a + b*x)^2,x]","\frac{3 a^2 x^2}{2 b^4}+\frac{a^5}{b^6 (a+b x)}-\frac{4 a^3 x}{b^5}+\frac{5 a^4 \log (a+b x)}{b^6}-\frac{2 a x^3}{3 b^3}+\frac{x^4}{4 b^2}","\frac{3 a^2 x^2}{2 b^4}+\frac{a^5}{b^6 (a+b x)}-\frac{4 a^3 x}{b^5}+\frac{5 a^4 \log (a+b x)}{b^6}-\frac{2 a x^3}{3 b^3}+\frac{x^4}{4 b^2}",1,"(-4*a^3*x)/b^5 + (3*a^2*x^2)/(2*b^4) - (2*a*x^3)/(3*b^3) + x^4/(4*b^2) + a^5/(b^6*(a + b*x)) + (5*a^4*Log[a + b*x])/b^6","A",2,1,11,0.09091,1,"{43}"
170,1,58,0,0.0329027,"\int \frac{x^4}{(a+b x)^2} \, dx","Int[x^4/(a + b*x)^2,x]","-\frac{a^4}{b^5 (a+b x)}+\frac{3 a^2 x}{b^4}-\frac{4 a^3 \log (a+b x)}{b^5}-\frac{a x^2}{b^3}+\frac{x^3}{3 b^2}","-\frac{a^4}{b^5 (a+b x)}+\frac{3 a^2 x}{b^4}-\frac{4 a^3 \log (a+b x)}{b^5}-\frac{a x^2}{b^3}+\frac{x^3}{3 b^2}",1,"(3*a^2*x)/b^4 - (a*x^2)/b^3 + x^3/(3*b^2) - a^4/(b^5*(a + b*x)) - (4*a^3*Log[a + b*x])/b^5","A",2,1,11,0.09091,1,"{43}"
171,1,46,0,0.0268024,"\int \frac{x^3}{(a+b x)^2} \, dx","Int[x^3/(a + b*x)^2,x]","\frac{a^3}{b^4 (a+b x)}+\frac{3 a^2 \log (a+b x)}{b^4}-\frac{2 a x}{b^3}+\frac{x^2}{2 b^2}","\frac{a^3}{b^4 (a+b x)}+\frac{3 a^2 \log (a+b x)}{b^4}-\frac{2 a x}{b^3}+\frac{x^2}{2 b^2}",1,"(-2*a*x)/b^3 + x^2/(2*b^2) + a^3/(b^4*(a + b*x)) + (3*a^2*Log[a + b*x])/b^4","A",2,1,11,0.09091,1,"{43}"
172,1,33,0,0.0179673,"\int \frac{x^2}{(a+b x)^2} \, dx","Int[x^2/(a + b*x)^2,x]","-\frac{a^2}{b^3 (a+b x)}-\frac{2 a \log (a+b x)}{b^3}+\frac{x}{b^2}","-\frac{a^2}{b^3 (a+b x)}-\frac{2 a \log (a+b x)}{b^3}+\frac{x}{b^2}",1,"x/b^2 - a^2/(b^3*(a + b*x)) - (2*a*Log[a + b*x])/b^3","A",2,1,11,0.09091,1,"{43}"
173,1,23,0,0.0119928,"\int \frac{x}{(a+b x)^2} \, dx","Int[x/(a + b*x)^2,x]","\frac{a}{b^2 (a+b x)}+\frac{\log (a+b x)}{b^2}","\frac{a}{b^2 (a+b x)}+\frac{\log (a+b x)}{b^2}",1,"a/(b^2*(a + b*x)) + Log[a + b*x]/b^2","A",2,1,9,0.1111,1,"{43}"
174,1,12,0,0.0017349,"\int \frac{1}{(a+b x)^2} \, dx","Int[(a + b*x)^(-2),x]","-\frac{1}{b (a+b x)}","-\frac{1}{b (a+b x)}",1,"-(1/(b*(a + b*x)))","A",1,1,7,0.1429,1,"{32}"
175,1,29,0,0.014131,"\int \frac{1}{x (a+b x)^2} \, dx","Int[1/(x*(a + b*x)^2),x]","-\frac{\log (a+b x)}{a^2}+\frac{\log (x)}{a^2}+\frac{1}{a (a+b x)}","-\frac{\log (a+b x)}{a^2}+\frac{\log (x)}{a^2}+\frac{1}{a (a+b x)}",1,"1/(a*(a + b*x)) + Log[x]/a^2 - Log[a + b*x]/a^2","A",2,1,11,0.09091,1,"{44}"
176,1,42,0,0.0208581,"\int \frac{1}{x^2 (a+b x)^2} \, dx","Int[1/(x^2*(a + b*x)^2),x]","-\frac{b}{a^2 (a+b x)}-\frac{2 b \log (x)}{a^3}+\frac{2 b \log (a+b x)}{a^3}-\frac{1}{a^2 x}","-\frac{b}{a^2 (a+b x)}-\frac{2 b \log (x)}{a^3}+\frac{2 b \log (a+b x)}{a^3}-\frac{1}{a^2 x}",1,"-(1/(a^2*x)) - b/(a^2*(a + b*x)) - (2*b*Log[x])/a^3 + (2*b*Log[a + b*x])/a^3","A",2,1,11,0.09091,1,"{44}"
177,1,58,0,0.0276379,"\int \frac{1}{x^3 (a+b x)^2} \, dx","Int[1/(x^3*(a + b*x)^2),x]","\frac{b^2}{a^3 (a+b x)}+\frac{3 b^2 \log (x)}{a^4}-\frac{3 b^2 \log (a+b x)}{a^4}+\frac{2 b}{a^3 x}-\frac{1}{2 a^2 x^2}","\frac{b^2}{a^3 (a+b x)}+\frac{3 b^2 \log (x)}{a^4}-\frac{3 b^2 \log (a+b x)}{a^4}+\frac{2 b}{a^3 x}-\frac{1}{2 a^2 x^2}",1,"-1/(2*a^2*x^2) + (2*b)/(a^3*x) + b^2/(a^3*(a + b*x)) + (3*b^2*Log[x])/a^4 - (3*b^2*Log[a + b*x])/a^4","A",2,1,11,0.09091,1,"{44}"
178,1,69,0,0.0347626,"\int \frac{1}{x^4 (a+b x)^2} \, dx","Int[1/(x^4*(a + b*x)^2),x]","-\frac{b^3}{a^4 (a+b x)}-\frac{3 b^2}{a^4 x}-\frac{4 b^3 \log (x)}{a^5}+\frac{4 b^3 \log (a+b x)}{a^5}+\frac{b}{a^3 x^2}-\frac{1}{3 a^2 x^3}","-\frac{b^3}{a^4 (a+b x)}-\frac{3 b^2}{a^4 x}-\frac{4 b^3 \log (x)}{a^5}+\frac{4 b^3 \log (a+b x)}{a^5}+\frac{b}{a^3 x^2}-\frac{1}{3 a^2 x^3}",1,"-1/(3*a^2*x^3) + b/(a^3*x^2) - (3*b^2)/(a^4*x) - b^3/(a^4*(a + b*x)) - (4*b^3*Log[x])/a^5 + (4*b^3*Log[a + b*x])/a^5","A",2,1,11,0.09091,1,"{44}"
179,1,84,0,0.0428869,"\int \frac{1}{x^5 (a+b x)^2} \, dx","Int[1/(x^5*(a + b*x)^2),x]","-\frac{3 b^2}{2 a^4 x^2}+\frac{b^4}{a^5 (a+b x)}+\frac{4 b^3}{a^5 x}+\frac{5 b^4 \log (x)}{a^6}-\frac{5 b^4 \log (a+b x)}{a^6}+\frac{2 b}{3 a^3 x^3}-\frac{1}{4 a^2 x^4}","-\frac{3 b^2}{2 a^4 x^2}+\frac{b^4}{a^5 (a+b x)}+\frac{4 b^3}{a^5 x}+\frac{5 b^4 \log (x)}{a^6}-\frac{5 b^4 \log (a+b x)}{a^6}+\frac{2 b}{3 a^3 x^3}-\frac{1}{4 a^2 x^4}",1,"-1/(4*a^2*x^4) + (2*b)/(3*a^3*x^3) - (3*b^2)/(2*a^4*x^2) + (4*b^3)/(a^5*x) + b^4/(a^5*(a + b*x)) + (5*b^4*Log[x])/a^6 - (5*b^4*Log[a + b*x])/a^6","A",2,1,11,0.09091,1,"{44}"
180,1,99,0,0.0703669,"\int \frac{x^7}{(a+b x)^3} \, dx","Int[x^7/(a + b*x)^3,x]","-\frac{5 a^3 x^2}{b^6}+\frac{2 a^2 x^3}{b^5}+\frac{a^7}{2 b^8 (a+b x)^2}-\frac{7 a^6}{b^8 (a+b x)}+\frac{15 a^4 x}{b^7}-\frac{21 a^5 \log (a+b x)}{b^8}-\frac{3 a x^4}{4 b^4}+\frac{x^5}{5 b^3}","-\frac{5 a^3 x^2}{b^6}+\frac{2 a^2 x^3}{b^5}+\frac{a^7}{2 b^8 (a+b x)^2}-\frac{7 a^6}{b^8 (a+b x)}+\frac{15 a^4 x}{b^7}-\frac{21 a^5 \log (a+b x)}{b^8}-\frac{3 a x^4}{4 b^4}+\frac{x^5}{5 b^3}",1,"(15*a^4*x)/b^7 - (5*a^3*x^2)/b^6 + (2*a^2*x^3)/b^5 - (3*a*x^4)/(4*b^4) + x^5/(5*b^3) + a^7/(2*b^8*(a + b*x)^2) - (7*a^6)/(b^8*(a + b*x)) - (21*a^5*Log[a + b*x])/b^8","A",2,1,11,0.09091,1,"{43}"
181,1,86,0,0.0525685,"\int \frac{x^6}{(a+b x)^3} \, dx","Int[x^6/(a + b*x)^3,x]","\frac{3 a^2 x^2}{b^5}-\frac{a^6}{2 b^7 (a+b x)^2}+\frac{6 a^5}{b^7 (a+b x)}-\frac{10 a^3 x}{b^6}+\frac{15 a^4 \log (a+b x)}{b^7}-\frac{a x^3}{b^4}+\frac{x^4}{4 b^3}","\frac{3 a^2 x^2}{b^5}-\frac{a^6}{2 b^7 (a+b x)^2}+\frac{6 a^5}{b^7 (a+b x)}-\frac{10 a^3 x}{b^6}+\frac{15 a^4 \log (a+b x)}{b^7}-\frac{a x^3}{b^4}+\frac{x^4}{4 b^3}",1,"(-10*a^3*x)/b^6 + (3*a^2*x^2)/b^5 - (a*x^3)/b^4 + x^4/(4*b^3) - a^6/(2*b^7*(a + b*x)^2) + (6*a^5)/(b^7*(a + b*x)) + (15*a^4*Log[a + b*x])/b^7","A",2,1,11,0.09091,1,"{43}"
182,1,77,0,0.0460517,"\int \frac{x^5}{(a+b x)^3} \, dx","Int[x^5/(a + b*x)^3,x]","\frac{a^5}{2 b^6 (a+b x)^2}-\frac{5 a^4}{b^6 (a+b x)}+\frac{6 a^2 x}{b^5}-\frac{10 a^3 \log (a+b x)}{b^6}-\frac{3 a x^2}{2 b^4}+\frac{x^3}{3 b^3}","\frac{a^5}{2 b^6 (a+b x)^2}-\frac{5 a^4}{b^6 (a+b x)}+\frac{6 a^2 x}{b^5}-\frac{10 a^3 \log (a+b x)}{b^6}-\frac{3 a x^2}{2 b^4}+\frac{x^3}{3 b^3}",1,"(6*a^2*x)/b^5 - (3*a*x^2)/(2*b^4) + x^3/(3*b^3) + a^5/(2*b^6*(a + b*x)^2) - (5*a^4)/(b^6*(a + b*x)) - (10*a^3*Log[a + b*x])/b^6","A",2,1,11,0.09091,1,"{43}"
183,1,64,0,0.0361858,"\int \frac{x^4}{(a+b x)^3} \, dx","Int[x^4/(a + b*x)^3,x]","-\frac{a^4}{2 b^5 (a+b x)^2}+\frac{4 a^3}{b^5 (a+b x)}+\frac{6 a^2 \log (a+b x)}{b^5}-\frac{3 a x}{b^4}+\frac{x^2}{2 b^3}","-\frac{a^4}{2 b^5 (a+b x)^2}+\frac{4 a^3}{b^5 (a+b x)}+\frac{6 a^2 \log (a+b x)}{b^5}-\frac{3 a x}{b^4}+\frac{x^2}{2 b^3}",1,"(-3*a*x)/b^4 + x^2/(2*b^3) - a^4/(2*b^5*(a + b*x)^2) + (4*a^3)/(b^5*(a + b*x)) + (6*a^2*Log[a + b*x])/b^5","A",2,1,11,0.09091,1,"{43}"
184,1,50,0,0.0262389,"\int \frac{x^3}{(a+b x)^3} \, dx","Int[x^3/(a + b*x)^3,x]","\frac{a^3}{2 b^4 (a+b x)^2}-\frac{3 a^2}{b^4 (a+b x)}-\frac{3 a \log (a+b x)}{b^4}+\frac{x}{b^3}","\frac{a^3}{2 b^4 (a+b x)^2}-\frac{3 a^2}{b^4 (a+b x)}-\frac{3 a \log (a+b x)}{b^4}+\frac{x}{b^3}",1,"x/b^3 + a^3/(2*b^4*(a + b*x)^2) - (3*a^2)/(b^4*(a + b*x)) - (3*a*Log[a + b*x])/b^4","A",2,1,11,0.09091,1,"{43}"
185,1,41,0,0.020299,"\int \frac{x^2}{(a+b x)^3} \, dx","Int[x^2/(a + b*x)^3,x]","-\frac{a^2}{2 b^3 (a+b x)^2}+\frac{2 a}{b^3 (a+b x)}+\frac{\log (a+b x)}{b^3}","-\frac{a^2}{2 b^3 (a+b x)^2}+\frac{2 a}{b^3 (a+b x)}+\frac{\log (a+b x)}{b^3}",1,"-a^2/(2*b^3*(a + b*x)^2) + (2*a)/(b^3*(a + b*x)) + Log[a + b*x]/b^3","A",2,1,11,0.09091,1,"{43}"
186,1,17,0,0.0016454,"\int \frac{x}{(a+b x)^3} \, dx","Int[x/(a + b*x)^3,x]","\frac{x^2}{2 a (a+b x)^2}","\frac{x^2}{2 a (a+b x)^2}",1,"x^2/(2*a*(a + b*x)^2)","A",1,1,9,0.1111,1,"{37}"
187,1,14,0,0.0014833,"\int \frac{1}{(a+b x)^3} \, dx","Int[(a + b*x)^(-3),x]","-\frac{1}{2 b (a+b x)^2}","-\frac{1}{2 b (a+b x)^2}",1,"-1/(2*b*(a + b*x)^2)","A",1,1,7,0.1429,1,"{32}"
188,1,43,0,0.0194961,"\int \frac{1}{x (a+b x)^3} \, dx","Int[1/(x*(a + b*x)^3),x]","\frac{1}{a^2 (a+b x)}-\frac{\log (a+b x)}{a^3}+\frac{\log (x)}{a^3}+\frac{1}{2 a (a+b x)^2}","\frac{1}{a^2 (a+b x)}-\frac{\log (a+b x)}{a^3}+\frac{\log (x)}{a^3}+\frac{1}{2 a (a+b x)^2}",1,"1/(2*a*(a + b*x)^2) + 1/(a^2*(a + b*x)) + Log[x]/a^3 - Log[a + b*x]/a^3","A",2,1,11,0.09091,1,"{44}"
189,1,57,0,0.0292758,"\int \frac{1}{x^2 (a+b x)^3} \, dx","Int[1/(x^2*(a + b*x)^3),x]","-\frac{2 b}{a^3 (a+b x)}-\frac{b}{2 a^2 (a+b x)^2}-\frac{3 b \log (x)}{a^4}+\frac{3 b \log (a+b x)}{a^4}-\frac{1}{a^3 x}","-\frac{2 b}{a^3 (a+b x)}-\frac{b}{2 a^2 (a+b x)^2}-\frac{3 b \log (x)}{a^4}+\frac{3 b \log (a+b x)}{a^4}-\frac{1}{a^3 x}",1,"-(1/(a^3*x)) - b/(2*a^2*(a + b*x)^2) - (2*b)/(a^3*(a + b*x)) - (3*b*Log[x])/a^4 + (3*b*Log[a + b*x])/a^4","A",2,1,11,0.09091,1,"{44}"
190,1,76,0,0.0359509,"\int \frac{1}{x^3 (a+b x)^3} \, dx","Int[1/(x^3*(a + b*x)^3),x]","\frac{3 b^2}{a^4 (a+b x)}+\frac{b^2}{2 a^3 (a+b x)^2}+\frac{6 b^2 \log (x)}{a^5}-\frac{6 b^2 \log (a+b x)}{a^5}+\frac{3 b}{a^4 x}-\frac{1}{2 a^3 x^2}","\frac{3 b^2}{a^4 (a+b x)}+\frac{b^2}{2 a^3 (a+b x)^2}+\frac{6 b^2 \log (x)}{a^5}-\frac{6 b^2 \log (a+b x)}{a^5}+\frac{3 b}{a^4 x}-\frac{1}{2 a^3 x^2}",1,"-1/(2*a^3*x^2) + (3*b)/(a^4*x) + b^2/(2*a^3*(a + b*x)^2) + (3*b^2)/(a^4*(a + b*x)) + (6*b^2*Log[x])/a^5 - (6*b^2*Log[a + b*x])/a^5","A",2,1,11,0.09091,1,"{44}"
191,1,89,0,0.0477162,"\int \frac{1}{x^4 (a+b x)^3} \, dx","Int[1/(x^4*(a + b*x)^3),x]","-\frac{4 b^3}{a^5 (a+b x)}-\frac{b^3}{2 a^4 (a+b x)^2}-\frac{6 b^2}{a^5 x}-\frac{10 b^3 \log (x)}{a^6}+\frac{10 b^3 \log (a+b x)}{a^6}+\frac{3 b}{2 a^4 x^2}-\frac{1}{3 a^3 x^3}","-\frac{4 b^3}{a^5 (a+b x)}-\frac{b^3}{2 a^4 (a+b x)^2}-\frac{6 b^2}{a^5 x}-\frac{10 b^3 \log (x)}{a^6}+\frac{10 b^3 \log (a+b x)}{a^6}+\frac{3 b}{2 a^4 x^2}-\frac{1}{3 a^3 x^3}",1,"-1/(3*a^3*x^3) + (3*b)/(2*a^4*x^2) - (6*b^2)/(a^5*x) - b^3/(2*a^4*(a + b*x)^2) - (4*b^3)/(a^5*(a + b*x)) - (10*b^3*Log[x])/a^6 + (10*b^3*Log[a + b*x])/a^6","A",2,1,11,0.09091,1,"{44}"
192,1,97,0,0.052223,"\int \frac{1}{x^5 (a+b x)^3} \, dx","Int[1/(x^5*(a + b*x)^3),x]","-\frac{3 b^2}{a^5 x^2}+\frac{5 b^4}{a^6 (a+b x)}+\frac{b^4}{2 a^5 (a+b x)^2}+\frac{10 b^3}{a^6 x}+\frac{15 b^4 \log (x)}{a^7}-\frac{15 b^4 \log (a+b x)}{a^7}+\frac{b}{a^4 x^3}-\frac{1}{4 a^3 x^4}","-\frac{3 b^2}{a^5 x^2}+\frac{5 b^4}{a^6 (a+b x)}+\frac{b^4}{2 a^5 (a+b x)^2}+\frac{10 b^3}{a^6 x}+\frac{15 b^4 \log (x)}{a^7}-\frac{15 b^4 \log (a+b x)}{a^7}+\frac{b}{a^4 x^3}-\frac{1}{4 a^3 x^4}",1,"-1/(4*a^3*x^4) + b/(a^4*x^3) - (3*b^2)/(a^5*x^2) + (10*b^3)/(a^6*x) + b^4/(2*a^5*(a + b*x)^2) + (5*b^4)/(a^6*(a + b*x)) + (15*b^4*Log[x])/a^7 - (15*b^4*Log[a + b*x])/a^7","A",2,1,11,0.09091,1,"{44}"
193,1,114,0,0.08529,"\int \frac{x^8}{(a+b x)^4} \, dx","Int[x^8/(a + b*x)^4,x]","-\frac{10 a^3 x^2}{b^7}+\frac{10 a^2 x^3}{3 b^6}-\frac{a^8}{3 b^9 (a+b x)^3}+\frac{4 a^7}{b^9 (a+b x)^2}-\frac{28 a^6}{b^9 (a+b x)}+\frac{35 a^4 x}{b^8}-\frac{56 a^5 \log (a+b x)}{b^9}-\frac{a x^4}{b^5}+\frac{x^5}{5 b^4}","-\frac{10 a^3 x^2}{b^7}+\frac{10 a^2 x^3}{3 b^6}-\frac{a^8}{3 b^9 (a+b x)^3}+\frac{4 a^7}{b^9 (a+b x)^2}-\frac{28 a^6}{b^9 (a+b x)}+\frac{35 a^4 x}{b^8}-\frac{56 a^5 \log (a+b x)}{b^9}-\frac{a x^4}{b^5}+\frac{x^5}{5 b^4}",1,"(35*a^4*x)/b^8 - (10*a^3*x^2)/b^7 + (10*a^2*x^3)/(3*b^6) - (a*x^4)/b^5 + x^5/(5*b^4) - a^8/(3*b^9*(a + b*x)^3) + (4*a^7)/(b^9*(a + b*x)^2) - (28*a^6)/(b^9*(a + b*x)) - (56*a^5*Log[a + b*x])/b^9","A",2,1,11,0.09091,1,"{43}"
194,1,105,0,0.0701249,"\int \frac{x^7}{(a+b x)^4} \, dx","Int[x^7/(a + b*x)^4,x]","\frac{5 a^2 x^2}{b^6}+\frac{a^7}{3 b^8 (a+b x)^3}-\frac{7 a^6}{2 b^8 (a+b x)^2}+\frac{21 a^5}{b^8 (a+b x)}-\frac{20 a^3 x}{b^7}+\frac{35 a^4 \log (a+b x)}{b^8}-\frac{4 a x^3}{3 b^5}+\frac{x^4}{4 b^4}","\frac{5 a^2 x^2}{b^6}+\frac{a^7}{3 b^8 (a+b x)^3}-\frac{7 a^6}{2 b^8 (a+b x)^2}+\frac{21 a^5}{b^8 (a+b x)}-\frac{20 a^3 x}{b^7}+\frac{35 a^4 \log (a+b x)}{b^8}-\frac{4 a x^3}{3 b^5}+\frac{x^4}{4 b^4}",1,"(-20*a^3*x)/b^7 + (5*a^2*x^2)/b^6 - (4*a*x^3)/(3*b^5) + x^4/(4*b^4) + a^7/(3*b^8*(a + b*x)^3) - (7*a^6)/(2*b^8*(a + b*x)^2) + (21*a^5)/(b^8*(a + b*x)) + (35*a^4*Log[a + b*x])/b^8","A",2,1,11,0.09091,1,"{43}"
195,1,90,0,0.0565142,"\int \frac{x^6}{(a+b x)^4} \, dx","Int[x^6/(a + b*x)^4,x]","-\frac{a^6}{3 b^7 (a+b x)^3}+\frac{3 a^5}{b^7 (a+b x)^2}-\frac{15 a^4}{b^7 (a+b x)}+\frac{10 a^2 x}{b^6}-\frac{20 a^3 \log (a+b x)}{b^7}-\frac{2 a x^2}{b^5}+\frac{x^3}{3 b^4}","-\frac{a^6}{3 b^7 (a+b x)^3}+\frac{3 a^5}{b^7 (a+b x)^2}-\frac{15 a^4}{b^7 (a+b x)}+\frac{10 a^2 x}{b^6}-\frac{20 a^3 \log (a+b x)}{b^7}-\frac{2 a x^2}{b^5}+\frac{x^3}{3 b^4}",1,"(10*a^2*x)/b^6 - (2*a*x^2)/b^5 + x^3/(3*b^4) - a^6/(3*b^7*(a + b*x)^3) + (3*a^5)/(b^7*(a + b*x)^2) - (15*a^4)/(b^7*(a + b*x)) - (20*a^3*Log[a + b*x])/b^7","A",2,1,11,0.09091,1,"{43}"
196,1,81,0,0.0476785,"\int \frac{x^5}{(a+b x)^4} \, dx","Int[x^5/(a + b*x)^4,x]","\frac{a^5}{3 b^6 (a+b x)^3}-\frac{5 a^4}{2 b^6 (a+b x)^2}+\frac{10 a^3}{b^6 (a+b x)}+\frac{10 a^2 \log (a+b x)}{b^6}-\frac{4 a x}{b^5}+\frac{x^2}{2 b^4}","\frac{a^5}{3 b^6 (a+b x)^3}-\frac{5 a^4}{2 b^6 (a+b x)^2}+\frac{10 a^3}{b^6 (a+b x)}+\frac{10 a^2 \log (a+b x)}{b^6}-\frac{4 a x}{b^5}+\frac{x^2}{2 b^4}",1,"(-4*a*x)/b^5 + x^2/(2*b^4) + a^5/(3*b^6*(a + b*x)^3) - (5*a^4)/(2*b^6*(a + b*x)^2) + (10*a^3)/(b^6*(a + b*x)) + (10*a^2*Log[a + b*x])/b^6","A",2,1,11,0.09091,1,"{43}"
197,1,65,0,0.0363399,"\int \frac{x^4}{(a+b x)^4} \, dx","Int[x^4/(a + b*x)^4,x]","-\frac{a^4}{3 b^5 (a+b x)^3}+\frac{2 a^3}{b^5 (a+b x)^2}-\frac{6 a^2}{b^5 (a+b x)}-\frac{4 a \log (a+b x)}{b^5}+\frac{x}{b^4}","-\frac{a^4}{3 b^5 (a+b x)^3}+\frac{2 a^3}{b^5 (a+b x)^2}-\frac{6 a^2}{b^5 (a+b x)}-\frac{4 a \log (a+b x)}{b^5}+\frac{x}{b^4}",1,"x/b^4 - a^4/(3*b^5*(a + b*x)^3) + (2*a^3)/(b^5*(a + b*x)^2) - (6*a^2)/(b^5*(a + b*x)) - (4*a*Log[a + b*x])/b^5","A",2,1,11,0.09091,1,"{43}"
198,1,58,0,0.0303948,"\int \frac{x^3}{(a+b x)^4} \, dx","Int[x^3/(a + b*x)^4,x]","\frac{a^3}{3 b^4 (a+b x)^3}-\frac{3 a^2}{2 b^4 (a+b x)^2}+\frac{3 a}{b^4 (a+b x)}+\frac{\log (a+b x)}{b^4}","\frac{a^3}{3 b^4 (a+b x)^3}-\frac{3 a^2}{2 b^4 (a+b x)^2}+\frac{3 a}{b^4 (a+b x)}+\frac{\log (a+b x)}{b^4}",1,"a^3/(3*b^4*(a + b*x)^3) - (3*a^2)/(2*b^4*(a + b*x)^2) + (3*a)/(b^4*(a + b*x)) + Log[a + b*x]/b^4","A",2,1,11,0.09091,1,"{43}"
199,1,17,0,0.0016848,"\int \frac{x^2}{(a+b x)^4} \, dx","Int[x^2/(a + b*x)^4,x]","\frac{x^3}{3 a (a+b x)^3}","\frac{x^3}{3 a (a+b x)^3}",1,"x^3/(3*a*(a + b*x)^3)","A",1,1,11,0.09091,1,"{37}"
200,1,30,0,0.0128605,"\int \frac{x}{(a+b x)^4} \, dx","Int[x/(a + b*x)^4,x]","\frac{a}{3 b^2 (a+b x)^3}-\frac{1}{2 b^2 (a+b x)^2}","\frac{a}{3 b^2 (a+b x)^3}-\frac{1}{2 b^2 (a+b x)^2}",1,"a/(3*b^2*(a + b*x)^3) - 1/(2*b^2*(a + b*x)^2)","A",2,1,9,0.1111,1,"{43}"
201,1,14,0,0.0015438,"\int \frac{1}{(a+b x)^4} \, dx","Int[(a + b*x)^(-4),x]","-\frac{1}{3 b (a+b x)^3}","-\frac{1}{3 b (a+b x)^3}",1,"-1/(3*b*(a + b*x)^3)","A",1,1,7,0.1429,1,"{32}"
202,1,57,0,0.0283706,"\int \frac{1}{x (a+b x)^4} \, dx","Int[1/(x*(a + b*x)^4),x]","\frac{1}{a^3 (a+b x)}+\frac{1}{2 a^2 (a+b x)^2}-\frac{\log (a+b x)}{a^4}+\frac{\log (x)}{a^4}+\frac{1}{3 a (a+b x)^3}","\frac{1}{a^3 (a+b x)}+\frac{1}{2 a^2 (a+b x)^2}-\frac{\log (a+b x)}{a^4}+\frac{\log (x)}{a^4}+\frac{1}{3 a (a+b x)^3}",1,"1/(3*a*(a + b*x)^3) + 1/(2*a^2*(a + b*x)^2) + 1/(a^3*(a + b*x)) + Log[x]/a^4 - Log[a + b*x]/a^4","A",2,1,11,0.09091,1,"{44}"
203,1,70,0,0.0388295,"\int \frac{1}{x^2 (a+b x)^4} \, dx","Int[1/(x^2*(a + b*x)^4),x]","-\frac{3 b}{a^4 (a+b x)}-\frac{b}{a^3 (a+b x)^2}-\frac{b}{3 a^2 (a+b x)^3}-\frac{4 b \log (x)}{a^5}+\frac{4 b \log (a+b x)}{a^5}-\frac{1}{a^4 x}","-\frac{3 b}{a^4 (a+b x)}-\frac{b}{a^3 (a+b x)^2}-\frac{b}{3 a^2 (a+b x)^3}-\frac{4 b \log (x)}{a^5}+\frac{4 b \log (a+b x)}{a^5}-\frac{1}{a^4 x}",1,"-(1/(a^4*x)) - b/(3*a^2*(a + b*x)^3) - b/(a^3*(a + b*x)^2) - (3*b)/(a^4*(a + b*x)) - (4*b*Log[x])/a^5 + (4*b*Log[a + b*x])/a^5","A",2,1,11,0.09091,1,"{44}"
204,1,93,0,0.0481338,"\int \frac{1}{x^3 (a+b x)^4} \, dx","Int[1/(x^3*(a + b*x)^4),x]","\frac{6 b^2}{a^5 (a+b x)}+\frac{3 b^2}{2 a^4 (a+b x)^2}+\frac{b^2}{3 a^3 (a+b x)^3}+\frac{10 b^2 \log (x)}{a^6}-\frac{10 b^2 \log (a+b x)}{a^6}+\frac{4 b}{a^5 x}-\frac{1}{2 a^4 x^2}","\frac{6 b^2}{a^5 (a+b x)}+\frac{3 b^2}{2 a^4 (a+b x)^2}+\frac{b^2}{3 a^3 (a+b x)^3}+\frac{10 b^2 \log (x)}{a^6}-\frac{10 b^2 \log (a+b x)}{a^6}+\frac{4 b}{a^5 x}-\frac{1}{2 a^4 x^2}",1,"-1/(2*a^4*x^2) + (4*b)/(a^5*x) + b^2/(3*a^3*(a + b*x)^3) + (3*b^2)/(2*a^4*(a + b*x)^2) + (6*b^2)/(a^5*(a + b*x)) + (10*b^2*Log[x])/a^6 - (10*b^2*Log[a + b*x])/a^6","A",2,1,11,0.09091,1,"{44}"
205,1,102,0,0.0529369,"\int \frac{1}{x^4 (a+b x)^4} \, dx","Int[1/(x^4*(a + b*x)^4),x]","-\frac{10 b^3}{a^6 (a+b x)}-\frac{2 b^3}{a^5 (a+b x)^2}-\frac{b^3}{3 a^4 (a+b x)^3}-\frac{10 b^2}{a^6 x}-\frac{20 b^3 \log (x)}{a^7}+\frac{20 b^3 \log (a+b x)}{a^7}+\frac{2 b}{a^5 x^2}-\frac{1}{3 a^4 x^3}","-\frac{10 b^3}{a^6 (a+b x)}-\frac{2 b^3}{a^5 (a+b x)^2}-\frac{b^3}{3 a^4 (a+b x)^3}-\frac{10 b^2}{a^6 x}-\frac{20 b^3 \log (x)}{a^7}+\frac{20 b^3 \log (a+b x)}{a^7}+\frac{2 b}{a^5 x^2}-\frac{1}{3 a^4 x^3}",1,"-1/(3*a^4*x^3) + (2*b)/(a^5*x^2) - (10*b^2)/(a^6*x) - b^3/(3*a^4*(a + b*x)^3) - (2*b^3)/(a^5*(a + b*x)^2) - (10*b^3)/(a^6*(a + b*x)) - (20*b^3*Log[x])/a^7 + (20*b^3*Log[a + b*x])/a^7","A",2,1,11,0.09091,1,"{44}"
206,1,117,0,0.0702539,"\int \frac{1}{x^5 (a+b x)^4} \, dx","Int[1/(x^5*(a + b*x)^4),x]","-\frac{5 b^2}{a^6 x^2}+\frac{15 b^4}{a^7 (a+b x)}+\frac{5 b^4}{2 a^6 (a+b x)^2}+\frac{b^4}{3 a^5 (a+b x)^3}+\frac{20 b^3}{a^7 x}+\frac{35 b^4 \log (x)}{a^8}-\frac{35 b^4 \log (a+b x)}{a^8}+\frac{4 b}{3 a^5 x^3}-\frac{1}{4 a^4 x^4}","-\frac{5 b^2}{a^6 x^2}+\frac{15 b^4}{a^7 (a+b x)}+\frac{5 b^4}{2 a^6 (a+b x)^2}+\frac{b^4}{3 a^5 (a+b x)^3}+\frac{20 b^3}{a^7 x}+\frac{35 b^4 \log (x)}{a^8}-\frac{35 b^4 \log (a+b x)}{a^8}+\frac{4 b}{3 a^5 x^3}-\frac{1}{4 a^4 x^4}",1,"-1/(4*a^4*x^4) + (4*b)/(3*a^5*x^3) - (5*b^2)/(a^6*x^2) + (20*b^3)/(a^7*x) + b^4/(3*a^5*(a + b*x)^3) + (5*b^4)/(2*a^6*(a + b*x)^2) + (15*b^4)/(a^7*(a + b*x)) + (35*b^4*Log[x])/a^8 - (35*b^4*Log[a + b*x])/a^8","A",2,1,11,0.09091,1,"{44}"
207,1,150,0,0.1353397,"\int \frac{x^{10}}{(a+b x)^7} \, dx","Int[x^10/(a + b*x)^7,x]","\frac{14 a^2 x^2}{b^9}-\frac{a^{10}}{6 b^{11} (a+b x)^6}+\frac{2 a^9}{b^{11} (a+b x)^5}-\frac{45 a^8}{4 b^{11} (a+b x)^4}+\frac{40 a^7}{b^{11} (a+b x)^3}-\frac{105 a^6}{b^{11} (a+b x)^2}+\frac{252 a^5}{b^{11} (a+b x)}-\frac{84 a^3 x}{b^{10}}+\frac{210 a^4 \log (a+b x)}{b^{11}}-\frac{7 a x^3}{3 b^8}+\frac{x^4}{4 b^7}","\frac{14 a^2 x^2}{b^9}-\frac{a^{10}}{6 b^{11} (a+b x)^6}+\frac{2 a^9}{b^{11} (a+b x)^5}-\frac{45 a^8}{4 b^{11} (a+b x)^4}+\frac{40 a^7}{b^{11} (a+b x)^3}-\frac{105 a^6}{b^{11} (a+b x)^2}+\frac{252 a^5}{b^{11} (a+b x)}-\frac{84 a^3 x}{b^{10}}+\frac{210 a^4 \log (a+b x)}{b^{11}}-\frac{7 a x^3}{3 b^8}+\frac{x^4}{4 b^7}",1,"(-84*a^3*x)/b^10 + (14*a^2*x^2)/b^9 - (7*a*x^3)/(3*b^8) + x^4/(4*b^7) - a^10/(6*b^11*(a + b*x)^6) + (2*a^9)/(b^11*(a + b*x)^5) - (45*a^8)/(4*b^11*(a + b*x)^4) + (40*a^7)/(b^11*(a + b*x)^3) - (105*a^6)/(b^11*(a + b*x)^2) + (252*a^5)/(b^11*(a + b*x)) + (210*a^4*Log[a + b*x])/b^11","A",2,1,11,0.09091,1,"{43}"
208,1,139,0,0.1137176,"\int \frac{x^9}{(a+b x)^7} \, dx","Int[x^9/(a + b*x)^7,x]","\frac{a^9}{6 b^{10} (a+b x)^6}-\frac{9 a^8}{5 b^{10} (a+b x)^5}+\frac{9 a^7}{b^{10} (a+b x)^4}-\frac{28 a^6}{b^{10} (a+b x)^3}+\frac{63 a^5}{b^{10} (a+b x)^2}-\frac{126 a^4}{b^{10} (a+b x)}+\frac{28 a^2 x}{b^9}-\frac{84 a^3 \log (a+b x)}{b^{10}}-\frac{7 a x^2}{2 b^8}+\frac{x^3}{3 b^7}","\frac{a^9}{6 b^{10} (a+b x)^6}-\frac{9 a^8}{5 b^{10} (a+b x)^5}+\frac{9 a^7}{b^{10} (a+b x)^4}-\frac{28 a^6}{b^{10} (a+b x)^3}+\frac{63 a^5}{b^{10} (a+b x)^2}-\frac{126 a^4}{b^{10} (a+b x)}+\frac{28 a^2 x}{b^9}-\frac{84 a^3 \log (a+b x)}{b^{10}}-\frac{7 a x^2}{2 b^8}+\frac{x^3}{3 b^7}",1,"(28*a^2*x)/b^9 - (7*a*x^2)/(2*b^8) + x^3/(3*b^7) + a^9/(6*b^10*(a + b*x)^6) - (9*a^8)/(5*b^10*(a + b*x)^5) + (9*a^7)/(b^10*(a + b*x)^4) - (28*a^6)/(b^10*(a + b*x)^3) + (63*a^5)/(b^10*(a + b*x)^2) - (126*a^4)/(b^10*(a + b*x)) - (84*a^3*Log[a + b*x])/b^10","A",2,1,11,0.09091,1,"{43}"
209,1,128,0,0.0889429,"\int \frac{x^8}{(a+b x)^7} \, dx","Int[x^8/(a + b*x)^7,x]","-\frac{a^8}{6 b^9 (a+b x)^6}+\frac{8 a^7}{5 b^9 (a+b x)^5}-\frac{7 a^6}{b^9 (a+b x)^4}+\frac{56 a^5}{3 b^9 (a+b x)^3}-\frac{35 a^4}{b^9 (a+b x)^2}+\frac{56 a^3}{b^9 (a+b x)}+\frac{28 a^2 \log (a+b x)}{b^9}-\frac{7 a x}{b^8}+\frac{x^2}{2 b^7}","-\frac{a^8}{6 b^9 (a+b x)^6}+\frac{8 a^7}{5 b^9 (a+b x)^5}-\frac{7 a^6}{b^9 (a+b x)^4}+\frac{56 a^5}{3 b^9 (a+b x)^3}-\frac{35 a^4}{b^9 (a+b x)^2}+\frac{56 a^3}{b^9 (a+b x)}+\frac{28 a^2 \log (a+b x)}{b^9}-\frac{7 a x}{b^8}+\frac{x^2}{2 b^7}",1,"(-7*a*x)/b^8 + x^2/(2*b^7) - a^8/(6*b^9*(a + b*x)^6) + (8*a^7)/(5*b^9*(a + b*x)^5) - (7*a^6)/(b^9*(a + b*x)^4) + (56*a^5)/(3*b^9*(a + b*x)^3) - (35*a^4)/(b^9*(a + b*x)^2) + (56*a^3)/(b^9*(a + b*x)) + (28*a^2*Log[a + b*x])/b^9","A",2,1,11,0.09091,1,"{43}"
210,1,118,0,0.0705354,"\int \frac{x^7}{(a+b x)^7} \, dx","Int[x^7/(a + b*x)^7,x]","\frac{a^7}{6 b^8 (a+b x)^6}-\frac{7 a^6}{5 b^8 (a+b x)^5}+\frac{21 a^5}{4 b^8 (a+b x)^4}-\frac{35 a^4}{3 b^8 (a+b x)^3}+\frac{35 a^3}{2 b^8 (a+b x)^2}-\frac{21 a^2}{b^8 (a+b x)}-\frac{7 a \log (a+b x)}{b^8}+\frac{x}{b^7}","\frac{a^7}{6 b^8 (a+b x)^6}-\frac{7 a^6}{5 b^8 (a+b x)^5}+\frac{21 a^5}{4 b^8 (a+b x)^4}-\frac{35 a^4}{3 b^8 (a+b x)^3}+\frac{35 a^3}{2 b^8 (a+b x)^2}-\frac{21 a^2}{b^8 (a+b x)}-\frac{7 a \log (a+b x)}{b^8}+\frac{x}{b^7}",1,"x/b^7 + a^7/(6*b^8*(a + b*x)^6) - (7*a^6)/(5*b^8*(a + b*x)^5) + (21*a^5)/(4*b^8*(a + b*x)^4) - (35*a^4)/(3*b^8*(a + b*x)^3) + (35*a^3)/(2*b^8*(a + b*x)^2) - (21*a^2)/(b^8*(a + b*x)) - (7*a*Log[a + b*x])/b^8","A",2,1,11,0.09091,1,"{43}"
211,1,109,0,0.0642931,"\int \frac{x^6}{(a+b x)^7} \, dx","Int[x^6/(a + b*x)^7,x]","-\frac{a^6}{6 b^7 (a+b x)^6}+\frac{6 a^5}{5 b^7 (a+b x)^5}-\frac{15 a^4}{4 b^7 (a+b x)^4}+\frac{20 a^3}{3 b^7 (a+b x)^3}-\frac{15 a^2}{2 b^7 (a+b x)^2}+\frac{6 a}{b^7 (a+b x)}+\frac{\log (a+b x)}{b^7}","-\frac{a^6}{6 b^7 (a+b x)^6}+\frac{6 a^5}{5 b^7 (a+b x)^5}-\frac{15 a^4}{4 b^7 (a+b x)^4}+\frac{20 a^3}{3 b^7 (a+b x)^3}-\frac{15 a^2}{2 b^7 (a+b x)^2}+\frac{6 a}{b^7 (a+b x)}+\frac{\log (a+b x)}{b^7}",1,"-a^6/(6*b^7*(a + b*x)^6) + (6*a^5)/(5*b^7*(a + b*x)^5) - (15*a^4)/(4*b^7*(a + b*x)^4) + (20*a^3)/(3*b^7*(a + b*x)^3) - (15*a^2)/(2*b^7*(a + b*x)^2) + (6*a)/(b^7*(a + b*x)) + Log[a + b*x]/b^7","A",2,1,11,0.09091,1,"{43}"
212,1,17,0,0.0018992,"\int \frac{x^5}{(a+b x)^7} \, dx","Int[x^5/(a + b*x)^7,x]","\frac{x^6}{6 a (a+b x)^6}","\frac{x^6}{6 a (a+b x)^6}",1,"x^6/(6*a*(a + b*x)^6)","A",1,1,11,0.09091,1,"{37}"
213,1,35,0,0.0049189,"\int \frac{x^4}{(a+b x)^7} \, dx","Int[x^4/(a + b*x)^7,x]","\frac{x^5}{30 a^2 (a+b x)^5}+\frac{x^5}{6 a (a+b x)^6}","\frac{x^5}{30 a^2 (a+b x)^5}+\frac{x^5}{6 a (a+b x)^6}",1,"x^5/(6*a*(a + b*x)^6) + x^5/(30*a^2*(a + b*x)^5)","A",2,2,11,0.1818,1,"{45, 37}"
214,1,64,0,0.0293148,"\int \frac{x^3}{(a+b x)^7} \, dx","Int[x^3/(a + b*x)^7,x]","\frac{a^3}{6 b^4 (a+b x)^6}-\frac{3 a^2}{5 b^4 (a+b x)^5}+\frac{3 a}{4 b^4 (a+b x)^4}-\frac{1}{3 b^4 (a+b x)^3}","\frac{x^4}{60 a^3 (a+b x)^4}+\frac{x^4}{15 a^2 (a+b x)^5}+\frac{x^4}{6 a (a+b x)^6}",1,"a^3/(6*b^4*(a + b*x)^6) - (3*a^2)/(5*b^4*(a + b*x)^5) + (3*a)/(4*b^4*(a + b*x)^4) - 1/(3*b^4*(a + b*x)^3)","A",2,1,11,0.09091,1,"{43}"
215,1,47,0,0.0209128,"\int \frac{x^2}{(a+b x)^7} \, dx","Int[x^2/(a + b*x)^7,x]","-\frac{a^2}{6 b^3 (a+b x)^6}+\frac{2 a}{5 b^3 (a+b x)^5}-\frac{1}{4 b^3 (a+b x)^4}","-\frac{a^2}{6 b^3 (a+b x)^6}+\frac{2 a}{5 b^3 (a+b x)^5}-\frac{1}{4 b^3 (a+b x)^4}",1,"-a^2/(6*b^3*(a + b*x)^6) + (2*a)/(5*b^3*(a + b*x)^5) - 1/(4*b^3*(a + b*x)^4)","A",2,1,11,0.09091,1,"{43}"
216,1,30,0,0.0134989,"\int \frac{x}{(a+b x)^7} \, dx","Int[x/(a + b*x)^7,x]","\frac{a}{6 b^2 (a+b x)^6}-\frac{1}{5 b^2 (a+b x)^5}","\frac{a}{6 b^2 (a+b x)^6}-\frac{1}{5 b^2 (a+b x)^5}",1,"a/(6*b^2*(a + b*x)^6) - 1/(5*b^2*(a + b*x)^5)","A",2,1,9,0.1111,1,"{43}"
217,1,14,0,0.0017102,"\int \frac{1}{(a+b x)^7} \, dx","Int[(a + b*x)^(-7),x]","-\frac{1}{6 b (a+b x)^6}","-\frac{1}{6 b (a+b x)^6}",1,"-1/(6*b*(a + b*x)^6)","A",1,1,7,0.1429,1,"{32}"
218,1,99,0,0.0488924,"\int \frac{1}{x (a+b x)^7} \, dx","Int[1/(x*(a + b*x)^7),x]","\frac{1}{a^6 (a+b x)}+\frac{1}{2 a^5 (a+b x)^2}+\frac{1}{3 a^4 (a+b x)^3}+\frac{1}{4 a^3 (a+b x)^4}+\frac{1}{5 a^2 (a+b x)^5}-\frac{\log (a+b x)}{a^7}+\frac{\log (x)}{a^7}+\frac{1}{6 a (a+b x)^6}","\frac{1}{a^6 (a+b x)}+\frac{1}{2 a^5 (a+b x)^2}+\frac{1}{3 a^4 (a+b x)^3}+\frac{1}{4 a^3 (a+b x)^4}+\frac{1}{5 a^2 (a+b x)^5}-\frac{\log (a+b x)}{a^7}+\frac{\log (x)}{a^7}+\frac{1}{6 a (a+b x)^6}",1,"1/(6*a*(a + b*x)^6) + 1/(5*a^2*(a + b*x)^5) + 1/(4*a^3*(a + b*x)^4) + 1/(3*a^4*(a + b*x)^3) + 1/(2*a^5*(a + b*x)^2) + 1/(a^6*(a + b*x)) + Log[x]/a^7 - Log[a + b*x]/a^7","A",2,1,11,0.09091,1,"{44}"
219,1,117,0,0.0732826,"\int \frac{1}{x^2 (a+b x)^7} \, dx","Int[1/(x^2*(a + b*x)^7),x]","-\frac{6 b}{a^7 (a+b x)}-\frac{5 b}{2 a^6 (a+b x)^2}-\frac{4 b}{3 a^5 (a+b x)^3}-\frac{3 b}{4 a^4 (a+b x)^4}-\frac{2 b}{5 a^3 (a+b x)^5}-\frac{b}{6 a^2 (a+b x)^6}-\frac{7 b \log (x)}{a^8}+\frac{7 b \log (a+b x)}{a^8}-\frac{1}{a^7 x}","-\frac{6 b}{a^7 (a+b x)}-\frac{5 b}{2 a^6 (a+b x)^2}-\frac{4 b}{3 a^5 (a+b x)^3}-\frac{3 b}{4 a^4 (a+b x)^4}-\frac{2 b}{5 a^3 (a+b x)^5}-\frac{b}{6 a^2 (a+b x)^6}-\frac{7 b \log (x)}{a^8}+\frac{7 b \log (a+b x)}{a^8}-\frac{1}{a^7 x}",1,"-(1/(a^7*x)) - b/(6*a^2*(a + b*x)^6) - (2*b)/(5*a^3*(a + b*x)^5) - (3*b)/(4*a^4*(a + b*x)^4) - (4*b)/(3*a^5*(a + b*x)^3) - (5*b)/(2*a^6*(a + b*x)^2) - (6*b)/(a^7*(a + b*x)) - (7*b*Log[x])/a^8 + (7*b*Log[a + b*x])/a^8","A",2,1,11,0.09091,1,"{44}"
220,1,144,0,0.0892933,"\int \frac{1}{x^3 (a+b x)^7} \, dx","Int[1/(x^3*(a + b*x)^7),x]","\frac{21 b^2}{a^8 (a+b x)}+\frac{15 b^2}{2 a^7 (a+b x)^2}+\frac{10 b^2}{3 a^6 (a+b x)^3}+\frac{3 b^2}{2 a^5 (a+b x)^4}+\frac{3 b^2}{5 a^4 (a+b x)^5}+\frac{b^2}{6 a^3 (a+b x)^6}+\frac{28 b^2 \log (x)}{a^9}-\frac{28 b^2 \log (a+b x)}{a^9}+\frac{7 b}{a^8 x}-\frac{1}{2 a^7 x^2}","\frac{21 b^2}{a^8 (a+b x)}+\frac{15 b^2}{2 a^7 (a+b x)^2}+\frac{10 b^2}{3 a^6 (a+b x)^3}+\frac{3 b^2}{2 a^5 (a+b x)^4}+\frac{3 b^2}{5 a^4 (a+b x)^5}+\frac{b^2}{6 a^3 (a+b x)^6}+\frac{28 b^2 \log (x)}{a^9}-\frac{28 b^2 \log (a+b x)}{a^9}+\frac{7 b}{a^8 x}-\frac{1}{2 a^7 x^2}",1,"-1/(2*a^7*x^2) + (7*b)/(a^8*x) + b^2/(6*a^3*(a + b*x)^6) + (3*b^2)/(5*a^4*(a + b*x)^5) + (3*b^2)/(2*a^5*(a + b*x)^4) + (10*b^2)/(3*a^6*(a + b*x)^3) + (15*b^2)/(2*a^7*(a + b*x)^2) + (21*b^2)/(a^8*(a + b*x)) + (28*b^2*Log[x])/a^9 - (28*b^2*Log[a + b*x])/a^9","A",2,1,11,0.09091,1,"{44}"
221,1,157,0,0.102711,"\int \frac{1}{x^4 (a+b x)^7} \, dx","Int[1/(x^4*(a + b*x)^7),x]","-\frac{56 b^3}{a^9 (a+b x)}-\frac{35 b^3}{2 a^8 (a+b x)^2}-\frac{20 b^3}{3 a^7 (a+b x)^3}-\frac{5 b^3}{2 a^6 (a+b x)^4}-\frac{4 b^3}{5 a^5 (a+b x)^5}-\frac{b^3}{6 a^4 (a+b x)^6}-\frac{28 b^2}{a^9 x}-\frac{84 b^3 \log (x)}{a^{10}}+\frac{84 b^3 \log (a+b x)}{a^{10}}+\frac{7 b}{2 a^8 x^2}-\frac{1}{3 a^7 x^3}","-\frac{56 b^3}{a^9 (a+b x)}-\frac{35 b^3}{2 a^8 (a+b x)^2}-\frac{20 b^3}{3 a^7 (a+b x)^3}-\frac{5 b^3}{2 a^6 (a+b x)^4}-\frac{4 b^3}{5 a^5 (a+b x)^5}-\frac{b^3}{6 a^4 (a+b x)^6}-\frac{28 b^2}{a^9 x}-\frac{84 b^3 \log (x)}{a^{10}}+\frac{84 b^3 \log (a+b x)}{a^{10}}+\frac{7 b}{2 a^8 x^2}-\frac{1}{3 a^7 x^3}",1,"-1/(3*a^7*x^3) + (7*b)/(2*a^8*x^2) - (28*b^2)/(a^9*x) - b^3/(6*a^4*(a + b*x)^6) - (4*b^3)/(5*a^5*(a + b*x)^5) - (5*b^3)/(2*a^6*(a + b*x)^4) - (20*b^3)/(3*a^7*(a + b*x)^3) - (35*b^3)/(2*a^8*(a + b*x)^2) - (56*b^3)/(a^9*(a + b*x)) - (84*b^3*Log[x])/a^10 + (84*b^3*Log[a + b*x])/a^10","A",2,1,11,0.09091,1,"{44}"
222,1,186,0,0.1767618,"\int \frac{x^{12}}{(a+b x)^{10}} \, dx","Int[x^12/(a + b*x)^10,x]","-\frac{a^{12}}{9 b^{13} (a+b x)^9}+\frac{3 a^{11}}{2 b^{13} (a+b x)^8}-\frac{66 a^{10}}{7 b^{13} (a+b x)^7}+\frac{110 a^9}{3 b^{13} (a+b x)^6}-\frac{99 a^8}{b^{13} (a+b x)^5}+\frac{198 a^7}{b^{13} (a+b x)^4}-\frac{308 a^6}{b^{13} (a+b x)^3}+\frac{396 a^5}{b^{13} (a+b x)^2}-\frac{495 a^4}{b^{13} (a+b x)}+\frac{55 a^2 x}{b^{12}}-\frac{220 a^3 \log (a+b x)}{b^{13}}-\frac{5 a x^2}{b^{11}}+\frac{x^3}{3 b^{10}}","-\frac{a^{12}}{9 b^{13} (a+b x)^9}+\frac{3 a^{11}}{2 b^{13} (a+b x)^8}-\frac{66 a^{10}}{7 b^{13} (a+b x)^7}+\frac{110 a^9}{3 b^{13} (a+b x)^6}-\frac{99 a^8}{b^{13} (a+b x)^5}+\frac{198 a^7}{b^{13} (a+b x)^4}-\frac{308 a^6}{b^{13} (a+b x)^3}+\frac{396 a^5}{b^{13} (a+b x)^2}-\frac{495 a^4}{b^{13} (a+b x)}+\frac{55 a^2 x}{b^{12}}-\frac{220 a^3 \log (a+b x)}{b^{13}}-\frac{5 a x^2}{b^{11}}+\frac{x^3}{3 b^{10}}",1,"(55*a^2*x)/b^12 - (5*a*x^2)/b^11 + x^3/(3*b^10) - a^12/(9*b^13*(a + b*x)^9) + (3*a^11)/(2*b^13*(a + b*x)^8) - (66*a^10)/(7*b^13*(a + b*x)^7) + (110*a^9)/(3*b^13*(a + b*x)^6) - (99*a^8)/(b^13*(a + b*x)^5) + (198*a^7)/(b^13*(a + b*x)^4) - (308*a^6)/(b^13*(a + b*x)^3) + (396*a^5)/(b^13*(a + b*x)^2) - (495*a^4)/(b^13*(a + b*x)) - (220*a^3*Log[a + b*x])/b^13","A",2,1,11,0.09091,1,"{43}"
223,1,177,0,0.1423781,"\int \frac{x^{11}}{(a+b x)^{10}} \, dx","Int[x^11/(a + b*x)^10,x]","\frac{a^{11}}{9 b^{12} (a+b x)^9}-\frac{11 a^{10}}{8 b^{12} (a+b x)^8}+\frac{55 a^9}{7 b^{12} (a+b x)^7}-\frac{55 a^8}{2 b^{12} (a+b x)^6}+\frac{66 a^7}{b^{12} (a+b x)^5}-\frac{231 a^6}{2 b^{12} (a+b x)^4}+\frac{154 a^5}{b^{12} (a+b x)^3}-\frac{165 a^4}{b^{12} (a+b x)^2}+\frac{165 a^3}{b^{12} (a+b x)}+\frac{55 a^2 \log (a+b x)}{b^{12}}-\frac{10 a x}{b^{11}}+\frac{x^2}{2 b^{10}}","\frac{a^{11}}{9 b^{12} (a+b x)^9}-\frac{11 a^{10}}{8 b^{12} (a+b x)^8}+\frac{55 a^9}{7 b^{12} (a+b x)^7}-\frac{55 a^8}{2 b^{12} (a+b x)^6}+\frac{66 a^7}{b^{12} (a+b x)^5}-\frac{231 a^6}{2 b^{12} (a+b x)^4}+\frac{154 a^5}{b^{12} (a+b x)^3}-\frac{165 a^4}{b^{12} (a+b x)^2}+\frac{165 a^3}{b^{12} (a+b x)}+\frac{55 a^2 \log (a+b x)}{b^{12}}-\frac{10 a x}{b^{11}}+\frac{x^2}{2 b^{10}}",1,"(-10*a*x)/b^11 + x^2/(2*b^10) + a^11/(9*b^12*(a + b*x)^9) - (11*a^10)/(8*b^12*(a + b*x)^8) + (55*a^9)/(7*b^12*(a + b*x)^7) - (55*a^8)/(2*b^12*(a + b*x)^6) + (66*a^7)/(b^12*(a + b*x)^5) - (231*a^6)/(2*b^12*(a + b*x)^4) + (154*a^5)/(b^12*(a + b*x)^3) - (165*a^4)/(b^12*(a + b*x)^2) + (165*a^3)/(b^12*(a + b*x)) + (55*a^2*Log[a + b*x])/b^12","A",2,1,11,0.09091,1,"{43}"
224,1,159,0,0.1209246,"\int \frac{x^{10}}{(a+b x)^{10}} \, dx","Int[x^10/(a + b*x)^10,x]","-\frac{a^{10}}{9 b^{11} (a+b x)^9}+\frac{5 a^9}{4 b^{11} (a+b x)^8}-\frac{45 a^8}{7 b^{11} (a+b x)^7}+\frac{20 a^7}{b^{11} (a+b x)^6}-\frac{42 a^6}{b^{11} (a+b x)^5}+\frac{63 a^5}{b^{11} (a+b x)^4}-\frac{70 a^4}{b^{11} (a+b x)^3}+\frac{60 a^3}{b^{11} (a+b x)^2}-\frac{45 a^2}{b^{11} (a+b x)}-\frac{10 a \log (a+b x)}{b^{11}}+\frac{x}{b^{10}}","-\frac{a^{10}}{9 b^{11} (a+b x)^9}+\frac{5 a^9}{4 b^{11} (a+b x)^8}-\frac{45 a^8}{7 b^{11} (a+b x)^7}+\frac{20 a^7}{b^{11} (a+b x)^6}-\frac{42 a^6}{b^{11} (a+b x)^5}+\frac{63 a^5}{b^{11} (a+b x)^4}-\frac{70 a^4}{b^{11} (a+b x)^3}+\frac{60 a^3}{b^{11} (a+b x)^2}-\frac{45 a^2}{b^{11} (a+b x)}-\frac{10 a \log (a+b x)}{b^{11}}+\frac{x}{b^{10}}",1,"x/b^10 - a^10/(9*b^11*(a + b*x)^9) + (5*a^9)/(4*b^11*(a + b*x)^8) - (45*a^8)/(7*b^11*(a + b*x)^7) + (20*a^7)/(b^11*(a + b*x)^6) - (42*a^6)/(b^11*(a + b*x)^5) + (63*a^5)/(b^11*(a + b*x)^4) - (70*a^4)/(b^11*(a + b*x)^3) + (60*a^3)/(b^11*(a + b*x)^2) - (45*a^2)/(b^11*(a + b*x)) - (10*a*Log[a + b*x])/b^11","A",2,1,11,0.09091,1,"{43}"
225,1,154,0,0.1082286,"\int \frac{x^9}{(a+b x)^{10}} \, dx","Int[x^9/(a + b*x)^10,x]","\frac{a^9}{9 b^{10} (a+b x)^9}-\frac{9 a^8}{8 b^{10} (a+b x)^8}+\frac{36 a^7}{7 b^{10} (a+b x)^7}-\frac{14 a^6}{b^{10} (a+b x)^6}+\frac{126 a^5}{5 b^{10} (a+b x)^5}-\frac{63 a^4}{2 b^{10} (a+b x)^4}+\frac{28 a^3}{b^{10} (a+b x)^3}-\frac{18 a^2}{b^{10} (a+b x)^2}+\frac{9 a}{b^{10} (a+b x)}+\frac{\log (a+b x)}{b^{10}}","\frac{a^9}{9 b^{10} (a+b x)^9}-\frac{9 a^8}{8 b^{10} (a+b x)^8}+\frac{36 a^7}{7 b^{10} (a+b x)^7}-\frac{14 a^6}{b^{10} (a+b x)^6}+\frac{126 a^5}{5 b^{10} (a+b x)^5}-\frac{63 a^4}{2 b^{10} (a+b x)^4}+\frac{28 a^3}{b^{10} (a+b x)^3}-\frac{18 a^2}{b^{10} (a+b x)^2}+\frac{9 a}{b^{10} (a+b x)}+\frac{\log (a+b x)}{b^{10}}",1,"a^9/(9*b^10*(a + b*x)^9) - (9*a^8)/(8*b^10*(a + b*x)^8) + (36*a^7)/(7*b^10*(a + b*x)^7) - (14*a^6)/(b^10*(a + b*x)^6) + (126*a^5)/(5*b^10*(a + b*x)^5) - (63*a^4)/(2*b^10*(a + b*x)^4) + (28*a^3)/(b^10*(a + b*x)^3) - (18*a^2)/(b^10*(a + b*x)^2) + (9*a)/(b^10*(a + b*x)) + Log[a + b*x]/b^10","A",2,1,11,0.09091,1,"{43}"
226,1,17,0,0.0016771,"\int \frac{x^8}{(a+b x)^{10}} \, dx","Int[x^8/(a + b*x)^10,x]","\frac{x^9}{9 a (a+b x)^9}","\frac{x^9}{9 a (a+b x)^9}",1,"x^9/(9*a*(a + b*x)^9)","A",1,1,11,0.09091,1,"{37}"
227,1,35,0,0.0051056,"\int \frac{x^7}{(a+b x)^{10}} \, dx","Int[x^7/(a + b*x)^10,x]","\frac{x^8}{72 a^2 (a+b x)^8}+\frac{x^8}{9 a (a+b x)^9}","\frac{x^8}{72 a^2 (a+b x)^8}+\frac{x^8}{9 a (a+b x)^9}",1,"x^8/(9*a*(a + b*x)^9) + x^8/(72*a^2*(a + b*x)^8)","A",2,2,11,0.1818,1,"{45, 37}"
228,1,52,0,0.0096319,"\int \frac{x^6}{(a+b x)^{10}} \, dx","Int[x^6/(a + b*x)^10,x]","\frac{x^7}{252 a^3 (a+b x)^7}+\frac{x^7}{36 a^2 (a+b x)^8}+\frac{x^7}{9 a (a+b x)^9}","\frac{x^7}{252 a^3 (a+b x)^7}+\frac{x^7}{36 a^2 (a+b x)^8}+\frac{x^7}{9 a (a+b x)^9}",1,"x^7/(9*a*(a + b*x)^9) + x^7/(36*a^2*(a + b*x)^8) + x^7/(252*a^3*(a + b*x)^7)","A",3,2,11,0.1818,1,"{45, 37}"
229,1,69,0,0.0155327,"\int \frac{x^5}{(a+b x)^{10}} \, dx","Int[x^5/(a + b*x)^10,x]","\frac{x^6}{504 a^4 (a+b x)^6}+\frac{x^6}{84 a^3 (a+b x)^7}+\frac{x^6}{24 a^2 (a+b x)^8}+\frac{x^6}{9 a (a+b x)^9}","\frac{x^6}{504 a^4 (a+b x)^6}+\frac{x^6}{84 a^3 (a+b x)^7}+\frac{x^6}{24 a^2 (a+b x)^8}+\frac{x^6}{9 a (a+b x)^9}",1,"x^6/(9*a*(a + b*x)^9) + x^6/(24*a^2*(a + b*x)^8) + x^6/(84*a^3*(a + b*x)^7) + x^6/(504*a^4*(a + b*x)^6)","A",4,2,11,0.1818,1,"{45, 37}"
230,1,81,0,0.0401836,"\int \frac{x^4}{(a+b x)^{10}} \, dx","Int[x^4/(a + b*x)^10,x]","-\frac{a^4}{9 b^5 (a+b x)^9}+\frac{a^3}{2 b^5 (a+b x)^8}-\frac{6 a^2}{7 b^5 (a+b x)^7}+\frac{2 a}{3 b^5 (a+b x)^6}-\frac{1}{5 b^5 (a+b x)^5}","-\frac{a^4}{9 b^5 (a+b x)^9}+\frac{a^3}{2 b^5 (a+b x)^8}-\frac{6 a^2}{7 b^5 (a+b x)^7}+\frac{2 a}{3 b^5 (a+b x)^6}-\frac{1}{5 b^5 (a+b x)^5}",1,"-a^4/(9*b^5*(a + b*x)^9) + a^3/(2*b^5*(a + b*x)^8) - (6*a^2)/(7*b^5*(a + b*x)^7) + (2*a)/(3*b^5*(a + b*x)^6) - 1/(5*b^5*(a + b*x)^5)","A",2,1,11,0.09091,1,"{43}"
231,1,64,0,0.0297847,"\int \frac{x^3}{(a+b x)^{10}} \, dx","Int[x^3/(a + b*x)^10,x]","\frac{a^3}{9 b^4 (a+b x)^9}-\frac{3 a^2}{8 b^4 (a+b x)^8}+\frac{3 a}{7 b^4 (a+b x)^7}-\frac{1}{6 b^4 (a+b x)^6}","\frac{a^3}{9 b^4 (a+b x)^9}-\frac{3 a^2}{8 b^4 (a+b x)^8}+\frac{3 a}{7 b^4 (a+b x)^7}-\frac{1}{6 b^4 (a+b x)^6}",1,"a^3/(9*b^4*(a + b*x)^9) - (3*a^2)/(8*b^4*(a + b*x)^8) + (3*a)/(7*b^4*(a + b*x)^7) - 1/(6*b^4*(a + b*x)^6)","A",2,1,11,0.09091,1,"{43}"
232,1,47,0,0.0207929,"\int \frac{x^2}{(a+b x)^{10}} \, dx","Int[x^2/(a + b*x)^10,x]","-\frac{a^2}{9 b^3 (a+b x)^9}+\frac{a}{4 b^3 (a+b x)^8}-\frac{1}{7 b^3 (a+b x)^7}","-\frac{a^2}{9 b^3 (a+b x)^9}+\frac{a}{4 b^3 (a+b x)^8}-\frac{1}{7 b^3 (a+b x)^7}",1,"-a^2/(9*b^3*(a + b*x)^9) + a/(4*b^3*(a + b*x)^8) - 1/(7*b^3*(a + b*x)^7)","A",2,1,11,0.09091,1,"{43}"
233,1,30,0,0.0135037,"\int \frac{x}{(a+b x)^{10}} \, dx","Int[x/(a + b*x)^10,x]","\frac{a}{9 b^2 (a+b x)^9}-\frac{1}{8 b^2 (a+b x)^8}","\frac{a}{9 b^2 (a+b x)^9}-\frac{1}{8 b^2 (a+b x)^8}",1,"a/(9*b^2*(a + b*x)^9) - 1/(8*b^2*(a + b*x)^8)","A",2,1,9,0.1111,1,"{43}"
234,1,14,0,0.0015978,"\int \frac{1}{(a+b x)^{10}} \, dx","Int[(a + b*x)^(-10),x]","-\frac{1}{9 b (a+b x)^9}","-\frac{1}{9 b (a+b x)^9}",1,"-1/(9*b*(a + b*x)^9)","A",1,1,7,0.1429,1,"{32}"
235,1,141,0,0.0748266,"\int \frac{1}{x (a+b x)^{10}} \, dx","Int[1/(x*(a + b*x)^10),x]","\frac{1}{a^9 (a+b x)}+\frac{1}{2 a^8 (a+b x)^2}+\frac{1}{3 a^7 (a+b x)^3}+\frac{1}{4 a^6 (a+b x)^4}+\frac{1}{5 a^5 (a+b x)^5}+\frac{1}{6 a^4 (a+b x)^6}+\frac{1}{7 a^3 (a+b x)^7}+\frac{1}{8 a^2 (a+b x)^8}-\frac{\log (a+b x)}{a^{10}}+\frac{\log (x)}{a^{10}}+\frac{1}{9 a (a+b x)^9}","\frac{1}{a^9 (a+b x)}+\frac{1}{2 a^8 (a+b x)^2}+\frac{1}{3 a^7 (a+b x)^3}+\frac{1}{4 a^6 (a+b x)^4}+\frac{1}{5 a^5 (a+b x)^5}+\frac{1}{6 a^4 (a+b x)^6}+\frac{1}{7 a^3 (a+b x)^7}+\frac{1}{8 a^2 (a+b x)^8}-\frac{\log (a+b x)}{a^{10}}+\frac{\log (x)}{a^{10}}+\frac{1}{9 a (a+b x)^9}",1,"1/(9*a*(a + b*x)^9) + 1/(8*a^2*(a + b*x)^8) + 1/(7*a^3*(a + b*x)^7) + 1/(6*a^4*(a + b*x)^6) + 1/(5*a^5*(a + b*x)^5) + 1/(4*a^6*(a + b*x)^4) + 1/(3*a^7*(a + b*x)^3) + 1/(2*a^8*(a + b*x)^2) + 1/(a^9*(a + b*x)) + Log[x]/a^10 - Log[a + b*x]/a^10","A",2,1,11,0.09091,1,"{44}"
236,1,158,0,0.1248976,"\int \frac{1}{x^2 (a+b x)^{10}} \, dx","Int[1/(x^2*(a + b*x)^10),x]","-\frac{9 b}{a^{10} (a+b x)}-\frac{4 b}{a^9 (a+b x)^2}-\frac{7 b}{3 a^8 (a+b x)^3}-\frac{3 b}{2 a^7 (a+b x)^4}-\frac{b}{a^6 (a+b x)^5}-\frac{2 b}{3 a^5 (a+b x)^6}-\frac{3 b}{7 a^4 (a+b x)^7}-\frac{b}{4 a^3 (a+b x)^8}-\frac{b}{9 a^2 (a+b x)^9}-\frac{10 b \log (x)}{a^{11}}+\frac{10 b \log (a+b x)}{a^{11}}-\frac{1}{a^{10} x}","-\frac{9 b}{a^{10} (a+b x)}-\frac{4 b}{a^9 (a+b x)^2}-\frac{7 b}{3 a^8 (a+b x)^3}-\frac{3 b}{2 a^7 (a+b x)^4}-\frac{b}{a^6 (a+b x)^5}-\frac{2 b}{3 a^5 (a+b x)^6}-\frac{3 b}{7 a^4 (a+b x)^7}-\frac{b}{4 a^3 (a+b x)^8}-\frac{b}{9 a^2 (a+b x)^9}-\frac{10 b \log (x)}{a^{11}}+\frac{10 b \log (a+b x)}{a^{11}}-\frac{1}{a^{10} x}",1,"-(1/(a^10*x)) - b/(9*a^2*(a + b*x)^9) - b/(4*a^3*(a + b*x)^8) - (3*b)/(7*a^4*(a + b*x)^7) - (2*b)/(3*a^5*(a + b*x)^6) - b/(a^6*(a + b*x)^5) - (3*b)/(2*a^7*(a + b*x)^4) - (7*b)/(3*a^8*(a + b*x)^3) - (4*b)/(a^9*(a + b*x)^2) - (9*b)/(a^10*(a + b*x)) - (10*b*Log[x])/a^11 + (10*b*Log[a + b*x])/a^11","A",2,1,11,0.09091,1,"{44}"
237,1,191,0,0.1413981,"\int \frac{1}{x^3 (a+b x)^{10}} \, dx","Int[1/(x^3*(a + b*x)^10),x]","\frac{45 b^2}{a^{11} (a+b x)}+\frac{18 b^2}{a^{10} (a+b x)^2}+\frac{28 b^2}{3 a^9 (a+b x)^3}+\frac{21 b^2}{4 a^8 (a+b x)^4}+\frac{3 b^2}{a^7 (a+b x)^5}+\frac{5 b^2}{3 a^6 (a+b x)^6}+\frac{6 b^2}{7 a^5 (a+b x)^7}+\frac{3 b^2}{8 a^4 (a+b x)^8}+\frac{b^2}{9 a^3 (a+b x)^9}+\frac{55 b^2 \log (x)}{a^{12}}-\frac{55 b^2 \log (a+b x)}{a^{12}}+\frac{10 b}{a^{11} x}-\frac{1}{2 a^{10} x^2}","\frac{45 b^2}{a^{11} (a+b x)}+\frac{18 b^2}{a^{10} (a+b x)^2}+\frac{28 b^2}{3 a^9 (a+b x)^3}+\frac{21 b^2}{4 a^8 (a+b x)^4}+\frac{3 b^2}{a^7 (a+b x)^5}+\frac{5 b^2}{3 a^6 (a+b x)^6}+\frac{6 b^2}{7 a^5 (a+b x)^7}+\frac{3 b^2}{8 a^4 (a+b x)^8}+\frac{b^2}{9 a^3 (a+b x)^9}+\frac{55 b^2 \log (x)}{a^{12}}-\frac{55 b^2 \log (a+b x)}{a^{12}}+\frac{10 b}{a^{11} x}-\frac{1}{2 a^{10} x^2}",1,"-1/(2*a^10*x^2) + (10*b)/(a^11*x) + b^2/(9*a^3*(a + b*x)^9) + (3*b^2)/(8*a^4*(a + b*x)^8) + (6*b^2)/(7*a^5*(a + b*x)^7) + (5*b^2)/(3*a^6*(a + b*x)^6) + (3*b^2)/(a^7*(a + b*x)^5) + (21*b^2)/(4*a^8*(a + b*x)^4) + (28*b^2)/(3*a^9*(a + b*x)^3) + (18*b^2)/(a^10*(a + b*x)^2) + (45*b^2)/(a^11*(a + b*x)) + (55*b^2*Log[x])/a^12 - (55*b^2*Log[a + b*x])/a^12","A",2,1,11,0.09091,1,"{44}"
238,1,198,0,0.164663,"\int \frac{1}{x^4 (a+b x)^{10}} \, dx","Int[1/(x^4*(a + b*x)^10),x]","-\frac{165 b^3}{a^{12} (a+b x)}-\frac{60 b^3}{a^{11} (a+b x)^2}-\frac{28 b^3}{a^{10} (a+b x)^3}-\frac{14 b^3}{a^9 (a+b x)^4}-\frac{7 b^3}{a^8 (a+b x)^5}-\frac{10 b^3}{3 a^7 (a+b x)^6}-\frac{10 b^3}{7 a^6 (a+b x)^7}-\frac{b^3}{2 a^5 (a+b x)^8}-\frac{b^3}{9 a^4 (a+b x)^9}-\frac{55 b^2}{a^{12} x}-\frac{220 b^3 \log (x)}{a^{13}}+\frac{220 b^3 \log (a+b x)}{a^{13}}+\frac{5 b}{a^{11} x^2}-\frac{1}{3 a^{10} x^3}","-\frac{165 b^3}{a^{12} (a+b x)}-\frac{60 b^3}{a^{11} (a+b x)^2}-\frac{28 b^3}{a^{10} (a+b x)^3}-\frac{14 b^3}{a^9 (a+b x)^4}-\frac{7 b^3}{a^8 (a+b x)^5}-\frac{10 b^3}{3 a^7 (a+b x)^6}-\frac{10 b^3}{7 a^6 (a+b x)^7}-\frac{b^3}{2 a^5 (a+b x)^8}-\frac{b^3}{9 a^4 (a+b x)^9}-\frac{55 b^2}{a^{12} x}-\frac{220 b^3 \log (x)}{a^{13}}+\frac{220 b^3 \log (a+b x)}{a^{13}}+\frac{5 b}{a^{11} x^2}-\frac{1}{3 a^{10} x^3}",1,"-1/(3*a^10*x^3) + (5*b)/(a^11*x^2) - (55*b^2)/(a^12*x) - b^3/(9*a^4*(a + b*x)^9) - b^3/(2*a^5*(a + b*x)^8) - (10*b^3)/(7*a^6*(a + b*x)^7) - (10*b^3)/(3*a^7*(a + b*x)^6) - (7*b^3)/(a^8*(a + b*x)^5) - (14*b^3)/(a^9*(a + b*x)^4) - (28*b^3)/(a^10*(a + b*x)^3) - (60*b^3)/(a^11*(a + b*x)^2) - (165*b^3)/(a^12*(a + b*x)) - (220*b^3*Log[x])/a^13 + (220*b^3*Log[a + b*x])/a^13","A",2,1,11,0.09091,1,"{44}"
239,1,141,0,0.078976,"\int \frac{(a+b x)^{12}}{x^{10}} \, dx","Int[(a + b*x)^12/x^10,x]","-\frac{66 a^{10} b^2}{7 x^7}-\frac{110 a^9 b^3}{3 x^6}-\frac{99 a^8 b^4}{x^5}-\frac{198 a^7 b^5}{x^4}-\frac{308 a^6 b^6}{x^3}-\frac{396 a^5 b^7}{x^2}-\frac{495 a^4 b^8}{x}+66 a^2 b^{10} x+220 a^3 b^9 \log (x)-\frac{3 a^{11} b}{2 x^8}-\frac{a^{12}}{9 x^9}+6 a b^{11} x^2+\frac{b^{12} x^3}{3}","-\frac{66 a^{10} b^2}{7 x^7}-\frac{110 a^9 b^3}{3 x^6}-\frac{99 a^8 b^4}{x^5}-\frac{198 a^7 b^5}{x^4}-\frac{308 a^6 b^6}{x^3}-\frac{396 a^5 b^7}{x^2}-\frac{495 a^4 b^8}{x}+66 a^2 b^{10} x+220 a^3 b^9 \log (x)-\frac{3 a^{11} b}{2 x^8}-\frac{a^{12}}{9 x^9}+6 a b^{11} x^2+\frac{b^{12} x^3}{3}",1,"-a^12/(9*x^9) - (3*a^11*b)/(2*x^8) - (66*a^10*b^2)/(7*x^7) - (110*a^9*b^3)/(3*x^6) - (99*a^8*b^4)/x^5 - (198*a^7*b^5)/x^4 - (308*a^6*b^6)/x^3 - (396*a^5*b^7)/x^2 - (495*a^4*b^8)/x + 66*a^2*b^10*x + 6*a*b^11*x^2 + (b^12*x^3)/3 + 220*a^3*b^9*Log[x]","A",2,1,11,0.09091,1,"{43}"
240,1,132,0,0.0695941,"\int \frac{(a+b x)^{11}}{x^{10}} \, dx","Int[(a + b*x)^11/x^10,x]","-\frac{55 a^9 b^2}{7 x^7}-\frac{55 a^8 b^3}{2 x^6}-\frac{66 a^7 b^4}{x^5}-\frac{231 a^6 b^5}{2 x^4}-\frac{154 a^5 b^6}{x^3}-\frac{165 a^4 b^7}{x^2}-\frac{165 a^3 b^8}{x}+55 a^2 b^9 \log (x)-\frac{11 a^{10} b}{8 x^8}-\frac{a^{11}}{9 x^9}+11 a b^{10} x+\frac{b^{11} x^2}{2}","-\frac{55 a^9 b^2}{7 x^7}-\frac{55 a^8 b^3}{2 x^6}-\frac{66 a^7 b^4}{x^5}-\frac{231 a^6 b^5}{2 x^4}-\frac{154 a^5 b^6}{x^3}-\frac{165 a^4 b^7}{x^2}-\frac{165 a^3 b^8}{x}+55 a^2 b^9 \log (x)-\frac{11 a^{10} b}{8 x^8}-\frac{a^{11}}{9 x^9}+11 a b^{10} x+\frac{b^{11} x^2}{2}",1,"-a^11/(9*x^9) - (11*a^10*b)/(8*x^8) - (55*a^9*b^2)/(7*x^7) - (55*a^8*b^3)/(2*x^6) - (66*a^7*b^4)/x^5 - (231*a^6*b^5)/(2*x^4) - (154*a^5*b^6)/x^3 - (165*a^4*b^7)/x^2 - (165*a^3*b^8)/x + 11*a*b^10*x + (b^11*x^2)/2 + 55*a^2*b^9*Log[x]","A",2,1,11,0.09091,1,"{43}"
241,1,114,0,0.0577027,"\int \frac{(a+b x)^{10}}{x^{10}} \, dx","Int[(a + b*x)^10/x^10,x]","-\frac{45 a^8 b^2}{7 x^7}-\frac{20 a^7 b^3}{x^6}-\frac{42 a^6 b^4}{x^5}-\frac{63 a^5 b^5}{x^4}-\frac{70 a^4 b^6}{x^3}-\frac{60 a^3 b^7}{x^2}-\frac{45 a^2 b^8}{x}-\frac{5 a^9 b}{4 x^8}-\frac{a^{10}}{9 x^9}+10 a b^9 \log (x)+b^{10} x","-\frac{45 a^8 b^2}{7 x^7}-\frac{20 a^7 b^3}{x^6}-\frac{42 a^6 b^4}{x^5}-\frac{63 a^5 b^5}{x^4}-\frac{70 a^4 b^6}{x^3}-\frac{60 a^3 b^7}{x^2}-\frac{45 a^2 b^8}{x}-\frac{5 a^9 b}{4 x^8}-\frac{a^{10}}{9 x^9}+10 a b^9 \log (x)+b^{10} x",1,"-a^10/(9*x^9) - (5*a^9*b)/(4*x^8) - (45*a^8*b^2)/(7*x^7) - (20*a^7*b^3)/x^6 - (42*a^6*b^4)/x^5 - (63*a^5*b^5)/x^4 - (70*a^4*b^6)/x^3 - (60*a^3*b^7)/x^2 - (45*a^2*b^8)/x + b^10*x + 10*a*b^9*Log[x]","A",2,1,11,0.09091,1,"{43}"
242,1,109,0,0.0516384,"\int \frac{(a+b x)^9}{x^{10}} \, dx","Int[(a + b*x)^9/x^10,x]","-\frac{36 a^7 b^2}{7 x^7}-\frac{14 a^6 b^3}{x^6}-\frac{126 a^5 b^4}{5 x^5}-\frac{63 a^4 b^5}{2 x^4}-\frac{28 a^3 b^6}{x^3}-\frac{18 a^2 b^7}{x^2}-\frac{9 a^8 b}{8 x^8}-\frac{a^9}{9 x^9}-\frac{9 a b^8}{x}+b^9 \log (x)","-\frac{36 a^7 b^2}{7 x^7}-\frac{14 a^6 b^3}{x^6}-\frac{126 a^5 b^4}{5 x^5}-\frac{63 a^4 b^5}{2 x^4}-\frac{28 a^3 b^6}{x^3}-\frac{18 a^2 b^7}{x^2}-\frac{9 a^8 b}{8 x^8}-\frac{a^9}{9 x^9}-\frac{9 a b^8}{x}+b^9 \log (x)",1,"-a^9/(9*x^9) - (9*a^8*b)/(8*x^8) - (36*a^7*b^2)/(7*x^7) - (14*a^6*b^3)/x^6 - (126*a^5*b^4)/(5*x^5) - (63*a^4*b^5)/(2*x^4) - (28*a^3*b^6)/x^3 - (18*a^2*b^7)/x^2 - (9*a*b^8)/x + b^9*Log[x]","A",2,1,11,0.09091,1,"{43}"
243,1,17,0,0.0016689,"\int \frac{(a+b x)^8}{x^{10}} \, dx","Int[(a + b*x)^8/x^10,x]","-\frac{(a+b x)^9}{9 a x^9}","-\frac{(a+b x)^9}{9 a x^9}",1,"-(a + b*x)^9/(9*a*x^9)","A",1,1,11,0.09091,1,"{37}"
244,1,36,0,0.0055383,"\int \frac{(a+b x)^7}{x^{10}} \, dx","Int[(a + b*x)^7/x^10,x]","\frac{b (a+b x)^8}{72 a^2 x^8}-\frac{(a+b x)^8}{9 a x^9}","\frac{b (a+b x)^8}{72 a^2 x^8}-\frac{(a+b x)^8}{9 a x^9}",1,"-(a + b*x)^8/(9*a*x^9) + (b*(a + b*x)^8)/(72*a^2*x^8)","A",2,2,11,0.1818,1,"{45, 37}"
245,1,56,0,0.0101443,"\int \frac{(a+b x)^6}{x^{10}} \, dx","Int[(a + b*x)^6/x^10,x]","-\frac{b^2 (a+b x)^7}{252 a^3 x^7}+\frac{b (a+b x)^7}{36 a^2 x^8}-\frac{(a+b x)^7}{9 a x^9}","-\frac{b^2 (a+b x)^7}{252 a^3 x^7}+\frac{b (a+b x)^7}{36 a^2 x^8}-\frac{(a+b x)^7}{9 a x^9}",1,"-(a + b*x)^7/(9*a*x^9) + (b*(a + b*x)^7)/(36*a^2*x^8) - (b^2*(a + b*x)^7)/(252*a^3*x^7)","A",3,2,11,0.1818,1,"{45, 37}"
246,1,67,0,0.024606,"\int \frac{(a+b x)^5}{x^{10}} \, dx","Int[(a + b*x)^5/x^10,x]","-\frac{10 a^3 b^2}{7 x^7}-\frac{5 a^2 b^3}{3 x^6}-\frac{5 a^4 b}{8 x^8}-\frac{a^5}{9 x^9}-\frac{a b^4}{x^5}-\frac{b^5}{4 x^4}","-\frac{10 a^3 b^2}{7 x^7}-\frac{5 a^2 b^3}{3 x^6}-\frac{5 a^4 b}{8 x^8}-\frac{a^5}{9 x^9}-\frac{a b^4}{x^5}-\frac{b^5}{4 x^4}",1,"-a^5/(9*x^9) - (5*a^4*b)/(8*x^8) - (10*a^3*b^2)/(7*x^7) - (5*a^2*b^3)/(3*x^6) - (a*b^4)/x^5 - b^5/(4*x^4)","A",2,1,11,0.09091,1,"{43}"
247,1,56,0,0.0191013,"\int \frac{(a+b x)^4}{x^{10}} \, dx","Int[(a + b*x)^4/x^10,x]","-\frac{6 a^2 b^2}{7 x^7}-\frac{a^3 b}{2 x^8}-\frac{a^4}{9 x^9}-\frac{2 a b^3}{3 x^6}-\frac{b^4}{5 x^5}","-\frac{6 a^2 b^2}{7 x^7}-\frac{a^3 b}{2 x^8}-\frac{a^4}{9 x^9}-\frac{2 a b^3}{3 x^6}-\frac{b^4}{5 x^5}",1,"-a^4/(9*x^9) - (a^3*b)/(2*x^8) - (6*a^2*b^2)/(7*x^7) - (2*a*b^3)/(3*x^6) - b^4/(5*x^5)","A",2,1,11,0.09091,1,"{43}"
248,1,43,0,0.0140346,"\int \frac{(a+b x)^3}{x^{10}} \, dx","Int[(a + b*x)^3/x^10,x]","-\frac{3 a^2 b}{8 x^8}-\frac{a^3}{9 x^9}-\frac{3 a b^2}{7 x^7}-\frac{b^3}{6 x^6}","-\frac{3 a^2 b}{8 x^8}-\frac{a^3}{9 x^9}-\frac{3 a b^2}{7 x^7}-\frac{b^3}{6 x^6}",1,"-a^3/(9*x^9) - (3*a^2*b)/(8*x^8) - (3*a*b^2)/(7*x^7) - b^3/(6*x^6)","A",2,1,11,0.09091,1,"{43}"
249,1,30,0,0.009093,"\int \frac{(a+b x)^2}{x^{10}} \, dx","Int[(a + b*x)^2/x^10,x]","-\frac{a^2}{9 x^9}-\frac{a b}{4 x^8}-\frac{b^2}{7 x^7}","-\frac{a^2}{9 x^9}-\frac{a b}{4 x^8}-\frac{b^2}{7 x^7}",1,"-a^2/(9*x^9) - (a*b)/(4*x^8) - b^2/(7*x^7)","A",2,1,11,0.09091,1,"{43}"
250,1,17,0,0.0047767,"\int \frac{a+b x}{x^{10}} \, dx","Int[(a + b*x)/x^10,x]","-\frac{a}{9 x^9}-\frac{b}{8 x^8}","-\frac{a}{9 x^9}-\frac{b}{8 x^8}",1,"-a/(9*x^9) - b/(8*x^8)","A",2,1,9,0.1111,1,"{43}"
251,1,7,0,0.0004806,"\int \frac{1}{x^{10}} \, dx","Int[x^(-10),x]","-\frac{1}{9 x^9}","-\frac{1}{9 x^9}",1,"-1/(9*x^9)","A",1,1,3,0.3333,1,"{30}"
252,1,134,0,0.0608035,"\int \frac{1}{x^{10} (a+b x)} \, dx","Int[1/(x^10*(a + b*x)),x]","\frac{b^7}{2 a^8 x^2}-\frac{b^6}{3 a^7 x^3}+\frac{b^5}{4 a^6 x^4}-\frac{b^4}{5 a^5 x^5}+\frac{b^3}{6 a^4 x^6}-\frac{b^2}{7 a^3 x^7}-\frac{b^8}{a^9 x}-\frac{b^9 \log (x)}{a^{10}}+\frac{b^9 \log (a+b x)}{a^{10}}+\frac{b}{8 a^2 x^8}-\frac{1}{9 a x^9}","\frac{b^7}{2 a^8 x^2}-\frac{b^6}{3 a^7 x^3}+\frac{b^5}{4 a^6 x^4}-\frac{b^4}{5 a^5 x^5}+\frac{b^3}{6 a^4 x^6}-\frac{b^2}{7 a^3 x^7}-\frac{b^8}{a^9 x}-\frac{b^9 \log (x)}{a^{10}}+\frac{b^9 \log (a+b x)}{a^{10}}+\frac{b}{8 a^2 x^8}-\frac{1}{9 a x^9}",1,"-1/(9*a*x^9) + b/(8*a^2*x^8) - b^2/(7*a^3*x^7) + b^3/(6*a^4*x^6) - b^4/(5*a^5*x^5) + b^5/(4*a^6*x^4) - b^6/(3*a^7*x^3) + b^7/(2*a^8*x^2) - b^8/(a^9*x) - (b^9*Log[x])/a^10 + (b^9*Log[a + b*x])/a^10","A",2,1,11,0.09091,1,"{44}"
253,1,146,0,0.0896469,"\int \frac{1}{x^{10} (a+b x)^2} \, dx","Int[1/(x^10*(a + b*x)^2),x]","\frac{4 b^7}{a^9 x^2}-\frac{7 b^6}{3 a^8 x^3}+\frac{3 b^5}{2 a^7 x^4}-\frac{b^4}{a^6 x^5}+\frac{2 b^3}{3 a^5 x^6}-\frac{3 b^2}{7 a^4 x^7}-\frac{b^9}{a^{10} (a+b x)}-\frac{9 b^8}{a^{10} x}-\frac{10 b^9 \log (x)}{a^{11}}+\frac{10 b^9 \log (a+b x)}{a^{11}}+\frac{b}{4 a^3 x^8}-\frac{1}{9 a^2 x^9}","\frac{4 b^7}{a^9 x^2}-\frac{7 b^6}{3 a^8 x^3}+\frac{3 b^5}{2 a^7 x^4}-\frac{b^4}{a^6 x^5}+\frac{2 b^3}{3 a^5 x^6}-\frac{3 b^2}{7 a^4 x^7}-\frac{b^9}{a^{10} (a+b x)}-\frac{9 b^8}{a^{10} x}-\frac{10 b^9 \log (x)}{a^{11}}+\frac{10 b^9 \log (a+b x)}{a^{11}}+\frac{b}{4 a^3 x^8}-\frac{1}{9 a^2 x^9}",1,"-1/(9*a^2*x^9) + b/(4*a^3*x^8) - (3*b^2)/(7*a^4*x^7) + (2*b^3)/(3*a^5*x^6) - b^4/(a^6*x^5) + (3*b^5)/(2*a^7*x^4) - (7*b^6)/(3*a^8*x^3) + (4*b^7)/(a^9*x^2) - (9*b^8)/(a^10*x) - b^9/(a^10*(a + b*x)) - (10*b^9*Log[x])/a^11 + (10*b^9*Log[a + b*x])/a^11","A",2,1,11,0.09091,1,"{44}"
254,1,163,0,0.1082381,"\int \frac{1}{x^{10} (a+b x)^3} \, dx","Int[1/(x^10*(a + b*x)^3),x]","\frac{18 b^7}{a^{10} x^2}-\frac{28 b^6}{3 a^9 x^3}+\frac{21 b^5}{4 a^8 x^4}-\frac{3 b^4}{a^7 x^5}+\frac{5 b^3}{3 a^6 x^6}-\frac{6 b^2}{7 a^5 x^7}-\frac{10 b^9}{a^{11} (a+b x)}-\frac{b^9}{2 a^{10} (a+b x)^2}-\frac{45 b^8}{a^{11} x}-\frac{55 b^9 \log (x)}{a^{12}}+\frac{55 b^9 \log (a+b x)}{a^{12}}+\frac{3 b}{8 a^4 x^8}-\frac{1}{9 a^3 x^9}","\frac{18 b^7}{a^{10} x^2}-\frac{28 b^6}{3 a^9 x^3}+\frac{21 b^5}{4 a^8 x^4}-\frac{3 b^4}{a^7 x^5}+\frac{5 b^3}{3 a^6 x^6}-\frac{6 b^2}{7 a^5 x^7}-\frac{10 b^9}{a^{11} (a+b x)}-\frac{b^9}{2 a^{10} (a+b x)^2}-\frac{45 b^8}{a^{11} x}-\frac{55 b^9 \log (x)}{a^{12}}+\frac{55 b^9 \log (a+b x)}{a^{12}}+\frac{3 b}{8 a^4 x^8}-\frac{1}{9 a^3 x^9}",1,"-1/(9*a^3*x^9) + (3*b)/(8*a^4*x^8) - (6*b^2)/(7*a^5*x^7) + (5*b^3)/(3*a^6*x^6) - (3*b^4)/(a^7*x^5) + (21*b^5)/(4*a^8*x^4) - (28*b^6)/(3*a^9*x^3) + (18*b^7)/(a^10*x^2) - (45*b^8)/(a^11*x) - b^9/(2*a^10*(a + b*x)^2) - (10*b^9)/(a^11*(a + b*x)) - (55*b^9*Log[x])/a^12 + (55*b^9*Log[a + b*x])/a^12","A",2,1,11,0.09091,1,"{44}"
255,1,17,0,0.002297,"\int \frac{1}{x (2+3 x)} \, dx","Int[1/(x*(2 + 3*x)),x]","\frac{\log (x)}{2}-\frac{1}{2} \log (3 x+2)","\frac{\log (x)}{2}-\frac{1}{2} \log (3 x+2)",1,"Log[x]/2 - Log[2 + 3*x]/2","A",3,3,11,0.2727,1,"{36, 29, 31}"
256,1,17,0,0.0022819,"\int \frac{1}{x (4+6 x)} \, dx","Int[1/(x*(4 + 6*x)),x]","\frac{\log (x)}{4}-\frac{1}{4} \log (3 x+2)","\frac{\log (x)}{4}-\frac{1}{4} \log (3 x+2)",1,"Log[x]/4 - Log[2 + 3*x]/4","A",3,3,11,0.2727,1,"{36, 29, 31}"
257,1,24,0,0.0078345,"\int \frac{1}{x^2 (4+6 x)} \, dx","Int[1/(x^2*(4 + 6*x)),x]","-\frac{1}{4 x}-\frac{3 \log (x)}{8}+\frac{3}{8} \log (3 x+2)","-\frac{1}{4 x}-\frac{3 \log (x)}{8}+\frac{3}{8} \log (3 x+2)",1,"-1/(4*x) - (3*Log[x])/8 + (3*Log[2 + 3*x])/8","A",2,1,11,0.09091,1,"{44}"
258,1,31,0,0.0100174,"\int \frac{1}{x^3 (4+6 x)} \, dx","Int[1/(x^3*(4 + 6*x)),x]","-\frac{1}{8 x^2}+\frac{3}{8 x}+\frac{9 \log (x)}{16}-\frac{9}{16} \log (3 x+2)","-\frac{1}{8 x^2}+\frac{3}{8 x}+\frac{9 \log (x)}{16}-\frac{9}{16} \log (3 x+2)",1,"-1/(8*x^2) + 3/(8*x) + (9*Log[x])/16 - (9*Log[2 + 3*x])/16","A",2,1,11,0.09091,1,"{44}"
259,1,38,0,0.0117281,"\int \frac{1}{x^4 (4+6 x)} \, dx","Int[1/(x^4*(4 + 6*x)),x]","\frac{3}{16 x^2}-\frac{1}{12 x^3}-\frac{9}{16 x}-\frac{27 \log (x)}{32}+\frac{27}{32} \log (3 x+2)","\frac{3}{16 x^2}-\frac{1}{12 x^3}-\frac{9}{16 x}-\frac{27 \log (x)}{32}+\frac{27}{32} \log (3 x+2)",1,"-1/(12*x^3) + 3/(16*x^2) - 9/(16*x) - (27*Log[x])/32 + (27*Log[2 + 3*x])/32","A",2,1,11,0.09091,1,"{44}"
260,1,45,0,0.0117359,"\int \frac{1}{x^5 (4+6 x)} \, dx","Int[1/(x^5*(4 + 6*x)),x]","-\frac{9}{32 x^2}+\frac{1}{8 x^3}-\frac{1}{16 x^4}+\frac{27}{32 x}+\frac{81 \log (x)}{64}-\frac{81}{64} \log (3 x+2)","-\frac{9}{32 x^2}+\frac{1}{8 x^3}-\frac{1}{16 x^4}+\frac{27}{32 x}+\frac{81 \log (x)}{64}-\frac{81}{64} \log (3 x+2)",1,"-1/(16*x^4) + 1/(8*x^3) - 9/(32*x^2) + 27/(32*x) + (81*Log[x])/64 - (81*Log[2 + 3*x])/64","A",2,1,11,0.09091,1,"{44}"
261,1,28,0,0.0089128,"\int \frac{1}{x (4+6 x)^2} \, dx","Int[1/(x*(4 + 6*x)^2),x]","\frac{1}{8 (3 x+2)}+\frac{\log (x)}{16}-\frac{1}{16} \log (3 x+2)","\frac{1}{8 (3 x+2)}+\frac{\log (x)}{16}-\frac{1}{16} \log (3 x+2)",1,"1/(8*(2 + 3*x)) + Log[x]/16 - Log[2 + 3*x]/16","A",2,1,11,0.09091,1,"{44}"
262,1,35,0,0.0099562,"\int \frac{1}{x^2 (4+6 x)^2} \, dx","Int[1/(x^2*(4 + 6*x)^2),x]","-\frac{1}{16 x}-\frac{3}{16 (3 x+2)}-\frac{3 \log (x)}{16}+\frac{3}{16} \log (3 x+2)","-\frac{1}{16 x}-\frac{3}{16 (3 x+2)}-\frac{3 \log (x)}{16}+\frac{3}{16} \log (3 x+2)",1,"-1/(16*x) - 3/(16*(2 + 3*x)) - (3*Log[x])/16 + (3*Log[2 + 3*x])/16","A",2,1,11,0.09091,1,"{44}"
263,1,42,0,0.0135602,"\int \frac{1}{x^3 (4+6 x)^2} \, dx","Int[1/(x^3*(4 + 6*x)^2),x]","-\frac{1}{32 x^2}+\frac{3}{16 x}+\frac{9}{32 (3 x+2)}+\frac{27 \log (x)}{64}-\frac{27}{64} \log (3 x+2)","-\frac{1}{32 x^2}+\frac{3}{16 x}+\frac{9}{32 (3 x+2)}+\frac{27 \log (x)}{64}-\frac{27}{64} \log (3 x+2)",1,"-1/(32*x^2) + 3/(16*x) + 9/(32*(2 + 3*x)) + (27*Log[x])/64 - (27*Log[2 + 3*x])/64","A",2,1,11,0.09091,1,"{44}"
264,1,49,0,0.0164746,"\int \frac{1}{x^4 (4+6 x)^2} \, dx","Int[1/(x^4*(4 + 6*x)^2),x]","\frac{3}{32 x^2}-\frac{1}{48 x^3}-\frac{27}{64 x}-\frac{27}{64 (3 x+2)}-\frac{27 \log (x)}{32}+\frac{27}{32} \log (3 x+2)","\frac{3}{32 x^2}-\frac{1}{48 x^3}-\frac{27}{64 x}-\frac{27}{64 (3 x+2)}-\frac{27 \log (x)}{32}+\frac{27}{32} \log (3 x+2)",1,"-1/(48*x^3) + 3/(32*x^2) - 27/(64*x) - 27/(64*(2 + 3*x)) - (27*Log[x])/32 + (27*Log[2 + 3*x])/32","A",2,1,11,0.09091,1,"{44}"
265,1,56,0,0.019642,"\int \frac{1}{x^5 (4+6 x)^2} \, dx","Int[1/(x^5*(4 + 6*x)^2),x]","-\frac{27}{128 x^2}+\frac{1}{16 x^3}-\frac{1}{64 x^4}+\frac{27}{32 x}+\frac{81}{128 (3 x+2)}+\frac{405 \log (x)}{256}-\frac{405}{256} \log (3 x+2)","-\frac{27}{128 x^2}+\frac{1}{16 x^3}-\frac{1}{64 x^4}+\frac{27}{32 x}+\frac{81}{128 (3 x+2)}+\frac{405 \log (x)}{256}-\frac{405}{256} \log (3 x+2)",1,"-1/(64*x^4) + 1/(16*x^3) - 27/(128*x^2) + 27/(32*x) + 81/(128*(2 + 3*x)) + (405*Log[x])/256 - (405*Log[2 + 3*x])/256","A",2,1,11,0.09091,1,"{44}"
266,1,39,0,0.0119353,"\int \frac{1}{x (4+6 x)^3} \, dx","Int[1/(x*(4 + 6*x)^3),x]","\frac{1}{32 (3 x+2)}+\frac{1}{32 (3 x+2)^2}+\frac{\log (x)}{64}-\frac{1}{64} \log (3 x+2)","\frac{1}{32 (3 x+2)}+\frac{1}{32 (3 x+2)^2}+\frac{\log (x)}{64}-\frac{1}{64} \log (3 x+2)",1,"1/(32*(2 + 3*x)^2) + 1/(32*(2 + 3*x)) + Log[x]/64 - Log[2 + 3*x]/64","A",2,1,11,0.09091,1,"{44}"
267,1,46,0,0.0150952,"\int \frac{1}{x^2 (4+6 x)^3} \, dx","Int[1/(x^2*(4 + 6*x)^3),x]","-\frac{1}{64 x}-\frac{3}{32 (3 x+2)}-\frac{3}{64 (3 x+2)^2}-\frac{9 \log (x)}{128}+\frac{9}{128} \log (3 x+2)","-\frac{1}{64 x}-\frac{3}{32 (3 x+2)}-\frac{3}{64 (3 x+2)^2}-\frac{9 \log (x)}{128}+\frac{9}{128} \log (3 x+2)",1,"-1/(64*x) - 3/(64*(2 + 3*x)^2) - 3/(32*(2 + 3*x)) - (9*Log[x])/128 + (9*Log[2 + 3*x])/128","A",2,1,11,0.09091,1,"{44}"
268,1,53,0,0.015826,"\int \frac{1}{x^3 (4+6 x)^3} \, dx","Int[1/(x^3*(4 + 6*x)^3),x]","-\frac{1}{128 x^2}+\frac{9}{128 x}+\frac{27}{128 (3 x+2)}+\frac{9}{128 (3 x+2)^2}+\frac{27 \log (x)}{128}-\frac{27}{128} \log (3 x+2)","-\frac{1}{128 x^2}+\frac{9}{128 x}+\frac{27}{128 (3 x+2)}+\frac{9}{128 (3 x+2)^2}+\frac{27 \log (x)}{128}-\frac{27}{128} \log (3 x+2)",1,"-1/(128*x^2) + 9/(128*x) + 9/(128*(2 + 3*x)^2) + 27/(128*(2 + 3*x)) + (27*Log[x])/128 - (27*Log[2 + 3*x])/128","A",2,1,11,0.09091,1,"{44}"
269,1,60,0,0.0207767,"\int \frac{1}{x^4 (4+6 x)^3} \, dx","Int[1/(x^4*(4 + 6*x)^3),x]","\frac{9}{256 x^2}-\frac{1}{192 x^3}-\frac{27}{128 x}-\frac{27}{64 (3 x+2)}-\frac{27}{256 (3 x+2)^2}-\frac{135 \log (x)}{256}+\frac{135}{256} \log (3 x+2)","\frac{9}{256 x^2}-\frac{1}{192 x^3}-\frac{27}{128 x}-\frac{27}{64 (3 x+2)}-\frac{27}{256 (3 x+2)^2}-\frac{135 \log (x)}{256}+\frac{135}{256} \log (3 x+2)",1,"-1/(192*x^3) + 9/(256*x^2) - 27/(128*x) - 27/(256*(2 + 3*x)^2) - 27/(64*(2 + 3*x)) - (135*Log[x])/256 + (135*Log[2 + 3*x])/256","A",2,1,11,0.09091,1,"{44}"
270,1,67,0,0.0223792,"\int \frac{1}{x^5 (4+6 x)^3} \, dx","Int[1/(x^5*(4 + 6*x)^3),x]","-\frac{27}{256 x^2}+\frac{3}{128 x^3}-\frac{1}{256 x^4}+\frac{135}{256 x}+\frac{405}{512 (3 x+2)}+\frac{81}{512 (3 x+2)^2}+\frac{1215 \log (x)}{1024}-\frac{1215 \log (3 x+2)}{1024}","-\frac{27}{256 x^2}+\frac{3}{128 x^3}-\frac{1}{256 x^4}+\frac{135}{256 x}+\frac{405}{512 (3 x+2)}+\frac{81}{512 (3 x+2)^2}+\frac{1215 \log (x)}{1024}-\frac{1215 \log (3 x+2)}{1024}",1,"-1/(256*x^4) + 3/(128*x^3) - 27/(256*x^2) + 135/(256*x) + 81/(512*(2 + 3*x)^2) + 405/(512*(2 + 3*x)) + (1215*Log[x])/1024 - (1215*Log[2 + 3*x])/1024","A",2,1,11,0.09091,1,"{44}"
271,1,8,0,0.0008358,"\int \frac{1}{2+2 x} \, dx","Int[(2 + 2*x)^(-1),x]","\frac{1}{2} \log (x+1)","\frac{1}{2} \log (x+1)",1,"Log[1 + x]/2","A",1,1,7,0.1429,1,"{31}"
272,1,10,0,0.0009693,"\int \frac{1}{4-6 x} \, dx","Int[(4 - 6*x)^(-1),x]","-\frac{1}{6} \log (2-3 x)","-\frac{1}{6} \log (2-3 x)",1,"-Log[2 - 3*x]/6","A",1,1,7,0.1429,1,"{31}"
273,1,14,0,0.0021261,"\int \frac{1}{a+\sqrt{a} x} \, dx","Int[(a + Sqrt[a]*x)^(-1),x]","\frac{\log \left(\sqrt{a}+x\right)}{\sqrt{a}}","\frac{\log \left(\sqrt{a}+x\right)}{\sqrt{a}}",1,"Log[Sqrt[a] + x]/Sqrt[a]","A",1,1,11,0.09091,1,"{31}"
274,1,20,0,0.0074811,"\int \frac{1}{a+\sqrt{-a} x} \, dx","Int[(a + Sqrt[-a]*x)^(-1),x]","\frac{\log \left(\sqrt{-a} x+a\right)}{\sqrt{-a}}","\frac{\log \left(\sqrt{-a} x+a\right)}{\sqrt{-a}}",1,"Log[a + Sqrt[-a]*x]/Sqrt[-a]","A",1,1,13,0.07692,1,"{31}"
275,1,22,0,0.0023876,"\int \frac{1}{a^2+\sqrt{-a} x} \, dx","Int[(a^2 + Sqrt[-a]*x)^(-1),x]","\frac{\log \left(a^2+\sqrt{-a} x\right)}{\sqrt{-a}}","\frac{\log \left(a^2+\sqrt{-a} x\right)}{\sqrt{-a}}",1,"Log[a^2 + Sqrt[-a]*x]/Sqrt[-a]","A",1,1,15,0.06667,1,"{31}"
276,1,22,0,0.0023425,"\int \frac{1}{a^3+\sqrt{-a} x} \, dx","Int[(a^3 + Sqrt[-a]*x)^(-1),x]","\frac{\log \left(a^3+\sqrt{-a} x\right)}{\sqrt{-a}}","\frac{\log \left(a^3+\sqrt{-a} x\right)}{\sqrt{-a}}",1,"Log[a^3 + Sqrt[-a]*x]/Sqrt[-a]","A",1,1,15,0.06667,1,"{31}"
277,1,21,0,0.0037768,"\int \frac{1}{\frac{1}{a}+\sqrt{-a} x} \, dx","Int[(a^(-1) + Sqrt[-a]*x)^(-1),x]","\frac{\log \left(1-(-a)^{3/2} x\right)}{\sqrt{-a}}","\frac{\log \left(1-(-a)^{3/2} x\right)}{\sqrt{-a}}",1,"Log[1 - (-a)^(3/2)*x]/Sqrt[-a]","A",1,1,15,0.06667,1,"{31}"
278,1,20,0,0.0042515,"\int \frac{1}{\frac{1}{a^2}+\sqrt{-a} x} \, dx","Int[(a^(-2) + Sqrt[-a]*x)^(-1),x]","\frac{\log \left((-a)^{5/2} x+1\right)}{\sqrt{-a}}","\frac{\log \left((-a)^{5/2} x+1\right)}{\sqrt{-a}}",1,"Log[1 + (-a)^(5/2)*x]/Sqrt[-a]","A",1,1,15,0.06667,1,"{31}"
279,1,11,0,0.0023277,"\int \frac{1}{x (1+b x)} \, dx","Int[1/(x*(1 + b*x)),x]","\log (x)-\log (b x+1)","\log (x)-\log (b x+1)",1,"Log[x] - Log[1 + b*x]","A",3,3,11,0.2727,1,"{36, 29, 31}"
280,1,12,0,0.0023875,"\int \frac{1}{x (-1+b x)} \, dx","Int[1/(x*(-1 + b*x)),x]","\log (1-b x)-\log (x)","\log (1-b x)-\log (x)",1,"-Log[x] + Log[1 - b*x]","A",3,3,11,0.2727,1,"{36, 29, 31}"
281,1,19,0,0.0080161,"\int \frac{1}{x^2 (1+b x)} \, dx","Int[1/(x^2*(1 + b*x)),x]","-b \log (x)+b \log (b x+1)-\frac{1}{x}","-b \log (x)+b \log (b x+1)-\frac{1}{x}",1,"-x^(-1) - b*Log[x] + b*Log[1 + b*x]","A",2,1,11,0.09091,1,"{44}"
282,1,18,0,0.0099948,"\int \frac{1}{x^2 (-1+b x)} \, dx","Int[1/(x^2*(-1 + b*x)),x]","-b \log (x)+b \log (1-b x)+\frac{1}{x}","-b \log (x)+b \log (1-b x)+\frac{1}{x}",1,"x^(-1) - b*Log[x] + b*Log[1 - b*x]","A",2,1,11,0.09091,1,"{44}"
283,1,14,0,0.0094408,"\int \left(\frac{b}{x}+\frac{1}{x^2 (1+b x)}\right) \, dx","Int[b/x + 1/(x^2*(1 + b*x)),x]","b \log (b x+1)-\frac{1}{x}","b \log (b x+1)-\frac{1}{x}",1,"-x^(-1) + b*Log[1 + b*x]","A",3,1,17,0.05882,1,"{44}"
284,1,72,0,0.018334,"\int x^3 \sqrt{a+b x} \, dx","Int[x^3*Sqrt[a + b*x],x]","\frac{6 a^2 (a+b x)^{5/2}}{5 b^4}-\frac{2 a^3 (a+b x)^{3/2}}{3 b^4}+\frac{2 (a+b x)^{9/2}}{9 b^4}-\frac{6 a (a+b x)^{7/2}}{7 b^4}","\frac{6 a^2 (a+b x)^{5/2}}{5 b^4}-\frac{2 a^3 (a+b x)^{3/2}}{3 b^4}+\frac{2 (a+b x)^{9/2}}{9 b^4}-\frac{6 a (a+b x)^{7/2}}{7 b^4}",1,"(-2*a^3*(a + b*x)^(3/2))/(3*b^4) + (6*a^2*(a + b*x)^(5/2))/(5*b^4) - (6*a*(a + b*x)^(7/2))/(7*b^4) + (2*(a + b*x)^(9/2))/(9*b^4)","A",2,1,13,0.07692,1,"{43}"
285,1,53,0,0.0129626,"\int x^2 \sqrt{a+b x} \, dx","Int[x^2*Sqrt[a + b*x],x]","\frac{2 a^2 (a+b x)^{3/2}}{3 b^3}+\frac{2 (a+b x)^{7/2}}{7 b^3}-\frac{4 a (a+b x)^{5/2}}{5 b^3}","\frac{2 a^2 (a+b x)^{3/2}}{3 b^3}+\frac{2 (a+b x)^{7/2}}{7 b^3}-\frac{4 a (a+b x)^{5/2}}{5 b^3}",1,"(2*a^2*(a + b*x)^(3/2))/(3*b^3) - (4*a*(a + b*x)^(5/2))/(5*b^3) + (2*(a + b*x)^(7/2))/(7*b^3)","A",2,1,13,0.07692,1,"{43}"
286,1,34,0,0.0077808,"\int x \sqrt{a+b x} \, dx","Int[x*Sqrt[a + b*x],x]","\frac{2 (a+b x)^{5/2}}{5 b^2}-\frac{2 a (a+b x)^{3/2}}{3 b^2}","\frac{2 (a+b x)^{5/2}}{5 b^2}-\frac{2 a (a+b x)^{3/2}}{3 b^2}",1,"(-2*a*(a + b*x)^(3/2))/(3*b^2) + (2*(a + b*x)^(5/2))/(5*b^2)","A",2,1,11,0.09091,1,"{43}"
287,1,16,0,0.0014043,"\int \sqrt{a+b x} \, dx","Int[Sqrt[a + b*x],x]","\frac{2 (a+b x)^{3/2}}{3 b}","\frac{2 (a+b x)^{3/2}}{3 b}",1,"(2*(a + b*x)^(3/2))/(3*b)","A",1,1,9,0.1111,1,"{32}"
288,1,35,0,0.0104539,"\int \frac{\sqrt{a+b x}}{x} \, dx","Int[Sqrt[a + b*x]/x,x]","2 \sqrt{a+b x}-2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)","2 \sqrt{a+b x}-2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)",1,"2*Sqrt[a + b*x] - 2*Sqrt[a]*ArcTanh[Sqrt[a + b*x]/Sqrt[a]]","A",3,3,13,0.2308,1,"{50, 63, 208}"
289,1,39,0,0.0106631,"\int \frac{\sqrt{a+b x}}{x^2} \, dx","Int[Sqrt[a + b*x]/x^2,x]","-\frac{\sqrt{a+b x}}{x}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{\sqrt{a}}","-\frac{\sqrt{a+b x}}{x}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{\sqrt{a}}",1,"-(Sqrt[a + b*x]/x) - (b*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/Sqrt[a]","A",3,3,13,0.2308,1,"{47, 63, 208}"
290,1,65,0,0.0183526,"\int \frac{\sqrt{a+b x}}{x^3} \, dx","Int[Sqrt[a + b*x]/x^3,x]","\frac{b^2 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{4 a^{3/2}}-\frac{\sqrt{a+b x}}{2 x^2}-\frac{b \sqrt{a+b x}}{4 a x}","\frac{b^2 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{4 a^{3/2}}-\frac{\sqrt{a+b x}}{2 x^2}-\frac{b \sqrt{a+b x}}{4 a x}",1,"-Sqrt[a + b*x]/(2*x^2) - (b*Sqrt[a + b*x])/(4*a*x) + (b^2*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/(4*a^(3/2))","A",4,4,13,0.3077,1,"{47, 51, 63, 208}"
291,1,87,0,0.0269141,"\int \frac{\sqrt{a+b x}}{x^4} \, dx","Int[Sqrt[a + b*x]/x^4,x]","\frac{b^2 \sqrt{a+b x}}{8 a^2 x}-\frac{b^3 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{8 a^{5/2}}-\frac{b \sqrt{a+b x}}{12 a x^2}-\frac{\sqrt{a+b x}}{3 x^3}","\frac{b^2 \sqrt{a+b x}}{8 a^2 x}-\frac{b^3 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{8 a^{5/2}}-\frac{b \sqrt{a+b x}}{12 a x^2}-\frac{\sqrt{a+b x}}{3 x^3}",1,"-Sqrt[a + b*x]/(3*x^3) - (b*Sqrt[a + b*x])/(12*a*x^2) + (b^2*Sqrt[a + b*x])/(8*a^2*x) - (b^3*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/(8*a^(5/2))","A",5,4,13,0.3077,1,"{47, 51, 63, 208}"
292,1,72,0,0.0188042,"\int x^3 (a+b x)^{3/2} \, dx","Int[x^3*(a + b*x)^(3/2),x]","\frac{6 a^2 (a+b x)^{7/2}}{7 b^4}-\frac{2 a^3 (a+b x)^{5/2}}{5 b^4}+\frac{2 (a+b x)^{11/2}}{11 b^4}-\frac{2 a (a+b x)^{9/2}}{3 b^4}","\frac{6 a^2 (a+b x)^{7/2}}{7 b^4}-\frac{2 a^3 (a+b x)^{5/2}}{5 b^4}+\frac{2 (a+b x)^{11/2}}{11 b^4}-\frac{2 a (a+b x)^{9/2}}{3 b^4}",1,"(-2*a^3*(a + b*x)^(5/2))/(5*b^4) + (6*a^2*(a + b*x)^(7/2))/(7*b^4) - (2*a*(a + b*x)^(9/2))/(3*b^4) + (2*(a + b*x)^(11/2))/(11*b^4)","A",2,1,13,0.07692,1,"{43}"
293,1,53,0,0.0128408,"\int x^2 (a+b x)^{3/2} \, dx","Int[x^2*(a + b*x)^(3/2),x]","\frac{2 a^2 (a+b x)^{5/2}}{5 b^3}+\frac{2 (a+b x)^{9/2}}{9 b^3}-\frac{4 a (a+b x)^{7/2}}{7 b^3}","\frac{2 a^2 (a+b x)^{5/2}}{5 b^3}+\frac{2 (a+b x)^{9/2}}{9 b^3}-\frac{4 a (a+b x)^{7/2}}{7 b^3}",1,"(2*a^2*(a + b*x)^(5/2))/(5*b^3) - (4*a*(a + b*x)^(7/2))/(7*b^3) + (2*(a + b*x)^(9/2))/(9*b^3)","A",2,1,13,0.07692,1,"{43}"
294,1,34,0,0.0077795,"\int x (a+b x)^{3/2} \, dx","Int[x*(a + b*x)^(3/2),x]","\frac{2 (a+b x)^{7/2}}{7 b^2}-\frac{2 a (a+b x)^{5/2}}{5 b^2}","\frac{2 (a+b x)^{7/2}}{7 b^2}-\frac{2 a (a+b x)^{5/2}}{5 b^2}",1,"(-2*a*(a + b*x)^(5/2))/(5*b^2) + (2*(a + b*x)^(7/2))/(7*b^2)","A",2,1,11,0.09091,1,"{43}"
295,1,16,0,0.0013847,"\int (a+b x)^{3/2} \, dx","Int[(a + b*x)^(3/2),x]","\frac{2 (a+b x)^{5/2}}{5 b}","\frac{2 (a+b x)^{5/2}}{5 b}",1,"(2*(a + b*x)^(5/2))/(5*b)","A",1,1,9,0.1111,1,"{32}"
296,1,49,0,0.0144803,"\int \frac{(a+b x)^{3/2}}{x} \, dx","Int[(a + b*x)^(3/2)/x,x]","-2 a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)+2 a \sqrt{a+b x}+\frac{2}{3} (a+b x)^{3/2}","-2 a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)+2 a \sqrt{a+b x}+\frac{2}{3} (a+b x)^{3/2}",1,"2*a*Sqrt[a + b*x] + (2*(a + b*x)^(3/2))/3 - 2*a^(3/2)*ArcTanh[Sqrt[a + b*x]/Sqrt[a]]","A",4,3,13,0.2308,1,"{50, 63, 208}"
297,1,51,0,0.0147685,"\int \frac{(a+b x)^{3/2}}{x^2} \, dx","Int[(a + b*x)^(3/2)/x^2,x]","-\frac{(a+b x)^{3/2}}{x}+3 b \sqrt{a+b x}-3 \sqrt{a} b \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)","-\frac{(a+b x)^{3/2}}{x}+3 b \sqrt{a+b x}-3 \sqrt{a} b \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)",1,"3*b*Sqrt[a + b*x] - (a + b*x)^(3/2)/x - 3*Sqrt[a]*b*ArcTanh[Sqrt[a + b*x]/Sqrt[a]]","A",4,4,13,0.3077,1,"{47, 50, 63, 208}"
298,1,62,0,0.0160989,"\int \frac{(a+b x)^{3/2}}{x^3} \, dx","Int[(a + b*x)^(3/2)/x^3,x]","-\frac{3 b^2 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{4 \sqrt{a}}-\frac{(a+b x)^{3/2}}{2 x^2}-\frac{3 b \sqrt{a+b x}}{4 x}","-\frac{3 b^2 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{4 \sqrt{a}}-\frac{(a+b x)^{3/2}}{2 x^2}-\frac{3 b \sqrt{a+b x}}{4 x}",1,"(-3*b*Sqrt[a + b*x])/(4*x) - (a + b*x)^(3/2)/(2*x^2) - (3*b^2*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/(4*Sqrt[a])","A",4,3,13,0.2308,1,"{47, 63, 208}"
299,1,84,0,0.0222849,"\int \frac{(a+b x)^{3/2}}{x^4} \, dx","Int[(a + b*x)^(3/2)/x^4,x]","\frac{b^3 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{8 a^{3/2}}-\frac{b^2 \sqrt{a+b x}}{8 a x}-\frac{b \sqrt{a+b x}}{4 x^2}-\frac{(a+b x)^{3/2}}{3 x^3}","\frac{b^3 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{8 a^{3/2}}-\frac{b^2 \sqrt{a+b x}}{8 a x}-\frac{b \sqrt{a+b x}}{4 x^2}-\frac{(a+b x)^{3/2}}{3 x^3}",1,"-(b*Sqrt[a + b*x])/(4*x^2) - (b^2*Sqrt[a + b*x])/(8*a*x) - (a + b*x)^(3/2)/(3*x^3) + (b^3*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/(8*a^(3/2))","A",5,4,13,0.3077,1,"{47, 51, 63, 208}"
300,1,72,0,0.0171271,"\int x^3 (a+b x)^{5/2} \, dx","Int[x^3*(a + b*x)^(5/2),x]","\frac{2 a^2 (a+b x)^{9/2}}{3 b^4}-\frac{2 a^3 (a+b x)^{7/2}}{7 b^4}+\frac{2 (a+b x)^{13/2}}{13 b^4}-\frac{6 a (a+b x)^{11/2}}{11 b^4}","\frac{2 a^2 (a+b x)^{9/2}}{3 b^4}-\frac{2 a^3 (a+b x)^{7/2}}{7 b^4}+\frac{2 (a+b x)^{13/2}}{13 b^4}-\frac{6 a (a+b x)^{11/2}}{11 b^4}",1,"(-2*a^3*(a + b*x)^(7/2))/(7*b^4) + (2*a^2*(a + b*x)^(9/2))/(3*b^4) - (6*a*(a + b*x)^(11/2))/(11*b^4) + (2*(a + b*x)^(13/2))/(13*b^4)","A",2,1,13,0.07692,1,"{43}"
301,1,53,0,0.0124758,"\int x^2 (a+b x)^{5/2} \, dx","Int[x^2*(a + b*x)^(5/2),x]","\frac{2 a^2 (a+b x)^{7/2}}{7 b^3}+\frac{2 (a+b x)^{11/2}}{11 b^3}-\frac{4 a (a+b x)^{9/2}}{9 b^3}","\frac{2 a^2 (a+b x)^{7/2}}{7 b^3}+\frac{2 (a+b x)^{11/2}}{11 b^3}-\frac{4 a (a+b x)^{9/2}}{9 b^3}",1,"(2*a^2*(a + b*x)^(7/2))/(7*b^3) - (4*a*(a + b*x)^(9/2))/(9*b^3) + (2*(a + b*x)^(11/2))/(11*b^3)","A",2,1,13,0.07692,1,"{43}"
302,1,34,0,0.0086827,"\int x (a+b x)^{5/2} \, dx","Int[x*(a + b*x)^(5/2),x]","\frac{2 (a+b x)^{9/2}}{9 b^2}-\frac{2 a (a+b x)^{7/2}}{7 b^2}","\frac{2 (a+b x)^{9/2}}{9 b^2}-\frac{2 a (a+b x)^{7/2}}{7 b^2}",1,"(-2*a*(a + b*x)^(7/2))/(7*b^2) + (2*(a + b*x)^(9/2))/(9*b^2)","A",2,1,11,0.09091,1,"{43}"
303,1,16,0,0.0013822,"\int (a+b x)^{5/2} \, dx","Int[(a + b*x)^(5/2),x]","\frac{2 (a+b x)^{7/2}}{7 b}","\frac{2 (a+b x)^{7/2}}{7 b}",1,"(2*(a + b*x)^(7/2))/(7*b)","A",1,1,9,0.1111,1,"{32}"
304,1,65,0,0.0208395,"\int \frac{(a+b x)^{5/2}}{x} \, dx","Int[(a + b*x)^(5/2)/x,x]","2 a^2 \sqrt{a+b x}-2 a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)+\frac{2}{3} a (a+b x)^{3/2}+\frac{2}{5} (a+b x)^{5/2}","2 a^2 \sqrt{a+b x}-2 a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)+\frac{2}{3} a (a+b x)^{3/2}+\frac{2}{5} (a+b x)^{5/2}",1,"2*a^2*Sqrt[a + b*x] + (2*a*(a + b*x)^(3/2))/3 + (2*(a + b*x)^(5/2))/5 - 2*a^(5/2)*ArcTanh[Sqrt[a + b*x]/Sqrt[a]]","A",5,3,13,0.2308,1,"{50, 63, 208}"
305,1,66,0,0.0204844,"\int \frac{(a+b x)^{5/2}}{x^2} \, dx","Int[(a + b*x)^(5/2)/x^2,x]","-5 a^{3/2} b \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)-\frac{(a+b x)^{5/2}}{x}+\frac{5}{3} b (a+b x)^{3/2}+5 a b \sqrt{a+b x}","-5 a^{3/2} b \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)-\frac{(a+b x)^{5/2}}{x}+\frac{5}{3} b (a+b x)^{3/2}+5 a b \sqrt{a+b x}",1,"5*a*b*Sqrt[a + b*x] + (5*b*(a + b*x)^(3/2))/3 - (a + b*x)^(5/2)/x - 5*a^(3/2)*b*ArcTanh[Sqrt[a + b*x]/Sqrt[a]]","A",5,4,13,0.3077,1,"{47, 50, 63, 208}"
306,1,78,0,0.0211749,"\int \frac{(a+b x)^{5/2}}{x^3} \, dx","Int[(a + b*x)^(5/2)/x^3,x]","\frac{15}{4} b^2 \sqrt{a+b x}-\frac{15}{4} \sqrt{a} b^2 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)-\frac{(a+b x)^{5/2}}{2 x^2}-\frac{5 b (a+b x)^{3/2}}{4 x}","\frac{15}{4} b^2 \sqrt{a+b x}-\frac{15}{4} \sqrt{a} b^2 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)-\frac{(a+b x)^{5/2}}{2 x^2}-\frac{5 b (a+b x)^{3/2}}{4 x}",1,"(15*b^2*Sqrt[a + b*x])/4 - (5*b*(a + b*x)^(3/2))/(4*x) - (a + b*x)^(5/2)/(2*x^2) - (15*Sqrt[a]*b^2*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/4","A",5,4,13,0.3077,1,"{47, 50, 63, 208}"
307,1,81,0,0.0226134,"\int \frac{(a+b x)^{5/2}}{x^4} \, dx","Int[(a + b*x)^(5/2)/x^4,x]","-\frac{5 b^2 \sqrt{a+b x}}{8 x}-\frac{5 b^3 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{8 \sqrt{a}}-\frac{5 b (a+b x)^{3/2}}{12 x^2}-\frac{(a+b x)^{5/2}}{3 x^3}","-\frac{5 b^2 \sqrt{a+b x}}{8 x}-\frac{5 b^3 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{8 \sqrt{a}}-\frac{5 b (a+b x)^{3/2}}{12 x^2}-\frac{(a+b x)^{5/2}}{3 x^3}",1,"(-5*b^2*Sqrt[a + b*x])/(8*x) - (5*b*(a + b*x)^(3/2))/(12*x^2) - (a + b*x)^(5/2)/(3*x^3) - (5*b^3*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/(8*Sqrt[a])","A",5,3,13,0.2308,1,"{47, 63, 208}"
308,1,103,0,0.0309203,"\int \frac{(a+b x)^{5/2}}{x^5} \, dx","Int[(a + b*x)^(5/2)/x^5,x]","\frac{5 b^4 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{64 a^{3/2}}-\frac{5 b^2 \sqrt{a+b x}}{32 x^2}-\frac{5 b^3 \sqrt{a+b x}}{64 a x}-\frac{5 b (a+b x)^{3/2}}{24 x^3}-\frac{(a+b x)^{5/2}}{4 x^4}","\frac{5 b^4 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{64 a^{3/2}}-\frac{5 b^2 \sqrt{a+b x}}{32 x^2}-\frac{5 b^3 \sqrt{a+b x}}{64 a x}-\frac{5 b (a+b x)^{3/2}}{24 x^3}-\frac{(a+b x)^{5/2}}{4 x^4}",1,"(-5*b^2*Sqrt[a + b*x])/(32*x^2) - (5*b^3*Sqrt[a + b*x])/(64*a*x) - (5*b*(a + b*x)^(3/2))/(24*x^3) - (a + b*x)^(5/2)/(4*x^4) + (5*b^4*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/(64*a^(3/2))","A",6,4,13,0.3077,1,"{47, 51, 63, 208}"
309,1,146,0,0.0424934,"\int x^7 (a+b x)^{9/2} \, dx","Int[x^7*(a + b*x)^(9/2),x]","\frac{2 a^2 (a+b x)^{21/2}}{b^8}-\frac{70 a^3 (a+b x)^{19/2}}{19 b^8}+\frac{70 a^4 (a+b x)^{17/2}}{17 b^8}-\frac{14 a^5 (a+b x)^{15/2}}{5 b^8}+\frac{14 a^6 (a+b x)^{13/2}}{13 b^8}-\frac{2 a^7 (a+b x)^{11/2}}{11 b^8}+\frac{2 (a+b x)^{25/2}}{25 b^8}-\frac{14 a (a+b x)^{23/2}}{23 b^8}","\frac{2 a^2 (a+b x)^{21/2}}{b^8}-\frac{70 a^3 (a+b x)^{19/2}}{19 b^8}+\frac{70 a^4 (a+b x)^{17/2}}{17 b^8}-\frac{14 a^5 (a+b x)^{15/2}}{5 b^8}+\frac{14 a^6 (a+b x)^{13/2}}{13 b^8}-\frac{2 a^7 (a+b x)^{11/2}}{11 b^8}+\frac{2 (a+b x)^{25/2}}{25 b^8}-\frac{14 a (a+b x)^{23/2}}{23 b^8}",1,"(-2*a^7*(a + b*x)^(11/2))/(11*b^8) + (14*a^6*(a + b*x)^(13/2))/(13*b^8) - (14*a^5*(a + b*x)^(15/2))/(5*b^8) + (70*a^4*(a + b*x)^(17/2))/(17*b^8) - (70*a^3*(a + b*x)^(19/2))/(19*b^8) + (2*a^2*(a + b*x)^(21/2))/b^8 - (14*a*(a + b*x)^(23/2))/(23*b^8) + (2*(a + b*x)^(25/2))/(25*b^8)","A",2,1,13,0.07692,1,"{43}"
310,1,127,0,0.0350039,"\int x^6 (a+b x)^{9/2} \, dx","Int[x^6*(a + b*x)^(9/2),x]","\frac{30 a^2 (a+b x)^{19/2}}{19 b^7}-\frac{40 a^3 (a+b x)^{17/2}}{17 b^7}+\frac{2 a^4 (a+b x)^{15/2}}{b^7}-\frac{12 a^5 (a+b x)^{13/2}}{13 b^7}+\frac{2 a^6 (a+b x)^{11/2}}{11 b^7}+\frac{2 (a+b x)^{23/2}}{23 b^7}-\frac{4 a (a+b x)^{21/2}}{7 b^7}","\frac{30 a^2 (a+b x)^{19/2}}{19 b^7}-\frac{40 a^3 (a+b x)^{17/2}}{17 b^7}+\frac{2 a^4 (a+b x)^{15/2}}{b^7}-\frac{12 a^5 (a+b x)^{13/2}}{13 b^7}+\frac{2 a^6 (a+b x)^{11/2}}{11 b^7}+\frac{2 (a+b x)^{23/2}}{23 b^7}-\frac{4 a (a+b x)^{21/2}}{7 b^7}",1,"(2*a^6*(a + b*x)^(11/2))/(11*b^7) - (12*a^5*(a + b*x)^(13/2))/(13*b^7) + (2*a^4*(a + b*x)^(15/2))/b^7 - (40*a^3*(a + b*x)^(17/2))/(17*b^7) + (30*a^2*(a + b*x)^(19/2))/(19*b^7) - (4*a*(a + b*x)^(21/2))/(7*b^7) + (2*(a + b*x)^(23/2))/(23*b^7)","A",2,1,13,0.07692,1,"{43}"
311,1,110,0,0.0321136,"\int x^5 (a+b x)^{9/2} \, dx","Int[x^5*(a + b*x)^(9/2),x]","\frac{20 a^2 (a+b x)^{17/2}}{17 b^6}-\frac{4 a^3 (a+b x)^{15/2}}{3 b^6}+\frac{10 a^4 (a+b x)^{13/2}}{13 b^6}-\frac{2 a^5 (a+b x)^{11/2}}{11 b^6}+\frac{2 (a+b x)^{21/2}}{21 b^6}-\frac{10 a (a+b x)^{19/2}}{19 b^6}","\frac{20 a^2 (a+b x)^{17/2}}{17 b^6}-\frac{4 a^3 (a+b x)^{15/2}}{3 b^6}+\frac{10 a^4 (a+b x)^{13/2}}{13 b^6}-\frac{2 a^5 (a+b x)^{11/2}}{11 b^6}+\frac{2 (a+b x)^{21/2}}{21 b^6}-\frac{10 a (a+b x)^{19/2}}{19 b^6}",1,"(-2*a^5*(a + b*x)^(11/2))/(11*b^6) + (10*a^4*(a + b*x)^(13/2))/(13*b^6) - (4*a^3*(a + b*x)^(15/2))/(3*b^6) + (20*a^2*(a + b*x)^(17/2))/(17*b^6) - (10*a*(a + b*x)^(19/2))/(19*b^6) + (2*(a + b*x)^(21/2))/(21*b^6)","A",2,1,13,0.07692,1,"{43}"
312,1,91,0,0.023489,"\int x^4 (a+b x)^{9/2} \, dx","Int[x^4*(a + b*x)^(9/2),x]","\frac{4 a^2 (a+b x)^{15/2}}{5 b^5}-\frac{8 a^3 (a+b x)^{13/2}}{13 b^5}+\frac{2 a^4 (a+b x)^{11/2}}{11 b^5}+\frac{2 (a+b x)^{19/2}}{19 b^5}-\frac{8 a (a+b x)^{17/2}}{17 b^5}","\frac{4 a^2 (a+b x)^{15/2}}{5 b^5}-\frac{8 a^3 (a+b x)^{13/2}}{13 b^5}+\frac{2 a^4 (a+b x)^{11/2}}{11 b^5}+\frac{2 (a+b x)^{19/2}}{19 b^5}-\frac{8 a (a+b x)^{17/2}}{17 b^5}",1,"(2*a^4*(a + b*x)^(11/2))/(11*b^5) - (8*a^3*(a + b*x)^(13/2))/(13*b^5) + (4*a^2*(a + b*x)^(15/2))/(5*b^5) - (8*a*(a + b*x)^(17/2))/(17*b^5) + (2*(a + b*x)^(19/2))/(19*b^5)","A",2,1,13,0.07692,1,"{43}"
313,1,72,0,0.0177268,"\int x^3 (a+b x)^{9/2} \, dx","Int[x^3*(a + b*x)^(9/2),x]","\frac{6 a^2 (a+b x)^{13/2}}{13 b^4}-\frac{2 a^3 (a+b x)^{11/2}}{11 b^4}+\frac{2 (a+b x)^{17/2}}{17 b^4}-\frac{2 a (a+b x)^{15/2}}{5 b^4}","\frac{6 a^2 (a+b x)^{13/2}}{13 b^4}-\frac{2 a^3 (a+b x)^{11/2}}{11 b^4}+\frac{2 (a+b x)^{17/2}}{17 b^4}-\frac{2 a (a+b x)^{15/2}}{5 b^4}",1,"(-2*a^3*(a + b*x)^(11/2))/(11*b^4) + (6*a^2*(a + b*x)^(13/2))/(13*b^4) - (2*a*(a + b*x)^(15/2))/(5*b^4) + (2*(a + b*x)^(17/2))/(17*b^4)","A",2,1,13,0.07692,1,"{43}"
314,1,53,0,0.0134202,"\int x^2 (a+b x)^{9/2} \, dx","Int[x^2*(a + b*x)^(9/2),x]","\frac{2 a^2 (a+b x)^{11/2}}{11 b^3}+\frac{2 (a+b x)^{15/2}}{15 b^3}-\frac{4 a (a+b x)^{13/2}}{13 b^3}","\frac{2 a^2 (a+b x)^{11/2}}{11 b^3}+\frac{2 (a+b x)^{15/2}}{15 b^3}-\frac{4 a (a+b x)^{13/2}}{13 b^3}",1,"(2*a^2*(a + b*x)^(11/2))/(11*b^3) - (4*a*(a + b*x)^(13/2))/(13*b^3) + (2*(a + b*x)^(15/2))/(15*b^3)","A",2,1,13,0.07692,1,"{43}"
315,1,34,0,0.0080125,"\int x (a+b x)^{9/2} \, dx","Int[x*(a + b*x)^(9/2),x]","\frac{2 (a+b x)^{13/2}}{13 b^2}-\frac{2 a (a+b x)^{11/2}}{11 b^2}","\frac{2 (a+b x)^{13/2}}{13 b^2}-\frac{2 a (a+b x)^{11/2}}{11 b^2}",1,"(-2*a*(a + b*x)^(11/2))/(11*b^2) + (2*(a + b*x)^(13/2))/(13*b^2)","A",2,1,11,0.09091,1,"{43}"
316,1,16,0,0.0015142,"\int (a+b x)^{9/2} \, dx","Int[(a + b*x)^(9/2),x]","\frac{2 (a+b x)^{11/2}}{11 b}","\frac{2 (a+b x)^{11/2}}{11 b}",1,"(2*(a + b*x)^(11/2))/(11*b)","A",1,1,9,0.1111,1,"{32}"
317,1,97,0,0.0342687,"\int \frac{(a+b x)^{9/2}}{x} \, dx","Int[(a + b*x)^(9/2)/x,x]","2 a^4 \sqrt{a+b x}+\frac{2}{3} a^3 (a+b x)^{3/2}+\frac{2}{5} a^2 (a+b x)^{5/2}-2 a^{9/2} \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)+\frac{2}{7} a (a+b x)^{7/2}+\frac{2}{9} (a+b x)^{9/2}","2 a^4 \sqrt{a+b x}+\frac{2}{3} a^3 (a+b x)^{3/2}+\frac{2}{5} a^2 (a+b x)^{5/2}-2 a^{9/2} \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)+\frac{2}{7} a (a+b x)^{7/2}+\frac{2}{9} (a+b x)^{9/2}",1,"2*a^4*Sqrt[a + b*x] + (2*a^3*(a + b*x)^(3/2))/3 + (2*a^2*(a + b*x)^(5/2))/5 + (2*a*(a + b*x)^(7/2))/7 + (2*(a + b*x)^(9/2))/9 - 2*a^(9/2)*ArcTanh[Sqrt[a + b*x]/Sqrt[a]]","A",7,3,13,0.2308,1,"{50, 63, 208}"
318,1,98,0,0.0340381,"\int \frac{(a+b x)^{9/2}}{x^2} \, dx","Int[(a + b*x)^(9/2)/x^2,x]","3 a^2 b (a+b x)^{3/2}+9 a^3 b \sqrt{a+b x}-9 a^{7/2} b \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)-\frac{(a+b x)^{9/2}}{x}+\frac{9}{7} b (a+b x)^{7/2}+\frac{9}{5} a b (a+b x)^{5/2}","3 a^2 b (a+b x)^{3/2}+9 a^3 b \sqrt{a+b x}-9 a^{7/2} b \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)-\frac{(a+b x)^{9/2}}{x}+\frac{9}{7} b (a+b x)^{7/2}+\frac{9}{5} a b (a+b x)^{5/2}",1,"9*a^3*b*Sqrt[a + b*x] + 3*a^2*b*(a + b*x)^(3/2) + (9*a*b*(a + b*x)^(5/2))/5 + (9*b*(a + b*x)^(7/2))/7 - (a + b*x)^(9/2)/x - 9*a^(7/2)*b*ArcTanh[Sqrt[a + b*x]/Sqrt[a]]","A",7,4,13,0.3077,1,"{47, 50, 63, 208}"
319,1,114,0,0.0350025,"\int \frac{(a+b x)^{9/2}}{x^3} \, dx","Int[(a + b*x)^(9/2)/x^3,x]","\frac{63}{4} a^2 b^2 \sqrt{a+b x}-\frac{63}{4} a^{5/2} b^2 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)+\frac{63}{20} b^2 (a+b x)^{5/2}+\frac{21}{4} a b^2 (a+b x)^{3/2}-\frac{(a+b x)^{9/2}}{2 x^2}-\frac{9 b (a+b x)^{7/2}}{4 x}","\frac{63}{4} a^2 b^2 \sqrt{a+b x}-\frac{63}{4} a^{5/2} b^2 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)+\frac{63}{20} b^2 (a+b x)^{5/2}+\frac{21}{4} a b^2 (a+b x)^{3/2}-\frac{(a+b x)^{9/2}}{2 x^2}-\frac{9 b (a+b x)^{7/2}}{4 x}",1,"(63*a^2*b^2*Sqrt[a + b*x])/4 + (21*a*b^2*(a + b*x)^(3/2))/4 + (63*b^2*(a + b*x)^(5/2))/20 - (9*b*(a + b*x)^(7/2))/(4*x) - (a + b*x)^(9/2)/(2*x^2) - (63*a^(5/2)*b^2*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/4","A",7,4,13,0.3077,1,"{47, 50, 63, 208}"
320,1,114,0,0.0357739,"\int \frac{(a+b x)^{9/2}}{x^4} \, dx","Int[(a + b*x)^(9/2)/x^4,x]","-\frac{105}{8} a^{3/2} b^3 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)-\frac{21 b^2 (a+b x)^{5/2}}{8 x}+\frac{35}{8} b^3 (a+b x)^{3/2}+\frac{105}{8} a b^3 \sqrt{a+b x}-\frac{(a+b x)^{9/2}}{3 x^3}-\frac{3 b (a+b x)^{7/2}}{4 x^2}","-\frac{105}{8} a^{3/2} b^3 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)-\frac{21 b^2 (a+b x)^{5/2}}{8 x}+\frac{35}{8} b^3 (a+b x)^{3/2}+\frac{105}{8} a b^3 \sqrt{a+b x}-\frac{(a+b x)^{9/2}}{3 x^3}-\frac{3 b (a+b x)^{7/2}}{4 x^2}",1,"(105*a*b^3*Sqrt[a + b*x])/8 + (35*b^3*(a + b*x)^(3/2))/8 - (21*b^2*(a + b*x)^(5/2))/(8*x) - (3*b*(a + b*x)^(7/2))/(4*x^2) - (a + b*x)^(9/2)/(3*x^3) - (105*a^(3/2)*b^3*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/8","A",7,4,13,0.3077,1,"{47, 50, 63, 208}"
321,1,116,0,0.0366599,"\int \frac{(a+b x)^{9/2}}{x^5} \, dx","Int[(a + b*x)^(9/2)/x^5,x]","-\frac{21 b^2 (a+b x)^{5/2}}{32 x^2}-\frac{105 b^3 (a+b x)^{3/2}}{64 x}+\frac{315}{64} b^4 \sqrt{a+b x}-\frac{315}{64} \sqrt{a} b^4 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)-\frac{(a+b x)^{9/2}}{4 x^4}-\frac{3 b (a+b x)^{7/2}}{8 x^3}","-\frac{21 b^2 (a+b x)^{5/2}}{32 x^2}-\frac{105 b^3 (a+b x)^{3/2}}{64 x}+\frac{315}{64} b^4 \sqrt{a+b x}-\frac{315}{64} \sqrt{a} b^4 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)-\frac{(a+b x)^{9/2}}{4 x^4}-\frac{3 b (a+b x)^{7/2}}{8 x^3}",1,"(315*b^4*Sqrt[a + b*x])/64 - (105*b^3*(a + b*x)^(3/2))/(64*x) - (21*b^2*(a + b*x)^(5/2))/(32*x^2) - (3*b*(a + b*x)^(7/2))/(8*x^3) - (a + b*x)^(9/2)/(4*x^4) - (315*Sqrt[a]*b^4*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/64","A",7,4,13,0.3077,1,"{47, 50, 63, 208}"
322,1,119,0,0.0385725,"\int \frac{(a+b x)^{9/2}}{x^6} \, dx","Int[(a + b*x)^(9/2)/x^6,x]","-\frac{21 b^3 (a+b x)^{3/2}}{64 x^2}-\frac{21 b^2 (a+b x)^{5/2}}{80 x^3}-\frac{63 b^4 \sqrt{a+b x}}{128 x}-\frac{63 b^5 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{128 \sqrt{a}}-\frac{9 b (a+b x)^{7/2}}{40 x^4}-\frac{(a+b x)^{9/2}}{5 x^5}","-\frac{21 b^3 (a+b x)^{3/2}}{64 x^2}-\frac{21 b^2 (a+b x)^{5/2}}{80 x^3}-\frac{63 b^4 \sqrt{a+b x}}{128 x}-\frac{63 b^5 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{128 \sqrt{a}}-\frac{9 b (a+b x)^{7/2}}{40 x^4}-\frac{(a+b x)^{9/2}}{5 x^5}",1,"(-63*b^4*Sqrt[a + b*x])/(128*x) - (21*b^3*(a + b*x)^(3/2))/(64*x^2) - (21*b^2*(a + b*x)^(5/2))/(80*x^3) - (9*b*(a + b*x)^(7/2))/(40*x^4) - (a + b*x)^(9/2)/(5*x^5) - (63*b^5*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/(128*Sqrt[a])","A",7,3,13,0.2308,1,"{47, 63, 208}"
323,1,141,0,0.0510884,"\int \frac{(a+b x)^{9/2}}{x^7} \, dx","Int[(a + b*x)^(9/2)/x^7,x]","\frac{21 b^6 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{512 a^{3/2}}-\frac{21 b^4 \sqrt{a+b x}}{256 x^2}-\frac{7 b^3 (a+b x)^{3/2}}{64 x^3}-\frac{21 b^2 (a+b x)^{5/2}}{160 x^4}-\frac{21 b^5 \sqrt{a+b x}}{512 a x}-\frac{3 b (a+b x)^{7/2}}{20 x^5}-\frac{(a+b x)^{9/2}}{6 x^6}","\frac{21 b^6 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{512 a^{3/2}}-\frac{21 b^4 \sqrt{a+b x}}{256 x^2}-\frac{7 b^3 (a+b x)^{3/2}}{64 x^3}-\frac{21 b^2 (a+b x)^{5/2}}{160 x^4}-\frac{21 b^5 \sqrt{a+b x}}{512 a x}-\frac{3 b (a+b x)^{7/2}}{20 x^5}-\frac{(a+b x)^{9/2}}{6 x^6}",1,"(-21*b^4*Sqrt[a + b*x])/(256*x^2) - (21*b^5*Sqrt[a + b*x])/(512*a*x) - (7*b^3*(a + b*x)^(3/2))/(64*x^3) - (21*b^2*(a + b*x)^(5/2))/(160*x^4) - (3*b*(a + b*x)^(7/2))/(20*x^5) - (a + b*x)^(9/2)/(6*x^6) + (21*b^6*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/(512*a^(3/2))","A",8,4,13,0.3077,1,"{47, 51, 63, 208}"
324,1,163,0,0.0675368,"\int \frac{(a+b x)^{9/2}}{x^8} \, dx","Int[(a + b*x)^(9/2)/x^8,x]","\frac{9 b^6 \sqrt{a+b x}}{1024 a^2 x}-\frac{9 b^7 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{1024 a^{5/2}}-\frac{3 b^5 \sqrt{a+b x}}{512 a x^2}-\frac{3 b^4 \sqrt{a+b x}}{128 x^3}-\frac{3 b^3 (a+b x)^{3/2}}{64 x^4}-\frac{3 b^2 (a+b x)^{5/2}}{40 x^5}-\frac{3 b (a+b x)^{7/2}}{28 x^6}-\frac{(a+b x)^{9/2}}{7 x^7}","\frac{9 b^6 \sqrt{a+b x}}{1024 a^2 x}-\frac{9 b^7 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{1024 a^{5/2}}-\frac{3 b^5 \sqrt{a+b x}}{512 a x^2}-\frac{3 b^4 \sqrt{a+b x}}{128 x^3}-\frac{3 b^3 (a+b x)^{3/2}}{64 x^4}-\frac{3 b^2 (a+b x)^{5/2}}{40 x^5}-\frac{3 b (a+b x)^{7/2}}{28 x^6}-\frac{(a+b x)^{9/2}}{7 x^7}",1,"(-3*b^4*Sqrt[a + b*x])/(128*x^3) - (3*b^5*Sqrt[a + b*x])/(512*a*x^2) + (9*b^6*Sqrt[a + b*x])/(1024*a^2*x) - (3*b^3*(a + b*x)^(3/2))/(64*x^4) - (3*b^2*(a + b*x)^(5/2))/(40*x^5) - (3*b*(a + b*x)^(7/2))/(28*x^6) - (a + b*x)^(9/2)/(7*x^7) - (9*b^7*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/(1024*a^(5/2))","A",9,4,13,0.3077,1,"{47, 51, 63, 208}"
325,1,39,0,0.0105244,"\int \frac{\sqrt{-a+b x}}{x} \, dx","Int[Sqrt[-a + b*x]/x,x]","2 \sqrt{b x-a}-2 \sqrt{a} \tan ^{-1}\left(\frac{\sqrt{b x-a}}{\sqrt{a}}\right)","2 \sqrt{b x-a}-2 \sqrt{a} \tan ^{-1}\left(\frac{\sqrt{b x-a}}{\sqrt{a}}\right)",1,"2*Sqrt[-a + b*x] - 2*Sqrt[a]*ArcTan[Sqrt[-a + b*x]/Sqrt[a]]","A",3,3,15,0.2000,1,"{50, 63, 205}"
326,1,42,0,0.0103159,"\int \frac{\sqrt{-a+b x}}{x^2} \, dx","Int[Sqrt[-a + b*x]/x^2,x]","\frac{b \tan ^{-1}\left(\frac{\sqrt{b x-a}}{\sqrt{a}}\right)}{\sqrt{a}}-\frac{\sqrt{b x-a}}{x}","\frac{b \tan ^{-1}\left(\frac{\sqrt{b x-a}}{\sqrt{a}}\right)}{\sqrt{a}}-\frac{\sqrt{b x-a}}{x}",1,"-(Sqrt[-a + b*x]/x) + (b*ArcTan[Sqrt[-a + b*x]/Sqrt[a]])/Sqrt[a]","A",3,3,15,0.2000,1,"{47, 63, 205}"
327,1,71,0,0.015946,"\int \frac{\sqrt{-a+b x}}{x^3} \, dx","Int[Sqrt[-a + b*x]/x^3,x]","\frac{b^2 \tan ^{-1}\left(\frac{\sqrt{b x-a}}{\sqrt{a}}\right)}{4 a^{3/2}}-\frac{\sqrt{b x-a}}{2 x^2}+\frac{b \sqrt{b x-a}}{4 a x}","\frac{b^2 \tan ^{-1}\left(\frac{\sqrt{b x-a}}{\sqrt{a}}\right)}{4 a^{3/2}}-\frac{\sqrt{b x-a}}{2 x^2}+\frac{b \sqrt{b x-a}}{4 a x}",1,"-Sqrt[-a + b*x]/(2*x^2) + (b*Sqrt[-a + b*x])/(4*a*x) + (b^2*ArcTan[Sqrt[-a + b*x]/Sqrt[a]])/(4*a^(3/2))","A",4,4,15,0.2667,1,"{47, 51, 63, 205}"
328,1,55,0,0.0145422,"\int \frac{(-a+b x)^{3/2}}{x} \, dx","Int[(-a + b*x)^(3/2)/x,x]","2 a^{3/2} \tan ^{-1}\left(\frac{\sqrt{b x-a}}{\sqrt{a}}\right)-2 a \sqrt{b x-a}+\frac{2}{3} (b x-a)^{3/2}","2 a^{3/2} \tan ^{-1}\left(\frac{\sqrt{b x-a}}{\sqrt{a}}\right)-2 a \sqrt{b x-a}+\frac{2}{3} (b x-a)^{3/2}",1,"-2*a*Sqrt[-a + b*x] + (2*(-a + b*x)^(3/2))/3 + 2*a^(3/2)*ArcTan[Sqrt[-a + b*x]/Sqrt[a]]","A",4,3,15,0.2000,1,"{50, 63, 205}"
329,1,57,0,0.0143466,"\int \frac{(-a+b x)^{3/2}}{x^2} \, dx","Int[(-a + b*x)^(3/2)/x^2,x]","-\frac{(b x-a)^{3/2}}{x}+3 b \sqrt{b x-a}-3 \sqrt{a} b \tan ^{-1}\left(\frac{\sqrt{b x-a}}{\sqrt{a}}\right)","-\frac{(b x-a)^{3/2}}{x}+3 b \sqrt{b x-a}-3 \sqrt{a} b \tan ^{-1}\left(\frac{\sqrt{b x-a}}{\sqrt{a}}\right)",1,"3*b*Sqrt[-a + b*x] - (-a + b*x)^(3/2)/x - 3*Sqrt[a]*b*ArcTan[Sqrt[-a + b*x]/Sqrt[a]]","A",4,4,15,0.2667,1,"{47, 50, 63, 205}"
330,1,68,0,0.0148347,"\int \frac{(-a+b x)^{3/2}}{x^3} \, dx","Int[(-a + b*x)^(3/2)/x^3,x]","\frac{3 b^2 \tan ^{-1}\left(\frac{\sqrt{b x-a}}{\sqrt{a}}\right)}{4 \sqrt{a}}-\frac{(b x-a)^{3/2}}{2 x^2}-\frac{3 b \sqrt{b x-a}}{4 x}","\frac{3 b^2 \tan ^{-1}\left(\frac{\sqrt{b x-a}}{\sqrt{a}}\right)}{4 \sqrt{a}}-\frac{(b x-a)^{3/2}}{2 x^2}-\frac{3 b \sqrt{b x-a}}{4 x}",1,"(-3*b*Sqrt[-a + b*x])/(4*x) - (-a + b*x)^(3/2)/(2*x^2) + (3*b^2*ArcTan[Sqrt[-a + b*x]/Sqrt[a]])/(4*Sqrt[a])","A",4,3,15,0.2000,1,"{47, 63, 205}"
331,1,73,0,0.0191096,"\int \frac{(-a+b x)^{5/2}}{x} \, dx","Int[(-a + b*x)^(5/2)/x,x]","2 a^2 \sqrt{b x-a}-2 a^{5/2} \tan ^{-1}\left(\frac{\sqrt{b x-a}}{\sqrt{a}}\right)-\frac{2}{3} a (b x-a)^{3/2}+\frac{2}{5} (b x-a)^{5/2}","2 a^2 \sqrt{b x-a}-2 a^{5/2} \tan ^{-1}\left(\frac{\sqrt{b x-a}}{\sqrt{a}}\right)-\frac{2}{3} a (b x-a)^{3/2}+\frac{2}{5} (b x-a)^{5/2}",1,"2*a^2*Sqrt[-a + b*x] - (2*a*(-a + b*x)^(3/2))/3 + (2*(-a + b*x)^(5/2))/5 - 2*a^(5/2)*ArcTan[Sqrt[-a + b*x]/Sqrt[a]]","A",5,3,15,0.2000,1,"{50, 63, 205}"
332,1,74,0,0.0197625,"\int \frac{(-a+b x)^{5/2}}{x^2} \, dx","Int[(-a + b*x)^(5/2)/x^2,x]","5 a^{3/2} b \tan ^{-1}\left(\frac{\sqrt{b x-a}}{\sqrt{a}}\right)-\frac{(b x-a)^{5/2}}{x}+\frac{5}{3} b (b x-a)^{3/2}-5 a b \sqrt{b x-a}","5 a^{3/2} b \tan ^{-1}\left(\frac{\sqrt{b x-a}}{\sqrt{a}}\right)-\frac{(b x-a)^{5/2}}{x}+\frac{5}{3} b (b x-a)^{3/2}-5 a b \sqrt{b x-a}",1,"-5*a*b*Sqrt[-a + b*x] + (5*b*(-a + b*x)^(3/2))/3 - (-a + b*x)^(5/2)/x + 5*a^(3/2)*b*ArcTan[Sqrt[-a + b*x]/Sqrt[a]]","A",5,4,15,0.2667,1,"{47, 50, 63, 205}"
333,1,86,0,0.022194,"\int \frac{(-a+b x)^{5/2}}{x^3} \, dx","Int[(-a + b*x)^(5/2)/x^3,x]","\frac{15}{4} b^2 \sqrt{b x-a}-\frac{15}{4} \sqrt{a} b^2 \tan ^{-1}\left(\frac{\sqrt{b x-a}}{\sqrt{a}}\right)-\frac{(b x-a)^{5/2}}{2 x^2}-\frac{5 b (b x-a)^{3/2}}{4 x}","\frac{15}{4} b^2 \sqrt{b x-a}-\frac{15}{4} \sqrt{a} b^2 \tan ^{-1}\left(\frac{\sqrt{b x-a}}{\sqrt{a}}\right)-\frac{(b x-a)^{5/2}}{2 x^2}-\frac{5 b (b x-a)^{3/2}}{4 x}",1,"(15*b^2*Sqrt[-a + b*x])/4 - (5*b*(-a + b*x)^(3/2))/(4*x) - (-a + b*x)^(5/2)/(2*x^2) - (15*Sqrt[a]*b^2*ArcTan[Sqrt[-a + b*x]/Sqrt[a]])/4","A",5,4,15,0.2667,1,"{47, 50, 63, 205}"
334,1,89,0,0.0222366,"\int \frac{x^4}{\sqrt{a+b x}} \, dx","Int[x^4/Sqrt[a + b*x],x]","\frac{12 a^2 (a+b x)^{5/2}}{5 b^5}-\frac{8 a^3 (a+b x)^{3/2}}{3 b^5}+\frac{2 a^4 \sqrt{a+b x}}{b^5}+\frac{2 (a+b x)^{9/2}}{9 b^5}-\frac{8 a (a+b x)^{7/2}}{7 b^5}","\frac{12 a^2 (a+b x)^{5/2}}{5 b^5}-\frac{8 a^3 (a+b x)^{3/2}}{3 b^5}+\frac{2 a^4 \sqrt{a+b x}}{b^5}+\frac{2 (a+b x)^{9/2}}{9 b^5}-\frac{8 a (a+b x)^{7/2}}{7 b^5}",1,"(2*a^4*Sqrt[a + b*x])/b^5 - (8*a^3*(a + b*x)^(3/2))/(3*b^5) + (12*a^2*(a + b*x)^(5/2))/(5*b^5) - (8*a*(a + b*x)^(7/2))/(7*b^5) + (2*(a + b*x)^(9/2))/(9*b^5)","A",2,1,13,0.07692,1,"{43}"
335,1,68,0,0.0178664,"\int \frac{x^3}{\sqrt{a+b x}} \, dx","Int[x^3/Sqrt[a + b*x],x]","\frac{2 a^2 (a+b x)^{3/2}}{b^4}-\frac{2 a^3 \sqrt{a+b x}}{b^4}+\frac{2 (a+b x)^{7/2}}{7 b^4}-\frac{6 a (a+b x)^{5/2}}{5 b^4}","\frac{2 a^2 (a+b x)^{3/2}}{b^4}-\frac{2 a^3 \sqrt{a+b x}}{b^4}+\frac{2 (a+b x)^{7/2}}{7 b^4}-\frac{6 a (a+b x)^{5/2}}{5 b^4}",1,"(-2*a^3*Sqrt[a + b*x])/b^4 + (2*a^2*(a + b*x)^(3/2))/b^4 - (6*a*(a + b*x)^(5/2))/(5*b^4) + (2*(a + b*x)^(7/2))/(7*b^4)","A",2,1,13,0.07692,1,"{43}"
336,1,51,0,0.0120363,"\int \frac{x^2}{\sqrt{a+b x}} \, dx","Int[x^2/Sqrt[a + b*x],x]","\frac{2 a^2 \sqrt{a+b x}}{b^3}+\frac{2 (a+b x)^{5/2}}{5 b^3}-\frac{4 a (a+b x)^{3/2}}{3 b^3}","\frac{2 a^2 \sqrt{a+b x}}{b^3}+\frac{2 (a+b x)^{5/2}}{5 b^3}-\frac{4 a (a+b x)^{3/2}}{3 b^3}",1,"(2*a^2*Sqrt[a + b*x])/b^3 - (4*a*(a + b*x)^(3/2))/(3*b^3) + (2*(a + b*x)^(5/2))/(5*b^3)","A",2,1,13,0.07692,1,"{43}"
337,1,32,0,0.0082382,"\int \frac{x}{\sqrt{a+b x}} \, dx","Int[x/Sqrt[a + b*x],x]","\frac{2 (a+b x)^{3/2}}{3 b^2}-\frac{2 a \sqrt{a+b x}}{b^2}","\frac{2 (a+b x)^{3/2}}{3 b^2}-\frac{2 a \sqrt{a+b x}}{b^2}",1,"(-2*a*Sqrt[a + b*x])/b^2 + (2*(a + b*x)^(3/2))/(3*b^2)","A",2,1,11,0.09091,1,"{43}"
338,1,14,0,0.0013527,"\int \frac{1}{\sqrt{a+b x}} \, dx","Int[1/Sqrt[a + b*x],x]","\frac{2 \sqrt{a+b x}}{b}","\frac{2 \sqrt{a+b x}}{b}",1,"(2*Sqrt[a + b*x])/b","A",1,1,9,0.1111,1,"{32}"
339,1,23,0,0.0072444,"\int \frac{1}{x \sqrt{a+b x}} \, dx","Int[1/(x*Sqrt[a + b*x]),x]","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{\sqrt{a}}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{\sqrt{a}}",1,"(-2*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/Sqrt[a]","A",2,2,13,0.1538,1,"{63, 208}"
340,1,41,0,0.01085,"\int \frac{1}{x^2 \sqrt{a+b x}} \, dx","Int[1/(x^2*Sqrt[a + b*x]),x]","\frac{b \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{a^{3/2}}-\frac{\sqrt{a+b x}}{a x}","\frac{b \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{a^{3/2}}-\frac{\sqrt{a+b x}}{a x}",1,"-(Sqrt[a + b*x]/(a*x)) + (b*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/a^(3/2)","A",3,3,13,0.2308,1,"{51, 63, 208}"
341,1,68,0,0.0165941,"\int \frac{1}{x^3 \sqrt{a+b x}} \, dx","Int[1/(x^3*Sqrt[a + b*x]),x]","-\frac{3 b^2 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{4 a^{5/2}}+\frac{3 b \sqrt{a+b x}}{4 a^2 x}-\frac{\sqrt{a+b x}}{2 a x^2}","-\frac{3 b^2 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{4 a^{5/2}}+\frac{3 b \sqrt{a+b x}}{4 a^2 x}-\frac{\sqrt{a+b x}}{2 a x^2}",1,"-Sqrt[a + b*x]/(2*a*x^2) + (3*b*Sqrt[a + b*x])/(4*a^2*x) - (3*b^2*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/(4*a^(5/2))","A",4,3,13,0.2308,1,"{51, 63, 208}"
342,1,90,0,0.0253039,"\int \frac{1}{x^4 \sqrt{a+b x}} \, dx","Int[1/(x^4*Sqrt[a + b*x]),x]","-\frac{5 b^2 \sqrt{a+b x}}{8 a^3 x}+\frac{5 b^3 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{8 a^{7/2}}+\frac{5 b \sqrt{a+b x}}{12 a^2 x^2}-\frac{\sqrt{a+b x}}{3 a x^3}","-\frac{5 b^2 \sqrt{a+b x}}{8 a^3 x}+\frac{5 b^3 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{8 a^{7/2}}+\frac{5 b \sqrt{a+b x}}{12 a^2 x^2}-\frac{\sqrt{a+b x}}{3 a x^3}",1,"-Sqrt[a + b*x]/(3*a*x^3) + (5*b*Sqrt[a + b*x])/(12*a^2*x^2) - (5*b^2*Sqrt[a + b*x])/(8*a^3*x) + (5*b^3*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/(8*a^(7/2))","A",5,3,13,0.2308,1,"{51, 63, 208}"
343,1,85,0,0.0235158,"\int \frac{x^4}{(a+b x)^{3/2}} \, dx","Int[x^4/(a + b*x)^(3/2),x]","-\frac{2 a^4}{b^5 \sqrt{a+b x}}-\frac{8 a^3 \sqrt{a+b x}}{b^5}+\frac{4 a^2 (a+b x)^{3/2}}{b^5}-\frac{8 a (a+b x)^{5/2}}{5 b^5}+\frac{2 (a+b x)^{7/2}}{7 b^5}","-\frac{2 a^4}{b^5 \sqrt{a+b x}}-\frac{8 a^3 \sqrt{a+b x}}{b^5}+\frac{4 a^2 (a+b x)^{3/2}}{b^5}-\frac{8 a (a+b x)^{5/2}}{5 b^5}+\frac{2 (a+b x)^{7/2}}{7 b^5}",1,"(-2*a^4)/(b^5*Sqrt[a + b*x]) - (8*a^3*Sqrt[a + b*x])/b^5 + (4*a^2*(a + b*x)^(3/2))/b^5 - (8*a*(a + b*x)^(5/2))/(5*b^5) + (2*(a + b*x)^(7/2))/(7*b^5)","A",2,1,13,0.07692,1,"{43}"
344,1,66,0,0.0172614,"\int \frac{x^3}{(a+b x)^{3/2}} \, dx","Int[x^3/(a + b*x)^(3/2),x]","\frac{2 a^3}{b^4 \sqrt{a+b x}}+\frac{6 a^2 \sqrt{a+b x}}{b^4}-\frac{2 a (a+b x)^{3/2}}{b^4}+\frac{2 (a+b x)^{5/2}}{5 b^4}","\frac{2 a^3}{b^4 \sqrt{a+b x}}+\frac{6 a^2 \sqrt{a+b x}}{b^4}-\frac{2 a (a+b x)^{3/2}}{b^4}+\frac{2 (a+b x)^{5/2}}{5 b^4}",1,"(2*a^3)/(b^4*Sqrt[a + b*x]) + (6*a^2*Sqrt[a + b*x])/b^4 - (2*a*(a + b*x)^(3/2))/b^4 + (2*(a + b*x)^(5/2))/(5*b^4)","A",2,1,13,0.07692,1,"{43}"
345,1,49,0,0.0130437,"\int \frac{x^2}{(a+b x)^{3/2}} \, dx","Int[x^2/(a + b*x)^(3/2),x]","-\frac{2 a^2}{b^3 \sqrt{a+b x}}-\frac{4 a \sqrt{a+b x}}{b^3}+\frac{2 (a+b x)^{3/2}}{3 b^3}","-\frac{2 a^2}{b^3 \sqrt{a+b x}}-\frac{4 a \sqrt{a+b x}}{b^3}+\frac{2 (a+b x)^{3/2}}{3 b^3}",1,"(-2*a^2)/(b^3*Sqrt[a + b*x]) - (4*a*Sqrt[a + b*x])/b^3 + (2*(a + b*x)^(3/2))/(3*b^3)","A",2,1,13,0.07692,1,"{43}"
346,1,30,0,0.0076305,"\int \frac{x}{(a+b x)^{3/2}} \, dx","Int[x/(a + b*x)^(3/2),x]","\frac{2 a}{b^2 \sqrt{a+b x}}+\frac{2 \sqrt{a+b x}}{b^2}","\frac{2 a}{b^2 \sqrt{a+b x}}+\frac{2 \sqrt{a+b x}}{b^2}",1,"(2*a)/(b^2*Sqrt[a + b*x]) + (2*Sqrt[a + b*x])/b^2","A",2,1,11,0.09091,1,"{43}"
347,1,14,0,0.0013755,"\int \frac{1}{(a+b x)^{3/2}} \, dx","Int[(a + b*x)^(-3/2),x]","-\frac{2}{b \sqrt{a+b x}}","-\frac{2}{b \sqrt{a+b x}}",1,"-2/(b*Sqrt[a + b*x])","A",1,1,9,0.1111,1,"{32}"
348,1,38,0,0.0110024,"\int \frac{1}{x (a+b x)^{3/2}} \, dx","Int[1/(x*(a + b*x)^(3/2)),x]","\frac{2}{a \sqrt{a+b x}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{a^{3/2}}","\frac{2}{a \sqrt{a+b x}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{a^{3/2}}",1,"2/(a*Sqrt[a + b*x]) - (2*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/a^(3/2)","A",3,3,13,0.2308,1,"{51, 63, 208}"
349,1,59,0,0.0165216,"\int \frac{1}{x^2 (a+b x)^{3/2}} \, dx","Int[1/(x^2*(a + b*x)^(3/2)),x]","-\frac{3 \sqrt{a+b x}}{a^2 x}+\frac{3 b \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{a^{5/2}}+\frac{2}{a x \sqrt{a+b x}}","-\frac{3 b}{a^2 \sqrt{a+b x}}+\frac{3 b \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{a^{5/2}}-\frac{1}{a x \sqrt{a+b x}}",1,"2/(a*x*Sqrt[a + b*x]) - (3*Sqrt[a + b*x])/(a^2*x) + (3*b*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/a^(5/2)","A",4,3,13,0.2308,1,"{51, 63, 208}"
350,1,85,0,0.0231892,"\int \frac{1}{x^3 (a+b x)^{3/2}} \, dx","Int[1/(x^3*(a + b*x)^(3/2)),x]","-\frac{15 b^2 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{4 a^{7/2}}-\frac{5 \sqrt{a+b x}}{2 a^2 x^2}+\frac{15 b \sqrt{a+b x}}{4 a^3 x}+\frac{2}{a x^2 \sqrt{a+b x}}","\frac{15 b^2}{4 a^3 \sqrt{a+b x}}-\frac{15 b^2 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{4 a^{7/2}}+\frac{5 b}{4 a^2 x \sqrt{a+b x}}-\frac{1}{2 a x^2 \sqrt{a+b x}}",1,"2/(a*x^2*Sqrt[a + b*x]) - (5*Sqrt[a + b*x])/(2*a^2*x^2) + (15*b*Sqrt[a + b*x])/(4*a^3*x) - (15*b^2*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/(4*a^(7/2))","A",5,3,13,0.2308,1,"{51, 63, 208}"
351,1,87,0,0.0217943,"\int \frac{x^4}{(a+b x)^{5/2}} \, dx","Int[x^4/(a + b*x)^(5/2),x]","-\frac{2 a^4}{3 b^5 (a+b x)^{3/2}}+\frac{8 a^3}{b^5 \sqrt{a+b x}}+\frac{12 a^2 \sqrt{a+b x}}{b^5}-\frac{8 a (a+b x)^{3/2}}{3 b^5}+\frac{2 (a+b x)^{5/2}}{5 b^5}","-\frac{2 a^4}{3 b^5 (a+b x)^{3/2}}+\frac{8 a^3}{b^5 \sqrt{a+b x}}+\frac{12 a^2 \sqrt{a+b x}}{b^5}-\frac{8 a (a+b x)^{3/2}}{3 b^5}+\frac{2 (a+b x)^{5/2}}{5 b^5}",1,"(-2*a^4)/(3*b^5*(a + b*x)^(3/2)) + (8*a^3)/(b^5*Sqrt[a + b*x]) + (12*a^2*Sqrt[a + b*x])/b^5 - (8*a*(a + b*x)^(3/2))/(3*b^5) + (2*(a + b*x)^(5/2))/(5*b^5)","A",2,1,13,0.07692,1,"{43}"
352,1,68,0,0.0169521,"\int \frac{x^3}{(a+b x)^{5/2}} \, dx","Int[x^3/(a + b*x)^(5/2),x]","\frac{2 a^3}{3 b^4 (a+b x)^{3/2}}-\frac{6 a^2}{b^4 \sqrt{a+b x}}-\frac{6 a \sqrt{a+b x}}{b^4}+\frac{2 (a+b x)^{3/2}}{3 b^4}","\frac{2 a^3}{3 b^4 (a+b x)^{3/2}}-\frac{6 a^2}{b^4 \sqrt{a+b x}}-\frac{6 a \sqrt{a+b x}}{b^4}+\frac{2 (a+b x)^{3/2}}{3 b^4}",1,"(2*a^3)/(3*b^4*(a + b*x)^(3/2)) - (6*a^2)/(b^4*Sqrt[a + b*x]) - (6*a*Sqrt[a + b*x])/b^4 + (2*(a + b*x)^(3/2))/(3*b^4)","A",2,1,13,0.07692,1,"{43}"
353,1,49,0,0.0130616,"\int \frac{x^2}{(a+b x)^{5/2}} \, dx","Int[x^2/(a + b*x)^(5/2),x]","-\frac{2 a^2}{3 b^3 (a+b x)^{3/2}}+\frac{4 a}{b^3 \sqrt{a+b x}}+\frac{2 \sqrt{a+b x}}{b^3}","-\frac{2 a^2}{3 b^3 (a+b x)^{3/2}}+\frac{4 a}{b^3 \sqrt{a+b x}}+\frac{2 \sqrt{a+b x}}{b^3}",1,"(-2*a^2)/(3*b^3*(a + b*x)^(3/2)) + (4*a)/(b^3*Sqrt[a + b*x]) + (2*Sqrt[a + b*x])/b^3","A",2,1,13,0.07692,1,"{43}"
354,1,32,0,0.0084376,"\int \frac{x}{(a+b x)^{5/2}} \, dx","Int[x/(a + b*x)^(5/2),x]","\frac{2 a}{3 b^2 (a+b x)^{3/2}}-\frac{2}{b^2 \sqrt{a+b x}}","\frac{2 a}{3 b^2 (a+b x)^{3/2}}-\frac{2}{b^2 \sqrt{a+b x}}",1,"(2*a)/(3*b^2*(a + b*x)^(3/2)) - 2/(b^2*Sqrt[a + b*x])","A",2,1,11,0.09091,1,"{43}"
355,1,16,0,0.0014716,"\int \frac{1}{(a+b x)^{5/2}} \, dx","Int[(a + b*x)^(-5/2),x]","-\frac{2}{3 b (a+b x)^{3/2}}","-\frac{2}{3 b (a+b x)^{3/2}}",1,"-2/(3*b*(a + b*x)^(3/2))","A",1,1,9,0.1111,1,"{32}"
356,1,54,0,0.0152049,"\int \frac{1}{x (a+b x)^{5/2}} \, dx","Int[1/(x*(a + b*x)^(5/2)),x]","\frac{2}{a^2 \sqrt{a+b x}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{a^{5/2}}+\frac{2}{3 a (a+b x)^{3/2}}","\frac{2}{a^2 \sqrt{a+b x}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{a^{5/2}}+\frac{2}{3 a (a+b x)^{3/2}}",1,"2/(3*a*(a + b*x)^(3/2)) + 2/(a^2*Sqrt[a + b*x]) - (2*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/a^(5/2)","A",4,3,13,0.2308,1,"{51, 63, 208}"
357,1,80,0,0.0242279,"\int \frac{1}{x^2 (a+b x)^{5/2}} \, dx","Int[1/(x^2*(a + b*x)^(5/2)),x]","-\frac{5 \sqrt{a+b x}}{a^3 x}+\frac{10}{3 a^2 x \sqrt{a+b x}}+\frac{5 b \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{a^{7/2}}+\frac{2}{3 a x (a+b x)^{3/2}}","-\frac{5 b}{a^3 \sqrt{a+b x}}-\frac{5 b}{3 a^2 (a+b x)^{3/2}}+\frac{5 b \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{a^{7/2}}-\frac{1}{a x (a+b x)^{3/2}}",1,"2/(3*a*x*(a + b*x)^(3/2)) + 10/(3*a^2*x*Sqrt[a + b*x]) - (5*Sqrt[a + b*x])/(a^3*x) + (5*b*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/a^(7/2)","A",5,3,13,0.2308,1,"{51, 63, 208}"
358,1,106,0,0.0339514,"\int \frac{1}{x^3 (a+b x)^{5/2}} \, dx","Int[1/(x^3*(a + b*x)^(5/2)),x]","-\frac{35 b^2 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{4 a^{9/2}}-\frac{35 \sqrt{a+b x}}{6 a^3 x^2}+\frac{14}{3 a^2 x^2 \sqrt{a+b x}}+\frac{35 b \sqrt{a+b x}}{4 a^4 x}+\frac{2}{3 a x^2 (a+b x)^{3/2}}","\frac{35 b^2}{4 a^4 \sqrt{a+b x}}+\frac{35 b^2}{12 a^3 (a+b x)^{3/2}}-\frac{35 b^2 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{4 a^{9/2}}+\frac{7 b}{4 a^2 x (a+b x)^{3/2}}-\frac{1}{2 a x^2 (a+b x)^{3/2}}",1,"2/(3*a*x^2*(a + b*x)^(3/2)) + 14/(3*a^2*x^2*Sqrt[a + b*x]) - (35*Sqrt[a + b*x])/(6*a^3*x^2) + (35*b*Sqrt[a + b*x])/(4*a^4*x) - (35*b^2*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/(4*a^(9/2))","A",6,3,13,0.2308,1,"{51, 63, 208}"
359,1,25,0,0.0064869,"\int \frac{1}{x \sqrt{-a+b x}} \, dx","Int[1/(x*Sqrt[-a + b*x]),x]","\frac{2 \tan ^{-1}\left(\frac{\sqrt{b x-a}}{\sqrt{a}}\right)}{\sqrt{a}}","\frac{2 \tan ^{-1}\left(\frac{\sqrt{b x-a}}{\sqrt{a}}\right)}{\sqrt{a}}",1,"(2*ArcTan[Sqrt[-a + b*x]/Sqrt[a]])/Sqrt[a]","A",2,2,15,0.1333,1,"{63, 205}"
360,1,44,0,0.0108631,"\int \frac{1}{x^2 \sqrt{-a+b x}} \, dx","Int[1/(x^2*Sqrt[-a + b*x]),x]","\frac{b \tan ^{-1}\left(\frac{\sqrt{b x-a}}{\sqrt{a}}\right)}{a^{3/2}}+\frac{\sqrt{b x-a}}{a x}","\frac{b \tan ^{-1}\left(\frac{\sqrt{b x-a}}{\sqrt{a}}\right)}{a^{3/2}}+\frac{\sqrt{b x-a}}{a x}",1,"Sqrt[-a + b*x]/(a*x) + (b*ArcTan[Sqrt[-a + b*x]/Sqrt[a]])/a^(3/2)","A",3,3,15,0.2000,1,"{51, 63, 205}"
361,1,74,0,0.0170277,"\int \frac{1}{x^3 \sqrt{-a+b x}} \, dx","Int[1/(x^3*Sqrt[-a + b*x]),x]","\frac{3 b^2 \tan ^{-1}\left(\frac{\sqrt{b x-a}}{\sqrt{a}}\right)}{4 a^{5/2}}+\frac{3 b \sqrt{b x-a}}{4 a^2 x}+\frac{\sqrt{b x-a}}{2 a x^2}","\frac{3 b^2 \tan ^{-1}\left(\frac{\sqrt{b x-a}}{\sqrt{a}}\right)}{4 a^{5/2}}+\frac{3 b \sqrt{b x-a}}{4 a^2 x}+\frac{\sqrt{b x-a}}{2 a x^2}",1,"Sqrt[-a + b*x]/(2*a*x^2) + (3*b*Sqrt[-a + b*x])/(4*a^2*x) + (3*b^2*ArcTan[Sqrt[-a + b*x]/Sqrt[a]])/(4*a^(5/2))","A",4,3,15,0.2000,1,"{51, 63, 205}"
362,1,42,0,0.0099389,"\int \frac{1}{x (-a+b x)^{3/2}} \, dx","Int[1/(x*(-a + b*x)^(3/2)),x]","-\frac{2 \tan ^{-1}\left(\frac{\sqrt{b x-a}}{\sqrt{a}}\right)}{a^{3/2}}-\frac{2}{a \sqrt{b x-a}}","-\frac{2 \tan ^{-1}\left(\frac{\sqrt{b x-a}}{\sqrt{a}}\right)}{a^{3/2}}-\frac{2}{a \sqrt{b x-a}}",1,"-2/(a*Sqrt[-a + b*x]) - (2*ArcTan[Sqrt[-a + b*x]/Sqrt[a]])/a^(3/2)","A",3,3,15,0.2000,1,"{51, 63, 205}"
363,1,65,0,0.0157637,"\int \frac{1}{x^2 (-a+b x)^{3/2}} \, dx","Int[1/(x^2*(-a + b*x)^(3/2)),x]","-\frac{3 \sqrt{b x-a}}{a^2 x}-\frac{3 b \tan ^{-1}\left(\frac{\sqrt{b x-a}}{\sqrt{a}}\right)}{a^{5/2}}-\frac{2}{a x \sqrt{b x-a}}","-\frac{3 b}{a^2 \sqrt{b x-a}}-\frac{3 b \tan ^{-1}\left(\frac{\sqrt{b x-a}}{\sqrt{a}}\right)}{a^{5/2}}+\frac{1}{a x \sqrt{b x-a}}",1,"-2/(a*x*Sqrt[-a + b*x]) - (3*Sqrt[-a + b*x])/(a^2*x) - (3*b*ArcTan[Sqrt[-a + b*x]/Sqrt[a]])/a^(5/2)","A",4,3,15,0.2000,1,"{51, 63, 205}"
364,1,93,0,0.0231135,"\int \frac{1}{x^3 (-a+b x)^{3/2}} \, dx","Int[1/(x^3*(-a + b*x)^(3/2)),x]","-\frac{15 b^2 \tan ^{-1}\left(\frac{\sqrt{b x-a}}{\sqrt{a}}\right)}{4 a^{7/2}}-\frac{5 \sqrt{b x-a}}{2 a^2 x^2}-\frac{15 b \sqrt{b x-a}}{4 a^3 x}-\frac{2}{a x^2 \sqrt{b x-a}}","-\frac{15 b^2}{4 a^3 \sqrt{b x-a}}-\frac{15 b^2 \tan ^{-1}\left(\frac{\sqrt{b x-a}}{\sqrt{a}}\right)}{4 a^{7/2}}+\frac{5 b}{4 a^2 x \sqrt{b x-a}}+\frac{1}{2 a x^2 \sqrt{b x-a}}",1,"-2/(a*x^2*Sqrt[-a + b*x]) - (5*Sqrt[-a + b*x])/(2*a^2*x^2) - (15*b*Sqrt[-a + b*x])/(4*a^3*x) - (15*b^2*ArcTan[Sqrt[-a + b*x]/Sqrt[a]])/(4*a^(7/2))","A",5,3,15,0.2000,1,"{51, 63, 205}"
365,1,60,0,0.0151089,"\int \frac{1}{x (-a+b x)^{5/2}} \, dx","Int[1/(x*(-a + b*x)^(5/2)),x]","\frac{2}{a^2 \sqrt{b x-a}}+\frac{2 \tan ^{-1}\left(\frac{\sqrt{b x-a}}{\sqrt{a}}\right)}{a^{5/2}}-\frac{2}{3 a (b x-a)^{3/2}}","\frac{2}{a^2 \sqrt{b x-a}}+\frac{2 \tan ^{-1}\left(\frac{\sqrt{b x-a}}{\sqrt{a}}\right)}{a^{5/2}}-\frac{2}{3 a (b x-a)^{3/2}}",1,"-2/(3*a*(-a + b*x)^(3/2)) + 2/(a^2*Sqrt[-a + b*x]) + (2*ArcTan[Sqrt[-a + b*x]/Sqrt[a]])/a^(5/2)","A",4,3,15,0.2000,1,"{51, 63, 205}"
366,1,88,0,0.0234259,"\int \frac{1}{x^2 (-a+b x)^{5/2}} \, dx","Int[1/(x^2*(-a + b*x)^(5/2)),x]","\frac{5 \sqrt{b x-a}}{a^3 x}+\frac{10}{3 a^2 x \sqrt{b x-a}}+\frac{5 b \tan ^{-1}\left(\frac{\sqrt{b x-a}}{\sqrt{a}}\right)}{a^{7/2}}-\frac{2}{3 a x (b x-a)^{3/2}}","\frac{5 b}{a^3 \sqrt{b x-a}}-\frac{5 b}{3 a^2 (b x-a)^{3/2}}+\frac{5 b \tan ^{-1}\left(\frac{\sqrt{b x-a}}{\sqrt{a}}\right)}{a^{7/2}}+\frac{1}{a x (b x-a)^{3/2}}",1,"-2/(3*a*x*(-a + b*x)^(3/2)) + 10/(3*a^2*x*Sqrt[-a + b*x]) + (5*Sqrt[-a + b*x])/(a^3*x) + (5*b*ArcTan[Sqrt[-a + b*x]/Sqrt[a]])/a^(7/2)","A",5,3,15,0.2000,1,"{51, 63, 205}"
367,1,116,0,0.0331239,"\int \frac{1}{x^3 (-a+b x)^{5/2}} \, dx","Int[1/(x^3*(-a + b*x)^(5/2)),x]","\frac{35 b^2 \tan ^{-1}\left(\frac{\sqrt{b x-a}}{\sqrt{a}}\right)}{4 a^{9/2}}+\frac{35 \sqrt{b x-a}}{6 a^3 x^2}+\frac{14}{3 a^2 x^2 \sqrt{b x-a}}+\frac{35 b \sqrt{b x-a}}{4 a^4 x}-\frac{2}{3 a x^2 (b x-a)^{3/2}}","\frac{35 b^2}{4 a^4 \sqrt{b x-a}}-\frac{35 b^2}{12 a^3 (b x-a)^{3/2}}+\frac{35 b^2 \tan ^{-1}\left(\frac{\sqrt{b x-a}}{\sqrt{a}}\right)}{4 a^{9/2}}+\frac{7 b}{4 a^2 x (b x-a)^{3/2}}+\frac{1}{2 a x^2 (b x-a)^{3/2}}",1,"-2/(3*a*x^2*(-a + b*x)^(3/2)) + 14/(3*a^2*x^2*Sqrt[-a + b*x]) + (35*Sqrt[-a + b*x])/(6*a^3*x^2) + (35*b*Sqrt[-a + b*x])/(4*a^4*x) + (35*b^2*ArcTan[Sqrt[-a + b*x]/Sqrt[a]])/(4*a^(9/2))","A",6,3,15,0.2000,1,"{51, 63, 205}"
368,1,13,0,0.0062557,"\int \frac{x^{-1+m} (2 a m+b (-1+2 m) x)}{2 (a+b x)^{3/2}} \, dx","Int[(x^(-1 + m)*(2*a*m + b*(-1 + 2*m)*x))/(2*(a + b*x)^(3/2)),x]","\frac{x^m}{\sqrt{a+b x}}","\frac{x^m}{\sqrt{a+b x}}",1,"x^m/Sqrt[a + b*x]","A",2,2,31,0.06452,1,"{12, 74}"
369,1,92,0,0.0446209,"\int \left(-\frac{b x^m}{2 (a+b x)^{3/2}}+\frac{m x^{-1+m}}{\sqrt{a+b x}}\right) \, dx","Int[-(b*x^m)/(2*(a + b*x)^(3/2)) + (m*x^(-1 + m))/Sqrt[a + b*x],x]","\frac{x^m \left(-\frac{b x}{a}\right)^{-m} \, _2F_1\left(-\frac{1}{2},-m;\frac{1}{2};\frac{b x}{a}+1\right)}{\sqrt{a+b x}}-\frac{2 m x^m \sqrt{a+b x} \left(-\frac{b x}{a}\right)^{-m} \, _2F_1\left(\frac{1}{2},1-m;\frac{3}{2};\frac{b x}{a}+1\right)}{a}","\frac{x^m}{\sqrt{a+b x}}",1,"(x^m*Hypergeometric2F1[-1/2, -m, 1/2, 1 + (b*x)/a])/((-((b*x)/a))^m*Sqrt[a + b*x]) - (2*m*x^m*Sqrt[a + b*x]*Hypergeometric2F1[1/2, 1 - m, 3/2, 1 + (b*x)/a])/(a*(-((b*x)/a))^m)","C",5,2,34,0.05882,1,"{67, 65}"
370,1,23,0,0.0077666,"\int \frac{x^{\frac{1-n}{2}+\frac{1}{2} (-3+n)}}{\sqrt{a+b x}} \, dx","Int[x^((1 - n)/2 + (-3 + n)/2)/Sqrt[a + b*x],x]","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{\sqrt{a}}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{\sqrt{a}}",1,"(-2*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/Sqrt[a]","A",3,3,29,0.1034,1,"{7, 63, 208}"
371,1,72,0,0.0186468,"\int x^3 \sqrt[3]{a+b x} \, dx","Int[x^3*(a + b*x)^(1/3),x]","\frac{9 a^2 (a+b x)^{7/3}}{7 b^4}-\frac{3 a^3 (a+b x)^{4/3}}{4 b^4}+\frac{3 (a+b x)^{13/3}}{13 b^4}-\frac{9 a (a+b x)^{10/3}}{10 b^4}","\frac{9 a^2 (a+b x)^{7/3}}{7 b^4}-\frac{3 a^3 (a+b x)^{4/3}}{4 b^4}+\frac{3 (a+b x)^{13/3}}{13 b^4}-\frac{9 a (a+b x)^{10/3}}{10 b^4}",1,"(-3*a^3*(a + b*x)^(4/3))/(4*b^4) + (9*a^2*(a + b*x)^(7/3))/(7*b^4) - (9*a*(a + b*x)^(10/3))/(10*b^4) + (3*(a + b*x)^(13/3))/(13*b^4)","A",2,1,13,0.07692,1,"{43}"
372,1,53,0,0.0123199,"\int x^2 \sqrt[3]{a+b x} \, dx","Int[x^2*(a + b*x)^(1/3),x]","\frac{3 a^2 (a+b x)^{4/3}}{4 b^3}+\frac{3 (a+b x)^{10/3}}{10 b^3}-\frac{6 a (a+b x)^{7/3}}{7 b^3}","\frac{3 a^2 (a+b x)^{4/3}}{4 b^3}+\frac{3 (a+b x)^{10/3}}{10 b^3}-\frac{6 a (a+b x)^{7/3}}{7 b^3}",1,"(3*a^2*(a + b*x)^(4/3))/(4*b^3) - (6*a*(a + b*x)^(7/3))/(7*b^3) + (3*(a + b*x)^(10/3))/(10*b^3)","A",2,1,13,0.07692,1,"{43}"
373,1,34,0,0.0082427,"\int x \sqrt[3]{a+b x} \, dx","Int[x*(a + b*x)^(1/3),x]","\frac{3 (a+b x)^{7/3}}{7 b^2}-\frac{3 a (a+b x)^{4/3}}{4 b^2}","\frac{3 (a+b x)^{7/3}}{7 b^2}-\frac{3 a (a+b x)^{4/3}}{4 b^2}",1,"(-3*a*(a + b*x)^(4/3))/(4*b^2) + (3*(a + b*x)^(7/3))/(7*b^2)","A",2,1,11,0.09091,1,"{43}"
374,1,16,0,0.001431,"\int \sqrt[3]{a+b x} \, dx","Int[(a + b*x)^(1/3),x]","\frac{3 (a+b x)^{4/3}}{4 b}","\frac{3 (a+b x)^{4/3}}{4 b}",1,"(3*(a + b*x)^(4/3))/(4*b)","A",1,1,9,0.1111,1,"{32}"
375,1,91,0,0.0470565,"\int \frac{\sqrt[3]{a+b x}}{x} \, dx","Int[(a + b*x)^(1/3)/x,x]","3 \sqrt[3]{a+b x}+\frac{3}{2} \sqrt[3]{a} \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x}\right)-\sqrt{3} \sqrt[3]{a} \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)-\frac{1}{2} \sqrt[3]{a} \log (x)","3 \sqrt[3]{a+b x}+\frac{3}{2} \sqrt[3]{a} \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x}\right)-\sqrt{3} \sqrt[3]{a} \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)-\frac{1}{2} \sqrt[3]{a} \log (x)",1,"3*(a + b*x)^(1/3) - Sqrt[3]*a^(1/3)*ArcTan[(a^(1/3) + 2*(a + b*x)^(1/3))/(Sqrt[3]*a^(1/3))] - (a^(1/3)*Log[x])/2 + (3*a^(1/3)*Log[a^(1/3) - (a + b*x)^(1/3)])/2","A",5,5,13,0.3846,1,"{50, 57, 617, 204, 31}"
376,1,97,0,0.0334369,"\int \frac{\sqrt[3]{a+b x}}{x^2} \, dx","Int[(a + b*x)^(1/3)/x^2,x]","-\frac{b \log (x)}{6 a^{2/3}}+\frac{b \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x}\right)}{2 a^{2/3}}-\frac{b \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3}}-\frac{\sqrt[3]{a+b x}}{x}","-\frac{b \log (x)}{6 a^{2/3}}+\frac{b \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x}\right)}{2 a^{2/3}}-\frac{b \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3}}-\frac{\sqrt[3]{a+b x}}{x}",1,"-((a + b*x)^(1/3)/x) - (b*ArcTan[(a^(1/3) + 2*(a + b*x)^(1/3))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(2/3)) - (b*Log[x])/(6*a^(2/3)) + (b*Log[a^(1/3) - (a + b*x)^(1/3)])/(2*a^(2/3))","A",5,5,13,0.3846,1,"{47, 57, 617, 204, 31}"
377,1,127,0,0.0494358,"\int \frac{\sqrt[3]{a+b x}}{x^3} \, dx","Int[(a + b*x)^(1/3)/x^3,x]","\frac{b^2 \log (x)}{18 a^{5/3}}-\frac{b^2 \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x}\right)}{6 a^{5/3}}+\frac{b^2 \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{5/3}}-\frac{\sqrt[3]{a+b x}}{2 x^2}-\frac{b \sqrt[3]{a+b x}}{6 a x}","\frac{b^2 \log (x)}{18 a^{5/3}}-\frac{b^2 \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x}\right)}{6 a^{5/3}}+\frac{b^2 \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{5/3}}-\frac{\sqrt[3]{a+b x}}{2 x^2}-\frac{b \sqrt[3]{a+b x}}{6 a x}",1,"-(a + b*x)^(1/3)/(2*x^2) - (b*(a + b*x)^(1/3))/(6*a*x) + (b^2*ArcTan[(a^(1/3) + 2*(a + b*x)^(1/3))/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(5/3)) + (b^2*Log[x])/(18*a^(5/3)) - (b^2*Log[a^(1/3) - (a + b*x)^(1/3)])/(6*a^(5/3))","A",6,6,13,0.4615,1,"{47, 51, 57, 617, 204, 31}"
378,1,72,0,0.018402,"\int x^3 (a+b x)^{2/3} \, dx","Int[x^3*(a + b*x)^(2/3),x]","\frac{9 a^2 (a+b x)^{8/3}}{8 b^4}-\frac{3 a^3 (a+b x)^{5/3}}{5 b^4}+\frac{3 (a+b x)^{14/3}}{14 b^4}-\frac{9 a (a+b x)^{11/3}}{11 b^4}","\frac{9 a^2 (a+b x)^{8/3}}{8 b^4}-\frac{3 a^3 (a+b x)^{5/3}}{5 b^4}+\frac{3 (a+b x)^{14/3}}{14 b^4}-\frac{9 a (a+b x)^{11/3}}{11 b^4}",1,"(-3*a^3*(a + b*x)^(5/3))/(5*b^4) + (9*a^2*(a + b*x)^(8/3))/(8*b^4) - (9*a*(a + b*x)^(11/3))/(11*b^4) + (3*(a + b*x)^(14/3))/(14*b^4)","A",2,1,13,0.07692,1,"{43}"
379,1,53,0,0.0126484,"\int x^2 (a+b x)^{2/3} \, dx","Int[x^2*(a + b*x)^(2/3),x]","\frac{3 a^2 (a+b x)^{5/3}}{5 b^3}+\frac{3 (a+b x)^{11/3}}{11 b^3}-\frac{3 a (a+b x)^{8/3}}{4 b^3}","\frac{3 a^2 (a+b x)^{5/3}}{5 b^3}+\frac{3 (a+b x)^{11/3}}{11 b^3}-\frac{3 a (a+b x)^{8/3}}{4 b^3}",1,"(3*a^2*(a + b*x)^(5/3))/(5*b^3) - (3*a*(a + b*x)^(8/3))/(4*b^3) + (3*(a + b*x)^(11/3))/(11*b^3)","A",2,1,13,0.07692,1,"{43}"
380,1,34,0,0.0078079,"\int x (a+b x)^{2/3} \, dx","Int[x*(a + b*x)^(2/3),x]","\frac{3 (a+b x)^{8/3}}{8 b^2}-\frac{3 a (a+b x)^{5/3}}{5 b^2}","\frac{3 (a+b x)^{8/3}}{8 b^2}-\frac{3 a (a+b x)^{5/3}}{5 b^2}",1,"(-3*a*(a + b*x)^(5/3))/(5*b^2) + (3*(a + b*x)^(8/3))/(8*b^2)","A",2,1,11,0.09091,1,"{43}"
381,1,16,0,0.0015048,"\int (a+b x)^{2/3} \, dx","Int[(a + b*x)^(2/3),x]","\frac{3 (a+b x)^{5/3}}{5 b}","\frac{3 (a+b x)^{5/3}}{5 b}",1,"(3*(a + b*x)^(5/3))/(5*b)","A",1,1,9,0.1111,1,"{32}"
382,1,92,0,0.0320364,"\int \frac{(a+b x)^{2/3}}{x} \, dx","Int[(a + b*x)^(2/3)/x,x]","\frac{3}{2} a^{2/3} \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x}\right)+\sqrt{3} a^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)-\frac{1}{2} a^{2/3} \log (x)+\frac{3}{2} (a+b x)^{2/3}","\frac{3}{2} a^{2/3} \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x}\right)+\sqrt{3} a^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)-\frac{1}{2} a^{2/3} \log (x)+\frac{3}{2} (a+b x)^{2/3}",1,"(3*(a + b*x)^(2/3))/2 + Sqrt[3]*a^(2/3)*ArcTan[(a^(1/3) + 2*(a + b*x)^(1/3))/(Sqrt[3]*a^(1/3))] - (a^(2/3)*Log[x])/2 + (3*a^(2/3)*Log[a^(1/3) - (a + b*x)^(1/3)])/2","A",5,5,13,0.3846,1,"{50, 55, 617, 204, 31}"
383,1,94,0,0.0332543,"\int \frac{(a+b x)^{2/3}}{x^2} \, dx","Int[(a + b*x)^(2/3)/x^2,x]","-\frac{(a+b x)^{2/3}}{x}-\frac{b \log (x)}{3 \sqrt[3]{a}}+\frac{b \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x}\right)}{\sqrt[3]{a}}+\frac{2 b \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} \sqrt[3]{a}}","-\frac{(a+b x)^{2/3}}{x}-\frac{b \log (x)}{3 \sqrt[3]{a}}+\frac{b \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x}\right)}{\sqrt[3]{a}}+\frac{2 b \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} \sqrt[3]{a}}",1,"-((a + b*x)^(2/3)/x) + (2*b*ArcTan[(a^(1/3) + 2*(a + b*x)^(1/3))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(1/3)) - (b*Log[x])/(3*a^(1/3)) + (b*Log[a^(1/3) - (a + b*x)^(1/3)])/a^(1/3)","A",5,5,13,0.3846,1,"{47, 55, 617, 204, 31}"
384,1,127,0,0.0470729,"\int \frac{(a+b x)^{2/3}}{x^3} \, dx","Int[(a + b*x)^(2/3)/x^3,x]","\frac{b^2 \log (x)}{18 a^{4/3}}-\frac{b^2 \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x}\right)}{6 a^{4/3}}-\frac{b^2 \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{4/3}}-\frac{(a+b x)^{2/3}}{2 x^2}-\frac{b (a+b x)^{2/3}}{3 a x}","\frac{b^2 \log (x)}{18 a^{4/3}}-\frac{b^2 \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x}\right)}{6 a^{4/3}}-\frac{b^2 \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{4/3}}-\frac{(a+b x)^{2/3}}{2 x^2}-\frac{b (a+b x)^{2/3}}{3 a x}",1,"-(a + b*x)^(2/3)/(2*x^2) - (b*(a + b*x)^(2/3))/(3*a*x) - (b^2*ArcTan[(a^(1/3) + 2*(a + b*x)^(1/3))/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(4/3)) + (b^2*Log[x])/(18*a^(4/3)) - (b^2*Log[a^(1/3) - (a + b*x)^(1/3)])/(6*a^(4/3))","A",6,6,13,0.4615,1,"{47, 51, 55, 617, 204, 31}"
385,1,72,0,0.0179075,"\int x^3 (a+b x)^{4/3} \, dx","Int[x^3*(a + b*x)^(4/3),x]","\frac{9 a^2 (a+b x)^{10/3}}{10 b^4}-\frac{3 a^3 (a+b x)^{7/3}}{7 b^4}+\frac{3 (a+b x)^{16/3}}{16 b^4}-\frac{9 a (a+b x)^{13/3}}{13 b^4}","\frac{9 a^2 (a+b x)^{10/3}}{10 b^4}-\frac{3 a^3 (a+b x)^{7/3}}{7 b^4}+\frac{3 (a+b x)^{16/3}}{16 b^4}-\frac{9 a (a+b x)^{13/3}}{13 b^4}",1,"(-3*a^3*(a + b*x)^(7/3))/(7*b^4) + (9*a^2*(a + b*x)^(10/3))/(10*b^4) - (9*a*(a + b*x)^(13/3))/(13*b^4) + (3*(a + b*x)^(16/3))/(16*b^4)","A",2,1,13,0.07692,1,"{43}"
386,1,53,0,0.0128579,"\int x^2 (a+b x)^{4/3} \, dx","Int[x^2*(a + b*x)^(4/3),x]","\frac{3 a^2 (a+b x)^{7/3}}{7 b^3}+\frac{3 (a+b x)^{13/3}}{13 b^3}-\frac{3 a (a+b x)^{10/3}}{5 b^3}","\frac{3 a^2 (a+b x)^{7/3}}{7 b^3}+\frac{3 (a+b x)^{13/3}}{13 b^3}-\frac{3 a (a+b x)^{10/3}}{5 b^3}",1,"(3*a^2*(a + b*x)^(7/3))/(7*b^3) - (3*a*(a + b*x)^(10/3))/(5*b^3) + (3*(a + b*x)^(13/3))/(13*b^3)","A",2,1,13,0.07692,1,"{43}"
387,1,34,0,0.0087666,"\int x (a+b x)^{4/3} \, dx","Int[x*(a + b*x)^(4/3),x]","\frac{3 (a+b x)^{10/3}}{10 b^2}-\frac{3 a (a+b x)^{7/3}}{7 b^2}","\frac{3 (a+b x)^{10/3}}{10 b^2}-\frac{3 a (a+b x)^{7/3}}{7 b^2}",1,"(-3*a*(a + b*x)^(7/3))/(7*b^2) + (3*(a + b*x)^(10/3))/(10*b^2)","A",2,1,11,0.09091,1,"{43}"
388,1,16,0,0.0015413,"\int (a+b x)^{4/3} \, dx","Int[(a + b*x)^(4/3),x]","\frac{3 (a+b x)^{7/3}}{7 b}","\frac{3 (a+b x)^{7/3}}{7 b}",1,"(3*(a + b*x)^(7/3))/(7*b)","A",1,1,9,0.1111,1,"{32}"
389,1,105,0,0.0406306,"\int \frac{(a+b x)^{4/3}}{x} \, dx","Int[(a + b*x)^(4/3)/x,x]","\frac{3}{2} a^{4/3} \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x}\right)-\sqrt{3} a^{4/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)-\frac{1}{2} a^{4/3} \log (x)+3 a \sqrt[3]{a+b x}+\frac{3}{4} (a+b x)^{4/3}","\frac{3}{2} a^{4/3} \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x}\right)-\sqrt{3} a^{4/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)-\frac{1}{2} a^{4/3} \log (x)+3 a \sqrt[3]{a+b x}+\frac{3}{4} (a+b x)^{4/3}",1,"3*a*(a + b*x)^(1/3) + (3*(a + b*x)^(4/3))/4 - Sqrt[3]*a^(4/3)*ArcTan[(a^(1/3) + 2*(a + b*x)^(1/3))/(Sqrt[3]*a^(1/3))] - (a^(4/3)*Log[x])/2 + (3*a^(4/3)*Log[a^(1/3) - (a + b*x)^(1/3)])/2","A",6,5,13,0.3846,1,"{50, 57, 617, 204, 31}"
390,1,107,0,0.0416443,"\int \frac{(a+b x)^{4/3}}{x^2} \, dx","Int[(a + b*x)^(4/3)/x^2,x]","-\frac{(a+b x)^{4/3}}{x}+4 b \sqrt[3]{a+b x}-\frac{2}{3} \sqrt[3]{a} b \log (x)+2 \sqrt[3]{a} b \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x}\right)-\frac{4 \sqrt[3]{a} b \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3}}","-\frac{(a+b x)^{4/3}}{x}+4 b \sqrt[3]{a+b x}-\frac{2}{3} \sqrt[3]{a} b \log (x)+2 \sqrt[3]{a} b \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x}\right)-\frac{4 \sqrt[3]{a} b \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3}}",1,"4*b*(a + b*x)^(1/3) - (a + b*x)^(4/3)/x - (4*a^(1/3)*b*ArcTan[(a^(1/3) + 2*(a + b*x)^(1/3))/(Sqrt[3]*a^(1/3))])/Sqrt[3] - (2*a^(1/3)*b*Log[x])/3 + 2*a^(1/3)*b*Log[a^(1/3) - (a + b*x)^(1/3)]","A",6,6,13,0.4615,1,"{47, 50, 57, 617, 204, 31}"
391,1,124,0,0.0443007,"\int \frac{(a+b x)^{4/3}}{x^3} \, dx","Int[(a + b*x)^(4/3)/x^3,x]","-\frac{b^2 \log (x)}{9 a^{2/3}}+\frac{b^2 \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x}\right)}{3 a^{2/3}}-\frac{2 b^2 \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{2/3}}-\frac{(a+b x)^{4/3}}{2 x^2}-\frac{2 b \sqrt[3]{a+b x}}{3 x}","-\frac{b^2 \log (x)}{9 a^{2/3}}+\frac{b^2 \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x}\right)}{3 a^{2/3}}-\frac{2 b^2 \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{2/3}}-\frac{(a+b x)^{4/3}}{2 x^2}-\frac{2 b \sqrt[3]{a+b x}}{3 x}",1,"(-2*b*(a + b*x)^(1/3))/(3*x) - (a + b*x)^(4/3)/(2*x^2) - (2*b^2*ArcTan[(a^(1/3) + 2*(a + b*x)^(1/3))/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(2/3)) - (b^2*Log[x])/(9*a^(2/3)) + (b^2*Log[a^(1/3) - (a + b*x)^(1/3)])/(3*a^(2/3))","A",6,5,13,0.3846,1,"{47, 57, 617, 204, 31}"
392,1,72,0,0.0179759,"\int \frac{x^3}{\sqrt[3]{a+b x}} \, dx","Int[x^3/(a + b*x)^(1/3),x]","\frac{9 a^2 (a+b x)^{5/3}}{5 b^4}-\frac{3 a^3 (a+b x)^{2/3}}{2 b^4}+\frac{3 (a+b x)^{11/3}}{11 b^4}-\frac{9 a (a+b x)^{8/3}}{8 b^4}","\frac{9 a^2 (a+b x)^{5/3}}{5 b^4}-\frac{3 a^3 (a+b x)^{2/3}}{2 b^4}+\frac{3 (a+b x)^{11/3}}{11 b^4}-\frac{9 a (a+b x)^{8/3}}{8 b^4}",1,"(-3*a^3*(a + b*x)^(2/3))/(2*b^4) + (9*a^2*(a + b*x)^(5/3))/(5*b^4) - (9*a*(a + b*x)^(8/3))/(8*b^4) + (3*(a + b*x)^(11/3))/(11*b^4)","A",2,1,13,0.07692,1,"{43}"
393,1,53,0,0.0124392,"\int \frac{x^2}{\sqrt[3]{a+b x}} \, dx","Int[x^2/(a + b*x)^(1/3),x]","\frac{3 a^2 (a+b x)^{2/3}}{2 b^3}+\frac{3 (a+b x)^{8/3}}{8 b^3}-\frac{6 a (a+b x)^{5/3}}{5 b^3}","\frac{3 a^2 (a+b x)^{2/3}}{2 b^3}+\frac{3 (a+b x)^{8/3}}{8 b^3}-\frac{6 a (a+b x)^{5/3}}{5 b^3}",1,"(3*a^2*(a + b*x)^(2/3))/(2*b^3) - (6*a*(a + b*x)^(5/3))/(5*b^3) + (3*(a + b*x)^(8/3))/(8*b^3)","A",2,1,13,0.07692,1,"{43}"
394,1,34,0,0.0078093,"\int \frac{x}{\sqrt[3]{a+b x}} \, dx","Int[x/(a + b*x)^(1/3),x]","\frac{3 (a+b x)^{5/3}}{5 b^2}-\frac{3 a (a+b x)^{2/3}}{2 b^2}","\frac{3 (a+b x)^{5/3}}{5 b^2}-\frac{3 a (a+b x)^{2/3}}{2 b^2}",1,"(-3*a*(a + b*x)^(2/3))/(2*b^2) + (3*(a + b*x)^(5/3))/(5*b^2)","A",2,1,11,0.09091,1,"{43}"
395,1,16,0,0.0017111,"\int \frac{1}{\sqrt[3]{a+b x}} \, dx","Int[(a + b*x)^(-1/3),x]","\frac{3 (a+b x)^{2/3}}{2 b}","\frac{3 (a+b x)^{2/3}}{2 b}",1,"(3*(a + b*x)^(2/3))/(2*b)","A",1,1,9,0.1111,1,"{32}"
396,1,79,0,0.0250843,"\int \frac{1}{x \sqrt[3]{a+b x}} \, dx","Int[1/(x*(a + b*x)^(1/3)),x]","\frac{3 \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x}\right)}{2 \sqrt[3]{a}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt[3]{a}}-\frac{\log (x)}{2 \sqrt[3]{a}}","\frac{3 \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x}\right)}{2 \sqrt[3]{a}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt[3]{a}}-\frac{\log (x)}{2 \sqrt[3]{a}}",1,"(Sqrt[3]*ArcTan[(a^(1/3) + 2*(a + b*x)^(1/3))/(Sqrt[3]*a^(1/3))])/a^(1/3) - Log[x]/(2*a^(1/3)) + (3*Log[a^(1/3) - (a + b*x)^(1/3)])/(2*a^(1/3))","A",4,4,13,0.3077,1,"{55, 617, 204, 31}"
397,1,100,0,0.0334924,"\int \frac{1}{x^2 \sqrt[3]{a+b x}} \, dx","Int[1/(x^2*(a + b*x)^(1/3)),x]","\frac{b \log (x)}{6 a^{4/3}}-\frac{b \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x}\right)}{2 a^{4/3}}-\frac{b \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{4/3}}-\frac{(a+b x)^{2/3}}{a x}","\frac{b \log (x)}{6 a^{4/3}}-\frac{b \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x}\right)}{2 a^{4/3}}-\frac{b \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{4/3}}-\frac{(a+b x)^{2/3}}{a x}",1,"-((a + b*x)^(2/3)/(a*x)) - (b*ArcTan[(a^(1/3) + 2*(a + b*x)^(1/3))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(4/3)) + (b*Log[x])/(6*a^(4/3)) - (b*Log[a^(1/3) - (a + b*x)^(1/3)])/(2*a^(4/3))","A",5,5,13,0.3846,1,"{51, 55, 617, 204, 31}"
398,1,130,0,0.047821,"\int \frac{1}{x^3 \sqrt[3]{a+b x}} \, dx","Int[1/(x^3*(a + b*x)^(1/3)),x]","-\frac{b^2 \log (x)}{9 a^{7/3}}+\frac{b^2 \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x}\right)}{3 a^{7/3}}+\frac{2 b^2 \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{7/3}}+\frac{2 b (a+b x)^{2/3}}{3 a^2 x}-\frac{(a+b x)^{2/3}}{2 a x^2}","-\frac{b^2 \log (x)}{9 a^{7/3}}+\frac{b^2 \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x}\right)}{3 a^{7/3}}+\frac{2 b^2 \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{7/3}}+\frac{2 b (a+b x)^{2/3}}{3 a^2 x}-\frac{(a+b x)^{2/3}}{2 a x^2}",1,"-(a + b*x)^(2/3)/(2*a*x^2) + (2*b*(a + b*x)^(2/3))/(3*a^2*x) + (2*b^2*ArcTan[(a^(1/3) + 2*(a + b*x)^(1/3))/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(7/3)) - (b^2*Log[x])/(9*a^(7/3)) + (b^2*Log[a^(1/3) - (a + b*x)^(1/3)])/(3*a^(7/3))","A",6,5,13,0.3846,1,"{51, 55, 617, 204, 31}"
399,1,80,0,0.018856,"\int \frac{x^3}{\sqrt[3]{-a+b x}} \, dx","Int[x^3/(-a + b*x)^(1/3),x]","\frac{9 a^2 (b x-a)^{5/3}}{5 b^4}+\frac{3 a^3 (b x-a)^{2/3}}{2 b^4}+\frac{3 (b x-a)^{11/3}}{11 b^4}+\frac{9 a (b x-a)^{8/3}}{8 b^4}","\frac{9 a^2 (b x-a)^{5/3}}{5 b^4}+\frac{3 a^3 (b x-a)^{2/3}}{2 b^4}+\frac{3 (b x-a)^{11/3}}{11 b^4}+\frac{9 a (b x-a)^{8/3}}{8 b^4}",1,"(3*a^3*(-a + b*x)^(2/3))/(2*b^4) + (9*a^2*(-a + b*x)^(5/3))/(5*b^4) + (9*a*(-a + b*x)^(8/3))/(8*b^4) + (3*(-a + b*x)^(11/3))/(11*b^4)","A",2,1,15,0.06667,1,"{43}"
400,1,59,0,0.0129849,"\int \frac{x^2}{\sqrt[3]{-a+b x}} \, dx","Int[x^2/(-a + b*x)^(1/3),x]","\frac{3 a^2 (b x-a)^{2/3}}{2 b^3}+\frac{3 (b x-a)^{8/3}}{8 b^3}+\frac{6 a (b x-a)^{5/3}}{5 b^3}","\frac{3 a^2 (b x-a)^{2/3}}{2 b^3}+\frac{3 (b x-a)^{8/3}}{8 b^3}+\frac{6 a (b x-a)^{5/3}}{5 b^3}",1,"(3*a^2*(-a + b*x)^(2/3))/(2*b^3) + (6*a*(-a + b*x)^(5/3))/(5*b^3) + (3*(-a + b*x)^(8/3))/(8*b^3)","A",2,1,15,0.06667,1,"{43}"
401,1,38,0,0.0088401,"\int \frac{x}{\sqrt[3]{-a+b x}} \, dx","Int[x/(-a + b*x)^(1/3),x]","\frac{3 (b x-a)^{5/3}}{5 b^2}+\frac{3 a (b x-a)^{2/3}}{2 b^2}","\frac{3 (b x-a)^{5/3}}{5 b^2}+\frac{3 a (b x-a)^{2/3}}{2 b^2}",1,"(3*a*(-a + b*x)^(2/3))/(2*b^2) + (3*(-a + b*x)^(5/3))/(5*b^2)","A",2,1,13,0.07692,1,"{43}"
402,1,18,0,0.0014808,"\int \frac{1}{\sqrt[3]{-a+b x}} \, dx","Int[(-a + b*x)^(-1/3),x]","\frac{3 (b x-a)^{2/3}}{2 b}","\frac{3 (b x-a)^{2/3}}{2 b}",1,"(3*(-a + b*x)^(2/3))/(2*b)","A",1,1,11,0.09091,1,"{32}"
403,1,82,0,0.0325087,"\int \frac{1}{x \sqrt[3]{-a+b x}} \, dx","Int[1/(x*(-a + b*x)^(1/3)),x]","-\frac{3 \log \left(\sqrt[3]{b x-a}+\sqrt[3]{a}\right)}{2 \sqrt[3]{a}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b x-a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt[3]{a}}+\frac{\log (x)}{2 \sqrt[3]{a}}","-\frac{3 \log \left(\sqrt[3]{b x-a}+\sqrt[3]{a}\right)}{2 \sqrt[3]{a}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b x-a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt[3]{a}}+\frac{\log (x)}{2 \sqrt[3]{a}}",1,"-((Sqrt[3]*ArcTan[(a^(1/3) - 2*(-a + b*x)^(1/3))/(Sqrt[3]*a^(1/3))])/a^(1/3)) + Log[x]/(2*a^(1/3)) - (3*Log[a^(1/3) + (-a + b*x)^(1/3)])/(2*a^(1/3))","A",4,4,15,0.2667,1,"{56, 617, 204, 31}"
404,1,103,0,0.0340923,"\int \frac{1}{x^2 \sqrt[3]{-a+b x}} \, dx","Int[1/(x^2*(-a + b*x)^(1/3)),x]","\frac{b \log (x)}{6 a^{4/3}}-\frac{b \log \left(\sqrt[3]{b x-a}+\sqrt[3]{a}\right)}{2 a^{4/3}}-\frac{b \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b x-a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{4/3}}+\frac{(b x-a)^{2/3}}{a x}","\frac{b \log (x)}{6 a^{4/3}}-\frac{b \log \left(\sqrt[3]{b x-a}+\sqrt[3]{a}\right)}{2 a^{4/3}}-\frac{b \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b x-a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{4/3}}+\frac{(b x-a)^{2/3}}{a x}",1,"(-a + b*x)^(2/3)/(a*x) - (b*ArcTan[(a^(1/3) - 2*(-a + b*x)^(1/3))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(4/3)) + (b*Log[x])/(6*a^(4/3)) - (b*Log[a^(1/3) + (-a + b*x)^(1/3)])/(2*a^(4/3))","A",5,5,15,0.3333,1,"{51, 56, 617, 204, 31}"
405,1,136,0,0.0440761,"\int \frac{1}{x^3 \sqrt[3]{-a+b x}} \, dx","Int[1/(x^3*(-a + b*x)^(1/3)),x]","\frac{b^2 \log (x)}{9 a^{7/3}}-\frac{b^2 \log \left(\sqrt[3]{b x-a}+\sqrt[3]{a}\right)}{3 a^{7/3}}-\frac{2 b^2 \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b x-a}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{7/3}}+\frac{2 b (b x-a)^{2/3}}{3 a^2 x}+\frac{(b x-a)^{2/3}}{2 a x^2}","\frac{b^2 \log (x)}{9 a^{7/3}}-\frac{b^2 \log \left(\sqrt[3]{b x-a}+\sqrt[3]{a}\right)}{3 a^{7/3}}-\frac{2 b^2 \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b x-a}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{7/3}}+\frac{2 b (b x-a)^{2/3}}{3 a^2 x}+\frac{(b x-a)^{2/3}}{2 a x^2}",1,"(-a + b*x)^(2/3)/(2*a*x^2) + (2*b*(-a + b*x)^(2/3))/(3*a^2*x) - (2*b^2*ArcTan[(a^(1/3) - 2*(-a + b*x)^(1/3))/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(7/3)) + (b^2*Log[x])/(9*a^(7/3)) - (b^2*Log[a^(1/3) + (-a + b*x)^(1/3)])/(3*a^(7/3))","A",6,5,15,0.3333,1,"{51, 56, 617, 204, 31}"
406,1,70,0,0.0182285,"\int \frac{x^3}{(a+b x)^{2/3}} \, dx","Int[x^3/(a + b*x)^(2/3),x]","\frac{9 a^2 (a+b x)^{4/3}}{4 b^4}-\frac{3 a^3 \sqrt[3]{a+b x}}{b^4}+\frac{3 (a+b x)^{10/3}}{10 b^4}-\frac{9 a (a+b x)^{7/3}}{7 b^4}","\frac{9 a^2 (a+b x)^{4/3}}{4 b^4}-\frac{3 a^3 \sqrt[3]{a+b x}}{b^4}+\frac{3 (a+b x)^{10/3}}{10 b^4}-\frac{9 a (a+b x)^{7/3}}{7 b^4}",1,"(-3*a^3*(a + b*x)^(1/3))/b^4 + (9*a^2*(a + b*x)^(4/3))/(4*b^4) - (9*a*(a + b*x)^(7/3))/(7*b^4) + (3*(a + b*x)^(10/3))/(10*b^4)","A",2,1,13,0.07692,1,"{43}"
407,1,51,0,0.0119599,"\int \frac{x^2}{(a+b x)^{2/3}} \, dx","Int[x^2/(a + b*x)^(2/3),x]","\frac{3 a^2 \sqrt[3]{a+b x}}{b^3}+\frac{3 (a+b x)^{7/3}}{7 b^3}-\frac{3 a (a+b x)^{4/3}}{2 b^3}","\frac{3 a^2 \sqrt[3]{a+b x}}{b^3}+\frac{3 (a+b x)^{7/3}}{7 b^3}-\frac{3 a (a+b x)^{4/3}}{2 b^3}",1,"(3*a^2*(a + b*x)^(1/3))/b^3 - (3*a*(a + b*x)^(4/3))/(2*b^3) + (3*(a + b*x)^(7/3))/(7*b^3)","A",2,1,13,0.07692,1,"{43}"
408,1,32,0,0.0074868,"\int \frac{x}{(a+b x)^{2/3}} \, dx","Int[x/(a + b*x)^(2/3),x]","\frac{3 (a+b x)^{4/3}}{4 b^2}-\frac{3 a \sqrt[3]{a+b x}}{b^2}","\frac{3 (a+b x)^{4/3}}{4 b^2}-\frac{3 a \sqrt[3]{a+b x}}{b^2}",1,"(-3*a*(a + b*x)^(1/3))/b^2 + (3*(a + b*x)^(4/3))/(4*b^2)","A",2,1,11,0.09091,1,"{43}"
409,1,14,0,0.001359,"\int \frac{1}{(a+b x)^{2/3}} \, dx","Int[(a + b*x)^(-2/3),x]","\frac{3 \sqrt[3]{a+b x}}{b}","\frac{3 \sqrt[3]{a+b x}}{b}",1,"(3*(a + b*x)^(1/3))/b","A",1,1,9,0.1111,1,"{32}"
410,1,80,0,0.0238317,"\int \frac{1}{x (a+b x)^{2/3}} \, dx","Int[1/(x*(a + b*x)^(2/3)),x]","\frac{3 \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x}\right)}{2 a^{2/3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{a^{2/3}}-\frac{\log (x)}{2 a^{2/3}}","\frac{3 \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x}\right)}{2 a^{2/3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{a^{2/3}}-\frac{\log (x)}{2 a^{2/3}}",1,"-((Sqrt[3]*ArcTan[(a^(1/3) + 2*(a + b*x)^(1/3))/(Sqrt[3]*a^(1/3))])/a^(2/3)) - Log[x]/(2*a^(2/3)) + (3*Log[a^(1/3) - (a + b*x)^(1/3)])/(2*a^(2/3))","A",4,4,13,0.3077,1,"{57, 617, 204, 31}"
411,1,98,0,0.0328974,"\int \frac{1}{x^2 (a+b x)^{2/3}} \, dx","Int[1/(x^2*(a + b*x)^(2/3)),x]","\frac{b \log (x)}{3 a^{5/3}}-\frac{b \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x}\right)}{a^{5/3}}+\frac{2 b \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{5/3}}-\frac{\sqrt[3]{a+b x}}{a x}","\frac{b \log (x)}{3 a^{5/3}}-\frac{b \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x}\right)}{a^{5/3}}+\frac{2 b \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{5/3}}-\frac{\sqrt[3]{a+b x}}{a x}",1,"-((a + b*x)^(1/3)/(a*x)) + (2*b*ArcTan[(a^(1/3) + 2*(a + b*x)^(1/3))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(5/3)) + (b*Log[x])/(3*a^(5/3)) - (b*Log[a^(1/3) - (a + b*x)^(1/3)])/a^(5/3)","A",5,5,13,0.3846,1,"{51, 57, 617, 204, 31}"
412,1,130,0,0.0475448,"\int \frac{1}{x^3 (a+b x)^{2/3}} \, dx","Int[1/(x^3*(a + b*x)^(2/3)),x]","-\frac{5 b^2 \log (x)}{18 a^{8/3}}+\frac{5 b^2 \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x}\right)}{6 a^{8/3}}-\frac{5 b^2 \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{8/3}}+\frac{5 b \sqrt[3]{a+b x}}{6 a^2 x}-\frac{\sqrt[3]{a+b x}}{2 a x^2}","-\frac{5 b^2 \log (x)}{18 a^{8/3}}+\frac{5 b^2 \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x}\right)}{6 a^{8/3}}-\frac{5 b^2 \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{8/3}}+\frac{5 b \sqrt[3]{a+b x}}{6 a^2 x}-\frac{\sqrt[3]{a+b x}}{2 a x^2}",1,"-(a + b*x)^(1/3)/(2*a*x^2) + (5*b*(a + b*x)^(1/3))/(6*a^2*x) - (5*b^2*ArcTan[(a^(1/3) + 2*(a + b*x)^(1/3))/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(8/3)) - (5*b^2*Log[x])/(18*a^(8/3)) + (5*b^2*Log[a^(1/3) - (a + b*x)^(1/3)])/(6*a^(8/3))","A",6,5,13,0.3846,1,"{51, 57, 617, 204, 31}"
413,1,70,0,0.0178824,"\int \frac{x^3}{(a+b x)^{4/3}} \, dx","Int[x^3/(a + b*x)^(4/3),x]","\frac{3 a^3}{b^4 \sqrt[3]{a+b x}}+\frac{9 a^2 (a+b x)^{2/3}}{2 b^4}-\frac{9 a (a+b x)^{5/3}}{5 b^4}+\frac{3 (a+b x)^{8/3}}{8 b^4}","\frac{3 a^3}{b^4 \sqrt[3]{a+b x}}+\frac{9 a^2 (a+b x)^{2/3}}{2 b^4}-\frac{9 a (a+b x)^{5/3}}{5 b^4}+\frac{3 (a+b x)^{8/3}}{8 b^4}",1,"(3*a^3)/(b^4*(a + b*x)^(1/3)) + (9*a^2*(a + b*x)^(2/3))/(2*b^4) - (9*a*(a + b*x)^(5/3))/(5*b^4) + (3*(a + b*x)^(8/3))/(8*b^4)","A",2,1,13,0.07692,1,"{43}"
414,1,49,0,0.0133071,"\int \frac{x^2}{(a+b x)^{4/3}} \, dx","Int[x^2/(a + b*x)^(4/3),x]","-\frac{3 a^2}{b^3 \sqrt[3]{a+b x}}-\frac{3 a (a+b x)^{2/3}}{b^3}+\frac{3 (a+b x)^{5/3}}{5 b^3}","-\frac{3 a^2}{b^3 \sqrt[3]{a+b x}}-\frac{3 a (a+b x)^{2/3}}{b^3}+\frac{3 (a+b x)^{5/3}}{5 b^3}",1,"(-3*a^2)/(b^3*(a + b*x)^(1/3)) - (3*a*(a + b*x)^(2/3))/b^3 + (3*(a + b*x)^(5/3))/(5*b^3)","A",2,1,13,0.07692,1,"{43}"
415,1,32,0,0.0085798,"\int \frac{x}{(a+b x)^{4/3}} \, dx","Int[x/(a + b*x)^(4/3),x]","\frac{3 a}{b^2 \sqrt[3]{a+b x}}+\frac{3 (a+b x)^{2/3}}{2 b^2}","\frac{3 a}{b^2 \sqrt[3]{a+b x}}+\frac{3 (a+b x)^{2/3}}{2 b^2}",1,"(3*a)/(b^2*(a + b*x)^(1/3)) + (3*(a + b*x)^(2/3))/(2*b^2)","A",2,1,11,0.09091,1,"{43}"
416,1,14,0,0.0013637,"\int \frac{1}{(a+b x)^{4/3}} \, dx","Int[(a + b*x)^(-4/3),x]","-\frac{3}{b \sqrt[3]{a+b x}}","-\frac{3}{b \sqrt[3]{a+b x}}",1,"-3/(b*(a + b*x)^(1/3))","A",1,1,9,0.1111,1,"{32}"
417,1,93,0,0.0331465,"\int \frac{1}{x (a+b x)^{4/3}} \, dx","Int[1/(x*(a + b*x)^(4/3)),x]","\frac{3 \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x}\right)}{2 a^{4/3}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{a^{4/3}}-\frac{\log (x)}{2 a^{4/3}}+\frac{3}{a \sqrt[3]{a+b x}}","\frac{3 \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x}\right)}{2 a^{4/3}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{a^{4/3}}-\frac{\log (x)}{2 a^{4/3}}+\frac{3}{a \sqrt[3]{a+b x}}",1,"3/(a*(a + b*x)^(1/3)) + (Sqrt[3]*ArcTan[(a^(1/3) + 2*(a + b*x)^(1/3))/(Sqrt[3]*a^(1/3))])/a^(4/3) - Log[x]/(2*a^(4/3)) + (3*Log[a^(1/3) - (a + b*x)^(1/3)])/(2*a^(4/3))","A",5,5,13,0.3846,1,"{51, 55, 617, 204, 31}"
418,1,115,0,0.0437349,"\int \frac{1}{x^2 (a+b x)^{4/3}} \, dx","Int[1/(x^2*(a + b*x)^(4/3)),x]","-\frac{4 (a+b x)^{2/3}}{a^2 x}+\frac{2 b \log (x)}{3 a^{7/3}}-\frac{2 b \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x}\right)}{a^{7/3}}-\frac{4 b \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{7/3}}+\frac{3}{a x \sqrt[3]{a+b x}}","-\frac{4 b}{a^2 \sqrt[3]{a+b x}}+\frac{2 b \log (x)}{3 a^{7/3}}-\frac{2 b \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x}\right)}{a^{7/3}}-\frac{4 b \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{7/3}}-\frac{1}{a x \sqrt[3]{a+b x}}",1,"3/(a*x*(a + b*x)^(1/3)) - (4*(a + b*x)^(2/3))/(a^2*x) - (4*b*ArcTan[(a^(1/3) + 2*(a + b*x)^(1/3))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(7/3)) + (2*b*Log[x])/(3*a^(7/3)) - (2*b*Log[a^(1/3) - (a + b*x)^(1/3)])/a^(7/3)","A",6,5,13,0.3846,1,"{51, 55, 617, 204, 31}"
419,1,147,0,0.0579336,"\int \frac{1}{x^3 (a+b x)^{4/3}} \, dx","Int[1/(x^3*(a + b*x)^(4/3)),x]","-\frac{7 b^2 \log (x)}{9 a^{10/3}}+\frac{7 b^2 \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x}\right)}{3 a^{10/3}}+\frac{14 b^2 \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{10/3}}-\frac{7 (a+b x)^{2/3}}{2 a^2 x^2}+\frac{14 b (a+b x)^{2/3}}{3 a^3 x}+\frac{3}{a x^2 \sqrt[3]{a+b x}}","\frac{14 b^2}{3 a^3 \sqrt[3]{a+b x}}-\frac{7 b^2 \log (x)}{9 a^{10/3}}+\frac{7 b^2 \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x}\right)}{3 a^{10/3}}+\frac{14 b^2 \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{10/3}}+\frac{7 b}{6 a^2 x \sqrt[3]{a+b x}}-\frac{1}{2 a x^2 \sqrt[3]{a+b x}}",1,"3/(a*x^2*(a + b*x)^(1/3)) - (7*(a + b*x)^(2/3))/(2*a^2*x^2) + (14*b*(a + b*x)^(2/3))/(3*a^3*x) + (14*b^2*ArcTan[(a^(1/3) + 2*(a + b*x)^(1/3))/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(10/3)) - (7*b^2*Log[x])/(9*a^(10/3)) + (7*b^2*Log[a^(1/3) - (a + b*x)^(1/3)])/(3*a^(10/3))","A",7,5,13,0.3846,1,"{51, 55, 617, 204, 31}"
420,1,71,0,0.0310501,"\int \frac{1}{x \sqrt[3]{a^3+b^3 x}} \, dx","Int[1/(x*(a^3 + b^3*x)^(1/3)),x]","\frac{3 \log \left(a-\sqrt[3]{a^3+b^3 x}\right)}{2 a}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3+b^3 x}+a}{\sqrt{3} a}\right)}{a}-\frac{\log (x)}{2 a}","\frac{3 \log \left(a-\sqrt[3]{a^3+b^3 x}\right)}{2 a}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3+b^3 x}+a}{\sqrt{3} a}\right)}{a}-\frac{\log (x)}{2 a}",1,"(Sqrt[3]*ArcTan[(a + 2*(a^3 + b^3*x)^(1/3))/(Sqrt[3]*a)])/a - Log[x]/(2*a) + (3*Log[a - (a^3 + b^3*x)^(1/3)])/(2*a)","A",4,4,17,0.2353,1,"{55, 617, 204, 31}"
421,1,73,0,0.030922,"\int \frac{1}{x \sqrt[3]{a^3-b^3 x}} \, dx","Int[1/(x*(a^3 - b^3*x)^(1/3)),x]","\frac{3 \log \left(a-\sqrt[3]{a^3-b^3 x}\right)}{2 a}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3-b^3 x}+a}{\sqrt{3} a}\right)}{a}-\frac{\log (x)}{2 a}","\frac{3 \log \left(a-\sqrt[3]{a^3-b^3 x}\right)}{2 a}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3-b^3 x}+a}{\sqrt{3} a}\right)}{a}-\frac{\log (x)}{2 a}",1,"(Sqrt[3]*ArcTan[(a + 2*(a^3 - b^3*x)^(1/3))/(Sqrt[3]*a)])/a - Log[x]/(2*a) + (3*Log[a - (a^3 - b^3*x)^(1/3)])/(2*a)","A",4,4,18,0.2222,1,"{55, 617, 204, 31}"
422,1,74,0,0.0316239,"\int \frac{1}{x \sqrt[3]{-a^3+b^3 x}} \, dx","Int[1/(x*(-a^3 + b^3*x)^(1/3)),x]","-\frac{3 \log \left(\sqrt[3]{b^3 x-a^3}+a\right)}{2 a}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{a-2 \sqrt[3]{b^3 x-a^3}}{\sqrt{3} a}\right)}{a}+\frac{\log (x)}{2 a}","-\frac{3 \log \left(\sqrt[3]{b^3 x-a^3}+a\right)}{2 a}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{a-2 \sqrt[3]{b^3 x-a^3}}{\sqrt{3} a}\right)}{a}+\frac{\log (x)}{2 a}",1,"-((Sqrt[3]*ArcTan[(a - 2*(-a^3 + b^3*x)^(1/3))/(Sqrt[3]*a)])/a) + Log[x]/(2*a) - (3*Log[a + (-a^3 + b^3*x)^(1/3)])/(2*a)","A",4,4,19,0.2105,1,"{56, 617, 204, 31}"
423,1,76,0,0.0283408,"\int \frac{1}{x \sqrt[3]{-a^3-b^3 x}} \, dx","Int[1/(x*(-a^3 - b^3*x)^(1/3)),x]","-\frac{3 \log \left(\sqrt[3]{-a^3-b^3 x}+a\right)}{2 a}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{a-2 \sqrt[3]{-a^3-b^3 x}}{\sqrt{3} a}\right)}{a}+\frac{\log (x)}{2 a}","-\frac{3 \log \left(\sqrt[3]{-a^3-b^3 x}+a\right)}{2 a}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{a-2 \sqrt[3]{-a^3-b^3 x}}{\sqrt{3} a}\right)}{a}+\frac{\log (x)}{2 a}",1,"-((Sqrt[3]*ArcTan[(a - 2*(-a^3 - b^3*x)^(1/3))/(Sqrt[3]*a)])/a) + Log[x]/(2*a) - (3*Log[a + (-a^3 - b^3*x)^(1/3)])/(2*a)","A",4,4,20,0.2000,1,"{56, 617, 204, 31}"
424,1,72,0,0.0238681,"\int \frac{1}{x \left(a^3+b^3 x\right)^{2/3}} \, dx","Int[1/(x*(a^3 + b^3*x)^(2/3)),x]","\frac{3 \log \left(a-\sqrt[3]{a^3+b^3 x}\right)}{2 a^2}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3+b^3 x}+a}{\sqrt{3} a}\right)}{a^2}-\frac{\log (x)}{2 a^2}","\frac{3 \log \left(a-\sqrt[3]{a^3+b^3 x}\right)}{2 a^2}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3+b^3 x}+a}{\sqrt{3} a}\right)}{a^2}-\frac{\log (x)}{2 a^2}",1,"-((Sqrt[3]*ArcTan[(a + 2*(a^3 + b^3*x)^(1/3))/(Sqrt[3]*a)])/a^2) - Log[x]/(2*a^2) + (3*Log[a - (a^3 + b^3*x)^(1/3)])/(2*a^2)","A",4,4,17,0.2353,1,"{57, 617, 204, 31}"
425,1,74,0,0.0248979,"\int \frac{1}{x \left(a^3-b^3 x\right)^{2/3}} \, dx","Int[1/(x*(a^3 - b^3*x)^(2/3)),x]","\frac{3 \log \left(a-\sqrt[3]{a^3-b^3 x}\right)}{2 a^2}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3-b^3 x}+a}{\sqrt{3} a}\right)}{a^2}-\frac{\log (x)}{2 a^2}","\frac{3 \log \left(a-\sqrt[3]{a^3-b^3 x}\right)}{2 a^2}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3-b^3 x}+a}{\sqrt{3} a}\right)}{a^2}-\frac{\log (x)}{2 a^2}",1,"-((Sqrt[3]*ArcTan[(a + 2*(a^3 - b^3*x)^(1/3))/(Sqrt[3]*a)])/a^2) - Log[x]/(2*a^2) + (3*Log[a - (a^3 - b^3*x)^(1/3)])/(2*a^2)","A",4,4,18,0.2222,1,"{57, 617, 204, 31}"
426,1,74,0,0.0232063,"\int \frac{1}{x \left(-a^3+b^3 x\right)^{2/3}} \, dx","Int[1/(x*(-a^3 + b^3*x)^(2/3)),x]","\frac{3 \log \left(\sqrt[3]{b^3 x-a^3}+a\right)}{2 a^2}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{a-2 \sqrt[3]{b^3 x-a^3}}{\sqrt{3} a}\right)}{a^2}-\frac{\log (x)}{2 a^2}","\frac{3 \log \left(\sqrt[3]{b^3 x-a^3}+a\right)}{2 a^2}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{a-2 \sqrt[3]{b^3 x-a^3}}{\sqrt{3} a}\right)}{a^2}-\frac{\log (x)}{2 a^2}",1,"-((Sqrt[3]*ArcTan[(a - 2*(-a^3 + b^3*x)^(1/3))/(Sqrt[3]*a)])/a^2) - Log[x]/(2*a^2) + (3*Log[a + (-a^3 + b^3*x)^(1/3)])/(2*a^2)","A",4,4,19,0.2105,1,"{58, 617, 204, 31}"
427,1,76,0,0.0233589,"\int \frac{1}{x \left(-a^3-b^3 x\right)^{2/3}} \, dx","Int[1/(x*(-a^3 - b^3*x)^(2/3)),x]","\frac{3 \log \left(\sqrt[3]{-a^3-b^3 x}+a\right)}{2 a^2}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{a-2 \sqrt[3]{-a^3-b^3 x}}{\sqrt{3} a}\right)}{a^2}-\frac{\log (x)}{2 a^2}","\frac{3 \log \left(\sqrt[3]{-a^3-b^3 x}+a\right)}{2 a^2}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{a-2 \sqrt[3]{-a^3-b^3 x}}{\sqrt{3} a}\right)}{a^2}-\frac{\log (x)}{2 a^2}",1,"-((Sqrt[3]*ArcTan[(a - 2*(-a^3 - b^3*x)^(1/3))/(Sqrt[3]*a)])/a^2) - Log[x]/(2*a^2) + (3*Log[a + (-a^3 - b^3*x)^(1/3)])/(2*a^2)","A",4,4,20,0.2000,1,"{58, 617, 204, 31}"
428,1,25,0,0.0083796,"\int x^m (a+b x) \, dx","Int[x^m*(a + b*x),x]","\frac{a x^{m+1}}{m+1}+\frac{b x^{m+2}}{m+2}","\frac{a x^{m+1}}{m+1}+\frac{b x^{m+2}}{m+2}",1,"(a*x^(1 + m))/(1 + m) + (b*x^(2 + m))/(2 + m)","A",2,1,9,0.1111,1,"{43}"
429,1,21,0,0.0040576,"\int x^{5/2} (a+b x) \, dx","Int[x^(5/2)*(a + b*x),x]","\frac{2}{7} a x^{7/2}+\frac{2}{9} b x^{9/2}","\frac{2}{7} a x^{7/2}+\frac{2}{9} b x^{9/2}",1,"(2*a*x^(7/2))/7 + (2*b*x^(9/2))/9","A",2,1,11,0.09091,1,"{43}"
430,1,21,0,0.0036704,"\int x^{3/2} (a+b x) \, dx","Int[x^(3/2)*(a + b*x),x]","\frac{2}{5} a x^{5/2}+\frac{2}{7} b x^{7/2}","\frac{2}{5} a x^{5/2}+\frac{2}{7} b x^{7/2}",1,"(2*a*x^(5/2))/5 + (2*b*x^(7/2))/7","A",2,1,11,0.09091,1,"{43}"
431,1,21,0,0.0041047,"\int \sqrt{x} (a+b x) \, dx","Int[Sqrt[x]*(a + b*x),x]","\frac{2}{3} a x^{3/2}+\frac{2}{5} b x^{5/2}","\frac{2}{3} a x^{3/2}+\frac{2}{5} b x^{5/2}",1,"(2*a*x^(3/2))/3 + (2*b*x^(5/2))/5","A",2,1,11,0.09091,1,"{43}"
432,1,19,0,0.0036023,"\int \frac{a+b x}{\sqrt{x}} \, dx","Int[(a + b*x)/Sqrt[x],x]","2 a \sqrt{x}+\frac{2}{3} b x^{3/2}","2 a \sqrt{x}+\frac{2}{3} b x^{3/2}",1,"2*a*Sqrt[x] + (2*b*x^(3/2))/3","A",2,1,11,0.09091,1,"{43}"
433,1,17,0,0.0040094,"\int \frac{a+b x}{x^{3/2}} \, dx","Int[(a + b*x)/x^(3/2),x]","2 b \sqrt{x}-\frac{2 a}{\sqrt{x}}","2 b \sqrt{x}-\frac{2 a}{\sqrt{x}}",1,"(-2*a)/Sqrt[x] + 2*b*Sqrt[x]","A",2,1,11,0.09091,1,"{43}"
434,1,19,0,0.0036581,"\int \frac{a+b x}{x^{5/2}} \, dx","Int[(a + b*x)/x^(5/2),x]","-\frac{2 a}{3 x^{3/2}}-\frac{2 b}{\sqrt{x}}","-\frac{2 a}{3 x^{3/2}}-\frac{2 b}{\sqrt{x}}",1,"(-2*a)/(3*x^(3/2)) - (2*b)/Sqrt[x]","A",2,1,11,0.09091,1,"{43}"
435,1,43,0,0.0142616,"\int x^m (a+b x)^2 \, dx","Int[x^m*(a + b*x)^2,x]","\frac{a^2 x^{m+1}}{m+1}+\frac{2 a b x^{m+2}}{m+2}+\frac{b^2 x^{m+3}}{m+3}","\frac{a^2 x^{m+1}}{m+1}+\frac{2 a b x^{m+2}}{m+2}+\frac{b^2 x^{m+3}}{m+3}",1,"(a^2*x^(1 + m))/(1 + m) + (2*a*b*x^(2 + m))/(2 + m) + (b^2*x^(3 + m))/(3 + m)","A",2,1,11,0.09091,1,"{43}"
436,1,36,0,0.0071863,"\int x^{5/2} (a+b x)^2 \, dx","Int[x^(5/2)*(a + b*x)^2,x]","\frac{2}{7} a^2 x^{7/2}+\frac{4}{9} a b x^{9/2}+\frac{2}{11} b^2 x^{11/2}","\frac{2}{7} a^2 x^{7/2}+\frac{4}{9} a b x^{9/2}+\frac{2}{11} b^2 x^{11/2}",1,"(2*a^2*x^(7/2))/7 + (4*a*b*x^(9/2))/9 + (2*b^2*x^(11/2))/11","A",2,1,13,0.07692,1,"{43}"
437,1,36,0,0.007302,"\int x^{3/2} (a+b x)^2 \, dx","Int[x^(3/2)*(a + b*x)^2,x]","\frac{2}{5} a^2 x^{5/2}+\frac{4}{7} a b x^{7/2}+\frac{2}{9} b^2 x^{9/2}","\frac{2}{5} a^2 x^{5/2}+\frac{4}{7} a b x^{7/2}+\frac{2}{9} b^2 x^{9/2}",1,"(2*a^2*x^(5/2))/5 + (4*a*b*x^(7/2))/7 + (2*b^2*x^(9/2))/9","A",2,1,13,0.07692,1,"{43}"
438,1,36,0,0.0073302,"\int \sqrt{x} (a+b x)^2 \, dx","Int[Sqrt[x]*(a + b*x)^2,x]","\frac{2}{3} a^2 x^{3/2}+\frac{4}{5} a b x^{5/2}+\frac{2}{7} b^2 x^{7/2}","\frac{2}{3} a^2 x^{3/2}+\frac{4}{5} a b x^{5/2}+\frac{2}{7} b^2 x^{7/2}",1,"(2*a^2*x^(3/2))/3 + (4*a*b*x^(5/2))/5 + (2*b^2*x^(7/2))/7","A",2,1,13,0.07692,1,"{43}"
439,1,34,0,0.0069611,"\int \frac{(a+b x)^2}{\sqrt{x}} \, dx","Int[(a + b*x)^2/Sqrt[x],x]","2 a^2 \sqrt{x}+\frac{4}{3} a b x^{3/2}+\frac{2}{5} b^2 x^{5/2}","2 a^2 \sqrt{x}+\frac{4}{3} a b x^{3/2}+\frac{2}{5} b^2 x^{5/2}",1,"2*a^2*Sqrt[x] + (4*a*b*x^(3/2))/3 + (2*b^2*x^(5/2))/5","A",2,1,13,0.07692,1,"{43}"
440,1,32,0,0.0067661,"\int \frac{(a+b x)^2}{x^{3/2}} \, dx","Int[(a + b*x)^2/x^(3/2),x]","-\frac{2 a^2}{\sqrt{x}}+4 a b \sqrt{x}+\frac{2}{3} b^2 x^{3/2}","-\frac{2 a^2}{\sqrt{x}}+4 a b \sqrt{x}+\frac{2}{3} b^2 x^{3/2}",1,"(-2*a^2)/Sqrt[x] + 4*a*b*Sqrt[x] + (2*b^2*x^(3/2))/3","A",2,1,13,0.07692,1,"{43}"
441,1,32,0,0.0074047,"\int \frac{(a+b x)^2}{x^{5/2}} \, dx","Int[(a + b*x)^2/x^(5/2),x]","-\frac{2 a^2}{3 x^{3/2}}-\frac{4 a b}{\sqrt{x}}+2 b^2 \sqrt{x}","-\frac{2 a^2}{3 x^{3/2}}-\frac{4 a b}{\sqrt{x}}+2 b^2 \sqrt{x}",1,"(-2*a^2)/(3*x^(3/2)) - (4*a*b)/Sqrt[x] + 2*b^2*Sqrt[x]","A",2,1,13,0.07692,1,"{43}"
442,1,61,0,0.0199992,"\int x^m (a+b x)^3 \, dx","Int[x^m*(a + b*x)^3,x]","\frac{3 a^2 b x^{m+2}}{m+2}+\frac{a^3 x^{m+1}}{m+1}+\frac{3 a b^2 x^{m+3}}{m+3}+\frac{b^3 x^{m+4}}{m+4}","\frac{3 a^2 b x^{m+2}}{m+2}+\frac{a^3 x^{m+1}}{m+1}+\frac{3 a b^2 x^{m+3}}{m+3}+\frac{b^3 x^{m+4}}{m+4}",1,"(a^3*x^(1 + m))/(1 + m) + (3*a^2*b*x^(2 + m))/(2 + m) + (3*a*b^2*x^(3 + m))/(3 + m) + (b^3*x^(4 + m))/(4 + m)","A",2,1,11,0.09091,1,"{43}"
443,1,51,0,0.0106187,"\int x^{5/2} (a+b x)^3 \, dx","Int[x^(5/2)*(a + b*x)^3,x]","\frac{2}{3} a^2 b x^{9/2}+\frac{2}{7} a^3 x^{7/2}+\frac{6}{11} a b^2 x^{11/2}+\frac{2}{13} b^3 x^{13/2}","\frac{2}{3} a^2 b x^{9/2}+\frac{2}{7} a^3 x^{7/2}+\frac{6}{11} a b^2 x^{11/2}+\frac{2}{13} b^3 x^{13/2}",1,"(2*a^3*x^(7/2))/7 + (2*a^2*b*x^(9/2))/3 + (6*a*b^2*x^(11/2))/11 + (2*b^3*x^(13/2))/13","A",2,1,13,0.07692,1,"{43}"
444,1,51,0,0.0115775,"\int x^{3/2} (a+b x)^3 \, dx","Int[x^(3/2)*(a + b*x)^3,x]","\frac{6}{7} a^2 b x^{7/2}+\frac{2}{5} a^3 x^{5/2}+\frac{2}{3} a b^2 x^{9/2}+\frac{2}{11} b^3 x^{11/2}","\frac{6}{7} a^2 b x^{7/2}+\frac{2}{5} a^3 x^{5/2}+\frac{2}{3} a b^2 x^{9/2}+\frac{2}{11} b^3 x^{11/2}",1,"(2*a^3*x^(5/2))/5 + (6*a^2*b*x^(7/2))/7 + (2*a*b^2*x^(9/2))/3 + (2*b^3*x^(11/2))/11","A",2,1,13,0.07692,1,"{43}"
445,1,51,0,0.0111421,"\int \sqrt{x} (a+b x)^3 \, dx","Int[Sqrt[x]*(a + b*x)^3,x]","\frac{6}{5} a^2 b x^{5/2}+\frac{2}{3} a^3 x^{3/2}+\frac{6}{7} a b^2 x^{7/2}+\frac{2}{9} b^3 x^{9/2}","\frac{6}{5} a^2 b x^{5/2}+\frac{2}{3} a^3 x^{3/2}+\frac{6}{7} a b^2 x^{7/2}+\frac{2}{9} b^3 x^{9/2}",1,"(2*a^3*x^(3/2))/3 + (6*a^2*b*x^(5/2))/5 + (6*a*b^2*x^(7/2))/7 + (2*b^3*x^(9/2))/9","A",2,1,13,0.07692,1,"{43}"
446,1,47,0,0.0114421,"\int \frac{(a+b x)^3}{\sqrt{x}} \, dx","Int[(a + b*x)^3/Sqrt[x],x]","2 a^2 b x^{3/2}+2 a^3 \sqrt{x}+\frac{6}{5} a b^2 x^{5/2}+\frac{2}{7} b^3 x^{7/2}","2 a^2 b x^{3/2}+2 a^3 \sqrt{x}+\frac{6}{5} a b^2 x^{5/2}+\frac{2}{7} b^3 x^{7/2}",1,"2*a^3*Sqrt[x] + 2*a^2*b*x^(3/2) + (6*a*b^2*x^(5/2))/5 + (2*b^3*x^(7/2))/7","A",2,1,13,0.07692,1,"{43}"
447,1,45,0,0.0111342,"\int \frac{(a+b x)^3}{x^{3/2}} \, dx","Int[(a + b*x)^3/x^(3/2),x]","6 a^2 b \sqrt{x}-\frac{2 a^3}{\sqrt{x}}+2 a b^2 x^{3/2}+\frac{2}{5} b^3 x^{5/2}","6 a^2 b \sqrt{x}-\frac{2 a^3}{\sqrt{x}}+2 a b^2 x^{3/2}+\frac{2}{5} b^3 x^{5/2}",1,"(-2*a^3)/Sqrt[x] + 6*a^2*b*Sqrt[x] + 2*a*b^2*x^(3/2) + (2*b^3*x^(5/2))/5","A",2,1,13,0.07692,1,"{43}"
448,1,47,0,0.0107336,"\int \frac{(a+b x)^3}{x^{5/2}} \, dx","Int[(a + b*x)^3/x^(5/2),x]","-\frac{6 a^2 b}{\sqrt{x}}-\frac{2 a^3}{3 x^{3/2}}+6 a b^2 \sqrt{x}+\frac{2}{3} b^3 x^{3/2}","-\frac{6 a^2 b}{\sqrt{x}}-\frac{2 a^3}{3 x^{3/2}}+6 a b^2 \sqrt{x}+\frac{2}{3} b^3 x^{3/2}",1,"(-2*a^3)/(3*x^(3/2)) - (6*a^2*b)/Sqrt[x] + 6*a*b^2*Sqrt[x] + (2*b^3*x^(3/2))/3","A",2,1,13,0.07692,1,"{43}"
449,1,68,0,0.0319405,"\int \frac{x^{5/2}}{a+b x} \, dx","Int[x^(5/2)/(a + b*x),x]","\frac{2 a^2 \sqrt{x}}{b^3}-\frac{2 a^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{7/2}}-\frac{2 a x^{3/2}}{3 b^2}+\frac{2 x^{5/2}}{5 b}","\frac{2 a^2 \sqrt{x}}{b^3}-\frac{2 a^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{7/2}}-\frac{2 a x^{3/2}}{3 b^2}+\frac{2 x^{5/2}}{5 b}",1,"(2*a^2*Sqrt[x])/b^3 - (2*a*x^(3/2))/(3*b^2) + (2*x^(5/2))/(5*b) - (2*a^(5/2)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/b^(7/2)","A",5,3,13,0.2308,1,"{50, 63, 205}"
450,1,53,0,0.0166034,"\int \frac{x^{3/2}}{a+b x} \, dx","Int[x^(3/2)/(a + b*x),x]","\frac{2 a^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{5/2}}-\frac{2 a \sqrt{x}}{b^2}+\frac{2 x^{3/2}}{3 b}","\frac{2 a^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{5/2}}-\frac{2 a \sqrt{x}}{b^2}+\frac{2 x^{3/2}}{3 b}",1,"(-2*a*Sqrt[x])/b^2 + (2*x^(3/2))/(3*b) + (2*a^(3/2)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/b^(5/2)","A",4,3,13,0.2308,1,"{50, 63, 205}"
451,1,40,0,0.0117361,"\int \frac{\sqrt{x}}{a+b x} \, dx","Int[Sqrt[x]/(a + b*x),x]","\frac{2 \sqrt{x}}{b}-\frac{2 \sqrt{a} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{3/2}}","\frac{2 \sqrt{x}}{b}-\frac{2 \sqrt{a} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{3/2}}",1,"(2*Sqrt[x])/b - (2*Sqrt[a]*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/b^(3/2)","A",3,3,13,0.2308,1,"{50, 63, 205}"
452,1,29,0,0.0082801,"\int \frac{1}{\sqrt{x} (a+b x)} \, dx","Int[1/(Sqrt[x]*(a + b*x)),x]","\frac{2 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b}}","\frac{2 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b}}",1,"(2*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(Sqrt[a]*Sqrt[b])","A",2,2,13,0.1538,1,"{63, 205}"
453,1,40,0,0.0129225,"\int \frac{1}{x^{3/2} (a+b x)} \, dx","Int[1/(x^(3/2)*(a + b*x)),x]","-\frac{2 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{a^{3/2}}-\frac{2}{a \sqrt{x}}","-\frac{2 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{a^{3/2}}-\frac{2}{a \sqrt{x}}",1,"-2/(a*Sqrt[x]) - (2*Sqrt[b]*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/a^(3/2)","A",3,3,13,0.2308,1,"{51, 63, 205}"
454,1,53,0,0.0176221,"\int \frac{1}{x^{5/2} (a+b x)} \, dx","Int[1/(x^(5/2)*(a + b*x)),x]","\frac{2 b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{a^{5/2}}+\frac{2 b}{a^2 \sqrt{x}}-\frac{2}{3 a x^{3/2}}","\frac{2 b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{a^{5/2}}+\frac{2 b}{a^2 \sqrt{x}}-\frac{2}{3 a x^{3/2}}",1,"-2/(3*a*x^(3/2)) + (2*b)/(a^2*Sqrt[x]) + (2*b^(3/2)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/a^(5/2)","A",4,3,13,0.2308,1,"{51, 63, 205}"
455,1,68,0,0.0232084,"\int \frac{1}{x^{7/2} (a+b x)} \, dx","Int[1/(x^(7/2)*(a + b*x)),x]","-\frac{2 b^2}{a^3 \sqrt{x}}-\frac{2 b^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{a^{7/2}}+\frac{2 b}{3 a^2 x^{3/2}}-\frac{2}{5 a x^{5/2}}","-\frac{2 b^2}{a^3 \sqrt{x}}-\frac{2 b^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{a^{7/2}}+\frac{2 b}{3 a^2 x^{3/2}}-\frac{2}{5 a x^{5/2}}",1,"-2/(5*a*x^(5/2)) + (2*b)/(3*a^2*x^(3/2)) - (2*b^2)/(a^3*Sqrt[x]) - (2*b^(5/2)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/a^(7/2)","A",5,3,13,0.2308,1,"{51, 63, 205}"
456,1,70,0,0.0221569,"\int \frac{x^{5/2}}{(a+b x)^2} \, dx","Int[x^(5/2)/(a + b*x)^2,x]","\frac{5 a^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{7/2}}-\frac{5 a \sqrt{x}}{b^3}-\frac{x^{5/2}}{b (a+b x)}+\frac{5 x^{3/2}}{3 b^2}","\frac{5 a^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{7/2}}-\frac{5 a \sqrt{x}}{b^3}-\frac{x^{5/2}}{b (a+b x)}+\frac{5 x^{3/2}}{3 b^2}",1,"(-5*a*Sqrt[x])/b^3 + (5*x^(3/2))/(3*b^2) - x^(5/2)/(b*(a + b*x)) + (5*a^(3/2)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/b^(7/2)","A",5,4,13,0.3077,1,"{47, 50, 63, 205}"
457,1,57,0,0.0168536,"\int \frac{x^{3/2}}{(a+b x)^2} \, dx","Int[x^(3/2)/(a + b*x)^2,x]","-\frac{3 \sqrt{a} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{5/2}}-\frac{x^{3/2}}{b (a+b x)}+\frac{3 \sqrt{x}}{b^2}","-\frac{3 \sqrt{a} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{5/2}}-\frac{x^{3/2}}{b (a+b x)}+\frac{3 \sqrt{x}}{b^2}",1,"(3*Sqrt[x])/b^2 - x^(3/2)/(b*(a + b*x)) - (3*Sqrt[a]*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/b^(5/2)","A",4,4,13,0.3077,1,"{47, 50, 63, 205}"
458,1,46,0,0.0133927,"\int \frac{\sqrt{x}}{(a+b x)^2} \, dx","Int[Sqrt[x]/(a + b*x)^2,x]","\frac{\tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{\sqrt{a} b^{3/2}}-\frac{\sqrt{x}}{b (a+b x)}","\frac{\tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{\sqrt{a} b^{3/2}}-\frac{\sqrt{x}}{b (a+b x)}",1,"-(Sqrt[x]/(b*(a + b*x))) + ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]]/(Sqrt[a]*b^(3/2))","A",3,3,13,0.2308,1,"{47, 63, 205}"
459,1,45,0,0.0128271,"\int \frac{1}{\sqrt{x} (a+b x)^2} \, dx","Int[1/(Sqrt[x]*(a + b*x)^2),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{a^{3/2} \sqrt{b}}+\frac{\sqrt{x}}{a (a+b x)}","\frac{\tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{a^{3/2} \sqrt{b}}+\frac{\sqrt{x}}{a (a+b x)}",1,"Sqrt[x]/(a*(a + b*x)) + ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]]/(a^(3/2)*Sqrt[b])","A",3,3,13,0.2308,1,"{51, 63, 205}"
460,1,56,0,0.0168896,"\int \frac{1}{x^{3/2} (a+b x)^2} \, dx","Int[1/(x^(3/2)*(a + b*x)^2),x]","-\frac{3 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{a^{5/2}}-\frac{3}{a^2 \sqrt{x}}+\frac{1}{a \sqrt{x} (a+b x)}","-\frac{3 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{a^{5/2}}-\frac{3}{a^2 \sqrt{x}}+\frac{1}{a \sqrt{x} (a+b x)}",1,"-3/(a^2*Sqrt[x]) + 1/(a*Sqrt[x]*(a + b*x)) - (3*Sqrt[b]*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/a^(5/2)","A",4,3,13,0.2308,1,"{51, 63, 205}"
461,1,69,0,0.0218529,"\int \frac{1}{x^{5/2} (a+b x)^2} \, dx","Int[1/(x^(5/2)*(a + b*x)^2),x]","\frac{5 b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{a^{7/2}}+\frac{5 b}{a^3 \sqrt{x}}-\frac{5}{3 a^2 x^{3/2}}+\frac{1}{a x^{3/2} (a+b x)}","\frac{5 b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{a^{7/2}}+\frac{5 b}{a^3 \sqrt{x}}-\frac{5}{3 a^2 x^{3/2}}+\frac{1}{a x^{3/2} (a+b x)}",1,"-5/(3*a^2*x^(3/2)) + (5*b)/(a^3*Sqrt[x]) + 1/(a*x^(3/2)*(a + b*x)) + (5*b^(3/2)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/a^(7/2)","A",5,3,13,0.2308,1,"{51, 63, 205}"
462,1,95,0,0.0326997,"\int \frac{x^{7/2}}{(a+b x)^3} \, dx","Int[x^(7/2)/(a + b*x)^3,x]","\frac{35 a^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 b^{9/2}}-\frac{7 x^{5/2}}{4 b^2 (a+b x)}-\frac{35 a \sqrt{x}}{4 b^4}-\frac{x^{7/2}}{2 b (a+b x)^2}+\frac{35 x^{3/2}}{12 b^3}","\frac{35 a^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 b^{9/2}}-\frac{7 x^{5/2}}{4 b^2 (a+b x)}-\frac{35 a \sqrt{x}}{4 b^4}-\frac{x^{7/2}}{2 b (a+b x)^2}+\frac{35 x^{3/2}}{12 b^3}",1,"(-35*a*Sqrt[x])/(4*b^4) + (35*x^(3/2))/(12*b^3) - x^(7/2)/(2*b*(a + b*x)^2) - (7*x^(5/2))/(4*b^2*(a + b*x)) + (35*a^(3/2)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(4*b^(9/2))","A",6,4,13,0.3077,1,"{47, 50, 63, 205}"
463,1,82,0,0.0234385,"\int \frac{x^{5/2}}{(a+b x)^3} \, dx","Int[x^(5/2)/(a + b*x)^3,x]","-\frac{5 x^{3/2}}{4 b^2 (a+b x)}-\frac{15 \sqrt{a} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 b^{7/2}}-\frac{x^{5/2}}{2 b (a+b x)^2}+\frac{15 \sqrt{x}}{4 b^3}","-\frac{5 x^{3/2}}{4 b^2 (a+b x)}-\frac{15 \sqrt{a} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 b^{7/2}}-\frac{x^{5/2}}{2 b (a+b x)^2}+\frac{15 \sqrt{x}}{4 b^3}",1,"(15*Sqrt[x])/(4*b^3) - x^(5/2)/(2*b*(a + b*x)^2) - (5*x^(3/2))/(4*b^2*(a + b*x)) - (15*Sqrt[a]*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(4*b^(7/2))","A",5,4,13,0.3077,1,"{47, 50, 63, 205}"
464,1,70,0,0.0192098,"\int \frac{x^{3/2}}{(a+b x)^3} \, dx","Int[x^(3/2)/(a + b*x)^3,x]","-\frac{3 \sqrt{x}}{4 b^2 (a+b x)}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 \sqrt{a} b^{5/2}}-\frac{x^{3/2}}{2 b (a+b x)^2}","-\frac{3 \sqrt{x}}{4 b^2 (a+b x)}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 \sqrt{a} b^{5/2}}-\frac{x^{3/2}}{2 b (a+b x)^2}",1,"-x^(3/2)/(2*b*(a + b*x)^2) - (3*Sqrt[x])/(4*b^2*(a + b*x)) + (3*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(4*Sqrt[a]*b^(5/2))","A",4,3,13,0.2308,1,"{47, 63, 205}"
465,1,73,0,0.0194928,"\int \frac{\sqrt{x}}{(a+b x)^3} \, dx","Int[Sqrt[x]/(a + b*x)^3,x]","\frac{\tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 a^{3/2} b^{3/2}}+\frac{\sqrt{x}}{4 a b (a+b x)}-\frac{\sqrt{x}}{2 b (a+b x)^2}","\frac{\tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 a^{3/2} b^{3/2}}+\frac{\sqrt{x}}{4 a b (a+b x)}-\frac{\sqrt{x}}{2 b (a+b x)^2}",1,"-Sqrt[x]/(2*b*(a + b*x)^2) + Sqrt[x]/(4*a*b*(a + b*x)) + ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]]/(4*a^(3/2)*b^(3/2))","A",4,4,13,0.3077,1,"{47, 51, 63, 205}"
466,1,70,0,0.0191969,"\int \frac{1}{\sqrt{x} (a+b x)^3} \, dx","Int[1/(Sqrt[x]*(a + b*x)^3),x]","\frac{3 \sqrt{x}}{4 a^2 (a+b x)}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 a^{5/2} \sqrt{b}}+\frac{\sqrt{x}}{2 a (a+b x)^2}","\frac{3 \sqrt{x}}{4 a^2 (a+b x)}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 a^{5/2} \sqrt{b}}+\frac{\sqrt{x}}{2 a (a+b x)^2}",1,"Sqrt[x]/(2*a*(a + b*x)^2) + (3*Sqrt[x])/(4*a^2*(a + b*x)) + (3*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(4*a^(5/2)*Sqrt[b])","A",4,3,13,0.2308,1,"{51, 63, 205}"
467,1,82,0,0.0251132,"\int \frac{1}{x^{3/2} (a+b x)^3} \, dx","Int[1/(x^(3/2)*(a + b*x)^3),x]","\frac{5}{4 a^2 \sqrt{x} (a+b x)}-\frac{15 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 a^{7/2}}-\frac{15}{4 a^3 \sqrt{x}}+\frac{1}{2 a \sqrt{x} (a+b x)^2}","\frac{5}{4 a^2 \sqrt{x} (a+b x)}-\frac{15 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 a^{7/2}}-\frac{15}{4 a^3 \sqrt{x}}+\frac{1}{2 a \sqrt{x} (a+b x)^2}",1,"-15/(4*a^3*Sqrt[x]) + 1/(2*a*Sqrt[x]*(a + b*x)^2) + 5/(4*a^2*Sqrt[x]*(a + b*x)) - (15*Sqrt[b]*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(4*a^(7/2))","A",5,3,13,0.2308,1,"{51, 63, 205}"
468,1,95,0,0.0289663,"\int \frac{1}{x^{5/2} (a+b x)^3} \, dx","Int[1/(x^(5/2)*(a + b*x)^3),x]","\frac{35 b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 a^{9/2}}+\frac{7}{4 a^2 x^{3/2} (a+b x)}+\frac{35 b}{4 a^4 \sqrt{x}}-\frac{35}{12 a^3 x^{3/2}}+\frac{1}{2 a x^{3/2} (a+b x)^2}","\frac{35 b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 a^{9/2}}+\frac{7}{4 a^2 x^{3/2} (a+b x)}+\frac{35 b}{4 a^4 \sqrt{x}}-\frac{35}{12 a^3 x^{3/2}}+\frac{1}{2 a x^{3/2} (a+b x)^2}",1,"-35/(12*a^3*x^(3/2)) + (35*b)/(4*a^4*Sqrt[x]) + 1/(2*a*x^(3/2)*(a + b*x)^2) + 7/(4*a^2*x^(3/2)*(a + b*x)) + (35*b^(3/2)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(4*a^(9/2))","A",6,3,13,0.2308,1,"{51, 63, 205}"
469,1,68,0,0.02392,"\int \frac{x^{5/2}}{-a+b x} \, dx","Int[x^(5/2)/(-a + b*x),x]","\frac{2 a^2 \sqrt{x}}{b^3}-\frac{2 a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{7/2}}+\frac{2 a x^{3/2}}{3 b^2}+\frac{2 x^{5/2}}{5 b}","\frac{2 a^2 \sqrt{x}}{b^3}-\frac{2 a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{7/2}}+\frac{2 a x^{3/2}}{3 b^2}+\frac{2 x^{5/2}}{5 b}",1,"(2*a^2*Sqrt[x])/b^3 + (2*a*x^(3/2))/(3*b^2) + (2*x^(5/2))/(5*b) - (2*a^(5/2)*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/b^(7/2)","A",5,3,15,0.2000,1,"{50, 63, 208}"
470,1,53,0,0.017739,"\int \frac{x^{3/2}}{-a+b x} \, dx","Int[x^(3/2)/(-a + b*x),x]","-\frac{2 a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{5/2}}+\frac{2 a \sqrt{x}}{b^2}+\frac{2 x^{3/2}}{3 b}","-\frac{2 a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{5/2}}+\frac{2 a \sqrt{x}}{b^2}+\frac{2 x^{3/2}}{3 b}",1,"(2*a*Sqrt[x])/b^2 + (2*x^(3/2))/(3*b) - (2*a^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/b^(5/2)","A",4,3,15,0.2000,1,"{50, 63, 208}"
471,1,40,0,0.0138221,"\int \frac{\sqrt{x}}{-a+b x} \, dx","Int[Sqrt[x]/(-a + b*x),x]","\frac{2 \sqrt{x}}{b}-\frac{2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{3/2}}","\frac{2 \sqrt{x}}{b}-\frac{2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{3/2}}",1,"(2*Sqrt[x])/b - (2*Sqrt[a]*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/b^(3/2)","A",3,3,15,0.2000,1,"{50, 63, 208}"
472,1,29,0,0.0106771,"\int \frac{1}{\sqrt{x} (-a+b x)} \, dx","Int[1/(Sqrt[x]*(-a + b*x)),x]","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b}}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b}}",1,"(-2*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(Sqrt[a]*Sqrt[b])","A",2,2,15,0.1333,1,"{63, 208}"
473,1,40,0,0.0141089,"\int \frac{1}{x^{3/2} (-a+b x)} \, dx","Int[1/(x^(3/2)*(-a + b*x)),x]","\frac{2}{a \sqrt{x}}-\frac{2 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{a^{3/2}}","\frac{2}{a \sqrt{x}}-\frac{2 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{a^{3/2}}",1,"2/(a*Sqrt[x]) - (2*Sqrt[b]*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/a^(3/2)","A",3,3,15,0.2000,1,"{51, 63, 208}"
474,1,53,0,0.0183376,"\int \frac{1}{x^{5/2} (-a+b x)} \, dx","Int[1/(x^(5/2)*(-a + b*x)),x]","-\frac{2 b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{a^{5/2}}+\frac{2 b}{a^2 \sqrt{x}}+\frac{2}{3 a x^{3/2}}","-\frac{2 b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{a^{5/2}}+\frac{2 b}{a^2 \sqrt{x}}+\frac{2}{3 a x^{3/2}}",1,"2/(3*a*x^(3/2)) + (2*b)/(a^2*Sqrt[x]) - (2*b^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/a^(5/2)","A",4,3,15,0.2000,1,"{51, 63, 208}"
475,1,68,0,0.0224059,"\int \frac{1}{x^{7/2} (-a+b x)} \, dx","Int[1/(x^(7/2)*(-a + b*x)),x]","\frac{2 b^2}{a^3 \sqrt{x}}-\frac{2 b^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{a^{7/2}}+\frac{2 b}{3 a^2 x^{3/2}}+\frac{2}{5 a x^{5/2}}","\frac{2 b^2}{a^3 \sqrt{x}}-\frac{2 b^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{a^{7/2}}+\frac{2 b}{3 a^2 x^{3/2}}+\frac{2}{5 a x^{5/2}}",1,"2/(5*a*x^(5/2)) + (2*b)/(3*a^2*x^(3/2)) + (2*b^2)/(a^3*Sqrt[x]) - (2*b^(5/2)*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/a^(7/2)","A",5,3,15,0.2000,1,"{51, 63, 208}"
476,1,70,0,0.0246949,"\int \frac{x^{5/2}}{(-a+b x)^2} \, dx","Int[x^(5/2)/(-a + b*x)^2,x]","-\frac{5 a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{7/2}}+\frac{5 a \sqrt{x}}{b^3}+\frac{x^{5/2}}{b (a-b x)}+\frac{5 x^{3/2}}{3 b^2}","-\frac{5 a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{7/2}}+\frac{5 a \sqrt{x}}{b^3}+\frac{x^{5/2}}{b (a-b x)}+\frac{5 x^{3/2}}{3 b^2}",1,"(5*a*Sqrt[x])/b^3 + (5*x^(3/2))/(3*b^2) + x^(5/2)/(b*(a - b*x)) - (5*a^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/b^(7/2)","A",5,4,15,0.2667,1,"{47, 50, 63, 208}"
477,1,57,0,0.0175417,"\int \frac{x^{3/2}}{(-a+b x)^2} \, dx","Int[x^(3/2)/(-a + b*x)^2,x]","-\frac{3 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{5/2}}+\frac{x^{3/2}}{b (a-b x)}+\frac{3 \sqrt{x}}{b^2}","-\frac{3 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{5/2}}+\frac{x^{3/2}}{b (a-b x)}+\frac{3 \sqrt{x}}{b^2}",1,"(3*Sqrt[x])/b^2 + x^(3/2)/(b*(a - b*x)) - (3*Sqrt[a]*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/b^(5/2)","A",4,4,15,0.2667,1,"{47, 50, 63, 208}"
478,1,47,0,0.0147455,"\int \frac{\sqrt{x}}{(-a+b x)^2} \, dx","Int[Sqrt[x]/(-a + b*x)^2,x]","\frac{\sqrt{x}}{b (a-b x)}-\frac{\tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{\sqrt{a} b^{3/2}}","\frac{\sqrt{x}}{b (a-b x)}-\frac{\tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{\sqrt{a} b^{3/2}}",1,"Sqrt[x]/(b*(a - b*x)) - ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a]]/(Sqrt[a]*b^(3/2))","A",3,3,15,0.2000,1,"{47, 63, 208}"
479,1,46,0,0.0142779,"\int \frac{1}{\sqrt{x} (-a+b x)^2} \, dx","Int[1/(Sqrt[x]*(-a + b*x)^2),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{a^{3/2} \sqrt{b}}+\frac{\sqrt{x}}{a (a-b x)}","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{a^{3/2} \sqrt{b}}+\frac{\sqrt{x}}{a (a-b x)}",1,"Sqrt[x]/(a*(a - b*x)) + ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a]]/(a^(3/2)*Sqrt[b])","A",3,3,15,0.2000,1,"{51, 63, 208}"
480,1,57,0,0.0179159,"\int \frac{1}{x^{3/2} (-a+b x)^2} \, dx","Int[1/(x^(3/2)*(-a + b*x)^2),x]","\frac{3 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{a^{5/2}}-\frac{3}{a^2 \sqrt{x}}+\frac{1}{a \sqrt{x} (a-b x)}","\frac{3 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{a^{5/2}}-\frac{3}{a^2 \sqrt{x}}+\frac{1}{a \sqrt{x} (a-b x)}",1,"-3/(a^2*Sqrt[x]) + 1/(a*Sqrt[x]*(a - b*x)) + (3*Sqrt[b]*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/a^(5/2)","A",4,3,15,0.2000,1,"{51, 63, 208}"
481,1,70,0,0.0224064,"\int \frac{1}{x^{5/2} (-a+b x)^2} \, dx","Int[1/(x^(5/2)*(-a + b*x)^2),x]","\frac{5 b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{a^{7/2}}-\frac{5 b}{a^3 \sqrt{x}}-\frac{5}{3 a^2 x^{3/2}}+\frac{1}{a x^{3/2} (a-b x)}","\frac{5 b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{a^{7/2}}-\frac{5 b}{a^3 \sqrt{x}}-\frac{5}{3 a^2 x^{3/2}}+\frac{1}{a x^{3/2} (a-b x)}",1,"-5/(3*a^2*x^(3/2)) - (5*b)/(a^3*Sqrt[x]) + 1/(a*x^(3/2)*(a - b*x)) + (5*b^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/a^(7/2)","A",5,3,15,0.2000,1,"{51, 63, 208}"
482,1,97,0,0.0301179,"\int \frac{x^{7/2}}{(-a+b x)^3} \, dx","Int[x^(7/2)/(-a + b*x)^3,x]","-\frac{35 a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 b^{9/2}}+\frac{7 x^{5/2}}{4 b^2 (a-b x)}+\frac{35 a \sqrt{x}}{4 b^4}-\frac{x^{7/2}}{2 b (a-b x)^2}+\frac{35 x^{3/2}}{12 b^3}","-\frac{35 a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 b^{9/2}}+\frac{7 x^{5/2}}{4 b^2 (a-b x)}+\frac{35 a \sqrt{x}}{4 b^4}-\frac{x^{7/2}}{2 b (a-b x)^2}+\frac{35 x^{3/2}}{12 b^3}",1,"(35*a*Sqrt[x])/(4*b^4) + (35*x^(3/2))/(12*b^3) - x^(7/2)/(2*b*(a - b*x)^2) + (7*x^(5/2))/(4*b^2*(a - b*x)) - (35*a^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(4*b^(9/2))","A",6,4,15,0.2667,1,"{47, 50, 63, 208}"
483,1,84,0,0.0260807,"\int \frac{x^{5/2}}{(-a+b x)^3} \, dx","Int[x^(5/2)/(-a + b*x)^3,x]","\frac{5 x^{3/2}}{4 b^2 (a-b x)}-\frac{15 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 b^{7/2}}-\frac{x^{5/2}}{2 b (a-b x)^2}+\frac{15 \sqrt{x}}{4 b^3}","\frac{5 x^{3/2}}{4 b^2 (a-b x)}-\frac{15 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 b^{7/2}}-\frac{x^{5/2}}{2 b (a-b x)^2}+\frac{15 \sqrt{x}}{4 b^3}",1,"(15*Sqrt[x])/(4*b^3) - x^(5/2)/(2*b*(a - b*x)^2) + (5*x^(3/2))/(4*b^2*(a - b*x)) - (15*Sqrt[a]*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(4*b^(7/2))","A",5,4,15,0.2667,1,"{47, 50, 63, 208}"
484,1,72,0,0.0208706,"\int \frac{x^{3/2}}{(-a+b x)^3} \, dx","Int[x^(3/2)/(-a + b*x)^3,x]","\frac{3 \sqrt{x}}{4 b^2 (a-b x)}-\frac{3 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 \sqrt{a} b^{5/2}}-\frac{x^{3/2}}{2 b (a-b x)^2}","\frac{3 \sqrt{x}}{4 b^2 (a-b x)}-\frac{3 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 \sqrt{a} b^{5/2}}-\frac{x^{3/2}}{2 b (a-b x)^2}",1,"-x^(3/2)/(2*b*(a - b*x)^2) + (3*Sqrt[x])/(4*b^2*(a - b*x)) - (3*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(4*Sqrt[a]*b^(5/2))","A",4,3,15,0.2000,1,"{47, 63, 208}"
485,1,75,0,0.0199319,"\int \frac{\sqrt{x}}{(-a+b x)^3} \, dx","Int[Sqrt[x]/(-a + b*x)^3,x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 a^{3/2} b^{3/2}}+\frac{\sqrt{x}}{4 a b (a-b x)}-\frac{\sqrt{x}}{2 b (a-b x)^2}","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 a^{3/2} b^{3/2}}+\frac{\sqrt{x}}{4 a b (a-b x)}-\frac{\sqrt{x}}{2 b (a-b x)^2}",1,"-Sqrt[x]/(2*b*(a - b*x)^2) + Sqrt[x]/(4*a*b*(a - b*x)) + ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a]]/(4*a^(3/2)*b^(3/2))","A",4,4,15,0.2667,1,"{47, 51, 63, 208}"
486,1,72,0,0.0196717,"\int \frac{1}{\sqrt{x} (-a+b x)^3} \, dx","Int[1/(Sqrt[x]*(-a + b*x)^3),x]","-\frac{3 \sqrt{x}}{4 a^2 (a-b x)}-\frac{3 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 a^{5/2} \sqrt{b}}-\frac{\sqrt{x}}{2 a (a-b x)^2}","-\frac{3 \sqrt{x}}{4 a^2 (a-b x)}-\frac{3 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 a^{5/2} \sqrt{b}}-\frac{\sqrt{x}}{2 a (a-b x)^2}",1,"-Sqrt[x]/(2*a*(a - b*x)^2) - (3*Sqrt[x])/(4*a^2*(a - b*x)) - (3*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(4*a^(5/2)*Sqrt[b])","A",4,3,15,0.2000,1,"{51, 63, 208}"
487,1,84,0,0.0239046,"\int \frac{1}{x^{3/2} (-a+b x)^3} \, dx","Int[1/(x^(3/2)*(-a + b*x)^3),x]","-\frac{5}{4 a^2 \sqrt{x} (a-b x)}-\frac{15 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 a^{7/2}}+\frac{15}{4 a^3 \sqrt{x}}-\frac{1}{2 a \sqrt{x} (a-b x)^2}","-\frac{5}{4 a^2 \sqrt{x} (a-b x)}-\frac{15 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 a^{7/2}}+\frac{15}{4 a^3 \sqrt{x}}-\frac{1}{2 a \sqrt{x} (a-b x)^2}",1,"15/(4*a^3*Sqrt[x]) - 1/(2*a*Sqrt[x]*(a - b*x)^2) - 5/(4*a^2*Sqrt[x]*(a - b*x)) - (15*Sqrt[b]*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(4*a^(7/2))","A",5,3,15,0.2000,1,"{51, 63, 208}"
488,1,97,0,0.0303405,"\int \frac{1}{x^{5/2} (-a+b x)^3} \, dx","Int[1/(x^(5/2)*(-a + b*x)^3),x]","-\frac{35 b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 a^{9/2}}-\frac{7}{4 a^2 x^{3/2} (a-b x)}+\frac{35 b}{4 a^4 \sqrt{x}}+\frac{35}{12 a^3 x^{3/2}}-\frac{1}{2 a x^{3/2} (a-b x)^2}","-\frac{35 b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 a^{9/2}}-\frac{7}{4 a^2 x^{3/2} (a-b x)}+\frac{35 b}{4 a^4 \sqrt{x}}+\frac{35}{12 a^3 x^{3/2}}-\frac{1}{2 a x^{3/2} (a-b x)^2}",1,"35/(12*a^3*x^(3/2)) + (35*b)/(4*a^4*Sqrt[x]) - 1/(2*a*x^(3/2)*(a - b*x)^2) - 7/(4*a^2*x^(3/2)*(a - b*x)) - (35*b^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(4*a^(9/2))","A",6,3,15,0.2000,1,"{51, 63, 208}"
489,1,122,0,0.0417613,"\int x^{5/2} \sqrt{a+b x} \, dx","Int[x^(5/2)*Sqrt[a + b*x],x]","-\frac{5 a^2 x^{3/2} \sqrt{a+b x}}{96 b^2}+\frac{5 a^3 \sqrt{x} \sqrt{a+b x}}{64 b^3}-\frac{5 a^4 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{64 b^{7/2}}+\frac{a x^{5/2} \sqrt{a+b x}}{24 b}+\frac{1}{4} x^{7/2} \sqrt{a+b x}","-\frac{5 a^2 x^{3/2} \sqrt{a+b x}}{96 b^2}+\frac{5 a^3 \sqrt{x} \sqrt{a+b x}}{64 b^3}-\frac{5 a^4 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{64 b^{7/2}}+\frac{a x^{5/2} \sqrt{a+b x}}{24 b}+\frac{1}{4} x^{7/2} \sqrt{a+b x}",1,"(5*a^3*Sqrt[x]*Sqrt[a + b*x])/(64*b^3) - (5*a^2*x^(3/2)*Sqrt[a + b*x])/(96*b^2) + (a*x^(5/2)*Sqrt[a + b*x])/(24*b) + (x^(7/2)*Sqrt[a + b*x])/4 - (5*a^4*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a + b*x]])/(64*b^(7/2))","A",7,4,15,0.2667,1,"{50, 63, 217, 206}"
490,1,98,0,0.0307894,"\int x^{3/2} \sqrt{a+b x} \, dx","Int[x^(3/2)*Sqrt[a + b*x],x]","-\frac{a^2 \sqrt{x} \sqrt{a+b x}}{8 b^2}+\frac{a^3 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{8 b^{5/2}}+\frac{a x^{3/2} \sqrt{a+b x}}{12 b}+\frac{1}{3} x^{5/2} \sqrt{a+b x}","-\frac{a^2 \sqrt{x} \sqrt{a+b x}}{8 b^2}+\frac{a^3 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{8 b^{5/2}}+\frac{a x^{3/2} \sqrt{a+b x}}{12 b}+\frac{1}{3} x^{5/2} \sqrt{a+b x}",1,"-(a^2*Sqrt[x]*Sqrt[a + b*x])/(8*b^2) + (a*x^(3/2)*Sqrt[a + b*x])/(12*b) + (x^(5/2)*Sqrt[a + b*x])/3 + (a^3*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a + b*x]])/(8*b^(5/2))","A",6,4,15,0.2667,1,"{50, 63, 217, 206}"
491,1,74,0,0.0226927,"\int \sqrt{x} \sqrt{a+b x} \, dx","Int[Sqrt[x]*Sqrt[a + b*x],x]","-\frac{a^2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{4 b^{3/2}}+\frac{1}{2} x^{3/2} \sqrt{a+b x}+\frac{a \sqrt{x} \sqrt{a+b x}}{4 b}","-\frac{a^2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{4 b^{3/2}}+\frac{1}{2} x^{3/2} \sqrt{a+b x}+\frac{a \sqrt{x} \sqrt{a+b x}}{4 b}",1,"(a*Sqrt[x]*Sqrt[a + b*x])/(4*b) + (x^(3/2)*Sqrt[a + b*x])/2 - (a^2*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a + b*x]])/(4*b^(3/2))","A",5,4,15,0.2667,1,"{50, 63, 217, 206}"
492,1,44,0,0.0171004,"\int \frac{\sqrt{a+b x}}{\sqrt{x}} \, dx","Int[Sqrt[a + b*x]/Sqrt[x],x]","\sqrt{x} \sqrt{a+b x}+\frac{a \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{\sqrt{b}}","\sqrt{x} \sqrt{a+b x}+\frac{a \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{\sqrt{b}}",1,"Sqrt[x]*Sqrt[a + b*x] + (a*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a + b*x]])/Sqrt[b]","A",4,4,15,0.2667,1,"{50, 63, 217, 206}"
493,1,45,0,0.0166056,"\int \frac{\sqrt{a+b x}}{x^{3/2}} \, dx","Int[Sqrt[a + b*x]/x^(3/2),x]","2 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)-\frac{2 \sqrt{a+b x}}{\sqrt{x}}","2 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)-\frac{2 \sqrt{a+b x}}{\sqrt{x}}",1,"(-2*Sqrt[a + b*x])/Sqrt[x] + 2*Sqrt[b]*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a + b*x]]","A",4,4,15,0.2667,1,"{47, 63, 217, 206}"
494,1,21,0,0.0019194,"\int \frac{\sqrt{a+b x}}{x^{5/2}} \, dx","Int[Sqrt[a + b*x]/x^(5/2),x]","-\frac{2 (a+b x)^{3/2}}{3 a x^{3/2}}","-\frac{2 (a+b x)^{3/2}}{3 a x^{3/2}}",1,"(-2*(a + b*x)^(3/2))/(3*a*x^(3/2))","A",1,1,15,0.06667,1,"{37}"
495,1,44,0,0.0053334,"\int \frac{\sqrt{a+b x}}{x^{7/2}} \, dx","Int[Sqrt[a + b*x]/x^(7/2),x]","\frac{4 b (a+b x)^{3/2}}{15 a^2 x^{3/2}}-\frac{2 (a+b x)^{3/2}}{5 a x^{5/2}}","\frac{4 b (a+b x)^{3/2}}{15 a^2 x^{3/2}}-\frac{2 (a+b x)^{3/2}}{5 a x^{5/2}}",1,"(-2*(a + b*x)^(3/2))/(5*a*x^(5/2)) + (4*b*(a + b*x)^(3/2))/(15*a^2*x^(3/2))","A",2,2,15,0.1333,1,"{45, 37}"
496,1,68,0,0.0096716,"\int \frac{\sqrt{a+b x}}{x^{9/2}} \, dx","Int[Sqrt[a + b*x]/x^(9/2),x]","-\frac{16 b^2 (a+b x)^{3/2}}{105 a^3 x^{3/2}}+\frac{8 b (a+b x)^{3/2}}{35 a^2 x^{5/2}}-\frac{2 (a+b x)^{3/2}}{7 a x^{7/2}}","-\frac{16 b^2 (a+b x)^{3/2}}{105 a^3 x^{3/2}}+\frac{8 b (a+b x)^{3/2}}{35 a^2 x^{5/2}}-\frac{2 (a+b x)^{3/2}}{7 a x^{7/2}}",1,"(-2*(a + b*x)^(3/2))/(7*a*x^(7/2)) + (8*b*(a + b*x)^(3/2))/(35*a^2*x^(5/2)) - (16*b^2*(a + b*x)^(3/2))/(105*a^3*x^(3/2))","A",3,2,15,0.1333,1,"{45, 37}"
497,1,127,0,0.0422133,"\int x^{5/2} \sqrt{a-b x} \, dx","Int[x^(5/2)*Sqrt[a - b*x],x]","-\frac{5 a^2 x^{3/2} \sqrt{a-b x}}{96 b^2}-\frac{5 a^3 \sqrt{x} \sqrt{a-b x}}{64 b^3}+\frac{5 a^4 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)}{64 b^{7/2}}-\frac{a x^{5/2} \sqrt{a-b x}}{24 b}+\frac{1}{4} x^{7/2} \sqrt{a-b x}","-\frac{5 a^2 x^{3/2} \sqrt{a-b x}}{96 b^2}-\frac{5 a^3 \sqrt{x} \sqrt{a-b x}}{64 b^3}+\frac{5 a^4 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)}{64 b^{7/2}}-\frac{a x^{5/2} \sqrt{a-b x}}{24 b}+\frac{1}{4} x^{7/2} \sqrt{a-b x}",1,"(-5*a^3*Sqrt[x]*Sqrt[a - b*x])/(64*b^3) - (5*a^2*x^(3/2)*Sqrt[a - b*x])/(96*b^2) - (a*x^(5/2)*Sqrt[a - b*x])/(24*b) + (x^(7/2)*Sqrt[a - b*x])/4 + (5*a^4*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a - b*x]])/(64*b^(7/2))","A",7,4,16,0.2500,1,"{50, 63, 217, 203}"
498,1,102,0,0.0296454,"\int x^{3/2} \sqrt{a-b x} \, dx","Int[x^(3/2)*Sqrt[a - b*x],x]","-\frac{a^2 \sqrt{x} \sqrt{a-b x}}{8 b^2}+\frac{a^3 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)}{8 b^{5/2}}-\frac{a x^{3/2} \sqrt{a-b x}}{12 b}+\frac{1}{3} x^{5/2} \sqrt{a-b x}","-\frac{a^2 \sqrt{x} \sqrt{a-b x}}{8 b^2}+\frac{a^3 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)}{8 b^{5/2}}-\frac{a x^{3/2} \sqrt{a-b x}}{12 b}+\frac{1}{3} x^{5/2} \sqrt{a-b x}",1,"-(a^2*Sqrt[x]*Sqrt[a - b*x])/(8*b^2) - (a*x^(3/2)*Sqrt[a - b*x])/(12*b) + (x^(5/2)*Sqrt[a - b*x])/3 + (a^3*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a - b*x]])/(8*b^(5/2))","A",6,4,16,0.2500,1,"{50, 63, 217, 203}"
499,1,77,0,0.0236496,"\int \sqrt{x} \sqrt{a-b x} \, dx","Int[Sqrt[x]*Sqrt[a - b*x],x]","\frac{a^2 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)}{4 b^{3/2}}+\frac{1}{2} x^{3/2} \sqrt{a-b x}-\frac{a \sqrt{x} \sqrt{a-b x}}{4 b}","\frac{a^2 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)}{4 b^{3/2}}+\frac{1}{2} x^{3/2} \sqrt{a-b x}-\frac{a \sqrt{x} \sqrt{a-b x}}{4 b}",1,"-(a*Sqrt[x]*Sqrt[a - b*x])/(4*b) + (x^(3/2)*Sqrt[a - b*x])/2 + (a^2*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a - b*x]])/(4*b^(3/2))","A",5,4,16,0.2500,1,"{50, 63, 217, 203}"
500,1,46,0,0.0169224,"\int \frac{\sqrt{a-b x}}{\sqrt{x}} \, dx","Int[Sqrt[a - b*x]/Sqrt[x],x]","\sqrt{x} \sqrt{a-b x}+\frac{a \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)}{\sqrt{b}}","\sqrt{x} \sqrt{a-b x}+\frac{a \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)}{\sqrt{b}}",1,"Sqrt[x]*Sqrt[a - b*x] + (a*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a - b*x]])/Sqrt[b]","A",4,4,16,0.2500,1,"{50, 63, 217, 203}"
501,1,47,0,0.0163847,"\int \frac{\sqrt{a-b x}}{x^{3/2}} \, dx","Int[Sqrt[a - b*x]/x^(3/2),x]","-\frac{2 \sqrt{a-b x}}{\sqrt{x}}-2 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)","-\frac{2 \sqrt{a-b x}}{\sqrt{x}}-2 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)",1,"(-2*Sqrt[a - b*x])/Sqrt[x] - 2*Sqrt[b]*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a - b*x]]","A",4,4,16,0.2500,1,"{47, 63, 217, 203}"
502,1,22,0,0.0017392,"\int \frac{\sqrt{a-b x}}{x^{5/2}} \, dx","Int[Sqrt[a - b*x]/x^(5/2),x]","-\frac{2 (a-b x)^{3/2}}{3 a x^{3/2}}","-\frac{2 (a-b x)^{3/2}}{3 a x^{3/2}}",1,"(-2*(a - b*x)^(3/2))/(3*a*x^(3/2))","A",1,1,16,0.06250,1,"{37}"
503,1,46,0,0.0051817,"\int \frac{\sqrt{a-b x}}{x^{7/2}} \, dx","Int[Sqrt[a - b*x]/x^(7/2),x]","-\frac{4 b (a-b x)^{3/2}}{15 a^2 x^{3/2}}-\frac{2 (a-b x)^{3/2}}{5 a x^{5/2}}","-\frac{4 b (a-b x)^{3/2}}{15 a^2 x^{3/2}}-\frac{2 (a-b x)^{3/2}}{5 a x^{5/2}}",1,"(-2*(a - b*x)^(3/2))/(5*a*x^(5/2)) - (4*b*(a - b*x)^(3/2))/(15*a^2*x^(3/2))","A",2,2,16,0.1250,1,"{45, 37}"
504,1,71,0,0.0104142,"\int \frac{\sqrt{a-b x}}{x^{9/2}} \, dx","Int[Sqrt[a - b*x]/x^(9/2),x]","-\frac{16 b^2 (a-b x)^{3/2}}{105 a^3 x^{3/2}}-\frac{8 b (a-b x)^{3/2}}{35 a^2 x^{5/2}}-\frac{2 (a-b x)^{3/2}}{7 a x^{7/2}}","-\frac{16 b^2 (a-b x)^{3/2}}{105 a^3 x^{3/2}}-\frac{8 b (a-b x)^{3/2}}{35 a^2 x^{5/2}}-\frac{2 (a-b x)^{3/2}}{7 a x^{7/2}}",1,"(-2*(a - b*x)^(3/2))/(7*a*x^(7/2)) - (8*b*(a - b*x)^(3/2))/(35*a^2*x^(5/2)) - (16*b^2*(a - b*x)^(3/2))/(105*a^3*x^(3/2))","A",3,2,16,0.1250,1,"{45, 37}"
505,1,108,0,0.0315586,"\int x^{5/2} \sqrt{2+b x} \, dx","Int[x^(5/2)*Sqrt[2 + b*x],x]","-\frac{5 x^{3/2} \sqrt{b x+2}}{24 b^2}+\frac{5 \sqrt{x} \sqrt{b x+2}}{8 b^3}-\frac{5 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{4 b^{7/2}}+\frac{1}{4} x^{7/2} \sqrt{b x+2}+\frac{x^{5/2} \sqrt{b x+2}}{12 b}","-\frac{5 x^{3/2} \sqrt{b x+2}}{24 b^2}+\frac{5 \sqrt{x} \sqrt{b x+2}}{8 b^3}-\frac{5 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{4 b^{7/2}}+\frac{1}{4} x^{7/2} \sqrt{b x+2}+\frac{x^{5/2} \sqrt{b x+2}}{12 b}",1,"(5*Sqrt[x]*Sqrt[2 + b*x])/(8*b^3) - (5*x^(3/2)*Sqrt[2 + b*x])/(24*b^2) + (x^(5/2)*Sqrt[2 + b*x])/(12*b) + (x^(7/2)*Sqrt[2 + b*x])/4 - (5*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/(4*b^(7/2))","A",6,3,15,0.2000,1,"{50, 54, 215}"
506,1,84,0,0.0200607,"\int x^{3/2} \sqrt{2+b x} \, dx","Int[x^(3/2)*Sqrt[2 + b*x],x]","-\frac{\sqrt{x} \sqrt{b x+2}}{2 b^2}+\frac{\sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{5/2}}+\frac{1}{3} x^{5/2} \sqrt{b x+2}+\frac{x^{3/2} \sqrt{b x+2}}{6 b}","-\frac{\sqrt{x} \sqrt{b x+2}}{2 b^2}+\frac{\sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{5/2}}+\frac{1}{3} x^{5/2} \sqrt{b x+2}+\frac{x^{3/2} \sqrt{b x+2}}{6 b}",1,"-(Sqrt[x]*Sqrt[2 + b*x])/(2*b^2) + (x^(3/2)*Sqrt[2 + b*x])/(6*b) + (x^(5/2)*Sqrt[2 + b*x])/3 + ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[2]]/b^(5/2)","A",5,3,15,0.2000,1,"{50, 54, 215}"
507,1,64,0,0.014512,"\int \sqrt{x} \sqrt{2+b x} \, dx","Int[Sqrt[x]*Sqrt[2 + b*x],x]","-\frac{\sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{3/2}}+\frac{1}{2} x^{3/2} \sqrt{b x+2}+\frac{\sqrt{x} \sqrt{b x+2}}{2 b}","-\frac{\sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{3/2}}+\frac{1}{2} x^{3/2} \sqrt{b x+2}+\frac{\sqrt{x} \sqrt{b x+2}}{2 b}",1,"(Sqrt[x]*Sqrt[2 + b*x])/(2*b) + (x^(3/2)*Sqrt[2 + b*x])/2 - ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[2]]/b^(3/2)","A",4,3,15,0.2000,1,"{50, 54, 215}"
508,1,40,0,0.007761,"\int \frac{\sqrt{2+b x}}{\sqrt{x}} \, dx","Int[Sqrt[2 + b*x]/Sqrt[x],x]","\sqrt{x} \sqrt{b x+2}+\frac{2 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{\sqrt{b}}","\sqrt{x} \sqrt{b x+2}+\frac{2 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{\sqrt{b}}",1,"Sqrt[x]*Sqrt[2 + b*x] + (2*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/Sqrt[b]","A",3,3,15,0.2000,1,"{50, 54, 215}"
509,1,41,0,0.009401,"\int \frac{\sqrt{2+b x}}{x^{3/2}} \, dx","Int[Sqrt[2 + b*x]/x^(3/2),x]","2 \sqrt{b} \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)-\frac{2 \sqrt{b x+2}}{\sqrt{x}}","2 \sqrt{b} \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)-\frac{2 \sqrt{b x+2}}{\sqrt{x}}",1,"(-2*Sqrt[2 + b*x])/Sqrt[x] + 2*Sqrt[b]*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[2]]","A",3,3,15,0.2000,1,"{47, 54, 215}"
510,1,18,0,0.0014173,"\int \frac{\sqrt{2+b x}}{x^{5/2}} \, dx","Int[Sqrt[2 + b*x]/x^(5/2),x]","-\frac{(b x+2)^{3/2}}{3 x^{3/2}}","-\frac{(b x+2)^{3/2}}{3 x^{3/2}}",1,"-(2 + b*x)^(3/2)/(3*x^(3/2))","A",1,1,15,0.06667,1,"{37}"
511,1,38,0,0.0039924,"\int \frac{\sqrt{2+b x}}{x^{7/2}} \, dx","Int[Sqrt[2 + b*x]/x^(7/2),x]","\frac{b (b x+2)^{3/2}}{15 x^{3/2}}-\frac{(b x+2)^{3/2}}{5 x^{5/2}}","\frac{b (b x+2)^{3/2}}{15 x^{3/2}}-\frac{(b x+2)^{3/2}}{5 x^{5/2}}",1,"-(2 + b*x)^(3/2)/(5*x^(5/2)) + (b*(2 + b*x)^(3/2))/(15*x^(3/2))","A",2,2,15,0.1333,1,"{45, 37}"
512,1,59,0,0.0082292,"\int \frac{\sqrt{2+b x}}{x^{9/2}} \, dx","Int[Sqrt[2 + b*x]/x^(9/2),x]","-\frac{2 b^2 (b x+2)^{3/2}}{105 x^{3/2}}+\frac{2 b (b x+2)^{3/2}}{35 x^{5/2}}-\frac{(b x+2)^{3/2}}{7 x^{7/2}}","-\frac{2 b^2 (b x+2)^{3/2}}{105 x^{3/2}}+\frac{2 b (b x+2)^{3/2}}{35 x^{5/2}}-\frac{(b x+2)^{3/2}}{7 x^{7/2}}",1,"-(2 + b*x)^(3/2)/(7*x^(7/2)) + (2*b*(2 + b*x)^(3/2))/(35*x^(5/2)) - (2*b^2*(2 + b*x)^(3/2))/(105*x^(3/2))","A",3,2,15,0.1333,1,"{45, 37}"
513,1,112,0,0.0286051,"\int x^{5/2} \sqrt{2-b x} \, dx","Int[x^(5/2)*Sqrt[2 - b*x],x]","-\frac{5 x^{3/2} \sqrt{2-b x}}{24 b^2}-\frac{5 \sqrt{x} \sqrt{2-b x}}{8 b^3}+\frac{5 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{4 b^{7/2}}+\frac{1}{4} x^{7/2} \sqrt{2-b x}-\frac{x^{5/2} \sqrt{2-b x}}{12 b}","-\frac{5 x^{3/2} \sqrt{2-b x}}{24 b^2}-\frac{5 \sqrt{x} \sqrt{2-b x}}{8 b^3}+\frac{5 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{4 b^{7/2}}+\frac{1}{4} x^{7/2} \sqrt{2-b x}-\frac{x^{5/2} \sqrt{2-b x}}{12 b}",1,"(-5*Sqrt[x]*Sqrt[2 - b*x])/(8*b^3) - (5*x^(3/2)*Sqrt[2 - b*x])/(24*b^2) - (x^(5/2)*Sqrt[2 - b*x])/(12*b) + (x^(7/2)*Sqrt[2 - b*x])/4 + (5*ArcSin[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/(4*b^(7/2))","A",6,3,16,0.1875,1,"{50, 54, 216}"
514,1,87,0,0.022504,"\int x^{3/2} \sqrt{2-b x} \, dx","Int[x^(3/2)*Sqrt[2 - b*x],x]","-\frac{\sqrt{x} \sqrt{2-b x}}{2 b^2}+\frac{\sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{5/2}}+\frac{1}{3} x^{5/2} \sqrt{2-b x}-\frac{x^{3/2} \sqrt{2-b x}}{6 b}","-\frac{\sqrt{x} \sqrt{2-b x}}{2 b^2}+\frac{\sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{5/2}}+\frac{1}{3} x^{5/2} \sqrt{2-b x}-\frac{x^{3/2} \sqrt{2-b x}}{6 b}",1,"-(Sqrt[x]*Sqrt[2 - b*x])/(2*b^2) - (x^(3/2)*Sqrt[2 - b*x])/(6*b) + (x^(5/2)*Sqrt[2 - b*x])/3 + ArcSin[(Sqrt[b]*Sqrt[x])/Sqrt[2]]/b^(5/2)","A",5,3,16,0.1875,1,"{50, 54, 216}"
515,1,65,0,0.0149726,"\int \sqrt{x} \sqrt{2-b x} \, dx","Int[Sqrt[x]*Sqrt[2 - b*x],x]","\frac{\sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{3/2}}+\frac{1}{2} x^{3/2} \sqrt{2-b x}-\frac{\sqrt{x} \sqrt{2-b x}}{2 b}","\frac{\sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{3/2}}+\frac{1}{2} x^{3/2} \sqrt{2-b x}-\frac{\sqrt{x} \sqrt{2-b x}}{2 b}",1,"-(Sqrt[x]*Sqrt[2 - b*x])/(2*b) + (x^(3/2)*Sqrt[2 - b*x])/2 + ArcSin[(Sqrt[b]*Sqrt[x])/Sqrt[2]]/b^(3/2)","A",4,3,16,0.1875,1,"{50, 54, 216}"
516,1,41,0,0.0076871,"\int \frac{\sqrt{2-b x}}{\sqrt{x}} \, dx","Int[Sqrt[2 - b*x]/Sqrt[x],x]","\sqrt{x} \sqrt{2-b x}+\frac{2 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{\sqrt{b}}","\sqrt{x} \sqrt{2-b x}+\frac{2 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{\sqrt{b}}",1,"Sqrt[x]*Sqrt[2 - b*x] + (2*ArcSin[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/Sqrt[b]","A",3,3,16,0.1875,1,"{50, 54, 216}"
517,1,42,0,0.0091793,"\int \frac{\sqrt{2-b x}}{x^{3/2}} \, dx","Int[Sqrt[2 - b*x]/x^(3/2),x]","-\frac{2 \sqrt{2-b x}}{\sqrt{x}}-2 \sqrt{b} \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)","-\frac{2 \sqrt{2-b x}}{\sqrt{x}}-2 \sqrt{b} \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)",1,"(-2*Sqrt[2 - b*x])/Sqrt[x] - 2*Sqrt[b]*ArcSin[(Sqrt[b]*Sqrt[x])/Sqrt[2]]","A",3,3,16,0.1875,1,"{47, 54, 216}"
518,1,19,0,0.0014399,"\int \frac{\sqrt{2-b x}}{x^{5/2}} \, dx","Int[Sqrt[2 - b*x]/x^(5/2),x]","-\frac{(2-b x)^{3/2}}{3 x^{3/2}}","-\frac{(2-b x)^{3/2}}{3 x^{3/2}}",1,"-(2 - b*x)^(3/2)/(3*x^(3/2))","A",1,1,16,0.06250,1,"{37}"
519,1,40,0,0.0041434,"\int \frac{\sqrt{2-b x}}{x^{7/2}} \, dx","Int[Sqrt[2 - b*x]/x^(7/2),x]","-\frac{b (2-b x)^{3/2}}{15 x^{3/2}}-\frac{(2-b x)^{3/2}}{5 x^{5/2}}","-\frac{b (2-b x)^{3/2}}{15 x^{3/2}}-\frac{(2-b x)^{3/2}}{5 x^{5/2}}",1,"-(2 - b*x)^(3/2)/(5*x^(5/2)) - (b*(2 - b*x)^(3/2))/(15*x^(3/2))","A",2,2,16,0.1250,1,"{45, 37}"
520,1,62,0,0.0080486,"\int \frac{\sqrt{2-b x}}{x^{9/2}} \, dx","Int[Sqrt[2 - b*x]/x^(9/2),x]","-\frac{2 b^2 (2-b x)^{3/2}}{105 x^{3/2}}-\frac{2 b (2-b x)^{3/2}}{35 x^{5/2}}-\frac{(2-b x)^{3/2}}{7 x^{7/2}}","-\frac{2 b^2 (2-b x)^{3/2}}{105 x^{3/2}}-\frac{2 b (2-b x)^{3/2}}{35 x^{5/2}}-\frac{(2-b x)^{3/2}}{7 x^{7/2}}",1,"-(2 - b*x)^(3/2)/(7*x^(7/2)) - (2*b*(2 - b*x)^(3/2))/(35*x^(5/2)) - (2*b^2*(2 - b*x)^(3/2))/(105*x^(3/2))","A",3,2,16,0.1250,1,"{45, 37}"
521,1,143,0,0.051225,"\int x^{5/2} (a+b x)^{3/2} \, dx","Int[x^(5/2)*(a + b*x)^(3/2),x]","-\frac{a^3 x^{3/2} \sqrt{a+b x}}{64 b^2}+\frac{3 a^4 \sqrt{x} \sqrt{a+b x}}{128 b^3}-\frac{3 a^5 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{128 b^{7/2}}+\frac{a^2 x^{5/2} \sqrt{a+b x}}{80 b}+\frac{3}{40} a x^{7/2} \sqrt{a+b x}+\frac{1}{5} x^{7/2} (a+b x)^{3/2}","-\frac{a^3 x^{3/2} \sqrt{a+b x}}{64 b^2}+\frac{3 a^4 \sqrt{x} \sqrt{a+b x}}{128 b^3}-\frac{3 a^5 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{128 b^{7/2}}+\frac{a^2 x^{5/2} \sqrt{a+b x}}{80 b}+\frac{3}{40} a x^{7/2} \sqrt{a+b x}+\frac{1}{5} x^{7/2} (a+b x)^{3/2}",1,"(3*a^4*Sqrt[x]*Sqrt[a + b*x])/(128*b^3) - (a^3*x^(3/2)*Sqrt[a + b*x])/(64*b^2) + (a^2*x^(5/2)*Sqrt[a + b*x])/(80*b) + (3*a*x^(7/2)*Sqrt[a + b*x])/40 + (x^(7/2)*(a + b*x)^(3/2))/5 - (3*a^5*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a + b*x]])/(128*b^(7/2))","A",8,4,15,0.2667,1,"{50, 63, 217, 206}"
522,1,119,0,0.0379329,"\int x^{3/2} (a+b x)^{3/2} \, dx","Int[x^(3/2)*(a + b*x)^(3/2),x]","-\frac{3 a^3 \sqrt{x} \sqrt{a+b x}}{64 b^2}+\frac{3 a^4 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{64 b^{5/2}}+\frac{a^2 x^{3/2} \sqrt{a+b x}}{32 b}+\frac{1}{8} a x^{5/2} \sqrt{a+b x}+\frac{1}{4} x^{5/2} (a+b x)^{3/2}","-\frac{3 a^3 \sqrt{x} \sqrt{a+b x}}{64 b^2}+\frac{3 a^4 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{64 b^{5/2}}+\frac{a^2 x^{3/2} \sqrt{a+b x}}{32 b}+\frac{1}{8} a x^{5/2} \sqrt{a+b x}+\frac{1}{4} x^{5/2} (a+b x)^{3/2}",1,"(-3*a^3*Sqrt[x]*Sqrt[a + b*x])/(64*b^2) + (a^2*x^(3/2)*Sqrt[a + b*x])/(32*b) + (a*x^(5/2)*Sqrt[a + b*x])/8 + (x^(5/2)*(a + b*x)^(3/2))/4 + (3*a^4*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a + b*x]])/(64*b^(5/2))","A",7,4,15,0.2667,1,"{50, 63, 217, 206}"
523,1,95,0,0.0290658,"\int \sqrt{x} (a+b x)^{3/2} \, dx","Int[Sqrt[x]*(a + b*x)^(3/2),x]","-\frac{a^3 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{8 b^{3/2}}+\frac{a^2 \sqrt{x} \sqrt{a+b x}}{8 b}+\frac{1}{4} a x^{3/2} \sqrt{a+b x}+\frac{1}{3} x^{3/2} (a+b x)^{3/2}","-\frac{a^3 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{8 b^{3/2}}+\frac{a^2 \sqrt{x} \sqrt{a+b x}}{8 b}+\frac{1}{4} a x^{3/2} \sqrt{a+b x}+\frac{1}{3} x^{3/2} (a+b x)^{3/2}",1,"(a^2*Sqrt[x]*Sqrt[a + b*x])/(8*b) + (a*x^(3/2)*Sqrt[a + b*x])/4 + (x^(3/2)*(a + b*x)^(3/2))/3 - (a^3*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a + b*x]])/(8*b^(3/2))","A",6,4,15,0.2667,1,"{50, 63, 217, 206}"
524,1,71,0,0.0215816,"\int \frac{(a+b x)^{3/2}}{\sqrt{x}} \, dx","Int[(a + b*x)^(3/2)/Sqrt[x],x]","\frac{3 a^2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{4 \sqrt{b}}+\frac{3}{4} a \sqrt{x} \sqrt{a+b x}+\frac{1}{2} \sqrt{x} (a+b x)^{3/2}","\frac{3 a^2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{4 \sqrt{b}}+\frac{3}{4} a \sqrt{x} \sqrt{a+b x}+\frac{1}{2} \sqrt{x} (a+b x)^{3/2}",1,"(3*a*Sqrt[x]*Sqrt[a + b*x])/4 + (Sqrt[x]*(a + b*x)^(3/2))/2 + (3*a^2*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a + b*x]])/(4*Sqrt[b])","A",5,4,15,0.2667,1,"{50, 63, 217, 206}"
525,1,63,0,0.021407,"\int \frac{(a+b x)^{3/2}}{x^{3/2}} \, dx","Int[(a + b*x)^(3/2)/x^(3/2),x]","-\frac{2 (a+b x)^{3/2}}{\sqrt{x}}+3 b \sqrt{x} \sqrt{a+b x}+3 a \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)","-\frac{2 (a+b x)^{3/2}}{\sqrt{x}}+3 b \sqrt{x} \sqrt{a+b x}+3 a \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)",1,"3*b*Sqrt[x]*Sqrt[a + b*x] - (2*(a + b*x)^(3/2))/Sqrt[x] + 3*a*Sqrt[b]*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a + b*x]]","A",5,5,15,0.3333,1,"{47, 50, 63, 217, 206}"
526,1,64,0,0.0214081,"\int \frac{(a+b x)^{3/2}}{x^{5/2}} \, dx","Int[(a + b*x)^(3/2)/x^(5/2),x]","2 b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)-\frac{2 (a+b x)^{3/2}}{3 x^{3/2}}-\frac{2 b \sqrt{a+b x}}{\sqrt{x}}","2 b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)-\frac{2 (a+b x)^{3/2}}{3 x^{3/2}}-\frac{2 b \sqrt{a+b x}}{\sqrt{x}}",1,"(-2*b*Sqrt[a + b*x])/Sqrt[x] - (2*(a + b*x)^(3/2))/(3*x^(3/2)) + 2*b^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a + b*x]]","A",5,4,15,0.2667,1,"{47, 63, 217, 206}"
527,1,149,0,0.0532699,"\int x^{5/2} (a-b x)^{3/2} \, dx","Int[x^(5/2)*(a - b*x)^(3/2),x]","-\frac{a^3 x^{3/2} \sqrt{a-b x}}{64 b^2}-\frac{3 a^4 \sqrt{x} \sqrt{a-b x}}{128 b^3}+\frac{3 a^5 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)}{128 b^{7/2}}-\frac{a^2 x^{5/2} \sqrt{a-b x}}{80 b}+\frac{3}{40} a x^{7/2} \sqrt{a-b x}+\frac{1}{5} x^{7/2} (a-b x)^{3/2}","-\frac{a^3 x^{3/2} \sqrt{a-b x}}{64 b^2}-\frac{3 a^4 \sqrt{x} \sqrt{a-b x}}{128 b^3}+\frac{3 a^5 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)}{128 b^{7/2}}-\frac{a^2 x^{5/2} \sqrt{a-b x}}{80 b}+\frac{3}{40} a x^{7/2} \sqrt{a-b x}+\frac{1}{5} x^{7/2} (a-b x)^{3/2}",1,"(-3*a^4*Sqrt[x]*Sqrt[a - b*x])/(128*b^3) - (a^3*x^(3/2)*Sqrt[a - b*x])/(64*b^2) - (a^2*x^(5/2)*Sqrt[a - b*x])/(80*b) + (3*a*x^(7/2)*Sqrt[a - b*x])/40 + (x^(7/2)*(a - b*x)^(3/2))/5 + (3*a^5*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a - b*x]])/(128*b^(7/2))","A",8,4,16,0.2500,1,"{50, 63, 217, 203}"
528,1,124,0,0.0414726,"\int x^{3/2} (a-b x)^{3/2} \, dx","Int[x^(3/2)*(a - b*x)^(3/2),x]","-\frac{3 a^3 \sqrt{x} \sqrt{a-b x}}{64 b^2}+\frac{3 a^4 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)}{64 b^{5/2}}-\frac{a^2 x^{3/2} \sqrt{a-b x}}{32 b}+\frac{1}{8} a x^{5/2} \sqrt{a-b x}+\frac{1}{4} x^{5/2} (a-b x)^{3/2}","-\frac{3 a^3 \sqrt{x} \sqrt{a-b x}}{64 b^2}+\frac{3 a^4 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)}{64 b^{5/2}}-\frac{a^2 x^{3/2} \sqrt{a-b x}}{32 b}+\frac{1}{8} a x^{5/2} \sqrt{a-b x}+\frac{1}{4} x^{5/2} (a-b x)^{3/2}",1,"(-3*a^3*Sqrt[x]*Sqrt[a - b*x])/(64*b^2) - (a^2*x^(3/2)*Sqrt[a - b*x])/(32*b) + (a*x^(5/2)*Sqrt[a - b*x])/8 + (x^(5/2)*(a - b*x)^(3/2))/4 + (3*a^4*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a - b*x]])/(64*b^(5/2))","A",7,4,16,0.2500,1,"{50, 63, 217, 203}"
529,1,99,0,0.0309863,"\int \sqrt{x} (a-b x)^{3/2} \, dx","Int[Sqrt[x]*(a - b*x)^(3/2),x]","\frac{a^3 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)}{8 b^{3/2}}-\frac{a^2 \sqrt{x} \sqrt{a-b x}}{8 b}+\frac{1}{4} a x^{3/2} \sqrt{a-b x}+\frac{1}{3} x^{3/2} (a-b x)^{3/2}","\frac{a^3 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)}{8 b^{3/2}}-\frac{a^2 \sqrt{x} \sqrt{a-b x}}{8 b}+\frac{1}{4} a x^{3/2} \sqrt{a-b x}+\frac{1}{3} x^{3/2} (a-b x)^{3/2}",1,"-(a^2*Sqrt[x]*Sqrt[a - b*x])/(8*b) + (a*x^(3/2)*Sqrt[a - b*x])/4 + (x^(3/2)*(a - b*x)^(3/2))/3 + (a^3*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a - b*x]])/(8*b^(3/2))","A",6,4,16,0.2500,1,"{50, 63, 217, 203}"
530,1,74,0,0.021048,"\int \frac{(a-b x)^{3/2}}{\sqrt{x}} \, dx","Int[(a - b*x)^(3/2)/Sqrt[x],x]","\frac{3 a^2 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)}{4 \sqrt{b}}+\frac{3}{4} a \sqrt{x} \sqrt{a-b x}+\frac{1}{2} \sqrt{x} (a-b x)^{3/2}","\frac{3 a^2 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)}{4 \sqrt{b}}+\frac{3}{4} a \sqrt{x} \sqrt{a-b x}+\frac{1}{2} \sqrt{x} (a-b x)^{3/2}",1,"(3*a*Sqrt[x]*Sqrt[a - b*x])/4 + (Sqrt[x]*(a - b*x)^(3/2))/2 + (3*a^2*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a - b*x]])/(4*Sqrt[b])","A",5,4,16,0.2500,1,"{50, 63, 217, 203}"
531,1,66,0,0.0203585,"\int \frac{(a-b x)^{3/2}}{x^{3/2}} \, dx","Int[(a - b*x)^(3/2)/x^(3/2),x]","-\frac{2 (a-b x)^{3/2}}{\sqrt{x}}-3 b \sqrt{x} \sqrt{a-b x}-3 a \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)","-\frac{2 (a-b x)^{3/2}}{\sqrt{x}}-3 b \sqrt{x} \sqrt{a-b x}-3 a \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)",1,"-3*b*Sqrt[x]*Sqrt[a - b*x] - (2*(a - b*x)^(3/2))/Sqrt[x] - 3*a*Sqrt[b]*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a - b*x]]","A",5,5,16,0.3125,1,"{47, 50, 63, 217, 203}"
532,1,67,0,0.0215647,"\int \frac{(a-b x)^{3/2}}{x^{5/2}} \, dx","Int[(a - b*x)^(3/2)/x^(5/2),x]","2 b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)-\frac{2 (a-b x)^{3/2}}{3 x^{3/2}}+\frac{2 b \sqrt{a-b x}}{\sqrt{x}}","2 b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)-\frac{2 (a-b x)^{3/2}}{3 x^{3/2}}+\frac{2 b \sqrt{a-b x}}{\sqrt{x}}",1,"(2*b*Sqrt[a - b*x])/Sqrt[x] - (2*(a - b*x)^(3/2))/(3*x^(3/2)) + 2*b^(3/2)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a - b*x]]","A",5,4,16,0.2500,1,"{47, 63, 217, 203}"
533,1,126,0,0.034079,"\int x^{5/2} (2+b x)^{3/2} \, dx","Int[x^(5/2)*(2 + b*x)^(3/2),x]","-\frac{x^{3/2} \sqrt{b x+2}}{8 b^2}+\frac{3 \sqrt{x} \sqrt{b x+2}}{8 b^3}-\frac{3 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{4 b^{7/2}}+\frac{1}{5} x^{7/2} (b x+2)^{3/2}+\frac{3}{20} x^{7/2} \sqrt{b x+2}+\frac{x^{5/2} \sqrt{b x+2}}{20 b}","-\frac{x^{3/2} \sqrt{b x+2}}{8 b^2}+\frac{3 \sqrt{x} \sqrt{b x+2}}{8 b^3}-\frac{3 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{4 b^{7/2}}+\frac{1}{5} x^{7/2} (b x+2)^{3/2}+\frac{3}{20} x^{7/2} \sqrt{b x+2}+\frac{x^{5/2} \sqrt{b x+2}}{20 b}",1,"(3*Sqrt[x]*Sqrt[2 + b*x])/(8*b^3) - (x^(3/2)*Sqrt[2 + b*x])/(8*b^2) + (x^(5/2)*Sqrt[2 + b*x])/(20*b) + (3*x^(7/2)*Sqrt[2 + b*x])/20 + (x^(7/2)*(2 + b*x)^(3/2))/5 - (3*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/(4*b^(7/2))","A",7,3,15,0.2000,1,"{50, 54, 215}"
534,1,105,0,0.0255435,"\int x^{3/2} (2+b x)^{3/2} \, dx","Int[x^(3/2)*(2 + b*x)^(3/2),x]","-\frac{3 \sqrt{x} \sqrt{b x+2}}{8 b^2}+\frac{3 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{4 b^{5/2}}+\frac{1}{4} x^{5/2} (b x+2)^{3/2}+\frac{1}{4} x^{5/2} \sqrt{b x+2}+\frac{x^{3/2} \sqrt{b x+2}}{8 b}","-\frac{3 \sqrt{x} \sqrt{b x+2}}{8 b^2}+\frac{3 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{4 b^{5/2}}+\frac{1}{4} x^{5/2} (b x+2)^{3/2}+\frac{1}{4} x^{5/2} \sqrt{b x+2}+\frac{x^{3/2} \sqrt{b x+2}}{8 b}",1,"(-3*Sqrt[x]*Sqrt[2 + b*x])/(8*b^2) + (x^(3/2)*Sqrt[2 + b*x])/(8*b) + (x^(5/2)*Sqrt[2 + b*x])/4 + (x^(5/2)*(2 + b*x)^(3/2))/4 + (3*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/(4*b^(5/2))","A",6,3,15,0.2000,1,"{50, 54, 215}"
535,1,82,0,0.0163102,"\int \sqrt{x} (2+b x)^{3/2} \, dx","Int[Sqrt[x]*(2 + b*x)^(3/2),x]","-\frac{\sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{3/2}}+\frac{1}{3} x^{3/2} (b x+2)^{3/2}+\frac{1}{2} x^{3/2} \sqrt{b x+2}+\frac{\sqrt{x} \sqrt{b x+2}}{2 b}","-\frac{\sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{3/2}}+\frac{1}{3} x^{3/2} (b x+2)^{3/2}+\frac{1}{2} x^{3/2} \sqrt{b x+2}+\frac{\sqrt{x} \sqrt{b x+2}}{2 b}",1,"(Sqrt[x]*Sqrt[2 + b*x])/(2*b) + (x^(3/2)*Sqrt[2 + b*x])/2 + (x^(3/2)*(2 + b*x)^(3/2))/3 - ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[2]]/b^(3/2)","A",5,3,15,0.2000,1,"{50, 54, 215}"
536,1,61,0,0.0109375,"\int \frac{(2+b x)^{3/2}}{\sqrt{x}} \, dx","Int[(2 + b*x)^(3/2)/Sqrt[x],x]","\frac{1}{2} \sqrt{x} (b x+2)^{3/2}+\frac{3}{2} \sqrt{x} \sqrt{b x+2}+\frac{3 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{\sqrt{b}}","\frac{1}{2} \sqrt{x} (b x+2)^{3/2}+\frac{3}{2} \sqrt{x} \sqrt{b x+2}+\frac{3 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{\sqrt{b}}",1,"(3*Sqrt[x]*Sqrt[2 + b*x])/2 + (Sqrt[x]*(2 + b*x)^(3/2))/2 + (3*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/Sqrt[b]","A",4,3,15,0.2000,1,"{50, 54, 215}"
537,1,58,0,0.0117686,"\int \frac{(2+b x)^{3/2}}{x^{3/2}} \, dx","Int[(2 + b*x)^(3/2)/x^(3/2),x]","-\frac{2 (b x+2)^{3/2}}{\sqrt{x}}+3 b \sqrt{x} \sqrt{b x+2}+6 \sqrt{b} \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)","-\frac{2 (b x+2)^{3/2}}{\sqrt{x}}+3 b \sqrt{x} \sqrt{b x+2}+6 \sqrt{b} \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)",1,"3*b*Sqrt[x]*Sqrt[2 + b*x] - (2*(2 + b*x)^(3/2))/Sqrt[x] + 6*Sqrt[b]*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[2]]","A",4,4,15,0.2667,1,"{47, 50, 54, 215}"
538,1,60,0,0.013916,"\int \frac{(2+b x)^{3/2}}{x^{5/2}} \, dx","Int[(2 + b*x)^(3/2)/x^(5/2),x]","2 b^{3/2} \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)-\frac{2 (b x+2)^{3/2}}{3 x^{3/2}}-\frac{2 b \sqrt{b x+2}}{\sqrt{x}}","2 b^{3/2} \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)-\frac{2 (b x+2)^{3/2}}{3 x^{3/2}}-\frac{2 b \sqrt{b x+2}}{\sqrt{x}}",1,"(-2*b*Sqrt[2 + b*x])/Sqrt[x] - (2*(2 + b*x)^(3/2))/(3*x^(3/2)) + 2*b^(3/2)*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[2]]","A",4,3,15,0.2000,1,"{47, 54, 215}"
539,1,131,0,0.0399673,"\int x^{5/2} (2-b x)^{3/2} \, dx","Int[x^(5/2)*(2 - b*x)^(3/2),x]","-\frac{x^{3/2} \sqrt{2-b x}}{8 b^2}-\frac{3 \sqrt{x} \sqrt{2-b x}}{8 b^3}+\frac{3 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{4 b^{7/2}}+\frac{1}{5} x^{7/2} (2-b x)^{3/2}+\frac{3}{20} x^{7/2} \sqrt{2-b x}-\frac{x^{5/2} \sqrt{2-b x}}{20 b}","-\frac{x^{3/2} \sqrt{2-b x}}{8 b^2}-\frac{3 \sqrt{x} \sqrt{2-b x}}{8 b^3}+\frac{3 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{4 b^{7/2}}+\frac{1}{5} x^{7/2} (2-b x)^{3/2}+\frac{3}{20} x^{7/2} \sqrt{2-b x}-\frac{x^{5/2} \sqrt{2-b x}}{20 b}",1,"(-3*Sqrt[x]*Sqrt[2 - b*x])/(8*b^3) - (x^(3/2)*Sqrt[2 - b*x])/(8*b^2) - (x^(5/2)*Sqrt[2 - b*x])/(20*b) + (3*x^(7/2)*Sqrt[2 - b*x])/20 + (x^(7/2)*(2 - b*x)^(3/2))/5 + (3*ArcSin[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/(4*b^(7/2))","A",7,3,16,0.1875,1,"{50, 54, 216}"
540,1,109,0,0.0279175,"\int x^{3/2} (2-b x)^{3/2} \, dx","Int[x^(3/2)*(2 - b*x)^(3/2),x]","-\frac{3 \sqrt{x} \sqrt{2-b x}}{8 b^2}+\frac{3 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{4 b^{5/2}}+\frac{1}{4} x^{5/2} (2-b x)^{3/2}+\frac{1}{4} x^{5/2} \sqrt{2-b x}-\frac{x^{3/2} \sqrt{2-b x}}{8 b}","-\frac{3 \sqrt{x} \sqrt{2-b x}}{8 b^2}+\frac{3 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{4 b^{5/2}}+\frac{1}{4} x^{5/2} (2-b x)^{3/2}+\frac{1}{4} x^{5/2} \sqrt{2-b x}-\frac{x^{3/2} \sqrt{2-b x}}{8 b}",1,"(-3*Sqrt[x]*Sqrt[2 - b*x])/(8*b^2) - (x^(3/2)*Sqrt[2 - b*x])/(8*b) + (x^(5/2)*Sqrt[2 - b*x])/4 + (x^(5/2)*(2 - b*x)^(3/2))/4 + (3*ArcSin[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/(4*b^(5/2))","A",6,3,16,0.1875,1,"{50, 54, 216}"
541,1,84,0,0.0157307,"\int \sqrt{x} (2-b x)^{3/2} \, dx","Int[Sqrt[x]*(2 - b*x)^(3/2),x]","\frac{\sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{3/2}}+\frac{1}{3} x^{3/2} (2-b x)^{3/2}+\frac{1}{2} x^{3/2} \sqrt{2-b x}-\frac{\sqrt{x} \sqrt{2-b x}}{2 b}","\frac{\sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{3/2}}+\frac{1}{3} x^{3/2} (2-b x)^{3/2}+\frac{1}{2} x^{3/2} \sqrt{2-b x}-\frac{\sqrt{x} \sqrt{2-b x}}{2 b}",1,"-(Sqrt[x]*Sqrt[2 - b*x])/(2*b) + (x^(3/2)*Sqrt[2 - b*x])/2 + (x^(3/2)*(2 - b*x)^(3/2))/3 + ArcSin[(Sqrt[b]*Sqrt[x])/Sqrt[2]]/b^(3/2)","A",5,3,16,0.1875,1,"{50, 54, 216}"
542,1,63,0,0.011925,"\int \frac{(2-b x)^{3/2}}{\sqrt{x}} \, dx","Int[(2 - b*x)^(3/2)/Sqrt[x],x]","\frac{1}{2} \sqrt{x} (2-b x)^{3/2}+\frac{3}{2} \sqrt{x} \sqrt{2-b x}+\frac{3 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{\sqrt{b}}","\frac{1}{2} \sqrt{x} (2-b x)^{3/2}+\frac{3}{2} \sqrt{x} \sqrt{2-b x}+\frac{3 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{\sqrt{b}}",1,"(3*Sqrt[x]*Sqrt[2 - b*x])/2 + (Sqrt[x]*(2 - b*x)^(3/2))/2 + (3*ArcSin[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/Sqrt[b]","A",4,3,16,0.1875,1,"{50, 54, 216}"
543,1,60,0,0.0115209,"\int \frac{(2-b x)^{3/2}}{x^{3/2}} \, dx","Int[(2 - b*x)^(3/2)/x^(3/2),x]","-\frac{2 (2-b x)^{3/2}}{\sqrt{x}}-3 b \sqrt{x} \sqrt{2-b x}-6 \sqrt{b} \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)","-\frac{2 (2-b x)^{3/2}}{\sqrt{x}}-3 b \sqrt{x} \sqrt{2-b x}-6 \sqrt{b} \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)",1,"-3*b*Sqrt[x]*Sqrt[2 - b*x] - (2*(2 - b*x)^(3/2))/Sqrt[x] - 6*Sqrt[b]*ArcSin[(Sqrt[b]*Sqrt[x])/Sqrt[2]]","A",4,4,16,0.2500,1,"{47, 50, 54, 216}"
544,1,62,0,0.0132896,"\int \frac{(2-b x)^{3/2}}{x^{5/2}} \, dx","Int[(2 - b*x)^(3/2)/x^(5/2),x]","2 b^{3/2} \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)-\frac{2 (2-b x)^{3/2}}{3 x^{3/2}}+\frac{2 b \sqrt{2-b x}}{\sqrt{x}}","2 b^{3/2} \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)-\frac{2 (2-b x)^{3/2}}{3 x^{3/2}}+\frac{2 b \sqrt{2-b x}}{\sqrt{x}}",1,"(2*b*Sqrt[2 - b*x])/Sqrt[x] - (2*(2 - b*x)^(3/2))/(3*x^(3/2)) + 2*b^(3/2)*ArcSin[(Sqrt[b]*Sqrt[x])/Sqrt[2]]","A",4,3,16,0.1875,1,"{47, 54, 216}"
545,1,164,0,0.0632622,"\int x^{5/2} (a+b x)^{5/2} \, dx","Int[x^(5/2)*(a + b*x)^(5/2),x]","-\frac{5 a^4 x^{3/2} \sqrt{a+b x}}{768 b^2}+\frac{5 a^5 \sqrt{x} \sqrt{a+b x}}{512 b^3}-\frac{5 a^6 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{512 b^{7/2}}+\frac{a^3 x^{5/2} \sqrt{a+b x}}{192 b}+\frac{1}{32} a^2 x^{7/2} \sqrt{a+b x}+\frac{1}{12} a x^{7/2} (a+b x)^{3/2}+\frac{1}{6} x^{7/2} (a+b x)^{5/2}","-\frac{5 a^4 x^{3/2} \sqrt{a+b x}}{768 b^2}+\frac{5 a^5 \sqrt{x} \sqrt{a+b x}}{512 b^3}-\frac{5 a^6 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{512 b^{7/2}}+\frac{a^3 x^{5/2} \sqrt{a+b x}}{192 b}+\frac{1}{32} a^2 x^{7/2} \sqrt{a+b x}+\frac{1}{12} a x^{7/2} (a+b x)^{3/2}+\frac{1}{6} x^{7/2} (a+b x)^{5/2}",1,"(5*a^5*Sqrt[x]*Sqrt[a + b*x])/(512*b^3) - (5*a^4*x^(3/2)*Sqrt[a + b*x])/(768*b^2) + (a^3*x^(5/2)*Sqrt[a + b*x])/(192*b) + (a^2*x^(7/2)*Sqrt[a + b*x])/32 + (a*x^(7/2)*(a + b*x)^(3/2))/12 + (x^(7/2)*(a + b*x)^(5/2))/6 - (5*a^6*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a + b*x]])/(512*b^(7/2))","A",9,4,15,0.2667,1,"{50, 63, 217, 206}"
546,1,140,0,0.0476703,"\int x^{3/2} (a+b x)^{5/2} \, dx","Int[x^(3/2)*(a + b*x)^(5/2),x]","-\frac{3 a^4 \sqrt{x} \sqrt{a+b x}}{128 b^2}+\frac{3 a^5 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{128 b^{5/2}}+\frac{a^3 x^{3/2} \sqrt{a+b x}}{64 b}+\frac{1}{16} a^2 x^{5/2} \sqrt{a+b x}+\frac{1}{8} a x^{5/2} (a+b x)^{3/2}+\frac{1}{5} x^{5/2} (a+b x)^{5/2}","-\frac{3 a^4 \sqrt{x} \sqrt{a+b x}}{128 b^2}+\frac{3 a^5 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{128 b^{5/2}}+\frac{a^3 x^{3/2} \sqrt{a+b x}}{64 b}+\frac{1}{16} a^2 x^{5/2} \sqrt{a+b x}+\frac{1}{8} a x^{5/2} (a+b x)^{3/2}+\frac{1}{5} x^{5/2} (a+b x)^{5/2}",1,"(-3*a^4*Sqrt[x]*Sqrt[a + b*x])/(128*b^2) + (a^3*x^(3/2)*Sqrt[a + b*x])/(64*b) + (a^2*x^(5/2)*Sqrt[a + b*x])/16 + (a*x^(5/2)*(a + b*x)^(3/2))/8 + (x^(5/2)*(a + b*x)^(5/2))/5 + (3*a^5*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a + b*x]])/(128*b^(5/2))","A",8,4,15,0.2667,1,"{50, 63, 217, 206}"
547,1,116,0,0.0382128,"\int \sqrt{x} (a+b x)^{5/2} \, dx","Int[Sqrt[x]*(a + b*x)^(5/2),x]","-\frac{5 a^4 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{64 b^{3/2}}+\frac{5}{32} a^2 x^{3/2} \sqrt{a+b x}+\frac{5 a^3 \sqrt{x} \sqrt{a+b x}}{64 b}+\frac{5}{24} a x^{3/2} (a+b x)^{3/2}+\frac{1}{4} x^{3/2} (a+b x)^{5/2}","-\frac{5 a^4 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{64 b^{3/2}}+\frac{5}{32} a^2 x^{3/2} \sqrt{a+b x}+\frac{5 a^3 \sqrt{x} \sqrt{a+b x}}{64 b}+\frac{5}{24} a x^{3/2} (a+b x)^{3/2}+\frac{1}{4} x^{3/2} (a+b x)^{5/2}",1,"(5*a^3*Sqrt[x]*Sqrt[a + b*x])/(64*b) + (5*a^2*x^(3/2)*Sqrt[a + b*x])/32 + (5*a*x^(3/2)*(a + b*x)^(3/2))/24 + (x^(3/2)*(a + b*x)^(5/2))/4 - (5*a^4*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a + b*x]])/(64*b^(3/2))","A",7,4,15,0.2667,1,"{50, 63, 217, 206}"
548,1,92,0,0.0277851,"\int \frac{(a+b x)^{5/2}}{\sqrt{x}} \, dx","Int[(a + b*x)^(5/2)/Sqrt[x],x]","\frac{5}{8} a^2 \sqrt{x} \sqrt{a+b x}+\frac{5 a^3 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{8 \sqrt{b}}+\frac{5}{12} a \sqrt{x} (a+b x)^{3/2}+\frac{1}{3} \sqrt{x} (a+b x)^{5/2}","\frac{5}{8} a^2 \sqrt{x} \sqrt{a+b x}+\frac{5 a^3 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{8 \sqrt{b}}+\frac{5}{12} a \sqrt{x} (a+b x)^{3/2}+\frac{1}{3} \sqrt{x} (a+b x)^{5/2}",1,"(5*a^2*Sqrt[x]*Sqrt[a + b*x])/8 + (5*a*Sqrt[x]*(a + b*x)^(3/2))/12 + (Sqrt[x]*(a + b*x)^(5/2))/3 + (5*a^3*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a + b*x]])/(8*Sqrt[b])","A",6,4,15,0.2667,1,"{50, 63, 217, 206}"
549,1,89,0,0.0279171,"\int \frac{(a+b x)^{5/2}}{x^{3/2}} \, dx","Int[(a + b*x)^(5/2)/x^(3/2),x]","\frac{15}{4} a^2 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)-\frac{2 (a+b x)^{5/2}}{\sqrt{x}}+\frac{5}{2} b \sqrt{x} (a+b x)^{3/2}+\frac{15}{4} a b \sqrt{x} \sqrt{a+b x}","\frac{15}{4} a^2 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)-\frac{2 (a+b x)^{5/2}}{\sqrt{x}}+\frac{5}{2} b \sqrt{x} (a+b x)^{3/2}+\frac{15}{4} a b \sqrt{x} \sqrt{a+b x}",1,"(15*a*b*Sqrt[x]*Sqrt[a + b*x])/4 + (5*b*Sqrt[x]*(a + b*x)^(3/2))/2 - (2*(a + b*x)^(5/2))/Sqrt[x] + (15*a^2*Sqrt[b]*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a + b*x]])/4","A",6,5,15,0.3333,1,"{47, 50, 63, 217, 206}"
550,1,86,0,0.0262959,"\int \frac{(a+b x)^{5/2}}{x^{5/2}} \, dx","Int[(a + b*x)^(5/2)/x^(5/2),x]","5 b^2 \sqrt{x} \sqrt{a+b x}+5 a b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)-\frac{2 (a+b x)^{5/2}}{3 x^{3/2}}-\frac{10 b (a+b x)^{3/2}}{3 \sqrt{x}}","5 b^2 \sqrt{x} \sqrt{a+b x}+5 a b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)-\frac{2 (a+b x)^{5/2}}{3 x^{3/2}}-\frac{10 b (a+b x)^{3/2}}{3 \sqrt{x}}",1,"5*b^2*Sqrt[x]*Sqrt[a + b*x] - (10*b*(a + b*x)^(3/2))/(3*Sqrt[x]) - (2*(a + b*x)^(5/2))/(3*x^(3/2)) + 5*a*b^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a + b*x]]","A",6,5,15,0.3333,1,"{47, 50, 63, 217, 206}"
551,1,171,0,0.0608304,"\int x^{5/2} (a-b x)^{5/2} \, dx","Int[x^(5/2)*(a - b*x)^(5/2),x]","-\frac{5 a^4 x^{3/2} \sqrt{a-b x}}{768 b^2}-\frac{5 a^5 \sqrt{x} \sqrt{a-b x}}{512 b^3}+\frac{5 a^6 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)}{512 b^{7/2}}-\frac{a^3 x^{5/2} \sqrt{a-b x}}{192 b}+\frac{1}{32} a^2 x^{7/2} \sqrt{a-b x}+\frac{1}{12} a x^{7/2} (a-b x)^{3/2}+\frac{1}{6} x^{7/2} (a-b x)^{5/2}","-\frac{5 a^4 x^{3/2} \sqrt{a-b x}}{768 b^2}-\frac{5 a^5 \sqrt{x} \sqrt{a-b x}}{512 b^3}+\frac{5 a^6 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)}{512 b^{7/2}}-\frac{a^3 x^{5/2} \sqrt{a-b x}}{192 b}+\frac{1}{32} a^2 x^{7/2} \sqrt{a-b x}+\frac{1}{12} a x^{7/2} (a-b x)^{3/2}+\frac{1}{6} x^{7/2} (a-b x)^{5/2}",1,"(-5*a^5*Sqrt[x]*Sqrt[a - b*x])/(512*b^3) - (5*a^4*x^(3/2)*Sqrt[a - b*x])/(768*b^2) - (a^3*x^(5/2)*Sqrt[a - b*x])/(192*b) + (a^2*x^(7/2)*Sqrt[a - b*x])/32 + (a*x^(7/2)*(a - b*x)^(3/2))/12 + (x^(7/2)*(a - b*x)^(5/2))/6 + (5*a^6*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a - b*x]])/(512*b^(7/2))","A",9,4,16,0.2500,1,"{50, 63, 217, 203}"
552,1,146,0,0.0505688,"\int x^{3/2} (a-b x)^{5/2} \, dx","Int[x^(3/2)*(a - b*x)^(5/2),x]","-\frac{3 a^4 \sqrt{x} \sqrt{a-b x}}{128 b^2}+\frac{3 a^5 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)}{128 b^{5/2}}-\frac{a^3 x^{3/2} \sqrt{a-b x}}{64 b}+\frac{1}{16} a^2 x^{5/2} \sqrt{a-b x}+\frac{1}{8} a x^{5/2} (a-b x)^{3/2}+\frac{1}{5} x^{5/2} (a-b x)^{5/2}","-\frac{3 a^4 \sqrt{x} \sqrt{a-b x}}{128 b^2}+\frac{3 a^5 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)}{128 b^{5/2}}-\frac{a^3 x^{3/2} \sqrt{a-b x}}{64 b}+\frac{1}{16} a^2 x^{5/2} \sqrt{a-b x}+\frac{1}{8} a x^{5/2} (a-b x)^{3/2}+\frac{1}{5} x^{5/2} (a-b x)^{5/2}",1,"(-3*a^4*Sqrt[x]*Sqrt[a - b*x])/(128*b^2) - (a^3*x^(3/2)*Sqrt[a - b*x])/(64*b) + (a^2*x^(5/2)*Sqrt[a - b*x])/16 + (a*x^(5/2)*(a - b*x)^(3/2))/8 + (x^(5/2)*(a - b*x)^(5/2))/5 + (3*a^5*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a - b*x]])/(128*b^(5/2))","A",8,4,16,0.2500,1,"{50, 63, 217, 203}"
553,1,121,0,0.0377049,"\int \sqrt{x} (a-b x)^{5/2} \, dx","Int[Sqrt[x]*(a - b*x)^(5/2),x]","\frac{5 a^4 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)}{64 b^{3/2}}+\frac{5}{32} a^2 x^{3/2} \sqrt{a-b x}-\frac{5 a^3 \sqrt{x} \sqrt{a-b x}}{64 b}+\frac{5}{24} a x^{3/2} (a-b x)^{3/2}+\frac{1}{4} x^{3/2} (a-b x)^{5/2}","\frac{5 a^4 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)}{64 b^{3/2}}+\frac{5}{32} a^2 x^{3/2} \sqrt{a-b x}-\frac{5 a^3 \sqrt{x} \sqrt{a-b x}}{64 b}+\frac{5}{24} a x^{3/2} (a-b x)^{3/2}+\frac{1}{4} x^{3/2} (a-b x)^{5/2}",1,"(-5*a^3*Sqrt[x]*Sqrt[a - b*x])/(64*b) + (5*a^2*x^(3/2)*Sqrt[a - b*x])/32 + (5*a*x^(3/2)*(a - b*x)^(3/2))/24 + (x^(3/2)*(a - b*x)^(5/2))/4 + (5*a^4*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a - b*x]])/(64*b^(3/2))","A",7,4,16,0.2500,1,"{50, 63, 217, 203}"
554,1,96,0,0.0304088,"\int \frac{(a-b x)^{5/2}}{\sqrt{x}} \, dx","Int[(a - b*x)^(5/2)/Sqrt[x],x]","\frac{5}{8} a^2 \sqrt{x} \sqrt{a-b x}+\frac{5 a^3 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)}{8 \sqrt{b}}+\frac{5}{12} a \sqrt{x} (a-b x)^{3/2}+\frac{1}{3} \sqrt{x} (a-b x)^{5/2}","\frac{5}{8} a^2 \sqrt{x} \sqrt{a-b x}+\frac{5 a^3 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)}{8 \sqrt{b}}+\frac{5}{12} a \sqrt{x} (a-b x)^{3/2}+\frac{1}{3} \sqrt{x} (a-b x)^{5/2}",1,"(5*a^2*Sqrt[x]*Sqrt[a - b*x])/8 + (5*a*Sqrt[x]*(a - b*x)^(3/2))/12 + (Sqrt[x]*(a - b*x)^(5/2))/3 + (5*a^3*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a - b*x]])/(8*Sqrt[b])","A",6,4,16,0.2500,1,"{50, 63, 217, 203}"
555,1,93,0,0.0281738,"\int \frac{(a-b x)^{5/2}}{x^{3/2}} \, dx","Int[(a - b*x)^(5/2)/x^(3/2),x]","-\frac{15}{4} a^2 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)-\frac{2 (a-b x)^{5/2}}{\sqrt{x}}-\frac{5}{2} b \sqrt{x} (a-b x)^{3/2}-\frac{15}{4} a b \sqrt{x} \sqrt{a-b x}","-\frac{15}{4} a^2 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)-\frac{2 (a-b x)^{5/2}}{\sqrt{x}}-\frac{5}{2} b \sqrt{x} (a-b x)^{3/2}-\frac{15}{4} a b \sqrt{x} \sqrt{a-b x}",1,"(-15*a*b*Sqrt[x]*Sqrt[a - b*x])/4 - (5*b*Sqrt[x]*(a - b*x)^(3/2))/2 - (2*(a - b*x)^(5/2))/Sqrt[x] - (15*a^2*Sqrt[b]*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a - b*x]])/4","A",6,5,16,0.3125,1,"{47, 50, 63, 217, 203}"
556,1,90,0,0.0296783,"\int \frac{(a-b x)^{5/2}}{x^{5/2}} \, dx","Int[(a - b*x)^(5/2)/x^(5/2),x]","5 b^2 \sqrt{x} \sqrt{a-b x}+5 a b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)-\frac{2 (a-b x)^{5/2}}{3 x^{3/2}}+\frac{10 b (a-b x)^{3/2}}{3 \sqrt{x}}","5 b^2 \sqrt{x} \sqrt{a-b x}+5 a b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)-\frac{2 (a-b x)^{5/2}}{3 x^{3/2}}+\frac{10 b (a-b x)^{3/2}}{3 \sqrt{x}}",1,"5*b^2*Sqrt[x]*Sqrt[a - b*x] + (10*b*(a - b*x)^(3/2))/(3*Sqrt[x]) - (2*(a - b*x)^(5/2))/(3*x^(3/2)) + 5*a*b^(3/2)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a - b*x]]","A",6,5,16,0.3125,1,"{47, 50, 63, 217, 203}"
557,1,144,0,0.0450716,"\int x^{5/2} (2+b x)^{5/2} \, dx","Int[x^(5/2)*(2 + b*x)^(5/2),x]","-\frac{5 x^{3/2} \sqrt{b x+2}}{48 b^2}+\frac{5 \sqrt{x} \sqrt{b x+2}}{16 b^3}-\frac{5 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{8 b^{7/2}}+\frac{1}{6} x^{7/2} (b x+2)^{5/2}+\frac{1}{6} x^{7/2} (b x+2)^{3/2}+\frac{1}{8} x^{7/2} \sqrt{b x+2}+\frac{x^{5/2} \sqrt{b x+2}}{24 b}","-\frac{5 x^{3/2} \sqrt{b x+2}}{48 b^2}+\frac{5 \sqrt{x} \sqrt{b x+2}}{16 b^3}-\frac{5 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{8 b^{7/2}}+\frac{1}{6} x^{7/2} (b x+2)^{5/2}+\frac{1}{6} x^{7/2} (b x+2)^{3/2}+\frac{1}{8} x^{7/2} \sqrt{b x+2}+\frac{x^{5/2} \sqrt{b x+2}}{24 b}",1,"(5*Sqrt[x]*Sqrt[2 + b*x])/(16*b^3) - (5*x^(3/2)*Sqrt[2 + b*x])/(48*b^2) + (x^(5/2)*Sqrt[2 + b*x])/(24*b) + (x^(7/2)*Sqrt[2 + b*x])/8 + (x^(7/2)*(2 + b*x)^(3/2))/6 + (x^(7/2)*(2 + b*x)^(5/2))/6 - (5*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/(8*b^(7/2))","A",8,3,15,0.2000,1,"{50, 54, 215}"
558,1,123,0,0.0282731,"\int x^{3/2} (2+b x)^{5/2} \, dx","Int[x^(3/2)*(2 + b*x)^(5/2),x]","-\frac{3 \sqrt{x} \sqrt{b x+2}}{8 b^2}+\frac{3 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{4 b^{5/2}}+\frac{1}{5} x^{5/2} (b x+2)^{5/2}+\frac{1}{4} x^{5/2} (b x+2)^{3/2}+\frac{1}{4} x^{5/2} \sqrt{b x+2}+\frac{x^{3/2} \sqrt{b x+2}}{8 b}","-\frac{3 \sqrt{x} \sqrt{b x+2}}{8 b^2}+\frac{3 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{4 b^{5/2}}+\frac{1}{5} x^{5/2} (b x+2)^{5/2}+\frac{1}{4} x^{5/2} (b x+2)^{3/2}+\frac{1}{4} x^{5/2} \sqrt{b x+2}+\frac{x^{3/2} \sqrt{b x+2}}{8 b}",1,"(-3*Sqrt[x]*Sqrt[2 + b*x])/(8*b^2) + (x^(3/2)*Sqrt[2 + b*x])/(8*b) + (x^(5/2)*Sqrt[2 + b*x])/4 + (x^(5/2)*(2 + b*x)^(3/2))/4 + (x^(5/2)*(2 + b*x)^(5/2))/5 + (3*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/(4*b^(5/2))","A",7,3,15,0.2000,1,"{50, 54, 215}"
559,1,102,0,0.0221546,"\int \sqrt{x} (2+b x)^{5/2} \, dx","Int[Sqrt[x]*(2 + b*x)^(5/2),x]","-\frac{5 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{4 b^{3/2}}+\frac{1}{4} x^{3/2} (b x+2)^{5/2}+\frac{5}{12} x^{3/2} (b x+2)^{3/2}+\frac{5}{8} x^{3/2} \sqrt{b x+2}+\frac{5 \sqrt{x} \sqrt{b x+2}}{8 b}","-\frac{5 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{4 b^{3/2}}+\frac{1}{4} x^{3/2} (b x+2)^{5/2}+\frac{5}{12} x^{3/2} (b x+2)^{3/2}+\frac{5}{8} x^{3/2} \sqrt{b x+2}+\frac{5 \sqrt{x} \sqrt{b x+2}}{8 b}",1,"(5*Sqrt[x]*Sqrt[2 + b*x])/(8*b) + (5*x^(3/2)*Sqrt[2 + b*x])/8 + (5*x^(3/2)*(2 + b*x)^(3/2))/12 + (x^(3/2)*(2 + b*x)^(5/2))/4 - (5*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/(4*b^(3/2))","A",6,3,15,0.2000,1,"{50, 54, 215}"
560,1,79,0,0.0159358,"\int \frac{(2+b x)^{5/2}}{\sqrt{x}} \, dx","Int[(2 + b*x)^(5/2)/Sqrt[x],x]","\frac{1}{3} \sqrt{x} (b x+2)^{5/2}+\frac{5}{6} \sqrt{x} (b x+2)^{3/2}+\frac{5}{2} \sqrt{x} \sqrt{b x+2}+\frac{5 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{\sqrt{b}}","\frac{1}{3} \sqrt{x} (b x+2)^{5/2}+\frac{5}{6} \sqrt{x} (b x+2)^{3/2}+\frac{5}{2} \sqrt{x} \sqrt{b x+2}+\frac{5 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{\sqrt{b}}",1,"(5*Sqrt[x]*Sqrt[2 + b*x])/2 + (5*Sqrt[x]*(2 + b*x)^(3/2))/6 + (Sqrt[x]*(2 + b*x)^(5/2))/3 + (5*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/Sqrt[b]","A",5,3,15,0.2000,1,"{50, 54, 215}"
561,1,79,0,0.0162733,"\int \frac{(2+b x)^{5/2}}{x^{3/2}} \, dx","Int[(2 + b*x)^(5/2)/x^(3/2),x]","-\frac{2 (b x+2)^{5/2}}{\sqrt{x}}+\frac{5}{2} b \sqrt{x} (b x+2)^{3/2}+\frac{15}{2} b \sqrt{x} \sqrt{b x+2}+15 \sqrt{b} \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)","-\frac{2 (b x+2)^{5/2}}{\sqrt{x}}+\frac{5}{2} b \sqrt{x} (b x+2)^{3/2}+\frac{15}{2} b \sqrt{x} \sqrt{b x+2}+15 \sqrt{b} \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)",1,"(15*b*Sqrt[x]*Sqrt[2 + b*x])/2 + (5*b*Sqrt[x]*(2 + b*x)^(3/2))/2 - (2*(2 + b*x)^(5/2))/Sqrt[x] + 15*Sqrt[b]*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[2]]","A",5,4,15,0.2667,1,"{47, 50, 54, 215}"
562,1,81,0,0.0171751,"\int \frac{(2+b x)^{5/2}}{x^{5/2}} \, dx","Int[(2 + b*x)^(5/2)/x^(5/2),x]","5 b^2 \sqrt{x} \sqrt{b x+2}+10 b^{3/2} \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)-\frac{2 (b x+2)^{5/2}}{3 x^{3/2}}-\frac{10 b (b x+2)^{3/2}}{3 \sqrt{x}}","5 b^2 \sqrt{x} \sqrt{b x+2}+10 b^{3/2} \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)-\frac{2 (b x+2)^{5/2}}{3 x^{3/2}}-\frac{10 b (b x+2)^{3/2}}{3 \sqrt{x}}",1,"5*b^2*Sqrt[x]*Sqrt[2 + b*x] - (10*b*(2 + b*x)^(3/2))/(3*Sqrt[x]) - (2*(2 + b*x)^(5/2))/(3*x^(3/2)) + 10*b^(3/2)*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[2]]","A",5,4,15,0.2667,1,"{47, 50, 54, 215}"
563,1,150,0,0.0452038,"\int x^{5/2} (2-b x)^{5/2} \, dx","Int[x^(5/2)*(2 - b*x)^(5/2),x]","-\frac{5 x^{3/2} \sqrt{2-b x}}{48 b^2}-\frac{5 \sqrt{x} \sqrt{2-b x}}{16 b^3}+\frac{5 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{8 b^{7/2}}+\frac{1}{6} x^{7/2} (2-b x)^{5/2}+\frac{1}{6} x^{7/2} (2-b x)^{3/2}+\frac{1}{8} x^{7/2} \sqrt{2-b x}-\frac{x^{5/2} \sqrt{2-b x}}{24 b}","-\frac{5 x^{3/2} \sqrt{2-b x}}{48 b^2}-\frac{5 \sqrt{x} \sqrt{2-b x}}{16 b^3}+\frac{5 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{8 b^{7/2}}+\frac{1}{6} x^{7/2} (2-b x)^{5/2}+\frac{1}{6} x^{7/2} (2-b x)^{3/2}+\frac{1}{8} x^{7/2} \sqrt{2-b x}-\frac{x^{5/2} \sqrt{2-b x}}{24 b}",1,"(-5*Sqrt[x]*Sqrt[2 - b*x])/(16*b^3) - (5*x^(3/2)*Sqrt[2 - b*x])/(48*b^2) - (x^(5/2)*Sqrt[2 - b*x])/(24*b) + (x^(7/2)*Sqrt[2 - b*x])/8 + (x^(7/2)*(2 - b*x)^(3/2))/6 + (x^(7/2)*(2 - b*x)^(5/2))/6 + (5*ArcSin[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/(8*b^(7/2))","A",8,3,16,0.1875,1,"{50, 54, 216}"
564,1,128,0,0.0285975,"\int x^{3/2} (2-b x)^{5/2} \, dx","Int[x^(3/2)*(2 - b*x)^(5/2),x]","-\frac{3 \sqrt{x} \sqrt{2-b x}}{8 b^2}+\frac{3 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{4 b^{5/2}}+\frac{1}{5} x^{5/2} (2-b x)^{5/2}+\frac{1}{4} x^{5/2} (2-b x)^{3/2}+\frac{1}{4} x^{5/2} \sqrt{2-b x}-\frac{x^{3/2} \sqrt{2-b x}}{8 b}","-\frac{3 \sqrt{x} \sqrt{2-b x}}{8 b^2}+\frac{3 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{4 b^{5/2}}+\frac{1}{5} x^{5/2} (2-b x)^{5/2}+\frac{1}{4} x^{5/2} (2-b x)^{3/2}+\frac{1}{4} x^{5/2} \sqrt{2-b x}-\frac{x^{3/2} \sqrt{2-b x}}{8 b}",1,"(-3*Sqrt[x]*Sqrt[2 - b*x])/(8*b^2) - (x^(3/2)*Sqrt[2 - b*x])/(8*b) + (x^(5/2)*Sqrt[2 - b*x])/4 + (x^(5/2)*(2 - b*x)^(3/2))/4 + (x^(5/2)*(2 - b*x)^(5/2))/5 + (3*ArcSin[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/(4*b^(5/2))","A",7,3,16,0.1875,1,"{50, 54, 216}"
565,1,106,0,0.022558,"\int \sqrt{x} (2-b x)^{5/2} \, dx","Int[Sqrt[x]*(2 - b*x)^(5/2),x]","\frac{5 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{4 b^{3/2}}+\frac{1}{4} x^{3/2} (2-b x)^{5/2}+\frac{5}{12} x^{3/2} (2-b x)^{3/2}+\frac{5}{8} x^{3/2} \sqrt{2-b x}-\frac{5 \sqrt{x} \sqrt{2-b x}}{8 b}","\frac{5 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{4 b^{3/2}}+\frac{1}{4} x^{3/2} (2-b x)^{5/2}+\frac{5}{12} x^{3/2} (2-b x)^{3/2}+\frac{5}{8} x^{3/2} \sqrt{2-b x}-\frac{5 \sqrt{x} \sqrt{2-b x}}{8 b}",1,"(-5*Sqrt[x]*Sqrt[2 - b*x])/(8*b) + (5*x^(3/2)*Sqrt[2 - b*x])/8 + (5*x^(3/2)*(2 - b*x)^(3/2))/12 + (x^(3/2)*(2 - b*x)^(5/2))/4 + (5*ArcSin[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/(4*b^(3/2))","A",6,3,16,0.1875,1,"{50, 54, 216}"
566,1,82,0,0.0165851,"\int \frac{(2-b x)^{5/2}}{\sqrt{x}} \, dx","Int[(2 - b*x)^(5/2)/Sqrt[x],x]","\frac{1}{3} \sqrt{x} (2-b x)^{5/2}+\frac{5}{6} \sqrt{x} (2-b x)^{3/2}+\frac{5}{2} \sqrt{x} \sqrt{2-b x}+\frac{5 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{\sqrt{b}}","\frac{1}{3} \sqrt{x} (2-b x)^{5/2}+\frac{5}{6} \sqrt{x} (2-b x)^{3/2}+\frac{5}{2} \sqrt{x} \sqrt{2-b x}+\frac{5 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{\sqrt{b}}",1,"(5*Sqrt[x]*Sqrt[2 - b*x])/2 + (5*Sqrt[x]*(2 - b*x)^(3/2))/6 + (Sqrt[x]*(2 - b*x)^(5/2))/3 + (5*ArcSin[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/Sqrt[b]","A",5,3,16,0.1875,1,"{50, 54, 216}"
567,1,82,0,0.0169737,"\int \frac{(2-b x)^{5/2}}{x^{3/2}} \, dx","Int[(2 - b*x)^(5/2)/x^(3/2),x]","-\frac{2 (2-b x)^{5/2}}{\sqrt{x}}-\frac{5}{2} b \sqrt{x} (2-b x)^{3/2}-\frac{15}{2} b \sqrt{x} \sqrt{2-b x}-15 \sqrt{b} \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)","-\frac{2 (2-b x)^{5/2}}{\sqrt{x}}-\frac{5}{2} b \sqrt{x} (2-b x)^{3/2}-\frac{15}{2} b \sqrt{x} \sqrt{2-b x}-15 \sqrt{b} \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)",1,"(-15*b*Sqrt[x]*Sqrt[2 - b*x])/2 - (5*b*Sqrt[x]*(2 - b*x)^(3/2))/2 - (2*(2 - b*x)^(5/2))/Sqrt[x] - 15*Sqrt[b]*ArcSin[(Sqrt[b]*Sqrt[x])/Sqrt[2]]","A",5,4,16,0.2500,1,"{47, 50, 54, 216}"
568,1,84,0,0.0172905,"\int \frac{(2-b x)^{5/2}}{x^{5/2}} \, dx","Int[(2 - b*x)^(5/2)/x^(5/2),x]","5 b^2 \sqrt{x} \sqrt{2-b x}+10 b^{3/2} \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)-\frac{2 (2-b x)^{5/2}}{3 x^{3/2}}+\frac{10 b (2-b x)^{3/2}}{3 \sqrt{x}}","5 b^2 \sqrt{x} \sqrt{2-b x}+10 b^{3/2} \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)-\frac{2 (2-b x)^{5/2}}{3 x^{3/2}}+\frac{10 b (2-b x)^{3/2}}{3 \sqrt{x}}",1,"5*b^2*Sqrt[x]*Sqrt[2 - b*x] + (10*b*(2 - b*x)^(3/2))/(3*Sqrt[x]) - (2*(2 - b*x)^(5/2))/(3*x^(3/2)) + 10*b^(3/2)*ArcSin[(Sqrt[b]*Sqrt[x])/Sqrt[2]]","A",5,4,16,0.2500,1,"{47, 50, 54, 216}"
569,1,101,0,0.0304051,"\int \frac{x^{5/2}}{\sqrt{a+b x}} \, dx","Int[x^(5/2)/Sqrt[a + b*x],x]","\frac{5 a^2 \sqrt{x} \sqrt{a+b x}}{8 b^3}-\frac{5 a^3 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{8 b^{7/2}}-\frac{5 a x^{3/2} \sqrt{a+b x}}{12 b^2}+\frac{x^{5/2} \sqrt{a+b x}}{3 b}","\frac{5 a^2 \sqrt{x} \sqrt{a+b x}}{8 b^3}-\frac{5 a^3 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{8 b^{7/2}}-\frac{5 a x^{3/2} \sqrt{a+b x}}{12 b^2}+\frac{x^{5/2} \sqrt{a+b x}}{3 b}",1,"(5*a^2*Sqrt[x]*Sqrt[a + b*x])/(8*b^3) - (5*a*x^(3/2)*Sqrt[a + b*x])/(12*b^2) + (x^(5/2)*Sqrt[a + b*x])/(3*b) - (5*a^3*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a + b*x]])/(8*b^(7/2))","A",6,4,15,0.2667,1,"{50, 63, 217, 206}"
570,1,77,0,0.0224716,"\int \frac{x^{3/2}}{\sqrt{a+b x}} \, dx","Int[x^(3/2)/Sqrt[a + b*x],x]","\frac{3 a^2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{4 b^{5/2}}-\frac{3 a \sqrt{x} \sqrt{a+b x}}{4 b^2}+\frac{x^{3/2} \sqrt{a+b x}}{2 b}","\frac{3 a^2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{4 b^{5/2}}-\frac{3 a \sqrt{x} \sqrt{a+b x}}{4 b^2}+\frac{x^{3/2} \sqrt{a+b x}}{2 b}",1,"(-3*a*Sqrt[x]*Sqrt[a + b*x])/(4*b^2) + (x^(3/2)*Sqrt[a + b*x])/(2*b) + (3*a^2*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a + b*x]])/(4*b^(5/2))","A",5,4,15,0.2667,1,"{50, 63, 217, 206}"
571,1,48,0,0.0162688,"\int \frac{\sqrt{x}}{\sqrt{a+b x}} \, dx","Int[Sqrt[x]/Sqrt[a + b*x],x]","\frac{\sqrt{x} \sqrt{a+b x}}{b}-\frac{a \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{b^{3/2}}","\frac{\sqrt{x} \sqrt{a+b x}}{b}-\frac{a \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{b^{3/2}}",1,"(Sqrt[x]*Sqrt[a + b*x])/b - (a*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a + b*x]])/b^(3/2)","A",4,4,15,0.2667,1,"{50, 63, 217, 206}"
572,1,28,0,0.0127668,"\int \frac{1}{\sqrt{x} \sqrt{a+b x}} \, dx","Int[1/(Sqrt[x]*Sqrt[a + b*x]),x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{\sqrt{b}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{\sqrt{b}}",1,"(2*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a + b*x]])/Sqrt[b]","A",3,3,15,0.2000,1,"{63, 217, 206}"
573,1,19,0,0.001619,"\int \frac{1}{x^{3/2} \sqrt{a+b x}} \, dx","Int[1/(x^(3/2)*Sqrt[a + b*x]),x]","-\frac{2 \sqrt{a+b x}}{a \sqrt{x}}","-\frac{2 \sqrt{a+b x}}{a \sqrt{x}}",1,"(-2*Sqrt[a + b*x])/(a*Sqrt[x])","A",1,1,15,0.06667,1,"{37}"
574,1,44,0,0.0047552,"\int \frac{1}{x^{5/2} \sqrt{a+b x}} \, dx","Int[1/(x^(5/2)*Sqrt[a + b*x]),x]","\frac{4 b \sqrt{a+b x}}{3 a^2 \sqrt{x}}-\frac{2 \sqrt{a+b x}}{3 a x^{3/2}}","\frac{4 b \sqrt{a+b x}}{3 a^2 \sqrt{x}}-\frac{2 \sqrt{a+b x}}{3 a x^{3/2}}",1,"(-2*Sqrt[a + b*x])/(3*a*x^(3/2)) + (4*b*Sqrt[a + b*x])/(3*a^2*Sqrt[x])","A",2,2,15,0.1333,1,"{45, 37}"
575,1,68,0,0.0102229,"\int \frac{1}{x^{7/2} \sqrt{a+b x}} \, dx","Int[1/(x^(7/2)*Sqrt[a + b*x]),x]","-\frac{16 b^2 \sqrt{a+b x}}{15 a^3 \sqrt{x}}+\frac{8 b \sqrt{a+b x}}{15 a^2 x^{3/2}}-\frac{2 \sqrt{a+b x}}{5 a x^{5/2}}","-\frac{16 b^2 \sqrt{a+b x}}{15 a^3 \sqrt{x}}+\frac{8 b \sqrt{a+b x}}{15 a^2 x^{3/2}}-\frac{2 \sqrt{a+b x}}{5 a x^{5/2}}",1,"(-2*Sqrt[a + b*x])/(5*a*x^(5/2)) + (8*b*Sqrt[a + b*x])/(15*a^2*x^(3/2)) - (16*b^2*Sqrt[a + b*x])/(15*a^3*Sqrt[x])","A",3,2,15,0.1333,1,"{45, 37}"
576,1,92,0,0.0163696,"\int \frac{1}{x^{9/2} \sqrt{a+b x}} \, dx","Int[1/(x^(9/2)*Sqrt[a + b*x]),x]","-\frac{16 b^2 \sqrt{a+b x}}{35 a^3 x^{3/2}}+\frac{32 b^3 \sqrt{a+b x}}{35 a^4 \sqrt{x}}+\frac{12 b \sqrt{a+b x}}{35 a^2 x^{5/2}}-\frac{2 \sqrt{a+b x}}{7 a x^{7/2}}","-\frac{16 b^2 \sqrt{a+b x}}{35 a^3 x^{3/2}}+\frac{32 b^3 \sqrt{a+b x}}{35 a^4 \sqrt{x}}+\frac{12 b \sqrt{a+b x}}{35 a^2 x^{5/2}}-\frac{2 \sqrt{a+b x}}{7 a x^{7/2}}",1,"(-2*Sqrt[a + b*x])/(7*a*x^(7/2)) + (12*b*Sqrt[a + b*x])/(35*a^2*x^(5/2)) - (16*b^2*Sqrt[a + b*x])/(35*a^3*x^(3/2)) + (32*b^3*Sqrt[a + b*x])/(35*a^4*Sqrt[x])","A",4,2,15,0.1333,1,"{45, 37}"
577,1,96,0,0.0293033,"\int \frac{x^{5/2}}{(a+b x)^{3/2}} \, dx","Int[x^(5/2)/(a + b*x)^(3/2),x]","\frac{15 a^2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{4 b^{7/2}}+\frac{5 x^{3/2} \sqrt{a+b x}}{2 b^2}-\frac{15 a \sqrt{x} \sqrt{a+b x}}{4 b^3}-\frac{2 x^{5/2}}{b \sqrt{a+b x}}","\frac{15 a^2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{4 b^{7/2}}+\frac{5 x^{3/2} \sqrt{a+b x}}{2 b^2}-\frac{15 a \sqrt{x} \sqrt{a+b x}}{4 b^3}-\frac{2 x^{5/2}}{b \sqrt{a+b x}}",1,"(-2*x^(5/2))/(b*Sqrt[a + b*x]) - (15*a*Sqrt[x]*Sqrt[a + b*x])/(4*b^3) + (5*x^(3/2)*Sqrt[a + b*x])/(2*b^2) + (15*a^2*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a + b*x]])/(4*b^(7/2))","A",6,5,15,0.3333,1,"{47, 50, 63, 217, 206}"
578,1,68,0,0.0215275,"\int \frac{x^{3/2}}{(a+b x)^{3/2}} \, dx","Int[x^(3/2)/(a + b*x)^(3/2),x]","\frac{3 \sqrt{x} \sqrt{a+b x}}{b^2}-\frac{3 a \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{b^{5/2}}-\frac{2 x^{3/2}}{b \sqrt{a+b x}}","\frac{3 \sqrt{x} \sqrt{a+b x}}{b^2}-\frac{3 a \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{b^{5/2}}-\frac{2 x^{3/2}}{b \sqrt{a+b x}}",1,"(-2*x^(3/2))/(b*Sqrt[a + b*x]) + (3*Sqrt[x]*Sqrt[a + b*x])/b^2 - (3*a*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a + b*x]])/b^(5/2)","A",5,5,15,0.3333,1,"{47, 50, 63, 217, 206}"
579,1,48,0,0.0161718,"\int \frac{\sqrt{x}}{(a+b x)^{3/2}} \, dx","Int[Sqrt[x]/(a + b*x)^(3/2),x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{b^{3/2}}-\frac{2 \sqrt{x}}{b \sqrt{a+b x}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{b^{3/2}}-\frac{2 \sqrt{x}}{b \sqrt{a+b x}}",1,"(-2*Sqrt[x])/(b*Sqrt[a + b*x]) + (2*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a + b*x]])/b^(3/2)","A",4,4,15,0.2667,1,"{47, 63, 217, 206}"
580,1,19,0,0.001838,"\int \frac{1}{\sqrt{x} (a+b x)^{3/2}} \, dx","Int[1/(Sqrt[x]*(a + b*x)^(3/2)),x]","\frac{2 \sqrt{x}}{a \sqrt{a+b x}}","\frac{2 \sqrt{x}}{a \sqrt{a+b x}}",1,"(2*Sqrt[x])/(a*Sqrt[a + b*x])","A",1,1,15,0.06667,1,"{37}"
581,1,39,0,0.0047896,"\int \frac{1}{x^{3/2} (a+b x)^{3/2}} \, dx","Int[1/(x^(3/2)*(a + b*x)^(3/2)),x]","\frac{2}{a \sqrt{x} \sqrt{a+b x}}-\frac{4 \sqrt{a+b x}}{a^2 \sqrt{x}}","\frac{2}{a \sqrt{x} \sqrt{a+b x}}-\frac{4 \sqrt{a+b x}}{a^2 \sqrt{x}}",1,"2/(a*Sqrt[x]*Sqrt[a + b*x]) - (4*Sqrt[a + b*x])/(a^2*Sqrt[x])","A",2,2,15,0.1333,1,"{45, 37}"
582,1,63,0,0.0098531,"\int \frac{1}{x^{5/2} (a+b x)^{3/2}} \, dx","Int[1/(x^(5/2)*(a + b*x)^(3/2)),x]","-\frac{8 \sqrt{a+b x}}{3 a^2 x^{3/2}}+\frac{16 b \sqrt{a+b x}}{3 a^3 \sqrt{x}}+\frac{2}{a x^{3/2} \sqrt{a+b x}}","-\frac{8 \sqrt{a+b x}}{3 a^2 x^{3/2}}+\frac{16 b \sqrt{a+b x}}{3 a^3 \sqrt{x}}+\frac{2}{a x^{3/2} \sqrt{a+b x}}",1,"2/(a*x^(3/2)*Sqrt[a + b*x]) - (8*Sqrt[a + b*x])/(3*a^2*x^(3/2)) + (16*b*Sqrt[a + b*x])/(3*a^3*Sqrt[x])","A",3,2,15,0.1333,1,"{45, 37}"
583,1,87,0,0.016875,"\int \frac{1}{x^{7/2} (a+b x)^{3/2}} \, dx","Int[1/(x^(7/2)*(a + b*x)^(3/2)),x]","-\frac{32 b^2 \sqrt{a+b x}}{5 a^4 \sqrt{x}}+\frac{16 b \sqrt{a+b x}}{5 a^3 x^{3/2}}-\frac{12 \sqrt{a+b x}}{5 a^2 x^{5/2}}+\frac{2}{a x^{5/2} \sqrt{a+b x}}","-\frac{32 b^2 \sqrt{a+b x}}{5 a^4 \sqrt{x}}+\frac{16 b \sqrt{a+b x}}{5 a^3 x^{3/2}}-\frac{12 \sqrt{a+b x}}{5 a^2 x^{5/2}}+\frac{2}{a x^{5/2} \sqrt{a+b x}}",1,"2/(a*x^(5/2)*Sqrt[a + b*x]) - (12*Sqrt[a + b*x])/(5*a^2*x^(5/2)) + (16*b*Sqrt[a + b*x])/(5*a^3*x^(3/2)) - (32*b^2*Sqrt[a + b*x])/(5*a^4*Sqrt[x])","A",4,2,15,0.1333,1,"{45, 37}"
584,1,91,0,0.0281517,"\int \frac{x^{5/2}}{(a+b x)^{5/2}} \, dx","Int[x^(5/2)/(a + b*x)^(5/2),x]","-\frac{10 x^{3/2}}{3 b^2 \sqrt{a+b x}}+\frac{5 \sqrt{x} \sqrt{a+b x}}{b^3}-\frac{5 a \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{b^{7/2}}-\frac{2 x^{5/2}}{3 b (a+b x)^{3/2}}","-\frac{10 x^{3/2}}{3 b^2 \sqrt{a+b x}}+\frac{5 \sqrt{x} \sqrt{a+b x}}{b^3}-\frac{5 a \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{b^{7/2}}-\frac{2 x^{5/2}}{3 b (a+b x)^{3/2}}",1,"(-2*x^(5/2))/(3*b*(a + b*x)^(3/2)) - (10*x^(3/2))/(3*b^2*Sqrt[a + b*x]) + (5*Sqrt[x]*Sqrt[a + b*x])/b^3 - (5*a*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a + b*x]])/b^(7/2)","A",6,5,15,0.3333,1,"{47, 50, 63, 217, 206}"
585,1,69,0,0.021607,"\int \frac{x^{3/2}}{(a+b x)^{5/2}} \, dx","Int[x^(3/2)/(a + b*x)^(5/2),x]","-\frac{2 \sqrt{x}}{b^2 \sqrt{a+b x}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{b^{5/2}}-\frac{2 x^{3/2}}{3 b (a+b x)^{3/2}}","-\frac{2 \sqrt{x}}{b^2 \sqrt{a+b x}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{b^{5/2}}-\frac{2 x^{3/2}}{3 b (a+b x)^{3/2}}",1,"(-2*x^(3/2))/(3*b*(a + b*x)^(3/2)) - (2*Sqrt[x])/(b^2*Sqrt[a + b*x]) + (2*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a + b*x]])/b^(5/2)","A",5,4,15,0.2667,1,"{47, 63, 217, 206}"
586,1,21,0,0.001626,"\int \frac{\sqrt{x}}{(a+b x)^{5/2}} \, dx","Int[Sqrt[x]/(a + b*x)^(5/2),x]","\frac{2 x^{3/2}}{3 a (a+b x)^{3/2}}","\frac{2 x^{3/2}}{3 a (a+b x)^{3/2}}",1,"(2*x^(3/2))/(3*a*(a + b*x)^(3/2))","A",1,1,15,0.06667,1,"{37}"
587,1,43,0,0.0046125,"\int \frac{1}{\sqrt{x} (a+b x)^{5/2}} \, dx","Int[1/(Sqrt[x]*(a + b*x)^(5/2)),x]","\frac{4 \sqrt{x}}{3 a^2 \sqrt{a+b x}}+\frac{2 \sqrt{x}}{3 a (a+b x)^{3/2}}","\frac{4 \sqrt{x}}{3 a^2 \sqrt{a+b x}}+\frac{2 \sqrt{x}}{3 a (a+b x)^{3/2}}",1,"(2*Sqrt[x])/(3*a*(a + b*x)^(3/2)) + (4*Sqrt[x])/(3*a^2*Sqrt[a + b*x])","A",2,2,15,0.1333,1,"{45, 37}"
588,1,64,0,0.0091767,"\int \frac{1}{x^{3/2} (a+b x)^{5/2}} \, dx","Int[1/(x^(3/2)*(a + b*x)^(5/2)),x]","-\frac{16 \sqrt{a+b x}}{3 a^3 \sqrt{x}}+\frac{8}{3 a^2 \sqrt{x} \sqrt{a+b x}}+\frac{2}{3 a \sqrt{x} (a+b x)^{3/2}}","-\frac{16 \sqrt{a+b x}}{3 a^3 \sqrt{x}}+\frac{8}{3 a^2 \sqrt{x} \sqrt{a+b x}}+\frac{2}{3 a \sqrt{x} (a+b x)^{3/2}}",1,"2/(3*a*Sqrt[x]*(a + b*x)^(3/2)) + 8/(3*a^2*Sqrt[x]*Sqrt[a + b*x]) - (16*Sqrt[a + b*x])/(3*a^3*Sqrt[x])","A",3,2,15,0.1333,1,"{45, 37}"
589,1,84,0,0.0153343,"\int \frac{1}{x^{5/2} (a+b x)^{5/2}} \, dx","Int[1/(x^(5/2)*(a + b*x)^(5/2)),x]","-\frac{16 \sqrt{a+b x}}{3 a^3 x^{3/2}}+\frac{4}{a^2 x^{3/2} \sqrt{a+b x}}+\frac{32 b \sqrt{a+b x}}{3 a^4 \sqrt{x}}+\frac{2}{3 a x^{3/2} (a+b x)^{3/2}}","-\frac{16 \sqrt{a+b x}}{3 a^3 x^{3/2}}+\frac{4}{a^2 x^{3/2} \sqrt{a+b x}}+\frac{32 b \sqrt{a+b x}}{3 a^4 \sqrt{x}}+\frac{2}{3 a x^{3/2} (a+b x)^{3/2}}",1,"2/(3*a*x^(3/2)*(a + b*x)^(3/2)) + 4/(a^2*x^(3/2)*Sqrt[a + b*x]) - (16*Sqrt[a + b*x])/(3*a^3*x^(3/2)) + (32*b*Sqrt[a + b*x])/(3*a^4*Sqrt[x])","A",4,2,15,0.1333,1,"{45, 37}"
590,1,105,0,0.0303057,"\int \frac{x^{5/2}}{\sqrt{a-b x}} \, dx","Int[x^(5/2)/Sqrt[a - b*x],x]","-\frac{5 a^2 \sqrt{x} \sqrt{a-b x}}{8 b^3}+\frac{5 a^3 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)}{8 b^{7/2}}-\frac{5 a x^{3/2} \sqrt{a-b x}}{12 b^2}-\frac{x^{5/2} \sqrt{a-b x}}{3 b}","-\frac{5 a^2 \sqrt{x} \sqrt{a-b x}}{8 b^3}+\frac{5 a^3 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)}{8 b^{7/2}}-\frac{5 a x^{3/2} \sqrt{a-b x}}{12 b^2}-\frac{x^{5/2} \sqrt{a-b x}}{3 b}",1,"(-5*a^2*Sqrt[x]*Sqrt[a - b*x])/(8*b^3) - (5*a*x^(3/2)*Sqrt[a - b*x])/(12*b^2) - (x^(5/2)*Sqrt[a - b*x])/(3*b) + (5*a^3*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a - b*x]])/(8*b^(7/2))","A",6,4,16,0.2500,1,"{50, 63, 217, 203}"
591,1,80,0,0.0228779,"\int \frac{x^{3/2}}{\sqrt{a-b x}} \, dx","Int[x^(3/2)/Sqrt[a - b*x],x]","\frac{3 a^2 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)}{4 b^{5/2}}-\frac{3 a \sqrt{x} \sqrt{a-b x}}{4 b^2}-\frac{x^{3/2} \sqrt{a-b x}}{2 b}","\frac{3 a^2 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)}{4 b^{5/2}}-\frac{3 a \sqrt{x} \sqrt{a-b x}}{4 b^2}-\frac{x^{3/2} \sqrt{a-b x}}{2 b}",1,"(-3*a*Sqrt[x]*Sqrt[a - b*x])/(4*b^2) - (x^(3/2)*Sqrt[a - b*x])/(2*b) + (3*a^2*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a - b*x]])/(4*b^(5/2))","A",5,4,16,0.2500,1,"{50, 63, 217, 203}"
592,1,50,0,0.0171857,"\int \frac{\sqrt{x}}{\sqrt{a-b x}} \, dx","Int[Sqrt[x]/Sqrt[a - b*x],x]","\frac{a \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)}{b^{3/2}}-\frac{\sqrt{x} \sqrt{a-b x}}{b}","\frac{a \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)}{b^{3/2}}-\frac{\sqrt{x} \sqrt{a-b x}}{b}",1,"-((Sqrt[x]*Sqrt[a - b*x])/b) + (a*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a - b*x]])/b^(3/2)","A",4,4,16,0.2500,1,"{50, 63, 217, 203}"
593,1,29,0,0.0125623,"\int \frac{1}{\sqrt{x} \sqrt{a-b x}} \, dx","Int[1/(Sqrt[x]*Sqrt[a - b*x]),x]","\frac{2 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)}{\sqrt{b}}","\frac{2 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)}{\sqrt{b}}",1,"(2*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a - b*x]])/Sqrt[b]","A",3,3,16,0.1875,1,"{63, 217, 203}"
594,1,20,0,0.0017315,"\int \frac{1}{x^{3/2} \sqrt{a-b x}} \, dx","Int[1/(x^(3/2)*Sqrt[a - b*x]),x]","-\frac{2 \sqrt{a-b x}}{a \sqrt{x}}","-\frac{2 \sqrt{a-b x}}{a \sqrt{x}}",1,"(-2*Sqrt[a - b*x])/(a*Sqrt[x])","A",1,1,16,0.06250,1,"{37}"
595,1,46,0,0.005001,"\int \frac{1}{x^{5/2} \sqrt{a-b x}} \, dx","Int[1/(x^(5/2)*Sqrt[a - b*x]),x]","-\frac{4 b \sqrt{a-b x}}{3 a^2 \sqrt{x}}-\frac{2 \sqrt{a-b x}}{3 a x^{3/2}}","-\frac{4 b \sqrt{a-b x}}{3 a^2 \sqrt{x}}-\frac{2 \sqrt{a-b x}}{3 a x^{3/2}}",1,"(-2*Sqrt[a - b*x])/(3*a*x^(3/2)) - (4*b*Sqrt[a - b*x])/(3*a^2*Sqrt[x])","A",2,2,16,0.1250,1,"{45, 37}"
596,1,100,0,0.0300671,"\int \frac{x^{5/2}}{(a-b x)^{3/2}} \, dx","Int[x^(5/2)/(a - b*x)^(3/2),x]","-\frac{15 a^2 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)}{4 b^{7/2}}+\frac{5 x^{3/2} \sqrt{a-b x}}{2 b^2}+\frac{15 a \sqrt{x} \sqrt{a-b x}}{4 b^3}+\frac{2 x^{5/2}}{b \sqrt{a-b x}}","-\frac{15 a^2 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)}{4 b^{7/2}}+\frac{5 x^{3/2} \sqrt{a-b x}}{2 b^2}+\frac{15 a \sqrt{x} \sqrt{a-b x}}{4 b^3}+\frac{2 x^{5/2}}{b \sqrt{a-b x}}",1,"(2*x^(5/2))/(b*Sqrt[a - b*x]) + (15*a*Sqrt[x]*Sqrt[a - b*x])/(4*b^3) + (5*x^(3/2)*Sqrt[a - b*x])/(2*b^2) - (15*a^2*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a - b*x]])/(4*b^(7/2))","A",6,5,16,0.3125,1,"{47, 50, 63, 217, 203}"
597,1,71,0,0.0220824,"\int \frac{x^{3/2}}{(a-b x)^{3/2}} \, dx","Int[x^(3/2)/(a - b*x)^(3/2),x]","\frac{3 \sqrt{x} \sqrt{a-b x}}{b^2}-\frac{3 a \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)}{b^{5/2}}+\frac{2 x^{3/2}}{b \sqrt{a-b x}}","\frac{3 \sqrt{x} \sqrt{a-b x}}{b^2}-\frac{3 a \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)}{b^{5/2}}+\frac{2 x^{3/2}}{b \sqrt{a-b x}}",1,"(2*x^(3/2))/(b*Sqrt[a - b*x]) + (3*Sqrt[x]*Sqrt[a - b*x])/b^2 - (3*a*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a - b*x]])/b^(5/2)","A",5,5,16,0.3125,1,"{47, 50, 63, 217, 203}"
598,1,50,0,0.0162758,"\int \frac{\sqrt{x}}{(a-b x)^{3/2}} \, dx","Int[Sqrt[x]/(a - b*x)^(3/2),x]","\frac{2 \sqrt{x}}{b \sqrt{a-b x}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)}{b^{3/2}}","\frac{2 \sqrt{x}}{b \sqrt{a-b x}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)}{b^{3/2}}",1,"(2*Sqrt[x])/(b*Sqrt[a - b*x]) - (2*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a - b*x]])/b^(3/2)","A",4,4,16,0.2500,1,"{47, 63, 217, 203}"
599,1,20,0,0.0017072,"\int \frac{1}{\sqrt{x} (a-b x)^{3/2}} \, dx","Int[1/(Sqrt[x]*(a - b*x)^(3/2)),x]","\frac{2 \sqrt{x}}{a \sqrt{a-b x}}","\frac{2 \sqrt{x}}{a \sqrt{a-b x}}",1,"(2*Sqrt[x])/(a*Sqrt[a - b*x])","A",1,1,16,0.06250,1,"{37}"
600,1,41,0,0.0049461,"\int \frac{1}{x^{3/2} (a-b x)^{3/2}} \, dx","Int[1/(x^(3/2)*(a - b*x)^(3/2)),x]","\frac{2}{a \sqrt{x} \sqrt{a-b x}}-\frac{4 \sqrt{a-b x}}{a^2 \sqrt{x}}","\frac{2}{a \sqrt{x} \sqrt{a-b x}}-\frac{4 \sqrt{a-b x}}{a^2 \sqrt{x}}",1,"2/(a*Sqrt[x]*Sqrt[a - b*x]) - (4*Sqrt[a - b*x])/(a^2*Sqrt[x])","A",2,2,16,0.1250,1,"{45, 37}"
601,1,66,0,0.0104674,"\int \frac{1}{x^{5/2} (a-b x)^{3/2}} \, dx","Int[1/(x^(5/2)*(a - b*x)^(3/2)),x]","-\frac{8 \sqrt{a-b x}}{3 a^2 x^{3/2}}-\frac{16 b \sqrt{a-b x}}{3 a^3 \sqrt{x}}+\frac{2}{a x^{3/2} \sqrt{a-b x}}","-\frac{8 \sqrt{a-b x}}{3 a^2 x^{3/2}}-\frac{16 b \sqrt{a-b x}}{3 a^3 \sqrt{x}}+\frac{2}{a x^{3/2} \sqrt{a-b x}}",1,"2/(a*x^(3/2)*Sqrt[a - b*x]) - (8*Sqrt[a - b*x])/(3*a^2*x^(3/2)) - (16*b*Sqrt[a - b*x])/(3*a^3*Sqrt[x])","A",3,2,16,0.1250,1,"{45, 37}"
602,1,95,0,0.0285071,"\int \frac{x^{5/2}}{(a-b x)^{5/2}} \, dx","Int[x^(5/2)/(a - b*x)^(5/2),x]","-\frac{10 x^{3/2}}{3 b^2 \sqrt{a-b x}}-\frac{5 \sqrt{x} \sqrt{a-b x}}{b^3}+\frac{5 a \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)}{b^{7/2}}+\frac{2 x^{5/2}}{3 b (a-b x)^{3/2}}","-\frac{10 x^{3/2}}{3 b^2 \sqrt{a-b x}}-\frac{5 \sqrt{x} \sqrt{a-b x}}{b^3}+\frac{5 a \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)}{b^{7/2}}+\frac{2 x^{5/2}}{3 b (a-b x)^{3/2}}",1,"(2*x^(5/2))/(3*b*(a - b*x)^(3/2)) - (10*x^(3/2))/(3*b^2*Sqrt[a - b*x]) - (5*Sqrt[x]*Sqrt[a - b*x])/b^3 + (5*a*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a - b*x]])/b^(7/2)","A",6,5,16,0.3125,1,"{47, 50, 63, 217, 203}"
603,1,72,0,0.0220513,"\int \frac{x^{3/2}}{(a-b x)^{5/2}} \, dx","Int[x^(3/2)/(a - b*x)^(5/2),x]","-\frac{2 \sqrt{x}}{b^2 \sqrt{a-b x}}+\frac{2 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)}{b^{5/2}}+\frac{2 x^{3/2}}{3 b (a-b x)^{3/2}}","-\frac{2 \sqrt{x}}{b^2 \sqrt{a-b x}}+\frac{2 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)}{b^{5/2}}+\frac{2 x^{3/2}}{3 b (a-b x)^{3/2}}",1,"(2*x^(3/2))/(3*b*(a - b*x)^(3/2)) - (2*Sqrt[x])/(b^2*Sqrt[a - b*x]) + (2*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a - b*x]])/b^(5/2)","A",5,4,16,0.2500,1,"{47, 63, 217, 203}"
604,1,22,0,0.0016898,"\int \frac{\sqrt{x}}{(a-b x)^{5/2}} \, dx","Int[Sqrt[x]/(a - b*x)^(5/2),x]","\frac{2 x^{3/2}}{3 a (a-b x)^{3/2}}","\frac{2 x^{3/2}}{3 a (a-b x)^{3/2}}",1,"(2*x^(3/2))/(3*a*(a - b*x)^(3/2))","A",1,1,16,0.06250,1,"{37}"
605,1,45,0,0.0050084,"\int \frac{1}{\sqrt{x} (a-b x)^{5/2}} \, dx","Int[1/(Sqrt[x]*(a - b*x)^(5/2)),x]","\frac{4 \sqrt{x}}{3 a^2 \sqrt{a-b x}}+\frac{2 \sqrt{x}}{3 a (a-b x)^{3/2}}","\frac{4 \sqrt{x}}{3 a^2 \sqrt{a-b x}}+\frac{2 \sqrt{x}}{3 a (a-b x)^{3/2}}",1,"(2*Sqrt[x])/(3*a*(a - b*x)^(3/2)) + (4*Sqrt[x])/(3*a^2*Sqrt[a - b*x])","A",2,2,16,0.1250,1,"{45, 37}"
606,1,67,0,0.009829,"\int \frac{1}{x^{3/2} (a-b x)^{5/2}} \, dx","Int[1/(x^(3/2)*(a - b*x)^(5/2)),x]","-\frac{16 \sqrt{a-b x}}{3 a^3 \sqrt{x}}+\frac{8}{3 a^2 \sqrt{x} \sqrt{a-b x}}+\frac{2}{3 a \sqrt{x} (a-b x)^{3/2}}","-\frac{16 \sqrt{a-b x}}{3 a^3 \sqrt{x}}+\frac{8}{3 a^2 \sqrt{x} \sqrt{a-b x}}+\frac{2}{3 a \sqrt{x} (a-b x)^{3/2}}",1,"2/(3*a*Sqrt[x]*(a - b*x)^(3/2)) + 8/(3*a^2*Sqrt[x]*Sqrt[a - b*x]) - (16*Sqrt[a - b*x])/(3*a^3*Sqrt[x])","A",3,2,16,0.1250,1,"{45, 37}"
607,1,88,0,0.0163789,"\int \frac{1}{x^{5/2} (a-b x)^{5/2}} \, dx","Int[1/(x^(5/2)*(a - b*x)^(5/2)),x]","-\frac{16 \sqrt{a-b x}}{3 a^3 x^{3/2}}+\frac{4}{a^2 x^{3/2} \sqrt{a-b x}}-\frac{32 b \sqrt{a-b x}}{3 a^4 \sqrt{x}}+\frac{2}{3 a x^{3/2} (a-b x)^{3/2}}","-\frac{16 \sqrt{a-b x}}{3 a^3 x^{3/2}}+\frac{4}{a^2 x^{3/2} \sqrt{a-b x}}-\frac{32 b \sqrt{a-b x}}{3 a^4 \sqrt{x}}+\frac{2}{3 a x^{3/2} (a-b x)^{3/2}}",1,"2/(3*a*x^(3/2)*(a - b*x)^(3/2)) + 4/(a^2*x^(3/2)*Sqrt[a - b*x]) - (16*Sqrt[a - b*x])/(3*a^3*x^(3/2)) - (32*b*Sqrt[a - b*x])/(3*a^4*Sqrt[x])","A",4,2,16,0.1250,1,"{45, 37}"
608,1,88,0,0.021807,"\int \frac{x^{5/2}}{\sqrt{2+b x}} \, dx","Int[x^(5/2)/Sqrt[2 + b*x],x]","-\frac{5 x^{3/2} \sqrt{b x+2}}{6 b^2}+\frac{5 \sqrt{x} \sqrt{b x+2}}{2 b^3}-\frac{5 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{7/2}}+\frac{x^{5/2} \sqrt{b x+2}}{3 b}","-\frac{5 x^{3/2} \sqrt{b x+2}}{6 b^2}+\frac{5 \sqrt{x} \sqrt{b x+2}}{2 b^3}-\frac{5 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{7/2}}+\frac{x^{5/2} \sqrt{b x+2}}{3 b}",1,"(5*Sqrt[x]*Sqrt[2 + b*x])/(2*b^3) - (5*x^(3/2)*Sqrt[2 + b*x])/(6*b^2) + (x^(5/2)*Sqrt[2 + b*x])/(3*b) - (5*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/b^(7/2)","A",5,3,15,0.2000,1,"{50, 54, 215}"
609,1,67,0,0.0135392,"\int \frac{x^{3/2}}{\sqrt{2+b x}} \, dx","Int[x^(3/2)/Sqrt[2 + b*x],x]","-\frac{3 \sqrt{x} \sqrt{b x+2}}{2 b^2}+\frac{3 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{5/2}}+\frac{x^{3/2} \sqrt{b x+2}}{2 b}","-\frac{3 \sqrt{x} \sqrt{b x+2}}{2 b^2}+\frac{3 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{5/2}}+\frac{x^{3/2} \sqrt{b x+2}}{2 b}",1,"(-3*Sqrt[x]*Sqrt[2 + b*x])/(2*b^2) + (x^(3/2)*Sqrt[2 + b*x])/(2*b) + (3*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/b^(5/2)","A",4,3,15,0.2000,1,"{50, 54, 215}"
610,1,43,0,0.0087786,"\int \frac{\sqrt{x}}{\sqrt{2+b x}} \, dx","Int[Sqrt[x]/Sqrt[2 + b*x],x]","\frac{\sqrt{x} \sqrt{b x+2}}{b}-\frac{2 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{3/2}}","\frac{\sqrt{x} \sqrt{b x+2}}{b}-\frac{2 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{3/2}}",1,"(Sqrt[x]*Sqrt[2 + b*x])/b - (2*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/b^(3/2)","A",3,3,15,0.2000,1,"{50, 54, 215}"
611,1,24,0,0.0055053,"\int \frac{1}{\sqrt{x} \sqrt{2+b x}} \, dx","Int[1/(Sqrt[x]*Sqrt[2 + b*x]),x]","\frac{2 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{\sqrt{b}}","\frac{2 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{\sqrt{b}}",1,"(2*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/Sqrt[b]","A",2,2,15,0.1333,1,"{54, 215}"
612,1,16,0,0.0012056,"\int \frac{1}{x^{3/2} \sqrt{2+b x}} \, dx","Int[1/(x^(3/2)*Sqrt[2 + b*x]),x]","-\frac{\sqrt{b x+2}}{\sqrt{x}}","-\frac{\sqrt{b x+2}}{\sqrt{x}}",1,"-(Sqrt[2 + b*x]/Sqrt[x])","A",1,1,15,0.06667,1,"{37}"
613,1,38,0,0.0035665,"\int \frac{1}{x^{5/2} \sqrt{2+b x}} \, dx","Int[1/(x^(5/2)*Sqrt[2 + b*x]),x]","\frac{b \sqrt{b x+2}}{3 \sqrt{x}}-\frac{\sqrt{b x+2}}{3 x^{3/2}}","\frac{b \sqrt{b x+2}}{3 \sqrt{x}}-\frac{\sqrt{b x+2}}{3 x^{3/2}}",1,"-Sqrt[2 + b*x]/(3*x^(3/2)) + (b*Sqrt[2 + b*x])/(3*Sqrt[x])","A",2,2,15,0.1333,1,"{45, 37}"
614,1,59,0,0.0074262,"\int \frac{1}{x^{7/2} \sqrt{2+b x}} \, dx","Int[1/(x^(7/2)*Sqrt[2 + b*x]),x]","-\frac{2 b^2 \sqrt{b x+2}}{15 \sqrt{x}}+\frac{2 b \sqrt{b x+2}}{15 x^{3/2}}-\frac{\sqrt{b x+2}}{5 x^{5/2}}","-\frac{2 b^2 \sqrt{b x+2}}{15 \sqrt{x}}+\frac{2 b \sqrt{b x+2}}{15 x^{3/2}}-\frac{\sqrt{b x+2}}{5 x^{5/2}}",1,"-Sqrt[2 + b*x]/(5*x^(5/2)) + (2*b*Sqrt[2 + b*x])/(15*x^(3/2)) - (2*b^2*Sqrt[2 + b*x])/(15*Sqrt[x])","A",3,2,15,0.1333,1,"{45, 37}"
615,1,80,0,0.0123568,"\int \frac{1}{x^{9/2} \sqrt{2+b x}} \, dx","Int[1/(x^(9/2)*Sqrt[2 + b*x]),x]","-\frac{2 b^2 \sqrt{b x+2}}{35 x^{3/2}}+\frac{2 b^3 \sqrt{b x+2}}{35 \sqrt{x}}+\frac{3 b \sqrt{b x+2}}{35 x^{5/2}}-\frac{\sqrt{b x+2}}{7 x^{7/2}}","-\frac{2 b^2 \sqrt{b x+2}}{35 x^{3/2}}+\frac{2 b^3 \sqrt{b x+2}}{35 \sqrt{x}}+\frac{3 b \sqrt{b x+2}}{35 x^{5/2}}-\frac{\sqrt{b x+2}}{7 x^{7/2}}",1,"-Sqrt[2 + b*x]/(7*x^(7/2)) + (3*b*Sqrt[2 + b*x])/(35*x^(5/2)) - (2*b^2*Sqrt[2 + b*x])/(35*x^(3/2)) + (2*b^3*Sqrt[2 + b*x])/(35*Sqrt[x])","A",4,2,15,0.1333,1,"{45, 37}"
616,1,86,0,0.0204427,"\int \frac{x^{5/2}}{(2+b x)^{3/2}} \, dx","Int[x^(5/2)/(2 + b*x)^(3/2),x]","\frac{5 x^{3/2} \sqrt{b x+2}}{2 b^2}-\frac{15 \sqrt{x} \sqrt{b x+2}}{2 b^3}+\frac{15 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{7/2}}-\frac{2 x^{5/2}}{b \sqrt{b x+2}}","\frac{5 x^{3/2} \sqrt{b x+2}}{2 b^2}-\frac{15 \sqrt{x} \sqrt{b x+2}}{2 b^3}+\frac{15 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{7/2}}-\frac{2 x^{5/2}}{b \sqrt{b x+2}}",1,"(-2*x^(5/2))/(b*Sqrt[2 + b*x]) - (15*Sqrt[x]*Sqrt[2 + b*x])/(2*b^3) + (5*x^(3/2)*Sqrt[2 + b*x])/(2*b^2) + (15*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/b^(7/2)","A",5,4,15,0.2667,1,"{47, 50, 54, 215}"
617,1,63,0,0.0138479,"\int \frac{x^{3/2}}{(2+b x)^{3/2}} \, dx","Int[x^(3/2)/(2 + b*x)^(3/2),x]","\frac{3 \sqrt{x} \sqrt{b x+2}}{b^2}-\frac{6 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{5/2}}-\frac{2 x^{3/2}}{b \sqrt{b x+2}}","\frac{3 \sqrt{x} \sqrt{b x+2}}{b^2}-\frac{6 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{5/2}}-\frac{2 x^{3/2}}{b \sqrt{b x+2}}",1,"(-2*x^(3/2))/(b*Sqrt[2 + b*x]) + (3*Sqrt[x]*Sqrt[2 + b*x])/b^2 - (6*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/b^(5/2)","A",4,4,15,0.2667,1,"{47, 50, 54, 215}"
618,1,44,0,0.0093868,"\int \frac{\sqrt{x}}{(2+b x)^{3/2}} \, dx","Int[Sqrt[x]/(2 + b*x)^(3/2),x]","\frac{2 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{3/2}}-\frac{2 \sqrt{x}}{b \sqrt{b x+2}}","\frac{2 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{3/2}}-\frac{2 \sqrt{x}}{b \sqrt{b x+2}}",1,"(-2*Sqrt[x])/(b*Sqrt[2 + b*x]) + (2*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/b^(3/2)","A",3,3,15,0.2000,1,"{47, 54, 215}"
619,1,15,0,0.0013378,"\int \frac{1}{\sqrt{x} (2+b x)^{3/2}} \, dx","Int[1/(Sqrt[x]*(2 + b*x)^(3/2)),x]","\frac{\sqrt{x}}{\sqrt{b x+2}}","\frac{\sqrt{x}}{\sqrt{b x+2}}",1,"Sqrt[x]/Sqrt[2 + b*x]","A",1,1,15,0.06667,1,"{37}"
620,1,32,0,0.0030264,"\int \frac{1}{x^{3/2} (2+b x)^{3/2}} \, dx","Int[1/(x^(3/2)*(2 + b*x)^(3/2)),x]","\frac{1}{\sqrt{x} \sqrt{b x+2}}-\frac{\sqrt{b x+2}}{\sqrt{x}}","\frac{1}{\sqrt{x} \sqrt{b x+2}}-\frac{\sqrt{b x+2}}{\sqrt{x}}",1,"1/(Sqrt[x]*Sqrt[2 + b*x]) - Sqrt[2 + b*x]/Sqrt[x]","A",2,2,15,0.1333,1,"{45, 37}"
621,1,53,0,0.0073547,"\int \frac{1}{x^{5/2} (2+b x)^{3/2}} \, dx","Int[1/(x^(5/2)*(2 + b*x)^(3/2)),x]","-\frac{2 \sqrt{b x+2}}{3 x^{3/2}}+\frac{1}{x^{3/2} \sqrt{b x+2}}+\frac{2 b \sqrt{b x+2}}{3 \sqrt{x}}","-\frac{2 \sqrt{b x+2}}{3 x^{3/2}}+\frac{1}{x^{3/2} \sqrt{b x+2}}+\frac{2 b \sqrt{b x+2}}{3 \sqrt{x}}",1,"1/(x^(3/2)*Sqrt[2 + b*x]) - (2*Sqrt[2 + b*x])/(3*x^(3/2)) + (2*b*Sqrt[2 + b*x])/(3*Sqrt[x])","A",3,2,15,0.1333,1,"{45, 37}"
622,1,74,0,0.013534,"\int \frac{1}{x^{7/2} (2+b x)^{3/2}} \, dx","Int[1/(x^(7/2)*(2 + b*x)^(3/2)),x]","-\frac{2 b^2 \sqrt{b x+2}}{5 \sqrt{x}}+\frac{2 b \sqrt{b x+2}}{5 x^{3/2}}-\frac{3 \sqrt{b x+2}}{5 x^{5/2}}+\frac{1}{x^{5/2} \sqrt{b x+2}}","-\frac{2 b^2 \sqrt{b x+2}}{5 \sqrt{x}}+\frac{2 b \sqrt{b x+2}}{5 x^{3/2}}-\frac{3 \sqrt{b x+2}}{5 x^{5/2}}+\frac{1}{x^{5/2} \sqrt{b x+2}}",1,"1/(x^(5/2)*Sqrt[2 + b*x]) - (3*Sqrt[2 + b*x])/(5*x^(5/2)) + (2*b*Sqrt[2 + b*x])/(5*x^(3/2)) - (2*b^2*Sqrt[2 + b*x])/(5*Sqrt[x])","A",4,2,15,0.1333,1,"{45, 37}"
623,1,86,0,0.0201415,"\int \frac{x^{5/2}}{(2+b x)^{5/2}} \, dx","Int[x^(5/2)/(2 + b*x)^(5/2),x]","-\frac{10 x^{3/2}}{3 b^2 \sqrt{b x+2}}+\frac{5 \sqrt{x} \sqrt{b x+2}}{b^3}-\frac{10 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{7/2}}-\frac{2 x^{5/2}}{3 b (b x+2)^{3/2}}","-\frac{10 x^{3/2}}{3 b^2 \sqrt{b x+2}}+\frac{5 \sqrt{x} \sqrt{b x+2}}{b^3}-\frac{10 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{7/2}}-\frac{2 x^{5/2}}{3 b (b x+2)^{3/2}}",1,"(-2*x^(5/2))/(3*b*(2 + b*x)^(3/2)) - (10*x^(3/2))/(3*b^2*Sqrt[2 + b*x]) + (5*Sqrt[x]*Sqrt[2 + b*x])/b^3 - (10*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/b^(7/2)","A",5,4,15,0.2667,1,"{47, 50, 54, 215}"
624,1,65,0,0.0144139,"\int \frac{x^{3/2}}{(2+b x)^{5/2}} \, dx","Int[x^(3/2)/(2 + b*x)^(5/2),x]","-\frac{2 \sqrt{x}}{b^2 \sqrt{b x+2}}+\frac{2 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{5/2}}-\frac{2 x^{3/2}}{3 b (b x+2)^{3/2}}","-\frac{2 \sqrt{x}}{b^2 \sqrt{b x+2}}+\frac{2 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{5/2}}-\frac{2 x^{3/2}}{3 b (b x+2)^{3/2}}",1,"(-2*x^(3/2))/(3*b*(2 + b*x)^(3/2)) - (2*Sqrt[x])/(b^2*Sqrt[2 + b*x]) + (2*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/b^(5/2)","A",4,3,15,0.2000,1,"{47, 54, 215}"
625,1,18,0,0.0012821,"\int \frac{\sqrt{x}}{(2+b x)^{5/2}} \, dx","Int[Sqrt[x]/(2 + b*x)^(5/2),x]","\frac{x^{3/2}}{3 (b x+2)^{3/2}}","\frac{x^{3/2}}{3 (b x+2)^{3/2}}",1,"x^(3/2)/(3*(2 + b*x)^(3/2))","A",1,1,15,0.06667,1,"{37}"
626,1,37,0,0.0034164,"\int \frac{1}{\sqrt{x} (2+b x)^{5/2}} \, dx","Int[1/(Sqrt[x]*(2 + b*x)^(5/2)),x]","\frac{\sqrt{x}}{3 \sqrt{b x+2}}+\frac{\sqrt{x}}{3 (b x+2)^{3/2}}","\frac{\sqrt{x}}{3 \sqrt{b x+2}}+\frac{\sqrt{x}}{3 (b x+2)^{3/2}}",1,"Sqrt[x]/(3*(2 + b*x)^(3/2)) + Sqrt[x]/(3*Sqrt[2 + b*x])","A",2,2,15,0.1333,1,"{45, 37}"
627,1,55,0,0.0059313,"\int \frac{1}{x^{3/2} (2+b x)^{5/2}} \, dx","Int[1/(x^(3/2)*(2 + b*x)^(5/2)),x]","-\frac{2 \sqrt{b x+2}}{3 \sqrt{x}}+\frac{2}{3 \sqrt{x} \sqrt{b x+2}}+\frac{1}{3 \sqrt{x} (b x+2)^{3/2}}","-\frac{2 \sqrt{b x+2}}{3 \sqrt{x}}+\frac{2}{3 \sqrt{x} \sqrt{b x+2}}+\frac{1}{3 \sqrt{x} (b x+2)^{3/2}}",1,"1/(3*Sqrt[x]*(2 + b*x)^(3/2)) + 2/(3*Sqrt[x]*Sqrt[2 + b*x]) - (2*Sqrt[2 + b*x])/(3*Sqrt[x])","A",3,2,15,0.1333,1,"{45, 37}"
628,1,71,0,0.0089598,"\int \frac{1}{x^{5/2} (2+b x)^{5/2}} \, dx","Int[1/(x^(5/2)*(2 + b*x)^(5/2)),x]","-\frac{2 \sqrt{b x+2}}{3 x^{3/2}}+\frac{1}{x^{3/2} \sqrt{b x+2}}+\frac{1}{3 x^{3/2} (b x+2)^{3/2}}+\frac{2 b \sqrt{b x+2}}{3 \sqrt{x}}","-\frac{2 \sqrt{b x+2}}{3 x^{3/2}}+\frac{1}{x^{3/2} \sqrt{b x+2}}+\frac{1}{3 x^{3/2} (b x+2)^{3/2}}+\frac{2 b \sqrt{b x+2}}{3 \sqrt{x}}",1,"1/(3*x^(3/2)*(2 + b*x)^(3/2)) + 1/(x^(3/2)*Sqrt[2 + b*x]) - (2*Sqrt[2 + b*x])/(3*x^(3/2)) + (2*b*Sqrt[2 + b*x])/(3*Sqrt[x])","A",4,2,15,0.1333,1,"{45, 37}"
629,1,91,0,0.0205853,"\int \frac{x^{5/2}}{\sqrt{2-b x}} \, dx","Int[x^(5/2)/Sqrt[2 - b*x],x]","-\frac{5 x^{3/2} \sqrt{2-b x}}{6 b^2}-\frac{5 \sqrt{x} \sqrt{2-b x}}{2 b^3}+\frac{5 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{7/2}}-\frac{x^{5/2} \sqrt{2-b x}}{3 b}","-\frac{5 x^{3/2} \sqrt{2-b x}}{6 b^2}-\frac{5 \sqrt{x} \sqrt{2-b x}}{2 b^3}+\frac{5 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{7/2}}-\frac{x^{5/2} \sqrt{2-b x}}{3 b}",1,"(-5*Sqrt[x]*Sqrt[2 - b*x])/(2*b^3) - (5*x^(3/2)*Sqrt[2 - b*x])/(6*b^2) - (x^(5/2)*Sqrt[2 - b*x])/(3*b) + (5*ArcSin[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/b^(7/2)","A",5,3,16,0.1875,1,"{50, 54, 216}"
630,1,69,0,0.01492,"\int \frac{x^{3/2}}{\sqrt{2-b x}} \, dx","Int[x^(3/2)/Sqrt[2 - b*x],x]","-\frac{3 \sqrt{x} \sqrt{2-b x}}{2 b^2}+\frac{3 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{5/2}}-\frac{x^{3/2} \sqrt{2-b x}}{2 b}","-\frac{3 \sqrt{x} \sqrt{2-b x}}{2 b^2}+\frac{3 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{5/2}}-\frac{x^{3/2} \sqrt{2-b x}}{2 b}",1,"(-3*Sqrt[x]*Sqrt[2 - b*x])/(2*b^2) - (x^(3/2)*Sqrt[2 - b*x])/(2*b) + (3*ArcSin[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/b^(5/2)","A",4,3,16,0.1875,1,"{50, 54, 216}"
631,1,45,0,0.009505,"\int \frac{\sqrt{x}}{\sqrt{2-b x}} \, dx","Int[Sqrt[x]/Sqrt[2 - b*x],x]","\frac{2 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{3/2}}-\frac{\sqrt{x} \sqrt{2-b x}}{b}","\frac{2 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{3/2}}-\frac{\sqrt{x} \sqrt{2-b x}}{b}",1,"-((Sqrt[x]*Sqrt[2 - b*x])/b) + (2*ArcSin[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/b^(3/2)","A",3,3,16,0.1875,1,"{50, 54, 216}"
632,1,24,0,0.0067891,"\int \frac{1}{\sqrt{x} \sqrt{2-b x}} \, dx","Int[1/(Sqrt[x]*Sqrt[2 - b*x]),x]","\frac{2 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{\sqrt{b}}","\frac{2 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{\sqrt{b}}",1,"(2*ArcSin[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/Sqrt[b]","A",2,2,16,0.1250,1,"{54, 216}"
633,1,17,0,0.001366,"\int \frac{1}{x^{3/2} \sqrt{2-b x}} \, dx","Int[1/(x^(3/2)*Sqrt[2 - b*x]),x]","-\frac{\sqrt{2-b x}}{\sqrt{x}}","-\frac{\sqrt{2-b x}}{\sqrt{x}}",1,"-(Sqrt[2 - b*x]/Sqrt[x])","A",1,1,16,0.06250,1,"{37}"
634,1,40,0,0.0039226,"\int \frac{1}{x^{5/2} \sqrt{2-b x}} \, dx","Int[1/(x^(5/2)*Sqrt[2 - b*x]),x]","-\frac{\sqrt{2-b x}}{3 x^{3/2}}-\frac{b \sqrt{2-b x}}{3 \sqrt{x}}","-\frac{\sqrt{2-b x}}{3 x^{3/2}}-\frac{b \sqrt{2-b x}}{3 \sqrt{x}}",1,"-Sqrt[2 - b*x]/(3*x^(3/2)) - (b*Sqrt[2 - b*x])/(3*Sqrt[x])","A",2,2,16,0.1250,1,"{45, 37}"
635,1,89,0,0.0207852,"\int \frac{x^{5/2}}{(2-b x)^{3/2}} \, dx","Int[x^(5/2)/(2 - b*x)^(3/2),x]","\frac{5 x^{3/2} \sqrt{2-b x}}{2 b^2}+\frac{15 \sqrt{x} \sqrt{2-b x}}{2 b^3}-\frac{15 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{7/2}}+\frac{2 x^{5/2}}{b \sqrt{2-b x}}","\frac{5 x^{3/2} \sqrt{2-b x}}{2 b^2}+\frac{15 \sqrt{x} \sqrt{2-b x}}{2 b^3}-\frac{15 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{7/2}}+\frac{2 x^{5/2}}{b \sqrt{2-b x}}",1,"(2*x^(5/2))/(b*Sqrt[2 - b*x]) + (15*Sqrt[x]*Sqrt[2 - b*x])/(2*b^3) + (5*x^(3/2)*Sqrt[2 - b*x])/(2*b^2) - (15*ArcSin[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/b^(7/2)","A",5,4,16,0.2500,1,"{47, 50, 54, 216}"
636,1,65,0,0.0144168,"\int \frac{x^{3/2}}{(2-b x)^{3/2}} \, dx","Int[x^(3/2)/(2 - b*x)^(3/2),x]","\frac{3 \sqrt{x} \sqrt{2-b x}}{b^2}-\frac{6 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{5/2}}+\frac{2 x^{3/2}}{b \sqrt{2-b x}}","\frac{3 \sqrt{x} \sqrt{2-b x}}{b^2}-\frac{6 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{5/2}}+\frac{2 x^{3/2}}{b \sqrt{2-b x}}",1,"(2*x^(3/2))/(b*Sqrt[2 - b*x]) + (3*Sqrt[x]*Sqrt[2 - b*x])/b^2 - (6*ArcSin[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/b^(5/2)","A",4,4,16,0.2500,1,"{47, 50, 54, 216}"
637,1,45,0,0.0094423,"\int \frac{\sqrt{x}}{(2-b x)^{3/2}} \, dx","Int[Sqrt[x]/(2 - b*x)^(3/2),x]","\frac{2 \sqrt{x}}{b \sqrt{2-b x}}-\frac{2 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{3/2}}","\frac{2 \sqrt{x}}{b \sqrt{2-b x}}-\frac{2 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{3/2}}",1,"(2*Sqrt[x])/(b*Sqrt[2 - b*x]) - (2*ArcSin[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/b^(3/2)","A",3,3,16,0.1875,1,"{47, 54, 216}"
638,1,16,0,0.0013493,"\int \frac{1}{\sqrt{x} (2-b x)^{3/2}} \, dx","Int[1/(Sqrt[x]*(2 - b*x)^(3/2)),x]","\frac{\sqrt{x}}{\sqrt{2-b x}}","\frac{\sqrt{x}}{\sqrt{2-b x}}",1,"Sqrt[x]/Sqrt[2 - b*x]","A",1,1,16,0.06250,1,"{37}"
639,1,34,0,0.0028815,"\int \frac{1}{x^{3/2} (2-b x)^{3/2}} \, dx","Int[1/(x^(3/2)*(2 - b*x)^(3/2)),x]","\frac{1}{\sqrt{x} \sqrt{2-b x}}-\frac{\sqrt{2-b x}}{\sqrt{x}}","\frac{1}{\sqrt{x} \sqrt{2-b x}}-\frac{\sqrt{2-b x}}{\sqrt{x}}",1,"1/(Sqrt[x]*Sqrt[2 - b*x]) - Sqrt[2 - b*x]/Sqrt[x]","A",2,2,16,0.1250,1,"{45, 37}"
640,1,56,0,0.0076754,"\int \frac{1}{x^{5/2} (2-b x)^{3/2}} \, dx","Int[1/(x^(5/2)*(2 - b*x)^(3/2)),x]","-\frac{2 \sqrt{2-b x}}{3 x^{3/2}}+\frac{1}{x^{3/2} \sqrt{2-b x}}-\frac{2 b \sqrt{2-b x}}{3 \sqrt{x}}","-\frac{2 \sqrt{2-b x}}{3 x^{3/2}}+\frac{1}{x^{3/2} \sqrt{2-b x}}-\frac{2 b \sqrt{2-b x}}{3 \sqrt{x}}",1,"1/(x^(3/2)*Sqrt[2 - b*x]) - (2*Sqrt[2 - b*x])/(3*x^(3/2)) - (2*b*Sqrt[2 - b*x])/(3*Sqrt[x])","A",3,2,16,0.1250,1,"{45, 37}"
641,1,89,0,0.0216252,"\int \frac{x^{5/2}}{(2-b x)^{5/2}} \, dx","Int[x^(5/2)/(2 - b*x)^(5/2),x]","-\frac{10 x^{3/2}}{3 b^2 \sqrt{2-b x}}-\frac{5 \sqrt{x} \sqrt{2-b x}}{b^3}+\frac{10 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{7/2}}+\frac{2 x^{5/2}}{3 b (2-b x)^{3/2}}","-\frac{10 x^{3/2}}{3 b^2 \sqrt{2-b x}}-\frac{5 \sqrt{x} \sqrt{2-b x}}{b^3}+\frac{10 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{7/2}}+\frac{2 x^{5/2}}{3 b (2-b x)^{3/2}}",1,"(2*x^(5/2))/(3*b*(2 - b*x)^(3/2)) - (10*x^(3/2))/(3*b^2*Sqrt[2 - b*x]) - (5*Sqrt[x]*Sqrt[2 - b*x])/b^3 + (10*ArcSin[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/b^(7/2)","A",5,4,16,0.2500,1,"{47, 50, 54, 216}"
642,1,67,0,0.0145247,"\int \frac{x^{3/2}}{(2-b x)^{5/2}} \, dx","Int[x^(3/2)/(2 - b*x)^(5/2),x]","-\frac{2 \sqrt{x}}{b^2 \sqrt{2-b x}}+\frac{2 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{5/2}}+\frac{2 x^{3/2}}{3 b (2-b x)^{3/2}}","-\frac{2 \sqrt{x}}{b^2 \sqrt{2-b x}}+\frac{2 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{5/2}}+\frac{2 x^{3/2}}{3 b (2-b x)^{3/2}}",1,"(2*x^(3/2))/(3*b*(2 - b*x)^(3/2)) - (2*Sqrt[x])/(b^2*Sqrt[2 - b*x]) + (2*ArcSin[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/b^(5/2)","A",4,3,16,0.1875,1,"{47, 54, 216}"
643,1,19,0,0.001343,"\int \frac{\sqrt{x}}{(2-b x)^{5/2}} \, dx","Int[Sqrt[x]/(2 - b*x)^(5/2),x]","\frac{x^{3/2}}{3 (2-b x)^{3/2}}","\frac{x^{3/2}}{3 (2-b x)^{3/2}}",1,"x^(3/2)/(3*(2 - b*x)^(3/2))","A",1,1,16,0.06250,1,"{37}"
644,1,39,0,0.003746,"\int \frac{1}{\sqrt{x} (2-b x)^{5/2}} \, dx","Int[1/(Sqrt[x]*(2 - b*x)^(5/2)),x]","\frac{\sqrt{x}}{3 \sqrt{2-b x}}+\frac{\sqrt{x}}{3 (2-b x)^{3/2}}","\frac{\sqrt{x}}{3 \sqrt{2-b x}}+\frac{\sqrt{x}}{3 (2-b x)^{3/2}}",1,"Sqrt[x]/(3*(2 - b*x)^(3/2)) + Sqrt[x]/(3*Sqrt[2 - b*x])","A",2,2,16,0.1250,1,"{45, 37}"
645,1,58,0,0.0063941,"\int \frac{1}{x^{3/2} (2-b x)^{5/2}} \, dx","Int[1/(x^(3/2)*(2 - b*x)^(5/2)),x]","-\frac{2 \sqrt{2-b x}}{3 \sqrt{x}}+\frac{2}{3 \sqrt{x} \sqrt{2-b x}}+\frac{1}{3 \sqrt{x} (2-b x)^{3/2}}","-\frac{2 \sqrt{2-b x}}{3 \sqrt{x}}+\frac{2}{3 \sqrt{x} \sqrt{2-b x}}+\frac{1}{3 \sqrt{x} (2-b x)^{3/2}}",1,"1/(3*Sqrt[x]*(2 - b*x)^(3/2)) + 2/(3*Sqrt[x]*Sqrt[2 - b*x]) - (2*Sqrt[2 - b*x])/(3*Sqrt[x])","A",3,2,16,0.1250,1,"{45, 37}"
646,1,75,0,0.0095324,"\int \frac{1}{x^{5/2} (2-b x)^{5/2}} \, dx","Int[1/(x^(5/2)*(2 - b*x)^(5/2)),x]","-\frac{2 \sqrt{2-b x}}{3 x^{3/2}}+\frac{1}{x^{3/2} \sqrt{2-b x}}+\frac{1}{3 x^{3/2} (2-b x)^{3/2}}-\frac{2 b \sqrt{2-b x}}{3 \sqrt{x}}","-\frac{2 \sqrt{2-b x}}{3 x^{3/2}}+\frac{1}{x^{3/2} \sqrt{2-b x}}+\frac{1}{3 x^{3/2} (2-b x)^{3/2}}-\frac{2 b \sqrt{2-b x}}{3 \sqrt{x}}",1,"1/(3*x^(3/2)*(2 - b*x)^(3/2)) + 1/(x^(3/2)*Sqrt[2 - b*x]) - (2*Sqrt[2 - b*x])/(3*x^(3/2)) - (2*b*Sqrt[2 - b*x])/(3*Sqrt[x])","A",4,2,16,0.1250,1,"{45, 37}"
647,1,27,0,0.005159,"\int \frac{\sqrt{x}}{\sqrt{1-x}} \, dx","Int[Sqrt[x]/Sqrt[1 - x],x]","-\sqrt{1-x} \sqrt{x}-\frac{1}{2} \sin ^{-1}(1-2 x)","-\sqrt{1-x} \sqrt{x}-\frac{1}{2} \sin ^{-1}(1-2 x)",1,"-(Sqrt[1 - x]*Sqrt[x]) - ArcSin[1 - 2*x]/2","A",4,4,15,0.2667,1,"{50, 53, 619, 216}"
648,1,8,0,0.0030581,"\int \frac{1}{\sqrt{1-x} \sqrt{x}} \, dx","Int[1/(Sqrt[1 - x]*Sqrt[x]),x]","-\sin ^{-1}(1-2 x)","-\sin ^{-1}(1-2 x)",1,"-ArcSin[1 - 2*x]","A",3,3,15,0.2000,1,"{53, 619, 216}"
649,1,19,0,0.004793,"\int \frac{1}{\sqrt{x} \sqrt{1-b x}} \, dx","Int[1/(Sqrt[x]*Sqrt[1 - b*x]),x]","\frac{2 \sin ^{-1}\left(\sqrt{b} \sqrt{x}\right)}{\sqrt{b}}","\frac{2 \sin ^{-1}\left(\sqrt{b} \sqrt{x}\right)}{\sqrt{b}}",1,"(2*ArcSin[Sqrt[b]*Sqrt[x]])/Sqrt[b]","A",2,2,16,0.1250,1,"{54, 216}"
650,1,21,0,0.0035423,"\int x^{5/3} (a+b x) \, dx","Int[x^(5/3)*(a + b*x),x]","\frac{3}{8} a x^{8/3}+\frac{3}{11} b x^{11/3}","\frac{3}{8} a x^{8/3}+\frac{3}{11} b x^{11/3}",1,"(3*a*x^(8/3))/8 + (3*b*x^(11/3))/11","A",2,1,11,0.09091,1,"{43}"
651,1,21,0,0.0035655,"\int x^{4/3} (a+b x) \, dx","Int[x^(4/3)*(a + b*x),x]","\frac{3}{7} a x^{7/3}+\frac{3}{10} b x^{10/3}","\frac{3}{7} a x^{7/3}+\frac{3}{10} b x^{10/3}",1,"(3*a*x^(7/3))/7 + (3*b*x^(10/3))/10","A",2,1,11,0.09091,1,"{43}"
652,1,21,0,0.003643,"\int x^{2/3} (a+b x) \, dx","Int[x^(2/3)*(a + b*x),x]","\frac{3}{5} a x^{5/3}+\frac{3}{8} b x^{8/3}","\frac{3}{5} a x^{5/3}+\frac{3}{8} b x^{8/3}",1,"(3*a*x^(5/3))/5 + (3*b*x^(8/3))/8","A",2,1,11,0.09091,1,"{43}"
653,1,21,0,0.0035914,"\int \sqrt[3]{x} (a+b x) \, dx","Int[x^(1/3)*(a + b*x),x]","\frac{3}{4} a x^{4/3}+\frac{3}{7} b x^{7/3}","\frac{3}{4} a x^{4/3}+\frac{3}{7} b x^{7/3}",1,"(3*a*x^(4/3))/4 + (3*b*x^(7/3))/7","A",2,1,11,0.09091,1,"{43}"
654,1,21,0,0.0038604,"\int \frac{a+b x}{\sqrt[3]{x}} \, dx","Int[(a + b*x)/x^(1/3),x]","\frac{3}{2} a x^{2/3}+\frac{3}{5} b x^{5/3}","\frac{3}{2} a x^{2/3}+\frac{3}{5} b x^{5/3}",1,"(3*a*x^(2/3))/2 + (3*b*x^(5/3))/5","A",2,1,11,0.09091,1,"{43}"
655,1,19,0,0.0034785,"\int \frac{a+b x}{x^{2/3}} \, dx","Int[(a + b*x)/x^(2/3),x]","3 a \sqrt[3]{x}+\frac{3}{4} b x^{4/3}","3 a \sqrt[3]{x}+\frac{3}{4} b x^{4/3}",1,"3*a*x^(1/3) + (3*b*x^(4/3))/4","A",2,1,11,0.09091,1,"{43}"
656,1,19,0,0.0036323,"\int \frac{a+b x}{x^{4/3}} \, dx","Int[(a + b*x)/x^(4/3),x]","\frac{3}{2} b x^{2/3}-\frac{3 a}{\sqrt[3]{x}}","\frac{3}{2} b x^{2/3}-\frac{3 a}{\sqrt[3]{x}}",1,"(-3*a)/x^(1/3) + (3*b*x^(2/3))/2","A",2,1,11,0.09091,1,"{43}"
657,1,19,0,0.0035201,"\int \frac{a+b x}{x^{5/3}} \, dx","Int[(a + b*x)/x^(5/3),x]","3 b \sqrt[3]{x}-\frac{3 a}{2 x^{2/3}}","3 b \sqrt[3]{x}-\frac{3 a}{2 x^{2/3}}",1,"(-3*a)/(2*x^(2/3)) + 3*b*x^(1/3)","A",2,1,11,0.09091,1,"{43}"
658,1,36,0,0.0067997,"\int x^{5/3} (a+b x)^2 \, dx","Int[x^(5/3)*(a + b*x)^2,x]","\frac{3}{8} a^2 x^{8/3}+\frac{6}{11} a b x^{11/3}+\frac{3}{14} b^2 x^{14/3}","\frac{3}{8} a^2 x^{8/3}+\frac{6}{11} a b x^{11/3}+\frac{3}{14} b^2 x^{14/3}",1,"(3*a^2*x^(8/3))/8 + (6*a*b*x^(11/3))/11 + (3*b^2*x^(14/3))/14","A",2,1,13,0.07692,1,"{43}"
659,1,36,0,0.0070806,"\int x^{4/3} (a+b x)^2 \, dx","Int[x^(4/3)*(a + b*x)^2,x]","\frac{3}{7} a^2 x^{7/3}+\frac{3}{5} a b x^{10/3}+\frac{3}{13} b^2 x^{13/3}","\frac{3}{7} a^2 x^{7/3}+\frac{3}{5} a b x^{10/3}+\frac{3}{13} b^2 x^{13/3}",1,"(3*a^2*x^(7/3))/7 + (3*a*b*x^(10/3))/5 + (3*b^2*x^(13/3))/13","A",2,1,13,0.07692,1,"{43}"
660,1,36,0,0.0068258,"\int x^{2/3} (a+b x)^2 \, dx","Int[x^(2/3)*(a + b*x)^2,x]","\frac{3}{5} a^2 x^{5/3}+\frac{3}{4} a b x^{8/3}+\frac{3}{11} b^2 x^{11/3}","\frac{3}{5} a^2 x^{5/3}+\frac{3}{4} a b x^{8/3}+\frac{3}{11} b^2 x^{11/3}",1,"(3*a^2*x^(5/3))/5 + (3*a*b*x^(8/3))/4 + (3*b^2*x^(11/3))/11","A",2,1,13,0.07692,1,"{43}"
661,1,36,0,0.0069011,"\int \sqrt[3]{x} (a+b x)^2 \, dx","Int[x^(1/3)*(a + b*x)^2,x]","\frac{3}{4} a^2 x^{4/3}+\frac{6}{7} a b x^{7/3}+\frac{3}{10} b^2 x^{10/3}","\frac{3}{4} a^2 x^{4/3}+\frac{6}{7} a b x^{7/3}+\frac{3}{10} b^2 x^{10/3}",1,"(3*a^2*x^(4/3))/4 + (6*a*b*x^(7/3))/7 + (3*b^2*x^(10/3))/10","A",2,1,13,0.07692,1,"{43}"
662,1,36,0,0.0076617,"\int \frac{(a+b x)^2}{\sqrt[3]{x}} \, dx","Int[(a + b*x)^2/x^(1/3),x]","\frac{3}{2} a^2 x^{2/3}+\frac{6}{5} a b x^{5/3}+\frac{3}{8} b^2 x^{8/3}","\frac{3}{2} a^2 x^{2/3}+\frac{6}{5} a b x^{5/3}+\frac{3}{8} b^2 x^{8/3}",1,"(3*a^2*x^(2/3))/2 + (6*a*b*x^(5/3))/5 + (3*b^2*x^(8/3))/8","A",2,1,13,0.07692,1,"{43}"
663,1,34,0,0.0066598,"\int \frac{(a+b x)^2}{x^{2/3}} \, dx","Int[(a + b*x)^2/x^(2/3),x]","3 a^2 \sqrt[3]{x}+\frac{3}{2} a b x^{4/3}+\frac{3}{7} b^2 x^{7/3}","3 a^2 \sqrt[3]{x}+\frac{3}{2} a b x^{4/3}+\frac{3}{7} b^2 x^{7/3}",1,"3*a^2*x^(1/3) + (3*a*b*x^(4/3))/2 + (3*b^2*x^(7/3))/7","A",2,1,13,0.07692,1,"{43}"
664,1,32,0,0.0067156,"\int \frac{(a+b x)^2}{x^{4/3}} \, dx","Int[(a + b*x)^2/x^(4/3),x]","-\frac{3 a^2}{\sqrt[3]{x}}+3 a b x^{2/3}+\frac{3}{5} b^2 x^{5/3}","-\frac{3 a^2}{\sqrt[3]{x}}+3 a b x^{2/3}+\frac{3}{5} b^2 x^{5/3}",1,"(-3*a^2)/x^(1/3) + 3*a*b*x^(2/3) + (3*b^2*x^(5/3))/5","A",2,1,13,0.07692,1,"{43}"
665,1,34,0,0.0071943,"\int \frac{(a+b x)^2}{x^{5/3}} \, dx","Int[(a + b*x)^2/x^(5/3),x]","-\frac{3 a^2}{2 x^{2/3}}+6 a b \sqrt[3]{x}+\frac{3}{4} b^2 x^{4/3}","-\frac{3 a^2}{2 x^{2/3}}+6 a b \sqrt[3]{x}+\frac{3}{4} b^2 x^{4/3}",1,"(-3*a^2)/(2*x^(2/3)) + 6*a*b*x^(1/3) + (3*b^2*x^(4/3))/4","A",2,1,13,0.07692,1,"{43}"
666,1,51,0,0.0104423,"\int x^{5/3} (a+b x)^3 \, dx","Int[x^(5/3)*(a + b*x)^3,x]","\frac{9}{11} a^2 b x^{11/3}+\frac{3}{8} a^3 x^{8/3}+\frac{9}{14} a b^2 x^{14/3}+\frac{3}{17} b^3 x^{17/3}","\frac{9}{11} a^2 b x^{11/3}+\frac{3}{8} a^3 x^{8/3}+\frac{9}{14} a b^2 x^{14/3}+\frac{3}{17} b^3 x^{17/3}",1,"(3*a^3*x^(8/3))/8 + (9*a^2*b*x^(11/3))/11 + (9*a*b^2*x^(14/3))/14 + (3*b^3*x^(17/3))/17","A",2,1,13,0.07692,1,"{43}"
667,1,51,0,0.0109155,"\int x^{4/3} (a+b x)^3 \, dx","Int[x^(4/3)*(a + b*x)^3,x]","\frac{9}{10} a^2 b x^{10/3}+\frac{3}{7} a^3 x^{7/3}+\frac{9}{13} a b^2 x^{13/3}+\frac{3}{16} b^3 x^{16/3}","\frac{9}{10} a^2 b x^{10/3}+\frac{3}{7} a^3 x^{7/3}+\frac{9}{13} a b^2 x^{13/3}+\frac{3}{16} b^3 x^{16/3}",1,"(3*a^3*x^(7/3))/7 + (9*a^2*b*x^(10/3))/10 + (9*a*b^2*x^(13/3))/13 + (3*b^3*x^(16/3))/16","A",2,1,13,0.07692,1,"{43}"
668,1,51,0,0.010782,"\int x^{2/3} (a+b x)^3 \, dx","Int[x^(2/3)*(a + b*x)^3,x]","\frac{9}{8} a^2 b x^{8/3}+\frac{3}{5} a^3 x^{5/3}+\frac{9}{11} a b^2 x^{11/3}+\frac{3}{14} b^3 x^{14/3}","\frac{9}{8} a^2 b x^{8/3}+\frac{3}{5} a^3 x^{5/3}+\frac{9}{11} a b^2 x^{11/3}+\frac{3}{14} b^3 x^{14/3}",1,"(3*a^3*x^(5/3))/5 + (9*a^2*b*x^(8/3))/8 + (9*a*b^2*x^(11/3))/11 + (3*b^3*x^(14/3))/14","A",2,1,13,0.07692,1,"{43}"
669,1,51,0,0.0111296,"\int \sqrt[3]{x} (a+b x)^3 \, dx","Int[x^(1/3)*(a + b*x)^3,x]","\frac{9}{7} a^2 b x^{7/3}+\frac{3}{4} a^3 x^{4/3}+\frac{9}{10} a b^2 x^{10/3}+\frac{3}{13} b^3 x^{13/3}","\frac{9}{7} a^2 b x^{7/3}+\frac{3}{4} a^3 x^{4/3}+\frac{9}{10} a b^2 x^{10/3}+\frac{3}{13} b^3 x^{13/3}",1,"(3*a^3*x^(4/3))/4 + (9*a^2*b*x^(7/3))/7 + (9*a*b^2*x^(10/3))/10 + (3*b^3*x^(13/3))/13","A",2,1,13,0.07692,1,"{43}"
670,1,51,0,0.0104117,"\int \frac{(a+b x)^3}{\sqrt[3]{x}} \, dx","Int[(a + b*x)^3/x^(1/3),x]","\frac{9}{5} a^2 b x^{5/3}+\frac{3}{2} a^3 x^{2/3}+\frac{9}{8} a b^2 x^{8/3}+\frac{3}{11} b^3 x^{11/3}","\frac{9}{5} a^2 b x^{5/3}+\frac{3}{2} a^3 x^{2/3}+\frac{9}{8} a b^2 x^{8/3}+\frac{3}{11} b^3 x^{11/3}",1,"(3*a^3*x^(2/3))/2 + (9*a^2*b*x^(5/3))/5 + (9*a*b^2*x^(8/3))/8 + (3*b^3*x^(11/3))/11","A",2,1,13,0.07692,1,"{43}"
671,1,49,0,0.010978,"\int \frac{(a+b x)^3}{x^{2/3}} \, dx","Int[(a + b*x)^3/x^(2/3),x]","\frac{9}{4} a^2 b x^{4/3}+3 a^3 \sqrt[3]{x}+\frac{9}{7} a b^2 x^{7/3}+\frac{3}{10} b^3 x^{10/3}","\frac{9}{4} a^2 b x^{4/3}+3 a^3 \sqrt[3]{x}+\frac{9}{7} a b^2 x^{7/3}+\frac{3}{10} b^3 x^{10/3}",1,"3*a^3*x^(1/3) + (9*a^2*b*x^(4/3))/4 + (9*a*b^2*x^(7/3))/7 + (3*b^3*x^(10/3))/10","A",2,1,13,0.07692,1,"{43}"
672,1,49,0,0.0109002,"\int \frac{(a+b x)^3}{x^{4/3}} \, dx","Int[(a + b*x)^3/x^(4/3),x]","\frac{9}{2} a^2 b x^{2/3}-\frac{3 a^3}{\sqrt[3]{x}}+\frac{9}{5} a b^2 x^{5/3}+\frac{3}{8} b^3 x^{8/3}","\frac{9}{2} a^2 b x^{2/3}-\frac{3 a^3}{\sqrt[3]{x}}+\frac{9}{5} a b^2 x^{5/3}+\frac{3}{8} b^3 x^{8/3}",1,"(-3*a^3)/x^(1/3) + (9*a^2*b*x^(2/3))/2 + (9*a*b^2*x^(5/3))/5 + (3*b^3*x^(8/3))/8","A",2,1,13,0.07692,1,"{43}"
673,1,49,0,0.0107705,"\int \frac{(a+b x)^3}{x^{5/3}} \, dx","Int[(a + b*x)^3/x^(5/3),x]","9 a^2 b \sqrt[3]{x}-\frac{3 a^3}{2 x^{2/3}}+\frac{9}{4} a b^2 x^{4/3}+\frac{3}{7} b^3 x^{7/3}","9 a^2 b \sqrt[3]{x}-\frac{3 a^3}{2 x^{2/3}}+\frac{9}{4} a b^2 x^{4/3}+\frac{3}{7} b^3 x^{7/3}",1,"(-3*a^3)/(2*x^(2/3)) + 9*a^2*b*x^(1/3) + (9*a*b^2*x^(4/3))/4 + (3*b^3*x^(7/3))/7","A",2,1,13,0.07692,1,"{43}"
674,1,125,0,0.0700581,"\int \frac{x^{5/3}}{a+b x} \, dx","Int[x^(5/3)/(a + b*x),x]","-\frac{3 a^{5/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{2 b^{8/3}}+\frac{a^{5/3} \log (a+b x)}{2 b^{8/3}}-\frac{\sqrt{3} a^{5/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a}}\right)}{b^{8/3}}-\frac{3 a x^{2/3}}{2 b^2}+\frac{3 x^{5/3}}{5 b}","-\frac{3 a^{5/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{2 b^{8/3}}+\frac{a^{5/3} \log (a+b x)}{2 b^{8/3}}-\frac{\sqrt{3} a^{5/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a}}\right)}{b^{8/3}}-\frac{3 a x^{2/3}}{2 b^2}+\frac{3 x^{5/3}}{5 b}",1,"(-3*a*x^(2/3))/(2*b^2) + (3*x^(5/3))/(5*b) - (Sqrt[3]*a^(5/3)*ArcTan[(a^(1/3) - 2*b^(1/3)*x^(1/3))/(Sqrt[3]*a^(1/3))])/b^(8/3) - (3*a^(5/3)*Log[a^(1/3) + b^(1/3)*x^(1/3)])/(2*b^(8/3)) + (a^(5/3)*Log[a + b*x])/(2*b^(8/3))","A",6,5,13,0.3846,1,"{50, 56, 617, 204, 31}"
675,1,123,0,0.0563835,"\int \frac{x^{4/3}}{a+b x} \, dx","Int[x^(4/3)/(a + b*x),x]","\frac{3 a^{4/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{2 b^{7/3}}-\frac{a^{4/3} \log (a+b x)}{2 b^{7/3}}-\frac{\sqrt{3} a^{4/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a}}\right)}{b^{7/3}}-\frac{3 a \sqrt[3]{x}}{b^2}+\frac{3 x^{4/3}}{4 b}","\frac{3 a^{4/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{2 b^{7/3}}-\frac{a^{4/3} \log (a+b x)}{2 b^{7/3}}-\frac{\sqrt{3} a^{4/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a}}\right)}{b^{7/3}}-\frac{3 a \sqrt[3]{x}}{b^2}+\frac{3 x^{4/3}}{4 b}",1,"(-3*a*x^(1/3))/b^2 + (3*x^(4/3))/(4*b) - (Sqrt[3]*a^(4/3)*ArcTan[(a^(1/3) - 2*b^(1/3)*x^(1/3))/(Sqrt[3]*a^(1/3))])/b^(7/3) + (3*a^(4/3)*Log[a^(1/3) + b^(1/3)*x^(1/3)])/(2*b^(7/3)) - (a^(4/3)*Log[a + b*x])/(2*b^(7/3))","A",6,5,13,0.3846,1,"{50, 58, 617, 204, 31}"
676,1,111,0,0.0396263,"\int \frac{x^{2/3}}{a+b x} \, dx","Int[x^(2/3)/(a + b*x),x]","\frac{3 a^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{2 b^{5/3}}-\frac{a^{2/3} \log (a+b x)}{2 b^{5/3}}+\frac{\sqrt{3} a^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a}}\right)}{b^{5/3}}+\frac{3 x^{2/3}}{2 b}","\frac{3 a^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{2 b^{5/3}}-\frac{a^{2/3} \log (a+b x)}{2 b^{5/3}}+\frac{\sqrt{3} a^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a}}\right)}{b^{5/3}}+\frac{3 x^{2/3}}{2 b}",1,"(3*x^(2/3))/(2*b) + (Sqrt[3]*a^(2/3)*ArcTan[(a^(1/3) - 2*b^(1/3)*x^(1/3))/(Sqrt[3]*a^(1/3))])/b^(5/3) + (3*a^(2/3)*Log[a^(1/3) + b^(1/3)*x^(1/3)])/(2*b^(5/3)) - (a^(2/3)*Log[a + b*x])/(2*b^(5/3))","A",5,5,13,0.3846,1,"{50, 56, 617, 204, 31}"
677,1,109,0,0.0389769,"\int \frac{\sqrt[3]{x}}{a+b x} \, dx","Int[x^(1/3)/(a + b*x),x]","-\frac{3 \sqrt[3]{a} \log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{2 b^{4/3}}+\frac{\sqrt[3]{a} \log (a+b x)}{2 b^{4/3}}+\frac{\sqrt{3} \sqrt[3]{a} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a}}\right)}{b^{4/3}}+\frac{3 \sqrt[3]{x}}{b}","-\frac{3 \sqrt[3]{a} \log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{2 b^{4/3}}+\frac{\sqrt[3]{a} \log (a+b x)}{2 b^{4/3}}+\frac{\sqrt{3} \sqrt[3]{a} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a}}\right)}{b^{4/3}}+\frac{3 \sqrt[3]{x}}{b}",1,"(3*x^(1/3))/b + (Sqrt[3]*a^(1/3)*ArcTan[(a^(1/3) - 2*b^(1/3)*x^(1/3))/(Sqrt[3]*a^(1/3))])/b^(4/3) - (3*a^(1/3)*Log[a^(1/3) + b^(1/3)*x^(1/3)])/(2*b^(4/3)) + (a^(1/3)*Log[a + b*x])/(2*b^(4/3))","A",5,5,13,0.3846,1,"{50, 58, 617, 204, 31}"
678,1,100,0,0.0284094,"\int \frac{1}{\sqrt[3]{x} (a+b x)} \, dx","Int[1/(x^(1/3)*(a + b*x)),x]","-\frac{3 \log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{2 \sqrt[3]{a} b^{2/3}}+\frac{\log (a+b x)}{2 \sqrt[3]{a} b^{2/3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt[3]{a} b^{2/3}}","-\frac{3 \log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{2 \sqrt[3]{a} b^{2/3}}+\frac{\log (a+b x)}{2 \sqrt[3]{a} b^{2/3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt[3]{a} b^{2/3}}",1,"-((Sqrt[3]*ArcTan[(a^(1/3) - 2*b^(1/3)*x^(1/3))/(Sqrt[3]*a^(1/3))])/(a^(1/3)*b^(2/3))) - (3*Log[a^(1/3) + b^(1/3)*x^(1/3)])/(2*a^(1/3)*b^(2/3)) + Log[a + b*x]/(2*a^(1/3)*b^(2/3))","A",4,4,13,0.3077,1,"{56, 617, 204, 31}"
679,1,100,0,0.02787,"\int \frac{1}{x^{2/3} (a+b x)} \, dx","Int[1/(x^(2/3)*(a + b*x)),x]","\frac{3 \log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{2 a^{2/3} \sqrt[3]{b}}-\frac{\log (a+b x)}{2 a^{2/3} \sqrt[3]{b}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a}}\right)}{a^{2/3} \sqrt[3]{b}}","\frac{3 \log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{2 a^{2/3} \sqrt[3]{b}}-\frac{\log (a+b x)}{2 a^{2/3} \sqrt[3]{b}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a}}\right)}{a^{2/3} \sqrt[3]{b}}",1,"-((Sqrt[3]*ArcTan[(a^(1/3) - 2*b^(1/3)*x^(1/3))/(Sqrt[3]*a^(1/3))])/(a^(2/3)*b^(1/3))) + (3*Log[a^(1/3) + b^(1/3)*x^(1/3)])/(2*a^(2/3)*b^(1/3)) - Log[a + b*x]/(2*a^(2/3)*b^(1/3))","A",4,4,13,0.3077,1,"{58, 617, 204, 31}"
680,1,109,0,0.0375527,"\int \frac{1}{x^{4/3} (a+b x)} \, dx","Int[1/(x^(4/3)*(a + b*x)),x]","\frac{3 \sqrt[3]{b} \log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{2 a^{4/3}}-\frac{\sqrt[3]{b} \log (a+b x)}{2 a^{4/3}}+\frac{\sqrt{3} \sqrt[3]{b} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a}}\right)}{a^{4/3}}-\frac{3}{a \sqrt[3]{x}}","\frac{3 \sqrt[3]{b} \log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{2 a^{4/3}}-\frac{\sqrt[3]{b} \log (a+b x)}{2 a^{4/3}}+\frac{\sqrt{3} \sqrt[3]{b} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a}}\right)}{a^{4/3}}-\frac{3}{a \sqrt[3]{x}}",1,"-3/(a*x^(1/3)) + (Sqrt[3]*b^(1/3)*ArcTan[(a^(1/3) - 2*b^(1/3)*x^(1/3))/(Sqrt[3]*a^(1/3))])/a^(4/3) + (3*b^(1/3)*Log[a^(1/3) + b^(1/3)*x^(1/3)])/(2*a^(4/3)) - (b^(1/3)*Log[a + b*x])/(2*a^(4/3))","A",5,5,13,0.3846,1,"{51, 56, 617, 204, 31}"
681,1,111,0,0.0391327,"\int \frac{1}{x^{5/3} (a+b x)} \, dx","Int[1/(x^(5/3)*(a + b*x)),x]","-\frac{3 b^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{2 a^{5/3}}+\frac{b^{2/3} \log (a+b x)}{2 a^{5/3}}+\frac{\sqrt{3} b^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a}}\right)}{a^{5/3}}-\frac{3}{2 a x^{2/3}}","-\frac{3 b^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{2 a^{5/3}}+\frac{b^{2/3} \log (a+b x)}{2 a^{5/3}}+\frac{\sqrt{3} b^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a}}\right)}{a^{5/3}}-\frac{3}{2 a x^{2/3}}",1,"-3/(2*a*x^(2/3)) + (Sqrt[3]*b^(2/3)*ArcTan[(a^(1/3) - 2*b^(1/3)*x^(1/3))/(Sqrt[3]*a^(1/3))])/a^(5/3) - (3*b^(2/3)*Log[a^(1/3) + b^(1/3)*x^(1/3)])/(2*a^(5/3)) + (b^(2/3)*Log[a + b*x])/(2*a^(5/3))","A",5,5,13,0.3846,1,"{51, 58, 617, 204, 31}"
682,1,129,0,0.0470636,"\int \frac{x^{5/3}}{(a+b x)^2} \, dx","Int[x^(5/3)/(a + b*x)^2,x]","\frac{5 a^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{2 b^{8/3}}-\frac{5 a^{2/3} \log (a+b x)}{6 b^{8/3}}+\frac{5 a^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} b^{8/3}}-\frac{x^{5/3}}{b (a+b x)}+\frac{5 x^{2/3}}{2 b^2}","\frac{5 a^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{2 b^{8/3}}-\frac{5 a^{2/3} \log (a+b x)}{6 b^{8/3}}+\frac{5 a^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} b^{8/3}}-\frac{x^{5/3}}{b (a+b x)}+\frac{5 x^{2/3}}{2 b^2}",1,"(5*x^(2/3))/(2*b^2) - x^(5/3)/(b*(a + b*x)) + (5*a^(2/3)*ArcTan[(a^(1/3) - 2*b^(1/3)*x^(1/3))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*b^(8/3)) + (5*a^(2/3)*Log[a^(1/3) + b^(1/3)*x^(1/3)])/(2*b^(8/3)) - (5*a^(2/3)*Log[a + b*x])/(6*b^(8/3))","A",6,6,13,0.4615,1,"{47, 50, 56, 617, 204, 31}"
683,1,125,0,0.0465502,"\int \frac{x^{4/3}}{(a+b x)^2} \, dx","Int[x^(4/3)/(a + b*x)^2,x]","-\frac{2 \sqrt[3]{a} \log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{b^{7/3}}+\frac{2 \sqrt[3]{a} \log (a+b x)}{3 b^{7/3}}+\frac{4 \sqrt[3]{a} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} b^{7/3}}-\frac{x^{4/3}}{b (a+b x)}+\frac{4 \sqrt[3]{x}}{b^2}","-\frac{2 \sqrt[3]{a} \log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{b^{7/3}}+\frac{2 \sqrt[3]{a} \log (a+b x)}{3 b^{7/3}}+\frac{4 \sqrt[3]{a} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} b^{7/3}}-\frac{x^{4/3}}{b (a+b x)}+\frac{4 \sqrt[3]{x}}{b^2}",1,"(4*x^(1/3))/b^2 - x^(4/3)/(b*(a + b*x)) + (4*a^(1/3)*ArcTan[(a^(1/3) - 2*b^(1/3)*x^(1/3))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*b^(7/3)) - (2*a^(1/3)*Log[a^(1/3) + b^(1/3)*x^(1/3)])/b^(7/3) + (2*a^(1/3)*Log[a + b*x])/(3*b^(7/3))","A",6,6,13,0.4615,1,"{47, 50, 58, 617, 204, 31}"
684,1,115,0,0.0377792,"\int \frac{x^{2/3}}{(a+b x)^2} \, dx","Int[x^(2/3)/(a + b*x)^2,x]","-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{\sqrt[3]{a} b^{5/3}}+\frac{\log (a+b x)}{3 \sqrt[3]{a} b^{5/3}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} \sqrt[3]{a} b^{5/3}}-\frac{x^{2/3}}{b (a+b x)}","-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{\sqrt[3]{a} b^{5/3}}+\frac{\log (a+b x)}{3 \sqrt[3]{a} b^{5/3}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} \sqrt[3]{a} b^{5/3}}-\frac{x^{2/3}}{b (a+b x)}",1,"-(x^(2/3)/(b*(a + b*x))) - (2*ArcTan[(a^(1/3) - 2*b^(1/3)*x^(1/3))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(1/3)*b^(5/3)) - Log[a^(1/3) + b^(1/3)*x^(1/3)]/(a^(1/3)*b^(5/3)) + Log[a + b*x]/(3*a^(1/3)*b^(5/3))","A",5,5,13,0.3846,1,"{47, 56, 617, 204, 31}"
685,1,117,0,0.0379469,"\int \frac{\sqrt[3]{x}}{(a+b x)^2} \, dx","Int[x^(1/3)/(a + b*x)^2,x]","\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{2 a^{2/3} b^{4/3}}-\frac{\log (a+b x)}{6 a^{2/3} b^{4/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} b^{4/3}}-\frac{\sqrt[3]{x}}{b (a+b x)}","\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{2 a^{2/3} b^{4/3}}-\frac{\log (a+b x)}{6 a^{2/3} b^{4/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} b^{4/3}}-\frac{\sqrt[3]{x}}{b (a+b x)}",1,"-(x^(1/3)/(b*(a + b*x))) - ArcTan[(a^(1/3) - 2*b^(1/3)*x^(1/3))/(Sqrt[3]*a^(1/3))]/(Sqrt[3]*a^(2/3)*b^(4/3)) + Log[a^(1/3) + b^(1/3)*x^(1/3)]/(2*a^(2/3)*b^(4/3)) - Log[a + b*x]/(6*a^(2/3)*b^(4/3))","A",5,5,13,0.3846,1,"{47, 58, 617, 204, 31}"
686,1,116,0,0.0414263,"\int \frac{1}{\sqrt[3]{x} (a+b x)^2} \, dx","Int[1/(x^(1/3)*(a + b*x)^2),x]","-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{2 a^{4/3} b^{2/3}}+\frac{\log (a+b x)}{6 a^{4/3} b^{2/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{4/3} b^{2/3}}+\frac{x^{2/3}}{a (a+b x)}","-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{2 a^{4/3} b^{2/3}}+\frac{\log (a+b x)}{6 a^{4/3} b^{2/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{4/3} b^{2/3}}+\frac{x^{2/3}}{a (a+b x)}",1,"x^(2/3)/(a*(a + b*x)) - ArcTan[(a^(1/3) - 2*b^(1/3)*x^(1/3))/(Sqrt[3]*a^(1/3))]/(Sqrt[3]*a^(4/3)*b^(2/3)) - Log[a^(1/3) + b^(1/3)*x^(1/3)]/(2*a^(4/3)*b^(2/3)) + Log[a + b*x]/(6*a^(4/3)*b^(2/3))","A",5,5,13,0.3846,1,"{51, 56, 617, 204, 31}"
687,1,113,0,0.0404265,"\int \frac{1}{x^{2/3} (a+b x)^2} \, dx","Int[1/(x^(2/3)*(a + b*x)^2),x]","\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{a^{5/3} \sqrt[3]{b}}-\frac{\log (a+b x)}{3 a^{5/3} \sqrt[3]{b}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{5/3} \sqrt[3]{b}}+\frac{\sqrt[3]{x}}{a (a+b x)}","\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{a^{5/3} \sqrt[3]{b}}-\frac{\log (a+b x)}{3 a^{5/3} \sqrt[3]{b}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{5/3} \sqrt[3]{b}}+\frac{\sqrt[3]{x}}{a (a+b x)}",1,"x^(1/3)/(a*(a + b*x)) - (2*ArcTan[(a^(1/3) - 2*b^(1/3)*x^(1/3))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(5/3)*b^(1/3)) + Log[a^(1/3) + b^(1/3)*x^(1/3)]/(a^(5/3)*b^(1/3)) - Log[a + b*x]/(3*a^(5/3)*b^(1/3))","A",5,5,13,0.3846,1,"{51, 58, 617, 204, 31}"
688,1,124,0,0.0491247,"\int \frac{1}{x^{4/3} (a+b x)^2} \, dx","Int[1/(x^(4/3)*(a + b*x)^2),x]","\frac{2 \sqrt[3]{b} \log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{a^{7/3}}-\frac{2 \sqrt[3]{b} \log (a+b x)}{3 a^{7/3}}+\frac{4 \sqrt[3]{b} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{7/3}}-\frac{4}{a^2 \sqrt[3]{x}}+\frac{1}{a \sqrt[3]{x} (a+b x)}","\frac{2 \sqrt[3]{b} \log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{a^{7/3}}-\frac{2 \sqrt[3]{b} \log (a+b x)}{3 a^{7/3}}+\frac{4 \sqrt[3]{b} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{7/3}}-\frac{4}{a^2 \sqrt[3]{x}}+\frac{1}{a \sqrt[3]{x} (a+b x)}",1,"-4/(a^2*x^(1/3)) + 1/(a*x^(1/3)*(a + b*x)) + (4*b^(1/3)*ArcTan[(a^(1/3) - 2*b^(1/3)*x^(1/3))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(7/3)) + (2*b^(1/3)*Log[a^(1/3) + b^(1/3)*x^(1/3)])/a^(7/3) - (2*b^(1/3)*Log[a + b*x])/(3*a^(7/3))","A",6,5,13,0.3846,1,"{51, 56, 617, 204, 31}"
689,1,128,0,0.0501187,"\int \frac{1}{x^{5/3} (a+b x)^2} \, dx","Int[1/(x^(5/3)*(a + b*x)^2),x]","-\frac{5 b^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{2 a^{8/3}}+\frac{5 b^{2/3} \log (a+b x)}{6 a^{8/3}}+\frac{5 b^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{8/3}}-\frac{5}{2 a^2 x^{2/3}}+\frac{1}{a x^{2/3} (a+b x)}","-\frac{5 b^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{2 a^{8/3}}+\frac{5 b^{2/3} \log (a+b x)}{6 a^{8/3}}+\frac{5 b^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{8/3}}-\frac{5}{2 a^2 x^{2/3}}+\frac{1}{a x^{2/3} (a+b x)}",1,"-5/(2*a^2*x^(2/3)) + 1/(a*x^(2/3)*(a + b*x)) + (5*b^(2/3)*ArcTan[(a^(1/3) - 2*b^(1/3)*x^(1/3))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(8/3)) - (5*b^(2/3)*Log[a^(1/3) + b^(1/3)*x^(1/3)])/(2*a^(8/3)) + (5*b^(2/3)*Log[a + b*x])/(6*a^(8/3))","A",6,5,13,0.3846,1,"{51, 58, 617, 204, 31}"
690,1,140,0,0.0486111,"\int \frac{x^{5/3}}{(a+b x)^3} \, dx","Int[x^(5/3)/(a + b*x)^3,x]","-\frac{5 x^{2/3}}{6 b^2 (a+b x)}-\frac{5 \log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{6 \sqrt[3]{a} b^{8/3}}+\frac{5 \log (a+b x)}{18 \sqrt[3]{a} b^{8/3}}-\frac{5 \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} \sqrt[3]{a} b^{8/3}}-\frac{x^{5/3}}{2 b (a+b x)^2}","-\frac{5 x^{2/3}}{6 b^2 (a+b x)}-\frac{5 \log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{6 \sqrt[3]{a} b^{8/3}}+\frac{5 \log (a+b x)}{18 \sqrt[3]{a} b^{8/3}}-\frac{5 \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} \sqrt[3]{a} b^{8/3}}-\frac{x^{5/3}}{2 b (a+b x)^2}",1,"-x^(5/3)/(2*b*(a + b*x)^2) - (5*x^(2/3))/(6*b^2*(a + b*x)) - (5*ArcTan[(a^(1/3) - 2*b^(1/3)*x^(1/3))/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(1/3)*b^(8/3)) - (5*Log[a^(1/3) + b^(1/3)*x^(1/3)])/(6*a^(1/3)*b^(8/3)) + (5*Log[a + b*x])/(18*a^(1/3)*b^(8/3))","A",6,5,13,0.3846,1,"{47, 56, 617, 204, 31}"
691,1,140,0,0.053599,"\int \frac{x^{4/3}}{(a+b x)^3} \, dx","Int[x^(4/3)/(a + b*x)^3,x]","\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{3 a^{2/3} b^{7/3}}-\frac{\log (a+b x)}{9 a^{2/3} b^{7/3}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{2/3} b^{7/3}}-\frac{2 \sqrt[3]{x}}{3 b^2 (a+b x)}-\frac{x^{4/3}}{2 b (a+b x)^2}","\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{3 a^{2/3} b^{7/3}}-\frac{\log (a+b x)}{9 a^{2/3} b^{7/3}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{2/3} b^{7/3}}-\frac{2 \sqrt[3]{x}}{3 b^2 (a+b x)}-\frac{x^{4/3}}{2 b (a+b x)^2}",1,"-x^(4/3)/(2*b*(a + b*x)^2) - (2*x^(1/3))/(3*b^2*(a + b*x)) - (2*ArcTan[(a^(1/3) - 2*b^(1/3)*x^(1/3))/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(2/3)*b^(7/3)) + Log[a^(1/3) + b^(1/3)*x^(1/3)]/(3*a^(2/3)*b^(7/3)) - Log[a + b*x]/(9*a^(2/3)*b^(7/3))","A",6,5,13,0.3846,1,"{47, 58, 617, 204, 31}"
692,1,143,0,0.0499361,"\int \frac{x^{2/3}}{(a+b x)^3} \, dx","Int[x^(2/3)/(a + b*x)^3,x]","-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{6 a^{4/3} b^{5/3}}+\frac{\log (a+b x)}{18 a^{4/3} b^{5/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{4/3} b^{5/3}}+\frac{x^{2/3}}{3 a b (a+b x)}-\frac{x^{2/3}}{2 b (a+b x)^2}","-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{6 a^{4/3} b^{5/3}}+\frac{\log (a+b x)}{18 a^{4/3} b^{5/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{4/3} b^{5/3}}+\frac{x^{2/3}}{3 a b (a+b x)}-\frac{x^{2/3}}{2 b (a+b x)^2}",1,"-x^(2/3)/(2*b*(a + b*x)^2) + x^(2/3)/(3*a*b*(a + b*x)) - ArcTan[(a^(1/3) - 2*b^(1/3)*x^(1/3))/(Sqrt[3]*a^(1/3))]/(3*Sqrt[3]*a^(4/3)*b^(5/3)) - Log[a^(1/3) + b^(1/3)*x^(1/3)]/(6*a^(4/3)*b^(5/3)) + Log[a + b*x]/(18*a^(4/3)*b^(5/3))","A",6,6,13,0.4615,1,"{47, 51, 56, 617, 204, 31}"
693,1,143,0,0.0519344,"\int \frac{\sqrt[3]{x}}{(a+b x)^3} \, dx","Int[x^(1/3)/(a + b*x)^3,x]","\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{6 a^{5/3} b^{4/3}}-\frac{\log (a+b x)}{18 a^{5/3} b^{4/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{5/3} b^{4/3}}+\frac{\sqrt[3]{x}}{6 a b (a+b x)}-\frac{\sqrt[3]{x}}{2 b (a+b x)^2}","\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{6 a^{5/3} b^{4/3}}-\frac{\log (a+b x)}{18 a^{5/3} b^{4/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{5/3} b^{4/3}}+\frac{\sqrt[3]{x}}{6 a b (a+b x)}-\frac{\sqrt[3]{x}}{2 b (a+b x)^2}",1,"-x^(1/3)/(2*b*(a + b*x)^2) + x^(1/3)/(6*a*b*(a + b*x)) - ArcTan[(a^(1/3) - 2*b^(1/3)*x^(1/3))/(Sqrt[3]*a^(1/3))]/(3*Sqrt[3]*a^(5/3)*b^(4/3)) + Log[a^(1/3) + b^(1/3)*x^(1/3)]/(6*a^(5/3)*b^(4/3)) - Log[a + b*x]/(18*a^(5/3)*b^(4/3))","A",6,6,13,0.4615,1,"{47, 51, 58, 617, 204, 31}"
694,1,140,0,0.0528097,"\int \frac{1}{\sqrt[3]{x} (a+b x)^3} \, dx","Int[1/(x^(1/3)*(a + b*x)^3),x]","-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{3 a^{7/3} b^{2/3}}+\frac{\log (a+b x)}{9 a^{7/3} b^{2/3}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{7/3} b^{2/3}}+\frac{2 x^{2/3}}{3 a^2 (a+b x)}+\frac{x^{2/3}}{2 a (a+b x)^2}","-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{3 a^{7/3} b^{2/3}}+\frac{\log (a+b x)}{9 a^{7/3} b^{2/3}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{7/3} b^{2/3}}+\frac{2 x^{2/3}}{3 a^2 (a+b x)}+\frac{x^{2/3}}{2 a (a+b x)^2}",1,"x^(2/3)/(2*a*(a + b*x)^2) + (2*x^(2/3))/(3*a^2*(a + b*x)) - (2*ArcTan[(a^(1/3) - 2*b^(1/3)*x^(1/3))/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(7/3)*b^(2/3)) - Log[a^(1/3) + b^(1/3)*x^(1/3)]/(3*a^(7/3)*b^(2/3)) + Log[a + b*x]/(9*a^(7/3)*b^(2/3))","A",6,5,13,0.3846,1,"{51, 56, 617, 204, 31}"
695,1,140,0,0.0496618,"\int \frac{1}{x^{2/3} (a+b x)^3} \, dx","Int[1/(x^(2/3)*(a + b*x)^3),x]","\frac{5 \sqrt[3]{x}}{6 a^2 (a+b x)}+\frac{5 \log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{6 a^{8/3} \sqrt[3]{b}}-\frac{5 \log (a+b x)}{18 a^{8/3} \sqrt[3]{b}}-\frac{5 \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{8/3} \sqrt[3]{b}}+\frac{\sqrt[3]{x}}{2 a (a+b x)^2}","\frac{5 \sqrt[3]{x}}{6 a^2 (a+b x)}+\frac{5 \log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{6 a^{8/3} \sqrt[3]{b}}-\frac{5 \log (a+b x)}{18 a^{8/3} \sqrt[3]{b}}-\frac{5 \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{8/3} \sqrt[3]{b}}+\frac{\sqrt[3]{x}}{2 a (a+b x)^2}",1,"x^(1/3)/(2*a*(a + b*x)^2) + (5*x^(1/3))/(6*a^2*(a + b*x)) - (5*ArcTan[(a^(1/3) - 2*b^(1/3)*x^(1/3))/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(8/3)*b^(1/3)) + (5*Log[a^(1/3) + b^(1/3)*x^(1/3)])/(6*a^(8/3)*b^(1/3)) - (5*Log[a + b*x])/(18*a^(8/3)*b^(1/3))","A",6,5,13,0.3846,1,"{51, 58, 617, 204, 31}"
696,1,152,0,0.0596014,"\int \frac{1}{x^{4/3} (a+b x)^3} \, dx","Int[1/(x^(4/3)*(a + b*x)^3),x]","\frac{7}{6 a^2 \sqrt[3]{x} (a+b x)}+\frac{7 \sqrt[3]{b} \log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{3 a^{10/3}}-\frac{7 \sqrt[3]{b} \log (a+b x)}{9 a^{10/3}}+\frac{14 \sqrt[3]{b} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{10/3}}-\frac{14}{3 a^3 \sqrt[3]{x}}+\frac{1}{2 a \sqrt[3]{x} (a+b x)^2}","\frac{7}{6 a^2 \sqrt[3]{x} (a+b x)}+\frac{7 \sqrt[3]{b} \log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{3 a^{10/3}}-\frac{7 \sqrt[3]{b} \log (a+b x)}{9 a^{10/3}}+\frac{14 \sqrt[3]{b} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{10/3}}-\frac{14}{3 a^3 \sqrt[3]{x}}+\frac{1}{2 a \sqrt[3]{x} (a+b x)^2}",1,"-14/(3*a^3*x^(1/3)) + 1/(2*a*x^(1/3)*(a + b*x)^2) + 7/(6*a^2*x^(1/3)*(a + b*x)) + (14*b^(1/3)*ArcTan[(a^(1/3) - 2*b^(1/3)*x^(1/3))/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(10/3)) + (7*b^(1/3)*Log[a^(1/3) + b^(1/3)*x^(1/3)])/(3*a^(10/3)) - (7*b^(1/3)*Log[a + b*x])/(9*a^(10/3))","A",7,5,13,0.3846,1,"{51, 56, 617, 204, 31}"
697,1,152,0,0.0606935,"\int \frac{1}{x^{5/3} (a+b x)^3} \, dx","Int[1/(x^(5/3)*(a + b*x)^3),x]","-\frac{10 b^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{3 a^{11/3}}+\frac{10 b^{2/3} \log (a+b x)}{9 a^{11/3}}+\frac{20 b^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{11/3}}+\frac{4}{3 a^2 x^{2/3} (a+b x)}-\frac{10}{3 a^3 x^{2/3}}+\frac{1}{2 a x^{2/3} (a+b x)^2}","-\frac{10 b^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{3 a^{11/3}}+\frac{10 b^{2/3} \log (a+b x)}{9 a^{11/3}}+\frac{20 b^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{11/3}}+\frac{4}{3 a^2 x^{2/3} (a+b x)}-\frac{10}{3 a^3 x^{2/3}}+\frac{1}{2 a x^{2/3} (a+b x)^2}",1,"-10/(3*a^3*x^(2/3)) + 1/(2*a*x^(2/3)*(a + b*x)^2) + 4/(3*a^2*x^(2/3)*(a + b*x)) + (20*b^(2/3)*ArcTan[(a^(1/3) - 2*b^(1/3)*x^(1/3))/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(11/3)) - (10*b^(2/3)*Log[a^(1/3) + b^(1/3)*x^(1/3)])/(3*a^(11/3)) + (10*b^(2/3)*Log[a + b*x])/(9*a^(11/3))","A",7,5,13,0.3846,1,"{51, 58, 617, 204, 31}"
698,1,58,0,0.0209206,"\int \frac{\sqrt[4]{1-x}}{1+x} \, dx","Int[(1 - x)^(1/4)/(1 + x),x]","4 \sqrt[4]{1-x}-2 \sqrt[4]{2} \tan ^{-1}\left(\frac{\sqrt[4]{1-x}}{\sqrt[4]{2}}\right)-2 \sqrt[4]{2} \tanh ^{-1}\left(\frac{\sqrt[4]{1-x}}{\sqrt[4]{2}}\right)","4 \sqrt[4]{1-x}-2 \sqrt[4]{2} \tan ^{-1}\left(\frac{\sqrt[4]{1-x}}{\sqrt[4]{2}}\right)-2 \sqrt[4]{2} \tanh ^{-1}\left(\frac{\sqrt[4]{1-x}}{\sqrt[4]{2}}\right)",1,"4*(1 - x)^(1/4) - 2*2^(1/4)*ArcTan[(1 - x)^(1/4)/2^(1/4)] - 2*2^(1/4)*ArcTanh[(1 - x)^(1/4)/2^(1/4)]","A",5,5,15,0.3333,1,"{50, 63, 212, 206, 203}"
699,1,187,0,0.0846196,"\int x^m (a+b x)^{10} \, dx","Int[x^m*(a + b*x)^10,x]","\frac{45 a^8 b^2 x^{m+3}}{m+3}+\frac{120 a^7 b^3 x^{m+4}}{m+4}+\frac{210 a^6 b^4 x^{m+5}}{m+5}+\frac{252 a^5 b^5 x^{m+6}}{m+6}+\frac{210 a^4 b^6 x^{m+7}}{m+7}+\frac{120 a^3 b^7 x^{m+8}}{m+8}+\frac{45 a^2 b^8 x^{m+9}}{m+9}+\frac{10 a^9 b x^{m+2}}{m+2}+\frac{a^{10} x^{m+1}}{m+1}+\frac{10 a b^9 x^{m+10}}{m+10}+\frac{b^{10} x^{m+11}}{m+11}","\frac{45 a^8 b^2 x^{m+3}}{m+3}+\frac{120 a^7 b^3 x^{m+4}}{m+4}+\frac{210 a^6 b^4 x^{m+5}}{m+5}+\frac{252 a^5 b^5 x^{m+6}}{m+6}+\frac{210 a^4 b^6 x^{m+7}}{m+7}+\frac{120 a^3 b^7 x^{m+8}}{m+8}+\frac{45 a^2 b^8 x^{m+9}}{m+9}+\frac{10 a^9 b x^{m+2}}{m+2}+\frac{a^{10} x^{m+1}}{m+1}+\frac{10 a b^9 x^{m+10}}{m+10}+\frac{b^{10} x^{m+11}}{m+11}",1,"(a^10*x^(1 + m))/(1 + m) + (10*a^9*b*x^(2 + m))/(2 + m) + (45*a^8*b^2*x^(3 + m))/(3 + m) + (120*a^7*b^3*x^(4 + m))/(4 + m) + (210*a^6*b^4*x^(5 + m))/(5 + m) + (252*a^5*b^5*x^(6 + m))/(6 + m) + (210*a^4*b^6*x^(7 + m))/(7 + m) + (120*a^3*b^7*x^(8 + m))/(8 + m) + (45*a^2*b^8*x^(9 + m))/(9 + m) + (10*a*b^9*x^(10 + m))/(10 + m) + (b^10*x^(11 + m))/(11 + m)","A",2,1,11,0.09091,1,"{43}"
700,1,133,0,0.0500478,"\int x^m (a+b x)^7 \, dx","Int[x^m*(a + b*x)^7,x]","\frac{21 a^5 b^2 x^{m+3}}{m+3}+\frac{35 a^4 b^3 x^{m+4}}{m+4}+\frac{35 a^3 b^4 x^{m+5}}{m+5}+\frac{21 a^2 b^5 x^{m+6}}{m+6}+\frac{7 a^6 b x^{m+2}}{m+2}+\frac{a^7 x^{m+1}}{m+1}+\frac{7 a b^6 x^{m+7}}{m+7}+\frac{b^7 x^{m+8}}{m+8}","\frac{21 a^5 b^2 x^{m+3}}{m+3}+\frac{35 a^4 b^3 x^{m+4}}{m+4}+\frac{35 a^3 b^4 x^{m+5}}{m+5}+\frac{21 a^2 b^5 x^{m+6}}{m+6}+\frac{7 a^6 b x^{m+2}}{m+2}+\frac{a^7 x^{m+1}}{m+1}+\frac{7 a b^6 x^{m+7}}{m+7}+\frac{b^7 x^{m+8}}{m+8}",1,"(a^7*x^(1 + m))/(1 + m) + (7*a^6*b*x^(2 + m))/(2 + m) + (21*a^5*b^2*x^(3 + m))/(3 + m) + (35*a^4*b^3*x^(4 + m))/(4 + m) + (35*a^3*b^4*x^(5 + m))/(5 + m) + (21*a^2*b^5*x^(6 + m))/(6 + m) + (7*a*b^6*x^(7 + m))/(7 + m) + (b^7*x^(8 + m))/(8 + m)","A",2,1,11,0.09091,1,"{43}"
701,1,61,0,0.0182403,"\int x^m (a+b x)^3 \, dx","Int[x^m*(a + b*x)^3,x]","\frac{3 a^2 b x^{m+2}}{m+2}+\frac{a^3 x^{m+1}}{m+1}+\frac{3 a b^2 x^{m+3}}{m+3}+\frac{b^3 x^{m+4}}{m+4}","\frac{3 a^2 b x^{m+2}}{m+2}+\frac{a^3 x^{m+1}}{m+1}+\frac{3 a b^2 x^{m+3}}{m+3}+\frac{b^3 x^{m+4}}{m+4}",1,"(a^3*x^(1 + m))/(1 + m) + (3*a^2*b*x^(2 + m))/(2 + m) + (3*a*b^2*x^(3 + m))/(3 + m) + (b^3*x^(4 + m))/(4 + m)","A",2,1,11,0.09091,1,"{43}"
702,1,43,0,0.012549,"\int x^m (a+b x)^2 \, dx","Int[x^m*(a + b*x)^2,x]","\frac{a^2 x^{m+1}}{m+1}+\frac{2 a b x^{m+2}}{m+2}+\frac{b^2 x^{m+3}}{m+3}","\frac{a^2 x^{m+1}}{m+1}+\frac{2 a b x^{m+2}}{m+2}+\frac{b^2 x^{m+3}}{m+3}",1,"(a^2*x^(1 + m))/(1 + m) + (2*a*b*x^(2 + m))/(2 + m) + (b^2*x^(3 + m))/(3 + m)","A",2,1,11,0.09091,1,"{43}"
703,1,25,0,0.0064292,"\int x^m (a+b x) \, dx","Int[x^m*(a + b*x),x]","\frac{a x^{m+1}}{m+1}+\frac{b x^{m+2}}{m+2}","\frac{a x^{m+1}}{m+1}+\frac{b x^{m+2}}{m+2}",1,"(a*x^(1 + m))/(1 + m) + (b*x^(2 + m))/(2 + m)","A",2,1,9,0.1111,1,"{43}"
704,1,29,0,0.0056343,"\int \frac{x^m}{a+b x} \, dx","Int[x^m/(a + b*x),x]","\frac{x^{m+1} \, _2F_1\left(1,m+1;m+2;-\frac{b x}{a}\right)}{a (m+1)}","\frac{x^{m+1} \, _2F_1\left(1,m+1;m+2;-\frac{b x}{a}\right)}{a (m+1)}",1,"(x^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, -((b*x)/a)])/(a*(1 + m))","A",1,1,11,0.09091,1,"{64}"
705,1,29,0,0.0052433,"\int \frac{x^m}{(a+b x)^2} \, dx","Int[x^m/(a + b*x)^2,x]","\frac{x^{m+1} \, _2F_1\left(2,m+1;m+2;-\frac{b x}{a}\right)}{a^2 (m+1)}","\frac{x^{m+1} \, _2F_1\left(2,m+1;m+2;-\frac{b x}{a}\right)}{a^2 (m+1)}",1,"(x^(1 + m)*Hypergeometric2F1[2, 1 + m, 2 + m, -((b*x)/a)])/(a^2*(1 + m))","A",1,1,11,0.09091,1,"{64}"
706,1,29,0,0.0054327,"\int \frac{x^m}{(a+b x)^3} \, dx","Int[x^m/(a + b*x)^3,x]","\frac{x^{m+1} \, _2F_1\left(3,m+1;m+2;-\frac{b x}{a}\right)}{a^3 (m+1)}","\frac{x^{m+1} \, _2F_1\left(3,m+1;m+2;-\frac{b x}{a}\right)}{a^3 (m+1)}",1,"(x^(1 + m)*Hypergeometric2F1[3, 1 + m, 2 + m, -((b*x)/a)])/(a^3*(1 + m))","A",1,1,11,0.09091,1,"{64}"
707,1,48,0,0.0112384,"\int x^m (a+b x)^{5/2} \, dx","Int[x^m*(a + b*x)^(5/2),x]","\frac{2 x^m (a+b x)^{7/2} \left(-\frac{b x}{a}\right)^{-m} \, _2F_1\left(\frac{7}{2},-m;\frac{9}{2};\frac{b x}{a}+1\right)}{7 b}","\frac{2 x^m (a+b x)^{7/2} \left(-\frac{b x}{a}\right)^{-m} \, _2F_1\left(\frac{7}{2},-m;\frac{9}{2};\frac{b x}{a}+1\right)}{7 b}",1,"(2*x^m*(a + b*x)^(7/2)*Hypergeometric2F1[7/2, -m, 9/2, 1 + (b*x)/a])/(7*b*(-((b*x)/a))^m)","A",2,2,13,0.1538,1,"{67, 65}"
708,1,48,0,0.0115617,"\int x^m (a+b x)^{3/2} \, dx","Int[x^m*(a + b*x)^(3/2),x]","\frac{2 x^m (a+b x)^{5/2} \left(-\frac{b x}{a}\right)^{-m} \, _2F_1\left(\frac{5}{2},-m;\frac{7}{2};\frac{b x}{a}+1\right)}{5 b}","\frac{2 x^m (a+b x)^{5/2} \left(-\frac{b x}{a}\right)^{-m} \, _2F_1\left(\frac{5}{2},-m;\frac{7}{2};\frac{b x}{a}+1\right)}{5 b}",1,"(2*x^m*(a + b*x)^(5/2)*Hypergeometric2F1[5/2, -m, 7/2, 1 + (b*x)/a])/(5*b*(-((b*x)/a))^m)","A",2,2,13,0.1538,1,"{67, 65}"
709,1,48,0,0.0109918,"\int x^m \sqrt{a+b x} \, dx","Int[x^m*Sqrt[a + b*x],x]","\frac{2 x^m (a+b x)^{3/2} \left(-\frac{b x}{a}\right)^{-m} \, _2F_1\left(\frac{3}{2},-m;\frac{5}{2};\frac{b x}{a}+1\right)}{3 b}","\frac{2 x^m (a+b x)^{3/2} \left(-\frac{b x}{a}\right)^{-m} \, _2F_1\left(\frac{3}{2},-m;\frac{5}{2};\frac{b x}{a}+1\right)}{3 b}",1,"(2*x^m*(a + b*x)^(3/2)*Hypergeometric2F1[3/2, -m, 5/2, 1 + (b*x)/a])/(3*b*(-((b*x)/a))^m)","A",2,2,13,0.1538,1,"{67, 65}"
710,1,46,0,0.010974,"\int \frac{x^m}{\sqrt{a+b x}} \, dx","Int[x^m/Sqrt[a + b*x],x]","\frac{2 x^m \sqrt{a+b x} \left(-\frac{b x}{a}\right)^{-m} \, _2F_1\left(\frac{1}{2},-m;\frac{3}{2};\frac{b x}{a}+1\right)}{b}","\frac{2 x^m \sqrt{a+b x} \left(-\frac{b x}{a}\right)^{-m} \, _2F_1\left(\frac{1}{2},-m;\frac{3}{2};\frac{b x}{a}+1\right)}{b}",1,"(2*x^m*Sqrt[a + b*x]*Hypergeometric2F1[1/2, -m, 3/2, 1 + (b*x)/a])/(b*(-((b*x)/a))^m)","A",2,2,13,0.1538,1,"{67, 65}"
711,1,46,0,0.010546,"\int \frac{x^m}{(a+b x)^{3/2}} \, dx","Int[x^m/(a + b*x)^(3/2),x]","-\frac{2 x^m \left(-\frac{b x}{a}\right)^{-m} \, _2F_1\left(-\frac{1}{2},-m;\frac{1}{2};\frac{b x}{a}+1\right)}{b \sqrt{a+b x}}","-\frac{2 x^m \left(-\frac{b x}{a}\right)^{-m} \, _2F_1\left(-\frac{1}{2},-m;\frac{1}{2};\frac{b x}{a}+1\right)}{b \sqrt{a+b x}}",1,"(-2*x^m*Hypergeometric2F1[-1/2, -m, 1/2, 1 + (b*x)/a])/(b*(-((b*x)/a))^m*Sqrt[a + b*x])","A",2,2,13,0.1538,1,"{67, 65}"
712,1,48,0,0.0110132,"\int \frac{x^m}{(a+b x)^{5/2}} \, dx","Int[x^m/(a + b*x)^(5/2),x]","-\frac{2 x^m \left(-\frac{b x}{a}\right)^{-m} \, _2F_1\left(-\frac{3}{2},-m;-\frac{1}{2};\frac{b x}{a}+1\right)}{3 b (a+b x)^{3/2}}","-\frac{2 x^m \left(-\frac{b x}{a}\right)^{-m} \, _2F_1\left(-\frac{3}{2},-m;-\frac{1}{2};\frac{b x}{a}+1\right)}{3 b (a+b x)^{3/2}}",1,"(-2*x^m*Hypergeometric2F1[-3/2, -m, -1/2, 1 + (b*x)/a])/(3*b*(-((b*x)/a))^m*(a + b*x)^(3/2))","A",2,2,13,0.1538,1,"{67, 65}"
713,1,51,0,0.0118605,"\int \frac{x^{2+m}}{\sqrt{a+b x}} \, dx","Int[x^(2 + m)/Sqrt[a + b*x],x]","\frac{2 a^2 x^m \sqrt{a+b x} \left(-\frac{b x}{a}\right)^{-m} \, _2F_1\left(\frac{1}{2},-m-2;\frac{3}{2};\frac{b x}{a}+1\right)}{b^3}","\frac{2 a^2 x^m \sqrt{a+b x} \left(-\frac{b x}{a}\right)^{-m} \, _2F_1\left(\frac{1}{2},-m-2;\frac{3}{2};\frac{b x}{a}+1\right)}{b^3}",1,"(2*a^2*x^m*Sqrt[a + b*x]*Hypergeometric2F1[1/2, -2 - m, 3/2, 1 + (b*x)/a])/(b^3*(-((b*x)/a))^m)","A",2,2,15,0.1333,1,"{67, 65}"
714,1,49,0,0.0121783,"\int \frac{x^{1+m}}{\sqrt{a+b x}} \, dx","Int[x^(1 + m)/Sqrt[a + b*x],x]","-\frac{2 a x^m \sqrt{a+b x} \left(-\frac{b x}{a}\right)^{-m} \, _2F_1\left(\frac{1}{2},-m-1;\frac{3}{2};\frac{b x}{a}+1\right)}{b^2}","-\frac{2 a x^m \sqrt{a+b x} \left(-\frac{b x}{a}\right)^{-m} \, _2F_1\left(\frac{1}{2},-m-1;\frac{3}{2};\frac{b x}{a}+1\right)}{b^2}",1,"(-2*a*x^m*Sqrt[a + b*x]*Hypergeometric2F1[1/2, -1 - m, 3/2, 1 + (b*x)/a])/(b^2*(-((b*x)/a))^m)","A",2,2,15,0.1333,1,"{67, 65}"
715,1,46,0,0.010804,"\int \frac{x^m}{\sqrt{a+b x}} \, dx","Int[x^m/Sqrt[a + b*x],x]","\frac{2 x^m \sqrt{a+b x} \left(-\frac{b x}{a}\right)^{-m} \, _2F_1\left(\frac{1}{2},-m;\frac{3}{2};\frac{b x}{a}+1\right)}{b}","\frac{2 x^m \sqrt{a+b x} \left(-\frac{b x}{a}\right)^{-m} \, _2F_1\left(\frac{1}{2},-m;\frac{3}{2};\frac{b x}{a}+1\right)}{b}",1,"(2*x^m*Sqrt[a + b*x]*Hypergeometric2F1[1/2, -m, 3/2, 1 + (b*x)/a])/(b*(-((b*x)/a))^m)","A",2,2,13,0.1538,1,"{67, 65}"
716,1,48,0,0.0116183,"\int \frac{x^{-1+m}}{\sqrt{a+b x}} \, dx","Int[x^(-1 + m)/Sqrt[a + b*x],x]","-\frac{2 x^m \sqrt{a+b x} \left(-\frac{b x}{a}\right)^{-m} \, _2F_1\left(\frac{1}{2},1-m;\frac{3}{2};\frac{b x}{a}+1\right)}{a}","-\frac{2 x^m \sqrt{a+b x} \left(-\frac{b x}{a}\right)^{-m} \, _2F_1\left(\frac{1}{2},1-m;\frac{3}{2};\frac{b x}{a}+1\right)}{a}",1,"(-2*x^m*Sqrt[a + b*x]*Hypergeometric2F1[1/2, 1 - m, 3/2, 1 + (b*x)/a])/(a*(-((b*x)/a))^m)","A",2,2,15,0.1333,1,"{67, 65}"
717,1,49,0,0.011609,"\int \frac{x^{-2+m}}{\sqrt{a+b x}} \, dx","Int[x^(-2 + m)/Sqrt[a + b*x],x]","\frac{2 b x^m \sqrt{a+b x} \left(-\frac{b x}{a}\right)^{-m} \, _2F_1\left(\frac{1}{2},2-m;\frac{3}{2};\frac{b x}{a}+1\right)}{a^2}","\frac{2 b x^m \sqrt{a+b x} \left(-\frac{b x}{a}\right)^{-m} \, _2F_1\left(\frac{1}{2},2-m;\frac{3}{2};\frac{b x}{a}+1\right)}{a^2}",1,"(2*b*x^m*Sqrt[a + b*x]*Hypergeometric2F1[1/2, 2 - m, 3/2, 1 + (b*x)/a])/(a^2*(-((b*x)/a))^m)","A",2,2,15,0.1333,1,"{67, 65}"
718,1,51,0,0.0125032,"\int \frac{x^{-3+m}}{\sqrt{a+b x}} \, dx","Int[x^(-3 + m)/Sqrt[a + b*x],x]","-\frac{2 b^2 x^m \sqrt{a+b x} \left(-\frac{b x}{a}\right)^{-m} \, _2F_1\left(\frac{1}{2},3-m;\frac{3}{2};\frac{b x}{a}+1\right)}{a^3}","-\frac{2 b^2 x^m \sqrt{a+b x} \left(-\frac{b x}{a}\right)^{-m} \, _2F_1\left(\frac{1}{2},3-m;\frac{3}{2};\frac{b x}{a}+1\right)}{a^3}",1,"(-2*b^2*x^m*Sqrt[a + b*x]*Hypergeometric2F1[1/2, 3 - m, 3/2, 1 + (b*x)/a])/(a^3*(-((b*x)/a))^m)","A",2,2,15,0.1333,1,"{67, 65}"
719,1,31,0,0.0055908,"\int \frac{x^m}{\sqrt{2+3 x}} \, dx","Int[x^m/Sqrt[2 + 3*x],x]","\frac{x^{m+1} \, _2F_1\left(\frac{1}{2},m+1;m+2;-\frac{3 x}{2}\right)}{\sqrt{2} (m+1)}","\frac{x^{m+1} \, _2F_1\left(\frac{1}{2},m+1;m+2;-\frac{3 x}{2}\right)}{\sqrt{2} (m+1)}",1,"(x^(1 + m)*Hypergeometric2F1[1/2, 1 + m, 2 + m, (-3*x)/2])/(Sqrt[2]*(1 + m))","A",1,1,13,0.07692,1,"{64}"
720,1,31,0,0.0040992,"\int \frac{x^m}{\sqrt{2-3 x}} \, dx","Int[x^m/Sqrt[2 - 3*x],x]","\frac{x^{m+1} \, _2F_1\left(\frac{1}{2},m+1;m+2;\frac{3 x}{2}\right)}{\sqrt{2} (m+1)}","\frac{x^{m+1} \, _2F_1\left(\frac{1}{2},m+1;m+2;\frac{3 x}{2}\right)}{\sqrt{2} (m+1)}",1,"(x^(1 + m)*Hypergeometric2F1[1/2, 1 + m, 2 + m, (3*x)/2])/(Sqrt[2]*(1 + m))","A",1,1,13,0.07692,1,"{64}"
721,1,36,0,0.0083152,"\int \frac{x^m}{\sqrt{-2+3 x}} \, dx","Int[x^m/Sqrt[-2 + 3*x],x]","\left(\frac{3}{2}\right)^{-m-1} \sqrt{3 x-2} \, _2F_1\left(\frac{1}{2},-m;\frac{3}{2};1-\frac{3 x}{2}\right)","\left(\frac{3}{2}\right)^{-m-1} \sqrt{3 x-2} \, _2F_1\left(\frac{1}{2},-m;\frac{3}{2};1-\frac{3 x}{2}\right)",1,"(3/2)^(-1 - m)*Sqrt[-2 + 3*x]*Hypergeometric2F1[1/2, -m, 3/2, 1 - (3*x)/2]","A",1,1,13,0.07692,1,"{65}"
722,1,50,0,0.0109464,"\int \frac{x^m}{\sqrt{-2-3 x}} \, dx","Int[x^m/Sqrt[-2 - 3*x],x]","-2^{m+1} 3^{-m-1} \sqrt{-3 x-2} (-x)^{-m} x^m \, _2F_1\left(\frac{1}{2},-m;\frac{3}{2};\frac{3 x}{2}+1\right)","-2^{m+1} 3^{-m-1} \sqrt{-3 x-2} (-x)^{-m} x^m \, _2F_1\left(\frac{1}{2},-m;\frac{3}{2};\frac{3 x}{2}+1\right)",1,"-((2^(1 + m)*3^(-1 - m)*Sqrt[-2 - 3*x]*x^m*Hypergeometric2F1[1/2, -m, 3/2, 1 + (3*x)/2])/(-x)^m)","A",3,3,13,0.2308,1,"{67, 12, 65}"
723,1,48,0,0.0108051,"\int \frac{(-x)^m}{\sqrt{a+b x}} \, dx","Int[(-x)^m/Sqrt[a + b*x],x]","\frac{2 (-x)^m \sqrt{a+b x} \left(-\frac{b x}{a}\right)^{-m} \, _2F_1\left(\frac{1}{2},-m;\frac{3}{2};\frac{b x}{a}+1\right)}{b}","\frac{2 (-x)^m \sqrt{a+b x} \left(-\frac{b x}{a}\right)^{-m} \, _2F_1\left(\frac{1}{2},-m;\frac{3}{2};\frac{b x}{a}+1\right)}{b}",1,"(2*(-x)^m*Sqrt[a + b*x]*Hypergeometric2F1[1/2, -m, 3/2, 1 + (b*x)/a])/(b*(-((b*x)/a))^m)","A",2,2,15,0.1333,1,"{67, 65}"
724,1,34,0,0.0060438,"\int \frac{(-x)^m}{\sqrt{2+3 x}} \, dx","Int[(-x)^m/Sqrt[2 + 3*x],x]","-\frac{(-x)^{m+1} \, _2F_1\left(\frac{1}{2},m+1;m+2;-\frac{3 x}{2}\right)}{\sqrt{2} (m+1)}","-\frac{(-x)^{m+1} \, _2F_1\left(\frac{1}{2},m+1;m+2;-\frac{3 x}{2}\right)}{\sqrt{2} (m+1)}",1,"-(((-x)^(1 + m)*Hypergeometric2F1[1/2, 1 + m, 2 + m, (-3*x)/2])/(Sqrt[2]*(1 + m)))","A",1,1,15,0.06667,1,"{64}"
725,1,34,0,0.0048189,"\int \frac{(-x)^m}{\sqrt{2-3 x}} \, dx","Int[(-x)^m/Sqrt[2 - 3*x],x]","-\frac{(-x)^{m+1} \, _2F_1\left(\frac{1}{2},m+1;m+2;\frac{3 x}{2}\right)}{\sqrt{2} (m+1)}","-\frac{(-x)^{m+1} \, _2F_1\left(\frac{1}{2},m+1;m+2;\frac{3 x}{2}\right)}{\sqrt{2} (m+1)}",1,"-(((-x)^(1 + m)*Hypergeometric2F1[1/2, 1 + m, 2 + m, (3*x)/2])/(Sqrt[2]*(1 + m)))","A",1,1,15,0.06667,1,"{64}"
726,1,49,0,0.0110271,"\int \frac{(-x)^m}{\sqrt{-2+3 x}} \, dx","Int[(-x)^m/Sqrt[-2 + 3*x],x]","2^{m+1} 3^{-m-1} \sqrt{3 x-2} (-x)^m x^{-m} \, _2F_1\left(\frac{1}{2},-m;\frac{3}{2};1-\frac{3 x}{2}\right)","2^{m+1} 3^{-m-1} \sqrt{3 x-2} (-x)^m x^{-m} \, _2F_1\left(\frac{1}{2},-m;\frac{3}{2};1-\frac{3 x}{2}\right)",1,"(2^(1 + m)*3^(-1 - m)*(-x)^m*Sqrt[-2 + 3*x]*Hypergeometric2F1[1/2, -m, 3/2, 1 - (3*x)/2])/x^m","A",3,3,15,0.2000,1,"{67, 12, 65}"
727,1,37,0,0.0046895,"\int \frac{(-x)^m}{\sqrt{-2-3 x}} \, dx","Int[(-x)^m/Sqrt[-2 - 3*x],x]","-\left(\frac{3}{2}\right)^{-m-1} \sqrt{-3 x-2} \, _2F_1\left(\frac{1}{2},-m;\frac{3}{2};\frac{3 x}{2}+1\right)","-\left(\frac{3}{2}\right)^{-m-1} \sqrt{-3 x-2} \, _2F_1\left(\frac{1}{2},-m;\frac{3}{2};\frac{3 x}{2}+1\right)",1,"-((3/2)^(-1 - m)*Sqrt[-2 - 3*x]*Hypergeometric2F1[1/2, -m, 3/2, 1 + (3*x)/2])","A",1,1,15,0.06667,1,"{65}"
728,1,26,0,0.0042752,"\int \frac{x^n}{\sqrt{1-x}} \, dx","Int[x^n/Sqrt[1 - x],x]","-2 \sqrt{1-x} \, _2F_1\left(\frac{1}{2},-n;\frac{3}{2};1-x\right)","-2 \sqrt{1-x} \, _2F_1\left(\frac{1}{2},-n;\frac{3}{2};1-x\right)",1,"-2*Sqrt[1 - x]*Hypergeometric2F1[1/2, -n, 3/2, 1 - x]","A",1,1,13,0.07692,1,"{65}"
729,1,30,0,0.0044462,"\int \frac{x^n}{\sqrt{a-a x}} \, dx","Int[x^n/Sqrt[a - a*x],x]","-\frac{2 \sqrt{a-a x} \, _2F_1\left(\frac{1}{2},-n;\frac{3}{2};1-x\right)}{a}","-\frac{2 \sqrt{a-a x} \, _2F_1\left(\frac{1}{2},-n;\frac{3}{2};1-x\right)}{a}",1,"(-2*Sqrt[a - a*x]*Hypergeometric2F1[1/2, -n, 3/2, 1 - x])/a","A",1,1,14,0.07143,1,"{65}"
730,1,47,0,0.0111344,"\int x^m (a+b x)^n \, dx","Int[x^m*(a + b*x)^n,x]","\frac{x^{m+1} (a+b x)^n \left(\frac{b x}{a}+1\right)^{-n} \, _2F_1\left(m+1,-n;m+2;-\frac{b x}{a}\right)}{m+1}","\frac{x^{m+1} (a+b x)^n \left(\frac{b x}{a}+1\right)^{-n} \, _2F_1\left(m+1,-n;m+2;-\frac{b x}{a}\right)}{m+1}",1,"(x^(1 + m)*(a + b*x)^n*Hypergeometric2F1[1 + m, -n, 2 + m, -((b*x)/a)])/((1 + m)*(1 + (b*x)/a)^n)","A",2,2,11,0.1818,1,"{66, 64}"
731,1,52,0,0.0135314,"\int (c x)^m (a+b x)^n \, dx","Int[(c*x)^m*(a + b*x)^n,x]","\frac{(c x)^{m+1} (a+b x)^n \left(\frac{b x}{a}+1\right)^{-n} \, _2F_1\left(m+1,-n;m+2;-\frac{b x}{a}\right)}{c (m+1)}","\frac{(c x)^{m+1} (a+b x)^n \left(\frac{b x}{a}+1\right)^{-n} \, _2F_1\left(m+1,-n;m+2;-\frac{b x}{a}\right)}{c (m+1)}",1,"((c*x)^(1 + m)*(a + b*x)^n*Hypergeometric2F1[1 + m, -n, 2 + m, -((b*x)/a)])/(c*(1 + m)*(1 + (b*x)/a)^n)","A",2,2,13,0.1538,1,"{66, 64}"
732,1,83,0,0.031316,"\int x^3 (a+b x)^n \, dx","Int[x^3*(a + b*x)^n,x]","-\frac{a^3 (a+b x)^{n+1}}{b^4 (n+1)}+\frac{3 a^2 (a+b x)^{n+2}}{b^4 (n+2)}-\frac{3 a (a+b x)^{n+3}}{b^4 (n+3)}+\frac{(a+b x)^{n+4}}{b^4 (n+4)}","-\frac{a^3 (a+b x)^{n+1}}{b^4 (n+1)}+\frac{3 a^2 (a+b x)^{n+2}}{b^4 (n+2)}-\frac{3 a (a+b x)^{n+3}}{b^4 (n+3)}+\frac{(a+b x)^{n+4}}{b^4 (n+4)}",1,"-((a^3*(a + b*x)^(1 + n))/(b^4*(1 + n))) + (3*a^2*(a + b*x)^(2 + n))/(b^4*(2 + n)) - (3*a*(a + b*x)^(3 + n))/(b^4*(3 + n)) + (a + b*x)^(4 + n)/(b^4*(4 + n))","A",2,1,11,0.09091,1,"{43}"
733,1,60,0,0.0189535,"\int x^2 (a+b x)^n \, dx","Int[x^2*(a + b*x)^n,x]","\frac{a^2 (a+b x)^{n+1}}{b^3 (n+1)}-\frac{2 a (a+b x)^{n+2}}{b^3 (n+2)}+\frac{(a+b x)^{n+3}}{b^3 (n+3)}","\frac{a^2 (a+b x)^{n+1}}{b^3 (n+1)}-\frac{2 a (a+b x)^{n+2}}{b^3 (n+2)}+\frac{(a+b x)^{n+3}}{b^3 (n+3)}",1,"(a^2*(a + b*x)^(1 + n))/(b^3*(1 + n)) - (2*a*(a + b*x)^(2 + n))/(b^3*(2 + n)) + (a + b*x)^(3 + n)/(b^3*(3 + n))","A",2,1,11,0.09091,1,"{43}"
734,1,39,0,0.0115666,"\int x (a+b x)^n \, dx","Int[x*(a + b*x)^n,x]","\frac{(a+b x)^{n+2}}{b^2 (n+2)}-\frac{a (a+b x)^{n+1}}{b^2 (n+1)}","\frac{(a+b x)^{n+2}}{b^2 (n+2)}-\frac{a (a+b x)^{n+1}}{b^2 (n+1)}",1,"-((a*(a + b*x)^(1 + n))/(b^2*(1 + n))) + (a + b*x)^(2 + n)/(b^2*(2 + n))","A",2,1,9,0.1111,1,"{43}"
735,1,18,0,0.003058,"\int (a+b x)^n \, dx","Int[(a + b*x)^n,x]","\frac{(a+b x)^{n+1}}{b (n+1)}","\frac{(a+b x)^{n+1}}{b (n+1)}",1,"(a + b*x)^(1 + n)/(b*(1 + n))","A",1,1,7,0.1429,1,"{32}"
736,1,35,0,0.0062213,"\int \frac{(a+b x)^n}{x} \, dx","Int[(a + b*x)^n/x,x]","-\frac{(a+b x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b x}{a}+1\right)}{a (n+1)}","-\frac{(a+b x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b x}{a}+1\right)}{a (n+1)}",1,"-(((a + b*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, 1 + (b*x)/a])/(a*(1 + n)))","A",1,1,11,0.09091,1,"{65}"
737,1,35,0,0.0068788,"\int \frac{(a+b x)^n}{x^2} \, dx","Int[(a + b*x)^n/x^2,x]","\frac{b (a+b x)^{n+1} \, _2F_1\left(2,n+1;n+2;\frac{b x}{a}+1\right)}{a^2 (n+1)}","\frac{b (a+b x)^{n+1} \, _2F_1\left(2,n+1;n+2;\frac{b x}{a}+1\right)}{a^2 (n+1)}",1,"(b*(a + b*x)^(1 + n)*Hypergeometric2F1[2, 1 + n, 2 + n, 1 + (b*x)/a])/(a^2*(1 + n))","A",1,1,11,0.09091,1,"{65}"
738,1,38,0,0.0076062,"\int \frac{(a+b x)^n}{x^3} \, dx","Int[(a + b*x)^n/x^3,x]","-\frac{b^2 (a+b x)^{n+1} \, _2F_1\left(3,n+1;n+2;\frac{b x}{a}+1\right)}{a^3 (n+1)}","-\frac{b^2 (a+b x)^{n+1} \, _2F_1\left(3,n+1;n+2;\frac{b x}{a}+1\right)}{a^3 (n+1)}",1,"-((b^2*(a + b*x)^(1 + n)*Hypergeometric2F1[3, 1 + n, 2 + n, 1 + (b*x)/a])/(a^3*(1 + n)))","A",1,1,11,0.09091,1,"{65}"
739,1,110,0,0.0356771,"\int x^{-4+n} (a+b x)^{-n} \, dx","Int[x^(-4 + n)/(a + b*x)^n,x]","-\frac{2 b^2 x^{n-1} (a+b x)^{1-n}}{a^3 (1-n) (2-n) (3-n)}+\frac{2 b x^{n-2} (a+b x)^{1-n}}{a^2 (2-n) (3-n)}-\frac{x^{n-3} (a+b x)^{1-n}}{a (3-n)}","-\frac{2 b^2 x^{n-1} (a+b x)^{1-n}}{a^3 (1-n) (2-n) (3-n)}+\frac{2 b x^{n-2} (a+b x)^{1-n}}{a^2 (2-n) (3-n)}-\frac{x^{n-3} (a+b x)^{1-n}}{a (3-n)}",1,"-((x^(-3 + n)*(a + b*x)^(1 - n))/(a*(3 - n))) + (2*b*x^(-2 + n)*(a + b*x)^(1 - n))/(a^2*(2 - n)*(3 - n)) - (2*b^2*x^(-1 + n)*(a + b*x)^(1 - n))/(a^3*(1 - n)*(2 - n)*(3 - n))","A",3,2,15,0.1333,1,"{45, 37}"
740,1,64,0,0.0091874,"\int x^{-3+n} (a+b x)^{-n} \, dx","Int[x^(-3 + n)/(a + b*x)^n,x]","\frac{b x^{n-1} (a+b x)^{1-n}}{a^2 (1-n) (2-n)}-\frac{x^{n-2} (a+b x)^{1-n}}{a (2-n)}","\frac{b x^{n-1} (a+b x)^{1-n}}{a^2 (1-n) (2-n)}-\frac{x^{n-2} (a+b x)^{1-n}}{a (2-n)}",1,"-((x^(-2 + n)*(a + b*x)^(1 - n))/(a*(2 - n))) + (b*x^(-1 + n)*(a + b*x)^(1 - n))/(a^2*(1 - n)*(2 - n))","A",2,2,15,0.1333,1,"{45, 37}"
741,1,28,0,0.0027961,"\int x^{-2+n} (a+b x)^{-n} \, dx","Int[x^(-2 + n)/(a + b*x)^n,x]","-\frac{x^{n-1} (a+b x)^{1-n}}{a (1-n)}","-\frac{x^{n-1} (a+b x)^{1-n}}{a (1-n)}",1,"-((x^(-1 + n)*(a + b*x)^(1 - n))/(a*(1 - n)))","A",1,1,15,0.06667,1,"{37}"
742,1,39,0,0.0097928,"\int x^{-1+n} (a+b x)^{-n} \, dx","Int[x^(-1 + n)/(a + b*x)^n,x]","\frac{x^n (a+b x)^{-n} \left(\frac{b x}{a}+1\right)^n \, _2F_1\left(n,n;n+1;-\frac{b x}{a}\right)}{n}","\frac{x^n (a+b x)^{-n} \left(\frac{b x}{a}+1\right)^n \, _2F_1\left(n,n;n+1;-\frac{b x}{a}\right)}{n}",1,"(x^n*(1 + (b*x)/a)^n*Hypergeometric2F1[n, n, 1 + n, -((b*x)/a)])/(n*(a + b*x)^n)","A",2,2,15,0.1333,1,"{66, 64}"
743,1,45,0,0.0102049,"\int x^n (a+b x)^{-n} \, dx","Int[x^n/(a + b*x)^n,x]","\frac{x^{n+1} (a+b x)^{-n} \left(\frac{b x}{a}+1\right)^n \, _2F_1\left(n,n+1;n+2;-\frac{b x}{a}\right)}{n+1}","\frac{x^{n+1} (a+b x)^{-n} \left(\frac{b x}{a}+1\right)^n \, _2F_1\left(n,n+1;n+2;-\frac{b x}{a}\right)}{n+1}",1,"(x^(1 + n)*(1 + (b*x)/a)^n*Hypergeometric2F1[n, 1 + n, 2 + n, -((b*x)/a)])/((1 + n)*(a + b*x)^n)","A",2,2,13,0.1538,1,"{66, 64}"
744,1,45,0,0.0105547,"\int x^{1+n} (a+b x)^{-n} \, dx","Int[x^(1 + n)/(a + b*x)^n,x]","\frac{x^{n+2} (a+b x)^{-n} \left(\frac{b x}{a}+1\right)^n \, _2F_1\left(n,n+2;n+3;-\frac{b x}{a}\right)}{n+2}","\frac{x^{n+2} (a+b x)^{-n} \left(\frac{b x}{a}+1\right)^n \, _2F_1\left(n,n+2;n+3;-\frac{b x}{a}\right)}{n+2}",1,"(x^(2 + n)*(1 + (b*x)/a)^n*Hypergeometric2F1[n, 2 + n, 3 + n, -((b*x)/a)])/((2 + n)*(a + b*x)^n)","A",2,2,15,0.1333,1,"{66, 64}"
745,1,45,0,0.0087233,"\int x^{3/2} (a+b x)^n \, dx","Int[x^(3/2)*(a + b*x)^n,x]","\frac{2}{5} x^{5/2} (a+b x)^n \left(\frac{b x}{a}+1\right)^{-n} \, _2F_1\left(\frac{5}{2},-n;\frac{7}{2};-\frac{b x}{a}\right)","\frac{2}{5} x^{5/2} (a+b x)^n \left(\frac{b x}{a}+1\right)^{-n} \, _2F_1\left(\frac{5}{2},-n;\frac{7}{2};-\frac{b x}{a}\right)",1,"(2*x^(5/2)*(a + b*x)^n*Hypergeometric2F1[5/2, -n, 7/2, -((b*x)/a)])/(5*(1 + (b*x)/a)^n)","A",2,2,13,0.1538,1,"{66, 64}"
746,1,45,0,0.0087533,"\int \sqrt{x} (a+b x)^n \, dx","Int[Sqrt[x]*(a + b*x)^n,x]","\frac{2}{3} x^{3/2} (a+b x)^n \left(\frac{b x}{a}+1\right)^{-n} \, _2F_1\left(\frac{3}{2},-n;\frac{5}{2};-\frac{b x}{a}\right)","\frac{2}{3} x^{3/2} (a+b x)^n \left(\frac{b x}{a}+1\right)^{-n} \, _2F_1\left(\frac{3}{2},-n;\frac{5}{2};-\frac{b x}{a}\right)",1,"(2*x^(3/2)*(a + b*x)^n*Hypergeometric2F1[3/2, -n, 5/2, -((b*x)/a)])/(3*(1 + (b*x)/a)^n)","A",2,2,13,0.1538,1,"{66, 64}"
747,1,43,0,0.0086755,"\int \frac{(a+b x)^n}{\sqrt{x}} \, dx","Int[(a + b*x)^n/Sqrt[x],x]","2 \sqrt{x} (a+b x)^n \left(\frac{b x}{a}+1\right)^{-n} \, _2F_1\left(\frac{1}{2},-n;\frac{3}{2};-\frac{b x}{a}\right)","2 \sqrt{x} (a+b x)^n \left(\frac{b x}{a}+1\right)^{-n} \, _2F_1\left(\frac{1}{2},-n;\frac{3}{2};-\frac{b x}{a}\right)",1,"(2*Sqrt[x]*(a + b*x)^n*Hypergeometric2F1[1/2, -n, 3/2, -((b*x)/a)])/(1 + (b*x)/a)^n","A",2,2,13,0.1538,1,"{66, 64}"
748,1,43,0,0.0086445,"\int \frac{(a+b x)^n}{x^{3/2}} \, dx","Int[(a + b*x)^n/x^(3/2),x]","-\frac{2 (a+b x)^n \left(\frac{b x}{a}+1\right)^{-n} \, _2F_1\left(-\frac{1}{2},-n;\frac{1}{2};-\frac{b x}{a}\right)}{\sqrt{x}}","-\frac{2 (a+b x)^n \left(\frac{b x}{a}+1\right)^{-n} \, _2F_1\left(-\frac{1}{2},-n;\frac{1}{2};-\frac{b x}{a}\right)}{\sqrt{x}}",1,"(-2*(a + b*x)^n*Hypergeometric2F1[-1/2, -n, 1/2, -((b*x)/a)])/(Sqrt[x]*(1 + (b*x)/a)^n)","A",2,2,13,0.1538,1,"{66, 64}"
749,1,45,0,0.0090092,"\int \frac{(a+b x)^n}{x^{5/2}} \, dx","Int[(a + b*x)^n/x^(5/2),x]","-\frac{2 (a+b x)^n \left(\frac{b x}{a}+1\right)^{-n} \, _2F_1\left(-\frac{3}{2},-n;-\frac{1}{2};-\frac{b x}{a}\right)}{3 x^{3/2}}","-\frac{2 (a+b x)^n \left(\frac{b x}{a}+1\right)^{-n} \, _2F_1\left(-\frac{3}{2},-n;-\frac{1}{2};-\frac{b x}{a}\right)}{3 x^{3/2}}",1,"(-2*(a + b*x)^n*Hypergeometric2F1[-3/2, -n, -1/2, -((b*x)/a)])/(3*x^(3/2)*(1 + (b*x)/a)^n)","A",2,2,13,0.1538,1,"{66, 64}"
750,1,35,0,0.0108964,"\int (b x)^m (2+d x)^n \, dx","Int[(b*x)^m*(2 + d*x)^n,x]","\frac{2^n (b x)^{m+1} \, _2F_1\left(m+1,-n;m+2;-\frac{d x}{2}\right)}{b (m+1)}","\frac{2^n (b x)^{m+1} \, _2F_1\left(m+1,-n;m+2;-\frac{d x}{2}\right)}{b (m+1)}",1,"(2^n*(b*x)^(1 + m)*Hypergeometric2F1[1 + m, -n, 2 + m, -(d*x)/2])/(b*(1 + m))","A",1,1,13,0.07692,1,"{64}"
751,1,40,0,0.0091687,"\int (b x)^m (c-b c x)^n \, dx","Int[(b*x)^m*(c - b*c*x)^n,x]","-\frac{(c-b c x)^{n+1} \, _2F_1(-m,n+1;n+2;1-b x)}{b c (n+1)}","-\frac{(c-b c x)^{n+1} \, _2F_1(-m,n+1;n+2;1-b x)}{b c (n+1)}",1,"-(((c - b*c*x)^(1 + n)*Hypergeometric2F1[-m, 1 + n, 2 + n, 1 - b*x])/(b*c*(1 + n)))","A",1,1,15,0.06667,1,"{65}"
752,1,52,0,0.0128916,"\int (b x)^m (c+d x)^n \, dx","Int[(b*x)^m*(c + d*x)^n,x]","\frac{(b x)^{m+1} (c+d x)^n \left(\frac{d x}{c}+1\right)^{-n} \, _2F_1\left(m+1,-n;m+2;-\frac{d x}{c}\right)}{b (m+1)}","\frac{(b x)^{m+1} (c+d x)^n \left(\frac{d x}{c}+1\right)^{-n} \, _2F_1\left(m+1,-n;m+2;-\frac{d x}{c}\right)}{b (m+1)}",1,"((b*x)^(1 + m)*(c + d*x)^n*Hypergeometric2F1[1 + m, -n, 2 + m, -((d*x)/c)])/(b*(1 + m)*(1 + (d*x)/c)^n)","A",2,2,13,0.1538,1,"{66, 64}"
753,1,19,0,0.00262,"\int x^{-1+n} (a+b x)^{-1-n} \, dx","Int[x^(-1 + n)*(a + b*x)^(-1 - n),x]","\frac{x^n (a+b x)^{-n}}{a n}","\frac{x^n (a+b x)^{-n}}{a n}",1,"x^n/(a*n*(a + b*x)^n)","A",1,1,17,0.05882,1,"{37}"
754,1,58,0,0.0134934,"\int x^{-3-n} (a+b x)^n \, dx","Int[x^(-3 - n)*(a + b*x)^n,x]","\frac{b x^{-n-1} (a+b x)^{n+1}}{a^2 (n+1) (n+2)}-\frac{x^{-n-2} (a+b x)^{n+1}}{a (n+2)}","\frac{b x^{-n-1} (a+b x)^{n+1}}{a^2 (n+1) (n+2)}-\frac{x^{-n-2} (a+b x)^{n+1}}{a (n+2)}",1,"-((x^(-2 - n)*(a + b*x)^(1 + n))/(a*(2 + n))) + (b*x^(-1 - n)*(a + b*x)^(1 + n))/(a^2*(1 + n)*(2 + n))","A",2,2,15,0.1333,1,"{45, 37}"
755,1,58,0,0.0111185,"\int x^{2 n-3 (1+n)} (a+b x)^n \, dx","Int[x^(2*n - 3*(1 + n))*(a + b*x)^n,x]","\frac{b x^{-n-1} (a+b x)^{n+1}}{a^2 (n+1) (n+2)}-\frac{x^{-n-2} (a+b x)^{n+1}}{a (n+2)}","\frac{b x^{-n-1} (a+b x)^{n+1}}{a^2 (n+1) (n+2)}-\frac{x^{-n-2} (a+b x)^{n+1}}{a (n+2)}",1,"-((x^(-2 - n)*(a + b*x)^(1 + n))/(a*(2 + n))) + (b*x^(-1 - n)*(a + b*x)^(1 + n))/(a^2*(1 + n)*(2 + n))","A",2,2,19,0.1053,1,"{45, 37}"
756,1,35,0,0.0114102,"\int x^3 \sqrt{c x^2} (a+b x) \, dx","Int[x^3*Sqrt[c*x^2]*(a + b*x),x]","\frac{1}{5} a x^4 \sqrt{c x^2}+\frac{1}{6} b x^5 \sqrt{c x^2}","\frac{1}{5} a x^4 \sqrt{c x^2}+\frac{1}{6} b x^5 \sqrt{c x^2}",1,"(a*x^4*Sqrt[c*x^2])/5 + (b*x^5*Sqrt[c*x^2])/6","A",3,2,18,0.1111,1,"{15, 43}"
757,1,35,0,0.0099123,"\int x^2 \sqrt{c x^2} (a+b x) \, dx","Int[x^2*Sqrt[c*x^2]*(a + b*x),x]","\frac{1}{4} a x^3 \sqrt{c x^2}+\frac{1}{5} b x^4 \sqrt{c x^2}","\frac{1}{4} a x^3 \sqrt{c x^2}+\frac{1}{5} b x^4 \sqrt{c x^2}",1,"(a*x^3*Sqrt[c*x^2])/4 + (b*x^4*Sqrt[c*x^2])/5","A",3,2,18,0.1111,1,"{15, 43}"
758,1,35,0,0.0086389,"\int x \sqrt{c x^2} (a+b x) \, dx","Int[x*Sqrt[c*x^2]*(a + b*x),x]","\frac{1}{3} a x^2 \sqrt{c x^2}+\frac{1}{4} b x^3 \sqrt{c x^2}","\frac{1}{3} a x^2 \sqrt{c x^2}+\frac{1}{4} b x^3 \sqrt{c x^2}",1,"(a*x^2*Sqrt[c*x^2])/3 + (b*x^3*Sqrt[c*x^2])/4","A",3,2,16,0.1250,1,"{15, 43}"
759,1,33,0,0.0078348,"\int \sqrt{c x^2} (a+b x) \, dx","Int[Sqrt[c*x^2]*(a + b*x),x]","\frac{1}{2} a x \sqrt{c x^2}+\frac{1}{3} b x^2 \sqrt{c x^2}","\frac{1}{2} a x \sqrt{c x^2}+\frac{1}{3} b x^2 \sqrt{c x^2}",1,"(a*x*Sqrt[c*x^2])/2 + (b*x^2*Sqrt[c*x^2])/3","A",3,2,15,0.1333,1,"{15, 43}"
760,1,27,0,0.0040651,"\int \frac{\sqrt{c x^2} (a+b x)}{x} \, dx","Int[(Sqrt[c*x^2]*(a + b*x))/x,x]","a \sqrt{c x^2}+\frac{1}{2} b x \sqrt{c x^2}","a \sqrt{c x^2}+\frac{1}{2} b x \sqrt{c x^2}",1,"a*Sqrt[c*x^2] + (b*x*Sqrt[c*x^2])/2","A",2,1,18,0.05556,1,"{15}"
761,1,28,0,0.0049333,"\int \frac{\sqrt{c x^2} (a+b x)}{x^2} \, dx","Int[(Sqrt[c*x^2]*(a + b*x))/x^2,x]","\frac{a \sqrt{c x^2} \log (x)}{x}+b \sqrt{c x^2}","\frac{a \sqrt{c x^2} \log (x)}{x}+b \sqrt{c x^2}",1,"b*Sqrt[c*x^2] + (a*Sqrt[c*x^2]*Log[x])/x","A",3,2,18,0.1111,1,"{15, 43}"
762,1,32,0,0.0067455,"\int \frac{\sqrt{c x^2} (a+b x)}{x^3} \, dx","Int[(Sqrt[c*x^2]*(a + b*x))/x^3,x]","\frac{b \sqrt{c x^2} \log (x)}{x}-\frac{a \sqrt{c x^2}}{x^2}","\frac{b \sqrt{c x^2} \log (x)}{x}-\frac{a \sqrt{c x^2}}{x^2}",1,"-((a*Sqrt[c*x^2])/x^2) + (b*Sqrt[c*x^2]*Log[x])/x","A",3,2,18,0.1111,1,"{15, 43}"
763,1,26,0,0.0040421,"\int \frac{\sqrt{c x^2} (a+b x)}{x^4} \, dx","Int[(Sqrt[c*x^2]*(a + b*x))/x^4,x]","-\frac{\sqrt{c x^2} (a+b x)^2}{2 a x^3}","-\frac{\sqrt{c x^2} (a+b x)^2}{2 a x^3}",1,"-(Sqrt[c*x^2]*(a + b*x)^2)/(2*a*x^3)","A",2,2,18,0.1111,1,"{15, 37}"
764,1,37,0,0.0133218,"\int x^3 \left(c x^2\right)^{3/2} (a+b x) \, dx","Int[x^3*(c*x^2)^(3/2)*(a + b*x),x]","\frac{1}{7} a c x^6 \sqrt{c x^2}+\frac{1}{8} b c x^7 \sqrt{c x^2}","\frac{1}{7} a c x^6 \sqrt{c x^2}+\frac{1}{8} b c x^7 \sqrt{c x^2}",1,"(a*c*x^6*Sqrt[c*x^2])/7 + (b*c*x^7*Sqrt[c*x^2])/8","A",3,2,18,0.1111,1,"{15, 43}"
765,1,37,0,0.0124938,"\int x^2 \left(c x^2\right)^{3/2} (a+b x) \, dx","Int[x^2*(c*x^2)^(3/2)*(a + b*x),x]","\frac{1}{6} a c x^5 \sqrt{c x^2}+\frac{1}{7} b c x^6 \sqrt{c x^2}","\frac{1}{6} a c x^5 \sqrt{c x^2}+\frac{1}{7} b c x^6 \sqrt{c x^2}",1,"(a*c*x^5*Sqrt[c*x^2])/6 + (b*c*x^6*Sqrt[c*x^2])/7","A",3,2,18,0.1111,1,"{15, 43}"
766,1,37,0,0.0108016,"\int x \left(c x^2\right)^{3/2} (a+b x) \, dx","Int[x*(c*x^2)^(3/2)*(a + b*x),x]","\frac{1}{5} a c x^4 \sqrt{c x^2}+\frac{1}{6} b c x^5 \sqrt{c x^2}","\frac{1}{5} a c x^4 \sqrt{c x^2}+\frac{1}{6} b c x^5 \sqrt{c x^2}",1,"(a*c*x^4*Sqrt[c*x^2])/5 + (b*c*x^5*Sqrt[c*x^2])/6","A",3,2,16,0.1250,1,"{15, 43}"
767,1,37,0,0.0097555,"\int \left(c x^2\right)^{3/2} (a+b x) \, dx","Int[(c*x^2)^(3/2)*(a + b*x),x]","\frac{1}{4} a c x^3 \sqrt{c x^2}+\frac{1}{5} b c x^4 \sqrt{c x^2}","\frac{1}{4} a c x^3 \sqrt{c x^2}+\frac{1}{5} b c x^4 \sqrt{c x^2}",1,"(a*c*x^3*Sqrt[c*x^2])/4 + (b*c*x^4*Sqrt[c*x^2])/5","A",3,2,15,0.1333,1,"{15, 43}"
768,1,37,0,0.0088063,"\int \frac{\left(c x^2\right)^{3/2} (a+b x)}{x} \, dx","Int[((c*x^2)^(3/2)*(a + b*x))/x,x]","\frac{1}{3} a c x^2 \sqrt{c x^2}+\frac{1}{4} b c x^3 \sqrt{c x^2}","\frac{1}{3} a c x^2 \sqrt{c x^2}+\frac{1}{4} b c x^3 \sqrt{c x^2}",1,"(a*c*x^2*Sqrt[c*x^2])/3 + (b*c*x^3*Sqrt[c*x^2])/4","A",3,2,18,0.1111,1,"{15, 43}"
769,1,35,0,0.0084287,"\int \frac{\left(c x^2\right)^{3/2} (a+b x)}{x^2} \, dx","Int[((c*x^2)^(3/2)*(a + b*x))/x^2,x]","\frac{1}{2} a c x \sqrt{c x^2}+\frac{1}{3} b c x^2 \sqrt{c x^2}","\frac{1}{2} a c x \sqrt{c x^2}+\frac{1}{3} b c x^2 \sqrt{c x^2}",1,"(a*c*x*Sqrt[c*x^2])/2 + (b*c*x^2*Sqrt[c*x^2])/3","A",3,2,18,0.1111,1,"{15, 43}"
770,1,29,0,0.0043358,"\int \frac{\left(c x^2\right)^{3/2} (a+b x)}{x^3} \, dx","Int[((c*x^2)^(3/2)*(a + b*x))/x^3,x]","a c \sqrt{c x^2}+\frac{1}{2} b c x \sqrt{c x^2}","a c \sqrt{c x^2}+\frac{1}{2} b c x \sqrt{c x^2}",1,"a*c*Sqrt[c*x^2] + (b*c*x*Sqrt[c*x^2])/2","A",2,1,18,0.05556,1,"{15}"
771,1,30,0,0.0052881,"\int \frac{\left(c x^2\right)^{3/2} (a+b x)}{x^4} \, dx","Int[((c*x^2)^(3/2)*(a + b*x))/x^4,x]","\frac{a c \sqrt{c x^2} \log (x)}{x}+b c \sqrt{c x^2}","\frac{a c \sqrt{c x^2} \log (x)}{x}+b c \sqrt{c x^2}",1,"b*c*Sqrt[c*x^2] + (a*c*Sqrt[c*x^2]*Log[x])/x","A",3,2,18,0.1111,1,"{15, 43}"
772,1,41,0,0.0159981,"\int x^3 \left(c x^2\right)^{5/2} (a+b x) \, dx","Int[x^3*(c*x^2)^(5/2)*(a + b*x),x]","\frac{1}{9} a c^2 x^8 \sqrt{c x^2}+\frac{1}{10} b c^2 x^9 \sqrt{c x^2}","\frac{1}{9} a c^2 x^8 \sqrt{c x^2}+\frac{1}{10} b c^2 x^9 \sqrt{c x^2}",1,"(a*c^2*x^8*Sqrt[c*x^2])/9 + (b*c^2*x^9*Sqrt[c*x^2])/10","A",3,2,18,0.1111,1,"{15, 43}"
773,1,41,0,0.0150992,"\int x^2 \left(c x^2\right)^{5/2} (a+b x) \, dx","Int[x^2*(c*x^2)^(5/2)*(a + b*x),x]","\frac{1}{8} a c^2 x^7 \sqrt{c x^2}+\frac{1}{9} b c^2 x^8 \sqrt{c x^2}","\frac{1}{8} a c^2 x^7 \sqrt{c x^2}+\frac{1}{9} b c^2 x^8 \sqrt{c x^2}",1,"(a*c^2*x^7*Sqrt[c*x^2])/8 + (b*c^2*x^8*Sqrt[c*x^2])/9","A",3,2,18,0.1111,1,"{15, 43}"
774,1,41,0,0.0132595,"\int x \left(c x^2\right)^{5/2} (a+b x) \, dx","Int[x*(c*x^2)^(5/2)*(a + b*x),x]","\frac{1}{7} a c^2 x^6 \sqrt{c x^2}+\frac{1}{8} b c^2 x^7 \sqrt{c x^2}","\frac{1}{7} a c^2 x^6 \sqrt{c x^2}+\frac{1}{8} b c^2 x^7 \sqrt{c x^2}",1,"(a*c^2*x^6*Sqrt[c*x^2])/7 + (b*c^2*x^7*Sqrt[c*x^2])/8","A",3,2,16,0.1250,1,"{15, 43}"
775,1,41,0,0.0128006,"\int \left(c x^2\right)^{5/2} (a+b x) \, dx","Int[(c*x^2)^(5/2)*(a + b*x),x]","\frac{1}{6} a c^2 x^5 \sqrt{c x^2}+\frac{1}{7} b c^2 x^6 \sqrt{c x^2}","\frac{1}{6} a c^2 x^5 \sqrt{c x^2}+\frac{1}{7} b c^2 x^6 \sqrt{c x^2}",1,"(a*c^2*x^5*Sqrt[c*x^2])/6 + (b*c^2*x^6*Sqrt[c*x^2])/7","A",3,2,15,0.1333,1,"{15, 43}"
776,1,41,0,0.0120243,"\int \frac{\left(c x^2\right)^{5/2} (a+b x)}{x} \, dx","Int[((c*x^2)^(5/2)*(a + b*x))/x,x]","\frac{1}{5} a c^2 x^4 \sqrt{c x^2}+\frac{1}{6} b c^2 x^5 \sqrt{c x^2}","\frac{1}{5} a c^2 x^4 \sqrt{c x^2}+\frac{1}{6} b c^2 x^5 \sqrt{c x^2}",1,"(a*c^2*x^4*Sqrt[c*x^2])/5 + (b*c^2*x^5*Sqrt[c*x^2])/6","A",3,2,18,0.1111,1,"{15, 43}"
777,1,41,0,0.011029,"\int \frac{\left(c x^2\right)^{5/2} (a+b x)}{x^2} \, dx","Int[((c*x^2)^(5/2)*(a + b*x))/x^2,x]","\frac{1}{4} a c^2 x^3 \sqrt{c x^2}+\frac{1}{5} b c^2 x^4 \sqrt{c x^2}","\frac{1}{4} a c^2 x^3 \sqrt{c x^2}+\frac{1}{5} b c^2 x^4 \sqrt{c x^2}",1,"(a*c^2*x^3*Sqrt[c*x^2])/4 + (b*c^2*x^4*Sqrt[c*x^2])/5","A",3,2,18,0.1111,1,"{15, 43}"
778,1,41,0,0.0100404,"\int \frac{\left(c x^2\right)^{5/2} (a+b x)}{x^3} \, dx","Int[((c*x^2)^(5/2)*(a + b*x))/x^3,x]","\frac{1}{3} a c^2 x^2 \sqrt{c x^2}+\frac{1}{4} b c^2 x^3 \sqrt{c x^2}","\frac{1}{3} a c^2 x^2 \sqrt{c x^2}+\frac{1}{4} b c^2 x^3 \sqrt{c x^2}",1,"(a*c^2*x^2*Sqrt[c*x^2])/3 + (b*c^2*x^3*Sqrt[c*x^2])/4","A",3,2,18,0.1111,1,"{15, 43}"
779,1,39,0,0.0084051,"\int \frac{\left(c x^2\right)^{5/2} (a+b x)}{x^4} \, dx","Int[((c*x^2)^(5/2)*(a + b*x))/x^4,x]","\frac{1}{2} a c^2 x \sqrt{c x^2}+\frac{1}{3} b c^2 x^2 \sqrt{c x^2}","\frac{1}{2} a c^2 x \sqrt{c x^2}+\frac{1}{3} b c^2 x^2 \sqrt{c x^2}",1,"(a*c^2*x*Sqrt[c*x^2])/2 + (b*c^2*x^2*Sqrt[c*x^2])/3","A",3,2,18,0.1111,1,"{15, 43}"
780,1,35,0,0.008578,"\int \frac{x^3 (a+b x)}{\sqrt{c x^2}} \, dx","Int[(x^3*(a + b*x))/Sqrt[c*x^2],x]","\frac{a x^4}{3 \sqrt{c x^2}}+\frac{b x^5}{4 \sqrt{c x^2}}","\frac{a x^4}{3 \sqrt{c x^2}}+\frac{b x^5}{4 \sqrt{c x^2}}",1,"(a*x^4)/(3*Sqrt[c*x^2]) + (b*x^5)/(4*Sqrt[c*x^2])","A",3,2,18,0.1111,1,"{15, 43}"
781,1,35,0,0.0081311,"\int \frac{x^2 (a+b x)}{\sqrt{c x^2}} \, dx","Int[(x^2*(a + b*x))/Sqrt[c*x^2],x]","\frac{a x^3}{2 \sqrt{c x^2}}+\frac{b x^4}{3 \sqrt{c x^2}}","\frac{a x^3}{2 \sqrt{c x^2}}+\frac{b x^4}{3 \sqrt{c x^2}}",1,"(a*x^3)/(2*Sqrt[c*x^2]) + (b*x^4)/(3*Sqrt[c*x^2])","A",3,2,18,0.1111,1,"{15, 43}"
782,1,32,0,0.0042455,"\int \frac{x (a+b x)}{\sqrt{c x^2}} \, dx","Int[(x*(a + b*x))/Sqrt[c*x^2],x]","\frac{a x^2}{\sqrt{c x^2}}+\frac{b x^3}{2 \sqrt{c x^2}}","\frac{a x^2}{\sqrt{c x^2}}+\frac{b x^3}{2 \sqrt{c x^2}}",1,"(a*x^2)/Sqrt[c*x^2] + (b*x^3)/(2*Sqrt[c*x^2])","A",2,1,16,0.06250,1,"{15}"
783,1,29,0,0.0051277,"\int \frac{a+b x}{\sqrt{c x^2}} \, dx","Int[(a + b*x)/Sqrt[c*x^2],x]","\frac{a x \log (x)}{\sqrt{c x^2}}+\frac{b x^2}{\sqrt{c x^2}}","\frac{a x \log (x)}{\sqrt{c x^2}}+\frac{b x^2}{\sqrt{c x^2}}",1,"(b*x^2)/Sqrt[c*x^2] + (a*x*Log[x])/Sqrt[c*x^2]","A",3,2,15,0.1333,1,"{15, 43}"
784,1,27,0,0.0060676,"\int \frac{a+b x}{x \sqrt{c x^2}} \, dx","Int[(a + b*x)/(x*Sqrt[c*x^2]),x]","\frac{b x \log (x)}{\sqrt{c x^2}}-\frac{a}{\sqrt{c x^2}}","\frac{b x \log (x)}{\sqrt{c x^2}}-\frac{a}{\sqrt{c x^2}}",1,"-(a/Sqrt[c*x^2]) + (b*x*Log[x])/Sqrt[c*x^2]","A",3,2,18,0.1111,1,"{15, 43}"
785,1,26,0,0.0038607,"\int \frac{a+b x}{x^2 \sqrt{c x^2}} \, dx","Int[(a + b*x)/(x^2*Sqrt[c*x^2]),x]","-\frac{(a+b x)^2}{2 a x \sqrt{c x^2}}","-\frac{(a+b x)^2}{2 a x \sqrt{c x^2}}",1,"-(a + b*x)^2/(2*a*x*Sqrt[c*x^2])","A",2,2,18,0.1111,1,"{15, 37}"
786,1,35,0,0.0067594,"\int \frac{a+b x}{x^3 \sqrt{c x^2}} \, dx","Int[(a + b*x)/(x^3*Sqrt[c*x^2]),x]","-\frac{a}{3 x^2 \sqrt{c x^2}}-\frac{b}{2 x \sqrt{c x^2}}","-\frac{a}{3 x^2 \sqrt{c x^2}}-\frac{b}{2 x \sqrt{c x^2}}",1,"-a/(3*x^2*Sqrt[c*x^2]) - b/(2*x*Sqrt[c*x^2])","A",3,2,18,0.1111,1,"{15, 43}"
787,1,35,0,0.0067296,"\int \frac{a+b x}{x^4 \sqrt{c x^2}} \, dx","Int[(a + b*x)/(x^4*Sqrt[c*x^2]),x]","-\frac{a}{4 x^3 \sqrt{c x^2}}-\frac{b}{3 x^2 \sqrt{c x^2}}","-\frac{a}{4 x^3 \sqrt{c x^2}}-\frac{b}{3 x^2 \sqrt{c x^2}}",1,"-a/(4*x^3*Sqrt[c*x^2]) - b/(3*x^2*Sqrt[c*x^2])","A",3,2,18,0.1111,1,"{15, 43}"
788,1,38,0,0.0056526,"\int \frac{x^3 (a+b x)}{\left(c x^2\right)^{3/2}} \, dx","Int[(x^3*(a + b*x))/(c*x^2)^(3/2),x]","\frac{a x^2}{c \sqrt{c x^2}}+\frac{b x^3}{2 c \sqrt{c x^2}}","\frac{a x^2}{c \sqrt{c x^2}}+\frac{b x^3}{2 c \sqrt{c x^2}}",1,"(a*x^2)/(c*Sqrt[c*x^2]) + (b*x^3)/(2*c*Sqrt[c*x^2])","A",2,1,18,0.05556,1,"{15}"
789,1,35,0,0.005395,"\int \frac{x^2 (a+b x)}{\left(c x^2\right)^{3/2}} \, dx","Int[(x^2*(a + b*x))/(c*x^2)^(3/2),x]","\frac{a x \log (x)}{c \sqrt{c x^2}}+\frac{b x^2}{c \sqrt{c x^2}}","\frac{a x \log (x)}{c \sqrt{c x^2}}+\frac{b x^2}{c \sqrt{c x^2}}",1,"(b*x^2)/(c*Sqrt[c*x^2]) + (a*x*Log[x])/(c*Sqrt[c*x^2])","A",3,2,18,0.1111,1,"{15, 43}"
790,1,33,0,0.0067799,"\int \frac{x (a+b x)}{\left(c x^2\right)^{3/2}} \, dx","Int[(x*(a + b*x))/(c*x^2)^(3/2),x]","\frac{b x \log (x)}{c \sqrt{c x^2}}-\frac{a}{c \sqrt{c x^2}}","\frac{b x \log (x)}{c \sqrt{c x^2}}-\frac{a}{c \sqrt{c x^2}}",1,"-(a/(c*Sqrt[c*x^2])) + (b*x*Log[x])/(c*Sqrt[c*x^2])","A",3,2,16,0.1250,1,"{15, 43}"
791,1,29,0,0.0043576,"\int \frac{a+b x}{\left(c x^2\right)^{3/2}} \, dx","Int[(a + b*x)/(c*x^2)^(3/2),x]","-\frac{(a+b x)^2}{2 a c x \sqrt{c x^2}}","-\frac{(a+b x)^2}{2 a c x \sqrt{c x^2}}",1,"-(a + b*x)^2/(2*a*c*x*Sqrt[c*x^2])","A",2,2,15,0.1333,1,"{15, 37}"
792,1,41,0,0.0077756,"\int \frac{a+b x}{x \left(c x^2\right)^{3/2}} \, dx","Int[(a + b*x)/(x*(c*x^2)^(3/2)),x]","-\frac{a}{3 c x^2 \sqrt{c x^2}}-\frac{b}{2 c x \sqrt{c x^2}}","-\frac{a}{3 c x^2 \sqrt{c x^2}}-\frac{b}{2 c x \sqrt{c x^2}}",1,"-a/(3*c*x^2*Sqrt[c*x^2]) - b/(2*c*x*Sqrt[c*x^2])","A",3,2,18,0.1111,1,"{15, 43}"
793,1,41,0,0.0074609,"\int \frac{a+b x}{x^2 \left(c x^2\right)^{3/2}} \, dx","Int[(a + b*x)/(x^2*(c*x^2)^(3/2)),x]","-\frac{a}{4 c x^3 \sqrt{c x^2}}-\frac{b}{3 c x^2 \sqrt{c x^2}}","-\frac{a}{4 c x^3 \sqrt{c x^2}}-\frac{b}{3 c x^2 \sqrt{c x^2}}",1,"-a/(4*c*x^3*Sqrt[c*x^2]) - b/(3*c*x^2*Sqrt[c*x^2])","A",3,2,18,0.1111,1,"{15, 43}"
794,1,41,0,0.0075206,"\int \frac{a+b x}{x^3 \left(c x^2\right)^{3/2}} \, dx","Int[(a + b*x)/(x^3*(c*x^2)^(3/2)),x]","-\frac{a}{5 c x^4 \sqrt{c x^2}}-\frac{b}{4 c x^3 \sqrt{c x^2}}","-\frac{a}{5 c x^4 \sqrt{c x^2}}-\frac{b}{4 c x^3 \sqrt{c x^2}}",1,"-a/(5*c*x^4*Sqrt[c*x^2]) - b/(4*c*x^3*Sqrt[c*x^2])","A",3,2,18,0.1111,1,"{15, 43}"
795,1,41,0,0.0074406,"\int \frac{a+b x}{x^4 \left(c x^2\right)^{3/2}} \, dx","Int[(a + b*x)/(x^4*(c*x^2)^(3/2)),x]","-\frac{a}{6 c x^5 \sqrt{c x^2}}-\frac{b}{5 c x^4 \sqrt{c x^2}}","-\frac{a}{6 c x^5 \sqrt{c x^2}}-\frac{b}{5 c x^4 \sqrt{c x^2}}",1,"-a/(6*c*x^5*Sqrt[c*x^2]) - b/(5*c*x^4*Sqrt[c*x^2])","A",3,2,18,0.1111,1,"{15, 43}"
796,1,33,0,0.0075182,"\int \frac{x^3 (a+b x)}{\left(c x^2\right)^{5/2}} \, dx","Int[(x^3*(a + b*x))/(c*x^2)^(5/2),x]","\frac{b x \log (x)}{c^2 \sqrt{c x^2}}-\frac{a}{c^2 \sqrt{c x^2}}","\frac{b x \log (x)}{c^2 \sqrt{c x^2}}-\frac{a}{c^2 \sqrt{c x^2}}",1,"-(a/(c^2*Sqrt[c*x^2])) + (b*x*Log[x])/(c^2*Sqrt[c*x^2])","A",3,2,18,0.1111,1,"{15, 43}"
797,1,29,0,0.0048614,"\int \frac{x^2 (a+b x)}{\left(c x^2\right)^{5/2}} \, dx","Int[(x^2*(a + b*x))/(c*x^2)^(5/2),x]","-\frac{(a+b x)^2}{2 a c^2 x \sqrt{c x^2}}","-\frac{(a+b x)^2}{2 a c^2 x \sqrt{c x^2}}",1,"-(a + b*x)^2/(2*a*c^2*x*Sqrt[c*x^2])","A",2,2,18,0.1111,1,"{15, 37}"
798,1,41,0,0.0082408,"\int \frac{x (a+b x)}{\left(c x^2\right)^{5/2}} \, dx","Int[(x*(a + b*x))/(c*x^2)^(5/2),x]","-\frac{a}{3 c^2 x^2 \sqrt{c x^2}}-\frac{b}{2 c^2 x \sqrt{c x^2}}","-\frac{a}{3 c^2 x^2 \sqrt{c x^2}}-\frac{b}{2 c^2 x \sqrt{c x^2}}",1,"-a/(3*c^2*x^2*Sqrt[c*x^2]) - b/(2*c^2*x*Sqrt[c*x^2])","A",3,2,16,0.1250,1,"{15, 43}"
799,1,41,0,0.0072754,"\int \frac{a+b x}{\left(c x^2\right)^{5/2}} \, dx","Int[(a + b*x)/(c*x^2)^(5/2),x]","-\frac{a}{4 c^2 x^3 \sqrt{c x^2}}-\frac{b}{3 c^2 x^2 \sqrt{c x^2}}","-\frac{a}{4 c^2 x^3 \sqrt{c x^2}}-\frac{b}{3 c^2 x^2 \sqrt{c x^2}}",1,"-a/(4*c^2*x^3*Sqrt[c*x^2]) - b/(3*c^2*x^2*Sqrt[c*x^2])","A",3,2,15,0.1333,1,"{15, 43}"
800,1,41,0,0.0081763,"\int \frac{a+b x}{x \left(c x^2\right)^{5/2}} \, dx","Int[(a + b*x)/(x*(c*x^2)^(5/2)),x]","-\frac{a}{5 c^2 x^4 \sqrt{c x^2}}-\frac{b}{4 c^2 x^3 \sqrt{c x^2}}","-\frac{a}{5 c^2 x^4 \sqrt{c x^2}}-\frac{b}{4 c^2 x^3 \sqrt{c x^2}}",1,"-a/(5*c^2*x^4*Sqrt[c*x^2]) - b/(4*c^2*x^3*Sqrt[c*x^2])","A",3,2,18,0.1111,1,"{15, 43}"
801,1,41,0,0.0076584,"\int \frac{a+b x}{x^2 \left(c x^2\right)^{5/2}} \, dx","Int[(a + b*x)/(x^2*(c*x^2)^(5/2)),x]","-\frac{a}{6 c^2 x^5 \sqrt{c x^2}}-\frac{b}{5 c^2 x^4 \sqrt{c x^2}}","-\frac{a}{6 c^2 x^5 \sqrt{c x^2}}-\frac{b}{5 c^2 x^4 \sqrt{c x^2}}",1,"-a/(6*c^2*x^5*Sqrt[c*x^2]) - b/(5*c^2*x^4*Sqrt[c*x^2])","A",3,2,18,0.1111,1,"{15, 43}"
802,1,41,0,0.0088245,"\int \frac{a+b x}{x^3 \left(c x^2\right)^{5/2}} \, dx","Int[(a + b*x)/(x^3*(c*x^2)^(5/2)),x]","-\frac{a}{7 c^2 x^6 \sqrt{c x^2}}-\frac{b}{6 c^2 x^5 \sqrt{c x^2}}","-\frac{a}{7 c^2 x^6 \sqrt{c x^2}}-\frac{b}{6 c^2 x^5 \sqrt{c x^2}}",1,"-a/(7*c^2*x^6*Sqrt[c*x^2]) - b/(6*c^2*x^5*Sqrt[c*x^2])","A",3,2,18,0.1111,1,"{15, 43}"
803,1,41,0,0.0083773,"\int \frac{a+b x}{x^4 \left(c x^2\right)^{5/2}} \, dx","Int[(a + b*x)/(x^4*(c*x^2)^(5/2)),x]","-\frac{a}{8 c^2 x^7 \sqrt{c x^2}}-\frac{b}{7 c^2 x^6 \sqrt{c x^2}}","-\frac{a}{8 c^2 x^7 \sqrt{c x^2}}-\frac{b}{7 c^2 x^6 \sqrt{c x^2}}",1,"-a/(8*c^2*x^7*Sqrt[c*x^2]) - b/(7*c^2*x^6*Sqrt[c*x^2])","A",3,2,18,0.1111,1,"{15, 43}"
804,1,57,0,0.0154403,"\int x^3 \sqrt{c x^2} (a+b x)^2 \, dx","Int[x^3*Sqrt[c*x^2]*(a + b*x)^2,x]","\frac{1}{5} a^2 x^4 \sqrt{c x^2}+\frac{1}{3} a b x^5 \sqrt{c x^2}+\frac{1}{7} b^2 x^6 \sqrt{c x^2}","\frac{1}{5} a^2 x^4 \sqrt{c x^2}+\frac{1}{3} a b x^5 \sqrt{c x^2}+\frac{1}{7} b^2 x^6 \sqrt{c x^2}",1,"(a^2*x^4*Sqrt[c*x^2])/5 + (a*b*x^5*Sqrt[c*x^2])/3 + (b^2*x^6*Sqrt[c*x^2])/7","A",3,2,20,0.1000,1,"{15, 43}"
805,1,57,0,0.0146784,"\int x^2 \sqrt{c x^2} (a+b x)^2 \, dx","Int[x^2*Sqrt[c*x^2]*(a + b*x)^2,x]","\frac{1}{4} a^2 x^3 \sqrt{c x^2}+\frac{2}{5} a b x^4 \sqrt{c x^2}+\frac{1}{6} b^2 x^5 \sqrt{c x^2}","\frac{1}{4} a^2 x^3 \sqrt{c x^2}+\frac{2}{5} a b x^4 \sqrt{c x^2}+\frac{1}{6} b^2 x^5 \sqrt{c x^2}",1,"(a^2*x^3*Sqrt[c*x^2])/4 + (2*a*b*x^4*Sqrt[c*x^2])/5 + (b^2*x^5*Sqrt[c*x^2])/6","A",3,2,20,0.1000,1,"{15, 43}"
806,1,57,0,0.0134847,"\int x \sqrt{c x^2} (a+b x)^2 \, dx","Int[x*Sqrt[c*x^2]*(a + b*x)^2,x]","\frac{1}{3} a^2 x^2 \sqrt{c x^2}+\frac{1}{2} a b x^3 \sqrt{c x^2}+\frac{1}{5} b^2 x^4 \sqrt{c x^2}","\frac{1}{3} a^2 x^2 \sqrt{c x^2}+\frac{1}{2} a b x^3 \sqrt{c x^2}+\frac{1}{5} b^2 x^4 \sqrt{c x^2}",1,"(a^2*x^2*Sqrt[c*x^2])/3 + (a*b*x^3*Sqrt[c*x^2])/2 + (b^2*x^4*Sqrt[c*x^2])/5","A",3,2,18,0.1111,1,"{15, 43}"
807,1,55,0,0.0136003,"\int \sqrt{c x^2} (a+b x)^2 \, dx","Int[Sqrt[c*x^2]*(a + b*x)^2,x]","\frac{1}{2} a^2 x \sqrt{c x^2}+\frac{2}{3} a b x^2 \sqrt{c x^2}+\frac{1}{4} b^2 x^3 \sqrt{c x^2}","\frac{1}{2} a^2 x \sqrt{c x^2}+\frac{2}{3} a b x^2 \sqrt{c x^2}+\frac{1}{4} b^2 x^3 \sqrt{c x^2}",1,"(a^2*x*Sqrt[c*x^2])/2 + (2*a*b*x^2*Sqrt[c*x^2])/3 + (b^2*x^3*Sqrt[c*x^2])/4","A",3,2,17,0.1176,1,"{15, 43}"
808,1,26,0,0.0036536,"\int \frac{\sqrt{c x^2} (a+b x)^2}{x} \, dx","Int[(Sqrt[c*x^2]*(a + b*x)^2)/x,x]","\frac{\sqrt{c x^2} (a+b x)^3}{3 b x}","\frac{\sqrt{c x^2} (a+b x)^3}{3 b x}",1,"(Sqrt[c*x^2]*(a + b*x)^3)/(3*b*x)","A",2,2,20,0.1000,1,"{15, 32}"
809,1,49,0,0.009421,"\int \frac{\sqrt{c x^2} (a+b x)^2}{x^2} \, dx","Int[(Sqrt[c*x^2]*(a + b*x)^2)/x^2,x]","\frac{a^2 \sqrt{c x^2} \log (x)}{x}+2 a b \sqrt{c x^2}+\frac{1}{2} b^2 x \sqrt{c x^2}","\frac{a^2 \sqrt{c x^2} \log (x)}{x}+2 a b \sqrt{c x^2}+\frac{1}{2} b^2 x \sqrt{c x^2}",1,"2*a*b*Sqrt[c*x^2] + (b^2*x*Sqrt[c*x^2])/2 + (a^2*Sqrt[c*x^2]*Log[x])/x","A",3,2,20,0.1000,1,"{15, 43}"
810,1,49,0,0.0113116,"\int \frac{\sqrt{c x^2} (a+b x)^2}{x^3} \, dx","Int[(Sqrt[c*x^2]*(a + b*x)^2)/x^3,x]","-\frac{a^2 \sqrt{c x^2}}{x^2}+\frac{2 a b \sqrt{c x^2} \log (x)}{x}+b^2 \sqrt{c x^2}","-\frac{a^2 \sqrt{c x^2}}{x^2}+\frac{2 a b \sqrt{c x^2} \log (x)}{x}+b^2 \sqrt{c x^2}",1,"b^2*Sqrt[c*x^2] - (a^2*Sqrt[c*x^2])/x^2 + (2*a*b*Sqrt[c*x^2]*Log[x])/x","A",3,2,20,0.1000,1,"{15, 43}"
811,1,54,0,0.0115592,"\int \frac{\sqrt{c x^2} (a+b x)^2}{x^4} \, dx","Int[(Sqrt[c*x^2]*(a + b*x)^2)/x^4,x]","-\frac{a^2 \sqrt{c x^2}}{2 x^3}-\frac{2 a b \sqrt{c x^2}}{x^2}+\frac{b^2 \sqrt{c x^2} \log (x)}{x}","-\frac{a^2 \sqrt{c x^2}}{2 x^3}-\frac{2 a b \sqrt{c x^2}}{x^2}+\frac{b^2 \sqrt{c x^2} \log (x)}{x}",1,"-(a^2*Sqrt[c*x^2])/(2*x^3) - (2*a*b*Sqrt[c*x^2])/x^2 + (b^2*Sqrt[c*x^2]*Log[x])/x","A",3,2,20,0.1000,1,"{15, 43}"
812,1,60,0,0.0187081,"\int x^3 \left(c x^2\right)^{3/2} (a+b x)^2 \, dx","Int[x^3*(c*x^2)^(3/2)*(a + b*x)^2,x]","\frac{1}{7} a^2 c x^6 \sqrt{c x^2}+\frac{1}{4} a b c x^7 \sqrt{c x^2}+\frac{1}{9} b^2 c x^8 \sqrt{c x^2}","\frac{1}{7} a^2 c x^6 \sqrt{c x^2}+\frac{1}{4} a b c x^7 \sqrt{c x^2}+\frac{1}{9} b^2 c x^8 \sqrt{c x^2}",1,"(a^2*c*x^6*Sqrt[c*x^2])/7 + (a*b*c*x^7*Sqrt[c*x^2])/4 + (b^2*c*x^8*Sqrt[c*x^2])/9","A",3,2,20,0.1000,1,"{15, 43}"
813,1,60,0,0.017045,"\int x^2 \left(c x^2\right)^{3/2} (a+b x)^2 \, dx","Int[x^2*(c*x^2)^(3/2)*(a + b*x)^2,x]","\frac{1}{6} a^2 c x^5 \sqrt{c x^2}+\frac{2}{7} a b c x^6 \sqrt{c x^2}+\frac{1}{8} b^2 c x^7 \sqrt{c x^2}","\frac{1}{6} a^2 c x^5 \sqrt{c x^2}+\frac{2}{7} a b c x^6 \sqrt{c x^2}+\frac{1}{8} b^2 c x^7 \sqrt{c x^2}",1,"(a^2*c*x^5*Sqrt[c*x^2])/6 + (2*a*b*c*x^6*Sqrt[c*x^2])/7 + (b^2*c*x^7*Sqrt[c*x^2])/8","A",3,2,20,0.1000,1,"{15, 43}"
814,1,60,0,0.0161078,"\int x \left(c x^2\right)^{3/2} (a+b x)^2 \, dx","Int[x*(c*x^2)^(3/2)*(a + b*x)^2,x]","\frac{1}{5} a^2 c x^4 \sqrt{c x^2}+\frac{1}{3} a b c x^5 \sqrt{c x^2}+\frac{1}{7} b^2 c x^6 \sqrt{c x^2}","\frac{1}{5} a^2 c x^4 \sqrt{c x^2}+\frac{1}{3} a b c x^5 \sqrt{c x^2}+\frac{1}{7} b^2 c x^6 \sqrt{c x^2}",1,"(a^2*c*x^4*Sqrt[c*x^2])/5 + (a*b*c*x^5*Sqrt[c*x^2])/3 + (b^2*c*x^6*Sqrt[c*x^2])/7","A",3,2,18,0.1111,1,"{15, 43}"
815,1,60,0,0.0146034,"\int \left(c x^2\right)^{3/2} (a+b x)^2 \, dx","Int[(c*x^2)^(3/2)*(a + b*x)^2,x]","\frac{1}{4} a^2 c x^3 \sqrt{c x^2}+\frac{2}{5} a b c x^4 \sqrt{c x^2}+\frac{1}{6} b^2 c x^5 \sqrt{c x^2}","\frac{1}{4} a^2 c x^3 \sqrt{c x^2}+\frac{2}{5} a b c x^4 \sqrt{c x^2}+\frac{1}{6} b^2 c x^5 \sqrt{c x^2}",1,"(a^2*c*x^3*Sqrt[c*x^2])/4 + (2*a*b*c*x^4*Sqrt[c*x^2])/5 + (b^2*c*x^5*Sqrt[c*x^2])/6","A",3,2,17,0.1176,1,"{15, 43}"
816,1,60,0,0.0146076,"\int \frac{\left(c x^2\right)^{3/2} (a+b x)^2}{x} \, dx","Int[((c*x^2)^(3/2)*(a + b*x)^2)/x,x]","\frac{1}{3} a^2 c x^2 \sqrt{c x^2}+\frac{1}{2} a b c x^3 \sqrt{c x^2}+\frac{1}{5} b^2 c x^4 \sqrt{c x^2}","\frac{1}{3} a^2 c x^2 \sqrt{c x^2}+\frac{1}{2} a b c x^3 \sqrt{c x^2}+\frac{1}{5} b^2 c x^4 \sqrt{c x^2}",1,"(a^2*c*x^2*Sqrt[c*x^2])/3 + (a*b*c*x^3*Sqrt[c*x^2])/2 + (b^2*c*x^4*Sqrt[c*x^2])/5","A",3,2,20,0.1000,1,"{15, 43}"
817,1,58,0,0.0131542,"\int \frac{\left(c x^2\right)^{3/2} (a+b x)^2}{x^2} \, dx","Int[((c*x^2)^(3/2)*(a + b*x)^2)/x^2,x]","\frac{1}{2} a^2 c x \sqrt{c x^2}+\frac{2}{3} a b c x^2 \sqrt{c x^2}+\frac{1}{4} b^2 c x^3 \sqrt{c x^2}","\frac{1}{2} a^2 c x \sqrt{c x^2}+\frac{2}{3} a b c x^2 \sqrt{c x^2}+\frac{1}{4} b^2 c x^3 \sqrt{c x^2}",1,"(a^2*c*x*Sqrt[c*x^2])/2 + (2*a*b*c*x^2*Sqrt[c*x^2])/3 + (b^2*c*x^3*Sqrt[c*x^2])/4","A",3,2,20,0.1000,1,"{15, 43}"
818,1,27,0,0.0044034,"\int \frac{\left(c x^2\right)^{3/2} (a+b x)^2}{x^3} \, dx","Int[((c*x^2)^(3/2)*(a + b*x)^2)/x^3,x]","\frac{c \sqrt{c x^2} (a+b x)^3}{3 b x}","\frac{c \sqrt{c x^2} (a+b x)^3}{3 b x}",1,"(c*Sqrt[c*x^2]*(a + b*x)^3)/(3*b*x)","A",2,2,20,0.1000,1,"{15, 32}"
819,1,52,0,0.0097471,"\int \frac{\left(c x^2\right)^{3/2} (a+b x)^2}{x^4} \, dx","Int[((c*x^2)^(3/2)*(a + b*x)^2)/x^4,x]","\frac{a^2 c \sqrt{c x^2} \log (x)}{x}+2 a b c \sqrt{c x^2}+\frac{1}{2} b^2 c x \sqrt{c x^2}","\frac{a^2 c \sqrt{c x^2} \log (x)}{x}+2 a b c \sqrt{c x^2}+\frac{1}{2} b^2 c x \sqrt{c x^2}",1,"2*a*b*c*Sqrt[c*x^2] + (b^2*c*x*Sqrt[c*x^2])/2 + (a^2*c*Sqrt[c*x^2]*Log[x])/x","A",3,2,20,0.1000,1,"{15, 43}"
820,1,66,0,0.0190345,"\int x \left(c x^2\right)^{5/2} (a+b x)^2 \, dx","Int[x*(c*x^2)^(5/2)*(a + b*x)^2,x]","\frac{1}{7} a^2 c^2 x^6 \sqrt{c x^2}+\frac{1}{4} a b c^2 x^7 \sqrt{c x^2}+\frac{1}{9} b^2 c^2 x^8 \sqrt{c x^2}","\frac{1}{7} a^2 c^2 x^6 \sqrt{c x^2}+\frac{1}{4} a b c^2 x^7 \sqrt{c x^2}+\frac{1}{9} b^2 c^2 x^8 \sqrt{c x^2}",1,"(a^2*c^2*x^6*Sqrt[c*x^2])/7 + (a*b*c^2*x^7*Sqrt[c*x^2])/4 + (b^2*c^2*x^8*Sqrt[c*x^2])/9","A",3,2,18,0.1111,1,"{15, 43}"
821,1,66,0,0.0169404,"\int \left(c x^2\right)^{5/2} (a+b x)^2 \, dx","Int[(c*x^2)^(5/2)*(a + b*x)^2,x]","\frac{1}{6} a^2 c^2 x^5 \sqrt{c x^2}+\frac{2}{7} a b c^2 x^6 \sqrt{c x^2}+\frac{1}{8} b^2 c^2 x^7 \sqrt{c x^2}","\frac{1}{6} a^2 c^2 x^5 \sqrt{c x^2}+\frac{2}{7} a b c^2 x^6 \sqrt{c x^2}+\frac{1}{8} b^2 c^2 x^7 \sqrt{c x^2}",1,"(a^2*c^2*x^5*Sqrt[c*x^2])/6 + (2*a*b*c^2*x^6*Sqrt[c*x^2])/7 + (b^2*c^2*x^7*Sqrt[c*x^2])/8","A",3,2,17,0.1176,1,"{15, 43}"
822,1,66,0,0.0163015,"\int \frac{\left(c x^2\right)^{5/2} (a+b x)^2}{x} \, dx","Int[((c*x^2)^(5/2)*(a + b*x)^2)/x,x]","\frac{1}{5} a^2 c^2 x^4 \sqrt{c x^2}+\frac{1}{3} a b c^2 x^5 \sqrt{c x^2}+\frac{1}{7} b^2 c^2 x^6 \sqrt{c x^2}","\frac{1}{5} a^2 c^2 x^4 \sqrt{c x^2}+\frac{1}{3} a b c^2 x^5 \sqrt{c x^2}+\frac{1}{7} b^2 c^2 x^6 \sqrt{c x^2}",1,"(a^2*c^2*x^4*Sqrt[c*x^2])/5 + (a*b*c^2*x^5*Sqrt[c*x^2])/3 + (b^2*c^2*x^6*Sqrt[c*x^2])/7","A",3,2,20,0.1000,1,"{15, 43}"
823,1,66,0,0.0151678,"\int \frac{\left(c x^2\right)^{5/2} (a+b x)^2}{x^2} \, dx","Int[((c*x^2)^(5/2)*(a + b*x)^2)/x^2,x]","\frac{1}{4} a^2 c^2 x^3 \sqrt{c x^2}+\frac{2}{5} a b c^2 x^4 \sqrt{c x^2}+\frac{1}{6} b^2 c^2 x^5 \sqrt{c x^2}","\frac{1}{4} a^2 c^2 x^3 \sqrt{c x^2}+\frac{2}{5} a b c^2 x^4 \sqrt{c x^2}+\frac{1}{6} b^2 c^2 x^5 \sqrt{c x^2}",1,"(a^2*c^2*x^3*Sqrt[c*x^2])/4 + (2*a*b*c^2*x^4*Sqrt[c*x^2])/5 + (b^2*c^2*x^5*Sqrt[c*x^2])/6","A",3,2,20,0.1000,1,"{15, 43}"
824,1,66,0,0.0142389,"\int \frac{\left(c x^2\right)^{5/2} (a+b x)^2}{x^3} \, dx","Int[((c*x^2)^(5/2)*(a + b*x)^2)/x^3,x]","\frac{1}{3} a^2 c^2 x^2 \sqrt{c x^2}+\frac{1}{2} a b c^2 x^3 \sqrt{c x^2}+\frac{1}{5} b^2 c^2 x^4 \sqrt{c x^2}","\frac{1}{3} a^2 c^2 x^2 \sqrt{c x^2}+\frac{1}{2} a b c^2 x^3 \sqrt{c x^2}+\frac{1}{5} b^2 c^2 x^4 \sqrt{c x^2}",1,"(a^2*c^2*x^2*Sqrt[c*x^2])/3 + (a*b*c^2*x^3*Sqrt[c*x^2])/2 + (b^2*c^2*x^4*Sqrt[c*x^2])/5","A",3,2,20,0.1000,1,"{15, 43}"
825,1,64,0,0.0146246,"\int \frac{\left(c x^2\right)^{5/2} (a+b x)^2}{x^4} \, dx","Int[((c*x^2)^(5/2)*(a + b*x)^2)/x^4,x]","\frac{1}{2} a^2 c^2 x \sqrt{c x^2}+\frac{2}{3} a b c^2 x^2 \sqrt{c x^2}+\frac{1}{4} b^2 c^2 x^3 \sqrt{c x^2}","\frac{1}{2} a^2 c^2 x \sqrt{c x^2}+\frac{2}{3} a b c^2 x^2 \sqrt{c x^2}+\frac{1}{4} b^2 c^2 x^3 \sqrt{c x^2}",1,"(a^2*c^2*x*Sqrt[c*x^2])/2 + (2*a*b*c^2*x^2*Sqrt[c*x^2])/3 + (b^2*c^2*x^3*Sqrt[c*x^2])/4","A",3,2,20,0.1000,1,"{15, 43}"
826,1,29,0,0.0042798,"\int \frac{\left(c x^2\right)^{5/2} (a+b x)^2}{x^5} \, dx","Int[((c*x^2)^(5/2)*(a + b*x)^2)/x^5,x]","\frac{c^2 \sqrt{c x^2} (a+b x)^3}{3 b x}","\frac{c^2 \sqrt{c x^2} (a+b x)^3}{3 b x}",1,"(c^2*Sqrt[c*x^2]*(a + b*x)^3)/(3*b*x)","A",2,2,20,0.1000,1,"{15, 32}"
827,1,58,0,0.0114799,"\int \frac{\left(c x^2\right)^{5/2} (a+b x)^2}{x^6} \, dx","Int[((c*x^2)^(5/2)*(a + b*x)^2)/x^6,x]","\frac{a^2 c^2 \sqrt{c x^2} \log (x)}{x}+2 a b c^2 \sqrt{c x^2}+\frac{1}{2} b^2 c^2 x \sqrt{c x^2}","\frac{a^2 c^2 \sqrt{c x^2} \log (x)}{x}+2 a b c^2 \sqrt{c x^2}+\frac{1}{2} b^2 c^2 x \sqrt{c x^2}",1,"2*a*b*c^2*Sqrt[c*x^2] + (b^2*c^2*x*Sqrt[c*x^2])/2 + (a^2*c^2*Sqrt[c*x^2]*Log[x])/x","A",3,2,20,0.1000,1,"{15, 43}"
828,1,57,0,0.0132603,"\int \frac{x^3 (a+b x)^2}{\sqrt{c x^2}} \, dx","Int[(x^3*(a + b*x)^2)/Sqrt[c*x^2],x]","\frac{a^2 x^4}{3 \sqrt{c x^2}}+\frac{a b x^5}{2 \sqrt{c x^2}}+\frac{b^2 x^6}{5 \sqrt{c x^2}}","\frac{a^2 x^4}{3 \sqrt{c x^2}}+\frac{a b x^5}{2 \sqrt{c x^2}}+\frac{b^2 x^6}{5 \sqrt{c x^2}}",1,"(a^2*x^4)/(3*Sqrt[c*x^2]) + (a*b*x^5)/(2*Sqrt[c*x^2]) + (b^2*x^6)/(5*Sqrt[c*x^2])","A",3,2,20,0.1000,1,"{15, 43}"
829,1,57,0,0.0121125,"\int \frac{x^2 (a+b x)^2}{\sqrt{c x^2}} \, dx","Int[(x^2*(a + b*x)^2)/Sqrt[c*x^2],x]","\frac{a^2 x^3}{2 \sqrt{c x^2}}+\frac{2 a b x^4}{3 \sqrt{c x^2}}+\frac{b^2 x^5}{4 \sqrt{c x^2}}","\frac{a^2 x^3}{2 \sqrt{c x^2}}+\frac{2 a b x^4}{3 \sqrt{c x^2}}+\frac{b^2 x^5}{4 \sqrt{c x^2}}",1,"(a^2*x^3)/(2*Sqrt[c*x^2]) + (2*a*b*x^4)/(3*Sqrt[c*x^2]) + (b^2*x^5)/(4*Sqrt[c*x^2])","A",3,2,20,0.1000,1,"{15, 43}"
830,1,24,0,0.0033883,"\int \frac{x (a+b x)^2}{\sqrt{c x^2}} \, dx","Int[(x*(a + b*x)^2)/Sqrt[c*x^2],x]","\frac{x (a+b x)^3}{3 b \sqrt{c x^2}}","\frac{x (a+b x)^3}{3 b \sqrt{c x^2}}",1,"(x*(a + b*x)^3)/(3*b*Sqrt[c*x^2])","A",2,2,18,0.1111,1,"{15, 32}"
831,1,52,0,0.0100162,"\int \frac{(a+b x)^2}{\sqrt{c x^2}} \, dx","Int[(a + b*x)^2/Sqrt[c*x^2],x]","\frac{a^2 x \log (x)}{\sqrt{c x^2}}+\frac{2 a b x^2}{\sqrt{c x^2}}+\frac{b^2 x^3}{2 \sqrt{c x^2}}","\frac{a^2 x \log (x)}{\sqrt{c x^2}}+\frac{2 a b x^2}{\sqrt{c x^2}}+\frac{b^2 x^3}{2 \sqrt{c x^2}}",1,"(2*a*b*x^2)/Sqrt[c*x^2] + (b^2*x^3)/(2*Sqrt[c*x^2]) + (a^2*x*Log[x])/Sqrt[c*x^2]","A",3,2,17,0.1176,1,"{15, 43}"
832,1,47,0,0.0105107,"\int \frac{(a+b x)^2}{x \sqrt{c x^2}} \, dx","Int[(a + b*x)^2/(x*Sqrt[c*x^2]),x]","-\frac{a^2}{\sqrt{c x^2}}+\frac{2 a b x \log (x)}{\sqrt{c x^2}}+\frac{b^2 x^2}{\sqrt{c x^2}}","-\frac{a^2}{\sqrt{c x^2}}+\frac{2 a b x \log (x)}{\sqrt{c x^2}}+\frac{b^2 x^2}{\sqrt{c x^2}}",1,"-(a^2/Sqrt[c*x^2]) + (b^2*x^2)/Sqrt[c*x^2] + (2*a*b*x*Log[x])/Sqrt[c*x^2]","A",3,2,20,0.1000,1,"{15, 43}"
833,1,49,0,0.0113112,"\int \frac{(a+b x)^2}{x^2 \sqrt{c x^2}} \, dx","Int[(a + b*x)^2/(x^2*Sqrt[c*x^2]),x]","-\frac{a^2}{2 x \sqrt{c x^2}}-\frac{2 a b}{\sqrt{c x^2}}+\frac{b^2 x \log (x)}{\sqrt{c x^2}}","-\frac{a^2}{2 x \sqrt{c x^2}}-\frac{2 a b}{\sqrt{c x^2}}+\frac{b^2 x \log (x)}{\sqrt{c x^2}}",1,"(-2*a*b)/Sqrt[c*x^2] - a^2/(2*x*Sqrt[c*x^2]) + (b^2*x*Log[x])/Sqrt[c*x^2]","A",3,2,20,0.1000,1,"{15, 43}"
834,1,26,0,0.0036094,"\int \frac{(a+b x)^2}{x^3 \sqrt{c x^2}} \, dx","Int[(a + b*x)^2/(x^3*Sqrt[c*x^2]),x]","-\frac{(a+b x)^3}{3 a x^2 \sqrt{c x^2}}","-\frac{(a+b x)^3}{3 a x^2 \sqrt{c x^2}}",1,"-(a + b*x)^3/(3*a*x^2*Sqrt[c*x^2])","A",2,2,20,0.1000,1,"{15, 37}"
835,1,57,0,0.0128204,"\int \frac{(a+b x)^2}{x^4 \sqrt{c x^2}} \, dx","Int[(a + b*x)^2/(x^4*Sqrt[c*x^2]),x]","-\frac{a^2}{4 x^3 \sqrt{c x^2}}-\frac{2 a b}{3 x^2 \sqrt{c x^2}}-\frac{b^2}{2 x \sqrt{c x^2}}","-\frac{a^2}{4 x^3 \sqrt{c x^2}}-\frac{2 a b}{3 x^2 \sqrt{c x^2}}-\frac{b^2}{2 x \sqrt{c x^2}}",1,"-a^2/(4*x^3*Sqrt[c*x^2]) - (2*a*b)/(3*x^2*Sqrt[c*x^2]) - b^2/(2*x*Sqrt[c*x^2])","A",3,2,20,0.1000,1,"{15, 43}"
836,1,27,0,0.0042818,"\int \frac{x^3 (a+b x)^2}{\left(c x^2\right)^{3/2}} \, dx","Int[(x^3*(a + b*x)^2)/(c*x^2)^(3/2),x]","\frac{x (a+b x)^3}{3 b c \sqrt{c x^2}}","\frac{x (a+b x)^3}{3 b c \sqrt{c x^2}}",1,"(x*(a + b*x)^3)/(3*b*c*Sqrt[c*x^2])","A",2,2,20,0.1000,1,"{15, 32}"
837,1,61,0,0.0109616,"\int \frac{x^2 (a+b x)^2}{\left(c x^2\right)^{3/2}} \, dx","Int[(x^2*(a + b*x)^2)/(c*x^2)^(3/2),x]","\frac{a^2 x \log (x)}{c \sqrt{c x^2}}+\frac{2 a b x^2}{c \sqrt{c x^2}}+\frac{b^2 x^3}{2 c \sqrt{c x^2}}","\frac{a^2 x \log (x)}{c \sqrt{c x^2}}+\frac{2 a b x^2}{c \sqrt{c x^2}}+\frac{b^2 x^3}{2 c \sqrt{c x^2}}",1,"(2*a*b*x^2)/(c*Sqrt[c*x^2]) + (b^2*x^3)/(2*c*Sqrt[c*x^2]) + (a^2*x*Log[x])/(c*Sqrt[c*x^2])","A",3,2,20,0.1000,1,"{15, 43}"
838,1,56,0,0.0120212,"\int \frac{x (a+b x)^2}{\left(c x^2\right)^{3/2}} \, dx","Int[(x*(a + b*x)^2)/(c*x^2)^(3/2),x]","-\frac{a^2}{c \sqrt{c x^2}}+\frac{2 a b x \log (x)}{c \sqrt{c x^2}}+\frac{b^2 x^2}{c \sqrt{c x^2}}","-\frac{a^2}{c \sqrt{c x^2}}+\frac{2 a b x \log (x)}{c \sqrt{c x^2}}+\frac{b^2 x^2}{c \sqrt{c x^2}}",1,"-(a^2/(c*Sqrt[c*x^2])) + (b^2*x^2)/(c*Sqrt[c*x^2]) + (2*a*b*x*Log[x])/(c*Sqrt[c*x^2])","A",3,2,18,0.1111,1,"{15, 43}"
839,1,58,0,0.0122137,"\int \frac{(a+b x)^2}{\left(c x^2\right)^{3/2}} \, dx","Int[(a + b*x)^2/(c*x^2)^(3/2),x]","-\frac{a^2}{2 c x \sqrt{c x^2}}-\frac{2 a b}{c \sqrt{c x^2}}+\frac{b^2 x \log (x)}{c \sqrt{c x^2}}","-\frac{a^2}{2 c x \sqrt{c x^2}}-\frac{2 a b}{c \sqrt{c x^2}}+\frac{b^2 x \log (x)}{c \sqrt{c x^2}}",1,"(-2*a*b)/(c*Sqrt[c*x^2]) - a^2/(2*c*x*Sqrt[c*x^2]) + (b^2*x*Log[x])/(c*Sqrt[c*x^2])","A",3,2,17,0.1176,1,"{15, 43}"
840,1,29,0,0.0043833,"\int \frac{(a+b x)^2}{x \left(c x^2\right)^{3/2}} \, dx","Int[(a + b*x)^2/(x*(c*x^2)^(3/2)),x]","-\frac{(a+b x)^3}{3 a c x^2 \sqrt{c x^2}}","-\frac{(a+b x)^3}{3 a c x^2 \sqrt{c x^2}}",1,"-(a + b*x)^3/(3*a*c*x^2*Sqrt[c*x^2])","A",2,2,20,0.1000,1,"{15, 37}"
841,1,66,0,0.0128758,"\int \frac{(a+b x)^2}{x^2 \left(c x^2\right)^{3/2}} \, dx","Int[(a + b*x)^2/(x^2*(c*x^2)^(3/2)),x]","-\frac{a^2}{4 c x^3 \sqrt{c x^2}}-\frac{2 a b}{3 c x^2 \sqrt{c x^2}}-\frac{b^2}{2 c x \sqrt{c x^2}}","-\frac{a^2}{4 c x^3 \sqrt{c x^2}}-\frac{2 a b}{3 c x^2 \sqrt{c x^2}}-\frac{b^2}{2 c x \sqrt{c x^2}}",1,"-a^2/(4*c*x^3*Sqrt[c*x^2]) - (2*a*b)/(3*c*x^2*Sqrt[c*x^2]) - b^2/(2*c*x*Sqrt[c*x^2])","A",3,2,20,0.1000,1,"{15, 43}"
842,1,66,0,0.0126852,"\int \frac{(a+b x)^2}{x^3 \left(c x^2\right)^{3/2}} \, dx","Int[(a + b*x)^2/(x^3*(c*x^2)^(3/2)),x]","-\frac{a^2}{5 c x^4 \sqrt{c x^2}}-\frac{a b}{2 c x^3 \sqrt{c x^2}}-\frac{b^2}{3 c x^2 \sqrt{c x^2}}","-\frac{a^2}{5 c x^4 \sqrt{c x^2}}-\frac{a b}{2 c x^3 \sqrt{c x^2}}-\frac{b^2}{3 c x^2 \sqrt{c x^2}}",1,"-a^2/(5*c*x^4*Sqrt[c*x^2]) - (a*b)/(2*c*x^3*Sqrt[c*x^2]) - b^2/(3*c*x^2*Sqrt[c*x^2])","A",3,2,20,0.1000,1,"{15, 43}"
843,1,66,0,0.0139281,"\int \frac{(a+b x)^2}{x^4 \left(c x^2\right)^{3/2}} \, dx","Int[(a + b*x)^2/(x^4*(c*x^2)^(3/2)),x]","-\frac{a^2}{6 c x^5 \sqrt{c x^2}}-\frac{2 a b}{5 c x^4 \sqrt{c x^2}}-\frac{b^2}{4 c x^3 \sqrt{c x^2}}","-\frac{a^2}{6 c x^5 \sqrt{c x^2}}-\frac{2 a b}{5 c x^4 \sqrt{c x^2}}-\frac{b^2}{4 c x^3 \sqrt{c x^2}}",1,"-a^2/(6*c*x^5*Sqrt[c*x^2]) - (2*a*b)/(5*c*x^4*Sqrt[c*x^2]) - b^2/(4*c*x^3*Sqrt[c*x^2])","A",3,2,20,0.1000,1,"{15, 43}"
844,1,56,0,0.0126618,"\int \frac{x^3 (a+b x)^2}{\left(c x^2\right)^{5/2}} \, dx","Int[(x^3*(a + b*x)^2)/(c*x^2)^(5/2),x]","-\frac{a^2}{c^2 \sqrt{c x^2}}+\frac{2 a b x \log (x)}{c^2 \sqrt{c x^2}}+\frac{b^2 x^2}{c^2 \sqrt{c x^2}}","-\frac{a^2}{c^2 \sqrt{c x^2}}+\frac{2 a b x \log (x)}{c^2 \sqrt{c x^2}}+\frac{b^2 x^2}{c^2 \sqrt{c x^2}}",1,"-(a^2/(c^2*Sqrt[c*x^2])) + (b^2*x^2)/(c^2*Sqrt[c*x^2]) + (2*a*b*x*Log[x])/(c^2*Sqrt[c*x^2])","A",3,2,20,0.1000,1,"{15, 43}"
845,1,58,0,0.0122728,"\int \frac{x^2 (a+b x)^2}{\left(c x^2\right)^{5/2}} \, dx","Int[(x^2*(a + b*x)^2)/(c*x^2)^(5/2),x]","-\frac{a^2}{2 c^2 x \sqrt{c x^2}}-\frac{2 a b}{c^2 \sqrt{c x^2}}+\frac{b^2 x \log (x)}{c^2 \sqrt{c x^2}}","-\frac{a^2}{2 c^2 x \sqrt{c x^2}}-\frac{2 a b}{c^2 \sqrt{c x^2}}+\frac{b^2 x \log (x)}{c^2 \sqrt{c x^2}}",1,"(-2*a*b)/(c^2*Sqrt[c*x^2]) - a^2/(2*c^2*x*Sqrt[c*x^2]) + (b^2*x*Log[x])/(c^2*Sqrt[c*x^2])","A",3,2,20,0.1000,1,"{15, 43}"
846,1,29,0,0.0041975,"\int \frac{x (a+b x)^2}{\left(c x^2\right)^{5/2}} \, dx","Int[(x*(a + b*x)^2)/(c*x^2)^(5/2),x]","-\frac{(a+b x)^3}{3 a c^2 x^2 \sqrt{c x^2}}","-\frac{(a+b x)^3}{3 a c^2 x^2 \sqrt{c x^2}}",1,"-(a + b*x)^3/(3*a*c^2*x^2*Sqrt[c*x^2])","A",2,2,18,0.1111,1,"{15, 37}"
847,1,66,0,0.0125624,"\int \frac{(a+b x)^2}{\left(c x^2\right)^{5/2}} \, dx","Int[(a + b*x)^2/(c*x^2)^(5/2),x]","-\frac{a^2}{4 c^2 x^3 \sqrt{c x^2}}-\frac{2 a b}{3 c^2 x^2 \sqrt{c x^2}}-\frac{b^2}{2 c^2 x \sqrt{c x^2}}","-\frac{a^2}{4 c^2 x^3 \sqrt{c x^2}}-\frac{2 a b}{3 c^2 x^2 \sqrt{c x^2}}-\frac{b^2}{2 c^2 x \sqrt{c x^2}}",1,"-a^2/(4*c^2*x^3*Sqrt[c*x^2]) - (2*a*b)/(3*c^2*x^2*Sqrt[c*x^2]) - b^2/(2*c^2*x*Sqrt[c*x^2])","A",3,2,17,0.1176,1,"{15, 43}"
848,1,66,0,0.0124531,"\int \frac{(a+b x)^2}{x \left(c x^2\right)^{5/2}} \, dx","Int[(a + b*x)^2/(x*(c*x^2)^(5/2)),x]","-\frac{a^2}{5 c^2 x^4 \sqrt{c x^2}}-\frac{a b}{2 c^2 x^3 \sqrt{c x^2}}-\frac{b^2}{3 c^2 x^2 \sqrt{c x^2}}","-\frac{a^2}{5 c^2 x^4 \sqrt{c x^2}}-\frac{a b}{2 c^2 x^3 \sqrt{c x^2}}-\frac{b^2}{3 c^2 x^2 \sqrt{c x^2}}",1,"-a^2/(5*c^2*x^4*Sqrt[c*x^2]) - (a*b)/(2*c^2*x^3*Sqrt[c*x^2]) - b^2/(3*c^2*x^2*Sqrt[c*x^2])","A",3,2,20,0.1000,1,"{15, 43}"
849,1,66,0,0.013062,"\int \frac{(a+b x)^2}{x^2 \left(c x^2\right)^{5/2}} \, dx","Int[(a + b*x)^2/(x^2*(c*x^2)^(5/2)),x]","-\frac{a^2}{6 c^2 x^5 \sqrt{c x^2}}-\frac{2 a b}{5 c^2 x^4 \sqrt{c x^2}}-\frac{b^2}{4 c^2 x^3 \sqrt{c x^2}}","-\frac{a^2}{6 c^2 x^5 \sqrt{c x^2}}-\frac{2 a b}{5 c^2 x^4 \sqrt{c x^2}}-\frac{b^2}{4 c^2 x^3 \sqrt{c x^2}}",1,"-a^2/(6*c^2*x^5*Sqrt[c*x^2]) - (2*a*b)/(5*c^2*x^4*Sqrt[c*x^2]) - b^2/(4*c^2*x^3*Sqrt[c*x^2])","A",3,2,20,0.1000,1,"{15, 43}"
850,1,66,0,0.0133345,"\int \frac{(a+b x)^2}{x^3 \left(c x^2\right)^{5/2}} \, dx","Int[(a + b*x)^2/(x^3*(c*x^2)^(5/2)),x]","-\frac{a^2}{7 c^2 x^6 \sqrt{c x^2}}-\frac{a b}{3 c^2 x^5 \sqrt{c x^2}}-\frac{b^2}{5 c^2 x^4 \sqrt{c x^2}}","-\frac{a^2}{7 c^2 x^6 \sqrt{c x^2}}-\frac{a b}{3 c^2 x^5 \sqrt{c x^2}}-\frac{b^2}{5 c^2 x^4 \sqrt{c x^2}}",1,"-a^2/(7*c^2*x^6*Sqrt[c*x^2]) - (a*b)/(3*c^2*x^5*Sqrt[c*x^2]) - b^2/(5*c^2*x^4*Sqrt[c*x^2])","A",3,2,20,0.1000,1,"{15, 43}"
851,1,66,0,0.0134873,"\int \frac{(a+b x)^2}{x^4 \left(c x^2\right)^{5/2}} \, dx","Int[(a + b*x)^2/(x^4*(c*x^2)^(5/2)),x]","-\frac{a^2}{8 c^2 x^7 \sqrt{c x^2}}-\frac{2 a b}{7 c^2 x^6 \sqrt{c x^2}}-\frac{b^2}{6 c^2 x^5 \sqrt{c x^2}}","-\frac{a^2}{8 c^2 x^7 \sqrt{c x^2}}-\frac{2 a b}{7 c^2 x^6 \sqrt{c x^2}}-\frac{b^2}{6 c^2 x^5 \sqrt{c x^2}}",1,"-a^2/(8*c^2*x^7*Sqrt[c*x^2]) - (2*a*b)/(7*c^2*x^6*Sqrt[c*x^2]) - b^2/(6*c^2*x^5*Sqrt[c*x^2])","A",3,2,20,0.1000,1,"{15, 43}"
852,1,102,0,0.035834,"\int \frac{x^3 \sqrt{c x^2}}{a+b x} \, dx","Int[(x^3*Sqrt[c*x^2])/(a + b*x),x]","-\frac{a^3 \sqrt{c x^2}}{b^4}+\frac{a^2 x \sqrt{c x^2}}{2 b^3}+\frac{a^4 \sqrt{c x^2} \log (a+b x)}{b^5 x}-\frac{a x^2 \sqrt{c x^2}}{3 b^2}+\frac{x^3 \sqrt{c x^2}}{4 b}","-\frac{a^3 \sqrt{c x^2}}{b^4}+\frac{a^2 x \sqrt{c x^2}}{2 b^3}+\frac{a^4 \sqrt{c x^2} \log (a+b x)}{b^5 x}-\frac{a x^2 \sqrt{c x^2}}{3 b^2}+\frac{x^3 \sqrt{c x^2}}{4 b}",1,"-((a^3*Sqrt[c*x^2])/b^4) + (a^2*x*Sqrt[c*x^2])/(2*b^3) - (a*x^2*Sqrt[c*x^2])/(3*b^2) + (x^3*Sqrt[c*x^2])/(4*b) + (a^4*Sqrt[c*x^2]*Log[a + b*x])/(b^5*x)","A",3,2,20,0.1000,1,"{15, 43}"
853,1,80,0,0.0249259,"\int \frac{x^2 \sqrt{c x^2}}{a+b x} \, dx","Int[(x^2*Sqrt[c*x^2])/(a + b*x),x]","\frac{a^2 \sqrt{c x^2}}{b^3}-\frac{a^3 \sqrt{c x^2} \log (a+b x)}{b^4 x}-\frac{a x \sqrt{c x^2}}{2 b^2}+\frac{x^2 \sqrt{c x^2}}{3 b}","\frac{a^2 \sqrt{c x^2}}{b^3}-\frac{a^3 \sqrt{c x^2} \log (a+b x)}{b^4 x}-\frac{a x \sqrt{c x^2}}{2 b^2}+\frac{x^2 \sqrt{c x^2}}{3 b}",1,"(a^2*Sqrt[c*x^2])/b^3 - (a*x*Sqrt[c*x^2])/(2*b^2) + (x^2*Sqrt[c*x^2])/(3*b) - (a^3*Sqrt[c*x^2]*Log[a + b*x])/(b^4*x)","A",3,2,20,0.1000,1,"{15, 43}"
854,1,58,0,0.0182118,"\int \frac{x \sqrt{c x^2}}{a+b x} \, dx","Int[(x*Sqrt[c*x^2])/(a + b*x),x]","\frac{a^2 \sqrt{c x^2} \log (a+b x)}{b^3 x}-\frac{a \sqrt{c x^2}}{b^2}+\frac{x \sqrt{c x^2}}{2 b}","\frac{a^2 \sqrt{c x^2} \log (a+b x)}{b^3 x}-\frac{a \sqrt{c x^2}}{b^2}+\frac{x \sqrt{c x^2}}{2 b}",1,"-((a*Sqrt[c*x^2])/b^2) + (x*Sqrt[c*x^2])/(2*b) + (a^2*Sqrt[c*x^2]*Log[a + b*x])/(b^3*x)","A",3,2,18,0.1111,1,"{15, 43}"
855,1,38,0,0.0124095,"\int \frac{\sqrt{c x^2}}{a+b x} \, dx","Int[Sqrt[c*x^2]/(a + b*x),x]","\frac{\sqrt{c x^2}}{b}-\frac{a \sqrt{c x^2} \log (a+b x)}{b^2 x}","\frac{\sqrt{c x^2}}{b}-\frac{a \sqrt{c x^2} \log (a+b x)}{b^2 x}",1,"Sqrt[c*x^2]/b - (a*Sqrt[c*x^2]*Log[a + b*x])/(b^2*x)","A",3,2,17,0.1176,1,"{15, 43}"
856,1,22,0,0.0032198,"\int \frac{\sqrt{c x^2}}{x (a+b x)} \, dx","Int[Sqrt[c*x^2]/(x*(a + b*x)),x]","\frac{\sqrt{c x^2} \log (a+b x)}{b x}","\frac{\sqrt{c x^2} \log (a+b x)}{b x}",1,"(Sqrt[c*x^2]*Log[a + b*x])/(b*x)","A",2,2,20,0.1000,1,"{15, 31}"
857,1,42,0,0.007027,"\int \frac{\sqrt{c x^2}}{x^2 (a+b x)} \, dx","Int[Sqrt[c*x^2]/(x^2*(a + b*x)),x]","\frac{\sqrt{c x^2} \log (x)}{a x}-\frac{\sqrt{c x^2} \log (a+b x)}{a x}","\frac{\sqrt{c x^2} \log (x)}{a x}-\frac{\sqrt{c x^2} \log (a+b x)}{a x}",1,"(Sqrt[c*x^2]*Log[x])/(a*x) - (Sqrt[c*x^2]*Log[a + b*x])/(a*x)","A",4,4,20,0.2000,1,"{15, 36, 29, 31}"
858,1,61,0,0.017243,"\int \frac{\sqrt{c x^2}}{x^3 (a+b x)} \, dx","Int[Sqrt[c*x^2]/(x^3*(a + b*x)),x]","-\frac{b \sqrt{c x^2} \log (x)}{a^2 x}+\frac{b \sqrt{c x^2} \log (a+b x)}{a^2 x}-\frac{\sqrt{c x^2}}{a x^2}","-\frac{b \sqrt{c x^2} \log (x)}{a^2 x}+\frac{b \sqrt{c x^2} \log (a+b x)}{a^2 x}-\frac{\sqrt{c x^2}}{a x^2}",1,"-(Sqrt[c*x^2]/(a*x^2)) - (b*Sqrt[c*x^2]*Log[x])/(a^2*x) + (b*Sqrt[c*x^2]*Log[a + b*x])/(a^2*x)","A",3,2,20,0.1000,1,"{15, 44}"
859,1,84,0,0.0226037,"\int \frac{\sqrt{c x^2}}{x^4 (a+b x)} \, dx","Int[Sqrt[c*x^2]/(x^4*(a + b*x)),x]","\frac{b^2 \sqrt{c x^2} \log (x)}{a^3 x}-\frac{b^2 \sqrt{c x^2} \log (a+b x)}{a^3 x}+\frac{b \sqrt{c x^2}}{a^2 x^2}-\frac{\sqrt{c x^2}}{2 a x^3}","\frac{b^2 \sqrt{c x^2} \log (x)}{a^3 x}-\frac{b^2 \sqrt{c x^2} \log (a+b x)}{a^3 x}+\frac{b \sqrt{c x^2}}{a^2 x^2}-\frac{\sqrt{c x^2}}{2 a x^3}",1,"-Sqrt[c*x^2]/(2*a*x^3) + (b*Sqrt[c*x^2])/(a^2*x^2) + (b^2*Sqrt[c*x^2]*Log[x])/(a^3*x) - (b^2*Sqrt[c*x^2]*Log[a + b*x])/(a^3*x)","A",3,2,20,0.1000,1,"{15, 44}"
860,1,107,0,0.0321806,"\int \frac{x \left(c x^2\right)^{3/2}}{a+b x} \, dx","Int[(x*(c*x^2)^(3/2))/(a + b*x),x]","-\frac{a^3 c \sqrt{c x^2}}{b^4}+\frac{a^2 c x \sqrt{c x^2}}{2 b^3}+\frac{a^4 c \sqrt{c x^2} \log (a+b x)}{b^5 x}-\frac{a c x^2 \sqrt{c x^2}}{3 b^2}+\frac{c x^3 \sqrt{c x^2}}{4 b}","-\frac{a^3 c \sqrt{c x^2}}{b^4}+\frac{a^2 c x \sqrt{c x^2}}{2 b^3}+\frac{a^4 c \sqrt{c x^2} \log (a+b x)}{b^5 x}-\frac{a c x^2 \sqrt{c x^2}}{3 b^2}+\frac{c x^3 \sqrt{c x^2}}{4 b}",1,"-((a^3*c*Sqrt[c*x^2])/b^4) + (a^2*c*x*Sqrt[c*x^2])/(2*b^3) - (a*c*x^2*Sqrt[c*x^2])/(3*b^2) + (c*x^3*Sqrt[c*x^2])/(4*b) + (a^4*c*Sqrt[c*x^2]*Log[a + b*x])/(b^5*x)","A",3,2,18,0.1111,1,"{15, 43}"
861,1,84,0,0.0246509,"\int \frac{\left(c x^2\right)^{3/2}}{a+b x} \, dx","Int[(c*x^2)^(3/2)/(a + b*x),x]","\frac{a^2 c \sqrt{c x^2}}{b^3}-\frac{a^3 c \sqrt{c x^2} \log (a+b x)}{b^4 x}-\frac{a c x \sqrt{c x^2}}{2 b^2}+\frac{c x^2 \sqrt{c x^2}}{3 b}","\frac{a^2 c \sqrt{c x^2}}{b^3}-\frac{a^3 c \sqrt{c x^2} \log (a+b x)}{b^4 x}-\frac{a c x \sqrt{c x^2}}{2 b^2}+\frac{c x^2 \sqrt{c x^2}}{3 b}",1,"(a^2*c*Sqrt[c*x^2])/b^3 - (a*c*x*Sqrt[c*x^2])/(2*b^2) + (c*x^2*Sqrt[c*x^2])/(3*b) - (a^3*c*Sqrt[c*x^2]*Log[a + b*x])/(b^4*x)","A",3,2,17,0.1176,1,"{15, 43}"
862,1,61,0,0.0185233,"\int \frac{\left(c x^2\right)^{3/2}}{x (a+b x)} \, dx","Int[(c*x^2)^(3/2)/(x*(a + b*x)),x]","\frac{a^2 c \sqrt{c x^2} \log (a+b x)}{b^3 x}-\frac{a c \sqrt{c x^2}}{b^2}+\frac{c x \sqrt{c x^2}}{2 b}","\frac{a^2 c \sqrt{c x^2} \log (a+b x)}{b^3 x}-\frac{a c \sqrt{c x^2}}{b^2}+\frac{c x \sqrt{c x^2}}{2 b}",1,"-((a*c*Sqrt[c*x^2])/b^2) + (c*x*Sqrt[c*x^2])/(2*b) + (a^2*c*Sqrt[c*x^2]*Log[a + b*x])/(b^3*x)","A",3,2,20,0.1000,1,"{15, 43}"
863,1,40,0,0.0116974,"\int \frac{\left(c x^2\right)^{3/2}}{x^2 (a+b x)} \, dx","Int[(c*x^2)^(3/2)/(x^2*(a + b*x)),x]","\frac{c \sqrt{c x^2}}{b}-\frac{a c \sqrt{c x^2} \log (a+b x)}{b^2 x}","\frac{c \sqrt{c x^2}}{b}-\frac{a c \sqrt{c x^2} \log (a+b x)}{b^2 x}",1,"(c*Sqrt[c*x^2])/b - (a*c*Sqrt[c*x^2]*Log[a + b*x])/(b^2*x)","A",3,2,20,0.1000,1,"{15, 43}"
864,1,23,0,0.0038999,"\int \frac{\left(c x^2\right)^{3/2}}{x^3 (a+b x)} \, dx","Int[(c*x^2)^(3/2)/(x^3*(a + b*x)),x]","\frac{c \sqrt{c x^2} \log (a+b x)}{b x}","\frac{c \sqrt{c x^2} \log (a+b x)}{b x}",1,"(c*Sqrt[c*x^2]*Log[a + b*x])/(b*x)","A",2,2,20,0.1000,1,"{15, 31}"
865,1,44,0,0.0068632,"\int \frac{\left(c x^2\right)^{3/2}}{x^4 (a+b x)} \, dx","Int[(c*x^2)^(3/2)/(x^4*(a + b*x)),x]","\frac{c \sqrt{c x^2} \log (x)}{a x}-\frac{c \sqrt{c x^2} \log (a+b x)}{a x}","\frac{c \sqrt{c x^2} \log (x)}{a x}-\frac{c \sqrt{c x^2} \log (a+b x)}{a x}",1,"(c*Sqrt[c*x^2]*Log[x])/(a*x) - (c*Sqrt[c*x^2]*Log[a + b*x])/(a*x)","A",4,4,20,0.2000,1,"{15, 36, 29, 31}"
866,1,64,0,0.016311,"\int \frac{\left(c x^2\right)^{3/2}}{x^5 (a+b x)} \, dx","Int[(c*x^2)^(3/2)/(x^5*(a + b*x)),x]","-\frac{b c \sqrt{c x^2} \log (x)}{a^2 x}+\frac{b c \sqrt{c x^2} \log (a+b x)}{a^2 x}-\frac{c \sqrt{c x^2}}{a x^2}","-\frac{b c \sqrt{c x^2} \log (x)}{a^2 x}+\frac{b c \sqrt{c x^2} \log (a+b x)}{a^2 x}-\frac{c \sqrt{c x^2}}{a x^2}",1,"-((c*Sqrt[c*x^2])/(a*x^2)) - (b*c*Sqrt[c*x^2]*Log[x])/(a^2*x) + (b*c*Sqrt[c*x^2]*Log[a + b*x])/(a^2*x)","A",3,2,20,0.1000,1,"{15, 44}"
867,1,88,0,0.0236948,"\int \frac{\left(c x^2\right)^{3/2}}{x^6 (a+b x)} \, dx","Int[(c*x^2)^(3/2)/(x^6*(a + b*x)),x]","\frac{b^2 c \sqrt{c x^2} \log (x)}{a^3 x}-\frac{b^2 c \sqrt{c x^2} \log (a+b x)}{a^3 x}+\frac{b c \sqrt{c x^2}}{a^2 x^2}-\frac{c \sqrt{c x^2}}{2 a x^3}","\frac{b^2 c \sqrt{c x^2} \log (x)}{a^3 x}-\frac{b^2 c \sqrt{c x^2} \log (a+b x)}{a^3 x}+\frac{b c \sqrt{c x^2}}{a^2 x^2}-\frac{c \sqrt{c x^2}}{2 a x^3}",1,"-(c*Sqrt[c*x^2])/(2*a*x^3) + (b*c*Sqrt[c*x^2])/(a^2*x^2) + (b^2*c*Sqrt[c*x^2]*Log[x])/(a^3*x) - (b^2*c*Sqrt[c*x^2]*Log[a + b*x])/(a^3*x)","A",3,2,20,0.1000,1,"{15, 44}"
868,1,112,0,0.0310682,"\int \frac{\left(c x^2\right)^{3/2}}{x^7 (a+b x)} \, dx","Int[(c*x^2)^(3/2)/(x^7*(a + b*x)),x]","-\frac{b^2 c \sqrt{c x^2}}{a^3 x^2}-\frac{b^3 c \sqrt{c x^2} \log (x)}{a^4 x}+\frac{b^3 c \sqrt{c x^2} \log (a+b x)}{a^4 x}+\frac{b c \sqrt{c x^2}}{2 a^2 x^3}-\frac{c \sqrt{c x^2}}{3 a x^4}","-\frac{b^2 c \sqrt{c x^2}}{a^3 x^2}-\frac{b^3 c \sqrt{c x^2} \log (x)}{a^4 x}+\frac{b^3 c \sqrt{c x^2} \log (a+b x)}{a^4 x}+\frac{b c \sqrt{c x^2}}{2 a^2 x^3}-\frac{c \sqrt{c x^2}}{3 a x^4}",1,"-(c*Sqrt[c*x^2])/(3*a*x^4) + (b*c*Sqrt[c*x^2])/(2*a^2*x^3) - (b^2*c*Sqrt[c*x^2])/(a^3*x^2) - (b^3*c*Sqrt[c*x^2]*Log[x])/(a^4*x) + (b^3*c*Sqrt[c*x^2]*Log[a + b*x])/(a^4*x)","A",3,2,20,0.1000,1,"{15, 44}"
869,1,142,0,0.044857,"\int \frac{\left(c x^2\right)^{5/2}}{a+b x} \, dx","Int[(c*x^2)^(5/2)/(a + b*x),x]","\frac{a^4 c^2 \sqrt{c x^2}}{b^5}-\frac{a^3 c^2 x \sqrt{c x^2}}{2 b^4}+\frac{a^2 c^2 x^2 \sqrt{c x^2}}{3 b^3}-\frac{a^5 c^2 \sqrt{c x^2} \log (a+b x)}{b^6 x}-\frac{a c^2 x^3 \sqrt{c x^2}}{4 b^2}+\frac{c^2 x^4 \sqrt{c x^2}}{5 b}","\frac{a^4 c^2 \sqrt{c x^2}}{b^5}-\frac{a^3 c^2 x \sqrt{c x^2}}{2 b^4}+\frac{a^2 c^2 x^2 \sqrt{c x^2}}{3 b^3}-\frac{a^5 c^2 \sqrt{c x^2} \log (a+b x)}{b^6 x}-\frac{a c^2 x^3 \sqrt{c x^2}}{4 b^2}+\frac{c^2 x^4 \sqrt{c x^2}}{5 b}",1,"(a^4*c^2*Sqrt[c*x^2])/b^5 - (a^3*c^2*x*Sqrt[c*x^2])/(2*b^4) + (a^2*c^2*x^2*Sqrt[c*x^2])/(3*b^3) - (a*c^2*x^3*Sqrt[c*x^2])/(4*b^2) + (c^2*x^4*Sqrt[c*x^2])/(5*b) - (a^5*c^2*Sqrt[c*x^2]*Log[a + b*x])/(b^6*x)","A",3,2,17,0.1176,1,"{15, 43}"
870,1,117,0,0.0510223,"\int \frac{\left(c x^2\right)^{5/2}}{x (a+b x)} \, dx","Int[(c*x^2)^(5/2)/(x*(a + b*x)),x]","-\frac{a^3 c^2 \sqrt{c x^2}}{b^4}+\frac{a^2 c^2 x \sqrt{c x^2}}{2 b^3}+\frac{a^4 c^2 \sqrt{c x^2} \log (a+b x)}{b^5 x}-\frac{a c^2 x^2 \sqrt{c x^2}}{3 b^2}+\frac{c^2 x^3 \sqrt{c x^2}}{4 b}","-\frac{a^3 c^2 \sqrt{c x^2}}{b^4}+\frac{a^2 c^2 x \sqrt{c x^2}}{2 b^3}+\frac{a^4 c^2 \sqrt{c x^2} \log (a+b x)}{b^5 x}-\frac{a c^2 x^2 \sqrt{c x^2}}{3 b^2}+\frac{c^2 x^3 \sqrt{c x^2}}{4 b}",1,"-((a^3*c^2*Sqrt[c*x^2])/b^4) + (a^2*c^2*x*Sqrt[c*x^2])/(2*b^3) - (a*c^2*x^2*Sqrt[c*x^2])/(3*b^2) + (c^2*x^3*Sqrt[c*x^2])/(4*b) + (a^4*c^2*Sqrt[c*x^2]*Log[a + b*x])/(b^5*x)","A",3,2,20,0.1000,1,"{15, 43}"
871,1,92,0,0.0303088,"\int \frac{\left(c x^2\right)^{5/2}}{x^2 (a+b x)} \, dx","Int[(c*x^2)^(5/2)/(x^2*(a + b*x)),x]","\frac{a^2 c^2 \sqrt{c x^2}}{b^3}-\frac{a^3 c^2 \sqrt{c x^2} \log (a+b x)}{b^4 x}-\frac{a c^2 x \sqrt{c x^2}}{2 b^2}+\frac{c^2 x^2 \sqrt{c x^2}}{3 b}","\frac{a^2 c^2 \sqrt{c x^2}}{b^3}-\frac{a^3 c^2 \sqrt{c x^2} \log (a+b x)}{b^4 x}-\frac{a c^2 x \sqrt{c x^2}}{2 b^2}+\frac{c^2 x^2 \sqrt{c x^2}}{3 b}",1,"(a^2*c^2*Sqrt[c*x^2])/b^3 - (a*c^2*x*Sqrt[c*x^2])/(2*b^2) + (c^2*x^2*Sqrt[c*x^2])/(3*b) - (a^3*c^2*Sqrt[c*x^2]*Log[a + b*x])/(b^4*x)","A",3,2,20,0.1000,1,"{15, 43}"
872,1,67,0,0.0197543,"\int \frac{\left(c x^2\right)^{5/2}}{x^3 (a+b x)} \, dx","Int[(c*x^2)^(5/2)/(x^3*(a + b*x)),x]","\frac{a^2 c^2 \sqrt{c x^2} \log (a+b x)}{b^3 x}-\frac{a c^2 \sqrt{c x^2}}{b^2}+\frac{c^2 x \sqrt{c x^2}}{2 b}","\frac{a^2 c^2 \sqrt{c x^2} \log (a+b x)}{b^3 x}-\frac{a c^2 \sqrt{c x^2}}{b^2}+\frac{c^2 x \sqrt{c x^2}}{2 b}",1,"-((a*c^2*Sqrt[c*x^2])/b^2) + (c^2*x*Sqrt[c*x^2])/(2*b) + (a^2*c^2*Sqrt[c*x^2]*Log[a + b*x])/(b^3*x)","A",3,2,20,0.1000,1,"{15, 43}"
873,1,44,0,0.0122541,"\int \frac{\left(c x^2\right)^{5/2}}{x^4 (a+b x)} \, dx","Int[(c*x^2)^(5/2)/(x^4*(a + b*x)),x]","\frac{c^2 \sqrt{c x^2}}{b}-\frac{a c^2 \sqrt{c x^2} \log (a+b x)}{b^2 x}","\frac{c^2 \sqrt{c x^2}}{b}-\frac{a c^2 \sqrt{c x^2} \log (a+b x)}{b^2 x}",1,"(c^2*Sqrt[c*x^2])/b - (a*c^2*Sqrt[c*x^2]*Log[a + b*x])/(b^2*x)","A",3,2,20,0.1000,1,"{15, 43}"
874,1,25,0,0.0043513,"\int \frac{\left(c x^2\right)^{5/2}}{x^5 (a+b x)} \, dx","Int[(c*x^2)^(5/2)/(x^5*(a + b*x)),x]","\frac{c^2 \sqrt{c x^2} \log (a+b x)}{b x}","\frac{c^2 \sqrt{c x^2} \log (a+b x)}{b x}",1,"(c^2*Sqrt[c*x^2]*Log[a + b*x])/(b*x)","A",2,2,20,0.1000,1,"{15, 31}"
875,1,48,0,0.0080137,"\int \frac{\left(c x^2\right)^{5/2}}{x^6 (a+b x)} \, dx","Int[(c*x^2)^(5/2)/(x^6*(a + b*x)),x]","\frac{c^2 \sqrt{c x^2} \log (x)}{a x}-\frac{c^2 \sqrt{c x^2} \log (a+b x)}{a x}","\frac{c^2 \sqrt{c x^2} \log (x)}{a x}-\frac{c^2 \sqrt{c x^2} \log (a+b x)}{a x}",1,"(c^2*Sqrt[c*x^2]*Log[x])/(a*x) - (c^2*Sqrt[c*x^2]*Log[a + b*x])/(a*x)","A",4,4,20,0.2000,1,"{15, 36, 29, 31}"
876,1,70,0,0.0169617,"\int \frac{\left(c x^2\right)^{5/2}}{x^7 (a+b x)} \, dx","Int[(c*x^2)^(5/2)/(x^7*(a + b*x)),x]","-\frac{b c^2 \sqrt{c x^2} \log (x)}{a^2 x}+\frac{b c^2 \sqrt{c x^2} \log (a+b x)}{a^2 x}-\frac{c^2 \sqrt{c x^2}}{a x^2}","-\frac{b c^2 \sqrt{c x^2} \log (x)}{a^2 x}+\frac{b c^2 \sqrt{c x^2} \log (a+b x)}{a^2 x}-\frac{c^2 \sqrt{c x^2}}{a x^2}",1,"-((c^2*Sqrt[c*x^2])/(a*x^2)) - (b*c^2*Sqrt[c*x^2]*Log[x])/(a^2*x) + (b*c^2*Sqrt[c*x^2]*Log[a + b*x])/(a^2*x)","A",3,2,20,0.1000,1,"{15, 44}"
877,1,83,0,0.0240749,"\int \frac{x^4}{\sqrt{c x^2} (a+b x)} \, dx","Int[x^4/(Sqrt[c*x^2]*(a + b*x)),x]","\frac{a^2 x^2}{b^3 \sqrt{c x^2}}-\frac{a^3 x \log (a+b x)}{b^4 \sqrt{c x^2}}-\frac{a x^3}{2 b^2 \sqrt{c x^2}}+\frac{x^4}{3 b \sqrt{c x^2}}","\frac{a^2 x^2}{b^3 \sqrt{c x^2}}-\frac{a^3 x \log (a+b x)}{b^4 \sqrt{c x^2}}-\frac{a x^3}{2 b^2 \sqrt{c x^2}}+\frac{x^4}{3 b \sqrt{c x^2}}",1,"(a^2*x^2)/(b^3*Sqrt[c*x^2]) - (a*x^3)/(2*b^2*Sqrt[c*x^2]) + x^4/(3*b*Sqrt[c*x^2]) - (a^3*x*Log[a + b*x])/(b^4*Sqrt[c*x^2])","A",3,2,20,0.1000,1,"{15, 43}"
878,1,61,0,0.0170711,"\int \frac{x^3}{\sqrt{c x^2} (a+b x)} \, dx","Int[x^3/(Sqrt[c*x^2]*(a + b*x)),x]","\frac{a^2 x \log (a+b x)}{b^3 \sqrt{c x^2}}-\frac{a x^2}{b^2 \sqrt{c x^2}}+\frac{x^3}{2 b \sqrt{c x^2}}","\frac{a^2 x \log (a+b x)}{b^3 \sqrt{c x^2}}-\frac{a x^2}{b^2 \sqrt{c x^2}}+\frac{x^3}{2 b \sqrt{c x^2}}",1,"-((a*x^2)/(b^2*Sqrt[c*x^2])) + x^3/(2*b*Sqrt[c*x^2]) + (a^2*x*Log[a + b*x])/(b^3*Sqrt[c*x^2])","A",3,2,20,0.1000,1,"{15, 43}"
879,1,39,0,0.0121325,"\int \frac{x^2}{\sqrt{c x^2} (a+b x)} \, dx","Int[x^2/(Sqrt[c*x^2]*(a + b*x)),x]","\frac{x^2}{b \sqrt{c x^2}}-\frac{a x \log (a+b x)}{b^2 \sqrt{c x^2}}","\frac{x^2}{b \sqrt{c x^2}}-\frac{a x \log (a+b x)}{b^2 \sqrt{c x^2}}",1,"x^2/(b*Sqrt[c*x^2]) - (a*x*Log[a + b*x])/(b^2*Sqrt[c*x^2])","A",3,2,20,0.1000,1,"{15, 43}"
880,1,20,0,0.0037139,"\int \frac{x}{\sqrt{c x^2} (a+b x)} \, dx","Int[x/(Sqrt[c*x^2]*(a + b*x)),x]","\frac{x \log (a+b x)}{b \sqrt{c x^2}}","\frac{x \log (a+b x)}{b \sqrt{c x^2}}",1,"(x*Log[a + b*x])/(b*Sqrt[c*x^2])","A",2,2,18,0.1111,1,"{15, 31}"
881,1,38,0,0.0071107,"\int \frac{1}{\sqrt{c x^2} (a+b x)} \, dx","Int[1/(Sqrt[c*x^2]*(a + b*x)),x]","\frac{x \log (x)}{a \sqrt{c x^2}}-\frac{x \log (a+b x)}{a \sqrt{c x^2}}","\frac{x \log (x)}{a \sqrt{c x^2}}-\frac{x \log (a+b x)}{a \sqrt{c x^2}}",1,"(x*Log[x])/(a*Sqrt[c*x^2]) - (x*Log[a + b*x])/(a*Sqrt[c*x^2])","A",4,4,17,0.2353,1,"{15, 36, 29, 31}"
882,1,54,0,0.0155541,"\int \frac{1}{x \sqrt{c x^2} (a+b x)} \, dx","Int[1/(x*Sqrt[c*x^2]*(a + b*x)),x]","-\frac{b x \log (x)}{a^2 \sqrt{c x^2}}+\frac{b x \log (a+b x)}{a^2 \sqrt{c x^2}}-\frac{1}{a \sqrt{c x^2}}","-\frac{b x \log (x)}{a^2 \sqrt{c x^2}}+\frac{b x \log (a+b x)}{a^2 \sqrt{c x^2}}-\frac{1}{a \sqrt{c x^2}}",1,"-(1/(a*Sqrt[c*x^2])) - (b*x*Log[x])/(a^2*Sqrt[c*x^2]) + (b*x*Log[a + b*x])/(a^2*Sqrt[c*x^2])","A",3,2,20,0.1000,1,"{15, 44}"
883,1,77,0,0.0285021,"\int \frac{1}{x^2 \sqrt{c x^2} (a+b x)} \, dx","Int[1/(x^2*Sqrt[c*x^2]*(a + b*x)),x]","\frac{b^2 x \log (x)}{a^3 \sqrt{c x^2}}-\frac{b^2 x \log (a+b x)}{a^3 \sqrt{c x^2}}+\frac{b}{a^2 \sqrt{c x^2}}-\frac{1}{2 a x \sqrt{c x^2}}","\frac{b^2 x \log (x)}{a^3 \sqrt{c x^2}}-\frac{b^2 x \log (a+b x)}{a^3 \sqrt{c x^2}}+\frac{b}{a^2 \sqrt{c x^2}}-\frac{1}{2 a x \sqrt{c x^2}}",1,"b/(a^2*Sqrt[c*x^2]) - 1/(2*a*x*Sqrt[c*x^2]) + (b^2*x*Log[x])/(a^3*Sqrt[c*x^2]) - (b^2*x*Log[a + b*x])/(a^3*Sqrt[c*x^2])","A",3,2,20,0.1000,1,"{15, 44}"
884,1,100,0,0.0263064,"\int \frac{1}{x^3 \sqrt{c x^2} (a+b x)} \, dx","Int[1/(x^3*Sqrt[c*x^2]*(a + b*x)),x]","-\frac{b^2}{a^3 \sqrt{c x^2}}-\frac{b^3 x \log (x)}{a^4 \sqrt{c x^2}}+\frac{b^3 x \log (a+b x)}{a^4 \sqrt{c x^2}}+\frac{b}{2 a^2 x \sqrt{c x^2}}-\frac{1}{3 a x^2 \sqrt{c x^2}}","-\frac{b^2}{a^3 \sqrt{c x^2}}-\frac{b^3 x \log (x)}{a^4 \sqrt{c x^2}}+\frac{b^3 x \log (a+b x)}{a^4 \sqrt{c x^2}}+\frac{b}{2 a^2 x \sqrt{c x^2}}-\frac{1}{3 a x^2 \sqrt{c x^2}}",1,"-(b^2/(a^3*Sqrt[c*x^2])) - 1/(3*a*x^2*Sqrt[c*x^2]) + b/(2*a^2*x*Sqrt[c*x^2]) - (b^3*x*Log[x])/(a^4*Sqrt[c*x^2]) + (b^3*x*Log[a + b*x])/(a^4*Sqrt[c*x^2])","A",3,2,20,0.1000,1,"{15, 44}"
885,1,95,0,0.0271292,"\int \frac{x^6}{\left(c x^2\right)^{3/2} (a+b x)} \, dx","Int[x^6/((c*x^2)^(3/2)*(a + b*x)),x]","\frac{a^2 x^2}{b^3 c \sqrt{c x^2}}-\frac{a^3 x \log (a+b x)}{b^4 c \sqrt{c x^2}}-\frac{a x^3}{2 b^2 c \sqrt{c x^2}}+\frac{x^4}{3 b c \sqrt{c x^2}}","\frac{a^2 x^2}{b^3 c \sqrt{c x^2}}-\frac{a^3 x \log (a+b x)}{b^4 c \sqrt{c x^2}}-\frac{a x^3}{2 b^2 c \sqrt{c x^2}}+\frac{x^4}{3 b c \sqrt{c x^2}}",1,"(a^2*x^2)/(b^3*c*Sqrt[c*x^2]) - (a*x^3)/(2*b^2*c*Sqrt[c*x^2]) + x^4/(3*b*c*Sqrt[c*x^2]) - (a^3*x*Log[a + b*x])/(b^4*c*Sqrt[c*x^2])","A",3,2,20,0.1000,1,"{15, 43}"
886,1,70,0,0.0200026,"\int \frac{x^5}{\left(c x^2\right)^{3/2} (a+b x)} \, dx","Int[x^5/((c*x^2)^(3/2)*(a + b*x)),x]","\frac{a^2 x \log (a+b x)}{b^3 c \sqrt{c x^2}}-\frac{a x^2}{b^2 c \sqrt{c x^2}}+\frac{x^3}{2 b c \sqrt{c x^2}}","\frac{a^2 x \log (a+b x)}{b^3 c \sqrt{c x^2}}-\frac{a x^2}{b^2 c \sqrt{c x^2}}+\frac{x^3}{2 b c \sqrt{c x^2}}",1,"-((a*x^2)/(b^2*c*Sqrt[c*x^2])) + x^3/(2*b*c*Sqrt[c*x^2]) + (a^2*x*Log[a + b*x])/(b^3*c*Sqrt[c*x^2])","A",3,2,20,0.1000,1,"{15, 43}"
887,1,45,0,0.0131412,"\int \frac{x^4}{\left(c x^2\right)^{3/2} (a+b x)} \, dx","Int[x^4/((c*x^2)^(3/2)*(a + b*x)),x]","\frac{x^2}{b c \sqrt{c x^2}}-\frac{a x \log (a+b x)}{b^2 c \sqrt{c x^2}}","\frac{x^2}{b c \sqrt{c x^2}}-\frac{a x \log (a+b x)}{b^2 c \sqrt{c x^2}}",1,"x^2/(b*c*Sqrt[c*x^2]) - (a*x*Log[a + b*x])/(b^2*c*Sqrt[c*x^2])","A",3,2,20,0.1000,1,"{15, 43}"
888,1,23,0,0.0039192,"\int \frac{x^3}{\left(c x^2\right)^{3/2} (a+b x)} \, dx","Int[x^3/((c*x^2)^(3/2)*(a + b*x)),x]","\frac{x \log (a+b x)}{b c \sqrt{c x^2}}","\frac{x \log (a+b x)}{b c \sqrt{c x^2}}",1,"(x*Log[a + b*x])/(b*c*Sqrt[c*x^2])","A",2,2,20,0.1000,1,"{15, 31}"
889,1,44,0,0.0080417,"\int \frac{x^2}{\left(c x^2\right)^{3/2} (a+b x)} \, dx","Int[x^2/((c*x^2)^(3/2)*(a + b*x)),x]","\frac{x \log (x)}{a c \sqrt{c x^2}}-\frac{x \log (a+b x)}{a c \sqrt{c x^2}}","\frac{x \log (x)}{a c \sqrt{c x^2}}-\frac{x \log (a+b x)}{a c \sqrt{c x^2}}",1,"(x*Log[x])/(a*c*Sqrt[c*x^2]) - (x*Log[a + b*x])/(a*c*Sqrt[c*x^2])","A",4,4,20,0.2000,1,"{15, 36, 29, 31}"
890,1,63,0,0.0169767,"\int \frac{x}{\left(c x^2\right)^{3/2} (a+b x)} \, dx","Int[x/((c*x^2)^(3/2)*(a + b*x)),x]","-\frac{b x \log (x)}{a^2 c \sqrt{c x^2}}+\frac{b x \log (a+b x)}{a^2 c \sqrt{c x^2}}-\frac{1}{a c \sqrt{c x^2}}","-\frac{b x \log (x)}{a^2 c \sqrt{c x^2}}+\frac{b x \log (a+b x)}{a^2 c \sqrt{c x^2}}-\frac{1}{a c \sqrt{c x^2}}",1,"-(1/(a*c*Sqrt[c*x^2])) - (b*x*Log[x])/(a^2*c*Sqrt[c*x^2]) + (b*x*Log[a + b*x])/(a^2*c*Sqrt[c*x^2])","A",3,2,18,0.1111,1,"{15, 44}"
891,1,89,0,0.0222743,"\int \frac{1}{\left(c x^2\right)^{3/2} (a+b x)} \, dx","Int[1/((c*x^2)^(3/2)*(a + b*x)),x]","\frac{b^2 x \log (x)}{a^3 c \sqrt{c x^2}}-\frac{b^2 x \log (a+b x)}{a^3 c \sqrt{c x^2}}+\frac{b}{a^2 c \sqrt{c x^2}}-\frac{1}{2 a c x \sqrt{c x^2}}","\frac{b^2 x \log (x)}{a^3 c \sqrt{c x^2}}-\frac{b^2 x \log (a+b x)}{a^3 c \sqrt{c x^2}}+\frac{b}{a^2 c \sqrt{c x^2}}-\frac{1}{2 a c x \sqrt{c x^2}}",1,"b/(a^2*c*Sqrt[c*x^2]) - 1/(2*a*c*x*Sqrt[c*x^2]) + (b^2*x*Log[x])/(a^3*c*Sqrt[c*x^2]) - (b^2*x*Log[a + b*x])/(a^3*c*Sqrt[c*x^2])","A",3,2,17,0.1176,1,"{15, 44}"
892,1,115,0,0.0283939,"\int \frac{1}{x \left(c x^2\right)^{3/2} (a+b x)} \, dx","Int[1/(x*(c*x^2)^(3/2)*(a + b*x)),x]","-\frac{b^2}{a^3 c \sqrt{c x^2}}-\frac{b^3 x \log (x)}{a^4 c \sqrt{c x^2}}+\frac{b^3 x \log (a+b x)}{a^4 c \sqrt{c x^2}}+\frac{b}{2 a^2 c x \sqrt{c x^2}}-\frac{1}{3 a c x^2 \sqrt{c x^2}}","-\frac{b^2}{a^3 c \sqrt{c x^2}}-\frac{b^3 x \log (x)}{a^4 c \sqrt{c x^2}}+\frac{b^3 x \log (a+b x)}{a^4 c \sqrt{c x^2}}+\frac{b}{2 a^2 c x \sqrt{c x^2}}-\frac{1}{3 a c x^2 \sqrt{c x^2}}",1,"-(b^2/(a^3*c*Sqrt[c*x^2])) - 1/(3*a*c*x^2*Sqrt[c*x^2]) + b/(2*a^2*c*x*Sqrt[c*x^2]) - (b^3*x*Log[x])/(a^4*c*Sqrt[c*x^2]) + (b^3*x*Log[a + b*x])/(a^4*c*Sqrt[c*x^2])","A",3,2,20,0.1000,1,"{15, 44}"
893,1,106,0,0.039058,"\int \frac{x^3 \sqrt{c x^2}}{(a+b x)^2} \, dx","Int[(x^3*Sqrt[c*x^2])/(a + b*x)^2,x]","-\frac{a^4 \sqrt{c x^2}}{b^5 x (a+b x)}+\frac{3 a^2 \sqrt{c x^2}}{b^4}-\frac{4 a^3 \sqrt{c x^2} \log (a+b x)}{b^5 x}-\frac{a x \sqrt{c x^2}}{b^3}+\frac{x^2 \sqrt{c x^2}}{3 b^2}","-\frac{a^4 \sqrt{c x^2}}{b^5 x (a+b x)}+\frac{3 a^2 \sqrt{c x^2}}{b^4}-\frac{4 a^3 \sqrt{c x^2} \log (a+b x)}{b^5 x}-\frac{a x \sqrt{c x^2}}{b^3}+\frac{x^2 \sqrt{c x^2}}{3 b^2}",1,"(3*a^2*Sqrt[c*x^2])/b^4 - (a*x*Sqrt[c*x^2])/b^3 + (x^2*Sqrt[c*x^2])/(3*b^2) - (a^4*Sqrt[c*x^2])/(b^5*x*(a + b*x)) - (4*a^3*Sqrt[c*x^2]*Log[a + b*x])/(b^5*x)","A",3,2,20,0.1000,1,"{15, 43}"
894,1,85,0,0.032175,"\int \frac{x^2 \sqrt{c x^2}}{(a+b x)^2} \, dx","Int[(x^2*Sqrt[c*x^2])/(a + b*x)^2,x]","\frac{a^3 \sqrt{c x^2}}{b^4 x (a+b x)}+\frac{3 a^2 \sqrt{c x^2} \log (a+b x)}{b^4 x}-\frac{2 a \sqrt{c x^2}}{b^3}+\frac{x \sqrt{c x^2}}{2 b^2}","\frac{a^3 \sqrt{c x^2}}{b^4 x (a+b x)}+\frac{3 a^2 \sqrt{c x^2} \log (a+b x)}{b^4 x}-\frac{2 a \sqrt{c x^2}}{b^3}+\frac{x \sqrt{c x^2}}{2 b^2}",1,"(-2*a*Sqrt[c*x^2])/b^3 + (x*Sqrt[c*x^2])/(2*b^2) + (a^3*Sqrt[c*x^2])/(b^4*x*(a + b*x)) + (3*a^2*Sqrt[c*x^2]*Log[a + b*x])/(b^4*x)","A",3,2,20,0.1000,1,"{15, 43}"
895,1,65,0,0.021723,"\int \frac{x \sqrt{c x^2}}{(a+b x)^2} \, dx","Int[(x*Sqrt[c*x^2])/(a + b*x)^2,x]","-\frac{a^2 \sqrt{c x^2}}{b^3 x (a+b x)}-\frac{2 a \sqrt{c x^2} \log (a+b x)}{b^3 x}+\frac{\sqrt{c x^2}}{b^2}","-\frac{a^2 \sqrt{c x^2}}{b^3 x (a+b x)}-\frac{2 a \sqrt{c x^2} \log (a+b x)}{b^3 x}+\frac{\sqrt{c x^2}}{b^2}",1,"Sqrt[c*x^2]/b^2 - (a^2*Sqrt[c*x^2])/(b^3*x*(a + b*x)) - (2*a*Sqrt[c*x^2]*Log[a + b*x])/(b^3*x)","A",3,2,18,0.1111,1,"{15, 43}"
896,1,47,0,0.0162818,"\int \frac{\sqrt{c x^2}}{(a+b x)^2} \, dx","Int[Sqrt[c*x^2]/(a + b*x)^2,x]","\frac{a \sqrt{c x^2}}{b^2 x (a+b x)}+\frac{\sqrt{c x^2} \log (a+b x)}{b^2 x}","\frac{a \sqrt{c x^2}}{b^2 x (a+b x)}+\frac{\sqrt{c x^2} \log (a+b x)}{b^2 x}",1,"(a*Sqrt[c*x^2])/(b^2*x*(a + b*x)) + (Sqrt[c*x^2]*Log[a + b*x])/(b^2*x)","A",3,2,17,0.1176,1,"{15, 43}"
897,1,24,0,0.0036378,"\int \frac{\sqrt{c x^2}}{x (a+b x)^2} \, dx","Int[Sqrt[c*x^2]/(x*(a + b*x)^2),x]","-\frac{\sqrt{c x^2}}{b x (a+b x)}","-\frac{\sqrt{c x^2}}{b x (a+b x)}",1,"-(Sqrt[c*x^2]/(b*x*(a + b*x)))","A",2,2,20,0.1000,1,"{15, 32}"
898,1,65,0,0.0179407,"\int \frac{\sqrt{c x^2}}{x^2 (a+b x)^2} \, dx","Int[Sqrt[c*x^2]/(x^2*(a + b*x)^2),x]","-\frac{\sqrt{c x^2} \log (a+b x)}{a^2 x}+\frac{\sqrt{c x^2} \log (x)}{a^2 x}+\frac{\sqrt{c x^2}}{a x (a+b x)}","-\frac{\sqrt{c x^2} \log (a+b x)}{a^2 x}+\frac{\sqrt{c x^2} \log (x)}{a^2 x}+\frac{\sqrt{c x^2}}{a x (a+b x)}",1,"Sqrt[c*x^2]/(a*x*(a + b*x)) + (Sqrt[c*x^2]*Log[x])/(a^2*x) - (Sqrt[c*x^2]*Log[a + b*x])/(a^2*x)","A",3,2,20,0.1000,1,"{15, 44}"
899,1,87,0,0.0270424,"\int \frac{\sqrt{c x^2}}{x^3 (a+b x)^2} \, dx","Int[Sqrt[c*x^2]/(x^3*(a + b*x)^2),x]","-\frac{b \sqrt{c x^2}}{a^2 x (a+b x)}-\frac{2 b \sqrt{c x^2} \log (x)}{a^3 x}+\frac{2 b \sqrt{c x^2} \log (a+b x)}{a^3 x}-\frac{\sqrt{c x^2}}{a^2 x^2}","-\frac{b \sqrt{c x^2}}{a^2 x (a+b x)}-\frac{2 b \sqrt{c x^2} \log (x)}{a^3 x}+\frac{2 b \sqrt{c x^2} \log (a+b x)}{a^3 x}-\frac{\sqrt{c x^2}}{a^2 x^2}",1,"-(Sqrt[c*x^2]/(a^2*x^2)) - (b*Sqrt[c*x^2])/(a^2*x*(a + b*x)) - (2*b*Sqrt[c*x^2]*Log[x])/(a^3*x) + (2*b*Sqrt[c*x^2]*Log[a + b*x])/(a^3*x)","A",3,2,20,0.1000,1,"{15, 44}"
900,1,112,0,0.0356999,"\int \frac{\sqrt{c x^2}}{x^4 (a+b x)^2} \, dx","Int[Sqrt[c*x^2]/(x^4*(a + b*x)^2),x]","\frac{b^2 \sqrt{c x^2}}{a^3 x (a+b x)}+\frac{3 b^2 \sqrt{c x^2} \log (x)}{a^4 x}-\frac{3 b^2 \sqrt{c x^2} \log (a+b x)}{a^4 x}+\frac{2 b \sqrt{c x^2}}{a^3 x^2}-\frac{\sqrt{c x^2}}{2 a^2 x^3}","\frac{b^2 \sqrt{c x^2}}{a^3 x (a+b x)}+\frac{3 b^2 \sqrt{c x^2} \log (x)}{a^4 x}-\frac{3 b^2 \sqrt{c x^2} \log (a+b x)}{a^4 x}+\frac{2 b \sqrt{c x^2}}{a^3 x^2}-\frac{\sqrt{c x^2}}{2 a^2 x^3}",1,"-Sqrt[c*x^2]/(2*a^2*x^3) + (2*b*Sqrt[c*x^2])/(a^3*x^2) + (b^2*Sqrt[c*x^2])/(a^3*x*(a + b*x)) + (3*b^2*Sqrt[c*x^2]*Log[x])/(a^4*x) - (3*b^2*Sqrt[c*x^2]*Log[a + b*x])/(a^4*x)","A",3,2,20,0.1000,1,"{15, 44}"
901,1,111,0,0.0373899,"\int \frac{x \left(c x^2\right)^{3/2}}{(a+b x)^2} \, dx","Int[(x*(c*x^2)^(3/2))/(a + b*x)^2,x]","-\frac{a^4 c \sqrt{c x^2}}{b^5 x (a+b x)}+\frac{3 a^2 c \sqrt{c x^2}}{b^4}-\frac{4 a^3 c \sqrt{c x^2} \log (a+b x)}{b^5 x}-\frac{a c x \sqrt{c x^2}}{b^3}+\frac{c x^2 \sqrt{c x^2}}{3 b^2}","-\frac{a^4 c \sqrt{c x^2}}{b^5 x (a+b x)}+\frac{3 a^2 c \sqrt{c x^2}}{b^4}-\frac{4 a^3 c \sqrt{c x^2} \log (a+b x)}{b^5 x}-\frac{a c x \sqrt{c x^2}}{b^3}+\frac{c x^2 \sqrt{c x^2}}{3 b^2}",1,"(3*a^2*c*Sqrt[c*x^2])/b^4 - (a*c*x*Sqrt[c*x^2])/b^3 + (c*x^2*Sqrt[c*x^2])/(3*b^2) - (a^4*c*Sqrt[c*x^2])/(b^5*x*(a + b*x)) - (4*a^3*c*Sqrt[c*x^2]*Log[a + b*x])/(b^5*x)","A",3,2,18,0.1111,1,"{15, 43}"
902,1,89,0,0.0285655,"\int \frac{\left(c x^2\right)^{3/2}}{(a+b x)^2} \, dx","Int[(c*x^2)^(3/2)/(a + b*x)^2,x]","\frac{a^3 c \sqrt{c x^2}}{b^4 x (a+b x)}+\frac{3 a^2 c \sqrt{c x^2} \log (a+b x)}{b^4 x}-\frac{2 a c \sqrt{c x^2}}{b^3}+\frac{c x \sqrt{c x^2}}{2 b^2}","\frac{a^3 c \sqrt{c x^2}}{b^4 x (a+b x)}+\frac{3 a^2 c \sqrt{c x^2} \log (a+b x)}{b^4 x}-\frac{2 a c \sqrt{c x^2}}{b^3}+\frac{c x \sqrt{c x^2}}{2 b^2}",1,"(-2*a*c*Sqrt[c*x^2])/b^3 + (c*x*Sqrt[c*x^2])/(2*b^2) + (a^3*c*Sqrt[c*x^2])/(b^4*x*(a + b*x)) + (3*a^2*c*Sqrt[c*x^2]*Log[a + b*x])/(b^4*x)","A",3,2,17,0.1176,1,"{15, 43}"
903,1,68,0,0.020345,"\int \frac{\left(c x^2\right)^{3/2}}{x (a+b x)^2} \, dx","Int[(c*x^2)^(3/2)/(x*(a + b*x)^2),x]","-\frac{a^2 c \sqrt{c x^2}}{b^3 x (a+b x)}-\frac{2 a c \sqrt{c x^2} \log (a+b x)}{b^3 x}+\frac{c \sqrt{c x^2}}{b^2}","-\frac{a^2 c \sqrt{c x^2}}{b^3 x (a+b x)}-\frac{2 a c \sqrt{c x^2} \log (a+b x)}{b^3 x}+\frac{c \sqrt{c x^2}}{b^2}",1,"(c*Sqrt[c*x^2])/b^2 - (a^2*c*Sqrt[c*x^2])/(b^3*x*(a + b*x)) - (2*a*c*Sqrt[c*x^2]*Log[a + b*x])/(b^3*x)","A",3,2,20,0.1000,1,"{15, 43}"
904,1,49,0,0.0145969,"\int \frac{\left(c x^2\right)^{3/2}}{x^2 (a+b x)^2} \, dx","Int[(c*x^2)^(3/2)/(x^2*(a + b*x)^2),x]","\frac{a c \sqrt{c x^2}}{b^2 x (a+b x)}+\frac{c \sqrt{c x^2} \log (a+b x)}{b^2 x}","\frac{a c \sqrt{c x^2}}{b^2 x (a+b x)}+\frac{c \sqrt{c x^2} \log (a+b x)}{b^2 x}",1,"(a*c*Sqrt[c*x^2])/(b^2*x*(a + b*x)) + (c*Sqrt[c*x^2]*Log[a + b*x])/(b^2*x)","A",3,2,20,0.1000,1,"{15, 43}"
905,1,25,0,0.004015,"\int \frac{\left(c x^2\right)^{3/2}}{x^3 (a+b x)^2} \, dx","Int[(c*x^2)^(3/2)/(x^3*(a + b*x)^2),x]","-\frac{c \sqrt{c x^2}}{b x (a+b x)}","-\frac{c \sqrt{c x^2}}{b x (a+b x)}",1,"-((c*Sqrt[c*x^2])/(b*x*(a + b*x)))","A",2,2,20,0.1000,1,"{15, 32}"
906,1,68,0,0.0177966,"\int \frac{\left(c x^2\right)^{3/2}}{x^4 (a+b x)^2} \, dx","Int[(c*x^2)^(3/2)/(x^4*(a + b*x)^2),x]","-\frac{c \sqrt{c x^2} \log (a+b x)}{a^2 x}+\frac{c \sqrt{c x^2} \log (x)}{a^2 x}+\frac{c \sqrt{c x^2}}{a x (a+b x)}","-\frac{c \sqrt{c x^2} \log (a+b x)}{a^2 x}+\frac{c \sqrt{c x^2} \log (x)}{a^2 x}+\frac{c \sqrt{c x^2}}{a x (a+b x)}",1,"(c*Sqrt[c*x^2])/(a*x*(a + b*x)) + (c*Sqrt[c*x^2]*Log[x])/(a^2*x) - (c*Sqrt[c*x^2]*Log[a + b*x])/(a^2*x)","A",3,2,20,0.1000,1,"{15, 44}"
907,1,91,0,0.0239688,"\int \frac{\left(c x^2\right)^{3/2}}{x^5 (a+b x)^2} \, dx","Int[(c*x^2)^(3/2)/(x^5*(a + b*x)^2),x]","-\frac{b c \sqrt{c x^2}}{a^2 x (a+b x)}-\frac{2 b c \sqrt{c x^2} \log (x)}{a^3 x}+\frac{2 b c \sqrt{c x^2} \log (a+b x)}{a^3 x}-\frac{c \sqrt{c x^2}}{a^2 x^2}","-\frac{b c \sqrt{c x^2}}{a^2 x (a+b x)}-\frac{2 b c \sqrt{c x^2} \log (x)}{a^3 x}+\frac{2 b c \sqrt{c x^2} \log (a+b x)}{a^3 x}-\frac{c \sqrt{c x^2}}{a^2 x^2}",1,"-((c*Sqrt[c*x^2])/(a^2*x^2)) - (b*c*Sqrt[c*x^2])/(a^2*x*(a + b*x)) - (2*b*c*Sqrt[c*x^2]*Log[x])/(a^3*x) + (2*b*c*Sqrt[c*x^2]*Log[a + b*x])/(a^3*x)","A",3,2,20,0.1000,1,"{15, 44}"
908,1,117,0,0.0317061,"\int \frac{\left(c x^2\right)^{3/2}}{x^6 (a+b x)^2} \, dx","Int[(c*x^2)^(3/2)/(x^6*(a + b*x)^2),x]","\frac{b^2 c \sqrt{c x^2}}{a^3 x (a+b x)}+\frac{3 b^2 c \sqrt{c x^2} \log (x)}{a^4 x}-\frac{3 b^2 c \sqrt{c x^2} \log (a+b x)}{a^4 x}+\frac{2 b c \sqrt{c x^2}}{a^3 x^2}-\frac{c \sqrt{c x^2}}{2 a^2 x^3}","\frac{b^2 c \sqrt{c x^2}}{a^3 x (a+b x)}+\frac{3 b^2 c \sqrt{c x^2} \log (x)}{a^4 x}-\frac{3 b^2 c \sqrt{c x^2} \log (a+b x)}{a^4 x}+\frac{2 b c \sqrt{c x^2}}{a^3 x^2}-\frac{c \sqrt{c x^2}}{2 a^2 x^3}",1,"-(c*Sqrt[c*x^2])/(2*a^2*x^3) + (2*b*c*Sqrt[c*x^2])/(a^3*x^2) + (b^2*c*Sqrt[c*x^2])/(a^3*x*(a + b*x)) + (3*b^2*c*Sqrt[c*x^2]*Log[x])/(a^4*x) - (3*b^2*c*Sqrt[c*x^2]*Log[a + b*x])/(a^4*x)","A",3,2,20,0.1000,1,"{15, 44}"
909,1,107,0,0.032868,"\int \frac{x^5}{\sqrt{c x^2} (a+b x)^2} \, dx","Int[x^5/(Sqrt[c*x^2]*(a + b*x)^2),x]","-\frac{a^4 x}{b^5 \sqrt{c x^2} (a+b x)}+\frac{3 a^2 x^2}{b^4 \sqrt{c x^2}}-\frac{4 a^3 x \log (a+b x)}{b^5 \sqrt{c x^2}}-\frac{a x^3}{b^3 \sqrt{c x^2}}+\frac{x^4}{3 b^2 \sqrt{c x^2}}","-\frac{a^4 x}{b^5 \sqrt{c x^2} (a+b x)}+\frac{3 a^2 x^2}{b^4 \sqrt{c x^2}}-\frac{4 a^3 x \log (a+b x)}{b^5 \sqrt{c x^2}}-\frac{a x^3}{b^3 \sqrt{c x^2}}+\frac{x^4}{3 b^2 \sqrt{c x^2}}",1,"(3*a^2*x^2)/(b^4*Sqrt[c*x^2]) - (a*x^3)/(b^3*Sqrt[c*x^2]) + x^4/(3*b^2*Sqrt[c*x^2]) - (a^4*x)/(b^5*Sqrt[c*x^2]*(a + b*x)) - (4*a^3*x*Log[a + b*x])/(b^5*Sqrt[c*x^2])","A",3,2,20,0.1000,1,"{15, 43}"
910,1,86,0,0.02566,"\int \frac{x^4}{\sqrt{c x^2} (a+b x)^2} \, dx","Int[x^4/(Sqrt[c*x^2]*(a + b*x)^2),x]","\frac{a^3 x}{b^4 \sqrt{c x^2} (a+b x)}+\frac{3 a^2 x \log (a+b x)}{b^4 \sqrt{c x^2}}-\frac{2 a x^2}{b^3 \sqrt{c x^2}}+\frac{x^3}{2 b^2 \sqrt{c x^2}}","\frac{a^3 x}{b^4 \sqrt{c x^2} (a+b x)}+\frac{3 a^2 x \log (a+b x)}{b^4 \sqrt{c x^2}}-\frac{2 a x^2}{b^3 \sqrt{c x^2}}+\frac{x^3}{2 b^2 \sqrt{c x^2}}",1,"(-2*a*x^2)/(b^3*Sqrt[c*x^2]) + x^3/(2*b^2*Sqrt[c*x^2]) + (a^3*x)/(b^4*Sqrt[c*x^2]*(a + b*x)) + (3*a^2*x*Log[a + b*x])/(b^4*Sqrt[c*x^2])","A",3,2,20,0.1000,1,"{15, 43}"
911,1,64,0,0.0196238,"\int \frac{x^3}{\sqrt{c x^2} (a+b x)^2} \, dx","Int[x^3/(Sqrt[c*x^2]*(a + b*x)^2),x]","-\frac{a^2 x}{b^3 \sqrt{c x^2} (a+b x)}-\frac{2 a x \log (a+b x)}{b^3 \sqrt{c x^2}}+\frac{x^2}{b^2 \sqrt{c x^2}}","-\frac{a^2 x}{b^3 \sqrt{c x^2} (a+b x)}-\frac{2 a x \log (a+b x)}{b^3 \sqrt{c x^2}}+\frac{x^2}{b^2 \sqrt{c x^2}}",1,"x^2/(b^2*Sqrt[c*x^2]) - (a^2*x)/(b^3*Sqrt[c*x^2]*(a + b*x)) - (2*a*x*Log[a + b*x])/(b^3*Sqrt[c*x^2])","A",3,2,20,0.1000,1,"{15, 43}"
912,1,43,0,0.0131761,"\int \frac{x^2}{\sqrt{c x^2} (a+b x)^2} \, dx","Int[x^2/(Sqrt[c*x^2]*(a + b*x)^2),x]","\frac{a x}{b^2 \sqrt{c x^2} (a+b x)}+\frac{x \log (a+b x)}{b^2 \sqrt{c x^2}}","\frac{a x}{b^2 \sqrt{c x^2} (a+b x)}+\frac{x \log (a+b x)}{b^2 \sqrt{c x^2}}",1,"(a*x)/(b^2*Sqrt[c*x^2]*(a + b*x)) + (x*Log[a + b*x])/(b^2*Sqrt[c*x^2])","A",3,2,20,0.1000,1,"{15, 43}"
913,1,22,0,0.0033827,"\int \frac{x}{\sqrt{c x^2} (a+b x)^2} \, dx","Int[x/(Sqrt[c*x^2]*(a + b*x)^2),x]","-\frac{x}{b \sqrt{c x^2} (a+b x)}","-\frac{x}{b \sqrt{c x^2} (a+b x)}",1,"-(x/(b*Sqrt[c*x^2]*(a + b*x)))","A",2,2,18,0.1111,1,"{15, 32}"
914,1,59,0,0.0164084,"\int \frac{1}{\sqrt{c x^2} (a+b x)^2} \, dx","Int[1/(Sqrt[c*x^2]*(a + b*x)^2),x]","-\frac{x \log (a+b x)}{a^2 \sqrt{c x^2}}+\frac{x \log (x)}{a^2 \sqrt{c x^2}}+\frac{x}{a \sqrt{c x^2} (a+b x)}","-\frac{x \log (a+b x)}{a^2 \sqrt{c x^2}}+\frac{x \log (x)}{a^2 \sqrt{c x^2}}+\frac{x}{a \sqrt{c x^2} (a+b x)}",1,"x/(a*Sqrt[c*x^2]*(a + b*x)) + (x*Log[x])/(a^2*Sqrt[c*x^2]) - (x*Log[a + b*x])/(a^2*Sqrt[c*x^2])","A",3,2,17,0.1176,1,"{15, 44}"
915,1,78,0,0.0224452,"\int \frac{1}{x \sqrt{c x^2} (a+b x)^2} \, dx","Int[1/(x*Sqrt[c*x^2]*(a + b*x)^2),x]","-\frac{b x}{a^2 \sqrt{c x^2} (a+b x)}-\frac{2 b x \log (x)}{a^3 \sqrt{c x^2}}+\frac{2 b x \log (a+b x)}{a^3 \sqrt{c x^2}}-\frac{1}{a^2 \sqrt{c x^2}}","-\frac{b x}{a^2 \sqrt{c x^2} (a+b x)}-\frac{2 b x \log (x)}{a^3 \sqrt{c x^2}}+\frac{2 b x \log (a+b x)}{a^3 \sqrt{c x^2}}-\frac{1}{a^2 \sqrt{c x^2}}",1,"-(1/(a^2*Sqrt[c*x^2])) - (b*x)/(a^2*Sqrt[c*x^2]*(a + b*x)) - (2*b*x*Log[x])/(a^3*Sqrt[c*x^2]) + (2*b*x*Log[a + b*x])/(a^3*Sqrt[c*x^2])","A",3,2,20,0.1000,1,"{15, 44}"
916,1,103,0,0.0316542,"\int \frac{1}{x^2 \sqrt{c x^2} (a+b x)^2} \, dx","Int[1/(x^2*Sqrt[c*x^2]*(a + b*x)^2),x]","\frac{b^2 x}{a^3 \sqrt{c x^2} (a+b x)}+\frac{3 b^2 x \log (x)}{a^4 \sqrt{c x^2}}-\frac{3 b^2 x \log (a+b x)}{a^4 \sqrt{c x^2}}+\frac{2 b}{a^3 \sqrt{c x^2}}-\frac{1}{2 a^2 x \sqrt{c x^2}}","\frac{b^2 x}{a^3 \sqrt{c x^2} (a+b x)}+\frac{3 b^2 x \log (x)}{a^4 \sqrt{c x^2}}-\frac{3 b^2 x \log (a+b x)}{a^4 \sqrt{c x^2}}+\frac{2 b}{a^3 \sqrt{c x^2}}-\frac{1}{2 a^2 x \sqrt{c x^2}}",1,"(2*b)/(a^3*Sqrt[c*x^2]) - 1/(2*a^2*x*Sqrt[c*x^2]) + (b^2*x)/(a^3*Sqrt[c*x^2]*(a + b*x)) + (3*b^2*x*Log[x])/(a^4*Sqrt[c*x^2]) - (3*b^2*x*Log[a + b*x])/(a^4*Sqrt[c*x^2])","A",3,2,20,0.1000,1,"{15, 44}"
917,1,73,0,0.02105,"\int \frac{x^5}{\left(c x^2\right)^{3/2} (a+b x)^2} \, dx","Int[x^5/((c*x^2)^(3/2)*(a + b*x)^2),x]","-\frac{a^2 x}{b^3 c \sqrt{c x^2} (a+b x)}-\frac{2 a x \log (a+b x)}{b^3 c \sqrt{c x^2}}+\frac{x^2}{b^2 c \sqrt{c x^2}}","-\frac{a^2 x}{b^3 c \sqrt{c x^2} (a+b x)}-\frac{2 a x \log (a+b x)}{b^3 c \sqrt{c x^2}}+\frac{x^2}{b^2 c \sqrt{c x^2}}",1,"x^2/(b^2*c*Sqrt[c*x^2]) - (a^2*x)/(b^3*c*Sqrt[c*x^2]*(a + b*x)) - (2*a*x*Log[a + b*x])/(b^3*c*Sqrt[c*x^2])","A",3,2,20,0.1000,1,"{15, 43}"
918,1,49,0,0.0138987,"\int \frac{x^4}{\left(c x^2\right)^{3/2} (a+b x)^2} \, dx","Int[x^4/((c*x^2)^(3/2)*(a + b*x)^2),x]","\frac{a x}{b^2 c \sqrt{c x^2} (a+b x)}+\frac{x \log (a+b x)}{b^2 c \sqrt{c x^2}}","\frac{a x}{b^2 c \sqrt{c x^2} (a+b x)}+\frac{x \log (a+b x)}{b^2 c \sqrt{c x^2}}",1,"(a*x)/(b^2*c*Sqrt[c*x^2]*(a + b*x)) + (x*Log[a + b*x])/(b^2*c*Sqrt[c*x^2])","A",3,2,20,0.1000,1,"{15, 43}"
919,1,25,0,0.0038696,"\int \frac{x^3}{\left(c x^2\right)^{3/2} (a+b x)^2} \, dx","Int[x^3/((c*x^2)^(3/2)*(a + b*x)^2),x]","-\frac{x}{b c \sqrt{c x^2} (a+b x)}","-\frac{x}{b c \sqrt{c x^2} (a+b x)}",1,"-(x/(b*c*Sqrt[c*x^2]*(a + b*x)))","A",2,2,20,0.1000,1,"{15, 32}"
920,1,68,0,0.0167383,"\int \frac{x^2}{\left(c x^2\right)^{3/2} (a+b x)^2} \, dx","Int[x^2/((c*x^2)^(3/2)*(a + b*x)^2),x]","-\frac{x \log (a+b x)}{a^2 c \sqrt{c x^2}}+\frac{x \log (x)}{a^2 c \sqrt{c x^2}}+\frac{x}{a c \sqrt{c x^2} (a+b x)}","-\frac{x \log (a+b x)}{a^2 c \sqrt{c x^2}}+\frac{x \log (x)}{a^2 c \sqrt{c x^2}}+\frac{x}{a c \sqrt{c x^2} (a+b x)}",1,"x/(a*c*Sqrt[c*x^2]*(a + b*x)) + (x*Log[x])/(a^2*c*Sqrt[c*x^2]) - (x*Log[a + b*x])/(a^2*c*Sqrt[c*x^2])","A",3,2,20,0.1000,1,"{15, 44}"
921,1,90,0,0.0236142,"\int \frac{x}{\left(c x^2\right)^{3/2} (a+b x)^2} \, dx","Int[x/((c*x^2)^(3/2)*(a + b*x)^2),x]","-\frac{b x}{a^2 c \sqrt{c x^2} (a+b x)}-\frac{2 b x \log (x)}{a^3 c \sqrt{c x^2}}+\frac{2 b x \log (a+b x)}{a^3 c \sqrt{c x^2}}-\frac{1}{a^2 c \sqrt{c x^2}}","-\frac{b x}{a^2 c \sqrt{c x^2} (a+b x)}-\frac{2 b x \log (x)}{a^3 c \sqrt{c x^2}}+\frac{2 b x \log (a+b x)}{a^3 c \sqrt{c x^2}}-\frac{1}{a^2 c \sqrt{c x^2}}",1,"-(1/(a^2*c*Sqrt[c*x^2])) - (b*x)/(a^2*c*Sqrt[c*x^2]*(a + b*x)) - (2*b*x*Log[x])/(a^3*c*Sqrt[c*x^2]) + (2*b*x*Log[a + b*x])/(a^3*c*Sqrt[c*x^2])","A",3,2,18,0.1111,1,"{15, 44}"
922,1,118,0,0.0323105,"\int \frac{1}{\left(c x^2\right)^{3/2} (a+b x)^2} \, dx","Int[1/((c*x^2)^(3/2)*(a + b*x)^2),x]","\frac{b^2 x}{a^3 c \sqrt{c x^2} (a+b x)}+\frac{3 b^2 x \log (x)}{a^4 c \sqrt{c x^2}}-\frac{3 b^2 x \log (a+b x)}{a^4 c \sqrt{c x^2}}+\frac{2 b}{a^3 c \sqrt{c x^2}}-\frac{1}{2 a^2 c x \sqrt{c x^2}}","\frac{b^2 x}{a^3 c \sqrt{c x^2} (a+b x)}+\frac{3 b^2 x \log (x)}{a^4 c \sqrt{c x^2}}-\frac{3 b^2 x \log (a+b x)}{a^4 c \sqrt{c x^2}}+\frac{2 b}{a^3 c \sqrt{c x^2}}-\frac{1}{2 a^2 c x \sqrt{c x^2}}",1,"(2*b)/(a^3*c*Sqrt[c*x^2]) - 1/(2*a^2*c*x*Sqrt[c*x^2]) + (b^2*x)/(a^3*c*Sqrt[c*x^2]*(a + b*x)) + (3*b^2*x*Log[x])/(a^4*c*Sqrt[c*x^2]) - (3*b^2*x*Log[a + b*x])/(a^4*c*Sqrt[c*x^2])","A",3,2,17,0.1176,1,"{15, 44}"
923,1,131,0,0.0374866,"\int x^2 \sqrt{c x^2} (a+b x)^n \, dx","Int[x^2*Sqrt[c*x^2]*(a + b*x)^n,x]","-\frac{a^3 \sqrt{c x^2} (a+b x)^{n+1}}{b^4 (n+1) x}+\frac{3 a^2 \sqrt{c x^2} (a+b x)^{n+2}}{b^4 (n+2) x}-\frac{3 a \sqrt{c x^2} (a+b x)^{n+3}}{b^4 (n+3) x}+\frac{\sqrt{c x^2} (a+b x)^{n+4}}{b^4 (n+4) x}","-\frac{a^3 \sqrt{c x^2} (a+b x)^{n+1}}{b^4 (n+1) x}+\frac{3 a^2 \sqrt{c x^2} (a+b x)^{n+2}}{b^4 (n+2) x}-\frac{3 a \sqrt{c x^2} (a+b x)^{n+3}}{b^4 (n+3) x}+\frac{\sqrt{c x^2} (a+b x)^{n+4}}{b^4 (n+4) x}",1,"-((a^3*Sqrt[c*x^2]*(a + b*x)^(1 + n))/(b^4*(1 + n)*x)) + (3*a^2*Sqrt[c*x^2]*(a + b*x)^(2 + n))/(b^4*(2 + n)*x) - (3*a*Sqrt[c*x^2]*(a + b*x)^(3 + n))/(b^4*(3 + n)*x) + (Sqrt[c*x^2]*(a + b*x)^(4 + n))/(b^4*(4 + n)*x)","A",3,2,20,0.1000,1,"{15, 43}"
924,1,96,0,0.0287581,"\int x \sqrt{c x^2} (a+b x)^n \, dx","Int[x*Sqrt[c*x^2]*(a + b*x)^n,x]","\frac{a^2 \sqrt{c x^2} (a+b x)^{n+1}}{b^3 (n+1) x}-\frac{2 a \sqrt{c x^2} (a+b x)^{n+2}}{b^3 (n+2) x}+\frac{\sqrt{c x^2} (a+b x)^{n+3}}{b^3 (n+3) x}","\frac{a^2 \sqrt{c x^2} (a+b x)^{n+1}}{b^3 (n+1) x}-\frac{2 a \sqrt{c x^2} (a+b x)^{n+2}}{b^3 (n+2) x}+\frac{\sqrt{c x^2} (a+b x)^{n+3}}{b^3 (n+3) x}",1,"(a^2*Sqrt[c*x^2]*(a + b*x)^(1 + n))/(b^3*(1 + n)*x) - (2*a*Sqrt[c*x^2]*(a + b*x)^(2 + n))/(b^3*(2 + n)*x) + (Sqrt[c*x^2]*(a + b*x)^(3 + n))/(b^3*(3 + n)*x)","A",3,2,18,0.1111,1,"{15, 43}"
925,1,63,0,0.0169286,"\int \sqrt{c x^2} (a+b x)^n \, dx","Int[Sqrt[c*x^2]*(a + b*x)^n,x]","\frac{\sqrt{c x^2} (a+b x)^{n+2}}{b^2 (n+2) x}-\frac{a \sqrt{c x^2} (a+b x)^{n+1}}{b^2 (n+1) x}","\frac{\sqrt{c x^2} (a+b x)^{n+2}}{b^2 (n+2) x}-\frac{a \sqrt{c x^2} (a+b x)^{n+1}}{b^2 (n+1) x}",1,"-((a*Sqrt[c*x^2]*(a + b*x)^(1 + n))/(b^2*(1 + n)*x)) + (Sqrt[c*x^2]*(a + b*x)^(2 + n))/(b^2*(2 + n)*x)","A",3,2,17,0.1176,1,"{15, 43}"
926,1,30,0,0.0056715,"\int \frac{\sqrt{c x^2} (a+b x)^n}{x} \, dx","Int[(Sqrt[c*x^2]*(a + b*x)^n)/x,x]","\frac{\sqrt{c x^2} (a+b x)^{n+1}}{b (n+1) x}","\frac{\sqrt{c x^2} (a+b x)^{n+1}}{b (n+1) x}",1,"(Sqrt[c*x^2]*(a + b*x)^(1 + n))/(b*(1 + n)*x)","A",2,2,20,0.1000,1,"{15, 32}"
927,1,47,0,0.0110567,"\int \frac{\sqrt{c x^2} (a+b x)^n}{x^2} \, dx","Int[(Sqrt[c*x^2]*(a + b*x)^n)/x^2,x]","-\frac{\sqrt{c x^2} (a+b x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b x}{a}+1\right)}{a (n+1) x}","-\frac{\sqrt{c x^2} (a+b x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b x}{a}+1\right)}{a (n+1) x}",1,"-((Sqrt[c*x^2]*(a + b*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, 1 + (b*x)/a])/(a*(1 + n)*x))","A",2,2,20,0.1000,1,"{15, 65}"
928,1,47,0,0.0106019,"\int \frac{\sqrt{c x^2} (a+b x)^n}{x^3} \, dx","Int[(Sqrt[c*x^2]*(a + b*x)^n)/x^3,x]","\frac{b \sqrt{c x^2} (a+b x)^{n+1} \, _2F_1\left(2,n+1;n+2;\frac{b x}{a}+1\right)}{a^2 (n+1) x}","\frac{b \sqrt{c x^2} (a+b x)^{n+1} \, _2F_1\left(2,n+1;n+2;\frac{b x}{a}+1\right)}{a^2 (n+1) x}",1,"(b*Sqrt[c*x^2]*(a + b*x)^(1 + n)*Hypergeometric2F1[2, 1 + n, 2 + n, 1 + (b*x)/a])/(a^2*(1 + n)*x)","A",2,2,20,0.1000,1,"{15, 65}"
929,1,50,0,0.0115907,"\int \frac{\sqrt{c x^2} (a+b x)^n}{x^4} \, dx","Int[(Sqrt[c*x^2]*(a + b*x)^n)/x^4,x]","-\frac{b^2 \sqrt{c x^2} (a+b x)^{n+1} \, _2F_1\left(3,n+1;n+2;\frac{b x}{a}+1\right)}{a^3 (n+1) x}","-\frac{b^2 \sqrt{c x^2} (a+b x)^{n+1} \, _2F_1\left(3,n+1;n+2;\frac{b x}{a}+1\right)}{a^3 (n+1) x}",1,"-((b^2*Sqrt[c*x^2]*(a + b*x)^(1 + n)*Hypergeometric2F1[3, 1 + n, 2 + n, 1 + (b*x)/a])/(a^3*(1 + n)*x))","A",2,2,20,0.1000,1,"{15, 65}"
930,1,169,0,0.0553475,"\int x \left(c x^2\right)^{3/2} (a+b x)^n \, dx","Int[x*(c*x^2)^(3/2)*(a + b*x)^n,x]","\frac{a^4 c \sqrt{c x^2} (a+b x)^{n+1}}{b^5 (n+1) x}-\frac{4 a^3 c \sqrt{c x^2} (a+b x)^{n+2}}{b^5 (n+2) x}+\frac{6 a^2 c \sqrt{c x^2} (a+b x)^{n+3}}{b^5 (n+3) x}-\frac{4 a c \sqrt{c x^2} (a+b x)^{n+4}}{b^5 (n+4) x}+\frac{c \sqrt{c x^2} (a+b x)^{n+5}}{b^5 (n+5) x}","\frac{a^4 c \sqrt{c x^2} (a+b x)^{n+1}}{b^5 (n+1) x}-\frac{4 a^3 c \sqrt{c x^2} (a+b x)^{n+2}}{b^5 (n+2) x}+\frac{6 a^2 c \sqrt{c x^2} (a+b x)^{n+3}}{b^5 (n+3) x}-\frac{4 a c \sqrt{c x^2} (a+b x)^{n+4}}{b^5 (n+4) x}+\frac{c \sqrt{c x^2} (a+b x)^{n+5}}{b^5 (n+5) x}",1,"(a^4*c*Sqrt[c*x^2]*(a + b*x)^(1 + n))/(b^5*(1 + n)*x) - (4*a^3*c*Sqrt[c*x^2]*(a + b*x)^(2 + n))/(b^5*(2 + n)*x) + (6*a^2*c*Sqrt[c*x^2]*(a + b*x)^(3 + n))/(b^5*(3 + n)*x) - (4*a*c*Sqrt[c*x^2]*(a + b*x)^(4 + n))/(b^5*(4 + n)*x) + (c*Sqrt[c*x^2]*(a + b*x)^(5 + n))/(b^5*(5 + n)*x)","A",3,2,18,0.1111,1,"{15, 43}"
931,1,135,0,0.0386992,"\int \left(c x^2\right)^{3/2} (a+b x)^n \, dx","Int[(c*x^2)^(3/2)*(a + b*x)^n,x]","-\frac{a^3 c \sqrt{c x^2} (a+b x)^{n+1}}{b^4 (n+1) x}+\frac{3 a^2 c \sqrt{c x^2} (a+b x)^{n+2}}{b^4 (n+2) x}-\frac{3 a c \sqrt{c x^2} (a+b x)^{n+3}}{b^4 (n+3) x}+\frac{c \sqrt{c x^2} (a+b x)^{n+4}}{b^4 (n+4) x}","-\frac{a^3 c \sqrt{c x^2} (a+b x)^{n+1}}{b^4 (n+1) x}+\frac{3 a^2 c \sqrt{c x^2} (a+b x)^{n+2}}{b^4 (n+2) x}-\frac{3 a c \sqrt{c x^2} (a+b x)^{n+3}}{b^4 (n+3) x}+\frac{c \sqrt{c x^2} (a+b x)^{n+4}}{b^4 (n+4) x}",1,"-((a^3*c*Sqrt[c*x^2]*(a + b*x)^(1 + n))/(b^4*(1 + n)*x)) + (3*a^2*c*Sqrt[c*x^2]*(a + b*x)^(2 + n))/(b^4*(2 + n)*x) - (3*a*c*Sqrt[c*x^2]*(a + b*x)^(3 + n))/(b^4*(3 + n)*x) + (c*Sqrt[c*x^2]*(a + b*x)^(4 + n))/(b^4*(4 + n)*x)","A",3,2,17,0.1176,1,"{15, 43}"
932,1,99,0,0.0284546,"\int \frac{\left(c x^2\right)^{3/2} (a+b x)^n}{x} \, dx","Int[((c*x^2)^(3/2)*(a + b*x)^n)/x,x]","\frac{a^2 c \sqrt{c x^2} (a+b x)^{n+1}}{b^3 (n+1) x}-\frac{2 a c \sqrt{c x^2} (a+b x)^{n+2}}{b^3 (n+2) x}+\frac{c \sqrt{c x^2} (a+b x)^{n+3}}{b^3 (n+3) x}","\frac{a^2 c \sqrt{c x^2} (a+b x)^{n+1}}{b^3 (n+1) x}-\frac{2 a c \sqrt{c x^2} (a+b x)^{n+2}}{b^3 (n+2) x}+\frac{c \sqrt{c x^2} (a+b x)^{n+3}}{b^3 (n+3) x}",1,"(a^2*c*Sqrt[c*x^2]*(a + b*x)^(1 + n))/(b^3*(1 + n)*x) - (2*a*c*Sqrt[c*x^2]*(a + b*x)^(2 + n))/(b^3*(2 + n)*x) + (c*Sqrt[c*x^2]*(a + b*x)^(3 + n))/(b^3*(3 + n)*x)","A",3,2,20,0.1000,1,"{15, 43}"
933,1,65,0,0.0179092,"\int \frac{\left(c x^2\right)^{3/2} (a+b x)^n}{x^2} \, dx","Int[((c*x^2)^(3/2)*(a + b*x)^n)/x^2,x]","\frac{c \sqrt{c x^2} (a+b x)^{n+2}}{b^2 (n+2) x}-\frac{a c \sqrt{c x^2} (a+b x)^{n+1}}{b^2 (n+1) x}","\frac{c \sqrt{c x^2} (a+b x)^{n+2}}{b^2 (n+2) x}-\frac{a c \sqrt{c x^2} (a+b x)^{n+1}}{b^2 (n+1) x}",1,"-((a*c*Sqrt[c*x^2]*(a + b*x)^(1 + n))/(b^2*(1 + n)*x)) + (c*Sqrt[c*x^2]*(a + b*x)^(2 + n))/(b^2*(2 + n)*x)","A",3,2,20,0.1000,1,"{15, 43}"
934,1,31,0,0.0059132,"\int \frac{\left(c x^2\right)^{3/2} (a+b x)^n}{x^3} \, dx","Int[((c*x^2)^(3/2)*(a + b*x)^n)/x^3,x]","\frac{c \sqrt{c x^2} (a+b x)^{n+1}}{b (n+1) x}","\frac{c \sqrt{c x^2} (a+b x)^{n+1}}{b (n+1) x}",1,"(c*Sqrt[c*x^2]*(a + b*x)^(1 + n))/(b*(1 + n)*x)","A",2,2,20,0.1000,1,"{15, 32}"
935,1,48,0,0.0113252,"\int \frac{\left(c x^2\right)^{3/2} (a+b x)^n}{x^4} \, dx","Int[((c*x^2)^(3/2)*(a + b*x)^n)/x^4,x]","-\frac{c \sqrt{c x^2} (a+b x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b x}{a}+1\right)}{a (n+1) x}","-\frac{c \sqrt{c x^2} (a+b x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b x}{a}+1\right)}{a (n+1) x}",1,"-((c*Sqrt[c*x^2]*(a + b*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, 1 + (b*x)/a])/(a*(1 + n)*x))","A",2,2,20,0.1000,1,"{15, 65}"
936,1,48,0,0.0111331,"\int \frac{\left(c x^2\right)^{3/2} (a+b x)^n}{x^5} \, dx","Int[((c*x^2)^(3/2)*(a + b*x)^n)/x^5,x]","\frac{b c \sqrt{c x^2} (a+b x)^{n+1} \, _2F_1\left(2,n+1;n+2;\frac{b x}{a}+1\right)}{a^2 (n+1) x}","\frac{b c \sqrt{c x^2} (a+b x)^{n+1} \, _2F_1\left(2,n+1;n+2;\frac{b x}{a}+1\right)}{a^2 (n+1) x}",1,"(b*c*Sqrt[c*x^2]*(a + b*x)^(1 + n)*Hypergeometric2F1[2, 1 + n, 2 + n, 1 + (b*x)/a])/(a^2*(1 + n)*x)","A",2,2,20,0.1000,1,"{15, 65}"
937,1,51,0,0.0130143,"\int \frac{\left(c x^2\right)^{3/2} (a+b x)^n}{x^6} \, dx","Int[((c*x^2)^(3/2)*(a + b*x)^n)/x^6,x]","-\frac{b^2 c \sqrt{c x^2} (a+b x)^{n+1} \, _2F_1\left(3,n+1;n+2;\frac{b x}{a}+1\right)}{a^3 (n+1) x}","-\frac{b^2 c \sqrt{c x^2} (a+b x)^{n+1} \, _2F_1\left(3,n+1;n+2;\frac{b x}{a}+1\right)}{a^3 (n+1) x}",1,"-((b^2*c*Sqrt[c*x^2]*(a + b*x)^(1 + n)*Hypergeometric2F1[3, 1 + n, 2 + n, 1 + (b*x)/a])/(a^3*(1 + n)*x))","A",2,2,20,0.1000,1,"{15, 65}"
938,1,217,0,0.073794,"\int \left(c x^2\right)^{5/2} (a+b x)^n \, dx","Int[(c*x^2)^(5/2)*(a + b*x)^n,x]","-\frac{a^5 c^2 \sqrt{c x^2} (a+b x)^{n+1}}{b^6 (n+1) x}+\frac{5 a^4 c^2 \sqrt{c x^2} (a+b x)^{n+2}}{b^6 (n+2) x}-\frac{10 a^3 c^2 \sqrt{c x^2} (a+b x)^{n+3}}{b^6 (n+3) x}+\frac{10 a^2 c^2 \sqrt{c x^2} (a+b x)^{n+4}}{b^6 (n+4) x}-\frac{5 a c^2 \sqrt{c x^2} (a+b x)^{n+5}}{b^6 (n+5) x}+\frac{c^2 \sqrt{c x^2} (a+b x)^{n+6}}{b^6 (n+6) x}","-\frac{a^5 c^2 \sqrt{c x^2} (a+b x)^{n+1}}{b^6 (n+1) x}+\frac{5 a^4 c^2 \sqrt{c x^2} (a+b x)^{n+2}}{b^6 (n+2) x}-\frac{10 a^3 c^2 \sqrt{c x^2} (a+b x)^{n+3}}{b^6 (n+3) x}+\frac{10 a^2 c^2 \sqrt{c x^2} (a+b x)^{n+4}}{b^6 (n+4) x}-\frac{5 a c^2 \sqrt{c x^2} (a+b x)^{n+5}}{b^6 (n+5) x}+\frac{c^2 \sqrt{c x^2} (a+b x)^{n+6}}{b^6 (n+6) x}",1,"-((a^5*c^2*Sqrt[c*x^2]*(a + b*x)^(1 + n))/(b^6*(1 + n)*x)) + (5*a^4*c^2*Sqrt[c*x^2]*(a + b*x)^(2 + n))/(b^6*(2 + n)*x) - (10*a^3*c^2*Sqrt[c*x^2]*(a + b*x)^(3 + n))/(b^6*(3 + n)*x) + (10*a^2*c^2*Sqrt[c*x^2]*(a + b*x)^(4 + n))/(b^6*(4 + n)*x) - (5*a*c^2*Sqrt[c*x^2]*(a + b*x)^(5 + n))/(b^6*(5 + n)*x) + (c^2*Sqrt[c*x^2]*(a + b*x)^(6 + n))/(b^6*(6 + n)*x)","A",3,2,17,0.1176,1,"{15, 43}"
939,1,179,0,0.051275,"\int \frac{\left(c x^2\right)^{5/2} (a+b x)^n}{x} \, dx","Int[((c*x^2)^(5/2)*(a + b*x)^n)/x,x]","\frac{a^4 c^2 \sqrt{c x^2} (a+b x)^{n+1}}{b^5 (n+1) x}-\frac{4 a^3 c^2 \sqrt{c x^2} (a+b x)^{n+2}}{b^5 (n+2) x}+\frac{6 a^2 c^2 \sqrt{c x^2} (a+b x)^{n+3}}{b^5 (n+3) x}-\frac{4 a c^2 \sqrt{c x^2} (a+b x)^{n+4}}{b^5 (n+4) x}+\frac{c^2 \sqrt{c x^2} (a+b x)^{n+5}}{b^5 (n+5) x}","\frac{a^4 c^2 \sqrt{c x^2} (a+b x)^{n+1}}{b^5 (n+1) x}-\frac{4 a^3 c^2 \sqrt{c x^2} (a+b x)^{n+2}}{b^5 (n+2) x}+\frac{6 a^2 c^2 \sqrt{c x^2} (a+b x)^{n+3}}{b^5 (n+3) x}-\frac{4 a c^2 \sqrt{c x^2} (a+b x)^{n+4}}{b^5 (n+4) x}+\frac{c^2 \sqrt{c x^2} (a+b x)^{n+5}}{b^5 (n+5) x}",1,"(a^4*c^2*Sqrt[c*x^2]*(a + b*x)^(1 + n))/(b^5*(1 + n)*x) - (4*a^3*c^2*Sqrt[c*x^2]*(a + b*x)^(2 + n))/(b^5*(2 + n)*x) + (6*a^2*c^2*Sqrt[c*x^2]*(a + b*x)^(3 + n))/(b^5*(3 + n)*x) - (4*a*c^2*Sqrt[c*x^2]*(a + b*x)^(4 + n))/(b^5*(4 + n)*x) + (c^2*Sqrt[c*x^2]*(a + b*x)^(5 + n))/(b^5*(5 + n)*x)","A",3,2,20,0.1000,1,"{15, 43}"
940,1,143,0,0.0424376,"\int \frac{\left(c x^2\right)^{5/2} (a+b x)^n}{x^2} \, dx","Int[((c*x^2)^(5/2)*(a + b*x)^n)/x^2,x]","-\frac{a^3 c^2 \sqrt{c x^2} (a+b x)^{n+1}}{b^4 (n+1) x}+\frac{3 a^2 c^2 \sqrt{c x^2} (a+b x)^{n+2}}{b^4 (n+2) x}-\frac{3 a c^2 \sqrt{c x^2} (a+b x)^{n+3}}{b^4 (n+3) x}+\frac{c^2 \sqrt{c x^2} (a+b x)^{n+4}}{b^4 (n+4) x}","-\frac{a^3 c^2 \sqrt{c x^2} (a+b x)^{n+1}}{b^4 (n+1) x}+\frac{3 a^2 c^2 \sqrt{c x^2} (a+b x)^{n+2}}{b^4 (n+2) x}-\frac{3 a c^2 \sqrt{c x^2} (a+b x)^{n+3}}{b^4 (n+3) x}+\frac{c^2 \sqrt{c x^2} (a+b x)^{n+4}}{b^4 (n+4) x}",1,"-((a^3*c^2*Sqrt[c*x^2]*(a + b*x)^(1 + n))/(b^4*(1 + n)*x)) + (3*a^2*c^2*Sqrt[c*x^2]*(a + b*x)^(2 + n))/(b^4*(2 + n)*x) - (3*a*c^2*Sqrt[c*x^2]*(a + b*x)^(3 + n))/(b^4*(3 + n)*x) + (c^2*Sqrt[c*x^2]*(a + b*x)^(4 + n))/(b^4*(4 + n)*x)","A",3,2,20,0.1000,1,"{15, 43}"
941,1,105,0,0.029299,"\int \frac{\left(c x^2\right)^{5/2} (a+b x)^n}{x^3} \, dx","Int[((c*x^2)^(5/2)*(a + b*x)^n)/x^3,x]","\frac{a^2 c^2 \sqrt{c x^2} (a+b x)^{n+1}}{b^3 (n+1) x}-\frac{2 a c^2 \sqrt{c x^2} (a+b x)^{n+2}}{b^3 (n+2) x}+\frac{c^2 \sqrt{c x^2} (a+b x)^{n+3}}{b^3 (n+3) x}","\frac{a^2 c^2 \sqrt{c x^2} (a+b x)^{n+1}}{b^3 (n+1) x}-\frac{2 a c^2 \sqrt{c x^2} (a+b x)^{n+2}}{b^3 (n+2) x}+\frac{c^2 \sqrt{c x^2} (a+b x)^{n+3}}{b^3 (n+3) x}",1,"(a^2*c^2*Sqrt[c*x^2]*(a + b*x)^(1 + n))/(b^3*(1 + n)*x) - (2*a*c^2*Sqrt[c*x^2]*(a + b*x)^(2 + n))/(b^3*(2 + n)*x) + (c^2*Sqrt[c*x^2]*(a + b*x)^(3 + n))/(b^3*(3 + n)*x)","A",3,2,20,0.1000,1,"{15, 43}"
942,1,69,0,0.0187664,"\int \frac{\left(c x^2\right)^{5/2} (a+b x)^n}{x^4} \, dx","Int[((c*x^2)^(5/2)*(a + b*x)^n)/x^4,x]","\frac{c^2 \sqrt{c x^2} (a+b x)^{n+2}}{b^2 (n+2) x}-\frac{a c^2 \sqrt{c x^2} (a+b x)^{n+1}}{b^2 (n+1) x}","\frac{c^2 \sqrt{c x^2} (a+b x)^{n+2}}{b^2 (n+2) x}-\frac{a c^2 \sqrt{c x^2} (a+b x)^{n+1}}{b^2 (n+1) x}",1,"-((a*c^2*Sqrt[c*x^2]*(a + b*x)^(1 + n))/(b^2*(1 + n)*x)) + (c^2*Sqrt[c*x^2]*(a + b*x)^(2 + n))/(b^2*(2 + n)*x)","A",3,2,20,0.1000,1,"{15, 43}"
943,1,33,0,0.0064947,"\int \frac{\left(c x^2\right)^{5/2} (a+b x)^n}{x^5} \, dx","Int[((c*x^2)^(5/2)*(a + b*x)^n)/x^5,x]","\frac{c^2 \sqrt{c x^2} (a+b x)^{n+1}}{b (n+1) x}","\frac{c^2 \sqrt{c x^2} (a+b x)^{n+1}}{b (n+1) x}",1,"(c^2*Sqrt[c*x^2]*(a + b*x)^(1 + n))/(b*(1 + n)*x)","A",2,2,20,0.1000,1,"{15, 32}"
944,1,50,0,0.0117057,"\int \frac{\left(c x^2\right)^{5/2} (a+b x)^n}{x^6} \, dx","Int[((c*x^2)^(5/2)*(a + b*x)^n)/x^6,x]","-\frac{c^2 \sqrt{c x^2} (a+b x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b x}{a}+1\right)}{a (n+1) x}","-\frac{c^2 \sqrt{c x^2} (a+b x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b x}{a}+1\right)}{a (n+1) x}",1,"-((c^2*Sqrt[c*x^2]*(a + b*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, 1 + (b*x)/a])/(a*(1 + n)*x))","A",2,2,20,0.1000,1,"{15, 65}"
945,1,50,0,0.0117204,"\int \frac{\left(c x^2\right)^{5/2} (a+b x)^n}{x^7} \, dx","Int[((c*x^2)^(5/2)*(a + b*x)^n)/x^7,x]","\frac{b c^2 \sqrt{c x^2} (a+b x)^{n+1} \, _2F_1\left(2,n+1;n+2;\frac{b x}{a}+1\right)}{a^2 (n+1) x}","\frac{b c^2 \sqrt{c x^2} (a+b x)^{n+1} \, _2F_1\left(2,n+1;n+2;\frac{b x}{a}+1\right)}{a^2 (n+1) x}",1,"(b*c^2*Sqrt[c*x^2]*(a + b*x)^(1 + n)*Hypergeometric2F1[2, 1 + n, 2 + n, 1 + (b*x)/a])/(a^2*(1 + n)*x)","A",2,2,20,0.1000,1,"{15, 65}"
946,1,123,0,0.0371531,"\int \frac{x^4 (a+b x)^n}{\sqrt{c x^2}} \, dx","Int[(x^4*(a + b*x)^n)/Sqrt[c*x^2],x]","-\frac{a^3 x (a+b x)^{n+1}}{b^4 (n+1) \sqrt{c x^2}}+\frac{3 a^2 x (a+b x)^{n+2}}{b^4 (n+2) \sqrt{c x^2}}-\frac{3 a x (a+b x)^{n+3}}{b^4 (n+3) \sqrt{c x^2}}+\frac{x (a+b x)^{n+4}}{b^4 (n+4) \sqrt{c x^2}}","-\frac{a^3 x (a+b x)^{n+1}}{b^4 (n+1) \sqrt{c x^2}}+\frac{3 a^2 x (a+b x)^{n+2}}{b^4 (n+2) \sqrt{c x^2}}-\frac{3 a x (a+b x)^{n+3}}{b^4 (n+3) \sqrt{c x^2}}+\frac{x (a+b x)^{n+4}}{b^4 (n+4) \sqrt{c x^2}}",1,"-((a^3*x*(a + b*x)^(1 + n))/(b^4*(1 + n)*Sqrt[c*x^2])) + (3*a^2*x*(a + b*x)^(2 + n))/(b^4*(2 + n)*Sqrt[c*x^2]) - (3*a*x*(a + b*x)^(3 + n))/(b^4*(3 + n)*Sqrt[c*x^2]) + (x*(a + b*x)^(4 + n))/(b^4*(4 + n)*Sqrt[c*x^2])","A",3,2,20,0.1000,1,"{15, 43}"
947,1,90,0,0.0258797,"\int \frac{x^3 (a+b x)^n}{\sqrt{c x^2}} \, dx","Int[(x^3*(a + b*x)^n)/Sqrt[c*x^2],x]","\frac{a^2 x (a+b x)^{n+1}}{b^3 (n+1) \sqrt{c x^2}}-\frac{2 a x (a+b x)^{n+2}}{b^3 (n+2) \sqrt{c x^2}}+\frac{x (a+b x)^{n+3}}{b^3 (n+3) \sqrt{c x^2}}","\frac{a^2 x (a+b x)^{n+1}}{b^3 (n+1) \sqrt{c x^2}}-\frac{2 a x (a+b x)^{n+2}}{b^3 (n+2) \sqrt{c x^2}}+\frac{x (a+b x)^{n+3}}{b^3 (n+3) \sqrt{c x^2}}",1,"(a^2*x*(a + b*x)^(1 + n))/(b^3*(1 + n)*Sqrt[c*x^2]) - (2*a*x*(a + b*x)^(2 + n))/(b^3*(2 + n)*Sqrt[c*x^2]) + (x*(a + b*x)^(3 + n))/(b^3*(3 + n)*Sqrt[c*x^2])","A",3,2,20,0.1000,1,"{15, 43}"
948,1,59,0,0.0157513,"\int \frac{x^2 (a+b x)^n}{\sqrt{c x^2}} \, dx","Int[(x^2*(a + b*x)^n)/Sqrt[c*x^2],x]","\frac{x (a+b x)^{n+2}}{b^2 (n+2) \sqrt{c x^2}}-\frac{a x (a+b x)^{n+1}}{b^2 (n+1) \sqrt{c x^2}}","\frac{x (a+b x)^{n+2}}{b^2 (n+2) \sqrt{c x^2}}-\frac{a x (a+b x)^{n+1}}{b^2 (n+1) \sqrt{c x^2}}",1,"-((a*x*(a + b*x)^(1 + n))/(b^2*(1 + n)*Sqrt[c*x^2])) + (x*(a + b*x)^(2 + n))/(b^2*(2 + n)*Sqrt[c*x^2])","A",3,2,20,0.1000,1,"{15, 43}"
949,1,28,0,0.0048816,"\int \frac{x (a+b x)^n}{\sqrt{c x^2}} \, dx","Int[(x*(a + b*x)^n)/Sqrt[c*x^2],x]","\frac{x (a+b x)^{n+1}}{b (n+1) \sqrt{c x^2}}","\frac{x (a+b x)^{n+1}}{b (n+1) \sqrt{c x^2}}",1,"(x*(a + b*x)^(1 + n))/(b*(1 + n)*Sqrt[c*x^2])","A",2,2,18,0.1111,1,"{15, 32}"
950,1,45,0,0.0097081,"\int \frac{(a+b x)^n}{\sqrt{c x^2}} \, dx","Int[(a + b*x)^n/Sqrt[c*x^2],x]","-\frac{x (a+b x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b x}{a}+1\right)}{a (n+1) \sqrt{c x^2}}","-\frac{x (a+b x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b x}{a}+1\right)}{a (n+1) \sqrt{c x^2}}",1,"-((x*(a + b*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, 1 + (b*x)/a])/(a*(1 + n)*Sqrt[c*x^2]))","A",2,2,17,0.1176,1,"{15, 65}"
951,1,45,0,0.0100599,"\int \frac{(a+b x)^n}{x \sqrt{c x^2}} \, dx","Int[(a + b*x)^n/(x*Sqrt[c*x^2]),x]","\frac{b x (a+b x)^{n+1} \, _2F_1\left(2,n+1;n+2;\frac{b x}{a}+1\right)}{a^2 (n+1) \sqrt{c x^2}}","\frac{b x (a+b x)^{n+1} \, _2F_1\left(2,n+1;n+2;\frac{b x}{a}+1\right)}{a^2 (n+1) \sqrt{c x^2}}",1,"(b*x*(a + b*x)^(1 + n)*Hypergeometric2F1[2, 1 + n, 2 + n, 1 + (b*x)/a])/(a^2*(1 + n)*Sqrt[c*x^2])","A",2,2,20,0.1000,1,"{15, 65}"
952,1,48,0,0.011783,"\int \frac{(a+b x)^n}{x^2 \sqrt{c x^2}} \, dx","Int[(a + b*x)^n/(x^2*Sqrt[c*x^2]),x]","-\frac{b^2 x (a+b x)^{n+1} \, _2F_1\left(3,n+1;n+2;\frac{b x}{a}+1\right)}{a^3 (n+1) \sqrt{c x^2}}","-\frac{b^2 x (a+b x)^{n+1} \, _2F_1\left(3,n+1;n+2;\frac{b x}{a}+1\right)}{a^3 (n+1) \sqrt{c x^2}}",1,"-((b^2*x*(a + b*x)^(1 + n)*Hypergeometric2F1[3, 1 + n, 2 + n, 1 + (b*x)/a])/(a^3*(1 + n)*Sqrt[c*x^2]))","A",2,2,20,0.1000,1,"{15, 65}"
953,1,135,0,0.0436374,"\int \frac{x^6 (a+b x)^n}{\left(c x^2\right)^{3/2}} \, dx","Int[(x^6*(a + b*x)^n)/(c*x^2)^(3/2),x]","-\frac{a^3 x (a+b x)^{n+1}}{b^4 c (n+1) \sqrt{c x^2}}+\frac{3 a^2 x (a+b x)^{n+2}}{b^4 c (n+2) \sqrt{c x^2}}-\frac{3 a x (a+b x)^{n+3}}{b^4 c (n+3) \sqrt{c x^2}}+\frac{x (a+b x)^{n+4}}{b^4 c (n+4) \sqrt{c x^2}}","-\frac{a^3 x (a+b x)^{n+1}}{b^4 c (n+1) \sqrt{c x^2}}+\frac{3 a^2 x (a+b x)^{n+2}}{b^4 c (n+2) \sqrt{c x^2}}-\frac{3 a x (a+b x)^{n+3}}{b^4 c (n+3) \sqrt{c x^2}}+\frac{x (a+b x)^{n+4}}{b^4 c (n+4) \sqrt{c x^2}}",1,"-((a^3*x*(a + b*x)^(1 + n))/(b^4*c*(1 + n)*Sqrt[c*x^2])) + (3*a^2*x*(a + b*x)^(2 + n))/(b^4*c*(2 + n)*Sqrt[c*x^2]) - (3*a*x*(a + b*x)^(3 + n))/(b^4*c*(3 + n)*Sqrt[c*x^2]) + (x*(a + b*x)^(4 + n))/(b^4*c*(4 + n)*Sqrt[c*x^2])","A",3,2,20,0.1000,1,"{15, 43}"
954,1,99,0,0.0311947,"\int \frac{x^5 (a+b x)^n}{\left(c x^2\right)^{3/2}} \, dx","Int[(x^5*(a + b*x)^n)/(c*x^2)^(3/2),x]","\frac{a^2 x (a+b x)^{n+1}}{b^3 c (n+1) \sqrt{c x^2}}-\frac{2 a x (a+b x)^{n+2}}{b^3 c (n+2) \sqrt{c x^2}}+\frac{x (a+b x)^{n+3}}{b^3 c (n+3) \sqrt{c x^2}}","\frac{a^2 x (a+b x)^{n+1}}{b^3 c (n+1) \sqrt{c x^2}}-\frac{2 a x (a+b x)^{n+2}}{b^3 c (n+2) \sqrt{c x^2}}+\frac{x (a+b x)^{n+3}}{b^3 c (n+3) \sqrt{c x^2}}",1,"(a^2*x*(a + b*x)^(1 + n))/(b^3*c*(1 + n)*Sqrt[c*x^2]) - (2*a*x*(a + b*x)^(2 + n))/(b^3*c*(2 + n)*Sqrt[c*x^2]) + (x*(a + b*x)^(3 + n))/(b^3*c*(3 + n)*Sqrt[c*x^2])","A",3,2,20,0.1000,1,"{15, 43}"
955,1,65,0,0.018915,"\int \frac{x^4 (a+b x)^n}{\left(c x^2\right)^{3/2}} \, dx","Int[(x^4*(a + b*x)^n)/(c*x^2)^(3/2),x]","\frac{x (a+b x)^{n+2}}{b^2 c (n+2) \sqrt{c x^2}}-\frac{a x (a+b x)^{n+1}}{b^2 c (n+1) \sqrt{c x^2}}","\frac{x (a+b x)^{n+2}}{b^2 c (n+2) \sqrt{c x^2}}-\frac{a x (a+b x)^{n+1}}{b^2 c (n+1) \sqrt{c x^2}}",1,"-((a*x*(a + b*x)^(1 + n))/(b^2*c*(1 + n)*Sqrt[c*x^2])) + (x*(a + b*x)^(2 + n))/(b^2*c*(2 + n)*Sqrt[c*x^2])","A",3,2,20,0.1000,1,"{15, 43}"
956,1,31,0,0.0067218,"\int \frac{x^3 (a+b x)^n}{\left(c x^2\right)^{3/2}} \, dx","Int[(x^3*(a + b*x)^n)/(c*x^2)^(3/2),x]","\frac{x (a+b x)^{n+1}}{b c (n+1) \sqrt{c x^2}}","\frac{x (a+b x)^{n+1}}{b c (n+1) \sqrt{c x^2}}",1,"(x*(a + b*x)^(1 + n))/(b*c*(1 + n)*Sqrt[c*x^2])","A",2,2,20,0.1000,1,"{15, 32}"
957,1,48,0,0.0124052,"\int \frac{x^2 (a+b x)^n}{\left(c x^2\right)^{3/2}} \, dx","Int[(x^2*(a + b*x)^n)/(c*x^2)^(3/2),x]","-\frac{x (a+b x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b x}{a}+1\right)}{a c (n+1) \sqrt{c x^2}}","-\frac{x (a+b x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b x}{a}+1\right)}{a c (n+1) \sqrt{c x^2}}",1,"-((x*(a + b*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, 1 + (b*x)/a])/(a*c*(1 + n)*Sqrt[c*x^2]))","A",2,2,20,0.1000,1,"{15, 65}"
958,1,48,0,0.0120192,"\int \frac{x (a+b x)^n}{\left(c x^2\right)^{3/2}} \, dx","Int[(x*(a + b*x)^n)/(c*x^2)^(3/2),x]","\frac{b x (a+b x)^{n+1} \, _2F_1\left(2,n+1;n+2;\frac{b x}{a}+1\right)}{a^2 c (n+1) \sqrt{c x^2}}","\frac{b x (a+b x)^{n+1} \, _2F_1\left(2,n+1;n+2;\frac{b x}{a}+1\right)}{a^2 c (n+1) \sqrt{c x^2}}",1,"(b*x*(a + b*x)^(1 + n)*Hypergeometric2F1[2, 1 + n, 2 + n, 1 + (b*x)/a])/(a^2*c*(1 + n)*Sqrt[c*x^2])","A",2,2,18,0.1111,1,"{15, 65}"
959,1,51,0,0.0136584,"\int \frac{(a+b x)^n}{\left(c x^2\right)^{3/2}} \, dx","Int[(a + b*x)^n/(c*x^2)^(3/2),x]","-\frac{b^2 x (a+b x)^{n+1} \, _2F_1\left(3,n+1;n+2;\frac{b x}{a}+1\right)}{a^3 c (n+1) \sqrt{c x^2}}","-\frac{b^2 x (a+b x)^{n+1} \, _2F_1\left(3,n+1;n+2;\frac{b x}{a}+1\right)}{a^3 c (n+1) \sqrt{c x^2}}",1,"-((b^2*x*(a + b*x)^(1 + n)*Hypergeometric2F1[3, 1 + n, 2 + n, 1 + (b*x)/a])/(a^3*c*(1 + n)*Sqrt[c*x^2]))","A",2,2,17,0.1176,1,"{15, 65}"
960,1,50,0,0.0141199,"\int \frac{(a+b x)^n}{x \left(c x^2\right)^{3/2}} \, dx","Int[(a + b*x)^n/(x*(c*x^2)^(3/2)),x]","\frac{b^3 x (a+b x)^{n+1} \, _2F_1\left(4,n+1;n+2;\frac{b x}{a}+1\right)}{a^4 c (n+1) \sqrt{c x^2}}","\frac{b^3 x (a+b x)^{n+1} \, _2F_1\left(4,n+1;n+2;\frac{b x}{a}+1\right)}{a^4 c (n+1) \sqrt{c x^2}}",1,"(b^3*x*(a + b*x)^(1 + n)*Hypergeometric2F1[4, 1 + n, 2 + n, 1 + (b*x)/a])/(a^4*c*(1 + n)*Sqrt[c*x^2])","A",2,2,20,0.1000,1,"{15, 65}"
961,1,135,0,0.0460681,"\int \frac{x^8 (a+b x)^n}{\left(c x^2\right)^{5/2}} \, dx","Int[(x^8*(a + b*x)^n)/(c*x^2)^(5/2),x]","-\frac{a^3 x (a+b x)^{n+1}}{b^4 c^2 (n+1) \sqrt{c x^2}}+\frac{3 a^2 x (a+b x)^{n+2}}{b^4 c^2 (n+2) \sqrt{c x^2}}-\frac{3 a x (a+b x)^{n+3}}{b^4 c^2 (n+3) \sqrt{c x^2}}+\frac{x (a+b x)^{n+4}}{b^4 c^2 (n+4) \sqrt{c x^2}}","-\frac{a^3 x (a+b x)^{n+1}}{b^4 c^2 (n+1) \sqrt{c x^2}}+\frac{3 a^2 x (a+b x)^{n+2}}{b^4 c^2 (n+2) \sqrt{c x^2}}-\frac{3 a x (a+b x)^{n+3}}{b^4 c^2 (n+3) \sqrt{c x^2}}+\frac{x (a+b x)^{n+4}}{b^4 c^2 (n+4) \sqrt{c x^2}}",1,"-((a^3*x*(a + b*x)^(1 + n))/(b^4*c^2*(1 + n)*Sqrt[c*x^2])) + (3*a^2*x*(a + b*x)^(2 + n))/(b^4*c^2*(2 + n)*Sqrt[c*x^2]) - (3*a*x*(a + b*x)^(3 + n))/(b^4*c^2*(3 + n)*Sqrt[c*x^2]) + (x*(a + b*x)^(4 + n))/(b^4*c^2*(4 + n)*Sqrt[c*x^2])","A",3,2,20,0.1000,1,"{15, 43}"
962,1,99,0,0.0307015,"\int \frac{x^7 (a+b x)^n}{\left(c x^2\right)^{5/2}} \, dx","Int[(x^7*(a + b*x)^n)/(c*x^2)^(5/2),x]","\frac{a^2 x (a+b x)^{n+1}}{b^3 c^2 (n+1) \sqrt{c x^2}}-\frac{2 a x (a+b x)^{n+2}}{b^3 c^2 (n+2) \sqrt{c x^2}}+\frac{x (a+b x)^{n+3}}{b^3 c^2 (n+3) \sqrt{c x^2}}","\frac{a^2 x (a+b x)^{n+1}}{b^3 c^2 (n+1) \sqrt{c x^2}}-\frac{2 a x (a+b x)^{n+2}}{b^3 c^2 (n+2) \sqrt{c x^2}}+\frac{x (a+b x)^{n+3}}{b^3 c^2 (n+3) \sqrt{c x^2}}",1,"(a^2*x*(a + b*x)^(1 + n))/(b^3*c^2*(1 + n)*Sqrt[c*x^2]) - (2*a*x*(a + b*x)^(2 + n))/(b^3*c^2*(2 + n)*Sqrt[c*x^2]) + (x*(a + b*x)^(3 + n))/(b^3*c^2*(3 + n)*Sqrt[c*x^2])","A",3,2,20,0.1000,1,"{15, 43}"
963,1,65,0,0.0202965,"\int \frac{x^6 (a+b x)^n}{\left(c x^2\right)^{5/2}} \, dx","Int[(x^6*(a + b*x)^n)/(c*x^2)^(5/2),x]","\frac{x (a+b x)^{n+2}}{b^2 c^2 (n+2) \sqrt{c x^2}}-\frac{a x (a+b x)^{n+1}}{b^2 c^2 (n+1) \sqrt{c x^2}}","\frac{x (a+b x)^{n+2}}{b^2 c^2 (n+2) \sqrt{c x^2}}-\frac{a x (a+b x)^{n+1}}{b^2 c^2 (n+1) \sqrt{c x^2}}",1,"-((a*x*(a + b*x)^(1 + n))/(b^2*c^2*(1 + n)*Sqrt[c*x^2])) + (x*(a + b*x)^(2 + n))/(b^2*c^2*(2 + n)*Sqrt[c*x^2])","A",3,2,20,0.1000,1,"{15, 43}"
964,1,31,0,0.0066318,"\int \frac{x^5 (a+b x)^n}{\left(c x^2\right)^{5/2}} \, dx","Int[(x^5*(a + b*x)^n)/(c*x^2)^(5/2),x]","\frac{x (a+b x)^{n+1}}{b c^2 (n+1) \sqrt{c x^2}}","\frac{x (a+b x)^{n+1}}{b c^2 (n+1) \sqrt{c x^2}}",1,"(x*(a + b*x)^(1 + n))/(b*c^2*(1 + n)*Sqrt[c*x^2])","A",2,2,20,0.1000,1,"{15, 32}"
965,1,48,0,0.0125406,"\int \frac{x^4 (a+b x)^n}{\left(c x^2\right)^{5/2}} \, dx","Int[(x^4*(a + b*x)^n)/(c*x^2)^(5/2),x]","-\frac{x (a+b x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b x}{a}+1\right)}{a c^2 (n+1) \sqrt{c x^2}}","-\frac{x (a+b x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b x}{a}+1\right)}{a c^2 (n+1) \sqrt{c x^2}}",1,"-((x*(a + b*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, 1 + (b*x)/a])/(a*c^2*(1 + n)*Sqrt[c*x^2]))","A",2,2,20,0.1000,1,"{15, 65}"
966,1,48,0,0.0126808,"\int \frac{x^3 (a+b x)^n}{\left(c x^2\right)^{5/2}} \, dx","Int[(x^3*(a + b*x)^n)/(c*x^2)^(5/2),x]","\frac{b x (a+b x)^{n+1} \, _2F_1\left(2,n+1;n+2;\frac{b x}{a}+1\right)}{a^2 c^2 (n+1) \sqrt{c x^2}}","\frac{b x (a+b x)^{n+1} \, _2F_1\left(2,n+1;n+2;\frac{b x}{a}+1\right)}{a^2 c^2 (n+1) \sqrt{c x^2}}",1,"(b*x*(a + b*x)^(1 + n)*Hypergeometric2F1[2, 1 + n, 2 + n, 1 + (b*x)/a])/(a^2*c^2*(1 + n)*Sqrt[c*x^2])","A",2,2,20,0.1000,1,"{15, 65}"
967,1,51,0,0.0146581,"\int \frac{x^2 (a+b x)^n}{\left(c x^2\right)^{5/2}} \, dx","Int[(x^2*(a + b*x)^n)/(c*x^2)^(5/2),x]","-\frac{b^2 x (a+b x)^{n+1} \, _2F_1\left(3,n+1;n+2;\frac{b x}{a}+1\right)}{a^3 c^2 (n+1) \sqrt{c x^2}}","-\frac{b^2 x (a+b x)^{n+1} \, _2F_1\left(3,n+1;n+2;\frac{b x}{a}+1\right)}{a^3 c^2 (n+1) \sqrt{c x^2}}",1,"-((b^2*x*(a + b*x)^(1 + n)*Hypergeometric2F1[3, 1 + n, 2 + n, 1 + (b*x)/a])/(a^3*c^2*(1 + n)*Sqrt[c*x^2]))","A",2,2,20,0.1000,1,"{15, 65}"
968,1,50,0,0.013246,"\int \frac{x (a+b x)^n}{\left(c x^2\right)^{5/2}} \, dx","Int[(x*(a + b*x)^n)/(c*x^2)^(5/2),x]","\frac{b^3 x (a+b x)^{n+1} \, _2F_1\left(4,n+1;n+2;\frac{b x}{a}+1\right)}{a^4 c^2 (n+1) \sqrt{c x^2}}","\frac{b^3 x (a+b x)^{n+1} \, _2F_1\left(4,n+1;n+2;\frac{b x}{a}+1\right)}{a^4 c^2 (n+1) \sqrt{c x^2}}",1,"(b^3*x*(a + b*x)^(1 + n)*Hypergeometric2F1[4, 1 + n, 2 + n, 1 + (b*x)/a])/(a^4*c^2*(1 + n)*Sqrt[c*x^2])","A",2,2,18,0.1111,1,"{15, 65}"
969,1,65,0,0.0304476,"\int (d x)^m \left(c x^2\right)^{5/2} (a+b x) \, dx","Int[(d*x)^m*(c*x^2)^(5/2)*(a + b*x),x]","\frac{a c^2 \sqrt{c x^2} (d x)^{m+6}}{d^6 (m+6) x}+\frac{b c^2 \sqrt{c x^2} (d x)^{m+7}}{d^7 (m+7) x}","\frac{a c^2 \sqrt{c x^2} (d x)^{m+6}}{d^6 (m+6) x}+\frac{b c^2 \sqrt{c x^2} (d x)^{m+7}}{d^7 (m+7) x}",1,"(a*c^2*(d*x)^(6 + m)*Sqrt[c*x^2])/(d^6*(6 + m)*x) + (b*c^2*(d*x)^(7 + m)*Sqrt[c*x^2])/(d^7*(7 + m)*x)","A",4,3,20,0.1500,1,"{15, 16, 43}"
970,1,61,0,0.0294383,"\int (d x)^m \left(c x^2\right)^{3/2} (a+b x) \, dx","Int[(d*x)^m*(c*x^2)^(3/2)*(a + b*x),x]","\frac{a c \sqrt{c x^2} (d x)^{m+4}}{d^4 (m+4) x}+\frac{b c \sqrt{c x^2} (d x)^{m+5}}{d^5 (m+5) x}","\frac{a c \sqrt{c x^2} (d x)^{m+4}}{d^4 (m+4) x}+\frac{b c \sqrt{c x^2} (d x)^{m+5}}{d^5 (m+5) x}",1,"(a*c*(d*x)^(4 + m)*Sqrt[c*x^2])/(d^4*(4 + m)*x) + (b*c*(d*x)^(5 + m)*Sqrt[c*x^2])/(d^5*(5 + m)*x)","A",4,3,20,0.1500,1,"{15, 16, 43}"
971,1,59,0,0.0267448,"\int (d x)^m \sqrt{c x^2} (a+b x) \, dx","Int[(d*x)^m*Sqrt[c*x^2]*(a + b*x),x]","\frac{a \sqrt{c x^2} (d x)^{m+2}}{d^2 (m+2) x}+\frac{b \sqrt{c x^2} (d x)^{m+3}}{d^3 (m+3) x}","\frac{a \sqrt{c x^2} (d x)^{m+2}}{d^2 (m+2) x}+\frac{b \sqrt{c x^2} (d x)^{m+3}}{d^3 (m+3) x}",1,"(a*(d*x)^(2 + m)*Sqrt[c*x^2])/(d^2*(2 + m)*x) + (b*(d*x)^(3 + m)*Sqrt[c*x^2])/(d^3*(3 + m)*x)","A",4,3,20,0.1500,1,"{15, 16, 43}"
972,1,48,0,0.0193592,"\int \frac{(d x)^m (a+b x)}{\sqrt{c x^2}} \, dx","Int[((d*x)^m*(a + b*x))/Sqrt[c*x^2],x]","\frac{a x (d x)^m}{m \sqrt{c x^2}}+\frac{b x (d x)^{m+1}}{d (m+1) \sqrt{c x^2}}","\frac{a x (d x)^m}{m \sqrt{c x^2}}+\frac{b x (d x)^{m+1}}{d (m+1) \sqrt{c x^2}}",1,"(a*x*(d*x)^m)/(m*Sqrt[c*x^2]) + (b*x*(d*x)^(1 + m))/(d*(1 + m)*Sqrt[c*x^2])","A",4,3,20,0.1500,1,"{15, 16, 43}"
973,1,65,0,0.0358064,"\int \frac{(d x)^m (a+b x)}{\left(c x^2\right)^{3/2}} \, dx","Int[((d*x)^m*(a + b*x))/(c*x^2)^(3/2),x]","-\frac{a d^2 x (d x)^{m-2}}{c (2-m) \sqrt{c x^2}}-\frac{b d x (d x)^{m-1}}{c (1-m) \sqrt{c x^2}}","-\frac{a d^2 x (d x)^{m-2}}{c (2-m) \sqrt{c x^2}}-\frac{b d x (d x)^{m-1}}{c (1-m) \sqrt{c x^2}}",1,"-((a*d^2*x*(d*x)^(-2 + m))/(c*(2 - m)*Sqrt[c*x^2])) - (b*d*x*(d*x)^(-1 + m))/(c*(1 - m)*Sqrt[c*x^2])","A",4,3,20,0.1500,1,"{15, 16, 43}"
974,1,67,0,0.0365748,"\int \frac{(d x)^m (a+b x)}{\left(c x^2\right)^{5/2}} \, dx","Int[((d*x)^m*(a + b*x))/(c*x^2)^(5/2),x]","-\frac{a d^4 x (d x)^{m-4}}{c^2 (4-m) \sqrt{c x^2}}-\frac{b d^3 x (d x)^{m-3}}{c^2 (3-m) \sqrt{c x^2}}","-\frac{a d^4 x (d x)^{m-4}}{c^2 (4-m) \sqrt{c x^2}}-\frac{b d^3 x (d x)^{m-3}}{c^2 (3-m) \sqrt{c x^2}}",1,"-((a*d^4*x*(d*x)^(-4 + m))/(c^2*(4 - m)*Sqrt[c*x^2])) - (b*d^3*x*(d*x)^(-3 + m))/(c^2*(3 - m)*Sqrt[c*x^2])","A",4,3,20,0.1500,1,"{15, 16, 43}"
975,1,103,0,0.0489113,"\int (d x)^m \left(c x^2\right)^{5/2} (a+b x)^2 \, dx","Int[(d*x)^m*(c*x^2)^(5/2)*(a + b*x)^2,x]","\frac{a^2 c^2 \sqrt{c x^2} (d x)^{m+6}}{d^6 (m+6) x}+\frac{2 a b c^2 \sqrt{c x^2} (d x)^{m+7}}{d^7 (m+7) x}+\frac{b^2 c^2 \sqrt{c x^2} (d x)^{m+8}}{d^8 (m+8) x}","\frac{a^2 c^2 \sqrt{c x^2} (d x)^{m+6}}{d^6 (m+6) x}+\frac{2 a b c^2 \sqrt{c x^2} (d x)^{m+7}}{d^7 (m+7) x}+\frac{b^2 c^2 \sqrt{c x^2} (d x)^{m+8}}{d^8 (m+8) x}",1,"(a^2*c^2*(d*x)^(6 + m)*Sqrt[c*x^2])/(d^6*(6 + m)*x) + (2*a*b*c^2*(d*x)^(7 + m)*Sqrt[c*x^2])/(d^7*(7 + m)*x) + (b^2*c^2*(d*x)^(8 + m)*Sqrt[c*x^2])/(d^8*(8 + m)*x)","A",4,3,22,0.1364,1,"{15, 16, 43}"
976,1,97,0,0.0446737,"\int (d x)^m \left(c x^2\right)^{3/2} (a+b x)^2 \, dx","Int[(d*x)^m*(c*x^2)^(3/2)*(a + b*x)^2,x]","\frac{a^2 c \sqrt{c x^2} (d x)^{m+4}}{d^4 (m+4) x}+\frac{2 a b c \sqrt{c x^2} (d x)^{m+5}}{d^5 (m+5) x}+\frac{b^2 c \sqrt{c x^2} (d x)^{m+6}}{d^6 (m+6) x}","\frac{a^2 c \sqrt{c x^2} (d x)^{m+4}}{d^4 (m+4) x}+\frac{2 a b c \sqrt{c x^2} (d x)^{m+5}}{d^5 (m+5) x}+\frac{b^2 c \sqrt{c x^2} (d x)^{m+6}}{d^6 (m+6) x}",1,"(a^2*c*(d*x)^(4 + m)*Sqrt[c*x^2])/(d^4*(4 + m)*x) + (2*a*b*c*(d*x)^(5 + m)*Sqrt[c*x^2])/(d^5*(5 + m)*x) + (b^2*c*(d*x)^(6 + m)*Sqrt[c*x^2])/(d^6*(6 + m)*x)","A",4,3,22,0.1364,1,"{15, 16, 43}"
977,1,94,0,0.0410875,"\int (d x)^m \sqrt{c x^2} (a+b x)^2 \, dx","Int[(d*x)^m*Sqrt[c*x^2]*(a + b*x)^2,x]","\frac{a^2 \sqrt{c x^2} (d x)^{m+2}}{d^2 (m+2) x}+\frac{2 a b \sqrt{c x^2} (d x)^{m+3}}{d^3 (m+3) x}+\frac{b^2 \sqrt{c x^2} (d x)^{m+4}}{d^4 (m+4) x}","\frac{a^2 \sqrt{c x^2} (d x)^{m+2}}{d^2 (m+2) x}+\frac{2 a b \sqrt{c x^2} (d x)^{m+3}}{d^3 (m+3) x}+\frac{b^2 \sqrt{c x^2} (d x)^{m+4}}{d^4 (m+4) x}",1,"(a^2*(d*x)^(2 + m)*Sqrt[c*x^2])/(d^2*(2 + m)*x) + (2*a*b*(d*x)^(3 + m)*Sqrt[c*x^2])/(d^3*(3 + m)*x) + (b^2*(d*x)^(4 + m)*Sqrt[c*x^2])/(d^4*(4 + m)*x)","A",4,3,22,0.1364,1,"{15, 16, 43}"
978,1,81,0,0.0355124,"\int \frac{(d x)^m (a+b x)^2}{\sqrt{c x^2}} \, dx","Int[((d*x)^m*(a + b*x)^2)/Sqrt[c*x^2],x]","\frac{a^2 x (d x)^m}{m \sqrt{c x^2}}+\frac{2 a b x (d x)^{m+1}}{d (m+1) \sqrt{c x^2}}+\frac{b^2 x (d x)^{m+2}}{d^2 (m+2) \sqrt{c x^2}}","\frac{a^2 x (d x)^m}{m \sqrt{c x^2}}+\frac{2 a b x (d x)^{m+1}}{d (m+1) \sqrt{c x^2}}+\frac{b^2 x (d x)^{m+2}}{d^2 (m+2) \sqrt{c x^2}}",1,"(a^2*x*(d*x)^m)/(m*Sqrt[c*x^2]) + (2*a*b*x*(d*x)^(1 + m))/(d*(1 + m)*Sqrt[c*x^2]) + (b^2*x*(d*x)^(2 + m))/(d^2*(2 + m)*Sqrt[c*x^2])","A",4,3,22,0.1364,1,"{15, 16, 43}"
979,1,93,0,0.0450581,"\int \frac{(d x)^m (a+b x)^2}{\left(c x^2\right)^{3/2}} \, dx","Int[((d*x)^m*(a + b*x)^2)/(c*x^2)^(3/2),x]","-\frac{a^2 d^2 x (d x)^{m-2}}{c (2-m) \sqrt{c x^2}}-\frac{2 a b d x (d x)^{m-1}}{c (1-m) \sqrt{c x^2}}+\frac{b^2 x (d x)^m}{c m \sqrt{c x^2}}","-\frac{a^2 d^2 x (d x)^{m-2}}{c (2-m) \sqrt{c x^2}}-\frac{2 a b d x (d x)^{m-1}}{c (1-m) \sqrt{c x^2}}+\frac{b^2 x (d x)^m}{c m \sqrt{c x^2}}",1,"-((a^2*d^2*x*(d*x)^(-2 + m))/(c*(2 - m)*Sqrt[c*x^2])) - (2*a*b*d*x*(d*x)^(-1 + m))/(c*(1 - m)*Sqrt[c*x^2]) + (b^2*x*(d*x)^m)/(c*m*Sqrt[c*x^2])","A",4,3,22,0.1364,1,"{15, 16, 43}"
980,1,105,0,0.0542726,"\int \frac{(d x)^m (a+b x)^2}{\left(c x^2\right)^{5/2}} \, dx","Int[((d*x)^m*(a + b*x)^2)/(c*x^2)^(5/2),x]","-\frac{a^2 d^4 x (d x)^{m-4}}{c^2 (4-m) \sqrt{c x^2}}-\frac{2 a b d^3 x (d x)^{m-3}}{c^2 (3-m) \sqrt{c x^2}}-\frac{b^2 d^2 x (d x)^{m-2}}{c^2 (2-m) \sqrt{c x^2}}","-\frac{a^2 d^4 x (d x)^{m-4}}{c^2 (4-m) \sqrt{c x^2}}-\frac{2 a b d^3 x (d x)^{m-3}}{c^2 (3-m) \sqrt{c x^2}}-\frac{b^2 d^2 x (d x)^{m-2}}{c^2 (2-m) \sqrt{c x^2}}",1,"-((a^2*d^4*x*(d*x)^(-4 + m))/(c^2*(4 - m)*Sqrt[c*x^2])) - (2*a*b*d^3*x*(d*x)^(-3 + m))/(c^2*(3 - m)*Sqrt[c*x^2]) - (b^2*d^2*x*(d*x)^(-2 + m))/(c^2*(2 - m)*Sqrt[c*x^2])","A",4,3,22,0.1364,1,"{15, 16, 43}"
981,1,67,0,0.028676,"\int (d x)^m \left(c x^2\right)^{5/2} (a+b x)^n \, dx","Int[(d*x)^m*(c*x^2)^(5/2)*(a + b*x)^n,x]","\frac{c^2 \sqrt{c x^2} (d x)^{m+6} (a+b x)^n \left(\frac{b x}{a}+1\right)^{-n} \, _2F_1\left(m+6,-n;m+7;-\frac{b x}{a}\right)}{d^6 (m+6) x}","\frac{c^2 \sqrt{c x^2} (d x)^{m+6} (a+b x)^n \left(\frac{b x}{a}+1\right)^{-n} \, _2F_1\left(m+6,-n;m+7;-\frac{b x}{a}\right)}{d^6 (m+6) x}",1,"(c^2*(d*x)^(6 + m)*Sqrt[c*x^2]*(a + b*x)^n*Hypergeometric2F1[6 + m, -n, 7 + m, -((b*x)/a)])/(d^6*(6 + m)*x*(1 + (b*x)/a)^n)","A",4,4,22,0.1818,1,"{15, 16, 66, 64}"
982,1,65,0,0.0285395,"\int (d x)^m \left(c x^2\right)^{3/2} (a+b x)^n \, dx","Int[(d*x)^m*(c*x^2)^(3/2)*(a + b*x)^n,x]","\frac{c \sqrt{c x^2} (d x)^{m+4} (a+b x)^n \left(\frac{b x}{a}+1\right)^{-n} \, _2F_1\left(m+4,-n;m+5;-\frac{b x}{a}\right)}{d^4 (m+4) x}","\frac{c \sqrt{c x^2} (d x)^{m+4} (a+b x)^n \left(\frac{b x}{a}+1\right)^{-n} \, _2F_1\left(m+4,-n;m+5;-\frac{b x}{a}\right)}{d^4 (m+4) x}",1,"(c*(d*x)^(4 + m)*Sqrt[c*x^2]*(a + b*x)^n*Hypergeometric2F1[4 + m, -n, 5 + m, -((b*x)/a)])/(d^4*(4 + m)*x*(1 + (b*x)/a)^n)","A",4,4,22,0.1818,1,"{15, 16, 66, 64}"
983,1,64,0,0.0281022,"\int (d x)^m \sqrt{c x^2} (a+b x)^n \, dx","Int[(d*x)^m*Sqrt[c*x^2]*(a + b*x)^n,x]","\frac{\sqrt{c x^2} (d x)^{m+2} (a+b x)^n \left(\frac{b x}{a}+1\right)^{-n} \, _2F_1\left(m+2,-n;m+3;-\frac{b x}{a}\right)}{d^2 (m+2) x}","\frac{\sqrt{c x^2} (d x)^{m+2} (a+b x)^n \left(\frac{b x}{a}+1\right)^{-n} \, _2F_1\left(m+2,-n;m+3;-\frac{b x}{a}\right)}{d^2 (m+2) x}",1,"((d*x)^(2 + m)*Sqrt[c*x^2]*(a + b*x)^n*Hypergeometric2F1[2 + m, -n, 3 + m, -((b*x)/a)])/(d^2*(2 + m)*x*(1 + (b*x)/a)^n)","A",4,4,22,0.1818,1,"{15, 16, 66, 64}"
984,1,53,0,0.0213641,"\int \frac{(d x)^m (a+b x)^n}{\sqrt{c x^2}} \, dx","Int[((d*x)^m*(a + b*x)^n)/Sqrt[c*x^2],x]","\frac{x (d x)^m (a+b x)^n \left(\frac{b x}{a}+1\right)^{-n} \, _2F_1\left(m,-n;m+1;-\frac{b x}{a}\right)}{m \sqrt{c x^2}}","\frac{x (d x)^m (a+b x)^n \left(\frac{b x}{a}+1\right)^{-n} \, _2F_1\left(m,-n;m+1;-\frac{b x}{a}\right)}{m \sqrt{c x^2}}",1,"(x*(d*x)^m*(a + b*x)^n*Hypergeometric2F1[m, -n, 1 + m, -((b*x)/a)])/(m*Sqrt[c*x^2]*(1 + (b*x)/a)^n)","A",4,4,22,0.1818,1,"{15, 16, 66, 64}"
985,1,68,0,0.0315716,"\int \frac{(d x)^m (a+b x)^n}{\left(c x^2\right)^{3/2}} \, dx","Int[((d*x)^m*(a + b*x)^n)/(c*x^2)^(3/2),x]","-\frac{d^2 x (d x)^{m-2} (a+b x)^n \left(\frac{b x}{a}+1\right)^{-n} \, _2F_1\left(m-2,-n;m-1;-\frac{b x}{a}\right)}{c (2-m) \sqrt{c x^2}}","-\frac{d^2 x (d x)^{m-2} (a+b x)^n \left(\frac{b x}{a}+1\right)^{-n} \, _2F_1\left(m-2,-n;m-1;-\frac{b x}{a}\right)}{c (2-m) \sqrt{c x^2}}",1,"-((d^2*x*(d*x)^(-2 + m)*(a + b*x)^n*Hypergeometric2F1[-2 + m, -n, -1 + m, -((b*x)/a)])/(c*(2 - m)*Sqrt[c*x^2]*(1 + (b*x)/a)^n))","A",4,4,22,0.1818,1,"{15, 16, 66, 64}"
986,1,68,0,0.0309549,"\int \frac{(d x)^m (a+b x)^n}{\left(c x^2\right)^{5/2}} \, dx","Int[((d*x)^m*(a + b*x)^n)/(c*x^2)^(5/2),x]","-\frac{d^4 x (d x)^{m-4} (a+b x)^n \left(\frac{b x}{a}+1\right)^{-n} \, _2F_1\left(m-4,-n;m-3;-\frac{b x}{a}\right)}{c^2 (4-m) \sqrt{c x^2}}","-\frac{d^4 x (d x)^{m-4} (a+b x)^n \left(\frac{b x}{a}+1\right)^{-n} \, _2F_1\left(m-4,-n;m-3;-\frac{b x}{a}\right)}{c^2 (4-m) \sqrt{c x^2}}",1,"-((d^4*x*(d*x)^(-4 + m)*(a + b*x)^n*Hypergeometric2F1[-4 + m, -n, -3 + m, -((b*x)/a)])/(c^2*(4 - m)*Sqrt[c*x^2]*(1 + (b*x)/a)^n))","A",4,4,22,0.1818,1,"{15, 16, 66, 64}"
987,1,33,0,0.0095883,"\int x^3 \left(c x^2\right)^p (a+b x)^{-5-2 p} \, dx","Int[x^3*(c*x^2)^p*(a + b*x)^(-5 - 2*p),x]","\frac{x^4 \left(c x^2\right)^p (a+b x)^{-2 (p+2)}}{2 a (p+2)}","\frac{x^4 \left(c x^2\right)^p (a+b x)^{-2 (p+2)}}{2 a (p+2)}",1,"(x^4*(c*x^2)^p)/(2*a*(2 + p)*(a + b*x)^(2*(2 + p)))","A",2,2,22,0.09091,1,"{15, 37}"
988,1,32,0,0.0086787,"\int x^2 \left(c x^2\right)^p (a+b x)^{-4-2 p} \, dx","Int[x^2*(c*x^2)^p*(a + b*x)^(-4 - 2*p),x]","\frac{x^3 \left(c x^2\right)^p (a+b x)^{-2 p-3}}{a (2 p+3)}","\frac{x^3 \left(c x^2\right)^p (a+b x)^{-2 p-3}}{a (2 p+3)}",1,"(x^3*(c*x^2)^p*(a + b*x)^(-3 - 2*p))/(a*(3 + 2*p))","A",2,2,22,0.09091,1,"{15, 37}"
989,1,33,0,0.0097638,"\int x \left(c x^2\right)^p (a+b x)^{-3-2 p} \, dx","Int[x*(c*x^2)^p*(a + b*x)^(-3 - 2*p),x]","\frac{x^2 \left(c x^2\right)^p (a+b x)^{-2 (p+1)}}{2 a (p+1)}","\frac{x^2 \left(c x^2\right)^p (a+b x)^{-2 (p+1)}}{2 a (p+1)}",1,"(x^2*(c*x^2)^p)/(2*a*(1 + p)*(a + b*x)^(2*(1 + p)))","A",2,2,20,0.1000,1,"{15, 37}"
990,1,30,0,0.0079995,"\int \left(c x^2\right)^p (a+b x)^{-2-2 p} \, dx","Int[(c*x^2)^p*(a + b*x)^(-2 - 2*p),x]","\frac{x \left(c x^2\right)^p (a+b x)^{-2 p-1}}{a (2 p+1)}","\frac{x \left(c x^2\right)^p (a+b x)^{-2 p-1}}{a (2 p+1)}",1,"(x*(c*x^2)^p*(a + b*x)^(-1 - 2*p))/(a*(1 + 2*p))","A",2,2,19,0.1053,1,"{15, 37}"
991,1,26,0,0.0061454,"\int \frac{\left(c x^2\right)^p (a+b x)^{-1-2 p}}{x} \, dx","Int[((c*x^2)^p*(a + b*x)^(-1 - 2*p))/x,x]","\frac{\left(c x^2\right)^p (a+b x)^{-2 p}}{2 a p}","\frac{\left(c x^2\right)^p (a+b x)^{-2 p}}{2 a p}",1,"(c*x^2)^p/(2*a*p*(a + b*x)^(2*p))","A",2,2,22,0.09091,1,"{15, 37}"
992,1,33,0,0.0108223,"\int \frac{\left(c x^2\right)^p (a+b x)^{-2 p}}{x^2} \, dx","Int[(c*x^2)^p/(x^2*(a + b*x)^(2*p)),x]","-\frac{\left(c x^2\right)^p (a+b x)^{1-2 p}}{a (1-2 p) x}","-\frac{\left(c x^2\right)^p (a+b x)^{1-2 p}}{a (1-2 p) x}",1,"-(((c*x^2)^p*(a + b*x)^(1 - 2*p))/(a*(1 - 2*p)*x))","A",2,2,20,0.1000,1,"{15, 37}"
993,1,35,0,0.01086,"\int \frac{\left(c x^2\right)^p (a+b x)^{1-2 p}}{x^3} \, dx","Int[((c*x^2)^p*(a + b*x)^(1 - 2*p))/x^3,x]","-\frac{\left(c x^2\right)^p (a+b x)^{2-2 p}}{2 a (1-p) x^2}","-\frac{\left(c x^2\right)^p (a+b x)^{2-2 p}}{2 a (1-p) x^2}",1,"-((c*x^2)^p*(a + b*x)^(2 - 2*p))/(2*a*(1 - p)*x^2)","A",2,2,22,0.09091,1,"{15, 37}"
994,1,33,0,0.0104211,"\int \frac{\left(c x^2\right)^p (a+b x)^{2-2 p}}{x^4} \, dx","Int[((c*x^2)^p*(a + b*x)^(2 - 2*p))/x^4,x]","-\frac{\left(c x^2\right)^p (a+b x)^{3-2 p}}{a (3-2 p) x^3}","-\frac{\left(c x^2\right)^p (a+b x)^{3-2 p}}{a (3-2 p) x^3}",1,"-(((c*x^2)^p*(a + b*x)^(3 - 2*p))/(a*(3 - 2*p)*x^3))","A",2,2,22,0.09091,1,"{15, 37}"
995,1,38,0,0.0102633,"\int x^m \left(c x^2\right)^p (a+b x)^{-2-m-2 p} \, dx","Int[x^m*(c*x^2)^p*(a + b*x)^(-2 - m - 2*p),x]","\frac{x^{m+1} \left(c x^2\right)^p (a+b x)^{-m-2 p-1}}{a (m+2 p+1)}","\frac{x^{m+1} \left(c x^2\right)^p (a+b x)^{-m-2 p-1}}{a (m+2 p+1)}",1,"(x^(1 + m)*(c*x^2)^p*(a + b*x)^(-1 - m - 2*p))/(a*(1 + m + 2*p))","A",2,2,25,0.08000,1,"{15, 37}"
996,1,39,0,0.0103912,"\int (d x)^m \left(c x^2\right)^p (a+b x)^{-2-m-2 p} \, dx","Int[(d*x)^m*(c*x^2)^p*(a + b*x)^(-2 - m - 2*p),x]","\frac{x \left(c x^2\right)^p (d x)^m (a+b x)^{-m-2 p-1}}{a (m+2 p+1)}","\frac{x \left(c x^2\right)^p (d x)^m (a+b x)^{-m-2 p-1}}{a (m+2 p+1)}",1,"(x*(d*x)^m*(c*x^2)^p*(a + b*x)^(-1 - m - 2*p))/(a*(1 + m + 2*p))","A",3,3,27,0.1111,1,"{15, 20, 37}"
997,1,63,0,0.0188879,"\int x^m \left(c x^2\right)^p (a+b x)^n \, dx","Int[x^m*(c*x^2)^p*(a + b*x)^n,x]","\frac{x^{m+1} \left(c x^2\right)^p (a+b x)^n \left(\frac{b x}{a}+1\right)^{-n} \, _2F_1\left(-n,m+2 p+1;m+2 p+2;-\frac{b x}{a}\right)}{m+2 p+1}","\frac{x^{m+1} \left(c x^2\right)^p (a+b x)^n \left(\frac{b x}{a}+1\right)^{-n} \, _2F_1\left(-n,m+2 p+1;m+2 p+2;-\frac{b x}{a}\right)}{m+2 p+1}",1,"(x^(1 + m)*(c*x^2)^p*(a + b*x)^n*Hypergeometric2F1[-n, 1 + m + 2*p, 2 + m + 2*p, -((b*x)/a)])/((1 + m + 2*p)*(1 + (b*x)/a)^n)","A",3,3,18,0.1667,1,"{15, 66, 64}"
998,1,64,0,0.0219284,"\int (d x)^m \left(c x^2\right)^p (a+b x)^n \, dx","Int[(d*x)^m*(c*x^2)^p*(a + b*x)^n,x]","\frac{x \left(c x^2\right)^p (d x)^m (a+b x)^n \left(\frac{b x}{a}+1\right)^{-n} \, _2F_1\left(-n,m+2 p+1;m+2 p+2;-\frac{b x}{a}\right)}{m+2 p+1}","\frac{\left(c x^2\right)^p (d x)^{m+1} (a+b x)^n \left(\frac{b x}{a}+1\right)^{-n} \, _2F_1\left(-n,m+2 p+1;m+2 p+2;-\frac{b x}{a}\right)}{d (m+2 p+1)}",1,"(x*(d*x)^m*(c*x^2)^p*(a + b*x)^n*Hypergeometric2F1[-n, 1 + m + 2*p, 2 + m + 2*p, -((b*x)/a)])/((1 + m + 2*p)*(1 + (b*x)/a)^n)","A",4,4,20,0.2000,1,"{15, 20, 66, 64}"
999,1,17,0,0.0037963,"\int \frac{(a+b x)^5}{\left(\frac{a d}{b}+d x\right)^3} \, dx","Int[(a + b*x)^5/((a*d)/b + d*x)^3,x]","\frac{b^2 (a+b x)^3}{3 d^3}","\frac{b^2 (a+b x)^3}{3 d^3}",1,"(b^2*(a + b*x)^3)/(3*d^3)","A",2,2,20,0.1000,1,"{21, 32}"
1000,1,23,0,0.0057754,"\int \frac{(a+b x)^4}{\left(\frac{a d}{b}+d x\right)^3} \, dx","Int[(a + b*x)^4/((a*d)/b + d*x)^3,x]","\frac{a b^3 x}{d^3}+\frac{b^4 x^2}{2 d^3}","\frac{a b^3 x}{d^3}+\frac{b^4 x^2}{2 d^3}",1,"(a*b^3*x)/d^3 + (b^4*x^2)/(2*d^3)","A",2,1,20,0.05000,1,"{21}"
1001,1,8,0,0.001698,"\int \frac{(a+b x)^3}{\left(\frac{a d}{b}+d x\right)^3} \, dx","Int[(a + b*x)^3/((a*d)/b + d*x)^3,x]","\frac{b^3 x}{d^3}","\frac{b^3 x}{d^3}",1,"(b^3*x)/d^3","A",2,2,20,0.1000,1,"{21, 8}"
1002,1,13,0,0.0033044,"\int \frac{(a+b x)^2}{\left(\frac{a d}{b}+d x\right)^3} \, dx","Int[(a + b*x)^2/((a*d)/b + d*x)^3,x]","\frac{b^2 \log (a+b x)}{d^3}","\frac{b^2 \log (a+b x)}{d^3}",1,"(b^2*Log[a + b*x])/d^3","A",2,2,20,0.1000,1,"{21, 31}"
1003,1,15,0,0.0033476,"\int \frac{a+b x}{\left(\frac{a d}{b}+d x\right)^3} \, dx","Int[(a + b*x)/((a*d)/b + d*x)^3,x]","-\frac{b^2}{d^3 (a+b x)}","-\frac{b^2}{d^3 (a+b x)}",1,"-(b^2/(d^3*(a + b*x)))","A",2,2,18,0.1111,1,"{21, 32}"
1004,1,17,0,0.0033228,"\int \frac{1}{(a+b x) \left(\frac{a d}{b}+d x\right)^3} \, dx","Int[1/((a + b*x)*((a*d)/b + d*x)^3),x]","-\frac{b^2}{3 d^3 (a+b x)^3}","-\frac{b^2}{3 d^3 (a+b x)^3}",1,"-b^2/(3*d^3*(a + b*x)^3)","A",2,2,20,0.1000,1,"{21, 32}"
1005,1,17,0,0.0032718,"\int \frac{1}{(a+b x)^2 \left(\frac{a d}{b}+d x\right)^3} \, dx","Int[1/((a + b*x)^2*((a*d)/b + d*x)^3),x]","-\frac{b^2}{4 d^3 (a+b x)^4}","-\frac{b^2}{4 d^3 (a+b x)^4}",1,"-b^2/(4*d^3*(a + b*x)^4)","A",2,2,20,0.1000,1,"{21, 32}"
1006,1,17,0,0.003293,"\int \frac{1}{(a+b x)^3 \left(\frac{a d}{b}+d x\right)^3} \, dx","Int[1/((a + b*x)^3*((a*d)/b + d*x)^3),x]","-\frac{b^2}{5 d^3 (a+b x)^5}","-\frac{b^2}{5 d^3 (a+b x)^5}",1,"-b^2/(5*d^3*(a + b*x)^5)","A",2,2,20,0.1000,1,"{21, 32}"
1007,1,17,0,0.0036141,"\int \frac{\left(\frac{b c}{d}+b x\right)^5}{(c+d x)^3} \, dx","Int[((b*c)/d + b*x)^5/(c + d*x)^3,x]","\frac{b^5 (c+d x)^3}{3 d^6}","\frac{b^5 (c+d x)^3}{3 d^6}",1,"(b^5*(c + d*x)^3)/(3*d^6)","A",2,2,20,0.1000,1,"{21, 32}"
1008,1,23,0,0.0049852,"\int \frac{\left(\frac{b c}{d}+b x\right)^4}{(c+d x)^3} \, dx","Int[((b*c)/d + b*x)^4/(c + d*x)^3,x]","\frac{b^4 c x}{d^4}+\frac{b^4 x^2}{2 d^3}","\frac{b^4 c x}{d^4}+\frac{b^4 x^2}{2 d^3}",1,"(b^4*c*x)/d^4 + (b^4*x^2)/(2*d^3)","A",2,1,20,0.05000,1,"{21}"
1009,1,8,0,0.0014703,"\int \frac{\left(\frac{b c}{d}+b x\right)^3}{(c+d x)^3} \, dx","Int[((b*c)/d + b*x)^3/(c + d*x)^3,x]","\frac{b^3 x}{d^3}","\frac{b^3 x}{d^3}",1,"(b^3*x)/d^3","A",2,2,20,0.1000,1,"{21, 8}"
1010,1,13,0,0.0030361,"\int \frac{\left(\frac{b c}{d}+b x\right)^2}{(c+d x)^3} \, dx","Int[((b*c)/d + b*x)^2/(c + d*x)^3,x]","\frac{b^2 \log (c+d x)}{d^3}","\frac{b^2 \log (c+d x)}{d^3}",1,"(b^2*Log[c + d*x])/d^3","A",2,2,20,0.1000,1,"{21, 31}"
1011,1,13,0,0.0032366,"\int \frac{\frac{b c}{d}+b x}{(c+d x)^3} \, dx","Int[((b*c)/d + b*x)/(c + d*x)^3,x]","-\frac{b}{d^2 (c+d x)}","-\frac{b}{d^2 (c+d x)}",1,"-(b/(d^2*(c + d*x)))","A",2,2,18,0.1111,1,"{21, 32}"
1012,1,14,0,0.0029554,"\int \frac{1}{\left(\frac{b c}{d}+b x\right) (c+d x)^3} \, dx","Int[1/(((b*c)/d + b*x)*(c + d*x)^3),x]","-\frac{1}{3 b (c+d x)^3}","-\frac{1}{3 b (c+d x)^3}",1,"-1/(3*b*(c + d*x)^3)","A",2,2,20,0.1000,1,"{21, 32}"
1013,1,15,0,0.0032222,"\int \frac{1}{\left(\frac{b c}{d}+b x\right)^2 (c+d x)^3} \, dx","Int[1/(((b*c)/d + b*x)^2*(c + d*x)^3),x]","-\frac{d}{4 b^2 (c+d x)^4}","-\frac{d}{4 b^2 (c+d x)^4}",1,"-d/(4*b^2*(c + d*x)^4)","A",2,2,20,0.1000,1,"{21, 32}"
1014,1,17,0,0.0034984,"\int \frac{1}{\left(\frac{b c}{d}+b x\right)^3 (c+d x)^3} \, dx","Int[1/(((b*c)/d + b*x)^3*(c + d*x)^3),x]","-\frac{d^2}{5 b^3 (c+d x)^5}","-\frac{d^2}{5 b^3 (c+d x)^5}",1,"-d^2/(5*b^3*(c + d*x)^5)","A",2,2,20,0.1000,1,"{21, 32}"
1015,1,24,0,0.0088863,"\int (a+b x)^5 (a c+b c x)^n \, dx","Int[(a + b*x)^5*(a*c + b*c*x)^n,x]","\frac{(a c+b c x)^{n+6}}{b c^6 (n+6)}","\frac{(a c+b c x)^{n+6}}{b c^6 (n+6)}",1,"(a*c + b*c*x)^(6 + n)/(b*c^6*(6 + n))","A",2,2,18,0.1111,1,"{21, 32}"
1016,1,17,0,0.0038523,"\int (a+b x)^5 (a c+b c x)^3 \, dx","Int[(a + b*x)^5*(a*c + b*c*x)^3,x]","\frac{c^3 (a+b x)^9}{9 b}","\frac{c^3 (a+b x)^9}{9 b}",1,"(c^3*(a + b*x)^9)/(9*b)","A",2,2,18,0.1111,1,"{21, 32}"
1017,1,17,0,0.0037584,"\int (a+b x)^5 (a c+b c x)^2 \, dx","Int[(a + b*x)^5*(a*c + b*c*x)^2,x]","\frac{c^2 (a+b x)^8}{8 b}","\frac{c^2 (a+b x)^8}{8 b}",1,"(c^2*(a + b*x)^8)/(8*b)","A",2,2,18,0.1111,1,"{21, 32}"
1018,1,15,0,0.0029926,"\int (a+b x)^5 (a c+b c x) \, dx","Int[(a + b*x)^5*(a*c + b*c*x),x]","\frac{c (a+b x)^7}{7 b}","\frac{c (a+b x)^7}{7 b}",1,"(c*(a + b*x)^7)/(7*b)","A",2,2,16,0.1250,1,"{21, 32}"
1019,1,17,0,0.0035367,"\int \frac{(a+b x)^5}{a c+b c x} \, dx","Int[(a + b*x)^5/(a*c + b*c*x),x]","\frac{(a+b x)^5}{5 b c}","\frac{(a+b x)^5}{5 b c}",1,"(a + b*x)^5/(5*b*c)","A",2,2,18,0.1111,1,"{21, 32}"
1020,1,17,0,0.0040407,"\int \frac{(a+b x)^5}{(a c+b c x)^2} \, dx","Int[(a + b*x)^5/(a*c + b*c*x)^2,x]","\frac{(a+b x)^4}{4 b c^2}","\frac{(a+b x)^4}{4 b c^2}",1,"(a + b*x)^4/(4*b*c^2)","A",2,2,18,0.1111,1,"{21, 32}"
1021,1,17,0,0.0040241,"\int \frac{(a+b x)^5}{(a c+b c x)^3} \, dx","Int[(a + b*x)^5/(a*c + b*c*x)^3,x]","\frac{(a+b x)^3}{3 b c^3}","\frac{(a+b x)^3}{3 b c^3}",1,"(a + b*x)^3/(3*b*c^3)","A",2,2,18,0.1111,1,"{21, 32}"
1022,1,18,0,0.004596,"\int \frac{(a+b x)^5}{(a c+b c x)^4} \, dx","Int[(a + b*x)^5/(a*c + b*c*x)^4,x]","\frac{a x}{c^4}+\frac{b x^2}{2 c^4}","\frac{a x}{c^4}+\frac{b x^2}{2 c^4}",1,"(a*x)/c^4 + (b*x^2)/(2*c^4)","A",2,1,18,0.05556,1,"{21}"
1023,1,5,0,0.0013297,"\int \frac{(a+b x)^5}{(a c+b c x)^5} \, dx","Int[(a + b*x)^5/(a*c + b*c*x)^5,x]","\frac{x}{c^5}","\frac{x}{c^5}",1,"x/c^5","A",2,2,18,0.1111,1,"{21, 8}"
1024,1,13,0,0.0037264,"\int \frac{(a+b x)^5}{(a c+b c x)^6} \, dx","Int[(a + b*x)^5/(a*c + b*c*x)^6,x]","\frac{\log (a+b x)}{b c^6}","\frac{\log (a+b x)}{b c^6}",1,"Log[a + b*x]/(b*c^6)","A",2,2,18,0.1111,1,"{21, 31}"
1025,1,15,0,0.0041574,"\int \frac{(a+b x)^5}{(a c+b c x)^7} \, dx","Int[(a + b*x)^5/(a*c + b*c*x)^7,x]","-\frac{1}{b c^7 (a+b x)}","-\frac{1}{b c^7 (a+b x)}",1,"-(1/(b*c^7*(a + b*x)))","A",2,2,18,0.1111,1,"{21, 32}"
1026,1,17,0,0.0038258,"\int \frac{(a+b x)^5}{(a c+b c x)^8} \, dx","Int[(a + b*x)^5/(a*c + b*c*x)^8,x]","-\frac{1}{2 b c^8 (a+b x)^2}","-\frac{1}{2 b c^8 (a+b x)^2}",1,"-1/(2*b*c^8*(a + b*x)^2)","A",2,2,18,0.1111,1,"{21, 32}"
1027,1,28,0,0.0030387,"\int \frac{1}{\sqrt{-2-3 x} \sqrt{2+3 x}} \, dx","Int[1/(Sqrt[-2 - 3*x]*Sqrt[2 + 3*x]),x]","\frac{\sqrt{3 x+2} \log (3 x+2)}{3 \sqrt{-3 x-2}}","\frac{\sqrt{3 x+2} \log (3 x+2)}{3 \sqrt{-3 x-2}}",1,"(Sqrt[2 + 3*x]*Log[2 + 3*x])/(3*Sqrt[-2 - 3*x])","A",2,2,19,0.1053,1,"{23, 31}"
1028,1,38,0,0.0116105,"\int (a+b x) (a c-b c x)^3 \, dx","Int[(a + b*x)*(a*c - b*c*x)^3,x]","\frac{c^3 (a-b x)^5}{5 b}-\frac{a c^3 (a-b x)^4}{2 b}","\frac{c^3 (a-b x)^5}{5 b}-\frac{a c^3 (a-b x)^4}{2 b}",1,"-(a*c^3*(a - b*x)^4)/(2*b) + (c^3*(a - b*x)^5)/(5*b)","A",2,1,17,0.05882,1,"{43}"
1029,1,38,0,0.0170622,"\int (a+b x) (a c-b c x)^2 \, dx","Int[(a + b*x)*(a*c - b*c*x)^2,x]","\frac{c^2 (a-b x)^4}{4 b}-\frac{2 a c^2 (a-b x)^3}{3 b}","\frac{c^2 (a-b x)^4}{4 b}-\frac{2 a c^2 (a-b x)^3}{3 b}",1,"(-2*a*c^2*(a - b*x)^3)/(3*b) + (c^2*(a - b*x)^4)/(4*b)","A",2,1,17,0.05882,1,"{43}"
1030,1,18,0,0.0042267,"\int (a+b x) (a c-b c x) \, dx","Int[(a + b*x)*(a*c - b*c*x),x]","a^2 c x-\frac{1}{3} b^2 c x^3","a^2 c x-\frac{1}{3} b^2 c x^3",1,"a^2*c*x - (b^2*c*x^3)/3","A",2,1,15,0.06667,1,"{41}"
1031,1,12,0,0.0020981,"\int (a+b x) \, dx","Int[a + b*x,x]","a x+\frac{b x^2}{2}","a x+\frac{b x^2}{2}",1,"a*x + (b*x^2)/2","A",1,0,5,0,1,"{}"
1032,1,23,0,0.012133,"\int \frac{a+b x}{a c-b c x} \, dx","Int[(a + b*x)/(a*c - b*c*x),x]","-\frac{2 a \log (a-b x)}{b c}-\frac{x}{c}","-\frac{2 a \log (a-b x)}{b c}-\frac{x}{c}",1,"-(x/c) - (2*a*Log[a - b*x])/(b*c)","A",2,1,17,0.05882,1,"{43}"
1033,1,32,0,0.017297,"\int \frac{a+b x}{(a c-b c x)^2} \, dx","Int[(a + b*x)/(a*c - b*c*x)^2,x]","\frac{2 a}{b c^2 (a-b x)}+\frac{\log (a-b x)}{b c^2}","\frac{2 a}{b c^2 (a-b x)}+\frac{\log (a-b x)}{b c^2}",1,"(2*a)/(b*c^2*(a - b*x)) + Log[a - b*x]/(b*c^2)","A",2,1,17,0.05882,1,"{43}"
1034,1,13,0,0.0021911,"\int \frac{a+b x}{(a c-b c x)^3} \, dx","Int[(a + b*x)/(a*c - b*c*x)^3,x]","\frac{x}{c^3 (a-b x)^2}","\frac{x}{c^3 (a-b x)^2}",1,"x/(c^3*(a - b*x)^2)","A",1,1,17,0.05882,1,"{34}"
1035,1,38,0,0.0187421,"\int \frac{a+b x}{(a c-b c x)^4} \, dx","Int[(a + b*x)/(a*c - b*c*x)^4,x]","\frac{2 a}{3 b c^4 (a-b x)^3}-\frac{1}{2 b c^4 (a-b x)^2}","\frac{2 a}{3 b c^4 (a-b x)^3}-\frac{1}{2 b c^4 (a-b x)^2}",1,"(2*a)/(3*b*c^4*(a - b*x)^3) - 1/(2*b*c^4*(a - b*x)^2)","A",2,1,17,0.05882,1,"{43}"
1036,1,38,0,0.018712,"\int \frac{a+b x}{(a c-b c x)^5} \, dx","Int[(a + b*x)/(a*c - b*c*x)^5,x]","\frac{a}{2 b c^5 (a-b x)^4}-\frac{1}{3 b c^5 (a-b x)^3}","\frac{a}{2 b c^5 (a-b x)^4}-\frac{1}{3 b c^5 (a-b x)^3}",1,"a/(2*b*c^5*(a - b*x)^4) - 1/(3*b*c^5*(a - b*x)^3)","A",2,1,17,0.05882,1,"{43}"
1037,1,38,0,0.0189225,"\int \frac{a+b x}{(a c-b c x)^6} \, dx","Int[(a + b*x)/(a*c - b*c*x)^6,x]","\frac{2 a}{5 b c^6 (a-b x)^5}-\frac{1}{4 b c^6 (a-b x)^4}","\frac{2 a}{5 b c^6 (a-b x)^5}-\frac{1}{4 b c^6 (a-b x)^4}",1,"(2*a)/(5*b*c^6*(a - b*x)^5) - 1/(4*b*c^6*(a - b*x)^4)","A",2,1,17,0.05882,1,"{43}"
1038,1,57,0,0.0303072,"\int (a+b x)^2 (a c-b c x)^3 \, dx","Int[(a + b*x)^2*(a*c - b*c*x)^3,x]","-\frac{a^2 c^3 (a-b x)^4}{b}-\frac{c^3 (a-b x)^6}{6 b}+\frac{4 a c^3 (a-b x)^5}{5 b}","-\frac{a^2 c^3 (a-b x)^4}{b}-\frac{c^3 (a-b x)^6}{6 b}+\frac{4 a c^3 (a-b x)^5}{5 b}",1,"-((a^2*c^3*(a - b*x)^4)/b) + (4*a*c^3*(a - b*x)^5)/(5*b) - (c^3*(a - b*x)^6)/(6*b)","A",2,1,19,0.05263,1,"{43}"
1039,1,38,0,0.0171346,"\int (a+b x)^2 (a c-b c x)^2 \, dx","Int[(a + b*x)^2*(a*c - b*c*x)^2,x]","-\frac{2}{3} a^2 b^2 c^2 x^3+a^4 c^2 x+\frac{1}{5} b^4 c^2 x^5","-\frac{2}{3} a^2 b^2 c^2 x^3+a^4 c^2 x+\frac{1}{5} b^4 c^2 x^5",1,"a^4*c^2*x - (2*a^2*b^2*c^2*x^3)/3 + (b^4*c^2*x^5)/5","A",3,2,19,0.1053,1,"{41, 194}"
1040,1,32,0,0.0149207,"\int (a+b x)^2 (a c-b c x) \, dx","Int[(a + b*x)^2*(a*c - b*c*x),x]","\frac{2 a c (a+b x)^3}{3 b}-\frac{c (a+b x)^4}{4 b}","\frac{2 a c (a+b x)^3}{3 b}-\frac{c (a+b x)^4}{4 b}",1,"(2*a*c*(a + b*x)^3)/(3*b) - (c*(a + b*x)^4)/(4*b)","A",2,1,17,0.05882,1,"{43}"
1041,1,14,0,0.0014589,"\int (a+b x)^2 \, dx","Int[(a + b*x)^2,x]","\frac{(a+b x)^3}{3 b}","\frac{(a+b x)^3}{3 b}",1,"(a + b*x)^3/(3*b)","A",1,1,7,0.1429,1,"{32}"
1042,1,43,0,0.0137355,"\int \frac{(a+b x)^2}{a c-b c x} \, dx","Int[(a + b*x)^2/(a*c - b*c*x),x]","-\frac{4 a^2 \log (a-b x)}{b c}-\frac{(a+b x)^2}{2 b c}-\frac{2 a x}{c}","-\frac{4 a^2 \log (a-b x)}{b c}-\frac{(a+b x)^2}{2 b c}-\frac{2 a x}{c}",1,"(-2*a*x)/c - (a + b*x)^2/(2*b*c) - (4*a^2*Log[a - b*x])/(b*c)","A",2,1,19,0.05263,1,"{43}"
1043,1,41,0,0.0221189,"\int \frac{(a+b x)^2}{(a c-b c x)^2} \, dx","Int[(a + b*x)^2/(a*c - b*c*x)^2,x]","\frac{4 a^2}{b c^2 (a-b x)}+\frac{4 a \log (a-b x)}{b c^2}+\frac{x}{c^2}","\frac{4 a^2}{b c^2 (a-b x)}+\frac{4 a \log (a-b x)}{b c^2}+\frac{x}{c^2}",1,"x/c^2 + (4*a^2)/(b*c^2*(a - b*x)) + (4*a*Log[a - b*x])/(b*c^2)","A",2,1,19,0.05263,1,"{43}"
1044,1,52,0,0.0280616,"\int \frac{(a+b x)^2}{(a c-b c x)^3} \, dx","Int[(a + b*x)^2/(a*c - b*c*x)^3,x]","\frac{2 a^2}{b c^3 (a-b x)^2}-\frac{4 a}{b c^3 (a-b x)}-\frac{\log (a-b x)}{b c^3}","\frac{2 a^2}{b c^3 (a-b x)^2}-\frac{4 a}{b c^3 (a-b x)}-\frac{\log (a-b x)}{b c^3}",1,"(2*a^2)/(b*c^3*(a - b*x)^2) - (4*a)/(b*c^3*(a - b*x)) - Log[a - b*x]/(b*c^3)","A",2,1,19,0.05263,1,"{43}"
1045,1,28,0,0.0051261,"\int \frac{(a+b x)^2}{(a c-b c x)^4} \, dx","Int[(a + b*x)^2/(a*c - b*c*x)^4,x]","\frac{(a+b x)^3}{6 a b c^4 (a-b x)^3}","\frac{(a+b x)^3}{6 a b c^4 (a-b x)^3}",1,"(a + b*x)^3/(6*a*b*c^4*(a - b*x)^3)","A",1,1,19,0.05263,1,"{37}"
1046,1,56,0,0.0237935,"\int \frac{(a+b x)^2}{(a c-b c x)^5} \, dx","Int[(a + b*x)^2/(a*c - b*c*x)^5,x]","\frac{a^2}{b c^5 (a-b x)^4}-\frac{4 a}{3 b c^5 (a-b x)^3}+\frac{1}{2 b c^5 (a-b x)^2}","\frac{a^2}{b c^5 (a-b x)^4}-\frac{4 a}{3 b c^5 (a-b x)^3}+\frac{1}{2 b c^5 (a-b x)^2}",1,"a^2/(b*c^5*(a - b*x)^4) - (4*a)/(3*b*c^5*(a - b*x)^3) + 1/(2*b*c^5*(a - b*x)^2)","A",2,1,19,0.05263,1,"{43}"
1047,1,57,0,0.0248059,"\int \frac{(a+b x)^2}{(a c-b c x)^6} \, dx","Int[(a + b*x)^2/(a*c - b*c*x)^6,x]","\frac{4 a^2}{5 b c^6 (a-b x)^5}-\frac{a}{b c^6 (a-b x)^4}+\frac{1}{3 b c^6 (a-b x)^3}","\frac{4 a^2}{5 b c^6 (a-b x)^5}-\frac{a}{b c^6 (a-b x)^4}+\frac{1}{3 b c^6 (a-b x)^3}",1,"(4*a^2)/(5*b*c^6*(a - b*x)^5) - a/(b*c^6*(a - b*x)^4) + 1/(3*b*c^6*(a - b*x)^3)","A",2,1,19,0.05263,1,"{43}"
1048,1,59,0,0.0290148,"\int \frac{(a+b x)^2}{(a c-b c x)^7} \, dx","Int[(a + b*x)^2/(a*c - b*c*x)^7,x]","\frac{2 a^2}{3 b c^7 (a-b x)^6}-\frac{4 a}{5 b c^7 (a-b x)^5}+\frac{1}{4 b c^7 (a-b x)^4}","\frac{2 a^2}{3 b c^7 (a-b x)^6}-\frac{4 a}{5 b c^7 (a-b x)^5}+\frac{1}{4 b c^7 (a-b x)^4}",1,"(2*a^2)/(3*b*c^7*(a - b*x)^6) - (4*a)/(5*b*c^7*(a - b*x)^5) + 1/(4*b*c^7*(a - b*x)^4)","A",2,1,19,0.05263,1,"{43}"
1049,1,61,0,0.0212865,"\int \frac{(a c-b c x)^3}{a+b x} \, dx","Int[(a*c - b*c*x)^3/(a + b*x),x]","\frac{8 a^3 c^3 \log (a+b x)}{b}-4 a^2 c^3 x+\frac{c^3 (a-b x)^3}{3 b}+\frac{a c^3 (a-b x)^2}{b}","\frac{8 a^3 c^3 \log (a+b x)}{b}-4 a^2 c^3 x+\frac{c^3 (a-b x)^3}{3 b}+\frac{a c^3 (a-b x)^2}{b}",1,"-4*a^2*c^3*x + (a*c^3*(a - b*x)^2)/b + (c^3*(a - b*x)^3)/(3*b) + (8*a^3*c^3*Log[a + b*x])/b","A",2,1,19,0.05263,1,"{43}"
1050,1,43,0,0.0143916,"\int \frac{(a c-b c x)^2}{a+b x} \, dx","Int[(a*c - b*c*x)^2/(a + b*x),x]","\frac{4 a^2 c^2 \log (a+b x)}{b}+\frac{c^2 (a-b x)^2}{2 b}-2 a c^2 x","\frac{4 a^2 c^2 \log (a+b x)}{b}+\frac{c^2 (a-b x)^2}{2 b}-2 a c^2 x",1,"-2*a*c^2*x + (c^2*(a - b*x)^2)/(2*b) + (4*a^2*c^2*Log[a + b*x])/b","A",2,1,19,0.05263,1,"{43}"
1051,1,18,0,0.0103672,"\int \frac{a c-b c x}{a+b x} \, dx","Int[(a*c - b*c*x)/(a + b*x),x]","\frac{2 a c \log (a+b x)}{b}-c x","\frac{2 a c \log (a+b x)}{b}-c x",1,"-(c*x) + (2*a*c*Log[a + b*x])/b","A",2,1,17,0.05882,1,"{43}"
1052,1,10,0,0.0015238,"\int \frac{1}{a+b x} \, dx","Int[(a + b*x)^(-1),x]","\frac{\log (a+b x)}{b}","\frac{\log (a+b x)}{b}",1,"Log[a + b*x]/b","A",1,1,7,0.1429,1,"{31}"
1053,1,17,0,0.0085704,"\int \frac{1}{(a+b x) (a c-b c x)} \, dx","Int[1/((a + b*x)*(a*c - b*c*x)),x]","\frac{\tanh ^{-1}\left(\frac{b x}{a}\right)}{a b c}","\frac{\tanh ^{-1}\left(\frac{b x}{a}\right)}{a b c}",1,"ArcTanh[(b*x)/a]/(a*b*c)","A",2,2,19,0.1053,1,"{35, 208}"
1054,1,42,0,0.0292954,"\int \frac{1}{(a+b x) (a c-b c x)^2} \, dx","Int[1/((a + b*x)*(a*c - b*c*x)^2),x]","\frac{\tanh ^{-1}\left(\frac{b x}{a}\right)}{2 a^2 b c^2}+\frac{1}{2 a b c^2 (a-b x)}","\frac{\tanh ^{-1}\left(\frac{b x}{a}\right)}{2 a^2 b c^2}+\frac{1}{2 a b c^2 (a-b x)}",1,"1/(2*a*b*c^2*(a - b*x)) + ArcTanh[(b*x)/a]/(2*a^2*b*c^2)","A",3,2,19,0.1053,1,"{44, 208}"
1055,1,63,0,0.0385831,"\int \frac{1}{(a+b x) (a c-b c x)^3} \, dx","Int[1/((a + b*x)*(a*c - b*c*x)^3),x]","\frac{1}{4 a^2 b c^3 (a-b x)}+\frac{\tanh ^{-1}\left(\frac{b x}{a}\right)}{4 a^3 b c^3}+\frac{1}{4 a b c^3 (a-b x)^2}","\frac{1}{4 a^2 b c^3 (a-b x)}+\frac{\tanh ^{-1}\left(\frac{b x}{a}\right)}{4 a^3 b c^3}+\frac{1}{4 a b c^3 (a-b x)^2}",1,"1/(4*a*b*c^3*(a - b*x)^2) + 1/(4*a^2*b*c^3*(a - b*x)) + ArcTanh[(b*x)/a]/(4*a^3*b*c^3)","A",3,2,19,0.1053,1,"{44, 208}"
1056,1,54,0,0.0313632,"\int \frac{(a c-b c x)^3}{(a+b x)^2} \, dx","Int[(a*c - b*c*x)^3/(a + b*x)^2,x]","-\frac{8 a^3 c^3}{b (a+b x)}-\frac{12 a^2 c^3 \log (a+b x)}{b}+5 a c^3 x-\frac{1}{2} b c^3 x^2","-\frac{8 a^3 c^3}{b (a+b x)}-\frac{12 a^2 c^3 \log (a+b x)}{b}+5 a c^3 x-\frac{1}{2} b c^3 x^2",1,"5*a*c^3*x - (b*c^3*x^2)/2 - (8*a^3*c^3)/(b*(a + b*x)) - (12*a^2*c^3*Log[a + b*x])/b","A",2,1,19,0.05263,1,"{43}"
1057,1,39,0,0.0209701,"\int \frac{(a c-b c x)^2}{(a+b x)^2} \, dx","Int[(a*c - b*c*x)^2/(a + b*x)^2,x]","-\frac{4 a^2 c^2}{b (a+b x)}-\frac{4 a c^2 \log (a+b x)}{b}+c^2 x","-\frac{4 a^2 c^2}{b (a+b x)}-\frac{4 a c^2 \log (a+b x)}{b}+c^2 x",1,"c^2*x - (4*a^2*c^2)/(b*(a + b*x)) - (4*a*c^2*Log[a + b*x])/b","A",2,1,19,0.05263,1,"{43}"
1058,1,27,0,0.0132458,"\int \frac{a c-b c x}{(a+b x)^2} \, dx","Int[(a*c - b*c*x)/(a + b*x)^2,x]","-\frac{2 a c}{b (a+b x)}-\frac{c \log (a+b x)}{b}","-\frac{2 a c}{b (a+b x)}-\frac{c \log (a+b x)}{b}",1,"(-2*a*c)/(b*(a + b*x)) - (c*Log[a + b*x])/b","A",2,1,17,0.05882,1,"{43}"
1059,1,12,0,0.0014791,"\int \frac{1}{(a+b x)^2} \, dx","Int[(a + b*x)^(-2),x]","-\frac{1}{b (a+b x)}","-\frac{1}{b (a+b x)}",1,"-(1/(b*(a + b*x)))","A",1,1,7,0.1429,1,"{32}"
1060,1,41,0,0.0279136,"\int \frac{1}{(a+b x)^2 (a c-b c x)} \, dx","Int[1/((a + b*x)^2*(a*c - b*c*x)),x]","\frac{\tanh ^{-1}\left(\frac{b x}{a}\right)}{2 a^2 b c}-\frac{1}{2 a b c (a+b x)}","\frac{\tanh ^{-1}\left(\frac{b x}{a}\right)}{2 a^2 b c}-\frac{1}{2 a b c (a+b x)}",1,"-1/(2*a*b*c*(a + b*x)) + ArcTanh[(b*x)/a]/(2*a^2*b*c)","A",3,2,19,0.1053,1,"{44, 208}"
1061,1,46,0,0.0166867,"\int \frac{1}{(a+b x)^2 (a c-b c x)^2} \, dx","Int[1/((a + b*x)^2*(a*c - b*c*x)^2),x]","\frac{x}{2 a^2 c^2 \left(a^2-b^2 x^2\right)}+\frac{\tanh ^{-1}\left(\frac{b x}{a}\right)}{2 a^3 b c^2}","\frac{x}{2 a^2 c^2 \left(a^2-b^2 x^2\right)}+\frac{\tanh ^{-1}\left(\frac{b x}{a}\right)}{2 a^3 b c^2}",1,"x/(2*a^2*c^2*(a^2 - b^2*x^2)) + ArcTanh[(b*x)/a]/(2*a^3*b*c^2)","A",3,3,19,0.1579,1,"{41, 199, 208}"
1062,1,83,0,0.0495295,"\int \frac{1}{(a+b x)^2 (a c-b c x)^3} \, dx","Int[1/((a + b*x)^2*(a*c - b*c*x)^3),x]","\frac{1}{4 a^3 b c^3 (a-b x)}-\frac{1}{8 a^3 b c^3 (a+b x)}+\frac{1}{8 a^2 b c^3 (a-b x)^2}+\frac{3 \tanh ^{-1}\left(\frac{b x}{a}\right)}{8 a^4 b c^3}","\frac{1}{4 a^3 b c^3 (a-b x)}-\frac{1}{8 a^3 b c^3 (a+b x)}+\frac{1}{8 a^2 b c^3 (a-b x)^2}+\frac{3 \tanh ^{-1}\left(\frac{b x}{a}\right)}{8 a^4 b c^3}",1,"1/(8*a^2*b*c^3*(a - b*x)^2) + 1/(4*a^3*b*c^3*(a - b*x)) - 1/(8*a^3*b*c^3*(a + b*x)) + (3*ArcTanh[(b*x)/a])/(8*a^4*b*c^3)","A",3,2,19,0.1053,1,"{44, 208}"
1063,1,108,0,0.02088,"\int (1-x)^{9/2} \sqrt{1+x} \, dx","Int[(1 - x)^(9/2)*Sqrt[1 + x],x]","\frac{1}{6} (x+1)^{3/2} (1-x)^{9/2}+\frac{3}{10} (x+1)^{3/2} (1-x)^{7/2}+\frac{21}{40} (x+1)^{3/2} (1-x)^{5/2}+\frac{7}{8} (x+1)^{3/2} (1-x)^{3/2}+\frac{21}{16} x \sqrt{x+1} \sqrt{1-x}+\frac{21}{16} \sin ^{-1}(x)","\frac{1}{6} (x+1)^{3/2} (1-x)^{9/2}+\frac{3}{10} (x+1)^{3/2} (1-x)^{7/2}+\frac{21}{40} (x+1)^{3/2} (1-x)^{5/2}+\frac{7}{8} (x+1)^{3/2} (1-x)^{3/2}+\frac{21}{16} x \sqrt{x+1} \sqrt{1-x}+\frac{21}{16} \sin ^{-1}(x)",1,"(21*Sqrt[1 - x]*x*Sqrt[1 + x])/16 + (7*(1 - x)^(3/2)*(1 + x)^(3/2))/8 + (21*(1 - x)^(5/2)*(1 + x)^(3/2))/40 + (3*(1 - x)^(7/2)*(1 + x)^(3/2))/10 + ((1 - x)^(9/2)*(1 + x)^(3/2))/6 + (21*ArcSin[x])/16","A",7,4,17,0.2353,1,"{49, 38, 41, 216}"
1064,1,88,0,0.0153782,"\int (1-x)^{7/2} \sqrt{1+x} \, dx","Int[(1 - x)^(7/2)*Sqrt[1 + x],x]","\frac{1}{5} (x+1)^{3/2} (1-x)^{7/2}+\frac{7}{20} (x+1)^{3/2} (1-x)^{5/2}+\frac{7}{12} (x+1)^{3/2} (1-x)^{3/2}+\frac{7}{8} x \sqrt{x+1} \sqrt{1-x}+\frac{7}{8} \sin ^{-1}(x)","\frac{1}{5} (x+1)^{3/2} (1-x)^{7/2}+\frac{7}{20} (x+1)^{3/2} (1-x)^{5/2}+\frac{7}{12} (x+1)^{3/2} (1-x)^{3/2}+\frac{7}{8} x \sqrt{x+1} \sqrt{1-x}+\frac{7}{8} \sin ^{-1}(x)",1,"(7*Sqrt[1 - x]*x*Sqrt[1 + x])/8 + (7*(1 - x)^(3/2)*(1 + x)^(3/2))/12 + (7*(1 - x)^(5/2)*(1 + x)^(3/2))/20 + ((1 - x)^(7/2)*(1 + x)^(3/2))/5 + (7*ArcSin[x])/8","A",6,4,17,0.2353,1,"{49, 38, 41, 216}"
1065,1,68,0,0.010737,"\int (1-x)^{5/2} \sqrt{1+x} \, dx","Int[(1 - x)^(5/2)*Sqrt[1 + x],x]","\frac{1}{4} (x+1)^{3/2} (1-x)^{5/2}+\frac{5}{12} (x+1)^{3/2} (1-x)^{3/2}+\frac{5}{8} x \sqrt{x+1} \sqrt{1-x}+\frac{5}{8} \sin ^{-1}(x)","\frac{1}{4} (x+1)^{3/2} (1-x)^{5/2}+\frac{5}{12} (x+1)^{3/2} (1-x)^{3/2}+\frac{5}{8} x \sqrt{x+1} \sqrt{1-x}+\frac{5}{8} \sin ^{-1}(x)",1,"(5*Sqrt[1 - x]*x*Sqrt[1 + x])/8 + (5*(1 - x)^(3/2)*(1 + x)^(3/2))/12 + ((1 - x)^(5/2)*(1 + x)^(3/2))/4 + (5*ArcSin[x])/8","A",5,4,17,0.2353,1,"{49, 38, 41, 216}"
1066,1,48,0,0.0056664,"\int (1-x)^{3/2} \sqrt{1+x} \, dx","Int[(1 - x)^(3/2)*Sqrt[1 + x],x]","\frac{1}{3} (1-x)^{3/2} (x+1)^{3/2}+\frac{1}{2} \sqrt{1-x} x \sqrt{x+1}+\frac{1}{2} \sin ^{-1}(x)","\frac{1}{3} (1-x)^{3/2} (x+1)^{3/2}+\frac{1}{2} \sqrt{1-x} x \sqrt{x+1}+\frac{1}{2} \sin ^{-1}(x)",1,"(Sqrt[1 - x]*x*Sqrt[1 + x])/2 + ((1 - x)^(3/2)*(1 + x)^(3/2))/3 + ArcSin[x]/2","A",4,4,17,0.2353,1,"{49, 38, 41, 216}"
1067,1,28,0,0.0035754,"\int \sqrt{1-x} \sqrt{1+x} \, dx","Int[Sqrt[1 - x]*Sqrt[1 + x],x]","\frac{1}{2} \sqrt{1-x} \sqrt{x+1} x+\frac{1}{2} \sin ^{-1}(x)","\frac{1}{2} \sqrt{1-x} \sqrt{x+1} x+\frac{1}{2} \sin ^{-1}(x)",1,"(Sqrt[1 - x]*x*Sqrt[1 + x])/2 + ArcSin[x]/2","A",3,3,17,0.1765,1,"{38, 41, 216}"
1068,1,21,0,0.00379,"\int \frac{\sqrt{1+x}}{\sqrt{1-x}} \, dx","Int[Sqrt[1 + x]/Sqrt[1 - x],x]","\sin ^{-1}(x)-\sqrt{1-x} \sqrt{x+1}","\sin ^{-1}(x)-\sqrt{1-x} \sqrt{x+1}",1,"-(Sqrt[1 - x]*Sqrt[1 + x]) + ArcSin[x]","A",3,3,17,0.1765,1,"{50, 41, 216}"
1069,1,23,0,0.0037246,"\int \frac{\sqrt{1+x}}{(1-x)^{3/2}} \, dx","Int[Sqrt[1 + x]/(1 - x)^(3/2),x]","\frac{2 \sqrt{x+1}}{\sqrt{1-x}}-\sin ^{-1}(x)","\frac{2 \sqrt{x+1}}{\sqrt{1-x}}-\sin ^{-1}(x)",1,"(2*Sqrt[1 + x])/Sqrt[1 - x] - ArcSin[x]","A",3,3,17,0.1765,1,"{47, 41, 216}"
1070,1,20,0,0.0015894,"\int \frac{\sqrt{1+x}}{(1-x)^{5/2}} \, dx","Int[Sqrt[1 + x]/(1 - x)^(5/2),x]","\frac{(x+1)^{3/2}}{3 (1-x)^{3/2}}","\frac{(x+1)^{3/2}}{3 (1-x)^{3/2}}",1,"(1 + x)^(3/2)/(3*(1 - x)^(3/2))","A",1,1,17,0.05882,1,"{37}"
1071,1,41,0,0.0042463,"\int \frac{\sqrt{1+x}}{(1-x)^{7/2}} \, dx","Int[Sqrt[1 + x]/(1 - x)^(7/2),x]","\frac{(x+1)^{3/2}}{15 (1-x)^{3/2}}+\frac{(x+1)^{3/2}}{5 (1-x)^{5/2}}","\frac{(x+1)^{3/2}}{15 (1-x)^{3/2}}+\frac{(x+1)^{3/2}}{5 (1-x)^{5/2}}",1,"(1 + x)^(3/2)/(5*(1 - x)^(5/2)) + (1 + x)^(3/2)/(15*(1 - x)^(3/2))","A",2,2,17,0.1176,1,"{45, 37}"
1072,1,61,0,0.0082057,"\int \frac{\sqrt{1+x}}{(1-x)^{9/2}} \, dx","Int[Sqrt[1 + x]/(1 - x)^(9/2),x]","\frac{2 (x+1)^{3/2}}{105 (1-x)^{3/2}}+\frac{2 (x+1)^{3/2}}{35 (1-x)^{5/2}}+\frac{(x+1)^{3/2}}{7 (1-x)^{7/2}}","\frac{2 (x+1)^{3/2}}{105 (1-x)^{3/2}}+\frac{2 (x+1)^{3/2}}{35 (1-x)^{5/2}}+\frac{(x+1)^{3/2}}{7 (1-x)^{7/2}}",1,"(1 + x)^(3/2)/(7*(1 - x)^(7/2)) + (2*(1 + x)^(3/2))/(35*(1 - x)^(5/2)) + (2*(1 + x)^(3/2))/(105*(1 - x)^(3/2))","A",3,2,17,0.1176,1,"{45, 37}"
1073,1,81,0,0.0130847,"\int \frac{\sqrt{1+x}}{(1-x)^{11/2}} \, dx","Int[Sqrt[1 + x]/(1 - x)^(11/2),x]","\frac{2 (x+1)^{3/2}}{315 (1-x)^{3/2}}+\frac{2 (x+1)^{3/2}}{105 (1-x)^{5/2}}+\frac{(x+1)^{3/2}}{21 (1-x)^{7/2}}+\frac{(x+1)^{3/2}}{9 (1-x)^{9/2}}","\frac{2 (x+1)^{3/2}}{315 (1-x)^{3/2}}+\frac{2 (x+1)^{3/2}}{105 (1-x)^{5/2}}+\frac{(x+1)^{3/2}}{21 (1-x)^{7/2}}+\frac{(x+1)^{3/2}}{9 (1-x)^{9/2}}",1,"(1 + x)^(3/2)/(9*(1 - x)^(9/2)) + (1 + x)^(3/2)/(21*(1 - x)^(7/2)) + (2*(1 + x)^(3/2))/(105*(1 - x)^(5/2)) + (2*(1 + x)^(3/2))/(315*(1 - x)^(3/2))","A",4,2,17,0.1176,1,"{45, 37}"
1074,1,101,0,0.0186567,"\int \frac{\sqrt{1+x}}{(1-x)^{13/2}} \, dx","Int[Sqrt[1 + x]/(1 - x)^(13/2),x]","\frac{8 (x+1)^{3/2}}{3465 (1-x)^{3/2}}+\frac{8 (x+1)^{3/2}}{1155 (1-x)^{5/2}}+\frac{4 (x+1)^{3/2}}{231 (1-x)^{7/2}}+\frac{4 (x+1)^{3/2}}{99 (1-x)^{9/2}}+\frac{(x+1)^{3/2}}{11 (1-x)^{11/2}}","\frac{8 (x+1)^{3/2}}{3465 (1-x)^{3/2}}+\frac{8 (x+1)^{3/2}}{1155 (1-x)^{5/2}}+\frac{4 (x+1)^{3/2}}{231 (1-x)^{7/2}}+\frac{4 (x+1)^{3/2}}{99 (1-x)^{9/2}}+\frac{(x+1)^{3/2}}{11 (1-x)^{11/2}}",1,"(1 + x)^(3/2)/(11*(1 - x)^(11/2)) + (4*(1 + x)^(3/2))/(99*(1 - x)^(9/2)) + (4*(1 + x)^(3/2))/(231*(1 - x)^(7/2)) + (8*(1 + x)^(3/2))/(1155*(1 - x)^(5/2)) + (8*(1 + x)^(3/2))/(3465*(1 - x)^(3/2))","A",5,2,17,0.1176,1,"{45, 37}"
1075,1,109,0,0.0197551,"\int (1-x)^{9/2} (1+x)^{3/2} \, dx","Int[(1 - x)^(9/2)*(1 + x)^(3/2),x]","\frac{1}{7} (x+1)^{5/2} (1-x)^{9/2}+\frac{3}{14} (x+1)^{5/2} (1-x)^{7/2}+\frac{3}{10} (x+1)^{5/2} (1-x)^{5/2}+\frac{3}{8} x (x+1)^{3/2} (1-x)^{3/2}+\frac{9}{16} x \sqrt{x+1} \sqrt{1-x}+\frac{9}{16} \sin ^{-1}(x)","\frac{1}{7} (x+1)^{5/2} (1-x)^{9/2}+\frac{3}{14} (x+1)^{5/2} (1-x)^{7/2}+\frac{3}{10} (x+1)^{5/2} (1-x)^{5/2}+\frac{3}{8} x (x+1)^{3/2} (1-x)^{3/2}+\frac{9}{16} x \sqrt{x+1} \sqrt{1-x}+\frac{9}{16} \sin ^{-1}(x)",1,"(9*Sqrt[1 - x]*x*Sqrt[1 + x])/16 + (3*(1 - x)^(3/2)*x*(1 + x)^(3/2))/8 + (3*(1 - x)^(5/2)*(1 + x)^(5/2))/10 + (3*(1 - x)^(7/2)*(1 + x)^(5/2))/14 + ((1 - x)^(9/2)*(1 + x)^(5/2))/7 + (9*ArcSin[x])/16","A",7,4,17,0.2353,1,"{49, 38, 41, 216}"
1076,1,89,0,0.0133954,"\int (1-x)^{7/2} (1+x)^{3/2} \, dx","Int[(1 - x)^(7/2)*(1 + x)^(3/2),x]","\frac{1}{6} (x+1)^{5/2} (1-x)^{7/2}+\frac{7}{30} (x+1)^{5/2} (1-x)^{5/2}+\frac{7}{24} x (x+1)^{3/2} (1-x)^{3/2}+\frac{7}{16} x \sqrt{x+1} \sqrt{1-x}+\frac{7}{16} \sin ^{-1}(x)","\frac{1}{6} (x+1)^{5/2} (1-x)^{7/2}+\frac{7}{30} (x+1)^{5/2} (1-x)^{5/2}+\frac{7}{24} x (x+1)^{3/2} (1-x)^{3/2}+\frac{7}{16} x \sqrt{x+1} \sqrt{1-x}+\frac{7}{16} \sin ^{-1}(x)",1,"(7*Sqrt[1 - x]*x*Sqrt[1 + x])/16 + (7*(1 - x)^(3/2)*x*(1 + x)^(3/2))/24 + (7*(1 - x)^(5/2)*(1 + x)^(5/2))/30 + ((1 - x)^(7/2)*(1 + x)^(5/2))/6 + (7*ArcSin[x])/16","A",6,4,17,0.2353,1,"{49, 38, 41, 216}"
1077,1,69,0,0.0081353,"\int (1-x)^{5/2} (1+x)^{3/2} \, dx","Int[(1 - x)^(5/2)*(1 + x)^(3/2),x]","\frac{1}{5} (1-x)^{5/2} (x+1)^{5/2}+\frac{1}{4} (1-x)^{3/2} x (x+1)^{3/2}+\frac{3}{8} \sqrt{1-x} x \sqrt{x+1}+\frac{3}{8} \sin ^{-1}(x)","\frac{1}{5} (1-x)^{5/2} (x+1)^{5/2}+\frac{1}{4} (1-x)^{3/2} x (x+1)^{3/2}+\frac{3}{8} \sqrt{1-x} x \sqrt{x+1}+\frac{3}{8} \sin ^{-1}(x)",1,"(3*Sqrt[1 - x]*x*Sqrt[1 + x])/8 + ((1 - x)^(3/2)*x*(1 + x)^(3/2))/4 + ((1 - x)^(5/2)*(1 + x)^(5/2))/5 + (3*ArcSin[x])/8","A",5,4,17,0.2353,1,"{49, 38, 41, 216}"
1078,1,49,0,0.0066708,"\int (1-x)^{3/2} (1+x)^{3/2} \, dx","Int[(1 - x)^(3/2)*(1 + x)^(3/2),x]","\frac{1}{4} (1-x)^{3/2} x (x+1)^{3/2}+\frac{3}{8} \sqrt{1-x} x \sqrt{x+1}+\frac{3}{8} \sin ^{-1}(x)","\frac{1}{4} (1-x)^{3/2} x (x+1)^{3/2}+\frac{3}{8} \sqrt{1-x} x \sqrt{x+1}+\frac{3}{8} \sin ^{-1}(x)",1,"(3*Sqrt[1 - x]*x*Sqrt[1 + x])/8 + ((1 - x)^(3/2)*x*(1 + x)^(3/2))/4 + (3*ArcSin[x])/8","A",4,3,17,0.1765,1,"{38, 41, 216}"
1079,1,48,0,0.0055341,"\int \sqrt{1-x} (1+x)^{3/2} \, dx","Int[Sqrt[1 - x]*(1 + x)^(3/2),x]","-\frac{1}{3} (1-x)^{3/2} (x+1)^{3/2}+\frac{1}{2} \sqrt{1-x} x \sqrt{x+1}+\frac{1}{2} \sin ^{-1}(x)","-\frac{1}{3} (1-x)^{3/2} (x+1)^{3/2}+\frac{1}{2} \sqrt{1-x} x \sqrt{x+1}+\frac{1}{2} \sin ^{-1}(x)",1,"(Sqrt[1 - x]*x*Sqrt[1 + x])/2 - ((1 - x)^(3/2)*(1 + x)^(3/2))/3 + ArcSin[x]/2","A",4,4,17,0.2353,1,"{49, 38, 41, 216}"
1080,1,47,0,0.006518,"\int \frac{(1+x)^{3/2}}{\sqrt{1-x}} \, dx","Int[(1 + x)^(3/2)/Sqrt[1 - x],x]","-\frac{1}{2} \sqrt{1-x} (x+1)^{3/2}-\frac{3}{2} \sqrt{1-x} \sqrt{x+1}+\frac{3}{2} \sin ^{-1}(x)","-\frac{1}{2} \sqrt{1-x} (x+1)^{3/2}-\frac{3}{2} \sqrt{1-x} \sqrt{x+1}+\frac{3}{2} \sin ^{-1}(x)",1,"(-3*Sqrt[1 - x]*Sqrt[1 + x])/2 - (Sqrt[1 - x]*(1 + x)^(3/2))/2 + (3*ArcSin[x])/2","A",4,3,17,0.1765,1,"{50, 41, 216}"
1081,1,41,0,0.0065135,"\int \frac{(1+x)^{3/2}}{(1-x)^{3/2}} \, dx","Int[(1 + x)^(3/2)/(1 - x)^(3/2),x]","\frac{2 (x+1)^{3/2}}{\sqrt{1-x}}+3 \sqrt{1-x} \sqrt{x+1}-3 \sin ^{-1}(x)","\frac{2 (x+1)^{3/2}}{\sqrt{1-x}}+3 \sqrt{1-x} \sqrt{x+1}-3 \sin ^{-1}(x)",1,"3*Sqrt[1 - x]*Sqrt[1 + x] + (2*(1 + x)^(3/2))/Sqrt[1 - x] - 3*ArcSin[x]","A",4,4,17,0.2353,1,"{47, 50, 41, 216}"
1082,1,41,0,0.0050945,"\int \frac{(1+x)^{3/2}}{(1-x)^{5/2}} \, dx","Int[(1 + x)^(3/2)/(1 - x)^(5/2),x]","\frac{2 (x+1)^{3/2}}{3 (1-x)^{3/2}}-\frac{2 \sqrt{x+1}}{\sqrt{1-x}}+\sin ^{-1}(x)","\frac{2 (x+1)^{3/2}}{3 (1-x)^{3/2}}-\frac{2 \sqrt{x+1}}{\sqrt{1-x}}+\sin ^{-1}(x)",1,"(-2*Sqrt[1 + x])/Sqrt[1 - x] + (2*(1 + x)^(3/2))/(3*(1 - x)^(3/2)) + ArcSin[x]","A",4,3,17,0.1765,1,"{47, 41, 216}"
1083,1,20,0,0.0016671,"\int \frac{(1+x)^{3/2}}{(1-x)^{7/2}} \, dx","Int[(1 + x)^(3/2)/(1 - x)^(7/2),x]","\frac{(x+1)^{5/2}}{5 (1-x)^{5/2}}","\frac{(x+1)^{5/2}}{5 (1-x)^{5/2}}",1,"(1 + x)^(5/2)/(5*(1 - x)^(5/2))","A",1,1,17,0.05882,1,"{37}"
1084,1,41,0,0.0041896,"\int \frac{(1+x)^{3/2}}{(1-x)^{9/2}} \, dx","Int[(1 + x)^(3/2)/(1 - x)^(9/2),x]","\frac{(x+1)^{5/2}}{35 (1-x)^{5/2}}+\frac{(x+1)^{5/2}}{7 (1-x)^{7/2}}","\frac{(x+1)^{5/2}}{35 (1-x)^{5/2}}+\frac{(x+1)^{5/2}}{7 (1-x)^{7/2}}",1,"(1 + x)^(5/2)/(7*(1 - x)^(7/2)) + (1 + x)^(5/2)/(35*(1 - x)^(5/2))","A",2,2,17,0.1176,1,"{45, 37}"
1085,1,61,0,0.0080453,"\int \frac{(1+x)^{3/2}}{(1-x)^{11/2}} \, dx","Int[(1 + x)^(3/2)/(1 - x)^(11/2),x]","\frac{2 (x+1)^{5/2}}{315 (1-x)^{5/2}}+\frac{2 (x+1)^{5/2}}{63 (1-x)^{7/2}}+\frac{(x+1)^{5/2}}{9 (1-x)^{9/2}}","\frac{2 (x+1)^{5/2}}{315 (1-x)^{5/2}}+\frac{2 (x+1)^{5/2}}{63 (1-x)^{7/2}}+\frac{(x+1)^{5/2}}{9 (1-x)^{9/2}}",1,"(1 + x)^(5/2)/(9*(1 - x)^(9/2)) + (2*(1 + x)^(5/2))/(63*(1 - x)^(7/2)) + (2*(1 + x)^(5/2))/(315*(1 - x)^(5/2))","A",3,2,17,0.1176,1,"{45, 37}"
1086,1,81,0,0.0131675,"\int \frac{(1+x)^{3/2}}{(1-x)^{13/2}} \, dx","Int[(1 + x)^(3/2)/(1 - x)^(13/2),x]","\frac{2 (x+1)^{5/2}}{1155 (1-x)^{5/2}}+\frac{2 (x+1)^{5/2}}{231 (1-x)^{7/2}}+\frac{(x+1)^{5/2}}{33 (1-x)^{9/2}}+\frac{(x+1)^{5/2}}{11 (1-x)^{11/2}}","\frac{2 (x+1)^{5/2}}{1155 (1-x)^{5/2}}+\frac{2 (x+1)^{5/2}}{231 (1-x)^{7/2}}+\frac{(x+1)^{5/2}}{33 (1-x)^{9/2}}+\frac{(x+1)^{5/2}}{11 (1-x)^{11/2}}",1,"(1 + x)^(5/2)/(11*(1 - x)^(11/2)) + (1 + x)^(5/2)/(33*(1 - x)^(9/2)) + (2*(1 + x)^(5/2))/(231*(1 - x)^(7/2)) + (2*(1 + x)^(5/2))/(1155*(1 - x)^(5/2))","A",4,2,17,0.1176,1,"{45, 37}"
1087,1,101,0,0.0192798,"\int \frac{(1+x)^{3/2}}{(1-x)^{15/2}} \, dx","Int[(1 + x)^(3/2)/(1 - x)^(15/2),x]","\frac{8 (x+1)^{5/2}}{15015 (1-x)^{5/2}}+\frac{8 (x+1)^{5/2}}{3003 (1-x)^{7/2}}+\frac{4 (x+1)^{5/2}}{429 (1-x)^{9/2}}+\frac{4 (x+1)^{5/2}}{143 (1-x)^{11/2}}+\frac{(x+1)^{5/2}}{13 (1-x)^{13/2}}","\frac{8 (x+1)^{5/2}}{15015 (1-x)^{5/2}}+\frac{8 (x+1)^{5/2}}{3003 (1-x)^{7/2}}+\frac{4 (x+1)^{5/2}}{429 (1-x)^{9/2}}+\frac{4 (x+1)^{5/2}}{143 (1-x)^{11/2}}+\frac{(x+1)^{5/2}}{13 (1-x)^{13/2}}",1,"(1 + x)^(5/2)/(13*(1 - x)^(13/2)) + (4*(1 + x)^(5/2))/(143*(1 - x)^(11/2)) + (4*(1 + x)^(5/2))/(429*(1 - x)^(9/2)) + (8*(1 + x)^(5/2))/(3003*(1 - x)^(7/2)) + (8*(1 + x)^(5/2))/(15015*(1 - x)^(5/2))","A",5,2,17,0.1176,1,"{45, 37}"
1088,1,130,0,0.0254404,"\int (1-x)^{11/2} (1+x)^{5/2} \, dx","Int[(1 - x)^(11/2)*(1 + x)^(5/2),x]","\frac{1}{9} (x+1)^{7/2} (1-x)^{11/2}+\frac{11}{72} (x+1)^{7/2} (1-x)^{9/2}+\frac{11}{56} (x+1)^{7/2} (1-x)^{7/2}+\frac{11}{48} x (x+1)^{5/2} (1-x)^{5/2}+\frac{55}{192} x (x+1)^{3/2} (1-x)^{3/2}+\frac{55}{128} x \sqrt{x+1} \sqrt{1-x}+\frac{55}{128} \sin ^{-1}(x)","\frac{1}{9} (x+1)^{7/2} (1-x)^{11/2}+\frac{11}{72} (x+1)^{7/2} (1-x)^{9/2}+\frac{11}{56} (x+1)^{7/2} (1-x)^{7/2}+\frac{11}{48} x (x+1)^{5/2} (1-x)^{5/2}+\frac{55}{192} x (x+1)^{3/2} (1-x)^{3/2}+\frac{55}{128} x \sqrt{x+1} \sqrt{1-x}+\frac{55}{128} \sin ^{-1}(x)",1,"(55*Sqrt[1 - x]*x*Sqrt[1 + x])/128 + (55*(1 - x)^(3/2)*x*(1 + x)^(3/2))/192 + (11*(1 - x)^(5/2)*x*(1 + x)^(5/2))/48 + (11*(1 - x)^(7/2)*(1 + x)^(7/2))/56 + (11*(1 - x)^(9/2)*(1 + x)^(7/2))/72 + ((1 - x)^(11/2)*(1 + x)^(7/2))/9 + (55*ArcSin[x])/128","A",8,4,17,0.2353,1,"{49, 38, 41, 216}"
1089,1,110,0,0.0191855,"\int (1-x)^{9/2} (1+x)^{5/2} \, dx","Int[(1 - x)^(9/2)*(1 + x)^(5/2),x]","\frac{1}{8} (x+1)^{7/2} (1-x)^{9/2}+\frac{9}{56} (x+1)^{7/2} (1-x)^{7/2}+\frac{3}{16} x (x+1)^{5/2} (1-x)^{5/2}+\frac{15}{64} x (x+1)^{3/2} (1-x)^{3/2}+\frac{45}{128} x \sqrt{x+1} \sqrt{1-x}+\frac{45}{128} \sin ^{-1}(x)","\frac{1}{8} (x+1)^{7/2} (1-x)^{9/2}+\frac{9}{56} (x+1)^{7/2} (1-x)^{7/2}+\frac{3}{16} x (x+1)^{5/2} (1-x)^{5/2}+\frac{15}{64} x (x+1)^{3/2} (1-x)^{3/2}+\frac{45}{128} x \sqrt{x+1} \sqrt{1-x}+\frac{45}{128} \sin ^{-1}(x)",1,"(45*Sqrt[1 - x]*x*Sqrt[1 + x])/128 + (15*(1 - x)^(3/2)*x*(1 + x)^(3/2))/64 + (3*(1 - x)^(5/2)*x*(1 + x)^(5/2))/16 + (9*(1 - x)^(7/2)*(1 + x)^(7/2))/56 + ((1 - x)^(9/2)*(1 + x)^(7/2))/8 + (45*ArcSin[x])/128","A",7,4,17,0.2353,1,"{49, 38, 41, 216}"
1090,1,90,0,0.0119287,"\int (1-x)^{7/2} (1+x)^{5/2} \, dx","Int[(1 - x)^(7/2)*(1 + x)^(5/2),x]","\frac{1}{7} (1-x)^{7/2} (x+1)^{7/2}+\frac{1}{6} (1-x)^{5/2} x (x+1)^{5/2}+\frac{5}{24} (1-x)^{3/2} x (x+1)^{3/2}+\frac{5}{16} \sqrt{1-x} x \sqrt{x+1}+\frac{5}{16} \sin ^{-1}(x)","\frac{1}{7} (1-x)^{7/2} (x+1)^{7/2}+\frac{1}{6} (1-x)^{5/2} x (x+1)^{5/2}+\frac{5}{24} (1-x)^{3/2} x (x+1)^{3/2}+\frac{5}{16} \sqrt{1-x} x \sqrt{x+1}+\frac{5}{16} \sin ^{-1}(x)",1,"(5*Sqrt[1 - x]*x*Sqrt[1 + x])/16 + (5*(1 - x)^(3/2)*x*(1 + x)^(3/2))/24 + ((1 - x)^(5/2)*x*(1 + x)^(5/2))/6 + ((1 - x)^(7/2)*(1 + x)^(7/2))/7 + (5*ArcSin[x])/16","A",6,4,17,0.2353,1,"{49, 38, 41, 216}"
1091,1,70,0,0.0107479,"\int (1-x)^{5/2} (1+x)^{5/2} \, dx","Int[(1 - x)^(5/2)*(1 + x)^(5/2),x]","\frac{1}{6} (1-x)^{5/2} x (x+1)^{5/2}+\frac{5}{24} (1-x)^{3/2} x (x+1)^{3/2}+\frac{5}{16} \sqrt{1-x} x \sqrt{x+1}+\frac{5}{16} \sin ^{-1}(x)","\frac{1}{6} (1-x)^{5/2} x (x+1)^{5/2}+\frac{5}{24} (1-x)^{3/2} x (x+1)^{3/2}+\frac{5}{16} \sqrt{1-x} x \sqrt{x+1}+\frac{5}{16} \sin ^{-1}(x)",1,"(5*Sqrt[1 - x]*x*Sqrt[1 + x])/16 + (5*(1 - x)^(3/2)*x*(1 + x)^(3/2))/24 + ((1 - x)^(5/2)*x*(1 + x)^(5/2))/6 + (5*ArcSin[x])/16","A",5,3,17,0.1765,1,"{38, 41, 216}"
1092,1,69,0,0.0080006,"\int (1-x)^{3/2} (1+x)^{5/2} \, dx","Int[(1 - x)^(3/2)*(1 + x)^(5/2),x]","-\frac{1}{5} (1-x)^{5/2} (x+1)^{5/2}+\frac{1}{4} (1-x)^{3/2} x (x+1)^{3/2}+\frac{3}{8} \sqrt{1-x} x \sqrt{x+1}+\frac{3}{8} \sin ^{-1}(x)","-\frac{1}{5} (1-x)^{5/2} (x+1)^{5/2}+\frac{1}{4} (1-x)^{3/2} x (x+1)^{3/2}+\frac{3}{8} \sqrt{1-x} x \sqrt{x+1}+\frac{3}{8} \sin ^{-1}(x)",1,"(3*Sqrt[1 - x]*x*Sqrt[1 + x])/8 + ((1 - x)^(3/2)*x*(1 + x)^(3/2))/4 - ((1 - x)^(5/2)*(1 + x)^(5/2))/5 + (3*ArcSin[x])/8","A",5,4,17,0.2353,1,"{49, 38, 41, 216}"
1093,1,68,0,0.0091997,"\int \sqrt{1-x} (1+x)^{5/2} \, dx","Int[Sqrt[1 - x]*(1 + x)^(5/2),x]","-\frac{1}{4} (1-x)^{3/2} (x+1)^{5/2}-\frac{5}{12} (1-x)^{3/2} (x+1)^{3/2}+\frac{5}{8} \sqrt{1-x} x \sqrt{x+1}+\frac{5}{8} \sin ^{-1}(x)","-\frac{1}{4} (1-x)^{3/2} (x+1)^{5/2}-\frac{5}{12} (1-x)^{3/2} (x+1)^{3/2}+\frac{5}{8} \sqrt{1-x} x \sqrt{x+1}+\frac{5}{8} \sin ^{-1}(x)",1,"(5*Sqrt[1 - x]*x*Sqrt[1 + x])/8 - (5*(1 - x)^(3/2)*(1 + x)^(3/2))/12 - ((1 - x)^(3/2)*(1 + x)^(5/2))/4 + (5*ArcSin[x])/8","A",5,4,17,0.2353,1,"{49, 38, 41, 216}"
1094,1,67,0,0.0103963,"\int \frac{(1+x)^{5/2}}{\sqrt{1-x}} \, dx","Int[(1 + x)^(5/2)/Sqrt[1 - x],x]","-\frac{1}{3} \sqrt{1-x} (x+1)^{5/2}-\frac{5}{6} \sqrt{1-x} (x+1)^{3/2}-\frac{5}{2} \sqrt{1-x} \sqrt{x+1}+\frac{5}{2} \sin ^{-1}(x)","-\frac{1}{3} \sqrt{1-x} (x+1)^{5/2}-\frac{5}{6} \sqrt{1-x} (x+1)^{3/2}-\frac{5}{2} \sqrt{1-x} \sqrt{x+1}+\frac{5}{2} \sin ^{-1}(x)",1,"(-5*Sqrt[1 - x]*Sqrt[1 + x])/2 - (5*Sqrt[1 - x]*(1 + x)^(3/2))/6 - (Sqrt[1 - x]*(1 + x)^(5/2))/3 + (5*ArcSin[x])/2","A",5,3,17,0.1765,1,"{50, 41, 216}"
1095,1,65,0,0.0103244,"\int \frac{(1+x)^{5/2}}{(1-x)^{3/2}} \, dx","Int[(1 + x)^(5/2)/(1 - x)^(3/2),x]","\frac{2 (x+1)^{5/2}}{\sqrt{1-x}}+\frac{5}{2} \sqrt{1-x} (x+1)^{3/2}+\frac{15}{2} \sqrt{1-x} \sqrt{x+1}-\frac{15}{2} \sin ^{-1}(x)","\frac{2 (x+1)^{5/2}}{\sqrt{1-x}}+\frac{5}{2} \sqrt{1-x} (x+1)^{3/2}+\frac{15}{2} \sqrt{1-x} \sqrt{x+1}-\frac{15}{2} \sin ^{-1}(x)",1,"(15*Sqrt[1 - x]*Sqrt[1 + x])/2 + (5*Sqrt[1 - x]*(1 + x)^(3/2))/2 + (2*(1 + x)^(5/2))/Sqrt[1 - x] - (15*ArcSin[x])/2","A",5,4,17,0.2353,1,"{47, 50, 41, 216}"
1096,1,63,0,0.0101658,"\int \frac{(1+x)^{5/2}}{(1-x)^{5/2}} \, dx","Int[(1 + x)^(5/2)/(1 - x)^(5/2),x]","\frac{2 (x+1)^{5/2}}{3 (1-x)^{3/2}}-\frac{10 (x+1)^{3/2}}{3 \sqrt{1-x}}-5 \sqrt{1-x} \sqrt{x+1}+5 \sin ^{-1}(x)","\frac{2 (x+1)^{5/2}}{3 (1-x)^{3/2}}-\frac{10 (x+1)^{3/2}}{3 \sqrt{1-x}}-5 \sqrt{1-x} \sqrt{x+1}+5 \sin ^{-1}(x)",1,"-5*Sqrt[1 - x]*Sqrt[1 + x] - (10*(1 + x)^(3/2))/(3*Sqrt[1 - x]) + (2*(1 + x)^(5/2))/(3*(1 - x)^(3/2)) + 5*ArcSin[x]","A",5,4,17,0.2353,1,"{47, 50, 41, 216}"
1097,1,63,0,0.0073775,"\int \frac{(1+x)^{5/2}}{(1-x)^{7/2}} \, dx","Int[(1 + x)^(5/2)/(1 - x)^(7/2),x]","\frac{2 (x+1)^{5/2}}{5 (1-x)^{5/2}}-\frac{2 (x+1)^{3/2}}{3 (1-x)^{3/2}}+\frac{2 \sqrt{x+1}}{\sqrt{1-x}}-\sin ^{-1}(x)","\frac{2 (x+1)^{5/2}}{5 (1-x)^{5/2}}-\frac{2 (x+1)^{3/2}}{3 (1-x)^{3/2}}+\frac{2 \sqrt{x+1}}{\sqrt{1-x}}-\sin ^{-1}(x)",1,"(2*Sqrt[1 + x])/Sqrt[1 - x] - (2*(1 + x)^(3/2))/(3*(1 - x)^(3/2)) + (2*(1 + x)^(5/2))/(5*(1 - x)^(5/2)) - ArcSin[x]","A",5,3,17,0.1765,1,"{47, 41, 216}"
1098,1,20,0,0.0017708,"\int \frac{(1+x)^{5/2}}{(1-x)^{9/2}} \, dx","Int[(1 + x)^(5/2)/(1 - x)^(9/2),x]","\frac{(x+1)^{7/2}}{7 (1-x)^{7/2}}","\frac{(x+1)^{7/2}}{7 (1-x)^{7/2}}",1,"(1 + x)^(7/2)/(7*(1 - x)^(7/2))","A",1,1,17,0.05882,1,"{37}"
1099,1,41,0,0.0043577,"\int \frac{(1+x)^{5/2}}{(1-x)^{11/2}} \, dx","Int[(1 + x)^(5/2)/(1 - x)^(11/2),x]","\frac{(x+1)^{7/2}}{63 (1-x)^{7/2}}+\frac{(x+1)^{7/2}}{9 (1-x)^{9/2}}","\frac{(x+1)^{7/2}}{63 (1-x)^{7/2}}+\frac{(x+1)^{7/2}}{9 (1-x)^{9/2}}",1,"(1 + x)^(7/2)/(9*(1 - x)^(9/2)) + (1 + x)^(7/2)/(63*(1 - x)^(7/2))","A",2,2,17,0.1176,1,"{45, 37}"
1100,1,61,0,0.0079077,"\int \frac{(1+x)^{5/2}}{(1-x)^{13/2}} \, dx","Int[(1 + x)^(5/2)/(1 - x)^(13/2),x]","\frac{2 (x+1)^{7/2}}{693 (1-x)^{7/2}}+\frac{2 (x+1)^{7/2}}{99 (1-x)^{9/2}}+\frac{(x+1)^{7/2}}{11 (1-x)^{11/2}}","\frac{2 (x+1)^{7/2}}{693 (1-x)^{7/2}}+\frac{2 (x+1)^{7/2}}{99 (1-x)^{9/2}}+\frac{(x+1)^{7/2}}{11 (1-x)^{11/2}}",1,"(1 + x)^(7/2)/(11*(1 - x)^(11/2)) + (2*(1 + x)^(7/2))/(99*(1 - x)^(9/2)) + (2*(1 + x)^(7/2))/(693*(1 - x)^(7/2))","A",3,2,17,0.1176,1,"{45, 37}"
1101,1,81,0,0.0127514,"\int \frac{(1+x)^{5/2}}{(1-x)^{15/2}} \, dx","Int[(1 + x)^(5/2)/(1 - x)^(15/2),x]","\frac{2 (x+1)^{7/2}}{3003 (1-x)^{7/2}}+\frac{2 (x+1)^{7/2}}{429 (1-x)^{9/2}}+\frac{3 (x+1)^{7/2}}{143 (1-x)^{11/2}}+\frac{(x+1)^{7/2}}{13 (1-x)^{13/2}}","\frac{2 (x+1)^{7/2}}{3003 (1-x)^{7/2}}+\frac{2 (x+1)^{7/2}}{429 (1-x)^{9/2}}+\frac{3 (x+1)^{7/2}}{143 (1-x)^{11/2}}+\frac{(x+1)^{7/2}}{13 (1-x)^{13/2}}",1,"(1 + x)^(7/2)/(13*(1 - x)^(13/2)) + (3*(1 + x)^(7/2))/(143*(1 - x)^(11/2)) + (2*(1 + x)^(7/2))/(429*(1 - x)^(9/2)) + (2*(1 + x)^(7/2))/(3003*(1 - x)^(7/2))","A",4,2,17,0.1176,1,"{45, 37}"
1102,1,101,0,0.0192351,"\int \frac{(1+x)^{5/2}}{(1-x)^{17/2}} \, dx","Int[(1 + x)^(5/2)/(1 - x)^(17/2),x]","\frac{8 (x+1)^{7/2}}{45045 (1-x)^{7/2}}+\frac{8 (x+1)^{7/2}}{6435 (1-x)^{9/2}}+\frac{4 (x+1)^{7/2}}{715 (1-x)^{11/2}}+\frac{4 (x+1)^{7/2}}{195 (1-x)^{13/2}}+\frac{(x+1)^{7/2}}{15 (1-x)^{15/2}}","\frac{8 (x+1)^{7/2}}{45045 (1-x)^{7/2}}+\frac{8 (x+1)^{7/2}}{6435 (1-x)^{9/2}}+\frac{4 (x+1)^{7/2}}{715 (1-x)^{11/2}}+\frac{4 (x+1)^{7/2}}{195 (1-x)^{13/2}}+\frac{(x+1)^{7/2}}{15 (1-x)^{15/2}}",1,"(1 + x)^(7/2)/(15*(1 - x)^(15/2)) + (4*(1 + x)^(7/2))/(195*(1 - x)^(13/2)) + (4*(1 + x)^(7/2))/(715*(1 - x)^(11/2)) + (8*(1 + x)^(7/2))/(6435*(1 - x)^(9/2)) + (8*(1 + x)^(7/2))/(45045*(1 - x)^(7/2))","A",5,2,17,0.1176,1,"{45, 37}"
1103,1,121,0,0.0246597,"\int \frac{(1+x)^{5/2}}{(1-x)^{19/2}} \, dx","Int[(1 + x)^(5/2)/(1 - x)^(19/2),x]","\frac{8 (x+1)^{7/2}}{153153 (1-x)^{7/2}}+\frac{8 (x+1)^{7/2}}{21879 (1-x)^{9/2}}+\frac{4 (x+1)^{7/2}}{2431 (1-x)^{11/2}}+\frac{4 (x+1)^{7/2}}{663 (1-x)^{13/2}}+\frac{(x+1)^{7/2}}{51 (1-x)^{15/2}}+\frac{(x+1)^{7/2}}{17 (1-x)^{17/2}}","\frac{8 (x+1)^{7/2}}{153153 (1-x)^{7/2}}+\frac{8 (x+1)^{7/2}}{21879 (1-x)^{9/2}}+\frac{4 (x+1)^{7/2}}{2431 (1-x)^{11/2}}+\frac{4 (x+1)^{7/2}}{663 (1-x)^{13/2}}+\frac{(x+1)^{7/2}}{51 (1-x)^{15/2}}+\frac{(x+1)^{7/2}}{17 (1-x)^{17/2}}",1,"(1 + x)^(7/2)/(17*(1 - x)^(17/2)) + (1 + x)^(7/2)/(51*(1 - x)^(15/2)) + (4*(1 + x)^(7/2))/(663*(1 - x)^(13/2)) + (4*(1 + x)^(7/2))/(2431*(1 - x)^(11/2)) + (8*(1 + x)^(7/2))/(21879*(1 - x)^(9/2)) + (8*(1 + x)^(7/2))/(153153*(1 - x)^(7/2))","A",6,2,17,0.1176,1,"{45, 37}"
1104,1,64,0,0.0117152,"\int \frac{(1+a x)^{3/2}}{\sqrt{1-a x}} \, dx","Int[(1 + a*x)^(3/2)/Sqrt[1 - a*x],x]","-\frac{\sqrt{1-a x} (a x+1)^{3/2}}{2 a}-\frac{3 \sqrt{1-a x} \sqrt{a x+1}}{2 a}+\frac{3 \sin ^{-1}(a x)}{2 a}","-\frac{\sqrt{1-a x} (a x+1)^{3/2}}{2 a}-\frac{3 \sqrt{1-a x} \sqrt{a x+1}}{2 a}+\frac{3 \sin ^{-1}(a x)}{2 a}",1,"(-3*Sqrt[1 - a*x]*Sqrt[1 + a*x])/(2*a) - (Sqrt[1 - a*x]*(1 + a*x)^(3/2))/(2*a) + (3*ArcSin[a*x])/(2*a)","A",4,3,20,0.1500,1,"{50, 41, 216}"
1105,1,62,0,0.028291,"\int \frac{(1+a x) \sqrt{1-a^2 x^2}}{1-a x} \, dx","Int[((1 + a*x)*Sqrt[1 - a^2*x^2])/(1 - a*x),x]","-\frac{\left(1-a^2 x^2\right)^{3/2}}{2 a (1-a x)}-\frac{3 \sqrt{1-a^2 x^2}}{2 a}+\frac{3 \sin ^{-1}(a x)}{2 a}","-\frac{\left(1-a^2 x^2\right)^{3/2}}{2 a (1-a x)}-\frac{3 \sqrt{1-a^2 x^2}}{2 a}+\frac{3 \sin ^{-1}(a x)}{2 a}",1,"(-3*Sqrt[1 - a^2*x^2])/(2*a) - (1 - a^2*x^2)^(3/2)/(2*a*(1 - a*x)) + (3*ArcSin[a*x])/(2*a)","A",3,3,28,0.1071,1,"{795, 665, 216}"
1106,1,87,0,0.0176468,"\int \frac{(1-x)^{7/2}}{\sqrt{1+x}} \, dx","Int[(1 - x)^(7/2)/Sqrt[1 + x],x]","\frac{1}{4} \sqrt{x+1} (1-x)^{7/2}+\frac{7}{12} \sqrt{x+1} (1-x)^{5/2}+\frac{35}{24} \sqrt{x+1} (1-x)^{3/2}+\frac{35}{8} \sqrt{x+1} \sqrt{1-x}+\frac{35}{8} \sin ^{-1}(x)","\frac{1}{4} \sqrt{x+1} (1-x)^{7/2}+\frac{7}{12} \sqrt{x+1} (1-x)^{5/2}+\frac{35}{24} \sqrt{x+1} (1-x)^{3/2}+\frac{35}{8} \sqrt{x+1} \sqrt{1-x}+\frac{35}{8} \sin ^{-1}(x)",1,"(35*Sqrt[1 - x]*Sqrt[1 + x])/8 + (35*(1 - x)^(3/2)*Sqrt[1 + x])/24 + (7*(1 - x)^(5/2)*Sqrt[1 + x])/12 + ((1 - x)^(7/2)*Sqrt[1 + x])/4 + (35*ArcSin[x])/8","A",6,3,17,0.1765,1,"{50, 41, 216}"
1107,1,67,0,0.0106446,"\int \frac{(1-x)^{5/2}}{\sqrt{1+x}} \, dx","Int[(1 - x)^(5/2)/Sqrt[1 + x],x]","\frac{1}{3} \sqrt{x+1} (1-x)^{5/2}+\frac{5}{6} \sqrt{x+1} (1-x)^{3/2}+\frac{5}{2} \sqrt{x+1} \sqrt{1-x}+\frac{5}{2} \sin ^{-1}(x)","\frac{1}{3} \sqrt{x+1} (1-x)^{5/2}+\frac{5}{6} \sqrt{x+1} (1-x)^{3/2}+\frac{5}{2} \sqrt{x+1} \sqrt{1-x}+\frac{5}{2} \sin ^{-1}(x)",1,"(5*Sqrt[1 - x]*Sqrt[1 + x])/2 + (5*(1 - x)^(3/2)*Sqrt[1 + x])/6 + ((1 - x)^(5/2)*Sqrt[1 + x])/3 + (5*ArcSin[x])/2","A",5,3,17,0.1765,1,"{50, 41, 216}"
1108,1,47,0,0.0069494,"\int \frac{(1-x)^{3/2}}{\sqrt{1+x}} \, dx","Int[(1 - x)^(3/2)/Sqrt[1 + x],x]","\frac{1}{2} \sqrt{x+1} (1-x)^{3/2}+\frac{3}{2} \sqrt{x+1} \sqrt{1-x}+\frac{3}{2} \sin ^{-1}(x)","\frac{1}{2} \sqrt{x+1} (1-x)^{3/2}+\frac{3}{2} \sqrt{x+1} \sqrt{1-x}+\frac{3}{2} \sin ^{-1}(x)",1,"(3*Sqrt[1 - x]*Sqrt[1 + x])/2 + ((1 - x)^(3/2)*Sqrt[1 + x])/2 + (3*ArcSin[x])/2","A",4,3,17,0.1765,1,"{50, 41, 216}"
1109,1,20,0,0.0034088,"\int \frac{\sqrt{1-x}}{\sqrt{1+x}} \, dx","Int[Sqrt[1 - x]/Sqrt[1 + x],x]","\sqrt{1-x} \sqrt{x+1}+\sin ^{-1}(x)","\sqrt{1-x} \sqrt{x+1}+\sin ^{-1}(x)",1,"Sqrt[1 - x]*Sqrt[1 + x] + ArcSin[x]","A",3,3,17,0.1765,1,"{50, 41, 216}"
1110,1,2,0,0.0014997,"\int \frac{1}{\sqrt{1-x} \sqrt{1+x}} \, dx","Int[1/(Sqrt[1 - x]*Sqrt[1 + x]),x]","\sin ^{-1}(x)","\sin ^{-1}(x)",1,"ArcSin[x]","A",2,2,17,0.1176,1,"{41, 216}"
1111,1,17,0,0.0031938,"\int \frac{1}{(1-x)^{3/2} \sqrt{1+x}} \, dx","Int[1/((1 - x)^(3/2)*Sqrt[1 + x]),x]","\frac{\sqrt{x+1}}{\sqrt{1-x}}","\frac{\sqrt{x+1}}{\sqrt{1-x}}",1,"Sqrt[1 + x]/Sqrt[1 - x]","A",1,1,17,0.05882,1,"{37}"
1112,1,41,0,0.0043011,"\int \frac{1}{(1-x)^{5/2} \sqrt{1+x}} \, dx","Int[1/((1 - x)^(5/2)*Sqrt[1 + x]),x]","\frac{\sqrt{x+1}}{3 \sqrt{1-x}}+\frac{\sqrt{x+1}}{3 (1-x)^{3/2}}","\frac{\sqrt{x+1}}{3 \sqrt{1-x}}+\frac{\sqrt{x+1}}{3 (1-x)^{3/2}}",1,"Sqrt[1 + x]/(3*(1 - x)^(3/2)) + Sqrt[1 + x]/(3*Sqrt[1 - x])","A",2,2,17,0.1176,1,"{45, 37}"
1113,1,61,0,0.0078398,"\int \frac{1}{(1-x)^{7/2} \sqrt{1+x}} \, dx","Int[1/((1 - x)^(7/2)*Sqrt[1 + x]),x]","\frac{2 \sqrt{x+1}}{15 \sqrt{1-x}}+\frac{2 \sqrt{x+1}}{15 (1-x)^{3/2}}+\frac{\sqrt{x+1}}{5 (1-x)^{5/2}}","\frac{2 \sqrt{x+1}}{15 \sqrt{1-x}}+\frac{2 \sqrt{x+1}}{15 (1-x)^{3/2}}+\frac{\sqrt{x+1}}{5 (1-x)^{5/2}}",1,"Sqrt[1 + x]/(5*(1 - x)^(5/2)) + (2*Sqrt[1 + x])/(15*(1 - x)^(3/2)) + (2*Sqrt[1 + x])/(15*Sqrt[1 - x])","A",3,2,17,0.1176,1,"{45, 37}"
1114,1,81,0,0.0138147,"\int \frac{1}{(1-x)^{9/2} \sqrt{1+x}} \, dx","Int[1/((1 - x)^(9/2)*Sqrt[1 + x]),x]","\frac{2 \sqrt{x+1}}{35 \sqrt{1-x}}+\frac{2 \sqrt{x+1}}{35 (1-x)^{3/2}}+\frac{3 \sqrt{x+1}}{35 (1-x)^{5/2}}+\frac{\sqrt{x+1}}{7 (1-x)^{7/2}}","\frac{2 \sqrt{x+1}}{35 \sqrt{1-x}}+\frac{2 \sqrt{x+1}}{35 (1-x)^{3/2}}+\frac{3 \sqrt{x+1}}{35 (1-x)^{5/2}}+\frac{\sqrt{x+1}}{7 (1-x)^{7/2}}",1,"Sqrt[1 + x]/(7*(1 - x)^(7/2)) + (3*Sqrt[1 + x])/(35*(1 - x)^(5/2)) + (2*Sqrt[1 + x])/(35*(1 - x)^(3/2)) + (2*Sqrt[1 + x])/(35*Sqrt[1 - x])","A",4,2,17,0.1176,1,"{45, 37}"
1115,1,101,0,0.0182229,"\int \frac{1}{(1-x)^{11/2} \sqrt{1+x}} \, dx","Int[1/((1 - x)^(11/2)*Sqrt[1 + x]),x]","\frac{8 \sqrt{x+1}}{315 \sqrt{1-x}}+\frac{8 \sqrt{x+1}}{315 (1-x)^{3/2}}+\frac{4 \sqrt{x+1}}{105 (1-x)^{5/2}}+\frac{4 \sqrt{x+1}}{63 (1-x)^{7/2}}+\frac{\sqrt{x+1}}{9 (1-x)^{9/2}}","\frac{8 \sqrt{x+1}}{315 \sqrt{1-x}}+\frac{8 \sqrt{x+1}}{315 (1-x)^{3/2}}+\frac{4 \sqrt{x+1}}{105 (1-x)^{5/2}}+\frac{4 \sqrt{x+1}}{63 (1-x)^{7/2}}+\frac{\sqrt{x+1}}{9 (1-x)^{9/2}}",1,"Sqrt[1 + x]/(9*(1 - x)^(9/2)) + (4*Sqrt[1 + x])/(63*(1 - x)^(7/2)) + (4*Sqrt[1 + x])/(105*(1 - x)^(5/2)) + (8*Sqrt[1 + x])/(315*(1 - x)^(3/2)) + (8*Sqrt[1 + x])/(315*Sqrt[1 - x])","A",5,2,17,0.1176,1,"{45, 37}"
1116,1,85,0,0.0162829,"\int \frac{(1-x)^{7/2}}{(1+x)^{3/2}} \, dx","Int[(1 - x)^(7/2)/(1 + x)^(3/2),x]","-\frac{2 (1-x)^{7/2}}{\sqrt{x+1}}-\frac{7}{3} \sqrt{x+1} (1-x)^{5/2}-\frac{35}{6} \sqrt{x+1} (1-x)^{3/2}-\frac{35}{2} \sqrt{x+1} \sqrt{1-x}-\frac{35}{2} \sin ^{-1}(x)","-\frac{2 (1-x)^{7/2}}{\sqrt{x+1}}-\frac{7}{3} \sqrt{x+1} (1-x)^{5/2}-\frac{35}{6} \sqrt{x+1} (1-x)^{3/2}-\frac{35}{2} \sqrt{x+1} \sqrt{1-x}-\frac{35}{2} \sin ^{-1}(x)",1,"(-2*(1 - x)^(7/2))/Sqrt[1 + x] - (35*Sqrt[1 - x]*Sqrt[1 + x])/2 - (35*(1 - x)^(3/2)*Sqrt[1 + x])/6 - (7*(1 - x)^(5/2)*Sqrt[1 + x])/3 - (35*ArcSin[x])/2","A",6,4,17,0.2353,1,"{47, 50, 41, 216}"
1117,1,65,0,0.0108989,"\int \frac{(1-x)^{5/2}}{(1+x)^{3/2}} \, dx","Int[(1 - x)^(5/2)/(1 + x)^(3/2),x]","-\frac{2 (1-x)^{5/2}}{\sqrt{x+1}}-\frac{5}{2} \sqrt{x+1} (1-x)^{3/2}-\frac{15}{2} \sqrt{x+1} \sqrt{1-x}-\frac{15}{2} \sin ^{-1}(x)","-\frac{2 (1-x)^{5/2}}{\sqrt{x+1}}-\frac{5}{2} \sqrt{x+1} (1-x)^{3/2}-\frac{15}{2} \sqrt{x+1} \sqrt{1-x}-\frac{15}{2} \sin ^{-1}(x)",1,"(-2*(1 - x)^(5/2))/Sqrt[1 + x] - (15*Sqrt[1 - x]*Sqrt[1 + x])/2 - (5*(1 - x)^(3/2)*Sqrt[1 + x])/2 - (15*ArcSin[x])/2","A",5,4,17,0.2353,1,"{47, 50, 41, 216}"
1118,1,41,0,0.0065795,"\int \frac{(1-x)^{3/2}}{(1+x)^{3/2}} \, dx","Int[(1 - x)^(3/2)/(1 + x)^(3/2),x]","-\frac{2 (1-x)^{3/2}}{\sqrt{x+1}}-3 \sqrt{x+1} \sqrt{1-x}-3 \sin ^{-1}(x)","-\frac{2 (1-x)^{3/2}}{\sqrt{x+1}}-3 \sqrt{x+1} \sqrt{1-x}-3 \sin ^{-1}(x)",1,"(-2*(1 - x)^(3/2))/Sqrt[1 + x] - 3*Sqrt[1 - x]*Sqrt[1 + x] - 3*ArcSin[x]","A",4,4,17,0.2353,1,"{47, 50, 41, 216}"
1119,1,23,0,0.0033808,"\int \frac{\sqrt{1-x}}{(1+x)^{3/2}} \, dx","Int[Sqrt[1 - x]/(1 + x)^(3/2),x]","-\frac{2 \sqrt{1-x}}{\sqrt{x+1}}-\sin ^{-1}(x)","-\frac{2 \sqrt{1-x}}{\sqrt{x+1}}-\sin ^{-1}(x)",1,"(-2*Sqrt[1 - x])/Sqrt[1 + x] - ArcSin[x]","A",3,3,17,0.1765,1,"{47, 41, 216}"
1120,1,18,0,0.0015644,"\int \frac{1}{\sqrt{1-x} (1+x)^{3/2}} \, dx","Int[1/(Sqrt[1 - x]*(1 + x)^(3/2)),x]","-\frac{\sqrt{1-x}}{\sqrt{x+1}}","-\frac{\sqrt{1-x}}{\sqrt{x+1}}",1,"-(Sqrt[1 - x]/Sqrt[1 + x])","A",1,1,17,0.05882,1,"{37}"
1121,1,18,0,0.0016086,"\int \frac{1}{(1-x)^{3/2} (1+x)^{3/2}} \, dx","Int[1/((1 - x)^(3/2)*(1 + x)^(3/2)),x]","\frac{x}{\sqrt{1-x} \sqrt{x+1}}","\frac{x}{\sqrt{1-x} \sqrt{x+1}}",1,"x/(Sqrt[1 - x]*Sqrt[1 + x])","A",1,1,17,0.05882,1,"{39}"
1122,1,42,0,0.0045252,"\int \frac{1}{(1-x)^{5/2} (1+x)^{3/2}} \, dx","Int[1/((1 - x)^(5/2)*(1 + x)^(3/2)),x]","\frac{2 x}{3 \sqrt{1-x} \sqrt{x+1}}+\frac{1}{3 (1-x)^{3/2} \sqrt{x+1}}","\frac{2 x}{3 \sqrt{1-x} \sqrt{x+1}}+\frac{1}{3 (1-x)^{3/2} \sqrt{x+1}}",1,"1/(3*(1 - x)^(3/2)*Sqrt[1 + x]) + (2*x)/(3*Sqrt[1 - x]*Sqrt[1 + x])","A",2,2,17,0.1176,1,"{45, 39}"
1123,1,62,0,0.008368,"\int \frac{1}{(1-x)^{7/2} (1+x)^{3/2}} \, dx","Int[1/((1 - x)^(7/2)*(1 + x)^(3/2)),x]","\frac{2 x}{5 \sqrt{1-x} \sqrt{x+1}}+\frac{1}{5 (1-x)^{3/2} \sqrt{x+1}}+\frac{1}{5 (1-x)^{5/2} \sqrt{x+1}}","\frac{2 x}{5 \sqrt{1-x} \sqrt{x+1}}+\frac{1}{5 (1-x)^{3/2} \sqrt{x+1}}+\frac{1}{5 (1-x)^{5/2} \sqrt{x+1}}",1,"1/(5*(1 - x)^(5/2)*Sqrt[1 + x]) + 1/(5*(1 - x)^(3/2)*Sqrt[1 + x]) + (2*x)/(5*Sqrt[1 - x]*Sqrt[1 + x])","A",3,2,17,0.1176,1,"{45, 39}"
1124,1,82,0,0.0134444,"\int \frac{1}{(1-x)^{9/2} (1+x)^{3/2}} \, dx","Int[1/((1 - x)^(9/2)*(1 + x)^(3/2)),x]","\frac{8 x}{35 \sqrt{1-x} \sqrt{x+1}}+\frac{4}{35 (1-x)^{3/2} \sqrt{x+1}}+\frac{4}{35 (1-x)^{5/2} \sqrt{x+1}}+\frac{1}{7 (1-x)^{7/2} \sqrt{x+1}}","\frac{8 x}{35 \sqrt{1-x} \sqrt{x+1}}+\frac{4}{35 (1-x)^{3/2} \sqrt{x+1}}+\frac{4}{35 (1-x)^{5/2} \sqrt{x+1}}+\frac{1}{7 (1-x)^{7/2} \sqrt{x+1}}",1,"1/(7*(1 - x)^(7/2)*Sqrt[1 + x]) + 4/(35*(1 - x)^(5/2)*Sqrt[1 + x]) + 4/(35*(1 - x)^(3/2)*Sqrt[1 + x]) + (8*x)/(35*Sqrt[1 - x]*Sqrt[1 + x])","A",4,2,17,0.1176,1,"{45, 39}"
1125,1,102,0,0.0203065,"\int \frac{1}{(1-x)^{11/2} (1+x)^{3/2}} \, dx","Int[1/((1 - x)^(11/2)*(1 + x)^(3/2)),x]","\frac{8 x}{63 \sqrt{1-x} \sqrt{x+1}}+\frac{4}{63 (1-x)^{3/2} \sqrt{x+1}}+\frac{4}{63 (1-x)^{5/2} \sqrt{x+1}}+\frac{5}{63 (1-x)^{7/2} \sqrt{x+1}}+\frac{1}{9 (1-x)^{9/2} \sqrt{x+1}}","\frac{8 x}{63 \sqrt{1-x} \sqrt{x+1}}+\frac{4}{63 (1-x)^{3/2} \sqrt{x+1}}+\frac{4}{63 (1-x)^{5/2} \sqrt{x+1}}+\frac{5}{63 (1-x)^{7/2} \sqrt{x+1}}+\frac{1}{9 (1-x)^{9/2} \sqrt{x+1}}",1,"1/(9*(1 - x)^(9/2)*Sqrt[1 + x]) + 5/(63*(1 - x)^(7/2)*Sqrt[1 + x]) + 4/(63*(1 - x)^(5/2)*Sqrt[1 + x]) + 4/(63*(1 - x)^(3/2)*Sqrt[1 + x]) + (8*x)/(63*Sqrt[1 - x]*Sqrt[1 + x])","A",5,2,17,0.1176,1,"{45, 39}"
1126,1,103,0,0.0214789,"\int \frac{(1-x)^{9/2}}{(1+x)^{5/2}} \, dx","Int[(1 - x)^(9/2)/(1 + x)^(5/2),x]","-\frac{2 (1-x)^{9/2}}{3 (x+1)^{3/2}}+\frac{6 (1-x)^{7/2}}{\sqrt{x+1}}+7 \sqrt{x+1} (1-x)^{5/2}+\frac{35}{2} \sqrt{x+1} (1-x)^{3/2}+\frac{105}{2} \sqrt{x+1} \sqrt{1-x}+\frac{105}{2} \sin ^{-1}(x)","-\frac{2 (1-x)^{9/2}}{3 (x+1)^{3/2}}+\frac{6 (1-x)^{7/2}}{\sqrt{x+1}}+7 \sqrt{x+1} (1-x)^{5/2}+\frac{35}{2} \sqrt{x+1} (1-x)^{3/2}+\frac{105}{2} \sqrt{x+1} \sqrt{1-x}+\frac{105}{2} \sin ^{-1}(x)",1,"(-2*(1 - x)^(9/2))/(3*(1 + x)^(3/2)) + (6*(1 - x)^(7/2))/Sqrt[1 + x] + (105*Sqrt[1 - x]*Sqrt[1 + x])/2 + (35*(1 - x)^(3/2)*Sqrt[1 + x])/2 + 7*(1 - x)^(5/2)*Sqrt[1 + x] + (105*ArcSin[x])/2","A",7,4,17,0.2353,1,"{47, 50, 41, 216}"
1127,1,87,0,0.0152415,"\int \frac{(1-x)^{7/2}}{(1+x)^{5/2}} \, dx","Int[(1 - x)^(7/2)/(1 + x)^(5/2),x]","-\frac{2 (1-x)^{7/2}}{3 (x+1)^{3/2}}+\frac{14 (1-x)^{5/2}}{3 \sqrt{x+1}}+\frac{35}{6} \sqrt{x+1} (1-x)^{3/2}+\frac{35}{2} \sqrt{x+1} \sqrt{1-x}+\frac{35}{2} \sin ^{-1}(x)","-\frac{2 (1-x)^{7/2}}{3 (x+1)^{3/2}}+\frac{14 (1-x)^{5/2}}{3 \sqrt{x+1}}+\frac{35}{6} \sqrt{x+1} (1-x)^{3/2}+\frac{35}{2} \sqrt{x+1} \sqrt{1-x}+\frac{35}{2} \sin ^{-1}(x)",1,"(-2*(1 - x)^(7/2))/(3*(1 + x)^(3/2)) + (14*(1 - x)^(5/2))/(3*Sqrt[1 + x]) + (35*Sqrt[1 - x]*Sqrt[1 + x])/2 + (35*(1 - x)^(3/2)*Sqrt[1 + x])/6 + (35*ArcSin[x])/2","A",6,4,17,0.2353,1,"{47, 50, 41, 216}"
1128,1,63,0,0.010729,"\int \frac{(1-x)^{5/2}}{(1+x)^{5/2}} \, dx","Int[(1 - x)^(5/2)/(1 + x)^(5/2),x]","-\frac{2 (1-x)^{5/2}}{3 (x+1)^{3/2}}+\frac{10 (1-x)^{3/2}}{3 \sqrt{x+1}}+5 \sqrt{x+1} \sqrt{1-x}+5 \sin ^{-1}(x)","-\frac{2 (1-x)^{5/2}}{3 (x+1)^{3/2}}+\frac{10 (1-x)^{3/2}}{3 \sqrt{x+1}}+5 \sqrt{x+1} \sqrt{1-x}+5 \sin ^{-1}(x)",1,"(-2*(1 - x)^(5/2))/(3*(1 + x)^(3/2)) + (10*(1 - x)^(3/2))/(3*Sqrt[1 + x]) + 5*Sqrt[1 - x]*Sqrt[1 + x] + 5*ArcSin[x]","A",5,4,17,0.2353,1,"{47, 50, 41, 216}"
1129,1,41,0,0.0055739,"\int \frac{(1-x)^{3/2}}{(1+x)^{5/2}} \, dx","Int[(1 - x)^(3/2)/(1 + x)^(5/2),x]","-\frac{2 (1-x)^{3/2}}{3 (x+1)^{3/2}}+\frac{2 \sqrt{1-x}}{\sqrt{x+1}}+\sin ^{-1}(x)","-\frac{2 (1-x)^{3/2}}{3 (x+1)^{3/2}}+\frac{2 \sqrt{1-x}}{\sqrt{x+1}}+\sin ^{-1}(x)",1,"(-2*(1 - x)^(3/2))/(3*(1 + x)^(3/2)) + (2*Sqrt[1 - x])/Sqrt[1 + x] + ArcSin[x]","A",4,3,17,0.1765,1,"{47, 41, 216}"
1130,1,20,0,0.0015594,"\int \frac{\sqrt{1-x}}{(1+x)^{5/2}} \, dx","Int[Sqrt[1 - x]/(1 + x)^(5/2),x]","-\frac{(1-x)^{3/2}}{3 (x+1)^{3/2}}","-\frac{(1-x)^{3/2}}{3 (x+1)^{3/2}}",1,"-(1 - x)^(3/2)/(3*(1 + x)^(3/2))","A",1,1,17,0.05882,1,"{37}"
1131,1,41,0,0.0043043,"\int \frac{1}{\sqrt{1-x} (1+x)^{5/2}} \, dx","Int[1/(Sqrt[1 - x]*(1 + x)^(5/2)),x]","-\frac{\sqrt{1-x}}{3 \sqrt{x+1}}-\frac{\sqrt{1-x}}{3 (x+1)^{3/2}}","-\frac{\sqrt{1-x}}{3 \sqrt{x+1}}-\frac{\sqrt{1-x}}{3 (x+1)^{3/2}}",1,"-Sqrt[1 - x]/(3*(1 + x)^(3/2)) - Sqrt[1 - x]/(3*Sqrt[1 + x])","A",2,2,17,0.1176,1,"{45, 37}"
1132,1,58,0,0.0084024,"\int \frac{1}{(1-x)^{3/2} (1+x)^{5/2}} \, dx","Int[1/((1 - x)^(3/2)*(1 + x)^(5/2)),x]","-\frac{2 \sqrt{1-x}}{3 \sqrt{x+1}}-\frac{2 \sqrt{1-x}}{3 (x+1)^{3/2}}+\frac{1}{(x+1)^{3/2} \sqrt{1-x}}","-\frac{2 \sqrt{1-x}}{3 \sqrt{x+1}}-\frac{2 \sqrt{1-x}}{3 (x+1)^{3/2}}+\frac{1}{(x+1)^{3/2} \sqrt{1-x}}",1,"1/(Sqrt[1 - x]*(1 + x)^(3/2)) - (2*Sqrt[1 - x])/(3*(1 + x)^(3/2)) - (2*Sqrt[1 - x])/(3*Sqrt[1 + x])","A",3,2,17,0.1176,1,"{45, 37}"
1133,1,43,0,0.0047007,"\int \frac{1}{(1-x)^{5/2} (1+x)^{5/2}} \, dx","Int[1/((1 - x)^(5/2)*(1 + x)^(5/2)),x]","\frac{2 x}{3 \sqrt{1-x} \sqrt{x+1}}+\frac{x}{3 (1-x)^{3/2} (x+1)^{3/2}}","\frac{2 x}{3 \sqrt{1-x} \sqrt{x+1}}+\frac{x}{3 (1-x)^{3/2} (x+1)^{3/2}}",1,"x/(3*(1 - x)^(3/2)*(1 + x)^(3/2)) + (2*x)/(3*Sqrt[1 - x]*Sqrt[1 + x])","A",2,2,17,0.1176,1,"{40, 39}"
1134,1,63,0,0.0081462,"\int \frac{1}{(1-x)^{7/2} (1+x)^{5/2}} \, dx","Int[1/((1 - x)^(7/2)*(1 + x)^(5/2)),x]","\frac{8 x}{15 \sqrt{1-x} \sqrt{x+1}}+\frac{4 x}{15 (1-x)^{3/2} (x+1)^{3/2}}+\frac{1}{5 (1-x)^{5/2} (x+1)^{3/2}}","\frac{8 x}{15 \sqrt{1-x} \sqrt{x+1}}+\frac{4 x}{15 (1-x)^{3/2} (x+1)^{3/2}}+\frac{1}{5 (1-x)^{5/2} (x+1)^{3/2}}",1,"1/(5*(1 - x)^(5/2)*(1 + x)^(3/2)) + (4*x)/(15*(1 - x)^(3/2)*(1 + x)^(3/2)) + (8*x)/(15*Sqrt[1 - x]*Sqrt[1 + x])","A",3,3,17,0.1765,1,"{45, 40, 39}"
1135,1,83,0,0.0137007,"\int \frac{1}{(1-x)^{9/2} (1+x)^{5/2}} \, dx","Int[1/((1 - x)^(9/2)*(1 + x)^(5/2)),x]","\frac{8 x}{21 \sqrt{1-x} \sqrt{x+1}}+\frac{4 x}{21 (1-x)^{3/2} (x+1)^{3/2}}+\frac{1}{7 (1-x)^{5/2} (x+1)^{3/2}}+\frac{1}{7 (1-x)^{7/2} (x+1)^{3/2}}","\frac{8 x}{21 \sqrt{1-x} \sqrt{x+1}}+\frac{4 x}{21 (1-x)^{3/2} (x+1)^{3/2}}+\frac{1}{7 (1-x)^{5/2} (x+1)^{3/2}}+\frac{1}{7 (1-x)^{7/2} (x+1)^{3/2}}",1,"1/(7*(1 - x)^(7/2)*(1 + x)^(3/2)) + 1/(7*(1 - x)^(5/2)*(1 + x)^(3/2)) + (4*x)/(21*(1 - x)^(3/2)*(1 + x)^(3/2)) + (8*x)/(21*Sqrt[1 - x]*Sqrt[1 + x])","A",4,3,17,0.1765,1,"{45, 40, 39}"
1136,1,103,0,0.0193206,"\int \frac{1}{(1-x)^{11/2} (1+x)^{5/2}} \, dx","Int[1/((1 - x)^(11/2)*(1 + x)^(5/2)),x]","\frac{16 x}{63 \sqrt{1-x} \sqrt{x+1}}+\frac{8 x}{63 (1-x)^{3/2} (x+1)^{3/2}}+\frac{2}{21 (1-x)^{5/2} (x+1)^{3/2}}+\frac{2}{21 (1-x)^{7/2} (x+1)^{3/2}}+\frac{1}{9 (1-x)^{9/2} (x+1)^{3/2}}","\frac{16 x}{63 \sqrt{1-x} \sqrt{x+1}}+\frac{8 x}{63 (1-x)^{3/2} (x+1)^{3/2}}+\frac{2}{21 (1-x)^{5/2} (x+1)^{3/2}}+\frac{2}{21 (1-x)^{7/2} (x+1)^{3/2}}+\frac{1}{9 (1-x)^{9/2} (x+1)^{3/2}}",1,"1/(9*(1 - x)^(9/2)*(1 + x)^(3/2)) + 2/(21*(1 - x)^(7/2)*(1 + x)^(3/2)) + 2/(21*(1 - x)^(5/2)*(1 + x)^(3/2)) + (8*x)/(63*(1 - x)^(3/2)*(1 + x)^(3/2)) + (16*x)/(63*Sqrt[1 - x]*Sqrt[1 + x])","A",5,3,17,0.1765,1,"{45, 40, 39}"
1137,1,126,0,0.0548007,"\int (a+a x)^{5/2} (c-c x)^{5/2} \, dx","Int[(a + a*x)^(5/2)*(c - c*x)^(5/2),x]","\frac{5}{16} a^2 c^2 x \sqrt{a x+a} \sqrt{c-c x}+\frac{5}{8} a^{5/2} c^{5/2} \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a x+a}}{\sqrt{a} \sqrt{c-c x}}\right)+\frac{5}{24} a c x (a x+a)^{3/2} (c-c x)^{3/2}+\frac{1}{6} x (a x+a)^{5/2} (c-c x)^{5/2}","\frac{5}{16} a^2 c^2 x \sqrt{a x+a} \sqrt{c-c x}+\frac{5}{8} a^{5/2} c^{5/2} \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a x+a}}{\sqrt{a} \sqrt{c-c x}}\right)+\frac{5}{24} a c x (a x+a)^{3/2} (c-c x)^{3/2}+\frac{1}{6} x (a x+a)^{5/2} (c-c x)^{5/2}",1,"(5*a^2*c^2*x*Sqrt[a + a*x]*Sqrt[c - c*x])/16 + (5*a*c*x*(a + a*x)^(3/2)*(c - c*x)^(3/2))/24 + (x*(a + a*x)^(5/2)*(c - c*x)^(5/2))/6 + (5*a^(5/2)*c^(5/2)*ArcTan[(Sqrt[c]*Sqrt[a + a*x])/(Sqrt[a]*Sqrt[c - c*x])])/8","A",6,4,20,0.2000,1,"{38, 63, 217, 203}"
1138,1,96,0,0.0365369,"\int (a+a x)^{3/2} (c-c x)^{3/2} \, dx","Int[(a + a*x)^(3/2)*(c - c*x)^(3/2),x]","\frac{3}{4} a^{3/2} c^{3/2} \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a x+a}}{\sqrt{a} \sqrt{c-c x}}\right)+\frac{3}{8} a c x \sqrt{a x+a} \sqrt{c-c x}+\frac{1}{4} x (a x+a)^{3/2} (c-c x)^{3/2}","\frac{3}{4} a^{3/2} c^{3/2} \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a x+a}}{\sqrt{a} \sqrt{c-c x}}\right)+\frac{3}{8} a c x \sqrt{a x+a} \sqrt{c-c x}+\frac{1}{4} x (a x+a)^{3/2} (c-c x)^{3/2}",1,"(3*a*c*x*Sqrt[a + a*x]*Sqrt[c - c*x])/8 + (x*(a + a*x)^(3/2)*(c - c*x)^(3/2))/4 + (3*a^(3/2)*c^(3/2)*ArcTan[(Sqrt[c]*Sqrt[a + a*x])/(Sqrt[a]*Sqrt[c - c*x])])/4","A",5,4,20,0.2000,1,"{38, 63, 217, 203}"
1139,1,67,0,0.0292047,"\int \sqrt{a+a x} \sqrt{c-c x} \, dx","Int[Sqrt[a + a*x]*Sqrt[c - c*x],x]","\frac{1}{2} x \sqrt{a x+a} \sqrt{c-c x}+\sqrt{a} \sqrt{c} \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a x+a}}{\sqrt{a} \sqrt{c-c x}}\right)","\frac{1}{2} x \sqrt{a x+a} \sqrt{c-c x}+\sqrt{a} \sqrt{c} \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a x+a}}{\sqrt{a} \sqrt{c-c x}}\right)",1,"(x*Sqrt[a + a*x]*Sqrt[c - c*x])/2 + Sqrt[a]*Sqrt[c]*ArcTan[(Sqrt[c]*Sqrt[a + a*x])/(Sqrt[a]*Sqrt[c - c*x])]","A",4,4,20,0.2000,1,"{38, 63, 217, 203}"
1140,1,43,0,0.0239438,"\int \frac{1}{\sqrt{a+a x} \sqrt{c-c x}} \, dx","Int[1/(Sqrt[a + a*x]*Sqrt[c - c*x]),x]","\frac{2 \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a x+a}}{\sqrt{a} \sqrt{c-c x}}\right)}{\sqrt{a} \sqrt{c}}","\frac{2 \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a x+a}}{\sqrt{a} \sqrt{c-c x}}\right)}{\sqrt{a} \sqrt{c}}",1,"(2*ArcTan[(Sqrt[c]*Sqrt[a + a*x])/(Sqrt[a]*Sqrt[c - c*x])])/(Sqrt[a]*Sqrt[c])","A",3,3,20,0.1500,1,"{63, 217, 203}"
1141,1,27,0,0.0031864,"\int \frac{1}{(a+a x)^{3/2} (c-c x)^{3/2}} \, dx","Int[1/((a + a*x)^(3/2)*(c - c*x)^(3/2)),x]","\frac{x}{a c \sqrt{a x+a} \sqrt{c-c x}}","\frac{x}{a c \sqrt{a x+a} \sqrt{c-c x}}",1,"x/(a*c*Sqrt[a + a*x]*Sqrt[c - c*x])","A",1,1,20,0.05000,1,"{39}"
1142,1,61,0,0.0098129,"\int \frac{1}{(a+a x)^{5/2} (c-c x)^{5/2}} \, dx","Int[1/((a + a*x)^(5/2)*(c - c*x)^(5/2)),x]","\frac{2 x}{3 a^2 c^2 \sqrt{a x+a} \sqrt{c-c x}}+\frac{x}{3 a c (a x+a)^{3/2} (c-c x)^{3/2}}","\frac{2 x}{3 a^2 c^2 \sqrt{a x+a} \sqrt{c-c x}}+\frac{x}{3 a c (a x+a)^{3/2} (c-c x)^{3/2}}",1,"x/(3*a*c*(a + a*x)^(3/2)*(c - c*x)^(3/2)) + (2*x)/(3*a^2*c^2*Sqrt[a + a*x]*Sqrt[c - c*x])","A",2,2,20,0.1000,1,"{40, 39}"
1143,1,91,0,0.0179005,"\int \frac{1}{(a+a x)^{7/2} (c-c x)^{7/2}} \, dx","Int[1/((a + a*x)^(7/2)*(c - c*x)^(7/2)),x]","\frac{8 x}{15 a^3 c^3 \sqrt{a x+a} \sqrt{c-c x}}+\frac{4 x}{15 a^2 c^2 (a x+a)^{3/2} (c-c x)^{3/2}}+\frac{x}{5 a c (a x+a)^{5/2} (c-c x)^{5/2}}","\frac{8 x}{15 a^3 c^3 \sqrt{a x+a} \sqrt{c-c x}}+\frac{4 x}{15 a^2 c^2 (a x+a)^{3/2} (c-c x)^{3/2}}+\frac{x}{5 a c (a x+a)^{5/2} (c-c x)^{5/2}}",1,"x/(5*a*c*(a + a*x)^(5/2)*(c - c*x)^(5/2)) + (4*x)/(15*a^2*c^2*(a + a*x)^(3/2)*(c - c*x)^(3/2)) + (8*x)/(15*a^3*c^3*Sqrt[a + a*x]*Sqrt[c - c*x])","A",3,2,20,0.1000,1,"{40, 39}"
1144,1,121,0,0.0276369,"\int \frac{1}{(a+a x)^{9/2} (c-c x)^{9/2}} \, dx","Int[1/((a + a*x)^(9/2)*(c - c*x)^(9/2)),x]","\frac{16 x}{35 a^4 c^4 \sqrt{a x+a} \sqrt{c-c x}}+\frac{8 x}{35 a^3 c^3 (a x+a)^{3/2} (c-c x)^{3/2}}+\frac{6 x}{35 a^2 c^2 (a x+a)^{5/2} (c-c x)^{5/2}}+\frac{x}{7 a c (a x+a)^{7/2} (c-c x)^{7/2}}","\frac{16 x}{35 a^4 c^4 \sqrt{a x+a} \sqrt{c-c x}}+\frac{8 x}{35 a^3 c^3 (a x+a)^{3/2} (c-c x)^{3/2}}+\frac{6 x}{35 a^2 c^2 (a x+a)^{5/2} (c-c x)^{5/2}}+\frac{x}{7 a c (a x+a)^{7/2} (c-c x)^{7/2}}",1,"x/(7*a*c*(a + a*x)^(7/2)*(c - c*x)^(7/2)) + (6*x)/(35*a^2*c^2*(a + a*x)^(5/2)*(c - c*x)^(5/2)) + (8*x)/(35*a^3*c^3*(a + a*x)^(3/2)*(c - c*x)^(3/2)) + (16*x)/(35*a^4*c^4*Sqrt[a + a*x]*Sqrt[c - c*x])","A",4,2,20,0.1000,1,"{40, 39}"
1145,1,135,0,0.0522339,"\int (a+b x)^{5/2} (a c-b c x)^{5/2} \, dx","Int[(a + b*x)^(5/2)*(a*c - b*c*x)^(5/2),x]","\frac{5}{16} a^4 c^2 x \sqrt{a+b x} \sqrt{a c-b c x}+\frac{5 a^6 c^{5/2} \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{c (a-b x)}}\right)}{8 b}+\frac{5}{24} a^2 c x (a+b x)^{3/2} (a c-b c x)^{3/2}+\frac{1}{6} x (a+b x)^{5/2} (a c-b c x)^{5/2}","\frac{5}{16} a^4 c^2 x \sqrt{a+b x} \sqrt{a c-b c x}+\frac{5 a^6 c^{5/2} \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{c (a-b x)}}\right)}{8 b}+\frac{5}{24} a^2 c x (a+b x)^{3/2} (a c-b c x)^{3/2}+\frac{1}{6} x (a+b x)^{5/2} (a c-b c x)^{5/2}",1,"(5*a^4*c^2*x*Sqrt[a + b*x]*Sqrt[a*c - b*c*x])/16 + (5*a^2*c*x*(a + b*x)^(3/2)*(a*c - b*c*x)^(3/2))/24 + (x*(a + b*x)^(5/2)*(a*c - b*c*x)^(5/2))/6 + (5*a^6*c^(5/2)*ArcTan[(Sqrt[c]*Sqrt[a + b*x])/Sqrt[c*(a - b*x)]])/(8*b)","A",6,4,23,0.1739,1,"{38, 63, 217, 203}"
1146,1,102,0,0.0361188,"\int (a+b x)^{3/2} (a c-b c x)^{3/2} \, dx","Int[(a + b*x)^(3/2)*(a*c - b*c*x)^(3/2),x]","\frac{3 a^4 c^{3/2} \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{c (a-b x)}}\right)}{4 b}+\frac{3}{8} a^2 c x \sqrt{a+b x} \sqrt{a c-b c x}+\frac{1}{4} x (a+b x)^{3/2} (a c-b c x)^{3/2}","\frac{3 a^4 c^{3/2} \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{c (a-b x)}}\right)}{4 b}+\frac{3}{8} a^2 c x \sqrt{a+b x} \sqrt{a c-b c x}+\frac{1}{4} x (a+b x)^{3/2} (a c-b c x)^{3/2}",1,"(3*a^2*c*x*Sqrt[a + b*x]*Sqrt[a*c - b*c*x])/8 + (x*(a + b*x)^(3/2)*(a*c - b*c*x)^(3/2))/4 + (3*a^4*c^(3/2)*ArcTan[(Sqrt[c]*Sqrt[a + b*x])/Sqrt[c*(a - b*x)]])/(4*b)","A",5,4,23,0.1739,1,"{38, 63, 217, 203}"
1147,1,68,0,0.0265255,"\int \sqrt{a+b x} \sqrt{a c-b c x} \, dx","Int[Sqrt[a + b*x]*Sqrt[a*c - b*c*x],x]","\frac{a^2 \sqrt{c} \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{c (a-b x)}}\right)}{b}+\frac{1}{2} x \sqrt{a+b x} \sqrt{a c-b c x}","\frac{a^2 \sqrt{c} \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{c (a-b x)}}\right)}{b}+\frac{1}{2} x \sqrt{a+b x} \sqrt{a c-b c x}",1,"(x*Sqrt[a + b*x]*Sqrt[a*c - b*c*x])/2 + (a^2*Sqrt[c]*ArcTan[(Sqrt[c]*Sqrt[a + b*x])/Sqrt[c*(a - b*x)]])/b","A",4,4,23,0.1739,1,"{38, 63, 217, 203}"
1148,1,38,0,0.0199325,"\int \frac{1}{\sqrt{a+b x} \sqrt{a c-b c x}} \, dx","Int[1/(Sqrt[a + b*x]*Sqrt[a*c - b*c*x]),x]","\frac{2 \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{c (a-b x)}}\right)}{b \sqrt{c}}","\frac{2 \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{c (a-b x)}}\right)}{b \sqrt{c}}",1,"(2*ArcTan[(Sqrt[c]*Sqrt[a + b*x])/Sqrt[c*(a - b*x)]])/(b*Sqrt[c])","A",3,3,23,0.1304,1,"{63, 217, 203}"
1149,1,30,0,0.0038488,"\int \frac{1}{(a+b x)^{3/2} (a c-b c x)^{3/2}} \, dx","Int[1/((a + b*x)^(3/2)*(a*c - b*c*x)^(3/2)),x]","\frac{x}{a^2 c \sqrt{a+b x} \sqrt{a c-b c x}}","\frac{x}{a^2 c \sqrt{a+b x} \sqrt{a c-b c x}}",1,"x/(a^2*c*Sqrt[a + b*x]*Sqrt[a*c - b*c*x])","A",1,1,23,0.04348,1,"{39}"
1150,1,67,0,0.011025,"\int \frac{1}{(a+b x)^{5/2} (a c-b c x)^{5/2}} \, dx","Int[1/((a + b*x)^(5/2)*(a*c - b*c*x)^(5/2)),x]","\frac{2 x}{3 a^4 c^2 \sqrt{a+b x} \sqrt{a c-b c x}}+\frac{x}{3 a^2 c (a+b x)^{3/2} (a c-b c x)^{3/2}}","\frac{2 x}{3 a^4 c^2 \sqrt{a+b x} \sqrt{a c-b c x}}+\frac{x}{3 a^2 c (a+b x)^{3/2} (a c-b c x)^{3/2}}",1,"x/(3*a^2*c*(a + b*x)^(3/2)*(a*c - b*c*x)^(3/2)) + (2*x)/(3*a^4*c^2*Sqrt[a + b*x]*Sqrt[a*c - b*c*x])","A",2,2,23,0.08696,1,"{40, 39}"
1151,1,100,0,0.0199559,"\int \frac{1}{(a+b x)^{7/2} (a c-b c x)^{7/2}} \, dx","Int[1/((a + b*x)^(7/2)*(a*c - b*c*x)^(7/2)),x]","\frac{8 x}{15 a^6 c^3 \sqrt{a+b x} \sqrt{a c-b c x}}+\frac{4 x}{15 a^4 c^2 (a+b x)^{3/2} (a c-b c x)^{3/2}}+\frac{x}{5 a^2 c (a+b x)^{5/2} (a c-b c x)^{5/2}}","\frac{8 x}{15 a^6 c^3 \sqrt{a+b x} \sqrt{a c-b c x}}+\frac{4 x}{15 a^4 c^2 (a+b x)^{3/2} (a c-b c x)^{3/2}}+\frac{x}{5 a^2 c (a+b x)^{5/2} (a c-b c x)^{5/2}}",1,"x/(5*a^2*c*(a + b*x)^(5/2)*(a*c - b*c*x)^(5/2)) + (4*x)/(15*a^4*c^2*(a + b*x)^(3/2)*(a*c - b*c*x)^(3/2)) + (8*x)/(15*a^6*c^3*Sqrt[a + b*x]*Sqrt[a*c - b*c*x])","A",3,2,23,0.08696,1,"{40, 39}"
1152,1,133,0,0.033947,"\int \frac{1}{(a+b x)^{9/2} (a c-b c x)^{9/2}} \, dx","Int[1/((a + b*x)^(9/2)*(a*c - b*c*x)^(9/2)),x]","\frac{16 x}{35 a^8 c^4 \sqrt{a+b x} \sqrt{a c-b c x}}+\frac{8 x}{35 a^6 c^3 (a+b x)^{3/2} (a c-b c x)^{3/2}}+\frac{6 x}{35 a^4 c^2 (a+b x)^{5/2} (a c-b c x)^{5/2}}+\frac{x}{7 a^2 c (a+b x)^{7/2} (a c-b c x)^{7/2}}","\frac{16 x}{35 a^8 c^4 \sqrt{a+b x} \sqrt{a c-b c x}}+\frac{8 x}{35 a^6 c^3 (a+b x)^{3/2} (a c-b c x)^{3/2}}+\frac{6 x}{35 a^4 c^2 (a+b x)^{5/2} (a c-b c x)^{5/2}}+\frac{x}{7 a^2 c (a+b x)^{7/2} (a c-b c x)^{7/2}}",1,"x/(7*a^2*c*(a + b*x)^(7/2)*(a*c - b*c*x)^(7/2)) + (6*x)/(35*a^4*c^2*(a + b*x)^(5/2)*(a*c - b*c*x)^(5/2)) + (8*x)/(35*a^6*c^3*(a + b*x)^(3/2)*(a*c - b*c*x)^(3/2)) + (16*x)/(35*a^8*c^4*Sqrt[a + b*x]*Sqrt[a*c - b*c*x])","A",4,2,23,0.08696,1,"{40, 39}"
1153,1,100,0,0.0166831,"\int (3-6 x)^{5/2} (2+4 x)^{5/2} \, dx","Int[(3 - 6*x)^(5/2)*(2 + 4*x)^(5/2),x]","6 \sqrt{6} (1-2 x)^{5/2} x (2 x+1)^{5/2}+15 \sqrt{\frac{3}{2}} (1-2 x)^{3/2} x (2 x+1)^{3/2}+\frac{45}{2} \sqrt{\frac{3}{2}} \sqrt{1-2 x} x \sqrt{2 x+1}+\frac{45}{4} \sqrt{\frac{3}{2}} \sin ^{-1}(2 x)","6 \sqrt{6} (1-2 x)^{5/2} x (2 x+1)^{5/2}+15 \sqrt{\frac{3}{2}} (1-2 x)^{3/2} x (2 x+1)^{3/2}+\frac{45}{2} \sqrt{\frac{3}{2}} \sqrt{1-2 x} x \sqrt{2 x+1}+\frac{45}{4} \sqrt{\frac{3}{2}} \sin ^{-1}(2 x)",1,"(45*Sqrt[3/2]*Sqrt[1 - 2*x]*x*Sqrt[1 + 2*x])/2 + 15*Sqrt[3/2]*(1 - 2*x)^(3/2)*x*(1 + 2*x)^(3/2) + 6*Sqrt[6]*(1 - 2*x)^(5/2)*x*(1 + 2*x)^(5/2) + (45*Sqrt[3/2]*ArcSin[2*x])/4","A",5,3,19,0.1579,1,"{38, 41, 216}"
1154,1,74,0,0.0100821,"\int (3-6 x)^{3/2} (2+4 x)^{3/2} \, dx","Int[(3 - 6*x)^(3/2)*(2 + 4*x)^(3/2),x]","3 \sqrt{\frac{3}{2}} (1-2 x)^{3/2} x (2 x+1)^{3/2}+\frac{9}{2} \sqrt{\frac{3}{2}} \sqrt{1-2 x} x \sqrt{2 x+1}+\frac{9}{4} \sqrt{\frac{3}{2}} \sin ^{-1}(2 x)","3 \sqrt{\frac{3}{2}} (1-2 x)^{3/2} x (2 x+1)^{3/2}+\frac{9}{2} \sqrt{\frac{3}{2}} \sqrt{1-2 x} x \sqrt{2 x+1}+\frac{9}{4} \sqrt{\frac{3}{2}} \sin ^{-1}(2 x)",1,"(9*Sqrt[3/2]*Sqrt[1 - 2*x]*x*Sqrt[1 + 2*x])/2 + 3*Sqrt[3/2]*(1 - 2*x)^(3/2)*x*(1 + 2*x)^(3/2) + (9*Sqrt[3/2]*ArcSin[2*x])/4","A",4,3,19,0.1579,1,"{38, 41, 216}"
1155,1,43,0,0.0057703,"\int \sqrt{3-6 x} \sqrt{2+4 x} \, dx","Int[Sqrt[3 - 6*x]*Sqrt[2 + 4*x],x]","\sqrt{\frac{3}{2}} \sqrt{1-2 x} \sqrt{2 x+1} x+\frac{1}{2} \sqrt{\frac{3}{2}} \sin ^{-1}(2 x)","\sqrt{\frac{3}{2}} \sqrt{1-2 x} \sqrt{2 x+1} x+\frac{1}{2} \sqrt{\frac{3}{2}} \sin ^{-1}(2 x)",1,"Sqrt[3/2]*Sqrt[1 - 2*x]*x*Sqrt[1 + 2*x] + (Sqrt[3/2]*ArcSin[2*x])/2","A",3,3,19,0.1579,1,"{38, 41, 216}"
1156,1,13,0,0.0025095,"\int \frac{1}{\sqrt{3-6 x} \sqrt{2+4 x}} \, dx","Int[1/(Sqrt[3 - 6*x]*Sqrt[2 + 4*x]),x]","\frac{\sin ^{-1}(2 x)}{2 \sqrt{6}}","\frac{\sin ^{-1}(2 x)}{2 \sqrt{6}}",1,"ArcSin[2*x]/(2*Sqrt[6])","A",2,2,19,0.1053,1,"{41, 216}"
1157,1,28,0,0.0019949,"\int \frac{1}{(3-6 x)^{3/2} (2+4 x)^{3/2}} \, dx","Int[1/((3 - 6*x)^(3/2)*(2 + 4*x)^(3/2)),x]","\frac{x}{6 \sqrt{6} \sqrt{1-2 x} \sqrt{2 x+1}}","\frac{x}{6 \sqrt{6} \sqrt{1-2 x} \sqrt{2 x+1}}",1,"x/(6*Sqrt[6]*Sqrt[1 - 2*x]*Sqrt[1 + 2*x])","A",1,1,19,0.05263,1,"{39}"
1158,1,57,0,0.0062288,"\int \frac{1}{(3-6 x)^{5/2} (2+4 x)^{5/2}} \, dx","Int[1/((3 - 6*x)^(5/2)*(2 + 4*x)^(5/2)),x]","\frac{x}{54 \sqrt{6} \sqrt{1-2 x} \sqrt{2 x+1}}+\frac{x}{108 \sqrt{6} (1-2 x)^{3/2} (2 x+1)^{3/2}}","\frac{x}{54 \sqrt{6} \sqrt{1-2 x} \sqrt{2 x+1}}+\frac{x}{108 \sqrt{6} (1-2 x)^{3/2} (2 x+1)^{3/2}}",1,"x/(108*Sqrt[6]*(1 - 2*x)^(3/2)*(1 + 2*x)^(3/2)) + x/(54*Sqrt[6]*Sqrt[1 - 2*x]*Sqrt[1 + 2*x])","A",2,2,19,0.1053,1,"{40, 39}"
1159,1,85,0,0.0110413,"\int \frac{1}{(3-6 x)^{7/2} (2+4 x)^{7/2}} \, dx","Int[1/((3 - 6*x)^(7/2)*(2 + 4*x)^(7/2)),x]","\frac{x}{405 \sqrt{6} \sqrt{1-2 x} \sqrt{2 x+1}}+\frac{x}{810 \sqrt{6} (1-2 x)^{3/2} (2 x+1)^{3/2}}+\frac{x}{1080 \sqrt{6} (1-2 x)^{5/2} (2 x+1)^{5/2}}","\frac{x}{405 \sqrt{6} \sqrt{1-2 x} \sqrt{2 x+1}}+\frac{x}{810 \sqrt{6} (1-2 x)^{3/2} (2 x+1)^{3/2}}+\frac{x}{1080 \sqrt{6} (1-2 x)^{5/2} (2 x+1)^{5/2}}",1,"x/(1080*Sqrt[6]*(1 - 2*x)^(5/2)*(1 + 2*x)^(5/2)) + x/(810*Sqrt[6]*(1 - 2*x)^(3/2)*(1 + 2*x)^(3/2)) + x/(405*Sqrt[6]*Sqrt[1 - 2*x]*Sqrt[1 + 2*x])","A",3,2,19,0.1053,1,"{40, 39}"
1160,1,91,0,0.0220188,"\int (3-x)^{3/2} (-2+x)^{3/2} \, dx","Int[(3 - x)^(3/2)*(-2 + x)^(3/2),x]","-\frac{1}{4} (x-2)^{3/2} (3-x)^{5/2}-\frac{1}{8} \sqrt{x-2} (3-x)^{5/2}+\frac{1}{32} \sqrt{x-2} (3-x)^{3/2}+\frac{3}{64} \sqrt{x-2} \sqrt{3-x}-\frac{3}{128} \sin ^{-1}(5-2 x)","-\frac{1}{4} (x-2)^{3/2} (3-x)^{5/2}-\frac{1}{8} \sqrt{x-2} (3-x)^{5/2}+\frac{1}{32} \sqrt{x-2} (3-x)^{3/2}+\frac{3}{64} \sqrt{x-2} \sqrt{3-x}-\frac{3}{128} \sin ^{-1}(5-2 x)",1,"(3*Sqrt[3 - x]*Sqrt[-2 + x])/64 + ((3 - x)^(3/2)*Sqrt[-2 + x])/32 - ((3 - x)^(5/2)*Sqrt[-2 + x])/8 - ((3 - x)^(5/2)*(-2 + x)^(3/2))/4 - (3*ArcSin[5 - 2*x])/128","A",7,4,17,0.2353,1,"{50, 53, 619, 216}"
1161,1,51,0,0.0097638,"\int \sqrt{3-x} \sqrt{-2+x} \, dx","Int[Sqrt[3 - x]*Sqrt[-2 + x],x]","-\frac{1}{2} \sqrt{x-2} (3-x)^{3/2}+\frac{1}{4} \sqrt{x-2} \sqrt{3-x}-\frac{1}{8} \sin ^{-1}(5-2 x)","-\frac{1}{2} \sqrt{x-2} (3-x)^{3/2}+\frac{1}{4} \sqrt{x-2} \sqrt{3-x}-\frac{1}{8} \sin ^{-1}(5-2 x)",1,"(Sqrt[3 - x]*Sqrt[-2 + x])/4 - ((3 - x)^(3/2)*Sqrt[-2 + x])/2 - ArcSin[5 - 2*x]/8","A",5,4,17,0.2353,1,"{50, 53, 619, 216}"
1162,1,8,0,0.0041647,"\int \frac{1}{\sqrt{3-x} \sqrt{-2+x}} \, dx","Int[1/(Sqrt[3 - x]*Sqrt[-2 + x]),x]","-\sin ^{-1}(5-2 x)","-\sin ^{-1}(5-2 x)",1,"-ArcSin[5 - 2*x]","A",3,3,17,0.1765,1,"{53, 619, 216}"
1163,1,37,0,0.0044166,"\int \frac{1}{(3-x)^{3/2} (-2+x)^{3/2}} \, dx","Int[1/((3 - x)^(3/2)*(-2 + x)^(3/2)),x]","\frac{2}{\sqrt{3-x} \sqrt{x-2}}-\frac{4 \sqrt{3-x}}{\sqrt{x-2}}","\frac{2}{\sqrt{3-x} \sqrt{x-2}}-\frac{4 \sqrt{3-x}}{\sqrt{x-2}}",1,"2/(Sqrt[3 - x]*Sqrt[-2 + x]) - (4*Sqrt[3 - x])/Sqrt[-2 + x]","A",2,2,17,0.1176,1,"{45, 37}"
1164,1,79,0,0.0127822,"\int \frac{1}{(3-x)^{5/2} (-2+x)^{5/2}} \, dx","Int[1/((3 - x)^(5/2)*(-2 + x)^(5/2)),x]","-\frac{32 \sqrt{3-x}}{3 \sqrt{x-2}}-\frac{16 \sqrt{3-x}}{3 (x-2)^{3/2}}+\frac{4}{(x-2)^{3/2} \sqrt{3-x}}+\frac{2}{3 (x-2)^{3/2} (3-x)^{3/2}}","-\frac{32 \sqrt{3-x}}{3 \sqrt{x-2}}-\frac{16 \sqrt{3-x}}{3 (x-2)^{3/2}}+\frac{4}{(x-2)^{3/2} \sqrt{3-x}}+\frac{2}{3 (x-2)^{3/2} (3-x)^{3/2}}",1,"2/(3*(3 - x)^(3/2)*(-2 + x)^(3/2)) + 4/(Sqrt[3 - x]*(-2 + x)^(3/2)) - (16*Sqrt[3 - x])/(3*(-2 + x)^(3/2)) - (32*Sqrt[3 - x])/(3*Sqrt[-2 + x])","A",4,2,17,0.1176,1,"{45, 37}"
1165,1,21,0,0.0016875,"\int \frac{1}{(3-x)^{3/2} (3+x)^{3/2}} \, dx","Int[1/((3 - x)^(3/2)*(3 + x)^(3/2)),x]","\frac{x}{9 \sqrt{3-x} \sqrt{x+3}}","\frac{x}{9 \sqrt{3-x} \sqrt{x+3}}",1,"x/(9*Sqrt[3 - x]*Sqrt[3 + x])","A",1,1,17,0.05882,1,"{39}"
1166,1,24,0,0.0025522,"\int \frac{1}{(3-b x)^{3/2} (3+b x)^{3/2}} \, dx","Int[1/((3 - b*x)^(3/2)*(3 + b*x)^(3/2)),x]","\frac{x}{9 \sqrt{3-b x} \sqrt{b x+3}}","\frac{x}{9 \sqrt{3-b x} \sqrt{b x+3}}",1,"x/(9*Sqrt[3 - b*x]*Sqrt[3 + b*x])","A",1,1,20,0.05000,1,"{39}"
1167,1,26,0,0.0016731,"\int \frac{1}{(6-2 x)^{3/2} (3+x)^{3/2}} \, dx","Int[1/((6 - 2*x)^(3/2)*(3 + x)^(3/2)),x]","\frac{x}{18 \sqrt{2} \sqrt{3-x} \sqrt{x+3}}","\frac{x}{18 \sqrt{2} \sqrt{3-x} \sqrt{x+3}}",1,"x/(18*Sqrt[2]*Sqrt[3 - x]*Sqrt[3 + x])","A",1,1,17,0.05882,1,"{39}"
1168,1,29,0,0.0025479,"\int \frac{1}{(6-2 b x)^{3/2} (3+b x)^{3/2}} \, dx","Int[1/((6 - 2*b*x)^(3/2)*(3 + b*x)^(3/2)),x]","\frac{x}{18 \sqrt{2} \sqrt{3-b x} \sqrt{b x+3}}","\frac{x}{18 \sqrt{2} \sqrt{3-b x} \sqrt{b x+3}}",1,"x/(18*Sqrt[2]*Sqrt[3 - b*x]*Sqrt[3 + b*x])","A",1,1,20,0.05000,1,"{39}"
1169,1,39,0,0.024387,"\int \frac{1}{\sqrt{a+b x} \sqrt{-a d+b d x}} \, dx","Int[1/(Sqrt[a + b*x]*Sqrt[-(a*d) + b*d*x]),x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b d x-a d}}\right)}{b \sqrt{d}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b d x-a d}}\right)}{b \sqrt{d}}",1,"(2*ArcTanh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[-(a*d) + b*d*x]])/(b*Sqrt[d])","A",3,3,23,0.1304,1,"{63, 217, 206}"
1170,1,241,0,0.2542856,"\int \frac{1}{\sqrt[4]{6-3 e x} (2+e x)^{3/4}} \, dx","Int[1/((6 - 3*e*x)^(1/4)*(2 + e*x)^(3/4)),x]","-\frac{\log \left(\frac{\sqrt{6-3 e x}+\sqrt{3} \sqrt{e x+2}-\sqrt{6} \sqrt[4]{2-e x} \sqrt[4]{e x+2}}{\sqrt{e x+2}}\right)}{\sqrt{2} \sqrt[4]{3} e}+\frac{\log \left(\frac{\sqrt{6-3 e x}+\sqrt{3} \sqrt{e x+2}+\sqrt{6} \sqrt[4]{2-e x} \sqrt[4]{e x+2}}{\sqrt{e x+2}}\right)}{\sqrt{2} \sqrt[4]{3} e}+\frac{\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{2-e x}}{\sqrt[4]{e x+2}}\right)}{\sqrt[4]{3} e}-\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{2-e x}}{\sqrt[4]{e x+2}}+1\right)}{\sqrt[4]{3} e}","-\frac{\log \left(\frac{\sqrt{6-3 e x}+\sqrt{3} \sqrt{e x+2}-\sqrt{6} \sqrt[4]{2-e x} \sqrt[4]{e x+2}}{\sqrt{e x+2}}\right)}{\sqrt{2} \sqrt[4]{3} e}+\frac{\log \left(\frac{\sqrt{6-3 e x}+\sqrt{3} \sqrt{e x+2}+\sqrt{6} \sqrt[4]{2-e x} \sqrt[4]{e x+2}}{\sqrt{e x+2}}\right)}{\sqrt{2} \sqrt[4]{3} e}+\frac{\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{2-e x}}{\sqrt[4]{e x+2}}\right)}{\sqrt[4]{3} e}-\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{2-e x}}{\sqrt[4]{e x+2}}+1\right)}{\sqrt[4]{3} e}",1,"(Sqrt[2]*ArcTan[1 - (Sqrt[2]*(2 - e*x)^(1/4))/(2 + e*x)^(1/4)])/(3^(1/4)*e) - (Sqrt[2]*ArcTan[1 + (Sqrt[2]*(2 - e*x)^(1/4))/(2 + e*x)^(1/4)])/(3^(1/4)*e) - Log[(Sqrt[6 - 3*e*x] - Sqrt[6]*(2 - e*x)^(1/4)*(2 + e*x)^(1/4) + Sqrt[3]*Sqrt[2 + e*x])/Sqrt[2 + e*x]]/(Sqrt[2]*3^(1/4)*e) + Log[(Sqrt[6 - 3*e*x] + Sqrt[6]*(2 - e*x)^(1/4)*(2 + e*x)^(1/4) + Sqrt[3]*Sqrt[2 + e*x])/Sqrt[2 + e*x]]/(Sqrt[2]*3^(1/4)*e)","A",11,8,20,0.4000,1,"{63, 331, 297, 1162, 617, 204, 1165, 628}"
1171,1,144,0,0.0343024,"\int \frac{(a-i a x)^{7/4}}{\sqrt[4]{a+i a x}} \, dx","Int[(a - I*a*x)^(7/4)/(a + I*a*x)^(1/4),x]","-\frac{14 a^2 \sqrt[4]{x^2+1} E\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{5 \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}+\frac{14 a^2 x}{5 \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}-\frac{14}{15} i (a-i a x)^{3/4} (a+i a x)^{3/4}-\frac{2 i (a-i a x)^{7/4} (a+i a x)^{3/4}}{5 a}","-\frac{14 a^2 \sqrt[4]{x^2+1} E\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{5 \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}+\frac{14 a^2 x}{5 \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}-\frac{14}{15} i (a-i a x)^{3/4} (a+i a x)^{3/4}-\frac{2 i (a-i a x)^{7/4} (a+i a x)^{3/4}}{5 a}",1,"(14*a^2*x)/(5*(a - I*a*x)^(1/4)*(a + I*a*x)^(1/4)) - ((14*I)/15)*(a - I*a*x)^(3/4)*(a + I*a*x)^(3/4) - (((2*I)/5)*(a - I*a*x)^(7/4)*(a + I*a*x)^(3/4))/a - (14*a^2*(1 + x^2)^(1/4)*EllipticE[ArcTan[x]/2, 2])/(5*(a - I*a*x)^(1/4)*(a + I*a*x)^(1/4))","A",6,5,25,0.2000,1,"{50, 42, 229, 227, 196}"
1172,1,106,0,0.0223588,"\int \frac{(a-i a x)^{3/4}}{\sqrt[4]{a+i a x}} \, dx","Int[(a - I*a*x)^(3/4)/(a + I*a*x)^(1/4),x]","-\frac{2 a \sqrt[4]{x^2+1} E\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{\sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}+\frac{2 a x}{\sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}-\frac{2 i (a-i a x)^{3/4} (a+i a x)^{3/4}}{3 a}","-\frac{2 a \sqrt[4]{x^2+1} E\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{\sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}+\frac{2 a x}{\sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}-\frac{2 i (a-i a x)^{3/4} (a+i a x)^{3/4}}{3 a}",1,"(2*a*x)/((a - I*a*x)^(1/4)*(a + I*a*x)^(1/4)) - (((2*I)/3)*(a - I*a*x)^(3/4)*(a + I*a*x)^(3/4))/a - (2*a*(1 + x^2)^(1/4)*EllipticE[ArcTan[x]/2, 2])/((a - I*a*x)^(1/4)*(a + I*a*x)^(1/4))","A",5,5,25,0.2000,1,"{50, 42, 229, 227, 196}"
1173,1,71,0,0.0119873,"\int \frac{1}{\sqrt[4]{a-i a x} \sqrt[4]{a+i a x}} \, dx","Int[1/((a - I*a*x)^(1/4)*(a + I*a*x)^(1/4)),x]","\frac{2 x}{\sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}-\frac{2 \sqrt[4]{x^2+1} E\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{\sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}","\frac{2 x}{\sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}-\frac{2 \sqrt[4]{x^2+1} E\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{\sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}",1,"(2*x)/((a - I*a*x)^(1/4)*(a + I*a*x)^(1/4)) - (2*(1 + x^2)^(1/4)*EllipticE[ArcTan[x]/2, 2])/((a - I*a*x)^(1/4)*(a + I*a*x)^(1/4))","A",4,4,25,0.1600,1,"{42, 229, 227, 196}"
1174,1,78,0,0.0159803,"\int \frac{1}{(a-i a x)^{5/4} \sqrt[4]{a+i a x}} \, dx","Int[1/((a - I*a*x)^(5/4)*(a + I*a*x)^(1/4)),x]","\frac{2 \sqrt[4]{x^2+1} E\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{a \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}-\frac{2 i}{a \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}","\frac{2 \sqrt[4]{x^2+1} E\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{a \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}-\frac{2 i}{a \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}",1,"(-2*I)/(a*(a - I*a*x)^(1/4)*(a + I*a*x)^(1/4)) + (2*(1 + x^2)^(1/4)*EllipticE[ArcTan[x]/2, 2])/(a*(a - I*a*x)^(1/4)*(a + I*a*x)^(1/4))","A",4,4,25,0.1600,1,"{48, 42, 197, 196}"
1175,1,82,0,0.0165606,"\int \frac{1}{(a-i a x)^{9/4} \sqrt[4]{a+i a x}} \, dx","Int[1/((a - I*a*x)^(9/4)*(a + I*a*x)^(1/4)),x]","\frac{2 \sqrt[4]{x^2+1} E\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{5 a^2 \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}-\frac{4 i}{5 a (a-i a x)^{5/4} \sqrt[4]{a+i a x}}","\frac{2 \sqrt[4]{x^2+1} E\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{5 a^2 \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}-\frac{4 i}{5 a (a-i a x)^{5/4} \sqrt[4]{a+i a x}}",1,"((-4*I)/5)/(a*(a - I*a*x)^(5/4)*(a + I*a*x)^(1/4)) + (2*(1 + x^2)^(1/4)*EllipticE[ArcTan[x]/2, 2])/(5*a^2*(a - I*a*x)^(1/4)*(a + I*a*x)^(1/4))","A",4,4,25,0.1600,1,"{46, 42, 197, 196}"
1176,1,115,0,0.02639,"\int \frac{1}{(a-i a x)^{13/4} \sqrt[4]{a+i a x}} \, dx","Int[1/((a - I*a*x)^(13/4)*(a + I*a*x)^(1/4)),x]","\frac{2 \sqrt[4]{x^2+1} E\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{15 a^3 \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}-\frac{2 i (a+i a x)^{3/4}}{9 a^2 (a-i a x)^{9/4}}-\frac{4 i}{15 a^2 (a-i a x)^{5/4} \sqrt[4]{a+i a x}}","\frac{2 \sqrt[4]{x^2+1} E\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{15 a^3 \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}-\frac{2 i (a+i a x)^{3/4}}{9 a^2 (a-i a x)^{9/4}}-\frac{4 i}{15 a^2 (a-i a x)^{5/4} \sqrt[4]{a+i a x}}",1,"((-4*I)/15)/(a^2*(a - I*a*x)^(5/4)*(a + I*a*x)^(1/4)) - (((2*I)/9)*(a + I*a*x)^(3/4))/(a^2*(a - I*a*x)^(9/4)) + (2*(1 + x^2)^(1/4)*EllipticE[ArcTan[x]/2, 2])/(15*a^3*(a - I*a*x)^(1/4)*(a + I*a*x)^(1/4))","A",5,5,25,0.2000,1,"{51, 46, 42, 197, 196}"
1177,1,148,0,0.0384858,"\int \frac{1}{(a-i a x)^{17/4} \sqrt[4]{a+i a x}} \, dx","Int[1/((a - I*a*x)^(17/4)*(a + I*a*x)^(1/4)),x]","\frac{2 \sqrt[4]{x^2+1} E\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{39 a^4 \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}-\frac{10 i (a+i a x)^{3/4}}{117 a^3 (a-i a x)^{9/4}}-\frac{2 i (a+i a x)^{3/4}}{13 a^2 (a-i a x)^{13/4}}-\frac{4 i}{39 a^3 (a-i a x)^{5/4} \sqrt[4]{a+i a x}}","\frac{2 \sqrt[4]{x^2+1} E\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{39 a^4 \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}-\frac{10 i (a+i a x)^{3/4}}{117 a^3 (a-i a x)^{9/4}}-\frac{2 i (a+i a x)^{3/4}}{13 a^2 (a-i a x)^{13/4}}-\frac{4 i}{39 a^3 (a-i a x)^{5/4} \sqrt[4]{a+i a x}}",1,"((-4*I)/39)/(a^3*(a - I*a*x)^(5/4)*(a + I*a*x)^(1/4)) - (((2*I)/13)*(a + I*a*x)^(3/4))/(a^2*(a - I*a*x)^(13/4)) - (((10*I)/117)*(a + I*a*x)^(3/4))/(a^3*(a - I*a*x)^(9/4)) + (2*(1 + x^2)^(1/4)*EllipticE[ArcTan[x]/2, 2])/(39*a^4*(a - I*a*x)^(1/4)*(a + I*a*x)^(1/4))","A",6,5,25,0.2000,1,"{51, 46, 42, 197, 196}"
1178,1,256,0,0.1729159,"\int \frac{\sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}} \, dx","Int[(a - I*a*x)^(1/4)/(a + I*a*x)^(1/4),x]","-\frac{i \sqrt[4]{a-i a x} (a+i a x)^{3/4}}{a}-\frac{i \log \left(\frac{\sqrt{a-i a x}}{\sqrt{a+i a x}}-\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}+1\right)}{2 \sqrt{2}}+\frac{i \log \left(\frac{\sqrt{a-i a x}}{\sqrt{a+i a x}}+\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}+1\right)}{2 \sqrt{2}}-\frac{i \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}\right)}{\sqrt{2}}+\frac{i \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}\right)}{\sqrt{2}}","-\frac{i \sqrt[4]{a-i a x} (a+i a x)^{3/4}}{a}-\frac{i \log \left(\frac{\sqrt{a-i a x}}{\sqrt{a+i a x}}-\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}+1\right)}{2 \sqrt{2}}+\frac{i \log \left(\frac{\sqrt{a-i a x}}{\sqrt{a+i a x}}+\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}+1\right)}{2 \sqrt{2}}-\frac{i \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}\right)}{\sqrt{2}}+\frac{i \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}\right)}{\sqrt{2}}",1,"((-I)*(a - I*a*x)^(1/4)*(a + I*a*x)^(3/4))/a - (I*ArcTan[1 - (Sqrt[2]*(a - I*a*x)^(1/4))/(a + I*a*x)^(1/4)])/Sqrt[2] + (I*ArcTan[1 + (Sqrt[2]*(a - I*a*x)^(1/4))/(a + I*a*x)^(1/4)])/Sqrt[2] - ((I/2)*Log[1 + Sqrt[a - I*a*x]/Sqrt[a + I*a*x] - (Sqrt[2]*(a - I*a*x)^(1/4))/(a + I*a*x)^(1/4)])/Sqrt[2] + ((I/2)*Log[1 + Sqrt[a - I*a*x]/Sqrt[a + I*a*x] + (Sqrt[2]*(a - I*a*x)^(1/4))/(a + I*a*x)^(1/4)])/Sqrt[2]","A",12,9,25,0.3600,1,"{50, 63, 240, 211, 1165, 628, 1162, 617, 204}"
1179,1,233,0,0.1306967,"\int \frac{1}{(a-i a x)^{3/4} \sqrt[4]{a+i a x}} \, dx","Int[1/((a - I*a*x)^(3/4)*(a + I*a*x)^(1/4)),x]","-\frac{i \log \left(\frac{\sqrt{a-i a x}}{\sqrt{a+i a x}}-\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}+1\right)}{\sqrt{2} a}+\frac{i \log \left(\frac{\sqrt{a-i a x}}{\sqrt{a+i a x}}+\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}+1\right)}{\sqrt{2} a}-\frac{i \sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}\right)}{a}+\frac{i \sqrt{2} \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}\right)}{a}","-\frac{i \log \left(\frac{\sqrt{a-i a x}}{\sqrt{a+i a x}}-\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}+1\right)}{\sqrt{2} a}+\frac{i \log \left(\frac{\sqrt{a-i a x}}{\sqrt{a+i a x}}+\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}+1\right)}{\sqrt{2} a}-\frac{i \sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}\right)}{a}+\frac{i \sqrt{2} \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}\right)}{a}",1,"((-I)*Sqrt[2]*ArcTan[1 - (Sqrt[2]*(a - I*a*x)^(1/4))/(a + I*a*x)^(1/4)])/a + (I*Sqrt[2]*ArcTan[1 + (Sqrt[2]*(a - I*a*x)^(1/4))/(a + I*a*x)^(1/4)])/a - (I*Log[1 + Sqrt[a - I*a*x]/Sqrt[a + I*a*x] - (Sqrt[2]*(a - I*a*x)^(1/4))/(a + I*a*x)^(1/4)])/(Sqrt[2]*a) + (I*Log[1 + Sqrt[a - I*a*x]/Sqrt[a + I*a*x] + (Sqrt[2]*(a - I*a*x)^(1/4))/(a + I*a*x)^(1/4)])/(Sqrt[2]*a)","A",11,8,25,0.3200,1,"{63, 240, 211, 1165, 628, 1162, 617, 204}"
1180,1,33,0,0.0032194,"\int \frac{1}{(a-i a x)^{7/4} \sqrt[4]{a+i a x}} \, dx","Int[1/((a - I*a*x)^(7/4)*(a + I*a*x)^(1/4)),x]","-\frac{2 i (a+i a x)^{3/4}}{3 a^2 (a-i a x)^{3/4}}","-\frac{2 i (a+i a x)^{3/4}}{3 a^2 (a-i a x)^{3/4}}",1,"(((-2*I)/3)*(a + I*a*x)^(3/4))/(a^2*(a - I*a*x)^(3/4))","A",1,1,25,0.04000,1,"{37}"
1181,1,67,0,0.0094478,"\int \frac{1}{(a-i a x)^{11/4} \sqrt[4]{a+i a x}} \, dx","Int[1/((a - I*a*x)^(11/4)*(a + I*a*x)^(1/4)),x]","-\frac{4 i (a+i a x)^{3/4}}{21 a^3 (a-i a x)^{3/4}}-\frac{2 i (a+i a x)^{3/4}}{7 a^2 (a-i a x)^{7/4}}","-\frac{4 i (a+i a x)^{3/4}}{21 a^3 (a-i a x)^{3/4}}-\frac{2 i (a+i a x)^{3/4}}{7 a^2 (a-i a x)^{7/4}}",1,"(((-2*I)/7)*(a + I*a*x)^(3/4))/(a^2*(a - I*a*x)^(7/4)) - (((4*I)/21)*(a + I*a*x)^(3/4))/(a^3*(a - I*a*x)^(3/4))","A",2,2,25,0.08000,1,"{45, 37}"
1182,1,100,0,0.0182027,"\int \frac{1}{(a-i a x)^{15/4} \sqrt[4]{a+i a x}} \, dx","Int[1/((a - I*a*x)^(15/4)*(a + I*a*x)^(1/4)),x]","-\frac{16 i (a+i a x)^{3/4}}{231 a^4 (a-i a x)^{3/4}}-\frac{8 i (a+i a x)^{3/4}}{77 a^3 (a-i a x)^{7/4}}-\frac{2 i (a+i a x)^{3/4}}{11 a^2 (a-i a x)^{11/4}}","-\frac{16 i (a+i a x)^{3/4}}{231 a^4 (a-i a x)^{3/4}}-\frac{8 i (a+i a x)^{3/4}}{77 a^3 (a-i a x)^{7/4}}-\frac{2 i (a+i a x)^{3/4}}{11 a^2 (a-i a x)^{11/4}}",1,"(((-2*I)/11)*(a + I*a*x)^(3/4))/(a^2*(a - I*a*x)^(11/4)) - (((8*I)/77)*(a + I*a*x)^(3/4))/(a^3*(a - I*a*x)^(7/4)) - (((16*I)/231)*(a + I*a*x)^(3/4))/(a^4*(a - I*a*x)^(3/4))","A",3,2,25,0.08000,1,"{45, 37}"
1183,1,133,0,0.0283329,"\int \frac{1}{(a-i a x)^{19/4} \sqrt[4]{a+i a x}} \, dx","Int[1/((a - I*a*x)^(19/4)*(a + I*a*x)^(1/4)),x]","-\frac{32 i (a+i a x)^{3/4}}{1155 a^5 (a-i a x)^{3/4}}-\frac{16 i (a+i a x)^{3/4}}{385 a^4 (a-i a x)^{7/4}}-\frac{4 i (a+i a x)^{3/4}}{55 a^3 (a-i a x)^{11/4}}-\frac{2 i (a+i a x)^{3/4}}{15 a^2 (a-i a x)^{15/4}}","-\frac{32 i (a+i a x)^{3/4}}{1155 a^5 (a-i a x)^{3/4}}-\frac{16 i (a+i a x)^{3/4}}{385 a^4 (a-i a x)^{7/4}}-\frac{4 i (a+i a x)^{3/4}}{55 a^3 (a-i a x)^{11/4}}-\frac{2 i (a+i a x)^{3/4}}{15 a^2 (a-i a x)^{15/4}}",1,"(((-2*I)/15)*(a + I*a*x)^(3/4))/(a^2*(a - I*a*x)^(15/4)) - (((4*I)/55)*(a + I*a*x)^(3/4))/(a^3*(a - I*a*x)^(11/4)) - (((16*I)/385)*(a + I*a*x)^(3/4))/(a^4*(a - I*a*x)^(7/4)) - (((32*I)/1155)*(a + I*a*x)^(3/4))/(a^5*(a - I*a*x)^(3/4))","A",4,2,25,0.08000,1,"{45, 37}"
1184,1,256,0,0.1582508,"\int \frac{(a-i a x)^{3/4}}{(a+i a x)^{3/4}} \, dx","Int[(a - I*a*x)^(3/4)/(a + I*a*x)^(3/4),x]","-\frac{i (a-i a x)^{3/4} \sqrt[4]{a+i a x}}{a}+\frac{3 i \log \left(\frac{\sqrt{a-i a x}}{\sqrt{a+i a x}}-\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}+1\right)}{2 \sqrt{2}}-\frac{3 i \log \left(\frac{\sqrt{a-i a x}}{\sqrt{a+i a x}}+\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}+1\right)}{2 \sqrt{2}}-\frac{3 i \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}\right)}{\sqrt{2}}+\frac{3 i \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}\right)}{\sqrt{2}}","-\frac{i (a-i a x)^{3/4} \sqrt[4]{a+i a x}}{a}+\frac{3 i \log \left(\frac{\sqrt{a-i a x}}{\sqrt{a+i a x}}-\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}+1\right)}{2 \sqrt{2}}-\frac{3 i \log \left(\frac{\sqrt{a-i a x}}{\sqrt{a+i a x}}+\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}+1\right)}{2 \sqrt{2}}-\frac{3 i \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}\right)}{\sqrt{2}}+\frac{3 i \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}\right)}{\sqrt{2}}",1,"((-I)*(a - I*a*x)^(3/4)*(a + I*a*x)^(1/4))/a - ((3*I)*ArcTan[1 - (Sqrt[2]*(a - I*a*x)^(1/4))/(a + I*a*x)^(1/4)])/Sqrt[2] + ((3*I)*ArcTan[1 + (Sqrt[2]*(a - I*a*x)^(1/4))/(a + I*a*x)^(1/4)])/Sqrt[2] + (((3*I)/2)*Log[1 + Sqrt[a - I*a*x]/Sqrt[a + I*a*x] - (Sqrt[2]*(a - I*a*x)^(1/4))/(a + I*a*x)^(1/4)])/Sqrt[2] - (((3*I)/2)*Log[1 + Sqrt[a - I*a*x]/Sqrt[a + I*a*x] + (Sqrt[2]*(a - I*a*x)^(1/4))/(a + I*a*x)^(1/4)])/Sqrt[2]","A",12,9,25,0.3600,1,"{50, 63, 331, 297, 1162, 617, 204, 1165, 628}"
1185,1,233,0,0.1350979,"\int \frac{1}{\sqrt[4]{a-i a x} (a+i a x)^{3/4}} \, dx","Int[1/((a - I*a*x)^(1/4)*(a + I*a*x)^(3/4)),x]","\frac{i \log \left(\frac{\sqrt{a-i a x}}{\sqrt{a+i a x}}-\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}+1\right)}{\sqrt{2} a}-\frac{i \log \left(\frac{\sqrt{a-i a x}}{\sqrt{a+i a x}}+\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}+1\right)}{\sqrt{2} a}-\frac{i \sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}\right)}{a}+\frac{i \sqrt{2} \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}\right)}{a}","\frac{i \log \left(\frac{\sqrt{a-i a x}}{\sqrt{a+i a x}}-\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}+1\right)}{\sqrt{2} a}-\frac{i \log \left(\frac{\sqrt{a-i a x}}{\sqrt{a+i a x}}+\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}+1\right)}{\sqrt{2} a}-\frac{i \sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}\right)}{a}+\frac{i \sqrt{2} \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}\right)}{a}",1,"((-I)*Sqrt[2]*ArcTan[1 - (Sqrt[2]*(a - I*a*x)^(1/4))/(a + I*a*x)^(1/4)])/a + (I*Sqrt[2]*ArcTan[1 + (Sqrt[2]*(a - I*a*x)^(1/4))/(a + I*a*x)^(1/4)])/a + (I*Log[1 + Sqrt[a - I*a*x]/Sqrt[a + I*a*x] - (Sqrt[2]*(a - I*a*x)^(1/4))/(a + I*a*x)^(1/4)])/(Sqrt[2]*a) - (I*Log[1 + Sqrt[a - I*a*x]/Sqrt[a + I*a*x] + (Sqrt[2]*(a - I*a*x)^(1/4))/(a + I*a*x)^(1/4)])/(Sqrt[2]*a)","A",11,8,25,0.3200,1,"{63, 331, 297, 1162, 617, 204, 1165, 628}"
1186,1,31,0,0.0031736,"\int \frac{1}{(a-i a x)^{5/4} (a+i a x)^{3/4}} \, dx","Int[1/((a - I*a*x)^(5/4)*(a + I*a*x)^(3/4)),x]","-\frac{2 i \sqrt[4]{a+i a x}}{a^2 \sqrt[4]{a-i a x}}","-\frac{2 i \sqrt[4]{a+i a x}}{a^2 \sqrt[4]{a-i a x}}",1,"((-2*I)*(a + I*a*x)^(1/4))/(a^2*(a - I*a*x)^(1/4))","A",1,1,25,0.04000,1,"{37}"
1187,1,67,0,0.0098718,"\int \frac{1}{(a-i a x)^{9/4} (a+i a x)^{3/4}} \, dx","Int[1/((a - I*a*x)^(9/4)*(a + I*a*x)^(3/4)),x]","-\frac{4 i \sqrt[4]{a+i a x}}{5 a^3 \sqrt[4]{a-i a x}}-\frac{2 i \sqrt[4]{a+i a x}}{5 a^2 (a-i a x)^{5/4}}","-\frac{4 i \sqrt[4]{a+i a x}}{5 a^3 \sqrt[4]{a-i a x}}-\frac{2 i \sqrt[4]{a+i a x}}{5 a^2 (a-i a x)^{5/4}}",1,"(((-2*I)/5)*(a + I*a*x)^(1/4))/(a^2*(a - I*a*x)^(5/4)) - (((4*I)/5)*(a + I*a*x)^(1/4))/(a^3*(a - I*a*x)^(1/4))","A",2,2,25,0.08000,1,"{45, 37}"
1188,1,100,0,0.0179842,"\int \frac{1}{(a-i a x)^{13/4} (a+i a x)^{3/4}} \, dx","Int[1/((a - I*a*x)^(13/4)*(a + I*a*x)^(3/4)),x]","-\frac{16 i \sqrt[4]{a+i a x}}{45 a^4 \sqrt[4]{a-i a x}}-\frac{8 i \sqrt[4]{a+i a x}}{45 a^3 (a-i a x)^{5/4}}-\frac{2 i \sqrt[4]{a+i a x}}{9 a^2 (a-i a x)^{9/4}}","-\frac{16 i \sqrt[4]{a+i a x}}{45 a^4 \sqrt[4]{a-i a x}}-\frac{8 i \sqrt[4]{a+i a x}}{45 a^3 (a-i a x)^{5/4}}-\frac{2 i \sqrt[4]{a+i a x}}{9 a^2 (a-i a x)^{9/4}}",1,"(((-2*I)/9)*(a + I*a*x)^(1/4))/(a^2*(a - I*a*x)^(9/4)) - (((8*I)/45)*(a + I*a*x)^(1/4))/(a^3*(a - I*a*x)^(5/4)) - (((16*I)/45)*(a + I*a*x)^(1/4))/(a^4*(a - I*a*x)^(1/4))","A",3,2,25,0.08000,1,"{45, 37}"
1189,1,112,0,0.0241203,"\int \frac{(a-i a x)^{5/4}}{(a+i a x)^{3/4}} \, dx","Int[(a - I*a*x)^(5/4)/(a + I*a*x)^(3/4),x]","\frac{10 a^2 \left(x^2+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{3 (a-i a x)^{3/4} (a+i a x)^{3/4}}-\frac{10}{3} i \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}-\frac{2 i (a-i a x)^{5/4} \sqrt[4]{a+i a x}}{3 a}","\frac{10 a^2 \left(x^2+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{3 (a-i a x)^{3/4} (a+i a x)^{3/4}}-\frac{10}{3} i \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}-\frac{2 i (a-i a x)^{5/4} \sqrt[4]{a+i a x}}{3 a}",1,"((-10*I)/3)*(a - I*a*x)^(1/4)*(a + I*a*x)^(1/4) - (((2*I)/3)*(a - I*a*x)^(5/4)*(a + I*a*x)^(1/4))/a + (10*a^2*(1 + x^2)^(3/4)*EllipticF[ArcTan[x]/2, 2])/(3*(a - I*a*x)^(3/4)*(a + I*a*x)^(3/4))","A",5,4,25,0.1600,1,"{50, 42, 233, 231}"
1190,1,76,0,0.0145622,"\int \frac{\sqrt[4]{a-i a x}}{(a+i a x)^{3/4}} \, dx","Int[(a - I*a*x)^(1/4)/(a + I*a*x)^(3/4),x]","\frac{2 a \left(x^2+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{(a-i a x)^{3/4} (a+i a x)^{3/4}}-\frac{2 i \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}{a}","\frac{2 a \left(x^2+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{(a-i a x)^{3/4} (a+i a x)^{3/4}}-\frac{2 i \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}{a}",1,"((-2*I)*(a - I*a*x)^(1/4)*(a + I*a*x)^(1/4))/a + (2*a*(1 + x^2)^(3/4)*EllipticF[ArcTan[x]/2, 2])/((a - I*a*x)^(3/4)*(a + I*a*x)^(3/4))","A",4,4,25,0.1600,1,"{50, 42, 233, 231}"
1191,1,43,0,0.0081492,"\int \frac{1}{(a-i a x)^{3/4} (a+i a x)^{3/4}} \, dx","Int[1/((a - I*a*x)^(3/4)*(a + I*a*x)^(3/4)),x]","\frac{2 \left(x^2+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{(a-i a x)^{3/4} (a+i a x)^{3/4}}","\frac{2 \left(x^2+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{(a-i a x)^{3/4} (a+i a x)^{3/4}}",1,"(2*(1 + x^2)^(3/4)*EllipticF[ArcTan[x]/2, 2])/((a - I*a*x)^(3/4)*(a + I*a*x)^(3/4))","A",3,3,25,0.1200,1,"{42, 233, 231}"
1192,1,82,0,0.0147231,"\int \frac{1}{(a-i a x)^{7/4} (a+i a x)^{3/4}} \, dx","Int[1/((a - I*a*x)^(7/4)*(a + I*a*x)^(3/4)),x]","\frac{2 \left(x^2+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{3 a (a-i a x)^{3/4} (a+i a x)^{3/4}}-\frac{2 i \sqrt[4]{a+i a x}}{3 a^2 (a-i a x)^{3/4}}","\frac{2 \left(x^2+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{3 a (a-i a x)^{3/4} (a+i a x)^{3/4}}-\frac{2 i \sqrt[4]{a+i a x}}{3 a^2 (a-i a x)^{3/4}}",1,"(((-2*I)/3)*(a + I*a*x)^(1/4))/(a^2*(a - I*a*x)^(3/4)) + (2*(1 + x^2)^(3/4)*EllipticF[ArcTan[x]/2, 2])/(3*a*(a - I*a*x)^(3/4)*(a + I*a*x)^(3/4))","A",4,4,25,0.1600,1,"{51, 42, 233, 231}"
1193,1,115,0,0.0250462,"\int \frac{1}{(a-i a x)^{11/4} (a+i a x)^{3/4}} \, dx","Int[1/((a - I*a*x)^(11/4)*(a + I*a*x)^(3/4)),x]","\frac{2 \left(x^2+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{7 a^2 (a-i a x)^{3/4} (a+i a x)^{3/4}}-\frac{2 i \sqrt[4]{a+i a x}}{7 a^3 (a-i a x)^{3/4}}-\frac{2 i \sqrt[4]{a+i a x}}{7 a^2 (a-i a x)^{7/4}}","\frac{2 \left(x^2+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{7 a^2 (a-i a x)^{3/4} (a+i a x)^{3/4}}-\frac{2 i \sqrt[4]{a+i a x}}{7 a^3 (a-i a x)^{3/4}}-\frac{2 i \sqrt[4]{a+i a x}}{7 a^2 (a-i a x)^{7/4}}",1,"(((-2*I)/7)*(a + I*a*x)^(1/4))/(a^2*(a - I*a*x)^(7/4)) - (((2*I)/7)*(a + I*a*x)^(1/4))/(a^3*(a - I*a*x)^(3/4)) + (2*(1 + x^2)^(3/4)*EllipticF[ArcTan[x]/2, 2])/(7*a^2*(a - I*a*x)^(3/4)*(a + I*a*x)^(3/4))","A",5,4,25,0.1600,1,"{51, 42, 233, 231}"
1194,1,291,0,0.1808313,"\int \frac{(a-i a x)^{7/4}}{(a+i a x)^{7/4}} \, dx","Int[(a - I*a*x)^(7/4)/(a + I*a*x)^(7/4),x]","\frac{4 i (a-i a x)^{7/4}}{3 a (a+i a x)^{3/4}}+\frac{7 i \sqrt[4]{a+i a x} (a-i a x)^{3/4}}{3 a}-\frac{7 i \log \left(\frac{\sqrt{a-i a x}}{\sqrt{a+i a x}}-\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}+1\right)}{2 \sqrt{2}}+\frac{7 i \log \left(\frac{\sqrt{a-i a x}}{\sqrt{a+i a x}}+\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}+1\right)}{2 \sqrt{2}}+\frac{7 i \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}\right)}{\sqrt{2}}-\frac{7 i \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}\right)}{\sqrt{2}}","\frac{4 i (a-i a x)^{7/4}}{3 a (a+i a x)^{3/4}}+\frac{7 i \sqrt[4]{a+i a x} (a-i a x)^{3/4}}{3 a}-\frac{7 i \log \left(\frac{\sqrt{a-i a x}}{\sqrt{a+i a x}}-\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}+1\right)}{2 \sqrt{2}}+\frac{7 i \log \left(\frac{\sqrt{a-i a x}}{\sqrt{a+i a x}}+\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}+1\right)}{2 \sqrt{2}}+\frac{7 i \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}\right)}{\sqrt{2}}-\frac{7 i \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}\right)}{\sqrt{2}}",1,"(((4*I)/3)*(a - I*a*x)^(7/4))/(a*(a + I*a*x)^(3/4)) + (((7*I)/3)*(a - I*a*x)^(3/4)*(a + I*a*x)^(1/4))/a + ((7*I)*ArcTan[1 - (Sqrt[2]*(a - I*a*x)^(1/4))/(a + I*a*x)^(1/4)])/Sqrt[2] - ((7*I)*ArcTan[1 + (Sqrt[2]*(a - I*a*x)^(1/4))/(a + I*a*x)^(1/4)])/Sqrt[2] - (((7*I)/2)*Log[1 + Sqrt[a - I*a*x]/Sqrt[a + I*a*x] - (Sqrt[2]*(a - I*a*x)^(1/4))/(a + I*a*x)^(1/4)])/Sqrt[2] + (((7*I)/2)*Log[1 + Sqrt[a - I*a*x]/Sqrt[a + I*a*x] + (Sqrt[2]*(a - I*a*x)^(1/4))/(a + I*a*x)^(1/4)])/Sqrt[2]","A",13,10,25,0.4000,1,"{47, 50, 63, 331, 297, 1162, 617, 204, 1165, 628}"
1195,1,266,0,0.1399885,"\int \frac{(a-i a x)^{3/4}}{(a+i a x)^{7/4}} \, dx","Int[(a - I*a*x)^(3/4)/(a + I*a*x)^(7/4),x]","\frac{4 i (a-i a x)^{3/4}}{3 a (a+i a x)^{3/4}}-\frac{i \log \left(\frac{\sqrt{a-i a x}}{\sqrt{a+i a x}}-\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}+1\right)}{\sqrt{2} a}+\frac{i \log \left(\frac{\sqrt{a-i a x}}{\sqrt{a+i a x}}+\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}+1\right)}{\sqrt{2} a}+\frac{i \sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}\right)}{a}-\frac{i \sqrt{2} \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}\right)}{a}","\frac{4 i (a-i a x)^{3/4}}{3 a (a+i a x)^{3/4}}-\frac{i \log \left(\frac{\sqrt{a-i a x}}{\sqrt{a+i a x}}-\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}+1\right)}{\sqrt{2} a}+\frac{i \log \left(\frac{\sqrt{a-i a x}}{\sqrt{a+i a x}}+\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}+1\right)}{\sqrt{2} a}+\frac{i \sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}\right)}{a}-\frac{i \sqrt{2} \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}\right)}{a}",1,"(((4*I)/3)*(a - I*a*x)^(3/4))/(a*(a + I*a*x)^(3/4)) + (I*Sqrt[2]*ArcTan[1 - (Sqrt[2]*(a - I*a*x)^(1/4))/(a + I*a*x)^(1/4)])/a - (I*Sqrt[2]*ArcTan[1 + (Sqrt[2]*(a - I*a*x)^(1/4))/(a + I*a*x)^(1/4)])/a - (I*Log[1 + Sqrt[a - I*a*x]/Sqrt[a + I*a*x] - (Sqrt[2]*(a - I*a*x)^(1/4))/(a + I*a*x)^(1/4)])/(Sqrt[2]*a) + (I*Log[1 + Sqrt[a - I*a*x]/Sqrt[a + I*a*x] + (Sqrt[2]*(a - I*a*x)^(1/4))/(a + I*a*x)^(1/4)])/(Sqrt[2]*a)","A",12,9,25,0.3600,1,"{47, 63, 331, 297, 1162, 617, 204, 1165, 628}"
1196,1,33,0,0.0034473,"\int \frac{1}{\sqrt[4]{a-i a x} (a+i a x)^{7/4}} \, dx","Int[1/((a - I*a*x)^(1/4)*(a + I*a*x)^(7/4)),x]","\frac{2 i (a-i a x)^{3/4}}{3 a^2 (a+i a x)^{3/4}}","\frac{2 i (a-i a x)^{3/4}}{3 a^2 (a+i a x)^{3/4}}",1,"(((2*I)/3)*(a - I*a*x)^(3/4))/(a^2*(a + I*a*x)^(3/4))","A",1,1,25,0.04000,1,"{37}"
1197,1,65,0,0.0090441,"\int \frac{1}{(a-i a x)^{5/4} (a+i a x)^{7/4}} \, dx","Int[1/((a - I*a*x)^(5/4)*(a + I*a*x)^(7/4)),x]","\frac{4 i (a-i a x)^{3/4}}{3 a^3 (a+i a x)^{3/4}}-\frac{2 i}{a^2 \sqrt[4]{a-i a x} (a+i a x)^{3/4}}","\frac{4 i (a-i a x)^{3/4}}{3 a^3 (a+i a x)^{3/4}}-\frac{2 i}{a^2 \sqrt[4]{a-i a x} (a+i a x)^{3/4}}",1,"(-2*I)/(a^2*(a - I*a*x)^(1/4)*(a + I*a*x)^(3/4)) + (((4*I)/3)*(a - I*a*x)^(3/4))/(a^3*(a + I*a*x)^(3/4))","A",2,2,25,0.08000,1,"{45, 37}"
1198,1,100,0,0.0173897,"\int \frac{1}{(a-i a x)^{9/4} (a+i a x)^{7/4}} \, dx","Int[1/((a - I*a*x)^(9/4)*(a + I*a*x)^(7/4)),x]","\frac{16 i (a-i a x)^{3/4}}{15 a^4 (a+i a x)^{3/4}}-\frac{8 i}{5 a^3 (a+i a x)^{3/4} \sqrt[4]{a-i a x}}-\frac{2 i}{5 a^2 (a+i a x)^{3/4} (a-i a x)^{5/4}}","\frac{16 i (a-i a x)^{3/4}}{15 a^4 (a+i a x)^{3/4}}-\frac{8 i}{5 a^3 (a+i a x)^{3/4} \sqrt[4]{a-i a x}}-\frac{2 i}{5 a^2 (a+i a x)^{3/4} (a-i a x)^{5/4}}",1,"((-2*I)/5)/(a^2*(a - I*a*x)^(5/4)*(a + I*a*x)^(3/4)) - ((8*I)/5)/(a^3*(a - I*a*x)^(1/4)*(a + I*a*x)^(3/4)) + (((16*I)/15)*(a - I*a*x)^(3/4))/(a^4*(a + I*a*x)^(3/4))","A",3,2,25,0.08000,1,"{45, 37}"
1199,1,139,0,0.033715,"\int \frac{(a-i a x)^{9/4}}{(a+i a x)^{7/4}} \, dx","Int[(a - I*a*x)^(9/4)/(a + I*a*x)^(7/4),x]","-\frac{10 a^2 \left(x^2+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{(a+i a x)^{3/4} (a-i a x)^{3/4}}+\frac{4 i (a-i a x)^{9/4}}{3 a (a+i a x)^{3/4}}+\frac{2 i \sqrt[4]{a+i a x} (a-i a x)^{5/4}}{a}+10 i \sqrt[4]{a+i a x} \sqrt[4]{a-i a x}","-\frac{10 a^2 \left(x^2+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{(a+i a x)^{3/4} (a-i a x)^{3/4}}+\frac{4 i (a-i a x)^{9/4}}{3 a (a+i a x)^{3/4}}+\frac{2 i \sqrt[4]{a+i a x} (a-i a x)^{5/4}}{a}+10 i \sqrt[4]{a+i a x} \sqrt[4]{a-i a x}",1,"(((4*I)/3)*(a - I*a*x)^(9/4))/(a*(a + I*a*x)^(3/4)) + (10*I)*(a - I*a*x)^(1/4)*(a + I*a*x)^(1/4) + ((2*I)*(a - I*a*x)^(5/4)*(a + I*a*x)^(1/4))/a - (10*a^2*(1 + x^2)^(3/4)*EllipticF[ArcTan[x]/2, 2])/((a - I*a*x)^(3/4)*(a + I*a*x)^(3/4))","A",6,5,25,0.2000,1,"{47, 50, 42, 233, 231}"
1200,1,113,0,0.0242478,"\int \frac{(a-i a x)^{5/4}}{(a+i a x)^{7/4}} \, dx","Int[(a - I*a*x)^(5/4)/(a + I*a*x)^(7/4),x]","-\frac{10 a \left(x^2+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{3 (a+i a x)^{3/4} (a-i a x)^{3/4}}+\frac{4 i (a-i a x)^{5/4}}{3 a (a+i a x)^{3/4}}+\frac{10 i \sqrt[4]{a+i a x} \sqrt[4]{a-i a x}}{3 a}","-\frac{10 a \left(x^2+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{3 (a+i a x)^{3/4} (a-i a x)^{3/4}}+\frac{4 i (a-i a x)^{5/4}}{3 a (a+i a x)^{3/4}}+\frac{10 i \sqrt[4]{a+i a x} \sqrt[4]{a-i a x}}{3 a}",1,"(((4*I)/3)*(a - I*a*x)^(5/4))/(a*(a + I*a*x)^(3/4)) + (((10*I)/3)*(a - I*a*x)^(1/4)*(a + I*a*x)^(1/4))/a - (10*a*(1 + x^2)^(3/4)*EllipticF[ArcTan[x]/2, 2])/(3*(a - I*a*x)^(3/4)*(a + I*a*x)^(3/4))","A",5,5,25,0.2000,1,"{47, 50, 42, 233, 231}"
1201,1,79,0,0.0139069,"\int \frac{\sqrt[4]{a-i a x}}{(a+i a x)^{7/4}} \, dx","Int[(a - I*a*x)^(1/4)/(a + I*a*x)^(7/4),x]","\frac{4 i \sqrt[4]{a-i a x}}{3 a (a+i a x)^{3/4}}-\frac{2 \left(x^2+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{3 (a-i a x)^{3/4} (a+i a x)^{3/4}}","\frac{4 i \sqrt[4]{a-i a x}}{3 a (a+i a x)^{3/4}}-\frac{2 \left(x^2+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{3 (a-i a x)^{3/4} (a+i a x)^{3/4}}",1,"(((4*I)/3)*(a - I*a*x)^(1/4))/(a*(a + I*a*x)^(3/4)) - (2*(1 + x^2)^(3/4)*EllipticF[ArcTan[x]/2, 2])/(3*(a - I*a*x)^(3/4)*(a + I*a*x)^(3/4))","A",4,4,25,0.1600,1,"{47, 42, 233, 231}"
1202,1,82,0,0.0154676,"\int \frac{1}{(a-i a x)^{3/4} (a+i a x)^{7/4}} \, dx","Int[1/((a - I*a*x)^(3/4)*(a + I*a*x)^(7/4)),x]","\frac{2 i \sqrt[4]{a-i a x}}{3 a^2 (a+i a x)^{3/4}}+\frac{2 \left(x^2+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{3 a (a-i a x)^{3/4} (a+i a x)^{3/4}}","\frac{2 i \sqrt[4]{a-i a x}}{3 a^2 (a+i a x)^{3/4}}+\frac{2 \left(x^2+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{3 a (a-i a x)^{3/4} (a+i a x)^{3/4}}",1,"(((2*I)/3)*(a - I*a*x)^(1/4))/(a^2*(a + I*a*x)^(3/4)) + (2*(1 + x^2)^(3/4)*EllipticF[ArcTan[x]/2, 2])/(3*a*(a - I*a*x)^(3/4)*(a + I*a*x)^(3/4))","A",4,4,25,0.1600,1,"{51, 42, 233, 231}"
1203,1,81,0,0.0148509,"\int \frac{1}{(a-i a x)^{7/4} (a+i a x)^{7/4}} \, dx","Int[1/((a - I*a*x)^(7/4)*(a + I*a*x)^(7/4)),x]","\frac{2 \left(x^2+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{3 a^2 (a-i a x)^{3/4} (a+i a x)^{3/4}}+\frac{2 x}{3 a^2 (a-i a x)^{3/4} (a+i a x)^{3/4}}","\frac{2 \left(x^2+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{3 a^2 (a-i a x)^{3/4} (a+i a x)^{3/4}}+\frac{2 x}{3 a^2 (a-i a x)^{3/4} (a+i a x)^{3/4}}",1,"(2*x)/(3*a^2*(a - I*a*x)^(3/4)*(a + I*a*x)^(3/4)) + (2*(1 + x^2)^(3/4)*EllipticF[ArcTan[x]/2, 2])/(3*a^2*(a - I*a*x)^(3/4)*(a + I*a*x)^(3/4))","A",4,4,25,0.1600,1,"{42, 199, 233, 231}"
1204,1,114,0,0.0246717,"\int \frac{1}{(a-i a x)^{11/4} (a+i a x)^{7/4}} \, dx","Int[1/((a - I*a*x)^(11/4)*(a + I*a*x)^(7/4)),x]","\frac{10 \left(x^2+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{21 a^3 (a-i a x)^{3/4} (a+i a x)^{3/4}}+\frac{10 x}{21 a^3 (a-i a x)^{3/4} (a+i a x)^{3/4}}-\frac{2 i}{7 a^2 (a-i a x)^{7/4} (a+i a x)^{3/4}}","\frac{10 \left(x^2+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{21 a^3 (a-i a x)^{3/4} (a+i a x)^{3/4}}+\frac{10 x}{21 a^3 (a-i a x)^{3/4} (a+i a x)^{3/4}}-\frac{2 i}{7 a^2 (a-i a x)^{7/4} (a+i a x)^{3/4}}",1,"((-2*I)/7)/(a^2*(a - I*a*x)^(7/4)*(a + I*a*x)^(3/4)) + (10*x)/(21*a^3*(a - I*a*x)^(3/4)*(a + I*a*x)^(3/4)) + (10*(1 + x^2)^(3/4)*EllipticF[ArcTan[x]/2, 2])/(21*a^3*(a - I*a*x)^(3/4)*(a + I*a*x)^(3/4))","A",5,5,25,0.2000,1,"{51, 42, 199, 233, 231}"
1205,1,147,0,0.0352481,"\int \frac{1}{(a-i a x)^{15/4} (a+i a x)^{7/4}} \, dx","Int[1/((a - I*a*x)^(15/4)*(a + I*a*x)^(7/4)),x]","\frac{10 \left(x^2+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{33 a^4 (a-i a x)^{3/4} (a+i a x)^{3/4}}+\frac{10 x}{33 a^4 (a-i a x)^{3/4} (a+i a x)^{3/4}}-\frac{2 i}{11 a^3 (a-i a x)^{7/4} (a+i a x)^{3/4}}-\frac{2 i}{11 a^2 (a-i a x)^{11/4} (a+i a x)^{3/4}}","\frac{10 \left(x^2+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{33 a^4 (a-i a x)^{3/4} (a+i a x)^{3/4}}+\frac{10 x}{33 a^4 (a-i a x)^{3/4} (a+i a x)^{3/4}}-\frac{2 i}{11 a^3 (a-i a x)^{7/4} (a+i a x)^{3/4}}-\frac{2 i}{11 a^2 (a-i a x)^{11/4} (a+i a x)^{3/4}}",1,"((-2*I)/11)/(a^2*(a - I*a*x)^(11/4)*(a + I*a*x)^(3/4)) - ((2*I)/11)/(a^3*(a - I*a*x)^(7/4)*(a + I*a*x)^(3/4)) + (10*x)/(33*a^4*(a - I*a*x)^(3/4)*(a + I*a*x)^(3/4)) + (10*(1 + x^2)^(3/4)*EllipticF[ArcTan[x]/2, 2])/(33*a^4*(a - I*a*x)^(3/4)*(a + I*a*x)^(3/4))","A",6,5,25,0.2000,1,"{51, 42, 199, 233, 231}"
1206,1,137,0,0.0320576,"\int \frac{(a-i a x)^{7/4}}{(a+i a x)^{5/4}} \, dx","Int[(a - I*a*x)^(7/4)/(a + I*a*x)^(5/4),x]","\frac{14 a \sqrt[4]{x^2+1} E\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{\sqrt[4]{a+i a x} \sqrt[4]{a-i a x}}+\frac{4 i (a-i a x)^{7/4}}{a \sqrt[4]{a+i a x}}+\frac{14 i (a+i a x)^{3/4} (a-i a x)^{3/4}}{3 a}-\frac{14 a x}{\sqrt[4]{a+i a x} \sqrt[4]{a-i a x}}","\frac{14 a \sqrt[4]{x^2+1} E\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{\sqrt[4]{a+i a x} \sqrt[4]{a-i a x}}+\frac{4 i (a-i a x)^{7/4}}{a \sqrt[4]{a+i a x}}+\frac{14 i (a+i a x)^{3/4} (a-i a x)^{3/4}}{3 a}-\frac{14 a x}{\sqrt[4]{a+i a x} \sqrt[4]{a-i a x}}",1,"(-14*a*x)/((a - I*a*x)^(1/4)*(a + I*a*x)^(1/4)) + ((4*I)*(a - I*a*x)^(7/4))/(a*(a + I*a*x)^(1/4)) + (((14*I)/3)*(a - I*a*x)^(3/4)*(a + I*a*x)^(3/4))/a + (14*a*(1 + x^2)^(1/4)*EllipticE[ArcTan[x]/2, 2])/((a - I*a*x)^(1/4)*(a + I*a*x)^(1/4))","A",6,6,25,0.2400,1,"{47, 50, 42, 229, 227, 196}"
1207,1,102,0,0.0199544,"\int \frac{(a-i a x)^{3/4}}{(a+i a x)^{5/4}} \, dx","Int[(a - I*a*x)^(3/4)/(a + I*a*x)^(5/4),x]","\frac{6 \sqrt[4]{x^2+1} E\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{\sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}-\frac{6 x}{\sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}+\frac{4 i (a-i a x)^{3/4}}{a \sqrt[4]{a+i a x}}","\frac{6 \sqrt[4]{x^2+1} E\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{\sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}-\frac{6 x}{\sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}+\frac{4 i (a-i a x)^{3/4}}{a \sqrt[4]{a+i a x}}",1,"(-6*x)/((a - I*a*x)^(1/4)*(a + I*a*x)^(1/4)) + ((4*I)*(a - I*a*x)^(3/4))/(a*(a + I*a*x)^(1/4)) + (6*(1 + x^2)^(1/4)*EllipticE[ArcTan[x]/2, 2])/((a - I*a*x)^(1/4)*(a + I*a*x)^(1/4))","A",5,5,25,0.2000,1,"{47, 42, 229, 227, 196}"
1208,1,78,0,0.0158888,"\int \frac{1}{\sqrt[4]{a-i a x} (a+i a x)^{5/4}} \, dx","Int[1/((a - I*a*x)^(1/4)*(a + I*a*x)^(5/4)),x]","\frac{2 \sqrt[4]{x^2+1} E\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{a \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}+\frac{2 i}{a \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}","\frac{2 \sqrt[4]{x^2+1} E\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{a \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}+\frac{2 i}{a \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}",1,"(2*I)/(a*(a - I*a*x)^(1/4)*(a + I*a*x)^(1/4)) + (2*(1 + x^2)^(1/4)*EllipticE[ArcTan[x]/2, 2])/(a*(a - I*a*x)^(1/4)*(a + I*a*x)^(1/4))","A",4,4,25,0.1600,1,"{48, 42, 197, 196}"
1209,1,46,0,0.0085974,"\int \frac{1}{(a-i a x)^{5/4} (a+i a x)^{5/4}} \, dx","Int[1/((a - I*a*x)^(5/4)*(a + I*a*x)^(5/4)),x]","\frac{2 \sqrt[4]{x^2+1} E\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{a^2 \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}","\frac{2 \sqrt[4]{x^2+1} E\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{a^2 \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}",1,"(2*(1 + x^2)^(1/4)*EllipticE[ArcTan[x]/2, 2])/(a^2*(a - I*a*x)^(1/4)*(a + I*a*x)^(1/4))","A",3,3,25,0.1200,1,"{42, 197, 196}"
1210,1,82,0,0.0160064,"\int \frac{1}{(a-i a x)^{9/4} (a+i a x)^{5/4}} \, dx","Int[1/((a - I*a*x)^(9/4)*(a + I*a*x)^(5/4)),x]","\frac{6 \sqrt[4]{x^2+1} E\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{5 a^3 \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}-\frac{2 i}{5 a^2 (a-i a x)^{5/4} \sqrt[4]{a+i a x}}","\frac{6 \sqrt[4]{x^2+1} E\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{5 a^3 \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}-\frac{2 i}{5 a^2 (a-i a x)^{5/4} \sqrt[4]{a+i a x}}",1,"((-2*I)/5)/(a^2*(a - I*a*x)^(5/4)*(a + I*a*x)^(1/4)) + (6*(1 + x^2)^(1/4)*EllipticE[ArcTan[x]/2, 2])/(5*a^3*(a - I*a*x)^(1/4)*(a + I*a*x)^(1/4))","A",4,4,25,0.1600,1,"{51, 42, 197, 196}"
1211,1,115,0,0.0264505,"\int \frac{1}{(a-i a x)^{13/4} (a+i a x)^{5/4}} \, dx","Int[1/((a - I*a*x)^(13/4)*(a + I*a*x)^(5/4)),x]","\frac{2 \sqrt[4]{x^2+1} E\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{3 a^4 \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}-\frac{2 i}{9 a^3 (a-i a x)^{5/4} \sqrt[4]{a+i a x}}-\frac{2 i}{9 a^2 (a-i a x)^{9/4} \sqrt[4]{a+i a x}}","\frac{2 \sqrt[4]{x^2+1} E\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{3 a^4 \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}-\frac{2 i}{9 a^3 (a-i a x)^{5/4} \sqrt[4]{a+i a x}}-\frac{2 i}{9 a^2 (a-i a x)^{9/4} \sqrt[4]{a+i a x}}",1,"((-2*I)/9)/(a^2*(a - I*a*x)^(9/4)*(a + I*a*x)^(1/4)) - ((2*I)/9)/(a^3*(a - I*a*x)^(5/4)*(a + I*a*x)^(1/4)) + (2*(1 + x^2)^(1/4)*EllipticE[ArcTan[x]/2, 2])/(3*a^4*(a - I*a*x)^(1/4)*(a + I*a*x)^(1/4))","A",5,4,25,0.1600,1,"{51, 42, 197, 196}"
1212,1,287,0,0.1779511,"\int \frac{(a-i a x)^{5/4}}{(a+i a x)^{5/4}} \, dx","Int[(a - I*a*x)^(5/4)/(a + I*a*x)^(5/4),x]","\frac{4 i (a-i a x)^{5/4}}{a \sqrt[4]{a+i a x}}+\frac{5 i (a+i a x)^{3/4} \sqrt[4]{a-i a x}}{a}+\frac{5 i \log \left(\frac{\sqrt{a-i a x}}{\sqrt{a+i a x}}-\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}+1\right)}{2 \sqrt{2}}-\frac{5 i \log \left(\frac{\sqrt{a-i a x}}{\sqrt{a+i a x}}+\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}+1\right)}{2 \sqrt{2}}+\frac{5 i \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}\right)}{\sqrt{2}}-\frac{5 i \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}\right)}{\sqrt{2}}","\frac{4 i (a-i a x)^{5/4}}{a \sqrt[4]{a+i a x}}+\frac{5 i (a+i a x)^{3/4} \sqrt[4]{a-i a x}}{a}+\frac{5 i \log \left(\frac{\sqrt{a-i a x}}{\sqrt{a+i a x}}-\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}+1\right)}{2 \sqrt{2}}-\frac{5 i \log \left(\frac{\sqrt{a-i a x}}{\sqrt{a+i a x}}+\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}+1\right)}{2 \sqrt{2}}+\frac{5 i \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}\right)}{\sqrt{2}}-\frac{5 i \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}\right)}{\sqrt{2}}",1,"((4*I)*(a - I*a*x)^(5/4))/(a*(a + I*a*x)^(1/4)) + ((5*I)*(a - I*a*x)^(1/4)*(a + I*a*x)^(3/4))/a + ((5*I)*ArcTan[1 - (Sqrt[2]*(a - I*a*x)^(1/4))/(a + I*a*x)^(1/4)])/Sqrt[2] - ((5*I)*ArcTan[1 + (Sqrt[2]*(a - I*a*x)^(1/4))/(a + I*a*x)^(1/4)])/Sqrt[2] + (((5*I)/2)*Log[1 + Sqrt[a - I*a*x]/Sqrt[a + I*a*x] - (Sqrt[2]*(a - I*a*x)^(1/4))/(a + I*a*x)^(1/4)])/Sqrt[2] - (((5*I)/2)*Log[1 + Sqrt[a - I*a*x]/Sqrt[a + I*a*x] + (Sqrt[2]*(a - I*a*x)^(1/4))/(a + I*a*x)^(1/4)])/Sqrt[2]","A",13,10,25,0.4000,1,"{47, 50, 63, 240, 211, 1165, 628, 1162, 617, 204}"
1213,1,264,0,0.1386315,"\int \frac{\sqrt[4]{a-i a x}}{(a+i a x)^{5/4}} \, dx","Int[(a - I*a*x)^(1/4)/(a + I*a*x)^(5/4),x]","\frac{4 i \sqrt[4]{a-i a x}}{a \sqrt[4]{a+i a x}}+\frac{i \log \left(\frac{\sqrt{a-i a x}}{\sqrt{a+i a x}}-\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}+1\right)}{\sqrt{2} a}-\frac{i \log \left(\frac{\sqrt{a-i a x}}{\sqrt{a+i a x}}+\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}+1\right)}{\sqrt{2} a}+\frac{i \sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}\right)}{a}-\frac{i \sqrt{2} \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}\right)}{a}","\frac{4 i \sqrt[4]{a-i a x}}{a \sqrt[4]{a+i a x}}+\frac{i \log \left(\frac{\sqrt{a-i a x}}{\sqrt{a+i a x}}-\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}+1\right)}{\sqrt{2} a}-\frac{i \log \left(\frac{\sqrt{a-i a x}}{\sqrt{a+i a x}}+\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}+1\right)}{\sqrt{2} a}+\frac{i \sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}\right)}{a}-\frac{i \sqrt{2} \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}\right)}{a}",1,"((4*I)*(a - I*a*x)^(1/4))/(a*(a + I*a*x)^(1/4)) + (I*Sqrt[2]*ArcTan[1 - (Sqrt[2]*(a - I*a*x)^(1/4))/(a + I*a*x)^(1/4)])/a - (I*Sqrt[2]*ArcTan[1 + (Sqrt[2]*(a - I*a*x)^(1/4))/(a + I*a*x)^(1/4)])/a + (I*Log[1 + Sqrt[a - I*a*x]/Sqrt[a + I*a*x] - (Sqrt[2]*(a - I*a*x)^(1/4))/(a + I*a*x)^(1/4)])/(Sqrt[2]*a) - (I*Log[1 + Sqrt[a - I*a*x]/Sqrt[a + I*a*x] + (Sqrt[2]*(a - I*a*x)^(1/4))/(a + I*a*x)^(1/4)])/(Sqrt[2]*a)","A",12,9,25,0.3600,1,"{47, 63, 240, 211, 1165, 628, 1162, 617, 204}"
1214,1,31,0,0.003278,"\int \frac{1}{(a-i a x)^{3/4} (a+i a x)^{5/4}} \, dx","Int[1/((a - I*a*x)^(3/4)*(a + I*a*x)^(5/4)),x]","\frac{2 i \sqrt[4]{a-i a x}}{a^2 \sqrt[4]{a+i a x}}","\frac{2 i \sqrt[4]{a-i a x}}{a^2 \sqrt[4]{a+i a x}}",1,"((2*I)*(a - I*a*x)^(1/4))/(a^2*(a + I*a*x)^(1/4))","A",1,1,25,0.04000,1,"{37}"
1215,1,67,0,0.0094655,"\int \frac{1}{(a-i a x)^{7/4} (a+i a x)^{5/4}} \, dx","Int[1/((a - I*a*x)^(7/4)*(a + I*a*x)^(5/4)),x]","\frac{4 i \sqrt[4]{a-i a x}}{3 a^3 \sqrt[4]{a+i a x}}-\frac{2 i}{3 a^2 (a-i a x)^{3/4} \sqrt[4]{a+i a x}}","\frac{4 i \sqrt[4]{a-i a x}}{3 a^3 \sqrt[4]{a+i a x}}-\frac{2 i}{3 a^2 (a-i a x)^{3/4} \sqrt[4]{a+i a x}}",1,"((-2*I)/3)/(a^2*(a - I*a*x)^(3/4)*(a + I*a*x)^(1/4)) + (((4*I)/3)*(a - I*a*x)^(1/4))/(a^3*(a + I*a*x)^(1/4))","A",2,2,25,0.08000,1,"{45, 37}"
1216,1,100,0,0.0181517,"\int \frac{1}{(a-i a x)^{11/4} (a+i a x)^{5/4}} \, dx","Int[1/((a - I*a*x)^(11/4)*(a + I*a*x)^(5/4)),x]","\frac{16 i \sqrt[4]{a-i a x}}{21 a^4 \sqrt[4]{a+i a x}}-\frac{8 i}{21 a^3 \sqrt[4]{a+i a x} (a-i a x)^{3/4}}-\frac{2 i}{7 a^2 \sqrt[4]{a+i a x} (a-i a x)^{7/4}}","\frac{16 i \sqrt[4]{a-i a x}}{21 a^4 \sqrt[4]{a+i a x}}-\frac{8 i}{21 a^3 \sqrt[4]{a+i a x} (a-i a x)^{3/4}}-\frac{2 i}{7 a^2 \sqrt[4]{a+i a x} (a-i a x)^{7/4}}",1,"((-2*I)/7)/(a^2*(a - I*a*x)^(7/4)*(a + I*a*x)^(1/4)) - ((8*I)/21)/(a^3*(a - I*a*x)^(3/4)*(a + I*a*x)^(1/4)) + (((16*I)/21)*(a - I*a*x)^(1/4))/(a^4*(a + I*a*x)^(1/4))","A",3,2,25,0.08000,1,"{45, 37}"
1217,1,141,0,0.0303233,"\int \frac{(a-i a x)^{7/4}}{(a+i a x)^{9/4}} \, dx","Int[(a - I*a*x)^(7/4)/(a + I*a*x)^(9/4),x]","-\frac{42 \sqrt[4]{x^2+1} E\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{5 \sqrt[4]{a+i a x} \sqrt[4]{a-i a x}}+\frac{4 i (a-i a x)^{7/4}}{5 a (a+i a x)^{5/4}}-\frac{28 i (a-i a x)^{3/4}}{5 a \sqrt[4]{a+i a x}}+\frac{42 x}{5 \sqrt[4]{a+i a x} \sqrt[4]{a-i a x}}","-\frac{42 \sqrt[4]{x^2+1} E\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{5 \sqrt[4]{a+i a x} \sqrt[4]{a-i a x}}+\frac{4 i (a-i a x)^{7/4}}{5 a (a+i a x)^{5/4}}-\frac{28 i (a-i a x)^{3/4}}{5 a \sqrt[4]{a+i a x}}+\frac{42 x}{5 \sqrt[4]{a+i a x} \sqrt[4]{a-i a x}}",1,"(((4*I)/5)*(a - I*a*x)^(7/4))/(a*(a + I*a*x)^(5/4)) + (42*x)/(5*(a - I*a*x)^(1/4)*(a + I*a*x)^(1/4)) - (((28*I)/5)*(a - I*a*x)^(3/4))/(a*(a + I*a*x)^(1/4)) - (42*(1 + x^2)^(1/4)*EllipticE[ArcTan[x]/2, 2])/(5*(a - I*a*x)^(1/4)*(a + I*a*x)^(1/4))","A",6,5,25,0.2000,1,"{47, 42, 229, 227, 196}"
1218,1,115,0,0.0252828,"\int \frac{(a-i a x)^{3/4}}{(a+i a x)^{9/4}} \, dx","Int[(a - I*a*x)^(3/4)/(a + I*a*x)^(9/4),x]","-\frac{6 \sqrt[4]{x^2+1} E\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{5 a \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}-\frac{6 i}{5 a \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}+\frac{4 i (a-i a x)^{3/4}}{5 a (a+i a x)^{5/4}}","-\frac{6 \sqrt[4]{x^2+1} E\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{5 a \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}-\frac{6 i}{5 a \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}+\frac{4 i (a-i a x)^{3/4}}{5 a (a+i a x)^{5/4}}",1,"(((4*I)/5)*(a - I*a*x)^(3/4))/(a*(a + I*a*x)^(5/4)) - ((6*I)/5)/(a*(a - I*a*x)^(1/4)*(a + I*a*x)^(1/4)) - (6*(1 + x^2)^(1/4)*EllipticE[ArcTan[x]/2, 2])/(5*a*(a - I*a*x)^(1/4)*(a + I*a*x)^(1/4))","A",5,5,25,0.2000,1,"{47, 48, 42, 197, 196}"
1219,1,82,0,0.0156894,"\int \frac{1}{\sqrt[4]{a-i a x} (a+i a x)^{9/4}} \, dx","Int[1/((a - I*a*x)^(1/4)*(a + I*a*x)^(9/4)),x]","\frac{2 \sqrt[4]{x^2+1} E\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{5 a^2 \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}+\frac{4 i}{5 a \sqrt[4]{a-i a x} (a+i a x)^{5/4}}","\frac{2 \sqrt[4]{x^2+1} E\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{5 a^2 \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}+\frac{4 i}{5 a \sqrt[4]{a-i a x} (a+i a x)^{5/4}}",1,"((4*I)/5)/(a*(a - I*a*x)^(1/4)*(a + I*a*x)^(5/4)) + (2*(1 + x^2)^(1/4)*EllipticE[ArcTan[x]/2, 2])/(5*a^2*(a - I*a*x)^(1/4)*(a + I*a*x)^(1/4))","A",4,4,25,0.1600,1,"{46, 42, 197, 196}"
1220,1,82,0,0.0246731,"\int \frac{1}{(a-i a x)^{5/4} (a+i a x)^{9/4}} \, dx","Int[1/((a - I*a*x)^(5/4)*(a + I*a*x)^(9/4)),x]","\frac{6 \sqrt[4]{x^2+1} E\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{5 a^3 \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}+\frac{2 i}{5 a^2 \sqrt[4]{a-i a x} (a+i a x)^{5/4}}","\frac{6 \sqrt[4]{x^2+1} E\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{5 a^3 \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}+\frac{2 i}{5 a^2 \sqrt[4]{a-i a x} (a+i a x)^{5/4}}",1,"((2*I)/5)/(a^2*(a - I*a*x)^(1/4)*(a + I*a*x)^(5/4)) + (6*(1 + x^2)^(1/4)*EllipticE[ArcTan[x]/2, 2])/(5*a^3*(a - I*a*x)^(1/4)*(a + I*a*x)^(1/4))","A",5,5,25,0.2000,1,"{51, 46, 42, 197, 196}"
1221,1,88,0,0.0158891,"\int \frac{1}{(a-i a x)^{9/4} (a+i a x)^{9/4}} \, dx","Int[1/((a - I*a*x)^(9/4)*(a + I*a*x)^(9/4)),x]","\frac{2 x}{5 a^4 \left(x^2+1\right) \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}+\frac{6 \sqrt[4]{x^2+1} E\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{5 a^4 \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}","\frac{2 x}{5 a^4 \left(x^2+1\right) \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}+\frac{6 \sqrt[4]{x^2+1} E\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{5 a^4 \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}",1,"(2*x)/(5*a^4*(a - I*a*x)^(1/4)*(a + I*a*x)^(1/4)*(1 + x^2)) + (6*(1 + x^2)^(1/4)*EllipticE[ArcTan[x]/2, 2])/(5*a^4*(a - I*a*x)^(1/4)*(a + I*a*x)^(1/4))","A",4,4,25,0.1600,1,"{42, 199, 197, 196}"
1222,1,121,0,0.0257717,"\int \frac{1}{(a-i a x)^{13/4} (a+i a x)^{9/4}} \, dx","Int[1/((a - I*a*x)^(13/4)*(a + I*a*x)^(9/4)),x]","\frac{14 x}{45 a^5 \left(x^2+1\right) \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}+\frac{14 \sqrt[4]{x^2+1} E\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{15 a^5 \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}-\frac{2 i}{9 a^2 (a-i a x)^{9/4} (a+i a x)^{5/4}}","\frac{14 x}{45 a^5 \left(x^2+1\right) \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}+\frac{14 \sqrt[4]{x^2+1} E\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{15 a^5 \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}-\frac{2 i}{9 a^2 (a-i a x)^{9/4} (a+i a x)^{5/4}}",1,"((-2*I)/9)/(a^2*(a - I*a*x)^(9/4)*(a + I*a*x)^(5/4)) + (14*x)/(45*a^5*(a - I*a*x)^(1/4)*(a + I*a*x)^(1/4)*(1 + x^2)) + (14*(1 + x^2)^(1/4)*EllipticE[ArcTan[x]/2, 2])/(15*a^5*(a - I*a*x)^(1/4)*(a + I*a*x)^(1/4))","A",5,5,25,0.2000,1,"{51, 42, 199, 197, 196}"
1223,1,154,0,0.0399608,"\int \frac{1}{(a-i a x)^{17/4} (a+i a x)^{9/4}} \, dx","Int[1/((a - I*a*x)^(17/4)*(a + I*a*x)^(9/4)),x]","\frac{14 x}{65 a^6 \left(x^2+1\right) \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}+\frac{42 \sqrt[4]{x^2+1} E\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{65 a^6 \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}-\frac{2 i}{13 a^3 (a-i a x)^{9/4} (a+i a x)^{5/4}}-\frac{2 i}{13 a^2 (a-i a x)^{13/4} (a+i a x)^{5/4}}","\frac{14 x}{65 a^6 \left(x^2+1\right) \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}+\frac{42 \sqrt[4]{x^2+1} E\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{65 a^6 \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}-\frac{2 i}{13 a^3 (a-i a x)^{9/4} (a+i a x)^{5/4}}-\frac{2 i}{13 a^2 (a-i a x)^{13/4} (a+i a x)^{5/4}}",1,"((-2*I)/13)/(a^2*(a - I*a*x)^(13/4)*(a + I*a*x)^(5/4)) - ((2*I)/13)/(a^3*(a - I*a*x)^(9/4)*(a + I*a*x)^(5/4)) + (14*x)/(65*a^6*(a - I*a*x)^(1/4)*(a + I*a*x)^(1/4)*(1 + x^2)) + (42*(1 + x^2)^(1/4)*EllipticE[ArcTan[x]/2, 2])/(65*a^6*(a - I*a*x)^(1/4)*(a + I*a*x)^(1/4))","A",6,5,25,0.2000,1,"{51, 42, 199, 197, 196}"
1224,1,297,0,0.140118,"\int \frac{(a-i a x)^{5/4}}{(a+i a x)^{9/4}} \, dx","Int[(a - I*a*x)^(5/4)/(a + I*a*x)^(9/4),x]","\frac{4 i (a-i a x)^{5/4}}{5 a (a+i a x)^{5/4}}-\frac{4 i \sqrt[4]{a-i a x}}{a \sqrt[4]{a+i a x}}-\frac{i \log \left(\frac{\sqrt{a-i a x}}{\sqrt{a+i a x}}-\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}+1\right)}{\sqrt{2} a}+\frac{i \log \left(\frac{\sqrt{a-i a x}}{\sqrt{a+i a x}}+\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}+1\right)}{\sqrt{2} a}-\frac{i \sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}\right)}{a}+\frac{i \sqrt{2} \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}\right)}{a}","\frac{4 i (a-i a x)^{5/4}}{5 a (a+i a x)^{5/4}}-\frac{4 i \sqrt[4]{a-i a x}}{a \sqrt[4]{a+i a x}}-\frac{i \log \left(\frac{\sqrt{a-i a x}}{\sqrt{a+i a x}}-\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}+1\right)}{\sqrt{2} a}+\frac{i \log \left(\frac{\sqrt{a-i a x}}{\sqrt{a+i a x}}+\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}+1\right)}{\sqrt{2} a}-\frac{i \sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}\right)}{a}+\frac{i \sqrt{2} \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}\right)}{a}",1,"(((4*I)/5)*(a - I*a*x)^(5/4))/(a*(a + I*a*x)^(5/4)) - ((4*I)*(a - I*a*x)^(1/4))/(a*(a + I*a*x)^(1/4)) - (I*Sqrt[2]*ArcTan[1 - (Sqrt[2]*(a - I*a*x)^(1/4))/(a + I*a*x)^(1/4)])/a + (I*Sqrt[2]*ArcTan[1 + (Sqrt[2]*(a - I*a*x)^(1/4))/(a + I*a*x)^(1/4)])/a - (I*Log[1 + Sqrt[a - I*a*x]/Sqrt[a + I*a*x] - (Sqrt[2]*(a - I*a*x)^(1/4))/(a + I*a*x)^(1/4)])/(Sqrt[2]*a) + (I*Log[1 + Sqrt[a - I*a*x]/Sqrt[a + I*a*x] + (Sqrt[2]*(a - I*a*x)^(1/4))/(a + I*a*x)^(1/4)])/(Sqrt[2]*a)","A",13,9,25,0.3600,1,"{47, 63, 240, 211, 1165, 628, 1162, 617, 204}"
1225,1,33,0,0.0032964,"\int \frac{\sqrt[4]{a-i a x}}{(a+i a x)^{9/4}} \, dx","Int[(a - I*a*x)^(1/4)/(a + I*a*x)^(9/4),x]","\frac{2 i (a-i a x)^{5/4}}{5 a^2 (a+i a x)^{5/4}}","\frac{2 i (a-i a x)^{5/4}}{5 a^2 (a+i a x)^{5/4}}",1,"(((2*I)/5)*(a - I*a*x)^(5/4))/(a^2*(a + I*a*x)^(5/4))","A",1,1,25,0.04000,1,"{37}"
1226,1,67,0,0.0098011,"\int \frac{1}{(a-i a x)^{3/4} (a+i a x)^{9/4}} \, dx","Int[1/((a - I*a*x)^(3/4)*(a + I*a*x)^(9/4)),x]","\frac{4 i \sqrt[4]{a-i a x}}{5 a^3 \sqrt[4]{a+i a x}}+\frac{2 i \sqrt[4]{a-i a x}}{5 a^2 (a+i a x)^{5/4}}","\frac{4 i \sqrt[4]{a-i a x}}{5 a^3 \sqrt[4]{a+i a x}}+\frac{2 i \sqrt[4]{a-i a x}}{5 a^2 (a+i a x)^{5/4}}",1,"(((2*I)/5)*(a - I*a*x)^(1/4))/(a^2*(a + I*a*x)^(5/4)) + (((4*I)/5)*(a - I*a*x)^(1/4))/(a^3*(a + I*a*x)^(1/4))","A",2,2,25,0.08000,1,"{45, 37}"
1227,1,100,0,0.018242,"\int \frac{1}{(a-i a x)^{7/4} (a+i a x)^{9/4}} \, dx","Int[1/((a - I*a*x)^(7/4)*(a + I*a*x)^(9/4)),x]","\frac{16 i \sqrt[4]{a-i a x}}{15 a^4 \sqrt[4]{a+i a x}}+\frac{8 i \sqrt[4]{a-i a x}}{15 a^3 (a+i a x)^{5/4}}-\frac{2 i}{3 a^2 (a+i a x)^{5/4} (a-i a x)^{3/4}}","\frac{16 i \sqrt[4]{a-i a x}}{15 a^4 \sqrt[4]{a+i a x}}+\frac{8 i \sqrt[4]{a-i a x}}{15 a^3 (a+i a x)^{5/4}}-\frac{2 i}{3 a^2 (a+i a x)^{5/4} (a-i a x)^{3/4}}",1,"((-2*I)/3)/(a^2*(a - I*a*x)^(3/4)*(a + I*a*x)^(5/4)) + (((8*I)/15)*(a - I*a*x)^(1/4))/(a^3*(a + I*a*x)^(5/4)) + (((16*I)/15)*(a - I*a*x)^(1/4))/(a^4*(a + I*a*x)^(1/4))","A",3,2,25,0.08000,1,"{45, 37}"
1228,1,133,0,0.0294059,"\int \frac{1}{(a-i a x)^{11/4} (a+i a x)^{9/4}} \, dx","Int[1/((a - I*a*x)^(11/4)*(a + I*a*x)^(9/4)),x]","\frac{32 i \sqrt[4]{a-i a x}}{35 a^5 \sqrt[4]{a+i a x}}+\frac{16 i \sqrt[4]{a-i a x}}{35 a^4 (a+i a x)^{5/4}}-\frac{4 i}{7 a^3 (a+i a x)^{5/4} (a-i a x)^{3/4}}-\frac{2 i}{7 a^2 (a+i a x)^{5/4} (a-i a x)^{7/4}}","\frac{32 i \sqrt[4]{a-i a x}}{35 a^5 \sqrt[4]{a+i a x}}+\frac{16 i \sqrt[4]{a-i a x}}{35 a^4 (a+i a x)^{5/4}}-\frac{4 i}{7 a^3 (a+i a x)^{5/4} (a-i a x)^{3/4}}-\frac{2 i}{7 a^2 (a+i a x)^{5/4} (a-i a x)^{7/4}}",1,"((-2*I)/7)/(a^2*(a - I*a*x)^(7/4)*(a + I*a*x)^(5/4)) - ((4*I)/7)/(a^3*(a - I*a*x)^(3/4)*(a + I*a*x)^(5/4)) + (((16*I)/35)*(a - I*a*x)^(1/4))/(a^4*(a + I*a*x)^(5/4)) + (((32*I)/35)*(a - I*a*x)^(1/4))/(a^5*(a + I*a*x)^(1/4))","A",4,2,25,0.08000,1,"{45, 37}"
1229,1,83,0,0.0285228,"\int (a+b x)^2 (a c-b c x)^n \, dx","Int[(a + b*x)^2*(a*c - b*c*x)^n,x]","-\frac{4 a^2 (a c-b c x)^{n+1}}{b c (n+1)}+\frac{4 a (a c-b c x)^{n+2}}{b c^2 (n+2)}-\frac{(a c-b c x)^{n+3}}{b c^3 (n+3)}","-\frac{4 a^2 (a c-b c x)^{n+1}}{b c (n+1)}+\frac{4 a (a c-b c x)^{n+2}}{b c^2 (n+2)}-\frac{(a c-b c x)^{n+3}}{b c^3 (n+3)}",1,"(-4*a^2*(a*c - b*c*x)^(1 + n))/(b*c*(1 + n)) + (4*a*(a*c - b*c*x)^(2 + n))/(b*c^2*(2 + n)) - (a*c - b*c*x)^(3 + n)/(b*c^3*(3 + n))","A",2,1,19,0.05263,1,"{43}"
1230,1,53,0,0.0170643,"\int (a+b x) (a c-b c x)^n \, dx","Int[(a + b*x)*(a*c - b*c*x)^n,x]","\frac{(a c-b c x)^{n+2}}{b c^2 (n+2)}-\frac{2 a (a c-b c x)^{n+1}}{b c (n+1)}","\frac{(a c-b c x)^{n+2}}{b c^2 (n+2)}-\frac{2 a (a c-b c x)^{n+1}}{b c (n+1)}",1,"(-2*a*(a*c - b*c*x)^(1 + n))/(b*c*(1 + n)) + (a*c - b*c*x)^(2 + n)/(b*c^2*(2 + n))","A",2,1,17,0.05882,1,"{43}"
1231,1,52,0,0.0145496,"\int \frac{(a c-b c x)^n}{a+b x} \, dx","Int[(a*c - b*c*x)^n/(a + b*x),x]","-\frac{(a c-b c x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{a-b x}{2 a}\right)}{2 a b c (n+1)}","-\frac{(a c-b c x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{a-b x}{2 a}\right)}{2 a b c (n+1)}",1,"-((a*c - b*c*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (a - b*x)/(2*a)])/(2*a*b*c*(1 + n))","A",1,1,19,0.05263,1,"{68}"
1232,1,52,0,0.0114906,"\int \frac{(a c-b c x)^n}{(a+b x)^2} \, dx","Int[(a*c - b*c*x)^n/(a + b*x)^2,x]","-\frac{(a c-b c x)^{n+1} \, _2F_1\left(2,n+1;n+2;\frac{a-b x}{2 a}\right)}{4 a^2 b c (n+1)}","-\frac{(a c-b c x)^{n+1} \, _2F_1\left(2,n+1;n+2;\frac{a-b x}{2 a}\right)}{4 a^2 b c (n+1)}",1,"-((a*c - b*c*x)^(1 + n)*Hypergeometric2F1[2, 1 + n, 2 + n, (a - b*x)/(2*a)])/(4*a^2*b*c*(1 + n))","A",1,1,19,0.05263,1,"{68}"
1233,1,41,0,0.0116055,"\int (a+a x)^m (c-c x)^m \, dx","Int[(a + a*x)^m*(c - c*x)^m,x]","x \left(1-x^2\right)^{-m} (a x+a)^m (c-c x)^m \, _2F_1\left(\frac{1}{2},-m;\frac{3}{2};x^2\right)","x \left(1-x^2\right)^{-m} (a x+a)^m (c-c x)^m \, _2F_1\left(\frac{1}{2},-m;\frac{3}{2};x^2\right)",1,"(x*(a + a*x)^m*(c - c*x)^m*Hypergeometric2F1[1/2, -m, 3/2, x^2])/(1 - x^2)^m","A",3,3,16,0.1875,1,"{42, 246, 245}"
1234,1,57,0,0.0179656,"\int (a+b x)^m (a c-b c x)^m \, dx","Int[(a + b*x)^m*(a*c - b*c*x)^m,x]","x (a+b x)^m \left(1-\frac{b^2 x^2}{a^2}\right)^{-m} (a c-b c x)^m \, _2F_1\left(\frac{1}{2},-m;\frac{3}{2};\frac{b^2 x^2}{a^2}\right)","x (a+b x)^m \left(1-\frac{b^2 x^2}{a^2}\right)^{-m} (a c-b c x)^m \, _2F_1\left(\frac{1}{2},-m;\frac{3}{2};\frac{b^2 x^2}{a^2}\right)",1,"(x*(a + b*x)^m*(a*c - b*c*x)^m*Hypergeometric2F1[1/2, -m, 3/2, (b^2*x^2)/a^2])/(1 - (b^2*x^2)/a^2)^m","A",3,3,19,0.1579,1,"{42, 246, 245}"
1235,1,20,0,0.0057414,"\int (3-6 x)^m (2+4 x)^m \, dx","Int[(3 - 6*x)^m*(2 + 4*x)^m,x]","6^m x \, _2F_1\left(\frac{1}{2},-m;\frac{3}{2};4 x^2\right)","6^m x \, _2F_1\left(\frac{1}{2},-m;\frac{3}{2};4 x^2\right)",1,"6^m*x*Hypergeometric2F1[1/2, -m, 3/2, 4*x^2]","A",2,2,15,0.1333,1,"{41, 245}"
1236,1,38,0,0.0147325,"\int (a+b x)^4 (c+d x) \, dx","Int[(a + b*x)^4*(c + d*x),x]","\frac{(a+b x)^5 (b c-a d)}{5 b^2}+\frac{d (a+b x)^6}{6 b^2}","\frac{(a+b x)^5 (b c-a d)}{5 b^2}+\frac{d (a+b x)^6}{6 b^2}",1,"((b*c - a*d)*(a + b*x)^5)/(5*b^2) + (d*(a + b*x)^6)/(6*b^2)","A",2,1,13,0.07692,1,"{43}"
1237,1,38,0,0.01236,"\int (a+b x)^3 (c+d x) \, dx","Int[(a + b*x)^3*(c + d*x),x]","\frac{(a+b x)^4 (b c-a d)}{4 b^2}+\frac{d (a+b x)^5}{5 b^2}","\frac{(a+b x)^4 (b c-a d)}{4 b^2}+\frac{d (a+b x)^5}{5 b^2}",1,"((b*c - a*d)*(a + b*x)^4)/(4*b^2) + (d*(a + b*x)^5)/(5*b^2)","A",2,1,13,0.07692,1,"{43}"
1238,1,38,0,0.0268233,"\int (a+b x)^2 (c+d x) \, dx","Int[(a + b*x)^2*(c + d*x),x]","\frac{(a+b x)^3 (b c-a d)}{3 b^2}+\frac{d (a+b x)^4}{4 b^2}","\frac{(a+b x)^3 (b c-a d)}{3 b^2}+\frac{d (a+b x)^4}{4 b^2}",1,"((b*c - a*d)*(a + b*x)^3)/(3*b^2) + (d*(a + b*x)^4)/(4*b^2)","A",2,1,13,0.07692,1,"{43}"
1239,1,28,0,0.015441,"\int (a+b x) (c+d x) \, dx","Int[(a + b*x)*(c + d*x),x]","\frac{1}{2} x^2 (a d+b c)+a c x+\frac{1}{3} b d x^3","\frac{1}{2} x^2 (a d+b c)+a c x+\frac{1}{3} b d x^3",1,"a*c*x + ((b*c + a*d)*x^2)/2 + (b*d*x^3)/3","A",2,1,11,0.09091,1,"{43}"
1240,1,12,0,0.0021542,"\int (c+d x) \, dx","Int[c + d*x,x]","c x+\frac{d x^2}{2}","c x+\frac{d x^2}{2}",1,"c*x + (d*x^2)/2","A",1,0,5,0,1,"{}"
1241,1,25,0,0.0170204,"\int \frac{c+d x}{a+b x} \, dx","Int[(c + d*x)/(a + b*x),x]","\frac{(b c-a d) \log (a+b x)}{b^2}+\frac{d x}{b}","\frac{(b c-a d) \log (a+b x)}{b^2}+\frac{d x}{b}",1,"(d*x)/b + ((b*c - a*d)*Log[a + b*x])/b^2","A",2,1,13,0.07692,1,"{43}"
1242,1,32,0,0.0193538,"\int \frac{c+d x}{(a+b x)^2} \, dx","Int[(c + d*x)/(a + b*x)^2,x]","\frac{d \log (a+b x)}{b^2}-\frac{b c-a d}{b^2 (a+b x)}","\frac{d \log (a+b x)}{b^2}-\frac{b c-a d}{b^2 (a+b x)}",1,"-((b*c - a*d)/(b^2*(a + b*x))) + (d*Log[a + b*x])/b^2","A",2,1,13,0.07692,1,"{43}"
1243,1,28,0,0.0043352,"\int \frac{c+d x}{(a+b x)^3} \, dx","Int[(c + d*x)/(a + b*x)^3,x]","-\frac{(c+d x)^2}{2 (a+b x)^2 (b c-a d)}","-\frac{(c+d x)^2}{2 (a+b x)^2 (b c-a d)}",1,"-(c + d*x)^2/(2*(b*c - a*d)*(a + b*x)^2)","A",1,1,13,0.07692,1,"{37}"
1244,1,38,0,0.0199422,"\int \frac{c+d x}{(a+b x)^4} \, dx","Int[(c + d*x)/(a + b*x)^4,x]","-\frac{b c-a d}{3 b^2 (a+b x)^3}-\frac{d}{2 b^2 (a+b x)^2}","-\frac{b c-a d}{3 b^2 (a+b x)^3}-\frac{d}{2 b^2 (a+b x)^2}",1,"-(b*c - a*d)/(3*b^2*(a + b*x)^3) - d/(2*b^2*(a + b*x)^2)","A",2,1,13,0.07692,1,"{43}"
1245,1,38,0,0.019943,"\int \frac{c+d x}{(a+b x)^5} \, dx","Int[(c + d*x)/(a + b*x)^5,x]","-\frac{b c-a d}{4 b^2 (a+b x)^4}-\frac{d}{3 b^2 (a+b x)^3}","-\frac{b c-a d}{4 b^2 (a+b x)^4}-\frac{d}{3 b^2 (a+b x)^3}",1,"-(b*c - a*d)/(4*b^2*(a + b*x)^4) - d/(3*b^2*(a + b*x)^3)","A",2,1,13,0.07692,1,"{43}"
1246,1,65,0,0.0877685,"\int (a+b x)^4 (c+d x)^2 \, dx","Int[(a + b*x)^4*(c + d*x)^2,x]","\frac{d (a+b x)^6 (b c-a d)}{3 b^3}+\frac{(a+b x)^5 (b c-a d)^2}{5 b^3}+\frac{d^2 (a+b x)^7}{7 b^3}","\frac{d (a+b x)^6 (b c-a d)}{3 b^3}+\frac{(a+b x)^5 (b c-a d)^2}{5 b^3}+\frac{d^2 (a+b x)^7}{7 b^3}",1,"((b*c - a*d)^2*(a + b*x)^5)/(5*b^3) + (d*(b*c - a*d)*(a + b*x)^6)/(3*b^3) + (d^2*(a + b*x)^7)/(7*b^3)","A",2,1,15,0.06667,1,"{43}"
1247,1,65,0,0.0636893,"\int (a+b x)^3 (c+d x)^2 \, dx","Int[(a + b*x)^3*(c + d*x)^2,x]","\frac{2 d (a+b x)^5 (b c-a d)}{5 b^3}+\frac{(a+b x)^4 (b c-a d)^2}{4 b^3}+\frac{d^2 (a+b x)^6}{6 b^3}","\frac{2 d (a+b x)^5 (b c-a d)}{5 b^3}+\frac{(a+b x)^4 (b c-a d)^2}{4 b^3}+\frac{d^2 (a+b x)^6}{6 b^3}",1,"((b*c - a*d)^2*(a + b*x)^4)/(4*b^3) + (2*d*(b*c - a*d)*(a + b*x)^5)/(5*b^3) + (d^2*(a + b*x)^6)/(6*b^3)","A",2,1,15,0.06667,1,"{43}"
1248,1,65,0,0.0454584,"\int (a+b x)^2 (c+d x)^2 \, dx","Int[(a + b*x)^2*(c + d*x)^2,x]","\frac{d (a+b x)^4 (b c-a d)}{2 b^3}+\frac{(a+b x)^3 (b c-a d)^2}{3 b^3}+\frac{d^2 (a+b x)^5}{5 b^3}","\frac{d (a+b x)^4 (b c-a d)}{2 b^3}+\frac{(a+b x)^3 (b c-a d)^2}{3 b^3}+\frac{d^2 (a+b x)^5}{5 b^3}",1,"((b*c - a*d)^2*(a + b*x)^3)/(3*b^3) + (d*(b*c - a*d)*(a + b*x)^4)/(2*b^3) + (d^2*(a + b*x)^5)/(5*b^3)","A",2,1,15,0.06667,1,"{43}"
1249,1,38,0,0.0273636,"\int (a+b x) (c+d x)^2 \, dx","Int[(a + b*x)*(c + d*x)^2,x]","\frac{b (c+d x)^4}{4 d^2}-\frac{(c+d x)^3 (b c-a d)}{3 d^2}","\frac{b (c+d x)^4}{4 d^2}-\frac{(c+d x)^3 (b c-a d)}{3 d^2}",1,"-((b*c - a*d)*(c + d*x)^3)/(3*d^2) + (b*(c + d*x)^4)/(4*d^2)","A",2,1,13,0.07692,1,"{43}"
1250,1,14,0,0.0015332,"\int (c+d x)^2 \, dx","Int[(c + d*x)^2,x]","\frac{(c+d x)^3}{3 d}","\frac{(c+d x)^3}{3 d}",1,"(c + d*x)^3/(3*d)","A",1,1,7,0.1429,1,"{32}"
1251,1,49,0,0.0186455,"\int \frac{(c+d x)^2}{a+b x} \, dx","Int[(c + d*x)^2/(a + b*x),x]","\frac{d x (b c-a d)}{b^2}+\frac{(b c-a d)^2 \log (a+b x)}{b^3}+\frac{(c+d x)^2}{2 b}","\frac{d x (b c-a d)}{b^2}+\frac{(b c-a d)^2 \log (a+b x)}{b^3}+\frac{(c+d x)^2}{2 b}",1,"(d*(b*c - a*d)*x)/b^2 + (c + d*x)^2/(2*b) + ((b*c - a*d)^2*Log[a + b*x])/b^3","A",2,1,15,0.06667,1,"{43}"
1252,1,51,0,0.0346731,"\int \frac{(c+d x)^2}{(a+b x)^2} \, dx","Int[(c + d*x)^2/(a + b*x)^2,x]","-\frac{(b c-a d)^2}{b^3 (a+b x)}+\frac{2 d (b c-a d) \log (a+b x)}{b^3}+\frac{d^2 x}{b^2}","-\frac{(b c-a d)^2}{b^3 (a+b x)}+\frac{2 d (b c-a d) \log (a+b x)}{b^3}+\frac{d^2 x}{b^2}",1,"(d^2*x)/b^2 - (b*c - a*d)^2/(b^3*(a + b*x)) + (2*d*(b*c - a*d)*Log[a + b*x])/b^3","A",2,1,15,0.06667,1,"{43}"
1253,1,59,0,0.0350432,"\int \frac{(c+d x)^2}{(a+b x)^3} \, dx","Int[(c + d*x)^2/(a + b*x)^3,x]","-\frac{2 d (b c-a d)}{b^3 (a+b x)}-\frac{(b c-a d)^2}{2 b^3 (a+b x)^2}+\frac{d^2 \log (a+b x)}{b^3}","-\frac{2 d (b c-a d)}{b^3 (a+b x)}-\frac{(b c-a d)^2}{2 b^3 (a+b x)^2}+\frac{d^2 \log (a+b x)}{b^3}",1,"-(b*c - a*d)^2/(2*b^3*(a + b*x)^2) - (2*d*(b*c - a*d))/(b^3*(a + b*x)) + (d^2*Log[a + b*x])/b^3","A",2,1,15,0.06667,1,"{43}"
1254,1,28,0,0.0042436,"\int \frac{(c+d x)^2}{(a+b x)^4} \, dx","Int[(c + d*x)^2/(a + b*x)^4,x]","-\frac{(c+d x)^3}{3 (a+b x)^3 (b c-a d)}","-\frac{(c+d x)^3}{3 (a+b x)^3 (b c-a d)}",1,"-(c + d*x)^3/(3*(b*c - a*d)*(a + b*x)^3)","A",1,1,15,0.06667,1,"{37}"
1255,1,65,0,0.0331657,"\int \frac{(c+d x)^2}{(a+b x)^5} \, dx","Int[(c + d*x)^2/(a + b*x)^5,x]","-\frac{2 d (b c-a d)}{3 b^3 (a+b x)^3}-\frac{(b c-a d)^2}{4 b^3 (a+b x)^4}-\frac{d^2}{2 b^3 (a+b x)^2}","-\frac{2 d (b c-a d)}{3 b^3 (a+b x)^3}-\frac{(b c-a d)^2}{4 b^3 (a+b x)^4}-\frac{d^2}{2 b^3 (a+b x)^2}",1,"-(b*c - a*d)^2/(4*b^3*(a + b*x)^4) - (2*d*(b*c - a*d))/(3*b^3*(a + b*x)^3) - d^2/(2*b^3*(a + b*x)^2)","A",2,1,15,0.06667,1,"{43}"
1256,1,65,0,0.0334299,"\int \frac{(c+d x)^2}{(a+b x)^6} \, dx","Int[(c + d*x)^2/(a + b*x)^6,x]","-\frac{d (b c-a d)}{2 b^3 (a+b x)^4}-\frac{(b c-a d)^2}{5 b^3 (a+b x)^5}-\frac{d^2}{3 b^3 (a+b x)^3}","-\frac{d (b c-a d)}{2 b^3 (a+b x)^4}-\frac{(b c-a d)^2}{5 b^3 (a+b x)^5}-\frac{d^2}{3 b^3 (a+b x)^3}",1,"-(b*c - a*d)^2/(5*b^3*(a + b*x)^5) - (d*(b*c - a*d))/(2*b^3*(a + b*x)^4) - d^2/(3*b^3*(a + b*x)^3)","A",2,1,15,0.06667,1,"{43}"
1257,1,65,0,0.0329904,"\int \frac{(c+d x)^2}{(a+b x)^7} \, dx","Int[(c + d*x)^2/(a + b*x)^7,x]","-\frac{2 d (b c-a d)}{5 b^3 (a+b x)^5}-\frac{(b c-a d)^2}{6 b^3 (a+b x)^6}-\frac{d^2}{4 b^3 (a+b x)^4}","-\frac{2 d (b c-a d)}{5 b^3 (a+b x)^5}-\frac{(b c-a d)^2}{6 b^3 (a+b x)^6}-\frac{d^2}{4 b^3 (a+b x)^4}",1,"-(b*c - a*d)^2/(6*b^3*(a + b*x)^6) - (2*d*(b*c - a*d))/(5*b^3*(a + b*x)^5) - d^2/(4*b^3*(a + b*x)^4)","A",2,1,15,0.06667,1,"{43}"
1258,1,92,0,0.1571892,"\int (a+b x)^5 (c+d x)^3 \, dx","Int[(a + b*x)^5*(c + d*x)^3,x]","\frac{3 d^2 (a+b x)^8 (b c-a d)}{8 b^4}+\frac{3 d (a+b x)^7 (b c-a d)^2}{7 b^4}+\frac{(a+b x)^6 (b c-a d)^3}{6 b^4}+\frac{d^3 (a+b x)^9}{9 b^4}","\frac{3 d^2 (a+b x)^8 (b c-a d)}{8 b^4}+\frac{3 d (a+b x)^7 (b c-a d)^2}{7 b^4}+\frac{(a+b x)^6 (b c-a d)^3}{6 b^4}+\frac{d^3 (a+b x)^9}{9 b^4}",1,"((b*c - a*d)^3*(a + b*x)^6)/(6*b^4) + (3*d*(b*c - a*d)^2*(a + b*x)^7)/(7*b^4) + (3*d^2*(b*c - a*d)*(a + b*x)^8)/(8*b^4) + (d^3*(a + b*x)^9)/(9*b^4)","A",2,1,15,0.06667,1,"{43}"
1259,1,92,0,0.1142265,"\int (a+b x)^4 (c+d x)^3 \, dx","Int[(a + b*x)^4*(c + d*x)^3,x]","\frac{3 d^2 (a+b x)^7 (b c-a d)}{7 b^4}+\frac{d (a+b x)^6 (b c-a d)^2}{2 b^4}+\frac{(a+b x)^5 (b c-a d)^3}{5 b^4}+\frac{d^3 (a+b x)^8}{8 b^4}","\frac{3 d^2 (a+b x)^7 (b c-a d)}{7 b^4}+\frac{d (a+b x)^6 (b c-a d)^2}{2 b^4}+\frac{(a+b x)^5 (b c-a d)^3}{5 b^4}+\frac{d^3 (a+b x)^8}{8 b^4}",1,"((b*c - a*d)^3*(a + b*x)^5)/(5*b^4) + (d*(b*c - a*d)^2*(a + b*x)^6)/(2*b^4) + (3*d^2*(b*c - a*d)*(a + b*x)^7)/(7*b^4) + (d^3*(a + b*x)^8)/(8*b^4)","A",2,1,15,0.06667,1,"{43}"
1260,1,92,0,0.0826116,"\int (a+b x)^3 (c+d x)^3 \, dx","Int[(a + b*x)^3*(c + d*x)^3,x]","\frac{d^2 (a+b x)^6 (b c-a d)}{2 b^4}+\frac{3 d (a+b x)^5 (b c-a d)^2}{5 b^4}+\frac{(a+b x)^4 (b c-a d)^3}{4 b^4}+\frac{d^3 (a+b x)^7}{7 b^4}","\frac{d^2 (a+b x)^6 (b c-a d)}{2 b^4}+\frac{3 d (a+b x)^5 (b c-a d)^2}{5 b^4}+\frac{(a+b x)^4 (b c-a d)^3}{4 b^4}+\frac{d^3 (a+b x)^7}{7 b^4}",1,"((b*c - a*d)^3*(a + b*x)^4)/(4*b^4) + (3*d*(b*c - a*d)^2*(a + b*x)^5)/(5*b^4) + (d^2*(b*c - a*d)*(a + b*x)^6)/(2*b^4) + (d^3*(a + b*x)^7)/(7*b^4)","A",2,1,15,0.06667,1,"{43}"
1261,1,65,0,0.0644285,"\int (a+b x)^2 (c+d x)^3 \, dx","Int[(a + b*x)^2*(c + d*x)^3,x]","-\frac{2 b (c+d x)^5 (b c-a d)}{5 d^3}+\frac{(c+d x)^4 (b c-a d)^2}{4 d^3}+\frac{b^2 (c+d x)^6}{6 d^3}","-\frac{2 b (c+d x)^5 (b c-a d)}{5 d^3}+\frac{(c+d x)^4 (b c-a d)^2}{4 d^3}+\frac{b^2 (c+d x)^6}{6 d^3}",1,"((b*c - a*d)^2*(c + d*x)^4)/(4*d^3) - (2*b*(b*c - a*d)*(c + d*x)^5)/(5*d^3) + (b^2*(c + d*x)^6)/(6*d^3)","A",2,1,15,0.06667,1,"{43}"
1262,1,38,0,0.0150808,"\int (a+b x) (c+d x)^3 \, dx","Int[(a + b*x)*(c + d*x)^3,x]","\frac{b (c+d x)^5}{5 d^2}-\frac{(c+d x)^4 (b c-a d)}{4 d^2}","\frac{b (c+d x)^5}{5 d^2}-\frac{(c+d x)^4 (b c-a d)}{4 d^2}",1,"-((b*c - a*d)*(c + d*x)^4)/(4*d^2) + (b*(c + d*x)^5)/(5*d^2)","A",2,1,13,0.07692,1,"{43}"
1263,1,14,0,0.0015485,"\int (c+d x)^3 \, dx","Int[(c + d*x)^3,x]","\frac{(c+d x)^4}{4 d}","\frac{(c+d x)^4}{4 d}",1,"(c + d*x)^4/(4*d)","A",1,1,7,0.1429,1,"{32}"
1264,1,73,0,0.0276175,"\int \frac{(c+d x)^3}{a+b x} \, dx","Int[(c + d*x)^3/(a + b*x),x]","\frac{d x (b c-a d)^2}{b^3}+\frac{(c+d x)^2 (b c-a d)}{2 b^2}+\frac{(b c-a d)^3 \log (a+b x)}{b^4}+\frac{(c+d x)^3}{3 b}","\frac{d x (b c-a d)^2}{b^3}+\frac{(c+d x)^2 (b c-a d)}{2 b^2}+\frac{(b c-a d)^3 \log (a+b x)}{b^4}+\frac{(c+d x)^3}{3 b}",1,"(d*(b*c - a*d)^2*x)/b^3 + ((b*c - a*d)*(c + d*x)^2)/(2*b^2) + (c + d*x)^3/(3*b) + ((b*c - a*d)^3*Log[a + b*x])/b^4","A",2,1,15,0.06667,1,"{43}"
1265,1,75,0,0.0550575,"\int \frac{(c+d x)^3}{(a+b x)^2} \, dx","Int[(c + d*x)^3/(a + b*x)^2,x]","\frac{d^2 x (3 b c-2 a d)}{b^3}-\frac{(b c-a d)^3}{b^4 (a+b x)}+\frac{3 d (b c-a d)^2 \log (a+b x)}{b^4}+\frac{d^3 x^2}{2 b^2}","\frac{d^2 x (3 b c-2 a d)}{b^3}-\frac{(b c-a d)^3}{b^4 (a+b x)}+\frac{3 d (b c-a d)^2 \log (a+b x)}{b^4}+\frac{d^3 x^2}{2 b^2}",1,"(d^2*(3*b*c - 2*a*d)*x)/b^3 + (d^3*x^2)/(2*b^2) - (b*c - a*d)^3/(b^4*(a + b*x)) + (3*d*(b*c - a*d)^2*Log[a + b*x])/b^4","A",2,1,15,0.06667,1,"{43}"
1266,1,78,0,0.0523061,"\int \frac{(c+d x)^3}{(a+b x)^3} \, dx","Int[(c + d*x)^3/(a + b*x)^3,x]","\frac{3 d^2 (b c-a d) \log (a+b x)}{b^4}-\frac{3 d (b c-a d)^2}{b^4 (a+b x)}-\frac{(b c-a d)^3}{2 b^4 (a+b x)^2}+\frac{d^3 x}{b^3}","\frac{3 d^2 (b c-a d) \log (a+b x)}{b^4}-\frac{3 d (b c-a d)^2}{b^4 (a+b x)}-\frac{(b c-a d)^3}{2 b^4 (a+b x)^2}+\frac{d^3 x}{b^3}",1,"(d^3*x)/b^3 - (b*c - a*d)^3/(2*b^4*(a + b*x)^2) - (3*d*(b*c - a*d)^2)/(b^4*(a + b*x)) + (3*d^2*(b*c - a*d)*Log[a + b*x])/b^4","A",2,1,15,0.06667,1,"{43}"
1267,1,86,0,0.0501509,"\int \frac{(c+d x)^3}{(a+b x)^4} \, dx","Int[(c + d*x)^3/(a + b*x)^4,x]","-\frac{3 d^2 (b c-a d)}{b^4 (a+b x)}-\frac{3 d (b c-a d)^2}{2 b^4 (a+b x)^2}-\frac{(b c-a d)^3}{3 b^4 (a+b x)^3}+\frac{d^3 \log (a+b x)}{b^4}","-\frac{3 d^2 (b c-a d)}{b^4 (a+b x)}-\frac{3 d (b c-a d)^2}{2 b^4 (a+b x)^2}-\frac{(b c-a d)^3}{3 b^4 (a+b x)^3}+\frac{d^3 \log (a+b x)}{b^4}",1,"-(b*c - a*d)^3/(3*b^4*(a + b*x)^3) - (3*d*(b*c - a*d)^2)/(2*b^4*(a + b*x)^2) - (3*d^2*(b*c - a*d))/(b^4*(a + b*x)) + (d^3*Log[a + b*x])/b^4","A",2,1,15,0.06667,1,"{43}"
1268,1,28,0,0.0029669,"\int \frac{(c+d x)^3}{(a+b x)^5} \, dx","Int[(c + d*x)^3/(a + b*x)^5,x]","-\frac{(c+d x)^4}{4 (a+b x)^4 (b c-a d)}","-\frac{(c+d x)^4}{4 (a+b x)^4 (b c-a d)}",1,"-(c + d*x)^4/(4*(b*c - a*d)*(a + b*x)^4)","A",1,1,15,0.06667,1,"{37}"
1269,1,58,0,0.0103058,"\int \frac{(c+d x)^3}{(a+b x)^6} \, dx","Int[(c + d*x)^3/(a + b*x)^6,x]","\frac{d (c+d x)^4}{20 (a+b x)^4 (b c-a d)^2}-\frac{(c+d x)^4}{5 (a+b x)^5 (b c-a d)}","\frac{d (c+d x)^4}{20 (a+b x)^4 (b c-a d)^2}-\frac{(c+d x)^4}{5 (a+b x)^5 (b c-a d)}",1,"-(c + d*x)^4/(5*(b*c - a*d)*(a + b*x)^5) + (d*(c + d*x)^4)/(20*(b*c - a*d)^2*(a + b*x)^4)","A",2,2,15,0.1333,1,"{45, 37}"
1270,1,92,0,0.0504132,"\int \frac{(c+d x)^3}{(a+b x)^7} \, dx","Int[(c + d*x)^3/(a + b*x)^7,x]","-\frac{3 d^2 (b c-a d)}{4 b^4 (a+b x)^4}-\frac{3 d (b c-a d)^2}{5 b^4 (a+b x)^5}-\frac{(b c-a d)^3}{6 b^4 (a+b x)^6}-\frac{d^3}{3 b^4 (a+b x)^3}","-\frac{3 d^2 (b c-a d)}{4 b^4 (a+b x)^4}-\frac{3 d (b c-a d)^2}{5 b^4 (a+b x)^5}-\frac{(b c-a d)^3}{6 b^4 (a+b x)^6}-\frac{d^3}{3 b^4 (a+b x)^3}",1,"-(b*c - a*d)^3/(6*b^4*(a + b*x)^6) - (3*d*(b*c - a*d)^2)/(5*b^4*(a + b*x)^5) - (3*d^2*(b*c - a*d))/(4*b^4*(a + b*x)^4) - d^3/(3*b^4*(a + b*x)^3)","A",2,1,15,0.06667,1,"{43}"
1271,1,92,0,0.049082,"\int \frac{(c+d x)^3}{(a+b x)^8} \, dx","Int[(c + d*x)^3/(a + b*x)^8,x]","-\frac{3 d^2 (b c-a d)}{5 b^4 (a+b x)^5}-\frac{d (b c-a d)^2}{2 b^4 (a+b x)^6}-\frac{(b c-a d)^3}{7 b^4 (a+b x)^7}-\frac{d^3}{4 b^4 (a+b x)^4}","-\frac{3 d^2 (b c-a d)}{5 b^4 (a+b x)^5}-\frac{d (b c-a d)^2}{2 b^4 (a+b x)^6}-\frac{(b c-a d)^3}{7 b^4 (a+b x)^7}-\frac{d^3}{4 b^4 (a+b x)^4}",1,"-(b*c - a*d)^3/(7*b^4*(a + b*x)^7) - (d*(b*c - a*d)^2)/(2*b^4*(a + b*x)^6) - (3*d^2*(b*c - a*d))/(5*b^4*(a + b*x)^5) - d^3/(4*b^4*(a + b*x)^4)","A",2,1,15,0.06667,1,"{43}"
1272,1,92,0,0.0463985,"\int \frac{(c+d x)^3}{(a+b x)^9} \, dx","Int[(c + d*x)^3/(a + b*x)^9,x]","-\frac{d^2 (b c-a d)}{2 b^4 (a+b x)^6}-\frac{3 d (b c-a d)^2}{7 b^4 (a+b x)^7}-\frac{(b c-a d)^3}{8 b^4 (a+b x)^8}-\frac{d^3}{5 b^4 (a+b x)^5}","-\frac{d^2 (b c-a d)}{2 b^4 (a+b x)^6}-\frac{3 d (b c-a d)^2}{7 b^4 (a+b x)^7}-\frac{(b c-a d)^3}{8 b^4 (a+b x)^8}-\frac{d^3}{5 b^4 (a+b x)^5}",1,"-(b*c - a*d)^3/(8*b^4*(a + b*x)^8) - (3*d*(b*c - a*d)^2)/(7*b^4*(a + b*x)^7) - (d^2*(b*c - a*d))/(2*b^4*(a + b*x)^6) - d^3/(5*b^4*(a + b*x)^5)","A",2,1,15,0.06667,1,"{43}"
1273,1,200,0,0.6764662,"\int (a+b x)^9 (c+d x)^7 \, dx","Int[(a + b*x)^9*(c + d*x)^7,x]","\frac{7 d^6 (a+b x)^{16} (b c-a d)}{16 b^8}+\frac{7 d^5 (a+b x)^{15} (b c-a d)^2}{5 b^8}+\frac{5 d^4 (a+b x)^{14} (b c-a d)^3}{2 b^8}+\frac{35 d^3 (a+b x)^{13} (b c-a d)^4}{13 b^8}+\frac{7 d^2 (a+b x)^{12} (b c-a d)^5}{4 b^8}+\frac{7 d (a+b x)^{11} (b c-a d)^6}{11 b^8}+\frac{(a+b x)^{10} (b c-a d)^7}{10 b^8}+\frac{d^7 (a+b x)^{17}}{17 b^8}","\frac{7 d^6 (a+b x)^{16} (b c-a d)}{16 b^8}+\frac{7 d^5 (a+b x)^{15} (b c-a d)^2}{5 b^8}+\frac{5 d^4 (a+b x)^{14} (b c-a d)^3}{2 b^8}+\frac{35 d^3 (a+b x)^{13} (b c-a d)^4}{13 b^8}+\frac{7 d^2 (a+b x)^{12} (b c-a d)^5}{4 b^8}+\frac{7 d (a+b x)^{11} (b c-a d)^6}{11 b^8}+\frac{(a+b x)^{10} (b c-a d)^7}{10 b^8}+\frac{d^7 (a+b x)^{17}}{17 b^8}",1,"((b*c - a*d)^7*(a + b*x)^10)/(10*b^8) + (7*d*(b*c - a*d)^6*(a + b*x)^11)/(11*b^8) + (7*d^2*(b*c - a*d)^5*(a + b*x)^12)/(4*b^8) + (35*d^3*(b*c - a*d)^4*(a + b*x)^13)/(13*b^8) + (5*d^4*(b*c - a*d)^3*(a + b*x)^14)/(2*b^8) + (7*d^5*(b*c - a*d)^2*(a + b*x)^15)/(5*b^8) + (7*d^6*(b*c - a*d)*(a + b*x)^16)/(16*b^8) + (d^7*(a + b*x)^17)/(17*b^8)","A",2,1,15,0.06667,1,"{43}"
1274,1,200,0,0.5736631,"\int (a+b x)^8 (c+d x)^7 \, dx","Int[(a + b*x)^8*(c + d*x)^7,x]","\frac{7 d^6 (a+b x)^{15} (b c-a d)}{15 b^8}+\frac{3 d^5 (a+b x)^{14} (b c-a d)^2}{2 b^8}+\frac{35 d^4 (a+b x)^{13} (b c-a d)^3}{13 b^8}+\frac{35 d^3 (a+b x)^{12} (b c-a d)^4}{12 b^8}+\frac{21 d^2 (a+b x)^{11} (b c-a d)^5}{11 b^8}+\frac{7 d (a+b x)^{10} (b c-a d)^6}{10 b^8}+\frac{(a+b x)^9 (b c-a d)^7}{9 b^8}+\frac{d^7 (a+b x)^{16}}{16 b^8}","\frac{7 d^6 (a+b x)^{15} (b c-a d)}{15 b^8}+\frac{3 d^5 (a+b x)^{14} (b c-a d)^2}{2 b^8}+\frac{35 d^4 (a+b x)^{13} (b c-a d)^3}{13 b^8}+\frac{35 d^3 (a+b x)^{12} (b c-a d)^4}{12 b^8}+\frac{21 d^2 (a+b x)^{11} (b c-a d)^5}{11 b^8}+\frac{7 d (a+b x)^{10} (b c-a d)^6}{10 b^8}+\frac{(a+b x)^9 (b c-a d)^7}{9 b^8}+\frac{d^7 (a+b x)^{16}}{16 b^8}",1,"((b*c - a*d)^7*(a + b*x)^9)/(9*b^8) + (7*d*(b*c - a*d)^6*(a + b*x)^10)/(10*b^8) + (21*d^2*(b*c - a*d)^5*(a + b*x)^11)/(11*b^8) + (35*d^3*(b*c - a*d)^4*(a + b*x)^12)/(12*b^8) + (35*d^4*(b*c - a*d)^3*(a + b*x)^13)/(13*b^8) + (3*d^5*(b*c - a*d)^2*(a + b*x)^14)/(2*b^8) + (7*d^6*(b*c - a*d)*(a + b*x)^15)/(15*b^8) + (d^7*(a + b*x)^16)/(16*b^8)","A",2,1,15,0.06667,1,"{43}"
1275,1,200,0,0.4536972,"\int (a+b x)^7 (c+d x)^7 \, dx","Int[(a + b*x)^7*(c + d*x)^7,x]","\frac{d^6 (a+b x)^{14} (b c-a d)}{2 b^8}+\frac{21 d^5 (a+b x)^{13} (b c-a d)^2}{13 b^8}+\frac{35 d^4 (a+b x)^{12} (b c-a d)^3}{12 b^8}+\frac{35 d^3 (a+b x)^{11} (b c-a d)^4}{11 b^8}+\frac{21 d^2 (a+b x)^{10} (b c-a d)^5}{10 b^8}+\frac{7 d (a+b x)^9 (b c-a d)^6}{9 b^8}+\frac{(a+b x)^8 (b c-a d)^7}{8 b^8}+\frac{d^7 (a+b x)^{15}}{15 b^8}","\frac{d^6 (a+b x)^{14} (b c-a d)}{2 b^8}+\frac{21 d^5 (a+b x)^{13} (b c-a d)^2}{13 b^8}+\frac{35 d^4 (a+b x)^{12} (b c-a d)^3}{12 b^8}+\frac{35 d^3 (a+b x)^{11} (b c-a d)^4}{11 b^8}+\frac{21 d^2 (a+b x)^{10} (b c-a d)^5}{10 b^8}+\frac{7 d (a+b x)^9 (b c-a d)^6}{9 b^8}+\frac{(a+b x)^8 (b c-a d)^7}{8 b^8}+\frac{d^7 (a+b x)^{15}}{15 b^8}",1,"((b*c - a*d)^7*(a + b*x)^8)/(8*b^8) + (7*d*(b*c - a*d)^6*(a + b*x)^9)/(9*b^8) + (21*d^2*(b*c - a*d)^5*(a + b*x)^10)/(10*b^8) + (35*d^3*(b*c - a*d)^4*(a + b*x)^11)/(11*b^8) + (35*d^4*(b*c - a*d)^3*(a + b*x)^12)/(12*b^8) + (21*d^5*(b*c - a*d)^2*(a + b*x)^13)/(13*b^8) + (d^6*(b*c - a*d)*(a + b*x)^14)/(2*b^8) + (d^7*(a + b*x)^15)/(15*b^8)","A",2,1,15,0.06667,1,"{43}"
1276,1,173,0,0.4345921,"\int (a+b x)^6 (c+d x)^7 \, dx","Int[(a + b*x)^6*(c + d*x)^7,x]","-\frac{6 b^5 (c+d x)^{13} (b c-a d)}{13 d^7}+\frac{5 b^4 (c+d x)^{12} (b c-a d)^2}{4 d^7}-\frac{20 b^3 (c+d x)^{11} (b c-a d)^3}{11 d^7}+\frac{3 b^2 (c+d x)^{10} (b c-a d)^4}{2 d^7}-\frac{2 b (c+d x)^9 (b c-a d)^5}{3 d^7}+\frac{(c+d x)^8 (b c-a d)^6}{8 d^7}+\frac{b^6 (c+d x)^{14}}{14 d^7}","-\frac{6 b^5 (c+d x)^{13} (b c-a d)}{13 d^7}+\frac{5 b^4 (c+d x)^{12} (b c-a d)^2}{4 d^7}-\frac{20 b^3 (c+d x)^{11} (b c-a d)^3}{11 d^7}+\frac{3 b^2 (c+d x)^{10} (b c-a d)^4}{2 d^7}-\frac{2 b (c+d x)^9 (b c-a d)^5}{3 d^7}+\frac{(c+d x)^8 (b c-a d)^6}{8 d^7}+\frac{b^6 (c+d x)^{14}}{14 d^7}",1,"((b*c - a*d)^6*(c + d*x)^8)/(8*d^7) - (2*b*(b*c - a*d)^5*(c + d*x)^9)/(3*d^7) + (3*b^2*(b*c - a*d)^4*(c + d*x)^10)/(2*d^7) - (20*b^3*(b*c - a*d)^3*(c + d*x)^11)/(11*d^7) + (5*b^4*(b*c - a*d)^2*(c + d*x)^12)/(4*d^7) - (6*b^5*(b*c - a*d)*(c + d*x)^13)/(13*d^7) + (b^6*(c + d*x)^14)/(14*d^7)","A",2,1,15,0.06667,1,"{43}"
1277,1,144,0,0.3596663,"\int (a+b x)^5 (c+d x)^7 \, dx","Int[(a + b*x)^5*(c + d*x)^7,x]","-\frac{5 b^4 (c+d x)^{12} (b c-a d)}{12 d^6}+\frac{10 b^3 (c+d x)^{11} (b c-a d)^2}{11 d^6}-\frac{b^2 (c+d x)^{10} (b c-a d)^3}{d^6}+\frac{5 b (c+d x)^9 (b c-a d)^4}{9 d^6}-\frac{(c+d x)^8 (b c-a d)^5}{8 d^6}+\frac{b^5 (c+d x)^{13}}{13 d^6}","-\frac{5 b^4 (c+d x)^{12} (b c-a d)}{12 d^6}+\frac{10 b^3 (c+d x)^{11} (b c-a d)^2}{11 d^6}-\frac{b^2 (c+d x)^{10} (b c-a d)^3}{d^6}+\frac{5 b (c+d x)^9 (b c-a d)^4}{9 d^6}-\frac{(c+d x)^8 (b c-a d)^5}{8 d^6}+\frac{b^5 (c+d x)^{13}}{13 d^6}",1,"-((b*c - a*d)^5*(c + d*x)^8)/(8*d^6) + (5*b*(b*c - a*d)^4*(c + d*x)^9)/(9*d^6) - (b^2*(b*c - a*d)^3*(c + d*x)^10)/d^6 + (10*b^3*(b*c - a*d)^2*(c + d*x)^11)/(11*d^6) - (5*b^4*(b*c - a*d)*(c + d*x)^12)/(12*d^6) + (b^5*(c + d*x)^13)/(13*d^6)","A",2,1,15,0.06667,1,"{43}"
1278,1,119,0,0.2793508,"\int (a+b x)^4 (c+d x)^7 \, dx","Int[(a + b*x)^4*(c + d*x)^7,x]","-\frac{4 b^3 (c+d x)^{11} (b c-a d)}{11 d^5}+\frac{3 b^2 (c+d x)^{10} (b c-a d)^2}{5 d^5}-\frac{4 b (c+d x)^9 (b c-a d)^3}{9 d^5}+\frac{(c+d x)^8 (b c-a d)^4}{8 d^5}+\frac{b^4 (c+d x)^{12}}{12 d^5}","-\frac{4 b^3 (c+d x)^{11} (b c-a d)}{11 d^5}+\frac{3 b^2 (c+d x)^{10} (b c-a d)^2}{5 d^5}-\frac{4 b (c+d x)^9 (b c-a d)^3}{9 d^5}+\frac{(c+d x)^8 (b c-a d)^4}{8 d^5}+\frac{b^4 (c+d x)^{12}}{12 d^5}",1,"((b*c - a*d)^4*(c + d*x)^8)/(8*d^5) - (4*b*(b*c - a*d)^3*(c + d*x)^9)/(9*d^5) + (3*b^2*(b*c - a*d)^2*(c + d*x)^10)/(5*d^5) - (4*b^3*(b*c - a*d)*(c + d*x)^11)/(11*d^5) + (b^4*(c + d*x)^12)/(12*d^5)","A",2,1,15,0.06667,1,"{43}"
1279,1,92,0,0.2182334,"\int (a+b x)^3 (c+d x)^7 \, dx","Int[(a + b*x)^3*(c + d*x)^7,x]","-\frac{3 b^2 (c+d x)^{10} (b c-a d)}{10 d^4}+\frac{b (c+d x)^9 (b c-a d)^2}{3 d^4}-\frac{(c+d x)^8 (b c-a d)^3}{8 d^4}+\frac{b^3 (c+d x)^{11}}{11 d^4}","-\frac{3 b^2 (c+d x)^{10} (b c-a d)}{10 d^4}+\frac{b (c+d x)^9 (b c-a d)^2}{3 d^4}-\frac{(c+d x)^8 (b c-a d)^3}{8 d^4}+\frac{b^3 (c+d x)^{11}}{11 d^4}",1,"-((b*c - a*d)^3*(c + d*x)^8)/(8*d^4) + (b*(b*c - a*d)^2*(c + d*x)^9)/(3*d^4) - (3*b^2*(b*c - a*d)*(c + d*x)^10)/(10*d^4) + (b^3*(c + d*x)^11)/(11*d^4)","A",2,1,15,0.06667,1,"{43}"
1280,1,65,0,0.1593417,"\int (a+b x)^2 (c+d x)^7 \, dx","Int[(a + b*x)^2*(c + d*x)^7,x]","-\frac{2 b (c+d x)^9 (b c-a d)}{9 d^3}+\frac{(c+d x)^8 (b c-a d)^2}{8 d^3}+\frac{b^2 (c+d x)^{10}}{10 d^3}","-\frac{2 b (c+d x)^9 (b c-a d)}{9 d^3}+\frac{(c+d x)^8 (b c-a d)^2}{8 d^3}+\frac{b^2 (c+d x)^{10}}{10 d^3}",1,"((b*c - a*d)^2*(c + d*x)^8)/(8*d^3) - (2*b*(b*c - a*d)*(c + d*x)^9)/(9*d^3) + (b^2*(c + d*x)^10)/(10*d^3)","A",2,1,15,0.06667,1,"{43}"
1281,1,38,0,0.0164614,"\int (a+b x) (c+d x)^7 \, dx","Int[(a + b*x)*(c + d*x)^7,x]","\frac{b (c+d x)^9}{9 d^2}-\frac{(c+d x)^8 (b c-a d)}{8 d^2}","\frac{b (c+d x)^9}{9 d^2}-\frac{(c+d x)^8 (b c-a d)}{8 d^2}",1,"-((b*c - a*d)*(c + d*x)^8)/(8*d^2) + (b*(c + d*x)^9)/(9*d^2)","A",2,1,13,0.07692,1,"{43}"
1282,1,14,0,0.0015101,"\int (c+d x)^7 \, dx","Int[(c + d*x)^7,x]","\frac{(c+d x)^8}{8 d}","\frac{(c+d x)^8}{8 d}",1,"(c + d*x)^8/(8*d)","A",1,1,7,0.1429,1,"{32}"
1283,1,169,0,0.0725765,"\int \frac{(c+d x)^7}{a+b x} \, dx","Int[(c + d*x)^7/(a + b*x),x]","\frac{d x (b c-a d)^6}{b^7}+\frac{(c+d x)^2 (b c-a d)^5}{2 b^6}+\frac{(c+d x)^3 (b c-a d)^4}{3 b^5}+\frac{(c+d x)^4 (b c-a d)^3}{4 b^4}+\frac{(c+d x)^5 (b c-a d)^2}{5 b^3}+\frac{(c+d x)^6 (b c-a d)}{6 b^2}+\frac{(b c-a d)^7 \log (a+b x)}{b^8}+\frac{(c+d x)^7}{7 b}","\frac{d x (b c-a d)^6}{b^7}+\frac{(c+d x)^2 (b c-a d)^5}{2 b^6}+\frac{(c+d x)^3 (b c-a d)^4}{3 b^5}+\frac{(c+d x)^4 (b c-a d)^3}{4 b^4}+\frac{(c+d x)^5 (b c-a d)^2}{5 b^3}+\frac{(c+d x)^6 (b c-a d)}{6 b^2}+\frac{(b c-a d)^7 \log (a+b x)}{b^8}+\frac{(c+d x)^7}{7 b}",1,"(d*(b*c - a*d)^6*x)/b^7 + ((b*c - a*d)^5*(c + d*x)^2)/(2*b^6) + ((b*c - a*d)^4*(c + d*x)^3)/(3*b^5) + ((b*c - a*d)^3*(c + d*x)^4)/(4*b^4) + ((b*c - a*d)^2*(c + d*x)^5)/(5*b^3) + ((b*c - a*d)*(c + d*x)^6)/(6*b^2) + (c + d*x)^7/(7*b) + ((b*c - a*d)^7*Log[a + b*x])/b^8","A",2,1,15,0.06667,1,"{43}"
1284,1,187,0,0.2347592,"\int \frac{(c+d x)^7}{(a+b x)^2} \, dx","Int[(c + d*x)^7/(a + b*x)^2,x]","\frac{7 d^6 (a+b x)^5 (b c-a d)}{5 b^8}+\frac{21 d^5 (a+b x)^4 (b c-a d)^2}{4 b^8}+\frac{35 d^4 (a+b x)^3 (b c-a d)^3}{3 b^8}+\frac{35 d^3 (a+b x)^2 (b c-a d)^4}{2 b^8}+\frac{21 d^2 x (b c-a d)^5}{b^7}-\frac{(b c-a d)^7}{b^8 (a+b x)}+\frac{7 d (b c-a d)^6 \log (a+b x)}{b^8}+\frac{d^7 (a+b x)^6}{6 b^8}","\frac{7 d^6 (a+b x)^5 (b c-a d)}{5 b^8}+\frac{21 d^5 (a+b x)^4 (b c-a d)^2}{4 b^8}+\frac{35 d^4 (a+b x)^3 (b c-a d)^3}{3 b^8}+\frac{35 d^3 (a+b x)^2 (b c-a d)^4}{2 b^8}+\frac{21 d^2 x (b c-a d)^5}{b^7}-\frac{(b c-a d)^7}{b^8 (a+b x)}+\frac{7 d (b c-a d)^6 \log (a+b x)}{b^8}+\frac{d^7 (a+b x)^6}{6 b^8}",1,"(21*d^2*(b*c - a*d)^5*x)/b^7 - (b*c - a*d)^7/(b^8*(a + b*x)) + (35*d^3*(b*c - a*d)^4*(a + b*x)^2)/(2*b^8) + (35*d^4*(b*c - a*d)^3*(a + b*x)^3)/(3*b^8) + (21*d^5*(b*c - a*d)^2*(a + b*x)^4)/(4*b^8) + (7*d^6*(b*c - a*d)*(a + b*x)^5)/(5*b^8) + (d^7*(a + b*x)^6)/(6*b^8) + (7*d*(b*c - a*d)^6*Log[a + b*x])/b^8","A",2,1,15,0.06667,1,"{43}"
1285,1,185,0,0.2171199,"\int \frac{(c+d x)^7}{(a+b x)^3} \, dx","Int[(c + d*x)^7/(a + b*x)^3,x]","\frac{7 d^6 (a+b x)^4 (b c-a d)}{4 b^8}+\frac{7 d^5 (a+b x)^3 (b c-a d)^2}{b^8}+\frac{35 d^4 (a+b x)^2 (b c-a d)^3}{2 b^8}+\frac{35 d^3 x (b c-a d)^4}{b^7}+\frac{21 d^2 (b c-a d)^5 \log (a+b x)}{b^8}-\frac{7 d (b c-a d)^6}{b^8 (a+b x)}-\frac{(b c-a d)^7}{2 b^8 (a+b x)^2}+\frac{d^7 (a+b x)^5}{5 b^8}","\frac{7 d^6 (a+b x)^4 (b c-a d)}{4 b^8}+\frac{7 d^5 (a+b x)^3 (b c-a d)^2}{b^8}+\frac{35 d^4 (a+b x)^2 (b c-a d)^3}{2 b^8}+\frac{35 d^3 x (b c-a d)^4}{b^7}+\frac{21 d^2 (b c-a d)^5 \log (a+b x)}{b^8}-\frac{7 d (b c-a d)^6}{b^8 (a+b x)}-\frac{(b c-a d)^7}{2 b^8 (a+b x)^2}+\frac{d^7 (a+b x)^5}{5 b^8}",1,"(35*d^3*(b*c - a*d)^4*x)/b^7 - (b*c - a*d)^7/(2*b^8*(a + b*x)^2) - (7*d*(b*c - a*d)^6)/(b^8*(a + b*x)) + (35*d^4*(b*c - a*d)^3*(a + b*x)^2)/(2*b^8) + (7*d^5*(b*c - a*d)^2*(a + b*x)^3)/b^8 + (7*d^6*(b*c - a*d)*(a + b*x)^4)/(4*b^8) + (d^7*(a + b*x)^5)/(5*b^8) + (21*d^2*(b*c - a*d)^5*Log[a + b*x])/b^8","A",2,1,15,0.06667,1,"{43}"
1286,1,187,0,0.2126296,"\int \frac{(c+d x)^7}{(a+b x)^4} \, dx","Int[(c + d*x)^7/(a + b*x)^4,x]","\frac{7 d^6 (a+b x)^3 (b c-a d)}{3 b^8}+\frac{21 d^5 (a+b x)^2 (b c-a d)^2}{2 b^8}+\frac{35 d^4 x (b c-a d)^3}{b^7}-\frac{21 d^2 (b c-a d)^5}{b^8 (a+b x)}+\frac{35 d^3 (b c-a d)^4 \log (a+b x)}{b^8}-\frac{7 d (b c-a d)^6}{2 b^8 (a+b x)^2}-\frac{(b c-a d)^7}{3 b^8 (a+b x)^3}+\frac{d^7 (a+b x)^4}{4 b^8}","\frac{7 d^6 (a+b x)^3 (b c-a d)}{3 b^8}+\frac{21 d^5 (a+b x)^2 (b c-a d)^2}{2 b^8}+\frac{35 d^4 x (b c-a d)^3}{b^7}-\frac{21 d^2 (b c-a d)^5}{b^8 (a+b x)}+\frac{35 d^3 (b c-a d)^4 \log (a+b x)}{b^8}-\frac{7 d (b c-a d)^6}{2 b^8 (a+b x)^2}-\frac{(b c-a d)^7}{3 b^8 (a+b x)^3}+\frac{d^7 (a+b x)^4}{4 b^8}",1,"(35*d^4*(b*c - a*d)^3*x)/b^7 - (b*c - a*d)^7/(3*b^8*(a + b*x)^3) - (7*d*(b*c - a*d)^6)/(2*b^8*(a + b*x)^2) - (21*d^2*(b*c - a*d)^5)/(b^8*(a + b*x)) + (21*d^5*(b*c - a*d)^2*(a + b*x)^2)/(2*b^8) + (7*d^6*(b*c - a*d)*(a + b*x)^3)/(3*b^8) + (d^7*(a + b*x)^4)/(4*b^8) + (35*d^3*(b*c - a*d)^4*Log[a + b*x])/b^8","A",2,1,15,0.06667,1,"{43}"
1287,1,187,0,0.1976034,"\int \frac{(c+d x)^7}{(a+b x)^5} \, dx","Int[(c + d*x)^7/(a + b*x)^5,x]","\frac{7 d^6 (a+b x)^2 (b c-a d)}{2 b^8}+\frac{21 d^5 x (b c-a d)^2}{b^7}-\frac{35 d^3 (b c-a d)^4}{b^8 (a+b x)}-\frac{21 d^2 (b c-a d)^5}{2 b^8 (a+b x)^2}+\frac{35 d^4 (b c-a d)^3 \log (a+b x)}{b^8}-\frac{7 d (b c-a d)^6}{3 b^8 (a+b x)^3}-\frac{(b c-a d)^7}{4 b^8 (a+b x)^4}+\frac{d^7 (a+b x)^3}{3 b^8}","\frac{7 d^6 (a+b x)^2 (b c-a d)}{2 b^8}+\frac{21 d^5 x (b c-a d)^2}{b^7}-\frac{35 d^3 (b c-a d)^4}{b^8 (a+b x)}-\frac{21 d^2 (b c-a d)^5}{2 b^8 (a+b x)^2}+\frac{35 d^4 (b c-a d)^3 \log (a+b x)}{b^8}-\frac{7 d (b c-a d)^6}{3 b^8 (a+b x)^3}-\frac{(b c-a d)^7}{4 b^8 (a+b x)^4}+\frac{d^7 (a+b x)^3}{3 b^8}",1,"(21*d^5*(b*c - a*d)^2*x)/b^7 - (b*c - a*d)^7/(4*b^8*(a + b*x)^4) - (7*d*(b*c - a*d)^6)/(3*b^8*(a + b*x)^3) - (21*d^2*(b*c - a*d)^5)/(2*b^8*(a + b*x)^2) - (35*d^3*(b*c - a*d)^4)/(b^8*(a + b*x)) + (7*d^6*(b*c - a*d)*(a + b*x)^2)/(2*b^8) + (d^7*(a + b*x)^3)/(3*b^8) + (35*d^4*(b*c - a*d)^3*Log[a + b*x])/b^8","A",2,1,15,0.06667,1,"{43}"
1288,1,181,0,0.191197,"\int \frac{(c+d x)^7}{(a+b x)^6} \, dx","Int[(c + d*x)^7/(a + b*x)^6,x]","\frac{d^6 x (7 b c-6 a d)}{b^7}-\frac{35 d^4 (b c-a d)^3}{b^8 (a+b x)}-\frac{35 d^3 (b c-a d)^4}{2 b^8 (a+b x)^2}-\frac{7 d^2 (b c-a d)^5}{b^8 (a+b x)^3}+\frac{21 d^5 (b c-a d)^2 \log (a+b x)}{b^8}-\frac{7 d (b c-a d)^6}{4 b^8 (a+b x)^4}-\frac{(b c-a d)^7}{5 b^8 (a+b x)^5}+\frac{d^7 x^2}{2 b^6}","\frac{d^6 x (7 b c-6 a d)}{b^7}-\frac{35 d^4 (b c-a d)^3}{b^8 (a+b x)}-\frac{35 d^3 (b c-a d)^4}{2 b^8 (a+b x)^2}-\frac{7 d^2 (b c-a d)^5}{b^8 (a+b x)^3}+\frac{21 d^5 (b c-a d)^2 \log (a+b x)}{b^8}-\frac{7 d (b c-a d)^6}{4 b^8 (a+b x)^4}-\frac{(b c-a d)^7}{5 b^8 (a+b x)^5}+\frac{d^7 x^2}{2 b^6}",1,"(d^6*(7*b*c - 6*a*d)*x)/b^7 + (d^7*x^2)/(2*b^6) - (b*c - a*d)^7/(5*b^8*(a + b*x)^5) - (7*d*(b*c - a*d)^6)/(4*b^8*(a + b*x)^4) - (7*d^2*(b*c - a*d)^5)/(b^8*(a + b*x)^3) - (35*d^3*(b*c - a*d)^4)/(2*b^8*(a + b*x)^2) - (35*d^4*(b*c - a*d)^3)/(b^8*(a + b*x)) + (21*d^5*(b*c - a*d)^2*Log[a + b*x])/b^8","A",2,1,15,0.06667,1,"{43}"
1289,1,186,0,0.1721352,"\int \frac{(c+d x)^7}{(a+b x)^7} \, dx","Int[(c + d*x)^7/(a + b*x)^7,x]","-\frac{21 d^5 (b c-a d)^2}{b^8 (a+b x)}-\frac{35 d^4 (b c-a d)^3}{2 b^8 (a+b x)^2}-\frac{35 d^3 (b c-a d)^4}{3 b^8 (a+b x)^3}-\frac{21 d^2 (b c-a d)^5}{4 b^8 (a+b x)^4}+\frac{7 d^6 (b c-a d) \log (a+b x)}{b^8}-\frac{7 d (b c-a d)^6}{5 b^8 (a+b x)^5}-\frac{(b c-a d)^7}{6 b^8 (a+b x)^6}+\frac{d^7 x}{b^7}","-\frac{21 d^5 (b c-a d)^2}{b^8 (a+b x)}-\frac{35 d^4 (b c-a d)^3}{2 b^8 (a+b x)^2}-\frac{35 d^3 (b c-a d)^4}{3 b^8 (a+b x)^3}-\frac{21 d^2 (b c-a d)^5}{4 b^8 (a+b x)^4}+\frac{7 d^6 (b c-a d) \log (a+b x)}{b^8}-\frac{7 d (b c-a d)^6}{5 b^8 (a+b x)^5}-\frac{(b c-a d)^7}{6 b^8 (a+b x)^6}+\frac{d^7 x}{b^7}",1,"(d^7*x)/b^7 - (b*c - a*d)^7/(6*b^8*(a + b*x)^6) - (7*d*(b*c - a*d)^6)/(5*b^8*(a + b*x)^5) - (21*d^2*(b*c - a*d)^5)/(4*b^8*(a + b*x)^4) - (35*d^3*(b*c - a*d)^4)/(3*b^8*(a + b*x)^3) - (35*d^4*(b*c - a*d)^3)/(2*b^8*(a + b*x)^2) - (21*d^5*(b*c - a*d)^2)/(b^8*(a + b*x)) + (7*d^6*(b*c - a*d)*Log[a + b*x])/b^8","A",2,1,15,0.06667,1,"{43}"
1290,1,194,0,0.1559081,"\int \frac{(c+d x)^7}{(a+b x)^8} \, dx","Int[(c + d*x)^7/(a + b*x)^8,x]","-\frac{7 d^6 (b c-a d)}{b^8 (a+b x)}-\frac{21 d^5 (b c-a d)^2}{2 b^8 (a+b x)^2}-\frac{35 d^4 (b c-a d)^3}{3 b^8 (a+b x)^3}-\frac{35 d^3 (b c-a d)^4}{4 b^8 (a+b x)^4}-\frac{21 d^2 (b c-a d)^5}{5 b^8 (a+b x)^5}-\frac{7 d (b c-a d)^6}{6 b^8 (a+b x)^6}-\frac{(b c-a d)^7}{7 b^8 (a+b x)^7}+\frac{d^7 \log (a+b x)}{b^8}","-\frac{7 d^6 (b c-a d)}{b^8 (a+b x)}-\frac{21 d^5 (b c-a d)^2}{2 b^8 (a+b x)^2}-\frac{35 d^4 (b c-a d)^3}{3 b^8 (a+b x)^3}-\frac{35 d^3 (b c-a d)^4}{4 b^8 (a+b x)^4}-\frac{21 d^2 (b c-a d)^5}{5 b^8 (a+b x)^5}-\frac{7 d (b c-a d)^6}{6 b^8 (a+b x)^6}-\frac{(b c-a d)^7}{7 b^8 (a+b x)^7}+\frac{d^7 \log (a+b x)}{b^8}",1,"-(b*c - a*d)^7/(7*b^8*(a + b*x)^7) - (7*d*(b*c - a*d)^6)/(6*b^8*(a + b*x)^6) - (21*d^2*(b*c - a*d)^5)/(5*b^8*(a + b*x)^5) - (35*d^3*(b*c - a*d)^4)/(4*b^8*(a + b*x)^4) - (35*d^4*(b*c - a*d)^3)/(3*b^8*(a + b*x)^3) - (21*d^5*(b*c - a*d)^2)/(2*b^8*(a + b*x)^2) - (7*d^6*(b*c - a*d))/(b^8*(a + b*x)) + (d^7*Log[a + b*x])/b^8","A",2,1,15,0.06667,1,"{43}"
1291,1,28,0,0.0034644,"\int \frac{(c+d x)^7}{(a+b x)^9} \, dx","Int[(c + d*x)^7/(a + b*x)^9,x]","-\frac{(c+d x)^8}{8 (a+b x)^8 (b c-a d)}","-\frac{(c+d x)^8}{8 (a+b x)^8 (b c-a d)}",1,"-(c + d*x)^8/(8*(b*c - a*d)*(a + b*x)^8)","A",1,1,15,0.06667,1,"{37}"
1292,1,58,0,0.009459,"\int \frac{(c+d x)^7}{(a+b x)^{10}} \, dx","Int[(c + d*x)^7/(a + b*x)^10,x]","\frac{d (c+d x)^8}{72 (a+b x)^8 (b c-a d)^2}-\frac{(c+d x)^8}{9 (a+b x)^9 (b c-a d)}","\frac{d (c+d x)^8}{72 (a+b x)^8 (b c-a d)^2}-\frac{(c+d x)^8}{9 (a+b x)^9 (b c-a d)}",1,"-(c + d*x)^8/(9*(b*c - a*d)*(a + b*x)^9) + (d*(c + d*x)^8)/(72*(b*c - a*d)^2*(a + b*x)^8)","A",2,2,15,0.1333,1,"{45, 37}"
1293,1,89,0,0.0218066,"\int \frac{(c+d x)^7}{(a+b x)^{11}} \, dx","Int[(c + d*x)^7/(a + b*x)^11,x]","-\frac{d^2 (c+d x)^8}{360 (a+b x)^8 (b c-a d)^3}+\frac{d (c+d x)^8}{45 (a+b x)^9 (b c-a d)^2}-\frac{(c+d x)^8}{10 (a+b x)^{10} (b c-a d)}","-\frac{d^2 (c+d x)^8}{360 (a+b x)^8 (b c-a d)^3}+\frac{d (c+d x)^8}{45 (a+b x)^9 (b c-a d)^2}-\frac{(c+d x)^8}{10 (a+b x)^{10} (b c-a d)}",1,"-(c + d*x)^8/(10*(b*c - a*d)*(a + b*x)^10) + (d*(c + d*x)^8)/(45*(b*c - a*d)^2*(a + b*x)^9) - (d^2*(c + d*x)^8)/(360*(b*c - a*d)^3*(a + b*x)^8)","A",3,2,15,0.1333,1,"{45, 37}"
1294,1,120,0,0.0334245,"\int \frac{(c+d x)^7}{(a+b x)^{12}} \, dx","Int[(c + d*x)^7/(a + b*x)^12,x]","\frac{d^3 (c+d x)^8}{1320 (a+b x)^8 (b c-a d)^4}-\frac{d^2 (c+d x)^8}{165 (a+b x)^9 (b c-a d)^3}+\frac{3 d (c+d x)^8}{110 (a+b x)^{10} (b c-a d)^2}-\frac{(c+d x)^8}{11 (a+b x)^{11} (b c-a d)}","\frac{d^3 (c+d x)^8}{1320 (a+b x)^8 (b c-a d)^4}-\frac{d^2 (c+d x)^8}{165 (a+b x)^9 (b c-a d)^3}+\frac{3 d (c+d x)^8}{110 (a+b x)^{10} (b c-a d)^2}-\frac{(c+d x)^8}{11 (a+b x)^{11} (b c-a d)}",1,"-(c + d*x)^8/(11*(b*c - a*d)*(a + b*x)^11) + (3*d*(c + d*x)^8)/(110*(b*c - a*d)^2*(a + b*x)^10) - (d^2*(c + d*x)^8)/(165*(b*c - a*d)^3*(a + b*x)^9) + (d^3*(c + d*x)^8)/(1320*(b*c - a*d)^4*(a + b*x)^8)","A",4,2,15,0.1333,1,"{45, 37}"
1295,1,151,0,0.0466408,"\int \frac{(c+d x)^7}{(a+b x)^{13}} \, dx","Int[(c + d*x)^7/(a + b*x)^13,x]","-\frac{d^4 (c+d x)^8}{3960 (a+b x)^8 (b c-a d)^5}+\frac{d^3 (c+d x)^8}{495 (a+b x)^9 (b c-a d)^4}-\frac{d^2 (c+d x)^8}{110 (a+b x)^{10} (b c-a d)^3}+\frac{d (c+d x)^8}{33 (a+b x)^{11} (b c-a d)^2}-\frac{(c+d x)^8}{12 (a+b x)^{12} (b c-a d)}","-\frac{d^4 (c+d x)^8}{3960 (a+b x)^8 (b c-a d)^5}+\frac{d^3 (c+d x)^8}{495 (a+b x)^9 (b c-a d)^4}-\frac{d^2 (c+d x)^8}{110 (a+b x)^{10} (b c-a d)^3}+\frac{d (c+d x)^8}{33 (a+b x)^{11} (b c-a d)^2}-\frac{(c+d x)^8}{12 (a+b x)^{12} (b c-a d)}",1,"-(c + d*x)^8/(12*(b*c - a*d)*(a + b*x)^12) + (d*(c + d*x)^8)/(33*(b*c - a*d)^2*(a + b*x)^11) - (d^2*(c + d*x)^8)/(110*(b*c - a*d)^3*(a + b*x)^10) + (d^3*(c + d*x)^8)/(495*(b*c - a*d)^4*(a + b*x)^9) - (d^4*(c + d*x)^8)/(3960*(b*c - a*d)^5*(a + b*x)^8)","A",5,2,15,0.1333,1,"{45, 37}"
1296,1,198,0,0.1534461,"\int \frac{(c+d x)^7}{(a+b x)^{14}} \, dx","Int[(c + d*x)^7/(a + b*x)^14,x]","-\frac{d^6 (b c-a d)}{b^8 (a+b x)^7}-\frac{21 d^5 (b c-a d)^2}{8 b^8 (a+b x)^8}-\frac{35 d^4 (b c-a d)^3}{9 b^8 (a+b x)^9}-\frac{7 d^3 (b c-a d)^4}{2 b^8 (a+b x)^{10}}-\frac{21 d^2 (b c-a d)^5}{11 b^8 (a+b x)^{11}}-\frac{7 d (b c-a d)^6}{12 b^8 (a+b x)^{12}}-\frac{(b c-a d)^7}{13 b^8 (a+b x)^{13}}-\frac{d^7}{6 b^8 (a+b x)^6}","-\frac{d^6 (b c-a d)}{b^8 (a+b x)^7}-\frac{21 d^5 (b c-a d)^2}{8 b^8 (a+b x)^8}-\frac{35 d^4 (b c-a d)^3}{9 b^8 (a+b x)^9}-\frac{7 d^3 (b c-a d)^4}{2 b^8 (a+b x)^{10}}-\frac{21 d^2 (b c-a d)^5}{11 b^8 (a+b x)^{11}}-\frac{7 d (b c-a d)^6}{12 b^8 (a+b x)^{12}}-\frac{(b c-a d)^7}{13 b^8 (a+b x)^{13}}-\frac{d^7}{6 b^8 (a+b x)^6}",1,"-(b*c - a*d)^7/(13*b^8*(a + b*x)^13) - (7*d*(b*c - a*d)^6)/(12*b^8*(a + b*x)^12) - (21*d^2*(b*c - a*d)^5)/(11*b^8*(a + b*x)^11) - (7*d^3*(b*c - a*d)^4)/(2*b^8*(a + b*x)^10) - (35*d^4*(b*c - a*d)^3)/(9*b^8*(a + b*x)^9) - (21*d^5*(b*c - a*d)^2)/(8*b^8*(a + b*x)^8) - (d^6*(b*c - a*d))/(b^8*(a + b*x)^7) - d^7/(6*b^8*(a + b*x)^6)","A",2,1,15,0.06667,1,"{43}"
1297,1,200,0,0.1428192,"\int \frac{(c+d x)^7}{(a+b x)^{15}} \, dx","Int[(c + d*x)^7/(a + b*x)^15,x]","-\frac{7 d^6 (b c-a d)}{8 b^8 (a+b x)^8}-\frac{7 d^5 (b c-a d)^2}{3 b^8 (a+b x)^9}-\frac{7 d^4 (b c-a d)^3}{2 b^8 (a+b x)^{10}}-\frac{35 d^3 (b c-a d)^4}{11 b^8 (a+b x)^{11}}-\frac{7 d^2 (b c-a d)^5}{4 b^8 (a+b x)^{12}}-\frac{7 d (b c-a d)^6}{13 b^8 (a+b x)^{13}}-\frac{(b c-a d)^7}{14 b^8 (a+b x)^{14}}-\frac{d^7}{7 b^8 (a+b x)^7}","-\frac{7 d^6 (b c-a d)}{8 b^8 (a+b x)^8}-\frac{7 d^5 (b c-a d)^2}{3 b^8 (a+b x)^9}-\frac{7 d^4 (b c-a d)^3}{2 b^8 (a+b x)^{10}}-\frac{35 d^3 (b c-a d)^4}{11 b^8 (a+b x)^{11}}-\frac{7 d^2 (b c-a d)^5}{4 b^8 (a+b x)^{12}}-\frac{7 d (b c-a d)^6}{13 b^8 (a+b x)^{13}}-\frac{(b c-a d)^7}{14 b^8 (a+b x)^{14}}-\frac{d^7}{7 b^8 (a+b x)^7}",1,"-(b*c - a*d)^7/(14*b^8*(a + b*x)^14) - (7*d*(b*c - a*d)^6)/(13*b^8*(a + b*x)^13) - (7*d^2*(b*c - a*d)^5)/(4*b^8*(a + b*x)^12) - (35*d^3*(b*c - a*d)^4)/(11*b^8*(a + b*x)^11) - (7*d^4*(b*c - a*d)^3)/(2*b^8*(a + b*x)^10) - (7*d^5*(b*c - a*d)^2)/(3*b^8*(a + b*x)^9) - (7*d^6*(b*c - a*d))/(8*b^8*(a + b*x)^8) - d^7/(7*b^8*(a + b*x)^7)","A",2,1,15,0.06667,1,"{43}"
1298,1,200,0,0.1396355,"\int \frac{(c+d x)^7}{(a+b x)^{16}} \, dx","Int[(c + d*x)^7/(a + b*x)^16,x]","-\frac{7 d^6 (b c-a d)}{9 b^8 (a+b x)^9}-\frac{21 d^5 (b c-a d)^2}{10 b^8 (a+b x)^{10}}-\frac{35 d^4 (b c-a d)^3}{11 b^8 (a+b x)^{11}}-\frac{35 d^3 (b c-a d)^4}{12 b^8 (a+b x)^{12}}-\frac{21 d^2 (b c-a d)^5}{13 b^8 (a+b x)^{13}}-\frac{d (b c-a d)^6}{2 b^8 (a+b x)^{14}}-\frac{(b c-a d)^7}{15 b^8 (a+b x)^{15}}-\frac{d^7}{8 b^8 (a+b x)^8}","-\frac{7 d^6 (b c-a d)}{9 b^8 (a+b x)^9}-\frac{21 d^5 (b c-a d)^2}{10 b^8 (a+b x)^{10}}-\frac{35 d^4 (b c-a d)^3}{11 b^8 (a+b x)^{11}}-\frac{35 d^3 (b c-a d)^4}{12 b^8 (a+b x)^{12}}-\frac{21 d^2 (b c-a d)^5}{13 b^8 (a+b x)^{13}}-\frac{d (b c-a d)^6}{2 b^8 (a+b x)^{14}}-\frac{(b c-a d)^7}{15 b^8 (a+b x)^{15}}-\frac{d^7}{8 b^8 (a+b x)^8}",1,"-(b*c - a*d)^7/(15*b^8*(a + b*x)^15) - (d*(b*c - a*d)^6)/(2*b^8*(a + b*x)^14) - (21*d^2*(b*c - a*d)^5)/(13*b^8*(a + b*x)^13) - (35*d^3*(b*c - a*d)^4)/(12*b^8*(a + b*x)^12) - (35*d^4*(b*c - a*d)^3)/(11*b^8*(a + b*x)^11) - (21*d^5*(b*c - a*d)^2)/(10*b^8*(a + b*x)^10) - (7*d^6*(b*c - a*d))/(9*b^8*(a + b*x)^9) - d^7/(8*b^8*(a + b*x)^8)","A",2,1,15,0.06667,1,"{43}"
1299,1,275,0,1.4651663,"\int (a+b x)^{12} (c+d x)^{10} \, dx","Int[(a + b*x)^12*(c + d*x)^10,x]","\frac{5 d^9 (a+b x)^{22} (b c-a d)}{11 b^{11}}+\frac{15 d^8 (a+b x)^{21} (b c-a d)^2}{7 b^{11}}+\frac{6 d^7 (a+b x)^{20} (b c-a d)^3}{b^{11}}+\frac{210 d^6 (a+b x)^{19} (b c-a d)^4}{19 b^{11}}+\frac{14 d^5 (a+b x)^{18} (b c-a d)^5}{b^{11}}+\frac{210 d^4 (a+b x)^{17} (b c-a d)^6}{17 b^{11}}+\frac{15 d^3 (a+b x)^{16} (b c-a d)^7}{2 b^{11}}+\frac{3 d^2 (a+b x)^{15} (b c-a d)^8}{b^{11}}+\frac{5 d (a+b x)^{14} (b c-a d)^9}{7 b^{11}}+\frac{(a+b x)^{13} (b c-a d)^{10}}{13 b^{11}}+\frac{d^{10} (a+b x)^{23}}{23 b^{11}}","\frac{5 d^9 (a+b x)^{22} (b c-a d)}{11 b^{11}}+\frac{15 d^8 (a+b x)^{21} (b c-a d)^2}{7 b^{11}}+\frac{6 d^7 (a+b x)^{20} (b c-a d)^3}{b^{11}}+\frac{210 d^6 (a+b x)^{19} (b c-a d)^4}{19 b^{11}}+\frac{14 d^5 (a+b x)^{18} (b c-a d)^5}{b^{11}}+\frac{210 d^4 (a+b x)^{17} (b c-a d)^6}{17 b^{11}}+\frac{15 d^3 (a+b x)^{16} (b c-a d)^7}{2 b^{11}}+\frac{3 d^2 (a+b x)^{15} (b c-a d)^8}{b^{11}}+\frac{5 d (a+b x)^{14} (b c-a d)^9}{7 b^{11}}+\frac{(a+b x)^{13} (b c-a d)^{10}}{13 b^{11}}+\frac{d^{10} (a+b x)^{23}}{23 b^{11}}",1,"((b*c - a*d)^10*(a + b*x)^13)/(13*b^11) + (5*d*(b*c - a*d)^9*(a + b*x)^14)/(7*b^11) + (3*d^2*(b*c - a*d)^8*(a + b*x)^15)/b^11 + (15*d^3*(b*c - a*d)^7*(a + b*x)^16)/(2*b^11) + (210*d^4*(b*c - a*d)^6*(a + b*x)^17)/(17*b^11) + (14*d^5*(b*c - a*d)^5*(a + b*x)^18)/b^11 + (210*d^6*(b*c - a*d)^4*(a + b*x)^19)/(19*b^11) + (6*d^7*(b*c - a*d)^3*(a + b*x)^20)/b^11 + (15*d^8*(b*c - a*d)^2*(a + b*x)^21)/(7*b^11) + (5*d^9*(b*c - a*d)*(a + b*x)^22)/(11*b^11) + (d^10*(a + b*x)^23)/(23*b^11)","A",2,1,15,0.06667,1,"{43}"
1300,1,279,0,1.2753039,"\int (a+b x)^{11} (c+d x)^{10} \, dx","Int[(a + b*x)^11*(c + d*x)^10,x]","\frac{10 d^9 (a+b x)^{21} (b c-a d)}{21 b^{11}}+\frac{9 d^8 (a+b x)^{20} (b c-a d)^2}{4 b^{11}}+\frac{120 d^7 (a+b x)^{19} (b c-a d)^3}{19 b^{11}}+\frac{35 d^6 (a+b x)^{18} (b c-a d)^4}{3 b^{11}}+\frac{252 d^5 (a+b x)^{17} (b c-a d)^5}{17 b^{11}}+\frac{105 d^4 (a+b x)^{16} (b c-a d)^6}{8 b^{11}}+\frac{8 d^3 (a+b x)^{15} (b c-a d)^7}{b^{11}}+\frac{45 d^2 (a+b x)^{14} (b c-a d)^8}{14 b^{11}}+\frac{10 d (a+b x)^{13} (b c-a d)^9}{13 b^{11}}+\frac{(a+b x)^{12} (b c-a d)^{10}}{12 b^{11}}+\frac{d^{10} (a+b x)^{22}}{22 b^{11}}","\frac{10 d^9 (a+b x)^{21} (b c-a d)}{21 b^{11}}+\frac{9 d^8 (a+b x)^{20} (b c-a d)^2}{4 b^{11}}+\frac{120 d^7 (a+b x)^{19} (b c-a d)^3}{19 b^{11}}+\frac{35 d^6 (a+b x)^{18} (b c-a d)^4}{3 b^{11}}+\frac{252 d^5 (a+b x)^{17} (b c-a d)^5}{17 b^{11}}+\frac{105 d^4 (a+b x)^{16} (b c-a d)^6}{8 b^{11}}+\frac{8 d^3 (a+b x)^{15} (b c-a d)^7}{b^{11}}+\frac{45 d^2 (a+b x)^{14} (b c-a d)^8}{14 b^{11}}+\frac{10 d (a+b x)^{13} (b c-a d)^9}{13 b^{11}}+\frac{(a+b x)^{12} (b c-a d)^{10}}{12 b^{11}}+\frac{d^{10} (a+b x)^{22}}{22 b^{11}}",1,"((b*c - a*d)^10*(a + b*x)^12)/(12*b^11) + (10*d*(b*c - a*d)^9*(a + b*x)^13)/(13*b^11) + (45*d^2*(b*c - a*d)^8*(a + b*x)^14)/(14*b^11) + (8*d^3*(b*c - a*d)^7*(a + b*x)^15)/b^11 + (105*d^4*(b*c - a*d)^6*(a + b*x)^16)/(8*b^11) + (252*d^5*(b*c - a*d)^5*(a + b*x)^17)/(17*b^11) + (35*d^6*(b*c - a*d)^4*(a + b*x)^18)/(3*b^11) + (120*d^7*(b*c - a*d)^3*(a + b*x)^19)/(19*b^11) + (9*d^8*(b*c - a*d)^2*(a + b*x)^20)/(4*b^11) + (10*d^9*(b*c - a*d)*(a + b*x)^21)/(21*b^11) + (d^10*(a + b*x)^22)/(22*b^11)","A",2,1,15,0.06667,1,"{43}"
1301,1,279,0,1.1122081,"\int (a+b x)^{10} (c+d x)^{10} \, dx","Int[(a + b*x)^10*(c + d*x)^10,x]","\frac{d^9 (a+b x)^{20} (b c-a d)}{2 b^{11}}+\frac{45 d^8 (a+b x)^{19} (b c-a d)^2}{19 b^{11}}+\frac{20 d^7 (a+b x)^{18} (b c-a d)^3}{3 b^{11}}+\frac{210 d^6 (a+b x)^{17} (b c-a d)^4}{17 b^{11}}+\frac{63 d^5 (a+b x)^{16} (b c-a d)^5}{4 b^{11}}+\frac{14 d^4 (a+b x)^{15} (b c-a d)^6}{b^{11}}+\frac{60 d^3 (a+b x)^{14} (b c-a d)^7}{7 b^{11}}+\frac{45 d^2 (a+b x)^{13} (b c-a d)^8}{13 b^{11}}+\frac{5 d (a+b x)^{12} (b c-a d)^9}{6 b^{11}}+\frac{(a+b x)^{11} (b c-a d)^{10}}{11 b^{11}}+\frac{d^{10} (a+b x)^{21}}{21 b^{11}}","\frac{d^9 (a+b x)^{20} (b c-a d)}{2 b^{11}}+\frac{45 d^8 (a+b x)^{19} (b c-a d)^2}{19 b^{11}}+\frac{20 d^7 (a+b x)^{18} (b c-a d)^3}{3 b^{11}}+\frac{210 d^6 (a+b x)^{17} (b c-a d)^4}{17 b^{11}}+\frac{63 d^5 (a+b x)^{16} (b c-a d)^5}{4 b^{11}}+\frac{14 d^4 (a+b x)^{15} (b c-a d)^6}{b^{11}}+\frac{60 d^3 (a+b x)^{14} (b c-a d)^7}{7 b^{11}}+\frac{45 d^2 (a+b x)^{13} (b c-a d)^8}{13 b^{11}}+\frac{5 d (a+b x)^{12} (b c-a d)^9}{6 b^{11}}+\frac{(a+b x)^{11} (b c-a d)^{10}}{11 b^{11}}+\frac{d^{10} (a+b x)^{21}}{21 b^{11}}",1,"((b*c - a*d)^10*(a + b*x)^11)/(11*b^11) + (5*d*(b*c - a*d)^9*(a + b*x)^12)/(6*b^11) + (45*d^2*(b*c - a*d)^8*(a + b*x)^13)/(13*b^11) + (60*d^3*(b*c - a*d)^7*(a + b*x)^14)/(7*b^11) + (14*d^4*(b*c - a*d)^6*(a + b*x)^15)/b^11 + (63*d^5*(b*c - a*d)^5*(a + b*x)^16)/(4*b^11) + (210*d^6*(b*c - a*d)^4*(a + b*x)^17)/(17*b^11) + (20*d^7*(b*c - a*d)^3*(a + b*x)^18)/(3*b^11) + (45*d^8*(b*c - a*d)^2*(a + b*x)^19)/(19*b^11) + (d^9*(b*c - a*d)*(a + b*x)^20)/(2*b^11) + (d^10*(a + b*x)^21)/(21*b^11)","A",2,1,15,0.06667,1,"{43}"
1302,1,250,0,1.0420219,"\int (a+b x)^9 (c+d x)^{10} \, dx","Int[(a + b*x)^9*(c + d*x)^10,x]","-\frac{9 b^8 (c+d x)^{19} (b c-a d)}{19 d^{10}}+\frac{2 b^7 (c+d x)^{18} (b c-a d)^2}{d^{10}}-\frac{84 b^6 (c+d x)^{17} (b c-a d)^3}{17 d^{10}}+\frac{63 b^5 (c+d x)^{16} (b c-a d)^4}{8 d^{10}}-\frac{42 b^4 (c+d x)^{15} (b c-a d)^5}{5 d^{10}}+\frac{6 b^3 (c+d x)^{14} (b c-a d)^6}{d^{10}}-\frac{36 b^2 (c+d x)^{13} (b c-a d)^7}{13 d^{10}}+\frac{3 b (c+d x)^{12} (b c-a d)^8}{4 d^{10}}-\frac{(c+d x)^{11} (b c-a d)^9}{11 d^{10}}+\frac{b^9 (c+d x)^{20}}{20 d^{10}}","-\frac{9 b^8 (c+d x)^{19} (b c-a d)}{19 d^{10}}+\frac{2 b^7 (c+d x)^{18} (b c-a d)^2}{d^{10}}-\frac{84 b^6 (c+d x)^{17} (b c-a d)^3}{17 d^{10}}+\frac{63 b^5 (c+d x)^{16} (b c-a d)^4}{8 d^{10}}-\frac{42 b^4 (c+d x)^{15} (b c-a d)^5}{5 d^{10}}+\frac{6 b^3 (c+d x)^{14} (b c-a d)^6}{d^{10}}-\frac{36 b^2 (c+d x)^{13} (b c-a d)^7}{13 d^{10}}+\frac{3 b (c+d x)^{12} (b c-a d)^8}{4 d^{10}}-\frac{(c+d x)^{11} (b c-a d)^9}{11 d^{10}}+\frac{b^9 (c+d x)^{20}}{20 d^{10}}",1,"-((b*c - a*d)^9*(c + d*x)^11)/(11*d^10) + (3*b*(b*c - a*d)^8*(c + d*x)^12)/(4*d^10) - (36*b^2*(b*c - a*d)^7*(c + d*x)^13)/(13*d^10) + (6*b^3*(b*c - a*d)^6*(c + d*x)^14)/d^10 - (42*b^4*(b*c - a*d)^5*(c + d*x)^15)/(5*d^10) + (63*b^5*(b*c - a*d)^4*(c + d*x)^16)/(8*d^10) - (84*b^6*(b*c - a*d)^3*(c + d*x)^17)/(17*d^10) + (2*b^7*(b*c - a*d)^2*(c + d*x)^18)/d^10 - (9*b^8*(b*c - a*d)*(c + d*x)^19)/(19*d^10) + (b^9*(c + d*x)^20)/(20*d^10)","A",2,1,15,0.06667,1,"{43}"
1303,1,225,0,0.8993811,"\int (a+b x)^8 (c+d x)^{10} \, dx","Int[(a + b*x)^8*(c + d*x)^10,x]","-\frac{4 b^7 (c+d x)^{18} (b c-a d)}{9 d^9}+\frac{28 b^6 (c+d x)^{17} (b c-a d)^2}{17 d^9}-\frac{7 b^5 (c+d x)^{16} (b c-a d)^3}{2 d^9}+\frac{14 b^4 (c+d x)^{15} (b c-a d)^4}{3 d^9}-\frac{4 b^3 (c+d x)^{14} (b c-a d)^5}{d^9}+\frac{28 b^2 (c+d x)^{13} (b c-a d)^6}{13 d^9}-\frac{2 b (c+d x)^{12} (b c-a d)^7}{3 d^9}+\frac{(c+d x)^{11} (b c-a d)^8}{11 d^9}+\frac{b^8 (c+d x)^{19}}{19 d^9}","-\frac{4 b^7 (c+d x)^{18} (b c-a d)}{9 d^9}+\frac{28 b^6 (c+d x)^{17} (b c-a d)^2}{17 d^9}-\frac{7 b^5 (c+d x)^{16} (b c-a d)^3}{2 d^9}+\frac{14 b^4 (c+d x)^{15} (b c-a d)^4}{3 d^9}-\frac{4 b^3 (c+d x)^{14} (b c-a d)^5}{d^9}+\frac{28 b^2 (c+d x)^{13} (b c-a d)^6}{13 d^9}-\frac{2 b (c+d x)^{12} (b c-a d)^7}{3 d^9}+\frac{(c+d x)^{11} (b c-a d)^8}{11 d^9}+\frac{b^8 (c+d x)^{19}}{19 d^9}",1,"((b*c - a*d)^8*(c + d*x)^11)/(11*d^9) - (2*b*(b*c - a*d)^7*(c + d*x)^12)/(3*d^9) + (28*b^2*(b*c - a*d)^6*(c + d*x)^13)/(13*d^9) - (4*b^3*(b*c - a*d)^5*(c + d*x)^14)/d^9 + (14*b^4*(b*c - a*d)^4*(c + d*x)^15)/(3*d^9) - (7*b^5*(b*c - a*d)^3*(c + d*x)^16)/(2*d^9) + (28*b^6*(b*c - a*d)^2*(c + d*x)^17)/(17*d^9) - (4*b^7*(b*c - a*d)*(c + d*x)^18)/(9*d^9) + (b^8*(c + d*x)^19)/(19*d^9)","A",2,1,15,0.06667,1,"{43}"
1304,1,200,0,0.7658095,"\int (a+b x)^7 (c+d x)^{10} \, dx","Int[(a + b*x)^7*(c + d*x)^10,x]","-\frac{7 b^6 (c+d x)^{17} (b c-a d)}{17 d^8}+\frac{21 b^5 (c+d x)^{16} (b c-a d)^2}{16 d^8}-\frac{7 b^4 (c+d x)^{15} (b c-a d)^3}{3 d^8}+\frac{5 b^3 (c+d x)^{14} (b c-a d)^4}{2 d^8}-\frac{21 b^2 (c+d x)^{13} (b c-a d)^5}{13 d^8}+\frac{7 b (c+d x)^{12} (b c-a d)^6}{12 d^8}-\frac{(c+d x)^{11} (b c-a d)^7}{11 d^8}+\frac{b^7 (c+d x)^{18}}{18 d^8}","-\frac{7 b^6 (c+d x)^{17} (b c-a d)}{17 d^8}+\frac{21 b^5 (c+d x)^{16} (b c-a d)^2}{16 d^8}-\frac{7 b^4 (c+d x)^{15} (b c-a d)^3}{3 d^8}+\frac{5 b^3 (c+d x)^{14} (b c-a d)^4}{2 d^8}-\frac{21 b^2 (c+d x)^{13} (b c-a d)^5}{13 d^8}+\frac{7 b (c+d x)^{12} (b c-a d)^6}{12 d^8}-\frac{(c+d x)^{11} (b c-a d)^7}{11 d^8}+\frac{b^7 (c+d x)^{18}}{18 d^8}",1,"-((b*c - a*d)^7*(c + d*x)^11)/(11*d^8) + (7*b*(b*c - a*d)^6*(c + d*x)^12)/(12*d^8) - (21*b^2*(b*c - a*d)^5*(c + d*x)^13)/(13*d^8) + (5*b^3*(b*c - a*d)^4*(c + d*x)^14)/(2*d^8) - (7*b^4*(b*c - a*d)^3*(c + d*x)^15)/(3*d^8) + (21*b^5*(b*c - a*d)^2*(c + d*x)^16)/(16*d^8) - (7*b^6*(b*c - a*d)*(c + d*x)^17)/(17*d^8) + (b^7*(c + d*x)^18)/(18*d^8)","A",2,1,15,0.06667,1,"{43}"
1305,1,170,0,0.6728391,"\int (a+b x)^6 (c+d x)^{10} \, dx","Int[(a + b*x)^6*(c + d*x)^10,x]","-\frac{3 b^5 (c+d x)^{16} (b c-a d)}{8 d^7}+\frac{b^4 (c+d x)^{15} (b c-a d)^2}{d^7}-\frac{10 b^3 (c+d x)^{14} (b c-a d)^3}{7 d^7}+\frac{15 b^2 (c+d x)^{13} (b c-a d)^4}{13 d^7}-\frac{b (c+d x)^{12} (b c-a d)^5}{2 d^7}+\frac{(c+d x)^{11} (b c-a d)^6}{11 d^7}+\frac{b^6 (c+d x)^{17}}{17 d^7}","-\frac{3 b^5 (c+d x)^{16} (b c-a d)}{8 d^7}+\frac{b^4 (c+d x)^{15} (b c-a d)^2}{d^7}-\frac{10 b^3 (c+d x)^{14} (b c-a d)^3}{7 d^7}+\frac{15 b^2 (c+d x)^{13} (b c-a d)^4}{13 d^7}-\frac{b (c+d x)^{12} (b c-a d)^5}{2 d^7}+\frac{(c+d x)^{11} (b c-a d)^6}{11 d^7}+\frac{b^6 (c+d x)^{17}}{17 d^7}",1,"((b*c - a*d)^6*(c + d*x)^11)/(11*d^7) - (b*(b*c - a*d)^5*(c + d*x)^12)/(2*d^7) + (15*b^2*(b*c - a*d)^4*(c + d*x)^13)/(13*d^7) - (10*b^3*(b*c - a*d)^3*(c + d*x)^14)/(7*d^7) + (b^4*(b*c - a*d)^2*(c + d*x)^15)/d^7 - (3*b^5*(b*c - a*d)*(c + d*x)^16)/(8*d^7) + (b^6*(c + d*x)^17)/(17*d^7)","A",2,1,15,0.06667,1,"{43}"
1306,1,146,0,0.5293856,"\int (a+b x)^5 (c+d x)^{10} \, dx","Int[(a + b*x)^5*(c + d*x)^10,x]","-\frac{b^4 (c+d x)^{15} (b c-a d)}{3 d^6}+\frac{5 b^3 (c+d x)^{14} (b c-a d)^2}{7 d^6}-\frac{10 b^2 (c+d x)^{13} (b c-a d)^3}{13 d^6}+\frac{5 b (c+d x)^{12} (b c-a d)^4}{12 d^6}-\frac{(c+d x)^{11} (b c-a d)^5}{11 d^6}+\frac{b^5 (c+d x)^{16}}{16 d^6}","-\frac{b^4 (c+d x)^{15} (b c-a d)}{3 d^6}+\frac{5 b^3 (c+d x)^{14} (b c-a d)^2}{7 d^6}-\frac{10 b^2 (c+d x)^{13} (b c-a d)^3}{13 d^6}+\frac{5 b (c+d x)^{12} (b c-a d)^4}{12 d^6}-\frac{(c+d x)^{11} (b c-a d)^5}{11 d^6}+\frac{b^5 (c+d x)^{16}}{16 d^6}",1,"-((b*c - a*d)^5*(c + d*x)^11)/(11*d^6) + (5*b*(b*c - a*d)^4*(c + d*x)^12)/(12*d^6) - (10*b^2*(b*c - a*d)^3*(c + d*x)^13)/(13*d^6) + (5*b^3*(b*c - a*d)^2*(c + d*x)^14)/(7*d^6) - (b^4*(b*c - a*d)*(c + d*x)^15)/(3*d^6) + (b^5*(c + d*x)^16)/(16*d^6)","A",2,1,15,0.06667,1,"{43}"
1307,1,119,0,0.437197,"\int (a+b x)^4 (c+d x)^{10} \, dx","Int[(a + b*x)^4*(c + d*x)^10,x]","-\frac{2 b^3 (c+d x)^{14} (b c-a d)}{7 d^5}+\frac{6 b^2 (c+d x)^{13} (b c-a d)^2}{13 d^5}-\frac{b (c+d x)^{12} (b c-a d)^3}{3 d^5}+\frac{(c+d x)^{11} (b c-a d)^4}{11 d^5}+\frac{b^4 (c+d x)^{15}}{15 d^5}","-\frac{2 b^3 (c+d x)^{14} (b c-a d)}{7 d^5}+\frac{6 b^2 (c+d x)^{13} (b c-a d)^2}{13 d^5}-\frac{b (c+d x)^{12} (b c-a d)^3}{3 d^5}+\frac{(c+d x)^{11} (b c-a d)^4}{11 d^5}+\frac{b^4 (c+d x)^{15}}{15 d^5}",1,"((b*c - a*d)^4*(c + d*x)^11)/(11*d^5) - (b*(b*c - a*d)^3*(c + d*x)^12)/(3*d^5) + (6*b^2*(b*c - a*d)^2*(c + d*x)^13)/(13*d^5) - (2*b^3*(b*c - a*d)*(c + d*x)^14)/(7*d^5) + (b^4*(c + d*x)^15)/(15*d^5)","A",2,1,15,0.06667,1,"{43}"
1308,1,92,0,0.3487878,"\int (a+b x)^3 (c+d x)^{10} \, dx","Int[(a + b*x)^3*(c + d*x)^10,x]","-\frac{3 b^2 (c+d x)^{13} (b c-a d)}{13 d^4}+\frac{b (c+d x)^{12} (b c-a d)^2}{4 d^4}-\frac{(c+d x)^{11} (b c-a d)^3}{11 d^4}+\frac{b^3 (c+d x)^{14}}{14 d^4}","-\frac{3 b^2 (c+d x)^{13} (b c-a d)}{13 d^4}+\frac{b (c+d x)^{12} (b c-a d)^2}{4 d^4}-\frac{(c+d x)^{11} (b c-a d)^3}{11 d^4}+\frac{b^3 (c+d x)^{14}}{14 d^4}",1,"-((b*c - a*d)^3*(c + d*x)^11)/(11*d^4) + (b*(b*c - a*d)^2*(c + d*x)^12)/(4*d^4) - (3*b^2*(b*c - a*d)*(c + d*x)^13)/(13*d^4) + (b^3*(c + d*x)^14)/(14*d^4)","A",2,1,15,0.06667,1,"{43}"
1309,1,65,0,0.2507411,"\int (a+b x)^2 (c+d x)^{10} \, dx","Int[(a + b*x)^2*(c + d*x)^10,x]","-\frac{b (c+d x)^{12} (b c-a d)}{6 d^3}+\frac{(c+d x)^{11} (b c-a d)^2}{11 d^3}+\frac{b^2 (c+d x)^{13}}{13 d^3}","-\frac{b (c+d x)^{12} (b c-a d)}{6 d^3}+\frac{(c+d x)^{11} (b c-a d)^2}{11 d^3}+\frac{b^2 (c+d x)^{13}}{13 d^3}",1,"((b*c - a*d)^2*(c + d*x)^11)/(11*d^3) - (b*(b*c - a*d)*(c + d*x)^12)/(6*d^3) + (b^2*(c + d*x)^13)/(13*d^3)","A",2,1,15,0.06667,1,"{43}"
1310,1,38,0,0.0164524,"\int (a+b x) (c+d x)^{10} \, dx","Int[(a + b*x)*(c + d*x)^10,x]","\frac{b (c+d x)^{12}}{12 d^2}-\frac{(c+d x)^{11} (b c-a d)}{11 d^2}","\frac{b (c+d x)^{12}}{12 d^2}-\frac{(c+d x)^{11} (b c-a d)}{11 d^2}",1,"-((b*c - a*d)*(c + d*x)^11)/(11*d^2) + (b*(c + d*x)^12)/(12*d^2)","A",2,1,13,0.07692,1,"{43}"
1311,1,14,0,0.0017762,"\int (c+d x)^{10} \, dx","Int[(c + d*x)^10,x]","\frac{(c+d x)^{11}}{11 d}","\frac{(c+d x)^{11}}{11 d}",1,"(c + d*x)^11/(11*d)","A",1,1,7,0.1429,1,"{32}"
1312,1,241,0,0.097776,"\int \frac{(c+d x)^{10}}{a+b x} \, dx","Int[(c + d*x)^10/(a + b*x),x]","\frac{d x (b c-a d)^9}{b^{10}}+\frac{(c+d x)^2 (b c-a d)^8}{2 b^9}+\frac{(c+d x)^3 (b c-a d)^7}{3 b^8}+\frac{(c+d x)^4 (b c-a d)^6}{4 b^7}+\frac{(c+d x)^5 (b c-a d)^5}{5 b^6}+\frac{(c+d x)^6 (b c-a d)^4}{6 b^5}+\frac{(c+d x)^7 (b c-a d)^3}{7 b^4}+\frac{(c+d x)^8 (b c-a d)^2}{8 b^3}+\frac{(c+d x)^9 (b c-a d)}{9 b^2}+\frac{(b c-a d)^{10} \log (a+b x)}{b^{11}}+\frac{(c+d x)^{10}}{10 b}","\frac{d x (b c-a d)^9}{b^{10}}+\frac{(c+d x)^2 (b c-a d)^8}{2 b^9}+\frac{(c+d x)^3 (b c-a d)^7}{3 b^8}+\frac{(c+d x)^4 (b c-a d)^6}{4 b^7}+\frac{(c+d x)^5 (b c-a d)^5}{5 b^6}+\frac{(c+d x)^6 (b c-a d)^4}{6 b^5}+\frac{(c+d x)^7 (b c-a d)^3}{7 b^4}+\frac{(c+d x)^8 (b c-a d)^2}{8 b^3}+\frac{(c+d x)^9 (b c-a d)}{9 b^2}+\frac{(b c-a d)^{10} \log (a+b x)}{b^{11}}+\frac{(c+d x)^{10}}{10 b}",1,"(d*(b*c - a*d)^9*x)/b^10 + ((b*c - a*d)^8*(c + d*x)^2)/(2*b^9) + ((b*c - a*d)^7*(c + d*x)^3)/(3*b^8) + ((b*c - a*d)^6*(c + d*x)^4)/(4*b^7) + ((b*c - a*d)^5*(c + d*x)^5)/(5*b^6) + ((b*c - a*d)^4*(c + d*x)^6)/(6*b^5) + ((b*c - a*d)^3*(c + d*x)^7)/(7*b^4) + ((b*c - a*d)^2*(c + d*x)^8)/(8*b^3) + ((b*c - a*d)*(c + d*x)^9)/(9*b^2) + (c + d*x)^10/(10*b) + ((b*c - a*d)^10*Log[a + b*x])/b^11","A",2,1,15,0.06667,1,"{43}"
1313,1,258,0,0.4726236,"\int \frac{(c+d x)^{10}}{(a+b x)^2} \, dx","Int[(c + d*x)^10/(a + b*x)^2,x]","\frac{5 d^9 (a+b x)^8 (b c-a d)}{4 b^{11}}+\frac{45 d^8 (a+b x)^7 (b c-a d)^2}{7 b^{11}}+\frac{20 d^7 (a+b x)^6 (b c-a d)^3}{b^{11}}+\frac{42 d^6 (a+b x)^5 (b c-a d)^4}{b^{11}}+\frac{63 d^5 (a+b x)^4 (b c-a d)^5}{b^{11}}+\frac{70 d^4 (a+b x)^3 (b c-a d)^6}{b^{11}}+\frac{60 d^3 (a+b x)^2 (b c-a d)^7}{b^{11}}+\frac{45 d^2 x (b c-a d)^8}{b^{10}}-\frac{(b c-a d)^{10}}{b^{11} (a+b x)}+\frac{10 d (b c-a d)^9 \log (a+b x)}{b^{11}}+\frac{d^{10} (a+b x)^9}{9 b^{11}}","\frac{5 d^9 (a+b x)^8 (b c-a d)}{4 b^{11}}+\frac{45 d^8 (a+b x)^7 (b c-a d)^2}{7 b^{11}}+\frac{20 d^7 (a+b x)^6 (b c-a d)^3}{b^{11}}+\frac{42 d^6 (a+b x)^5 (b c-a d)^4}{b^{11}}+\frac{63 d^5 (a+b x)^4 (b c-a d)^5}{b^{11}}+\frac{70 d^4 (a+b x)^3 (b c-a d)^6}{b^{11}}+\frac{60 d^3 (a+b x)^2 (b c-a d)^7}{b^{11}}+\frac{45 d^2 x (b c-a d)^8}{b^{10}}-\frac{(b c-a d)^{10}}{b^{11} (a+b x)}+\frac{10 d (b c-a d)^9 \log (a+b x)}{b^{11}}+\frac{d^{10} (a+b x)^9}{9 b^{11}}",1,"(45*d^2*(b*c - a*d)^8*x)/b^10 - (b*c - a*d)^10/(b^11*(a + b*x)) + (60*d^3*(b*c - a*d)^7*(a + b*x)^2)/b^11 + (70*d^4*(b*c - a*d)^6*(a + b*x)^3)/b^11 + (63*d^5*(b*c - a*d)^5*(a + b*x)^4)/b^11 + (42*d^6*(b*c - a*d)^4*(a + b*x)^5)/b^11 + (20*d^7*(b*c - a*d)^3*(a + b*x)^6)/b^11 + (45*d^8*(b*c - a*d)^2*(a + b*x)^7)/(7*b^11) + (5*d^9*(b*c - a*d)*(a + b*x)^8)/(4*b^11) + (d^10*(a + b*x)^9)/(9*b^11) + (10*d*(b*c - a*d)^9*Log[a + b*x])/b^11","A",2,1,15,0.06667,1,"{43}"
1314,1,262,0,0.4442945,"\int \frac{(c+d x)^{10}}{(a+b x)^3} \, dx","Int[(c + d*x)^10/(a + b*x)^3,x]","\frac{10 d^9 (a+b x)^7 (b c-a d)}{7 b^{11}}+\frac{15 d^8 (a+b x)^6 (b c-a d)^2}{2 b^{11}}+\frac{24 d^7 (a+b x)^5 (b c-a d)^3}{b^{11}}+\frac{105 d^6 (a+b x)^4 (b c-a d)^4}{2 b^{11}}+\frac{84 d^5 (a+b x)^3 (b c-a d)^5}{b^{11}}+\frac{105 d^4 (a+b x)^2 (b c-a d)^6}{b^{11}}+\frac{120 d^3 x (b c-a d)^7}{b^{10}}+\frac{45 d^2 (b c-a d)^8 \log (a+b x)}{b^{11}}-\frac{10 d (b c-a d)^9}{b^{11} (a+b x)}-\frac{(b c-a d)^{10}}{2 b^{11} (a+b x)^2}+\frac{d^{10} (a+b x)^8}{8 b^{11}}","\frac{10 d^9 (a+b x)^7 (b c-a d)}{7 b^{11}}+\frac{15 d^8 (a+b x)^6 (b c-a d)^2}{2 b^{11}}+\frac{24 d^7 (a+b x)^5 (b c-a d)^3}{b^{11}}+\frac{105 d^6 (a+b x)^4 (b c-a d)^4}{2 b^{11}}+\frac{84 d^5 (a+b x)^3 (b c-a d)^5}{b^{11}}+\frac{105 d^4 (a+b x)^2 (b c-a d)^6}{b^{11}}+\frac{120 d^3 x (b c-a d)^7}{b^{10}}+\frac{45 d^2 (b c-a d)^8 \log (a+b x)}{b^{11}}-\frac{10 d (b c-a d)^9}{b^{11} (a+b x)}-\frac{(b c-a d)^{10}}{2 b^{11} (a+b x)^2}+\frac{d^{10} (a+b x)^8}{8 b^{11}}",1,"(120*d^3*(b*c - a*d)^7*x)/b^10 - (b*c - a*d)^10/(2*b^11*(a + b*x)^2) - (10*d*(b*c - a*d)^9)/(b^11*(a + b*x)) + (105*d^4*(b*c - a*d)^6*(a + b*x)^2)/b^11 + (84*d^5*(b*c - a*d)^5*(a + b*x)^3)/b^11 + (105*d^6*(b*c - a*d)^4*(a + b*x)^4)/(2*b^11) + (24*d^7*(b*c - a*d)^3*(a + b*x)^5)/b^11 + (15*d^8*(b*c - a*d)^2*(a + b*x)^6)/(2*b^11) + (10*d^9*(b*c - a*d)*(a + b*x)^7)/(7*b^11) + (d^10*(a + b*x)^8)/(8*b^11) + (45*d^2*(b*c - a*d)^8*Log[a + b*x])/b^11","A",2,1,15,0.06667,1,"{43}"
1315,1,258,0,0.4408243,"\int \frac{(c+d x)^{10}}{(a+b x)^4} \, dx","Int[(c + d*x)^10/(a + b*x)^4,x]","\frac{5 d^9 (a+b x)^6 (b c-a d)}{3 b^{11}}+\frac{9 d^8 (a+b x)^5 (b c-a d)^2}{b^{11}}+\frac{30 d^7 (a+b x)^4 (b c-a d)^3}{b^{11}}+\frac{70 d^6 (a+b x)^3 (b c-a d)^4}{b^{11}}+\frac{126 d^5 (a+b x)^2 (b c-a d)^5}{b^{11}}+\frac{210 d^4 x (b c-a d)^6}{b^{10}}-\frac{45 d^2 (b c-a d)^8}{b^{11} (a+b x)}+\frac{120 d^3 (b c-a d)^7 \log (a+b x)}{b^{11}}-\frac{5 d (b c-a d)^9}{b^{11} (a+b x)^2}-\frac{(b c-a d)^{10}}{3 b^{11} (a+b x)^3}+\frac{d^{10} (a+b x)^7}{7 b^{11}}","\frac{5 d^9 (a+b x)^6 (b c-a d)}{3 b^{11}}+\frac{9 d^8 (a+b x)^5 (b c-a d)^2}{b^{11}}+\frac{30 d^7 (a+b x)^4 (b c-a d)^3}{b^{11}}+\frac{70 d^6 (a+b x)^3 (b c-a d)^4}{b^{11}}+\frac{126 d^5 (a+b x)^2 (b c-a d)^5}{b^{11}}+\frac{210 d^4 x (b c-a d)^6}{b^{10}}-\frac{45 d^2 (b c-a d)^8}{b^{11} (a+b x)}+\frac{120 d^3 (b c-a d)^7 \log (a+b x)}{b^{11}}-\frac{5 d (b c-a d)^9}{b^{11} (a+b x)^2}-\frac{(b c-a d)^{10}}{3 b^{11} (a+b x)^3}+\frac{d^{10} (a+b x)^7}{7 b^{11}}",1,"(210*d^4*(b*c - a*d)^6*x)/b^10 - (b*c - a*d)^10/(3*b^11*(a + b*x)^3) - (5*d*(b*c - a*d)^9)/(b^11*(a + b*x)^2) - (45*d^2*(b*c - a*d)^8)/(b^11*(a + b*x)) + (126*d^5*(b*c - a*d)^5*(a + b*x)^2)/b^11 + (70*d^6*(b*c - a*d)^4*(a + b*x)^3)/b^11 + (30*d^7*(b*c - a*d)^3*(a + b*x)^4)/b^11 + (9*d^8*(b*c - a*d)^2*(a + b*x)^5)/b^11 + (5*d^9*(b*c - a*d)*(a + b*x)^6)/(3*b^11) + (d^10*(a + b*x)^7)/(7*b^11) + (120*d^3*(b*c - a*d)^7*Log[a + b*x])/b^11","A",2,1,15,0.06667,1,"{43}"
1316,1,262,0,0.4219477,"\int \frac{(c+d x)^{10}}{(a+b x)^5} \, dx","Int[(c + d*x)^10/(a + b*x)^5,x]","\frac{2 d^9 (a+b x)^5 (b c-a d)}{b^{11}}+\frac{45 d^8 (a+b x)^4 (b c-a d)^2}{4 b^{11}}+\frac{40 d^7 (a+b x)^3 (b c-a d)^3}{b^{11}}+\frac{105 d^6 (a+b x)^2 (b c-a d)^4}{b^{11}}+\frac{252 d^5 x (b c-a d)^5}{b^{10}}-\frac{120 d^3 (b c-a d)^7}{b^{11} (a+b x)}-\frac{45 d^2 (b c-a d)^8}{2 b^{11} (a+b x)^2}+\frac{210 d^4 (b c-a d)^6 \log (a+b x)}{b^{11}}-\frac{10 d (b c-a d)^9}{3 b^{11} (a+b x)^3}-\frac{(b c-a d)^{10}}{4 b^{11} (a+b x)^4}+\frac{d^{10} (a+b x)^6}{6 b^{11}}","\frac{2 d^9 (a+b x)^5 (b c-a d)}{b^{11}}+\frac{45 d^8 (a+b x)^4 (b c-a d)^2}{4 b^{11}}+\frac{40 d^7 (a+b x)^3 (b c-a d)^3}{b^{11}}+\frac{105 d^6 (a+b x)^2 (b c-a d)^4}{b^{11}}+\frac{252 d^5 x (b c-a d)^5}{b^{10}}-\frac{120 d^3 (b c-a d)^7}{b^{11} (a+b x)}-\frac{45 d^2 (b c-a d)^8}{2 b^{11} (a+b x)^2}+\frac{210 d^4 (b c-a d)^6 \log (a+b x)}{b^{11}}-\frac{10 d (b c-a d)^9}{3 b^{11} (a+b x)^3}-\frac{(b c-a d)^{10}}{4 b^{11} (a+b x)^4}+\frac{d^{10} (a+b x)^6}{6 b^{11}}",1,"(252*d^5*(b*c - a*d)^5*x)/b^10 - (b*c - a*d)^10/(4*b^11*(a + b*x)^4) - (10*d*(b*c - a*d)^9)/(3*b^11*(a + b*x)^3) - (45*d^2*(b*c - a*d)^8)/(2*b^11*(a + b*x)^2) - (120*d^3*(b*c - a*d)^7)/(b^11*(a + b*x)) + (105*d^6*(b*c - a*d)^4*(a + b*x)^2)/b^11 + (40*d^7*(b*c - a*d)^3*(a + b*x)^3)/b^11 + (45*d^8*(b*c - a*d)^2*(a + b*x)^4)/(4*b^11) + (2*d^9*(b*c - a*d)*(a + b*x)^5)/b^11 + (d^10*(a + b*x)^6)/(6*b^11) + (210*d^4*(b*c - a*d)^6*Log[a + b*x])/b^11","A",2,1,15,0.06667,1,"{43}"
1317,1,260,0,0.4209052,"\int \frac{(c+d x)^{10}}{(a+b x)^6} \, dx","Int[(c + d*x)^10/(a + b*x)^6,x]","\frac{5 d^9 (a+b x)^4 (b c-a d)}{2 b^{11}}+\frac{15 d^8 (a+b x)^3 (b c-a d)^2}{b^{11}}+\frac{60 d^7 (a+b x)^2 (b c-a d)^3}{b^{11}}+\frac{210 d^6 x (b c-a d)^4}{b^{10}}-\frac{210 d^4 (b c-a d)^6}{b^{11} (a+b x)}-\frac{60 d^3 (b c-a d)^7}{b^{11} (a+b x)^2}-\frac{15 d^2 (b c-a d)^8}{b^{11} (a+b x)^3}+\frac{252 d^5 (b c-a d)^5 \log (a+b x)}{b^{11}}-\frac{5 d (b c-a d)^9}{2 b^{11} (a+b x)^4}-\frac{(b c-a d)^{10}}{5 b^{11} (a+b x)^5}+\frac{d^{10} (a+b x)^5}{5 b^{11}}","\frac{5 d^9 (a+b x)^4 (b c-a d)}{2 b^{11}}+\frac{15 d^8 (a+b x)^3 (b c-a d)^2}{b^{11}}+\frac{60 d^7 (a+b x)^2 (b c-a d)^3}{b^{11}}+\frac{210 d^6 x (b c-a d)^4}{b^{10}}-\frac{210 d^4 (b c-a d)^6}{b^{11} (a+b x)}-\frac{60 d^3 (b c-a d)^7}{b^{11} (a+b x)^2}-\frac{15 d^2 (b c-a d)^8}{b^{11} (a+b x)^3}+\frac{252 d^5 (b c-a d)^5 \log (a+b x)}{b^{11}}-\frac{5 d (b c-a d)^9}{2 b^{11} (a+b x)^4}-\frac{(b c-a d)^{10}}{5 b^{11} (a+b x)^5}+\frac{d^{10} (a+b x)^5}{5 b^{11}}",1,"(210*d^6*(b*c - a*d)^4*x)/b^10 - (b*c - a*d)^10/(5*b^11*(a + b*x)^5) - (5*d*(b*c - a*d)^9)/(2*b^11*(a + b*x)^4) - (15*d^2*(b*c - a*d)^8)/(b^11*(a + b*x)^3) - (60*d^3*(b*c - a*d)^7)/(b^11*(a + b*x)^2) - (210*d^4*(b*c - a*d)^6)/(b^11*(a + b*x)) + (60*d^7*(b*c - a*d)^3*(a + b*x)^2)/b^11 + (15*d^8*(b*c - a*d)^2*(a + b*x)^3)/b^11 + (5*d^9*(b*c - a*d)*(a + b*x)^4)/(2*b^11) + (d^10*(a + b*x)^5)/(5*b^11) + (252*d^5*(b*c - a*d)^5*Log[a + b*x])/b^11","A",2,1,15,0.06667,1,"{43}"
1318,1,262,0,0.3865936,"\int \frac{(c+d x)^{10}}{(a+b x)^7} \, dx","Int[(c + d*x)^10/(a + b*x)^7,x]","\frac{10 d^9 (a+b x)^3 (b c-a d)}{3 b^{11}}+\frac{45 d^8 (a+b x)^2 (b c-a d)^2}{2 b^{11}}+\frac{120 d^7 x (b c-a d)^3}{b^{10}}-\frac{252 d^5 (b c-a d)^5}{b^{11} (a+b x)}-\frac{105 d^4 (b c-a d)^6}{b^{11} (a+b x)^2}-\frac{40 d^3 (b c-a d)^7}{b^{11} (a+b x)^3}-\frac{45 d^2 (b c-a d)^8}{4 b^{11} (a+b x)^4}+\frac{210 d^6 (b c-a d)^4 \log (a+b x)}{b^{11}}-\frac{2 d (b c-a d)^9}{b^{11} (a+b x)^5}-\frac{(b c-a d)^{10}}{6 b^{11} (a+b x)^6}+\frac{d^{10} (a+b x)^4}{4 b^{11}}","\frac{10 d^9 (a+b x)^3 (b c-a d)}{3 b^{11}}+\frac{45 d^8 (a+b x)^2 (b c-a d)^2}{2 b^{11}}+\frac{120 d^7 x (b c-a d)^3}{b^{10}}-\frac{252 d^5 (b c-a d)^5}{b^{11} (a+b x)}-\frac{105 d^4 (b c-a d)^6}{b^{11} (a+b x)^2}-\frac{40 d^3 (b c-a d)^7}{b^{11} (a+b x)^3}-\frac{45 d^2 (b c-a d)^8}{4 b^{11} (a+b x)^4}+\frac{210 d^6 (b c-a d)^4 \log (a+b x)}{b^{11}}-\frac{2 d (b c-a d)^9}{b^{11} (a+b x)^5}-\frac{(b c-a d)^{10}}{6 b^{11} (a+b x)^6}+\frac{d^{10} (a+b x)^4}{4 b^{11}}",1,"(120*d^7*(b*c - a*d)^3*x)/b^10 - (b*c - a*d)^10/(6*b^11*(a + b*x)^6) - (2*d*(b*c - a*d)^9)/(b^11*(a + b*x)^5) - (45*d^2*(b*c - a*d)^8)/(4*b^11*(a + b*x)^4) - (40*d^3*(b*c - a*d)^7)/(b^11*(a + b*x)^3) - (105*d^4*(b*c - a*d)^6)/(b^11*(a + b*x)^2) - (252*d^5*(b*c - a*d)^5)/(b^11*(a + b*x)) + (45*d^8*(b*c - a*d)^2*(a + b*x)^2)/(2*b^11) + (10*d^9*(b*c - a*d)*(a + b*x)^3)/(3*b^11) + (d^10*(a + b*x)^4)/(4*b^11) + (210*d^6*(b*c - a*d)^4*Log[a + b*x])/b^11","A",2,1,15,0.06667,1,"{43}"
1319,1,258,0,0.3649,"\int \frac{(c+d x)^{10}}{(a+b x)^8} \, dx","Int[(c + d*x)^10/(a + b*x)^8,x]","\frac{5 d^9 (a+b x)^2 (b c-a d)}{b^{11}}+\frac{45 d^8 x (b c-a d)^2}{b^{10}}-\frac{210 d^6 (b c-a d)^4}{b^{11} (a+b x)}-\frac{126 d^5 (b c-a d)^5}{b^{11} (a+b x)^2}-\frac{70 d^4 (b c-a d)^6}{b^{11} (a+b x)^3}-\frac{30 d^3 (b c-a d)^7}{b^{11} (a+b x)^4}-\frac{9 d^2 (b c-a d)^8}{b^{11} (a+b x)^5}+\frac{120 d^7 (b c-a d)^3 \log (a+b x)}{b^{11}}-\frac{5 d (b c-a d)^9}{3 b^{11} (a+b x)^6}-\frac{(b c-a d)^{10}}{7 b^{11} (a+b x)^7}+\frac{d^{10} (a+b x)^3}{3 b^{11}}","\frac{5 d^9 (a+b x)^2 (b c-a d)}{b^{11}}+\frac{45 d^8 x (b c-a d)^2}{b^{10}}-\frac{210 d^6 (b c-a d)^4}{b^{11} (a+b x)}-\frac{126 d^5 (b c-a d)^5}{b^{11} (a+b x)^2}-\frac{70 d^4 (b c-a d)^6}{b^{11} (a+b x)^3}-\frac{30 d^3 (b c-a d)^7}{b^{11} (a+b x)^4}-\frac{9 d^2 (b c-a d)^8}{b^{11} (a+b x)^5}+\frac{120 d^7 (b c-a d)^3 \log (a+b x)}{b^{11}}-\frac{5 d (b c-a d)^9}{3 b^{11} (a+b x)^6}-\frac{(b c-a d)^{10}}{7 b^{11} (a+b x)^7}+\frac{d^{10} (a+b x)^3}{3 b^{11}}",1,"(45*d^8*(b*c - a*d)^2*x)/b^10 - (b*c - a*d)^10/(7*b^11*(a + b*x)^7) - (5*d*(b*c - a*d)^9)/(3*b^11*(a + b*x)^6) - (9*d^2*(b*c - a*d)^8)/(b^11*(a + b*x)^5) - (30*d^3*(b*c - a*d)^7)/(b^11*(a + b*x)^4) - (70*d^4*(b*c - a*d)^6)/(b^11*(a + b*x)^3) - (126*d^5*(b*c - a*d)^5)/(b^11*(a + b*x)^2) - (210*d^6*(b*c - a*d)^4)/(b^11*(a + b*x)) + (5*d^9*(b*c - a*d)*(a + b*x)^2)/b^11 + (d^10*(a + b*x)^3)/(3*b^11) + (120*d^7*(b*c - a*d)^3*Log[a + b*x])/b^11","A",2,1,15,0.06667,1,"{43}"
1320,1,258,0,0.3408474,"\int \frac{(c+d x)^{10}}{(a+b x)^9} \, dx","Int[(c + d*x)^10/(a + b*x)^9,x]","\frac{d^9 x (10 b c-9 a d)}{b^{10}}-\frac{120 d^7 (b c-a d)^3}{b^{11} (a+b x)}-\frac{105 d^6 (b c-a d)^4}{b^{11} (a+b x)^2}-\frac{84 d^5 (b c-a d)^5}{b^{11} (a+b x)^3}-\frac{105 d^4 (b c-a d)^6}{2 b^{11} (a+b x)^4}-\frac{24 d^3 (b c-a d)^7}{b^{11} (a+b x)^5}-\frac{15 d^2 (b c-a d)^8}{2 b^{11} (a+b x)^6}+\frac{45 d^8 (b c-a d)^2 \log (a+b x)}{b^{11}}-\frac{10 d (b c-a d)^9}{7 b^{11} (a+b x)^7}-\frac{(b c-a d)^{10}}{8 b^{11} (a+b x)^8}+\frac{d^{10} x^2}{2 b^9}","\frac{d^9 x (10 b c-9 a d)}{b^{10}}-\frac{120 d^7 (b c-a d)^3}{b^{11} (a+b x)}-\frac{105 d^6 (b c-a d)^4}{b^{11} (a+b x)^2}-\frac{84 d^5 (b c-a d)^5}{b^{11} (a+b x)^3}-\frac{105 d^4 (b c-a d)^6}{2 b^{11} (a+b x)^4}-\frac{24 d^3 (b c-a d)^7}{b^{11} (a+b x)^5}-\frac{15 d^2 (b c-a d)^8}{2 b^{11} (a+b x)^6}+\frac{45 d^8 (b c-a d)^2 \log (a+b x)}{b^{11}}-\frac{10 d (b c-a d)^9}{7 b^{11} (a+b x)^7}-\frac{(b c-a d)^{10}}{8 b^{11} (a+b x)^8}+\frac{d^{10} x^2}{2 b^9}",1,"(d^9*(10*b*c - 9*a*d)*x)/b^10 + (d^10*x^2)/(2*b^9) - (b*c - a*d)^10/(8*b^11*(a + b*x)^8) - (10*d*(b*c - a*d)^9)/(7*b^11*(a + b*x)^7) - (15*d^2*(b*c - a*d)^8)/(2*b^11*(a + b*x)^6) - (24*d^3*(b*c - a*d)^7)/(b^11*(a + b*x)^5) - (105*d^4*(b*c - a*d)^6)/(2*b^11*(a + b*x)^4) - (84*d^5*(b*c - a*d)^5)/(b^11*(a + b*x)^3) - (105*d^6*(b*c - a*d)^4)/(b^11*(a + b*x)^2) - (120*d^7*(b*c - a*d)^3)/(b^11*(a + b*x)) + (45*d^8*(b*c - a*d)^2*Log[a + b*x])/b^11","A",2,1,15,0.06667,1,"{43}"
1321,1,257,0,0.3112672,"\int \frac{(c+d x)^{10}}{(a+b x)^{10}} \, dx","Int[(c + d*x)^10/(a + b*x)^10,x]","-\frac{45 d^8 (b c-a d)^2}{b^{11} (a+b x)}-\frac{60 d^7 (b c-a d)^3}{b^{11} (a+b x)^2}-\frac{70 d^6 (b c-a d)^4}{b^{11} (a+b x)^3}-\frac{63 d^5 (b c-a d)^5}{b^{11} (a+b x)^4}-\frac{42 d^4 (b c-a d)^6}{b^{11} (a+b x)^5}-\frac{20 d^3 (b c-a d)^7}{b^{11} (a+b x)^6}-\frac{45 d^2 (b c-a d)^8}{7 b^{11} (a+b x)^7}+\frac{10 d^9 (b c-a d) \log (a+b x)}{b^{11}}-\frac{5 d (b c-a d)^9}{4 b^{11} (a+b x)^8}-\frac{(b c-a d)^{10}}{9 b^{11} (a+b x)^9}+\frac{d^{10} x}{b^{10}}","-\frac{45 d^8 (b c-a d)^2}{b^{11} (a+b x)}-\frac{60 d^7 (b c-a d)^3}{b^{11} (a+b x)^2}-\frac{70 d^6 (b c-a d)^4}{b^{11} (a+b x)^3}-\frac{63 d^5 (b c-a d)^5}{b^{11} (a+b x)^4}-\frac{42 d^4 (b c-a d)^6}{b^{11} (a+b x)^5}-\frac{20 d^3 (b c-a d)^7}{b^{11} (a+b x)^6}-\frac{45 d^2 (b c-a d)^8}{7 b^{11} (a+b x)^7}+\frac{10 d^9 (b c-a d) \log (a+b x)}{b^{11}}-\frac{5 d (b c-a d)^9}{4 b^{11} (a+b x)^8}-\frac{(b c-a d)^{10}}{9 b^{11} (a+b x)^9}+\frac{d^{10} x}{b^{10}}",1,"(d^10*x)/b^10 - (b*c - a*d)^10/(9*b^11*(a + b*x)^9) - (5*d*(b*c - a*d)^9)/(4*b^11*(a + b*x)^8) - (45*d^2*(b*c - a*d)^8)/(7*b^11*(a + b*x)^7) - (20*d^3*(b*c - a*d)^7)/(b^11*(a + b*x)^6) - (42*d^4*(b*c - a*d)^6)/(b^11*(a + b*x)^5) - (63*d^5*(b*c - a*d)^5)/(b^11*(a + b*x)^4) - (70*d^6*(b*c - a*d)^4)/(b^11*(a + b*x)^3) - (60*d^7*(b*c - a*d)^3)/(b^11*(a + b*x)^2) - (45*d^8*(b*c - a*d)^2)/(b^11*(a + b*x)) + (10*d^9*(b*c - a*d)*Log[a + b*x])/b^11","A",2,1,15,0.06667,1,"{43}"
1322,1,271,0,0.2868442,"\int \frac{(c+d x)^{10}}{(a+b x)^{11}} \, dx","Int[(c + d*x)^10/(a + b*x)^11,x]","-\frac{10 d^9 (b c-a d)}{b^{11} (a+b x)}-\frac{45 d^8 (b c-a d)^2}{2 b^{11} (a+b x)^2}-\frac{40 d^7 (b c-a d)^3}{b^{11} (a+b x)^3}-\frac{105 d^6 (b c-a d)^4}{2 b^{11} (a+b x)^4}-\frac{252 d^5 (b c-a d)^5}{5 b^{11} (a+b x)^5}-\frac{35 d^4 (b c-a d)^6}{b^{11} (a+b x)^6}-\frac{120 d^3 (b c-a d)^7}{7 b^{11} (a+b x)^7}-\frac{45 d^2 (b c-a d)^8}{8 b^{11} (a+b x)^8}-\frac{10 d (b c-a d)^9}{9 b^{11} (a+b x)^9}-\frac{(b c-a d)^{10}}{10 b^{11} (a+b x)^{10}}+\frac{d^{10} \log (a+b x)}{b^{11}}","-\frac{10 d^9 (b c-a d)}{b^{11} (a+b x)}-\frac{45 d^8 (b c-a d)^2}{2 b^{11} (a+b x)^2}-\frac{40 d^7 (b c-a d)^3}{b^{11} (a+b x)^3}-\frac{105 d^6 (b c-a d)^4}{2 b^{11} (a+b x)^4}-\frac{252 d^5 (b c-a d)^5}{5 b^{11} (a+b x)^5}-\frac{35 d^4 (b c-a d)^6}{b^{11} (a+b x)^6}-\frac{120 d^3 (b c-a d)^7}{7 b^{11} (a+b x)^7}-\frac{45 d^2 (b c-a d)^8}{8 b^{11} (a+b x)^8}-\frac{10 d (b c-a d)^9}{9 b^{11} (a+b x)^9}-\frac{(b c-a d)^{10}}{10 b^{11} (a+b x)^{10}}+\frac{d^{10} \log (a+b x)}{b^{11}}",1,"-(b*c - a*d)^10/(10*b^11*(a + b*x)^10) - (10*d*(b*c - a*d)^9)/(9*b^11*(a + b*x)^9) - (45*d^2*(b*c - a*d)^8)/(8*b^11*(a + b*x)^8) - (120*d^3*(b*c - a*d)^7)/(7*b^11*(a + b*x)^7) - (35*d^4*(b*c - a*d)^6)/(b^11*(a + b*x)^6) - (252*d^5*(b*c - a*d)^5)/(5*b^11*(a + b*x)^5) - (105*d^6*(b*c - a*d)^4)/(2*b^11*(a + b*x)^4) - (40*d^7*(b*c - a*d)^3)/(b^11*(a + b*x)^3) - (45*d^8*(b*c - a*d)^2)/(2*b^11*(a + b*x)^2) - (10*d^9*(b*c - a*d))/(b^11*(a + b*x)) + (d^10*Log[a + b*x])/b^11","A",2,1,15,0.06667,1,"{43}"
1323,1,28,0,0.0030368,"\int \frac{(c+d x)^{10}}{(a+b x)^{12}} \, dx","Int[(c + d*x)^10/(a + b*x)^12,x]","-\frac{(c+d x)^{11}}{11 (a+b x)^{11} (b c-a d)}","-\frac{(c+d x)^{11}}{11 (a+b x)^{11} (b c-a d)}",1,"-(c + d*x)^11/(11*(b*c - a*d)*(a + b*x)^11)","A",1,1,15,0.06667,1,"{37}"
1324,1,58,0,0.0101382,"\int \frac{(c+d x)^{10}}{(a+b x)^{13}} \, dx","Int[(c + d*x)^10/(a + b*x)^13,x]","\frac{d (c+d x)^{11}}{132 (a+b x)^{11} (b c-a d)^2}-\frac{(c+d x)^{11}}{12 (a+b x)^{12} (b c-a d)}","\frac{d (c+d x)^{11}}{132 (a+b x)^{11} (b c-a d)^2}-\frac{(c+d x)^{11}}{12 (a+b x)^{12} (b c-a d)}",1,"-(c + d*x)^11/(12*(b*c - a*d)*(a + b*x)^12) + (d*(c + d*x)^11)/(132*(b*c - a*d)^2*(a + b*x)^11)","A",2,2,15,0.1333,1,"{45, 37}"
1325,1,89,0,0.0199106,"\int \frac{(c+d x)^{10}}{(a+b x)^{14}} \, dx","Int[(c + d*x)^10/(a + b*x)^14,x]","-\frac{d^2 (c+d x)^{11}}{858 (a+b x)^{11} (b c-a d)^3}+\frac{d (c+d x)^{11}}{78 (a+b x)^{12} (b c-a d)^2}-\frac{(c+d x)^{11}}{13 (a+b x)^{13} (b c-a d)}","-\frac{d^2 (c+d x)^{11}}{858 (a+b x)^{11} (b c-a d)^3}+\frac{d (c+d x)^{11}}{78 (a+b x)^{12} (b c-a d)^2}-\frac{(c+d x)^{11}}{13 (a+b x)^{13} (b c-a d)}",1,"-(c + d*x)^11/(13*(b*c - a*d)*(a + b*x)^13) + (d*(c + d*x)^11)/(78*(b*c - a*d)^2*(a + b*x)^12) - (d^2*(c + d*x)^11)/(858*(b*c - a*d)^3*(a + b*x)^11)","A",3,2,15,0.1333,1,"{45, 37}"
1326,1,120,0,0.029914,"\int \frac{(c+d x)^{10}}{(a+b x)^{15}} \, dx","Int[(c + d*x)^10/(a + b*x)^15,x]","\frac{d^3 (c+d x)^{11}}{4004 (a+b x)^{11} (b c-a d)^4}-\frac{d^2 (c+d x)^{11}}{364 (a+b x)^{12} (b c-a d)^3}+\frac{3 d (c+d x)^{11}}{182 (a+b x)^{13} (b c-a d)^2}-\frac{(c+d x)^{11}}{14 (a+b x)^{14} (b c-a d)}","\frac{d^3 (c+d x)^{11}}{4004 (a+b x)^{11} (b c-a d)^4}-\frac{d^2 (c+d x)^{11}}{364 (a+b x)^{12} (b c-a d)^3}+\frac{3 d (c+d x)^{11}}{182 (a+b x)^{13} (b c-a d)^2}-\frac{(c+d x)^{11}}{14 (a+b x)^{14} (b c-a d)}",1,"-(c + d*x)^11/(14*(b*c - a*d)*(a + b*x)^14) + (3*d*(c + d*x)^11)/(182*(b*c - a*d)^2*(a + b*x)^13) - (d^2*(c + d*x)^11)/(364*(b*c - a*d)^3*(a + b*x)^12) + (d^3*(c + d*x)^11)/(4004*(b*c - a*d)^4*(a + b*x)^11)","A",4,2,15,0.1333,1,"{45, 37}"
1327,1,151,0,0.0444379,"\int \frac{(c+d x)^{10}}{(a+b x)^{16}} \, dx","Int[(c + d*x)^10/(a + b*x)^16,x]","-\frac{d^4 (c+d x)^{11}}{15015 (a+b x)^{11} (b c-a d)^5}+\frac{d^3 (c+d x)^{11}}{1365 (a+b x)^{12} (b c-a d)^4}-\frac{2 d^2 (c+d x)^{11}}{455 (a+b x)^{13} (b c-a d)^3}+\frac{2 d (c+d x)^{11}}{105 (a+b x)^{14} (b c-a d)^2}-\frac{(c+d x)^{11}}{15 (a+b x)^{15} (b c-a d)}","-\frac{d^4 (c+d x)^{11}}{15015 (a+b x)^{11} (b c-a d)^5}+\frac{d^3 (c+d x)^{11}}{1365 (a+b x)^{12} (b c-a d)^4}-\frac{2 d^2 (c+d x)^{11}}{455 (a+b x)^{13} (b c-a d)^3}+\frac{2 d (c+d x)^{11}}{105 (a+b x)^{14} (b c-a d)^2}-\frac{(c+d x)^{11}}{15 (a+b x)^{15} (b c-a d)}",1,"-(c + d*x)^11/(15*(b*c - a*d)*(a + b*x)^15) + (2*d*(c + d*x)^11)/(105*(b*c - a*d)^2*(a + b*x)^14) - (2*d^2*(c + d*x)^11)/(455*(b*c - a*d)^3*(a + b*x)^13) + (d^3*(c + d*x)^11)/(1365*(b*c - a*d)^4*(a + b*x)^12) - (d^4*(c + d*x)^11)/(15015*(b*c - a*d)^5*(a + b*x)^11)","A",5,2,15,0.1333,1,"{45, 37}"
1328,1,182,0,0.062674,"\int \frac{(c+d x)^{10}}{(a+b x)^{17}} \, dx","Int[(c + d*x)^10/(a + b*x)^17,x]","\frac{d^5 (c+d x)^{11}}{48048 (a+b x)^{11} (b c-a d)^6}-\frac{d^4 (c+d x)^{11}}{4368 (a+b x)^{12} (b c-a d)^5}+\frac{d^3 (c+d x)^{11}}{728 (a+b x)^{13} (b c-a d)^4}-\frac{d^2 (c+d x)^{11}}{168 (a+b x)^{14} (b c-a d)^3}+\frac{d (c+d x)^{11}}{48 (a+b x)^{15} (b c-a d)^2}-\frac{(c+d x)^{11}}{16 (a+b x)^{16} (b c-a d)}","\frac{d^5 (c+d x)^{11}}{48048 (a+b x)^{11} (b c-a d)^6}-\frac{d^4 (c+d x)^{11}}{4368 (a+b x)^{12} (b c-a d)^5}+\frac{d^3 (c+d x)^{11}}{728 (a+b x)^{13} (b c-a d)^4}-\frac{d^2 (c+d x)^{11}}{168 (a+b x)^{14} (b c-a d)^3}+\frac{d (c+d x)^{11}}{48 (a+b x)^{15} (b c-a d)^2}-\frac{(c+d x)^{11}}{16 (a+b x)^{16} (b c-a d)}",1,"-(c + d*x)^11/(16*(b*c - a*d)*(a + b*x)^16) + (d*(c + d*x)^11)/(48*(b*c - a*d)^2*(a + b*x)^15) - (d^2*(c + d*x)^11)/(168*(b*c - a*d)^3*(a + b*x)^14) + (d^3*(c + d*x)^11)/(728*(b*c - a*d)^4*(a + b*x)^13) - (d^4*(c + d*x)^11)/(4368*(b*c - a*d)^5*(a + b*x)^12) + (d^5*(c + d*x)^11)/(48048*(b*c - a*d)^6*(a + b*x)^11)","A",6,2,15,0.1333,1,"{45, 37}"
1329,1,213,0,0.0787245,"\int \frac{(c+d x)^{10}}{(a+b x)^{18}} \, dx","Int[(c + d*x)^10/(a + b*x)^18,x]","-\frac{d^6 (c+d x)^{11}}{136136 (a+b x)^{11} (b c-a d)^7}+\frac{d^5 (c+d x)^{11}}{12376 (a+b x)^{12} (b c-a d)^6}-\frac{3 d^4 (c+d x)^{11}}{6188 (a+b x)^{13} (b c-a d)^5}+\frac{d^3 (c+d x)^{11}}{476 (a+b x)^{14} (b c-a d)^4}-\frac{d^2 (c+d x)^{11}}{136 (a+b x)^{15} (b c-a d)^3}+\frac{3 d (c+d x)^{11}}{136 (a+b x)^{16} (b c-a d)^2}-\frac{(c+d x)^{11}}{17 (a+b x)^{17} (b c-a d)}","-\frac{d^6 (c+d x)^{11}}{136136 (a+b x)^{11} (b c-a d)^7}+\frac{d^5 (c+d x)^{11}}{12376 (a+b x)^{12} (b c-a d)^6}-\frac{3 d^4 (c+d x)^{11}}{6188 (a+b x)^{13} (b c-a d)^5}+\frac{d^3 (c+d x)^{11}}{476 (a+b x)^{14} (b c-a d)^4}-\frac{d^2 (c+d x)^{11}}{136 (a+b x)^{15} (b c-a d)^3}+\frac{3 d (c+d x)^{11}}{136 (a+b x)^{16} (b c-a d)^2}-\frac{(c+d x)^{11}}{17 (a+b x)^{17} (b c-a d)}",1,"-(c + d*x)^11/(17*(b*c - a*d)*(a + b*x)^17) + (3*d*(c + d*x)^11)/(136*(b*c - a*d)^2*(a + b*x)^16) - (d^2*(c + d*x)^11)/(136*(b*c - a*d)^3*(a + b*x)^15) + (d^3*(c + d*x)^11)/(476*(b*c - a*d)^4*(a + b*x)^14) - (3*d^4*(c + d*x)^11)/(6188*(b*c - a*d)^5*(a + b*x)^13) + (d^5*(c + d*x)^11)/(12376*(b*c - a*d)^6*(a + b*x)^12) - (d^6*(c + d*x)^11)/(136136*(b*c - a*d)^7*(a + b*x)^11)","A",7,2,15,0.1333,1,"{45, 37}"
1330,1,244,0,0.1049756,"\int \frac{(c+d x)^{10}}{(a+b x)^{19}} \, dx","Int[(c + d*x)^10/(a + b*x)^19,x]","\frac{d^7 (c+d x)^{11}}{350064 (a+b x)^{11} (b c-a d)^8}-\frac{d^6 (c+d x)^{11}}{31824 (a+b x)^{12} (b c-a d)^7}+\frac{d^5 (c+d x)^{11}}{5304 (a+b x)^{13} (b c-a d)^6}-\frac{d^4 (c+d x)^{11}}{1224 (a+b x)^{14} (b c-a d)^5}+\frac{7 d^3 (c+d x)^{11}}{2448 (a+b x)^{15} (b c-a d)^4}-\frac{7 d^2 (c+d x)^{11}}{816 (a+b x)^{16} (b c-a d)^3}+\frac{7 d (c+d x)^{11}}{306 (a+b x)^{17} (b c-a d)^2}-\frac{(c+d x)^{11}}{18 (a+b x)^{18} (b c-a d)}","\frac{d^7 (c+d x)^{11}}{350064 (a+b x)^{11} (b c-a d)^8}-\frac{d^6 (c+d x)^{11}}{31824 (a+b x)^{12} (b c-a d)^7}+\frac{d^5 (c+d x)^{11}}{5304 (a+b x)^{13} (b c-a d)^6}-\frac{d^4 (c+d x)^{11}}{1224 (a+b x)^{14} (b c-a d)^5}+\frac{7 d^3 (c+d x)^{11}}{2448 (a+b x)^{15} (b c-a d)^4}-\frac{7 d^2 (c+d x)^{11}}{816 (a+b x)^{16} (b c-a d)^3}+\frac{7 d (c+d x)^{11}}{306 (a+b x)^{17} (b c-a d)^2}-\frac{(c+d x)^{11}}{18 (a+b x)^{18} (b c-a d)}",1,"-(c + d*x)^11/(18*(b*c - a*d)*(a + b*x)^18) + (7*d*(c + d*x)^11)/(306*(b*c - a*d)^2*(a + b*x)^17) - (7*d^2*(c + d*x)^11)/(816*(b*c - a*d)^3*(a + b*x)^16) + (7*d^3*(c + d*x)^11)/(2448*(b*c - a*d)^4*(a + b*x)^15) - (d^4*(c + d*x)^11)/(1224*(b*c - a*d)^5*(a + b*x)^14) + (d^5*(c + d*x)^11)/(5304*(b*c - a*d)^6*(a + b*x)^13) - (d^6*(c + d*x)^11)/(31824*(b*c - a*d)^7*(a + b*x)^12) + (d^7*(c + d*x)^11)/(350064*(b*c - a*d)^8*(a + b*x)^11)","A",8,2,15,0.1333,1,"{45, 37}"
1331,1,273,0,0.2841171,"\int \frac{(c+d x)^{10}}{(a+b x)^{20}} \, dx","Int[(c + d*x)^10/(a + b*x)^20,x]","-\frac{d^9 (b c-a d)}{b^{11} (a+b x)^{10}}-\frac{45 d^8 (b c-a d)^2}{11 b^{11} (a+b x)^{11}}-\frac{10 d^7 (b c-a d)^3}{b^{11} (a+b x)^{12}}-\frac{210 d^6 (b c-a d)^4}{13 b^{11} (a+b x)^{13}}-\frac{18 d^5 (b c-a d)^5}{b^{11} (a+b x)^{14}}-\frac{14 d^4 (b c-a d)^6}{b^{11} (a+b x)^{15}}-\frac{15 d^3 (b c-a d)^7}{2 b^{11} (a+b x)^{16}}-\frac{45 d^2 (b c-a d)^8}{17 b^{11} (a+b x)^{17}}-\frac{5 d (b c-a d)^9}{9 b^{11} (a+b x)^{18}}-\frac{(b c-a d)^{10}}{19 b^{11} (a+b x)^{19}}-\frac{d^{10}}{9 b^{11} (a+b x)^9}","-\frac{d^9 (b c-a d)}{b^{11} (a+b x)^{10}}-\frac{45 d^8 (b c-a d)^2}{11 b^{11} (a+b x)^{11}}-\frac{10 d^7 (b c-a d)^3}{b^{11} (a+b x)^{12}}-\frac{210 d^6 (b c-a d)^4}{13 b^{11} (a+b x)^{13}}-\frac{18 d^5 (b c-a d)^5}{b^{11} (a+b x)^{14}}-\frac{14 d^4 (b c-a d)^6}{b^{11} (a+b x)^{15}}-\frac{15 d^3 (b c-a d)^7}{2 b^{11} (a+b x)^{16}}-\frac{45 d^2 (b c-a d)^8}{17 b^{11} (a+b x)^{17}}-\frac{5 d (b c-a d)^9}{9 b^{11} (a+b x)^{18}}-\frac{(b c-a d)^{10}}{19 b^{11} (a+b x)^{19}}-\frac{d^{10}}{9 b^{11} (a+b x)^9}",1,"-(b*c - a*d)^10/(19*b^11*(a + b*x)^19) - (5*d*(b*c - a*d)^9)/(9*b^11*(a + b*x)^18) - (45*d^2*(b*c - a*d)^8)/(17*b^11*(a + b*x)^17) - (15*d^3*(b*c - a*d)^7)/(2*b^11*(a + b*x)^16) - (14*d^4*(b*c - a*d)^6)/(b^11*(a + b*x)^15) - (18*d^5*(b*c - a*d)^5)/(b^11*(a + b*x)^14) - (210*d^6*(b*c - a*d)^4)/(13*b^11*(a + b*x)^13) - (10*d^7*(b*c - a*d)^3)/(b^11*(a + b*x)^12) - (45*d^8*(b*c - a*d)^2)/(11*b^11*(a + b*x)^11) - (d^9*(b*c - a*d))/(b^11*(a + b*x)^10) - d^10/(9*b^11*(a + b*x)^9)","A",2,1,15,0.06667,1,"{43}"
1332,1,279,0,0.2724359,"\int \frac{(c+d x)^{10}}{(a+b x)^{21}} \, dx","Int[(c + d*x)^10/(a + b*x)^21,x]","-\frac{10 d^9 (b c-a d)}{11 b^{11} (a+b x)^{11}}-\frac{15 d^8 (b c-a d)^2}{4 b^{11} (a+b x)^{12}}-\frac{120 d^7 (b c-a d)^3}{13 b^{11} (a+b x)^{13}}-\frac{15 d^6 (b c-a d)^4}{b^{11} (a+b x)^{14}}-\frac{84 d^5 (b c-a d)^5}{5 b^{11} (a+b x)^{15}}-\frac{105 d^4 (b c-a d)^6}{8 b^{11} (a+b x)^{16}}-\frac{120 d^3 (b c-a d)^7}{17 b^{11} (a+b x)^{17}}-\frac{5 d^2 (b c-a d)^8}{2 b^{11} (a+b x)^{18}}-\frac{10 d (b c-a d)^9}{19 b^{11} (a+b x)^{19}}-\frac{(b c-a d)^{10}}{20 b^{11} (a+b x)^{20}}-\frac{d^{10}}{10 b^{11} (a+b x)^{10}}","-\frac{10 d^9 (b c-a d)}{11 b^{11} (a+b x)^{11}}-\frac{15 d^8 (b c-a d)^2}{4 b^{11} (a+b x)^{12}}-\frac{120 d^7 (b c-a d)^3}{13 b^{11} (a+b x)^{13}}-\frac{15 d^6 (b c-a d)^4}{b^{11} (a+b x)^{14}}-\frac{84 d^5 (b c-a d)^5}{5 b^{11} (a+b x)^{15}}-\frac{105 d^4 (b c-a d)^6}{8 b^{11} (a+b x)^{16}}-\frac{120 d^3 (b c-a d)^7}{17 b^{11} (a+b x)^{17}}-\frac{5 d^2 (b c-a d)^8}{2 b^{11} (a+b x)^{18}}-\frac{10 d (b c-a d)^9}{19 b^{11} (a+b x)^{19}}-\frac{(b c-a d)^{10}}{20 b^{11} (a+b x)^{20}}-\frac{d^{10}}{10 b^{11} (a+b x)^{10}}",1,"-(b*c - a*d)^10/(20*b^11*(a + b*x)^20) - (10*d*(b*c - a*d)^9)/(19*b^11*(a + b*x)^19) - (5*d^2*(b*c - a*d)^8)/(2*b^11*(a + b*x)^18) - (120*d^3*(b*c - a*d)^7)/(17*b^11*(a + b*x)^17) - (105*d^4*(b*c - a*d)^6)/(8*b^11*(a + b*x)^16) - (84*d^5*(b*c - a*d)^5)/(5*b^11*(a + b*x)^15) - (15*d^6*(b*c - a*d)^4)/(b^11*(a + b*x)^14) - (120*d^7*(b*c - a*d)^3)/(13*b^11*(a + b*x)^13) - (15*d^8*(b*c - a*d)^2)/(4*b^11*(a + b*x)^12) - (10*d^9*(b*c - a*d))/(11*b^11*(a + b*x)^11) - d^10/(10*b^11*(a + b*x)^10)","A",2,1,15,0.06667,1,"{43}"
1333,1,279,0,0.2705681,"\int \frac{(c+d x)^{10}}{(a+b x)^{22}} \, dx","Int[(c + d*x)^10/(a + b*x)^22,x]","-\frac{5 d^9 (b c-a d)}{6 b^{11} (a+b x)^{12}}-\frac{45 d^8 (b c-a d)^2}{13 b^{11} (a+b x)^{13}}-\frac{60 d^7 (b c-a d)^3}{7 b^{11} (a+b x)^{14}}-\frac{14 d^6 (b c-a d)^4}{b^{11} (a+b x)^{15}}-\frac{63 d^5 (b c-a d)^5}{4 b^{11} (a+b x)^{16}}-\frac{210 d^4 (b c-a d)^6}{17 b^{11} (a+b x)^{17}}-\frac{20 d^3 (b c-a d)^7}{3 b^{11} (a+b x)^{18}}-\frac{45 d^2 (b c-a d)^8}{19 b^{11} (a+b x)^{19}}-\frac{d (b c-a d)^9}{2 b^{11} (a+b x)^{20}}-\frac{(b c-a d)^{10}}{21 b^{11} (a+b x)^{21}}-\frac{d^{10}}{11 b^{11} (a+b x)^{11}}","-\frac{5 d^9 (b c-a d)}{6 b^{11} (a+b x)^{12}}-\frac{45 d^8 (b c-a d)^2}{13 b^{11} (a+b x)^{13}}-\frac{60 d^7 (b c-a d)^3}{7 b^{11} (a+b x)^{14}}-\frac{14 d^6 (b c-a d)^4}{b^{11} (a+b x)^{15}}-\frac{63 d^5 (b c-a d)^5}{4 b^{11} (a+b x)^{16}}-\frac{210 d^4 (b c-a d)^6}{17 b^{11} (a+b x)^{17}}-\frac{20 d^3 (b c-a d)^7}{3 b^{11} (a+b x)^{18}}-\frac{45 d^2 (b c-a d)^8}{19 b^{11} (a+b x)^{19}}-\frac{d (b c-a d)^9}{2 b^{11} (a+b x)^{20}}-\frac{(b c-a d)^{10}}{21 b^{11} (a+b x)^{21}}-\frac{d^{10}}{11 b^{11} (a+b x)^{11}}",1,"-(b*c - a*d)^10/(21*b^11*(a + b*x)^21) - (d*(b*c - a*d)^9)/(2*b^11*(a + b*x)^20) - (45*d^2*(b*c - a*d)^8)/(19*b^11*(a + b*x)^19) - (20*d^3*(b*c - a*d)^7)/(3*b^11*(a + b*x)^18) - (210*d^4*(b*c - a*d)^6)/(17*b^11*(a + b*x)^17) - (63*d^5*(b*c - a*d)^5)/(4*b^11*(a + b*x)^16) - (14*d^6*(b*c - a*d)^4)/(b^11*(a + b*x)^15) - (60*d^7*(b*c - a*d)^3)/(7*b^11*(a + b*x)^14) - (45*d^8*(b*c - a*d)^2)/(13*b^11*(a + b*x)^13) - (5*d^9*(b*c - a*d))/(6*b^11*(a + b*x)^12) - d^10/(11*b^11*(a + b*x)^11)","A",2,1,15,0.06667,1,"{43}"
1334,1,122,0,0.0533321,"\int \frac{(a+b x)^5}{c+d x} \, dx","Int[(a + b*x)^5/(c + d*x),x]","\frac{b x (b c-a d)^4}{d^5}-\frac{(a+b x)^2 (b c-a d)^3}{2 d^4}+\frac{(a+b x)^3 (b c-a d)^2}{3 d^3}-\frac{(a+b x)^4 (b c-a d)}{4 d^2}-\frac{(b c-a d)^5 \log (c+d x)}{d^6}+\frac{(a+b x)^5}{5 d}","\frac{b x (b c-a d)^4}{d^5}-\frac{(a+b x)^2 (b c-a d)^3}{2 d^4}+\frac{(a+b x)^3 (b c-a d)^2}{3 d^3}-\frac{(a+b x)^4 (b c-a d)}{4 d^2}-\frac{(b c-a d)^5 \log (c+d x)}{d^6}+\frac{(a+b x)^5}{5 d}",1,"(b*(b*c - a*d)^4*x)/d^5 - ((b*c - a*d)^3*(a + b*x)^2)/(2*d^4) + ((b*c - a*d)^2*(a + b*x)^3)/(3*d^3) - ((b*c - a*d)*(a + b*x)^4)/(4*d^2) + (a + b*x)^5/(5*d) - ((b*c - a*d)^5*Log[c + d*x])/d^6","A",2,1,15,0.06667,1,"{43}"
1335,1,98,0,0.0383132,"\int \frac{(a+b x)^4}{c+d x} \, dx","Int[(a + b*x)^4/(c + d*x),x]","-\frac{b x (b c-a d)^3}{d^4}+\frac{(a+b x)^2 (b c-a d)^2}{2 d^3}-\frac{(a+b x)^3 (b c-a d)}{3 d^2}+\frac{(b c-a d)^4 \log (c+d x)}{d^5}+\frac{(a+b x)^4}{4 d}","-\frac{b x (b c-a d)^3}{d^4}+\frac{(a+b x)^2 (b c-a d)^2}{2 d^3}-\frac{(a+b x)^3 (b c-a d)}{3 d^2}+\frac{(b c-a d)^4 \log (c+d x)}{d^5}+\frac{(a+b x)^4}{4 d}",1,"-((b*(b*c - a*d)^3*x)/d^4) + ((b*c - a*d)^2*(a + b*x)^2)/(2*d^3) - ((b*c - a*d)*(a + b*x)^3)/(3*d^2) + (a + b*x)^4/(4*d) + ((b*c - a*d)^4*Log[c + d*x])/d^5","A",2,1,15,0.06667,1,"{43}"
1336,1,74,0,0.0298652,"\int \frac{(a+b x)^3}{c+d x} \, dx","Int[(a + b*x)^3/(c + d*x),x]","\frac{b x (b c-a d)^2}{d^3}-\frac{(a+b x)^2 (b c-a d)}{2 d^2}-\frac{(b c-a d)^3 \log (c+d x)}{d^4}+\frac{(a+b x)^3}{3 d}","\frac{b x (b c-a d)^2}{d^3}-\frac{(a+b x)^2 (b c-a d)}{2 d^2}-\frac{(b c-a d)^3 \log (c+d x)}{d^4}+\frac{(a+b x)^3}{3 d}",1,"(b*(b*c - a*d)^2*x)/d^3 - ((b*c - a*d)*(a + b*x)^2)/(2*d^2) + (a + b*x)^3/(3*d) - ((b*c - a*d)^3*Log[c + d*x])/d^4","A",2,1,15,0.06667,1,"{43}"
1337,1,50,0,0.0208861,"\int \frac{(a+b x)^2}{c+d x} \, dx","Int[(a + b*x)^2/(c + d*x),x]","-\frac{b x (b c-a d)}{d^2}+\frac{(b c-a d)^2 \log (c+d x)}{d^3}+\frac{(a+b x)^2}{2 d}","-\frac{b x (b c-a d)}{d^2}+\frac{(b c-a d)^2 \log (c+d x)}{d^3}+\frac{(a+b x)^2}{2 d}",1,"-((b*(b*c - a*d)*x)/d^2) + (a + b*x)^2/(2*d) + ((b*c - a*d)^2*Log[c + d*x])/d^3","A",2,1,15,0.06667,1,"{43}"
1338,1,26,0,0.0178974,"\int \frac{a+b x}{c+d x} \, dx","Int[(a + b*x)/(c + d*x),x]","\frac{b x}{d}-\frac{(b c-a d) \log (c+d x)}{d^2}","\frac{b x}{d}-\frac{(b c-a d) \log (c+d x)}{d^2}",1,"(b*x)/d - ((b*c - a*d)*Log[c + d*x])/d^2","A",2,1,13,0.07692,1,"{43}"
1339,1,10,0,0.0014583,"\int \frac{1}{c+d x} \, dx","Int[(c + d*x)^(-1),x]","\frac{\log (c+d x)}{d}","\frac{\log (c+d x)}{d}",1,"Log[c + d*x]/d","A",1,1,7,0.1429,1,"{31}"
1340,1,36,0,0.0076648,"\int \frac{1}{(a+b x) (c+d x)} \, dx","Int[1/((a + b*x)*(c + d*x)),x]","\frac{\log (a+b x)}{b c-a d}-\frac{\log (c+d x)}{b c-a d}","\frac{\log (a+b x)}{b c-a d}-\frac{\log (c+d x)}{b c-a d}",1,"Log[a + b*x]/(b*c - a*d) - Log[c + d*x]/(b*c - a*d)","A",3,2,15,0.1333,1,"{36, 31}"
1341,1,57,0,0.0317131,"\int \frac{1}{(a+b x)^2 (c+d x)} \, dx","Int[1/((a + b*x)^2*(c + d*x)),x]","-\frac{1}{(a+b x) (b c-a d)}-\frac{d \log (a+b x)}{(b c-a d)^2}+\frac{d \log (c+d x)}{(b c-a d)^2}","-\frac{1}{(a+b x) (b c-a d)}-\frac{d \log (a+b x)}{(b c-a d)^2}+\frac{d \log (c+d x)}{(b c-a d)^2}",1,"-(1/((b*c - a*d)*(a + b*x))) - (d*Log[a + b*x])/(b*c - a*d)^2 + (d*Log[c + d*x])/(b*c - a*d)^2","A",2,1,15,0.06667,1,"{44}"
1342,1,82,0,0.0454462,"\int \frac{1}{(a+b x)^3 (c+d x)} \, dx","Int[1/((a + b*x)^3*(c + d*x)),x]","\frac{d^2 \log (a+b x)}{(b c-a d)^3}-\frac{d^2 \log (c+d x)}{(b c-a d)^3}+\frac{d}{(a+b x) (b c-a d)^2}-\frac{1}{2 (a+b x)^2 (b c-a d)}","\frac{d^2 \log (a+b x)}{(b c-a d)^3}-\frac{d^2 \log (c+d x)}{(b c-a d)^3}+\frac{d}{(a+b x) (b c-a d)^2}-\frac{1}{2 (a+b x)^2 (b c-a d)}",1,"-1/(2*(b*c - a*d)*(a + b*x)^2) + d/((b*c - a*d)^2*(a + b*x)) + (d^2*Log[a + b*x])/(b*c - a*d)^3 - (d^2*Log[c + d*x])/(b*c - a*d)^3","A",2,1,15,0.06667,1,"{44}"
1343,1,130,0,0.1391649,"\int \frac{(a+b x)^5}{(c+d x)^2} \, dx","Int[(a + b*x)^5/(c + d*x)^2,x]","-\frac{5 b^4 (c+d x)^3 (b c-a d)}{3 d^6}+\frac{5 b^3 (c+d x)^2 (b c-a d)^2}{d^6}-\frac{10 b^2 x (b c-a d)^3}{d^5}+\frac{(b c-a d)^5}{d^6 (c+d x)}+\frac{5 b (b c-a d)^4 \log (c+d x)}{d^6}+\frac{b^5 (c+d x)^4}{4 d^6}","-\frac{5 b^4 (c+d x)^3 (b c-a d)}{3 d^6}+\frac{5 b^3 (c+d x)^2 (b c-a d)^2}{d^6}-\frac{10 b^2 x (b c-a d)^3}{d^5}+\frac{(b c-a d)^5}{d^6 (c+d x)}+\frac{5 b (b c-a d)^4 \log (c+d x)}{d^6}+\frac{b^5 (c+d x)^4}{4 d^6}",1,"(-10*b^2*(b*c - a*d)^3*x)/d^5 + (b*c - a*d)^5/(d^6*(c + d*x)) + (5*b^3*(b*c - a*d)^2*(c + d*x)^2)/d^6 - (5*b^4*(b*c - a*d)*(c + d*x)^3)/(3*d^6) + (b^5*(c + d*x)^4)/(4*d^6) + (5*b*(b*c - a*d)^4*Log[c + d*x])/d^6","A",2,1,15,0.06667,1,"{43}"
1344,1,104,0,0.100315,"\int \frac{(a+b x)^4}{(c+d x)^2} \, dx","Int[(a + b*x)^4/(c + d*x)^2,x]","-\frac{2 b^3 (c+d x)^2 (b c-a d)}{d^5}+\frac{6 b^2 x (b c-a d)^2}{d^4}-\frac{(b c-a d)^4}{d^5 (c+d x)}-\frac{4 b (b c-a d)^3 \log (c+d x)}{d^5}+\frac{b^4 (c+d x)^3}{3 d^5}","-\frac{2 b^3 (c+d x)^2 (b c-a d)}{d^5}+\frac{6 b^2 x (b c-a d)^2}{d^4}-\frac{(b c-a d)^4}{d^5 (c+d x)}-\frac{4 b (b c-a d)^3 \log (c+d x)}{d^5}+\frac{b^4 (c+d x)^3}{3 d^5}",1,"(6*b^2*(b*c - a*d)^2*x)/d^4 - (b*c - a*d)^4/(d^5*(c + d*x)) - (2*b^3*(b*c - a*d)*(c + d*x)^2)/d^5 + (b^4*(c + d*x)^3)/(3*d^5) - (4*b*(b*c - a*d)^3*Log[c + d*x])/d^5","A",2,1,15,0.06667,1,"{43}"
1345,1,75,0,0.0621689,"\int \frac{(a+b x)^3}{(c+d x)^2} \, dx","Int[(a + b*x)^3/(c + d*x)^2,x]","-\frac{b^2 x (2 b c-3 a d)}{d^3}+\frac{(b c-a d)^3}{d^4 (c+d x)}+\frac{3 b (b c-a d)^2 \log (c+d x)}{d^4}+\frac{b^3 x^2}{2 d^2}","-\frac{b^2 x (2 b c-3 a d)}{d^3}+\frac{(b c-a d)^3}{d^4 (c+d x)}+\frac{3 b (b c-a d)^2 \log (c+d x)}{d^4}+\frac{b^3 x^2}{2 d^2}",1,"-((b^2*(2*b*c - 3*a*d)*x)/d^3) + (b^3*x^2)/(2*d^2) + (b*c - a*d)^3/(d^4*(c + d*x)) + (3*b*(b*c - a*d)^2*Log[c + d*x])/d^4","A",2,1,15,0.06667,1,"{43}"
1346,1,51,0,0.0385264,"\int \frac{(a+b x)^2}{(c+d x)^2} \, dx","Int[(a + b*x)^2/(c + d*x)^2,x]","-\frac{(b c-a d)^2}{d^3 (c+d x)}-\frac{2 b (b c-a d) \log (c+d x)}{d^3}+\frac{b^2 x}{d^2}","-\frac{(b c-a d)^2}{d^3 (c+d x)}-\frac{2 b (b c-a d) \log (c+d x)}{d^3}+\frac{b^2 x}{d^2}",1,"(b^2*x)/d^2 - (b*c - a*d)^2/(d^3*(c + d*x)) - (2*b*(b*c - a*d)*Log[c + d*x])/d^3","A",2,1,15,0.06667,1,"{43}"
1347,1,31,0,0.0208401,"\int \frac{a+b x}{(c+d x)^2} \, dx","Int[(a + b*x)/(c + d*x)^2,x]","\frac{b c-a d}{d^2 (c+d x)}+\frac{b \log (c+d x)}{d^2}","\frac{b c-a d}{d^2 (c+d x)}+\frac{b \log (c+d x)}{d^2}",1,"(b*c - a*d)/(d^2*(c + d*x)) + (b*Log[c + d*x])/d^2","A",2,1,13,0.07692,1,"{43}"
1348,1,12,0,0.0016551,"\int \frac{1}{(c+d x)^2} \, dx","Int[(c + d*x)^(-2),x]","-\frac{1}{d (c+d x)}","-\frac{1}{d (c+d x)}",1,"-(1/(d*(c + d*x)))","A",1,1,7,0.1429,1,"{32}"
1349,1,56,0,0.0322105,"\int \frac{1}{(a+b x) (c+d x)^2} \, dx","Int[1/((a + b*x)*(c + d*x)^2),x]","\frac{1}{(c+d x) (b c-a d)}+\frac{b \log (a+b x)}{(b c-a d)^2}-\frac{b \log (c+d x)}{(b c-a d)^2}","\frac{1}{(c+d x) (b c-a d)}+\frac{b \log (a+b x)}{(b c-a d)^2}-\frac{b \log (c+d x)}{(b c-a d)^2}",1,"1/((b*c - a*d)*(c + d*x)) + (b*Log[a + b*x])/(b*c - a*d)^2 - (b*Log[c + d*x])/(b*c - a*d)^2","A",2,1,15,0.06667,1,"{44}"
1350,1,81,0,0.0496297,"\int \frac{1}{(a+b x)^2 (c+d x)^2} \, dx","Int[1/((a + b*x)^2*(c + d*x)^2),x]","-\frac{b}{(a+b x) (b c-a d)^2}-\frac{d}{(c+d x) (b c-a d)^2}-\frac{2 b d \log (a+b x)}{(b c-a d)^3}+\frac{2 b d \log (c+d x)}{(b c-a d)^3}","-\frac{b}{(a+b x) (b c-a d)^2}-\frac{d}{(c+d x) (b c-a d)^2}-\frac{2 b d \log (a+b x)}{(b c-a d)^3}+\frac{2 b d \log (c+d x)}{(b c-a d)^3}",1,"-(b/((b*c - a*d)^2*(a + b*x))) - d/((b*c - a*d)^2*(c + d*x)) - (2*b*d*Log[a + b*x])/(b*c - a*d)^3 + (2*b*d*Log[c + d*x])/(b*c - a*d)^3","A",2,1,15,0.06667,1,"{44}"
1351,1,109,0,0.0760537,"\int \frac{1}{(a+b x)^3 (c+d x)^2} \, dx","Int[1/((a + b*x)^3*(c + d*x)^2),x]","\frac{d^2}{(c+d x) (b c-a d)^3}+\frac{3 b d^2 \log (a+b x)}{(b c-a d)^4}-\frac{3 b d^2 \log (c+d x)}{(b c-a d)^4}+\frac{2 b d}{(a+b x) (b c-a d)^3}-\frac{b}{2 (a+b x)^2 (b c-a d)^2}","\frac{d^2}{(c+d x) (b c-a d)^3}+\frac{3 b d^2 \log (a+b x)}{(b c-a d)^4}-\frac{3 b d^2 \log (c+d x)}{(b c-a d)^4}+\frac{2 b d}{(a+b x) (b c-a d)^3}-\frac{b}{2 (a+b x)^2 (b c-a d)^2}",1,"-b/(2*(b*c - a*d)^2*(a + b*x)^2) + (2*b*d)/((b*c - a*d)^3*(a + b*x)) + d^2/((b*c - a*d)^3*(c + d*x)) + (3*b*d^2*Log[a + b*x])/(b*c - a*d)^4 - (3*b*d^2*Log[c + d*x])/(b*c - a*d)^4","A",2,1,15,0.06667,1,"{44}"
1352,1,158,0,0.2023703,"\int \frac{(a+b x)^6}{(c+d x)^3} \, dx","Int[(a + b*x)^6/(c + d*x)^3,x]","-\frac{2 b^5 (c+d x)^3 (b c-a d)}{d^7}+\frac{15 b^4 (c+d x)^2 (b c-a d)^2}{2 d^7}-\frac{20 b^3 x (b c-a d)^3}{d^6}+\frac{15 b^2 (b c-a d)^4 \log (c+d x)}{d^7}+\frac{6 b (b c-a d)^5}{d^7 (c+d x)}-\frac{(b c-a d)^6}{2 d^7 (c+d x)^2}+\frac{b^6 (c+d x)^4}{4 d^7}","-\frac{2 b^5 (c+d x)^3 (b c-a d)}{d^7}+\frac{15 b^4 (c+d x)^2 (b c-a d)^2}{2 d^7}-\frac{20 b^3 x (b c-a d)^3}{d^6}+\frac{15 b^2 (b c-a d)^4 \log (c+d x)}{d^7}+\frac{6 b (b c-a d)^5}{d^7 (c+d x)}-\frac{(b c-a d)^6}{2 d^7 (c+d x)^2}+\frac{b^6 (c+d x)^4}{4 d^7}",1,"(-20*b^3*(b*c - a*d)^3*x)/d^6 - (b*c - a*d)^6/(2*d^7*(c + d*x)^2) + (6*b*(b*c - a*d)^5)/(d^7*(c + d*x)) + (15*b^4*(b*c - a*d)^2*(c + d*x)^2)/(2*d^7) - (2*b^5*(b*c - a*d)*(c + d*x)^3)/d^7 + (b^6*(c + d*x)^4)/(4*d^7) + (15*b^2*(b*c - a*d)^4*Log[c + d*x])/d^7","A",2,1,15,0.06667,1,"{43}"
1353,1,133,0,0.1206187,"\int \frac{(a+b x)^5}{(c+d x)^3} \, dx","Int[(a + b*x)^5/(c + d*x)^3,x]","-\frac{5 b^4 (c+d x)^2 (b c-a d)}{2 d^6}+\frac{10 b^3 x (b c-a d)^2}{d^5}-\frac{10 b^2 (b c-a d)^3 \log (c+d x)}{d^6}-\frac{5 b (b c-a d)^4}{d^6 (c+d x)}+\frac{(b c-a d)^5}{2 d^6 (c+d x)^2}+\frac{b^5 (c+d x)^3}{3 d^6}","-\frac{5 b^4 (c+d x)^2 (b c-a d)}{2 d^6}+\frac{10 b^3 x (b c-a d)^2}{d^5}-\frac{10 b^2 (b c-a d)^3 \log (c+d x)}{d^6}-\frac{5 b (b c-a d)^4}{d^6 (c+d x)}+\frac{(b c-a d)^5}{2 d^6 (c+d x)^2}+\frac{b^5 (c+d x)^3}{3 d^6}",1,"(10*b^3*(b*c - a*d)^2*x)/d^5 + (b*c - a*d)^5/(2*d^6*(c + d*x)^2) - (5*b*(b*c - a*d)^4)/(d^6*(c + d*x)) - (5*b^4*(b*c - a*d)*(c + d*x)^2)/(2*d^6) + (b^5*(c + d*x)^3)/(3*d^6) - (10*b^2*(b*c - a*d)^3*Log[c + d*x])/d^6","A",2,1,15,0.06667,1,"{43}"
1354,1,103,0,0.0871533,"\int \frac{(a+b x)^4}{(c+d x)^3} \, dx","Int[(a + b*x)^4/(c + d*x)^3,x]","-\frac{b^3 x (3 b c-4 a d)}{d^4}+\frac{6 b^2 (b c-a d)^2 \log (c+d x)}{d^5}+\frac{4 b (b c-a d)^3}{d^5 (c+d x)}-\frac{(b c-a d)^4}{2 d^5 (c+d x)^2}+\frac{b^4 x^2}{2 d^3}","-\frac{b^3 x (3 b c-4 a d)}{d^4}+\frac{6 b^2 (b c-a d)^2 \log (c+d x)}{d^5}+\frac{4 b (b c-a d)^3}{d^5 (c+d x)}-\frac{(b c-a d)^4}{2 d^5 (c+d x)^2}+\frac{b^4 x^2}{2 d^3}",1,"-((b^3*(3*b*c - 4*a*d)*x)/d^4) + (b^4*x^2)/(2*d^3) - (b*c - a*d)^4/(2*d^5*(c + d*x)^2) + (4*b*(b*c - a*d)^3)/(d^5*(c + d*x)) + (6*b^2*(b*c - a*d)^2*Log[c + d*x])/d^5","A",2,1,15,0.06667,1,"{43}"
1355,1,78,0,0.055235,"\int \frac{(a+b x)^3}{(c+d x)^3} \, dx","Int[(a + b*x)^3/(c + d*x)^3,x]","-\frac{3 b^2 (b c-a d) \log (c+d x)}{d^4}-\frac{3 b (b c-a d)^2}{d^4 (c+d x)}+\frac{(b c-a d)^3}{2 d^4 (c+d x)^2}+\frac{b^3 x}{d^3}","-\frac{3 b^2 (b c-a d) \log (c+d x)}{d^4}-\frac{3 b (b c-a d)^2}{d^4 (c+d x)}+\frac{(b c-a d)^3}{2 d^4 (c+d x)^2}+\frac{b^3 x}{d^3}",1,"(b^3*x)/d^3 + (b*c - a*d)^3/(2*d^4*(c + d*x)^2) - (3*b*(b*c - a*d)^2)/(d^4*(c + d*x)) - (3*b^2*(b*c - a*d)*Log[c + d*x])/d^4","A",2,1,15,0.06667,1,"{43}"
1356,1,59,0,0.0382741,"\int \frac{(a+b x)^2}{(c+d x)^3} \, dx","Int[(a + b*x)^2/(c + d*x)^3,x]","\frac{2 b (b c-a d)}{d^3 (c+d x)}-\frac{(b c-a d)^2}{2 d^3 (c+d x)^2}+\frac{b^2 \log (c+d x)}{d^3}","\frac{2 b (b c-a d)}{d^3 (c+d x)}-\frac{(b c-a d)^2}{2 d^3 (c+d x)^2}+\frac{b^2 \log (c+d x)}{d^3}",1,"-(b*c - a*d)^2/(2*d^3*(c + d*x)^2) + (2*b*(b*c - a*d))/(d^3*(c + d*x)) + (b^2*Log[c + d*x])/d^3","A",2,1,15,0.06667,1,"{43}"
1357,1,28,0,0.0029068,"\int \frac{a+b x}{(c+d x)^3} \, dx","Int[(a + b*x)/(c + d*x)^3,x]","\frac{(a+b x)^2}{2 (c+d x)^2 (b c-a d)}","\frac{(a+b x)^2}{2 (c+d x)^2 (b c-a d)}",1,"(a + b*x)^2/(2*(b*c - a*d)*(c + d*x)^2)","A",1,1,13,0.07692,1,"{37}"
1358,1,14,0,0.0017357,"\int \frac{1}{(c+d x)^3} \, dx","Int[(c + d*x)^(-3),x]","-\frac{1}{2 d (c+d x)^2}","-\frac{1}{2 d (c+d x)^2}",1,"-1/(2*d*(c + d*x)^2)","A",1,1,7,0.1429,1,"{32}"
1359,1,82,0,0.0459267,"\int \frac{1}{(a+b x) (c+d x)^3} \, dx","Int[1/((a + b*x)*(c + d*x)^3),x]","\frac{b^2 \log (a+b x)}{(b c-a d)^3}-\frac{b^2 \log (c+d x)}{(b c-a d)^3}+\frac{b}{(c+d x) (b c-a d)^2}+\frac{1}{2 (c+d x)^2 (b c-a d)}","\frac{b^2 \log (a+b x)}{(b c-a d)^3}-\frac{b^2 \log (c+d x)}{(b c-a d)^3}+\frac{b}{(c+d x) (b c-a d)^2}+\frac{1}{2 (c+d x)^2 (b c-a d)}",1,"1/(2*(b*c - a*d)*(c + d*x)^2) + b/((b*c - a*d)^2*(c + d*x)) + (b^2*Log[a + b*x])/(b*c - a*d)^3 - (b^2*Log[c + d*x])/(b*c - a*d)^3","A",2,1,15,0.06667,1,"{44}"
1360,1,110,0,0.0741628,"\int \frac{1}{(a+b x)^2 (c+d x)^3} \, dx","Int[1/((a + b*x)^2*(c + d*x)^3),x]","-\frac{b^2}{(a+b x) (b c-a d)^3}-\frac{3 b^2 d \log (a+b x)}{(b c-a d)^4}+\frac{3 b^2 d \log (c+d x)}{(b c-a d)^4}-\frac{2 b d}{(c+d x) (b c-a d)^3}-\frac{d}{2 (c+d x)^2 (b c-a d)^2}","-\frac{b^2}{(a+b x) (b c-a d)^3}-\frac{3 b^2 d \log (a+b x)}{(b c-a d)^4}+\frac{3 b^2 d \log (c+d x)}{(b c-a d)^4}-\frac{2 b d}{(c+d x) (b c-a d)^3}-\frac{d}{2 (c+d x)^2 (b c-a d)^2}",1,"-(b^2/((b*c - a*d)^3*(a + b*x))) - d/(2*(b*c - a*d)^2*(c + d*x)^2) - (2*b*d)/((b*c - a*d)^3*(c + d*x)) - (3*b^2*d*Log[a + b*x])/(b*c - a*d)^4 + (3*b^2*d*Log[c + d*x])/(b*c - a*d)^4","A",2,1,15,0.06667,1,"{44}"
1361,1,143,0,0.1017621,"\int \frac{1}{(a+b x)^3 (c+d x)^3} \, dx","Int[1/((a + b*x)^3*(c + d*x)^3),x]","\frac{6 b^2 d^2 \log (a+b x)}{(b c-a d)^5}-\frac{6 b^2 d^2 \log (c+d x)}{(b c-a d)^5}+\frac{3 b^2 d}{(a+b x) (b c-a d)^4}-\frac{b^2}{2 (a+b x)^2 (b c-a d)^3}+\frac{3 b d^2}{(c+d x) (b c-a d)^4}+\frac{d^2}{2 (c+d x)^2 (b c-a d)^3}","\frac{6 b^2 d^2 \log (a+b x)}{(b c-a d)^5}-\frac{6 b^2 d^2 \log (c+d x)}{(b c-a d)^5}+\frac{3 b^2 d}{(a+b x) (b c-a d)^4}-\frac{b^2}{2 (a+b x)^2 (b c-a d)^3}+\frac{3 b d^2}{(c+d x) (b c-a d)^4}+\frac{d^2}{2 (c+d x)^2 (b c-a d)^3}",1,"-b^2/(2*(b*c - a*d)^3*(a + b*x)^2) + (3*b^2*d)/((b*c - a*d)^4*(a + b*x)) + d^2/(2*(b*c - a*d)^3*(c + d*x)^2) + (3*b*d^2)/((b*c - a*d)^4*(c + d*x)) + (6*b^2*d^2*Log[a + b*x])/(b*c - a*d)^5 - (6*b^2*d^2*Log[c + d*x])/(b*c - a*d)^5","A",2,1,15,0.06667,1,"{44}"
1362,1,232,0,0.3568822,"\int \frac{(a+b x)^9}{(c+d x)^8} \, dx","Int[(a + b*x)^9/(c + d*x)^8,x]","-\frac{b^8 x (8 b c-9 a d)}{d^9}+\frac{84 b^6 (b c-a d)^3}{d^{10} (c+d x)}-\frac{63 b^5 (b c-a d)^4}{d^{10} (c+d x)^2}+\frac{42 b^4 (b c-a d)^5}{d^{10} (c+d x)^3}-\frac{21 b^3 (b c-a d)^6}{d^{10} (c+d x)^4}+\frac{36 b^2 (b c-a d)^7}{5 d^{10} (c+d x)^5}+\frac{36 b^7 (b c-a d)^2 \log (c+d x)}{d^{10}}-\frac{3 b (b c-a d)^8}{2 d^{10} (c+d x)^6}+\frac{(b c-a d)^9}{7 d^{10} (c+d x)^7}+\frac{b^9 x^2}{2 d^8}","-\frac{b^8 x (8 b c-9 a d)}{d^9}+\frac{84 b^6 (b c-a d)^3}{d^{10} (c+d x)}-\frac{63 b^5 (b c-a d)^4}{d^{10} (c+d x)^2}+\frac{42 b^4 (b c-a d)^5}{d^{10} (c+d x)^3}-\frac{21 b^3 (b c-a d)^6}{d^{10} (c+d x)^4}+\frac{36 b^2 (b c-a d)^7}{5 d^{10} (c+d x)^5}+\frac{36 b^7 (b c-a d)^2 \log (c+d x)}{d^{10}}-\frac{3 b (b c-a d)^8}{2 d^{10} (c+d x)^6}+\frac{(b c-a d)^9}{7 d^{10} (c+d x)^7}+\frac{b^9 x^2}{2 d^8}",1,"-((b^8*(8*b*c - 9*a*d)*x)/d^9) + (b^9*x^2)/(2*d^8) + (b*c - a*d)^9/(7*d^10*(c + d*x)^7) - (3*b*(b*c - a*d)^8)/(2*d^10*(c + d*x)^6) + (36*b^2*(b*c - a*d)^7)/(5*d^10*(c + d*x)^5) - (21*b^3*(b*c - a*d)^6)/(d^10*(c + d*x)^4) + (42*b^4*(b*c - a*d)^5)/(d^10*(c + d*x)^3) - (63*b^5*(b*c - a*d)^4)/(d^10*(c + d*x)^2) + (84*b^6*(b*c - a*d)^3)/(d^10*(c + d*x)) + (36*b^7*(b*c - a*d)^2*Log[c + d*x])/d^10","A",2,1,15,0.06667,1,"{43}"
1363,1,209,0,0.2775553,"\int \frac{(a+b x)^8}{(c+d x)^8} \, dx","Int[(a + b*x)^8/(c + d*x)^8,x]","-\frac{28 b^6 (b c-a d)^2}{d^9 (c+d x)}+\frac{28 b^5 (b c-a d)^3}{d^9 (c+d x)^2}-\frac{70 b^4 (b c-a d)^4}{3 d^9 (c+d x)^3}+\frac{14 b^3 (b c-a d)^5}{d^9 (c+d x)^4}-\frac{28 b^2 (b c-a d)^6}{5 d^9 (c+d x)^5}-\frac{8 b^7 (b c-a d) \log (c+d x)}{d^9}+\frac{4 b (b c-a d)^7}{3 d^9 (c+d x)^6}-\frac{(b c-a d)^8}{7 d^9 (c+d x)^7}+\frac{b^8 x}{d^8}","-\frac{28 b^6 (b c-a d)^2}{d^9 (c+d x)}+\frac{28 b^5 (b c-a d)^3}{d^9 (c+d x)^2}-\frac{70 b^4 (b c-a d)^4}{3 d^9 (c+d x)^3}+\frac{14 b^3 (b c-a d)^5}{d^9 (c+d x)^4}-\frac{28 b^2 (b c-a d)^6}{5 d^9 (c+d x)^5}-\frac{8 b^7 (b c-a d) \log (c+d x)}{d^9}+\frac{4 b (b c-a d)^7}{3 d^9 (c+d x)^6}-\frac{(b c-a d)^8}{7 d^9 (c+d x)^7}+\frac{b^8 x}{d^8}",1,"(b^8*x)/d^8 - (b*c - a*d)^8/(7*d^9*(c + d*x)^7) + (4*b*(b*c - a*d)^7)/(3*d^9*(c + d*x)^6) - (28*b^2*(b*c - a*d)^6)/(5*d^9*(c + d*x)^5) + (14*b^3*(b*c - a*d)^5)/(d^9*(c + d*x)^4) - (70*b^4*(b*c - a*d)^4)/(3*d^9*(c + d*x)^3) + (28*b^5*(b*c - a*d)^3)/(d^9*(c + d*x)^2) - (28*b^6*(b*c - a*d)^2)/(d^9*(c + d*x)) - (8*b^7*(b*c - a*d)*Log[c + d*x])/d^9","A",2,1,15,0.06667,1,"{43}"
1364,1,194,0,0.209351,"\int \frac{(a+b x)^7}{(c+d x)^8} \, dx","Int[(a + b*x)^7/(c + d*x)^8,x]","\frac{7 b^6 (b c-a d)}{d^8 (c+d x)}-\frac{21 b^5 (b c-a d)^2}{2 d^8 (c+d x)^2}+\frac{35 b^4 (b c-a d)^3}{3 d^8 (c+d x)^3}-\frac{35 b^3 (b c-a d)^4}{4 d^8 (c+d x)^4}+\frac{21 b^2 (b c-a d)^5}{5 d^8 (c+d x)^5}-\frac{7 b (b c-a d)^6}{6 d^8 (c+d x)^6}+\frac{(b c-a d)^7}{7 d^8 (c+d x)^7}+\frac{b^7 \log (c+d x)}{d^8}","\frac{7 b^6 (b c-a d)}{d^8 (c+d x)}-\frac{21 b^5 (b c-a d)^2}{2 d^8 (c+d x)^2}+\frac{35 b^4 (b c-a d)^3}{3 d^8 (c+d x)^3}-\frac{35 b^3 (b c-a d)^4}{4 d^8 (c+d x)^4}+\frac{21 b^2 (b c-a d)^5}{5 d^8 (c+d x)^5}-\frac{7 b (b c-a d)^6}{6 d^8 (c+d x)^6}+\frac{(b c-a d)^7}{7 d^8 (c+d x)^7}+\frac{b^7 \log (c+d x)}{d^8}",1,"(b*c - a*d)^7/(7*d^8*(c + d*x)^7) - (7*b*(b*c - a*d)^6)/(6*d^8*(c + d*x)^6) + (21*b^2*(b*c - a*d)^5)/(5*d^8*(c + d*x)^5) - (35*b^3*(b*c - a*d)^4)/(4*d^8*(c + d*x)^4) + (35*b^4*(b*c - a*d)^3)/(3*d^8*(c + d*x)^3) - (21*b^5*(b*c - a*d)^2)/(2*d^8*(c + d*x)^2) + (7*b^6*(b*c - a*d))/(d^8*(c + d*x)) + (b^7*Log[c + d*x])/d^8","A",2,1,15,0.06667,1,"{43}"
1365,1,28,0,0.0029524,"\int \frac{(a+b x)^6}{(c+d x)^8} \, dx","Int[(a + b*x)^6/(c + d*x)^8,x]","\frac{(a+b x)^7}{7 (c+d x)^7 (b c-a d)}","\frac{(a+b x)^7}{7 (c+d x)^7 (b c-a d)}",1,"(a + b*x)^7/(7*(b*c - a*d)*(c + d*x)^7)","A",1,1,15,0.06667,1,"{37}"
1366,1,58,0,0.0112179,"\int \frac{(a+b x)^5}{(c+d x)^8} \, dx","Int[(a + b*x)^5/(c + d*x)^8,x]","\frac{b (a+b x)^6}{42 (c+d x)^6 (b c-a d)^2}+\frac{(a+b x)^6}{7 (c+d x)^7 (b c-a d)}","\frac{b (a+b x)^6}{42 (c+d x)^6 (b c-a d)^2}+\frac{(a+b x)^6}{7 (c+d x)^7 (b c-a d)}",1,"(a + b*x)^6/(7*(b*c - a*d)*(c + d*x)^7) + (b*(a + b*x)^6)/(42*(b*c - a*d)^2*(c + d*x)^6)","A",2,2,15,0.1333,1,"{45, 37}"
1367,1,89,0,0.0192818,"\int \frac{(a+b x)^4}{(c+d x)^8} \, dx","Int[(a + b*x)^4/(c + d*x)^8,x]","\frac{b^2 (a+b x)^5}{105 (c+d x)^5 (b c-a d)^3}+\frac{b (a+b x)^5}{21 (c+d x)^6 (b c-a d)^2}+\frac{(a+b x)^5}{7 (c+d x)^7 (b c-a d)}","\frac{b^2 (a+b x)^5}{105 (c+d x)^5 (b c-a d)^3}+\frac{b (a+b x)^5}{21 (c+d x)^6 (b c-a d)^2}+\frac{(a+b x)^5}{7 (c+d x)^7 (b c-a d)}",1,"(a + b*x)^5/(7*(b*c - a*d)*(c + d*x)^7) + (b*(a + b*x)^5)/(21*(b*c - a*d)^2*(c + d*x)^6) + (b^2*(a + b*x)^5)/(105*(b*c - a*d)^3*(c + d*x)^5)","A",3,2,15,0.1333,1,"{45, 37}"
1368,1,92,0,0.057465,"\int \frac{(a+b x)^3}{(c+d x)^8} \, dx","Int[(a + b*x)^3/(c + d*x)^8,x]","\frac{3 b^2 (b c-a d)}{5 d^4 (c+d x)^5}-\frac{b (b c-a d)^2}{2 d^4 (c+d x)^6}+\frac{(b c-a d)^3}{7 d^4 (c+d x)^7}-\frac{b^3}{4 d^4 (c+d x)^4}","\frac{3 b^2 (b c-a d)}{5 d^4 (c+d x)^5}-\frac{b (b c-a d)^2}{2 d^4 (c+d x)^6}+\frac{(b c-a d)^3}{7 d^4 (c+d x)^7}-\frac{b^3}{4 d^4 (c+d x)^4}",1,"(b*c - a*d)^3/(7*d^4*(c + d*x)^7) - (b*(b*c - a*d)^2)/(2*d^4*(c + d*x)^6) + (3*b^2*(b*c - a*d))/(5*d^4*(c + d*x)^5) - b^3/(4*d^4*(c + d*x)^4)","A",2,1,15,0.06667,1,"{43}"
1369,1,65,0,0.0398526,"\int \frac{(a+b x)^2}{(c+d x)^8} \, dx","Int[(a + b*x)^2/(c + d*x)^8,x]","\frac{b (b c-a d)}{3 d^3 (c+d x)^6}-\frac{(b c-a d)^2}{7 d^3 (c+d x)^7}-\frac{b^2}{5 d^3 (c+d x)^5}","\frac{b (b c-a d)}{3 d^3 (c+d x)^6}-\frac{(b c-a d)^2}{7 d^3 (c+d x)^7}-\frac{b^2}{5 d^3 (c+d x)^5}",1,"-(b*c - a*d)^2/(7*d^3*(c + d*x)^7) + (b*(b*c - a*d))/(3*d^3*(c + d*x)^6) - b^2/(5*d^3*(c + d*x)^5)","A",2,1,15,0.06667,1,"{43}"
1370,1,38,0,0.0220319,"\int \frac{a+b x}{(c+d x)^8} \, dx","Int[(a + b*x)/(c + d*x)^8,x]","\frac{b c-a d}{7 d^2 (c+d x)^7}-\frac{b}{6 d^2 (c+d x)^6}","\frac{b c-a d}{7 d^2 (c+d x)^7}-\frac{b}{6 d^2 (c+d x)^6}",1,"(b*c - a*d)/(7*d^2*(c + d*x)^7) - b/(6*d^2*(c + d*x)^6)","A",2,1,13,0.07692,1,"{43}"
1371,1,14,0,0.0016125,"\int \frac{1}{(c+d x)^8} \, dx","Int[(c + d*x)^(-8),x]","-\frac{1}{7 d (c+d x)^7}","-\frac{1}{7 d (c+d x)^7}",1,"-1/(7*d*(c + d*x)^7)","A",1,1,7,0.1429,1,"{32}"
1372,1,202,0,0.1691232,"\int \frac{1}{(a+b x) (c+d x)^8} \, dx","Int[1/((a + b*x)*(c + d*x)^8),x]","\frac{b^6}{(c+d x) (b c-a d)^7}+\frac{b^5}{2 (c+d x)^2 (b c-a d)^6}+\frac{b^4}{3 (c+d x)^3 (b c-a d)^5}+\frac{b^3}{4 (c+d x)^4 (b c-a d)^4}+\frac{b^2}{5 (c+d x)^5 (b c-a d)^3}+\frac{b^7 \log (a+b x)}{(b c-a d)^8}-\frac{b^7 \log (c+d x)}{(b c-a d)^8}+\frac{b}{6 (c+d x)^6 (b c-a d)^2}+\frac{1}{7 (c+d x)^7 (b c-a d)}","\frac{b^6}{(c+d x) (b c-a d)^7}+\frac{b^5}{2 (c+d x)^2 (b c-a d)^6}+\frac{b^4}{3 (c+d x)^3 (b c-a d)^5}+\frac{b^3}{4 (c+d x)^4 (b c-a d)^4}+\frac{b^2}{5 (c+d x)^5 (b c-a d)^3}+\frac{b^7 \log (a+b x)}{(b c-a d)^8}-\frac{b^7 \log (c+d x)}{(b c-a d)^8}+\frac{b}{6 (c+d x)^6 (b c-a d)^2}+\frac{1}{7 (c+d x)^7 (b c-a d)}",1,"1/(7*(b*c - a*d)*(c + d*x)^7) + b/(6*(b*c - a*d)^2*(c + d*x)^6) + b^2/(5*(b*c - a*d)^3*(c + d*x)^5) + b^3/(4*(b*c - a*d)^4*(c + d*x)^4) + b^4/(3*(b*c - a*d)^5*(c + d*x)^3) + b^5/(2*(b*c - a*d)^6*(c + d*x)^2) + b^6/((b*c - a*d)^7*(c + d*x)) + (b^7*Log[a + b*x])/(b*c - a*d)^8 - (b^7*Log[c + d*x])/(b*c - a*d)^8","A",2,1,15,0.06667,1,"{44}"
1373,1,231,0,0.270129,"\int \frac{1}{(a+b x)^2 (c+d x)^8} \, dx","Int[1/((a + b*x)^2*(c + d*x)^8),x]","-\frac{b^7}{(a+b x) (b c-a d)^8}-\frac{7 b^6 d}{(c+d x) (b c-a d)^8}-\frac{3 b^5 d}{(c+d x)^2 (b c-a d)^7}-\frac{5 b^4 d}{3 (c+d x)^3 (b c-a d)^6}-\frac{b^3 d}{(c+d x)^4 (b c-a d)^5}-\frac{3 b^2 d}{5 (c+d x)^5 (b c-a d)^4}-\frac{8 b^7 d \log (a+b x)}{(b c-a d)^9}+\frac{8 b^7 d \log (c+d x)}{(b c-a d)^9}-\frac{b d}{3 (c+d x)^6 (b c-a d)^3}-\frac{d}{7 (c+d x)^7 (b c-a d)^2}","-\frac{b^7}{(a+b x) (b c-a d)^8}-\frac{7 b^6 d}{(c+d x) (b c-a d)^8}-\frac{3 b^5 d}{(c+d x)^2 (b c-a d)^7}-\frac{5 b^4 d}{3 (c+d x)^3 (b c-a d)^6}-\frac{b^3 d}{(c+d x)^4 (b c-a d)^5}-\frac{3 b^2 d}{5 (c+d x)^5 (b c-a d)^4}-\frac{8 b^7 d \log (a+b x)}{(b c-a d)^9}+\frac{8 b^7 d \log (c+d x)}{(b c-a d)^9}-\frac{b d}{3 (c+d x)^6 (b c-a d)^3}-\frac{d}{7 (c+d x)^7 (b c-a d)^2}",1,"-(b^7/((b*c - a*d)^8*(a + b*x))) - d/(7*(b*c - a*d)^2*(c + d*x)^7) - (b*d)/(3*(b*c - a*d)^3*(c + d*x)^6) - (3*b^2*d)/(5*(b*c - a*d)^4*(c + d*x)^5) - (b^3*d)/((b*c - a*d)^5*(c + d*x)^4) - (5*b^4*d)/(3*(b*c - a*d)^6*(c + d*x)^3) - (3*b^5*d)/((b*c - a*d)^7*(c + d*x)^2) - (7*b^6*d)/((b*c - a*d)^8*(c + d*x)) - (8*b^7*d*Log[a + b*x])/(b*c - a*d)^9 + (8*b^7*d*Log[c + d*x])/(b*c - a*d)^9","A",2,1,15,0.06667,1,"{44}"
1374,1,276,0,0.3560382,"\int \frac{1}{(a+b x)^3 (c+d x)^8} \, dx","Int[1/((a + b*x)^3*(c + d*x)^8),x]","\frac{28 b^6 d^2}{(c+d x) (b c-a d)^9}+\frac{21 b^5 d^2}{2 (c+d x)^2 (b c-a d)^8}+\frac{5 b^4 d^2}{(c+d x)^3 (b c-a d)^7}+\frac{5 b^3 d^2}{2 (c+d x)^4 (b c-a d)^6}+\frac{6 b^2 d^2}{5 (c+d x)^5 (b c-a d)^5}+\frac{36 b^7 d^2 \log (a+b x)}{(b c-a d)^{10}}-\frac{36 b^7 d^2 \log (c+d x)}{(b c-a d)^{10}}+\frac{8 b^7 d}{(a+b x) (b c-a d)^9}-\frac{b^7}{2 (a+b x)^2 (b c-a d)^8}+\frac{b d^2}{2 (c+d x)^6 (b c-a d)^4}+\frac{d^2}{7 (c+d x)^7 (b c-a d)^3}","\frac{28 b^6 d^2}{(c+d x) (b c-a d)^9}+\frac{21 b^5 d^2}{2 (c+d x)^2 (b c-a d)^8}+\frac{5 b^4 d^2}{(c+d x)^3 (b c-a d)^7}+\frac{5 b^3 d^2}{2 (c+d x)^4 (b c-a d)^6}+\frac{6 b^2 d^2}{5 (c+d x)^5 (b c-a d)^5}+\frac{36 b^7 d^2 \log (a+b x)}{(b c-a d)^{10}}-\frac{36 b^7 d^2 \log (c+d x)}{(b c-a d)^{10}}+\frac{8 b^7 d}{(a+b x) (b c-a d)^9}-\frac{b^7}{2 (a+b x)^2 (b c-a d)^8}+\frac{b d^2}{2 (c+d x)^6 (b c-a d)^4}+\frac{d^2}{7 (c+d x)^7 (b c-a d)^3}",1,"-b^7/(2*(b*c - a*d)^8*(a + b*x)^2) + (8*b^7*d)/((b*c - a*d)^9*(a + b*x)) + d^2/(7*(b*c - a*d)^3*(c + d*x)^7) + (b*d^2)/(2*(b*c - a*d)^4*(c + d*x)^6) + (6*b^2*d^2)/(5*(b*c - a*d)^5*(c + d*x)^5) + (5*b^3*d^2)/(2*(b*c - a*d)^6*(c + d*x)^4) + (5*b^4*d^2)/((b*c - a*d)^7*(c + d*x)^3) + (21*b^5*d^2)/(2*(b*c - a*d)^8*(c + d*x)^2) + (28*b^6*d^2)/((b*c - a*d)^9*(c + d*x)) + (36*b^7*d^2*Log[a + b*x])/(b*c - a*d)^10 - (36*b^7*d^2*Log[c + d*x])/(b*c - a*d)^10","A",2,1,15,0.06667,1,"{44}"
1375,1,156,0,0.0627983,"\int (a+b x)^5 \sqrt{c+d x} \, dx","Int[(a + b*x)^5*Sqrt[c + d*x],x]","-\frac{10 b^4 (c+d x)^{11/2} (b c-a d)}{11 d^6}+\frac{20 b^3 (c+d x)^{9/2} (b c-a d)^2}{9 d^6}-\frac{20 b^2 (c+d x)^{7/2} (b c-a d)^3}{7 d^6}+\frac{2 b (c+d x)^{5/2} (b c-a d)^4}{d^6}-\frac{2 (c+d x)^{3/2} (b c-a d)^5}{3 d^6}+\frac{2 b^5 (c+d x)^{13/2}}{13 d^6}","-\frac{10 b^4 (c+d x)^{11/2} (b c-a d)}{11 d^6}+\frac{20 b^3 (c+d x)^{9/2} (b c-a d)^2}{9 d^6}-\frac{20 b^2 (c+d x)^{7/2} (b c-a d)^3}{7 d^6}+\frac{2 b (c+d x)^{5/2} (b c-a d)^4}{d^6}-\frac{2 (c+d x)^{3/2} (b c-a d)^5}{3 d^6}+\frac{2 b^5 (c+d x)^{13/2}}{13 d^6}",1,"(-2*(b*c - a*d)^5*(c + d*x)^(3/2))/(3*d^6) + (2*b*(b*c - a*d)^4*(c + d*x)^(5/2))/d^6 - (20*b^2*(b*c - a*d)^3*(c + d*x)^(7/2))/(7*d^6) + (20*b^3*(b*c - a*d)^2*(c + d*x)^(9/2))/(9*d^6) - (10*b^4*(b*c - a*d)*(c + d*x)^(11/2))/(11*d^6) + (2*b^5*(c + d*x)^(13/2))/(13*d^6)","A",2,1,17,0.05882,1,"{43}"
1376,1,129,0,0.0519554,"\int (a+b x)^4 \sqrt{c+d x} \, dx","Int[(a + b*x)^4*Sqrt[c + d*x],x]","-\frac{8 b^3 (c+d x)^{9/2} (b c-a d)}{9 d^5}+\frac{12 b^2 (c+d x)^{7/2} (b c-a d)^2}{7 d^5}-\frac{8 b (c+d x)^{5/2} (b c-a d)^3}{5 d^5}+\frac{2 (c+d x)^{3/2} (b c-a d)^4}{3 d^5}+\frac{2 b^4 (c+d x)^{11/2}}{11 d^5}","-\frac{8 b^3 (c+d x)^{9/2} (b c-a d)}{9 d^5}+\frac{12 b^2 (c+d x)^{7/2} (b c-a d)^2}{7 d^5}-\frac{8 b (c+d x)^{5/2} (b c-a d)^3}{5 d^5}+\frac{2 (c+d x)^{3/2} (b c-a d)^4}{3 d^5}+\frac{2 b^4 (c+d x)^{11/2}}{11 d^5}",1,"(2*(b*c - a*d)^4*(c + d*x)^(3/2))/(3*d^5) - (8*b*(b*c - a*d)^3*(c + d*x)^(5/2))/(5*d^5) + (12*b^2*(b*c - a*d)^2*(c + d*x)^(7/2))/(7*d^5) - (8*b^3*(b*c - a*d)*(c + d*x)^(9/2))/(9*d^5) + (2*b^4*(c + d*x)^(11/2))/(11*d^5)","A",2,1,17,0.05882,1,"{43}"
1377,1,100,0,0.0355149,"\int (a+b x)^3 \sqrt{c+d x} \, dx","Int[(a + b*x)^3*Sqrt[c + d*x],x]","-\frac{6 b^2 (c+d x)^{7/2} (b c-a d)}{7 d^4}+\frac{6 b (c+d x)^{5/2} (b c-a d)^2}{5 d^4}-\frac{2 (c+d x)^{3/2} (b c-a d)^3}{3 d^4}+\frac{2 b^3 (c+d x)^{9/2}}{9 d^4}","-\frac{6 b^2 (c+d x)^{7/2} (b c-a d)}{7 d^4}+\frac{6 b (c+d x)^{5/2} (b c-a d)^2}{5 d^4}-\frac{2 (c+d x)^{3/2} (b c-a d)^3}{3 d^4}+\frac{2 b^3 (c+d x)^{9/2}}{9 d^4}",1,"(-2*(b*c - a*d)^3*(c + d*x)^(3/2))/(3*d^4) + (6*b*(b*c - a*d)^2*(c + d*x)^(5/2))/(5*d^4) - (6*b^2*(b*c - a*d)*(c + d*x)^(7/2))/(7*d^4) + (2*b^3*(c + d*x)^(9/2))/(9*d^4)","A",2,1,17,0.05882,1,"{43}"
1378,1,71,0,0.0247449,"\int (a+b x)^2 \sqrt{c+d x} \, dx","Int[(a + b*x)^2*Sqrt[c + d*x],x]","-\frac{4 b (c+d x)^{5/2} (b c-a d)}{5 d^3}+\frac{2 (c+d x)^{3/2} (b c-a d)^2}{3 d^3}+\frac{2 b^2 (c+d x)^{7/2}}{7 d^3}","-\frac{4 b (c+d x)^{5/2} (b c-a d)}{5 d^3}+\frac{2 (c+d x)^{3/2} (b c-a d)^2}{3 d^3}+\frac{2 b^2 (c+d x)^{7/2}}{7 d^3}",1,"(2*(b*c - a*d)^2*(c + d*x)^(3/2))/(3*d^3) - (4*b*(b*c - a*d)*(c + d*x)^(5/2))/(5*d^3) + (2*b^2*(c + d*x)^(7/2))/(7*d^3)","A",2,1,17,0.05882,1,"{43}"
1379,1,42,0,0.0139514,"\int (a+b x) \sqrt{c+d x} \, dx","Int[(a + b*x)*Sqrt[c + d*x],x]","\frac{2 b (c+d x)^{5/2}}{5 d^2}-\frac{2 (c+d x)^{3/2} (b c-a d)}{3 d^2}","\frac{2 b (c+d x)^{5/2}}{5 d^2}-\frac{2 (c+d x)^{3/2} (b c-a d)}{3 d^2}",1,"(-2*(b*c - a*d)*(c + d*x)^(3/2))/(3*d^2) + (2*b*(c + d*x)^(5/2))/(5*d^2)","A",2,1,15,0.06667,1,"{43}"
1380,1,16,0,0.0015467,"\int \sqrt{c+d x} \, dx","Int[Sqrt[c + d*x],x]","\frac{2 (c+d x)^{3/2}}{3 d}","\frac{2 (c+d x)^{3/2}}{3 d}",1,"(2*(c + d*x)^(3/2))/(3*d)","A",1,1,9,0.1111,1,"{32}"
1381,1,62,0,0.0527786,"\int \frac{\sqrt{c+d x}}{a+b x} \, dx","Int[Sqrt[c + d*x]/(a + b*x),x]","\frac{2 \sqrt{c+d x}}{b}-\frac{2 \sqrt{b c-a d} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{b^{3/2}}","\frac{2 \sqrt{c+d x}}{b}-\frac{2 \sqrt{b c-a d} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{b^{3/2}}",1,"(2*Sqrt[c + d*x])/b - (2*Sqrt[b*c - a*d]*ArcTanh[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[b*c - a*d]])/b^(3/2)","A",3,3,17,0.1765,1,"{50, 63, 208}"
1382,1,70,0,0.030299,"\int \frac{\sqrt{c+d x}}{(a+b x)^2} \, dx","Int[Sqrt[c + d*x]/(a + b*x)^2,x]","-\frac{d \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{b^{3/2} \sqrt{b c-a d}}-\frac{\sqrt{c+d x}}{b (a+b x)}","-\frac{d \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{b^{3/2} \sqrt{b c-a d}}-\frac{\sqrt{c+d x}}{b (a+b x)}",1,"-(Sqrt[c + d*x]/(b*(a + b*x))) - (d*ArcTanh[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[b*c - a*d]])/(b^(3/2)*Sqrt[b*c - a*d])","A",3,3,17,0.1765,1,"{47, 63, 208}"
1383,1,110,0,0.0780258,"\int \frac{\sqrt{c+d x}}{(a+b x)^3} \, dx","Int[Sqrt[c + d*x]/(a + b*x)^3,x]","\frac{d^2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{4 b^{3/2} (b c-a d)^{3/2}}-\frac{d \sqrt{c+d x}}{4 b (a+b x) (b c-a d)}-\frac{\sqrt{c+d x}}{2 b (a+b x)^2}","\frac{d^2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{4 b^{3/2} (b c-a d)^{3/2}}-\frac{d \sqrt{c+d x}}{4 b (a+b x) (b c-a d)}-\frac{\sqrt{c+d x}}{2 b (a+b x)^2}",1,"-Sqrt[c + d*x]/(2*b*(a + b*x)^2) - (d*Sqrt[c + d*x])/(4*b*(b*c - a*d)*(a + b*x)) + (d^2*ArcTanh[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[b*c - a*d]])/(4*b^(3/2)*(b*c - a*d)^(3/2))","A",4,4,17,0.2353,1,"{47, 51, 63, 208}"
1384,1,146,0,0.0978502,"\int \frac{\sqrt{c+d x}}{(a+b x)^4} \, dx","Int[Sqrt[c + d*x]/(a + b*x)^4,x]","-\frac{d^3 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{8 b^{3/2} (b c-a d)^{5/2}}+\frac{d^2 \sqrt{c+d x}}{8 b (a+b x) (b c-a d)^2}-\frac{d \sqrt{c+d x}}{12 b (a+b x)^2 (b c-a d)}-\frac{\sqrt{c+d x}}{3 b (a+b x)^3}","-\frac{d^3 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{8 b^{3/2} (b c-a d)^{5/2}}+\frac{d^2 \sqrt{c+d x}}{8 b (a+b x) (b c-a d)^2}-\frac{d \sqrt{c+d x}}{12 b (a+b x)^2 (b c-a d)}-\frac{\sqrt{c+d x}}{3 b (a+b x)^3}",1,"-Sqrt[c + d*x]/(3*b*(a + b*x)^3) - (d*Sqrt[c + d*x])/(12*b*(b*c - a*d)*(a + b*x)^2) + (d^2*Sqrt[c + d*x])/(8*b*(b*c - a*d)^2*(a + b*x)) - (d^3*ArcTanh[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[b*c - a*d]])/(8*b^(3/2)*(b*c - a*d)^(5/2))","A",5,4,17,0.2353,1,"{47, 51, 63, 208}"
1385,1,182,0,0.1229984,"\int \frac{\sqrt{c+d x}}{(a+b x)^5} \, dx","Int[Sqrt[c + d*x]/(a + b*x)^5,x]","\frac{5 d^4 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{64 b^{3/2} (b c-a d)^{7/2}}-\frac{5 d^3 \sqrt{c+d x}}{64 b (a+b x) (b c-a d)^3}+\frac{5 d^2 \sqrt{c+d x}}{96 b (a+b x)^2 (b c-a d)^2}-\frac{d \sqrt{c+d x}}{24 b (a+b x)^3 (b c-a d)}-\frac{\sqrt{c+d x}}{4 b (a+b x)^4}","\frac{5 d^4 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{64 b^{3/2} (b c-a d)^{7/2}}-\frac{5 d^3 \sqrt{c+d x}}{64 b (a+b x) (b c-a d)^3}+\frac{5 d^2 \sqrt{c+d x}}{96 b (a+b x)^2 (b c-a d)^2}-\frac{d \sqrt{c+d x}}{24 b (a+b x)^3 (b c-a d)}-\frac{\sqrt{c+d x}}{4 b (a+b x)^4}",1,"-Sqrt[c + d*x]/(4*b*(a + b*x)^4) - (d*Sqrt[c + d*x])/(24*b*(b*c - a*d)*(a + b*x)^3) + (5*d^2*Sqrt[c + d*x])/(96*b*(b*c - a*d)^2*(a + b*x)^2) - (5*d^3*Sqrt[c + d*x])/(64*b*(b*c - a*d)^3*(a + b*x)) + (5*d^4*ArcTanh[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[b*c - a*d]])/(64*b^(3/2)*(b*c - a*d)^(7/2))","A",6,4,17,0.2353,1,"{47, 51, 63, 208}"
1386,1,218,0,0.1514298,"\int \frac{\sqrt{c+d x}}{(a+b x)^6} \, dx","Int[Sqrt[c + d*x]/(a + b*x)^6,x]","-\frac{7 d^5 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{128 b^{3/2} (b c-a d)^{9/2}}+\frac{7 d^4 \sqrt{c+d x}}{128 b (a+b x) (b c-a d)^4}-\frac{7 d^3 \sqrt{c+d x}}{192 b (a+b x)^2 (b c-a d)^3}+\frac{7 d^2 \sqrt{c+d x}}{240 b (a+b x)^3 (b c-a d)^2}-\frac{d \sqrt{c+d x}}{40 b (a+b x)^4 (b c-a d)}-\frac{\sqrt{c+d x}}{5 b (a+b x)^5}","-\frac{7 d^5 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{128 b^{3/2} (b c-a d)^{9/2}}+\frac{7 d^4 \sqrt{c+d x}}{128 b (a+b x) (b c-a d)^4}-\frac{7 d^3 \sqrt{c+d x}}{192 b (a+b x)^2 (b c-a d)^3}+\frac{7 d^2 \sqrt{c+d x}}{240 b (a+b x)^3 (b c-a d)^2}-\frac{d \sqrt{c+d x}}{40 b (a+b x)^4 (b c-a d)}-\frac{\sqrt{c+d x}}{5 b (a+b x)^5}",1,"-Sqrt[c + d*x]/(5*b*(a + b*x)^5) - (d*Sqrt[c + d*x])/(40*b*(b*c - a*d)*(a + b*x)^4) + (7*d^2*Sqrt[c + d*x])/(240*b*(b*c - a*d)^2*(a + b*x)^3) - (7*d^3*Sqrt[c + d*x])/(192*b*(b*c - a*d)^3*(a + b*x)^2) + (7*d^4*Sqrt[c + d*x])/(128*b*(b*c - a*d)^4*(a + b*x)) - (7*d^5*ArcTanh[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[b*c - a*d]])/(128*b^(3/2)*(b*c - a*d)^(9/2))","A",7,4,17,0.2353,1,"{47, 51, 63, 208}"
1387,1,158,0,0.0526392,"\int (a+b x)^5 (c+d x)^{3/2} \, dx","Int[(a + b*x)^5*(c + d*x)^(3/2),x]","-\frac{10 b^4 (c+d x)^{13/2} (b c-a d)}{13 d^6}+\frac{20 b^3 (c+d x)^{11/2} (b c-a d)^2}{11 d^6}-\frac{20 b^2 (c+d x)^{9/2} (b c-a d)^3}{9 d^6}+\frac{10 b (c+d x)^{7/2} (b c-a d)^4}{7 d^6}-\frac{2 (c+d x)^{5/2} (b c-a d)^5}{5 d^6}+\frac{2 b^5 (c+d x)^{15/2}}{15 d^6}","-\frac{10 b^4 (c+d x)^{13/2} (b c-a d)}{13 d^6}+\frac{20 b^3 (c+d x)^{11/2} (b c-a d)^2}{11 d^6}-\frac{20 b^2 (c+d x)^{9/2} (b c-a d)^3}{9 d^6}+\frac{10 b (c+d x)^{7/2} (b c-a d)^4}{7 d^6}-\frac{2 (c+d x)^{5/2} (b c-a d)^5}{5 d^6}+\frac{2 b^5 (c+d x)^{15/2}}{15 d^6}",1,"(-2*(b*c - a*d)^5*(c + d*x)^(5/2))/(5*d^6) + (10*b*(b*c - a*d)^4*(c + d*x)^(7/2))/(7*d^6) - (20*b^2*(b*c - a*d)^3*(c + d*x)^(9/2))/(9*d^6) + (20*b^3*(b*c - a*d)^2*(c + d*x)^(11/2))/(11*d^6) - (10*b^4*(b*c - a*d)*(c + d*x)^(13/2))/(13*d^6) + (2*b^5*(c + d*x)^(15/2))/(15*d^6)","A",2,1,17,0.05882,1,"{43}"
1388,1,129,0,0.0419296,"\int (a+b x)^4 (c+d x)^{3/2} \, dx","Int[(a + b*x)^4*(c + d*x)^(3/2),x]","-\frac{8 b^3 (c+d x)^{11/2} (b c-a d)}{11 d^5}+\frac{4 b^2 (c+d x)^{9/2} (b c-a d)^2}{3 d^5}-\frac{8 b (c+d x)^{7/2} (b c-a d)^3}{7 d^5}+\frac{2 (c+d x)^{5/2} (b c-a d)^4}{5 d^5}+\frac{2 b^4 (c+d x)^{13/2}}{13 d^5}","-\frac{8 b^3 (c+d x)^{11/2} (b c-a d)}{11 d^5}+\frac{4 b^2 (c+d x)^{9/2} (b c-a d)^2}{3 d^5}-\frac{8 b (c+d x)^{7/2} (b c-a d)^3}{7 d^5}+\frac{2 (c+d x)^{5/2} (b c-a d)^4}{5 d^5}+\frac{2 b^4 (c+d x)^{13/2}}{13 d^5}",1,"(2*(b*c - a*d)^4*(c + d*x)^(5/2))/(5*d^5) - (8*b*(b*c - a*d)^3*(c + d*x)^(7/2))/(7*d^5) + (4*b^2*(b*c - a*d)^2*(c + d*x)^(9/2))/(3*d^5) - (8*b^3*(b*c - a*d)*(c + d*x)^(11/2))/(11*d^5) + (2*b^4*(c + d*x)^(13/2))/(13*d^5)","A",2,1,17,0.05882,1,"{43}"
1389,1,100,0,0.0338238,"\int (a+b x)^3 (c+d x)^{3/2} \, dx","Int[(a + b*x)^3*(c + d*x)^(3/2),x]","-\frac{2 b^2 (c+d x)^{9/2} (b c-a d)}{3 d^4}+\frac{6 b (c+d x)^{7/2} (b c-a d)^2}{7 d^4}-\frac{2 (c+d x)^{5/2} (b c-a d)^3}{5 d^4}+\frac{2 b^3 (c+d x)^{11/2}}{11 d^4}","-\frac{2 b^2 (c+d x)^{9/2} (b c-a d)}{3 d^4}+\frac{6 b (c+d x)^{7/2} (b c-a d)^2}{7 d^4}-\frac{2 (c+d x)^{5/2} (b c-a d)^3}{5 d^4}+\frac{2 b^3 (c+d x)^{11/2}}{11 d^4}",1,"(-2*(b*c - a*d)^3*(c + d*x)^(5/2))/(5*d^4) + (6*b*(b*c - a*d)^2*(c + d*x)^(7/2))/(7*d^4) - (2*b^2*(b*c - a*d)*(c + d*x)^(9/2))/(3*d^4) + (2*b^3*(c + d*x)^(11/2))/(11*d^4)","A",2,1,17,0.05882,1,"{43}"
1390,1,71,0,0.0237218,"\int (a+b x)^2 (c+d x)^{3/2} \, dx","Int[(a + b*x)^2*(c + d*x)^(3/2),x]","-\frac{4 b (c+d x)^{7/2} (b c-a d)}{7 d^3}+\frac{2 (c+d x)^{5/2} (b c-a d)^2}{5 d^3}+\frac{2 b^2 (c+d x)^{9/2}}{9 d^3}","-\frac{4 b (c+d x)^{7/2} (b c-a d)}{7 d^3}+\frac{2 (c+d x)^{5/2} (b c-a d)^2}{5 d^3}+\frac{2 b^2 (c+d x)^{9/2}}{9 d^3}",1,"(2*(b*c - a*d)^2*(c + d*x)^(5/2))/(5*d^3) - (4*b*(b*c - a*d)*(c + d*x)^(7/2))/(7*d^3) + (2*b^2*(c + d*x)^(9/2))/(9*d^3)","A",2,1,17,0.05882,1,"{43}"
1391,1,42,0,0.0139126,"\int (a+b x) (c+d x)^{3/2} \, dx","Int[(a + b*x)*(c + d*x)^(3/2),x]","\frac{2 b (c+d x)^{7/2}}{7 d^2}-\frac{2 (c+d x)^{5/2} (b c-a d)}{5 d^2}","\frac{2 b (c+d x)^{7/2}}{7 d^2}-\frac{2 (c+d x)^{5/2} (b c-a d)}{5 d^2}",1,"(-2*(b*c - a*d)*(c + d*x)^(5/2))/(5*d^2) + (2*b*(c + d*x)^(7/2))/(7*d^2)","A",2,1,15,0.06667,1,"{43}"
1392,1,16,0,0.0014835,"\int (c+d x)^{3/2} \, dx","Int[(c + d*x)^(3/2),x]","\frac{2 (c+d x)^{5/2}}{5 d}","\frac{2 (c+d x)^{5/2}}{5 d}",1,"(2*(c + d*x)^(5/2))/(5*d)","A",1,1,9,0.1111,1,"{32}"
1393,1,86,0,0.0455595,"\int \frac{(c+d x)^{3/2}}{a+b x} \, dx","Int[(c + d*x)^(3/2)/(a + b*x),x]","\frac{2 \sqrt{c+d x} (b c-a d)}{b^2}-\frac{2 (b c-a d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{b^{5/2}}+\frac{2 (c+d x)^{3/2}}{3 b}","\frac{2 \sqrt{c+d x} (b c-a d)}{b^2}-\frac{2 (b c-a d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{b^{5/2}}+\frac{2 (c+d x)^{3/2}}{3 b}",1,"(2*(b*c - a*d)*Sqrt[c + d*x])/b^2 + (2*(c + d*x)^(3/2))/(3*b) - (2*(b*c - a*d)^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[b*c - a*d]])/b^(5/2)","A",4,3,17,0.1765,1,"{50, 63, 208}"
1394,1,85,0,0.0381649,"\int \frac{(c+d x)^{3/2}}{(a+b x)^2} \, dx","Int[(c + d*x)^(3/2)/(a + b*x)^2,x]","-\frac{3 d \sqrt{b c-a d} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{b^{5/2}}-\frac{(c+d x)^{3/2}}{b (a+b x)}+\frac{3 d \sqrt{c+d x}}{b^2}","-\frac{3 d \sqrt{b c-a d} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{b^{5/2}}-\frac{(c+d x)^{3/2}}{b (a+b x)}+\frac{3 d \sqrt{c+d x}}{b^2}",1,"(3*d*Sqrt[c + d*x])/b^2 - (c + d*x)^(3/2)/(b*(a + b*x)) - (3*d*Sqrt[b*c - a*d]*ArcTanh[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[b*c - a*d]])/b^(5/2)","A",4,4,17,0.2353,1,"{47, 50, 63, 208}"
1395,1,100,0,0.0475181,"\int \frac{(c+d x)^{3/2}}{(a+b x)^3} \, dx","Int[(c + d*x)^(3/2)/(a + b*x)^3,x]","-\frac{3 d^2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{4 b^{5/2} \sqrt{b c-a d}}-\frac{3 d \sqrt{c+d x}}{4 b^2 (a+b x)}-\frac{(c+d x)^{3/2}}{2 b (a+b x)^2}","-\frac{3 d^2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{4 b^{5/2} \sqrt{b c-a d}}-\frac{3 d \sqrt{c+d x}}{4 b^2 (a+b x)}-\frac{(c+d x)^{3/2}}{2 b (a+b x)^2}",1,"(-3*d*Sqrt[c + d*x])/(4*b^2*(a + b*x)) - (c + d*x)^(3/2)/(2*b*(a + b*x)^2) - (3*d^2*ArcTanh[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[b*c - a*d]])/(4*b^(5/2)*Sqrt[b*c - a*d])","A",4,3,17,0.1765,1,"{47, 63, 208}"
1396,1,136,0,0.0571202,"\int \frac{(c+d x)^{3/2}}{(a+b x)^4} \, dx","Int[(c + d*x)^(3/2)/(a + b*x)^4,x]","-\frac{d^2 \sqrt{c+d x}}{8 b^2 (a+b x) (b c-a d)}+\frac{d^3 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{8 b^{5/2} (b c-a d)^{3/2}}-\frac{d \sqrt{c+d x}}{4 b^2 (a+b x)^2}-\frac{(c+d x)^{3/2}}{3 b (a+b x)^3}","-\frac{d^2 \sqrt{c+d x}}{8 b^2 (a+b x) (b c-a d)}+\frac{d^3 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{8 b^{5/2} (b c-a d)^{3/2}}-\frac{d \sqrt{c+d x}}{4 b^2 (a+b x)^2}-\frac{(c+d x)^{3/2}}{3 b (a+b x)^3}",1,"-(d*Sqrt[c + d*x])/(4*b^2*(a + b*x)^2) - (d^2*Sqrt[c + d*x])/(8*b^2*(b*c - a*d)*(a + b*x)) - (c + d*x)^(3/2)/(3*b*(a + b*x)^3) + (d^3*ArcTanh[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[b*c - a*d]])/(8*b^(5/2)*(b*c - a*d)^(3/2))","A",5,4,17,0.2353,1,"{47, 51, 63, 208}"
1397,1,172,0,0.0737483,"\int \frac{(c+d x)^{3/2}}{(a+b x)^5} \, dx","Int[(c + d*x)^(3/2)/(a + b*x)^5,x]","\frac{3 d^3 \sqrt{c+d x}}{64 b^2 (a+b x) (b c-a d)^2}-\frac{d^2 \sqrt{c+d x}}{32 b^2 (a+b x)^2 (b c-a d)}-\frac{3 d^4 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{64 b^{5/2} (b c-a d)^{5/2}}-\frac{d \sqrt{c+d x}}{8 b^2 (a+b x)^3}-\frac{(c+d x)^{3/2}}{4 b (a+b x)^4}","\frac{3 d^3 \sqrt{c+d x}}{64 b^2 (a+b x) (b c-a d)^2}-\frac{d^2 \sqrt{c+d x}}{32 b^2 (a+b x)^2 (b c-a d)}-\frac{3 d^4 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{64 b^{5/2} (b c-a d)^{5/2}}-\frac{d \sqrt{c+d x}}{8 b^2 (a+b x)^3}-\frac{(c+d x)^{3/2}}{4 b (a+b x)^4}",1,"-(d*Sqrt[c + d*x])/(8*b^2*(a + b*x)^3) - (d^2*Sqrt[c + d*x])/(32*b^2*(b*c - a*d)*(a + b*x)^2) + (3*d^3*Sqrt[c + d*x])/(64*b^2*(b*c - a*d)^2*(a + b*x)) - (c + d*x)^(3/2)/(4*b*(a + b*x)^4) - (3*d^4*ArcTanh[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[b*c - a*d]])/(64*b^(5/2)*(b*c - a*d)^(5/2))","A",6,4,17,0.2353,1,"{47, 51, 63, 208}"
1398,1,208,0,0.093295,"\int \frac{(c+d x)^{3/2}}{(a+b x)^6} \, dx","Int[(c + d*x)^(3/2)/(a + b*x)^6,x]","-\frac{3 d^4 \sqrt{c+d x}}{128 b^2 (a+b x) (b c-a d)^3}+\frac{d^3 \sqrt{c+d x}}{64 b^2 (a+b x)^2 (b c-a d)^2}-\frac{d^2 \sqrt{c+d x}}{80 b^2 (a+b x)^3 (b c-a d)}+\frac{3 d^5 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{128 b^{5/2} (b c-a d)^{7/2}}-\frac{3 d \sqrt{c+d x}}{40 b^2 (a+b x)^4}-\frac{(c+d x)^{3/2}}{5 b (a+b x)^5}","-\frac{3 d^4 \sqrt{c+d x}}{128 b^2 (a+b x) (b c-a d)^3}+\frac{d^3 \sqrt{c+d x}}{64 b^2 (a+b x)^2 (b c-a d)^2}-\frac{d^2 \sqrt{c+d x}}{80 b^2 (a+b x)^3 (b c-a d)}+\frac{3 d^5 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{128 b^{5/2} (b c-a d)^{7/2}}-\frac{3 d \sqrt{c+d x}}{40 b^2 (a+b x)^4}-\frac{(c+d x)^{3/2}}{5 b (a+b x)^5}",1,"(-3*d*Sqrt[c + d*x])/(40*b^2*(a + b*x)^4) - (d^2*Sqrt[c + d*x])/(80*b^2*(b*c - a*d)*(a + b*x)^3) + (d^3*Sqrt[c + d*x])/(64*b^2*(b*c - a*d)^2*(a + b*x)^2) - (3*d^4*Sqrt[c + d*x])/(128*b^2*(b*c - a*d)^3*(a + b*x)) - (c + d*x)^(3/2)/(5*b*(a + b*x)^5) + (3*d^5*ArcTanh[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[b*c - a*d]])/(128*b^(5/2)*(b*c - a*d)^(7/2))","A",7,4,17,0.2353,1,"{47, 51, 63, 208}"
1399,1,158,0,0.050514,"\int (a+b x)^5 (c+d x)^{5/2} \, dx","Int[(a + b*x)^5*(c + d*x)^(5/2),x]","-\frac{2 b^4 (c+d x)^{15/2} (b c-a d)}{3 d^6}+\frac{20 b^3 (c+d x)^{13/2} (b c-a d)^2}{13 d^6}-\frac{20 b^2 (c+d x)^{11/2} (b c-a d)^3}{11 d^6}+\frac{10 b (c+d x)^{9/2} (b c-a d)^4}{9 d^6}-\frac{2 (c+d x)^{7/2} (b c-a d)^5}{7 d^6}+\frac{2 b^5 (c+d x)^{17/2}}{17 d^6}","-\frac{2 b^4 (c+d x)^{15/2} (b c-a d)}{3 d^6}+\frac{20 b^3 (c+d x)^{13/2} (b c-a d)^2}{13 d^6}-\frac{20 b^2 (c+d x)^{11/2} (b c-a d)^3}{11 d^6}+\frac{10 b (c+d x)^{9/2} (b c-a d)^4}{9 d^6}-\frac{2 (c+d x)^{7/2} (b c-a d)^5}{7 d^6}+\frac{2 b^5 (c+d x)^{17/2}}{17 d^6}",1,"(-2*(b*c - a*d)^5*(c + d*x)^(7/2))/(7*d^6) + (10*b*(b*c - a*d)^4*(c + d*x)^(9/2))/(9*d^6) - (20*b^2*(b*c - a*d)^3*(c + d*x)^(11/2))/(11*d^6) + (20*b^3*(b*c - a*d)^2*(c + d*x)^(13/2))/(13*d^6) - (2*b^4*(b*c - a*d)*(c + d*x)^(15/2))/(3*d^6) + (2*b^5*(c + d*x)^(17/2))/(17*d^6)","A",2,1,17,0.05882,1,"{43}"
1400,1,129,0,0.0427892,"\int (a+b x)^4 (c+d x)^{5/2} \, dx","Int[(a + b*x)^4*(c + d*x)^(5/2),x]","-\frac{8 b^3 (c+d x)^{13/2} (b c-a d)}{13 d^5}+\frac{12 b^2 (c+d x)^{11/2} (b c-a d)^2}{11 d^5}-\frac{8 b (c+d x)^{9/2} (b c-a d)^3}{9 d^5}+\frac{2 (c+d x)^{7/2} (b c-a d)^4}{7 d^5}+\frac{2 b^4 (c+d x)^{15/2}}{15 d^5}","-\frac{8 b^3 (c+d x)^{13/2} (b c-a d)}{13 d^5}+\frac{12 b^2 (c+d x)^{11/2} (b c-a d)^2}{11 d^5}-\frac{8 b (c+d x)^{9/2} (b c-a d)^3}{9 d^5}+\frac{2 (c+d x)^{7/2} (b c-a d)^4}{7 d^5}+\frac{2 b^4 (c+d x)^{15/2}}{15 d^5}",1,"(2*(b*c - a*d)^4*(c + d*x)^(7/2))/(7*d^5) - (8*b*(b*c - a*d)^3*(c + d*x)^(9/2))/(9*d^5) + (12*b^2*(b*c - a*d)^2*(c + d*x)^(11/2))/(11*d^5) - (8*b^3*(b*c - a*d)*(c + d*x)^(13/2))/(13*d^5) + (2*b^4*(c + d*x)^(15/2))/(15*d^5)","A",2,1,17,0.05882,1,"{43}"
1401,1,100,0,0.0312856,"\int (a+b x)^3 (c+d x)^{5/2} \, dx","Int[(a + b*x)^3*(c + d*x)^(5/2),x]","-\frac{6 b^2 (c+d x)^{11/2} (b c-a d)}{11 d^4}+\frac{2 b (c+d x)^{9/2} (b c-a d)^2}{3 d^4}-\frac{2 (c+d x)^{7/2} (b c-a d)^3}{7 d^4}+\frac{2 b^3 (c+d x)^{13/2}}{13 d^4}","-\frac{6 b^2 (c+d x)^{11/2} (b c-a d)}{11 d^4}+\frac{2 b (c+d x)^{9/2} (b c-a d)^2}{3 d^4}-\frac{2 (c+d x)^{7/2} (b c-a d)^3}{7 d^4}+\frac{2 b^3 (c+d x)^{13/2}}{13 d^4}",1,"(-2*(b*c - a*d)^3*(c + d*x)^(7/2))/(7*d^4) + (2*b*(b*c - a*d)^2*(c + d*x)^(9/2))/(3*d^4) - (6*b^2*(b*c - a*d)*(c + d*x)^(11/2))/(11*d^4) + (2*b^3*(c + d*x)^(13/2))/(13*d^4)","A",2,1,17,0.05882,1,"{43}"
1402,1,71,0,0.0229477,"\int (a+b x)^2 (c+d x)^{5/2} \, dx","Int[(a + b*x)^2*(c + d*x)^(5/2),x]","-\frac{4 b (c+d x)^{9/2} (b c-a d)}{9 d^3}+\frac{2 (c+d x)^{7/2} (b c-a d)^2}{7 d^3}+\frac{2 b^2 (c+d x)^{11/2}}{11 d^3}","-\frac{4 b (c+d x)^{9/2} (b c-a d)}{9 d^3}+\frac{2 (c+d x)^{7/2} (b c-a d)^2}{7 d^3}+\frac{2 b^2 (c+d x)^{11/2}}{11 d^3}",1,"(2*(b*c - a*d)^2*(c + d*x)^(7/2))/(7*d^3) - (4*b*(b*c - a*d)*(c + d*x)^(9/2))/(9*d^3) + (2*b^2*(c + d*x)^(11/2))/(11*d^3)","A",2,1,17,0.05882,1,"{43}"
1403,1,42,0,0.0148131,"\int (a+b x) (c+d x)^{5/2} \, dx","Int[(a + b*x)*(c + d*x)^(5/2),x]","\frac{2 b (c+d x)^{9/2}}{9 d^2}-\frac{2 (c+d x)^{7/2} (b c-a d)}{7 d^2}","\frac{2 b (c+d x)^{9/2}}{9 d^2}-\frac{2 (c+d x)^{7/2} (b c-a d)}{7 d^2}",1,"(-2*(b*c - a*d)*(c + d*x)^(7/2))/(7*d^2) + (2*b*(c + d*x)^(9/2))/(9*d^2)","A",2,1,15,0.06667,1,"{43}"
1404,1,16,0,0.0014248,"\int (c+d x)^{5/2} \, dx","Int[(c + d*x)^(5/2),x]","\frac{2 (c+d x)^{7/2}}{7 d}","\frac{2 (c+d x)^{7/2}}{7 d}",1,"(2*(c + d*x)^(7/2))/(7*d)","A",1,1,9,0.1111,1,"{32}"
1405,1,112,0,0.0579813,"\int \frac{(c+d x)^{5/2}}{a+b x} \, dx","Int[(c + d*x)^(5/2)/(a + b*x),x]","\frac{2 \sqrt{c+d x} (b c-a d)^2}{b^3}+\frac{2 (c+d x)^{3/2} (b c-a d)}{3 b^2}-\frac{2 (b c-a d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{b^{7/2}}+\frac{2 (c+d x)^{5/2}}{5 b}","\frac{2 \sqrt{c+d x} (b c-a d)^2}{b^3}+\frac{2 (c+d x)^{3/2} (b c-a d)}{3 b^2}-\frac{2 (b c-a d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{b^{7/2}}+\frac{2 (c+d x)^{5/2}}{5 b}",1,"(2*(b*c - a*d)^2*Sqrt[c + d*x])/b^3 + (2*(b*c - a*d)*(c + d*x)^(3/2))/(3*b^2) + (2*(c + d*x)^(5/2))/(5*b) - (2*(b*c - a*d)^(5/2)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[b*c - a*d]])/b^(7/2)","A",5,3,17,0.1765,1,"{50, 63, 208}"
1406,1,110,0,0.0547527,"\int \frac{(c+d x)^{5/2}}{(a+b x)^2} \, dx","Int[(c + d*x)^(5/2)/(a + b*x)^2,x]","\frac{5 d \sqrt{c+d x} (b c-a d)}{b^3}-\frac{5 d (b c-a d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{b^{7/2}}-\frac{(c+d x)^{5/2}}{b (a+b x)}+\frac{5 d (c+d x)^{3/2}}{3 b^2}","\frac{5 d \sqrt{c+d x} (b c-a d)}{b^3}-\frac{5 d (b c-a d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{b^{7/2}}-\frac{(c+d x)^{5/2}}{b (a+b x)}+\frac{5 d (c+d x)^{3/2}}{3 b^2}",1,"(5*d*(b*c - a*d)*Sqrt[c + d*x])/b^3 + (5*d*(c + d*x)^(3/2))/(3*b^2) - (c + d*x)^(5/2)/(b*(a + b*x)) - (5*d*(b*c - a*d)^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[b*c - a*d]])/b^(7/2)","A",5,4,17,0.2353,1,"{47, 50, 63, 208}"
1407,1,119,0,0.0493503,"\int \frac{(c+d x)^{5/2}}{(a+b x)^3} \, dx","Int[(c + d*x)^(5/2)/(a + b*x)^3,x]","-\frac{15 d^2 \sqrt{b c-a d} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{4 b^{7/2}}-\frac{5 d (c+d x)^{3/2}}{4 b^2 (a+b x)}-\frac{(c+d x)^{5/2}}{2 b (a+b x)^2}+\frac{15 d^2 \sqrt{c+d x}}{4 b^3}","-\frac{15 d^2 \sqrt{b c-a d} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{4 b^{7/2}}-\frac{5 d (c+d x)^{3/2}}{4 b^2 (a+b x)}-\frac{(c+d x)^{5/2}}{2 b (a+b x)^2}+\frac{15 d^2 \sqrt{c+d x}}{4 b^3}",1,"(15*d^2*Sqrt[c + d*x])/(4*b^3) - (5*d*(c + d*x)^(3/2))/(4*b^2*(a + b*x)) - (c + d*x)^(5/2)/(2*b*(a + b*x)^2) - (15*d^2*Sqrt[b*c - a*d]*ArcTanh[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[b*c - a*d]])/(4*b^(7/2))","A",5,4,17,0.2353,1,"{47, 50, 63, 208}"
1408,1,126,0,0.0501402,"\int \frac{(c+d x)^{5/2}}{(a+b x)^4} \, dx","Int[(c + d*x)^(5/2)/(a + b*x)^4,x]","-\frac{5 d^2 \sqrt{c+d x}}{8 b^3 (a+b x)}-\frac{5 d^3 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{8 b^{7/2} \sqrt{b c-a d}}-\frac{5 d (c+d x)^{3/2}}{12 b^2 (a+b x)^2}-\frac{(c+d x)^{5/2}}{3 b (a+b x)^3}","-\frac{5 d^2 \sqrt{c+d x}}{8 b^3 (a+b x)}-\frac{5 d^3 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{8 b^{7/2} \sqrt{b c-a d}}-\frac{5 d (c+d x)^{3/2}}{12 b^2 (a+b x)^2}-\frac{(c+d x)^{5/2}}{3 b (a+b x)^3}",1,"(-5*d^2*Sqrt[c + d*x])/(8*b^3*(a + b*x)) - (5*d*(c + d*x)^(3/2))/(12*b^2*(a + b*x)^2) - (c + d*x)^(5/2)/(3*b*(a + b*x)^3) - (5*d^3*ArcTanh[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[b*c - a*d]])/(8*b^(7/2)*Sqrt[b*c - a*d])","A",5,3,17,0.1765,1,"{47, 63, 208}"
1409,1,162,0,0.0703069,"\int \frac{(c+d x)^{5/2}}{(a+b x)^5} \, dx","Int[(c + d*x)^(5/2)/(a + b*x)^5,x]","-\frac{5 d^3 \sqrt{c+d x}}{64 b^3 (a+b x) (b c-a d)}-\frac{5 d^2 \sqrt{c+d x}}{32 b^3 (a+b x)^2}+\frac{5 d^4 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{64 b^{7/2} (b c-a d)^{3/2}}-\frac{5 d (c+d x)^{3/2}}{24 b^2 (a+b x)^3}-\frac{(c+d x)^{5/2}}{4 b (a+b x)^4}","-\frac{5 d^3 \sqrt{c+d x}}{64 b^3 (a+b x) (b c-a d)}-\frac{5 d^2 \sqrt{c+d x}}{32 b^3 (a+b x)^2}+\frac{5 d^4 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{64 b^{7/2} (b c-a d)^{3/2}}-\frac{5 d (c+d x)^{3/2}}{24 b^2 (a+b x)^3}-\frac{(c+d x)^{5/2}}{4 b (a+b x)^4}",1,"(-5*d^2*Sqrt[c + d*x])/(32*b^3*(a + b*x)^2) - (5*d^3*Sqrt[c + d*x])/(64*b^3*(b*c - a*d)*(a + b*x)) - (5*d*(c + d*x)^(3/2))/(24*b^2*(a + b*x)^3) - (c + d*x)^(5/2)/(4*b*(a + b*x)^4) + (5*d^4*ArcTanh[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[b*c - a*d]])/(64*b^(7/2)*(b*c - a*d)^(3/2))","A",6,4,17,0.2353,1,"{47, 51, 63, 208}"
1410,1,198,0,0.0922634,"\int \frac{(c+d x)^{5/2}}{(a+b x)^6} \, dx","Int[(c + d*x)^(5/2)/(a + b*x)^6,x]","\frac{3 d^4 \sqrt{c+d x}}{128 b^3 (a+b x) (b c-a d)^2}-\frac{d^3 \sqrt{c+d x}}{64 b^3 (a+b x)^2 (b c-a d)}-\frac{d^2 \sqrt{c+d x}}{16 b^3 (a+b x)^3}-\frac{3 d^5 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{128 b^{7/2} (b c-a d)^{5/2}}-\frac{d (c+d x)^{3/2}}{8 b^2 (a+b x)^4}-\frac{(c+d x)^{5/2}}{5 b (a+b x)^5}","\frac{3 d^4 \sqrt{c+d x}}{128 b^3 (a+b x) (b c-a d)^2}-\frac{d^3 \sqrt{c+d x}}{64 b^3 (a+b x)^2 (b c-a d)}-\frac{d^2 \sqrt{c+d x}}{16 b^3 (a+b x)^3}-\frac{3 d^5 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{128 b^{7/2} (b c-a d)^{5/2}}-\frac{d (c+d x)^{3/2}}{8 b^2 (a+b x)^4}-\frac{(c+d x)^{5/2}}{5 b (a+b x)^5}",1,"-(d^2*Sqrt[c + d*x])/(16*b^3*(a + b*x)^3) - (d^3*Sqrt[c + d*x])/(64*b^3*(b*c - a*d)*(a + b*x)^2) + (3*d^4*Sqrt[c + d*x])/(128*b^3*(b*c - a*d)^2*(a + b*x)) - (d*(c + d*x)^(3/2))/(8*b^2*(a + b*x)^4) - (c + d*x)^(5/2)/(5*b*(a + b*x)^5) - (3*d^5*ArcTanh[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[b*c - a*d]])/(128*b^(7/2)*(b*c - a*d)^(5/2))","A",7,4,17,0.2353,1,"{47, 51, 63, 208}"
1411,1,35,0,0.0081189,"\int \frac{\sqrt{-1+x}}{(1+x)^2} \, dx","Int[Sqrt[-1 + x]/(1 + x)^2,x]","\frac{\tan ^{-1}\left(\frac{\sqrt{x-1}}{\sqrt{2}}\right)}{\sqrt{2}}-\frac{\sqrt{x-1}}{x+1}","\frac{\tan ^{-1}\left(\frac{\sqrt{x-1}}{\sqrt{2}}\right)}{\sqrt{2}}-\frac{\sqrt{x-1}}{x+1}",1,"-(Sqrt[-1 + x]/(1 + x)) + ArcTan[Sqrt[-1 + x]/Sqrt[2]]/Sqrt[2]","A",3,3,13,0.2308,1,"{47, 63, 203}"
1412,1,56,0,0.0130528,"\int \frac{\sqrt{-1+x}}{(1+x)^3} \, dx","Int[Sqrt[-1 + x]/(1 + x)^3,x]","\frac{\sqrt{x-1}}{8 (x+1)}-\frac{\sqrt{x-1}}{2 (x+1)^2}+\frac{\tan ^{-1}\left(\frac{\sqrt{x-1}}{\sqrt{2}}\right)}{8 \sqrt{2}}","\frac{\sqrt{x-1}}{8 (x+1)}-\frac{\sqrt{x-1}}{2 (x+1)^2}+\frac{\tan ^{-1}\left(\frac{\sqrt{x-1}}{\sqrt{2}}\right)}{8 \sqrt{2}}",1,"-Sqrt[-1 + x]/(2*(1 + x)^2) + Sqrt[-1 + x]/(8*(1 + x)) + ArcTan[Sqrt[-1 + x]/Sqrt[2]]/(8*Sqrt[2])","A",4,4,13,0.3077,1,"{47, 51, 63, 203}"
1413,1,154,0,0.0507118,"\int \frac{(a+b x)^5}{\sqrt{c+d x}} \, dx","Int[(a + b*x)^5/Sqrt[c + d*x],x]","-\frac{10 b^4 (c+d x)^{9/2} (b c-a d)}{9 d^6}+\frac{20 b^3 (c+d x)^{7/2} (b c-a d)^2}{7 d^6}-\frac{4 b^2 (c+d x)^{5/2} (b c-a d)^3}{d^6}+\frac{10 b (c+d x)^{3/2} (b c-a d)^4}{3 d^6}-\frac{2 \sqrt{c+d x} (b c-a d)^5}{d^6}+\frac{2 b^5 (c+d x)^{11/2}}{11 d^6}","-\frac{10 b^4 (c+d x)^{9/2} (b c-a d)}{9 d^6}+\frac{20 b^3 (c+d x)^{7/2} (b c-a d)^2}{7 d^6}-\frac{4 b^2 (c+d x)^{5/2} (b c-a d)^3}{d^6}+\frac{10 b (c+d x)^{3/2} (b c-a d)^4}{3 d^6}-\frac{2 \sqrt{c+d x} (b c-a d)^5}{d^6}+\frac{2 b^5 (c+d x)^{11/2}}{11 d^6}",1,"(-2*(b*c - a*d)^5*Sqrt[c + d*x])/d^6 + (10*b*(b*c - a*d)^4*(c + d*x)^(3/2))/(3*d^6) - (4*b^2*(b*c - a*d)^3*(c + d*x)^(5/2))/d^6 + (20*b^3*(b*c - a*d)^2*(c + d*x)^(7/2))/(7*d^6) - (10*b^4*(b*c - a*d)*(c + d*x)^(9/2))/(9*d^6) + (2*b^5*(c + d*x)^(11/2))/(11*d^6)","A",2,1,17,0.05882,1,"{43}"
1414,1,127,0,0.0410394,"\int \frac{(a+b x)^4}{\sqrt{c+d x}} \, dx","Int[(a + b*x)^4/Sqrt[c + d*x],x]","-\frac{8 b^3 (c+d x)^{7/2} (b c-a d)}{7 d^5}+\frac{12 b^2 (c+d x)^{5/2} (b c-a d)^2}{5 d^5}-\frac{8 b (c+d x)^{3/2} (b c-a d)^3}{3 d^5}+\frac{2 \sqrt{c+d x} (b c-a d)^4}{d^5}+\frac{2 b^4 (c+d x)^{9/2}}{9 d^5}","-\frac{8 b^3 (c+d x)^{7/2} (b c-a d)}{7 d^5}+\frac{12 b^2 (c+d x)^{5/2} (b c-a d)^2}{5 d^5}-\frac{8 b (c+d x)^{3/2} (b c-a d)^3}{3 d^5}+\frac{2 \sqrt{c+d x} (b c-a d)^4}{d^5}+\frac{2 b^4 (c+d x)^{9/2}}{9 d^5}",1,"(2*(b*c - a*d)^4*Sqrt[c + d*x])/d^5 - (8*b*(b*c - a*d)^3*(c + d*x)^(3/2))/(3*d^5) + (12*b^2*(b*c - a*d)^2*(c + d*x)^(5/2))/(5*d^5) - (8*b^3*(b*c - a*d)*(c + d*x)^(7/2))/(7*d^5) + (2*b^4*(c + d*x)^(9/2))/(9*d^5)","A",2,1,17,0.05882,1,"{43}"
1415,1,96,0,0.0308993,"\int \frac{(a+b x)^3}{\sqrt{c+d x}} \, dx","Int[(a + b*x)^3/Sqrt[c + d*x],x]","-\frac{6 b^2 (c+d x)^{5/2} (b c-a d)}{5 d^4}+\frac{2 b (c+d x)^{3/2} (b c-a d)^2}{d^4}-\frac{2 \sqrt{c+d x} (b c-a d)^3}{d^4}+\frac{2 b^3 (c+d x)^{7/2}}{7 d^4}","-\frac{6 b^2 (c+d x)^{5/2} (b c-a d)}{5 d^4}+\frac{2 b (c+d x)^{3/2} (b c-a d)^2}{d^4}-\frac{2 \sqrt{c+d x} (b c-a d)^3}{d^4}+\frac{2 b^3 (c+d x)^{7/2}}{7 d^4}",1,"(-2*(b*c - a*d)^3*Sqrt[c + d*x])/d^4 + (2*b*(b*c - a*d)^2*(c + d*x)^(3/2))/d^4 - (6*b^2*(b*c - a*d)*(c + d*x)^(5/2))/(5*d^4) + (2*b^3*(c + d*x)^(7/2))/(7*d^4)","A",2,1,17,0.05882,1,"{43}"
1416,1,69,0,0.021249,"\int \frac{(a+b x)^2}{\sqrt{c+d x}} \, dx","Int[(a + b*x)^2/Sqrt[c + d*x],x]","-\frac{4 b (c+d x)^{3/2} (b c-a d)}{3 d^3}+\frac{2 \sqrt{c+d x} (b c-a d)^2}{d^3}+\frac{2 b^2 (c+d x)^{5/2}}{5 d^3}","-\frac{4 b (c+d x)^{3/2} (b c-a d)}{3 d^3}+\frac{2 \sqrt{c+d x} (b c-a d)^2}{d^3}+\frac{2 b^2 (c+d x)^{5/2}}{5 d^3}",1,"(2*(b*c - a*d)^2*Sqrt[c + d*x])/d^3 - (4*b*(b*c - a*d)*(c + d*x)^(3/2))/(3*d^3) + (2*b^2*(c + d*x)^(5/2))/(5*d^3)","A",2,1,17,0.05882,1,"{43}"
1417,1,40,0,0.0129204,"\int \frac{a+b x}{\sqrt{c+d x}} \, dx","Int[(a + b*x)/Sqrt[c + d*x],x]","\frac{2 b (c+d x)^{3/2}}{3 d^2}-\frac{2 \sqrt{c+d x} (b c-a d)}{d^2}","\frac{2 b (c+d x)^{3/2}}{3 d^2}-\frac{2 \sqrt{c+d x} (b c-a d)}{d^2}",1,"(-2*(b*c - a*d)*Sqrt[c + d*x])/d^2 + (2*b*(c + d*x)^(3/2))/(3*d^2)","A",2,1,15,0.06667,1,"{43}"
1418,1,14,0,0.0013672,"\int \frac{1}{\sqrt{c+d x}} \, dx","Int[1/Sqrt[c + d*x],x]","\frac{2 \sqrt{c+d x}}{d}","\frac{2 \sqrt{c+d x}}{d}",1,"(2*Sqrt[c + d*x])/d","A",1,1,9,0.1111,1,"{32}"
1419,1,47,0,0.0203073,"\int \frac{1}{(a+b x) \sqrt{c+d x}} \, dx","Int[1/((a + b*x)*Sqrt[c + d*x]),x]","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{\sqrt{b} \sqrt{b c-a d}}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{\sqrt{b} \sqrt{b c-a d}}",1,"(-2*ArcTanh[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[b*c - a*d]])/(Sqrt[b]*Sqrt[b*c - a*d])","A",2,2,17,0.1176,1,"{63, 208}"
1420,1,76,0,0.0269979,"\int \frac{1}{(a+b x)^2 \sqrt{c+d x}} \, dx","Int[1/((a + b*x)^2*Sqrt[c + d*x]),x]","\frac{d \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{\sqrt{b} (b c-a d)^{3/2}}-\frac{\sqrt{c+d x}}{(a+b x) (b c-a d)}","\frac{d \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{\sqrt{b} (b c-a d)^{3/2}}-\frac{\sqrt{c+d x}}{(a+b x) (b c-a d)}",1,"-(Sqrt[c + d*x]/((b*c - a*d)*(a + b*x))) + (d*ArcTanh[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[b*c - a*d]])/(Sqrt[b]*(b*c - a*d)^(3/2))","A",3,3,17,0.1765,1,"{51, 63, 208}"
1421,1,114,0,0.0372377,"\int \frac{1}{(a+b x)^3 \sqrt{c+d x}} \, dx","Int[1/((a + b*x)^3*Sqrt[c + d*x]),x]","-\frac{3 d^2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{4 \sqrt{b} (b c-a d)^{5/2}}+\frac{3 d \sqrt{c+d x}}{4 (a+b x) (b c-a d)^2}-\frac{\sqrt{c+d x}}{2 (a+b x)^2 (b c-a d)}","-\frac{3 d^2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{4 \sqrt{b} (b c-a d)^{5/2}}+\frac{3 d \sqrt{c+d x}}{4 (a+b x) (b c-a d)^2}-\frac{\sqrt{c+d x}}{2 (a+b x)^2 (b c-a d)}",1,"-Sqrt[c + d*x]/(2*(b*c - a*d)*(a + b*x)^2) + (3*d*Sqrt[c + d*x])/(4*(b*c - a*d)^2*(a + b*x)) - (3*d^2*ArcTanh[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[b*c - a*d]])/(4*Sqrt[b]*(b*c - a*d)^(5/2))","A",4,3,17,0.1765,1,"{51, 63, 208}"
1422,1,147,0,0.0504401,"\int \frac{1}{(a+b x)^4 \sqrt{c+d x}} \, dx","Int[1/((a + b*x)^4*Sqrt[c + d*x]),x]","-\frac{5 d^2 \sqrt{c+d x}}{8 (a+b x) (b c-a d)^3}+\frac{5 d^3 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{8 \sqrt{b} (b c-a d)^{7/2}}+\frac{5 d \sqrt{c+d x}}{12 (a+b x)^2 (b c-a d)^2}-\frac{\sqrt{c+d x}}{3 (a+b x)^3 (b c-a d)}","-\frac{5 d^2 \sqrt{c+d x}}{8 (a+b x) (b c-a d)^3}+\frac{5 d^3 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{8 \sqrt{b} (b c-a d)^{7/2}}+\frac{5 d \sqrt{c+d x}}{12 (a+b x)^2 (b c-a d)^2}-\frac{\sqrt{c+d x}}{3 (a+b x)^3 (b c-a d)}",1,"-Sqrt[c + d*x]/(3*(b*c - a*d)*(a + b*x)^3) + (5*d*Sqrt[c + d*x])/(12*(b*c - a*d)^2*(a + b*x)^2) - (5*d^2*Sqrt[c + d*x])/(8*(b*c - a*d)^3*(a + b*x)) + (5*d^3*ArcTanh[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[b*c - a*d]])/(8*Sqrt[b]*(b*c - a*d)^(7/2))","A",5,3,17,0.1765,1,"{51, 63, 208}"
1423,1,180,0,0.0647658,"\int \frac{1}{(a+b x)^5 \sqrt{c+d x}} \, dx","Int[1/((a + b*x)^5*Sqrt[c + d*x]),x]","\frac{35 d^3 \sqrt{c+d x}}{64 (a+b x) (b c-a d)^4}-\frac{35 d^2 \sqrt{c+d x}}{96 (a+b x)^2 (b c-a d)^3}-\frac{35 d^4 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{64 \sqrt{b} (b c-a d)^{9/2}}+\frac{7 d \sqrt{c+d x}}{24 (a+b x)^3 (b c-a d)^2}-\frac{\sqrt{c+d x}}{4 (a+b x)^4 (b c-a d)}","\frac{35 d^3 \sqrt{c+d x}}{64 (a+b x) (b c-a d)^4}-\frac{35 d^2 \sqrt{c+d x}}{96 (a+b x)^2 (b c-a d)^3}-\frac{35 d^4 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{64 \sqrt{b} (b c-a d)^{9/2}}+\frac{7 d \sqrt{c+d x}}{24 (a+b x)^3 (b c-a d)^2}-\frac{\sqrt{c+d x}}{4 (a+b x)^4 (b c-a d)}",1,"-Sqrt[c + d*x]/(4*(b*c - a*d)*(a + b*x)^4) + (7*d*Sqrt[c + d*x])/(24*(b*c - a*d)^2*(a + b*x)^3) - (35*d^2*Sqrt[c + d*x])/(96*(b*c - a*d)^3*(a + b*x)^2) + (35*d^3*Sqrt[c + d*x])/(64*(b*c - a*d)^4*(a + b*x)) - (35*d^4*ArcTanh[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[b*c - a*d]])/(64*Sqrt[b]*(b*c - a*d)^(9/2))","A",6,3,17,0.1765,1,"{51, 63, 208}"
1424,1,152,0,0.0486974,"\int \frac{(a+b x)^5}{(c+d x)^{3/2}} \, dx","Int[(a + b*x)^5/(c + d*x)^(3/2),x]","-\frac{10 b^4 (c+d x)^{7/2} (b c-a d)}{7 d^6}+\frac{4 b^3 (c+d x)^{5/2} (b c-a d)^2}{d^6}-\frac{20 b^2 (c+d x)^{3/2} (b c-a d)^3}{3 d^6}+\frac{10 b \sqrt{c+d x} (b c-a d)^4}{d^6}+\frac{2 (b c-a d)^5}{d^6 \sqrt{c+d x}}+\frac{2 b^5 (c+d x)^{9/2}}{9 d^6}","-\frac{10 b^4 (c+d x)^{7/2} (b c-a d)}{7 d^6}+\frac{4 b^3 (c+d x)^{5/2} (b c-a d)^2}{d^6}-\frac{20 b^2 (c+d x)^{3/2} (b c-a d)^3}{3 d^6}+\frac{10 b \sqrt{c+d x} (b c-a d)^4}{d^6}+\frac{2 (b c-a d)^5}{d^6 \sqrt{c+d x}}+\frac{2 b^5 (c+d x)^{9/2}}{9 d^6}",1,"(2*(b*c - a*d)^5)/(d^6*Sqrt[c + d*x]) + (10*b*(b*c - a*d)^4*Sqrt[c + d*x])/d^6 - (20*b^2*(b*c - a*d)^3*(c + d*x)^(3/2))/(3*d^6) + (4*b^3*(b*c - a*d)^2*(c + d*x)^(5/2))/d^6 - (10*b^4*(b*c - a*d)*(c + d*x)^(7/2))/(7*d^6) + (2*b^5*(c + d*x)^(9/2))/(9*d^6)","A",2,1,17,0.05882,1,"{43}"
1425,1,123,0,0.0371394,"\int \frac{(a+b x)^4}{(c+d x)^{3/2}} \, dx","Int[(a + b*x)^4/(c + d*x)^(3/2),x]","-\frac{8 b^3 (c+d x)^{5/2} (b c-a d)}{5 d^5}+\frac{4 b^2 (c+d x)^{3/2} (b c-a d)^2}{d^5}-\frac{8 b \sqrt{c+d x} (b c-a d)^3}{d^5}-\frac{2 (b c-a d)^4}{d^5 \sqrt{c+d x}}+\frac{2 b^4 (c+d x)^{7/2}}{7 d^5}","-\frac{8 b^3 (c+d x)^{5/2} (b c-a d)}{5 d^5}+\frac{4 b^2 (c+d x)^{3/2} (b c-a d)^2}{d^5}-\frac{8 b \sqrt{c+d x} (b c-a d)^3}{d^5}-\frac{2 (b c-a d)^4}{d^5 \sqrt{c+d x}}+\frac{2 b^4 (c+d x)^{7/2}}{7 d^5}",1,"(-2*(b*c - a*d)^4)/(d^5*Sqrt[c + d*x]) - (8*b*(b*c - a*d)^3*Sqrt[c + d*x])/d^5 + (4*b^2*(b*c - a*d)^2*(c + d*x)^(3/2))/d^5 - (8*b^3*(b*c - a*d)*(c + d*x)^(5/2))/(5*d^5) + (2*b^4*(c + d*x)^(7/2))/(7*d^5)","A",2,1,17,0.05882,1,"{43}"
1426,1,94,0,0.0297938,"\int \frac{(a+b x)^3}{(c+d x)^{3/2}} \, dx","Int[(a + b*x)^3/(c + d*x)^(3/2),x]","-\frac{2 b^2 (c+d x)^{3/2} (b c-a d)}{d^4}+\frac{6 b \sqrt{c+d x} (b c-a d)^2}{d^4}+\frac{2 (b c-a d)^3}{d^4 \sqrt{c+d x}}+\frac{2 b^3 (c+d x)^{5/2}}{5 d^4}","-\frac{2 b^2 (c+d x)^{3/2} (b c-a d)}{d^4}+\frac{6 b \sqrt{c+d x} (b c-a d)^2}{d^4}+\frac{2 (b c-a d)^3}{d^4 \sqrt{c+d x}}+\frac{2 b^3 (c+d x)^{5/2}}{5 d^4}",1,"(2*(b*c - a*d)^3)/(d^4*Sqrt[c + d*x]) + (6*b*(b*c - a*d)^2*Sqrt[c + d*x])/d^4 - (2*b^2*(b*c - a*d)*(c + d*x)^(3/2))/d^4 + (2*b^3*(c + d*x)^(5/2))/(5*d^4)","A",2,1,17,0.05882,1,"{43}"
1427,1,67,0,0.0206038,"\int \frac{(a+b x)^2}{(c+d x)^{3/2}} \, dx","Int[(a + b*x)^2/(c + d*x)^(3/2),x]","-\frac{4 b \sqrt{c+d x} (b c-a d)}{d^3}-\frac{2 (b c-a d)^2}{d^3 \sqrt{c+d x}}+\frac{2 b^2 (c+d x)^{3/2}}{3 d^3}","-\frac{4 b \sqrt{c+d x} (b c-a d)}{d^3}-\frac{2 (b c-a d)^2}{d^3 \sqrt{c+d x}}+\frac{2 b^2 (c+d x)^{3/2}}{3 d^3}",1,"(-2*(b*c - a*d)^2)/(d^3*Sqrt[c + d*x]) - (4*b*(b*c - a*d)*Sqrt[c + d*x])/d^3 + (2*b^2*(c + d*x)^(3/2))/(3*d^3)","A",2,1,17,0.05882,1,"{43}"
1428,1,38,0,0.0142636,"\int \frac{a+b x}{(c+d x)^{3/2}} \, dx","Int[(a + b*x)/(c + d*x)^(3/2),x]","\frac{2 (b c-a d)}{d^2 \sqrt{c+d x}}+\frac{2 b \sqrt{c+d x}}{d^2}","\frac{2 (b c-a d)}{d^2 \sqrt{c+d x}}+\frac{2 b \sqrt{c+d x}}{d^2}",1,"(2*(b*c - a*d))/(d^2*Sqrt[c + d*x]) + (2*b*Sqrt[c + d*x])/d^2","A",2,1,15,0.06667,1,"{43}"
1429,1,14,0,0.0015836,"\int \frac{1}{(c+d x)^{3/2}} \, dx","Int[(c + d*x)^(-3/2),x]","-\frac{2}{d \sqrt{c+d x}}","-\frac{2}{d \sqrt{c+d x}}",1,"-2/(d*Sqrt[c + d*x])","A",1,1,9,0.1111,1,"{32}"
1430,1,69,0,0.0273585,"\int \frac{1}{(a+b x) (c+d x)^{3/2}} \, dx","Int[1/((a + b*x)*(c + d*x)^(3/2)),x]","\frac{2}{\sqrt{c+d x} (b c-a d)}-\frac{2 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{(b c-a d)^{3/2}}","\frac{2}{\sqrt{c+d x} (b c-a d)}-\frac{2 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{(b c-a d)^{3/2}}",1,"2/((b*c - a*d)*Sqrt[c + d*x]) - (2*Sqrt[b]*ArcTanh[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[b*c - a*d]])/(b*c - a*d)^(3/2)","A",3,3,17,0.1765,1,"{51, 63, 208}"
1431,1,99,0,0.0384196,"\int \frac{1}{(a+b x)^2 (c+d x)^{3/2}} \, dx","Int[1/((a + b*x)^2*(c + d*x)^(3/2)),x]","-\frac{3 d}{\sqrt{c+d x} (b c-a d)^2}-\frac{1}{(a+b x) \sqrt{c+d x} (b c-a d)}+\frac{3 \sqrt{b} d \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{(b c-a d)^{5/2}}","-\frac{3 d}{\sqrt{c+d x} (b c-a d)^2}-\frac{1}{(a+b x) \sqrt{c+d x} (b c-a d)}+\frac{3 \sqrt{b} d \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{(b c-a d)^{5/2}}",1,"(-3*d)/((b*c - a*d)^2*Sqrt[c + d*x]) - 1/((b*c - a*d)*(a + b*x)*Sqrt[c + d*x]) + (3*Sqrt[b]*d*ArcTanh[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[b*c - a*d]])/(b*c - a*d)^(5/2)","A",4,3,17,0.1765,1,"{51, 63, 208}"
1432,1,140,0,0.0515628,"\int \frac{1}{(a+b x)^3 (c+d x)^{3/2}} \, dx","Int[1/((a + b*x)^3*(c + d*x)^(3/2)),x]","\frac{15 d^2}{4 \sqrt{c+d x} (b c-a d)^3}-\frac{15 \sqrt{b} d^2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{4 (b c-a d)^{7/2}}+\frac{5 d}{4 (a+b x) \sqrt{c+d x} (b c-a d)^2}-\frac{1}{2 (a+b x)^2 \sqrt{c+d x} (b c-a d)}","\frac{15 d^2}{4 \sqrt{c+d x} (b c-a d)^3}-\frac{15 \sqrt{b} d^2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{4 (b c-a d)^{7/2}}+\frac{5 d}{4 (a+b x) \sqrt{c+d x} (b c-a d)^2}-\frac{1}{2 (a+b x)^2 \sqrt{c+d x} (b c-a d)}",1,"(15*d^2)/(4*(b*c - a*d)^3*Sqrt[c + d*x]) - 1/(2*(b*c - a*d)*(a + b*x)^2*Sqrt[c + d*x]) + (5*d)/(4*(b*c - a*d)^2*(a + b*x)*Sqrt[c + d*x]) - (15*Sqrt[b]*d^2*ArcTanh[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[b*c - a*d]])/(4*(b*c - a*d)^(7/2))","A",5,3,17,0.1765,1,"{51, 63, 208}"
1433,1,173,0,0.0660012,"\int \frac{1}{(a+b x)^4 (c+d x)^{3/2}} \, dx","Int[1/((a + b*x)^4*(c + d*x)^(3/2)),x]","-\frac{35 d^3}{8 \sqrt{c+d x} (b c-a d)^4}-\frac{35 d^2}{24 (a+b x) \sqrt{c+d x} (b c-a d)^3}+\frac{35 \sqrt{b} d^3 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{8 (b c-a d)^{9/2}}+\frac{7 d}{12 (a+b x)^2 \sqrt{c+d x} (b c-a d)^2}-\frac{1}{3 (a+b x)^3 \sqrt{c+d x} (b c-a d)}","-\frac{35 d^3}{8 \sqrt{c+d x} (b c-a d)^4}-\frac{35 d^2}{24 (a+b x) \sqrt{c+d x} (b c-a d)^3}+\frac{35 \sqrt{b} d^3 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{8 (b c-a d)^{9/2}}+\frac{7 d}{12 (a+b x)^2 \sqrt{c+d x} (b c-a d)^2}-\frac{1}{3 (a+b x)^3 \sqrt{c+d x} (b c-a d)}",1,"(-35*d^3)/(8*(b*c - a*d)^4*Sqrt[c + d*x]) - 1/(3*(b*c - a*d)*(a + b*x)^3*Sqrt[c + d*x]) + (7*d)/(12*(b*c - a*d)^2*(a + b*x)^2*Sqrt[c + d*x]) - (35*d^2)/(24*(b*c - a*d)^3*(a + b*x)*Sqrt[c + d*x]) + (35*Sqrt[b]*d^3*ArcTanh[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[b*c - a*d]])/(8*(b*c - a*d)^(9/2))","A",6,3,17,0.1765,1,"{51, 63, 208}"
1434,1,152,0,0.0483056,"\int \frac{(a+b x)^5}{(c+d x)^{5/2}} \, dx","Int[(a + b*x)^5/(c + d*x)^(5/2),x]","-\frac{2 b^4 (c+d x)^{5/2} (b c-a d)}{d^6}+\frac{20 b^3 (c+d x)^{3/2} (b c-a d)^2}{3 d^6}-\frac{20 b^2 \sqrt{c+d x} (b c-a d)^3}{d^6}-\frac{10 b (b c-a d)^4}{d^6 \sqrt{c+d x}}+\frac{2 (b c-a d)^5}{3 d^6 (c+d x)^{3/2}}+\frac{2 b^5 (c+d x)^{7/2}}{7 d^6}","-\frac{2 b^4 (c+d x)^{5/2} (b c-a d)}{d^6}+\frac{20 b^3 (c+d x)^{3/2} (b c-a d)^2}{3 d^6}-\frac{20 b^2 \sqrt{c+d x} (b c-a d)^3}{d^6}-\frac{10 b (b c-a d)^4}{d^6 \sqrt{c+d x}}+\frac{2 (b c-a d)^5}{3 d^6 (c+d x)^{3/2}}+\frac{2 b^5 (c+d x)^{7/2}}{7 d^6}",1,"(2*(b*c - a*d)^5)/(3*d^6*(c + d*x)^(3/2)) - (10*b*(b*c - a*d)^4)/(d^6*Sqrt[c + d*x]) - (20*b^2*(b*c - a*d)^3*Sqrt[c + d*x])/d^6 + (20*b^3*(b*c - a*d)^2*(c + d*x)^(3/2))/(3*d^6) - (2*b^4*(b*c - a*d)*(c + d*x)^(5/2))/d^6 + (2*b^5*(c + d*x)^(7/2))/(7*d^6)","A",2,1,17,0.05882,1,"{43}"
1435,1,125,0,0.0385926,"\int \frac{(a+b x)^4}{(c+d x)^{5/2}} \, dx","Int[(a + b*x)^4/(c + d*x)^(5/2),x]","-\frac{8 b^3 (c+d x)^{3/2} (b c-a d)}{3 d^5}+\frac{12 b^2 \sqrt{c+d x} (b c-a d)^2}{d^5}+\frac{8 b (b c-a d)^3}{d^5 \sqrt{c+d x}}-\frac{2 (b c-a d)^4}{3 d^5 (c+d x)^{3/2}}+\frac{2 b^4 (c+d x)^{5/2}}{5 d^5}","-\frac{8 b^3 (c+d x)^{3/2} (b c-a d)}{3 d^5}+\frac{12 b^2 \sqrt{c+d x} (b c-a d)^2}{d^5}+\frac{8 b (b c-a d)^3}{d^5 \sqrt{c+d x}}-\frac{2 (b c-a d)^4}{3 d^5 (c+d x)^{3/2}}+\frac{2 b^4 (c+d x)^{5/2}}{5 d^5}",1,"(-2*(b*c - a*d)^4)/(3*d^5*(c + d*x)^(3/2)) + (8*b*(b*c - a*d)^3)/(d^5*Sqrt[c + d*x]) + (12*b^2*(b*c - a*d)^2*Sqrt[c + d*x])/d^5 - (8*b^3*(b*c - a*d)*(c + d*x)^(3/2))/(3*d^5) + (2*b^4*(c + d*x)^(5/2))/(5*d^5)","A",2,1,17,0.05882,1,"{43}"
1436,1,96,0,0.0309867,"\int \frac{(a+b x)^3}{(c+d x)^{5/2}} \, dx","Int[(a + b*x)^3/(c + d*x)^(5/2),x]","-\frac{6 b^2 \sqrt{c+d x} (b c-a d)}{d^4}-\frac{6 b (b c-a d)^2}{d^4 \sqrt{c+d x}}+\frac{2 (b c-a d)^3}{3 d^4 (c+d x)^{3/2}}+\frac{2 b^3 (c+d x)^{3/2}}{3 d^4}","-\frac{6 b^2 \sqrt{c+d x} (b c-a d)}{d^4}-\frac{6 b (b c-a d)^2}{d^4 \sqrt{c+d x}}+\frac{2 (b c-a d)^3}{3 d^4 (c+d x)^{3/2}}+\frac{2 b^3 (c+d x)^{3/2}}{3 d^4}",1,"(2*(b*c - a*d)^3)/(3*d^4*(c + d*x)^(3/2)) - (6*b*(b*c - a*d)^2)/(d^4*Sqrt[c + d*x]) - (6*b^2*(b*c - a*d)*Sqrt[c + d*x])/d^4 + (2*b^3*(c + d*x)^(3/2))/(3*d^4)","A",2,1,17,0.05882,1,"{43}"
1437,1,67,0,0.0211512,"\int \frac{(a+b x)^2}{(c+d x)^{5/2}} \, dx","Int[(a + b*x)^2/(c + d*x)^(5/2),x]","\frac{4 b (b c-a d)}{d^3 \sqrt{c+d x}}-\frac{2 (b c-a d)^2}{3 d^3 (c+d x)^{3/2}}+\frac{2 b^2 \sqrt{c+d x}}{d^3}","\frac{4 b (b c-a d)}{d^3 \sqrt{c+d x}}-\frac{2 (b c-a d)^2}{3 d^3 (c+d x)^{3/2}}+\frac{2 b^2 \sqrt{c+d x}}{d^3}",1,"(-2*(b*c - a*d)^2)/(3*d^3*(c + d*x)^(3/2)) + (4*b*(b*c - a*d))/(d^3*Sqrt[c + d*x]) + (2*b^2*Sqrt[c + d*x])/d^3","A",2,1,17,0.05882,1,"{43}"
1438,1,40,0,0.0139255,"\int \frac{a+b x}{(c+d x)^{5/2}} \, dx","Int[(a + b*x)/(c + d*x)^(5/2),x]","\frac{2 (b c-a d)}{3 d^2 (c+d x)^{3/2}}-\frac{2 b}{d^2 \sqrt{c+d x}}","\frac{2 (b c-a d)}{3 d^2 (c+d x)^{3/2}}-\frac{2 b}{d^2 \sqrt{c+d x}}",1,"(2*(b*c - a*d))/(3*d^2*(c + d*x)^(3/2)) - (2*b)/(d^2*Sqrt[c + d*x])","A",2,1,15,0.06667,1,"{43}"
1439,1,16,0,0.0013823,"\int \frac{1}{(c+d x)^{5/2}} \, dx","Int[(c + d*x)^(-5/2),x]","-\frac{2}{3 d (c+d x)^{3/2}}","-\frac{2}{3 d (c+d x)^{3/2}}",1,"-2/(3*d*(c + d*x)^(3/2))","A",1,1,9,0.1111,1,"{32}"
1440,1,93,0,0.0387108,"\int \frac{1}{(a+b x) (c+d x)^{5/2}} \, dx","Int[1/((a + b*x)*(c + d*x)^(5/2)),x]","-\frac{2 b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{(b c-a d)^{5/2}}+\frac{2 b}{\sqrt{c+d x} (b c-a d)^2}+\frac{2}{3 (c+d x)^{3/2} (b c-a d)}","-\frac{2 b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{(b c-a d)^{5/2}}+\frac{2 b}{\sqrt{c+d x} (b c-a d)^2}+\frac{2}{3 (c+d x)^{3/2} (b c-a d)}",1,"2/(3*(b*c - a*d)*(c + d*x)^(3/2)) + (2*b)/((b*c - a*d)^2*Sqrt[c + d*x]) - (2*b^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[b*c - a*d]])/(b*c - a*d)^(5/2)","A",4,3,17,0.1765,1,"{51, 63, 208}"
1441,1,124,0,0.0497228,"\int \frac{1}{(a+b x)^2 (c+d x)^{5/2}} \, dx","Int[1/((a + b*x)^2*(c + d*x)^(5/2)),x]","\frac{5 b^{3/2} d \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{(b c-a d)^{7/2}}-\frac{5 b d}{\sqrt{c+d x} (b c-a d)^3}-\frac{1}{(a+b x) (c+d x)^{3/2} (b c-a d)}-\frac{5 d}{3 (c+d x)^{3/2} (b c-a d)^2}","\frac{5 b^{3/2} d \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{(b c-a d)^{7/2}}-\frac{5 b d}{\sqrt{c+d x} (b c-a d)^3}-\frac{1}{(a+b x) (c+d x)^{3/2} (b c-a d)}-\frac{5 d}{3 (c+d x)^{3/2} (b c-a d)^2}",1,"(-5*d)/(3*(b*c - a*d)^2*(c + d*x)^(3/2)) - 1/((b*c - a*d)*(a + b*x)*(c + d*x)^(3/2)) - (5*b*d)/((b*c - a*d)^3*Sqrt[c + d*x]) + (5*b^(3/2)*d*ArcTanh[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[b*c - a*d]])/(b*c - a*d)^(7/2)","A",5,3,17,0.1765,1,"{51, 63, 208}"
1442,1,167,0,0.0616835,"\int \frac{1}{(a+b x)^3 (c+d x)^{5/2}} \, dx","Int[1/((a + b*x)^3*(c + d*x)^(5/2)),x]","-\frac{35 b^{3/2} d^2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{4 (b c-a d)^{9/2}}+\frac{35 b d^2}{4 \sqrt{c+d x} (b c-a d)^4}+\frac{35 d^2}{12 (c+d x)^{3/2} (b c-a d)^3}+\frac{7 d}{4 (a+b x) (c+d x)^{3/2} (b c-a d)^2}-\frac{1}{2 (a+b x)^2 (c+d x)^{3/2} (b c-a d)}","-\frac{35 b^{3/2} d^2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{4 (b c-a d)^{9/2}}+\frac{35 b d^2}{4 \sqrt{c+d x} (b c-a d)^4}+\frac{35 d^2}{12 (c+d x)^{3/2} (b c-a d)^3}+\frac{7 d}{4 (a+b x) (c+d x)^{3/2} (b c-a d)^2}-\frac{1}{2 (a+b x)^2 (c+d x)^{3/2} (b c-a d)}",1,"(35*d^2)/(12*(b*c - a*d)^3*(c + d*x)^(3/2)) - 1/(2*(b*c - a*d)*(a + b*x)^2*(c + d*x)^(3/2)) + (7*d)/(4*(b*c - a*d)^2*(a + b*x)*(c + d*x)^(3/2)) + (35*b*d^2)/(4*(b*c - a*d)^4*Sqrt[c + d*x]) - (35*b^(3/2)*d^2*ArcTanh[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[b*c - a*d]])/(4*(b*c - a*d)^(9/2))","A",6,3,17,0.1765,1,"{51, 63, 208}"
1443,1,200,0,0.1344472,"\int \frac{1}{(a+b x)^4 (c+d x)^{5/2}} \, dx","Int[1/((a + b*x)^4*(c + d*x)^(5/2)),x]","\frac{105 b^{3/2} d^3 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{8 (b c-a d)^{11/2}}-\frac{105 b d^3}{8 \sqrt{c+d x} (b c-a d)^5}-\frac{35 d^3}{8 (c+d x)^{3/2} (b c-a d)^4}-\frac{21 d^2}{8 (a+b x) (c+d x)^{3/2} (b c-a d)^3}+\frac{3 d}{4 (a+b x)^2 (c+d x)^{3/2} (b c-a d)^2}-\frac{1}{3 (a+b x)^3 (c+d x)^{3/2} (b c-a d)}","\frac{105 b^{3/2} d^3 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{8 (b c-a d)^{11/2}}-\frac{105 b d^3}{8 \sqrt{c+d x} (b c-a d)^5}-\frac{35 d^3}{8 (c+d x)^{3/2} (b c-a d)^4}-\frac{21 d^2}{8 (a+b x) (c+d x)^{3/2} (b c-a d)^3}+\frac{3 d}{4 (a+b x)^2 (c+d x)^{3/2} (b c-a d)^2}-\frac{1}{3 (a+b x)^3 (c+d x)^{3/2} (b c-a d)}",1,"(-35*d^3)/(8*(b*c - a*d)^4*(c + d*x)^(3/2)) - 1/(3*(b*c - a*d)*(a + b*x)^3*(c + d*x)^(3/2)) + (3*d)/(4*(b*c - a*d)^2*(a + b*x)^2*(c + d*x)^(3/2)) - (21*d^2)/(8*(b*c - a*d)^3*(a + b*x)*(c + d*x)^(3/2)) - (105*b*d^3)/(8*(b*c - a*d)^5*Sqrt[c + d*x]) + (105*b^(3/2)*d^3*ArcTanh[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[b*c - a*d]])/(8*(b*c - a*d)^(11/2))","A",7,3,17,0.1765,1,"{51, 63, 208}"
1444,1,22,0,0.0045903,"\int (a+b x)^5 (a c+b c x)^{3/2} \, dx","Int[(a + b*x)^5*(a*c + b*c*x)^(3/2),x]","\frac{2 (a c+b c x)^{15/2}}{15 b c^6}","\frac{2 (a c+b c x)^{15/2}}{15 b c^6}",1,"(2*(a*c + b*c*x)^(15/2))/(15*b*c^6)","A",2,2,20,0.1000,1,"{21, 32}"
1445,1,22,0,0.0045631,"\int (a+b x)^5 \sqrt{a c+b c x} \, dx","Int[(a + b*x)^5*Sqrt[a*c + b*c*x],x]","\frac{2 (a c+b c x)^{13/2}}{13 b c^6}","\frac{2 (a c+b c x)^{13/2}}{13 b c^6}",1,"(2*(a*c + b*c*x)^(13/2))/(13*b*c^6)","A",2,2,20,0.1000,1,"{21, 32}"
1446,1,22,0,0.0044284,"\int \frac{(a+b x)^5}{\sqrt{a c+b c x}} \, dx","Int[(a + b*x)^5/Sqrt[a*c + b*c*x],x]","\frac{2 (a c+b c x)^{11/2}}{11 b c^6}","\frac{2 (a c+b c x)^{11/2}}{11 b c^6}",1,"(2*(a*c + b*c*x)^(11/2))/(11*b*c^6)","A",2,2,20,0.1000,1,"{21, 32}"
1447,1,22,0,0.0043641,"\int \frac{(a+b x)^5}{(a c+b c x)^{3/2}} \, dx","Int[(a + b*x)^5/(a*c + b*c*x)^(3/2),x]","\frac{2 (a c+b c x)^{9/2}}{9 b c^6}","\frac{2 (a c+b c x)^{9/2}}{9 b c^6}",1,"(2*(a*c + b*c*x)^(9/2))/(9*b*c^6)","A",2,2,20,0.1000,1,"{21, 32}"
1448,1,22,0,0.0042334,"\int \frac{(a+b x)^5}{(a c+b c x)^{5/2}} \, dx","Int[(a + b*x)^5/(a*c + b*c*x)^(5/2),x]","\frac{2 (a c+b c x)^{7/2}}{7 b c^6}","\frac{2 (a c+b c x)^{7/2}}{7 b c^6}",1,"(2*(a*c + b*c*x)^(7/2))/(7*b*c^6)","A",2,2,20,0.1000,1,"{21, 32}"
1449,1,22,0,0.0042234,"\int \frac{(a+b x)^5}{(a c+b c x)^{7/2}} \, dx","Int[(a + b*x)^5/(a*c + b*c*x)^(7/2),x]","\frac{2 (a c+b c x)^{5/2}}{5 b c^6}","\frac{2 (a c+b c x)^{5/2}}{5 b c^6}",1,"(2*(a*c + b*c*x)^(5/2))/(5*b*c^6)","A",2,2,20,0.1000,1,"{21, 32}"
1450,1,22,0,0.0041991,"\int \frac{(a+b x)^5}{(a c+b c x)^{9/2}} \, dx","Int[(a + b*x)^5/(a*c + b*c*x)^(9/2),x]","\frac{2 (a c+b c x)^{3/2}}{3 b c^6}","\frac{2 (a c+b c x)^{3/2}}{3 b c^6}",1,"(2*(a*c + b*c*x)^(3/2))/(3*b*c^6)","A",2,2,20,0.1000,1,"{21, 32}"
1451,1,20,0,0.0041583,"\int \frac{(a+b x)^5}{(a c+b c x)^{11/2}} \, dx","Int[(a + b*x)^5/(a*c + b*c*x)^(11/2),x]","\frac{2 \sqrt{a c+b c x}}{b c^6}","\frac{2 \sqrt{a c+b c x}}{b c^6}",1,"(2*Sqrt[a*c + b*c*x])/(b*c^6)","A",2,2,20,0.1000,1,"{21, 32}"
1452,1,20,0,0.0045802,"\int \frac{(a+b x)^5}{(a c+b c x)^{13/2}} \, dx","Int[(a + b*x)^5/(a*c + b*c*x)^(13/2),x]","-\frac{2}{b c^6 \sqrt{a c+b c x}}","-\frac{2}{b c^6 \sqrt{a c+b c x}}",1,"-2/(b*c^6*Sqrt[a*c + b*c*x])","A",2,2,20,0.1000,1,"{21, 32}"
1453,1,14,0,0.0038494,"\int \frac{1}{(-2+x) \sqrt{2+x}} \, dx","Int[1/((-2 + x)*Sqrt[2 + x]),x]","-\tanh ^{-1}\left(\frac{\sqrt{x+2}}{2}\right)","-\tanh ^{-1}\left(\frac{\sqrt{x+2}}{2}\right)",1,"-ArcTanh[Sqrt[2 + x]/2]","A",2,2,13,0.1538,1,"{63, 207}"
1454,1,25,0,0.0086591,"\int \frac{1}{(2+3 x) \sqrt{1+5 x}} \, dx","Int[1/((2 + 3*x)*Sqrt[1 + 5*x]),x]","\frac{2 \tan ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{5 x+1}\right)}{\sqrt{21}}","\frac{2 \tan ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{5 x+1}\right)}{\sqrt{21}}",1,"(2*ArcTan[Sqrt[3/7]*Sqrt[1 + 5*x]])/Sqrt[21]","A",2,2,17,0.1176,1,"{63, 203}"
1455,1,84,0,0.0377397,"\int \frac{\sqrt[3]{1-x}}{1+x} \, dx","Int[(1 - x)^(1/3)/(1 + x),x]","3 \sqrt[3]{1-x}+\frac{3 \log \left(\sqrt[3]{2}-\sqrt[3]{1-x}\right)}{2^{2/3}}-\frac{\log (x+1)}{2^{2/3}}-\sqrt[3]{2} \sqrt{3} \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{1-x}+1}{\sqrt{3}}\right)","3 \sqrt[3]{1-x}+\frac{3 \log \left(\sqrt[3]{2}-\sqrt[3]{1-x}\right)}{2^{2/3}}-\frac{\log (x+1)}{2^{2/3}}-\sqrt[3]{2} \sqrt{3} \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{1-x}+1}{\sqrt{3}}\right)",1,"3*(1 - x)^(1/3) - 2^(1/3)*Sqrt[3]*ArcTan[(1 + 2^(2/3)*(1 - x)^(1/3))/Sqrt[3]] + (3*Log[2^(1/3) - (1 - x)^(1/3)])/2^(2/3) - Log[1 + x]/2^(2/3)","A",5,5,15,0.3333,1,"{50, 57, 617, 204, 31}"
1456,1,27,0,0.0048718,"\int \sqrt[3]{3-2 x} (7+x) \, dx","Int[(3 - 2*x)^(1/3)*(7 + x),x]","\frac{3}{28} (3-2 x)^{7/3}-\frac{51}{16} (3-2 x)^{4/3}","\frac{3}{28} (3-2 x)^{7/3}-\frac{51}{16} (3-2 x)^{4/3}",1,"(-51*(3 - 2*x)^(4/3))/16 + (3*(3 - 2*x)^(7/3))/28","A",2,1,13,0.07692,1,"{43}"
1457,1,38,0,0.0068215,"\int \sqrt[3]{1-x} (1+x)^2 \, dx","Int[(1 - x)^(1/3)*(1 + x)^2,x]","-\frac{3}{10} (1-x)^{10/3}+\frac{12}{7} (1-x)^{7/3}-3 (1-x)^{4/3}","-\frac{3}{10} (1-x)^{10/3}+\frac{12}{7} (1-x)^{7/3}-3 (1-x)^{4/3}",1,"-3*(1 - x)^(4/3) + (12*(1 - x)^(7/3))/7 - (3*(1 - x)^(10/3))/10","A",2,1,15,0.06667,1,"{43}"
1458,1,139,0,0.1084454,"\int \frac{1}{(a+b x) \sqrt[3]{c+d x}} \, dx","Int[1/((a + b*x)*(c + d*x)^(1/3)),x]","-\frac{\log (a+b x)}{2 b^{2/3} \sqrt[3]{b c-a d}}+\frac{3 \log \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{2 b^{2/3} \sqrt[3]{b c-a d}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}}+1}{\sqrt{3}}\right)}{b^{2/3} \sqrt[3]{b c-a d}}","-\frac{\log (a+b x)}{2 b^{2/3} \sqrt[3]{b c-a d}}+\frac{3 \log \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{2 b^{2/3} \sqrt[3]{b c-a d}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}}+1}{\sqrt{3}}\right)}{b^{2/3} \sqrt[3]{b c-a d}}",1,"(Sqrt[3]*ArcTan[(1 + (2*b^(1/3)*(c + d*x)^(1/3))/(b*c - a*d)^(1/3))/Sqrt[3]])/(b^(2/3)*(b*c - a*d)^(1/3)) - Log[a + b*x]/(2*b^(2/3)*(b*c - a*d)^(1/3)) + (3*Log[(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)])/(2*b^(2/3)*(b*c - a*d)^(1/3))","A",4,4,17,0.2353,1,"{55, 617, 204, 31}"
1459,1,140,0,0.0744044,"\int \frac{1}{(a+b x) (c+d x)^{2/3}} \, dx","Int[1/((a + b*x)*(c + d*x)^(2/3)),x]","-\frac{\log (a+b x)}{2 \sqrt[3]{b} (b c-a d)^{2/3}}+\frac{3 \log \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{2 \sqrt[3]{b} (b c-a d)^{2/3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}}+1}{\sqrt{3}}\right)}{\sqrt[3]{b} (b c-a d)^{2/3}}","-\frac{\log (a+b x)}{2 \sqrt[3]{b} (b c-a d)^{2/3}}+\frac{3 \log \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{2 \sqrt[3]{b} (b c-a d)^{2/3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}}+1}{\sqrt{3}}\right)}{\sqrt[3]{b} (b c-a d)^{2/3}}",1,"-((Sqrt[3]*ArcTan[(1 + (2*b^(1/3)*(c + d*x)^(1/3))/(b*c - a*d)^(1/3))/Sqrt[3]])/(b^(1/3)*(b*c - a*d)^(2/3))) - Log[a + b*x]/(2*b^(1/3)*(b*c - a*d)^(2/3)) + (3*Log[(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)])/(2*b^(1/3)*(b*c - a*d)^(2/3))","A",4,4,17,0.2353,1,"{57, 617, 204, 31}"
1460,1,230,0,0.1603161,"\int (a+b x)^{7/2} \sqrt{c+d x} \, dx","Int[(a + b*x)^(7/2)*Sqrt[c + d*x],x]","\frac{7 (b c-a d)^5 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{128 b^{3/2} d^{9/2}}-\frac{7 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^4}{128 b d^4}+\frac{7 (a+b x)^{3/2} \sqrt{c+d x} (b c-a d)^3}{192 b d^3}-\frac{7 (a+b x)^{5/2} \sqrt{c+d x} (b c-a d)^2}{240 b d^2}+\frac{(a+b x)^{7/2} \sqrt{c+d x} (b c-a d)}{40 b d}+\frac{(a+b x)^{9/2} \sqrt{c+d x}}{5 b}","\frac{7 (b c-a d)^5 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{128 b^{3/2} d^{9/2}}-\frac{7 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^4}{128 b d^4}+\frac{7 (a+b x)^{3/2} \sqrt{c+d x} (b c-a d)^3}{192 b d^3}-\frac{7 (a+b x)^{5/2} \sqrt{c+d x} (b c-a d)^2}{240 b d^2}+\frac{(a+b x)^{7/2} \sqrt{c+d x} (b c-a d)}{40 b d}+\frac{(a+b x)^{9/2} \sqrt{c+d x}}{5 b}",1,"(-7*(b*c - a*d)^4*Sqrt[a + b*x]*Sqrt[c + d*x])/(128*b*d^4) + (7*(b*c - a*d)^3*(a + b*x)^(3/2)*Sqrt[c + d*x])/(192*b*d^3) - (7*(b*c - a*d)^2*(a + b*x)^(5/2)*Sqrt[c + d*x])/(240*b*d^2) + ((b*c - a*d)*(a + b*x)^(7/2)*Sqrt[c + d*x])/(40*b*d) + ((a + b*x)^(9/2)*Sqrt[c + d*x])/(5*b) + (7*(b*c - a*d)^5*ArcTanh[(Sqrt[d]*Sqrt[a + b*x])/(Sqrt[b]*Sqrt[c + d*x])])/(128*b^(3/2)*d^(9/2))","A",8,4,19,0.2105,1,"{50, 63, 217, 206}"
1461,1,192,0,0.0946061,"\int (a+b x)^{5/2} \sqrt{c+d x} \, dx","Int[(a + b*x)^(5/2)*Sqrt[c + d*x],x]","-\frac{5 (b c-a d)^4 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{64 b^{3/2} d^{7/2}}+\frac{5 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^3}{64 b d^3}-\frac{5 (a+b x)^{3/2} \sqrt{c+d x} (b c-a d)^2}{96 b d^2}+\frac{(a+b x)^{5/2} \sqrt{c+d x} (b c-a d)}{24 b d}+\frac{(a+b x)^{7/2} \sqrt{c+d x}}{4 b}","-\frac{5 (b c-a d)^4 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{64 b^{3/2} d^{7/2}}+\frac{5 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^3}{64 b d^3}-\frac{5 (a+b x)^{3/2} \sqrt{c+d x} (b c-a d)^2}{96 b d^2}+\frac{(a+b x)^{5/2} \sqrt{c+d x} (b c-a d)}{24 b d}+\frac{(a+b x)^{7/2} \sqrt{c+d x}}{4 b}",1,"(5*(b*c - a*d)^3*Sqrt[a + b*x]*Sqrt[c + d*x])/(64*b*d^3) - (5*(b*c - a*d)^2*(a + b*x)^(3/2)*Sqrt[c + d*x])/(96*b*d^2) + ((b*c - a*d)*(a + b*x)^(5/2)*Sqrt[c + d*x])/(24*b*d) + ((a + b*x)^(7/2)*Sqrt[c + d*x])/(4*b) - (5*(b*c - a*d)^4*ArcTanh[(Sqrt[d]*Sqrt[a + b*x])/(Sqrt[b]*Sqrt[c + d*x])])/(64*b^(3/2)*d^(7/2))","A",7,4,19,0.2105,1,"{50, 63, 217, 206}"
1462,1,154,0,0.0718098,"\int (a+b x)^{3/2} \sqrt{c+d x} \, dx","Int[(a + b*x)^(3/2)*Sqrt[c + d*x],x]","\frac{(b c-a d)^3 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{8 b^{3/2} d^{5/2}}-\frac{\sqrt{a+b x} \sqrt{c+d x} (b c-a d)^2}{8 b d^2}+\frac{(a+b x)^{3/2} \sqrt{c+d x} (b c-a d)}{12 b d}+\frac{(a+b x)^{5/2} \sqrt{c+d x}}{3 b}","\frac{(b c-a d)^3 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{8 b^{3/2} d^{5/2}}-\frac{\sqrt{a+b x} \sqrt{c+d x} (b c-a d)^2}{8 b d^2}+\frac{(a+b x)^{3/2} \sqrt{c+d x} (b c-a d)}{12 b d}+\frac{(a+b x)^{5/2} \sqrt{c+d x}}{3 b}",1,"-((b*c - a*d)^2*Sqrt[a + b*x]*Sqrt[c + d*x])/(8*b*d^2) + ((b*c - a*d)*(a + b*x)^(3/2)*Sqrt[c + d*x])/(12*b*d) + ((a + b*x)^(5/2)*Sqrt[c + d*x])/(3*b) + ((b*c - a*d)^3*ArcTanh[(Sqrt[d]*Sqrt[a + b*x])/(Sqrt[b]*Sqrt[c + d*x])])/(8*b^(3/2)*d^(5/2))","A",6,4,19,0.2105,1,"{50, 63, 217, 206}"
1463,1,116,0,0.0545892,"\int \sqrt{a+b x} \sqrt{c+d x} \, dx","Int[Sqrt[a + b*x]*Sqrt[c + d*x],x]","-\frac{(b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{4 b^{3/2} d^{3/2}}+\frac{\sqrt{a+b x} \sqrt{c+d x} (b c-a d)}{4 b d}+\frac{(a+b x)^{3/2} \sqrt{c+d x}}{2 b}","-\frac{(b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{4 b^{3/2} d^{3/2}}+\frac{\sqrt{a+b x} \sqrt{c+d x} (b c-a d)}{4 b d}+\frac{(a+b x)^{3/2} \sqrt{c+d x}}{2 b}",1,"((b*c - a*d)*Sqrt[a + b*x]*Sqrt[c + d*x])/(4*b*d) + ((a + b*x)^(3/2)*Sqrt[c + d*x])/(2*b) - ((b*c - a*d)^2*ArcTanh[(Sqrt[d]*Sqrt[a + b*x])/(Sqrt[b]*Sqrt[c + d*x])])/(4*b^(3/2)*d^(3/2))","A",5,4,19,0.2105,1,"{50, 63, 217, 206}"
1464,1,72,0,0.0377266,"\int \frac{\sqrt{c+d x}}{\sqrt{a+b x}} \, dx","Int[Sqrt[c + d*x]/Sqrt[a + b*x],x]","\frac{(b c-a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{b^{3/2} \sqrt{d}}+\frac{\sqrt{a+b x} \sqrt{c+d x}}{b}","\frac{(b c-a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{b^{3/2} \sqrt{d}}+\frac{\sqrt{a+b x} \sqrt{c+d x}}{b}",1,"(Sqrt[a + b*x]*Sqrt[c + d*x])/b + ((b*c - a*d)*ArcTanh[(Sqrt[d]*Sqrt[a + b*x])/(Sqrt[b]*Sqrt[c + d*x])])/(b^(3/2)*Sqrt[d])","A",4,4,19,0.2105,1,"{50, 63, 217, 206}"
1465,1,66,0,0.0332162,"\int \frac{\sqrt{c+d x}}{(a+b x)^{3/2}} \, dx","Int[Sqrt[c + d*x]/(a + b*x)^(3/2),x]","\frac{2 \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{b^{3/2}}-\frac{2 \sqrt{c+d x}}{b \sqrt{a+b x}}","\frac{2 \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{b^{3/2}}-\frac{2 \sqrt{c+d x}}{b \sqrt{a+b x}}",1,"(-2*Sqrt[c + d*x])/(b*Sqrt[a + b*x]) + (2*Sqrt[d]*ArcTanh[(Sqrt[d]*Sqrt[a + b*x])/(Sqrt[b]*Sqrt[c + d*x])])/b^(3/2)","A",4,4,19,0.2105,1,"{47, 63, 217, 206}"
1466,1,32,0,0.0029979,"\int \frac{\sqrt{c+d x}}{(a+b x)^{5/2}} \, dx","Int[Sqrt[c + d*x]/(a + b*x)^(5/2),x]","-\frac{2 (c+d x)^{3/2}}{3 (a+b x)^{3/2} (b c-a d)}","-\frac{2 (c+d x)^{3/2}}{3 (a+b x)^{3/2} (b c-a d)}",1,"(-2*(c + d*x)^(3/2))/(3*(b*c - a*d)*(a + b*x)^(3/2))","A",1,1,19,0.05263,1,"{37}"
1467,1,66,0,0.0086535,"\int \frac{\sqrt{c+d x}}{(a+b x)^{7/2}} \, dx","Int[Sqrt[c + d*x]/(a + b*x)^(7/2),x]","\frac{4 d (c+d x)^{3/2}}{15 (a+b x)^{3/2} (b c-a d)^2}-\frac{2 (c+d x)^{3/2}}{5 (a+b x)^{5/2} (b c-a d)}","\frac{4 d (c+d x)^{3/2}}{15 (a+b x)^{3/2} (b c-a d)^2}-\frac{2 (c+d x)^{3/2}}{5 (a+b x)^{5/2} (b c-a d)}",1,"(-2*(c + d*x)^(3/2))/(5*(b*c - a*d)*(a + b*x)^(5/2)) + (4*d*(c + d*x)^(3/2))/(15*(b*c - a*d)^2*(a + b*x)^(3/2))","A",2,2,19,0.1053,1,"{45, 37}"
1468,1,101,0,0.016475,"\int \frac{\sqrt{c+d x}}{(a+b x)^{9/2}} \, dx","Int[Sqrt[c + d*x]/(a + b*x)^(9/2),x]","-\frac{16 d^2 (c+d x)^{3/2}}{105 (a+b x)^{3/2} (b c-a d)^3}+\frac{8 d (c+d x)^{3/2}}{35 (a+b x)^{5/2} (b c-a d)^2}-\frac{2 (c+d x)^{3/2}}{7 (a+b x)^{7/2} (b c-a d)}","-\frac{16 d^2 (c+d x)^{3/2}}{105 (a+b x)^{3/2} (b c-a d)^3}+\frac{8 d (c+d x)^{3/2}}{35 (a+b x)^{5/2} (b c-a d)^2}-\frac{2 (c+d x)^{3/2}}{7 (a+b x)^{7/2} (b c-a d)}",1,"(-2*(c + d*x)^(3/2))/(7*(b*c - a*d)*(a + b*x)^(7/2)) + (8*d*(c + d*x)^(3/2))/(35*(b*c - a*d)^2*(a + b*x)^(5/2)) - (16*d^2*(c + d*x)^(3/2))/(105*(b*c - a*d)^3*(a + b*x)^(3/2))","A",3,2,19,0.1053,1,"{45, 37}"
1469,1,136,0,0.0285565,"\int \frac{\sqrt{c+d x}}{(a+b x)^{11/2}} \, dx","Int[Sqrt[c + d*x]/(a + b*x)^(11/2),x]","\frac{32 d^3 (c+d x)^{3/2}}{315 (a+b x)^{3/2} (b c-a d)^4}-\frac{16 d^2 (c+d x)^{3/2}}{105 (a+b x)^{5/2} (b c-a d)^3}+\frac{4 d (c+d x)^{3/2}}{21 (a+b x)^{7/2} (b c-a d)^2}-\frac{2 (c+d x)^{3/2}}{9 (a+b x)^{9/2} (b c-a d)}","\frac{32 d^3 (c+d x)^{3/2}}{315 (a+b x)^{3/2} (b c-a d)^4}-\frac{16 d^2 (c+d x)^{3/2}}{105 (a+b x)^{5/2} (b c-a d)^3}+\frac{4 d (c+d x)^{3/2}}{21 (a+b x)^{7/2} (b c-a d)^2}-\frac{2 (c+d x)^{3/2}}{9 (a+b x)^{9/2} (b c-a d)}",1,"(-2*(c + d*x)^(3/2))/(9*(b*c - a*d)*(a + b*x)^(9/2)) + (4*d*(c + d*x)^(3/2))/(21*(b*c - a*d)^2*(a + b*x)^(7/2)) - (16*d^2*(c + d*x)^(3/2))/(105*(b*c - a*d)^3*(a + b*x)^(5/2)) + (32*d^3*(c + d*x)^(3/2))/(315*(b*c - a*d)^4*(a + b*x)^(3/2))","A",4,2,19,0.1053,1,"{45, 37}"
1470,1,171,0,0.0414111,"\int \frac{\sqrt{c+d x}}{(a+b x)^{13/2}} \, dx","Int[Sqrt[c + d*x]/(a + b*x)^(13/2),x]","-\frac{256 d^4 (c+d x)^{3/2}}{3465 (a+b x)^{3/2} (b c-a d)^5}+\frac{128 d^3 (c+d x)^{3/2}}{1155 (a+b x)^{5/2} (b c-a d)^4}-\frac{32 d^2 (c+d x)^{3/2}}{231 (a+b x)^{7/2} (b c-a d)^3}+\frac{16 d (c+d x)^{3/2}}{99 (a+b x)^{9/2} (b c-a d)^2}-\frac{2 (c+d x)^{3/2}}{11 (a+b x)^{11/2} (b c-a d)}","-\frac{256 d^4 (c+d x)^{3/2}}{3465 (a+b x)^{3/2} (b c-a d)^5}+\frac{128 d^3 (c+d x)^{3/2}}{1155 (a+b x)^{5/2} (b c-a d)^4}-\frac{32 d^2 (c+d x)^{3/2}}{231 (a+b x)^{7/2} (b c-a d)^3}+\frac{16 d (c+d x)^{3/2}}{99 (a+b x)^{9/2} (b c-a d)^2}-\frac{2 (c+d x)^{3/2}}{11 (a+b x)^{11/2} (b c-a d)}",1,"(-2*(c + d*x)^(3/2))/(11*(b*c - a*d)*(a + b*x)^(11/2)) + (16*d*(c + d*x)^(3/2))/(99*(b*c - a*d)^2*(a + b*x)^(9/2)) - (32*d^2*(c + d*x)^(3/2))/(231*(b*c - a*d)^3*(a + b*x)^(7/2)) + (128*d^3*(c + d*x)^(3/2))/(1155*(b*c - a*d)^4*(a + b*x)^(5/2)) - (256*d^4*(c + d*x)^(3/2))/(3465*(b*c - a*d)^5*(a + b*x)^(3/2))","A",5,2,19,0.1053,1,"{45, 37}"
1471,1,227,0,0.1302241,"\int (a+b x)^{5/2} (c+d x)^{3/2} \, dx","Int[(a + b*x)^(5/2)*(c + d*x)^(3/2),x]","\frac{3 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^4}{128 b^2 d^3}-\frac{(a+b x)^{3/2} \sqrt{c+d x} (b c-a d)^3}{64 b^2 d^2}-\frac{3 (b c-a d)^5 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{128 b^{5/2} d^{7/2}}+\frac{(a+b x)^{5/2} \sqrt{c+d x} (b c-a d)^2}{80 b^2 d}+\frac{3 (a+b x)^{7/2} \sqrt{c+d x} (b c-a d)}{40 b^2}+\frac{(a+b x)^{7/2} (c+d x)^{3/2}}{5 b}","\frac{3 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^4}{128 b^2 d^3}-\frac{(a+b x)^{3/2} \sqrt{c+d x} (b c-a d)^3}{64 b^2 d^2}-\frac{3 (b c-a d)^5 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{128 b^{5/2} d^{7/2}}+\frac{(a+b x)^{5/2} \sqrt{c+d x} (b c-a d)^2}{80 b^2 d}+\frac{3 (a+b x)^{7/2} \sqrt{c+d x} (b c-a d)}{40 b^2}+\frac{(a+b x)^{7/2} (c+d x)^{3/2}}{5 b}",1,"(3*(b*c - a*d)^4*Sqrt[a + b*x]*Sqrt[c + d*x])/(128*b^2*d^3) - ((b*c - a*d)^3*(a + b*x)^(3/2)*Sqrt[c + d*x])/(64*b^2*d^2) + ((b*c - a*d)^2*(a + b*x)^(5/2)*Sqrt[c + d*x])/(80*b^2*d) + (3*(b*c - a*d)*(a + b*x)^(7/2)*Sqrt[c + d*x])/(40*b^2) + ((a + b*x)^(7/2)*(c + d*x)^(3/2))/(5*b) - (3*(b*c - a*d)^5*ArcTanh[(Sqrt[d]*Sqrt[a + b*x])/(Sqrt[b]*Sqrt[c + d*x])])/(128*b^(5/2)*d^(7/2))","A",8,4,19,0.2105,1,"{50, 63, 217, 206}"
1472,1,189,0,0.0898839,"\int (a+b x)^{3/2} (c+d x)^{3/2} \, dx","Int[(a + b*x)^(3/2)*(c + d*x)^(3/2),x]","-\frac{3 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^3}{64 b^2 d^2}+\frac{3 (b c-a d)^4 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{64 b^{5/2} d^{5/2}}+\frac{(a+b x)^{3/2} \sqrt{c+d x} (b c-a d)^2}{32 b^2 d}+\frac{(a+b x)^{5/2} \sqrt{c+d x} (b c-a d)}{8 b^2}+\frac{(a+b x)^{5/2} (c+d x)^{3/2}}{4 b}","-\frac{3 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^3}{64 b^2 d^2}+\frac{3 (b c-a d)^4 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{64 b^{5/2} d^{5/2}}+\frac{(a+b x)^{3/2} \sqrt{c+d x} (b c-a d)^2}{32 b^2 d}+\frac{(a+b x)^{5/2} \sqrt{c+d x} (b c-a d)}{8 b^2}+\frac{(a+b x)^{5/2} (c+d x)^{3/2}}{4 b}",1,"(-3*(b*c - a*d)^3*Sqrt[a + b*x]*Sqrt[c + d*x])/(64*b^2*d^2) + ((b*c - a*d)^2*(a + b*x)^(3/2)*Sqrt[c + d*x])/(32*b^2*d) + ((b*c - a*d)*(a + b*x)^(5/2)*Sqrt[c + d*x])/(8*b^2) + ((a + b*x)^(5/2)*(c + d*x)^(3/2))/(4*b) + (3*(b*c - a*d)^4*ArcTanh[(Sqrt[d]*Sqrt[a + b*x])/(Sqrt[b]*Sqrt[c + d*x])])/(64*b^(5/2)*d^(5/2))","A",7,4,19,0.2105,1,"{50, 63, 217, 206}"
1473,1,151,0,0.0676236,"\int \sqrt{a+b x} (c+d x)^{3/2} \, dx","Int[Sqrt[a + b*x]*(c + d*x)^(3/2),x]","-\frac{(b c-a d)^3 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{8 b^{5/2} d^{3/2}}+\frac{\sqrt{a+b x} \sqrt{c+d x} (b c-a d)^2}{8 b^2 d}+\frac{(a+b x)^{3/2} \sqrt{c+d x} (b c-a d)}{4 b^2}+\frac{(a+b x)^{3/2} (c+d x)^{3/2}}{3 b}","-\frac{(b c-a d)^3 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{8 b^{5/2} d^{3/2}}+\frac{\sqrt{a+b x} \sqrt{c+d x} (b c-a d)^2}{8 b^2 d}+\frac{(a+b x)^{3/2} \sqrt{c+d x} (b c-a d)}{4 b^2}+\frac{(a+b x)^{3/2} (c+d x)^{3/2}}{3 b}",1,"((b*c - a*d)^2*Sqrt[a + b*x]*Sqrt[c + d*x])/(8*b^2*d) + ((b*c - a*d)*(a + b*x)^(3/2)*Sqrt[c + d*x])/(4*b^2) + ((a + b*x)^(3/2)*(c + d*x)^(3/2))/(3*b) - ((b*c - a*d)^3*ArcTanh[(Sqrt[d]*Sqrt[a + b*x])/(Sqrt[b]*Sqrt[c + d*x])])/(8*b^(5/2)*d^(3/2))","A",6,4,19,0.2105,1,"{50, 63, 217, 206}"
1474,1,113,0,0.0510619,"\int \frac{(c+d x)^{3/2}}{\sqrt{a+b x}} \, dx","Int[(c + d*x)^(3/2)/Sqrt[a + b*x],x]","\frac{3 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)}{4 b^2}+\frac{3 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{4 b^{5/2} \sqrt{d}}+\frac{\sqrt{a+b x} (c+d x)^{3/2}}{2 b}","\frac{3 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)}{4 b^2}+\frac{3 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{4 b^{5/2} \sqrt{d}}+\frac{\sqrt{a+b x} (c+d x)^{3/2}}{2 b}",1,"(3*(b*c - a*d)*Sqrt[a + b*x]*Sqrt[c + d*x])/(4*b^2) + (Sqrt[a + b*x]*(c + d*x)^(3/2))/(2*b) + (3*(b*c - a*d)^2*ArcTanh[(Sqrt[d]*Sqrt[a + b*x])/(Sqrt[b]*Sqrt[c + d*x])])/(4*b^(5/2)*Sqrt[d])","A",5,4,19,0.2105,1,"{50, 63, 217, 206}"
1475,1,98,0,0.046969,"\int \frac{(c+d x)^{3/2}}{(a+b x)^{3/2}} \, dx","Int[(c + d*x)^(3/2)/(a + b*x)^(3/2),x]","\frac{3 d \sqrt{a+b x} \sqrt{c+d x}}{b^2}+\frac{3 \sqrt{d} (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{b^{5/2}}-\frac{2 (c+d x)^{3/2}}{b \sqrt{a+b x}}","\frac{3 d \sqrt{a+b x} \sqrt{c+d x}}{b^2}+\frac{3 \sqrt{d} (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{b^{5/2}}-\frac{2 (c+d x)^{3/2}}{b \sqrt{a+b x}}",1,"(3*d*Sqrt[a + b*x]*Sqrt[c + d*x])/b^2 - (2*(c + d*x)^(3/2))/(b*Sqrt[a + b*x]) + (3*Sqrt[d]*(b*c - a*d)*ArcTanh[(Sqrt[d]*Sqrt[a + b*x])/(Sqrt[b]*Sqrt[c + d*x])])/b^(5/2)","A",5,5,19,0.2632,1,"{47, 50, 63, 217, 206}"
1476,1,92,0,0.0397725,"\int \frac{(c+d x)^{3/2}}{(a+b x)^{5/2}} \, dx","Int[(c + d*x)^(3/2)/(a + b*x)^(5/2),x]","\frac{2 d^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{b^{5/2}}-\frac{2 d \sqrt{c+d x}}{b^2 \sqrt{a+b x}}-\frac{2 (c+d x)^{3/2}}{3 b (a+b x)^{3/2}}","\frac{2 d^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{b^{5/2}}-\frac{2 d \sqrt{c+d x}}{b^2 \sqrt{a+b x}}-\frac{2 (c+d x)^{3/2}}{3 b (a+b x)^{3/2}}",1,"(-2*d*Sqrt[c + d*x])/(b^2*Sqrt[a + b*x]) - (2*(c + d*x)^(3/2))/(3*b*(a + b*x)^(3/2)) + (2*d^(3/2)*ArcTanh[(Sqrt[d]*Sqrt[a + b*x])/(Sqrt[b]*Sqrt[c + d*x])])/b^(5/2)","A",5,4,19,0.2105,1,"{47, 63, 217, 206}"
1477,1,32,0,0.0030631,"\int \frac{(c+d x)^{3/2}}{(a+b x)^{7/2}} \, dx","Int[(c + d*x)^(3/2)/(a + b*x)^(7/2),x]","-\frac{2 (c+d x)^{5/2}}{5 (a+b x)^{5/2} (b c-a d)}","-\frac{2 (c+d x)^{5/2}}{5 (a+b x)^{5/2} (b c-a d)}",1,"(-2*(c + d*x)^(5/2))/(5*(b*c - a*d)*(a + b*x)^(5/2))","A",1,1,19,0.05263,1,"{37}"
1478,1,66,0,0.0082446,"\int \frac{(c+d x)^{3/2}}{(a+b x)^{9/2}} \, dx","Int[(c + d*x)^(3/2)/(a + b*x)^(9/2),x]","\frac{4 d (c+d x)^{5/2}}{35 (a+b x)^{5/2} (b c-a d)^2}-\frac{2 (c+d x)^{5/2}}{7 (a+b x)^{7/2} (b c-a d)}","\frac{4 d (c+d x)^{5/2}}{35 (a+b x)^{5/2} (b c-a d)^2}-\frac{2 (c+d x)^{5/2}}{7 (a+b x)^{7/2} (b c-a d)}",1,"(-2*(c + d*x)^(5/2))/(7*(b*c - a*d)*(a + b*x)^(7/2)) + (4*d*(c + d*x)^(5/2))/(35*(b*c - a*d)^2*(a + b*x)^(5/2))","A",2,2,19,0.1053,1,"{45, 37}"
1479,1,101,0,0.015951,"\int \frac{(c+d x)^{3/2}}{(a+b x)^{11/2}} \, dx","Int[(c + d*x)^(3/2)/(a + b*x)^(11/2),x]","-\frac{16 d^2 (c+d x)^{5/2}}{315 (a+b x)^{5/2} (b c-a d)^3}+\frac{8 d (c+d x)^{5/2}}{63 (a+b x)^{7/2} (b c-a d)^2}-\frac{2 (c+d x)^{5/2}}{9 (a+b x)^{9/2} (b c-a d)}","-\frac{16 d^2 (c+d x)^{5/2}}{315 (a+b x)^{5/2} (b c-a d)^3}+\frac{8 d (c+d x)^{5/2}}{63 (a+b x)^{7/2} (b c-a d)^2}-\frac{2 (c+d x)^{5/2}}{9 (a+b x)^{9/2} (b c-a d)}",1,"(-2*(c + d*x)^(5/2))/(9*(b*c - a*d)*(a + b*x)^(9/2)) + (8*d*(c + d*x)^(5/2))/(63*(b*c - a*d)^2*(a + b*x)^(7/2)) - (16*d^2*(c + d*x)^(5/2))/(315*(b*c - a*d)^3*(a + b*x)^(5/2))","A",3,2,19,0.1053,1,"{45, 37}"
1480,1,136,0,0.0283103,"\int \frac{(c+d x)^{3/2}}{(a+b x)^{13/2}} \, dx","Int[(c + d*x)^(3/2)/(a + b*x)^(13/2),x]","\frac{32 d^3 (c+d x)^{5/2}}{1155 (a+b x)^{5/2} (b c-a d)^4}-\frac{16 d^2 (c+d x)^{5/2}}{231 (a+b x)^{7/2} (b c-a d)^3}+\frac{4 d (c+d x)^{5/2}}{33 (a+b x)^{9/2} (b c-a d)^2}-\frac{2 (c+d x)^{5/2}}{11 (a+b x)^{11/2} (b c-a d)}","\frac{32 d^3 (c+d x)^{5/2}}{1155 (a+b x)^{5/2} (b c-a d)^4}-\frac{16 d^2 (c+d x)^{5/2}}{231 (a+b x)^{7/2} (b c-a d)^3}+\frac{4 d (c+d x)^{5/2}}{33 (a+b x)^{9/2} (b c-a d)^2}-\frac{2 (c+d x)^{5/2}}{11 (a+b x)^{11/2} (b c-a d)}",1,"(-2*(c + d*x)^(5/2))/(11*(b*c - a*d)*(a + b*x)^(11/2)) + (4*d*(c + d*x)^(5/2))/(33*(b*c - a*d)^2*(a + b*x)^(9/2)) - (16*d^2*(c + d*x)^(5/2))/(231*(b*c - a*d)^3*(a + b*x)^(7/2)) + (32*d^3*(c + d*x)^(5/2))/(1155*(b*c - a*d)^4*(a + b*x)^(5/2))","A",4,2,19,0.1053,1,"{45, 37}"
1481,1,262,0,0.1492998,"\int (a+b x)^{5/2} (c+d x)^{5/2} \, dx","Int[(a + b*x)^(5/2)*(c + d*x)^(5/2),x]","\frac{5 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^5}{512 b^3 d^3}-\frac{5 (a+b x)^{3/2} \sqrt{c+d x} (b c-a d)^4}{768 b^3 d^2}-\frac{5 (b c-a d)^6 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{512 b^{7/2} d^{7/2}}+\frac{(a+b x)^{5/2} \sqrt{c+d x} (b c-a d)^3}{192 b^3 d}+\frac{(a+b x)^{7/2} \sqrt{c+d x} (b c-a d)^2}{32 b^3}+\frac{(a+b x)^{7/2} (c+d x)^{3/2} (b c-a d)}{12 b^2}+\frac{(a+b x)^{7/2} (c+d x)^{5/2}}{6 b}","\frac{5 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^5}{512 b^3 d^3}-\frac{5 (a+b x)^{3/2} \sqrt{c+d x} (b c-a d)^4}{768 b^3 d^2}-\frac{5 (b c-a d)^6 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{512 b^{7/2} d^{7/2}}+\frac{(a+b x)^{5/2} \sqrt{c+d x} (b c-a d)^3}{192 b^3 d}+\frac{(a+b x)^{7/2} \sqrt{c+d x} (b c-a d)^2}{32 b^3}+\frac{(a+b x)^{7/2} (c+d x)^{3/2} (b c-a d)}{12 b^2}+\frac{(a+b x)^{7/2} (c+d x)^{5/2}}{6 b}",1,"(5*(b*c - a*d)^5*Sqrt[a + b*x]*Sqrt[c + d*x])/(512*b^3*d^3) - (5*(b*c - a*d)^4*(a + b*x)^(3/2)*Sqrt[c + d*x])/(768*b^3*d^2) + ((b*c - a*d)^3*(a + b*x)^(5/2)*Sqrt[c + d*x])/(192*b^3*d) + ((b*c - a*d)^2*(a + b*x)^(7/2)*Sqrt[c + d*x])/(32*b^3) + ((b*c - a*d)*(a + b*x)^(7/2)*(c + d*x)^(3/2))/(12*b^2) + ((a + b*x)^(7/2)*(c + d*x)^(5/2))/(6*b) - (5*(b*c - a*d)^6*ArcTanh[(Sqrt[d]*Sqrt[a + b*x])/(Sqrt[b]*Sqrt[c + d*x])])/(512*b^(7/2)*d^(7/2))","A",9,4,19,0.2105,1,"{50, 63, 217, 206}"
1482,1,224,0,0.1194477,"\int (a+b x)^{3/2} (c+d x)^{5/2} \, dx","Int[(a + b*x)^(3/2)*(c + d*x)^(5/2),x]","-\frac{3 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^4}{128 b^3 d^2}+\frac{3 (b c-a d)^5 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{128 b^{7/2} d^{5/2}}+\frac{(a+b x)^{3/2} \sqrt{c+d x} (b c-a d)^3}{64 b^3 d}+\frac{(a+b x)^{5/2} \sqrt{c+d x} (b c-a d)^2}{16 b^3}+\frac{(a+b x)^{5/2} (c+d x)^{3/2} (b c-a d)}{8 b^2}+\frac{(a+b x)^{5/2} (c+d x)^{5/2}}{5 b}","-\frac{3 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^4}{128 b^3 d^2}+\frac{3 (b c-a d)^5 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{128 b^{7/2} d^{5/2}}+\frac{(a+b x)^{3/2} \sqrt{c+d x} (b c-a d)^3}{64 b^3 d}+\frac{(a+b x)^{5/2} \sqrt{c+d x} (b c-a d)^2}{16 b^3}+\frac{(a+b x)^{5/2} (c+d x)^{3/2} (b c-a d)}{8 b^2}+\frac{(a+b x)^{5/2} (c+d x)^{5/2}}{5 b}",1,"(-3*(b*c - a*d)^4*Sqrt[a + b*x]*Sqrt[c + d*x])/(128*b^3*d^2) + ((b*c - a*d)^3*(a + b*x)^(3/2)*Sqrt[c + d*x])/(64*b^3*d) + ((b*c - a*d)^2*(a + b*x)^(5/2)*Sqrt[c + d*x])/(16*b^3) + ((b*c - a*d)*(a + b*x)^(5/2)*(c + d*x)^(3/2))/(8*b^2) + ((a + b*x)^(5/2)*(c + d*x)^(5/2))/(5*b) + (3*(b*c - a*d)^5*ArcTanh[(Sqrt[d]*Sqrt[a + b*x])/(Sqrt[b]*Sqrt[c + d*x])])/(128*b^(7/2)*d^(5/2))","A",8,4,19,0.2105,1,"{50, 63, 217, 206}"
1483,1,186,0,0.0863186,"\int \sqrt{a+b x} (c+d x)^{5/2} \, dx","Int[Sqrt[a + b*x]*(c + d*x)^(5/2),x]","-\frac{5 (b c-a d)^4 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{64 b^{7/2} d^{3/2}}+\frac{5 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^3}{64 b^3 d}+\frac{5 (a+b x)^{3/2} \sqrt{c+d x} (b c-a d)^2}{32 b^3}+\frac{5 (a+b x)^{3/2} (c+d x)^{3/2} (b c-a d)}{24 b^2}+\frac{(a+b x)^{3/2} (c+d x)^{5/2}}{4 b}","-\frac{5 (b c-a d)^4 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{64 b^{7/2} d^{3/2}}+\frac{5 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^3}{64 b^3 d}+\frac{5 (a+b x)^{3/2} \sqrt{c+d x} (b c-a d)^2}{32 b^3}+\frac{5 (a+b x)^{3/2} (c+d x)^{3/2} (b c-a d)}{24 b^2}+\frac{(a+b x)^{3/2} (c+d x)^{5/2}}{4 b}",1,"(5*(b*c - a*d)^3*Sqrt[a + b*x]*Sqrt[c + d*x])/(64*b^3*d) + (5*(b*c - a*d)^2*(a + b*x)^(3/2)*Sqrt[c + d*x])/(32*b^3) + (5*(b*c - a*d)*(a + b*x)^(3/2)*(c + d*x)^(3/2))/(24*b^2) + ((a + b*x)^(3/2)*(c + d*x)^(5/2))/(4*b) - (5*(b*c - a*d)^4*ArcTanh[(Sqrt[d]*Sqrt[a + b*x])/(Sqrt[b]*Sqrt[c + d*x])])/(64*b^(7/2)*d^(3/2))","A",7,4,19,0.2105,1,"{50, 63, 217, 206}"
1484,1,148,0,0.0663875,"\int \frac{(c+d x)^{5/2}}{\sqrt{a+b x}} \, dx","Int[(c + d*x)^(5/2)/Sqrt[a + b*x],x]","\frac{5 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^2}{8 b^3}+\frac{5 \sqrt{a+b x} (c+d x)^{3/2} (b c-a d)}{12 b^2}+\frac{5 (b c-a d)^3 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{8 b^{7/2} \sqrt{d}}+\frac{\sqrt{a+b x} (c+d x)^{5/2}}{3 b}","\frac{5 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^2}{8 b^3}+\frac{5 \sqrt{a+b x} (c+d x)^{3/2} (b c-a d)}{12 b^2}+\frac{5 (b c-a d)^3 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{8 b^{7/2} \sqrt{d}}+\frac{\sqrt{a+b x} (c+d x)^{5/2}}{3 b}",1,"(5*(b*c - a*d)^2*Sqrt[a + b*x]*Sqrt[c + d*x])/(8*b^3) + (5*(b*c - a*d)*Sqrt[a + b*x]*(c + d*x)^(3/2))/(12*b^2) + (Sqrt[a + b*x]*(c + d*x)^(5/2))/(3*b) + (5*(b*c - a*d)^3*ArcTanh[(Sqrt[d]*Sqrt[a + b*x])/(Sqrt[b]*Sqrt[c + d*x])])/(8*b^(7/2)*Sqrt[d])","A",6,4,19,0.2105,1,"{50, 63, 217, 206}"
1485,1,138,0,0.0628883,"\int \frac{(c+d x)^{5/2}}{(a+b x)^{3/2}} \, dx","Int[(c + d*x)^(5/2)/(a + b*x)^(3/2),x]","\frac{5 d \sqrt{a+b x} (c+d x)^{3/2}}{2 b^2}+\frac{15 d \sqrt{a+b x} \sqrt{c+d x} (b c-a d)}{4 b^3}+\frac{15 \sqrt{d} (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{4 b^{7/2}}-\frac{2 (c+d x)^{5/2}}{b \sqrt{a+b x}}","\frac{5 d \sqrt{a+b x} (c+d x)^{3/2}}{2 b^2}+\frac{15 d \sqrt{a+b x} \sqrt{c+d x} (b c-a d)}{4 b^3}+\frac{15 \sqrt{d} (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{4 b^{7/2}}-\frac{2 (c+d x)^{5/2}}{b \sqrt{a+b x}}",1,"(15*d*(b*c - a*d)*Sqrt[a + b*x]*Sqrt[c + d*x])/(4*b^3) + (5*d*Sqrt[a + b*x]*(c + d*x)^(3/2))/(2*b^2) - (2*(c + d*x)^(5/2))/(b*Sqrt[a + b*x]) + (15*Sqrt[d]*(b*c - a*d)^2*ArcTanh[(Sqrt[d]*Sqrt[a + b*x])/(Sqrt[b]*Sqrt[c + d*x])])/(4*b^(7/2))","A",6,5,19,0.2632,1,"{47, 50, 63, 217, 206}"
1486,1,128,0,0.0615877,"\int \frac{(c+d x)^{5/2}}{(a+b x)^{5/2}} \, dx","Int[(c + d*x)^(5/2)/(a + b*x)^(5/2),x]","\frac{5 d^2 \sqrt{a+b x} \sqrt{c+d x}}{b^3}+\frac{5 d^{3/2} (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{b^{7/2}}-\frac{10 d (c+d x)^{3/2}}{3 b^2 \sqrt{a+b x}}-\frac{2 (c+d x)^{5/2}}{3 b (a+b x)^{3/2}}","\frac{5 d^2 \sqrt{a+b x} \sqrt{c+d x}}{b^3}+\frac{5 d^{3/2} (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{b^{7/2}}-\frac{10 d (c+d x)^{3/2}}{3 b^2 \sqrt{a+b x}}-\frac{2 (c+d x)^{5/2}}{3 b (a+b x)^{3/2}}",1,"(5*d^2*Sqrt[a + b*x]*Sqrt[c + d*x])/b^3 - (10*d*(c + d*x)^(3/2))/(3*b^2*Sqrt[a + b*x]) - (2*(c + d*x)^(5/2))/(3*b*(a + b*x)^(3/2)) + (5*d^(3/2)*(b*c - a*d)*ArcTanh[(Sqrt[d]*Sqrt[a + b*x])/(Sqrt[b]*Sqrt[c + d*x])])/b^(7/2)","A",6,5,19,0.2632,1,"{47, 50, 63, 217, 206}"
1487,1,120,0,0.0519115,"\int \frac{(c+d x)^{5/2}}{(a+b x)^{7/2}} \, dx","Int[(c + d*x)^(5/2)/(a + b*x)^(7/2),x]","-\frac{2 d^2 \sqrt{c+d x}}{b^3 \sqrt{a+b x}}+\frac{2 d^{5/2} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{b^{7/2}}-\frac{2 d (c+d x)^{3/2}}{3 b^2 (a+b x)^{3/2}}-\frac{2 (c+d x)^{5/2}}{5 b (a+b x)^{5/2}}","-\frac{2 d^2 \sqrt{c+d x}}{b^3 \sqrt{a+b x}}+\frac{2 d^{5/2} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{b^{7/2}}-\frac{2 d (c+d x)^{3/2}}{3 b^2 (a+b x)^{3/2}}-\frac{2 (c+d x)^{5/2}}{5 b (a+b x)^{5/2}}",1,"(-2*d^2*Sqrt[c + d*x])/(b^3*Sqrt[a + b*x]) - (2*d*(c + d*x)^(3/2))/(3*b^2*(a + b*x)^(3/2)) - (2*(c + d*x)^(5/2))/(5*b*(a + b*x)^(5/2)) + (2*d^(5/2)*ArcTanh[(Sqrt[d]*Sqrt[a + b*x])/(Sqrt[b]*Sqrt[c + d*x])])/b^(7/2)","A",6,4,19,0.2105,1,"{47, 63, 217, 206}"
1488,1,32,0,0.0028235,"\int \frac{(c+d x)^{5/2}}{(a+b x)^{9/2}} \, dx","Int[(c + d*x)^(5/2)/(a + b*x)^(9/2),x]","-\frac{2 (c+d x)^{7/2}}{7 (a+b x)^{7/2} (b c-a d)}","-\frac{2 (c+d x)^{7/2}}{7 (a+b x)^{7/2} (b c-a d)}",1,"(-2*(c + d*x)^(7/2))/(7*(b*c - a*d)*(a + b*x)^(7/2))","A",1,1,19,0.05263,1,"{37}"
1489,1,66,0,0.0090831,"\int \frac{(c+d x)^{5/2}}{(a+b x)^{11/2}} \, dx","Int[(c + d*x)^(5/2)/(a + b*x)^(11/2),x]","\frac{4 d (c+d x)^{7/2}}{63 (a+b x)^{7/2} (b c-a d)^2}-\frac{2 (c+d x)^{7/2}}{9 (a+b x)^{9/2} (b c-a d)}","\frac{4 d (c+d x)^{7/2}}{63 (a+b x)^{7/2} (b c-a d)^2}-\frac{2 (c+d x)^{7/2}}{9 (a+b x)^{9/2} (b c-a d)}",1,"(-2*(c + d*x)^(7/2))/(9*(b*c - a*d)*(a + b*x)^(9/2)) + (4*d*(c + d*x)^(7/2))/(63*(b*c - a*d)^2*(a + b*x)^(7/2))","A",2,2,19,0.1053,1,"{45, 37}"
1490,1,101,0,0.0162974,"\int \frac{(c+d x)^{5/2}}{(a+b x)^{13/2}} \, dx","Int[(c + d*x)^(5/2)/(a + b*x)^(13/2),x]","-\frac{16 d^2 (c+d x)^{7/2}}{693 (a+b x)^{7/2} (b c-a d)^3}+\frac{8 d (c+d x)^{7/2}}{99 (a+b x)^{9/2} (b c-a d)^2}-\frac{2 (c+d x)^{7/2}}{11 (a+b x)^{11/2} (b c-a d)}","-\frac{16 d^2 (c+d x)^{7/2}}{693 (a+b x)^{7/2} (b c-a d)^3}+\frac{8 d (c+d x)^{7/2}}{99 (a+b x)^{9/2} (b c-a d)^2}-\frac{2 (c+d x)^{7/2}}{11 (a+b x)^{11/2} (b c-a d)}",1,"(-2*(c + d*x)^(7/2))/(11*(b*c - a*d)*(a + b*x)^(11/2)) + (8*d*(c + d*x)^(7/2))/(99*(b*c - a*d)^2*(a + b*x)^(9/2)) - (16*d^2*(c + d*x)^(7/2))/(693*(b*c - a*d)^3*(a + b*x)^(7/2))","A",3,2,19,0.1053,1,"{45, 37}"
1491,1,136,0,0.0278713,"\int \frac{(c+d x)^{5/2}}{(a+b x)^{15/2}} \, dx","Int[(c + d*x)^(5/2)/(a + b*x)^(15/2),x]","\frac{32 d^3 (c+d x)^{7/2}}{3003 (a+b x)^{7/2} (b c-a d)^4}-\frac{16 d^2 (c+d x)^{7/2}}{429 (a+b x)^{9/2} (b c-a d)^3}+\frac{12 d (c+d x)^{7/2}}{143 (a+b x)^{11/2} (b c-a d)^2}-\frac{2 (c+d x)^{7/2}}{13 (a+b x)^{13/2} (b c-a d)}","\frac{32 d^3 (c+d x)^{7/2}}{3003 (a+b x)^{7/2} (b c-a d)^4}-\frac{16 d^2 (c+d x)^{7/2}}{429 (a+b x)^{9/2} (b c-a d)^3}+\frac{12 d (c+d x)^{7/2}}{143 (a+b x)^{11/2} (b c-a d)^2}-\frac{2 (c+d x)^{7/2}}{13 (a+b x)^{13/2} (b c-a d)}",1,"(-2*(c + d*x)^(7/2))/(13*(b*c - a*d)*(a + b*x)^(13/2)) + (12*d*(c + d*x)^(7/2))/(143*(b*c - a*d)^2*(a + b*x)^(11/2)) - (16*d^2*(c + d*x)^(7/2))/(429*(b*c - a*d)^3*(a + b*x)^(9/2)) + (32*d^3*(c + d*x)^(7/2))/(3003*(b*c - a*d)^4*(a + b*x)^(7/2))","A",4,2,19,0.1053,1,"{45, 37}"
1492,1,183,0,0.0967502,"\int \frac{(a+b x)^{7/2}}{\sqrt{c+d x}} \, dx","Int[(a + b*x)^(7/2)/Sqrt[c + d*x],x]","-\frac{35 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^3}{64 d^4}+\frac{35 (a+b x)^{3/2} \sqrt{c+d x} (b c-a d)^2}{96 d^3}-\frac{7 (a+b x)^{5/2} \sqrt{c+d x} (b c-a d)}{24 d^2}+\frac{35 (b c-a d)^4 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{64 \sqrt{b} d^{9/2}}+\frac{(a+b x)^{7/2} \sqrt{c+d x}}{4 d}","-\frac{35 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^3}{64 d^4}+\frac{35 (a+b x)^{3/2} \sqrt{c+d x} (b c-a d)^2}{96 d^3}-\frac{7 (a+b x)^{5/2} \sqrt{c+d x} (b c-a d)}{24 d^2}+\frac{35 (b c-a d)^4 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{64 \sqrt{b} d^{9/2}}+\frac{(a+b x)^{7/2} \sqrt{c+d x}}{4 d}",1,"(-35*(b*c - a*d)^3*Sqrt[a + b*x]*Sqrt[c + d*x])/(64*d^4) + (35*(b*c - a*d)^2*(a + b*x)^(3/2)*Sqrt[c + d*x])/(96*d^3) - (7*(b*c - a*d)*(a + b*x)^(5/2)*Sqrt[c + d*x])/(24*d^2) + ((a + b*x)^(7/2)*Sqrt[c + d*x])/(4*d) + (35*(b*c - a*d)^4*ArcTanh[(Sqrt[d]*Sqrt[a + b*x])/(Sqrt[b]*Sqrt[c + d*x])])/(64*Sqrt[b]*d^(9/2))","A",7,4,19,0.2105,1,"{50, 63, 217, 206}"
1493,1,148,0,0.0723475,"\int \frac{(a+b x)^{5/2}}{\sqrt{c+d x}} \, dx","Int[(a + b*x)^(5/2)/Sqrt[c + d*x],x]","\frac{5 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^2}{8 d^3}-\frac{5 (a+b x)^{3/2} \sqrt{c+d x} (b c-a d)}{12 d^2}-\frac{5 (b c-a d)^3 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{8 \sqrt{b} d^{7/2}}+\frac{(a+b x)^{5/2} \sqrt{c+d x}}{3 d}","\frac{5 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^2}{8 d^3}-\frac{5 (a+b x)^{3/2} \sqrt{c+d x} (b c-a d)}{12 d^2}-\frac{5 (b c-a d)^3 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{8 \sqrt{b} d^{7/2}}+\frac{(a+b x)^{5/2} \sqrt{c+d x}}{3 d}",1,"(5*(b*c - a*d)^2*Sqrt[a + b*x]*Sqrt[c + d*x])/(8*d^3) - (5*(b*c - a*d)*(a + b*x)^(3/2)*Sqrt[c + d*x])/(12*d^2) + ((a + b*x)^(5/2)*Sqrt[c + d*x])/(3*d) - (5*(b*c - a*d)^3*ArcTanh[(Sqrt[d]*Sqrt[a + b*x])/(Sqrt[b]*Sqrt[c + d*x])])/(8*Sqrt[b]*d^(7/2))","A",6,4,19,0.2105,1,"{50, 63, 217, 206}"
1494,1,113,0,0.0500458,"\int \frac{(a+b x)^{3/2}}{\sqrt{c+d x}} \, dx","Int[(a + b*x)^(3/2)/Sqrt[c + d*x],x]","-\frac{3 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)}{4 d^2}+\frac{3 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{4 \sqrt{b} d^{5/2}}+\frac{(a+b x)^{3/2} \sqrt{c+d x}}{2 d}","-\frac{3 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)}{4 d^2}+\frac{3 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{4 \sqrt{b} d^{5/2}}+\frac{(a+b x)^{3/2} \sqrt{c+d x}}{2 d}",1,"(-3*(b*c - a*d)*Sqrt[a + b*x]*Sqrt[c + d*x])/(4*d^2) + ((a + b*x)^(3/2)*Sqrt[c + d*x])/(2*d) + (3*(b*c - a*d)^2*ArcTanh[(Sqrt[d]*Sqrt[a + b*x])/(Sqrt[b]*Sqrt[c + d*x])])/(4*Sqrt[b]*d^(5/2))","A",5,4,19,0.2105,1,"{50, 63, 217, 206}"
1495,1,73,0,0.0352477,"\int \frac{\sqrt{a+b x}}{\sqrt{c+d x}} \, dx","Int[Sqrt[a + b*x]/Sqrt[c + d*x],x]","\frac{\sqrt{a+b x} \sqrt{c+d x}}{d}-\frac{(b c-a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{\sqrt{b} d^{3/2}}","\frac{\sqrt{a+b x} \sqrt{c+d x}}{d}-\frac{(b c-a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{\sqrt{b} d^{3/2}}",1,"(Sqrt[a + b*x]*Sqrt[c + d*x])/d - ((b*c - a*d)*ArcTanh[(Sqrt[d]*Sqrt[a + b*x])/(Sqrt[b]*Sqrt[c + d*x])])/(Sqrt[b]*d^(3/2))","A",4,4,19,0.2105,1,"{50, 63, 217, 206}"
1496,1,42,0,0.0260562,"\int \frac{1}{\sqrt{a+b x} \sqrt{c+d x}} \, dx","Int[1/(Sqrt[a + b*x]*Sqrt[c + d*x]),x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{\sqrt{b} \sqrt{d}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{\sqrt{b} \sqrt{d}}",1,"(2*ArcTanh[(Sqrt[d]*Sqrt[a + b*x])/(Sqrt[b]*Sqrt[c + d*x])])/(Sqrt[b]*Sqrt[d])","A",3,3,19,0.1579,1,"{63, 217, 206}"
1497,1,30,0,0.0028276,"\int \frac{1}{(a+b x)^{3/2} \sqrt{c+d x}} \, dx","Int[1/((a + b*x)^(3/2)*Sqrt[c + d*x]),x]","-\frac{2 \sqrt{c+d x}}{\sqrt{a+b x} (b c-a d)}","-\frac{2 \sqrt{c+d x}}{\sqrt{a+b x} (b c-a d)}",1,"(-2*Sqrt[c + d*x])/((b*c - a*d)*Sqrt[a + b*x])","A",1,1,19,0.05263,1,"{37}"
1498,1,66,0,0.0083011,"\int \frac{1}{(a+b x)^{5/2} \sqrt{c+d x}} \, dx","Int[1/((a + b*x)^(5/2)*Sqrt[c + d*x]),x]","\frac{4 d \sqrt{c+d x}}{3 \sqrt{a+b x} (b c-a d)^2}-\frac{2 \sqrt{c+d x}}{3 (a+b x)^{3/2} (b c-a d)}","\frac{4 d \sqrt{c+d x}}{3 \sqrt{a+b x} (b c-a d)^2}-\frac{2 \sqrt{c+d x}}{3 (a+b x)^{3/2} (b c-a d)}",1,"(-2*Sqrt[c + d*x])/(3*(b*c - a*d)*(a + b*x)^(3/2)) + (4*d*Sqrt[c + d*x])/(3*(b*c - a*d)^2*Sqrt[a + b*x])","A",2,2,19,0.1053,1,"{45, 37}"
1499,1,101,0,0.016225,"\int \frac{1}{(a+b x)^{7/2} \sqrt{c+d x}} \, dx","Int[1/((a + b*x)^(7/2)*Sqrt[c + d*x]),x]","-\frac{16 d^2 \sqrt{c+d x}}{15 \sqrt{a+b x} (b c-a d)^3}+\frac{8 d \sqrt{c+d x}}{15 (a+b x)^{3/2} (b c-a d)^2}-\frac{2 \sqrt{c+d x}}{5 (a+b x)^{5/2} (b c-a d)}","-\frac{16 d^2 \sqrt{c+d x}}{15 \sqrt{a+b x} (b c-a d)^3}+\frac{8 d \sqrt{c+d x}}{15 (a+b x)^{3/2} (b c-a d)^2}-\frac{2 \sqrt{c+d x}}{5 (a+b x)^{5/2} (b c-a d)}",1,"(-2*Sqrt[c + d*x])/(5*(b*c - a*d)*(a + b*x)^(5/2)) + (8*d*Sqrt[c + d*x])/(15*(b*c - a*d)^2*(a + b*x)^(3/2)) - (16*d^2*Sqrt[c + d*x])/(15*(b*c - a*d)^3*Sqrt[a + b*x])","A",3,2,19,0.1053,1,"{45, 37}"
1500,1,136,0,0.0280244,"\int \frac{1}{(a+b x)^{9/2} \sqrt{c+d x}} \, dx","Int[1/((a + b*x)^(9/2)*Sqrt[c + d*x]),x]","\frac{32 d^3 \sqrt{c+d x}}{35 \sqrt{a+b x} (b c-a d)^4}-\frac{16 d^2 \sqrt{c+d x}}{35 (a+b x)^{3/2} (b c-a d)^3}+\frac{12 d \sqrt{c+d x}}{35 (a+b x)^{5/2} (b c-a d)^2}-\frac{2 \sqrt{c+d x}}{7 (a+b x)^{7/2} (b c-a d)}","\frac{32 d^3 \sqrt{c+d x}}{35 \sqrt{a+b x} (b c-a d)^4}-\frac{16 d^2 \sqrt{c+d x}}{35 (a+b x)^{3/2} (b c-a d)^3}+\frac{12 d \sqrt{c+d x}}{35 (a+b x)^{5/2} (b c-a d)^2}-\frac{2 \sqrt{c+d x}}{7 (a+b x)^{7/2} (b c-a d)}",1,"(-2*Sqrt[c + d*x])/(7*(b*c - a*d)*(a + b*x)^(7/2)) + (12*d*Sqrt[c + d*x])/(35*(b*c - a*d)^2*(a + b*x)^(5/2)) - (16*d^2*Sqrt[c + d*x])/(35*(b*c - a*d)^3*(a + b*x)^(3/2)) + (32*d^3*Sqrt[c + d*x])/(35*(b*c - a*d)^4*Sqrt[a + b*x])","A",4,2,19,0.1053,1,"{45, 37}"
1501,1,171,0,0.0409882,"\int \frac{1}{(a+b x)^{11/2} \sqrt{c+d x}} \, dx","Int[1/((a + b*x)^(11/2)*Sqrt[c + d*x]),x]","-\frac{256 d^4 \sqrt{c+d x}}{315 \sqrt{a+b x} (b c-a d)^5}+\frac{128 d^3 \sqrt{c+d x}}{315 (a+b x)^{3/2} (b c-a d)^4}-\frac{32 d^2 \sqrt{c+d x}}{105 (a+b x)^{5/2} (b c-a d)^3}+\frac{16 d \sqrt{c+d x}}{63 (a+b x)^{7/2} (b c-a d)^2}-\frac{2 \sqrt{c+d x}}{9 (a+b x)^{9/2} (b c-a d)}","-\frac{256 d^4 \sqrt{c+d x}}{315 \sqrt{a+b x} (b c-a d)^5}+\frac{128 d^3 \sqrt{c+d x}}{315 (a+b x)^{3/2} (b c-a d)^4}-\frac{32 d^2 \sqrt{c+d x}}{105 (a+b x)^{5/2} (b c-a d)^3}+\frac{16 d \sqrt{c+d x}}{63 (a+b x)^{7/2} (b c-a d)^2}-\frac{2 \sqrt{c+d x}}{9 (a+b x)^{9/2} (b c-a d)}",1,"(-2*Sqrt[c + d*x])/(9*(b*c - a*d)*(a + b*x)^(9/2)) + (16*d*Sqrt[c + d*x])/(63*(b*c - a*d)^2*(a + b*x)^(7/2)) - (32*d^2*Sqrt[c + d*x])/(105*(b*c - a*d)^3*(a + b*x)^(5/2)) + (128*d^3*Sqrt[c + d*x])/(315*(b*c - a*d)^4*(a + b*x)^(3/2)) - (256*d^4*Sqrt[c + d*x])/(315*(b*c - a*d)^5*Sqrt[a + b*x])","A",5,2,19,0.1053,1,"{45, 37}"
1502,1,174,0,0.0891534,"\int \frac{(a+b x)^{7/2}}{(c+d x)^{3/2}} \, dx","Int[(a + b*x)^(7/2)/(c + d*x)^(3/2),x]","\frac{7 b (a+b x)^{5/2} \sqrt{c+d x}}{3 d^2}-\frac{35 b (a+b x)^{3/2} \sqrt{c+d x} (b c-a d)}{12 d^3}+\frac{35 b \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^2}{8 d^4}-\frac{35 \sqrt{b} (b c-a d)^3 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{8 d^{9/2}}-\frac{2 (a+b x)^{7/2}}{d \sqrt{c+d x}}","\frac{7 b (a+b x)^{5/2} \sqrt{c+d x}}{3 d^2}-\frac{35 b (a+b x)^{3/2} \sqrt{c+d x} (b c-a d)}{12 d^3}+\frac{35 b \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^2}{8 d^4}-\frac{35 \sqrt{b} (b c-a d)^3 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{8 d^{9/2}}-\frac{2 (a+b x)^{7/2}}{d \sqrt{c+d x}}",1,"(-2*(a + b*x)^(7/2))/(d*Sqrt[c + d*x]) + (35*b*(b*c - a*d)^2*Sqrt[a + b*x]*Sqrt[c + d*x])/(8*d^4) - (35*b*(b*c - a*d)*(a + b*x)^(3/2)*Sqrt[c + d*x])/(12*d^3) + (7*b*(a + b*x)^(5/2)*Sqrt[c + d*x])/(3*d^2) - (35*Sqrt[b]*(b*c - a*d)^3*ArcTanh[(Sqrt[d]*Sqrt[a + b*x])/(Sqrt[b]*Sqrt[c + d*x])])/(8*d^(9/2))","A",7,5,19,0.2632,1,"{47, 50, 63, 217, 206}"
1503,1,138,0,0.0666129,"\int \frac{(a+b x)^{5/2}}{(c+d x)^{3/2}} \, dx","Int[(a + b*x)^(5/2)/(c + d*x)^(3/2),x]","\frac{5 b (a+b x)^{3/2} \sqrt{c+d x}}{2 d^2}-\frac{15 b \sqrt{a+b x} \sqrt{c+d x} (b c-a d)}{4 d^3}+\frac{15 \sqrt{b} (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{4 d^{7/2}}-\frac{2 (a+b x)^{5/2}}{d \sqrt{c+d x}}","\frac{5 b (a+b x)^{3/2} \sqrt{c+d x}}{2 d^2}-\frac{15 b \sqrt{a+b x} \sqrt{c+d x} (b c-a d)}{4 d^3}+\frac{15 \sqrt{b} (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{4 d^{7/2}}-\frac{2 (a+b x)^{5/2}}{d \sqrt{c+d x}}",1,"(-2*(a + b*x)^(5/2))/(d*Sqrt[c + d*x]) - (15*b*(b*c - a*d)*Sqrt[a + b*x]*Sqrt[c + d*x])/(4*d^3) + (5*b*(a + b*x)^(3/2)*Sqrt[c + d*x])/(2*d^2) + (15*Sqrt[b]*(b*c - a*d)^2*ArcTanh[(Sqrt[d]*Sqrt[a + b*x])/(Sqrt[b]*Sqrt[c + d*x])])/(4*d^(7/2))","A",6,5,19,0.2632,1,"{47, 50, 63, 217, 206}"
1504,1,98,0,0.0471672,"\int \frac{(a+b x)^{3/2}}{(c+d x)^{3/2}} \, dx","Int[(a + b*x)^(3/2)/(c + d*x)^(3/2),x]","\frac{3 b \sqrt{a+b x} \sqrt{c+d x}}{d^2}-\frac{3 \sqrt{b} (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{d^{5/2}}-\frac{2 (a+b x)^{3/2}}{d \sqrt{c+d x}}","\frac{3 b \sqrt{a+b x} \sqrt{c+d x}}{d^2}-\frac{3 \sqrt{b} (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{d^{5/2}}-\frac{2 (a+b x)^{3/2}}{d \sqrt{c+d x}}",1,"(-2*(a + b*x)^(3/2))/(d*Sqrt[c + d*x]) + (3*b*Sqrt[a + b*x]*Sqrt[c + d*x])/d^2 - (3*Sqrt[b]*(b*c - a*d)*ArcTanh[(Sqrt[d]*Sqrt[a + b*x])/(Sqrt[b]*Sqrt[c + d*x])])/d^(5/2)","A",5,5,19,0.2632,1,"{47, 50, 63, 217, 206}"
1505,1,66,0,0.0318719,"\int \frac{\sqrt{a+b x}}{(c+d x)^{3/2}} \, dx","Int[Sqrt[a + b*x]/(c + d*x)^(3/2),x]","\frac{2 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{d^{3/2}}-\frac{2 \sqrt{a+b x}}{d \sqrt{c+d x}}","\frac{2 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{d^{3/2}}-\frac{2 \sqrt{a+b x}}{d \sqrt{c+d x}}",1,"(-2*Sqrt[a + b*x])/(d*Sqrt[c + d*x]) + (2*Sqrt[b]*ArcTanh[(Sqrt[d]*Sqrt[a + b*x])/(Sqrt[b]*Sqrt[c + d*x])])/d^(3/2)","A",4,4,19,0.2105,1,"{47, 63, 217, 206}"
1506,1,30,0,0.0027923,"\int \frac{1}{\sqrt{a+b x} (c+d x)^{3/2}} \, dx","Int[1/(Sqrt[a + b*x]*(c + d*x)^(3/2)),x]","\frac{2 \sqrt{a+b x}}{\sqrt{c+d x} (b c-a d)}","\frac{2 \sqrt{a+b x}}{\sqrt{c+d x} (b c-a d)}",1,"(2*Sqrt[a + b*x])/((b*c - a*d)*Sqrt[c + d*x])","A",1,1,19,0.05263,1,"{37}"
1507,1,62,0,0.0090855,"\int \frac{1}{(a+b x)^{3/2} (c+d x)^{3/2}} \, dx","Int[1/((a + b*x)^(3/2)*(c + d*x)^(3/2)),x]","-\frac{4 d \sqrt{a+b x}}{\sqrt{c+d x} (b c-a d)^2}-\frac{2}{\sqrt{a+b x} \sqrt{c+d x} (b c-a d)}","-\frac{4 d \sqrt{a+b x}}{\sqrt{c+d x} (b c-a d)^2}-\frac{2}{\sqrt{a+b x} \sqrt{c+d x} (b c-a d)}",1,"-2/((b*c - a*d)*Sqrt[a + b*x]*Sqrt[c + d*x]) - (4*d*Sqrt[a + b*x])/((b*c - a*d)^2*Sqrt[c + d*x])","A",2,2,19,0.1053,1,"{45, 37}"
1508,1,101,0,0.0178873,"\int \frac{1}{(a+b x)^{5/2} (c+d x)^{3/2}} \, dx","Int[1/((a + b*x)^(5/2)*(c + d*x)^(3/2)),x]","\frac{16 d^2 \sqrt{a+b x}}{3 \sqrt{c+d x} (b c-a d)^3}+\frac{8 d}{3 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^2}-\frac{2}{3 (a+b x)^{3/2} \sqrt{c+d x} (b c-a d)}","\frac{16 d^2 \sqrt{a+b x}}{3 \sqrt{c+d x} (b c-a d)^3}+\frac{8 d}{3 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^2}-\frac{2}{3 (a+b x)^{3/2} \sqrt{c+d x} (b c-a d)}",1,"-2/(3*(b*c - a*d)*(a + b*x)^(3/2)*Sqrt[c + d*x]) + (8*d)/(3*(b*c - a*d)^2*Sqrt[a + b*x]*Sqrt[c + d*x]) + (16*d^2*Sqrt[a + b*x])/(3*(b*c - a*d)^3*Sqrt[c + d*x])","A",3,2,19,0.1053,1,"{45, 37}"
1509,1,136,0,0.0270072,"\int \frac{1}{(a+b x)^{7/2} (c+d x)^{3/2}} \, dx","Int[1/((a + b*x)^(7/2)*(c + d*x)^(3/2)),x]","-\frac{32 d^3 \sqrt{a+b x}}{5 \sqrt{c+d x} (b c-a d)^4}-\frac{16 d^2}{5 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^3}+\frac{4 d}{5 (a+b x)^{3/2} \sqrt{c+d x} (b c-a d)^2}-\frac{2}{5 (a+b x)^{5/2} \sqrt{c+d x} (b c-a d)}","-\frac{32 d^3 \sqrt{a+b x}}{5 \sqrt{c+d x} (b c-a d)^4}-\frac{16 d^2}{5 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^3}+\frac{4 d}{5 (a+b x)^{3/2} \sqrt{c+d x} (b c-a d)^2}-\frac{2}{5 (a+b x)^{5/2} \sqrt{c+d x} (b c-a d)}",1,"-2/(5*(b*c - a*d)*(a + b*x)^(5/2)*Sqrt[c + d*x]) + (4*d)/(5*(b*c - a*d)^2*(a + b*x)^(3/2)*Sqrt[c + d*x]) - (16*d^2)/(5*(b*c - a*d)^3*Sqrt[a + b*x]*Sqrt[c + d*x]) - (32*d^3*Sqrt[a + b*x])/(5*(b*c - a*d)^4*Sqrt[c + d*x])","A",4,2,19,0.1053,1,"{45, 37}"
1510,1,171,0,0.0432695,"\int \frac{1}{(a+b x)^{9/2} (c+d x)^{3/2}} \, dx","Int[1/((a + b*x)^(9/2)*(c + d*x)^(3/2)),x]","\frac{256 d^4 \sqrt{a+b x}}{35 \sqrt{c+d x} (b c-a d)^5}+\frac{128 d^3}{35 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^4}-\frac{32 d^2}{35 (a+b x)^{3/2} \sqrt{c+d x} (b c-a d)^3}+\frac{16 d}{35 (a+b x)^{5/2} \sqrt{c+d x} (b c-a d)^2}-\frac{2}{7 (a+b x)^{7/2} \sqrt{c+d x} (b c-a d)}","\frac{256 d^4 \sqrt{a+b x}}{35 \sqrt{c+d x} (b c-a d)^5}+\frac{128 d^3}{35 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^4}-\frac{32 d^2}{35 (a+b x)^{3/2} \sqrt{c+d x} (b c-a d)^3}+\frac{16 d}{35 (a+b x)^{5/2} \sqrt{c+d x} (b c-a d)^2}-\frac{2}{7 (a+b x)^{7/2} \sqrt{c+d x} (b c-a d)}",1,"-2/(7*(b*c - a*d)*(a + b*x)^(7/2)*Sqrt[c + d*x]) + (16*d)/(35*(b*c - a*d)^2*(a + b*x)^(5/2)*Sqrt[c + d*x]) - (32*d^2)/(35*(b*c - a*d)^3*(a + b*x)^(3/2)*Sqrt[c + d*x]) + (128*d^3)/(35*(b*c - a*d)^4*Sqrt[a + b*x]*Sqrt[c + d*x]) + (256*d^4*Sqrt[a + b*x])/(35*(b*c - a*d)^5*Sqrt[c + d*x])","A",5,2,19,0.1053,1,"{45, 37}"
1511,1,206,0,0.0565066,"\int \frac{1}{(a+b x)^{11/2} (c+d x)^{3/2}} \, dx","Int[1/((a + b*x)^(11/2)*(c + d*x)^(3/2)),x]","-\frac{512 d^5 \sqrt{a+b x}}{63 \sqrt{c+d x} (b c-a d)^6}-\frac{256 d^4}{63 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^5}+\frac{64 d^3}{63 (a+b x)^{3/2} \sqrt{c+d x} (b c-a d)^4}-\frac{32 d^2}{63 (a+b x)^{5/2} \sqrt{c+d x} (b c-a d)^3}+\frac{20 d}{63 (a+b x)^{7/2} \sqrt{c+d x} (b c-a d)^2}-\frac{2}{9 (a+b x)^{9/2} \sqrt{c+d x} (b c-a d)}","-\frac{512 d^5 \sqrt{a+b x}}{63 \sqrt{c+d x} (b c-a d)^6}-\frac{256 d^4}{63 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^5}+\frac{64 d^3}{63 (a+b x)^{3/2} \sqrt{c+d x} (b c-a d)^4}-\frac{32 d^2}{63 (a+b x)^{5/2} \sqrt{c+d x} (b c-a d)^3}+\frac{20 d}{63 (a+b x)^{7/2} \sqrt{c+d x} (b c-a d)^2}-\frac{2}{9 (a+b x)^{9/2} \sqrt{c+d x} (b c-a d)}",1,"-2/(9*(b*c - a*d)*(a + b*x)^(9/2)*Sqrt[c + d*x]) + (20*d)/(63*(b*c - a*d)^2*(a + b*x)^(7/2)*Sqrt[c + d*x]) - (32*d^2)/(63*(b*c - a*d)^3*(a + b*x)^(5/2)*Sqrt[c + d*x]) + (64*d^3)/(63*(b*c - a*d)^4*(a + b*x)^(3/2)*Sqrt[c + d*x]) - (256*d^4)/(63*(b*c - a*d)^5*Sqrt[a + b*x]*Sqrt[c + d*x]) - (512*d^5*Sqrt[a + b*x])/(63*(b*c - a*d)^6*Sqrt[c + d*x])","A",6,2,19,0.1053,1,"{45, 37}"
1512,1,204,0,0.1086612,"\int \frac{(a+b x)^{9/2}}{(c+d x)^{5/2}} \, dx","Int[(a + b*x)^(9/2)/(c + d*x)^(5/2),x]","\frac{7 b^2 (a+b x)^{5/2} \sqrt{c+d x}}{d^3}-\frac{35 b^2 (a+b x)^{3/2} \sqrt{c+d x} (b c-a d)}{4 d^4}+\frac{105 b^2 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^2}{8 d^5}-\frac{105 b^{3/2} (b c-a d)^3 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{8 d^{11/2}}-\frac{6 b (a+b x)^{7/2}}{d^2 \sqrt{c+d x}}-\frac{2 (a+b x)^{9/2}}{3 d (c+d x)^{3/2}}","\frac{7 b^2 (a+b x)^{5/2} \sqrt{c+d x}}{d^3}-\frac{35 b^2 (a+b x)^{3/2} \sqrt{c+d x} (b c-a d)}{4 d^4}+\frac{105 b^2 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^2}{8 d^5}-\frac{105 b^{3/2} (b c-a d)^3 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{8 d^{11/2}}-\frac{6 b (a+b x)^{7/2}}{d^2 \sqrt{c+d x}}-\frac{2 (a+b x)^{9/2}}{3 d (c+d x)^{3/2}}",1,"(-2*(a + b*x)^(9/2))/(3*d*(c + d*x)^(3/2)) - (6*b*(a + b*x)^(7/2))/(d^2*Sqrt[c + d*x]) + (105*b^2*(b*c - a*d)^2*Sqrt[a + b*x]*Sqrt[c + d*x])/(8*d^5) - (35*b^2*(b*c - a*d)*(a + b*x)^(3/2)*Sqrt[c + d*x])/(4*d^4) + (7*b^2*(a + b*x)^(5/2)*Sqrt[c + d*x])/d^3 - (105*b^(3/2)*(b*c - a*d)^3*ArcTanh[(Sqrt[d]*Sqrt[a + b*x])/(Sqrt[b]*Sqrt[c + d*x])])/(8*d^(11/2))","A",8,5,19,0.2632,1,"{47, 50, 63, 217, 206}"
1513,1,170,0,0.0788944,"\int \frac{(a+b x)^{7/2}}{(c+d x)^{5/2}} \, dx","Int[(a + b*x)^(7/2)/(c + d*x)^(5/2),x]","\frac{35 b^2 (a+b x)^{3/2} \sqrt{c+d x}}{6 d^3}-\frac{35 b^2 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)}{4 d^4}+\frac{35 b^{3/2} (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{4 d^{9/2}}-\frac{14 b (a+b x)^{5/2}}{3 d^2 \sqrt{c+d x}}-\frac{2 (a+b x)^{7/2}}{3 d (c+d x)^{3/2}}","\frac{35 b^2 (a+b x)^{3/2} \sqrt{c+d x}}{6 d^3}-\frac{35 b^2 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)}{4 d^4}+\frac{35 b^{3/2} (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{4 d^{9/2}}-\frac{14 b (a+b x)^{5/2}}{3 d^2 \sqrt{c+d x}}-\frac{2 (a+b x)^{7/2}}{3 d (c+d x)^{3/2}}",1,"(-2*(a + b*x)^(7/2))/(3*d*(c + d*x)^(3/2)) - (14*b*(a + b*x)^(5/2))/(3*d^2*Sqrt[c + d*x]) - (35*b^2*(b*c - a*d)*Sqrt[a + b*x]*Sqrt[c + d*x])/(4*d^4) + (35*b^2*(a + b*x)^(3/2)*Sqrt[c + d*x])/(6*d^3) + (35*b^(3/2)*(b*c - a*d)^2*ArcTanh[(Sqrt[d]*Sqrt[a + b*x])/(Sqrt[b]*Sqrt[c + d*x])])/(4*d^(9/2))","A",7,5,19,0.2632,1,"{47, 50, 63, 217, 206}"
1514,1,128,0,0.0583784,"\int \frac{(a+b x)^{5/2}}{(c+d x)^{5/2}} \, dx","Int[(a + b*x)^(5/2)/(c + d*x)^(5/2),x]","\frac{5 b^2 \sqrt{a+b x} \sqrt{c+d x}}{d^3}-\frac{5 b^{3/2} (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{d^{7/2}}-\frac{10 b (a+b x)^{3/2}}{3 d^2 \sqrt{c+d x}}-\frac{2 (a+b x)^{5/2}}{3 d (c+d x)^{3/2}}","\frac{5 b^2 \sqrt{a+b x} \sqrt{c+d x}}{d^3}-\frac{5 b^{3/2} (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{d^{7/2}}-\frac{10 b (a+b x)^{3/2}}{3 d^2 \sqrt{c+d x}}-\frac{2 (a+b x)^{5/2}}{3 d (c+d x)^{3/2}}",1,"(-2*(a + b*x)^(5/2))/(3*d*(c + d*x)^(3/2)) - (10*b*(a + b*x)^(3/2))/(3*d^2*Sqrt[c + d*x]) + (5*b^2*Sqrt[a + b*x]*Sqrt[c + d*x])/d^3 - (5*b^(3/2)*(b*c - a*d)*ArcTanh[(Sqrt[d]*Sqrt[a + b*x])/(Sqrt[b]*Sqrt[c + d*x])])/d^(7/2)","A",6,5,19,0.2632,1,"{47, 50, 63, 217, 206}"
1515,1,92,0,0.0398938,"\int \frac{(a+b x)^{3/2}}{(c+d x)^{5/2}} \, dx","Int[(a + b*x)^(3/2)/(c + d*x)^(5/2),x]","\frac{2 b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{d^{5/2}}-\frac{2 b \sqrt{a+b x}}{d^2 \sqrt{c+d x}}-\frac{2 (a+b x)^{3/2}}{3 d (c+d x)^{3/2}}","\frac{2 b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{d^{5/2}}-\frac{2 b \sqrt{a+b x}}{d^2 \sqrt{c+d x}}-\frac{2 (a+b x)^{3/2}}{3 d (c+d x)^{3/2}}",1,"(-2*(a + b*x)^(3/2))/(3*d*(c + d*x)^(3/2)) - (2*b*Sqrt[a + b*x])/(d^2*Sqrt[c + d*x]) + (2*b^(3/2)*ArcTanh[(Sqrt[d]*Sqrt[a + b*x])/(Sqrt[b]*Sqrt[c + d*x])])/d^(5/2)","A",5,4,19,0.2105,1,"{47, 63, 217, 206}"
1516,1,32,0,0.0027823,"\int \frac{\sqrt{a+b x}}{(c+d x)^{5/2}} \, dx","Int[Sqrt[a + b*x]/(c + d*x)^(5/2),x]","\frac{2 (a+b x)^{3/2}}{3 (c+d x)^{3/2} (b c-a d)}","\frac{2 (a+b x)^{3/2}}{3 (c+d x)^{3/2} (b c-a d)}",1,"(2*(a + b*x)^(3/2))/(3*(b*c - a*d)*(c + d*x)^(3/2))","A",1,1,19,0.05263,1,"{37}"
1517,1,66,0,0.0082581,"\int \frac{1}{\sqrt{a+b x} (c+d x)^{5/2}} \, dx","Int[1/(Sqrt[a + b*x]*(c + d*x)^(5/2)),x]","\frac{4 b \sqrt{a+b x}}{3 \sqrt{c+d x} (b c-a d)^2}+\frac{2 \sqrt{a+b x}}{3 (c+d x)^{3/2} (b c-a d)}","\frac{4 b \sqrt{a+b x}}{3 \sqrt{c+d x} (b c-a d)^2}+\frac{2 \sqrt{a+b x}}{3 (c+d x)^{3/2} (b c-a d)}",1,"(2*Sqrt[a + b*x])/(3*(b*c - a*d)*(c + d*x)^(3/2)) + (4*b*Sqrt[a + b*x])/(3*(b*c - a*d)^2*Sqrt[c + d*x])","A",2,2,19,0.1053,1,"{45, 37}"
1518,1,98,0,0.0172845,"\int \frac{1}{(a+b x)^{3/2} (c+d x)^{5/2}} \, dx","Int[1/((a + b*x)^(3/2)*(c + d*x)^(5/2)),x]","-\frac{16 b d \sqrt{a+b x}}{3 \sqrt{c+d x} (b c-a d)^3}-\frac{8 d \sqrt{a+b x}}{3 (c+d x)^{3/2} (b c-a d)^2}-\frac{2}{\sqrt{a+b x} (c+d x)^{3/2} (b c-a d)}","-\frac{16 b d \sqrt{a+b x}}{3 \sqrt{c+d x} (b c-a d)^3}-\frac{8 d \sqrt{a+b x}}{3 (c+d x)^{3/2} (b c-a d)^2}-\frac{2}{\sqrt{a+b x} (c+d x)^{3/2} (b c-a d)}",1,"-2/((b*c - a*d)*Sqrt[a + b*x]*(c + d*x)^(3/2)) - (8*d*Sqrt[a + b*x])/(3*(b*c - a*d)^2*(c + d*x)^(3/2)) - (16*b*d*Sqrt[a + b*x])/(3*(b*c - a*d)^3*Sqrt[c + d*x])","A",3,2,19,0.1053,1,"{45, 37}"
1519,1,135,0,0.0284987,"\int \frac{1}{(a+b x)^{5/2} (c+d x)^{5/2}} \, dx","Int[1/((a + b*x)^(5/2)*(c + d*x)^(5/2)),x]","\frac{32 b d^2 \sqrt{a+b x}}{3 \sqrt{c+d x} (b c-a d)^4}+\frac{16 d^2 \sqrt{a+b x}}{3 (c+d x)^{3/2} (b c-a d)^3}+\frac{4 d}{\sqrt{a+b x} (c+d x)^{3/2} (b c-a d)^2}-\frac{2}{3 (a+b x)^{3/2} (c+d x)^{3/2} (b c-a d)}","\frac{32 b d^2 \sqrt{a+b x}}{3 \sqrt{c+d x} (b c-a d)^4}+\frac{16 d^2 \sqrt{a+b x}}{3 (c+d x)^{3/2} (b c-a d)^3}+\frac{4 d}{\sqrt{a+b x} (c+d x)^{3/2} (b c-a d)^2}-\frac{2}{3 (a+b x)^{3/2} (c+d x)^{3/2} (b c-a d)}",1,"-2/(3*(b*c - a*d)*(a + b*x)^(3/2)*(c + d*x)^(3/2)) + (4*d)/((b*c - a*d)^2*Sqrt[a + b*x]*(c + d*x)^(3/2)) + (16*d^2*Sqrt[a + b*x])/(3*(b*c - a*d)^3*(c + d*x)^(3/2)) + (32*b*d^2*Sqrt[a + b*x])/(3*(b*c - a*d)^4*Sqrt[c + d*x])","A",4,2,19,0.1053,1,"{45, 37}"
1520,1,172,0,0.0441092,"\int \frac{1}{(a+b x)^{7/2} (c+d x)^{5/2}} \, dx","Int[1/((a + b*x)^(7/2)*(c + d*x)^(5/2)),x]","-\frac{256 b d^3 \sqrt{a+b x}}{15 \sqrt{c+d x} (b c-a d)^5}-\frac{128 d^3 \sqrt{a+b x}}{15 (c+d x)^{3/2} (b c-a d)^4}-\frac{32 d^2}{5 \sqrt{a+b x} (c+d x)^{3/2} (b c-a d)^3}+\frac{16 d}{15 (a+b x)^{3/2} (c+d x)^{3/2} (b c-a d)^2}-\frac{2}{5 (a+b x)^{5/2} (c+d x)^{3/2} (b c-a d)}","-\frac{256 b d^3 \sqrt{a+b x}}{15 \sqrt{c+d x} (b c-a d)^5}-\frac{128 d^3 \sqrt{a+b x}}{15 (c+d x)^{3/2} (b c-a d)^4}-\frac{32 d^2}{5 \sqrt{a+b x} (c+d x)^{3/2} (b c-a d)^3}+\frac{16 d}{15 (a+b x)^{3/2} (c+d x)^{3/2} (b c-a d)^2}-\frac{2}{5 (a+b x)^{5/2} (c+d x)^{3/2} (b c-a d)}",1,"-2/(5*(b*c - a*d)*(a + b*x)^(5/2)*(c + d*x)^(3/2)) + (16*d)/(15*(b*c - a*d)^2*(a + b*x)^(3/2)*(c + d*x)^(3/2)) - (32*d^2)/(5*(b*c - a*d)^3*Sqrt[a + b*x]*(c + d*x)^(3/2)) - (128*d^3*Sqrt[a + b*x])/(15*(b*c - a*d)^4*(c + d*x)^(3/2)) - (256*b*d^3*Sqrt[a + b*x])/(15*(b*c - a*d)^5*Sqrt[c + d*x])","A",5,2,19,0.1053,1,"{45, 37}"
1521,1,207,0,0.0610089,"\int \frac{1}{(a+b x)^{9/2} (c+d x)^{5/2}} \, dx","Int[1/((a + b*x)^(9/2)*(c + d*x)^(5/2)),x]","\frac{512 b d^4 \sqrt{a+b x}}{21 \sqrt{c+d x} (b c-a d)^6}+\frac{256 d^4 \sqrt{a+b x}}{21 (c+d x)^{3/2} (b c-a d)^5}+\frac{64 d^3}{7 \sqrt{a+b x} (c+d x)^{3/2} (b c-a d)^4}-\frac{32 d^2}{21 (a+b x)^{3/2} (c+d x)^{3/2} (b c-a d)^3}+\frac{4 d}{7 (a+b x)^{5/2} (c+d x)^{3/2} (b c-a d)^2}-\frac{2}{7 (a+b x)^{7/2} (c+d x)^{3/2} (b c-a d)}","\frac{512 b d^4 \sqrt{a+b x}}{21 \sqrt{c+d x} (b c-a d)^6}+\frac{256 d^4 \sqrt{a+b x}}{21 (c+d x)^{3/2} (b c-a d)^5}+\frac{64 d^3}{7 \sqrt{a+b x} (c+d x)^{3/2} (b c-a d)^4}-\frac{32 d^2}{21 (a+b x)^{3/2} (c+d x)^{3/2} (b c-a d)^3}+\frac{4 d}{7 (a+b x)^{5/2} (c+d x)^{3/2} (b c-a d)^2}-\frac{2}{7 (a+b x)^{7/2} (c+d x)^{3/2} (b c-a d)}",1,"-2/(7*(b*c - a*d)*(a + b*x)^(7/2)*(c + d*x)^(3/2)) + (4*d)/(7*(b*c - a*d)^2*(a + b*x)^(5/2)*(c + d*x)^(3/2)) - (32*d^2)/(21*(b*c - a*d)^3*(a + b*x)^(3/2)*(c + d*x)^(3/2)) + (64*d^3)/(7*(b*c - a*d)^4*Sqrt[a + b*x]*(c + d*x)^(3/2)) + (256*d^4*Sqrt[a + b*x])/(21*(b*c - a*d)^5*(c + d*x)^(3/2)) + (512*b*d^4*Sqrt[a + b*x])/(21*(b*c - a*d)^6*Sqrt[c + d*x])","A",6,2,19,0.1053,1,"{45, 37}"
1522,1,19,0,0.0061986,"\int \frac{1}{\sqrt{a+b x} \sqrt{4+a+b x}} \, dx","Int[1/(Sqrt[a + b*x]*Sqrt[4 + a + b*x]),x]","\frac{2 \sinh ^{-1}\left(\frac{1}{2} \sqrt{a+b x}\right)}{b}","\frac{2 \sinh ^{-1}\left(\frac{1}{2} \sqrt{a+b x}\right)}{b}",1,"(2*ArcSinh[Sqrt[a + b*x]/2])/b","A",2,2,20,0.1000,1,"{63, 215}"
1523,1,19,0,0.0049453,"\int \frac{1}{\sqrt{2+b x} \sqrt{6+b x}} \, dx","Int[1/(Sqrt[2 + b*x]*Sqrt[6 + b*x]),x]","\frac{2 \sinh ^{-1}\left(\frac{1}{2} \sqrt{b x+2}\right)}{b}","\frac{2 \sinh ^{-1}\left(\frac{1}{2} \sqrt{b x+2}\right)}{b}",1,"(2*ArcSinh[Sqrt[2 + b*x]/2])/b","A",2,2,19,0.1053,1,"{63, 215}"
1524,1,19,0,0.0049356,"\int \frac{1}{\sqrt{1+b x} \sqrt{5+b x}} \, dx","Int[1/(Sqrt[1 + b*x]*Sqrt[5 + b*x]),x]","\frac{2 \sinh ^{-1}\left(\frac{1}{2} \sqrt{b x+1}\right)}{b}","\frac{2 \sinh ^{-1}\left(\frac{1}{2} \sqrt{b x+1}\right)}{b}",1,"(2*ArcSinh[Sqrt[1 + b*x]/2])/b","A",2,2,19,0.1053,1,"{63, 215}"
1525,1,17,0,0.0038164,"\int \frac{1}{\sqrt{b x} \sqrt{4+b x}} \, dx","Int[1/(Sqrt[b*x]*Sqrt[4 + b*x]),x]","\frac{2 \sinh ^{-1}\left(\frac{\sqrt{b x}}{2}\right)}{b}","\frac{2 \sinh ^{-1}\left(\frac{\sqrt{b x}}{2}\right)}{b}",1,"(2*ArcSinh[Sqrt[b*x]/2])/b","A",2,2,17,0.1176,1,"{63, 215}"
1526,1,19,0,0.0050002,"\int \frac{1}{\sqrt{-1+b x} \sqrt{3+b x}} \, dx","Int[1/(Sqrt[-1 + b*x]*Sqrt[3 + b*x]),x]","\frac{2 \sinh ^{-1}\left(\frac{1}{2} \sqrt{b x-1}\right)}{b}","\frac{2 \sinh ^{-1}\left(\frac{1}{2} \sqrt{b x-1}\right)}{b}",1,"(2*ArcSinh[Sqrt[-1 + b*x]/2])/b","A",2,2,19,0.1053,1,"{63, 215}"
1527,1,11,0,0.0026196,"\int \frac{1}{\sqrt{-2+b x} \sqrt{2+b x}} \, dx","Int[1/(Sqrt[-2 + b*x]*Sqrt[2 + b*x]),x]","\frac{\cosh ^{-1}\left(\frac{b x}{2}\right)}{b}","\frac{\cosh ^{-1}\left(\frac{b x}{2}\right)}{b}",1,"ArcCosh[(b*x)/2]/b","A",1,1,19,0.05263,1,"{52}"
1528,1,19,0,0.0049623,"\int \frac{1}{\sqrt{-3+b x} \sqrt{1+b x}} \, dx","Int[1/(Sqrt[-3 + b*x]*Sqrt[1 + b*x]),x]","\frac{2 \sinh ^{-1}\left(\frac{1}{2} \sqrt{b x-3}\right)}{b}","\frac{2 \sinh ^{-1}\left(\frac{1}{2} \sqrt{b x-3}\right)}{b}",1,"(2*ArcSinh[Sqrt[-3 + b*x]/2])/b","A",2,2,19,0.1053,1,"{63, 215}"
1529,1,15,0,0.004099,"\int \frac{1}{\sqrt{2+b x} \sqrt{3+b x}} \, dx","Int[1/(Sqrt[2 + b*x]*Sqrt[3 + b*x]),x]","\frac{2 \sinh ^{-1}\left(\sqrt{b x+2}\right)}{b}","\frac{2 \sinh ^{-1}\left(\sqrt{b x+2}\right)}{b}",1,"(2*ArcSinh[Sqrt[2 + b*x]])/b","A",2,2,19,0.1053,1,"{63, 215}"
1530,1,10,0,0.0013725,"\int \frac{1}{2+b x} \, dx","Int[(2 + b*x)^(-1),x]","\frac{\log (b x+2)}{b}","\frac{\log (b x+2)}{b}",1,"Log[2 + b*x]/b","A",1,1,7,0.1429,1,"{31}"
1531,1,15,0,0.0040925,"\int \frac{1}{\sqrt{1+b x} \sqrt{2+b x}} \, dx","Int[1/(Sqrt[1 + b*x]*Sqrt[2 + b*x]),x]","\frac{2 \sinh ^{-1}\left(\sqrt{b x+1}\right)}{b}","\frac{2 \sinh ^{-1}\left(\sqrt{b x+1}\right)}{b}",1,"(2*ArcSinh[Sqrt[1 + b*x]])/b","A",2,2,19,0.1053,1,"{63, 215}"
1532,1,19,0,0.004641,"\int \frac{1}{\sqrt{b x} \sqrt{2+b x}} \, dx","Int[1/(Sqrt[b*x]*Sqrt[2 + b*x]),x]","\frac{2 \sinh ^{-1}\left(\frac{\sqrt{b x}}{\sqrt{2}}\right)}{b}","\frac{2 \sinh ^{-1}\left(\frac{\sqrt{b x}}{\sqrt{2}}\right)}{b}",1,"(2*ArcSinh[Sqrt[b*x]/Sqrt[2]])/b","A",2,2,17,0.1176,1,"{63, 215}"
1533,1,21,0,0.0062222,"\int \frac{1}{\sqrt{-1+b x} \sqrt{2+b x}} \, dx","Int[1/(Sqrt[-1 + b*x]*Sqrt[2 + b*x]),x]","\frac{2 \sinh ^{-1}\left(\frac{\sqrt{b x-1}}{\sqrt{3}}\right)}{b}","\frac{2 \sinh ^{-1}\left(\frac{\sqrt{b x-1}}{\sqrt{3}}\right)}{b}",1,"(2*ArcSinh[Sqrt[-1 + b*x]/Sqrt[3]])/b","A",2,2,19,0.1053,1,"{63, 215}"
1534,1,11,0,0.0022657,"\int \frac{1}{\sqrt{-2+b x} \sqrt{2+b x}} \, dx","Int[1/(Sqrt[-2 + b*x]*Sqrt[2 + b*x]),x]","\frac{\cosh ^{-1}\left(\frac{b x}{2}\right)}{b}","\frac{\cosh ^{-1}\left(\frac{b x}{2}\right)}{b}",1,"ArcCosh[(b*x)/2]/b","A",1,1,19,0.05263,1,"{52}"
1535,1,21,0,0.0057734,"\int \frac{1}{\sqrt{-3+b x} \sqrt{2+b x}} \, dx","Int[1/(Sqrt[-3 + b*x]*Sqrt[2 + b*x]),x]","\frac{2 \sinh ^{-1}\left(\frac{\sqrt{b x-3}}{\sqrt{5}}\right)}{b}","\frac{2 \sinh ^{-1}\left(\frac{\sqrt{b x-3}}{\sqrt{5}}\right)}{b}",1,"(2*ArcSinh[Sqrt[-3 + b*x]/Sqrt[5]])/b","A",2,2,19,0.1053,1,"{63, 215}"
1536,1,16,0,0.0137068,"\int \frac{1}{\sqrt{3-b x} \sqrt{2+b x}} \, dx","Int[1/(Sqrt[3 - b*x]*Sqrt[2 + b*x]),x]","-\frac{\sin ^{-1}\left(\frac{1}{5} (1-2 b x)\right)}{b}","-\frac{\sin ^{-1}\left(\frac{1}{5} (1-2 b x)\right)}{b}",1,"-(ArcSin[(1 - 2*b*x)/5]/b)","A",3,3,20,0.1500,1,"{53, 619, 216}"
1537,1,11,0,0.0033367,"\int \frac{1}{\sqrt{2-b x} \sqrt{2+b x}} \, dx","Int[1/(Sqrt[2 - b*x]*Sqrt[2 + b*x]),x]","\frac{\sin ^{-1}\left(\frac{b x}{2}\right)}{b}","\frac{\sin ^{-1}\left(\frac{b x}{2}\right)}{b}",1,"ArcSin[(b*x)/2]/b","A",2,2,20,0.1000,1,"{41, 216}"
1538,1,16,0,0.0133358,"\int \frac{1}{\sqrt{1-b x} \sqrt{2+b x}} \, dx","Int[1/(Sqrt[1 - b*x]*Sqrt[2 + b*x]),x]","-\frac{\sin ^{-1}\left(\frac{1}{3} (-2 b x-1)\right)}{b}","-\frac{\sin ^{-1}\left(\frac{1}{3} (-2 b x-1)\right)}{b}",1,"-(ArcSin[(-1 - 2*b*x)/3]/b)","A",3,3,20,0.1500,1,"{53, 619, 216}"
1539,1,10,0,0.009602,"\int \frac{1}{\sqrt{-b x} \sqrt{2+b x}} \, dx","Int[1/(Sqrt[-(b*x)]*Sqrt[2 + b*x]),x]","\frac{\sin ^{-1}(b x+1)}{b}","\frac{\sin ^{-1}(b x+1)}{b}",1,"ArcSin[1 + b*x]/b","A",3,3,18,0.1667,1,"{53, 619, 216}"
1540,1,11,0,0.0100564,"\int \frac{1}{\sqrt{-1-b x} \sqrt{2+b x}} \, dx","Int[1/(Sqrt[-1 - b*x]*Sqrt[2 + b*x]),x]","\frac{\sin ^{-1}(2 b x+3)}{b}","\frac{\sin ^{-1}(2 b x+3)}{b}",1,"ArcSin[3 + 2*b*x]/b","A",3,3,20,0.1500,1,"{53, 619, 216}"
1541,1,29,0,0.0042249,"\int \frac{1}{\sqrt{-2-b x} \sqrt{2+b x}} \, dx","Int[1/(Sqrt[-2 - b*x]*Sqrt[2 + b*x]),x]","\frac{\sqrt{b x+2} \log (b x+2)}{b \sqrt{-b x-2}}","\frac{\sqrt{b x+2} \log (b x+2)}{b \sqrt{-b x-2}}",1,"(Sqrt[2 + b*x]*Log[2 + b*x])/(b*Sqrt[-2 - b*x])","A",2,2,20,0.1000,1,"{23, 31}"
1542,1,26,0,0.0137541,"\int \frac{1}{\sqrt{-3-b x} \sqrt{2+b x}} \, dx","Int[1/(Sqrt[-3 - b*x]*Sqrt[2 + b*x]),x]","-\frac{2 \tan ^{-1}\left(\frac{\sqrt{-b x-3}}{\sqrt{b x+2}}\right)}{b}","-\frac{2 \tan ^{-1}\left(\frac{\sqrt{-b x-3}}{\sqrt{b x+2}}\right)}{b}",1,"(-2*ArcTan[Sqrt[-3 - b*x]/Sqrt[2 + b*x]])/b","A",3,3,20,0.1500,1,"{63, 217, 203}"
1543,1,16,0,0.0054359,"\int \frac{1}{\sqrt{2-b x} \sqrt{3-b x}} \, dx","Int[1/(Sqrt[2 - b*x]*Sqrt[3 - b*x]),x]","-\frac{2 \sinh ^{-1}\left(\sqrt{2-b x}\right)}{b}","-\frac{2 \sinh ^{-1}\left(\sqrt{2-b x}\right)}{b}",1,"(-2*ArcSinh[Sqrt[2 - b*x]])/b","A",2,2,21,0.09524,1,"{63, 215}"
1544,1,12,0,0.0014485,"\int \frac{1}{2-b x} \, dx","Int[(2 - b*x)^(-1),x]","-\frac{\log (2-b x)}{b}","-\frac{\log (2-b x)}{b}",1,"-(Log[2 - b*x]/b)","A",1,1,8,0.1250,1,"{31}"
1545,1,16,0,0.0052831,"\int \frac{1}{\sqrt{1-b x} \sqrt{2-b x}} \, dx","Int[1/(Sqrt[1 - b*x]*Sqrt[2 - b*x]),x]","-\frac{2 \sinh ^{-1}\left(\sqrt{1-b x}\right)}{b}","-\frac{2 \sinh ^{-1}\left(\sqrt{1-b x}\right)}{b}",1,"(-2*ArcSinh[Sqrt[1 - b*x]])/b","A",2,2,21,0.09524,1,"{63, 215}"
1546,1,20,0,0.0053592,"\int \frac{1}{\sqrt{-b x} \sqrt{2-b x}} \, dx","Int[1/(Sqrt[-(b*x)]*Sqrt[2 - b*x]),x]","-\frac{2 \sinh ^{-1}\left(\frac{\sqrt{-b x}}{\sqrt{2}}\right)}{b}","-\frac{2 \sinh ^{-1}\left(\frac{\sqrt{-b x}}{\sqrt{2}}\right)}{b}",1,"(-2*ArcSinh[Sqrt[-(b*x)]/Sqrt[2]])/b","A",2,2,19,0.1053,1,"{63, 215}"
1547,1,22,0,0.0071565,"\int \frac{1}{\sqrt{-1-b x} \sqrt{2-b x}} \, dx","Int[1/(Sqrt[-1 - b*x]*Sqrt[2 - b*x]),x]","-\frac{2 \sinh ^{-1}\left(\frac{\sqrt{-b x-1}}{\sqrt{3}}\right)}{b}","-\frac{2 \sinh ^{-1}\left(\frac{\sqrt{-b x-1}}{\sqrt{3}}\right)}{b}",1,"(-2*ArcSinh[Sqrt[-1 - b*x]/Sqrt[3]])/b","A",2,2,21,0.09524,1,"{63, 215}"
1548,1,12,0,0.003148,"\int \frac{1}{\sqrt{-2-b x} \sqrt{2-b x}} \, dx","Int[1/(Sqrt[-2 - b*x]*Sqrt[2 - b*x]),x]","-\frac{\cosh ^{-1}\left(-\frac{b x}{2}\right)}{b}","-\frac{\cosh ^{-1}\left(-\frac{b x}{2}\right)}{b}",1,"-(ArcCosh[-(b*x)/2]/b)","A",1,1,21,0.04762,1,"{52}"
1549,1,22,0,0.0068181,"\int \frac{1}{\sqrt{-3-b x} \sqrt{2-b x}} \, dx","Int[1/(Sqrt[-3 - b*x]*Sqrt[2 - b*x]),x]","-\frac{2 \sinh ^{-1}\left(\frac{\sqrt{-b x-3}}{\sqrt{5}}\right)}{b}","-\frac{2 \sinh ^{-1}\left(\frac{\sqrt{-b x-3}}{\sqrt{5}}\right)}{b}",1,"(-2*ArcSinh[Sqrt[-3 - b*x]/Sqrt[5]])/b","A",2,2,21,0.09524,1,"{63, 215}"
1550,1,11,0,0.0022748,"\int \frac{1}{\sqrt{-4+b x} \sqrt{4+b x}} \, dx","Int[1/(Sqrt[-4 + b*x]*Sqrt[4 + b*x]),x]","\frac{\cosh ^{-1}\left(\frac{b x}{4}\right)}{b}","\frac{\cosh ^{-1}\left(\frac{b x}{4}\right)}{b}",1,"ArcCosh[(b*x)/4]/b","A",1,1,19,0.05263,1,"{52}"
1551,1,43,0,0.0153134,"\int \frac{1}{\sqrt{\frac{-b+b c}{d}+b x} \sqrt{c+d x}} \, dx","Int[1/(Sqrt[(-b + b*c)/d + b*x]*Sqrt[c + d*x]),x]","\frac{2 \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{b x-\frac{b (1-c)}{d}}}{\sqrt{b}}\right)}{\sqrt{b} \sqrt{d}}","\frac{2 \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{b x-\frac{b (1-c)}{d}}}{\sqrt{b}}\right)}{\sqrt{b} \sqrt{d}}",1,"(2*ArcSinh[(Sqrt[d]*Sqrt[-((b*(1 - c))/d) + b*x])/Sqrt[b]])/(Sqrt[b]*Sqrt[d])","A",2,2,29,0.06897,1,"{63, 215}"
1552,1,22,0,0.0040966,"\int \frac{1}{\sqrt{x} \sqrt{-3+2 x}} \, dx","Int[1/(Sqrt[x]*Sqrt[-3 + 2*x]),x]","\sqrt{2} \sinh ^{-1}\left(\frac{\sqrt{2 x-3}}{\sqrt{3}}\right)","\sqrt{2} \sinh ^{-1}\left(\frac{\sqrt{2 x-3}}{\sqrt{3}}\right)",1,"Sqrt[2]*ArcSinh[Sqrt[-3 + 2*x]/Sqrt[3]]","A",2,2,15,0.1333,1,"{54, 215}"
1553,1,26,0,0.0080107,"\int \frac{1}{\sqrt{-3+2 x} \sqrt{2+3 x}} \, dx","Int[1/(Sqrt[-3 + 2*x]*Sqrt[2 + 3*x]),x]","\sqrt{\frac{2}{3}} \sinh ^{-1}\left(\sqrt{\frac{3}{13}} \sqrt{2 x-3}\right)","\sqrt{\frac{2}{3}} \sinh ^{-1}\left(\sqrt{\frac{3}{13}} \sqrt{2 x-3}\right)",1,"Sqrt[2/3]*ArcSinh[Sqrt[3/13]*Sqrt[-3 + 2*x]]","A",2,2,19,0.1053,1,"{54, 215}"
1554,1,42,0,0.0161989,"\int \frac{1}{\sqrt{\frac{b-b c}{d}+b x} \sqrt{c-d x}} \, dx","Int[1/(Sqrt[(b - b*c)/d + b*x]*Sqrt[c - d*x]),x]","\frac{2 \sin ^{-1}\left(\frac{\sqrt{d} \sqrt{\frac{b (1-c)}{d}+b x}}{\sqrt{b}}\right)}{\sqrt{b} \sqrt{d}}","\frac{2 \sin ^{-1}\left(\frac{\sqrt{d} \sqrt{\frac{b (1-c)}{d}+b x}}{\sqrt{b}}\right)}{\sqrt{b} \sqrt{d}}",1,"(2*ArcSin[(Sqrt[d]*Sqrt[(b*(1 - c))/d + b*x])/Sqrt[b]])/(Sqrt[b]*Sqrt[d])","A",2,2,29,0.06897,1,"{63, 216}"
1555,1,10,0,0.0074331,"\int \frac{1}{\sqrt{4-x} \sqrt{x}} \, dx","Int[1/(Sqrt[4 - x]*Sqrt[x]),x]","-\sin ^{-1}\left(1-\frac{x}{2}\right)","-\sin ^{-1}\left(1-\frac{x}{2}\right)",1,"-ArcSin[1 - x/2]","A",3,3,15,0.2000,1,"{53, 619, 216}"
1556,1,20,0,0.0067617,"\int \frac{1}{\sqrt{3-2 x} \sqrt{x}} \, dx","Int[1/(Sqrt[3 - 2*x]*Sqrt[x]),x]","\sqrt{2} \sin ^{-1}\left(\sqrt{\frac{2}{3}} \sqrt{x}\right)","\sqrt{2} \sin ^{-1}\left(\sqrt{\frac{2}{3}} \sqrt{x}\right)",1,"Sqrt[2]*ArcSin[Sqrt[2/3]*Sqrt[x]]","A",2,2,15,0.1333,1,"{54, 216}"
1557,1,26,0,0.0089491,"\int \frac{1}{\sqrt{3-2 x} \sqrt{3+5 x}} \, dx","Int[1/(Sqrt[3 - 2*x]*Sqrt[3 + 5*x]),x]","\sqrt{\frac{2}{5}} \sin ^{-1}\left(\sqrt{\frac{2}{21}} \sqrt{5 x+3}\right)","\sqrt{\frac{2}{5}} \sin ^{-1}\left(\sqrt{\frac{2}{21}} \sqrt{5 x+3}\right)",1,"Sqrt[2/5]*ArcSin[Sqrt[2/21]*Sqrt[3 + 5*x]]","A",2,2,19,0.1053,1,"{54, 216}"
1558,1,43,0,0.0277071,"\int \frac{1}{\sqrt{a-b x} \sqrt{c+d x}} \, dx","Int[1/(Sqrt[a - b*x]*Sqrt[c + d*x]),x]","-\frac{2 \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{a-b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{\sqrt{b} \sqrt{d}}","-\frac{2 \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{a-b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{\sqrt{b} \sqrt{d}}",1,"(-2*ArcTan[(Sqrt[d]*Sqrt[a - b*x])/(Sqrt[b]*Sqrt[c + d*x])])/(Sqrt[b]*Sqrt[d])","A",3,3,20,0.1500,1,"{63, 217, 203}"
1559,1,457,0,0.6271753,"\int (a+b x)^{3/2} \sqrt[3]{c+d x} \, dx","Int[(a + b*x)^(3/2)*(c + d*x)^(1/3),x]","-\frac{108\ 3^{3/4} \sqrt{2-\sqrt{3}} (b c-a d)^3 \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+(b c-a d)^{2/3}+b^{2/3} (c+d x)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}{\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}\right)|-7+4 \sqrt{3}\right)}{935 b^{4/3} d^3 \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b c-a d} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{108 \sqrt{a+b x} \sqrt[3]{c+d x} (b c-a d)^2}{935 b d^2}+\frac{12 (a+b x)^{3/2} \sqrt[3]{c+d x} (b c-a d)}{187 b d}+\frac{6 (a+b x)^{5/2} \sqrt[3]{c+d x}}{17 b}","-\frac{108\ 3^{3/4} \sqrt{2-\sqrt{3}} (b c-a d)^3 \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+(b c-a d)^{2/3}+b^{2/3} (c+d x)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}{\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}\right)|-7+4 \sqrt{3}\right)}{935 b^{4/3} d^3 \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b c-a d} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{108 \sqrt{a+b x} \sqrt[3]{c+d x} (b c-a d)^2}{935 b d^2}+\frac{12 (a+b x)^{3/2} \sqrt[3]{c+d x} (b c-a d)}{187 b d}+\frac{6 (a+b x)^{5/2} \sqrt[3]{c+d x}}{17 b}",1,"(-108*(b*c - a*d)^2*Sqrt[a + b*x]*(c + d*x)^(1/3))/(935*b*d^2) + (12*(b*c - a*d)*(a + b*x)^(3/2)*(c + d*x)^(1/3))/(187*b*d) + (6*(a + b*x)^(5/2)*(c + d*x)^(1/3))/(17*b) - (108*3^(3/4)*Sqrt[2 - Sqrt[3]]*(b*c - a*d)^3*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))^2]*EllipticF[ArcSin[((1 + Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))/((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))], -7 + 4*Sqrt[3]])/(935*b^(4/3)*d^3*Sqrt[a + b*x]*Sqrt[-(((b*c - a*d)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))^2)])","A",5,3,19,0.1579,1,"{50, 63, 219}"
1560,1,419,0,0.3735584,"\int \sqrt{a+b x} \sqrt[3]{c+d x} \, dx","Int[Sqrt[a + b*x]*(c + d*x)^(1/3),x]","\frac{12\ 3^{3/4} \sqrt{2-\sqrt{3}} (b c-a d)^2 \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+(b c-a d)^{2/3}+b^{2/3} (c+d x)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}{\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}\right)|-7+4 \sqrt{3}\right)}{55 b^{4/3} d^2 \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b c-a d} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{12 \sqrt{a+b x} \sqrt[3]{c+d x} (b c-a d)}{55 b d}+\frac{6 (a+b x)^{3/2} \sqrt[3]{c+d x}}{11 b}","\frac{12\ 3^{3/4} \sqrt{2-\sqrt{3}} (b c-a d)^2 \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+(b c-a d)^{2/3}+b^{2/3} (c+d x)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}{\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}\right)|-7+4 \sqrt{3}\right)}{55 b^{4/3} d^2 \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b c-a d} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{12 \sqrt{a+b x} \sqrt[3]{c+d x} (b c-a d)}{55 b d}+\frac{6 (a+b x)^{3/2} \sqrt[3]{c+d x}}{11 b}",1,"(12*(b*c - a*d)*Sqrt[a + b*x]*(c + d*x)^(1/3))/(55*b*d) + (6*(a + b*x)^(3/2)*(c + d*x)^(1/3))/(11*b) + (12*3^(3/4)*Sqrt[2 - Sqrt[3]]*(b*c - a*d)^2*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))^2]*EllipticF[ArcSin[((1 + Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))/((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))], -7 + 4*Sqrt[3]])/(55*b^(4/3)*d^2*Sqrt[a + b*x]*Sqrt[-(((b*c - a*d)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))^2)])","A",4,3,19,0.1579,1,"{50, 63, 219}"
1561,1,381,0,0.2716547,"\int \frac{\sqrt[3]{c+d x}}{\sqrt{a+b x}} \, dx","Int[(c + d*x)^(1/3)/Sqrt[a + b*x],x]","\frac{6 \sqrt{a+b x} \sqrt[3]{c+d x}}{5 b}-\frac{4\ 3^{3/4} \sqrt{2-\sqrt{3}} (b c-a d) \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+(b c-a d)^{2/3}+b^{2/3} (c+d x)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}{\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}\right)|-7+4 \sqrt{3}\right)}{5 b^{4/3} d \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b c-a d} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}","\frac{6 \sqrt{a+b x} \sqrt[3]{c+d x}}{5 b}-\frac{4\ 3^{3/4} \sqrt{2-\sqrt{3}} (b c-a d) \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+(b c-a d)^{2/3}+b^{2/3} (c+d x)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}{\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}\right)|-7+4 \sqrt{3}\right)}{5 b^{4/3} d \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b c-a d} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}",1,"(6*Sqrt[a + b*x]*(c + d*x)^(1/3))/(5*b) - (4*3^(3/4)*Sqrt[2 - Sqrt[3]]*(b*c - a*d)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))^2]*EllipticF[ArcSin[((1 + Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))/((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))], -7 + 4*Sqrt[3]])/(5*b^(4/3)*d*Sqrt[a + b*x]*Sqrt[-(((b*c - a*d)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))^2)])","A",3,3,19,0.1579,1,"{50, 63, 219}"
1562,1,366,0,0.2618126,"\int \frac{\sqrt[3]{c+d x}}{(a+b x)^{3/2}} \, dx","Int[(c + d*x)^(1/3)/(a + b*x)^(3/2),x]","-\frac{4 \sqrt{2-\sqrt{3}} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+(b c-a d)^{2/3}+b^{2/3} (c+d x)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}{\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} b^{4/3} \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b c-a d} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{2 \sqrt[3]{c+d x}}{b \sqrt{a+b x}}","-\frac{4 \sqrt{2-\sqrt{3}} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+(b c-a d)^{2/3}+b^{2/3} (c+d x)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}{\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} b^{4/3} \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b c-a d} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{2 \sqrt[3]{c+d x}}{b \sqrt{a+b x}}",1,"(-2*(c + d*x)^(1/3))/(b*Sqrt[a + b*x]) - (4*Sqrt[2 - Sqrt[3]]*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))^2]*EllipticF[ArcSin[((1 + Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))/((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))], -7 + 4*Sqrt[3]])/(3^(1/4)*b^(4/3)*Sqrt[a + b*x]*Sqrt[-(((b*c - a*d)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))^2)])","A",3,3,19,0.1579,1,"{47, 63, 219}"
1563,1,417,0,0.3657541,"\int \frac{\sqrt[3]{c+d x}}{(a+b x)^{5/2}} \, dx","Int[(c + d*x)^(1/3)/(a + b*x)^(5/2),x]","\frac{4 \sqrt{2-\sqrt{3}} d \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+(b c-a d)^{2/3}+b^{2/3} (c+d x)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}{\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}\right)|-7+4 \sqrt{3}\right)}{9 \sqrt[4]{3} b^{4/3} \sqrt{a+b x} (b c-a d) \sqrt{-\frac{\sqrt[3]{b c-a d} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{4 d \sqrt[3]{c+d x}}{9 b \sqrt{a+b x} (b c-a d)}-\frac{2 \sqrt[3]{c+d x}}{3 b (a+b x)^{3/2}}","\frac{4 \sqrt{2-\sqrt{3}} d \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+(b c-a d)^{2/3}+b^{2/3} (c+d x)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}{\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}\right)|-7+4 \sqrt{3}\right)}{9 \sqrt[4]{3} b^{4/3} \sqrt{a+b x} (b c-a d) \sqrt{-\frac{\sqrt[3]{b c-a d} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{4 d \sqrt[3]{c+d x}}{9 b \sqrt{a+b x} (b c-a d)}-\frac{2 \sqrt[3]{c+d x}}{3 b (a+b x)^{3/2}}",1,"(-2*(c + d*x)^(1/3))/(3*b*(a + b*x)^(3/2)) - (4*d*(c + d*x)^(1/3))/(9*b*(b*c - a*d)*Sqrt[a + b*x]) + (4*Sqrt[2 - Sqrt[3]]*d*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))^2]*EllipticF[ArcSin[((1 + Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))/((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))], -7 + 4*Sqrt[3]])/(9*3^(1/4)*b^(4/3)*(b*c - a*d)*Sqrt[a + b*x]*Sqrt[-(((b*c - a*d)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))^2)])","A",4,4,19,0.2105,1,"{47, 51, 63, 219}"
1564,1,457,0,0.4470218,"\int \frac{\sqrt[3]{c+d x}}{(a+b x)^{7/2}} \, dx","Int[(c + d*x)^(1/3)/(a + b*x)^(7/2),x]","-\frac{28 \sqrt{2-\sqrt{3}} d^2 \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+(b c-a d)^{2/3}+b^{2/3} (c+d x)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}{\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}\right)|-7+4 \sqrt{3}\right)}{135 \sqrt[4]{3} b^{4/3} \sqrt{a+b x} (b c-a d)^2 \sqrt{-\frac{\sqrt[3]{b c-a d} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{28 d^2 \sqrt[3]{c+d x}}{135 b \sqrt{a+b x} (b c-a d)^2}-\frac{4 d \sqrt[3]{c+d x}}{45 b (a+b x)^{3/2} (b c-a d)}-\frac{2 \sqrt[3]{c+d x}}{5 b (a+b x)^{5/2}}","-\frac{28 \sqrt{2-\sqrt{3}} d^2 \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+(b c-a d)^{2/3}+b^{2/3} (c+d x)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}{\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}\right)|-7+4 \sqrt{3}\right)}{135 \sqrt[4]{3} b^{4/3} \sqrt{a+b x} (b c-a d)^2 \sqrt{-\frac{\sqrt[3]{b c-a d} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{28 d^2 \sqrt[3]{c+d x}}{135 b \sqrt{a+b x} (b c-a d)^2}-\frac{4 d \sqrt[3]{c+d x}}{45 b (a+b x)^{3/2} (b c-a d)}-\frac{2 \sqrt[3]{c+d x}}{5 b (a+b x)^{5/2}}",1,"(-2*(c + d*x)^(1/3))/(5*b*(a + b*x)^(5/2)) - (4*d*(c + d*x)^(1/3))/(45*b*(b*c - a*d)*(a + b*x)^(3/2)) + (28*d^2*(c + d*x)^(1/3))/(135*b*(b*c - a*d)^2*Sqrt[a + b*x]) - (28*Sqrt[2 - Sqrt[3]]*d^2*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))^2]*EllipticF[ArcSin[((1 + Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))/((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))], -7 + 4*Sqrt[3]])/(135*3^(1/4)*b^(4/3)*(b*c - a*d)^2*Sqrt[a + b*x]*Sqrt[-(((b*c - a*d)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))^2)])","A",5,4,19,0.2105,1,"{47, 51, 63, 219}"
1565,1,839,0,0.937686,"\int \frac{(a+b x)^{3/2}}{\sqrt[3]{c+d x}} \, dx","Int[(a + b*x)^(3/2)/(c + d*x)^(1/3),x]","\frac{81 \sqrt[4]{3} \sqrt{2+\sqrt{3}} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}{\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}\right)|-7+4 \sqrt{3}\right) (b c-a d)^{7/3}}{91 b^{2/3} d^3 \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b c-a d} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{54 \sqrt{2} 3^{3/4} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}{\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}\right)|-7+4 \sqrt{3}\right) (b c-a d)^{7/3}}{91 b^{2/3} d^3 \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b c-a d} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{162 \sqrt{a+b x} (b c-a d)^2}{91 b^{2/3} d^2 \left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}-\frac{54 \sqrt{a+b x} (c+d x)^{2/3} (b c-a d)}{91 d^2}+\frac{6 (a+b x)^{3/2} (c+d x)^{2/3}}{13 d}","\frac{81 \sqrt[4]{3} \sqrt{2+\sqrt{3}} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}{\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}\right)|-7+4 \sqrt{3}\right) (b c-a d)^{7/3}}{91 b^{2/3} d^3 \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b c-a d} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{54 \sqrt{2} 3^{3/4} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}{\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}\right)|-7+4 \sqrt{3}\right) (b c-a d)^{7/3}}{91 b^{2/3} d^3 \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b c-a d} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{162 \sqrt{a+b x} (b c-a d)^2}{91 b^{2/3} d^2 \left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}-\frac{54 \sqrt{a+b x} (c+d x)^{2/3} (b c-a d)}{91 d^2}+\frac{6 (a+b x)^{3/2} (c+d x)^{2/3}}{13 d}",1,"(-54*(b*c - a*d)*Sqrt[a + b*x]*(c + d*x)^(2/3))/(91*d^2) + (6*(a + b*x)^(3/2)*(c + d*x)^(2/3))/(13*d) - (162*(b*c - a*d)^2*Sqrt[a + b*x])/(91*b^(2/3)*d^2*((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))) + (81*3^(1/4)*Sqrt[2 + Sqrt[3]]*(b*c - a*d)^(7/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))^2]*EllipticE[ArcSin[((1 + Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))/((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))], -7 + 4*Sqrt[3]])/(91*b^(2/3)*d^3*Sqrt[a + b*x]*Sqrt[-(((b*c - a*d)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))^2)]) - (54*Sqrt[2]*3^(3/4)*(b*c - a*d)^(7/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))^2]*EllipticF[ArcSin[((1 + Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))/((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))], -7 + 4*Sqrt[3]])/(91*b^(2/3)*d^3*Sqrt[a + b*x]*Sqrt[-(((b*c - a*d)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))^2)])","A",6,5,19,0.2632,1,"{50, 63, 304, 219, 1879}"
1566,1,804,0,0.6679533,"\int \frac{\sqrt{a+b x}}{\sqrt[3]{c+d x}} \, dx","Int[Sqrt[a + b*x]/(c + d*x)^(1/3),x]","-\frac{9 \sqrt[4]{3} \sqrt{2+\sqrt{3}} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}{\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}\right)|-7+4 \sqrt{3}\right) (b c-a d)^{4/3}}{7 b^{2/3} d^2 \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b c-a d} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{6 \sqrt{2} 3^{3/4} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}{\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}\right)|-7+4 \sqrt{3}\right) (b c-a d)^{4/3}}{7 b^{2/3} d^2 \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b c-a d} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{18 \sqrt{a+b x} (b c-a d)}{7 b^{2/3} d \left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}+\frac{6 \sqrt{a+b x} (c+d x)^{2/3}}{7 d}","-\frac{9 \sqrt[4]{3} \sqrt{2+\sqrt{3}} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}{\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}\right)|-7+4 \sqrt{3}\right) (b c-a d)^{4/3}}{7 b^{2/3} d^2 \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b c-a d} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{6 \sqrt{2} 3^{3/4} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}{\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}\right)|-7+4 \sqrt{3}\right) (b c-a d)^{4/3}}{7 b^{2/3} d^2 \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b c-a d} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{18 \sqrt{a+b x} (b c-a d)}{7 b^{2/3} d \left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}+\frac{6 \sqrt{a+b x} (c+d x)^{2/3}}{7 d}",1,"(6*Sqrt[a + b*x]*(c + d*x)^(2/3))/(7*d) + (18*(b*c - a*d)*Sqrt[a + b*x])/(7*b^(2/3)*d*((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))) - (9*3^(1/4)*Sqrt[2 + Sqrt[3]]*(b*c - a*d)^(4/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))^2]*EllipticE[ArcSin[((1 + Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))/((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))], -7 + 4*Sqrt[3]])/(7*b^(2/3)*d^2*Sqrt[a + b*x]*Sqrt[-(((b*c - a*d)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))^2)]) + (6*Sqrt[2]*3^(3/4)*(b*c - a*d)^(4/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))^2]*EllipticF[ArcSin[((1 + Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))/((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))], -7 + 4*Sqrt[3]])/(7*b^(2/3)*d^2*Sqrt[a + b*x]*Sqrt[-(((b*c - a*d)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))^2)])","A",5,5,19,0.2632,1,"{50, 63, 304, 219, 1879}"
1567,1,762,0,0.5780892,"\int \frac{1}{\sqrt{a+b x} \sqrt[3]{c+d x}} \, dx","Int[1/(Sqrt[a + b*x]*(c + d*x)^(1/3)),x]","-\frac{6 \sqrt{a+b x}}{b^{2/3} \left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}-\frac{2 \sqrt{2} 3^{3/4} \sqrt[3]{b c-a d} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+(b c-a d)^{2/3}+b^{2/3} (c+d x)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}{\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}\right)|-7+4 \sqrt{3}\right)}{b^{2/3} d \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b c-a d} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{3 \sqrt[4]{3} \sqrt{2+\sqrt{3}} \sqrt[3]{b c-a d} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+(b c-a d)^{2/3}+b^{2/3} (c+d x)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}{\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}\right)|-7+4 \sqrt{3}\right)}{b^{2/3} d \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b c-a d} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}","-\frac{6 \sqrt{a+b x}}{b^{2/3} \left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}-\frac{2 \sqrt{2} 3^{3/4} \sqrt[3]{b c-a d} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+(b c-a d)^{2/3}+b^{2/3} (c+d x)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}{\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}\right)|-7+4 \sqrt{3}\right)}{b^{2/3} d \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b c-a d} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{3 \sqrt[4]{3} \sqrt{2+\sqrt{3}} \sqrt[3]{b c-a d} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+(b c-a d)^{2/3}+b^{2/3} (c+d x)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}{\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}\right)|-7+4 \sqrt{3}\right)}{b^{2/3} d \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b c-a d} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}",1,"(-6*Sqrt[a + b*x])/(b^(2/3)*((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))) + (3*3^(1/4)*Sqrt[2 + Sqrt[3]]*(b*c - a*d)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))^2]*EllipticE[ArcSin[((1 + Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))/((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))], -7 + 4*Sqrt[3]])/(b^(2/3)*d*Sqrt[a + b*x]*Sqrt[-(((b*c - a*d)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))^2)]) - (2*Sqrt[2]*3^(3/4)*(b*c - a*d)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))^2]*EllipticF[ArcSin[((1 + Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))/((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))], -7 + 4*Sqrt[3]])/(b^(2/3)*d*Sqrt[a + b*x]*Sqrt[-(((b*c - a*d)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))^2)])","A",4,4,19,0.2105,1,"{63, 304, 219, 1879}"
1568,1,796,0,0.6898365,"\int \frac{1}{(a+b x)^{3/2} \sqrt[3]{c+d x}} \, dx","Int[1/((a + b*x)^(3/2)*(c + d*x)^(1/3)),x]","-\frac{2 \sqrt{a+b x} d}{b^{2/3} (b c-a d) \left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}+\frac{\sqrt[4]{3} \sqrt{2+\sqrt{3}} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}{\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}\right)|-7+4 \sqrt{3}\right)}{b^{2/3} (b c-a d)^{2/3} \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b c-a d} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{2 \sqrt{2} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}{\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} b^{2/3} (b c-a d)^{2/3} \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b c-a d} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{2 (c+d x)^{2/3}}{(b c-a d) \sqrt{a+b x}}","-\frac{2 \sqrt{a+b x} d}{b^{2/3} (b c-a d) \left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}+\frac{\sqrt[4]{3} \sqrt{2+\sqrt{3}} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}{\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}\right)|-7+4 \sqrt{3}\right)}{b^{2/3} (b c-a d)^{2/3} \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b c-a d} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{2 \sqrt{2} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}{\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} b^{2/3} (b c-a d)^{2/3} \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b c-a d} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{2 (c+d x)^{2/3}}{(b c-a d) \sqrt{a+b x}}",1,"(-2*(c + d*x)^(2/3))/((b*c - a*d)*Sqrt[a + b*x]) - (2*d*Sqrt[a + b*x])/(b^(2/3)*(b*c - a*d)*((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))) + (3^(1/4)*Sqrt[2 + Sqrt[3]]*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))^2]*EllipticE[ArcSin[((1 + Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))/((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))], -7 + 4*Sqrt[3]])/(b^(2/3)*(b*c - a*d)^(2/3)*Sqrt[a + b*x]*Sqrt[-(((b*c - a*d)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))^2)]) - (2*Sqrt[2]*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))^2]*EllipticF[ArcSin[((1 + Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))/((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))], -7 + 4*Sqrt[3]])/(3^(1/4)*b^(2/3)*(b*c - a*d)^(2/3)*Sqrt[a + b*x]*Sqrt[-(((b*c - a*d)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))^2)])","A",5,5,19,0.2632,1,"{51, 63, 304, 219, 1879}"
1569,1,842,0,0.833726,"\int \frac{1}{(a+b x)^{5/2} \sqrt[3]{c+d x}} \, dx","Int[1/((a + b*x)^(5/2)*(c + d*x)^(1/3)),x]","\frac{10 \sqrt{a+b x} d^2}{9 b^{2/3} (b c-a d)^2 \left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}-\frac{5 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}{\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}\right)|-7+4 \sqrt{3}\right) d}{3\ 3^{3/4} b^{2/3} (b c-a d)^{5/3} \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b c-a d} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{10 \sqrt{2} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}{\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}\right)|-7+4 \sqrt{3}\right) d}{9 \sqrt[4]{3} b^{2/3} (b c-a d)^{5/3} \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b c-a d} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{10 (c+d x)^{2/3} d}{9 (b c-a d)^2 \sqrt{a+b x}}-\frac{2 (c+d x)^{2/3}}{3 (b c-a d) (a+b x)^{3/2}}","\frac{10 \sqrt{a+b x} d^2}{9 b^{2/3} (b c-a d)^2 \left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}-\frac{5 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}{\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}\right)|-7+4 \sqrt{3}\right) d}{3\ 3^{3/4} b^{2/3} (b c-a d)^{5/3} \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b c-a d} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{10 \sqrt{2} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}{\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}\right)|-7+4 \sqrt{3}\right) d}{9 \sqrt[4]{3} b^{2/3} (b c-a d)^{5/3} \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b c-a d} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{10 (c+d x)^{2/3} d}{9 (b c-a d)^2 \sqrt{a+b x}}-\frac{2 (c+d x)^{2/3}}{3 (b c-a d) (a+b x)^{3/2}}",1,"(-2*(c + d*x)^(2/3))/(3*(b*c - a*d)*(a + b*x)^(3/2)) + (10*d*(c + d*x)^(2/3))/(9*(b*c - a*d)^2*Sqrt[a + b*x]) + (10*d^2*Sqrt[a + b*x])/(9*b^(2/3)*(b*c - a*d)^2*((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))) - (5*Sqrt[2 + Sqrt[3]]*d*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))^2]*EllipticE[ArcSin[((1 + Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))/((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))], -7 + 4*Sqrt[3]])/(3*3^(3/4)*b^(2/3)*(b*c - a*d)^(5/3)*Sqrt[a + b*x]*Sqrt[-(((b*c - a*d)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))^2)]) + (10*Sqrt[2]*d*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))^2]*EllipticF[ArcSin[((1 + Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))/((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))], -7 + 4*Sqrt[3]])/(9*3^(1/4)*b^(2/3)*(b*c - a*d)^(5/3)*Sqrt[a + b*x]*Sqrt[-(((b*c - a*d)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))^2)])","A",6,5,19,0.2632,1,"{51, 63, 304, 219, 1879}"
1570,1,416,0,0.3851288,"\int \frac{(a+b x)^{3/2}}{(c+d x)^{2/3}} \, dx","Int[(a + b*x)^(3/2)/(c + d*x)^(2/3),x]","-\frac{54\ 3^{3/4} \sqrt{2-\sqrt{3}} (b c-a d)^2 \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+(b c-a d)^{2/3}+b^{2/3} (c+d x)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}{\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}\right)|-7+4 \sqrt{3}\right)}{55 \sqrt[3]{b} d^3 \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b c-a d} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{54 \sqrt{a+b x} \sqrt[3]{c+d x} (b c-a d)}{55 d^2}+\frac{6 (a+b x)^{3/2} \sqrt[3]{c+d x}}{11 d}","-\frac{54\ 3^{3/4} \sqrt{2-\sqrt{3}} (b c-a d)^2 \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+(b c-a d)^{2/3}+b^{2/3} (c+d x)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}{\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}\right)|-7+4 \sqrt{3}\right)}{55 \sqrt[3]{b} d^3 \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b c-a d} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{54 \sqrt{a+b x} \sqrt[3]{c+d x} (b c-a d)}{55 d^2}+\frac{6 (a+b x)^{3/2} \sqrt[3]{c+d x}}{11 d}",1,"(-54*(b*c - a*d)*Sqrt[a + b*x]*(c + d*x)^(1/3))/(55*d^2) + (6*(a + b*x)^(3/2)*(c + d*x)^(1/3))/(11*d) - (54*3^(3/4)*Sqrt[2 - Sqrt[3]]*(b*c - a*d)^2*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))^2]*EllipticF[ArcSin[((1 + Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))/((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))], -7 + 4*Sqrt[3]])/(55*b^(1/3)*d^3*Sqrt[a + b*x]*Sqrt[-(((b*c - a*d)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))^2)])","A",4,3,19,0.1579,1,"{50, 63, 219}"
1571,1,381,0,0.2964501,"\int \frac{\sqrt{a+b x}}{(c+d x)^{2/3}} \, dx","Int[Sqrt[a + b*x]/(c + d*x)^(2/3),x]","\frac{6\ 3^{3/4} \sqrt{2-\sqrt{3}} (b c-a d) \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+(b c-a d)^{2/3}+b^{2/3} (c+d x)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}{\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}\right)|-7+4 \sqrt{3}\right)}{5 \sqrt[3]{b} d^2 \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b c-a d} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{6 \sqrt{a+b x} \sqrt[3]{c+d x}}{5 d}","\frac{6\ 3^{3/4} \sqrt{2-\sqrt{3}} (b c-a d) \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+(b c-a d)^{2/3}+b^{2/3} (c+d x)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}{\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}\right)|-7+4 \sqrt{3}\right)}{5 \sqrt[3]{b} d^2 \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b c-a d} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{6 \sqrt{a+b x} \sqrt[3]{c+d x}}{5 d}",1,"(6*Sqrt[a + b*x]*(c + d*x)^(1/3))/(5*d) + (6*3^(3/4)*Sqrt[2 - Sqrt[3]]*(b*c - a*d)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))^2]*EllipticF[ArcSin[((1 + Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))/((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))], -7 + 4*Sqrt[3]])/(5*b^(1/3)*d^2*Sqrt[a + b*x]*Sqrt[-(((b*c - a*d)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))^2)])","A",3,3,19,0.1579,1,"{50, 63, 219}"
1572,1,345,0,0.2234034,"\int \frac{1}{\sqrt{a+b x} (c+d x)^{2/3}} \, dx","Int[1/(Sqrt[a + b*x]*(c + d*x)^(2/3)),x]","-\frac{2\ 3^{3/4} \sqrt{2-\sqrt{3}} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+(b c-a d)^{2/3}+b^{2/3} (c+d x)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}{\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}\right)|-7+4 \sqrt{3}\right)}{\sqrt[3]{b} d \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b c-a d} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}","-\frac{2\ 3^{3/4} \sqrt{2-\sqrt{3}} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+(b c-a d)^{2/3}+b^{2/3} (c+d x)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}{\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}\right)|-7+4 \sqrt{3}\right)}{\sqrt[3]{b} d \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b c-a d} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}",1,"(-2*3^(3/4)*Sqrt[2 - Sqrt[3]]*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))^2]*EllipticF[ArcSin[((1 + Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))/((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))], -7 + 4*Sqrt[3]])/(b^(1/3)*d*Sqrt[a + b*x]*Sqrt[-(((b*c - a*d)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))^2)])","A",2,2,19,0.1053,1,"{63, 219}"
1573,1,383,0,0.2935883,"\int \frac{1}{(a+b x)^{3/2} (c+d x)^{2/3}} \, dx","Int[1/((a + b*x)^(3/2)*(c + d*x)^(2/3)),x]","\frac{2 \sqrt{2-\sqrt{3}} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+(b c-a d)^{2/3}+b^{2/3} (c+d x)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}{\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt[3]{b} \sqrt{a+b x} (b c-a d) \sqrt{-\frac{\sqrt[3]{b c-a d} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{2 \sqrt[3]{c+d x}}{\sqrt{a+b x} (b c-a d)}","\frac{2 \sqrt{2-\sqrt{3}} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+(b c-a d)^{2/3}+b^{2/3} (c+d x)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}{\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt[3]{b} \sqrt{a+b x} (b c-a d) \sqrt{-\frac{\sqrt[3]{b c-a d} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{2 \sqrt[3]{c+d x}}{\sqrt{a+b x} (b c-a d)}",1,"(-2*(c + d*x)^(1/3))/((b*c - a*d)*Sqrt[a + b*x]) + (2*Sqrt[2 - Sqrt[3]]*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))^2]*EllipticF[ArcSin[((1 + Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))/((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))], -7 + 4*Sqrt[3]])/(3^(1/4)*b^(1/3)*(b*c - a*d)*Sqrt[a + b*x]*Sqrt[-(((b*c - a*d)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))^2)])","A",3,3,19,0.1579,1,"{51, 63, 219}"
1574,1,421,0,0.3681911,"\int \frac{1}{(a+b x)^{5/2} (c+d x)^{2/3}} \, dx","Int[1/((a + b*x)^(5/2)*(c + d*x)^(2/3)),x]","-\frac{14 \sqrt{2-\sqrt{3}} d \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+(b c-a d)^{2/3}+b^{2/3} (c+d x)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}{\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}\right)|-7+4 \sqrt{3}\right)}{9 \sqrt[4]{3} \sqrt[3]{b} \sqrt{a+b x} (b c-a d)^2 \sqrt{-\frac{\sqrt[3]{b c-a d} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{14 d \sqrt[3]{c+d x}}{9 \sqrt{a+b x} (b c-a d)^2}-\frac{2 \sqrt[3]{c+d x}}{3 (a+b x)^{3/2} (b c-a d)}","-\frac{14 \sqrt{2-\sqrt{3}} d \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+(b c-a d)^{2/3}+b^{2/3} (c+d x)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}{\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}\right)|-7+4 \sqrt{3}\right)}{9 \sqrt[4]{3} \sqrt[3]{b} \sqrt{a+b x} (b c-a d)^2 \sqrt{-\frac{\sqrt[3]{b c-a d} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{14 d \sqrt[3]{c+d x}}{9 \sqrt{a+b x} (b c-a d)^2}-\frac{2 \sqrt[3]{c+d x}}{3 (a+b x)^{3/2} (b c-a d)}",1,"(-2*(c + d*x)^(1/3))/(3*(b*c - a*d)*(a + b*x)^(3/2)) + (14*d*(c + d*x)^(1/3))/(9*(b*c - a*d)^2*Sqrt[a + b*x]) - (14*Sqrt[2 - Sqrt[3]]*d*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))^2]*EllipticF[ArcSin[((1 + Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))/((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))], -7 + 4*Sqrt[3]])/(9*3^(1/4)*b^(1/3)*(b*c - a*d)^2*Sqrt[a + b*x]*Sqrt[-(((b*c - a*d)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((1 - Sqrt[3])*(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))^2)])","A",4,3,19,0.1579,1,"{51, 63, 219}"
1575,1,219,0,0.0875222,"\int (a+b x)^{2/3} \sqrt[3]{c+d x} \, dx","Int[(a + b*x)^(2/3)*(c + d*x)^(1/3),x]","\frac{(b c-a d)^2 \log (c+d x)}{18 b^{4/3} d^{5/3}}+\frac{(b c-a d)^2 \log \left(\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{b} \sqrt[3]{c+d x}}-1\right)}{6 b^{4/3} d^{5/3}}+\frac{(b c-a d)^2 \tan ^{-1}\left(\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt{3} \sqrt[3]{b} \sqrt[3]{c+d x}}+\frac{1}{\sqrt{3}}\right)}{3 \sqrt{3} b^{4/3} d^{5/3}}+\frac{(a+b x)^{2/3} \sqrt[3]{c+d x} (b c-a d)}{6 b d}+\frac{(a+b x)^{5/3} \sqrt[3]{c+d x}}{2 b}","\frac{(b c-a d)^2 \log (c+d x)}{18 b^{4/3} d^{5/3}}+\frac{(b c-a d)^2 \log \left(\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{b} \sqrt[3]{c+d x}}-1\right)}{6 b^{4/3} d^{5/3}}+\frac{(b c-a d)^2 \tan ^{-1}\left(\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt{3} \sqrt[3]{b} \sqrt[3]{c+d x}}+\frac{1}{\sqrt{3}}\right)}{3 \sqrt{3} b^{4/3} d^{5/3}}+\frac{(a+b x)^{2/3} \sqrt[3]{c+d x} (b c-a d)}{6 b d}+\frac{(a+b x)^{5/3} \sqrt[3]{c+d x}}{2 b}",1,"((b*c - a*d)*(a + b*x)^(2/3)*(c + d*x)^(1/3))/(6*b*d) + ((a + b*x)^(5/3)*(c + d*x)^(1/3))/(2*b) + ((b*c - a*d)^2*ArcTan[1/Sqrt[3] + (2*d^(1/3)*(a + b*x)^(1/3))/(Sqrt[3]*b^(1/3)*(c + d*x)^(1/3))])/(3*Sqrt[3]*b^(4/3)*d^(5/3)) + ((b*c - a*d)^2*Log[c + d*x])/(18*b^(4/3)*d^(5/3)) + ((b*c - a*d)^2*Log[-1 + (d^(1/3)*(a + b*x)^(1/3))/(b^(1/3)*(c + d*x)^(1/3))])/(6*b^(4/3)*d^(5/3))","A",3,2,19,0.1053,1,"{50, 59}"
1576,1,172,0,0.0455278,"\int \frac{\sqrt[3]{c+d x}}{\sqrt[3]{a+b x}} \, dx","Int[(c + d*x)^(1/3)/(a + b*x)^(1/3),x]","-\frac{(b c-a d) \log (c+d x)}{6 b^{4/3} d^{2/3}}-\frac{(b c-a d) \log \left(\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{b} \sqrt[3]{c+d x}}-1\right)}{2 b^{4/3} d^{2/3}}-\frac{(b c-a d) \tan ^{-1}\left(\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt{3} \sqrt[3]{b} \sqrt[3]{c+d x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3} b^{4/3} d^{2/3}}+\frac{(a+b x)^{2/3} \sqrt[3]{c+d x}}{b}","-\frac{(b c-a d) \log (c+d x)}{6 b^{4/3} d^{2/3}}-\frac{(b c-a d) \log \left(\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{b} \sqrt[3]{c+d x}}-1\right)}{2 b^{4/3} d^{2/3}}-\frac{(b c-a d) \tan ^{-1}\left(\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt{3} \sqrt[3]{b} \sqrt[3]{c+d x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3} b^{4/3} d^{2/3}}+\frac{(a+b x)^{2/3} \sqrt[3]{c+d x}}{b}",1,"((a + b*x)^(2/3)*(c + d*x)^(1/3))/b - ((b*c - a*d)*ArcTan[1/Sqrt[3] + (2*d^(1/3)*(a + b*x)^(1/3))/(Sqrt[3]*b^(1/3)*(c + d*x)^(1/3))])/(Sqrt[3]*b^(4/3)*d^(2/3)) - ((b*c - a*d)*Log[c + d*x])/(6*b^(4/3)*d^(2/3)) - ((b*c - a*d)*Log[-1 + (d^(1/3)*(a + b*x)^(1/3))/(b^(1/3)*(c + d*x)^(1/3))])/(2*b^(4/3)*d^(2/3))","A",2,2,19,0.1053,1,"{50, 59}"
1577,1,149,0,0.032848,"\int \frac{\sqrt[3]{c+d x}}{(a+b x)^{4/3}} \, dx","Int[(c + d*x)^(1/3)/(a + b*x)^(4/3),x]","-\frac{3 \sqrt[3]{d} \log \left(\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{b} \sqrt[3]{c+d x}}-1\right)}{2 b^{4/3}}-\frac{\sqrt{3} \sqrt[3]{d} \tan ^{-1}\left(\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt{3} \sqrt[3]{b} \sqrt[3]{c+d x}}+\frac{1}{\sqrt{3}}\right)}{b^{4/3}}-\frac{3 \sqrt[3]{c+d x}}{b \sqrt[3]{a+b x}}-\frac{\sqrt[3]{d} \log (c+d x)}{2 b^{4/3}}","-\frac{3 \sqrt[3]{d} \log \left(\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{b} \sqrt[3]{c+d x}}-1\right)}{2 b^{4/3}}-\frac{\sqrt{3} \sqrt[3]{d} \tan ^{-1}\left(\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt{3} \sqrt[3]{b} \sqrt[3]{c+d x}}+\frac{1}{\sqrt{3}}\right)}{b^{4/3}}-\frac{3 \sqrt[3]{c+d x}}{b \sqrt[3]{a+b x}}-\frac{\sqrt[3]{d} \log (c+d x)}{2 b^{4/3}}",1,"(-3*(c + d*x)^(1/3))/(b*(a + b*x)^(1/3)) - (Sqrt[3]*d^(1/3)*ArcTan[1/Sqrt[3] + (2*d^(1/3)*(a + b*x)^(1/3))/(Sqrt[3]*b^(1/3)*(c + d*x)^(1/3))])/b^(4/3) - (d^(1/3)*Log[c + d*x])/(2*b^(4/3)) - (3*d^(1/3)*Log[-1 + (d^(1/3)*(a + b*x)^(1/3))/(b^(1/3)*(c + d*x)^(1/3))])/(2*b^(4/3))","A",2,2,19,0.1053,1,"{47, 59}"
1578,1,32,0,0.0029945,"\int \frac{\sqrt[3]{c+d x}}{(a+b x)^{7/3}} \, dx","Int[(c + d*x)^(1/3)/(a + b*x)^(7/3),x]","-\frac{3 (c+d x)^{4/3}}{4 (a+b x)^{4/3} (b c-a d)}","-\frac{3 (c+d x)^{4/3}}{4 (a+b x)^{4/3} (b c-a d)}",1,"(-3*(c + d*x)^(4/3))/(4*(b*c - a*d)*(a + b*x)^(4/3))","A",1,1,19,0.05263,1,"{37}"
1579,1,66,0,0.0086674,"\int \frac{\sqrt[3]{c+d x}}{(a+b x)^{10/3}} \, dx","Int[(c + d*x)^(1/3)/(a + b*x)^(10/3),x]","\frac{9 d (c+d x)^{4/3}}{28 (a+b x)^{4/3} (b c-a d)^2}-\frac{3 (c+d x)^{4/3}}{7 (a+b x)^{7/3} (b c-a d)}","\frac{9 d (c+d x)^{4/3}}{28 (a+b x)^{4/3} (b c-a d)^2}-\frac{3 (c+d x)^{4/3}}{7 (a+b x)^{7/3} (b c-a d)}",1,"(-3*(c + d*x)^(4/3))/(7*(b*c - a*d)*(a + b*x)^(7/3)) + (9*d*(c + d*x)^(4/3))/(28*(b*c - a*d)^2*(a + b*x)^(4/3))","A",2,2,19,0.1053,1,"{45, 37}"
1580,1,101,0,0.0173515,"\int \frac{\sqrt[3]{c+d x}}{(a+b x)^{13/3}} \, dx","Int[(c + d*x)^(1/3)/(a + b*x)^(13/3),x]","-\frac{27 d^2 (c+d x)^{4/3}}{140 (a+b x)^{4/3} (b c-a d)^3}+\frac{9 d (c+d x)^{4/3}}{35 (a+b x)^{7/3} (b c-a d)^2}-\frac{3 (c+d x)^{4/3}}{10 (a+b x)^{10/3} (b c-a d)}","-\frac{27 d^2 (c+d x)^{4/3}}{140 (a+b x)^{4/3} (b c-a d)^3}+\frac{9 d (c+d x)^{4/3}}{35 (a+b x)^{7/3} (b c-a d)^2}-\frac{3 (c+d x)^{4/3}}{10 (a+b x)^{10/3} (b c-a d)}",1,"(-3*(c + d*x)^(4/3))/(10*(b*c - a*d)*(a + b*x)^(10/3)) + (9*d*(c + d*x)^(4/3))/(35*(b*c - a*d)^2*(a + b*x)^(7/3)) - (27*d^2*(c + d*x)^(4/3))/(140*(b*c - a*d)^3*(a + b*x)^(4/3))","A",3,2,19,0.1053,1,"{45, 37}"
1581,1,136,0,0.0283204,"\int \frac{\sqrt[3]{c+d x}}{(a+b x)^{16/3}} \, dx","Int[(c + d*x)^(1/3)/(a + b*x)^(16/3),x]","\frac{243 d^3 (c+d x)^{4/3}}{1820 (a+b x)^{4/3} (b c-a d)^4}-\frac{81 d^2 (c+d x)^{4/3}}{455 (a+b x)^{7/3} (b c-a d)^3}+\frac{27 d (c+d x)^{4/3}}{130 (a+b x)^{10/3} (b c-a d)^2}-\frac{3 (c+d x)^{4/3}}{13 (a+b x)^{13/3} (b c-a d)}","\frac{243 d^3 (c+d x)^{4/3}}{1820 (a+b x)^{4/3} (b c-a d)^4}-\frac{81 d^2 (c+d x)^{4/3}}{455 (a+b x)^{7/3} (b c-a d)^3}+\frac{27 d (c+d x)^{4/3}}{130 (a+b x)^{10/3} (b c-a d)^2}-\frac{3 (c+d x)^{4/3}}{13 (a+b x)^{13/3} (b c-a d)}",1,"(-3*(c + d*x)^(4/3))/(13*(b*c - a*d)*(a + b*x)^(13/3)) + (27*d*(c + d*x)^(4/3))/(130*(b*c - a*d)^2*(a + b*x)^(10/3)) - (81*d^2*(c + d*x)^(4/3))/(455*(b*c - a*d)^3*(a + b*x)^(7/3)) + (243*d^3*(c + d*x)^(4/3))/(1820*(b*c - a*d)^4*(a + b*x)^(4/3))","A",4,2,19,0.1053,1,"{45, 37}"
1582,1,655,0,1.4164623,"\int (a+b x)^{4/3} \sqrt[3]{c+d x} \, dx","Int[(a + b*x)^(4/3)*(c + d*x)^(1/3),x]","\frac{3^{3/4} \sqrt{2+\sqrt{3}} (b c-a d)^3 ((a+b x) (c+d x))^{2/3} \sqrt{(a d+b c+2 b d x)^2} \left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{2/3}\right) \sqrt{\frac{2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} (b c-a d)^{2/3} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{4/3}}{\left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right)}{10\ 2^{2/3} b^{4/3} d^{7/3} (a+b x)^{2/3} (c+d x)^{2/3} (a d+b c+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{2/3}\right)}{\left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}-\frac{3 \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c-a d)^2}{20 b d^2}+\frac{3 (a+b x)^{4/3} \sqrt[3]{c+d x} (b c-a d)}{40 b d}+\frac{3 (a+b x)^{7/3} \sqrt[3]{c+d x}}{8 b}","\frac{3^{3/4} \sqrt{2+\sqrt{3}} (b c-a d)^3 ((a+b x) (c+d x))^{2/3} \sqrt{(a d+b c+2 b d x)^2} \left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{2/3}\right) \sqrt{\frac{2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} (b c-a d)^{2/3} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{4/3}}{\left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right)}{10\ 2^{2/3} b^{4/3} d^{7/3} (a+b x)^{2/3} (c+d x)^{2/3} (a d+b c+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{2/3}\right)}{\left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}-\frac{3 \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c-a d)^2}{20 b d^2}+\frac{3 (a+b x)^{4/3} \sqrt[3]{c+d x} (b c-a d)}{40 b d}+\frac{3 (a+b x)^{7/3} \sqrt[3]{c+d x}}{8 b}",1,"(-3*(b*c - a*d)^2*(a + b*x)^(1/3)*(c + d*x)^(1/3))/(20*b*d^2) + (3*(b*c - a*d)*(a + b*x)^(4/3)*(c + d*x)^(1/3))/(40*b*d) + (3*(a + b*x)^(7/3)*(c + d*x)^(1/3))/(8*b) + (3^(3/4)*Sqrt[2 + Sqrt[3]]*(b*c - a*d)^3*((a + b*x)*(c + d*x))^(2/3)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))*Sqrt[((b*c - a*d)^(4/3) - 2^(2/3)*b^(1/3)*d^(1/3)*(b*c - a*d)^(2/3)*((a + b*x)*(c + d*x))^(1/3) + 2*2^(1/3)*b^(2/3)*d^(2/3)*((a + b*x)*(c + d*x))^(2/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*EllipticF[ArcSin[((1 - Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))], -7 - 4*Sqrt[3]])/(10*2^(2/3)*b^(4/3)*d^(7/3)*(a + b*x)^(2/3)*(c + d*x)^(2/3)*(b*c + a*d + 2*b*d*x)*Sqrt[((b*c - a*d)^(2/3)*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3)))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*Sqrt[(a*d + b*(c + 2*d*x))^2])","A",6,4,19,0.2105,1,"{50, 62, 623, 218}"
1583,1,617,0,0.8490558,"\int \sqrt[3]{a+b x} \sqrt[3]{c+d x} \, dx","Int[(a + b*x)^(1/3)*(c + d*x)^(1/3),x]","-\frac{3^{3/4} \sqrt{2+\sqrt{3}} (b c-a d)^2 ((a+b x) (c+d x))^{2/3} \sqrt{(a d+b c+2 b d x)^2} \left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{2/3}\right) \sqrt{\frac{2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} (b c-a d)^{2/3} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{4/3}}{\left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right)}{5\ 2^{2/3} b^{4/3} d^{4/3} (a+b x)^{2/3} (c+d x)^{2/3} (a d+b c+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{2/3}\right)}{\left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}+\frac{3 \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c-a d)}{10 b d}+\frac{3 (a+b x)^{4/3} \sqrt[3]{c+d x}}{5 b}","-\frac{3^{3/4} \sqrt{2+\sqrt{3}} (b c-a d)^2 ((a+b x) (c+d x))^{2/3} \sqrt{(a d+b c+2 b d x)^2} \left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{2/3}\right) \sqrt{\frac{2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} (b c-a d)^{2/3} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{4/3}}{\left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right)}{5\ 2^{2/3} b^{4/3} d^{4/3} (a+b x)^{2/3} (c+d x)^{2/3} (a d+b c+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{2/3}\right)}{\left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}+\frac{3 \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c-a d)}{10 b d}+\frac{3 (a+b x)^{4/3} \sqrt[3]{c+d x}}{5 b}",1,"(3*(b*c - a*d)*(a + b*x)^(1/3)*(c + d*x)^(1/3))/(10*b*d) + (3*(a + b*x)^(4/3)*(c + d*x)^(1/3))/(5*b) - (3^(3/4)*Sqrt[2 + Sqrt[3]]*(b*c - a*d)^2*((a + b*x)*(c + d*x))^(2/3)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))*Sqrt[((b*c - a*d)^(4/3) - 2^(2/3)*b^(1/3)*d^(1/3)*(b*c - a*d)^(2/3)*((a + b*x)*(c + d*x))^(1/3) + 2*2^(1/3)*b^(2/3)*d^(2/3)*((a + b*x)*(c + d*x))^(2/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*EllipticF[ArcSin[((1 - Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))], -7 - 4*Sqrt[3]])/(5*2^(2/3)*b^(4/3)*d^(4/3)*(a + b*x)^(2/3)*(c + d*x)^(2/3)*(b*c + a*d + 2*b*d*x)*Sqrt[((b*c - a*d)^(2/3)*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3)))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*Sqrt[(a*d + b*(c + 2*d*x))^2])","A",5,4,19,0.2105,1,"{50, 62, 623, 218}"
1584,1,576,0,0.5625961,"\int \frac{\sqrt[3]{c+d x}}{(a+b x)^{2/3}} \, dx","Int[(c + d*x)^(1/3)/(a + b*x)^(2/3),x]","\frac{3^{3/4} \sqrt{2+\sqrt{3}} (b c-a d) ((a+b x) (c+d x))^{2/3} \sqrt{(a d+b c+2 b d x)^2} \left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{2/3}\right) \sqrt{\frac{2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} (b c-a d)^{2/3} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{4/3}}{\left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right)}{2^{2/3} b^{4/3} \sqrt[3]{d} (a+b x)^{2/3} (c+d x)^{2/3} (a d+b c+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{2/3}\right)}{\left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}+\frac{3 \sqrt[3]{a+b x} \sqrt[3]{c+d x}}{2 b}","\frac{3^{3/4} \sqrt{2+\sqrt{3}} (b c-a d) ((a+b x) (c+d x))^{2/3} \sqrt{(a d+b c+2 b d x)^2} \left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{2/3}\right) \sqrt{\frac{2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} (b c-a d)^{2/3} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{4/3}}{\left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right)}{2^{2/3} b^{4/3} \sqrt[3]{d} (a+b x)^{2/3} (c+d x)^{2/3} (a d+b c+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{2/3}\right)}{\left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}+\frac{3 \sqrt[3]{a+b x} \sqrt[3]{c+d x}}{2 b}",1,"(3*(a + b*x)^(1/3)*(c + d*x)^(1/3))/(2*b) + (3^(3/4)*Sqrt[2 + Sqrt[3]]*(b*c - a*d)*((a + b*x)*(c + d*x))^(2/3)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))*Sqrt[((b*c - a*d)^(4/3) - 2^(2/3)*b^(1/3)*d^(1/3)*(b*c - a*d)^(2/3)*((a + b*x)*(c + d*x))^(1/3) + 2*2^(1/3)*b^(2/3)*d^(2/3)*((a + b*x)*(c + d*x))^(2/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*EllipticF[ArcSin[((1 - Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))], -7 - 4*Sqrt[3]])/(2^(2/3)*b^(4/3)*d^(1/3)*(a + b*x)^(2/3)*(c + d*x)^(2/3)*(b*c + a*d + 2*b*d*x)*Sqrt[((b*c - a*d)^(2/3)*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3)))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*Sqrt[(a*d + b*(c + 2*d*x))^2])","A",4,4,19,0.2105,1,"{50, 62, 623, 218}"
1585,1,568,0,0.5944283,"\int \frac{\sqrt[3]{c+d x}}{(a+b x)^{5/3}} \, dx","Int[(c + d*x)^(1/3)/(a + b*x)^(5/3),x]","\frac{3^{3/4} \sqrt{2+\sqrt{3}} d^{2/3} ((a+b x) (c+d x))^{2/3} \sqrt{(a d+b c+2 b d x)^2} \left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{2/3}\right) \sqrt{\frac{2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} (b c-a d)^{2/3} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{4/3}}{\left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right)}{2^{2/3} b^{4/3} (a+b x)^{2/3} (c+d x)^{2/3} (a d+b c+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{2/3}\right)}{\left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}-\frac{3 \sqrt[3]{c+d x}}{2 b (a+b x)^{2/3}}","\frac{3^{3/4} \sqrt{2+\sqrt{3}} d^{2/3} ((a+b x) (c+d x))^{2/3} \sqrt{(a d+b c+2 b d x)^2} \left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{2/3}\right) \sqrt{\frac{2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} (b c-a d)^{2/3} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{4/3}}{\left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right)}{2^{2/3} b^{4/3} (a+b x)^{2/3} (c+d x)^{2/3} (a d+b c+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{2/3}\right)}{\left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}-\frac{3 \sqrt[3]{c+d x}}{2 b (a+b x)^{2/3}}",1,"(-3*(c + d*x)^(1/3))/(2*b*(a + b*x)^(2/3)) + (3^(3/4)*Sqrt[2 + Sqrt[3]]*d^(2/3)*((a + b*x)*(c + d*x))^(2/3)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))*Sqrt[((b*c - a*d)^(4/3) - 2^(2/3)*b^(1/3)*d^(1/3)*(b*c - a*d)^(2/3)*((a + b*x)*(c + d*x))^(1/3) + 2*2^(1/3)*b^(2/3)*d^(2/3)*((a + b*x)*(c + d*x))^(2/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*EllipticF[ArcSin[((1 - Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))], -7 - 4*Sqrt[3]])/(2^(2/3)*b^(4/3)*(a + b*x)^(2/3)*(c + d*x)^(2/3)*(b*c + a*d + 2*b*d*x)*Sqrt[((b*c - a*d)^(2/3)*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3)))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*Sqrt[(a*d + b*(c + 2*d*x))^2])","A",4,4,19,0.2105,1,"{47, 62, 623, 218}"
1586,1,617,0,0.8433779,"\int \frac{\sqrt[3]{c+d x}}{(a+b x)^{8/3}} \, dx","Int[(c + d*x)^(1/3)/(a + b*x)^(8/3),x]","-\frac{3^{3/4} \sqrt{2+\sqrt{3}} d^{5/3} ((a+b x) (c+d x))^{2/3} \sqrt{(a d+b c+2 b d x)^2} \left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{2/3}\right) \sqrt{\frac{2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} (b c-a d)^{2/3} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{4/3}}{\left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right)}{5\ 2^{2/3} b^{4/3} (a+b x)^{2/3} (c+d x)^{2/3} (b c-a d) (a d+b c+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{2/3}\right)}{\left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}-\frac{3 d \sqrt[3]{c+d x}}{10 b (a+b x)^{2/3} (b c-a d)}-\frac{3 \sqrt[3]{c+d x}}{5 b (a+b x)^{5/3}}","-\frac{3^{3/4} \sqrt{2+\sqrt{3}} d^{5/3} ((a+b x) (c+d x))^{2/3} \sqrt{(a d+b c+2 b d x)^2} \left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{2/3}\right) \sqrt{\frac{2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} (b c-a d)^{2/3} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{4/3}}{\left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right)}{5\ 2^{2/3} b^{4/3} (a+b x)^{2/3} (c+d x)^{2/3} (b c-a d) (a d+b c+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{2/3}\right)}{\left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}-\frac{3 d \sqrt[3]{c+d x}}{10 b (a+b x)^{2/3} (b c-a d)}-\frac{3 \sqrt[3]{c+d x}}{5 b (a+b x)^{5/3}}",1,"(-3*(c + d*x)^(1/3))/(5*b*(a + b*x)^(5/3)) - (3*d*(c + d*x)^(1/3))/(10*b*(b*c - a*d)*(a + b*x)^(2/3)) - (3^(3/4)*Sqrt[2 + Sqrt[3]]*d^(5/3)*((a + b*x)*(c + d*x))^(2/3)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))*Sqrt[((b*c - a*d)^(4/3) - 2^(2/3)*b^(1/3)*d^(1/3)*(b*c - a*d)^(2/3)*((a + b*x)*(c + d*x))^(1/3) + 2*2^(1/3)*b^(2/3)*d^(2/3)*((a + b*x)*(c + d*x))^(2/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*EllipticF[ArcSin[((1 - Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))], -7 - 4*Sqrt[3]])/(5*2^(2/3)*b^(4/3)*(b*c - a*d)*(a + b*x)^(2/3)*(c + d*x)^(2/3)*(b*c + a*d + 2*b*d*x)*Sqrt[((b*c - a*d)^(2/3)*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3)))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*Sqrt[(a*d + b*(c + 2*d*x))^2])","A",5,5,19,0.2632,1,"{47, 51, 62, 623, 218}"
1587,1,216,0,0.0903724,"\int \frac{(a+b x)^{4/3}}{\sqrt[3]{c+d x}} \, dx","Int[(a + b*x)^(4/3)/(c + d*x)^(1/3),x]","-\frac{(b c-a d)^2 \log (a+b x)}{9 b^{2/3} d^{7/3}}-\frac{(b c-a d)^2 \log \left(\frac{\sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{d} \sqrt[3]{a+b x}}-1\right)}{3 b^{2/3} d^{7/3}}-\frac{2 (b c-a d)^2 \tan ^{-1}\left(\frac{2 \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt{3} \sqrt[3]{d} \sqrt[3]{a+b x}}+\frac{1}{\sqrt{3}}\right)}{3 \sqrt{3} b^{2/3} d^{7/3}}-\frac{2 \sqrt[3]{a+b x} (c+d x)^{2/3} (b c-a d)}{3 d^2}+\frac{(a+b x)^{4/3} (c+d x)^{2/3}}{2 d}","-\frac{(b c-a d)^2 \log (a+b x)}{9 b^{2/3} d^{7/3}}-\frac{(b c-a d)^2 \log \left(\frac{\sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{d} \sqrt[3]{a+b x}}-1\right)}{3 b^{2/3} d^{7/3}}-\frac{2 (b c-a d)^2 \tan ^{-1}\left(\frac{2 \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt{3} \sqrt[3]{d} \sqrt[3]{a+b x}}+\frac{1}{\sqrt{3}}\right)}{3 \sqrt{3} b^{2/3} d^{7/3}}-\frac{2 \sqrt[3]{a+b x} (c+d x)^{2/3} (b c-a d)}{3 d^2}+\frac{(a+b x)^{4/3} (c+d x)^{2/3}}{2 d}",1,"(-2*(b*c - a*d)*(a + b*x)^(1/3)*(c + d*x)^(2/3))/(3*d^2) + ((a + b*x)^(4/3)*(c + d*x)^(2/3))/(2*d) - (2*(b*c - a*d)^2*ArcTan[1/Sqrt[3] + (2*b^(1/3)*(c + d*x)^(1/3))/(Sqrt[3]*d^(1/3)*(a + b*x)^(1/3))])/(3*Sqrt[3]*b^(2/3)*d^(7/3)) - ((b*c - a*d)^2*Log[a + b*x])/(9*b^(2/3)*d^(7/3)) - ((b*c - a*d)^2*Log[-1 + (b^(1/3)*(c + d*x)^(1/3))/(d^(1/3)*(a + b*x)^(1/3))])/(3*b^(2/3)*d^(7/3))","A",3,2,19,0.1053,1,"{50, 59}"
1588,1,171,0,0.040657,"\int \frac{\sqrt[3]{a+b x}}{\sqrt[3]{c+d x}} \, dx","Int[(a + b*x)^(1/3)/(c + d*x)^(1/3),x]","\frac{(b c-a d) \log (a+b x)}{6 b^{2/3} d^{4/3}}+\frac{(b c-a d) \log \left(\frac{\sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{d} \sqrt[3]{a+b x}}-1\right)}{2 b^{2/3} d^{4/3}}+\frac{(b c-a d) \tan ^{-1}\left(\frac{2 \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt{3} \sqrt[3]{d} \sqrt[3]{a+b x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3} b^{2/3} d^{4/3}}+\frac{\sqrt[3]{a+b x} (c+d x)^{2/3}}{d}","\frac{(b c-a d) \log (a+b x)}{6 b^{2/3} d^{4/3}}+\frac{(b c-a d) \log \left(\frac{\sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{d} \sqrt[3]{a+b x}}-1\right)}{2 b^{2/3} d^{4/3}}+\frac{(b c-a d) \tan ^{-1}\left(\frac{2 \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt{3} \sqrt[3]{d} \sqrt[3]{a+b x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3} b^{2/3} d^{4/3}}+\frac{\sqrt[3]{a+b x} (c+d x)^{2/3}}{d}",1,"((a + b*x)^(1/3)*(c + d*x)^(2/3))/d + ((b*c - a*d)*ArcTan[1/Sqrt[3] + (2*b^(1/3)*(c + d*x)^(1/3))/(Sqrt[3]*d^(1/3)*(a + b*x)^(1/3))])/(Sqrt[3]*b^(2/3)*d^(4/3)) + ((b*c - a*d)*Log[a + b*x])/(6*b^(2/3)*d^(4/3)) + ((b*c - a*d)*Log[-1 + (b^(1/3)*(c + d*x)^(1/3))/(d^(1/3)*(a + b*x)^(1/3))])/(2*b^(2/3)*d^(4/3))","A",2,2,19,0.1053,1,"{50, 59}"
1589,1,126,0,0.014312,"\int \frac{1}{(a+b x)^{2/3} \sqrt[3]{c+d x}} \, dx","Int[1/((a + b*x)^(2/3)*(c + d*x)^(1/3)),x]","-\frac{3 \log \left(\frac{\sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{d} \sqrt[3]{a+b x}}-1\right)}{2 b^{2/3} \sqrt[3]{d}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt{3} \sqrt[3]{d} \sqrt[3]{a+b x}}+\frac{1}{\sqrt{3}}\right)}{b^{2/3} \sqrt[3]{d}}-\frac{\log (a+b x)}{2 b^{2/3} \sqrt[3]{d}}","-\frac{3 \log \left(\frac{\sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{d} \sqrt[3]{a+b x}}-1\right)}{2 b^{2/3} \sqrt[3]{d}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt{3} \sqrt[3]{d} \sqrt[3]{a+b x}}+\frac{1}{\sqrt{3}}\right)}{b^{2/3} \sqrt[3]{d}}-\frac{\log (a+b x)}{2 b^{2/3} \sqrt[3]{d}}",1,"-((Sqrt[3]*ArcTan[1/Sqrt[3] + (2*b^(1/3)*(c + d*x)^(1/3))/(Sqrt[3]*d^(1/3)*(a + b*x)^(1/3))])/(b^(2/3)*d^(1/3))) - Log[a + b*x]/(2*b^(2/3)*d^(1/3)) - (3*Log[-1 + (b^(1/3)*(c + d*x)^(1/3))/(d^(1/3)*(a + b*x)^(1/3))])/(2*b^(2/3)*d^(1/3))","A",1,1,19,0.05263,1,"{59}"
1590,1,32,0,0.0029671,"\int \frac{1}{(a+b x)^{5/3} \sqrt[3]{c+d x}} \, dx","Int[1/((a + b*x)^(5/3)*(c + d*x)^(1/3)),x]","-\frac{3 (c+d x)^{2/3}}{2 (a+b x)^{2/3} (b c-a d)}","-\frac{3 (c+d x)^{2/3}}{2 (a+b x)^{2/3} (b c-a d)}",1,"(-3*(c + d*x)^(2/3))/(2*(b*c - a*d)*(a + b*x)^(2/3))","A",1,1,19,0.05263,1,"{37}"
1591,1,66,0,0.0090983,"\int \frac{1}{(a+b x)^{8/3} \sqrt[3]{c+d x}} \, dx","Int[1/((a + b*x)^(8/3)*(c + d*x)^(1/3)),x]","\frac{9 d (c+d x)^{2/3}}{10 (a+b x)^{2/3} (b c-a d)^2}-\frac{3 (c+d x)^{2/3}}{5 (a+b x)^{5/3} (b c-a d)}","\frac{9 d (c+d x)^{2/3}}{10 (a+b x)^{2/3} (b c-a d)^2}-\frac{3 (c+d x)^{2/3}}{5 (a+b x)^{5/3} (b c-a d)}",1,"(-3*(c + d*x)^(2/3))/(5*(b*c - a*d)*(a + b*x)^(5/3)) + (9*d*(c + d*x)^(2/3))/(10*(b*c - a*d)^2*(a + b*x)^(2/3))","A",2,2,19,0.1053,1,"{45, 37}"
1592,1,101,0,0.0176758,"\int \frac{1}{(a+b x)^{11/3} \sqrt[3]{c+d x}} \, dx","Int[1/((a + b*x)^(11/3)*(c + d*x)^(1/3)),x]","-\frac{27 d^2 (c+d x)^{2/3}}{40 (a+b x)^{2/3} (b c-a d)^3}+\frac{9 d (c+d x)^{2/3}}{20 (a+b x)^{5/3} (b c-a d)^2}-\frac{3 (c+d x)^{2/3}}{8 (a+b x)^{8/3} (b c-a d)}","-\frac{27 d^2 (c+d x)^{2/3}}{40 (a+b x)^{2/3} (b c-a d)^3}+\frac{9 d (c+d x)^{2/3}}{20 (a+b x)^{5/3} (b c-a d)^2}-\frac{3 (c+d x)^{2/3}}{8 (a+b x)^{8/3} (b c-a d)}",1,"(-3*(c + d*x)^(2/3))/(8*(b*c - a*d)*(a + b*x)^(8/3)) + (9*d*(c + d*x)^(2/3))/(20*(b*c - a*d)^2*(a + b*x)^(5/3)) - (27*d^2*(c + d*x)^(2/3))/(40*(b*c - a*d)^3*(a + b*x)^(2/3))","A",3,2,19,0.1053,1,"{45, 37}"
1593,1,136,0,0.0282084,"\int \frac{1}{(a+b x)^{14/3} \sqrt[3]{c+d x}} \, dx","Int[1/((a + b*x)^(14/3)*(c + d*x)^(1/3)),x]","\frac{243 d^3 (c+d x)^{2/3}}{440 (a+b x)^{2/3} (b c-a d)^4}-\frac{81 d^2 (c+d x)^{2/3}}{220 (a+b x)^{5/3} (b c-a d)^3}+\frac{27 d (c+d x)^{2/3}}{88 (a+b x)^{8/3} (b c-a d)^2}-\frac{3 (c+d x)^{2/3}}{11 (a+b x)^{11/3} (b c-a d)}","\frac{243 d^3 (c+d x)^{2/3}}{440 (a+b x)^{2/3} (b c-a d)^4}-\frac{81 d^2 (c+d x)^{2/3}}{220 (a+b x)^{5/3} (b c-a d)^3}+\frac{27 d (c+d x)^{2/3}}{88 (a+b x)^{8/3} (b c-a d)^2}-\frac{3 (c+d x)^{2/3}}{11 (a+b x)^{11/3} (b c-a d)}",1,"(-3*(c + d*x)^(2/3))/(11*(b*c - a*d)*(a + b*x)^(11/3)) + (27*d*(c + d*x)^(2/3))/(88*(b*c - a*d)^2*(a + b*x)^(8/3)) - (81*d^2*(c + d*x)^(2/3))/(220*(b*c - a*d)^3*(a + b*x)^(5/3)) + (243*d^3*(c + d*x)^(2/3))/(440*(b*c - a*d)^4*(a + b*x)^(2/3))","A",4,2,19,0.1053,1,"{45, 37}"
1594,1,1365,0,2.8032829,"\int \frac{(a+b x)^{8/3}}{\sqrt[3]{c+d x}} \, dx","Int[(a + b*x)^(8/3)/(c + d*x)^(1/3),x]","\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right) (b c-a d)^{11/3}}{7 \sqrt[3]{2} b^{2/3} d^{11/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}-\frac{2 \sqrt[6]{2} 3^{3/4} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right) (b c-a d)^{11/3}}{7 b^{2/3} d^{11/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}-\frac{3\ 2^{2/3} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \sqrt{(a d+b (c+2 d x))^2} (b c-a d)^3}{7 b^{2/3} d^{11/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}+\frac{3 (a+b x)^{2/3} (c+d x)^{2/3} (b c-a d)^2}{7 d^3}-\frac{12 (a+b x)^{5/3} (c+d x)^{2/3} (b c-a d)}{35 d^2}+\frac{3 (a+b x)^{8/3} (c+d x)^{2/3}}{10 d}","\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right) (b c-a d)^{11/3}}{7 \sqrt[3]{2} b^{2/3} d^{11/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}-\frac{2 \sqrt[6]{2} 3^{3/4} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right) (b c-a d)^{11/3}}{7 b^{2/3} d^{11/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}-\frac{3\ 2^{2/3} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \sqrt{(a d+b (c+2 d x))^2} (b c-a d)^3}{7 b^{2/3} d^{11/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}+\frac{3 (a+b x)^{2/3} (c+d x)^{2/3} (b c-a d)^2}{7 d^3}-\frac{12 (a+b x)^{5/3} (c+d x)^{2/3} (b c-a d)}{35 d^2}+\frac{3 (a+b x)^{8/3} (c+d x)^{2/3}}{10 d}",1,"(3*(b*c - a*d)^2*(a + b*x)^(2/3)*(c + d*x)^(2/3))/(7*d^3) - (12*(b*c - a*d)*(a + b*x)^(5/3)*(c + d*x)^(2/3))/(35*d^2) + (3*(a + b*x)^(8/3)*(c + d*x)^(2/3))/(10*d) - (3*2^(2/3)*(b*c - a*d)^3*((a + b*x)*(c + d*x))^(1/3)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*Sqrt[(a*d + b*(c + 2*d*x))^2])/(7*b^(2/3)*d^(11/3)*(a + b*x)^(1/3)*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)*((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))) + (3*3^(1/4)*Sqrt[2 - Sqrt[3]]*(b*c - a*d)^(11/3)*((a + b*x)*(c + d*x))^(1/3)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))*Sqrt[((b*c - a*d)^(4/3) - 2^(2/3)*b^(1/3)*d^(1/3)*(b*c - a*d)^(2/3)*((a + b*x)*(c + d*x))^(1/3) + 2*2^(1/3)*b^(2/3)*d^(2/3)*((a + b*x)*(c + d*x))^(2/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*EllipticE[ArcSin[((1 - Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))], -7 - 4*Sqrt[3]])/(7*2^(1/3)*b^(2/3)*d^(11/3)*(a + b*x)^(1/3)*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)*Sqrt[((b*c - a*d)^(2/3)*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3)))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*Sqrt[(a*d + b*(c + 2*d*x))^2]) - (2*2^(1/6)*3^(3/4)*(b*c - a*d)^(11/3)*((a + b*x)*(c + d*x))^(1/3)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))*Sqrt[((b*c - a*d)^(4/3) - 2^(2/3)*b^(1/3)*d^(1/3)*(b*c - a*d)^(2/3)*((a + b*x)*(c + d*x))^(1/3) + 2*2^(1/3)*b^(2/3)*d^(2/3)*((a + b*x)*(c + d*x))^(2/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*EllipticF[ArcSin[((1 - Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))], -7 - 4*Sqrt[3]])/(7*b^(2/3)*d^(11/3)*(a + b*x)^(1/3)*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)*Sqrt[((b*c - a*d)^(2/3)*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3)))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*Sqrt[(a*d + b*(c + 2*d*x))^2])","A",8,6,19,0.3158,1,"{50, 62, 623, 303, 218, 1877}"
1595,1,1330,0,2.0099071,"\int \frac{(a+b x)^{5/3}}{\sqrt[3]{c+d x}} \, dx","Int[(a + b*x)^(5/3)/(c + d*x)^(1/3),x]","-\frac{15 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right) (b c-a d)^{8/3}}{28 \sqrt[3]{2} b^{2/3} d^{8/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}+\frac{5\ 3^{3/4} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right) (b c-a d)^{8/3}}{7\ 2^{5/6} b^{2/3} d^{8/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}+\frac{15 \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \sqrt{(a d+b (c+2 d x))^2} (b c-a d)^2}{14 \sqrt[3]{2} b^{2/3} d^{8/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}-\frac{15 (a+b x)^{2/3} (c+d x)^{2/3} (b c-a d)}{28 d^2}+\frac{3 (a+b x)^{5/3} (c+d x)^{2/3}}{7 d}","-\frac{15 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right) (b c-a d)^{8/3}}{28 \sqrt[3]{2} b^{2/3} d^{8/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}+\frac{5\ 3^{3/4} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right) (b c-a d)^{8/3}}{7\ 2^{5/6} b^{2/3} d^{8/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}+\frac{15 \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \sqrt{(a d+b (c+2 d x))^2} (b c-a d)^2}{14 \sqrt[3]{2} b^{2/3} d^{8/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}-\frac{15 (a+b x)^{2/3} (c+d x)^{2/3} (b c-a d)}{28 d^2}+\frac{3 (a+b x)^{5/3} (c+d x)^{2/3}}{7 d}",1,"(-15*(b*c - a*d)*(a + b*x)^(2/3)*(c + d*x)^(2/3))/(28*d^2) + (3*(a + b*x)^(5/3)*(c + d*x)^(2/3))/(7*d) + (15*(b*c - a*d)^2*((a + b*x)*(c + d*x))^(1/3)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*Sqrt[(a*d + b*(c + 2*d*x))^2])/(14*2^(1/3)*b^(2/3)*d^(8/3)*(a + b*x)^(1/3)*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)*((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))) - (15*3^(1/4)*Sqrt[2 - Sqrt[3]]*(b*c - a*d)^(8/3)*((a + b*x)*(c + d*x))^(1/3)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))*Sqrt[((b*c - a*d)^(4/3) - 2^(2/3)*b^(1/3)*d^(1/3)*(b*c - a*d)^(2/3)*((a + b*x)*(c + d*x))^(1/3) + 2*2^(1/3)*b^(2/3)*d^(2/3)*((a + b*x)*(c + d*x))^(2/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*EllipticE[ArcSin[((1 - Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))], -7 - 4*Sqrt[3]])/(28*2^(1/3)*b^(2/3)*d^(8/3)*(a + b*x)^(1/3)*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)*Sqrt[((b*c - a*d)^(2/3)*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3)))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*Sqrt[(a*d + b*(c + 2*d*x))^2]) + (5*3^(3/4)*(b*c - a*d)^(8/3)*((a + b*x)*(c + d*x))^(1/3)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))*Sqrt[((b*c - a*d)^(4/3) - 2^(2/3)*b^(1/3)*d^(1/3)*(b*c - a*d)^(2/3)*((a + b*x)*(c + d*x))^(1/3) + 2*2^(1/3)*b^(2/3)*d^(2/3)*((a + b*x)*(c + d*x))^(2/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*EllipticF[ArcSin[((1 - Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))], -7 - 4*Sqrt[3]])/(7*2^(5/6)*b^(2/3)*d^(8/3)*(a + b*x)^(1/3)*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)*Sqrt[((b*c - a*d)^(2/3)*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3)))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*Sqrt[(a*d + b*(c + 2*d*x))^2])","A",7,6,19,0.3158,1,"{50, 62, 623, 303, 218, 1877}"
1596,1,1293,0,1.5630769,"\int \frac{(a+b x)^{2/3}}{\sqrt[3]{c+d x}} \, dx","Int[(a + b*x)^(2/3)/(c + d*x)^(1/3),x]","\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right) (b c-a d)^{5/3}}{4 \sqrt[3]{2} b^{2/3} d^{5/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}-\frac{3^{3/4} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right) (b c-a d)^{5/3}}{2^{5/6} b^{2/3} d^{5/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}-\frac{3 \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \sqrt{(a d+b (c+2 d x))^2} (b c-a d)}{2 \sqrt[3]{2} b^{2/3} d^{5/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}+\frac{3 (a+b x)^{2/3} (c+d x)^{2/3}}{4 d}","\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right) (b c-a d)^{5/3}}{4 \sqrt[3]{2} b^{2/3} d^{5/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}-\frac{3^{3/4} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right) (b c-a d)^{5/3}}{2^{5/6} b^{2/3} d^{5/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}-\frac{3 \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \sqrt{(a d+b (c+2 d x))^2} (b c-a d)}{2 \sqrt[3]{2} b^{2/3} d^{5/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}+\frac{3 (a+b x)^{2/3} (c+d x)^{2/3}}{4 d}",1,"(3*(a + b*x)^(2/3)*(c + d*x)^(2/3))/(4*d) - (3*(b*c - a*d)*((a + b*x)*(c + d*x))^(1/3)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*Sqrt[(a*d + b*(c + 2*d*x))^2])/(2*2^(1/3)*b^(2/3)*d^(5/3)*(a + b*x)^(1/3)*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)*((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))) + (3*3^(1/4)*Sqrt[2 - Sqrt[3]]*(b*c - a*d)^(5/3)*((a + b*x)*(c + d*x))^(1/3)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))*Sqrt[((b*c - a*d)^(4/3) - 2^(2/3)*b^(1/3)*d^(1/3)*(b*c - a*d)^(2/3)*((a + b*x)*(c + d*x))^(1/3) + 2*2^(1/3)*b^(2/3)*d^(2/3)*((a + b*x)*(c + d*x))^(2/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*EllipticE[ArcSin[((1 - Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))], -7 - 4*Sqrt[3]])/(4*2^(1/3)*b^(2/3)*d^(5/3)*(a + b*x)^(1/3)*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)*Sqrt[((b*c - a*d)^(2/3)*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3)))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*Sqrt[(a*d + b*(c + 2*d*x))^2]) - (3^(3/4)*(b*c - a*d)^(5/3)*((a + b*x)*(c + d*x))^(1/3)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))*Sqrt[((b*c - a*d)^(4/3) - 2^(2/3)*b^(1/3)*d^(1/3)*(b*c - a*d)^(2/3)*((a + b*x)*(c + d*x))^(1/3) + 2*2^(1/3)*b^(2/3)*d^(2/3)*((a + b*x)*(c + d*x))^(2/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*EllipticF[ArcSin[((1 - Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))], -7 - 4*Sqrt[3]])/(2^(5/6)*b^(2/3)*d^(5/3)*(a + b*x)^(1/3)*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)*Sqrt[((b*c - a*d)^(2/3)*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3)))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*Sqrt[(a*d + b*(c + 2*d*x))^2])","A",6,6,19,0.3158,1,"{50, 62, 623, 303, 218, 1877}"
1597,1,1257,0,1.1785149,"\int \frac{1}{\sqrt[3]{a+b x} \sqrt[3]{c+d x}} \, dx","Int[1/((a + b*x)^(1/3)*(c + d*x)^(1/3)),x]","-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} (b c-a d)^{2/3} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right)}{2 \sqrt[3]{2} b^{2/3} d^{2/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}+\frac{\sqrt[6]{2} 3^{3/4} (b c-a d)^{2/3} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right)}{b^{2/3} d^{2/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}+\frac{3 \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \sqrt{(a d+b (c+2 d x))^2}}{\sqrt[3]{2} b^{2/3} d^{2/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}","-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} (b c-a d)^{2/3} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right)}{2 \sqrt[3]{2} b^{2/3} d^{2/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}+\frac{\sqrt[6]{2} 3^{3/4} (b c-a d)^{2/3} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right)}{b^{2/3} d^{2/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}+\frac{3 \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \sqrt{(a d+b (c+2 d x))^2}}{\sqrt[3]{2} b^{2/3} d^{2/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}",1,"(3*((a + b*x)*(c + d*x))^(1/3)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*Sqrt[(a*d + b*(c + 2*d*x))^2])/(2^(1/3)*b^(2/3)*d^(2/3)*(a + b*x)^(1/3)*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)*((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))) - (3*3^(1/4)*Sqrt[2 - Sqrt[3]]*(b*c - a*d)^(2/3)*((a + b*x)*(c + d*x))^(1/3)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))*Sqrt[((b*c - a*d)^(4/3) - 2^(2/3)*b^(1/3)*d^(1/3)*(b*c - a*d)^(2/3)*((a + b*x)*(c + d*x))^(1/3) + 2*2^(1/3)*b^(2/3)*d^(2/3)*((a + b*x)*(c + d*x))^(2/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*EllipticE[ArcSin[((1 - Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))], -7 - 4*Sqrt[3]])/(2*2^(1/3)*b^(2/3)*d^(2/3)*(a + b*x)^(1/3)*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)*Sqrt[((b*c - a*d)^(2/3)*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3)))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*Sqrt[(a*d + b*(c + 2*d*x))^2]) + (2^(1/6)*3^(3/4)*(b*c - a*d)^(2/3)*((a + b*x)*(c + d*x))^(1/3)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))*Sqrt[((b*c - a*d)^(4/3) - 2^(2/3)*b^(1/3)*d^(1/3)*(b*c - a*d)^(2/3)*((a + b*x)*(c + d*x))^(1/3) + 2*2^(1/3)*b^(2/3)*d^(2/3)*((a + b*x)*(c + d*x))^(2/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*EllipticF[ArcSin[((1 - Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))], -7 - 4*Sqrt[3]])/(b^(2/3)*d^(2/3)*(a + b*x)^(1/3)*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)*Sqrt[((b*c - a*d)^(2/3)*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3)))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*Sqrt[(a*d + b*(c + 2*d*x))^2])","A",5,5,19,0.2632,1,"{62, 623, 303, 218, 1877}"
1598,1,1297,0,1.5864182,"\int \frac{1}{(a+b x)^{4/3} \sqrt[3]{c+d x}} \, dx","Int[1/((a + b*x)^(4/3)*(c + d*x)^(1/3)),x]","-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right)}{2 \sqrt[3]{2} b^{2/3} \sqrt[3]{b c-a d} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}+\frac{\sqrt[6]{2} 3^{3/4} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right)}{b^{2/3} \sqrt[3]{b c-a d} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}-\frac{3 (c+d x)^{2/3}}{(b c-a d) \sqrt[3]{a+b x}}+\frac{3 \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \sqrt{(a d+b (c+2 d x))^2}}{\sqrt[3]{2} b^{2/3} (b c-a d) \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}","-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right)}{2 \sqrt[3]{2} b^{2/3} \sqrt[3]{b c-a d} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}+\frac{\sqrt[6]{2} 3^{3/4} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right)}{b^{2/3} \sqrt[3]{b c-a d} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}-\frac{3 (c+d x)^{2/3}}{(b c-a d) \sqrt[3]{a+b x}}+\frac{3 \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \sqrt{(a d+b (c+2 d x))^2}}{\sqrt[3]{2} b^{2/3} (b c-a d) \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}",1,"(-3*(c + d*x)^(2/3))/((b*c - a*d)*(a + b*x)^(1/3)) + (3*d^(1/3)*((a + b*x)*(c + d*x))^(1/3)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*Sqrt[(a*d + b*(c + 2*d*x))^2])/(2^(1/3)*b^(2/3)*(b*c - a*d)*(a + b*x)^(1/3)*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)*((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))) - (3*3^(1/4)*Sqrt[2 - Sqrt[3]]*d^(1/3)*((a + b*x)*(c + d*x))^(1/3)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))*Sqrt[((b*c - a*d)^(4/3) - 2^(2/3)*b^(1/3)*d^(1/3)*(b*c - a*d)^(2/3)*((a + b*x)*(c + d*x))^(1/3) + 2*2^(1/3)*b^(2/3)*d^(2/3)*((a + b*x)*(c + d*x))^(2/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*EllipticE[ArcSin[((1 - Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))], -7 - 4*Sqrt[3]])/(2*2^(1/3)*b^(2/3)*(b*c - a*d)^(1/3)*(a + b*x)^(1/3)*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)*Sqrt[((b*c - a*d)^(2/3)*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3)))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*Sqrt[(a*d + b*(c + 2*d*x))^2]) + (2^(1/6)*3^(3/4)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))*Sqrt[((b*c - a*d)^(4/3) - 2^(2/3)*b^(1/3)*d^(1/3)*(b*c - a*d)^(2/3)*((a + b*x)*(c + d*x))^(1/3) + 2*2^(1/3)*b^(2/3)*d^(2/3)*((a + b*x)*(c + d*x))^(2/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*EllipticF[ArcSin[((1 - Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))], -7 - 4*Sqrt[3]])/(b^(2/3)*(b*c - a*d)^(1/3)*(a + b*x)^(1/3)*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)*Sqrt[((b*c - a*d)^(2/3)*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3)))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*Sqrt[(a*d + b*(c + 2*d*x))^2])","A",6,6,19,0.3158,1,"{51, 62, 623, 303, 218, 1877}"
1599,1,1335,0,2.0124718,"\int \frac{1}{(a+b x)^{7/3} \sqrt[3]{c+d x}} \, dx","Int[1/((a + b*x)^(7/3)*(c + d*x)^(1/3)),x]","\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right) d^{4/3}}{4 \sqrt[3]{2} b^{2/3} (b c-a d)^{4/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}-\frac{3^{3/4} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right) d^{4/3}}{2^{5/6} b^{2/3} (b c-a d)^{4/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}-\frac{3 \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \sqrt{(a d+b (c+2 d x))^2} d^{4/3}}{2 \sqrt[3]{2} b^{2/3} (b c-a d)^2 \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}+\frac{3 (c+d x)^{2/3} d}{2 (b c-a d)^2 \sqrt[3]{a+b x}}-\frac{3 (c+d x)^{2/3}}{4 (b c-a d) (a+b x)^{4/3}}","\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right) d^{4/3}}{4 \sqrt[3]{2} b^{2/3} (b c-a d)^{4/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}-\frac{3^{3/4} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right) d^{4/3}}{2^{5/6} b^{2/3} (b c-a d)^{4/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}-\frac{3 \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \sqrt{(a d+b (c+2 d x))^2} d^{4/3}}{2 \sqrt[3]{2} b^{2/3} (b c-a d)^2 \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}+\frac{3 (c+d x)^{2/3} d}{2 (b c-a d)^2 \sqrt[3]{a+b x}}-\frac{3 (c+d x)^{2/3}}{4 (b c-a d) (a+b x)^{4/3}}",1,"(-3*(c + d*x)^(2/3))/(4*(b*c - a*d)*(a + b*x)^(4/3)) + (3*d*(c + d*x)^(2/3))/(2*(b*c - a*d)^2*(a + b*x)^(1/3)) - (3*d^(4/3)*((a + b*x)*(c + d*x))^(1/3)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*Sqrt[(a*d + b*(c + 2*d*x))^2])/(2*2^(1/3)*b^(2/3)*(b*c - a*d)^2*(a + b*x)^(1/3)*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)*((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))) + (3*3^(1/4)*Sqrt[2 - Sqrt[3]]*d^(4/3)*((a + b*x)*(c + d*x))^(1/3)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))*Sqrt[((b*c - a*d)^(4/3) - 2^(2/3)*b^(1/3)*d^(1/3)*(b*c - a*d)^(2/3)*((a + b*x)*(c + d*x))^(1/3) + 2*2^(1/3)*b^(2/3)*d^(2/3)*((a + b*x)*(c + d*x))^(2/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*EllipticE[ArcSin[((1 - Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))], -7 - 4*Sqrt[3]])/(4*2^(1/3)*b^(2/3)*(b*c - a*d)^(4/3)*(a + b*x)^(1/3)*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)*Sqrt[((b*c - a*d)^(2/3)*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3)))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*Sqrt[(a*d + b*(c + 2*d*x))^2]) - (3^(3/4)*d^(4/3)*((a + b*x)*(c + d*x))^(1/3)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))*Sqrt[((b*c - a*d)^(4/3) - 2^(2/3)*b^(1/3)*d^(1/3)*(b*c - a*d)^(2/3)*((a + b*x)*(c + d*x))^(1/3) + 2*2^(1/3)*b^(2/3)*d^(2/3)*((a + b*x)*(c + d*x))^(2/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*EllipticF[ArcSin[((1 - Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))], -7 - 4*Sqrt[3]])/(2^(5/6)*b^(2/3)*(b*c - a*d)^(4/3)*(a + b*x)^(1/3)*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)*Sqrt[((b*c - a*d)^(2/3)*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3)))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*Sqrt[(a*d + b*(c + 2*d*x))^2])","A",7,6,19,0.3158,1,"{51, 62, 623, 303, 218, 1877}"
1600,1,1372,0,2.4420586,"\int \frac{1}{(a+b x)^{10/3} \sqrt[3]{c+d x}} \, dx","Int[1/((a + b*x)^(10/3)*(c + d*x)^(1/3)),x]","-\frac{15 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right) d^{7/3}}{28 \sqrt[3]{2} b^{2/3} (b c-a d)^{7/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}+\frac{5\ 3^{3/4} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right) d^{7/3}}{7\ 2^{5/6} b^{2/3} (b c-a d)^{7/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}+\frac{15 \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \sqrt{(a d+b (c+2 d x))^2} d^{7/3}}{14 \sqrt[3]{2} b^{2/3} (b c-a d)^3 \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}-\frac{15 (c+d x)^{2/3} d^2}{14 (b c-a d)^3 \sqrt[3]{a+b x}}+\frac{15 (c+d x)^{2/3} d}{28 (b c-a d)^2 (a+b x)^{4/3}}-\frac{3 (c+d x)^{2/3}}{7 (b c-a d) (a+b x)^{7/3}}","-\frac{15 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right) d^{7/3}}{28 \sqrt[3]{2} b^{2/3} (b c-a d)^{7/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}+\frac{5\ 3^{3/4} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right) d^{7/3}}{7\ 2^{5/6} b^{2/3} (b c-a d)^{7/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}+\frac{15 \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \sqrt{(a d+b (c+2 d x))^2} d^{7/3}}{14 \sqrt[3]{2} b^{2/3} (b c-a d)^3 \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}-\frac{15 (c+d x)^{2/3} d^2}{14 (b c-a d)^3 \sqrt[3]{a+b x}}+\frac{15 (c+d x)^{2/3} d}{28 (b c-a d)^2 (a+b x)^{4/3}}-\frac{3 (c+d x)^{2/3}}{7 (b c-a d) (a+b x)^{7/3}}",1,"(-3*(c + d*x)^(2/3))/(7*(b*c - a*d)*(a + b*x)^(7/3)) + (15*d*(c + d*x)^(2/3))/(28*(b*c - a*d)^2*(a + b*x)^(4/3)) - (15*d^2*(c + d*x)^(2/3))/(14*(b*c - a*d)^3*(a + b*x)^(1/3)) + (15*d^(7/3)*((a + b*x)*(c + d*x))^(1/3)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*Sqrt[(a*d + b*(c + 2*d*x))^2])/(14*2^(1/3)*b^(2/3)*(b*c - a*d)^3*(a + b*x)^(1/3)*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)*((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))) - (15*3^(1/4)*Sqrt[2 - Sqrt[3]]*d^(7/3)*((a + b*x)*(c + d*x))^(1/3)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))*Sqrt[((b*c - a*d)^(4/3) - 2^(2/3)*b^(1/3)*d^(1/3)*(b*c - a*d)^(2/3)*((a + b*x)*(c + d*x))^(1/3) + 2*2^(1/3)*b^(2/3)*d^(2/3)*((a + b*x)*(c + d*x))^(2/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*EllipticE[ArcSin[((1 - Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))], -7 - 4*Sqrt[3]])/(28*2^(1/3)*b^(2/3)*(b*c - a*d)^(7/3)*(a + b*x)^(1/3)*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)*Sqrt[((b*c - a*d)^(2/3)*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3)))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*Sqrt[(a*d + b*(c + 2*d*x))^2]) + (5*3^(3/4)*d^(7/3)*((a + b*x)*(c + d*x))^(1/3)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))*Sqrt[((b*c - a*d)^(4/3) - 2^(2/3)*b^(1/3)*d^(1/3)*(b*c - a*d)^(2/3)*((a + b*x)*(c + d*x))^(1/3) + 2*2^(1/3)*b^(2/3)*d^(2/3)*((a + b*x)*(c + d*x))^(2/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*EllipticF[ArcSin[((1 - Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))], -7 - 4*Sqrt[3]])/(7*2^(5/6)*b^(2/3)*(b*c - a*d)^(7/3)*(a + b*x)^(1/3)*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)*Sqrt[((b*c - a*d)^(2/3)*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3)))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*Sqrt[(a*d + b*(c + 2*d*x))^2])","A",8,6,19,0.3158,1,"{51, 62, 623, 303, 218, 1877}"
1601,1,216,0,0.080201,"\int \frac{(a+b x)^{5/3}}{(c+d x)^{2/3}} \, dx","Int[(a + b*x)^(5/3)/(c + d*x)^(2/3),x]","-\frac{5 (a+b x)^{2/3} \sqrt[3]{c+d x} (b c-a d)}{6 d^2}-\frac{5 (b c-a d)^2 \log (c+d x)}{18 \sqrt[3]{b} d^{8/3}}-\frac{5 (b c-a d)^2 \log \left(\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{b} \sqrt[3]{c+d x}}-1\right)}{6 \sqrt[3]{b} d^{8/3}}-\frac{5 (b c-a d)^2 \tan ^{-1}\left(\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt{3} \sqrt[3]{b} \sqrt[3]{c+d x}}+\frac{1}{\sqrt{3}}\right)}{3 \sqrt{3} \sqrt[3]{b} d^{8/3}}+\frac{(a+b x)^{5/3} \sqrt[3]{c+d x}}{2 d}","-\frac{5 (a+b x)^{2/3} \sqrt[3]{c+d x} (b c-a d)}{6 d^2}-\frac{5 (b c-a d)^2 \log (c+d x)}{18 \sqrt[3]{b} d^{8/3}}-\frac{5 (b c-a d)^2 \log \left(\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{b} \sqrt[3]{c+d x}}-1\right)}{6 \sqrt[3]{b} d^{8/3}}-\frac{5 (b c-a d)^2 \tan ^{-1}\left(\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt{3} \sqrt[3]{b} \sqrt[3]{c+d x}}+\frac{1}{\sqrt{3}}\right)}{3 \sqrt{3} \sqrt[3]{b} d^{8/3}}+\frac{(a+b x)^{5/3} \sqrt[3]{c+d x}}{2 d}",1,"(-5*(b*c - a*d)*(a + b*x)^(2/3)*(c + d*x)^(1/3))/(6*d^2) + ((a + b*x)^(5/3)*(c + d*x)^(1/3))/(2*d) - (5*(b*c - a*d)^2*ArcTan[1/Sqrt[3] + (2*d^(1/3)*(a + b*x)^(1/3))/(Sqrt[3]*b^(1/3)*(c + d*x)^(1/3))])/(3*Sqrt[3]*b^(1/3)*d^(8/3)) - (5*(b*c - a*d)^2*Log[c + d*x])/(18*b^(1/3)*d^(8/3)) - (5*(b*c - a*d)^2*Log[-1 + (d^(1/3)*(a + b*x)^(1/3))/(b^(1/3)*(c + d*x)^(1/3))])/(6*b^(1/3)*d^(8/3))","A",3,2,19,0.1053,1,"{50, 59}"
1602,1,169,0,0.0407949,"\int \frac{(a+b x)^{2/3}}{(c+d x)^{2/3}} \, dx","Int[(a + b*x)^(2/3)/(c + d*x)^(2/3),x]","\frac{(b c-a d) \log (c+d x)}{3 \sqrt[3]{b} d^{5/3}}+\frac{(b c-a d) \log \left(\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{b} \sqrt[3]{c+d x}}-1\right)}{\sqrt[3]{b} d^{5/3}}+\frac{2 (b c-a d) \tan ^{-1}\left(\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt{3} \sqrt[3]{b} \sqrt[3]{c+d x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{b} d^{5/3}}+\frac{(a+b x)^{2/3} \sqrt[3]{c+d x}}{d}","\frac{(b c-a d) \log (c+d x)}{3 \sqrt[3]{b} d^{5/3}}+\frac{(b c-a d) \log \left(\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{b} \sqrt[3]{c+d x}}-1\right)}{\sqrt[3]{b} d^{5/3}}+\frac{2 (b c-a d) \tan ^{-1}\left(\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt{3} \sqrt[3]{b} \sqrt[3]{c+d x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{b} d^{5/3}}+\frac{(a+b x)^{2/3} \sqrt[3]{c+d x}}{d}",1,"((a + b*x)^(2/3)*(c + d*x)^(1/3))/d + (2*(b*c - a*d)*ArcTan[1/Sqrt[3] + (2*d^(1/3)*(a + b*x)^(1/3))/(Sqrt[3]*b^(1/3)*(c + d*x)^(1/3))])/(Sqrt[3]*b^(1/3)*d^(5/3)) + ((b*c - a*d)*Log[c + d*x])/(3*b^(1/3)*d^(5/3)) + ((b*c - a*d)*Log[-1 + (d^(1/3)*(a + b*x)^(1/3))/(b^(1/3)*(c + d*x)^(1/3))])/(b^(1/3)*d^(5/3))","A",2,2,19,0.1053,1,"{50, 59}"
1603,1,126,0,0.0151174,"\int \frac{1}{\sqrt[3]{a+b x} (c+d x)^{2/3}} \, dx","Int[1/((a + b*x)^(1/3)*(c + d*x)^(2/3)),x]","-\frac{3 \log \left(\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{b} \sqrt[3]{c+d x}}-1\right)}{2 \sqrt[3]{b} d^{2/3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt{3} \sqrt[3]{b} \sqrt[3]{c+d x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt[3]{b} d^{2/3}}-\frac{\log (c+d x)}{2 \sqrt[3]{b} d^{2/3}}","-\frac{3 \log \left(\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{b} \sqrt[3]{c+d x}}-1\right)}{2 \sqrt[3]{b} d^{2/3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt{3} \sqrt[3]{b} \sqrt[3]{c+d x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt[3]{b} d^{2/3}}-\frac{\log (c+d x)}{2 \sqrt[3]{b} d^{2/3}}",1,"-((Sqrt[3]*ArcTan[1/Sqrt[3] + (2*d^(1/3)*(a + b*x)^(1/3))/(Sqrt[3]*b^(1/3)*(c + d*x)^(1/3))])/(b^(1/3)*d^(2/3))) - Log[c + d*x]/(2*b^(1/3)*d^(2/3)) - (3*Log[-1 + (d^(1/3)*(a + b*x)^(1/3))/(b^(1/3)*(c + d*x)^(1/3))])/(2*b^(1/3)*d^(2/3))","A",1,1,19,0.05263,1,"{59}"
1604,1,30,0,0.0030281,"\int \frac{1}{(a+b x)^{4/3} (c+d x)^{2/3}} \, dx","Int[1/((a + b*x)^(4/3)*(c + d*x)^(2/3)),x]","-\frac{3 \sqrt[3]{c+d x}}{\sqrt[3]{a+b x} (b c-a d)}","-\frac{3 \sqrt[3]{c+d x}}{\sqrt[3]{a+b x} (b c-a d)}",1,"(-3*(c + d*x)^(1/3))/((b*c - a*d)*(a + b*x)^(1/3))","A",1,1,19,0.05263,1,"{37}"
1605,1,66,0,0.0095416,"\int \frac{1}{(a+b x)^{7/3} (c+d x)^{2/3}} \, dx","Int[1/((a + b*x)^(7/3)*(c + d*x)^(2/3)),x]","\frac{9 d \sqrt[3]{c+d x}}{4 \sqrt[3]{a+b x} (b c-a d)^2}-\frac{3 \sqrt[3]{c+d x}}{4 (a+b x)^{4/3} (b c-a d)}","\frac{9 d \sqrt[3]{c+d x}}{4 \sqrt[3]{a+b x} (b c-a d)^2}-\frac{3 \sqrt[3]{c+d x}}{4 (a+b x)^{4/3} (b c-a d)}",1,"(-3*(c + d*x)^(1/3))/(4*(b*c - a*d)*(a + b*x)^(4/3)) + (9*d*(c + d*x)^(1/3))/(4*(b*c - a*d)^2*(a + b*x)^(1/3))","A",2,2,19,0.1053,1,"{45, 37}"
1606,1,101,0,0.017218,"\int \frac{1}{(a+b x)^{10/3} (c+d x)^{2/3}} \, dx","Int[1/((a + b*x)^(10/3)*(c + d*x)^(2/3)),x]","-\frac{27 d^2 \sqrt[3]{c+d x}}{14 \sqrt[3]{a+b x} (b c-a d)^3}+\frac{9 d \sqrt[3]{c+d x}}{14 (a+b x)^{4/3} (b c-a d)^2}-\frac{3 \sqrt[3]{c+d x}}{7 (a+b x)^{7/3} (b c-a d)}","-\frac{27 d^2 \sqrt[3]{c+d x}}{14 \sqrt[3]{a+b x} (b c-a d)^3}+\frac{9 d \sqrt[3]{c+d x}}{14 (a+b x)^{4/3} (b c-a d)^2}-\frac{3 \sqrt[3]{c+d x}}{7 (a+b x)^{7/3} (b c-a d)}",1,"(-3*(c + d*x)^(1/3))/(7*(b*c - a*d)*(a + b*x)^(7/3)) + (9*d*(c + d*x)^(1/3))/(14*(b*c - a*d)^2*(a + b*x)^(4/3)) - (27*d^2*(c + d*x)^(1/3))/(14*(b*c - a*d)^3*(a + b*x)^(1/3))","A",3,2,19,0.1053,1,"{45, 37}"
1607,1,136,0,0.0295051,"\int \frac{1}{(a+b x)^{13/3} (c+d x)^{2/3}} \, dx","Int[1/((a + b*x)^(13/3)*(c + d*x)^(2/3)),x]","\frac{243 d^3 \sqrt[3]{c+d x}}{140 \sqrt[3]{a+b x} (b c-a d)^4}-\frac{81 d^2 \sqrt[3]{c+d x}}{140 (a+b x)^{4/3} (b c-a d)^3}+\frac{27 d \sqrt[3]{c+d x}}{70 (a+b x)^{7/3} (b c-a d)^2}-\frac{3 \sqrt[3]{c+d x}}{10 (a+b x)^{10/3} (b c-a d)}","\frac{243 d^3 \sqrt[3]{c+d x}}{140 \sqrt[3]{a+b x} (b c-a d)^4}-\frac{81 d^2 \sqrt[3]{c+d x}}{140 (a+b x)^{4/3} (b c-a d)^3}+\frac{27 d \sqrt[3]{c+d x}}{70 (a+b x)^{7/3} (b c-a d)^2}-\frac{3 \sqrt[3]{c+d x}}{10 (a+b x)^{10/3} (b c-a d)}",1,"(-3*(c + d*x)^(1/3))/(10*(b*c - a*d)*(a + b*x)^(10/3)) + (27*d*(c + d*x)^(1/3))/(70*(b*c - a*d)^2*(a + b*x)^(7/3)) - (81*d^2*(c + d*x)^(1/3))/(140*(b*c - a*d)^3*(a + b*x)^(4/3)) + (243*d^3*(c + d*x)^(1/3))/(140*(b*c - a*d)^4*(a + b*x)^(1/3))","A",4,2,19,0.1053,1,"{45, 37}"
1608,1,649,0,1.1178548,"\int \frac{(a+b x)^{7/3}}{(c+d x)^{2/3}} \, dx","Int[(a + b*x)^(7/3)/(c + d*x)^(2/3),x]","-\frac{7\ 3^{3/4} \sqrt{2+\sqrt{3}} (b c-a d)^3 ((a+b x) (c+d x))^{2/3} \sqrt{(a d+b c+2 b d x)^2} \left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{2/3}\right) \sqrt{\frac{2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} (b c-a d)^{2/3} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{4/3}}{\left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right)}{10\ 2^{2/3} \sqrt[3]{b} d^{10/3} (a+b x)^{2/3} (c+d x)^{2/3} (a d+b c+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{2/3}\right)}{\left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}+\frac{21 \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c-a d)^2}{20 d^3}-\frac{21 (a+b x)^{4/3} \sqrt[3]{c+d x} (b c-a d)}{40 d^2}+\frac{3 (a+b x)^{7/3} \sqrt[3]{c+d x}}{8 d}","-\frac{7\ 3^{3/4} \sqrt{2+\sqrt{3}} (b c-a d)^3 ((a+b x) (c+d x))^{2/3} \sqrt{(a d+b c+2 b d x)^2} \left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{2/3}\right) \sqrt{\frac{2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} (b c-a d)^{2/3} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{4/3}}{\left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right)}{10\ 2^{2/3} \sqrt[3]{b} d^{10/3} (a+b x)^{2/3} (c+d x)^{2/3} (a d+b c+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{2/3}\right)}{\left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}+\frac{21 \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c-a d)^2}{20 d^3}-\frac{21 (a+b x)^{4/3} \sqrt[3]{c+d x} (b c-a d)}{40 d^2}+\frac{3 (a+b x)^{7/3} \sqrt[3]{c+d x}}{8 d}",1,"(21*(b*c - a*d)^2*(a + b*x)^(1/3)*(c + d*x)^(1/3))/(20*d^3) - (21*(b*c - a*d)*(a + b*x)^(4/3)*(c + d*x)^(1/3))/(40*d^2) + (3*(a + b*x)^(7/3)*(c + d*x)^(1/3))/(8*d) - (7*3^(3/4)*Sqrt[2 + Sqrt[3]]*(b*c - a*d)^3*((a + b*x)*(c + d*x))^(2/3)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))*Sqrt[((b*c - a*d)^(4/3) - 2^(2/3)*b^(1/3)*d^(1/3)*(b*c - a*d)^(2/3)*((a + b*x)*(c + d*x))^(1/3) + 2*2^(1/3)*b^(2/3)*d^(2/3)*((a + b*x)*(c + d*x))^(2/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*EllipticF[ArcSin[((1 - Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))], -7 - 4*Sqrt[3]])/(10*2^(2/3)*b^(1/3)*d^(10/3)*(a + b*x)^(2/3)*(c + d*x)^(2/3)*(b*c + a*d + 2*b*d*x)*Sqrt[((b*c - a*d)^(2/3)*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3)))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*Sqrt[(a*d + b*(c + 2*d*x))^2])","A",6,4,19,0.2105,1,"{50, 62, 623, 218}"
1609,1,614,0,0.8174565,"\int \frac{(a+b x)^{4/3}}{(c+d x)^{2/3}} \, dx","Int[(a + b*x)^(4/3)/(c + d*x)^(2/3),x]","\frac{2 \sqrt[3]{2} 3^{3/4} \sqrt{2+\sqrt{3}} (b c-a d)^2 ((a+b x) (c+d x))^{2/3} \sqrt{(a d+b c+2 b d x)^2} \left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{2/3}\right) \sqrt{\frac{2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} (b c-a d)^{2/3} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{4/3}}{\left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right)}{5 \sqrt[3]{b} d^{7/3} (a+b x)^{2/3} (c+d x)^{2/3} (a d+b c+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{2/3}\right)}{\left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}-\frac{6 \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c-a d)}{5 d^2}+\frac{3 (a+b x)^{4/3} \sqrt[3]{c+d x}}{5 d}","\frac{2 \sqrt[3]{2} 3^{3/4} \sqrt{2+\sqrt{3}} (b c-a d)^2 ((a+b x) (c+d x))^{2/3} \sqrt{(a d+b c+2 b d x)^2} \left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{2/3}\right) \sqrt{\frac{2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} (b c-a d)^{2/3} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{4/3}}{\left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right)}{5 \sqrt[3]{b} d^{7/3} (a+b x)^{2/3} (c+d x)^{2/3} (a d+b c+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{2/3}\right)}{\left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}-\frac{6 \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c-a d)}{5 d^2}+\frac{3 (a+b x)^{4/3} \sqrt[3]{c+d x}}{5 d}",1,"(-6*(b*c - a*d)*(a + b*x)^(1/3)*(c + d*x)^(1/3))/(5*d^2) + (3*(a + b*x)^(4/3)*(c + d*x)^(1/3))/(5*d) + (2*2^(1/3)*3^(3/4)*Sqrt[2 + Sqrt[3]]*(b*c - a*d)^2*((a + b*x)*(c + d*x))^(2/3)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))*Sqrt[((b*c - a*d)^(4/3) - 2^(2/3)*b^(1/3)*d^(1/3)*(b*c - a*d)^(2/3)*((a + b*x)*(c + d*x))^(1/3) + 2*2^(1/3)*b^(2/3)*d^(2/3)*((a + b*x)*(c + d*x))^(2/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*EllipticF[ArcSin[((1 - Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))], -7 - 4*Sqrt[3]])/(5*b^(1/3)*d^(7/3)*(a + b*x)^(2/3)*(c + d*x)^(2/3)*(b*c + a*d + 2*b*d*x)*Sqrt[((b*c - a*d)^(2/3)*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3)))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*Sqrt[(a*d + b*(c + 2*d*x))^2])","A",5,4,19,0.2105,1,"{50, 62, 623, 218}"
1610,1,577,0,0.5470715,"\int \frac{\sqrt[3]{a+b x}}{(c+d x)^{2/3}} \, dx","Int[(a + b*x)^(1/3)/(c + d*x)^(2/3),x]","\frac{3 \sqrt[3]{a+b x} \sqrt[3]{c+d x}}{2 d}-\frac{3^{3/4} \sqrt{2+\sqrt{3}} (b c-a d) ((a+b x) (c+d x))^{2/3} \sqrt{(a d+b c+2 b d x)^2} \left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{2/3}\right) \sqrt{\frac{2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} (b c-a d)^{2/3} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{4/3}}{\left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right)}{2^{2/3} \sqrt[3]{b} d^{4/3} (a+b x)^{2/3} (c+d x)^{2/3} (a d+b c+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{2/3}\right)}{\left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}","\frac{3 \sqrt[3]{a+b x} \sqrt[3]{c+d x}}{2 d}-\frac{3^{3/4} \sqrt{2+\sqrt{3}} (b c-a d) ((a+b x) (c+d x))^{2/3} \sqrt{(a d+b c+2 b d x)^2} \left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{2/3}\right) \sqrt{\frac{2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} (b c-a d)^{2/3} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{4/3}}{\left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right)}{2^{2/3} \sqrt[3]{b} d^{4/3} (a+b x)^{2/3} (c+d x)^{2/3} (a d+b c+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{2/3}\right)}{\left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}",1,"(3*(a + b*x)^(1/3)*(c + d*x)^(1/3))/(2*d) - (3^(3/4)*Sqrt[2 + Sqrt[3]]*(b*c - a*d)*((a + b*x)*(c + d*x))^(2/3)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))*Sqrt[((b*c - a*d)^(4/3) - 2^(2/3)*b^(1/3)*d^(1/3)*(b*c - a*d)^(2/3)*((a + b*x)*(c + d*x))^(1/3) + 2*2^(1/3)*b^(2/3)*d^(2/3)*((a + b*x)*(c + d*x))^(2/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*EllipticF[ArcSin[((1 - Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))], -7 - 4*Sqrt[3]])/(2^(2/3)*b^(1/3)*d^(4/3)*(a + b*x)^(2/3)*(c + d*x)^(2/3)*(b*c + a*d + 2*b*d*x)*Sqrt[((b*c - a*d)^(2/3)*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3)))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*Sqrt[(a*d + b*(c + 2*d*x))^2])","A",4,4,19,0.2105,1,"{50, 62, 623, 218}"
1611,1,542,0,0.4298224,"\int \frac{1}{(a+b x)^{2/3} (c+d x)^{2/3}} \, dx","Int[1/((a + b*x)^(2/3)*(c + d*x)^(2/3)),x]","\frac{\sqrt[3]{2} 3^{3/4} \sqrt{2+\sqrt{3}} ((a+b x) (c+d x))^{2/3} \sqrt{(a d+b c+2 b d x)^2} \left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{2/3}\right) \sqrt{\frac{2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} (b c-a d)^{2/3} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{4/3}}{\left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right)}{\sqrt[3]{b} \sqrt[3]{d} (a+b x)^{2/3} (c+d x)^{2/3} (a d+b c+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{2/3}\right)}{\left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}","\frac{\sqrt[3]{2} 3^{3/4} \sqrt{2+\sqrt{3}} ((a+b x) (c+d x))^{2/3} \sqrt{(a d+b c+2 b d x)^2} \left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{2/3}\right) \sqrt{\frac{2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} (b c-a d)^{2/3} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{4/3}}{\left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right)}{\sqrt[3]{b} \sqrt[3]{d} (a+b x)^{2/3} (c+d x)^{2/3} (a d+b c+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{2/3}\right)}{\left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}",1,"(2^(1/3)*3^(3/4)*Sqrt[2 + Sqrt[3]]*((a + b*x)*(c + d*x))^(2/3)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))*Sqrt[((b*c - a*d)^(4/3) - 2^(2/3)*b^(1/3)*d^(1/3)*(b*c - a*d)^(2/3)*((a + b*x)*(c + d*x))^(1/3) + 2*2^(1/3)*b^(2/3)*d^(2/3)*((a + b*x)*(c + d*x))^(2/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*EllipticF[ArcSin[((1 - Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))], -7 - 4*Sqrt[3]])/(b^(1/3)*d^(1/3)*(a + b*x)^(2/3)*(c + d*x)^(2/3)*(b*c + a*d + 2*b*d*x)*Sqrt[((b*c - a*d)^(2/3)*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3)))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*Sqrt[(a*d + b*(c + 2*d*x))^2])","A",3,3,19,0.1579,1,"{62, 623, 218}"
1612,1,586,0,0.5497423,"\int \frac{1}{(a+b x)^{5/3} (c+d x)^{2/3}} \, dx","Int[1/((a + b*x)^(5/3)*(c + d*x)^(2/3)),x]","-\frac{3^{3/4} \sqrt{2+\sqrt{3}} d^{2/3} ((a+b x) (c+d x))^{2/3} \sqrt{(a d+b c+2 b d x)^2} \left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{2/3}\right) \sqrt{\frac{2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} (b c-a d)^{2/3} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{4/3}}{\left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right)}{2^{2/3} \sqrt[3]{b} (a+b x)^{2/3} (c+d x)^{2/3} (b c-a d) (a d+b c+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{2/3}\right)}{\left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}-\frac{3 \sqrt[3]{c+d x}}{2 (a+b x)^{2/3} (b c-a d)}","-\frac{3^{3/4} \sqrt{2+\sqrt{3}} d^{2/3} ((a+b x) (c+d x))^{2/3} \sqrt{(a d+b c+2 b d x)^2} \left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{2/3}\right) \sqrt{\frac{2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} (b c-a d)^{2/3} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{4/3}}{\left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right)}{2^{2/3} \sqrt[3]{b} (a+b x)^{2/3} (c+d x)^{2/3} (b c-a d) (a d+b c+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{2/3}\right)}{\left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}-\frac{3 \sqrt[3]{c+d x}}{2 (a+b x)^{2/3} (b c-a d)}",1,"(-3*(c + d*x)^(1/3))/(2*(b*c - a*d)*(a + b*x)^(2/3)) - (3^(3/4)*Sqrt[2 + Sqrt[3]]*d^(2/3)*((a + b*x)*(c + d*x))^(2/3)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))*Sqrt[((b*c - a*d)^(4/3) - 2^(2/3)*b^(1/3)*d^(1/3)*(b*c - a*d)^(2/3)*((a + b*x)*(c + d*x))^(1/3) + 2*2^(1/3)*b^(2/3)*d^(2/3)*((a + b*x)*(c + d*x))^(2/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*EllipticF[ArcSin[((1 - Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))], -7 - 4*Sqrt[3]])/(2^(2/3)*b^(1/3)*(b*c - a*d)*(a + b*x)^(2/3)*(c + d*x)^(2/3)*(b*c + a*d + 2*b*d*x)*Sqrt[((b*c - a*d)^(2/3)*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3)))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*Sqrt[(a*d + b*(c + 2*d*x))^2])","A",4,4,19,0.2105,1,"{51, 62, 623, 218}"
1613,1,621,0,0.8121544,"\int \frac{1}{(a+b x)^{8/3} (c+d x)^{2/3}} \, dx","Int[1/((a + b*x)^(8/3)*(c + d*x)^(2/3)),x]","\frac{2 \sqrt[3]{2} 3^{3/4} \sqrt{2+\sqrt{3}} d^{5/3} ((a+b x) (c+d x))^{2/3} \sqrt{(a d+b c+2 b d x)^2} \left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{2/3}\right) \sqrt{\frac{2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} (b c-a d)^{2/3} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{4/3}}{\left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right)}{5 \sqrt[3]{b} (a+b x)^{2/3} (c+d x)^{2/3} (b c-a d)^2 (a d+b c+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{2/3}\right)}{\left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}+\frac{6 d \sqrt[3]{c+d x}}{5 (a+b x)^{2/3} (b c-a d)^2}-\frac{3 \sqrt[3]{c+d x}}{5 (a+b x)^{5/3} (b c-a d)}","\frac{2 \sqrt[3]{2} 3^{3/4} \sqrt{2+\sqrt{3}} d^{5/3} ((a+b x) (c+d x))^{2/3} \sqrt{(a d+b c+2 b d x)^2} \left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{2/3}\right) \sqrt{\frac{2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} (b c-a d)^{2/3} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{4/3}}{\left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right)}{5 \sqrt[3]{b} (a+b x)^{2/3} (c+d x)^{2/3} (b c-a d)^2 (a d+b c+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{2/3}\right)}{\left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}+\frac{6 d \sqrt[3]{c+d x}}{5 (a+b x)^{2/3} (b c-a d)^2}-\frac{3 \sqrt[3]{c+d x}}{5 (a+b x)^{5/3} (b c-a d)}",1,"(-3*(c + d*x)^(1/3))/(5*(b*c - a*d)*(a + b*x)^(5/3)) + (6*d*(c + d*x)^(1/3))/(5*(b*c - a*d)^2*(a + b*x)^(2/3)) + (2*2^(1/3)*3^(3/4)*Sqrt[2 + Sqrt[3]]*d^(5/3)*((a + b*x)*(c + d*x))^(2/3)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))*Sqrt[((b*c - a*d)^(4/3) - 2^(2/3)*b^(1/3)*d^(1/3)*(b*c - a*d)^(2/3)*((a + b*x)*(c + d*x))^(1/3) + 2*2^(1/3)*b^(2/3)*d^(2/3)*((a + b*x)*(c + d*x))^(2/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*EllipticF[ArcSin[((1 - Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))], -7 - 4*Sqrt[3]])/(5*b^(1/3)*(b*c - a*d)^2*(a + b*x)^(2/3)*(c + d*x)^(2/3)*(b*c + a*d + 2*b*d*x)*Sqrt[((b*c - a*d)^(2/3)*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3)))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*Sqrt[(a*d + b*(c + 2*d*x))^2])","A",5,4,19,0.2105,1,"{51, 62, 623, 218}"
1614,1,656,0,1.0901461,"\int \frac{1}{(a+b x)^{11/3} (c+d x)^{2/3}} \, dx","Int[1/((a + b*x)^(11/3)*(c + d*x)^(2/3)),x]","-\frac{7\ 3^{3/4} \sqrt{2+\sqrt{3}} d^{8/3} ((a+b x) (c+d x))^{2/3} \sqrt{(a d+b c+2 b d x)^2} \left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{2/3}\right) \sqrt{\frac{2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} (b c-a d)^{2/3} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{4/3}}{\left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right)}{10\ 2^{2/3} \sqrt[3]{b} (a+b x)^{2/3} (c+d x)^{2/3} (b c-a d)^3 (a d+b c+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{2/3}\right)}{\left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}-\frac{21 d^2 \sqrt[3]{c+d x}}{20 (a+b x)^{2/3} (b c-a d)^3}+\frac{21 d \sqrt[3]{c+d x}}{40 (a+b x)^{5/3} (b c-a d)^2}-\frac{3 \sqrt[3]{c+d x}}{8 (a+b x)^{8/3} (b c-a d)}","-\frac{7\ 3^{3/4} \sqrt{2+\sqrt{3}} d^{8/3} ((a+b x) (c+d x))^{2/3} \sqrt{(a d+b c+2 b d x)^2} \left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{2/3}\right) \sqrt{\frac{2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} (b c-a d)^{2/3} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{4/3}}{\left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right)}{10\ 2^{2/3} \sqrt[3]{b} (a+b x)^{2/3} (c+d x)^{2/3} (b c-a d)^3 (a d+b c+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{2/3}\right)}{\left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}-\frac{21 d^2 \sqrt[3]{c+d x}}{20 (a+b x)^{2/3} (b c-a d)^3}+\frac{21 d \sqrt[3]{c+d x}}{40 (a+b x)^{5/3} (b c-a d)^2}-\frac{3 \sqrt[3]{c+d x}}{8 (a+b x)^{8/3} (b c-a d)}",1,"(-3*(c + d*x)^(1/3))/(8*(b*c - a*d)*(a + b*x)^(8/3)) + (21*d*(c + d*x)^(1/3))/(40*(b*c - a*d)^2*(a + b*x)^(5/3)) - (21*d^2*(c + d*x)^(1/3))/(20*(b*c - a*d)^3*(a + b*x)^(2/3)) - (7*3^(3/4)*Sqrt[2 + Sqrt[3]]*d^(8/3)*((a + b*x)*(c + d*x))^(2/3)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))*Sqrt[((b*c - a*d)^(4/3) - 2^(2/3)*b^(1/3)*d^(1/3)*(b*c - a*d)^(2/3)*((a + b*x)*(c + d*x))^(1/3) + 2*2^(1/3)*b^(2/3)*d^(2/3)*((a + b*x)*(c + d*x))^(2/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*EllipticF[ArcSin[((1 - Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))], -7 - 4*Sqrt[3]])/(10*2^(2/3)*b^(1/3)*(b*c - a*d)^3*(a + b*x)^(2/3)*(c + d*x)^(2/3)*(b*c + a*d + 2*b*d*x)*Sqrt[((b*c - a*d)^(2/3)*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3)))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*Sqrt[(a*d + b*(c + 2*d*x))^2])","A",6,4,19,0.2105,1,"{51, 62, 623, 218}"
1615,1,241,0,0.1069964,"\int \frac{(a+b x)^{7/3}}{(c+d x)^{4/3}} \, dx","Int[(a + b*x)^(7/3)/(c + d*x)^(4/3),x]","\frac{7 b (a+b x)^{4/3} (c+d x)^{2/3}}{2 d^2}-\frac{14 b \sqrt[3]{a+b x} (c+d x)^{2/3} (b c-a d)}{3 d^3}-\frac{7 \sqrt[3]{b} (b c-a d)^2 \log (a+b x)}{9 d^{10/3}}-\frac{7 \sqrt[3]{b} (b c-a d)^2 \log \left(\frac{\sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{d} \sqrt[3]{a+b x}}-1\right)}{3 d^{10/3}}-\frac{14 \sqrt[3]{b} (b c-a d)^2 \tan ^{-1}\left(\frac{2 \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt{3} \sqrt[3]{d} \sqrt[3]{a+b x}}+\frac{1}{\sqrt{3}}\right)}{3 \sqrt{3} d^{10/3}}-\frac{3 (a+b x)^{7/3}}{d \sqrt[3]{c+d x}}","\frac{7 b (a+b x)^{4/3} (c+d x)^{2/3}}{2 d^2}-\frac{14 b \sqrt[3]{a+b x} (c+d x)^{2/3} (b c-a d)}{3 d^3}-\frac{7 \sqrt[3]{b} (b c-a d)^2 \log (a+b x)}{9 d^{10/3}}-\frac{7 \sqrt[3]{b} (b c-a d)^2 \log \left(\frac{\sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{d} \sqrt[3]{a+b x}}-1\right)}{3 d^{10/3}}-\frac{14 \sqrt[3]{b} (b c-a d)^2 \tan ^{-1}\left(\frac{2 \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt{3} \sqrt[3]{d} \sqrt[3]{a+b x}}+\frac{1}{\sqrt{3}}\right)}{3 \sqrt{3} d^{10/3}}-\frac{3 (a+b x)^{7/3}}{d \sqrt[3]{c+d x}}",1,"(-3*(a + b*x)^(7/3))/(d*(c + d*x)^(1/3)) - (14*b*(b*c - a*d)*(a + b*x)^(1/3)*(c + d*x)^(2/3))/(3*d^3) + (7*b*(a + b*x)^(4/3)*(c + d*x)^(2/3))/(2*d^2) - (14*b^(1/3)*(b*c - a*d)^2*ArcTan[1/Sqrt[3] + (2*b^(1/3)*(c + d*x)^(1/3))/(Sqrt[3]*d^(1/3)*(a + b*x)^(1/3))])/(3*Sqrt[3]*d^(10/3)) - (7*b^(1/3)*(b*c - a*d)^2*Log[a + b*x])/(9*d^(10/3)) - (7*b^(1/3)*(b*c - a*d)^2*Log[-1 + (b^(1/3)*(c + d*x)^(1/3))/(d^(1/3)*(a + b*x)^(1/3))])/(3*d^(10/3))","A",4,3,19,0.1579,1,"{47, 50, 59}"
1616,1,195,0,0.0706522,"\int \frac{(a+b x)^{4/3}}{(c+d x)^{4/3}} \, dx","Int[(a + b*x)^(4/3)/(c + d*x)^(4/3),x]","\frac{4 b \sqrt[3]{a+b x} (c+d x)^{2/3}}{d^2}+\frac{2 \sqrt[3]{b} (b c-a d) \log (a+b x)}{3 d^{7/3}}+\frac{2 \sqrt[3]{b} (b c-a d) \log \left(\frac{\sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{d} \sqrt[3]{a+b x}}-1\right)}{d^{7/3}}+\frac{4 \sqrt[3]{b} (b c-a d) \tan ^{-1}\left(\frac{2 \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt{3} \sqrt[3]{d} \sqrt[3]{a+b x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3} d^{7/3}}-\frac{3 (a+b x)^{4/3}}{d \sqrt[3]{c+d x}}","\frac{4 b \sqrt[3]{a+b x} (c+d x)^{2/3}}{d^2}+\frac{2 \sqrt[3]{b} (b c-a d) \log (a+b x)}{3 d^{7/3}}+\frac{2 \sqrt[3]{b} (b c-a d) \log \left(\frac{\sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{d} \sqrt[3]{a+b x}}-1\right)}{d^{7/3}}+\frac{4 \sqrt[3]{b} (b c-a d) \tan ^{-1}\left(\frac{2 \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt{3} \sqrt[3]{d} \sqrt[3]{a+b x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3} d^{7/3}}-\frac{3 (a+b x)^{4/3}}{d \sqrt[3]{c+d x}}",1,"(-3*(a + b*x)^(4/3))/(d*(c + d*x)^(1/3)) + (4*b*(a + b*x)^(1/3)*(c + d*x)^(2/3))/d^2 + (4*b^(1/3)*(b*c - a*d)*ArcTan[1/Sqrt[3] + (2*b^(1/3)*(c + d*x)^(1/3))/(Sqrt[3]*d^(1/3)*(a + b*x)^(1/3))])/(Sqrt[3]*d^(7/3)) + (2*b^(1/3)*(b*c - a*d)*Log[a + b*x])/(3*d^(7/3)) + (2*b^(1/3)*(b*c - a*d)*Log[-1 + (b^(1/3)*(c + d*x)^(1/3))/(d^(1/3)*(a + b*x)^(1/3))])/d^(7/3)","A",3,3,19,0.1579,1,"{47, 50, 59}"
1617,1,149,0,0.0308381,"\int \frac{\sqrt[3]{a+b x}}{(c+d x)^{4/3}} \, dx","Int[(a + b*x)^(1/3)/(c + d*x)^(4/3),x]","-\frac{3 \sqrt[3]{b} \log \left(\frac{\sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{d} \sqrt[3]{a+b x}}-1\right)}{2 d^{4/3}}-\frac{\sqrt{3} \sqrt[3]{b} \tan ^{-1}\left(\frac{2 \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt{3} \sqrt[3]{d} \sqrt[3]{a+b x}}+\frac{1}{\sqrt{3}}\right)}{d^{4/3}}-\frac{3 \sqrt[3]{a+b x}}{d \sqrt[3]{c+d x}}-\frac{\sqrt[3]{b} \log (a+b x)}{2 d^{4/3}}","-\frac{3 \sqrt[3]{b} \log \left(\frac{\sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{d} \sqrt[3]{a+b x}}-1\right)}{2 d^{4/3}}-\frac{\sqrt{3} \sqrt[3]{b} \tan ^{-1}\left(\frac{2 \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt{3} \sqrt[3]{d} \sqrt[3]{a+b x}}+\frac{1}{\sqrt{3}}\right)}{d^{4/3}}-\frac{3 \sqrt[3]{a+b x}}{d \sqrt[3]{c+d x}}-\frac{\sqrt[3]{b} \log (a+b x)}{2 d^{4/3}}",1,"(-3*(a + b*x)^(1/3))/(d*(c + d*x)^(1/3)) - (Sqrt[3]*b^(1/3)*ArcTan[1/Sqrt[3] + (2*b^(1/3)*(c + d*x)^(1/3))/(Sqrt[3]*d^(1/3)*(a + b*x)^(1/3))])/d^(4/3) - (b^(1/3)*Log[a + b*x])/(2*d^(4/3)) - (3*b^(1/3)*Log[-1 + (b^(1/3)*(c + d*x)^(1/3))/(d^(1/3)*(a + b*x)^(1/3))])/(2*d^(4/3))","A",2,2,19,0.1053,1,"{47, 59}"
1618,1,30,0,0.0031594,"\int \frac{1}{(a+b x)^{2/3} (c+d x)^{4/3}} \, dx","Int[1/((a + b*x)^(2/3)*(c + d*x)^(4/3)),x]","\frac{3 \sqrt[3]{a+b x}}{\sqrt[3]{c+d x} (b c-a d)}","\frac{3 \sqrt[3]{a+b x}}{\sqrt[3]{c+d x} (b c-a d)}",1,"(3*(a + b*x)^(1/3))/((b*c - a*d)*(c + d*x)^(1/3))","A",1,1,19,0.05263,1,"{37}"
1619,1,66,0,0.0086929,"\int \frac{1}{(a+b x)^{5/3} (c+d x)^{4/3}} \, dx","Int[1/((a + b*x)^(5/3)*(c + d*x)^(4/3)),x]","-\frac{9 d \sqrt[3]{a+b x}}{2 \sqrt[3]{c+d x} (b c-a d)^2}-\frac{3}{2 (a+b x)^{2/3} \sqrt[3]{c+d x} (b c-a d)}","-\frac{9 d \sqrt[3]{a+b x}}{2 \sqrt[3]{c+d x} (b c-a d)^2}-\frac{3}{2 (a+b x)^{2/3} \sqrt[3]{c+d x} (b c-a d)}",1,"-3/(2*(b*c - a*d)*(a + b*x)^(2/3)*(c + d*x)^(1/3)) - (9*d*(a + b*x)^(1/3))/(2*(b*c - a*d)^2*(c + d*x)^(1/3))","A",2,2,19,0.1053,1,"{45, 37}"
1620,1,101,0,0.0180775,"\int \frac{1}{(a+b x)^{8/3} (c+d x)^{4/3}} \, dx","Int[1/((a + b*x)^(8/3)*(c + d*x)^(4/3)),x]","\frac{27 d^2 \sqrt[3]{a+b x}}{5 \sqrt[3]{c+d x} (b c-a d)^3}+\frac{9 d}{5 (a+b x)^{2/3} \sqrt[3]{c+d x} (b c-a d)^2}-\frac{3}{5 (a+b x)^{5/3} \sqrt[3]{c+d x} (b c-a d)}","\frac{27 d^2 \sqrt[3]{a+b x}}{5 \sqrt[3]{c+d x} (b c-a d)^3}+\frac{9 d}{5 (a+b x)^{2/3} \sqrt[3]{c+d x} (b c-a d)^2}-\frac{3}{5 (a+b x)^{5/3} \sqrt[3]{c+d x} (b c-a d)}",1,"-3/(5*(b*c - a*d)*(a + b*x)^(5/3)*(c + d*x)^(1/3)) + (9*d)/(5*(b*c - a*d)^2*(a + b*x)^(2/3)*(c + d*x)^(1/3)) + (27*d^2*(a + b*x)^(1/3))/(5*(b*c - a*d)^3*(c + d*x)^(1/3))","A",3,2,19,0.1053,1,"{45, 37}"
1621,1,136,0,0.0296401,"\int \frac{1}{(a+b x)^{11/3} (c+d x)^{4/3}} \, dx","Int[1/((a + b*x)^(11/3)*(c + d*x)^(4/3)),x]","-\frac{243 d^3 \sqrt[3]{a+b x}}{40 \sqrt[3]{c+d x} (b c-a d)^4}-\frac{81 d^2}{40 (a+b x)^{2/3} \sqrt[3]{c+d x} (b c-a d)^3}+\frac{27 d}{40 (a+b x)^{5/3} \sqrt[3]{c+d x} (b c-a d)^2}-\frac{3}{8 (a+b x)^{8/3} \sqrt[3]{c+d x} (b c-a d)}","-\frac{243 d^3 \sqrt[3]{a+b x}}{40 \sqrt[3]{c+d x} (b c-a d)^4}-\frac{81 d^2}{40 (a+b x)^{2/3} \sqrt[3]{c+d x} (b c-a d)^3}+\frac{27 d}{40 (a+b x)^{5/3} \sqrt[3]{c+d x} (b c-a d)^2}-\frac{3}{8 (a+b x)^{8/3} \sqrt[3]{c+d x} (b c-a d)}",1,"-3/(8*(b*c - a*d)*(a + b*x)^(8/3)*(c + d*x)^(1/3)) + (27*d)/(40*(b*c - a*d)^2*(a + b*x)^(5/3)*(c + d*x)^(1/3)) - (81*d^2)/(40*(b*c - a*d)^3*(a + b*x)^(2/3)*(c + d*x)^(1/3)) - (243*d^3*(a + b*x)^(1/3))/(40*(b*c - a*d)^4*(c + d*x)^(1/3))","A",4,2,19,0.1053,1,"{45, 37}"
1622,1,1355,0,2.5106439,"\int \frac{(a+b x)^{8/3}}{(c+d x)^{4/3}} \, dx","Int[(a + b*x)^(8/3)/(c + d*x)^(4/3),x]","-\frac{15\ 2^{2/3} \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{b} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right) (b c-a d)^{8/3}}{7 d^{11/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}+\frac{20 \sqrt[6]{2} 3^{3/4} \sqrt[3]{b} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right) (b c-a d)^{8/3}}{7 d^{11/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}+\frac{30\ 2^{2/3} \sqrt[3]{b} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \sqrt{(a d+b (c+2 d x))^2} (b c-a d)^2}{7 d^{11/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}-\frac{30 b (a+b x)^{2/3} (c+d x)^{2/3} (b c-a d)}{7 d^3}+\frac{24 b (a+b x)^{5/3} (c+d x)^{2/3}}{7 d^2}-\frac{3 (a+b x)^{8/3}}{d \sqrt[3]{c+d x}}","-\frac{15\ 2^{2/3} \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{b} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right) (b c-a d)^{8/3}}{7 d^{11/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}+\frac{20 \sqrt[6]{2} 3^{3/4} \sqrt[3]{b} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right) (b c-a d)^{8/3}}{7 d^{11/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}+\frac{30\ 2^{2/3} \sqrt[3]{b} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \sqrt{(a d+b (c+2 d x))^2} (b c-a d)^2}{7 d^{11/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}-\frac{30 b (a+b x)^{2/3} (c+d x)^{2/3} (b c-a d)}{7 d^3}+\frac{24 b (a+b x)^{5/3} (c+d x)^{2/3}}{7 d^2}-\frac{3 (a+b x)^{8/3}}{d \sqrt[3]{c+d x}}",1,"(-3*(a + b*x)^(8/3))/(d*(c + d*x)^(1/3)) - (30*b*(b*c - a*d)*(a + b*x)^(2/3)*(c + d*x)^(2/3))/(7*d^3) + (24*b*(a + b*x)^(5/3)*(c + d*x)^(2/3))/(7*d^2) + (30*2^(2/3)*b^(1/3)*(b*c - a*d)^2*((a + b*x)*(c + d*x))^(1/3)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*Sqrt[(a*d + b*(c + 2*d*x))^2])/(7*d^(11/3)*(a + b*x)^(1/3)*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)*((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))) - (15*2^(2/3)*3^(1/4)*Sqrt[2 - Sqrt[3]]*b^(1/3)*(b*c - a*d)^(8/3)*((a + b*x)*(c + d*x))^(1/3)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))*Sqrt[((b*c - a*d)^(4/3) - 2^(2/3)*b^(1/3)*d^(1/3)*(b*c - a*d)^(2/3)*((a + b*x)*(c + d*x))^(1/3) + 2*2^(1/3)*b^(2/3)*d^(2/3)*((a + b*x)*(c + d*x))^(2/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*EllipticE[ArcSin[((1 - Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))], -7 - 4*Sqrt[3]])/(7*d^(11/3)*(a + b*x)^(1/3)*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)*Sqrt[((b*c - a*d)^(2/3)*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3)))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*Sqrt[(a*d + b*(c + 2*d*x))^2]) + (20*2^(1/6)*3^(3/4)*b^(1/3)*(b*c - a*d)^(8/3)*((a + b*x)*(c + d*x))^(1/3)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))*Sqrt[((b*c - a*d)^(4/3) - 2^(2/3)*b^(1/3)*d^(1/3)*(b*c - a*d)^(2/3)*((a + b*x)*(c + d*x))^(1/3) + 2*2^(1/3)*b^(2/3)*d^(2/3)*((a + b*x)*(c + d*x))^(2/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*EllipticF[ArcSin[((1 - Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))], -7 - 4*Sqrt[3]])/(7*d^(11/3)*(a + b*x)^(1/3)*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)*Sqrt[((b*c - a*d)^(2/3)*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3)))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*Sqrt[(a*d + b*(c + 2*d*x))^2])","A",8,7,19,0.3684,1,"{47, 50, 62, 623, 303, 218, 1877}"
1623,1,1317,0,1.9980537,"\int \frac{(a+b x)^{5/3}}{(c+d x)^{4/3}} \, dx","Int[(a + b*x)^(5/3)/(c + d*x)^(4/3),x]","\frac{15 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{b} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right) (b c-a d)^{5/3}}{4 \sqrt[3]{2} d^{8/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}-\frac{5\ 3^{3/4} \sqrt[3]{b} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right) (b c-a d)^{5/3}}{2^{5/6} d^{8/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}-\frac{15 \sqrt[3]{b} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \sqrt{(a d+b (c+2 d x))^2} (b c-a d)}{2 \sqrt[3]{2} d^{8/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}+\frac{15 b (a+b x)^{2/3} (c+d x)^{2/3}}{4 d^2}-\frac{3 (a+b x)^{5/3}}{d \sqrt[3]{c+d x}}","\frac{15 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{b} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right) (b c-a d)^{5/3}}{4 \sqrt[3]{2} d^{8/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}-\frac{5\ 3^{3/4} \sqrt[3]{b} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right) (b c-a d)^{5/3}}{2^{5/6} d^{8/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}-\frac{15 \sqrt[3]{b} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \sqrt{(a d+b (c+2 d x))^2} (b c-a d)}{2 \sqrt[3]{2} d^{8/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}+\frac{15 b (a+b x)^{2/3} (c+d x)^{2/3}}{4 d^2}-\frac{3 (a+b x)^{5/3}}{d \sqrt[3]{c+d x}}",1,"(-3*(a + b*x)^(5/3))/(d*(c + d*x)^(1/3)) + (15*b*(a + b*x)^(2/3)*(c + d*x)^(2/3))/(4*d^2) - (15*b^(1/3)*(b*c - a*d)*((a + b*x)*(c + d*x))^(1/3)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*Sqrt[(a*d + b*(c + 2*d*x))^2])/(2*2^(1/3)*d^(8/3)*(a + b*x)^(1/3)*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)*((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))) + (15*3^(1/4)*Sqrt[2 - Sqrt[3]]*b^(1/3)*(b*c - a*d)^(5/3)*((a + b*x)*(c + d*x))^(1/3)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))*Sqrt[((b*c - a*d)^(4/3) - 2^(2/3)*b^(1/3)*d^(1/3)*(b*c - a*d)^(2/3)*((a + b*x)*(c + d*x))^(1/3) + 2*2^(1/3)*b^(2/3)*d^(2/3)*((a + b*x)*(c + d*x))^(2/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*EllipticE[ArcSin[((1 - Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))], -7 - 4*Sqrt[3]])/(4*2^(1/3)*d^(8/3)*(a + b*x)^(1/3)*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)*Sqrt[((b*c - a*d)^(2/3)*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3)))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*Sqrt[(a*d + b*(c + 2*d*x))^2]) - (5*3^(3/4)*b^(1/3)*(b*c - a*d)^(5/3)*((a + b*x)*(c + d*x))^(1/3)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))*Sqrt[((b*c - a*d)^(4/3) - 2^(2/3)*b^(1/3)*d^(1/3)*(b*c - a*d)^(2/3)*((a + b*x)*(c + d*x))^(1/3) + 2*2^(1/3)*b^(2/3)*d^(2/3)*((a + b*x)*(c + d*x))^(2/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*EllipticF[ArcSin[((1 - Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))], -7 - 4*Sqrt[3]])/(2^(5/6)*d^(8/3)*(a + b*x)^(1/3)*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)*Sqrt[((b*c - a*d)^(2/3)*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3)))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*Sqrt[(a*d + b*(c + 2*d*x))^2])","A",7,7,19,0.3684,1,"{47, 50, 62, 623, 303, 218, 1877}"
1624,1,1279,0,1.5412191,"\int \frac{(a+b x)^{2/3}}{(c+d x)^{4/3}} \, dx","Int[(a + b*x)^(2/3)/(c + d*x)^(4/3),x]","-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{b} (b c-a d)^{2/3} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right)}{\sqrt[3]{2} d^{5/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}+\frac{2 \sqrt[6]{2} 3^{3/4} \sqrt[3]{b} (b c-a d)^{2/3} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right)}{d^{5/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}+\frac{3\ 2^{2/3} \sqrt[3]{b} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \sqrt{(a d+b (c+2 d x))^2}}{d^{5/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}-\frac{3 (a+b x)^{2/3}}{d \sqrt[3]{c+d x}}","-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{b} (b c-a d)^{2/3} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right)}{\sqrt[3]{2} d^{5/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}+\frac{2 \sqrt[6]{2} 3^{3/4} \sqrt[3]{b} (b c-a d)^{2/3} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right)}{d^{5/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}+\frac{3\ 2^{2/3} \sqrt[3]{b} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \sqrt{(a d+b (c+2 d x))^2}}{d^{5/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}-\frac{3 (a+b x)^{2/3}}{d \sqrt[3]{c+d x}}",1,"(-3*(a + b*x)^(2/3))/(d*(c + d*x)^(1/3)) + (3*2^(2/3)*b^(1/3)*((a + b*x)*(c + d*x))^(1/3)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*Sqrt[(a*d + b*(c + 2*d*x))^2])/(d^(5/3)*(a + b*x)^(1/3)*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)*((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))) - (3*3^(1/4)*Sqrt[2 - Sqrt[3]]*b^(1/3)*(b*c - a*d)^(2/3)*((a + b*x)*(c + d*x))^(1/3)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))*Sqrt[((b*c - a*d)^(4/3) - 2^(2/3)*b^(1/3)*d^(1/3)*(b*c - a*d)^(2/3)*((a + b*x)*(c + d*x))^(1/3) + 2*2^(1/3)*b^(2/3)*d^(2/3)*((a + b*x)*(c + d*x))^(2/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*EllipticE[ArcSin[((1 - Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))], -7 - 4*Sqrt[3]])/(2^(1/3)*d^(5/3)*(a + b*x)^(1/3)*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)*Sqrt[((b*c - a*d)^(2/3)*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3)))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*Sqrt[(a*d + b*(c + 2*d*x))^2]) + (2*2^(1/6)*3^(3/4)*b^(1/3)*(b*c - a*d)^(2/3)*((a + b*x)*(c + d*x))^(1/3)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))*Sqrt[((b*c - a*d)^(4/3) - 2^(2/3)*b^(1/3)*d^(1/3)*(b*c - a*d)^(2/3)*((a + b*x)*(c + d*x))^(1/3) + 2*2^(1/3)*b^(2/3)*d^(2/3)*((a + b*x)*(c + d*x))^(2/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*EllipticF[ArcSin[((1 - Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))], -7 - 4*Sqrt[3]])/(d^(5/3)*(a + b*x)^(1/3)*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)*Sqrt[((b*c - a*d)^(2/3)*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3)))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*Sqrt[(a*d + b*(c + 2*d*x))^2])","A",6,6,19,0.3158,1,"{47, 62, 623, 303, 218, 1877}"
1625,1,1298,0,1.5236476,"\int \frac{1}{\sqrt[3]{a+b x} (c+d x)^{4/3}} \, dx","Int[1/((a + b*x)^(1/3)*(c + d*x)^(4/3)),x]","\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{b} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right)}{2 \sqrt[3]{2} d^{2/3} \sqrt[3]{b c-a d} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}-\frac{\sqrt[6]{2} 3^{3/4} \sqrt[3]{b} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right)}{d^{2/3} \sqrt[3]{b c-a d} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}-\frac{3 \sqrt[3]{b} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \sqrt{(a d+b (c+2 d x))^2}}{\sqrt[3]{2} d^{2/3} (b c-a d) \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}+\frac{3 (a+b x)^{2/3}}{(b c-a d) \sqrt[3]{c+d x}}","\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{b} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right)}{2 \sqrt[3]{2} d^{2/3} \sqrt[3]{b c-a d} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}-\frac{\sqrt[6]{2} 3^{3/4} \sqrt[3]{b} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right)}{d^{2/3} \sqrt[3]{b c-a d} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}-\frac{3 \sqrt[3]{b} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \sqrt{(a d+b (c+2 d x))^2}}{\sqrt[3]{2} d^{2/3} (b c-a d) \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}+\frac{3 (a+b x)^{2/3}}{(b c-a d) \sqrt[3]{c+d x}}",1,"(3*(a + b*x)^(2/3))/((b*c - a*d)*(c + d*x)^(1/3)) - (3*b^(1/3)*((a + b*x)*(c + d*x))^(1/3)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*Sqrt[(a*d + b*(c + 2*d*x))^2])/(2^(1/3)*d^(2/3)*(b*c - a*d)*(a + b*x)^(1/3)*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)*((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))) + (3*3^(1/4)*Sqrt[2 - Sqrt[3]]*b^(1/3)*((a + b*x)*(c + d*x))^(1/3)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))*Sqrt[((b*c - a*d)^(4/3) - 2^(2/3)*b^(1/3)*d^(1/3)*(b*c - a*d)^(2/3)*((a + b*x)*(c + d*x))^(1/3) + 2*2^(1/3)*b^(2/3)*d^(2/3)*((a + b*x)*(c + d*x))^(2/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*EllipticE[ArcSin[((1 - Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))], -7 - 4*Sqrt[3]])/(2*2^(1/3)*d^(2/3)*(b*c - a*d)^(1/3)*(a + b*x)^(1/3)*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)*Sqrt[((b*c - a*d)^(2/3)*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3)))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*Sqrt[(a*d + b*(c + 2*d*x))^2]) - (2^(1/6)*3^(3/4)*b^(1/3)*((a + b*x)*(c + d*x))^(1/3)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))*Sqrt[((b*c - a*d)^(4/3) - 2^(2/3)*b^(1/3)*d^(1/3)*(b*c - a*d)^(2/3)*((a + b*x)*(c + d*x))^(1/3) + 2*2^(1/3)*b^(2/3)*d^(2/3)*((a + b*x)*(c + d*x))^(2/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*EllipticF[ArcSin[((1 - Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))], -7 - 4*Sqrt[3]])/(d^(2/3)*(b*c - a*d)^(1/3)*(a + b*x)^(1/3)*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)*Sqrt[((b*c - a*d)^(2/3)*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3)))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*Sqrt[(a*d + b*(c + 2*d*x))^2])","A",6,6,19,0.3158,1,"{51, 62, 623, 303, 218, 1877}"
1626,1,1327,0,1.9584581,"\int \frac{1}{(a+b x)^{4/3} (c+d x)^{4/3}} \, dx","Int[1/((a + b*x)^(4/3)*(c + d*x)^(4/3)),x]","-\frac{6 (a+b x)^{2/3} d}{(b c-a d)^2 \sqrt[3]{c+d x}}-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{b} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right) \sqrt[3]{d}}{\sqrt[3]{2} (b c-a d)^{4/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}+\frac{2 \sqrt[6]{2} 3^{3/4} \sqrt[3]{b} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right) \sqrt[3]{d}}{(b c-a d)^{4/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}+\frac{3\ 2^{2/3} \sqrt[3]{b} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \sqrt{(a d+b (c+2 d x))^2} \sqrt[3]{d}}{(b c-a d)^2 \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}-\frac{3}{(b c-a d) \sqrt[3]{a+b x} \sqrt[3]{c+d x}}","-\frac{6 (a+b x)^{2/3} d}{(b c-a d)^2 \sqrt[3]{c+d x}}-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{b} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right) \sqrt[3]{d}}{\sqrt[3]{2} (b c-a d)^{4/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}+\frac{2 \sqrt[6]{2} 3^{3/4} \sqrt[3]{b} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right) \sqrt[3]{d}}{(b c-a d)^{4/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}+\frac{3\ 2^{2/3} \sqrt[3]{b} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \sqrt{(a d+b (c+2 d x))^2} \sqrt[3]{d}}{(b c-a d)^2 \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}-\frac{3}{(b c-a d) \sqrt[3]{a+b x} \sqrt[3]{c+d x}}",1,"-3/((b*c - a*d)*(a + b*x)^(1/3)*(c + d*x)^(1/3)) - (6*d*(a + b*x)^(2/3))/((b*c - a*d)^2*(c + d*x)^(1/3)) + (3*2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*Sqrt[(a*d + b*(c + 2*d*x))^2])/((b*c - a*d)^2*(a + b*x)^(1/3)*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)*((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))) - (3*3^(1/4)*Sqrt[2 - Sqrt[3]]*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))*Sqrt[((b*c - a*d)^(4/3) - 2^(2/3)*b^(1/3)*d^(1/3)*(b*c - a*d)^(2/3)*((a + b*x)*(c + d*x))^(1/3) + 2*2^(1/3)*b^(2/3)*d^(2/3)*((a + b*x)*(c + d*x))^(2/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*EllipticE[ArcSin[((1 - Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))], -7 - 4*Sqrt[3]])/(2^(1/3)*(b*c - a*d)^(4/3)*(a + b*x)^(1/3)*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)*Sqrt[((b*c - a*d)^(2/3)*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3)))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*Sqrt[(a*d + b*(c + 2*d*x))^2]) + (2*2^(1/6)*3^(3/4)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))*Sqrt[((b*c - a*d)^(4/3) - 2^(2/3)*b^(1/3)*d^(1/3)*(b*c - a*d)^(2/3)*((a + b*x)*(c + d*x))^(1/3) + 2*2^(1/3)*b^(2/3)*d^(2/3)*((a + b*x)*(c + d*x))^(2/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*EllipticF[ArcSin[((1 - Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))], -7 - 4*Sqrt[3]])/((b*c - a*d)^(4/3)*(a + b*x)^(1/3)*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)*Sqrt[((b*c - a*d)^(2/3)*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3)))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*Sqrt[(a*d + b*(c + 2*d*x))^2])","A",7,6,19,0.3158,1,"{51, 62, 623, 303, 218, 1877}"
1627,1,1370,0,2.4179631,"\int \frac{1}{(a+b x)^{7/3} (c+d x)^{4/3}} \, dx","Int[1/((a + b*x)^(7/3)*(c + d*x)^(4/3)),x]","\frac{15 (a+b x)^{2/3} d^2}{2 (b c-a d)^3 \sqrt[3]{c+d x}}+\frac{15 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{b} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right) d^{4/3}}{4 \sqrt[3]{2} (b c-a d)^{7/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}-\frac{5\ 3^{3/4} \sqrt[3]{b} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right) d^{4/3}}{2^{5/6} (b c-a d)^{7/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}-\frac{15 \sqrt[3]{b} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \sqrt{(a d+b (c+2 d x))^2} d^{4/3}}{2 \sqrt[3]{2} (b c-a d)^3 \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}+\frac{15 d}{4 (b c-a d)^2 \sqrt[3]{a+b x} \sqrt[3]{c+d x}}-\frac{3}{4 (b c-a d) (a+b x)^{4/3} \sqrt[3]{c+d x}}","\frac{15 (a+b x)^{2/3} d^2}{2 (b c-a d)^3 \sqrt[3]{c+d x}}+\frac{15 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{b} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right) d^{4/3}}{4 \sqrt[3]{2} (b c-a d)^{7/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}-\frac{5\ 3^{3/4} \sqrt[3]{b} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right) d^{4/3}}{2^{5/6} (b c-a d)^{7/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}-\frac{15 \sqrt[3]{b} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \sqrt{(a d+b (c+2 d x))^2} d^{4/3}}{2 \sqrt[3]{2} (b c-a d)^3 \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}+\frac{15 d}{4 (b c-a d)^2 \sqrt[3]{a+b x} \sqrt[3]{c+d x}}-\frac{3}{4 (b c-a d) (a+b x)^{4/3} \sqrt[3]{c+d x}}",1,"-3/(4*(b*c - a*d)*(a + b*x)^(4/3)*(c + d*x)^(1/3)) + (15*d)/(4*(b*c - a*d)^2*(a + b*x)^(1/3)*(c + d*x)^(1/3)) + (15*d^2*(a + b*x)^(2/3))/(2*(b*c - a*d)^3*(c + d*x)^(1/3)) - (15*b^(1/3)*d^(4/3)*((a + b*x)*(c + d*x))^(1/3)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*Sqrt[(a*d + b*(c + 2*d*x))^2])/(2*2^(1/3)*(b*c - a*d)^3*(a + b*x)^(1/3)*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)*((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))) + (15*3^(1/4)*Sqrt[2 - Sqrt[3]]*b^(1/3)*d^(4/3)*((a + b*x)*(c + d*x))^(1/3)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))*Sqrt[((b*c - a*d)^(4/3) - 2^(2/3)*b^(1/3)*d^(1/3)*(b*c - a*d)^(2/3)*((a + b*x)*(c + d*x))^(1/3) + 2*2^(1/3)*b^(2/3)*d^(2/3)*((a + b*x)*(c + d*x))^(2/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*EllipticE[ArcSin[((1 - Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))], -7 - 4*Sqrt[3]])/(4*2^(1/3)*(b*c - a*d)^(7/3)*(a + b*x)^(1/3)*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)*Sqrt[((b*c - a*d)^(2/3)*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3)))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*Sqrt[(a*d + b*(c + 2*d*x))^2]) - (5*3^(3/4)*b^(1/3)*d^(4/3)*((a + b*x)*(c + d*x))^(1/3)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))*Sqrt[((b*c - a*d)^(4/3) - 2^(2/3)*b^(1/3)*d^(1/3)*(b*c - a*d)^(2/3)*((a + b*x)*(c + d*x))^(1/3) + 2*2^(1/3)*b^(2/3)*d^(2/3)*((a + b*x)*(c + d*x))^(2/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*EllipticF[ArcSin[((1 - Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))], -7 - 4*Sqrt[3]])/(2^(5/6)*(b*c - a*d)^(7/3)*(a + b*x)^(1/3)*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)*Sqrt[((b*c - a*d)^(2/3)*((b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3)))/((1 + Sqrt[3])*(b*c - a*d)^(2/3) + 2^(2/3)*b^(1/3)*d^(1/3)*((a + b*x)*(c + d*x))^(1/3))^2]*Sqrt[(a*d + b*(c + 2*d*x))^2])","A",8,6,19,0.3158,1,"{51, 62, 623, 303, 218, 1877}"
1628,1,77,0,0.0138222,"\int \frac{\sqrt[3]{-1+x}}{\sqrt[3]{1+x}} \, dx","Int[(-1 + x)^(1/3)/(1 + x)^(1/3),x]","\sqrt[3]{x-1} (x+1)^{2/3}+\frac{1}{3} \log (x-1)+\log \left(\frac{\sqrt[3]{x+1}}{\sqrt[3]{x-1}}-1\right)+\frac{2 \tan ^{-1}\left(\frac{2 \sqrt[3]{x+1}}{\sqrt{3} \sqrt[3]{x-1}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3}}","\sqrt[3]{x-1} (x+1)^{2/3}+\frac{1}{3} \log (x-1)+\log \left(\frac{\sqrt[3]{x+1}}{\sqrt[3]{x-1}}-1\right)+\frac{2 \tan ^{-1}\left(\frac{2 \sqrt[3]{x+1}}{\sqrt{3} \sqrt[3]{x-1}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3}}",1,"(-1 + x)^(1/3)*(1 + x)^(2/3) + (2*ArcTan[1/Sqrt[3] + (2*(1 + x)^(1/3))/(Sqrt[3]*(-1 + x)^(1/3))])/Sqrt[3] + Log[-1 + x]/3 + Log[-1 + (1 + x)^(1/3)/(-1 + x)^(1/3)]","A",2,2,15,0.1333,1,"{50, 59}"
1629,1,185,0,0.2124648,"\int (a+b x)^{3/2} \sqrt[4]{c+d x} \, dx","Int[(a + b*x)^(3/2)*(c + d*x)^(1/4),x]","\frac{16 (b c-a d)^{13/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{77 b^{5/4} d^3 \sqrt{a+b x}}-\frac{8 \sqrt{a+b x} \sqrt[4]{c+d x} (b c-a d)^2}{77 b d^2}+\frac{4 (a+b x)^{3/2} \sqrt[4]{c+d x} (b c-a d)}{77 b d}+\frac{4 (a+b x)^{5/2} \sqrt[4]{c+d x}}{11 b}","\frac{16 (b c-a d)^{13/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{77 b^{5/4} d^3 \sqrt{a+b x}}-\frac{8 \sqrt{a+b x} \sqrt[4]{c+d x} (b c-a d)^2}{77 b d^2}+\frac{4 (a+b x)^{3/2} \sqrt[4]{c+d x} (b c-a d)}{77 b d}+\frac{4 (a+b x)^{5/2} \sqrt[4]{c+d x}}{11 b}",1,"(-8*(b*c - a*d)^2*Sqrt[a + b*x]*(c + d*x)^(1/4))/(77*b*d^2) + (4*(b*c - a*d)*(a + b*x)^(3/2)*(c + d*x)^(1/4))/(77*b*d) + (4*(a + b*x)^(5/2)*(c + d*x)^(1/4))/(11*b) + (16*(b*c - a*d)^(13/4)*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticF[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(77*b^(5/4)*d^3*Sqrt[a + b*x])","A",6,4,19,0.2105,1,"{50, 63, 224, 221}"
1630,1,147,0,0.0888444,"\int \sqrt{a+b x} \sqrt[4]{c+d x} \, dx","Int[Sqrt[a + b*x]*(c + d*x)^(1/4),x]","-\frac{8 (b c-a d)^{9/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{21 b^{5/4} d^2 \sqrt{a+b x}}+\frac{4 \sqrt{a+b x} \sqrt[4]{c+d x} (b c-a d)}{21 b d}+\frac{4 (a+b x)^{3/2} \sqrt[4]{c+d x}}{7 b}","-\frac{8 (b c-a d)^{9/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{21 b^{5/4} d^2 \sqrt{a+b x}}+\frac{4 \sqrt{a+b x} \sqrt[4]{c+d x} (b c-a d)}{21 b d}+\frac{4 (a+b x)^{3/2} \sqrt[4]{c+d x}}{7 b}",1,"(4*(b*c - a*d)*Sqrt[a + b*x]*(c + d*x)^(1/4))/(21*b*d) + (4*(a + b*x)^(3/2)*(c + d*x)^(1/4))/(7*b) - (8*(b*c - a*d)^(9/4)*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticF[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(21*b^(5/4)*d^2*Sqrt[a + b*x])","A",5,4,19,0.2105,1,"{50, 63, 224, 221}"
1631,1,111,0,0.0673849,"\int \frac{\sqrt[4]{c+d x}}{\sqrt{a+b x}} \, dx","Int[(c + d*x)^(1/4)/Sqrt[a + b*x],x]","\frac{4 (b c-a d)^{5/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{3 b^{5/4} d \sqrt{a+b x}}+\frac{4 \sqrt{a+b x} \sqrt[4]{c+d x}}{3 b}","\frac{4 (b c-a d)^{5/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{3 b^{5/4} d \sqrt{a+b x}}+\frac{4 \sqrt{a+b x} \sqrt[4]{c+d x}}{3 b}",1,"(4*Sqrt[a + b*x]*(c + d*x)^(1/4))/(3*b) + (4*(b*c - a*d)^(5/4)*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticF[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(3*b^(5/4)*d*Sqrt[a + b*x])","A",4,4,19,0.2105,1,"{50, 63, 224, 221}"
1632,1,104,0,0.0642513,"\int \frac{\sqrt[4]{c+d x}}{(a+b x)^{3/2}} \, dx","Int[(c + d*x)^(1/4)/(a + b*x)^(3/2),x]","\frac{2 \sqrt[4]{b c-a d} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{b^{5/4} \sqrt{a+b x}}-\frac{2 \sqrt[4]{c+d x}}{b \sqrt{a+b x}}","\frac{2 \sqrt[4]{b c-a d} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{b^{5/4} \sqrt{a+b x}}-\frac{2 \sqrt[4]{c+d x}}{b \sqrt{a+b x}}",1,"(-2*(c + d*x)^(1/4))/(b*Sqrt[a + b*x]) + (2*(b*c - a*d)^(1/4)*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticF[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(b^(5/4)*Sqrt[a + b*x])","A",4,4,19,0.2105,1,"{47, 63, 224, 221}"
1633,1,145,0,0.0942337,"\int \frac{\sqrt[4]{c+d x}}{(a+b x)^{5/2}} \, dx","Int[(c + d*x)^(1/4)/(a + b*x)^(5/2),x]","-\frac{d \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{3 b^{5/4} \sqrt{a+b x} (b c-a d)^{3/4}}-\frac{d \sqrt[4]{c+d x}}{3 b \sqrt{a+b x} (b c-a d)}-\frac{2 \sqrt[4]{c+d x}}{3 b (a+b x)^{3/2}}","-\frac{d \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{3 b^{5/4} \sqrt{a+b x} (b c-a d)^{3/4}}-\frac{d \sqrt[4]{c+d x}}{3 b \sqrt{a+b x} (b c-a d)}-\frac{2 \sqrt[4]{c+d x}}{3 b (a+b x)^{3/2}}",1,"(-2*(c + d*x)^(1/4))/(3*b*(a + b*x)^(3/2)) - (d*(c + d*x)^(1/4))/(3*b*(b*c - a*d)*Sqrt[a + b*x]) - (d*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticF[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(3*b^(5/4)*(b*c - a*d)^(3/4)*Sqrt[a + b*x])","A",5,5,19,0.2632,1,"{47, 51, 63, 224, 221}"
1634,1,185,0,0.1283417,"\int \frac{\sqrt[4]{c+d x}}{(a+b x)^{7/2}} \, dx","Int[(c + d*x)^(1/4)/(a + b*x)^(7/2),x]","\frac{d^2 \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{6 b^{5/4} \sqrt{a+b x} (b c-a d)^{7/4}}+\frac{d^2 \sqrt[4]{c+d x}}{6 b \sqrt{a+b x} (b c-a d)^2}-\frac{d \sqrt[4]{c+d x}}{15 b (a+b x)^{3/2} (b c-a d)}-\frac{2 \sqrt[4]{c+d x}}{5 b (a+b x)^{5/2}}","\frac{d^2 \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{6 b^{5/4} \sqrt{a+b x} (b c-a d)^{7/4}}+\frac{d^2 \sqrt[4]{c+d x}}{6 b \sqrt{a+b x} (b c-a d)^2}-\frac{d \sqrt[4]{c+d x}}{15 b (a+b x)^{3/2} (b c-a d)}-\frac{2 \sqrt[4]{c+d x}}{5 b (a+b x)^{5/2}}",1,"(-2*(c + d*x)^(1/4))/(5*b*(a + b*x)^(5/2)) - (d*(c + d*x)^(1/4))/(15*b*(b*c - a*d)*(a + b*x)^(3/2)) + (d^2*(c + d*x)^(1/4))/(6*b*(b*c - a*d)^2*Sqrt[a + b*x]) + (d^2*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticF[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(6*b^(5/4)*(b*c - a*d)^(7/4)*Sqrt[a + b*x])","A",6,5,19,0.2632,1,"{47, 51, 63, 224, 221}"
1635,1,270,0,0.3647432,"\int (a+b x)^{3/2} (c+d x)^{3/4} \, dx","Int[(a + b*x)^(3/2)*(c + d*x)^(3/4),x]","-\frac{16 (b c-a d)^{15/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{65 b^{7/4} d^3 \sqrt{a+b x}}+\frac{16 (b c-a d)^{15/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{65 b^{7/4} d^3 \sqrt{a+b x}}-\frac{8 \sqrt{a+b x} (c+d x)^{3/4} (b c-a d)^2}{65 b d^2}+\frac{4 (a+b x)^{3/2} (c+d x)^{3/4} (b c-a d)}{39 b d}+\frac{4 (a+b x)^{5/2} (c+d x)^{3/4}}{13 b}","-\frac{16 (b c-a d)^{15/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{65 b^{7/4} d^3 \sqrt{a+b x}}+\frac{16 (b c-a d)^{15/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{65 b^{7/4} d^3 \sqrt{a+b x}}-\frac{8 \sqrt{a+b x} (c+d x)^{3/4} (b c-a d)^2}{65 b d^2}+\frac{4 (a+b x)^{3/2} (c+d x)^{3/4} (b c-a d)}{39 b d}+\frac{4 (a+b x)^{5/2} (c+d x)^{3/4}}{13 b}",1,"(-8*(b*c - a*d)^2*Sqrt[a + b*x]*(c + d*x)^(3/4))/(65*b*d^2) + (4*(b*c - a*d)*(a + b*x)^(3/2)*(c + d*x)^(3/4))/(39*b*d) + (4*(a + b*x)^(5/2)*(c + d*x)^(3/4))/(13*b) + (16*(b*c - a*d)^(15/4)*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticE[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(65*b^(7/4)*d^3*Sqrt[a + b*x]) - (16*(b*c - a*d)^(15/4)*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticF[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(65*b^(7/4)*d^3*Sqrt[a + b*x])","A",10,8,19,0.4211,1,"{50, 63, 307, 224, 221, 1200, 1199, 424}"
1636,1,232,0,0.245906,"\int \sqrt{a+b x} (c+d x)^{3/4} \, dx","Int[Sqrt[a + b*x]*(c + d*x)^(3/4),x]","\frac{8 (b c-a d)^{11/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{15 b^{7/4} d^2 \sqrt{a+b x}}-\frac{8 (b c-a d)^{11/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{15 b^{7/4} d^2 \sqrt{a+b x}}+\frac{4 \sqrt{a+b x} (c+d x)^{3/4} (b c-a d)}{15 b d}+\frac{4 (a+b x)^{3/2} (c+d x)^{3/4}}{9 b}","\frac{8 (b c-a d)^{11/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{15 b^{7/4} d^2 \sqrt{a+b x}}-\frac{8 (b c-a d)^{11/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{15 b^{7/4} d^2 \sqrt{a+b x}}+\frac{4 \sqrt{a+b x} (c+d x)^{3/4} (b c-a d)}{15 b d}+\frac{4 (a+b x)^{3/2} (c+d x)^{3/4}}{9 b}",1,"(4*(b*c - a*d)*Sqrt[a + b*x]*(c + d*x)^(3/4))/(15*b*d) + (4*(a + b*x)^(3/2)*(c + d*x)^(3/4))/(9*b) - (8*(b*c - a*d)^(11/4)*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticE[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(15*b^(7/4)*d^2*Sqrt[a + b*x]) + (8*(b*c - a*d)^(11/4)*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticF[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(15*b^(7/4)*d^2*Sqrt[a + b*x])","A",9,8,19,0.4211,1,"{50, 63, 307, 224, 221, 1200, 1199, 424}"
1637,1,196,0,0.2219091,"\int \frac{(c+d x)^{3/4}}{\sqrt{a+b x}} \, dx","Int[(c + d*x)^(3/4)/Sqrt[a + b*x],x]","-\frac{12 (b c-a d)^{7/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{5 b^{7/4} d \sqrt{a+b x}}+\frac{12 (b c-a d)^{7/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{5 b^{7/4} d \sqrt{a+b x}}+\frac{4 \sqrt{a+b x} (c+d x)^{3/4}}{5 b}","-\frac{12 (b c-a d)^{7/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{5 b^{7/4} d \sqrt{a+b x}}+\frac{12 (b c-a d)^{7/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{5 b^{7/4} d \sqrt{a+b x}}+\frac{4 \sqrt{a+b x} (c+d x)^{3/4}}{5 b}",1,"(4*Sqrt[a + b*x]*(c + d*x)^(3/4))/(5*b) + (12*(b*c - a*d)^(7/4)*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticE[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(5*b^(7/4)*d*Sqrt[a + b*x]) - (12*(b*c - a*d)^(7/4)*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticF[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(5*b^(7/4)*d*Sqrt[a + b*x])","A",8,8,19,0.4211,1,"{50, 63, 307, 224, 221, 1200, 1199, 424}"
1638,1,184,0,0.214829,"\int \frac{(c+d x)^{3/4}}{(a+b x)^{3/2}} \, dx","Int[(c + d*x)^(3/4)/(a + b*x)^(3/2),x]","-\frac{6 (b c-a d)^{3/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{b^{7/4} \sqrt{a+b x}}+\frac{6 (b c-a d)^{3/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{b^{7/4} \sqrt{a+b x}}-\frac{2 (c+d x)^{3/4}}{b \sqrt{a+b x}}","-\frac{6 (b c-a d)^{3/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{b^{7/4} \sqrt{a+b x}}+\frac{6 (b c-a d)^{3/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{b^{7/4} \sqrt{a+b x}}-\frac{2 (c+d x)^{3/4}}{b \sqrt{a+b x}}",1,"(-2*(c + d*x)^(3/4))/(b*Sqrt[a + b*x]) + (6*(b*c - a*d)^(3/4)*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticE[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(b^(7/4)*Sqrt[a + b*x]) - (6*(b*c - a*d)^(3/4)*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticF[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(b^(7/4)*Sqrt[a + b*x])","A",8,8,19,0.4211,1,"{47, 63, 307, 224, 221, 1200, 1199, 424}"
1639,1,221,0,0.2357176,"\int \frac{(c+d x)^{3/4}}{(a+b x)^{5/2}} \, dx","Int[(c + d*x)^(3/4)/(a + b*x)^(5/2),x]","-\frac{d \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{b^{7/4} \sqrt{a+b x} \sqrt[4]{b c-a d}}+\frac{d \sqrt{-\frac{d (a+b x)}{b c-a d}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{b^{7/4} \sqrt{a+b x} \sqrt[4]{b c-a d}}-\frac{d (c+d x)^{3/4}}{b \sqrt{a+b x} (b c-a d)}-\frac{2 (c+d x)^{3/4}}{3 b (a+b x)^{3/2}}","-\frac{d \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{b^{7/4} \sqrt{a+b x} \sqrt[4]{b c-a d}}+\frac{d \sqrt{-\frac{d (a+b x)}{b c-a d}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{b^{7/4} \sqrt{a+b x} \sqrt[4]{b c-a d}}-\frac{d (c+d x)^{3/4}}{b \sqrt{a+b x} (b c-a d)}-\frac{2 (c+d x)^{3/4}}{3 b (a+b x)^{3/2}}",1,"(-2*(c + d*x)^(3/4))/(3*b*(a + b*x)^(3/2)) - (d*(c + d*x)^(3/4))/(b*(b*c - a*d)*Sqrt[a + b*x]) + (d*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticE[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(b^(7/4)*(b*c - a*d)^(1/4)*Sqrt[a + b*x]) - (d*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticF[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(b^(7/4)*(b*c - a*d)^(1/4)*Sqrt[a + b*x])","A",9,9,19,0.4737,1,"{47, 51, 63, 307, 224, 221, 1200, 1199, 424}"
1640,1,270,0,0.2847747,"\int \frac{(c+d x)^{3/4}}{(a+b x)^{7/2}} \, dx","Int[(c + d*x)^(3/4)/(a + b*x)^(7/2),x]","\frac{3 d^2 \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{10 b^{7/4} \sqrt{a+b x} (b c-a d)^{5/4}}-\frac{3 d^2 \sqrt{-\frac{d (a+b x)}{b c-a d}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{10 b^{7/4} \sqrt{a+b x} (b c-a d)^{5/4}}+\frac{3 d^2 (c+d x)^{3/4}}{10 b \sqrt{a+b x} (b c-a d)^2}-\frac{d (c+d x)^{3/4}}{5 b (a+b x)^{3/2} (b c-a d)}-\frac{2 (c+d x)^{3/4}}{5 b (a+b x)^{5/2}}","\frac{3 d^2 \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{10 b^{7/4} \sqrt{a+b x} (b c-a d)^{5/4}}-\frac{3 d^2 \sqrt{-\frac{d (a+b x)}{b c-a d}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{10 b^{7/4} \sqrt{a+b x} (b c-a d)^{5/4}}+\frac{3 d^2 (c+d x)^{3/4}}{10 b \sqrt{a+b x} (b c-a d)^2}-\frac{d (c+d x)^{3/4}}{5 b (a+b x)^{3/2} (b c-a d)}-\frac{2 (c+d x)^{3/4}}{5 b (a+b x)^{5/2}}",1,"(-2*(c + d*x)^(3/4))/(5*b*(a + b*x)^(5/2)) - (d*(c + d*x)^(3/4))/(5*b*(b*c - a*d)*(a + b*x)^(3/2)) + (3*d^2*(c + d*x)^(3/4))/(10*b*(b*c - a*d)^2*Sqrt[a + b*x]) - (3*d^2*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticE[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(10*b^(7/4)*(b*c - a*d)^(5/4)*Sqrt[a + b*x]) + (3*d^2*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticF[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(10*b^(7/4)*(b*c - a*d)^(5/4)*Sqrt[a + b*x])","A",10,9,19,0.4737,1,"{47, 51, 63, 307, 224, 221, 1200, 1199, 424}"
1641,1,220,0,0.1680366,"\int (a+b x)^{3/2} (c+d x)^{5/4} \, dx","Int[(a + b*x)^(3/2)*(c + d*x)^(5/4),x]","-\frac{8 \sqrt{a+b x} \sqrt[4]{c+d x} (b c-a d)^3}{231 b^2 d^2}+\frac{16 (b c-a d)^{17/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{231 b^{9/4} d^3 \sqrt{a+b x}}+\frac{4 (a+b x)^{3/2} \sqrt[4]{c+d x} (b c-a d)^2}{231 b^2 d}+\frac{4 (a+b x)^{5/2} \sqrt[4]{c+d x} (b c-a d)}{33 b^2}+\frac{4 (a+b x)^{5/2} (c+d x)^{5/4}}{15 b}","-\frac{8 \sqrt{a+b x} \sqrt[4]{c+d x} (b c-a d)^3}{231 b^2 d^2}+\frac{16 (b c-a d)^{17/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{231 b^{9/4} d^3 \sqrt{a+b x}}+\frac{4 (a+b x)^{3/2} \sqrt[4]{c+d x} (b c-a d)^2}{231 b^2 d}+\frac{4 (a+b x)^{5/2} \sqrt[4]{c+d x} (b c-a d)}{33 b^2}+\frac{4 (a+b x)^{5/2} (c+d x)^{5/4}}{15 b}",1,"(-8*(b*c - a*d)^3*Sqrt[a + b*x]*(c + d*x)^(1/4))/(231*b^2*d^2) + (4*(b*c - a*d)^2*(a + b*x)^(3/2)*(c + d*x)^(1/4))/(231*b^2*d) + (4*(b*c - a*d)*(a + b*x)^(5/2)*(c + d*x)^(1/4))/(33*b^2) + (4*(a + b*x)^(5/2)*(c + d*x)^(5/4))/(15*b) + (16*(b*c - a*d)^(17/4)*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticF[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(231*b^(9/4)*d^3*Sqrt[a + b*x])","A",7,4,19,0.2105,1,"{50, 63, 224, 221}"
1642,1,182,0,0.1040159,"\int \sqrt{a+b x} (c+d x)^{5/4} \, dx","Int[Sqrt[a + b*x]*(c + d*x)^(5/4),x]","-\frac{40 (b c-a d)^{13/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{231 b^{9/4} d^2 \sqrt{a+b x}}+\frac{20 \sqrt{a+b x} \sqrt[4]{c+d x} (b c-a d)^2}{231 b^2 d}+\frac{20 (a+b x)^{3/2} \sqrt[4]{c+d x} (b c-a d)}{77 b^2}+\frac{4 (a+b x)^{3/2} (c+d x)^{5/4}}{11 b}","-\frac{40 (b c-a d)^{13/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{231 b^{9/4} d^2 \sqrt{a+b x}}+\frac{20 \sqrt{a+b x} \sqrt[4]{c+d x} (b c-a d)^2}{231 b^2 d}+\frac{20 (a+b x)^{3/2} \sqrt[4]{c+d x} (b c-a d)}{77 b^2}+\frac{4 (a+b x)^{3/2} (c+d x)^{5/4}}{11 b}",1,"(20*(b*c - a*d)^2*Sqrt[a + b*x]*(c + d*x)^(1/4))/(231*b^2*d) + (20*(b*c - a*d)*(a + b*x)^(3/2)*(c + d*x)^(1/4))/(77*b^2) + (4*(a + b*x)^(3/2)*(c + d*x)^(5/4))/(11*b) - (40*(b*c - a*d)^(13/4)*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticF[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(231*b^(9/4)*d^2*Sqrt[a + b*x])","A",6,4,19,0.2105,1,"{50, 63, 224, 221}"
1643,1,144,0,0.0835383,"\int \frac{(c+d x)^{5/4}}{\sqrt{a+b x}} \, dx","Int[(c + d*x)^(5/4)/Sqrt[a + b*x],x]","\frac{20 \sqrt{a+b x} \sqrt[4]{c+d x} (b c-a d)}{21 b^2}+\frac{20 (b c-a d)^{9/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{21 b^{9/4} d \sqrt{a+b x}}+\frac{4 \sqrt{a+b x} (c+d x)^{5/4}}{7 b}","\frac{20 \sqrt{a+b x} \sqrt[4]{c+d x} (b c-a d)}{21 b^2}+\frac{20 (b c-a d)^{9/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{21 b^{9/4} d \sqrt{a+b x}}+\frac{4 \sqrt{a+b x} (c+d x)^{5/4}}{7 b}",1,"(20*(b*c - a*d)*Sqrt[a + b*x]*(c + d*x)^(1/4))/(21*b^2) + (4*Sqrt[a + b*x]*(c + d*x)^(5/4))/(7*b) + (20*(b*c - a*d)^(9/4)*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticF[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(21*b^(9/4)*d*Sqrt[a + b*x])","A",5,4,19,0.2105,1,"{50, 63, 224, 221}"
1644,1,132,0,0.0783782,"\int \frac{(c+d x)^{5/4}}{(a+b x)^{3/2}} \, dx","Int[(c + d*x)^(5/4)/(a + b*x)^(3/2),x]","\frac{10 d \sqrt{a+b x} \sqrt[4]{c+d x}}{3 b^2}+\frac{10 (b c-a d)^{5/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{3 b^{9/4} \sqrt{a+b x}}-\frac{2 (c+d x)^{5/4}}{b \sqrt{a+b x}}","\frac{10 d \sqrt{a+b x} \sqrt[4]{c+d x}}{3 b^2}+\frac{10 (b c-a d)^{5/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{3 b^{9/4} \sqrt{a+b x}}-\frac{2 (c+d x)^{5/4}}{b \sqrt{a+b x}}",1,"(10*d*Sqrt[a + b*x]*(c + d*x)^(1/4))/(3*b^2) - (2*(c + d*x)^(5/4))/(b*Sqrt[a + b*x]) + (10*(b*c - a*d)^(5/4)*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticF[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(3*b^(9/4)*Sqrt[a + b*x])","A",5,5,19,0.2632,1,"{47, 50, 63, 224, 221}"
1645,1,135,0,0.076054,"\int \frac{(c+d x)^{5/4}}{(a+b x)^{5/2}} \, dx","Int[(c + d*x)^(5/4)/(a + b*x)^(5/2),x]","-\frac{5 d \sqrt[4]{c+d x}}{3 b^2 \sqrt{a+b x}}+\frac{5 d \sqrt[4]{b c-a d} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{3 b^{9/4} \sqrt{a+b x}}-\frac{2 (c+d x)^{5/4}}{3 b (a+b x)^{3/2}}","-\frac{5 d \sqrt[4]{c+d x}}{3 b^2 \sqrt{a+b x}}+\frac{5 d \sqrt[4]{b c-a d} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{3 b^{9/4} \sqrt{a+b x}}-\frac{2 (c+d x)^{5/4}}{3 b (a+b x)^{3/2}}",1,"(-5*d*(c + d*x)^(1/4))/(3*b^2*Sqrt[a + b*x]) - (2*(c + d*x)^(5/4))/(3*b*(a + b*x)^(3/2)) + (5*d*(b*c - a*d)^(1/4)*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticF[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(3*b^(9/4)*Sqrt[a + b*x])","A",5,4,19,0.2105,1,"{47, 63, 224, 221}"
1646,1,175,0,0.1039063,"\int \frac{(c+d x)^{5/4}}{(a+b x)^{7/2}} \, dx","Int[(c + d*x)^(5/4)/(a + b*x)^(7/2),x]","-\frac{d^2 \sqrt[4]{c+d x}}{6 b^2 \sqrt{a+b x} (b c-a d)}-\frac{d^2 \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{6 b^{9/4} \sqrt{a+b x} (b c-a d)^{3/4}}-\frac{d \sqrt[4]{c+d x}}{3 b^2 (a+b x)^{3/2}}-\frac{2 (c+d x)^{5/4}}{5 b (a+b x)^{5/2}}","-\frac{d^2 \sqrt[4]{c+d x}}{6 b^2 \sqrt{a+b x} (b c-a d)}-\frac{d^2 \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{6 b^{9/4} \sqrt{a+b x} (b c-a d)^{3/4}}-\frac{d \sqrt[4]{c+d x}}{3 b^2 (a+b x)^{3/2}}-\frac{2 (c+d x)^{5/4}}{5 b (a+b x)^{5/2}}",1,"-(d*(c + d*x)^(1/4))/(3*b^2*(a + b*x)^(3/2)) - (d^2*(c + d*x)^(1/4))/(6*b^2*(b*c - a*d)*Sqrt[a + b*x]) - (2*(c + d*x)^(5/4))/(5*b*(a + b*x)^(5/2)) - (d^2*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticF[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(6*b^(9/4)*(b*c - a*d)^(3/4)*Sqrt[a + b*x])","A",6,5,19,0.2632,1,"{47, 51, 63, 224, 221}"
1647,1,213,0,0.1202522,"\int \frac{(c+d x)^{5/4}}{(a+b x)^{9/2}} \, dx","Int[(c + d*x)^(5/4)/(a + b*x)^(9/2),x]","\frac{5 d^3 \sqrt[4]{c+d x}}{84 b^2 \sqrt{a+b x} (b c-a d)^2}-\frac{d^2 \sqrt[4]{c+d x}}{42 b^2 (a+b x)^{3/2} (b c-a d)}+\frac{5 d^3 \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{84 b^{9/4} \sqrt{a+b x} (b c-a d)^{7/4}}-\frac{d \sqrt[4]{c+d x}}{7 b^2 (a+b x)^{5/2}}-\frac{2 (c+d x)^{5/4}}{7 b (a+b x)^{7/2}}","\frac{5 d^3 \sqrt[4]{c+d x}}{84 b^2 \sqrt{a+b x} (b c-a d)^2}-\frac{d^2 \sqrt[4]{c+d x}}{42 b^2 (a+b x)^{3/2} (b c-a d)}+\frac{5 d^3 \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{84 b^{9/4} \sqrt{a+b x} (b c-a d)^{7/4}}-\frac{d \sqrt[4]{c+d x}}{7 b^2 (a+b x)^{5/2}}-\frac{2 (c+d x)^{5/4}}{7 b (a+b x)^{7/2}}",1,"-(d*(c + d*x)^(1/4))/(7*b^2*(a + b*x)^(5/2)) - (d^2*(c + d*x)^(1/4))/(42*b^2*(b*c - a*d)*(a + b*x)^(3/2)) + (5*d^3*(c + d*x)^(1/4))/(84*b^2*(b*c - a*d)^2*Sqrt[a + b*x]) - (2*(c + d*x)^(5/4))/(7*b*(a + b*x)^(7/2)) + (5*d^3*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticF[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(84*b^(9/4)*(b*c - a*d)^(7/4)*Sqrt[a + b*x])","A",7,5,19,0.2632,1,"{47, 51, 63, 224, 221}"
1648,1,264,0,0.2984637,"\int \frac{(a+b x)^{5/2}}{\sqrt[4]{c+d x}} \, dx","Int[(a + b*x)^(5/2)/(c + d*x)^(1/4),x]","\frac{32 (b c-a d)^{15/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{39 b^{3/4} d^4 \sqrt{a+b x}}-\frac{32 (b c-a d)^{15/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{39 b^{3/4} d^4 \sqrt{a+b x}}+\frac{16 \sqrt{a+b x} (c+d x)^{3/4} (b c-a d)^2}{39 d^3}-\frac{40 (a+b x)^{3/2} (c+d x)^{3/4} (b c-a d)}{117 d^2}+\frac{4 (a+b x)^{5/2} (c+d x)^{3/4}}{13 d}","\frac{32 (b c-a d)^{15/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{39 b^{3/4} d^4 \sqrt{a+b x}}-\frac{32 (b c-a d)^{15/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{39 b^{3/4} d^4 \sqrt{a+b x}}+\frac{16 \sqrt{a+b x} (c+d x)^{3/4} (b c-a d)^2}{39 d^3}-\frac{40 (a+b x)^{3/2} (c+d x)^{3/4} (b c-a d)}{117 d^2}+\frac{4 (a+b x)^{5/2} (c+d x)^{3/4}}{13 d}",1,"(16*(b*c - a*d)^2*Sqrt[a + b*x]*(c + d*x)^(3/4))/(39*d^3) - (40*(b*c - a*d)*(a + b*x)^(3/2)*(c + d*x)^(3/4))/(117*d^2) + (4*(a + b*x)^(5/2)*(c + d*x)^(3/4))/(13*d) - (32*(b*c - a*d)^(15/4)*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticE[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(39*b^(3/4)*d^4*Sqrt[a + b*x]) + (32*(b*c - a*d)^(15/4)*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticF[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(39*b^(3/4)*d^4*Sqrt[a + b*x])","A",10,8,19,0.4211,1,"{50, 63, 307, 224, 221, 1200, 1199, 424}"
1649,1,229,0,0.2447806,"\int \frac{(a+b x)^{3/2}}{\sqrt[4]{c+d x}} \, dx","Int[(a + b*x)^(3/2)/(c + d*x)^(1/4),x]","-\frac{16 (b c-a d)^{11/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{15 b^{3/4} d^3 \sqrt{a+b x}}+\frac{16 (b c-a d)^{11/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{15 b^{3/4} d^3 \sqrt{a+b x}}-\frac{8 \sqrt{a+b x} (c+d x)^{3/4} (b c-a d)}{15 d^2}+\frac{4 (a+b x)^{3/2} (c+d x)^{3/4}}{9 d}","-\frac{16 (b c-a d)^{11/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{15 b^{3/4} d^3 \sqrt{a+b x}}+\frac{16 (b c-a d)^{11/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{15 b^{3/4} d^3 \sqrt{a+b x}}-\frac{8 \sqrt{a+b x} (c+d x)^{3/4} (b c-a d)}{15 d^2}+\frac{4 (a+b x)^{3/2} (c+d x)^{3/4}}{9 d}",1,"(-8*(b*c - a*d)*Sqrt[a + b*x]*(c + d*x)^(3/4))/(15*d^2) + (4*(a + b*x)^(3/2)*(c + d*x)^(3/4))/(9*d) + (16*(b*c - a*d)^(11/4)*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticE[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(15*b^(3/4)*d^3*Sqrt[a + b*x]) - (16*(b*c - a*d)^(11/4)*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticF[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(15*b^(3/4)*d^3*Sqrt[a + b*x])","A",9,8,19,0.4211,1,"{50, 63, 307, 224, 221, 1200, 1199, 424}"
1650,1,196,0,0.2155701,"\int \frac{\sqrt{a+b x}}{\sqrt[4]{c+d x}} \, dx","Int[Sqrt[a + b*x]/(c + d*x)^(1/4),x]","\frac{8 (b c-a d)^{7/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{5 b^{3/4} d^2 \sqrt{a+b x}}-\frac{8 (b c-a d)^{7/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{5 b^{3/4} d^2 \sqrt{a+b x}}+\frac{4 \sqrt{a+b x} (c+d x)^{3/4}}{5 d}","\frac{8 (b c-a d)^{7/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{5 b^{3/4} d^2 \sqrt{a+b x}}-\frac{8 (b c-a d)^{7/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{5 b^{3/4} d^2 \sqrt{a+b x}}+\frac{4 \sqrt{a+b x} (c+d x)^{3/4}}{5 d}",1,"(4*Sqrt[a + b*x]*(c + d*x)^(3/4))/(5*d) - (8*(b*c - a*d)^(7/4)*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticE[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(5*b^(3/4)*d^2*Sqrt[a + b*x]) + (8*(b*c - a*d)^(7/4)*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticF[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(5*b^(3/4)*d^2*Sqrt[a + b*x])","A",8,8,19,0.4211,1,"{50, 63, 307, 224, 221, 1200, 1199, 424}"
1651,1,167,0,0.1940738,"\int \frac{1}{\sqrt{a+b x} \sqrt[4]{c+d x}} \, dx","Int[1/(Sqrt[a + b*x]*(c + d*x)^(1/4)),x]","\frac{4 (b c-a d)^{3/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{b^{3/4} d \sqrt{a+b x}}-\frac{4 (b c-a d)^{3/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{b^{3/4} d \sqrt{a+b x}}","\frac{4 (b c-a d)^{3/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{b^{3/4} d \sqrt{a+b x}}-\frac{4 (b c-a d)^{3/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{b^{3/4} d \sqrt{a+b x}}",1,"(4*(b*c - a*d)^(3/4)*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticE[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(b^(3/4)*d*Sqrt[a + b*x]) - (4*(b*c - a*d)^(3/4)*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticF[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(b^(3/4)*d*Sqrt[a + b*x])","A",7,7,19,0.3684,1,"{63, 307, 224, 221, 1200, 1199, 424}"
1652,1,191,0,0.224496,"\int \frac{1}{(a+b x)^{3/2} \sqrt[4]{c+d x}} \, dx","Int[1/((a + b*x)^(3/2)*(c + d*x)^(1/4)),x]","-\frac{2 \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{b^{3/4} \sqrt{a+b x} \sqrt[4]{b c-a d}}+\frac{2 \sqrt{-\frac{d (a+b x)}{b c-a d}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{b^{3/4} \sqrt{a+b x} \sqrt[4]{b c-a d}}-\frac{2 (c+d x)^{3/4}}{\sqrt{a+b x} (b c-a d)}","-\frac{2 \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{b^{3/4} \sqrt{a+b x} \sqrt[4]{b c-a d}}+\frac{2 \sqrt{-\frac{d (a+b x)}{b c-a d}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{b^{3/4} \sqrt{a+b x} \sqrt[4]{b c-a d}}-\frac{2 (c+d x)^{3/4}}{\sqrt{a+b x} (b c-a d)}",1,"(-2*(c + d*x)^(3/4))/((b*c - a*d)*Sqrt[a + b*x]) + (2*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticE[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(b^(3/4)*(b*c - a*d)^(1/4)*Sqrt[a + b*x]) - (2*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticF[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(b^(3/4)*(b*c - a*d)^(1/4)*Sqrt[a + b*x])","A",8,8,19,0.4211,1,"{51, 63, 307, 224, 221, 1200, 1199, 424}"
1653,1,224,0,0.2620062,"\int \frac{1}{(a+b x)^{5/2} \sqrt[4]{c+d x}} \, dx","Int[1/((a + b*x)^(5/2)*(c + d*x)^(1/4)),x]","\frac{d \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{b^{3/4} \sqrt{a+b x} (b c-a d)^{5/4}}-\frac{d \sqrt{-\frac{d (a+b x)}{b c-a d}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{b^{3/4} \sqrt{a+b x} (b c-a d)^{5/4}}+\frac{d (c+d x)^{3/4}}{\sqrt{a+b x} (b c-a d)^2}-\frac{2 (c+d x)^{3/4}}{3 (a+b x)^{3/2} (b c-a d)}","\frac{d \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{b^{3/4} \sqrt{a+b x} (b c-a d)^{5/4}}-\frac{d \sqrt{-\frac{d (a+b x)}{b c-a d}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{b^{3/4} \sqrt{a+b x} (b c-a d)^{5/4}}+\frac{d (c+d x)^{3/4}}{\sqrt{a+b x} (b c-a d)^2}-\frac{2 (c+d x)^{3/4}}{3 (a+b x)^{3/2} (b c-a d)}",1,"(-2*(c + d*x)^(3/4))/(3*(b*c - a*d)*(a + b*x)^(3/2)) + (d*(c + d*x)^(3/4))/((b*c - a*d)^2*Sqrt[a + b*x]) - (d*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticE[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(b^(3/4)*(b*c - a*d)^(5/4)*Sqrt[a + b*x]) + (d*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticF[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(b^(3/4)*(b*c - a*d)^(5/4)*Sqrt[a + b*x])","A",9,8,19,0.4211,1,"{51, 63, 307, 224, 221, 1200, 1199, 424}"
1654,1,144,0,0.083312,"\int \frac{(a+b x)^{3/2}}{(c+d x)^{3/4}} \, dx","Int[(a + b*x)^(3/2)/(c + d*x)^(3/4),x]","-\frac{8 \sqrt{a+b x} \sqrt[4]{c+d x} (b c-a d)}{7 d^2}+\frac{16 (b c-a d)^{9/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{7 \sqrt[4]{b} d^3 \sqrt{a+b x}}+\frac{4 (a+b x)^{3/2} \sqrt[4]{c+d x}}{7 d}","-\frac{8 \sqrt{a+b x} \sqrt[4]{c+d x} (b c-a d)}{7 d^2}+\frac{16 (b c-a d)^{9/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{7 \sqrt[4]{b} d^3 \sqrt{a+b x}}+\frac{4 (a+b x)^{3/2} \sqrt[4]{c+d x}}{7 d}",1,"(-8*(b*c - a*d)*Sqrt[a + b*x]*(c + d*x)^(1/4))/(7*d^2) + (4*(a + b*x)^(3/2)*(c + d*x)^(1/4))/(7*d) + (16*(b*c - a*d)^(9/4)*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticF[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(7*b^(1/4)*d^3*Sqrt[a + b*x])","A",5,4,19,0.2105,1,"{50, 63, 224, 221}"
1655,1,111,0,0.0672476,"\int \frac{\sqrt{a+b x}}{(c+d x)^{3/4}} \, dx","Int[Sqrt[a + b*x]/(c + d*x)^(3/4),x]","\frac{4 \sqrt{a+b x} \sqrt[4]{c+d x}}{3 d}-\frac{8 (b c-a d)^{5/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{3 \sqrt[4]{b} d^2 \sqrt{a+b x}}","\frac{4 \sqrt{a+b x} \sqrt[4]{c+d x}}{3 d}-\frac{8 (b c-a d)^{5/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{3 \sqrt[4]{b} d^2 \sqrt{a+b x}}",1,"(4*Sqrt[a + b*x]*(c + d*x)^(1/4))/(3*d) - (8*(b*c - a*d)^(5/4)*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticF[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(3*b^(1/4)*d^2*Sqrt[a + b*x])","A",4,4,19,0.2105,1,"{50, 63, 224, 221}"
1656,1,83,0,0.0510196,"\int \frac{1}{\sqrt{a+b x} (c+d x)^{3/4}} \, dx","Int[1/(Sqrt[a + b*x]*(c + d*x)^(3/4)),x]","\frac{4 \sqrt[4]{b c-a d} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{\sqrt[4]{b} d \sqrt{a+b x}}","\frac{4 \sqrt[4]{b c-a d} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{\sqrt[4]{b} d \sqrt{a+b x}}",1,"(4*(b*c - a*d)^(1/4)*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticF[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(b^(1/4)*d*Sqrt[a + b*x])","A",3,3,19,0.1579,1,"{63, 224, 221}"
1657,1,111,0,0.0602431,"\int \frac{1}{(a+b x)^{3/2} (c+d x)^{3/4}} \, dx","Int[1/((a + b*x)^(3/2)*(c + d*x)^(3/4)),x]","-\frac{2 \sqrt[4]{c+d x}}{\sqrt{a+b x} (b c-a d)}-\frac{2 \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{\sqrt[4]{b} \sqrt{a+b x} (b c-a d)^{3/4}}","-\frac{2 \sqrt[4]{c+d x}}{\sqrt{a+b x} (b c-a d)}-\frac{2 \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{\sqrt[4]{b} \sqrt{a+b x} (b c-a d)^{3/4}}",1,"(-2*(c + d*x)^(1/4))/((b*c - a*d)*Sqrt[a + b*x]) - (2*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticF[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(b^(1/4)*(b*c - a*d)^(3/4)*Sqrt[a + b*x])","A",4,4,19,0.2105,1,"{51, 63, 224, 221}"
1658,1,149,0,0.0745647,"\int \frac{1}{(a+b x)^{5/2} (c+d x)^{3/4}} \, dx","Int[1/((a + b*x)^(5/2)*(c + d*x)^(3/4)),x]","\frac{5 d \sqrt[4]{c+d x}}{3 \sqrt{a+b x} (b c-a d)^2}-\frac{2 \sqrt[4]{c+d x}}{3 (a+b x)^{3/2} (b c-a d)}+\frac{5 d \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{3 \sqrt[4]{b} \sqrt{a+b x} (b c-a d)^{7/4}}","\frac{5 d \sqrt[4]{c+d x}}{3 \sqrt{a+b x} (b c-a d)^2}-\frac{2 \sqrt[4]{c+d x}}{3 (a+b x)^{3/2} (b c-a d)}+\frac{5 d \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{3 \sqrt[4]{b} \sqrt{a+b x} (b c-a d)^{7/4}}",1,"(-2*(c + d*x)^(1/4))/(3*(b*c - a*d)*(a + b*x)^(3/2)) + (5*d*(c + d*x)^(1/4))/(3*(b*c - a*d)^2*Sqrt[a + b*x]) + (5*d*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticF[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(3*b^(1/4)*(b*c - a*d)^(7/4)*Sqrt[a + b*x])","A",5,4,19,0.2105,1,"{51, 63, 224, 221}"
1659,1,254,0,0.2620134,"\int \frac{(a+b x)^{5/2}}{(c+d x)^{5/4}} \, dx","Int[(a + b*x)^(5/2)/(c + d*x)^(5/4),x]","-\frac{16 b \sqrt{a+b x} (c+d x)^{3/4} (b c-a d)}{3 d^3}+\frac{40 b (a+b x)^{3/2} (c+d x)^{3/4}}{9 d^2}-\frac{32 \sqrt[4]{b} (b c-a d)^{11/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{3 d^4 \sqrt{a+b x}}+\frac{32 \sqrt[4]{b} (b c-a d)^{11/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{3 d^4 \sqrt{a+b x}}-\frac{4 (a+b x)^{5/2}}{d \sqrt[4]{c+d x}}","-\frac{16 b \sqrt{a+b x} (c+d x)^{3/4} (b c-a d)}{3 d^3}+\frac{40 b (a+b x)^{3/2} (c+d x)^{3/4}}{9 d^2}-\frac{32 \sqrt[4]{b} (b c-a d)^{11/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{3 d^4 \sqrt{a+b x}}+\frac{32 \sqrt[4]{b} (b c-a d)^{11/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{3 d^4 \sqrt{a+b x}}-\frac{4 (a+b x)^{5/2}}{d \sqrt[4]{c+d x}}",1,"(-4*(a + b*x)^(5/2))/(d*(c + d*x)^(1/4)) - (16*b*(b*c - a*d)*Sqrt[a + b*x]*(c + d*x)^(3/4))/(3*d^3) + (40*b*(a + b*x)^(3/2)*(c + d*x)^(3/4))/(9*d^2) + (32*b^(1/4)*(b*c - a*d)^(11/4)*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticE[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(3*d^4*Sqrt[a + b*x]) - (32*b^(1/4)*(b*c - a*d)^(11/4)*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticF[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(3*d^4*Sqrt[a + b*x])","A",10,9,19,0.4737,1,"{47, 50, 63, 307, 224, 221, 1200, 1199, 424}"
1660,1,220,0,0.2349477,"\int \frac{(a+b x)^{3/2}}{(c+d x)^{5/4}} \, dx","Int[(a + b*x)^(3/2)/(c + d*x)^(5/4),x]","\frac{24 b \sqrt{a+b x} (c+d x)^{3/4}}{5 d^2}+\frac{48 \sqrt[4]{b} (b c-a d)^{7/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{5 d^3 \sqrt{a+b x}}-\frac{48 \sqrt[4]{b} (b c-a d)^{7/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{5 d^3 \sqrt{a+b x}}-\frac{4 (a+b x)^{3/2}}{d \sqrt[4]{c+d x}}","\frac{24 b \sqrt{a+b x} (c+d x)^{3/4}}{5 d^2}+\frac{48 \sqrt[4]{b} (b c-a d)^{7/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{5 d^3 \sqrt{a+b x}}-\frac{48 \sqrt[4]{b} (b c-a d)^{7/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{5 d^3 \sqrt{a+b x}}-\frac{4 (a+b x)^{3/2}}{d \sqrt[4]{c+d x}}",1,"(-4*(a + b*x)^(3/2))/(d*(c + d*x)^(1/4)) + (24*b*Sqrt[a + b*x]*(c + d*x)^(3/4))/(5*d^2) - (48*b^(1/4)*(b*c - a*d)^(7/4)*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticE[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(5*d^3*Sqrt[a + b*x]) + (48*b^(1/4)*(b*c - a*d)^(7/4)*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticF[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(5*d^3*Sqrt[a + b*x])","A",9,9,19,0.4737,1,"{47, 50, 63, 307, 224, 221, 1200, 1199, 424}"
1661,1,190,0,0.2073222,"\int \frac{\sqrt{a+b x}}{(c+d x)^{5/4}} \, dx","Int[Sqrt[a + b*x]/(c + d*x)^(5/4),x]","-\frac{8 \sqrt[4]{b} (b c-a d)^{3/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{d^2 \sqrt{a+b x}}+\frac{8 \sqrt[4]{b} (b c-a d)^{3/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{d^2 \sqrt{a+b x}}-\frac{4 \sqrt{a+b x}}{d \sqrt[4]{c+d x}}","-\frac{8 \sqrt[4]{b} (b c-a d)^{3/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{d^2 \sqrt{a+b x}}+\frac{8 \sqrt[4]{b} (b c-a d)^{3/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{d^2 \sqrt{a+b x}}-\frac{4 \sqrt{a+b x}}{d \sqrt[4]{c+d x}}",1,"(-4*Sqrt[a + b*x])/(d*(c + d*x)^(1/4)) + (8*b^(1/4)*(b*c - a*d)^(3/4)*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticE[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(d^2*Sqrt[a + b*x]) - (8*b^(1/4)*(b*c - a*d)^(3/4)*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticF[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(d^2*Sqrt[a + b*x])","A",8,8,19,0.4211,1,"{47, 63, 307, 224, 221, 1200, 1199, 424}"
1662,1,197,0,0.2110941,"\int \frac{1}{\sqrt{a+b x} (c+d x)^{5/4}} \, dx","Int[1/(Sqrt[a + b*x]*(c + d*x)^(5/4)),x]","\frac{4 \sqrt{a+b x}}{\sqrt[4]{c+d x} (b c-a d)}+\frac{4 \sqrt[4]{b} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{d \sqrt{a+b x} \sqrt[4]{b c-a d}}-\frac{4 \sqrt[4]{b} \sqrt{-\frac{d (a+b x)}{b c-a d}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{d \sqrt{a+b x} \sqrt[4]{b c-a d}}","\frac{4 \sqrt{a+b x}}{\sqrt[4]{c+d x} (b c-a d)}+\frac{4 \sqrt[4]{b} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{d \sqrt{a+b x} \sqrt[4]{b c-a d}}-\frac{4 \sqrt[4]{b} \sqrt{-\frac{d (a+b x)}{b c-a d}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{d \sqrt{a+b x} \sqrt[4]{b c-a d}}",1,"(4*Sqrt[a + b*x])/((b*c - a*d)*(c + d*x)^(1/4)) - (4*b^(1/4)*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticE[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(d*(b*c - a*d)^(1/4)*Sqrt[a + b*x]) + (4*b^(1/4)*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticF[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(d*(b*c - a*d)^(1/4)*Sqrt[a + b*x])","A",8,8,19,0.4211,1,"{51, 63, 307, 224, 221, 1200, 1199, 424}"
1663,1,222,0,0.231177,"\int \frac{1}{(a+b x)^{3/2} (c+d x)^{5/4}} \, dx","Int[1/((a + b*x)^(3/2)*(c + d*x)^(5/4)),x]","-\frac{6 d \sqrt{a+b x}}{\sqrt[4]{c+d x} (b c-a d)^2}-\frac{2}{\sqrt{a+b x} \sqrt[4]{c+d x} (b c-a d)}-\frac{6 \sqrt[4]{b} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{\sqrt{a+b x} (b c-a d)^{5/4}}+\frac{6 \sqrt[4]{b} \sqrt{-\frac{d (a+b x)}{b c-a d}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{\sqrt{a+b x} (b c-a d)^{5/4}}","-\frac{6 d \sqrt{a+b x}}{\sqrt[4]{c+d x} (b c-a d)^2}-\frac{2}{\sqrt{a+b x} \sqrt[4]{c+d x} (b c-a d)}-\frac{6 \sqrt[4]{b} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{\sqrt{a+b x} (b c-a d)^{5/4}}+\frac{6 \sqrt[4]{b} \sqrt{-\frac{d (a+b x)}{b c-a d}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{\sqrt{a+b x} (b c-a d)^{5/4}}",1,"-2/((b*c - a*d)*Sqrt[a + b*x]*(c + d*x)^(1/4)) - (6*d*Sqrt[a + b*x])/((b*c - a*d)^2*(c + d*x)^(1/4)) + (6*b^(1/4)*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticE[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/((b*c - a*d)^(5/4)*Sqrt[a + b*x]) - (6*b^(1/4)*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticF[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/((b*c - a*d)^(5/4)*Sqrt[a + b*x])","A",9,8,19,0.4211,1,"{51, 63, 307, 224, 221, 1200, 1199, 424}"
1664,1,261,0,0.2601695,"\int \frac{1}{(a+b x)^{5/2} (c+d x)^{5/4}} \, dx","Int[1/((a + b*x)^(5/2)*(c + d*x)^(5/4)),x]","\frac{7 d^2 \sqrt{a+b x}}{\sqrt[4]{c+d x} (b c-a d)^3}+\frac{7 d}{3 \sqrt{a+b x} \sqrt[4]{c+d x} (b c-a d)^2}-\frac{2}{3 (a+b x)^{3/2} \sqrt[4]{c+d x} (b c-a d)}+\frac{7 \sqrt[4]{b} d \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{\sqrt{a+b x} (b c-a d)^{9/4}}-\frac{7 \sqrt[4]{b} d \sqrt{-\frac{d (a+b x)}{b c-a d}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{\sqrt{a+b x} (b c-a d)^{9/4}}","\frac{7 d^2 \sqrt{a+b x}}{\sqrt[4]{c+d x} (b c-a d)^3}+\frac{7 d}{3 \sqrt{a+b x} \sqrt[4]{c+d x} (b c-a d)^2}-\frac{2}{3 (a+b x)^{3/2} \sqrt[4]{c+d x} (b c-a d)}+\frac{7 \sqrt[4]{b} d \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{\sqrt{a+b x} (b c-a d)^{9/4}}-\frac{7 \sqrt[4]{b} d \sqrt{-\frac{d (a+b x)}{b c-a d}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{\sqrt{a+b x} (b c-a d)^{9/4}}",1,"-2/(3*(b*c - a*d)*(a + b*x)^(3/2)*(c + d*x)^(1/4)) + (7*d)/(3*(b*c - a*d)^2*Sqrt[a + b*x]*(c + d*x)^(1/4)) + (7*d^2*Sqrt[a + b*x])/((b*c - a*d)^3*(c + d*x)^(1/4)) - (7*b^(1/4)*d*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticE[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/((b*c - a*d)^(9/4)*Sqrt[a + b*x]) + (7*b^(1/4)*d*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticF[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/((b*c - a*d)^(9/4)*Sqrt[a + b*x])","A",10,8,19,0.4211,1,"{51, 63, 307, 224, 221, 1200, 1199, 424}"
1665,1,207,0,0.1363125,"\int \frac{(a+b x)^{7/2}}{(c+d x)^{7/4}} \, dx","Int[(a + b*x)^(7/2)/(c + d*x)^(7/4),x]","-\frac{320 b^{3/4} (b c-a d)^{13/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{33 d^5 \sqrt{a+b x}}+\frac{56 b (a+b x)^{5/2} \sqrt[4]{c+d x}}{33 d^2}-\frac{80 b (a+b x)^{3/2} \sqrt[4]{c+d x} (b c-a d)}{33 d^3}+\frac{160 b \sqrt{a+b x} \sqrt[4]{c+d x} (b c-a d)^2}{33 d^4}-\frac{4 (a+b x)^{7/2}}{3 d (c+d x)^{3/4}}","-\frac{320 b^{3/4} (b c-a d)^{13/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{33 d^5 \sqrt{a+b x}}+\frac{56 b (a+b x)^{5/2} \sqrt[4]{c+d x}}{33 d^2}-\frac{80 b (a+b x)^{3/2} \sqrt[4]{c+d x} (b c-a d)}{33 d^3}+\frac{160 b \sqrt{a+b x} \sqrt[4]{c+d x} (b c-a d)^2}{33 d^4}-\frac{4 (a+b x)^{7/2}}{3 d (c+d x)^{3/4}}",1,"(-4*(a + b*x)^(7/2))/(3*d*(c + d*x)^(3/4)) + (160*b*(b*c - a*d)^2*Sqrt[a + b*x]*(c + d*x)^(1/4))/(33*d^4) - (80*b*(b*c - a*d)*(a + b*x)^(3/2)*(c + d*x)^(1/4))/(33*d^3) + (56*b*(a + b*x)^(5/2)*(c + d*x)^(1/4))/(33*d^2) - (320*b^(3/4)*(b*c - a*d)^(13/4)*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticF[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(33*d^5*Sqrt[a + b*x])","A",7,5,19,0.2632,1,"{47, 50, 63, 224, 221}"
1666,1,137,0,0.0804734,"\int \frac{(a+b x)^{3/2}}{(c+d x)^{7/4}} \, dx","Int[(a + b*x)^(3/2)/(c + d*x)^(7/4),x]","-\frac{16 b^{3/4} (b c-a d)^{5/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{3 d^3 \sqrt{a+b x}}+\frac{8 b \sqrt{a+b x} \sqrt[4]{c+d x}}{3 d^2}-\frac{4 (a+b x)^{3/2}}{3 d (c+d x)^{3/4}}","-\frac{16 b^{3/4} (b c-a d)^{5/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{3 d^3 \sqrt{a+b x}}+\frac{8 b \sqrt{a+b x} \sqrt[4]{c+d x}}{3 d^2}-\frac{4 (a+b x)^{3/2}}{3 d (c+d x)^{3/4}}",1,"(-4*(a + b*x)^(3/2))/(3*d*(c + d*x)^(3/4)) + (8*b*Sqrt[a + b*x]*(c + d*x)^(1/4))/(3*d^2) - (16*b^(3/4)*(b*c - a*d)^(5/4)*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticF[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(3*d^3*Sqrt[a + b*x])","A",5,5,19,0.2632,1,"{47, 50, 63, 224, 221}"
1667,1,111,0,0.0637834,"\int \frac{\sqrt{a+b x}}{(c+d x)^{7/4}} \, dx","Int[Sqrt[a + b*x]/(c + d*x)^(7/4),x]","\frac{8 b^{3/4} \sqrt[4]{b c-a d} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{3 d^2 \sqrt{a+b x}}-\frac{4 \sqrt{a+b x}}{3 d (c+d x)^{3/4}}","\frac{8 b^{3/4} \sqrt[4]{b c-a d} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{3 d^2 \sqrt{a+b x}}-\frac{4 \sqrt{a+b x}}{3 d (c+d x)^{3/4}}",1,"(-4*Sqrt[a + b*x])/(3*d*(c + d*x)^(3/4)) + (8*b^(3/4)*(b*c - a*d)^(1/4)*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticF[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(3*d^2*Sqrt[a + b*x])","A",4,4,19,0.2105,1,"{47, 63, 224, 221}"
1668,1,118,0,0.0700133,"\int \frac{1}{\sqrt{a+b x} (c+d x)^{7/4}} \, dx","Int[1/(Sqrt[a + b*x]*(c + d*x)^(7/4)),x]","\frac{4 b^{3/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{3 d \sqrt{a+b x} (b c-a d)^{3/4}}+\frac{4 \sqrt{a+b x}}{3 (c+d x)^{3/4} (b c-a d)}","\frac{4 b^{3/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{3 d \sqrt{a+b x} (b c-a d)^{3/4}}+\frac{4 \sqrt{a+b x}}{3 (c+d x)^{3/4} (b c-a d)}",1,"(4*Sqrt[a + b*x])/(3*(b*c - a*d)*(c + d*x)^(3/4)) + (4*b^(3/4)*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticF[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(3*d*(b*c - a*d)^(3/4)*Sqrt[a + b*x])","A",4,4,19,0.2105,1,"{51, 63, 224, 221}"
1669,1,146,0,0.0784827,"\int \frac{1}{(a+b x)^{3/2} (c+d x)^{7/4}} \, dx","Int[1/((a + b*x)^(3/2)*(c + d*x)^(7/4)),x]","-\frac{10 b^{3/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{3 \sqrt{a+b x} (b c-a d)^{7/4}}-\frac{10 d \sqrt{a+b x}}{3 (c+d x)^{3/4} (b c-a d)^2}-\frac{2}{\sqrt{a+b x} (c+d x)^{3/4} (b c-a d)}","-\frac{10 b^{3/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{3 \sqrt{a+b x} (b c-a d)^{7/4}}-\frac{10 d \sqrt{a+b x}}{3 (c+d x)^{3/4} (b c-a d)^2}-\frac{2}{\sqrt{a+b x} (c+d x)^{3/4} (b c-a d)}",1,"-2/((b*c - a*d)*Sqrt[a + b*x]*(c + d*x)^(3/4)) - (10*d*Sqrt[a + b*x])/(3*(b*c - a*d)^2*(c + d*x)^(3/4)) - (10*b^(3/4)*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticF[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(3*(b*c - a*d)^(7/4)*Sqrt[a + b*x])","A",5,4,19,0.2105,1,"{51, 63, 224, 221}"
1670,1,178,0,0.1031641,"\int \frac{1}{(a+b x)^{5/2} (c+d x)^{7/4}} \, dx","Int[1/((a + b*x)^(5/2)*(c + d*x)^(7/4)),x]","\frac{5 b^{3/4} d \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{\sqrt{a+b x} (b c-a d)^{11/4}}+\frac{5 d^2 \sqrt{a+b x}}{(c+d x)^{3/4} (b c-a d)^3}+\frac{3 d}{\sqrt{a+b x} (c+d x)^{3/4} (b c-a d)^2}-\frac{2}{3 (a+b x)^{3/2} (c+d x)^{3/4} (b c-a d)}","\frac{5 b^{3/4} d \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{\sqrt{a+b x} (b c-a d)^{11/4}}+\frac{5 d^2 \sqrt{a+b x}}{(c+d x)^{3/4} (b c-a d)^3}+\frac{3 d}{\sqrt{a+b x} (c+d x)^{3/4} (b c-a d)^2}-\frac{2}{3 (a+b x)^{3/2} (c+d x)^{3/4} (b c-a d)}",1,"-2/(3*(b*c - a*d)*(a + b*x)^(3/2)*(c + d*x)^(3/4)) + (3*d)/((b*c - a*d)^2*Sqrt[a + b*x]*(c + d*x)^(3/4)) + (5*d^2*Sqrt[a + b*x])/((b*c - a*d)^3*(c + d*x)^(3/4)) + (5*b^(3/4)*d*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticF[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/((b*c - a*d)^(11/4)*Sqrt[a + b*x])","A",6,4,19,0.2105,1,"{51, 63, 224, 221}"
1671,1,286,0,0.2969894,"\int \frac{(a+b x)^{7/2}}{(c+d x)^{9/4}} \, dx","Int[(a + b*x)^(7/2)/(c + d*x)^(9/4),x]","\frac{112 b^2 (a+b x)^{3/2} (c+d x)^{3/4}}{9 d^3}-\frac{224 b^2 \sqrt{a+b x} (c+d x)^{3/4} (b c-a d)}{15 d^4}-\frac{448 b^{5/4} (b c-a d)^{11/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{15 d^5 \sqrt{a+b x}}+\frac{448 b^{5/4} (b c-a d)^{11/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{15 d^5 \sqrt{a+b x}}-\frac{56 b (a+b x)^{5/2}}{5 d^2 \sqrt[4]{c+d x}}-\frac{4 (a+b x)^{7/2}}{5 d (c+d x)^{5/4}}","\frac{112 b^2 (a+b x)^{3/2} (c+d x)^{3/4}}{9 d^3}-\frac{224 b^2 \sqrt{a+b x} (c+d x)^{3/4} (b c-a d)}{15 d^4}-\frac{448 b^{5/4} (b c-a d)^{11/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{15 d^5 \sqrt{a+b x}}+\frac{448 b^{5/4} (b c-a d)^{11/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{15 d^5 \sqrt{a+b x}}-\frac{56 b (a+b x)^{5/2}}{5 d^2 \sqrt[4]{c+d x}}-\frac{4 (a+b x)^{7/2}}{5 d (c+d x)^{5/4}}",1,"(-4*(a + b*x)^(7/2))/(5*d*(c + d*x)^(5/4)) - (56*b*(a + b*x)^(5/2))/(5*d^2*(c + d*x)^(1/4)) - (224*b^2*(b*c - a*d)*Sqrt[a + b*x]*(c + d*x)^(3/4))/(15*d^4) + (112*b^2*(a + b*x)^(3/2)*(c + d*x)^(3/4))/(9*d^3) + (448*b^(5/4)*(b*c - a*d)^(11/4)*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticE[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(15*d^5*Sqrt[a + b*x]) - (448*b^(5/4)*(b*c - a*d)^(11/4)*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticF[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(15*d^5*Sqrt[a + b*x])","A",11,9,19,0.4737,1,"{47, 50, 63, 307, 224, 221, 1200, 1199, 424}"
1672,1,248,0,0.2573929,"\int \frac{(a+b x)^{5/2}}{(c+d x)^{9/4}} \, dx","Int[(a + b*x)^(5/2)/(c + d*x)^(9/4),x]","\frac{48 b^2 \sqrt{a+b x} (c+d x)^{3/4}}{5 d^3}+\frac{96 b^{5/4} (b c-a d)^{7/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{5 d^4 \sqrt{a+b x}}-\frac{96 b^{5/4} (b c-a d)^{7/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{5 d^4 \sqrt{a+b x}}-\frac{8 b (a+b x)^{3/2}}{d^2 \sqrt[4]{c+d x}}-\frac{4 (a+b x)^{5/2}}{5 d (c+d x)^{5/4}}","\frac{48 b^2 \sqrt{a+b x} (c+d x)^{3/4}}{5 d^3}+\frac{96 b^{5/4} (b c-a d)^{7/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{5 d^4 \sqrt{a+b x}}-\frac{96 b^{5/4} (b c-a d)^{7/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{5 d^4 \sqrt{a+b x}}-\frac{8 b (a+b x)^{3/2}}{d^2 \sqrt[4]{c+d x}}-\frac{4 (a+b x)^{5/2}}{5 d (c+d x)^{5/4}}",1,"(-4*(a + b*x)^(5/2))/(5*d*(c + d*x)^(5/4)) - (8*b*(a + b*x)^(3/2))/(d^2*(c + d*x)^(1/4)) + (48*b^2*Sqrt[a + b*x]*(c + d*x)^(3/4))/(5*d^3) - (96*b^(5/4)*(b*c - a*d)^(7/4)*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticE[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(5*d^4*Sqrt[a + b*x]) + (96*b^(5/4)*(b*c - a*d)^(7/4)*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticF[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(5*d^4*Sqrt[a + b*x])","A",10,9,19,0.4737,1,"{47, 50, 63, 307, 224, 221, 1200, 1199, 424}"
1673,1,222,0,0.23486,"\int \frac{(a+b x)^{3/2}}{(c+d x)^{9/4}} \, dx","Int[(a + b*x)^(3/2)/(c + d*x)^(9/4),x]","-\frac{48 b^{5/4} (b c-a d)^{3/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{5 d^3 \sqrt{a+b x}}+\frac{48 b^{5/4} (b c-a d)^{3/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{5 d^3 \sqrt{a+b x}}-\frac{24 b \sqrt{a+b x}}{5 d^2 \sqrt[4]{c+d x}}-\frac{4 (a+b x)^{3/2}}{5 d (c+d x)^{5/4}}","-\frac{48 b^{5/4} (b c-a d)^{3/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{5 d^3 \sqrt{a+b x}}+\frac{48 b^{5/4} (b c-a d)^{3/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{5 d^3 \sqrt{a+b x}}-\frac{24 b \sqrt{a+b x}}{5 d^2 \sqrt[4]{c+d x}}-\frac{4 (a+b x)^{3/2}}{5 d (c+d x)^{5/4}}",1,"(-4*(a + b*x)^(3/2))/(5*d*(c + d*x)^(5/4)) - (24*b*Sqrt[a + b*x])/(5*d^2*(c + d*x)^(1/4)) + (48*b^(5/4)*(b*c - a*d)^(3/4)*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticE[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(5*d^3*Sqrt[a + b*x]) - (48*b^(5/4)*(b*c - a*d)^(3/4)*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticF[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(5*d^3*Sqrt[a + b*x])","A",9,8,19,0.4211,1,"{47, 63, 307, 224, 221, 1200, 1199, 424}"
1674,1,232,0,0.2330559,"\int \frac{\sqrt{a+b x}}{(c+d x)^{9/4}} \, dx","Int[Sqrt[a + b*x]/(c + d*x)^(9/4),x]","\frac{8 b^{5/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{5 d^2 \sqrt{a+b x} \sqrt[4]{b c-a d}}-\frac{8 b^{5/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{5 d^2 \sqrt{a+b x} \sqrt[4]{b c-a d}}+\frac{8 b \sqrt{a+b x}}{5 d \sqrt[4]{c+d x} (b c-a d)}-\frac{4 \sqrt{a+b x}}{5 d (c+d x)^{5/4}}","\frac{8 b^{5/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{5 d^2 \sqrt{a+b x} \sqrt[4]{b c-a d}}-\frac{8 b^{5/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{5 d^2 \sqrt{a+b x} \sqrt[4]{b c-a d}}+\frac{8 b \sqrt{a+b x}}{5 d \sqrt[4]{c+d x} (b c-a d)}-\frac{4 \sqrt{a+b x}}{5 d (c+d x)^{5/4}}",1,"(-4*Sqrt[a + b*x])/(5*d*(c + d*x)^(5/4)) + (8*b*Sqrt[a + b*x])/(5*d*(b*c - a*d)*(c + d*x)^(1/4)) - (8*b^(5/4)*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticE[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(5*d^2*(b*c - a*d)^(1/4)*Sqrt[a + b*x]) + (8*b^(5/4)*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticF[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(5*d^2*(b*c - a*d)^(1/4)*Sqrt[a + b*x])","A",9,9,19,0.4737,1,"{47, 51, 63, 307, 224, 221, 1200, 1199, 424}"
1675,1,236,0,0.2358816,"\int \frac{1}{\sqrt{a+b x} (c+d x)^{9/4}} \, dx","Int[1/(Sqrt[a + b*x]*(c + d*x)^(9/4)),x]","\frac{12 b^{5/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{5 d \sqrt{a+b x} (b c-a d)^{5/4}}-\frac{12 b^{5/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{5 d \sqrt{a+b x} (b c-a d)^{5/4}}+\frac{12 b \sqrt{a+b x}}{5 \sqrt[4]{c+d x} (b c-a d)^2}+\frac{4 \sqrt{a+b x}}{5 (c+d x)^{5/4} (b c-a d)}","\frac{12 b^{5/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{5 d \sqrt{a+b x} (b c-a d)^{5/4}}-\frac{12 b^{5/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{5 d \sqrt{a+b x} (b c-a d)^{5/4}}+\frac{12 b \sqrt{a+b x}}{5 \sqrt[4]{c+d x} (b c-a d)^2}+\frac{4 \sqrt{a+b x}}{5 (c+d x)^{5/4} (b c-a d)}",1,"(4*Sqrt[a + b*x])/(5*(b*c - a*d)*(c + d*x)^(5/4)) + (12*b*Sqrt[a + b*x])/(5*(b*c - a*d)^2*(c + d*x)^(1/4)) - (12*b^(5/4)*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticE[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(5*d*(b*c - a*d)^(5/4)*Sqrt[a + b*x]) + (12*b^(5/4)*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticF[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(5*d*(b*c - a*d)^(5/4)*Sqrt[a + b*x])","A",9,8,19,0.4211,1,"{51, 63, 307, 224, 221, 1200, 1199, 424}"
1676,1,262,0,0.2568443,"\int \frac{1}{(a+b x)^{3/2} (c+d x)^{9/4}} \, dx","Int[1/((a + b*x)^(3/2)*(c + d*x)^(9/4)),x]","-\frac{42 b^{5/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{5 \sqrt{a+b x} (b c-a d)^{9/4}}+\frac{42 b^{5/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{5 \sqrt{a+b x} (b c-a d)^{9/4}}-\frac{42 b d \sqrt{a+b x}}{5 \sqrt[4]{c+d x} (b c-a d)^3}-\frac{14 d \sqrt{a+b x}}{5 (c+d x)^{5/4} (b c-a d)^2}-\frac{2}{\sqrt{a+b x} (c+d x)^{5/4} (b c-a d)}","-\frac{42 b^{5/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{5 \sqrt{a+b x} (b c-a d)^{9/4}}+\frac{42 b^{5/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{5 \sqrt{a+b x} (b c-a d)^{9/4}}-\frac{42 b d \sqrt{a+b x}}{5 \sqrt[4]{c+d x} (b c-a d)^3}-\frac{14 d \sqrt{a+b x}}{5 (c+d x)^{5/4} (b c-a d)^2}-\frac{2}{\sqrt{a+b x} (c+d x)^{5/4} (b c-a d)}",1,"-2/((b*c - a*d)*Sqrt[a + b*x]*(c + d*x)^(5/4)) - (14*d*Sqrt[a + b*x])/(5*(b*c - a*d)^2*(c + d*x)^(5/4)) - (42*b*d*Sqrt[a + b*x])/(5*(b*c - a*d)^3*(c + d*x)^(1/4)) + (42*b^(5/4)*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticE[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(5*(b*c - a*d)^(9/4)*Sqrt[a + b*x]) - (42*b^(5/4)*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticF[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(5*(b*c - a*d)^(9/4)*Sqrt[a + b*x])","A",10,8,19,0.4211,1,"{51, 63, 307, 224, 221, 1200, 1199, 424}"
1677,1,303,0,0.2899966,"\int \frac{1}{(a+b x)^{5/2} (c+d x)^{9/4}} \, dx","Int[1/((a + b*x)^(5/2)*(c + d*x)^(9/4)),x]","\frac{77 b^{5/4} d \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{5 \sqrt{a+b x} (b c-a d)^{13/4}}-\frac{77 b^{5/4} d \sqrt{-\frac{d (a+b x)}{b c-a d}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{5 \sqrt{a+b x} (b c-a d)^{13/4}}+\frac{77 b d^2 \sqrt{a+b x}}{5 \sqrt[4]{c+d x} (b c-a d)^4}+\frac{77 d^2 \sqrt{a+b x}}{15 (c+d x)^{5/4} (b c-a d)^3}+\frac{11 d}{3 \sqrt{a+b x} (c+d x)^{5/4} (b c-a d)^2}-\frac{2}{3 (a+b x)^{3/2} (c+d x)^{5/4} (b c-a d)}","\frac{77 b^{5/4} d \sqrt{-\frac{d (a+b x)}{b c-a d}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{5 \sqrt{a+b x} (b c-a d)^{13/4}}-\frac{77 b^{5/4} d \sqrt{-\frac{d (a+b x)}{b c-a d}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{5 \sqrt{a+b x} (b c-a d)^{13/4}}+\frac{77 b d^2 \sqrt{a+b x}}{5 \sqrt[4]{c+d x} (b c-a d)^4}+\frac{77 d^2 \sqrt{a+b x}}{15 (c+d x)^{5/4} (b c-a d)^3}+\frac{11 d}{3 \sqrt{a+b x} (c+d x)^{5/4} (b c-a d)^2}-\frac{2}{3 (a+b x)^{3/2} (c+d x)^{5/4} (b c-a d)}",1,"-2/(3*(b*c - a*d)*(a + b*x)^(3/2)*(c + d*x)^(5/4)) + (11*d)/(3*(b*c - a*d)^2*Sqrt[a + b*x]*(c + d*x)^(5/4)) + (77*d^2*Sqrt[a + b*x])/(15*(b*c - a*d)^3*(c + d*x)^(5/4)) + (77*b*d^2*Sqrt[a + b*x])/(5*(b*c - a*d)^4*(c + d*x)^(1/4)) - (77*b^(5/4)*d*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticE[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(5*(b*c - a*d)^(13/4)*Sqrt[a + b*x]) + (77*b^(5/4)*d*Sqrt[-((d*(a + b*x))/(b*c - a*d))]*EllipticF[ArcSin[(b^(1/4)*(c + d*x)^(1/4))/(b*c - a*d)^(1/4)], -1])/(5*(b*c - a*d)^(13/4)*Sqrt[a + b*x])","A",11,8,19,0.4211,1,"{51, 63, 307, 224, 221, 1200, 1199, 424}"
1678,1,205,0,0.1392199,"\int (a+b x)^{3/4} (c+d x)^{5/4} \, dx","Int[(a + b*x)^(3/4)*(c + d*x)^(5/4),x]","\frac{5 (b c-a d)^3 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{64 b^{9/4} d^{7/4}}-\frac{5 (b c-a d)^3 \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{64 b^{9/4} d^{7/4}}+\frac{5 (a+b x)^{3/4} \sqrt[4]{c+d x} (b c-a d)^2}{96 b^2 d}+\frac{5 (a+b x)^{7/4} \sqrt[4]{c+d x} (b c-a d)}{24 b^2}+\frac{(a+b x)^{7/4} (c+d x)^{5/4}}{3 b}","\frac{5 (b c-a d)^3 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{64 b^{9/4} d^{7/4}}-\frac{5 (b c-a d)^3 \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{64 b^{9/4} d^{7/4}}+\frac{5 (a+b x)^{3/4} \sqrt[4]{c+d x} (b c-a d)^2}{96 b^2 d}+\frac{5 (a+b x)^{7/4} \sqrt[4]{c+d x} (b c-a d)}{24 b^2}+\frac{(a+b x)^{7/4} (c+d x)^{5/4}}{3 b}",1,"(5*(b*c - a*d)^2*(a + b*x)^(3/4)*(c + d*x)^(1/4))/(96*b^2*d) + (5*(b*c - a*d)*(a + b*x)^(7/4)*(c + d*x)^(1/4))/(24*b^2) + ((a + b*x)^(7/4)*(c + d*x)^(5/4))/(3*b) + (5*(b*c - a*d)^3*ArcTan[(d^(1/4)*(a + b*x)^(1/4))/(b^(1/4)*(c + d*x)^(1/4))])/(64*b^(9/4)*d^(7/4)) - (5*(b*c - a*d)^3*ArcTanh[(d^(1/4)*(a + b*x)^(1/4))/(b^(1/4)*(c + d*x)^(1/4))])/(64*b^(9/4)*d^(7/4))","A",8,6,19,0.3158,1,"{50, 63, 331, 298, 205, 208}"
1679,1,167,0,0.1023892,"\int \frac{(c+d x)^{5/4}}{\sqrt[4]{a+b x}} \, dx","Int[(c + d*x)^(5/4)/(a + b*x)^(1/4),x]","-\frac{5 (b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{16 b^{9/4} d^{3/4}}+\frac{5 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{16 b^{9/4} d^{3/4}}+\frac{5 (a+b x)^{3/4} \sqrt[4]{c+d x} (b c-a d)}{8 b^2}+\frac{(a+b x)^{3/4} (c+d x)^{5/4}}{2 b}","-\frac{5 (b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{16 b^{9/4} d^{3/4}}+\frac{5 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{16 b^{9/4} d^{3/4}}+\frac{5 (a+b x)^{3/4} \sqrt[4]{c+d x} (b c-a d)}{8 b^2}+\frac{(a+b x)^{3/4} (c+d x)^{5/4}}{2 b}",1,"(5*(b*c - a*d)*(a + b*x)^(3/4)*(c + d*x)^(1/4))/(8*b^2) + ((a + b*x)^(3/4)*(c + d*x)^(5/4))/(2*b) - (5*(b*c - a*d)^2*ArcTan[(d^(1/4)*(a + b*x)^(1/4))/(b^(1/4)*(c + d*x)^(1/4))])/(16*b^(9/4)*d^(3/4)) + (5*(b*c - a*d)^2*ArcTanh[(d^(1/4)*(a + b*x)^(1/4))/(b^(1/4)*(c + d*x)^(1/4))])/(16*b^(9/4)*d^(3/4))","A",7,6,19,0.3158,1,"{50, 63, 331, 298, 205, 208}"
1680,1,152,0,0.0975301,"\int \frac{(c+d x)^{5/4}}{(a+b x)^{5/4}} \, dx","Int[(c + d*x)^(5/4)/(a + b*x)^(5/4),x]","\frac{5 d (a+b x)^{3/4} \sqrt[4]{c+d x}}{b^2}-\frac{5 \sqrt[4]{d} (b c-a d) \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{2 b^{9/4}}+\frac{5 \sqrt[4]{d} (b c-a d) \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{2 b^{9/4}}-\frac{4 (c+d x)^{5/4}}{b \sqrt[4]{a+b x}}","\frac{5 d (a+b x)^{3/4} \sqrt[4]{c+d x}}{b^2}-\frac{5 \sqrt[4]{d} (b c-a d) \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{2 b^{9/4}}+\frac{5 \sqrt[4]{d} (b c-a d) \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{2 b^{9/4}}-\frac{4 (c+d x)^{5/4}}{b \sqrt[4]{a+b x}}",1,"(5*d*(a + b*x)^(3/4)*(c + d*x)^(1/4))/b^2 - (4*(c + d*x)^(5/4))/(b*(a + b*x)^(1/4)) - (5*d^(1/4)*(b*c - a*d)*ArcTan[(d^(1/4)*(a + b*x)^(1/4))/(b^(1/4)*(c + d*x)^(1/4))])/(2*b^(9/4)) + (5*d^(1/4)*(b*c - a*d)*ArcTanh[(d^(1/4)*(a + b*x)^(1/4))/(b^(1/4)*(c + d*x)^(1/4))])/(2*b^(9/4))","A",7,7,19,0.3684,1,"{47, 50, 63, 331, 298, 205, 208}"
1681,1,134,0,0.0876632,"\int \frac{(c+d x)^{5/4}}{(a+b x)^{9/4}} \, dx","Int[(c + d*x)^(5/4)/(a + b*x)^(9/4),x]","-\frac{2 d^{5/4} \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{b^{9/4}}+\frac{2 d^{5/4} \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{b^{9/4}}-\frac{4 d \sqrt[4]{c+d x}}{b^2 \sqrt[4]{a+b x}}-\frac{4 (c+d x)^{5/4}}{5 b (a+b x)^{5/4}}","-\frac{2 d^{5/4} \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{b^{9/4}}+\frac{2 d^{5/4} \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{b^{9/4}}-\frac{4 d \sqrt[4]{c+d x}}{b^2 \sqrt[4]{a+b x}}-\frac{4 (c+d x)^{5/4}}{5 b (a+b x)^{5/4}}",1,"(-4*d*(c + d*x)^(1/4))/(b^2*(a + b*x)^(1/4)) - (4*(c + d*x)^(5/4))/(5*b*(a + b*x)^(5/4)) - (2*d^(5/4)*ArcTan[(d^(1/4)*(a + b*x)^(1/4))/(b^(1/4)*(c + d*x)^(1/4))])/b^(9/4) + (2*d^(5/4)*ArcTanh[(d^(1/4)*(a + b*x)^(1/4))/(b^(1/4)*(c + d*x)^(1/4))])/b^(9/4)","A",7,6,19,0.3158,1,"{47, 63, 331, 298, 205, 208}"
1682,1,32,0,0.002907,"\int \frac{(c+d x)^{5/4}}{(a+b x)^{13/4}} \, dx","Int[(c + d*x)^(5/4)/(a + b*x)^(13/4),x]","-\frac{4 (c+d x)^{9/4}}{9 (a+b x)^{9/4} (b c-a d)}","-\frac{4 (c+d x)^{9/4}}{9 (a+b x)^{9/4} (b c-a d)}",1,"(-4*(c + d*x)^(9/4))/(9*(b*c - a*d)*(a + b*x)^(9/4))","A",1,1,19,0.05263,1,"{37}"
1683,1,66,0,0.0093824,"\int \frac{(c+d x)^{5/4}}{(a+b x)^{17/4}} \, dx","Int[(c + d*x)^(5/4)/(a + b*x)^(17/4),x]","\frac{16 d (c+d x)^{9/4}}{117 (a+b x)^{9/4} (b c-a d)^2}-\frac{4 (c+d x)^{9/4}}{13 (a+b x)^{13/4} (b c-a d)}","\frac{16 d (c+d x)^{9/4}}{117 (a+b x)^{9/4} (b c-a d)^2}-\frac{4 (c+d x)^{9/4}}{13 (a+b x)^{13/4} (b c-a d)}",1,"(-4*(c + d*x)^(9/4))/(13*(b*c - a*d)*(a + b*x)^(13/4)) + (16*d*(c + d*x)^(9/4))/(117*(b*c - a*d)^2*(a + b*x)^(9/4))","A",2,2,19,0.1053,1,"{45, 37}"
1684,1,101,0,0.0173348,"\int \frac{(c+d x)^{5/4}}{(a+b x)^{21/4}} \, dx","Int[(c + d*x)^(5/4)/(a + b*x)^(21/4),x]","-\frac{128 d^2 (c+d x)^{9/4}}{1989 (a+b x)^{9/4} (b c-a d)^3}+\frac{32 d (c+d x)^{9/4}}{221 (a+b x)^{13/4} (b c-a d)^2}-\frac{4 (c+d x)^{9/4}}{17 (a+b x)^{17/4} (b c-a d)}","-\frac{128 d^2 (c+d x)^{9/4}}{1989 (a+b x)^{9/4} (b c-a d)^3}+\frac{32 d (c+d x)^{9/4}}{221 (a+b x)^{13/4} (b c-a d)^2}-\frac{4 (c+d x)^{9/4}}{17 (a+b x)^{17/4} (b c-a d)}",1,"(-4*(c + d*x)^(9/4))/(17*(b*c - a*d)*(a + b*x)^(17/4)) + (32*d*(c + d*x)^(9/4))/(221*(b*c - a*d)^2*(a + b*x)^(13/4)) - (128*d^2*(c + d*x)^(9/4))/(1989*(b*c - a*d)^3*(a + b*x)^(9/4))","A",3,2,19,0.1053,1,"{45, 37}"
1685,1,136,0,0.0289592,"\int \frac{(c+d x)^{5/4}}{(a+b x)^{25/4}} \, dx","Int[(c + d*x)^(5/4)/(a + b*x)^(25/4),x]","\frac{512 d^3 (c+d x)^{9/4}}{13923 (a+b x)^{9/4} (b c-a d)^4}-\frac{128 d^2 (c+d x)^{9/4}}{1547 (a+b x)^{13/4} (b c-a d)^3}+\frac{16 d (c+d x)^{9/4}}{119 (a+b x)^{17/4} (b c-a d)^2}-\frac{4 (c+d x)^{9/4}}{21 (a+b x)^{21/4} (b c-a d)}","\frac{512 d^3 (c+d x)^{9/4}}{13923 (a+b x)^{9/4} (b c-a d)^4}-\frac{128 d^2 (c+d x)^{9/4}}{1547 (a+b x)^{13/4} (b c-a d)^3}+\frac{16 d (c+d x)^{9/4}}{119 (a+b x)^{17/4} (b c-a d)^2}-\frac{4 (c+d x)^{9/4}}{21 (a+b x)^{21/4} (b c-a d)}",1,"(-4*(c + d*x)^(9/4))/(21*(b*c - a*d)*(a + b*x)^(21/4)) + (16*d*(c + d*x)^(9/4))/(119*(b*c - a*d)^2*(a + b*x)^(17/4)) - (128*d^2*(c + d*x)^(9/4))/(1547*(b*c - a*d)^3*(a + b*x)^(13/4)) + (512*d^3*(c + d*x)^(9/4))/(13923*(b*c - a*d)^4*(a + b*x)^(9/4))","A",4,2,19,0.1053,1,"{45, 37}"
1686,1,408,0,0.5902311,"\int (a+b x)^{5/4} (c+d x)^{5/4} \, dx","Int[(a + b*x)^(5/4)*(c + d*x)^(5/4),x]","-\frac{5 \sqrt[4]{a+b x} \sqrt[4]{c+d x} (b c-a d)^3}{84 b^2 d^2}+\frac{5 (b c-a d)^{9/2} ((a+b x) (c+d x))^{3/4} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{168 \sqrt{2} b^{9/4} d^{9/4} (a+b x)^{3/4} (c+d x)^{3/4} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}+\frac{(a+b x)^{5/4} \sqrt[4]{c+d x} (b c-a d)^2}{42 b^2 d}+\frac{(a+b x)^{9/4} \sqrt[4]{c+d x} (b c-a d)}{7 b^2}+\frac{2 (a+b x)^{9/4} (c+d x)^{5/4}}{7 b}","-\frac{5 \sqrt[4]{a+b x} \sqrt[4]{c+d x} (b c-a d)^3}{84 b^2 d^2}+\frac{5 (b c-a d)^{9/2} ((a+b x) (c+d x))^{3/4} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{168 \sqrt{2} b^{9/4} d^{9/4} (a+b x)^{3/4} (c+d x)^{3/4} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}+\frac{(a+b x)^{5/4} \sqrt[4]{c+d x} (b c-a d)^2}{42 b^2 d}+\frac{(a+b x)^{9/4} \sqrt[4]{c+d x} (b c-a d)}{7 b^2}+\frac{2 (a+b x)^{9/4} (c+d x)^{5/4}}{7 b}",1,"(-5*(b*c - a*d)^3*(a + b*x)^(1/4)*(c + d*x)^(1/4))/(84*b^2*d^2) + ((b*c - a*d)^2*(a + b*x)^(5/4)*(c + d*x)^(1/4))/(42*b^2*d) + ((b*c - a*d)*(a + b*x)^(9/4)*(c + d*x)^(1/4))/(7*b^2) + (2*(a + b*x)^(9/4)*(c + d*x)^(5/4))/(7*b) + (5*(b*c - a*d)^(9/2)*((a + b*x)*(c + d*x))^(3/4)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))*Sqrt[(a*d + b*(c + 2*d*x))^2/((b*c - a*d)^2*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))^2)]*EllipticF[2*ArcTan[(Sqrt[2]*b^(1/4)*d^(1/4)*((a + b*x)*(c + d*x))^(1/4))/Sqrt[b*c - a*d]], 1/2])/(168*Sqrt[2]*b^(9/4)*d^(9/4)*(a + b*x)^(3/4)*(c + d*x)^(3/4)*(b*c + a*d + 2*b*d*x)*Sqrt[(a*d + b*(c + 2*d*x))^2])","A",7,4,19,0.2105,1,"{50, 62, 623, 220}"
1687,1,370,0,0.3782935,"\int \sqrt[4]{a+b x} (c+d x)^{5/4} \, dx","Int[(a + b*x)^(1/4)*(c + d*x)^(5/4),x]","-\frac{(b c-a d)^{7/2} ((a+b x) (c+d x))^{3/4} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{12 \sqrt{2} b^{9/4} d^{5/4} (a+b x)^{3/4} (c+d x)^{3/4} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}+\frac{\sqrt[4]{a+b x} \sqrt[4]{c+d x} (b c-a d)^2}{6 b^2 d}+\frac{(a+b x)^{5/4} \sqrt[4]{c+d x} (b c-a d)}{3 b^2}+\frac{2 (a+b x)^{5/4} (c+d x)^{5/4}}{5 b}","-\frac{(b c-a d)^{7/2} ((a+b x) (c+d x))^{3/4} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{12 \sqrt{2} b^{9/4} d^{5/4} (a+b x)^{3/4} (c+d x)^{3/4} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}+\frac{\sqrt[4]{a+b x} \sqrt[4]{c+d x} (b c-a d)^2}{6 b^2 d}+\frac{(a+b x)^{5/4} \sqrt[4]{c+d x} (b c-a d)}{3 b^2}+\frac{2 (a+b x)^{5/4} (c+d x)^{5/4}}{5 b}",1,"((b*c - a*d)^2*(a + b*x)^(1/4)*(c + d*x)^(1/4))/(6*b^2*d) + ((b*c - a*d)*(a + b*x)^(5/4)*(c + d*x)^(1/4))/(3*b^2) + (2*(a + b*x)^(5/4)*(c + d*x)^(5/4))/(5*b) - ((b*c - a*d)^(7/2)*((a + b*x)*(c + d*x))^(3/4)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))*Sqrt[(a*d + b*(c + 2*d*x))^2/((b*c - a*d)^2*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))^2)]*EllipticF[2*ArcTan[(Sqrt[2]*b^(1/4)*d^(1/4)*((a + b*x)*(c + d*x))^(1/4))/Sqrt[b*c - a*d]], 1/2])/(12*Sqrt[2]*b^(9/4)*d^(5/4)*(a + b*x)^(3/4)*(c + d*x)^(3/4)*(b*c + a*d + 2*b*d*x)*Sqrt[(a*d + b*(c + 2*d*x))^2])","A",6,4,19,0.2105,1,"{50, 62, 623, 220}"
1688,1,332,0,0.2872167,"\int \frac{(c+d x)^{5/4}}{(a+b x)^{3/4}} \, dx","Int[(c + d*x)^(5/4)/(a + b*x)^(3/4),x]","\frac{5 \sqrt[4]{a+b x} \sqrt[4]{c+d x} (b c-a d)}{3 b^2}+\frac{5 (b c-a d)^{5/2} ((a+b x) (c+d x))^{3/4} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{6 \sqrt{2} b^{9/4} \sqrt[4]{d} (a+b x)^{3/4} (c+d x)^{3/4} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}+\frac{2 \sqrt[4]{a+b x} (c+d x)^{5/4}}{3 b}","\frac{5 \sqrt[4]{a+b x} \sqrt[4]{c+d x} (b c-a d)}{3 b^2}+\frac{5 (b c-a d)^{5/2} ((a+b x) (c+d x))^{3/4} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{6 \sqrt{2} b^{9/4} \sqrt[4]{d} (a+b x)^{3/4} (c+d x)^{3/4} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}+\frac{2 \sqrt[4]{a+b x} (c+d x)^{5/4}}{3 b}",1,"(5*(b*c - a*d)*(a + b*x)^(1/4)*(c + d*x)^(1/4))/(3*b^2) + (2*(a + b*x)^(1/4)*(c + d*x)^(5/4))/(3*b) + (5*(b*c - a*d)^(5/2)*((a + b*x)*(c + d*x))^(3/4)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))*Sqrt[(a*d + b*(c + 2*d*x))^2/((b*c - a*d)^2*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))^2)]*EllipticF[2*ArcTan[(Sqrt[2]*b^(1/4)*d^(1/4)*((a + b*x)*(c + d*x))^(1/4))/Sqrt[b*c - a*d]], 1/2])/(6*Sqrt[2]*b^(9/4)*d^(1/4)*(a + b*x)^(3/4)*(c + d*x)^(3/4)*(b*c + a*d + 2*b*d*x)*Sqrt[(a*d + b*(c + 2*d*x))^2])","A",5,4,19,0.2105,1,"{50, 62, 623, 220}"
1689,1,325,0,0.2784597,"\int \frac{(c+d x)^{5/4}}{(a+b x)^{7/4}} \, dx","Int[(c + d*x)^(5/4)/(a + b*x)^(7/4),x]","\frac{5 d^{3/4} (b c-a d)^{3/2} ((a+b x) (c+d x))^{3/4} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{3 \sqrt{2} b^{9/4} (a+b x)^{3/4} (c+d x)^{3/4} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}+\frac{10 d \sqrt[4]{a+b x} \sqrt[4]{c+d x}}{3 b^2}-\frac{4 (c+d x)^{5/4}}{3 b (a+b x)^{3/4}}","\frac{5 d^{3/4} (b c-a d)^{3/2} ((a+b x) (c+d x))^{3/4} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{3 \sqrt{2} b^{9/4} (a+b x)^{3/4} (c+d x)^{3/4} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}+\frac{10 d \sqrt[4]{a+b x} \sqrt[4]{c+d x}}{3 b^2}-\frac{4 (c+d x)^{5/4}}{3 b (a+b x)^{3/4}}",1,"(10*d*(a + b*x)^(1/4)*(c + d*x)^(1/4))/(3*b^2) - (4*(c + d*x)^(5/4))/(3*b*(a + b*x)^(3/4)) + (5*d^(3/4)*(b*c - a*d)^(3/2)*((a + b*x)*(c + d*x))^(3/4)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))*Sqrt[(a*d + b*(c + 2*d*x))^2/((b*c - a*d)^2*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))^2)]*EllipticF[2*ArcTan[(Sqrt[2]*b^(1/4)*d^(1/4)*((a + b*x)*(c + d*x))^(1/4))/Sqrt[b*c - a*d]], 1/2])/(3*Sqrt[2]*b^(9/4)*(a + b*x)^(3/4)*(c + d*x)^(3/4)*(b*c + a*d + 2*b*d*x)*Sqrt[(a*d + b*(c + 2*d*x))^2])","A",5,5,19,0.2632,1,"{47, 50, 62, 623, 220}"
1690,1,325,0,0.2994792,"\int \frac{(c+d x)^{5/4}}{(a+b x)^{11/4}} \, dx","Int[(c + d*x)^(5/4)/(a + b*x)^(11/4),x]","\frac{5 \sqrt{2} d^{7/4} \sqrt{b c-a d} ((a+b x) (c+d x))^{3/4} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{21 b^{9/4} (a+b x)^{3/4} (c+d x)^{3/4} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}-\frac{20 d \sqrt[4]{c+d x}}{21 b^2 (a+b x)^{3/4}}-\frac{4 (c+d x)^{5/4}}{7 b (a+b x)^{7/4}}","\frac{5 \sqrt{2} d^{7/4} \sqrt{b c-a d} ((a+b x) (c+d x))^{3/4} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{21 b^{9/4} (a+b x)^{3/4} (c+d x)^{3/4} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}-\frac{20 d \sqrt[4]{c+d x}}{21 b^2 (a+b x)^{3/4}}-\frac{4 (c+d x)^{5/4}}{7 b (a+b x)^{7/4}}",1,"(-20*d*(c + d*x)^(1/4))/(21*b^2*(a + b*x)^(3/4)) - (4*(c + d*x)^(5/4))/(7*b*(a + b*x)^(7/4)) + (5*Sqrt[2]*d^(7/4)*Sqrt[b*c - a*d]*((a + b*x)*(c + d*x))^(3/4)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))*Sqrt[(a*d + b*(c + 2*d*x))^2/((b*c - a*d)^2*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))^2)]*EllipticF[2*ArcTan[(Sqrt[2]*b^(1/4)*d^(1/4)*((a + b*x)*(c + d*x))^(1/4))/Sqrt[b*c - a*d]], 1/2])/(21*b^(9/4)*(a + b*x)^(3/4)*(c + d*x)^(3/4)*(b*c + a*d + 2*b*d*x)*Sqrt[(a*d + b*(c + 2*d*x))^2])","A",5,4,19,0.2105,1,"{47, 62, 623, 220}"
1691,1,363,0,0.3521482,"\int \frac{(c+d x)^{5/4}}{(a+b x)^{15/4}} \, dx","Int[(c + d*x)^(5/4)/(a + b*x)^(15/4),x]","-\frac{20 d^2 \sqrt[4]{c+d x}}{231 b^2 (a+b x)^{3/4} (b c-a d)}-\frac{10 \sqrt{2} d^{11/4} ((a+b x) (c+d x))^{3/4} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{231 b^{9/4} (a+b x)^{3/4} (c+d x)^{3/4} \sqrt{b c-a d} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}-\frac{20 d \sqrt[4]{c+d x}}{77 b^2 (a+b x)^{7/4}}-\frac{4 (c+d x)^{5/4}}{11 b (a+b x)^{11/4}}","-\frac{20 d^2 \sqrt[4]{c+d x}}{231 b^2 (a+b x)^{3/4} (b c-a d)}-\frac{10 \sqrt{2} d^{11/4} ((a+b x) (c+d x))^{3/4} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{231 b^{9/4} (a+b x)^{3/4} (c+d x)^{3/4} \sqrt{b c-a d} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}-\frac{20 d \sqrt[4]{c+d x}}{77 b^2 (a+b x)^{7/4}}-\frac{4 (c+d x)^{5/4}}{11 b (a+b x)^{11/4}}",1,"(-20*d*(c + d*x)^(1/4))/(77*b^2*(a + b*x)^(7/4)) - (20*d^2*(c + d*x)^(1/4))/(231*b^2*(b*c - a*d)*(a + b*x)^(3/4)) - (4*(c + d*x)^(5/4))/(11*b*(a + b*x)^(11/4)) - (10*Sqrt[2]*d^(11/4)*((a + b*x)*(c + d*x))^(3/4)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))*Sqrt[(a*d + b*(c + 2*d*x))^2/((b*c - a*d)^2*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))^2)]*EllipticF[2*ArcTan[(Sqrt[2]*b^(1/4)*d^(1/4)*((a + b*x)*(c + d*x))^(1/4))/Sqrt[b*c - a*d]], 1/2])/(231*b^(9/4)*Sqrt[b*c - a*d]*(a + b*x)^(3/4)*(c + d*x)^(3/4)*(b*c + a*d + 2*b*d*x)*Sqrt[(a*d + b*(c + 2*d*x))^2])","A",6,5,19,0.2632,1,"{47, 51, 62, 623, 220}"
1692,1,401,0,0.4251964,"\int \frac{(c+d x)^{5/4}}{(a+b x)^{19/4}} \, dx","Int[(c + d*x)^(5/4)/(a + b*x)^(19/4),x]","\frac{8 d^3 \sqrt[4]{c+d x}}{231 b^2 (a+b x)^{3/4} (b c-a d)^2}-\frac{4 d^2 \sqrt[4]{c+d x}}{231 b^2 (a+b x)^{7/4} (b c-a d)}+\frac{4 \sqrt{2} d^{15/4} ((a+b x) (c+d x))^{3/4} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{231 b^{9/4} (a+b x)^{3/4} (c+d x)^{3/4} (b c-a d)^{3/2} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}-\frac{4 d \sqrt[4]{c+d x}}{33 b^2 (a+b x)^{11/4}}-\frac{4 (c+d x)^{5/4}}{15 b (a+b x)^{15/4}}","\frac{8 d^3 \sqrt[4]{c+d x}}{231 b^2 (a+b x)^{3/4} (b c-a d)^2}-\frac{4 d^2 \sqrt[4]{c+d x}}{231 b^2 (a+b x)^{7/4} (b c-a d)}+\frac{4 \sqrt{2} d^{15/4} ((a+b x) (c+d x))^{3/4} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{231 b^{9/4} (a+b x)^{3/4} (c+d x)^{3/4} (b c-a d)^{3/2} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}-\frac{4 d \sqrt[4]{c+d x}}{33 b^2 (a+b x)^{11/4}}-\frac{4 (c+d x)^{5/4}}{15 b (a+b x)^{15/4}}",1,"(-4*d*(c + d*x)^(1/4))/(33*b^2*(a + b*x)^(11/4)) - (4*d^2*(c + d*x)^(1/4))/(231*b^2*(b*c - a*d)*(a + b*x)^(7/4)) + (8*d^3*(c + d*x)^(1/4))/(231*b^2*(b*c - a*d)^2*(a + b*x)^(3/4)) - (4*(c + d*x)^(5/4))/(15*b*(a + b*x)^(15/4)) + (4*Sqrt[2]*d^(15/4)*((a + b*x)*(c + d*x))^(3/4)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))*Sqrt[(a*d + b*(c + 2*d*x))^2/((b*c - a*d)^2*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))^2)]*EllipticF[2*ArcTan[(Sqrt[2]*b^(1/4)*d^(1/4)*((a + b*x)*(c + d*x))^(1/4))/Sqrt[b*c - a*d]], 1/2])/(231*b^(9/4)*(b*c - a*d)^(3/2)*(a + b*x)^(3/4)*(c + d*x)^(3/4)*(b*c + a*d + 2*b*d*x)*Sqrt[(a*d + b*(c + 2*d*x))^2])","A",7,5,19,0.2632,1,"{47, 51, 62, 623, 220}"
1693,1,167,0,0.1022444,"\int \frac{(a+b x)^{5/4}}{\sqrt[4]{c+d x}} \, dx","Int[(a + b*x)^(5/4)/(c + d*x)^(1/4),x]","\frac{5 (b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{16 b^{3/4} d^{9/4}}+\frac{5 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{16 b^{3/4} d^{9/4}}-\frac{5 \sqrt[4]{a+b x} (c+d x)^{3/4} (b c-a d)}{8 d^2}+\frac{(a+b x)^{5/4} (c+d x)^{3/4}}{2 d}","\frac{5 (b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{16 b^{3/4} d^{9/4}}+\frac{5 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{16 b^{3/4} d^{9/4}}-\frac{5 \sqrt[4]{a+b x} (c+d x)^{3/4} (b c-a d)}{8 d^2}+\frac{(a+b x)^{5/4} (c+d x)^{3/4}}{2 d}",1,"(-5*(b*c - a*d)*(a + b*x)^(1/4)*(c + d*x)^(3/4))/(8*d^2) + ((a + b*x)^(5/4)*(c + d*x)^(3/4))/(2*d) + (5*(b*c - a*d)^2*ArcTan[(d^(1/4)*(a + b*x)^(1/4))/(b^(1/4)*(c + d*x)^(1/4))])/(16*b^(3/4)*d^(9/4)) + (5*(b*c - a*d)^2*ArcTanh[(d^(1/4)*(a + b*x)^(1/4))/(b^(1/4)*(c + d*x)^(1/4))])/(16*b^(3/4)*d^(9/4))","A",7,6,19,0.3158,1,"{50, 63, 240, 212, 208, 205}"
1694,1,127,0,0.0738602,"\int \frac{\sqrt[4]{a+b x}}{\sqrt[4]{c+d x}} \, dx","Int[(a + b*x)^(1/4)/(c + d*x)^(1/4),x]","-\frac{(b c-a d) \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{2 b^{3/4} d^{5/4}}-\frac{(b c-a d) \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{2 b^{3/4} d^{5/4}}+\frac{\sqrt[4]{a+b x} (c+d x)^{3/4}}{d}","-\frac{(b c-a d) \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{2 b^{3/4} d^{5/4}}-\frac{(b c-a d) \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{2 b^{3/4} d^{5/4}}+\frac{\sqrt[4]{a+b x} (c+d x)^{3/4}}{d}",1,"((a + b*x)^(1/4)*(c + d*x)^(3/4))/d - ((b*c - a*d)*ArcTan[(d^(1/4)*(a + b*x)^(1/4))/(b^(1/4)*(c + d*x)^(1/4))])/(2*b^(3/4)*d^(5/4)) - ((b*c - a*d)*ArcTanh[(d^(1/4)*(a + b*x)^(1/4))/(b^(1/4)*(c + d*x)^(1/4))])/(2*b^(3/4)*d^(5/4))","A",6,6,19,0.3158,1,"{50, 63, 240, 212, 208, 205}"
1695,1,85,0,0.0583946,"\int \frac{1}{(a+b x)^{3/4} \sqrt[4]{c+d x}} \, dx","Int[1/((a + b*x)^(3/4)*(c + d*x)^(1/4)),x]","\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{b^{3/4} \sqrt[4]{d}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{b^{3/4} \sqrt[4]{d}}","\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{b^{3/4} \sqrt[4]{d}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{b^{3/4} \sqrt[4]{d}}",1,"(2*ArcTan[(d^(1/4)*(a + b*x)^(1/4))/(b^(1/4)*(c + d*x)^(1/4))])/(b^(3/4)*d^(1/4)) + (2*ArcTanh[(d^(1/4)*(a + b*x)^(1/4))/(b^(1/4)*(c + d*x)^(1/4))])/(b^(3/4)*d^(1/4))","A",5,5,19,0.2632,1,"{63, 240, 212, 208, 205}"
1696,1,32,0,0.0032892,"\int \frac{1}{(a+b x)^{7/4} \sqrt[4]{c+d x}} \, dx","Int[1/((a + b*x)^(7/4)*(c + d*x)^(1/4)),x]","-\frac{4 (c+d x)^{3/4}}{3 (a+b x)^{3/4} (b c-a d)}","-\frac{4 (c+d x)^{3/4}}{3 (a+b x)^{3/4} (b c-a d)}",1,"(-4*(c + d*x)^(3/4))/(3*(b*c - a*d)*(a + b*x)^(3/4))","A",1,1,19,0.05263,1,"{37}"
1697,1,66,0,0.0090494,"\int \frac{1}{(a+b x)^{11/4} \sqrt[4]{c+d x}} \, dx","Int[1/((a + b*x)^(11/4)*(c + d*x)^(1/4)),x]","\frac{16 d (c+d x)^{3/4}}{21 (a+b x)^{3/4} (b c-a d)^2}-\frac{4 (c+d x)^{3/4}}{7 (a+b x)^{7/4} (b c-a d)}","\frac{16 d (c+d x)^{3/4}}{21 (a+b x)^{3/4} (b c-a d)^2}-\frac{4 (c+d x)^{3/4}}{7 (a+b x)^{7/4} (b c-a d)}",1,"(-4*(c + d*x)^(3/4))/(7*(b*c - a*d)*(a + b*x)^(7/4)) + (16*d*(c + d*x)^(3/4))/(21*(b*c - a*d)^2*(a + b*x)^(3/4))","A",2,2,19,0.1053,1,"{45, 37}"
1698,1,101,0,0.0171828,"\int \frac{1}{(a+b x)^{15/4} \sqrt[4]{c+d x}} \, dx","Int[1/((a + b*x)^(15/4)*(c + d*x)^(1/4)),x]","-\frac{128 d^2 (c+d x)^{3/4}}{231 (a+b x)^{3/4} (b c-a d)^3}+\frac{32 d (c+d x)^{3/4}}{77 (a+b x)^{7/4} (b c-a d)^2}-\frac{4 (c+d x)^{3/4}}{11 (a+b x)^{11/4} (b c-a d)}","-\frac{128 d^2 (c+d x)^{3/4}}{231 (a+b x)^{3/4} (b c-a d)^3}+\frac{32 d (c+d x)^{3/4}}{77 (a+b x)^{7/4} (b c-a d)^2}-\frac{4 (c+d x)^{3/4}}{11 (a+b x)^{11/4} (b c-a d)}",1,"(-4*(c + d*x)^(3/4))/(11*(b*c - a*d)*(a + b*x)^(11/4)) + (32*d*(c + d*x)^(3/4))/(77*(b*c - a*d)^2*(a + b*x)^(7/4)) - (128*d^2*(c + d*x)^(3/4))/(231*(b*c - a*d)^3*(a + b*x)^(3/4))","A",3,2,19,0.1053,1,"{45, 37}"
1699,1,136,0,0.0305414,"\int \frac{1}{(a+b x)^{19/4} \sqrt[4]{c+d x}} \, dx","Int[1/((a + b*x)^(19/4)*(c + d*x)^(1/4)),x]","\frac{512 d^3 (c+d x)^{3/4}}{1155 (a+b x)^{3/4} (b c-a d)^4}-\frac{128 d^2 (c+d x)^{3/4}}{385 (a+b x)^{7/4} (b c-a d)^3}+\frac{16 d (c+d x)^{3/4}}{55 (a+b x)^{11/4} (b c-a d)^2}-\frac{4 (c+d x)^{3/4}}{15 (a+b x)^{15/4} (b c-a d)}","\frac{512 d^3 (c+d x)^{3/4}}{1155 (a+b x)^{3/4} (b c-a d)^4}-\frac{128 d^2 (c+d x)^{3/4}}{385 (a+b x)^{7/4} (b c-a d)^3}+\frac{16 d (c+d x)^{3/4}}{55 (a+b x)^{11/4} (b c-a d)^2}-\frac{4 (c+d x)^{3/4}}{15 (a+b x)^{15/4} (b c-a d)}",1,"(-4*(c + d*x)^(3/4))/(15*(b*c - a*d)*(a + b*x)^(15/4)) + (16*d*(c + d*x)^(3/4))/(55*(b*c - a*d)^2*(a + b*x)^(11/4)) - (128*d^2*(c + d*x)^(3/4))/(385*(b*c - a*d)^3*(a + b*x)^(7/4)) + (512*d^3*(c + d*x)^(3/4))/(1155*(b*c - a*d)^4*(a + b*x)^(3/4))","A",4,2,19,0.1053,1,"{45, 37}"
1700,1,751,0,0.7888866,"\int \frac{(a+b x)^{7/4}}{\sqrt[4]{c+d x}} \, dx","Int[(a + b*x)^(7/4)/(c + d*x)^(1/4),x]","\frac{7 (b c-a d)^{7/2} \sqrt[4]{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{20 \sqrt{2} b^{3/4} d^{11/4} \sqrt[4]{a+b x} \sqrt[4]{c+d x} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}-\frac{7 (b c-a d)^{7/2} \sqrt[4]{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{10 \sqrt{2} b^{3/4} d^{11/4} \sqrt[4]{a+b x} \sqrt[4]{c+d x} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}-\frac{7 (a+b x)^{3/4} (c+d x)^{3/4} (b c-a d)}{15 d^2}+\frac{7 (b c-a d) \sqrt{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \sqrt{(a d+b (c+2 d x))^2}}{10 \sqrt{b} d^{5/2} \sqrt[4]{a+b x} \sqrt[4]{c+d x} (a d+b c+2 b d x) \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)}+\frac{2 (a+b x)^{7/4} (c+d x)^{3/4}}{5 d}","\frac{7 (b c-a d)^{7/2} \sqrt[4]{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{20 \sqrt{2} b^{3/4} d^{11/4} \sqrt[4]{a+b x} \sqrt[4]{c+d x} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}-\frac{7 (b c-a d)^{7/2} \sqrt[4]{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{10 \sqrt{2} b^{3/4} d^{11/4} \sqrt[4]{a+b x} \sqrt[4]{c+d x} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}-\frac{7 (a+b x)^{3/4} (c+d x)^{3/4} (b c-a d)}{15 d^2}+\frac{7 (b c-a d) \sqrt{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \sqrt{(a d+b (c+2 d x))^2}}{10 \sqrt{b} d^{5/2} \sqrt[4]{a+b x} \sqrt[4]{c+d x} (a d+b c+2 b d x) \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)}+\frac{2 (a+b x)^{7/4} (c+d x)^{3/4}}{5 d}",1,"(-7*(b*c - a*d)*(a + b*x)^(3/4)*(c + d*x)^(3/4))/(15*d^2) + (2*(a + b*x)^(7/4)*(c + d*x)^(3/4))/(5*d) + (7*(b*c - a*d)*Sqrt[(a + b*x)*(c + d*x)]*Sqrt[(b*c + a*d + 2*b*d*x)^2]*Sqrt[(a*d + b*(c + 2*d*x))^2])/(10*Sqrt[b]*d^(5/2)*(a + b*x)^(1/4)*(c + d*x)^(1/4)*(b*c + a*d + 2*b*d*x)*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))) - (7*(b*c - a*d)^(7/2)*((a + b*x)*(c + d*x))^(1/4)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))*Sqrt[(a*d + b*(c + 2*d*x))^2/((b*c - a*d)^2*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))^2)]*EllipticE[2*ArcTan[(Sqrt[2]*b^(1/4)*d^(1/4)*((a + b*x)*(c + d*x))^(1/4))/Sqrt[b*c - a*d]], 1/2])/(10*Sqrt[2]*b^(3/4)*d^(11/4)*(a + b*x)^(1/4)*(c + d*x)^(1/4)*(b*c + a*d + 2*b*d*x)*Sqrt[(a*d + b*(c + 2*d*x))^2]) + (7*(b*c - a*d)^(7/2)*((a + b*x)*(c + d*x))^(1/4)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))*Sqrt[(a*d + b*(c + 2*d*x))^2/((b*c - a*d)^2*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))^2)]*EllipticF[2*ArcTan[(Sqrt[2]*b^(1/4)*d^(1/4)*((a + b*x)*(c + d*x))^(1/4))/Sqrt[b*c - a*d]], 1/2])/(20*Sqrt[2]*b^(3/4)*d^(11/4)*(a + b*x)^(1/4)*(c + d*x)^(1/4)*(b*c + a*d + 2*b*d*x)*Sqrt[(a*d + b*(c + 2*d*x))^2])","A",7,6,19,0.3158,1,"{50, 62, 623, 305, 220, 1196}"
1701,1,705,0,0.6168579,"\int \frac{(a+b x)^{3/4}}{\sqrt[4]{c+d x}} \, dx","Int[(a + b*x)^(3/4)/(c + d*x)^(1/4),x]","-\frac{(b c-a d)^{5/2} \sqrt[4]{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{2 \sqrt{2} b^{3/4} d^{7/4} \sqrt[4]{a+b x} \sqrt[4]{c+d x} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}+\frac{(b c-a d)^{5/2} \sqrt[4]{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{\sqrt{2} b^{3/4} d^{7/4} \sqrt[4]{a+b x} \sqrt[4]{c+d x} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}-\frac{\sqrt{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \sqrt{(a d+b (c+2 d x))^2}}{\sqrt{b} d^{3/2} \sqrt[4]{a+b x} \sqrt[4]{c+d x} (a d+b c+2 b d x) \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)}+\frac{2 (a+b x)^{3/4} (c+d x)^{3/4}}{3 d}","-\frac{(b c-a d)^{5/2} \sqrt[4]{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{2 \sqrt{2} b^{3/4} d^{7/4} \sqrt[4]{a+b x} \sqrt[4]{c+d x} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}+\frac{(b c-a d)^{5/2} \sqrt[4]{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{\sqrt{2} b^{3/4} d^{7/4} \sqrt[4]{a+b x} \sqrt[4]{c+d x} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}-\frac{\sqrt{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \sqrt{(a d+b (c+2 d x))^2}}{\sqrt{b} d^{3/2} \sqrt[4]{a+b x} \sqrt[4]{c+d x} (a d+b c+2 b d x) \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)}+\frac{2 (a+b x)^{3/4} (c+d x)^{3/4}}{3 d}",1,"(2*(a + b*x)^(3/4)*(c + d*x)^(3/4))/(3*d) - (Sqrt[(a + b*x)*(c + d*x)]*Sqrt[(b*c + a*d + 2*b*d*x)^2]*Sqrt[(a*d + b*(c + 2*d*x))^2])/(Sqrt[b]*d^(3/2)*(a + b*x)^(1/4)*(c + d*x)^(1/4)*(b*c + a*d + 2*b*d*x)*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))) + ((b*c - a*d)^(5/2)*((a + b*x)*(c + d*x))^(1/4)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))*Sqrt[(a*d + b*(c + 2*d*x))^2/((b*c - a*d)^2*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))^2)]*EllipticE[2*ArcTan[(Sqrt[2]*b^(1/4)*d^(1/4)*((a + b*x)*(c + d*x))^(1/4))/Sqrt[b*c - a*d]], 1/2])/(Sqrt[2]*b^(3/4)*d^(7/4)*(a + b*x)^(1/4)*(c + d*x)^(1/4)*(b*c + a*d + 2*b*d*x)*Sqrt[(a*d + b*(c + 2*d*x))^2]) - ((b*c - a*d)^(5/2)*((a + b*x)*(c + d*x))^(1/4)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))*Sqrt[(a*d + b*(c + 2*d*x))^2/((b*c - a*d)^2*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))^2)]*EllipticF[2*ArcTan[(Sqrt[2]*b^(1/4)*d^(1/4)*((a + b*x)*(c + d*x))^(1/4))/Sqrt[b*c - a*d]], 1/2])/(2*Sqrt[2]*b^(3/4)*d^(7/4)*(a + b*x)^(1/4)*(c + d*x)^(1/4)*(b*c + a*d + 2*b*d*x)*Sqrt[(a*d + b*(c + 2*d*x))^2])","A",6,6,19,0.3158,1,"{50, 62, 623, 305, 220, 1196}"
1702,1,688,0,0.4954645,"\int \frac{1}{\sqrt[4]{a+b x} \sqrt[4]{c+d x}} \, dx","Int[1/((a + b*x)^(1/4)*(c + d*x)^(1/4)),x]","\frac{(b c-a d)^{3/2} \sqrt[4]{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{\sqrt{2} b^{3/4} d^{3/4} \sqrt[4]{a+b x} \sqrt[4]{c+d x} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}-\frac{\sqrt{2} (b c-a d)^{3/2} \sqrt[4]{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{b^{3/4} d^{3/4} \sqrt[4]{a+b x} \sqrt[4]{c+d x} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}+\frac{2 \sqrt{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \sqrt{(a d+b (c+2 d x))^2}}{\sqrt{b} \sqrt{d} \sqrt[4]{a+b x} \sqrt[4]{c+d x} (b c-a d) (a d+b c+2 b d x) \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)}","\frac{(b c-a d)^{3/2} \sqrt[4]{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{\sqrt{2} b^{3/4} d^{3/4} \sqrt[4]{a+b x} \sqrt[4]{c+d x} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}-\frac{\sqrt{2} (b c-a d)^{3/2} \sqrt[4]{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{b^{3/4} d^{3/4} \sqrt[4]{a+b x} \sqrt[4]{c+d x} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}+\frac{2 \sqrt{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \sqrt{(a d+b (c+2 d x))^2}}{\sqrt{b} \sqrt{d} \sqrt[4]{a+b x} \sqrt[4]{c+d x} (b c-a d) (a d+b c+2 b d x) \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)}",1,"(2*Sqrt[(a + b*x)*(c + d*x)]*Sqrt[(b*c + a*d + 2*b*d*x)^2]*Sqrt[(a*d + b*(c + 2*d*x))^2])/(Sqrt[b]*Sqrt[d]*(b*c - a*d)*(a + b*x)^(1/4)*(c + d*x)^(1/4)*(b*c + a*d + 2*b*d*x)*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))) - (Sqrt[2]*(b*c - a*d)^(3/2)*((a + b*x)*(c + d*x))^(1/4)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))*Sqrt[(a*d + b*(c + 2*d*x))^2/((b*c - a*d)^2*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))^2)]*EllipticE[2*ArcTan[(Sqrt[2]*b^(1/4)*d^(1/4)*((a + b*x)*(c + d*x))^(1/4))/Sqrt[b*c - a*d]], 1/2])/(b^(3/4)*d^(3/4)*(a + b*x)^(1/4)*(c + d*x)^(1/4)*(b*c + a*d + 2*b*d*x)*Sqrt[(a*d + b*(c + 2*d*x))^2]) + ((b*c - a*d)^(3/2)*((a + b*x)*(c + d*x))^(1/4)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))*Sqrt[(a*d + b*(c + 2*d*x))^2/((b*c - a*d)^2*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))^2)]*EllipticF[2*ArcTan[(Sqrt[2]*b^(1/4)*d^(1/4)*((a + b*x)*(c + d*x))^(1/4))/Sqrt[b*c - a*d]], 1/2])/(Sqrt[2]*b^(3/4)*d^(3/4)*(a + b*x)^(1/4)*(c + d*x)^(1/4)*(b*c + a*d + 2*b*d*x)*Sqrt[(a*d + b*(c + 2*d*x))^2])","A",5,5,19,0.2632,1,"{62, 623, 305, 220, 1196}"
1703,1,718,0,0.6091573,"\int \frac{1}{(a+b x)^{5/4} \sqrt[4]{c+d x}} \, dx","Int[1/((a + b*x)^(5/4)*(c + d*x)^(1/4)),x]","\frac{\sqrt{2} \sqrt[4]{d} \sqrt{b c-a d} \sqrt[4]{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{b^{3/4} \sqrt[4]{a+b x} \sqrt[4]{c+d x} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}-\frac{2 \sqrt{2} \sqrt[4]{d} \sqrt{b c-a d} \sqrt[4]{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{b^{3/4} \sqrt[4]{a+b x} \sqrt[4]{c+d x} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}-\frac{4 (c+d x)^{3/4}}{\sqrt[4]{a+b x} (b c-a d)}+\frac{4 \sqrt{d} \sqrt{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \sqrt{(a d+b (c+2 d x))^2}}{\sqrt{b} \sqrt[4]{a+b x} \sqrt[4]{c+d x} (b c-a d)^2 (a d+b c+2 b d x) \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)}","\frac{\sqrt{2} \sqrt[4]{d} \sqrt{b c-a d} \sqrt[4]{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{b^{3/4} \sqrt[4]{a+b x} \sqrt[4]{c+d x} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}-\frac{2 \sqrt{2} \sqrt[4]{d} \sqrt{b c-a d} \sqrt[4]{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{b^{3/4} \sqrt[4]{a+b x} \sqrt[4]{c+d x} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}-\frac{4 (c+d x)^{3/4}}{\sqrt[4]{a+b x} (b c-a d)}+\frac{4 \sqrt{d} \sqrt{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \sqrt{(a d+b (c+2 d x))^2}}{\sqrt{b} \sqrt[4]{a+b x} \sqrt[4]{c+d x} (b c-a d)^2 (a d+b c+2 b d x) \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)}",1,"(-4*(c + d*x)^(3/4))/((b*c - a*d)*(a + b*x)^(1/4)) + (4*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)]*Sqrt[(b*c + a*d + 2*b*d*x)^2]*Sqrt[(a*d + b*(c + 2*d*x))^2])/(Sqrt[b]*(b*c - a*d)^2*(a + b*x)^(1/4)*(c + d*x)^(1/4)*(b*c + a*d + 2*b*d*x)*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))) - (2*Sqrt[2]*d^(1/4)*Sqrt[b*c - a*d]*((a + b*x)*(c + d*x))^(1/4)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))*Sqrt[(a*d + b*(c + 2*d*x))^2/((b*c - a*d)^2*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))^2)]*EllipticE[2*ArcTan[(Sqrt[2]*b^(1/4)*d^(1/4)*((a + b*x)*(c + d*x))^(1/4))/Sqrt[b*c - a*d]], 1/2])/(b^(3/4)*(a + b*x)^(1/4)*(c + d*x)^(1/4)*(b*c + a*d + 2*b*d*x)*Sqrt[(a*d + b*(c + 2*d*x))^2]) + (Sqrt[2]*d^(1/4)*Sqrt[b*c - a*d]*((a + b*x)*(c + d*x))^(1/4)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))*Sqrt[(a*d + b*(c + 2*d*x))^2/((b*c - a*d)^2*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))^2)]*EllipticF[2*ArcTan[(Sqrt[2]*b^(1/4)*d^(1/4)*((a + b*x)*(c + d*x))^(1/4))/Sqrt[b*c - a*d]], 1/2])/(b^(3/4)*(a + b*x)^(1/4)*(c + d*x)^(1/4)*(b*c + a*d + 2*b*d*x)*Sqrt[(a*d + b*(c + 2*d*x))^2])","A",6,6,19,0.3158,1,"{51, 62, 623, 305, 220, 1196}"
1704,1,760,0,0.7260721,"\int \frac{1}{(a+b x)^{9/4} \sqrt[4]{c+d x}} \, dx","Int[1/((a + b*x)^(9/4)*(c + d*x)^(1/4)),x]","-\frac{2 \sqrt{2} d^{5/4} \sqrt[4]{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{5 b^{3/4} \sqrt[4]{a+b x} \sqrt[4]{c+d x} \sqrt{b c-a d} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}+\frac{4 \sqrt{2} d^{5/4} \sqrt[4]{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{5 b^{3/4} \sqrt[4]{a+b x} \sqrt[4]{c+d x} \sqrt{b c-a d} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}-\frac{8 d^{3/2} \sqrt{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \sqrt{(a d+b (c+2 d x))^2}}{5 \sqrt{b} \sqrt[4]{a+b x} \sqrt[4]{c+d x} (b c-a d)^3 (a d+b c+2 b d x) \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)}+\frac{8 d (c+d x)^{3/4}}{5 \sqrt[4]{a+b x} (b c-a d)^2}-\frac{4 (c+d x)^{3/4}}{5 (a+b x)^{5/4} (b c-a d)}","-\frac{2 \sqrt{2} d^{5/4} \sqrt[4]{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{5 b^{3/4} \sqrt[4]{a+b x} \sqrt[4]{c+d x} \sqrt{b c-a d} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}+\frac{4 \sqrt{2} d^{5/4} \sqrt[4]{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{5 b^{3/4} \sqrt[4]{a+b x} \sqrt[4]{c+d x} \sqrt{b c-a d} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}-\frac{8 d^{3/2} \sqrt{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \sqrt{(a d+b (c+2 d x))^2}}{5 \sqrt{b} \sqrt[4]{a+b x} \sqrt[4]{c+d x} (b c-a d)^3 (a d+b c+2 b d x) \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)}+\frac{8 d (c+d x)^{3/4}}{5 \sqrt[4]{a+b x} (b c-a d)^2}-\frac{4 (c+d x)^{3/4}}{5 (a+b x)^{5/4} (b c-a d)}",1,"(-4*(c + d*x)^(3/4))/(5*(b*c - a*d)*(a + b*x)^(5/4)) + (8*d*(c + d*x)^(3/4))/(5*(b*c - a*d)^2*(a + b*x)^(1/4)) - (8*d^(3/2)*Sqrt[(a + b*x)*(c + d*x)]*Sqrt[(b*c + a*d + 2*b*d*x)^2]*Sqrt[(a*d + b*(c + 2*d*x))^2])/(5*Sqrt[b]*(b*c - a*d)^3*(a + b*x)^(1/4)*(c + d*x)^(1/4)*(b*c + a*d + 2*b*d*x)*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))) + (4*Sqrt[2]*d^(5/4)*((a + b*x)*(c + d*x))^(1/4)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))*Sqrt[(a*d + b*(c + 2*d*x))^2/((b*c - a*d)^2*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))^2)]*EllipticE[2*ArcTan[(Sqrt[2]*b^(1/4)*d^(1/4)*((a + b*x)*(c + d*x))^(1/4))/Sqrt[b*c - a*d]], 1/2])/(5*b^(3/4)*Sqrt[b*c - a*d]*(a + b*x)^(1/4)*(c + d*x)^(1/4)*(b*c + a*d + 2*b*d*x)*Sqrt[(a*d + b*(c + 2*d*x))^2]) - (2*Sqrt[2]*d^(5/4)*((a + b*x)*(c + d*x))^(1/4)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))*Sqrt[(a*d + b*(c + 2*d*x))^2/((b*c - a*d)^2*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))^2)]*EllipticF[2*ArcTan[(Sqrt[2]*b^(1/4)*d^(1/4)*((a + b*x)*(c + d*x))^(1/4))/Sqrt[b*c - a*d]], 1/2])/(5*b^(3/4)*Sqrt[b*c - a*d]*(a + b*x)^(1/4)*(c + d*x)^(1/4)*(b*c + a*d + 2*b*d*x)*Sqrt[(a*d + b*(c + 2*d*x))^2])","A",7,6,19,0.3158,1,"{51, 62, 623, 305, 220, 1196}"
1705,1,167,0,0.1050181,"\int \frac{(a+b x)^{7/4}}{(c+d x)^{3/4}} \, dx","Int[(a + b*x)^(7/4)/(c + d*x)^(3/4),x]","-\frac{7 (a+b x)^{3/4} \sqrt[4]{c+d x} (b c-a d)}{8 d^2}-\frac{21 (b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{16 \sqrt[4]{b} d^{11/4}}+\frac{21 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{16 \sqrt[4]{b} d^{11/4}}+\frac{(a+b x)^{7/4} \sqrt[4]{c+d x}}{2 d}","-\frac{7 (a+b x)^{3/4} \sqrt[4]{c+d x} (b c-a d)}{8 d^2}-\frac{21 (b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{16 \sqrt[4]{b} d^{11/4}}+\frac{21 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{16 \sqrt[4]{b} d^{11/4}}+\frac{(a+b x)^{7/4} \sqrt[4]{c+d x}}{2 d}",1,"(-7*(b*c - a*d)*(a + b*x)^(3/4)*(c + d*x)^(1/4))/(8*d^2) + ((a + b*x)^(7/4)*(c + d*x)^(1/4))/(2*d) - (21*(b*c - a*d)^2*ArcTan[(d^(1/4)*(a + b*x)^(1/4))/(b^(1/4)*(c + d*x)^(1/4))])/(16*b^(1/4)*d^(11/4)) + (21*(b*c - a*d)^2*ArcTanh[(d^(1/4)*(a + b*x)^(1/4))/(b^(1/4)*(c + d*x)^(1/4))])/(16*b^(1/4)*d^(11/4))","A",7,6,19,0.3158,1,"{50, 63, 331, 298, 205, 208}"
1706,1,127,0,0.080577,"\int \frac{(a+b x)^{3/4}}{(c+d x)^{3/4}} \, dx","Int[(a + b*x)^(3/4)/(c + d*x)^(3/4),x]","\frac{3 (b c-a d) \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{2 \sqrt[4]{b} d^{7/4}}-\frac{3 (b c-a d) \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{2 \sqrt[4]{b} d^{7/4}}+\frac{(a+b x)^{3/4} \sqrt[4]{c+d x}}{d}","\frac{3 (b c-a d) \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{2 \sqrt[4]{b} d^{7/4}}-\frac{3 (b c-a d) \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{2 \sqrt[4]{b} d^{7/4}}+\frac{(a+b x)^{3/4} \sqrt[4]{c+d x}}{d}",1,"((a + b*x)^(3/4)*(c + d*x)^(1/4))/d + (3*(b*c - a*d)*ArcTan[(d^(1/4)*(a + b*x)^(1/4))/(b^(1/4)*(c + d*x)^(1/4))])/(2*b^(1/4)*d^(7/4)) - (3*(b*c - a*d)*ArcTanh[(d^(1/4)*(a + b*x)^(1/4))/(b^(1/4)*(c + d*x)^(1/4))])/(2*b^(1/4)*d^(7/4))","A",6,6,19,0.3158,1,"{50, 63, 331, 298, 205, 208}"
1707,1,85,0,0.0665139,"\int \frac{1}{\sqrt[4]{a+b x} (c+d x)^{3/4}} \, dx","Int[1/((a + b*x)^(1/4)*(c + d*x)^(3/4)),x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{\sqrt[4]{b} d^{3/4}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{\sqrt[4]{b} d^{3/4}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{\sqrt[4]{b} d^{3/4}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{\sqrt[4]{b} d^{3/4}}",1,"(-2*ArcTan[(d^(1/4)*(a + b*x)^(1/4))/(b^(1/4)*(c + d*x)^(1/4))])/(b^(1/4)*d^(3/4)) + (2*ArcTanh[(d^(1/4)*(a + b*x)^(1/4))/(b^(1/4)*(c + d*x)^(1/4))])/(b^(1/4)*d^(3/4))","A",5,5,19,0.2632,1,"{63, 331, 298, 205, 208}"
1708,1,30,0,0.0030378,"\int \frac{1}{(a+b x)^{5/4} (c+d x)^{3/4}} \, dx","Int[1/((a + b*x)^(5/4)*(c + d*x)^(3/4)),x]","-\frac{4 \sqrt[4]{c+d x}}{\sqrt[4]{a+b x} (b c-a d)}","-\frac{4 \sqrt[4]{c+d x}}{\sqrt[4]{a+b x} (b c-a d)}",1,"(-4*(c + d*x)^(1/4))/((b*c - a*d)*(a + b*x)^(1/4))","A",1,1,19,0.05263,1,"{37}"
1709,1,66,0,0.0093289,"\int \frac{1}{(a+b x)^{9/4} (c+d x)^{3/4}} \, dx","Int[1/((a + b*x)^(9/4)*(c + d*x)^(3/4)),x]","\frac{16 d \sqrt[4]{c+d x}}{5 \sqrt[4]{a+b x} (b c-a d)^2}-\frac{4 \sqrt[4]{c+d x}}{5 (a+b x)^{5/4} (b c-a d)}","\frac{16 d \sqrt[4]{c+d x}}{5 \sqrt[4]{a+b x} (b c-a d)^2}-\frac{4 \sqrt[4]{c+d x}}{5 (a+b x)^{5/4} (b c-a d)}",1,"(-4*(c + d*x)^(1/4))/(5*(b*c - a*d)*(a + b*x)^(5/4)) + (16*d*(c + d*x)^(1/4))/(5*(b*c - a*d)^2*(a + b*x)^(1/4))","A",2,2,19,0.1053,1,"{45, 37}"
1710,1,101,0,0.0174494,"\int \frac{1}{(a+b x)^{13/4} (c+d x)^{3/4}} \, dx","Int[1/((a + b*x)^(13/4)*(c + d*x)^(3/4)),x]","-\frac{128 d^2 \sqrt[4]{c+d x}}{45 \sqrt[4]{a+b x} (b c-a d)^3}+\frac{32 d \sqrt[4]{c+d x}}{45 (a+b x)^{5/4} (b c-a d)^2}-\frac{4 \sqrt[4]{c+d x}}{9 (a+b x)^{9/4} (b c-a d)}","-\frac{128 d^2 \sqrt[4]{c+d x}}{45 \sqrt[4]{a+b x} (b c-a d)^3}+\frac{32 d \sqrt[4]{c+d x}}{45 (a+b x)^{5/4} (b c-a d)^2}-\frac{4 \sqrt[4]{c+d x}}{9 (a+b x)^{9/4} (b c-a d)}",1,"(-4*(c + d*x)^(1/4))/(9*(b*c - a*d)*(a + b*x)^(9/4)) + (32*d*(c + d*x)^(1/4))/(45*(b*c - a*d)^2*(a + b*x)^(5/4)) - (128*d^2*(c + d*x)^(1/4))/(45*(b*c - a*d)^3*(a + b*x)^(1/4))","A",3,2,19,0.1053,1,"{45, 37}"
1711,1,136,0,0.0281114,"\int \frac{1}{(a+b x)^{17/4} (c+d x)^{3/4}} \, dx","Int[1/((a + b*x)^(17/4)*(c + d*x)^(3/4)),x]","\frac{512 d^3 \sqrt[4]{c+d x}}{195 \sqrt[4]{a+b x} (b c-a d)^4}-\frac{128 d^2 \sqrt[4]{c+d x}}{195 (a+b x)^{5/4} (b c-a d)^3}+\frac{16 d \sqrt[4]{c+d x}}{39 (a+b x)^{9/4} (b c-a d)^2}-\frac{4 \sqrt[4]{c+d x}}{13 (a+b x)^{13/4} (b c-a d)}","\frac{512 d^3 \sqrt[4]{c+d x}}{195 \sqrt[4]{a+b x} (b c-a d)^4}-\frac{128 d^2 \sqrt[4]{c+d x}}{195 (a+b x)^{5/4} (b c-a d)^3}+\frac{16 d \sqrt[4]{c+d x}}{39 (a+b x)^{9/4} (b c-a d)^2}-\frac{4 \sqrt[4]{c+d x}}{13 (a+b x)^{13/4} (b c-a d)}",1,"(-4*(c + d*x)^(1/4))/(13*(b*c - a*d)*(a + b*x)^(13/4)) + (16*d*(c + d*x)^(1/4))/(39*(b*c - a*d)^2*(a + b*x)^(9/4)) - (128*d^2*(c + d*x)^(1/4))/(195*(b*c - a*d)^3*(a + b*x)^(5/4)) + (512*d^3*(c + d*x)^(1/4))/(195*(b*c - a*d)^4*(a + b*x)^(1/4))","A",4,2,19,0.1053,1,"{45, 37}"
1712,1,332,0,0.2861695,"\int \frac{(a+b x)^{5/4}}{(c+d x)^{3/4}} \, dx","Int[(a + b*x)^(5/4)/(c + d*x)^(3/4),x]","-\frac{5 \sqrt[4]{a+b x} \sqrt[4]{c+d x} (b c-a d)}{3 d^2}+\frac{5 (b c-a d)^{5/2} ((a+b x) (c+d x))^{3/4} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{6 \sqrt{2} \sqrt[4]{b} d^{9/4} (a+b x)^{3/4} (c+d x)^{3/4} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}+\frac{2 (a+b x)^{5/4} \sqrt[4]{c+d x}}{3 d}","-\frac{5 \sqrt[4]{a+b x} \sqrt[4]{c+d x} (b c-a d)}{3 d^2}+\frac{5 (b c-a d)^{5/2} ((a+b x) (c+d x))^{3/4} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{6 \sqrt{2} \sqrt[4]{b} d^{9/4} (a+b x)^{3/4} (c+d x)^{3/4} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}+\frac{2 (a+b x)^{5/4} \sqrt[4]{c+d x}}{3 d}",1,"(-5*(b*c - a*d)*(a + b*x)^(1/4)*(c + d*x)^(1/4))/(3*d^2) + (2*(a + b*x)^(5/4)*(c + d*x)^(1/4))/(3*d) + (5*(b*c - a*d)^(5/2)*((a + b*x)*(c + d*x))^(3/4)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))*Sqrt[(a*d + b*(c + 2*d*x))^2/((b*c - a*d)^2*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))^2)]*EllipticF[2*ArcTan[(Sqrt[2]*b^(1/4)*d^(1/4)*((a + b*x)*(c + d*x))^(1/4))/Sqrt[b*c - a*d]], 1/2])/(6*Sqrt[2]*b^(1/4)*d^(9/4)*(a + b*x)^(3/4)*(c + d*x)^(3/4)*(b*c + a*d + 2*b*d*x)*Sqrt[(a*d + b*(c + 2*d*x))^2])","A",5,4,19,0.2105,1,"{50, 62, 623, 220}"
1713,1,295,0,0.2235178,"\int \frac{\sqrt[4]{a+b x}}{(c+d x)^{3/4}} \, dx","Int[(a + b*x)^(1/4)/(c + d*x)^(3/4),x]","\frac{2 \sqrt[4]{a+b x} \sqrt[4]{c+d x}}{d}-\frac{(b c-a d)^{3/2} ((a+b x) (c+d x))^{3/4} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{\sqrt{2} \sqrt[4]{b} d^{5/4} (a+b x)^{3/4} (c+d x)^{3/4} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}","\frac{2 \sqrt[4]{a+b x} \sqrt[4]{c+d x}}{d}-\frac{(b c-a d)^{3/2} ((a+b x) (c+d x))^{3/4} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{\sqrt{2} \sqrt[4]{b} d^{5/4} (a+b x)^{3/4} (c+d x)^{3/4} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}",1,"(2*(a + b*x)^(1/4)*(c + d*x)^(1/4))/d - ((b*c - a*d)^(3/2)*((a + b*x)*(c + d*x))^(3/4)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))*Sqrt[(a*d + b*(c + 2*d*x))^2/((b*c - a*d)^2*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))^2)]*EllipticF[2*ArcTan[(Sqrt[2]*b^(1/4)*d^(1/4)*((a + b*x)*(c + d*x))^(1/4))/Sqrt[b*c - a*d]], 1/2])/(Sqrt[2]*b^(1/4)*d^(5/4)*(a + b*x)^(3/4)*(c + d*x)^(3/4)*(b*c + a*d + 2*b*d*x)*Sqrt[(a*d + b*(c + 2*d*x))^2])","A",4,4,19,0.2105,1,"{50, 62, 623, 220}"
1714,1,270,0,0.1750625,"\int \frac{1}{(a+b x)^{3/4} (c+d x)^{3/4}} \, dx","Int[1/((a + b*x)^(3/4)*(c + d*x)^(3/4)),x]","\frac{\sqrt{2} \sqrt{b c-a d} ((a+b x) (c+d x))^{3/4} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{\sqrt[4]{b} \sqrt[4]{d} (a+b x)^{3/4} (c+d x)^{3/4} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}","\frac{\sqrt{2} \sqrt{b c-a d} ((a+b x) (c+d x))^{3/4} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{\sqrt[4]{b} \sqrt[4]{d} (a+b x)^{3/4} (c+d x)^{3/4} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}",1,"(Sqrt[2]*Sqrt[b*c - a*d]*((a + b*x)*(c + d*x))^(3/4)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))*Sqrt[(a*d + b*(c + 2*d*x))^2/((b*c - a*d)^2*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))^2)]*EllipticF[2*ArcTan[(Sqrt[2]*b^(1/4)*d^(1/4)*((a + b*x)*(c + d*x))^(1/4))/Sqrt[b*c - a*d]], 1/2])/(b^(1/4)*d^(1/4)*(a + b*x)^(3/4)*(c + d*x)^(3/4)*(b*c + a*d + 2*b*d*x)*Sqrt[(a*d + b*(c + 2*d*x))^2])","A",3,3,19,0.1579,1,"{62, 623, 220}"
1715,1,306,0,0.2151701,"\int \frac{1}{(a+b x)^{7/4} (c+d x)^{3/4}} \, dx","Int[1/((a + b*x)^(7/4)*(c + d*x)^(3/4)),x]","-\frac{2 \sqrt{2} d^{3/4} ((a+b x) (c+d x))^{3/4} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{3 \sqrt[4]{b} (a+b x)^{3/4} (c+d x)^{3/4} \sqrt{b c-a d} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}-\frac{4 \sqrt[4]{c+d x}}{3 (a+b x)^{3/4} (b c-a d)}","-\frac{2 \sqrt{2} d^{3/4} ((a+b x) (c+d x))^{3/4} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{3 \sqrt[4]{b} (a+b x)^{3/4} (c+d x)^{3/4} \sqrt{b c-a d} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}-\frac{4 \sqrt[4]{c+d x}}{3 (a+b x)^{3/4} (b c-a d)}",1,"(-4*(c + d*x)^(1/4))/(3*(b*c - a*d)*(a + b*x)^(3/4)) - (2*Sqrt[2]*d^(3/4)*((a + b*x)*(c + d*x))^(3/4)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))*Sqrt[(a*d + b*(c + 2*d*x))^2/((b*c - a*d)^2*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))^2)]*EllipticF[2*ArcTan[(Sqrt[2]*b^(1/4)*d^(1/4)*((a + b*x)*(c + d*x))^(1/4))/Sqrt[b*c - a*d]], 1/2])/(3*b^(1/4)*Sqrt[b*c - a*d]*(a + b*x)^(3/4)*(c + d*x)^(3/4)*(b*c + a*d + 2*b*d*x)*Sqrt[(a*d + b*(c + 2*d*x))^2])","A",4,4,19,0.2105,1,"{51, 62, 623, 220}"
1716,1,339,0,0.2796115,"\int \frac{1}{(a+b x)^{11/4} (c+d x)^{3/4}} \, dx","Int[1/((a + b*x)^(11/4)*(c + d*x)^(3/4)),x]","\frac{4 \sqrt{2} d^{7/4} ((a+b x) (c+d x))^{3/4} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{7 \sqrt[4]{b} (a+b x)^{3/4} (c+d x)^{3/4} (b c-a d)^{3/2} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}+\frac{8 d \sqrt[4]{c+d x}}{7 (a+b x)^{3/4} (b c-a d)^2}-\frac{4 \sqrt[4]{c+d x}}{7 (a+b x)^{7/4} (b c-a d)}","\frac{4 \sqrt{2} d^{7/4} ((a+b x) (c+d x))^{3/4} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{7 \sqrt[4]{b} (a+b x)^{3/4} (c+d x)^{3/4} (b c-a d)^{3/2} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}+\frac{8 d \sqrt[4]{c+d x}}{7 (a+b x)^{3/4} (b c-a d)^2}-\frac{4 \sqrt[4]{c+d x}}{7 (a+b x)^{7/4} (b c-a d)}",1,"(-4*(c + d*x)^(1/4))/(7*(b*c - a*d)*(a + b*x)^(7/4)) + (8*d*(c + d*x)^(1/4))/(7*(b*c - a*d)^2*(a + b*x)^(3/4)) + (4*Sqrt[2]*d^(7/4)*((a + b*x)*(c + d*x))^(3/4)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))*Sqrt[(a*d + b*(c + 2*d*x))^2/((b*c - a*d)^2*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))^2)]*EllipticF[2*ArcTan[(Sqrt[2]*b^(1/4)*d^(1/4)*((a + b*x)*(c + d*x))^(1/4))/Sqrt[b*c - a*d]], 1/2])/(7*b^(1/4)*(b*c - a*d)^(3/2)*(a + b*x)^(3/4)*(c + d*x)^(3/4)*(b*c + a*d + 2*b*d*x)*Sqrt[(a*d + b*(c + 2*d*x))^2])","A",5,4,19,0.2105,1,"{51, 62, 623, 220}"
1717,1,152,0,0.0871252,"\int \frac{(a+b x)^{5/4}}{(c+d x)^{5/4}} \, dx","Int[(a + b*x)^(5/4)/(c + d*x)^(5/4),x]","\frac{5 b \sqrt[4]{a+b x} (c+d x)^{3/4}}{d^2}-\frac{5 \sqrt[4]{b} (b c-a d) \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{2 d^{9/4}}-\frac{5 \sqrt[4]{b} (b c-a d) \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{2 d^{9/4}}-\frac{4 (a+b x)^{5/4}}{d \sqrt[4]{c+d x}}","\frac{5 b \sqrt[4]{a+b x} (c+d x)^{3/4}}{d^2}-\frac{5 \sqrt[4]{b} (b c-a d) \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{2 d^{9/4}}-\frac{5 \sqrt[4]{b} (b c-a d) \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{2 d^{9/4}}-\frac{4 (a+b x)^{5/4}}{d \sqrt[4]{c+d x}}",1,"(-4*(a + b*x)^(5/4))/(d*(c + d*x)^(1/4)) + (5*b*(a + b*x)^(1/4)*(c + d*x)^(3/4))/d^2 - (5*b^(1/4)*(b*c - a*d)*ArcTan[(d^(1/4)*(a + b*x)^(1/4))/(b^(1/4)*(c + d*x)^(1/4))])/(2*d^(9/4)) - (5*b^(1/4)*(b*c - a*d)*ArcTanh[(d^(1/4)*(a + b*x)^(1/4))/(b^(1/4)*(c + d*x)^(1/4))])/(2*d^(9/4))","A",7,7,19,0.3684,1,"{47, 50, 63, 240, 212, 208, 205}"
1718,1,108,0,0.0652558,"\int \frac{\sqrt[4]{a+b x}}{(c+d x)^{5/4}} \, dx","Int[(a + b*x)^(1/4)/(c + d*x)^(5/4),x]","\frac{2 \sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{d^{5/4}}+\frac{2 \sqrt[4]{b} \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{d^{5/4}}-\frac{4 \sqrt[4]{a+b x}}{d \sqrt[4]{c+d x}}","\frac{2 \sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{d^{5/4}}+\frac{2 \sqrt[4]{b} \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{d^{5/4}}-\frac{4 \sqrt[4]{a+b x}}{d \sqrt[4]{c+d x}}",1,"(-4*(a + b*x)^(1/4))/(d*(c + d*x)^(1/4)) + (2*b^(1/4)*ArcTan[(d^(1/4)*(a + b*x)^(1/4))/(b^(1/4)*(c + d*x)^(1/4))])/d^(5/4) + (2*b^(1/4)*ArcTanh[(d^(1/4)*(a + b*x)^(1/4))/(b^(1/4)*(c + d*x)^(1/4))])/d^(5/4)","A",6,6,19,0.3158,1,"{47, 63, 240, 212, 208, 205}"
1719,1,30,0,0.002851,"\int \frac{1}{(a+b x)^{3/4} (c+d x)^{5/4}} \, dx","Int[1/((a + b*x)^(3/4)*(c + d*x)^(5/4)),x]","\frac{4 \sqrt[4]{a+b x}}{\sqrt[4]{c+d x} (b c-a d)}","\frac{4 \sqrt[4]{a+b x}}{\sqrt[4]{c+d x} (b c-a d)}",1,"(4*(a + b*x)^(1/4))/((b*c - a*d)*(c + d*x)^(1/4))","A",1,1,19,0.05263,1,"{37}"
1720,1,66,0,0.008442,"\int \frac{1}{(a+b x)^{7/4} (c+d x)^{5/4}} \, dx","Int[1/((a + b*x)^(7/4)*(c + d*x)^(5/4)),x]","-\frac{16 d \sqrt[4]{a+b x}}{3 \sqrt[4]{c+d x} (b c-a d)^2}-\frac{4}{3 (a+b x)^{3/4} \sqrt[4]{c+d x} (b c-a d)}","-\frac{16 d \sqrt[4]{a+b x}}{3 \sqrt[4]{c+d x} (b c-a d)^2}-\frac{4}{3 (a+b x)^{3/4} \sqrt[4]{c+d x} (b c-a d)}",1,"-4/(3*(b*c - a*d)*(a + b*x)^(3/4)*(c + d*x)^(1/4)) - (16*d*(a + b*x)^(1/4))/(3*(b*c - a*d)^2*(c + d*x)^(1/4))","A",2,2,19,0.1053,1,"{45, 37}"
1721,1,101,0,0.0165107,"\int \frac{1}{(a+b x)^{11/4} (c+d x)^{5/4}} \, dx","Int[1/((a + b*x)^(11/4)*(c + d*x)^(5/4)),x]","\frac{128 d^2 \sqrt[4]{a+b x}}{21 \sqrt[4]{c+d x} (b c-a d)^3}+\frac{32 d}{21 (a+b x)^{3/4} \sqrt[4]{c+d x} (b c-a d)^2}-\frac{4}{7 (a+b x)^{7/4} \sqrt[4]{c+d x} (b c-a d)}","\frac{128 d^2 \sqrt[4]{a+b x}}{21 \sqrt[4]{c+d x} (b c-a d)^3}+\frac{32 d}{21 (a+b x)^{3/4} \sqrt[4]{c+d x} (b c-a d)^2}-\frac{4}{7 (a+b x)^{7/4} \sqrt[4]{c+d x} (b c-a d)}",1,"-4/(7*(b*c - a*d)*(a + b*x)^(7/4)*(c + d*x)^(1/4)) + (32*d)/(21*(b*c - a*d)^2*(a + b*x)^(3/4)*(c + d*x)^(1/4)) + (128*d^2*(a + b*x)^(1/4))/(21*(b*c - a*d)^3*(c + d*x)^(1/4))","A",3,2,19,0.1053,1,"{45, 37}"
1722,1,136,0,0.027462,"\int \frac{1}{(a+b x)^{15/4} (c+d x)^{5/4}} \, dx","Int[1/((a + b*x)^(15/4)*(c + d*x)^(5/4)),x]","-\frac{512 d^3 \sqrt[4]{a+b x}}{77 \sqrt[4]{c+d x} (b c-a d)^4}-\frac{128 d^2}{77 (a+b x)^{3/4} \sqrt[4]{c+d x} (b c-a d)^3}+\frac{48 d}{77 (a+b x)^{7/4} \sqrt[4]{c+d x} (b c-a d)^2}-\frac{4}{11 (a+b x)^{11/4} \sqrt[4]{c+d x} (b c-a d)}","-\frac{512 d^3 \sqrt[4]{a+b x}}{77 \sqrt[4]{c+d x} (b c-a d)^4}-\frac{128 d^2}{77 (a+b x)^{3/4} \sqrt[4]{c+d x} (b c-a d)^3}+\frac{48 d}{77 (a+b x)^{7/4} \sqrt[4]{c+d x} (b c-a d)^2}-\frac{4}{11 (a+b x)^{11/4} \sqrt[4]{c+d x} (b c-a d)}",1,"-4/(11*(b*c - a*d)*(a + b*x)^(11/4)*(c + d*x)^(1/4)) + (48*d)/(77*(b*c - a*d)^2*(a + b*x)^(7/4)*(c + d*x)^(1/4)) - (128*d^2)/(77*(b*c - a*d)^3*(a + b*x)^(3/4)*(c + d*x)^(1/4)) - (512*d^3*(a + b*x)^(1/4))/(77*(b*c - a*d)^4*(c + d*x)^(1/4))","A",4,2,19,0.1053,1,"{45, 37}"
1723,1,776,0,0.8799762,"\int \frac{(a+b x)^{11/4}}{(c+d x)^{5/4}} \, dx","Int[(a + b*x)^(11/4)/(c + d*x)^(5/4),x]","-\frac{77 b (a+b x)^{3/4} (c+d x)^{3/4} (b c-a d)}{15 d^3}+\frac{77 \sqrt{b} (b c-a d) \sqrt{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \sqrt{(a d+b (c+2 d x))^2}}{10 d^{7/2} \sqrt[4]{a+b x} \sqrt[4]{c+d x} (a d+b c+2 b d x) \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)}+\frac{22 b (a+b x)^{7/4} (c+d x)^{3/4}}{5 d^2}+\frac{77 \sqrt[4]{b} (b c-a d)^{7/2} \sqrt[4]{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{20 \sqrt{2} d^{15/4} \sqrt[4]{a+b x} \sqrt[4]{c+d x} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}-\frac{77 \sqrt[4]{b} (b c-a d)^{7/2} \sqrt[4]{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{10 \sqrt{2} d^{15/4} \sqrt[4]{a+b x} \sqrt[4]{c+d x} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}-\frac{4 (a+b x)^{11/4}}{d \sqrt[4]{c+d x}}","-\frac{77 b (a+b x)^{3/4} (c+d x)^{3/4} (b c-a d)}{15 d^3}+\frac{77 \sqrt{b} (b c-a d) \sqrt{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \sqrt{(a d+b (c+2 d x))^2}}{10 d^{7/2} \sqrt[4]{a+b x} \sqrt[4]{c+d x} (a d+b c+2 b d x) \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)}+\frac{22 b (a+b x)^{7/4} (c+d x)^{3/4}}{5 d^2}+\frac{77 \sqrt[4]{b} (b c-a d)^{7/2} \sqrt[4]{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{20 \sqrt{2} d^{15/4} \sqrt[4]{a+b x} \sqrt[4]{c+d x} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}-\frac{77 \sqrt[4]{b} (b c-a d)^{7/2} \sqrt[4]{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{10 \sqrt{2} d^{15/4} \sqrt[4]{a+b x} \sqrt[4]{c+d x} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}-\frac{4 (a+b x)^{11/4}}{d \sqrt[4]{c+d x}}",1,"(-4*(a + b*x)^(11/4))/(d*(c + d*x)^(1/4)) - (77*b*(b*c - a*d)*(a + b*x)^(3/4)*(c + d*x)^(3/4))/(15*d^3) + (22*b*(a + b*x)^(7/4)*(c + d*x)^(3/4))/(5*d^2) + (77*Sqrt[b]*(b*c - a*d)*Sqrt[(a + b*x)*(c + d*x)]*Sqrt[(b*c + a*d + 2*b*d*x)^2]*Sqrt[(a*d + b*(c + 2*d*x))^2])/(10*d^(7/2)*(a + b*x)^(1/4)*(c + d*x)^(1/4)*(b*c + a*d + 2*b*d*x)*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))) - (77*b^(1/4)*(b*c - a*d)^(7/2)*((a + b*x)*(c + d*x))^(1/4)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))*Sqrt[(a*d + b*(c + 2*d*x))^2/((b*c - a*d)^2*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))^2)]*EllipticE[2*ArcTan[(Sqrt[2]*b^(1/4)*d^(1/4)*((a + b*x)*(c + d*x))^(1/4))/Sqrt[b*c - a*d]], 1/2])/(10*Sqrt[2]*d^(15/4)*(a + b*x)^(1/4)*(c + d*x)^(1/4)*(b*c + a*d + 2*b*d*x)*Sqrt[(a*d + b*(c + 2*d*x))^2]) + (77*b^(1/4)*(b*c - a*d)^(7/2)*((a + b*x)*(c + d*x))^(1/4)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))*Sqrt[(a*d + b*(c + 2*d*x))^2/((b*c - a*d)^2*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))^2)]*EllipticF[2*ArcTan[(Sqrt[2]*b^(1/4)*d^(1/4)*((a + b*x)*(c + d*x))^(1/4))/Sqrt[b*c - a*d]], 1/2])/(20*Sqrt[2]*d^(15/4)*(a + b*x)^(1/4)*(c + d*x)^(1/4)*(b*c + a*d + 2*b*d*x)*Sqrt[(a*d + b*(c + 2*d*x))^2])","A",8,7,19,0.3684,1,"{47, 50, 62, 623, 305, 220, 1196}"
1724,1,730,0,0.7252117,"\int \frac{(a+b x)^{7/4}}{(c+d x)^{5/4}} \, dx","Int[(a + b*x)^(7/4)/(c + d*x)^(5/4),x]","\frac{14 b (a+b x)^{3/4} (c+d x)^{3/4}}{3 d^2}-\frac{7 \sqrt{b} \sqrt{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \sqrt{(a d+b (c+2 d x))^2}}{d^{5/2} \sqrt[4]{a+b x} \sqrt[4]{c+d x} (a d+b c+2 b d x) \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)}-\frac{7 \sqrt[4]{b} (b c-a d)^{5/2} \sqrt[4]{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{2 \sqrt{2} d^{11/4} \sqrt[4]{a+b x} \sqrt[4]{c+d x} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}+\frac{7 \sqrt[4]{b} (b c-a d)^{5/2} \sqrt[4]{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{\sqrt{2} d^{11/4} \sqrt[4]{a+b x} \sqrt[4]{c+d x} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}-\frac{4 (a+b x)^{7/4}}{d \sqrt[4]{c+d x}}","\frac{14 b (a+b x)^{3/4} (c+d x)^{3/4}}{3 d^2}-\frac{7 \sqrt{b} \sqrt{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \sqrt{(a d+b (c+2 d x))^2}}{d^{5/2} \sqrt[4]{a+b x} \sqrt[4]{c+d x} (a d+b c+2 b d x) \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)}-\frac{7 \sqrt[4]{b} (b c-a d)^{5/2} \sqrt[4]{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{2 \sqrt{2} d^{11/4} \sqrt[4]{a+b x} \sqrt[4]{c+d x} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}+\frac{7 \sqrt[4]{b} (b c-a d)^{5/2} \sqrt[4]{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{\sqrt{2} d^{11/4} \sqrt[4]{a+b x} \sqrt[4]{c+d x} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}-\frac{4 (a+b x)^{7/4}}{d \sqrt[4]{c+d x}}",1,"(-4*(a + b*x)^(7/4))/(d*(c + d*x)^(1/4)) + (14*b*(a + b*x)^(3/4)*(c + d*x)^(3/4))/(3*d^2) - (7*Sqrt[b]*Sqrt[(a + b*x)*(c + d*x)]*Sqrt[(b*c + a*d + 2*b*d*x)^2]*Sqrt[(a*d + b*(c + 2*d*x))^2])/(d^(5/2)*(a + b*x)^(1/4)*(c + d*x)^(1/4)*(b*c + a*d + 2*b*d*x)*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))) + (7*b^(1/4)*(b*c - a*d)^(5/2)*((a + b*x)*(c + d*x))^(1/4)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))*Sqrt[(a*d + b*(c + 2*d*x))^2/((b*c - a*d)^2*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))^2)]*EllipticE[2*ArcTan[(Sqrt[2]*b^(1/4)*d^(1/4)*((a + b*x)*(c + d*x))^(1/4))/Sqrt[b*c - a*d]], 1/2])/(Sqrt[2]*d^(11/4)*(a + b*x)^(1/4)*(c + d*x)^(1/4)*(b*c + a*d + 2*b*d*x)*Sqrt[(a*d + b*(c + 2*d*x))^2]) - (7*b^(1/4)*(b*c - a*d)^(5/2)*((a + b*x)*(c + d*x))^(1/4)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))*Sqrt[(a*d + b*(c + 2*d*x))^2/((b*c - a*d)^2*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))^2)]*EllipticF[2*ArcTan[(Sqrt[2]*b^(1/4)*d^(1/4)*((a + b*x)*(c + d*x))^(1/4))/Sqrt[b*c - a*d]], 1/2])/(2*Sqrt[2]*d^(11/4)*(a + b*x)^(1/4)*(c + d*x)^(1/4)*(b*c + a*d + 2*b*d*x)*Sqrt[(a*d + b*(c + 2*d*x))^2])","A",7,7,19,0.3684,1,"{47, 50, 62, 623, 305, 220, 1196}"
1725,1,712,0,0.6086525,"\int \frac{(a+b x)^{3/4}}{(c+d x)^{5/4}} \, dx","Int[(a + b*x)^(3/4)/(c + d*x)^(5/4),x]","\frac{6 \sqrt{b} \sqrt{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \sqrt{(a d+b (c+2 d x))^2}}{d^{3/2} \sqrt[4]{a+b x} \sqrt[4]{c+d x} (b c-a d) (a d+b c+2 b d x) \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)}+\frac{3 \sqrt[4]{b} (b c-a d)^{3/2} \sqrt[4]{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{\sqrt{2} d^{7/4} \sqrt[4]{a+b x} \sqrt[4]{c+d x} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}-\frac{3 \sqrt{2} \sqrt[4]{b} (b c-a d)^{3/2} \sqrt[4]{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{d^{7/4} \sqrt[4]{a+b x} \sqrt[4]{c+d x} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}-\frac{4 (a+b x)^{3/4}}{d \sqrt[4]{c+d x}}","\frac{6 \sqrt{b} \sqrt{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \sqrt{(a d+b (c+2 d x))^2}}{d^{3/2} \sqrt[4]{a+b x} \sqrt[4]{c+d x} (b c-a d) (a d+b c+2 b d x) \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)}+\frac{3 \sqrt[4]{b} (b c-a d)^{3/2} \sqrt[4]{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{\sqrt{2} d^{7/4} \sqrt[4]{a+b x} \sqrt[4]{c+d x} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}-\frac{3 \sqrt{2} \sqrt[4]{b} (b c-a d)^{3/2} \sqrt[4]{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{d^{7/4} \sqrt[4]{a+b x} \sqrt[4]{c+d x} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}-\frac{4 (a+b x)^{3/4}}{d \sqrt[4]{c+d x}}",1,"(-4*(a + b*x)^(3/4))/(d*(c + d*x)^(1/4)) + (6*Sqrt[b]*Sqrt[(a + b*x)*(c + d*x)]*Sqrt[(b*c + a*d + 2*b*d*x)^2]*Sqrt[(a*d + b*(c + 2*d*x))^2])/(d^(3/2)*(b*c - a*d)*(a + b*x)^(1/4)*(c + d*x)^(1/4)*(b*c + a*d + 2*b*d*x)*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))) - (3*Sqrt[2]*b^(1/4)*(b*c - a*d)^(3/2)*((a + b*x)*(c + d*x))^(1/4)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))*Sqrt[(a*d + b*(c + 2*d*x))^2/((b*c - a*d)^2*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))^2)]*EllipticE[2*ArcTan[(Sqrt[2]*b^(1/4)*d^(1/4)*((a + b*x)*(c + d*x))^(1/4))/Sqrt[b*c - a*d]], 1/2])/(d^(7/4)*(a + b*x)^(1/4)*(c + d*x)^(1/4)*(b*c + a*d + 2*b*d*x)*Sqrt[(a*d + b*(c + 2*d*x))^2]) + (3*b^(1/4)*(b*c - a*d)^(3/2)*((a + b*x)*(c + d*x))^(1/4)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))*Sqrt[(a*d + b*(c + 2*d*x))^2/((b*c - a*d)^2*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))^2)]*EllipticF[2*ArcTan[(Sqrt[2]*b^(1/4)*d^(1/4)*((a + b*x)*(c + d*x))^(1/4))/Sqrt[b*c - a*d]], 1/2])/(Sqrt[2]*d^(7/4)*(a + b*x)^(1/4)*(c + d*x)^(1/4)*(b*c + a*d + 2*b*d*x)*Sqrt[(a*d + b*(c + 2*d*x))^2])","A",6,6,19,0.3158,1,"{47, 62, 623, 305, 220, 1196}"
1726,1,719,0,0.6116069,"\int \frac{1}{\sqrt[4]{a+b x} (c+d x)^{5/4}} \, dx","Int[1/((a + b*x)^(1/4)*(c + d*x)^(5/4)),x]","-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{b c-a d} \sqrt[4]{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{d^{3/4} \sqrt[4]{a+b x} \sqrt[4]{c+d x} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}+\frac{2 \sqrt{2} \sqrt[4]{b} \sqrt{b c-a d} \sqrt[4]{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{d^{3/4} \sqrt[4]{a+b x} \sqrt[4]{c+d x} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}-\frac{4 \sqrt{b} \sqrt{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \sqrt{(a d+b (c+2 d x))^2}}{\sqrt{d} \sqrt[4]{a+b x} \sqrt[4]{c+d x} (b c-a d)^2 (a d+b c+2 b d x) \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)}+\frac{4 (a+b x)^{3/4}}{\sqrt[4]{c+d x} (b c-a d)}","-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{b c-a d} \sqrt[4]{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{d^{3/4} \sqrt[4]{a+b x} \sqrt[4]{c+d x} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}+\frac{2 \sqrt{2} \sqrt[4]{b} \sqrt{b c-a d} \sqrt[4]{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{d^{3/4} \sqrt[4]{a+b x} \sqrt[4]{c+d x} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}-\frac{4 \sqrt{b} \sqrt{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \sqrt{(a d+b (c+2 d x))^2}}{\sqrt{d} \sqrt[4]{a+b x} \sqrt[4]{c+d x} (b c-a d)^2 (a d+b c+2 b d x) \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)}+\frac{4 (a+b x)^{3/4}}{\sqrt[4]{c+d x} (b c-a d)}",1,"(4*(a + b*x)^(3/4))/((b*c - a*d)*(c + d*x)^(1/4)) - (4*Sqrt[b]*Sqrt[(a + b*x)*(c + d*x)]*Sqrt[(b*c + a*d + 2*b*d*x)^2]*Sqrt[(a*d + b*(c + 2*d*x))^2])/(Sqrt[d]*(b*c - a*d)^2*(a + b*x)^(1/4)*(c + d*x)^(1/4)*(b*c + a*d + 2*b*d*x)*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))) + (2*Sqrt[2]*b^(1/4)*Sqrt[b*c - a*d]*((a + b*x)*(c + d*x))^(1/4)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))*Sqrt[(a*d + b*(c + 2*d*x))^2/((b*c - a*d)^2*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))^2)]*EllipticE[2*ArcTan[(Sqrt[2]*b^(1/4)*d^(1/4)*((a + b*x)*(c + d*x))^(1/4))/Sqrt[b*c - a*d]], 1/2])/(d^(3/4)*(a + b*x)^(1/4)*(c + d*x)^(1/4)*(b*c + a*d + 2*b*d*x)*Sqrt[(a*d + b*(c + 2*d*x))^2]) - (Sqrt[2]*b^(1/4)*Sqrt[b*c - a*d]*((a + b*x)*(c + d*x))^(1/4)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))*Sqrt[(a*d + b*(c + 2*d*x))^2/((b*c - a*d)^2*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))^2)]*EllipticF[2*ArcTan[(Sqrt[2]*b^(1/4)*d^(1/4)*((a + b*x)*(c + d*x))^(1/4))/Sqrt[b*c - a*d]], 1/2])/(d^(3/4)*(a + b*x)^(1/4)*(c + d*x)^(1/4)*(b*c + a*d + 2*b*d*x)*Sqrt[(a*d + b*(c + 2*d*x))^2])","A",6,6,19,0.3158,1,"{51, 62, 623, 305, 220, 1196}"
1727,1,750,0,0.739789,"\int \frac{1}{(a+b x)^{5/4} (c+d x)^{5/4}} \, dx","Int[1/((a + b*x)^(5/4)*(c + d*x)^(5/4)),x]","-\frac{8 d (a+b x)^{3/4}}{\sqrt[4]{c+d x} (b c-a d)^2}+\frac{8 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \sqrt{(a d+b (c+2 d x))^2}}{\sqrt[4]{a+b x} \sqrt[4]{c+d x} (b c-a d)^3 (a d+b c+2 b d x) \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)}-\frac{4}{\sqrt[4]{a+b x} \sqrt[4]{c+d x} (b c-a d)}+\frac{2 \sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{\sqrt[4]{a+b x} \sqrt[4]{c+d x} \sqrt{b c-a d} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}-\frac{4 \sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{\sqrt[4]{a+b x} \sqrt[4]{c+d x} \sqrt{b c-a d} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}","-\frac{8 d (a+b x)^{3/4}}{\sqrt[4]{c+d x} (b c-a d)^2}+\frac{8 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \sqrt{(a d+b (c+2 d x))^2}}{\sqrt[4]{a+b x} \sqrt[4]{c+d x} (b c-a d)^3 (a d+b c+2 b d x) \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)}-\frac{4}{\sqrt[4]{a+b x} \sqrt[4]{c+d x} (b c-a d)}+\frac{2 \sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{\sqrt[4]{a+b x} \sqrt[4]{c+d x} \sqrt{b c-a d} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}-\frac{4 \sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{\sqrt[4]{a+b x} \sqrt[4]{c+d x} \sqrt{b c-a d} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}",1,"-4/((b*c - a*d)*(a + b*x)^(1/4)*(c + d*x)^(1/4)) - (8*d*(a + b*x)^(3/4))/((b*c - a*d)^2*(c + d*x)^(1/4)) + (8*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)]*Sqrt[(b*c + a*d + 2*b*d*x)^2]*Sqrt[(a*d + b*(c + 2*d*x))^2])/((b*c - a*d)^3*(a + b*x)^(1/4)*(c + d*x)^(1/4)*(b*c + a*d + 2*b*d*x)*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))) - (4*Sqrt[2]*b^(1/4)*d^(1/4)*((a + b*x)*(c + d*x))^(1/4)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))*Sqrt[(a*d + b*(c + 2*d*x))^2/((b*c - a*d)^2*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))^2)]*EllipticE[2*ArcTan[(Sqrt[2]*b^(1/4)*d^(1/4)*((a + b*x)*(c + d*x))^(1/4))/Sqrt[b*c - a*d]], 1/2])/(Sqrt[b*c - a*d]*(a + b*x)^(1/4)*(c + d*x)^(1/4)*(b*c + a*d + 2*b*d*x)*Sqrt[(a*d + b*(c + 2*d*x))^2]) + (2*Sqrt[2]*b^(1/4)*d^(1/4)*((a + b*x)*(c + d*x))^(1/4)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))*Sqrt[(a*d + b*(c + 2*d*x))^2/((b*c - a*d)^2*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))^2)]*EllipticF[2*ArcTan[(Sqrt[2]*b^(1/4)*d^(1/4)*((a + b*x)*(c + d*x))^(1/4))/Sqrt[b*c - a*d]], 1/2])/(Sqrt[b*c - a*d]*(a + b*x)^(1/4)*(c + d*x)^(1/4)*(b*c + a*d + 2*b*d*x)*Sqrt[(a*d + b*(c + 2*d*x))^2])","A",7,6,19,0.3158,1,"{51, 62, 623, 305, 220, 1196}"
1728,1,795,0,0.864912,"\int \frac{1}{(a+b x)^{9/4} (c+d x)^{5/4}} \, dx","Int[1/((a + b*x)^(9/4)*(c + d*x)^(5/4)),x]","\frac{48 (a+b x)^{3/4} d^2}{5 (b c-a d)^3 \sqrt[4]{c+d x}}-\frac{48 \sqrt{b} \sqrt{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \sqrt{(a d+b (c+2 d x))^2} d^{3/2}}{5 (b c-a d)^4 \sqrt[4]{a+b x} \sqrt[4]{c+d x} (b c+a d+2 b d x) \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)}+\frac{24 \sqrt{2} \sqrt[4]{b} \sqrt[4]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right) d^{5/4}}{5 (b c-a d)^{3/2} \sqrt[4]{a+b x} \sqrt[4]{c+d x} (b c+a d+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}-\frac{12 \sqrt{2} \sqrt[4]{b} \sqrt[4]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right) d^{5/4}}{5 (b c-a d)^{3/2} \sqrt[4]{a+b x} \sqrt[4]{c+d x} (b c+a d+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}+\frac{24 d}{5 (b c-a d)^2 \sqrt[4]{a+b x} \sqrt[4]{c+d x}}-\frac{4}{5 (b c-a d) (a+b x)^{5/4} \sqrt[4]{c+d x}}","\frac{48 (a+b x)^{3/4} d^2}{5 (b c-a d)^3 \sqrt[4]{c+d x}}-\frac{48 \sqrt{b} \sqrt{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \sqrt{(a d+b (c+2 d x))^2} d^{3/2}}{5 (b c-a d)^4 \sqrt[4]{a+b x} \sqrt[4]{c+d x} (b c+a d+2 b d x) \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)}+\frac{24 \sqrt{2} \sqrt[4]{b} \sqrt[4]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right) d^{5/4}}{5 (b c-a d)^{3/2} \sqrt[4]{a+b x} \sqrt[4]{c+d x} (b c+a d+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}-\frac{12 \sqrt{2} \sqrt[4]{b} \sqrt[4]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right) d^{5/4}}{5 (b c-a d)^{3/2} \sqrt[4]{a+b x} \sqrt[4]{c+d x} (b c+a d+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}+\frac{24 d}{5 (b c-a d)^2 \sqrt[4]{a+b x} \sqrt[4]{c+d x}}-\frac{4}{5 (b c-a d) (a+b x)^{5/4} \sqrt[4]{c+d x}}",1,"-4/(5*(b*c - a*d)*(a + b*x)^(5/4)*(c + d*x)^(1/4)) + (24*d)/(5*(b*c - a*d)^2*(a + b*x)^(1/4)*(c + d*x)^(1/4)) + (48*d^2*(a + b*x)^(3/4))/(5*(b*c - a*d)^3*(c + d*x)^(1/4)) - (48*Sqrt[b]*d^(3/2)*Sqrt[(a + b*x)*(c + d*x)]*Sqrt[(b*c + a*d + 2*b*d*x)^2]*Sqrt[(a*d + b*(c + 2*d*x))^2])/(5*(b*c - a*d)^4*(a + b*x)^(1/4)*(c + d*x)^(1/4)*(b*c + a*d + 2*b*d*x)*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))) + (24*Sqrt[2]*b^(1/4)*d^(5/4)*((a + b*x)*(c + d*x))^(1/4)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))*Sqrt[(a*d + b*(c + 2*d*x))^2/((b*c - a*d)^2*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))^2)]*EllipticE[2*ArcTan[(Sqrt[2]*b^(1/4)*d^(1/4)*((a + b*x)*(c + d*x))^(1/4))/Sqrt[b*c - a*d]], 1/2])/(5*(b*c - a*d)^(3/2)*(a + b*x)^(1/4)*(c + d*x)^(1/4)*(b*c + a*d + 2*b*d*x)*Sqrt[(a*d + b*(c + 2*d*x))^2]) - (12*Sqrt[2]*b^(1/4)*d^(5/4)*((a + b*x)*(c + d*x))^(1/4)*Sqrt[(b*c + a*d + 2*b*d*x)^2]*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))*Sqrt[(a*d + b*(c + 2*d*x))^2/((b*c - a*d)^2*(1 + (2*Sqrt[b]*Sqrt[d]*Sqrt[(a + b*x)*(c + d*x)])/(b*c - a*d))^2)]*EllipticF[2*ArcTan[(Sqrt[2]*b^(1/4)*d^(1/4)*((a + b*x)*(c + d*x))^(1/4))/Sqrt[b*c - a*d]], 1/2])/(5*(b*c - a*d)^(3/2)*(a + b*x)^(1/4)*(c + d*x)^(1/4)*(b*c + a*d + 2*b*d*x)*Sqrt[(a*d + b*(c + 2*d*x))^2])","A",8,6,19,0.3158,1,"{51, 62, 623, 305, 220, 1196}"
1729,1,279,0,0.3039881,"\int \frac{1}{\sqrt[4]{1-a x} (1+b x)^{3/4}} \, dx","Int[1/((1 - a*x)^(1/4)*(1 + b*x)^(3/4)),x]","-\frac{\log \left(-\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt[4]{1-a x}}{\sqrt[4]{b x+1}}+\frac{\sqrt{b} \sqrt{1-a x}}{\sqrt{b x+1}}+\sqrt{a}\right)}{\sqrt{2} \sqrt[4]{a} b^{3/4}}+\frac{\log \left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt[4]{1-a x}}{\sqrt[4]{b x+1}}+\frac{\sqrt{b} \sqrt{1-a x}}{\sqrt{b x+1}}+\sqrt{a}\right)}{\sqrt{2} \sqrt[4]{a} b^{3/4}}+\frac{\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{1-a x}}{\sqrt[4]{a} \sqrt[4]{b x+1}}\right)}{\sqrt[4]{a} b^{3/4}}-\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{1-a x}}{\sqrt[4]{a} \sqrt[4]{b x+1}}+1\right)}{\sqrt[4]{a} b^{3/4}}","-\frac{\log \left(-\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt[4]{1-a x}}{\sqrt[4]{b x+1}}+\frac{\sqrt{b} \sqrt{1-a x}}{\sqrt{b x+1}}+\sqrt{a}\right)}{\sqrt{2} \sqrt[4]{a} b^{3/4}}+\frac{\log \left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt[4]{1-a x}}{\sqrt[4]{b x+1}}+\frac{\sqrt{b} \sqrt{1-a x}}{\sqrt{b x+1}}+\sqrt{a}\right)}{\sqrt{2} \sqrt[4]{a} b^{3/4}}+\frac{\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{1-a x}}{\sqrt[4]{a} \sqrt[4]{b x+1}}\right)}{\sqrt[4]{a} b^{3/4}}-\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{1-a x}}{\sqrt[4]{a} \sqrt[4]{b x+1}}+1\right)}{\sqrt[4]{a} b^{3/4}}",1,"(Sqrt[2]*ArcTan[1 - (Sqrt[2]*b^(1/4)*(1 - a*x)^(1/4))/(a^(1/4)*(1 + b*x)^(1/4))])/(a^(1/4)*b^(3/4)) - (Sqrt[2]*ArcTan[1 + (Sqrt[2]*b^(1/4)*(1 - a*x)^(1/4))/(a^(1/4)*(1 + b*x)^(1/4))])/(a^(1/4)*b^(3/4)) - Log[Sqrt[a] + (Sqrt[b]*Sqrt[1 - a*x])/Sqrt[1 + b*x] - (Sqrt[2]*a^(1/4)*b^(1/4)*(1 - a*x)^(1/4))/(1 + b*x)^(1/4)]/(Sqrt[2]*a^(1/4)*b^(3/4)) + Log[Sqrt[a] + (Sqrt[b]*Sqrt[1 - a*x])/Sqrt[1 + b*x] + (Sqrt[2]*a^(1/4)*b^(1/4)*(1 - a*x)^(1/4))/(1 + b*x)^(1/4)]/(Sqrt[2]*a^(1/4)*b^(3/4))","A",11,8,20,0.4000,1,"{63, 331, 297, 1162, 617, 204, 1165, 628}"
1730,1,193,0,0.138051,"\int \frac{1}{\sqrt[4]{1-a x} (1+a x)^{3/4}} \, dx","Int[1/((1 - a*x)^(1/4)*(1 + a*x)^(3/4)),x]","-\frac{\log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{\sqrt{2} a}+\frac{\log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}+\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{\sqrt{2} a}+\frac{\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}\right)}{a}-\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{a}","-\frac{\log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{\sqrt{2} a}+\frac{\log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}+\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{\sqrt{2} a}+\frac{\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}\right)}{a}-\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{a}",1,"(Sqrt[2]*ArcTan[1 - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/a - (Sqrt[2]*ArcTan[1 + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/a - Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)]/(Sqrt[2]*a) + Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)]/(Sqrt[2]*a)","A",11,8,20,0.4000,1,"{63, 331, 297, 1162, 617, 204, 1165, 628}"
1731,1,74,0,0.0290308,"\int \frac{(a+b x)^{3/2}}{\sqrt[5]{c+d x}} \, dx","Int[(a + b*x)^(3/2)/(c + d*x)^(1/5),x]","\frac{2 (a+b x)^{5/2} \sqrt[5]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{1}{5},\frac{5}{2};\frac{7}{2};-\frac{d (a+b x)}{b c-a d}\right)}{5 b \sqrt[5]{c+d x}}","\frac{2 (a+b x)^{5/2} \sqrt[5]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{1}{5},\frac{5}{2};\frac{7}{2};-\frac{d (a+b x)}{b c-a d}\right)}{5 b \sqrt[5]{c+d x}}",1,"(2*(a + b*x)^(5/2)*((b*(c + d*x))/(b*c - a*d))^(1/5)*Hypergeometric2F1[1/5, 5/2, 7/2, -((d*(a + b*x))/(b*c - a*d))])/(5*b*(c + d*x)^(1/5))","A",2,2,19,0.1053,1,"{70, 69}"
1732,1,74,0,0.019703,"\int \frac{\sqrt{a+b x}}{\sqrt[5]{c+d x}} \, dx","Int[Sqrt[a + b*x]/(c + d*x)^(1/5),x]","\frac{2 (a+b x)^{3/2} \sqrt[5]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{1}{5},\frac{3}{2};\frac{5}{2};-\frac{d (a+b x)}{b c-a d}\right)}{3 b \sqrt[5]{c+d x}}","\frac{2 (a+b x)^{3/2} \sqrt[5]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{1}{5},\frac{3}{2};\frac{5}{2};-\frac{d (a+b x)}{b c-a d}\right)}{3 b \sqrt[5]{c+d x}}",1,"(2*(a + b*x)^(3/2)*((b*(c + d*x))/(b*c - a*d))^(1/5)*Hypergeometric2F1[1/5, 3/2, 5/2, -((d*(a + b*x))/(b*c - a*d))])/(3*b*(c + d*x)^(1/5))","A",2,2,19,0.1053,1,"{70, 69}"
1733,1,72,0,0.0196033,"\int \frac{1}{\sqrt{a+b x} \sqrt[5]{c+d x}} \, dx","Int[1/(Sqrt[a + b*x]*(c + d*x)^(1/5)),x]","\frac{2 \sqrt{a+b x} \sqrt[5]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{1}{5},\frac{1}{2};\frac{3}{2};-\frac{d (a+b x)}{b c-a d}\right)}{b \sqrt[5]{c+d x}}","\frac{2 \sqrt{a+b x} \sqrt[5]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{1}{5},\frac{1}{2};\frac{3}{2};-\frac{d (a+b x)}{b c-a d}\right)}{b \sqrt[5]{c+d x}}",1,"(2*Sqrt[a + b*x]*((b*(c + d*x))/(b*c - a*d))^(1/5)*Hypergeometric2F1[1/5, 1/2, 3/2, -((d*(a + b*x))/(b*c - a*d))])/(b*(c + d*x)^(1/5))","A",2,2,19,0.1053,1,"{70, 69}"
1734,1,72,0,0.0198808,"\int \frac{1}{(a+b x)^{3/2} \sqrt[5]{c+d x}} \, dx","Int[1/((a + b*x)^(3/2)*(c + d*x)^(1/5)),x]","-\frac{2 \sqrt[5]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(-\frac{1}{2},\frac{1}{5};\frac{1}{2};-\frac{d (a+b x)}{b c-a d}\right)}{b \sqrt{a+b x} \sqrt[5]{c+d x}}","-\frac{2 \sqrt[5]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(-\frac{1}{2},\frac{1}{5};\frac{1}{2};-\frac{d (a+b x)}{b c-a d}\right)}{b \sqrt{a+b x} \sqrt[5]{c+d x}}",1,"(-2*((b*(c + d*x))/(b*c - a*d))^(1/5)*Hypergeometric2F1[-1/2, 1/5, 1/2, -((d*(a + b*x))/(b*c - a*d))])/(b*Sqrt[a + b*x]*(c + d*x)^(1/5))","A",2,2,19,0.1053,1,"{70, 69}"
1735,1,74,0,0.0205612,"\int \frac{1}{(a+b x)^{5/2} \sqrt[5]{c+d x}} \, dx","Int[1/((a + b*x)^(5/2)*(c + d*x)^(1/5)),x]","-\frac{2 \sqrt[5]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(-\frac{3}{2},\frac{1}{5};-\frac{1}{2};-\frac{d (a+b x)}{b c-a d}\right)}{3 b (a+b x)^{3/2} \sqrt[5]{c+d x}}","-\frac{2 \sqrt[5]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(-\frac{3}{2},\frac{1}{5};-\frac{1}{2};-\frac{d (a+b x)}{b c-a d}\right)}{3 b (a+b x)^{3/2} \sqrt[5]{c+d x}}",1,"(-2*((b*(c + d*x))/(b*c - a*d))^(1/5)*Hypergeometric2F1[-3/2, 1/5, -1/2, -((d*(a + b*x))/(b*c - a*d))])/(3*b*(a + b*x)^(3/2)*(c + d*x)^(1/5))","A",2,2,19,0.1053,1,"{70, 69}"
1736,1,487,0,0.5221354,"\int (a+b x)^{5/2} \sqrt[6]{c+d x} \, dx","Int[(a + b*x)^(5/2)*(c + d*x)^(1/6),x]","-\frac{81\ 3^{3/4} \sqrt[6]{c+d x} (b c-a d)^{11/3} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+(b c-a d)^{2/3}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{2816 b d^4 \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{81 \sqrt{a+b x} \sqrt[6]{c+d x} (b c-a d)^3}{1408 b d^3}-\frac{9 (a+b x)^{3/2} \sqrt[6]{c+d x} (b c-a d)^2}{352 b d^2}+\frac{3 (a+b x)^{5/2} \sqrt[6]{c+d x} (b c-a d)}{176 b d}+\frac{3 (a+b x)^{7/2} \sqrt[6]{c+d x}}{11 b}","-\frac{81\ 3^{3/4} \sqrt[6]{c+d x} (b c-a d)^{11/3} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+(b c-a d)^{2/3}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{2816 b d^4 \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{81 \sqrt{a+b x} \sqrt[6]{c+d x} (b c-a d)^3}{1408 b d^3}-\frac{9 (a+b x)^{3/2} \sqrt[6]{c+d x} (b c-a d)^2}{352 b d^2}+\frac{3 (a+b x)^{5/2} \sqrt[6]{c+d x} (b c-a d)}{176 b d}+\frac{3 (a+b x)^{7/2} \sqrt[6]{c+d x}}{11 b}",1,"(81*(b*c - a*d)^3*Sqrt[a + b*x]*(c + d*x)^(1/6))/(1408*b*d^3) - (9*(b*c - a*d)^2*(a + b*x)^(3/2)*(c + d*x)^(1/6))/(352*b*d^2) + (3*(b*c - a*d)*(a + b*x)^(5/2)*(c + d*x)^(1/6))/(176*b*d) + (3*(a + b*x)^(7/2)*(c + d*x)^(1/6))/(11*b) - (81*3^(3/4)*(b*c - a*d)^(11/3)*(c + d*x)^(1/6)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2]*EllipticF[ArcCos[((b*c - a*d)^(1/3) - (1 - Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))], (2 + Sqrt[3])/4])/(2816*b*d^4*Sqrt[a + b*x]*Sqrt[-((b^(1/3)*(c + d*x)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2)])","A",6,3,19,0.1579,1,"{50, 63, 225}"
1737,1,449,0,0.3363533,"\int (a+b x)^{3/2} \sqrt[6]{c+d x} \, dx","Int[(a + b*x)^(3/2)*(c + d*x)^(1/6),x]","\frac{27\ 3^{3/4} \sqrt[6]{c+d x} (b c-a d)^{8/3} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+(b c-a d)^{2/3}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{640 b d^3 \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{27 \sqrt{a+b x} \sqrt[6]{c+d x} (b c-a d)^2}{320 b d^2}+\frac{3 (a+b x)^{3/2} \sqrt[6]{c+d x} (b c-a d)}{80 b d}+\frac{3 (a+b x)^{5/2} \sqrt[6]{c+d x}}{8 b}","\frac{27\ 3^{3/4} \sqrt[6]{c+d x} (b c-a d)^{8/3} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+(b c-a d)^{2/3}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{640 b d^3 \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{27 \sqrt{a+b x} \sqrt[6]{c+d x} (b c-a d)^2}{320 b d^2}+\frac{3 (a+b x)^{3/2} \sqrt[6]{c+d x} (b c-a d)}{80 b d}+\frac{3 (a+b x)^{5/2} \sqrt[6]{c+d x}}{8 b}",1,"(-27*(b*c - a*d)^2*Sqrt[a + b*x]*(c + d*x)^(1/6))/(320*b*d^2) + (3*(b*c - a*d)*(a + b*x)^(3/2)*(c + d*x)^(1/6))/(80*b*d) + (3*(a + b*x)^(5/2)*(c + d*x)^(1/6))/(8*b) + (27*3^(3/4)*(b*c - a*d)^(8/3)*(c + d*x)^(1/6)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2]*EllipticF[ArcCos[((b*c - a*d)^(1/3) - (1 - Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))], (2 + Sqrt[3])/4])/(640*b*d^3*Sqrt[a + b*x]*Sqrt[-((b^(1/3)*(c + d*x)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2)])","A",5,3,19,0.1579,1,"{50, 63, 225}"
1738,1,411,0,0.2838301,"\int \sqrt{a+b x} \sqrt[6]{c+d x} \, dx","Int[Sqrt[a + b*x]*(c + d*x)^(1/6),x]","-\frac{3\ 3^{3/4} \sqrt[6]{c+d x} (b c-a d)^{5/3} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+(b c-a d)^{2/3}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{40 b d^2 \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{3 \sqrt{a+b x} \sqrt[6]{c+d x} (b c-a d)}{20 b d}+\frac{3 (a+b x)^{3/2} \sqrt[6]{c+d x}}{5 b}","-\frac{3\ 3^{3/4} \sqrt[6]{c+d x} (b c-a d)^{5/3} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+(b c-a d)^{2/3}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{40 b d^2 \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{3 \sqrt{a+b x} \sqrt[6]{c+d x} (b c-a d)}{20 b d}+\frac{3 (a+b x)^{3/2} \sqrt[6]{c+d x}}{5 b}",1,"(3*(b*c - a*d)*Sqrt[a + b*x]*(c + d*x)^(1/6))/(20*b*d) + (3*(a + b*x)^(3/2)*(c + d*x)^(1/6))/(5*b) - (3*3^(3/4)*(b*c - a*d)^(5/3)*(c + d*x)^(1/6)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2]*EllipticF[ArcCos[((b*c - a*d)^(1/3) - (1 - Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))], (2 + Sqrt[3])/4])/(40*b*d^2*Sqrt[a + b*x]*Sqrt[-((b^(1/3)*(c + d*x)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2)])","A",4,3,19,0.1579,1,"{50, 63, 225}"
1739,1,375,0,0.2329123,"\int \frac{\sqrt[6]{c+d x}}{\sqrt{a+b x}} \, dx","Int[(c + d*x)^(1/6)/Sqrt[a + b*x],x]","\frac{3^{3/4} \sqrt[6]{c+d x} (b c-a d)^{2/3} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+(b c-a d)^{2/3}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{4 b d \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{3 \sqrt{a+b x} \sqrt[6]{c+d x}}{2 b}","\frac{3^{3/4} \sqrt[6]{c+d x} (b c-a d)^{2/3} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+(b c-a d)^{2/3}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{4 b d \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{3 \sqrt{a+b x} \sqrt[6]{c+d x}}{2 b}",1,"(3*Sqrt[a + b*x]*(c + d*x)^(1/6))/(2*b) + (3^(3/4)*(b*c - a*d)^(2/3)*(c + d*x)^(1/6)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2]*EllipticF[ArcCos[((b*c - a*d)^(1/3) - (1 - Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))], (2 + Sqrt[3])/4])/(4*b*d*Sqrt[a + b*x]*Sqrt[-((b^(1/3)*(c + d*x)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2)])","A",3,3,19,0.1579,1,"{50, 63, 225}"
1740,1,367,0,0.2292408,"\int \frac{\sqrt[6]{c+d x}}{(a+b x)^{3/2}} \, dx","Int[(c + d*x)^(1/6)/(a + b*x)^(3/2),x]","\frac{\sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+(b c-a d)^{2/3}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{\sqrt[4]{3} b \sqrt{a+b x} \sqrt[3]{b c-a d} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{2 \sqrt[6]{c+d x}}{b \sqrt{a+b x}}","\frac{\sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+(b c-a d)^{2/3}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{\sqrt[4]{3} b \sqrt{a+b x} \sqrt[3]{b c-a d} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{2 \sqrt[6]{c+d x}}{b \sqrt{a+b x}}",1,"(-2*(c + d*x)^(1/6))/(b*Sqrt[a + b*x]) + ((c + d*x)^(1/6)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2]*EllipticF[ArcCos[((b*c - a*d)^(1/3) - (1 - Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))], (2 + Sqrt[3])/4])/(3^(1/4)*b*(b*c - a*d)^(1/3)*Sqrt[a + b*x]*Sqrt[-((b^(1/3)*(c + d*x)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2)])","A",3,3,19,0.1579,1,"{47, 63, 225}"
1741,1,409,0,0.2796058,"\int \frac{\sqrt[6]{c+d x}}{(a+b x)^{5/2}} \, dx","Int[(c + d*x)^(1/6)/(a + b*x)^(5/2),x]","-\frac{2 d \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+(b c-a d)^{2/3}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{9 \sqrt[4]{3} b \sqrt{a+b x} (b c-a d)^{4/3} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{2 d \sqrt[6]{c+d x}}{9 b \sqrt{a+b x} (b c-a d)}-\frac{2 \sqrt[6]{c+d x}}{3 b (a+b x)^{3/2}}","-\frac{2 d \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+(b c-a d)^{2/3}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{9 \sqrt[4]{3} b \sqrt{a+b x} (b c-a d)^{4/3} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{2 d \sqrt[6]{c+d x}}{9 b \sqrt{a+b x} (b c-a d)}-\frac{2 \sqrt[6]{c+d x}}{3 b (a+b x)^{3/2}}",1,"(-2*(c + d*x)^(1/6))/(3*b*(a + b*x)^(3/2)) - (2*d*(c + d*x)^(1/6))/(9*b*(b*c - a*d)*Sqrt[a + b*x]) - (2*d*(c + d*x)^(1/6)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2]*EllipticF[ArcCos[((b*c - a*d)^(1/3) - (1 - Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))], (2 + Sqrt[3])/4])/(9*3^(1/4)*b*(b*c - a*d)^(4/3)*Sqrt[a + b*x]*Sqrt[-((b^(1/3)*(c + d*x)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2)])","A",4,4,19,0.2105,1,"{47, 51, 63, 225}"
1742,1,896,0,1.0783926,"\int (a+b x)^{3/2} (c+d x)^{5/6} \, dx","Int[(a + b*x)^(3/2)*(c + d*x)^(5/6),x]","-\frac{81 \sqrt[4]{3} \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} E\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right) (b c-a d)^{10/3}}{448 b^{5/3} d^3 \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{27\ 3^{3/4} \left(1-\sqrt{3}\right) \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right) (b c-a d)^{10/3}}{896 b^{5/3} d^3 \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{81 \left(1+\sqrt{3}\right) \sqrt{a+b x} \sqrt[6]{c+d x} (b c-a d)^3}{448 b^{5/3} d^2 \left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)}-\frac{27 \sqrt{a+b x} (c+d x)^{5/6} (b c-a d)^2}{224 b d^2}+\frac{3 (a+b x)^{3/2} (c+d x)^{5/6} (b c-a d)}{28 b d}+\frac{3 (a+b x)^{5/2} (c+d x)^{5/6}}{10 b}","-\frac{81 \sqrt[4]{3} \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} E\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right) (b c-a d)^{10/3}}{448 b^{5/3} d^3 \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{27\ 3^{3/4} \left(1-\sqrt{3}\right) \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right) (b c-a d)^{10/3}}{896 b^{5/3} d^3 \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{81 \left(1+\sqrt{3}\right) \sqrt{a+b x} \sqrt[6]{c+d x} (b c-a d)^3}{448 b^{5/3} d^2 \left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)}-\frac{27 \sqrt{a+b x} (c+d x)^{5/6} (b c-a d)^2}{224 b d^2}+\frac{3 (a+b x)^{3/2} (c+d x)^{5/6} (b c-a d)}{28 b d}+\frac{3 (a+b x)^{5/2} (c+d x)^{5/6}}{10 b}",1,"(-27*(b*c - a*d)^2*Sqrt[a + b*x]*(c + d*x)^(5/6))/(224*b*d^2) + (3*(b*c - a*d)*(a + b*x)^(3/2)*(c + d*x)^(5/6))/(28*b*d) + (3*(a + b*x)^(5/2)*(c + d*x)^(5/6))/(10*b) - (81*(1 + Sqrt[3])*(b*c - a*d)^3*Sqrt[a + b*x]*(c + d*x)^(1/6))/(448*b^(5/3)*d^2*((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))) - (81*3^(1/4)*(b*c - a*d)^(10/3)*(c + d*x)^(1/6)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2]*EllipticE[ArcCos[((b*c - a*d)^(1/3) - (1 - Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))], (2 + Sqrt[3])/4])/(448*b^(5/3)*d^3*Sqrt[a + b*x]*Sqrt[-((b^(1/3)*(c + d*x)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2)]) - (27*3^(3/4)*(1 - Sqrt[3])*(b*c - a*d)^(10/3)*(c + d*x)^(1/6)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2]*EllipticF[ArcCos[((b*c - a*d)^(1/3) - (1 - Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))], (2 + Sqrt[3])/4])/(896*b^(5/3)*d^3*Sqrt[a + b*x]*Sqrt[-((b^(1/3)*(c + d*x)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2)])","A",7,5,19,0.2632,1,"{50, 63, 308, 225, 1881}"
1743,1,858,0,0.8225885,"\int \sqrt{a+b x} (c+d x)^{5/6} \, dx","Int[Sqrt[a + b*x]*(c + d*x)^(5/6),x]","\frac{45 \sqrt[4]{3} \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} E\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right) (b c-a d)^{7/3}}{112 b^{5/3} d^2 \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{15\ 3^{3/4} \left(1-\sqrt{3}\right) \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right) (b c-a d)^{7/3}}{224 b^{5/3} d^2 \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{45 \left(1+\sqrt{3}\right) \sqrt{a+b x} \sqrt[6]{c+d x} (b c-a d)^2}{112 b^{5/3} d \left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)}+\frac{15 \sqrt{a+b x} (c+d x)^{5/6} (b c-a d)}{56 b d}+\frac{3 (a+b x)^{3/2} (c+d x)^{5/6}}{7 b}","\frac{45 \sqrt[4]{3} \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} E\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right) (b c-a d)^{7/3}}{112 b^{5/3} d^2 \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{15\ 3^{3/4} \left(1-\sqrt{3}\right) \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right) (b c-a d)^{7/3}}{224 b^{5/3} d^2 \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{45 \left(1+\sqrt{3}\right) \sqrt{a+b x} \sqrt[6]{c+d x} (b c-a d)^2}{112 b^{5/3} d \left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)}+\frac{15 \sqrt{a+b x} (c+d x)^{5/6} (b c-a d)}{56 b d}+\frac{3 (a+b x)^{3/2} (c+d x)^{5/6}}{7 b}",1,"(15*(b*c - a*d)*Sqrt[a + b*x]*(c + d*x)^(5/6))/(56*b*d) + (3*(a + b*x)^(3/2)*(c + d*x)^(5/6))/(7*b) + (45*(1 + Sqrt[3])*(b*c - a*d)^2*Sqrt[a + b*x]*(c + d*x)^(1/6))/(112*b^(5/3)*d*((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))) + (45*3^(1/4)*(b*c - a*d)^(7/3)*(c + d*x)^(1/6)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2]*EllipticE[ArcCos[((b*c - a*d)^(1/3) - (1 - Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))], (2 + Sqrt[3])/4])/(112*b^(5/3)*d^2*Sqrt[a + b*x]*Sqrt[-((b^(1/3)*(c + d*x)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2)]) + (15*3^(3/4)*(1 - Sqrt[3])*(b*c - a*d)^(7/3)*(c + d*x)^(1/6)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2]*EllipticF[ArcCos[((b*c - a*d)^(1/3) - (1 - Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))], (2 + Sqrt[3])/4])/(224*b^(5/3)*d^2*Sqrt[a + b*x]*Sqrt[-((b^(1/3)*(c + d*x)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2)])","A",6,5,19,0.2632,1,"{50, 63, 308, 225, 1881}"
1744,1,817,0,0.7095197,"\int \frac{(c+d x)^{5/6}}{\sqrt{a+b x}} \, dx","Int[(c + d*x)^(5/6)/Sqrt[a + b*x],x]","-\frac{15 \sqrt[4]{3} \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} E\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right) (b c-a d)^{4/3}}{8 b^{5/3} d \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{5\ 3^{3/4} \left(1-\sqrt{3}\right) \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right) (b c-a d)^{4/3}}{16 b^{5/3} d \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{15 \left(1+\sqrt{3}\right) \sqrt{a+b x} \sqrt[6]{c+d x} (b c-a d)}{8 b^{5/3} \left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)}+\frac{3 \sqrt{a+b x} (c+d x)^{5/6}}{4 b}","-\frac{15 \sqrt[4]{3} \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} E\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right) (b c-a d)^{4/3}}{8 b^{5/3} d \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{5\ 3^{3/4} \left(1-\sqrt{3}\right) \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right) (b c-a d)^{4/3}}{16 b^{5/3} d \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{15 \left(1+\sqrt{3}\right) \sqrt{a+b x} \sqrt[6]{c+d x} (b c-a d)}{8 b^{5/3} \left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)}+\frac{3 \sqrt{a+b x} (c+d x)^{5/6}}{4 b}",1,"(3*Sqrt[a + b*x]*(c + d*x)^(5/6))/(4*b) - (15*(1 + Sqrt[3])*(b*c - a*d)*Sqrt[a + b*x]*(c + d*x)^(1/6))/(8*b^(5/3)*((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))) - (15*3^(1/4)*(b*c - a*d)^(4/3)*(c + d*x)^(1/6)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2]*EllipticE[ArcCos[((b*c - a*d)^(1/3) - (1 - Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))], (2 + Sqrt[3])/4])/(8*b^(5/3)*d*Sqrt[a + b*x]*Sqrt[-((b^(1/3)*(c + d*x)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2)]) - (5*3^(3/4)*(1 - Sqrt[3])*(b*c - a*d)^(4/3)*(c + d*x)^(1/6)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2]*EllipticF[ArcCos[((b*c - a*d)^(1/3) - (1 - Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))], (2 + Sqrt[3])/4])/(16*b^(5/3)*d*Sqrt[a + b*x]*Sqrt[-((b^(1/3)*(c + d*x)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2)])","A",5,5,19,0.2632,1,"{50, 63, 308, 225, 1881}"
1745,1,798,0,0.6839552,"\int \frac{(c+d x)^{5/6}}{(a+b x)^{3/2}} \, dx","Int[(c + d*x)^(5/6)/(a + b*x)^(3/2),x]","-\frac{5 \left(1+\sqrt{3}\right) \sqrt{a+b x} \sqrt[6]{c+d x} d}{b^{5/3} \left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)}-\frac{5 \sqrt[4]{3} \sqrt[3]{b c-a d} \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} E\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{b^{5/3} \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{5 \left(1-\sqrt{3}\right) \sqrt[3]{b c-a d} \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{2 \sqrt[4]{3} b^{5/3} \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{2 (c+d x)^{5/6}}{b \sqrt{a+b x}}","-\frac{5 \left(1+\sqrt{3}\right) \sqrt{a+b x} \sqrt[6]{c+d x} d}{b^{5/3} \left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)}-\frac{5 \sqrt[4]{3} \sqrt[3]{b c-a d} \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} E\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{b^{5/3} \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{5 \left(1-\sqrt{3}\right) \sqrt[3]{b c-a d} \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{2 \sqrt[4]{3} b^{5/3} \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{2 (c+d x)^{5/6}}{b \sqrt{a+b x}}",1,"(-2*(c + d*x)^(5/6))/(b*Sqrt[a + b*x]) - (5*(1 + Sqrt[3])*d*Sqrt[a + b*x]*(c + d*x)^(1/6))/(b^(5/3)*((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))) - (5*3^(1/4)*(b*c - a*d)^(1/3)*(c + d*x)^(1/6)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2]*EllipticE[ArcCos[((b*c - a*d)^(1/3) - (1 - Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))], (2 + Sqrt[3])/4])/(b^(5/3)*Sqrt[a + b*x]*Sqrt[-((b^(1/3)*(c + d*x)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2)]) - (5*(1 - Sqrt[3])*(b*c - a*d)^(1/3)*(c + d*x)^(1/6)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2]*EllipticF[ArcCos[((b*c - a*d)^(1/3) - (1 - Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))], (2 + Sqrt[3])/4])/(2*3^(1/4)*b^(5/3)*Sqrt[a + b*x]*Sqrt[-((b^(1/3)*(c + d*x)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2)])","A",5,5,19,0.2632,1,"{47, 63, 308, 225, 1881}"
1746,1,854,0,0.7975783,"\int \frac{(c+d x)^{5/6}}{(a+b x)^{5/2}} \, dx","Int[(c + d*x)^(5/6)/(a + b*x)^(5/2),x]","-\frac{10 \left(1+\sqrt{3}\right) \sqrt{a+b x} \sqrt[6]{c+d x} d^2}{9 b^{5/3} (b c-a d) \left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)}-\frac{10 \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} E\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right) d}{3\ 3^{3/4} b^{5/3} (b c-a d)^{2/3} \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{5 \left(1-\sqrt{3}\right) \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right) d}{9 \sqrt[4]{3} b^{5/3} (b c-a d)^{2/3} \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{10 (c+d x)^{5/6} d}{9 b (b c-a d) \sqrt{a+b x}}-\frac{2 (c+d x)^{5/6}}{3 b (a+b x)^{3/2}}","-\frac{10 \left(1+\sqrt{3}\right) \sqrt{a+b x} \sqrt[6]{c+d x} d^2}{9 b^{5/3} (b c-a d) \left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)}-\frac{10 \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} E\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right) d}{3\ 3^{3/4} b^{5/3} (b c-a d)^{2/3} \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{5 \left(1-\sqrt{3}\right) \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right) d}{9 \sqrt[4]{3} b^{5/3} (b c-a d)^{2/3} \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{10 (c+d x)^{5/6} d}{9 b (b c-a d) \sqrt{a+b x}}-\frac{2 (c+d x)^{5/6}}{3 b (a+b x)^{3/2}}",1,"(-2*(c + d*x)^(5/6))/(3*b*(a + b*x)^(3/2)) - (10*d*(c + d*x)^(5/6))/(9*b*(b*c - a*d)*Sqrt[a + b*x]) - (10*(1 + Sqrt[3])*d^2*Sqrt[a + b*x]*(c + d*x)^(1/6))/(9*b^(5/3)*(b*c - a*d)*((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))) - (10*d*(c + d*x)^(1/6)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2]*EllipticE[ArcCos[((b*c - a*d)^(1/3) - (1 - Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))], (2 + Sqrt[3])/4])/(3*3^(3/4)*b^(5/3)*(b*c - a*d)^(2/3)*Sqrt[a + b*x]*Sqrt[-((b^(1/3)*(c + d*x)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2)]) - (5*(1 - Sqrt[3])*d*(c + d*x)^(1/6)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2]*EllipticF[ArcCos[((b*c - a*d)^(1/3) - (1 - Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))], (2 + Sqrt[3])/4])/(9*3^(1/4)*b^(5/3)*(b*c - a*d)^(2/3)*Sqrt[a + b*x]*Sqrt[-((b^(1/3)*(c + d*x)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2)])","A",6,6,19,0.3158,1,"{47, 51, 63, 308, 225, 1881}"
1747,1,896,0,0.9014704,"\int \frac{(c+d x)^{5/6}}{(a+b x)^{7/2}} \, dx","Int[(c + d*x)^(5/6)/(a + b*x)^(7/2),x]","\frac{8 \left(1+\sqrt{3}\right) \sqrt{a+b x} \sqrt[6]{c+d x} d^3}{27 b^{5/3} (b c-a d)^2 \left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)}+\frac{8 \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} E\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right) d^2}{9\ 3^{3/4} b^{5/3} (b c-a d)^{5/3} \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{4 \left(1-\sqrt{3}\right) \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right) d^2}{27 \sqrt[4]{3} b^{5/3} (b c-a d)^{5/3} \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{8 (c+d x)^{5/6} d^2}{27 b (b c-a d)^2 \sqrt{a+b x}}-\frac{2 (c+d x)^{5/6} d}{9 b (b c-a d) (a+b x)^{3/2}}-\frac{2 (c+d x)^{5/6}}{5 b (a+b x)^{5/2}}","\frac{8 \left(1+\sqrt{3}\right) \sqrt{a+b x} \sqrt[6]{c+d x} d^3}{27 b^{5/3} (b c-a d)^2 \left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)}+\frac{8 \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} E\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right) d^2}{9\ 3^{3/4} b^{5/3} (b c-a d)^{5/3} \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{4 \left(1-\sqrt{3}\right) \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right) d^2}{27 \sqrt[4]{3} b^{5/3} (b c-a d)^{5/3} \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{8 (c+d x)^{5/6} d^2}{27 b (b c-a d)^2 \sqrt{a+b x}}-\frac{2 (c+d x)^{5/6} d}{9 b (b c-a d) (a+b x)^{3/2}}-\frac{2 (c+d x)^{5/6}}{5 b (a+b x)^{5/2}}",1,"(-2*(c + d*x)^(5/6))/(5*b*(a + b*x)^(5/2)) - (2*d*(c + d*x)^(5/6))/(9*b*(b*c - a*d)*(a + b*x)^(3/2)) + (8*d^2*(c + d*x)^(5/6))/(27*b*(b*c - a*d)^2*Sqrt[a + b*x]) + (8*(1 + Sqrt[3])*d^3*Sqrt[a + b*x]*(c + d*x)^(1/6))/(27*b^(5/3)*(b*c - a*d)^2*((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))) + (8*d^2*(c + d*x)^(1/6)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2]*EllipticE[ArcCos[((b*c - a*d)^(1/3) - (1 - Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))], (2 + Sqrt[3])/4])/(9*3^(3/4)*b^(5/3)*(b*c - a*d)^(5/3)*Sqrt[a + b*x]*Sqrt[-((b^(1/3)*(c + d*x)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2)]) + (4*(1 - Sqrt[3])*d^2*(c + d*x)^(1/6)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2]*EllipticF[ArcCos[((b*c - a*d)^(1/3) - (1 - Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))], (2 + Sqrt[3])/4])/(27*3^(1/4)*b^(5/3)*(b*c - a*d)^(5/3)*Sqrt[a + b*x]*Sqrt[-((b^(1/3)*(c + d*x)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2)])","A",7,6,19,0.3158,1,"{47, 51, 63, 308, 225, 1881}"
1748,1,890,0,0.9522387,"\int \frac{(a+b x)^{5/2}}{\sqrt[6]{c+d x}} \, dx","Int[(a + b*x)^(5/2)/(c + d*x)^(1/6),x]","\frac{243 \sqrt[4]{3} \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} E\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right) (b c-a d)^{10/3}}{448 b^{2/3} d^4 \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{81\ 3^{3/4} \left(1-\sqrt{3}\right) \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right) (b c-a d)^{10/3}}{896 b^{2/3} d^4 \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{243 \left(1+\sqrt{3}\right) \sqrt{a+b x} \sqrt[6]{c+d x} (b c-a d)^3}{448 b^{2/3} d^3 \left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)}+\frac{81 \sqrt{a+b x} (c+d x)^{5/6} (b c-a d)^2}{224 d^3}-\frac{9 (a+b x)^{3/2} (c+d x)^{5/6} (b c-a d)}{28 d^2}+\frac{3 (a+b x)^{5/2} (c+d x)^{5/6}}{10 d}","\frac{243 \sqrt[4]{3} \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} E\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right) (b c-a d)^{10/3}}{448 b^{2/3} d^4 \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{81\ 3^{3/4} \left(1-\sqrt{3}\right) \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right) (b c-a d)^{10/3}}{896 b^{2/3} d^4 \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{243 \left(1+\sqrt{3}\right) \sqrt{a+b x} \sqrt[6]{c+d x} (b c-a d)^3}{448 b^{2/3} d^3 \left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)}+\frac{81 \sqrt{a+b x} (c+d x)^{5/6} (b c-a d)^2}{224 d^3}-\frac{9 (a+b x)^{3/2} (c+d x)^{5/6} (b c-a d)}{28 d^2}+\frac{3 (a+b x)^{5/2} (c+d x)^{5/6}}{10 d}",1,"(81*(b*c - a*d)^2*Sqrt[a + b*x]*(c + d*x)^(5/6))/(224*d^3) - (9*(b*c - a*d)*(a + b*x)^(3/2)*(c + d*x)^(5/6))/(28*d^2) + (3*(a + b*x)^(5/2)*(c + d*x)^(5/6))/(10*d) + (243*(1 + Sqrt[3])*(b*c - a*d)^3*Sqrt[a + b*x]*(c + d*x)^(1/6))/(448*b^(2/3)*d^3*((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))) + (243*3^(1/4)*(b*c - a*d)^(10/3)*(c + d*x)^(1/6)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2]*EllipticE[ArcCos[((b*c - a*d)^(1/3) - (1 - Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))], (2 + Sqrt[3])/4])/(448*b^(2/3)*d^4*Sqrt[a + b*x]*Sqrt[-((b^(1/3)*(c + d*x)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2)]) + (81*3^(3/4)*(1 - Sqrt[3])*(b*c - a*d)^(10/3)*(c + d*x)^(1/6)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2]*EllipticF[ArcCos[((b*c - a*d)^(1/3) - (1 - Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))], (2 + Sqrt[3])/4])/(896*b^(2/3)*d^4*Sqrt[a + b*x]*Sqrt[-((b^(1/3)*(c + d*x)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2)])","A",7,5,19,0.2632,1,"{50, 63, 308, 225, 1881}"
1749,1,855,0,0.7904954,"\int \frac{(a+b x)^{3/2}}{\sqrt[6]{c+d x}} \, dx","Int[(a + b*x)^(3/2)/(c + d*x)^(1/6),x]","-\frac{81 \sqrt[4]{3} \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} E\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right) (b c-a d)^{7/3}}{112 b^{2/3} d^3 \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{27\ 3^{3/4} \left(1-\sqrt{3}\right) \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right) (b c-a d)^{7/3}}{224 b^{2/3} d^3 \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{81 \left(1+\sqrt{3}\right) \sqrt{a+b x} \sqrt[6]{c+d x} (b c-a d)^2}{112 b^{2/3} d^2 \left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)}-\frac{27 \sqrt{a+b x} (c+d x)^{5/6} (b c-a d)}{56 d^2}+\frac{3 (a+b x)^{3/2} (c+d x)^{5/6}}{7 d}","-\frac{81 \sqrt[4]{3} \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} E\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right) (b c-a d)^{7/3}}{112 b^{2/3} d^3 \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{27\ 3^{3/4} \left(1-\sqrt{3}\right) \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right) (b c-a d)^{7/3}}{224 b^{2/3} d^3 \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{81 \left(1+\sqrt{3}\right) \sqrt{a+b x} \sqrt[6]{c+d x} (b c-a d)^2}{112 b^{2/3} d^2 \left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)}-\frac{27 \sqrt{a+b x} (c+d x)^{5/6} (b c-a d)}{56 d^2}+\frac{3 (a+b x)^{3/2} (c+d x)^{5/6}}{7 d}",1,"(-27*(b*c - a*d)*Sqrt[a + b*x]*(c + d*x)^(5/6))/(56*d^2) + (3*(a + b*x)^(3/2)*(c + d*x)^(5/6))/(7*d) - (81*(1 + Sqrt[3])*(b*c - a*d)^2*Sqrt[a + b*x]*(c + d*x)^(1/6))/(112*b^(2/3)*d^2*((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))) - (81*3^(1/4)*(b*c - a*d)^(7/3)*(c + d*x)^(1/6)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2]*EllipticE[ArcCos[((b*c - a*d)^(1/3) - (1 - Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))], (2 + Sqrt[3])/4])/(112*b^(2/3)*d^3*Sqrt[a + b*x]*Sqrt[-((b^(1/3)*(c + d*x)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2)]) - (27*3^(3/4)*(1 - Sqrt[3])*(b*c - a*d)^(7/3)*(c + d*x)^(1/6)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2]*EllipticF[ArcCos[((b*c - a*d)^(1/3) - (1 - Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))], (2 + Sqrt[3])/4])/(224*b^(2/3)*d^3*Sqrt[a + b*x]*Sqrt[-((b^(1/3)*(c + d*x)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2)])","A",6,5,19,0.2632,1,"{50, 63, 308, 225, 1881}"
1750,1,820,0,0.6897187,"\int \frac{\sqrt{a+b x}}{\sqrt[6]{c+d x}} \, dx","Int[Sqrt[a + b*x]/(c + d*x)^(1/6),x]","\frac{9 \sqrt[4]{3} \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} E\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right) (b c-a d)^{4/3}}{8 b^{2/3} d^2 \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{3\ 3^{3/4} \left(1-\sqrt{3}\right) \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right) (b c-a d)^{4/3}}{16 b^{2/3} d^2 \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{9 \left(1+\sqrt{3}\right) \sqrt{a+b x} \sqrt[6]{c+d x} (b c-a d)}{8 b^{2/3} d \left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)}+\frac{3 \sqrt{a+b x} (c+d x)^{5/6}}{4 d}","\frac{9 \sqrt[4]{3} \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} E\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right) (b c-a d)^{4/3}}{8 b^{2/3} d^2 \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{3\ 3^{3/4} \left(1-\sqrt{3}\right) \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right) (b c-a d)^{4/3}}{16 b^{2/3} d^2 \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{9 \left(1+\sqrt{3}\right) \sqrt{a+b x} \sqrt[6]{c+d x} (b c-a d)}{8 b^{2/3} d \left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)}+\frac{3 \sqrt{a+b x} (c+d x)^{5/6}}{4 d}",1,"(3*Sqrt[a + b*x]*(c + d*x)^(5/6))/(4*d) + (9*(1 + Sqrt[3])*(b*c - a*d)*Sqrt[a + b*x]*(c + d*x)^(1/6))/(8*b^(2/3)*d*((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))) + (9*3^(1/4)*(b*c - a*d)^(4/3)*(c + d*x)^(1/6)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2]*EllipticE[ArcCos[((b*c - a*d)^(1/3) - (1 - Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))], (2 + Sqrt[3])/4])/(8*b^(2/3)*d^2*Sqrt[a + b*x]*Sqrt[-((b^(1/3)*(c + d*x)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2)]) + (3*3^(3/4)*(1 - Sqrt[3])*(b*c - a*d)^(4/3)*(c + d*x)^(1/6)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2]*EllipticF[ArcCos[((b*c - a*d)^(1/3) - (1 - Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))], (2 + Sqrt[3])/4])/(16*b^(2/3)*d^2*Sqrt[a + b*x]*Sqrt[-((b^(1/3)*(c + d*x)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2)])","A",5,5,19,0.2632,1,"{50, 63, 308, 225, 1881}"
1751,1,780,0,0.5819848,"\int \frac{1}{\sqrt{a+b x} \sqrt[6]{c+d x}} \, dx","Int[1/(Sqrt[a + b*x]*(c + d*x)^(1/6)),x]","-\frac{3 \left(1+\sqrt{3}\right) \sqrt{a+b x} \sqrt[6]{c+d x}}{b^{2/3} \left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)}-\frac{3^{3/4} \left(1-\sqrt{3}\right) \sqrt[6]{c+d x} \sqrt[3]{b c-a d} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+(b c-a d)^{2/3}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{2 b^{2/3} d \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{3 \sqrt[4]{3} \sqrt[6]{c+d x} \sqrt[3]{b c-a d} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+(b c-a d)^{2/3}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} E\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{b^{2/3} d \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}","-\frac{3 \left(1+\sqrt{3}\right) \sqrt{a+b x} \sqrt[6]{c+d x}}{b^{2/3} \left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)}-\frac{3^{3/4} \left(1-\sqrt{3}\right) \sqrt[6]{c+d x} \sqrt[3]{b c-a d} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+(b c-a d)^{2/3}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{2 b^{2/3} d \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{3 \sqrt[4]{3} \sqrt[6]{c+d x} \sqrt[3]{b c-a d} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+(b c-a d)^{2/3}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} E\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{b^{2/3} d \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}",1,"(-3*(1 + Sqrt[3])*Sqrt[a + b*x]*(c + d*x)^(1/6))/(b^(2/3)*((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))) - (3*3^(1/4)*(b*c - a*d)^(1/3)*(c + d*x)^(1/6)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2]*EllipticE[ArcCos[((b*c - a*d)^(1/3) - (1 - Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))], (2 + Sqrt[3])/4])/(b^(2/3)*d*Sqrt[a + b*x]*Sqrt[-((b^(1/3)*(c + d*x)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2)]) - (3^(3/4)*(1 - Sqrt[3])*(b*c - a*d)^(1/3)*(c + d*x)^(1/6)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2]*EllipticF[ArcCos[((b*c - a*d)^(1/3) - (1 - Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))], (2 + Sqrt[3])/4])/(2*b^(2/3)*d*Sqrt[a + b*x]*Sqrt[-((b^(1/3)*(c + d*x)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2)])","A",4,4,19,0.2105,1,"{63, 308, 225, 1881}"
1752,1,813,0,0.6768433,"\int \frac{1}{(a+b x)^{3/2} \sqrt[6]{c+d x}} \, dx","Int[1/((a + b*x)^(3/2)*(c + d*x)^(1/6)),x]","-\frac{2 \left(1+\sqrt{3}\right) \sqrt{a+b x} \sqrt[6]{c+d x} d}{b^{2/3} (b c-a d) \left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)}-\frac{2 \sqrt[4]{3} \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} E\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{b^{2/3} (b c-a d)^{2/3} \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{\left(1-\sqrt{3}\right) \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{\sqrt[4]{3} b^{2/3} (b c-a d)^{2/3} \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{2 (c+d x)^{5/6}}{(b c-a d) \sqrt{a+b x}}","-\frac{2 \left(1+\sqrt{3}\right) \sqrt{a+b x} \sqrt[6]{c+d x} d}{b^{2/3} (b c-a d) \left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)}-\frac{2 \sqrt[4]{3} \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} E\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{b^{2/3} (b c-a d)^{2/3} \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{\left(1-\sqrt{3}\right) \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{\sqrt[4]{3} b^{2/3} (b c-a d)^{2/3} \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{2 (c+d x)^{5/6}}{(b c-a d) \sqrt{a+b x}}",1,"(-2*(c + d*x)^(5/6))/((b*c - a*d)*Sqrt[a + b*x]) - (2*(1 + Sqrt[3])*d*Sqrt[a + b*x]*(c + d*x)^(1/6))/(b^(2/3)*(b*c - a*d)*((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))) - (2*3^(1/4)*(c + d*x)^(1/6)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2]*EllipticE[ArcCos[((b*c - a*d)^(1/3) - (1 - Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))], (2 + Sqrt[3])/4])/(b^(2/3)*(b*c - a*d)^(2/3)*Sqrt[a + b*x]*Sqrt[-((b^(1/3)*(c + d*x)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2)]) - ((1 - Sqrt[3])*(c + d*x)^(1/6)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2]*EllipticF[ArcCos[((b*c - a*d)^(1/3) - (1 - Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))], (2 + Sqrt[3])/4])/(3^(1/4)*b^(2/3)*(b*c - a*d)^(2/3)*Sqrt[a + b*x]*Sqrt[-((b^(1/3)*(c + d*x)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2)])","A",5,5,19,0.2632,1,"{51, 63, 308, 225, 1881}"
1753,1,858,0,0.7522021,"\int \frac{1}{(a+b x)^{5/2} \sqrt[6]{c+d x}} \, dx","Int[1/((a + b*x)^(5/2)*(c + d*x)^(1/6)),x]","\frac{8 \left(1+\sqrt{3}\right) \sqrt{a+b x} \sqrt[6]{c+d x} d^2}{9 b^{2/3} (b c-a d)^2 \left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)}+\frac{8 \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} E\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right) d}{3\ 3^{3/4} b^{2/3} (b c-a d)^{5/3} \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{4 \left(1-\sqrt{3}\right) \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right) d}{9 \sqrt[4]{3} b^{2/3} (b c-a d)^{5/3} \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{8 (c+d x)^{5/6} d}{9 (b c-a d)^2 \sqrt{a+b x}}-\frac{2 (c+d x)^{5/6}}{3 (b c-a d) (a+b x)^{3/2}}","\frac{8 \left(1+\sqrt{3}\right) \sqrt{a+b x} \sqrt[6]{c+d x} d^2}{9 b^{2/3} (b c-a d)^2 \left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)}+\frac{8 \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} E\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right) d}{3\ 3^{3/4} b^{2/3} (b c-a d)^{5/3} \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{4 \left(1-\sqrt{3}\right) \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right) d}{9 \sqrt[4]{3} b^{2/3} (b c-a d)^{5/3} \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{8 (c+d x)^{5/6} d}{9 (b c-a d)^2 \sqrt{a+b x}}-\frac{2 (c+d x)^{5/6}}{3 (b c-a d) (a+b x)^{3/2}}",1,"(-2*(c + d*x)^(5/6))/(3*(b*c - a*d)*(a + b*x)^(3/2)) + (8*d*(c + d*x)^(5/6))/(9*(b*c - a*d)^2*Sqrt[a + b*x]) + (8*(1 + Sqrt[3])*d^2*Sqrt[a + b*x]*(c + d*x)^(1/6))/(9*b^(2/3)*(b*c - a*d)^2*((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))) + (8*d*(c + d*x)^(1/6)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2]*EllipticE[ArcCos[((b*c - a*d)^(1/3) - (1 - Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))], (2 + Sqrt[3])/4])/(3*3^(3/4)*b^(2/3)*(b*c - a*d)^(5/3)*Sqrt[a + b*x]*Sqrt[-((b^(1/3)*(c + d*x)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2)]) + (4*(1 - Sqrt[3])*d*(c + d*x)^(1/6)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2]*EllipticF[ArcCos[((b*c - a*d)^(1/3) - (1 - Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))], (2 + Sqrt[3])/4])/(9*3^(1/4)*b^(2/3)*(b*c - a*d)^(5/3)*Sqrt[a + b*x]*Sqrt[-((b^(1/3)*(c + d*x)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2)])","A",6,5,19,0.2632,1,"{51, 63, 308, 225, 1881}"
1754,1,440,0,0.3272301,"\int \frac{(a+b x)^{5/2}}{(c+d x)^{5/6}} \, dx","Int[(a + b*x)^(5/2)/(c + d*x)^(5/6),x]","-\frac{81\ 3^{3/4} \sqrt[6]{c+d x} (b c-a d)^{8/3} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+(b c-a d)^{2/3}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{128 d^4 \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{81 \sqrt{a+b x} \sqrt[6]{c+d x} (b c-a d)^2}{64 d^3}-\frac{9 (a+b x)^{3/2} \sqrt[6]{c+d x} (b c-a d)}{16 d^2}+\frac{3 (a+b x)^{5/2} \sqrt[6]{c+d x}}{8 d}","-\frac{81\ 3^{3/4} \sqrt[6]{c+d x} (b c-a d)^{8/3} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+(b c-a d)^{2/3}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{128 d^4 \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{81 \sqrt{a+b x} \sqrt[6]{c+d x} (b c-a d)^2}{64 d^3}-\frac{9 (a+b x)^{3/2} \sqrt[6]{c+d x} (b c-a d)}{16 d^2}+\frac{3 (a+b x)^{5/2} \sqrt[6]{c+d x}}{8 d}",1,"(81*(b*c - a*d)^2*Sqrt[a + b*x]*(c + d*x)^(1/6))/(64*d^3) - (9*(b*c - a*d)*(a + b*x)^(3/2)*(c + d*x)^(1/6))/(16*d^2) + (3*(a + b*x)^(5/2)*(c + d*x)^(1/6))/(8*d) - (81*3^(3/4)*(b*c - a*d)^(8/3)*(c + d*x)^(1/6)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2]*EllipticF[ArcCos[((b*c - a*d)^(1/3) - (1 - Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))], (2 + Sqrt[3])/4])/(128*d^4*Sqrt[a + b*x]*Sqrt[-((b^(1/3)*(c + d*x)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2)])","A",5,3,19,0.1579,1,"{50, 63, 225}"
1755,1,405,0,0.279166,"\int \frac{(a+b x)^{3/2}}{(c+d x)^{5/6}} \, dx","Int[(a + b*x)^(3/2)/(c + d*x)^(5/6),x]","\frac{27\ 3^{3/4} \sqrt[6]{c+d x} (b c-a d)^{5/3} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+(b c-a d)^{2/3}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{40 d^3 \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{27 \sqrt{a+b x} \sqrt[6]{c+d x} (b c-a d)}{20 d^2}+\frac{3 (a+b x)^{3/2} \sqrt[6]{c+d x}}{5 d}","\frac{27\ 3^{3/4} \sqrt[6]{c+d x} (b c-a d)^{5/3} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+(b c-a d)^{2/3}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{40 d^3 \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{27 \sqrt{a+b x} \sqrt[6]{c+d x} (b c-a d)}{20 d^2}+\frac{3 (a+b x)^{3/2} \sqrt[6]{c+d x}}{5 d}",1,"(-27*(b*c - a*d)*Sqrt[a + b*x]*(c + d*x)^(1/6))/(20*d^2) + (3*(a + b*x)^(3/2)*(c + d*x)^(1/6))/(5*d) + (27*3^(3/4)*(b*c - a*d)^(5/3)*(c + d*x)^(1/6)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2]*EllipticF[ArcCos[((b*c - a*d)^(1/3) - (1 - Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))], (2 + Sqrt[3])/4])/(40*d^3*Sqrt[a + b*x]*Sqrt[-((b^(1/3)*(c + d*x)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2)])","A",4,3,19,0.1579,1,"{50, 63, 225}"
1756,1,372,0,0.2355138,"\int \frac{\sqrt{a+b x}}{(c+d x)^{5/6}} \, dx","Int[Sqrt[a + b*x]/(c + d*x)^(5/6),x]","\frac{3 \sqrt{a+b x} \sqrt[6]{c+d x}}{2 d}-\frac{3\ 3^{3/4} \sqrt[6]{c+d x} (b c-a d)^{2/3} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+(b c-a d)^{2/3}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{4 d^2 \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}","\frac{3 \sqrt{a+b x} \sqrt[6]{c+d x}}{2 d}-\frac{3\ 3^{3/4} \sqrt[6]{c+d x} (b c-a d)^{2/3} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+(b c-a d)^{2/3}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{4 d^2 \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}",1,"(3*Sqrt[a + b*x]*(c + d*x)^(1/6))/(2*d) - (3*3^(3/4)*(b*c - a*d)^(2/3)*(c + d*x)^(1/6)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2]*EllipticF[ArcCos[((b*c - a*d)^(1/3) - (1 - Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))], (2 + Sqrt[3])/4])/(4*d^2*Sqrt[a + b*x]*Sqrt[-((b^(1/3)*(c + d*x)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2)])","A",3,3,19,0.1579,1,"{50, 63, 225}"
1757,1,343,0,0.1940584,"\int \frac{1}{\sqrt{a+b x} (c+d x)^{5/6}} \, dx","Int[1/(Sqrt[a + b*x]*(c + d*x)^(5/6)),x]","\frac{3^{3/4} \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+(b c-a d)^{2/3}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{d \sqrt{a+b x} \sqrt[3]{b c-a d} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}","\frac{3^{3/4} \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+(b c-a d)^{2/3}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{d \sqrt{a+b x} \sqrt[3]{b c-a d} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}",1,"(3^(3/4)*(c + d*x)^(1/6)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2]*EllipticF[ArcCos[((b*c - a*d)^(1/3) - (1 - Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))], (2 + Sqrt[3])/4])/(d*(b*c - a*d)^(1/3)*Sqrt[a + b*x]*Sqrt[-((b^(1/3)*(c + d*x)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2)])","A",2,2,19,0.1053,1,"{63, 225}"
1758,1,372,0,0.2306085,"\int \frac{1}{(a+b x)^{3/2} (c+d x)^{5/6}} \, dx","Int[1/((a + b*x)^(3/2)*(c + d*x)^(5/6)),x]","-\frac{2 \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+(b c-a d)^{2/3}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{\sqrt[4]{3} \sqrt{a+b x} (b c-a d)^{4/3} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{2 \sqrt[6]{c+d x}}{\sqrt{a+b x} (b c-a d)}","-\frac{2 \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+(b c-a d)^{2/3}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{\sqrt[4]{3} \sqrt{a+b x} (b c-a d)^{4/3} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{2 \sqrt[6]{c+d x}}{\sqrt{a+b x} (b c-a d)}",1,"(-2*(c + d*x)^(1/6))/((b*c - a*d)*Sqrt[a + b*x]) - (2*(c + d*x)^(1/6)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2]*EllipticF[ArcCos[((b*c - a*d)^(1/3) - (1 - Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))], (2 + Sqrt[3])/4])/(3^(1/4)*(b*c - a*d)^(4/3)*Sqrt[a + b*x]*Sqrt[-((b^(1/3)*(c + d*x)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2)])","A",3,3,19,0.1579,1,"{51, 63, 225}"
1759,1,410,0,0.2684035,"\int \frac{1}{(a+b x)^{5/2} (c+d x)^{5/6}} \, dx","Int[1/((a + b*x)^(5/2)*(c + d*x)^(5/6)),x]","\frac{16 d \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+(b c-a d)^{2/3}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{9 \sqrt[4]{3} \sqrt{a+b x} (b c-a d)^{7/3} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{16 d \sqrt[6]{c+d x}}{9 \sqrt{a+b x} (b c-a d)^2}-\frac{2 \sqrt[6]{c+d x}}{3 (a+b x)^{3/2} (b c-a d)}","\frac{16 d \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+(b c-a d)^{2/3}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{9 \sqrt[4]{3} \sqrt{a+b x} (b c-a d)^{7/3} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{16 d \sqrt[6]{c+d x}}{9 \sqrt{a+b x} (b c-a d)^2}-\frac{2 \sqrt[6]{c+d x}}{3 (a+b x)^{3/2} (b c-a d)}",1,"(-2*(c + d*x)^(1/6))/(3*(b*c - a*d)*(a + b*x)^(3/2)) + (16*d*(c + d*x)^(1/6))/(9*(b*c - a*d)^2*Sqrt[a + b*x]) + (16*d*(c + d*x)^(1/6)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2]*EllipticF[ArcCos[((b*c - a*d)^(1/3) - (1 - Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))], (2 + Sqrt[3])/4])/(9*3^(1/4)*(b*c - a*d)^(7/3)*Sqrt[a + b*x]*Sqrt[-((b^(1/3)*(c + d*x)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2)])","A",4,3,19,0.1579,1,"{51, 63, 225}"
1760,1,880,0,0.9014279,"\int \frac{(a+b x)^{5/2}}{(c+d x)^{7/6}} \, dx","Int[(a + b*x)^(5/2)/(c + d*x)^(7/6),x]","-\frac{6 (a+b x)^{5/2}}{d \sqrt[6]{c+d x}}+\frac{45 b (c+d x)^{5/6} (a+b x)^{3/2}}{7 d^2}-\frac{405 b (b c-a d) (c+d x)^{5/6} \sqrt{a+b x}}{56 d^3}-\frac{1215 \left(1+\sqrt{3}\right) \sqrt[3]{b} (b c-a d)^2 \sqrt[6]{c+d x} \sqrt{a+b x}}{112 d^3 \left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)}-\frac{1215 \sqrt[4]{3} \sqrt[3]{b} (b c-a d)^{7/3} \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} E\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{112 d^4 \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} \sqrt{a+b x}}-\frac{405\ 3^{3/4} \left(1-\sqrt{3}\right) \sqrt[3]{b} (b c-a d)^{7/3} \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{224 d^4 \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} \sqrt{a+b x}}","-\frac{6 (a+b x)^{5/2}}{d \sqrt[6]{c+d x}}+\frac{45 b (c+d x)^{5/6} (a+b x)^{3/2}}{7 d^2}-\frac{405 b (b c-a d) (c+d x)^{5/6} \sqrt{a+b x}}{56 d^3}-\frac{1215 \left(1+\sqrt{3}\right) \sqrt[3]{b} (b c-a d)^2 \sqrt[6]{c+d x} \sqrt{a+b x}}{112 d^3 \left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)}-\frac{1215 \sqrt[4]{3} \sqrt[3]{b} (b c-a d)^{7/3} \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} E\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{112 d^4 \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} \sqrt{a+b x}}-\frac{405\ 3^{3/4} \left(1-\sqrt{3}\right) \sqrt[3]{b} (b c-a d)^{7/3} \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{224 d^4 \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} \sqrt{a+b x}}",1,"(-6*(a + b*x)^(5/2))/(d*(c + d*x)^(1/6)) - (405*b*(b*c - a*d)*Sqrt[a + b*x]*(c + d*x)^(5/6))/(56*d^3) + (45*b*(a + b*x)^(3/2)*(c + d*x)^(5/6))/(7*d^2) - (1215*(1 + Sqrt[3])*b^(1/3)*(b*c - a*d)^2*Sqrt[a + b*x]*(c + d*x)^(1/6))/(112*d^3*((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))) - (1215*3^(1/4)*b^(1/3)*(b*c - a*d)^(7/3)*(c + d*x)^(1/6)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2]*EllipticE[ArcCos[((b*c - a*d)^(1/3) - (1 - Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))], (2 + Sqrt[3])/4])/(112*d^4*Sqrt[a + b*x]*Sqrt[-((b^(1/3)*(c + d*x)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2)]) - (405*3^(3/4)*(1 - Sqrt[3])*b^(1/3)*(b*c - a*d)^(7/3)*(c + d*x)^(1/6)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2]*EllipticF[ArcCos[((b*c - a*d)^(1/3) - (1 - Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))], (2 + Sqrt[3])/4])/(224*d^4*Sqrt[a + b*x]*Sqrt[-((b^(1/3)*(c + d*x)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2)])","A",7,6,19,0.3158,1,"{47, 50, 63, 308, 225, 1881}"
1761,1,844,0,0.7725398,"\int \frac{(a+b x)^{3/2}}{(c+d x)^{7/6}} \, dx","Int[(a + b*x)^(3/2)/(c + d*x)^(7/6),x]","-\frac{6 (a+b x)^{3/2}}{d \sqrt[6]{c+d x}}+\frac{27 b (c+d x)^{5/6} \sqrt{a+b x}}{4 d^2}+\frac{81 \left(1+\sqrt{3}\right) \sqrt[3]{b} (b c-a d) \sqrt[6]{c+d x} \sqrt{a+b x}}{8 d^2 \left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)}+\frac{81 \sqrt[4]{3} \sqrt[3]{b} (b c-a d)^{4/3} \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} E\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{8 d^3 \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} \sqrt{a+b x}}+\frac{27\ 3^{3/4} \left(1-\sqrt{3}\right) \sqrt[3]{b} (b c-a d)^{4/3} \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{16 d^3 \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} \sqrt{a+b x}}","-\frac{6 (a+b x)^{3/2}}{d \sqrt[6]{c+d x}}+\frac{27 b (c+d x)^{5/6} \sqrt{a+b x}}{4 d^2}+\frac{81 \left(1+\sqrt{3}\right) \sqrt[3]{b} (b c-a d) \sqrt[6]{c+d x} \sqrt{a+b x}}{8 d^2 \left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)}+\frac{81 \sqrt[4]{3} \sqrt[3]{b} (b c-a d)^{4/3} \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} E\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{8 d^3 \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} \sqrt{a+b x}}+\frac{27\ 3^{3/4} \left(1-\sqrt{3}\right) \sqrt[3]{b} (b c-a d)^{4/3} \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{16 d^3 \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} \sqrt{a+b x}}",1,"(-6*(a + b*x)^(3/2))/(d*(c + d*x)^(1/6)) + (27*b*Sqrt[a + b*x]*(c + d*x)^(5/6))/(4*d^2) + (81*(1 + Sqrt[3])*b^(1/3)*(b*c - a*d)*Sqrt[a + b*x]*(c + d*x)^(1/6))/(8*d^2*((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))) + (81*3^(1/4)*b^(1/3)*(b*c - a*d)^(4/3)*(c + d*x)^(1/6)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2]*EllipticE[ArcCos[((b*c - a*d)^(1/3) - (1 - Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))], (2 + Sqrt[3])/4])/(8*d^3*Sqrt[a + b*x]*Sqrt[-((b^(1/3)*(c + d*x)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2)]) + (27*3^(3/4)*(1 - Sqrt[3])*b^(1/3)*(b*c - a*d)^(4/3)*(c + d*x)^(1/6)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2]*EllipticF[ArcCos[((b*c - a*d)^(1/3) - (1 - Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))], (2 + Sqrt[3])/4])/(16*d^3*Sqrt[a + b*x]*Sqrt[-((b^(1/3)*(c + d*x)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2)])","A",6,6,19,0.3158,1,"{47, 50, 63, 308, 225, 1881}"
1762,1,806,0,0.6679209,"\int \frac{\sqrt{a+b x}}{(c+d x)^{7/6}} \, dx","Int[Sqrt[a + b*x]/(c + d*x)^(7/6),x]","-\frac{9 \sqrt[4]{3} \sqrt[3]{b} \sqrt[3]{b c-a d} \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} E\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{d^2 \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{3\ 3^{3/4} \left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{b c-a d} \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{2 d^2 \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{6 \sqrt{a+b x}}{d \sqrt[6]{c+d x}}-\frac{9 \left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt{a+b x} \sqrt[6]{c+d x}}{d \left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)}","-\frac{9 \sqrt[4]{3} \sqrt[3]{b} \sqrt[3]{b c-a d} \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} E\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{d^2 \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{3\ 3^{3/4} \left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{b c-a d} \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{2 d^2 \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{6 \sqrt{a+b x}}{d \sqrt[6]{c+d x}}-\frac{9 \left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt{a+b x} \sqrt[6]{c+d x}}{d \left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)}",1,"(-6*Sqrt[a + b*x])/(d*(c + d*x)^(1/6)) - (9*(1 + Sqrt[3])*b^(1/3)*Sqrt[a + b*x]*(c + d*x)^(1/6))/(d*((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))) - (9*3^(1/4)*b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/6)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2]*EllipticE[ArcCos[((b*c - a*d)^(1/3) - (1 - Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))], (2 + Sqrt[3])/4])/(d^2*Sqrt[a + b*x]*Sqrt[-((b^(1/3)*(c + d*x)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2)]) - (3*3^(3/4)*(1 - Sqrt[3])*b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/6)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2]*EllipticF[ArcCos[((b*c - a*d)^(1/3) - (1 - Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))], (2 + Sqrt[3])/4])/(2*d^2*Sqrt[a + b*x]*Sqrt[-((b^(1/3)*(c + d*x)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2)])","A",5,5,19,0.2632,1,"{47, 63, 308, 225, 1881}"
1763,1,817,0,0.6716767,"\int \frac{1}{\sqrt{a+b x} (c+d x)^{7/6}} \, dx","Int[1/(Sqrt[a + b*x]*(c + d*x)^(7/6)),x]","\frac{6 \sqrt[4]{3} \sqrt[3]{b} \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} E\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{d (b c-a d)^{2/3} \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{3^{3/4} \left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{d (b c-a d)^{2/3} \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{6 \sqrt{a+b x}}{(b c-a d) \sqrt[6]{c+d x}}+\frac{6 \left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt{a+b x} \sqrt[6]{c+d x}}{(b c-a d) \left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)}","\frac{6 \sqrt[4]{3} \sqrt[3]{b} \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} E\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{d (b c-a d)^{2/3} \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{3^{3/4} \left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{d (b c-a d)^{2/3} \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{6 \sqrt{a+b x}}{(b c-a d) \sqrt[6]{c+d x}}+\frac{6 \left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt{a+b x} \sqrt[6]{c+d x}}{(b c-a d) \left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)}",1,"(6*Sqrt[a + b*x])/((b*c - a*d)*(c + d*x)^(1/6)) + (6*(1 + Sqrt[3])*b^(1/3)*Sqrt[a + b*x]*(c + d*x)^(1/6))/((b*c - a*d)*((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))) + (6*3^(1/4)*b^(1/3)*(c + d*x)^(1/6)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2]*EllipticE[ArcCos[((b*c - a*d)^(1/3) - (1 - Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))], (2 + Sqrt[3])/4])/(d*(b*c - a*d)^(2/3)*Sqrt[a + b*x]*Sqrt[-((b^(1/3)*(c + d*x)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2)]) + (3^(3/4)*(1 - Sqrt[3])*b^(1/3)*(c + d*x)^(1/6)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2]*EllipticF[ArcCos[((b*c - a*d)^(1/3) - (1 - Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))], (2 + Sqrt[3])/4])/(d*(b*c - a*d)^(2/3)*Sqrt[a + b*x]*Sqrt[-((b^(1/3)*(c + d*x)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2)])","A",5,5,19,0.2632,1,"{51, 63, 308, 225, 1881}"
1764,1,844,0,0.7585123,"\int \frac{1}{(a+b x)^{3/2} (c+d x)^{7/6}} \, dx","Int[1/((a + b*x)^(3/2)*(c + d*x)^(7/6)),x]","-\frac{8 \sqrt{a+b x} d}{(b c-a d)^2 \sqrt[6]{c+d x}}-\frac{8 \left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt{a+b x} \sqrt[6]{c+d x} d}{(b c-a d)^2 \left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)}-\frac{8 \sqrt[4]{3} \sqrt[3]{b} \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} E\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{(b c-a d)^{5/3} \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{4 \left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{\sqrt[4]{3} (b c-a d)^{5/3} \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{2}{(b c-a d) \sqrt{a+b x} \sqrt[6]{c+d x}}","-\frac{8 \sqrt{a+b x} d}{(b c-a d)^2 \sqrt[6]{c+d x}}-\frac{8 \left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt{a+b x} \sqrt[6]{c+d x} d}{(b c-a d)^2 \left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)}-\frac{8 \sqrt[4]{3} \sqrt[3]{b} \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} E\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{(b c-a d)^{5/3} \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{4 \left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{\sqrt[4]{3} (b c-a d)^{5/3} \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{2}{(b c-a d) \sqrt{a+b x} \sqrt[6]{c+d x}}",1,"-2/((b*c - a*d)*Sqrt[a + b*x]*(c + d*x)^(1/6)) - (8*d*Sqrt[a + b*x])/((b*c - a*d)^2*(c + d*x)^(1/6)) - (8*(1 + Sqrt[3])*b^(1/3)*d*Sqrt[a + b*x]*(c + d*x)^(1/6))/((b*c - a*d)^2*((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))) - (8*3^(1/4)*b^(1/3)*(c + d*x)^(1/6)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2]*EllipticE[ArcCos[((b*c - a*d)^(1/3) - (1 - Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))], (2 + Sqrt[3])/4])/((b*c - a*d)^(5/3)*Sqrt[a + b*x]*Sqrt[-((b^(1/3)*(c + d*x)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2)]) - (4*(1 - Sqrt[3])*b^(1/3)*(c + d*x)^(1/6)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2]*EllipticF[ArcCos[((b*c - a*d)^(1/3) - (1 - Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))], (2 + Sqrt[3])/4])/(3^(1/4)*(b*c - a*d)^(5/3)*Sqrt[a + b*x]*Sqrt[-((b^(1/3)*(c + d*x)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2)])","A",6,5,19,0.2632,1,"{51, 63, 308, 225, 1881}"
1765,1,893,0,0.8684238,"\int \frac{1}{(a+b x)^{5/2} (c+d x)^{7/6}} \, dx","Int[1/((a + b*x)^(5/2)*(c + d*x)^(7/6)),x]","\frac{80 \sqrt{a+b x} d^2}{9 (b c-a d)^3 \sqrt[6]{c+d x}}+\frac{80 \left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt{a+b x} \sqrt[6]{c+d x} d^2}{9 (b c-a d)^3 \left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)}+\frac{80 \sqrt[3]{b} \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} E\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right) d}{3\ 3^{3/4} (b c-a d)^{8/3} \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{40 \left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right) d}{9 \sqrt[4]{3} (b c-a d)^{8/3} \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{20 d}{9 (b c-a d)^2 \sqrt{a+b x} \sqrt[6]{c+d x}}-\frac{2}{3 (b c-a d) (a+b x)^{3/2} \sqrt[6]{c+d x}}","\frac{80 \sqrt{a+b x} d^2}{9 (b c-a d)^3 \sqrt[6]{c+d x}}+\frac{80 \left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt{a+b x} \sqrt[6]{c+d x} d^2}{9 (b c-a d)^3 \left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)}+\frac{80 \sqrt[3]{b} \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} E\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right) d}{3\ 3^{3/4} (b c-a d)^{8/3} \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{40 \left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} F\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right) d}{9 \sqrt[4]{3} (b c-a d)^{8/3} \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{20 d}{9 (b c-a d)^2 \sqrt{a+b x} \sqrt[6]{c+d x}}-\frac{2}{3 (b c-a d) (a+b x)^{3/2} \sqrt[6]{c+d x}}",1,"-2/(3*(b*c - a*d)*(a + b*x)^(3/2)*(c + d*x)^(1/6)) + (20*d)/(9*(b*c - a*d)^2*Sqrt[a + b*x]*(c + d*x)^(1/6)) + (80*d^2*Sqrt[a + b*x])/(9*(b*c - a*d)^3*(c + d*x)^(1/6)) + (80*(1 + Sqrt[3])*b^(1/3)*d^2*Sqrt[a + b*x]*(c + d*x)^(1/6))/(9*(b*c - a*d)^3*((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))) + (80*b^(1/3)*d*(c + d*x)^(1/6)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2]*EllipticE[ArcCos[((b*c - a*d)^(1/3) - (1 - Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))], (2 + Sqrt[3])/4])/(3*3^(3/4)*(b*c - a*d)^(8/3)*Sqrt[a + b*x]*Sqrt[-((b^(1/3)*(c + d*x)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2)]) + (40*(1 - Sqrt[3])*b^(1/3)*d*(c + d*x)^(1/6)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3))*Sqrt[((b*c - a*d)^(2/3) + b^(1/3)*(b*c - a*d)^(1/3)*(c + d*x)^(1/3) + b^(2/3)*(c + d*x)^(2/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2]*EllipticF[ArcCos[((b*c - a*d)^(1/3) - (1 - Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))], (2 + Sqrt[3])/4])/(9*3^(1/4)*(b*c - a*d)^(8/3)*Sqrt[a + b*x]*Sqrt[-((b^(1/3)*(c + d*x)^(1/3)*((b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)))/((b*c - a*d)^(1/3) - (1 + Sqrt[3])*b^(1/3)*(c + d*x)^(1/3))^2)])","A",7,5,19,0.2632,1,"{51, 63, 308, 225, 1881}"
1766,1,84,0,0.0211692,"\int \sqrt[6]{a+b x} (c+d x)^{13/6} \, dx","Int[(a + b*x)^(1/6)*(c + d*x)^(13/6),x]","\frac{6 (a+b x)^{7/6} \sqrt[6]{c+d x} (b c-a d)^2 \, _2F_1\left(-\frac{13}{6},\frac{7}{6};\frac{13}{6};-\frac{d (a+b x)}{b c-a d}\right)}{7 b^3 \sqrt[6]{\frac{b (c+d x)}{b c-a d}}}","\frac{6 (a+b x)^{7/6} \sqrt[6]{c+d x} (b c-a d)^2 \, _2F_1\left(-\frac{13}{6},\frac{7}{6};\frac{13}{6};-\frac{d (a+b x)}{b c-a d}\right)}{7 b^3 \sqrt[6]{\frac{b (c+d x)}{b c-a d}}}",1,"(6*(b*c - a*d)^2*(a + b*x)^(7/6)*(c + d*x)^(1/6)*Hypergeometric2F1[-13/6, 7/6, 13/6, -((d*(a + b*x))/(b*c - a*d))])/(7*b^3*((b*(c + d*x))/(b*c - a*d))^(1/6))","A",2,2,19,0.1053,1,"{70, 69}"
1767,1,82,0,0.0241791,"\int \sqrt[6]{a+b x} (c+d x)^{7/6} \, dx","Int[(a + b*x)^(1/6)*(c + d*x)^(7/6),x]","\frac{6 (a+b x)^{7/6} \sqrt[6]{c+d x} (b c-a d) \, _2F_1\left(-\frac{7}{6},\frac{7}{6};\frac{13}{6};-\frac{d (a+b x)}{b c-a d}\right)}{7 b^2 \sqrt[6]{\frac{b (c+d x)}{b c-a d}}}","\frac{6 (a+b x)^{7/6} \sqrt[6]{c+d x} (b c-a d) \, _2F_1\left(-\frac{7}{6},\frac{7}{6};\frac{13}{6};-\frac{d (a+b x)}{b c-a d}\right)}{7 b^2 \sqrt[6]{\frac{b (c+d x)}{b c-a d}}}",1,"(6*(b*c - a*d)*(a + b*x)^(7/6)*(c + d*x)^(1/6)*Hypergeometric2F1[-7/6, 7/6, 13/6, -((d*(a + b*x))/(b*c - a*d))])/(7*b^2*((b*(c + d*x))/(b*c - a*d))^(1/6))","A",2,2,19,0.1053,1,"{70, 69}"
1768,1,74,0,0.0204714,"\int \sqrt[6]{a+b x} \sqrt[6]{c+d x} \, dx","Int[(a + b*x)^(1/6)*(c + d*x)^(1/6),x]","\frac{6 (a+b x)^{7/6} \sqrt[6]{c+d x} \, _2F_1\left(-\frac{1}{6},\frac{7}{6};\frac{13}{6};-\frac{d (a+b x)}{b c-a d}\right)}{7 b \sqrt[6]{\frac{b (c+d x)}{b c-a d}}}","\frac{6 (a+b x)^{7/6} \sqrt[6]{c+d x} \, _2F_1\left(-\frac{1}{6},\frac{7}{6};\frac{13}{6};-\frac{d (a+b x)}{b c-a d}\right)}{7 b \sqrt[6]{\frac{b (c+d x)}{b c-a d}}}",1,"(6*(a + b*x)^(7/6)*(c + d*x)^(1/6)*Hypergeometric2F1[-1/6, 7/6, 13/6, -((d*(a + b*x))/(b*c - a*d))])/(7*b*((b*(c + d*x))/(b*c - a*d))^(1/6))","A",2,2,19,0.1053,1,"{70, 69}"
1769,1,74,0,0.0201391,"\int \frac{\sqrt[6]{a+b x}}{(c+d x)^{5/6}} \, dx","Int[(a + b*x)^(1/6)/(c + d*x)^(5/6),x]","\frac{6 (a+b x)^{7/6} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6} \, _2F_1\left(\frac{5}{6},\frac{7}{6};\frac{13}{6};-\frac{d (a+b x)}{b c-a d}\right)}{7 b (c+d x)^{5/6}}","\frac{6 (a+b x)^{7/6} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6} \, _2F_1\left(\frac{5}{6},\frac{7}{6};\frac{13}{6};-\frac{d (a+b x)}{b c-a d}\right)}{7 b (c+d x)^{5/6}}",1,"(6*(a + b*x)^(7/6)*((b*(c + d*x))/(b*c - a*d))^(5/6)*Hypergeometric2F1[5/6, 7/6, 13/6, -((d*(a + b*x))/(b*c - a*d))])/(7*b*(c + d*x)^(5/6))","A",2,2,19,0.1053,1,"{70, 69}"
1770,1,81,0,0.0205303,"\int \frac{\sqrt[6]{a+b x}}{(c+d x)^{11/6}} \, dx","Int[(a + b*x)^(1/6)/(c + d*x)^(11/6),x]","\frac{6 (a+b x)^{7/6} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6} \, _2F_1\left(\frac{7}{6},\frac{11}{6};\frac{13}{6};-\frac{d (a+b x)}{b c-a d}\right)}{7 (c+d x)^{5/6} (b c-a d)}","\frac{6 (a+b x)^{7/6} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6} \, _2F_1\left(\frac{7}{6},\frac{11}{6};\frac{13}{6};-\frac{d (a+b x)}{b c-a d}\right)}{7 (c+d x)^{5/6} (b c-a d)}",1,"(6*(a + b*x)^(7/6)*((b*(c + d*x))/(b*c - a*d))^(5/6)*Hypergeometric2F1[7/6, 11/6, 13/6, -((d*(a + b*x))/(b*c - a*d))])/(7*(b*c - a*d)*(c + d*x)^(5/6))","A",2,2,19,0.1053,1,"{70, 69}"
1771,1,82,0,0.0212505,"\int \frac{\sqrt[6]{a+b x}}{(c+d x)^{17/6}} \, dx","Int[(a + b*x)^(1/6)/(c + d*x)^(17/6),x]","\frac{6 b (a+b x)^{7/6} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6} \, _2F_1\left(\frac{7}{6},\frac{17}{6};\frac{13}{6};-\frac{d (a+b x)}{b c-a d}\right)}{7 (c+d x)^{5/6} (b c-a d)^2}","\frac{6 b (a+b x)^{7/6} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6} \, _2F_1\left(\frac{7}{6},\frac{17}{6};\frac{13}{6};-\frac{d (a+b x)}{b c-a d}\right)}{7 (c+d x)^{5/6} (b c-a d)^2}",1,"(6*b*(a + b*x)^(7/6)*((b*(c + d*x))/(b*c - a*d))^(5/6)*Hypergeometric2F1[7/6, 17/6, 13/6, -((d*(a + b*x))/(b*c - a*d))])/(7*(b*c - a*d)^2*(c + d*x)^(5/6))","A",2,2,19,0.1053,1,"{70, 69}"
1772,1,427,0,0.6431882,"\int \sqrt[6]{a+b x} (c+d x)^{5/6} \, dx","Int[(a + b*x)^(1/6)*(c + d*x)^(5/6),x]","\frac{5 (b c-a d)^2 \log \left(-\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{144 b^{11/6} d^{7/6}}-\frac{5 (b c-a d)^2 \log \left(\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{144 b^{11/6} d^{7/6}}+\frac{5 (b c-a d)^2 \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{24 \sqrt{3} b^{11/6} d^{7/6}}-\frac{5 (b c-a d)^2 \tan ^{-1}\left(\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}+\frac{1}{\sqrt{3}}\right)}{24 \sqrt{3} b^{11/6} d^{7/6}}-\frac{5 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{36 b^{11/6} d^{7/6}}+\frac{5 \sqrt[6]{a+b x} (c+d x)^{5/6} (b c-a d)}{12 b d}+\frac{(a+b x)^{7/6} (c+d x)^{5/6}}{2 b}","\frac{5 (b c-a d)^2 \log \left(-\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{144 b^{11/6} d^{7/6}}-\frac{5 (b c-a d)^2 \log \left(\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{144 b^{11/6} d^{7/6}}+\frac{5 (b c-a d)^2 \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{24 \sqrt{3} b^{11/6} d^{7/6}}-\frac{5 (b c-a d)^2 \tan ^{-1}\left(\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}+\frac{1}{\sqrt{3}}\right)}{24 \sqrt{3} b^{11/6} d^{7/6}}-\frac{5 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{36 b^{11/6} d^{7/6}}+\frac{5 \sqrt[6]{a+b x} (c+d x)^{5/6} (b c-a d)}{12 b d}+\frac{(a+b x)^{7/6} (c+d x)^{5/6}}{2 b}",1,"(5*(b*c - a*d)*(a + b*x)^(1/6)*(c + d*x)^(5/6))/(12*b*d) + ((a + b*x)^(7/6)*(c + d*x)^(5/6))/(2*b) + (5*(b*c - a*d)^2*ArcTan[1/Sqrt[3] - (2*d^(1/6)*(a + b*x)^(1/6))/(Sqrt[3]*b^(1/6)*(c + d*x)^(1/6))])/(24*Sqrt[3]*b^(11/6)*d^(7/6)) - (5*(b*c - a*d)^2*ArcTan[1/Sqrt[3] + (2*d^(1/6)*(a + b*x)^(1/6))/(Sqrt[3]*b^(1/6)*(c + d*x)^(1/6))])/(24*Sqrt[3]*b^(11/6)*d^(7/6)) - (5*(b*c - a*d)^2*ArcTanh[(d^(1/6)*(a + b*x)^(1/6))/(b^(1/6)*(c + d*x)^(1/6))])/(36*b^(11/6)*d^(7/6)) + (5*(b*c - a*d)^2*Log[b^(1/3) + (d^(1/3)*(a + b*x)^(1/3))/(c + d*x)^(1/3) - (b^(1/6)*d^(1/6)*(a + b*x)^(1/6))/(c + d*x)^(1/6)])/(144*b^(11/6)*d^(7/6)) - (5*(b*c - a*d)^2*Log[b^(1/3) + (d^(1/3)*(a + b*x)^(1/3))/(c + d*x)^(1/3) + (b^(1/6)*d^(1/6)*(a + b*x)^(1/6))/(c + d*x)^(1/6)])/(144*b^(11/6)*d^(7/6))","A",14,9,19,0.4737,1,"{50, 63, 240, 210, 634, 618, 204, 628, 208}"
1773,1,378,0,0.4970566,"\int \frac{\sqrt[6]{a+b x}}{\sqrt[6]{c+d x}} \, dx","Int[(a + b*x)^(1/6)/(c + d*x)^(1/6),x]","\frac{(b c-a d) \log \left(-\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{12 b^{5/6} d^{7/6}}-\frac{(b c-a d) \log \left(\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{12 b^{5/6} d^{7/6}}+\frac{(b c-a d) \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{2 \sqrt{3} b^{5/6} d^{7/6}}-\frac{(b c-a d) \tan ^{-1}\left(\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} b^{5/6} d^{7/6}}-\frac{(b c-a d) \tanh ^{-1}\left(\frac{\sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{3 b^{5/6} d^{7/6}}+\frac{\sqrt[6]{a+b x} (c+d x)^{5/6}}{d}","\frac{(b c-a d) \log \left(-\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{12 b^{5/6} d^{7/6}}-\frac{(b c-a d) \log \left(\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{12 b^{5/6} d^{7/6}}+\frac{(b c-a d) \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{2 \sqrt{3} b^{5/6} d^{7/6}}-\frac{(b c-a d) \tan ^{-1}\left(\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} b^{5/6} d^{7/6}}-\frac{(b c-a d) \tanh ^{-1}\left(\frac{\sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{3 b^{5/6} d^{7/6}}+\frac{\sqrt[6]{a+b x} (c+d x)^{5/6}}{d}",1,"((a + b*x)^(1/6)*(c + d*x)^(5/6))/d + ((b*c - a*d)*ArcTan[1/Sqrt[3] - (2*d^(1/6)*(a + b*x)^(1/6))/(Sqrt[3]*b^(1/6)*(c + d*x)^(1/6))])/(2*Sqrt[3]*b^(5/6)*d^(7/6)) - ((b*c - a*d)*ArcTan[1/Sqrt[3] + (2*d^(1/6)*(a + b*x)^(1/6))/(Sqrt[3]*b^(1/6)*(c + d*x)^(1/6))])/(2*Sqrt[3]*b^(5/6)*d^(7/6)) - ((b*c - a*d)*ArcTanh[(d^(1/6)*(a + b*x)^(1/6))/(b^(1/6)*(c + d*x)^(1/6))])/(3*b^(5/6)*d^(7/6)) + ((b*c - a*d)*Log[b^(1/3) + (d^(1/3)*(a + b*x)^(1/3))/(c + d*x)^(1/3) - (b^(1/6)*d^(1/6)*(a + b*x)^(1/6))/(c + d*x)^(1/6)])/(12*b^(5/6)*d^(7/6)) - ((b*c - a*d)*Log[b^(1/3) + (d^(1/3)*(a + b*x)^(1/3))/(c + d*x)^(1/3) + (b^(1/6)*d^(1/6)*(a + b*x)^(1/6))/(c + d*x)^(1/6)])/(12*b^(5/6)*d^(7/6))","A",13,9,19,0.4737,1,"{50, 63, 240, 210, 634, 618, 204, 628, 208}"
1774,1,332,0,0.4871189,"\int \frac{\sqrt[6]{a+b x}}{(c+d x)^{7/6}} \, dx","Int[(a + b*x)^(1/6)/(c + d*x)^(7/6),x]","-\frac{\sqrt[6]{b} \log \left(-\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{2 d^{7/6}}+\frac{\sqrt[6]{b} \log \left(\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{2 d^{7/6}}-\frac{\sqrt{3} \sqrt[6]{b} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{d^{7/6}}+\frac{\sqrt{3} \sqrt[6]{b} \tan ^{-1}\left(\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}+\frac{1}{\sqrt{3}}\right)}{d^{7/6}}+\frac{2 \sqrt[6]{b} \tanh ^{-1}\left(\frac{\sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{d^{7/6}}-\frac{6 \sqrt[6]{a+b x}}{d \sqrt[6]{c+d x}}","-\frac{\sqrt[6]{b} \log \left(-\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{2 d^{7/6}}+\frac{\sqrt[6]{b} \log \left(\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{2 d^{7/6}}-\frac{\sqrt{3} \sqrt[6]{b} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{d^{7/6}}+\frac{\sqrt{3} \sqrt[6]{b} \tan ^{-1}\left(\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}+\frac{1}{\sqrt{3}}\right)}{d^{7/6}}+\frac{2 \sqrt[6]{b} \tanh ^{-1}\left(\frac{\sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{d^{7/6}}-\frac{6 \sqrt[6]{a+b x}}{d \sqrt[6]{c+d x}}",1,"(-6*(a + b*x)^(1/6))/(d*(c + d*x)^(1/6)) - (Sqrt[3]*b^(1/6)*ArcTan[1/Sqrt[3] - (2*d^(1/6)*(a + b*x)^(1/6))/(Sqrt[3]*b^(1/6)*(c + d*x)^(1/6))])/d^(7/6) + (Sqrt[3]*b^(1/6)*ArcTan[1/Sqrt[3] + (2*d^(1/6)*(a + b*x)^(1/6))/(Sqrt[3]*b^(1/6)*(c + d*x)^(1/6))])/d^(7/6) + (2*b^(1/6)*ArcTanh[(d^(1/6)*(a + b*x)^(1/6))/(b^(1/6)*(c + d*x)^(1/6))])/d^(7/6) - (b^(1/6)*Log[b^(1/3) + (d^(1/3)*(a + b*x)^(1/3))/(c + d*x)^(1/3) - (b^(1/6)*d^(1/6)*(a + b*x)^(1/6))/(c + d*x)^(1/6)])/(2*d^(7/6)) + (b^(1/6)*Log[b^(1/3) + (d^(1/3)*(a + b*x)^(1/3))/(c + d*x)^(1/3) + (b^(1/6)*d^(1/6)*(a + b*x)^(1/6))/(c + d*x)^(1/6)])/(2*d^(7/6))","A",13,9,19,0.4737,1,"{47, 63, 240, 210, 634, 618, 204, 628, 208}"
1775,1,32,0,0.0032505,"\int \frac{\sqrt[6]{a+b x}}{(c+d x)^{13/6}} \, dx","Int[(a + b*x)^(1/6)/(c + d*x)^(13/6),x]","\frac{6 (a+b x)^{7/6}}{7 (c+d x)^{7/6} (b c-a d)}","\frac{6 (a+b x)^{7/6}}{7 (c+d x)^{7/6} (b c-a d)}",1,"(6*(a + b*x)^(7/6))/(7*(b*c - a*d)*(c + d*x)^(7/6))","A",1,1,19,0.05263,1,"{37}"
1776,1,66,0,0.0090521,"\int \frac{\sqrt[6]{a+b x}}{(c+d x)^{19/6}} \, dx","Int[(a + b*x)^(1/6)/(c + d*x)^(19/6),x]","\frac{36 b (a+b x)^{7/6}}{91 (c+d x)^{7/6} (b c-a d)^2}+\frac{6 (a+b x)^{7/6}}{13 (c+d x)^{13/6} (b c-a d)}","\frac{36 b (a+b x)^{7/6}}{91 (c+d x)^{7/6} (b c-a d)^2}+\frac{6 (a+b x)^{7/6}}{13 (c+d x)^{13/6} (b c-a d)}",1,"(6*(a + b*x)^(7/6))/(13*(b*c - a*d)*(c + d*x)^(13/6)) + (36*b*(a + b*x)^(7/6))/(91*(b*c - a*d)^2*(c + d*x)^(7/6))","A",2,2,19,0.1053,1,"{45, 37}"
1777,1,101,0,0.0209129,"\int \frac{\sqrt[6]{a+b x}}{(c+d x)^{25/6}} \, dx","Int[(a + b*x)^(1/6)/(c + d*x)^(25/6),x]","\frac{432 b^2 (a+b x)^{7/6}}{1729 (c+d x)^{7/6} (b c-a d)^3}+\frac{72 b (a+b x)^{7/6}}{247 (c+d x)^{13/6} (b c-a d)^2}+\frac{6 (a+b x)^{7/6}}{19 (c+d x)^{19/6} (b c-a d)}","\frac{432 b^2 (a+b x)^{7/6}}{1729 (c+d x)^{7/6} (b c-a d)^3}+\frac{72 b (a+b x)^{7/6}}{247 (c+d x)^{13/6} (b c-a d)^2}+\frac{6 (a+b x)^{7/6}}{19 (c+d x)^{19/6} (b c-a d)}",1,"(6*(a + b*x)^(7/6))/(19*(b*c - a*d)*(c + d*x)^(19/6)) + (72*b*(a + b*x)^(7/6))/(247*(b*c - a*d)^2*(c + d*x)^(13/6)) + (432*b^2*(a + b*x)^(7/6))/(1729*(b*c - a*d)^3*(c + d*x)^(7/6))","A",3,2,19,0.1053,1,"{45, 37}"
1778,1,136,0,0.0339152,"\int \frac{\sqrt[6]{a+b x}}{(c+d x)^{31/6}} \, dx","Int[(a + b*x)^(1/6)/(c + d*x)^(31/6),x]","\frac{7776 b^3 (a+b x)^{7/6}}{43225 (c+d x)^{7/6} (b c-a d)^4}+\frac{1296 b^2 (a+b x)^{7/6}}{6175 (c+d x)^{13/6} (b c-a d)^3}+\frac{108 b (a+b x)^{7/6}}{475 (c+d x)^{19/6} (b c-a d)^2}+\frac{6 (a+b x)^{7/6}}{25 (c+d x)^{25/6} (b c-a d)}","\frac{7776 b^3 (a+b x)^{7/6}}{43225 (c+d x)^{7/6} (b c-a d)^4}+\frac{1296 b^2 (a+b x)^{7/6}}{6175 (c+d x)^{13/6} (b c-a d)^3}+\frac{108 b (a+b x)^{7/6}}{475 (c+d x)^{19/6} (b c-a d)^2}+\frac{6 (a+b x)^{7/6}}{25 (c+d x)^{25/6} (b c-a d)}",1,"(6*(a + b*x)^(7/6))/(25*(b*c - a*d)*(c + d*x)^(25/6)) + (108*b*(a + b*x)^(7/6))/(475*(b*c - a*d)^2*(c + d*x)^(19/6)) + (1296*b^2*(a + b*x)^(7/6))/(6175*(b*c - a*d)^3*(c + d*x)^(13/6)) + (7776*b^3*(a + b*x)^(7/6))/(43225*(b*c - a*d)^4*(c + d*x)^(7/6))","A",4,2,19,0.1053,1,"{45, 37}"
1779,1,427,0,0.6423474,"\int (a+b x)^{5/6} \sqrt[6]{c+d x} \, dx","Int[(a + b*x)^(5/6)*(c + d*x)^(1/6),x]","\frac{5 (b c-a d)^2 \log \left(-\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{144 b^{7/6} d^{11/6}}-\frac{5 (b c-a d)^2 \log \left(\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{144 b^{7/6} d^{11/6}}-\frac{5 (b c-a d)^2 \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{24 \sqrt{3} b^{7/6} d^{11/6}}+\frac{5 (b c-a d)^2 \tan ^{-1}\left(\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}+\frac{1}{\sqrt{3}}\right)}{24 \sqrt{3} b^{7/6} d^{11/6}}-\frac{5 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{36 b^{7/6} d^{11/6}}+\frac{(a+b x)^{5/6} \sqrt[6]{c+d x} (b c-a d)}{12 b d}+\frac{(a+b x)^{11/6} \sqrt[6]{c+d x}}{2 b}","\frac{5 (b c-a d)^2 \log \left(-\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{144 b^{7/6} d^{11/6}}-\frac{5 (b c-a d)^2 \log \left(\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{144 b^{7/6} d^{11/6}}-\frac{5 (b c-a d)^2 \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{24 \sqrt{3} b^{7/6} d^{11/6}}+\frac{5 (b c-a d)^2 \tan ^{-1}\left(\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}+\frac{1}{\sqrt{3}}\right)}{24 \sqrt{3} b^{7/6} d^{11/6}}-\frac{5 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{36 b^{7/6} d^{11/6}}+\frac{(a+b x)^{5/6} \sqrt[6]{c+d x} (b c-a d)}{12 b d}+\frac{(a+b x)^{11/6} \sqrt[6]{c+d x}}{2 b}",1,"((b*c - a*d)*(a + b*x)^(5/6)*(c + d*x)^(1/6))/(12*b*d) + ((a + b*x)^(11/6)*(c + d*x)^(1/6))/(2*b) - (5*(b*c - a*d)^2*ArcTan[1/Sqrt[3] - (2*d^(1/6)*(a + b*x)^(1/6))/(Sqrt[3]*b^(1/6)*(c + d*x)^(1/6))])/(24*Sqrt[3]*b^(7/6)*d^(11/6)) + (5*(b*c - a*d)^2*ArcTan[1/Sqrt[3] + (2*d^(1/6)*(a + b*x)^(1/6))/(Sqrt[3]*b^(1/6)*(c + d*x)^(1/6))])/(24*Sqrt[3]*b^(7/6)*d^(11/6)) - (5*(b*c - a*d)^2*ArcTanh[(d^(1/6)*(a + b*x)^(1/6))/(b^(1/6)*(c + d*x)^(1/6))])/(36*b^(7/6)*d^(11/6)) + (5*(b*c - a*d)^2*Log[b^(1/3) + (d^(1/3)*(a + b*x)^(1/3))/(c + d*x)^(1/3) - (b^(1/6)*d^(1/6)*(a + b*x)^(1/6))/(c + d*x)^(1/6)])/(144*b^(7/6)*d^(11/6)) - (5*(b*c - a*d)^2*Log[b^(1/3) + (d^(1/3)*(a + b*x)^(1/3))/(c + d*x)^(1/3) + (b^(1/6)*d^(1/6)*(a + b*x)^(1/6))/(c + d*x)^(1/6)])/(144*b^(7/6)*d^(11/6))","A",14,9,19,0.4737,1,"{50, 63, 331, 296, 634, 618, 204, 628, 208}"
1780,1,378,0,0.5567902,"\int \frac{(a+b x)^{5/6}}{(c+d x)^{5/6}} \, dx","Int[(a + b*x)^(5/6)/(c + d*x)^(5/6),x]","\frac{5 (b c-a d) \log \left(-\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{12 \sqrt[6]{b} d^{11/6}}-\frac{5 (b c-a d) \log \left(\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{12 \sqrt[6]{b} d^{11/6}}-\frac{5 (b c-a d) \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{2 \sqrt{3} \sqrt[6]{b} d^{11/6}}+\frac{5 (b c-a d) \tan ^{-1}\left(\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} \sqrt[6]{b} d^{11/6}}-\frac{5 (b c-a d) \tanh ^{-1}\left(\frac{\sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{3 \sqrt[6]{b} d^{11/6}}+\frac{(a+b x)^{5/6} \sqrt[6]{c+d x}}{d}","\frac{5 (b c-a d) \log \left(-\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{12 \sqrt[6]{b} d^{11/6}}-\frac{5 (b c-a d) \log \left(\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{12 \sqrt[6]{b} d^{11/6}}-\frac{5 (b c-a d) \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{2 \sqrt{3} \sqrt[6]{b} d^{11/6}}+\frac{5 (b c-a d) \tan ^{-1}\left(\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} \sqrt[6]{b} d^{11/6}}-\frac{5 (b c-a d) \tanh ^{-1}\left(\frac{\sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{3 \sqrt[6]{b} d^{11/6}}+\frac{(a+b x)^{5/6} \sqrt[6]{c+d x}}{d}",1,"((a + b*x)^(5/6)*(c + d*x)^(1/6))/d - (5*(b*c - a*d)*ArcTan[1/Sqrt[3] - (2*d^(1/6)*(a + b*x)^(1/6))/(Sqrt[3]*b^(1/6)*(c + d*x)^(1/6))])/(2*Sqrt[3]*b^(1/6)*d^(11/6)) + (5*(b*c - a*d)*ArcTan[1/Sqrt[3] + (2*d^(1/6)*(a + b*x)^(1/6))/(Sqrt[3]*b^(1/6)*(c + d*x)^(1/6))])/(2*Sqrt[3]*b^(1/6)*d^(11/6)) - (5*(b*c - a*d)*ArcTanh[(d^(1/6)*(a + b*x)^(1/6))/(b^(1/6)*(c + d*x)^(1/6))])/(3*b^(1/6)*d^(11/6)) + (5*(b*c - a*d)*Log[b^(1/3) + (d^(1/3)*(a + b*x)^(1/3))/(c + d*x)^(1/3) - (b^(1/6)*d^(1/6)*(a + b*x)^(1/6))/(c + d*x)^(1/6)])/(12*b^(1/6)*d^(11/6)) - (5*(b*c - a*d)*Log[b^(1/3) + (d^(1/3)*(a + b*x)^(1/3))/(c + d*x)^(1/3) + (b^(1/6)*d^(1/6)*(a + b*x)^(1/6))/(c + d*x)^(1/6)])/(12*b^(1/6)*d^(11/6))","A",13,9,19,0.4737,1,"{50, 63, 331, 296, 634, 618, 204, 628, 208}"
1781,1,334,0,0.5608907,"\int \frac{(a+b x)^{5/6}}{(c+d x)^{11/6}} \, dx","Int[(a + b*x)^(5/6)/(c + d*x)^(11/6),x]","-\frac{b^{5/6} \log \left(-\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{2 d^{11/6}}+\frac{b^{5/6} \log \left(\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{2 d^{11/6}}+\frac{\sqrt{3} b^{5/6} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{d^{11/6}}-\frac{\sqrt{3} b^{5/6} \tan ^{-1}\left(\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}+\frac{1}{\sqrt{3}}\right)}{d^{11/6}}+\frac{2 b^{5/6} \tanh ^{-1}\left(\frac{\sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{d^{11/6}}-\frac{6 (a+b x)^{5/6}}{5 d (c+d x)^{5/6}}","-\frac{b^{5/6} \log \left(-\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{2 d^{11/6}}+\frac{b^{5/6} \log \left(\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{2 d^{11/6}}+\frac{\sqrt{3} b^{5/6} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{d^{11/6}}-\frac{\sqrt{3} b^{5/6} \tan ^{-1}\left(\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}+\frac{1}{\sqrt{3}}\right)}{d^{11/6}}+\frac{2 b^{5/6} \tanh ^{-1}\left(\frac{\sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{d^{11/6}}-\frac{6 (a+b x)^{5/6}}{5 d (c+d x)^{5/6}}",1,"(-6*(a + b*x)^(5/6))/(5*d*(c + d*x)^(5/6)) + (Sqrt[3]*b^(5/6)*ArcTan[1/Sqrt[3] - (2*d^(1/6)*(a + b*x)^(1/6))/(Sqrt[3]*b^(1/6)*(c + d*x)^(1/6))])/d^(11/6) - (Sqrt[3]*b^(5/6)*ArcTan[1/Sqrt[3] + (2*d^(1/6)*(a + b*x)^(1/6))/(Sqrt[3]*b^(1/6)*(c + d*x)^(1/6))])/d^(11/6) + (2*b^(5/6)*ArcTanh[(d^(1/6)*(a + b*x)^(1/6))/(b^(1/6)*(c + d*x)^(1/6))])/d^(11/6) - (b^(5/6)*Log[b^(1/3) + (d^(1/3)*(a + b*x)^(1/3))/(c + d*x)^(1/3) - (b^(1/6)*d^(1/6)*(a + b*x)^(1/6))/(c + d*x)^(1/6)])/(2*d^(11/6)) + (b^(5/6)*Log[b^(1/3) + (d^(1/3)*(a + b*x)^(1/3))/(c + d*x)^(1/3) + (b^(1/6)*d^(1/6)*(a + b*x)^(1/6))/(c + d*x)^(1/6)])/(2*d^(11/6))","A",13,9,19,0.4737,1,"{47, 63, 331, 296, 634, 618, 204, 628, 208}"
1782,1,32,0,0.0032335,"\int \frac{(a+b x)^{5/6}}{(c+d x)^{17/6}} \, dx","Int[(a + b*x)^(5/6)/(c + d*x)^(17/6),x]","\frac{6 (a+b x)^{11/6}}{11 (c+d x)^{11/6} (b c-a d)}","\frac{6 (a+b x)^{11/6}}{11 (c+d x)^{11/6} (b c-a d)}",1,"(6*(a + b*x)^(11/6))/(11*(b*c - a*d)*(c + d*x)^(11/6))","A",1,1,19,0.05263,1,"{37}"
1783,1,66,0,0.0090605,"\int \frac{(a+b x)^{5/6}}{(c+d x)^{23/6}} \, dx","Int[(a + b*x)^(5/6)/(c + d*x)^(23/6),x]","\frac{36 b (a+b x)^{11/6}}{187 (c+d x)^{11/6} (b c-a d)^2}+\frac{6 (a+b x)^{11/6}}{17 (c+d x)^{17/6} (b c-a d)}","\frac{36 b (a+b x)^{11/6}}{187 (c+d x)^{11/6} (b c-a d)^2}+\frac{6 (a+b x)^{11/6}}{17 (c+d x)^{17/6} (b c-a d)}",1,"(6*(a + b*x)^(11/6))/(17*(b*c - a*d)*(c + d*x)^(17/6)) + (36*b*(a + b*x)^(11/6))/(187*(b*c - a*d)^2*(c + d*x)^(11/6))","A",2,2,19,0.1053,1,"{45, 37}"
1784,1,101,0,0.0197437,"\int \frac{(a+b x)^{5/6}}{(c+d x)^{29/6}} \, dx","Int[(a + b*x)^(5/6)/(c + d*x)^(29/6),x]","\frac{432 b^2 (a+b x)^{11/6}}{4301 (c+d x)^{11/6} (b c-a d)^3}+\frac{72 b (a+b x)^{11/6}}{391 (c+d x)^{17/6} (b c-a d)^2}+\frac{6 (a+b x)^{11/6}}{23 (c+d x)^{23/6} (b c-a d)}","\frac{432 b^2 (a+b x)^{11/6}}{4301 (c+d x)^{11/6} (b c-a d)^3}+\frac{72 b (a+b x)^{11/6}}{391 (c+d x)^{17/6} (b c-a d)^2}+\frac{6 (a+b x)^{11/6}}{23 (c+d x)^{23/6} (b c-a d)}",1,"(6*(a + b*x)^(11/6))/(23*(b*c - a*d)*(c + d*x)^(23/6)) + (72*b*(a + b*x)^(11/6))/(391*(b*c - a*d)^2*(c + d*x)^(17/6)) + (432*b^2*(a + b*x)^(11/6))/(4301*(b*c - a*d)^3*(c + d*x)^(11/6))","A",3,2,19,0.1053,1,"{45, 37}"
1785,1,136,0,0.0334923,"\int \frac{(a+b x)^{5/6}}{(c+d x)^{35/6}} \, dx","Int[(a + b*x)^(5/6)/(c + d*x)^(35/6),x]","\frac{7776 b^3 (a+b x)^{11/6}}{124729 (c+d x)^{11/6} (b c-a d)^4}+\frac{1296 b^2 (a+b x)^{11/6}}{11339 (c+d x)^{17/6} (b c-a d)^3}+\frac{108 b (a+b x)^{11/6}}{667 (c+d x)^{23/6} (b c-a d)^2}+\frac{6 (a+b x)^{11/6}}{29 (c+d x)^{29/6} (b c-a d)}","\frac{7776 b^3 (a+b x)^{11/6}}{124729 (c+d x)^{11/6} (b c-a d)^4}+\frac{1296 b^2 (a+b x)^{11/6}}{11339 (c+d x)^{17/6} (b c-a d)^3}+\frac{108 b (a+b x)^{11/6}}{667 (c+d x)^{23/6} (b c-a d)^2}+\frac{6 (a+b x)^{11/6}}{29 (c+d x)^{29/6} (b c-a d)}",1,"(6*(a + b*x)^(11/6))/(29*(b*c - a*d)*(c + d*x)^(29/6)) + (108*b*(a + b*x)^(11/6))/(667*(b*c - a*d)^2*(c + d*x)^(23/6)) + (1296*b^2*(a + b*x)^(11/6))/(11339*(b*c - a*d)^3*(c + d*x)^(17/6)) + (7776*b^3*(a + b*x)^(11/6))/(124729*(b*c - a*d)^4*(c + d*x)^(11/6))","A",4,2,19,0.1053,1,"{45, 37}"
1786,1,82,0,0.0262025,"\int (a+b x)^{5/6} (c+d x)^{11/6} \, dx","Int[(a + b*x)^(5/6)*(c + d*x)^(11/6),x]","\frac{6 (a+b x)^{11/6} (c+d x)^{5/6} (b c-a d) \, _2F_1\left(-\frac{11}{6},\frac{11}{6};\frac{17}{6};-\frac{d (a+b x)}{b c-a d}\right)}{11 b^2 \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6}}","\frac{6 (a+b x)^{11/6} (c+d x)^{5/6} (b c-a d) \, _2F_1\left(-\frac{11}{6},\frac{11}{6};\frac{17}{6};-\frac{d (a+b x)}{b c-a d}\right)}{11 b^2 \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6}}",1,"(6*(b*c - a*d)*(a + b*x)^(11/6)*(c + d*x)^(5/6)*Hypergeometric2F1[-11/6, 11/6, 17/6, -((d*(a + b*x))/(b*c - a*d))])/(11*b^2*((b*(c + d*x))/(b*c - a*d))^(5/6))","A",2,2,19,0.1053,1,"{70, 69}"
1787,1,74,0,0.0205306,"\int (a+b x)^{5/6} (c+d x)^{5/6} \, dx","Int[(a + b*x)^(5/6)*(c + d*x)^(5/6),x]","\frac{6 (a+b x)^{11/6} (c+d x)^{5/6} \, _2F_1\left(-\frac{5}{6},\frac{11}{6};\frac{17}{6};-\frac{d (a+b x)}{b c-a d}\right)}{11 b \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6}}","\frac{6 (a+b x)^{11/6} (c+d x)^{5/6} \, _2F_1\left(-\frac{5}{6},\frac{11}{6};\frac{17}{6};-\frac{d (a+b x)}{b c-a d}\right)}{11 b \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6}}",1,"(6*(a + b*x)^(11/6)*(c + d*x)^(5/6)*Hypergeometric2F1[-5/6, 11/6, 17/6, -((d*(a + b*x))/(b*c - a*d))])/(11*b*((b*(c + d*x))/(b*c - a*d))^(5/6))","A",2,2,19,0.1053,1,"{70, 69}"
1788,1,74,0,0.0198072,"\int \frac{(a+b x)^{5/6}}{\sqrt[6]{c+d x}} \, dx","Int[(a + b*x)^(5/6)/(c + d*x)^(1/6),x]","\frac{6 (a+b x)^{11/6} \sqrt[6]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{1}{6},\frac{11}{6};\frac{17}{6};-\frac{d (a+b x)}{b c-a d}\right)}{11 b \sqrt[6]{c+d x}}","\frac{6 (a+b x)^{11/6} \sqrt[6]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{1}{6},\frac{11}{6};\frac{17}{6};-\frac{d (a+b x)}{b c-a d}\right)}{11 b \sqrt[6]{c+d x}}",1,"(6*(a + b*x)^(11/6)*((b*(c + d*x))/(b*c - a*d))^(1/6)*Hypergeometric2F1[1/6, 11/6, 17/6, -((d*(a + b*x))/(b*c - a*d))])/(11*b*(c + d*x)^(1/6))","A",2,2,19,0.1053,1,"{70, 69}"
1789,1,81,0,0.0203077,"\int \frac{(a+b x)^{5/6}}{(c+d x)^{7/6}} \, dx","Int[(a + b*x)^(5/6)/(c + d*x)^(7/6),x]","\frac{6 (a+b x)^{11/6} \sqrt[6]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{7}{6},\frac{11}{6};\frac{17}{6};-\frac{d (a+b x)}{b c-a d}\right)}{11 \sqrt[6]{c+d x} (b c-a d)}","\frac{6 (a+b x)^{11/6} \sqrt[6]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{7}{6},\frac{11}{6};\frac{17}{6};-\frac{d (a+b x)}{b c-a d}\right)}{11 \sqrt[6]{c+d x} (b c-a d)}",1,"(6*(a + b*x)^(11/6)*((b*(c + d*x))/(b*c - a*d))^(1/6)*Hypergeometric2F1[7/6, 11/6, 17/6, -((d*(a + b*x))/(b*c - a*d))])/(11*(b*c - a*d)*(c + d*x)^(1/6))","A",2,2,19,0.1053,1,"{70, 69}"
1790,1,82,0,0.0215203,"\int \frac{(a+b x)^{5/6}}{(c+d x)^{13/6}} \, dx","Int[(a + b*x)^(5/6)/(c + d*x)^(13/6),x]","\frac{6 b (a+b x)^{11/6} \sqrt[6]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{11}{6},\frac{13}{6};\frac{17}{6};-\frac{d (a+b x)}{b c-a d}\right)}{11 \sqrt[6]{c+d x} (b c-a d)^2}","\frac{6 b (a+b x)^{11/6} \sqrt[6]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{11}{6},\frac{13}{6};\frac{17}{6};-\frac{d (a+b x)}{b c-a d}\right)}{11 \sqrt[6]{c+d x} (b c-a d)^2}",1,"(6*b*(a + b*x)^(11/6)*((b*(c + d*x))/(b*c - a*d))^(1/6)*Hypergeometric2F1[11/6, 13/6, 17/6, -((d*(a + b*x))/(b*c - a*d))])/(11*(b*c - a*d)^2*(c + d*x)^(1/6))","A",2,2,19,0.1053,1,"{70, 69}"
1791,1,84,0,0.0219392,"\int \frac{(a+b x)^{5/6}}{(c+d x)^{19/6}} \, dx","Int[(a + b*x)^(5/6)/(c + d*x)^(19/6),x]","\frac{6 b^2 (a+b x)^{11/6} \sqrt[6]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{11}{6},\frac{19}{6};\frac{17}{6};-\frac{d (a+b x)}{b c-a d}\right)}{11 \sqrt[6]{c+d x} (b c-a d)^3}","\frac{6 b^2 (a+b x)^{11/6} \sqrt[6]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{11}{6},\frac{19}{6};\frac{17}{6};-\frac{d (a+b x)}{b c-a d}\right)}{11 \sqrt[6]{c+d x} (b c-a d)^3}",1,"(6*b^2*(a + b*x)^(11/6)*((b*(c + d*x))/(b*c - a*d))^(1/6)*Hypergeometric2F1[11/6, 19/6, 17/6, -((d*(a + b*x))/(b*c - a*d))])/(11*(b*c - a*d)^3*(c + d*x)^(1/6))","A",2,2,19,0.1053,1,"{70, 69}"
1792,1,84,0,0.02099,"\int (a+b x)^{7/6} (c+d x)^{13/6} \, dx","Int[(a + b*x)^(7/6)*(c + d*x)^(13/6),x]","\frac{6 (a+b x)^{13/6} \sqrt[6]{c+d x} (b c-a d)^2 \, _2F_1\left(-\frac{13}{6},\frac{13}{6};\frac{19}{6};-\frac{d (a+b x)}{b c-a d}\right)}{13 b^3 \sqrt[6]{\frac{b (c+d x)}{b c-a d}}}","\frac{6 (a+b x)^{13/6} \sqrt[6]{c+d x} (b c-a d)^2 \, _2F_1\left(-\frac{13}{6},\frac{13}{6};\frac{19}{6};-\frac{d (a+b x)}{b c-a d}\right)}{13 b^3 \sqrt[6]{\frac{b (c+d x)}{b c-a d}}}",1,"(6*(b*c - a*d)^2*(a + b*x)^(13/6)*(c + d*x)^(1/6)*Hypergeometric2F1[-13/6, 13/6, 19/6, -((d*(a + b*x))/(b*c - a*d))])/(13*b^3*((b*(c + d*x))/(b*c - a*d))^(1/6))","A",2,2,19,0.1053,1,"{70, 69}"
1793,1,82,0,0.0222514,"\int (a+b x)^{7/6} (c+d x)^{7/6} \, dx","Int[(a + b*x)^(7/6)*(c + d*x)^(7/6),x]","\frac{6 (a+b x)^{13/6} \sqrt[6]{c+d x} (b c-a d) \, _2F_1\left(-\frac{7}{6},\frac{13}{6};\frac{19}{6};-\frac{d (a+b x)}{b c-a d}\right)}{13 b^2 \sqrt[6]{\frac{b (c+d x)}{b c-a d}}}","\frac{6 (a+b x)^{13/6} \sqrt[6]{c+d x} (b c-a d) \, _2F_1\left(-\frac{7}{6},\frac{13}{6};\frac{19}{6};-\frac{d (a+b x)}{b c-a d}\right)}{13 b^2 \sqrt[6]{\frac{b (c+d x)}{b c-a d}}}",1,"(6*(b*c - a*d)*(a + b*x)^(13/6)*(c + d*x)^(1/6)*Hypergeometric2F1[-7/6, 13/6, 19/6, -((d*(a + b*x))/(b*c - a*d))])/(13*b^2*((b*(c + d*x))/(b*c - a*d))^(1/6))","A",2,2,19,0.1053,1,"{70, 69}"
1794,1,74,0,0.0196854,"\int (a+b x)^{7/6} \sqrt[6]{c+d x} \, dx","Int[(a + b*x)^(7/6)*(c + d*x)^(1/6),x]","\frac{6 (a+b x)^{13/6} \sqrt[6]{c+d x} \, _2F_1\left(-\frac{1}{6},\frac{13}{6};\frac{19}{6};-\frac{d (a+b x)}{b c-a d}\right)}{13 b \sqrt[6]{\frac{b (c+d x)}{b c-a d}}}","\frac{6 (a+b x)^{13/6} \sqrt[6]{c+d x} \, _2F_1\left(-\frac{1}{6},\frac{13}{6};\frac{19}{6};-\frac{d (a+b x)}{b c-a d}\right)}{13 b \sqrt[6]{\frac{b (c+d x)}{b c-a d}}}",1,"(6*(a + b*x)^(13/6)*(c + d*x)^(1/6)*Hypergeometric2F1[-1/6, 13/6, 19/6, -((d*(a + b*x))/(b*c - a*d))])/(13*b*((b*(c + d*x))/(b*c - a*d))^(1/6))","A",2,2,19,0.1053,1,"{70, 69}"
1795,1,74,0,0.0184608,"\int \frac{(a+b x)^{7/6}}{(c+d x)^{5/6}} \, dx","Int[(a + b*x)^(7/6)/(c + d*x)^(5/6),x]","\frac{6 (a+b x)^{13/6} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6} \, _2F_1\left(\frac{5}{6},\frac{13}{6};\frac{19}{6};-\frac{d (a+b x)}{b c-a d}\right)}{13 b (c+d x)^{5/6}}","\frac{6 (a+b x)^{13/6} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6} \, _2F_1\left(\frac{5}{6},\frac{13}{6};\frac{19}{6};-\frac{d (a+b x)}{b c-a d}\right)}{13 b (c+d x)^{5/6}}",1,"(6*(a + b*x)^(13/6)*((b*(c + d*x))/(b*c - a*d))^(5/6)*Hypergeometric2F1[5/6, 13/6, 19/6, -((d*(a + b*x))/(b*c - a*d))])/(13*b*(c + d*x)^(5/6))","A",2,2,19,0.1053,1,"{70, 69}"
1796,1,81,0,0.0193788,"\int \frac{(a+b x)^{7/6}}{(c+d x)^{11/6}} \, dx","Int[(a + b*x)^(7/6)/(c + d*x)^(11/6),x]","\frac{6 (a+b x)^{13/6} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6} \, _2F_1\left(\frac{11}{6},\frac{13}{6};\frac{19}{6};-\frac{d (a+b x)}{b c-a d}\right)}{13 (c+d x)^{5/6} (b c-a d)}","\frac{6 (a+b x)^{13/6} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6} \, _2F_1\left(\frac{11}{6},\frac{13}{6};\frac{19}{6};-\frac{d (a+b x)}{b c-a d}\right)}{13 (c+d x)^{5/6} (b c-a d)}",1,"(6*(a + b*x)^(13/6)*((b*(c + d*x))/(b*c - a*d))^(5/6)*Hypergeometric2F1[11/6, 13/6, 19/6, -((d*(a + b*x))/(b*c - a*d))])/(13*(b*c - a*d)*(c + d*x)^(5/6))","A",2,2,19,0.1053,1,"{70, 69}"
1797,1,82,0,0.0201316,"\int \frac{(a+b x)^{7/6}}{(c+d x)^{17/6}} \, dx","Int[(a + b*x)^(7/6)/(c + d*x)^(17/6),x]","\frac{6 b (a+b x)^{13/6} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6} \, _2F_1\left(\frac{13}{6},\frac{17}{6};\frac{19}{6};-\frac{d (a+b x)}{b c-a d}\right)}{13 (c+d x)^{5/6} (b c-a d)^2}","\frac{6 b (a+b x)^{13/6} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6} \, _2F_1\left(\frac{13}{6},\frac{17}{6};\frac{19}{6};-\frac{d (a+b x)}{b c-a d}\right)}{13 (c+d x)^{5/6} (b c-a d)^2}",1,"(6*b*(a + b*x)^(13/6)*((b*(c + d*x))/(b*c - a*d))^(5/6)*Hypergeometric2F1[13/6, 17/6, 19/6, -((d*(a + b*x))/(b*c - a*d))])/(13*(b*c - a*d)^2*(c + d*x)^(5/6))","A",2,2,19,0.1053,1,"{70, 69}"
1798,1,424,0,0.5522346,"\int \frac{(a+b x)^{7/6}}{\sqrt[6]{c+d x}} \, dx","Int[(a + b*x)^(7/6)/(c + d*x)^(1/6),x]","-\frac{7 (b c-a d)^2 \log \left(-\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{144 b^{5/6} d^{13/6}}+\frac{7 (b c-a d)^2 \log \left(\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{144 b^{5/6} d^{13/6}}-\frac{7 (b c-a d)^2 \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{24 \sqrt{3} b^{5/6} d^{13/6}}+\frac{7 (b c-a d)^2 \tan ^{-1}\left(\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}+\frac{1}{\sqrt{3}}\right)}{24 \sqrt{3} b^{5/6} d^{13/6}}+\frac{7 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{36 b^{5/6} d^{13/6}}-\frac{7 \sqrt[6]{a+b x} (c+d x)^{5/6} (b c-a d)}{12 d^2}+\frac{(a+b x)^{7/6} (c+d x)^{5/6}}{2 d}","-\frac{7 (b c-a d)^2 \log \left(-\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{144 b^{5/6} d^{13/6}}+\frac{7 (b c-a d)^2 \log \left(\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{144 b^{5/6} d^{13/6}}-\frac{7 (b c-a d)^2 \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{24 \sqrt{3} b^{5/6} d^{13/6}}+\frac{7 (b c-a d)^2 \tan ^{-1}\left(\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}+\frac{1}{\sqrt{3}}\right)}{24 \sqrt{3} b^{5/6} d^{13/6}}+\frac{7 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{36 b^{5/6} d^{13/6}}-\frac{7 \sqrt[6]{a+b x} (c+d x)^{5/6} (b c-a d)}{12 d^2}+\frac{(a+b x)^{7/6} (c+d x)^{5/6}}{2 d}",1,"(-7*(b*c - a*d)*(a + b*x)^(1/6)*(c + d*x)^(5/6))/(12*d^2) + ((a + b*x)^(7/6)*(c + d*x)^(5/6))/(2*d) - (7*(b*c - a*d)^2*ArcTan[1/Sqrt[3] - (2*d^(1/6)*(a + b*x)^(1/6))/(Sqrt[3]*b^(1/6)*(c + d*x)^(1/6))])/(24*Sqrt[3]*b^(5/6)*d^(13/6)) + (7*(b*c - a*d)^2*ArcTan[1/Sqrt[3] + (2*d^(1/6)*(a + b*x)^(1/6))/(Sqrt[3]*b^(1/6)*(c + d*x)^(1/6))])/(24*Sqrt[3]*b^(5/6)*d^(13/6)) + (7*(b*c - a*d)^2*ArcTanh[(d^(1/6)*(a + b*x)^(1/6))/(b^(1/6)*(c + d*x)^(1/6))])/(36*b^(5/6)*d^(13/6)) - (7*(b*c - a*d)^2*Log[b^(1/3) + (d^(1/3)*(a + b*x)^(1/3))/(c + d*x)^(1/3) - (b^(1/6)*d^(1/6)*(a + b*x)^(1/6))/(c + d*x)^(1/6)])/(144*b^(5/6)*d^(13/6)) + (7*(b*c - a*d)^2*Log[b^(1/3) + (d^(1/3)*(a + b*x)^(1/3))/(c + d*x)^(1/3) + (b^(1/6)*d^(1/6)*(a + b*x)^(1/6))/(c + d*x)^(1/6)])/(144*b^(5/6)*d^(13/6))","A",14,9,19,0.4737,1,"{50, 63, 240, 210, 634, 618, 204, 628, 208}"
1799,1,403,0,0.5260331,"\int \frac{(a+b x)^{7/6}}{(c+d x)^{7/6}} \, dx","Int[(a + b*x)^(7/6)/(c + d*x)^(7/6),x]","\frac{7 b \sqrt[6]{a+b x} (c+d x)^{5/6}}{d^2}+\frac{7 \sqrt[6]{b} (b c-a d) \log \left(-\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{12 d^{13/6}}-\frac{7 \sqrt[6]{b} (b c-a d) \log \left(\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{12 d^{13/6}}+\frac{7 \sqrt[6]{b} (b c-a d) \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{2 \sqrt{3} d^{13/6}}-\frac{7 \sqrt[6]{b} (b c-a d) \tan ^{-1}\left(\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} d^{13/6}}-\frac{7 \sqrt[6]{b} (b c-a d) \tanh ^{-1}\left(\frac{\sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{3 d^{13/6}}-\frac{6 (a+b x)^{7/6}}{d \sqrt[6]{c+d x}}","\frac{7 b \sqrt[6]{a+b x} (c+d x)^{5/6}}{d^2}+\frac{7 \sqrt[6]{b} (b c-a d) \log \left(-\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{12 d^{13/6}}-\frac{7 \sqrt[6]{b} (b c-a d) \log \left(\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{12 d^{13/6}}+\frac{7 \sqrt[6]{b} (b c-a d) \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{2 \sqrt{3} d^{13/6}}-\frac{7 \sqrt[6]{b} (b c-a d) \tan ^{-1}\left(\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} d^{13/6}}-\frac{7 \sqrt[6]{b} (b c-a d) \tanh ^{-1}\left(\frac{\sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{3 d^{13/6}}-\frac{6 (a+b x)^{7/6}}{d \sqrt[6]{c+d x}}",1,"(-6*(a + b*x)^(7/6))/(d*(c + d*x)^(1/6)) + (7*b*(a + b*x)^(1/6)*(c + d*x)^(5/6))/d^2 + (7*b^(1/6)*(b*c - a*d)*ArcTan[1/Sqrt[3] - (2*d^(1/6)*(a + b*x)^(1/6))/(Sqrt[3]*b^(1/6)*(c + d*x)^(1/6))])/(2*Sqrt[3]*d^(13/6)) - (7*b^(1/6)*(b*c - a*d)*ArcTan[1/Sqrt[3] + (2*d^(1/6)*(a + b*x)^(1/6))/(Sqrt[3]*b^(1/6)*(c + d*x)^(1/6))])/(2*Sqrt[3]*d^(13/6)) - (7*b^(1/6)*(b*c - a*d)*ArcTanh[(d^(1/6)*(a + b*x)^(1/6))/(b^(1/6)*(c + d*x)^(1/6))])/(3*d^(13/6)) + (7*b^(1/6)*(b*c - a*d)*Log[b^(1/3) + (d^(1/3)*(a + b*x)^(1/3))/(c + d*x)^(1/3) - (b^(1/6)*d^(1/6)*(a + b*x)^(1/6))/(c + d*x)^(1/6)])/(12*d^(13/6)) - (7*b^(1/6)*(b*c - a*d)*Log[b^(1/3) + (d^(1/3)*(a + b*x)^(1/3))/(c + d*x)^(1/3) + (b^(1/6)*d^(1/6)*(a + b*x)^(1/6))/(c + d*x)^(1/6)])/(12*d^(13/6))","A",14,10,19,0.5263,1,"{47, 50, 63, 240, 210, 634, 618, 204, 628, 208}"
1800,1,358,0,0.5010666,"\int \frac{(a+b x)^{7/6}}{(c+d x)^{13/6}} \, dx","Int[(a + b*x)^(7/6)/(c + d*x)^(13/6),x]","-\frac{b^{7/6} \log \left(-\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{2 d^{13/6}}+\frac{b^{7/6} \log \left(\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{2 d^{13/6}}-\frac{\sqrt{3} b^{7/6} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{d^{13/6}}+\frac{\sqrt{3} b^{7/6} \tan ^{-1}\left(\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}+\frac{1}{\sqrt{3}}\right)}{d^{13/6}}+\frac{2 b^{7/6} \tanh ^{-1}\left(\frac{\sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{d^{13/6}}-\frac{6 b \sqrt[6]{a+b x}}{d^2 \sqrt[6]{c+d x}}-\frac{6 (a+b x)^{7/6}}{7 d (c+d x)^{7/6}}","-\frac{b^{7/6} \log \left(-\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{2 d^{13/6}}+\frac{b^{7/6} \log \left(\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{2 d^{13/6}}-\frac{\sqrt{3} b^{7/6} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{d^{13/6}}+\frac{\sqrt{3} b^{7/6} \tan ^{-1}\left(\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}+\frac{1}{\sqrt{3}}\right)}{d^{13/6}}+\frac{2 b^{7/6} \tanh ^{-1}\left(\frac{\sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{d^{13/6}}-\frac{6 b \sqrt[6]{a+b x}}{d^2 \sqrt[6]{c+d x}}-\frac{6 (a+b x)^{7/6}}{7 d (c+d x)^{7/6}}",1,"(-6*(a + b*x)^(7/6))/(7*d*(c + d*x)^(7/6)) - (6*b*(a + b*x)^(1/6))/(d^2*(c + d*x)^(1/6)) - (Sqrt[3]*b^(7/6)*ArcTan[1/Sqrt[3] - (2*d^(1/6)*(a + b*x)^(1/6))/(Sqrt[3]*b^(1/6)*(c + d*x)^(1/6))])/d^(13/6) + (Sqrt[3]*b^(7/6)*ArcTan[1/Sqrt[3] + (2*d^(1/6)*(a + b*x)^(1/6))/(Sqrt[3]*b^(1/6)*(c + d*x)^(1/6))])/d^(13/6) + (2*b^(7/6)*ArcTanh[(d^(1/6)*(a + b*x)^(1/6))/(b^(1/6)*(c + d*x)^(1/6))])/d^(13/6) - (b^(7/6)*Log[b^(1/3) + (d^(1/3)*(a + b*x)^(1/3))/(c + d*x)^(1/3) - (b^(1/6)*d^(1/6)*(a + b*x)^(1/6))/(c + d*x)^(1/6)])/(2*d^(13/6)) + (b^(7/6)*Log[b^(1/3) + (d^(1/3)*(a + b*x)^(1/3))/(c + d*x)^(1/3) + (b^(1/6)*d^(1/6)*(a + b*x)^(1/6))/(c + d*x)^(1/6)])/(2*d^(13/6))","A",14,9,19,0.4737,1,"{47, 63, 240, 210, 634, 618, 204, 628, 208}"
1801,1,32,0,0.0030103,"\int \frac{(a+b x)^{7/6}}{(c+d x)^{19/6}} \, dx","Int[(a + b*x)^(7/6)/(c + d*x)^(19/6),x]","\frac{6 (a+b x)^{13/6}}{13 (c+d x)^{13/6} (b c-a d)}","\frac{6 (a+b x)^{13/6}}{13 (c+d x)^{13/6} (b c-a d)}",1,"(6*(a + b*x)^(13/6))/(13*(b*c - a*d)*(c + d*x)^(13/6))","A",1,1,19,0.05263,1,"{37}"
1802,1,66,0,0.0092703,"\int \frac{(a+b x)^{7/6}}{(c+d x)^{25/6}} \, dx","Int[(a + b*x)^(7/6)/(c + d*x)^(25/6),x]","\frac{36 b (a+b x)^{13/6}}{247 (c+d x)^{13/6} (b c-a d)^2}+\frac{6 (a+b x)^{13/6}}{19 (c+d x)^{19/6} (b c-a d)}","\frac{36 b (a+b x)^{13/6}}{247 (c+d x)^{13/6} (b c-a d)^2}+\frac{6 (a+b x)^{13/6}}{19 (c+d x)^{19/6} (b c-a d)}",1,"(6*(a + b*x)^(13/6))/(19*(b*c - a*d)*(c + d*x)^(19/6)) + (36*b*(a + b*x)^(13/6))/(247*(b*c - a*d)^2*(c + d*x)^(13/6))","A",2,2,19,0.1053,1,"{45, 37}"
1803,1,101,0,0.0182365,"\int \frac{(a+b x)^{7/6}}{(c+d x)^{31/6}} \, dx","Int[(a + b*x)^(7/6)/(c + d*x)^(31/6),x]","\frac{432 b^2 (a+b x)^{13/6}}{6175 (c+d x)^{13/6} (b c-a d)^3}+\frac{72 b (a+b x)^{13/6}}{475 (c+d x)^{19/6} (b c-a d)^2}+\frac{6 (a+b x)^{13/6}}{25 (c+d x)^{25/6} (b c-a d)}","\frac{432 b^2 (a+b x)^{13/6}}{6175 (c+d x)^{13/6} (b c-a d)^3}+\frac{72 b (a+b x)^{13/6}}{475 (c+d x)^{19/6} (b c-a d)^2}+\frac{6 (a+b x)^{13/6}}{25 (c+d x)^{25/6} (b c-a d)}",1,"(6*(a + b*x)^(13/6))/(25*(b*c - a*d)*(c + d*x)^(25/6)) + (72*b*(a + b*x)^(13/6))/(475*(b*c - a*d)^2*(c + d*x)^(19/6)) + (432*b^2*(a + b*x)^(13/6))/(6175*(b*c - a*d)^3*(c + d*x)^(13/6))","A",3,2,19,0.1053,1,"{45, 37}"
1804,1,136,0,0.0296088,"\int \frac{(a+b x)^{7/6}}{(c+d x)^{37/6}} \, dx","Int[(a + b*x)^(7/6)/(c + d*x)^(37/6),x]","\frac{7776 b^3 (a+b x)^{13/6}}{191425 (c+d x)^{13/6} (b c-a d)^4}+\frac{1296 b^2 (a+b x)^{13/6}}{14725 (c+d x)^{19/6} (b c-a d)^3}+\frac{108 b (a+b x)^{13/6}}{775 (c+d x)^{25/6} (b c-a d)^2}+\frac{6 (a+b x)^{13/6}}{31 (c+d x)^{31/6} (b c-a d)}","\frac{7776 b^3 (a+b x)^{13/6}}{191425 (c+d x)^{13/6} (b c-a d)^4}+\frac{1296 b^2 (a+b x)^{13/6}}{14725 (c+d x)^{19/6} (b c-a d)^3}+\frac{108 b (a+b x)^{13/6}}{775 (c+d x)^{25/6} (b c-a d)^2}+\frac{6 (a+b x)^{13/6}}{31 (c+d x)^{31/6} (b c-a d)}",1,"(6*(a + b*x)^(13/6))/(31*(b*c - a*d)*(c + d*x)^(31/6)) + (108*b*(a + b*x)^(13/6))/(775*(b*c - a*d)^2*(c + d*x)^(25/6)) + (1296*b^2*(a + b*x)^(13/6))/(14725*(b*c - a*d)^3*(c + d*x)^(19/6)) + (7776*b^3*(a + b*x)^(13/6))/(191425*(b*c - a*d)^4*(c + d*x)^(13/6))","A",4,2,19,0.1053,1,"{45, 37}"
1805,1,424,0,0.6098877,"\int \frac{(c+d x)^{7/6}}{\sqrt[6]{a+b x}} \, dx","Int[(c + d*x)^(7/6)/(a + b*x)^(1/6),x]","-\frac{7 (b c-a d)^2 \log \left(-\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{144 b^{13/6} d^{5/6}}+\frac{7 (b c-a d)^2 \log \left(\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{144 b^{13/6} d^{5/6}}+\frac{7 (b c-a d)^2 \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{24 \sqrt{3} b^{13/6} d^{5/6}}-\frac{7 (b c-a d)^2 \tan ^{-1}\left(\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}+\frac{1}{\sqrt{3}}\right)}{24 \sqrt{3} b^{13/6} d^{5/6}}+\frac{7 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{36 b^{13/6} d^{5/6}}+\frac{7 (a+b x)^{5/6} \sqrt[6]{c+d x} (b c-a d)}{12 b^2}+\frac{(a+b x)^{5/6} (c+d x)^{7/6}}{2 b}","-\frac{7 (b c-a d)^2 \log \left(-\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{144 b^{13/6} d^{5/6}}+\frac{7 (b c-a d)^2 \log \left(\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{144 b^{13/6} d^{5/6}}+\frac{7 (b c-a d)^2 \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{24 \sqrt{3} b^{13/6} d^{5/6}}-\frac{7 (b c-a d)^2 \tan ^{-1}\left(\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}+\frac{1}{\sqrt{3}}\right)}{24 \sqrt{3} b^{13/6} d^{5/6}}+\frac{7 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{36 b^{13/6} d^{5/6}}+\frac{7 (a+b x)^{5/6} \sqrt[6]{c+d x} (b c-a d)}{12 b^2}+\frac{(a+b x)^{5/6} (c+d x)^{7/6}}{2 b}",1,"(7*(b*c - a*d)*(a + b*x)^(5/6)*(c + d*x)^(1/6))/(12*b^2) + ((a + b*x)^(5/6)*(c + d*x)^(7/6))/(2*b) + (7*(b*c - a*d)^2*ArcTan[1/Sqrt[3] - (2*d^(1/6)*(a + b*x)^(1/6))/(Sqrt[3]*b^(1/6)*(c + d*x)^(1/6))])/(24*Sqrt[3]*b^(13/6)*d^(5/6)) - (7*(b*c - a*d)^2*ArcTan[1/Sqrt[3] + (2*d^(1/6)*(a + b*x)^(1/6))/(Sqrt[3]*b^(1/6)*(c + d*x)^(1/6))])/(24*Sqrt[3]*b^(13/6)*d^(5/6)) + (7*(b*c - a*d)^2*ArcTanh[(d^(1/6)*(a + b*x)^(1/6))/(b^(1/6)*(c + d*x)^(1/6))])/(36*b^(13/6)*d^(5/6)) - (7*(b*c - a*d)^2*Log[b^(1/3) + (d^(1/3)*(a + b*x)^(1/3))/(c + d*x)^(1/3) - (b^(1/6)*d^(1/6)*(a + b*x)^(1/6))/(c + d*x)^(1/6)])/(144*b^(13/6)*d^(5/6)) + (7*(b*c - a*d)^2*Log[b^(1/3) + (d^(1/3)*(a + b*x)^(1/3))/(c + d*x)^(1/3) + (b^(1/6)*d^(1/6)*(a + b*x)^(1/6))/(c + d*x)^(1/6)])/(144*b^(13/6)*d^(5/6))","A",14,9,19,0.4737,1,"{50, 63, 331, 296, 634, 618, 204, 628, 208}"
1806,1,378,0,0.5595385,"\int \frac{\sqrt[6]{c+d x}}{\sqrt[6]{a+b x}} \, dx","Int[(c + d*x)^(1/6)/(a + b*x)^(1/6),x]","-\frac{(b c-a d) \log \left(-\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{12 b^{7/6} d^{5/6}}+\frac{(b c-a d) \log \left(\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{12 b^{7/6} d^{5/6}}+\frac{(b c-a d) \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{2 \sqrt{3} b^{7/6} d^{5/6}}-\frac{(b c-a d) \tan ^{-1}\left(\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} b^{7/6} d^{5/6}}+\frac{(b c-a d) \tanh ^{-1}\left(\frac{\sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{3 b^{7/6} d^{5/6}}+\frac{(a+b x)^{5/6} \sqrt[6]{c+d x}}{b}","-\frac{(b c-a d) \log \left(-\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{12 b^{7/6} d^{5/6}}+\frac{(b c-a d) \log \left(\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{12 b^{7/6} d^{5/6}}+\frac{(b c-a d) \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{2 \sqrt{3} b^{7/6} d^{5/6}}-\frac{(b c-a d) \tan ^{-1}\left(\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} b^{7/6} d^{5/6}}+\frac{(b c-a d) \tanh ^{-1}\left(\frac{\sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{3 b^{7/6} d^{5/6}}+\frac{(a+b x)^{5/6} \sqrt[6]{c+d x}}{b}",1,"((a + b*x)^(5/6)*(c + d*x)^(1/6))/b + ((b*c - a*d)*ArcTan[1/Sqrt[3] - (2*d^(1/6)*(a + b*x)^(1/6))/(Sqrt[3]*b^(1/6)*(c + d*x)^(1/6))])/(2*Sqrt[3]*b^(7/6)*d^(5/6)) - ((b*c - a*d)*ArcTan[1/Sqrt[3] + (2*d^(1/6)*(a + b*x)^(1/6))/(Sqrt[3]*b^(1/6)*(c + d*x)^(1/6))])/(2*Sqrt[3]*b^(7/6)*d^(5/6)) + ((b*c - a*d)*ArcTanh[(d^(1/6)*(a + b*x)^(1/6))/(b^(1/6)*(c + d*x)^(1/6))])/(3*b^(7/6)*d^(5/6)) - ((b*c - a*d)*Log[b^(1/3) + (d^(1/3)*(a + b*x)^(1/3))/(c + d*x)^(1/3) - (b^(1/6)*d^(1/6)*(a + b*x)^(1/6))/(c + d*x)^(1/6)])/(12*b^(7/6)*d^(5/6)) + ((b*c - a*d)*Log[b^(1/3) + (d^(1/3)*(a + b*x)^(1/3))/(c + d*x)^(1/3) + (b^(1/6)*d^(1/6)*(a + b*x)^(1/6))/(c + d*x)^(1/6)])/(12*b^(7/6)*d^(5/6))","A",13,9,19,0.4737,1,"{50, 63, 331, 296, 634, 618, 204, 628, 208}"
1807,1,309,0,0.5093485,"\int \frac{1}{\sqrt[6]{a+b x} (c+d x)^{5/6}} \, dx","Int[1/((a + b*x)^(1/6)*(c + d*x)^(5/6)),x]","-\frac{\log \left(-\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{2 \sqrt[6]{b} d^{5/6}}+\frac{\log \left(\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{2 \sqrt[6]{b} d^{5/6}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{\sqrt[6]{b} d^{5/6}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt[6]{b} d^{5/6}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{\sqrt[6]{b} d^{5/6}}","-\frac{\log \left(-\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{2 \sqrt[6]{b} d^{5/6}}+\frac{\log \left(\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{2 \sqrt[6]{b} d^{5/6}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{\sqrt[6]{b} d^{5/6}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt[6]{b} d^{5/6}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{\sqrt[6]{b} d^{5/6}}",1,"(Sqrt[3]*ArcTan[1/Sqrt[3] - (2*d^(1/6)*(a + b*x)^(1/6))/(Sqrt[3]*b^(1/6)*(c + d*x)^(1/6))])/(b^(1/6)*d^(5/6)) - (Sqrt[3]*ArcTan[1/Sqrt[3] + (2*d^(1/6)*(a + b*x)^(1/6))/(Sqrt[3]*b^(1/6)*(c + d*x)^(1/6))])/(b^(1/6)*d^(5/6)) + (2*ArcTanh[(d^(1/6)*(a + b*x)^(1/6))/(b^(1/6)*(c + d*x)^(1/6))])/(b^(1/6)*d^(5/6)) - Log[b^(1/3) + (d^(1/3)*(a + b*x)^(1/3))/(c + d*x)^(1/3) - (b^(1/6)*d^(1/6)*(a + b*x)^(1/6))/(c + d*x)^(1/6)]/(2*b^(1/6)*d^(5/6)) + Log[b^(1/3) + (d^(1/3)*(a + b*x)^(1/3))/(c + d*x)^(1/3) + (b^(1/6)*d^(1/6)*(a + b*x)^(1/6))/(c + d*x)^(1/6)]/(2*b^(1/6)*d^(5/6))","A",12,8,19,0.4211,1,"{63, 331, 296, 634, 618, 204, 628, 208}"
1808,1,32,0,0.0031016,"\int \frac{1}{\sqrt[6]{a+b x} (c+d x)^{11/6}} \, dx","Int[1/((a + b*x)^(1/6)*(c + d*x)^(11/6)),x]","\frac{6 (a+b x)^{5/6}}{5 (c+d x)^{5/6} (b c-a d)}","\frac{6 (a+b x)^{5/6}}{5 (c+d x)^{5/6} (b c-a d)}",1,"(6*(a + b*x)^(5/6))/(5*(b*c - a*d)*(c + d*x)^(5/6))","A",1,1,19,0.05263,1,"{37}"
1809,1,66,0,0.0104578,"\int \frac{1}{\sqrt[6]{a+b x} (c+d x)^{17/6}} \, dx","Int[1/((a + b*x)^(1/6)*(c + d*x)^(17/6)),x]","\frac{36 b (a+b x)^{5/6}}{55 (c+d x)^{5/6} (b c-a d)^2}+\frac{6 (a+b x)^{5/6}}{11 (c+d x)^{11/6} (b c-a d)}","\frac{36 b (a+b x)^{5/6}}{55 (c+d x)^{5/6} (b c-a d)^2}+\frac{6 (a+b x)^{5/6}}{11 (c+d x)^{11/6} (b c-a d)}",1,"(6*(a + b*x)^(5/6))/(11*(b*c - a*d)*(c + d*x)^(11/6)) + (36*b*(a + b*x)^(5/6))/(55*(b*c - a*d)^2*(c + d*x)^(5/6))","A",2,2,19,0.1053,1,"{45, 37}"
1810,1,101,0,0.0201421,"\int \frac{1}{\sqrt[6]{a+b x} (c+d x)^{23/6}} \, dx","Int[1/((a + b*x)^(1/6)*(c + d*x)^(23/6)),x]","\frac{432 b^2 (a+b x)^{5/6}}{935 (c+d x)^{5/6} (b c-a d)^3}+\frac{72 b (a+b x)^{5/6}}{187 (c+d x)^{11/6} (b c-a d)^2}+\frac{6 (a+b x)^{5/6}}{17 (c+d x)^{17/6} (b c-a d)}","\frac{432 b^2 (a+b x)^{5/6}}{935 (c+d x)^{5/6} (b c-a d)^3}+\frac{72 b (a+b x)^{5/6}}{187 (c+d x)^{11/6} (b c-a d)^2}+\frac{6 (a+b x)^{5/6}}{17 (c+d x)^{17/6} (b c-a d)}",1,"(6*(a + b*x)^(5/6))/(17*(b*c - a*d)*(c + d*x)^(17/6)) + (72*b*(a + b*x)^(5/6))/(187*(b*c - a*d)^2*(c + d*x)^(11/6)) + (432*b^2*(a + b*x)^(5/6))/(935*(b*c - a*d)^3*(c + d*x)^(5/6))","A",3,2,19,0.1053,1,"{45, 37}"
1811,1,136,0,0.0301452,"\int \frac{1}{\sqrt[6]{a+b x} (c+d x)^{29/6}} \, dx","Int[1/((a + b*x)^(1/6)*(c + d*x)^(29/6)),x]","\frac{7776 b^3 (a+b x)^{5/6}}{21505 (c+d x)^{5/6} (b c-a d)^4}+\frac{1296 b^2 (a+b x)^{5/6}}{4301 (c+d x)^{11/6} (b c-a d)^3}+\frac{108 b (a+b x)^{5/6}}{391 (c+d x)^{17/6} (b c-a d)^2}+\frac{6 (a+b x)^{5/6}}{23 (c+d x)^{23/6} (b c-a d)}","\frac{7776 b^3 (a+b x)^{5/6}}{21505 (c+d x)^{5/6} (b c-a d)^4}+\frac{1296 b^2 (a+b x)^{5/6}}{4301 (c+d x)^{11/6} (b c-a d)^3}+\frac{108 b (a+b x)^{5/6}}{391 (c+d x)^{17/6} (b c-a d)^2}+\frac{6 (a+b x)^{5/6}}{23 (c+d x)^{23/6} (b c-a d)}",1,"(6*(a + b*x)^(5/6))/(23*(b*c - a*d)*(c + d*x)^(23/6)) + (108*b*(a + b*x)^(5/6))/(391*(b*c - a*d)^2*(c + d*x)^(17/6)) + (1296*b^2*(a + b*x)^(5/6))/(4301*(b*c - a*d)^3*(c + d*x)^(11/6)) + (7776*b^3*(a + b*x)^(5/6))/(21505*(b*c - a*d)^4*(c + d*x)^(5/6))","A",4,2,19,0.1053,1,"{45, 37}"
1812,1,82,0,0.0235723,"\int \frac{(c+d x)^{11/6}}{\sqrt[6]{a+b x}} \, dx","Int[(c + d*x)^(11/6)/(a + b*x)^(1/6),x]","\frac{6 (a+b x)^{5/6} (c+d x)^{5/6} (b c-a d) \, _2F_1\left(-\frac{11}{6},\frac{5}{6};\frac{11}{6};-\frac{d (a+b x)}{b c-a d}\right)}{5 b^2 \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6}}","\frac{6 (a+b x)^{5/6} (c+d x)^{5/6} (b c-a d) \, _2F_1\left(-\frac{11}{6},\frac{5}{6};\frac{11}{6};-\frac{d (a+b x)}{b c-a d}\right)}{5 b^2 \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6}}",1,"(6*(b*c - a*d)*(a + b*x)^(5/6)*(c + d*x)^(5/6)*Hypergeometric2F1[-11/6, 5/6, 11/6, -((d*(a + b*x))/(b*c - a*d))])/(5*b^2*((b*(c + d*x))/(b*c - a*d))^(5/6))","A",2,2,19,0.1053,1,"{70, 69}"
1813,1,74,0,0.0202515,"\int \frac{(c+d x)^{5/6}}{\sqrt[6]{a+b x}} \, dx","Int[(c + d*x)^(5/6)/(a + b*x)^(1/6),x]","\frac{6 (a+b x)^{5/6} (c+d x)^{5/6} \, _2F_1\left(-\frac{5}{6},\frac{5}{6};\frac{11}{6};-\frac{d (a+b x)}{b c-a d}\right)}{5 b \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6}}","\frac{6 (a+b x)^{5/6} (c+d x)^{5/6} \, _2F_1\left(-\frac{5}{6},\frac{5}{6};\frac{11}{6};-\frac{d (a+b x)}{b c-a d}\right)}{5 b \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6}}",1,"(6*(a + b*x)^(5/6)*(c + d*x)^(5/6)*Hypergeometric2F1[-5/6, 5/6, 11/6, -((d*(a + b*x))/(b*c - a*d))])/(5*b*((b*(c + d*x))/(b*c - a*d))^(5/6))","A",2,2,19,0.1053,1,"{70, 69}"
1814,1,74,0,0.0205361,"\int \frac{1}{\sqrt[6]{a+b x} \sqrt[6]{c+d x}} \, dx","Int[1/((a + b*x)^(1/6)*(c + d*x)^(1/6)),x]","\frac{6 (a+b x)^{5/6} \sqrt[6]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{1}{6},\frac{5}{6};\frac{11}{6};-\frac{d (a+b x)}{b c-a d}\right)}{5 b \sqrt[6]{c+d x}}","\frac{6 (a+b x)^{5/6} \sqrt[6]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{1}{6},\frac{5}{6};\frac{11}{6};-\frac{d (a+b x)}{b c-a d}\right)}{5 b \sqrt[6]{c+d x}}",1,"(6*(a + b*x)^(5/6)*((b*(c + d*x))/(b*c - a*d))^(1/6)*Hypergeometric2F1[1/6, 5/6, 11/6, -((d*(a + b*x))/(b*c - a*d))])/(5*b*(c + d*x)^(1/6))","A",2,2,19,0.1053,1,"{70, 69}"
1815,1,81,0,0.0204251,"\int \frac{1}{\sqrt[6]{a+b x} (c+d x)^{7/6}} \, dx","Int[1/((a + b*x)^(1/6)*(c + d*x)^(7/6)),x]","\frac{6 (a+b x)^{5/6} \sqrt[6]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{5}{6},\frac{7}{6};\frac{11}{6};-\frac{d (a+b x)}{b c-a d}\right)}{5 \sqrt[6]{c+d x} (b c-a d)}","\frac{6 (a+b x)^{5/6} \sqrt[6]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{5}{6},\frac{7}{6};\frac{11}{6};-\frac{d (a+b x)}{b c-a d}\right)}{5 \sqrt[6]{c+d x} (b c-a d)}",1,"(6*(a + b*x)^(5/6)*((b*(c + d*x))/(b*c - a*d))^(1/6)*Hypergeometric2F1[5/6, 7/6, 11/6, -((d*(a + b*x))/(b*c - a*d))])/(5*(b*c - a*d)*(c + d*x)^(1/6))","A",2,2,19,0.1053,1,"{70, 69}"
1816,1,82,0,0.0201833,"\int \frac{1}{\sqrt[6]{a+b x} (c+d x)^{13/6}} \, dx","Int[1/((a + b*x)^(1/6)*(c + d*x)^(13/6)),x]","\frac{6 b (a+b x)^{5/6} \sqrt[6]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{5}{6},\frac{13}{6};\frac{11}{6};-\frac{d (a+b x)}{b c-a d}\right)}{5 \sqrt[6]{c+d x} (b c-a d)^2}","\frac{6 b (a+b x)^{5/6} \sqrt[6]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{5}{6},\frac{13}{6};\frac{11}{6};-\frac{d (a+b x)}{b c-a d}\right)}{5 \sqrt[6]{c+d x} (b c-a d)^2}",1,"(6*b*(a + b*x)^(5/6)*((b*(c + d*x))/(b*c - a*d))^(1/6)*Hypergeometric2F1[5/6, 13/6, 11/6, -((d*(a + b*x))/(b*c - a*d))])/(5*(b*c - a*d)^2*(c + d*x)^(1/6))","A",2,2,19,0.1053,1,"{70, 69}"
1817,1,84,0,0.0204141,"\int \frac{1}{\sqrt[6]{a+b x} (c+d x)^{19/6}} \, dx","Int[1/((a + b*x)^(1/6)*(c + d*x)^(19/6)),x]","\frac{6 b^2 (a+b x)^{5/6} \sqrt[6]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{5}{6},\frac{19}{6};\frac{11}{6};-\frac{d (a+b x)}{b c-a d}\right)}{5 \sqrt[6]{c+d x} (b c-a d)^3}","\frac{6 b^2 (a+b x)^{5/6} \sqrt[6]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{5}{6},\frac{19}{6};\frac{11}{6};-\frac{d (a+b x)}{b c-a d}\right)}{5 \sqrt[6]{c+d x} (b c-a d)^3}",1,"(6*b^2*(a + b*x)^(5/6)*((b*(c + d*x))/(b*c - a*d))^(1/6)*Hypergeometric2F1[5/6, 19/6, 11/6, -((d*(a + b*x))/(b*c - a*d))])/(5*(b*c - a*d)^3*(c + d*x)^(1/6))","A",2,2,19,0.1053,1,"{70, 69}"
1818,1,82,0,0.0198021,"\int \frac{(c+d x)^{13/6}}{(a+b x)^{5/6}} \, dx","Int[(c + d*x)^(13/6)/(a + b*x)^(5/6),x]","\frac{6 \sqrt[6]{a+b x} \sqrt[6]{c+d x} (b c-a d)^2 \, _2F_1\left(-\frac{13}{6},\frac{1}{6};\frac{7}{6};-\frac{d (a+b x)}{b c-a d}\right)}{b^3 \sqrt[6]{\frac{b (c+d x)}{b c-a d}}}","\frac{6 \sqrt[6]{a+b x} \sqrt[6]{c+d x} (b c-a d)^2 \, _2F_1\left(-\frac{13}{6},\frac{1}{6};\frac{7}{6};-\frac{d (a+b x)}{b c-a d}\right)}{b^3 \sqrt[6]{\frac{b (c+d x)}{b c-a d}}}",1,"(6*(b*c - a*d)^2*(a + b*x)^(1/6)*(c + d*x)^(1/6)*Hypergeometric2F1[-13/6, 1/6, 7/6, -((d*(a + b*x))/(b*c - a*d))])/(b^3*((b*(c + d*x))/(b*c - a*d))^(1/6))","A",2,2,19,0.1053,1,"{70, 69}"
1819,1,80,0,0.0215323,"\int \frac{(c+d x)^{7/6}}{(a+b x)^{5/6}} \, dx","Int[(c + d*x)^(7/6)/(a + b*x)^(5/6),x]","\frac{6 \sqrt[6]{a+b x} \sqrt[6]{c+d x} (b c-a d) \, _2F_1\left(-\frac{7}{6},\frac{1}{6};\frac{7}{6};-\frac{d (a+b x)}{b c-a d}\right)}{b^2 \sqrt[6]{\frac{b (c+d x)}{b c-a d}}}","\frac{6 \sqrt[6]{a+b x} \sqrt[6]{c+d x} (b c-a d) \, _2F_1\left(-\frac{7}{6},\frac{1}{6};\frac{7}{6};-\frac{d (a+b x)}{b c-a d}\right)}{b^2 \sqrt[6]{\frac{b (c+d x)}{b c-a d}}}",1,"(6*(b*c - a*d)*(a + b*x)^(1/6)*(c + d*x)^(1/6)*Hypergeometric2F1[-7/6, 1/6, 7/6, -((d*(a + b*x))/(b*c - a*d))])/(b^2*((b*(c + d*x))/(b*c - a*d))^(1/6))","A",2,2,19,0.1053,1,"{70, 69}"
1820,1,72,0,0.0193598,"\int \frac{\sqrt[6]{c+d x}}{(a+b x)^{5/6}} \, dx","Int[(c + d*x)^(1/6)/(a + b*x)^(5/6),x]","\frac{6 \sqrt[6]{a+b x} \sqrt[6]{c+d x} \, _2F_1\left(-\frac{1}{6},\frac{1}{6};\frac{7}{6};-\frac{d (a+b x)}{b c-a d}\right)}{b \sqrt[6]{\frac{b (c+d x)}{b c-a d}}}","\frac{6 \sqrt[6]{a+b x} \sqrt[6]{c+d x} \, _2F_1\left(-\frac{1}{6},\frac{1}{6};\frac{7}{6};-\frac{d (a+b x)}{b c-a d}\right)}{b \sqrt[6]{\frac{b (c+d x)}{b c-a d}}}",1,"(6*(a + b*x)^(1/6)*(c + d*x)^(1/6)*Hypergeometric2F1[-1/6, 1/6, 7/6, -((d*(a + b*x))/(b*c - a*d))])/(b*((b*(c + d*x))/(b*c - a*d))^(1/6))","A",2,2,19,0.1053,1,"{70, 69}"
1821,1,72,0,0.0199112,"\int \frac{1}{(a+b x)^{5/6} (c+d x)^{5/6}} \, dx","Int[1/((a + b*x)^(5/6)*(c + d*x)^(5/6)),x]","\frac{6 \sqrt[6]{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6} \, _2F_1\left(\frac{1}{6},\frac{5}{6};\frac{7}{6};-\frac{d (a+b x)}{b c-a d}\right)}{b (c+d x)^{5/6}}","\frac{6 \sqrt[6]{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6} \, _2F_1\left(\frac{1}{6},\frac{5}{6};\frac{7}{6};-\frac{d (a+b x)}{b c-a d}\right)}{b (c+d x)^{5/6}}",1,"(6*(a + b*x)^(1/6)*((b*(c + d*x))/(b*c - a*d))^(5/6)*Hypergeometric2F1[1/6, 5/6, 7/6, -((d*(a + b*x))/(b*c - a*d))])/(b*(c + d*x)^(5/6))","A",2,2,19,0.1053,1,"{70, 69}"
1822,1,79,0,0.018723,"\int \frac{1}{(a+b x)^{5/6} (c+d x)^{11/6}} \, dx","Int[1/((a + b*x)^(5/6)*(c + d*x)^(11/6)),x]","\frac{6 \sqrt[6]{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6} \, _2F_1\left(\frac{1}{6},\frac{11}{6};\frac{7}{6};-\frac{d (a+b x)}{b c-a d}\right)}{(c+d x)^{5/6} (b c-a d)}","\frac{6 \sqrt[6]{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6} \, _2F_1\left(\frac{1}{6},\frac{11}{6};\frac{7}{6};-\frac{d (a+b x)}{b c-a d}\right)}{(c+d x)^{5/6} (b c-a d)}",1,"(6*(a + b*x)^(1/6)*((b*(c + d*x))/(b*c - a*d))^(5/6)*Hypergeometric2F1[1/6, 11/6, 7/6, -((d*(a + b*x))/(b*c - a*d))])/((b*c - a*d)*(c + d*x)^(5/6))","A",2,2,19,0.1053,1,"{70, 69}"
1823,1,80,0,0.0200252,"\int \frac{1}{(a+b x)^{5/6} (c+d x)^{17/6}} \, dx","Int[1/((a + b*x)^(5/6)*(c + d*x)^(17/6)),x]","\frac{6 b \sqrt[6]{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6} \, _2F_1\left(\frac{1}{6},\frac{17}{6};\frac{7}{6};-\frac{d (a+b x)}{b c-a d}\right)}{(c+d x)^{5/6} (b c-a d)^2}","\frac{6 b \sqrt[6]{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6} \, _2F_1\left(\frac{1}{6},\frac{17}{6};\frac{7}{6};-\frac{d (a+b x)}{b c-a d}\right)}{(c+d x)^{5/6} (b c-a d)^2}",1,"(6*b*(a + b*x)^(1/6)*((b*(c + d*x))/(b*c - a*d))^(5/6)*Hypergeometric2F1[1/6, 17/6, 7/6, -((d*(a + b*x))/(b*c - a*d))])/((b*c - a*d)^2*(c + d*x)^(5/6))","A",2,2,19,0.1053,1,"{70, 69}"
1824,1,424,0,0.5491836,"\int \frac{(c+d x)^{11/6}}{(a+b x)^{5/6}} \, dx","Int[(c + d*x)^(11/6)/(a + b*x)^(5/6),x]","\frac{11 \sqrt[6]{a+b x} (c+d x)^{5/6} (b c-a d)}{12 b^2}-\frac{55 (b c-a d)^2 \log \left(-\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{144 b^{17/6} \sqrt[6]{d}}+\frac{55 (b c-a d)^2 \log \left(\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{144 b^{17/6} \sqrt[6]{d}}-\frac{55 (b c-a d)^2 \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{24 \sqrt{3} b^{17/6} \sqrt[6]{d}}+\frac{55 (b c-a d)^2 \tan ^{-1}\left(\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}+\frac{1}{\sqrt{3}}\right)}{24 \sqrt{3} b^{17/6} \sqrt[6]{d}}+\frac{55 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{36 b^{17/6} \sqrt[6]{d}}+\frac{\sqrt[6]{a+b x} (c+d x)^{11/6}}{2 b}","\frac{11 \sqrt[6]{a+b x} (c+d x)^{5/6} (b c-a d)}{12 b^2}-\frac{55 (b c-a d)^2 \log \left(-\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{144 b^{17/6} \sqrt[6]{d}}+\frac{55 (b c-a d)^2 \log \left(\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{144 b^{17/6} \sqrt[6]{d}}-\frac{55 (b c-a d)^2 \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{24 \sqrt{3} b^{17/6} \sqrt[6]{d}}+\frac{55 (b c-a d)^2 \tan ^{-1}\left(\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}+\frac{1}{\sqrt{3}}\right)}{24 \sqrt{3} b^{17/6} \sqrt[6]{d}}+\frac{55 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{36 b^{17/6} \sqrt[6]{d}}+\frac{\sqrt[6]{a+b x} (c+d x)^{11/6}}{2 b}",1,"(11*(b*c - a*d)*(a + b*x)^(1/6)*(c + d*x)^(5/6))/(12*b^2) + ((a + b*x)^(1/6)*(c + d*x)^(11/6))/(2*b) - (55*(b*c - a*d)^2*ArcTan[1/Sqrt[3] - (2*d^(1/6)*(a + b*x)^(1/6))/(Sqrt[3]*b^(1/6)*(c + d*x)^(1/6))])/(24*Sqrt[3]*b^(17/6)*d^(1/6)) + (55*(b*c - a*d)^2*ArcTan[1/Sqrt[3] + (2*d^(1/6)*(a + b*x)^(1/6))/(Sqrt[3]*b^(1/6)*(c + d*x)^(1/6))])/(24*Sqrt[3]*b^(17/6)*d^(1/6)) + (55*(b*c - a*d)^2*ArcTanh[(d^(1/6)*(a + b*x)^(1/6))/(b^(1/6)*(c + d*x)^(1/6))])/(36*b^(17/6)*d^(1/6)) - (55*(b*c - a*d)^2*Log[b^(1/3) + (d^(1/3)*(a + b*x)^(1/3))/(c + d*x)^(1/3) - (b^(1/6)*d^(1/6)*(a + b*x)^(1/6))/(c + d*x)^(1/6)])/(144*b^(17/6)*d^(1/6)) + (55*(b*c - a*d)^2*Log[b^(1/3) + (d^(1/3)*(a + b*x)^(1/3))/(c + d*x)^(1/3) + (b^(1/6)*d^(1/6)*(a + b*x)^(1/6))/(c + d*x)^(1/6)])/(144*b^(17/6)*d^(1/6))","A",14,9,19,0.4737,1,"{50, 63, 240, 210, 634, 618, 204, 628, 208}"
1825,1,378,0,0.4794068,"\int \frac{(c+d x)^{5/6}}{(a+b x)^{5/6}} \, dx","Int[(c + d*x)^(5/6)/(a + b*x)^(5/6),x]","-\frac{5 (b c-a d) \log \left(-\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{12 b^{11/6} \sqrt[6]{d}}+\frac{5 (b c-a d) \log \left(\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{12 b^{11/6} \sqrt[6]{d}}-\frac{5 (b c-a d) \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{2 \sqrt{3} b^{11/6} \sqrt[6]{d}}+\frac{5 (b c-a d) \tan ^{-1}\left(\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} b^{11/6} \sqrt[6]{d}}+\frac{5 (b c-a d) \tanh ^{-1}\left(\frac{\sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{3 b^{11/6} \sqrt[6]{d}}+\frac{\sqrt[6]{a+b x} (c+d x)^{5/6}}{b}","-\frac{5 (b c-a d) \log \left(-\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{12 b^{11/6} \sqrt[6]{d}}+\frac{5 (b c-a d) \log \left(\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{12 b^{11/6} \sqrt[6]{d}}-\frac{5 (b c-a d) \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{2 \sqrt{3} b^{11/6} \sqrt[6]{d}}+\frac{5 (b c-a d) \tan ^{-1}\left(\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} b^{11/6} \sqrt[6]{d}}+\frac{5 (b c-a d) \tanh ^{-1}\left(\frac{\sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{3 b^{11/6} \sqrt[6]{d}}+\frac{\sqrt[6]{a+b x} (c+d x)^{5/6}}{b}",1,"((a + b*x)^(1/6)*(c + d*x)^(5/6))/b - (5*(b*c - a*d)*ArcTan[1/Sqrt[3] - (2*d^(1/6)*(a + b*x)^(1/6))/(Sqrt[3]*b^(1/6)*(c + d*x)^(1/6))])/(2*Sqrt[3]*b^(11/6)*d^(1/6)) + (5*(b*c - a*d)*ArcTan[1/Sqrt[3] + (2*d^(1/6)*(a + b*x)^(1/6))/(Sqrt[3]*b^(1/6)*(c + d*x)^(1/6))])/(2*Sqrt[3]*b^(11/6)*d^(1/6)) + (5*(b*c - a*d)*ArcTanh[(d^(1/6)*(a + b*x)^(1/6))/(b^(1/6)*(c + d*x)^(1/6))])/(3*b^(11/6)*d^(1/6)) - (5*(b*c - a*d)*Log[b^(1/3) + (d^(1/3)*(a + b*x)^(1/3))/(c + d*x)^(1/3) - (b^(1/6)*d^(1/6)*(a + b*x)^(1/6))/(c + d*x)^(1/6)])/(12*b^(11/6)*d^(1/6)) + (5*(b*c - a*d)*Log[b^(1/3) + (d^(1/3)*(a + b*x)^(1/3))/(c + d*x)^(1/3) + (b^(1/6)*d^(1/6)*(a + b*x)^(1/6))/(c + d*x)^(1/6)])/(12*b^(11/6)*d^(1/6))","A",13,9,19,0.4737,1,"{50, 63, 240, 210, 634, 618, 204, 628, 208}"
1826,1,309,0,0.4438333,"\int \frac{1}{(a+b x)^{5/6} \sqrt[6]{c+d x}} \, dx","Int[1/((a + b*x)^(5/6)*(c + d*x)^(1/6)),x]","-\frac{\log \left(-\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{2 b^{5/6} \sqrt[6]{d}}+\frac{\log \left(\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{2 b^{5/6} \sqrt[6]{d}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{b^{5/6} \sqrt[6]{d}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}+\frac{1}{\sqrt{3}}\right)}{b^{5/6} \sqrt[6]{d}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{b^{5/6} \sqrt[6]{d}}","-\frac{\log \left(-\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{2 b^{5/6} \sqrt[6]{d}}+\frac{\log \left(\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{2 b^{5/6} \sqrt[6]{d}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{b^{5/6} \sqrt[6]{d}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}+\frac{1}{\sqrt{3}}\right)}{b^{5/6} \sqrt[6]{d}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{b^{5/6} \sqrt[6]{d}}",1,"-((Sqrt[3]*ArcTan[1/Sqrt[3] - (2*d^(1/6)*(a + b*x)^(1/6))/(Sqrt[3]*b^(1/6)*(c + d*x)^(1/6))])/(b^(5/6)*d^(1/6))) + (Sqrt[3]*ArcTan[1/Sqrt[3] + (2*d^(1/6)*(a + b*x)^(1/6))/(Sqrt[3]*b^(1/6)*(c + d*x)^(1/6))])/(b^(5/6)*d^(1/6)) + (2*ArcTanh[(d^(1/6)*(a + b*x)^(1/6))/(b^(1/6)*(c + d*x)^(1/6))])/(b^(5/6)*d^(1/6)) - Log[b^(1/3) + (d^(1/3)*(a + b*x)^(1/3))/(c + d*x)^(1/3) - (b^(1/6)*d^(1/6)*(a + b*x)^(1/6))/(c + d*x)^(1/6)]/(2*b^(5/6)*d^(1/6)) + Log[b^(1/3) + (d^(1/3)*(a + b*x)^(1/3))/(c + d*x)^(1/3) + (b^(1/6)*d^(1/6)*(a + b*x)^(1/6))/(c + d*x)^(1/6)]/(2*b^(5/6)*d^(1/6))","A",12,8,19,0.4211,1,"{63, 240, 210, 634, 618, 204, 628, 208}"
1827,1,30,0,0.0029776,"\int \frac{1}{(a+b x)^{5/6} (c+d x)^{7/6}} \, dx","Int[1/((a + b*x)^(5/6)*(c + d*x)^(7/6)),x]","\frac{6 \sqrt[6]{a+b x}}{\sqrt[6]{c+d x} (b c-a d)}","\frac{6 \sqrt[6]{a+b x}}{\sqrt[6]{c+d x} (b c-a d)}",1,"(6*(a + b*x)^(1/6))/((b*c - a*d)*(c + d*x)^(1/6))","A",1,1,19,0.05263,1,"{37}"
1828,1,66,0,0.0092258,"\int \frac{1}{(a+b x)^{5/6} (c+d x)^{13/6}} \, dx","Int[1/((a + b*x)^(5/6)*(c + d*x)^(13/6)),x]","\frac{36 b \sqrt[6]{a+b x}}{7 \sqrt[6]{c+d x} (b c-a d)^2}+\frac{6 \sqrt[6]{a+b x}}{7 (c+d x)^{7/6} (b c-a d)}","\frac{36 b \sqrt[6]{a+b x}}{7 \sqrt[6]{c+d x} (b c-a d)^2}+\frac{6 \sqrt[6]{a+b x}}{7 (c+d x)^{7/6} (b c-a d)}",1,"(6*(a + b*x)^(1/6))/(7*(b*c - a*d)*(c + d*x)^(7/6)) + (36*b*(a + b*x)^(1/6))/(7*(b*c - a*d)^2*(c + d*x)^(1/6))","A",2,2,19,0.1053,1,"{45, 37}"
1829,1,101,0,0.0175022,"\int \frac{1}{(a+b x)^{5/6} (c+d x)^{19/6}} \, dx","Int[1/((a + b*x)^(5/6)*(c + d*x)^(19/6)),x]","\frac{432 b^2 \sqrt[6]{a+b x}}{91 \sqrt[6]{c+d x} (b c-a d)^3}+\frac{72 b \sqrt[6]{a+b x}}{91 (c+d x)^{7/6} (b c-a d)^2}+\frac{6 \sqrt[6]{a+b x}}{13 (c+d x)^{13/6} (b c-a d)}","\frac{432 b^2 \sqrt[6]{a+b x}}{91 \sqrt[6]{c+d x} (b c-a d)^3}+\frac{72 b \sqrt[6]{a+b x}}{91 (c+d x)^{7/6} (b c-a d)^2}+\frac{6 \sqrt[6]{a+b x}}{13 (c+d x)^{13/6} (b c-a d)}",1,"(6*(a + b*x)^(1/6))/(13*(b*c - a*d)*(c + d*x)^(13/6)) + (72*b*(a + b*x)^(1/6))/(91*(b*c - a*d)^2*(c + d*x)^(7/6)) + (432*b^2*(a + b*x)^(1/6))/(91*(b*c - a*d)^3*(c + d*x)^(1/6))","A",3,2,19,0.1053,1,"{45, 37}"
1830,1,136,0,0.030887,"\int \frac{1}{(a+b x)^{5/6} (c+d x)^{25/6}} \, dx","Int[1/((a + b*x)^(5/6)*(c + d*x)^(25/6)),x]","\frac{7776 b^3 \sqrt[6]{a+b x}}{1729 \sqrt[6]{c+d x} (b c-a d)^4}+\frac{1296 b^2 \sqrt[6]{a+b x}}{1729 (c+d x)^{7/6} (b c-a d)^3}+\frac{108 b \sqrt[6]{a+b x}}{247 (c+d x)^{13/6} (b c-a d)^2}+\frac{6 \sqrt[6]{a+b x}}{19 (c+d x)^{19/6} (b c-a d)}","\frac{7776 b^3 \sqrt[6]{a+b x}}{1729 \sqrt[6]{c+d x} (b c-a d)^4}+\frac{1296 b^2 \sqrt[6]{a+b x}}{1729 (c+d x)^{7/6} (b c-a d)^3}+\frac{108 b \sqrt[6]{a+b x}}{247 (c+d x)^{13/6} (b c-a d)^2}+\frac{6 \sqrt[6]{a+b x}}{19 (c+d x)^{19/6} (b c-a d)}",1,"(6*(a + b*x)^(1/6))/(19*(b*c - a*d)*(c + d*x)^(19/6)) + (108*b*(a + b*x)^(1/6))/(247*(b*c - a*d)^2*(c + d*x)^(13/6)) + (1296*b^2*(a + b*x)^(1/6))/(1729*(b*c - a*d)^3*(c + d*x)^(7/6)) + (7776*b^3*(a + b*x)^(1/6))/(1729*(b*c - a*d)^4*(c + d*x)^(1/6))","A",4,2,19,0.1053,1,"{45, 37}"
1831,1,449,0,0.6600123,"\int \frac{(c+d x)^{13/6}}{(a+b x)^{7/6}} \, dx","Int[(c + d*x)^(13/6)/(a + b*x)^(7/6),x]","\frac{13 d (a+b x)^{5/6} (c+d x)^{7/6}}{2 b^2}+\frac{91 d (a+b x)^{5/6} \sqrt[6]{c+d x} (b c-a d)}{12 b^3}-\frac{91 \sqrt[6]{d} (b c-a d)^2 \log \left(-\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{144 b^{19/6}}+\frac{91 \sqrt[6]{d} (b c-a d)^2 \log \left(\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{144 b^{19/6}}+\frac{91 \sqrt[6]{d} (b c-a d)^2 \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{24 \sqrt{3} b^{19/6}}-\frac{91 \sqrt[6]{d} (b c-a d)^2 \tan ^{-1}\left(\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}+\frac{1}{\sqrt{3}}\right)}{24 \sqrt{3} b^{19/6}}+\frac{91 \sqrt[6]{d} (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{36 b^{19/6}}-\frac{6 (c+d x)^{13/6}}{b \sqrt[6]{a+b x}}","\frac{13 d (a+b x)^{5/6} (c+d x)^{7/6}}{2 b^2}+\frac{91 d (a+b x)^{5/6} \sqrt[6]{c+d x} (b c-a d)}{12 b^3}-\frac{91 \sqrt[6]{d} (b c-a d)^2 \log \left(-\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{144 b^{19/6}}+\frac{91 \sqrt[6]{d} (b c-a d)^2 \log \left(\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{144 b^{19/6}}+\frac{91 \sqrt[6]{d} (b c-a d)^2 \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{24 \sqrt{3} b^{19/6}}-\frac{91 \sqrt[6]{d} (b c-a d)^2 \tan ^{-1}\left(\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}+\frac{1}{\sqrt{3}}\right)}{24 \sqrt{3} b^{19/6}}+\frac{91 \sqrt[6]{d} (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{36 b^{19/6}}-\frac{6 (c+d x)^{13/6}}{b \sqrt[6]{a+b x}}",1,"(91*d*(b*c - a*d)*(a + b*x)^(5/6)*(c + d*x)^(1/6))/(12*b^3) + (13*d*(a + b*x)^(5/6)*(c + d*x)^(7/6))/(2*b^2) - (6*(c + d*x)^(13/6))/(b*(a + b*x)^(1/6)) + (91*d^(1/6)*(b*c - a*d)^2*ArcTan[1/Sqrt[3] - (2*d^(1/6)*(a + b*x)^(1/6))/(Sqrt[3]*b^(1/6)*(c + d*x)^(1/6))])/(24*Sqrt[3]*b^(19/6)) - (91*d^(1/6)*(b*c - a*d)^2*ArcTan[1/Sqrt[3] + (2*d^(1/6)*(a + b*x)^(1/6))/(Sqrt[3]*b^(1/6)*(c + d*x)^(1/6))])/(24*Sqrt[3]*b^(19/6)) + (91*d^(1/6)*(b*c - a*d)^2*ArcTanh[(d^(1/6)*(a + b*x)^(1/6))/(b^(1/6)*(c + d*x)^(1/6))])/(36*b^(19/6)) - (91*d^(1/6)*(b*c - a*d)^2*Log[b^(1/3) + (d^(1/3)*(a + b*x)^(1/3))/(c + d*x)^(1/3) - (b^(1/6)*d^(1/6)*(a + b*x)^(1/6))/(c + d*x)^(1/6)])/(144*b^(19/6)) + (91*d^(1/6)*(b*c - a*d)^2*Log[b^(1/3) + (d^(1/3)*(a + b*x)^(1/3))/(c + d*x)^(1/3) + (b^(1/6)*d^(1/6)*(a + b*x)^(1/6))/(c + d*x)^(1/6)])/(144*b^(19/6))","A",15,10,19,0.5263,1,"{47, 50, 63, 331, 296, 634, 618, 204, 628, 208}"
1832,1,403,0,0.5956274,"\int \frac{(c+d x)^{7/6}}{(a+b x)^{7/6}} \, dx","Int[(c + d*x)^(7/6)/(a + b*x)^(7/6),x]","\frac{7 d (a+b x)^{5/6} \sqrt[6]{c+d x}}{b^2}-\frac{7 \sqrt[6]{d} (b c-a d) \log \left(-\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{12 b^{13/6}}+\frac{7 \sqrt[6]{d} (b c-a d) \log \left(\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{12 b^{13/6}}+\frac{7 \sqrt[6]{d} (b c-a d) \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{2 \sqrt{3} b^{13/6}}-\frac{7 \sqrt[6]{d} (b c-a d) \tan ^{-1}\left(\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} b^{13/6}}+\frac{7 \sqrt[6]{d} (b c-a d) \tanh ^{-1}\left(\frac{\sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{3 b^{13/6}}-\frac{6 (c+d x)^{7/6}}{b \sqrt[6]{a+b x}}","\frac{7 d (a+b x)^{5/6} \sqrt[6]{c+d x}}{b^2}-\frac{7 \sqrt[6]{d} (b c-a d) \log \left(-\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{12 b^{13/6}}+\frac{7 \sqrt[6]{d} (b c-a d) \log \left(\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{12 b^{13/6}}+\frac{7 \sqrt[6]{d} (b c-a d) \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{2 \sqrt{3} b^{13/6}}-\frac{7 \sqrt[6]{d} (b c-a d) \tan ^{-1}\left(\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} b^{13/6}}+\frac{7 \sqrt[6]{d} (b c-a d) \tanh ^{-1}\left(\frac{\sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{3 b^{13/6}}-\frac{6 (c+d x)^{7/6}}{b \sqrt[6]{a+b x}}",1,"(7*d*(a + b*x)^(5/6)*(c + d*x)^(1/6))/b^2 - (6*(c + d*x)^(7/6))/(b*(a + b*x)^(1/6)) + (7*d^(1/6)*(b*c - a*d)*ArcTan[1/Sqrt[3] - (2*d^(1/6)*(a + b*x)^(1/6))/(Sqrt[3]*b^(1/6)*(c + d*x)^(1/6))])/(2*Sqrt[3]*b^(13/6)) - (7*d^(1/6)*(b*c - a*d)*ArcTan[1/Sqrt[3] + (2*d^(1/6)*(a + b*x)^(1/6))/(Sqrt[3]*b^(1/6)*(c + d*x)^(1/6))])/(2*Sqrt[3]*b^(13/6)) + (7*d^(1/6)*(b*c - a*d)*ArcTanh[(d^(1/6)*(a + b*x)^(1/6))/(b^(1/6)*(c + d*x)^(1/6))])/(3*b^(13/6)) - (7*d^(1/6)*(b*c - a*d)*Log[b^(1/3) + (d^(1/3)*(a + b*x)^(1/3))/(c + d*x)^(1/3) - (b^(1/6)*d^(1/6)*(a + b*x)^(1/6))/(c + d*x)^(1/6)])/(12*b^(13/6)) + (7*d^(1/6)*(b*c - a*d)*Log[b^(1/3) + (d^(1/3)*(a + b*x)^(1/3))/(c + d*x)^(1/3) + (b^(1/6)*d^(1/6)*(a + b*x)^(1/6))/(c + d*x)^(1/6)])/(12*b^(13/6))","A",14,10,19,0.5263,1,"{47, 50, 63, 331, 296, 634, 618, 204, 628, 208}"
1833,1,332,0,0.5405816,"\int \frac{\sqrt[6]{c+d x}}{(a+b x)^{7/6}} \, dx","Int[(c + d*x)^(1/6)/(a + b*x)^(7/6),x]","-\frac{\sqrt[6]{d} \log \left(-\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{2 b^{7/6}}+\frac{\sqrt[6]{d} \log \left(\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{2 b^{7/6}}+\frac{\sqrt{3} \sqrt[6]{d} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{b^{7/6}}-\frac{\sqrt{3} \sqrt[6]{d} \tan ^{-1}\left(\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}+\frac{1}{\sqrt{3}}\right)}{b^{7/6}}+\frac{2 \sqrt[6]{d} \tanh ^{-1}\left(\frac{\sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{b^{7/6}}-\frac{6 \sqrt[6]{c+d x}}{b \sqrt[6]{a+b x}}","-\frac{\sqrt[6]{d} \log \left(-\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{2 b^{7/6}}+\frac{\sqrt[6]{d} \log \left(\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{2 b^{7/6}}+\frac{\sqrt{3} \sqrt[6]{d} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{b^{7/6}}-\frac{\sqrt{3} \sqrt[6]{d} \tan ^{-1}\left(\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}+\frac{1}{\sqrt{3}}\right)}{b^{7/6}}+\frac{2 \sqrt[6]{d} \tanh ^{-1}\left(\frac{\sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{b^{7/6}}-\frac{6 \sqrt[6]{c+d x}}{b \sqrt[6]{a+b x}}",1,"(-6*(c + d*x)^(1/6))/(b*(a + b*x)^(1/6)) + (Sqrt[3]*d^(1/6)*ArcTan[1/Sqrt[3] - (2*d^(1/6)*(a + b*x)^(1/6))/(Sqrt[3]*b^(1/6)*(c + d*x)^(1/6))])/b^(7/6) - (Sqrt[3]*d^(1/6)*ArcTan[1/Sqrt[3] + (2*d^(1/6)*(a + b*x)^(1/6))/(Sqrt[3]*b^(1/6)*(c + d*x)^(1/6))])/b^(7/6) + (2*d^(1/6)*ArcTanh[(d^(1/6)*(a + b*x)^(1/6))/(b^(1/6)*(c + d*x)^(1/6))])/b^(7/6) - (d^(1/6)*Log[b^(1/3) + (d^(1/3)*(a + b*x)^(1/3))/(c + d*x)^(1/3) - (b^(1/6)*d^(1/6)*(a + b*x)^(1/6))/(c + d*x)^(1/6)])/(2*b^(7/6)) + (d^(1/6)*Log[b^(1/3) + (d^(1/3)*(a + b*x)^(1/3))/(c + d*x)^(1/3) + (b^(1/6)*d^(1/6)*(a + b*x)^(1/6))/(c + d*x)^(1/6)])/(2*b^(7/6))","A",13,9,19,0.4737,1,"{47, 63, 331, 296, 634, 618, 204, 628, 208}"
1834,1,30,0,0.0033471,"\int \frac{1}{(a+b x)^{7/6} (c+d x)^{5/6}} \, dx","Int[1/((a + b*x)^(7/6)*(c + d*x)^(5/6)),x]","-\frac{6 \sqrt[6]{c+d x}}{\sqrt[6]{a+b x} (b c-a d)}","-\frac{6 \sqrt[6]{c+d x}}{\sqrt[6]{a+b x} (b c-a d)}",1,"(-6*(c + d*x)^(1/6))/((b*c - a*d)*(a + b*x)^(1/6))","A",1,1,19,0.05263,1,"{37}"
1835,1,64,0,0.0105572,"\int \frac{1}{(a+b x)^{7/6} (c+d x)^{11/6}} \, dx","Int[1/((a + b*x)^(7/6)*(c + d*x)^(11/6)),x]","-\frac{36 d (a+b x)^{5/6}}{5 (c+d x)^{5/6} (b c-a d)^2}-\frac{6}{\sqrt[6]{a+b x} (c+d x)^{5/6} (b c-a d)}","-\frac{36 d (a+b x)^{5/6}}{5 (c+d x)^{5/6} (b c-a d)^2}-\frac{6}{\sqrt[6]{a+b x} (c+d x)^{5/6} (b c-a d)}",1,"-6/((b*c - a*d)*(a + b*x)^(1/6)*(c + d*x)^(5/6)) - (36*d*(a + b*x)^(5/6))/(5*(b*c - a*d)^2*(c + d*x)^(5/6))","A",2,2,19,0.1053,1,"{45, 37}"
1836,1,98,0,0.0202185,"\int \frac{1}{(a+b x)^{7/6} (c+d x)^{17/6}} \, dx","Int[1/((a + b*x)^(7/6)*(c + d*x)^(17/6)),x]","-\frac{432 b d (a+b x)^{5/6}}{55 (c+d x)^{5/6} (b c-a d)^3}-\frac{72 d (a+b x)^{5/6}}{11 (c+d x)^{11/6} (b c-a d)^2}-\frac{6}{\sqrt[6]{a+b x} (c+d x)^{11/6} (b c-a d)}","-\frac{432 b d (a+b x)^{5/6}}{55 (c+d x)^{5/6} (b c-a d)^3}-\frac{72 d (a+b x)^{5/6}}{11 (c+d x)^{11/6} (b c-a d)^2}-\frac{6}{\sqrt[6]{a+b x} (c+d x)^{11/6} (b c-a d)}",1,"-6/((b*c - a*d)*(a + b*x)^(1/6)*(c + d*x)^(11/6)) - (72*d*(a + b*x)^(5/6))/(11*(b*c - a*d)^2*(c + d*x)^(11/6)) - (432*b*d*(a + b*x)^(5/6))/(55*(b*c - a*d)^3*(c + d*x)^(5/6))","A",3,2,19,0.1053,1,"{45, 37}"
1837,1,134,0,0.0327841,"\int \frac{1}{(a+b x)^{7/6} (c+d x)^{23/6}} \, dx","Int[1/((a + b*x)^(7/6)*(c + d*x)^(23/6)),x]","-\frac{7776 b^2 d (a+b x)^{5/6}}{935 (c+d x)^{5/6} (b c-a d)^4}-\frac{1296 b d (a+b x)^{5/6}}{187 (c+d x)^{11/6} (b c-a d)^3}-\frac{108 d (a+b x)^{5/6}}{17 (c+d x)^{17/6} (b c-a d)^2}-\frac{6}{\sqrt[6]{a+b x} (c+d x)^{17/6} (b c-a d)}","-\frac{7776 b^2 d (a+b x)^{5/6}}{935 (c+d x)^{5/6} (b c-a d)^4}-\frac{1296 b d (a+b x)^{5/6}}{187 (c+d x)^{11/6} (b c-a d)^3}-\frac{108 d (a+b x)^{5/6}}{17 (c+d x)^{17/6} (b c-a d)^2}-\frac{6}{\sqrt[6]{a+b x} (c+d x)^{17/6} (b c-a d)}",1,"-6/((b*c - a*d)*(a + b*x)^(1/6)*(c + d*x)^(17/6)) - (108*d*(a + b*x)^(5/6))/(17*(b*c - a*d)^2*(c + d*x)^(17/6)) - (1296*b*d*(a + b*x)^(5/6))/(187*(b*c - a*d)^3*(c + d*x)^(11/6)) - (7776*b^2*d*(a + b*x)^(5/6))/(935*(b*c - a*d)^4*(c + d*x)^(5/6))","A",4,2,19,0.1053,1,"{45, 37}"
1838,1,80,0,0.0238371,"\int \frac{(c+d x)^{11/6}}{(a+b x)^{7/6}} \, dx","Int[(c + d*x)^(11/6)/(a + b*x)^(7/6),x]","-\frac{6 (c+d x)^{5/6} (b c-a d) \, _2F_1\left(-\frac{11}{6},-\frac{1}{6};\frac{5}{6};-\frac{d (a+b x)}{b c-a d}\right)}{b^2 \sqrt[6]{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6}}","-\frac{6 (c+d x)^{5/6} (b c-a d) \, _2F_1\left(-\frac{11}{6},-\frac{1}{6};\frac{5}{6};-\frac{d (a+b x)}{b c-a d}\right)}{b^2 \sqrt[6]{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6}}",1,"(-6*(b*c - a*d)*(c + d*x)^(5/6)*Hypergeometric2F1[-11/6, -1/6, 5/6, -((d*(a + b*x))/(b*c - a*d))])/(b^2*(a + b*x)^(1/6)*((b*(c + d*x))/(b*c - a*d))^(5/6))","A",2,2,19,0.1053,1,"{70, 69}"
1839,1,72,0,0.020786,"\int \frac{(c+d x)^{5/6}}{(a+b x)^{7/6}} \, dx","Int[(c + d*x)^(5/6)/(a + b*x)^(7/6),x]","-\frac{6 (c+d x)^{5/6} \, _2F_1\left(-\frac{5}{6},-\frac{1}{6};\frac{5}{6};-\frac{d (a+b x)}{b c-a d}\right)}{b \sqrt[6]{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6}}","-\frac{6 (c+d x)^{5/6} \, _2F_1\left(-\frac{5}{6},-\frac{1}{6};\frac{5}{6};-\frac{d (a+b x)}{b c-a d}\right)}{b \sqrt[6]{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6}}",1,"(-6*(c + d*x)^(5/6)*Hypergeometric2F1[-5/6, -1/6, 5/6, -((d*(a + b*x))/(b*c - a*d))])/(b*(a + b*x)^(1/6)*((b*(c + d*x))/(b*c - a*d))^(5/6))","A",2,2,19,0.1053,1,"{70, 69}"
1840,1,72,0,0.0205284,"\int \frac{1}{(a+b x)^{7/6} \sqrt[6]{c+d x}} \, dx","Int[1/((a + b*x)^(7/6)*(c + d*x)^(1/6)),x]","-\frac{6 \sqrt[6]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(-\frac{1}{6},\frac{1}{6};\frac{5}{6};-\frac{d (a+b x)}{b c-a d}\right)}{b \sqrt[6]{a+b x} \sqrt[6]{c+d x}}","-\frac{6 \sqrt[6]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(-\frac{1}{6},\frac{1}{6};\frac{5}{6};-\frac{d (a+b x)}{b c-a d}\right)}{b \sqrt[6]{a+b x} \sqrt[6]{c+d x}}",1,"(-6*((b*(c + d*x))/(b*c - a*d))^(1/6)*Hypergeometric2F1[-1/6, 1/6, 5/6, -((d*(a + b*x))/(b*c - a*d))])/(b*(a + b*x)^(1/6)*(c + d*x)^(1/6))","A",2,2,19,0.1053,1,"{70, 69}"
1841,1,79,0,0.0206713,"\int \frac{1}{(a+b x)^{7/6} (c+d x)^{7/6}} \, dx","Int[1/((a + b*x)^(7/6)*(c + d*x)^(7/6)),x]","-\frac{6 \sqrt[6]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(-\frac{1}{6},\frac{7}{6};\frac{5}{6};-\frac{d (a+b x)}{b c-a d}\right)}{\sqrt[6]{a+b x} \sqrt[6]{c+d x} (b c-a d)}","-\frac{6 \sqrt[6]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(-\frac{1}{6},\frac{7}{6};\frac{5}{6};-\frac{d (a+b x)}{b c-a d}\right)}{\sqrt[6]{a+b x} \sqrt[6]{c+d x} (b c-a d)}",1,"(-6*((b*(c + d*x))/(b*c - a*d))^(1/6)*Hypergeometric2F1[-1/6, 7/6, 5/6, -((d*(a + b*x))/(b*c - a*d))])/((b*c - a*d)*(a + b*x)^(1/6)*(c + d*x)^(1/6))","A",2,2,19,0.1053,1,"{70, 69}"
1842,1,80,0,0.0209196,"\int \frac{1}{(a+b x)^{7/6} (c+d x)^{13/6}} \, dx","Int[1/((a + b*x)^(7/6)*(c + d*x)^(13/6)),x]","-\frac{6 b \sqrt[6]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(-\frac{1}{6},\frac{13}{6};\frac{5}{6};-\frac{d (a+b x)}{b c-a d}\right)}{\sqrt[6]{a+b x} \sqrt[6]{c+d x} (b c-a d)^2}","-\frac{6 b \sqrt[6]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(-\frac{1}{6},\frac{13}{6};\frac{5}{6};-\frac{d (a+b x)}{b c-a d}\right)}{\sqrt[6]{a+b x} \sqrt[6]{c+d x} (b c-a d)^2}",1,"(-6*b*((b*(c + d*x))/(b*c - a*d))^(1/6)*Hypergeometric2F1[-1/6, 13/6, 5/6, -((d*(a + b*x))/(b*c - a*d))])/((b*c - a*d)^2*(a + b*x)^(1/6)*(c + d*x)^(1/6))","A",2,2,19,0.1053,1,"{70, 69}"
1843,1,82,0,0.0223072,"\int \frac{1}{(a+b x)^{7/6} (c+d x)^{19/6}} \, dx","Int[1/((a + b*x)^(7/6)*(c + d*x)^(19/6)),x]","-\frac{6 b^2 \sqrt[6]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(-\frac{1}{6},\frac{19}{6};\frac{5}{6};-\frac{d (a+b x)}{b c-a d}\right)}{\sqrt[6]{a+b x} \sqrt[6]{c+d x} (b c-a d)^3}","-\frac{6 b^2 \sqrt[6]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(-\frac{1}{6},\frac{19}{6};\frac{5}{6};-\frac{d (a+b x)}{b c-a d}\right)}{\sqrt[6]{a+b x} \sqrt[6]{c+d x} (b c-a d)^3}",1,"(-6*b^2*((b*(c + d*x))/(b*c - a*d))^(1/6)*Hypergeometric2F1[-1/6, 19/6, 5/6, -((d*(a + b*x))/(b*c - a*d))])/((b*c - a*d)^3*(a + b*x)^(1/6)*(c + d*x)^(1/6))","A",2,2,19,0.1053,1,"{70, 69}"
1844,1,11,0,0.0022903,"\int (a+b x)^m (a+b (2+m) x) \, dx","Int[(a + b*x)^m*(a + b*(2 + m)*x),x]","x (a+b x)^{m+1}","x (a+b x)^{m+1}",1,"x*(a + b*x)^(1 + m)","A",1,1,16,0.06250,1,"{34}"
1845,1,74,0,0.0256269,"\int (a+b x)^m (c+d x)^n \, dx","Int[(a + b*x)^m*(c + d*x)^n,x]","\frac{(a+b x)^{m+1} (c+d x)^n \left(\frac{b (c+d x)}{b c-a d}\right)^{-n} \, _2F_1\left(m+1,-n;m+2;-\frac{d (a+b x)}{b c-a d}\right)}{b (m+1)}","-\frac{(a+b x)^{m+1} (c+d x)^{n+1} \, _2F_1\left(1,m+n+2;n+2;\frac{b (c+d x)}{b c-a d}\right)}{(n+1) (b c-a d)}",1,"((a + b*x)^(1 + m)*(c + d*x)^n*Hypergeometric2F1[1 + m, -n, 2 + m, -((d*(a + b*x))/(b*c - a*d))])/(b*(1 + m)*((b*(c + d*x))/(b*c - a*d))^n)","A",2,2,15,0.1333,1,"{70, 69}"
1846,1,110,0,0.0545642,"\int (a+b x)^m (c+d x)^3 \, dx","Int[(a + b*x)^m*(c + d*x)^3,x]","\frac{3 d^2 (b c-a d) (a+b x)^{m+3}}{b^4 (m+3)}+\frac{(b c-a d)^3 (a+b x)^{m+1}}{b^4 (m+1)}+\frac{3 d (b c-a d)^2 (a+b x)^{m+2}}{b^4 (m+2)}+\frac{d^3 (a+b x)^{m+4}}{b^4 (m+4)}","\frac{3 d^2 (b c-a d) (a+b x)^{m+3}}{b^4 (m+3)}+\frac{(b c-a d)^3 (a+b x)^{m+1}}{b^4 (m+1)}+\frac{3 d (b c-a d)^2 (a+b x)^{m+2}}{b^4 (m+2)}+\frac{d^3 (a+b x)^{m+4}}{b^4 (m+4)}",1,"((b*c - a*d)^3*(a + b*x)^(1 + m))/(b^4*(1 + m)) + (3*d*(b*c - a*d)^2*(a + b*x)^(2 + m))/(b^4*(2 + m)) + (3*d^2*(b*c - a*d)*(a + b*x)^(3 + m))/(b^4*(3 + m)) + (d^3*(a + b*x)^(4 + m))/(b^4*(4 + m))","A",2,1,15,0.06667,1,"{43}"
1847,1,78,0,0.0318711,"\int (a+b x)^m (c+d x)^2 \, dx","Int[(a + b*x)^m*(c + d*x)^2,x]","\frac{(b c-a d)^2 (a+b x)^{m+1}}{b^3 (m+1)}+\frac{2 d (b c-a d) (a+b x)^{m+2}}{b^3 (m+2)}+\frac{d^2 (a+b x)^{m+3}}{b^3 (m+3)}","\frac{(b c-a d)^2 (a+b x)^{m+1}}{b^3 (m+1)}+\frac{2 d (b c-a d) (a+b x)^{m+2}}{b^3 (m+2)}+\frac{d^2 (a+b x)^{m+3}}{b^3 (m+3)}",1,"((b*c - a*d)^2*(a + b*x)^(1 + m))/(b^3*(1 + m)) + (2*d*(b*c - a*d)*(a + b*x)^(2 + m))/(b^3*(2 + m)) + (d^2*(a + b*x)^(3 + m))/(b^3*(3 + m))","A",2,1,15,0.06667,1,"{43}"
1848,1,46,0,0.0182928,"\int (a+b x)^m (c+d x) \, dx","Int[(a + b*x)^m*(c + d*x),x]","\frac{(b c-a d) (a+b x)^{m+1}}{b^2 (m+1)}+\frac{d (a+b x)^{m+2}}{b^2 (m+2)}","\frac{(b c-a d) (a+b x)^{m+1}}{b^2 (m+1)}+\frac{d (a+b x)^{m+2}}{b^2 (m+2)}",1,"((b*c - a*d)*(a + b*x)^(1 + m))/(b^2*(1 + m)) + (d*(a + b*x)^(2 + m))/(b^2*(2 + m))","A",2,1,13,0.07692,1,"{43}"
1849,1,51,0,0.0106833,"\int \frac{(a+b x)^m}{c+d x} \, dx","Int[(a + b*x)^m/(c + d*x),x]","\frac{(a+b x)^{m+1} \, _2F_1\left(1,m+1;m+2;-\frac{d (a+b x)}{b c-a d}\right)}{(m+1) (b c-a d)}","\frac{(a+b x)^{m+1} \, _2F_1\left(1,m+1;m+2;-\frac{d (a+b x)}{b c-a d}\right)}{(m+1) (b c-a d)}",1,"((a + b*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, -((d*(a + b*x))/(b*c - a*d))])/((b*c - a*d)*(1 + m))","A",1,1,15,0.06667,1,"{68}"
1850,1,52,0,0.0108203,"\int \frac{(a+b x)^m}{(c+d x)^2} \, dx","Int[(a + b*x)^m/(c + d*x)^2,x]","\frac{b (a+b x)^{m+1} \, _2F_1\left(2,m+1;m+2;-\frac{d (a+b x)}{b c-a d}\right)}{(m+1) (b c-a d)^2}","\frac{b (a+b x)^{m+1} \, _2F_1\left(2,m+1;m+2;-\frac{d (a+b x)}{b c-a d}\right)}{(m+1) (b c-a d)^2}",1,"(b*(a + b*x)^(1 + m)*Hypergeometric2F1[2, 1 + m, 2 + m, -((d*(a + b*x))/(b*c - a*d))])/((b*c - a*d)^2*(1 + m))","A",1,1,15,0.06667,1,"{68}"
1851,1,54,0,0.0131582,"\int \frac{(a+b x)^m}{(c+d x)^3} \, dx","Int[(a + b*x)^m/(c + d*x)^3,x]","\frac{b^2 (a+b x)^{m+1} \, _2F_1\left(3,m+1;m+2;-\frac{d (a+b x)}{b c-a d}\right)}{(m+1) (b c-a d)^3}","\frac{b^2 (a+b x)^{m+1} \, _2F_1\left(3,m+1;m+2;-\frac{d (a+b x)}{b c-a d}\right)}{(m+1) (b c-a d)^3}",1,"(b^2*(a + b*x)^(1 + m)*Hypergeometric2F1[3, 1 + m, 2 + m, -((d*(a + b*x))/(b*c - a*d))])/((b*c - a*d)^3*(1 + m))","A",1,1,15,0.06667,1,"{68}"
1852,1,111,0,0.0566002,"\int (a+b x)^3 (c+d x)^n \, dx","Int[(a + b*x)^3*(c + d*x)^n,x]","-\frac{3 b^2 (b c-a d) (c+d x)^{n+3}}{d^4 (n+3)}-\frac{(b c-a d)^3 (c+d x)^{n+1}}{d^4 (n+1)}+\frac{3 b (b c-a d)^2 (c+d x)^{n+2}}{d^4 (n+2)}+\frac{b^3 (c+d x)^{n+4}}{d^4 (n+4)}","-\frac{3 b^2 (b c-a d) (c+d x)^{n+3}}{d^4 (n+3)}-\frac{(b c-a d)^3 (c+d x)^{n+1}}{d^4 (n+1)}+\frac{3 b (b c-a d)^2 (c+d x)^{n+2}}{d^4 (n+2)}+\frac{b^3 (c+d x)^{n+4}}{d^4 (n+4)}",1,"-(((b*c - a*d)^3*(c + d*x)^(1 + n))/(d^4*(1 + n))) + (3*b*(b*c - a*d)^2*(c + d*x)^(2 + n))/(d^4*(2 + n)) - (3*b^2*(b*c - a*d)*(c + d*x)^(3 + n))/(d^4*(3 + n)) + (b^3*(c + d*x)^(4 + n))/(d^4*(4 + n))","A",2,1,15,0.06667,1,"{43}"
1853,1,78,0,0.0320649,"\int (a+b x)^2 (c+d x)^n \, dx","Int[(a + b*x)^2*(c + d*x)^n,x]","\frac{(b c-a d)^2 (c+d x)^{n+1}}{d^3 (n+1)}-\frac{2 b (b c-a d) (c+d x)^{n+2}}{d^3 (n+2)}+\frac{b^2 (c+d x)^{n+3}}{d^3 (n+3)}","\frac{(b c-a d)^2 (c+d x)^{n+1}}{d^3 (n+1)}-\frac{2 b (b c-a d) (c+d x)^{n+2}}{d^3 (n+2)}+\frac{b^2 (c+d x)^{n+3}}{d^3 (n+3)}",1,"((b*c - a*d)^2*(c + d*x)^(1 + n))/(d^3*(1 + n)) - (2*b*(b*c - a*d)*(c + d*x)^(2 + n))/(d^3*(2 + n)) + (b^2*(c + d*x)^(3 + n))/(d^3*(3 + n))","A",2,1,15,0.06667,1,"{43}"
1854,1,47,0,0.018252,"\int (a+b x) (c+d x)^n \, dx","Int[(a + b*x)*(c + d*x)^n,x]","\frac{b (c+d x)^{n+2}}{d^2 (n+2)}-\frac{(b c-a d) (c+d x)^{n+1}}{d^2 (n+1)}","\frac{b (c+d x)^{n+2}}{d^2 (n+2)}-\frac{(b c-a d) (c+d x)^{n+1}}{d^2 (n+1)}",1,"-(((b*c - a*d)*(c + d*x)^(1 + n))/(d^2*(1 + n))) + (b*(c + d*x)^(2 + n))/(d^2*(2 + n))","A",2,1,13,0.07692,1,"{43}"
1855,1,18,0,0.0029468,"\int (c+d x)^n \, dx","Int[(c + d*x)^n,x]","\frac{(c+d x)^{n+1}}{d (n+1)}","\frac{(c+d x)^{n+1}}{d (n+1)}",1,"(c + d*x)^(1 + n)/(d*(1 + n))","A",1,1,7,0.1429,1,"{32}"
1856,1,51,0,0.0116944,"\int \frac{(c+d x)^n}{a+b x} \, dx","Int[(c + d*x)^n/(a + b*x),x]","-\frac{(c+d x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b (c+d x)}{b c-a d}\right)}{(n+1) (b c-a d)}","-\frac{(c+d x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b (c+d x)}{b c-a d}\right)}{(n+1) (b c-a d)}",1,"-(((c + d*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (b*(c + d*x))/(b*c - a*d)])/((b*c - a*d)*(1 + n)))","A",1,1,15,0.06667,1,"{68}"
1857,1,51,0,0.0111316,"\int \frac{(c+d x)^n}{(a+b x)^2} \, dx","Int[(c + d*x)^n/(a + b*x)^2,x]","\frac{d (c+d x)^{n+1} \, _2F_1\left(2,n+1;n+2;\frac{b (c+d x)}{b c-a d}\right)}{(n+1) (b c-a d)^2}","\frac{d (c+d x)^{n+1} \, _2F_1\left(2,n+1;n+2;\frac{b (c+d x)}{b c-a d}\right)}{(n+1) (b c-a d)^2}",1,"(d*(c + d*x)^(1 + n)*Hypergeometric2F1[2, 1 + n, 2 + n, (b*(c + d*x))/(b*c - a*d)])/((b*c - a*d)^2*(1 + n))","A",1,1,15,0.06667,1,"{68}"
1858,1,54,0,0.0153957,"\int \frac{(c+d x)^n}{(a+b x)^3} \, dx","Int[(c + d*x)^n/(a + b*x)^3,x]","-\frac{d^2 (c+d x)^{n+1} \, _2F_1\left(3,n+1;n+2;\frac{b (c+d x)}{b c-a d}\right)}{(n+1) (b c-a d)^3}","-\frac{d^2 (c+d x)^{n+1} \, _2F_1\left(3,n+1;n+2;\frac{b (c+d x)}{b c-a d}\right)}{(n+1) (b c-a d)^3}",1,"-((d^2*(c + d*x)^(1 + n)*Hypergeometric2F1[3, 1 + n, 2 + n, (b*(c + d*x))/(b*c - a*d)])/((b*c - a*d)^3*(1 + n)))","A",1,1,15,0.06667,1,"{68}"
1859,1,143,0,0.0627202,"\int (a+b x)^{-4+n} (c+d x)^{-n} \, dx","Int[(a + b*x)^(-4 + n)/(c + d*x)^n,x]","-\frac{2 d^2 (a+b x)^{n-1} (c+d x)^{1-n}}{(1-n) (2-n) (3-n) (b c-a d)^3}-\frac{(a+b x)^{n-3} (c+d x)^{1-n}}{(3-n) (b c-a d)}+\frac{2 d (a+b x)^{n-2} (c+d x)^{1-n}}{(2-n) (3-n) (b c-a d)^2}","-\frac{2 d^2 (a+b x)^{n-1} (c+d x)^{1-n}}{(1-n) (2-n) (3-n) (b c-a d)^3}-\frac{(a+b x)^{n-3} (c+d x)^{1-n}}{(3-n) (b c-a d)}+\frac{2 d (a+b x)^{n-2} (c+d x)^{1-n}}{(2-n) (3-n) (b c-a d)^2}",1,"-(((a + b*x)^(-3 + n)*(c + d*x)^(1 - n))/((b*c - a*d)*(3 - n))) + (2*d*(a + b*x)^(-2 + n)*(c + d*x)^(1 - n))/((b*c - a*d)^2*(2 - n)*(3 - n)) - (2*d^2*(a + b*x)^(-1 + n)*(c + d*x)^(1 - n))/((b*c - a*d)^3*(1 - n)*(2 - n)*(3 - n))","A",3,2,19,0.1053,1,"{45, 37}"
1860,1,86,0,0.0124284,"\int (a+b x)^{-3+n} (c+d x)^{-n} \, dx","Int[(a + b*x)^(-3 + n)/(c + d*x)^n,x]","\frac{d (a+b x)^{n-1} (c+d x)^{1-n}}{(1-n) (2-n) (b c-a d)^2}-\frac{(a+b x)^{n-2} (c+d x)^{1-n}}{(2-n) (b c-a d)}","\frac{d (a+b x)^{n-1} (c+d x)^{1-n}}{(1-n) (2-n) (b c-a d)^2}-\frac{(a+b x)^{n-2} (c+d x)^{1-n}}{(2-n) (b c-a d)}",1,"-(((a + b*x)^(-2 + n)*(c + d*x)^(1 - n))/((b*c - a*d)*(2 - n))) + (d*(a + b*x)^(-1 + n)*(c + d*x)^(1 - n))/((b*c - a*d)^2*(1 - n)*(2 - n))","A",2,2,19,0.1053,1,"{45, 37}"
1861,1,39,0,0.0041875,"\int (a+b x)^{-2+n} (c+d x)^{-n} \, dx","Int[(a + b*x)^(-2 + n)/(c + d*x)^n,x]","-\frac{(a+b x)^{n-1} (c+d x)^{1-n}}{(1-n) (b c-a d)}","-\frac{(a+b x)^{n-1} (c+d x)^{1-n}}{(1-n) (b c-a d)}",1,"-(((a + b*x)^(-1 + n)*(c + d*x)^(1 - n))/((b*c - a*d)*(1 - n)))","A",1,1,19,0.05263,1,"{37}"
1862,1,66,0,0.0237162,"\int (a+b x)^{-1+n} (c+d x)^{-n} \, dx","Int[(a + b*x)^(-1 + n)/(c + d*x)^n,x]","\frac{(a+b x)^n (c+d x)^{-n} \left(\frac{b (c+d x)}{b c-a d}\right)^n \, _2F_1\left(n,n;n+1;-\frac{d (a+b x)}{b c-a d}\right)}{b n}","\frac{(a+b x)^n (c+d x)^{-n} \left(\frac{b (c+d x)}{b c-a d}\right)^n \, _2F_1\left(n,n;n+1;-\frac{d (a+b x)}{b c-a d}\right)}{b n}",1,"((a + b*x)^n*((b*(c + d*x))/(b*c - a*d))^n*Hypergeometric2F1[n, n, 1 + n, -((d*(a + b*x))/(b*c - a*d))])/(b*n*(c + d*x)^n)","A",2,2,19,0.1053,1,"{70, 69}"
1863,1,72,0,0.0232951,"\int (a+b x)^n (c+d x)^{-n} \, dx","Int[(a + b*x)^n/(c + d*x)^n,x]","\frac{(a+b x)^{n+1} (c+d x)^{-n} \left(\frac{b (c+d x)}{b c-a d}\right)^n \, _2F_1\left(n,n+1;n+2;-\frac{d (a+b x)}{b c-a d}\right)}{b (n+1)}","\frac{(a+b x)^{n+1} (c+d x)^{-n} \left(\frac{b (c+d x)}{b c-a d}\right)^n \, _2F_1\left(n,n+1;n+2;-\frac{d (a+b x)}{b c-a d}\right)}{b (n+1)}",1,"((a + b*x)^(1 + n)*((b*(c + d*x))/(b*c - a*d))^n*Hypergeometric2F1[n, 1 + n, 2 + n, -((d*(a + b*x))/(b*c - a*d))])/(b*(1 + n)*(c + d*x)^n)","A",2,2,17,0.1176,1,"{70, 69}"
1864,1,72,0,0.0229974,"\int (a+b x)^{1+n} (c+d x)^{-n} \, dx","Int[(a + b*x)^(1 + n)/(c + d*x)^n,x]","\frac{(a+b x)^{n+2} (c+d x)^{-n} \left(\frac{b (c+d x)}{b c-a d}\right)^n \, _2F_1\left(n,n+2;n+3;-\frac{d (a+b x)}{b c-a d}\right)}{b (n+2)}","\frac{(a+b x)^{n+2} (c+d x)^{-n} \left(\frac{b (c+d x)}{b c-a d}\right)^n \, _2F_1\left(n,n+2;n+3;-\frac{d (a+b x)}{b c-a d}\right)}{b (n+2)}",1,"((a + b*x)^(2 + n)*((b*(c + d*x))/(b*c - a*d))^n*Hypergeometric2F1[n, 2 + n, 3 + n, -((d*(a + b*x))/(b*c - a*d))])/(b*(2 + n)*(c + d*x)^n)","A",2,2,19,0.1053,1,"{70, 69}"
1865,1,72,0,0.0227955,"\int (a+b x)^{2+n} (c+d x)^{-n} \, dx","Int[(a + b*x)^(2 + n)/(c + d*x)^n,x]","\frac{(a+b x)^{n+3} (c+d x)^{-n} \left(\frac{b (c+d x)}{b c-a d}\right)^n \, _2F_1\left(n,n+3;n+4;-\frac{d (a+b x)}{b c-a d}\right)}{b (n+3)}","\frac{(a+b x)^{n+3} (c+d x)^{-n} \left(\frac{b (c+d x)}{b c-a d}\right)^n \, _2F_1\left(n,n+3;n+4;-\frac{d (a+b x)}{b c-a d}\right)}{b (n+3)}",1,"((a + b*x)^(3 + n)*((b*(c + d*x))/(b*c - a*d))^n*Hypergeometric2F1[n, 3 + n, 4 + n, -((d*(a + b*x))/(b*c - a*d))])/(b*(3 + n)*(c + d*x)^n)","A",2,2,19,0.1053,1,"{70, 69}"
1866,1,72,0,0.0305638,"\int (a+b x)^{-n} (c+d x)^n \, dx","Int[(c + d*x)^n/(a + b*x)^n,x]","\frac{(a+b x)^{-n} (c+d x)^{n+1} \left(-\frac{d (a+b x)}{b c-a d}\right)^n \, _2F_1\left(n,n+1;n+2;\frac{b (c+d x)}{b c-a d}\right)}{d (n+1)}","\frac{(a+b x)^{-n} (c+d x)^{n+1} \left(-\frac{d (a+b x)}{b c-a d}\right)^n \, _2F_1\left(n,n+1;n+2;\frac{b (c+d x)}{b c-a d}\right)}{d (n+1)}",1,"((-((d*(a + b*x))/(b*c - a*d)))^n*(c + d*x)^(1 + n)*Hypergeometric2F1[n, 1 + n, 2 + n, (b*(c + d*x))/(b*c - a*d)])/(d*(1 + n)*(a + b*x)^n)","A",2,2,17,0.1176,1,"{70, 69}"
1867,1,75,0,0.0238464,"\int (a+b x)^{-1-n} (c+d x)^n \, dx","Int[(a + b*x)^(-1 - n)*(c + d*x)^n,x]","-\frac{(a+b x)^{-n} (c+d x)^n \left(\frac{b (c+d x)}{b c-a d}\right)^{-n} \, _2F_1\left(-n,-n;1-n;-\frac{d (a+b x)}{b c-a d}\right)}{b n}","-\frac{(a+b x)^{-n} (c+d x)^n \left(\frac{b (c+d x)}{b c-a d}\right)^{-n} \, _2F_1\left(-n,-n;1-n;-\frac{d (a+b x)}{b c-a d}\right)}{b n}",1,"-(((c + d*x)^n*Hypergeometric2F1[-n, -n, 1 - n, -((d*(a + b*x))/(b*c - a*d))])/(b*n*(a + b*x)^n*((b*(c + d*x))/(b*c - a*d))^n))","A",2,2,19,0.1053,1,"{70, 69}"
1868,1,37,0,0.0059839,"\int (a+b x)^{-2-n} (c+d x)^n \, dx","Int[(a + b*x)^(-2 - n)*(c + d*x)^n,x]","-\frac{(a+b x)^{-n-1} (c+d x)^{n+1}}{(n+1) (b c-a d)}","-\frac{(a+b x)^{-n-1} (c+d x)^{n+1}}{(n+1) (b c-a d)}",1,"-(((a + b*x)^(-1 - n)*(c + d*x)^(1 + n))/((b*c - a*d)*(1 + n)))","A",1,1,19,0.05263,1,"{37}"
1869,1,80,0,0.0197497,"\int (a+b x)^{-3-n} (c+d x)^n \, dx","Int[(a + b*x)^(-3 - n)*(c + d*x)^n,x]","\frac{d (a+b x)^{-n-1} (c+d x)^{n+1}}{(n+1) (n+2) (b c-a d)^2}-\frac{(a+b x)^{-n-2} (c+d x)^{n+1}}{(n+2) (b c-a d)}","\frac{d (a+b x)^{-n-1} (c+d x)^{n+1}}{(n+1) (n+2) (b c-a d)^2}-\frac{(a+b x)^{-n-2} (c+d x)^{n+1}}{(n+2) (b c-a d)}",1,"-(((a + b*x)^(-2 - n)*(c + d*x)^(1 + n))/((b*c - a*d)*(2 + n))) + (d*(a + b*x)^(-1 - n)*(c + d*x)^(1 + n))/((b*c - a*d)^2*(1 + n)*(2 + n))","A",2,2,19,0.1053,1,"{45, 37}"
1870,1,131,0,0.046199,"\int (a+b x)^{-4-n} (c+d x)^n \, dx","Int[(a + b*x)^(-4 - n)*(c + d*x)^n,x]","-\frac{2 d^2 (a+b x)^{-n-1} (c+d x)^{n+1}}{(n+1) (n+2) (n+3) (b c-a d)^3}-\frac{(a+b x)^{-n-3} (c+d x)^{n+1}}{(n+3) (b c-a d)}+\frac{2 d (a+b x)^{-n-2} (c+d x)^{n+1}}{(n+2) (n+3) (b c-a d)^2}","-\frac{2 d^2 (a+b x)^{-n-1} (c+d x)^{n+1}}{(n+1) (n+2) (n+3) (b c-a d)^3}-\frac{(a+b x)^{-n-3} (c+d x)^{n+1}}{(n+3) (b c-a d)}+\frac{2 d (a+b x)^{-n-2} (c+d x)^{n+1}}{(n+2) (n+3) (b c-a d)^2}",1,"-(((a + b*x)^(-3 - n)*(c + d*x)^(1 + n))/((b*c - a*d)*(3 + n))) + (2*d*(a + b*x)^(-2 - n)*(c + d*x)^(1 + n))/((b*c - a*d)^2*(2 + n)*(3 + n)) - (2*d^2*(a + b*x)^(-1 - n)*(c + d*x)^(1 + n))/((b*c - a*d)^3*(1 + n)*(2 + n)*(3 + n))","A",3,2,19,0.1053,1,"{45, 37}"
1871,1,186,0,0.0862265,"\int (a+b x)^{-5-n} (c+d x)^n \, dx","Int[(a + b*x)^(-5 - n)*(c + d*x)^n,x]","-\frac{6 d^2 (a+b x)^{-n-2} (c+d x)^{n+1}}{(n+2) (n+3) (n+4) (b c-a d)^3}+\frac{6 d^3 (a+b x)^{-n-1} (c+d x)^{n+1}}{(n+1) (n+2) (n+3) (n+4) (b c-a d)^4}-\frac{(a+b x)^{-n-4} (c+d x)^{n+1}}{(n+4) (b c-a d)}+\frac{3 d (a+b x)^{-n-3} (c+d x)^{n+1}}{(n+3) (n+4) (b c-a d)^2}","-\frac{6 d^2 (a+b x)^{-n-2} (c+d x)^{n+1}}{(n+2) (n+3) (n+4) (b c-a d)^3}+\frac{6 d^3 (a+b x)^{-n-1} (c+d x)^{n+1}}{(n+1) (n+2) (n+3) (n+4) (b c-a d)^4}-\frac{(a+b x)^{-n-4} (c+d x)^{n+1}}{(n+4) (b c-a d)}+\frac{3 d (a+b x)^{-n-3} (c+d x)^{n+1}}{(n+3) (n+4) (b c-a d)^2}",1,"-(((a + b*x)^(-4 - n)*(c + d*x)^(1 + n))/((b*c - a*d)*(4 + n))) + (3*d*(a + b*x)^(-3 - n)*(c + d*x)^(1 + n))/((b*c - a*d)^2*(3 + n)*(4 + n)) - (6*d^2*(a + b*x)^(-2 - n)*(c + d*x)^(1 + n))/((b*c - a*d)^3*(2 + n)*(3 + n)*(4 + n)) + (6*d^3*(a + b*x)^(-1 - n)*(c + d*x)^(1 + n))/((b*c - a*d)^4*(1 + n)*(2 + n)*(3 + n)*(4 + n))","A",4,2,19,0.1053,1,"{45, 37}"
1872,1,72,0,0.0226195,"\int (a+b x)^n (c+d x)^{-n} \, dx","Int[(a + b*x)^n/(c + d*x)^n,x]","\frac{(a+b x)^{n+1} (c+d x)^{-n} \left(\frac{b (c+d x)}{b c-a d}\right)^n \, _2F_1\left(n,n+1;n+2;-\frac{d (a+b x)}{b c-a d}\right)}{b (n+1)}","\frac{(a+b x)^{n+1} (c+d x)^{-n} \left(\frac{b (c+d x)}{b c-a d}\right)^n \, _2F_1\left(n,n+1;n+2;-\frac{d (a+b x)}{b c-a d}\right)}{b (n+1)}",1,"((a + b*x)^(1 + n)*((b*(c + d*x))/(b*c - a*d))^n*Hypergeometric2F1[n, 1 + n, 2 + n, -((d*(a + b*x))/(b*c - a*d))])/(b*(1 + n)*(c + d*x)^n)","A",2,2,17,0.1176,1,"{70, 69}"
1873,1,75,0,0.0262994,"\int (a+b x)^n (c+d x)^{-1-n} \, dx","Int[(a + b*x)^n*(c + d*x)^(-1 - n),x]","-\frac{(a+b x)^n (c+d x)^{-n} \left(-\frac{d (a+b x)}{b c-a d}\right)^{-n} \, _2F_1\left(-n,-n;1-n;\frac{b (c+d x)}{b c-a d}\right)}{d n}","-\frac{(a+b x)^n (c+d x)^{-n} \left(-\frac{d (a+b x)}{b c-a d}\right)^{-n} \, _2F_1\left(-n,-n;1-n;\frac{b (c+d x)}{b c-a d}\right)}{d n}",1,"-(((a + b*x)^n*Hypergeometric2F1[-n, -n, 1 - n, (b*(c + d*x))/(b*c - a*d)])/(d*n*(-((d*(a + b*x))/(b*c - a*d)))^n*(c + d*x)^n))","A",2,2,19,0.1053,1,"{70, 69}"
1874,1,36,0,0.0045702,"\int (a+b x)^n (c+d x)^{-2-n} \, dx","Int[(a + b*x)^n*(c + d*x)^(-2 - n),x]","\frac{(a+b x)^{n+1} (c+d x)^{-n-1}}{(n+1) (b c-a d)}","\frac{(a+b x)^{n+1} (c+d x)^{-n-1}}{(n+1) (b c-a d)}",1,"((a + b*x)^(1 + n)*(c + d*x)^(-1 - n))/((b*c - a*d)*(1 + n))","A",1,1,19,0.05263,1,"{37}"
1875,1,79,0,0.0169357,"\int (a+b x)^n (c+d x)^{-3-n} \, dx","Int[(a + b*x)^n*(c + d*x)^(-3 - n),x]","\frac{(a+b x)^{n+1} (c+d x)^{-n-2}}{(n+2) (b c-a d)}+\frac{b (a+b x)^{n+1} (c+d x)^{-n-1}}{(n+1) (n+2) (b c-a d)^2}","\frac{(a+b x)^{n+1} (c+d x)^{-n-2}}{(n+2) (b c-a d)}+\frac{b (a+b x)^{n+1} (c+d x)^{-n-1}}{(n+1) (n+2) (b c-a d)^2}",1,"((a + b*x)^(1 + n)*(c + d*x)^(-2 - n))/((b*c - a*d)*(2 + n)) + (b*(a + b*x)^(1 + n)*(c + d*x)^(-1 - n))/((b*c - a*d)^2*(1 + n)*(2 + n))","A",2,2,19,0.1053,1,"{45, 37}"
1876,1,130,0,0.0372081,"\int (a+b x)^n (c+d x)^{-4-n} \, dx","Int[(a + b*x)^n*(c + d*x)^(-4 - n),x]","\frac{2 b^2 (a+b x)^{n+1} (c+d x)^{-n-1}}{(n+1) (n+2) (n+3) (b c-a d)^3}+\frac{(a+b x)^{n+1} (c+d x)^{-n-3}}{(n+3) (b c-a d)}+\frac{2 b (a+b x)^{n+1} (c+d x)^{-n-2}}{(n+2) (n+3) (b c-a d)^2}","\frac{2 b^2 (a+b x)^{n+1} (c+d x)^{-n-1}}{(n+1) (n+2) (n+3) (b c-a d)^3}+\frac{(a+b x)^{n+1} (c+d x)^{-n-3}}{(n+3) (b c-a d)}+\frac{2 b (a+b x)^{n+1} (c+d x)^{-n-2}}{(n+2) (n+3) (b c-a d)^2}",1,"((a + b*x)^(1 + n)*(c + d*x)^(-3 - n))/((b*c - a*d)*(3 + n)) + (2*b*(a + b*x)^(1 + n)*(c + d*x)^(-2 - n))/((b*c - a*d)^2*(2 + n)*(3 + n)) + (2*b^2*(a + b*x)^(1 + n)*(c + d*x)^(-1 - n))/((b*c - a*d)^3*(1 + n)*(2 + n)*(3 + n))","A",3,2,19,0.1053,1,"{45, 37}"
1877,1,185,0,0.0616625,"\int (a+b x)^n (c+d x)^{-5-n} \, dx","Int[(a + b*x)^n*(c + d*x)^(-5 - n),x]","\frac{6 b^2 (a+b x)^{n+1} (c+d x)^{-n-2}}{(n+2) (n+3) (n+4) (b c-a d)^3}+\frac{6 b^3 (a+b x)^{n+1} (c+d x)^{-n-1}}{(n+1) (n+2) (n+3) (n+4) (b c-a d)^4}+\frac{(a+b x)^{n+1} (c+d x)^{-n-4}}{(n+4) (b c-a d)}+\frac{3 b (a+b x)^{n+1} (c+d x)^{-n-3}}{(n+3) (n+4) (b c-a d)^2}","\frac{6 b^2 (a+b x)^{n+1} (c+d x)^{-n-2}}{(n+2) (n+3) (n+4) (b c-a d)^3}+\frac{6 b^3 (a+b x)^{n+1} (c+d x)^{-n-1}}{(n+1) (n+2) (n+3) (n+4) (b c-a d)^4}+\frac{(a+b x)^{n+1} (c+d x)^{-n-4}}{(n+4) (b c-a d)}+\frac{3 b (a+b x)^{n+1} (c+d x)^{-n-3}}{(n+3) (n+4) (b c-a d)^2}",1,"((a + b*x)^(1 + n)*(c + d*x)^(-4 - n))/((b*c - a*d)*(4 + n)) + (3*b*(a + b*x)^(1 + n)*(c + d*x)^(-3 - n))/((b*c - a*d)^2*(3 + n)*(4 + n)) + (6*b^2*(a + b*x)^(1 + n)*(c + d*x)^(-2 - n))/((b*c - a*d)^3*(2 + n)*(3 + n)*(4 + n)) + (6*b^3*(a + b*x)^(1 + n)*(c + d*x)^(-1 - n))/((b*c - a*d)^4*(1 + n)*(2 + n)*(3 + n)*(4 + n))","A",4,2,19,0.1053,1,"{45, 37}"
1878,1,83,0,0.0287925,"\int (a+b x)^{-2+n} (c+d x)^{1-n} \, dx","Int[(a + b*x)^(-2 + n)*(c + d*x)^(1 - n),x]","-\frac{(b c-a d) (a+b x)^{n-1} (c+d x)^{-n} \left(\frac{b (c+d x)}{b c-a d}\right)^n \, _2F_1\left(n-1,n-1;n;-\frac{d (a+b x)}{b c-a d}\right)}{b^2 (1-n)}","-\frac{(b c-a d) (a+b x)^{n-1} (c+d x)^{-n} \left(\frac{b (c+d x)}{b c-a d}\right)^n \, _2F_1\left(n-1,n-1;n;-\frac{d (a+b x)}{b c-a d}\right)}{b^2 (1-n)}",1,"-(((b*c - a*d)*(a + b*x)^(-1 + n)*((b*(c + d*x))/(b*c - a*d))^n*Hypergeometric2F1[-1 + n, -1 + n, n, -((d*(a + b*x))/(b*c - a*d))])/(b^2*(1 - n)*(c + d*x)^n))","A",2,2,21,0.09524,1,"{70, 69}"
1879,1,84,0,0.0297747,"\int (a+b x)^{1+n} (c+d x)^{-1-n} \, dx","Int[(a + b*x)^(1 + n)*(c + d*x)^(-1 - n),x]","\frac{(b c-a d) (a+b x)^n (c+d x)^{-n} \left(-\frac{d (a+b x)}{b c-a d}\right)^{-n} \, _2F_1\left(-n-1,-n;1-n;\frac{b (c+d x)}{b c-a d}\right)}{d^2 n}","\frac{(b c-a d) (a+b x)^n (c+d x)^{-n} \left(-\frac{d (a+b x)}{b c-a d}\right)^{-n} \, _2F_1\left(-n-1,-n;1-n;\frac{b (c+d x)}{b c-a d}\right)}{d^2 n}",1,"((b*c - a*d)*(a + b*x)^n*Hypergeometric2F1[-1 - n, -n, 1 - n, (b*(c + d*x))/(b*c - a*d)])/(d^2*n*(-((d*(a + b*x))/(b*c - a*d)))^n*(c + d*x)^n)","A",2,2,21,0.09524,1,"{70, 69}"
1880,1,51,0,0.0091459,"\int (a+b x)^m (c+d x)^{1+2 n-2 (1+n)} \, dx","Int[(a + b*x)^m*(c + d*x)^(1 + 2*n - 2*(1 + n)),x]","\frac{(a+b x)^{m+1} \, _2F_1\left(1,m+1;m+2;-\frac{d (a+b x)}{b c-a d}\right)}{(m+1) (b c-a d)}","\frac{(a+b x)^{m+1} \, _2F_1\left(1,m+1;m+2;-\frac{d (a+b x)}{b c-a d}\right)}{(m+1) (b c-a d)}",1,"((a + b*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, -((d*(a + b*x))/(b*c - a*d))])/((b*c - a*d)*(1 + m))","A",2,2,24,0.08333,1,"{7, 68}"
1881,1,57,0,0.0301914,"\int \frac{(c+d x)^{1+2 n-2 (1+n)}}{(a+b x)^2} \, dx","Int[(c + d*x)^(1 + 2*n - 2*(1 + n))/(a + b*x)^2,x]","-\frac{1}{(a+b x) (b c-a d)}-\frac{d \log (a+b x)}{(b c-a d)^2}+\frac{d \log (c+d x)}{(b c-a d)^2}","-\frac{1}{(a+b x) (b c-a d)}-\frac{d \log (a+b x)}{(b c-a d)^2}+\frac{d \log (c+d x)}{(b c-a d)^2}",1,"-(1/((b*c - a*d)*(a + b*x))) - (d*Log[a + b*x])/(b*c - a*d)^2 + (d*Log[c + d*x])/(b*c - a*d)^2","A",3,2,24,0.08333,1,"{7, 44}"
1882,1,95,0,0.0360218,"\int (a+b x)^m (a c (1+m)+b c (2+m) x)^{-3-m} \, dx","Int[(a + b*x)^m*(a*c*(1 + m) + b*c*(2 + m)*x)^(-3 - m),x]","\frac{(a+b x)^{m+1} (a c (m+1)+b c (m+2) x)^{-m-1}}{a^2 b c^2 (m+1) (m+2)}-\frac{(a+b x)^{m+1} (a c (m+1)+b c (m+2) x)^{-m-2}}{a b c (m+2)}","\frac{(a+b x)^{m+1} (a c (m+1)+b c (m+2) x)^{-m-1}}{a^2 b c^2 (m+1) (m+2)}-\frac{(a+b x)^{m+1} (a c (m+1)+b c (m+2) x)^{-m-2}}{a b c (m+2)}",1,"-(((a + b*x)^(1 + m)*(a*c*(1 + m) + b*c*(2 + m)*x)^(-2 - m))/(a*b*c*(2 + m))) + ((a + b*x)^(1 + m)*(a*c*(1 + m) + b*c*(2 + m)*x)^(-1 - m))/(a^2*b*c^2*(1 + m)*(2 + m))","A",2,2,28,0.07143,1,"{45, 37}"
1883,1,97,0,0.0221451,"\int (a+b x)^{-1-\frac{b c}{b c-a d}} (c+d x)^{-1+\frac{a d}{b c-a d}} \, dx","Int[(a + b*x)^(-1 - (b*c)/(b*c - a*d))*(c + d*x)^(-1 + (a*d)/(b*c - a*d)),x]","\frac{(a+b x)^{-\frac{a d}{b c-a d}} (c+d x)^{\frac{a d}{b c-a d}}}{a b c}-\frac{(a+b x)^{-\frac{b c}{b c-a d}} (c+d x)^{\frac{a d}{b c-a d}}}{b c}","\frac{(a+b x)^{-\frac{a d}{b c-a d}} (c+d x)^{\frac{a d}{b c-a d}}}{a b c}-\frac{(a+b x)^{-\frac{b c}{b c-a d}} (c+d x)^{\frac{a d}{b c-a d}}}{b c}",1,"-((c + d*x)^((a*d)/(b*c - a*d))/(b*c*(a + b*x)^((b*c)/(b*c - a*d)))) + (c + d*x)^((a*d)/(b*c - a*d))/(a*b*c*(a + b*x)^((a*d)/(b*c - a*d)))","A",2,2,44,0.04545,1,"{45, 37}"
1884,1,97,0,0.018449,"\int (a+b x)^{\frac{-2 b c+a d}{b c-a d}} (c+d x)^{\frac{b c-2 a d}{-b c+a d}} \, dx","Int[(a + b*x)^((-2*b*c + a*d)/(b*c - a*d))*(c + d*x)^((b*c - 2*a*d)/(-(b*c) + a*d)),x]","\frac{(a+b x)^{-\frac{a d}{b c-a d}} (c+d x)^{\frac{a d}{b c-a d}}}{a b c}-\frac{(a+b x)^{-\frac{b c}{b c-a d}} (c+d x)^{\frac{a d}{b c-a d}}}{b c}","\frac{(a+b x)^{-\frac{a d}{b c-a d}} (c+d x)^{\frac{a d}{b c-a d}}}{a b c}-\frac{(a+b x)^{-\frac{b c}{b c-a d}} (c+d x)^{\frac{a d}{b c-a d}}}{b c}",1,"-((c + d*x)^((a*d)/(b*c - a*d))/(b*c*(a + b*x)^((b*c)/(b*c - a*d)))) + (c + d*x)^((a*d)/(b*c - a*d))/(a*b*c*(a + b*x)^((a*d)/(b*c - a*d)))","A",2,2,51,0.03922,1,"{45, 37}"
1885,1,30,0,0.0067607,"\int \frac{(1-x)^n}{\sqrt{1+x}} \, dx","Int[(1 - x)^n/Sqrt[1 + x],x]","2^{n+1} \sqrt{x+1} \, _2F_1\left(\frac{1}{2},-n;\frac{3}{2};\frac{x+1}{2}\right)","2^{n+1} \sqrt{x+1} \, _2F_1\left(\frac{1}{2},-n;\frac{3}{2};\frac{x+1}{2}\right)",1,"2^(1 + n)*Sqrt[1 + x]*Hypergeometric2F1[1/2, -n, 3/2, (1 + x)/2]","A",1,1,15,0.06667,1,"{69}"
1886,1,35,0,0.0055015,"\int \frac{(1+x)^n}{\sqrt{1-x}} \, dx","Int[(1 + x)^n/Sqrt[1 - x],x]","-2^{n+1} \sqrt{1-x} \, _2F_1\left(\frac{1}{2},-n;\frac{3}{2};\frac{1-x}{2}\right)","-2^{n+1} \sqrt{1-x} \, _2F_1\left(\frac{1}{2},-n;\frac{3}{2};\frac{1-x}{2}\right)",1,"-(2^(1 + n)*Sqrt[1 - x]*Hypergeometric2F1[1/2, -n, 3/2, (1 - x)/2])","A",1,1,15,0.06667,1,"{69}"
1887,1,33,0,0.007115,"\int (1-x)^n (1+x)^{7/3} \, dx","Int[(1 - x)^n*(1 + x)^(7/3),x]","\frac{3}{5} 2^{n-1} (x+1)^{10/3} \, _2F_1\left(\frac{10}{3},-n;\frac{13}{3};\frac{x+1}{2}\right)","\frac{3}{5} 2^{n-1} (x+1)^{10/3} \, _2F_1\left(\frac{10}{3},-n;\frac{13}{3};\frac{x+1}{2}\right)",1,"(3*2^(-1 + n)*(1 + x)^(10/3)*Hypergeometric2F1[10/3, -n, 13/3, (1 + x)/2])/5","A",1,1,15,0.06667,1,"{69}"
1888,1,37,0,0.0052561,"\int (1-x)^{7/3} (1+x)^n \, dx","Int[(1 - x)^(7/3)*(1 + x)^n,x]","-\frac{3}{5} 2^{n-1} (1-x)^{10/3} \, _2F_1\left(\frac{10}{3},-n;\frac{13}{3};\frac{1-x}{2}\right)","-\frac{3}{5} 2^{n-1} (1-x)^{10/3} \, _2F_1\left(\frac{10}{3},-n;\frac{13}{3};\frac{1-x}{2}\right)",1,"(-3*2^(-1 + n)*(1 - x)^(10/3)*Hypergeometric2F1[10/3, -n, 13/3, (1 - x)/2])/5","A",1,1,15,0.06667,1,"{69}"
1889,1,47,0,0.0144975,"\int (1+2 x)^{-m} (2+3 x)^m \, dx","Int[(2 + 3*x)^m/(1 + 2*x)^m,x]","\frac{2^{-m-1} (2 x+1)^{1-m} \, _2F_1(1-m,-m;2-m;-3 (2 x+1))}{1-m}","\frac{2^{-m-1} (2 x+1)^{1-m} \, _2F_1(1-m,-m;2-m;-3 (2 x+1))}{1-m}",1,"(2^(-1 - m)*(1 + 2*x)^(1 - m)*Hypergeometric2F1[1 - m, -m, 2 - m, -3*(1 + 2*x)])/(1 - m)","A",1,1,17,0.05882,1,"{69}"
1890,1,45,0,0.01852,"\int \left(\frac{d (a+b x)}{-b c+a d}\right)^m (c+d x)^n \, dx","Int[((d*(a + b*x))/(-(b*c) + a*d))^m*(c + d*x)^n,x]","\frac{(c+d x)^{n+1} \, _2F_1\left(-m,n+1;n+2;\frac{b (c+d x)}{b c-a d}\right)}{d (n+1)}","\frac{(c+d x)^{n+1} \, _2F_1\left(-m,n+1;n+2;\frac{b (c+d x)}{b c-a d}\right)}{d (n+1)}",1,"((c + d*x)^(1 + n)*Hypergeometric2F1[-m, 1 + n, 2 + n, (b*(c + d*x))/(b*c - a*d)])/(d*(1 + n))","A",2,2,27,0.07407,1,"{186, 69}"
1891,1,28,0,0.0046075,"\int \left(a+b x+c x^2+d x^3\right) \, dx","Int[a + b*x + c*x^2 + d*x^3,x]","a x+\frac{b x^2}{2}+\frac{c x^3}{3}+\frac{d x^4}{4}","a x+\frac{b x^2}{2}+\frac{c x^3}{3}+\frac{d x^4}{4}",1,"a*x + (b*x^2)/2 + (c*x^3)/3 + (d*x^4)/4","A",1,0,15,0,1,"{}"
1892,1,15,0,0.0019756,"\int \left(-x^3+x^4\right) \, dx","Int[-x^3 + x^4,x]","\frac{x^5}{5}-\frac{x^4}{4}","\frac{x^5}{5}-\frac{x^4}{4}",1,"-x^4/4 + x^5/5","A",1,0,9,0,1,"{}"
1893,1,11,0,0.00155,"\int \left(-1+x^5\right) \, dx","Int[-1 + x^5,x]","\frac{x^6}{6}-x","\frac{x^6}{6}-x",1,"-x + x^6/6","A",1,0,5,0,1,"{}"
1894,1,9,0,0.0014703,"\int (7+4 x) \, dx","Int[7 + 4*x,x]","2 x^2+7 x","2 x^2+7 x",1,"7*x + 2*x^2","A",1,0,5,0,1,"{}"
1895,1,14,0,0.002349,"\int \left(4 x+\pi  x^3\right) \, dx","Int[4*x + Pi*x^3,x]","\frac{\pi  x^4}{4}+2 x^2","\frac{\pi  x^4}{4}+2 x^2",1,"2*x^2 + (Pi*x^4)/4","A",1,0,9,0,1,"{}"
1896,1,11,0,0.0014909,"\int \left(2 x+5 x^2\right) \, dx","Int[2*x + 5*x^2,x]","\frac{5 x^3}{3}+x^2","\frac{5 x^3}{3}+x^2",1,"x^2 + (5*x^3)/3","A",1,0,9,0,1,"{}"
1897,1,15,0,0.0019564,"\int \left(\frac{x^2}{2}+\frac{x^3}{3}\right) \, dx","Int[x^2/2 + x^3/3,x]","\frac{x^4}{12}+\frac{x^3}{6}","\frac{x^4}{12}+\frac{x^3}{6}",1,"x^3/6 + x^4/12","A",1,0,15,0,1,"{}"
1898,1,18,0,0.0025386,"\int \left(3-5 x+2 x^2\right) \, dx","Int[3 - 5*x + 2*x^2,x]","\frac{2 x^3}{3}-\frac{5 x^2}{2}+3 x","\frac{2 x^3}{3}-\frac{5 x^2}{2}+3 x",1,"3*x - (5*x^2)/2 + (2*x^3)/3","A",1,0,10,0,1,"{}"
1899,1,20,0,0.002542,"\int \left(-2 x+x^2+x^3\right) \, dx","Int[-2*x + x^2 + x^3,x]","\frac{x^4}{4}+\frac{x^3}{3}-x^2","\frac{x^4}{4}+\frac{x^3}{3}-x^2",1,"-x^2 + x^3/3 + x^4/4","A",1,0,10,0,1,"{}"
1900,1,16,0,0.0018788,"\int \left(1-x^2-3 x^5\right) \, dx","Int[1 - x^2 - 3*x^5,x]","-\frac{x^6}{2}-\frac{x^3}{3}+x","-\frac{x^6}{2}-\frac{x^3}{3}+x",1,"x - x^3/3 - x^6/2","A",1,0,12,0,1,"{}"
1901,1,13,0,0.0018286,"\int \left(5+2 x+3 x^2+4 x^3\right) \, dx","Int[5 + 2*x + 3*x^2 + 4*x^3,x]","x^4+x^3+x^2+5 x","x^4+x^3+x^2+5 x",1,"5*x + x^2 + x^3 + x^4","A",1,0,15,0,1,"{}"
1902,1,22,0,0.0039866,"\int \left(a+\frac{d}{x^3}+\frac{c}{x^2}+\frac{b}{x}\right) \, dx","Int[a + d/x^3 + c/x^2 + b/x,x]","a x+b \log (x)-\frac{c}{x}-\frac{d}{2 x^2}","a x+b \log (x)-\frac{c}{x}-\frac{d}{2 x^2}",1,"-d/(2*x^2) - c/x + a*x + b*Log[x]","A",1,0,17,0,1,"{}"
1903,1,22,0,0.0026291,"\int \left(\frac{1}{x^5}+x+x^5\right) \, dx","Int[x^(-5) + x + x^5,x]","\frac{x^6}{6}+\frac{x^2}{2}-\frac{1}{4 x^4}","\frac{x^6}{6}+\frac{x^2}{2}-\frac{1}{4 x^4}",1,"-1/(4*x^4) + x^2/2 + x^6/6","A",1,0,8,0,1,"{}"
1904,1,15,0,0.0020757,"\int \left(\frac{1}{x^3}+\frac{1}{x^2}+\frac{1}{x}\right) \, dx","Int[x^(-3) + x^(-2) + x^(-1),x]","-\frac{1}{2 x^2}-\frac{1}{x}+\log (x)","-\frac{1}{2 x^2}-\frac{1}{x}+\log (x)",1,"-1/(2*x^2) - x^(-1) + Log[x]","A",1,0,10,0,1,"{}"
1905,1,10,0,0.0017358,"\int \left(-\frac{2}{x^2}+\frac{3}{x}\right) \, dx","Int[-2/x^2 + 3/x,x]","\frac{2}{x}+3 \log (x)","\frac{2}{x}+3 \log (x)",1,"2/x + 3*Log[x]","A",1,0,11,0,1,"{}"
1906,1,15,0,0.0018043,"\int \left(-\frac{1}{7 x^6}+x^6\right) \, dx","Int[-1/(7*x^6) + x^6,x]","\frac{x^7}{7}+\frac{1}{35 x^5}","\frac{x^7}{7}+\frac{1}{35 x^5}",1,"1/(35*x^5) + x^7/7","A",1,0,11,0,1,"{}"
1907,1,11,0,0.0013859,"\int \left(1+\frac{1}{x}+x\right) \, dx","Int[1 + x^(-1) + x,x]","\frac{x^2}{2}+x+\log (x)","\frac{x^2}{2}+x+\log (x)",1,"x + x^2/2 + Log[x]","A",1,0,6,0,1,"{}"
1908,1,13,0,0.0019179,"\int \left(-\frac{3}{x^3}+\frac{4}{x^2}\right) \, dx","Int[-3/x^3 + 4/x^2,x]","\frac{3}{2 x^2}-\frac{4}{x}","\frac{3}{2 x^2}-\frac{4}{x}",1,"3/(2*x^2) - 4/x","A",1,0,11,0,1,"{}"
1909,1,13,0,0.0016842,"\int \left(\frac{1}{x}+2 x+x^2\right) \, dx","Int[x^(-1) + 2*x + x^2,x]","\frac{x^3}{3}+x^2+\log (x)","\frac{x^3}{3}+x^2+\log (x)",1,"x^2 + x^3/3 + Log[x]","A",1,0,10,0,1,"{}"
1910,1,17,0,0.0018104,"\int \left(x^{5/6}-x^3\right) \, dx","Int[x^(5/6) - x^3,x]","\frac{6 x^{11/6}}{11}-\frac{x^4}{4}","\frac{6 x^{11/6}}{11}-\frac{x^4}{4}",1,"(6*x^(11/6))/11 - x^4/4","A",1,0,11,0,1,"{}"
1911,1,13,0,0.0016099,"\int \left(33+\sqrt[33]{x}\right) \, dx","Int[33 + x^(1/33),x]","\frac{33 x^{34/33}}{34}+33 x","\frac{33 x^{34/33}}{34}+33 x",1,"33*x + (33*x^(34/33))/34","A",1,0,7,0,1,"{}"
1912,1,15,0,0.0013879,"\int \left(\frac{1}{2 \sqrt{x}}+2 \sqrt{x}\right) \, dx","Int[1/(2*Sqrt[x]) + 2*Sqrt[x],x]","\frac{4 x^{3/2}}{3}+\sqrt{x}","\frac{4 x^{3/2}}{3}+\sqrt{x}",1,"Sqrt[x] + (4*x^(3/2))/3","A",1,0,17,0,1,"{}"
1913,1,15,0,0.002104,"\int \left(-\frac{1}{x^2}+\frac{10}{x}+6 \sqrt{x}\right) \, dx","Int[-x^(-2) + 10/x + 6*Sqrt[x],x]","4 x^{3/2}+\frac{1}{x}+10 \log (x)","4 x^{3/2}+\frac{1}{x}+10 \log (x)",1,"x^(-1) + 4*x^(3/2) + 10*Log[x]","A",1,0,18,0,1,"{}"
1914,1,17,0,0.0018102,"\int \left(\frac{1}{x^{3/2}}+x^{3/2}\right) \, dx","Int[x^(-3/2) + x^(3/2),x]","\frac{2 x^{5/2}}{5}-\frac{2}{\sqrt{x}}","\frac{2 x^{5/2}}{5}-\frac{2}{\sqrt{x}}",1,"-2/Sqrt[x] + (2*x^(5/2))/5","A",1,0,11,0,1,"{}"
1915,1,15,0,0.0018477,"\int \left(-5 x^{3/2}+7 x^{5/2}\right) \, dx","Int[-5*x^(3/2) + 7*x^(5/2),x]","2 x^{7/2}-2 x^{5/2}","2 x^{7/2}-2 x^{5/2}",1,"-2*x^(5/2) + 2*x^(7/2)","A",1,0,15,0,1,"{}"
1916,1,24,0,0.0024671,"\int \left(\frac{2}{\sqrt{x}}+\sqrt{x}-\frac{x}{2}\right) \, dx","Int[2/Sqrt[x] + Sqrt[x] - x/2,x]","-\frac{x^2}{4}+\frac{2 x^{3/2}}{3}+4 \sqrt{x}","-\frac{x^2}{4}+\frac{2 x^{3/2}}{3}+4 \sqrt{x}",1,"4*Sqrt[x] + (2*x^(3/2))/3 - x^2/4","A",1,0,18,0,1,"{}"
1917,1,23,0,0.0025672,"\int \left(-\frac{2}{x}+\frac{\sqrt{x}}{5}+x^{3/2}\right) \, dx","Int[-2/x + Sqrt[x]/5 + x^(3/2),x]","\frac{2 x^{5/2}}{5}+\frac{2 x^{3/2}}{15}-2 \log (x)","\frac{2 x^{5/2}}{5}+\frac{2 x^{3/2}}{15}-2 \log (x)",1,"(2*x^(3/2))/15 + (2*x^(5/2))/5 - 2*Log[x]","A",1,0,20,0,1,"{}"