1,1,1,1,0.0122427,"\int 0 \, dx","IntegrateAlgebraic[0,x]","0","0",1,"0","A",1
2,1,1,1,0.0008903,"\int 1 \, dx","IntegrateAlgebraic[1,x]","x","x",1,"x","A",1
3,1,3,3,0.0010493,"\int 5 \, dx","IntegrateAlgebraic[5,x]","5 x","5 x",1,"5*x","A",1
4,1,3,3,0.0009618,"\int -2 \, dx","IntegrateAlgebraic[-2,x]","-2 x","-2 x",1,"-2*x","A",1
5,1,5,5,0.0009161,"\int -\frac{3}{2} \, dx","IntegrateAlgebraic[-3/2,x]","-\frac{3 x}{2}","-\frac{3 x}{2}",1,"(-3*x)/2","A",1
6,1,3,3,0.0011358,"\int \pi  \, dx","IntegrateAlgebraic[Pi,x]","\pi  x","\pi  x",1,"Pi*x","A",1
7,1,3,3,0.0011221,"\int a \, dx","IntegrateAlgebraic[a,x]","a x","a x",1,"a*x","A",1
8,1,4,4,0.0011994,"\int 3 a \, dx","IntegrateAlgebraic[3*a,x]","3 a x","3 a x",1,"3*a*x","A",1
9,1,14,14,0.0035728,"\int \frac{\pi }{\sqrt{16-e^2}} \, dx","IntegrateAlgebraic[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
10,1,7,7,0.0010951,"\int x^{100} \, dx","IntegrateAlgebraic[x^100,x]","\frac{x^{101}}{101}","\frac{x^{101}}{101}",1,"x^101/101","A",1
11,1,7,7,0.0012435,"\int x^3 \, dx","IntegrateAlgebraic[x^3,x]","\frac{x^4}{4}","\frac{x^4}{4}",1,"x^4/4","A",1
12,1,7,7,0.0012268,"\int x^2 \, dx","IntegrateAlgebraic[x^2,x]","\frac{x^3}{3}","\frac{x^3}{3}",1,"x^3/3","A",1
13,1,7,7,0.0010356,"\int x \, dx","IntegrateAlgebraic[x,x]","\frac{x^2}{2}","\frac{x^2}{2}",1,"x^2/2","A",1
14,1,1,1,0.0000585,"\int 1 \, dx","IntegrateAlgebraic[1,x]","x","x",1,"x","A",1
15,1,2,2,0.0014183,"\int \frac{1}{x} \, dx","IntegrateAlgebraic[x^(-1),x]","\log (x)","\log (x)",1,"Log[x]","A",1
16,1,5,5,0.0014049,"\int \frac{1}{x^2} \, dx","IntegrateAlgebraic[x^(-2),x]","-\frac{1}{x}","-\frac{1}{x}",1,"-x^(-1)","A",1
17,1,7,7,0.0014287,"\int \frac{1}{x^3} \, dx","IntegrateAlgebraic[x^(-3),x]","-\frac{1}{2 x^2}","-\frac{1}{2 x^2}",1,"-1/2*1/x^2","A",1
18,1,7,7,0.0013399,"\int \frac{1}{x^4} \, dx","IntegrateAlgebraic[x^(-4),x]","-\frac{1}{3 x^3}","-\frac{1}{3 x^3}",1,"-1/3*1/x^3","A",1
19,1,7,7,0.0014448,"\int \frac{1}{x^{100}} \, dx","IntegrateAlgebraic[x^(-100),x]","-\frac{1}{99 x^{99}}","-\frac{1}{99 x^{99}}",1,"-1/99*1/x^99","A",1
20,1,9,9,0.0022365,"\int x^{5/2} \, dx","IntegrateAlgebraic[x^(5/2),x]","\frac{2 x^{7/2}}{7}","\frac{2 x^{7/2}}{7}",1,"(2*x^(7/2))/7","A",1
21,1,9,9,0.0020172,"\int x^{3/2} \, dx","IntegrateAlgebraic[x^(3/2),x]","\frac{2 x^{5/2}}{5}","\frac{2 x^{5/2}}{5}",1,"(2*x^(5/2))/5","A",1
22,1,9,9,0.0022199,"\int \sqrt{x} \, dx","IntegrateAlgebraic[Sqrt[x],x]","\frac{2 x^{3/2}}{3}","\frac{2 x^{3/2}}{3}",1,"(2*x^(3/2))/3","A",1
23,1,7,7,0.0020791,"\int \frac{1}{\sqrt{x}} \, dx","IntegrateAlgebraic[1/Sqrt[x],x]","2 \sqrt{x}","2 \sqrt{x}",1,"2*Sqrt[x]","A",1
24,1,7,7,0.0026862,"\int \frac{1}{x^{3/2}} \, dx","IntegrateAlgebraic[x^(-3/2),x]","-\frac{2}{\sqrt{x}}","-\frac{2}{\sqrt{x}}",1,"-2/Sqrt[x]","A",1
25,1,9,9,0.0025089,"\int \frac{1}{x^{5/2}} \, dx","IntegrateAlgebraic[x^(-5/2),x]","-\frac{2}{3 x^{3/2}}","-\frac{2}{3 x^{3/2}}",1,"-2/(3*x^(3/2))","A",1
26,1,9,9,0.0022962,"\int x^{5/3} \, dx","IntegrateAlgebraic[x^(5/3),x]","\frac{3 x^{8/3}}{8}","\frac{3 x^{8/3}}{8}",1,"(3*x^(8/3))/8","A",1
27,1,9,9,0.0020212,"\int x^{4/3} \, dx","IntegrateAlgebraic[x^(4/3),x]","\frac{3 x^{7/3}}{7}","\frac{3 x^{7/3}}{7}",1,"(3*x^(7/3))/7","A",1
28,1,9,9,0.0022455,"\int x^{2/3} \, dx","IntegrateAlgebraic[x^(2/3),x]","\frac{3 x^{5/3}}{5}","\frac{3 x^{5/3}}{5}",1,"(3*x^(5/3))/5","A",1
29,1,9,9,0.001794,"\int \sqrt[3]{x} \, dx","IntegrateAlgebraic[x^(1/3),x]","\frac{3 x^{4/3}}{4}","\frac{3 x^{4/3}}{4}",1,"(3*x^(4/3))/4","A",1
30,1,9,9,0.0020458,"\int \frac{1}{\sqrt[3]{x}} \, dx","IntegrateAlgebraic[x^(-1/3),x]","\frac{3 x^{2/3}}{2}","\frac{3 x^{2/3}}{2}",1,"(3*x^(2/3))/2","A",1
31,1,7,7,0.0028216,"\int \frac{1}{x^{2/3}} \, dx","IntegrateAlgebraic[x^(-2/3),x]","3 \sqrt[3]{x}","3 \sqrt[3]{x}",1,"3*x^(1/3)","A",1
32,1,7,7,0.0027201,"\int \frac{1}{x^{4/3}} \, dx","IntegrateAlgebraic[x^(-4/3),x]","-\frac{3}{\sqrt[3]{x}}","-\frac{3}{\sqrt[3]{x}}",1,"-3/x^(1/3)","A",1
33,1,9,9,0.0028234,"\int \frac{1}{x^{5/3}} \, dx","IntegrateAlgebraic[x^(-5/3),x]","-\frac{3}{2 x^{2/3}}","-\frac{3}{2 x^{2/3}}",1,"-3/(2*x^(2/3))","A",1
34,0,0,11,0.0000484,"\int x^n \, dx","IntegrateAlgebraic[x^n,x]","\int x^n \, dx","\frac{x^{n+1}}{n+1}",1,"Could not integrate","F",-1
35,0,0,16,0.0000568,"\int (b x)^n \, dx","IntegrateAlgebraic[(b*x)^n,x]","\int (b x)^n \, dx","\frac{(b x)^{n+1}}{b (n+1)}",1,"Could not integrate","F",-1
36,1,23,23,0.0158396,"\int \frac{1}{\sqrt{-a}+e (c+d x)} \, dx","IntegrateAlgebraic[(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",1
37,1,23,23,0.0087208,"\int (c+d (a+b x))^{5/2} \, dx","IntegrateAlgebraic[(c + d*(a + b*x))^(5/2),x]","\frac{2 (a d+b d x+c)^{7/2}}{7 b d}","\frac{2 (d (a+b x)+c)^{7/2}}{7 b d}",1,"(2*(c + a*d + b*d*x)^(7/2))/(7*b*d)","A",1
38,1,23,23,0.0082092,"\int (c+d (a+b x))^{3/2} \, dx","IntegrateAlgebraic[(c + d*(a + b*x))^(3/2),x]","\frac{2 (a d+b d x+c)^{5/2}}{5 b d}","\frac{2 (d (a+b x)+c)^{5/2}}{5 b d}",1,"(2*(c + a*d + b*d*x)^(5/2))/(5*b*d)","A",1
39,1,23,23,0.0075624,"\int \sqrt{c+d (a+b x)} \, dx","IntegrateAlgebraic[Sqrt[c + d*(a + b*x)],x]","\frac{2 (a d+b d x+c)^{3/2}}{3 b d}","\frac{2 (d (a+b x)+c)^{3/2}}{3 b d}",1,"(2*(c + a*d + b*d*x)^(3/2))/(3*b*d)","A",1
40,1,21,21,0.0075219,"\int \frac{1}{\sqrt{c+d (a+b x)}} \, dx","IntegrateAlgebraic[1/Sqrt[c + d*(a + b*x)],x]","\frac{2 \sqrt{a d+b d x+c}}{b d}","\frac{2 \sqrt{d (a+b x)+c}}{b d}",1,"(2*Sqrt[c + a*d + b*d*x])/(b*d)","A",1
41,1,21,21,0.0107803,"\int \frac{1}{(c+d (a+b x))^{3/2}} \, dx","IntegrateAlgebraic[(c + d*(a + b*x))^(-3/2),x]","-\frac{2}{b d \sqrt{a d+b d x+c}}","-\frac{2}{b d \sqrt{d (a+b x)+c}}",1,"-2/(b*d*Sqrt[c + a*d + b*d*x])","A",1
42,1,23,23,0.0088562,"\int \frac{1}{(c+d (a+b x))^{5/2}} \, dx","IntegrateAlgebraic[(c + d*(a + b*x))^(-5/2),x]","-\frac{2}{3 b d (a d+b d x+c)^{3/2}}","-\frac{2}{3 b d (d (a+b x)+c)^{3/2}}",1,"-2/(3*b*d*(c + a*d + b*d*x)^(3/2))","A",1
43,1,15,17,0.0042279,"\int x^3 (a+b x) \, dx","IntegrateAlgebraic[x^3*(a + b*x),x]","\frac{1}{20} x^4 (5 a+4 b x)","\frac{a x^4}{4}+\frac{b x^5}{5}",1,"(x^4*(5*a + 4*b*x))/20","A",1
44,1,15,17,0.0038371,"\int x^2 (a+b x) \, dx","IntegrateAlgebraic[x^2*(a + b*x),x]","\frac{1}{12} x^3 (4 a+3 b x)","\frac{a x^3}{3}+\frac{b x^4}{4}",1,"(x^3*(4*a + 3*b*x))/12","A",1
45,1,15,17,0.0037801,"\int x (a+b x) \, dx","IntegrateAlgebraic[x*(a + b*x),x]","\frac{1}{6} x^2 (3 a+2 b x)","\frac{a x^2}{2}+\frac{b x^3}{3}",1,"(x^2*(3*a + 2*b*x))/6","A",1
46,1,14,12,0.0029307,"\int (a+b x) \, dx","IntegrateAlgebraic[a + b*x,x]","\frac{1}{2} \left(2 a x+b x^2\right)","a x+\frac{b x^2}{2}",1,"(2*a*x + b*x^2)/2","A",1
47,1,8,8,0.0027008,"\int \frac{a+b x}{x} \, dx","IntegrateAlgebraic[(a + b*x)/x,x]","a \log (x)+b x","a \log (x)+b x",1,"b*x + a*Log[x]","A",1
48,1,11,11,0.0058373,"\int \frac{a+b x}{x^2} \, dx","IntegrateAlgebraic[(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",1
49,1,15,17,0.0037574,"\int \frac{a+b x}{x^3} \, dx","IntegrateAlgebraic[(a + b*x)/x^3,x]","\frac{-a-2 b x}{2 x^2}","-\frac{(a+b x)^2}{2 a x^2}",1,"(-a - 2*b*x)/(2*x^2)","A",1
50,1,15,17,0.0040605,"\int \frac{a+b x}{x^4} \, dx","IntegrateAlgebraic[(a + b*x)/x^4,x]","\frac{-2 a-3 b x}{6 x^3}","-\frac{a}{3 x^3}-\frac{b}{2 x^2}",1,"(-2*a - 3*b*x)/(6*x^3)","A",1
51,1,15,17,0.0037395,"\int \frac{a+b x}{x^5} \, dx","IntegrateAlgebraic[(a + b*x)/x^5,x]","\frac{-3 a-4 b x}{12 x^4}","-\frac{a}{4 x^4}-\frac{b}{3 x^3}",1,"(-3*a - 4*b*x)/(12*x^4)","A",1
52,1,26,30,0.0066617,"\int x^3 (a+b x)^2 \, dx","IntegrateAlgebraic[x^3*(a + b*x)^2,x]","\frac{1}{60} x^4 \left(15 a^2+24 a b x+10 b^2 x^2\right)","\frac{a^2 x^4}{4}+\frac{2}{5} a b x^5+\frac{b^2 x^6}{6}",1,"(x^4*(15*a^2 + 24*a*b*x + 10*b^2*x^2))/60","A",1
53,1,26,30,0.0062915,"\int x^2 (a+b x)^2 \, dx","IntegrateAlgebraic[x^2*(a + b*x)^2,x]","\frac{1}{30} x^3 \left(10 a^2+15 a b x+6 b^2 x^2\right)","\frac{a^2 x^3}{3}+\frac{1}{2} a b x^4+\frac{b^2 x^5}{5}",1,"(x^3*(10*a^2 + 15*a*b*x + 6*b^2*x^2))/30","A",1
54,1,26,30,0.0068528,"\int x (a+b x)^2 \, dx","IntegrateAlgebraic[x*(a + b*x)^2,x]","\frac{1}{12} x^2 \left(6 a^2+8 a b x+3 b^2 x^2\right)","\frac{a^2 x^2}{2}+\frac{2}{3} a b x^3+\frac{b^2 x^4}{4}",1,"(x^2*(6*a^2 + 8*a*b*x + 3*b^2*x^2))/12","A",1
55,1,14,14,0.0044905,"\int (a+b x)^2 \, dx","IntegrateAlgebraic[(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
56,1,20,22,0.0051769,"\int \frac{(a+b x)^2}{x} \, dx","IntegrateAlgebraic[(a + b*x)^2/x,x]","a^2 \log (x)+\frac{1}{2} b x (4 a+b x)","a^2 \log (x)+2 a b x+\frac{b^2 x^2}{2}",1,"(b*x*(4*a + b*x))/2 + a^2*Log[x]","A",1
57,1,24,20,0.0058918,"\int \frac{(a+b x)^2}{x^2} \, dx","IntegrateAlgebraic[(a + b*x)^2/x^2,x]","\frac{b^2 x^2-a^2}{x}+2 a b \log (x)","-\frac{a^2}{x}+2 a b \log (x)+b^2 x",1,"(-a^2 + b^2*x^2)/x + 2*a*b*Log[x]","A",1
58,1,21,24,0.0090812,"\int \frac{(a+b x)^2}{x^3} \, dx","IntegrateAlgebraic[(a + b*x)^2/x^3,x]","b^2 \log (x)-\frac{a (a+4 b x)}{2 x^2}","-\frac{a^2}{2 x^2}-\frac{2 a b}{x}+b^2 \log (x)",1,"-1/2*(a*(a + 4*b*x))/x^2 + b^2*Log[x]","A",1
59,1,26,17,0.0106504,"\int \frac{(a+b x)^2}{x^4} \, dx","IntegrateAlgebraic[(a + b*x)^2/x^4,x]","\frac{-a^2-3 a b x-3 b^2 x^2}{3 x^3}","-\frac{(a+b x)^3}{3 a x^3}",1,"(-a^2 - 3*a*b*x - 3*b^2*x^2)/(3*x^3)","A",1
60,1,26,30,0.0076278,"\int \frac{(a+b x)^2}{x^5} \, dx","IntegrateAlgebraic[(a + b*x)^2/x^5,x]","\frac{-3 a^2-8 a b x-6 b^2 x^2}{12 x^4}","-\frac{a^2}{4 x^4}-\frac{2 a b}{3 x^3}-\frac{b^2}{2 x^2}",1,"(-3*a^2 - 8*a*b*x - 6*b^2*x^2)/(12*x^4)","A",1
61,1,26,30,0.0103046,"\int \frac{(a+b x)^2}{x^6} \, dx","IntegrateAlgebraic[(a + b*x)^2/x^6,x]","\frac{-6 a^2-15 a b x-10 b^2 x^2}{30 x^5}","-\frac{a^2}{5 x^5}-\frac{a b}{2 x^4}-\frac{b^2}{3 x^3}",1,"(-6*a^2 - 15*a*b*x - 10*b^2*x^2)/(30*x^5)","A",1
62,1,26,30,0.0076343,"\int \frac{(a+b x)^2}{x^7} \, dx","IntegrateAlgebraic[(a + b*x)^2/x^7,x]","\frac{-10 a^2-24 a b x-15 b^2 x^2}{60 x^6}","-\frac{a^2}{6 x^6}-\frac{2 a b}{5 x^5}-\frac{b^2}{4 x^4}",1,"(-10*a^2 - 24*a*b*x - 15*b^2*x^2)/(60*x^6)","A",1
63,1,26,30,0.010185,"\int \frac{(a+b x)^2}{x^8} \, dx","IntegrateAlgebraic[(a + b*x)^2/x^8,x]","\frac{-15 a^2-35 a b x-21 b^2 x^2}{105 x^7}","-\frac{a^2}{7 x^7}-\frac{a b}{3 x^6}-\frac{b^2}{5 x^5}",1,"(-15*a^2 - 35*a*b*x - 21*b^2*x^2)/(105*x^7)","A",1
64,1,39,43,0.0080698,"\int x^4 (a+b x)^3 \, dx","IntegrateAlgebraic[x^4*(a + b*x)^3,x]","\frac{1}{280} \left(56 a^3 x^5+140 a^2 b x^6+120 a b^2 x^7+35 b^3 x^8\right)","\frac{a^3 x^5}{5}+\frac{1}{2} a^2 b x^6+\frac{3}{7} a b^2 x^7+\frac{b^3 x^8}{8}",1,"(56*a^3*x^5 + 140*a^2*b*x^6 + 120*a*b^2*x^7 + 35*b^3*x^8)/280","A",1
65,1,37,43,0.0086219,"\int x^3 (a+b x)^3 \, dx","IntegrateAlgebraic[x^3*(a + b*x)^3,x]","\frac{1}{140} x^4 \left(35 a^3+84 a^2 b x+70 a b^2 x^2+20 b^3 x^3\right)","\frac{a^3 x^4}{4}+\frac{3}{5} a^2 b x^5+\frac{1}{2} a b^2 x^6+\frac{b^3 x^7}{7}",1,"(x^4*(35*a^3 + 84*a^2*b*x + 70*a*b^2*x^2 + 20*b^3*x^3))/140","A",1
66,1,37,43,0.0089283,"\int x^2 (a+b x)^3 \, dx","IntegrateAlgebraic[x^2*(a + b*x)^3,x]","\frac{1}{60} x^3 \left(20 a^3+45 a^2 b x+36 a b^2 x^2+10 b^3 x^3\right)","\frac{a^3 x^3}{3}+\frac{3}{4} a^2 b x^4+\frac{3}{5} a b^2 x^5+\frac{b^3 x^6}{6}",1,"(x^3*(20*a^3 + 45*a^2*b*x + 36*a*b^2*x^2 + 10*b^3*x^3))/60","A",1
67,1,39,30,0.0074804,"\int x (a+b x)^3 \, dx","IntegrateAlgebraic[x*(a + b*x)^3,x]","\frac{1}{20} \left(10 a^3 x^2+20 a^2 b x^3+15 a b^2 x^4+4 b^3 x^5\right)","\frac{(a+b x)^5}{5 b^2}-\frac{a (a+b x)^4}{4 b^2}",1,"(10*a^3*x^2 + 20*a^2*b*x^3 + 15*a*b^2*x^4 + 4*b^3*x^5)/20","A",1
68,1,14,14,0.0043589,"\int (a+b x)^3 \, dx","IntegrateAlgebraic[(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
69,1,32,35,0.0088977,"\int \frac{(a+b x)^3}{x} \, dx","IntegrateAlgebraic[(a + b*x)^3/x,x]","a^3 \log (x)+\frac{1}{6} b x \left(18 a^2+9 a b x+2 b^2 x^2\right)","a^3 \log (x)+3 a^2 b x+\frac{3}{2} a b^2 x^2+\frac{b^3 x^3}{3}",1,"(b*x*(18*a^2 + 9*a*b*x + 2*b^2*x^2))/6 + a^3*Log[x]","A",1
70,1,38,34,0.0118963,"\int \frac{(a+b x)^3}{x^2} \, dx","IntegrateAlgebraic[(a + b*x)^3/x^2,x]","\frac{-2 a^3+6 a b^2 x^2+b^3 x^3}{2 x}+3 a^2 b \log (x)","-\frac{a^3}{x}+3 a^2 b \log (x)+3 a b^2 x+\frac{b^3 x^2}{2}",1,"(-2*a^3 + 6*a*b^2*x^2 + b^3*x^3)/(2*x) + 3*a^2*b*Log[x]","A",1
71,1,37,33,0.0138156,"\int \frac{(a+b x)^3}{x^3} \, dx","IntegrateAlgebraic[(a + b*x)^3/x^3,x]","\frac{-a^3-6 a^2 b x+2 b^3 x^3}{2 x^2}+3 a b^2 \log (x)","-\frac{a^3}{2 x^2}-\frac{3 a^2 b}{x}+3 a b^2 \log (x)+b^3 x",1,"(-a^3 - 6*a^2*b*x + 2*b^3*x^3)/(2*x^2) + 3*a*b^2*Log[x]","A",1
72,1,34,37,0.0113933,"\int \frac{(a+b x)^3}{x^4} \, dx","IntegrateAlgebraic[(a + b*x)^3/x^4,x]","b^3 \log (x)-\frac{a \left(2 a^2+9 a b x+18 b^2 x^2\right)}{6 x^3}","-\frac{a^3}{3 x^3}-\frac{3 a^2 b}{2 x^2}-\frac{3 a b^2}{x}+b^3 \log (x)",1,"-1/6*(a*(2*a^2 + 9*a*b*x + 18*b^2*x^2))/x^3 + b^3*Log[x]","A",1
73,1,37,17,0.008083,"\int \frac{(a+b x)^3}{x^5} \, dx","IntegrateAlgebraic[(a + b*x)^3/x^5,x]","\frac{-a^3-4 a^2 b x-6 a b^2 x^2-4 b^3 x^3}{4 x^4}","-\frac{(a+b x)^4}{4 a x^4}",1,"(-a^3 - 4*a^2*b*x - 6*a*b^2*x^2 - 4*b^3*x^3)/(4*x^4)","B",1
74,1,37,36,0.0098686,"\int \frac{(a+b x)^3}{x^6} \, dx","IntegrateAlgebraic[(a + b*x)^3/x^6,x]","\frac{-4 a^3-15 a^2 b x-20 a b^2 x^2-10 b^3 x^3}{20 x^5}","\frac{b (a+b x)^4}{20 a^2 x^4}-\frac{(a+b x)^4}{5 a x^5}",1,"(-4*a^3 - 15*a^2*b*x - 20*a*b^2*x^2 - 10*b^3*x^3)/(20*x^5)","A",1
75,1,37,43,0.007407,"\int \frac{(a+b x)^3}{x^7} \, dx","IntegrateAlgebraic[(a + b*x)^3/x^7,x]","\frac{-10 a^3-36 a^2 b x-45 a b^2 x^2-20 b^3 x^3}{60 x^6}","-\frac{a^3}{6 x^6}-\frac{3 a^2 b}{5 x^5}-\frac{3 a b^2}{4 x^4}-\frac{b^3}{3 x^3}",1,"(-10*a^3 - 36*a^2*b*x - 45*a*b^2*x^2 - 20*b^3*x^3)/(60*x^6)","A",1
76,1,37,43,0.0074717,"\int \frac{(a+b x)^3}{x^8} \, dx","IntegrateAlgebraic[(a + b*x)^3/x^8,x]","\frac{-20 a^3-70 a^2 b x-84 a b^2 x^2-35 b^3 x^3}{140 x^7}","-\frac{a^3}{7 x^7}-\frac{a^2 b}{2 x^6}-\frac{3 a b^2}{5 x^5}-\frac{b^3}{4 x^4}",1,"(-20*a^3 - 70*a^2*b*x - 84*a*b^2*x^2 - 35*b^3*x^3)/(140*x^7)","A",1
77,1,61,66,0.0105342,"\int x^6 (a+b x)^5 \, dx","IntegrateAlgebraic[x^6*(a + b*x)^5,x]","\frac{792 a^5 x^7+3465 a^4 b x^8+6160 a^3 b^2 x^9+5544 a^2 b^3 x^{10}+2520 a b^4 x^{11}+462 b^5 x^{12}}{5544}","\frac{a^5 x^7}{7}+\frac{5}{8} a^4 b x^8+\frac{10}{9} a^3 b^2 x^9+a^2 b^3 x^{10}+\frac{5}{11} a b^4 x^{11}+\frac{b^5 x^{12}}{12}",1,"(792*a^5*x^7 + 3465*a^4*b*x^8 + 6160*a^3*b^2*x^9 + 5544*a^2*b^3*x^10 + 2520*a*b^4*x^11 + 462*b^5*x^12)/5544","A",1
78,1,61,69,0.0095831,"\int x^5 (a+b x)^5 \, dx","IntegrateAlgebraic[x^5*(a + b*x)^5,x]","\frac{462 a^5 x^6+1980 a^4 b x^7+3465 a^3 b^2 x^8+3080 a^2 b^3 x^9+1386 a b^4 x^{10}+252 b^5 x^{11}}{2772}","\frac{a^5 x^6}{6}+\frac{5}{7} a^4 b x^7+\frac{5}{4} a^3 b^2 x^8+\frac{10}{9} a^2 b^3 x^9+\frac{1}{2} a b^4 x^{10}+\frac{b^5 x^{11}}{11}",1,"(462*a^5*x^6 + 1980*a^4*b*x^7 + 3465*a^3*b^2*x^8 + 3080*a^2*b^3*x^9 + 1386*a*b^4*x^10 + 252*b^5*x^11)/2772","A",1
79,1,61,69,0.01019,"\int x^4 (a+b x)^5 \, dx","IntegrateAlgebraic[x^4*(a + b*x)^5,x]","\frac{252 a^5 x^5+1050 a^4 b x^6+1800 a^3 b^2 x^7+1575 a^2 b^3 x^8+700 a b^4 x^9+126 b^5 x^{10}}{1260}","\frac{a^5 x^5}{5}+\frac{5}{6} a^4 b x^6+\frac{10}{7} a^3 b^2 x^7+\frac{5}{4} a^2 b^3 x^8+\frac{5}{9} a b^4 x^9+\frac{b^5 x^{10}}{10}",1,"(252*a^5*x^5 + 1050*a^4*b*x^6 + 1800*a^3*b^2*x^7 + 1575*a^2*b^3*x^8 + 700*a*b^4*x^9 + 126*b^5*x^10)/1260","A",1
80,1,61,64,0.010511,"\int x^3 (a+b x)^5 \, dx","IntegrateAlgebraic[x^3*(a + b*x)^5,x]","\frac{1}{504} \left(126 a^5 x^4+504 a^4 b x^5+840 a^3 b^2 x^6+720 a^2 b^3 x^7+315 a b^4 x^8+56 b^5 x^9\right)","-\frac{a^3 (a+b x)^6}{6 b^4}+\frac{3 a^2 (a+b x)^7}{7 b^4}+\frac{(a+b x)^9}{9 b^4}-\frac{3 a (a+b x)^8}{8 b^4}",1,"(126*a^5*x^4 + 504*a^4*b*x^5 + 840*a^3*b^2*x^6 + 720*a^2*b^3*x^7 + 315*a*b^4*x^8 + 56*b^5*x^9)/504","A",1
81,1,61,47,0.0099266,"\int x^2 (a+b x)^5 \, dx","IntegrateAlgebraic[x^2*(a + b*x)^5,x]","\frac{1}{168} \left(56 a^5 x^3+210 a^4 b x^4+336 a^3 b^2 x^5+280 a^2 b^3 x^6+120 a b^4 x^7+21 b^5 x^8\right)","\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,"(56*a^5*x^3 + 210*a^4*b*x^4 + 336*a^3*b^2*x^5 + 280*a^2*b^3*x^6 + 120*a*b^4*x^7 + 21*b^5*x^8)/168","A",1
82,1,59,30,0.0097783,"\int x (a+b x)^5 \, dx","IntegrateAlgebraic[x*(a + b*x)^5,x]","\frac{1}{42} x^2 \left(21 a^5+70 a^4 b x+105 a^3 b^2 x^2+84 a^2 b^3 x^3+35 a b^4 x^4+6 b^5 x^5\right)","\frac{(a+b x)^7}{7 b^2}-\frac{a (a+b x)^6}{6 b^2}",1,"(x^2*(21*a^5 + 70*a^4*b*x + 105*a^3*b^2*x^2 + 84*a^2*b^3*x^3 + 35*a*b^4*x^4 + 6*b^5*x^5))/42","A",1
83,1,14,14,0.0053671,"\int (a+b x)^5 \, dx","IntegrateAlgebraic[(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
84,1,58,59,0.010974,"\int \frac{(a+b x)^5}{x} \, dx","IntegrateAlgebraic[(a + b*x)^5/x,x]","a^5 \log (x)+\frac{1}{60} \left(300 a^4 b x+300 a^3 b^2 x^2+200 a^2 b^3 x^3+75 a b^4 x^4+12 b^5 x^5\right)","a^5 \log (x)+5 a^4 b x+5 a^3 b^2 x^2+\frac{10}{3} a^2 b^3 x^3+\frac{5}{4} a b^4 x^4+\frac{b^5 x^5}{5}",1,"(300*a^4*b*x + 300*a^3*b^2*x^2 + 200*a^2*b^3*x^3 + 75*a*b^4*x^4 + 12*b^5*x^5)/60 + a^5*Log[x]","A",1
85,1,61,58,0.0144887,"\int \frac{(a+b x)^5}{x^2} \, dx","IntegrateAlgebraic[(a + b*x)^5/x^2,x]","5 a^4 b \log (x)+\frac{-12 a^5+120 a^3 b^2 x^2+60 a^2 b^3 x^3+20 a b^4 x^4+3 b^5 x^5}{12 x}","-\frac{a^5}{x}+5 a^4 b \log (x)+10 a^3 b^2 x+5 a^2 b^3 x^2+\frac{5}{3} a b^4 x^3+\frac{b^5 x^4}{4}",1,"(-12*a^5 + 120*a^3*b^2*x^2 + 60*a^2*b^3*x^3 + 20*a*b^4*x^4 + 3*b^5*x^5)/(12*x) + 5*a^4*b*Log[x]","A",1
86,1,59,60,0.0127435,"\int \frac{(a+b x)^5}{x^3} \, dx","IntegrateAlgebraic[(a + b*x)^5/x^3,x]","10 a^3 b^2 \log (x)+\frac{-3 a^5-30 a^4 b x+60 a^2 b^3 x^3+15 a b^4 x^4+2 b^5 x^5}{6 x^2}","-\frac{a^5}{2 x^2}-\frac{5 a^4 b}{x}+10 a^3 b^2 \log (x)+10 a^2 b^3 x+\frac{5}{2} a b^4 x^2+\frac{b^5 x^3}{3}",1,"(-3*a^5 - 30*a^4*b*x + 60*a^2*b^3*x^3 + 15*a*b^4*x^4 + 2*b^5*x^5)/(6*x^2) + 10*a^3*b^2*Log[x]","A",1
87,1,59,60,0.0141502,"\int \frac{(a+b x)^5}{x^4} \, dx","IntegrateAlgebraic[(a + b*x)^5/x^4,x]","10 a^2 b^3 \log (x)+\frac{-2 a^5-15 a^4 b x-60 a^3 b^2 x^2+30 a b^4 x^4+3 b^5 x^5}{6 x^3}","-\frac{a^5}{3 x^3}-\frac{5 a^4 b}{2 x^2}-\frac{10 a^3 b^2}{x}+10 a^2 b^3 \log (x)+5 a b^4 x+\frac{b^5 x^2}{2}",1,"(-2*a^5 - 15*a^4*b*x - 60*a^3*b^2*x^2 + 30*a*b^4*x^4 + 3*b^5*x^5)/(6*x^3) + 10*a^2*b^3*Log[x]","A",1
88,1,59,57,0.017023,"\int \frac{(a+b x)^5}{x^5} \, dx","IntegrateAlgebraic[(a + b*x)^5/x^5,x]","\frac{-3 a^5-20 a^4 b x-60 a^3 b^2 x^2-120 a^2 b^3 x^3+12 b^5 x^5}{12 x^4}+5 a b^4 \log (x)","-\frac{a^5}{4 x^4}-\frac{5 a^4 b}{3 x^3}-\frac{5 a^3 b^2}{x^2}-\frac{10 a^2 b^3}{x}+5 a b^4 \log (x)+b^5 x",1,"(-3*a^5 - 20*a^4*b*x - 60*a^3*b^2*x^2 - 120*a^2*b^3*x^3 + 12*b^5*x^5)/(12*x^4) + 5*a*b^4*Log[x]","A",1
89,1,56,61,0.0154766,"\int \frac{(a+b x)^5}{x^6} \, dx","IntegrateAlgebraic[(a + b*x)^5/x^6,x]","b^5 \log (x)-\frac{a \left(12 a^4+75 a^3 b x+200 a^2 b^2 x^2+300 a b^3 x^3+300 b^4 x^4\right)}{60 x^5}","-\frac{a^5}{5 x^5}-\frac{5 a^4 b}{4 x^4}-\frac{10 a^3 b^2}{3 x^3}-\frac{5 a^2 b^3}{x^2}-\frac{5 a b^4}{x}+b^5 \log (x)",1,"-1/60*(a*(12*a^4 + 75*a^3*b*x + 200*a^2*b^2*x^2 + 300*a*b^3*x^3 + 300*b^4*x^4))/x^5 + b^5*Log[x]","A",1
90,1,59,17,0.0091466,"\int \frac{(a+b x)^5}{x^7} \, dx","IntegrateAlgebraic[(a + b*x)^5/x^7,x]","\frac{-a^5-6 a^4 b x-15 a^3 b^2 x^2-20 a^2 b^3 x^3-15 a b^4 x^4-6 b^5 x^5}{6 x^6}","-\frac{(a+b x)^6}{6 a x^6}",1,"(-a^5 - 6*a^4*b*x - 15*a^3*b^2*x^2 - 20*a^2*b^3*x^3 - 15*a*b^4*x^4 - 6*b^5*x^5)/(6*x^6)","B",1
91,1,59,36,0.0102215,"\int \frac{(a+b x)^5}{x^8} \, dx","IntegrateAlgebraic[(a + b*x)^5/x^8,x]","\frac{-6 a^5-35 a^4 b x-84 a^3 b^2 x^2-105 a^2 b^3 x^3-70 a b^4 x^4-21 b^5 x^5}{42 x^7}","\frac{b (a+b x)^6}{42 a^2 x^6}-\frac{(a+b x)^6}{7 a x^7}",1,"(-6*a^5 - 35*a^4*b*x - 84*a^3*b^2*x^2 - 105*a^2*b^3*x^3 - 70*a*b^4*x^4 - 21*b^5*x^5)/(42*x^7)","A",1
92,1,59,56,0.0092984,"\int \frac{(a+b x)^5}{x^9} \, dx","IntegrateAlgebraic[(a + b*x)^5/x^9,x]","\frac{-21 a^5-120 a^4 b x-280 a^3 b^2 x^2-336 a^2 b^3 x^3-210 a b^4 x^4-56 b^5 x^5}{168 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,"(-21*a^5 - 120*a^4*b*x - 280*a^3*b^2*x^2 - 336*a^2*b^3*x^3 - 210*a*b^4*x^4 - 56*b^5*x^5)/(168*x^8)","A",1
93,1,59,67,0.0121298,"\int \frac{(a+b x)^5}{x^{10}} \, dx","IntegrateAlgebraic[(a + b*x)^5/x^10,x]","\frac{-56 a^5-315 a^4 b x-720 a^3 b^2 x^2-840 a^2 b^3 x^3-504 a b^4 x^4-126 b^5 x^5}{504 x^9}","-\frac{a^5}{9 x^9}-\frac{5 a^4 b}{8 x^8}-\frac{10 a^3 b^2}{7 x^7}-\frac{5 a^2 b^3}{3 x^6}-\frac{a b^4}{x^5}-\frac{b^5}{4 x^4}",1,"(-56*a^5 - 315*a^4*b*x - 720*a^3*b^2*x^2 - 840*a^2*b^3*x^3 - 504*a*b^4*x^4 - 126*b^5*x^5)/(504*x^9)","A",1
94,1,59,69,0.0090334,"\int \frac{(a+b x)^5}{x^{11}} \, dx","IntegrateAlgebraic[(a + b*x)^5/x^11,x]","\frac{-126 a^5-700 a^4 b x-1575 a^3 b^2 x^2-1800 a^2 b^3 x^3-1050 a b^4 x^4-252 b^5 x^5}{1260 x^{10}}","-\frac{a^5}{10 x^{10}}-\frac{5 a^4 b}{9 x^9}-\frac{5 a^3 b^2}{4 x^8}-\frac{10 a^2 b^3}{7 x^7}-\frac{5 a b^4}{6 x^6}-\frac{b^5}{5 x^5}",1,"(-126*a^5 - 700*a^4*b*x - 1575*a^3*b^2*x^2 - 1800*a^2*b^3*x^3 - 1050*a*b^4*x^4 - 252*b^5*x^5)/(1260*x^10)","A",1
95,1,59,69,0.0097596,"\int \frac{(a+b x)^5}{x^{12}} \, dx","IntegrateAlgebraic[(a + b*x)^5/x^12,x]","\frac{-252 a^5-1386 a^4 b x-3080 a^3 b^2 x^2-3465 a^2 b^3 x^3-1980 a b^4 x^4-462 b^5 x^5}{2772 x^{11}}","-\frac{a^5}{11 x^{11}}-\frac{a^4 b}{2 x^{10}}-\frac{10 a^3 b^2}{9 x^9}-\frac{5 a^2 b^3}{4 x^8}-\frac{5 a b^4}{7 x^7}-\frac{b^5}{6 x^6}",1,"(-252*a^5 - 1386*a^4*b*x - 3080*a^3*b^2*x^2 - 3465*a^2*b^3*x^3 - 1980*a*b^4*x^4 - 462*b^5*x^5)/(2772*x^11)","A",1
96,1,59,67,0.0092794,"\int \frac{(a+b x)^5}{x^{13}} \, dx","IntegrateAlgebraic[(a + b*x)^5/x^13,x]","\frac{-462 a^5-2520 a^4 b x-5544 a^3 b^2 x^2-6160 a^2 b^3 x^3-3465 a b^4 x^4-792 b^5 x^5}{5544 x^{12}}","-\frac{a^5}{12 x^{12}}-\frac{5 a^4 b}{11 x^{11}}-\frac{a^3 b^2}{x^{10}}-\frac{10 a^2 b^3}{9 x^9}-\frac{5 a b^4}{8 x^8}-\frac{b^5}{7 x^7}",1,"(-462*a^5 - 2520*a^4*b*x - 5544*a^3*b^2*x^2 - 6160*a^2*b^3*x^3 - 3465*a*b^4*x^4 - 792*b^5*x^5)/(5544*x^12)","A",1
97,1,59,67,0.0100226,"\int \frac{(a+b x)^5}{x^{14}} \, dx","IntegrateAlgebraic[(a + b*x)^5/x^14,x]","\frac{-792 a^5-4290 a^4 b x-9360 a^3 b^2 x^2-10296 a^2 b^3 x^3-5720 a b^4 x^4-1287 b^5 x^5}{10296 x^{13}}","-\frac{a^5}{13 x^{13}}-\frac{5 a^4 b}{12 x^{12}}-\frac{10 a^3 b^2}{11 x^{11}}-\frac{a^2 b^3}{x^{10}}-\frac{5 a b^4}{9 x^9}-\frac{b^5}{8 x^8}",1,"(-792*a^5 - 4290*a^4*b*x - 9360*a^3*b^2*x^2 - 10296*a^2*b^3*x^3 - 5720*a*b^4*x^4 - 1287*b^5*x^5)/(10296*x^13)","A",1
98,1,83,95,0.0128652,"\int x^8 (a+b x)^7 \, dx","IntegrateAlgebraic[x^8*(a + b*x)^7,x]","\frac{11440 a^7 x^9+72072 a^6 b x^{10}+196560 a^5 b^2 x^{11}+300300 a^4 b^3 x^{12}+277200 a^3 b^4 x^{13}+154440 a^2 b^5 x^{14}+48048 a b^6 x^{15}+6435 b^7 x^{16}}{102960}","\frac{a^7 x^9}{9}+\frac{7}{10} a^6 b x^{10}+\frac{21}{11} a^5 b^2 x^{11}+\frac{35}{12} a^4 b^3 x^{12}+\frac{35}{13} a^3 b^4 x^{13}+\frac{3}{2} a^2 b^5 x^{14}+\frac{7}{15} a b^6 x^{15}+\frac{b^7 x^{16}}{16}",1,"(11440*a^7*x^9 + 72072*a^6*b*x^10 + 196560*a^5*b^2*x^11 + 300300*a^4*b^3*x^12 + 277200*a^3*b^4*x^13 + 154440*a^2*b^5*x^14 + 48048*a*b^6*x^15 + 6435*b^7*x^16)/102960","A",1
99,1,83,95,0.0128577,"\int x^7 (a+b x)^7 \, dx","IntegrateAlgebraic[x^7*(a + b*x)^7,x]","\frac{6435 a^7 x^8+40040 a^6 b x^9+108108 a^5 b^2 x^{10}+163800 a^4 b^3 x^{11}+150150 a^3 b^4 x^{12}+83160 a^2 b^5 x^{13}+25740 a b^6 x^{14}+3432 b^7 x^{15}}{51480}","\frac{a^7 x^8}{8}+\frac{7}{9} a^6 b x^9+\frac{21}{10} a^5 b^2 x^{10}+\frac{35}{11} a^4 b^3 x^{11}+\frac{35}{12} a^3 b^4 x^{12}+\frac{21}{13} a^2 b^5 x^{13}+\frac{1}{2} a b^6 x^{14}+\frac{b^7 x^{15}}{15}",1,"(6435*a^7*x^8 + 40040*a^6*b*x^9 + 108108*a^5*b^2*x^10 + 163800*a^4*b^3*x^11 + 150150*a^3*b^4*x^12 + 83160*a^2*b^5*x^13 + 25740*a*b^6*x^14 + 3432*b^7*x^15)/51480","A",1
100,1,83,95,0.0125029,"\int x^6 (a+b x)^7 \, dx","IntegrateAlgebraic[x^6*(a + b*x)^7,x]","\frac{3432 a^7 x^7+21021 a^6 b x^8+56056 a^5 b^2 x^9+84084 a^4 b^3 x^{10}+76440 a^3 b^4 x^{11}+42042 a^2 b^5 x^{12}+12936 a b^6 x^{13}+1716 b^7 x^{14}}{24024}","\frac{a^7 x^7}{7}+\frac{7}{8} a^6 b x^8+\frac{7}{3} a^5 b^2 x^9+\frac{7}{2} a^4 b^3 x^{10}+\frac{35}{11} a^3 b^4 x^{11}+\frac{7}{4} a^2 b^5 x^{12}+\frac{7}{13} a b^6 x^{13}+\frac{b^7 x^{14}}{14}",1,"(3432*a^7*x^7 + 21021*a^6*b*x^8 + 56056*a^5*b^2*x^9 + 84084*a^4*b^3*x^10 + 76440*a^3*b^4*x^11 + 42042*a^2*b^5*x^12 + 12936*a*b^6*x^13 + 1716*b^7*x^14)/24024","A",1
101,1,83,96,0.013631,"\int x^5 (a+b x)^7 \, dx","IntegrateAlgebraic[x^5*(a + b*x)^7,x]","\frac{1716 a^7 x^6+10296 a^6 b x^7+27027 a^5 b^2 x^8+40040 a^4 b^3 x^9+36036 a^3 b^4 x^{10}+19656 a^2 b^5 x^{11}+6006 a b^6 x^{12}+792 b^7 x^{13}}{10296}","-\frac{a^5 (a+b x)^8}{8 b^6}+\frac{5 a^4 (a+b x)^9}{9 b^6}-\frac{a^3 (a+b x)^{10}}{b^6}+\frac{10 a^2 (a+b x)^{11}}{11 b^6}+\frac{(a+b x)^{13}}{13 b^6}-\frac{5 a (a+b x)^{12}}{12 b^6}",1,"(1716*a^7*x^6 + 10296*a^6*b*x^7 + 27027*a^5*b^2*x^8 + 40040*a^4*b^3*x^9 + 36036*a^3*b^4*x^10 + 19656*a^2*b^5*x^11 + 6006*a*b^6*x^12 + 792*b^7*x^13)/10296","A",1
102,1,83,81,0.0123871,"\int x^4 (a+b x)^7 \, dx","IntegrateAlgebraic[x^4*(a + b*x)^7,x]","\frac{792 a^7 x^5+4620 a^6 b x^6+11880 a^5 b^2 x^7+17325 a^4 b^3 x^8+15400 a^3 b^4 x^9+8316 a^2 b^5 x^{10}+2520 a b^6 x^{11}+330 b^7 x^{12}}{3960}","\frac{a^4 (a+b x)^8}{8 b^5}-\frac{4 a^3 (a+b x)^9}{9 b^5}+\frac{3 a^2 (a+b x)^{10}}{5 b^5}+\frac{(a+b x)^{12}}{12 b^5}-\frac{4 a (a+b x)^{11}}{11 b^5}",1,"(792*a^7*x^5 + 4620*a^6*b*x^6 + 11880*a^5*b^2*x^7 + 17325*a^4*b^3*x^8 + 15400*a^3*b^4*x^9 + 8316*a^2*b^5*x^10 + 2520*a*b^6*x^11 + 330*b^7*x^12)/3960","A",1
103,1,83,64,0.0121355,"\int x^3 (a+b x)^7 \, dx","IntegrateAlgebraic[x^3*(a + b*x)^7,x]","\frac{330 a^7 x^4+1848 a^6 b x^5+4620 a^5 b^2 x^6+6600 a^4 b^3 x^7+5775 a^3 b^4 x^8+3080 a^2 b^5 x^9+924 a b^6 x^{10}+120 b^7 x^{11}}{1320}","-\frac{a^3 (a+b x)^8}{8 b^4}+\frac{a^2 (a+b x)^9}{3 b^4}+\frac{(a+b x)^{11}}{11 b^4}-\frac{3 a (a+b x)^{10}}{10 b^4}",1,"(330*a^7*x^4 + 1848*a^6*b*x^5 + 4620*a^5*b^2*x^6 + 6600*a^4*b^3*x^7 + 5775*a^3*b^4*x^8 + 3080*a^2*b^5*x^9 + 924*a*b^6*x^10 + 120*b^7*x^11)/1320","A",1
104,1,83,47,0.0123179,"\int x^2 (a+b x)^7 \, dx","IntegrateAlgebraic[x^2*(a + b*x)^7,x]","\frac{1}{360} \left(120 a^7 x^3+630 a^6 b x^4+1512 a^5 b^2 x^5+2100 a^4 b^3 x^6+1800 a^3 b^4 x^7+945 a^2 b^5 x^8+280 a b^6 x^9+36 b^7 x^{10}\right)","\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,"(120*a^7*x^3 + 630*a^6*b*x^4 + 1512*a^5*b^2*x^5 + 2100*a^4*b^3*x^6 + 1800*a^3*b^4*x^7 + 945*a^2*b^5*x^8 + 280*a*b^6*x^9 + 36*b^7*x^10)/360","A",1
105,1,83,30,0.0116721,"\int x (a+b x)^7 \, dx","IntegrateAlgebraic[x*(a + b*x)^7,x]","\frac{1}{72} \left(36 a^7 x^2+168 a^6 b x^3+378 a^5 b^2 x^4+504 a^4 b^3 x^5+420 a^3 b^4 x^6+216 a^2 b^5 x^7+63 a b^6 x^8+8 b^7 x^9\right)","\frac{(a+b x)^9}{9 b^2}-\frac{a (a+b x)^8}{8 b^2}",1,"(36*a^7*x^2 + 168*a^6*b*x^3 + 378*a^5*b^2*x^4 + 504*a^4*b^3*x^5 + 420*a^3*b^4*x^6 + 216*a^2*b^5*x^7 + 63*a*b^6*x^8 + 8*b^7*x^9)/72","B",1
106,1,14,14,0.0044734,"\int (a+b x)^7 \, dx","IntegrateAlgebraic[(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
107,1,80,87,0.01306,"\int \frac{(a+b x)^7}{x} \, dx","IntegrateAlgebraic[(a + b*x)^7/x,x]","a^7 \log (x)+\frac{1}{420} \left(2940 a^6 b x+4410 a^5 b^2 x^2+4900 a^4 b^3 x^3+3675 a^3 b^4 x^4+1764 a^2 b^5 x^5+490 a b^6 x^6+60 b^7 x^7\right)","a^7 \log (x)+7 a^6 b 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+\frac{7}{6} a b^6 x^6+\frac{b^7 x^7}{7}",1,"(2940*a^6*b*x + 4410*a^5*b^2*x^2 + 4900*a^4*b^3*x^3 + 3675*a^3*b^4*x^4 + 1764*a^2*b^5*x^5 + 490*a*b^6*x^6 + 60*b^7*x^7)/420 + a^7*Log[x]","A",1
108,1,83,86,0.0174528,"\int \frac{(a+b x)^7}{x^2} \, dx","IntegrateAlgebraic[(a + b*x)^7/x^2,x]","7 a^6 b \log (x)+\frac{-60 a^7+1260 a^5 b^2 x^2+1050 a^4 b^3 x^3+700 a^3 b^4 x^4+315 a^2 b^5 x^5+84 a b^6 x^6+10 b^7 x^7}{60 x}","-\frac{a^7}{x}+7 a^6 b \log (x)+21 a^5 b^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+\frac{7}{5} a b^6 x^5+\frac{b^7 x^6}{6}",1,"(-60*a^7 + 1260*a^5*b^2*x^2 + 1050*a^4*b^3*x^3 + 700*a^3*b^4*x^4 + 315*a^2*b^5*x^5 + 84*a*b^6*x^6 + 10*b^7*x^7)/(60*x) + 7*a^6*b*Log[x]","A",1
109,1,81,84,0.0163615,"\int \frac{(a+b x)^7}{x^3} \, dx","IntegrateAlgebraic[(a + b*x)^7/x^3,x]","21 a^5 b^2 \log (x)+\frac{-10 a^7-140 a^6 b x+700 a^4 b^3 x^3+350 a^3 b^4 x^4+140 a^2 b^5 x^5+35 a b^6 x^6+4 b^7 x^7}{20 x^2}","-\frac{a^7}{2 x^2}-\frac{7 a^6 b}{x}+21 a^5 b^2 \log (x)+35 a^4 b^3 x+\frac{35}{2} a^3 b^4 x^2+7 a^2 b^5 x^3+\frac{7}{4} a b^6 x^4+\frac{b^7 x^5}{5}",1,"(-10*a^7 - 140*a^6*b*x + 700*a^4*b^3*x^3 + 350*a^3*b^4*x^4 + 140*a^2*b^5*x^5 + 35*a*b^6*x^6 + 4*b^7*x^7)/(20*x^2) + 21*a^5*b^2*Log[x]","A",1
110,1,81,86,0.01469,"\int \frac{(a+b x)^7}{x^4} \, dx","IntegrateAlgebraic[(a + b*x)^7/x^4,x]","35 a^4 b^3 \log (x)+\frac{-4 a^7-42 a^6 b x-252 a^5 b^2 x^2+420 a^3 b^4 x^4+126 a^2 b^5 x^5+28 a b^6 x^6+3 b^7 x^7}{12 x^3}","-\frac{a^7}{3 x^3}-\frac{7 a^6 b}{2 x^2}-\frac{21 a^5 b^2}{x}+35 a^4 b^3 \log (x)+35 a^3 b^4 x+\frac{21}{2} a^2 b^5 x^2+\frac{7}{3} a b^6 x^3+\frac{b^7 x^4}{4}",1,"(-4*a^7 - 42*a^6*b*x - 252*a^5*b^2*x^2 + 420*a^3*b^4*x^4 + 126*a^2*b^5*x^5 + 28*a*b^6*x^6 + 3*b^7*x^7)/(12*x^3) + 35*a^4*b^3*Log[x]","A",1
111,1,81,86,0.0161425,"\int \frac{(a+b x)^7}{x^5} \, dx","IntegrateAlgebraic[(a + b*x)^7/x^5,x]","35 a^3 b^4 \log (x)+\frac{-3 a^7-28 a^6 b x-126 a^5 b^2 x^2-420 a^4 b^3 x^3+252 a^2 b^5 x^5+42 a b^6 x^6+4 b^7 x^7}{12 x^4}","-\frac{a^7}{4 x^4}-\frac{7 a^6 b}{3 x^3}-\frac{21 a^5 b^2}{2 x^2}-\frac{35 a^4 b^3}{x}+35 a^3 b^4 \log (x)+21 a^2 b^5 x+\frac{7}{2} a b^6 x^2+\frac{b^7 x^3}{3}",1,"(-3*a^7 - 28*a^6*b*x - 126*a^5*b^2*x^2 - 420*a^4*b^3*x^3 + 252*a^2*b^5*x^5 + 42*a*b^6*x^6 + 4*b^7*x^7)/(12*x^4) + 35*a^3*b^4*Log[x]","A",1
112,1,81,84,0.019567,"\int \frac{(a+b x)^7}{x^6} \, dx","IntegrateAlgebraic[(a + b*x)^7/x^6,x]","21 a^2 b^5 \log (x)+\frac{-4 a^7-35 a^6 b x-140 a^5 b^2 x^2-350 a^4 b^3 x^3-700 a^3 b^4 x^4+140 a b^6 x^6+10 b^7 x^7}{20 x^5}","-\frac{a^7}{5 x^5}-\frac{7 a^6 b}{4 x^4}-\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)+7 a b^6 x+\frac{b^7 x^2}{2}",1,"(-4*a^7 - 35*a^6*b*x - 140*a^5*b^2*x^2 - 350*a^4*b^3*x^3 - 700*a^3*b^4*x^4 + 140*a*b^6*x^6 + 10*b^7*x^7)/(20*x^5) + 21*a^2*b^5*Log[x]","A",1
113,1,81,85,0.0208533,"\int \frac{(a+b x)^7}{x^7} \, dx","IntegrateAlgebraic[(a + b*x)^7/x^7,x]","\frac{-10 a^7-84 a^6 b x-315 a^5 b^2 x^2-700 a^4 b^3 x^3-1050 a^3 b^4 x^4-1260 a^2 b^5 x^5+60 b^7 x^7}{60 x^6}+7 a b^6 \log (x)","-\frac{a^7}{6 x^6}-\frac{7 a^6 b}{5 x^5}-\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}+7 a b^6 \log (x)+b^7 x",1,"(-10*a^7 - 84*a^6*b*x - 315*a^5*b^2*x^2 - 700*a^4*b^3*x^3 - 1050*a^3*b^4*x^4 - 1260*a^2*b^5*x^5 + 60*b^7*x^7)/(60*x^6) + 7*a*b^6*Log[x]","A",1
114,1,78,89,0.0157897,"\int \frac{(a+b x)^7}{x^8} \, dx","IntegrateAlgebraic[(a + b*x)^7/x^8,x]","b^7 \log (x)-\frac{a \left(60 a^6+490 a^5 b x+1764 a^4 b^2 x^2+3675 a^3 b^3 x^3+4900 a^2 b^4 x^4+4410 a b^5 x^5+2940 b^6 x^6\right)}{420 x^7}","-\frac{a^7}{7 x^7}-\frac{7 a^6 b}{6 x^6}-\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 b^6}{x}+b^7 \log (x)",1,"-1/420*(a*(60*a^6 + 490*a^5*b*x + 1764*a^4*b^2*x^2 + 3675*a^3*b^3*x^3 + 4900*a^2*b^4*x^4 + 4410*a*b^5*x^5 + 2940*b^6*x^6))/x^7 + b^7*Log[x]","A",1
115,1,81,17,0.0101099,"\int \frac{(a+b x)^7}{x^9} \, dx","IntegrateAlgebraic[(a + b*x)^7/x^9,x]","\frac{-a^7-8 a^6 b x-28 a^5 b^2 x^2-56 a^4 b^3 x^3-70 a^3 b^4 x^4-56 a^2 b^5 x^5-28 a b^6 x^6-8 b^7 x^7}{8 x^8}","-\frac{(a+b x)^8}{8 a x^8}",1,"(-a^7 - 8*a^6*b*x - 28*a^5*b^2*x^2 - 56*a^4*b^3*x^3 - 70*a^3*b^4*x^4 - 56*a^2*b^5*x^5 - 28*a*b^6*x^6 - 8*b^7*x^7)/(8*x^8)","B",1
116,1,81,36,0.009998,"\int \frac{(a+b x)^7}{x^{10}} \, dx","IntegrateAlgebraic[(a + b*x)^7/x^10,x]","\frac{-8 a^7-63 a^6 b x-216 a^5 b^2 x^2-420 a^4 b^3 x^3-504 a^3 b^4 x^4-378 a^2 b^5 x^5-168 a b^6 x^6-36 b^7 x^7}{72 x^9}","\frac{b (a+b x)^8}{72 a^2 x^8}-\frac{(a+b x)^8}{9 a x^9}",1,"(-8*a^7 - 63*a^6*b*x - 216*a^5*b^2*x^2 - 420*a^4*b^3*x^3 - 504*a^3*b^4*x^4 - 378*a^2*b^5*x^5 - 168*a*b^6*x^6 - 36*b^7*x^7)/(72*x^9)","B",1
117,1,81,56,0.0100849,"\int \frac{(a+b x)^7}{x^{11}} \, dx","IntegrateAlgebraic[(a + b*x)^7/x^11,x]","\frac{-36 a^7-280 a^6 b x-945 a^5 b^2 x^2-1800 a^4 b^3 x^3-2100 a^3 b^4 x^4-1512 a^2 b^5 x^5-630 a b^6 x^6-120 b^7 x^7}{360 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,"(-36*a^7 - 280*a^6*b*x - 945*a^5*b^2*x^2 - 1800*a^4*b^3*x^3 - 2100*a^3*b^4*x^4 - 1512*a^2*b^5*x^5 - 630*a*b^6*x^6 - 120*b^7*x^7)/(360*x^10)","A",1
118,1,81,76,0.0100274,"\int \frac{(a+b x)^7}{x^{12}} \, dx","IntegrateAlgebraic[(a + b*x)^7/x^12,x]","\frac{-120 a^7-924 a^6 b x-3080 a^5 b^2 x^2-5775 a^4 b^3 x^3-6600 a^3 b^4 x^4-4620 a^2 b^5 x^5-1848 a b^6 x^6-330 b^7 x^7}{1320 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,"(-120*a^7 - 924*a^6*b*x - 3080*a^5*b^2*x^2 - 5775*a^4*b^3*x^3 - 6600*a^3*b^4*x^4 - 4620*a^2*b^5*x^5 - 1848*a*b^6*x^6 - 330*b^7*x^7)/(1320*x^11)","A",1
119,1,81,96,0.0102254,"\int \frac{(a+b x)^7}{x^{13}} \, dx","IntegrateAlgebraic[(a + b*x)^7/x^13,x]","\frac{-330 a^7-2520 a^6 b x-8316 a^5 b^2 x^2-15400 a^4 b^3 x^3-17325 a^3 b^4 x^4-11880 a^2 b^5 x^5-4620 a b^6 x^6-792 b^7 x^7}{3960 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,"(-330*a^7 - 2520*a^6*b*x - 8316*a^5*b^2*x^2 - 15400*a^4*b^3*x^3 - 17325*a^3*b^4*x^4 - 11880*a^2*b^5*x^5 - 4620*a*b^6*x^6 - 792*b^7*x^7)/(3960*x^12)","A",1
120,1,81,93,0.0126454,"\int \frac{(a+b x)^7}{x^{14}} \, dx","IntegrateAlgebraic[(a + b*x)^7/x^14,x]","\frac{-792 a^7-6006 a^6 b x-19656 a^5 b^2 x^2-36036 a^4 b^3 x^3-40040 a^3 b^4 x^4-27027 a^2 b^5 x^5-10296 a b^6 x^6-1716 b^7 x^7}{10296 x^{13}}","-\frac{a^7}{13 x^{13}}-\frac{7 a^6 b}{12 x^{12}}-\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{a b^6}{x^7}-\frac{b^7}{6 x^6}",1,"(-792*a^7 - 6006*a^6*b*x - 19656*a^5*b^2*x^2 - 36036*a^4*b^3*x^3 - 40040*a^3*b^4*x^4 - 27027*a^2*b^5*x^5 - 10296*a*b^6*x^6 - 1716*b^7*x^7)/(10296*x^13)","A",1
121,1,81,95,0.010059,"\int \frac{(a+b x)^7}{x^{15}} \, dx","IntegrateAlgebraic[(a + b*x)^7/x^15,x]","\frac{-1716 a^7-12936 a^6 b x-42042 a^5 b^2 x^2-76440 a^4 b^3 x^3-84084 a^3 b^4 x^4-56056 a^2 b^5 x^5-21021 a b^6 x^6-3432 b^7 x^7}{24024 x^{14}}","-\frac{a^7}{14 x^{14}}-\frac{7 a^6 b}{13 x^{13}}-\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 b^6}{8 x^8}-\frac{b^7}{7 x^7}",1,"(-1716*a^7 - 12936*a^6*b*x - 42042*a^5*b^2*x^2 - 76440*a^4*b^3*x^3 - 84084*a^3*b^4*x^4 - 56056*a^2*b^5*x^5 - 21021*a*b^6*x^6 - 3432*b^7*x^7)/(24024*x^14)","A",1
122,1,81,95,0.0102332,"\int \frac{(a+b x)^7}{x^{16}} \, dx","IntegrateAlgebraic[(a + b*x)^7/x^16,x]","\frac{-3432 a^7-25740 a^6 b x-83160 a^5 b^2 x^2-150150 a^4 b^3 x^3-163800 a^3 b^4 x^4-108108 a^2 b^5 x^5-40040 a b^6 x^6-6435 b^7 x^7}{51480 x^{15}}","-\frac{a^7}{15 x^{15}}-\frac{a^6 b}{2 x^{14}}-\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{7 a b^6}{9 x^9}-\frac{b^7}{8 x^8}",1,"(-3432*a^7 - 25740*a^6*b*x - 83160*a^5*b^2*x^2 - 150150*a^4*b^3*x^3 - 163800*a^3*b^4*x^4 - 108108*a^2*b^5*x^5 - 40040*a*b^6*x^6 - 6435*b^7*x^7)/(51480*x^15)","A",1
123,1,116,132,0.0148828,"\int x^{11} (a+b x)^{10} \, dx","IntegrateAlgebraic[x^11*(a + b*x)^10,x]","\frac{646646 a^{10} x^{12}+5969040 a^9 b x^{13}+24942060 a^8 b^2 x^{14}+62078016 a^7 b^3 x^{15}+101846745 a^6 b^4 x^{16}+115026912 a^5 b^5 x^{17}+90530440 a^4 b^6 x^{18}+49008960 a^3 b^7 x^{19}+17459442 a^2 b^8 x^{20}+3695120 a b^9 x^{21}+352716 b^{10} x^{22}}{7759752}","\frac{a^{10} x^{12}}{12}+\frac{10}{13} a^9 b x^{13}+\frac{45}{14} a^8 b^2 x^{14}+8 a^7 b^3 x^{15}+\frac{105}{8} a^6 b^4 x^{16}+\frac{252}{17} a^5 b^5 x^{17}+\frac{35}{3} a^4 b^6 x^{18}+\frac{120}{19} a^3 b^7 x^{19}+\frac{9}{4} a^2 b^8 x^{20}+\frac{10}{21} a b^9 x^{21}+\frac{b^{10} x^{22}}{22}",1,"(646646*a^10*x^12 + 5969040*a^9*b*x^13 + 24942060*a^8*b^2*x^14 + 62078016*a^7*b^3*x^15 + 101846745*a^6*b^4*x^16 + 115026912*a^5*b^5*x^17 + 90530440*a^4*b^6*x^18 + 49008960*a^3*b^7*x^19 + 17459442*a^2*b^8*x^20 + 3695120*a*b^9*x^21 + 352716*b^10*x^22)/7759752","A",1
124,1,116,132,0.0144992,"\int x^{10} (a+b x)^{10} \, dx","IntegrateAlgebraic[x^10*(a + b*x)^10,x]","\frac{352716 a^{10} x^{11}+3233230 a^9 b x^{12}+13430340 a^8 b^2 x^{13}+33256080 a^7 b^3 x^{14}+54318264 a^6 b^4 x^{15}+61108047 a^5 b^5 x^{16}+47927880 a^4 b^6 x^{17}+25865840 a^3 b^7 x^{18}+9189180 a^2 b^8 x^{19}+1939938 a b^9 x^{20}+184756 b^{10} x^{21}}{3879876}","\frac{a^{10} x^{11}}{11}+\frac{5}{6} a^9 b x^{12}+\frac{45}{13} a^8 b^2 x^{13}+\frac{60}{7} a^7 b^3 x^{14}+14 a^6 b^4 x^{15}+\frac{63}{4} a^5 b^5 x^{16}+\frac{210}{17} a^4 b^6 x^{17}+\frac{20}{3} a^3 b^7 x^{18}+\frac{45}{19} a^2 b^8 x^{19}+\frac{1}{2} a b^9 x^{20}+\frac{b^{10} x^{21}}{21}",1,"(352716*a^10*x^11 + 3233230*a^9*b*x^12 + 13430340*a^8*b^2*x^13 + 33256080*a^7*b^3*x^14 + 54318264*a^6*b^4*x^15 + 61108047*a^5*b^5*x^16 + 47927880*a^4*b^6*x^17 + 25865840*a^3*b^7*x^18 + 9189180*a^2*b^8*x^19 + 1939938*a*b^9*x^20 + 184756*b^10*x^21)/3879876","A",1
125,1,116,132,0.015119,"\int x^9 (a+b x)^{10} \, dx","IntegrateAlgebraic[x^9*(a + b*x)^10,x]","\frac{184756 a^{10} x^{10}+1679600 a^9 b x^{11}+6928350 a^8 b^2 x^{12}+17054400 a^7 b^3 x^{13}+27713400 a^6 b^4 x^{14}+31039008 a^5 b^5 x^{15}+24249225 a^4 b^6 x^{16}+13041600 a^3 b^7 x^{17}+4618900 a^2 b^8 x^{18}+972400 a b^9 x^{19}+92378 b^{10} x^{20}}{1847560}","\frac{a^{10} x^{10}}{10}+\frac{10}{11} a^9 b x^{11}+\frac{15}{4} a^8 b^2 x^{12}+\frac{120}{13} a^7 b^3 x^{13}+15 a^6 b^4 x^{14}+\frac{84}{5} a^5 b^5 x^{15}+\frac{105}{8} a^4 b^6 x^{16}+\frac{120}{17} a^3 b^7 x^{17}+\frac{5}{2} a^2 b^8 x^{18}+\frac{10}{19} a b^9 x^{19}+\frac{b^{10} x^{20}}{20}",1,"(184756*a^10*x^10 + 1679600*a^9*b*x^11 + 6928350*a^8*b^2*x^12 + 17054400*a^7*b^3*x^13 + 27713400*a^6*b^4*x^14 + 31039008*a^5*b^5*x^15 + 24249225*a^4*b^6*x^16 + 13041600*a^3*b^7*x^17 + 4618900*a^2*b^8*x^18 + 972400*a*b^9*x^19 + 92378*b^10*x^20)/1847560","A",1
126,1,116,147,0.0144037,"\int x^8 (a+b x)^{10} \, dx","IntegrateAlgebraic[x^8*(a + b*x)^10,x]","\frac{92378 a^{10} x^9+831402 a^9 b x^{10}+3401190 a^8 b^2 x^{11}+8314020 a^7 b^3 x^{12}+13430340 a^6 b^4 x^{13}+14965236 a^5 b^5 x^{14}+11639628 a^4 b^6 x^{15}+6235515 a^3 b^7 x^{16}+2200770 a^2 b^8 x^{17}+461890 a b^9 x^{18}+43758 b^{10} x^{19}}{831402}","\frac{a^8 (a+b x)^{11}}{11 b^9}-\frac{2 a^7 (a+b x)^{12}}{3 b^9}+\frac{28 a^6 (a+b x)^{13}}{13 b^9}-\frac{4 a^5 (a+b x)^{14}}{b^9}+\frac{14 a^4 (a+b x)^{15}}{3 b^9}-\frac{7 a^3 (a+b x)^{16}}{2 b^9}+\frac{28 a^2 (a+b x)^{17}}{17 b^9}+\frac{(a+b x)^{19}}{19 b^9}-\frac{4 a (a+b x)^{18}}{9 b^9}",1,"(92378*a^10*x^9 + 831402*a^9*b*x^10 + 3401190*a^8*b^2*x^11 + 8314020*a^7*b^3*x^12 + 13430340*a^6*b^4*x^13 + 14965236*a^5*b^5*x^14 + 11639628*a^4*b^6*x^15 + 6235515*a^3*b^7*x^16 + 2200770*a^2*b^8*x^17 + 461890*a*b^9*x^18 + 43758*b^10*x^19)/831402","A",1
127,1,116,132,0.014241,"\int x^7 (a+b x)^{10} \, dx","IntegrateAlgebraic[x^7*(a + b*x)^10,x]","\frac{43758 a^{10} x^8+388960 a^9 b x^9+1575288 a^8 b^2 x^{10}+3818880 a^7 b^3 x^{11}+6126120 a^6 b^4 x^{12}+6785856 a^5 b^5 x^{13}+5250960 a^4 b^6 x^{14}+2800512 a^3 b^7 x^{15}+984555 a^2 b^8 x^{16}+205920 a b^9 x^{17}+19448 b^{10} x^{18}}{350064}","-\frac{a^7 (a+b x)^{11}}{11 b^8}+\frac{7 a^6 (a+b x)^{12}}{12 b^8}-\frac{21 a^5 (a+b x)^{13}}{13 b^8}+\frac{5 a^4 (a+b x)^{14}}{2 b^8}-\frac{7 a^3 (a+b x)^{15}}{3 b^8}+\frac{21 a^2 (a+b x)^{16}}{16 b^8}+\frac{(a+b x)^{18}}{18 b^8}-\frac{7 a (a+b x)^{17}}{17 b^8}",1,"(43758*a^10*x^8 + 388960*a^9*b*x^9 + 1575288*a^8*b^2*x^10 + 3818880*a^7*b^3*x^11 + 6126120*a^6*b^4*x^12 + 6785856*a^5*b^5*x^13 + 5250960*a^4*b^6*x^14 + 2800512*a^3*b^7*x^15 + 984555*a^2*b^8*x^16 + 205920*a*b^9*x^17 + 19448*b^10*x^18)/350064","A",1
128,1,116,112,0.014925,"\int x^6 (a+b x)^{10} \, dx","IntegrateAlgebraic[x^6*(a + b*x)^10,x]","\frac{19448 a^{10} x^7+170170 a^9 b x^8+680680 a^8 b^2 x^9+1633632 a^7 b^3 x^{10}+2598960 a^6 b^4 x^{11}+2858856 a^5 b^5 x^{12}+2199120 a^4 b^6 x^{13}+1166880 a^3 b^7 x^{14}+408408 a^2 b^8 x^{15}+85085 a b^9 x^{16}+8008 b^{10} x^{17}}{136136}","\frac{a^6 (a+b x)^{11}}{11 b^7}-\frac{a^5 (a+b x)^{12}}{2 b^7}+\frac{15 a^4 (a+b x)^{13}}{13 b^7}-\frac{10 a^3 (a+b x)^{14}}{7 b^7}+\frac{a^2 (a+b x)^{15}}{b^7}+\frac{(a+b x)^{17}}{17 b^7}-\frac{3 a (a+b x)^{16}}{8 b^7}",1,"(19448*a^10*x^7 + 170170*a^9*b*x^8 + 680680*a^8*b^2*x^9 + 1633632*a^7*b^3*x^10 + 2598960*a^6*b^4*x^11 + 2858856*a^5*b^5*x^12 + 2199120*a^4*b^6*x^13 + 1166880*a^3*b^7*x^14 + 408408*a^2*b^8*x^15 + 85085*a*b^9*x^16 + 8008*b^10*x^17)/136136","A",1
129,1,116,98,0.015139,"\int x^5 (a+b x)^{10} \, dx","IntegrateAlgebraic[x^5*(a + b*x)^10,x]","\frac{8008 a^{10} x^6+68640 a^9 b x^7+270270 a^8 b^2 x^8+640640 a^7 b^3 x^9+1009008 a^6 b^4 x^{10}+1100736 a^5 b^5 x^{11}+840840 a^4 b^6 x^{12}+443520 a^3 b^7 x^{13}+154440 a^2 b^8 x^{14}+32032 a b^9 x^{15}+3003 b^{10} x^{16}}{48048}","-\frac{a^5 (a+b x)^{11}}{11 b^6}+\frac{5 a^4 (a+b x)^{12}}{12 b^6}-\frac{10 a^3 (a+b x)^{13}}{13 b^6}+\frac{5 a^2 (a+b x)^{14}}{7 b^6}+\frac{(a+b x)^{16}}{16 b^6}-\frac{a (a+b x)^{15}}{3 b^6}",1,"(8008*a^10*x^6 + 68640*a^9*b*x^7 + 270270*a^8*b^2*x^8 + 640640*a^7*b^3*x^9 + 1009008*a^6*b^4*x^10 + 1100736*a^5*b^5*x^11 + 840840*a^4*b^6*x^12 + 443520*a^3*b^7*x^13 + 154440*a^2*b^8*x^14 + 32032*a*b^9*x^15 + 3003*b^10*x^16)/48048","A",1
130,1,116,81,0.0148924,"\int x^4 (a+b x)^{10} \, dx","IntegrateAlgebraic[x^4*(a + b*x)^10,x]","\frac{3003 a^{10} x^5+25025 a^9 b x^6+96525 a^8 b^2 x^7+225225 a^7 b^3 x^8+350350 a^6 b^4 x^9+378378 a^5 b^5 x^{10}+286650 a^4 b^6 x^{11}+150150 a^3 b^7 x^{12}+51975 a^2 b^8 x^{13}+10725 a b^9 x^{14}+1001 b^{10} x^{15}}{15015}","\frac{a^4 (a+b x)^{11}}{11 b^5}-\frac{a^3 (a+b x)^{12}}{3 b^5}+\frac{6 a^2 (a+b x)^{13}}{13 b^5}+\frac{(a+b x)^{15}}{15 b^5}-\frac{2 a (a+b x)^{14}}{7 b^5}",1,"(3003*a^10*x^5 + 25025*a^9*b*x^6 + 96525*a^8*b^2*x^7 + 225225*a^7*b^3*x^8 + 350350*a^6*b^4*x^9 + 378378*a^5*b^5*x^10 + 286650*a^4*b^6*x^11 + 150150*a^3*b^7*x^12 + 51975*a^2*b^8*x^13 + 10725*a*b^9*x^14 + 1001*b^10*x^15)/15015","A",1
131,1,116,64,0.0147623,"\int x^3 (a+b x)^{10} \, dx","IntegrateAlgebraic[x^3*(a + b*x)^10,x]","\frac{1001 a^{10} x^4+8008 a^9 b x^5+30030 a^8 b^2 x^6+68640 a^7 b^3 x^7+105105 a^6 b^4 x^8+112112 a^5 b^5 x^9+84084 a^4 b^6 x^{10}+43680 a^3 b^7 x^{11}+15015 a^2 b^8 x^{12}+3080 a b^9 x^{13}+286 b^{10} x^{14}}{4004}","-\frac{a^3 (a+b x)^{11}}{11 b^4}+\frac{a^2 (a+b x)^{12}}{4 b^4}+\frac{(a+b x)^{14}}{14 b^4}-\frac{3 a (a+b x)^{13}}{13 b^4}",1,"(1001*a^10*x^4 + 8008*a^9*b*x^5 + 30030*a^8*b^2*x^6 + 68640*a^7*b^3*x^7 + 105105*a^6*b^4*x^8 + 112112*a^5*b^5*x^9 + 84084*a^4*b^6*x^10 + 43680*a^3*b^7*x^11 + 15015*a^2*b^8*x^12 + 3080*a*b^9*x^13 + 286*b^10*x^14)/4004","A",1
132,1,116,47,0.0143513,"\int x^2 (a+b x)^{10} \, dx","IntegrateAlgebraic[x^2*(a + b*x)^10,x]","\frac{1}{858} \left(286 a^{10} x^3+2145 a^9 b x^4+7722 a^8 b^2 x^5+17160 a^7 b^3 x^6+25740 a^6 b^4 x^7+27027 a^5 b^5 x^8+20020 a^4 b^6 x^9+10296 a^3 b^7 x^{10}+3510 a^2 b^8 x^{11}+715 a b^9 x^{12}+66 b^{10} x^{13}\right)","\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,"(286*a^10*x^3 + 2145*a^9*b*x^4 + 7722*a^8*b^2*x^5 + 17160*a^7*b^3*x^6 + 25740*a^6*b^4*x^7 + 27027*a^5*b^5*x^8 + 20020*a^4*b^6*x^9 + 10296*a^3*b^7*x^10 + 3510*a^2*b^8*x^11 + 715*a*b^9*x^12 + 66*b^10*x^13)/858","B",1
133,1,116,30,0.014846,"\int x (a+b x)^{10} \, dx","IntegrateAlgebraic[x*(a + b*x)^10,x]","\frac{1}{132} \left(66 a^{10} x^2+440 a^9 b x^3+1485 a^8 b^2 x^4+3168 a^7 b^3 x^5+4620 a^6 b^4 x^6+4752 a^5 b^5 x^7+3465 a^4 b^6 x^8+1760 a^3 b^7 x^9+594 a^2 b^8 x^{10}+120 a b^9 x^{11}+11 b^{10} x^{12}\right)","\frac{(a+b x)^{12}}{12 b^2}-\frac{a (a+b x)^{11}}{11 b^2}",1,"(66*a^10*x^2 + 440*a^9*b*x^3 + 1485*a^8*b^2*x^4 + 3168*a^7*b^3*x^5 + 4620*a^6*b^4*x^6 + 4752*a^5*b^5*x^7 + 3465*a^4*b^6*x^8 + 1760*a^3*b^7*x^9 + 594*a^2*b^8*x^10 + 120*a*b^9*x^11 + 11*b^10*x^12)/132","B",1
134,1,14,14,0.0045113,"\int (a+b x)^{10} \, dx","IntegrateAlgebraic[(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
135,1,113,122,0.0169461,"\int \frac{(a+b x)^{10}}{x} \, dx","IntegrateAlgebraic[(a + b*x)^10/x,x]","a^{10} \log (x)+\frac{25200 a^9 b x+56700 a^8 b^2 x^2+100800 a^7 b^3 x^3+132300 a^6 b^4 x^4+127008 a^5 b^5 x^5+88200 a^4 b^6 x^6+43200 a^3 b^7 x^7+14175 a^2 b^8 x^8+2800 a b^9 x^9+252 b^{10} x^{10}}{2520}","a^{10} \log (x)+10 a^9 b 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+\frac{10}{9} a b^9 x^9+\frac{b^{10} x^{10}}{10}",1,"(25200*a^9*b*x + 56700*a^8*b^2*x^2 + 100800*a^7*b^3*x^3 + 132300*a^6*b^4*x^4 + 127008*a^5*b^5*x^5 + 88200*a^4*b^6*x^6 + 43200*a^3*b^7*x^7 + 14175*a^2*b^8*x^8 + 2800*a*b^9*x^9 + 252*b^10*x^10)/2520 + a^10*Log[x]","A",1
136,1,116,115,0.0240935,"\int \frac{(a+b x)^{10}}{x^2} \, dx","IntegrateAlgebraic[(a + b*x)^10/x^2,x]","10 a^9 b \log (x)+\frac{-252 a^{10}+11340 a^8 b^2 x^2+15120 a^7 b^3 x^3+17640 a^6 b^4 x^4+15876 a^5 b^5 x^5+10584 a^4 b^6 x^6+5040 a^3 b^7 x^7+1620 a^2 b^8 x^8+315 a b^9 x^9+28 b^{10} x^{10}}{252 x}","-\frac{a^{10}}{x}+10 a^9 b \log (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+\frac{45}{7} a^2 b^8 x^7+\frac{5}{4} a b^9 x^8+\frac{b^{10} x^9}{9}",1,"(-252*a^10 + 11340*a^8*b^2*x^2 + 15120*a^7*b^3*x^3 + 17640*a^6*b^4*x^4 + 15876*a^5*b^5*x^5 + 10584*a^4*b^6*x^6 + 5040*a^3*b^7*x^7 + 1620*a^2*b^8*x^8 + 315*a*b^9*x^9 + 28*b^10*x^10)/(252*x) + 10*a^9*b*Log[x]","A",1
137,1,114,119,0.021265,"\int \frac{(a+b x)^{10}}{x^3} \, dx","IntegrateAlgebraic[(a + b*x)^10/x^3,x]","45 a^8 b^2 \log (x)+\frac{-28 a^{10}-560 a^9 b x+6720 a^7 b^3 x^3+5880 a^6 b^4 x^4+4704 a^5 b^5 x^5+2940 a^4 b^6 x^6+1344 a^3 b^7 x^7+420 a^2 b^8 x^8+80 a b^9 x^9+7 b^{10} x^{10}}{56 x^2}","-\frac{a^{10}}{2 x^2}-\frac{10 a^9 b}{x}+45 a^8 b^2 \log (x)+120 a^7 b^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+\frac{10}{7} a b^9 x^7+\frac{b^{10} x^8}{8}",1,"(-28*a^10 - 560*a^9*b*x + 6720*a^7*b^3*x^3 + 5880*a^6*b^4*x^4 + 4704*a^5*b^5*x^5 + 2940*a^4*b^6*x^6 + 1344*a^3*b^7*x^7 + 420*a^2*b^8*x^8 + 80*a*b^9*x^9 + 7*b^10*x^10)/(56*x^2) + 45*a^8*b^2*Log[x]","A",1
138,1,114,115,0.0271505,"\int \frac{(a+b x)^{10}}{x^4} \, dx","IntegrateAlgebraic[(a + b*x)^10/x^4,x]","120 a^7 b^3 \log (x)+\frac{-7 a^{10}-105 a^9 b x-945 a^8 b^2 x^2+4410 a^6 b^4 x^4+2646 a^5 b^5 x^5+1470 a^4 b^6 x^6+630 a^3 b^7 x^7+189 a^2 b^8 x^8+35 a b^9 x^9+3 b^{10} x^{10}}{21 x^3}","-\frac{a^{10}}{3 x^3}-\frac{5 a^9 b}{x^2}-\frac{45 a^8 b^2}{x}+120 a^7 b^3 \log (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+\frac{5}{3} a b^9 x^6+\frac{b^{10} x^7}{7}",1,"(-7*a^10 - 105*a^9*b*x - 945*a^8*b^2*x^2 + 4410*a^6*b^4*x^4 + 2646*a^5*b^5*x^5 + 1470*a^4*b^6*x^6 + 630*a^3*b^7*x^7 + 189*a^2*b^8*x^8 + 35*a*b^9*x^9 + 3*b^10*x^10)/(21*x^3) + 120*a^7*b^3*Log[x]","A",1
139,1,114,119,0.0242681,"\int \frac{(a+b x)^{10}}{x^5} \, dx","IntegrateAlgebraic[(a + b*x)^10/x^5,x]","210 a^6 b^4 \log (x)+\frac{-3 a^{10}-40 a^9 b x-270 a^8 b^2 x^2-1440 a^7 b^3 x^3+3024 a^5 b^5 x^5+1260 a^4 b^6 x^6+480 a^3 b^7 x^7+135 a^2 b^8 x^8+24 a b^9 x^9+2 b^{10} x^{10}}{12 x^4}","-\frac{a^{10}}{4 x^4}-\frac{10 a^9 b}{3 x^3}-\frac{45 a^8 b^2}{2 x^2}-\frac{120 a^7 b^3}{x}+210 a^6 b^4 \log (x)+252 a^5 b^5 x+105 a^4 b^6 x^2+40 a^3 b^7 x^3+\frac{45}{4} a^2 b^8 x^4+2 a b^9 x^5+\frac{b^{10} x^6}{6}",1,"(-3*a^10 - 40*a^9*b*x - 270*a^8*b^2*x^2 - 1440*a^7*b^3*x^3 + 3024*a^5*b^5*x^5 + 1260*a^4*b^6*x^6 + 480*a^3*b^7*x^7 + 135*a^2*b^8*x^8 + 24*a*b^9*x^9 + 2*b^10*x^10)/(12*x^4) + 210*a^6*b^4*Log[x]","A",1
140,1,114,117,0.0254261,"\int \frac{(a+b x)^{10}}{x^6} \, dx","IntegrateAlgebraic[(a + b*x)^10/x^6,x]","252 a^5 b^5 \log (x)+\frac{-2 a^{10}-25 a^9 b x-150 a^8 b^2 x^2-600 a^7 b^3 x^3-2100 a^6 b^4 x^4+2100 a^4 b^6 x^6+600 a^3 b^7 x^7+150 a^2 b^8 x^8+25 a b^9 x^9+2 b^{10} x^{10}}{10 x^5}","-\frac{a^{10}}{5 x^5}-\frac{5 a^9 b}{2 x^4}-\frac{15 a^8 b^2}{x^3}-\frac{60 a^7 b^3}{x^2}-\frac{210 a^6 b^4}{x}+252 a^5 b^5 \log (x)+210 a^4 b^6 x+60 a^3 b^7 x^2+15 a^2 b^8 x^3+\frac{5}{2} a b^9 x^4+\frac{b^{10} x^5}{5}",1,"(-2*a^10 - 25*a^9*b*x - 150*a^8*b^2*x^2 - 600*a^7*b^3*x^3 - 2100*a^6*b^4*x^4 + 2100*a^4*b^6*x^6 + 600*a^3*b^7*x^7 + 150*a^2*b^8*x^8 + 25*a*b^9*x^9 + 2*b^10*x^10)/(10*x^5) + 252*a^5*b^5*Log[x]","A",1
141,1,114,119,0.0236566,"\int \frac{(a+b x)^{10}}{x^7} \, dx","IntegrateAlgebraic[(a + b*x)^10/x^7,x]","210 a^4 b^6 \log (x)+\frac{-2 a^{10}-24 a^9 b x-135 a^8 b^2 x^2-480 a^7 b^3 x^3-1260 a^6 b^4 x^4-3024 a^5 b^5 x^5+1440 a^3 b^7 x^7+270 a^2 b^8 x^8+40 a b^9 x^9+3 b^{10} x^{10}}{12 x^6}","-\frac{a^{10}}{6 x^6}-\frac{2 a^9 b}{x^5}-\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{252 a^5 b^5}{x}+210 a^4 b^6 \log (x)+120 a^3 b^7 x+\frac{45}{2} a^2 b^8 x^2+\frac{10}{3} a b^9 x^3+\frac{b^{10} x^4}{4}",1,"(-2*a^10 - 24*a^9*b*x - 135*a^8*b^2*x^2 - 480*a^7*b^3*x^3 - 1260*a^6*b^4*x^4 - 3024*a^5*b^5*x^5 + 1440*a^3*b^7*x^7 + 270*a^2*b^8*x^8 + 40*a*b^9*x^9 + 3*b^10*x^10)/(12*x^6) + 210*a^4*b^6*Log[x]","A",1
142,1,114,115,0.030144,"\int \frac{(a+b x)^{10}}{x^8} \, dx","IntegrateAlgebraic[(a + b*x)^10/x^8,x]","120 a^3 b^7 \log (x)+\frac{-3 a^{10}-35 a^9 b x-189 a^8 b^2 x^2-630 a^7 b^3 x^3-1470 a^6 b^4 x^4-2646 a^5 b^5 x^5-4410 a^4 b^6 x^6+945 a^2 b^8 x^8+105 a b^9 x^9+7 b^{10} x^{10}}{21 x^7}","-\frac{a^{10}}{7 x^7}-\frac{5 a^9 b}{3 x^6}-\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}+120 a^3 b^7 \log (x)+45 a^2 b^8 x+5 a b^9 x^2+\frac{b^{10} x^3}{3}",1,"(-3*a^10 - 35*a^9*b*x - 189*a^8*b^2*x^2 - 630*a^7*b^3*x^3 - 1470*a^6*b^4*x^4 - 2646*a^5*b^5*x^5 - 4410*a^4*b^6*x^6 + 945*a^2*b^8*x^8 + 105*a*b^9*x^9 + 7*b^10*x^10)/(21*x^7) + 120*a^3*b^7*Log[x]","A",1
143,1,114,119,0.0239893,"\int \frac{(a+b x)^{10}}{x^9} \, dx","IntegrateAlgebraic[(a + b*x)^10/x^9,x]","45 a^2 b^8 \log (x)+\frac{-7 a^{10}-80 a^9 b x-420 a^8 b^2 x^2-1344 a^7 b^3 x^3-2940 a^6 b^4 x^4-4704 a^5 b^5 x^5-5880 a^4 b^6 x^6-6720 a^3 b^7 x^7+560 a b^9 x^9+28 b^{10} x^{10}}{56 x^8}","-\frac{a^{10}}{8 x^8}-\frac{10 a^9 b}{7 x^7}-\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)+10 a b^9 x+\frac{b^{10} x^2}{2}",1,"(-7*a^10 - 80*a^9*b*x - 420*a^8*b^2*x^2 - 1344*a^7*b^3*x^3 - 2940*a^6*b^4*x^4 - 4704*a^5*b^5*x^5 - 5880*a^4*b^6*x^6 - 6720*a^3*b^7*x^7 + 560*a*b^9*x^9 + 28*b^10*x^10)/(56*x^8) + 45*a^2*b^8*Log[x]","A",1
144,1,114,114,0.0255271,"\int \frac{(a+b x)^{10}}{x^{10}} \, dx","IntegrateAlgebraic[(a + b*x)^10/x^10,x]","\frac{-28 a^{10}-315 a^9 b x-1620 a^8 b^2 x^2-5040 a^7 b^3 x^3-10584 a^6 b^4 x^4-15876 a^5 b^5 x^5-17640 a^4 b^6 x^6-15120 a^3 b^7 x^7-11340 a^2 b^8 x^8+252 b^{10} x^{10}}{252 x^9}+10 a b^9 \log (x)","-\frac{a^{10}}{9 x^9}-\frac{5 a^9 b}{4 x^8}-\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}+10 a b^9 \log (x)+b^{10} x",1,"(-28*a^10 - 315*a^9*b*x - 1620*a^8*b^2*x^2 - 5040*a^7*b^3*x^3 - 10584*a^6*b^4*x^4 - 15876*a^5*b^5*x^5 - 17640*a^4*b^6*x^6 - 15120*a^3*b^7*x^7 - 11340*a^2*b^8*x^8 + 252*b^10*x^10)/(252*x^9) + 10*a*b^9*Log[x]","A",1
145,1,113,124,0.0254422,"\int \frac{(a+b x)^{10}}{x^{11}} \, dx","IntegrateAlgebraic[(a + b*x)^10/x^11,x]","\frac{-252 a^{10}-2800 a^9 b x-14175 a^8 b^2 x^2-43200 a^7 b^3 x^3-88200 a^6 b^4 x^4-127008 a^5 b^5 x^5-132300 a^4 b^6 x^6-100800 a^3 b^7 x^7-56700 a^2 b^8 x^8-25200 a b^9 x^9}{2520 x^{10}}+b^{10} \log (x)","-\frac{a^{10}}{10 x^{10}}-\frac{10 a^9 b}{9 x^9}-\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 b^9}{x}+b^{10} \log (x)",1,"(-252*a^10 - 2800*a^9*b*x - 14175*a^8*b^2*x^2 - 43200*a^7*b^3*x^3 - 88200*a^6*b^4*x^4 - 127008*a^5*b^5*x^5 - 132300*a^4*b^6*x^6 - 100800*a^3*b^7*x^7 - 56700*a^2*b^8*x^8 - 25200*a*b^9*x^9)/(2520*x^10) + b^10*Log[x]","A",1
146,1,114,17,0.01709,"\int \frac{(a+b x)^{10}}{x^{12}} \, dx","IntegrateAlgebraic[(a + b*x)^10/x^12,x]","\frac{-a^{10}-11 a^9 b x-55 a^8 b^2 x^2-165 a^7 b^3 x^3-330 a^6 b^4 x^4-462 a^5 b^5 x^5-462 a^4 b^6 x^6-330 a^3 b^7 x^7-165 a^2 b^8 x^8-55 a b^9 x^9-11 b^{10} x^{10}}{11 x^{11}}","-\frac{(a+b x)^{11}}{11 a x^{11}}",1,"(-a^10 - 11*a^9*b*x - 55*a^8*b^2*x^2 - 165*a^7*b^3*x^3 - 330*a^6*b^4*x^4 - 462*a^5*b^5*x^5 - 462*a^4*b^6*x^6 - 330*a^3*b^7*x^7 - 165*a^2*b^8*x^8 - 55*a*b^9*x^9 - 11*b^10*x^10)/(11*x^11)","B",1
147,1,114,36,0.0124487,"\int \frac{(a+b x)^{10}}{x^{13}} \, dx","IntegrateAlgebraic[(a + b*x)^10/x^13,x]","\frac{-11 a^{10}-120 a^9 b x-594 a^8 b^2 x^2-1760 a^7 b^3 x^3-3465 a^6 b^4 x^4-4752 a^5 b^5 x^5-4620 a^4 b^6 x^6-3168 a^3 b^7 x^7-1485 a^2 b^8 x^8-440 a b^9 x^9-66 b^{10} x^{10}}{132 x^{12}}","\frac{b (a+b x)^{11}}{132 a^2 x^{11}}-\frac{(a+b x)^{11}}{12 a x^{12}}",1,"(-11*a^10 - 120*a^9*b*x - 594*a^8*b^2*x^2 - 1760*a^7*b^3*x^3 - 3465*a^6*b^4*x^4 - 4752*a^5*b^5*x^5 - 4620*a^4*b^6*x^6 - 3168*a^3*b^7*x^7 - 1485*a^2*b^8*x^8 - 440*a*b^9*x^9 - 66*b^10*x^10)/(132*x^12)","B",1
148,1,114,56,0.0177034,"\int \frac{(a+b x)^{10}}{x^{14}} \, dx","IntegrateAlgebraic[(a + b*x)^10/x^14,x]","\frac{-66 a^{10}-715 a^9 b x-3510 a^8 b^2 x^2-10296 a^7 b^3 x^3-20020 a^6 b^4 x^4-27027 a^5 b^5 x^5-25740 a^4 b^6 x^6-17160 a^3 b^7 x^7-7722 a^2 b^8 x^8-2145 a b^9 x^9-286 b^{10} x^{10}}{858 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,"(-66*a^10 - 715*a^9*b*x - 3510*a^8*b^2*x^2 - 10296*a^7*b^3*x^3 - 20020*a^6*b^4*x^4 - 27027*a^5*b^5*x^5 - 25740*a^4*b^6*x^6 - 17160*a^3*b^7*x^7 - 7722*a^2*b^8*x^8 - 2145*a*b^9*x^9 - 286*b^10*x^10)/(858*x^13)","B",1
149,1,114,76,0.01876,"\int \frac{(a+b x)^{10}}{x^{15}} \, dx","IntegrateAlgebraic[(a + b*x)^10/x^15,x]","\frac{-286 a^{10}-3080 a^9 b x-15015 a^8 b^2 x^2-43680 a^7 b^3 x^3-84084 a^6 b^4 x^4-112112 a^5 b^5 x^5-105105 a^4 b^6 x^6-68640 a^3 b^7 x^7-30030 a^2 b^8 x^8-8008 a b^9 x^9-1001 b^{10} x^{10}}{4004 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,"(-286*a^10 - 3080*a^9*b*x - 15015*a^8*b^2*x^2 - 43680*a^7*b^3*x^3 - 84084*a^6*b^4*x^4 - 112112*a^5*b^5*x^5 - 105105*a^4*b^6*x^6 - 68640*a^3*b^7*x^7 - 30030*a^2*b^8*x^8 - 8008*a*b^9*x^9 - 1001*b^10*x^10)/(4004*x^14)","A",1
150,1,114,96,0.0178819,"\int \frac{(a+b x)^{10}}{x^{16}} \, dx","IntegrateAlgebraic[(a + b*x)^10/x^16,x]","\frac{-1001 a^{10}-10725 a^9 b x-51975 a^8 b^2 x^2-150150 a^7 b^3 x^3-286650 a^6 b^4 x^4-378378 a^5 b^5 x^5-350350 a^4 b^6 x^6-225225 a^3 b^7 x^7-96525 a^2 b^8 x^8-25025 a b^9 x^9-3003 b^{10} x^{10}}{15015 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,"(-1001*a^10 - 10725*a^9*b*x - 51975*a^8*b^2*x^2 - 150150*a^7*b^3*x^3 - 286650*a^6*b^4*x^4 - 378378*a^5*b^5*x^5 - 350350*a^4*b^6*x^6 - 225225*a^3*b^7*x^7 - 96525*a^2*b^8*x^8 - 25025*a*b^9*x^9 - 3003*b^10*x^10)/(15015*x^15)","A",1
151,1,114,116,0.0125146,"\int \frac{(a+b x)^{10}}{x^{17}} \, dx","IntegrateAlgebraic[(a + b*x)^10/x^17,x]","\frac{-3003 a^{10}-32032 a^9 b x-154440 a^8 b^2 x^2-443520 a^7 b^3 x^3-840840 a^6 b^4 x^4-1100736 a^5 b^5 x^5-1009008 a^4 b^6 x^6-640640 a^3 b^7 x^7-270270 a^2 b^8 x^8-68640 a b^9 x^9-8008 b^{10} x^{10}}{48048 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,"(-3003*a^10 - 32032*a^9*b*x - 154440*a^8*b^2*x^2 - 443520*a^7*b^3*x^3 - 840840*a^6*b^4*x^4 - 1100736*a^5*b^5*x^5 - 1009008*a^4*b^6*x^6 - 640640*a^3*b^7*x^7 - 270270*a^2*b^8*x^8 - 68640*a*b^9*x^9 - 8008*b^10*x^10)/(48048*x^16)","A",1
152,1,114,136,0.0183106,"\int \frac{(a+b x)^{10}}{x^{18}} \, dx","IntegrateAlgebraic[(a + b*x)^10/x^18,x]","\frac{-8008 a^{10}-85085 a^9 b x-408408 a^8 b^2 x^2-1166880 a^7 b^3 x^3-2199120 a^6 b^4 x^4-2858856 a^5 b^5 x^5-2598960 a^4 b^6 x^6-1633632 a^3 b^7 x^7-680680 a^2 b^8 x^8-170170 a b^9 x^9-19448 b^{10} x^{10}}{136136 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,"(-8008*a^10 - 85085*a^9*b*x - 408408*a^8*b^2*x^2 - 1166880*a^7*b^3*x^3 - 2199120*a^6*b^4*x^4 - 2858856*a^5*b^5*x^5 - 2598960*a^4*b^6*x^6 - 1633632*a^3*b^7*x^7 - 680680*a^2*b^8*x^8 - 170170*a*b^9*x^9 - 19448*b^10*x^10)/(136136*x^17)","A",1
153,1,114,130,0.0127237,"\int \frac{(a+b x)^{10}}{x^{19}} \, dx","IntegrateAlgebraic[(a + b*x)^10/x^19,x]","\frac{-19448 a^{10}-205920 a^9 b x-984555 a^8 b^2 x^2-2800512 a^7 b^3 x^3-5250960 a^6 b^4 x^4-6785856 a^5 b^5 x^5-6126120 a^4 b^6 x^6-3818880 a^3 b^7 x^7-1575288 a^2 b^8 x^8-388960 a b^9 x^9-43758 b^{10} x^{10}}{350064 x^{18}}","-\frac{a^{10}}{18 x^{18}}-\frac{10 a^9 b}{17 x^{17}}-\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 b^9}{9 x^9}-\frac{b^{10}}{8 x^8}",1,"(-19448*a^10 - 205920*a^9*b*x - 984555*a^8*b^2*x^2 - 2800512*a^7*b^3*x^3 - 5250960*a^6*b^4*x^4 - 6785856*a^5*b^5*x^5 - 6126120*a^4*b^6*x^6 - 3818880*a^3*b^7*x^7 - 1575288*a^2*b^8*x^8 - 388960*a*b^9*x^9 - 43758*b^10*x^10)/(350064*x^18)","A",1
154,1,114,126,0.0152835,"\int \frac{(a+b x)^{10}}{x^{20}} \, dx","IntegrateAlgebraic[(a + b*x)^10/x^20,x]","\frac{-43758 a^{10}-461890 a^9 b x-2200770 a^8 b^2 x^2-6235515 a^7 b^3 x^3-11639628 a^6 b^4 x^4-14965236 a^5 b^5 x^5-13430340 a^4 b^6 x^6-8314020 a^3 b^7 x^7-3401190 a^2 b^8 x^8-831402 a b^9 x^9-92378 b^{10} x^{10}}{831402 x^{19}}","-\frac{a^{10}}{19 x^{19}}-\frac{5 a^9 b}{9 x^{18}}-\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{a b^9}{x^{10}}-\frac{b^{10}}{9 x^9}",1,"(-43758*a^10 - 461890*a^9*b*x - 2200770*a^8*b^2*x^2 - 6235515*a^7*b^3*x^3 - 11639628*a^6*b^4*x^4 - 14965236*a^5*b^5*x^5 - 13430340*a^4*b^6*x^6 - 8314020*a^3*b^7*x^7 - 3401190*a^2*b^8*x^8 - 831402*a*b^9*x^9 - 92378*b^10*x^10)/(831402*x^19)","A",1
155,1,13,15,0.0031377,"\int c (a+b x) \, dx","IntegrateAlgebraic[c*(a + b*x),x]","\frac{1}{2} c x (2 a+b x)","\frac{c (a+b x)^2}{2 b}",1,"(c*x*(2*a + b*x))/2","A",1
156,1,18,20,0.0062652,"\int \frac{(c+d) (a+b x)}{e} \, dx","IntegrateAlgebraic[((c + d)*(a + b*x))/e,x]","\frac{x (c+d) (2 a+b x)}{2 e}","\frac{(c+d) (a+b x)^2}{2 b e}",1,"((c + d)*x*(2*a + b*x))/(2*e)","A",1
157,1,64,70,0.0138857,"\int \frac{x^5}{a+b x} \, dx","IntegrateAlgebraic[x^5/(a + b*x),x]","\frac{x \left(60 a^4-30 a^3 b x+20 a^2 b^2 x^2-15 a b^3 x^3+12 b^4 x^4\right)}{60 b^5}-\frac{a^5 \log (a+b x)}{b^6}","-\frac{a^5 \log (a+b x)}{b^6}+\frac{a^4 x}{b^5}-\frac{a^3 x^2}{2 b^4}+\frac{a^2 x^3}{3 b^3}-\frac{a x^4}{4 b^2}+\frac{x^5}{5 b}",1,"(x*(60*a^4 - 30*a^3*b*x + 20*a^2*b^2*x^2 - 15*a*b^3*x^3 + 12*b^4*x^4))/(60*b^5) - (a^5*Log[a + b*x])/b^6","A",1
158,1,52,57,0.0125322,"\int \frac{x^4}{a+b x} \, dx","IntegrateAlgebraic[x^4/(a + b*x),x]","\frac{a^4 \log (a+b x)}{b^5}+\frac{x \left(-12 a^3+6 a^2 b x-4 a b^2 x^2+3 b^3 x^3\right)}{12 b^4}","\frac{a^4 \log (a+b x)}{b^5}-\frac{a^3 x}{b^4}+\frac{a^2 x^2}{2 b^3}-\frac{a x^3}{3 b^2}+\frac{x^4}{4 b}",1,"(x*(-12*a^3 + 6*a^2*b*x - 4*a*b^2*x^2 + 3*b^3*x^3))/(12*b^4) + (a^4*Log[a + b*x])/b^5","A",1
159,1,42,44,0.0108489,"\int \frac{x^3}{a+b x} \, dx","IntegrateAlgebraic[x^3/(a + b*x),x]","\frac{x \left(6 a^2-3 a b x+2 b^2 x^2\right)}{6 b^3}-\frac{a^3 \log (a+b x)}{b^4}","-\frac{a^3 \log (a+b x)}{b^4}+\frac{a^2 x}{b^3}-\frac{a x^2}{2 b^2}+\frac{x^3}{3 b}",1,"(x*(6*a^2 - 3*a*b*x + 2*b^2*x^2))/(6*b^3) - (a^3*Log[a + b*x])/b^4","A",1
160,1,29,31,0.008918,"\int \frac{x^2}{a+b x} \, dx","IntegrateAlgebraic[x^2/(a + b*x),x]","\frac{a^2 \log (a+b x)}{b^3}+\frac{x (b x-2 a)}{2 b^2}","\frac{a^2 \log (a+b x)}{b^3}-\frac{a x}{b^2}+\frac{x^2}{2 b}",1,"(x*(-2*a + b*x))/(2*b^2) + (a^2*Log[a + b*x])/b^3","A",1
161,1,18,18,0.005778,"\int \frac{x}{a+b x} \, dx","IntegrateAlgebraic[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",1
162,1,10,10,0.0028005,"\int \frac{1}{a+b x} \, dx","IntegrateAlgebraic[(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
163,1,18,18,0.0083086,"\int \frac{1}{x (a+b x)} \, dx","IntegrateAlgebraic[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",1
164,1,28,28,0.0094618,"\int \frac{1}{x^2 (a+b x)} \, dx","IntegrateAlgebraic[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",1
165,1,42,42,0.0129522,"\int \frac{1}{x^3 (a+b x)} \, dx","IntegrateAlgebraic[1/(x^3*(a + b*x)),x]","\frac{b^2 \log (x)}{a^3}-\frac{b^2 \log (a+b x)}{a^3}+\frac{2 b x-a}{2 a^2 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,"(-a + 2*b*x)/(2*a^2*x^2) + (b^2*Log[x])/a^3 - (b^2*Log[a + b*x])/a^3","A",1
166,1,53,56,0.0154965,"\int \frac{1}{x^4 (a+b x)} \, dx","IntegrateAlgebraic[1/(x^4*(a + b*x)),x]","-\frac{b^3 \log (x)}{a^4}+\frac{b^3 \log (a+b x)}{a^4}+\frac{-2 a^2+3 a b x-6 b^2 x^2}{6 a^3 x^3}","-\frac{b^3 \log (x)}{a^4}+\frac{b^3 \log (a+b x)}{a^4}-\frac{b^2}{a^3 x}+\frac{b}{2 a^2 x^2}-\frac{1}{3 a x^3}",1,"(-2*a^2 + 3*a*b*x - 6*b^2*x^2)/(6*a^3*x^3) - (b^3*Log[x])/a^4 + (b^3*Log[a + b*x])/a^4","A",1
167,1,64,68,0.0157696,"\int \frac{1}{x^5 (a+b x)} \, dx","IntegrateAlgebraic[1/(x^5*(a + b*x)),x]","\frac{b^4 \log (x)}{a^5}-\frac{b^4 \log (a+b x)}{a^5}+\frac{-3 a^3+4 a^2 b x-6 a b^2 x^2+12 b^3 x^3}{12 a^4 x^4}","\frac{b^4 \log (x)}{a^5}-\frac{b^4 \log (a+b x)}{a^5}+\frac{b^3}{a^4 x}-\frac{b^2}{2 a^3 x^2}+\frac{b}{3 a^2 x^3}-\frac{1}{4 a x^4}",1,"(-3*a^3 + 4*a^2*b*x - 6*a*b^2*x^2 + 12*b^3*x^3)/(12*a^4*x^4) + (b^4*Log[x])/a^5 - (b^4*Log[a + b*x])/a^5","A",1
168,1,92,81,0.0340688,"\int \frac{x^6}{(a+b x)^2} \, dx","IntegrateAlgebraic[x^6/(a + b*x)^2,x]","\frac{-10 a^6+50 a^5 b x+30 a^4 b^2 x^2-10 a^3 b^3 x^3+5 a^2 b^4 x^4-3 a b^5 x^5+2 b^6 x^6}{10 b^7 (a+b x)}-\frac{6 a^5 \log (a+b x)}{b^7}","-\frac{a^6}{b^7 (a+b x)}-\frac{6 a^5 \log (a+b x)}{b^7}+\frac{5 a^4 x}{b^6}-\frac{2 a^3 x^2}{b^5}+\frac{a^2 x^3}{b^4}-\frac{a x^4}{2 b^3}+\frac{x^5}{5 b^2}",1,"(-10*a^6 + 50*a^5*b*x + 30*a^4*b^2*x^2 - 10*a^3*b^3*x^3 + 5*a^2*b^4*x^4 - 3*a*b^5*x^5 + 2*b^6*x^6)/(10*b^7*(a + b*x)) - (6*a^5*Log[a + b*x])/b^7","A",1
169,1,81,72,0.0262476,"\int \frac{x^5}{(a+b x)^2} \, dx","IntegrateAlgebraic[x^5/(a + b*x)^2,x]","\frac{5 a^4 \log (a+b x)}{b^6}+\frac{12 a^5-48 a^4 b x-30 a^3 b^2 x^2+10 a^2 b^3 x^3-5 a b^4 x^4+3 b^5 x^5}{12 b^6 (a+b x)}","\frac{a^5}{b^6 (a+b x)}+\frac{5 a^4 \log (a+b x)}{b^6}-\frac{4 a^3 x}{b^5}+\frac{3 a^2 x^2}{2 b^4}-\frac{2 a x^3}{3 b^3}+\frac{x^4}{4 b^2}",1,"(12*a^5 - 48*a^4*b*x - 30*a^3*b^2*x^2 + 10*a^2*b^3*x^3 - 5*a*b^4*x^4 + 3*b^5*x^5)/(12*b^6*(a + b*x)) + (5*a^4*Log[a + b*x])/b^6","A",1
170,1,69,58,0.0282668,"\int \frac{x^4}{(a+b x)^2} \, dx","IntegrateAlgebraic[x^4/(a + b*x)^2,x]","\frac{-3 a^4+9 a^3 b x+6 a^2 b^2 x^2-2 a b^3 x^3+b^4 x^4}{3 b^5 (a+b x)}-\frac{4 a^3 \log (a+b x)}{b^5}","-\frac{a^4}{b^5 (a+b x)}-\frac{4 a^3 \log (a+b x)}{b^5}+\frac{3 a^2 x}{b^4}-\frac{a x^2}{b^3}+\frac{x^3}{3 b^2}",1,"(-3*a^4 + 9*a^3*b*x + 6*a^2*b^2*x^2 - 2*a*b^3*x^3 + b^4*x^4)/(3*b^5*(a + b*x)) - (4*a^3*Log[a + b*x])/b^5","A",1
171,1,58,46,0.020839,"\int \frac{x^3}{(a+b x)^2} \, dx","IntegrateAlgebraic[x^3/(a + b*x)^2,x]","\frac{3 a^2 \log (a+b x)}{b^4}+\frac{2 a^3-4 a^2 b x-3 a b^2 x^2+b^3 x^3}{2 b^4 (a+b 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}",1,"(2*a^3 - 4*a^2*b*x - 3*a*b^2*x^2 + b^3*x^3)/(2*b^4*(a + b*x)) + (3*a^2*Log[a + b*x])/b^4","A",1
172,1,41,33,0.0191505,"\int \frac{x^2}{(a+b x)^2} \, dx","IntegrateAlgebraic[x^2/(a + b*x)^2,x]","\frac{-a^2+a b x+b^2 x^2}{b^3 (a+b x)}-\frac{2 a \log (a+b x)}{b^3}","-\frac{a^2}{b^3 (a+b x)}-\frac{2 a \log (a+b x)}{b^3}+\frac{x}{b^2}",1,"(-a^2 + a*b*x + b^2*x^2)/(b^3*(a + b*x)) - (2*a*Log[a + b*x])/b^3","A",1
173,1,23,23,0.0111888,"\int \frac{x}{(a+b x)^2} \, dx","IntegrateAlgebraic[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",1
174,1,12,12,0.0050878,"\int \frac{1}{(a+b x)^2} \, dx","IntegrateAlgebraic[(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
175,1,29,29,0.0190874,"\int \frac{1}{x (a+b x)^2} \, dx","IntegrateAlgebraic[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",1
176,1,43,42,0.0447287,"\int \frac{1}{x^2 (a+b x)^2} \, dx","IntegrateAlgebraic[1/(x^2*(a + b*x)^2),x]","-\frac{2 b \log (x)}{a^3}+\frac{2 b \log (a+b x)}{a^3}+\frac{-a-2 b x}{a^2 x (a+b x)}","-\frac{2 b \log (x)}{a^3}+\frac{2 b \log (a+b x)}{a^3}-\frac{b}{a^2 (a+b x)}-\frac{1}{a^2 x}",1,"(-a - 2*b*x)/(a^2*x*(a + b*x)) - (2*b*Log[x])/a^3 + (2*b*Log[a + b*x])/a^3","A",1
177,1,61,58,0.0528734,"\int \frac{1}{x^3 (a+b x)^2} \, dx","IntegrateAlgebraic[1/(x^3*(a + b*x)^2),x]","\frac{3 b^2 \log (x)}{a^4}-\frac{3 b^2 \log (a+b x)}{a^4}+\frac{-a^2+3 a b x+6 b^2 x^2}{2 a^3 x^2 (a+b x)}","\frac{3 b^2 \log (x)}{a^4}-\frac{3 b^2 \log (a+b x)}{a^4}+\frac{b^2}{a^3 (a+b x)}+\frac{2 b}{a^3 x}-\frac{1}{2 a^2 x^2}",1,"(-a^2 + 3*a*b*x + 6*b^2*x^2)/(2*a^3*x^2*(a + b*x)) + (3*b^2*Log[x])/a^4 - (3*b^2*Log[a + b*x])/a^4","A",1
178,1,72,69,0.0600831,"\int \frac{1}{x^4 (a+b x)^2} \, dx","IntegrateAlgebraic[1/(x^4*(a + b*x)^2),x]","-\frac{4 b^3 \log (x)}{a^5}+\frac{4 b^3 \log (a+b x)}{a^5}+\frac{-a^3+2 a^2 b x-6 a b^2 x^2-12 b^3 x^3}{3 a^4 x^3 (a+b x)}","-\frac{4 b^3 \log (x)}{a^5}+\frac{4 b^3 \log (a+b x)}{a^5}-\frac{b^3}{a^4 (a+b x)}-\frac{3 b^2}{a^4 x}+\frac{b}{a^3 x^2}-\frac{1}{3 a^2 x^3}",1,"(-a^3 + 2*a^2*b*x - 6*a*b^2*x^2 - 12*b^3*x^3)/(3*a^4*x^3*(a + b*x)) - (4*b^3*Log[x])/a^5 + (4*b^3*Log[a + b*x])/a^5","A",1
179,1,83,84,0.0509633,"\int \frac{1}{x^5 (a+b x)^2} \, dx","IntegrateAlgebraic[1/(x^5*(a + b*x)^2),x]","\frac{5 b^4 \log (x)}{a^6}-\frac{5 b^4 \log (a+b x)}{a^6}+\frac{-3 a^4+5 a^3 b x-10 a^2 b^2 x^2+30 a b^3 x^3+60 b^4 x^4}{12 a^5 x^4 (a+b x)}","\frac{5 b^4 \log (x)}{a^6}-\frac{5 b^4 \log (a+b x)}{a^6}+\frac{b^4}{a^5 (a+b x)}+\frac{4 b^3}{a^5 x}-\frac{3 b^2}{2 a^4 x^2}+\frac{2 b}{3 a^3 x^3}-\frac{1}{4 a^2 x^4}",1,"(-3*a^4 + 5*a^3*b*x - 10*a^2*b^2*x^2 + 30*a*b^3*x^3 + 60*b^4*x^4)/(12*a^5*x^4*(a + b*x)) + (5*b^4*Log[x])/a^6 - (5*b^4*Log[a + b*x])/a^6","A",1
180,1,103,99,0.0362128,"\int \frac{x^7}{(a+b x)^3} \, dx","IntegrateAlgebraic[x^7/(a + b*x)^3,x]","\frac{-130 a^7+160 a^6 b x+500 a^5 b^2 x^2+140 a^4 b^3 x^3-35 a^3 b^4 x^4+14 a^2 b^5 x^5-7 a b^6 x^6+4 b^7 x^7}{20 b^8 (a+b x)^2}-\frac{21 a^5 \log (a+b x)}{b^8}","\frac{a^7}{2 b^8 (a+b x)^2}-\frac{7 a^6}{b^8 (a+b x)}-\frac{21 a^5 \log (a+b x)}{b^8}+\frac{15 a^4 x}{b^7}-\frac{5 a^3 x^2}{b^6}+\frac{2 a^2 x^3}{b^5}-\frac{3 a x^4}{4 b^4}+\frac{x^5}{5 b^3}",1,"(-130*a^7 + 160*a^6*b*x + 500*a^5*b^2*x^2 + 140*a^4*b^3*x^3 - 35*a^3*b^4*x^4 + 14*a^2*b^5*x^5 - 7*a*b^6*x^6 + 4*b^7*x^7)/(20*b^8*(a + b*x)^2) - (21*a^5*Log[a + b*x])/b^8","A",1
181,1,91,86,0.0346769,"\int \frac{x^6}{(a+b x)^3} \, dx","IntegrateAlgebraic[x^6/(a + b*x)^3,x]","\frac{15 a^4 \log (a+b x)}{b^7}+\frac{22 a^6-16 a^5 b x-68 a^4 b^2 x^2-20 a^3 b^3 x^3+5 a^2 b^4 x^4-2 a b^5 x^5+b^6 x^6}{4 b^7 (a+b x)^2}","-\frac{a^6}{2 b^7 (a+b x)^2}+\frac{6 a^5}{b^7 (a+b x)}+\frac{15 a^4 \log (a+b x)}{b^7}-\frac{10 a^3 x}{b^6}+\frac{3 a^2 x^2}{b^5}-\frac{a x^3}{b^4}+\frac{x^4}{4 b^3}",1,"(22*a^6 - 16*a^5*b*x - 68*a^4*b^2*x^2 - 20*a^3*b^3*x^3 + 5*a^2*b^4*x^4 - 2*a*b^5*x^5 + b^6*x^6)/(4*b^7*(a + b*x)^2) + (15*a^4*Log[a + b*x])/b^7","A",1
182,1,81,77,0.0300451,"\int \frac{x^5}{(a+b x)^3} \, dx","IntegrateAlgebraic[x^5/(a + b*x)^3,x]","\frac{-27 a^5+6 a^4 b x+63 a^3 b^2 x^2+20 a^2 b^3 x^3-5 a b^4 x^4+2 b^5 x^5}{6 b^6 (a+b x)^2}-\frac{10 a^3 \log (a+b x)}{b^6}","\frac{a^5}{2 b^6 (a+b x)^2}-\frac{5 a^4}{b^6 (a+b x)}-\frac{10 a^3 \log (a+b x)}{b^6}+\frac{6 a^2 x}{b^5}-\frac{3 a x^2}{2 b^4}+\frac{x^3}{3 b^3}",1,"(-27*a^5 + 6*a^4*b*x + 63*a^3*b^2*x^2 + 20*a^2*b^3*x^3 - 5*a*b^4*x^4 + 2*b^5*x^5)/(6*b^6*(a + b*x)^2) - (10*a^3*Log[a + b*x])/b^6","A",1
183,1,69,64,0.0280336,"\int \frac{x^4}{(a+b x)^3} \, dx","IntegrateAlgebraic[x^4/(a + b*x)^3,x]","\frac{6 a^2 \log (a+b x)}{b^5}+\frac{7 a^4+2 a^3 b x-11 a^2 b^2 x^2-4 a b^3 x^3+b^4 x^4}{2 b^5 (a+b x)^2}","-\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,"(7*a^4 + 2*a^3*b*x - 11*a^2*b^2*x^2 - 4*a*b^3*x^3 + b^4*x^4)/(2*b^5*(a + b*x)^2) + (6*a^2*Log[a + b*x])/b^5","A",1
184,1,57,50,0.0460434,"\int \frac{x^3}{(a+b x)^3} \, dx","IntegrateAlgebraic[x^3/(a + b*x)^3,x]","\frac{-5 a^3-4 a^2 b x+4 a b^2 x^2+2 b^3 x^3}{2 b^4 (a+b x)^2}-\frac{3 a \log (a+b x)}{b^4}","\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,"(-5*a^3 - 4*a^2*b*x + 4*a*b^2*x^2 + 2*b^3*x^3)/(2*b^4*(a + b*x)^2) - (3*a*Log[a + b*x])/b^4","A",1
185,1,34,41,0.0207817,"\int \frac{x^2}{(a+b x)^3} \, dx","IntegrateAlgebraic[x^2/(a + b*x)^3,x]","\frac{a (3 a+4 b x)}{2 b^3 (a+b x)^2}+\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*(3*a + 4*b*x))/(2*b^3*(a + b*x)^2) + Log[a + b*x]/b^3","A",1
186,1,22,17,0.0082451,"\int \frac{x}{(a+b x)^3} \, dx","IntegrateAlgebraic[x/(a + b*x)^3,x]","\frac{-a-2 b x}{2 b^2 (a+b x)^2}","\frac{x^2}{2 a (a+b x)^2}",1,"(-a - 2*b*x)/(2*b^2*(a + b*x)^2)","A",1
187,1,14,14,0.0053577,"\int \frac{1}{(a+b x)^3} \, dx","IntegrateAlgebraic[(a + b*x)^(-3),x]","-\frac{1}{2 b (a+b x)^2}","-\frac{1}{2 b (a+b x)^2}",1,"-1/2*1/(b*(a + b*x)^2)","A",1
188,1,40,43,0.0337481,"\int \frac{1}{x (a+b x)^3} \, dx","IntegrateAlgebraic[1/(x*(a + b*x)^3),x]","-\frac{\log (a+b x)}{a^3}+\frac{\log (x)}{a^3}+\frac{3 a+2 b x}{2 a^2 (a+b x)^2}","-\frac{\log (a+b x)}{a^3}+\frac{\log (x)}{a^3}+\frac{1}{a^2 (a+b x)}+\frac{1}{2 a (a+b x)^2}",1,"(3*a + 2*b*x)/(2*a^2*(a + b*x)^2) + Log[x]/a^3 - Log[a + b*x]/a^3","A",1
189,1,57,57,0.0550375,"\int \frac{1}{x^2 (a+b x)^3} \, dx","IntegrateAlgebraic[1/(x^2*(a + b*x)^3),x]","-\frac{3 b \log (x)}{a^4}+\frac{3 b \log (a+b x)}{a^4}+\frac{-2 a^2-9 a b x-6 b^2 x^2}{2 a^3 x (a+b x)^2}","-\frac{3 b \log (x)}{a^4}+\frac{3 b \log (a+b x)}{a^4}-\frac{2 b}{a^3 (a+b x)}-\frac{1}{a^3 x}-\frac{b}{2 a^2 (a+b x)^2}",1,"(-2*a^2 - 9*a*b*x - 6*b^2*x^2)/(2*a^3*x*(a + b*x)^2) - (3*b*Log[x])/a^4 + (3*b*Log[a + b*x])/a^4","A",1
190,1,72,76,0.0536334,"\int \frac{1}{x^3 (a+b x)^3} \, dx","IntegrateAlgebraic[1/(x^3*(a + b*x)^3),x]","\frac{6 b^2 \log (x)}{a^5}-\frac{6 b^2 \log (a+b x)}{a^5}+\frac{-a^3+4 a^2 b x+18 a b^2 x^2+12 b^3 x^3}{2 a^4 x^2 (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^2}{a^4 (a+b x)}+\frac{3 b}{a^4 x}+\frac{b^2}{2 a^3 (a+b x)^2}-\frac{1}{2 a^3 x^2}",1,"(-a^3 + 4*a^2*b*x + 18*a*b^2*x^2 + 12*b^3*x^3)/(2*a^4*x^2*(a + b*x)^2) + (6*b^2*Log[x])/a^5 - (6*b^2*Log[a + b*x])/a^5","A",1
191,1,83,89,0.0728227,"\int \frac{1}{x^4 (a+b x)^3} \, dx","IntegrateAlgebraic[1/(x^4*(a + b*x)^3),x]","-\frac{10 b^3 \log (x)}{a^6}+\frac{10 b^3 \log (a+b x)}{a^6}+\frac{-2 a^4+5 a^3 b x-20 a^2 b^2 x^2-90 a b^3 x^3-60 b^4 x^4}{6 a^5 x^3 (a+b x)^2}","-\frac{10 b^3 \log (x)}{a^6}+\frac{10 b^3 \log (a+b x)}{a^6}-\frac{4 b^3}{a^5 (a+b x)}-\frac{6 b^2}{a^5 x}-\frac{b^3}{2 a^4 (a+b x)^2}+\frac{3 b}{2 a^4 x^2}-\frac{1}{3 a^3 x^3}",1,"(-2*a^4 + 5*a^3*b*x - 20*a^2*b^2*x^2 - 90*a*b^3*x^3 - 60*b^4*x^4)/(6*a^5*x^3*(a + b*x)^2) - (10*b^3*Log[x])/a^6 + (10*b^3*Log[a + b*x])/a^6","A",1
192,1,94,97,0.063356,"\int \frac{1}{x^5 (a+b x)^3} \, dx","IntegrateAlgebraic[1/(x^5*(a + b*x)^3),x]","\frac{15 b^4 \log (x)}{a^7}-\frac{15 b^4 \log (a+b x)}{a^7}+\frac{-a^5+2 a^4 b x-5 a^3 b^2 x^2+20 a^2 b^3 x^3+90 a b^4 x^4+60 b^5 x^5}{4 a^6 x^4 (a+b x)^2}","\frac{15 b^4 \log (x)}{a^7}-\frac{15 b^4 \log (a+b x)}{a^7}+\frac{5 b^4}{a^6 (a+b x)}+\frac{10 b^3}{a^6 x}+\frac{b^4}{2 a^5 (a+b x)^2}-\frac{3 b^2}{a^5 x^2}+\frac{b}{a^4 x^3}-\frac{1}{4 a^3 x^4}",1,"(-a^5 + 2*a^4*b*x - 5*a^3*b^2*x^2 + 20*a^2*b^3*x^3 + 90*a*b^4*x^4 + 60*b^5*x^5)/(4*a^6*x^4*(a + b*x)^2) + (15*b^4*Log[x])/a^7 - (15*b^4*Log[a + b*x])/a^7","A",1
193,1,114,114,0.0467532,"\int \frac{x^8}{(a+b x)^4} \, dx","IntegrateAlgebraic[x^8/(a + b*x)^4,x]","\frac{-365 a^8-255 a^7 b x+1005 a^6 b^2 x^2+1175 a^5 b^3 x^3+210 a^4 b^4 x^4-42 a^3 b^5 x^5+14 a^2 b^6 x^6-6 a b^7 x^7+3 b^8 x^8}{15 b^9 (a+b x)^3}-\frac{56 a^5 \log (a+b x)}{b^9}","-\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{56 a^5 \log (a+b x)}{b^9}+\frac{35 a^4 x}{b^8}-\frac{10 a^3 x^2}{b^7}+\frac{10 a^2 x^3}{3 b^6}-\frac{a x^4}{b^5}+\frac{x^5}{5 b^4}",1,"(-365*a^8 - 255*a^7*b*x + 1005*a^6*b^2*x^2 + 1175*a^5*b^3*x^3 + 210*a^4*b^4*x^4 - 42*a^3*b^5*x^5 + 14*a^2*b^6*x^6 - 6*a*b^7*x^7 + 3*b^8*x^8)/(15*b^9*(a + b*x)^3) - (56*a^5*Log[a + b*x])/b^9","A",1
194,1,103,105,0.0403592,"\int \frac{x^7}{(a+b x)^4} \, dx","IntegrateAlgebraic[x^7/(a + b*x)^4,x]","\frac{35 a^4 \log (a+b x)}{b^8}+\frac{214 a^7+222 a^6 b x-408 a^5 b^2 x^2-556 a^4 b^3 x^3-105 a^3 b^4 x^4+21 a^2 b^5 x^5-7 a b^6 x^6+3 b^7 x^7}{12 b^8 (a+b x)^3}","\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{35 a^4 \log (a+b x)}{b^8}-\frac{20 a^3 x}{b^7}+\frac{5 a^2 x^2}{b^6}-\frac{4 a x^3}{3 b^5}+\frac{x^4}{4 b^4}",1,"(214*a^7 + 222*a^6*b*x - 408*a^5*b^2*x^2 - 556*a^4*b^3*x^3 - 105*a^3*b^4*x^4 + 21*a^2*b^5*x^5 - 7*a*b^6*x^6 + 3*b^7*x^7)/(12*b^8*(a + b*x)^3) + (35*a^4*Log[a + b*x])/b^8","A",1
195,1,91,90,0.0304671,"\int \frac{x^6}{(a+b x)^4} \, dx","IntegrateAlgebraic[x^6/(a + b*x)^4,x]","\frac{-37 a^6-51 a^5 b x+39 a^4 b^2 x^2+73 a^3 b^3 x^3+15 a^2 b^4 x^4-3 a b^5 x^5+b^6 x^6}{3 b^7 (a+b x)^3}-\frac{20 a^3 \log (a+b x)}{b^7}","-\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{20 a^3 \log (a+b x)}{b^7}+\frac{10 a^2 x}{b^6}-\frac{2 a x^2}{b^5}+\frac{x^3}{3 b^4}",1,"(-37*a^6 - 51*a^5*b*x + 39*a^4*b^2*x^2 + 73*a^3*b^3*x^3 + 15*a^2*b^4*x^4 - 3*a*b^5*x^5 + b^6*x^6)/(3*b^7*(a + b*x)^3) - (20*a^3*Log[a + b*x])/b^7","A",1
196,1,81,81,0.0338633,"\int \frac{x^5}{(a+b x)^4} \, dx","IntegrateAlgebraic[x^5/(a + b*x)^4,x]","\frac{10 a^2 \log (a+b x)}{b^6}+\frac{47 a^5+81 a^4 b x-9 a^3 b^2 x^2-63 a^2 b^3 x^3-15 a b^4 x^4+3 b^5 x^5}{6 b^6 (a+b x)^3}","\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,"(47*a^5 + 81*a^4*b*x - 9*a^3*b^2*x^2 - 63*a^2*b^3*x^3 - 15*a*b^4*x^4 + 3*b^5*x^5)/(6*b^6*(a + b*x)^3) + (10*a^2*Log[a + b*x])/b^6","A",1
197,1,68,65,0.0517059,"\int \frac{x^4}{(a+b x)^4} \, dx","IntegrateAlgebraic[x^4/(a + b*x)^4,x]","\frac{-13 a^4-27 a^3 b x-9 a^2 b^2 x^2+9 a b^3 x^3+3 b^4 x^4}{3 b^5 (a+b x)^3}-\frac{4 a \log (a+b x)}{b^5}","-\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,"(-13*a^4 - 27*a^3*b*x - 9*a^2*b^2*x^2 + 9*a*b^3*x^3 + 3*b^4*x^4)/(3*b^5*(a + b*x)^3) - (4*a*Log[a + b*x])/b^5","A",1
198,1,45,58,0.0234482,"\int \frac{x^3}{(a+b x)^4} \, dx","IntegrateAlgebraic[x^3/(a + b*x)^4,x]","\frac{a \left(11 a^2+27 a b x+18 b^2 x^2\right)}{6 b^4 (a+b x)^3}+\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*(11*a^2 + 27*a*b*x + 18*b^2*x^2))/(6*b^4*(a + b*x)^3) + Log[a + b*x]/b^4","A",1
199,1,33,17,0.0137685,"\int \frac{x^2}{(a+b x)^4} \, dx","IntegrateAlgebraic[x^2/(a + b*x)^4,x]","\frac{-a^2-3 a b x-3 b^2 x^2}{3 b^3 (a+b x)^3}","\frac{x^3}{3 a (a+b x)^3}",1,"(-a^2 - 3*a*b*x - 3*b^2*x^2)/(3*b^3*(a + b*x)^3)","A",1
200,1,22,30,0.009271,"\int \frac{x}{(a+b x)^4} \, dx","IntegrateAlgebraic[x/(a + b*x)^4,x]","\frac{-a-3 b x}{6 b^2 (a+b x)^3}","\frac{a}{3 b^2 (a+b x)^3}-\frac{1}{2 b^2 (a+b x)^2}",1,"(-a - 3*b*x)/(6*b^2*(a + b*x)^3)","A",1
201,1,14,14,0.0059005,"\int \frac{1}{(a+b x)^4} \, dx","IntegrateAlgebraic[(a + b*x)^(-4),x]","-\frac{1}{3 b (a+b x)^3}","-\frac{1}{3 b (a+b x)^3}",1,"-1/3*1/(b*(a + b*x)^3)","A",1
202,1,51,57,0.0394219,"\int \frac{1}{x (a+b x)^4} \, dx","IntegrateAlgebraic[1/(x*(a + b*x)^4),x]","-\frac{\log (a+b x)}{a^4}+\frac{\log (x)}{a^4}+\frac{11 a^2+15 a b x+6 b^2 x^2}{6 a^3 (a+b x)^3}","-\frac{\log (a+b x)}{a^4}+\frac{\log (x)}{a^4}+\frac{1}{a^3 (a+b x)}+\frac{1}{2 a^2 (a+b x)^2}+\frac{1}{3 a (a+b x)^3}",1,"(11*a^2 + 15*a*b*x + 6*b^2*x^2)/(6*a^3*(a + b*x)^3) + Log[x]/a^4 - Log[a + b*x]/a^4","A",1
203,1,68,70,0.0651493,"\int \frac{1}{x^2 (a+b x)^4} \, dx","IntegrateAlgebraic[1/(x^2*(a + b*x)^4),x]","-\frac{4 b \log (x)}{a^5}+\frac{4 b \log (a+b x)}{a^5}+\frac{-3 a^3-22 a^2 b x-30 a b^2 x^2-12 b^3 x^3}{3 a^4 x (a+b x)^3}","-\frac{4 b \log (x)}{a^5}+\frac{4 b \log (a+b x)}{a^5}-\frac{3 b}{a^4 (a+b x)}-\frac{1}{a^4 x}-\frac{b}{a^3 (a+b x)^2}-\frac{b}{3 a^2 (a+b x)^3}",1,"(-3*a^3 - 22*a^2*b*x - 30*a*b^2*x^2 - 12*b^3*x^3)/(3*a^4*x*(a + b*x)^3) - (4*b*Log[x])/a^5 + (4*b*Log[a + b*x])/a^5","A",1
204,1,83,93,0.0617722,"\int \frac{1}{x^3 (a+b x)^4} \, dx","IntegrateAlgebraic[1/(x^3*(a + b*x)^4),x]","\frac{10 b^2 \log (x)}{a^6}-\frac{10 b^2 \log (a+b x)}{a^6}+\frac{-3 a^4+15 a^3 b x+110 a^2 b^2 x^2+150 a b^3 x^3+60 b^4 x^4}{6 a^5 x^2 (a+b x)^3}","\frac{10 b^2 \log (x)}{a^6}-\frac{10 b^2 \log (a+b x)}{a^6}+\frac{6 b^2}{a^5 (a+b x)}+\frac{4 b}{a^5 x}+\frac{3 b^2}{2 a^4 (a+b x)^2}-\frac{1}{2 a^4 x^2}+\frac{b^2}{3 a^3 (a+b x)^3}",1,"(-3*a^4 + 15*a^3*b*x + 110*a^2*b^2*x^2 + 150*a*b^3*x^3 + 60*b^4*x^4)/(6*a^5*x^2*(a + b*x)^3) + (10*b^2*Log[x])/a^6 - (10*b^2*Log[a + b*x])/a^6","A",1
205,1,94,102,0.0668781,"\int \frac{1}{x^4 (a+b x)^4} \, dx","IntegrateAlgebraic[1/(x^4*(a + b*x)^4),x]","-\frac{20 b^3 \log (x)}{a^7}+\frac{20 b^3 \log (a+b x)}{a^7}+\frac{-a^5+3 a^4 b x-15 a^3 b^2 x^2-110 a^2 b^3 x^3-150 a b^4 x^4-60 b^5 x^5}{3 a^6 x^3 (a+b x)^3}","-\frac{20 b^3 \log (x)}{a^7}+\frac{20 b^3 \log (a+b x)}{a^7}-\frac{10 b^3}{a^6 (a+b x)}-\frac{10 b^2}{a^6 x}-\frac{2 b^3}{a^5 (a+b x)^2}+\frac{2 b}{a^5 x^2}-\frac{b^3}{3 a^4 (a+b x)^3}-\frac{1}{3 a^4 x^3}",1,"(-a^5 + 3*a^4*b*x - 15*a^3*b^2*x^2 - 110*a^2*b^3*x^3 - 150*a*b^4*x^4 - 60*b^5*x^5)/(3*a^6*x^3*(a + b*x)^3) - (20*b^3*Log[x])/a^7 + (20*b^3*Log[a + b*x])/a^7","A",1
206,1,105,117,0.0742508,"\int \frac{1}{x^5 (a+b x)^4} \, dx","IntegrateAlgebraic[1/(x^5*(a + b*x)^4),x]","\frac{35 b^4 \log (x)}{a^8}-\frac{35 b^4 \log (a+b x)}{a^8}+\frac{-3 a^6+7 a^5 b x-21 a^4 b^2 x^2+105 a^3 b^3 x^3+770 a^2 b^4 x^4+1050 a b^5 x^5+420 b^6 x^6}{12 a^7 x^4 (a+b x)^3}","\frac{35 b^4 \log (x)}{a^8}-\frac{35 b^4 \log (a+b x)}{a^8}+\frac{15 b^4}{a^7 (a+b x)}+\frac{20 b^3}{a^7 x}+\frac{5 b^4}{2 a^6 (a+b x)^2}-\frac{5 b^2}{a^6 x^2}+\frac{b^4}{3 a^5 (a+b x)^3}+\frac{4 b}{3 a^5 x^3}-\frac{1}{4 a^4 x^4}",1,"(-3*a^6 + 7*a^5*b*x - 21*a^4*b^2*x^2 + 105*a^3*b^3*x^3 + 770*a^2*b^4*x^4 + 1050*a*b^5*x^5 + 420*b^6*x^6)/(12*a^7*x^4*(a + b*x)^3) + (35*b^4*Log[x])/a^8 - (35*b^4*Log[a + b*x])/a^8","A",1
207,1,136,150,0.040204,"\int \frac{x^{10}}{(a+b x)^7} \, dx","IntegrateAlgebraic[x^10/(a + b*x)^7,x]","\frac{210 a^4 \log (a+b x)}{b^{11}}+\frac{2131 a^{10}+10266 a^9 b x+18105 a^8 b^2 x^2+11540 a^7 b^3 x^3-3945 a^6 b^4 x^4-9138 a^5 b^5 x^5-4043 a^4 b^6 x^6-360 a^3 b^7 x^7+45 a^2 b^8 x^8-10 a b^9 x^9+3 b^{10} x^{10}}{12 b^{11} (a+b x)^6}","-\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{210 a^4 \log (a+b x)}{b^{11}}-\frac{84 a^3 x}{b^{10}}+\frac{14 a^2 x^2}{b^9}-\frac{7 a x^3}{3 b^8}+\frac{x^4}{4 b^7}",1,"(2131*a^10 + 10266*a^9*b*x + 18105*a^8*b^2*x^2 + 11540*a^7*b^3*x^3 - 3945*a^6*b^4*x^4 - 9138*a^5*b^5*x^5 - 4043*a^4*b^6*x^6 - 360*a^3*b^7*x^7 + 45*a^2*b^8*x^8 - 10*a*b^9*x^9 + 3*b^10*x^10)/(12*b^11*(a + b*x)^6) + (210*a^4*Log[a + b*x])/b^11","A",1
208,1,125,139,0.0492467,"\int \frac{x^9}{(a+b x)^7} \, dx","IntegrateAlgebraic[x^9/(a + b*x)^7,x]","\frac{-2509 a^9-12534 a^8 b x-23775 a^7 b^2 x^2-19100 a^6 b^3 x^3-1725 a^5 b^4 x^4+6870 a^4 b^5 x^5+3665 a^3 b^6 x^6+360 a^2 b^7 x^7-45 a b^8 x^8+10 b^9 x^9}{30 b^{10} (a+b x)^6}-\frac{84 a^3 \log (a+b x)}{b^{10}}","\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{84 a^3 \log (a+b x)}{b^{10}}+\frac{28 a^2 x}{b^9}-\frac{7 a x^2}{2 b^8}+\frac{x^3}{3 b^7}",1,"(-2509*a^9 - 12534*a^8*b*x - 23775*a^7*b^2*x^2 - 19100*a^6*b^3*x^3 - 1725*a^5*b^4*x^4 + 6870*a^4*b^5*x^5 + 3665*a^3*b^6*x^6 + 360*a^2*b^7*x^7 - 45*a*b^8*x^8 + 10*b^9*x^9)/(30*b^10*(a + b*x)^6) - (84*a^3*Log[a + b*x])/b^10","A",1
209,1,114,128,0.0586187,"\int \frac{x^8}{(a+b x)^7} \, dx","IntegrateAlgebraic[x^8/(a + b*x)^7,x]","\frac{28 a^2 \log (a+b x)}{b^9}+\frac{1023 a^8+5298 a^7 b x+10725 a^6 b^2 x^2+10100 a^5 b^3 x^3+3375 a^4 b^4 x^4-1170 a^3 b^5 x^5-1035 a^2 b^6 x^6-120 a b^7 x^7+15 b^8 x^8}{30 b^9 (a+b x)^6}","-\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,"(1023*a^8 + 5298*a^7*b*x + 10725*a^6*b^2*x^2 + 10100*a^5*b^3*x^3 + 3375*a^4*b^4*x^4 - 1170*a^3*b^5*x^5 - 1035*a^2*b^6*x^6 - 120*a*b^7*x^7 + 15*b^8*x^8)/(30*b^9*(a + b*x)^6) + (28*a^2*Log[a + b*x])/b^9","A",1
210,1,101,118,0.0444325,"\int \frac{x^7}{(a+b x)^7} \, dx","IntegrateAlgebraic[x^7/(a + b*x)^7,x]","\frac{-669 a^7-3594 a^6 b x-7725 a^5 b^2 x^2-8200 a^4 b^3 x^3-4050 a^3 b^4 x^4-360 a^2 b^5 x^5+360 a b^6 x^6+60 b^7 x^7}{60 b^8 (a+b x)^6}-\frac{7 a \log (a+b x)}{b^8}","\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,"(-669*a^7 - 3594*a^6*b*x - 7725*a^5*b^2*x^2 - 8200*a^4*b^3*x^3 - 4050*a^3*b^4*x^4 - 360*a^2*b^5*x^5 + 360*a*b^6*x^6 + 60*b^7*x^7)/(60*b^8*(a + b*x)^6) - (7*a*Log[a + b*x])/b^8","A",1
211,1,78,109,0.0356231,"\int \frac{x^6}{(a+b x)^7} \, dx","IntegrateAlgebraic[x^6/(a + b*x)^7,x]","\frac{a \left(147 a^5+822 a^4 b x+1875 a^3 b^2 x^2+2200 a^2 b^3 x^3+1350 a b^4 x^4+360 b^5 x^5\right)}{60 b^7 (a+b x)^6}+\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*(147*a^5 + 822*a^4*b*x + 1875*a^3*b^2*x^2 + 2200*a^2*b^3*x^3 + 1350*a*b^4*x^4 + 360*b^5*x^5))/(60*b^7*(a + b*x)^6) + Log[a + b*x]/b^7","A",1
212,1,66,17,0.0160855,"\int \frac{x^5}{(a+b x)^7} \, dx","IntegrateAlgebraic[x^5/(a + b*x)^7,x]","\frac{-a^5-6 a^4 b x-15 a^3 b^2 x^2-20 a^2 b^3 x^3-15 a b^4 x^4-6 b^5 x^5}{6 b^6 (a+b x)^6}","\frac{x^6}{6 a (a+b x)^6}",1,"(-a^5 - 6*a^4*b*x - 15*a^3*b^2*x^2 - 20*a^2*b^3*x^3 - 15*a*b^4*x^4 - 6*b^5*x^5)/(6*b^6*(a + b*x)^6)","B",1
213,1,55,35,0.0157041,"\int \frac{x^4}{(a+b x)^7} \, dx","IntegrateAlgebraic[x^4/(a + b*x)^7,x]","\frac{-a^4-6 a^3 b x-15 a^2 b^2 x^2-20 a b^3 x^3-15 b^4 x^4}{30 b^5 (a+b x)^6}","\frac{x^5}{30 a^2 (a+b x)^5}+\frac{x^5}{6 a (a+b x)^6}",1,"(-a^4 - 6*a^3*b*x - 15*a^2*b^2*x^2 - 20*a*b^3*x^3 - 15*b^4*x^4)/(30*b^5*(a + b*x)^6)","A",1
214,1,44,52,0.0140393,"\int \frac{x^3}{(a+b x)^7} \, dx","IntegrateAlgebraic[x^3/(a + b*x)^7,x]","\frac{-a^3-6 a^2 b x-15 a b^2 x^2-20 b^3 x^3}{60 b^4 (a+b x)^6}","\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*a^2*b*x - 15*a*b^2*x^2 - 20*b^3*x^3)/(60*b^4*(a + b*x)^6)","A",1
215,1,33,47,0.0118768,"\int \frac{x^2}{(a+b x)^7} \, dx","IntegrateAlgebraic[x^2/(a + b*x)^7,x]","\frac{-a^2-6 a b x-15 b^2 x^2}{60 b^3 (a+b x)^6}","-\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*a*b*x - 15*b^2*x^2)/(60*b^3*(a + b*x)^6)","A",1
216,1,22,30,0.0096329,"\int \frac{x}{(a+b x)^7} \, dx","IntegrateAlgebraic[x/(a + b*x)^7,x]","\frac{-a-6 b x}{30 b^2 (a+b x)^6}","\frac{a}{6 b^2 (a+b x)^6}-\frac{1}{5 b^2 (a+b x)^5}",1,"(-a - 6*b*x)/(30*b^2*(a + b*x)^6)","A",1
217,1,14,14,0.0058752,"\int \frac{1}{(a+b x)^7} \, dx","IntegrateAlgebraic[(a + b*x)^(-7),x]","-\frac{1}{6 b (a+b x)^6}","-\frac{1}{6 b (a+b x)^6}",1,"-1/6*1/(b*(a + b*x)^6)","A",1
218,1,84,99,0.0658769,"\int \frac{1}{x (a+b x)^7} \, dx","IntegrateAlgebraic[1/(x*(a + b*x)^7),x]","-\frac{\log (a+b x)}{a^7}+\frac{\log (x)}{a^7}+\frac{147 a^5+522 a^4 b x+855 a^3 b^2 x^2+740 a^2 b^3 x^3+330 a b^4 x^4+60 b^5 x^5}{60 a^6 (a+b x)^6}","-\frac{\log (a+b x)}{a^7}+\frac{\log (x)}{a^7}+\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{1}{6 a (a+b x)^6}",1,"(147*a^5 + 522*a^4*b*x + 855*a^3*b^2*x^2 + 740*a^2*b^3*x^3 + 330*a*b^4*x^4 + 60*b^5*x^5)/(60*a^6*(a + b*x)^6) + Log[x]/a^7 - Log[a + b*x]/a^7","A",1
219,1,101,117,0.1026395,"\int \frac{1}{x^2 (a+b x)^7} \, dx","IntegrateAlgebraic[1/(x^2*(a + b*x)^7),x]","-\frac{7 b \log (x)}{a^8}+\frac{7 b \log (a+b x)}{a^8}+\frac{-60 a^6-1029 a^5 b x-3654 a^4 b^2 x^2-5985 a^3 b^3 x^3-5180 a^2 b^4 x^4-2310 a b^5 x^5-420 b^6 x^6}{60 a^7 x (a+b x)^6}","-\frac{7 b \log (x)}{a^8}+\frac{7 b \log (a+b x)}{a^8}-\frac{6 b}{a^7 (a+b x)}-\frac{1}{a^7 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}",1,"(-60*a^6 - 1029*a^5*b*x - 3654*a^4*b^2*x^2 - 5985*a^3*b^3*x^3 - 5180*a^2*b^4*x^4 - 2310*a*b^5*x^5 - 420*b^6*x^6)/(60*a^7*x*(a + b*x)^6) - (7*b*Log[x])/a^8 + (7*b*Log[a + b*x])/a^8","A",1
220,1,116,144,0.0794308,"\int \frac{1}{x^3 (a+b x)^7} \, dx","IntegrateAlgebraic[1/(x^3*(a + b*x)^7),x]","\frac{28 b^2 \log (x)}{a^9}-\frac{28 b^2 \log (a+b x)}{a^9}+\frac{-15 a^7+120 a^6 b x+2058 a^5 b^2 x^2+7308 a^4 b^3 x^3+11970 a^3 b^4 x^4+10360 a^2 b^5 x^5+4620 a b^6 x^6+840 b^7 x^7}{30 a^8 x^2 (a+b x)^6}","\frac{28 b^2 \log (x)}{a^9}-\frac{28 b^2 \log (a+b x)}{a^9}+\frac{21 b^2}{a^8 (a+b x)}+\frac{7 b}{a^8 x}+\frac{15 b^2}{2 a^7 (a+b x)^2}-\frac{1}{2 a^7 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}",1,"(-15*a^7 + 120*a^6*b*x + 2058*a^5*b^2*x^2 + 7308*a^4*b^3*x^3 + 11970*a^3*b^4*x^4 + 10360*a^2*b^5*x^5 + 4620*a*b^6*x^6 + 840*b^7*x^7)/(30*a^8*x^2*(a + b*x)^6) + (28*b^2*Log[x])/a^9 - (28*b^2*Log[a + b*x])/a^9","A",1
221,1,127,157,0.1026696,"\int \frac{1}{x^4 (a+b x)^7} \, dx","IntegrateAlgebraic[1/(x^4*(a + b*x)^7),x]","-\frac{84 b^3 \log (x)}{a^{10}}+\frac{84 b^3 \log (a+b x)}{a^{10}}+\frac{-10 a^8+45 a^7 b x-360 a^6 b^2 x^2-6174 a^5 b^3 x^3-21924 a^4 b^4 x^4-35910 a^3 b^5 x^5-31080 a^2 b^6 x^6-13860 a b^7 x^7-2520 b^8 x^8}{30 a^9 x^3 (a+b x)^6}","-\frac{84 b^3 \log (x)}{a^{10}}+\frac{84 b^3 \log (a+b x)}{a^{10}}-\frac{56 b^3}{a^9 (a+b x)}-\frac{28 b^2}{a^9 x}-\frac{35 b^3}{2 a^8 (a+b x)^2}+\frac{7 b}{2 a^8 x^2}-\frac{20 b^3}{3 a^7 (a+b x)^3}-\frac{1}{3 a^7 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}",1,"(-10*a^8 + 45*a^7*b*x - 360*a^6*b^2*x^2 - 6174*a^5*b^3*x^3 - 21924*a^4*b^4*x^4 - 35910*a^3*b^5*x^5 - 31080*a^2*b^6*x^6 - 13860*a*b^7*x^7 - 2520*b^8*x^8)/(30*a^9*x^3*(a + b*x)^6) - (84*b^3*Log[x])/a^10 + (84*b^3*Log[a + b*x])/a^10","A",1
222,1,158,186,0.0850597,"\int \frac{x^{12}}{(a+b x)^{10}} \, dx","IntegrateAlgebraic[x^12/(a + b*x)^10,x]","\frac{-35201 a^{12}-289089 a^{11} b x-1031616 a^{10} b^2 x^2-2074464 a^9 b^3 x^3-2529576 a^8 b^4 x^4-1831032 a^7 b^5 x^5-638568 a^6 b^6 x^6+58968 a^5 b^7 x^7+139482 a^4 b^8 x^8+43218 a^3 b^9 x^9+2772 a^2 b^{10} x^{10}-252 a b^{11} x^{11}+42 b^{12} x^{12}}{126 b^{13} (a+b x)^9}-\frac{220 a^3 \log (a+b x)}{b^{13}}","-\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{220 a^3 \log (a+b x)}{b^{13}}+\frac{55 a^2 x}{b^{12}}-\frac{5 a x^2}{b^{11}}+\frac{x^3}{3 b^{10}}",1,"(-35201*a^12 - 289089*a^11*b*x - 1031616*a^10*b^2*x^2 - 2074464*a^9*b^3*x^3 - 2529576*a^8*b^4*x^4 - 1831032*a^7*b^5*x^5 - 638568*a^6*b^6*x^6 + 58968*a^5*b^7*x^7 + 139482*a^4*b^8*x^8 + 43218*a^3*b^9*x^9 + 2772*a^2*b^10*x^10 - 252*a*b^11*x^11 + 42*b^12*x^12)/(126*b^13*(a + b*x)^9) - (220*a^3*Log[a + b*x])/b^13","A",1
223,1,147,177,0.0447142,"\int \frac{x^{11}}{(a+b x)^{10}} \, dx","IntegrateAlgebraic[x^11/(a + b*x)^10,x]","\frac{55 a^2 \log (a+b x)}{b^{12}}+\frac{42131 a^{11}+351459 a^{10} b x+1281096 a^9 b^2 x^2+2656584 a^8 b^3 x^3+3402756 a^7 b^4 x^4+2704212 a^6 b^5 x^5+1220688 a^5 b^6 x^6+190512 a^4 b^7 x^7-77112 a^3 b^8 x^8-36288 a^2 b^9 x^9-2772 a b^{10} x^{10}+252 b^{11} x^{11}}{504 b^{12} (a+b x)^9}","\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,"(42131*a^11 + 351459*a^10*b*x + 1281096*a^9*b^2*x^2 + 2656584*a^8*b^3*x^3 + 3402756*a^7*b^4*x^4 + 2704212*a^6*b^5*x^5 + 1220688*a^5*b^6*x^6 + 190512*a^4*b^7*x^7 - 77112*a^3*b^8*x^8 - 36288*a^2*b^9*x^9 - 2772*a*b^10*x^10 + 252*b^11*x^11)/(504*b^12*(a + b*x)^9) + (55*a^2*Log[a + b*x])/b^12","A",1
224,1,134,159,0.0657365,"\int \frac{x^{10}}{(a+b x)^{10}} \, dx","IntegrateAlgebraic[x^10/(a + b*x)^10,x]","\frac{-4861 a^{10}-41229 a^9 b x-153576 a^8 b^2 x^2-328104 a^7 b^3 x^3-439236 a^6 b^4 x^4-375732 a^5 b^5 x^5-197568 a^4 b^6 x^6-54432 a^3 b^7 x^7-2268 a^2 b^8 x^8+2268 a b^9 x^9+252 b^{10} x^{10}}{252 b^{11} (a+b x)^9}-\frac{10 a \log (a+b x)}{b^{11}}","-\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,"(-4861*a^10 - 41229*a^9*b*x - 153576*a^8*b^2*x^2 - 328104*a^7*b^3*x^3 - 439236*a^6*b^4*x^4 - 375732*a^5*b^5*x^5 - 197568*a^4*b^6*x^6 - 54432*a^3*b^7*x^7 - 2268*a^2*b^8*x^8 + 2268*a*b^9*x^9 + 252*b^10*x^10)/(252*b^11*(a + b*x)^9) - (10*a*Log[a + b*x])/b^11","A",1
225,1,111,154,0.0465013,"\int \frac{x^9}{(a+b x)^{10}} \, dx","IntegrateAlgebraic[x^9/(a + b*x)^10,x]","\frac{a \left(7129 a^8+61641 a^7 b x+235224 a^6 b^2 x^2+518616 a^5 b^3 x^3+725004 a^4 b^4 x^4+661500 a^3 b^5 x^5+388080 a^2 b^6 x^6+136080 a b^7 x^7+22680 b^8 x^8\right)}{2520 b^{10} (a+b x)^9}+\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*(7129*a^8 + 61641*a^7*b*x + 235224*a^6*b^2*x^2 + 518616*a^5*b^3*x^3 + 725004*a^4*b^4*x^4 + 661500*a^3*b^5*x^5 + 388080*a^2*b^6*x^6 + 136080*a*b^7*x^7 + 22680*b^8*x^8))/(2520*b^10*(a + b*x)^9) + Log[a + b*x]/b^10","A",1
226,1,99,17,0.0268013,"\int \frac{x^8}{(a+b x)^{10}} \, dx","IntegrateAlgebraic[x^8/(a + b*x)^10,x]","\frac{-a^8-9 a^7 b x-36 a^6 b^2 x^2-84 a^5 b^3 x^3-126 a^4 b^4 x^4-126 a^3 b^5 x^5-84 a^2 b^6 x^6-36 a b^7 x^7-9 b^8 x^8}{9 b^9 (a+b x)^9}","\frac{x^9}{9 a (a+b x)^9}",1,"(-a^8 - 9*a^7*b*x - 36*a^6*b^2*x^2 - 84*a^5*b^3*x^3 - 126*a^4*b^4*x^4 - 126*a^3*b^5*x^5 - 84*a^2*b^6*x^6 - 36*a*b^7*x^7 - 9*b^8*x^8)/(9*b^9*(a + b*x)^9)","B",1
227,1,88,35,0.0203905,"\int \frac{x^7}{(a+b x)^{10}} \, dx","IntegrateAlgebraic[x^7/(a + b*x)^10,x]","\frac{-a^7-9 a^6 b x-36 a^5 b^2 x^2-84 a^4 b^3 x^3-126 a^3 b^4 x^4-126 a^2 b^5 x^5-84 a b^6 x^6-36 b^7 x^7}{72 b^8 (a+b x)^9}","\frac{x^8}{72 a^2 (a+b x)^8}+\frac{x^8}{9 a (a+b x)^9}",1,"(-a^7 - 9*a^6*b*x - 36*a^5*b^2*x^2 - 84*a^4*b^3*x^3 - 126*a^3*b^4*x^4 - 126*a^2*b^5*x^5 - 84*a*b^6*x^6 - 36*b^7*x^7)/(72*b^8*(a + b*x)^9)","B",1
228,1,77,52,0.0215202,"\int \frac{x^6}{(a+b x)^{10}} \, dx","IntegrateAlgebraic[x^6/(a + b*x)^10,x]","\frac{-a^6-9 a^5 b x-36 a^4 b^2 x^2-84 a^3 b^3 x^3-126 a^2 b^4 x^4-126 a b^5 x^5-84 b^6 x^6}{252 b^7 (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,"(-a^6 - 9*a^5*b*x - 36*a^4*b^2*x^2 - 84*a^3*b^3*x^3 - 126*a^2*b^4*x^4 - 126*a*b^5*x^5 - 84*b^6*x^6)/(252*b^7*(a + b*x)^9)","A",1
229,1,66,69,0.0194721,"\int \frac{x^5}{(a+b x)^{10}} \, dx","IntegrateAlgebraic[x^5/(a + b*x)^10,x]","\frac{-a^5-9 a^4 b x-36 a^3 b^2 x^2-84 a^2 b^3 x^3-126 a b^4 x^4-126 b^5 x^5}{504 b^6 (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,"(-a^5 - 9*a^4*b*x - 36*a^3*b^2*x^2 - 84*a^2*b^3*x^3 - 126*a*b^4*x^4 - 126*b^5*x^5)/(504*b^6*(a + b*x)^9)","A",1
230,1,55,81,0.0186477,"\int \frac{x^4}{(a+b x)^{10}} \, dx","IntegrateAlgebraic[x^4/(a + b*x)^10,x]","\frac{-a^4-9 a^3 b x-36 a^2 b^2 x^2-84 a b^3 x^3-126 b^4 x^4}{630 b^5 (a+b x)^9}","-\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*a^3*b*x - 36*a^2*b^2*x^2 - 84*a*b^3*x^3 - 126*b^4*x^4)/(630*b^5*(a + b*x)^9)","A",1
231,1,44,64,0.013299,"\int \frac{x^3}{(a+b x)^{10}} \, dx","IntegrateAlgebraic[x^3/(a + b*x)^10,x]","\frac{-a^3-9 a^2 b x-36 a b^2 x^2-84 b^3 x^3}{504 b^4 (a+b x)^9}","\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*a^2*b*x - 36*a*b^2*x^2 - 84*b^3*x^3)/(504*b^4*(a + b*x)^9)","A",1
232,1,33,47,0.0144041,"\int \frac{x^2}{(a+b x)^{10}} \, dx","IntegrateAlgebraic[x^2/(a + b*x)^10,x]","\frac{-a^2-9 a b x-36 b^2 x^2}{252 b^3 (a+b x)^9}","-\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*a*b*x - 36*b^2*x^2)/(252*b^3*(a + b*x)^9)","A",1
233,1,22,30,0.00944,"\int \frac{x}{(a+b x)^{10}} \, dx","IntegrateAlgebraic[x/(a + b*x)^10,x]","\frac{-a-9 b x}{72 b^2 (a+b x)^9}","\frac{a}{9 b^2 (a+b x)^9}-\frac{1}{8 b^2 (a+b x)^8}",1,"(-a - 9*b*x)/(72*b^2*(a + b*x)^9)","A",1
234,1,14,14,0.0061058,"\int \frac{1}{(a+b x)^{10}} \, dx","IntegrateAlgebraic[(a + b*x)^(-10),x]","-\frac{1}{9 b (a+b x)^9}","-\frac{1}{9 b (a+b x)^9}",1,"-1/9*1/(b*(a + b*x)^9)","A",1
235,1,117,141,0.1058585,"\int \frac{1}{x (a+b x)^{10}} \, dx","IntegrateAlgebraic[1/(x*(a + b*x)^10),x]","-\frac{\log (a+b x)}{a^{10}}+\frac{\log (x)}{a^{10}}+\frac{7129 a^8+41481 a^7 b x+120564 a^6 b^2 x^2+210756 a^5 b^3 x^3+236754 a^4 b^4 x^4+173250 a^3 b^5 x^5+80220 a^2 b^6 x^6+21420 a b^7 x^7+2520 b^8 x^8}{2520 a^9 (a+b x)^9}","-\frac{\log (a+b x)}{a^{10}}+\frac{\log (x)}{a^{10}}+\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{1}{9 a (a+b x)^9}",1,"(7129*a^8 + 41481*a^7*b*x + 120564*a^6*b^2*x^2 + 210756*a^5*b^3*x^3 + 236754*a^4*b^4*x^4 + 173250*a^3*b^5*x^5 + 80220*a^2*b^6*x^6 + 21420*a*b^7*x^7 + 2520*b^8*x^8)/(2520*a^9*(a + b*x)^9) + Log[x]/a^10 - Log[a + b*x]/a^10","A",1
236,1,134,158,0.1369122,"\int \frac{1}{x^2 (a+b x)^{10}} \, dx","IntegrateAlgebraic[1/(x^2*(a + b*x)^10),x]","-\frac{10 b \log (x)}{a^{11}}+\frac{10 b \log (a+b x)}{a^{11}}+\frac{-252 a^9-7129 a^8 b x-41481 a^7 b^2 x^2-120564 a^6 b^3 x^3-210756 a^5 b^4 x^4-236754 a^4 b^5 x^5-173250 a^3 b^6 x^6-80220 a^2 b^7 x^7-21420 a b^8 x^8-2520 b^9 x^9}{252 a^{10} x (a+b x)^9}","-\frac{10 b \log (x)}{a^{11}}+\frac{10 b \log (a+b x)}{a^{11}}-\frac{9 b}{a^{10} (a+b x)}-\frac{1}{a^{10} 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}",1,"(-252*a^9 - 7129*a^8*b*x - 41481*a^7*b^2*x^2 - 120564*a^6*b^3*x^3 - 210756*a^5*b^4*x^4 - 236754*a^4*b^5*x^5 - 173250*a^3*b^6*x^6 - 80220*a^2*b^7*x^7 - 21420*a*b^8*x^8 - 2520*b^9*x^9)/(252*a^10*x*(a + b*x)^9) - (10*b*Log[x])/a^11 + (10*b*Log[a + b*x])/a^11","A",1
237,1,149,191,0.117317,"\int \frac{1}{x^3 (a+b x)^{10}} \, dx","IntegrateAlgebraic[1/(x^3*(a + b*x)^10),x]","\frac{55 b^2 \log (x)}{a^{12}}-\frac{55 b^2 \log (a+b x)}{a^{12}}+\frac{-252 a^{10}+2772 a^9 b x+78419 a^8 b^2 x^2+456291 a^7 b^3 x^3+1326204 a^6 b^4 x^4+2318316 a^5 b^5 x^5+2604294 a^4 b^6 x^6+1905750 a^3 b^7 x^7+882420 a^2 b^8 x^8+235620 a b^9 x^9+27720 b^{10} x^{10}}{504 a^{11} x^2 (a+b x)^9}","\frac{55 b^2 \log (x)}{a^{12}}-\frac{55 b^2 \log (a+b x)}{a^{12}}+\frac{45 b^2}{a^{11} (a+b x)}+\frac{10 b}{a^{11} x}+\frac{18 b^2}{a^{10} (a+b x)^2}-\frac{1}{2 a^{10} 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}",1,"(-252*a^10 + 2772*a^9*b*x + 78419*a^8*b^2*x^2 + 456291*a^7*b^3*x^3 + 1326204*a^6*b^4*x^4 + 2318316*a^5*b^5*x^5 + 2604294*a^4*b^6*x^6 + 1905750*a^3*b^7*x^7 + 882420*a^2*b^8*x^8 + 235620*a*b^9*x^9 + 27720*b^10*x^10)/(504*a^11*x^2*(a + b*x)^9) + (55*b^2*Log[x])/a^12 - (55*b^2*Log[a + b*x])/a^12","A",1
238,1,160,198,0.1370889,"\int \frac{1}{x^4 (a+b x)^{10}} \, dx","IntegrateAlgebraic[1/(x^4*(a + b*x)^10),x]","-\frac{220 b^3 \log (x)}{a^{13}}+\frac{220 b^3 \log (a+b x)}{a^{13}}+\frac{-42 a^{11}+252 a^{10} b x-2772 a^9 b^2 x^2-78419 a^8 b^3 x^3-456291 a^7 b^4 x^4-1326204 a^6 b^5 x^5-2318316 a^5 b^6 x^6-2604294 a^4 b^7 x^7-1905750 a^3 b^8 x^8-882420 a^2 b^9 x^9-235620 a b^{10} x^{10}-27720 b^{11} x^{11}}{126 a^{12} x^3 (a+b x)^9}","-\frac{220 b^3 \log (x)}{a^{13}}+\frac{220 b^3 \log (a+b x)}{a^{13}}-\frac{165 b^3}{a^{12} (a+b x)}-\frac{55 b^2}{a^{12} x}-\frac{60 b^3}{a^{11} (a+b x)^2}+\frac{5 b}{a^{11} x^2}-\frac{28 b^3}{a^{10} (a+b x)^3}-\frac{1}{3 a^{10} 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}",1,"(-42*a^11 + 252*a^10*b*x - 2772*a^9*b^2*x^2 - 78419*a^8*b^3*x^3 - 456291*a^7*b^4*x^4 - 1326204*a^6*b^5*x^5 - 2318316*a^5*b^6*x^6 - 2604294*a^4*b^7*x^7 - 1905750*a^3*b^8*x^8 - 882420*a^2*b^9*x^9 - 235620*a*b^10*x^10 - 27720*b^11*x^11)/(126*a^12*x^3*(a + b*x)^9) - (220*b^3*Log[x])/a^13 + (220*b^3*Log[a + b*x])/a^13","A",1
239,1,136,141,0.0354147,"\int \frac{(a+b x)^{12}}{x^{10}} \, dx","IntegrateAlgebraic[(a + b*x)^12/x^10,x]","220 a^3 b^9 \log (x)+\frac{-14 a^{12}-189 a^{11} b x-1188 a^{10} b^2 x^2-4620 a^9 b^3 x^3-12474 a^8 b^4 x^4-24948 a^7 b^5 x^5-38808 a^6 b^6 x^6-49896 a^5 b^7 x^7-62370 a^4 b^8 x^8+8316 a^2 b^{10} x^{10}+756 a b^{11} x^{11}+42 b^{12} x^{12}}{126 x^9}","-\frac{a^{12}}{9 x^9}-\frac{3 a^{11} b}{2 x^8}-\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}+220 a^3 b^9 \log (x)+66 a^2 b^{10} x+6 a b^{11} x^2+\frac{b^{12} x^3}{3}",1,"(-14*a^12 - 189*a^11*b*x - 1188*a^10*b^2*x^2 - 4620*a^9*b^3*x^3 - 12474*a^8*b^4*x^4 - 24948*a^7*b^5*x^5 - 38808*a^6*b^6*x^6 - 49896*a^5*b^7*x^7 - 62370*a^4*b^8*x^8 + 8316*a^2*b^10*x^10 + 756*a*b^11*x^11 + 42*b^12*x^12)/(126*x^9) + 220*a^3*b^9*Log[x]","A",1
240,1,125,132,0.0273644,"\int \frac{(a+b x)^{11}}{x^{10}} \, dx","IntegrateAlgebraic[(a + b*x)^11/x^10,x]","55 a^2 b^9 \log (x)+\frac{-56 a^{11}-693 a^{10} b x-3960 a^9 b^2 x^2-13860 a^8 b^3 x^3-33264 a^7 b^4 x^4-58212 a^6 b^5 x^5-77616 a^5 b^6 x^6-83160 a^4 b^7 x^7-83160 a^3 b^8 x^8+5544 a b^{10} x^{10}+252 b^{11} x^{11}}{504 x^9}","-\frac{a^{11}}{9 x^9}-\frac{11 a^{10} b}{8 x^8}-\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)+11 a b^{10} x+\frac{b^{11} x^2}{2}",1,"(-56*a^11 - 693*a^10*b*x - 3960*a^9*b^2*x^2 - 13860*a^8*b^3*x^3 - 33264*a^7*b^4*x^4 - 58212*a^6*b^5*x^5 - 77616*a^5*b^6*x^6 - 83160*a^4*b^7*x^7 - 83160*a^3*b^8*x^8 + 5544*a*b^10*x^10 + 252*b^11*x^11)/(504*x^9) + 55*a^2*b^9*Log[x]","A",1
241,1,114,114,0.0001126,"\int \frac{(a+b x)^{10}}{x^{10}} \, dx","IntegrateAlgebraic[(a + b*x)^10/x^10,x]","\frac{-28 a^{10}-315 a^9 b x-1620 a^8 b^2 x^2-5040 a^7 b^3 x^3-10584 a^6 b^4 x^4-15876 a^5 b^5 x^5-17640 a^4 b^6 x^6-15120 a^3 b^7 x^7-11340 a^2 b^8 x^8+252 b^{10} x^{10}}{252 x^9}+10 a b^9 \log (x)","-\frac{a^{10}}{9 x^9}-\frac{5 a^9 b}{4 x^8}-\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}+10 a b^9 \log (x)+b^{10} x",1,"(-28*a^10 - 315*a^9*b*x - 1620*a^8*b^2*x^2 - 5040*a^7*b^3*x^3 - 10584*a^6*b^4*x^4 - 15876*a^5*b^5*x^5 - 17640*a^4*b^6*x^6 - 15120*a^3*b^7*x^7 - 11340*a^2*b^8*x^8 + 252*b^10*x^10)/(252*x^9) + 10*a*b^9*Log[x]","A",1
242,1,102,109,0.0253155,"\int \frac{(a+b x)^9}{x^{10}} \, dx","IntegrateAlgebraic[(a + b*x)^9/x^10,x]","\frac{-280 a^9-2835 a^8 b x-12960 a^7 b^2 x^2-35280 a^6 b^3 x^3-63504 a^5 b^4 x^4-79380 a^4 b^5 x^5-70560 a^3 b^6 x^6-45360 a^2 b^7 x^7-22680 a b^8 x^8}{2520 x^9}+b^9 \log (x)","-\frac{a^9}{9 x^9}-\frac{9 a^8 b}{8 x^8}-\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 b^8}{x}+b^9 \log (x)",1,"(-280*a^9 - 2835*a^8*b*x - 12960*a^7*b^2*x^2 - 35280*a^6*b^3*x^3 - 63504*a^5*b^4*x^4 - 79380*a^4*b^5*x^5 - 70560*a^3*b^6*x^6 - 45360*a^2*b^7*x^7 - 22680*a*b^8*x^8)/(2520*x^9) + b^9*Log[x]","A",1
243,1,92,17,0.0162595,"\int \frac{(a+b x)^8}{x^{10}} \, dx","IntegrateAlgebraic[(a + b*x)^8/x^10,x]","\frac{-a^8-9 a^7 b x-36 a^6 b^2 x^2-84 a^5 b^3 x^3-126 a^4 b^4 x^4-126 a^3 b^5 x^5-84 a^2 b^6 x^6-36 a b^7 x^7-9 b^8 x^8}{9 x^9}","-\frac{(a+b x)^9}{9 a x^9}",1,"(-a^8 - 9*a^7*b*x - 36*a^6*b^2*x^2 - 84*a^5*b^3*x^3 - 126*a^4*b^4*x^4 - 126*a^3*b^5*x^5 - 84*a^2*b^6*x^6 - 36*a*b^7*x^7 - 9*b^8*x^8)/(9*x^9)","B",1
244,1,81,36,0.0001089,"\int \frac{(a+b x)^7}{x^{10}} \, dx","IntegrateAlgebraic[(a + b*x)^7/x^10,x]","\frac{-8 a^7-63 a^6 b x-216 a^5 b^2 x^2-420 a^4 b^3 x^3-504 a^3 b^4 x^4-378 a^2 b^5 x^5-168 a b^6 x^6-36 b^7 x^7}{72 x^9}","\frac{b (a+b x)^8}{72 a^2 x^8}-\frac{(a+b x)^8}{9 a x^9}",1,"(-8*a^7 - 63*a^6*b*x - 216*a^5*b^2*x^2 - 420*a^4*b^3*x^3 - 504*a^3*b^4*x^4 - 378*a^2*b^5*x^5 - 168*a*b^6*x^6 - 36*b^7*x^7)/(72*x^9)","B",1
245,1,70,56,0.0149197,"\int \frac{(a+b x)^6}{x^{10}} \, dx","IntegrateAlgebraic[(a + b*x)^6/x^10,x]","\frac{-28 a^6-189 a^5 b x-540 a^4 b^2 x^2-840 a^3 b^3 x^3-756 a^2 b^4 x^4-378 a b^5 x^5-84 b^6 x^6}{252 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,"(-28*a^6 - 189*a^5*b*x - 540*a^4*b^2*x^2 - 840*a^3*b^3*x^3 - 756*a^2*b^4*x^4 - 378*a*b^5*x^5 - 84*b^6*x^6)/(252*x^9)","A",1
246,1,59,67,0.0001114,"\int \frac{(a+b x)^5}{x^{10}} \, dx","IntegrateAlgebraic[(a + b*x)^5/x^10,x]","\frac{-56 a^5-315 a^4 b x-720 a^3 b^2 x^2-840 a^2 b^3 x^3-504 a b^4 x^4-126 b^5 x^5}{504 x^9}","-\frac{a^5}{9 x^9}-\frac{5 a^4 b}{8 x^8}-\frac{10 a^3 b^2}{7 x^7}-\frac{5 a^2 b^3}{3 x^6}-\frac{a b^4}{x^5}-\frac{b^5}{4 x^4}",1,"(-56*a^5 - 315*a^4*b*x - 720*a^3*b^2*x^2 - 840*a^2*b^3*x^3 - 504*a*b^4*x^4 - 126*b^5*x^5)/(504*x^9)","A",1
247,1,48,56,0.0124026,"\int \frac{(a+b x)^4}{x^{10}} \, dx","IntegrateAlgebraic[(a + b*x)^4/x^10,x]","\frac{-70 a^4-315 a^3 b x-540 a^2 b^2 x^2-420 a b^3 x^3-126 b^4 x^4}{630 x^9}","-\frac{a^4}{9 x^9}-\frac{a^3 b}{2 x^8}-\frac{6 a^2 b^2}{7 x^7}-\frac{2 a b^3}{3 x^6}-\frac{b^4}{5 x^5}",1,"(-70*a^4 - 315*a^3*b*x - 540*a^2*b^2*x^2 - 420*a*b^3*x^3 - 126*b^4*x^4)/(630*x^9)","A",1
248,1,37,43,0.0079843,"\int \frac{(a+b x)^3}{x^{10}} \, dx","IntegrateAlgebraic[(a + b*x)^3/x^10,x]","\frac{-56 a^3-189 a^2 b x-216 a b^2 x^2-84 b^3 x^3}{504 x^9}","-\frac{a^3}{9 x^9}-\frac{3 a^2 b}{8 x^8}-\frac{3 a b^2}{7 x^7}-\frac{b^3}{6 x^6}",1,"(-56*a^3 - 189*a^2*b*x - 216*a*b^2*x^2 - 84*b^3*x^3)/(504*x^9)","A",1
249,1,26,30,0.0096014,"\int \frac{(a+b x)^2}{x^{10}} \, dx","IntegrateAlgebraic[(a + b*x)^2/x^10,x]","\frac{-28 a^2-63 a b x-36 b^2 x^2}{252 x^9}","-\frac{a^2}{9 x^9}-\frac{a b}{4 x^8}-\frac{b^2}{7 x^7}",1,"(-28*a^2 - 63*a*b*x - 36*b^2*x^2)/(252*x^9)","A",1
250,1,15,17,0.0044503,"\int \frac{a+b x}{x^{10}} \, dx","IntegrateAlgebraic[(a + b*x)/x^10,x]","\frac{-8 a-9 b x}{72 x^9}","-\frac{a}{9 x^9}-\frac{b}{8 x^8}",1,"(-8*a - 9*b*x)/(72*x^9)","A",1
251,1,7,7,0.0013776,"\int \frac{1}{x^{10}} \, dx","IntegrateAlgebraic[x^(-10),x]","-\frac{1}{9 x^9}","-\frac{1}{9 x^9}",1,"-1/9*1/x^9","A",1
252,1,119,134,0.0230257,"\int \frac{1}{x^{10} (a+b x)} \, dx","IntegrateAlgebraic[1/(x^10*(a + b*x)),x]","-\frac{b^9 \log (x)}{a^{10}}+\frac{b^9 \log (a+b x)}{a^{10}}+\frac{-280 a^8+315 a^7 b x-360 a^6 b^2 x^2+420 a^5 b^3 x^3-504 a^4 b^4 x^4+630 a^3 b^5 x^5-840 a^2 b^6 x^6+1260 a b^7 x^7-2520 b^8 x^8}{2520 a^9 x^9}","-\frac{b^9 \log (x)}{a^{10}}+\frac{b^9 \log (a+b x)}{a^{10}}-\frac{b^8}{a^9 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^2 x^8}-\frac{1}{9 a x^9}",1,"(-280*a^8 + 315*a^7*b*x - 360*a^6*b^2*x^2 + 420*a^5*b^3*x^3 - 504*a^4*b^4*x^4 + 630*a^3*b^5*x^5 - 840*a^2*b^6*x^6 + 1260*a*b^7*x^7 - 2520*b^8*x^8)/(2520*a^9*x^9) - (b^9*Log[x])/a^10 + (b^9*Log[a + b*x])/a^10","A",1
253,1,138,146,0.105269,"\int \frac{1}{x^{10} (a+b x)^2} \, dx","IntegrateAlgebraic[1/(x^10*(a + b*x)^2),x]","-\frac{10 b^9 \log (x)}{a^{11}}+\frac{10 b^9 \log (a+b x)}{a^{11}}+\frac{-28 a^9+35 a^8 b x-45 a^7 b^2 x^2+60 a^6 b^3 x^3-84 a^5 b^4 x^4+126 a^4 b^5 x^5-210 a^3 b^6 x^6+420 a^2 b^7 x^7-1260 a b^8 x^8-2520 b^9 x^9}{252 a^{10} x^9 (a+b x)}","-\frac{10 b^9 \log (x)}{a^{11}}+\frac{10 b^9 \log (a+b x)}{a^{11}}-\frac{b^9}{a^{10} (a+b x)}-\frac{9 b^8}{a^{10} 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}{4 a^3 x^8}-\frac{1}{9 a^2 x^9}",1,"(-28*a^9 + 35*a^8*b*x - 45*a^7*b^2*x^2 + 60*a^6*b^3*x^3 - 84*a^5*b^4*x^4 + 126*a^4*b^5*x^5 - 210*a^3*b^6*x^6 + 420*a^2*b^7*x^7 - 1260*a*b^8*x^8 - 2520*b^9*x^9)/(252*a^10*x^9*(a + b*x)) - (10*b^9*Log[x])/a^11 + (10*b^9*Log[a + b*x])/a^11","A",1
254,1,149,163,0.1188514,"\int \frac{1}{x^{10} (a+b x)^3} \, dx","IntegrateAlgebraic[1/(x^10*(a + b*x)^3),x]","-\frac{55 b^9 \log (x)}{a^{12}}+\frac{55 b^9 \log (a+b x)}{a^{12}}+\frac{-56 a^{10}+77 a^9 b x-110 a^8 b^2 x^2+165 a^7 b^3 x^3-264 a^6 b^4 x^4+462 a^5 b^5 x^5-924 a^4 b^6 x^6+2310 a^3 b^7 x^7-9240 a^2 b^8 x^8-41580 a b^9 x^9-27720 b^{10} x^{10}}{504 a^{11} x^9 (a+b x)^2}","-\frac{55 b^9 \log (x)}{a^{12}}+\frac{55 b^9 \log (a+b x)}{a^{12}}-\frac{10 b^9}{a^{11} (a+b x)}-\frac{45 b^8}{a^{11} x}-\frac{b^9}{2 a^{10} (a+b x)^2}+\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{3 b}{8 a^4 x^8}-\frac{1}{9 a^3 x^9}",1,"(-56*a^10 + 77*a^9*b*x - 110*a^8*b^2*x^2 + 165*a^7*b^3*x^3 - 264*a^6*b^4*x^4 + 462*a^5*b^5*x^5 - 924*a^4*b^6*x^6 + 2310*a^3*b^7*x^7 - 9240*a^2*b^8*x^8 - 41580*a*b^9*x^9 - 27720*b^10*x^10)/(504*a^11*x^9*(a + b*x)^2) - (55*b^9*Log[x])/a^12 + (55*b^9*Log[a + b*x])/a^12","A",1
255,1,17,17,0.0061503,"\int \frac{1}{x (2+3 x)} \, dx","IntegrateAlgebraic[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",1
256,1,17,17,0.0057302,"\int \frac{1}{x (4+6 x)} \, dx","IntegrateAlgebraic[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",1
257,1,24,24,0.0062009,"\int \frac{1}{x^2 (4+6 x)} \, dx","IntegrateAlgebraic[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*1/x - (3*Log[x])/8 + (3*Log[2 + 3*x])/8","A",1
258,1,29,31,0.0073354,"\int \frac{1}{x^3 (4+6 x)} \, dx","IntegrateAlgebraic[1/(x^3*(4 + 6*x)),x]","\frac{3 x-1}{8 x^2}+\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 + 3*x)/(8*x^2) + (9*Log[x])/16 - (9*Log[2 + 3*x])/16","A",1
259,1,34,38,0.0084206,"\int \frac{1}{x^4 (4+6 x)} \, dx","IntegrateAlgebraic[1/(x^4*(4 + 6*x)),x]","\frac{-27 x^2+9 x-4}{48 x^3}-\frac{27 \log (x)}{32}+\frac{27}{32} \log (3 x+2)","-\frac{1}{12 x^3}+\frac{3}{16 x^2}-\frac{9}{16 x}-\frac{27 \log (x)}{32}+\frac{27}{32} \log (3 x+2)",1,"(-4 + 9*x - 27*x^2)/(48*x^3) - (27*Log[x])/32 + (27*Log[2 + 3*x])/32","A",1
260,1,39,45,0.0090586,"\int \frac{1}{x^5 (4+6 x)} \, dx","IntegrateAlgebraic[1/(x^5*(4 + 6*x)),x]","\frac{27 x^3-9 x^2+4 x-2}{32 x^4}+\frac{81 \log (x)}{64}-\frac{81}{64} \log (3 x+2)","-\frac{1}{16 x^4}+\frac{1}{8 x^3}-\frac{9}{32 x^2}+\frac{27}{32 x}+\frac{81 \log (x)}{64}-\frac{81}{64} \log (3 x+2)",1,"(-2 + 4*x - 9*x^2 + 27*x^3)/(32*x^4) + (81*Log[x])/64 - (81*Log[2 + 3*x])/64","A",1
261,1,28,28,0.0187305,"\int \frac{1}{x (4+6 x)^2} \, dx","IntegrateAlgebraic[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",1
262,1,36,35,0.0194559,"\int \frac{1}{x^2 (4+6 x)^2} \, dx","IntegrateAlgebraic[1/(x^2*(4 + 6*x)^2),x]","\frac{-3 x-1}{8 x (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 - 3*x)/(8*x*(2 + 3*x)) - (3*Log[x])/16 + (3*Log[2 + 3*x])/16","A",1
263,1,41,42,0.0198912,"\int \frac{1}{x^3 (4+6 x)^2} \, dx","IntegrateAlgebraic[1/(x^3*(4 + 6*x)^2),x]","\frac{27 x^2+9 x-2}{32 x^2 (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,"(-2 + 9*x + 27*x^2)/(32*x^2*(2 + 3*x)) + (27*Log[x])/64 - (27*Log[2 + 3*x])/64","A",1
264,1,46,49,0.0379602,"\int \frac{1}{x^4 (4+6 x)^2} \, dx","IntegrateAlgebraic[1/(x^4*(4 + 6*x)^2),x]","\frac{-81 x^3-27 x^2+6 x-2}{48 x^3 (3 x+2)}-\frac{27 \log (x)}{32}+\frac{27}{32} \log (3 x+2)","-\frac{1}{48 x^3}+\frac{3}{32 x^2}-\frac{27}{64 x}-\frac{27}{64 (3 x+2)}-\frac{27 \log (x)}{32}+\frac{27}{32} \log (3 x+2)",1,"(-2 + 6*x - 27*x^2 - 81*x^3)/(48*x^3*(2 + 3*x)) - (27*Log[x])/32 + (27*Log[2 + 3*x])/32","A",1
265,1,51,56,0.0176142,"\int \frac{1}{x^5 (4+6 x)^2} \, dx","IntegrateAlgebraic[1/(x^5*(4 + 6*x)^2),x]","\frac{405 x^4+135 x^3-30 x^2+10 x-4}{128 x^4 (3 x+2)}+\frac{405 \log (x)}{256}-\frac{405}{256} \log (3 x+2)","-\frac{1}{64 x^4}+\frac{1}{16 x^3}-\frac{27}{128 x^2}+\frac{27}{32 x}+\frac{81}{128 (3 x+2)}+\frac{405 \log (x)}{256}-\frac{405}{256} \log (3 x+2)",1,"(-4 + 10*x - 30*x^2 + 135*x^3 + 405*x^4)/(128*x^4*(2 + 3*x)) + (405*Log[x])/256 - (405*Log[2 + 3*x])/256","A",1
266,1,31,39,0.0251871,"\int \frac{1}{x (4+6 x)^3} \, dx","IntegrateAlgebraic[1/(x*(4 + 6*x)^3),x]","\frac{3 (x+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,"(3*(1 + x))/(32*(2 + 3*x)^2) + Log[x]/64 - Log[2 + 3*x]/64","A",1
267,1,41,46,0.0280419,"\int \frac{1}{x^2 (4+6 x)^3} \, dx","IntegrateAlgebraic[1/(x^2*(4 + 6*x)^3),x]","\frac{-27 x^2-27 x-4}{64 x (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,"(-4 - 27*x - 27*x^2)/(64*x*(2 + 3*x)^2) - (9*Log[x])/128 + (9*Log[2 + 3*x])/128","A",1
268,1,46,53,0.0316004,"\int \frac{1}{x^3 (4+6 x)^3} \, dx","IntegrateAlgebraic[1/(x^3*(4 + 6*x)^3),x]","\frac{81 x^3+81 x^2+12 x-2}{64 x^2 (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,"(-2 + 12*x + 81*x^2 + 81*x^3)/(64*x^2*(2 + 3*x)^2) + (27*Log[x])/128 - (27*Log[2 + 3*x])/128","A",1
269,1,51,60,0.0259573,"\int \frac{1}{x^4 (4+6 x)^3} \, dx","IntegrateAlgebraic[1/(x^4*(4 + 6*x)^3),x]","\frac{-1215 x^4-1215 x^3-180 x^2+30 x-8}{384 x^3 (3 x+2)^2}-\frac{135 \log (x)}{256}+\frac{135}{256} \log (3 x+2)","-\frac{1}{192 x^3}+\frac{9}{256 x^2}-\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,"(-8 + 30*x - 180*x^2 - 1215*x^3 - 1215*x^4)/(384*x^3*(2 + 3*x)^2) - (135*Log[x])/256 + (135*Log[2 + 3*x])/256","A",1
270,1,56,67,0.0276536,"\int \frac{1}{x^5 (4+6 x)^3} \, dx","IntegrateAlgebraic[1/(x^5*(4 + 6*x)^3),x]","\frac{3645 x^5+3645 x^4+540 x^3-90 x^2+24 x-8}{512 x^4 (3 x+2)^2}+\frac{1215 \log (x)}{1024}-\frac{1215 \log (3 x+2)}{1024}","-\frac{1}{256 x^4}+\frac{3}{128 x^3}-\frac{27}{256 x^2}+\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,"(-8 + 24*x - 90*x^2 + 540*x^3 + 3645*x^4 + 3645*x^5)/(512*x^4*(2 + 3*x)^2) + (1215*Log[x])/1024 - (1215*Log[2 + 3*x])/1024","A",1
271,1,8,8,0.002849,"\int \frac{1}{2+2 x} \, dx","IntegrateAlgebraic[(2 + 2*x)^(-1),x]","\frac{1}{2} \log (x+1)","\frac{1}{2} \log (x+1)",1,"Log[1 + x]/2","A",1
272,1,10,10,0.0033663,"\int \frac{1}{4-6 x} \, dx","IntegrateAlgebraic[(4 - 6*x)^(-1),x]","-\frac{1}{6} \log (3 x-2)","-\frac{1}{6} \log (2-3 x)",1,"-1/6*Log[-2 + 3*x]","A",1
273,1,16,14,0.0069961,"\int \frac{1}{a+\sqrt{a} x} \, dx","IntegrateAlgebraic[(a + Sqrt[a]*x)^(-1),x]","\frac{\log \left(\sqrt{a} x+a\right)}{\sqrt{a}}","\frac{\log \left(\sqrt{a}+x\right)}{\sqrt{a}}",1,"Log[a + Sqrt[a]*x]/Sqrt[a]","A",1
274,1,20,20,0.0087916,"\int \frac{1}{a+\sqrt{-a} x} \, dx","IntegrateAlgebraic[(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
275,1,22,22,0.008437,"\int \frac{1}{a^2+\sqrt{-a} x} \, dx","IntegrateAlgebraic[(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
276,1,22,22,0.0089212,"\int \frac{1}{a^3+\sqrt{-a} x} \, dx","IntegrateAlgebraic[(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
277,1,21,21,0.0107881,"\int \frac{1}{\frac{1}{a}+\sqrt{-a} x} \, dx","IntegrateAlgebraic[(a^(-1) + Sqrt[-a]*x)^(-1),x]","\frac{\log \left(\sqrt{-a} a x+1\right)}{\sqrt{-a}}","\frac{\log \left(1-(-a)^{3/2} x\right)}{\sqrt{-a}}",1,"Log[1 + Sqrt[-a]*a*x]/Sqrt[-a]","A",1
278,1,23,20,0.0166412,"\int \frac{1}{\frac{1}{a^2}+\sqrt{-a} x} \, dx","IntegrateAlgebraic[(a^(-2) + Sqrt[-a]*x)^(-1),x]","\frac{\log \left(\sqrt{-a} a^2 x+1\right)}{\sqrt{-a}}","\frac{\log \left((-a)^{5/2} x+1\right)}{\sqrt{-a}}",1,"Log[1 + Sqrt[-a]*a^2*x]/Sqrt[-a]","A",1
279,1,11,11,0.0069675,"\int \frac{1}{x (1+b x)} \, dx","IntegrateAlgebraic[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",1
280,1,11,12,0.0064555,"\int \frac{1}{x (-1+b x)} \, dx","IntegrateAlgebraic[1/(x*(-1 + b*x)),x]","\log (b x-1)-\log (x)","\log (1-b x)-\log (x)",1,"-Log[x] + Log[-1 + b*x]","A",1
281,1,19,19,0.008169,"\int \frac{1}{x^2 (1+b x)} \, dx","IntegrateAlgebraic[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",1
282,1,17,18,0.0071741,"\int \frac{1}{x^2 (-1+b x)} \, dx","IntegrateAlgebraic[1/(x^2*(-1 + b*x)),x]","-b \log (x)+b \log (b x-1)+\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",1
283,1,14,14,0.0080752,"\int \left(\frac{b}{x}+\frac{1}{x^2 (1+b x)}\right) \, dx","IntegrateAlgebraic[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",1
284,1,57,72,0.0161391,"\int x^3 \sqrt{a+b x} \, dx","IntegrateAlgebraic[x^3*Sqrt[a + b*x],x]","-\frac{2 \sqrt{a+b x} \left(16 a^4-8 a^3 b x+6 a^2 b^2 x^2-5 a b^3 x^3-35 b^4 x^4\right)}{315 b^4}","-\frac{2 a^3 (a+b x)^{3/2}}{3 b^4}+\frac{6 a^2 (a+b x)^{5/2}}{5 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*Sqrt[a + b*x]*(16*a^4 - 8*a^3*b*x + 6*a^2*b^2*x^2 - 5*a*b^3*x^3 - 35*b^4*x^4))/(315*b^4)","A",1
285,1,46,53,0.0159876,"\int x^2 \sqrt{a+b x} \, dx","IntegrateAlgebraic[x^2*Sqrt[a + b*x],x]","\frac{2 \sqrt{a+b x} \left(8 a^3-4 a^2 b x+3 a b^2 x^2+15 b^3 x^3\right)}{105 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*Sqrt[a + b*x]*(8*a^3 - 4*a^2*b*x + 3*a*b^2*x^2 + 15*b^3*x^3))/(105*b^3)","A",1
286,1,35,34,0.0103327,"\int x \sqrt{a+b x} \, dx","IntegrateAlgebraic[x*Sqrt[a + b*x],x]","-\frac{2 \sqrt{a+b x} \left(2 a^2-a b x-3 b^2 x^2\right)}{15 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*Sqrt[a + b*x]*(2*a^2 - a*b*x - 3*b^2*x^2))/(15*b^2)","A",1
287,1,16,16,0.0045338,"\int \sqrt{a+b x} \, dx","IntegrateAlgebraic[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
288,1,35,35,0.021467,"\int \frac{\sqrt{a+b x}}{x} \, dx","IntegrateAlgebraic[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",1
289,1,39,39,0.0327758,"\int \frac{\sqrt{a+b x}}{x^2} \, dx","IntegrateAlgebraic[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",1
290,1,56,65,0.0409649,"\int \frac{\sqrt{a+b x}}{x^3} \, dx","IntegrateAlgebraic[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{(-2 a-b x) \sqrt{a+b x}}{4 a x^2}","\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,"((-2*a - b*x)*Sqrt[a + b*x])/(4*a*x^2) + (b^2*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/(4*a^(3/2))","A",1
291,1,67,87,0.0554258,"\int \frac{\sqrt{a+b x}}{x^4} \, dx","IntegrateAlgebraic[Sqrt[a + b*x]/x^4,x]","\frac{\sqrt{a+b x} \left(-8 a^2-2 a b x+3 b^2 x^2\right)}{24 a^2 x^3}-\frac{b^3 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{8 a^{5/2}}","-\frac{b^3 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{8 a^{5/2}}+\frac{b^2 \sqrt{a+b x}}{8 a^2 x}-\frac{\sqrt{a+b x}}{3 x^3}-\frac{b \sqrt{a+b x}}{12 a x^2}",1,"(Sqrt[a + b*x]*(-8*a^2 - 2*a*b*x + 3*b^2*x^2))/(24*a^2*x^3) - (b^3*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/(8*a^(5/2))","A",1
292,1,68,72,0.0169355,"\int x^3 (a+b x)^{3/2} \, dx","IntegrateAlgebraic[x^3*(a + b*x)^(3/2),x]","-\frac{2 \sqrt{a+b x} \left(16 a^5-8 a^4 b x+6 a^3 b^2 x^2-5 a^2 b^3 x^3-140 a b^4 x^4-105 b^5 x^5\right)}{1155 b^4}","-\frac{2 a^3 (a+b x)^{5/2}}{5 b^4}+\frac{6 a^2 (a+b x)^{7/2}}{7 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*Sqrt[a + b*x]*(16*a^5 - 8*a^4*b*x + 6*a^3*b^2*x^2 - 5*a^2*b^3*x^3 - 140*a*b^4*x^4 - 105*b^5*x^5))/(1155*b^4)","A",1
293,1,57,53,0.0140209,"\int x^2 (a+b x)^{3/2} \, dx","IntegrateAlgebraic[x^2*(a + b*x)^(3/2),x]","\frac{2 \sqrt{a+b x} \left(8 a^4-4 a^3 b x+3 a^2 b^2 x^2+50 a b^3 x^3+35 b^4 x^4\right)}{315 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*Sqrt[a + b*x]*(8*a^4 - 4*a^3*b*x + 3*a^2*b^2*x^2 + 50*a*b^3*x^3 + 35*b^4*x^4))/(315*b^3)","A",1
294,1,46,34,0.0121499,"\int x (a+b x)^{3/2} \, dx","IntegrateAlgebraic[x*(a + b*x)^(3/2),x]","-\frac{2 \sqrt{a+b x} \left(2 a^3-a^2 b x-8 a b^2 x^2-5 b^3 x^3\right)}{35 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*Sqrt[a + b*x]*(2*a^3 - a^2*b*x - 8*a*b^2*x^2 - 5*b^3*x^3))/(35*b^2)","A",1
295,1,16,16,0.0045261,"\int (a+b x)^{3/2} \, dx","IntegrateAlgebraic[(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
296,1,44,49,0.022928,"\int \frac{(a+b x)^{3/2}}{x} \, dx","IntegrateAlgebraic[(a + b*x)^(3/2)/x,x]","\frac{2}{3} \sqrt{a+b x} (4 a+b x)-2 a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)","-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*Sqrt[a + b*x]*(4*a + b*x))/3 - 2*a^(3/2)*ArcTanh[Sqrt[a + b*x]/Sqrt[a]]","A",1
297,1,46,51,0.0369593,"\int \frac{(a+b x)^{3/2}}{x^2} \, dx","IntegrateAlgebraic[(a + b*x)^(3/2)/x^2,x]","\frac{\sqrt{a+b x} (2 b x-a)}{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,"(Sqrt[a + b*x]*(-a + 2*b*x))/x - 3*Sqrt[a]*b*ArcTanh[Sqrt[a + b*x]/Sqrt[a]]","A",1
298,1,53,62,0.0528288,"\int \frac{(a+b x)^{3/2}}{x^3} \, dx","IntegrateAlgebraic[(a + b*x)^(3/2)/x^3,x]","\frac{(-2 a-5 b x) \sqrt{a+b x}}{4 x^2}-\frac{3 b^2 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{4 \sqrt{a}}","-\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,"((-2*a - 5*b*x)*Sqrt[a + b*x])/(4*x^2) - (3*b^2*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/(4*Sqrt[a])","A",1
299,1,67,84,0.0499754,"\int \frac{(a+b x)^{3/2}}{x^4} \, dx","IntegrateAlgebraic[(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{\sqrt{a+b x} \left(-8 a^2-14 a b x-3 b^2 x^2\right)}{24 a 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{(a+b x)^{3/2}}{3 x^3}-\frac{b \sqrt{a+b x}}{4 x^2}",1,"(Sqrt[a + b*x]*(-8*a^2 - 14*a*b*x - 3*b^2*x^2))/(24*a*x^3) + (b^3*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/(8*a^(3/2))","A",1
300,1,79,72,0.0211749,"\int x^3 (a+b x)^{5/2} \, dx","IntegrateAlgebraic[x^3*(a + b*x)^(5/2),x]","-\frac{2 \sqrt{a+b x} \left(16 a^6-8 a^5 b x+6 a^4 b^2 x^2-5 a^3 b^3 x^3-371 a^2 b^4 x^4-567 a b^5 x^5-231 b^6 x^6\right)}{3003 b^4}","-\frac{2 a^3 (a+b x)^{7/2}}{7 b^4}+\frac{2 a^2 (a+b x)^{9/2}}{3 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*Sqrt[a + b*x]*(16*a^6 - 8*a^5*b*x + 6*a^4*b^2*x^2 - 5*a^3*b^3*x^3 - 371*a^2*b^4*x^4 - 567*a*b^5*x^5 - 231*b^6*x^6))/(3003*b^4)","A",1
301,1,68,53,0.0147805,"\int x^2 (a+b x)^{5/2} \, dx","IntegrateAlgebraic[x^2*(a + b*x)^(5/2),x]","\frac{2 \sqrt{a+b x} \left(8 a^5-4 a^4 b x+3 a^3 b^2 x^2+113 a^2 b^3 x^3+161 a b^4 x^4+63 b^5 x^5\right)}{693 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*Sqrt[a + b*x]*(8*a^5 - 4*a^4*b*x + 3*a^3*b^2*x^2 + 113*a^2*b^3*x^3 + 161*a*b^4*x^4 + 63*b^5*x^5))/(693*b^3)","A",1
302,1,57,34,0.012238,"\int x (a+b x)^{5/2} \, dx","IntegrateAlgebraic[x*(a + b*x)^(5/2),x]","-\frac{2 \sqrt{a+b x} \left(2 a^4-a^3 b x-15 a^2 b^2 x^2-19 a b^3 x^3-7 b^4 x^4\right)}{63 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*Sqrt[a + b*x]*(2*a^4 - a^3*b*x - 15*a^2*b^2*x^2 - 19*a*b^3*x^3 - 7*b^4*x^4))/(63*b^2)","A",1
303,1,16,16,0.0047001,"\int (a+b x)^{5/2} \, dx","IntegrateAlgebraic[(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
304,1,56,65,0.0268057,"\int \frac{(a+b x)^{5/2}}{x} \, dx","IntegrateAlgebraic[(a + b*x)^(5/2)/x,x]","\frac{2}{15} \sqrt{a+b x} \left(23 a^2+11 a b x+3 b^2 x^2\right)-2 a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)","-2 a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)+2 a^2 \sqrt{a+b x}+\frac{2}{3} a (a+b x)^{3/2}+\frac{2}{5} (a+b x)^{5/2}",1,"(2*Sqrt[a + b*x]*(23*a^2 + 11*a*b*x + 3*b^2*x^2))/15 - 2*a^(5/2)*ArcTanh[Sqrt[a + b*x]/Sqrt[a]]","A",1
305,1,60,66,0.0473593,"\int \frac{(a+b x)^{5/2}}{x^2} \, dx","IntegrateAlgebraic[(a + b*x)^(5/2)/x^2,x]","\frac{\sqrt{a+b x} \left(-3 a^2+14 a b x+2 b^2 x^2\right)}{3 x}-5 a^{3/2} b \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)","-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,"(Sqrt[a + b*x]*(-3*a^2 + 14*a*b*x + 2*b^2*x^2))/(3*x) - 5*a^(3/2)*b*ArcTanh[Sqrt[a + b*x]/Sqrt[a]]","A",1
306,1,64,78,0.0638342,"\int \frac{(a+b x)^{5/2}}{x^3} \, dx","IntegrateAlgebraic[(a + b*x)^(5/2)/x^3,x]","\frac{\sqrt{a+b x} \left(-2 a^2-9 a b x+8 b^2 x^2\right)}{4 x^2}-\frac{15}{4} \sqrt{a} b^2 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)","\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,"(Sqrt[a + b*x]*(-2*a^2 - 9*a*b*x + 8*b^2*x^2))/(4*x^2) - (15*Sqrt[a]*b^2*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/4","A",1
307,1,64,81,0.0491256,"\int \frac{(a+b x)^{5/2}}{x^4} \, dx","IntegrateAlgebraic[(a + b*x)^(5/2)/x^4,x]","\frac{\sqrt{a+b x} \left(-8 a^2-26 a b x-33 b^2 x^2\right)}{24 x^3}-\frac{5 b^3 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{8 \sqrt{a}}","-\frac{5 b^3 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{8 \sqrt{a}}-\frac{5 b^2 \sqrt{a+b x}}{8 x}-\frac{(a+b x)^{5/2}}{3 x^3}-\frac{5 b (a+b x)^{3/2}}{12 x^2}",1,"(Sqrt[a + b*x]*(-8*a^2 - 26*a*b*x - 33*b^2*x^2))/(24*x^3) - (5*b^3*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/(8*Sqrt[a])","A",1
308,1,78,103,0.0702511,"\int \frac{(a+b x)^{5/2}}{x^5} \, dx","IntegrateAlgebraic[(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{\sqrt{a+b x} \left(-48 a^3-136 a^2 b x-118 a b^2 x^2-15 b^3 x^3\right)}{192 a x^4}","\frac{5 b^4 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{64 a^{3/2}}-\frac{5 b^3 \sqrt{a+b x}}{64 a x}-\frac{5 b^2 \sqrt{a+b x}}{32 x^2}-\frac{(a+b x)^{5/2}}{4 x^4}-\frac{5 b (a+b x)^{3/2}}{24 x^3}",1,"(Sqrt[a + b*x]*(-48*a^3 - 136*a^2*b*x - 118*a*b^2*x^2 - 15*b^3*x^3))/(192*a*x^4) + (5*b^4*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/(64*a^(3/2))","A",1
309,1,145,146,0.0272723,"\int x^7 (a+b x)^{9/2} \, dx","IntegrateAlgebraic[x^7*(a + b*x)^(9/2),x]","-\frac{2 \sqrt{a+b x} \left(2048 a^{12}-1024 a^{11} b x+768 a^{10} b^2 x^2-640 a^9 b^3 x^3+560 a^8 b^4 x^4-504 a^7 b^5 x^5+462 a^6 b^6 x^6-429 a^5 b^7 x^7-1659515 a^4 b^8 x^8-5810090 a^3 b^9 x^9-7759752 a^2 b^{10} x^{10}-4665089 a b^{11} x^{11}-1062347 b^{12} x^{12}\right)}{26558675 b^8}","-\frac{2 a^7 (a+b x)^{11/2}}{11 b^8}+\frac{14 a^6 (a+b x)^{13/2}}{13 b^8}-\frac{14 a^5 (a+b x)^{15/2}}{5 b^8}+\frac{70 a^4 (a+b x)^{17/2}}{17 b^8}-\frac{70 a^3 (a+b x)^{19/2}}{19 b^8}+\frac{2 a^2 (a+b x)^{21/2}}{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*Sqrt[a + b*x]*(2048*a^12 - 1024*a^11*b*x + 768*a^10*b^2*x^2 - 640*a^9*b^3*x^3 + 560*a^8*b^4*x^4 - 504*a^7*b^5*x^5 + 462*a^6*b^6*x^6 - 429*a^5*b^7*x^7 - 1659515*a^4*b^8*x^8 - 5810090*a^3*b^9*x^9 - 7759752*a^2*b^10*x^10 - 4665089*a*b^11*x^11 - 1062347*b^12*x^12))/(26558675*b^8)","A",1
310,1,134,127,0.0261497,"\int x^6 (a+b x)^{9/2} \, dx","IntegrateAlgebraic[x^6*(a + b*x)^(9/2),x]","\frac{2 \sqrt{a+b x} \left(1024 a^{11}-512 a^{10} b x+384 a^9 b^2 x^2-320 a^8 b^3 x^3+280 a^7 b^4 x^4-252 a^6 b^5 x^5+231 a^5 b^6 x^6+530959 a^4 b^7 x^7+1826110 a^3 b^8 x^8+2406690 a^2 b^9 x^9+1431859 a b^{10} x^{10}+323323 b^{11} x^{11}\right)}{7436429 b^7}","\frac{2 a^6 (a+b x)^{11/2}}{11 b^7}-\frac{12 a^5 (a+b x)^{13/2}}{13 b^7}+\frac{2 a^4 (a+b x)^{15/2}}{b^7}-\frac{40 a^3 (a+b x)^{17/2}}{17 b^7}+\frac{30 a^2 (a+b x)^{19/2}}{19 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*Sqrt[a + b*x]*(1024*a^11 - 512*a^10*b*x + 384*a^9*b^2*x^2 - 320*a^8*b^3*x^3 + 280*a^7*b^4*x^4 - 252*a^6*b^5*x^5 + 231*a^5*b^6*x^6 + 530959*a^4*b^7*x^7 + 1826110*a^3*b^8*x^8 + 2406690*a^2*b^9*x^9 + 1431859*a*b^10*x^10 + 323323*b^11*x^11))/(7436429*b^7)","A",1
311,1,123,110,0.0224156,"\int x^5 (a+b x)^{9/2} \, dx","IntegrateAlgebraic[x^5*(a + b*x)^(9/2),x]","-\frac{2 \sqrt{a+b x} \left(256 a^{10}-128 a^9 b x+96 a^8 b^2 x^2-80 a^7 b^3 x^3+70 a^6 b^4 x^4-63 a^5 b^5 x^5-80773 a^4 b^6 x^6-271414 a^3 b^7 x^7-351780 a^2 b^8 x^8-206635 a b^9 x^9-46189 b^{10} x^{10}\right)}{969969 b^6}","-\frac{2 a^5 (a+b x)^{11/2}}{11 b^6}+\frac{10 a^4 (a+b x)^{13/2}}{13 b^6}-\frac{4 a^3 (a+b x)^{15/2}}{3 b^6}+\frac{20 a^2 (a+b x)^{17/2}}{17 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*Sqrt[a + b*x]*(256*a^10 - 128*a^9*b*x + 96*a^8*b^2*x^2 - 80*a^7*b^3*x^3 + 70*a^6*b^4*x^4 - 63*a^5*b^5*x^5 - 80773*a^4*b^6*x^6 - 271414*a^3*b^7*x^7 - 351780*a^2*b^8*x^8 - 206635*a*b^9*x^9 - 46189*b^10*x^10))/(969969*b^6)","A",1
312,1,112,91,0.0222776,"\int x^4 (a+b x)^{9/2} \, dx","IntegrateAlgebraic[x^4*(a + b*x)^(9/2),x]","\frac{2 \sqrt{a+b x} \left(128 a^9-64 a^8 b x+48 a^7 b^2 x^2-40 a^6 b^3 x^3+35 a^5 b^4 x^4+23063 a^4 b^5 x^5+75086 a^3 b^6 x^6+95238 a^2 b^7 x^7+55055 a b^8 x^8+12155 b^9 x^9\right)}{230945 b^5}","\frac{2 a^4 (a+b x)^{11/2}}{11 b^5}-\frac{8 a^3 (a+b x)^{13/2}}{13 b^5}+\frac{4 a^2 (a+b x)^{15/2}}{5 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*Sqrt[a + b*x]*(128*a^9 - 64*a^8*b*x + 48*a^7*b^2*x^2 - 40*a^6*b^3*x^3 + 35*a^5*b^4*x^4 + 23063*a^4*b^5*x^5 + 75086*a^3*b^6*x^6 + 95238*a^2*b^7*x^7 + 55055*a*b^8*x^8 + 12155*b^9*x^9))/(230945*b^5)","A",1
313,1,101,72,0.0177676,"\int x^3 (a+b x)^{9/2} \, dx","IntegrateAlgebraic[x^3*(a + b*x)^(9/2),x]","-\frac{2 \sqrt{a+b x} \left(16 a^8-8 a^7 b x+6 a^6 b^2 x^2-5 a^5 b^3 x^3-1515 a^4 b^4 x^4-4714 a^3 b^5 x^5-5808 a^2 b^6 x^6-3289 a b^7 x^7-715 b^8 x^8\right)}{12155 b^4}","-\frac{2 a^3 (a+b x)^{11/2}}{11 b^4}+\frac{6 a^2 (a+b x)^{13/2}}{13 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*Sqrt[a + b*x]*(16*a^8 - 8*a^7*b*x + 6*a^6*b^2*x^2 - 5*a^5*b^3*x^3 - 1515*a^4*b^4*x^4 - 4714*a^3*b^5*x^5 - 5808*a^2*b^6*x^6 - 3289*a*b^7*x^7 - 715*b^8*x^8))/(12155*b^4)","A",1
314,1,90,53,0.0160845,"\int x^2 (a+b x)^{9/2} \, dx","IntegrateAlgebraic[x^2*(a + b*x)^(9/2),x]","\frac{2 \sqrt{a+b x} \left(8 a^7-4 a^6 b x+3 a^5 b^2 x^2+355 a^4 b^3 x^3+1030 a^3 b^4 x^4+1218 a^2 b^5 x^5+671 a b^6 x^6+143 b^7 x^7\right)}{2145 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*Sqrt[a + b*x]*(8*a^7 - 4*a^6*b*x + 3*a^5*b^2*x^2 + 355*a^4*b^3*x^3 + 1030*a^3*b^4*x^4 + 1218*a^2*b^5*x^5 + 671*a*b^6*x^6 + 143*b^7*x^7))/(2145*b^3)","A",1
315,1,79,34,0.0137062,"\int x (a+b x)^{9/2} \, dx","IntegrateAlgebraic[x*(a + b*x)^(9/2),x]","-\frac{2 \sqrt{a+b x} \left(2 a^6-a^5 b x-35 a^4 b^2 x^2-90 a^3 b^3 x^3-100 a^2 b^4 x^4-53 a b^5 x^5-11 b^6 x^6\right)}{143 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*Sqrt[a + b*x]*(2*a^6 - a^5*b*x - 35*a^4*b^2*x^2 - 90*a^3*b^3*x^3 - 100*a^2*b^4*x^4 - 53*a*b^5*x^5 - 11*b^6*x^6))/(143*b^2)","B",1
316,1,16,16,0.0046445,"\int (a+b x)^{9/2} \, dx","IntegrateAlgebraic[(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
317,1,78,97,0.0345424,"\int \frac{(a+b x)^{9/2}}{x} \, dx","IntegrateAlgebraic[(a + b*x)^(9/2)/x,x]","\frac{2}{315} \sqrt{a+b x} \left(563 a^4+506 a^3 b x+408 a^2 b^2 x^2+185 a b^3 x^3+35 b^4 x^4\right)-2 a^{9/2} \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)","-2 a^{9/2} \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)+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}+\frac{2}{7} a (a+b x)^{7/2}+\frac{2}{9} (a+b x)^{9/2}",1,"(2*Sqrt[a + b*x]*(563*a^4 + 506*a^3*b*x + 408*a^2*b^2*x^2 + 185*a*b^3*x^3 + 35*b^4*x^4))/315 - 2*a^(9/2)*ArcTanh[Sqrt[a + b*x]/Sqrt[a]]","A",1
318,1,82,98,0.0570518,"\int \frac{(a+b x)^{9/2}}{x^2} \, dx","IntegrateAlgebraic[(a + b*x)^(9/2)/x^2,x]","\frac{\sqrt{a+b x} \left(-35 a^4+388 a^3 b x+156 a^2 b^2 x^2+58 a b^3 x^3+10 b^4 x^4\right)}{35 x}-9 a^{7/2} b \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)","-9 a^{7/2} b \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)+9 a^3 b \sqrt{a+b x}+3 a^2 b (a+b x)^{3/2}-\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,"(Sqrt[a + b*x]*(-35*a^4 + 388*a^3*b*x + 156*a^2*b^2*x^2 + 58*a*b^3*x^3 + 10*b^4*x^4))/(35*x) - 9*a^(7/2)*b*ArcTanh[Sqrt[a + b*x]/Sqrt[a]]","A",1
319,1,86,114,0.0669368,"\int \frac{(a+b x)^{9/2}}{x^3} \, dx","IntegrateAlgebraic[(a + b*x)^(9/2)/x^3,x]","\frac{\sqrt{a+b x} \left(-10 a^4-85 a^3 b x+288 a^2 b^2 x^2+56 a b^3 x^3+8 b^4 x^4\right)}{20 x^2}-\frac{63}{4} a^{5/2} b^2 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)","-\frac{63}{4} a^{5/2} b^2 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)+\frac{63}{4} a^2 b^2 \sqrt{a+b x}+\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,"(Sqrt[a + b*x]*(-10*a^4 - 85*a^3*b*x + 288*a^2*b^2*x^2 + 56*a*b^3*x^3 + 8*b^4*x^4))/(20*x^2) - (63*a^(5/2)*b^2*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/4","A",1
320,1,86,114,0.0587017,"\int \frac{(a+b x)^{9/2}}{x^4} \, dx","IntegrateAlgebraic[(a + b*x)^(9/2)/x^4,x]","\frac{\sqrt{a+b x} \left(-8 a^4-50 a^3 b x-165 a^2 b^2 x^2+208 a b^3 x^3+16 b^4 x^4\right)}{24 x^3}-\frac{105}{8} a^{3/2} b^3 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)","-\frac{105}{8} a^{3/2} b^3 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)+\frac{35}{8} b^3 (a+b x)^{3/2}+\frac{105}{8} a b^3 \sqrt{a+b x}-\frac{21 b^2 (a+b x)^{5/2}}{8 x}-\frac{(a+b x)^{9/2}}{3 x^3}-\frac{3 b (a+b x)^{7/2}}{4 x^2}",1,"(Sqrt[a + b*x]*(-8*a^4 - 50*a^3*b*x - 165*a^2*b^2*x^2 + 208*a*b^3*x^3 + 16*b^4*x^4))/(24*x^3) - (105*a^(3/2)*b^3*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/8","A",1
321,1,86,116,0.0570929,"\int \frac{(a+b x)^{9/2}}{x^5} \, dx","IntegrateAlgebraic[(a + b*x)^(9/2)/x^5,x]","\frac{\sqrt{a+b x} \left(-16 a^4-88 a^3 b x-210 a^2 b^2 x^2-325 a b^3 x^3+128 b^4 x^4\right)}{64 x^4}-\frac{315}{64} \sqrt{a} b^4 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)","\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{105 b^3 (a+b x)^{3/2}}{64 x}-\frac{21 b^2 (a+b x)^{5/2}}{32 x^2}-\frac{(a+b x)^{9/2}}{4 x^4}-\frac{3 b (a+b x)^{7/2}}{8 x^3}",1,"(Sqrt[a + b*x]*(-16*a^4 - 88*a^3*b*x - 210*a^2*b^2*x^2 - 325*a*b^3*x^3 + 128*b^4*x^4))/(64*x^4) - (315*Sqrt[a]*b^4*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/64","A",1
322,1,86,119,0.0665871,"\int \frac{(a+b x)^{9/2}}{x^6} \, dx","IntegrateAlgebraic[(a + b*x)^(9/2)/x^6,x]","\frac{\sqrt{a+b x} \left(-128 a^4-656 a^3 b x-1368 a^2 b^2 x^2-1490 a b^3 x^3-965 b^4 x^4\right)}{640 x^5}-\frac{63 b^5 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{128 \sqrt{a}}","-\frac{63 b^5 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{128 \sqrt{a}}-\frac{63 b^4 \sqrt{a+b x}}{128 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{(a+b x)^{9/2}}{5 x^5}-\frac{9 b (a+b x)^{7/2}}{40 x^4}",1,"(Sqrt[a + b*x]*(-128*a^4 - 656*a^3*b*x - 1368*a^2*b^2*x^2 - 1490*a*b^3*x^3 - 965*b^4*x^4))/(640*x^5) - (63*b^5*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/(128*Sqrt[a])","A",1
323,1,100,141,0.0732606,"\int \frac{(a+b x)^{9/2}}{x^7} \, dx","IntegrateAlgebraic[(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{\sqrt{a+b x} \left(-1280 a^5-6272 a^4 b x-12144 a^3 b^2 x^2-11432 a^2 b^3 x^3-4910 a b^4 x^4-315 b^5 x^5\right)}{7680 a x^6}","\frac{21 b^6 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{512 a^{3/2}}-\frac{21 b^5 \sqrt{a+b x}}{512 a x}-\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{(a+b x)^{9/2}}{6 x^6}-\frac{3 b (a+b x)^{7/2}}{20 x^5}",1,"(Sqrt[a + b*x]*(-1280*a^5 - 6272*a^4*b*x - 12144*a^3*b^2*x^2 - 11432*a^2*b^3*x^3 - 4910*a*b^4*x^4 - 315*b^5*x^5))/(7680*a*x^6) + (21*b^6*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/(512*a^(3/2))","A",1
324,1,111,163,0.0733615,"\int \frac{(a+b x)^{9/2}}{x^8} \, dx","IntegrateAlgebraic[(a + b*x)^(9/2)/x^8,x]","\frac{\sqrt{a+b x} \left(-5120 a^6-24320 a^5 b x-44928 a^4 b^2 x^2-39056 a^3 b^3 x^3-14168 a^2 b^4 x^4-210 a b^5 x^5+315 b^6 x^6\right)}{35840 a^2 x^7}-\frac{9 b^7 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{1024 a^{5/2}}","-\frac{9 b^7 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{1024 a^{5/2}}+\frac{9 b^6 \sqrt{a+b x}}{1024 a^2 x}-\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{(a+b x)^{9/2}}{7 x^7}-\frac{3 b (a+b x)^{7/2}}{28 x^6}",1,"(Sqrt[a + b*x]*(-5120*a^6 - 24320*a^5*b*x - 44928*a^4*b^2*x^2 - 39056*a^3*b^3*x^3 - 14168*a^2*b^4*x^4 - 210*a*b^5*x^5 + 315*b^6*x^6))/(35840*a^2*x^7) - (9*b^7*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/(1024*a^(5/2))","A",1
325,1,39,39,0.0194384,"\int \frac{\sqrt{-a+b x}}{x} \, dx","IntegrateAlgebraic[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",1
326,1,42,42,0.0326634,"\int \frac{\sqrt{-a+b x}}{x^2} \, dx","IntegrateAlgebraic[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",1
327,1,59,71,0.0529854,"\int \frac{\sqrt{-a+b x}}{x^3} \, dx","IntegrateAlgebraic[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{(b x-2 a) \sqrt{b x-a}}{4 a x^2}","\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,"((-2*a + b*x)*Sqrt[-a + b*x])/(4*a*x^2) + (b^2*ArcTan[Sqrt[-a + b*x]/Sqrt[a]])/(4*a^(3/2))","A",1
328,1,49,55,0.025821,"\int \frac{(-a+b x)^{3/2}}{x} \, dx","IntegrateAlgebraic[(-a + b*x)^(3/2)/x,x]","2 a^{3/2} \tan ^{-1}\left(\frac{\sqrt{b x-a}}{\sqrt{a}}\right)-\frac{2}{3} (4 a-b x) \sqrt{b x-a}","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*(4*a - b*x)*Sqrt[-a + b*x])/3 + 2*a^(3/2)*ArcTan[Sqrt[-a + b*x]/Sqrt[a]]","A",1
329,1,48,57,0.033862,"\int \frac{(-a+b x)^{3/2}}{x^2} \, dx","IntegrateAlgebraic[(-a + b*x)^(3/2)/x^2,x]","\frac{\sqrt{b x-a} (a+2 b x)}{x}-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,"(Sqrt[-a + b*x]*(a + 2*b*x))/x - 3*Sqrt[a]*b*ArcTan[Sqrt[-a + b*x]/Sqrt[a]]","A",1
330,1,57,68,0.04948,"\int \frac{(-a+b x)^{3/2}}{x^3} \, dx","IntegrateAlgebraic[(-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{(2 a-5 b x) \sqrt{b x-a}}{4 x^2}","\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,"((2*a - 5*b*x)*Sqrt[-a + b*x])/(4*x^2) + (3*b^2*ArcTan[Sqrt[-a + b*x]/Sqrt[a]])/(4*Sqrt[a])","A",1
331,1,60,73,0.0306562,"\int \frac{(-a+b x)^{5/2}}{x} \, dx","IntegrateAlgebraic[(-a + b*x)^(5/2)/x,x]","\frac{2}{15} \sqrt{b x-a} \left(23 a^2-11 a b x+3 b^2 x^2\right)-2 a^{5/2} \tan ^{-1}\left(\frac{\sqrt{b x-a}}{\sqrt{a}}\right)","-2 a^{5/2} \tan ^{-1}\left(\frac{\sqrt{b x-a}}{\sqrt{a}}\right)+2 a^2 \sqrt{b x-a}-\frac{2}{3} a (b x-a)^{3/2}+\frac{2}{5} (b x-a)^{5/2}",1,"(2*Sqrt[-a + b*x]*(23*a^2 - 11*a*b*x + 3*b^2*x^2))/15 - 2*a^(5/2)*ArcTan[Sqrt[-a + b*x]/Sqrt[a]]","A",1
332,1,64,74,0.0435563,"\int \frac{(-a+b x)^{5/2}}{x^2} \, dx","IntegrateAlgebraic[(-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{\sqrt{b x-a} \left(-3 a^2-14 a b x+2 b^2 x^2\right)}{3 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}",1,"(Sqrt[-a + b*x]*(-3*a^2 - 14*a*b*x + 2*b^2*x^2))/(3*x) + 5*a^(3/2)*b*ArcTan[Sqrt[-a + b*x]/Sqrt[a]]","A",1
333,1,68,86,0.0553177,"\int \frac{(-a+b x)^{5/2}}{x^3} \, dx","IntegrateAlgebraic[(-a + b*x)^(5/2)/x^3,x]","\frac{\sqrt{b x-a} \left(-2 a^2+9 a b x+8 b^2 x^2\right)}{4 x^2}-\frac{15}{4} \sqrt{a} b^2 \tan ^{-1}\left(\frac{\sqrt{b x-a}}{\sqrt{a}}\right)","\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,"(Sqrt[-a + b*x]*(-2*a^2 + 9*a*b*x + 8*b^2*x^2))/(4*x^2) - (15*Sqrt[a]*b^2*ArcTan[Sqrt[-a + b*x]/Sqrt[a]])/4","A",1
334,1,57,89,0.0179288,"\int \frac{x^4}{\sqrt{a+b x}} \, dx","IntegrateAlgebraic[x^4/Sqrt[a + b*x],x]","\frac{2 \sqrt{a+b x} \left(128 a^4-64 a^3 b x+48 a^2 b^2 x^2-40 a b^3 x^3+35 b^4 x^4\right)}{315 b^5}","\frac{2 a^4 \sqrt{a+b x}}{b^5}-\frac{8 a^3 (a+b x)^{3/2}}{3 b^5}+\frac{12 a^2 (a+b x)^{5/2}}{5 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*Sqrt[a + b*x]*(128*a^4 - 64*a^3*b*x + 48*a^2*b^2*x^2 - 40*a*b^3*x^3 + 35*b^4*x^4))/(315*b^5)","A",1
335,1,46,68,0.0164499,"\int \frac{x^3}{\sqrt{a+b x}} \, dx","IntegrateAlgebraic[x^3/Sqrt[a + b*x],x]","-\frac{2 \sqrt{a+b x} \left(16 a^3-8 a^2 b x+6 a b^2 x^2-5 b^3 x^3\right)}{35 b^4}","-\frac{2 a^3 \sqrt{a+b x}}{b^4}+\frac{2 a^2 (a+b x)^{3/2}}{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*Sqrt[a + b*x]*(16*a^3 - 8*a^2*b*x + 6*a*b^2*x^2 - 5*b^3*x^3))/(35*b^4)","A",1
336,1,35,51,0.0129167,"\int \frac{x^2}{\sqrt{a+b x}} \, dx","IntegrateAlgebraic[x^2/Sqrt[a + b*x],x]","\frac{2 \sqrt{a+b x} \left(8 a^2-4 a b x+3 b^2 x^2\right)}{15 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*Sqrt[a + b*x]*(8*a^2 - 4*a*b*x + 3*b^2*x^2))/(15*b^3)","A",1
337,1,24,32,0.0098332,"\int \frac{x}{\sqrt{a+b x}} \, dx","IntegrateAlgebraic[x/Sqrt[a + b*x],x]","-\frac{2 (2 a-b x) \sqrt{a+b x}}{3 b^2}","\frac{2 (a+b x)^{3/2}}{3 b^2}-\frac{2 a \sqrt{a+b x}}{b^2}",1,"(-2*(2*a - b*x)*Sqrt[a + b*x])/(3*b^2)","A",1
338,1,14,14,0.0042091,"\int \frac{1}{\sqrt{a+b x}} \, dx","IntegrateAlgebraic[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
339,1,23,23,0.0107145,"\int \frac{1}{x \sqrt{a+b x}} \, dx","IntegrateAlgebraic[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",1
340,1,41,41,0.0316114,"\int \frac{1}{x^2 \sqrt{a+b x}} \, dx","IntegrateAlgebraic[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",1
341,1,56,68,0.0484582,"\int \frac{1}{x^3 \sqrt{a+b x}} \, dx","IntegrateAlgebraic[1/(x^3*Sqrt[a + b*x]),x]","\frac{\sqrt{a+b x} (3 b x-2 a)}{4 a^2 x^2}-\frac{3 b^2 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{4 a^{5/2}}","-\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 + 3*b*x))/(4*a^2*x^2) - (3*b^2*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/(4*a^(5/2))","A",1
342,1,67,90,0.0481675,"\int \frac{1}{x^4 \sqrt{a+b x}} \, dx","IntegrateAlgebraic[1/(x^4*Sqrt[a + b*x]),x]","\frac{5 b^3 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{8 a^{7/2}}+\frac{\sqrt{a+b x} \left(-8 a^2+10 a b x-15 b^2 x^2\right)}{24 a^3 x^3}","\frac{5 b^3 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{8 a^{7/2}}-\frac{5 b^2 \sqrt{a+b x}}{8 a^3 x}+\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]*(-8*a^2 + 10*a*b*x - 15*b^2*x^2))/(24*a^3*x^3) + (5*b^3*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/(8*a^(7/2))","A",1
343,1,57,85,0.0247629,"\int \frac{x^4}{(a+b x)^{3/2}} \, dx","IntegrateAlgebraic[x^4/(a + b*x)^(3/2),x]","-\frac{2 \left(128 a^4+64 a^3 b x-16 a^2 b^2 x^2+8 a b^3 x^3-5 b^4 x^4\right)}{35 b^5 \sqrt{a+b 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}",1,"(-2*(128*a^4 + 64*a^3*b*x - 16*a^2*b^2*x^2 + 8*a*b^3*x^3 - 5*b^4*x^4))/(35*b^5*Sqrt[a + b*x])","A",1
344,1,45,66,0.0177647,"\int \frac{x^3}{(a+b x)^{3/2}} \, dx","IntegrateAlgebraic[x^3/(a + b*x)^(3/2),x]","\frac{2 \left(16 a^3+8 a^2 b x-2 a b^2 x^2+b^3 x^3\right)}{5 b^4 \sqrt{a+b 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}",1,"(2*(16*a^3 + 8*a^2*b*x - 2*a*b^2*x^2 + b^3*x^3))/(5*b^4*Sqrt[a + b*x])","A",1
345,1,35,49,0.0144212,"\int \frac{x^2}{(a+b x)^{3/2}} \, dx","IntegrateAlgebraic[x^2/(a + b*x)^(3/2),x]","-\frac{2 \left(8 a^2+4 a b x-b^2 x^2\right)}{3 b^3 \sqrt{a+b 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}",1,"(-2*(8*a^2 + 4*a*b*x - b^2*x^2))/(3*b^3*Sqrt[a + b*x])","A",1
346,1,21,30,0.0110751,"\int \frac{x}{(a+b x)^{3/2}} \, dx","IntegrateAlgebraic[x/(a + b*x)^(3/2),x]","\frac{2 (2 a+b x)}{b^2 \sqrt{a+b x}}","\frac{2 a}{b^2 \sqrt{a+b x}}+\frac{2 \sqrt{a+b x}}{b^2}",1,"(2*(2*a + b*x))/(b^2*Sqrt[a + b*x])","A",1
347,1,14,14,0.0060797,"\int \frac{1}{(a+b x)^{3/2}} \, dx","IntegrateAlgebraic[(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
348,1,38,38,0.0251038,"\int \frac{1}{x (a+b x)^{3/2}} \, dx","IntegrateAlgebraic[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",1
349,1,49,57,0.0500154,"\int \frac{1}{x^2 (a+b x)^{3/2}} \, dx","IntegrateAlgebraic[1/(x^2*(a + b*x)^(3/2)),x]","\frac{3 b \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{a^{5/2}}+\frac{-a-3 b x}{a^2 x \sqrt{a+b x}}","\frac{3 b \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{a^{5/2}}-\frac{3 b}{a^2 \sqrt{a+b x}}-\frac{1}{a x \sqrt{a+b x}}",1,"(-a - 3*b*x)/(a^2*x*Sqrt[a + b*x]) + (3*b*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/a^(5/2)","A",1
350,1,67,87,0.0570141,"\int \frac{1}{x^3 (a+b x)^{3/2}} \, dx","IntegrateAlgebraic[1/(x^3*(a + b*x)^(3/2)),x]","\frac{-2 a^2+5 a b x+15 b^2 x^2}{4 a^3 x^2 \sqrt{a+b x}}-\frac{15 b^2 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{4 a^{7/2}}","-\frac{15 b^2 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{4 a^{7/2}}+\frac{15 b^2}{4 a^3 \sqrt{a+b x}}+\frac{5 b}{4 a^2 x \sqrt{a+b x}}-\frac{1}{2 a x^2 \sqrt{a+b x}}",1,"(-2*a^2 + 5*a*b*x + 15*b^2*x^2)/(4*a^3*x^2*Sqrt[a + b*x]) - (15*b^2*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/(4*a^(7/2))","A",1
351,1,57,87,0.0245381,"\int \frac{x^4}{(a+b x)^{5/2}} \, dx","IntegrateAlgebraic[x^4/(a + b*x)^(5/2),x]","\frac{2 \left(128 a^4+192 a^3 b x+48 a^2 b^2 x^2-8 a b^3 x^3+3 b^4 x^4\right)}{15 b^5 (a+b x)^{3/2}}","-\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*(128*a^4 + 192*a^3*b*x + 48*a^2*b^2*x^2 - 8*a*b^3*x^3 + 3*b^4*x^4))/(15*b^5*(a + b*x)^(3/2))","A",1
352,1,46,68,0.0180355,"\int \frac{x^3}{(a+b x)^{5/2}} \, dx","IntegrateAlgebraic[x^3/(a + b*x)^(5/2),x]","-\frac{2 \left(16 a^3+24 a^2 b x+6 a b^2 x^2-b^3 x^3\right)}{3 b^4 (a+b x)^{3/2}}","\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*(16*a^3 + 24*a^2*b*x + 6*a*b^2*x^2 - b^3*x^3))/(3*b^4*(a + b*x)^(3/2))","A",1
353,1,35,49,0.0142186,"\int \frac{x^2}{(a+b x)^{5/2}} \, dx","IntegrateAlgebraic[x^2/(a + b*x)^(5/2),x]","\frac{2 \left(8 a^2+12 a b x+3 b^2 x^2\right)}{3 b^3 (a+b x)^{3/2}}","-\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*(8*a^2 + 12*a*b*x + 3*b^2*x^2))/(3*b^3*(a + b*x)^(3/2))","A",1
354,1,24,32,0.0127575,"\int \frac{x}{(a+b x)^{5/2}} \, dx","IntegrateAlgebraic[x/(a + b*x)^(5/2),x]","-\frac{2 (2 a+3 b x)}{3 b^2 (a+b x)^{3/2}}","\frac{2 a}{3 b^2 (a+b x)^{3/2}}-\frac{2}{b^2 \sqrt{a+b x}}",1,"(-2*(2*a + 3*b*x))/(3*b^2*(a + b*x)^(3/2))","A",1
355,1,16,16,0.0056784,"\int \frac{1}{(a+b x)^{5/2}} \, dx","IntegrateAlgebraic[(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
356,1,48,54,0.0380522,"\int \frac{1}{x (a+b x)^{5/2}} \, dx","IntegrateAlgebraic[1/(x*(a + b*x)^(5/2)),x]","\frac{2 (4 a+3 b x)}{3 a^2 (a+b x)^{3/2}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{a^{5/2}}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{a^{5/2}}+\frac{2}{a^2 \sqrt{a+b x}}+\frac{2}{3 a (a+b x)^{3/2}}",1,"(2*(4*a + 3*b*x))/(3*a^2*(a + b*x)^(3/2)) - (2*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/a^(5/2)","A",1
357,1,63,74,0.0656266,"\int \frac{1}{x^2 (a+b x)^{5/2}} \, dx","IntegrateAlgebraic[1/(x^2*(a + b*x)^(5/2)),x]","\frac{5 b \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{a^{7/2}}+\frac{-3 a^2-20 a b x-15 b^2 x^2}{3 a^3 x (a+b x)^{3/2}}","\frac{5 b \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{a^{7/2}}-\frac{5 b}{a^3 \sqrt{a+b x}}-\frac{5 b}{3 a^2 (a+b x)^{3/2}}-\frac{1}{a x (a+b x)^{3/2}}",1,"(-3*a^2 - 20*a*b*x - 15*b^2*x^2)/(3*a^3*x*(a + b*x)^(3/2)) + (5*b*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/a^(7/2)","A",1
358,1,78,106,0.0689146,"\int \frac{1}{x^3 (a+b x)^{5/2}} \, dx","IntegrateAlgebraic[1/(x^3*(a + b*x)^(5/2)),x]","\frac{-6 a^3+21 a^2 b x+140 a b^2 x^2+105 b^3 x^3}{12 a^4 x^2 (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{35 b^2 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{4 a^{9/2}}+\frac{35 b^2}{4 a^4 \sqrt{a+b x}}+\frac{35 b^2}{12 a^3 (a+b x)^{3/2}}+\frac{7 b}{4 a^2 x (a+b x)^{3/2}}-\frac{1}{2 a x^2 (a+b x)^{3/2}}",1,"(-6*a^3 + 21*a^2*b*x + 140*a*b^2*x^2 + 105*b^3*x^3)/(12*a^4*x^2*(a + b*x)^(3/2)) - (35*b^2*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/(4*a^(9/2))","A",1
359,1,25,25,0.0114895,"\int \frac{1}{x \sqrt{-a+b x}} \, dx","IntegrateAlgebraic[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",1
360,1,44,44,0.0257879,"\int \frac{1}{x^2 \sqrt{-a+b x}} \, dx","IntegrateAlgebraic[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",1
361,1,60,74,0.0469604,"\int \frac{1}{x^3 \sqrt{-a+b x}} \, dx","IntegrateAlgebraic[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{\sqrt{b x-a} (2 a+3 b x)}{4 a^2 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 + 3*b*x))/(4*a^2*x^2) + (3*b^2*ArcTan[Sqrt[-a + b*x]/Sqrt[a]])/(4*a^(5/2))","A",1
362,1,50,42,0.0308009,"\int \frac{1}{x (-a+b x)^{3/2}} \, dx","IntegrateAlgebraic[1/(x*(-a + b*x)^(3/2)),x]","\frac{2 \sqrt{b x-a}}{a (a-b x)}-\frac{2 \tan ^{-1}\left(\frac{\sqrt{b x-a}}{\sqrt{a}}\right)}{a^{3/2}}","-\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*Sqrt[-a + b*x])/(a*(a - b*x)) - (2*ArcTan[Sqrt[-a + b*x]/Sqrt[a]])/a^(3/2)","A",1
363,1,61,62,0.0516022,"\int \frac{1}{x^2 (-a+b x)^{3/2}} \, dx","IntegrateAlgebraic[1/(x^2*(-a + b*x)^(3/2)),x]","\frac{\sqrt{b x-a} (3 b x-a)}{a^2 x (a-b x)}-\frac{3 b \tan ^{-1}\left(\frac{\sqrt{b x-a}}{\sqrt{a}}\right)}{a^{5/2}}","-\frac{3 b \tan ^{-1}\left(\frac{\sqrt{b x-a}}{\sqrt{a}}\right)}{a^{5/2}}-\frac{3 b}{a^2 \sqrt{b x-a}}+\frac{1}{a x \sqrt{b x-a}}",1,"(Sqrt[-a + b*x]*(-a + 3*b*x))/(a^2*x*(a - b*x)) - (3*b*ArcTan[Sqrt[-a + b*x]/Sqrt[a]])/a^(5/2)","A",1
364,1,79,95,0.0574261,"\int \frac{1}{x^3 (-a+b x)^{3/2}} \, dx","IntegrateAlgebraic[1/(x^3*(-a + b*x)^(3/2)),x]","\frac{\sqrt{b x-a} \left(-2 a^2-5 a b x+15 b^2 x^2\right)}{4 a^3 x^2 (a-b x)}-\frac{15 b^2 \tan ^{-1}\left(\frac{\sqrt{b x-a}}{\sqrt{a}}\right)}{4 a^{7/2}}","-\frac{15 b^2 \tan ^{-1}\left(\frac{\sqrt{b x-a}}{\sqrt{a}}\right)}{4 a^{7/2}}-\frac{15 b^2}{4 a^3 \sqrt{b x-a}}+\frac{5 b}{4 a^2 x \sqrt{b x-a}}+\frac{1}{2 a x^2 \sqrt{b x-a}}",1,"(Sqrt[-a + b*x]*(-2*a^2 - 5*a*b*x + 15*b^2*x^2))/(4*a^3*x^2*(a - b*x)) - (15*b^2*ArcTan[Sqrt[-a + b*x]/Sqrt[a]])/(4*a^(7/2))","A",1
365,1,60,60,0.043402,"\int \frac{1}{x (-a+b x)^{5/2}} \, dx","IntegrateAlgebraic[1/(x*(-a + b*x)^(5/2)),x]","\frac{2 \tan ^{-1}\left(\frac{\sqrt{b x-a}}{\sqrt{a}}\right)}{a^{5/2}}-\frac{2 (4 a-3 b x) \sqrt{b x-a}}{3 a^2 (a-b x)^2}","\frac{2 \tan ^{-1}\left(\frac{\sqrt{b x-a}}{\sqrt{a}}\right)}{a^{5/2}}+\frac{2}{a^2 \sqrt{b x-a}}-\frac{2}{3 a (b x-a)^{3/2}}",1,"(-2*(4*a - 3*b*x)*Sqrt[-a + b*x])/(3*a^2*(a - b*x)^2) + (2*ArcTan[Sqrt[-a + b*x]/Sqrt[a]])/a^(5/2)","A",1
366,1,75,81,0.0598695,"\int \frac{1}{x^2 (-a+b x)^{5/2}} \, dx","IntegrateAlgebraic[1/(x^2*(-a + b*x)^(5/2)),x]","\frac{5 b \tan ^{-1}\left(\frac{\sqrt{b x-a}}{\sqrt{a}}\right)}{a^{7/2}}+\frac{\sqrt{b x-a} \left(3 a^2-20 a b x+15 b^2 x^2\right)}{3 a^3 x (a-b x)^2}","\frac{5 b \tan ^{-1}\left(\frac{\sqrt{b x-a}}{\sqrt{a}}\right)}{a^{7/2}}+\frac{5 b}{a^3 \sqrt{b x-a}}-\frac{5 b}{3 a^2 (b x-a)^{3/2}}+\frac{1}{a x (b x-a)^{3/2}}",1,"(Sqrt[-a + b*x]*(3*a^2 - 20*a*b*x + 15*b^2*x^2))/(3*a^3*x*(a - b*x)^2) + (5*b*ArcTan[Sqrt[-a + b*x]/Sqrt[a]])/a^(7/2)","A",1
367,1,90,116,0.0658465,"\int \frac{1}{x^3 (-a+b x)^{5/2}} \, dx","IntegrateAlgebraic[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{\sqrt{b x-a} \left(6 a^3+21 a^2 b x-140 a b^2 x^2+105 b^3 x^3\right)}{12 a^4 x^2 (a-b x)^2}","\frac{35 b^2 \tan ^{-1}\left(\frac{\sqrt{b x-a}}{\sqrt{a}}\right)}{4 a^{9/2}}+\frac{35 b^2}{4 a^4 \sqrt{b x-a}}-\frac{35 b^2}{12 a^3 (b x-a)^{3/2}}+\frac{7 b}{4 a^2 x (b x-a)^{3/2}}+\frac{1}{2 a x^2 (b x-a)^{3/2}}",1,"(Sqrt[-a + b*x]*(6*a^3 + 21*a^2*b*x - 140*a*b^2*x^2 + 105*b^3*x^3))/(12*a^4*x^2*(a - b*x)^2) + (35*b^2*ArcTan[Sqrt[-a + b*x]/Sqrt[a]])/(4*a^(9/2))","A",1
368,0,0,13,0.0000791,"\int \frac{x^{-1+m} (2 a m+b (-1+2 m) x)}{2 (a+b x)^{3/2}} \, dx","IntegrateAlgebraic[(x^(-1 + m)*(2*a*m + b*(-1 + 2*m)*x))/(2*(a + b*x)^(3/2)),x]","\int \frac{x^{-1+m} (2 a m+b (-1+2 m) x)}{2 (a+b x)^{3/2}} \, dx","\frac{x^m}{\sqrt{a+b x}}",1,"Could not integrate","F",-1
369,0,0,13,0.0000771,"\int \left(-\frac{b x^m}{2 (a+b x)^{3/2}}+\frac{m x^{-1+m}}{\sqrt{a+b x}}\right) \, dx","IntegrateAlgebraic[-1/2*(b*x^m)/(a + b*x)^(3/2) + (m*x^(-1 + m))/Sqrt[a + b*x],x]","\int \left(-\frac{b x^m}{2 (a+b x)^{3/2}}+\frac{m x^{-1+m}}{\sqrt{a+b x}}\right) \, dx","\frac{x^m}{\sqrt{a+b x}}",1,"Could not integrate","F",-1
370,0,0,23,0.0000648,"\int \frac{x^{\frac{1-n}{2}+\frac{1}{2} (-3+n)}}{\sqrt{a+b x}} \, dx","IntegrateAlgebraic[x^((1 - n)/2 + (-3 + n)/2)/Sqrt[a + b*x],x]","\int \frac{x^{\frac{1-n}{2}+\frac{1}{2} (-3+n)}}{\sqrt{a+b x}} \, dx","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{\sqrt{a}}",1,"Could not integrate","F",-1
371,1,57,72,0.020082,"\int x^3 \sqrt[3]{a+b x} \, dx","IntegrateAlgebraic[x^3*(a + b*x)^(1/3),x]","-\frac{3 \sqrt[3]{a+b x} \left(81 a^4-27 a^3 b x+18 a^2 b^2 x^2-14 a b^3 x^3-140 b^4 x^4\right)}{1820 b^4}","-\frac{3 a^3 (a+b x)^{4/3}}{4 b^4}+\frac{9 a^2 (a+b x)^{7/3}}{7 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 + b*x)^(1/3)*(81*a^4 - 27*a^3*b*x + 18*a^2*b^2*x^2 - 14*a*b^3*x^3 - 140*b^4*x^4))/(1820*b^4)","A",1
372,1,46,53,0.0138633,"\int x^2 \sqrt[3]{a+b x} \, dx","IntegrateAlgebraic[x^2*(a + b*x)^(1/3),x]","\frac{3 \sqrt[3]{a+b x} \left(9 a^3-3 a^2 b x+2 a b^2 x^2+14 b^3 x^3\right)}{140 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 + b*x)^(1/3)*(9*a^3 - 3*a^2*b*x + 2*a*b^2*x^2 + 14*b^3*x^3))/(140*b^3)","A",1
373,1,35,34,0.0118293,"\int x \sqrt[3]{a+b x} \, dx","IntegrateAlgebraic[x*(a + b*x)^(1/3),x]","-\frac{3 \sqrt[3]{a+b x} \left(3 a^2-a b x-4 b^2 x^2\right)}{28 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 + b*x)^(1/3)*(3*a^2 - a*b*x - 4*b^2*x^2))/(28*b^2)","A",1
374,1,16,16,0.0047481,"\int \sqrt[3]{a+b x} \, dx","IntegrateAlgebraic[(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
375,1,116,91,0.0781738,"\int \frac{\sqrt[3]{a+b x}}{x} \, dx","IntegrateAlgebraic[(a + b*x)^(1/3)/x,x]","-\frac{1}{2} \sqrt[3]{a} \log \left(a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x}+(a+b x)^{2/3}\right)+3 \sqrt[3]{a+b x}+\sqrt[3]{a} \log \left(\sqrt[3]{a+b x}-\sqrt[3]{a}\right)-\sqrt{3} \sqrt[3]{a} \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x}}{\sqrt{3} \sqrt[3]{a}}+\frac{1}{\sqrt{3}}\right)","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[1/Sqrt[3] + (2*(a + b*x)^(1/3))/(Sqrt[3]*a^(1/3))] + a^(1/3)*Log[-a^(1/3) + (a + b*x)^(1/3)] - (a^(1/3)*Log[a^(2/3) + a^(1/3)*(a + b*x)^(1/3) + (a + b*x)^(2/3)])/2","A",1
376,1,125,97,0.1016388,"\int \frac{\sqrt[3]{a+b x}}{x^2} \, dx","IntegrateAlgebraic[(a + b*x)^(1/3)/x^2,x]","\frac{b \log \left(\sqrt[3]{a+b x}-\sqrt[3]{a}\right)}{3 a^{2/3}}-\frac{b \log \left(a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x}+(a+b x)^{2/3}\right)}{6 a^{2/3}}-\frac{b \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x}}{\sqrt{3} \sqrt[3]{a}}+\frac{1}{\sqrt{3}}\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[1/Sqrt[3] + (2*(a + b*x)^(1/3))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(2/3)) + (b*Log[-a^(1/3) + (a + b*x)^(1/3)])/(3*a^(2/3)) - (b*Log[a^(2/3) + a^(1/3)*(a + b*x)^(1/3) + (a + b*x)^(2/3)])/(6*a^(2/3))","A",1
377,1,146,127,0.1044249,"\int \frac{\sqrt[3]{a+b x}}{x^3} \, dx","IntegrateAlgebraic[(a + b*x)^(1/3)/x^3,x]","-\frac{b^2 \log \left(\sqrt[3]{a+b x}-\sqrt[3]{a}\right)}{9 a^{5/3}}+\frac{b^2 \log \left(a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x}+(a+b x)^{2/3}\right)}{18 a^{5/3}}+\frac{b^2 \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x}}{\sqrt{3} \sqrt[3]{a}}+\frac{1}{\sqrt{3}}\right)}{3 \sqrt{3} a^{5/3}}+\frac{(-3 a-b x) \sqrt[3]{a+b x}}{6 a x^2}","\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,"((-3*a - b*x)*(a + b*x)^(1/3))/(6*a*x^2) + (b^2*ArcTan[1/Sqrt[3] + (2*(a + b*x)^(1/3))/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(5/3)) - (b^2*Log[-a^(1/3) + (a + b*x)^(1/3)])/(9*a^(5/3)) + (b^2*Log[a^(2/3) + a^(1/3)*(a + b*x)^(1/3) + (a + b*x)^(2/3)])/(18*a^(5/3))","A",1
378,1,57,72,0.0165349,"\int x^3 (a+b x)^{2/3} \, dx","IntegrateAlgebraic[x^3*(a + b*x)^(2/3),x]","-\frac{3 (a+b x)^{2/3} \left(81 a^4-54 a^3 b x+45 a^2 b^2 x^2-40 a b^3 x^3-220 b^4 x^4\right)}{3080 b^4}","-\frac{3 a^3 (a+b x)^{5/3}}{5 b^4}+\frac{9 a^2 (a+b x)^{8/3}}{8 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 + b*x)^(2/3)*(81*a^4 - 54*a^3*b*x + 45*a^2*b^2*x^2 - 40*a*b^3*x^3 - 220*b^4*x^4))/(3080*b^4)","A",1
379,1,46,53,0.0137553,"\int x^2 (a+b x)^{2/3} \, dx","IntegrateAlgebraic[x^2*(a + b*x)^(2/3),x]","\frac{3 (a+b x)^{2/3} \left(9 a^3-6 a^2 b x+5 a b^2 x^2+20 b^3 x^3\right)}{220 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 + b*x)^(2/3)*(9*a^3 - 6*a^2*b*x + 5*a*b^2*x^2 + 20*b^3*x^3))/(220*b^3)","A",1
380,1,35,34,0.0112516,"\int x (a+b x)^{2/3} \, dx","IntegrateAlgebraic[x*(a + b*x)^(2/3),x]","-\frac{3 (a+b x)^{2/3} \left(3 a^2-2 a b x-5 b^2 x^2\right)}{40 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 + b*x)^(2/3)*(3*a^2 - 2*a*b*x - 5*b^2*x^2))/(40*b^2)","A",1
381,1,16,16,0.00505,"\int (a+b x)^{2/3} \, dx","IntegrateAlgebraic[(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
382,1,117,92,0.054514,"\int \frac{(a+b x)^{2/3}}{x} \, dx","IntegrateAlgebraic[(a + b*x)^(2/3)/x,x]","a^{2/3} \log \left(\sqrt[3]{a+b x}-\sqrt[3]{a}\right)-\frac{1}{2} a^{2/3} \log \left(a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x}+(a+b x)^{2/3}\right)+\sqrt{3} a^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x}}{\sqrt{3} \sqrt[3]{a}}+\frac{1}{\sqrt{3}}\right)+\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[1/Sqrt[3] + (2*(a + b*x)^(1/3))/(Sqrt[3]*a^(1/3))] + a^(2/3)*Log[-a^(1/3) + (a + b*x)^(1/3)] - (a^(2/3)*Log[a^(2/3) + a^(1/3)*(a + b*x)^(1/3) + (a + b*x)^(2/3)])/2","A",1
383,1,125,94,0.0948772,"\int \frac{(a+b x)^{2/3}}{x^2} \, dx","IntegrateAlgebraic[(a + b*x)^(2/3)/x^2,x]","-\frac{b \log \left(a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x}+(a+b x)^{2/3}\right)}{3 \sqrt[3]{a}}-\frac{(a+b x)^{2/3}}{x}+\frac{2 b \log \left(\sqrt[3]{a+b x}-\sqrt[3]{a}\right)}{3 \sqrt[3]{a}}+\frac{2 b \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x}}{\sqrt{3} \sqrt[3]{a}}+\frac{1}{\sqrt{3}}\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[1/Sqrt[3] + (2*(a + b*x)^(1/3))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(1/3)) + (2*b*Log[-a^(1/3) + (a + b*x)^(1/3)])/(3*a^(1/3)) - (b*Log[a^(2/3) + a^(1/3)*(a + b*x)^(1/3) + (a + b*x)^(2/3)])/(3*a^(1/3))","A",1
384,1,146,127,0.1277879,"\int \frac{(a+b x)^{2/3}}{x^3} \, dx","IntegrateAlgebraic[(a + b*x)^(2/3)/x^3,x]","-\frac{b^2 \log \left(\sqrt[3]{a+b x}-\sqrt[3]{a}\right)}{9 a^{4/3}}+\frac{b^2 \log \left(a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x}+(a+b x)^{2/3}\right)}{18 a^{4/3}}-\frac{b^2 \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x}}{\sqrt{3} \sqrt[3]{a}}+\frac{1}{\sqrt{3}}\right)}{3 \sqrt{3} a^{4/3}}+\frac{(-3 a-2 b x) (a+b x)^{2/3}}{6 a x^2}","\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,"((-3*a - 2*b*x)*(a + b*x)^(2/3))/(6*a*x^2) - (b^2*ArcTan[1/Sqrt[3] + (2*(a + b*x)^(1/3))/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(4/3)) - (b^2*Log[-a^(1/3) + (a + b*x)^(1/3)])/(9*a^(4/3)) + (b^2*Log[a^(2/3) + a^(1/3)*(a + b*x)^(1/3) + (a + b*x)^(2/3)])/(18*a^(4/3))","A",1
385,1,68,72,0.0170477,"\int x^3 (a+b x)^{4/3} \, dx","IntegrateAlgebraic[x^3*(a + b*x)^(4/3),x]","-\frac{3 \sqrt[3]{a+b x} \left(81 a^5-27 a^4 b x+18 a^3 b^2 x^2-14 a^2 b^3 x^3-595 a b^4 x^4-455 b^5 x^5\right)}{7280 b^4}","-\frac{3 a^3 (a+b x)^{7/3}}{7 b^4}+\frac{9 a^2 (a+b x)^{10/3}}{10 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 + b*x)^(1/3)*(81*a^5 - 27*a^4*b*x + 18*a^3*b^2*x^2 - 14*a^2*b^3*x^3 - 595*a*b^4*x^4 - 455*b^5*x^5))/(7280*b^4)","A",1
386,1,57,53,0.0147574,"\int x^2 (a+b x)^{4/3} \, dx","IntegrateAlgebraic[x^2*(a + b*x)^(4/3),x]","\frac{3 \sqrt[3]{a+b x} \left(9 a^4-3 a^3 b x+2 a^2 b^2 x^2+49 a b^3 x^3+35 b^4 x^4\right)}{455 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 + b*x)^(1/3)*(9*a^4 - 3*a^3*b*x + 2*a^2*b^2*x^2 + 49*a*b^3*x^3 + 35*b^4*x^4))/(455*b^3)","A",1
387,1,46,34,0.0127131,"\int x (a+b x)^{4/3} \, dx","IntegrateAlgebraic[x*(a + b*x)^(4/3),x]","-\frac{3 \sqrt[3]{a+b x} \left(3 a^3-a^2 b x-11 a b^2 x^2-7 b^3 x^3\right)}{70 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 + b*x)^(1/3)*(3*a^3 - a^2*b*x - 11*a*b^2*x^2 - 7*b^3*x^3))/(70*b^2)","A",1
388,1,16,16,0.0048658,"\int (a+b x)^{4/3} \, dx","IntegrateAlgebraic[(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
389,1,125,105,0.0609674,"\int \frac{(a+b x)^{4/3}}{x} \, dx","IntegrateAlgebraic[(a + b*x)^(4/3)/x,x]","a^{4/3} \log \left(\sqrt[3]{a+b x}-\sqrt[3]{a}\right)-\frac{1}{2} a^{4/3} \log \left(a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x}+(a+b x)^{2/3}\right)-\sqrt{3} a^{4/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x}}{\sqrt{3} \sqrt[3]{a}}+\frac{1}{\sqrt{3}}\right)+\frac{3}{4} \sqrt[3]{a+b x} (5 a+b 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}",1,"(3*(a + b*x)^(1/3)*(5*a + b*x))/4 - Sqrt[3]*a^(4/3)*ArcTan[1/Sqrt[3] + (2*(a + b*x)^(1/3))/(Sqrt[3]*a^(1/3))] + a^(4/3)*Log[-a^(1/3) + (a + b*x)^(1/3)] - (a^(4/3)*Log[a^(2/3) + a^(1/3)*(a + b*x)^(1/3) + (a + b*x)^(2/3)])/2","A",1
390,1,132,107,0.1081919,"\int \frac{(a+b x)^{4/3}}{x^2} \, dx","IntegrateAlgebraic[(a + b*x)^(4/3)/x^2,x]","-\frac{2}{3} \sqrt[3]{a} b \log \left(a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x}+(a+b x)^{2/3}\right)+\frac{\sqrt[3]{a+b x} (3 b x-a)}{x}+\frac{4}{3} \sqrt[3]{a} b \log \left(\sqrt[3]{a+b x}-\sqrt[3]{a}\right)-\frac{4 \sqrt[3]{a} b \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x}}{\sqrt{3} \sqrt[3]{a}}+\frac{1}{\sqrt{3}}\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,"((a + b*x)^(1/3)*(-a + 3*b*x))/x - (4*a^(1/3)*b*ArcTan[1/Sqrt[3] + (2*(a + b*x)^(1/3))/(Sqrt[3]*a^(1/3))])/Sqrt[3] + (4*a^(1/3)*b*Log[-a^(1/3) + (a + b*x)^(1/3)])/3 - (2*a^(1/3)*b*Log[a^(2/3) + a^(1/3)*(a + b*x)^(1/3) + (a + b*x)^(2/3)])/3","A",1
391,1,143,124,0.1065475,"\int \frac{(a+b x)^{4/3}}{x^3} \, dx","IntegrateAlgebraic[(a + b*x)^(4/3)/x^3,x]","\frac{2 b^2 \log \left(\sqrt[3]{a+b x}-\sqrt[3]{a}\right)}{9 a^{2/3}}-\frac{b^2 \log \left(a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x}+(a+b x)^{2/3}\right)}{9 a^{2/3}}-\frac{2 b^2 \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x}}{\sqrt{3} \sqrt[3]{a}}+\frac{1}{\sqrt{3}}\right)}{3 \sqrt{3} a^{2/3}}+\frac{(-3 a-7 b x) \sqrt[3]{a+b x}}{6 x^2}","-\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,"((-3*a - 7*b*x)*(a + b*x)^(1/3))/(6*x^2) - (2*b^2*ArcTan[1/Sqrt[3] + (2*(a + b*x)^(1/3))/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(2/3)) + (2*b^2*Log[-a^(1/3) + (a + b*x)^(1/3)])/(9*a^(2/3)) - (b^2*Log[a^(2/3) + a^(1/3)*(a + b*x)^(1/3) + (a + b*x)^(2/3)])/(9*a^(2/3))","A",1
392,1,46,72,0.0160263,"\int \frac{x^3}{\sqrt[3]{a+b x}} \, dx","IntegrateAlgebraic[x^3/(a + b*x)^(1/3),x]","-\frac{3 (a+b x)^{2/3} \left(81 a^3-54 a^2 b x+45 a b^2 x^2-40 b^3 x^3\right)}{440 b^4}","-\frac{3 a^3 (a+b x)^{2/3}}{2 b^4}+\frac{9 a^2 (a+b x)^{5/3}}{5 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 + b*x)^(2/3)*(81*a^3 - 54*a^2*b*x + 45*a*b^2*x^2 - 40*b^3*x^3))/(440*b^4)","A",1
393,1,35,53,0.0147104,"\int \frac{x^2}{\sqrt[3]{a+b x}} \, dx","IntegrateAlgebraic[x^2/(a + b*x)^(1/3),x]","\frac{3 (a+b x)^{2/3} \left(9 a^2-6 a b x+5 b^2 x^2\right)}{40 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 + b*x)^(2/3)*(9*a^2 - 6*a*b*x + 5*b^2*x^2))/(40*b^3)","A",1
394,1,24,34,0.0105772,"\int \frac{x}{\sqrt[3]{a+b x}} \, dx","IntegrateAlgebraic[x/(a + b*x)^(1/3),x]","-\frac{3 (3 a-2 b x) (a+b x)^{2/3}}{10 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*(3*a - 2*b*x)*(a + b*x)^(2/3))/(10*b^2)","A",1
395,1,16,16,0.0052882,"\int \frac{1}{\sqrt[3]{a+b x}} \, dx","IntegrateAlgebraic[(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
396,1,104,79,0.0457282,"\int \frac{1}{x \sqrt[3]{a+b x}} \, dx","IntegrateAlgebraic[1/(x*(a + b*x)^(1/3)),x]","-\frac{\log \left(a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x}+(a+b x)^{2/3}\right)}{2 \sqrt[3]{a}}+\frac{\log \left(\sqrt[3]{a+b x}-\sqrt[3]{a}\right)}{\sqrt[3]{a}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x}}{\sqrt{3} \sqrt[3]{a}}+\frac{1}{\sqrt{3}}\right)}{\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[1/Sqrt[3] + (2*(a + b*x)^(1/3))/(Sqrt[3]*a^(1/3))])/a^(1/3) + Log[-a^(1/3) + (a + b*x)^(1/3)]/a^(1/3) - Log[a^(2/3) + a^(1/3)*(a + b*x)^(1/3) + (a + b*x)^(2/3)]/(2*a^(1/3))","A",1
397,1,128,100,0.1028055,"\int \frac{1}{x^2 \sqrt[3]{a+b x}} \, dx","IntegrateAlgebraic[1/(x^2*(a + b*x)^(1/3)),x]","-\frac{b \log \left(\sqrt[3]{a+b x}-\sqrt[3]{a}\right)}{3 a^{4/3}}+\frac{b \log \left(a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x}+(a+b x)^{2/3}\right)}{6 a^{4/3}}-\frac{b \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x}}{\sqrt{3} \sqrt[3]{a}}+\frac{1}{\sqrt{3}}\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[1/Sqrt[3] + (2*(a + b*x)^(1/3))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(4/3)) - (b*Log[-a^(1/3) + (a + b*x)^(1/3)])/(3*a^(4/3)) + (b*Log[a^(2/3) + a^(1/3)*(a + b*x)^(1/3) + (a + b*x)^(2/3)])/(6*a^(4/3))","A",1
398,1,146,130,0.1231345,"\int \frac{1}{x^3 \sqrt[3]{a+b x}} \, dx","IntegrateAlgebraic[1/(x^3*(a + b*x)^(1/3)),x]","\frac{2 b^2 \log \left(\sqrt[3]{a+b x}-\sqrt[3]{a}\right)}{9 a^{7/3}}-\frac{b^2 \log \left(a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x}+(a+b x)^{2/3}\right)}{9 a^{7/3}}+\frac{2 b^2 \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x}}{\sqrt{3} \sqrt[3]{a}}+\frac{1}{\sqrt{3}}\right)}{3 \sqrt{3} a^{7/3}}+\frac{(a+b x)^{2/3} (4 b x-3 a)}{6 a^2 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)*(-3*a + 4*b*x))/(6*a^2*x^2) + (2*b^2*ArcTan[1/Sqrt[3] + (2*(a + b*x)^(1/3))/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(7/3)) + (2*b^2*Log[-a^(1/3) + (a + b*x)^(1/3)])/(9*a^(7/3)) - (b^2*Log[a^(2/3) + a^(1/3)*(a + b*x)^(1/3) + (a + b*x)^(2/3)])/(9*a^(7/3))","A",1
399,1,48,80,0.0173966,"\int \frac{x^3}{\sqrt[3]{-a+b x}} \, dx","IntegrateAlgebraic[x^3/(-a + b*x)^(1/3),x]","\frac{3 (b x-a)^{2/3} \left(81 a^3+54 a^2 b x+45 a b^2 x^2+40 b^3 x^3\right)}{440 b^4}","\frac{3 a^3 (b x-a)^{2/3}}{2 b^4}+\frac{9 a^2 (b x-a)^{5/3}}{5 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 + b*x)^(2/3)*(81*a^3 + 54*a^2*b*x + 45*a*b^2*x^2 + 40*b^3*x^3))/(440*b^4)","A",1
400,1,37,59,0.0146014,"\int \frac{x^2}{\sqrt[3]{-a+b x}} \, dx","IntegrateAlgebraic[x^2/(-a + b*x)^(1/3),x]","\frac{3 (b x-a)^{2/3} \left(9 a^2+6 a b x+5 b^2 x^2\right)}{40 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 + b*x)^(2/3)*(9*a^2 + 6*a*b*x + 5*b^2*x^2))/(40*b^3)","A",1
401,1,26,38,0.0115427,"\int \frac{x}{\sqrt[3]{-a+b x}} \, dx","IntegrateAlgebraic[x/(-a + b*x)^(1/3),x]","\frac{3 (b x-a)^{2/3} (3 a+2 b x)}{10 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 + b*x)^(2/3)*(3*a + 2*b*x))/(10*b^2)","A",1
402,1,18,18,0.005453,"\int \frac{1}{\sqrt[3]{-a+b x}} \, dx","IntegrateAlgebraic[(-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
403,1,113,82,0.0721957,"\int \frac{1}{x \sqrt[3]{-a+b x}} \, dx","IntegrateAlgebraic[1/(x*(-a + b*x)^(1/3)),x]","\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b x-a}+(b x-a)^{2/3}\right)}{2 \sqrt[3]{a}}-\frac{\log \left(\sqrt[3]{b x-a}+\sqrt[3]{a}\right)}{\sqrt[3]{a}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{b x-a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\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[1/Sqrt[3] - (2*(-a + b*x)^(1/3))/(Sqrt[3]*a^(1/3))])/a^(1/3)) - Log[a^(1/3) + (-a + b*x)^(1/3)]/a^(1/3) + Log[a^(2/3) - a^(1/3)*(-a + b*x)^(1/3) + (-a + b*x)^(2/3)]/(2*a^(1/3))","A",1
404,1,136,103,0.0945569,"\int \frac{1}{x^2 \sqrt[3]{-a+b x}} \, dx","IntegrateAlgebraic[1/(x^2*(-a + b*x)^(1/3)),x]","-\frac{b \log \left(\sqrt[3]{b x-a}+\sqrt[3]{a}\right)}{3 a^{4/3}}+\frac{b \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b x-a}+(b x-a)^{2/3}\right)}{6 a^{4/3}}-\frac{b \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{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[1/Sqrt[3] - (2*(-a + b*x)^(1/3))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(4/3)) - (b*Log[a^(1/3) + (-a + b*x)^(1/3)])/(3*a^(4/3)) + (b*Log[a^(2/3) - a^(1/3)*(-a + b*x)^(1/3) + (-a + b*x)^(2/3)])/(6*a^(4/3))","A",1
405,1,155,136,0.0988964,"\int \frac{1}{x^3 \sqrt[3]{-a+b x}} \, dx","IntegrateAlgebraic[1/(x^3*(-a + b*x)^(1/3)),x]","-\frac{2 b^2 \log \left(\sqrt[3]{b x-a}+\sqrt[3]{a}\right)}{9 a^{7/3}}+\frac{b^2 \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b x-a}+(b x-a)^{2/3}\right)}{9 a^{7/3}}-\frac{2 b^2 \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{b x-a}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{7/3}}+\frac{(b x-a)^{2/3} (3 a+4 b x)}{6 a^2 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)*(3*a + 4*b*x))/(6*a^2*x^2) - (2*b^2*ArcTan[1/Sqrt[3] - (2*(-a + b*x)^(1/3))/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(7/3)) - (2*b^2*Log[a^(1/3) + (-a + b*x)^(1/3)])/(9*a^(7/3)) + (b^2*Log[a^(2/3) - a^(1/3)*(-a + b*x)^(1/3) + (-a + b*x)^(2/3)])/(9*a^(7/3))","A",1
406,1,46,70,0.0151175,"\int \frac{x^3}{(a+b x)^{2/3}} \, dx","IntegrateAlgebraic[x^3/(a + b*x)^(2/3),x]","-\frac{3 \sqrt[3]{a+b x} \left(81 a^3-27 a^2 b x+18 a b^2 x^2-14 b^3 x^3\right)}{140 b^4}","-\frac{3 a^3 \sqrt[3]{a+b x}}{b^4}+\frac{9 a^2 (a+b x)^{4/3}}{4 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 + b*x)^(1/3)*(81*a^3 - 27*a^2*b*x + 18*a*b^2*x^2 - 14*b^3*x^3))/(140*b^4)","A",1
407,1,35,51,0.012254,"\int \frac{x^2}{(a+b x)^{2/3}} \, dx","IntegrateAlgebraic[x^2/(a + b*x)^(2/3),x]","\frac{3 \sqrt[3]{a+b x} \left(9 a^2-3 a b x+2 b^2 x^2\right)}{14 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 + b*x)^(1/3)*(9*a^2 - 3*a*b*x + 2*b^2*x^2))/(14*b^3)","A",1
408,1,24,32,0.009899,"\int \frac{x}{(a+b x)^{2/3}} \, dx","IntegrateAlgebraic[x/(a + b*x)^(2/3),x]","-\frac{3 (3 a-b x) \sqrt[3]{a+b x}}{4 b^2}","\frac{3 (a+b x)^{4/3}}{4 b^2}-\frac{3 a \sqrt[3]{a+b x}}{b^2}",1,"(-3*(3*a - b*x)*(a + b*x)^(1/3))/(4*b^2)","A",1
409,1,14,14,0.0046368,"\int \frac{1}{(a+b x)^{2/3}} \, dx","IntegrateAlgebraic[(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
410,1,105,80,0.046435,"\int \frac{1}{x (a+b x)^{2/3}} \, dx","IntegrateAlgebraic[1/(x*(a + b*x)^(2/3)),x]","\frac{\log \left(\sqrt[3]{a+b x}-\sqrt[3]{a}\right)}{a^{2/3}}-\frac{\log \left(a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x}+(a+b x)^{2/3}\right)}{2 a^{2/3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x}}{\sqrt{3} \sqrt[3]{a}}+\frac{1}{\sqrt{3}}\right)}{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[1/Sqrt[3] + (2*(a + b*x)^(1/3))/(Sqrt[3]*a^(1/3))])/a^(2/3)) + Log[-a^(1/3) + (a + b*x)^(1/3)]/a^(2/3) - Log[a^(2/3) + a^(1/3)*(a + b*x)^(1/3) + (a + b*x)^(2/3)]/(2*a^(2/3))","A",1
411,1,128,98,0.1019826,"\int \frac{1}{x^2 (a+b x)^{2/3}} \, dx","IntegrateAlgebraic[1/(x^2*(a + b*x)^(2/3)),x]","-\frac{2 b \log \left(\sqrt[3]{a+b x}-\sqrt[3]{a}\right)}{3 a^{5/3}}+\frac{b \log \left(a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x}+(a+b x)^{2/3}\right)}{3 a^{5/3}}+\frac{2 b \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x}}{\sqrt{3} \sqrt[3]{a}}+\frac{1}{\sqrt{3}}\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[1/Sqrt[3] + (2*(a + b*x)^(1/3))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(5/3)) - (2*b*Log[-a^(1/3) + (a + b*x)^(1/3)])/(3*a^(5/3)) + (b*Log[a^(2/3) + a^(1/3)*(a + b*x)^(1/3) + (a + b*x)^(2/3)])/(3*a^(5/3))","A",1
412,1,146,130,0.1004395,"\int \frac{1}{x^3 (a+b x)^{2/3}} \, dx","IntegrateAlgebraic[1/(x^3*(a + b*x)^(2/3)),x]","\frac{5 b^2 \log \left(\sqrt[3]{a+b x}-\sqrt[3]{a}\right)}{9 a^{8/3}}-\frac{5 b^2 \log \left(a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x}+(a+b x)^{2/3}\right)}{18 a^{8/3}}-\frac{5 b^2 \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x}}{\sqrt{3} \sqrt[3]{a}}+\frac{1}{\sqrt{3}}\right)}{3 \sqrt{3} a^{8/3}}+\frac{\sqrt[3]{a+b x} (5 b x-3 a)}{6 a^2 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)*(-3*a + 5*b*x))/(6*a^2*x^2) - (5*b^2*ArcTan[1/Sqrt[3] + (2*(a + b*x)^(1/3))/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(8/3)) + (5*b^2*Log[-a^(1/3) + (a + b*x)^(1/3)])/(9*a^(8/3)) - (5*b^2*Log[a^(2/3) + a^(1/3)*(a + b*x)^(1/3) + (a + b*x)^(2/3)])/(18*a^(8/3))","A",1
413,1,46,70,0.0182934,"\int \frac{x^3}{(a+b x)^{4/3}} \, dx","IntegrateAlgebraic[x^3/(a + b*x)^(4/3),x]","\frac{3 \left(81 a^3+27 a^2 b x-9 a b^2 x^2+5 b^3 x^3\right)}{40 b^4 \sqrt[3]{a+b 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}",1,"(3*(81*a^3 + 27*a^2*b*x - 9*a*b^2*x^2 + 5*b^3*x^3))/(40*b^4*(a + b*x)^(1/3))","A",1
414,1,35,49,0.0149727,"\int \frac{x^2}{(a+b x)^{4/3}} \, dx","IntegrateAlgebraic[x^2/(a + b*x)^(4/3),x]","-\frac{3 \left(9 a^2+3 a b x-b^2 x^2\right)}{5 b^3 \sqrt[3]{a+b 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}",1,"(-3*(9*a^2 + 3*a*b*x - b^2*x^2))/(5*b^3*(a + b*x)^(1/3))","A",1
415,1,23,32,0.0127579,"\int \frac{x}{(a+b x)^{4/3}} \, dx","IntegrateAlgebraic[x/(a + b*x)^(4/3),x]","\frac{3 (3 a+b x)}{2 b^2 \sqrt[3]{a+b x}}","\frac{3 a}{b^2 \sqrt[3]{a+b x}}+\frac{3 (a+b x)^{2/3}}{2 b^2}",1,"(3*(3*a + b*x))/(2*b^2*(a + b*x)^(1/3))","A",1
416,1,14,14,0.0063502,"\int \frac{1}{(a+b x)^{4/3}} \, dx","IntegrateAlgebraic[(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
417,1,118,93,0.0643096,"\int \frac{1}{x (a+b x)^{4/3}} \, dx","IntegrateAlgebraic[1/(x*(a + b*x)^(4/3)),x]","\frac{\log \left(\sqrt[3]{a+b x}-\sqrt[3]{a}\right)}{a^{4/3}}-\frac{\log \left(a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x}+(a+b x)^{2/3}\right)}{2 a^{4/3}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x}}{\sqrt{3} \sqrt[3]{a}}+\frac{1}{\sqrt{3}}\right)}{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[1/Sqrt[3] + (2*(a + b*x)^(1/3))/(Sqrt[3]*a^(1/3))])/a^(4/3) + Log[-a^(1/3) + (a + b*x)^(1/3)]/a^(4/3) - Log[a^(2/3) + a^(1/3)*(a + b*x)^(1/3) + (a + b*x)^(2/3)]/(2*a^(4/3))","A",1
418,1,135,113,0.1336989,"\int \frac{1}{x^2 (a+b x)^{4/3}} \, dx","IntegrateAlgebraic[1/(x^2*(a + b*x)^(4/3)),x]","-\frac{4 b \log \left(\sqrt[3]{a+b x}-\sqrt[3]{a}\right)}{3 a^{7/3}}+\frac{2 b \log \left(a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x}+(a+b x)^{2/3}\right)}{3 a^{7/3}}-\frac{4 b \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x}}{\sqrt{3} \sqrt[3]{a}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3} a^{7/3}}+\frac{-a-4 b x}{a^2 x \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{4 b}{a^2 \sqrt[3]{a+b x}}-\frac{1}{a x \sqrt[3]{a+b x}}",1,"(-a - 4*b*x)/(a^2*x*(a + b*x)^(1/3)) - (4*b*ArcTan[1/Sqrt[3] + (2*(a + b*x)^(1/3))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(7/3)) - (4*b*Log[-a^(1/3) + (a + b*x)^(1/3)])/(3*a^(7/3)) + (2*b*Log[a^(2/3) + a^(1/3)*(a + b*x)^(1/3) + (a + b*x)^(2/3)])/(3*a^(7/3))","A",1
419,1,157,149,0.1403991,"\int \frac{1}{x^3 (a+b x)^{4/3}} \, dx","IntegrateAlgebraic[1/(x^3*(a + b*x)^(4/3)),x]","\frac{14 b^2 \log \left(\sqrt[3]{a+b x}-\sqrt[3]{a}\right)}{9 a^{10/3}}-\frac{7 b^2 \log \left(a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x}+(a+b x)^{2/3}\right)}{9 a^{10/3}}+\frac{14 b^2 \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x}}{\sqrt{3} \sqrt[3]{a}}+\frac{1}{\sqrt{3}}\right)}{3 \sqrt{3} a^{10/3}}+\frac{-3 a^2+7 a b x+28 b^2 x^2}{6 a^3 x^2 \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{14 b^2}{3 a^3 \sqrt[3]{a+b x}}+\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^2 + 7*a*b*x + 28*b^2*x^2)/(6*a^3*x^2*(a + b*x)^(1/3)) + (14*b^2*ArcTan[1/Sqrt[3] + (2*(a + b*x)^(1/3))/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(10/3)) + (14*b^2*Log[-a^(1/3) + (a + b*x)^(1/3)])/(9*a^(10/3)) - (7*b^2*Log[a^(2/3) + a^(1/3)*(a + b*x)^(1/3) + (a + b*x)^(2/3)])/(9*a^(10/3))","A",1
420,1,102,71,0.0591246,"\int \frac{1}{x \sqrt[3]{a^3+b^3 x}} \, dx","IntegrateAlgebraic[1/(x*(a^3 + b^3*x)^(1/3)),x]","\frac{\log \left(\sqrt[3]{a^3+b^3 x}-a\right)}{a}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3+b^3 x}}{\sqrt{3} a}+\frac{1}{\sqrt{3}}\right)}{a}-\frac{\log \left(a \sqrt[3]{a^3+b^3 x}+\left(a^3+b^3 x\right)^{2/3}+a^2\right)}{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[1/Sqrt[3] + (2*(a^3 + b^3*x)^(1/3))/(Sqrt[3]*a)])/a + Log[-a + (a^3 + b^3*x)^(1/3)]/a - Log[a^2 + a*(a^3 + b^3*x)^(1/3) + (a^3 + b^3*x)^(2/3)]/(2*a)","A",1
421,1,106,73,0.0529096,"\int \frac{1}{x \sqrt[3]{a^3-b^3 x}} \, dx","IntegrateAlgebraic[1/(x*(a^3 - b^3*x)^(1/3)),x]","\frac{\log \left(\sqrt[3]{a^3-b^3 x}-a\right)}{a}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3-b^3 x}}{\sqrt{3} a}+\frac{1}{\sqrt{3}}\right)}{a}-\frac{\log \left(a \sqrt[3]{a^3-b^3 x}+\left(a^3-b^3 x\right)^{2/3}+a^2\right)}{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[1/Sqrt[3] + (2*(a^3 - b^3*x)^(1/3))/(Sqrt[3]*a)])/a + Log[-a + (a^3 - b^3*x)^(1/3)]/a - Log[a^2 + a*(a^3 - b^3*x)^(1/3) + (a^3 - b^3*x)^(2/3)]/(2*a)","A",1
422,1,111,74,0.0604246,"\int \frac{1}{x \sqrt[3]{-a^3+b^3 x}} \, dx","IntegrateAlgebraic[1/(x*(-a^3 + b^3*x)^(1/3)),x]","-\frac{\log \left(\sqrt[3]{b^3 x-a^3}+a\right)}{a}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{b^3 x-a^3}}{\sqrt{3} a}\right)}{a}+\frac{\log \left(-a \sqrt[3]{b^3 x-a^3}+\left(b^3 x-a^3\right)^{2/3}+a^2\right)}{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[1/Sqrt[3] - (2*(-a^3 + b^3*x)^(1/3))/(Sqrt[3]*a)])/a) - Log[a + (-a^3 + b^3*x)^(1/3)]/a + Log[a^2 - a*(-a^3 + b^3*x)^(1/3) + (-a^3 + b^3*x)^(2/3)]/(2*a)","A",1
423,1,115,76,0.0527562,"\int \frac{1}{x \sqrt[3]{-a^3-b^3 x}} \, dx","IntegrateAlgebraic[1/(x*(-a^3 - b^3*x)^(1/3)),x]","-\frac{\log \left(\sqrt[3]{-a^3-b^3 x}+a\right)}{a}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{-a^3-b^3 x}}{\sqrt{3} a}\right)}{a}+\frac{\log \left(-a \sqrt[3]{-a^3-b^3 x}+\left(-a^3-b^3 x\right)^{2/3}+a^2\right)}{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[1/Sqrt[3] - (2*(-a^3 - b^3*x)^(1/3))/(Sqrt[3]*a)])/a) - Log[a + (-a^3 - b^3*x)^(1/3)]/a + Log[a^2 - a*(-a^3 - b^3*x)^(1/3) + (-a^3 - b^3*x)^(2/3)]/(2*a)","A",1
424,1,103,72,0.0438035,"\int \frac{1}{x \left(a^3+b^3 x\right)^{2/3}} \, dx","IntegrateAlgebraic[1/(x*(a^3 + b^3*x)^(2/3)),x]","\frac{\log \left(\sqrt[3]{a^3+b^3 x}-a\right)}{a^2}-\frac{\log \left(a \sqrt[3]{a^3+b^3 x}+\left(a^3+b^3 x\right)^{2/3}+a^2\right)}{2 a^2}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3+b^3 x}}{\sqrt{3} a}+\frac{1}{\sqrt{3}}\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}",1,"-((Sqrt[3]*ArcTan[1/Sqrt[3] + (2*(a^3 + b^3*x)^(1/3))/(Sqrt[3]*a)])/a^2) + Log[-a + (a^3 + b^3*x)^(1/3)]/a^2 - Log[a^2 + a*(a^3 + b^3*x)^(1/3) + (a^3 + b^3*x)^(2/3)]/(2*a^2)","A",1
425,1,107,74,0.0424084,"\int \frac{1}{x \left(a^3-b^3 x\right)^{2/3}} \, dx","IntegrateAlgebraic[1/(x*(a^3 - b^3*x)^(2/3)),x]","\frac{\log \left(\sqrt[3]{a^3-b^3 x}-a\right)}{a^2}-\frac{\log \left(a \sqrt[3]{a^3-b^3 x}+\left(a^3-b^3 x\right)^{2/3}+a^2\right)}{2 a^2}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3-b^3 x}}{\sqrt{3} a}+\frac{1}{\sqrt{3}}\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}",1,"-((Sqrt[3]*ArcTan[1/Sqrt[3] + (2*(a^3 - b^3*x)^(1/3))/(Sqrt[3]*a)])/a^2) + Log[-a + (a^3 - b^3*x)^(1/3)]/a^2 - Log[a^2 + a*(a^3 - b^3*x)^(1/3) + (a^3 - b^3*x)^(2/3)]/(2*a^2)","A",1
426,1,110,74,0.0447131,"\int \frac{1}{x \left(-a^3+b^3 x\right)^{2/3}} \, dx","IntegrateAlgebraic[1/(x*(-a^3 + b^3*x)^(2/3)),x]","\frac{\log \left(\sqrt[3]{b^3 x-a^3}+a\right)}{a^2}-\frac{\log \left(-a \sqrt[3]{b^3 x-a^3}+\left(b^3 x-a^3\right)^{2/3}+a^2\right)}{2 a^2}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{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}",1,"-((Sqrt[3]*ArcTan[1/Sqrt[3] - (2*(-a^3 + b^3*x)^(1/3))/(Sqrt[3]*a)])/a^2) + Log[a + (-a^3 + b^3*x)^(1/3)]/a^2 - Log[a^2 - a*(-a^3 + b^3*x)^(1/3) + (-a^3 + b^3*x)^(2/3)]/(2*a^2)","A",1
427,1,114,76,0.0409664,"\int \frac{1}{x \left(-a^3-b^3 x\right)^{2/3}} \, dx","IntegrateAlgebraic[1/(x*(-a^3 - b^3*x)^(2/3)),x]","\frac{\log \left(\sqrt[3]{-a^3-b^3 x}+a\right)}{a^2}-\frac{\log \left(-a \sqrt[3]{-a^3-b^3 x}+\left(-a^3-b^3 x\right)^{2/3}+a^2\right)}{2 a^2}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{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}",1,"-((Sqrt[3]*ArcTan[1/Sqrt[3] - (2*(-a^3 - b^3*x)^(1/3))/(Sqrt[3]*a)])/a^2) + Log[a + (-a^3 - b^3*x)^(1/3)]/a^2 - Log[a^2 - a*(-a^3 - b^3*x)^(1/3) + (-a^3 - b^3*x)^(2/3)]/(2*a^2)","A",1
428,0,0,25,0.0000531,"\int x^m (a+b x) \, dx","IntegrateAlgebraic[x^m*(a + b*x),x]","\int x^m (a+b x) \, dx","\frac{a x^{m+1}}{m+1}+\frac{b x^{m+2}}{m+2}",1,"Could not integrate","F",-1
429,1,21,21,0.0077667,"\int x^{5/2} (a+b x) \, dx","IntegrateAlgebraic[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",1
430,1,21,21,0.0074197,"\int x^{3/2} (a+b x) \, dx","IntegrateAlgebraic[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",1
431,1,21,21,0.0074863,"\int \sqrt{x} (a+b x) \, dx","IntegrateAlgebraic[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",1
432,1,19,19,0.0060018,"\int \frac{a+b x}{\sqrt{x}} \, dx","IntegrateAlgebraic[(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",1
433,1,17,17,0.0085341,"\int \frac{a+b x}{x^{3/2}} \, dx","IntegrateAlgebraic[(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",1
434,1,19,19,0.0089234,"\int \frac{a+b x}{x^{5/2}} \, dx","IntegrateAlgebraic[(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",1
435,0,0,43,0.0000532,"\int x^m (a+b x)^2 \, dx","IntegrateAlgebraic[x^m*(a + b*x)^2,x]","\int x^m (a+b x)^2 \, dx","\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,"Could not integrate","F",-1
436,1,36,36,0.0098298,"\int x^{5/2} (a+b x)^2 \, dx","IntegrateAlgebraic[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",1
437,1,36,36,0.0095154,"\int x^{3/2} (a+b x)^2 \, dx","IntegrateAlgebraic[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",1
438,1,36,36,0.0094028,"\int \sqrt{x} (a+b x)^2 \, dx","IntegrateAlgebraic[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",1
439,1,34,34,0.0103746,"\int \frac{(a+b x)^2}{\sqrt{x}} \, dx","IntegrateAlgebraic[(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",1
440,1,32,32,0.0103665,"\int \frac{(a+b x)^2}{x^{3/2}} \, dx","IntegrateAlgebraic[(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",1
441,1,32,32,0.0101363,"\int \frac{(a+b x)^2}{x^{5/2}} \, dx","IntegrateAlgebraic[(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",1
442,0,0,61,0.0000523,"\int x^m (a+b x)^3 \, dx","IntegrateAlgebraic[x^m*(a + b*x)^3,x]","\int x^m (a+b x)^3 \, dx","\frac{a^3 x^{m+1}}{m+1}+\frac{3 a^2 b x^{m+2}}{m+2}+\frac{3 a b^2 x^{m+3}}{m+3}+\frac{b^3 x^{m+4}}{m+4}",1,"Could not integrate","F",-1
443,1,51,51,0.0127561,"\int x^{5/2} (a+b x)^3 \, dx","IntegrateAlgebraic[x^(5/2)*(a + b*x)^3,x]","\frac{2}{7} a^3 x^{7/2}+\frac{2}{3} a^2 b x^{9/2}+\frac{6}{11} a b^2 x^{11/2}+\frac{2}{13} b^3 x^{13/2}","\frac{2}{7} a^3 x^{7/2}+\frac{2}{3} a^2 b x^{9/2}+\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",1
444,1,51,51,0.0135871,"\int x^{3/2} (a+b x)^3 \, dx","IntegrateAlgebraic[x^(3/2)*(a + b*x)^3,x]","\frac{2}{5} a^3 x^{5/2}+\frac{6}{7} a^2 b x^{7/2}+\frac{2}{3} a b^2 x^{9/2}+\frac{2}{11} b^3 x^{11/2}","\frac{2}{5} a^3 x^{5/2}+\frac{6}{7} a^2 b x^{7/2}+\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",1
445,1,51,51,0.0125784,"\int \sqrt{x} (a+b x)^3 \, dx","IntegrateAlgebraic[Sqrt[x]*(a + b*x)^3,x]","\frac{2}{3} a^3 x^{3/2}+\frac{6}{5} a^2 b x^{5/2}+\frac{6}{7} a b^2 x^{7/2}+\frac{2}{9} b^3 x^{9/2}","\frac{2}{3} a^3 x^{3/2}+\frac{6}{5} a^2 b x^{5/2}+\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",1
446,1,47,47,0.0122809,"\int \frac{(a+b x)^3}{\sqrt{x}} \, dx","IntegrateAlgebraic[(a + b*x)^3/Sqrt[x],x]","2 a^3 \sqrt{x}+2 a^2 b x^{3/2}+\frac{6}{5} a b^2 x^{5/2}+\frac{2}{7} b^3 x^{7/2}","2 a^3 \sqrt{x}+2 a^2 b x^{3/2}+\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",1
447,1,45,45,0.0153275,"\int \frac{(a+b x)^3}{x^{3/2}} \, dx","IntegrateAlgebraic[(a + b*x)^3/x^(3/2),x]","-\frac{2 a^3}{\sqrt{x}}+6 a^2 b \sqrt{x}+2 a b^2 x^{3/2}+\frac{2}{5} b^3 x^{5/2}","-\frac{2 a^3}{\sqrt{x}}+6 a^2 b \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",1
448,1,47,47,0.0173977,"\int \frac{(a+b x)^3}{x^{5/2}} \, dx","IntegrateAlgebraic[(a + b*x)^3/x^(5/2),x]","-\frac{2 a^3}{3 x^{3/2}}-\frac{6 a^2 b}{\sqrt{x}}+6 a b^2 \sqrt{x}+\frac{2}{3} b^3 x^{3/2}","-\frac{2 a^3}{3 x^{3/2}}-\frac{6 a^2 b}{\sqrt{x}}+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",1
449,1,68,68,0.0402946,"\int \frac{x^{5/2}}{a+b x} \, dx","IntegrateAlgebraic[x^(5/2)/(a + b*x),x]","-\frac{2 a^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{7/2}}+\frac{2 a^2 \sqrt{x}}{b^3}-\frac{2 a x^{3/2}}{3 b^2}+\frac{2 x^{5/2}}{5 b}","-\frac{2 a^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{7/2}}+\frac{2 a^2 \sqrt{x}}{b^3}-\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",1
450,1,53,53,0.030771,"\int \frac{x^{3/2}}{a+b x} \, dx","IntegrateAlgebraic[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",1
451,1,40,40,0.0171159,"\int \frac{\sqrt{x}}{a+b x} \, dx","IntegrateAlgebraic[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",1
452,1,29,29,0.0103212,"\int \frac{1}{\sqrt{x} (a+b x)} \, dx","IntegrateAlgebraic[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",1
453,1,40,40,0.0211778,"\int \frac{1}{x^{3/2} (a+b x)} \, dx","IntegrateAlgebraic[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",1
454,1,53,53,0.031945,"\int \frac{1}{x^{5/2} (a+b x)} \, dx","IntegrateAlgebraic[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",1
455,1,68,68,0.0381214,"\int \frac{1}{x^{7/2} (a+b x)} \, dx","IntegrateAlgebraic[1/(x^(7/2)*(a + b*x)),x]","-\frac{2 b^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{a^{7/2}}-\frac{2 b^2}{a^3 \sqrt{x}}+\frac{2 b}{3 a^2 x^{3/2}}-\frac{2}{5 a x^{5/2}}","-\frac{2 b^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{a^{7/2}}-\frac{2 b^2}{a^3 \sqrt{x}}+\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",1
456,1,71,70,0.0580731,"\int \frac{x^{5/2}}{(a+b x)^2} \, dx","IntegrateAlgebraic[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{\sqrt{x} \left(-\frac{5 a^2}{b^3}-\frac{10 a x}{3 b^2}+\frac{2 x^2}{3 b}\right)}{a+b 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}",1,"(Sqrt[x]*((-5*a^2)/b^3 - (10*a*x)/(3*b^2) + (2*x^2)/(3*b)))/(a + b*x) + (5*a^(3/2)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/b^(7/2)","A",1
457,1,57,57,0.0434686,"\int \frac{x^{3/2}}{(a+b x)^2} \, dx","IntegrateAlgebraic[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{a \sqrt{x}}{b^2 (a+b x)}+\frac{2 \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,"(2*Sqrt[x])/b^2 + (a*Sqrt[x])/(b^2*(a + b*x)) - (3*Sqrt[a]*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/b^(5/2)","A",1
458,1,46,46,0.031515,"\int \frac{\sqrt{x}}{(a+b x)^2} \, dx","IntegrateAlgebraic[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",1
459,1,45,45,0.0334693,"\int \frac{1}{\sqrt{x} (a+b x)^2} \, dx","IntegrateAlgebraic[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",1
460,1,58,56,0.0484514,"\int \frac{1}{x^{3/2} (a+b x)^2} \, dx","IntegrateAlgebraic[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{b \sqrt{x}}{a^2 (a+b x)}-\frac{2}{a^2 \sqrt{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,"-2/(a^2*Sqrt[x]) - (b*Sqrt[x])/(a^2*(a + b*x)) - (3*Sqrt[b]*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/a^(5/2)","A",1
461,1,72,69,0.0532347,"\int \frac{1}{x^{5/2} (a+b x)^2} \, dx","IntegrateAlgebraic[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{b^2 \sqrt{x}}{a^3 (a+b x)}+\frac{4 b}{a^3 \sqrt{x}}-\frac{2}{3 a^2 x^{3/2}}","\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,"-2/(3*a^2*x^(3/2)) + (4*b)/(a^3*Sqrt[x]) + (b^2*Sqrt[x])/(a^3*(a + b*x)) + (5*b^(3/2)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/a^(7/2)","A",1
462,1,89,95,0.0697244,"\int \frac{x^{7/2}}{(a+b x)^3} \, dx","IntegrateAlgebraic[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{-105 a^3 \sqrt{x}-175 a^2 b x^{3/2}-56 a b^2 x^{5/2}+8 b^3 x^{7/2}}{12 b^4 (a+b x)^2}","\frac{35 a^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 b^{9/2}}-\frac{35 a \sqrt{x}}{4 b^4}-\frac{7 x^{5/2}}{4 b^2 (a+b x)}-\frac{x^{7/2}}{2 b (a+b x)^2}+\frac{35 x^{3/2}}{12 b^3}",1,"(-105*a^3*Sqrt[x] - 175*a^2*b*x^(3/2) - 56*a*b^2*x^(5/2) + 8*b^3*x^(7/2))/(12*b^4*(a + b*x)^2) + (35*a^(3/2)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(4*b^(9/2))","A",1
463,1,76,82,0.0612634,"\int \frac{x^{5/2}}{(a+b x)^3} \, dx","IntegrateAlgebraic[x^(5/2)/(a + b*x)^3,x]","\frac{15 a^2 \sqrt{x}+25 a b x^{3/2}+8 b^2 x^{5/2}}{4 b^3 (a+b x)^2}-\frac{15 \sqrt{a} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 b^{7/2}}","-\frac{15 \sqrt{a} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 b^{7/2}}-\frac{5 x^{3/2}}{4 b^2 (a+b x)}-\frac{x^{5/2}}{2 b (a+b x)^2}+\frac{15 \sqrt{x}}{4 b^3}",1,"(15*a^2*Sqrt[x] + 25*a*b*x^(3/2) + 8*b^2*x^(5/2))/(4*b^3*(a + b*x)^2) - (15*Sqrt[a]*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(4*b^(7/2))","A",1
464,1,63,70,0.0551877,"\int \frac{x^{3/2}}{(a+b x)^3} \, dx","IntegrateAlgebraic[x^(3/2)/(a + b*x)^3,x]","\frac{3 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 \sqrt{a} b^{5/2}}+\frac{-3 a \sqrt{x}-5 b x^{3/2}}{4 b^2 (a+b x)^2}","\frac{3 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 \sqrt{a} b^{5/2}}-\frac{3 \sqrt{x}}{4 b^2 (a+b x)}-\frac{x^{3/2}}{2 b (a+b x)^2}",1,"(-3*a*Sqrt[x] - 5*b*x^(3/2))/(4*b^2*(a + b*x)^2) + (3*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(4*Sqrt[a]*b^(5/2))","A",1
465,1,61,73,0.0419425,"\int \frac{\sqrt{x}}{(a+b x)^3} \, dx","IntegrateAlgebraic[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} \left(\frac{x}{4 a}-\frac{1}{4 b}\right)}{(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]*(-1/4*1/b + x/(4*a)))/(a + b*x)^2 + ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]]/(4*a^(3/2)*b^(3/2))","A",1
466,1,63,70,0.0453839,"\int \frac{1}{\sqrt{x} (a+b x)^3} \, dx","IntegrateAlgebraic[1/(Sqrt[x]*(a + b*x)^3),x]","\frac{3 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 a^{5/2} \sqrt{b}}+\frac{5 a \sqrt{x}+3 b x^{3/2}}{4 a^2 (a+b x)^2}","\frac{3 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 a^{5/2} \sqrt{b}}+\frac{3 \sqrt{x}}{4 a^2 (a+b x)}+\frac{\sqrt{x}}{2 a (a+b x)^2}",1,"(5*a*Sqrt[x] + 3*b*x^(3/2))/(4*a^2*(a + b*x)^2) + (3*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(4*a^(5/2)*Sqrt[b])","A",1
467,1,73,82,0.0561179,"\int \frac{1}{x^{3/2} (a+b x)^3} \, dx","IntegrateAlgebraic[1/(x^(3/2)*(a + b*x)^3),x]","\frac{-\frac{15 b^2 x^2}{4 a^3}-\frac{25 b x}{4 a^2}-\frac{2}{a}}{\sqrt{x} (a+b x)^2}-\frac{15 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 a^{7/2}}","-\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{5}{4 a^2 \sqrt{x} (a+b x)}+\frac{1}{2 a \sqrt{x} (a+b x)^2}",1,"(-2/a - (25*b*x)/(4*a^2) - (15*b^2*x^2)/(4*a^3))/(Sqrt[x]*(a + b*x)^2) - (15*Sqrt[b]*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(4*a^(7/2))","A",1
468,1,88,95,0.059814,"\int \frac{1}{x^{5/2} (a+b x)^3} \, dx","IntegrateAlgebraic[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{\frac{35 b^3 x^3}{4 a^4}+\frac{175 b^2 x^2}{12 a^3}+\frac{14 b x}{3 a^2}-\frac{2}{3 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{35 b}{4 a^4 \sqrt{x}}-\frac{35}{12 a^3 x^{3/2}}+\frac{7}{4 a^2 x^{3/2} (a+b x)}+\frac{1}{2 a x^{3/2} (a+b x)^2}",1,"(-2/(3*a) + (14*b*x)/(3*a^2) + (175*b^2*x^2)/(12*a^3) + (35*b^3*x^3)/(4*a^4))/(x^(3/2)*(a + b*x)^2) + (35*b^(3/2)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(4*a^(9/2))","A",1
469,1,68,68,0.04191,"\int \frac{x^{5/2}}{-a+b x} \, dx","IntegrateAlgebraic[x^(5/2)/(-a + b*x),x]","-\frac{2 a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{7/2}}+\frac{2 a^2 \sqrt{x}}{b^3}+\frac{2 a x^{3/2}}{3 b^2}+\frac{2 x^{5/2}}{5 b}","-\frac{2 a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{7/2}}+\frac{2 a^2 \sqrt{x}}{b^3}+\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",1
470,1,53,53,0.0317835,"\int \frac{x^{3/2}}{-a+b x} \, dx","IntegrateAlgebraic[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",1
471,1,40,40,0.0167951,"\int \frac{\sqrt{x}}{-a+b x} \, dx","IntegrateAlgebraic[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",1
472,1,29,29,0.011139,"\int \frac{1}{\sqrt{x} (-a+b x)} \, dx","IntegrateAlgebraic[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",1
473,1,40,40,0.0214926,"\int \frac{1}{x^{3/2} (-a+b x)} \, dx","IntegrateAlgebraic[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",1
474,1,53,53,0.0329937,"\int \frac{1}{x^{5/2} (-a+b x)} \, dx","IntegrateAlgebraic[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",1
475,1,68,68,0.0381415,"\int \frac{1}{x^{7/2} (-a+b x)} \, dx","IntegrateAlgebraic[1/(x^(7/2)*(-a + b*x)),x]","-\frac{2 b^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{a^{7/2}}+\frac{2 b^2}{a^3 \sqrt{x}}+\frac{2 b}{3 a^2 x^{3/2}}+\frac{2}{5 a x^{5/2}}","-\frac{2 b^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{a^{7/2}}+\frac{2 b^2}{a^3 \sqrt{x}}+\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",1
476,1,72,70,0.0664569,"\int \frac{x^{5/2}}{(-a+b x)^2} \, dx","IntegrateAlgebraic[x^(5/2)/(-a + b*x)^2,x]","\frac{\sqrt{x} \left(\frac{5 a^2}{b^3}-\frac{10 a x}{3 b^2}-\frac{2 x^2}{3 b}\right)}{a-b x}-\frac{5 a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{7/2}}","-\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,"(Sqrt[x]*((5*a^2)/b^3 - (10*a*x)/(3*b^2) - (2*x^2)/(3*b)))/(a - b*x) - (5*a^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/b^(7/2)","A",1
477,1,57,57,0.0516204,"\int \frac{x^{3/2}}{(-a+b x)^2} \, dx","IntegrateAlgebraic[x^(3/2)/(-a + b*x)^2,x]","\frac{\sqrt{x} \left(\frac{3 a}{b^2}-\frac{2 x}{b}\right)}{a-b x}-\frac{3 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{5/2}}","-\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,"(Sqrt[x]*((3*a)/b^2 - (2*x)/b))/(a - b*x) - (3*Sqrt[a]*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/b^(5/2)","A",1
478,1,49,47,0.0405046,"\int \frac{\sqrt{x}}{(-a+b x)^2} \, dx","IntegrateAlgebraic[Sqrt[x]/(-a + b*x)^2,x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{\sqrt{a} b^{3/2}}-\frac{\sqrt{x}}{b (b x-a)}","\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",1
479,1,46,46,0.0284408,"\int \frac{1}{\sqrt{x} (-a+b x)^2} \, dx","IntegrateAlgebraic[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",1
480,1,60,57,0.0515716,"\int \frac{1}{x^{3/2} (-a+b x)^2} \, dx","IntegrateAlgebraic[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{b \sqrt{x}}{a^2 (b x-a)}-\frac{2}{a^2 \sqrt{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,"-2/(a^2*Sqrt[x]) - (b*Sqrt[x])/(a^2*(-a + b*x)) + (3*Sqrt[b]*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/a^(5/2)","A",1
481,1,74,70,0.0680432,"\int \frac{1}{x^{5/2} (-a+b x)^2} \, dx","IntegrateAlgebraic[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{-2 a^2-10 a b x+15 b^2 x^2}{3 a^4 x^{3/2}-3 a^3 b x^{5/2}}","\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,"(-2*a^2 - 10*a*b*x + 15*b^2*x^2)/(3*a^4*x^(3/2) - 3*a^3*b*x^(5/2)) + (5*b^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/a^(7/2)","A",1
482,1,91,97,0.0743247,"\int \frac{x^{7/2}}{(-a+b x)^3} \, dx","IntegrateAlgebraic[x^(7/2)/(-a + b*x)^3,x]","\frac{105 a^3 \sqrt{x}-175 a^2 b x^{3/2}+56 a b^2 x^{5/2}+8 b^3 x^{7/2}}{12 b^4 (b x-a)^2}-\frac{35 a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 b^{9/2}}","-\frac{35 a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 b^{9/2}}+\frac{35 a \sqrt{x}}{4 b^4}+\frac{7 x^{5/2}}{4 b^2 (a-b x)}-\frac{x^{7/2}}{2 b (a-b x)^2}+\frac{35 x^{3/2}}{12 b^3}",1,"(105*a^3*Sqrt[x] - 175*a^2*b*x^(3/2) + 56*a*b^2*x^(5/2) + 8*b^3*x^(7/2))/(12*b^4*(-a + b*x)^2) - (35*a^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(4*b^(9/2))","A",1
483,1,78,84,0.0649855,"\int \frac{x^{5/2}}{(-a+b x)^3} \, dx","IntegrateAlgebraic[x^(5/2)/(-a + b*x)^3,x]","\frac{15 a^2 \sqrt{x}-25 a b x^{3/2}+8 b^2 x^{5/2}}{4 b^3 (b x-a)^2}-\frac{15 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 b^{7/2}}","-\frac{15 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 b^{7/2}}+\frac{5 x^{3/2}}{4 b^2 (a-b x)}-\frac{x^{5/2}}{2 b (a-b x)^2}+\frac{15 \sqrt{x}}{4 b^3}",1,"(15*a^2*Sqrt[x] - 25*a*b*x^(3/2) + 8*b^2*x^(5/2))/(4*b^3*(-a + b*x)^2) - (15*Sqrt[a]*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(4*b^(7/2))","A",1
484,1,65,72,0.0547499,"\int \frac{x^{3/2}}{(-a+b x)^3} \, dx","IntegrateAlgebraic[x^(3/2)/(-a + b*x)^3,x]","\frac{3 a \sqrt{x}-5 b x^{3/2}}{4 b^2 (b x-a)^2}-\frac{3 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 \sqrt{a} b^{5/2}}","-\frac{3 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 \sqrt{a} b^{5/2}}+\frac{3 \sqrt{x}}{4 b^2 (a-b x)}-\frac{x^{3/2}}{2 b (a-b x)^2}",1,"(3*a*Sqrt[x] - 5*b*x^(3/2))/(4*b^2*(-a + b*x)^2) - (3*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(4*Sqrt[a]*b^(5/2))","A",1
485,1,62,75,0.0431465,"\int \frac{\sqrt{x}}{(-a+b x)^3} \, dx","IntegrateAlgebraic[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} \left(-\frac{x}{4 a}-\frac{1}{4 b}\right)}{(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]*(-1/4*1/b - x/(4*a)))/(a - b*x)^2 + ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a]]/(4*a^(3/2)*b^(3/2))","A",1
486,1,64,72,0.051042,"\int \frac{1}{\sqrt{x} (-a+b x)^3} \, dx","IntegrateAlgebraic[1/(Sqrt[x]*(-a + b*x)^3),x]","\frac{3 b x^{3/2}-5 a \sqrt{x}}{4 a^2 (a-b x)^2}-\frac{3 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 a^{5/2} \sqrt{b}}","-\frac{3 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 a^{5/2} \sqrt{b}}-\frac{3 \sqrt{x}}{4 a^2 (a-b x)}-\frac{\sqrt{x}}{2 a (a-b x)^2}",1,"(-5*a*Sqrt[x] + 3*b*x^(3/2))/(4*a^2*(a - b*x)^2) - (3*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(4*a^(5/2)*Sqrt[b])","A",1
487,1,74,84,0.0596739,"\int \frac{1}{x^{3/2} (-a+b x)^3} \, dx","IntegrateAlgebraic[1/(x^(3/2)*(-a + b*x)^3),x]","\frac{\frac{15 b^2 x^2}{4 a^3}-\frac{25 b x}{4 a^2}+\frac{2}{a}}{\sqrt{x} (a-b x)^2}-\frac{15 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 a^{7/2}}","-\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{5}{4 a^2 \sqrt{x} (a-b x)}-\frac{1}{2 a \sqrt{x} (a-b x)^2}",1,"(2/a - (25*b*x)/(4*a^2) + (15*b^2*x^2)/(4*a^3))/(Sqrt[x]*(a - b*x)^2) - (15*Sqrt[b]*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(4*a^(7/2))","A",1
488,1,89,97,0.0690011,"\int \frac{1}{x^{5/2} (-a+b x)^3} \, dx","IntegrateAlgebraic[1/(x^(5/2)*(-a + b*x)^3),x]","\frac{\frac{35 b^3 x^3}{4 a^4}-\frac{175 b^2 x^2}{12 a^3}+\frac{14 b x}{3 a^2}+\frac{2}{3 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{35 b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 a^{9/2}}+\frac{35 b}{4 a^4 \sqrt{x}}+\frac{35}{12 a^3 x^{3/2}}-\frac{7}{4 a^2 x^{3/2} (a-b x)}-\frac{1}{2 a x^{3/2} (a-b x)^2}",1,"(2/(3*a) + (14*b*x)/(3*a^2) - (175*b^2*x^2)/(12*a^3) + (35*b^3*x^3)/(4*a^4))/(x^(3/2)*(a - b*x)^2) - (35*b^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(4*a^(9/2))","A",1
489,1,2817,122,3.7930498,"\int x^{5/2} \sqrt{a+b x} \, dx","IntegrateAlgebraic[x^(5/2)*Sqrt[a + b*x],x]","\text{Result too large to show}","-\frac{5 a^4 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{64 b^{7/2}}+\frac{5 a^3 \sqrt{x} \sqrt{a+b x}}{64 b^3}-\frac{5 a^2 x^{3/2} \sqrt{a+b x}}{96 b^2}+\frac{a x^{5/2} \sqrt{a+b x}}{24 b}+\frac{1}{4} x^{7/2} \sqrt{a+b x}",1,"((-1920*a^11 - 3520*a^10*b - 1904*a^9*b^2 - 7304*a^8*b^3 - 16776*a^7*b^4 - 13680*a^6*b^5 - 4288*a^5*b^6 - 384*a^4*b^7)*Sqrt[a + b*x] + (1920*a^11 - 3840*a^10*b - 9760*a^9*b^2 - 4576*a^8*b^3 - 28457*a^7*b^4 - 60072*a^6*b^5 - 41456*a^5*b^6 - 9664*a^4*b^7 - 384*a^3*b^8)*Sqrt[x]*Sqrt[a + b*x] + (4800*a^10*b - 6240*a^9*b^2 - 15336*a^8*b^3 - 15696*a^7*b^4 - 77904*a^6*b^5 - 120000*a^5*b^6 - 62592*a^4*b^7 - 9216*a^3*b^8)*x*Sqrt[a + b*x] + (2560*a^10*b + 9920*a^9*b^2 - 7200*a^8*b^3 - 15780*a^7*b^4 - 38130*a^6*b^5 - 136480*a^5*b^6 - 152480*a^4*b^7 - 56320*a^3*b^8 - 3840*a^2*b^9)*x^(3/2)*Sqrt[a + b*x] + (7120*a^9*b^2 + 14760*a^8*b^3 - 5760*a^7*b^4 - 15360*a^6*b^5 - 63680*a^5*b^6 - 158080*a^4*b^7 - 128000*a^3*b^8 - 30720*a^2*b^9)*x^2*Sqrt[a + b*x] + (864*a^9*b^2 + 10848*a^8*b^3 + 15570*a^7*b^4 - 3120*a^6*b^5 - 15624*a^5*b^6 - 68160*a^4*b^7 - 121344*a^3*b^8 - 70656*a^2*b^9 - 9216*a*b^10)*x^(5/2)*Sqrt[a + b*x] + (1736*a^8*b^3 + 10128*a^7*b^4 + 11520*a^6*b^5 - 1536*a^5*b^6 - 12416*a^4*b^7 - 44032*a^3*b^8 - 59392*a^2*b^9 - 24576*a*b^10)*x^3*Sqrt[a + b*x] + (7072*a^8*b^3 + 15404*a^7*b^4 + 14220*a^6*b^5 + 7584*a^5*b^6 - 624*a^4*b^7 - 5120*a^3*b^8 - 14336*a^2*b^9 - 16384*a*b^10 - 6144*b^11)*x^(7/2)*Sqrt[a + b*x] + (28104*a^7*b^4 + 49392*a^6*b^5 + 25536*a^5*b^6 + 4992*a^4*b^7)*x^4*Sqrt[a + b*x] + (13263*a^7*b^4 + 79176*a^6*b^5 + 95440*a^5*b^6 + 32192*a^4*b^7 + 2176*a^3*b^8)*x^(9/2)*Sqrt[a + b*x] + (46032*a^6*b^5 + 142016*a^5*b^6 + 117376*a^4*b^7 + 23552*a^3*b^8)*x^5*Sqrt[a + b*x] + (7926*a^6*b^5 + 88992*a^5*b^6 + 169440*a^4*b^7 + 93696*a^3*b^8 + 8448*a^2*b^9)*x^(11/2)*Sqrt[a + b*x] + (21952*a^5*b^6 + 108416*a^4*b^7 + 136192*a^3*b^8 + 47104*a^2*b^9)*x^6*Sqrt[a + b*x] + (1544*a^5*b^6 + 29248*a^4*b^7 + 85760*a^3*b^8 + 72704*a^2*b^9 + 13312*a*b^10)*x^(13/2)*Sqrt[a + b*x] + (2688*a^4*b^7 + 21504*a^3*b^8 + 43008*a^2*b^9 + 24576*a*b^10)*x^7*Sqrt[a + b*x] + (48*a^4*b^7 + 1536*a^3*b^8 + 7680*a^2*b^9 + 12288*a*b^10 + 6144*b^11)*x^(15/2)*Sqrt[a + b*x] + Sqrt[a + b]*(1920*a^11 + 2560*a^10*b + 864*a^9*b^2 + 7072*a^8*b^3 + 13263*a^7*b^4 + 7926*a^6*b^5 + 1544*a^5*b^6 + 48*a^4*b^7 + (-1920*a^11 + 4800*a^10*b + 7120*a^9*b^2 + 1736*a^8*b^3 + 28104*a^7*b^4 + 46032*a^6*b^5 + 21952*a^5*b^6 + 2688*a^4*b^7)*Sqrt[x] + (-3840*a^10*b + 9920*a^9*b^2 + 10848*a^8*b^3 + 15404*a^7*b^4 + 79176*a^6*b^5 + 88992*a^5*b^6 + 29248*a^4*b^7 + 1536*a^3*b^8)*x + (-3520*a^10*b - 6240*a^9*b^2 + 14760*a^8*b^3 + 10128*a^7*b^4 + 49392*a^6*b^5 + 142016*a^5*b^6 + 108416*a^4*b^7 + 21504*a^3*b^8)*x^(3/2) + (-9760*a^9*b^2 - 7200*a^8*b^3 + 15570*a^7*b^4 + 14220*a^6*b^5 + 95440*a^5*b^6 + 169440*a^4*b^7 + 85760*a^3*b^8 + 7680*a^2*b^9)*x^2 + (-1904*a^9*b^2 - 15336*a^8*b^3 - 5760*a^7*b^4 + 11520*a^6*b^5 + 25536*a^5*b^6 + 117376*a^4*b^7 + 136192*a^3*b^8 + 43008*a^2*b^9)*x^(5/2) + (-4576*a^8*b^3 - 15780*a^7*b^4 - 3120*a^6*b^5 + 7584*a^5*b^6 + 32192*a^4*b^7 + 93696*a^3*b^8 + 72704*a^2*b^9 + 12288*a*b^10)*x^3 + (-7304*a^8*b^3 - 15696*a^7*b^4 - 15360*a^6*b^5 - 1536*a^5*b^6 + 4992*a^4*b^7 + 23552*a^3*b^8 + 47104*a^2*b^9 + 24576*a*b^10)*x^(7/2) + (-28457*a^7*b^4 - 38130*a^6*b^5 - 15624*a^5*b^6 - 624*a^4*b^7 + 2176*a^3*b^8 + 8448*a^2*b^9 + 13312*a*b^10 + 6144*b^11)*x^4 + (-16776*a^7*b^4 - 77904*a^6*b^5 - 63680*a^5*b^6 - 12416*a^4*b^7)*x^(9/2) + (-60072*a^6*b^5 - 136480*a^5*b^6 - 68160*a^4*b^7 - 5120*a^3*b^8)*x^5 + (-13680*a^6*b^5 - 120000*a^5*b^6 - 158080*a^4*b^7 - 44032*a^3*b^8)*x^(11/2) + (-41456*a^5*b^6 - 152480*a^4*b^7 - 121344*a^3*b^8 - 14336*a^2*b^9)*x^6 + (-4288*a^5*b^6 - 62592*a^4*b^7 - 128000*a^3*b^8 - 59392*a^2*b^9)*x^(13/2) + (-9664*a^4*b^7 - 56320*a^3*b^8 - 70656*a^2*b^9 - 16384*a*b^10)*x^7 + (-384*a^4*b^7 - 9216*a^3*b^8 - 30720*a^2*b^9 - 24576*a*b^10)*x^(15/2) + (-384*a^3*b^8 - 3840*a^2*b^9 - 9216*a*b^10 - 6144*b^11)*x^8))/(192*b^3*(128*a^8 + 256*a^7*b + 160*a^6*b^2 + 32*a^5*b^3 + a^4*b^4) + 192*b^3*(a^4*b^4 + 32*a^3*b^5 + 160*a^2*b^6 + 256*a*b^7 + 128*b^8)*x^4 + 192*b^3*Sqrt[a + b]*(-128*a^7 - 192*a^6*b - 80*a^5*b^2 - 8*a^4*b^3)*Sqrt[a + b*x] + x*(192*b^3*(256*a^7*b + 1472*a^6*b^2 + 1760*a^5*b^3 + 604*a^4*b^4 + 32*a^3*b^5) + 192*b^3*Sqrt[a + b]*(-192*a^6*b - 1248*a^5*b^2 - 1080*a^4*b^3 - 192*a^3*b^4)*Sqrt[a + b*x]) + Sqrt[x]*(192*b^3*(512*a^7*b + 896*a^6*b^2 + 448*a^5*b^3 + 56*a^4*b^4) + 192*b^3*Sqrt[a + b]*(-512*a^6*b - 640*a^5*b^2 - 192*a^4*b^3 - 8*a^3*b^4)*Sqrt[a + b*x]) + x^2*(192*b^3*(160*a^6*b^2 + 1760*a^5*b^3 + 3270*a^4*b^4 + 1760*a^3*b^5 + 160*a^2*b^6) + 192*b^3*Sqrt[a + b]*(-80*a^5*b^2 - 1080*a^4*b^3 - 1920*a^3*b^4 - 640*a^2*b^5)*Sqrt[a + b*x]) + x^(3/2)*(192*b^3*(896*a^6*b^2 + 2688*a^5*b^3 + 2184*a^4*b^4 + 448*a^3*b^5) + 192*b^3*Sqrt[a + b]*(-640*a^5*b^2 - 1920*a^4*b^3 - 1080*a^3*b^4 - 80*a^2*b^5)*Sqrt[a + b*x]) + x^3*(192*b^3*(32*a^5*b^3 + 604*a^4*b^4 + 1760*a^3*b^5 + 1472*a^2*b^6 + 256*a*b^7) + 192*b^3*Sqrt[a + b]*(-8*a^4*b^3 - 192*a^3*b^4 - 640*a^2*b^5 - 512*a*b^6)*Sqrt[a + b*x]) + x^(5/2)*(192*b^3*(448*a^5*b^3 + 2184*a^4*b^4 + 2688*a^3*b^5 + 896*a^2*b^6) + 192*b^3*Sqrt[a + b]*(-192*a^4*b^3 - 1080*a^3*b^4 - 1248*a^2*b^5 - 192*a*b^6)*Sqrt[a + b*x]) + x^(7/2)*(192*b^3*(56*a^4*b^4 + 448*a^3*b^5 + 896*a^2*b^6 + 512*a*b^7) + 192*b^3*Sqrt[a + b]*(-8*a^3*b^4 - 80*a^2*b^5 - 192*a*b^6 - 128*b^7)*Sqrt[a + b*x])) + (5*a^4*ArcTanh[(Sqrt[a + b]/Sqrt[b] - Sqrt[a + b*x]/Sqrt[b])/(-1 + Sqrt[x])])/(32*b^(7/2))","B",1
490,1,1705,98,2.2683028,"\int x^{3/2} \sqrt{a+b x} \, dx","IntegrateAlgebraic[x^(3/2)*Sqrt[a + b*x],x]","\frac{\left(256 b^8+384 a b^7+144 a^2 b^6+8 a^3 b^5\right) \sqrt{a+b x} x^{11/2}+\left(768 a b^7+960 a^2 b^6+240 a^3 b^5\right) \sqrt{a+b x} x^5+\left(448 a b^7+1728 a^2 b^6+1308 a^3 b^5+146 a^4 b^4\right) \sqrt{a+b x} x^{9/2}+\left(1152 a^2 b^6+2320 a^3 b^5+1020 a^4 b^4\right) \sqrt{a+b x} x^4+\left(144 a^2 b^6+1536 a^3 b^5+1896 a^4 b^4+417 a^5 b^3\right) \sqrt{a+b x} x^{7/2}+\left(918 b^3 a^5+1120 b^4 a^4+192 b^5 a^3\right) \sqrt{a+b x} x^3+\left(-256 b^8-576 a b^7-336 a^2 b^6-32 a^3 b^5-48 a^4 b^4+333 a^5 b^3+298 a^6 b^2\right) \sqrt{a+b x} x^{5/2}+\left(-768 a b^7-1536 a^2 b^6-672 a^3 b^5-318 a^5 b^3-150 a^6 b^2\right) \sqrt{a+b x} x^2+\left(-80 b a^7-300 b^2 a^6+123 b^3 a^5-512 b^4 a^4-2184 b^5 a^3-1632 b^6 a^2-256 b^7 a\right) \sqrt{a+b x} x^{3/2}+\left(-192 b a^7+164 b^2 a^6-30 b^3 a^5-1824 b^4 a^4-2032 b^5 a^3-576 b^6 a^2\right) \sqrt{a+b x} x+\left(-96 a^8+144 b a^7+258 b^2 a^6-873 b^3 a^5-1482 b^4 a^4-636 b^5 a^3-48 b^6 a^2\right) \sqrt{a+b x} \sqrt{x}+\sqrt{a+b} \left(-96 a^8-80 b a^7+298 b^2 a^6+417 b^3 a^5+146 b^4 a^4+8 b^5 a^3+\left(-256 b^8-256 a b^7-48 a^2 b^6\right) x^6+\left(-768 a b^7-576 a^2 b^6-48 a^3 b^5\right) x^{11/2}+\left(-576 a b^7-1632 a^2 b^6-636 a^3 b^5\right) x^5+\left(-1536 a^2 b^6-2032 a^3 b^5-316 a^4 b^4\right) x^{9/2}+\left(-336 a^2 b^6-2184 a^3 b^5-1482 a^4 b^4\right) x^4+\left(-570 b^3 a^5-1824 b^4 a^4-672 b^5 a^3\right) x^{7/2}+\left(256 b^8+448 a b^7+144 a^2 b^6-32 a^3 b^5-512 a^4 b^4-873 a^5 b^3\right) x^3+\left(768 a b^7+1152 a^2 b^6+192 a^3 b^5-30 a^5 b^3-270 a^6 b^2\right) x^{5/2}+\left(384 a b^7+1728 a^2 b^6+1536 a^3 b^5-48 a^4 b^4+123 a^5 b^3+258 a^6 b^2\right) x^2+\left(128 b a^7+164 b^2 a^6-318 b^3 a^5+1120 b^4 a^4+2320 b^5 a^3+960 b^6 a^2\right) x^{3/2}+\left(144 b a^7-300 b^2 a^6+333 b^3 a^5+1896 b^4 a^4+1308 b^5 a^3+144 b^6 a^2\right) x+\left(96 a^8-192 b a^7-150 b^2 a^6+918 b^3 a^5+1020 b^4 a^4+240 b^5 a^3\right) \sqrt{x}\right)+\left(96 a^8+128 b a^7-270 b^2 a^6-570 b^3 a^5-316 b^4 a^4-48 b^5 a^3\right) \sqrt{a+b x}}{24 b^2 \left(32 b^6+48 a b^5+18 a^2 b^4+a^3 b^3\right) x^3+\left(24 \left(96 a b^5+120 a^2 b^4+30 a^3 b^3\right) b^2+24 \sqrt{a+b} \left(-32 b^5-32 a b^4-6 a^2 b^3\right) \sqrt{a+b x} b^2\right) x^{5/2}+\left(24 \left(48 a b^5+204 a^2 b^4+159 a^3 b^3+18 a^4 b^2\right) b^2+24 \sqrt{a+b} \left(-96 a b^4-72 a^2 b^3-6 a^3 b^2\right) \sqrt{a+b x} b^2\right) x^2+\left(24 \left(120 b^2 a^4+260 b^3 a^3+120 b^4 a^2\right) b^2+24 \sqrt{a+b} \left(-32 a b^4-164 a^2 b^3-72 a^3 b^2\right) \sqrt{a+b x} b^2\right) x^{3/2}+\left(24 \left(48 b a^5+204 b^2 a^4+159 b^3 a^3+18 b^4 a^2\right) b^2+24 \sqrt{a+b} \left(-32 b a^4-164 b^2 a^3-72 b^3 a^2\right) \sqrt{a+b x} b^2\right) x+\left(24 \left(96 b a^5+120 b^2 a^4+30 b^3 a^3\right) b^2+24 \sqrt{a+b} \left(-96 b a^4-72 b^2 a^3-6 b^3 a^2\right) \sqrt{a+b x} b^2\right) \sqrt{x}+24 b^2 \left(32 a^6+48 b a^5+18 b^2 a^4+b^3 a^3\right)+24 b^2 \sqrt{a+b} \left(-32 a^5-32 b a^4-6 b^2 a^3\right) \sqrt{a+b x}}-\frac{a^3 \tanh ^{-1}\left(\frac{\frac{\sqrt{a+b}}{\sqrt{b}}-\frac{\sqrt{a+b x}}{\sqrt{b}}}{\sqrt{x}-1}\right)}{4 b^{5/2}}","\frac{a^3 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{8 b^{5/2}}-\frac{a^2 \sqrt{x} \sqrt{a+b x}}{8 b^2}+\frac{a x^{3/2} \sqrt{a+b x}}{12 b}+\frac{1}{3} x^{5/2} \sqrt{a+b x}",1,"((96*a^8 + 128*a^7*b - 270*a^6*b^2 - 570*a^5*b^3 - 316*a^4*b^4 - 48*a^3*b^5)*Sqrt[a + b*x] + (-96*a^8 + 144*a^7*b + 258*a^6*b^2 - 873*a^5*b^3 - 1482*a^4*b^4 - 636*a^3*b^5 - 48*a^2*b^6)*Sqrt[x]*Sqrt[a + b*x] + (-192*a^7*b + 164*a^6*b^2 - 30*a^5*b^3 - 1824*a^4*b^4 - 2032*a^3*b^5 - 576*a^2*b^6)*x*Sqrt[a + b*x] + (-80*a^7*b - 300*a^6*b^2 + 123*a^5*b^3 - 512*a^4*b^4 - 2184*a^3*b^5 - 1632*a^2*b^6 - 256*a*b^7)*x^(3/2)*Sqrt[a + b*x] + (-150*a^6*b^2 - 318*a^5*b^3 - 672*a^3*b^5 - 1536*a^2*b^6 - 768*a*b^7)*x^2*Sqrt[a + b*x] + (298*a^6*b^2 + 333*a^5*b^3 - 48*a^4*b^4 - 32*a^3*b^5 - 336*a^2*b^6 - 576*a*b^7 - 256*b^8)*x^(5/2)*Sqrt[a + b*x] + (918*a^5*b^3 + 1120*a^4*b^4 + 192*a^3*b^5)*x^3*Sqrt[a + b*x] + (417*a^5*b^3 + 1896*a^4*b^4 + 1536*a^3*b^5 + 144*a^2*b^6)*x^(7/2)*Sqrt[a + b*x] + (1020*a^4*b^4 + 2320*a^3*b^5 + 1152*a^2*b^6)*x^4*Sqrt[a + b*x] + (146*a^4*b^4 + 1308*a^3*b^5 + 1728*a^2*b^6 + 448*a*b^7)*x^(9/2)*Sqrt[a + b*x] + (240*a^3*b^5 + 960*a^2*b^6 + 768*a*b^7)*x^5*Sqrt[a + b*x] + (8*a^3*b^5 + 144*a^2*b^6 + 384*a*b^7 + 256*b^8)*x^(11/2)*Sqrt[a + b*x] + Sqrt[a + b]*(-96*a^8 - 80*a^7*b + 298*a^6*b^2 + 417*a^5*b^3 + 146*a^4*b^4 + 8*a^3*b^5 + (96*a^8 - 192*a^7*b - 150*a^6*b^2 + 918*a^5*b^3 + 1020*a^4*b^4 + 240*a^3*b^5)*Sqrt[x] + (144*a^7*b - 300*a^6*b^2 + 333*a^5*b^3 + 1896*a^4*b^4 + 1308*a^3*b^5 + 144*a^2*b^6)*x + (128*a^7*b + 164*a^6*b^2 - 318*a^5*b^3 + 1120*a^4*b^4 + 2320*a^3*b^5 + 960*a^2*b^6)*x^(3/2) + (258*a^6*b^2 + 123*a^5*b^3 - 48*a^4*b^4 + 1536*a^3*b^5 + 1728*a^2*b^6 + 384*a*b^7)*x^2 + (-270*a^6*b^2 - 30*a^5*b^3 + 192*a^3*b^5 + 1152*a^2*b^6 + 768*a*b^7)*x^(5/2) + (-873*a^5*b^3 - 512*a^4*b^4 - 32*a^3*b^5 + 144*a^2*b^6 + 448*a*b^7 + 256*b^8)*x^3 + (-570*a^5*b^3 - 1824*a^4*b^4 - 672*a^3*b^5)*x^(7/2) + (-1482*a^4*b^4 - 2184*a^3*b^5 - 336*a^2*b^6)*x^4 + (-316*a^4*b^4 - 2032*a^3*b^5 - 1536*a^2*b^6)*x^(9/2) + (-636*a^3*b^5 - 1632*a^2*b^6 - 576*a*b^7)*x^5 + (-48*a^3*b^5 - 576*a^2*b^6 - 768*a*b^7)*x^(11/2) + (-48*a^2*b^6 - 256*a*b^7 - 256*b^8)*x^6))/(24*b^2*(32*a^6 + 48*a^5*b + 18*a^4*b^2 + a^3*b^3) + 24*b^2*(a^3*b^3 + 18*a^2*b^4 + 48*a*b^5 + 32*b^6)*x^3 + 24*b^2*Sqrt[a + b]*(-32*a^5 - 32*a^4*b - 6*a^3*b^2)*Sqrt[a + b*x] + x*(24*b^2*(48*a^5*b + 204*a^4*b^2 + 159*a^3*b^3 + 18*a^2*b^4) + 24*b^2*Sqrt[a + b]*(-32*a^4*b - 164*a^3*b^2 - 72*a^2*b^3)*Sqrt[a + b*x]) + Sqrt[x]*(24*b^2*(96*a^5*b + 120*a^4*b^2 + 30*a^3*b^3) + 24*b^2*Sqrt[a + b]*(-96*a^4*b - 72*a^3*b^2 - 6*a^2*b^3)*Sqrt[a + b*x]) + x^2*(24*b^2*(18*a^4*b^2 + 159*a^3*b^3 + 204*a^2*b^4 + 48*a*b^5) + 24*b^2*Sqrt[a + b]*(-6*a^3*b^2 - 72*a^2*b^3 - 96*a*b^4)*Sqrt[a + b*x]) + x^(3/2)*(24*b^2*(120*a^4*b^2 + 260*a^3*b^3 + 120*a^2*b^4) + 24*b^2*Sqrt[a + b]*(-72*a^3*b^2 - 164*a^2*b^3 - 32*a*b^4)*Sqrt[a + b*x]) + x^(5/2)*(24*b^2*(30*a^3*b^3 + 120*a^2*b^4 + 96*a*b^5) + 24*b^2*Sqrt[a + b]*(-6*a^2*b^3 - 32*a*b^4 - 32*b^5)*Sqrt[a + b*x])) - (a^3*ArcTanh[(Sqrt[a + b]/Sqrt[b] - Sqrt[a + b*x]/Sqrt[b])/(-1 + Sqrt[x])])/(4*b^(5/2))","B",1
491,1,475,74,0.8175996,"\int \sqrt{x} \sqrt{a+b x} \, dx","IntegrateAlgebraic[Sqrt[x]*Sqrt[a + b*x],x]","\frac{a^2 \tanh ^{-1}\left(\frac{\frac{\sqrt{a+b}}{\sqrt{b}}-\frac{\sqrt{a+b x}}{\sqrt{b}}}{\sqrt{x}-1}\right)}{2 b^{3/2}}+\frac{\left(\frac{1}{4 b}-\frac{\sqrt{x}}{4 b}\right) \left(\sqrt{a+b}-\sqrt{a+b x}\right) \left(\sqrt{a+b} \sqrt{a+b x}-a-b x+b \sqrt{x}-b\right) \left(-2 a^4-5 a^3 b x-10 a^3 b \sqrt{x}+2 a^3 \sqrt{a+b} \sqrt{a+b x}-5 a^3 b-12 a^2 b^2 x^{3/2}-2 a^2 b^2 x^2-22 a^2 b^2 x-12 a^2 b^2 \sqrt{x}-2 a^2 b^2+4 a^2 b x \sqrt{a+b} \sqrt{a+b x}+4 a^2 b \sqrt{a+b} \sqrt{a+b x}+10 a^2 b \sqrt{x} \sqrt{a+b} \sqrt{a+b x}-16 a b^3 x^{3/2}+16 b^3 x^{3/2} \sqrt{a+b} \sqrt{a+b x}-16 a b^3 x^2-16 a b^3 x+8 a b^2 x^{3/2} \sqrt{a+b} \sqrt{a+b x}+16 a b^2 x \sqrt{a+b} \sqrt{a+b x}+8 a b^2 \sqrt{x} \sqrt{a+b} \sqrt{a+b x}-16 b^4 x^2\right)}{\left(\sqrt{a+b} \sqrt{a+b x}-a-b \sqrt{x}\right)^4}","-\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,"((1/(4*b) - Sqrt[x]/(4*b))*(Sqrt[a + b] - Sqrt[a + b*x])*(-a - b + b*Sqrt[x] - b*x + Sqrt[a + b]*Sqrt[a + b*x])*(-2*a^4 - 5*a^3*b - 2*a^2*b^2 - 10*a^3*b*Sqrt[x] - 12*a^2*b^2*Sqrt[x] - 5*a^3*b*x - 22*a^2*b^2*x - 16*a*b^3*x - 12*a^2*b^2*x^(3/2) - 16*a*b^3*x^(3/2) - 2*a^2*b^2*x^2 - 16*a*b^3*x^2 - 16*b^4*x^2 + 2*a^3*Sqrt[a + b]*Sqrt[a + b*x] + 4*a^2*b*Sqrt[a + b]*Sqrt[a + b*x] + 10*a^2*b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 8*a*b^2*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 4*a^2*b*Sqrt[a + b]*x*Sqrt[a + b*x] + 16*a*b^2*Sqrt[a + b]*x*Sqrt[a + b*x] + 8*a*b^2*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] + 16*b^3*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x]))/(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x])^4 + (a^2*ArcTanh[(Sqrt[a + b]/Sqrt[b] - Sqrt[a + b*x]/Sqrt[b])/(-1 + Sqrt[x])])/(2*b^(3/2))","B",1
492,1,178,44,0.2926349,"\int \frac{\sqrt{a+b x}}{\sqrt{x}} \, dx","IntegrateAlgebraic[Sqrt[a + b*x]/Sqrt[x],x]","\frac{\left(1-\sqrt{x}\right) \left(\sqrt{a+b}-\sqrt{a+b x}\right) \left(a^2+a b x+a b \sqrt{x}-a \sqrt{a+b} \sqrt{a+b x}-2 b \sqrt{x} \sqrt{a+b} \sqrt{a+b x}+a b+2 b^2 x\right)}{\left(\sqrt{a+b} \sqrt{a+b x}-a-b \sqrt{x}\right)^2}-\frac{2 a \tanh ^{-1}\left(\frac{\frac{\sqrt{a+b}}{\sqrt{b}}-\frac{\sqrt{a+b x}}{\sqrt{b}}}{\sqrt{x}-1}\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,"((1 - Sqrt[x])*(Sqrt[a + b] - Sqrt[a + b*x])*(a^2 + a*b + a*b*Sqrt[x] + a*b*x + 2*b^2*x - a*Sqrt[a + b]*Sqrt[a + b*x] - 2*b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x]))/(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x])^2 - (2*a*ArcTanh[(Sqrt[a + b]/Sqrt[b] - Sqrt[a + b*x]/Sqrt[b])/(-1 + Sqrt[x])])/Sqrt[b]","B",1
493,1,269,45,0.4417292,"\int \frac{\sqrt{a+b x}}{x^{3/2}} \, dx","IntegrateAlgebraic[Sqrt[a + b*x]/x^(3/2),x]","\frac{\left(2 a-2 a \sqrt{x}\right) \left(\sqrt{a+b}-\sqrt{a+b x}\right) \left(-2 \sqrt{a+b} \sqrt{a+b x}+\sqrt{x} \sqrt{a+b} \sqrt{a+b x}+a \left(-\sqrt{x}\right)+2 a+b x-2 b \sqrt{x}+2 b\right)}{\sqrt{x} \left(-2 a^2 \sqrt{x}+4 a^2-a b x^{3/2}+2 a b x-a b \sqrt{x}-4 a \sqrt{a+b} \sqrt{a+b x}+2 a \sqrt{x} \sqrt{a+b} \sqrt{a+b x}-2 b \sqrt{a+b} \sqrt{a+b x}+4 a b+2 b^2 \sqrt{x}\right)}-4 \sqrt{b} \tanh ^{-1}\left(\frac{\frac{\sqrt{a+b}}{\sqrt{b}}-\frac{\sqrt{a+b x}}{\sqrt{b}}}{\sqrt{x}-1}\right)","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*a - 2*a*Sqrt[x])*(Sqrt[a + b] - Sqrt[a + b*x])*(2*a + 2*b - a*Sqrt[x] - 2*b*Sqrt[x] + b*x - 2*Sqrt[a + b]*Sqrt[a + b*x] + Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x]))/(Sqrt[x]*(4*a^2 + 4*a*b - 2*a^2*Sqrt[x] - a*b*Sqrt[x] + 2*b^2*Sqrt[x] + 2*a*b*x - a*b*x^(3/2) - 4*a*Sqrt[a + b]*Sqrt[a + b*x] - 2*b*Sqrt[a + b]*Sqrt[a + b*x] + 2*a*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x])) - 4*Sqrt[b]*ArcTanh[(Sqrt[a + b]/Sqrt[b] - Sqrt[a + b*x]/Sqrt[b])/(-1 + Sqrt[x])]","B",1
494,1,946,21,8.3402176,"\int \frac{\sqrt{a+b x}}{x^{5/2}} \, dx","IntegrateAlgebraic[Sqrt[a + b*x]/x^(5/2),x]","\frac{\left(\frac{\sqrt{x}}{48}-\frac{1}{48}\right) \left(\sqrt{a+b}-\sqrt{a+b x}\right)^{12} \left(-\frac{32 a^3 \sqrt{a+b} \left(\sqrt{x}-1\right)^5}{\left(\sqrt{a+b}-\sqrt{a+b x}\right)^5}-\frac{32 a^2 \left(-12 \sqrt{x} a^3+8 a^3-5 b x^{3/2} a^2+2 b a^2-24 b x a^2+15 b \sqrt{x} a^2-8 \sqrt{a+b} \sqrt{a+b x} a^2+12 \sqrt{a+b} \sqrt{x} \sqrt{a+b x} a^2+3 b^2 x^{5/2} a-8 b^2 a-21 b^2 x^2 a+14 b^2 x^{3/2} a-33 b^2 x a+33 b^2 \sqrt{x} a-b \sqrt{a+b} x^{3/2} \sqrt{a+b x} a+28 b \sqrt{a+b} x \sqrt{a+b x} a+2 b \sqrt{a+b} \sqrt{a+b x} a-21 b \sqrt{a+b} \sqrt{x} \sqrt{a+b x} a-2 b^3-b^3 x^3+6 b^3 x^{5/2}-24 b^3 x^2+20 b^3 x^{3/2}-9 b^3 x+6 b^3 \sqrt{x}-b^2 \sqrt{a+b} x^{5/2} \sqrt{a+b x}+6 b^2 \sqrt{a+b} x^2 \sqrt{a+b x}-6 b^2 \sqrt{a+b} x^{3/2} \sqrt{a+b x}+20 b^2 \sqrt{a+b} x \sqrt{a+b x}+6 b^2 \sqrt{a+b} \sqrt{a+b x}-21 b^2 \sqrt{a+b} \sqrt{x} \sqrt{a+b x}\right) \left(\sqrt{x}-1\right)^2}{\left(\sqrt{a+b}-\sqrt{a+b x}\right)^8}+\frac{96 b \left(-a-b \sqrt{x}+\sqrt{a+b} \sqrt{a+b x}\right)^4 \left(-\sqrt{x} a+2 a+2 b+b x-2 b \sqrt{x}-2 \sqrt{a+b} \sqrt{a+b x}+\sqrt{a+b} \sqrt{x} \sqrt{a+b x}\right)}{\left(\sqrt{a+b}-\sqrt{a+b x}\right)^{10}}+\frac{96 a \left(-a-b \sqrt{x}+\sqrt{a+b} \sqrt{a+b x}\right)^4 \left(-2 \sqrt{x} a+3 a+3 b+b x-3 b \sqrt{x}-3 \sqrt{a+b} \sqrt{a+b x}+2 \sqrt{a+b} \sqrt{x} \sqrt{a+b x}\right)}{\left(\sqrt{a+b}-\sqrt{a+b x}\right)^{10}}\right)}{\left(\sqrt{a+b x}-\sqrt{a+b}\right) \left(-2 x a^2+4 \sqrt{x} a^2-b x^2 a+2 b x^{3/2} a-b x a+4 b \sqrt{x} a+2 \sqrt{a+b} x \sqrt{a+b x} a-4 \sqrt{a+b} \sqrt{x} \sqrt{a+b x} a+2 b^2 x-2 b \sqrt{a+b} \sqrt{x} \sqrt{a+b x}\right)^3}","-\frac{2 (a+b x)^{3/2}}{3 a x^{3/2}}",1,"((-1/48 + Sqrt[x]/48)*(Sqrt[a + b] - Sqrt[a + b*x])^12*((-32*a^3*Sqrt[a + b]*(-1 + Sqrt[x])^5)/(Sqrt[a + b] - Sqrt[a + b*x])^5 + (96*b*(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x])^4*(2*a + 2*b - a*Sqrt[x] - 2*b*Sqrt[x] + b*x - 2*Sqrt[a + b]*Sqrt[a + b*x] + Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x]))/(Sqrt[a + b] - Sqrt[a + b*x])^10 + (96*a*(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x])^4*(3*a + 3*b - 2*a*Sqrt[x] - 3*b*Sqrt[x] + b*x - 3*Sqrt[a + b]*Sqrt[a + b*x] + 2*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x]))/(Sqrt[a + b] - Sqrt[a + b*x])^10 - (32*a^2*(-1 + Sqrt[x])^2*(8*a^3 + 2*a^2*b - 8*a*b^2 - 2*b^3 - 12*a^3*Sqrt[x] + 15*a^2*b*Sqrt[x] + 33*a*b^2*Sqrt[x] + 6*b^3*Sqrt[x] - 24*a^2*b*x - 33*a*b^2*x - 9*b^3*x - 5*a^2*b*x^(3/2) + 14*a*b^2*x^(3/2) + 20*b^3*x^(3/2) - 21*a*b^2*x^2 - 24*b^3*x^2 + 3*a*b^2*x^(5/2) + 6*b^3*x^(5/2) - b^3*x^3 - 8*a^2*Sqrt[a + b]*Sqrt[a + b*x] + 2*a*b*Sqrt[a + b]*Sqrt[a + b*x] + 6*b^2*Sqrt[a + b]*Sqrt[a + b*x] + 12*a^2*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 21*a*b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 21*b^2*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 28*a*b*Sqrt[a + b]*x*Sqrt[a + b*x] + 20*b^2*Sqrt[a + b]*x*Sqrt[a + b*x] - a*b*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] - 6*b^2*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] + 6*b^2*Sqrt[a + b]*x^2*Sqrt[a + b*x] - b^2*Sqrt[a + b]*x^(5/2)*Sqrt[a + b*x]))/(Sqrt[a + b] - Sqrt[a + b*x])^8))/((-Sqrt[a + b] + Sqrt[a + b*x])*(4*a^2*Sqrt[x] + 4*a*b*Sqrt[x] - 2*a^2*x - a*b*x + 2*b^2*x + 2*a*b*x^(3/2) - a*b*x^2 - 4*a*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 2*b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 2*a*Sqrt[a + b]*x*Sqrt[a + b*x])^3)","B",1
495,1,4326,44,122.3233144,"\int \frac{\sqrt{a+b x}}{x^{7/2}} \, dx","IntegrateAlgebraic[Sqrt[a + b*x]/x^(7/2),x]","\text{Result too large to show}","\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,"((-1/3840 + Sqrt[x]/3840)*(Sqrt[a + b] - Sqrt[a + b*x])^20*((-1536*a^5*Sqrt[a + b]*(-1 + Sqrt[x])^9)/(Sqrt[a + b] - Sqrt[a + b*x])^9 - (512*a^4*Sqrt[a + b]*(-1 + Sqrt[x])^7*(-30*a^2 - 13*a*b + b^2 - 34*a*b*Sqrt[x] - 2*b^2*Sqrt[x] - 13*a*b*x - 28*b^2*x - 2*b^2*x^(3/2) + b^2*x^2 + 30*a*Sqrt[a + b]*Sqrt[a + b*x] - 2*b*Sqrt[a + b]*Sqrt[a + b*x] + 34*b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 2*b*Sqrt[a + b]*x*Sqrt[a + b*x]))/(Sqrt[a + b] - Sqrt[a + b*x])^11 - (7680*b*(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x])^6*(-a - b + b*Sqrt[x] - b*x + Sqrt[a + b]*Sqrt[a + b*x])*(6*a^2 + 11*a*b + 4*b^2 - 4*a^2*Sqrt[x] - 14*a*b*Sqrt[x] - 8*b^2*Sqrt[x] + 11*a*b*x + 12*b^2*x - 4*a*b*x^(3/2) - 8*b^2*x^(3/2) + 2*b^2*x^2 - 6*a*Sqrt[a + b]*Sqrt[a + b*x] - 8*b*Sqrt[a + b]*Sqrt[a + b*x] + 4*a*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 12*b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 8*b*Sqrt[a + b]*x*Sqrt[a + b*x] + 2*b*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x]))/(Sqrt[a + b] - Sqrt[a + b*x])^18 + (512*a^3*(-1 + Sqrt[x])^4*(528*a^5 + 860*a^4*b + 253*a^3*b^2 - 131*a^2*b^3 - 56*a*b^4 - 4*b^5 - 480*a^5*Sqrt[x] + 400*a^4*b*Sqrt[x] + 1750*a^3*b^2*Sqrt[x] + 1080*a^2*b^3*Sqrt[x] + 230*a*b^4*Sqrt[x] + 20*b^5*Sqrt[x] - 500*a^4*b*x - 170*a^3*b^2*x + 75*a^2*b^3*x - 345*a*b^4*x - 90*b^5*x - 520*a^4*b*x^(3/2) - 180*a^3*b^2*x^(3/2) + 1905*a^2*b^3*x^(3/2) + 1810*a*b^4*x^(3/2) + 240*b^5*x^(3/2) - 1155*a^3*b^2*x^2 - 2165*a^2*b^3*x^2 - 1175*a*b^4*x^2 - 140*b^5*x^2 - 18*a^3*b^2*x^(5/2) + 6*a^2*b^3*x^(5/2) + 576*a*b^4*x^(5/2) + 504*b^5*x^(5/2) - 355*a^2*b^3*x^3 - 1055*a*b^4*x^3 - 660*b^5*x^3 + 65*a^2*b^3*x^(7/2) + 310*a*b^4*x^(7/2) + 240*b^5*x^(7/2) - 65*a*b^4*x^4 - 80*b^5*x^4 + 10*a*b^4*x^(9/2) + 20*b^5*x^(9/2) - 2*b^5*x^5 - 528*a^4*Sqrt[a + b]*Sqrt[a + b*x] - 596*a^3*b*Sqrt[a + b]*Sqrt[a + b*x] - 21*a^2*b^2*Sqrt[a + b]*Sqrt[a + b*x] + 100*a*b^3*Sqrt[a + b]*Sqrt[a + b*x] + 20*b^4*Sqrt[a + b]*Sqrt[a + b*x] + 480*a^4*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 640*a^3*b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 1370*a^2*b^2*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 505*a*b^3*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 90*b^4*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 764*a^3*b*Sqrt[a + b]*x*Sqrt[a + b*x] + 218*a^2*b^2*Sqrt[a + b]*x*Sqrt[a + b*x] + 38*a*b^3*Sqrt[a + b]*x*Sqrt[a + b*x] + 240*b^4*Sqrt[a + b]*x*Sqrt[a + b*x] + 280*a^3*b*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] + 240*a^2*b^2*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] - 1115*a*b^3*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] - 700*b^4*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] + 707*a^2*b^2*Sqrt[a + b]*x^2*Sqrt[a + b*x] + 1404*a*b^3*Sqrt[a + b]*x^2*Sqrt[a + b*x] + 504*b^4*Sqrt[a + b]*x^2*Sqrt[a + b*x] - 62*a^2*b^2*Sqrt[a + b]*x^(5/2)*Sqrt[a + b*x] - 215*a*b^3*Sqrt[a + b]*x^(5/2)*Sqrt[a + b*x] - 180*b^4*Sqrt[a + b]*x^(5/2)*Sqrt[a + b*x] + 130*a*b^3*Sqrt[a + b]*x^3*Sqrt[a + b*x] + 240*b^4*Sqrt[a + b]*x^3*Sqrt[a + b*x] - 29*a*b^3*Sqrt[a + b]*x^(7/2)*Sqrt[a + b*x] - 100*b^4*Sqrt[a + b]*x^(7/2)*Sqrt[a + b*x] + 20*b^4*Sqrt[a + b]*x^4*Sqrt[a + b*x] - 2*b^4*Sqrt[a + b]*x^(9/2)*Sqrt[a + b*x]))/(Sqrt[a + b] - Sqrt[a + b*x])^14 - (2560*a^2*(-1 + Sqrt[x])^2*(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x])^2*(-48*a^5 - 244*a^4*b - 383*a^3*b^2 - 245*a^2*b^3 - 62*a*b^4 - 4*b^5 - 48*a^5*Sqrt[x] + 268*a^4*b*Sqrt[x] + 733*a^3*b^2*Sqrt[x] + 600*a^2*b^3*Sqrt[x] + 200*a*b^4*Sqrt[x] + 20*b^5*Sqrt[x] - 524*a^4*b*x - 1274*a^3*b^2*x - 1308*a^2*b^3*x - 645*a*b^4*x - 102*b^5*x + 20*a^4*b*x^(3/2) + 558*a^3*b^2*x^(3/2) + 1449*a^2*b^3*x^(3/2) + 1120*a*b^4*x^(3/2) + 240*b^5*x^(3/2) - 711*a^3*b^2*x^2 - 1793*a^2*b^3*x^2 - 1463*a*b^4*x^2 - 416*b^5*x^2 + 117*a^3*b^2*x^(5/2) + 606*a^2*b^3*x^(5/2) + 966*a*b^4*x^(5/2) + 504*b^5*x^(5/2) - 334*a^2*b^3*x^3 - 815*a*b^4*x^3 - 504*b^5*x^3 + 65*a^2*b^3*x^(7/2) + 280*a*b^4*x^(7/2) + 240*b^5*x^(7/2) - 71*a*b^4*x^4 - 92*b^5*x^4 + 10*a*b^4*x^(9/2) + 20*b^5*x^(9/2) - 2*b^5*x^5 + 48*a^4*Sqrt[a + b]*Sqrt[a + b*x] + 220*a^3*b*Sqrt[a + b]*Sqrt[a + b*x] + 279*a^2*b^2*Sqrt[a + b]*Sqrt[a + b*x] + 130*a*b^3*Sqrt[a + b]*Sqrt[a + b*x] + 20*b^4*Sqrt[a + b]*Sqrt[a + b*x] + 48*a^4*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 292*a^3*b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 581*a^2*b^2*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 349*a*b^3*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 78*b^4*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 500*a^3*b*Sqrt[a + b]*x*Sqrt[a + b*x] + 902*a^2*b^2*Sqrt[a + b]*x*Sqrt[a + b*x] + 728*a*b^3*Sqrt[a + b]*x*Sqrt[a + b*x] + 240*b^4*Sqrt[a + b]*x*Sqrt[a + b*x] - 44*a^3*b*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] - 402*a^2*b^2*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] - 887*a*b^3*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] - 424*b^4*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] + 467*a^2*b^2*Sqrt[a + b]*x^2*Sqrt[a + b*x] + 1014*a*b^3*Sqrt[a + b]*x^2*Sqrt[a + b*x] + 504*b^4*Sqrt[a + b]*x^2*Sqrt[a + b*x] - 89*a^2*b^2*Sqrt[a + b]*x^(5/2)*Sqrt[a + b*x] - 383*a*b^3*Sqrt[a + b]*x^(5/2)*Sqrt[a + b*x] - 336*b^4*Sqrt[a + b]*x^(5/2)*Sqrt[a + b*x] + 160*a*b^3*Sqrt[a + b]*x^3*Sqrt[a + b*x] + 240*b^4*Sqrt[a + b]*x^3*Sqrt[a + b*x] - 29*a*b^3*Sqrt[a + b]*x^(7/2)*Sqrt[a + b*x] - 88*b^4*Sqrt[a + b]*x^(7/2)*Sqrt[a + b*x] + 20*b^4*Sqrt[a + b]*x^4*Sqrt[a + b*x] - 2*b^4*Sqrt[a + b]*x^(9/2)*Sqrt[a + b*x]))/(Sqrt[a + b] - Sqrt[a + b*x])^16 + (2560*a*(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x])^4*(192*a^5 + 656*a^4*b + 780*a^3*b^2 + 384*a^2*b^3 + 72*a*b^4 + 4*b^5 - 144*a^5*Sqrt[x] - 676*a^4*b*Sqrt[x] - 993*a^3*b^2*Sqrt[x] - 585*a^2*b^3*Sqrt[x] - 150*a*b^4*Sqrt[x] - 20*b^5*Sqrt[x] + 584*a^4*b*x + 1744*a^3*b^2*x + 1733*a^2*b^3*x + 725*a*b^4*x + 122*b^5*x - 324*a^4*b*x^(3/2) - 1486*a^3*b^2*x^(3/2) - 1899*a^2*b^3*x^(3/2) - 1030*a*b^4*x^(3/2) - 240*b^5*x^(3/2) + 692*a^3*b^2*x^2 + 1606*a^2*b^3*x^2 + 1391*a*b^4*x^2 + 452*b^5*x^2 - 257*a^3*b^2*x^(5/2) - 1031*a^2*b^3*x^(5/2) - 1236*a*b^4*x^(5/2) - 504*b^5*x^(5/2) + 357*a^2*b^3*x^3 + 679*a*b^4*x^3 + 396*b^5*x^3 - 85*a^2*b^3*x^(7/2) - 270*a*b^4*x^(7/2) - 240*b^5*x^(7/2) + 69*a*b^4*x^4 + 96*b^5*x^4 - 10*a*b^4*x^(9/2) - 20*b^5*x^(9/2) + 2*b^5*x^5 - 192*a^4*Sqrt[a + b]*Sqrt[a + b*x] - 560*a^3*b*Sqrt[a + b]*Sqrt[a + b*x] - 524*a^2*b^2*Sqrt[a + b]*Sqrt[a + b*x] - 180*a*b^3*Sqrt[a + b]*Sqrt[a + b*x] - 20*b^4*Sqrt[a + b]*Sqrt[a + b*x] + 144*a^4*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 604*a^3*b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 709*a^2*b^2*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 297*a*b^3*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 58*b^4*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 488*a^3*b*Sqrt[a + b]*x*Sqrt[a + b*x] - 1172*a^2*b^2*Sqrt[a + b]*x*Sqrt[a + b*x] - 818*a*b^3*Sqrt[a + b]*x*Sqrt[a + b*x] - 240*b^4*Sqrt[a + b]*x*Sqrt[a + b*x] + 252*a^3*b*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] + 1022*a^2*b^2*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] + 923*a*b^3*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] + 388*b^4*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] - 472*a^2*b^2*Sqrt[a + b]*x^2*Sqrt[a + b*x] - 744*a*b^3*Sqrt[a + b]*x^2*Sqrt[a + b*x] - 504*b^4*Sqrt[a + b]*x^2*Sqrt[a + b*x] + 149*a^2*b^2*Sqrt[a + b]*x^(5/2)*Sqrt[a + b*x] + 467*a*b^3*Sqrt[a + b]*x^(5/2)*Sqrt[a + b*x] + 444*b^4*Sqrt[a + b]*x^(5/2)*Sqrt[a + b*x] - 170*a*b^3*Sqrt[a + b]*x^3*Sqrt[a + b*x] - 240*b^4*Sqrt[a + b]*x^3*Sqrt[a + b*x] + 33*a*b^3*Sqrt[a + b]*x^(7/2)*Sqrt[a + b*x] + 84*b^4*Sqrt[a + b]*x^(7/2)*Sqrt[a + b*x] - 20*b^4*Sqrt[a + b]*x^4*Sqrt[a + b*x] + 2*b^4*Sqrt[a + b]*x^(9/2)*Sqrt[a + b*x]))/(Sqrt[a + b] - Sqrt[a + b*x])^18))/((-Sqrt[a + b] + Sqrt[a + b*x])*(4*a^2*Sqrt[x] + 4*a*b*Sqrt[x] - 2*a^2*x - a*b*x + 2*b^2*x + 2*a*b*x^(3/2) - a*b*x^2 - 4*a*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 2*b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 2*a*Sqrt[a + b]*x*Sqrt[a + b*x])^5)","B",1
496,-1,0,68,180.1189184,"\int \frac{\sqrt{a+b x}}{x^{9/2}} \, dx","IntegrateAlgebraic[Sqrt[a + b*x]/x^(9/2),x]","\text{\$Aborted}","-\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,"$Aborted","F",-1
497,1,2862,127,4.0529287,"\int x^{5/2} \sqrt{a-b x} \, dx","IntegrateAlgebraic[x^(5/2)*Sqrt[a - b*x],x]","\text{Result too large to show}","\frac{5 a^4 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)}{64 b^{7/2}}-\frac{5 a^3 \sqrt{x} \sqrt{a-b x}}{64 b^3}-\frac{5 a^2 x^{3/2} \sqrt{a-b x}}{96 b^2}-\frac{a x^{5/2} \sqrt{a-b x}}{24 b}+\frac{1}{4} x^{7/2} \sqrt{a-b x}",1,"((1920*a^11 - 3520*a^10*b + 1904*a^9*b^2 - 7304*a^8*b^3 + 16776*a^7*b^4 - 13680*a^6*b^5 + 4288*a^5*b^6 - 384*a^4*b^7)*Sqrt[a - b*x] + (-1920*a^11 - 3840*a^10*b + 9760*a^9*b^2 - 4576*a^8*b^3 + 28457*a^7*b^4 - 60072*a^6*b^5 + 41456*a^5*b^6 - 9664*a^4*b^7 + 384*a^3*b^8)*Sqrt[x]*Sqrt[a - b*x] + (4800*a^10*b + 6240*a^9*b^2 - 15336*a^8*b^3 + 15696*a^7*b^4 - 77904*a^6*b^5 + 120000*a^5*b^6 - 62592*a^4*b^7 + 9216*a^3*b^8)*x*Sqrt[a - b*x] + (2560*a^10*b - 9920*a^9*b^2 - 7200*a^8*b^3 + 15780*a^7*b^4 - 38130*a^6*b^5 + 136480*a^5*b^6 - 152480*a^4*b^7 + 56320*a^3*b^8 - 3840*a^2*b^9)*x^(3/2)*Sqrt[a - b*x] + (-7120*a^9*b^2 + 14760*a^8*b^3 + 5760*a^7*b^4 - 15360*a^6*b^5 + 63680*a^5*b^6 - 158080*a^4*b^7 + 128000*a^3*b^8 - 30720*a^2*b^9)*x^2*Sqrt[a - b*x] + (-864*a^9*b^2 + 10848*a^8*b^3 - 15570*a^7*b^4 - 3120*a^6*b^5 + 15624*a^5*b^6 - 68160*a^4*b^7 + 121344*a^3*b^8 - 70656*a^2*b^9 + 9216*a*b^10)*x^(5/2)*Sqrt[a - b*x] + (1736*a^8*b^3 - 10128*a^7*b^4 + 11520*a^6*b^5 + 1536*a^5*b^6 - 12416*a^4*b^7 + 44032*a^3*b^8 - 59392*a^2*b^9 + 24576*a*b^10)*x^3*Sqrt[a - b*x] + (7072*a^8*b^3 - 15404*a^7*b^4 + 14220*a^6*b^5 - 7584*a^5*b^6 - 624*a^4*b^7 + 5120*a^3*b^8 - 14336*a^2*b^9 + 16384*a*b^10 - 6144*b^11)*x^(7/2)*Sqrt[a - b*x] + (-28104*a^7*b^4 + 49392*a^6*b^5 - 25536*a^5*b^6 + 4992*a^4*b^7)*x^4*Sqrt[a - b*x] + (-13263*a^7*b^4 + 79176*a^6*b^5 - 95440*a^5*b^6 + 32192*a^4*b^7 - 2176*a^3*b^8)*x^(9/2)*Sqrt[a - b*x] + (46032*a^6*b^5 - 142016*a^5*b^6 + 117376*a^4*b^7 - 23552*a^3*b^8)*x^5*Sqrt[a - b*x] + (7926*a^6*b^5 - 88992*a^5*b^6 + 169440*a^4*b^7 - 93696*a^3*b^8 + 8448*a^2*b^9)*x^(11/2)*Sqrt[a - b*x] + (-21952*a^5*b^6 + 108416*a^4*b^7 - 136192*a^3*b^8 + 47104*a^2*b^9)*x^6*Sqrt[a - b*x] + (-1544*a^5*b^6 + 29248*a^4*b^7 - 85760*a^3*b^8 + 72704*a^2*b^9 - 13312*a*b^10)*x^(13/2)*Sqrt[a - b*x] + (2688*a^4*b^7 - 21504*a^3*b^8 + 43008*a^2*b^9 - 24576*a*b^10)*x^7*Sqrt[a - b*x] + (48*a^4*b^7 - 1536*a^3*b^8 + 7680*a^2*b^9 - 12288*a*b^10 + 6144*b^11)*x^(15/2)*Sqrt[a - b*x] + Sqrt[a - b]*(-1920*a^11 + 2560*a^10*b - 864*a^9*b^2 + 7072*a^8*b^3 - 13263*a^7*b^4 + 7926*a^6*b^5 - 1544*a^5*b^6 + 48*a^4*b^7 + (1920*a^11 + 4800*a^10*b - 7120*a^9*b^2 + 1736*a^8*b^3 - 28104*a^7*b^4 + 46032*a^6*b^5 - 21952*a^5*b^6 + 2688*a^4*b^7)*Sqrt[x] + (-3840*a^10*b - 9920*a^9*b^2 + 10848*a^8*b^3 - 15404*a^7*b^4 + 79176*a^6*b^5 - 88992*a^5*b^6 + 29248*a^4*b^7 - 1536*a^3*b^8)*x + (-3520*a^10*b + 6240*a^9*b^2 + 14760*a^8*b^3 - 10128*a^7*b^4 + 49392*a^6*b^5 - 142016*a^5*b^6 + 108416*a^4*b^7 - 21504*a^3*b^8)*x^(3/2) + (9760*a^9*b^2 - 7200*a^8*b^3 - 15570*a^7*b^4 + 14220*a^6*b^5 - 95440*a^5*b^6 + 169440*a^4*b^7 - 85760*a^3*b^8 + 7680*a^2*b^9)*x^2 + (1904*a^9*b^2 - 15336*a^8*b^3 + 5760*a^7*b^4 + 11520*a^6*b^5 - 25536*a^5*b^6 + 117376*a^4*b^7 - 136192*a^3*b^8 + 43008*a^2*b^9)*x^(5/2) + (-4576*a^8*b^3 + 15780*a^7*b^4 - 3120*a^6*b^5 - 7584*a^5*b^6 + 32192*a^4*b^7 - 93696*a^3*b^8 + 72704*a^2*b^9 - 12288*a*b^10)*x^3 + (-7304*a^8*b^3 + 15696*a^7*b^4 - 15360*a^6*b^5 + 1536*a^5*b^6 + 4992*a^4*b^7 - 23552*a^3*b^8 + 47104*a^2*b^9 - 24576*a*b^10)*x^(7/2) + (28457*a^7*b^4 - 38130*a^6*b^5 + 15624*a^5*b^6 - 624*a^4*b^7 - 2176*a^3*b^8 + 8448*a^2*b^9 - 13312*a*b^10 + 6144*b^11)*x^4 + (16776*a^7*b^4 - 77904*a^6*b^5 + 63680*a^5*b^6 - 12416*a^4*b^7)*x^(9/2) + (-60072*a^6*b^5 + 136480*a^5*b^6 - 68160*a^4*b^7 + 5120*a^3*b^8)*x^5 + (-13680*a^6*b^5 + 120000*a^5*b^6 - 158080*a^4*b^7 + 44032*a^3*b^8)*x^(11/2) + (41456*a^5*b^6 - 152480*a^4*b^7 + 121344*a^3*b^8 - 14336*a^2*b^9)*x^6 + (4288*a^5*b^6 - 62592*a^4*b^7 + 128000*a^3*b^8 - 59392*a^2*b^9)*x^(13/2) + (-9664*a^4*b^7 + 56320*a^3*b^8 - 70656*a^2*b^9 + 16384*a*b^10)*x^7 + (-384*a^4*b^7 + 9216*a^3*b^8 - 30720*a^2*b^9 + 24576*a*b^10)*x^(15/2) + (384*a^3*b^8 - 3840*a^2*b^9 + 9216*a*b^10 - 6144*b^11)*x^8))/(192*b^3*(128*a^8 - 256*a^7*b + 160*a^6*b^2 - 32*a^5*b^3 + a^4*b^4) + 192*b^3*(a^4*b^4 - 32*a^3*b^5 + 160*a^2*b^6 - 256*a*b^7 + 128*b^8)*x^4 + 192*Sqrt[a - b]*b^3*(-128*a^7 + 192*a^6*b - 80*a^5*b^2 + 8*a^4*b^3)*Sqrt[a - b*x] + x*(192*b^3*(-256*a^7*b + 1472*a^6*b^2 - 1760*a^5*b^3 + 604*a^4*b^4 - 32*a^3*b^5) + 192*Sqrt[a - b]*b^3*(192*a^6*b - 1248*a^5*b^2 + 1080*a^4*b^3 - 192*a^3*b^4)*Sqrt[a - b*x]) + Sqrt[x]*(192*b^3*(-512*a^7*b + 896*a^6*b^2 - 448*a^5*b^3 + 56*a^4*b^4) + 192*Sqrt[a - b]*b^3*(512*a^6*b - 640*a^5*b^2 + 192*a^4*b^3 - 8*a^3*b^4)*Sqrt[a - b*x]) + x^(3/2)*(192*b^3*(896*a^6*b^2 - 2688*a^5*b^3 + 2184*a^4*b^4 - 448*a^3*b^5) + 192*Sqrt[a - b]*b^3*(-640*a^5*b^2 + 1920*a^4*b^3 - 1080*a^3*b^4 + 80*a^2*b^5)*Sqrt[a - b*x]) + x^2*(192*b^3*(160*a^6*b^2 - 1760*a^5*b^3 + 3270*a^4*b^4 - 1760*a^3*b^5 + 160*a^2*b^6) + 192*Sqrt[a - b]*b^3*(-80*a^5*b^2 + 1080*a^4*b^3 - 1920*a^3*b^4 + 640*a^2*b^5)*Sqrt[a - b*x]) + x^3*(192*b^3*(-32*a^5*b^3 + 604*a^4*b^4 - 1760*a^3*b^5 + 1472*a^2*b^6 - 256*a*b^7) + 192*Sqrt[a - b]*b^3*(8*a^4*b^3 - 192*a^3*b^4 + 640*a^2*b^5 - 512*a*b^6)*Sqrt[a - b*x]) + x^(5/2)*(192*b^3*(-448*a^5*b^3 + 2184*a^4*b^4 - 2688*a^3*b^5 + 896*a^2*b^6) + 192*Sqrt[a - b]*b^3*(192*a^4*b^3 - 1080*a^3*b^4 + 1248*a^2*b^5 - 192*a*b^6)*Sqrt[a - b*x]) + x^(7/2)*(192*b^3*(56*a^4*b^4 - 448*a^3*b^5 + 896*a^2*b^6 - 512*a*b^7) + 192*Sqrt[a - b]*b^3*(-8*a^3*b^4 + 80*a^2*b^5 - 192*a*b^6 + 128*b^7)*Sqrt[a - b*x])) + (5*a^4*ArcTan[(Sqrt[a - b]/Sqrt[b] - Sqrt[a - b*x]/Sqrt[b])/(-1 + Sqrt[x])])/(32*b^(7/2))","B",1
498,1,1742,102,2.1295179,"\int x^{3/2} \sqrt{a-b x} \, dx","IntegrateAlgebraic[x^(3/2)*Sqrt[a - b*x],x]","\frac{\tan ^{-1}\left(\frac{\frac{\sqrt{a-b}}{\sqrt{b}}-\frac{\sqrt{a-b x}}{\sqrt{b}}}{\sqrt{x}-1}\right) a^3}{4 b^{5/2}}+\frac{\left(256 b^8-384 a b^7+144 a^2 b^6-8 a^3 b^5\right) \sqrt{a-b x} x^{11/2}+\left(-768 a b^7+960 a^2 b^6-240 a^3 b^5\right) \sqrt{a-b x} x^5+\left(-448 a b^7+1728 a^2 b^6-1308 a^3 b^5+146 a^4 b^4\right) \sqrt{a-b x} x^{9/2}+\left(1152 a^2 b^6-2320 a^3 b^5+1020 a^4 b^4\right) \sqrt{a-b x} x^4+\left(144 a^2 b^6-1536 a^3 b^5+1896 a^4 b^4-417 a^5 b^3\right) \sqrt{a-b x} x^{7/2}+\left(-918 b^3 a^5+1120 b^4 a^4-192 b^5 a^3\right) \sqrt{a-b x} x^3+\left(-256 b^8+576 a b^7-336 a^2 b^6+32 a^3 b^5-48 a^4 b^4-333 a^5 b^3+298 a^6 b^2\right) \sqrt{a-b x} x^{5/2}+\left(768 a b^7-1536 a^2 b^6+672 a^3 b^5+318 a^5 b^3-150 a^6 b^2\right) \sqrt{a-b x} x^2+\left(80 b a^7-300 b^2 a^6-123 b^3 a^5-512 b^4 a^4+2184 b^5 a^3-1632 b^6 a^2+256 b^7 a\right) \sqrt{a-b x} x^{3/2}+\left(192 b a^7+164 b^2 a^6+30 b^3 a^5-1824 b^4 a^4+2032 b^5 a^3-576 b^6 a^2\right) \sqrt{a-b x} x+\left(-96 a^8-144 b a^7+258 b^2 a^6+873 b^3 a^5-1482 b^4 a^4+636 b^5 a^3-48 b^6 a^2\right) \sqrt{a-b x} \sqrt{x}+\sqrt{a-b} \left(-96 a^8+80 b a^7+298 b^2 a^6-417 b^3 a^5+146 b^4 a^4-8 b^5 a^3+\left(-256 b^8+256 a b^7-48 a^2 b^6\right) x^6+\left(768 a b^7-576 a^2 b^6+48 a^3 b^5\right) x^{11/2}+\left(576 a b^7-1632 a^2 b^6+636 a^3 b^5\right) x^5+\left(-1536 a^2 b^6+2032 a^3 b^5-316 a^4 b^4\right) x^{9/2}+\left(-336 a^2 b^6+2184 a^3 b^5-1482 a^4 b^4\right) x^4+\left(570 b^3 a^5-1824 b^4 a^4+672 b^5 a^3\right) x^{7/2}+\left(256 b^8-448 a b^7+144 a^2 b^6+32 a^3 b^5-512 a^4 b^4+873 a^5 b^3\right) x^3+\left(-768 a b^7+1152 a^2 b^6-192 a^3 b^5+30 a^5 b^3-270 a^6 b^2\right) x^{5/2}+\left(-384 a b^7+1728 a^2 b^6-1536 a^3 b^5-48 a^4 b^4-123 a^5 b^3+258 a^6 b^2\right) x^2+\left(-128 b a^7+164 b^2 a^6+318 b^3 a^5+1120 b^4 a^4-2320 b^5 a^3+960 b^6 a^2\right) x^{3/2}+\left(-144 b a^7-300 b^2 a^6-333 b^3 a^5+1896 b^4 a^4-1308 b^5 a^3+144 b^6 a^2\right) x+\left(96 a^8+192 b a^7-150 b^2 a^6-918 b^3 a^5+1020 b^4 a^4-240 b^5 a^3\right) \sqrt{x}\right)+\left(96 a^8-128 b a^7-270 b^2 a^6+570 b^3 a^5-316 b^4 a^4+48 b^5 a^3\right) \sqrt{a-b x}}{24 b^2 \left(32 b^6-48 a b^5+18 a^2 b^4-a^3 b^3\right) x^3+\left(24 \left(-96 a b^5+120 a^2 b^4-30 a^3 b^3\right) b^2+24 \sqrt{a-b} \left(32 b^5-32 a b^4+6 a^2 b^3\right) \sqrt{a-b x} b^2\right) x^{5/2}+\left(24 \left(-48 a b^5+204 a^2 b^4-159 a^3 b^3+18 a^4 b^2\right) b^2+24 \sqrt{a-b} \left(-96 a b^4+72 a^2 b^3-6 a^3 b^2\right) \sqrt{a-b x} b^2\right) x^2+\left(24 \left(120 b^2 a^4-260 b^3 a^3+120 b^4 a^2\right) b^2+24 \sqrt{a-b} \left(-32 a b^4+164 a^2 b^3-72 a^3 b^2\right) \sqrt{a-b x} b^2\right) x^{3/2}+\left(24 \left(-48 b a^5+204 b^2 a^4-159 b^3 a^3+18 b^4 a^2\right) b^2+24 \sqrt{a-b} \left(32 b a^4-164 b^2 a^3+72 b^3 a^2\right) \sqrt{a-b x} b^2\right) x+\left(24 \left(-96 b a^5+120 b^2 a^4-30 b^3 a^3\right) b^2+24 \sqrt{a-b} \left(96 b a^4-72 b^2 a^3+6 b^3 a^2\right) \sqrt{a-b x} b^2\right) \sqrt{x}+24 b^2 \left(32 a^6-48 b a^5+18 b^2 a^4-b^3 a^3\right)+24 \sqrt{a-b} b^2 \left(-32 a^5+32 b a^4-6 b^2 a^3\right) \sqrt{a-b x}}","\frac{a^3 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)}{8 b^{5/2}}-\frac{a^2 \sqrt{x} \sqrt{a-b x}}{8 b^2}-\frac{a x^{3/2} \sqrt{a-b x}}{12 b}+\frac{1}{3} x^{5/2} \sqrt{a-b x}",1,"((96*a^8 - 128*a^7*b - 270*a^6*b^2 + 570*a^5*b^3 - 316*a^4*b^4 + 48*a^3*b^5)*Sqrt[a - b*x] + (-96*a^8 - 144*a^7*b + 258*a^6*b^2 + 873*a^5*b^3 - 1482*a^4*b^4 + 636*a^3*b^5 - 48*a^2*b^6)*Sqrt[x]*Sqrt[a - b*x] + (192*a^7*b + 164*a^6*b^2 + 30*a^5*b^3 - 1824*a^4*b^4 + 2032*a^3*b^5 - 576*a^2*b^6)*x*Sqrt[a - b*x] + (80*a^7*b - 300*a^6*b^2 - 123*a^5*b^3 - 512*a^4*b^4 + 2184*a^3*b^5 - 1632*a^2*b^6 + 256*a*b^7)*x^(3/2)*Sqrt[a - b*x] + (-150*a^6*b^2 + 318*a^5*b^3 + 672*a^3*b^5 - 1536*a^2*b^6 + 768*a*b^7)*x^2*Sqrt[a - b*x] + (298*a^6*b^2 - 333*a^5*b^3 - 48*a^4*b^4 + 32*a^3*b^5 - 336*a^2*b^6 + 576*a*b^7 - 256*b^8)*x^(5/2)*Sqrt[a - b*x] + (-918*a^5*b^3 + 1120*a^4*b^4 - 192*a^3*b^5)*x^3*Sqrt[a - b*x] + (-417*a^5*b^3 + 1896*a^4*b^4 - 1536*a^3*b^5 + 144*a^2*b^6)*x^(7/2)*Sqrt[a - b*x] + (1020*a^4*b^4 - 2320*a^3*b^5 + 1152*a^2*b^6)*x^4*Sqrt[a - b*x] + (146*a^4*b^4 - 1308*a^3*b^5 + 1728*a^2*b^6 - 448*a*b^7)*x^(9/2)*Sqrt[a - b*x] + (-240*a^3*b^5 + 960*a^2*b^6 - 768*a*b^7)*x^5*Sqrt[a - b*x] + (-8*a^3*b^5 + 144*a^2*b^6 - 384*a*b^7 + 256*b^8)*x^(11/2)*Sqrt[a - b*x] + Sqrt[a - b]*(-96*a^8 + 80*a^7*b + 298*a^6*b^2 - 417*a^5*b^3 + 146*a^4*b^4 - 8*a^3*b^5 + (96*a^8 + 192*a^7*b - 150*a^6*b^2 - 918*a^5*b^3 + 1020*a^4*b^4 - 240*a^3*b^5)*Sqrt[x] + (-144*a^7*b - 300*a^6*b^2 - 333*a^5*b^3 + 1896*a^4*b^4 - 1308*a^3*b^5 + 144*a^2*b^6)*x + (-128*a^7*b + 164*a^6*b^2 + 318*a^5*b^3 + 1120*a^4*b^4 - 2320*a^3*b^5 + 960*a^2*b^6)*x^(3/2) + (258*a^6*b^2 - 123*a^5*b^3 - 48*a^4*b^4 - 1536*a^3*b^5 + 1728*a^2*b^6 - 384*a*b^7)*x^2 + (-270*a^6*b^2 + 30*a^5*b^3 - 192*a^3*b^5 + 1152*a^2*b^6 - 768*a*b^7)*x^(5/2) + (873*a^5*b^3 - 512*a^4*b^4 + 32*a^3*b^5 + 144*a^2*b^6 - 448*a*b^7 + 256*b^8)*x^3 + (570*a^5*b^3 - 1824*a^4*b^4 + 672*a^3*b^5)*x^(7/2) + (-1482*a^4*b^4 + 2184*a^3*b^5 - 336*a^2*b^6)*x^4 + (-316*a^4*b^4 + 2032*a^3*b^5 - 1536*a^2*b^6)*x^(9/2) + (636*a^3*b^5 - 1632*a^2*b^6 + 576*a*b^7)*x^5 + (48*a^3*b^5 - 576*a^2*b^6 + 768*a*b^7)*x^(11/2) + (-48*a^2*b^6 + 256*a*b^7 - 256*b^8)*x^6))/(24*b^2*(32*a^6 - 48*a^5*b + 18*a^4*b^2 - a^3*b^3) + 24*b^2*(-(a^3*b^3) + 18*a^2*b^4 - 48*a*b^5 + 32*b^6)*x^3 + 24*Sqrt[a - b]*b^2*(-32*a^5 + 32*a^4*b - 6*a^3*b^2)*Sqrt[a - b*x] + Sqrt[x]*(24*b^2*(-96*a^5*b + 120*a^4*b^2 - 30*a^3*b^3) + 24*Sqrt[a - b]*b^2*(96*a^4*b - 72*a^3*b^2 + 6*a^2*b^3)*Sqrt[a - b*x]) + x*(24*b^2*(-48*a^5*b + 204*a^4*b^2 - 159*a^3*b^3 + 18*a^2*b^4) + 24*Sqrt[a - b]*b^2*(32*a^4*b - 164*a^3*b^2 + 72*a^2*b^3)*Sqrt[a - b*x]) + x^2*(24*b^2*(18*a^4*b^2 - 159*a^3*b^3 + 204*a^2*b^4 - 48*a*b^5) + 24*Sqrt[a - b]*b^2*(-6*a^3*b^2 + 72*a^2*b^3 - 96*a*b^4)*Sqrt[a - b*x]) + x^(3/2)*(24*b^2*(120*a^4*b^2 - 260*a^3*b^3 + 120*a^2*b^4) + 24*Sqrt[a - b]*b^2*(-72*a^3*b^2 + 164*a^2*b^3 - 32*a*b^4)*Sqrt[a - b*x]) + x^(5/2)*(24*b^2*(-30*a^3*b^3 + 120*a^2*b^4 - 96*a*b^5) + 24*Sqrt[a - b]*b^2*(6*a^2*b^3 - 32*a*b^4 + 32*b^5)*Sqrt[a - b*x])) + (a^3*ArcTan[(Sqrt[a - b]/Sqrt[b] - Sqrt[a - b*x]/Sqrt[b])/(-1 + Sqrt[x])])/(4*b^(5/2))","B",1
499,1,508,77,0.7805355,"\int \sqrt{x} \sqrt{a-b x} \, dx","IntegrateAlgebraic[Sqrt[x]*Sqrt[a - b*x],x]","\frac{a^2 \tan ^{-1}\left(\frac{\frac{\sqrt{a-b}}{\sqrt{b}}-\frac{\sqrt{a-b x}}{\sqrt{b}}}{\sqrt{x}-1}\right)}{2 b^{3/2}}+\frac{\left(\frac{\sqrt{x}}{4 b}-\frac{1}{4 b}\right) \left(\sqrt{a-b}-\sqrt{a-b x}\right) \left(\sqrt{a-b} \sqrt{a-b x}-a+b x-b \sqrt{x}+b\right) \left(-2 a^4+5 a^3 b x+10 a^3 b \sqrt{x}+2 a^3 \sqrt{a-b} \sqrt{a-b x}+5 a^3 b-12 a^2 b^2 x^{3/2}-2 a^2 b^2 x^2-22 a^2 b^2 x-12 a^2 b^2 \sqrt{x}-2 a^2 b^2-4 a^2 b \sqrt{a-b} \sqrt{a-b x}-4 a^2 b x \sqrt{a-b} \sqrt{a-b x}-10 a^2 b \sqrt{x} \sqrt{a-b} \sqrt{a-b x}+16 a b^3 x^{3/2}-16 b^3 x^{3/2} \sqrt{a-b} \sqrt{a-b x}+16 a b^3 x^2+16 a b^3 x+8 a b^2 x^{3/2} \sqrt{a-b} \sqrt{a-b x}+16 a b^2 x \sqrt{a-b} \sqrt{a-b x}+8 a b^2 \sqrt{x} \sqrt{a-b} \sqrt{a-b x}-16 b^4 x^2\right)}{\left(\sqrt{a-b} \sqrt{a-b x}-a+b \sqrt{x}\right)^4}","\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,"((-1/4*1/b + Sqrt[x]/(4*b))*(Sqrt[a - b] - Sqrt[a - b*x])*(-a + b - b*Sqrt[x] + b*x + Sqrt[a - b]*Sqrt[a - b*x])*(-2*a^4 + 5*a^3*b - 2*a^2*b^2 + 10*a^3*b*Sqrt[x] - 12*a^2*b^2*Sqrt[x] + 5*a^3*b*x - 22*a^2*b^2*x + 16*a*b^3*x - 12*a^2*b^2*x^(3/2) + 16*a*b^3*x^(3/2) - 2*a^2*b^2*x^2 + 16*a*b^3*x^2 - 16*b^4*x^2 + 2*a^3*Sqrt[a - b]*Sqrt[a - b*x] - 4*a^2*Sqrt[a - b]*b*Sqrt[a - b*x] - 10*a^2*Sqrt[a - b]*b*Sqrt[x]*Sqrt[a - b*x] + 8*a*Sqrt[a - b]*b^2*Sqrt[x]*Sqrt[a - b*x] - 4*a^2*Sqrt[a - b]*b*x*Sqrt[a - b*x] + 16*a*Sqrt[a - b]*b^2*x*Sqrt[a - b*x] + 8*a*Sqrt[a - b]*b^2*x^(3/2)*Sqrt[a - b*x] - 16*Sqrt[a - b]*b^3*x^(3/2)*Sqrt[a - b*x]))/(-a + b*Sqrt[x] + Sqrt[a - b]*Sqrt[a - b*x])^4 + (a^2*ArcTan[(Sqrt[a - b]/Sqrt[b] - Sqrt[a - b*x]/Sqrt[b])/(-1 + Sqrt[x])])/(2*b^(3/2))","B",1
500,1,195,46,0.314208,"\int \frac{\sqrt{a-b x}}{\sqrt{x}} \, dx","IntegrateAlgebraic[Sqrt[a - b*x]/Sqrt[x],x]","\frac{\left(1-\sqrt{x}\right) \left(\sqrt{a-b}-\sqrt{a-b x}\right) \left(a^2-a b x-a b \sqrt{x}-a \sqrt{a-b} \sqrt{a-b x}+2 b \sqrt{x} \sqrt{a-b} \sqrt{a-b x}-a b+2 b^2 x\right)}{\left(\sqrt{a-b} \sqrt{a-b x}-a+b \sqrt{x}\right)^2}+\frac{2 a \tan ^{-1}\left(\frac{\frac{\sqrt{a-b}}{\sqrt{b}}-\frac{\sqrt{a-b x}}{\sqrt{b}}}{\sqrt{x}-1}\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,"((1 - Sqrt[x])*(Sqrt[a - b] - Sqrt[a - b*x])*(a^2 - a*b - a*b*Sqrt[x] - a*b*x + 2*b^2*x - a*Sqrt[a - b]*Sqrt[a - b*x] + 2*Sqrt[a - b]*b*Sqrt[x]*Sqrt[a - b*x]))/(-a + b*Sqrt[x] + Sqrt[a - b]*Sqrt[a - b*x])^2 + (2*a*ArcTan[(Sqrt[a - b]/Sqrt[b] - Sqrt[a - b*x]/Sqrt[b])/(-1 + Sqrt[x])])/Sqrt[b]","B",1
501,1,289,47,0.4191979,"\int \frac{\sqrt{a-b x}}{x^{3/2}} \, dx","IntegrateAlgebraic[Sqrt[a - b*x]/x^(3/2),x]","\frac{\left(2 a-2 a \sqrt{x}\right) \left(\sqrt{a-b}-\sqrt{a-b x}\right) \left(-2 \sqrt{a-b} \sqrt{a-b x}+\sqrt{x} \sqrt{a-b} \sqrt{a-b x}+a \left(-\sqrt{x}\right)+2 a-b x+2 b \sqrt{x}-2 b\right)}{\sqrt{x} \left(-2 a^2 \sqrt{x}+4 a^2+a b x^{3/2}-2 a b x+a b \sqrt{x}-4 a \sqrt{a-b} \sqrt{a-b x}+2 a \sqrt{x} \sqrt{a-b} \sqrt{a-b x}+2 b \sqrt{a-b} \sqrt{a-b x}-4 a b+2 b^2 \sqrt{x}\right)}-4 \sqrt{b} \tan ^{-1}\left(\frac{\frac{\sqrt{a-b}}{\sqrt{b}}-\frac{\sqrt{a-b x}}{\sqrt{b}}}{\sqrt{x}-1}\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*a - 2*a*Sqrt[x])*(Sqrt[a - b] - Sqrt[a - b*x])*(2*a - 2*b - a*Sqrt[x] + 2*b*Sqrt[x] - b*x - 2*Sqrt[a - b]*Sqrt[a - b*x] + Sqrt[a - b]*Sqrt[x]*Sqrt[a - b*x]))/(Sqrt[x]*(4*a^2 - 4*a*b - 2*a^2*Sqrt[x] + a*b*Sqrt[x] + 2*b^2*Sqrt[x] - 2*a*b*x + a*b*x^(3/2) - 4*a*Sqrt[a - b]*Sqrt[a - b*x] + 2*Sqrt[a - b]*b*Sqrt[a - b*x] + 2*a*Sqrt[a - b]*Sqrt[x]*Sqrt[a - b*x])) - 4*Sqrt[b]*ArcTan[(Sqrt[a - b]/Sqrt[b] - Sqrt[a - b*x]/Sqrt[b])/(-1 + Sqrt[x])]","B",1
502,1,1006,22,7.0042436,"\int \frac{\sqrt{a-b x}}{x^{5/2}} \, dx","IntegrateAlgebraic[Sqrt[a - b*x]/x^(5/2),x]","\frac{\left(\sqrt{a-b}-\sqrt{a-b x}\right)^{12} \left(\frac{2 a^3 \sqrt{a-b} \left(\sqrt{x}-1\right)^6}{3 \left(\sqrt{a-b}-\sqrt{a-b x}\right)^6}+\frac{2 a^2 \left(-12 \sqrt{x} a^3+8 a^3+5 b x^{3/2} a^2-2 b a^2+24 b x a^2-15 b \sqrt{x} a^2-8 \sqrt{a-b} \sqrt{a-b x} a^2+12 \sqrt{a-b} \sqrt{x} \sqrt{a-b x} a^2+3 b^2 x^{5/2} a-8 b^2 a-21 b^2 x^2 a+14 b^2 x^{3/2} a-33 b^2 x a+33 b^2 \sqrt{x} a+\sqrt{a-b} b x^{3/2} \sqrt{a-b x} a-2 \sqrt{a-b} b \sqrt{a-b x} a-28 \sqrt{a-b} b x \sqrt{a-b x} a+21 \sqrt{a-b} b \sqrt{x} \sqrt{a-b x} a+2 b^3+b^3 x^3-6 b^3 x^{5/2}+24 b^3 x^2-20 b^3 x^{3/2}+9 b^3 x-6 b^3 \sqrt{x}-\sqrt{a-b} b^2 x^{5/2} \sqrt{a-b x}+6 \sqrt{a-b} b^2 \sqrt{a-b x}+6 \sqrt{a-b} b^2 x^2 \sqrt{a-b x}-6 \sqrt{a-b} b^2 x^{3/2} \sqrt{a-b x}+20 \sqrt{a-b} b^2 x \sqrt{a-b x}-21 \sqrt{a-b} b^2 \sqrt{x} \sqrt{a-b x}\right) \left(\sqrt{x}-1\right)^3}{3 \left(\sqrt{a-b}-\sqrt{a-b x}\right)^9}+\frac{2 b \left(-a+b \sqrt{x}+\sqrt{a-b} \sqrt{a-b x}\right)^4 \left(-\sqrt{x} a+2 a-2 b-b x+2 b \sqrt{x}-2 \sqrt{a-b} \sqrt{a-b x}+\sqrt{a-b} \sqrt{x} \sqrt{a-b x}\right) \left(\sqrt{x}-1\right)}{\left(\sqrt{a-b}-\sqrt{a-b x}\right)^{11}}-\frac{2 a \left(-a+b \sqrt{x}+\sqrt{a-b} \sqrt{a-b x}\right)^4 \left(-2 \sqrt{x} a+3 a-3 b-b x+3 b \sqrt{x}-3 \sqrt{a-b} \sqrt{a-b x}+2 \sqrt{a-b} \sqrt{x} \sqrt{a-b x}\right) \left(\sqrt{x}-1\right)}{\left(\sqrt{a-b}-\sqrt{a-b x}\right)^{11}}\right)}{\left(-2 x a^2+4 \sqrt{x} a^2+b x^2 a-2 b x^{3/2} a+b x a-4 b \sqrt{x} a+2 \sqrt{a-b} x \sqrt{a-b x} a-4 \sqrt{a-b} \sqrt{x} \sqrt{a-b x} a+2 b^2 x+2 \sqrt{a-b} b \sqrt{x} \sqrt{a-b x}\right)^3}","-\frac{2 (a-b x)^{3/2}}{3 a x^{3/2}}",1,"((Sqrt[a - b] - Sqrt[a - b*x])^12*((2*a^3*Sqrt[a - b]*(-1 + Sqrt[x])^6)/(3*(Sqrt[a - b] - Sqrt[a - b*x])^6) + (2*b*(-1 + Sqrt[x])*(-a + b*Sqrt[x] + Sqrt[a - b]*Sqrt[a - b*x])^4*(2*a - 2*b - a*Sqrt[x] + 2*b*Sqrt[x] - b*x - 2*Sqrt[a - b]*Sqrt[a - b*x] + Sqrt[a - b]*Sqrt[x]*Sqrt[a - b*x]))/(Sqrt[a - b] - Sqrt[a - b*x])^11 - (2*a*(-1 + Sqrt[x])*(-a + b*Sqrt[x] + Sqrt[a - b]*Sqrt[a - b*x])^4*(3*a - 3*b - 2*a*Sqrt[x] + 3*b*Sqrt[x] - b*x - 3*Sqrt[a - b]*Sqrt[a - b*x] + 2*Sqrt[a - b]*Sqrt[x]*Sqrt[a - b*x]))/(Sqrt[a - b] - Sqrt[a - b*x])^11 + (2*a^2*(-1 + Sqrt[x])^3*(8*a^3 - 2*a^2*b - 8*a*b^2 + 2*b^3 - 12*a^3*Sqrt[x] - 15*a^2*b*Sqrt[x] + 33*a*b^2*Sqrt[x] - 6*b^3*Sqrt[x] + 24*a^2*b*x - 33*a*b^2*x + 9*b^3*x + 5*a^2*b*x^(3/2) + 14*a*b^2*x^(3/2) - 20*b^3*x^(3/2) - 21*a*b^2*x^2 + 24*b^3*x^2 + 3*a*b^2*x^(5/2) - 6*b^3*x^(5/2) + b^3*x^3 - 8*a^2*Sqrt[a - b]*Sqrt[a - b*x] - 2*a*Sqrt[a - b]*b*Sqrt[a - b*x] + 6*Sqrt[a - b]*b^2*Sqrt[a - b*x] + 12*a^2*Sqrt[a - b]*Sqrt[x]*Sqrt[a - b*x] + 21*a*Sqrt[a - b]*b*Sqrt[x]*Sqrt[a - b*x] - 21*Sqrt[a - b]*b^2*Sqrt[x]*Sqrt[a - b*x] - 28*a*Sqrt[a - b]*b*x*Sqrt[a - b*x] + 20*Sqrt[a - b]*b^2*x*Sqrt[a - b*x] + a*Sqrt[a - b]*b*x^(3/2)*Sqrt[a - b*x] - 6*Sqrt[a - b]*b^2*x^(3/2)*Sqrt[a - b*x] + 6*Sqrt[a - b]*b^2*x^2*Sqrt[a - b*x] - Sqrt[a - b]*b^2*x^(5/2)*Sqrt[a - b*x]))/(3*(Sqrt[a - b] - Sqrt[a - b*x])^9)))/(4*a^2*Sqrt[x] - 4*a*b*Sqrt[x] - 2*a^2*x + a*b*x + 2*b^2*x - 2*a*b*x^(3/2) + a*b*x^2 - 4*a*Sqrt[a - b]*Sqrt[x]*Sqrt[a - b*x] + 2*Sqrt[a - b]*b*Sqrt[x]*Sqrt[a - b*x] + 2*a*Sqrt[a - b]*x*Sqrt[a - b*x])^3","B",1
503,1,4668,46,121.5956302,"\int \frac{\sqrt{a-b x}}{x^{7/2}} \, dx","IntegrateAlgebraic[Sqrt[a - b*x]/x^(7/2),x]","\text{Result too large to show}","-\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,"((-1/3840 + Sqrt[x]/3840)*(Sqrt[a - b] - Sqrt[a - b*x])^20*((-1536*a^5*Sqrt[a - b]*(-1 + Sqrt[x])^9)/(Sqrt[a - b] - Sqrt[a - b*x])^9 - (512*a^4*Sqrt[a - b]*(-1 + Sqrt[x])^7*(-30*a^2 + 13*a*b + b^2 + 34*a*b*Sqrt[x] - 2*b^2*Sqrt[x] + 13*a*b*x - 28*b^2*x - 2*b^2*x^(3/2) + b^2*x^2 + 30*a*Sqrt[a - b]*Sqrt[a - b*x] + 2*Sqrt[a - b]*b*Sqrt[a - b*x] - 34*Sqrt[a - b]*b*Sqrt[x]*Sqrt[a - b*x] + 2*Sqrt[a - b]*b*x*Sqrt[a - b*x]))/(Sqrt[a - b] - Sqrt[a - b*x])^11 - (7680*b*(-a + b*Sqrt[x] + Sqrt[a - b]*Sqrt[a - b*x])^6*(-a + b - b*Sqrt[x] + b*x + Sqrt[a - b]*Sqrt[a - b*x])*(-6*a^2 + 11*a*b - 4*b^2 + 4*a^2*Sqrt[x] - 14*a*b*Sqrt[x] + 8*b^2*Sqrt[x] + 11*a*b*x - 12*b^2*x - 4*a*b*x^(3/2) + 8*b^2*x^(3/2) - 2*b^2*x^2 + 6*a*Sqrt[a - b]*Sqrt[a - b*x] - 8*Sqrt[a - b]*b*Sqrt[a - b*x] - 4*a*Sqrt[a - b]*Sqrt[x]*Sqrt[a - b*x] + 12*Sqrt[a - b]*b*Sqrt[x]*Sqrt[a - b*x] - 8*Sqrt[a - b]*b*x*Sqrt[a - b*x] + 2*Sqrt[a - b]*b*x^(3/2)*Sqrt[a - b*x]))/(Sqrt[a - b] - Sqrt[a - b*x])^18 + (512*a^3*(-1 + Sqrt[x])^4*(528*a^5 - 860*a^4*b + 253*a^3*b^2 + 131*a^2*b^3 - 56*a*b^4 + 4*b^5 - 480*a^5*Sqrt[x] - 400*a^4*b*Sqrt[x] + 1750*a^3*b^2*Sqrt[x] - 1080*a^2*b^3*Sqrt[x] + 230*a*b^4*Sqrt[x] - 20*b^5*Sqrt[x] + 500*a^4*b*x - 170*a^3*b^2*x - 75*a^2*b^3*x - 345*a*b^4*x + 90*b^5*x + 520*a^4*b*x^(3/2) - 180*a^3*b^2*x^(3/2) - 1905*a^2*b^3*x^(3/2) + 1810*a*b^4*x^(3/2) - 240*b^5*x^(3/2) - 1155*a^3*b^2*x^2 + 2165*a^2*b^3*x^2 - 1175*a*b^4*x^2 + 140*b^5*x^2 - 18*a^3*b^2*x^(5/2) - 6*a^2*b^3*x^(5/2) + 576*a*b^4*x^(5/2) - 504*b^5*x^(5/2) + 355*a^2*b^3*x^3 - 1055*a*b^4*x^3 + 660*b^5*x^3 - 65*a^2*b^3*x^(7/2) + 310*a*b^4*x^(7/2) - 240*b^5*x^(7/2) - 65*a*b^4*x^4 + 80*b^5*x^4 + 10*a*b^4*x^(9/2) - 20*b^5*x^(9/2) + 2*b^5*x^5 - 528*a^4*Sqrt[a - b]*Sqrt[a - b*x] + 596*a^3*Sqrt[a - b]*b*Sqrt[a - b*x] - 21*a^2*Sqrt[a - b]*b^2*Sqrt[a - b*x] - 100*a*Sqrt[a - b]*b^3*Sqrt[a - b*x] + 20*Sqrt[a - b]*b^4*Sqrt[a - b*x] + 480*a^4*Sqrt[a - b]*Sqrt[x]*Sqrt[a - b*x] + 640*a^3*Sqrt[a - b]*b*Sqrt[x]*Sqrt[a - b*x] - 1370*a^2*Sqrt[a - b]*b^2*Sqrt[x]*Sqrt[a - b*x] + 505*a*Sqrt[a - b]*b^3*Sqrt[x]*Sqrt[a - b*x] - 90*Sqrt[a - b]*b^4*Sqrt[x]*Sqrt[a - b*x] - 764*a^3*Sqrt[a - b]*b*x*Sqrt[a - b*x] + 218*a^2*Sqrt[a - b]*b^2*x*Sqrt[a - b*x] - 38*a*Sqrt[a - b]*b^3*x*Sqrt[a - b*x] + 240*Sqrt[a - b]*b^4*x*Sqrt[a - b*x] - 280*a^3*Sqrt[a - b]*b*x^(3/2)*Sqrt[a - b*x] + 240*a^2*Sqrt[a - b]*b^2*x^(3/2)*Sqrt[a - b*x] + 1115*a*Sqrt[a - b]*b^3*x^(3/2)*Sqrt[a - b*x] - 700*Sqrt[a - b]*b^4*x^(3/2)*Sqrt[a - b*x] + 707*a^2*Sqrt[a - b]*b^2*x^2*Sqrt[a - b*x] - 1404*a*Sqrt[a - b]*b^3*x^2*Sqrt[a - b*x] + 504*Sqrt[a - b]*b^4*x^2*Sqrt[a - b*x] - 62*a^2*Sqrt[a - b]*b^2*x^(5/2)*Sqrt[a - b*x] + 215*a*Sqrt[a - b]*b^3*x^(5/2)*Sqrt[a - b*x] - 180*Sqrt[a - b]*b^4*x^(5/2)*Sqrt[a - b*x] - 130*a*Sqrt[a - b]*b^3*x^3*Sqrt[a - b*x] + 240*Sqrt[a - b]*b^4*x^3*Sqrt[a - b*x] + 29*a*Sqrt[a - b]*b^3*x^(7/2)*Sqrt[a - b*x] - 100*Sqrt[a - b]*b^4*x^(7/2)*Sqrt[a - b*x] + 20*Sqrt[a - b]*b^4*x^4*Sqrt[a - b*x] - 2*Sqrt[a - b]*b^4*x^(9/2)*Sqrt[a - b*x]))/(Sqrt[a - b] - Sqrt[a - b*x])^14 - (2560*a^2*(-1 + Sqrt[x])^2*(-a + b*Sqrt[x] + Sqrt[a - b]*Sqrt[a - b*x])^2*(-48*a^5 + 244*a^4*b - 383*a^3*b^2 + 245*a^2*b^3 - 62*a*b^4 + 4*b^5 - 48*a^5*Sqrt[x] - 268*a^4*b*Sqrt[x] + 733*a^3*b^2*Sqrt[x] - 600*a^2*b^3*Sqrt[x] + 200*a*b^4*Sqrt[x] - 20*b^5*Sqrt[x] + 524*a^4*b*x - 1274*a^3*b^2*x + 1308*a^2*b^3*x - 645*a*b^4*x + 102*b^5*x - 20*a^4*b*x^(3/2) + 558*a^3*b^2*x^(3/2) - 1449*a^2*b^3*x^(3/2) + 1120*a*b^4*x^(3/2) - 240*b^5*x^(3/2) - 711*a^3*b^2*x^2 + 1793*a^2*b^3*x^2 - 1463*a*b^4*x^2 + 416*b^5*x^2 + 117*a^3*b^2*x^(5/2) - 606*a^2*b^3*x^(5/2) + 966*a*b^4*x^(5/2) - 504*b^5*x^(5/2) + 334*a^2*b^3*x^3 - 815*a*b^4*x^3 + 504*b^5*x^3 - 65*a^2*b^3*x^(7/2) + 280*a*b^4*x^(7/2) - 240*b^5*x^(7/2) - 71*a*b^4*x^4 + 92*b^5*x^4 + 10*a*b^4*x^(9/2) - 20*b^5*x^(9/2) + 2*b^5*x^5 + 48*a^4*Sqrt[a - b]*Sqrt[a - b*x] - 220*a^3*Sqrt[a - b]*b*Sqrt[a - b*x] + 279*a^2*Sqrt[a - b]*b^2*Sqrt[a - b*x] - 130*a*Sqrt[a - b]*b^3*Sqrt[a - b*x] + 20*Sqrt[a - b]*b^4*Sqrt[a - b*x] + 48*a^4*Sqrt[a - b]*Sqrt[x]*Sqrt[a - b*x] + 292*a^3*Sqrt[a - b]*b*Sqrt[x]*Sqrt[a - b*x] - 581*a^2*Sqrt[a - b]*b^2*Sqrt[x]*Sqrt[a - b*x] + 349*a*Sqrt[a - b]*b^3*Sqrt[x]*Sqrt[a - b*x] - 78*Sqrt[a - b]*b^4*Sqrt[x]*Sqrt[a - b*x] - 500*a^3*Sqrt[a - b]*b*x*Sqrt[a - b*x] + 902*a^2*Sqrt[a - b]*b^2*x*Sqrt[a - b*x] - 728*a*Sqrt[a - b]*b^3*x*Sqrt[a - b*x] + 240*Sqrt[a - b]*b^4*x*Sqrt[a - b*x] + 44*a^3*Sqrt[a - b]*b*x^(3/2)*Sqrt[a - b*x] - 402*a^2*Sqrt[a - b]*b^2*x^(3/2)*Sqrt[a - b*x] + 887*a*Sqrt[a - b]*b^3*x^(3/2)*Sqrt[a - b*x] - 424*Sqrt[a - b]*b^4*x^(3/2)*Sqrt[a - b*x] + 467*a^2*Sqrt[a - b]*b^2*x^2*Sqrt[a - b*x] - 1014*a*Sqrt[a - b]*b^3*x^2*Sqrt[a - b*x] + 504*Sqrt[a - b]*b^4*x^2*Sqrt[a - b*x] - 89*a^2*Sqrt[a - b]*b^2*x^(5/2)*Sqrt[a - b*x] + 383*a*Sqrt[a - b]*b^3*x^(5/2)*Sqrt[a - b*x] - 336*Sqrt[a - b]*b^4*x^(5/2)*Sqrt[a - b*x] - 160*a*Sqrt[a - b]*b^3*x^3*Sqrt[a - b*x] + 240*Sqrt[a - b]*b^4*x^3*Sqrt[a - b*x] + 29*a*Sqrt[a - b]*b^3*x^(7/2)*Sqrt[a - b*x] - 88*Sqrt[a - b]*b^4*x^(7/2)*Sqrt[a - b*x] + 20*Sqrt[a - b]*b^4*x^4*Sqrt[a - b*x] - 2*Sqrt[a - b]*b^4*x^(9/2)*Sqrt[a - b*x]))/(Sqrt[a - b] - Sqrt[a - b*x])^16 + (2560*a*(-a + b*Sqrt[x] + Sqrt[a - b]*Sqrt[a - b*x])^4*(192*a^5 - 656*a^4*b + 780*a^3*b^2 - 384*a^2*b^3 + 72*a*b^4 - 4*b^5 - 144*a^5*Sqrt[x] + 676*a^4*b*Sqrt[x] - 993*a^3*b^2*Sqrt[x] + 585*a^2*b^3*Sqrt[x] - 150*a*b^4*Sqrt[x] + 20*b^5*Sqrt[x] - 584*a^4*b*x + 1744*a^3*b^2*x - 1733*a^2*b^3*x + 725*a*b^4*x - 122*b^5*x + 324*a^4*b*x^(3/2) - 1486*a^3*b^2*x^(3/2) + 1899*a^2*b^3*x^(3/2) - 1030*a*b^4*x^(3/2) + 240*b^5*x^(3/2) + 692*a^3*b^2*x^2 - 1606*a^2*b^3*x^2 + 1391*a*b^4*x^2 - 452*b^5*x^2 - 257*a^3*b^2*x^(5/2) + 1031*a^2*b^3*x^(5/2) - 1236*a*b^4*x^(5/2) + 504*b^5*x^(5/2) - 357*a^2*b^3*x^3 + 679*a*b^4*x^3 - 396*b^5*x^3 + 85*a^2*b^3*x^(7/2) - 270*a*b^4*x^(7/2) + 240*b^5*x^(7/2) + 69*a*b^4*x^4 - 96*b^5*x^4 - 10*a*b^4*x^(9/2) + 20*b^5*x^(9/2) - 2*b^5*x^5 - 192*a^4*Sqrt[a - b]*Sqrt[a - b*x] + 560*a^3*Sqrt[a - b]*b*Sqrt[a - b*x] - 524*a^2*Sqrt[a - b]*b^2*Sqrt[a - b*x] + 180*a*Sqrt[a - b]*b^3*Sqrt[a - b*x] - 20*Sqrt[a - b]*b^4*Sqrt[a - b*x] + 144*a^4*Sqrt[a - b]*Sqrt[x]*Sqrt[a - b*x] - 604*a^3*Sqrt[a - b]*b*Sqrt[x]*Sqrt[a - b*x] + 709*a^2*Sqrt[a - b]*b^2*Sqrt[x]*Sqrt[a - b*x] - 297*a*Sqrt[a - b]*b^3*Sqrt[x]*Sqrt[a - b*x] + 58*Sqrt[a - b]*b^4*Sqrt[x]*Sqrt[a - b*x] + 488*a^3*Sqrt[a - b]*b*x*Sqrt[a - b*x] - 1172*a^2*Sqrt[a - b]*b^2*x*Sqrt[a - b*x] + 818*a*Sqrt[a - b]*b^3*x*Sqrt[a - b*x] - 240*Sqrt[a - b]*b^4*x*Sqrt[a - b*x] - 252*a^3*Sqrt[a - b]*b*x^(3/2)*Sqrt[a - b*x] + 1022*a^2*Sqrt[a - b]*b^2*x^(3/2)*Sqrt[a - b*x] - 923*a*Sqrt[a - b]*b^3*x^(3/2)*Sqrt[a - b*x] + 388*Sqrt[a - b]*b^4*x^(3/2)*Sqrt[a - b*x] - 472*a^2*Sqrt[a - b]*b^2*x^2*Sqrt[a - b*x] + 744*a*Sqrt[a - b]*b^3*x^2*Sqrt[a - b*x] - 504*Sqrt[a - b]*b^4*x^2*Sqrt[a - b*x] + 149*a^2*Sqrt[a - b]*b^2*x^(5/2)*Sqrt[a - b*x] - 467*a*Sqrt[a - b]*b^3*x^(5/2)*Sqrt[a - b*x] + 444*Sqrt[a - b]*b^4*x^(5/2)*Sqrt[a - b*x] + 170*a*Sqrt[a - b]*b^3*x^3*Sqrt[a - b*x] - 240*Sqrt[a - b]*b^4*x^3*Sqrt[a - b*x] - 33*a*Sqrt[a - b]*b^3*x^(7/2)*Sqrt[a - b*x] + 84*Sqrt[a - b]*b^4*x^(7/2)*Sqrt[a - b*x] - 20*Sqrt[a - b]*b^4*x^4*Sqrt[a - b*x] + 2*Sqrt[a - b]*b^4*x^(9/2)*Sqrt[a - b*x]))/(Sqrt[a - b] - Sqrt[a - b*x])^18))/((-Sqrt[a - b] + Sqrt[a - b*x])*(4*a^2*Sqrt[x] - 4*a*b*Sqrt[x] - 2*a^2*x + a*b*x + 2*b^2*x - 2*a*b*x^(3/2) + a*b*x^2 - 4*a*Sqrt[a - b]*Sqrt[x]*Sqrt[a - b*x] + 2*Sqrt[a - b]*b*Sqrt[x]*Sqrt[a - b*x] + 2*a*Sqrt[a - b]*x*Sqrt[a - b*x])^5)","B",1
504,-1,0,71,180.1474937,"\int \frac{\sqrt{a-b x}}{x^{9/2}} \, dx","IntegrateAlgebraic[Sqrt[a - b*x]/x^(9/2),x]","\text{\$Aborted}","-\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,"$Aborted","F",-1
505,1,2056,108,3.6143637,"\int x^{5/2} \sqrt{2+b x} \, dx","IntegrateAlgebraic[x^(5/2)*Sqrt[2 + b*x],x]","\text{Result too large to show}","-\frac{5 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{4 b^{7/2}}+\frac{5 \sqrt{x} \sqrt{b x+2}}{8 b^3}-\frac{5 x^{3/2} \sqrt{b x+2}}{24 b^2}+\frac{1}{4} x^{7/2} \sqrt{b x+2}+\frac{x^{5/2} \sqrt{b x+2}}{12 b}",1,"(2*(-30720 - 28160*b - 7616*b^2 - 14608*b^3 - 16776*b^4 - 6840*b^5 - 1072*b^6 - 48*b^7)*Sqrt[2 + b*x] + 2*(30720 - 30720*b - 39040*b^2 - 9152*b^3 - 28457*b^4 - 30036*b^5 - 10364*b^6 - 1208*b^7 - 24*b^8)*Sqrt[x]*Sqrt[2 + b*x] + 2*(38400*b - 24960*b^2 - 30672*b^3 - 15696*b^4 - 38952*b^5 - 30000*b^6 - 7824*b^7 - 576*b^8)*x*Sqrt[2 + b*x] + 2*(20480*b + 39680*b^2 - 14400*b^3 - 15780*b^4 - 19065*b^5 - 34120*b^6 - 19060*b^7 - 3520*b^8 - 120*b^9)*x^(3/2)*Sqrt[2 + b*x] + 2*(28480*b^2 + 29520*b^3 - 5760*b^4 - 7680*b^5 - 15920*b^6 - 19760*b^7 - 8000*b^8 - 960*b^9)*x^2*Sqrt[2 + b*x] + 2*(3456*b^2 + 21696*b^3 + 15570*b^4 - 1560*b^5 - 3906*b^6 - 8520*b^7 - 7584*b^8 - 2208*b^9 - 144*b^10)*x^(5/2)*Sqrt[2 + b*x] + 2*(3472*b^3 + 10128*b^4 + 5760*b^5 - 384*b^6 - 1552*b^7 - 2752*b^8 - 1856*b^9 - 384*b^10)*x^3*Sqrt[2 + b*x] + 2*(14144*b^3 + 15404*b^4 + 7110*b^5 + 1896*b^6 - 78*b^7 - 320*b^8 - 448*b^9 - 256*b^10 - 48*b^11)*x^(7/2)*Sqrt[2 + b*x] + 2*(28104*b^4 + 24696*b^5 + 6384*b^6 + 624*b^7)*x^4*Sqrt[2 + b*x] + 2*(13263*b^4 + 39588*b^5 + 23860*b^6 + 4024*b^7 + 136*b^8)*x^(9/2)*Sqrt[2 + b*x] + 2*(23016*b^5 + 35504*b^6 + 14672*b^7 + 1472*b^8)*x^5*Sqrt[2 + b*x] + 2*(3963*b^5 + 22248*b^6 + 21180*b^7 + 5856*b^8 + 264*b^9)*x^(11/2)*Sqrt[2 + b*x] + 2*(5488*b^6 + 13552*b^7 + 8512*b^8 + 1472*b^9)*x^6*Sqrt[2 + b*x] + 2*(386*b^6 + 3656*b^7 + 5360*b^8 + 2272*b^9 + 208*b^10)*x^(13/2)*Sqrt[2 + b*x] + 2*(336*b^7 + 1344*b^8 + 1344*b^9 + 384*b^10)*x^7*Sqrt[2 + b*x] + 2*(6*b^7 + 96*b^8 + 240*b^9 + 192*b^10 + 48*b^11)*x^(15/2)*Sqrt[2 + b*x] + Sqrt[2 + b]*(2*(30720 + 20480*b + 3456*b^2 + 14144*b^3 + 13263*b^4 + 3963*b^5 + 386*b^6 + 6*b^7) + 2*(-30720 + 38400*b + 28480*b^2 + 3472*b^3 + 28104*b^4 + 23016*b^5 + 5488*b^6 + 336*b^7)*Sqrt[x] + 2*(-30720*b + 39680*b^2 + 21696*b^3 + 15404*b^4 + 39588*b^5 + 22248*b^6 + 3656*b^7 + 96*b^8)*x + 2*(-28160*b - 24960*b^2 + 29520*b^3 + 10128*b^4 + 24696*b^5 + 35504*b^6 + 13552*b^7 + 1344*b^8)*x^(3/2) + 2*(-39040*b^2 - 14400*b^3 + 15570*b^4 + 7110*b^5 + 23860*b^6 + 21180*b^7 + 5360*b^8 + 240*b^9)*x^2 + 2*(-7616*b^2 - 30672*b^3 - 5760*b^4 + 5760*b^5 + 6384*b^6 + 14672*b^7 + 8512*b^8 + 1344*b^9)*x^(5/2) + 2*(-9152*b^3 - 15780*b^4 - 1560*b^5 + 1896*b^6 + 4024*b^7 + 5856*b^8 + 2272*b^9 + 192*b^10)*x^3 + 2*(-14608*b^3 - 15696*b^4 - 7680*b^5 - 384*b^6 + 624*b^7 + 1472*b^8 + 1472*b^9 + 384*b^10)*x^(7/2) + 2*(-28457*b^4 - 19065*b^5 - 3906*b^6 - 78*b^7 + 136*b^8 + 264*b^9 + 208*b^10 + 48*b^11)*x^4 + 2*(-16776*b^4 - 38952*b^5 - 15920*b^6 - 1552*b^7)*x^(9/2) + 2*(-30036*b^5 - 34120*b^6 - 8520*b^7 - 320*b^8)*x^5 + 2*(-6840*b^5 - 30000*b^6 - 19760*b^7 - 2752*b^8)*x^(11/2) + 2*(-10364*b^6 - 19060*b^7 - 7584*b^8 - 448*b^9)*x^6 + 2*(-1072*b^6 - 7824*b^7 - 8000*b^8 - 1856*b^9)*x^(13/2) + 2*(-1208*b^7 - 3520*b^8 - 2208*b^9 - 256*b^10)*x^7 + 2*(-48*b^7 - 576*b^8 - 960*b^9 - 384*b^10)*x^(15/2) + 2*(-24*b^8 - 120*b^9 - 144*b^10 - 48*b^11)*x^8))/(3*b^3*(32768 + 32768*b + 10240*b^2 + 1024*b^3 + 16*b^4) + 3*b^3*(16*b^4 + 256*b^5 + 640*b^6 + 512*b^7 + 128*b^8)*x^4 + 3*b^3*Sqrt[2 + b]*(-16384 - 12288*b - 2560*b^2 - 128*b^3)*Sqrt[2 + b*x] + x*(3*b^3*(32768*b + 94208*b^2 + 56320*b^3 + 9664*b^4 + 256*b^5) + 3*b^3*Sqrt[2 + b]*(-12288*b - 39936*b^2 - 17280*b^3 - 1536*b^4)*Sqrt[2 + b*x]) + Sqrt[x]*(3*b^3*(65536*b + 57344*b^2 + 14336*b^3 + 896*b^4) + 3*b^3*Sqrt[2 + b]*(-32768*b - 20480*b^2 - 3072*b^3 - 64*b^4)*Sqrt[2 + b*x]) + x^2*(3*b^3*(10240*b^2 + 56320*b^3 + 52320*b^4 + 14080*b^5 + 640*b^6) + 3*b^3*Sqrt[2 + b]*(-2560*b^2 - 17280*b^3 - 15360*b^4 - 2560*b^5)*Sqrt[2 + b*x]) + x^(3/2)*(3*b^3*(57344*b^2 + 86016*b^3 + 34944*b^4 + 3584*b^5) + 3*b^3*Sqrt[2 + b]*(-20480*b^2 - 30720*b^3 - 8640*b^4 - 320*b^5)*Sqrt[2 + b*x]) + x^3*(3*b^3*(1024*b^3 + 9664*b^4 + 14080*b^5 + 5888*b^6 + 512*b^7) + 3*b^3*Sqrt[2 + b]*(-128*b^3 - 1536*b^4 - 2560*b^5 - 1024*b^6)*Sqrt[2 + b*x]) + x^(5/2)*(3*b^3*(14336*b^3 + 34944*b^4 + 21504*b^5 + 3584*b^6) + 3*b^3*Sqrt[2 + b]*(-3072*b^3 - 8640*b^4 - 4992*b^5 - 384*b^6)*Sqrt[2 + b*x]) + x^(7/2)*(3*b^3*(896*b^4 + 3584*b^5 + 3584*b^6 + 1024*b^7) + 3*b^3*Sqrt[2 + b]*(-64*b^4 - 320*b^5 - 384*b^6 - 128*b^7)*Sqrt[2 + b*x])) + (5*ArcTanh[(Sqrt[2 + b]/Sqrt[b] - Sqrt[2 + b*x]/Sqrt[b])/(-1 + Sqrt[x])])/(2*b^(7/2))","B",1
506,1,1294,84,1.7794581,"\int x^{3/2} \sqrt{2+b x} \, dx","IntegrateAlgebraic[x^(3/2)*Sqrt[2 + b*x],x]","\frac{4 \left(8 b^8+24 b^7+18 b^6+2 b^5\right) \sqrt{b x+2} x^{11/2}+4 \left(48 b^7+120 b^6+60 b^5\right) \sqrt{b x+2} x^5+4 \left(28 b^7+216 b^6+327 b^5+73 b^4\right) \sqrt{b x+2} x^{9/2}+4 \left(144 b^6+580 b^5+510 b^4\right) \sqrt{b x+2} x^4+4 \left(18 b^6+384 b^5+948 b^4+417 b^3\right) \sqrt{b x+2} x^{7/2}+4 \left(48 b^5+560 b^4+918 b^3\right) \sqrt{b x+2} x^3+4 \left(-8 b^8-36 b^7-42 b^6-8 b^5-24 b^4+333 b^3+596 b^2\right) \sqrt{b x+2} x^{5/2}+4 \left(-48 b^7-192 b^6-168 b^5-318 b^3-300 b^2\right) \sqrt{b x+2} x^2+4 \left(-16 b^7-204 b^6-546 b^5-256 b^4+123 b^3-600 b^2-320 b\right) \sqrt{b x+2} x^{3/2}+4 \left(-72 b^6-508 b^5-912 b^4-30 b^3+328 b^2-768 b\right) \sqrt{b x+2} x+4 \left(-6 b^6-159 b^5-741 b^4-873 b^3+516 b^2+576 b-768\right) \sqrt{b x+2} \sqrt{x}+\sqrt{b+2} \left(4 \left(-8 b^8-16 b^7-6 b^6\right) x^6+4 \left(-48 b^7-72 b^6-12 b^5\right) x^{11/2}+4 \left(-36 b^7-204 b^6-159 b^5\right) x^5+4 \left(-192 b^6-508 b^5-158 b^4\right) x^{9/2}+4 \left(-42 b^6-546 b^5-741 b^4\right) x^4+4 \left(-168 b^5-912 b^4-570 b^3\right) x^{7/2}+4 \left(8 b^8+28 b^7+18 b^6-8 b^5-256 b^4-873 b^3\right) x^3+4 \left(48 b^7+144 b^6+48 b^5-30 b^3-540 b^2\right) x^{5/2}+4 \left(24 b^7+216 b^6+384 b^5-24 b^4+123 b^3+516 b^2\right) x^2+4 \left(120 b^6+580 b^5+560 b^4-318 b^3+328 b^2+512 b\right) x^{3/2}+4 \left(18 b^6+327 b^5+948 b^4+333 b^3-600 b^2+576 b\right) x+4 \left(60 b^5+510 b^4+918 b^3-300 b^2-768 b+768\right) \sqrt{x}+4 \left(2 b^5+73 b^4+417 b^3+596 b^2-320 b-768\right)\right)+4 \left(-12 b^5-158 b^4-570 b^3-540 b^2+512 b+768\right) \sqrt{b x+2}}{3 b^2 \left(32 b^6+96 b^5+72 b^4+8 b^3\right) x^3+\left(3 \left(192 b^5+480 b^4+240 b^3\right) b^2+3 \sqrt{b+2} \left(-32 b^5-64 b^4-24 b^3\right) \sqrt{b x+2} b^2\right) x^{5/2}+\left(3 \left(96 b^5+816 b^4+1272 b^3+288 b^2\right) b^2+3 \sqrt{b+2} \left(-192 b^4-288 b^3-48 b^2\right) \sqrt{b x+2} b^2\right) x^2+\left(3 \left(480 b^4+2080 b^3+1920 b^2\right) b^2+3 \sqrt{b+2} \left(-64 b^4-656 b^3-576 b^2\right) \sqrt{b x+2} b^2\right) x^{3/2}+\left(3 \left(72 b^4+1272 b^3+3264 b^2+1536 b\right) b^2+3 \sqrt{b+2} \left(-288 b^3-1312 b^2-512 b\right) \sqrt{b x+2} b^2\right) x+\left(3 \left(240 b^3+1920 b^2+3072 b\right) b^2+3 \sqrt{b+2} \left(-24 b^3-576 b^2-1536 b\right) \sqrt{b x+2} b^2\right) \sqrt{x}+3 b^2 \left(8 b^3+288 b^2+1536 b+2048\right)+3 b^2 \sqrt{b+2} \left(-48 b^2-512 b-1024\right) \sqrt{b x+2}}-\frac{2 \tanh ^{-1}\left(\frac{\frac{\sqrt{b+2}}{\sqrt{b}}-\frac{\sqrt{b x+2}}{\sqrt{b}}}{\sqrt{x}-1}\right)}{b^{5/2}}","\frac{\sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{5/2}}-\frac{\sqrt{x} \sqrt{b x+2}}{2 b^2}+\frac{1}{3} x^{5/2} \sqrt{b x+2}+\frac{x^{3/2} \sqrt{b x+2}}{6 b}",1,"(4*(768 + 512*b - 540*b^2 - 570*b^3 - 158*b^4 - 12*b^5)*Sqrt[2 + b*x] + 4*(-768 + 576*b + 516*b^2 - 873*b^3 - 741*b^4 - 159*b^5 - 6*b^6)*Sqrt[x]*Sqrt[2 + b*x] + 4*(-768*b + 328*b^2 - 30*b^3 - 912*b^4 - 508*b^5 - 72*b^6)*x*Sqrt[2 + b*x] + 4*(-320*b - 600*b^2 + 123*b^3 - 256*b^4 - 546*b^5 - 204*b^6 - 16*b^7)*x^(3/2)*Sqrt[2 + b*x] + 4*(-300*b^2 - 318*b^3 - 168*b^5 - 192*b^6 - 48*b^7)*x^2*Sqrt[2 + b*x] + 4*(596*b^2 + 333*b^3 - 24*b^4 - 8*b^5 - 42*b^6 - 36*b^7 - 8*b^8)*x^(5/2)*Sqrt[2 + b*x] + 4*(918*b^3 + 560*b^4 + 48*b^5)*x^3*Sqrt[2 + b*x] + 4*(417*b^3 + 948*b^4 + 384*b^5 + 18*b^6)*x^(7/2)*Sqrt[2 + b*x] + 4*(510*b^4 + 580*b^5 + 144*b^6)*x^4*Sqrt[2 + b*x] + 4*(73*b^4 + 327*b^5 + 216*b^6 + 28*b^7)*x^(9/2)*Sqrt[2 + b*x] + 4*(60*b^5 + 120*b^6 + 48*b^7)*x^5*Sqrt[2 + b*x] + 4*(2*b^5 + 18*b^6 + 24*b^7 + 8*b^8)*x^(11/2)*Sqrt[2 + b*x] + Sqrt[2 + b]*(4*(-768 - 320*b + 596*b^2 + 417*b^3 + 73*b^4 + 2*b^5) + 4*(768 - 768*b - 300*b^2 + 918*b^3 + 510*b^4 + 60*b^5)*Sqrt[x] + 4*(576*b - 600*b^2 + 333*b^3 + 948*b^4 + 327*b^5 + 18*b^6)*x + 4*(512*b + 328*b^2 - 318*b^3 + 560*b^4 + 580*b^5 + 120*b^6)*x^(3/2) + 4*(516*b^2 + 123*b^3 - 24*b^4 + 384*b^5 + 216*b^6 + 24*b^7)*x^2 + 4*(-540*b^2 - 30*b^3 + 48*b^5 + 144*b^6 + 48*b^7)*x^(5/2) + 4*(-873*b^3 - 256*b^4 - 8*b^5 + 18*b^6 + 28*b^7 + 8*b^8)*x^3 + 4*(-570*b^3 - 912*b^4 - 168*b^5)*x^(7/2) + 4*(-741*b^4 - 546*b^5 - 42*b^6)*x^4 + 4*(-158*b^4 - 508*b^5 - 192*b^6)*x^(9/2) + 4*(-159*b^5 - 204*b^6 - 36*b^7)*x^5 + 4*(-12*b^5 - 72*b^6 - 48*b^7)*x^(11/2) + 4*(-6*b^6 - 16*b^7 - 8*b^8)*x^6))/(3*b^2*(2048 + 1536*b + 288*b^2 + 8*b^3) + 3*b^2*(8*b^3 + 72*b^4 + 96*b^5 + 32*b^6)*x^3 + 3*b^2*Sqrt[2 + b]*(-1024 - 512*b - 48*b^2)*Sqrt[2 + b*x] + x*(3*b^2*(1536*b + 3264*b^2 + 1272*b^3 + 72*b^4) + 3*b^2*Sqrt[2 + b]*(-512*b - 1312*b^2 - 288*b^3)*Sqrt[2 + b*x]) + Sqrt[x]*(3*b^2*(3072*b + 1920*b^2 + 240*b^3) + 3*b^2*Sqrt[2 + b]*(-1536*b - 576*b^2 - 24*b^3)*Sqrt[2 + b*x]) + x^2*(3*b^2*(288*b^2 + 1272*b^3 + 816*b^4 + 96*b^5) + 3*b^2*Sqrt[2 + b]*(-48*b^2 - 288*b^3 - 192*b^4)*Sqrt[2 + b*x]) + x^(3/2)*(3*b^2*(1920*b^2 + 2080*b^3 + 480*b^4) + 3*b^2*Sqrt[2 + b]*(-576*b^2 - 656*b^3 - 64*b^4)*Sqrt[2 + b*x]) + x^(5/2)*(3*b^2*(240*b^3 + 480*b^4 + 192*b^5) + 3*b^2*Sqrt[2 + b]*(-24*b^3 - 64*b^4 - 32*b^5)*Sqrt[2 + b*x])) - (2*ArcTanh[(Sqrt[2 + b]/Sqrt[b] - Sqrt[2 + b*x]/Sqrt[b])/(-1 + Sqrt[x])])/b^(5/2)","B",1
507,1,416,64,0.5813948,"\int \sqrt{x} \sqrt{2+b x} \, dx","IntegrateAlgebraic[Sqrt[x]*Sqrt[2 + b*x],x]","\frac{2 \tanh ^{-1}\left(\frac{\frac{\sqrt{b+2}}{\sqrt{b}}-\frac{\sqrt{b x+2}}{\sqrt{b}}}{\sqrt{x}-1}\right)}{b^{3/2}}+\frac{\left(\frac{2}{b}-\frac{2 \sqrt{x}}{b}\right) \left(\sqrt{b+2}-\sqrt{b x+2}\right) \left(b (-x)+b \sqrt{x}+\sqrt{b+2} \sqrt{b x+2}-b-2\right) \left(-2 b^4 x^2-4 b^3 x^{3/2}+2 \sqrt{b+2} b^3 x^{3/2} \sqrt{b x+2}-4 b^3 x^2-4 b^3 x-6 b^2 x^{3/2}+2 \sqrt{b+2} b^2 x^{3/2} \sqrt{b x+2}-b^2 x^2-11 b^2 x-6 b^2 \sqrt{x}+4 \sqrt{b+2} b^2 x \sqrt{b x+2}+2 \sqrt{b+2} b^2 \sqrt{x} \sqrt{b x+2}-b^2-5 b x-10 b \sqrt{x}+2 \sqrt{b+2} b x \sqrt{b x+2}+2 \sqrt{b+2} b \sqrt{b x+2}+5 \sqrt{b+2} b \sqrt{x} \sqrt{b x+2}+2 \sqrt{b+2} \sqrt{b x+2}-5 b-4\right)}{\left(b \left(-\sqrt{x}\right)+\sqrt{b+2} \sqrt{b x+2}-2\right)^4}","-\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,"((2/b - (2*Sqrt[x])/b)*(Sqrt[2 + b] - Sqrt[2 + b*x])*(-2 - b + b*Sqrt[x] - b*x + Sqrt[2 + b]*Sqrt[2 + b*x])*(-4 - 5*b - b^2 - 10*b*Sqrt[x] - 6*b^2*Sqrt[x] - 5*b*x - 11*b^2*x - 4*b^3*x - 6*b^2*x^(3/2) - 4*b^3*x^(3/2) - b^2*x^2 - 4*b^3*x^2 - 2*b^4*x^2 + 2*Sqrt[2 + b]*Sqrt[2 + b*x] + 2*b*Sqrt[2 + b]*Sqrt[2 + b*x] + 5*b*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] + 2*b^2*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] + 2*b*Sqrt[2 + b]*x*Sqrt[2 + b*x] + 4*b^2*Sqrt[2 + b]*x*Sqrt[2 + b*x] + 2*b^2*Sqrt[2 + b]*x^(3/2)*Sqrt[2 + b*x] + 2*b^3*Sqrt[2 + b]*x^(3/2)*Sqrt[2 + b*x]))/(-2 - b*Sqrt[x] + Sqrt[2 + b]*Sqrt[2 + b*x])^4 + (2*ArcTanh[(Sqrt[2 + b]/Sqrt[b] - Sqrt[2 + b*x]/Sqrt[b])/(-1 + Sqrt[x])])/b^(3/2)","B",1
508,1,167,40,0.2270962,"\int \frac{\sqrt{2+b x}}{\sqrt{x}} \, dx","IntegrateAlgebraic[Sqrt[2 + b*x]/Sqrt[x],x]","\frac{\left(2-2 \sqrt{x}\right) \left(\sqrt{b+2}-\sqrt{b x+2}\right) \left(b^2 x+b x+b \sqrt{x}-\sqrt{b+2} b \sqrt{x} \sqrt{b x+2}-\sqrt{b+2} \sqrt{b x+2}+b+2\right)}{\left(b \left(-\sqrt{x}\right)+\sqrt{b+2} \sqrt{b x+2}-2\right)^2}-\frac{4 \tanh ^{-1}\left(\frac{\frac{\sqrt{b+2}}{\sqrt{b}}-\frac{\sqrt{b x+2}}{\sqrt{b}}}{\sqrt{x}-1}\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,"((2 - 2*Sqrt[x])*(Sqrt[2 + b] - Sqrt[2 + b*x])*(2 + b + b*Sqrt[x] + b*x + b^2*x - Sqrt[2 + b]*Sqrt[2 + b*x] - b*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x]))/(-2 - b*Sqrt[x] + Sqrt[2 + b]*Sqrt[2 + b*x])^2 - (4*ArcTanh[(Sqrt[2 + b]/Sqrt[b] - Sqrt[2 + b*x]/Sqrt[b])/(-1 + Sqrt[x])])/Sqrt[b]","B",1
509,1,247,41,0.295142,"\int \frac{\sqrt{2+b x}}{x^{3/2}} \, dx","IntegrateAlgebraic[Sqrt[2 + b*x]/x^(3/2),x]","\frac{\left(2 \sqrt{x}-2\right) \left(\sqrt{b+2}-\sqrt{b x+2}\right) \left(b x-2 b \sqrt{x}-2 \sqrt{b+2} \sqrt{b x+2}+\sqrt{b+2} \sqrt{x} \sqrt{b x+2}+2 b-2 \sqrt{x}+4\right)}{\sqrt{x} \left(b^2 \left(-\sqrt{x}\right)+b x^{3/2}-2 b x+b \sqrt{x}+\sqrt{b+2} b \sqrt{b x+2}+4 \sqrt{b+2} \sqrt{b x+2}-2 \sqrt{b+2} \sqrt{x} \sqrt{b x+2}-4 b+4 \sqrt{x}-8\right)}-4 \sqrt{b} \tanh ^{-1}\left(\frac{\frac{\sqrt{b+2}}{\sqrt{b}}-\frac{\sqrt{b x+2}}{\sqrt{b}}}{\sqrt{x}-1}\right)","2 \sqrt{b} \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)-\frac{2 \sqrt{b x+2}}{\sqrt{x}}",1,"((-2 + 2*Sqrt[x])*(Sqrt[2 + b] - Sqrt[2 + b*x])*(4 + 2*b - 2*Sqrt[x] - 2*b*Sqrt[x] + b*x - 2*Sqrt[2 + b]*Sqrt[2 + b*x] + Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x]))/(Sqrt[x]*(-8 - 4*b + 4*Sqrt[x] + b*Sqrt[x] - b^2*Sqrt[x] - 2*b*x + b*x^(3/2) + 4*Sqrt[2 + b]*Sqrt[2 + b*x] + b*Sqrt[2 + b]*Sqrt[2 + b*x] - 2*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x])) - 4*Sqrt[b]*ArcTanh[(Sqrt[2 + b]/Sqrt[b] - Sqrt[2 + b*x]/Sqrt[b])/(-1 + Sqrt[x])]","B",1
510,1,1964,18,6.3784566,"\int \frac{\sqrt{2+b x}}{x^{5/2}} \, dx","IntegrateAlgebraic[Sqrt[2 + b*x]/x^(5/2),x]","\frac{\left(\frac{1}{384}-\frac{\sqrt{x}}{384}\right) \left(\sqrt{b+2}-\sqrt{b x+2}\right)^{12} \left(\frac{3 b^6 \left(\sqrt{x}-1\right)^{10}}{\left(\sqrt{b+2}-\sqrt{b x+2}\right)^{10}}+\frac{3 b^5 \left(-3 x b-2 \sqrt{x} b-b+2 x-8 \sqrt{x}+4 \sqrt{b+2} \sqrt{b x+2}+2 \sqrt{b+2} \sqrt{x} \sqrt{b x+2}-6\right) \left(\sqrt{x}-1\right)^8}{\left(\sqrt{b+2}-\sqrt{b x+2}\right)^{10}}+\frac{6 b^4 \left(4 b \sqrt{b+2} x^{3/2}-4 \sqrt{b+2} x^{3/2}-b \sqrt{b+2} x+9 \sqrt{b+2} x-b \sqrt{b x+2} x+3 \sqrt{b x+2} x+4 b \sqrt{b+2} \sqrt{x}+10 \sqrt{b+2} \sqrt{x}-8 b \sqrt{b x+2} \sqrt{x}-22 \sqrt{b x+2} \sqrt{x}-3 b \sqrt{b+2}-7 \sqrt{b+2}+5 b \sqrt{b x+2}+11 \sqrt{b x+2}\right) \left(\sqrt{x}-1\right)^6}{\left(\sqrt{b+2}-\sqrt{b x+2}\right)^9}-\frac{256 \sqrt{b+2} \left(\sqrt{x}-1\right)^5}{\left(\sqrt{b+2}-\sqrt{b x+2}\right)^5}+\frac{2 b^3 \left(3 x^2 b^2-54 x^{3/2} b^2+72 x b^2-18 \sqrt{x} b^2+21 b^2+6 x^2 b-72 x^{3/2} b+24 x b-48 \sqrt{x} b+18 \sqrt{b+2} x^{3/2} \sqrt{b x+2} b-30 \sqrt{b+2} x \sqrt{b x+2} b-66 \sqrt{b+2} \sqrt{b x+2} b+54 \sqrt{b+2} \sqrt{x} \sqrt{b x+2} b+186 b+8 x^2+64 x^{3/2}-216 x-80 \sqrt{x}-48 \sqrt{b+2} x^{3/2} \sqrt{b x+2}+132 \sqrt{b+2} x \sqrt{b x+2}-156 \sqrt{b+2} \sqrt{b x+2}+24 \sqrt{b+2} \sqrt{x} \sqrt{b x+2}+320\right) \left(\sqrt{x}-1\right)^4}{\left(\sqrt{b+2}-\sqrt{b x+2}\right)^8}+\frac{96 \sqrt{b+2} \left(\sqrt{x}-1\right)^3}{\left(\sqrt{b+2}-\sqrt{b x+2}\right)^3}+\frac{3 b^2 \left(8 b^2 \sqrt{b+2} x^{5/2}-48 b \sqrt{b+2} x^{5/2}+32 \sqrt{b+2} x^{5/2}-23 b^2 \sqrt{b+2} x^2+156 b \sqrt{b+2} x^2-144 \sqrt{b+2} x^2+3 b^2 \sqrt{b x+2} x^2-4 b \sqrt{b x+2} x^2-16 \sqrt{b x+2} x^2+48 b^2 \sqrt{b+2} x^{3/2}-88 b \sqrt{b+2} x^{3/2}+64 \sqrt{b+2} x^{3/2}-32 b^2 \sqrt{b x+2} x^{3/2}+40 b \sqrt{b x+2} x^{3/2}+256 \sqrt{b x+2} x^{3/2}-78 b^2 \sqrt{b+2} x-40 b \sqrt{b+2} x+384 \sqrt{b+2} x+62 b^2 \sqrt{b x+2} x-168 b \sqrt{b x+2} x-704 \sqrt{b x+2} x+8 b^2 \sqrt{b+2} \sqrt{x}-24 b \sqrt{b+2} \sqrt{x}-288 \sqrt{b+2} \sqrt{x}-32 b^2 \sqrt{b x+2} \sqrt{x}+120 b \sqrt{b x+2} \sqrt{x}+448 \sqrt{b x+2} \sqrt{x}-11 b^2 \sqrt{b+2}-148 b \sqrt{b+2}-240 \sqrt{b+2}+47 b^2 \sqrt{b x+2}+204 b \sqrt{b x+2}+208 \sqrt{b x+2}\right) \left(\sqrt{x}-1\right)^2}{\left(\sqrt{b+2}-\sqrt{b x+2}\right)^7}+\frac{16 \left(\sqrt{x}-1\right)^2}{\left(\sqrt{b+2}-\sqrt{b x+2}\right)^2}-\frac{24 \sqrt{b+2} \left(\sqrt{x}-1\right)}{\sqrt{b+2}-\sqrt{b x+2}}-\frac{b \left(6 b^2 \sqrt{b+2} x^{5/2}-96 b \sqrt{b+2} x^{5/2}+320 \sqrt{b+2} x^{5/2}-21 b^2 \sqrt{b+2} x^2+342 b \sqrt{b+2} x^2-1648 \sqrt{b+2} x^2+3 b^2 \sqrt{b x+2} x^2-18 b \sqrt{b x+2} x^2+48 \sqrt{b x+2} x^2+36 b^2 \sqrt{b+2} x^{3/2}-396 b \sqrt{b+2} x^{3/2}+3008 \sqrt{b+2} x^{3/2}-24 b^2 \sqrt{b x+2} x^{3/2}+180 b \sqrt{b x+2} x^{3/2}+192 \sqrt{b x+2} x^{3/2}-66 b^2 \sqrt{b+2} x+240 b \sqrt{b+2} x-2192 \sqrt{b+2} x+54 b^2 \sqrt{b x+2} x-528 b \sqrt{b x+2} x-1008 \sqrt{b x+2} x+6 b^2 \sqrt{b+2} \sqrt{x}-228 b \sqrt{b+2} \sqrt{x}+544 \sqrt{b+2} \sqrt{x}-24 b^2 \sqrt{b x+2} \sqrt{x}+540 b \sqrt{b x+2} \sqrt{x}+1056 \sqrt{b x+2} \sqrt{x}-9 b^2 \sqrt{b+2}-54 b \sqrt{b+2}-224 \sqrt{b+2}+39 b^2 \sqrt{b x+2}+18 b \sqrt{b x+2}-96 \sqrt{b x+2}\right)}{\left(\sqrt{b+2}-\sqrt{b x+2}\right)^5}+6\right)}{\left(\sqrt{b x+2}-\sqrt{b+2}\right) \left(-x b^2+x^2 b-2 x^{3/2} b+x b-4 \sqrt{x} b+\sqrt{b+2} \sqrt{x} \sqrt{b x+2} b+4 x-8 \sqrt{x}-2 \sqrt{b+2} x \sqrt{b x+2}+4 \sqrt{b+2} \sqrt{x} \sqrt{b x+2}\right)^3}","-\frac{(b x+2)^{3/2}}{3 x^{3/2}}",1,"((1/384 - Sqrt[x]/384)*(Sqrt[2 + b] - Sqrt[2 + b*x])^12*(6 + (3*b^6*(-1 + Sqrt[x])^10)/(Sqrt[2 + b] - Sqrt[2 + b*x])^10 - (256*Sqrt[2 + b]*(-1 + Sqrt[x])^5)/(Sqrt[2 + b] - Sqrt[2 + b*x])^5 + (96*Sqrt[2 + b]*(-1 + Sqrt[x])^3)/(Sqrt[2 + b] - Sqrt[2 + b*x])^3 + (16*(-1 + Sqrt[x])^2)/(Sqrt[2 + b] - Sqrt[2 + b*x])^2 - (24*Sqrt[2 + b]*(-1 + Sqrt[x]))/(Sqrt[2 + b] - Sqrt[2 + b*x]) + (3*b^5*(-1 + Sqrt[x])^8*(-6 - b - 8*Sqrt[x] - 2*b*Sqrt[x] + 2*x - 3*b*x + 4*Sqrt[2 + b]*Sqrt[2 + b*x] + 2*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x]))/(Sqrt[2 + b] - Sqrt[2 + b*x])^10 + (6*b^4*(-1 + Sqrt[x])^6*(-7*Sqrt[2 + b] - 3*b*Sqrt[2 + b] + 10*Sqrt[2 + b]*Sqrt[x] + 4*b*Sqrt[2 + b]*Sqrt[x] + 9*Sqrt[2 + b]*x - b*Sqrt[2 + b]*x - 4*Sqrt[2 + b]*x^(3/2) + 4*b*Sqrt[2 + b]*x^(3/2) + 11*Sqrt[2 + b*x] + 5*b*Sqrt[2 + b*x] - 22*Sqrt[x]*Sqrt[2 + b*x] - 8*b*Sqrt[x]*Sqrt[2 + b*x] + 3*x*Sqrt[2 + b*x] - b*x*Sqrt[2 + b*x]))/(Sqrt[2 + b] - Sqrt[2 + b*x])^9 + (2*b^3*(-1 + Sqrt[x])^4*(320 + 186*b + 21*b^2 - 80*Sqrt[x] - 48*b*Sqrt[x] - 18*b^2*Sqrt[x] - 216*x + 24*b*x + 72*b^2*x + 64*x^(3/2) - 72*b*x^(3/2) - 54*b^2*x^(3/2) + 8*x^2 + 6*b*x^2 + 3*b^2*x^2 - 156*Sqrt[2 + b]*Sqrt[2 + b*x] - 66*b*Sqrt[2 + b]*Sqrt[2 + b*x] + 24*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] + 54*b*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] + 132*Sqrt[2 + b]*x*Sqrt[2 + b*x] - 30*b*Sqrt[2 + b]*x*Sqrt[2 + b*x] - 48*Sqrt[2 + b]*x^(3/2)*Sqrt[2 + b*x] + 18*b*Sqrt[2 + b]*x^(3/2)*Sqrt[2 + b*x]))/(Sqrt[2 + b] - Sqrt[2 + b*x])^8 - (b*(-224*Sqrt[2 + b] - 54*b*Sqrt[2 + b] - 9*b^2*Sqrt[2 + b] + 544*Sqrt[2 + b]*Sqrt[x] - 228*b*Sqrt[2 + b]*Sqrt[x] + 6*b^2*Sqrt[2 + b]*Sqrt[x] - 2192*Sqrt[2 + b]*x + 240*b*Sqrt[2 + b]*x - 66*b^2*Sqrt[2 + b]*x + 3008*Sqrt[2 + b]*x^(3/2) - 396*b*Sqrt[2 + b]*x^(3/2) + 36*b^2*Sqrt[2 + b]*x^(3/2) - 1648*Sqrt[2 + b]*x^2 + 342*b*Sqrt[2 + b]*x^2 - 21*b^2*Sqrt[2 + b]*x^2 + 320*Sqrt[2 + b]*x^(5/2) - 96*b*Sqrt[2 + b]*x^(5/2) + 6*b^2*Sqrt[2 + b]*x^(5/2) - 96*Sqrt[2 + b*x] + 18*b*Sqrt[2 + b*x] + 39*b^2*Sqrt[2 + b*x] + 1056*Sqrt[x]*Sqrt[2 + b*x] + 540*b*Sqrt[x]*Sqrt[2 + b*x] - 24*b^2*Sqrt[x]*Sqrt[2 + b*x] - 1008*x*Sqrt[2 + b*x] - 528*b*x*Sqrt[2 + b*x] + 54*b^2*x*Sqrt[2 + b*x] + 192*x^(3/2)*Sqrt[2 + b*x] + 180*b*x^(3/2)*Sqrt[2 + b*x] - 24*b^2*x^(3/2)*Sqrt[2 + b*x] + 48*x^2*Sqrt[2 + b*x] - 18*b*x^2*Sqrt[2 + b*x] + 3*b^2*x^2*Sqrt[2 + b*x]))/(Sqrt[2 + b] - Sqrt[2 + b*x])^5 + (3*b^2*(-1 + Sqrt[x])^2*(-240*Sqrt[2 + b] - 148*b*Sqrt[2 + b] - 11*b^2*Sqrt[2 + b] - 288*Sqrt[2 + b]*Sqrt[x] - 24*b*Sqrt[2 + b]*Sqrt[x] + 8*b^2*Sqrt[2 + b]*Sqrt[x] + 384*Sqrt[2 + b]*x - 40*b*Sqrt[2 + b]*x - 78*b^2*Sqrt[2 + b]*x + 64*Sqrt[2 + b]*x^(3/2) - 88*b*Sqrt[2 + b]*x^(3/2) + 48*b^2*Sqrt[2 + b]*x^(3/2) - 144*Sqrt[2 + b]*x^2 + 156*b*Sqrt[2 + b]*x^2 - 23*b^2*Sqrt[2 + b]*x^2 + 32*Sqrt[2 + b]*x^(5/2) - 48*b*Sqrt[2 + b]*x^(5/2) + 8*b^2*Sqrt[2 + b]*x^(5/2) + 208*Sqrt[2 + b*x] + 204*b*Sqrt[2 + b*x] + 47*b^2*Sqrt[2 + b*x] + 448*Sqrt[x]*Sqrt[2 + b*x] + 120*b*Sqrt[x]*Sqrt[2 + b*x] - 32*b^2*Sqrt[x]*Sqrt[2 + b*x] - 704*x*Sqrt[2 + b*x] - 168*b*x*Sqrt[2 + b*x] + 62*b^2*x*Sqrt[2 + b*x] + 256*x^(3/2)*Sqrt[2 + b*x] + 40*b*x^(3/2)*Sqrt[2 + b*x] - 32*b^2*x^(3/2)*Sqrt[2 + b*x] - 16*x^2*Sqrt[2 + b*x] - 4*b*x^2*Sqrt[2 + b*x] + 3*b^2*x^2*Sqrt[2 + b*x]))/(Sqrt[2 + b] - Sqrt[2 + b*x])^7))/((-Sqrt[2 + b] + Sqrt[2 + b*x])*(-8*Sqrt[x] - 4*b*Sqrt[x] + 4*x + b*x - b^2*x - 2*b*x^(3/2) + b*x^2 + 4*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] + b*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] - 2*Sqrt[2 + b]*x*Sqrt[2 + b*x])^3)","B",1
511,1,8209,38,51.3924536,"\int \frac{\sqrt{2+b x}}{x^{7/2}} \, dx","IntegrateAlgebraic[Sqrt[2 + b*x]/x^(7/2),x]","\text{Result too large to show}","\frac{b (b x+2)^{3/2}}{15 x^{3/2}}-\frac{(b x+2)^{3/2}}{5 x^{5/2}}",1,"Result too large to show","B",1
512,-1,0,59,180.0156976,"\int \frac{\sqrt{2+b x}}{x^{9/2}} \, dx","IntegrateAlgebraic[Sqrt[2 + b*x]/x^(9/2),x]","\text{\$Aborted}","-\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,"$Aborted","F",-1
513,1,2101,112,3.4875268,"\int x^{5/2} \sqrt{2-b x} \, dx","IntegrateAlgebraic[x^(5/2)*Sqrt[2 - b*x],x]","\text{Result too large to show}","\frac{5 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{4 b^{7/2}}-\frac{5 \sqrt{x} \sqrt{2-b x}}{8 b^3}-\frac{5 x^{3/2} \sqrt{2-b x}}{24 b^2}+\frac{1}{4} x^{7/2} \sqrt{2-b x}-\frac{x^{5/2} \sqrt{2-b x}}{12 b}",1,"(-2*(-30720 + 28160*b - 7616*b^2 + 14608*b^3 - 16776*b^4 + 6840*b^5 - 1072*b^6 + 48*b^7)*Sqrt[2 - b*x] - 2*(30720 + 30720*b - 39040*b^2 + 9152*b^3 - 28457*b^4 + 30036*b^5 - 10364*b^6 + 1208*b^7 - 24*b^8)*Sqrt[x]*Sqrt[2 - b*x] - 2*(-38400*b - 24960*b^2 + 30672*b^3 - 15696*b^4 + 38952*b^5 - 30000*b^6 + 7824*b^7 - 576*b^8)*x*Sqrt[2 - b*x] - 2*(-20480*b + 39680*b^2 + 14400*b^3 - 15780*b^4 + 19065*b^5 - 34120*b^6 + 19060*b^7 - 3520*b^8 + 120*b^9)*x^(3/2)*Sqrt[2 - b*x] - 2*(28480*b^2 - 29520*b^3 - 5760*b^4 + 7680*b^5 - 15920*b^6 + 19760*b^7 - 8000*b^8 + 960*b^9)*x^2*Sqrt[2 - b*x] - 2*(3456*b^2 - 21696*b^3 + 15570*b^4 + 1560*b^5 - 3906*b^6 + 8520*b^7 - 7584*b^8 + 2208*b^9 - 144*b^10)*x^(5/2)*Sqrt[2 - b*x] - 2*(-3472*b^3 + 10128*b^4 - 5760*b^5 - 384*b^6 + 1552*b^7 - 2752*b^8 + 1856*b^9 - 384*b^10)*x^3*Sqrt[2 - b*x] - 2*(-14144*b^3 + 15404*b^4 - 7110*b^5 + 1896*b^6 + 78*b^7 - 320*b^8 + 448*b^9 - 256*b^10 + 48*b^11)*x^(7/2)*Sqrt[2 - b*x] - 2*(28104*b^4 - 24696*b^5 + 6384*b^6 - 624*b^7)*x^4*Sqrt[2 - b*x] - 2*(13263*b^4 - 39588*b^5 + 23860*b^6 - 4024*b^7 + 136*b^8)*x^(9/2)*Sqrt[2 - b*x] - 2*(-23016*b^5 + 35504*b^6 - 14672*b^7 + 1472*b^8)*x^5*Sqrt[2 - b*x] - 2*(-3963*b^5 + 22248*b^6 - 21180*b^7 + 5856*b^8 - 264*b^9)*x^(11/2)*Sqrt[2 - b*x] - 2*(5488*b^6 - 13552*b^7 + 8512*b^8 - 1472*b^9)*x^6*Sqrt[2 - b*x] - 2*(386*b^6 - 3656*b^7 + 5360*b^8 - 2272*b^9 + 208*b^10)*x^(13/2)*Sqrt[2 - b*x] - 2*(-336*b^7 + 1344*b^8 - 1344*b^9 + 384*b^10)*x^7*Sqrt[2 - b*x] - 2*(-6*b^7 + 96*b^8 - 240*b^9 + 192*b^10 - 48*b^11)*x^(15/2)*Sqrt[2 - b*x] + Sqrt[2 - b]*(-2*(30720 - 20480*b + 3456*b^2 - 14144*b^3 + 13263*b^4 - 3963*b^5 + 386*b^6 - 6*b^7) - 2*(-30720 - 38400*b + 28480*b^2 - 3472*b^3 + 28104*b^4 - 23016*b^5 + 5488*b^6 - 336*b^7)*Sqrt[x] - 2*(30720*b + 39680*b^2 - 21696*b^3 + 15404*b^4 - 39588*b^5 + 22248*b^6 - 3656*b^7 + 96*b^8)*x - 2*(28160*b - 24960*b^2 - 29520*b^3 + 10128*b^4 - 24696*b^5 + 35504*b^6 - 13552*b^7 + 1344*b^8)*x^(3/2) - 2*(-39040*b^2 + 14400*b^3 + 15570*b^4 - 7110*b^5 + 23860*b^6 - 21180*b^7 + 5360*b^8 - 240*b^9)*x^2 - 2*(-7616*b^2 + 30672*b^3 - 5760*b^4 - 5760*b^5 + 6384*b^6 - 14672*b^7 + 8512*b^8 - 1344*b^9)*x^(5/2) - 2*(9152*b^3 - 15780*b^4 + 1560*b^5 + 1896*b^6 - 4024*b^7 + 5856*b^8 - 2272*b^9 + 192*b^10)*x^3 - 2*(14608*b^3 - 15696*b^4 + 7680*b^5 - 384*b^6 - 624*b^7 + 1472*b^8 - 1472*b^9 + 384*b^10)*x^(7/2) - 2*(-28457*b^4 + 19065*b^5 - 3906*b^6 + 78*b^7 + 136*b^8 - 264*b^9 + 208*b^10 - 48*b^11)*x^4 - 2*(-16776*b^4 + 38952*b^5 - 15920*b^6 + 1552*b^7)*x^(9/2) - 2*(30036*b^5 - 34120*b^6 + 8520*b^7 - 320*b^8)*x^5 - 2*(6840*b^5 - 30000*b^6 + 19760*b^7 - 2752*b^8)*x^(11/2) - 2*(-10364*b^6 + 19060*b^7 - 7584*b^8 + 448*b^9)*x^6 - 2*(-1072*b^6 + 7824*b^7 - 8000*b^8 + 1856*b^9)*x^(13/2) - 2*(1208*b^7 - 3520*b^8 + 2208*b^9 - 256*b^10)*x^7 - 2*(48*b^7 - 576*b^8 + 960*b^9 - 384*b^10)*x^(15/2) - 2*(-24*b^8 + 120*b^9 - 144*b^10 + 48*b^11)*x^8))/(3*b^3*(32768 - 32768*b + 10240*b^2 - 1024*b^3 + 16*b^4) + 3*b^3*(16*b^4 - 256*b^5 + 640*b^6 - 512*b^7 + 128*b^8)*x^4 + 3*Sqrt[2 - b]*b^3*(-16384 + 12288*b - 2560*b^2 + 128*b^3)*Sqrt[2 - b*x] + x*(3*b^3*(-32768*b + 94208*b^2 - 56320*b^3 + 9664*b^4 - 256*b^5) + 3*Sqrt[2 - b]*b^3*(12288*b - 39936*b^2 + 17280*b^3 - 1536*b^4)*Sqrt[2 - b*x]) + Sqrt[x]*(3*b^3*(-65536*b + 57344*b^2 - 14336*b^3 + 896*b^4) + 3*Sqrt[2 - b]*b^3*(32768*b - 20480*b^2 + 3072*b^3 - 64*b^4)*Sqrt[2 - b*x]) + x^(3/2)*(3*b^3*(57344*b^2 - 86016*b^3 + 34944*b^4 - 3584*b^5) + 3*Sqrt[2 - b]*b^3*(-20480*b^2 + 30720*b^3 - 8640*b^4 + 320*b^5)*Sqrt[2 - b*x]) + x^2*(3*b^3*(10240*b^2 - 56320*b^3 + 52320*b^4 - 14080*b^5 + 640*b^6) + 3*Sqrt[2 - b]*b^3*(-2560*b^2 + 17280*b^3 - 15360*b^4 + 2560*b^5)*Sqrt[2 - b*x]) + x^3*(3*b^3*(-1024*b^3 + 9664*b^4 - 14080*b^5 + 5888*b^6 - 512*b^7) + 3*Sqrt[2 - b]*b^3*(128*b^3 - 1536*b^4 + 2560*b^5 - 1024*b^6)*Sqrt[2 - b*x]) + x^(5/2)*(3*b^3*(-14336*b^3 + 34944*b^4 - 21504*b^5 + 3584*b^6) + 3*Sqrt[2 - b]*b^3*(3072*b^3 - 8640*b^4 + 4992*b^5 - 384*b^6)*Sqrt[2 - b*x]) + x^(7/2)*(3*b^3*(896*b^4 - 3584*b^5 + 3584*b^6 - 1024*b^7) + 3*Sqrt[2 - b]*b^3*(-64*b^4 + 320*b^5 - 384*b^6 + 128*b^7)*Sqrt[2 - b*x])) + (5*ArcTan[(Sqrt[2 - b]/Sqrt[b] - Sqrt[2 - b*x]/Sqrt[b])/(-1 + Sqrt[x])])/(2*b^(7/2))","B",1
514,1,1329,87,1.7936227,"\int x^{3/2} \sqrt{2-b x} \, dx","IntegrateAlgebraic[x^(3/2)*Sqrt[2 - b*x],x]","\frac{-4 \left(-8 b^8+24 b^7-18 b^6+2 b^5\right) \sqrt{2-b x} x^{11/2}-4 \left(48 b^7-120 b^6+60 b^5\right) \sqrt{2-b x} x^5-4 \left(28 b^7-216 b^6+327 b^5-73 b^4\right) \sqrt{2-b x} x^{9/2}-4 \left(-144 b^6+580 b^5-510 b^4\right) \sqrt{2-b x} x^4-4 \left(-18 b^6+384 b^5-948 b^4+417 b^3\right) \sqrt{2-b x} x^{7/2}-4 \left(48 b^5-560 b^4+918 b^3\right) \sqrt{2-b x} x^3-4 \left(8 b^8-36 b^7+42 b^6-8 b^5+24 b^4+333 b^3-596 b^2\right) \sqrt{2-b x} x^{5/2}-4 \left(-48 b^7+192 b^6-168 b^5-318 b^3+300 b^2\right) \sqrt{2-b x} x^2-4 \left(-16 b^7+204 b^6-546 b^5+256 b^4+123 b^3+600 b^2-320 b\right) \sqrt{2-b x} x^{3/2}-4 \left(72 b^6-508 b^5+912 b^4-30 b^3-328 b^2-768 b\right) \sqrt{2-b x} x-4 \left(6 b^6-159 b^5+741 b^4-873 b^3-516 b^2+576 b+768\right) \sqrt{2-b x} \sqrt{x}+\sqrt{2-b} \left(-4 \left(8 b^8-16 b^7+6 b^6\right) x^6-4 \left(-48 b^7+72 b^6-12 b^5\right) x^{11/2}-4 \left(-36 b^7+204 b^6-159 b^5\right) x^5-4 \left(192 b^6-508 b^5+158 b^4\right) x^{9/2}-4 \left(42 b^6-546 b^5+741 b^4\right) x^4-4 \left(-168 b^5+912 b^4-570 b^3\right) x^{7/2}-4 \left(-8 b^8+28 b^7-18 b^6-8 b^5+256 b^4-873 b^3\right) x^3-4 \left(48 b^7-144 b^6+48 b^5-30 b^3+540 b^2\right) x^{5/2}-4 \left(24 b^7-216 b^6+384 b^5+24 b^4+123 b^3-516 b^2\right) x^2-4 \left(-120 b^6+580 b^5-560 b^4-318 b^3-328 b^2+512 b\right) x^{3/2}-4 \left(-18 b^6+327 b^5-948 b^4+333 b^3+600 b^2+576 b\right) x-4 \left(60 b^5-510 b^4+918 b^3+300 b^2-768 b-768\right) \sqrt{x}-4 \left(2 b^5-73 b^4+417 b^3-596 b^2-320 b+768\right)\right)-4 \left(-12 b^5+158 b^4-570 b^3+540 b^2+512 b-768\right) \sqrt{2-b x}}{3 b^2 \left(32 b^6-96 b^5+72 b^4-8 b^3\right) x^3+\left(3 \left(-192 b^5+480 b^4-240 b^3\right) b^2+3 \sqrt{2-b} \left(32 b^5-64 b^4+24 b^3\right) \sqrt{2-b x} b^2\right) x^{5/2}+\left(3 \left(-96 b^5+816 b^4-1272 b^3+288 b^2\right) b^2+3 \sqrt{2-b} \left(-192 b^4+288 b^3-48 b^2\right) \sqrt{2-b x} b^2\right) x^2+\left(3 \left(480 b^4-2080 b^3+1920 b^2\right) b^2+3 \sqrt{2-b} \left(-64 b^4+656 b^3-576 b^2\right) \sqrt{2-b x} b^2\right) x^{3/2}+\left(3 \left(72 b^4-1272 b^3+3264 b^2-1536 b\right) b^2+3 \sqrt{2-b} \left(288 b^3-1312 b^2+512 b\right) \sqrt{2-b x} b^2\right) x+\left(3 \left(-240 b^3+1920 b^2-3072 b\right) b^2+3 \sqrt{2-b} \left(24 b^3-576 b^2+1536 b\right) \sqrt{2-b x} b^2\right) \sqrt{x}+3 b^2 \left(-8 b^3+288 b^2-1536 b+2048\right)+3 \sqrt{2-b} b^2 \left(-48 b^2+512 b-1024\right) \sqrt{2-b x}}+\frac{2 \tan ^{-1}\left(\frac{\frac{\sqrt{2-b}}{\sqrt{b}}-\frac{\sqrt{2-b x}}{\sqrt{b}}}{\sqrt{x}-1}\right)}{b^{5/2}}","\frac{\sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{5/2}}-\frac{\sqrt{x} \sqrt{2-b x}}{2 b^2}+\frac{1}{3} x^{5/2} \sqrt{2-b x}-\frac{x^{3/2} \sqrt{2-b x}}{6 b}",1,"(-4*(-768 + 512*b + 540*b^2 - 570*b^3 + 158*b^4 - 12*b^5)*Sqrt[2 - b*x] - 4*(768 + 576*b - 516*b^2 - 873*b^3 + 741*b^4 - 159*b^5 + 6*b^6)*Sqrt[x]*Sqrt[2 - b*x] - 4*(-768*b - 328*b^2 - 30*b^3 + 912*b^4 - 508*b^5 + 72*b^6)*x*Sqrt[2 - b*x] - 4*(-320*b + 600*b^2 + 123*b^3 + 256*b^4 - 546*b^5 + 204*b^6 - 16*b^7)*x^(3/2)*Sqrt[2 - b*x] - 4*(300*b^2 - 318*b^3 - 168*b^5 + 192*b^6 - 48*b^7)*x^2*Sqrt[2 - b*x] - 4*(-596*b^2 + 333*b^3 + 24*b^4 - 8*b^5 + 42*b^6 - 36*b^7 + 8*b^8)*x^(5/2)*Sqrt[2 - b*x] - 4*(918*b^3 - 560*b^4 + 48*b^5)*x^3*Sqrt[2 - b*x] - 4*(417*b^3 - 948*b^4 + 384*b^5 - 18*b^6)*x^(7/2)*Sqrt[2 - b*x] - 4*(-510*b^4 + 580*b^5 - 144*b^6)*x^4*Sqrt[2 - b*x] - 4*(-73*b^4 + 327*b^5 - 216*b^6 + 28*b^7)*x^(9/2)*Sqrt[2 - b*x] - 4*(60*b^5 - 120*b^6 + 48*b^7)*x^5*Sqrt[2 - b*x] - 4*(2*b^5 - 18*b^6 + 24*b^7 - 8*b^8)*x^(11/2)*Sqrt[2 - b*x] + Sqrt[2 - b]*(-4*(768 - 320*b - 596*b^2 + 417*b^3 - 73*b^4 + 2*b^5) - 4*(-768 - 768*b + 300*b^2 + 918*b^3 - 510*b^4 + 60*b^5)*Sqrt[x] - 4*(576*b + 600*b^2 + 333*b^3 - 948*b^4 + 327*b^5 - 18*b^6)*x - 4*(512*b - 328*b^2 - 318*b^3 - 560*b^4 + 580*b^5 - 120*b^6)*x^(3/2) - 4*(-516*b^2 + 123*b^3 + 24*b^4 + 384*b^5 - 216*b^6 + 24*b^7)*x^2 - 4*(540*b^2 - 30*b^3 + 48*b^5 - 144*b^6 + 48*b^7)*x^(5/2) - 4*(-873*b^3 + 256*b^4 - 8*b^5 - 18*b^6 + 28*b^7 - 8*b^8)*x^3 - 4*(-570*b^3 + 912*b^4 - 168*b^5)*x^(7/2) - 4*(741*b^4 - 546*b^5 + 42*b^6)*x^4 - 4*(158*b^4 - 508*b^5 + 192*b^6)*x^(9/2) - 4*(-159*b^5 + 204*b^6 - 36*b^7)*x^5 - 4*(-12*b^5 + 72*b^6 - 48*b^7)*x^(11/2) - 4*(6*b^6 - 16*b^7 + 8*b^8)*x^6))/(3*b^2*(2048 - 1536*b + 288*b^2 - 8*b^3) + 3*b^2*(-8*b^3 + 72*b^4 - 96*b^5 + 32*b^6)*x^3 + 3*Sqrt[2 - b]*b^2*(-1024 + 512*b - 48*b^2)*Sqrt[2 - b*x] + Sqrt[x]*(3*b^2*(-3072*b + 1920*b^2 - 240*b^3) + 3*Sqrt[2 - b]*b^2*(1536*b - 576*b^2 + 24*b^3)*Sqrt[2 - b*x]) + x*(3*b^2*(-1536*b + 3264*b^2 - 1272*b^3 + 72*b^4) + 3*Sqrt[2 - b]*b^2*(512*b - 1312*b^2 + 288*b^3)*Sqrt[2 - b*x]) + x^2*(3*b^2*(288*b^2 - 1272*b^3 + 816*b^4 - 96*b^5) + 3*Sqrt[2 - b]*b^2*(-48*b^2 + 288*b^3 - 192*b^4)*Sqrt[2 - b*x]) + x^(3/2)*(3*b^2*(1920*b^2 - 2080*b^3 + 480*b^4) + 3*Sqrt[2 - b]*b^2*(-576*b^2 + 656*b^3 - 64*b^4)*Sqrt[2 - b*x]) + x^(5/2)*(3*b^2*(-240*b^3 + 480*b^4 - 192*b^5) + 3*Sqrt[2 - b]*b^2*(24*b^3 - 64*b^4 + 32*b^5)*Sqrt[2 - b*x])) + (2*ArcTan[(Sqrt[2 - b]/Sqrt[b] - Sqrt[2 - b*x]/Sqrt[b])/(-1 + Sqrt[x])])/b^(5/2)","B",1
515,1,446,65,0.669255,"\int \sqrt{x} \sqrt{2-b x} \, dx","IntegrateAlgebraic[Sqrt[x]*Sqrt[2 - b*x],x]","\frac{2 \tan ^{-1}\left(\frac{\frac{\sqrt{2-b}}{\sqrt{b}}-\frac{\sqrt{2-b x}}{\sqrt{b}}}{\sqrt{x}-1}\right)}{b^{3/2}}+\frac{\left(\frac{2}{b}-\frac{2 \sqrt{x}}{b}\right) \left(\sqrt{2-b}-\sqrt{2-b x}\right) \left(b x-b \sqrt{x}+\sqrt{2-b} \sqrt{2-b x}+b-2\right) \left(2 b^4 x^2-4 b^3 x^{3/2}+2 \sqrt{2-b} b^3 x^{3/2} \sqrt{2-b x}-4 b^3 x^2-4 b^3 x+6 b^2 x^{3/2}-2 \sqrt{2-b} b^2 x^{3/2} \sqrt{2-b x}+b^2 x^2+11 b^2 x+6 b^2 \sqrt{x}-4 \sqrt{2-b} b^2 x \sqrt{2-b x}-2 \sqrt{2-b} b^2 \sqrt{x} \sqrt{2-b x}+b^2-5 b x-10 b \sqrt{x}+2 \sqrt{2-b} b x \sqrt{2-b x}+2 \sqrt{2-b} b \sqrt{2-b x}+5 \sqrt{2-b} b \sqrt{x} \sqrt{2-b x}-2 \sqrt{2-b} \sqrt{2-b x}-5 b+4\right)}{\left(b \sqrt{x}+\sqrt{2-b} \sqrt{2-b x}-2\right)^4}","\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,"((2/b - (2*Sqrt[x])/b)*(Sqrt[2 - b] - Sqrt[2 - b*x])*(-2 + b - b*Sqrt[x] + b*x + Sqrt[2 - b]*Sqrt[2 - b*x])*(4 - 5*b + b^2 - 10*b*Sqrt[x] + 6*b^2*Sqrt[x] - 5*b*x + 11*b^2*x - 4*b^3*x + 6*b^2*x^(3/2) - 4*b^3*x^(3/2) + b^2*x^2 - 4*b^3*x^2 + 2*b^4*x^2 - 2*Sqrt[2 - b]*Sqrt[2 - b*x] + 2*Sqrt[2 - b]*b*Sqrt[2 - b*x] + 5*Sqrt[2 - b]*b*Sqrt[x]*Sqrt[2 - b*x] - 2*Sqrt[2 - b]*b^2*Sqrt[x]*Sqrt[2 - b*x] + 2*Sqrt[2 - b]*b*x*Sqrt[2 - b*x] - 4*Sqrt[2 - b]*b^2*x*Sqrt[2 - b*x] - 2*Sqrt[2 - b]*b^2*x^(3/2)*Sqrt[2 - b*x] + 2*Sqrt[2 - b]*b^3*x^(3/2)*Sqrt[2 - b*x]))/(-2 + b*Sqrt[x] + Sqrt[2 - b]*Sqrt[2 - b*x])^4 + (2*ArcTan[(Sqrt[2 - b]/Sqrt[b] - Sqrt[2 - b*x]/Sqrt[b])/(-1 + Sqrt[x])])/b^(3/2)","B",1
516,1,184,41,0.2679378,"\int \frac{\sqrt{2-b x}}{\sqrt{x}} \, dx","IntegrateAlgebraic[Sqrt[2 - b*x]/Sqrt[x],x]","\frac{\left(2-2 \sqrt{x}\right) \left(\sqrt{2-b}-\sqrt{2-b x}\right) \left(b^2 x-b x-b \sqrt{x}+\sqrt{2-b} b \sqrt{x} \sqrt{2-b x}-\sqrt{2-b} \sqrt{2-b x}-b+2\right)}{\left(b \sqrt{x}+\sqrt{2-b} \sqrt{2-b x}-2\right)^2}+\frac{4 \tan ^{-1}\left(\frac{\frac{\sqrt{2-b}}{\sqrt{b}}-\frac{\sqrt{2-b x}}{\sqrt{b}}}{\sqrt{x}-1}\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,"((2 - 2*Sqrt[x])*(Sqrt[2 - b] - Sqrt[2 - b*x])*(2 - b - b*Sqrt[x] - b*x + b^2*x - Sqrt[2 - b]*Sqrt[2 - b*x] + Sqrt[2 - b]*b*Sqrt[x]*Sqrt[2 - b*x]))/(-2 + b*Sqrt[x] + Sqrt[2 - b]*Sqrt[2 - b*x])^2 + (4*ArcTan[(Sqrt[2 - b]/Sqrt[b] - Sqrt[2 - b*x]/Sqrt[b])/(-1 + Sqrt[x])])/Sqrt[b]","B",1
517,1,260,42,0.2964913,"\int \frac{\sqrt{2-b x}}{x^{3/2}} \, dx","IntegrateAlgebraic[Sqrt[2 - b*x]/x^(3/2),x]","\frac{-2 b x^{3/2} \sqrt{2-b x}+\sqrt{2-b} \left(8 b x^{3/2}-2 b x^2-2 (5 b-4) x-2 (12-4 b) \sqrt{x}-2 (2 b-8)\right)-2 (4-4 b) x \sqrt{2-b x}-2 (7 b-12) \sqrt{x} \sqrt{2-b x}-2 (8-4 b) \sqrt{2-b x}}{x \left(b^2+2 \sqrt{2-b} \sqrt{2-b x}+b-4\right)-2 b x^{3/2}+b x^2+\sqrt{x} \left(\sqrt{2-b} (b-4) \sqrt{2-b x}-4 b+8\right)}-4 \sqrt{b} \tan ^{-1}\left(\frac{\frac{\sqrt{2-b}}{\sqrt{b}}-\frac{\sqrt{2-b x}}{\sqrt{b}}}{\sqrt{x}-1}\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*(8 - 4*b)*Sqrt[2 - b*x] - 2*(-12 + 7*b)*Sqrt[x]*Sqrt[2 - b*x] - 2*(4 - 4*b)*x*Sqrt[2 - b*x] - 2*b*x^(3/2)*Sqrt[2 - b*x] + Sqrt[2 - b]*(-2*(-8 + 2*b) - 2*(12 - 4*b)*Sqrt[x] - 2*(-4 + 5*b)*x + 8*b*x^(3/2) - 2*b*x^2))/(-2*b*x^(3/2) + b*x^2 + x*(-4 + b + b^2 + 2*Sqrt[2 - b]*Sqrt[2 - b*x]) + Sqrt[x]*(8 - 4*b + Sqrt[2 - b]*(-4 + b)*Sqrt[2 - b*x])) - 4*Sqrt[b]*ArcTan[(Sqrt[2 - b]/Sqrt[b] - Sqrt[2 - b*x]/Sqrt[b])/(-1 + Sqrt[x])]","B",1
518,1,2165,19,6.7273303,"\int \frac{\sqrt{2-b x}}{x^{5/2}} \, dx","IntegrateAlgebraic[Sqrt[2 - b*x]/x^(5/2),x]","\text{Result too large to show}","-\frac{(2-b x)^{3/2}}{3 x^{3/2}}",1,"((-1/384 + Sqrt[x]/384)*(Sqrt[2 - b] - Sqrt[2 - b*x])^12*(6 + (3*b^6*(-1 + Sqrt[x])^10)/(Sqrt[2 - b] - Sqrt[2 - b*x])^10 - (256*Sqrt[2 - b]*(-1 + Sqrt[x])^5)/(Sqrt[2 - b] - Sqrt[2 - b*x])^5 + (96*Sqrt[2 - b]*(-1 + Sqrt[x])^3)/(Sqrt[2 - b] - Sqrt[2 - b*x])^3 + (16*(-1 + Sqrt[x])^2)/(Sqrt[2 - b] - Sqrt[2 - b*x])^2 - (24*Sqrt[2 - b]*(-1 + Sqrt[x]))/(Sqrt[2 - b] - Sqrt[2 - b*x]) - (3*b^5*(-1 + Sqrt[x])^8*(-6 + b - 8*Sqrt[x] + 2*b*Sqrt[x] + 2*x + 3*b*x + 4*Sqrt[2 - b]*Sqrt[2 - b*x] + 2*Sqrt[2 - b]*Sqrt[x]*Sqrt[2 - b*x]))/(Sqrt[2 - b] - Sqrt[2 - b*x])^10 - (6*b^4*(-1 + Sqrt[x])^6*(7*Sqrt[2 - b] - 3*Sqrt[2 - b]*b - 10*Sqrt[2 - b]*Sqrt[x] + 4*Sqrt[2 - b]*b*Sqrt[x] - 9*Sqrt[2 - b]*x - Sqrt[2 - b]*b*x + 4*Sqrt[2 - b]*x^(3/2) + 4*Sqrt[2 - b]*b*x^(3/2) - 11*Sqrt[2 - b*x] + 5*b*Sqrt[2 - b*x] + 22*Sqrt[x]*Sqrt[2 - b*x] - 8*b*Sqrt[x]*Sqrt[2 - b*x] - 3*x*Sqrt[2 - b*x] - b*x*Sqrt[2 - b*x]))/(Sqrt[2 - b] - Sqrt[2 - b*x])^9 + (2*b^3*(-1 + Sqrt[x])^4*(-320 + 186*b - 21*b^2 + 80*Sqrt[x] - 48*b*Sqrt[x] + 18*b^2*Sqrt[x] + 216*x + 24*b*x - 72*b^2*x - 64*x^(3/2) - 72*b*x^(3/2) + 54*b^2*x^(3/2) - 8*x^2 + 6*b*x^2 - 3*b^2*x^2 + 156*Sqrt[2 - b]*Sqrt[2 - b*x] - 66*Sqrt[2 - b]*b*Sqrt[2 - b*x] - 24*Sqrt[2 - b]*Sqrt[x]*Sqrt[2 - b*x] + 54*Sqrt[2 - b]*b*Sqrt[x]*Sqrt[2 - b*x] - 132*Sqrt[2 - b]*x*Sqrt[2 - b*x] - 30*Sqrt[2 - b]*b*x*Sqrt[2 - b*x] + 48*Sqrt[2 - b]*x^(3/2)*Sqrt[2 - b*x] + 18*Sqrt[2 - b]*b*x^(3/2)*Sqrt[2 - b*x]))/(Sqrt[2 - b] - Sqrt[2 - b*x])^8 + (3*b^2*(-1 + Sqrt[x])^2*(-240*Sqrt[2 - b] + 148*Sqrt[2 - b]*b - 11*Sqrt[2 - b]*b^2 - 288*Sqrt[2 - b]*Sqrt[x] + 24*Sqrt[2 - b]*b*Sqrt[x] + 8*Sqrt[2 - b]*b^2*Sqrt[x] + 384*Sqrt[2 - b]*x + 40*Sqrt[2 - b]*b*x - 78*Sqrt[2 - b]*b^2*x + 64*Sqrt[2 - b]*x^(3/2) + 88*Sqrt[2 - b]*b*x^(3/2) + 48*Sqrt[2 - b]*b^2*x^(3/2) - 144*Sqrt[2 - b]*x^2 - 156*Sqrt[2 - b]*b*x^2 - 23*Sqrt[2 - b]*b^2*x^2 + 32*Sqrt[2 - b]*x^(5/2) + 48*Sqrt[2 - b]*b*x^(5/2) + 8*Sqrt[2 - b]*b^2*x^(5/2) + 208*Sqrt[2 - b*x] - 204*b*Sqrt[2 - b*x] + 47*b^2*Sqrt[2 - b*x] + 448*Sqrt[x]*Sqrt[2 - b*x] - 120*b*Sqrt[x]*Sqrt[2 - b*x] - 32*b^2*Sqrt[x]*Sqrt[2 - b*x] - 704*x*Sqrt[2 - b*x] + 168*b*x*Sqrt[2 - b*x] + 62*b^2*x*Sqrt[2 - b*x] + 256*x^(3/2)*Sqrt[2 - b*x] - 40*b*x^(3/2)*Sqrt[2 - b*x] - 32*b^2*x^(3/2)*Sqrt[2 - b*x] - 16*x^2*Sqrt[2 - b*x] + 4*b*x^2*Sqrt[2 - b*x] + 3*b^2*x^2*Sqrt[2 - b*x]))/(Sqrt[2 - b] - Sqrt[2 - b*x])^7 + (b*(-224*Sqrt[2 - b] + 54*Sqrt[2 - b]*b - 9*Sqrt[2 - b]*b^2 + 544*Sqrt[2 - b]*Sqrt[x] + 228*Sqrt[2 - b]*b*Sqrt[x] + 6*Sqrt[2 - b]*b^2*Sqrt[x] - 2192*Sqrt[2 - b]*x - 240*Sqrt[2 - b]*b*x - 66*Sqrt[2 - b]*b^2*x + 3008*Sqrt[2 - b]*x^(3/2) + 396*Sqrt[2 - b]*b*x^(3/2) + 36*Sqrt[2 - b]*b^2*x^(3/2) - 1648*Sqrt[2 - b]*x^2 - 342*Sqrt[2 - b]*b*x^2 - 21*Sqrt[2 - b]*b^2*x^2 + 320*Sqrt[2 - b]*x^(5/2) + 96*Sqrt[2 - b]*b*x^(5/2) + 6*Sqrt[2 - b]*b^2*x^(5/2) - 96*Sqrt[2 - b*x] - 18*b*Sqrt[2 - b*x] + 39*b^2*Sqrt[2 - b*x] + 1056*Sqrt[x]*Sqrt[2 - b*x] - 540*b*Sqrt[x]*Sqrt[2 - b*x] - 24*b^2*Sqrt[x]*Sqrt[2 - b*x] - 1008*x*Sqrt[2 - b*x] + 528*b*x*Sqrt[2 - b*x] + 54*b^2*x*Sqrt[2 - b*x] + 192*x^(3/2)*Sqrt[2 - b*x] - 180*b*x^(3/2)*Sqrt[2 - b*x] - 24*b^2*x^(3/2)*Sqrt[2 - b*x] + 48*x^2*Sqrt[2 - b*x] + 18*b*x^2*Sqrt[2 - b*x] + 3*b^2*x^2*Sqrt[2 - b*x]))/(Sqrt[2 - b] - Sqrt[2 - b*x])^5))/((-Sqrt[2 - b] + Sqrt[2 - b*x])*(8*Sqrt[x] - 4*b*Sqrt[x] - 4*x + b*x + b^2*x - 2*b*x^(3/2) + b*x^2 - 4*Sqrt[2 - b]*Sqrt[x]*Sqrt[2 - b*x] + Sqrt[2 - b]*b*Sqrt[x]*Sqrt[2 - b*x] + 2*Sqrt[2 - b]*x*Sqrt[2 - b*x])^3)","B",1
519,1,9027,40,51.0550436,"\int \frac{\sqrt{2-b x}}{x^{7/2}} \, dx","IntegrateAlgebraic[Sqrt[2 - b*x]/x^(7/2),x]","\text{Result too large to show}","-\frac{b (2-b x)^{3/2}}{15 x^{3/2}}-\frac{(2-b x)^{3/2}}{5 x^{5/2}}",1,"Result too large to show","B",1
520,-1,0,62,180.0770305,"\int \frac{\sqrt{2-b x}}{x^{9/2}} \, dx","IntegrateAlgebraic[Sqrt[2 - b*x]/x^(9/2),x]","\text{\$Aborted}","-\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,"$Aborted","F",-1
521,1,4169,143,7.5543132,"\int x^{5/2} (a+b x)^{3/2} \, dx","IntegrateAlgebraic[x^(5/2)*(a + b*x)^(3/2),x]","\text{Result too large to show}","-\frac{3 a^5 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{128 b^{7/2}}+\frac{3 a^4 \sqrt{x} \sqrt{a+b x}}{128 b^3}-\frac{a^3 x^{3/2} \sqrt{a+b x}}{64 b^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,"((-7680*a^14 - 17920*a^13*b - 14176*a^12*b^2 - 97920*a^11*b^3 - 343670*a^10*b^4 - 500210*a^9*b^5 - 364780*a^8*b^6 - 136496*a^7*b^7 - 23520*a^6*b^8 - 1280*a^5*b^9)*Sqrt[a + b*x] + (7680*a^14 - 19200*a^13*b - 63200*a^12*b^2 - 47280*a^11*b^3 - 479330*a^10*b^4 - 1599895*a^9*b^5 - 2130450*a^8*b^6 - 1376620*a^7*b^7 - 430640*a^6*b^8 - 54240*a^5*b^9 - 1280*a^4*b^10)*Sqrt[x]*Sqrt[a + b*x] + (23040*a^13*b - 40640*a^12*b^2 - 130752*a^11*b^3 - 268280*a^10*b^4 - 1811170*a^9*b^5 - 4521120*a^8*b^6 - 4978720*a^7*b^7 - 2665472*a^6*b^8 - 648960*a^5*b^9 - 51200*a^4*b^10)*x*Sqrt[a + b*x] + (14080*a^13*b + 59200*a^12*b^2 - 63600*a^11*b^3 - 184840*a^10*b^4 - 906025*a^9*b^5 - 4473620*a^8*b^6 - 8592240*a^7*b^7 - 7671040*a^6*b^8 - 3278720*a^5*b^9 - 576000*a^4*b^10 - 20480*a^3*b^11)*x^(3/2)*Sqrt[a + b*x] + (50720*a^12*b^2 + 113280*a^11*b^3 - 72756*a^10*b^4 - 309780*a^9*b^5 - 2178060*a^8*b^6 - 7710240*a^7*b^7 - 11577600*a^6*b^8 - 8288256*a^5*b^9 - 2726400*a^4*b^10 - 307200*a^3*b^11)*x^2*Sqrt[a + b*x] + (8096*a^12*b^2 + 105840*a^11*b^3 + 160260*a^10*b^4 - 60630*a^9*b^5 - 575670*a^8*b^6 - 3608388*a^7*b^7 - 9494400*a^6*b^8 - 11293440*a^5*b^9 - 6408960*a^4*b^10 - 1543680*a^3*b^11 - 86016*a^2*b^12)*x^(5/2)*Sqrt[a + b*x] + (25280*a^11*b^3 + 147880*a^10*b^4 + 168060*a^9*b^5 - 65600*a^8*b^6 - 874000*a^7*b^7 - 4131840*a^6*b^8 - 8381440*a^5*b^9 - 7976960*a^4*b^10 - 3532800*a^3*b^11 - 573440*a^2*b^12)*x^3*Sqrt[a + b*x] + (95152*a^11*b^3 + 272920*a^10*b^4 + 347550*a^9*b^5 + 203240*a^8*b^6 - 79240*a^7*b^7 - 901376*a^6*b^8 - 3217920*a^5*b^9 - 5201920*a^4*b^10 - 3998720*a^3*b^11 - 1351680*a^2*b^12 - 131072*a*b^13)*x^(7/2)*Sqrt[a + b*x] + (471290*a^10*b^4 + 1087750*a^9*b^5 + 883260*a^8*b^6 + 290800*a^7*b^7 - 64000*a^6*b^8 - 568320*a^5*b^9 - 1600000*a^4*b^10 - 2140160*a^3*b^11 - 1351680*a^2*b^12 - 327680*a*b^13)*x^4*Sqrt[a + b*x] + (296526*a^10*b^4 + 1855325*a^9*b^5 + 2888450*a^8*b^6 + 1658620*a^7*b^7 + 334080*a^6*b^8 - 23808*a^5*b^9 - 174080*a^4*b^10 - 412160*a^3*b^11 - 491520*a^2*b^12 - 286720*a*b^13 - 65536*b^14)*x^(9/2)*Sqrt[a + b*x] + (1365350*a^9*b^5 + 4740000*a^8*b^6 + 5224416*a^7*b^7 + 2104320*a^6*b^8 + 238080*a^5*b^9)*x^5*Sqrt[a + b*x] + (363675*a^9*b^5 + 3873900*a^8*b^6 + 8496720*a^7*b^7 + 6647040*a^6*b^8 + 1770240*a^5*b^9 + 80640*a^4*b^10)*x^(11/2)*Sqrt[a + b*x] + (1506300*a^8*b^6 + 7419360*a^7*b^7 + 11012352*a^6*b^8 + 6005760*a^5*b^9 + 934400*a^4*b^10)*x^6*Sqrt[a + b*x] + (214150*a^8*b^6 + 3441140*a^7*b^7 + 10119040*a^6*b^8 + 10443520*a^5*b^9 + 3795200*a^4*b^10 + 253440*a^3*b^11)*x^(13/2)*Sqrt[a + b*x] + (764880*a^7*b^7 + 5176320*a^6*b^8 + 10054656*a^5*b^9 + 7219200*a^4*b^10 + 1587200*a^3*b^11)*x^7*Sqrt[a + b*x] + (60008*a^7*b^7 + 1390720*a^6*b^8 + 5434880*a^5*b^9 + 7308800*a^4*b^10 + 3558400*a^3*b^11 + 372736*a^2*b^12)*x^(15/2)*Sqrt[a + b*x] + (169440*a^6*b^8 + 1578240*a^5*b^9 + 4047360*a^4*b^10 + 3840000*a^3*b^11 + 1187840*a^2*b^12)*x^8*Sqrt[a + b*x] + (6576*a^6*b^8 + 219360*a^5*b^9 + 1171200*a^4*b^10 + 2112000*a^3*b^11 + 1413120*a^2*b^12 + 253952*a*b^13)*x^(17/2)*Sqrt[a + b*x] + (11520*a^5*b^9 + 153600*a^4*b^10 + 552960*a^3*b^11 + 737280*a^2*b^12 + 327680*a*b^13)*x^9*Sqrt[a + b*x] + (128*a^5*b^9 + 6400*a^4*b^10 + 51200*a^3*b^11 + 143360*a^2*b^12 + 163840*a*b^13 + 65536*b^14)*x^(19/2)*Sqrt[a + b*x] + Sqrt[a + b]*(7680*a^14 + 14080*a^13*b + 8096*a^12*b^2 + 95152*a^11*b^3 + 296526*a^10*b^4 + 363675*a^9*b^5 + 214150*a^8*b^6 + 60008*a^7*b^7 + 6576*a^6*b^8 + 128*a^5*b^9 + (-7680*a^14 + 23040*a^13*b + 50720*a^12*b^2 + 25280*a^11*b^3 + 471290*a^10*b^4 + 1365350*a^9*b^5 + 1506300*a^8*b^6 + 764880*a^7*b^7 + 169440*a^6*b^8 + 11520*a^5*b^9)*Sqrt[x] + (-19200*a^13*b + 59200*a^12*b^2 + 105840*a^11*b^3 + 272920*a^10*b^4 + 1855325*a^9*b^5 + 3873900*a^8*b^6 + 3441140*a^7*b^7 + 1390720*a^6*b^8 + 219360*a^5*b^9 + 6400*a^4*b^10)*x + (-17920*a^13*b - 40640*a^12*b^2 + 113280*a^11*b^3 + 147880*a^10*b^4 + 1087750*a^9*b^5 + 4740000*a^8*b^6 + 7419360*a^7*b^7 + 5176320*a^6*b^8 + 1578240*a^5*b^9 + 153600*a^4*b^10)*x^(3/2) + (-63200*a^12*b^2 - 63600*a^11*b^3 + 160260*a^10*b^4 + 347550*a^9*b^5 + 2888450*a^8*b^6 + 8496720*a^7*b^7 + 10119040*a^6*b^8 + 5434880*a^5*b^9 + 1171200*a^4*b^10 + 51200*a^3*b^11)*x^2 + (-14176*a^12*b^2 - 130752*a^11*b^3 - 72756*a^10*b^4 + 168060*a^9*b^5 + 883260*a^8*b^6 + 5224416*a^7*b^7 + 11012352*a^6*b^8 + 10054656*a^5*b^9 + 4047360*a^4*b^10 + 552960*a^3*b^11)*x^(5/2) + (-47280*a^11*b^3 - 184840*a^10*b^4 - 60630*a^9*b^5 + 203240*a^8*b^6 + 1658620*a^7*b^7 + 6647040*a^6*b^8 + 10443520*a^5*b^9 + 7308800*a^4*b^10 + 2112000*a^3*b^11 + 143360*a^2*b^12)*x^3 + (-97920*a^11*b^3 - 268280*a^10*b^4 - 309780*a^9*b^5 - 65600*a^8*b^6 + 290800*a^7*b^7 + 2104320*a^6*b^8 + 6005760*a^5*b^9 + 7219200*a^4*b^10 + 3840000*a^3*b^11 + 737280*a^2*b^12)*x^(7/2) + (-479330*a^10*b^4 - 906025*a^9*b^5 - 575670*a^8*b^6 - 79240*a^7*b^7 + 334080*a^6*b^8 + 1770240*a^5*b^9 + 3795200*a^4*b^10 + 3558400*a^3*b^11 + 1413120*a^2*b^12 + 163840*a*b^13)*x^4 + (-343670*a^10*b^4 - 1811170*a^9*b^5 - 2178060*a^8*b^6 - 874000*a^7*b^7 - 64000*a^6*b^8 + 238080*a^5*b^9 + 934400*a^4*b^10 + 1587200*a^3*b^11 + 1187840*a^2*b^12 + 327680*a*b^13)*x^(9/2) + (-1599895*a^9*b^5 - 4473620*a^8*b^6 - 3608388*a^7*b^7 - 901376*a^6*b^8 - 23808*a^5*b^9 + 80640*a^4*b^10 + 253440*a^3*b^11 + 372736*a^2*b^12 + 253952*a*b^13 + 65536*b^14)*x^5 + (-500210*a^9*b^5 - 4521120*a^8*b^6 - 7710240*a^7*b^7 - 4131840*a^6*b^8 - 568320*a^5*b^9)*x^(11/2) + (-2130450*a^8*b^6 - 8592240*a^7*b^7 - 9494400*a^6*b^8 - 3217920*a^5*b^9 - 174080*a^4*b^10)*x^6 + (-364780*a^8*b^6 - 4978720*a^7*b^7 - 11577600*a^6*b^8 - 8381440*a^5*b^9 - 1600000*a^4*b^10)*x^(13/2) + (-1376620*a^7*b^7 - 7671040*a^6*b^8 - 11293440*a^5*b^9 - 5201920*a^4*b^10 - 412160*a^3*b^11)*x^7 + (-136496*a^7*b^7 - 2665472*a^6*b^8 - 8288256*a^5*b^9 - 7976960*a^4*b^10 - 2140160*a^3*b^11)*x^(15/2) + (-430640*a^6*b^8 - 3278720*a^5*b^9 - 6408960*a^4*b^10 - 3998720*a^3*b^11 - 491520*a^2*b^12)*x^8 + (-23520*a^6*b^8 - 648960*a^5*b^9 - 2726400*a^4*b^10 - 3532800*a^3*b^11 - 1351680*a^2*b^12)*x^(17/2) + (-54240*a^5*b^9 - 576000*a^4*b^10 - 1543680*a^3*b^11 - 1351680*a^2*b^12 - 286720*a*b^13)*x^9 + (-1280*a^5*b^9 - 51200*a^4*b^10 - 307200*a^3*b^11 - 573440*a^2*b^12 - 327680*a*b^13)*x^(19/2) + (-1280*a^4*b^10 - 20480*a^3*b^11 - 86016*a^2*b^12 - 131072*a*b^13 - 65536*b^14)*x^10))/(640*b^3*(512*a^10 + 1280*a^9*b + 1120*a^8*b^2 + 400*a^7*b^3 + 50*a^6*b^4 + a^5*b^5) + 640*b^3*(a^5*b^5 + 50*a^4*b^6 + 400*a^3*b^7 + 1120*a^2*b^8 + 1280*a*b^9 + 512*b^10)*x^5 + 640*b^3*Sqrt[a + b]*(-512*a^9 - 1024*a^8*b - 672*a^7*b^2 - 160*a^6*b^3 - 10*a^5*b^4)*Sqrt[a + b*x] + x*(640*b^3*(1280*a^9*b + 9280*a^8*b^2 + 14960*a^7*b^3 + 8600*a^6*b^4 + 1645*a^5*b^5 + 50*a^4*b^6) + 640*b^3*Sqrt[a + b]*(-1024*a^8*b - 8128*a^7*b^2 - 10464*a^6*b^3 - 4120*a^5*b^4 - 400*a^4*b^5)*Sqrt[a + b*x]) + Sqrt[x]*(640*b^3*(2560*a^9*b + 5760*a^8*b^2 + 4320*a^7*b^3 + 1200*a^6*b^4 + 90*a^5*b^5) + 640*b^3*Sqrt[a + b]*(-2560*a^8*b - 4480*a^7*b^2 - 2400*a^6*b^3 - 400*a^5*b^4 - 10*a^4*b^5)*Sqrt[a + b*x]) + x^2*(640*b^3*(1120*a^8*b^2 + 14960*a^7*b^3 + 36460*a^6*b^4 + 30610*a^5*b^5 + 8600*a^4*b^6 + 400*a^3*b^7) + 640*b^3*Sqrt[a + b]*(-672*a^7*b^2 - 10464*a^6*b^3 - 24252*a^5*b^4 - 15600*a^4*b^5 - 2400*a^3*b^6)*Sqrt[a + b*x]) + x^(3/2)*(640*b^3*(5760*a^8*b^2 + 22080*a^7*b^3 + 25680*a^6*b^4 + 10680*a^5*b^5 + 1200*a^4*b^6) + 640*b^3*Sqrt[a + b]*(-4480*a^7*b^2 - 16960*a^6*b^3 - 15600*a^5*b^4 - 4120*a^4*b^5 - 160*a^3*b^6)*Sqrt[a + b*x]) + x^3*(640*b^3*(400*a^7*b^3 + 8600*a^6*b^4 + 30610*a^5*b^5 + 36460*a^4*b^6 + 14960*a^3*b^7 + 1120*a^2*b^8) + 640*b^3*Sqrt[a + b]*(-160*a^6*b^3 - 4120*a^5*b^4 - 15600*a^4*b^5 - 16960*a^3*b^6 - 4480*a^2*b^7)*Sqrt[a + b*x]) + x^(5/2)*(640*b^3*(4320*a^7*b^3 + 25680*a^6*b^4 + 42972*a^5*b^5 + 25680*a^4*b^6 + 4320*a^3*b^7) + 640*b^3*Sqrt[a + b]*(-2400*a^6*b^3 - 15600*a^5*b^4 - 24252*a^4*b^5 - 10464*a^3*b^6 - 672*a^2*b^7)*Sqrt[a + b*x]) + x^4*(640*b^3*(50*a^6*b^4 + 1645*a^5*b^5 + 8600*a^4*b^6 + 14960*a^3*b^7 + 9280*a^2*b^8 + 1280*a*b^9) + 640*b^3*Sqrt[a + b]*(-10*a^5*b^4 - 400*a^4*b^5 - 2400*a^3*b^6 - 4480*a^2*b^7 - 2560*a*b^8)*Sqrt[a + b*x]) + x^(7/2)*(640*b^3*(1200*a^6*b^4 + 10680*a^5*b^5 + 25680*a^4*b^6 + 22080*a^3*b^7 + 5760*a^2*b^8) + 640*b^3*Sqrt[a + b]*(-400*a^5*b^4 - 4120*a^4*b^5 - 10464*a^3*b^6 - 8128*a^2*b^7 - 1024*a*b^8)*Sqrt[a + b*x]) + x^(9/2)*(640*b^3*(90*a^5*b^5 + 1200*a^4*b^6 + 4320*a^3*b^7 + 5760*a^2*b^8 + 2560*a*b^9) + 640*b^3*Sqrt[a + b]*(-10*a^4*b^5 - 160*a^3*b^6 - 672*a^2*b^7 - 1024*a*b^8 - 512*b^9)*Sqrt[a + b*x])) + (3*a^5*ArcTanh[(Sqrt[a + b]/Sqrt[b] - Sqrt[a + b*x]/Sqrt[b])/(-1 + Sqrt[x])])/(64*b^(7/2))","B",1
522,1,2745,119,3.5798197,"\int x^{3/2} (a+b x)^{3/2} \, dx","IntegrateAlgebraic[x^(3/2)*(a + b*x)^(3/2),x]","\text{Result too large to show}","\frac{3 a^4 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{64 b^{5/2}}-\frac{3 a^3 \sqrt{x} \sqrt{a+b x}}{64 b^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,"((-1/64*1/b^2 + Sqrt[x]/(64*b^2))*(Sqrt[a + b] - Sqrt[a + b*x])*(-a - b + b*Sqrt[x] - b*x + Sqrt[a + b]*Sqrt[a + b*x])*(-96*a^10 - 80*a^9*b + 810*a^8*b^2 + 1697*a^7*b^3 + 1202*a^6*b^4 + 312*a^5*b^5 + 16*a^4*b^6 - 416*a^9*b*Sqrt[x] + 600*a^8*b^2*Sqrt[x] + 5374*a^7*b^3*Sqrt[x] + 7716*a^6*b^4*Sqrt[x] + 4048*a^5*b^5*Sqrt[x] + 672*a^4*b^6*Sqrt[x] - 80*a^9*b*x - 164*a^8*b^2*x + 6015*a^7*b^3*x + 17754*a^6*b^4*x + 17384*a^5*b^5*x + 6288*a^4*b^6*x + 512*a^3*b^7*x + 600*a^8*b^2*x^(3/2) + 4676*a^7*b^3*x^(3/2) + 20596*a^6*b^4*x^(3/2) + 34800*a^5*b^5*x^(3/2) + 23584*a^4*b^6*x^(3/2) + 5376*a^3*b^7*x^(3/2) + 810*a^8*b^2*x^2 + 6015*a^7*b^3*x^2 + 18712*a^6*b^4*x^2 + 39504*a^5*b^5*x^2 + 43840*a^4*b^6*x^2 + 20352*a^3*b^7*x^2 + 2560*a^2*b^8*x^2 + 5374*a^7*b^3*x^(5/2) + 20596*a^6*b^4*x^(5/2) + 36704*a^5*b^5*x^(5/2) + 47424*a^4*b^6*x^(5/2) + 36608*a^3*b^7*x^(5/2) + 10752*a^2*b^8*x^(5/2) + 1697*a^7*b^3*x^3 + 17754*a^6*b^4*x^3 + 39504*a^5*b^5*x^3 + 42976*a^4*b^6*x^3 + 36480*a^3*b^7*x^3 + 20736*a^2*b^8*x^3 + 4096*a*b^9*x^3 + 7716*a^6*b^4*x^(7/2) + 34800*a^5*b^5*x^(7/2) + 47424*a^4*b^6*x^(7/2) + 30720*a^3*b^7*x^(7/2) + 16896*a^2*b^8*x^(7/2) + 6144*a*b^9*x^(7/2) + 1202*a^6*b^4*x^4 + 17384*a^5*b^5*x^4 + 43840*a^4*b^6*x^4 + 36480*a^3*b^7*x^4 + 12800*a^2*b^8*x^4 + 6144*a*b^9*x^4 + 2048*b^10*x^4 + 4048*a^5*b^5*x^(9/2) + 23584*a^4*b^6*x^(9/2) + 36608*a^3*b^7*x^(9/2) + 16896*a^2*b^8*x^(9/2) + 312*a^5*b^5*x^5 + 6288*a^4*b^6*x^5 + 20352*a^3*b^7*x^5 + 20736*a^2*b^8*x^5 + 6144*a*b^9*x^5 + 672*a^4*b^6*x^(11/2) + 5376*a^3*b^7*x^(11/2) + 10752*a^2*b^8*x^(11/2) + 6144*a*b^9*x^(11/2) + 16*a^4*b^6*x^6 + 512*a^3*b^7*x^6 + 2560*a^2*b^8*x^6 + 4096*a*b^9*x^6 + 2048*b^10*x^6 + 96*a^9*Sqrt[a + b]*Sqrt[a + b*x] + 32*a^8*b*Sqrt[a + b]*Sqrt[a + b*x] - 814*a^7*b^2*Sqrt[a + b]*Sqrt[a + b*x] - 1292*a^6*b^3*Sqrt[a + b]*Sqrt[a + b*x] - 656*a^5*b^4*Sqrt[a + b]*Sqrt[a + b*x] - 96*a^4*b^5*Sqrt[a + b]*Sqrt[a + b*x] + 416*a^8*b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 808*a^7*b^2*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 4918*a^6*b^3*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 5384*a^5*b^4*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 1904*a^4*b^5*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 128*a^3*b^6*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 32*a^8*b*Sqrt[a + b]*x*Sqrt[a + b*x] + 108*a^7*b^2*Sqrt[a + b]*x*Sqrt[a + b*x] - 5660*a^6*b^3*Sqrt[a + b]*x*Sqrt[a + b*x] - 14064*a^5*b^4*Sqrt[a + b]*x*Sqrt[a + b*x] - 10464*a^4*b^5*Sqrt[a + b]*x*Sqrt[a + b*x] - 2304*a^3*b^6*Sqrt[a + b]*x*Sqrt[a + b*x] - 808*a^7*b^2*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] - 3972*a^6*b^3*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] - 16024*a^5*b^4*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] - 23376*a^4*b^5*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] - 11648*a^3*b^6*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] - 1280*a^2*b^7*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] - 814*a^7*b^2*Sqrt[a + b]*x^2*Sqrt[a + b*x] - 5660*a^6*b^3*Sqrt[a + b]*x^2*Sqrt[a + b*x] - 13280*a^5*b^4*Sqrt[a + b]*x^2*Sqrt[a + b*x] - 25280*a^4*b^5*Sqrt[a + b]*x^2*Sqrt[a + b*x] - 24320*a^3*b^6*Sqrt[a + b]*x^2*Sqrt[a + b*x] - 7680*a^2*b^7*Sqrt[a + b]*x^2*Sqrt[a + b*x] - 4918*a^6*b^3*Sqrt[a + b]*x^(5/2)*Sqrt[a + b*x] - 16024*a^5*b^4*Sqrt[a + b]*x^(5/2)*Sqrt[a + b*x] - 21024*a^4*b^5*Sqrt[a + b]*x^(5/2)*Sqrt[a + b*x] - 24064*a^3*b^6*Sqrt[a + b]*x^(5/2)*Sqrt[a + b*x] - 16128*a^2*b^7*Sqrt[a + b]*x^(5/2)*Sqrt[a + b*x] - 3072*a*b^8*Sqrt[a + b]*x^(5/2)*Sqrt[a + b*x] - 1292*a^6*b^3*Sqrt[a + b]*x^3*Sqrt[a + b*x] - 14064*a^5*b^4*Sqrt[a + b]*x^3*Sqrt[a + b*x] - 25280*a^4*b^5*Sqrt[a + b]*x^3*Sqrt[a + b*x] - 18432*a^3*b^6*Sqrt[a + b]*x^3*Sqrt[a + b*x] - 13824*a^2*b^7*Sqrt[a + b]*x^3*Sqrt[a + b*x] - 6144*a*b^8*Sqrt[a + b]*x^3*Sqrt[a + b*x] - 5384*a^5*b^4*Sqrt[a + b]*x^(7/2)*Sqrt[a + b*x] - 23376*a^4*b^5*Sqrt[a + b]*x^(7/2)*Sqrt[a + b*x] - 24064*a^3*b^6*Sqrt[a + b]*x^(7/2)*Sqrt[a + b*x] - 8192*a^2*b^7*Sqrt[a + b]*x^(7/2)*Sqrt[a + b*x] - 5120*a*b^8*Sqrt[a + b]*x^(7/2)*Sqrt[a + b*x] - 2048*b^9*Sqrt[a + b]*x^(7/2)*Sqrt[a + b*x] - 656*a^5*b^4*Sqrt[a + b]*x^4*Sqrt[a + b*x] - 10464*a^4*b^5*Sqrt[a + b]*x^4*Sqrt[a + b*x] - 24320*a^3*b^6*Sqrt[a + b]*x^4*Sqrt[a + b*x] - 13824*a^2*b^7*Sqrt[a + b]*x^4*Sqrt[a + b*x] - 1904*a^4*b^5*Sqrt[a + b]*x^(9/2)*Sqrt[a + b*x] - 11648*a^3*b^6*Sqrt[a + b]*x^(9/2)*Sqrt[a + b*x] - 16128*a^2*b^7*Sqrt[a + b]*x^(9/2)*Sqrt[a + b*x] - 5120*a*b^8*Sqrt[a + b]*x^(9/2)*Sqrt[a + b*x] - 96*a^4*b^5*Sqrt[a + b]*x^5*Sqrt[a + b*x] - 2304*a^3*b^6*Sqrt[a + b]*x^5*Sqrt[a + b*x] - 7680*a^2*b^7*Sqrt[a + b]*x^5*Sqrt[a + b*x] - 6144*a*b^8*Sqrt[a + b]*x^5*Sqrt[a + b*x] - 128*a^3*b^6*Sqrt[a + b]*x^(11/2)*Sqrt[a + b*x] - 1280*a^2*b^7*Sqrt[a + b]*x^(11/2)*Sqrt[a + b*x] - 3072*a*b^8*Sqrt[a + b]*x^(11/2)*Sqrt[a + b*x] - 2048*b^9*Sqrt[a + b]*x^(11/2)*Sqrt[a + b*x]))/(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x])^8 - (3*a^4*ArcTanh[(Sqrt[a + b]/Sqrt[b] - Sqrt[a + b*x]/Sqrt[b])/(-1 + Sqrt[x])])/(32*b^(5/2))","B",1
523,1,1695,95,2.1700456,"\int \sqrt{x} (a+b x)^{3/2} \, dx","IntegrateAlgebraic[Sqrt[x]*(a + b*x)^(3/2),x]","\frac{\tanh ^{-1}\left(\frac{\frac{\sqrt{a+b}}{\sqrt{b}}-\frac{\sqrt{a+b x}}{\sqrt{b}}}{\sqrt{x}-1}\right) a^3}{4 b^{3/2}}+\frac{\left(256 b^8+384 a b^7+144 a^2 b^6+8 a^3 b^5\right) \sqrt{a+b x} x^{11/2}+\left(768 a b^7+960 a^2 b^6+240 a^3 b^5\right) \sqrt{a+b x} x^5+\left(832 a b^7+2304 a^2 b^6+1524 a^3 b^5+158 a^4 b^4\right) \sqrt{a+b x} x^{9/2}+\left(2304 a^2 b^6+3760 a^3 b^5+1380 a^4 b^4\right) \sqrt{a+b x} x^4+\left(912 a^2 b^6+4272 a^3 b^5+3912 a^4 b^4+639 a^5 b^3\right) \sqrt{a+b x} x^{7/2}+\left(2538 b^3 a^5+4960 b^4 a^4+2208 b^5 a^3\right) \sqrt{a+b x} x^3+\left(-256 b^8-960 a b^7-1296 a^2 b^6-368 a^3 b^5+2784 a^4 b^4+3699 a^5 b^3+982 a^6 b^2\right) \sqrt{a+b x} x^{5/2}+\left(-768 a b^7-2688 a^2 b^6-3264 a^3 b^5-864 a^4 b^4+2142 a^5 b^3+1686 a^6 b^2\right) \sqrt{a+b x} x^2+\left(592 b a^7+1068 b^2 a^6-987 b^3 a^5-4400 b^4 a^4-4728 b^5 a^3-2016 b^6 a^2-256 b^7 a\right) \sqrt{a+b x} x^{3/2}+\left(192 b a^7-676 b^2 a^6-3618 b^3 a^5-5088 b^4 a^4-2896 b^5 a^3-576 b^6 a^2\right) \sqrt{a+b x} x+\left(96 a^8-144 b a^7-1794 b^2 a^6-3351 b^3 a^5-2454 b^4 a^4-708 b^5 a^3-48 b^6 a^2\right) \sqrt{a+b x} \sqrt{x}+\sqrt{a+b} \left(96 a^8+592 b a^7+982 b^2 a^6+639 b^3 a^5+158 b^4 a^4+8 b^5 a^3+\left(-256 b^8-256 a b^7-48 a^2 b^6\right) x^6+\left(-768 a b^7-576 a^2 b^6-48 a^3 b^5\right) x^{11/2}+\left(-960 a b^7-2016 a^2 b^6-708 a^3 b^5\right) x^5+\left(-2688 a^2 b^6-2896 a^3 b^5-388 a^4 b^4\right) x^{9/2}+\left(-1296 a^2 b^6-4728 a^3 b^5-2454 a^4 b^4\right) x^4+\left(-1062 b^3 a^5-5088 b^4 a^4-3264 b^5 a^3\right) x^{7/2}+\left(256 b^8+832 a b^7+912 a^2 b^6-368 a^3 b^5-4400 a^4 b^4-3351 a^5 b^3\right) x^3+\left(768 a b^7+2304 a^2 b^6+2208 a^3 b^5-864 a^4 b^4-3618 a^5 b^3-1266 a^6 b^2\right) x^{5/2}+\left(384 a b^7+2304 a^2 b^6+4272 a^3 b^5+2784 a^4 b^4-987 a^5 b^3-1794 a^6 b^2\right) x^2+\left(-640 b a^7-676 b^2 a^6+2142 b^3 a^5+4960 b^4 a^4+3760 b^5 a^3+960 b^6 a^2\right) x^{3/2}+\left(-144 b a^7+1068 b^2 a^6+3699 b^3 a^5+3912 b^4 a^4+1524 b^5 a^3+144 b^6 a^2\right) x+\left(-96 a^8+192 b a^7+1686 b^2 a^6+2538 b^3 a^5+1380 b^4 a^4+240 b^5 a^3\right) \sqrt{x}\right)+\left(-96 a^8-640 b a^7-1266 b^2 a^6-1062 b^3 a^5-388 b^4 a^4-48 b^5 a^3\right) \sqrt{a+b x}}{24 b \left(32 b^6+48 a b^5+18 a^2 b^4+a^3 b^3\right) x^3+\left(24 b \sqrt{a+b} \sqrt{a+b x} \left(-32 b^5-32 a b^4-6 a^2 b^3\right)+24 b \left(96 a b^5+120 a^2 b^4+30 a^3 b^3\right)\right) x^{5/2}+\left(24 b \sqrt{a+b} \sqrt{a+b x} \left(-96 a b^4-72 a^2 b^3-6 a^3 b^2\right)+24 b \left(48 a b^5+204 a^2 b^4+159 a^3 b^3+18 a^4 b^2\right)\right) x^2+\left(24 b \sqrt{a+b} \sqrt{a+b x} \left(-32 a b^4-164 a^2 b^3-72 a^3 b^2\right)+24 b \left(120 b^2 a^4+260 b^3 a^3+120 b^4 a^2\right)\right) x^{3/2}+\left(24 b \sqrt{a+b} \sqrt{a+b x} \left(-32 b a^4-164 b^2 a^3-72 b^3 a^2\right)+24 b \left(48 b a^5+204 b^2 a^4+159 b^3 a^3+18 b^4 a^2\right)\right) x+\left(24 b \sqrt{a+b} \sqrt{a+b x} \left(-96 b a^4-72 b^2 a^3-6 b^3 a^2\right)+24 b \left(96 b a^5+120 b^2 a^4+30 b^3 a^3\right)\right) \sqrt{x}+24 b \left(32 a^6+48 b a^5+18 b^2 a^4+b^3 a^3\right)+24 b \sqrt{a+b} \left(-32 a^5-32 b a^4-6 b^2 a^3\right) \sqrt{a+b 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}",1,"((-96*a^8 - 640*a^7*b - 1266*a^6*b^2 - 1062*a^5*b^3 - 388*a^4*b^4 - 48*a^3*b^5)*Sqrt[a + b*x] + (96*a^8 - 144*a^7*b - 1794*a^6*b^2 - 3351*a^5*b^3 - 2454*a^4*b^4 - 708*a^3*b^5 - 48*a^2*b^6)*Sqrt[x]*Sqrt[a + b*x] + (192*a^7*b - 676*a^6*b^2 - 3618*a^5*b^3 - 5088*a^4*b^4 - 2896*a^3*b^5 - 576*a^2*b^6)*x*Sqrt[a + b*x] + (592*a^7*b + 1068*a^6*b^2 - 987*a^5*b^3 - 4400*a^4*b^4 - 4728*a^3*b^5 - 2016*a^2*b^6 - 256*a*b^7)*x^(3/2)*Sqrt[a + b*x] + (1686*a^6*b^2 + 2142*a^5*b^3 - 864*a^4*b^4 - 3264*a^3*b^5 - 2688*a^2*b^6 - 768*a*b^7)*x^2*Sqrt[a + b*x] + (982*a^6*b^2 + 3699*a^5*b^3 + 2784*a^4*b^4 - 368*a^3*b^5 - 1296*a^2*b^6 - 960*a*b^7 - 256*b^8)*x^(5/2)*Sqrt[a + b*x] + (2538*a^5*b^3 + 4960*a^4*b^4 + 2208*a^3*b^5)*x^3*Sqrt[a + b*x] + (639*a^5*b^3 + 3912*a^4*b^4 + 4272*a^3*b^5 + 912*a^2*b^6)*x^(7/2)*Sqrt[a + b*x] + (1380*a^4*b^4 + 3760*a^3*b^5 + 2304*a^2*b^6)*x^4*Sqrt[a + b*x] + (158*a^4*b^4 + 1524*a^3*b^5 + 2304*a^2*b^6 + 832*a*b^7)*x^(9/2)*Sqrt[a + b*x] + (240*a^3*b^5 + 960*a^2*b^6 + 768*a*b^7)*x^5*Sqrt[a + b*x] + (8*a^3*b^5 + 144*a^2*b^6 + 384*a*b^7 + 256*b^8)*x^(11/2)*Sqrt[a + b*x] + Sqrt[a + b]*(96*a^8 + 592*a^7*b + 982*a^6*b^2 + 639*a^5*b^3 + 158*a^4*b^4 + 8*a^3*b^5 + (-96*a^8 + 192*a^7*b + 1686*a^6*b^2 + 2538*a^5*b^3 + 1380*a^4*b^4 + 240*a^3*b^5)*Sqrt[x] + (-144*a^7*b + 1068*a^6*b^2 + 3699*a^5*b^3 + 3912*a^4*b^4 + 1524*a^3*b^5 + 144*a^2*b^6)*x + (-640*a^7*b - 676*a^6*b^2 + 2142*a^5*b^3 + 4960*a^4*b^4 + 3760*a^3*b^5 + 960*a^2*b^6)*x^(3/2) + (-1794*a^6*b^2 - 987*a^5*b^3 + 2784*a^4*b^4 + 4272*a^3*b^5 + 2304*a^2*b^6 + 384*a*b^7)*x^2 + (-1266*a^6*b^2 - 3618*a^5*b^3 - 864*a^4*b^4 + 2208*a^3*b^5 + 2304*a^2*b^6 + 768*a*b^7)*x^(5/2) + (-3351*a^5*b^3 - 4400*a^4*b^4 - 368*a^3*b^5 + 912*a^2*b^6 + 832*a*b^7 + 256*b^8)*x^3 + (-1062*a^5*b^3 - 5088*a^4*b^4 - 3264*a^3*b^5)*x^(7/2) + (-2454*a^4*b^4 - 4728*a^3*b^5 - 1296*a^2*b^6)*x^4 + (-388*a^4*b^4 - 2896*a^3*b^5 - 2688*a^2*b^6)*x^(9/2) + (-708*a^3*b^5 - 2016*a^2*b^6 - 960*a*b^7)*x^5 + (-48*a^3*b^5 - 576*a^2*b^6 - 768*a*b^7)*x^(11/2) + (-48*a^2*b^6 - 256*a*b^7 - 256*b^8)*x^6))/(24*b*(32*a^6 + 48*a^5*b + 18*a^4*b^2 + a^3*b^3) + 24*b*(a^3*b^3 + 18*a^2*b^4 + 48*a*b^5 + 32*b^6)*x^3 + 24*b*Sqrt[a + b]*(-32*a^5 - 32*a^4*b - 6*a^3*b^2)*Sqrt[a + b*x] + x*(24*b*(48*a^5*b + 204*a^4*b^2 + 159*a^3*b^3 + 18*a^2*b^4) + 24*b*Sqrt[a + b]*(-32*a^4*b - 164*a^3*b^2 - 72*a^2*b^3)*Sqrt[a + b*x]) + Sqrt[x]*(24*b*(96*a^5*b + 120*a^4*b^2 + 30*a^3*b^3) + 24*b*Sqrt[a + b]*(-96*a^4*b - 72*a^3*b^2 - 6*a^2*b^3)*Sqrt[a + b*x]) + x^2*(24*b*(18*a^4*b^2 + 159*a^3*b^3 + 204*a^2*b^4 + 48*a*b^5) + 24*b*Sqrt[a + b]*(-6*a^3*b^2 - 72*a^2*b^3 - 96*a*b^4)*Sqrt[a + b*x]) + x^(3/2)*(24*b*(120*a^4*b^2 + 260*a^3*b^3 + 120*a^2*b^4) + 24*b*Sqrt[a + b]*(-72*a^3*b^2 - 164*a^2*b^3 - 32*a*b^4)*Sqrt[a + b*x]) + x^(5/2)*(24*b*(30*a^3*b^3 + 120*a^2*b^4 + 96*a*b^5) + 24*b*Sqrt[a + b]*(-6*a^2*b^3 - 32*a*b^4 - 32*b^5)*Sqrt[a + b*x])) + (a^3*ArcTanh[(Sqrt[a + b]/Sqrt[b] - Sqrt[a + b*x]/Sqrt[b])/(-1 + Sqrt[x])])/(4*b^(3/2))","B",1
524,1,751,71,0.9402469,"\int \frac{(a+b x)^{3/2}}{\sqrt{x}} \, dx","IntegrateAlgebraic[(a + b*x)^(3/2)/Sqrt[x],x]","\frac{\left(\frac{\sqrt{x}}{4}-\frac{1}{4}\right) \left(\sqrt{a+b}-\sqrt{a+b x}\right) \left(-20 a^5-33 a^4 b x-58 a^4 b \sqrt{x}+20 a^4 \sqrt{a+b} \sqrt{a+b x}-33 a^4 b-71 a^3 b^2 x^{3/2}-15 a^3 b^2 x^2-112 a^3 b^2 x-71 a^3 b^2 \sqrt{x}-15 a^3 b^2+23 a^3 b x \sqrt{a+b} \sqrt{a+b x}+23 a^3 b \sqrt{a+b} \sqrt{a+b x}+58 a^3 b \sqrt{x} \sqrt{a+b} \sqrt{a+b x}-18 a^2 b^3 x^{5/2}-108 a^2 b^3 x^{3/2}-2 a^2 b^3 x^3-80 a^2 b^3 x^2-80 a^2 b^3 x-18 a^2 b^3 \sqrt{x}-2 a^2 b^3+42 a^2 b^2 x^{3/2} \sqrt{a+b} \sqrt{a+b x}+6 a^2 b^2 x^2 \sqrt{a+b} \sqrt{a+b x}+84 a^2 b^2 x \sqrt{a+b} \sqrt{a+b x}+6 a^2 b^2 \sqrt{a+b} \sqrt{a+b x}+42 a^2 b^2 \sqrt{x} \sqrt{a+b} \sqrt{a+b x}-24 a b^4 x^{5/2}-24 a b^4 x^{3/2}+16 b^4 x^{5/2} \sqrt{a+b} \sqrt{a+b x}+16 b^4 x^{3/2} \sqrt{a+b} \sqrt{a+b x}-16 a b^4 x^3-80 a b^4 x^2-16 a b^4 x+8 a b^3 x^{5/2} \sqrt{a+b} \sqrt{a+b x}+64 a b^3 x^{3/2} \sqrt{a+b} \sqrt{a+b x}+24 a b^3 x^2 \sqrt{a+b} \sqrt{a+b x}+24 a b^3 x \sqrt{a+b} \sqrt{a+b x}+8 a b^3 \sqrt{x} \sqrt{a+b} \sqrt{a+b x}-16 b^5 x^3-16 b^5 x^2\right)}{\left(\sqrt{a+b} \sqrt{a+b x}-a-b \sqrt{x}\right)^4}-\frac{3 a^2 \tanh ^{-1}\left(\frac{\frac{\sqrt{a+b}}{\sqrt{b}}-\frac{\sqrt{a+b x}}{\sqrt{b}}}{\sqrt{x}-1}\right)}{2 \sqrt{b}}","\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,"((-1/4 + Sqrt[x]/4)*(Sqrt[a + b] - Sqrt[a + b*x])*(-20*a^5 - 33*a^4*b - 15*a^3*b^2 - 2*a^2*b^3 - 58*a^4*b*Sqrt[x] - 71*a^3*b^2*Sqrt[x] - 18*a^2*b^3*Sqrt[x] - 33*a^4*b*x - 112*a^3*b^2*x - 80*a^2*b^3*x - 16*a*b^4*x - 71*a^3*b^2*x^(3/2) - 108*a^2*b^3*x^(3/2) - 24*a*b^4*x^(3/2) - 15*a^3*b^2*x^2 - 80*a^2*b^3*x^2 - 80*a*b^4*x^2 - 16*b^5*x^2 - 18*a^2*b^3*x^(5/2) - 24*a*b^4*x^(5/2) - 2*a^2*b^3*x^3 - 16*a*b^4*x^3 - 16*b^5*x^3 + 20*a^4*Sqrt[a + b]*Sqrt[a + b*x] + 23*a^3*b*Sqrt[a + b]*Sqrt[a + b*x] + 6*a^2*b^2*Sqrt[a + b]*Sqrt[a + b*x] + 58*a^3*b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 42*a^2*b^2*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 8*a*b^3*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 23*a^3*b*Sqrt[a + b]*x*Sqrt[a + b*x] + 84*a^2*b^2*Sqrt[a + b]*x*Sqrt[a + b*x] + 24*a*b^3*Sqrt[a + b]*x*Sqrt[a + b*x] + 42*a^2*b^2*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] + 64*a*b^3*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] + 16*b^4*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] + 6*a^2*b^2*Sqrt[a + b]*x^2*Sqrt[a + b*x] + 24*a*b^3*Sqrt[a + b]*x^2*Sqrt[a + b*x] + 8*a*b^3*Sqrt[a + b]*x^(5/2)*Sqrt[a + b*x] + 16*b^4*Sqrt[a + b]*x^(5/2)*Sqrt[a + b*x]))/(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x])^4 - (3*a^2*ArcTanh[(Sqrt[a + b]/Sqrt[b] - Sqrt[a + b*x]/Sqrt[b])/(-1 + Sqrt[x])])/(2*Sqrt[b])","B",1
525,1,465,63,1.1900288,"\int \frac{(a+b x)^{3/2}}{x^{3/2}} \, dx","IntegrateAlgebraic[(a + b*x)^(3/2)/x^(3/2),x]","\frac{\left(2 a^2-2 a^2 \sqrt{x}\right) \left(-2 \sqrt{a+b} \sqrt{a+b x}+\sqrt{x} \sqrt{a+b} \sqrt{a+b x}+a \left(-\sqrt{x}\right)+2 a+b x-2 b \sqrt{x}+2 b\right) \left(\sqrt{a+b}-\sqrt{a+b x}\right)}{\sqrt{x} \left(-2 a^2 \sqrt{x}+4 a^2-a b x^{3/2}+2 a b x-a b \sqrt{x}-4 a \sqrt{a+b} \sqrt{a+b x}+2 a \sqrt{x} \sqrt{a+b} \sqrt{a+b x}-2 b \sqrt{a+b} \sqrt{a+b x}+4 a b+2 b^2 \sqrt{x}\right)}+\frac{\left(-a b \sqrt{x}+2 b \sqrt{a+b} \sqrt{a+b x}-a b-2 b^2 \sqrt{x}\right) \left(\sqrt{a+b}-\sqrt{a+b x}\right)^3}{\left(\sqrt{a+b} \sqrt{a+b x}-a-b \sqrt{x}\right)^2}+\frac{\left(b \sqrt{a+b}-b \sqrt{a+b x}\right) \left(4 \sqrt{a+b} \sqrt{a+b x}+a \left(-\sqrt{x}\right)-3 a-2 b \sqrt{x}-2 b\right)}{\sqrt{a+b} \sqrt{a+b x}-a-b \sqrt{x}}-6 a \sqrt{b} \tanh ^{-1}\left(\frac{\frac{\sqrt{a+b}}{\sqrt{b}}-\frac{\sqrt{a+b x}}{\sqrt{b}}}{\sqrt{x}-1}\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,"((b*Sqrt[a + b] - b*Sqrt[a + b*x])*(-3*a - 2*b - a*Sqrt[x] - 2*b*Sqrt[x] + 4*Sqrt[a + b]*Sqrt[a + b*x]))/(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x]) + ((Sqrt[a + b] - Sqrt[a + b*x])^3*(-(a*b) - a*b*Sqrt[x] - 2*b^2*Sqrt[x] + 2*b*Sqrt[a + b]*Sqrt[a + b*x]))/(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x])^2 + ((2*a^2 - 2*a^2*Sqrt[x])*(Sqrt[a + b] - Sqrt[a + b*x])*(2*a + 2*b - a*Sqrt[x] - 2*b*Sqrt[x] + b*x - 2*Sqrt[a + b]*Sqrt[a + b*x] + Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x]))/(Sqrt[x]*(4*a^2 + 4*a*b - 2*a^2*Sqrt[x] - a*b*Sqrt[x] + 2*b^2*Sqrt[x] + 2*a*b*x - a*b*x^(3/2) - 4*a*Sqrt[a + b]*Sqrt[a + b*x] - 2*b*Sqrt[a + b]*Sqrt[a + b*x] + 2*a*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x])) - 6*a*Sqrt[b]*ArcTanh[(Sqrt[a + b]/Sqrt[b] - Sqrt[a + b*x]/Sqrt[b])/(-1 + Sqrt[x])]","B",1
526,1,1759,64,2.3945651,"\int \frac{(a+b x)^{3/2}}{x^{5/2}} \, dx","IntegrateAlgebraic[(a + b*x)^(3/2)/x^(5/2),x]","\frac{\left(\frac{2 a}{3}-\frac{2 a \sqrt{x}}{3}\right) \left(\sqrt{a+b}-\sqrt{a+b x}\right) \left(-16 x^{5/2} a^6+80 x^2 a^6-112 x^{3/2} a^6+32 x a^6-64 \sqrt{x} a^6+128 a^6-20 b x^{7/2} a^5+100 b x^3 a^5-232 b x^{5/2} a^5+620 b x^2 a^5-1228 b x^{3/2} a^5+352 b a^5+824 b x a^5-80 b \sqrt{x} a^5+16 \sqrt{a+b} x^{5/2} \sqrt{a+b x} a^5-80 \sqrt{a+b} x^2 \sqrt{a+b x} a^5+112 \sqrt{a+b} x^{3/2} \sqrt{a+b x} a^5-32 \sqrt{a+b} x \sqrt{a+b x} a^5-128 \sqrt{a+b} \sqrt{a+b x} a^5+64 \sqrt{a+b} \sqrt{x} \sqrt{a+b x} a^5-5 b^2 x^{9/2} a^4+25 b^2 x^4 a^4-145 b^2 x^{7/2} a^4+728 b^2 x^3 a^4-1635 b^2 x^{5/2} a^4+328 b^2 a^4+1965 b^2 x^2 a^4-2467 b^2 x^{3/2} a^4+2042 b^2 x a^4+124 b^2 \sqrt{x} a^4+12 b \sqrt{a+b} x^{7/2} \sqrt{a+b x} a^4-60 b \sqrt{a+b} x^3 \sqrt{a+b x} a^4+168 b \sqrt{a+b} x^{5/2} \sqrt{a+b x} a^4-564 b \sqrt{a+b} x^2 \sqrt{a+b x} a^4+1140 b \sqrt{a+b} x^{3/2} \sqrt{a+b x} a^4-744 b \sqrt{a+b} x \sqrt{a+b x} a^4-288 b \sqrt{a+b} \sqrt{a+b x} a^4+48 b \sqrt{a+b} \sqrt{x} \sqrt{a+b x} a^4-25 b^3 x^{9/2} a^3+184 b^3 x^4 a^3-570 b^3 x^{7/2} a^3+112 b^3 a^3+1386 b^3 x^3 a^3-2613 b^3 x^{5/2} a^3+2316 b^3 x^2 a^3-1412 b^3 x^{3/2} a^3+1842 b^3 x a^3+220 b^3 \sqrt{x} a^3+b^2 \sqrt{a+b} x^{9/2} \sqrt{a+b x} a^3-5 b^2 \sqrt{a+b} x^4 \sqrt{a+b x} a^3+65 b^2 \sqrt{a+b} x^{7/2} \sqrt{a+b x} a^3-400 b^2 \sqrt{a+b} x^3 \sqrt{a+b x} a^3+963 b^2 \sqrt{a+b} x^{5/2} \sqrt{a+b x} a^3-1329 b^2 \sqrt{a+b} x^2 \sqrt{a+b x} a^3+1871 b^2 \sqrt{a+b} x^{3/2} \sqrt{a+b x} a^3-1498 b^2 \sqrt{a+b} x \sqrt{a+b x} a^3-200 b^2 \sqrt{a+b} \sqrt{a+b x} a^3-140 b^2 \sqrt{a+b} \sqrt{x} \sqrt{a+b x} a^3+4 b^4 x^5 a^2-40 b^4 x^{9/2} a^2+8 b^4 a^2+198 b^4 x^4 a^2-480 b^4 x^{7/2} a^2+696 b^4 x^3 a^2-1188 b^4 x^{5/2} a^2+1078 b^4 x^2 a^2+180 b^4 x^{3/2} a^2+664 b^4 x a^2+80 b^4 \sqrt{x} a^2+4 b^3 \sqrt{a+b} x^{9/2} \sqrt{a+b x} a^2-40 b^3 \sqrt{a+b} x^4 \sqrt{a+b x} a^2+162 b^3 \sqrt{a+b} x^{7/2} \sqrt{a+b x} a^2-480 b^3 \sqrt{a+b} x^3 \sqrt{a+b x} a^2+948 b^3 \sqrt{a+b} x^{5/2} \sqrt{a+b x} a^2-828 b^3 \sqrt{a+b} x^2 \sqrt{a+b x} a^2+674 b^3 \sqrt{a+b} x^{3/2} \sqrt{a+b x} a^2-1020 b^3 \sqrt{a+b} x \sqrt{a+b x} a^2-40 b^3 \sqrt{a+b} \sqrt{a+b x} a^2-148 b^3 \sqrt{a+b} \sqrt{x} \sqrt{a+b x} a^2-72 b^5 x^3 a+288 b^5 x^2 a+240 b^5 x^{3/2} a+72 b^5 x a+72 b^4 \sqrt{a+b} x^{5/2} \sqrt{a+b x} a-240 b^4 \sqrt{a+b} x^{3/2} \sqrt{a+b x} a-240 b^4 \sqrt{a+b} x \sqrt{a+b x} a-24 b^4 \sqrt{a+b} \sqrt{x} \sqrt{a+b x} a+96 b^6 x^2-96 b^5 \sqrt{a+b} x^{3/2} \sqrt{a+b x}\right)}{x^{3/2} \left(-2 \sqrt{x} a^2+4 a^2-b x^{3/2} a+4 b a+2 b x a-b \sqrt{x} a-4 \sqrt{a+b} \sqrt{a+b x} a+2 \sqrt{a+b} \sqrt{x} \sqrt{a+b x} a+2 b^2 \sqrt{x}-2 b \sqrt{a+b} \sqrt{a+b x}\right)^3}-4 b^{3/2} \tanh ^{-1}\left(\frac{\frac{\sqrt{a+b}}{\sqrt{b}}-\frac{\sqrt{a+b x}}{\sqrt{b}}}{\sqrt{x}-1}\right)","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*a)/3 - (2*a*Sqrt[x])/3)*(Sqrt[a + b] - Sqrt[a + b*x])*(128*a^6 + 352*a^5*b + 328*a^4*b^2 + 112*a^3*b^3 + 8*a^2*b^4 - 64*a^6*Sqrt[x] - 80*a^5*b*Sqrt[x] + 124*a^4*b^2*Sqrt[x] + 220*a^3*b^3*Sqrt[x] + 80*a^2*b^4*Sqrt[x] + 32*a^6*x + 824*a^5*b*x + 2042*a^4*b^2*x + 1842*a^3*b^3*x + 664*a^2*b^4*x + 72*a*b^5*x - 112*a^6*x^(3/2) - 1228*a^5*b*x^(3/2) - 2467*a^4*b^2*x^(3/2) - 1412*a^3*b^3*x^(3/2) + 180*a^2*b^4*x^(3/2) + 240*a*b^5*x^(3/2) + 80*a^6*x^2 + 620*a^5*b*x^2 + 1965*a^4*b^2*x^2 + 2316*a^3*b^3*x^2 + 1078*a^2*b^4*x^2 + 288*a*b^5*x^2 + 96*b^6*x^2 - 16*a^6*x^(5/2) - 232*a^5*b*x^(5/2) - 1635*a^4*b^2*x^(5/2) - 2613*a^3*b^3*x^(5/2) - 1188*a^2*b^4*x^(5/2) + 100*a^5*b*x^3 + 728*a^4*b^2*x^3 + 1386*a^3*b^3*x^3 + 696*a^2*b^4*x^3 - 72*a*b^5*x^3 - 20*a^5*b*x^(7/2) - 145*a^4*b^2*x^(7/2) - 570*a^3*b^3*x^(7/2) - 480*a^2*b^4*x^(7/2) + 25*a^4*b^2*x^4 + 184*a^3*b^3*x^4 + 198*a^2*b^4*x^4 - 5*a^4*b^2*x^(9/2) - 25*a^3*b^3*x^(9/2) - 40*a^2*b^4*x^(9/2) + 4*a^2*b^4*x^5 - 128*a^5*Sqrt[a + b]*Sqrt[a + b*x] - 288*a^4*b*Sqrt[a + b]*Sqrt[a + b*x] - 200*a^3*b^2*Sqrt[a + b]*Sqrt[a + b*x] - 40*a^2*b^3*Sqrt[a + b]*Sqrt[a + b*x] + 64*a^5*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 48*a^4*b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 140*a^3*b^2*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 148*a^2*b^3*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 24*a*b^4*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 32*a^5*Sqrt[a + b]*x*Sqrt[a + b*x] - 744*a^4*b*Sqrt[a + b]*x*Sqrt[a + b*x] - 1498*a^3*b^2*Sqrt[a + b]*x*Sqrt[a + b*x] - 1020*a^2*b^3*Sqrt[a + b]*x*Sqrt[a + b*x] - 240*a*b^4*Sqrt[a + b]*x*Sqrt[a + b*x] + 112*a^5*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] + 1140*a^4*b*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] + 1871*a^3*b^2*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] + 674*a^2*b^3*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] - 240*a*b^4*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] - 96*b^5*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] - 80*a^5*Sqrt[a + b]*x^2*Sqrt[a + b*x] - 564*a^4*b*Sqrt[a + b]*x^2*Sqrt[a + b*x] - 1329*a^3*b^2*Sqrt[a + b]*x^2*Sqrt[a + b*x] - 828*a^2*b^3*Sqrt[a + b]*x^2*Sqrt[a + b*x] + 16*a^5*Sqrt[a + b]*x^(5/2)*Sqrt[a + b*x] + 168*a^4*b*Sqrt[a + b]*x^(5/2)*Sqrt[a + b*x] + 963*a^3*b^2*Sqrt[a + b]*x^(5/2)*Sqrt[a + b*x] + 948*a^2*b^3*Sqrt[a + b]*x^(5/2)*Sqrt[a + b*x] + 72*a*b^4*Sqrt[a + b]*x^(5/2)*Sqrt[a + b*x] - 60*a^4*b*Sqrt[a + b]*x^3*Sqrt[a + b*x] - 400*a^3*b^2*Sqrt[a + b]*x^3*Sqrt[a + b*x] - 480*a^2*b^3*Sqrt[a + b]*x^3*Sqrt[a + b*x] + 12*a^4*b*Sqrt[a + b]*x^(7/2)*Sqrt[a + b*x] + 65*a^3*b^2*Sqrt[a + b]*x^(7/2)*Sqrt[a + b*x] + 162*a^2*b^3*Sqrt[a + b]*x^(7/2)*Sqrt[a + b*x] - 5*a^3*b^2*Sqrt[a + b]*x^4*Sqrt[a + b*x] - 40*a^2*b^3*Sqrt[a + b]*x^4*Sqrt[a + b*x] + a^3*b^2*Sqrt[a + b]*x^(9/2)*Sqrt[a + b*x] + 4*a^2*b^3*Sqrt[a + b]*x^(9/2)*Sqrt[a + b*x]))/(x^(3/2)*(4*a^2 + 4*a*b - 2*a^2*Sqrt[x] - a*b*Sqrt[x] + 2*b^2*Sqrt[x] + 2*a*b*x - a*b*x^(3/2) - 4*a*Sqrt[a + b]*Sqrt[a + b*x] - 2*b*Sqrt[a + b]*Sqrt[a + b*x] + 2*a*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x])^3) - 4*b^(3/2)*ArcTanh[(Sqrt[a + b]/Sqrt[b] - Sqrt[a + b*x]/Sqrt[b])/(-1 + Sqrt[x])]","B",1
527,1,4226,149,8.264482,"\int x^{5/2} (a-b x)^{3/2} \, dx","IntegrateAlgebraic[x^(5/2)*(a - b*x)^(3/2),x]","\text{Result too large to show}","\frac{3 a^5 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)}{128 b^{7/2}}-\frac{3 a^4 \sqrt{x} \sqrt{a-b x}}{128 b^3}-\frac{a^3 x^{3/2} \sqrt{a-b x}}{64 b^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,"((7680*a^14 - 17920*a^13*b + 14176*a^12*b^2 - 97920*a^11*b^3 + 343670*a^10*b^4 - 500210*a^9*b^5 + 364780*a^8*b^6 - 136496*a^7*b^7 + 23520*a^6*b^8 - 1280*a^5*b^9)*Sqrt[a - b*x] + (-7680*a^14 - 19200*a^13*b + 63200*a^12*b^2 - 47280*a^11*b^3 + 479330*a^10*b^4 - 1599895*a^9*b^5 + 2130450*a^8*b^6 - 1376620*a^7*b^7 + 430640*a^6*b^8 - 54240*a^5*b^9 + 1280*a^4*b^10)*Sqrt[x]*Sqrt[a - b*x] + (23040*a^13*b + 40640*a^12*b^2 - 130752*a^11*b^3 + 268280*a^10*b^4 - 1811170*a^9*b^5 + 4521120*a^8*b^6 - 4978720*a^7*b^7 + 2665472*a^6*b^8 - 648960*a^5*b^9 + 51200*a^4*b^10)*x*Sqrt[a - b*x] + (14080*a^13*b - 59200*a^12*b^2 - 63600*a^11*b^3 + 184840*a^10*b^4 - 906025*a^9*b^5 + 4473620*a^8*b^6 - 8592240*a^7*b^7 + 7671040*a^6*b^8 - 3278720*a^5*b^9 + 576000*a^4*b^10 - 20480*a^3*b^11)*x^(3/2)*Sqrt[a - b*x] + (-50720*a^12*b^2 + 113280*a^11*b^3 + 72756*a^10*b^4 - 309780*a^9*b^5 + 2178060*a^8*b^6 - 7710240*a^7*b^7 + 11577600*a^6*b^8 - 8288256*a^5*b^9 + 2726400*a^4*b^10 - 307200*a^3*b^11)*x^2*Sqrt[a - b*x] + (-8096*a^12*b^2 + 105840*a^11*b^3 - 160260*a^10*b^4 - 60630*a^9*b^5 + 575670*a^8*b^6 - 3608388*a^7*b^7 + 9494400*a^6*b^8 - 11293440*a^5*b^9 + 6408960*a^4*b^10 - 1543680*a^3*b^11 + 86016*a^2*b^12)*x^(5/2)*Sqrt[a - b*x] + (25280*a^11*b^3 - 147880*a^10*b^4 + 168060*a^9*b^5 + 65600*a^8*b^6 - 874000*a^7*b^7 + 4131840*a^6*b^8 - 8381440*a^5*b^9 + 7976960*a^4*b^10 - 3532800*a^3*b^11 + 573440*a^2*b^12)*x^3*Sqrt[a - b*x] + (95152*a^11*b^3 - 272920*a^10*b^4 + 347550*a^9*b^5 - 203240*a^8*b^6 - 79240*a^7*b^7 + 901376*a^6*b^8 - 3217920*a^5*b^9 + 5201920*a^4*b^10 - 3998720*a^3*b^11 + 1351680*a^2*b^12 - 131072*a*b^13)*x^(7/2)*Sqrt[a - b*x] + (-471290*a^10*b^4 + 1087750*a^9*b^5 - 883260*a^8*b^6 + 290800*a^7*b^7 + 64000*a^6*b^8 - 568320*a^5*b^9 + 1600000*a^4*b^10 - 2140160*a^3*b^11 + 1351680*a^2*b^12 - 327680*a*b^13)*x^4*Sqrt[a - b*x] + (-296526*a^10*b^4 + 1855325*a^9*b^5 - 2888450*a^8*b^6 + 1658620*a^7*b^7 - 334080*a^6*b^8 - 23808*a^5*b^9 + 174080*a^4*b^10 - 412160*a^3*b^11 + 491520*a^2*b^12 - 286720*a*b^13 + 65536*b^14)*x^(9/2)*Sqrt[a - b*x] + (1365350*a^9*b^5 - 4740000*a^8*b^6 + 5224416*a^7*b^7 - 2104320*a^6*b^8 + 238080*a^5*b^9)*x^5*Sqrt[a - b*x] + (363675*a^9*b^5 - 3873900*a^8*b^6 + 8496720*a^7*b^7 - 6647040*a^6*b^8 + 1770240*a^5*b^9 - 80640*a^4*b^10)*x^(11/2)*Sqrt[a - b*x] + (-1506300*a^8*b^6 + 7419360*a^7*b^7 - 11012352*a^6*b^8 + 6005760*a^5*b^9 - 934400*a^4*b^10)*x^6*Sqrt[a - b*x] + (-214150*a^8*b^6 + 3441140*a^7*b^7 - 10119040*a^6*b^8 + 10443520*a^5*b^9 - 3795200*a^4*b^10 + 253440*a^3*b^11)*x^(13/2)*Sqrt[a - b*x] + (764880*a^7*b^7 - 5176320*a^6*b^8 + 10054656*a^5*b^9 - 7219200*a^4*b^10 + 1587200*a^3*b^11)*x^7*Sqrt[a - b*x] + (60008*a^7*b^7 - 1390720*a^6*b^8 + 5434880*a^5*b^9 - 7308800*a^4*b^10 + 3558400*a^3*b^11 - 372736*a^2*b^12)*x^(15/2)*Sqrt[a - b*x] + (-169440*a^6*b^8 + 1578240*a^5*b^9 - 4047360*a^4*b^10 + 3840000*a^3*b^11 - 1187840*a^2*b^12)*x^8*Sqrt[a - b*x] + (-6576*a^6*b^8 + 219360*a^5*b^9 - 1171200*a^4*b^10 + 2112000*a^3*b^11 - 1413120*a^2*b^12 + 253952*a*b^13)*x^(17/2)*Sqrt[a - b*x] + (11520*a^5*b^9 - 153600*a^4*b^10 + 552960*a^3*b^11 - 737280*a^2*b^12 + 327680*a*b^13)*x^9*Sqrt[a - b*x] + (128*a^5*b^9 - 6400*a^4*b^10 + 51200*a^3*b^11 - 143360*a^2*b^12 + 163840*a*b^13 - 65536*b^14)*x^(19/2)*Sqrt[a - b*x] + Sqrt[a - b]*(-7680*a^14 + 14080*a^13*b - 8096*a^12*b^2 + 95152*a^11*b^3 - 296526*a^10*b^4 + 363675*a^9*b^5 - 214150*a^8*b^6 + 60008*a^7*b^7 - 6576*a^6*b^8 + 128*a^5*b^9 + (7680*a^14 + 23040*a^13*b - 50720*a^12*b^2 + 25280*a^11*b^3 - 471290*a^10*b^4 + 1365350*a^9*b^5 - 1506300*a^8*b^6 + 764880*a^7*b^7 - 169440*a^6*b^8 + 11520*a^5*b^9)*Sqrt[x] + (-19200*a^13*b - 59200*a^12*b^2 + 105840*a^11*b^3 - 272920*a^10*b^4 + 1855325*a^9*b^5 - 3873900*a^8*b^6 + 3441140*a^7*b^7 - 1390720*a^6*b^8 + 219360*a^5*b^9 - 6400*a^4*b^10)*x + (-17920*a^13*b + 40640*a^12*b^2 + 113280*a^11*b^3 - 147880*a^10*b^4 + 1087750*a^9*b^5 - 4740000*a^8*b^6 + 7419360*a^7*b^7 - 5176320*a^6*b^8 + 1578240*a^5*b^9 - 153600*a^4*b^10)*x^(3/2) + (63200*a^12*b^2 - 63600*a^11*b^3 - 160260*a^10*b^4 + 347550*a^9*b^5 - 2888450*a^8*b^6 + 8496720*a^7*b^7 - 10119040*a^6*b^8 + 5434880*a^5*b^9 - 1171200*a^4*b^10 + 51200*a^3*b^11)*x^2 + (14176*a^12*b^2 - 130752*a^11*b^3 + 72756*a^10*b^4 + 168060*a^9*b^5 - 883260*a^8*b^6 + 5224416*a^7*b^7 - 11012352*a^6*b^8 + 10054656*a^5*b^9 - 4047360*a^4*b^10 + 552960*a^3*b^11)*x^(5/2) + (-47280*a^11*b^3 + 184840*a^10*b^4 - 60630*a^9*b^5 - 203240*a^8*b^6 + 1658620*a^7*b^7 - 6647040*a^6*b^8 + 10443520*a^5*b^9 - 7308800*a^4*b^10 + 2112000*a^3*b^11 - 143360*a^2*b^12)*x^3 + (-97920*a^11*b^3 + 268280*a^10*b^4 - 309780*a^9*b^5 + 65600*a^8*b^6 + 290800*a^7*b^7 - 2104320*a^6*b^8 + 6005760*a^5*b^9 - 7219200*a^4*b^10 + 3840000*a^3*b^11 - 737280*a^2*b^12)*x^(7/2) + (479330*a^10*b^4 - 906025*a^9*b^5 + 575670*a^8*b^6 - 79240*a^7*b^7 - 334080*a^6*b^8 + 1770240*a^5*b^9 - 3795200*a^4*b^10 + 3558400*a^3*b^11 - 1413120*a^2*b^12 + 163840*a*b^13)*x^4 + (343670*a^10*b^4 - 1811170*a^9*b^5 + 2178060*a^8*b^6 - 874000*a^7*b^7 + 64000*a^6*b^8 + 238080*a^5*b^9 - 934400*a^4*b^10 + 1587200*a^3*b^11 - 1187840*a^2*b^12 + 327680*a*b^13)*x^(9/2) + (-1599895*a^9*b^5 + 4473620*a^8*b^6 - 3608388*a^7*b^7 + 901376*a^6*b^8 - 23808*a^5*b^9 - 80640*a^4*b^10 + 253440*a^3*b^11 - 372736*a^2*b^12 + 253952*a*b^13 - 65536*b^14)*x^5 + (-500210*a^9*b^5 + 4521120*a^8*b^6 - 7710240*a^7*b^7 + 4131840*a^6*b^8 - 568320*a^5*b^9)*x^(11/2) + (2130450*a^8*b^6 - 8592240*a^7*b^7 + 9494400*a^6*b^8 - 3217920*a^5*b^9 + 174080*a^4*b^10)*x^6 + (364780*a^8*b^6 - 4978720*a^7*b^7 + 11577600*a^6*b^8 - 8381440*a^5*b^9 + 1600000*a^4*b^10)*x^(13/2) + (-1376620*a^7*b^7 + 7671040*a^6*b^8 - 11293440*a^5*b^9 + 5201920*a^4*b^10 - 412160*a^3*b^11)*x^7 + (-136496*a^7*b^7 + 2665472*a^6*b^8 - 8288256*a^5*b^9 + 7976960*a^4*b^10 - 2140160*a^3*b^11)*x^(15/2) + (430640*a^6*b^8 - 3278720*a^5*b^9 + 6408960*a^4*b^10 - 3998720*a^3*b^11 + 491520*a^2*b^12)*x^8 + (23520*a^6*b^8 - 648960*a^5*b^9 + 2726400*a^4*b^10 - 3532800*a^3*b^11 + 1351680*a^2*b^12)*x^(17/2) + (-54240*a^5*b^9 + 576000*a^4*b^10 - 1543680*a^3*b^11 + 1351680*a^2*b^12 - 286720*a*b^13)*x^9 + (-1280*a^5*b^9 + 51200*a^4*b^10 - 307200*a^3*b^11 + 573440*a^2*b^12 - 327680*a*b^13)*x^(19/2) + (1280*a^4*b^10 - 20480*a^3*b^11 + 86016*a^2*b^12 - 131072*a*b^13 + 65536*b^14)*x^10))/(640*b^3*(512*a^10 - 1280*a^9*b + 1120*a^8*b^2 - 400*a^7*b^3 + 50*a^6*b^4 - a^5*b^5) + 640*b^3*(-(a^5*b^5) + 50*a^4*b^6 - 400*a^3*b^7 + 1120*a^2*b^8 - 1280*a*b^9 + 512*b^10)*x^5 + 640*Sqrt[a - b]*b^3*(-512*a^9 + 1024*a^8*b - 672*a^7*b^2 + 160*a^6*b^3 - 10*a^5*b^4)*Sqrt[a - b*x] + Sqrt[x]*(640*b^3*(-2560*a^9*b + 5760*a^8*b^2 - 4320*a^7*b^3 + 1200*a^6*b^4 - 90*a^5*b^5) + 640*Sqrt[a - b]*b^3*(2560*a^8*b - 4480*a^7*b^2 + 2400*a^6*b^3 - 400*a^5*b^4 + 10*a^4*b^5)*Sqrt[a - b*x]) + x*(640*b^3*(-1280*a^9*b + 9280*a^8*b^2 - 14960*a^7*b^3 + 8600*a^6*b^4 - 1645*a^5*b^5 + 50*a^4*b^6) + 640*Sqrt[a - b]*b^3*(1024*a^8*b - 8128*a^7*b^2 + 10464*a^6*b^3 - 4120*a^5*b^4 + 400*a^4*b^5)*Sqrt[a - b*x]) + x^2*(640*b^3*(1120*a^8*b^2 - 14960*a^7*b^3 + 36460*a^6*b^4 - 30610*a^5*b^5 + 8600*a^4*b^6 - 400*a^3*b^7) + 640*Sqrt[a - b]*b^3*(-672*a^7*b^2 + 10464*a^6*b^3 - 24252*a^5*b^4 + 15600*a^4*b^5 - 2400*a^3*b^6)*Sqrt[a - b*x]) + x^(3/2)*(640*b^3*(5760*a^8*b^2 - 22080*a^7*b^3 + 25680*a^6*b^4 - 10680*a^5*b^5 + 1200*a^4*b^6) + 640*Sqrt[a - b]*b^3*(-4480*a^7*b^2 + 16960*a^6*b^3 - 15600*a^5*b^4 + 4120*a^4*b^5 - 160*a^3*b^6)*Sqrt[a - b*x]) + x^(5/2)*(640*b^3*(-4320*a^7*b^3 + 25680*a^6*b^4 - 42972*a^5*b^5 + 25680*a^4*b^6 - 4320*a^3*b^7) + 640*Sqrt[a - b]*b^3*(2400*a^6*b^3 - 15600*a^5*b^4 + 24252*a^4*b^5 - 10464*a^3*b^6 + 672*a^2*b^7)*Sqrt[a - b*x]) + x^3*(640*b^3*(-400*a^7*b^3 + 8600*a^6*b^4 - 30610*a^5*b^5 + 36460*a^4*b^6 - 14960*a^3*b^7 + 1120*a^2*b^8) + 640*Sqrt[a - b]*b^3*(160*a^6*b^3 - 4120*a^5*b^4 + 15600*a^4*b^5 - 16960*a^3*b^6 + 4480*a^2*b^7)*Sqrt[a - b*x]) + x^4*(640*b^3*(50*a^6*b^4 - 1645*a^5*b^5 + 8600*a^4*b^6 - 14960*a^3*b^7 + 9280*a^2*b^8 - 1280*a*b^9) + 640*Sqrt[a - b]*b^3*(-10*a^5*b^4 + 400*a^4*b^5 - 2400*a^3*b^6 + 4480*a^2*b^7 - 2560*a*b^8)*Sqrt[a - b*x]) + x^(7/2)*(640*b^3*(1200*a^6*b^4 - 10680*a^5*b^5 + 25680*a^4*b^6 - 22080*a^3*b^7 + 5760*a^2*b^8) + 640*Sqrt[a - b]*b^3*(-400*a^5*b^4 + 4120*a^4*b^5 - 10464*a^3*b^6 + 8128*a^2*b^7 - 1024*a*b^8)*Sqrt[a - b*x]) + x^(9/2)*(640*b^3*(-90*a^5*b^5 + 1200*a^4*b^6 - 4320*a^3*b^7 + 5760*a^2*b^8 - 2560*a*b^9) + 640*Sqrt[a - b]*b^3*(10*a^4*b^5 - 160*a^3*b^6 + 672*a^2*b^7 - 1024*a*b^8 + 512*b^9)*Sqrt[a - b*x])) + (3*a^5*ArcTan[(Sqrt[a - b]/Sqrt[b] - Sqrt[a - b*x]/Sqrt[b])/(-1 + Sqrt[x])])/(64*b^(7/2))","B",1
528,1,2862,124,3.9355072,"\int x^{3/2} (a-b x)^{3/2} \, dx","IntegrateAlgebraic[x^(3/2)*(a - b*x)^(3/2),x]","\text{Result too large to show}","\frac{3 a^4 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)}{64 b^{5/2}}-\frac{3 a^3 \sqrt{x} \sqrt{a-b x}}{64 b^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,"((384*a^11 - 704*a^10*b - 2896*a^9*b^2 + 10008*a^8*b^3 - 11800*a^7*b^4 + 6480*a^6*b^5 - 1600*a^5*b^6 + 128*a^4*b^7)*Sqrt[a - b*x] + (-384*a^11 - 768*a^10*b + 1952*a^9*b^2 + 12192*a^8*b^3 - 36907*a^7*b^4 + 38776*a^6*b^5 - 18128*a^5*b^6 + 3392*a^4*b^7 - 128*a^3*b^8)*Sqrt[x]*Sqrt[a - b*x] + (960*a^10*b + 1248*a^9*b^2 + 1848*a^8*b^3 - 38640*a^7*b^4 + 80880*a^6*b^5 - 68160*a^5*b^6 + 24960*a^4*b^7 - 3072*a^3*b^8)*x*Sqrt[a - b*x] + (512*a^10*b - 1984*a^9*b^2 - 1440*a^8*b^3 - 13228*a^7*b^4 + 74294*a^6*b^5 - 115040*a^5*b^6 + 76000*a^4*b^7 - 20480*a^3*b^8 + 1280*a^2*b^9)*x^(3/2)*Sqrt[a - b*x] + (-1424*a^9*b^2 + 2952*a^8*b^3 - 896*a^7*b^4 + 28672*a^6*b^5 - 93760*a^5*b^6 + 110720*a^4*b^7 - 56320*a^3*b^8 + 10240*a^2*b^9)*x^2*Sqrt[a - b*x] + (3104*a^9*b^2 - 4384*a^8*b^3 + 982*a^7*b^4 + 3472*a^6*b^5 - 34328*a^5*b^6 + 78528*a^4*b^7 - 72192*a^3*b^8 + 27648*a^2*b^9 - 3072*a*b^10)*x^(5/2)*Sqrt[a - b*x] + (-12760*a^8*b^3 + 20912*a^7*b^4 - 8960*a^6*b^5 - 3584*a^5*b^6 + 23936*a^4*b^7 - 41984*a^3*b^8 + 30720*a^2*b^9 - 8192*a*b^10)*x^3*Sqrt[a - b*x] + (-8416*a^8*b^3 + 41156*a^7*b^4 - 46308*a^6*b^5 + 14560*a^5*b^6 + 1488*a^4*b^7 - 8192*a^3*b^8 + 12288*a^2*b^9 - 8192*a*b^10 + 2048*b^11)*x^(7/2)*Sqrt[a - b*x] + (30424*a^7*b^4 - 81872*a^6*b^5 + 62272*a^5*b^6 - 11904*a^4*b^7)*x^4*Sqrt[a - b*x] + (7997*a^7*b^4 - 66904*a^6*b^5 + 109680*a^5*b^6 - 54080*a^4*b^7 + 4480*a^3*b^8)*x^(9/2)*Sqrt[a - b*x] + (-25200*a^6*b^5 + 96320*a^5*b^6 - 101248*a^4*b^7 + 29696*a^3*b^8)*x^5*Sqrt[a - b*x] + (-3330*a^6*b^5 + 42720*a^5*b^6 - 94880*a^4*b^7 + 64000*a^3*b^8 - 8960*a^2*b^9)*x^(11/2)*Sqrt[a - b*x] + (8512*a^5*b^6 - 45696*a^4*b^7 + 64512*a^3*b^8 - 26624*a^2*b^9)*x^6*Sqrt[a - b*x] + (536*a^5*b^6 - 10432*a^4*b^7 + 32000*a^3*b^8 - 29696*a^2*b^9 + 7168*a*b^10)*x^(13/2)*Sqrt[a - b*x] + (-896*a^4*b^7 + 7168*a^3*b^8 - 14336*a^2*b^9 + 8192*a*b^10)*x^7*Sqrt[a - b*x] + (-16*a^4*b^7 + 512*a^3*b^8 - 2560*a^2*b^9 + 4096*a*b^10 - 2048*b^11)*x^(15/2)*Sqrt[a - b*x] + Sqrt[a - b]*(-384*a^11 + 512*a^10*b + 3104*a^9*b^2 - 8416*a^8*b^3 + 7997*a^7*b^4 - 3330*a^6*b^5 + 536*a^5*b^6 - 16*a^4*b^7 + (384*a^11 + 960*a^10*b - 1424*a^9*b^2 - 12760*a^8*b^3 + 30424*a^7*b^4 - 25200*a^6*b^5 + 8512*a^5*b^6 - 896*a^4*b^7)*Sqrt[x] + (-768*a^10*b - 1984*a^9*b^2 - 4384*a^8*b^3 + 41156*a^7*b^4 - 66904*a^6*b^5 + 42720*a^5*b^6 - 10432*a^4*b^7 + 512*a^3*b^8)*x + (-704*a^10*b + 1248*a^9*b^2 + 2952*a^8*b^3 + 20912*a^7*b^4 - 81872*a^6*b^5 + 96320*a^5*b^6 - 45696*a^4*b^7 + 7168*a^3*b^8)*x^(3/2) + (1952*a^9*b^2 - 1440*a^8*b^3 + 982*a^7*b^4 - 46308*a^6*b^5 + 109680*a^5*b^6 - 94880*a^4*b^7 + 32000*a^3*b^8 - 2560*a^2*b^9)*x^2 + (-2896*a^9*b^2 + 1848*a^8*b^3 - 896*a^7*b^4 - 8960*a^6*b^5 + 62272*a^5*b^6 - 101248*a^4*b^7 + 64512*a^3*b^8 - 14336*a^2*b^9)*x^(5/2) + (12192*a^8*b^3 - 13228*a^7*b^4 + 3472*a^6*b^5 + 14560*a^5*b^6 - 54080*a^4*b^7 + 64000*a^3*b^8 - 29696*a^2*b^9 + 4096*a*b^10)*x^3 + (10008*a^8*b^3 - 38640*a^7*b^4 + 28672*a^6*b^5 - 3584*a^5*b^6 - 11904*a^4*b^7 + 29696*a^3*b^8 - 26624*a^2*b^9 + 8192*a*b^10)*x^(7/2) + (-36907*a^7*b^4 + 74294*a^6*b^5 - 34328*a^5*b^6 + 1488*a^4*b^7 + 4480*a^3*b^8 - 8960*a^2*b^9 + 7168*a*b^10 - 2048*b^11)*x^4 + (-11800*a^7*b^4 + 80880*a^6*b^5 - 93760*a^5*b^6 + 23936*a^4*b^7)*x^(9/2) + (38776*a^6*b^5 - 115040*a^5*b^6 + 78528*a^4*b^7 - 8192*a^3*b^8)*x^5 + (6480*a^6*b^5 - 68160*a^5*b^6 + 110720*a^4*b^7 - 41984*a^3*b^8)*x^(11/2) + (-18128*a^5*b^6 + 76000*a^4*b^7 - 72192*a^3*b^8 + 12288*a^2*b^9)*x^6 + (-1600*a^5*b^6 + 24960*a^4*b^7 - 56320*a^3*b^8 + 30720*a^2*b^9)*x^(13/2) + (3392*a^4*b^7 - 20480*a^3*b^8 + 27648*a^2*b^9 - 8192*a*b^10)*x^7 + (128*a^4*b^7 - 3072*a^3*b^8 + 10240*a^2*b^9 - 8192*a*b^10)*x^(15/2) + (-128*a^3*b^8 + 1280*a^2*b^9 - 3072*a*b^10 + 2048*b^11)*x^8))/(64*b^2*(128*a^8 - 256*a^7*b + 160*a^6*b^2 - 32*a^5*b^3 + a^4*b^4) + 64*b^2*(a^4*b^4 - 32*a^3*b^5 + 160*a^2*b^6 - 256*a*b^7 + 128*b^8)*x^4 + 64*Sqrt[a - b]*b^2*(-128*a^7 + 192*a^6*b - 80*a^5*b^2 + 8*a^4*b^3)*Sqrt[a - b*x] + x*(64*b^2*(-256*a^7*b + 1472*a^6*b^2 - 1760*a^5*b^3 + 604*a^4*b^4 - 32*a^3*b^5) + 64*Sqrt[a - b]*b^2*(192*a^6*b - 1248*a^5*b^2 + 1080*a^4*b^3 - 192*a^3*b^4)*Sqrt[a - b*x]) + Sqrt[x]*(64*b^2*(-512*a^7*b + 896*a^6*b^2 - 448*a^5*b^3 + 56*a^4*b^4) + 64*Sqrt[a - b]*b^2*(512*a^6*b - 640*a^5*b^2 + 192*a^4*b^3 - 8*a^3*b^4)*Sqrt[a - b*x]) + x^(3/2)*(64*b^2*(896*a^6*b^2 - 2688*a^5*b^3 + 2184*a^4*b^4 - 448*a^3*b^5) + 64*Sqrt[a - b]*b^2*(-640*a^5*b^2 + 1920*a^4*b^3 - 1080*a^3*b^4 + 80*a^2*b^5)*Sqrt[a - b*x]) + x^2*(64*b^2*(160*a^6*b^2 - 1760*a^5*b^3 + 3270*a^4*b^4 - 1760*a^3*b^5 + 160*a^2*b^6) + 64*Sqrt[a - b]*b^2*(-80*a^5*b^2 + 1080*a^4*b^3 - 1920*a^3*b^4 + 640*a^2*b^5)*Sqrt[a - b*x]) + x^3*(64*b^2*(-32*a^5*b^3 + 604*a^4*b^4 - 1760*a^3*b^5 + 1472*a^2*b^6 - 256*a*b^7) + 64*Sqrt[a - b]*b^2*(8*a^4*b^3 - 192*a^3*b^4 + 640*a^2*b^5 - 512*a*b^6)*Sqrt[a - b*x]) + x^(5/2)*(64*b^2*(-448*a^5*b^3 + 2184*a^4*b^4 - 2688*a^3*b^5 + 896*a^2*b^6) + 64*Sqrt[a - b]*b^2*(192*a^4*b^3 - 1080*a^3*b^4 + 1248*a^2*b^5 - 192*a*b^6)*Sqrt[a - b*x]) + x^(7/2)*(64*b^2*(56*a^4*b^4 - 448*a^3*b^5 + 896*a^2*b^6 - 512*a*b^7) + 64*Sqrt[a - b]*b^2*(-8*a^3*b^4 + 80*a^2*b^5 - 192*a*b^6 + 128*b^7)*Sqrt[a - b*x])) + (3*a^4*ArcTan[(Sqrt[a - b]/Sqrt[b] - Sqrt[a - b*x]/Sqrt[b])/(-1 + Sqrt[x])])/(32*b^(5/2))","B",1
529,1,1732,99,2.2894702,"\int \sqrt{x} (a-b x)^{3/2} \, dx","IntegrateAlgebraic[Sqrt[x]*(a - b*x)^(3/2),x]","\frac{\tan ^{-1}\left(\frac{\frac{\sqrt{a-b}}{\sqrt{b}}-\frac{\sqrt{a-b x}}{\sqrt{b}}}{\sqrt{x}-1}\right) a^3}{4 b^{3/2}}+\frac{\left(-256 b^8+384 a b^7-144 a^2 b^6+8 a^3 b^5\right) \sqrt{a-b x} x^{11/2}+\left(768 a b^7-960 a^2 b^6+240 a^3 b^5\right) \sqrt{a-b x} x^5+\left(832 a b^7-2304 a^2 b^6+1524 a^3 b^5-158 a^4 b^4\right) \sqrt{a-b x} x^{9/2}+\left(-2304 a^2 b^6+3760 a^3 b^5-1380 a^4 b^4\right) \sqrt{a-b x} x^4+\left(-912 a^2 b^6+4272 a^3 b^5-3912 a^4 b^4+639 a^5 b^3\right) \sqrt{a-b x} x^{7/2}+\left(2538 b^3 a^5-4960 b^4 a^4+2208 b^5 a^3\right) \sqrt{a-b x} x^3+\left(256 b^8-960 a b^7+1296 a^2 b^6-368 a^3 b^5-2784 a^4 b^4+3699 a^5 b^3-982 a^6 b^2\right) \sqrt{a-b x} x^{5/2}+\left(-768 a b^7+2688 a^2 b^6-3264 a^3 b^5+864 a^4 b^4+2142 a^5 b^3-1686 a^6 b^2\right) \sqrt{a-b x} x^2+\left(592 b a^7-1068 b^2 a^6-987 b^3 a^5+4400 b^4 a^4-4728 b^5 a^3+2016 b^6 a^2-256 b^7 a\right) \sqrt{a-b x} x^{3/2}+\left(192 b a^7+676 b^2 a^6-3618 b^3 a^5+5088 b^4 a^4-2896 b^5 a^3+576 b^6 a^2\right) \sqrt{a-b x} x+\left(-96 a^8-144 b a^7+1794 b^2 a^6-3351 b^3 a^5+2454 b^4 a^4-708 b^5 a^3+48 b^6 a^2\right) \sqrt{a-b x} \sqrt{x}+\sqrt{a-b} \left(-96 a^8+592 b a^7-982 b^2 a^6+639 b^3 a^5-158 b^4 a^4+8 b^5 a^3+\left(256 b^8-256 a b^7+48 a^2 b^6\right) x^6+\left(-768 a b^7+576 a^2 b^6-48 a^3 b^5\right) x^{11/2}+\left(-960 a b^7+2016 a^2 b^6-708 a^3 b^5\right) x^5+\left(2688 a^2 b^6-2896 a^3 b^5+388 a^4 b^4\right) x^{9/2}+\left(1296 a^2 b^6-4728 a^3 b^5+2454 a^4 b^4\right) x^4+\left(-1062 b^3 a^5+5088 b^4 a^4-3264 b^5 a^3\right) x^{7/2}+\left(-256 b^8+832 a b^7-912 a^2 b^6-368 a^3 b^5+4400 a^4 b^4-3351 a^5 b^3\right) x^3+\left(768 a b^7-2304 a^2 b^6+2208 a^3 b^5+864 a^4 b^4-3618 a^5 b^3+1266 a^6 b^2\right) x^{5/2}+\left(384 a b^7-2304 a^2 b^6+4272 a^3 b^5-2784 a^4 b^4-987 a^5 b^3+1794 a^6 b^2\right) x^2+\left(-640 b a^7+676 b^2 a^6+2142 b^3 a^5-4960 b^4 a^4+3760 b^5 a^3-960 b^6 a^2\right) x^{3/2}+\left(-144 b a^7-1068 b^2 a^6+3699 b^3 a^5-3912 b^4 a^4+1524 b^5 a^3-144 b^6 a^2\right) x+\left(96 a^8+192 b a^7-1686 b^2 a^6+2538 b^3 a^5-1380 b^4 a^4+240 b^5 a^3\right) \sqrt{x}\right)+\left(96 a^8-640 b a^7+1266 b^2 a^6-1062 b^3 a^5+388 b^4 a^4-48 b^5 a^3\right) \sqrt{a-b x}}{24 b \left(32 b^6-48 a b^5+18 a^2 b^4-a^3 b^3\right) x^3+\left(24 \sqrt{a-b} b \sqrt{a-b x} \left(32 b^5-32 a b^4+6 a^2 b^3\right)+24 b \left(-96 a b^5+120 a^2 b^4-30 a^3 b^3\right)\right) x^{5/2}+\left(24 \sqrt{a-b} b \sqrt{a-b x} \left(-96 a b^4+72 a^2 b^3-6 a^3 b^2\right)+24 b \left(-48 a b^5+204 a^2 b^4-159 a^3 b^3+18 a^4 b^2\right)\right) x^2+\left(24 \sqrt{a-b} b \sqrt{a-b x} \left(-32 a b^4+164 a^2 b^3-72 a^3 b^2\right)+24 b \left(120 b^2 a^4-260 b^3 a^3+120 b^4 a^2\right)\right) x^{3/2}+\left(24 \sqrt{a-b} b \sqrt{a-b x} \left(32 b a^4-164 b^2 a^3+72 b^3 a^2\right)+24 b \left(-48 b a^5+204 b^2 a^4-159 b^3 a^3+18 b^4 a^2\right)\right) x+\left(24 \sqrt{a-b} b \sqrt{a-b x} \left(96 b a^4-72 b^2 a^3+6 b^3 a^2\right)+24 b \left(-96 b a^5+120 b^2 a^4-30 b^3 a^3\right)\right) \sqrt{x}+24 b \left(32 a^6-48 b a^5+18 b^2 a^4-b^3 a^3\right)+24 \sqrt{a-b} b \left(-32 a^5+32 b a^4-6 b^2 a^3\right) \sqrt{a-b 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}",1,"((96*a^8 - 640*a^7*b + 1266*a^6*b^2 - 1062*a^5*b^3 + 388*a^4*b^4 - 48*a^3*b^5)*Sqrt[a - b*x] + (-96*a^8 - 144*a^7*b + 1794*a^6*b^2 - 3351*a^5*b^3 + 2454*a^4*b^4 - 708*a^3*b^5 + 48*a^2*b^6)*Sqrt[x]*Sqrt[a - b*x] + (192*a^7*b + 676*a^6*b^2 - 3618*a^5*b^3 + 5088*a^4*b^4 - 2896*a^3*b^5 + 576*a^2*b^6)*x*Sqrt[a - b*x] + (592*a^7*b - 1068*a^6*b^2 - 987*a^5*b^3 + 4400*a^4*b^4 - 4728*a^3*b^5 + 2016*a^2*b^6 - 256*a*b^7)*x^(3/2)*Sqrt[a - b*x] + (-1686*a^6*b^2 + 2142*a^5*b^3 + 864*a^4*b^4 - 3264*a^3*b^5 + 2688*a^2*b^6 - 768*a*b^7)*x^2*Sqrt[a - b*x] + (-982*a^6*b^2 + 3699*a^5*b^3 - 2784*a^4*b^4 - 368*a^3*b^5 + 1296*a^2*b^6 - 960*a*b^7 + 256*b^8)*x^(5/2)*Sqrt[a - b*x] + (2538*a^5*b^3 - 4960*a^4*b^4 + 2208*a^3*b^5)*x^3*Sqrt[a - b*x] + (639*a^5*b^3 - 3912*a^4*b^4 + 4272*a^3*b^5 - 912*a^2*b^6)*x^(7/2)*Sqrt[a - b*x] + (-1380*a^4*b^4 + 3760*a^3*b^5 - 2304*a^2*b^6)*x^4*Sqrt[a - b*x] + (-158*a^4*b^4 + 1524*a^3*b^5 - 2304*a^2*b^6 + 832*a*b^7)*x^(9/2)*Sqrt[a - b*x] + (240*a^3*b^5 - 960*a^2*b^6 + 768*a*b^7)*x^5*Sqrt[a - b*x] + (8*a^3*b^5 - 144*a^2*b^6 + 384*a*b^7 - 256*b^8)*x^(11/2)*Sqrt[a - b*x] + Sqrt[a - b]*(-96*a^8 + 592*a^7*b - 982*a^6*b^2 + 639*a^5*b^3 - 158*a^4*b^4 + 8*a^3*b^5 + (96*a^8 + 192*a^7*b - 1686*a^6*b^2 + 2538*a^5*b^3 - 1380*a^4*b^4 + 240*a^3*b^5)*Sqrt[x] + (-144*a^7*b - 1068*a^6*b^2 + 3699*a^5*b^3 - 3912*a^4*b^4 + 1524*a^3*b^5 - 144*a^2*b^6)*x + (-640*a^7*b + 676*a^6*b^2 + 2142*a^5*b^3 - 4960*a^4*b^4 + 3760*a^3*b^5 - 960*a^2*b^6)*x^(3/2) + (1794*a^6*b^2 - 987*a^5*b^3 - 2784*a^4*b^4 + 4272*a^3*b^5 - 2304*a^2*b^6 + 384*a*b^7)*x^2 + (1266*a^6*b^2 - 3618*a^5*b^3 + 864*a^4*b^4 + 2208*a^3*b^5 - 2304*a^2*b^6 + 768*a*b^7)*x^(5/2) + (-3351*a^5*b^3 + 4400*a^4*b^4 - 368*a^3*b^5 - 912*a^2*b^6 + 832*a*b^7 - 256*b^8)*x^3 + (-1062*a^5*b^3 + 5088*a^4*b^4 - 3264*a^3*b^5)*x^(7/2) + (2454*a^4*b^4 - 4728*a^3*b^5 + 1296*a^2*b^6)*x^4 + (388*a^4*b^4 - 2896*a^3*b^5 + 2688*a^2*b^6)*x^(9/2) + (-708*a^3*b^5 + 2016*a^2*b^6 - 960*a*b^7)*x^5 + (-48*a^3*b^5 + 576*a^2*b^6 - 768*a*b^7)*x^(11/2) + (48*a^2*b^6 - 256*a*b^7 + 256*b^8)*x^6))/(24*b*(32*a^6 - 48*a^5*b + 18*a^4*b^2 - a^3*b^3) + 24*b*(-(a^3*b^3) + 18*a^2*b^4 - 48*a*b^5 + 32*b^6)*x^3 + 24*Sqrt[a - b]*b*(-32*a^5 + 32*a^4*b - 6*a^3*b^2)*Sqrt[a - b*x] + Sqrt[x]*(24*b*(-96*a^5*b + 120*a^4*b^2 - 30*a^3*b^3) + 24*Sqrt[a - b]*b*(96*a^4*b - 72*a^3*b^2 + 6*a^2*b^3)*Sqrt[a - b*x]) + x*(24*b*(-48*a^5*b + 204*a^4*b^2 - 159*a^3*b^3 + 18*a^2*b^4) + 24*Sqrt[a - b]*b*(32*a^4*b - 164*a^3*b^2 + 72*a^2*b^3)*Sqrt[a - b*x]) + x^2*(24*b*(18*a^4*b^2 - 159*a^3*b^3 + 204*a^2*b^4 - 48*a*b^5) + 24*Sqrt[a - b]*b*(-6*a^3*b^2 + 72*a^2*b^3 - 96*a*b^4)*Sqrt[a - b*x]) + x^(3/2)*(24*b*(120*a^4*b^2 - 260*a^3*b^3 + 120*a^2*b^4) + 24*Sqrt[a - b]*b*(-72*a^3*b^2 + 164*a^2*b^3 - 32*a*b^4)*Sqrt[a - b*x]) + x^(5/2)*(24*b*(-30*a^3*b^3 + 120*a^2*b^4 - 96*a*b^5) + 24*Sqrt[a - b]*b*(6*a^2*b^3 - 32*a*b^4 + 32*b^5)*Sqrt[a - b*x])) + (a^3*ArcTan[(Sqrt[a - b]/Sqrt[b] - Sqrt[a - b*x]/Sqrt[b])/(-1 + Sqrt[x])])/(4*b^(3/2))","B",1
530,1,807,74,0.9236444,"\int \frac{(a-b x)^{3/2}}{\sqrt{x}} \, dx","IntegrateAlgebraic[(a - b*x)^(3/2)/Sqrt[x],x]","\frac{3 \tan ^{-1}\left(\frac{\frac{\sqrt{a-b}}{\sqrt{b}}-\frac{\sqrt{a-b x}}{\sqrt{b}}}{\sqrt{x}-1}\right) a^2}{2 \sqrt{b}}+\frac{\left(\frac{\sqrt{x}}{4}-\frac{1}{4}\right) \left(\sqrt{a-b}-\sqrt{a-b x}\right) \left(-20 a^5+33 b a^4+33 b x a^4+58 b \sqrt{x} a^4+20 \sqrt{a-b} \sqrt{a-b x} a^4-15 b^2 a^3-15 b^2 x^2 a^3-71 b^2 x^{3/2} a^3-112 b^2 x a^3-71 b^2 \sqrt{x} a^3-23 \sqrt{a-b} b \sqrt{a-b x} a^3-23 \sqrt{a-b} b x \sqrt{a-b x} a^3-58 \sqrt{a-b} b \sqrt{x} \sqrt{a-b x} a^3+2 b^3 a^2+2 b^3 x^3 a^2+18 b^3 x^{5/2} a^2+80 b^3 x^2 a^2+108 b^3 x^{3/2} a^2+80 b^3 x a^2+18 b^3 \sqrt{x} a^2+6 \sqrt{a-b} b^2 \sqrt{a-b x} a^2+6 \sqrt{a-b} b^2 x^2 \sqrt{a-b x} a^2+42 \sqrt{a-b} b^2 x^{3/2} \sqrt{a-b x} a^2+84 \sqrt{a-b} b^2 x \sqrt{a-b x} a^2+42 \sqrt{a-b} b^2 \sqrt{x} \sqrt{a-b x} a^2-16 b^4 x^3 a-24 b^4 x^{5/2} a-80 b^4 x^2 a-24 b^4 x^{3/2} a-16 b^4 x a-8 \sqrt{a-b} b^3 x^{5/2} \sqrt{a-b x} a-24 \sqrt{a-b} b^3 x^2 \sqrt{a-b x} a-64 \sqrt{a-b} b^3 x^{3/2} \sqrt{a-b x} a-24 \sqrt{a-b} b^3 x \sqrt{a-b x} a-8 \sqrt{a-b} b^3 \sqrt{x} \sqrt{a-b x} a+16 b^5 x^3+16 b^5 x^2+16 \sqrt{a-b} b^4 x^{5/2} \sqrt{a-b x}+16 \sqrt{a-b} b^4 x^{3/2} \sqrt{a-b x}\right)}{\left(-a+b \sqrt{x}+\sqrt{a-b} \sqrt{a-b x}\right)^4}","\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,"((-1/4 + Sqrt[x]/4)*(Sqrt[a - b] - Sqrt[a - b*x])*(-20*a^5 + 33*a^4*b - 15*a^3*b^2 + 2*a^2*b^3 + 58*a^4*b*Sqrt[x] - 71*a^3*b^2*Sqrt[x] + 18*a^2*b^3*Sqrt[x] + 33*a^4*b*x - 112*a^3*b^2*x + 80*a^2*b^3*x - 16*a*b^4*x - 71*a^3*b^2*x^(3/2) + 108*a^2*b^3*x^(3/2) - 24*a*b^4*x^(3/2) - 15*a^3*b^2*x^2 + 80*a^2*b^3*x^2 - 80*a*b^4*x^2 + 16*b^5*x^2 + 18*a^2*b^3*x^(5/2) - 24*a*b^4*x^(5/2) + 2*a^2*b^3*x^3 - 16*a*b^4*x^3 + 16*b^5*x^3 + 20*a^4*Sqrt[a - b]*Sqrt[a - b*x] - 23*a^3*Sqrt[a - b]*b*Sqrt[a - b*x] + 6*a^2*Sqrt[a - b]*b^2*Sqrt[a - b*x] - 58*a^3*Sqrt[a - b]*b*Sqrt[x]*Sqrt[a - b*x] + 42*a^2*Sqrt[a - b]*b^2*Sqrt[x]*Sqrt[a - b*x] - 8*a*Sqrt[a - b]*b^3*Sqrt[x]*Sqrt[a - b*x] - 23*a^3*Sqrt[a - b]*b*x*Sqrt[a - b*x] + 84*a^2*Sqrt[a - b]*b^2*x*Sqrt[a - b*x] - 24*a*Sqrt[a - b]*b^3*x*Sqrt[a - b*x] + 42*a^2*Sqrt[a - b]*b^2*x^(3/2)*Sqrt[a - b*x] - 64*a*Sqrt[a - b]*b^3*x^(3/2)*Sqrt[a - b*x] + 16*Sqrt[a - b]*b^4*x^(3/2)*Sqrt[a - b*x] + 6*a^2*Sqrt[a - b]*b^2*x^2*Sqrt[a - b*x] - 24*a*Sqrt[a - b]*b^3*x^2*Sqrt[a - b*x] - 8*a*Sqrt[a - b]*b^3*x^(5/2)*Sqrt[a - b*x] + 16*Sqrt[a - b]*b^4*x^(5/2)*Sqrt[a - b*x]))/(-a + b*Sqrt[x] + Sqrt[a - b]*Sqrt[a - b*x])^4 + (3*a^2*ArcTan[(Sqrt[a - b]/Sqrt[b] - Sqrt[a - b*x]/Sqrt[b])/(-1 + Sqrt[x])])/(2*Sqrt[b])","B",1
531,1,499,66,1.1689052,"\int \frac{(a-b x)^{3/2}}{x^{3/2}} \, dx","IntegrateAlgebraic[(a - b*x)^(3/2)/x^(3/2),x]","\frac{\left(2 a^2-2 a^2 \sqrt{x}\right) \left(-2 \sqrt{a-b} \sqrt{a-b x}+\sqrt{x} \sqrt{a-b} \sqrt{a-b x}+a \left(-\sqrt{x}\right)+2 a-b x+2 b \sqrt{x}-2 b\right) \left(\sqrt{a-b}-\sqrt{a-b x}\right)}{\sqrt{x} \left(-2 a^2 \sqrt{x}+4 a^2+a b x^{3/2}-2 a b x+a b \sqrt{x}-4 a \sqrt{a-b} \sqrt{a-b x}+2 a \sqrt{x} \sqrt{a-b} \sqrt{a-b x}+2 b \sqrt{a-b} \sqrt{a-b x}-4 a b+2 b^2 \sqrt{x}\right)}+\frac{\left(a b \sqrt{x}-2 b \sqrt{a-b} \sqrt{a-b x}+a b-2 b^2 \sqrt{x}\right) \left(\sqrt{a-b}-\sqrt{a-b x}\right)^3}{\left(\sqrt{a-b} \sqrt{a-b x}-a+b \sqrt{x}\right)^2}+\frac{\left(4 \sqrt{a-b} \sqrt{a-b x}+a \left(-\sqrt{x}\right)-3 a+2 b \sqrt{x}+2 b\right) \left(b \sqrt{a-b x}-b \sqrt{a-b}\right)}{\sqrt{a-b} \sqrt{a-b x}-a+b \sqrt{x}}-6 a \sqrt{b} \tan ^{-1}\left(\frac{\frac{\sqrt{a-b}}{\sqrt{b}}-\frac{\sqrt{a-b x}}{\sqrt{b}}}{\sqrt{x}-1}\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*a + 2*b - a*Sqrt[x] + 2*b*Sqrt[x] + 4*Sqrt[a - b]*Sqrt[a - b*x])*(-(Sqrt[a - b]*b) + b*Sqrt[a - b*x]))/(-a + b*Sqrt[x] + Sqrt[a - b]*Sqrt[a - b*x]) + ((Sqrt[a - b] - Sqrt[a - b*x])^3*(a*b + a*b*Sqrt[x] - 2*b^2*Sqrt[x] - 2*Sqrt[a - b]*b*Sqrt[a - b*x]))/(-a + b*Sqrt[x] + Sqrt[a - b]*Sqrt[a - b*x])^2 + ((2*a^2 - 2*a^2*Sqrt[x])*(Sqrt[a - b] - Sqrt[a - b*x])*(2*a - 2*b - a*Sqrt[x] + 2*b*Sqrt[x] - b*x - 2*Sqrt[a - b]*Sqrt[a - b*x] + Sqrt[a - b]*Sqrt[x]*Sqrt[a - b*x]))/(Sqrt[x]*(4*a^2 - 4*a*b - 2*a^2*Sqrt[x] + a*b*Sqrt[x] + 2*b^2*Sqrt[x] - 2*a*b*x + a*b*x^(3/2) - 4*a*Sqrt[a - b]*Sqrt[a - b*x] + 2*Sqrt[a - b]*b*Sqrt[a - b*x] + 2*a*Sqrt[a - b]*Sqrt[x]*Sqrt[a - b*x])) - 6*a*Sqrt[b]*ArcTan[(Sqrt[a - b]/Sqrt[b] - Sqrt[a - b*x]/Sqrt[b])/(-1 + Sqrt[x])]","B",1
532,1,1889,67,2.2667357,"\int \frac{(a-b x)^{3/2}}{x^{5/2}} \, dx","IntegrateAlgebraic[(a - b*x)^(3/2)/x^(5/2),x]","4 \tan ^{-1}\left(\frac{\frac{\sqrt{a-b}}{\sqrt{b}}-\frac{\sqrt{a-b x}}{\sqrt{b}}}{\sqrt{x}-1}\right) b^{3/2}+\frac{\left(\frac{2 a}{3}-\frac{2 a \sqrt{x}}{3}\right) \left(\sqrt{a-b}-\sqrt{a-b x}\right) \left(-16 x^{5/2} a^6+80 x^2 a^6-112 x^{3/2} a^6+32 x a^6-64 \sqrt{x} a^6+128 a^6+20 b x^{7/2} a^5-100 b x^3 a^5+232 b x^{5/2} a^5-620 b x^2 a^5+1228 b x^{3/2} a^5-352 b a^5-824 b x a^5+80 b \sqrt{x} a^5+16 \sqrt{a-b} x^{5/2} \sqrt{a-b x} a^5-80 \sqrt{a-b} x^2 \sqrt{a-b x} a^5+112 \sqrt{a-b} x^{3/2} \sqrt{a-b x} a^5-32 \sqrt{a-b} x \sqrt{a-b x} a^5-128 \sqrt{a-b} \sqrt{a-b x} a^5+64 \sqrt{a-b} \sqrt{x} \sqrt{a-b x} a^5-5 b^2 x^{9/2} a^4+25 b^2 x^4 a^4-145 b^2 x^{7/2} a^4+728 b^2 x^3 a^4-1635 b^2 x^{5/2} a^4+328 b^2 a^4+1965 b^2 x^2 a^4-2467 b^2 x^{3/2} a^4+2042 b^2 x a^4+124 b^2 \sqrt{x} a^4-12 \sqrt{a-b} b x^{7/2} \sqrt{a-b x} a^4+60 \sqrt{a-b} b x^3 \sqrt{a-b x} a^4-168 \sqrt{a-b} b x^{5/2} \sqrt{a-b x} a^4+564 \sqrt{a-b} b x^2 \sqrt{a-b x} a^4-1140 \sqrt{a-b} b x^{3/2} \sqrt{a-b x} a^4+288 \sqrt{a-b} b \sqrt{a-b x} a^4+744 \sqrt{a-b} b x \sqrt{a-b x} a^4-48 \sqrt{a-b} b \sqrt{x} \sqrt{a-b x} a^4+25 b^3 x^{9/2} a^3-184 b^3 x^4 a^3+570 b^3 x^{7/2} a^3-112 b^3 a^3-1386 b^3 x^3 a^3+2613 b^3 x^{5/2} a^3-2316 b^3 x^2 a^3+1412 b^3 x^{3/2} a^3-1842 b^3 x a^3-220 b^3 \sqrt{x} a^3+\sqrt{a-b} b^2 x^{9/2} \sqrt{a-b x} a^3-5 \sqrt{a-b} b^2 x^4 \sqrt{a-b x} a^3+65 \sqrt{a-b} b^2 x^{7/2} \sqrt{a-b x} a^3-400 \sqrt{a-b} b^2 x^3 \sqrt{a-b x} a^3+963 \sqrt{a-b} b^2 x^{5/2} \sqrt{a-b x} a^3-200 \sqrt{a-b} b^2 \sqrt{a-b x} a^3-1329 \sqrt{a-b} b^2 x^2 \sqrt{a-b x} a^3+1871 \sqrt{a-b} b^2 x^{3/2} \sqrt{a-b x} a^3-1498 \sqrt{a-b} b^2 x \sqrt{a-b x} a^3-140 \sqrt{a-b} b^2 \sqrt{x} \sqrt{a-b x} a^3+4 b^4 x^5 a^2-40 b^4 x^{9/2} a^2+8 b^4 a^2+198 b^4 x^4 a^2-480 b^4 x^{7/2} a^2+696 b^4 x^3 a^2-1188 b^4 x^{5/2} a^2+1078 b^4 x^2 a^2+180 b^4 x^{3/2} a^2+664 b^4 x a^2+80 b^4 \sqrt{x} a^2-4 \sqrt{a-b} b^3 x^{9/2} \sqrt{a-b x} a^2+40 \sqrt{a-b} b^3 x^4 \sqrt{a-b x} a^2-162 \sqrt{a-b} b^3 x^{7/2} \sqrt{a-b x} a^2+40 \sqrt{a-b} b^3 \sqrt{a-b x} a^2+480 \sqrt{a-b} b^3 x^3 \sqrt{a-b x} a^2-948 \sqrt{a-b} b^3 x^{5/2} \sqrt{a-b x} a^2+828 \sqrt{a-b} b^3 x^2 \sqrt{a-b x} a^2-674 \sqrt{a-b} b^3 x^{3/2} \sqrt{a-b x} a^2+1020 \sqrt{a-b} b^3 x \sqrt{a-b x} a^2+148 \sqrt{a-b} b^3 \sqrt{x} \sqrt{a-b x} a^2+72 b^5 x^3 a-288 b^5 x^2 a-240 b^5 x^{3/2} a-72 b^5 x a+72 \sqrt{a-b} b^4 x^{5/2} \sqrt{a-b x} a-240 \sqrt{a-b} b^4 x^{3/2} \sqrt{a-b x} a-240 \sqrt{a-b} b^4 x \sqrt{a-b x} a-24 \sqrt{a-b} b^4 \sqrt{x} \sqrt{a-b x} a+96 b^6 x^2+96 \sqrt{a-b} b^5 x^{3/2} \sqrt{a-b x}\right)}{x^{3/2} \left(-2 \sqrt{x} a^2+4 a^2+b x^{3/2} a-4 b a-2 b x a+b \sqrt{x} a-4 \sqrt{a-b} \sqrt{a-b x} a+2 \sqrt{a-b} \sqrt{x} \sqrt{a-b x} a+2 b^2 \sqrt{x}+2 \sqrt{a-b} b \sqrt{a-b x}\right)^3}","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*a)/3 - (2*a*Sqrt[x])/3)*(Sqrt[a - b] - Sqrt[a - b*x])*(128*a^6 - 352*a^5*b + 328*a^4*b^2 - 112*a^3*b^3 + 8*a^2*b^4 - 64*a^6*Sqrt[x] + 80*a^5*b*Sqrt[x] + 124*a^4*b^2*Sqrt[x] - 220*a^3*b^3*Sqrt[x] + 80*a^2*b^4*Sqrt[x] + 32*a^6*x - 824*a^5*b*x + 2042*a^4*b^2*x - 1842*a^3*b^3*x + 664*a^2*b^4*x - 72*a*b^5*x - 112*a^6*x^(3/2) + 1228*a^5*b*x^(3/2) - 2467*a^4*b^2*x^(3/2) + 1412*a^3*b^3*x^(3/2) + 180*a^2*b^4*x^(3/2) - 240*a*b^5*x^(3/2) + 80*a^6*x^2 - 620*a^5*b*x^2 + 1965*a^4*b^2*x^2 - 2316*a^3*b^3*x^2 + 1078*a^2*b^4*x^2 - 288*a*b^5*x^2 + 96*b^6*x^2 - 16*a^6*x^(5/2) + 232*a^5*b*x^(5/2) - 1635*a^4*b^2*x^(5/2) + 2613*a^3*b^3*x^(5/2) - 1188*a^2*b^4*x^(5/2) - 100*a^5*b*x^3 + 728*a^4*b^2*x^3 - 1386*a^3*b^3*x^3 + 696*a^2*b^4*x^3 + 72*a*b^5*x^3 + 20*a^5*b*x^(7/2) - 145*a^4*b^2*x^(7/2) + 570*a^3*b^3*x^(7/2) - 480*a^2*b^4*x^(7/2) + 25*a^4*b^2*x^4 - 184*a^3*b^3*x^4 + 198*a^2*b^4*x^4 - 5*a^4*b^2*x^(9/2) + 25*a^3*b^3*x^(9/2) - 40*a^2*b^4*x^(9/2) + 4*a^2*b^4*x^5 - 128*a^5*Sqrt[a - b]*Sqrt[a - b*x] + 288*a^4*Sqrt[a - b]*b*Sqrt[a - b*x] - 200*a^3*Sqrt[a - b]*b^2*Sqrt[a - b*x] + 40*a^2*Sqrt[a - b]*b^3*Sqrt[a - b*x] + 64*a^5*Sqrt[a - b]*Sqrt[x]*Sqrt[a - b*x] - 48*a^4*Sqrt[a - b]*b*Sqrt[x]*Sqrt[a - b*x] - 140*a^3*Sqrt[a - b]*b^2*Sqrt[x]*Sqrt[a - b*x] + 148*a^2*Sqrt[a - b]*b^3*Sqrt[x]*Sqrt[a - b*x] - 24*a*Sqrt[a - b]*b^4*Sqrt[x]*Sqrt[a - b*x] - 32*a^5*Sqrt[a - b]*x*Sqrt[a - b*x] + 744*a^4*Sqrt[a - b]*b*x*Sqrt[a - b*x] - 1498*a^3*Sqrt[a - b]*b^2*x*Sqrt[a - b*x] + 1020*a^2*Sqrt[a - b]*b^3*x*Sqrt[a - b*x] - 240*a*Sqrt[a - b]*b^4*x*Sqrt[a - b*x] + 112*a^5*Sqrt[a - b]*x^(3/2)*Sqrt[a - b*x] - 1140*a^4*Sqrt[a - b]*b*x^(3/2)*Sqrt[a - b*x] + 1871*a^3*Sqrt[a - b]*b^2*x^(3/2)*Sqrt[a - b*x] - 674*a^2*Sqrt[a - b]*b^3*x^(3/2)*Sqrt[a - b*x] - 240*a*Sqrt[a - b]*b^4*x^(3/2)*Sqrt[a - b*x] + 96*Sqrt[a - b]*b^5*x^(3/2)*Sqrt[a - b*x] - 80*a^5*Sqrt[a - b]*x^2*Sqrt[a - b*x] + 564*a^4*Sqrt[a - b]*b*x^2*Sqrt[a - b*x] - 1329*a^3*Sqrt[a - b]*b^2*x^2*Sqrt[a - b*x] + 828*a^2*Sqrt[a - b]*b^3*x^2*Sqrt[a - b*x] + 16*a^5*Sqrt[a - b]*x^(5/2)*Sqrt[a - b*x] - 168*a^4*Sqrt[a - b]*b*x^(5/2)*Sqrt[a - b*x] + 963*a^3*Sqrt[a - b]*b^2*x^(5/2)*Sqrt[a - b*x] - 948*a^2*Sqrt[a - b]*b^3*x^(5/2)*Sqrt[a - b*x] + 72*a*Sqrt[a - b]*b^4*x^(5/2)*Sqrt[a - b*x] + 60*a^4*Sqrt[a - b]*b*x^3*Sqrt[a - b*x] - 400*a^3*Sqrt[a - b]*b^2*x^3*Sqrt[a - b*x] + 480*a^2*Sqrt[a - b]*b^3*x^3*Sqrt[a - b*x] - 12*a^4*Sqrt[a - b]*b*x^(7/2)*Sqrt[a - b*x] + 65*a^3*Sqrt[a - b]*b^2*x^(7/2)*Sqrt[a - b*x] - 162*a^2*Sqrt[a - b]*b^3*x^(7/2)*Sqrt[a - b*x] - 5*a^3*Sqrt[a - b]*b^2*x^4*Sqrt[a - b*x] + 40*a^2*Sqrt[a - b]*b^3*x^4*Sqrt[a - b*x] + a^3*Sqrt[a - b]*b^2*x^(9/2)*Sqrt[a - b*x] - 4*a^2*Sqrt[a - b]*b^3*x^(9/2)*Sqrt[a - b*x]))/(x^(3/2)*(4*a^2 - 4*a*b - 2*a^2*Sqrt[x] + a*b*Sqrt[x] + 2*b^2*Sqrt[x] - 2*a*b*x + a*b*x^(3/2) - 4*a*Sqrt[a - b]*Sqrt[a - b*x] + 2*Sqrt[a - b]*b*Sqrt[a - b*x] + 2*a*Sqrt[a - b]*Sqrt[x]*Sqrt[a - b*x])^3) + 4*b^(3/2)*ArcTan[(Sqrt[a - b]/Sqrt[b] - Sqrt[a - b*x]/Sqrt[b])/(-1 + Sqrt[x])]","B",1
533,1,2966,126,6.5393495,"\int x^{5/2} (2+b x)^{3/2} \, dx","IntegrateAlgebraic[x^(5/2)*(2 + b*x)^(3/2),x]","\text{Result too large to show}","-\frac{3 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{4 b^{7/2}}+\frac{3 \sqrt{x} \sqrt{b x+2}}{8 b^3}-\frac{x^{3/2} \sqrt{b x+2}}{8 b^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,"(4*(-245760 - 286720*b - 113408*b^2 - 391680*b^3 - 687340*b^4 - 500210*b^5 - 182390*b^6 - 34124*b^7 - 2940*b^8 - 80*b^9)*Sqrt[2 + b*x] + 4*(245760 - 307200*b - 505600*b^2 - 189120*b^3 - 958660*b^4 - 1599895*b^5 - 1065225*b^6 - 344155*b^7 - 53830*b^8 - 3390*b^9 - 40*b^10)*Sqrt[x]*Sqrt[2 + b*x] + 4*(368640*b - 325120*b^2 - 523008*b^3 - 536560*b^4 - 1811170*b^5 - 2260560*b^6 - 1244680*b^7 - 333184*b^8 - 40560*b^9 - 1600*b^10)*x*Sqrt[2 + b*x] + 4*(225280*b + 473600*b^2 - 254400*b^3 - 369680*b^4 - 906025*b^5 - 2236810*b^6 - 2148060*b^7 - 958880*b^8 - 204920*b^9 - 18000*b^10 - 320*b^11)*x^(3/2)*Sqrt[2 + b*x] + 4*(405760*b^2 + 453120*b^3 - 145512*b^4 - 309780*b^5 - 1089030*b^6 - 1927560*b^7 - 1447200*b^8 - 518016*b^9 - 85200*b^10 - 4800*b^11)*x^2*Sqrt[2 + b*x] + 4*(64768*b^2 + 423360*b^3 + 320520*b^4 - 60630*b^5 - 287835*b^6 - 902097*b^7 - 1186800*b^8 - 705840*b^9 - 200280*b^10 - 24120*b^11 - 672*b^12)*x^(5/2)*Sqrt[2 + b*x] + 4*(101120*b^3 + 295760*b^4 + 168060*b^5 - 32800*b^6 - 218500*b^7 - 516480*b^8 - 523840*b^9 - 249280*b^10 - 55200*b^11 - 4480*b^12)*x^3*Sqrt[2 + b*x] + 4*(380608*b^3 + 545840*b^4 + 347550*b^5 + 101620*b^6 - 19810*b^7 - 112672*b^8 - 201120*b^9 - 162560*b^10 - 62480*b^11 - 10560*b^12 - 512*b^13)*x^(7/2)*Sqrt[2 + b*x] + 4*(942580*b^4 + 1087750*b^5 + 441630*b^6 + 72700*b^7 - 8000*b^8 - 35520*b^9 - 50000*b^10 - 33440*b^11 - 10560*b^12 - 1280*b^13)*x^4*Sqrt[2 + b*x] + 4*(593052*b^4 + 1855325*b^5 + 1444225*b^6 + 414655*b^7 + 41760*b^8 - 1488*b^9 - 5440*b^10 - 6440*b^11 - 3840*b^12 - 1120*b^13 - 128*b^14)*x^(9/2)*Sqrt[2 + b*x] + 4*(1365350*b^5 + 2370000*b^6 + 1306104*b^7 + 263040*b^8 + 14880*b^9)*x^5*Sqrt[2 + b*x] + 4*(363675*b^5 + 1936950*b^6 + 2124180*b^7 + 830880*b^8 + 110640*b^9 + 2520*b^10)*x^(11/2)*Sqrt[2 + b*x] + 4*(753150*b^6 + 1854840*b^7 + 1376544*b^8 + 375360*b^9 + 29200*b^10)*x^6*Sqrt[2 + b*x] + 4*(107075*b^6 + 860285*b^7 + 1264880*b^8 + 652720*b^9 + 118600*b^10 + 3960*b^11)*x^(13/2)*Sqrt[2 + b*x] + 4*(191220*b^7 + 647040*b^8 + 628416*b^9 + 225600*b^10 + 24800*b^11)*x^7*Sqrt[2 + b*x] + 4*(15002*b^7 + 173840*b^8 + 339680*b^9 + 228400*b^10 + 55600*b^11 + 2912*b^12)*x^(15/2)*Sqrt[2 + b*x] + 4*(21180*b^8 + 98640*b^9 + 126480*b^10 + 60000*b^11 + 9280*b^12)*x^8*Sqrt[2 + b*x] + 4*(822*b^8 + 13710*b^9 + 36600*b^10 + 33000*b^11 + 11040*b^12 + 992*b^13)*x^(17/2)*Sqrt[2 + b*x] + 4*(720*b^9 + 4800*b^10 + 8640*b^11 + 5760*b^12 + 1280*b^13)*x^9*Sqrt[2 + b*x] + 4*(8*b^9 + 200*b^10 + 800*b^11 + 1120*b^12 + 640*b^13 + 128*b^14)*x^(19/2)*Sqrt[2 + b*x] + Sqrt[2 + b]*(4*(245760 + 225280*b + 64768*b^2 + 380608*b^3 + 593052*b^4 + 363675*b^5 + 107075*b^6 + 15002*b^7 + 822*b^8 + 8*b^9) + 4*(-245760 + 368640*b + 405760*b^2 + 101120*b^3 + 942580*b^4 + 1365350*b^5 + 753150*b^6 + 191220*b^7 + 21180*b^8 + 720*b^9)*Sqrt[x] + 4*(-307200*b + 473600*b^2 + 423360*b^3 + 545840*b^4 + 1855325*b^5 + 1936950*b^6 + 860285*b^7 + 173840*b^8 + 13710*b^9 + 200*b^10)*x + 4*(-286720*b - 325120*b^2 + 453120*b^3 + 295760*b^4 + 1087750*b^5 + 2370000*b^6 + 1854840*b^7 + 647040*b^8 + 98640*b^9 + 4800*b^10)*x^(3/2) + 4*(-505600*b^2 - 254400*b^3 + 320520*b^4 + 347550*b^5 + 1444225*b^6 + 2124180*b^7 + 1264880*b^8 + 339680*b^9 + 36600*b^10 + 800*b^11)*x^2 + 4*(-113408*b^2 - 523008*b^3 - 145512*b^4 + 168060*b^5 + 441630*b^6 + 1306104*b^7 + 1376544*b^8 + 628416*b^9 + 126480*b^10 + 8640*b^11)*x^(5/2) + 4*(-189120*b^3 - 369680*b^4 - 60630*b^5 + 101620*b^6 + 414655*b^7 + 830880*b^8 + 652720*b^9 + 228400*b^10 + 33000*b^11 + 1120*b^12)*x^3 + 4*(-391680*b^3 - 536560*b^4 - 309780*b^5 - 32800*b^6 + 72700*b^7 + 263040*b^8 + 375360*b^9 + 225600*b^10 + 60000*b^11 + 5760*b^12)*x^(7/2) + 4*(-958660*b^4 - 906025*b^5 - 287835*b^6 - 19810*b^7 + 41760*b^8 + 110640*b^9 + 118600*b^10 + 55600*b^11 + 11040*b^12 + 640*b^13)*x^4 + 4*(-687340*b^4 - 1811170*b^5 - 1089030*b^6 - 218500*b^7 - 8000*b^8 + 14880*b^9 + 29200*b^10 + 24800*b^11 + 9280*b^12 + 1280*b^13)*x^(9/2) + 4*(-1599895*b^5 - 2236810*b^6 - 902097*b^7 - 112672*b^8 - 1488*b^9 + 2520*b^10 + 3960*b^11 + 2912*b^12 + 992*b^13 + 128*b^14)*x^5 + 4*(-500210*b^5 - 2260560*b^6 - 1927560*b^7 - 516480*b^8 - 35520*b^9)*x^(11/2) + 4*(-1065225*b^6 - 2148060*b^7 - 1186800*b^8 - 201120*b^9 - 5440*b^10)*x^6 + 4*(-182390*b^6 - 1244680*b^7 - 1447200*b^8 - 523840*b^9 - 50000*b^10)*x^(13/2) + 4*(-344155*b^7 - 958880*b^8 - 705840*b^9 - 162560*b^10 - 6440*b^11)*x^7 + 4*(-34124*b^7 - 333184*b^8 - 518016*b^9 - 249280*b^10 - 33440*b^11)*x^(15/2) + 4*(-53830*b^8 - 204920*b^9 - 200280*b^10 - 62480*b^11 - 3840*b^12)*x^8 + 4*(-2940*b^8 - 40560*b^9 - 85200*b^10 - 55200*b^11 - 10560*b^12)*x^(17/2) + 4*(-3390*b^9 - 18000*b^10 - 24120*b^11 - 10560*b^12 - 1120*b^13)*x^9 + 4*(-80*b^9 - 1600*b^10 - 4800*b^11 - 4480*b^12 - 1280*b^13)*x^(19/2) + 4*(-40*b^10 - 320*b^11 - 672*b^12 - 512*b^13 - 128*b^14)*x^10))/(5*b^3*(524288 + 655360*b + 286720*b^2 + 51200*b^3 + 3200*b^4 + 32*b^5) + 5*b^3*(32*b^5 + 800*b^6 + 3200*b^7 + 4480*b^8 + 2560*b^9 + 512*b^10)*x^5 + 5*b^3*Sqrt[2 + b]*(-262144 - 262144*b - 86016*b^2 - 10240*b^3 - 320*b^4)*Sqrt[2 + b*x] + x*(5*b^3*(655360*b + 2375680*b^2 + 1914880*b^3 + 550400*b^4 + 52640*b^5 + 800*b^6) + 5*b^3*Sqrt[2 + b]*(-262144*b - 1040384*b^2 - 669696*b^3 - 131840*b^4 - 6400*b^5)*Sqrt[2 + b*x]) + Sqrt[x]*(5*b^3*(1310720*b + 1474560*b^2 + 552960*b^3 + 76800*b^4 + 2880*b^5) + 5*b^3*Sqrt[2 + b]*(-655360*b - 573440*b^2 - 153600*b^3 - 12800*b^4 - 160*b^5)*Sqrt[2 + b*x]) + x^2*(5*b^3*(286720*b^2 + 1914880*b^3 + 2333440*b^4 + 979520*b^5 + 137600*b^6 + 3200*b^7) + 5*b^3*Sqrt[2 + b]*(-86016*b^2 - 669696*b^3 - 776064*b^4 - 249600*b^5 - 19200*b^6)*Sqrt[2 + b*x]) + x^(3/2)*(5*b^3*(1474560*b^2 + 2826240*b^3 + 1643520*b^4 + 341760*b^5 + 19200*b^6) + 5*b^3*Sqrt[2 + b]*(-573440*b^2 - 1085440*b^3 - 499200*b^4 - 65920*b^5 - 1280*b^6)*Sqrt[2 + b*x]) + x^3*(5*b^3*(51200*b^3 + 550400*b^4 + 979520*b^5 + 583360*b^6 + 119680*b^7 + 4480*b^8) + 5*b^3*Sqrt[2 + b]*(-10240*b^3 - 131840*b^4 - 249600*b^5 - 135680*b^6 - 17920*b^7)*Sqrt[2 + b*x]) + x^(5/2)*(5*b^3*(552960*b^3 + 1643520*b^4 + 1375104*b^5 + 410880*b^6 + 34560*b^7) + 5*b^3*Sqrt[2 + b]*(-153600*b^3 - 499200*b^4 - 388032*b^5 - 83712*b^6 - 2688*b^7)*Sqrt[2 + b*x]) + x^4*(5*b^3*(3200*b^4 + 52640*b^5 + 137600*b^6 + 119680*b^7 + 37120*b^8 + 2560*b^9) + 5*b^3*Sqrt[2 + b]*(-320*b^4 - 6400*b^5 - 19200*b^6 - 17920*b^7 - 5120*b^8)*Sqrt[2 + b*x]) + x^(7/2)*(5*b^3*(76800*b^4 + 341760*b^5 + 410880*b^6 + 176640*b^7 + 23040*b^8) + 5*b^3*Sqrt[2 + b]*(-12800*b^4 - 65920*b^5 - 83712*b^6 - 32512*b^7 - 2048*b^8)*Sqrt[2 + b*x]) + x^(9/2)*(5*b^3*(2880*b^5 + 19200*b^6 + 34560*b^7 + 23040*b^8 + 5120*b^9) + 5*b^3*Sqrt[2 + b]*(-160*b^5 - 1280*b^6 - 2688*b^7 - 2048*b^8 - 512*b^9)*Sqrt[2 + b*x])) + (3*ArcTanh[(Sqrt[2 + b]/Sqrt[b] - Sqrt[2 + b*x]/Sqrt[b])/(-1 + Sqrt[x])])/(2*b^(7/2))","B",1
534,1,2039,105,3.3295332,"\int x^{3/2} (2+b x)^{3/2} \, dx","IntegrateAlgebraic[x^(3/2)*(2 + b*x)^(3/2),x]","\text{Result too large to show}","\frac{3 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{4 b^{5/2}}-\frac{3 \sqrt{x} \sqrt{b x+2}}{8 b^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,"(-2*(-6144 - 5632*b + 11584*b^2 + 20016*b^3 + 11800*b^4 + 3240*b^5 + 400*b^6 + 16*b^7)*Sqrt[2 + b*x] - 2*(6144 - 6144*b - 7808*b^2 + 24384*b^3 + 36907*b^4 + 19388*b^5 + 4532*b^6 + 424*b^7 + 8*b^8)*Sqrt[x]*Sqrt[2 + b*x] - 2*(7680*b - 4992*b^2 + 3696*b^3 + 38640*b^4 + 40440*b^5 + 17040*b^6 + 3120*b^7 + 192*b^8)*x*Sqrt[2 + b*x] - 2*(4096*b + 7936*b^2 - 2880*b^3 + 13228*b^4 + 37147*b^5 + 28760*b^6 + 9500*b^7 + 1280*b^8 + 40*b^9)*x^(3/2)*Sqrt[2 + b*x] - 2*(5696*b^2 + 5904*b^3 + 896*b^4 + 14336*b^5 + 23440*b^6 + 13840*b^7 + 3520*b^8 + 320*b^9)*x^2*Sqrt[2 + b*x] - 2*(-12416*b^2 - 8768*b^3 - 982*b^4 + 1736*b^5 + 8582*b^6 + 9816*b^7 + 4512*b^8 + 864*b^9 + 48*b^10)*x^(5/2)*Sqrt[2 + b*x] - 2*(-25520*b^3 - 20912*b^4 - 4480*b^5 + 896*b^6 + 2992*b^7 + 2624*b^8 + 960*b^9 + 128*b^10)*x^3*Sqrt[2 + b*x] - 2*(-16832*b^3 - 41156*b^4 - 23154*b^5 - 3640*b^6 + 186*b^7 + 512*b^8 + 384*b^9 + 128*b^10 + 16*b^11)*x^(7/2)*Sqrt[2 + b*x] - 2*(-30424*b^4 - 40936*b^5 - 15568*b^6 - 1488*b^7)*x^4*Sqrt[2 + b*x] - 2*(-7997*b^4 - 33452*b^5 - 27420*b^6 - 6760*b^7 - 280*b^8)*x^(9/2)*Sqrt[2 + b*x] - 2*(-12600*b^5 - 24080*b^6 - 12656*b^7 - 1856*b^8)*x^5*Sqrt[2 + b*x] - 2*(-1665*b^5 - 10680*b^6 - 11860*b^7 - 4000*b^8 - 280*b^9)*x^(11/2)*Sqrt[2 + b*x] - 2*(-2128*b^6 - 5712*b^7 - 4032*b^8 - 832*b^9)*x^6*Sqrt[2 + b*x] - 2*(-134*b^6 - 1304*b^7 - 2000*b^8 - 928*b^9 - 112*b^10)*x^(13/2)*Sqrt[2 + b*x] - 2*(-112*b^7 - 448*b^8 - 448*b^9 - 128*b^10)*x^7*Sqrt[2 + b*x] - 2*(-2*b^7 - 32*b^8 - 80*b^9 - 64*b^10 - 16*b^11)*x^(15/2)*Sqrt[2 + b*x] + Sqrt[2 + b]*(-2*(6144 + 4096*b - 12416*b^2 - 16832*b^3 - 7997*b^4 - 1665*b^5 - 134*b^6 - 2*b^7) - 2*(-6144 + 7680*b + 5696*b^2 - 25520*b^3 - 30424*b^4 - 12600*b^5 - 2128*b^6 - 112*b^7)*Sqrt[x] - 2*(-6144*b + 7936*b^2 - 8768*b^3 - 41156*b^4 - 33452*b^5 - 10680*b^6 - 1304*b^7 - 32*b^8)*x - 2*(-5632*b - 4992*b^2 + 5904*b^3 - 20912*b^4 - 40936*b^5 - 24080*b^6 - 5712*b^7 - 448*b^8)*x^(3/2) - 2*(-7808*b^2 - 2880*b^3 - 982*b^4 - 23154*b^5 - 27420*b^6 - 11860*b^7 - 2000*b^8 - 80*b^9)*x^2 - 2*(11584*b^2 + 3696*b^3 + 896*b^4 - 4480*b^5 - 15568*b^6 - 12656*b^7 - 4032*b^8 - 448*b^9)*x^(5/2) - 2*(24384*b^3 + 13228*b^4 + 1736*b^5 - 3640*b^6 - 6760*b^7 - 4000*b^8 - 928*b^9 - 64*b^10)*x^3 - 2*(20016*b^3 + 38640*b^4 + 14336*b^5 + 896*b^6 - 1488*b^7 - 1856*b^8 - 832*b^9 - 128*b^10)*x^(7/2) - 2*(36907*b^4 + 37147*b^5 + 8582*b^6 + 186*b^7 - 280*b^8 - 280*b^9 - 112*b^10 - 16*b^11)*x^4 - 2*(11800*b^4 + 40440*b^5 + 23440*b^6 + 2992*b^7)*x^(9/2) - 2*(19388*b^5 + 28760*b^6 + 9816*b^7 + 512*b^8)*x^5 - 2*(3240*b^5 + 17040*b^6 + 13840*b^7 + 2624*b^8)*x^(11/2) - 2*(4532*b^6 + 9500*b^7 + 4512*b^8 + 384*b^9)*x^6 - 2*(400*b^6 + 3120*b^7 + 3520*b^8 + 960*b^9)*x^(13/2) - 2*(424*b^7 + 1280*b^8 + 864*b^9 + 128*b^10)*x^7 - 2*(16*b^7 + 192*b^8 + 320*b^9 + 128*b^10)*x^(15/2) - 2*(8*b^8 + 40*b^9 + 48*b^10 + 16*b^11)*x^8))/(b^2*(32768 + 32768*b + 10240*b^2 + 1024*b^3 + 16*b^4) + b^2*(16*b^4 + 256*b^5 + 640*b^6 + 512*b^7 + 128*b^8)*x^4 + b^2*Sqrt[2 + b]*(-16384 - 12288*b - 2560*b^2 - 128*b^3)*Sqrt[2 + b*x] + x*(b^2*(32768*b + 94208*b^2 + 56320*b^3 + 9664*b^4 + 256*b^5) + b^2*Sqrt[2 + b]*(-12288*b - 39936*b^2 - 17280*b^3 - 1536*b^4)*Sqrt[2 + b*x]) + Sqrt[x]*(b^2*(65536*b + 57344*b^2 + 14336*b^3 + 896*b^4) + b^2*Sqrt[2 + b]*(-32768*b - 20480*b^2 - 3072*b^3 - 64*b^4)*Sqrt[2 + b*x]) + x^2*(b^2*(10240*b^2 + 56320*b^3 + 52320*b^4 + 14080*b^5 + 640*b^6) + b^2*Sqrt[2 + b]*(-2560*b^2 - 17280*b^3 - 15360*b^4 - 2560*b^5)*Sqrt[2 + b*x]) + x^(3/2)*(b^2*(57344*b^2 + 86016*b^3 + 34944*b^4 + 3584*b^5) + b^2*Sqrt[2 + b]*(-20480*b^2 - 30720*b^3 - 8640*b^4 - 320*b^5)*Sqrt[2 + b*x]) + x^3*(b^2*(1024*b^3 + 9664*b^4 + 14080*b^5 + 5888*b^6 + 512*b^7) + b^2*Sqrt[2 + b]*(-128*b^3 - 1536*b^4 - 2560*b^5 - 1024*b^6)*Sqrt[2 + b*x]) + x^(5/2)*(b^2*(14336*b^3 + 34944*b^4 + 21504*b^5 + 3584*b^6) + b^2*Sqrt[2 + b]*(-3072*b^3 - 8640*b^4 - 4992*b^5 - 384*b^6)*Sqrt[2 + b*x]) + x^(7/2)*(b^2*(896*b^4 + 3584*b^5 + 3584*b^6 + 1024*b^7) + b^2*Sqrt[2 + b]*(-64*b^4 - 320*b^5 - 384*b^6 - 128*b^7)*Sqrt[2 + b*x])) - (3*ArcTanh[(Sqrt[2 + b]/Sqrt[b] - Sqrt[2 + b*x]/Sqrt[b])/(-1 + Sqrt[x])])/(2*b^(5/2))","B",1
535,1,1278,82,1.9081903,"\int \sqrt{x} (2+b x)^{3/2} \, dx","IntegrateAlgebraic[Sqrt[x]*(2 + b*x)^(3/2),x]","\frac{4 \left(8 b^8+24 b^7+18 b^6+2 b^5\right) \sqrt{b x+2} x^{11/2}+4 \left(48 b^7+120 b^6+60 b^5\right) \sqrt{b x+2} x^5+4 \left(52 b^7+288 b^6+381 b^5+79 b^4\right) \sqrt{b x+2} x^{9/2}+4 \left(288 b^6+940 b^5+690 b^4\right) \sqrt{b x+2} x^4+4 \left(114 b^6+1068 b^5+1956 b^4+639 b^3\right) \sqrt{b x+2} x^{7/2}+4 \left(552 b^5+2480 b^4+2538 b^3\right) \sqrt{b x+2} x^3+4 \left(-8 b^8-60 b^7-162 b^6-92 b^5+1392 b^4+3699 b^3+1964 b^2\right) \sqrt{b x+2} x^{5/2}+4 \left(-48 b^7-336 b^6-816 b^5-432 b^4+2142 b^3+3372 b^2\right) \sqrt{b x+2} x^2+4 \left(-16 b^7-252 b^6-1182 b^5-2200 b^4-987 b^3+2136 b^2+2368 b\right) \sqrt{b x+2} x^{3/2}+4 \left(-72 b^6-724 b^5-2544 b^4-3618 b^3-1352 b^2+768 b\right) \sqrt{b x+2} x+4 \left(-6 b^6-177 b^5-1227 b^4-3351 b^3-3588 b^2-576 b+768\right) \sqrt{b x+2} \sqrt{x}+\sqrt{b+2} \left(4 \left(-8 b^8-16 b^7-6 b^6\right) x^6+4 \left(-48 b^7-72 b^6-12 b^5\right) x^{11/2}+4 \left(-60 b^7-252 b^6-177 b^5\right) x^5+4 \left(-336 b^6-724 b^5-194 b^4\right) x^{9/2}+4 \left(-162 b^6-1182 b^5-1227 b^4\right) x^4+4 \left(-816 b^5-2544 b^4-1062 b^3\right) x^{7/2}+4 \left(8 b^8+52 b^7+114 b^6-92 b^5-2200 b^4-3351 b^3\right) x^3+4 \left(48 b^7+288 b^6+552 b^5-432 b^4-3618 b^3-2532 b^2\right) x^{5/2}+4 \left(24 b^7+288 b^6+1068 b^5+1392 b^4-987 b^3-3588 b^2\right) x^2+4 \left(120 b^6+940 b^5+2480 b^4+2142 b^3-1352 b^2-2560 b\right) x^{3/2}+4 \left(18 b^6+381 b^5+1956 b^4+3699 b^3+2136 b^2-576 b\right) x+4 \left(60 b^5+690 b^4+2538 b^3+3372 b^2+768 b-768\right) \sqrt{x}+4 \left(2 b^5+79 b^4+639 b^3+1964 b^2+2368 b+768\right)\right)+4 \left(-12 b^5-194 b^4-1062 b^3-2532 b^2-2560 b-768\right) \sqrt{b x+2}}{3 b \left(32 b^6+96 b^5+72 b^4+8 b^3\right) x^3+\left(3 b \sqrt{b+2} \sqrt{b x+2} \left(-32 b^5-64 b^4-24 b^3\right)+3 b \left(192 b^5+480 b^4+240 b^3\right)\right) x^{5/2}+\left(3 b \sqrt{b+2} \sqrt{b x+2} \left(-192 b^4-288 b^3-48 b^2\right)+3 b \left(96 b^5+816 b^4+1272 b^3+288 b^2\right)\right) x^2+\left(3 b \sqrt{b+2} \sqrt{b x+2} \left(-64 b^4-656 b^3-576 b^2\right)+3 b \left(480 b^4+2080 b^3+1920 b^2\right)\right) x^{3/2}+\left(3 b \sqrt{b+2} \sqrt{b x+2} \left(-288 b^3-1312 b^2-512 b\right)+3 b \left(72 b^4+1272 b^3+3264 b^2+1536 b\right)\right) x+\left(3 b \sqrt{b+2} \sqrt{b x+2} \left(-24 b^3-576 b^2-1536 b\right)+3 b \left(240 b^3+1920 b^2+3072 b\right)\right) \sqrt{x}+3 b \left(8 b^3+288 b^2+1536 b+2048\right)+3 b \sqrt{b+2} \left(-48 b^2-512 b-1024\right) \sqrt{b x+2}}+\frac{2 \tanh ^{-1}\left(\frac{\frac{\sqrt{b+2}}{\sqrt{b}}-\frac{\sqrt{b x+2}}{\sqrt{b}}}{\sqrt{x}-1}\right)}{b^{3/2}}","-\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,"(4*(-768 - 2560*b - 2532*b^2 - 1062*b^3 - 194*b^4 - 12*b^5)*Sqrt[2 + b*x] + 4*(768 - 576*b - 3588*b^2 - 3351*b^3 - 1227*b^4 - 177*b^5 - 6*b^6)*Sqrt[x]*Sqrt[2 + b*x] + 4*(768*b - 1352*b^2 - 3618*b^3 - 2544*b^4 - 724*b^5 - 72*b^6)*x*Sqrt[2 + b*x] + 4*(2368*b + 2136*b^2 - 987*b^3 - 2200*b^4 - 1182*b^5 - 252*b^6 - 16*b^7)*x^(3/2)*Sqrt[2 + b*x] + 4*(3372*b^2 + 2142*b^3 - 432*b^4 - 816*b^5 - 336*b^6 - 48*b^7)*x^2*Sqrt[2 + b*x] + 4*(1964*b^2 + 3699*b^3 + 1392*b^4 - 92*b^5 - 162*b^6 - 60*b^7 - 8*b^8)*x^(5/2)*Sqrt[2 + b*x] + 4*(2538*b^3 + 2480*b^4 + 552*b^5)*x^3*Sqrt[2 + b*x] + 4*(639*b^3 + 1956*b^4 + 1068*b^5 + 114*b^6)*x^(7/2)*Sqrt[2 + b*x] + 4*(690*b^4 + 940*b^5 + 288*b^6)*x^4*Sqrt[2 + b*x] + 4*(79*b^4 + 381*b^5 + 288*b^6 + 52*b^7)*x^(9/2)*Sqrt[2 + b*x] + 4*(60*b^5 + 120*b^6 + 48*b^7)*x^5*Sqrt[2 + b*x] + 4*(2*b^5 + 18*b^6 + 24*b^7 + 8*b^8)*x^(11/2)*Sqrt[2 + b*x] + Sqrt[2 + b]*(4*(768 + 2368*b + 1964*b^2 + 639*b^3 + 79*b^4 + 2*b^5) + 4*(-768 + 768*b + 3372*b^2 + 2538*b^3 + 690*b^4 + 60*b^5)*Sqrt[x] + 4*(-576*b + 2136*b^2 + 3699*b^3 + 1956*b^4 + 381*b^5 + 18*b^6)*x + 4*(-2560*b - 1352*b^2 + 2142*b^3 + 2480*b^4 + 940*b^5 + 120*b^6)*x^(3/2) + 4*(-3588*b^2 - 987*b^3 + 1392*b^4 + 1068*b^5 + 288*b^6 + 24*b^7)*x^2 + 4*(-2532*b^2 - 3618*b^3 - 432*b^4 + 552*b^5 + 288*b^6 + 48*b^7)*x^(5/2) + 4*(-3351*b^3 - 2200*b^4 - 92*b^5 + 114*b^6 + 52*b^7 + 8*b^8)*x^3 + 4*(-1062*b^3 - 2544*b^4 - 816*b^5)*x^(7/2) + 4*(-1227*b^4 - 1182*b^5 - 162*b^6)*x^4 + 4*(-194*b^4 - 724*b^5 - 336*b^6)*x^(9/2) + 4*(-177*b^5 - 252*b^6 - 60*b^7)*x^5 + 4*(-12*b^5 - 72*b^6 - 48*b^7)*x^(11/2) + 4*(-6*b^6 - 16*b^7 - 8*b^8)*x^6))/(3*b*(2048 + 1536*b + 288*b^2 + 8*b^3) + 3*b*(8*b^3 + 72*b^4 + 96*b^5 + 32*b^6)*x^3 + 3*b*Sqrt[2 + b]*(-1024 - 512*b - 48*b^2)*Sqrt[2 + b*x] + x*(3*b*(1536*b + 3264*b^2 + 1272*b^3 + 72*b^4) + 3*b*Sqrt[2 + b]*(-512*b - 1312*b^2 - 288*b^3)*Sqrt[2 + b*x]) + Sqrt[x]*(3*b*(3072*b + 1920*b^2 + 240*b^3) + 3*b*Sqrt[2 + b]*(-1536*b - 576*b^2 - 24*b^3)*Sqrt[2 + b*x]) + x^2*(3*b*(288*b^2 + 1272*b^3 + 816*b^4 + 96*b^5) + 3*b*Sqrt[2 + b]*(-48*b^2 - 288*b^3 - 192*b^4)*Sqrt[2 + b*x]) + x^(3/2)*(3*b*(1920*b^2 + 2080*b^3 + 480*b^4) + 3*b*Sqrt[2 + b]*(-576*b^2 - 656*b^3 - 64*b^4)*Sqrt[2 + b*x]) + x^(5/2)*(3*b*(240*b^3 + 480*b^4 + 192*b^5) + 3*b*Sqrt[2 + b]*(-24*b^3 - 64*b^4 - 32*b^5)*Sqrt[2 + b*x])) + (2*ArcTanh[(Sqrt[2 + b]/Sqrt[b] - Sqrt[2 + b*x]/Sqrt[b])/(-1 + Sqrt[x])])/b^(3/2)","B",1
536,1,654,61,0.7644981,"\int \frac{(2+b x)^{3/2}}{\sqrt{x}} \, dx","IntegrateAlgebraic[(2 + b*x)^(3/2)/Sqrt[x],x]","\frac{\left(2 \sqrt{x}-2\right) \left(\sqrt{b+2}-\sqrt{b x+2}\right) \left(-2 b^5 x^3-2 b^5 x^2-6 b^4 x^{5/2}-6 b^4 x^{3/2}+2 \sqrt{b+2} b^4 x^{5/2} \sqrt{b x+2}+2 \sqrt{b+2} b^4 x^{3/2} \sqrt{b x+2}-4 b^4 x^3-20 b^4 x^2-4 b^4 x-9 b^3 x^{5/2}-54 b^3 x^{3/2}+2 \sqrt{b+2} b^3 x^{5/2} \sqrt{b x+2}+16 \sqrt{b+2} b^3 x^{3/2} \sqrt{b x+2}-b^3 x^3-40 b^3 x^2+6 \sqrt{b+2} b^3 x^2 \sqrt{b x+2}-40 b^3 x-9 b^3 \sqrt{x}+6 \sqrt{b+2} b^3 x \sqrt{b x+2}+2 \sqrt{b+2} b^3 \sqrt{x} \sqrt{b x+2}-b^3-71 b^2 x^{3/2}+21 \sqrt{b+2} b^2 x^{3/2} \sqrt{b x+2}-15 b^2 x^2+3 \sqrt{b+2} b^2 x^2 \sqrt{b x+2}-112 b^2 x-71 b^2 \sqrt{x}+42 \sqrt{b+2} b^2 x \sqrt{b x+2}+3 \sqrt{b+2} b^2 \sqrt{b x+2}+21 \sqrt{b+2} b^2 \sqrt{x} \sqrt{b x+2}-15 b^2-66 b x-116 b \sqrt{x}+23 \sqrt{b+2} b x \sqrt{b x+2}+23 \sqrt{b+2} b \sqrt{b x+2}+58 \sqrt{b+2} b \sqrt{x} \sqrt{b x+2}+40 \sqrt{b+2} \sqrt{b x+2}-66 b-80\right)}{\left(b \left(-\sqrt{x}\right)+\sqrt{b+2} \sqrt{b x+2}-2\right)^4}-\frac{6 \tanh ^{-1}\left(\frac{\frac{\sqrt{b+2}}{\sqrt{b}}-\frac{\sqrt{b x+2}}{\sqrt{b}}}{\sqrt{x}-1}\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,"((-2 + 2*Sqrt[x])*(Sqrt[2 + b] - Sqrt[2 + b*x])*(-80 - 66*b - 15*b^2 - b^3 - 116*b*Sqrt[x] - 71*b^2*Sqrt[x] - 9*b^3*Sqrt[x] - 66*b*x - 112*b^2*x - 40*b^3*x - 4*b^4*x - 71*b^2*x^(3/2) - 54*b^3*x^(3/2) - 6*b^4*x^(3/2) - 15*b^2*x^2 - 40*b^3*x^2 - 20*b^4*x^2 - 2*b^5*x^2 - 9*b^3*x^(5/2) - 6*b^4*x^(5/2) - b^3*x^3 - 4*b^4*x^3 - 2*b^5*x^3 + 40*Sqrt[2 + b]*Sqrt[2 + b*x] + 23*b*Sqrt[2 + b]*Sqrt[2 + b*x] + 3*b^2*Sqrt[2 + b]*Sqrt[2 + b*x] + 58*b*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] + 21*b^2*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] + 2*b^3*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] + 23*b*Sqrt[2 + b]*x*Sqrt[2 + b*x] + 42*b^2*Sqrt[2 + b]*x*Sqrt[2 + b*x] + 6*b^3*Sqrt[2 + b]*x*Sqrt[2 + b*x] + 21*b^2*Sqrt[2 + b]*x^(3/2)*Sqrt[2 + b*x] + 16*b^3*Sqrt[2 + b]*x^(3/2)*Sqrt[2 + b*x] + 2*b^4*Sqrt[2 + b]*x^(3/2)*Sqrt[2 + b*x] + 3*b^2*Sqrt[2 + b]*x^2*Sqrt[2 + b*x] + 6*b^3*Sqrt[2 + b]*x^2*Sqrt[2 + b*x] + 2*b^3*Sqrt[2 + b]*x^(5/2)*Sqrt[2 + b*x] + 2*b^4*Sqrt[2 + b]*x^(5/2)*Sqrt[2 + b*x]))/(-2 - b*Sqrt[x] + Sqrt[2 + b]*Sqrt[2 + b*x])^4 - (6*ArcTanh[(Sqrt[2 + b]/Sqrt[b] - Sqrt[2 + b*x]/Sqrt[b])/(-1 + Sqrt[x])])/Sqrt[b]","B",1
537,1,430,58,0.8567255,"\int \frac{(2+b x)^{3/2}}{x^{3/2}} \, dx","IntegrateAlgebraic[(2 + b*x)^(3/2)/x^(3/2),x]","\frac{\left(4 \sqrt{x}-4\right) \left(b x-2 b \sqrt{x}-2 \sqrt{b+2} \sqrt{b x+2}+\sqrt{b+2} \sqrt{x} \sqrt{b x+2}+2 b-2 \sqrt{x}+4\right) \left(\sqrt{b+2}-\sqrt{b x+2}\right)}{\sqrt{x} \left(b^2 \left(-\sqrt{x}\right)+b x^{3/2}-2 b x+b \sqrt{x}+\sqrt{b+2} b \sqrt{b x+2}+4 \sqrt{b+2} \sqrt{b x+2}-2 \sqrt{b+2} \sqrt{x} \sqrt{b x+2}-4 b+4 \sqrt{x}-8\right)}+\frac{\left(-2 b^2 \sqrt{x}-2 b \sqrt{x}+2 \sqrt{b+2} b \sqrt{b x+2}-2 b\right) \left(\sqrt{b+2}-\sqrt{b x+2}\right)^3}{\left(b \left(-\sqrt{x}\right)+\sqrt{b+2} \sqrt{b x+2}-2\right)^2}+\frac{\left(2 b \sqrt{b+2}-2 b \sqrt{b x+2}\right) \left(b \left(-\sqrt{x}\right)+2 \sqrt{b+2} \sqrt{b x+2}-b-\sqrt{x}-3\right)}{b \left(-\sqrt{x}\right)+\sqrt{b+2} \sqrt{b x+2}-2}-12 \sqrt{b} \tanh ^{-1}\left(\frac{\frac{\sqrt{b+2}}{\sqrt{b}}-\frac{\sqrt{b x+2}}{\sqrt{b}}}{\sqrt{x}-1}\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,"((2*b*Sqrt[2 + b] - 2*b*Sqrt[2 + b*x])*(-3 - b - Sqrt[x] - b*Sqrt[x] + 2*Sqrt[2 + b]*Sqrt[2 + b*x]))/(-2 - b*Sqrt[x] + Sqrt[2 + b]*Sqrt[2 + b*x]) + ((Sqrt[2 + b] - Sqrt[2 + b*x])^3*(-2*b - 2*b*Sqrt[x] - 2*b^2*Sqrt[x] + 2*b*Sqrt[2 + b]*Sqrt[2 + b*x]))/(-2 - b*Sqrt[x] + Sqrt[2 + b]*Sqrt[2 + b*x])^2 + ((-4 + 4*Sqrt[x])*(Sqrt[2 + b] - Sqrt[2 + b*x])*(4 + 2*b - 2*Sqrt[x] - 2*b*Sqrt[x] + b*x - 2*Sqrt[2 + b]*Sqrt[2 + b*x] + Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x]))/(Sqrt[x]*(-8 - 4*b + 4*Sqrt[x] + b*Sqrt[x] - b^2*Sqrt[x] - 2*b*x + b*x^(3/2) + 4*Sqrt[2 + b]*Sqrt[2 + b*x] + b*Sqrt[2 + b]*Sqrt[2 + b*x] - 2*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x])) - 12*Sqrt[b]*ArcTanh[(Sqrt[2 + b]/Sqrt[b] - Sqrt[2 + b*x]/Sqrt[b])/(-1 + Sqrt[x])]","B",1
538,1,1351,60,1.9142595,"\int \frac{(2+b x)^{3/2}}{x^{5/2}} \, dx","IntegrateAlgebraic[(2 + b*x)^(3/2)/x^(5/2),x]","\frac{-8 b^4 \sqrt{b x+2} x^{11/2}-4 \left(-24 b^4-30 b^3-12 b^2\right) \sqrt{b x+2} x^5-4 \left(141 b^4+259 b^3+72 b^2\right) \sqrt{b x+2} x^{9/2}-4 \left(-440 b^4-1026 b^3-504 b^2-128 b\right) \sqrt{b x+2} x^4-4 \left(-18 b^5+909 b^4+3063 b^3+2820 b^2+768 b\right) \sqrt{b x+2} x^{7/2}-4 \left(-1692 b^4-6790 b^3-7908 b^2-2304 b-256\right) \sqrt{b x+2} x^3-4 \left(12 b^6+90 b^5+2057 b^4+8997 b^3+13248 b^2+6720 b+1536\right) \sqrt{b x+2} x^{5/2}-4 \left(72 b^5-1080 b^4-8430 b^3-18672 b^2-14976 b-3072\right) \sqrt{b x+2} x^2-4 \left(-12 b^6-66 b^5+1089 b^4+8317 b^3+19524 b^2+16320 b+2304\right) \sqrt{b x+2} x^{3/2}-4 \left(-72 b^5-836 b^4-3852 b^3-8136 b^2-7168 b-1536\right) \sqrt{b x+2} x-4 \left(-6 b^5-102 b^4-156 b^3+1200 b^2+3840 b+3072\right) \sqrt{b x+2} \sqrt{x}+\sqrt{b+2} \left(-4 \left(2 b^4+b^3\right) x^6-4 \left(-24 b^4-6 b^3\right) x^{11/2}-4 \left(123 b^4+99 b^3+36 b^2\right) x^5-4 \left(-440 b^4-718 b^3-216 b^2\right) x^{9/2}-4 \left(18 b^5+1053 b^4+2319 b^3+936 b^2+192 b\right) x^4-4 \left(-1476 b^4-4890 b^3-4140 b^2-1152 b\right) x^{7/2}-4 \left(-12 b^6-78 b^5+1729 b^4+8627 b^3+10860 b^2+3008 b+256\right) x^3-4 \left(-72 b^5-2016 b^4-10074 b^3-15552 b^2-6912 b-1536\right) x^{5/2}-4 \left(12 b^6+42 b^5+765 b^4+6588 b^3+16848 b^2+14592 b+3072\right) x^2-4 \left(72 b^5-188 b^4-5008 b^3-16428 b^2-16512 b-2304\right) x^{3/2}-4 \left(18 b^5+420 b^4+2694 b^3+7128 b^2+7296 b+1536\right) x-4 \left(48 b^4+216 b^3-528 b^2-3072 b-3072\right) \sqrt{x}-4 \left(4 b^4+152 b^3+1056 b^2+2560 b+2048\right)\right)-4 \left(-24 b^4-352 b^3-1632 b^2-3072 b-2048\right) \sqrt{b x+2}}{3 b^3 x^6-18 b^3 x^{11/2}+\left(3 \left(-3 b^4+27 b^3+36 b^2\right)-18 b^2 \sqrt{b+2} \sqrt{b x+2}\right) x^5+\left(3 \left(-128 b^3-216 b^2\right)+3 \sqrt{b+2} \left(3 b^3+36 b^2\right) \sqrt{b x+2}\right) x^{9/2}+\left(3 \sqrt{b+2} \sqrt{b x+2} \left(-92 b^2-64 b\right)+3 \left(6 b^5+24 b^4+267 b^3+552 b^2+192 b\right)\right) x^4+\left(3 \sqrt{b+2} \sqrt{b x+2} \left(-6 b^4-18 b^3+240 b^2+384 b\right)+3 \left(36 b^4-270 b^3-1248 b^2-1152 b\right)\right) x^{7/2}+\left(3 \sqrt{b+2} \sqrt{b x+2} \left(-36 b^3-486 b^2-832 b-128\right)+3 \left(-4 b^6-24 b^5-39 b^4+565 b^3+2340 b^2+2496 b+256\right)\right) x^3+\left(3 \left(-24 b^5-132 b^4-588 b^3-1992 b^2-3072 b-1536\right)+3 \sqrt{b+2} \left(4 b^5+20 b^4+27 b^3+364 b^2+1088 b+768\right) \sqrt{b x+2}\right) x^{5/2}+\left(3 \sqrt{b+2} \sqrt{b x+2} \left(24 b^4+108 b^3-264 b^2-1536 b-1536\right)+3 \left(-6 b^5-102 b^4-156 b^3+1200 b^2+3840 b+3072\right)\right) x^2+\left(3 \left(-24 b^4-352 b^3-1632 b^2-3072 b-2048\right)+3 \sqrt{b+2} \left(2 b^4+76 b^3+528 b^2+1280 b+1024\right) \sqrt{b x+2}\right) x^{3/2}}-4 b^{3/2} \tanh ^{-1}\left(\frac{\frac{\sqrt{b+2}}{\sqrt{b}}-\frac{\sqrt{b x+2}}{\sqrt{b}}}{\sqrt{x}-1}\right)","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,"(-4*(-2048 - 3072*b - 1632*b^2 - 352*b^3 - 24*b^4)*Sqrt[2 + b*x] - 4*(3072 + 3840*b + 1200*b^2 - 156*b^3 - 102*b^4 - 6*b^5)*Sqrt[x]*Sqrt[2 + b*x] - 4*(-1536 - 7168*b - 8136*b^2 - 3852*b^3 - 836*b^4 - 72*b^5)*x*Sqrt[2 + b*x] - 4*(2304 + 16320*b + 19524*b^2 + 8317*b^3 + 1089*b^4 - 66*b^5 - 12*b^6)*x^(3/2)*Sqrt[2 + b*x] - 4*(-3072 - 14976*b - 18672*b^2 - 8430*b^3 - 1080*b^4 + 72*b^5)*x^2*Sqrt[2 + b*x] - 4*(1536 + 6720*b + 13248*b^2 + 8997*b^3 + 2057*b^4 + 90*b^5 + 12*b^6)*x^(5/2)*Sqrt[2 + b*x] - 4*(-256 - 2304*b - 7908*b^2 - 6790*b^3 - 1692*b^4)*x^3*Sqrt[2 + b*x] - 4*(768*b + 2820*b^2 + 3063*b^3 + 909*b^4 - 18*b^5)*x^(7/2)*Sqrt[2 + b*x] - 4*(-128*b - 504*b^2 - 1026*b^3 - 440*b^4)*x^4*Sqrt[2 + b*x] - 4*(72*b^2 + 259*b^3 + 141*b^4)*x^(9/2)*Sqrt[2 + b*x] - 4*(-12*b^2 - 30*b^3 - 24*b^4)*x^5*Sqrt[2 + b*x] - 8*b^4*x^(11/2)*Sqrt[2 + b*x] + Sqrt[2 + b]*(-4*(2048 + 2560*b + 1056*b^2 + 152*b^3 + 4*b^4) - 4*(-3072 - 3072*b - 528*b^2 + 216*b^3 + 48*b^4)*Sqrt[x] - 4*(1536 + 7296*b + 7128*b^2 + 2694*b^3 + 420*b^4 + 18*b^5)*x - 4*(-2304 - 16512*b - 16428*b^2 - 5008*b^3 - 188*b^4 + 72*b^5)*x^(3/2) - 4*(3072 + 14592*b + 16848*b^2 + 6588*b^3 + 765*b^4 + 42*b^5 + 12*b^6)*x^2 - 4*(-1536 - 6912*b - 15552*b^2 - 10074*b^3 - 2016*b^4 - 72*b^5)*x^(5/2) - 4*(256 + 3008*b + 10860*b^2 + 8627*b^3 + 1729*b^4 - 78*b^5 - 12*b^6)*x^3 - 4*(-1152*b - 4140*b^2 - 4890*b^3 - 1476*b^4)*x^(7/2) - 4*(192*b + 936*b^2 + 2319*b^3 + 1053*b^4 + 18*b^5)*x^4 - 4*(-216*b^2 - 718*b^3 - 440*b^4)*x^(9/2) - 4*(36*b^2 + 99*b^3 + 123*b^4)*x^5 - 4*(-6*b^3 - 24*b^4)*x^(11/2) - 4*(b^3 + 2*b^4)*x^6))/(-18*b^3*x^(11/2) + 3*b^3*x^6 + x^5*(3*(36*b^2 + 27*b^3 - 3*b^4) - 18*b^2*Sqrt[2 + b]*Sqrt[2 + b*x]) + x^4*(3*(192*b + 552*b^2 + 267*b^3 + 24*b^4 + 6*b^5) + 3*Sqrt[2 + b]*(-64*b - 92*b^2)*Sqrt[2 + b*x]) + x^3*(3*(256 + 2496*b + 2340*b^2 + 565*b^3 - 39*b^4 - 24*b^5 - 4*b^6) + 3*Sqrt[2 + b]*(-128 - 832*b - 486*b^2 - 36*b^3)*Sqrt[2 + b*x]) + x^(9/2)*(3*(-216*b^2 - 128*b^3) + 3*Sqrt[2 + b]*(36*b^2 + 3*b^3)*Sqrt[2 + b*x]) + x^(7/2)*(3*(-1152*b - 1248*b^2 - 270*b^3 + 36*b^4) + 3*Sqrt[2 + b]*(384*b + 240*b^2 - 18*b^3 - 6*b^4)*Sqrt[2 + b*x]) + x^(3/2)*(3*(-2048 - 3072*b - 1632*b^2 - 352*b^3 - 24*b^4) + 3*Sqrt[2 + b]*(1024 + 1280*b + 528*b^2 + 76*b^3 + 2*b^4)*Sqrt[2 + b*x]) + x^2*(3*(3072 + 3840*b + 1200*b^2 - 156*b^3 - 102*b^4 - 6*b^5) + 3*Sqrt[2 + b]*(-1536 - 1536*b - 264*b^2 + 108*b^3 + 24*b^4)*Sqrt[2 + b*x]) + x^(5/2)*(3*(-1536 - 3072*b - 1992*b^2 - 588*b^3 - 132*b^4 - 24*b^5) + 3*Sqrt[2 + b]*(768 + 1088*b + 364*b^2 + 27*b^3 + 20*b^4 + 4*b^5)*Sqrt[2 + b*x])) - 4*b^(3/2)*ArcTanh[(Sqrt[2 + b]/Sqrt[b] - Sqrt[2 + b*x]/Sqrt[b])/(-1 + Sqrt[x])]","B",1
539,1,3021,131,6.7842297,"\int x^{5/2} (2-b x)^{3/2} \, dx","IntegrateAlgebraic[x^(5/2)*(2 - b*x)^(3/2),x]","\text{Result too large to show}","\frac{3 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{4 b^{7/2}}-\frac{3 \sqrt{x} \sqrt{2-b x}}{8 b^3}-\frac{x^{3/2} \sqrt{2-b x}}{8 b^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,"(4*(245760 - 286720*b + 113408*b^2 - 391680*b^3 + 687340*b^4 - 500210*b^5 + 182390*b^6 - 34124*b^7 + 2940*b^8 - 80*b^9)*Sqrt[2 - b*x] + 4*(-245760 - 307200*b + 505600*b^2 - 189120*b^3 + 958660*b^4 - 1599895*b^5 + 1065225*b^6 - 344155*b^7 + 53830*b^8 - 3390*b^9 + 40*b^10)*Sqrt[x]*Sqrt[2 - b*x] + 4*(368640*b + 325120*b^2 - 523008*b^3 + 536560*b^4 - 1811170*b^5 + 2260560*b^6 - 1244680*b^7 + 333184*b^8 - 40560*b^9 + 1600*b^10)*x*Sqrt[2 - b*x] + 4*(225280*b - 473600*b^2 - 254400*b^3 + 369680*b^4 - 906025*b^5 + 2236810*b^6 - 2148060*b^7 + 958880*b^8 - 204920*b^9 + 18000*b^10 - 320*b^11)*x^(3/2)*Sqrt[2 - b*x] + 4*(-405760*b^2 + 453120*b^3 + 145512*b^4 - 309780*b^5 + 1089030*b^6 - 1927560*b^7 + 1447200*b^8 - 518016*b^9 + 85200*b^10 - 4800*b^11)*x^2*Sqrt[2 - b*x] + 4*(-64768*b^2 + 423360*b^3 - 320520*b^4 - 60630*b^5 + 287835*b^6 - 902097*b^7 + 1186800*b^8 - 705840*b^9 + 200280*b^10 - 24120*b^11 + 672*b^12)*x^(5/2)*Sqrt[2 - b*x] + 4*(101120*b^3 - 295760*b^4 + 168060*b^5 + 32800*b^6 - 218500*b^7 + 516480*b^8 - 523840*b^9 + 249280*b^10 - 55200*b^11 + 4480*b^12)*x^3*Sqrt[2 - b*x] + 4*(380608*b^3 - 545840*b^4 + 347550*b^5 - 101620*b^6 - 19810*b^7 + 112672*b^8 - 201120*b^9 + 162560*b^10 - 62480*b^11 + 10560*b^12 - 512*b^13)*x^(7/2)*Sqrt[2 - b*x] + 4*(-942580*b^4 + 1087750*b^5 - 441630*b^6 + 72700*b^7 + 8000*b^8 - 35520*b^9 + 50000*b^10 - 33440*b^11 + 10560*b^12 - 1280*b^13)*x^4*Sqrt[2 - b*x] + 4*(-593052*b^4 + 1855325*b^5 - 1444225*b^6 + 414655*b^7 - 41760*b^8 - 1488*b^9 + 5440*b^10 - 6440*b^11 + 3840*b^12 - 1120*b^13 + 128*b^14)*x^(9/2)*Sqrt[2 - b*x] + 4*(1365350*b^5 - 2370000*b^6 + 1306104*b^7 - 263040*b^8 + 14880*b^9)*x^5*Sqrt[2 - b*x] + 4*(363675*b^5 - 1936950*b^6 + 2124180*b^7 - 830880*b^8 + 110640*b^9 - 2520*b^10)*x^(11/2)*Sqrt[2 - b*x] + 4*(-753150*b^6 + 1854840*b^7 - 1376544*b^8 + 375360*b^9 - 29200*b^10)*x^6*Sqrt[2 - b*x] + 4*(-107075*b^6 + 860285*b^7 - 1264880*b^8 + 652720*b^9 - 118600*b^10 + 3960*b^11)*x^(13/2)*Sqrt[2 - b*x] + 4*(191220*b^7 - 647040*b^8 + 628416*b^9 - 225600*b^10 + 24800*b^11)*x^7*Sqrt[2 - b*x] + 4*(15002*b^7 - 173840*b^8 + 339680*b^9 - 228400*b^10 + 55600*b^11 - 2912*b^12)*x^(15/2)*Sqrt[2 - b*x] + 4*(-21180*b^8 + 98640*b^9 - 126480*b^10 + 60000*b^11 - 9280*b^12)*x^8*Sqrt[2 - b*x] + 4*(-822*b^8 + 13710*b^9 - 36600*b^10 + 33000*b^11 - 11040*b^12 + 992*b^13)*x^(17/2)*Sqrt[2 - b*x] + 4*(720*b^9 - 4800*b^10 + 8640*b^11 - 5760*b^12 + 1280*b^13)*x^9*Sqrt[2 - b*x] + 4*(8*b^9 - 200*b^10 + 800*b^11 - 1120*b^12 + 640*b^13 - 128*b^14)*x^(19/2)*Sqrt[2 - b*x] + Sqrt[2 - b]*(4*(-245760 + 225280*b - 64768*b^2 + 380608*b^3 - 593052*b^4 + 363675*b^5 - 107075*b^6 + 15002*b^7 - 822*b^8 + 8*b^9) + 4*(245760 + 368640*b - 405760*b^2 + 101120*b^3 - 942580*b^4 + 1365350*b^5 - 753150*b^6 + 191220*b^7 - 21180*b^8 + 720*b^9)*Sqrt[x] + 4*(-307200*b - 473600*b^2 + 423360*b^3 - 545840*b^4 + 1855325*b^5 - 1936950*b^6 + 860285*b^7 - 173840*b^8 + 13710*b^9 - 200*b^10)*x + 4*(-286720*b + 325120*b^2 + 453120*b^3 - 295760*b^4 + 1087750*b^5 - 2370000*b^6 + 1854840*b^7 - 647040*b^8 + 98640*b^9 - 4800*b^10)*x^(3/2) + 4*(505600*b^2 - 254400*b^3 - 320520*b^4 + 347550*b^5 - 1444225*b^6 + 2124180*b^7 - 1264880*b^8 + 339680*b^9 - 36600*b^10 + 800*b^11)*x^2 + 4*(113408*b^2 - 523008*b^3 + 145512*b^4 + 168060*b^5 - 441630*b^6 + 1306104*b^7 - 1376544*b^8 + 628416*b^9 - 126480*b^10 + 8640*b^11)*x^(5/2) + 4*(-189120*b^3 + 369680*b^4 - 60630*b^5 - 101620*b^6 + 414655*b^7 - 830880*b^8 + 652720*b^9 - 228400*b^10 + 33000*b^11 - 1120*b^12)*x^3 + 4*(-391680*b^3 + 536560*b^4 - 309780*b^5 + 32800*b^6 + 72700*b^7 - 263040*b^8 + 375360*b^9 - 225600*b^10 + 60000*b^11 - 5760*b^12)*x^(7/2) + 4*(958660*b^4 - 906025*b^5 + 287835*b^6 - 19810*b^7 - 41760*b^8 + 110640*b^9 - 118600*b^10 + 55600*b^11 - 11040*b^12 + 640*b^13)*x^4 + 4*(687340*b^4 - 1811170*b^5 + 1089030*b^6 - 218500*b^7 + 8000*b^8 + 14880*b^9 - 29200*b^10 + 24800*b^11 - 9280*b^12 + 1280*b^13)*x^(9/2) + 4*(-1599895*b^5 + 2236810*b^6 - 902097*b^7 + 112672*b^8 - 1488*b^9 - 2520*b^10 + 3960*b^11 - 2912*b^12 + 992*b^13 - 128*b^14)*x^5 + 4*(-500210*b^5 + 2260560*b^6 - 1927560*b^7 + 516480*b^8 - 35520*b^9)*x^(11/2) + 4*(1065225*b^6 - 2148060*b^7 + 1186800*b^8 - 201120*b^9 + 5440*b^10)*x^6 + 4*(182390*b^6 - 1244680*b^7 + 1447200*b^8 - 523840*b^9 + 50000*b^10)*x^(13/2) + 4*(-344155*b^7 + 958880*b^8 - 705840*b^9 + 162560*b^10 - 6440*b^11)*x^7 + 4*(-34124*b^7 + 333184*b^8 - 518016*b^9 + 249280*b^10 - 33440*b^11)*x^(15/2) + 4*(53830*b^8 - 204920*b^9 + 200280*b^10 - 62480*b^11 + 3840*b^12)*x^8 + 4*(2940*b^8 - 40560*b^9 + 85200*b^10 - 55200*b^11 + 10560*b^12)*x^(17/2) + 4*(-3390*b^9 + 18000*b^10 - 24120*b^11 + 10560*b^12 - 1120*b^13)*x^9 + 4*(-80*b^9 + 1600*b^10 - 4800*b^11 + 4480*b^12 - 1280*b^13)*x^(19/2) + 4*(40*b^10 - 320*b^11 + 672*b^12 - 512*b^13 + 128*b^14)*x^10))/(5*b^3*(524288 - 655360*b + 286720*b^2 - 51200*b^3 + 3200*b^4 - 32*b^5) + 5*b^3*(-32*b^5 + 800*b^6 - 3200*b^7 + 4480*b^8 - 2560*b^9 + 512*b^10)*x^5 + 5*Sqrt[2 - b]*b^3*(-262144 + 262144*b - 86016*b^2 + 10240*b^3 - 320*b^4)*Sqrt[2 - b*x] + Sqrt[x]*(5*b^3*(-1310720*b + 1474560*b^2 - 552960*b^3 + 76800*b^4 - 2880*b^5) + 5*Sqrt[2 - b]*b^3*(655360*b - 573440*b^2 + 153600*b^3 - 12800*b^4 + 160*b^5)*Sqrt[2 - b*x]) + x*(5*b^3*(-655360*b + 2375680*b^2 - 1914880*b^3 + 550400*b^4 - 52640*b^5 + 800*b^6) + 5*Sqrt[2 - b]*b^3*(262144*b - 1040384*b^2 + 669696*b^3 - 131840*b^4 + 6400*b^5)*Sqrt[2 - b*x]) + x^2*(5*b^3*(286720*b^2 - 1914880*b^3 + 2333440*b^4 - 979520*b^5 + 137600*b^6 - 3200*b^7) + 5*Sqrt[2 - b]*b^3*(-86016*b^2 + 669696*b^3 - 776064*b^4 + 249600*b^5 - 19200*b^6)*Sqrt[2 - b*x]) + x^(3/2)*(5*b^3*(1474560*b^2 - 2826240*b^3 + 1643520*b^4 - 341760*b^5 + 19200*b^6) + 5*Sqrt[2 - b]*b^3*(-573440*b^2 + 1085440*b^3 - 499200*b^4 + 65920*b^5 - 1280*b^6)*Sqrt[2 - b*x]) + x^(5/2)*(5*b^3*(-552960*b^3 + 1643520*b^4 - 1375104*b^5 + 410880*b^6 - 34560*b^7) + 5*Sqrt[2 - b]*b^3*(153600*b^3 - 499200*b^4 + 388032*b^5 - 83712*b^6 + 2688*b^7)*Sqrt[2 - b*x]) + x^3*(5*b^3*(-51200*b^3 + 550400*b^4 - 979520*b^5 + 583360*b^6 - 119680*b^7 + 4480*b^8) + 5*Sqrt[2 - b]*b^3*(10240*b^3 - 131840*b^4 + 249600*b^5 - 135680*b^6 + 17920*b^7)*Sqrt[2 - b*x]) + x^4*(5*b^3*(3200*b^4 - 52640*b^5 + 137600*b^6 - 119680*b^7 + 37120*b^8 - 2560*b^9) + 5*Sqrt[2 - b]*b^3*(-320*b^4 + 6400*b^5 - 19200*b^6 + 17920*b^7 - 5120*b^8)*Sqrt[2 - b*x]) + x^(7/2)*(5*b^3*(76800*b^4 - 341760*b^5 + 410880*b^6 - 176640*b^7 + 23040*b^8) + 5*Sqrt[2 - b]*b^3*(-12800*b^4 + 65920*b^5 - 83712*b^6 + 32512*b^7 - 2048*b^8)*Sqrt[2 - b*x]) + x^(9/2)*(5*b^3*(-2880*b^5 + 19200*b^6 - 34560*b^7 + 23040*b^8 - 5120*b^9) + 5*Sqrt[2 - b]*b^3*(160*b^5 - 1280*b^6 + 2688*b^7 - 2048*b^8 + 512*b^9)*Sqrt[2 - b*x])) + (3*ArcTan[(Sqrt[2 - b]/Sqrt[b] - Sqrt[2 - b*x]/Sqrt[b])/(-1 + Sqrt[x])])/(2*b^(7/2))","B",1
540,1,2084,109,3.105024,"\int x^{3/2} (2-b x)^{3/2} \, dx","IntegrateAlgebraic[x^(3/2)*(2 - b*x)^(3/2),x]","\text{Result too large to show}","\frac{3 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{4 b^{5/2}}-\frac{3 \sqrt{x} \sqrt{2-b x}}{8 b^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,"(2*(6144 - 5632*b - 11584*b^2 + 20016*b^3 - 11800*b^4 + 3240*b^5 - 400*b^6 + 16*b^7)*Sqrt[2 - b*x] + 2*(-6144 - 6144*b + 7808*b^2 + 24384*b^3 - 36907*b^4 + 19388*b^5 - 4532*b^6 + 424*b^7 - 8*b^8)*Sqrt[x]*Sqrt[2 - b*x] + 2*(7680*b + 4992*b^2 + 3696*b^3 - 38640*b^4 + 40440*b^5 - 17040*b^6 + 3120*b^7 - 192*b^8)*x*Sqrt[2 - b*x] + 2*(4096*b - 7936*b^2 - 2880*b^3 - 13228*b^4 + 37147*b^5 - 28760*b^6 + 9500*b^7 - 1280*b^8 + 40*b^9)*x^(3/2)*Sqrt[2 - b*x] + 2*(-5696*b^2 + 5904*b^3 - 896*b^4 + 14336*b^5 - 23440*b^6 + 13840*b^7 - 3520*b^8 + 320*b^9)*x^2*Sqrt[2 - b*x] + 2*(12416*b^2 - 8768*b^3 + 982*b^4 + 1736*b^5 - 8582*b^6 + 9816*b^7 - 4512*b^8 + 864*b^9 - 48*b^10)*x^(5/2)*Sqrt[2 - b*x] + 2*(-25520*b^3 + 20912*b^4 - 4480*b^5 - 896*b^6 + 2992*b^7 - 2624*b^8 + 960*b^9 - 128*b^10)*x^3*Sqrt[2 - b*x] + 2*(-16832*b^3 + 41156*b^4 - 23154*b^5 + 3640*b^6 + 186*b^7 - 512*b^8 + 384*b^9 - 128*b^10 + 16*b^11)*x^(7/2)*Sqrt[2 - b*x] + 2*(30424*b^4 - 40936*b^5 + 15568*b^6 - 1488*b^7)*x^4*Sqrt[2 - b*x] + 2*(7997*b^4 - 33452*b^5 + 27420*b^6 - 6760*b^7 + 280*b^8)*x^(9/2)*Sqrt[2 - b*x] + 2*(-12600*b^5 + 24080*b^6 - 12656*b^7 + 1856*b^8)*x^5*Sqrt[2 - b*x] + 2*(-1665*b^5 + 10680*b^6 - 11860*b^7 + 4000*b^8 - 280*b^9)*x^(11/2)*Sqrt[2 - b*x] + 2*(2128*b^6 - 5712*b^7 + 4032*b^8 - 832*b^9)*x^6*Sqrt[2 - b*x] + 2*(134*b^6 - 1304*b^7 + 2000*b^8 - 928*b^9 + 112*b^10)*x^(13/2)*Sqrt[2 - b*x] + 2*(-112*b^7 + 448*b^8 - 448*b^9 + 128*b^10)*x^7*Sqrt[2 - b*x] + 2*(-2*b^7 + 32*b^8 - 80*b^9 + 64*b^10 - 16*b^11)*x^(15/2)*Sqrt[2 - b*x] + Sqrt[2 - b]*(2*(-6144 + 4096*b + 12416*b^2 - 16832*b^3 + 7997*b^4 - 1665*b^5 + 134*b^6 - 2*b^7) + 2*(6144 + 7680*b - 5696*b^2 - 25520*b^3 + 30424*b^4 - 12600*b^5 + 2128*b^6 - 112*b^7)*Sqrt[x] + 2*(-6144*b - 7936*b^2 - 8768*b^3 + 41156*b^4 - 33452*b^5 + 10680*b^6 - 1304*b^7 + 32*b^8)*x + 2*(-5632*b + 4992*b^2 + 5904*b^3 + 20912*b^4 - 40936*b^5 + 24080*b^6 - 5712*b^7 + 448*b^8)*x^(3/2) + 2*(7808*b^2 - 2880*b^3 + 982*b^4 - 23154*b^5 + 27420*b^6 - 11860*b^7 + 2000*b^8 - 80*b^9)*x^2 + 2*(-11584*b^2 + 3696*b^3 - 896*b^4 - 4480*b^5 + 15568*b^6 - 12656*b^7 + 4032*b^8 - 448*b^9)*x^(5/2) + 2*(24384*b^3 - 13228*b^4 + 1736*b^5 + 3640*b^6 - 6760*b^7 + 4000*b^8 - 928*b^9 + 64*b^10)*x^3 + 2*(20016*b^3 - 38640*b^4 + 14336*b^5 - 896*b^6 - 1488*b^7 + 1856*b^8 - 832*b^9 + 128*b^10)*x^(7/2) + 2*(-36907*b^4 + 37147*b^5 - 8582*b^6 + 186*b^7 + 280*b^8 - 280*b^9 + 112*b^10 - 16*b^11)*x^4 + 2*(-11800*b^4 + 40440*b^5 - 23440*b^6 + 2992*b^7)*x^(9/2) + 2*(19388*b^5 - 28760*b^6 + 9816*b^7 - 512*b^8)*x^5 + 2*(3240*b^5 - 17040*b^6 + 13840*b^7 - 2624*b^8)*x^(11/2) + 2*(-4532*b^6 + 9500*b^7 - 4512*b^8 + 384*b^9)*x^6 + 2*(-400*b^6 + 3120*b^7 - 3520*b^8 + 960*b^9)*x^(13/2) + 2*(424*b^7 - 1280*b^8 + 864*b^9 - 128*b^10)*x^7 + 2*(16*b^7 - 192*b^8 + 320*b^9 - 128*b^10)*x^(15/2) + 2*(-8*b^8 + 40*b^9 - 48*b^10 + 16*b^11)*x^8))/(b^2*(32768 - 32768*b + 10240*b^2 - 1024*b^3 + 16*b^4) + b^2*(16*b^4 - 256*b^5 + 640*b^6 - 512*b^7 + 128*b^8)*x^4 + Sqrt[2 - b]*b^2*(-16384 + 12288*b - 2560*b^2 + 128*b^3)*Sqrt[2 - b*x] + x*(b^2*(-32768*b + 94208*b^2 - 56320*b^3 + 9664*b^4 - 256*b^5) + Sqrt[2 - b]*b^2*(12288*b - 39936*b^2 + 17280*b^3 - 1536*b^4)*Sqrt[2 - b*x]) + Sqrt[x]*(b^2*(-65536*b + 57344*b^2 - 14336*b^3 + 896*b^4) + Sqrt[2 - b]*b^2*(32768*b - 20480*b^2 + 3072*b^3 - 64*b^4)*Sqrt[2 - b*x]) + x^(3/2)*(b^2*(57344*b^2 - 86016*b^3 + 34944*b^4 - 3584*b^5) + Sqrt[2 - b]*b^2*(-20480*b^2 + 30720*b^3 - 8640*b^4 + 320*b^5)*Sqrt[2 - b*x]) + x^2*(b^2*(10240*b^2 - 56320*b^3 + 52320*b^4 - 14080*b^5 + 640*b^6) + Sqrt[2 - b]*b^2*(-2560*b^2 + 17280*b^3 - 15360*b^4 + 2560*b^5)*Sqrt[2 - b*x]) + x^3*(b^2*(-1024*b^3 + 9664*b^4 - 14080*b^5 + 5888*b^6 - 512*b^7) + Sqrt[2 - b]*b^2*(128*b^3 - 1536*b^4 + 2560*b^5 - 1024*b^6)*Sqrt[2 - b*x]) + x^(5/2)*(b^2*(-14336*b^3 + 34944*b^4 - 21504*b^5 + 3584*b^6) + Sqrt[2 - b]*b^2*(3072*b^3 - 8640*b^4 + 4992*b^5 - 384*b^6)*Sqrt[2 - b*x]) + x^(7/2)*(b^2*(896*b^4 - 3584*b^5 + 3584*b^6 - 1024*b^7) + Sqrt[2 - b]*b^2*(-64*b^4 + 320*b^5 - 384*b^6 + 128*b^7)*Sqrt[2 - b*x])) + (3*ArcTan[(Sqrt[2 - b]/Sqrt[b] - Sqrt[2 - b*x]/Sqrt[b])/(-1 + Sqrt[x])])/(2*b^(5/2))","B",1
541,1,1313,84,1.9452592,"\int \sqrt{x} (2-b x)^{3/2} \, dx","IntegrateAlgebraic[Sqrt[x]*(2 - b*x)^(3/2),x]","\frac{4 \left(-8 b^8+24 b^7-18 b^6+2 b^5\right) \sqrt{2-b x} x^{11/2}+4 \left(48 b^7-120 b^6+60 b^5\right) \sqrt{2-b x} x^5+4 \left(52 b^7-288 b^6+381 b^5-79 b^4\right) \sqrt{2-b x} x^{9/2}+4 \left(-288 b^6+940 b^5-690 b^4\right) \sqrt{2-b x} x^4+4 \left(-114 b^6+1068 b^5-1956 b^4+639 b^3\right) \sqrt{2-b x} x^{7/2}+4 \left(552 b^5-2480 b^4+2538 b^3\right) \sqrt{2-b x} x^3+4 \left(8 b^8-60 b^7+162 b^6-92 b^5-1392 b^4+3699 b^3-1964 b^2\right) \sqrt{2-b x} x^{5/2}+4 \left(-48 b^7+336 b^6-816 b^5+432 b^4+2142 b^3-3372 b^2\right) \sqrt{2-b x} x^2+4 \left(-16 b^7+252 b^6-1182 b^5+2200 b^4-987 b^3-2136 b^2+2368 b\right) \sqrt{2-b x} x^{3/2}+4 \left(72 b^6-724 b^5+2544 b^4-3618 b^3+1352 b^2+768 b\right) \sqrt{2-b x} x+4 \left(6 b^6-177 b^5+1227 b^4-3351 b^3+3588 b^2-576 b-768\right) \sqrt{2-b x} \sqrt{x}+\sqrt{2-b} \left(4 \left(8 b^8-16 b^7+6 b^6\right) x^6+4 \left(-48 b^7+72 b^6-12 b^5\right) x^{11/2}+4 \left(-60 b^7+252 b^6-177 b^5\right) x^5+4 \left(336 b^6-724 b^5+194 b^4\right) x^{9/2}+4 \left(162 b^6-1182 b^5+1227 b^4\right) x^4+4 \left(-816 b^5+2544 b^4-1062 b^3\right) x^{7/2}+4 \left(-8 b^8+52 b^7-114 b^6-92 b^5+2200 b^4-3351 b^3\right) x^3+4 \left(48 b^7-288 b^6+552 b^5+432 b^4-3618 b^3+2532 b^2\right) x^{5/2}+4 \left(24 b^7-288 b^6+1068 b^5-1392 b^4-987 b^3+3588 b^2\right) x^2+4 \left(-120 b^6+940 b^5-2480 b^4+2142 b^3+1352 b^2-2560 b\right) x^{3/2}+4 \left(-18 b^6+381 b^5-1956 b^4+3699 b^3-2136 b^2-576 b\right) x+4 \left(60 b^5-690 b^4+2538 b^3-3372 b^2+768 b+768\right) \sqrt{x}+4 \left(2 b^5-79 b^4+639 b^3-1964 b^2+2368 b-768\right)\right)+4 \left(-12 b^5+194 b^4-1062 b^3+2532 b^2-2560 b+768\right) \sqrt{2-b x}}{3 b \left(32 b^6-96 b^5+72 b^4-8 b^3\right) x^3+\left(3 b \left(-192 b^5+480 b^4-240 b^3\right)+3 \sqrt{2-b} b \left(32 b^5-64 b^4+24 b^3\right) \sqrt{2-b x}\right) x^{5/2}+\left(3 \sqrt{2-b} b \sqrt{2-b x} \left(-192 b^4+288 b^3-48 b^2\right)+3 b \left(-96 b^5+816 b^4-1272 b^3+288 b^2\right)\right) x^2+\left(3 \sqrt{2-b} b \sqrt{2-b x} \left(-64 b^4+656 b^3-576 b^2\right)+3 b \left(480 b^4-2080 b^3+1920 b^2\right)\right) x^{3/2}+\left(3 \sqrt{2-b} b \sqrt{2-b x} \left(288 b^3-1312 b^2+512 b\right)+3 b \left(72 b^4-1272 b^3+3264 b^2-1536 b\right)\right) x+\left(3 b \left(-240 b^3+1920 b^2-3072 b\right)+3 \sqrt{2-b} b \left(24 b^3-576 b^2+1536 b\right) \sqrt{2-b x}\right) \sqrt{x}+3 b \left(-8 b^3+288 b^2-1536 b+2048\right)+3 \sqrt{2-b} b \left(-48 b^2+512 b-1024\right) \sqrt{2-b x}}+\frac{2 \tan ^{-1}\left(\frac{\frac{\sqrt{2-b}}{\sqrt{b}}-\frac{\sqrt{2-b x}}{\sqrt{b}}}{\sqrt{x}-1}\right)}{b^{3/2}}","\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,"(4*(768 - 2560*b + 2532*b^2 - 1062*b^3 + 194*b^4 - 12*b^5)*Sqrt[2 - b*x] + 4*(-768 - 576*b + 3588*b^2 - 3351*b^3 + 1227*b^4 - 177*b^5 + 6*b^6)*Sqrt[x]*Sqrt[2 - b*x] + 4*(768*b + 1352*b^2 - 3618*b^3 + 2544*b^4 - 724*b^5 + 72*b^6)*x*Sqrt[2 - b*x] + 4*(2368*b - 2136*b^2 - 987*b^3 + 2200*b^4 - 1182*b^5 + 252*b^6 - 16*b^7)*x^(3/2)*Sqrt[2 - b*x] + 4*(-3372*b^2 + 2142*b^3 + 432*b^4 - 816*b^5 + 336*b^6 - 48*b^7)*x^2*Sqrt[2 - b*x] + 4*(-1964*b^2 + 3699*b^3 - 1392*b^4 - 92*b^5 + 162*b^6 - 60*b^7 + 8*b^8)*x^(5/2)*Sqrt[2 - b*x] + 4*(2538*b^3 - 2480*b^4 + 552*b^5)*x^3*Sqrt[2 - b*x] + 4*(639*b^3 - 1956*b^4 + 1068*b^5 - 114*b^6)*x^(7/2)*Sqrt[2 - b*x] + 4*(-690*b^4 + 940*b^5 - 288*b^6)*x^4*Sqrt[2 - b*x] + 4*(-79*b^4 + 381*b^5 - 288*b^6 + 52*b^7)*x^(9/2)*Sqrt[2 - b*x] + 4*(60*b^5 - 120*b^6 + 48*b^7)*x^5*Sqrt[2 - b*x] + 4*(2*b^5 - 18*b^6 + 24*b^7 - 8*b^8)*x^(11/2)*Sqrt[2 - b*x] + Sqrt[2 - b]*(4*(-768 + 2368*b - 1964*b^2 + 639*b^3 - 79*b^4 + 2*b^5) + 4*(768 + 768*b - 3372*b^2 + 2538*b^3 - 690*b^4 + 60*b^5)*Sqrt[x] + 4*(-576*b - 2136*b^2 + 3699*b^3 - 1956*b^4 + 381*b^5 - 18*b^6)*x + 4*(-2560*b + 1352*b^2 + 2142*b^3 - 2480*b^4 + 940*b^5 - 120*b^6)*x^(3/2) + 4*(3588*b^2 - 987*b^3 - 1392*b^4 + 1068*b^5 - 288*b^6 + 24*b^7)*x^2 + 4*(2532*b^2 - 3618*b^3 + 432*b^4 + 552*b^5 - 288*b^6 + 48*b^7)*x^(5/2) + 4*(-3351*b^3 + 2200*b^4 - 92*b^5 - 114*b^6 + 52*b^7 - 8*b^8)*x^3 + 4*(-1062*b^3 + 2544*b^4 - 816*b^5)*x^(7/2) + 4*(1227*b^4 - 1182*b^5 + 162*b^6)*x^4 + 4*(194*b^4 - 724*b^5 + 336*b^6)*x^(9/2) + 4*(-177*b^5 + 252*b^6 - 60*b^7)*x^5 + 4*(-12*b^5 + 72*b^6 - 48*b^7)*x^(11/2) + 4*(6*b^6 - 16*b^7 + 8*b^8)*x^6))/(3*b*(2048 - 1536*b + 288*b^2 - 8*b^3) + 3*b*(-8*b^3 + 72*b^4 - 96*b^5 + 32*b^6)*x^3 + 3*Sqrt[2 - b]*b*(-1024 + 512*b - 48*b^2)*Sqrt[2 - b*x] + Sqrt[x]*(3*b*(-3072*b + 1920*b^2 - 240*b^3) + 3*Sqrt[2 - b]*b*(1536*b - 576*b^2 + 24*b^3)*Sqrt[2 - b*x]) + x*(3*b*(-1536*b + 3264*b^2 - 1272*b^3 + 72*b^4) + 3*Sqrt[2 - b]*b*(512*b - 1312*b^2 + 288*b^3)*Sqrt[2 - b*x]) + x^2*(3*b*(288*b^2 - 1272*b^3 + 816*b^4 - 96*b^5) + 3*Sqrt[2 - b]*b*(-48*b^2 + 288*b^3 - 192*b^4)*Sqrt[2 - b*x]) + x^(3/2)*(3*b*(1920*b^2 - 2080*b^3 + 480*b^4) + 3*Sqrt[2 - b]*b*(-576*b^2 + 656*b^3 - 64*b^4)*Sqrt[2 - b*x]) + x^(5/2)*(3*b*(-240*b^3 + 480*b^4 - 192*b^5) + 3*Sqrt[2 - b]*b*(24*b^3 - 64*b^4 + 32*b^5)*Sqrt[2 - b*x])) + (2*ArcTan[(Sqrt[2 - b]/Sqrt[b] - Sqrt[2 - b*x]/Sqrt[b])/(-1 + Sqrt[x])])/b^(3/2)","B",1
542,1,695,63,0.8276799,"\int \frac{(2-b x)^{3/2}}{\sqrt{x}} \, dx","IntegrateAlgebraic[(2 - b*x)^(3/2)/Sqrt[x],x]","\frac{2 \left(8 b^4-12 b^3\right) x^3 \sqrt{2-b x}+2 \left(92 b^2-52 b^3\right) x^2 \sqrt{2-b x}+2 \left(4 b^3-44 b^2+152 b-160\right) \sqrt{2-b x}+2 \left(-2 b^5+4 b^4-b^3\right) x^{7/2} \sqrt{2-b x}+2 \left(14 b^4-42 b^3+21 b^2\right) x^{5/2} \sqrt{2-b x}+2 \left(-8 b^4+60 b^3-48 b^2-120 b\right) x \sqrt{2-b x}+2 \left(-2 b^4+30 b^3-127 b^2+80 b+160\right) \sqrt{x} \sqrt{2-b x}+2 \left(2 b^5-16 b^4+13 b^3+106 b^2-112 b\right) x^{3/2} \sqrt{2-b x}+\sqrt{2-b} \left(2 \left(2 b^5-2 b^4\right) x^4+2 \left(4 b^3-8 b^4\right) x^{7/2}+2 \left(30 b^3-16 b^4\right) x^3+2 \left(60 b^3-44 b^2\right) x^{5/2}+2 \left(-12 b^3+92 b^2-120 b-160\right) \sqrt{x}+2 \left(-b^3+21 b^2-112 b+160\right)+2 \left(8 b^4-52 b^3-48 b^2+152 b\right) x^{3/2}+2 \left(4 b^4-42 b^3+106 b^2+80 b\right) x+2 \left(-2 b^5+14 b^4+13 b^3-127 b^2\right) x^2\right)}{\sqrt{x} \left(\sqrt{2-b} \left(64 b-8 b^2\right) \sqrt{2-b x}+48 b^2-128 b\right)+4 b^2+x^{3/2} \left(-32 b^3+48 b^2+\sqrt{2-b} \left(8 b^3-8 b^2\right) \sqrt{2-b x}\right)+x \left(-16 b^3+\sqrt{2-b} \left(16 b-32 b^2\right) \sqrt{2-b x}+88 b^2-64 b\right)+\left(8 b^4-16 b^3+4 b^2\right) x^2+\sqrt{2-b} (16 b-64) \sqrt{2-b x}-64 b+128}+\frac{6 \tan ^{-1}\left(\frac{\frac{\sqrt{2-b}}{\sqrt{b}}-\frac{\sqrt{2-b x}}{\sqrt{b}}}{\sqrt{x}-1}\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,"(2*(-160 + 152*b - 44*b^2 + 4*b^3)*Sqrt[2 - b*x] + 2*(160 + 80*b - 127*b^2 + 30*b^3 - 2*b^4)*Sqrt[x]*Sqrt[2 - b*x] + 2*(-120*b - 48*b^2 + 60*b^3 - 8*b^4)*x*Sqrt[2 - b*x] + 2*(-112*b + 106*b^2 + 13*b^3 - 16*b^4 + 2*b^5)*x^(3/2)*Sqrt[2 - b*x] + 2*(92*b^2 - 52*b^3)*x^2*Sqrt[2 - b*x] + 2*(21*b^2 - 42*b^3 + 14*b^4)*x^(5/2)*Sqrt[2 - b*x] + 2*(-12*b^3 + 8*b^4)*x^3*Sqrt[2 - b*x] + 2*(-b^3 + 4*b^4 - 2*b^5)*x^(7/2)*Sqrt[2 - b*x] + Sqrt[2 - b]*(2*(160 - 112*b + 21*b^2 - b^3) + 2*(-160 - 120*b + 92*b^2 - 12*b^3)*Sqrt[x] + 2*(80*b + 106*b^2 - 42*b^3 + 4*b^4)*x + 2*(152*b - 48*b^2 - 52*b^3 + 8*b^4)*x^(3/2) + 2*(-127*b^2 + 13*b^3 + 14*b^4 - 2*b^5)*x^2 + 2*(-44*b^2 + 60*b^3)*x^(5/2) + 2*(30*b^3 - 16*b^4)*x^3 + 2*(4*b^3 - 8*b^4)*x^(7/2) + 2*(-2*b^4 + 2*b^5)*x^4))/(128 - 64*b + 4*b^2 + (4*b^2 - 16*b^3 + 8*b^4)*x^2 + Sqrt[2 - b]*(-64 + 16*b)*Sqrt[2 - b*x] + x*(-64*b + 88*b^2 - 16*b^3 + Sqrt[2 - b]*(16*b - 32*b^2)*Sqrt[2 - b*x]) + Sqrt[x]*(-128*b + 48*b^2 + Sqrt[2 - b]*(64*b - 8*b^2)*Sqrt[2 - b*x]) + x^(3/2)*(48*b^2 - 32*b^3 + Sqrt[2 - b]*(-8*b^2 + 8*b^3)*Sqrt[2 - b*x])) + (6*ArcTan[(Sqrt[2 - b]/Sqrt[b] - Sqrt[2 - b*x]/Sqrt[b])/(-1 + Sqrt[x])])/Sqrt[b]","B",1
543,1,464,60,0.9941971,"\int \frac{(2-b x)^{3/2}}{x^{3/2}} \, dx","IntegrateAlgebraic[(2 - b*x)^(3/2)/x^(3/2),x]","\frac{\left(4-4 \sqrt{x}\right) \left(b (-x)+2 b \sqrt{x}-2 \sqrt{2-b} \sqrt{2-b x}+\sqrt{2-b} \sqrt{x} \sqrt{2-b x}-2 b-2 \sqrt{x}+4\right) \left(\sqrt{2-b}-\sqrt{2-b x}\right)}{\sqrt{x} \left(b^2 \sqrt{x}+b x^{3/2}-2 b x+b \sqrt{x}+\sqrt{2-b} b \sqrt{2-b x}-4 \sqrt{2-b} \sqrt{2-b x}+2 \sqrt{2-b} \sqrt{x} \sqrt{2-b x}-4 b-4 \sqrt{x}+8\right)}+\frac{\left(-2 b^2 \sqrt{x}+2 b \sqrt{x}-2 \sqrt{2-b} b \sqrt{2-b x}+2 b\right) \left(\sqrt{2-b}-\sqrt{2-b x}\right)^3}{\left(b \sqrt{x}+\sqrt{2-b} \sqrt{2-b x}-2\right)^2}+\frac{\left(b \sqrt{x}+2 \sqrt{2-b} \sqrt{2-b x}+b-\sqrt{x}-3\right) \left(2 b \sqrt{2-b x}-2 \sqrt{2-b} b\right)}{b \sqrt{x}+\sqrt{2-b} \sqrt{2-b x}-2}-12 \sqrt{b} \tan ^{-1}\left(\frac{\frac{\sqrt{2-b}}{\sqrt{b}}-\frac{\sqrt{2-b x}}{\sqrt{b}}}{\sqrt{x}-1}\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] + b*Sqrt[x] + 2*Sqrt[2 - b]*Sqrt[2 - b*x])*(-2*Sqrt[2 - b]*b + 2*b*Sqrt[2 - b*x]))/(-2 + b*Sqrt[x] + Sqrt[2 - b]*Sqrt[2 - b*x]) + ((Sqrt[2 - b] - Sqrt[2 - b*x])^3*(2*b + 2*b*Sqrt[x] - 2*b^2*Sqrt[x] - 2*Sqrt[2 - b]*b*Sqrt[2 - b*x]))/(-2 + b*Sqrt[x] + Sqrt[2 - b]*Sqrt[2 - b*x])^2 + ((4 - 4*Sqrt[x])*(Sqrt[2 - b] - Sqrt[2 - b*x])*(4 - 2*b - 2*Sqrt[x] + 2*b*Sqrt[x] - b*x - 2*Sqrt[2 - b]*Sqrt[2 - b*x] + Sqrt[2 - b]*Sqrt[x]*Sqrt[2 - b*x]))/(Sqrt[x]*(8 - 4*b - 4*Sqrt[x] + b*Sqrt[x] + b^2*Sqrt[x] - 2*b*x + b*x^(3/2) - 4*Sqrt[2 - b]*Sqrt[2 - b*x] + Sqrt[2 - b]*b*Sqrt[2 - b*x] + 2*Sqrt[2 - b]*Sqrt[x]*Sqrt[2 - b*x])) - 12*Sqrt[b]*ArcTan[(Sqrt[2 - b]/Sqrt[b] - Sqrt[2 - b*x]/Sqrt[b])/(-1 + Sqrt[x])]","B",1
544,1,1392,62,2.0767421,"\int \frac{(2-b x)^{3/2}}{x^{5/2}} \, dx","IntegrateAlgebraic[(2 - b*x)^(3/2)/x^(5/2),x]","4 \tan ^{-1}\left(\frac{\frac{\sqrt{2-b}}{\sqrt{b}}-\frac{\sqrt{2-b x}}{\sqrt{b}}}{\sqrt{x}-1}\right) b^{3/2}+\frac{8 b^4 \sqrt{2-b x} x^{11/2}-4 \left(24 b^4-30 b^3+12 b^2\right) \sqrt{2-b x} x^5-4 \left(-141 b^4+259 b^3-72 b^2\right) \sqrt{2-b x} x^{9/2}-4 \left(440 b^4-1026 b^3+504 b^2-128 b\right) \sqrt{2-b x} x^4-4 \left(-18 b^5-909 b^4+3063 b^3-2820 b^2+768 b\right) \sqrt{2-b x} x^{7/2}-4 \left(1692 b^4-6790 b^3+7908 b^2-2304 b+256\right) \sqrt{2-b x} x^3-4 \left(-12 b^6+90 b^5-2057 b^4+8997 b^3-13248 b^2+6720 b-1536\right) \sqrt{2-b x} x^{5/2}-4 \left(72 b^5+1080 b^4-8430 b^3+18672 b^2-14976 b+3072\right) \sqrt{2-b x} x^2-4 \left(12 b^6-66 b^5-1089 b^4+8317 b^3-19524 b^2+16320 b-2304\right) \sqrt{2-b x} x^{3/2}-4 \left(-72 b^5+836 b^4-3852 b^3+8136 b^2-7168 b+1536\right) \sqrt{2-b x} x-4 \left(-6 b^5+102 b^4-156 b^3-1200 b^2+3840 b-3072\right) \sqrt{2-b x} \sqrt{x}+\sqrt{2-b} \left(-4 \left(b^3-2 b^4\right) x^6-4 \left(24 b^4-6 b^3\right) x^{11/2}-4 \left(-123 b^4+99 b^3-36 b^2\right) x^5-4 \left(440 b^4-718 b^3+216 b^2\right) x^{9/2}-4 \left(18 b^5-1053 b^4+2319 b^3-936 b^2+192 b\right) x^4-4 \left(1476 b^4-4890 b^3+4140 b^2-1152 b\right) x^{7/2}-4 \left(12 b^6-78 b^5-1729 b^4+8627 b^3-10860 b^2+3008 b-256\right) x^3-4 \left(-72 b^5+2016 b^4-10074 b^3+15552 b^2-6912 b+1536\right) x^{5/2}-4 \left(-12 b^6+42 b^5-765 b^4+6588 b^3-16848 b^2+14592 b-3072\right) x^2-4 \left(72 b^5+188 b^4-5008 b^3+16428 b^2-16512 b+2304\right) x^{3/2}-4 \left(18 b^5-420 b^4+2694 b^3-7128 b^2+7296 b-1536\right) x-4 \left(-48 b^4+216 b^3+528 b^2-3072 b+3072\right) \sqrt{x}-4 \left(-4 b^4+152 b^3-1056 b^2+2560 b-2048\right)\right)-4 \left(24 b^4-352 b^3+1632 b^2-3072 b+2048\right) \sqrt{2-b x}}{3 b^3 x^6-18 b^3 x^{11/2}+\left(18 \sqrt{2-b} \sqrt{2-b x} b^2+3 \left(3 b^4+27 b^3-36 b^2\right)\right) x^5+\left(3 \left(216 b^2-128 b^3\right)+3 \sqrt{2-b} \left(3 b^3-36 b^2\right) \sqrt{2-b x}\right) x^{9/2}+\left(3 \sqrt{2-b} \sqrt{2-b x} \left(92 b^2-64 b\right)+3 \left(6 b^5-24 b^4+267 b^3-552 b^2+192 b\right)\right) x^4+\left(3 \left(-36 b^4-270 b^3+1248 b^2-1152 b\right)+3 \sqrt{2-b} \left(6 b^4-18 b^3-240 b^2+384 b\right) \sqrt{2-b x}\right) x^{7/2}+\left(3 \sqrt{2-b} \sqrt{2-b x} \left(-36 b^3+486 b^2-832 b+128\right)+3 \left(4 b^6-24 b^5+39 b^4+565 b^3-2340 b^2+2496 b-256\right)\right) x^3+\left(3 \left(-24 b^5+132 b^4-588 b^3+1992 b^2-3072 b+1536\right)+3 \sqrt{2-b} \left(4 b^5-20 b^4+27 b^3-364 b^2+1088 b-768\right) \sqrt{2-b x}\right) x^{5/2}+\left(3 \sqrt{2-b} \sqrt{2-b x} \left(-24 b^4+108 b^3+264 b^2-1536 b+1536\right)+3 \left(-6 b^5+102 b^4-156 b^3-1200 b^2+3840 b-3072\right)\right) x^2+\left(3 \sqrt{2-b} \sqrt{2-b x} \left(-2 b^4+76 b^3-528 b^2+1280 b-1024\right)+3 \left(24 b^4-352 b^3+1632 b^2-3072 b+2048\right)\right) x^{3/2}}","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,"(-4*(2048 - 3072*b + 1632*b^2 - 352*b^3 + 24*b^4)*Sqrt[2 - b*x] - 4*(-3072 + 3840*b - 1200*b^2 - 156*b^3 + 102*b^4 - 6*b^5)*Sqrt[x]*Sqrt[2 - b*x] - 4*(1536 - 7168*b + 8136*b^2 - 3852*b^3 + 836*b^4 - 72*b^5)*x*Sqrt[2 - b*x] - 4*(-2304 + 16320*b - 19524*b^2 + 8317*b^3 - 1089*b^4 - 66*b^5 + 12*b^6)*x^(3/2)*Sqrt[2 - b*x] - 4*(3072 - 14976*b + 18672*b^2 - 8430*b^3 + 1080*b^4 + 72*b^5)*x^2*Sqrt[2 - b*x] - 4*(-1536 + 6720*b - 13248*b^2 + 8997*b^3 - 2057*b^4 + 90*b^5 - 12*b^6)*x^(5/2)*Sqrt[2 - b*x] - 4*(256 - 2304*b + 7908*b^2 - 6790*b^3 + 1692*b^4)*x^3*Sqrt[2 - b*x] - 4*(768*b - 2820*b^2 + 3063*b^3 - 909*b^4 - 18*b^5)*x^(7/2)*Sqrt[2 - b*x] - 4*(-128*b + 504*b^2 - 1026*b^3 + 440*b^4)*x^4*Sqrt[2 - b*x] - 4*(-72*b^2 + 259*b^3 - 141*b^4)*x^(9/2)*Sqrt[2 - b*x] - 4*(12*b^2 - 30*b^3 + 24*b^4)*x^5*Sqrt[2 - b*x] + 8*b^4*x^(11/2)*Sqrt[2 - b*x] + Sqrt[2 - b]*(-4*(-2048 + 2560*b - 1056*b^2 + 152*b^3 - 4*b^4) - 4*(3072 - 3072*b + 528*b^2 + 216*b^3 - 48*b^4)*Sqrt[x] - 4*(-1536 + 7296*b - 7128*b^2 + 2694*b^3 - 420*b^4 + 18*b^5)*x - 4*(2304 - 16512*b + 16428*b^2 - 5008*b^3 + 188*b^4 + 72*b^5)*x^(3/2) - 4*(-3072 + 14592*b - 16848*b^2 + 6588*b^3 - 765*b^4 + 42*b^5 - 12*b^6)*x^2 - 4*(1536 - 6912*b + 15552*b^2 - 10074*b^3 + 2016*b^4 - 72*b^5)*x^(5/2) - 4*(-256 + 3008*b - 10860*b^2 + 8627*b^3 - 1729*b^4 - 78*b^5 + 12*b^6)*x^3 - 4*(-1152*b + 4140*b^2 - 4890*b^3 + 1476*b^4)*x^(7/2) - 4*(192*b - 936*b^2 + 2319*b^3 - 1053*b^4 + 18*b^5)*x^4 - 4*(216*b^2 - 718*b^3 + 440*b^4)*x^(9/2) - 4*(-36*b^2 + 99*b^3 - 123*b^4)*x^5 - 4*(-6*b^3 + 24*b^4)*x^(11/2) - 4*(b^3 - 2*b^4)*x^6))/(-18*b^3*x^(11/2) + 3*b^3*x^6 + x^5*(3*(-36*b^2 + 27*b^3 + 3*b^4) + 18*Sqrt[2 - b]*b^2*Sqrt[2 - b*x]) + x^4*(3*(192*b - 552*b^2 + 267*b^3 - 24*b^4 + 6*b^5) + 3*Sqrt[2 - b]*(-64*b + 92*b^2)*Sqrt[2 - b*x]) + x^3*(3*(-256 + 2496*b - 2340*b^2 + 565*b^3 + 39*b^4 - 24*b^5 + 4*b^6) + 3*Sqrt[2 - b]*(128 - 832*b + 486*b^2 - 36*b^3)*Sqrt[2 - b*x]) + x^(9/2)*(3*(216*b^2 - 128*b^3) + 3*Sqrt[2 - b]*(-36*b^2 + 3*b^3)*Sqrt[2 - b*x]) + x^2*(3*(-3072 + 3840*b - 1200*b^2 - 156*b^3 + 102*b^4 - 6*b^5) + 3*Sqrt[2 - b]*(1536 - 1536*b + 264*b^2 + 108*b^3 - 24*b^4)*Sqrt[2 - b*x]) + x^(3/2)*(3*(2048 - 3072*b + 1632*b^2 - 352*b^3 + 24*b^4) + 3*Sqrt[2 - b]*(-1024 + 1280*b - 528*b^2 + 76*b^3 - 2*b^4)*Sqrt[2 - b*x]) + x^(7/2)*(3*(-1152*b + 1248*b^2 - 270*b^3 - 36*b^4) + 3*Sqrt[2 - b]*(384*b - 240*b^2 - 18*b^3 + 6*b^4)*Sqrt[2 - b*x]) + x^(5/2)*(3*(1536 - 3072*b + 1992*b^2 - 588*b^3 + 132*b^4 - 24*b^5) + 3*Sqrt[2 - b]*(-768 + 1088*b - 364*b^2 + 27*b^3 - 20*b^4 + 4*b^5)*Sqrt[2 - b*x])) + 4*b^(3/2)*ArcTan[(Sqrt[2 - b]/Sqrt[b] - Sqrt[2 - b*x]/Sqrt[b])/(-1 + Sqrt[x])]","B",1
545,1,5777,164,11.107185,"\int x^{5/2} (a+b x)^{5/2} \, dx","IntegrateAlgebraic[x^(5/2)*(a + b*x)^(5/2),x]","\text{Result too large to show}","-\frac{5 a^6 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{512 b^{7/2}}+\frac{5 a^5 \sqrt{x} \sqrt{a+b x}}{512 b^3}-\frac{5 a^4 x^{3/2} \sqrt{a+b x}}{768 b^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,"Result too large to show","B",1
546,1,4169,140,8.0352518,"\int x^{3/2} (a+b x)^{5/2} \, dx","IntegrateAlgebraic[x^(3/2)*(a + b*x)^(5/2),x]","\text{Result too large to show}","\frac{3 a^5 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{128 b^{5/2}}-\frac{3 a^4 \sqrt{x} \sqrt{a+b x}}{128 b^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,"((7680*a^14 + 17920*a^13*b - 116896*a^12*b^2 - 557440*a^11*b^3 - 1008010*a^10*b^4 - 974350*a^9*b^5 - 538900*a^8*b^6 - 166096*a^7*b^7 - 25120*a^6*b^8 - 1280*a^5*b^9)*Sqrt[a + b*x] + (-7680*a^14 + 19200*a^13*b + 63200*a^12*b^2 - 608080*a^11*b^3 - 2633630*a^10*b^4 - 4421225*a^9*b^5 - 3911150*a^8*b^6 - 1923220*a^7*b^7 - 498640*a^6*b^8 - 55840*a^5*b^9 - 1280*a^4*b^10)*Sqrt[x]*Sqrt[a + b*x] + (-23040*a^13*b + 40640*a^12*b^2 - 131392*a^11*b^3 - 2598920*a^10*b^4 - 7896350*a^9*b^5 - 11074400*a^8*b^6 - 8404960*a^7*b^7 - 3484672*a^6*b^8 - 712960*a^5*b^9 - 51200*a^4*b^10)*x*Sqrt[a + b*x] + (-14080*a^13*b - 59200*a^12*b^2 + 63600*a^11*b^3 - 962040*a^10*b^4 - 6876375*a^9*b^5 - 15985900*a^8*b^6 - 18615440*a^7*b^7 - 11856640*a^6*b^8 - 4001920*a^5*b^9 - 601600*a^4*b^10 - 20480*a^3*b^11)*x^(3/2)*Sqrt[a + b*x] + (-50720*a^12*b^2 - 113280*a^11*b^3 - 99276*a^10*b^4 - 2885100*a^9*b^5 - 12582900*a^8*b^6 - 23117280*a^7*b^7 - 22321920*a^6*b^8 - 11744256*a^5*b^9 - 3110400*a^4*b^10 - 307200*a^3*b^11)*x^2*Sqrt[a + b*x] + (122976*a^12*b^2 + 221840*a^11*b^3 + 126460*a^10*b^4 - 451370*a^9*b^5 - 5248330*a^8*b^6 - 16423868*a^7*b^7 - 24405120*a^6*b^8 - 19534080*a^5*b^9 - 8352000*a^4*b^10 - 1651200*a^3*b^11 - 86016*a^2*b^12)*x^(5/2)*Sqrt[a + b*x] + (630080*a^11*b^3 + 1326680*a^10*b^4 + 896900*a^9*b^5 - 804800*a^8*b^6 - 6383600*a^7*b^7 - 15395840*a^6*b^8 - 18826240*a^5*b^9 - 12482560*a^4*b^10 - 4249600*a^3*b^11 - 573440*a^2*b^12)*x^3*Sqrt[a + b*x] + (494672*a^11*b^3 + 2758120*a^10*b^4 + 4055650*a^9*b^5 + 2100760*a^8*b^6 - 835960*a^7*b^7 - 5235456*a^6*b^8 - 10165760*a^5*b^9 - 10393600*a^4*b^10 - 5708800*a^3*b^11 - 1515520*a^2*b^12 - 131072*a*b^13)*x^(7/2)*Sqrt[a + b*x] + (2313990*a^10*b^4 + 7513850*a^9*b^5 + 7900100*a^8*b^6 + 2947600*a^7*b^7 - 512000*a^6*b^8 - 2731520*a^5*b^9 - 4441600*a^4*b^10 - 3880960*a^3*b^11 - 1761280*a^2*b^12 - 327680*a*b^13)*x^4*Sqrt[a + b*x] + (776626*a^10*b^4 + 7053475*a^9*b^5 + 14391550*a^8*b^6 + 10680580*a^7*b^7 + 2673920*a^6*b^8 - 150528*a^5*b^9 - 729600*a^4*b^10 - 1062400*a^3*b^11 - 860160*a^2*b^12 - 368640*a*b^13 - 65536*b^14)*x^(9/2)*Sqrt[a + b*x] + (3345050*a^9*b^5 + 14613600*a^8*b^6 + 20030496*a^7*b^7 + 10245120*a^6*b^8 + 1505280*a^5*b^9)*x^5*Sqrt[a + b*x] + (639845*a^9*b^5 + 8362900*a^8*b^6 + 21836720*a^7*b^7 + 20560640*a^6*b^8 + 6883840*a^5*b^9 + 423680*a^4*b^10)*x^(11/2)*Sqrt[a + b*x] + (2487300*a^8*b^6 + 14115360*a^7*b^7 + 24137472*a^6*b^8 + 15528960*a^5*b^9 + 3059200*a^4*b^10)*x^6*Sqrt[a + b*x] + (290170*a^8*b^6 + 5212940*a^7*b^7 + 17088640*a^6*b^8 + 19889920*a^5*b^9 + 8441600*a^4*b^10 + 750080*a^3*b^11)*x^(13/2)*Sqrt[a + b*x] + (978480*a^7*b^7 + 7173120*a^6*b^8 + 15200256*a^5*b^9 + 12134400*a^4*b^10 + 3123200*a^3*b^11)*x^7*Sqrt[a + b*x] + (68248*a^7*b^7 + 1665920*a^6*b^8 + 6906880*a^5*b^9 + 9971200*a^4*b^10 + 5350400*a^3*b^11 + 700416*a^2*b^12)*x^(15/2)*Sqrt[a + b*x] + (183840*a^6*b^8 + 1770240*a^5*b^9 + 4738560*a^4*b^10 + 4761600*a^3*b^11 + 1597440*a^2*b^12)*x^8*Sqrt[a + b*x] + (6736*a^6*b^8 + 227360*a^5*b^9 + 1235200*a^4*b^10 + 2291200*a^3*b^11 + 1617920*a^2*b^12 + 335872*a*b^13)*x^(17/2)*Sqrt[a + b*x] + (11520*a^5*b^9 + 153600*a^4*b^10 + 552960*a^3*b^11 + 737280*a^2*b^12 + 327680*a*b^13)*x^9*Sqrt[a + b*x] + (128*a^5*b^9 + 6400*a^4*b^10 + 51200*a^3*b^11 + 143360*a^2*b^12 + 163840*a*b^13 + 65536*b^14)*x^(19/2)*Sqrt[a + b*x] + Sqrt[a + b]*(-7680*a^14 - 14080*a^13*b + 122976*a^12*b^2 + 494672*a^11*b^3 + 776626*a^10*b^4 + 639845*a^9*b^5 + 290170*a^8*b^6 + 68248*a^7*b^7 + 6736*a^6*b^8 + 128*a^5*b^9 + (7680*a^14 - 23040*a^13*b - 50720*a^12*b^2 + 630080*a^11*b^3 + 2313990*a^10*b^4 + 3345050*a^9*b^5 + 2487300*a^8*b^6 + 978480*a^7*b^7 + 183840*a^6*b^8 + 11520*a^5*b^9)*Sqrt[x] + (19200*a^13*b - 59200*a^12*b^2 + 221840*a^11*b^3 + 2758120*a^10*b^4 + 7053475*a^9*b^5 + 8362900*a^8*b^6 + 5212940*a^7*b^7 + 1665920*a^6*b^8 + 227360*a^5*b^9 + 6400*a^4*b^10)*x + (17920*a^13*b + 40640*a^12*b^2 - 113280*a^11*b^3 + 1326680*a^10*b^4 + 7513850*a^9*b^5 + 14613600*a^8*b^6 + 14115360*a^7*b^7 + 7173120*a^6*b^8 + 1770240*a^5*b^9 + 153600*a^4*b^10)*x^(3/2) + (63200*a^12*b^2 + 63600*a^11*b^3 + 126460*a^10*b^4 + 4055650*a^9*b^5 + 14391550*a^8*b^6 + 21836720*a^7*b^7 + 17088640*a^6*b^8 + 6906880*a^5*b^9 + 1235200*a^4*b^10 + 51200*a^3*b^11)*x^2 + (-116896*a^12*b^2 - 131392*a^11*b^3 - 99276*a^10*b^4 + 896900*a^9*b^5 + 7900100*a^8*b^6 + 20030496*a^7*b^7 + 24137472*a^6*b^8 + 15200256*a^5*b^9 + 4738560*a^4*b^10 + 552960*a^3*b^11)*x^(5/2) + (-608080*a^11*b^3 - 962040*a^10*b^4 - 451370*a^9*b^5 + 2100760*a^8*b^6 + 10680580*a^7*b^7 + 20560640*a^6*b^8 + 19889920*a^5*b^9 + 9971200*a^4*b^10 + 2291200*a^3*b^11 + 143360*a^2*b^12)*x^3 + (-557440*a^11*b^3 - 2598920*a^10*b^4 - 2885100*a^9*b^5 - 804800*a^8*b^6 + 2947600*a^7*b^7 + 10245120*a^6*b^8 + 15528960*a^5*b^9 + 12134400*a^4*b^10 + 4761600*a^3*b^11 + 737280*a^2*b^12)*x^(7/2) + (-2633630*a^10*b^4 - 6876375*a^9*b^5 - 5248330*a^8*b^6 - 835960*a^7*b^7 + 2673920*a^6*b^8 + 6883840*a^5*b^9 + 8441600*a^4*b^10 + 5350400*a^3*b^11 + 1617920*a^2*b^12 + 163840*a*b^13)*x^4 + (-1008010*a^10*b^4 - 7896350*a^9*b^5 - 12582900*a^8*b^6 - 6383600*a^7*b^7 - 512000*a^6*b^8 + 1505280*a^5*b^9 + 3059200*a^4*b^10 + 3123200*a^3*b^11 + 1597440*a^2*b^12 + 327680*a*b^13)*x^(9/2) + (-4421225*a^9*b^5 - 15985900*a^8*b^6 - 16423868*a^7*b^7 - 5235456*a^6*b^8 - 150528*a^5*b^9 + 423680*a^4*b^10 + 750080*a^3*b^11 + 700416*a^2*b^12 + 335872*a*b^13 + 65536*b^14)*x^5 + (-974350*a^9*b^5 - 11074400*a^8*b^6 - 23117280*a^7*b^7 - 15395840*a^6*b^8 - 2731520*a^5*b^9)*x^(11/2) + (-3911150*a^8*b^6 - 18615440*a^7*b^7 - 24405120*a^6*b^8 - 10165760*a^5*b^9 - 729600*a^4*b^10)*x^6 + (-538900*a^8*b^6 - 8404960*a^7*b^7 - 22321920*a^6*b^8 - 18826240*a^5*b^9 - 4441600*a^4*b^10)*x^(13/2) + (-1923220*a^7*b^7 - 11856640*a^6*b^8 - 19534080*a^5*b^9 - 10393600*a^4*b^10 - 1062400*a^3*b^11)*x^7 + (-166096*a^7*b^7 - 3484672*a^6*b^8 - 11744256*a^5*b^9 - 12482560*a^4*b^10 - 3880960*a^3*b^11)*x^(15/2) + (-498640*a^6*b^8 - 4001920*a^5*b^9 - 8352000*a^4*b^10 - 5708800*a^3*b^11 - 860160*a^2*b^12)*x^8 + (-25120*a^6*b^8 - 712960*a^5*b^9 - 3110400*a^4*b^10 - 4249600*a^3*b^11 - 1761280*a^2*b^12)*x^(17/2) + (-55840*a^5*b^9 - 601600*a^4*b^10 - 1651200*a^3*b^11 - 1515520*a^2*b^12 - 368640*a*b^13)*x^9 + (-1280*a^5*b^9 - 51200*a^4*b^10 - 307200*a^3*b^11 - 573440*a^2*b^12 - 327680*a*b^13)*x^(19/2) + (-1280*a^4*b^10 - 20480*a^3*b^11 - 86016*a^2*b^12 - 131072*a*b^13 - 65536*b^14)*x^10))/(640*b^2*(512*a^10 + 1280*a^9*b + 1120*a^8*b^2 + 400*a^7*b^3 + 50*a^6*b^4 + a^5*b^5) + 640*b^2*(a^5*b^5 + 50*a^4*b^6 + 400*a^3*b^7 + 1120*a^2*b^8 + 1280*a*b^9 + 512*b^10)*x^5 + 640*b^2*Sqrt[a + b]*(-512*a^9 - 1024*a^8*b - 672*a^7*b^2 - 160*a^6*b^3 - 10*a^5*b^4)*Sqrt[a + b*x] + x*(640*b^2*(1280*a^9*b + 9280*a^8*b^2 + 14960*a^7*b^3 + 8600*a^6*b^4 + 1645*a^5*b^5 + 50*a^4*b^6) + 640*b^2*Sqrt[a + b]*(-1024*a^8*b - 8128*a^7*b^2 - 10464*a^6*b^3 - 4120*a^5*b^4 - 400*a^4*b^5)*Sqrt[a + b*x]) + Sqrt[x]*(640*b^2*(2560*a^9*b + 5760*a^8*b^2 + 4320*a^7*b^3 + 1200*a^6*b^4 + 90*a^5*b^5) + 640*b^2*Sqrt[a + b]*(-2560*a^8*b - 4480*a^7*b^2 - 2400*a^6*b^3 - 400*a^5*b^4 - 10*a^4*b^5)*Sqrt[a + b*x]) + x^2*(640*b^2*(1120*a^8*b^2 + 14960*a^7*b^3 + 36460*a^6*b^4 + 30610*a^5*b^5 + 8600*a^4*b^6 + 400*a^3*b^7) + 640*b^2*Sqrt[a + b]*(-672*a^7*b^2 - 10464*a^6*b^3 - 24252*a^5*b^4 - 15600*a^4*b^5 - 2400*a^3*b^6)*Sqrt[a + b*x]) + x^(3/2)*(640*b^2*(5760*a^8*b^2 + 22080*a^7*b^3 + 25680*a^6*b^4 + 10680*a^5*b^5 + 1200*a^4*b^6) + 640*b^2*Sqrt[a + b]*(-4480*a^7*b^2 - 16960*a^6*b^3 - 15600*a^5*b^4 - 4120*a^4*b^5 - 160*a^3*b^6)*Sqrt[a + b*x]) + x^3*(640*b^2*(400*a^7*b^3 + 8600*a^6*b^4 + 30610*a^5*b^5 + 36460*a^4*b^6 + 14960*a^3*b^7 + 1120*a^2*b^8) + 640*b^2*Sqrt[a + b]*(-160*a^6*b^3 - 4120*a^5*b^4 - 15600*a^4*b^5 - 16960*a^3*b^6 - 4480*a^2*b^7)*Sqrt[a + b*x]) + x^(5/2)*(640*b^2*(4320*a^7*b^3 + 25680*a^6*b^4 + 42972*a^5*b^5 + 25680*a^4*b^6 + 4320*a^3*b^7) + 640*b^2*Sqrt[a + b]*(-2400*a^6*b^3 - 15600*a^5*b^4 - 24252*a^4*b^5 - 10464*a^3*b^6 - 672*a^2*b^7)*Sqrt[a + b*x]) + x^4*(640*b^2*(50*a^6*b^4 + 1645*a^5*b^5 + 8600*a^4*b^6 + 14960*a^3*b^7 + 9280*a^2*b^8 + 1280*a*b^9) + 640*b^2*Sqrt[a + b]*(-10*a^5*b^4 - 400*a^4*b^5 - 2400*a^3*b^6 - 4480*a^2*b^7 - 2560*a*b^8)*Sqrt[a + b*x]) + x^(7/2)*(640*b^2*(1200*a^6*b^4 + 10680*a^5*b^5 + 25680*a^4*b^6 + 22080*a^3*b^7 + 5760*a^2*b^8) + 640*b^2*Sqrt[a + b]*(-400*a^5*b^4 - 4120*a^4*b^5 - 10464*a^3*b^6 - 8128*a^2*b^7 - 1024*a*b^8)*Sqrt[a + b*x]) + x^(9/2)*(640*b^2*(90*a^5*b^5 + 1200*a^4*b^6 + 4320*a^3*b^7 + 5760*a^2*b^8 + 2560*a*b^9) + 640*b^2*Sqrt[a + b]*(-10*a^4*b^5 - 160*a^3*b^6 - 672*a^2*b^7 - 1024*a*b^8 - 512*b^9)*Sqrt[a + b*x])) - (3*a^5*ArcTanh[(Sqrt[a + b]/Sqrt[b] - Sqrt[a + b*x]/Sqrt[b])/(-1 + Sqrt[x])])/(64*b^(5/2))","B",1
547,1,2783,116,4.4485683,"\int \sqrt{x} (a+b x)^{5/2} \, dx","IntegrateAlgebraic[Sqrt[x]*(a + b*x)^(5/2),x]","\text{Result too large to show}","-\frac{5 a^4 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{64 b^{3/2}}+\frac{5 a^3 \sqrt{x} \sqrt{a+b x}}{64 b}+\frac{5}{32} a^2 x^{3/2} \sqrt{a+b x}+\frac{5}{24} a x^{3/2} (a+b x)^{3/2}+\frac{1}{4} x^{3/2} (a+b x)^{5/2}",1,"((-1920*a^11 - 19904*a^10*b - 59248*a^9*b^2 - 83080*a^8*b^3 - 62856*a^7*b^4 - 25968*a^6*b^5 - 5312*a^5*b^6 - 384*a^4*b^7)*Sqrt[a + b*x] + (1920*a^11 - 3840*a^10*b - 75296*a^9*b^2 - 217568*a^8*b^3 - 282409*a^7*b^4 - 192168*a^6*b^5 - 68080*a^5*b^6 - 10688*a^4*b^7 - 384*a^3*b^8)*Sqrt[x]*Sqrt[a + b*x] + (4800*a^10*b - 30816*a^9*b^2 - 224232*a^8*b^3 - 498000*a^7*b^4 - 538704*a^6*b^5 - 307392*a^5*b^6 - 87168*a^4*b^7 - 9216*a^3*b^8)*x*Sqrt[a + b*x] + (18944*a^10*b + 42688*a^9*b^2 - 68640*a^8*b^3 - 421284*a^7*b^4 - 749682*a^6*b^5 - 668960*a^5*b^6 - 311200*a^4*b^7 - 66560*a^3*b^8 - 3840*a^2*b^9)*x^(3/2)*Sqrt[a + b*x] + (72656*a^9*b^2 + 119208*a^8*b^3 - 107136*a^7*b^4 - 540672*a^6*b^5 - 775360*a^5*b^6 - 567680*a^4*b^7 - 209920*a^3*b^8 - 30720*a^2*b^9)*x^2*Sqrt[a + b*x] + (50016*a^9*b^2 + 232032*a^8*b^3 + 236754*a^7*b^4 - 109104*a^6*b^5 - 472200*a^5*b^6 - 550464*a^4*b^7 - 330240*a^3*b^8 - 95232*a^2*b^9 - 9216*a*b^10)*x^(5/2)*Sqrt[a + b*x] + (181960*a^8*b^3 + 467856*a^7*b^4 + 321792*a^6*b^5 - 69120*a^5*b^6 - 266368*a^4*b^7 - 257024*a^3*b^8 - 124928*a^2*b^9 - 24576*a*b^10)*x^3*Sqrt[a + b*x] + (60320*a^8*b^3 + 429100*a^7*b^4 + 657036*a^6*b^5 + 297888*a^5*b^6 - 22128*a^4*b^7 - 80896*a^3*b^8 - 71680*a^2*b^9 - 32768*a*b^10 - 6144*b^11)*x^(7/2)*Sqrt[a + b*x] + (200136*a^7*b^4 + 673008*a^6*b^5 + 649152*a^5*b^6 + 177024*a^4*b^7)*x^4*Sqrt[a + b*x] + (37839*a^7*b^4 + 381768*a^6*b^5 + 739280*a^5*b^6 + 445888*a^4*b^7 + 55424*a^3*b^8)*x^(9/2)*Sqrt[a + b*x] + (110544*a^6*b^5 + 478912*a^5*b^6 + 576128*a^4*b^7 + 203776*a^3*b^8)*x^5*Sqrt[a + b*x] + (12150*a^6*b^5 + 170400*a^5*b^6 + 415200*a^4*b^7 + 314880*a^3*b^8 + 57600*a^2*b^9)*x^(11/2)*Sqrt[a + b*x] + (29120*a^5*b^6 + 165760*a^4*b^7 + 250880*a^3*b^8 + 112640*a^2*b^9)*x^6*Sqrt[a + b*x] + (1672*a^5*b^6 + 33344*a^4*b^7 + 106240*a^3*b^8 + 105472*a^2*b^9 + 29696*a*b^10)*x^(13/2)*Sqrt[a + b*x] + (2688*a^4*b^7 + 21504*a^3*b^8 + 43008*a^2*b^9 + 24576*a*b^10)*x^7*Sqrt[a + b*x] + (48*a^4*b^7 + 1536*a^3*b^8 + 7680*a^2*b^9 + 12288*a*b^10 + 6144*b^11)*x^(15/2)*Sqrt[a + b*x] + Sqrt[a + b]*(1920*a^11 + 18944*a^10*b + 50016*a^9*b^2 + 60320*a^8*b^3 + 37839*a^7*b^4 + 12150*a^6*b^5 + 1672*a^5*b^6 + 48*a^4*b^7 + (-1920*a^11 + 4800*a^10*b + 72656*a^9*b^2 + 181960*a^8*b^3 + 200136*a^7*b^4 + 110544*a^6*b^5 + 29120*a^5*b^6 + 2688*a^4*b^7)*Sqrt[x] + (-3840*a^10*b + 42688*a^9*b^2 + 232032*a^8*b^3 + 429100*a^7*b^4 + 381768*a^6*b^5 + 170400*a^5*b^6 + 33344*a^4*b^7 + 1536*a^3*b^8)*x + (-19904*a^10*b - 30816*a^9*b^2 + 119208*a^8*b^3 + 467856*a^7*b^4 + 673008*a^6*b^5 + 478912*a^5*b^6 + 165760*a^4*b^7 + 21504*a^3*b^8)*x^(3/2) + (-75296*a^9*b^2 - 68640*a^8*b^3 + 236754*a^7*b^4 + 657036*a^6*b^5 + 739280*a^5*b^6 + 415200*a^4*b^7 + 106240*a^3*b^8 + 7680*a^2*b^9)*x^2 + (-59248*a^9*b^2 - 224232*a^8*b^3 - 107136*a^7*b^4 + 321792*a^6*b^5 + 649152*a^5*b^6 + 576128*a^4*b^7 + 250880*a^3*b^8 + 43008*a^2*b^9)*x^(5/2) + (-217568*a^8*b^3 - 421284*a^7*b^4 - 109104*a^6*b^5 + 297888*a^5*b^6 + 445888*a^4*b^7 + 314880*a^3*b^8 + 105472*a^2*b^9 + 12288*a*b^10)*x^3 + (-83080*a^8*b^3 - 498000*a^7*b^4 - 540672*a^6*b^5 - 69120*a^5*b^6 + 177024*a^4*b^7 + 203776*a^3*b^8 + 112640*a^2*b^9 + 24576*a*b^10)*x^(7/2) + (-282409*a^7*b^4 - 749682*a^6*b^5 - 472200*a^5*b^6 - 22128*a^4*b^7 + 55424*a^3*b^8 + 57600*a^2*b^9 + 29696*a*b^10 + 6144*b^11)*x^4 + (-62856*a^7*b^4 - 538704*a^6*b^5 - 775360*a^5*b^6 - 266368*a^4*b^7)*x^(9/2) + (-192168*a^6*b^5 - 668960*a^5*b^6 - 550464*a^4*b^7 - 80896*a^3*b^8)*x^5 + (-25968*a^6*b^5 - 307392*a^5*b^6 - 567680*a^4*b^7 - 257024*a^3*b^8)*x^(11/2) + (-68080*a^5*b^6 - 311200*a^4*b^7 - 330240*a^3*b^8 - 71680*a^2*b^9)*x^6 + (-5312*a^5*b^6 - 87168*a^4*b^7 - 209920*a^3*b^8 - 124928*a^2*b^9)*x^(13/2) + (-10688*a^4*b^7 - 66560*a^3*b^8 - 95232*a^2*b^9 - 32768*a*b^10)*x^7 + (-384*a^4*b^7 - 9216*a^3*b^8 - 30720*a^2*b^9 - 24576*a*b^10)*x^(15/2) + (-384*a^3*b^8 - 3840*a^2*b^9 - 9216*a*b^10 - 6144*b^11)*x^8))/(192*b*(128*a^8 + 256*a^7*b + 160*a^6*b^2 + 32*a^5*b^3 + a^4*b^4) + 192*b*(a^4*b^4 + 32*a^3*b^5 + 160*a^2*b^6 + 256*a*b^7 + 128*b^8)*x^4 + 192*b*Sqrt[a + b]*(-128*a^7 - 192*a^6*b - 80*a^5*b^2 - 8*a^4*b^3)*Sqrt[a + b*x] + x*(192*b*(256*a^7*b + 1472*a^6*b^2 + 1760*a^5*b^3 + 604*a^4*b^4 + 32*a^3*b^5) + 192*b*Sqrt[a + b]*(-192*a^6*b - 1248*a^5*b^2 - 1080*a^4*b^3 - 192*a^3*b^4)*Sqrt[a + b*x]) + Sqrt[x]*(192*b*(512*a^7*b + 896*a^6*b^2 + 448*a^5*b^3 + 56*a^4*b^4) + 192*b*Sqrt[a + b]*(-512*a^6*b - 640*a^5*b^2 - 192*a^4*b^3 - 8*a^3*b^4)*Sqrt[a + b*x]) + x^2*(192*b*(160*a^6*b^2 + 1760*a^5*b^3 + 3270*a^4*b^4 + 1760*a^3*b^5 + 160*a^2*b^6) + 192*b*Sqrt[a + b]*(-80*a^5*b^2 - 1080*a^4*b^3 - 1920*a^3*b^4 - 640*a^2*b^5)*Sqrt[a + b*x]) + x^(3/2)*(192*b*(896*a^6*b^2 + 2688*a^5*b^3 + 2184*a^4*b^4 + 448*a^3*b^5) + 192*b*Sqrt[a + b]*(-640*a^5*b^2 - 1920*a^4*b^3 - 1080*a^3*b^4 - 80*a^2*b^5)*Sqrt[a + b*x]) + x^3*(192*b*(32*a^5*b^3 + 604*a^4*b^4 + 1760*a^3*b^5 + 1472*a^2*b^6 + 256*a*b^7) + 192*b*Sqrt[a + b]*(-8*a^4*b^3 - 192*a^3*b^4 - 640*a^2*b^5 - 512*a*b^6)*Sqrt[a + b*x]) + x^(5/2)*(192*b*(448*a^5*b^3 + 2184*a^4*b^4 + 2688*a^3*b^5 + 896*a^2*b^6) + 192*b*Sqrt[a + b]*(-192*a^4*b^3 - 1080*a^3*b^4 - 1248*a^2*b^5 - 192*a*b^6)*Sqrt[a + b*x]) + x^(7/2)*(192*b*(56*a^4*b^4 + 448*a^3*b^5 + 896*a^2*b^6 + 512*a*b^7) + 192*b*Sqrt[a + b]*(-8*a^3*b^4 - 80*a^2*b^5 - 192*a*b^6 - 128*b^7)*Sqrt[a + b*x])) + (5*a^4*ArcTanh[(Sqrt[a + b]/Sqrt[b] - Sqrt[a + b*x]/Sqrt[b])/(-1 + Sqrt[x])])/(32*b^(3/2))","B",1
548,1,1682,92,2.4724909,"\int \frac{(a+b x)^{5/2}}{\sqrt{x}} \, dx","IntegrateAlgebraic[(a + b*x)^(5/2)/Sqrt[x],x]","\frac{\left(256 b^8+384 a b^7+144 a^2 b^6+8 a^3 b^5\right) \sqrt{a+b x} x^{11/2}+\left(768 a b^7+960 a^2 b^6+240 a^3 b^5\right) \sqrt{a+b x} x^5+\left(1216 a b^7+2880 a^2 b^6+1740 a^3 b^5+170 a^4 b^4\right) \sqrt{a+b x} x^{9/2}+\left(3456 a^2 b^6+5200 a^3 b^5+1740 a^4 b^4\right) \sqrt{a+b x} x^4+\left(2448 a^2 b^6+8160 a^3 b^5+6360 a^4 b^4+885 a^5 b^3\right) \sqrt{a+b x} x^{7/2}+\left(4878 b^3 a^5+11680 b^4 a^4+6528 b^5 a^3\right) \sqrt{a+b x} x^3+\left(-256 b^8-1344 a b^7-3024 a^2 b^6-1088 a^3 b^5+9600 a^4 b^4+10737 a^5 b^3+2098 a^6 b^2\right) \sqrt{a+b x} x^{5/2}+\left(-768 a b^7-3840 a^2 b^6-8160 a^3 b^5-2880 a^4 b^4+8970 a^5 b^3+6258 a^6 b^2\right) \sqrt{a+b x} x^2+\left(2416 b a^7+5604 b^2 a^6-3945 b^3 a^5-12560 b^4 a^4-8040 b^5 a^3-2400 b^6 a^2-256 b^7 a\right) \sqrt{a+b x} x^{3/2}+\left(2112 b a^7-3340 b^2 a^6-12150 b^3 a^5-10080 b^4 a^4-3760 b^5 a^3-576 b^6 a^2\right) \sqrt{a+b x} x+\left(1056 a^8-1584 b a^7-7446 b^2 a^6-7677 b^3 a^5-3570 b^4 a^4-780 b^5 a^3-48 b^6 a^2\right) \sqrt{a+b x} \sqrt{x}+\sqrt{a+b} \left(1056 a^8+2416 b a^7+2098 b^2 a^6+885 b^3 a^5+170 b^4 a^4+8 b^5 a^3+\left(-256 b^8-256 a b^7-48 a^2 b^6\right) x^6+\left(-768 a b^7-576 a^2 b^6-48 a^3 b^5\right) x^{11/2}+\left(-1344 a b^7-2400 a^2 b^6-780 a^3 b^5\right) x^5+\left(-3840 a^2 b^6-3760 a^3 b^5-460 a^4 b^4\right) x^{9/2}+\left(-3024 a^2 b^6-8040 a^3 b^5-3570 a^4 b^4\right) x^4+\left(-1698 b^3 a^5-10080 b^4 a^4-8160 b^5 a^3\right) x^{7/2}+\left(256 b^8+1216 a b^7+2448 a^2 b^6-1088 a^3 b^5-12560 a^4 b^4-7677 a^5 b^3\right) x^3+\left(768 a b^7+3456 a^2 b^6+6528 a^3 b^5-2880 a^4 b^4-12150 a^5 b^3-3174 a^6 b^2\right) x^{5/2}+\left(384 a b^7+2880 a^2 b^6+8160 a^3 b^5+9600 a^4 b^4-3945 a^5 b^3-7446 a^6 b^2\right) x^2+\left(-2944 b a^7-3340 b^2 a^6+8970 b^3 a^5+11680 b^4 a^4+5200 b^5 a^3+960 b^6 a^2\right) x^{3/2}+\left(-1584 b a^7+5604 b^2 a^6+10737 b^3 a^5+6360 b^4 a^4+1740 b^5 a^3+144 b^6 a^2\right) x+\left(-1056 a^8+2112 b a^7+6258 b^2 a^6+4878 b^3 a^5+1740 b^4 a^4+240 b^5 a^3\right) \sqrt{x}\right)+\left(-1056 a^8-2944 b a^7-3174 b^2 a^6-1698 b^3 a^5-460 b^4 a^4-48 b^5 a^3\right) \sqrt{a+b x}}{24 \left(32 b^6+48 a b^5+18 a^2 b^4+a^3 b^3\right) x^3+\left(24 \sqrt{a+b} \sqrt{a+b x} \left(-32 b^5-32 a b^4-6 a^2 b^3\right)+24 \left(96 a b^5+120 a^2 b^4+30 a^3 b^3\right)\right) x^{5/2}+\left(24 \sqrt{a+b} \sqrt{a+b x} \left(-96 a b^4-72 a^2 b^3-6 a^3 b^2\right)+24 \left(48 a b^5+204 a^2 b^4+159 a^3 b^3+18 a^4 b^2\right)\right) x^2+\left(24 \sqrt{a+b} \sqrt{a+b x} \left(-32 a b^4-164 a^2 b^3-72 a^3 b^2\right)+24 \left(120 b^2 a^4+260 b^3 a^3+120 b^4 a^2\right)\right) x^{3/2}+\left(24 \sqrt{a+b} \sqrt{a+b x} \left(-32 b a^4-164 b^2 a^3-72 b^3 a^2\right)+24 \left(48 b a^5+204 b^2 a^4+159 b^3 a^3+18 b^4 a^2\right)\right) x+\left(24 \sqrt{a+b} \sqrt{a+b x} \left(-96 b a^4-72 b^2 a^3-6 b^3 a^2\right)+24 \left(96 b a^5+120 b^2 a^4+30 b^3 a^3\right)\right) \sqrt{x}+24 \left(32 a^6+48 b a^5+18 b^2 a^4+b^3 a^3\right)+24 \sqrt{a+b} \left(-32 a^5-32 b a^4-6 b^2 a^3\right) \sqrt{a+b x}}-\frac{5 a^3 \tanh ^{-1}\left(\frac{\frac{\sqrt{a+b}}{\sqrt{b}}-\frac{\sqrt{a+b x}}{\sqrt{b}}}{\sqrt{x}-1}\right)}{4 \sqrt{b}}","\frac{5 a^3 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{8 \sqrt{b}}+\frac{5}{8} a^2 \sqrt{x} \sqrt{a+b x}+\frac{5}{12} a \sqrt{x} (a+b x)^{3/2}+\frac{1}{3} \sqrt{x} (a+b x)^{5/2}",1,"((-1056*a^8 - 2944*a^7*b - 3174*a^6*b^2 - 1698*a^5*b^3 - 460*a^4*b^4 - 48*a^3*b^5)*Sqrt[a + b*x] + (1056*a^8 - 1584*a^7*b - 7446*a^6*b^2 - 7677*a^5*b^3 - 3570*a^4*b^4 - 780*a^3*b^5 - 48*a^2*b^6)*Sqrt[x]*Sqrt[a + b*x] + (2112*a^7*b - 3340*a^6*b^2 - 12150*a^5*b^3 - 10080*a^4*b^4 - 3760*a^3*b^5 - 576*a^2*b^6)*x*Sqrt[a + b*x] + (2416*a^7*b + 5604*a^6*b^2 - 3945*a^5*b^3 - 12560*a^4*b^4 - 8040*a^3*b^5 - 2400*a^2*b^6 - 256*a*b^7)*x^(3/2)*Sqrt[a + b*x] + (6258*a^6*b^2 + 8970*a^5*b^3 - 2880*a^4*b^4 - 8160*a^3*b^5 - 3840*a^2*b^6 - 768*a*b^7)*x^2*Sqrt[a + b*x] + (2098*a^6*b^2 + 10737*a^5*b^3 + 9600*a^4*b^4 - 1088*a^3*b^5 - 3024*a^2*b^6 - 1344*a*b^7 - 256*b^8)*x^(5/2)*Sqrt[a + b*x] + (4878*a^5*b^3 + 11680*a^4*b^4 + 6528*a^3*b^5)*x^3*Sqrt[a + b*x] + (885*a^5*b^3 + 6360*a^4*b^4 + 8160*a^3*b^5 + 2448*a^2*b^6)*x^(7/2)*Sqrt[a + b*x] + (1740*a^4*b^4 + 5200*a^3*b^5 + 3456*a^2*b^6)*x^4*Sqrt[a + b*x] + (170*a^4*b^4 + 1740*a^3*b^5 + 2880*a^2*b^6 + 1216*a*b^7)*x^(9/2)*Sqrt[a + b*x] + (240*a^3*b^5 + 960*a^2*b^6 + 768*a*b^7)*x^5*Sqrt[a + b*x] + (8*a^3*b^5 + 144*a^2*b^6 + 384*a*b^7 + 256*b^8)*x^(11/2)*Sqrt[a + b*x] + Sqrt[a + b]*(1056*a^8 + 2416*a^7*b + 2098*a^6*b^2 + 885*a^5*b^3 + 170*a^4*b^4 + 8*a^3*b^5 + (-1056*a^8 + 2112*a^7*b + 6258*a^6*b^2 + 4878*a^5*b^3 + 1740*a^4*b^4 + 240*a^3*b^5)*Sqrt[x] + (-1584*a^7*b + 5604*a^6*b^2 + 10737*a^5*b^3 + 6360*a^4*b^4 + 1740*a^3*b^5 + 144*a^2*b^6)*x + (-2944*a^7*b - 3340*a^6*b^2 + 8970*a^5*b^3 + 11680*a^4*b^4 + 5200*a^3*b^5 + 960*a^2*b^6)*x^(3/2) + (-7446*a^6*b^2 - 3945*a^5*b^3 + 9600*a^4*b^4 + 8160*a^3*b^5 + 2880*a^2*b^6 + 384*a*b^7)*x^2 + (-3174*a^6*b^2 - 12150*a^5*b^3 - 2880*a^4*b^4 + 6528*a^3*b^5 + 3456*a^2*b^6 + 768*a*b^7)*x^(5/2) + (-7677*a^5*b^3 - 12560*a^4*b^4 - 1088*a^3*b^5 + 2448*a^2*b^6 + 1216*a*b^7 + 256*b^8)*x^3 + (-1698*a^5*b^3 - 10080*a^4*b^4 - 8160*a^3*b^5)*x^(7/2) + (-3570*a^4*b^4 - 8040*a^3*b^5 - 3024*a^2*b^6)*x^4 + (-460*a^4*b^4 - 3760*a^3*b^5 - 3840*a^2*b^6)*x^(9/2) + (-780*a^3*b^5 - 2400*a^2*b^6 - 1344*a*b^7)*x^5 + (-48*a^3*b^5 - 576*a^2*b^6 - 768*a*b^7)*x^(11/2) + (-48*a^2*b^6 - 256*a*b^7 - 256*b^8)*x^6))/(24*(32*a^6 + 48*a^5*b + 18*a^4*b^2 + a^3*b^3) + 24*(a^3*b^3 + 18*a^2*b^4 + 48*a*b^5 + 32*b^6)*x^3 + 24*Sqrt[a + b]*(-32*a^5 - 32*a^4*b - 6*a^3*b^2)*Sqrt[a + b*x] + x*(24*(48*a^5*b + 204*a^4*b^2 + 159*a^3*b^3 + 18*a^2*b^4) + 24*Sqrt[a + b]*(-32*a^4*b - 164*a^3*b^2 - 72*a^2*b^3)*Sqrt[a + b*x]) + Sqrt[x]*(24*(96*a^5*b + 120*a^4*b^2 + 30*a^3*b^3) + 24*Sqrt[a + b]*(-96*a^4*b - 72*a^3*b^2 - 6*a^2*b^3)*Sqrt[a + b*x]) + x^2*(24*(18*a^4*b^2 + 159*a^3*b^3 + 204*a^2*b^4 + 48*a*b^5) + 24*Sqrt[a + b]*(-6*a^3*b^2 - 72*a^2*b^3 - 96*a*b^4)*Sqrt[a + b*x]) + x^(3/2)*(24*(120*a^4*b^2 + 260*a^3*b^3 + 120*a^2*b^4) + 24*Sqrt[a + b]*(-72*a^3*b^2 - 164*a^2*b^3 - 32*a*b^4)*Sqrt[a + b*x]) + x^(5/2)*(24*(30*a^3*b^3 + 120*a^2*b^4 + 96*a*b^5) + 24*Sqrt[a + b]*(-6*a^2*b^3 - 32*a*b^4 - 32*b^5)*Sqrt[a + b*x])) - (5*a^3*ArcTanh[(Sqrt[a + b]/Sqrt[b] - Sqrt[a + b*x]/Sqrt[b])/(-1 + Sqrt[x])])/(4*Sqrt[b])","B",1
549,1,858,89,3.510793,"\int \frac{(a+b x)^{5/2}}{x^{3/2}} \, dx","IntegrateAlgebraic[(a + b*x)^(5/2)/x^(3/2),x]","\frac{\left(-4 \sqrt{x} b^3-2 a b^2-4 a \sqrt{x} b^2+4 \sqrt{a+b} \sqrt{a+b x} b^2-\frac{3 a^2 b}{2}-\frac{1}{2} a^2 \sqrt{x} b+2 a \sqrt{a+b} \sqrt{a+b x} b\right) \left(\sqrt{a+b}-\sqrt{a+b x}\right)^7}{\left(-a-b \sqrt{x}+\sqrt{a+b} \sqrt{a+b x}\right)^4}+\frac{\left(-12 \sqrt{x} b^3-4 b^3-12 a b^2-12 a \sqrt{x} b^2+16 \sqrt{a+b} \sqrt{a+b x} b^2-\frac{13 a^2 b}{2}-\frac{3}{2} a^2 \sqrt{x} b+8 a \sqrt{a+b} \sqrt{a+b x} b\right) \left(\sqrt{a+b}-\sqrt{a+b x}\right)^5}{\left(-a-b \sqrt{x}+\sqrt{a+b} \sqrt{a+b x}\right)^3}+\frac{\left(-10 \sqrt{x} b^3-10 b^3-20 a b^2-14 a \sqrt{x} b^2+20 \sqrt{a+b} \sqrt{a+b x} b^2-\frac{43 a^2 b}{4}-\frac{13}{4} a^2 \sqrt{x} b+14 a \sqrt{a+b} \sqrt{a+b x} b\right) \left(\sqrt{a+b}-\sqrt{a+b x}\right)^3}{\left(-a-b \sqrt{x}+\sqrt{a+b} \sqrt{a+b x}\right)^2}+\frac{\left(2 a^3-2 a^3 \sqrt{x}\right) \left(-\sqrt{x} a+2 a+2 b+b x-2 b \sqrt{x}-2 \sqrt{a+b} \sqrt{a+b x}+\sqrt{a+b} \sqrt{x} \sqrt{a+b x}\right) \left(\sqrt{a+b}-\sqrt{a+b x}\right)}{\sqrt{x} \left(-2 \sqrt{x} a^2+4 a^2-b x^{3/2} a+4 b a+2 b x a-b \sqrt{x} a-4 \sqrt{a+b} \sqrt{a+b x} a+2 \sqrt{a+b} \sqrt{x} \sqrt{a+b x} a+2 b^2 \sqrt{x}-2 b \sqrt{a+b} \sqrt{a+b x}\right)}+\frac{\left(\frac{1}{4} b \sqrt{a+b}-\frac{1}{4} b \sqrt{a+b x}\right) \left(-9 \sqrt{x} a^2-39 a^2-56 b a-24 b \sqrt{x} a+48 \sqrt{a+b} \sqrt{a+b x} a-24 b^2-8 b^2 \sqrt{x}+32 b \sqrt{a+b} \sqrt{a+b x}\right)}{-a-b \sqrt{x}+\sqrt{a+b} \sqrt{a+b x}}-\frac{15}{2} a^2 \sqrt{b} \tanh ^{-1}\left(\frac{\frac{\sqrt{a+b}}{\sqrt{b}}-\frac{\sqrt{a+b x}}{\sqrt{b}}}{\sqrt{x}-1}\right)","\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,"(((b*Sqrt[a + b])/4 - (b*Sqrt[a + b*x])/4)*(-39*a^2 - 56*a*b - 24*b^2 - 9*a^2*Sqrt[x] - 24*a*b*Sqrt[x] - 8*b^2*Sqrt[x] + 48*a*Sqrt[a + b]*Sqrt[a + b*x] + 32*b*Sqrt[a + b]*Sqrt[a + b*x]))/(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x]) + ((Sqrt[a + b] - Sqrt[a + b*x])^7*((-3*a^2*b)/2 - 2*a*b^2 - (a^2*b*Sqrt[x])/2 - 4*a*b^2*Sqrt[x] - 4*b^3*Sqrt[x] + 2*a*b*Sqrt[a + b]*Sqrt[a + b*x] + 4*b^2*Sqrt[a + b]*Sqrt[a + b*x]))/(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x])^4 + ((Sqrt[a + b] - Sqrt[a + b*x])^5*((-13*a^2*b)/2 - 12*a*b^2 - 4*b^3 - (3*a^2*b*Sqrt[x])/2 - 12*a*b^2*Sqrt[x] - 12*b^3*Sqrt[x] + 8*a*b*Sqrt[a + b]*Sqrt[a + b*x] + 16*b^2*Sqrt[a + b]*Sqrt[a + b*x]))/(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x])^3 + ((Sqrt[a + b] - Sqrt[a + b*x])^3*((-43*a^2*b)/4 - 20*a*b^2 - 10*b^3 - (13*a^2*b*Sqrt[x])/4 - 14*a*b^2*Sqrt[x] - 10*b^3*Sqrt[x] + 14*a*b*Sqrt[a + b]*Sqrt[a + b*x] + 20*b^2*Sqrt[a + b]*Sqrt[a + b*x]))/(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x])^2 + ((2*a^3 - 2*a^3*Sqrt[x])*(Sqrt[a + b] - Sqrt[a + b*x])*(2*a + 2*b - a*Sqrt[x] - 2*b*Sqrt[x] + b*x - 2*Sqrt[a + b]*Sqrt[a + b*x] + Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x]))/(Sqrt[x]*(4*a^2 + 4*a*b - 2*a^2*Sqrt[x] - a*b*Sqrt[x] + 2*b^2*Sqrt[x] + 2*a*b*x - a*b*x^(3/2) - 4*a*Sqrt[a + b]*Sqrt[a + b*x] - 2*b*Sqrt[a + b]*Sqrt[a + b*x] + 2*a*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x])) - (15*a^2*Sqrt[b]*ArcTanh[(Sqrt[a + b]/Sqrt[b] - Sqrt[a + b*x]/Sqrt[b])/(-1 + Sqrt[x])])/2","B",1
550,1,2127,86,11.9845593,"\int \frac{(a+b x)^{5/2}}{x^{5/2}} \, dx","IntegrateAlgebraic[(a + b*x)^(5/2)/x^(5/2),x]","\text{Result too large to show}","5 a b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)+5 b^2 \sqrt{x} \sqrt{a+b x}-\frac{2 (a+b x)^{5/2}}{3 x^{3/2}}-\frac{10 b (a+b x)^{3/2}}{3 \sqrt{x}}",1,"((b^2*Sqrt[a + b] - b^2*Sqrt[a + b*x])*(-3*a - 2*b - a*Sqrt[x] - 2*b*Sqrt[x] + 4*Sqrt[a + b]*Sqrt[a + b*x]))/(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x]) + ((Sqrt[a + b] - Sqrt[a + b*x])^3*(-(a*b^2) - a*b^2*Sqrt[x] - 2*b^3*Sqrt[x] + 2*b^2*Sqrt[a + b]*Sqrt[a + b*x]))/(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x])^2 + ((Sqrt[a + b] - Sqrt[a + b*x])^5*(72*a^4 + (512*a^8)/(3*b^4) + (512*a^7)/b^3 + (1664*a^6)/(3*b^2) + (832*a^5)/(3*b) + 8*a^3*b - 164*a^4*Sqrt[x] - (128*a^7*Sqrt[x])/(3*b^3) - (496*a^6*Sqrt[x])/(3*b^2) - (766*a^5*Sqrt[x])/(3*b) - 32*a^3*b*Sqrt[x] + (466*a^4*x)/3 + (128*a^7*x)/b^3 + (376*a^6*x)/b^2 + (1178*a^5*x)/(3*b) + 12*a^3*b*x - 34*a^4*x^(3/2) - (64*a^6*x^(3/2))/(3*b^2) - (52*a^5*x^(3/2))/b - 4*a^3*b*x^(3/2) + 8*a^3*Sqrt[a + b]*Sqrt[a + b*x] - (512*a^7*Sqrt[a + b]*Sqrt[a + b*x])/(3*b^4) - (1280*a^6*Sqrt[a + b]*Sqrt[a + b*x])/(3*b^3) - (1088*a^5*Sqrt[a + b]*Sqrt[a + b*x])/(3*b^2) - (96*a^4*Sqrt[a + b]*Sqrt[a + b*x])/b + 12*a^3*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + (128*a^6*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x])/(3*b^3) + (144*a^5*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x])/b^2 + (314*a^4*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x])/(3*b) - 4*a^3*Sqrt[a + b]*x*Sqrt[a + b*x] - (128*a^6*Sqrt[a + b]*x*Sqrt[a + b*x])/(3*b^3) - (296*a^5*Sqrt[a + b]*x*Sqrt[a + b*x])/(3*b^2) - (54*a^4*Sqrt[a + b]*x*Sqrt[a + b*x])/b))/(x*(4*a^2 + 4*a*b - 2*a^2*Sqrt[x] - a*b*Sqrt[x] + 2*b^2*Sqrt[x] + 2*a*b*x - a*b*x^(3/2) - 4*a*Sqrt[a + b]*Sqrt[a + b*x] - 2*b*Sqrt[a + b]*Sqrt[a + b*x] + 2*a*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x])^2) + ((Sqrt[a + b] - Sqrt[a + b*x])^9*((16*a^4)/3 + (64*a^7)/(3*b^3) + (48*a^6)/b^2 + (32*a^5)/b - 32*a^4*Sqrt[x] - (256*a^8*Sqrt[x])/(3*b^4) - (928*a^7*Sqrt[x])/(3*b^3) - (392*a^6*Sqrt[x])/b^2 - (200*a^5*Sqrt[x])/b + 8*a^4*x + (128*a^8*x)/(3*b^4) + (160*a^7*x)/b^3 + (584*a^6*x)/(3*b^2) + (256*a^5*x)/(3*b) - (8*a^4*x^(3/2))/3 - (64*a^7*x^(3/2))/(3*b^3) - (128*a^6*x^(3/2))/(3*b^2) - (24*a^5*x^(3/2))/b + (64*a^6*Sqrt[a + b]*Sqrt[a + b*x])/(3*b^3) + (112*a^5*Sqrt[a + b]*Sqrt[a + b*x])/(3*b^2) + (16*a^4*Sqrt[a + b]*Sqrt[a + b*x])/b + (256*a^7*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x])/(3*b^4) + (160*a^6*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x])/b^3 + (248*a^5*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x])/(3*b^2) + (8*a^4*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x])/b - (128*a^7*Sqrt[a + b]*x*Sqrt[a + b*x])/(3*b^4) - (224*a^6*Sqrt[a + b]*x*Sqrt[a + b*x])/(3*b^3) - (104*a^5*Sqrt[a + b]*x*Sqrt[a + b*x])/(3*b^2) - (8*a^4*Sqrt[a + b]*x*Sqrt[a + b*x])/(3*b)))/(x^(3/2)*(4*a^2 + 4*a*b - 2*a^2*Sqrt[x] - a*b*Sqrt[x] + 2*b^2*Sqrt[x] + 2*a*b*x - a*b*x^(3/2) - 4*a*Sqrt[a + b]*Sqrt[a + b*x] - 2*b*Sqrt[a + b]*Sqrt[a + b*x] + 2*a*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x])^3) + (((-2*a^2*Sqrt[a + b])/(3*b^2) + (2*a^2*Sqrt[a + b*x])/(3*b^2))*(-144*a^4 - 304*a^3*b - 203*a^2*b^2 - 63*a*b^3 - 18*b^4 + 28*a^3*b*Sqrt[x] + 53*a^2*b^2*Sqrt[x] + 57*a*b^3*Sqrt[x] + 36*b^4*Sqrt[x] - 108*a^3*b*x - 200*a^2*b^2*x - 105*a*b^3*x - 27*b^4*x + 14*a^2*b^2*x^(3/2) + 15*a*b^3*x^(3/2) + 9*b^4*x^(3/2) + 144*a^3*Sqrt[a + b]*Sqrt[a + b*x] + 232*a^2*b*Sqrt[a + b]*Sqrt[a + b*x] + 105*a*b^2*Sqrt[a + b]*Sqrt[a + b*x] + 18*b^3*Sqrt[a + b]*Sqrt[a + b*x] - 28*a^2*b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 39*a*b^2*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 27*b^3*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 36*a^2*b*Sqrt[a + b]*x*Sqrt[a + b*x] + 30*a*b^2*Sqrt[a + b]*x*Sqrt[a + b*x] + 9*b^3*Sqrt[a + b]*x*Sqrt[a + b*x]))/(Sqrt[x]*(4*a^2 + 4*a*b - 2*a^2*Sqrt[x] - a*b*Sqrt[x] + 2*b^2*Sqrt[x] + 2*a*b*x - a*b*x^(3/2) - 4*a*Sqrt[a + b]*Sqrt[a + b*x] - 2*b*Sqrt[a + b]*Sqrt[a + b*x] + 2*a*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x])) - 10*a*b^(3/2)*ArcTanh[(Sqrt[a + b]/Sqrt[b] - Sqrt[a + b*x]/Sqrt[b])/(-1 + Sqrt[x])]","B",1
551,1,5842,171,14.126425,"\int x^{5/2} (a-b x)^{5/2} \, dx","IntegrateAlgebraic[x^(5/2)*(a - b*x)^(5/2),x]","\text{Result too large to show}","\frac{5 a^6 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)}{512 b^{7/2}}-\frac{5 a^5 \sqrt{x} \sqrt{a-b x}}{512 b^3}-\frac{5 a^4 x^{3/2} \sqrt{a-b x}}{768 b^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,"Result too large to show","B",1
552,1,4226,146,9.347013,"\int x^{3/2} (a-b x)^{5/2} \, dx","IntegrateAlgebraic[x^(3/2)*(a - b*x)^(5/2),x]","\text{Result too large to show}","\frac{3 a^5 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)}{128 b^{5/2}}-\frac{3 a^4 \sqrt{x} \sqrt{a-b x}}{128 b^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,"((7680*a^14 - 17920*a^13*b - 116896*a^12*b^2 + 557440*a^11*b^3 - 1008010*a^10*b^4 + 974350*a^9*b^5 - 538900*a^8*b^6 + 166096*a^7*b^7 - 25120*a^6*b^8 + 1280*a^5*b^9)*Sqrt[a - b*x] + (-7680*a^14 - 19200*a^13*b + 63200*a^12*b^2 + 608080*a^11*b^3 - 2633630*a^10*b^4 + 4421225*a^9*b^5 - 3911150*a^8*b^6 + 1923220*a^7*b^7 - 498640*a^6*b^8 + 55840*a^5*b^9 - 1280*a^4*b^10)*Sqrt[x]*Sqrt[a - b*x] + (23040*a^13*b + 40640*a^12*b^2 + 131392*a^11*b^3 - 2598920*a^10*b^4 + 7896350*a^9*b^5 - 11074400*a^8*b^6 + 8404960*a^7*b^7 - 3484672*a^6*b^8 + 712960*a^5*b^9 - 51200*a^4*b^10)*x*Sqrt[a - b*x] + (14080*a^13*b - 59200*a^12*b^2 - 63600*a^11*b^3 - 962040*a^10*b^4 + 6876375*a^9*b^5 - 15985900*a^8*b^6 + 18615440*a^7*b^7 - 11856640*a^6*b^8 + 4001920*a^5*b^9 - 601600*a^4*b^10 + 20480*a^3*b^11)*x^(3/2)*Sqrt[a - b*x] + (-50720*a^12*b^2 + 113280*a^11*b^3 - 99276*a^10*b^4 + 2885100*a^9*b^5 - 12582900*a^8*b^6 + 23117280*a^7*b^7 - 22321920*a^6*b^8 + 11744256*a^5*b^9 - 3110400*a^4*b^10 + 307200*a^3*b^11)*x^2*Sqrt[a - b*x] + (122976*a^12*b^2 - 221840*a^11*b^3 + 126460*a^10*b^4 + 451370*a^9*b^5 - 5248330*a^8*b^6 + 16423868*a^7*b^7 - 24405120*a^6*b^8 + 19534080*a^5*b^9 - 8352000*a^4*b^10 + 1651200*a^3*b^11 - 86016*a^2*b^12)*x^(5/2)*Sqrt[a - b*x] + (-630080*a^11*b^3 + 1326680*a^10*b^4 - 896900*a^9*b^5 - 804800*a^8*b^6 + 6383600*a^7*b^7 - 15395840*a^6*b^8 + 18826240*a^5*b^9 - 12482560*a^4*b^10 + 4249600*a^3*b^11 - 573440*a^2*b^12)*x^3*Sqrt[a - b*x] + (-494672*a^11*b^3 + 2758120*a^10*b^4 - 4055650*a^9*b^5 + 2100760*a^8*b^6 + 835960*a^7*b^7 - 5235456*a^6*b^8 + 10165760*a^5*b^9 - 10393600*a^4*b^10 + 5708800*a^3*b^11 - 1515520*a^2*b^12 + 131072*a*b^13)*x^(7/2)*Sqrt[a - b*x] + (2313990*a^10*b^4 - 7513850*a^9*b^5 + 7900100*a^8*b^6 - 2947600*a^7*b^7 - 512000*a^6*b^8 + 2731520*a^5*b^9 - 4441600*a^4*b^10 + 3880960*a^3*b^11 - 1761280*a^2*b^12 + 327680*a*b^13)*x^4*Sqrt[a - b*x] + (776626*a^10*b^4 - 7053475*a^9*b^5 + 14391550*a^8*b^6 - 10680580*a^7*b^7 + 2673920*a^6*b^8 + 150528*a^5*b^9 - 729600*a^4*b^10 + 1062400*a^3*b^11 - 860160*a^2*b^12 + 368640*a*b^13 - 65536*b^14)*x^(9/2)*Sqrt[a - b*x] + (-3345050*a^9*b^5 + 14613600*a^8*b^6 - 20030496*a^7*b^7 + 10245120*a^6*b^8 - 1505280*a^5*b^9)*x^5*Sqrt[a - b*x] + (-639845*a^9*b^5 + 8362900*a^8*b^6 - 21836720*a^7*b^7 + 20560640*a^6*b^8 - 6883840*a^5*b^9 + 423680*a^4*b^10)*x^(11/2)*Sqrt[a - b*x] + (2487300*a^8*b^6 - 14115360*a^7*b^7 + 24137472*a^6*b^8 - 15528960*a^5*b^9 + 3059200*a^4*b^10)*x^6*Sqrt[a - b*x] + (290170*a^8*b^6 - 5212940*a^7*b^7 + 17088640*a^6*b^8 - 19889920*a^5*b^9 + 8441600*a^4*b^10 - 750080*a^3*b^11)*x^(13/2)*Sqrt[a - b*x] + (-978480*a^7*b^7 + 7173120*a^6*b^8 - 15200256*a^5*b^9 + 12134400*a^4*b^10 - 3123200*a^3*b^11)*x^7*Sqrt[a - b*x] + (-68248*a^7*b^7 + 1665920*a^6*b^8 - 6906880*a^5*b^9 + 9971200*a^4*b^10 - 5350400*a^3*b^11 + 700416*a^2*b^12)*x^(15/2)*Sqrt[a - b*x] + (183840*a^6*b^8 - 1770240*a^5*b^9 + 4738560*a^4*b^10 - 4761600*a^3*b^11 + 1597440*a^2*b^12)*x^8*Sqrt[a - b*x] + (6736*a^6*b^8 - 227360*a^5*b^9 + 1235200*a^4*b^10 - 2291200*a^3*b^11 + 1617920*a^2*b^12 - 335872*a*b^13)*x^(17/2)*Sqrt[a - b*x] + (-11520*a^5*b^9 + 153600*a^4*b^10 - 552960*a^3*b^11 + 737280*a^2*b^12 - 327680*a*b^13)*x^9*Sqrt[a - b*x] + (-128*a^5*b^9 + 6400*a^4*b^10 - 51200*a^3*b^11 + 143360*a^2*b^12 - 163840*a*b^13 + 65536*b^14)*x^(19/2)*Sqrt[a - b*x] + Sqrt[a - b]*(-7680*a^14 + 14080*a^13*b + 122976*a^12*b^2 - 494672*a^11*b^3 + 776626*a^10*b^4 - 639845*a^9*b^5 + 290170*a^8*b^6 - 68248*a^7*b^7 + 6736*a^6*b^8 - 128*a^5*b^9 + (7680*a^14 + 23040*a^13*b - 50720*a^12*b^2 - 630080*a^11*b^3 + 2313990*a^10*b^4 - 3345050*a^9*b^5 + 2487300*a^8*b^6 - 978480*a^7*b^7 + 183840*a^6*b^8 - 11520*a^5*b^9)*Sqrt[x] + (-19200*a^13*b - 59200*a^12*b^2 - 221840*a^11*b^3 + 2758120*a^10*b^4 - 7053475*a^9*b^5 + 8362900*a^8*b^6 - 5212940*a^7*b^7 + 1665920*a^6*b^8 - 227360*a^5*b^9 + 6400*a^4*b^10)*x + (-17920*a^13*b + 40640*a^12*b^2 + 113280*a^11*b^3 + 1326680*a^10*b^4 - 7513850*a^9*b^5 + 14613600*a^8*b^6 - 14115360*a^7*b^7 + 7173120*a^6*b^8 - 1770240*a^5*b^9 + 153600*a^4*b^10)*x^(3/2) + (63200*a^12*b^2 - 63600*a^11*b^3 + 126460*a^10*b^4 - 4055650*a^9*b^5 + 14391550*a^8*b^6 - 21836720*a^7*b^7 + 17088640*a^6*b^8 - 6906880*a^5*b^9 + 1235200*a^4*b^10 - 51200*a^3*b^11)*x^2 + (-116896*a^12*b^2 + 131392*a^11*b^3 - 99276*a^10*b^4 - 896900*a^9*b^5 + 7900100*a^8*b^6 - 20030496*a^7*b^7 + 24137472*a^6*b^8 - 15200256*a^5*b^9 + 4738560*a^4*b^10 - 552960*a^3*b^11)*x^(5/2) + (608080*a^11*b^3 - 962040*a^10*b^4 + 451370*a^9*b^5 + 2100760*a^8*b^6 - 10680580*a^7*b^7 + 20560640*a^6*b^8 - 19889920*a^5*b^9 + 9971200*a^4*b^10 - 2291200*a^3*b^11 + 143360*a^2*b^12)*x^3 + (557440*a^11*b^3 - 2598920*a^10*b^4 + 2885100*a^9*b^5 - 804800*a^8*b^6 - 2947600*a^7*b^7 + 10245120*a^6*b^8 - 15528960*a^5*b^9 + 12134400*a^4*b^10 - 4761600*a^3*b^11 + 737280*a^2*b^12)*x^(7/2) + (-2633630*a^10*b^4 + 6876375*a^9*b^5 - 5248330*a^8*b^6 + 835960*a^7*b^7 + 2673920*a^6*b^8 - 6883840*a^5*b^9 + 8441600*a^4*b^10 - 5350400*a^3*b^11 + 1617920*a^2*b^12 - 163840*a*b^13)*x^4 + (-1008010*a^10*b^4 + 7896350*a^9*b^5 - 12582900*a^8*b^6 + 6383600*a^7*b^7 - 512000*a^6*b^8 - 1505280*a^5*b^9 + 3059200*a^4*b^10 - 3123200*a^3*b^11 + 1597440*a^2*b^12 - 327680*a*b^13)*x^(9/2) + (4421225*a^9*b^5 - 15985900*a^8*b^6 + 16423868*a^7*b^7 - 5235456*a^6*b^8 + 150528*a^5*b^9 + 423680*a^4*b^10 - 750080*a^3*b^11 + 700416*a^2*b^12 - 335872*a*b^13 + 65536*b^14)*x^5 + (974350*a^9*b^5 - 11074400*a^8*b^6 + 23117280*a^7*b^7 - 15395840*a^6*b^8 + 2731520*a^5*b^9)*x^(11/2) + (-3911150*a^8*b^6 + 18615440*a^7*b^7 - 24405120*a^6*b^8 + 10165760*a^5*b^9 - 729600*a^4*b^10)*x^6 + (-538900*a^8*b^6 + 8404960*a^7*b^7 - 22321920*a^6*b^8 + 18826240*a^5*b^9 - 4441600*a^4*b^10)*x^(13/2) + (1923220*a^7*b^7 - 11856640*a^6*b^8 + 19534080*a^5*b^9 - 10393600*a^4*b^10 + 1062400*a^3*b^11)*x^7 + (166096*a^7*b^7 - 3484672*a^6*b^8 + 11744256*a^5*b^9 - 12482560*a^4*b^10 + 3880960*a^3*b^11)*x^(15/2) + (-498640*a^6*b^8 + 4001920*a^5*b^9 - 8352000*a^4*b^10 + 5708800*a^3*b^11 - 860160*a^2*b^12)*x^8 + (-25120*a^6*b^8 + 712960*a^5*b^9 - 3110400*a^4*b^10 + 4249600*a^3*b^11 - 1761280*a^2*b^12)*x^(17/2) + (55840*a^5*b^9 - 601600*a^4*b^10 + 1651200*a^3*b^11 - 1515520*a^2*b^12 + 368640*a*b^13)*x^9 + (1280*a^5*b^9 - 51200*a^4*b^10 + 307200*a^3*b^11 - 573440*a^2*b^12 + 327680*a*b^13)*x^(19/2) + (-1280*a^4*b^10 + 20480*a^3*b^11 - 86016*a^2*b^12 + 131072*a*b^13 - 65536*b^14)*x^10))/(640*b^2*(512*a^10 - 1280*a^9*b + 1120*a^8*b^2 - 400*a^7*b^3 + 50*a^6*b^4 - a^5*b^5) + 640*b^2*(-(a^5*b^5) + 50*a^4*b^6 - 400*a^3*b^7 + 1120*a^2*b^8 - 1280*a*b^9 + 512*b^10)*x^5 + 640*Sqrt[a - b]*b^2*(-512*a^9 + 1024*a^8*b - 672*a^7*b^2 + 160*a^6*b^3 - 10*a^5*b^4)*Sqrt[a - b*x] + Sqrt[x]*(640*b^2*(-2560*a^9*b + 5760*a^8*b^2 - 4320*a^7*b^3 + 1200*a^6*b^4 - 90*a^5*b^5) + 640*Sqrt[a - b]*b^2*(2560*a^8*b - 4480*a^7*b^2 + 2400*a^6*b^3 - 400*a^5*b^4 + 10*a^4*b^5)*Sqrt[a - b*x]) + x*(640*b^2*(-1280*a^9*b + 9280*a^8*b^2 - 14960*a^7*b^3 + 8600*a^6*b^4 - 1645*a^5*b^5 + 50*a^4*b^6) + 640*Sqrt[a - b]*b^2*(1024*a^8*b - 8128*a^7*b^2 + 10464*a^6*b^3 - 4120*a^5*b^4 + 400*a^4*b^5)*Sqrt[a - b*x]) + x^2*(640*b^2*(1120*a^8*b^2 - 14960*a^7*b^3 + 36460*a^6*b^4 - 30610*a^5*b^5 + 8600*a^4*b^6 - 400*a^3*b^7) + 640*Sqrt[a - b]*b^2*(-672*a^7*b^2 + 10464*a^6*b^3 - 24252*a^5*b^4 + 15600*a^4*b^5 - 2400*a^3*b^6)*Sqrt[a - b*x]) + x^(3/2)*(640*b^2*(5760*a^8*b^2 - 22080*a^7*b^3 + 25680*a^6*b^4 - 10680*a^5*b^5 + 1200*a^4*b^6) + 640*Sqrt[a - b]*b^2*(-4480*a^7*b^2 + 16960*a^6*b^3 - 15600*a^5*b^4 + 4120*a^4*b^5 - 160*a^3*b^6)*Sqrt[a - b*x]) + x^(5/2)*(640*b^2*(-4320*a^7*b^3 + 25680*a^6*b^4 - 42972*a^5*b^5 + 25680*a^4*b^6 - 4320*a^3*b^7) + 640*Sqrt[a - b]*b^2*(2400*a^6*b^3 - 15600*a^5*b^4 + 24252*a^4*b^5 - 10464*a^3*b^6 + 672*a^2*b^7)*Sqrt[a - b*x]) + x^3*(640*b^2*(-400*a^7*b^3 + 8600*a^6*b^4 - 30610*a^5*b^5 + 36460*a^4*b^6 - 14960*a^3*b^7 + 1120*a^2*b^8) + 640*Sqrt[a - b]*b^2*(160*a^6*b^3 - 4120*a^5*b^4 + 15600*a^4*b^5 - 16960*a^3*b^6 + 4480*a^2*b^7)*Sqrt[a - b*x]) + x^4*(640*b^2*(50*a^6*b^4 - 1645*a^5*b^5 + 8600*a^4*b^6 - 14960*a^3*b^7 + 9280*a^2*b^8 - 1280*a*b^9) + 640*Sqrt[a - b]*b^2*(-10*a^5*b^4 + 400*a^4*b^5 - 2400*a^3*b^6 + 4480*a^2*b^7 - 2560*a*b^8)*Sqrt[a - b*x]) + x^(7/2)*(640*b^2*(1200*a^6*b^4 - 10680*a^5*b^5 + 25680*a^4*b^6 - 22080*a^3*b^7 + 5760*a^2*b^8) + 640*Sqrt[a - b]*b^2*(-400*a^5*b^4 + 4120*a^4*b^5 - 10464*a^3*b^6 + 8128*a^2*b^7 - 1024*a*b^8)*Sqrt[a - b*x]) + x^(9/2)*(640*b^2*(-90*a^5*b^5 + 1200*a^4*b^6 - 4320*a^3*b^7 + 5760*a^2*b^8 - 2560*a*b^9) + 640*Sqrt[a - b]*b^2*(10*a^4*b^5 - 160*a^3*b^6 + 672*a^2*b^7 - 1024*a*b^8 + 512*b^9)*Sqrt[a - b*x])) + (3*a^5*ArcTan[(Sqrt[a - b]/Sqrt[b] - Sqrt[a - b*x]/Sqrt[b])/(-1 + Sqrt[x])])/(64*b^(5/2))","B",1
553,1,2828,121,4.8414989,"\int \sqrt{x} (a-b x)^{5/2} \, dx","IntegrateAlgebraic[Sqrt[x]*(a - b*x)^(5/2),x]","\text{Result too large to show}","\frac{5 a^4 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)}{64 b^{3/2}}-\frac{5 a^3 \sqrt{x} \sqrt{a-b x}}{64 b}+\frac{5}{32} a^2 x^{3/2} \sqrt{a-b x}+\frac{5}{24} a x^{3/2} (a-b x)^{3/2}+\frac{1}{4} x^{3/2} (a-b x)^{5/2}",1,"((1920*a^11 - 19904*a^10*b + 59248*a^9*b^2 - 83080*a^8*b^3 + 62856*a^7*b^4 - 25968*a^6*b^5 + 5312*a^5*b^6 - 384*a^4*b^7)*Sqrt[a - b*x] + (-1920*a^11 - 3840*a^10*b + 75296*a^9*b^2 - 217568*a^8*b^3 + 282409*a^7*b^4 - 192168*a^6*b^5 + 68080*a^5*b^6 - 10688*a^4*b^7 + 384*a^3*b^8)*Sqrt[x]*Sqrt[a - b*x] + (4800*a^10*b + 30816*a^9*b^2 - 224232*a^8*b^3 + 498000*a^7*b^4 - 538704*a^6*b^5 + 307392*a^5*b^6 - 87168*a^4*b^7 + 9216*a^3*b^8)*x*Sqrt[a - b*x] + (18944*a^10*b - 42688*a^9*b^2 - 68640*a^8*b^3 + 421284*a^7*b^4 - 749682*a^6*b^5 + 668960*a^5*b^6 - 311200*a^4*b^7 + 66560*a^3*b^8 - 3840*a^2*b^9)*x^(3/2)*Sqrt[a - b*x] + (-72656*a^9*b^2 + 119208*a^8*b^3 + 107136*a^7*b^4 - 540672*a^6*b^5 + 775360*a^5*b^6 - 567680*a^4*b^7 + 209920*a^3*b^8 - 30720*a^2*b^9)*x^2*Sqrt[a - b*x] + (-50016*a^9*b^2 + 232032*a^8*b^3 - 236754*a^7*b^4 - 109104*a^6*b^5 + 472200*a^5*b^6 - 550464*a^4*b^7 + 330240*a^3*b^8 - 95232*a^2*b^9 + 9216*a*b^10)*x^(5/2)*Sqrt[a - b*x] + (181960*a^8*b^3 - 467856*a^7*b^4 + 321792*a^6*b^5 + 69120*a^5*b^6 - 266368*a^4*b^7 + 257024*a^3*b^8 - 124928*a^2*b^9 + 24576*a*b^10)*x^3*Sqrt[a - b*x] + (60320*a^8*b^3 - 429100*a^7*b^4 + 657036*a^6*b^5 - 297888*a^5*b^6 - 22128*a^4*b^7 + 80896*a^3*b^8 - 71680*a^2*b^9 + 32768*a*b^10 - 6144*b^11)*x^(7/2)*Sqrt[a - b*x] + (-200136*a^7*b^4 + 673008*a^6*b^5 - 649152*a^5*b^6 + 177024*a^4*b^7)*x^4*Sqrt[a - b*x] + (-37839*a^7*b^4 + 381768*a^6*b^5 - 739280*a^5*b^6 + 445888*a^4*b^7 - 55424*a^3*b^8)*x^(9/2)*Sqrt[a - b*x] + (110544*a^6*b^5 - 478912*a^5*b^6 + 576128*a^4*b^7 - 203776*a^3*b^8)*x^5*Sqrt[a - b*x] + (12150*a^6*b^5 - 170400*a^5*b^6 + 415200*a^4*b^7 - 314880*a^3*b^8 + 57600*a^2*b^9)*x^(11/2)*Sqrt[a - b*x] + (-29120*a^5*b^6 + 165760*a^4*b^7 - 250880*a^3*b^8 + 112640*a^2*b^9)*x^6*Sqrt[a - b*x] + (-1672*a^5*b^6 + 33344*a^4*b^7 - 106240*a^3*b^8 + 105472*a^2*b^9 - 29696*a*b^10)*x^(13/2)*Sqrt[a - b*x] + (2688*a^4*b^7 - 21504*a^3*b^8 + 43008*a^2*b^9 - 24576*a*b^10)*x^7*Sqrt[a - b*x] + (48*a^4*b^7 - 1536*a^3*b^8 + 7680*a^2*b^9 - 12288*a*b^10 + 6144*b^11)*x^(15/2)*Sqrt[a - b*x] + Sqrt[a - b]*(-1920*a^11 + 18944*a^10*b - 50016*a^9*b^2 + 60320*a^8*b^3 - 37839*a^7*b^4 + 12150*a^6*b^5 - 1672*a^5*b^6 + 48*a^4*b^7 + (1920*a^11 + 4800*a^10*b - 72656*a^9*b^2 + 181960*a^8*b^3 - 200136*a^7*b^4 + 110544*a^6*b^5 - 29120*a^5*b^6 + 2688*a^4*b^7)*Sqrt[x] + (-3840*a^10*b - 42688*a^9*b^2 + 232032*a^8*b^3 - 429100*a^7*b^4 + 381768*a^6*b^5 - 170400*a^5*b^6 + 33344*a^4*b^7 - 1536*a^3*b^8)*x + (-19904*a^10*b + 30816*a^9*b^2 + 119208*a^8*b^3 - 467856*a^7*b^4 + 673008*a^6*b^5 - 478912*a^5*b^6 + 165760*a^4*b^7 - 21504*a^3*b^8)*x^(3/2) + (75296*a^9*b^2 - 68640*a^8*b^3 - 236754*a^7*b^4 + 657036*a^6*b^5 - 739280*a^5*b^6 + 415200*a^4*b^7 - 106240*a^3*b^8 + 7680*a^2*b^9)*x^2 + (59248*a^9*b^2 - 224232*a^8*b^3 + 107136*a^7*b^4 + 321792*a^6*b^5 - 649152*a^5*b^6 + 576128*a^4*b^7 - 250880*a^3*b^8 + 43008*a^2*b^9)*x^(5/2) + (-217568*a^8*b^3 + 421284*a^7*b^4 - 109104*a^6*b^5 - 297888*a^5*b^6 + 445888*a^4*b^7 - 314880*a^3*b^8 + 105472*a^2*b^9 - 12288*a*b^10)*x^3 + (-83080*a^8*b^3 + 498000*a^7*b^4 - 540672*a^6*b^5 + 69120*a^5*b^6 + 177024*a^4*b^7 - 203776*a^3*b^8 + 112640*a^2*b^9 - 24576*a*b^10)*x^(7/2) + (282409*a^7*b^4 - 749682*a^6*b^5 + 472200*a^5*b^6 - 22128*a^4*b^7 - 55424*a^3*b^8 + 57600*a^2*b^9 - 29696*a*b^10 + 6144*b^11)*x^4 + (62856*a^7*b^4 - 538704*a^6*b^5 + 775360*a^5*b^6 - 266368*a^4*b^7)*x^(9/2) + (-192168*a^6*b^5 + 668960*a^5*b^6 - 550464*a^4*b^7 + 80896*a^3*b^8)*x^5 + (-25968*a^6*b^5 + 307392*a^5*b^6 - 567680*a^4*b^7 + 257024*a^3*b^8)*x^(11/2) + (68080*a^5*b^6 - 311200*a^4*b^7 + 330240*a^3*b^8 - 71680*a^2*b^9)*x^6 + (5312*a^5*b^6 - 87168*a^4*b^7 + 209920*a^3*b^8 - 124928*a^2*b^9)*x^(13/2) + (-10688*a^4*b^7 + 66560*a^3*b^8 - 95232*a^2*b^9 + 32768*a*b^10)*x^7 + (-384*a^4*b^7 + 9216*a^3*b^8 - 30720*a^2*b^9 + 24576*a*b^10)*x^(15/2) + (384*a^3*b^8 - 3840*a^2*b^9 + 9216*a*b^10 - 6144*b^11)*x^8))/(192*b*(128*a^8 - 256*a^7*b + 160*a^6*b^2 - 32*a^5*b^3 + a^4*b^4) + 192*b*(a^4*b^4 - 32*a^3*b^5 + 160*a^2*b^6 - 256*a*b^7 + 128*b^8)*x^4 + 192*Sqrt[a - b]*b*(-128*a^7 + 192*a^6*b - 80*a^5*b^2 + 8*a^4*b^3)*Sqrt[a - b*x] + x*(192*b*(-256*a^7*b + 1472*a^6*b^2 - 1760*a^5*b^3 + 604*a^4*b^4 - 32*a^3*b^5) + 192*Sqrt[a - b]*b*(192*a^6*b - 1248*a^5*b^2 + 1080*a^4*b^3 - 192*a^3*b^4)*Sqrt[a - b*x]) + Sqrt[x]*(192*b*(-512*a^7*b + 896*a^6*b^2 - 448*a^5*b^3 + 56*a^4*b^4) + 192*Sqrt[a - b]*b*(512*a^6*b - 640*a^5*b^2 + 192*a^4*b^3 - 8*a^3*b^4)*Sqrt[a - b*x]) + x^(3/2)*(192*b*(896*a^6*b^2 - 2688*a^5*b^3 + 2184*a^4*b^4 - 448*a^3*b^5) + 192*Sqrt[a - b]*b*(-640*a^5*b^2 + 1920*a^4*b^3 - 1080*a^3*b^4 + 80*a^2*b^5)*Sqrt[a - b*x]) + x^2*(192*b*(160*a^6*b^2 - 1760*a^5*b^3 + 3270*a^4*b^4 - 1760*a^3*b^5 + 160*a^2*b^6) + 192*Sqrt[a - b]*b*(-80*a^5*b^2 + 1080*a^4*b^3 - 1920*a^3*b^4 + 640*a^2*b^5)*Sqrt[a - b*x]) + x^3*(192*b*(-32*a^5*b^3 + 604*a^4*b^4 - 1760*a^3*b^5 + 1472*a^2*b^6 - 256*a*b^7) + 192*Sqrt[a - b]*b*(8*a^4*b^3 - 192*a^3*b^4 + 640*a^2*b^5 - 512*a*b^6)*Sqrt[a - b*x]) + x^(5/2)*(192*b*(-448*a^5*b^3 + 2184*a^4*b^4 - 2688*a^3*b^5 + 896*a^2*b^6) + 192*Sqrt[a - b]*b*(192*a^4*b^3 - 1080*a^3*b^4 + 1248*a^2*b^5 - 192*a*b^6)*Sqrt[a - b*x]) + x^(7/2)*(192*b*(56*a^4*b^4 - 448*a^3*b^5 + 896*a^2*b^6 - 512*a*b^7) + 192*Sqrt[a - b]*b*(-8*a^3*b^4 + 80*a^2*b^5 - 192*a*b^6 + 128*b^7)*Sqrt[a - b*x])) + (5*a^4*ArcTan[(Sqrt[a - b]/Sqrt[b] - Sqrt[a - b*x]/Sqrt[b])/(-1 + Sqrt[x])])/(32*b^(3/2))","B",1
554,1,1719,96,2.5760595,"\int \frac{(a-b x)^{5/2}}{\sqrt{x}} \, dx","IntegrateAlgebraic[(a - b*x)^(5/2)/Sqrt[x],x]","\frac{5 \tan ^{-1}\left(\frac{\frac{\sqrt{a-b}}{\sqrt{b}}-\frac{\sqrt{a-b x}}{\sqrt{b}}}{\sqrt{x}-1}\right) a^3}{4 \sqrt{b}}+\frac{\left(256 b^8-384 a b^7+144 a^2 b^6-8 a^3 b^5\right) \sqrt{a-b x} x^{11/2}+\left(-768 a b^7+960 a^2 b^6-240 a^3 b^5\right) \sqrt{a-b x} x^5+\left(-1216 a b^7+2880 a^2 b^6-1740 a^3 b^5+170 a^4 b^4\right) \sqrt{a-b x} x^{9/2}+\left(3456 a^2 b^6-5200 a^3 b^5+1740 a^4 b^4\right) \sqrt{a-b x} x^4+\left(2448 a^2 b^6-8160 a^3 b^5+6360 a^4 b^4-885 a^5 b^3\right) \sqrt{a-b x} x^{7/2}+\left(-4878 b^3 a^5+11680 b^4 a^4-6528 b^5 a^3\right) \sqrt{a-b x} x^3+\left(-256 b^8+1344 a b^7-3024 a^2 b^6+1088 a^3 b^5+9600 a^4 b^4-10737 a^5 b^3+2098 a^6 b^2\right) \sqrt{a-b x} x^{5/2}+\left(768 a b^7-3840 a^2 b^6+8160 a^3 b^5-2880 a^4 b^4-8970 a^5 b^3+6258 a^6 b^2\right) \sqrt{a-b x} x^2+\left(-2416 b a^7+5604 b^2 a^6+3945 b^3 a^5-12560 b^4 a^4+8040 b^5 a^3-2400 b^6 a^2+256 b^7 a\right) \sqrt{a-b x} x^{3/2}+\left(-2112 b a^7-3340 b^2 a^6+12150 b^3 a^5-10080 b^4 a^4+3760 b^5 a^3-576 b^6 a^2\right) \sqrt{a-b x} x+\left(1056 a^8+1584 b a^7-7446 b^2 a^6+7677 b^3 a^5-3570 b^4 a^4+780 b^5 a^3-48 b^6 a^2\right) \sqrt{a-b x} \sqrt{x}+\sqrt{a-b} \left(1056 a^8-2416 b a^7+2098 b^2 a^6-885 b^3 a^5+170 b^4 a^4-8 b^5 a^3+\left(-256 b^8+256 a b^7-48 a^2 b^6\right) x^6+\left(768 a b^7-576 a^2 b^6+48 a^3 b^5\right) x^{11/2}+\left(1344 a b^7-2400 a^2 b^6+780 a^3 b^5\right) x^5+\left(-3840 a^2 b^6+3760 a^3 b^5-460 a^4 b^4\right) x^{9/2}+\left(-3024 a^2 b^6+8040 a^3 b^5-3570 a^4 b^4\right) x^4+\left(1698 b^3 a^5-10080 b^4 a^4+8160 b^5 a^3\right) x^{7/2}+\left(256 b^8-1216 a b^7+2448 a^2 b^6+1088 a^3 b^5-12560 a^4 b^4+7677 a^5 b^3\right) x^3+\left(-768 a b^7+3456 a^2 b^6-6528 a^3 b^5-2880 a^4 b^4+12150 a^5 b^3-3174 a^6 b^2\right) x^{5/2}+\left(-384 a b^7+2880 a^2 b^6-8160 a^3 b^5+9600 a^4 b^4+3945 a^5 b^3-7446 a^6 b^2\right) x^2+\left(2944 b a^7-3340 b^2 a^6-8970 b^3 a^5+11680 b^4 a^4-5200 b^5 a^3+960 b^6 a^2\right) x^{3/2}+\left(1584 b a^7+5604 b^2 a^6-10737 b^3 a^5+6360 b^4 a^4-1740 b^5 a^3+144 b^6 a^2\right) x+\left(-1056 a^8-2112 b a^7+6258 b^2 a^6-4878 b^3 a^5+1740 b^4 a^4-240 b^5 a^3\right) \sqrt{x}\right)+\left(-1056 a^8+2944 b a^7-3174 b^2 a^6+1698 b^3 a^5-460 b^4 a^4+48 b^5 a^3\right) \sqrt{a-b x}}{24 \left(32 b^6-48 a b^5+18 a^2 b^4-a^3 b^3\right) x^3+\left(24 \sqrt{a-b} \sqrt{a-b x} \left(32 b^5-32 a b^4+6 a^2 b^3\right)+24 \left(-96 a b^5+120 a^2 b^4-30 a^3 b^3\right)\right) x^{5/2}+\left(24 \sqrt{a-b} \sqrt{a-b x} \left(-96 a b^4+72 a^2 b^3-6 a^3 b^2\right)+24 \left(-48 a b^5+204 a^2 b^4-159 a^3 b^3+18 a^4 b^2\right)\right) x^2+\left(24 \sqrt{a-b} \sqrt{a-b x} \left(-32 a b^4+164 a^2 b^3-72 a^3 b^2\right)+24 \left(120 b^2 a^4-260 b^3 a^3+120 b^4 a^2\right)\right) x^{3/2}+\left(24 \sqrt{a-b} \sqrt{a-b x} \left(32 b a^4-164 b^2 a^3+72 b^3 a^2\right)+24 \left(-48 b a^5+204 b^2 a^4-159 b^3 a^3+18 b^4 a^2\right)\right) x+\left(24 \sqrt{a-b} \sqrt{a-b x} \left(96 b a^4-72 b^2 a^3+6 b^3 a^2\right)+24 \left(-96 b a^5+120 b^2 a^4-30 b^3 a^3\right)\right) \sqrt{x}+24 \left(32 a^6-48 b a^5+18 b^2 a^4-b^3 a^3\right)+24 \sqrt{a-b} \left(-32 a^5+32 b a^4-6 b^2 a^3\right) \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}{8} a^2 \sqrt{x} \sqrt{a-b x}+\frac{5}{12} a \sqrt{x} (a-b x)^{3/2}+\frac{1}{3} \sqrt{x} (a-b x)^{5/2}",1,"((-1056*a^8 + 2944*a^7*b - 3174*a^6*b^2 + 1698*a^5*b^3 - 460*a^4*b^4 + 48*a^3*b^5)*Sqrt[a - b*x] + (1056*a^8 + 1584*a^7*b - 7446*a^6*b^2 + 7677*a^5*b^3 - 3570*a^4*b^4 + 780*a^3*b^5 - 48*a^2*b^6)*Sqrt[x]*Sqrt[a - b*x] + (-2112*a^7*b - 3340*a^6*b^2 + 12150*a^5*b^3 - 10080*a^4*b^4 + 3760*a^3*b^5 - 576*a^2*b^6)*x*Sqrt[a - b*x] + (-2416*a^7*b + 5604*a^6*b^2 + 3945*a^5*b^3 - 12560*a^4*b^4 + 8040*a^3*b^5 - 2400*a^2*b^6 + 256*a*b^7)*x^(3/2)*Sqrt[a - b*x] + (6258*a^6*b^2 - 8970*a^5*b^3 - 2880*a^4*b^4 + 8160*a^3*b^5 - 3840*a^2*b^6 + 768*a*b^7)*x^2*Sqrt[a - b*x] + (2098*a^6*b^2 - 10737*a^5*b^3 + 9600*a^4*b^4 + 1088*a^3*b^5 - 3024*a^2*b^6 + 1344*a*b^7 - 256*b^8)*x^(5/2)*Sqrt[a - b*x] + (-4878*a^5*b^3 + 11680*a^4*b^4 - 6528*a^3*b^5)*x^3*Sqrt[a - b*x] + (-885*a^5*b^3 + 6360*a^4*b^4 - 8160*a^3*b^5 + 2448*a^2*b^6)*x^(7/2)*Sqrt[a - b*x] + (1740*a^4*b^4 - 5200*a^3*b^5 + 3456*a^2*b^6)*x^4*Sqrt[a - b*x] + (170*a^4*b^4 - 1740*a^3*b^5 + 2880*a^2*b^6 - 1216*a*b^7)*x^(9/2)*Sqrt[a - b*x] + (-240*a^3*b^5 + 960*a^2*b^6 - 768*a*b^7)*x^5*Sqrt[a - b*x] + (-8*a^3*b^5 + 144*a^2*b^6 - 384*a*b^7 + 256*b^8)*x^(11/2)*Sqrt[a - b*x] + Sqrt[a - b]*(1056*a^8 - 2416*a^7*b + 2098*a^6*b^2 - 885*a^5*b^3 + 170*a^4*b^4 - 8*a^3*b^5 + (-1056*a^8 - 2112*a^7*b + 6258*a^6*b^2 - 4878*a^5*b^3 + 1740*a^4*b^4 - 240*a^3*b^5)*Sqrt[x] + (1584*a^7*b + 5604*a^6*b^2 - 10737*a^5*b^3 + 6360*a^4*b^4 - 1740*a^3*b^5 + 144*a^2*b^6)*x + (2944*a^7*b - 3340*a^6*b^2 - 8970*a^5*b^3 + 11680*a^4*b^4 - 5200*a^3*b^5 + 960*a^2*b^6)*x^(3/2) + (-7446*a^6*b^2 + 3945*a^5*b^3 + 9600*a^4*b^4 - 8160*a^3*b^5 + 2880*a^2*b^6 - 384*a*b^7)*x^2 + (-3174*a^6*b^2 + 12150*a^5*b^3 - 2880*a^4*b^4 - 6528*a^3*b^5 + 3456*a^2*b^6 - 768*a*b^7)*x^(5/2) + (7677*a^5*b^3 - 12560*a^4*b^4 + 1088*a^3*b^5 + 2448*a^2*b^6 - 1216*a*b^7 + 256*b^8)*x^3 + (1698*a^5*b^3 - 10080*a^4*b^4 + 8160*a^3*b^5)*x^(7/2) + (-3570*a^4*b^4 + 8040*a^3*b^5 - 3024*a^2*b^6)*x^4 + (-460*a^4*b^4 + 3760*a^3*b^5 - 3840*a^2*b^6)*x^(9/2) + (780*a^3*b^5 - 2400*a^2*b^6 + 1344*a*b^7)*x^5 + (48*a^3*b^5 - 576*a^2*b^6 + 768*a*b^7)*x^(11/2) + (-48*a^2*b^6 + 256*a*b^7 - 256*b^8)*x^6))/(24*(32*a^6 - 48*a^5*b + 18*a^4*b^2 - a^3*b^3) + 24*(-(a^3*b^3) + 18*a^2*b^4 - 48*a*b^5 + 32*b^6)*x^3 + 24*Sqrt[a - b]*(-32*a^5 + 32*a^4*b - 6*a^3*b^2)*Sqrt[a - b*x] + Sqrt[x]*(24*(-96*a^5*b + 120*a^4*b^2 - 30*a^3*b^3) + 24*Sqrt[a - b]*(96*a^4*b - 72*a^3*b^2 + 6*a^2*b^3)*Sqrt[a - b*x]) + x*(24*(-48*a^5*b + 204*a^4*b^2 - 159*a^3*b^3 + 18*a^2*b^4) + 24*Sqrt[a - b]*(32*a^4*b - 164*a^3*b^2 + 72*a^2*b^3)*Sqrt[a - b*x]) + x^2*(24*(18*a^4*b^2 - 159*a^3*b^3 + 204*a^2*b^4 - 48*a*b^5) + 24*Sqrt[a - b]*(-6*a^3*b^2 + 72*a^2*b^3 - 96*a*b^4)*Sqrt[a - b*x]) + x^(3/2)*(24*(120*a^4*b^2 - 260*a^3*b^3 + 120*a^2*b^4) + 24*Sqrt[a - b]*(-72*a^3*b^2 + 164*a^2*b^3 - 32*a*b^4)*Sqrt[a - b*x]) + x^(5/2)*(24*(-30*a^3*b^3 + 120*a^2*b^4 - 96*a*b^5) + 24*Sqrt[a - b]*(6*a^2*b^3 - 32*a*b^4 + 32*b^5)*Sqrt[a - b*x])) + (5*a^3*ArcTan[(Sqrt[a - b]/Sqrt[b] - Sqrt[a - b*x]/Sqrt[b])/(-1 + Sqrt[x])])/(4*Sqrt[b])","B",1
555,1,922,93,3.6634541,"\int \frac{(a-b x)^{5/2}}{x^{3/2}} \, dx","IntegrateAlgebraic[(a - b*x)^(5/2)/x^(3/2),x]","\frac{\left(4 \sqrt{x} b^3-2 a b^2-4 a \sqrt{x} b^2+4 \sqrt{a-b} \sqrt{a-b x} b^2+\frac{3 a^2 b}{2}+\frac{1}{2} a^2 \sqrt{x} b-2 a \sqrt{a-b} \sqrt{a-b x} b\right) \left(\sqrt{a-b}-\sqrt{a-b x}\right)^7}{\left(-a+b \sqrt{x}+\sqrt{a-b} \sqrt{a-b x}\right)^4}+\frac{\left(12 \sqrt{x} b^3+4 b^3-12 a b^2-12 a \sqrt{x} b^2+16 \sqrt{a-b} \sqrt{a-b x} b^2+\frac{13 a^2 b}{2}+\frac{3}{2} a^2 \sqrt{x} b-8 a \sqrt{a-b} \sqrt{a-b x} b\right) \left(\sqrt{a-b}-\sqrt{a-b x}\right)^5}{\left(-a+b \sqrt{x}+\sqrt{a-b} \sqrt{a-b x}\right)^3}+\frac{\left(10 \sqrt{x} b^3+10 b^3-20 a b^2-14 a \sqrt{x} b^2+20 \sqrt{a-b} \sqrt{a-b x} b^2+\frac{43 a^2 b}{4}+\frac{13}{4} a^2 \sqrt{x} b-14 a \sqrt{a-b} \sqrt{a-b x} b\right) \left(\sqrt{a-b}-\sqrt{a-b x}\right)^3}{\left(-a+b \sqrt{x}+\sqrt{a-b} \sqrt{a-b x}\right)^2}+\frac{\left(2 a^3-2 a^3 \sqrt{x}\right) \left(-\sqrt{x} a+2 a-2 b-b x+2 b \sqrt{x}-2 \sqrt{a-b} \sqrt{a-b x}+\sqrt{a-b} \sqrt{x} \sqrt{a-b x}\right) \left(\sqrt{a-b}-\sqrt{a-b x}\right)}{\sqrt{x} \left(-2 \sqrt{x} a^2+4 a^2+b x^{3/2} a-4 b a-2 b x a+b \sqrt{x} a-4 \sqrt{a-b} \sqrt{a-b x} a+2 \sqrt{a-b} \sqrt{x} \sqrt{a-b x} a+2 b^2 \sqrt{x}+2 \sqrt{a-b} b \sqrt{a-b x}\right)}+\frac{\left(\frac{1}{4} b \sqrt{a-b x}-\frac{1}{4} \sqrt{a-b} b\right) \left(-9 \sqrt{x} a^2-39 a^2+56 b a+24 b \sqrt{x} a+48 \sqrt{a-b} \sqrt{a-b x} a-24 b^2-8 b^2 \sqrt{x}-32 \sqrt{a-b} b \sqrt{a-b x}\right)}{-a+b \sqrt{x}+\sqrt{a-b} \sqrt{a-b x}}-\frac{15}{2} a^2 \sqrt{b} \tan ^{-1}\left(\frac{\frac{\sqrt{a-b}}{\sqrt{b}}-\frac{\sqrt{a-b x}}{\sqrt{b}}}{\sqrt{x}-1}\right)","-\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,"((-1/4*(Sqrt[a - b]*b) + (b*Sqrt[a - b*x])/4)*(-39*a^2 + 56*a*b - 24*b^2 - 9*a^2*Sqrt[x] + 24*a*b*Sqrt[x] - 8*b^2*Sqrt[x] + 48*a*Sqrt[a - b]*Sqrt[a - b*x] - 32*Sqrt[a - b]*b*Sqrt[a - b*x]))/(-a + b*Sqrt[x] + Sqrt[a - b]*Sqrt[a - b*x]) + ((Sqrt[a - b] - Sqrt[a - b*x])^7*((3*a^2*b)/2 - 2*a*b^2 + (a^2*b*Sqrt[x])/2 - 4*a*b^2*Sqrt[x] + 4*b^3*Sqrt[x] - 2*a*Sqrt[a - b]*b*Sqrt[a - b*x] + 4*Sqrt[a - b]*b^2*Sqrt[a - b*x]))/(-a + b*Sqrt[x] + Sqrt[a - b]*Sqrt[a - b*x])^4 + ((Sqrt[a - b] - Sqrt[a - b*x])^5*((13*a^2*b)/2 - 12*a*b^2 + 4*b^3 + (3*a^2*b*Sqrt[x])/2 - 12*a*b^2*Sqrt[x] + 12*b^3*Sqrt[x] - 8*a*Sqrt[a - b]*b*Sqrt[a - b*x] + 16*Sqrt[a - b]*b^2*Sqrt[a - b*x]))/(-a + b*Sqrt[x] + Sqrt[a - b]*Sqrt[a - b*x])^3 + ((Sqrt[a - b] - Sqrt[a - b*x])^3*((43*a^2*b)/4 - 20*a*b^2 + 10*b^3 + (13*a^2*b*Sqrt[x])/4 - 14*a*b^2*Sqrt[x] + 10*b^3*Sqrt[x] - 14*a*Sqrt[a - b]*b*Sqrt[a - b*x] + 20*Sqrt[a - b]*b^2*Sqrt[a - b*x]))/(-a + b*Sqrt[x] + Sqrt[a - b]*Sqrt[a - b*x])^2 + ((2*a^3 - 2*a^3*Sqrt[x])*(Sqrt[a - b] - Sqrt[a - b*x])*(2*a - 2*b - a*Sqrt[x] + 2*b*Sqrt[x] - b*x - 2*Sqrt[a - b]*Sqrt[a - b*x] + Sqrt[a - b]*Sqrt[x]*Sqrt[a - b*x]))/(Sqrt[x]*(4*a^2 - 4*a*b - 2*a^2*Sqrt[x] + a*b*Sqrt[x] + 2*b^2*Sqrt[x] - 2*a*b*x + a*b*x^(3/2) - 4*a*Sqrt[a - b]*Sqrt[a - b*x] + 2*Sqrt[a - b]*b*Sqrt[a - b*x] + 2*a*Sqrt[a - b]*Sqrt[x]*Sqrt[a - b*x])) - (15*a^2*Sqrt[b]*ArcTan[(Sqrt[a - b]/Sqrt[b] - Sqrt[a - b*x]/Sqrt[b])/(-1 + Sqrt[x])])/2","B",1
556,1,2277,90,13.3020549,"\int \frac{(a-b x)^{5/2}}{x^{5/2}} \, dx","IntegrateAlgebraic[(a - b*x)^(5/2)/x^(5/2),x]","\text{Result too large to show}","5 a b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)+5 b^2 \sqrt{x} \sqrt{a-b x}-\frac{2 (a-b x)^{5/2}}{3 x^{3/2}}+\frac{10 b (a-b x)^{3/2}}{3 \sqrt{x}}",1,"((3*a - 2*b + a*Sqrt[x] - 2*b*Sqrt[x] - 4*Sqrt[a - b]*Sqrt[a - b*x])*(-(Sqrt[a - b]*b^2) + b^2*Sqrt[a - b*x]))/(-a + b*Sqrt[x] + Sqrt[a - b]*Sqrt[a - b*x]) + ((Sqrt[a - b] - Sqrt[a - b*x])^3*(-(a*b^2) - a*b^2*Sqrt[x] + 2*b^3*Sqrt[x] + 2*Sqrt[a - b]*b^2*Sqrt[a - b*x]))/(-a + b*Sqrt[x] + Sqrt[a - b]*Sqrt[a - b*x])^2 + ((Sqrt[a - b] - Sqrt[a - b*x])^9*((16*a^4)/3 - (64*a^7)/(3*b^3) + (48*a^6)/b^2 - (32*a^5)/b - 32*a^4*Sqrt[x] - (256*a^8*Sqrt[x])/(3*b^4) + (928*a^7*Sqrt[x])/(3*b^3) - (392*a^6*Sqrt[x])/b^2 + (200*a^5*Sqrt[x])/b + 8*a^4*x + (128*a^8*x)/(3*b^4) - (160*a^7*x)/b^3 + (584*a^6*x)/(3*b^2) - (256*a^5*x)/(3*b) - (8*a^4*x^(3/2))/3 + (64*a^7*x^(3/2))/(3*b^3) - (128*a^6*x^(3/2))/(3*b^2) + (24*a^5*x^(3/2))/b - (64*a^6*Sqrt[a - b]*Sqrt[a - b*x])/(3*b^3) + (112*a^5*Sqrt[a - b]*Sqrt[a - b*x])/(3*b^2) - (16*a^4*Sqrt[a - b]*Sqrt[a - b*x])/b + (256*a^7*Sqrt[a - b]*Sqrt[x]*Sqrt[a - b*x])/(3*b^4) - (160*a^6*Sqrt[a - b]*Sqrt[x]*Sqrt[a - b*x])/b^3 + (248*a^5*Sqrt[a - b]*Sqrt[x]*Sqrt[a - b*x])/(3*b^2) - (8*a^4*Sqrt[a - b]*Sqrt[x]*Sqrt[a - b*x])/b - (128*a^7*Sqrt[a - b]*x*Sqrt[a - b*x])/(3*b^4) + (224*a^6*Sqrt[a - b]*x*Sqrt[a - b*x])/(3*b^3) - (104*a^5*Sqrt[a - b]*x*Sqrt[a - b*x])/(3*b^2) + (8*a^4*Sqrt[a - b]*x*Sqrt[a - b*x])/(3*b)))/(x^(3/2)*(4*a^2 - 4*a*b - 2*a^2*Sqrt[x] + a*b*Sqrt[x] + 2*b^2*Sqrt[x] - 2*a*b*x + a*b*x^(3/2) - 4*a*Sqrt[a - b]*Sqrt[a - b*x] + 2*Sqrt[a - b]*b*Sqrt[a - b*x] + 2*a*Sqrt[a - b]*Sqrt[x]*Sqrt[a - b*x])^3) + ((Sqrt[a - b] - Sqrt[a - b*x])^5*(72*a^4 + (512*a^8)/(3*b^4) - (512*a^7)/b^3 + (1664*a^6)/(3*b^2) - (832*a^5)/(3*b) - 8*a^3*b - 164*a^4*Sqrt[x] + (128*a^7*Sqrt[x])/(3*b^3) - (496*a^6*Sqrt[x])/(3*b^2) + (766*a^5*Sqrt[x])/(3*b) + 32*a^3*b*Sqrt[x] + (466*a^4*x)/3 - (128*a^7*x)/b^3 + (376*a^6*x)/b^2 - (1178*a^5*x)/(3*b) - 12*a^3*b*x - 34*a^4*x^(3/2) - (64*a^6*x^(3/2))/(3*b^2) + (52*a^5*x^(3/2))/b + 4*a^3*b*x^(3/2) + 8*a^3*Sqrt[a - b]*Sqrt[a - b*x] - (512*a^7*Sqrt[a - b]*Sqrt[a - b*x])/(3*b^4) + (1280*a^6*Sqrt[a - b]*Sqrt[a - b*x])/(3*b^3) - (1088*a^5*Sqrt[a - b]*Sqrt[a - b*x])/(3*b^2) + (96*a^4*Sqrt[a - b]*Sqrt[a - b*x])/b + 12*a^3*Sqrt[a - b]*Sqrt[x]*Sqrt[a - b*x] - (128*a^6*Sqrt[a - b]*Sqrt[x]*Sqrt[a - b*x])/(3*b^3) + (144*a^5*Sqrt[a - b]*Sqrt[x]*Sqrt[a - b*x])/b^2 - (314*a^4*Sqrt[a - b]*Sqrt[x]*Sqrt[a - b*x])/(3*b) - 4*a^3*Sqrt[a - b]*x*Sqrt[a - b*x] + (128*a^6*Sqrt[a - b]*x*Sqrt[a - b*x])/(3*b^3) - (296*a^5*Sqrt[a - b]*x*Sqrt[a - b*x])/(3*b^2) + (54*a^4*Sqrt[a - b]*x*Sqrt[a - b*x])/b))/(x*(4*a^2 - 4*a*b - 2*a^2*Sqrt[x] + a*b*Sqrt[x] + 2*b^2*Sqrt[x] - 2*a*b*x + a*b*x^(3/2) - 4*a*Sqrt[a - b]*Sqrt[a - b*x] + 2*Sqrt[a - b]*b*Sqrt[a - b*x] + 2*a*Sqrt[a - b]*Sqrt[x]*Sqrt[a - b*x])^2) + (((-2*a^2*Sqrt[a - b])/(3*b^2) + (2*a^2*Sqrt[a - b*x])/(3*b^2))*(-144*a^4 + 304*a^3*b - 203*a^2*b^2 + 63*a*b^3 - 18*b^4 - 28*a^3*b*Sqrt[x] + 53*a^2*b^2*Sqrt[x] - 57*a*b^3*Sqrt[x] + 36*b^4*Sqrt[x] + 108*a^3*b*x - 200*a^2*b^2*x + 105*a*b^3*x - 27*b^4*x + 14*a^2*b^2*x^(3/2) - 15*a*b^3*x^(3/2) + 9*b^4*x^(3/2) + 144*a^3*Sqrt[a - b]*Sqrt[a - b*x] - 232*a^2*Sqrt[a - b]*b*Sqrt[a - b*x] + 105*a*Sqrt[a - b]*b^2*Sqrt[a - b*x] - 18*Sqrt[a - b]*b^3*Sqrt[a - b*x] + 28*a^2*Sqrt[a - b]*b*Sqrt[x]*Sqrt[a - b*x] - 39*a*Sqrt[a - b]*b^2*Sqrt[x]*Sqrt[a - b*x] + 27*Sqrt[a - b]*b^3*Sqrt[x]*Sqrt[a - b*x] - 36*a^2*Sqrt[a - b]*b*x*Sqrt[a - b*x] + 30*a*Sqrt[a - b]*b^2*x*Sqrt[a - b*x] - 9*Sqrt[a - b]*b^3*x*Sqrt[a - b*x]))/(Sqrt[x]*(4*a^2 - 4*a*b - 2*a^2*Sqrt[x] + a*b*Sqrt[x] + 2*b^2*Sqrt[x] - 2*a*b*x + a*b*x^(3/2) - 4*a*Sqrt[a - b]*Sqrt[a - b*x] + 2*Sqrt[a - b]*b*Sqrt[a - b*x] + 2*a*Sqrt[a - b]*Sqrt[x]*Sqrt[a - b*x])) + 10*a*b^(3/2)*ArcTan[(Sqrt[a - b]/Sqrt[b] - Sqrt[a - b*x]/Sqrt[b])/(-1 + Sqrt[x])]","B",1
557,1,4036,144,13.0631075,"\int x^{5/2} (2+b x)^{5/2} \, dx","IntegrateAlgebraic[x^(5/2)*(2 + b*x)^(5/2),x]","\text{Result too large to show}","-\frac{5 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{8 b^{7/2}}+\frac{5 \sqrt{x} \sqrt{b x+2}}{16 b^3}-\frac{5 x^{3/2} \sqrt{b x+2}}{48 b^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,"(-4*(1966080 + 2785280*b + 1449984*b^2 + 7526400*b^3 + 17808800*b^4 + 18698328*b^5 + 10839564*b^6 + 3741844*b^7 + 772680*b^8 + 90312*b^9 + 5152*b^10 + 96*b^11)*Sqrt[2 + b*x] - 4*(-1966080 + 2949120*b + 5959680*b^2 + 3059712*b^3 + 22188576*b^4 + 50676336*b^5 + 50100789*b^6 + 26963022*b^7 + 8466522*b^8 + 1537908*b^9 + 148644*b^10 + 6096*b^11 + 48*b^12)*Sqrt[x]*Sqrt[2 + b*x] - 4*(-3440640*b + 3850240*b^2 + 7649280*b^3 + 12433536*b^4 + 53782696*b^5 + 92304000*b^6 + 77439660*b^7 + 36405920*b^8 + 9937368*b^9 + 1519248*b^10 + 114080*b^11 + 2880*b^12)*x*Sqrt[2 + b*x] - 4*(-2293760*b - 5283840*b^2 + 3809280*b^3 + 6883456*b^4 + 26828016*b^5 + 85685670*b^6 + 115980675*b^7 + 81892080*b^8 + 32984958*b^9 + 7628968*b^10 + 944820*b^11 + 50880*b^12 + 560*b^13)*x^(3/2)*Sqrt[2 + b*x] - 4*(-5038080*b^2 - 6174720*b^3 + 2840256*b^4 + 8618736*b^5 + 42344940*b^6 + 98178660*b^7 + 106776000*b^8 + 63361728*b^9 + 21612768*b^10 + 4142880*b^11 + 397440*b^12 + 13440*b^13)*x^2*Sqrt[2 + b*x] - 4*(-937984*b^2 - 6598656*b^3 - 5473344*b^4 + 1604960*b^5 + 11730519*b^6 + 47519514*b^7 + 83424288*b^8 + 74138400*b^9 + 36988056*b^10 + 10575824*b^11 + 1639008*b^12 + 114240*b^13 + 1792*b^14)*x^(5/2)*Sqrt[2 + b*x] - 4*(-1923072*b^3 - 6006144*b^4 - 3712560*b^5 + 1474272*b^6 + 12991132*b^7 + 38772672*b^8 + 53433408*b^9 + 39324544*b^10 + 16495584*b^11 + 3908352*b^12 + 473984*b^13 + 21504*b^14)*x^3*Sqrt[2 + b*x] - 4*(-7348224*b^3 - 12853632*b^4 - 10051104*b^5 - 3509244*b^6 + 1512135*b^7 + 10365312*b^8 + 23245632*b^9 + 25881408*b^10 + 15945240*b^11 + 5618880*b^12 + 1087200*b^13 + 98304*b^14 + 2304*b^15)*x^(7/2)*Sqrt[2 + b*x] - 4*(-21833568*b^4 - 31089864*b^5 - 16783452*b^6 - 3957732*b^7 + 1126400*b^8 + 5811840*b^9 + 10183488*b^10 + 9379520*b^11 + 4884480*b^12 + 1443840*b^13 + 223744*b^14 + 13824*b^15)*x^4*Sqrt[2 + b*x] - 4*(-15987936*b^4 - 55179216*b^5 - 52907565*b^6 - 21154630*b^7 - 3594480*b^8 + 542784*b^9 + 2228144*b^10 + 3165600*b^11 + 2466000*b^12 + 1097600*b^13 + 272064*b^14 + 33024*b^15 + 1280*b^16)*x^(9/2)*Sqrt[2 + b*x] - 4*(-45248760*b^5 - 90714720*b^6 - 63282204*b^7 - 18971328*b^8 - 2285184*b^9 + 156672*b^10 + 541248*b^11 + 646848*b^12 + 437760*b^13 + 169728*b^14 + 35328*b^15 + 3072*b^16)*x^5*Sqrt[2 + b*x] - 4*(-14927568*b^5 - 83549322*b^6 - 107710575*b^7 - 55398272*b^8 - 12211632*b^9 - 972768*b^10 + 21424*b^11 + 65664*b^12 + 69264*b^13 + 42880*b^14 + 15552*b^15 + 3072*b^16 + 256*b^17)*x^(11/2)*Sqrt[2 + b*x] - 4*(-39464604*b^6 - 106769300*b^7 - 95527872*b^8 - 36248256*b^9 - 5648192*b^10 - 257088*b^11)*x^6*Sqrt[2 + b*x] - 4*(-7550847*b^6 - 60896802*b^7 - 100459080*b^8 - 64577184*b^9 - 17842032*b^10 - 1833504*b^11 - 33264*b^12)*x^(13/2)*Sqrt[2 + b*x] - 4*(-18342060*b^7 - 64540960*b^8 - 71742528*b^9 - 33568128*b^10 - 6550720*b^11 - 388800*b^12)*x^7*Sqrt[2 + b*x] - 4*(-2213339*b^7 - 24324816*b^8 - 50203512*b^9 - 39486272*b^10 - 13399440*b^11 - 1742688*b^12 - 43152*b^13)*x^(15/2)*Sqrt[2 + b*x] - 4*(-4813512*b^8 - 21667272*b^9 - 29562720*b^10 - 16829472*b^11 - 4055040*b^12 - 313344*b^13)*x^8*Sqrt[2 + b*x] - 4*(-371554*b^8 - 5424660*b^9 - 13942452*b^10 - 13356784*b^11 - 5529600*b^12 - 903168*b^13 - 31296*b^14)*x^(17/2)*Sqrt[2 + b*x] - 4*(-691416*b^9 - 3975312*b^10 - 6681312*b^11 - 4637952*b^12 - 1379840*b^13 - 139008*b^14)*x^9*Sqrt[2 + b*x] - 4*(-32694*b^9 - 630504*b^10 - 2038500*b^11 - 2405760*b^12 - 1226880*b^13 - 253824*b^14 - 12864*b^15)*x^(19/2)*Sqrt[2 + b*x] - 4*(-47520*b^10 - 353760*b^11 - 747648*b^12 - 646272*b^13 - 242176*b^14 - 32256*b^15)*x^10*Sqrt[2 + b*x] - 4*(-1192*b^10 - 30768*b^11 - 128880*b^12 - 193984*b^13 - 126336*b^14 - 34560*b^15 - 2816*b^16)*x^(21/2)*Sqrt[2 + b*x] - 4*(-1056*b^11 - 10560*b^12 - 29568*b^13 - 33792*b^14 - 16896*b^15 - 3072*b^16)*x^11*Sqrt[2 + b*x] - 4*(-8*b^11 - 288*b^12 - 1680*b^13 - 3584*b^14 - 3456*b^15 - 1536*b^16 - 256*b^17)*x^(23/2)*Sqrt[2 + b*x] + Sqrt[2 + b]*(-4*(-1966080 - 2293760*b - 937984*b^2 - 7348224*b^3 - 15987936*b^4 - 14927568*b^5 - 7550847*b^6 - 2213339*b^7 - 371554*b^8 - 32694*b^9 - 1192*b^10 - 8*b^11) - 4*(1966080 - 3440640*b - 5038080*b^2 - 1923072*b^3 - 21833568*b^4 - 45248760*b^5 - 39464604*b^6 - 18342060*b^7 - 4813512*b^8 - 691416*b^9 - 47520*b^10 - 1056*b^11)*Sqrt[x] - 4*(2949120*b - 5283840*b^2 - 6598656*b^3 - 12853632*b^4 - 55179216*b^5 - 83549322*b^6 - 60896802*b^7 - 24324816*b^8 - 5424660*b^9 - 630504*b^10 - 30768*b^11 - 288*b^12)*x - 4*(2785280*b + 3850240*b^2 - 6174720*b^3 - 6006144*b^4 - 31089864*b^5 - 90714720*b^6 - 106769300*b^7 - 64540960*b^8 - 21667272*b^9 - 3975312*b^10 - 353760*b^11 - 10560*b^12)*x^(3/2) - 4*(5959680*b^2 + 3809280*b^3 - 5473344*b^4 - 10051104*b^5 - 52907565*b^6 - 107710575*b^7 - 100459080*b^8 - 50203512*b^9 - 13942452*b^10 - 2038500*b^11 - 128880*b^12 - 1680*b^13)*x^2 - 4*(1449984*b^2 + 7649280*b^3 + 2840256*b^4 - 3712560*b^5 - 16783452*b^6 - 63282204*b^7 - 95527872*b^8 - 71742528*b^9 - 29562720*b^10 - 6681312*b^11 - 747648*b^12 - 29568*b^13)*x^(5/2) - 4*(3059712*b^3 + 6883456*b^4 + 1604960*b^5 - 3509244*b^6 - 21154630*b^7 - 55398272*b^8 - 64577184*b^9 - 39486272*b^10 - 13356784*b^11 - 2405760*b^12 - 193984*b^13 - 3584*b^14)*x^3 - 4*(7526400*b^3 + 12433536*b^4 + 8618736*b^5 + 1474272*b^6 - 3957732*b^7 - 18971328*b^8 - 36248256*b^9 - 33568128*b^10 - 16829472*b^11 - 4637952*b^12 - 646272*b^13 - 33792*b^14)*x^(7/2) - 4*(22188576*b^4 + 26828016*b^5 + 11730519*b^6 + 1512135*b^7 - 3594480*b^8 - 12211632*b^9 - 17842032*b^10 - 13399440*b^11 - 5529600*b^12 - 1226880*b^13 - 126336*b^14 - 3456*b^15)*x^4 - 4*(17808800*b^4 + 53782696*b^5 + 42344940*b^6 + 12991132*b^7 + 1126400*b^8 - 2285184*b^9 - 5648192*b^10 - 6550720*b^11 - 4055040*b^12 - 1379840*b^13 - 242176*b^14 - 16896*b^15)*x^(9/2) - 4*(50676336*b^5 + 85685670*b^6 + 47519514*b^7 + 10365312*b^8 + 542784*b^9 - 972768*b^10 - 1833504*b^11 - 1742688*b^12 - 903168*b^13 - 253824*b^14 - 34560*b^15 - 1536*b^16)*x^5 - 4*(18698328*b^5 + 92304000*b^6 + 98178660*b^7 + 38772672*b^8 + 5811840*b^9 + 156672*b^10 - 257088*b^11 - 388800*b^12 - 313344*b^13 - 139008*b^14 - 32256*b^15 - 3072*b^16)*x^(11/2) - 4*(50100789*b^6 + 115980675*b^7 + 83424288*b^8 + 23245632*b^9 + 2228144*b^10 + 21424*b^11 - 33264*b^12 - 43152*b^13 - 31296*b^14 - 12864*b^15 - 2816*b^16 - 256*b^17)*x^6 - 4*(10839564*b^6 + 77439660*b^7 + 106776000*b^8 + 53433408*b^9 + 10183488*b^10 + 541248*b^11)*x^(13/2) - 4*(26963022*b^7 + 81892080*b^8 + 74138400*b^9 + 25881408*b^10 + 3165600*b^11 + 65664*b^12)*x^7 - 4*(3741844*b^7 + 36405920*b^8 + 63361728*b^9 + 39324544*b^10 + 9379520*b^11 + 646848*b^12)*x^(15/2) - 4*(8466522*b^8 + 32984958*b^9 + 36988056*b^10 + 15945240*b^11 + 2466000*b^12 + 69264*b^13)*x^8 - 4*(772680*b^8 + 9937368*b^9 + 21612768*b^10 + 16495584*b^11 + 4884480*b^12 + 437760*b^13)*x^(17/2) - 4*(1537908*b^9 + 7628968*b^10 + 10575824*b^11 + 5618880*b^12 + 1097600*b^13 + 42880*b^14)*x^9 - 4*(90312*b^9 + 1519248*b^10 + 4142880*b^11 + 3908352*b^12 + 1443840*b^13 + 169728*b^14)*x^(19/2) - 4*(148644*b^10 + 944820*b^11 + 1639008*b^12 + 1087200*b^13 + 272064*b^14 + 15552*b^15)*x^10 - 4*(5152*b^10 + 114080*b^11 + 397440*b^12 + 473984*b^13 + 223744*b^14 + 35328*b^15)*x^(21/2) - 4*(6096*b^11 + 50880*b^12 + 114240*b^13 + 98304*b^14 + 33024*b^15 + 3072*b^16)*x^11 - 4*(96*b^11 + 2880*b^12 + 13440*b^13 + 21504*b^14 + 13824*b^15 + 3072*b^16)*x^(23/2) - 4*(48*b^12 + 560*b^13 + 1792*b^14 + 2304*b^15 + 1280*b^16 + 256*b^17)*x^12))/(3*b^3*(8388608 + 12582912*b + 7077888*b^2 + 1835008*b^3 + 215040*b^4 + 9216*b^5 + 64*b^6) + 3*b^3*(64*b^6 + 2304*b^7 + 13440*b^8 + 28672*b^9 + 27648*b^10 + 12288*b^11 + 2048*b^12)*x^6 + 3*b^3*Sqrt[2 + b]*(-4194304 - 5242880*b - 2359296*b^2 - 458752*b^3 - 35840*b^4 - 768*b^5)*Sqrt[2 + b*x] + x*(3*b^3*(12582912*b + 55050240*b^2 + 55836672*b^3 + 22536192*b^4 + 3855360*b^5 + 234624*b^6 + 2304*b^7) + 3*b^3*Sqrt[2 + b]*(-5242880*b - 24641536*b^2 - 21037056*b^3 - 6508544*b^4 - 751360*b^5 - 23040*b^6)*Sqrt[2 + b*x]) + Sqrt[x]*(3*b^3*(25165824*b + 34603008*b^2 + 17301504*b^3 + 3784704*b^4 + 337920*b^5 + 8448*b^6) + 3*b^3*Sqrt[2 + b]*(-12582912*b - 14155776*b^2 - 5505024*b^3 - 860160*b^4 - 46080*b^5 - 384*b^6)*Sqrt[2 + b*x]) + x^2*(3*b^3*(7077888*b^2 + 55836672*b^3 + 84258816*b^4 + 48039936*b^5 + 11398080*b^6 + 963840*b^7 + 13440*b^8) + 3*b^3*Sqrt[2 + b]*(-2359296*b^2 - 21037056*b^3 - 30296064*b^4 - 14353920*b^5 - 2426880*b^6 - 107520*b^7)*Sqrt[2 + b*x]) + x^(3/2)*(3*b^3*(34603008*b^2 + 80740352*b^3 + 61095936*b^4 + 19193856*b^5 + 2407680*b^6 + 84480*b^7) + 3*b^3*Sqrt[2 + b]*(-14155776*b^2 - 32505856*b^3 - 20701184*b^4 - 4853760*b^5 - 375680*b^6 - 4480*b^7)*Sqrt[2 + b*x]) + x^3*(3*b^3*(1835008*b^3 + 22536192*b^4 + 48039936*b^5 + 37289728*b^6 + 12009984*b^7 + 1408512*b^8 + 28672*b^9) + 3*b^3*Sqrt[2 + b]*(-458752*b^3 - 6508544*b^4 - 14353920*b^5 - 10271744*b^6 - 2587648*b^7 - 172032*b^8)*Sqrt[2 + b*x]) + x^(5/2)*(3*b^3*(17301504*b^3 + 61095936*b^4 + 64745472*b^5 + 27861504*b^6 + 4798464*b^7 + 236544*b^8) + 3*b^3*Sqrt[2 + b]*(-5505024*b^3 - 20701184*b^4 - 20543488*b^5 - 7176960*b^6 - 813568*b^7 - 14336*b^8)*Sqrt[2 + b*x]) + x^4*(3*b^3*(215040*b^4 + 3855360*b^5 + 11398080*b^6 + 12009984*b^7 + 5266176*b^8 + 872448*b^9 + 27648*b^10) + 3*b^3*Sqrt[2 + b]*(-35840*b^4 - 751360*b^5 - 2426880*b^6 - 2587648*b^7 - 1015808*b^8 - 110592*b^9)*Sqrt[2 + b*x]) + x^(7/2)*(3*b^3*(3784704*b^4 + 19193856*b^5 + 27861504*b^6 + 16186368*b^7 + 3818496*b^8 + 270336*b^9) + 3*b^3*Sqrt[2 + b]*(-860160*b^4 - 4853760*b^5 - 7176960*b^6 - 3787008*b^7 - 657408*b^8 - 18432*b^9)*Sqrt[2 + b*x]) + x^5*(3*b^3*(9216*b^5 + 234624*b^6 + 963840*b^7 + 1408512*b^8 + 872448*b^9 + 215040*b^10 + 12288*b^11) + 3*b^3*Sqrt[2 + b]*(-768*b^5 - 23040*b^6 - 107520*b^7 - 172032*b^8 - 110592*b^9 - 24576*b^10)*Sqrt[2 + b*x]) + x^(9/2)*(3*b^3*(337920*b^5 + 2407680*b^6 + 4798464*b^7 + 3818496*b^8 + 1261568*b^9 + 135168*b^10) + 3*b^3*Sqrt[2 + b]*(-46080*b^5 - 375680*b^6 - 813568*b^7 - 657408*b^8 - 192512*b^9 - 10240*b^10)*Sqrt[2 + b*x]) + x^(11/2)*(3*b^3*(8448*b^6 + 84480*b^7 + 236544*b^8 + 270336*b^9 + 135168*b^10 + 24576*b^11) + 3*b^3*Sqrt[2 + b]*(-384*b^6 - 4480*b^7 - 14336*b^8 - 18432*b^9 - 10240*b^10 - 2048*b^11)*Sqrt[2 + b*x])) + (5*ArcTanh[(Sqrt[2 + b]/Sqrt[b] - Sqrt[2 + b*x]/Sqrt[b])/(-1 + Sqrt[x])])/(4*b^(7/2))","B",1
558,1,2966,123,7.8590257,"\int x^{3/2} (2+b x)^{5/2} \, dx","IntegrateAlgebraic[x^(3/2)*(2 + b*x)^(5/2),x]","\text{Result too large to show}","\frac{3 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{4 b^{5/2}}-\frac{3 \sqrt{x} \sqrt{b x+2}}{8 b^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,"(4*(245760 + 286720*b - 935168*b^2 - 2229760*b^3 - 2016020*b^4 - 974350*b^5 - 269450*b^6 - 41524*b^7 - 3140*b^8 - 80*b^9)*Sqrt[2 + b*x] + 4*(-245760 + 307200*b + 505600*b^2 - 2432320*b^3 - 5267260*b^4 - 4421225*b^5 - 1955575*b^6 - 480805*b^7 - 62330*b^8 - 3490*b^9 - 40*b^10)*Sqrt[x]*Sqrt[2 + b*x] + 4*(-368640*b + 325120*b^2 - 525568*b^3 - 5197840*b^4 - 7896350*b^5 - 5537200*b^6 - 2101240*b^7 - 435584*b^8 - 44560*b^9 - 1600*b^10)*x*Sqrt[2 + b*x] + 4*(-225280*b - 473600*b^2 + 254400*b^3 - 1924080*b^4 - 6876375*b^5 - 7992950*b^6 - 4653860*b^7 - 1482080*b^8 - 250120*b^9 - 18800*b^10 - 320*b^11)*x^(3/2)*Sqrt[2 + b*x] + 4*(-405760*b^2 - 453120*b^3 - 198552*b^4 - 2885100*b^5 - 6291450*b^6 - 5779320*b^7 - 2790240*b^8 - 734016*b^9 - 97200*b^10 - 4800*b^11)*x^2*Sqrt[2 + b*x] + 4*(983808*b^2 + 887360*b^3 + 252920*b^4 - 451370*b^5 - 2624165*b^6 - 4105967*b^7 - 3050640*b^8 - 1220880*b^9 - 261000*b^10 - 25800*b^11 - 672*b^12)*x^(5/2)*Sqrt[2 + b*x] + 4*(2520320*b^3 + 2653360*b^4 + 896900*b^5 - 402400*b^6 - 1595900*b^7 - 1924480*b^8 - 1176640*b^9 - 390080*b^10 - 66400*b^11 - 4480*b^12)*x^3*Sqrt[2 + b*x] + 4*(1978688*b^3 + 5516240*b^4 + 4055650*b^5 + 1050380*b^6 - 208990*b^7 - 654432*b^8 - 635360*b^9 - 324800*b^10 - 89200*b^11 - 11840*b^12 - 512*b^13)*x^(7/2)*Sqrt[2 + b*x] + 4*(4627980*b^4 + 7513850*b^5 + 3950050*b^6 + 736900*b^7 - 64000*b^8 - 170720*b^9 - 138800*b^10 - 60640*b^11 - 13760*b^12 - 1280*b^13)*x^4*Sqrt[2 + b*x] + 4*(1553252*b^4 + 7053475*b^5 + 7195775*b^6 + 2670145*b^7 + 334240*b^8 - 9408*b^9 - 22800*b^10 - 16600*b^11 - 6720*b^12 - 1440*b^13 - 128*b^14)*x^(9/2)*Sqrt[2 + b*x] + 4*(3345050*b^5 + 7306800*b^6 + 5007624*b^7 + 1280640*b^8 + 94080*b^9)*x^5*Sqrt[2 + b*x] + 4*(639845*b^5 + 4181450*b^6 + 5459180*b^7 + 2570080*b^8 + 430240*b^9 + 13240*b^10)*x^(11/2)*Sqrt[2 + b*x] + 4*(1243650*b^6 + 3528840*b^7 + 3017184*b^8 + 970560*b^9 + 95600*b^10)*x^6*Sqrt[2 + b*x] + 4*(145085*b^6 + 1303235*b^7 + 2136080*b^8 + 1243120*b^9 + 263800*b^10 + 11720*b^11)*x^(13/2)*Sqrt[2 + b*x] + 4*(244620*b^7 + 896640*b^8 + 950016*b^9 + 379200*b^10 + 48800*b^11)*x^7*Sqrt[2 + b*x] + 4*(17062*b^7 + 208240*b^8 + 431680*b^9 + 311600*b^10 + 83600*b^11 + 5472*b^12)*x^(15/2)*Sqrt[2 + b*x] + 4*(22980*b^8 + 110640*b^9 + 148080*b^10 + 74400*b^11 + 12480*b^12)*x^8*Sqrt[2 + b*x] + 4*(842*b^8 + 14210*b^9 + 38600*b^10 + 35800*b^11 + 12640*b^12 + 1312*b^13)*x^(17/2)*Sqrt[2 + b*x] + 4*(720*b^9 + 4800*b^10 + 8640*b^11 + 5760*b^12 + 1280*b^13)*x^9*Sqrt[2 + b*x] + 4*(8*b^9 + 200*b^10 + 800*b^11 + 1120*b^12 + 640*b^13 + 128*b^14)*x^(19/2)*Sqrt[2 + b*x] + Sqrt[2 + b]*(4*(-245760 - 225280*b + 983808*b^2 + 1978688*b^3 + 1553252*b^4 + 639845*b^5 + 145085*b^6 + 17062*b^7 + 842*b^8 + 8*b^9) + 4*(245760 - 368640*b - 405760*b^2 + 2520320*b^3 + 4627980*b^4 + 3345050*b^5 + 1243650*b^6 + 244620*b^7 + 22980*b^8 + 720*b^9)*Sqrt[x] + 4*(307200*b - 473600*b^2 + 887360*b^3 + 5516240*b^4 + 7053475*b^5 + 4181450*b^6 + 1303235*b^7 + 208240*b^8 + 14210*b^9 + 200*b^10)*x + 4*(286720*b + 325120*b^2 - 453120*b^3 + 2653360*b^4 + 7513850*b^5 + 7306800*b^6 + 3528840*b^7 + 896640*b^8 + 110640*b^9 + 4800*b^10)*x^(3/2) + 4*(505600*b^2 + 254400*b^3 + 252920*b^4 + 4055650*b^5 + 7195775*b^6 + 5459180*b^7 + 2136080*b^8 + 431680*b^9 + 38600*b^10 + 800*b^11)*x^2 + 4*(-935168*b^2 - 525568*b^3 - 198552*b^4 + 896900*b^5 + 3950050*b^6 + 5007624*b^7 + 3017184*b^8 + 950016*b^9 + 148080*b^10 + 8640*b^11)*x^(5/2) + 4*(-2432320*b^3 - 1924080*b^4 - 451370*b^5 + 1050380*b^6 + 2670145*b^7 + 2570080*b^8 + 1243120*b^9 + 311600*b^10 + 35800*b^11 + 1120*b^12)*x^3 + 4*(-2229760*b^3 - 5197840*b^4 - 2885100*b^5 - 402400*b^6 + 736900*b^7 + 1280640*b^8 + 970560*b^9 + 379200*b^10 + 74400*b^11 + 5760*b^12)*x^(7/2) + 4*(-5267260*b^4 - 6876375*b^5 - 2624165*b^6 - 208990*b^7 + 334240*b^8 + 430240*b^9 + 263800*b^10 + 83600*b^11 + 12640*b^12 + 640*b^13)*x^4 + 4*(-2016020*b^4 - 7896350*b^5 - 6291450*b^6 - 1595900*b^7 - 64000*b^8 + 94080*b^9 + 95600*b^10 + 48800*b^11 + 12480*b^12 + 1280*b^13)*x^(9/2) + 4*(-4421225*b^5 - 7992950*b^6 - 4105967*b^7 - 654432*b^8 - 9408*b^9 + 13240*b^10 + 11720*b^11 + 5472*b^12 + 1312*b^13 + 128*b^14)*x^5 + 4*(-974350*b^5 - 5537200*b^6 - 5779320*b^7 - 1924480*b^8 - 170720*b^9)*x^(11/2) + 4*(-1955575*b^6 - 4653860*b^7 - 3050640*b^8 - 635360*b^9 - 22800*b^10)*x^6 + 4*(-269450*b^6 - 2101240*b^7 - 2790240*b^8 - 1176640*b^9 - 138800*b^10)*x^(13/2) + 4*(-480805*b^7 - 1482080*b^8 - 1220880*b^9 - 324800*b^10 - 16600*b^11)*x^7 + 4*(-41524*b^7 - 435584*b^8 - 734016*b^9 - 390080*b^10 - 60640*b^11)*x^(15/2) + 4*(-62330*b^8 - 250120*b^9 - 261000*b^10 - 89200*b^11 - 6720*b^12)*x^8 + 4*(-3140*b^8 - 44560*b^9 - 97200*b^10 - 66400*b^11 - 13760*b^12)*x^(17/2) + 4*(-3490*b^9 - 18800*b^10 - 25800*b^11 - 11840*b^12 - 1440*b^13)*x^9 + 4*(-80*b^9 - 1600*b^10 - 4800*b^11 - 4480*b^12 - 1280*b^13)*x^(19/2) + 4*(-40*b^10 - 320*b^11 - 672*b^12 - 512*b^13 - 128*b^14)*x^10))/(5*b^2*(524288 + 655360*b + 286720*b^2 + 51200*b^3 + 3200*b^4 + 32*b^5) + 5*b^2*(32*b^5 + 800*b^6 + 3200*b^7 + 4480*b^8 + 2560*b^9 + 512*b^10)*x^5 + 5*b^2*Sqrt[2 + b]*(-262144 - 262144*b - 86016*b^2 - 10240*b^3 - 320*b^4)*Sqrt[2 + b*x] + x*(5*b^2*(655360*b + 2375680*b^2 + 1914880*b^3 + 550400*b^4 + 52640*b^5 + 800*b^6) + 5*b^2*Sqrt[2 + b]*(-262144*b - 1040384*b^2 - 669696*b^3 - 131840*b^4 - 6400*b^5)*Sqrt[2 + b*x]) + Sqrt[x]*(5*b^2*(1310720*b + 1474560*b^2 + 552960*b^3 + 76800*b^4 + 2880*b^5) + 5*b^2*Sqrt[2 + b]*(-655360*b - 573440*b^2 - 153600*b^3 - 12800*b^4 - 160*b^5)*Sqrt[2 + b*x]) + x^2*(5*b^2*(286720*b^2 + 1914880*b^3 + 2333440*b^4 + 979520*b^5 + 137600*b^6 + 3200*b^7) + 5*b^2*Sqrt[2 + b]*(-86016*b^2 - 669696*b^3 - 776064*b^4 - 249600*b^5 - 19200*b^6)*Sqrt[2 + b*x]) + x^(3/2)*(5*b^2*(1474560*b^2 + 2826240*b^3 + 1643520*b^4 + 341760*b^5 + 19200*b^6) + 5*b^2*Sqrt[2 + b]*(-573440*b^2 - 1085440*b^3 - 499200*b^4 - 65920*b^5 - 1280*b^6)*Sqrt[2 + b*x]) + x^3*(5*b^2*(51200*b^3 + 550400*b^4 + 979520*b^5 + 583360*b^6 + 119680*b^7 + 4480*b^8) + 5*b^2*Sqrt[2 + b]*(-10240*b^3 - 131840*b^4 - 249600*b^5 - 135680*b^6 - 17920*b^7)*Sqrt[2 + b*x]) + x^(5/2)*(5*b^2*(552960*b^3 + 1643520*b^4 + 1375104*b^5 + 410880*b^6 + 34560*b^7) + 5*b^2*Sqrt[2 + b]*(-153600*b^3 - 499200*b^4 - 388032*b^5 - 83712*b^6 - 2688*b^7)*Sqrt[2 + b*x]) + x^4*(5*b^2*(3200*b^4 + 52640*b^5 + 137600*b^6 + 119680*b^7 + 37120*b^8 + 2560*b^9) + 5*b^2*Sqrt[2 + b]*(-320*b^4 - 6400*b^5 - 19200*b^6 - 17920*b^7 - 5120*b^8)*Sqrt[2 + b*x]) + x^(7/2)*(5*b^2*(76800*b^4 + 341760*b^5 + 410880*b^6 + 176640*b^7 + 23040*b^8) + 5*b^2*Sqrt[2 + b]*(-12800*b^4 - 65920*b^5 - 83712*b^6 - 32512*b^7 - 2048*b^8)*Sqrt[2 + b*x]) + x^(9/2)*(5*b^2*(2880*b^5 + 19200*b^6 + 34560*b^7 + 23040*b^8 + 5120*b^9) + 5*b^2*Sqrt[2 + b]*(-160*b^5 - 1280*b^6 - 2688*b^7 - 2048*b^8 - 512*b^9)*Sqrt[2 + b*x])) - (3*ArcTanh[(Sqrt[2 + b]/Sqrt[b] - Sqrt[2 + b*x]/Sqrt[b])/(-1 + Sqrt[x])])/(2*b^(5/2))","B",1
559,1,2022,102,4.0703068,"\int \sqrt{x} (2+b x)^{5/2} \, dx","IntegrateAlgebraic[Sqrt[x]*(2 + b*x)^(5/2),x]","\text{Result too large to show}","-\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,"(2*(-30720 - 159232*b - 236992*b^2 - 166160*b^3 - 62856*b^4 - 12984*b^5 - 1328*b^6 - 48*b^7)*Sqrt[2 + b*x] + 2*(30720 - 30720*b - 301184*b^2 - 435136*b^3 - 282409*b^4 - 96084*b^5 - 17020*b^6 - 1336*b^7 - 24*b^8)*Sqrt[x]*Sqrt[2 + b*x] + 2*(38400*b - 123264*b^2 - 448464*b^3 - 498000*b^4 - 269352*b^5 - 76848*b^6 - 10896*b^7 - 576*b^8)*x*Sqrt[2 + b*x] + 2*(151552*b + 170752*b^2 - 137280*b^3 - 421284*b^4 - 374841*b^5 - 167240*b^6 - 38900*b^7 - 4160*b^8 - 120*b^9)*x^(3/2)*Sqrt[2 + b*x] + 2*(290624*b^2 + 238416*b^3 - 107136*b^4 - 270336*b^5 - 193840*b^6 - 70960*b^7 - 13120*b^8 - 960*b^9)*x^2*Sqrt[2 + b*x] + 2*(200064*b^2 + 464064*b^3 + 236754*b^4 - 54552*b^5 - 118050*b^6 - 68808*b^7 - 20640*b^8 - 2976*b^9 - 144*b^10)*x^(5/2)*Sqrt[2 + b*x] + 2*(363920*b^3 + 467856*b^4 + 160896*b^5 - 17280*b^6 - 33296*b^7 - 16064*b^8 - 3904*b^9 - 384*b^10)*x^3*Sqrt[2 + b*x] + 2*(120640*b^3 + 429100*b^4 + 328518*b^5 + 74472*b^6 - 2766*b^7 - 5056*b^8 - 2240*b^9 - 512*b^10 - 48*b^11)*x^(7/2)*Sqrt[2 + b*x] + 2*(200136*b^4 + 336504*b^5 + 162288*b^6 + 22128*b^7)*x^4*Sqrt[2 + b*x] + 2*(37839*b^4 + 190884*b^5 + 184820*b^6 + 55736*b^7 + 3464*b^8)*x^(9/2)*Sqrt[2 + b*x] + 2*(55272*b^5 + 119728*b^6 + 72016*b^7 + 12736*b^8)*x^5*Sqrt[2 + b*x] + 2*(6075*b^5 + 42600*b^6 + 51900*b^7 + 19680*b^8 + 1800*b^9)*x^(11/2)*Sqrt[2 + b*x] + 2*(7280*b^6 + 20720*b^7 + 15680*b^8 + 3520*b^9)*x^6*Sqrt[2 + b*x] + 2*(418*b^6 + 4168*b^7 + 6640*b^8 + 3296*b^9 + 464*b^10)*x^(13/2)*Sqrt[2 + b*x] + 2*(336*b^7 + 1344*b^8 + 1344*b^9 + 384*b^10)*x^7*Sqrt[2 + b*x] + 2*(6*b^7 + 96*b^8 + 240*b^9 + 192*b^10 + 48*b^11)*x^(15/2)*Sqrt[2 + b*x] + Sqrt[2 + b]*(2*(30720 + 151552*b + 200064*b^2 + 120640*b^3 + 37839*b^4 + 6075*b^5 + 418*b^6 + 6*b^7) + 2*(-30720 + 38400*b + 290624*b^2 + 363920*b^3 + 200136*b^4 + 55272*b^5 + 7280*b^6 + 336*b^7)*Sqrt[x] + 2*(-30720*b + 170752*b^2 + 464064*b^3 + 429100*b^4 + 190884*b^5 + 42600*b^6 + 4168*b^7 + 96*b^8)*x + 2*(-159232*b - 123264*b^2 + 238416*b^3 + 467856*b^4 + 336504*b^5 + 119728*b^6 + 20720*b^7 + 1344*b^8)*x^(3/2) + 2*(-301184*b^2 - 137280*b^3 + 236754*b^4 + 328518*b^5 + 184820*b^6 + 51900*b^7 + 6640*b^8 + 240*b^9)*x^2 + 2*(-236992*b^2 - 448464*b^3 - 107136*b^4 + 160896*b^5 + 162288*b^6 + 72016*b^7 + 15680*b^8 + 1344*b^9)*x^(5/2) + 2*(-435136*b^3 - 421284*b^4 - 54552*b^5 + 74472*b^6 + 55736*b^7 + 19680*b^8 + 3296*b^9 + 192*b^10)*x^3 + 2*(-166160*b^3 - 498000*b^4 - 270336*b^5 - 17280*b^6 + 22128*b^7 + 12736*b^8 + 3520*b^9 + 384*b^10)*x^(7/2) + 2*(-282409*b^4 - 374841*b^5 - 118050*b^6 - 2766*b^7 + 3464*b^8 + 1800*b^9 + 464*b^10 + 48*b^11)*x^4 + 2*(-62856*b^4 - 269352*b^5 - 193840*b^6 - 33296*b^7)*x^(9/2) + 2*(-96084*b^5 - 167240*b^6 - 68808*b^7 - 5056*b^8)*x^5 + 2*(-12984*b^5 - 76848*b^6 - 70960*b^7 - 16064*b^8)*x^(11/2) + 2*(-17020*b^6 - 38900*b^7 - 20640*b^8 - 2240*b^9)*x^6 + 2*(-1328*b^6 - 10896*b^7 - 13120*b^8 - 3904*b^9)*x^(13/2) + 2*(-1336*b^7 - 4160*b^8 - 2976*b^9 - 512*b^10)*x^7 + 2*(-48*b^7 - 576*b^8 - 960*b^9 - 384*b^10)*x^(15/2) + 2*(-24*b^8 - 120*b^9 - 144*b^10 - 48*b^11)*x^8))/(3*b*(32768 + 32768*b + 10240*b^2 + 1024*b^3 + 16*b^4) + 3*b*(16*b^4 + 256*b^5 + 640*b^6 + 512*b^7 + 128*b^8)*x^4 + 3*b*Sqrt[2 + b]*(-16384 - 12288*b - 2560*b^2 - 128*b^3)*Sqrt[2 + b*x] + x*(3*b*(32768*b + 94208*b^2 + 56320*b^3 + 9664*b^4 + 256*b^5) + 3*b*Sqrt[2 + b]*(-12288*b - 39936*b^2 - 17280*b^3 - 1536*b^4)*Sqrt[2 + b*x]) + Sqrt[x]*(3*b*(65536*b + 57344*b^2 + 14336*b^3 + 896*b^4) + 3*b*Sqrt[2 + b]*(-32768*b - 20480*b^2 - 3072*b^3 - 64*b^4)*Sqrt[2 + b*x]) + x^2*(3*b*(10240*b^2 + 56320*b^3 + 52320*b^4 + 14080*b^5 + 640*b^6) + 3*b*Sqrt[2 + b]*(-2560*b^2 - 17280*b^3 - 15360*b^4 - 2560*b^5)*Sqrt[2 + b*x]) + x^(3/2)*(3*b*(57344*b^2 + 86016*b^3 + 34944*b^4 + 3584*b^5) + 3*b*Sqrt[2 + b]*(-20480*b^2 - 30720*b^3 - 8640*b^4 - 320*b^5)*Sqrt[2 + b*x]) + x^3*(3*b*(1024*b^3 + 9664*b^4 + 14080*b^5 + 5888*b^6 + 512*b^7) + 3*b*Sqrt[2 + b]*(-128*b^3 - 1536*b^4 - 2560*b^5 - 1024*b^6)*Sqrt[2 + b*x]) + x^(5/2)*(3*b*(14336*b^3 + 34944*b^4 + 21504*b^5 + 3584*b^6) + 3*b*Sqrt[2 + b]*(-3072*b^3 - 8640*b^4 - 4992*b^5 - 384*b^6)*Sqrt[2 + b*x]) + x^(7/2)*(3*b*(896*b^4 + 3584*b^5 + 3584*b^6 + 1024*b^7) + 3*b*Sqrt[2 + b]*(-64*b^4 - 320*b^5 - 384*b^6 - 128*b^7)*Sqrt[2 + b*x])) + (5*ArcTanh[(Sqrt[2 + b]/Sqrt[b] - Sqrt[2 + b*x]/Sqrt[b])/(-1 + Sqrt[x])])/(2*b^(3/2))","B",1
560,1,1265,79,1.9056184,"\int \frac{(2+b x)^{5/2}}{\sqrt{x}} \, dx","IntegrateAlgebraic[(2 + b*x)^(5/2)/Sqrt[x],x]","\frac{4 \left(8 b^8+24 b^7+18 b^6+2 b^5\right) \sqrt{b x+2} x^{11/2}+4 \left(48 b^7+120 b^6+60 b^5\right) \sqrt{b x+2} x^5+4 \left(76 b^7+360 b^6+435 b^5+85 b^4\right) \sqrt{b x+2} x^{9/2}+4 \left(432 b^6+1300 b^5+870 b^4\right) \sqrt{b x+2} x^4+4 \left(306 b^6+2040 b^5+3180 b^4+885 b^3\right) \sqrt{b x+2} x^{7/2}+4 \left(1632 b^5+5840 b^4+4878 b^3\right) \sqrt{b x+2} x^3+4 \left(-8 b^8-84 b^7-378 b^6-272 b^5+4800 b^4+10737 b^3+4196 b^2\right) \sqrt{b x+2} x^{5/2}+4 \left(-48 b^7-480 b^6-2040 b^5-1440 b^4+8970 b^3+12516 b^2\right) \sqrt{b x+2} x^2+4 \left(-16 b^7-300 b^6-2010 b^5-6280 b^4-3945 b^3+11208 b^2+9664 b\right) \sqrt{b x+2} x^{3/2}+4 \left(-72 b^6-940 b^5-5040 b^4-12150 b^3-6680 b^2+8448 b\right) \sqrt{b x+2} x+4 \left(-6 b^6-195 b^5-1785 b^4-7677 b^3-14892 b^2-6336 b+8448\right) \sqrt{b x+2} \sqrt{x}+\sqrt{b+2} \left(4 \left(-8 b^8-16 b^7-6 b^6\right) x^6+4 \left(-48 b^7-72 b^6-12 b^5\right) x^{11/2}+4 \left(-84 b^7-300 b^6-195 b^5\right) x^5+4 \left(-480 b^6-940 b^5-230 b^4\right) x^{9/2}+4 \left(-378 b^6-2010 b^5-1785 b^4\right) x^4+4 \left(-2040 b^5-5040 b^4-1698 b^3\right) x^{7/2}+4 \left(8 b^8+76 b^7+306 b^6-272 b^5-6280 b^4-7677 b^3\right) x^3+4 \left(48 b^7+432 b^6+1632 b^5-1440 b^4-12150 b^3-6348 b^2\right) x^{5/2}+4 \left(24 b^7+360 b^6+2040 b^5+4800 b^4-3945 b^3-14892 b^2\right) x^2+4 \left(120 b^6+1300 b^5+5840 b^4+8970 b^3-6680 b^2-11776 b\right) x^{3/2}+4 \left(18 b^6+435 b^5+3180 b^4+10737 b^3+11208 b^2-6336 b\right) x+4 \left(60 b^5+870 b^4+4878 b^3+12516 b^2+8448 b-8448\right) \sqrt{x}+4 \left(2 b^5+85 b^4+885 b^3+4196 b^2+9664 b+8448\right)\right)+4 \left(-12 b^5-230 b^4-1698 b^3-6348 b^2-11776 b-8448\right) \sqrt{b x+2}}{3 \left(32 b^6+96 b^5+72 b^4+8 b^3\right) x^3+\left(3 \sqrt{b+2} \sqrt{b x+2} \left(-32 b^5-64 b^4-24 b^3\right)+3 \left(192 b^5+480 b^4+240 b^3\right)\right) x^{5/2}+\left(3 \sqrt{b+2} \sqrt{b x+2} \left(-192 b^4-288 b^3-48 b^2\right)+3 \left(96 b^5+816 b^4+1272 b^3+288 b^2\right)\right) x^2+\left(3 \sqrt{b+2} \sqrt{b x+2} \left(-64 b^4-656 b^3-576 b^2\right)+3 \left(480 b^4+2080 b^3+1920 b^2\right)\right) x^{3/2}+\left(3 \sqrt{b+2} \sqrt{b x+2} \left(-288 b^3-1312 b^2-512 b\right)+3 \left(72 b^4+1272 b^3+3264 b^2+1536 b\right)\right) x+\left(3 \sqrt{b+2} \sqrt{b x+2} \left(-24 b^3-576 b^2-1536 b\right)+3 \left(240 b^3+1920 b^2+3072 b\right)\right) \sqrt{x}+3 \left(8 b^3+288 b^2+1536 b+2048\right)+3 \sqrt{b+2} \left(-48 b^2-512 b-1024\right) \sqrt{b x+2}}-\frac{10 \tanh ^{-1}\left(\frac{\frac{\sqrt{b+2}}{\sqrt{b}}-\frac{\sqrt{b x+2}}{\sqrt{b}}}{\sqrt{x}-1}\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,"(4*(-8448 - 11776*b - 6348*b^2 - 1698*b^3 - 230*b^4 - 12*b^5)*Sqrt[2 + b*x] + 4*(8448 - 6336*b - 14892*b^2 - 7677*b^3 - 1785*b^4 - 195*b^5 - 6*b^6)*Sqrt[x]*Sqrt[2 + b*x] + 4*(8448*b - 6680*b^2 - 12150*b^3 - 5040*b^4 - 940*b^5 - 72*b^6)*x*Sqrt[2 + b*x] + 4*(9664*b + 11208*b^2 - 3945*b^3 - 6280*b^4 - 2010*b^5 - 300*b^6 - 16*b^7)*x^(3/2)*Sqrt[2 + b*x] + 4*(12516*b^2 + 8970*b^3 - 1440*b^4 - 2040*b^5 - 480*b^6 - 48*b^7)*x^2*Sqrt[2 + b*x] + 4*(4196*b^2 + 10737*b^3 + 4800*b^4 - 272*b^5 - 378*b^6 - 84*b^7 - 8*b^8)*x^(5/2)*Sqrt[2 + b*x] + 4*(4878*b^3 + 5840*b^4 + 1632*b^5)*x^3*Sqrt[2 + b*x] + 4*(885*b^3 + 3180*b^4 + 2040*b^5 + 306*b^6)*x^(7/2)*Sqrt[2 + b*x] + 4*(870*b^4 + 1300*b^5 + 432*b^6)*x^4*Sqrt[2 + b*x] + 4*(85*b^4 + 435*b^5 + 360*b^6 + 76*b^7)*x^(9/2)*Sqrt[2 + b*x] + 4*(60*b^5 + 120*b^6 + 48*b^7)*x^5*Sqrt[2 + b*x] + 4*(2*b^5 + 18*b^6 + 24*b^7 + 8*b^8)*x^(11/2)*Sqrt[2 + b*x] + Sqrt[2 + b]*(4*(8448 + 9664*b + 4196*b^2 + 885*b^3 + 85*b^4 + 2*b^5) + 4*(-8448 + 8448*b + 12516*b^2 + 4878*b^3 + 870*b^4 + 60*b^5)*Sqrt[x] + 4*(-6336*b + 11208*b^2 + 10737*b^3 + 3180*b^4 + 435*b^5 + 18*b^6)*x + 4*(-11776*b - 6680*b^2 + 8970*b^3 + 5840*b^4 + 1300*b^5 + 120*b^6)*x^(3/2) + 4*(-14892*b^2 - 3945*b^3 + 4800*b^4 + 2040*b^5 + 360*b^6 + 24*b^7)*x^2 + 4*(-6348*b^2 - 12150*b^3 - 1440*b^4 + 1632*b^5 + 432*b^6 + 48*b^7)*x^(5/2) + 4*(-7677*b^3 - 6280*b^4 - 272*b^5 + 306*b^6 + 76*b^7 + 8*b^8)*x^3 + 4*(-1698*b^3 - 5040*b^4 - 2040*b^5)*x^(7/2) + 4*(-1785*b^4 - 2010*b^5 - 378*b^6)*x^4 + 4*(-230*b^4 - 940*b^5 - 480*b^6)*x^(9/2) + 4*(-195*b^5 - 300*b^6 - 84*b^7)*x^5 + 4*(-12*b^5 - 72*b^6 - 48*b^7)*x^(11/2) + 4*(-6*b^6 - 16*b^7 - 8*b^8)*x^6))/(3*(2048 + 1536*b + 288*b^2 + 8*b^3) + 3*(8*b^3 + 72*b^4 + 96*b^5 + 32*b^6)*x^3 + 3*Sqrt[2 + b]*(-1024 - 512*b - 48*b^2)*Sqrt[2 + b*x] + x*(3*(1536*b + 3264*b^2 + 1272*b^3 + 72*b^4) + 3*Sqrt[2 + b]*(-512*b - 1312*b^2 - 288*b^3)*Sqrt[2 + b*x]) + Sqrt[x]*(3*(3072*b + 1920*b^2 + 240*b^3) + 3*Sqrt[2 + b]*(-1536*b - 576*b^2 - 24*b^3)*Sqrt[2 + b*x]) + x^2*(3*(288*b^2 + 1272*b^3 + 816*b^4 + 96*b^5) + 3*Sqrt[2 + b]*(-48*b^2 - 288*b^3 - 192*b^4)*Sqrt[2 + b*x]) + x^(3/2)*(3*(1920*b^2 + 2080*b^3 + 480*b^4) + 3*Sqrt[2 + b]*(-576*b^2 - 656*b^3 - 64*b^4)*Sqrt[2 + b*x]) + x^(5/2)*(3*(240*b^3 + 480*b^4 + 192*b^5) + 3*Sqrt[2 + b]*(-24*b^3 - 64*b^4 - 32*b^5)*Sqrt[2 + b*x])) - (10*ArcTanh[(Sqrt[2 + b]/Sqrt[b] - Sqrt[2 + b*x]/Sqrt[b])/(-1 + Sqrt[x])])/Sqrt[b]","B",1
561,1,765,79,2.7336773,"\int \frac{(2+b x)^{5/2}}{x^{3/2}} \, dx","IntegrateAlgebraic[(2 + b*x)^(5/2)/x^(3/2),x]","\frac{\left(8 \sqrt{x}-8\right) \left(b x-2 b \sqrt{x}-2 \sqrt{b+2} \sqrt{b x+2}+\sqrt{b+2} \sqrt{x} \sqrt{b x+2}+2 b-2 \sqrt{x}+4\right) \left(\sqrt{b+2}-\sqrt{b x+2}\right)}{\sqrt{x} \left(b^2 \left(-\sqrt{x}\right)+b x^{3/2}-2 b x+b \sqrt{x}+\sqrt{b+2} b \sqrt{b x+2}+4 \sqrt{b+2} \sqrt{b x+2}-2 \sqrt{b+2} \sqrt{x} \sqrt{b x+2}-4 b+4 \sqrt{x}-8\right)}+\frac{\left(b \sqrt{b+2}-b \sqrt{b x+2}\right) \left(-2 b^2 \sqrt{x}-6 b^2-12 b \sqrt{x}+8 \sqrt{b+2} b \sqrt{b x+2}+24 \sqrt{b+2} \sqrt{b x+2}-28 b-9 \sqrt{x}-39\right)}{b \left(-\sqrt{x}\right)+\sqrt{b+2} \sqrt{b x+2}-2}+\frac{\left(-4 b^3 \sqrt{x}-8 b^2 \sqrt{x}+4 \sqrt{b+2} b^2 \sqrt{b x+2}-4 b^2-2 b \sqrt{x}+4 \sqrt{b+2} b \sqrt{b x+2}-6 b\right) \left(\sqrt{b+2}-\sqrt{b x+2}\right)^7}{\left(b \left(-\sqrt{x}\right)+\sqrt{b+2} \sqrt{b x+2}-2\right)^4}+\frac{\left(-12 b^3 \sqrt{x}-4 b^3-24 b^2 \sqrt{x}+16 \sqrt{b+2} b^2 \sqrt{b x+2}-24 b^2-6 b \sqrt{x}+16 \sqrt{b+2} b \sqrt{b x+2}-26 b\right) \left(\sqrt{b+2}-\sqrt{b x+2}\right)^5}{\left(b \left(-\sqrt{x}\right)+\sqrt{b+2} \sqrt{b x+2}-2\right)^3}+\frac{\left(-10 b^3 \sqrt{x}-10 b^3-28 b^2 \sqrt{x}+20 \sqrt{b+2} b^2 \sqrt{b x+2}-40 b^2-13 b \sqrt{x}+28 \sqrt{b+2} b \sqrt{b x+2}-43 b\right) \left(\sqrt{b+2}-\sqrt{b x+2}\right)^3}{\left(b \left(-\sqrt{x}\right)+\sqrt{b+2} \sqrt{b x+2}-2\right)^2}-30 \sqrt{b} \tanh ^{-1}\left(\frac{\frac{\sqrt{b+2}}{\sqrt{b}}-\frac{\sqrt{b x+2}}{\sqrt{b}}}{\sqrt{x}-1}\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,"((b*Sqrt[2 + b] - b*Sqrt[2 + b*x])*(-39 - 28*b - 6*b^2 - 9*Sqrt[x] - 12*b*Sqrt[x] - 2*b^2*Sqrt[x] + 24*Sqrt[2 + b]*Sqrt[2 + b*x] + 8*b*Sqrt[2 + b]*Sqrt[2 + b*x]))/(-2 - b*Sqrt[x] + Sqrt[2 + b]*Sqrt[2 + b*x]) + ((Sqrt[2 + b] - Sqrt[2 + b*x])^7*(-6*b - 4*b^2 - 2*b*Sqrt[x] - 8*b^2*Sqrt[x] - 4*b^3*Sqrt[x] + 4*b*Sqrt[2 + b]*Sqrt[2 + b*x] + 4*b^2*Sqrt[2 + b]*Sqrt[2 + b*x]))/(-2 - b*Sqrt[x] + Sqrt[2 + b]*Sqrt[2 + b*x])^4 + ((Sqrt[2 + b] - Sqrt[2 + b*x])^5*(-26*b - 24*b^2 - 4*b^3 - 6*b*Sqrt[x] - 24*b^2*Sqrt[x] - 12*b^3*Sqrt[x] + 16*b*Sqrt[2 + b]*Sqrt[2 + b*x] + 16*b^2*Sqrt[2 + b]*Sqrt[2 + b*x]))/(-2 - b*Sqrt[x] + Sqrt[2 + b]*Sqrt[2 + b*x])^3 + ((Sqrt[2 + b] - Sqrt[2 + b*x])^3*(-43*b - 40*b^2 - 10*b^3 - 13*b*Sqrt[x] - 28*b^2*Sqrt[x] - 10*b^3*Sqrt[x] + 28*b*Sqrt[2 + b]*Sqrt[2 + b*x] + 20*b^2*Sqrt[2 + b]*Sqrt[2 + b*x]))/(-2 - b*Sqrt[x] + Sqrt[2 + b]*Sqrt[2 + b*x])^2 + ((-8 + 8*Sqrt[x])*(Sqrt[2 + b] - Sqrt[2 + b*x])*(4 + 2*b - 2*Sqrt[x] - 2*b*Sqrt[x] + b*x - 2*Sqrt[2 + b]*Sqrt[2 + b*x] + Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x]))/(Sqrt[x]*(-8 - 4*b + 4*Sqrt[x] + b*Sqrt[x] - b^2*Sqrt[x] - 2*b*x + b*x^(3/2) + 4*Sqrt[2 + b]*Sqrt[2 + b*x] + b*Sqrt[2 + b]*Sqrt[2 + b*x] - 2*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x])) - 30*Sqrt[b]*ArcTanh[(Sqrt[2 + b]/Sqrt[b] - Sqrt[2 + b*x]/Sqrt[b])/(-1 + Sqrt[x])]","B",1
562,1,1832,81,8.6260212,"\int \frac{(2+b x)^{5/2}}{x^{5/2}} \, dx","IntegrateAlgebraic[(2 + b*x)^(5/2)/x^(5/2),x]","\frac{\left(\frac{96 x^{3/2}}{b}+\frac{1024 x^{3/2}}{3 b^2}+\frac{1024 x^{3/2}}{3 b^3}+\frac{16 x^{3/2}}{3}+\frac{16 \sqrt{b+2} \sqrt{b x+2} x}{3 b}+\frac{416 \sqrt{b+2} \sqrt{b x+2} x}{3 b^2}+\frac{1792 \sqrt{b+2} \sqrt{b x+2} x}{3 b^3}+\frac{2048 \sqrt{b+2} \sqrt{b x+2} x}{3 b^4}-\frac{1024 x}{3 b}-\frac{4672 x}{3 b^2}-\frac{2560 x}{b^3}-\frac{4096 x}{3 b^4}-16 x-\frac{16 \sqrt{b+2} \sqrt{b x+2} \sqrt{x}}{b}-\frac{992 \sqrt{b+2} \sqrt{b x+2} \sqrt{x}}{3 b^2}-\frac{1280 \sqrt{b+2} \sqrt{b x+2} \sqrt{x}}{b^3}-\frac{4096 \sqrt{b+2} \sqrt{b x+2} \sqrt{x}}{3 b^4}+\frac{800 \sqrt{x}}{b}+\frac{3136 \sqrt{x}}{b^2}+\frac{14848 \sqrt{x}}{3 b^3}+\frac{8192 \sqrt{x}}{3 b^4}+64 \sqrt{x}-\frac{32 \sqrt{b+2} \sqrt{b x+2}}{b}-\frac{448 \sqrt{b+2} \sqrt{b x+2}}{3 b^2}-\frac{512 \sqrt{b+2} \sqrt{b x+2}}{3 b^3}-\frac{128}{b}-\frac{384}{b^2}-\frac{1024}{3 b^3}-\frac{32}{3}\right) \left(\sqrt{b+2}-\sqrt{b x+2}\right)^9}{x^{3/2} \left(-\sqrt{x} b^2+x^{3/2} b-2 x b+\sqrt{x} b+\sqrt{b+2} \sqrt{b x+2} b-4 b+4 \sqrt{x}+4 \sqrt{b+2} \sqrt{b x+2}-2 \sqrt{b+2} \sqrt{x} \sqrt{b x+2}-8\right)^3}+\frac{\left(-8 b x^{3/2}-\frac{416 x^{3/2}}{b}-\frac{1024 x^{3/2}}{3 b^2}-136 x^{3/2}+24 b x-\frac{216 \sqrt{b+2} \sqrt{b x+2} x}{b}-\frac{2368 \sqrt{b+2} \sqrt{b x+2} x}{3 b^2}-\frac{2048 \sqrt{b+2} \sqrt{b x+2} x}{3 b^3}-8 \sqrt{b+2} \sqrt{b x+2} x+\frac{9424 x}{3 b}+\frac{6016 x}{b^2}+\frac{4096 x}{b^3}+\frac{1864 x}{3}-64 b \sqrt{x}+\frac{1256 \sqrt{b+2} \sqrt{b x+2} \sqrt{x}}{3 b}+\frac{1152 \sqrt{b+2} \sqrt{b x+2} \sqrt{x}}{b^2}+\frac{2048 \sqrt{b+2} \sqrt{b x+2} \sqrt{x}}{3 b^3}+24 \sqrt{b+2} \sqrt{b x+2} \sqrt{x}-\frac{6128 \sqrt{x}}{3 b}-\frac{7936 \sqrt{x}}{3 b^2}-\frac{4096 \sqrt{x}}{3 b^3}-656 \sqrt{x}+16 b-\frac{384 \sqrt{b+2} \sqrt{b x+2}}{b}-\frac{8704 \sqrt{b+2} \sqrt{b x+2}}{3 b^2}-\frac{20480 \sqrt{b+2} \sqrt{b x+2}}{3 b^3}-\frac{16384 \sqrt{b+2} \sqrt{b x+2}}{3 b^4}+16 \sqrt{b+2} \sqrt{b x+2}+\frac{6656}{3 b}+\frac{26624}{3 b^2}+\frac{16384}{b^3}+\frac{32768}{3 b^4}+288\right) \left(\sqrt{b+2}-\sqrt{b x+2}\right)^5}{x \left(-\sqrt{x} b^2+x^{3/2} b-2 x b+\sqrt{x} b+\sqrt{b+2} \sqrt{b x+2} b-4 b+4 \sqrt{x}+4 \sqrt{b+2} \sqrt{b x+2}-2 \sqrt{b+2} \sqrt{x} \sqrt{b x+2}-8\right)^2}+\frac{\left(-2 \sqrt{x} b^3-2 \sqrt{x} b^2+2 \sqrt{b+2} \sqrt{b x+2} b^2-2 b^2\right) \left(\sqrt{b+2}-\sqrt{b x+2}\right)^3}{\left(-\sqrt{x} b+\sqrt{b+2} \sqrt{b x+2}-2\right)^2}+\frac{\left(2 b^2 \sqrt{b+2}-2 b^2 \sqrt{b x+2}\right) \left(-\sqrt{x} b-b-\sqrt{x}+2 \sqrt{b+2} \sqrt{b x+2}-3\right)}{-\sqrt{x} b+\sqrt{b+2} \sqrt{b x+2}-2}+\frac{\left(\frac{4 \sqrt{b+2}}{3 b^2}-\frac{4 \sqrt{b x+2}}{3 b^2}\right) \left(9 x^{3/2} b^4-27 x b^4+36 \sqrt{x} b^4-18 b^4+30 x^{3/2} b^3-210 x b^3+114 \sqrt{x} b^3+9 \sqrt{b+2} x \sqrt{b x+2} b^3+18 \sqrt{b+2} \sqrt{b x+2} b^3-27 \sqrt{b+2} \sqrt{x} \sqrt{b x+2} b^3-126 b^3+56 x^{3/2} b^2-800 x b^2+212 \sqrt{x} b^2+60 \sqrt{b+2} x \sqrt{b x+2} b^2+210 \sqrt{b+2} \sqrt{b x+2} b^2-78 \sqrt{b+2} \sqrt{x} \sqrt{b x+2} b^2-812 b^2-864 x b+224 \sqrt{x} b+144 \sqrt{b+2} x \sqrt{b x+2} b+928 \sqrt{b+2} \sqrt{b x+2} b-112 \sqrt{b+2} \sqrt{x} \sqrt{b x+2} b-2432 b+1152 \sqrt{b+2} \sqrt{b x+2}-2304\right)}{\sqrt{x} \left(-\sqrt{x} b^2+x^{3/2} b-2 x b+\sqrt{x} b+\sqrt{b+2} \sqrt{b x+2} b-4 b+4 \sqrt{x}+4 \sqrt{b+2} \sqrt{b x+2}-2 \sqrt{b+2} \sqrt{x} \sqrt{b x+2}-8\right)}-20 b^{3/2} \tanh ^{-1}\left(\frac{\frac{\sqrt{b+2}}{\sqrt{b}}-\frac{\sqrt{b x+2}}{\sqrt{b}}}{\sqrt{x}-1}\right)","10 b^{3/2} \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)+5 b^2 \sqrt{x} \sqrt{b x+2}-\frac{2 (b x+2)^{5/2}}{3 x^{3/2}}-\frac{10 b (b x+2)^{3/2}}{3 \sqrt{x}}",1,"((2*b^2*Sqrt[2 + b] - 2*b^2*Sqrt[2 + b*x])*(-3 - b - Sqrt[x] - b*Sqrt[x] + 2*Sqrt[2 + b]*Sqrt[2 + b*x]))/(-2 - b*Sqrt[x] + Sqrt[2 + b]*Sqrt[2 + b*x]) + ((Sqrt[2 + b] - Sqrt[2 + b*x])^3*(-2*b^2 - 2*b^2*Sqrt[x] - 2*b^3*Sqrt[x] + 2*b^2*Sqrt[2 + b]*Sqrt[2 + b*x]))/(-2 - b*Sqrt[x] + Sqrt[2 + b]*Sqrt[2 + b*x])^2 + ((Sqrt[2 + b] - Sqrt[2 + b*x])^5*(288 + 32768/(3*b^4) + 16384/b^3 + 26624/(3*b^2) + 6656/(3*b) + 16*b - 656*Sqrt[x] - (4096*Sqrt[x])/(3*b^3) - (7936*Sqrt[x])/(3*b^2) - (6128*Sqrt[x])/(3*b) - 64*b*Sqrt[x] + (1864*x)/3 + (4096*x)/b^3 + (6016*x)/b^2 + (9424*x)/(3*b) + 24*b*x - 136*x^(3/2) - (1024*x^(3/2))/(3*b^2) - (416*x^(3/2))/b - 8*b*x^(3/2) + 16*Sqrt[2 + b]*Sqrt[2 + b*x] - (16384*Sqrt[2 + b]*Sqrt[2 + b*x])/(3*b^4) - (20480*Sqrt[2 + b]*Sqrt[2 + b*x])/(3*b^3) - (8704*Sqrt[2 + b]*Sqrt[2 + b*x])/(3*b^2) - (384*Sqrt[2 + b]*Sqrt[2 + b*x])/b + 24*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] + (2048*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x])/(3*b^3) + (1152*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x])/b^2 + (1256*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x])/(3*b) - 8*Sqrt[2 + b]*x*Sqrt[2 + b*x] - (2048*Sqrt[2 + b]*x*Sqrt[2 + b*x])/(3*b^3) - (2368*Sqrt[2 + b]*x*Sqrt[2 + b*x])/(3*b^2) - (216*Sqrt[2 + b]*x*Sqrt[2 + b*x])/b))/(x*(-8 - 4*b + 4*Sqrt[x] + b*Sqrt[x] - b^2*Sqrt[x] - 2*b*x + b*x^(3/2) + 4*Sqrt[2 + b]*Sqrt[2 + b*x] + b*Sqrt[2 + b]*Sqrt[2 + b*x] - 2*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x])^2) + ((Sqrt[2 + b] - Sqrt[2 + b*x])^9*(-32/3 - 1024/(3*b^3) - 384/b^2 - 128/b + 64*Sqrt[x] + (8192*Sqrt[x])/(3*b^4) + (14848*Sqrt[x])/(3*b^3) + (3136*Sqrt[x])/b^2 + (800*Sqrt[x])/b - 16*x - (4096*x)/(3*b^4) - (2560*x)/b^3 - (4672*x)/(3*b^2) - (1024*x)/(3*b) + (16*x^(3/2))/3 + (1024*x^(3/2))/(3*b^3) + (1024*x^(3/2))/(3*b^2) + (96*x^(3/2))/b - (512*Sqrt[2 + b]*Sqrt[2 + b*x])/(3*b^3) - (448*Sqrt[2 + b]*Sqrt[2 + b*x])/(3*b^2) - (32*Sqrt[2 + b]*Sqrt[2 + b*x])/b - (4096*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x])/(3*b^4) - (1280*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x])/b^3 - (992*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x])/(3*b^2) - (16*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x])/b + (2048*Sqrt[2 + b]*x*Sqrt[2 + b*x])/(3*b^4) + (1792*Sqrt[2 + b]*x*Sqrt[2 + b*x])/(3*b^3) + (416*Sqrt[2 + b]*x*Sqrt[2 + b*x])/(3*b^2) + (16*Sqrt[2 + b]*x*Sqrt[2 + b*x])/(3*b)))/(x^(3/2)*(-8 - 4*b + 4*Sqrt[x] + b*Sqrt[x] - b^2*Sqrt[x] - 2*b*x + b*x^(3/2) + 4*Sqrt[2 + b]*Sqrt[2 + b*x] + b*Sqrt[2 + b]*Sqrt[2 + b*x] - 2*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x])^3) + (((4*Sqrt[2 + b])/(3*b^2) - (4*Sqrt[2 + b*x])/(3*b^2))*(-2304 - 2432*b - 812*b^2 - 126*b^3 - 18*b^4 + 224*b*Sqrt[x] + 212*b^2*Sqrt[x] + 114*b^3*Sqrt[x] + 36*b^4*Sqrt[x] - 864*b*x - 800*b^2*x - 210*b^3*x - 27*b^4*x + 56*b^2*x^(3/2) + 30*b^3*x^(3/2) + 9*b^4*x^(3/2) + 1152*Sqrt[2 + b]*Sqrt[2 + b*x] + 928*b*Sqrt[2 + b]*Sqrt[2 + b*x] + 210*b^2*Sqrt[2 + b]*Sqrt[2 + b*x] + 18*b^3*Sqrt[2 + b]*Sqrt[2 + b*x] - 112*b*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] - 78*b^2*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] - 27*b^3*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] + 144*b*Sqrt[2 + b]*x*Sqrt[2 + b*x] + 60*b^2*Sqrt[2 + b]*x*Sqrt[2 + b*x] + 9*b^3*Sqrt[2 + b]*x*Sqrt[2 + b*x]))/(Sqrt[x]*(-8 - 4*b + 4*Sqrt[x] + b*Sqrt[x] - b^2*Sqrt[x] - 2*b*x + b*x^(3/2) + 4*Sqrt[2 + b]*Sqrt[2 + b*x] + b*Sqrt[2 + b]*Sqrt[2 + b*x] - 2*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x])) - 20*b^(3/2)*ArcTanh[(Sqrt[2 + b]/Sqrt[b] - Sqrt[2 + b*x]/Sqrt[b])/(-1 + Sqrt[x])]","B",1
563,1,4101,150,12.8580659,"\int x^{5/2} (2-b x)^{5/2} \, dx","IntegrateAlgebraic[x^(5/2)*(2 - b*x)^(5/2),x]","\text{Result too large to show}","\frac{5 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{8 b^{7/2}}-\frac{5 \sqrt{x} \sqrt{2-b x}}{16 b^3}-\frac{5 x^{3/2} \sqrt{2-b x}}{48 b^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,"(-4*(-1966080 + 2785280*b - 1449984*b^2 + 7526400*b^3 - 17808800*b^4 + 18698328*b^5 - 10839564*b^6 + 3741844*b^7 - 772680*b^8 + 90312*b^9 - 5152*b^10 + 96*b^11)*Sqrt[2 - b*x] - 4*(1966080 + 2949120*b - 5959680*b^2 + 3059712*b^3 - 22188576*b^4 + 50676336*b^5 - 50100789*b^6 + 26963022*b^7 - 8466522*b^8 + 1537908*b^9 - 148644*b^10 + 6096*b^11 - 48*b^12)*Sqrt[x]*Sqrt[2 - b*x] - 4*(-3440640*b - 3850240*b^2 + 7649280*b^3 - 12433536*b^4 + 53782696*b^5 - 92304000*b^6 + 77439660*b^7 - 36405920*b^8 + 9937368*b^9 - 1519248*b^10 + 114080*b^11 - 2880*b^12)*x*Sqrt[2 - b*x] - 4*(-2293760*b + 5283840*b^2 + 3809280*b^3 - 6883456*b^4 + 26828016*b^5 - 85685670*b^6 + 115980675*b^7 - 81892080*b^8 + 32984958*b^9 - 7628968*b^10 + 944820*b^11 - 50880*b^12 + 560*b^13)*x^(3/2)*Sqrt[2 - b*x] - 4*(5038080*b^2 - 6174720*b^3 - 2840256*b^4 + 8618736*b^5 - 42344940*b^6 + 98178660*b^7 - 106776000*b^8 + 63361728*b^9 - 21612768*b^10 + 4142880*b^11 - 397440*b^12 + 13440*b^13)*x^2*Sqrt[2 - b*x] - 4*(937984*b^2 - 6598656*b^3 + 5473344*b^4 + 1604960*b^5 - 11730519*b^6 + 47519514*b^7 - 83424288*b^8 + 74138400*b^9 - 36988056*b^10 + 10575824*b^11 - 1639008*b^12 + 114240*b^13 - 1792*b^14)*x^(5/2)*Sqrt[2 - b*x] - 4*(-1923072*b^3 + 6006144*b^4 - 3712560*b^5 - 1474272*b^6 + 12991132*b^7 - 38772672*b^8 + 53433408*b^9 - 39324544*b^10 + 16495584*b^11 - 3908352*b^12 + 473984*b^13 - 21504*b^14)*x^3*Sqrt[2 - b*x] - 4*(-7348224*b^3 + 12853632*b^4 - 10051104*b^5 + 3509244*b^6 + 1512135*b^7 - 10365312*b^8 + 23245632*b^9 - 25881408*b^10 + 15945240*b^11 - 5618880*b^12 + 1087200*b^13 - 98304*b^14 + 2304*b^15)*x^(7/2)*Sqrt[2 - b*x] - 4*(21833568*b^4 - 31089864*b^5 + 16783452*b^6 - 3957732*b^7 - 1126400*b^8 + 5811840*b^9 - 10183488*b^10 + 9379520*b^11 - 4884480*b^12 + 1443840*b^13 - 223744*b^14 + 13824*b^15)*x^4*Sqrt[2 - b*x] - 4*(15987936*b^4 - 55179216*b^5 + 52907565*b^6 - 21154630*b^7 + 3594480*b^8 + 542784*b^9 - 2228144*b^10 + 3165600*b^11 - 2466000*b^12 + 1097600*b^13 - 272064*b^14 + 33024*b^15 - 1280*b^16)*x^(9/2)*Sqrt[2 - b*x] - 4*(-45248760*b^5 + 90714720*b^6 - 63282204*b^7 + 18971328*b^8 - 2285184*b^9 - 156672*b^10 + 541248*b^11 - 646848*b^12 + 437760*b^13 - 169728*b^14 + 35328*b^15 - 3072*b^16)*x^5*Sqrt[2 - b*x] - 4*(-14927568*b^5 + 83549322*b^6 - 107710575*b^7 + 55398272*b^8 - 12211632*b^9 + 972768*b^10 + 21424*b^11 - 65664*b^12 + 69264*b^13 - 42880*b^14 + 15552*b^15 - 3072*b^16 + 256*b^17)*x^(11/2)*Sqrt[2 - b*x] - 4*(39464604*b^6 - 106769300*b^7 + 95527872*b^8 - 36248256*b^9 + 5648192*b^10 - 257088*b^11)*x^6*Sqrt[2 - b*x] - 4*(7550847*b^6 - 60896802*b^7 + 100459080*b^8 - 64577184*b^9 + 17842032*b^10 - 1833504*b^11 + 33264*b^12)*x^(13/2)*Sqrt[2 - b*x] - 4*(-18342060*b^7 + 64540960*b^8 - 71742528*b^9 + 33568128*b^10 - 6550720*b^11 + 388800*b^12)*x^7*Sqrt[2 - b*x] - 4*(-2213339*b^7 + 24324816*b^8 - 50203512*b^9 + 39486272*b^10 - 13399440*b^11 + 1742688*b^12 - 43152*b^13)*x^(15/2)*Sqrt[2 - b*x] - 4*(4813512*b^8 - 21667272*b^9 + 29562720*b^10 - 16829472*b^11 + 4055040*b^12 - 313344*b^13)*x^8*Sqrt[2 - b*x] - 4*(371554*b^8 - 5424660*b^9 + 13942452*b^10 - 13356784*b^11 + 5529600*b^12 - 903168*b^13 + 31296*b^14)*x^(17/2)*Sqrt[2 - b*x] - 4*(-691416*b^9 + 3975312*b^10 - 6681312*b^11 + 4637952*b^12 - 1379840*b^13 + 139008*b^14)*x^9*Sqrt[2 - b*x] - 4*(-32694*b^9 + 630504*b^10 - 2038500*b^11 + 2405760*b^12 - 1226880*b^13 + 253824*b^14 - 12864*b^15)*x^(19/2)*Sqrt[2 - b*x] - 4*(47520*b^10 - 353760*b^11 + 747648*b^12 - 646272*b^13 + 242176*b^14 - 32256*b^15)*x^10*Sqrt[2 - b*x] - 4*(1192*b^10 - 30768*b^11 + 128880*b^12 - 193984*b^13 + 126336*b^14 - 34560*b^15 + 2816*b^16)*x^(21/2)*Sqrt[2 - b*x] - 4*(-1056*b^11 + 10560*b^12 - 29568*b^13 + 33792*b^14 - 16896*b^15 + 3072*b^16)*x^11*Sqrt[2 - b*x] - 4*(-8*b^11 + 288*b^12 - 1680*b^13 + 3584*b^14 - 3456*b^15 + 1536*b^16 - 256*b^17)*x^(23/2)*Sqrt[2 - b*x] + Sqrt[2 - b]*(-4*(1966080 - 2293760*b + 937984*b^2 - 7348224*b^3 + 15987936*b^4 - 14927568*b^5 + 7550847*b^6 - 2213339*b^7 + 371554*b^8 - 32694*b^9 + 1192*b^10 - 8*b^11) - 4*(-1966080 - 3440640*b + 5038080*b^2 - 1923072*b^3 + 21833568*b^4 - 45248760*b^5 + 39464604*b^6 - 18342060*b^7 + 4813512*b^8 - 691416*b^9 + 47520*b^10 - 1056*b^11)*Sqrt[x] - 4*(2949120*b + 5283840*b^2 - 6598656*b^3 + 12853632*b^4 - 55179216*b^5 + 83549322*b^6 - 60896802*b^7 + 24324816*b^8 - 5424660*b^9 + 630504*b^10 - 30768*b^11 + 288*b^12)*x - 4*(2785280*b - 3850240*b^2 - 6174720*b^3 + 6006144*b^4 - 31089864*b^5 + 90714720*b^6 - 106769300*b^7 + 64540960*b^8 - 21667272*b^9 + 3975312*b^10 - 353760*b^11 + 10560*b^12)*x^(3/2) - 4*(-5959680*b^2 + 3809280*b^3 + 5473344*b^4 - 10051104*b^5 + 52907565*b^6 - 107710575*b^7 + 100459080*b^8 - 50203512*b^9 + 13942452*b^10 - 2038500*b^11 + 128880*b^12 - 1680*b^13)*x^2 - 4*(-1449984*b^2 + 7649280*b^3 - 2840256*b^4 - 3712560*b^5 + 16783452*b^6 - 63282204*b^7 + 95527872*b^8 - 71742528*b^9 + 29562720*b^10 - 6681312*b^11 + 747648*b^12 - 29568*b^13)*x^(5/2) - 4*(3059712*b^3 - 6883456*b^4 + 1604960*b^5 + 3509244*b^6 - 21154630*b^7 + 55398272*b^8 - 64577184*b^9 + 39486272*b^10 - 13356784*b^11 + 2405760*b^12 - 193984*b^13 + 3584*b^14)*x^3 - 4*(7526400*b^3 - 12433536*b^4 + 8618736*b^5 - 1474272*b^6 - 3957732*b^7 + 18971328*b^8 - 36248256*b^9 + 33568128*b^10 - 16829472*b^11 + 4637952*b^12 - 646272*b^13 + 33792*b^14)*x^(7/2) - 4*(-22188576*b^4 + 26828016*b^5 - 11730519*b^6 + 1512135*b^7 + 3594480*b^8 - 12211632*b^9 + 17842032*b^10 - 13399440*b^11 + 5529600*b^12 - 1226880*b^13 + 126336*b^14 - 3456*b^15)*x^4 - 4*(-17808800*b^4 + 53782696*b^5 - 42344940*b^6 + 12991132*b^7 - 1126400*b^8 - 2285184*b^9 + 5648192*b^10 - 6550720*b^11 + 4055040*b^12 - 1379840*b^13 + 242176*b^14 - 16896*b^15)*x^(9/2) - 4*(50676336*b^5 - 85685670*b^6 + 47519514*b^7 - 10365312*b^8 + 542784*b^9 + 972768*b^10 - 1833504*b^11 + 1742688*b^12 - 903168*b^13 + 253824*b^14 - 34560*b^15 + 1536*b^16)*x^5 - 4*(18698328*b^5 - 92304000*b^6 + 98178660*b^7 - 38772672*b^8 + 5811840*b^9 - 156672*b^10 - 257088*b^11 + 388800*b^12 - 313344*b^13 + 139008*b^14 - 32256*b^15 + 3072*b^16)*x^(11/2) - 4*(-50100789*b^6 + 115980675*b^7 - 83424288*b^8 + 23245632*b^9 - 2228144*b^10 + 21424*b^11 + 33264*b^12 - 43152*b^13 + 31296*b^14 - 12864*b^15 + 2816*b^16 - 256*b^17)*x^6 - 4*(-10839564*b^6 + 77439660*b^7 - 106776000*b^8 + 53433408*b^9 - 10183488*b^10 + 541248*b^11)*x^(13/2) - 4*(26963022*b^7 - 81892080*b^8 + 74138400*b^9 - 25881408*b^10 + 3165600*b^11 - 65664*b^12)*x^7 - 4*(3741844*b^7 - 36405920*b^8 + 63361728*b^9 - 39324544*b^10 + 9379520*b^11 - 646848*b^12)*x^(15/2) - 4*(-8466522*b^8 + 32984958*b^9 - 36988056*b^10 + 15945240*b^11 - 2466000*b^12 + 69264*b^13)*x^8 - 4*(-772680*b^8 + 9937368*b^9 - 21612768*b^10 + 16495584*b^11 - 4884480*b^12 + 437760*b^13)*x^(17/2) - 4*(1537908*b^9 - 7628968*b^10 + 10575824*b^11 - 5618880*b^12 + 1097600*b^13 - 42880*b^14)*x^9 - 4*(90312*b^9 - 1519248*b^10 + 4142880*b^11 - 3908352*b^12 + 1443840*b^13 - 169728*b^14)*x^(19/2) - 4*(-148644*b^10 + 944820*b^11 - 1639008*b^12 + 1087200*b^13 - 272064*b^14 + 15552*b^15)*x^10 - 4*(-5152*b^10 + 114080*b^11 - 397440*b^12 + 473984*b^13 - 223744*b^14 + 35328*b^15)*x^(21/2) - 4*(6096*b^11 - 50880*b^12 + 114240*b^13 - 98304*b^14 + 33024*b^15 - 3072*b^16)*x^11 - 4*(96*b^11 - 2880*b^12 + 13440*b^13 - 21504*b^14 + 13824*b^15 - 3072*b^16)*x^(23/2) - 4*(-48*b^12 + 560*b^13 - 1792*b^14 + 2304*b^15 - 1280*b^16 + 256*b^17)*x^12))/(3*b^3*(8388608 - 12582912*b + 7077888*b^2 - 1835008*b^3 + 215040*b^4 - 9216*b^5 + 64*b^6) + 3*b^3*(64*b^6 - 2304*b^7 + 13440*b^8 - 28672*b^9 + 27648*b^10 - 12288*b^11 + 2048*b^12)*x^6 + 3*Sqrt[2 - b]*b^3*(-4194304 + 5242880*b - 2359296*b^2 + 458752*b^3 - 35840*b^4 + 768*b^5)*Sqrt[2 - b*x] + x*(3*b^3*(-12582912*b + 55050240*b^2 - 55836672*b^3 + 22536192*b^4 - 3855360*b^5 + 234624*b^6 - 2304*b^7) + 3*Sqrt[2 - b]*b^3*(5242880*b - 24641536*b^2 + 21037056*b^3 - 6508544*b^4 + 751360*b^5 - 23040*b^6)*Sqrt[2 - b*x]) + Sqrt[x]*(3*b^3*(-25165824*b + 34603008*b^2 - 17301504*b^3 + 3784704*b^4 - 337920*b^5 + 8448*b^6) + 3*Sqrt[2 - b]*b^3*(12582912*b - 14155776*b^2 + 5505024*b^3 - 860160*b^4 + 46080*b^5 - 384*b^6)*Sqrt[2 - b*x]) + x^(3/2)*(3*b^3*(34603008*b^2 - 80740352*b^3 + 61095936*b^4 - 19193856*b^5 + 2407680*b^6 - 84480*b^7) + 3*Sqrt[2 - b]*b^3*(-14155776*b^2 + 32505856*b^3 - 20701184*b^4 + 4853760*b^5 - 375680*b^6 + 4480*b^7)*Sqrt[2 - b*x]) + x^2*(3*b^3*(7077888*b^2 - 55836672*b^3 + 84258816*b^4 - 48039936*b^5 + 11398080*b^6 - 963840*b^7 + 13440*b^8) + 3*Sqrt[2 - b]*b^3*(-2359296*b^2 + 21037056*b^3 - 30296064*b^4 + 14353920*b^5 - 2426880*b^6 + 107520*b^7)*Sqrt[2 - b*x]) + x^3*(3*b^3*(-1835008*b^3 + 22536192*b^4 - 48039936*b^5 + 37289728*b^6 - 12009984*b^7 + 1408512*b^8 - 28672*b^9) + 3*Sqrt[2 - b]*b^3*(458752*b^3 - 6508544*b^4 + 14353920*b^5 - 10271744*b^6 + 2587648*b^7 - 172032*b^8)*Sqrt[2 - b*x]) + x^(5/2)*(3*b^3*(-17301504*b^3 + 61095936*b^4 - 64745472*b^5 + 27861504*b^6 - 4798464*b^7 + 236544*b^8) + 3*Sqrt[2 - b]*b^3*(5505024*b^3 - 20701184*b^4 + 20543488*b^5 - 7176960*b^6 + 813568*b^7 - 14336*b^8)*Sqrt[2 - b*x]) + x^(7/2)*(3*b^3*(3784704*b^4 - 19193856*b^5 + 27861504*b^6 - 16186368*b^7 + 3818496*b^8 - 270336*b^9) + 3*Sqrt[2 - b]*b^3*(-860160*b^4 + 4853760*b^5 - 7176960*b^6 + 3787008*b^7 - 657408*b^8 + 18432*b^9)*Sqrt[2 - b*x]) + x^4*(3*b^3*(215040*b^4 - 3855360*b^5 + 11398080*b^6 - 12009984*b^7 + 5266176*b^8 - 872448*b^9 + 27648*b^10) + 3*Sqrt[2 - b]*b^3*(-35840*b^4 + 751360*b^5 - 2426880*b^6 + 2587648*b^7 - 1015808*b^8 + 110592*b^9)*Sqrt[2 - b*x]) + x^5*(3*b^3*(-9216*b^5 + 234624*b^6 - 963840*b^7 + 1408512*b^8 - 872448*b^9 + 215040*b^10 - 12288*b^11) + 3*Sqrt[2 - b]*b^3*(768*b^5 - 23040*b^6 + 107520*b^7 - 172032*b^8 + 110592*b^9 - 24576*b^10)*Sqrt[2 - b*x]) + x^(9/2)*(3*b^3*(-337920*b^5 + 2407680*b^6 - 4798464*b^7 + 3818496*b^8 - 1261568*b^9 + 135168*b^10) + 3*Sqrt[2 - b]*b^3*(46080*b^5 - 375680*b^6 + 813568*b^7 - 657408*b^8 + 192512*b^9 - 10240*b^10)*Sqrt[2 - b*x]) + x^(11/2)*(3*b^3*(8448*b^6 - 84480*b^7 + 236544*b^8 - 270336*b^9 + 135168*b^10 - 24576*b^11) + 3*Sqrt[2 - b]*b^3*(-384*b^6 + 4480*b^7 - 14336*b^8 + 18432*b^9 - 10240*b^10 + 2048*b^11)*Sqrt[2 - b*x])) + (5*ArcTan[(Sqrt[2 - b]/Sqrt[b] - Sqrt[2 - b*x]/Sqrt[b])/(-1 + Sqrt[x])])/(4*b^(7/2))","B",1
564,1,3021,128,8.6334752,"\int x^{3/2} (2-b x)^{5/2} \, dx","IntegrateAlgebraic[x^(3/2)*(2 - b*x)^(5/2),x]","\text{Result too large to show}","\frac{3 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{4 b^{5/2}}-\frac{3 \sqrt{x} \sqrt{2-b x}}{8 b^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,"(-4*(-245760 + 286720*b + 935168*b^2 - 2229760*b^3 + 2016020*b^4 - 974350*b^5 + 269450*b^6 - 41524*b^7 + 3140*b^8 - 80*b^9)*Sqrt[2 - b*x] - 4*(245760 + 307200*b - 505600*b^2 - 2432320*b^3 + 5267260*b^4 - 4421225*b^5 + 1955575*b^6 - 480805*b^7 + 62330*b^8 - 3490*b^9 + 40*b^10)*Sqrt[x]*Sqrt[2 - b*x] - 4*(-368640*b - 325120*b^2 - 525568*b^3 + 5197840*b^4 - 7896350*b^5 + 5537200*b^6 - 2101240*b^7 + 435584*b^8 - 44560*b^9 + 1600*b^10)*x*Sqrt[2 - b*x] - 4*(-225280*b + 473600*b^2 + 254400*b^3 + 1924080*b^4 - 6876375*b^5 + 7992950*b^6 - 4653860*b^7 + 1482080*b^8 - 250120*b^9 + 18800*b^10 - 320*b^11)*x^(3/2)*Sqrt[2 - b*x] - 4*(405760*b^2 - 453120*b^3 + 198552*b^4 - 2885100*b^5 + 6291450*b^6 - 5779320*b^7 + 2790240*b^8 - 734016*b^9 + 97200*b^10 - 4800*b^11)*x^2*Sqrt[2 - b*x] - 4*(-983808*b^2 + 887360*b^3 - 252920*b^4 - 451370*b^5 + 2624165*b^6 - 4105967*b^7 + 3050640*b^8 - 1220880*b^9 + 261000*b^10 - 25800*b^11 + 672*b^12)*x^(5/2)*Sqrt[2 - b*x] - 4*(2520320*b^3 - 2653360*b^4 + 896900*b^5 + 402400*b^6 - 1595900*b^7 + 1924480*b^8 - 1176640*b^9 + 390080*b^10 - 66400*b^11 + 4480*b^12)*x^3*Sqrt[2 - b*x] - 4*(1978688*b^3 - 5516240*b^4 + 4055650*b^5 - 1050380*b^6 - 208990*b^7 + 654432*b^8 - 635360*b^9 + 324800*b^10 - 89200*b^11 + 11840*b^12 - 512*b^13)*x^(7/2)*Sqrt[2 - b*x] - 4*(-4627980*b^4 + 7513850*b^5 - 3950050*b^6 + 736900*b^7 + 64000*b^8 - 170720*b^9 + 138800*b^10 - 60640*b^11 + 13760*b^12 - 1280*b^13)*x^4*Sqrt[2 - b*x] - 4*(-1553252*b^4 + 7053475*b^5 - 7195775*b^6 + 2670145*b^7 - 334240*b^8 - 9408*b^9 + 22800*b^10 - 16600*b^11 + 6720*b^12 - 1440*b^13 + 128*b^14)*x^(9/2)*Sqrt[2 - b*x] - 4*(3345050*b^5 - 7306800*b^6 + 5007624*b^7 - 1280640*b^8 + 94080*b^9)*x^5*Sqrt[2 - b*x] - 4*(639845*b^5 - 4181450*b^6 + 5459180*b^7 - 2570080*b^8 + 430240*b^9 - 13240*b^10)*x^(11/2)*Sqrt[2 - b*x] - 4*(-1243650*b^6 + 3528840*b^7 - 3017184*b^8 + 970560*b^9 - 95600*b^10)*x^6*Sqrt[2 - b*x] - 4*(-145085*b^6 + 1303235*b^7 - 2136080*b^8 + 1243120*b^9 - 263800*b^10 + 11720*b^11)*x^(13/2)*Sqrt[2 - b*x] - 4*(244620*b^7 - 896640*b^8 + 950016*b^9 - 379200*b^10 + 48800*b^11)*x^7*Sqrt[2 - b*x] - 4*(17062*b^7 - 208240*b^8 + 431680*b^9 - 311600*b^10 + 83600*b^11 - 5472*b^12)*x^(15/2)*Sqrt[2 - b*x] - 4*(-22980*b^8 + 110640*b^9 - 148080*b^10 + 74400*b^11 - 12480*b^12)*x^8*Sqrt[2 - b*x] - 4*(-842*b^8 + 14210*b^9 - 38600*b^10 + 35800*b^11 - 12640*b^12 + 1312*b^13)*x^(17/2)*Sqrt[2 - b*x] - 4*(720*b^9 - 4800*b^10 + 8640*b^11 - 5760*b^12 + 1280*b^13)*x^9*Sqrt[2 - b*x] - 4*(8*b^9 - 200*b^10 + 800*b^11 - 1120*b^12 + 640*b^13 - 128*b^14)*x^(19/2)*Sqrt[2 - b*x] + Sqrt[2 - b]*(-4*(245760 - 225280*b - 983808*b^2 + 1978688*b^3 - 1553252*b^4 + 639845*b^5 - 145085*b^6 + 17062*b^7 - 842*b^8 + 8*b^9) - 4*(-245760 - 368640*b + 405760*b^2 + 2520320*b^3 - 4627980*b^4 + 3345050*b^5 - 1243650*b^6 + 244620*b^7 - 22980*b^8 + 720*b^9)*Sqrt[x] - 4*(307200*b + 473600*b^2 + 887360*b^3 - 5516240*b^4 + 7053475*b^5 - 4181450*b^6 + 1303235*b^7 - 208240*b^8 + 14210*b^9 - 200*b^10)*x - 4*(286720*b - 325120*b^2 - 453120*b^3 - 2653360*b^4 + 7513850*b^5 - 7306800*b^6 + 3528840*b^7 - 896640*b^8 + 110640*b^9 - 4800*b^10)*x^(3/2) - 4*(-505600*b^2 + 254400*b^3 - 252920*b^4 + 4055650*b^5 - 7195775*b^6 + 5459180*b^7 - 2136080*b^8 + 431680*b^9 - 38600*b^10 + 800*b^11)*x^2 - 4*(935168*b^2 - 525568*b^3 + 198552*b^4 + 896900*b^5 - 3950050*b^6 + 5007624*b^7 - 3017184*b^8 + 950016*b^9 - 148080*b^10 + 8640*b^11)*x^(5/2) - 4*(-2432320*b^3 + 1924080*b^4 - 451370*b^5 - 1050380*b^6 + 2670145*b^7 - 2570080*b^8 + 1243120*b^9 - 311600*b^10 + 35800*b^11 - 1120*b^12)*x^3 - 4*(-2229760*b^3 + 5197840*b^4 - 2885100*b^5 + 402400*b^6 + 736900*b^7 - 1280640*b^8 + 970560*b^9 - 379200*b^10 + 74400*b^11 - 5760*b^12)*x^(7/2) - 4*(5267260*b^4 - 6876375*b^5 + 2624165*b^6 - 208990*b^7 - 334240*b^8 + 430240*b^9 - 263800*b^10 + 83600*b^11 - 12640*b^12 + 640*b^13)*x^4 - 4*(2016020*b^4 - 7896350*b^5 + 6291450*b^6 - 1595900*b^7 + 64000*b^8 + 94080*b^9 - 95600*b^10 + 48800*b^11 - 12480*b^12 + 1280*b^13)*x^(9/2) - 4*(-4421225*b^5 + 7992950*b^6 - 4105967*b^7 + 654432*b^8 - 9408*b^9 - 13240*b^10 + 11720*b^11 - 5472*b^12 + 1312*b^13 - 128*b^14)*x^5 - 4*(-974350*b^5 + 5537200*b^6 - 5779320*b^7 + 1924480*b^8 - 170720*b^9)*x^(11/2) - 4*(1955575*b^6 - 4653860*b^7 + 3050640*b^8 - 635360*b^9 + 22800*b^10)*x^6 - 4*(269450*b^6 - 2101240*b^7 + 2790240*b^8 - 1176640*b^9 + 138800*b^10)*x^(13/2) - 4*(-480805*b^7 + 1482080*b^8 - 1220880*b^9 + 324800*b^10 - 16600*b^11)*x^7 - 4*(-41524*b^7 + 435584*b^8 - 734016*b^9 + 390080*b^10 - 60640*b^11)*x^(15/2) - 4*(62330*b^8 - 250120*b^9 + 261000*b^10 - 89200*b^11 + 6720*b^12)*x^8 - 4*(3140*b^8 - 44560*b^9 + 97200*b^10 - 66400*b^11 + 13760*b^12)*x^(17/2) - 4*(-3490*b^9 + 18800*b^10 - 25800*b^11 + 11840*b^12 - 1440*b^13)*x^9 - 4*(-80*b^9 + 1600*b^10 - 4800*b^11 + 4480*b^12 - 1280*b^13)*x^(19/2) - 4*(40*b^10 - 320*b^11 + 672*b^12 - 512*b^13 + 128*b^14)*x^10))/(5*b^2*(524288 - 655360*b + 286720*b^2 - 51200*b^3 + 3200*b^4 - 32*b^5) + 5*b^2*(-32*b^5 + 800*b^6 - 3200*b^7 + 4480*b^8 - 2560*b^9 + 512*b^10)*x^5 + 5*Sqrt[2 - b]*b^2*(-262144 + 262144*b - 86016*b^2 + 10240*b^3 - 320*b^4)*Sqrt[2 - b*x] + Sqrt[x]*(5*b^2*(-1310720*b + 1474560*b^2 - 552960*b^3 + 76800*b^4 - 2880*b^5) + 5*Sqrt[2 - b]*b^2*(655360*b - 573440*b^2 + 153600*b^3 - 12800*b^4 + 160*b^5)*Sqrt[2 - b*x]) + x*(5*b^2*(-655360*b + 2375680*b^2 - 1914880*b^3 + 550400*b^4 - 52640*b^5 + 800*b^6) + 5*Sqrt[2 - b]*b^2*(262144*b - 1040384*b^2 + 669696*b^3 - 131840*b^4 + 6400*b^5)*Sqrt[2 - b*x]) + x^2*(5*b^2*(286720*b^2 - 1914880*b^3 + 2333440*b^4 - 979520*b^5 + 137600*b^6 - 3200*b^7) + 5*Sqrt[2 - b]*b^2*(-86016*b^2 + 669696*b^3 - 776064*b^4 + 249600*b^5 - 19200*b^6)*Sqrt[2 - b*x]) + x^(3/2)*(5*b^2*(1474560*b^2 - 2826240*b^3 + 1643520*b^4 - 341760*b^5 + 19200*b^6) + 5*Sqrt[2 - b]*b^2*(-573440*b^2 + 1085440*b^3 - 499200*b^4 + 65920*b^5 - 1280*b^6)*Sqrt[2 - b*x]) + x^(5/2)*(5*b^2*(-552960*b^3 + 1643520*b^4 - 1375104*b^5 + 410880*b^6 - 34560*b^7) + 5*Sqrt[2 - b]*b^2*(153600*b^3 - 499200*b^4 + 388032*b^5 - 83712*b^6 + 2688*b^7)*Sqrt[2 - b*x]) + x^3*(5*b^2*(-51200*b^3 + 550400*b^4 - 979520*b^5 + 583360*b^6 - 119680*b^7 + 4480*b^8) + 5*Sqrt[2 - b]*b^2*(10240*b^3 - 131840*b^4 + 249600*b^5 - 135680*b^6 + 17920*b^7)*Sqrt[2 - b*x]) + x^4*(5*b^2*(3200*b^4 - 52640*b^5 + 137600*b^6 - 119680*b^7 + 37120*b^8 - 2560*b^9) + 5*Sqrt[2 - b]*b^2*(-320*b^4 + 6400*b^5 - 19200*b^6 + 17920*b^7 - 5120*b^8)*Sqrt[2 - b*x]) + x^(7/2)*(5*b^2*(76800*b^4 - 341760*b^5 + 410880*b^6 - 176640*b^7 + 23040*b^8) + 5*Sqrt[2 - b]*b^2*(-12800*b^4 + 65920*b^5 - 83712*b^6 + 32512*b^7 - 2048*b^8)*Sqrt[2 - b*x]) + x^(9/2)*(5*b^2*(-2880*b^5 + 19200*b^6 - 34560*b^7 + 23040*b^8 - 5120*b^9) + 5*Sqrt[2 - b]*b^2*(160*b^5 - 1280*b^6 + 2688*b^7 - 2048*b^8 + 512*b^9)*Sqrt[2 - b*x])) + (3*ArcTan[(Sqrt[2 - b]/Sqrt[b] - Sqrt[2 - b*x]/Sqrt[b])/(-1 + Sqrt[x])])/(2*b^(5/2))","B",1
565,1,2067,106,4.2565255,"\int \sqrt{x} (2-b x)^{5/2} \, dx","IntegrateAlgebraic[Sqrt[x]*(2 - b*x)^(5/2),x]","\text{Result too large to show}","\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,"(-2*(-30720 + 159232*b - 236992*b^2 + 166160*b^3 - 62856*b^4 + 12984*b^5 - 1328*b^6 + 48*b^7)*Sqrt[2 - b*x] - 2*(30720 + 30720*b - 301184*b^2 + 435136*b^3 - 282409*b^4 + 96084*b^5 - 17020*b^6 + 1336*b^7 - 24*b^8)*Sqrt[x]*Sqrt[2 - b*x] - 2*(-38400*b - 123264*b^2 + 448464*b^3 - 498000*b^4 + 269352*b^5 - 76848*b^6 + 10896*b^7 - 576*b^8)*x*Sqrt[2 - b*x] - 2*(-151552*b + 170752*b^2 + 137280*b^3 - 421284*b^4 + 374841*b^5 - 167240*b^6 + 38900*b^7 - 4160*b^8 + 120*b^9)*x^(3/2)*Sqrt[2 - b*x] - 2*(290624*b^2 - 238416*b^3 - 107136*b^4 + 270336*b^5 - 193840*b^6 + 70960*b^7 - 13120*b^8 + 960*b^9)*x^2*Sqrt[2 - b*x] - 2*(200064*b^2 - 464064*b^3 + 236754*b^4 + 54552*b^5 - 118050*b^6 + 68808*b^7 - 20640*b^8 + 2976*b^9 - 144*b^10)*x^(5/2)*Sqrt[2 - b*x] - 2*(-363920*b^3 + 467856*b^4 - 160896*b^5 - 17280*b^6 + 33296*b^7 - 16064*b^8 + 3904*b^9 - 384*b^10)*x^3*Sqrt[2 - b*x] - 2*(-120640*b^3 + 429100*b^4 - 328518*b^5 + 74472*b^6 + 2766*b^7 - 5056*b^8 + 2240*b^9 - 512*b^10 + 48*b^11)*x^(7/2)*Sqrt[2 - b*x] - 2*(200136*b^4 - 336504*b^5 + 162288*b^6 - 22128*b^7)*x^4*Sqrt[2 - b*x] - 2*(37839*b^4 - 190884*b^5 + 184820*b^6 - 55736*b^7 + 3464*b^8)*x^(9/2)*Sqrt[2 - b*x] - 2*(-55272*b^5 + 119728*b^6 - 72016*b^7 + 12736*b^8)*x^5*Sqrt[2 - b*x] - 2*(-6075*b^5 + 42600*b^6 - 51900*b^7 + 19680*b^8 - 1800*b^9)*x^(11/2)*Sqrt[2 - b*x] - 2*(7280*b^6 - 20720*b^7 + 15680*b^8 - 3520*b^9)*x^6*Sqrt[2 - b*x] - 2*(418*b^6 - 4168*b^7 + 6640*b^8 - 3296*b^9 + 464*b^10)*x^(13/2)*Sqrt[2 - b*x] - 2*(-336*b^7 + 1344*b^8 - 1344*b^9 + 384*b^10)*x^7*Sqrt[2 - b*x] - 2*(-6*b^7 + 96*b^8 - 240*b^9 + 192*b^10 - 48*b^11)*x^(15/2)*Sqrt[2 - b*x] + Sqrt[2 - b]*(-2*(30720 - 151552*b + 200064*b^2 - 120640*b^3 + 37839*b^4 - 6075*b^5 + 418*b^6 - 6*b^7) - 2*(-30720 - 38400*b + 290624*b^2 - 363920*b^3 + 200136*b^4 - 55272*b^5 + 7280*b^6 - 336*b^7)*Sqrt[x] - 2*(30720*b + 170752*b^2 - 464064*b^3 + 429100*b^4 - 190884*b^5 + 42600*b^6 - 4168*b^7 + 96*b^8)*x - 2*(159232*b - 123264*b^2 - 238416*b^3 + 467856*b^4 - 336504*b^5 + 119728*b^6 - 20720*b^7 + 1344*b^8)*x^(3/2) - 2*(-301184*b^2 + 137280*b^3 + 236754*b^4 - 328518*b^5 + 184820*b^6 - 51900*b^7 + 6640*b^8 - 240*b^9)*x^2 - 2*(-236992*b^2 + 448464*b^3 - 107136*b^4 - 160896*b^5 + 162288*b^6 - 72016*b^7 + 15680*b^8 - 1344*b^9)*x^(5/2) - 2*(435136*b^3 - 421284*b^4 + 54552*b^5 + 74472*b^6 - 55736*b^7 + 19680*b^8 - 3296*b^9 + 192*b^10)*x^3 - 2*(166160*b^3 - 498000*b^4 + 270336*b^5 - 17280*b^6 - 22128*b^7 + 12736*b^8 - 3520*b^9 + 384*b^10)*x^(7/2) - 2*(-282409*b^4 + 374841*b^5 - 118050*b^6 + 2766*b^7 + 3464*b^8 - 1800*b^9 + 464*b^10 - 48*b^11)*x^4 - 2*(-62856*b^4 + 269352*b^5 - 193840*b^6 + 33296*b^7)*x^(9/2) - 2*(96084*b^5 - 167240*b^6 + 68808*b^7 - 5056*b^8)*x^5 - 2*(12984*b^5 - 76848*b^6 + 70960*b^7 - 16064*b^8)*x^(11/2) - 2*(-17020*b^6 + 38900*b^7 - 20640*b^8 + 2240*b^9)*x^6 - 2*(-1328*b^6 + 10896*b^7 - 13120*b^8 + 3904*b^9)*x^(13/2) - 2*(1336*b^7 - 4160*b^8 + 2976*b^9 - 512*b^10)*x^7 - 2*(48*b^7 - 576*b^8 + 960*b^9 - 384*b^10)*x^(15/2) - 2*(-24*b^8 + 120*b^9 - 144*b^10 + 48*b^11)*x^8))/(3*b*(32768 - 32768*b + 10240*b^2 - 1024*b^3 + 16*b^4) + 3*b*(16*b^4 - 256*b^5 + 640*b^6 - 512*b^7 + 128*b^8)*x^4 + 3*Sqrt[2 - b]*b*(-16384 + 12288*b - 2560*b^2 + 128*b^3)*Sqrt[2 - b*x] + x*(3*b*(-32768*b + 94208*b^2 - 56320*b^3 + 9664*b^4 - 256*b^5) + 3*Sqrt[2 - b]*b*(12288*b - 39936*b^2 + 17280*b^3 - 1536*b^4)*Sqrt[2 - b*x]) + Sqrt[x]*(3*b*(-65536*b + 57344*b^2 - 14336*b^3 + 896*b^4) + 3*Sqrt[2 - b]*b*(32768*b - 20480*b^2 + 3072*b^3 - 64*b^4)*Sqrt[2 - b*x]) + x^(3/2)*(3*b*(57344*b^2 - 86016*b^3 + 34944*b^4 - 3584*b^5) + 3*Sqrt[2 - b]*b*(-20480*b^2 + 30720*b^3 - 8640*b^4 + 320*b^5)*Sqrt[2 - b*x]) + x^2*(3*b*(10240*b^2 - 56320*b^3 + 52320*b^4 - 14080*b^5 + 640*b^6) + 3*Sqrt[2 - b]*b*(-2560*b^2 + 17280*b^3 - 15360*b^4 + 2560*b^5)*Sqrt[2 - b*x]) + x^3*(3*b*(-1024*b^3 + 9664*b^4 - 14080*b^5 + 5888*b^6 - 512*b^7) + 3*Sqrt[2 - b]*b*(128*b^3 - 1536*b^4 + 2560*b^5 - 1024*b^6)*Sqrt[2 - b*x]) + x^(5/2)*(3*b*(-14336*b^3 + 34944*b^4 - 21504*b^5 + 3584*b^6) + 3*Sqrt[2 - b]*b*(3072*b^3 - 8640*b^4 + 4992*b^5 - 384*b^6)*Sqrt[2 - b*x]) + x^(7/2)*(3*b*(896*b^4 - 3584*b^5 + 3584*b^6 - 1024*b^7) + 3*Sqrt[2 - b]*b*(-64*b^4 + 320*b^5 - 384*b^6 + 128*b^7)*Sqrt[2 - b*x])) + (5*ArcTan[(Sqrt[2 - b]/Sqrt[b] - Sqrt[2 - b*x]/Sqrt[b])/(-1 + Sqrt[x])])/(2*b^(3/2))","B",1
566,1,1300,82,2.0482039,"\int \frac{(2-b x)^{5/2}}{\sqrt{x}} \, dx","IntegrateAlgebraic[(2 - b*x)^(5/2)/Sqrt[x],x]","\frac{-4 \left(-8 b^8+24 b^7-18 b^6+2 b^5\right) \sqrt{2-b x} x^{11/2}-4 \left(48 b^7-120 b^6+60 b^5\right) \sqrt{2-b x} x^5-4 \left(76 b^7-360 b^6+435 b^5-85 b^4\right) \sqrt{2-b x} x^{9/2}-4 \left(-432 b^6+1300 b^5-870 b^4\right) \sqrt{2-b x} x^4-4 \left(-306 b^6+2040 b^5-3180 b^4+885 b^3\right) \sqrt{2-b x} x^{7/2}-4 \left(1632 b^5-5840 b^4+4878 b^3\right) \sqrt{2-b x} x^3-4 \left(8 b^8-84 b^7+378 b^6-272 b^5-4800 b^4+10737 b^3-4196 b^2\right) \sqrt{2-b x} x^{5/2}-4 \left(-48 b^7+480 b^6-2040 b^5+1440 b^4+8970 b^3-12516 b^2\right) \sqrt{2-b x} x^2-4 \left(-16 b^7+300 b^6-2010 b^5+6280 b^4-3945 b^3-11208 b^2+9664 b\right) \sqrt{2-b x} x^{3/2}-4 \left(72 b^6-940 b^5+5040 b^4-12150 b^3+6680 b^2+8448 b\right) \sqrt{2-b x} x-4 \left(6 b^6-195 b^5+1785 b^4-7677 b^3+14892 b^2-6336 b-8448\right) \sqrt{2-b x} \sqrt{x}+\sqrt{2-b} \left(-4 \left(8 b^8-16 b^7+6 b^6\right) x^6-4 \left(-48 b^7+72 b^6-12 b^5\right) x^{11/2}-4 \left(-84 b^7+300 b^6-195 b^5\right) x^5-4 \left(480 b^6-940 b^5+230 b^4\right) x^{9/2}-4 \left(378 b^6-2010 b^5+1785 b^4\right) x^4-4 \left(-2040 b^5+5040 b^4-1698 b^3\right) x^{7/2}-4 \left(-8 b^8+76 b^7-306 b^6-272 b^5+6280 b^4-7677 b^3\right) x^3-4 \left(48 b^7-432 b^6+1632 b^5+1440 b^4-12150 b^3+6348 b^2\right) x^{5/2}-4 \left(24 b^7-360 b^6+2040 b^5-4800 b^4-3945 b^3+14892 b^2\right) x^2-4 \left(-120 b^6+1300 b^5-5840 b^4+8970 b^3+6680 b^2-11776 b\right) x^{3/2}-4 \left(-18 b^6+435 b^5-3180 b^4+10737 b^3-11208 b^2-6336 b\right) x-4 \left(60 b^5-870 b^4+4878 b^3-12516 b^2+8448 b+8448\right) \sqrt{x}-4 \left(2 b^5-85 b^4+885 b^3-4196 b^2+9664 b-8448\right)\right)-4 \left(-12 b^5+230 b^4-1698 b^3+6348 b^2-11776 b+8448\right) \sqrt{2-b x}}{3 \left(32 b^6-96 b^5+72 b^4-8 b^3\right) x^3+\left(3 \left(-192 b^5+480 b^4-240 b^3\right)+3 \sqrt{2-b} \left(32 b^5-64 b^4+24 b^3\right) \sqrt{2-b x}\right) x^{5/2}+\left(3 \sqrt{2-b} \sqrt{2-b x} \left(-192 b^4+288 b^3-48 b^2\right)+3 \left(-96 b^5+816 b^4-1272 b^3+288 b^2\right)\right) x^2+\left(3 \sqrt{2-b} \sqrt{2-b x} \left(-64 b^4+656 b^3-576 b^2\right)+3 \left(480 b^4-2080 b^3+1920 b^2\right)\right) x^{3/2}+\left(3 \sqrt{2-b} \sqrt{2-b x} \left(288 b^3-1312 b^2+512 b\right)+3 \left(72 b^4-1272 b^3+3264 b^2-1536 b\right)\right) x+\left(3 \left(-240 b^3+1920 b^2-3072 b\right)+3 \sqrt{2-b} \left(24 b^3-576 b^2+1536 b\right) \sqrt{2-b x}\right) \sqrt{x}+3 \left(-8 b^3+288 b^2-1536 b+2048\right)+3 \sqrt{2-b} \left(-48 b^2+512 b-1024\right) \sqrt{2-b x}}+\frac{10 \tan ^{-1}\left(\frac{\frac{\sqrt{2-b}}{\sqrt{b}}-\frac{\sqrt{2-b x}}{\sqrt{b}}}{\sqrt{x}-1}\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,"(-4*(8448 - 11776*b + 6348*b^2 - 1698*b^3 + 230*b^4 - 12*b^5)*Sqrt[2 - b*x] - 4*(-8448 - 6336*b + 14892*b^2 - 7677*b^3 + 1785*b^4 - 195*b^5 + 6*b^6)*Sqrt[x]*Sqrt[2 - b*x] - 4*(8448*b + 6680*b^2 - 12150*b^3 + 5040*b^4 - 940*b^5 + 72*b^6)*x*Sqrt[2 - b*x] - 4*(9664*b - 11208*b^2 - 3945*b^3 + 6280*b^4 - 2010*b^5 + 300*b^6 - 16*b^7)*x^(3/2)*Sqrt[2 - b*x] - 4*(-12516*b^2 + 8970*b^3 + 1440*b^4 - 2040*b^5 + 480*b^6 - 48*b^7)*x^2*Sqrt[2 - b*x] - 4*(-4196*b^2 + 10737*b^3 - 4800*b^4 - 272*b^5 + 378*b^6 - 84*b^7 + 8*b^8)*x^(5/2)*Sqrt[2 - b*x] - 4*(4878*b^3 - 5840*b^4 + 1632*b^5)*x^3*Sqrt[2 - b*x] - 4*(885*b^3 - 3180*b^4 + 2040*b^5 - 306*b^6)*x^(7/2)*Sqrt[2 - b*x] - 4*(-870*b^4 + 1300*b^5 - 432*b^6)*x^4*Sqrt[2 - b*x] - 4*(-85*b^4 + 435*b^5 - 360*b^6 + 76*b^7)*x^(9/2)*Sqrt[2 - b*x] - 4*(60*b^5 - 120*b^6 + 48*b^7)*x^5*Sqrt[2 - b*x] - 4*(2*b^5 - 18*b^6 + 24*b^7 - 8*b^8)*x^(11/2)*Sqrt[2 - b*x] + Sqrt[2 - b]*(-4*(-8448 + 9664*b - 4196*b^2 + 885*b^3 - 85*b^4 + 2*b^5) - 4*(8448 + 8448*b - 12516*b^2 + 4878*b^3 - 870*b^4 + 60*b^5)*Sqrt[x] - 4*(-6336*b - 11208*b^2 + 10737*b^3 - 3180*b^4 + 435*b^5 - 18*b^6)*x - 4*(-11776*b + 6680*b^2 + 8970*b^3 - 5840*b^4 + 1300*b^5 - 120*b^6)*x^(3/2) - 4*(14892*b^2 - 3945*b^3 - 4800*b^4 + 2040*b^5 - 360*b^6 + 24*b^7)*x^2 - 4*(6348*b^2 - 12150*b^3 + 1440*b^4 + 1632*b^5 - 432*b^6 + 48*b^7)*x^(5/2) - 4*(-7677*b^3 + 6280*b^4 - 272*b^5 - 306*b^6 + 76*b^7 - 8*b^8)*x^3 - 4*(-1698*b^3 + 5040*b^4 - 2040*b^5)*x^(7/2) - 4*(1785*b^4 - 2010*b^5 + 378*b^6)*x^4 - 4*(230*b^4 - 940*b^5 + 480*b^6)*x^(9/2) - 4*(-195*b^5 + 300*b^6 - 84*b^7)*x^5 - 4*(-12*b^5 + 72*b^6 - 48*b^7)*x^(11/2) - 4*(6*b^6 - 16*b^7 + 8*b^8)*x^6))/(3*(2048 - 1536*b + 288*b^2 - 8*b^3) + 3*(-8*b^3 + 72*b^4 - 96*b^5 + 32*b^6)*x^3 + 3*Sqrt[2 - b]*(-1024 + 512*b - 48*b^2)*Sqrt[2 - b*x] + Sqrt[x]*(3*(-3072*b + 1920*b^2 - 240*b^3) + 3*Sqrt[2 - b]*(1536*b - 576*b^2 + 24*b^3)*Sqrt[2 - b*x]) + x*(3*(-1536*b + 3264*b^2 - 1272*b^3 + 72*b^4) + 3*Sqrt[2 - b]*(512*b - 1312*b^2 + 288*b^3)*Sqrt[2 - b*x]) + x^2*(3*(288*b^2 - 1272*b^3 + 816*b^4 - 96*b^5) + 3*Sqrt[2 - b]*(-48*b^2 + 288*b^3 - 192*b^4)*Sqrt[2 - b*x]) + x^(3/2)*(3*(1920*b^2 - 2080*b^3 + 480*b^4) + 3*Sqrt[2 - b]*(-576*b^2 + 656*b^3 - 64*b^4)*Sqrt[2 - b*x]) + x^(5/2)*(3*(-240*b^3 + 480*b^4 - 192*b^5) + 3*Sqrt[2 - b]*(24*b^3 - 64*b^4 + 32*b^5)*Sqrt[2 - b*x])) + (10*ArcTan[(Sqrt[2 - b]/Sqrt[b] - Sqrt[2 - b*x]/Sqrt[b])/(-1 + Sqrt[x])])/Sqrt[b]","B",1
567,1,830,82,2.6212315,"\int \frac{(2-b x)^{5/2}}{x^{3/2}} \, dx","IntegrateAlgebraic[(2 - b*x)^(5/2)/x^(3/2),x]","\frac{\left(4 \sqrt{x} b^3-8 \sqrt{x} b^2+4 \sqrt{2-b} \sqrt{2-b x} b^2-4 b^2+2 \sqrt{x} b-4 \sqrt{2-b} \sqrt{2-b x} b+6 b\right) \left(\sqrt{2-b}-\sqrt{2-b x}\right)^7}{\left(\sqrt{x} b+\sqrt{2-b} \sqrt{2-b x}-2\right)^4}+\frac{\left(12 \sqrt{x} b^3+4 b^3-24 \sqrt{x} b^2+16 \sqrt{2-b} \sqrt{2-b x} b^2-24 b^2+6 \sqrt{x} b-16 \sqrt{2-b} \sqrt{2-b x} b+26 b\right) \left(\sqrt{2-b}-\sqrt{2-b x}\right)^5}{\left(\sqrt{x} b+\sqrt{2-b} \sqrt{2-b x}-2\right)^3}+\frac{\left(10 \sqrt{x} b^3+10 b^3-28 \sqrt{x} b^2+20 \sqrt{2-b} \sqrt{2-b x} b^2-40 b^2+13 \sqrt{x} b-28 \sqrt{2-b} \sqrt{2-b x} b+43 b\right) \left(\sqrt{2-b}-\sqrt{2-b x}\right)^3}{\left(\sqrt{x} b+\sqrt{2-b} \sqrt{2-b x}-2\right)^2}+\frac{\left(8-8 \sqrt{x}\right) \left(-x b+2 \sqrt{x} b-2 b-2 \sqrt{x}-2 \sqrt{2-b} \sqrt{2-b x}+\sqrt{2-b} \sqrt{x} \sqrt{2-b x}+4\right) \left(\sqrt{2-b}-\sqrt{2-b x}\right)}{\sqrt{x} \left(\sqrt{x} b^2+x^{3/2} b-2 x b+\sqrt{x} b+\sqrt{2-b} \sqrt{2-b x} b-4 b-4 \sqrt{x}-4 \sqrt{2-b} \sqrt{2-b x}+2 \sqrt{2-b} \sqrt{x} \sqrt{2-b x}+8\right)}+\frac{\left(b \sqrt{2-b x}-\sqrt{2-b} b\right) \left(-2 \sqrt{x} b^2-6 b^2+12 \sqrt{x} b-8 \sqrt{2-b} \sqrt{2-b x} b+28 b-9 \sqrt{x}+24 \sqrt{2-b} \sqrt{2-b x}-39\right)}{\sqrt{x} b+\sqrt{2-b} \sqrt{2-b x}-2}-30 \sqrt{b} \tan ^{-1}\left(\frac{\frac{\sqrt{2-b}}{\sqrt{b}}-\frac{\sqrt{2-b x}}{\sqrt{b}}}{\sqrt{x}-1}\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,"((-(Sqrt[2 - b]*b) + b*Sqrt[2 - b*x])*(-39 + 28*b - 6*b^2 - 9*Sqrt[x] + 12*b*Sqrt[x] - 2*b^2*Sqrt[x] + 24*Sqrt[2 - b]*Sqrt[2 - b*x] - 8*Sqrt[2 - b]*b*Sqrt[2 - b*x]))/(-2 + b*Sqrt[x] + Sqrt[2 - b]*Sqrt[2 - b*x]) + ((Sqrt[2 - b] - Sqrt[2 - b*x])^7*(6*b - 4*b^2 + 2*b*Sqrt[x] - 8*b^2*Sqrt[x] + 4*b^3*Sqrt[x] - 4*Sqrt[2 - b]*b*Sqrt[2 - b*x] + 4*Sqrt[2 - b]*b^2*Sqrt[2 - b*x]))/(-2 + b*Sqrt[x] + Sqrt[2 - b]*Sqrt[2 - b*x])^4 + ((Sqrt[2 - b] - Sqrt[2 - b*x])^5*(26*b - 24*b^2 + 4*b^3 + 6*b*Sqrt[x] - 24*b^2*Sqrt[x] + 12*b^3*Sqrt[x] - 16*Sqrt[2 - b]*b*Sqrt[2 - b*x] + 16*Sqrt[2 - b]*b^2*Sqrt[2 - b*x]))/(-2 + b*Sqrt[x] + Sqrt[2 - b]*Sqrt[2 - b*x])^3 + ((Sqrt[2 - b] - Sqrt[2 - b*x])^3*(43*b - 40*b^2 + 10*b^3 + 13*b*Sqrt[x] - 28*b^2*Sqrt[x] + 10*b^3*Sqrt[x] - 28*Sqrt[2 - b]*b*Sqrt[2 - b*x] + 20*Sqrt[2 - b]*b^2*Sqrt[2 - b*x]))/(-2 + b*Sqrt[x] + Sqrt[2 - b]*Sqrt[2 - b*x])^2 + ((8 - 8*Sqrt[x])*(Sqrt[2 - b] - Sqrt[2 - b*x])*(4 - 2*b - 2*Sqrt[x] + 2*b*Sqrt[x] - b*x - 2*Sqrt[2 - b]*Sqrt[2 - b*x] + Sqrt[2 - b]*Sqrt[x]*Sqrt[2 - b*x]))/(Sqrt[x]*(8 - 4*b - 4*Sqrt[x] + b*Sqrt[x] + b^2*Sqrt[x] - 2*b*x + b*x^(3/2) - 4*Sqrt[2 - b]*Sqrt[2 - b*x] + Sqrt[2 - b]*b*Sqrt[2 - b*x] + 2*Sqrt[2 - b]*Sqrt[x]*Sqrt[2 - b*x])) - 30*Sqrt[b]*ArcTan[(Sqrt[2 - b]/Sqrt[b] - Sqrt[2 - b*x]/Sqrt[b])/(-1 + Sqrt[x])]","B",1
568,1,1984,84,8.4558999,"\int \frac{(2-b x)^{5/2}}{x^{5/2}} \, dx","IntegrateAlgebraic[(2 - b*x)^(5/2)/x^(5/2),x]","\frac{\left(\frac{96 x^{3/2}}{b}-\frac{1024 x^{3/2}}{3 b^2}+\frac{1024 x^{3/2}}{3 b^3}-\frac{16 x^{3/2}}{3}+\frac{16 \sqrt{2-b} \sqrt{2-b x} x}{3 b}-\frac{416 \sqrt{2-b} \sqrt{2-b x} x}{3 b^2}+\frac{1792 \sqrt{2-b} \sqrt{2-b x} x}{3 b^3}-\frac{2048 \sqrt{2-b} \sqrt{2-b x} x}{3 b^4}-\frac{1024 x}{3 b}+\frac{4672 x}{3 b^2}-\frac{2560 x}{b^3}+\frac{4096 x}{3 b^4}+16 x-\frac{16 \sqrt{2-b} \sqrt{2-b x} \sqrt{x}}{b}+\frac{992 \sqrt{2-b} \sqrt{2-b x} \sqrt{x}}{3 b^2}-\frac{1280 \sqrt{2-b} \sqrt{2-b x} \sqrt{x}}{b^3}+\frac{4096 \sqrt{2-b} \sqrt{2-b x} \sqrt{x}}{3 b^4}+\frac{800 \sqrt{x}}{b}-\frac{3136 \sqrt{x}}{b^2}+\frac{14848 \sqrt{x}}{3 b^3}-\frac{8192 \sqrt{x}}{3 b^4}-64 \sqrt{x}-\frac{32 \sqrt{2-b} \sqrt{2-b x}}{b}+\frac{448 \sqrt{2-b} \sqrt{2-b x}}{3 b^2}-\frac{512 \sqrt{2-b} \sqrt{2-b x}}{3 b^3}-\frac{128}{b}+\frac{384}{b^2}-\frac{1024}{3 b^3}+\frac{32}{3}\right) \left(\sqrt{2-b}-\sqrt{2-b x}\right)^9}{x^{3/2} \left(\sqrt{x} b^2+x^{3/2} b-2 x b+\sqrt{x} b+\sqrt{2-b} \sqrt{2-b x} b-4 b-4 \sqrt{x}-4 \sqrt{2-b} \sqrt{2-b x}+2 \sqrt{2-b} \sqrt{x} \sqrt{2-b x}+8\right)^3}+\frac{\left(8 b x^{3/2}+\frac{416 x^{3/2}}{b}-\frac{1024 x^{3/2}}{3 b^2}-136 x^{3/2}-24 b x-8 \sqrt{2-b} \sqrt{2-b x} x+\frac{216 \sqrt{2-b} \sqrt{2-b x} x}{b}-\frac{2368 \sqrt{2-b} \sqrt{2-b x} x}{3 b^2}+\frac{2048 \sqrt{2-b} \sqrt{2-b x} x}{3 b^3}-\frac{9424 x}{3 b}+\frac{6016 x}{b^2}-\frac{4096 x}{b^3}+\frac{1864 x}{3}+64 b \sqrt{x}+24 \sqrt{2-b} \sqrt{2-b x} \sqrt{x}-\frac{1256 \sqrt{2-b} \sqrt{2-b x} \sqrt{x}}{3 b}+\frac{1152 \sqrt{2-b} \sqrt{2-b x} \sqrt{x}}{b^2}-\frac{2048 \sqrt{2-b} \sqrt{2-b x} \sqrt{x}}{3 b^3}+\frac{6128 \sqrt{x}}{3 b}-\frac{7936 \sqrt{x}}{3 b^2}+\frac{4096 \sqrt{x}}{3 b^3}-656 \sqrt{x}-16 b+16 \sqrt{2-b} \sqrt{2-b x}+\frac{384 \sqrt{2-b} \sqrt{2-b x}}{b}-\frac{8704 \sqrt{2-b} \sqrt{2-b x}}{3 b^2}+\frac{20480 \sqrt{2-b} \sqrt{2-b x}}{3 b^3}-\frac{16384 \sqrt{2-b} \sqrt{2-b x}}{3 b^4}-\frac{6656}{3 b}+\frac{26624}{3 b^2}-\frac{16384}{b^3}+\frac{32768}{3 b^4}+288\right) \left(\sqrt{2-b}-\sqrt{2-b x}\right)^5}{x \left(\sqrt{x} b^2+x^{3/2} b-2 x b+\sqrt{x} b+\sqrt{2-b} \sqrt{2-b x} b-4 b-4 \sqrt{x}-4 \sqrt{2-b} \sqrt{2-b x}+2 \sqrt{2-b} \sqrt{x} \sqrt{2-b x}+8\right)^2}+\frac{\left(2 \sqrt{x} b^3-2 \sqrt{x} b^2+2 \sqrt{2-b} \sqrt{2-b x} b^2-2 b^2\right) \left(\sqrt{2-b}-\sqrt{2-b x}\right)^3}{\left(\sqrt{x} b+\sqrt{2-b} \sqrt{2-b x}-2\right)^2}+\frac{\left(-\sqrt{x} b-b+\sqrt{x}-2 \sqrt{2-b} \sqrt{2-b x}+3\right) \left(2 b^2 \sqrt{2-b x}-2 \sqrt{2-b} b^2\right)}{\sqrt{x} b+\sqrt{2-b} \sqrt{2-b x}-2}+\frac{\left(\frac{4 \sqrt{2-b}}{3 b^2}-\frac{4 \sqrt{2-b x}}{3 b^2}\right) \left(-9 x^{3/2} b^4+27 x b^4-36 \sqrt{x} b^4+18 b^4+30 x^{3/2} b^3-210 x b^3+114 \sqrt{x} b^3+9 \sqrt{2-b} x \sqrt{2-b x} b^3+18 \sqrt{2-b} \sqrt{2-b x} b^3-27 \sqrt{2-b} \sqrt{x} \sqrt{2-b x} b^3-126 b^3-56 x^{3/2} b^2+800 x b^2-212 \sqrt{x} b^2-60 \sqrt{2-b} x \sqrt{2-b x} b^2-210 \sqrt{2-b} \sqrt{2-b x} b^2+78 \sqrt{2-b} \sqrt{x} \sqrt{2-b x} b^2+812 b^2-864 x b+224 \sqrt{x} b+144 \sqrt{2-b} x \sqrt{2-b x} b+928 \sqrt{2-b} \sqrt{2-b x} b-112 \sqrt{2-b} \sqrt{x} \sqrt{2-b x} b-2432 b-1152 \sqrt{2-b} \sqrt{2-b x}+2304\right)}{\sqrt{x} \left(\sqrt{x} b^2+x^{3/2} b-2 x b+\sqrt{x} b+\sqrt{2-b} \sqrt{2-b x} b-4 b-4 \sqrt{x}-4 \sqrt{2-b} \sqrt{2-b x}+2 \sqrt{2-b} \sqrt{x} \sqrt{2-b x}+8\right)}+20 b^{3/2} \tan ^{-1}\left(\frac{\frac{\sqrt{2-b}}{\sqrt{b}}-\frac{\sqrt{2-b x}}{\sqrt{b}}}{\sqrt{x}-1}\right)","10 b^{3/2} \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)+5 b^2 \sqrt{x} \sqrt{2-b x}-\frac{2 (2-b x)^{5/2}}{3 x^{3/2}}+\frac{10 b (2-b x)^{3/2}}{3 \sqrt{x}}",1,"((3 - b + Sqrt[x] - b*Sqrt[x] - 2*Sqrt[2 - b]*Sqrt[2 - b*x])*(-2*Sqrt[2 - b]*b^2 + 2*b^2*Sqrt[2 - b*x]))/(-2 + b*Sqrt[x] + Sqrt[2 - b]*Sqrt[2 - b*x]) + ((Sqrt[2 - b] - Sqrt[2 - b*x])^3*(-2*b^2 - 2*b^2*Sqrt[x] + 2*b^3*Sqrt[x] + 2*Sqrt[2 - b]*b^2*Sqrt[2 - b*x]))/(-2 + b*Sqrt[x] + Sqrt[2 - b]*Sqrt[2 - b*x])^2 + ((Sqrt[2 - b] - Sqrt[2 - b*x])^9*(32/3 - 1024/(3*b^3) + 384/b^2 - 128/b - 64*Sqrt[x] - (8192*Sqrt[x])/(3*b^4) + (14848*Sqrt[x])/(3*b^3) - (3136*Sqrt[x])/b^2 + (800*Sqrt[x])/b + 16*x + (4096*x)/(3*b^4) - (2560*x)/b^3 + (4672*x)/(3*b^2) - (1024*x)/(3*b) - (16*x^(3/2))/3 + (1024*x^(3/2))/(3*b^3) - (1024*x^(3/2))/(3*b^2) + (96*x^(3/2))/b - (512*Sqrt[2 - b]*Sqrt[2 - b*x])/(3*b^3) + (448*Sqrt[2 - b]*Sqrt[2 - b*x])/(3*b^2) - (32*Sqrt[2 - b]*Sqrt[2 - b*x])/b + (4096*Sqrt[2 - b]*Sqrt[x]*Sqrt[2 - b*x])/(3*b^4) - (1280*Sqrt[2 - b]*Sqrt[x]*Sqrt[2 - b*x])/b^3 + (992*Sqrt[2 - b]*Sqrt[x]*Sqrt[2 - b*x])/(3*b^2) - (16*Sqrt[2 - b]*Sqrt[x]*Sqrt[2 - b*x])/b - (2048*Sqrt[2 - b]*x*Sqrt[2 - b*x])/(3*b^4) + (1792*Sqrt[2 - b]*x*Sqrt[2 - b*x])/(3*b^3) - (416*Sqrt[2 - b]*x*Sqrt[2 - b*x])/(3*b^2) + (16*Sqrt[2 - b]*x*Sqrt[2 - b*x])/(3*b)))/(x^(3/2)*(8 - 4*b - 4*Sqrt[x] + b*Sqrt[x] + b^2*Sqrt[x] - 2*b*x + b*x^(3/2) - 4*Sqrt[2 - b]*Sqrt[2 - b*x] + Sqrt[2 - b]*b*Sqrt[2 - b*x] + 2*Sqrt[2 - b]*Sqrt[x]*Sqrt[2 - b*x])^3) + ((Sqrt[2 - b] - Sqrt[2 - b*x])^5*(288 + 32768/(3*b^4) - 16384/b^3 + 26624/(3*b^2) - 6656/(3*b) - 16*b - 656*Sqrt[x] + (4096*Sqrt[x])/(3*b^3) - (7936*Sqrt[x])/(3*b^2) + (6128*Sqrt[x])/(3*b) + 64*b*Sqrt[x] + (1864*x)/3 - (4096*x)/b^3 + (6016*x)/b^2 - (9424*x)/(3*b) - 24*b*x - 136*x^(3/2) - (1024*x^(3/2))/(3*b^2) + (416*x^(3/2))/b + 8*b*x^(3/2) + 16*Sqrt[2 - b]*Sqrt[2 - b*x] - (16384*Sqrt[2 - b]*Sqrt[2 - b*x])/(3*b^4) + (20480*Sqrt[2 - b]*Sqrt[2 - b*x])/(3*b^3) - (8704*Sqrt[2 - b]*Sqrt[2 - b*x])/(3*b^2) + (384*Sqrt[2 - b]*Sqrt[2 - b*x])/b + 24*Sqrt[2 - b]*Sqrt[x]*Sqrt[2 - b*x] - (2048*Sqrt[2 - b]*Sqrt[x]*Sqrt[2 - b*x])/(3*b^3) + (1152*Sqrt[2 - b]*Sqrt[x]*Sqrt[2 - b*x])/b^2 - (1256*Sqrt[2 - b]*Sqrt[x]*Sqrt[2 - b*x])/(3*b) - 8*Sqrt[2 - b]*x*Sqrt[2 - b*x] + (2048*Sqrt[2 - b]*x*Sqrt[2 - b*x])/(3*b^3) - (2368*Sqrt[2 - b]*x*Sqrt[2 - b*x])/(3*b^2) + (216*Sqrt[2 - b]*x*Sqrt[2 - b*x])/b))/(x*(8 - 4*b - 4*Sqrt[x] + b*Sqrt[x] + b^2*Sqrt[x] - 2*b*x + b*x^(3/2) - 4*Sqrt[2 - b]*Sqrt[2 - b*x] + Sqrt[2 - b]*b*Sqrt[2 - b*x] + 2*Sqrt[2 - b]*Sqrt[x]*Sqrt[2 - b*x])^2) + (((4*Sqrt[2 - b])/(3*b^2) - (4*Sqrt[2 - b*x])/(3*b^2))*(2304 - 2432*b + 812*b^2 - 126*b^3 + 18*b^4 + 224*b*Sqrt[x] - 212*b^2*Sqrt[x] + 114*b^3*Sqrt[x] - 36*b^4*Sqrt[x] - 864*b*x + 800*b^2*x - 210*b^3*x + 27*b^4*x - 56*b^2*x^(3/2) + 30*b^3*x^(3/2) - 9*b^4*x^(3/2) - 1152*Sqrt[2 - b]*Sqrt[2 - b*x] + 928*Sqrt[2 - b]*b*Sqrt[2 - b*x] - 210*Sqrt[2 - b]*b^2*Sqrt[2 - b*x] + 18*Sqrt[2 - b]*b^3*Sqrt[2 - b*x] - 112*Sqrt[2 - b]*b*Sqrt[x]*Sqrt[2 - b*x] + 78*Sqrt[2 - b]*b^2*Sqrt[x]*Sqrt[2 - b*x] - 27*Sqrt[2 - b]*b^3*Sqrt[x]*Sqrt[2 - b*x] + 144*Sqrt[2 - b]*b*x*Sqrt[2 - b*x] - 60*Sqrt[2 - b]*b^2*x*Sqrt[2 - b*x] + 9*Sqrt[2 - b]*b^3*x*Sqrt[2 - b*x]))/(Sqrt[x]*(8 - 4*b - 4*Sqrt[x] + b*Sqrt[x] + b^2*Sqrt[x] - 2*b*x + b*x^(3/2) - 4*Sqrt[2 - b]*Sqrt[2 - b*x] + Sqrt[2 - b]*b*Sqrt[2 - b*x] + 2*Sqrt[2 - b]*Sqrt[x]*Sqrt[2 - b*x])) + 20*b^(3/2)*ArcTan[(Sqrt[2 - b]/Sqrt[b] - Sqrt[2 - b*x]/Sqrt[b])/(-1 + Sqrt[x])]","B",1
569,1,1705,101,2.1346196,"\int \frac{x^{5/2}}{\sqrt{a+b x}} \, dx","IntegrateAlgebraic[x^(5/2)/Sqrt[a + b*x],x]","\frac{5 \tanh ^{-1}\left(\frac{\frac{\sqrt{a+b}}{\sqrt{b}}-\frac{\sqrt{a+b x}}{\sqrt{b}}}{\sqrt{x}-1}\right) a^3}{4 b^{7/2}}+\frac{\left(256 b^8+384 a b^7+144 a^2 b^6+8 a^3 b^5\right) \sqrt{a+b x} x^{11/2}+\left(768 a b^7+960 a^2 b^6+240 a^3 b^5\right) \sqrt{a+b x} x^5+\left(64 a b^7+1152 a^2 b^6+1092 a^3 b^5+134 a^4 b^4\right) \sqrt{a+b x} x^{9/2}+\left(880 a^3 b^5+660 a^4 b^4\right) \sqrt{a+b x} x^4+\left(144 a^2 b^6-48 a^3 b^5+312 a^4 b^4+219 a^5 b^3\right) \sqrt{a+b x} x^{7/2}+\left(18 b^3 a^5+160 b^4 a^4+480 b^5 a^3\right) \sqrt{a+b x} x^3+\left(-256 b^8-192 a b^7-144 a^2 b^6-80 a^3 b^5+1104 a^4 b^4+639 a^5 b^3+46 a^6 b^2\right) \sqrt{a+b x} x^{5/2}+\left(-768 a b^7-384 a^2 b^6-384 a^3 b^5-288 a^4 b^4+1590 a^5 b^3+750 a^6 b^2\right) \sqrt{a+b x} x^2+\left(400 b a^7+1500 b^2 a^6-615 b^3 a^5-896 b^4 a^4-408 b^5 a^3-1248 b^6 a^2-256 b^7 a\right) \sqrt{a+b x} x^{3/2}+\left(960 b a^7-820 b^2 a^6-1386 b^3 a^5-288 b^4 a^4-1168 b^5 a^3-576 b^6 a^2\right) \sqrt{a+b x} x+\left(480 a^8-720 b a^7-1290 b^2 a^6-243 b^3 a^5-654 b^4 a^4-564 b^5 a^3-48 b^6 a^2\right) \sqrt{a+b x} \sqrt{x}+\sqrt{a+b} \left(480 a^8+400 b a^7+46 b^2 a^6+219 b^3 a^5+134 b^4 a^4+8 b^5 a^3+\left(-256 b^8-256 a b^7-48 a^2 b^6\right) x^6+\left(-768 a b^7-576 a^2 b^6-48 a^3 b^5\right) x^{11/2}+\left(-192 a b^7-1248 a^2 b^6-564 a^3 b^5\right) x^5+\left(-384 a^2 b^6-1168 a^3 b^5-244 a^4 b^4\right) x^{9/2}+\left(-144 a^2 b^6-408 a^3 b^5-654 a^4 b^4\right) x^4+\left(-222 b^3 a^5-288 b^4 a^4-384 b^5 a^3\right) x^{7/2}+\left(256 b^8+64 a b^7+144 a^2 b^6-80 a^3 b^5-896 a^4 b^4-243 a^5 b^3\right) x^3+\left(768 a b^7+480 a^3 b^5-288 a^4 b^4-1386 a^5 b^3-186 a^6 b^2\right) x^{5/2}+\left(384 a b^7+1152 a^2 b^6-48 a^3 b^5+1104 a^4 b^4-615 a^5 b^3-1290 a^6 b^2\right) x^2+\left(-640 b a^7-820 b^2 a^6+1590 b^3 a^5+160 b^4 a^4+880 b^5 a^3+960 b^6 a^2\right) x^{3/2}+\left(-720 b a^7+1500 b^2 a^6+639 b^3 a^5+312 b^4 a^4+1092 b^5 a^3+144 b^6 a^2\right) x+\left(-480 a^8+960 b a^7+750 b^2 a^6+18 b^3 a^5+660 b^4 a^4+240 b^5 a^3\right) \sqrt{x}\right)+\left(-480 a^8-640 b a^7-186 b^2 a^6-222 b^3 a^5-244 b^4 a^4-48 b^5 a^3\right) \sqrt{a+b x}}{24 \left(32 b^6+48 a b^5+18 a^2 b^4+a^3 b^3\right) x^3 b^3+24 \left(32 a^6+48 b a^5+18 b^2 a^4+b^3 a^3\right) b^3+24 \sqrt{a+b} \left(-32 a^5-32 b a^4-6 b^2 a^3\right) \sqrt{a+b x} b^3+x \left(24 \left(48 b a^5+204 b^2 a^4+159 b^3 a^3+18 b^4 a^2\right) b^3+24 \sqrt{a+b} \left(-32 b a^4-164 b^2 a^3-72 b^3 a^2\right) \sqrt{a+b x} b^3\right)+\sqrt{x} \left(24 \left(96 b a^5+120 b^2 a^4+30 b^3 a^3\right) b^3+24 \sqrt{a+b} \left(-96 b a^4-72 b^2 a^3-6 b^3 a^2\right) \sqrt{a+b x} b^3\right)+x^2 \left(24 \left(48 a b^5+204 a^2 b^4+159 a^3 b^3+18 a^4 b^2\right) b^3+24 \sqrt{a+b} \left(-96 a b^4-72 a^2 b^3-6 a^3 b^2\right) \sqrt{a+b x} b^3\right)+x^{3/2} \left(24 \left(120 b^2 a^4+260 b^3 a^3+120 b^4 a^2\right) b^3+24 \sqrt{a+b} \left(-32 a b^4-164 a^2 b^3-72 a^3 b^2\right) \sqrt{a+b x} b^3\right)+x^{5/2} \left(24 \left(96 a b^5+120 a^2 b^4+30 a^3 b^3\right) b^3+24 \sqrt{a+b} \left(-32 b^5-32 a b^4-6 a^2 b^3\right) \sqrt{a+b x} b^3\right)}","-\frac{5 a^3 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{8 b^{7/2}}+\frac{5 a^2 \sqrt{x} \sqrt{a+b x}}{8 b^3}-\frac{5 a x^{3/2} \sqrt{a+b x}}{12 b^2}+\frac{x^{5/2} \sqrt{a+b x}}{3 b}",1,"((-480*a^8 - 640*a^7*b - 186*a^6*b^2 - 222*a^5*b^3 - 244*a^4*b^4 - 48*a^3*b^5)*Sqrt[a + b*x] + (480*a^8 - 720*a^7*b - 1290*a^6*b^2 - 243*a^5*b^3 - 654*a^4*b^4 - 564*a^3*b^5 - 48*a^2*b^6)*Sqrt[x]*Sqrt[a + b*x] + (960*a^7*b - 820*a^6*b^2 - 1386*a^5*b^3 - 288*a^4*b^4 - 1168*a^3*b^5 - 576*a^2*b^6)*x*Sqrt[a + b*x] + (400*a^7*b + 1500*a^6*b^2 - 615*a^5*b^3 - 896*a^4*b^4 - 408*a^3*b^5 - 1248*a^2*b^6 - 256*a*b^7)*x^(3/2)*Sqrt[a + b*x] + (750*a^6*b^2 + 1590*a^5*b^3 - 288*a^4*b^4 - 384*a^3*b^5 - 384*a^2*b^6 - 768*a*b^7)*x^2*Sqrt[a + b*x] + (46*a^6*b^2 + 639*a^5*b^3 + 1104*a^4*b^4 - 80*a^3*b^5 - 144*a^2*b^6 - 192*a*b^7 - 256*b^8)*x^(5/2)*Sqrt[a + b*x] + (18*a^5*b^3 + 160*a^4*b^4 + 480*a^3*b^5)*x^3*Sqrt[a + b*x] + (219*a^5*b^3 + 312*a^4*b^4 - 48*a^3*b^5 + 144*a^2*b^6)*x^(7/2)*Sqrt[a + b*x] + (660*a^4*b^4 + 880*a^3*b^5)*x^4*Sqrt[a + b*x] + (134*a^4*b^4 + 1092*a^3*b^5 + 1152*a^2*b^6 + 64*a*b^7)*x^(9/2)*Sqrt[a + b*x] + (240*a^3*b^5 + 960*a^2*b^6 + 768*a*b^7)*x^5*Sqrt[a + b*x] + (8*a^3*b^5 + 144*a^2*b^6 + 384*a*b^7 + 256*b^8)*x^(11/2)*Sqrt[a + b*x] + Sqrt[a + b]*(480*a^8 + 400*a^7*b + 46*a^6*b^2 + 219*a^5*b^3 + 134*a^4*b^4 + 8*a^3*b^5 + (-480*a^8 + 960*a^7*b + 750*a^6*b^2 + 18*a^5*b^3 + 660*a^4*b^4 + 240*a^3*b^5)*Sqrt[x] + (-720*a^7*b + 1500*a^6*b^2 + 639*a^5*b^3 + 312*a^4*b^4 + 1092*a^3*b^5 + 144*a^2*b^6)*x + (-640*a^7*b - 820*a^6*b^2 + 1590*a^5*b^3 + 160*a^4*b^4 + 880*a^3*b^5 + 960*a^2*b^6)*x^(3/2) + (-1290*a^6*b^2 - 615*a^5*b^3 + 1104*a^4*b^4 - 48*a^3*b^5 + 1152*a^2*b^6 + 384*a*b^7)*x^2 + (-186*a^6*b^2 - 1386*a^5*b^3 - 288*a^4*b^4 + 480*a^3*b^5 + 768*a*b^7)*x^(5/2) + (-243*a^5*b^3 - 896*a^4*b^4 - 80*a^3*b^5 + 144*a^2*b^6 + 64*a*b^7 + 256*b^8)*x^3 + (-222*a^5*b^3 - 288*a^4*b^4 - 384*a^3*b^5)*x^(7/2) + (-654*a^4*b^4 - 408*a^3*b^5 - 144*a^2*b^6)*x^4 + (-244*a^4*b^4 - 1168*a^3*b^5 - 384*a^2*b^6)*x^(9/2) + (-564*a^3*b^5 - 1248*a^2*b^6 - 192*a*b^7)*x^5 + (-48*a^3*b^5 - 576*a^2*b^6 - 768*a*b^7)*x^(11/2) + (-48*a^2*b^6 - 256*a*b^7 - 256*b^8)*x^6))/(24*b^3*(32*a^6 + 48*a^5*b + 18*a^4*b^2 + a^3*b^3) + 24*b^3*(a^3*b^3 + 18*a^2*b^4 + 48*a*b^5 + 32*b^6)*x^3 + 24*b^3*Sqrt[a + b]*(-32*a^5 - 32*a^4*b - 6*a^3*b^2)*Sqrt[a + b*x] + x*(24*b^3*(48*a^5*b + 204*a^4*b^2 + 159*a^3*b^3 + 18*a^2*b^4) + 24*b^3*Sqrt[a + b]*(-32*a^4*b - 164*a^3*b^2 - 72*a^2*b^3)*Sqrt[a + b*x]) + Sqrt[x]*(24*b^3*(96*a^5*b + 120*a^4*b^2 + 30*a^3*b^3) + 24*b^3*Sqrt[a + b]*(-96*a^4*b - 72*a^3*b^2 - 6*a^2*b^3)*Sqrt[a + b*x]) + x^2*(24*b^3*(18*a^4*b^2 + 159*a^3*b^3 + 204*a^2*b^4 + 48*a*b^5) + 24*b^3*Sqrt[a + b]*(-6*a^3*b^2 - 72*a^2*b^3 - 96*a*b^4)*Sqrt[a + b*x]) + x^(3/2)*(24*b^3*(120*a^4*b^2 + 260*a^3*b^3 + 120*a^2*b^4) + 24*b^3*Sqrt[a + b]*(-72*a^3*b^2 - 164*a^2*b^3 - 32*a*b^4)*Sqrt[a + b*x]) + x^(5/2)*(24*b^3*(30*a^3*b^3 + 120*a^2*b^4 + 96*a*b^5) + 24*b^3*Sqrt[a + b]*(-6*a^2*b^3 - 32*a*b^4 - 32*b^5)*Sqrt[a + b*x])) + (5*a^3*ArcTanh[(Sqrt[a + b]/Sqrt[b] - Sqrt[a + b*x]/Sqrt[b])/(-1 + Sqrt[x])])/(4*b^(7/2))","B",1
570,1,729,77,0.9276496,"\int \frac{x^{3/2}}{\sqrt{a+b x}} \, dx","IntegrateAlgebraic[x^(3/2)/Sqrt[a + b*x],x]","\frac{\left(\frac{1}{4 b^2}-\frac{\sqrt{x}}{4 b^2}\right) \left(\sqrt{a+b}-\sqrt{a+b x}\right) \left(-12 a^5-7 a^4 b x-22 a^4 b \sqrt{x}+12 a^4 \sqrt{a+b} \sqrt{a+b x}-7 a^4 b-a^3 b^2 x^{3/2}+7 a^3 b^2 x^2-16 a^3 b^2 x-a^3 b^2 \sqrt{x}+7 a^3 b^2+a^3 b x \sqrt{a+b} \sqrt{a+b x}+a^3 b \sqrt{a+b} \sqrt{a+b x}+22 a^3 b \sqrt{x} \sqrt{a+b} \sqrt{a+b x}+18 a^2 b^3 x^{5/2}+12 a^2 b^3 x^{3/2}+2 a^2 b^3 x^3+16 a^2 b^3 x^2+16 a^2 b^3 x+18 a^2 b^3 \sqrt{x}+2 a^2 b^3-10 a^2 b^2 x^{3/2} \sqrt{a+b} \sqrt{a+b x}-6 a^2 b^2 x^2 \sqrt{a+b} \sqrt{a+b x}+12 a^2 b^2 x \sqrt{a+b} \sqrt{a+b x}-6 a^2 b^2 \sqrt{a+b} \sqrt{a+b x}-10 a^2 b^2 \sqrt{x} \sqrt{a+b} \sqrt{a+b x}+24 a b^4 x^{5/2}+24 a b^4 x^{3/2}-16 b^4 x^{5/2} \sqrt{a+b} \sqrt{a+b x}-16 b^4 x^{3/2} \sqrt{a+b} \sqrt{a+b x}+16 a b^4 x^3+16 a b^4 x^2+16 a b^4 x-8 a b^3 x^{5/2} \sqrt{a+b} \sqrt{a+b x}-24 a b^3 x^2 \sqrt{a+b} \sqrt{a+b x}-24 a b^3 x \sqrt{a+b} \sqrt{a+b x}-8 a b^3 \sqrt{x} \sqrt{a+b} \sqrt{a+b x}+16 b^5 x^3+16 b^5 x^2\right)}{\left(\sqrt{a+b} \sqrt{a+b x}-a-b \sqrt{x}\right)^4}-\frac{3 a^2 \tanh ^{-1}\left(\frac{\frac{\sqrt{a+b}}{\sqrt{b}}-\frac{\sqrt{a+b x}}{\sqrt{b}}}{\sqrt{x}-1}\right)}{2 b^{5/2}}","\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,"((1/(4*b^2) - Sqrt[x]/(4*b^2))*(Sqrt[a + b] - Sqrt[a + b*x])*(-12*a^5 - 7*a^4*b + 7*a^3*b^2 + 2*a^2*b^3 - 22*a^4*b*Sqrt[x] - a^3*b^2*Sqrt[x] + 18*a^2*b^3*Sqrt[x] - 7*a^4*b*x - 16*a^3*b^2*x + 16*a^2*b^3*x + 16*a*b^4*x - a^3*b^2*x^(3/2) + 12*a^2*b^3*x^(3/2) + 24*a*b^4*x^(3/2) + 7*a^3*b^2*x^2 + 16*a^2*b^3*x^2 + 16*a*b^4*x^2 + 16*b^5*x^2 + 18*a^2*b^3*x^(5/2) + 24*a*b^4*x^(5/2) + 2*a^2*b^3*x^3 + 16*a*b^4*x^3 + 16*b^5*x^3 + 12*a^4*Sqrt[a + b]*Sqrt[a + b*x] + a^3*b*Sqrt[a + b]*Sqrt[a + b*x] - 6*a^2*b^2*Sqrt[a + b]*Sqrt[a + b*x] + 22*a^3*b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 10*a^2*b^2*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 8*a*b^3*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + a^3*b*Sqrt[a + b]*x*Sqrt[a + b*x] + 12*a^2*b^2*Sqrt[a + b]*x*Sqrt[a + b*x] - 24*a*b^3*Sqrt[a + b]*x*Sqrt[a + b*x] - 10*a^2*b^2*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] - 16*b^4*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] - 6*a^2*b^2*Sqrt[a + b]*x^2*Sqrt[a + b*x] - 24*a*b^3*Sqrt[a + b]*x^2*Sqrt[a + b*x] - 8*a*b^3*Sqrt[a + b]*x^(5/2)*Sqrt[a + b*x] - 16*b^4*Sqrt[a + b]*x^(5/2)*Sqrt[a + b*x]))/(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x])^4 - (3*a^2*ArcTanh[(Sqrt[a + b]/Sqrt[b] - Sqrt[a + b*x]/Sqrt[b])/(-1 + Sqrt[x])])/(2*b^(5/2))","B",1
571,1,183,48,0.3064245,"\int \frac{\sqrt{x}}{\sqrt{a+b x}} \, dx","IntegrateAlgebraic[Sqrt[x]/Sqrt[a + b*x],x]","\frac{\left(\frac{1}{b}-\frac{\sqrt{x}}{b}\right) \left(\sqrt{a+b}-\sqrt{a+b x}\right) \left(a^2+a b x+a b \sqrt{x}-a \sqrt{a+b} \sqrt{a+b x}-2 b \sqrt{x} \sqrt{a+b} \sqrt{a+b x}+a b+2 b^2 x\right)}{\left(\sqrt{a+b} \sqrt{a+b x}-a-b \sqrt{x}\right)^2}+\frac{2 a \tanh ^{-1}\left(\frac{\frac{\sqrt{a+b}}{\sqrt{b}}-\frac{\sqrt{a+b x}}{\sqrt{b}}}{\sqrt{x}-1}\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,"((b^(-1) - Sqrt[x]/b)*(Sqrt[a + b] - Sqrt[a + b*x])*(a^2 + a*b + a*b*Sqrt[x] + a*b*x + 2*b^2*x - a*Sqrt[a + b]*Sqrt[a + b*x] - 2*b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x]))/(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x])^2 + (2*a*ArcTanh[(Sqrt[a + b]/Sqrt[b] - Sqrt[a + b*x]/Sqrt[b])/(-1 + Sqrt[x])])/b^(3/2)","B",1
572,1,48,28,0.1540018,"\int \frac{1}{\sqrt{x} \sqrt{a+b x}} \, dx","IntegrateAlgebraic[1/(Sqrt[x]*Sqrt[a + b*x]),x]","\frac{4 \tanh ^{-1}\left(\frac{\frac{\sqrt{a+b x}}{\sqrt{b}}-\frac{\sqrt{a+b}}{\sqrt{b}}}{\sqrt{x}-1}\right)}{\sqrt{b}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{\sqrt{b}}",1,"(4*ArcTanh[(-(Sqrt[a + b]/Sqrt[b]) + Sqrt[a + b*x]/Sqrt[b])/(-1 + Sqrt[x])])/Sqrt[b]","A",1
573,1,244,19,0.296883,"\int \frac{1}{x^{3/2} \sqrt{a+b x}} \, dx","IntegrateAlgebraic[1/(x^(3/2)*Sqrt[a + b*x]),x]","\frac{\left(\sqrt{x}-1\right) \left(\sqrt{a+b}-\sqrt{a+b x}\right)^4 \left(\frac{b \left(\sqrt{x}-1\right)^2}{\left(\sqrt{a+b}-\sqrt{a+b x}\right)^2}-\frac{2 \left(\sqrt{x}-1\right) \sqrt{a+b}}{\sqrt{a+b}-\sqrt{a+b x}}+1\right)}{\left(\sqrt{a+b x}-\sqrt{a+b}\right) \left(-2 a^2 x+4 a^2 \sqrt{x}+2 a b x^{3/2}-a b x^2-a b x+4 a b \sqrt{x}+2 a x \sqrt{a+b} \sqrt{a+b x}-4 a \sqrt{x} \sqrt{a+b} \sqrt{a+b x}-2 b \sqrt{x} \sqrt{a+b} \sqrt{a+b x}+2 b^2 x\right)}","-\frac{2 \sqrt{a+b x}}{a \sqrt{x}}",1,"((-1 + Sqrt[x])*(Sqrt[a + b] - Sqrt[a + b*x])^4*(1 + (b*(-1 + Sqrt[x])^2)/(Sqrt[a + b] - Sqrt[a + b*x])^2 - (2*Sqrt[a + b]*(-1 + Sqrt[x]))/(Sqrt[a + b] - Sqrt[a + b*x])))/((-Sqrt[a + b] + Sqrt[a + b*x])*(4*a^2*Sqrt[x] + 4*a*b*Sqrt[x] - 2*a^2*x - a*b*x + 2*b^2*x + 2*a*b*x^(3/2) - a*b*x^2 - 4*a*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 2*b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 2*a*Sqrt[a + b]*x*Sqrt[a + b*x]))","B",1
574,1,589,44,5.6112086,"\int \frac{1}{x^{5/2} \sqrt{a+b x}} \, dx","IntegrateAlgebraic[1/(x^(5/2)*Sqrt[a + b*x]),x]","\frac{\left(\frac{\sqrt{x}}{48}-\frac{1}{48}\right) \left(\sqrt{a+b}-\sqrt{a+b x}\right)^{12} \left(-\frac{8 \left(\sqrt{x}-1\right)^5 \sqrt{a+b} \left(4 a^2-2 a b-3 b^2\right)}{\left(\sqrt{a+b}-\sqrt{a+b x}\right)^5}+\frac{3 b^5 \left(\sqrt{x}-1\right)^{10}}{\left(\sqrt{a+b}-\sqrt{a+b x}\right)^{10}}-\frac{12 b^4 \left(\sqrt{x}-1\right)^9 \sqrt{a+b}}{\left(\sqrt{a+b}-\sqrt{a+b x}\right)^9}+\frac{b^3 \left(\sqrt{x}-1\right)^8 (4 a+15 b)}{\left(\sqrt{a+b}-\sqrt{a+b x}\right)^8}+\frac{24 a b^2 \left(\sqrt{x}-1\right)^7 \sqrt{a+b}}{\left(\sqrt{a+b}-\sqrt{a+b x}\right)^7}-\frac{18 b^2 \left(\sqrt{x}-1\right)^6 (2 a+b)}{\left(\sqrt{a+b}-\sqrt{a+b x}\right)^6}-\frac{18 b \left(\sqrt{x}-1\right)^4 (2 a+b)}{\left(\sqrt{a+b}-\sqrt{a+b x}\right)^4}+\frac{24 a \left(\sqrt{x}-1\right)^3 \sqrt{a+b}}{\left(\sqrt{a+b}-\sqrt{a+b x}\right)^3}+\frac{\left(\sqrt{x}-1\right)^2 (4 a+15 b)}{\left(\sqrt{a+b}-\sqrt{a+b x}\right)^2}-\frac{12 \left(\sqrt{x}-1\right) \sqrt{a+b}}{\sqrt{a+b}-\sqrt{a+b x}}+3\right)}{\left(\sqrt{a+b x}-\sqrt{a+b}\right) \left(-2 a^2 x+4 a^2 \sqrt{x}+2 a b x^{3/2}-a b x^2-a b x+4 a b \sqrt{x}+2 a x \sqrt{a+b} \sqrt{a+b x}-4 a \sqrt{x} \sqrt{a+b} \sqrt{a+b x}-2 b \sqrt{x} \sqrt{a+b} \sqrt{a+b x}+2 b^2 x\right)^3}","\frac{4 b \sqrt{a+b x}}{3 a^2 \sqrt{x}}-\frac{2 \sqrt{a+b x}}{3 a x^{3/2}}",1,"((-1/48 + Sqrt[x]/48)*(Sqrt[a + b] - Sqrt[a + b*x])^12*(3 + (3*b^5*(-1 + Sqrt[x])^10)/(Sqrt[a + b] - Sqrt[a + b*x])^10 - (12*b^4*Sqrt[a + b]*(-1 + Sqrt[x])^9)/(Sqrt[a + b] - Sqrt[a + b*x])^9 + (b^3*(4*a + 15*b)*(-1 + Sqrt[x])^8)/(Sqrt[a + b] - Sqrt[a + b*x])^8 + (24*a*b^2*Sqrt[a + b]*(-1 + Sqrt[x])^7)/(Sqrt[a + b] - Sqrt[a + b*x])^7 - (18*b^2*(2*a + b)*(-1 + Sqrt[x])^6)/(Sqrt[a + b] - Sqrt[a + b*x])^6 - (8*Sqrt[a + b]*(4*a^2 - 2*a*b - 3*b^2)*(-1 + Sqrt[x])^5)/(Sqrt[a + b] - Sqrt[a + b*x])^5 - (18*b*(2*a + b)*(-1 + Sqrt[x])^4)/(Sqrt[a + b] - Sqrt[a + b*x])^4 + (24*a*Sqrt[a + b]*(-1 + Sqrt[x])^3)/(Sqrt[a + b] - Sqrt[a + b*x])^3 + ((4*a + 15*b)*(-1 + Sqrt[x])^2)/(Sqrt[a + b] - Sqrt[a + b*x])^2 - (12*Sqrt[a + b]*(-1 + Sqrt[x]))/(Sqrt[a + b] - Sqrt[a + b*x])))/((-Sqrt[a + b] + Sqrt[a + b*x])*(4*a^2*Sqrt[x] + 4*a*b*Sqrt[x] - 2*a^2*x - a*b*x + 2*b^2*x + 2*a*b*x^(3/2) - a*b*x^2 - 4*a*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 2*b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 2*a*Sqrt[a + b]*x*Sqrt[a + b*x])^3)","B",1
575,1,1070,68,62.8801725,"\int \frac{1}{x^{7/2} \sqrt{a+b x}} \, dx","IntegrateAlgebraic[1/(x^(7/2)*Sqrt[a + b*x]),x]","\frac{\left(\frac{\sqrt{x}}{3840}-\frac{1}{3840}\right) \left(\sqrt{a+b}-\sqrt{a+b x}\right)^{20} \left(\frac{15 b^9 \left(\sqrt{x}-1\right)^{18}}{\left(\sqrt{a+b}-\sqrt{a+b x}\right)^{18}}-\frac{90 b^8 \sqrt{a+b} \left(\sqrt{x}-1\right)^{17}}{\left(\sqrt{a+b}-\sqrt{a+b x}\right)^{17}}+\frac{5 b^7 (24 a+43 b) \left(\sqrt{x}-1\right)^{16}}{\left(\sqrt{a+b}-\sqrt{a+b x}\right)^{16}}+\frac{120 (a-2 b) b^6 \sqrt{a+b} \left(\sqrt{x}-1\right)^{15}}{\left(\sqrt{a+b}-\sqrt{a+b x}\right)^{15}}-\frac{4 b^5 \left(-12 a^2+70 b a+5 b^2\right) \left(\sqrt{x}-1\right)^{14}}{\left(\sqrt{a+b}-\sqrt{a+b x}\right)^{14}}+\frac{40 b^4 \sqrt{a+b} \left(-24 a^2+14 b a+17 b^2\right) \left(\sqrt{x}-1\right)^{13}}{\left(\sqrt{a+b}-\sqrt{a+b x}\right)^{13}}-\frac{20 b^4 \left(20 a^2+122 b a+69 b^2\right) \left(\sqrt{x}-1\right)^{12}}{\left(\sqrt{a+b}-\sqrt{a+b x}\right)^{12}}+\frac{40 b^2 \sqrt{a+b} \left(48 a^3+32 b a^2+45 b^2 a+22 b^3\right) \left(\sqrt{x}-1\right)^{11}}{\left(\sqrt{a+b}-\sqrt{a+b x}\right)^{11}}+\frac{10 b^3 \left(240 a^2+260 b a+117 b^2\right) \left(\sqrt{x}-1\right)^{10}}{\left(\sqrt{a+b}-\sqrt{a+b x}\right)^{10}}-\frac{4 \sqrt{a+b} \left(384 a^4+448 b a^3+1184 b^2 a^2+1240 b^3 a+615 b^4\right) \left(\sqrt{x}-1\right)^9}{\left(\sqrt{a+b}-\sqrt{a+b x}\right)^9}+\frac{10 b^2 \left(240 a^2+260 b a+117 b^2\right) \left(\sqrt{x}-1\right)^8}{\left(\sqrt{a+b}-\sqrt{a+b x}\right)^8}+\frac{40 \sqrt{a+b} \left(48 a^3+32 b a^2+45 b^2 a+22 b^3\right) \left(\sqrt{x}-1\right)^7}{\left(\sqrt{a+b}-\sqrt{a+b x}\right)^7}-\frac{20 b \left(20 a^2+122 b a+69 b^2\right) \left(\sqrt{x}-1\right)^6}{\left(\sqrt{a+b}-\sqrt{a+b x}\right)^6}-\frac{40 \sqrt{a+b} \left(24 a^2-14 b a-17 b^2\right) \left(\sqrt{x}-1\right)^5}{\left(\sqrt{a+b}-\sqrt{a+b x}\right)^5}+\frac{4 \left(12 a^2-70 b a-5 b^2\right) \left(\sqrt{x}-1\right)^4}{\left(\sqrt{a+b}-\sqrt{a+b x}\right)^4}+\frac{120 (a-2 b) \sqrt{a+b} \left(\sqrt{x}-1\right)^3}{\left(\sqrt{a+b}-\sqrt{a+b x}\right)^3}+\frac{5 (24 a+43 b) \left(\sqrt{x}-1\right)^2}{\left(\sqrt{a+b}-\sqrt{a+b x}\right)^2}-\frac{90 \sqrt{a+b} \left(\sqrt{x}-1\right)}{\sqrt{a+b}-\sqrt{a+b x}}+15\right)}{\left(\sqrt{a+b x}-\sqrt{a+b}\right) \left(-2 x a^2+4 \sqrt{x} a^2-b x^2 a+2 b x^{3/2} a-b x a+4 b \sqrt{x} a+2 \sqrt{a+b} x \sqrt{a+b x} a-4 \sqrt{a+b} \sqrt{x} \sqrt{a+b x} a+2 b^2 x-2 b \sqrt{a+b} \sqrt{x} \sqrt{a+b x}\right)^5}","-\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,"((-1/3840 + Sqrt[x]/3840)*(Sqrt[a + b] - Sqrt[a + b*x])^20*(15 + (15*b^9*(-1 + Sqrt[x])^18)/(Sqrt[a + b] - Sqrt[a + b*x])^18 - (90*b^8*Sqrt[a + b]*(-1 + Sqrt[x])^17)/(Sqrt[a + b] - Sqrt[a + b*x])^17 + (5*b^7*(24*a + 43*b)*(-1 + Sqrt[x])^16)/(Sqrt[a + b] - Sqrt[a + b*x])^16 + (120*(a - 2*b)*b^6*Sqrt[a + b]*(-1 + Sqrt[x])^15)/(Sqrt[a + b] - Sqrt[a + b*x])^15 - (4*b^5*(-12*a^2 + 70*a*b + 5*b^2)*(-1 + Sqrt[x])^14)/(Sqrt[a + b] - Sqrt[a + b*x])^14 + (40*b^4*Sqrt[a + b]*(-24*a^2 + 14*a*b + 17*b^2)*(-1 + Sqrt[x])^13)/(Sqrt[a + b] - Sqrt[a + b*x])^13 - (20*b^4*(20*a^2 + 122*a*b + 69*b^2)*(-1 + Sqrt[x])^12)/(Sqrt[a + b] - Sqrt[a + b*x])^12 + (40*b^2*Sqrt[a + b]*(48*a^3 + 32*a^2*b + 45*a*b^2 + 22*b^3)*(-1 + Sqrt[x])^11)/(Sqrt[a + b] - Sqrt[a + b*x])^11 + (10*b^3*(240*a^2 + 260*a*b + 117*b^2)*(-1 + Sqrt[x])^10)/(Sqrt[a + b] - Sqrt[a + b*x])^10 - (4*Sqrt[a + b]*(384*a^4 + 448*a^3*b + 1184*a^2*b^2 + 1240*a*b^3 + 615*b^4)*(-1 + Sqrt[x])^9)/(Sqrt[a + b] - Sqrt[a + b*x])^9 + (10*b^2*(240*a^2 + 260*a*b + 117*b^2)*(-1 + Sqrt[x])^8)/(Sqrt[a + b] - Sqrt[a + b*x])^8 + (40*Sqrt[a + b]*(48*a^3 + 32*a^2*b + 45*a*b^2 + 22*b^3)*(-1 + Sqrt[x])^7)/(Sqrt[a + b] - Sqrt[a + b*x])^7 - (20*b*(20*a^2 + 122*a*b + 69*b^2)*(-1 + Sqrt[x])^6)/(Sqrt[a + b] - Sqrt[a + b*x])^6 - (40*Sqrt[a + b]*(24*a^2 - 14*a*b - 17*b^2)*(-1 + Sqrt[x])^5)/(Sqrt[a + b] - Sqrt[a + b*x])^5 + (4*(12*a^2 - 70*a*b - 5*b^2)*(-1 + Sqrt[x])^4)/(Sqrt[a + b] - Sqrt[a + b*x])^4 + (120*(a - 2*b)*Sqrt[a + b]*(-1 + Sqrt[x])^3)/(Sqrt[a + b] - Sqrt[a + b*x])^3 + (5*(24*a + 43*b)*(-1 + Sqrt[x])^2)/(Sqrt[a + b] - Sqrt[a + b*x])^2 - (90*Sqrt[a + b]*(-1 + Sqrt[x]))/(Sqrt[a + b] - Sqrt[a + b*x])))/((-Sqrt[a + b] + Sqrt[a + b*x])*(4*a^2*Sqrt[x] + 4*a*b*Sqrt[x] - 2*a^2*x - a*b*x + 2*b^2*x + 2*a*b*x^(3/2) - a*b*x^2 - 4*a*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 2*b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 2*a*Sqrt[a + b]*x*Sqrt[a + b*x])^5)","B",0
576,-1,0,92,180.0902657,"\int \frac{1}{x^{9/2} \sqrt{a+b x}} \, dx","IntegrateAlgebraic[1/(x^(9/2)*Sqrt[a + b*x]),x]","\text{\$Aborted}","\frac{32 b^3 \sqrt{a+b x}}{35 a^4 \sqrt{x}}-\frac{16 b^2 \sqrt{a+b x}}{35 a^3 x^{3/2}}+\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,"$Aborted","F",-1
577,1,994,96,3.6133061,"\int \frac{x^{5/2}}{(a+b x)^{3/2}} \, dx","IntegrateAlgebraic[x^(5/2)/(a + b*x)^(3/2),x]","\frac{\left(-\frac{\sqrt{x} a^2}{2 b^3}-\frac{3 a^2}{2 b^3}-\frac{4 \sqrt{x} a}{b^2}+\frac{2 \sqrt{a+b} \sqrt{a+b x} a}{b^3}-\frac{2 a}{b^2}-\frac{4 \sqrt{x}}{b}+\frac{4 \sqrt{a+b} \sqrt{a+b x}}{b^2}\right) \left(\sqrt{a+b}-\sqrt{a+b x}\right)^7}{\left(-a-b \sqrt{x}+\sqrt{a+b} \sqrt{a+b x}\right)^4}+\frac{\left(-\frac{3 \sqrt{x} a^2}{2 b^3}-\frac{13 a^2}{2 b^3}-\frac{12 \sqrt{x} a}{b^2}+\frac{8 \sqrt{a+b} \sqrt{a+b x} a}{b^3}-\frac{12 a}{b^2}-\frac{12 \sqrt{x}}{b}+\frac{16 \sqrt{a+b} \sqrt{a+b x}}{b^2}-\frac{4}{b}\right) \left(\sqrt{a+b}-\sqrt{a+b x}\right)^5}{\left(-a-b \sqrt{x}+\sqrt{a+b} \sqrt{a+b x}\right)^3}+\frac{\left(\frac{3 \sqrt{x} a^2}{4 b^3}-\frac{27 a^2}{4 b^3}-\frac{6 \sqrt{x} a}{b^2}+\frac{6 \sqrt{a+b} \sqrt{a+b x} a}{b^3}-\frac{20 a}{b^2}-\frac{10 \sqrt{x}}{b}+\frac{20 \sqrt{a+b} \sqrt{a+b x}}{b^2}-\frac{10}{b}\right) \left(\sqrt{a+b}-\sqrt{a+b x}\right)^3}{\left(-a-b \sqrt{x}+\sqrt{a+b} \sqrt{a+b x}\right)^2}+\frac{\left(\frac{2 a^3}{b^3 (a+b)}-\frac{2 a^3 \sqrt{x}}{b^3 (a+b)}\right) \left(a^2+3 b a+b x a-2 b \sqrt{x} a-\sqrt{a+b} \sqrt{a+b x} a+2 b^2+b^2 x-2 b^2 \sqrt{x}-2 b \sqrt{a+b} \sqrt{a+b x}+b \sqrt{a+b} \sqrt{x} \sqrt{a+b x}\right) \left(\sqrt{a+b}-\sqrt{a+b x}\right)}{-2 a^3-5 b a^2-3 b x a^2+2 b \sqrt{x} a^2+2 \sqrt{a+b} \sqrt{a+b x} a^2-2 b^2 a-b^2 x^2 a+2 b^2 x^{3/2} a-5 b^2 x a+2 b \sqrt{a+b} x \sqrt{a+b x} a+4 b \sqrt{a+b} \sqrt{a+b x} a-2 b \sqrt{a+b} \sqrt{x} \sqrt{a+b x} a-2 b^3 x+2 b^2 \sqrt{a+b} \sqrt{x} \sqrt{a+b x}}+\frac{\left(\frac{\sqrt{a+b}}{4 b^3}-\frac{\sqrt{a+b x}}{4 b^3}\right) \left(7 \sqrt{x} a^2+9 a^2-24 b a+8 b \sqrt{x} a-16 \sqrt{a+b} \sqrt{a+b x} a-24 b^2-8 b^2 \sqrt{x}+32 b \sqrt{a+b} \sqrt{a+b x}\right)}{-a-b \sqrt{x}+\sqrt{a+b} \sqrt{a+b x}}-\frac{15 a^2 \tanh ^{-1}\left(\frac{\frac{\sqrt{a+b}}{\sqrt{b}}-\frac{\sqrt{a+b x}}{\sqrt{b}}}{\sqrt{x}-1}\right)}{2 b^{7/2}}","\frac{15 a^2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{4 b^{7/2}}-\frac{15 a \sqrt{x} \sqrt{a+b x}}{4 b^3}+\frac{5 x^{3/2} \sqrt{a+b x}}{2 b^2}-\frac{2 x^{5/2}}{b \sqrt{a+b x}}",1,"((Sqrt[a + b] - Sqrt[a + b*x])^7*((-3*a^2)/(2*b^3) - (2*a)/b^2 - (a^2*Sqrt[x])/(2*b^3) - (4*a*Sqrt[x])/b^2 - (4*Sqrt[x])/b + (2*a*Sqrt[a + b]*Sqrt[a + b*x])/b^3 + (4*Sqrt[a + b]*Sqrt[a + b*x])/b^2))/(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x])^4 + ((Sqrt[a + b] - Sqrt[a + b*x])^5*((-13*a^2)/(2*b^3) - (12*a)/b^2 - 4/b - (3*a^2*Sqrt[x])/(2*b^3) - (12*a*Sqrt[x])/b^2 - (12*Sqrt[x])/b + (8*a*Sqrt[a + b]*Sqrt[a + b*x])/b^3 + (16*Sqrt[a + b]*Sqrt[a + b*x])/b^2))/(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x])^3 + ((Sqrt[a + b] - Sqrt[a + b*x])^3*((-27*a^2)/(4*b^3) - (20*a)/b^2 - 10/b + (3*a^2*Sqrt[x])/(4*b^3) - (6*a*Sqrt[x])/b^2 - (10*Sqrt[x])/b + (6*a*Sqrt[a + b]*Sqrt[a + b*x])/b^3 + (20*Sqrt[a + b]*Sqrt[a + b*x])/b^2))/(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x])^2 + ((Sqrt[a + b]/(4*b^3) - Sqrt[a + b*x]/(4*b^3))*(9*a^2 - 24*a*b - 24*b^2 + 7*a^2*Sqrt[x] + 8*a*b*Sqrt[x] - 8*b^2*Sqrt[x] - 16*a*Sqrt[a + b]*Sqrt[a + b*x] + 32*b*Sqrt[a + b]*Sqrt[a + b*x]))/(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x]) + (((2*a^3)/(b^3*(a + b)) - (2*a^3*Sqrt[x])/(b^3*(a + b)))*(Sqrt[a + b] - Sqrt[a + b*x])*(a^2 + 3*a*b + 2*b^2 - 2*a*b*Sqrt[x] - 2*b^2*Sqrt[x] + a*b*x + b^2*x - a*Sqrt[a + b]*Sqrt[a + b*x] - 2*b*Sqrt[a + b]*Sqrt[a + b*x] + b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x]))/(-2*a^3 - 5*a^2*b - 2*a*b^2 + 2*a^2*b*Sqrt[x] - 3*a^2*b*x - 5*a*b^2*x - 2*b^3*x + 2*a*b^2*x^(3/2) - a*b^2*x^2 + 2*a^2*Sqrt[a + b]*Sqrt[a + b*x] + 4*a*b*Sqrt[a + b]*Sqrt[a + b*x] - 2*a*b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 2*b^2*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 2*a*b*Sqrt[a + b]*x*Sqrt[a + b*x]) - (15*a^2*ArcTanh[(Sqrt[a + b]/Sqrt[b] - Sqrt[a + b*x]/Sqrt[b])/(-1 + Sqrt[x])])/(2*b^(7/2))","B",1
578,1,589,68,1.4945027,"\int \frac{x^{3/2}}{(a+b x)^{3/2}} \, dx","IntegrateAlgebraic[x^(3/2)/(a + b*x)^(3/2),x]","\frac{\left(\frac{2 a^2 \sqrt{x}}{b^2 (a+b)}-\frac{2 a^2}{b^2 (a+b)}\right) \left(a^2+a b x-2 a b \sqrt{x}-a \sqrt{a+b} \sqrt{a+b x}-2 b \sqrt{a+b} \sqrt{a+b x}+b \sqrt{x} \sqrt{a+b} \sqrt{a+b x}+3 a b+b^2 x-2 b^2 \sqrt{x}+2 b^2\right) \left(\sqrt{a+b}-\sqrt{a+b x}\right)}{-2 a^3-3 a^2 b x+2 a^2 b \sqrt{x}+2 a^2 \sqrt{a+b} \sqrt{a+b x}-5 a^2 b+2 a b^2 x^{3/2}-a b^2 x^2-5 a b^2 x+2 b^2 \sqrt{x} \sqrt{a+b} \sqrt{a+b x}-2 a b^2+2 a b x \sqrt{a+b} \sqrt{a+b x}+4 a b \sqrt{a+b} \sqrt{a+b x}-2 a b \sqrt{x} \sqrt{a+b} \sqrt{a+b x}-2 b^3 x}+\frac{6 a \tanh ^{-1}\left(\frac{\frac{\sqrt{a+b}}{\sqrt{b}}-\frac{\sqrt{a+b x}}{\sqrt{b}}}{\sqrt{x}-1}\right)}{b^{5/2}}+\frac{\left(-\frac{a \sqrt{x}}{b^2}+\frac{2 \sqrt{a+b} \sqrt{a+b x}}{b^2}-\frac{a}{b^2}-\frac{2 \sqrt{x}}{b}\right) \left(\sqrt{a+b}-\sqrt{a+b x}\right)^3}{\left(\sqrt{a+b} \sqrt{a+b x}-a-b \sqrt{x}\right)^2}+\frac{\left(\frac{\sqrt{a+b}}{b^2}-\frac{\sqrt{a+b x}}{b^2}\right) \left(4 \sqrt{a+b} \sqrt{a+b x}+a \left(-\sqrt{x}\right)-3 a-2 b \sqrt{x}-2 b\right)}{\sqrt{a+b} \sqrt{a+b x}-a-b \sqrt{x}}","-\frac{3 a \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{b^{5/2}}+\frac{3 \sqrt{x} \sqrt{a+b x}}{b^2}-\frac{2 x^{3/2}}{b \sqrt{a+b x}}",1,"((Sqrt[a + b]/b^2 - Sqrt[a + b*x]/b^2)*(-3*a - 2*b - a*Sqrt[x] - 2*b*Sqrt[x] + 4*Sqrt[a + b]*Sqrt[a + b*x]))/(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x]) + ((Sqrt[a + b] - Sqrt[a + b*x])^3*(-(a/b^2) - (a*Sqrt[x])/b^2 - (2*Sqrt[x])/b + (2*Sqrt[a + b]*Sqrt[a + b*x])/b^2))/(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x])^2 + (((-2*a^2)/(b^2*(a + b)) + (2*a^2*Sqrt[x])/(b^2*(a + b)))*(Sqrt[a + b] - Sqrt[a + b*x])*(a^2 + 3*a*b + 2*b^2 - 2*a*b*Sqrt[x] - 2*b^2*Sqrt[x] + a*b*x + b^2*x - a*Sqrt[a + b]*Sqrt[a + b*x] - 2*b*Sqrt[a + b]*Sqrt[a + b*x] + b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x]))/(-2*a^3 - 5*a^2*b - 2*a*b^2 + 2*a^2*b*Sqrt[x] - 3*a^2*b*x - 5*a*b^2*x - 2*b^3*x + 2*a*b^2*x^(3/2) - a*b^2*x^2 + 2*a^2*Sqrt[a + b]*Sqrt[a + b*x] + 4*a*b*Sqrt[a + b]*Sqrt[a + b*x] - 2*a*b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 2*b^2*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 2*a*b*Sqrt[a + b]*x*Sqrt[a + b*x]) + (6*a*ArcTanh[(Sqrt[a + b]/Sqrt[b] - Sqrt[a + b*x]/Sqrt[b])/(-1 + Sqrt[x])])/b^(5/2)","B",1
579,1,383,48,0.5483506,"\int \frac{\sqrt{x}}{(a+b x)^{3/2}} \, dx","IntegrateAlgebraic[Sqrt[x]/(a + b*x)^(3/2),x]","\frac{\left(\frac{2 a}{b (a+b)}-\frac{2 a \sqrt{x}}{b (a+b)}\right) \left(\sqrt{a+b}-\sqrt{a+b x}\right) \left(a^2+a b x-2 a b \sqrt{x}-a \sqrt{a+b} \sqrt{a+b x}-2 b \sqrt{a+b} \sqrt{a+b x}+b \sqrt{x} \sqrt{a+b} \sqrt{a+b x}+3 a b+b^2 x-2 b^2 \sqrt{x}+2 b^2\right)}{-2 a^3-3 a^2 b x+2 a^2 b \sqrt{x}+2 a^2 \sqrt{a+b} \sqrt{a+b x}-5 a^2 b+2 a b^2 x^{3/2}-a b^2 x^2-5 a b^2 x+2 b^2 \sqrt{x} \sqrt{a+b} \sqrt{a+b x}-2 a b^2+2 a b x \sqrt{a+b} \sqrt{a+b x}+4 a b \sqrt{a+b} \sqrt{a+b x}-2 a b \sqrt{x} \sqrt{a+b} \sqrt{a+b x}-2 b^3 x}-\frac{4 \tanh ^{-1}\left(\frac{\frac{\sqrt{a+b}}{\sqrt{b}}-\frac{\sqrt{a+b x}}{\sqrt{b}}}{\sqrt{x}-1}\right)}{b^{3/2}}","\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*a)/(b*(a + b)) - (2*a*Sqrt[x])/(b*(a + b)))*(Sqrt[a + b] - Sqrt[a + b*x])*(a^2 + 3*a*b + 2*b^2 - 2*a*b*Sqrt[x] - 2*b^2*Sqrt[x] + a*b*x + b^2*x - a*Sqrt[a + b]*Sqrt[a + b*x] - 2*b*Sqrt[a + b]*Sqrt[a + b*x] + b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x]))/(-2*a^3 - 5*a^2*b - 2*a*b^2 + 2*a^2*b*Sqrt[x] - 3*a^2*b*x - 5*a*b^2*x - 2*b^3*x + 2*a*b^2*x^(3/2) - a*b^2*x^2 + 2*a^2*Sqrt[a + b]*Sqrt[a + b*x] + 4*a*b*Sqrt[a + b]*Sqrt[a + b*x] - 2*a*b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 2*b^2*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 2*a*b*Sqrt[a + b]*x*Sqrt[a + b*x]) - (4*ArcTanh[(Sqrt[a + b]/Sqrt[b] - Sqrt[a + b*x]/Sqrt[b])/(-1 + Sqrt[x])])/b^(3/2)","B",1
580,1,370,19,0.3784252,"\int \frac{1}{\sqrt{x} (a+b x)^{3/2}} \, dx","IntegrateAlgebraic[1/(Sqrt[x]*(a + b*x)^(3/2)),x]","\frac{\left(\frac{1}{a+b}-\frac{\sqrt{x}}{a+b}\right) \left(\sqrt{a+b}-\sqrt{a+b x}\right)^4 \left(\frac{a b \left(\sqrt{x}-1\right)^2}{\left(\sqrt{a+b}-\sqrt{a+b x}\right)^2}+\frac{2 b \left(-2 \sqrt{a+b} \sqrt{a+b x}+\sqrt{x} \sqrt{a+b} \sqrt{a+b x}+a \left(-\sqrt{x}\right)+2 a+b x-2 b \sqrt{x}+2 b\right)}{\left(\sqrt{a+b}-\sqrt{a+b x}\right)^2}+a\right)}{\left(\sqrt{a+b x}-\sqrt{a+b}\right) \left(-2 a^3-3 a^2 b x+2 a^2 b \sqrt{x}+2 a^2 \sqrt{a+b} \sqrt{a+b x}-5 a^2 b+2 a b^2 x^{3/2}-a b^2 x^2-5 a b^2 x+2 b^2 \sqrt{x} \sqrt{a+b} \sqrt{a+b x}-2 a b^2+2 a b x \sqrt{a+b} \sqrt{a+b x}+4 a b \sqrt{a+b} \sqrt{a+b x}-2 a b \sqrt{x} \sqrt{a+b} \sqrt{a+b x}-2 b^3 x\right)}","\frac{2 \sqrt{x}}{a \sqrt{a+b x}}",1,"(((a + b)^(-1) - Sqrt[x]/(a + b))*(Sqrt[a + b] - Sqrt[a + b*x])^4*(a + (a*b*(-1 + Sqrt[x])^2)/(Sqrt[a + b] - Sqrt[a + b*x])^2 + (2*b*(2*a + 2*b - a*Sqrt[x] - 2*b*Sqrt[x] + b*x - 2*Sqrt[a + b]*Sqrt[a + b*x] + Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x]))/(Sqrt[a + b] - Sqrt[a + b*x])^2))/((-Sqrt[a + b] + Sqrt[a + b*x])*(-2*a^3 - 5*a^2*b - 2*a*b^2 + 2*a^2*b*Sqrt[x] - 3*a^2*b*x - 5*a*b^2*x - 2*b^3*x + 2*a*b^2*x^(3/2) - a*b^2*x^2 + 2*a^2*Sqrt[a + b]*Sqrt[a + b*x] + 4*a*b*Sqrt[a + b]*Sqrt[a + b*x] - 2*a*b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 2*b^2*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 2*a*b*Sqrt[a + b]*x*Sqrt[a + b*x]))","B",1
581,1,1248,39,4.630488,"\int \frac{1}{x^{3/2} (a+b x)^{3/2}} \, dx","IntegrateAlgebraic[1/(x^(3/2)*(a + b*x)^(3/2)),x]","\frac{\left(\frac{\sqrt{x}}{4 (a+b)}-\frac{1}{4 (a+b)}\right) \left(\sqrt{a+b}-\sqrt{a+b x}\right)^8 \left(\frac{b \left(\sqrt{x}-1\right)^2}{\left(\sqrt{a+b}-\sqrt{a+b x}\right)^2}+1\right) \left(\frac{4 a \left(-2 \sqrt{x} a^2+4 a^2-2 b x^{3/2} a+8 b a+8 b x a-10 b \sqrt{x} a-4 \sqrt{a+b} \sqrt{a+b x} a+2 \sqrt{a+b} \sqrt{x} \sqrt{a+b x} a+3 b^2+2 b^2 x^2-6 b^2 x^{3/2}+9 b^2 x-6 b^2 \sqrt{x}+b \sqrt{a+b} x^{3/2} \sqrt{a+b x}-6 b \sqrt{a+b} x \sqrt{a+b x}-6 b \sqrt{a+b} \sqrt{a+b x}+9 b \sqrt{a+b} \sqrt{x} \sqrt{a+b x}\right)}{\left(\sqrt{a+b}-\sqrt{a+b x}\right)^4}+\frac{4 b \left(-4 \sqrt{x} a^2+6 a^2-4 b x^{3/2} a+11 b a+11 b x a-14 b \sqrt{x} a-6 \sqrt{a+b} \sqrt{a+b x} a+4 \sqrt{a+b} \sqrt{x} \sqrt{a+b x} a+4 b^2+2 b^2 x^2-8 b^2 x^{3/2}+12 b^2 x-8 b^2 \sqrt{x}+2 b \sqrt{a+b} x^{3/2} \sqrt{a+b x}-8 b \sqrt{a+b} x \sqrt{a+b x}-8 b \sqrt{a+b} \sqrt{a+b x}+12 b \sqrt{a+b} \sqrt{x} \sqrt{a+b x}\right)}{\left(\sqrt{a+b}-\sqrt{a+b x}\right)^4}\right)}{\left(\sqrt{a+b x}-\sqrt{a+b}\right) \left(-8 x a^5+16 \sqrt{x} a^5-16 b x^2 a^4+40 b x^{3/2} a^4-40 b x a^4+56 b \sqrt{x} a^4+8 \sqrt{a+b} x \sqrt{a+b x} a^4-16 \sqrt{a+b} \sqrt{x} \sqrt{a+b x} a^4-9 b^2 x^3 a^3+28 b^2 x^{5/2} a^3-54 b^2 x^2 a^3+84 b^2 x^{3/2} a^3-25 b^2 x a^3+56 b^2 \sqrt{x} a^3+12 b \sqrt{a+b} x^2 \sqrt{a+b x} a^3-32 b \sqrt{a+b} x^{3/2} \sqrt{a+b x} a^3+36 b \sqrt{a+b} x \sqrt{a+b x} a^3-48 b \sqrt{a+b} \sqrt{x} \sqrt{a+b x} a^3-b^3 x^4 a^2+4 b^3 x^{7/2} a^2-14 b^3 x^3 a^2+28 b^3 x^{5/2} a^2-25 b^3 x^2 a^2+56 b^3 x^{3/2} a^2+16 b^3 x a^2+16 b^3 \sqrt{x} a^2+4 b^2 \sqrt{a+b} x^3 \sqrt{a+b x} a^2-14 b^2 \sqrt{a+b} x^{5/2} \sqrt{a+b x} a^2+28 b^2 \sqrt{a+b} x^2 \sqrt{a+b x} a^2-40 b^2 \sqrt{a+b} x^{3/2} \sqrt{a+b x} a^2+8 b^2 \sqrt{a+b} x \sqrt{a+b x} a^2-34 b^2 \sqrt{a+b} \sqrt{x} \sqrt{a+b x} a^2+16 b^4 x^2 a+16 b^4 x^{3/2} a+8 b^4 x a-12 b^3 \sqrt{a+b} x^{3/2} \sqrt{a+b x} a-16 b^3 \sqrt{a+b} x \sqrt{a+b x} a-4 b^3 \sqrt{a+b} \sqrt{x} \sqrt{a+b x} a+8 b^5 x^2-8 b^4 \sqrt{a+b} x^{3/2} \sqrt{a+b x}\right)}","\frac{2}{a \sqrt{x} \sqrt{a+b x}}-\frac{4 \sqrt{a+b x}}{a^2 \sqrt{x}}",1,"((-1/4*1/(a + b) + Sqrt[x]/(4*(a + b)))*(Sqrt[a + b] - Sqrt[a + b*x])^8*(1 + (b*(-1 + Sqrt[x])^2)/(Sqrt[a + b] - Sqrt[a + b*x])^2)*((4*a*(4*a^2 + 8*a*b + 3*b^2 - 2*a^2*Sqrt[x] - 10*a*b*Sqrt[x] - 6*b^2*Sqrt[x] + 8*a*b*x + 9*b^2*x - 2*a*b*x^(3/2) - 6*b^2*x^(3/2) + 2*b^2*x^2 - 4*a*Sqrt[a + b]*Sqrt[a + b*x] - 6*b*Sqrt[a + b]*Sqrt[a + b*x] + 2*a*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 9*b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 6*b*Sqrt[a + b]*x*Sqrt[a + b*x] + b*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x]))/(Sqrt[a + b] - Sqrt[a + b*x])^4 + (4*b*(6*a^2 + 11*a*b + 4*b^2 - 4*a^2*Sqrt[x] - 14*a*b*Sqrt[x] - 8*b^2*Sqrt[x] + 11*a*b*x + 12*b^2*x - 4*a*b*x^(3/2) - 8*b^2*x^(3/2) + 2*b^2*x^2 - 6*a*Sqrt[a + b]*Sqrt[a + b*x] - 8*b*Sqrt[a + b]*Sqrt[a + b*x] + 4*a*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 12*b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 8*b*Sqrt[a + b]*x*Sqrt[a + b*x] + 2*b*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x]))/(Sqrt[a + b] - Sqrt[a + b*x])^4))/((-Sqrt[a + b] + Sqrt[a + b*x])*(16*a^5*Sqrt[x] + 56*a^4*b*Sqrt[x] + 56*a^3*b^2*Sqrt[x] + 16*a^2*b^3*Sqrt[x] - 8*a^5*x - 40*a^4*b*x - 25*a^3*b^2*x + 16*a^2*b^3*x + 8*a*b^4*x + 40*a^4*b*x^(3/2) + 84*a^3*b^2*x^(3/2) + 56*a^2*b^3*x^(3/2) + 16*a*b^4*x^(3/2) - 16*a^4*b*x^2 - 54*a^3*b^2*x^2 - 25*a^2*b^3*x^2 + 16*a*b^4*x^2 + 8*b^5*x^2 + 28*a^3*b^2*x^(5/2) + 28*a^2*b^3*x^(5/2) - 9*a^3*b^2*x^3 - 14*a^2*b^3*x^3 + 4*a^2*b^3*x^(7/2) - a^2*b^3*x^4 - 16*a^4*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 48*a^3*b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 34*a^2*b^2*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 4*a*b^3*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 8*a^4*Sqrt[a + b]*x*Sqrt[a + b*x] + 36*a^3*b*Sqrt[a + b]*x*Sqrt[a + b*x] + 8*a^2*b^2*Sqrt[a + b]*x*Sqrt[a + b*x] - 16*a*b^3*Sqrt[a + b]*x*Sqrt[a + b*x] - 32*a^3*b*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] - 40*a^2*b^2*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] - 12*a*b^3*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] - 8*b^4*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] + 12*a^3*b*Sqrt[a + b]*x^2*Sqrt[a + b*x] + 28*a^2*b^2*Sqrt[a + b]*x^2*Sqrt[a + b*x] - 14*a^2*b^2*Sqrt[a + b]*x^(5/2)*Sqrt[a + b*x] + 4*a^2*b^2*Sqrt[a + b]*x^3*Sqrt[a + b*x]))","B",1
582,1,4495,63,48.3249429,"\int \frac{1}{x^{5/2} (a+b x)^{3/2}} \, dx","IntegrateAlgebraic[1/(x^(5/2)*(a + b*x)^(3/2)),x]","\text{Result too large to show}","\frac{16 b \sqrt{a+b x}}{3 a^3 \sqrt{x}}-\frac{8 \sqrt{a+b x}}{3 a^2 x^{3/2}}+\frac{2}{a x^{3/2} \sqrt{a+b x}}",1,"((1/(192*(a + b)) - Sqrt[x]/(192*(a + b)))*(Sqrt[a + b] - Sqrt[a + b*x])^16*((-128*a^3*Sqrt[a + b]*(-1 + Sqrt[x])^5*(-a - b + b*Sqrt[x] - b*x + Sqrt[a + b]*Sqrt[a + b*x])^2)/(Sqrt[a + b] - Sqrt[a + b*x])^9 - (128*b*(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x])^2*(-6*a^2 - 11*a*b - 4*b^2 + 10*a*b*Sqrt[x] + 8*b^2*Sqrt[x] - 11*a*b*x - 14*b^2*x + 8*b^2*x^(3/2) - 4*b^2*x^2 + 6*a*Sqrt[a + b]*Sqrt[a + b*x] + 8*b*Sqrt[a + b]*Sqrt[a + b*x] - 10*b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 8*b*Sqrt[a + b]*x*Sqrt[a + b*x])*(16*a^3 + 52*a^2*b + 44*a*b^2 + 8*b^3 - 12*a^3*Sqrt[x] - 81*a^2*b*Sqrt[x] - 96*a*b^2*Sqrt[x] - 24*b^3*Sqrt[x] + 66*a^2*b*x + 135*a*b^2*x + 60*b^3*x - 25*a^2*b*x^(3/2) - 110*a*b^2*x^(3/2) - 80*b^3*x^(3/2) + 51*a*b^2*x^2 + 60*b^3*x^2 - 12*a*b^2*x^(5/2) - 24*b^3*x^(5/2) + 4*b^3*x^3 - 16*a^2*Sqrt[a + b]*Sqrt[a + b*x] - 44*a*b*Sqrt[a + b]*Sqrt[a + b*x] - 24*b^2*Sqrt[a + b]*Sqrt[a + b*x] + 12*a^2*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 75*a*b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 60*b^2*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 58*a*b*Sqrt[a + b]*x*Sqrt[a + b*x] - 80*b^2*Sqrt[a + b]*x*Sqrt[a + b*x] + 19*a*b*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] + 60*b^2*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] - 24*b^2*Sqrt[a + b]*x^2*Sqrt[a + b*x] + 4*b^2*Sqrt[a + b]*x^(5/2)*Sqrt[a + b*x]))/(Sqrt[a + b] - Sqrt[a + b*x])^14 - (128*a^2*(-1 + Sqrt[x])^2*(32*a^5 + 216*a^4*b + 498*a^3*b^2 + 468*a^2*b^3 + 166*a*b^4 + 12*b^5 - 48*a^5*Sqrt[x] - 428*a^4*b*Sqrt[x] - 1367*a^3*b^2*Sqrt[x] - 1620*a^2*b^3*Sqrt[x] - 690*a*b^4*Sqrt[x] - 60*b^5*Sqrt[x] + 288*a^4*b*x + 1892*a^3*b^2*x + 3193*a^2*b^3*x + 1842*a*b^4*x + 268*b^5*x - 156*a^4*b*x^(3/2) - 1714*a^3*b^2*x^(3/2) - 4126*a^2*b^3*x^(3/2) - 3270*a*b^4*x^(3/2) - 720*b^5*x^(3/2) + 730*a^3*b^2*x^2 + 3410*a^2*b^3*x^2 + 3970*a*b^4*x^2 + 1260*b^5*x^2 - 199*a^3*b^2*x^(5/2) - 2032*a^2*b^3*x^(5/2) - 3442*a*b^4*x^(5/2) - 1512*b^5*x^(5/2) + 657*a^2*b^3*x^3 + 1978*a*b^4*x^3 + 1244*b^5*x^3 - 110*a^2*b^3*x^(7/2) - 810*a*b^4*x^(7/2) - 720*b^5*x^(7/2) + 196*a*b^4*x^4 + 264*b^5*x^4 - 20*a*b^4*x^(9/2) - 60*b^5*x^(9/2) + 8*b^5*x^5 - 32*a^4*Sqrt[a + b]*Sqrt[a + b*x] - 200*a^3*b*Sqrt[a + b]*Sqrt[a + b*x] - 402*a^2*b^2*Sqrt[a + b]*Sqrt[a + b*x] - 290*a*b^3*Sqrt[a + b]*Sqrt[a + b*x] - 60*b^4*Sqrt[a + b]*Sqrt[a + b*x] + 48*a^4*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 404*a^3*b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 1171*a^2*b^2*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 1082*a*b^3*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 272*b^4*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 272*a^3*b*Sqrt[a + b]*x*Sqrt[a + b*x] - 1648*a^2*b^2*Sqrt[a + b]*x*Sqrt[a + b*x] - 2154*a*b^3*Sqrt[a + b]*x*Sqrt[a + b*x] - 720*b^4*Sqrt[a + b]*x*Sqrt[a + b*x] + 132*a^3*b*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] + 1434*a^2*b^2*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] + 2742*a*b^3*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] + 1260*b^4*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] - 598*a^2*b^2*Sqrt[a + b]*x^2*Sqrt[a + b*x] - 2246*a*b^3*Sqrt[a + b]*x^2*Sqrt[a + b*x] - 1512*b^4*Sqrt[a + b]*x^2*Sqrt[a + b*x] + 139*a^2*b^2*Sqrt[a + b]*x^(5/2)*Sqrt[a + b*x] + 1266*a*b^3*Sqrt[a + b]*x^(5/2)*Sqrt[a + b*x] + 1276*b^4*Sqrt[a + b]*x^(5/2)*Sqrt[a + b*x] - 390*a*b^3*Sqrt[a + b]*x^3*Sqrt[a + b*x] - 720*b^4*Sqrt[a + b]*x^3*Sqrt[a + b*x] + 54*a*b^3*Sqrt[a + b]*x^(7/2)*Sqrt[a + b*x] + 276*b^4*Sqrt[a + b]*x^(7/2)*Sqrt[a + b*x] - 60*b^4*Sqrt[a + b]*x^4*Sqrt[a + b*x] + 4*b^4*Sqrt[a + b]*x^(9/2)*Sqrt[a + b*x]))/(Sqrt[a + b] - Sqrt[a + b*x])^12 + (128*a*(576*a^7 + 3152*a^6*b + 5880*a^5*b^2 + 3945*a^4*b^3 - 322*a^3*b^4 - 1335*a^2*b^5 - 388*a*b^6 - 16*b^7 - 384*a^7*Sqrt[x] - 3712*a^6*b*Sqrt[x] - 7296*a^5*b^2*Sqrt[x] + 1304*a^4*b^3*Sqrt[x] + 13867*a^3*b^4*Sqrt[x] + 11305*a^2*b^5*Sqrt[x] + 2828*a*b^6*Sqrt[x] + 112*b^7*Sqrt[x] + 3344*a^6*b*x + 10320*a^5*b^2*x - 4653*a^4*b^3*x - 35556*a^3*b^4*x - 33333*a^2*b^5*x - 10104*a*b^6*x - 656*b^7*x - 1440*a^6*b*x^(3/2) - 7824*a^5*b^2*x^(3/2) + 12870*a^4*b^3*x^(3/2) + 68909*a^3*b^4*x^(3/2) + 75544*a^2*b^5*x^(3/2) + 28896*a*b^6*x^(3/2) + 2912*b^7*x^(3/2) + 4632*a^5*b^2*x^2 - 11665*a^4*b^3*x^2 - 85294*a^3*b^4*x^2 - 118880*a^2*b^5*x^2 - 57844*a*b^6*x^2 - 7968*b^7*x^2 - 1680*a^5*b^2*x^(5/2) + 6540*a^4*b^3*x^(5/2) + 78625*a^3*b^4*x^(5/2) + 143134*a^2*b^5*x^(5/2) + 88340*a*b^6*x^(5/2) + 16016*b^7*x^(5/2) - 1419*a^4*b^3*x^3 - 51344*a^3*b^4*x^3 - 128648*a^2*b^5*x^3 - 101968*a*b^6*x^3 - 23952*b^7*x^3 - 202*a^4*b^3*x^(7/2) + 23419*a^3*b^4*x^(7/2) + 87352*a^2*b^5*x^(7/2) + 90892*a*b^6*x^(7/2) + 27456*b^7*x^(7/2) - 6396*a^3*b^4*x^4 - 43865*a^2*b^5*x^4 - 62068*a*b^6*x^4 - 24040*b^7*x^4 + 812*a^3*b^4*x^(9/2) + 16009*a^2*b^5*x^(9/2) + 32088*a*b^6*x^(9/2) + 16016*b^7*x^(9/2) - 3699*a^2*b^5*x^5 - 12136*a*b^6*x^5 - 7992*b^7*x^5 + 448*a^2*b^5*x^(11/2) + 3332*a*b^6*x^(11/2) + 2912*b^7*x^(11/2) - 580*a*b^6*x^6 - 712*b^7*x^6 + 56*a*b^6*x^(13/2) + 112*b^7*x^(13/2) - 8*b^7*x^7 - 576*a^6*Sqrt[a + b]*Sqrt[a + b*x] - 2864*a^5*b*Sqrt[a + b]*Sqrt[a + b*x] - 4520*a^4*b^2*Sqrt[a + b]*Sqrt[a + b*x] - 2007*a^3*b^3*Sqrt[a + b]*Sqrt[a + b*x] + 917*a^2*b^4*Sqrt[a + b]*Sqrt[a + b*x] + 812*a*b^5*Sqrt[a + b]*Sqrt[a + b*x] + 112*b^6*Sqrt[a + b]*Sqrt[a + b*x] + 384*a^6*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 3520*a^5*b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 5584*a^4*b^2*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 3680*a^3*b^3*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 11534*a^2*b^4*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 6220*a*b^5*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 800*b^6*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 3056*a^5*b*Sqrt[a + b]*x*Sqrt[a + b*x] - 7216*a^4*b^2*Sqrt[a + b]*x*Sqrt[a + b*x] + 10819*a^3*b^3*Sqrt[a + b]*x*Sqrt[a + b*x] + 31408*a^2*b^4*Sqrt[a + b]*x*Sqrt[a + b*x] + 19152*a*b^5*Sqrt[a + b]*x*Sqrt[a + b*x] + 2912*b^6*Sqrt[a + b]*x*Sqrt[a + b*x] + 1248*a^5*b*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] + 5344*a^4*b^2*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] - 19034*a^3*b^3*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] - 58150*a^2*b^4*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] - 42200*a*b^5*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] - 8048*b^6*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] - 3176*a^4*b^2*Sqrt[a + b]*x^2*Sqrt[a + b*x] + 17231*a^3*b^3*Sqrt[a + b]*x^2*Sqrt[a + b*x] + 71750*a^2*b^4*Sqrt[a + b]*x^2*Sqrt[a + b*x] + 66100*a*b^5*Sqrt[a + b]*x^2*Sqrt[a + b*x] + 16016*b^6*Sqrt[a + b]*x^2*Sqrt[a + b*x] + 1104*a^4*b^2*Sqrt[a + b]*x^(5/2)*Sqrt[a + b*x] - 9612*a^3*b^3*Sqrt[a + b]*x^(5/2)*Sqrt[a + b*x] - 64510*a^2*b^4*Sqrt[a + b]*x^(5/2)*Sqrt[a + b*x] - 78184*a*b^5*Sqrt[a + b]*x^(5/2)*Sqrt[a + b*x] - 24096*b^6*Sqrt[a + b]*x^(5/2)*Sqrt[a + b*x] + 2661*a^3*b^3*Sqrt[a + b]*x^3*Sqrt[a + b*x] + 41296*a^2*b^4*Sqrt[a + b]*x^3*Sqrt[a + b*x] + 69268*a*b^5*Sqrt[a + b]*x^3*Sqrt[a + b*x] + 27456*b^6*Sqrt[a + b]*x^3*Sqrt[a + b*x] - 218*a^3*b^3*Sqrt[a + b]*x^(7/2)*Sqrt[a + b*x] - 18266*a^2*b^4*Sqrt[a + b]*x^(7/2)*Sqrt[a + b*x] - 46040*a*b^5*Sqrt[a + b]*x^(7/2)*Sqrt[a + b*x] - 24008*b^6*Sqrt[a + b]*x^(7/2)*Sqrt[a + b*x] + 4837*a^2*b^4*Sqrt[a + b]*x^4*Sqrt[a + b*x] + 22512*a*b^5*Sqrt[a + b]*x^4*Sqrt[a + b*x] + 16016*b^6*Sqrt[a + b]*x^4*Sqrt[a + b*x] - 628*a^2*b^4*Sqrt[a + b]*x^(9/2)*Sqrt[a + b*x] - 7868*a*b^5*Sqrt[a + b]*x^(9/2)*Sqrt[a + b*x] - 8024*b^6*Sqrt[a + b]*x^(9/2)*Sqrt[a + b*x] + 1708*a*b^5*Sqrt[a + b]*x^5*Sqrt[a + b*x] + 2912*b^6*Sqrt[a + b]*x^5*Sqrt[a + b*x] - 192*a*b^5*Sqrt[a + b]*x^(11/2)*Sqrt[a + b*x] - 744*b^6*Sqrt[a + b]*x^(11/2)*Sqrt[a + b*x] + 112*b^6*Sqrt[a + b]*x^6*Sqrt[a + b*x] - 8*b^6*Sqrt[a + b]*x^(13/2)*Sqrt[a + b*x]))/(Sqrt[a + b] - Sqrt[a + b*x])^14))/((-Sqrt[a + b] + Sqrt[a + b*x])*(4*a^2*Sqrt[x] + 4*a*b*Sqrt[x] - 2*a^2*x - a*b*x + 2*b^2*x + 2*a*b*x^(3/2) - a*b*x^2 - 4*a*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 2*b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 2*a*Sqrt[a + b]*x*Sqrt[a + b*x])^3*(-2*a^3 - 5*a^2*b - 2*a*b^2 + 2*a^2*b*Sqrt[x] - 3*a^2*b*x - 5*a*b^2*x - 2*b^3*x + 2*a*b^2*x^(3/2) - a*b^2*x^2 + 2*a^2*Sqrt[a + b]*Sqrt[a + b*x] + 4*a*b*Sqrt[a + b]*Sqrt[a + b*x] - 2*a*b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 2*b^2*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 2*a*b*Sqrt[a + b]*x*Sqrt[a + b*x]))","B",1
583,-1,0,87,180.1303989,"\int \frac{1}{x^{7/2} (a+b x)^{3/2}} \, dx","IntegrateAlgebraic[1/(x^(7/2)*(a + b*x)^(3/2)),x]","\text{\$Aborted}","-\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,"$Aborted","F",-1
584,1,2597,91,47.3037221,"\int \frac{x^{5/2}}{(a+b x)^{5/2}} \, dx","IntegrateAlgebraic[x^(5/2)/(a + b*x)^(5/2),x]","\text{Result too large to show}","-\frac{5 a \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{b^{7/2}}+\frac{5 \sqrt{x} \sqrt{a+b x}}{b^3}-\frac{10 x^{3/2}}{3 b^2 \sqrt{a+b x}}-\frac{2 x^{5/2}}{3 b (a+b x)^{3/2}}",1,"((Sqrt[a + b]/b^3 - Sqrt[a + b*x]/b^3)*(-3*a - 2*b - a*Sqrt[x] - 2*b*Sqrt[x] + 4*Sqrt[a + b]*Sqrt[a + b*x]))/(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x]) + ((Sqrt[a + b] - Sqrt[a + b*x])^3*(-(a/b^3) - (a*Sqrt[x])/b^3 - (2*Sqrt[x])/b^2 + (2*Sqrt[a + b]*Sqrt[a + b*x])/b^3))/(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x])^2 + ((Sqrt[a + b] - Sqrt[a + b*x])^9*((184*a^6)/(3*(a + b)^4) - (24*a^8)/(b^2*(a + b)^4) - (104*a^7)/(3*b*(a + b)^4) + (200*a^5*b)/(3*(a + b)^4) - (16*a^4*b^2)/(3*(a + b)^4) - (88*a^6*Sqrt[x])/(a + b)^4 + (8*a^8*Sqrt[x])/(3*b^2*(a + b)^4) + (56*a^7*Sqrt[x])/(3*b*(a + b)^4) - (72*a^5*b*Sqrt[x])/(a + b)^4 + (32*a^4*b^2*Sqrt[x])/(a + b)^4 + (40*a^6*x)/(a + b)^4 - (88*a^7*x)/(3*b*(a + b)^4) + (184*a^5*b*x)/(3*(a + b)^4) - (8*a^4*b^2*x)/(a + b)^4 - (40*a^6*x^(3/2))/(3*(a + b)^4) + (8*a^7*x^(3/2))/(3*b*(a + b)^4) - (40*a^5*b*x^(3/2))/(3*(a + b)^4) + (8*a^4*b^2*x^(3/2))/(3*(a + b)^4) - (184*a^5*Sqrt[a + b*x])/(3*(a + b)^(7/2)) + (24*a^7*Sqrt[a + b*x])/(b^2*(a + b)^(7/2)) + (64*a^6*Sqrt[a + b*x])/(3*b*(a + b)^(7/2)) - (16*a^4*b*Sqrt[a + b*x])/(a + b)^(7/2) + (200*a^5*Sqrt[x]*Sqrt[a + b*x])/(3*(a + b)^(7/2)) - (8*a^7*Sqrt[x]*Sqrt[a + b*x])/(3*b^2*(a + b)^(7/2)) - (40*a^6*Sqrt[x]*Sqrt[a + b*x])/(3*b*(a + b)^(7/2)) - (8*a^4*b*Sqrt[x]*Sqrt[a + b*x])/(a + b)^(7/2) - (80*a^5*x*Sqrt[a + b*x])/(3*(a + b)^(7/2)) + (40*a^6*x*Sqrt[a + b*x])/(3*b*(a + b)^(7/2)) + (8*a^4*b*x*Sqrt[a + b*x])/(3*(a + b)^(7/2))))/(-2*a^3 - 5*a^2*b - 2*a*b^2 + 2*a^2*b*Sqrt[x] - 3*a^2*b*x - 5*a*b^2*x - 2*b^3*x + 2*a*b^2*x^(3/2) - a*b^2*x^2 + 2*a^2*Sqrt[a + b]*Sqrt[a + b*x] + 4*a*b*Sqrt[a + b]*Sqrt[a + b*x] - 2*a*b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 2*b^2*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 2*a*b*Sqrt[a + b]*x*Sqrt[a + b*x])^3 + ((Sqrt[a + b] - Sqrt[a + b*x])^5*((234*a^5)/(a + b)^4 - (26*a^8)/(3*b^3*(a + b)^4) - (326*a^7)/(3*b^2*(a + b)^4) + (50*a^6)/(b*(a + b)^4) + (76*a^4*b)/(a + b)^4 - (8*a^3*b^2)/(a + b)^4 - (470*a^5*Sqrt[x])/(3*(a + b)^4) + (2*a^8*Sqrt[x])/(3*b^3*(a + b)^4) + (18*a^7*Sqrt[x])/(b^2*(a + b)^4) - (238*a^6*Sqrt[x])/(3*b*(a + b)^4) - (28*a^4*b*Sqrt[x])/(a + b)^4 + (32*a^3*b^2*Sqrt[x])/(a + b)^4 + (98*a^5*x)/(a + b)^4 - (34*a^7*x)/(3*b^2*(a + b)^4) - (110*a^6*x)/(3*b*(a + b)^4) + (334*a^4*b*x)/(3*(a + b)^4) - (12*a^3*b^2*x)/(a + b)^4 - (26*a^5*x^(3/2))/(a + b)^4 + (2*a^7*x^(3/2))/(3*b^2*(a + b)^4) - (10*a^6*x^(3/2))/(3*b*(a + b)^4) - (18*a^4*b*x^(3/2))/(a + b)^4 + (4*a^3*b^2*x^(3/2))/(a + b)^4 - (156*a^4*Sqrt[a + b*x])/(a + b)^(7/2) + (26*a^7*Sqrt[a + b*x])/(3*b^3*(a + b)^(7/2)) + (104*a^6*Sqrt[a + b*x])/(b^2*(a + b)^(7/2)) - (286*a^5*Sqrt[a + b*x])/(3*b*(a + b)^(7/2)) - (8*a^3*b*Sqrt[a + b*x])/(a + b)^(7/2) + (218*a^4*Sqrt[x]*Sqrt[a + b*x])/(3*(a + b)^(7/2)) - (2*a^7*Sqrt[x]*Sqrt[a + b*x])/(3*b^3*(a + b)^(7/2)) - (50*a^6*Sqrt[x]*Sqrt[a + b*x])/(3*b^2*(a + b)^(7/2)) + (206*a^5*Sqrt[x]*Sqrt[a + b*x])/(3*b*(a + b)^(7/2)) - (12*a^3*b*Sqrt[x]*Sqrt[a + b*x])/(a + b)^(7/2) - (42*a^4*x*Sqrt[a + b*x])/(a + b)^(7/2) + (6*a^6*x*Sqrt[a + b*x])/(b^2*(a + b)^(7/2)) + (8*a^5*x*Sqrt[a + b*x])/(3*b*(a + b)^(7/2)) + (4*a^3*b*x*Sqrt[a + b*x])/(a + b)^(7/2)))/(-2*a^3 - 5*a^2*b - 2*a*b^2 + 2*a^2*b*Sqrt[x] - 3*a^2*b*x - 5*a*b^2*x - 2*b^3*x + 2*a*b^2*x^(3/2) - a*b^2*x^2 + 2*a^2*Sqrt[a + b]*Sqrt[a + b*x] + 4*a*b*Sqrt[a + b]*Sqrt[a + b*x] - 2*a*b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 2*b^2*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 2*a*b*Sqrt[a + b]*x*Sqrt[a + b*x])^2 + (((-2*a^2)/(3*b^3*(a + b)^(5/2)) + (2*a^2*Sqrt[a + b*x])/(3*b^3*(a + b)^3))*(58*a^4 - 24*a^3*b - 82*a^2*b^2 + 18*a*b^3 + 18*b^4 - 10*a^4*Sqrt[x] - 21*a^3*b*Sqrt[x] - 62*a^2*b^2*Sqrt[x] - 87*a*b^3*Sqrt[x] - 36*b^4*Sqrt[x] + 53*a^3*b*x + 11*a^2*b^2*x - 15*a*b^3*x + 27*b^4*x - 8*a^3*b*x^(3/2) - 11*a^2*b^2*x^(3/2) - 12*a*b^3*x^(3/2) - 9*b^4*x^(3/2) - 58*a^3*Sqrt[a + b]*Sqrt[a + b*x] + 56*a^2*b*Sqrt[a + b]*Sqrt[a + b*x] + 60*a*b^2*Sqrt[a + b]*Sqrt[a + b*x] - 18*b^3*Sqrt[a + b]*Sqrt[a + b*x] + 10*a^3*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 7*a^2*b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 24*a*b^2*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 27*b^3*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 15*a^2*b*Sqrt[a + b]*x*Sqrt[a + b*x] + 12*a*b^2*Sqrt[a + b]*x*Sqrt[a + b*x] - 9*b^3*Sqrt[a + b]*x*Sqrt[a + b*x]))/(-2*a^3 - 5*a^2*b - 2*a*b^2 + 2*a^2*b*Sqrt[x] - 3*a^2*b*x - 5*a*b^2*x - 2*b^3*x + 2*a*b^2*x^(3/2) - a*b^2*x^2 + 2*a^2*Sqrt[a + b]*Sqrt[a + b*x] + 4*a*b*Sqrt[a + b]*Sqrt[a + b*x] - 2*a*b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 2*b^2*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 2*a*b*Sqrt[a + b]*x*Sqrt[a + b*x]) + (10*a*ArcTanh[(Sqrt[a + b]/Sqrt[b] - Sqrt[a + b*x]/Sqrt[b])/(-1 + Sqrt[x])])/b^(7/2)","B",1
585,1,2380,69,14.2138869,"\int \frac{x^{3/2}}{(a+b x)^{5/2}} \, dx","IntegrateAlgebraic[x^(3/2)/(a + b*x)^(5/2),x]","\text{Result too large to show}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{b^{5/2}}-\frac{2 \sqrt{x}}{b^2 \sqrt{a+b x}}-\frac{2 x^{3/2}}{3 b (a+b x)^{3/2}}",1,"((Sqrt[a + b] - Sqrt[a + b*x])^9*((104*a^6)/(3*(a + b)^4) + (24*a^7)/(b*(a + b)^4) - (184*a^5*b)/(3*(a + b)^4) - (200*a^4*b^2)/(3*(a + b)^4) + (16*a^3*b^3)/(3*(a + b)^4) - (56*a^6*Sqrt[x])/(3*(a + b)^4) - (8*a^7*Sqrt[x])/(3*b*(a + b)^4) + (88*a^5*b*Sqrt[x])/(a + b)^4 + (72*a^4*b^2*Sqrt[x])/(a + b)^4 - (32*a^3*b^3*Sqrt[x])/(a + b)^4 + (88*a^6*x)/(3*(a + b)^4) - (40*a^5*b*x)/(a + b)^4 - (184*a^4*b^2*x)/(3*(a + b)^4) + (8*a^3*b^3*x)/(a + b)^4 - (8*a^6*x^(3/2))/(3*(a + b)^4) + (40*a^5*b*x^(3/2))/(3*(a + b)^4) + (40*a^4*b^2*x^(3/2))/(3*(a + b)^4) - (8*a^3*b^3*x^(3/2))/(3*(a + b)^4) - (64*a^5*Sqrt[a + b*x])/(3*(a + b)^(7/2)) - (24*a^6*Sqrt[a + b*x])/(b*(a + b)^(7/2)) + (184*a^4*b*Sqrt[a + b*x])/(3*(a + b)^(7/2)) + (16*a^3*b^2*Sqrt[a + b*x])/(a + b)^(7/2) + (40*a^5*Sqrt[x]*Sqrt[a + b*x])/(3*(a + b)^(7/2)) + (8*a^6*Sqrt[x]*Sqrt[a + b*x])/(3*b*(a + b)^(7/2)) - (200*a^4*b*Sqrt[x]*Sqrt[a + b*x])/(3*(a + b)^(7/2)) + (8*a^3*b^2*Sqrt[x]*Sqrt[a + b*x])/(a + b)^(7/2) - (40*a^5*x*Sqrt[a + b*x])/(3*(a + b)^(7/2)) + (80*a^4*b*x*Sqrt[a + b*x])/(3*(a + b)^(7/2)) - (8*a^3*b^2*x*Sqrt[a + b*x])/(3*(a + b)^(7/2))))/(-2*a^3 - 5*a^2*b - 2*a*b^2 + 2*a^2*b*Sqrt[x] - 3*a^2*b*x - 5*a*b^2*x - 2*b^3*x + 2*a*b^2*x^(3/2) - a*b^2*x^2 + 2*a^2*Sqrt[a + b]*Sqrt[a + b*x] + 4*a*b*Sqrt[a + b]*Sqrt[a + b*x] - 2*a*b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 2*b^2*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 2*a*b*Sqrt[a + b]*x*Sqrt[a + b*x])^3 + ((Sqrt[a + b] - Sqrt[a + b*x])^5*((-50*a^5)/(a + b)^4 + (26*a^7)/(3*b^2*(a + b)^4) + (326*a^6)/(3*b*(a + b)^4) - (234*a^4*b)/(a + b)^4 - (76*a^3*b^2)/(a + b)^4 + (8*a^2*b^3)/(a + b)^4 + (238*a^5*Sqrt[x])/(3*(a + b)^4) - (2*a^7*Sqrt[x])/(3*b^2*(a + b)^4) - (18*a^6*Sqrt[x])/(b*(a + b)^4) + (470*a^4*b*Sqrt[x])/(3*(a + b)^4) + (28*a^3*b^2*Sqrt[x])/(a + b)^4 - (32*a^2*b^3*Sqrt[x])/(a + b)^4 + (110*a^5*x)/(3*(a + b)^4) + (34*a^6*x)/(3*b*(a + b)^4) - (98*a^4*b*x)/(a + b)^4 - (334*a^3*b^2*x)/(3*(a + b)^4) + (12*a^2*b^3*x)/(a + b)^4 + (10*a^5*x^(3/2))/(3*(a + b)^4) - (2*a^6*x^(3/2))/(3*b*(a + b)^4) + (26*a^4*b*x^(3/2))/(a + b)^4 + (18*a^3*b^2*x^(3/2))/(a + b)^4 - (4*a^2*b^3*x^(3/2))/(a + b)^4 + (286*a^4*Sqrt[a + b*x])/(3*(a + b)^(7/2)) - (26*a^6*Sqrt[a + b*x])/(3*b^2*(a + b)^(7/2)) - (104*a^5*Sqrt[a + b*x])/(b*(a + b)^(7/2)) + (156*a^3*b*Sqrt[a + b*x])/(a + b)^(7/2) + (8*a^2*b^2*Sqrt[a + b*x])/(a + b)^(7/2) - (206*a^4*Sqrt[x]*Sqrt[a + b*x])/(3*(a + b)^(7/2)) + (2*a^6*Sqrt[x]*Sqrt[a + b*x])/(3*b^2*(a + b)^(7/2)) + (50*a^5*Sqrt[x]*Sqrt[a + b*x])/(3*b*(a + b)^(7/2)) - (218*a^3*b*Sqrt[x]*Sqrt[a + b*x])/(3*(a + b)^(7/2)) + (12*a^2*b^2*Sqrt[x]*Sqrt[a + b*x])/(a + b)^(7/2) - (8*a^4*x*Sqrt[a + b*x])/(3*(a + b)^(7/2)) - (6*a^5*x*Sqrt[a + b*x])/(b*(a + b)^(7/2)) + (42*a^3*b*x*Sqrt[a + b*x])/(a + b)^(7/2) - (4*a^2*b^2*x*Sqrt[a + b*x])/(a + b)^(7/2)))/(-2*a^3 - 5*a^2*b - 2*a*b^2 + 2*a^2*b*Sqrt[x] - 3*a^2*b*x - 5*a*b^2*x - 2*b^3*x + 2*a*b^2*x^(3/2) - a*b^2*x^2 + 2*a^2*Sqrt[a + b]*Sqrt[a + b*x] + 4*a*b*Sqrt[a + b]*Sqrt[a + b*x] - 2*a*b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 2*b^2*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 2*a*b*Sqrt[a + b]*x*Sqrt[a + b*x])^2 + (((2*a)/(3*b^2*(a + b)^(5/2)) - (2*a*Sqrt[a + b*x])/(3*b^2*(a + b)^3))*(55*a^4 - 39*a^3*b - 109*a^2*b^2 - 3*a*b^3 + 12*b^4 - 7*a^4*Sqrt[x] - 17*a^2*b^2*Sqrt[x] - 48*a*b^3*Sqrt[x] - 24*b^4*Sqrt[x] + 44*a^3*b*x - 16*a^2*b^2*x - 42*a*b^3*x + 18*b^4*x - 5*a^3*b*x^(3/2) - 2*a^2*b^2*x^(3/2) - 3*a*b^3*x^(3/2) - 6*b^4*x^(3/2) - 55*a^3*Sqrt[a + b]*Sqrt[a + b*x] + 68*a^2*b*Sqrt[a + b]*Sqrt[a + b*x] + 75*a*b^2*Sqrt[a + b]*Sqrt[a + b*x] - 12*b^3*Sqrt[a + b]*Sqrt[a + b*x] + 7*a^3*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 8*a^2*b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 3*a*b^2*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 18*b^3*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 12*a^2*b*Sqrt[a + b]*x*Sqrt[a + b*x] + 18*a*b^2*Sqrt[a + b]*x*Sqrt[a + b*x] - 6*b^3*Sqrt[a + b]*x*Sqrt[a + b*x]))/(-2*a^3 - 5*a^2*b - 2*a*b^2 + 2*a^2*b*Sqrt[x] - 3*a^2*b*x - 5*a*b^2*x - 2*b^3*x + 2*a*b^2*x^(3/2) - a*b^2*x^2 + 2*a^2*Sqrt[a + b]*Sqrt[a + b*x] + 4*a*b*Sqrt[a + b]*Sqrt[a + b*x] - 2*a*b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 2*b^2*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 2*a*b*Sqrt[a + b]*x*Sqrt[a + b*x]) - (4*ArcTanh[(Sqrt[a + b]/Sqrt[b] - Sqrt[a + b*x]/Sqrt[b])/(-1 + Sqrt[x])])/b^(5/2)","B",1
586,1,2870,21,9.3419582,"\int \frac{\sqrt{x}}{(a+b x)^{5/2}} \, dx","IntegrateAlgebraic[Sqrt[x]/(a + b*x)^(5/2),x]","\text{Result too large to show}","\frac{2 x^{3/2}}{3 a (a+b x)^{3/2}}",1,"((1/(48*(a + b)^2) - Sqrt[x]/(48*(a + b)^2))*(Sqrt[a + b] - Sqrt[a + b*x])^12*((-32*a^4*(-1 + Sqrt[x])^2*(-a - b + b*Sqrt[x] - b*x + Sqrt[a + b]*Sqrt[a + b*x])^3)/(Sqrt[a + b] - Sqrt[a + b*x])^8 + (96*a*b^2*(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x])^4*(4*a + 4*b - a*Sqrt[x] - 4*b*Sqrt[x] + 3*b*x - 4*Sqrt[a + b]*Sqrt[a + b*x] + Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x]))/(Sqrt[a + b] - Sqrt[a + b*x])^10 + (96*b^3*(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x])^4*(2*a + 2*b - a*Sqrt[x] - 2*b*Sqrt[x] + b*x - 2*Sqrt[a + b]*Sqrt[a + b*x] + Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x]))/(Sqrt[a + b] - Sqrt[a + b*x])^10 - (32*a^3*(16*a^4*b - 4*a^3*b^2 - 43*a^2*b^3 - 25*a*b^4 - 2*b^5 - 48*a^5*Sqrt[x] - 140*a^4*b*Sqrt[x] + 5*a^3*b^2*Sqrt[x] + 215*a^2*b^3*Sqrt[x] + 125*a*b^4*Sqrt[x] + 10*b^5*Sqrt[x] - 8*a^4*b*x - 224*a^3*b^2*x - 494*a^2*b^3*x - 303*a*b^4*x - 40*b^5*x - 108*a^4*b*x^(3/2) - 106*a^3*b^2*x^(3/2) + 395*a^2*b^3*x^(3/2) + 485*a*b^4*x^(3/2) + 120*b^5*x^(3/2) - 76*a^3*b^2*x^2 - 563*a^2*b^3*x^2 - 693*a*b^4*x^2 - 226*b^5*x^2 - 75*a^3*b^2*x^(5/2) + 125*a^2*b^3*x^(5/2) + 455*a*b^4*x^(5/2) + 252*b^5*x^(5/2) - 100*a^2*b^3*x^3 - 345*a*b^4*x^3 - 238*b^5*x^3 - 15*a^2*b^3*x^(7/2) + 95*a*b^4*x^(7/2) + 120*b^5*x^(7/2) - 34*a*b^4*x^4 - 52*b^5*x^4 + 10*b^5*x^(9/2) - 2*b^5*x^5 - 16*a^3*b*Sqrt[a + b]*Sqrt[a + b*x] + 12*a^2*b^2*Sqrt[a + b]*Sqrt[a + b*x] + 35*a*b^3*Sqrt[a + b]*Sqrt[a + b*x] + 10*b^4*Sqrt[a + b]*Sqrt[a + b*x] + 48*a^4*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 116*a^3*b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 57*a^2*b^2*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 175*a*b^3*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 50*b^4*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 8*a^3*b*Sqrt[a + b]*x*Sqrt[a + b*x] + 228*a^2*b^2*Sqrt[a + b]*x*Sqrt[a + b*x] + 379*a*b^3*Sqrt[a + b]*x*Sqrt[a + b*x] + 120*b^4*Sqrt[a + b]*x*Sqrt[a + b*x] + 84*a^3*b*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] - 6*a^2*b^2*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] - 379*a*b^3*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] - 194*b^4*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] + 72*a^2*b^2*Sqrt[a + b]*x^2*Sqrt[a + b*x] + 409*a*b^3*Sqrt[a + b]*x^2*Sqrt[a + b*x] + 252*b^4*Sqrt[a + b]*x^2*Sqrt[a + b*x] + 39*a^2*b^2*Sqrt[a + b]*x^(5/2)*Sqrt[a + b*x] - 145*a*b^3*Sqrt[a + b]*x^(5/2)*Sqrt[a + b*x] - 182*b^4*Sqrt[a + b]*x^(5/2)*Sqrt[a + b*x] + 65*a*b^3*Sqrt[a + b]*x^3*Sqrt[a + b*x] + 120*b^4*Sqrt[a + b]*x^3*Sqrt[a + b*x] + 3*a*b^3*Sqrt[a + b]*x^(7/2)*Sqrt[a + b*x] - 38*b^4*Sqrt[a + b]*x^(7/2)*Sqrt[a + b*x] + 10*b^4*Sqrt[a + b]*x^4*Sqrt[a + b*x]))/(Sqrt[a + b] - Sqrt[a + b*x])^10 - (32*a^2*b*(-96*a^5 - 136*a^4*b - 54*a^3*b^2 - 36*a^2*b^3 - 24*a*b^4 - 2*b^5 - 48*a^5*Sqrt[x] - 316*a^4*b*Sqrt[x] - 267*a^3*b^2*Sqrt[x] + 135*a^2*b^3*Sqrt[x] + 135*a*b^4*Sqrt[x] + 10*b^5*Sqrt[x] - 160*a^4*b*x - 572*a^3*b^2*x - 781*a^2*b^3*x - 361*a*b^4*x - 37*b^5*x - 108*a^4*b*x^(3/2) - 298*a^3*b^2*x^(3/2) + 159*a^2*b^3*x^(3/2) + 380*a*b^4*x^(3/2) + 120*b^5*x^(3/2) - 190*a^3*b^2*x^2 - 890*a^2*b^3*x^2 - 895*a*b^4*x^2 - 280*b^5*x^2 - 59*a^3*b^2*x^(5/2) + 133*a^2*b^3*x^(5/2) + 408*a*b^4*x^(5/2) + 252*b^5*x^(5/2) - 165*a^2*b^3*x^3 - 443*a*b^4*x^3 - 282*b^5*x^3 + 5*a^2*b^3*x^(7/2) + 120*a*b^4*x^(7/2) + 120*b^5*x^(7/2) - 45*a*b^4*x^4 - 54*b^5*x^4 + 5*a*b^4*x^(9/2) + 10*b^5*x^(9/2) - b^5*x^5 + 96*a^4*Sqrt[a + b]*Sqrt[a + b*x] + 88*a^3*b*Sqrt[a + b]*Sqrt[a + b*x] + 22*a^2*b^2*Sqrt[a + b]*Sqrt[a + b*x] + 30*a*b^3*Sqrt[a + b]*Sqrt[a + b*x] + 10*b^4*Sqrt[a + b]*Sqrt[a + b*x] + 48*a^4*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 292*a^3*b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 127*a^2*b^2*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 165*a*b^3*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 53*b^4*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 112*a^3*b*Sqrt[a + b]*x*Sqrt[a + b*x] + 448*a^2*b^2*Sqrt[a + b]*x*Sqrt[a + b*x] + 544*a*b^3*Sqrt[a + b]*x*Sqrt[a + b*x] + 120*b^4*Sqrt[a + b]*x*Sqrt[a + b*x] + 84*a^3*b*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] + 98*a^2*b^2*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] - 331*a*b^3*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] - 140*b^4*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] + 146*a^2*b^2*Sqrt[a + b]*x^2*Sqrt[a + b*x] + 582*a*b^3*Sqrt[a + b]*x^2*Sqrt[a + b*x] + 252*b^4*Sqrt[a + b]*x^2*Sqrt[a + b*x] + 23*a^2*b^2*Sqrt[a + b]*x^(5/2)*Sqrt[a + b*x] - 175*a*b^3*Sqrt[a + b]*x^(5/2)*Sqrt[a + b*x] - 138*b^4*Sqrt[a + b]*x^(5/2)*Sqrt[a + b*x] + 100*a*b^3*Sqrt[a + b]*x^3*Sqrt[a + b*x] + 120*b^4*Sqrt[a + b]*x^3*Sqrt[a + b*x] - 9*a*b^3*Sqrt[a + b]*x^(7/2)*Sqrt[a + b*x] - 36*b^4*Sqrt[a + b]*x^(7/2)*Sqrt[a + b*x] + 10*b^4*Sqrt[a + b]*x^4*Sqrt[a + b*x] - b^4*Sqrt[a + b]*x^(9/2)*Sqrt[a + b*x]))/(Sqrt[a + b] - Sqrt[a + b*x])^10))/((-Sqrt[a + b] + Sqrt[a + b*x])*(-2*a^3 - 5*a^2*b - 2*a*b^2 + 2*a^2*b*Sqrt[x] - 3*a^2*b*x - 5*a*b^2*x - 2*b^3*x + 2*a*b^2*x^(3/2) - a*b^2*x^2 + 2*a^2*Sqrt[a + b]*Sqrt[a + b*x] + 4*a*b*Sqrt[a + b]*Sqrt[a + b*x] - 2*a*b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 2*b^2*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 2*a*b*Sqrt[a + b]*x*Sqrt[a + b*x])^3)","B",1
587,1,2767,43,8.7021637,"\int \frac{1}{\sqrt{x} (a+b x)^{5/2}} \, dx","IntegrateAlgebraic[1/(Sqrt[x]*(a + b*x)^(5/2)),x]","\text{Result too large to show}","\frac{4 \sqrt{x}}{3 a^2 \sqrt{a+b x}}+\frac{2 \sqrt{x}}{3 a (a+b x)^{3/2}}",1,"((1/(48*(a + b)^2) - Sqrt[x]/(48*(a + b)^2))*(Sqrt[a + b] - Sqrt[a + b*x])^12*((32*a^3*(-a - b + b*Sqrt[x] - b*x + Sqrt[a + b]*Sqrt[a + b*x])^3*(-6*a^2 - 7*a*b - 2*b^2 + 2*a*b*Sqrt[x] + 4*b^2*Sqrt[x] - 7*a*b*x - 10*b^2*x + 4*b^2*x^(3/2) - 2*b^2*x^2 + 6*a*Sqrt[a + b]*Sqrt[a + b*x] + 4*b*Sqrt[a + b]*Sqrt[a + b*x] - 2*b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 4*b*Sqrt[a + b]*x*Sqrt[a + b*x]))/(Sqrt[a + b] - Sqrt[a + b*x])^10 - (96*b^3*(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x])^2*(-a - b + b*Sqrt[x] - b*x + Sqrt[a + b]*Sqrt[a + b*x])*(6*a^2 + 11*a*b + 4*b^2 - 4*a^2*Sqrt[x] - 14*a*b*Sqrt[x] - 8*b^2*Sqrt[x] + 11*a*b*x + 12*b^2*x - 4*a*b*x^(3/2) - 8*b^2*x^(3/2) + 2*b^2*x^2 - 6*a*Sqrt[a + b]*Sqrt[a + b*x] - 8*b*Sqrt[a + b]*Sqrt[a + b*x] + 4*a*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 12*b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 8*b*Sqrt[a + b]*x*Sqrt[a + b*x] + 2*b*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x]))/(Sqrt[a + b] - Sqrt[a + b*x])^10 - (32*a^2*b*(-a - b + b*Sqrt[x] - b*x + Sqrt[a + b]*Sqrt[a + b*x])*(120*a^4 + 320*a^3*b + 271*a^2*b^2 + 81*a*b^3 + 7*b^4 - 48*a^4*Sqrt[x] - 256*a^3*b*Sqrt[x] - 304*a^2*b^2*Sqrt[x] - 136*a*b^3*Sqrt[x] - 28*b^4*Sqrt[x] + 320*a^3*b*x + 666*a^2*b^2*x + 487*a*b^3*x + 131*b^4*x - 96*a^3*b*x^(3/2) - 412*a^2*b^2*x^(3/2) - 492*a*b^3*x^(3/2) - 196*b^4*x^(3/2) + 271*a^2*b^2*x^2 + 487*a*b^3*x^2 + 265*b^4*x^2 - 60*a^2*b^2*x^(5/2) - 208*a*b^3*x^(5/2) - 196*b^4*x^(5/2) + 81*a*b^3*x^3 + 113*b^4*x^3 - 12*a*b^3*x^(7/2) - 28*b^4*x^(7/2) + 4*b^4*x^4 - 120*a^3*Sqrt[a + b]*Sqrt[a + b*x] - 260*a^2*b*Sqrt[a + b]*Sqrt[a + b*x] - 156*a*b^2*Sqrt[a + b]*Sqrt[a + b*x] - 28*b^3*Sqrt[a + b]*Sqrt[a + b*x] + 48*a^3*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 232*a^2*b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 194*a*b^2*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 65*b^3*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 260*a^2*b*Sqrt[a + b]*x*Sqrt[a + b*x] - 376*a*b^2*Sqrt[a + b]*x*Sqrt[a + b*x] - 196*b^3*Sqrt[a + b]*x*Sqrt[a + b*x] + 72*a^2*b*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] + 248*a*b^2*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] + 225*b^3*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] - 156*a*b^2*Sqrt[a + b]*x^2*Sqrt[a + b*x] - 196*b^3*Sqrt[a + b]*x^2*Sqrt[a + b*x] + 30*a*b^2*Sqrt[a + b]*x^(5/2)*Sqrt[a + b*x] + 83*b^3*Sqrt[a + b]*x^(5/2)*Sqrt[a + b*x] - 28*b^3*Sqrt[a + b]*x^3*Sqrt[a + b*x] + 3*b^3*Sqrt[a + b]*x^(7/2)*Sqrt[a + b*x]))/(Sqrt[a + b] - Sqrt[a + b*x])^10 + (32*a*b^2*(336*a^5 + 1100*a^4*b + 1233*a^3*b^2 + 549*a^2*b^3 + 84*a*b^4 + 4*b^5 - 192*a^5*Sqrt[x] - 1000*a^4*b*Sqrt[x] - 1344*a^3*b^2*Sqrt[x] - 600*a^2*b^3*Sqrt[x] - 90*a*b^4*Sqrt[x] - 20*b^5*Sqrt[x] + 1100*a^4*b*x + 2686*a^3*b^2*x + 2213*a^2*b^3*x + 803*a*b^4*x + 146*b^5*x - 480*a^4*b*x^(3/2) - 1864*a^3*b^2*x^(3/2) - 2067*a^2*b^3*x^(3/2) - 970*a*b^4*x^(3/2) - 240*b^5*x^(3/2) + 1121*a^3*b^2*x^2 + 2143*a^2*b^3*x^2 + 1493*a*b^4*x^2 + 476*b^5*x^2 - 392*a^3*b^2*x^(5/2) - 1106*a^2*b^3*x^(5/2) - 1116*a*b^4*x^(5/2) - 504*b^5*x^(5/2) + 423*a^2*b^3*x^3 + 733*a*b^4*x^3 + 444*b^5*x^3 - 115*a^2*b^3*x^(7/2) - 270*a*b^4*x^(7/2) - 240*b^5*x^(7/2) + 63*a*b^4*x^4 + 96*b^5*x^4 - 10*a*b^4*x^(9/2) - 20*b^5*x^(9/2) + 2*b^5*x^5 - 336*a^4*Sqrt[a + b]*Sqrt[a + b*x] - 932*a^3*b*Sqrt[a + b]*Sqrt[a + b*x] - 809*a^2*b^2*Sqrt[a + b]*Sqrt[a + b*x] - 240*a*b^3*Sqrt[a + b]*Sqrt[a + b*x] - 20*b^4*Sqrt[a + b]*Sqrt[a + b*x] + 192*a^4*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 904*a^3*b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 916*a^2*b^2*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 243*a*b^3*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 34*b^4*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 932*a^3*b*Sqrt[a + b]*x*Sqrt[a + b*x] - 1670*a^2*b^2*Sqrt[a + b]*x*Sqrt[a + b*x] - 878*a*b^3*Sqrt[a + b]*x*Sqrt[a + b*x] - 240*b^4*Sqrt[a + b]*x*Sqrt[a + b*x] + 384*a^3*b*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] + 1172*a^2*b^2*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] + 857*a*b^3*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] + 364*b^4*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] - 697*a^2*b^2*Sqrt[a + b]*x^2*Sqrt[a + b*x] - 864*a*b^3*Sqrt[a + b]*x^2*Sqrt[a + b*x] - 504*b^4*Sqrt[a + b]*x^2*Sqrt[a + b*x] + 224*a^2*b^2*Sqrt[a + b]*x^(5/2)*Sqrt[a + b*x] + 437*a*b^3*Sqrt[a + b]*x^(5/2)*Sqrt[a + b*x] + 396*b^4*Sqrt[a + b]*x^(5/2)*Sqrt[a + b*x] - 170*a*b^3*Sqrt[a + b]*x^3*Sqrt[a + b*x] - 240*b^4*Sqrt[a + b]*x^3*Sqrt[a + b*x] + 39*a*b^3*Sqrt[a + b]*x^(7/2)*Sqrt[a + b*x] + 84*b^4*Sqrt[a + b]*x^(7/2)*Sqrt[a + b*x] - 20*b^4*Sqrt[a + b]*x^4*Sqrt[a + b*x] + 2*b^4*Sqrt[a + b]*x^(9/2)*Sqrt[a + b*x]))/(Sqrt[a + b] - Sqrt[a + b*x])^10))/((-Sqrt[a + b] + Sqrt[a + b*x])*(-2*a^3 - 5*a^2*b - 2*a*b^2 + 2*a^2*b*Sqrt[x] - 3*a^2*b*x - 5*a*b^2*x - 2*b^3*x + 2*a*b^2*x^(3/2) - a*b^2*x^2 + 2*a^2*Sqrt[a + b]*Sqrt[a + b*x] + 4*a*b*Sqrt[a + b]*Sqrt[a + b*x] - 2*a*b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 2*b^2*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 2*a*b*Sqrt[a + b]*x*Sqrt[a + b*x])^3)","B",1
588,1,5745,64,42.9540003,"\int \frac{1}{x^{3/2} (a+b x)^{5/2}} \, dx","IntegrateAlgebraic[1/(x^(3/2)*(a + b*x)^(5/2)),x]","\text{Result too large to show}","-\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,"Result too large to show","B",1
589,-1,0,84,180.3889469,"\int \frac{1}{x^{5/2} (a+b x)^{5/2}} \, dx","IntegrateAlgebraic[1/(x^(5/2)*(a + b*x)^(5/2)),x]","\text{\$Aborted}","\frac{32 b \sqrt{a+b x}}{3 a^4 \sqrt{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{2}{3 a x^{3/2} (a+b x)^{3/2}}",1,"$Aborted","F",-1
590,1,1742,105,1.9984237,"\int \frac{x^{5/2}}{\sqrt{a-b x}} \, dx","IntegrateAlgebraic[x^(5/2)/Sqrt[a - b*x],x]","\frac{5 \tan ^{-1}\left(\frac{\frac{\sqrt{a-b}}{\sqrt{b}}-\frac{\sqrt{a-b x}}{\sqrt{b}}}{\sqrt{x}-1}\right) a^3}{4 b^{7/2}}+\frac{\left(-256 b^8+384 a b^7-144 a^2 b^6+8 a^3 b^5\right) \sqrt{a-b x} x^{11/2}+\left(768 a b^7-960 a^2 b^6+240 a^3 b^5\right) \sqrt{a-b x} x^5+\left(64 a b^7-1152 a^2 b^6+1092 a^3 b^5-134 a^4 b^4\right) \sqrt{a-b x} x^{9/2}+\left(880 a^3 b^5-660 a^4 b^4\right) \sqrt{a-b x} x^4+\left(-144 a^2 b^6-48 a^3 b^5-312 a^4 b^4+219 a^5 b^3\right) \sqrt{a-b x} x^{7/2}+\left(18 b^3 a^5-160 b^4 a^4+480 b^5 a^3\right) \sqrt{a-b x} x^3+\left(256 b^8-192 a b^7+144 a^2 b^6-80 a^3 b^5-1104 a^4 b^4+639 a^5 b^3-46 a^6 b^2\right) \sqrt{a-b x} x^{5/2}+\left(-768 a b^7+384 a^2 b^6-384 a^3 b^5+288 a^4 b^4+1590 a^5 b^3-750 a^6 b^2\right) \sqrt{a-b x} x^2+\left(400 b a^7-1500 b^2 a^6-615 b^3 a^5+896 b^4 a^4-408 b^5 a^3+1248 b^6 a^2-256 b^7 a\right) \sqrt{a-b x} x^{3/2}+\left(960 b a^7+820 b^2 a^6-1386 b^3 a^5+288 b^4 a^4-1168 b^5 a^3+576 b^6 a^2\right) \sqrt{a-b x} x+\left(-480 a^8-720 b a^7+1290 b^2 a^6-243 b^3 a^5+654 b^4 a^4-564 b^5 a^3+48 b^6 a^2\right) \sqrt{a-b x} \sqrt{x}+\sqrt{a-b} \left(-480 a^8+400 b a^7-46 b^2 a^6+219 b^3 a^5-134 b^4 a^4+8 b^5 a^3+\left(256 b^8-256 a b^7+48 a^2 b^6\right) x^6+\left(-768 a b^7+576 a^2 b^6-48 a^3 b^5\right) x^{11/2}+\left(-192 a b^7+1248 a^2 b^6-564 a^3 b^5\right) x^5+\left(384 a^2 b^6-1168 a^3 b^5+244 a^4 b^4\right) x^{9/2}+\left(144 a^2 b^6-408 a^3 b^5+654 a^4 b^4\right) x^4+\left(-222 b^3 a^5+288 b^4 a^4-384 b^5 a^3\right) x^{7/2}+\left(-256 b^8+64 a b^7-144 a^2 b^6-80 a^3 b^5+896 a^4 b^4-243 a^5 b^3\right) x^3+\left(768 a b^7+480 a^3 b^5+288 a^4 b^4-1386 a^5 b^3+186 a^6 b^2\right) x^{5/2}+\left(384 a b^7-1152 a^2 b^6-48 a^3 b^5-1104 a^4 b^4-615 a^5 b^3+1290 a^6 b^2\right) x^2+\left(-640 b a^7+820 b^2 a^6+1590 b^3 a^5-160 b^4 a^4+880 b^5 a^3-960 b^6 a^2\right) x^{3/2}+\left(-720 b a^7-1500 b^2 a^6+639 b^3 a^5-312 b^4 a^4+1092 b^5 a^3-144 b^6 a^2\right) x+\left(480 a^8+960 b a^7-750 b^2 a^6+18 b^3 a^5-660 b^4 a^4+240 b^5 a^3\right) \sqrt{x}\right)+\left(480 a^8-640 b a^7+186 b^2 a^6-222 b^3 a^5+244 b^4 a^4-48 b^5 a^3\right) \sqrt{a-b x}}{24 \left(32 b^6-48 a b^5+18 a^2 b^4-a^3 b^3\right) x^3 b^3+24 \left(32 a^6-48 b a^5+18 b^2 a^4-b^3 a^3\right) b^3+24 \sqrt{a-b} \left(-32 a^5+32 b a^4-6 b^2 a^3\right) \sqrt{a-b x} b^3+\sqrt{x} \left(24 \left(-96 b a^5+120 b^2 a^4-30 b^3 a^3\right) b^3+24 \sqrt{a-b} \left(96 b a^4-72 b^2 a^3+6 b^3 a^2\right) \sqrt{a-b x} b^3\right)+x \left(24 \left(-48 b a^5+204 b^2 a^4-159 b^3 a^3+18 b^4 a^2\right) b^3+24 \sqrt{a-b} \left(32 b a^4-164 b^2 a^3+72 b^3 a^2\right) \sqrt{a-b x} b^3\right)+x^2 \left(24 \left(-48 a b^5+204 a^2 b^4-159 a^3 b^3+18 a^4 b^2\right) b^3+24 \sqrt{a-b} \left(-96 a b^4+72 a^2 b^3-6 a^3 b^2\right) \sqrt{a-b x} b^3\right)+x^{3/2} \left(24 \left(120 b^2 a^4-260 b^3 a^3+120 b^4 a^2\right) b^3+24 \sqrt{a-b} \left(-32 a b^4+164 a^2 b^3-72 a^3 b^2\right) \sqrt{a-b x} b^3\right)+x^{5/2} \left(24 \left(-96 a b^5+120 a^2 b^4-30 a^3 b^3\right) b^3+24 \sqrt{a-b} \left(32 b^5-32 a b^4+6 a^2 b^3\right) \sqrt{a-b x} b^3\right)}","\frac{5 a^3 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)}{8 b^{7/2}}-\frac{5 a^2 \sqrt{x} \sqrt{a-b x}}{8 b^3}-\frac{5 a x^{3/2} \sqrt{a-b x}}{12 b^2}-\frac{x^{5/2} \sqrt{a-b x}}{3 b}",1,"((480*a^8 - 640*a^7*b + 186*a^6*b^2 - 222*a^5*b^3 + 244*a^4*b^4 - 48*a^3*b^5)*Sqrt[a - b*x] + (-480*a^8 - 720*a^7*b + 1290*a^6*b^2 - 243*a^5*b^3 + 654*a^4*b^4 - 564*a^3*b^5 + 48*a^2*b^6)*Sqrt[x]*Sqrt[a - b*x] + (960*a^7*b + 820*a^6*b^2 - 1386*a^5*b^3 + 288*a^4*b^4 - 1168*a^3*b^5 + 576*a^2*b^6)*x*Sqrt[a - b*x] + (400*a^7*b - 1500*a^6*b^2 - 615*a^5*b^3 + 896*a^4*b^4 - 408*a^3*b^5 + 1248*a^2*b^6 - 256*a*b^7)*x^(3/2)*Sqrt[a - b*x] + (-750*a^6*b^2 + 1590*a^5*b^3 + 288*a^4*b^4 - 384*a^3*b^5 + 384*a^2*b^6 - 768*a*b^7)*x^2*Sqrt[a - b*x] + (-46*a^6*b^2 + 639*a^5*b^3 - 1104*a^4*b^4 - 80*a^3*b^5 + 144*a^2*b^6 - 192*a*b^7 + 256*b^8)*x^(5/2)*Sqrt[a - b*x] + (18*a^5*b^3 - 160*a^4*b^4 + 480*a^3*b^5)*x^3*Sqrt[a - b*x] + (219*a^5*b^3 - 312*a^4*b^4 - 48*a^3*b^5 - 144*a^2*b^6)*x^(7/2)*Sqrt[a - b*x] + (-660*a^4*b^4 + 880*a^3*b^5)*x^4*Sqrt[a - b*x] + (-134*a^4*b^4 + 1092*a^3*b^5 - 1152*a^2*b^6 + 64*a*b^7)*x^(9/2)*Sqrt[a - b*x] + (240*a^3*b^5 - 960*a^2*b^6 + 768*a*b^7)*x^5*Sqrt[a - b*x] + (8*a^3*b^5 - 144*a^2*b^6 + 384*a*b^7 - 256*b^8)*x^(11/2)*Sqrt[a - b*x] + Sqrt[a - b]*(-480*a^8 + 400*a^7*b - 46*a^6*b^2 + 219*a^5*b^3 - 134*a^4*b^4 + 8*a^3*b^5 + (480*a^8 + 960*a^7*b - 750*a^6*b^2 + 18*a^5*b^3 - 660*a^4*b^4 + 240*a^3*b^5)*Sqrt[x] + (-720*a^7*b - 1500*a^6*b^2 + 639*a^5*b^3 - 312*a^4*b^4 + 1092*a^3*b^5 - 144*a^2*b^6)*x + (-640*a^7*b + 820*a^6*b^2 + 1590*a^5*b^3 - 160*a^4*b^4 + 880*a^3*b^5 - 960*a^2*b^6)*x^(3/2) + (1290*a^6*b^2 - 615*a^5*b^3 - 1104*a^4*b^4 - 48*a^3*b^5 - 1152*a^2*b^6 + 384*a*b^7)*x^2 + (186*a^6*b^2 - 1386*a^5*b^3 + 288*a^4*b^4 + 480*a^3*b^5 + 768*a*b^7)*x^(5/2) + (-243*a^5*b^3 + 896*a^4*b^4 - 80*a^3*b^5 - 144*a^2*b^6 + 64*a*b^7 - 256*b^8)*x^3 + (-222*a^5*b^3 + 288*a^4*b^4 - 384*a^3*b^5)*x^(7/2) + (654*a^4*b^4 - 408*a^3*b^5 + 144*a^2*b^6)*x^4 + (244*a^4*b^4 - 1168*a^3*b^5 + 384*a^2*b^6)*x^(9/2) + (-564*a^3*b^5 + 1248*a^2*b^6 - 192*a*b^7)*x^5 + (-48*a^3*b^5 + 576*a^2*b^6 - 768*a*b^7)*x^(11/2) + (48*a^2*b^6 - 256*a*b^7 + 256*b^8)*x^6))/(24*b^3*(32*a^6 - 48*a^5*b + 18*a^4*b^2 - a^3*b^3) + 24*b^3*(-(a^3*b^3) + 18*a^2*b^4 - 48*a*b^5 + 32*b^6)*x^3 + 24*Sqrt[a - b]*b^3*(-32*a^5 + 32*a^4*b - 6*a^3*b^2)*Sqrt[a - b*x] + Sqrt[x]*(24*b^3*(-96*a^5*b + 120*a^4*b^2 - 30*a^3*b^3) + 24*Sqrt[a - b]*b^3*(96*a^4*b - 72*a^3*b^2 + 6*a^2*b^3)*Sqrt[a - b*x]) + x*(24*b^3*(-48*a^5*b + 204*a^4*b^2 - 159*a^3*b^3 + 18*a^2*b^4) + 24*Sqrt[a - b]*b^3*(32*a^4*b - 164*a^3*b^2 + 72*a^2*b^3)*Sqrt[a - b*x]) + x^2*(24*b^3*(18*a^4*b^2 - 159*a^3*b^3 + 204*a^2*b^4 - 48*a*b^5) + 24*Sqrt[a - b]*b^3*(-6*a^3*b^2 + 72*a^2*b^3 - 96*a*b^4)*Sqrt[a - b*x]) + x^(3/2)*(24*b^3*(120*a^4*b^2 - 260*a^3*b^3 + 120*a^2*b^4) + 24*Sqrt[a - b]*b^3*(-72*a^3*b^2 + 164*a^2*b^3 - 32*a*b^4)*Sqrt[a - b*x]) + x^(5/2)*(24*b^3*(-30*a^3*b^3 + 120*a^2*b^4 - 96*a*b^5) + 24*Sqrt[a - b]*b^3*(6*a^2*b^3 - 32*a*b^4 + 32*b^5)*Sqrt[a - b*x])) + (5*a^3*ArcTan[(Sqrt[a - b]/Sqrt[b] - Sqrt[a - b*x]/Sqrt[b])/(-1 + Sqrt[x])])/(4*b^(7/2))","B",1
591,1,784,80,0.8858696,"\int \frac{x^{3/2}}{\sqrt{a-b x}} \, dx","IntegrateAlgebraic[x^(3/2)/Sqrt[a - b*x],x]","\frac{3 a^2 \tan ^{-1}\left(\frac{\frac{\sqrt{a-b}}{\sqrt{b}}-\frac{\sqrt{a-b x}}{\sqrt{b}}}{\sqrt{x}-1}\right)}{2 b^{5/2}}+\frac{\left(\frac{1}{4 b^2}-\frac{\sqrt{x}}{4 b^2}\right) \left(\sqrt{a-b}-\sqrt{a-b x}\right) \left(-12 a^5+7 a^4 b x+22 a^4 b \sqrt{x}+12 a^4 \sqrt{a-b} \sqrt{a-b x}+7 a^4 b-a^3 b^2 x^{3/2}+7 a^3 b^2 x^2-16 a^3 b^2 x-a^3 b^2 \sqrt{x}+7 a^3 b^2-a^3 b \sqrt{a-b} \sqrt{a-b x}-a^3 b x \sqrt{a-b} \sqrt{a-b x}-22 a^3 b \sqrt{x} \sqrt{a-b} \sqrt{a-b x}-18 a^2 b^3 x^{5/2}-12 a^2 b^3 x^{3/2}-2 a^2 b^3 x^3-16 a^2 b^3 x^2-16 a^2 b^3 x-18 a^2 b^3 \sqrt{x}-2 a^2 b^3-10 a^2 b^2 x^{3/2} \sqrt{a-b} \sqrt{a-b x}-6 a^2 b^2 x^2 \sqrt{a-b} \sqrt{a-b x}-6 a^2 b^2 \sqrt{a-b} \sqrt{a-b x}+12 a^2 b^2 x \sqrt{a-b} \sqrt{a-b x}-10 a^2 b^2 \sqrt{x} \sqrt{a-b} \sqrt{a-b x}+24 a b^4 x^{5/2}+24 a b^4 x^{3/2}-16 b^4 x^{5/2} \sqrt{a-b} \sqrt{a-b x}-16 b^4 x^{3/2} \sqrt{a-b} \sqrt{a-b x}+16 a b^4 x^3+16 a b^4 x^2+16 a b^4 x+8 a b^3 x^{5/2} \sqrt{a-b} \sqrt{a-b x}+24 a b^3 x^2 \sqrt{a-b} \sqrt{a-b x}+24 a b^3 x \sqrt{a-b} \sqrt{a-b x}+8 a b^3 \sqrt{x} \sqrt{a-b} \sqrt{a-b x}-16 b^5 x^3-16 b^5 x^2\right)}{\left(\sqrt{a-b} \sqrt{a-b x}-a+b \sqrt{x}\right)^4}","\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,"((1/(4*b^2) - Sqrt[x]/(4*b^2))*(Sqrt[a - b] - Sqrt[a - b*x])*(-12*a^5 + 7*a^4*b + 7*a^3*b^2 - 2*a^2*b^3 + 22*a^4*b*Sqrt[x] - a^3*b^2*Sqrt[x] - 18*a^2*b^3*Sqrt[x] + 7*a^4*b*x - 16*a^3*b^2*x - 16*a^2*b^3*x + 16*a*b^4*x - a^3*b^2*x^(3/2) - 12*a^2*b^3*x^(3/2) + 24*a*b^4*x^(3/2) + 7*a^3*b^2*x^2 - 16*a^2*b^3*x^2 + 16*a*b^4*x^2 - 16*b^5*x^2 - 18*a^2*b^3*x^(5/2) + 24*a*b^4*x^(5/2) - 2*a^2*b^3*x^3 + 16*a*b^4*x^3 - 16*b^5*x^3 + 12*a^4*Sqrt[a - b]*Sqrt[a - b*x] - a^3*Sqrt[a - b]*b*Sqrt[a - b*x] - 6*a^2*Sqrt[a - b]*b^2*Sqrt[a - b*x] - 22*a^3*Sqrt[a - b]*b*Sqrt[x]*Sqrt[a - b*x] - 10*a^2*Sqrt[a - b]*b^2*Sqrt[x]*Sqrt[a - b*x] + 8*a*Sqrt[a - b]*b^3*Sqrt[x]*Sqrt[a - b*x] - a^3*Sqrt[a - b]*b*x*Sqrt[a - b*x] + 12*a^2*Sqrt[a - b]*b^2*x*Sqrt[a - b*x] + 24*a*Sqrt[a - b]*b^3*x*Sqrt[a - b*x] - 10*a^2*Sqrt[a - b]*b^2*x^(3/2)*Sqrt[a - b*x] - 16*Sqrt[a - b]*b^4*x^(3/2)*Sqrt[a - b*x] - 6*a^2*Sqrt[a - b]*b^2*x^2*Sqrt[a - b*x] + 24*a*Sqrt[a - b]*b^3*x^2*Sqrt[a - b*x] + 8*a*Sqrt[a - b]*b^3*x^(5/2)*Sqrt[a - b*x] - 16*Sqrt[a - b]*b^4*x^(5/2)*Sqrt[a - b*x]))/(-a + b*Sqrt[x] + Sqrt[a - b]*Sqrt[a - b*x])^4 + (3*a^2*ArcTan[(Sqrt[a - b]/Sqrt[b] - Sqrt[a - b*x]/Sqrt[b])/(-1 + Sqrt[x])])/(2*b^(5/2))","B",1
592,1,201,50,0.296896,"\int \frac{\sqrt{x}}{\sqrt{a-b x}} \, dx","IntegrateAlgebraic[Sqrt[x]/Sqrt[a - b*x],x]","\frac{\left(\frac{\sqrt{x}}{b}-\frac{1}{b}\right) \left(\sqrt{a-b}-\sqrt{a-b x}\right) \left(a^2-a b x-a b \sqrt{x}-a \sqrt{a-b} \sqrt{a-b x}+2 b \sqrt{x} \sqrt{a-b} \sqrt{a-b x}-a b+2 b^2 x\right)}{\left(\sqrt{a-b} \sqrt{a-b x}-a+b \sqrt{x}\right)^2}+\frac{2 a \tan ^{-1}\left(\frac{\frac{\sqrt{a-b}}{\sqrt{b}}-\frac{\sqrt{a-b x}}{\sqrt{b}}}{\sqrt{x}-1}\right)}{b^{3/2}}","\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,"((-b^(-1) + Sqrt[x]/b)*(Sqrt[a - b] - Sqrt[a - b*x])*(a^2 - a*b - a*b*Sqrt[x] - a*b*x + 2*b^2*x - a*Sqrt[a - b]*Sqrt[a - b*x] + 2*Sqrt[a - b]*b*Sqrt[x]*Sqrt[a - b*x]))/(-a + b*Sqrt[x] + Sqrt[a - b]*Sqrt[a - b*x])^2 + (2*a*ArcTan[(Sqrt[a - b]/Sqrt[b] - Sqrt[a - b*x]/Sqrt[b])/(-1 + Sqrt[x])])/b^(3/2)","B",1
593,1,51,29,0.1522201,"\int \frac{1}{\sqrt{x} \sqrt{a-b x}} \, dx","IntegrateAlgebraic[1/(Sqrt[x]*Sqrt[a - b*x]),x]","-\frac{4 \tan ^{-1}\left(\frac{\frac{\sqrt{a-b x}}{\sqrt{b}}-\frac{\sqrt{a-b}}{\sqrt{b}}}{\sqrt{x}-1}\right)}{\sqrt{b}}","\frac{2 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)}{\sqrt{b}}",1,"(-4*ArcTan[(-(Sqrt[a - b]/Sqrt[b]) + Sqrt[a - b*x]/Sqrt[b])/(-1 + Sqrt[x])])/Sqrt[b]","A",1
594,1,268,20,0.2643761,"\int \frac{1}{x^{3/2} \sqrt{a-b x}} \, dx","IntegrateAlgebraic[1/(x^(3/2)*Sqrt[a - b*x]),x]","\frac{\left(\sqrt{a-b}-\sqrt{a-b x}\right)^4 \left(\frac{b \left(\sqrt{x}-1\right)^3}{\left(\sqrt{a-b}-\sqrt{a-b x}\right)^3}+\frac{2 \left(\sqrt{x}-1\right)^2 \sqrt{a-b}}{\left(\sqrt{a-b}-\sqrt{a-b x}\right)^2}-\frac{\sqrt{x}-1}{\sqrt{a-b}-\sqrt{a-b x}}\right)}{-2 a^2 x+4 a^2 \sqrt{x}-2 a b x^{3/2}+a b x^2+a b x-4 a b \sqrt{x}+2 a x \sqrt{a-b} \sqrt{a-b x}-4 a \sqrt{x} \sqrt{a-b} \sqrt{a-b x}+2 b \sqrt{x} \sqrt{a-b} \sqrt{a-b x}+2 b^2 x}","-\frac{2 \sqrt{a-b x}}{a \sqrt{x}}",1,"((Sqrt[a - b] - Sqrt[a - b*x])^4*((b*(-1 + Sqrt[x])^3)/(Sqrt[a - b] - Sqrt[a - b*x])^3 + (2*Sqrt[a - b]*(-1 + Sqrt[x])^2)/(Sqrt[a - b] - Sqrt[a - b*x])^2 - (-1 + Sqrt[x])/(Sqrt[a - b] - Sqrt[a - b*x])))/(4*a^2*Sqrt[x] - 4*a*b*Sqrt[x] - 2*a^2*x + a*b*x + 2*b^2*x - 2*a*b*x^(3/2) + a*b*x^2 - 4*a*Sqrt[a - b]*Sqrt[x]*Sqrt[a - b*x] + 2*Sqrt[a - b]*b*Sqrt[x]*Sqrt[a - b*x] + 2*a*Sqrt[a - b]*x*Sqrt[a - b*x])","B",1
595,1,644,46,4.8734116,"\int \frac{1}{x^{5/2} \sqrt{a-b x}} \, dx","IntegrateAlgebraic[1/(x^(5/2)*Sqrt[a - b*x]),x]","\frac{\left(\frac{\sqrt{x}}{48}-\frac{1}{48}\right) \left(\sqrt{a-b}-\sqrt{a-b x}\right)^{12} \left(-\frac{8 \left(\sqrt{x}-1\right)^5 \sqrt{a-b} \left(4 a^2+2 a b-3 b^2\right)}{\left(\sqrt{a-b}-\sqrt{a-b x}\right)^5}-\frac{3 b^5 \left(\sqrt{x}-1\right)^{10}}{\left(\sqrt{a-b}-\sqrt{a-b x}\right)^{10}}-\frac{12 b^4 \left(\sqrt{x}-1\right)^9 \sqrt{a-b}}{\left(\sqrt{a-b}-\sqrt{a-b x}\right)^9}+\frac{b^3 \left(\sqrt{x}-1\right)^8 (15 b-4 a)}{\left(\sqrt{a-b}-\sqrt{a-b x}\right)^8}+\frac{24 a b^2 \left(\sqrt{x}-1\right)^7 \sqrt{a-b}}{\left(\sqrt{a-b}-\sqrt{a-b x}\right)^7}+\frac{18 b^2 \left(\sqrt{x}-1\right)^6 (b-2 a)}{\left(\sqrt{a-b}-\sqrt{a-b x}\right)^6}+\frac{18 b \left(\sqrt{x}-1\right)^4 (2 a-b)}{\left(\sqrt{a-b}-\sqrt{a-b x}\right)^4}+\frac{24 a \left(\sqrt{x}-1\right)^3 \sqrt{a-b}}{\left(\sqrt{a-b}-\sqrt{a-b x}\right)^3}+\frac{\left(\sqrt{x}-1\right)^2 (4 a-15 b)}{\left(\sqrt{a-b}-\sqrt{a-b x}\right)^2}-\frac{12 \left(\sqrt{x}-1\right) \sqrt{a-b}}{\sqrt{a-b}-\sqrt{a-b x}}+3\right)}{\left(\sqrt{a-b x}-\sqrt{a-b}\right) \left(-2 a^2 x+4 a^2 \sqrt{x}-2 a b x^{3/2}+a b x^2+a b x-4 a b \sqrt{x}+2 a x \sqrt{a-b} \sqrt{a-b x}-4 a \sqrt{x} \sqrt{a-b} \sqrt{a-b x}+2 b \sqrt{x} \sqrt{a-b} \sqrt{a-b x}+2 b^2 x\right)^3}","-\frac{4 b \sqrt{a-b x}}{3 a^2 \sqrt{x}}-\frac{2 \sqrt{a-b x}}{3 a x^{3/2}}",1,"((-1/48 + Sqrt[x]/48)*(Sqrt[a - b] - Sqrt[a - b*x])^12*(3 - (3*b^5*(-1 + Sqrt[x])^10)/(Sqrt[a - b] - Sqrt[a - b*x])^10 - (12*Sqrt[a - b]*b^4*(-1 + Sqrt[x])^9)/(Sqrt[a - b] - Sqrt[a - b*x])^9 + (b^3*(-4*a + 15*b)*(-1 + Sqrt[x])^8)/(Sqrt[a - b] - Sqrt[a - b*x])^8 + (24*a*Sqrt[a - b]*b^2*(-1 + Sqrt[x])^7)/(Sqrt[a - b] - Sqrt[a - b*x])^7 + (18*b^2*(-2*a + b)*(-1 + Sqrt[x])^6)/(Sqrt[a - b] - Sqrt[a - b*x])^6 - (8*Sqrt[a - b]*(4*a^2 + 2*a*b - 3*b^2)*(-1 + Sqrt[x])^5)/(Sqrt[a - b] - Sqrt[a - b*x])^5 + (18*(2*a - b)*b*(-1 + Sqrt[x])^4)/(Sqrt[a - b] - Sqrt[a - b*x])^4 + (24*a*Sqrt[a - b]*(-1 + Sqrt[x])^3)/(Sqrt[a - b] - Sqrt[a - b*x])^3 + ((4*a - 15*b)*(-1 + Sqrt[x])^2)/(Sqrt[a - b] - Sqrt[a - b*x])^2 - (12*Sqrt[a - b]*(-1 + Sqrt[x]))/(Sqrt[a - b] - Sqrt[a - b*x])))/((-Sqrt[a - b] + Sqrt[a - b*x])*(4*a^2*Sqrt[x] - 4*a*b*Sqrt[x] - 2*a^2*x + a*b*x + 2*b^2*x - 2*a*b*x^(3/2) + a*b*x^2 - 4*a*Sqrt[a - b]*Sqrt[x]*Sqrt[a - b*x] + 2*Sqrt[a - b]*b*Sqrt[x]*Sqrt[a - b*x] + 2*a*Sqrt[a - b]*x*Sqrt[a - b*x])^3)","B",1
596,1,1074,100,4.049662,"\int \frac{x^{5/2}}{(a-b x)^{3/2}} \, dx","IntegrateAlgebraic[x^(5/2)/(a - b*x)^(3/2),x]","\frac{\left(\frac{\sqrt{x} a^2}{2 b^3}+\frac{3 a^2}{2 b^3}-\frac{4 \sqrt{x} a}{b^2}-\frac{2 \sqrt{a-b} \sqrt{a-b x} a}{b^3}-\frac{2 a}{b^2}+\frac{4 \sqrt{x}}{b}+\frac{4 \sqrt{a-b} \sqrt{a-b x}}{b^2}\right) \left(\sqrt{a-b}-\sqrt{a-b x}\right)^7}{\left(-a+b \sqrt{x}+\sqrt{a-b} \sqrt{a-b x}\right)^4}+\frac{\left(\frac{3 \sqrt{x} a^2}{2 b^3}+\frac{13 a^2}{2 b^3}-\frac{12 \sqrt{x} a}{b^2}-\frac{8 \sqrt{a-b} \sqrt{a-b x} a}{b^3}-\frac{12 a}{b^2}+\frac{12 \sqrt{x}}{b}+\frac{16 \sqrt{a-b} \sqrt{a-b x}}{b^2}+\frac{4}{b}\right) \left(\sqrt{a-b}-\sqrt{a-b x}\right)^5}{\left(-a+b \sqrt{x}+\sqrt{a-b} \sqrt{a-b x}\right)^3}+\frac{\left(-\frac{3 \sqrt{x} a^2}{4 b^3}+\frac{27 a^2}{4 b^3}-\frac{6 \sqrt{x} a}{b^2}-\frac{6 \sqrt{a-b} \sqrt{a-b x} a}{b^3}-\frac{20 a}{b^2}+\frac{10 \sqrt{x}}{b}+\frac{20 \sqrt{a-b} \sqrt{a-b x}}{b^2}+\frac{10}{b}\right) \left(\sqrt{a-b}-\sqrt{a-b x}\right)^3}{\left(-a+b \sqrt{x}+\sqrt{a-b} \sqrt{a-b x}\right)^2}+\frac{\left(\frac{2 a^3}{(a-b) b^3}-\frac{2 a^3 \sqrt{x}}{(a-b) b^3}\right) \left(-a^2+3 b a+b x a-2 b \sqrt{x} a+\sqrt{a-b} \sqrt{a-b x} a-2 b^2-b^2 x+2 b^2 \sqrt{x}-2 \sqrt{a-b} b \sqrt{a-b x}+\sqrt{a-b} b \sqrt{x} \sqrt{a-b x}\right) \left(\sqrt{a-b}-\sqrt{a-b x}\right)}{-2 a^3+5 b a^2+3 b x a^2-2 b \sqrt{x} a^2+2 \sqrt{a-b} \sqrt{a-b x} a^2-2 b^2 a-b^2 x^2 a+2 b^2 x^{3/2} a-5 b^2 x a-4 \sqrt{a-b} b \sqrt{a-b x} a-2 \sqrt{a-b} b x \sqrt{a-b x} a+2 \sqrt{a-b} b \sqrt{x} \sqrt{a-b x} a+2 b^3 x+2 \sqrt{a-b} b^2 \sqrt{x} \sqrt{a-b x}}+\frac{\left(\frac{\sqrt{a-b x}}{4 b^3}-\frac{\sqrt{a-b}}{4 b^3}\right) \left(7 \sqrt{x} a^2+9 a^2+24 b a-8 b \sqrt{x} a-16 \sqrt{a-b} \sqrt{a-b x} a-24 b^2-8 b^2 \sqrt{x}-32 \sqrt{a-b} b \sqrt{a-b x}\right)}{-a+b \sqrt{x}+\sqrt{a-b} \sqrt{a-b x}}-\frac{15 a^2 \tan ^{-1}\left(\frac{\frac{\sqrt{a-b}}{\sqrt{b}}-\frac{\sqrt{a-b x}}{\sqrt{b}}}{\sqrt{x}-1}\right)}{2 b^{7/2}}","-\frac{15 a^2 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)}{4 b^{7/2}}+\frac{15 a \sqrt{x} \sqrt{a-b x}}{4 b^3}+\frac{5 x^{3/2} \sqrt{a-b x}}{2 b^2}+\frac{2 x^{5/2}}{b \sqrt{a-b x}}",1,"((Sqrt[a - b] - Sqrt[a - b*x])^7*((3*a^2)/(2*b^3) - (2*a)/b^2 + (a^2*Sqrt[x])/(2*b^3) - (4*a*Sqrt[x])/b^2 + (4*Sqrt[x])/b - (2*a*Sqrt[a - b]*Sqrt[a - b*x])/b^3 + (4*Sqrt[a - b]*Sqrt[a - b*x])/b^2))/(-a + b*Sqrt[x] + Sqrt[a - b]*Sqrt[a - b*x])^4 + ((Sqrt[a - b] - Sqrt[a - b*x])^5*((13*a^2)/(2*b^3) - (12*a)/b^2 + 4/b + (3*a^2*Sqrt[x])/(2*b^3) - (12*a*Sqrt[x])/b^2 + (12*Sqrt[x])/b - (8*a*Sqrt[a - b]*Sqrt[a - b*x])/b^3 + (16*Sqrt[a - b]*Sqrt[a - b*x])/b^2))/(-a + b*Sqrt[x] + Sqrt[a - b]*Sqrt[a - b*x])^3 + ((Sqrt[a - b] - Sqrt[a - b*x])^3*((27*a^2)/(4*b^3) - (20*a)/b^2 + 10/b - (3*a^2*Sqrt[x])/(4*b^3) - (6*a*Sqrt[x])/b^2 + (10*Sqrt[x])/b - (6*a*Sqrt[a - b]*Sqrt[a - b*x])/b^3 + (20*Sqrt[a - b]*Sqrt[a - b*x])/b^2))/(-a + b*Sqrt[x] + Sqrt[a - b]*Sqrt[a - b*x])^2 + ((-1/4*Sqrt[a - b]/b^3 + Sqrt[a - b*x]/(4*b^3))*(9*a^2 + 24*a*b - 24*b^2 + 7*a^2*Sqrt[x] - 8*a*b*Sqrt[x] - 8*b^2*Sqrt[x] - 16*a*Sqrt[a - b]*Sqrt[a - b*x] - 32*Sqrt[a - b]*b*Sqrt[a - b*x]))/(-a + b*Sqrt[x] + Sqrt[a - b]*Sqrt[a - b*x]) + (((2*a^3)/((a - b)*b^3) - (2*a^3*Sqrt[x])/((a - b)*b^3))*(Sqrt[a - b] - Sqrt[a - b*x])*(-a^2 + 3*a*b - 2*b^2 - 2*a*b*Sqrt[x] + 2*b^2*Sqrt[x] + a*b*x - b^2*x + a*Sqrt[a - b]*Sqrt[a - b*x] - 2*Sqrt[a - b]*b*Sqrt[a - b*x] + Sqrt[a - b]*b*Sqrt[x]*Sqrt[a - b*x]))/(-2*a^3 + 5*a^2*b - 2*a*b^2 - 2*a^2*b*Sqrt[x] + 3*a^2*b*x - 5*a*b^2*x + 2*b^3*x + 2*a*b^2*x^(3/2) - a*b^2*x^2 + 2*a^2*Sqrt[a - b]*Sqrt[a - b*x] - 4*a*Sqrt[a - b]*b*Sqrt[a - b*x] + 2*a*Sqrt[a - b]*b*Sqrt[x]*Sqrt[a - b*x] + 2*Sqrt[a - b]*b^2*Sqrt[x]*Sqrt[a - b*x] - 2*a*Sqrt[a - b]*b*x*Sqrt[a - b*x]) - (15*a^2*ArcTan[(Sqrt[a - b]/Sqrt[b] - Sqrt[a - b*x]/Sqrt[b])/(-1 + Sqrt[x])])/(2*b^(7/2))","B",1
597,1,640,71,1.4482057,"\int \frac{x^{3/2}}{(a-b x)^{3/2}} \, dx","IntegrateAlgebraic[x^(3/2)/(a - b*x)^(3/2),x]","\frac{\left(\frac{2 a^2}{b^2 (a-b)}-\frac{2 a^2 \sqrt{x}}{b^2 (a-b)}\right) \left(-a^2+a b x-2 a b \sqrt{x}+a \sqrt{a-b} \sqrt{a-b x}-2 b \sqrt{a-b} \sqrt{a-b x}+b \sqrt{x} \sqrt{a-b} \sqrt{a-b x}+3 a b-b^2 x+2 b^2 \sqrt{x}-2 b^2\right) \left(\sqrt{a-b}-\sqrt{a-b x}\right)}{-2 a^3+3 a^2 b x-2 a^2 b \sqrt{x}+2 a^2 \sqrt{a-b} \sqrt{a-b x}+5 a^2 b+2 a b^2 x^{3/2}-a b^2 x^2-5 a b^2 x+2 b^2 \sqrt{x} \sqrt{a-b} \sqrt{a-b x}-2 a b^2-4 a b \sqrt{a-b} \sqrt{a-b x}-2 a b x \sqrt{a-b} \sqrt{a-b x}+2 a b \sqrt{x} \sqrt{a-b} \sqrt{a-b x}+2 b^3 x}-\frac{6 a \tan ^{-1}\left(\frac{\frac{\sqrt{a-b}}{\sqrt{b}}-\frac{\sqrt{a-b x}}{\sqrt{b}}}{\sqrt{x}-1}\right)}{b^{5/2}}+\frac{\left(-\frac{a \sqrt{x}}{b^2}+\frac{2 \sqrt{a-b} \sqrt{a-b x}}{b^2}-\frac{a}{b^2}+\frac{2 \sqrt{x}}{b}\right) \left(\sqrt{a-b}-\sqrt{a-b x}\right)^3}{\left(\sqrt{a-b} \sqrt{a-b x}-a+b \sqrt{x}\right)^2}+\frac{\left(-4 \sqrt{a-b} \sqrt{a-b x}+a \sqrt{x}+3 a-2 b \sqrt{x}-2 b\right) \left(\frac{\sqrt{a-b x}}{b^2}-\frac{\sqrt{a-b}}{b^2}\right)}{\sqrt{a-b} \sqrt{a-b x}-a+b \sqrt{x}}","-\frac{3 a \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)}{b^{5/2}}+\frac{3 \sqrt{x} \sqrt{a-b x}}{b^2}+\frac{2 x^{3/2}}{b \sqrt{a-b x}}",1,"((3*a - 2*b + a*Sqrt[x] - 2*b*Sqrt[x] - 4*Sqrt[a - b]*Sqrt[a - b*x])*(-(Sqrt[a - b]/b^2) + Sqrt[a - b*x]/b^2))/(-a + b*Sqrt[x] + Sqrt[a - b]*Sqrt[a - b*x]) + ((Sqrt[a - b] - Sqrt[a - b*x])^3*(-(a/b^2) - (a*Sqrt[x])/b^2 + (2*Sqrt[x])/b + (2*Sqrt[a - b]*Sqrt[a - b*x])/b^2))/(-a + b*Sqrt[x] + Sqrt[a - b]*Sqrt[a - b*x])^2 + (((2*a^2)/((a - b)*b^2) - (2*a^2*Sqrt[x])/((a - b)*b^2))*(Sqrt[a - b] - Sqrt[a - b*x])*(-a^2 + 3*a*b - 2*b^2 - 2*a*b*Sqrt[x] + 2*b^2*Sqrt[x] + a*b*x - b^2*x + a*Sqrt[a - b]*Sqrt[a - b*x] - 2*Sqrt[a - b]*b*Sqrt[a - b*x] + Sqrt[a - b]*b*Sqrt[x]*Sqrt[a - b*x]))/(-2*a^3 + 5*a^2*b - 2*a*b^2 - 2*a^2*b*Sqrt[x] + 3*a^2*b*x - 5*a*b^2*x + 2*b^3*x + 2*a*b^2*x^(3/2) - a*b^2*x^2 + 2*a^2*Sqrt[a - b]*Sqrt[a - b*x] - 4*a*Sqrt[a - b]*b*Sqrt[a - b*x] + 2*a*Sqrt[a - b]*b*Sqrt[x]*Sqrt[a - b*x] + 2*Sqrt[a - b]*b^2*Sqrt[x]*Sqrt[a - b*x] - 2*a*Sqrt[a - b]*b*x*Sqrt[a - b*x]) - (6*a*ArcTan[(Sqrt[a - b]/Sqrt[b] - Sqrt[a - b*x]/Sqrt[b])/(-1 + Sqrt[x])])/b^(5/2)","B",1
598,1,419,50,0.5248898,"\int \frac{\sqrt{x}}{(a-b x)^{3/2}} \, dx","IntegrateAlgebraic[Sqrt[x]/(a - b*x)^(3/2),x]","\frac{\left(\frac{2 a}{b (b-a)}-\frac{2 a \sqrt{x}}{b (b-a)}\right) \left(\sqrt{a-b}-\sqrt{a-b x}\right) \left(a^2-a b x+2 a b \sqrt{x}-a \sqrt{a-b} \sqrt{a-b x}+2 b \sqrt{a-b} \sqrt{a-b x}-b \sqrt{x} \sqrt{a-b} \sqrt{a-b x}-3 a b+b^2 x-2 b^2 \sqrt{x}+2 b^2\right)}{-2 a^3+3 a^2 b x-2 a^2 b \sqrt{x}+2 a^2 \sqrt{a-b} \sqrt{a-b x}+5 a^2 b+2 a b^2 x^{3/2}-a b^2 x^2-5 a b^2 x+2 b^2 \sqrt{x} \sqrt{a-b} \sqrt{a-b x}-2 a b^2-4 a b \sqrt{a-b} \sqrt{a-b x}-2 a b x \sqrt{a-b} \sqrt{a-b x}+2 a b \sqrt{x} \sqrt{a-b} \sqrt{a-b x}+2 b^3 x}-\frac{4 \tan ^{-1}\left(\frac{\frac{\sqrt{a-b}}{\sqrt{b}}-\frac{\sqrt{a-b x}}{\sqrt{b}}}{\sqrt{x}-1}\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*a)/(b*(-a + b)) - (2*a*Sqrt[x])/(b*(-a + b)))*(Sqrt[a - b] - Sqrt[a - b*x])*(a^2 - 3*a*b + 2*b^2 + 2*a*b*Sqrt[x] - 2*b^2*Sqrt[x] - a*b*x + b^2*x - a*Sqrt[a - b]*Sqrt[a - b*x] + 2*Sqrt[a - b]*b*Sqrt[a - b*x] - Sqrt[a - b]*b*Sqrt[x]*Sqrt[a - b*x]))/(-2*a^3 + 5*a^2*b - 2*a*b^2 - 2*a^2*b*Sqrt[x] + 3*a^2*b*x - 5*a*b^2*x + 2*b^3*x + 2*a*b^2*x^(3/2) - a*b^2*x^2 + 2*a^2*Sqrt[a - b]*Sqrt[a - b*x] - 4*a*Sqrt[a - b]*b*Sqrt[a - b*x] + 2*a*Sqrt[a - b]*b*Sqrt[x]*Sqrt[a - b*x] + 2*Sqrt[a - b]*b^2*Sqrt[x]*Sqrt[a - b*x] - 2*a*Sqrt[a - b]*b*x*Sqrt[a - b*x]) - (4*ArcTan[(Sqrt[a - b]/Sqrt[b] - Sqrt[a - b*x]/Sqrt[b])/(-1 + Sqrt[x])])/b^(3/2)","B",1
599,1,409,20,0.3970279,"\int \frac{1}{\sqrt{x} (a-b x)^{3/2}} \, dx","IntegrateAlgebraic[1/(Sqrt[x]*(a - b*x)^(3/2)),x]","\frac{\left(\frac{1}{a-b}-\frac{\sqrt{x}}{a-b}\right) \left(\sqrt{a-b}-\sqrt{a-b x}\right)^4 \left(-\frac{a b \left(\sqrt{x}-1\right)^2}{\left(\sqrt{a-b}-\sqrt{a-b x}\right)^2}-\frac{2 b \left(-2 \sqrt{a-b} \sqrt{a-b x}+\sqrt{x} \sqrt{a-b} \sqrt{a-b x}+a \left(-\sqrt{x}\right)+2 a-b x+2 b \sqrt{x}-2 b\right)}{\left(\sqrt{a-b}-\sqrt{a-b x}\right)^2}+a\right)}{\left(\sqrt{a-b x}-\sqrt{a-b}\right) \left(-2 a^3+3 a^2 b x-2 a^2 b \sqrt{x}+2 a^2 \sqrt{a-b} \sqrt{a-b x}+5 a^2 b+2 a b^2 x^{3/2}-a b^2 x^2-5 a b^2 x+2 b^2 \sqrt{x} \sqrt{a-b} \sqrt{a-b x}-2 a b^2-4 a b \sqrt{a-b} \sqrt{a-b x}-2 a b x \sqrt{a-b} \sqrt{a-b x}+2 a b \sqrt{x} \sqrt{a-b} \sqrt{a-b x}+2 b^3 x\right)}","\frac{2 \sqrt{x}}{a \sqrt{a-b x}}",1,"(((a - b)^(-1) - Sqrt[x]/(a - b))*(Sqrt[a - b] - Sqrt[a - b*x])^4*(a - (a*b*(-1 + Sqrt[x])^2)/(Sqrt[a - b] - Sqrt[a - b*x])^2 - (2*b*(2*a - 2*b - a*Sqrt[x] + 2*b*Sqrt[x] - b*x - 2*Sqrt[a - b]*Sqrt[a - b*x] + Sqrt[a - b]*Sqrt[x]*Sqrt[a - b*x]))/(Sqrt[a - b] - Sqrt[a - b*x])^2))/((-Sqrt[a - b] + Sqrt[a - b*x])*(-2*a^3 + 5*a^2*b - 2*a*b^2 - 2*a^2*b*Sqrt[x] + 3*a^2*b*x - 5*a*b^2*x + 2*b^3*x + 2*a*b^2*x^(3/2) - a*b^2*x^2 + 2*a^2*Sqrt[a - b]*Sqrt[a - b*x] - 4*a*Sqrt[a - b]*b*Sqrt[a - b*x] + 2*a*Sqrt[a - b]*b*Sqrt[x]*Sqrt[a - b*x] + 2*Sqrt[a - b]*b^2*Sqrt[x]*Sqrt[a - b*x] - 2*a*Sqrt[a - b]*b*x*Sqrt[a - b*x]))","B",1
600,1,1351,41,4.677589,"\int \frac{1}{x^{3/2} (a-b x)^{3/2}} \, dx","IntegrateAlgebraic[1/(x^(3/2)*(a - b*x)^(3/2)),x]","\frac{\left(\frac{1}{4 (a-b)}-\frac{\sqrt{x}}{4 (a-b)}\right) \left(\sqrt{a-b}-\sqrt{a-b x}\right)^8 \left(\frac{b \left(\sqrt{x}-1\right)^2}{\left(\sqrt{a-b}-\sqrt{a-b x}\right)^2}-1\right) \left(\frac{4 a \left(-2 \sqrt{x} a^2+4 a^2+2 b x^{3/2} a-8 b a-8 b x a+10 b \sqrt{x} a-4 \sqrt{a-b} \sqrt{a-b x} a+2 \sqrt{a-b} \sqrt{x} \sqrt{a-b x} a+3 b^2+2 b^2 x^2-6 b^2 x^{3/2}+9 b^2 x-6 b^2 \sqrt{x}-\sqrt{a-b} b x^{3/2} \sqrt{a-b x}+6 \sqrt{a-b} b \sqrt{a-b x}+6 \sqrt{a-b} b x \sqrt{a-b x}-9 \sqrt{a-b} b \sqrt{x} \sqrt{a-b x}\right)}{\left(\sqrt{a-b}-\sqrt{a-b x}\right)^4}+\frac{4 b \left(4 \sqrt{x} a^2-6 a^2-4 b x^{3/2} a+11 b a+11 b x a-14 b \sqrt{x} a+6 \sqrt{a-b} \sqrt{a-b x} a-4 \sqrt{a-b} \sqrt{x} \sqrt{a-b x} a-4 b^2-2 b^2 x^2+8 b^2 x^{3/2}-12 b^2 x+8 b^2 \sqrt{x}+2 \sqrt{a-b} b x^{3/2} \sqrt{a-b x}-8 \sqrt{a-b} b \sqrt{a-b x}-8 \sqrt{a-b} b x \sqrt{a-b x}+12 \sqrt{a-b} b \sqrt{x} \sqrt{a-b x}\right)}{\left(\sqrt{a-b}-\sqrt{a-b x}\right)^4}\right)}{\left(\sqrt{a-b x}-\sqrt{a-b}\right) \left(-8 x a^5+16 \sqrt{x} a^5+16 b x^2 a^4-40 b x^{3/2} a^4+40 b x a^4-56 b \sqrt{x} a^4+8 \sqrt{a-b} x \sqrt{a-b x} a^4-16 \sqrt{a-b} \sqrt{x} \sqrt{a-b x} a^4-9 b^2 x^3 a^3+28 b^2 x^{5/2} a^3-54 b^2 x^2 a^3+84 b^2 x^{3/2} a^3-25 b^2 x a^3+56 b^2 \sqrt{x} a^3-12 \sqrt{a-b} b x^2 \sqrt{a-b x} a^3+32 \sqrt{a-b} b x^{3/2} \sqrt{a-b x} a^3-36 \sqrt{a-b} b x \sqrt{a-b x} a^3+48 \sqrt{a-b} b \sqrt{x} \sqrt{a-b x} a^3+b^3 x^4 a^2-4 b^3 x^{7/2} a^2+14 b^3 x^3 a^2-28 b^3 x^{5/2} a^2+25 b^3 x^2 a^2-56 b^3 x^{3/2} a^2-16 b^3 x a^2-16 b^3 \sqrt{x} a^2+4 \sqrt{a-b} b^2 x^3 \sqrt{a-b x} a^2-14 \sqrt{a-b} b^2 x^{5/2} \sqrt{a-b x} a^2+28 \sqrt{a-b} b^2 x^2 \sqrt{a-b x} a^2-40 \sqrt{a-b} b^2 x^{3/2} \sqrt{a-b x} a^2+8 \sqrt{a-b} b^2 x \sqrt{a-b x} a^2-34 \sqrt{a-b} b^2 \sqrt{x} \sqrt{a-b x} a^2+16 b^4 x^2 a+16 b^4 x^{3/2} a+8 b^4 x a+12 \sqrt{a-b} b^3 x^{3/2} \sqrt{a-b x} a+16 \sqrt{a-b} b^3 x \sqrt{a-b x} a+4 \sqrt{a-b} b^3 \sqrt{x} \sqrt{a-b x} a-8 b^5 x^2-8 \sqrt{a-b} b^4 x^{3/2} \sqrt{a-b x}\right)}","\frac{2}{a \sqrt{x} \sqrt{a-b x}}-\frac{4 \sqrt{a-b x}}{a^2 \sqrt{x}}",1,"((1/(4*(a - b)) - Sqrt[x]/(4*(a - b)))*(Sqrt[a - b] - Sqrt[a - b*x])^8*(-1 + (b*(-1 + Sqrt[x])^2)/(Sqrt[a - b] - Sqrt[a - b*x])^2)*((4*a*(4*a^2 - 8*a*b + 3*b^2 - 2*a^2*Sqrt[x] + 10*a*b*Sqrt[x] - 6*b^2*Sqrt[x] - 8*a*b*x + 9*b^2*x + 2*a*b*x^(3/2) - 6*b^2*x^(3/2) + 2*b^2*x^2 - 4*a*Sqrt[a - b]*Sqrt[a - b*x] + 6*Sqrt[a - b]*b*Sqrt[a - b*x] + 2*a*Sqrt[a - b]*Sqrt[x]*Sqrt[a - b*x] - 9*Sqrt[a - b]*b*Sqrt[x]*Sqrt[a - b*x] + 6*Sqrt[a - b]*b*x*Sqrt[a - b*x] - Sqrt[a - b]*b*x^(3/2)*Sqrt[a - b*x]))/(Sqrt[a - b] - Sqrt[a - b*x])^4 + (4*b*(-6*a^2 + 11*a*b - 4*b^2 + 4*a^2*Sqrt[x] - 14*a*b*Sqrt[x] + 8*b^2*Sqrt[x] + 11*a*b*x - 12*b^2*x - 4*a*b*x^(3/2) + 8*b^2*x^(3/2) - 2*b^2*x^2 + 6*a*Sqrt[a - b]*Sqrt[a - b*x] - 8*Sqrt[a - b]*b*Sqrt[a - b*x] - 4*a*Sqrt[a - b]*Sqrt[x]*Sqrt[a - b*x] + 12*Sqrt[a - b]*b*Sqrt[x]*Sqrt[a - b*x] - 8*Sqrt[a - b]*b*x*Sqrt[a - b*x] + 2*Sqrt[a - b]*b*x^(3/2)*Sqrt[a - b*x]))/(Sqrt[a - b] - Sqrt[a - b*x])^4))/((-Sqrt[a - b] + Sqrt[a - b*x])*(16*a^5*Sqrt[x] - 56*a^4*b*Sqrt[x] + 56*a^3*b^2*Sqrt[x] - 16*a^2*b^3*Sqrt[x] - 8*a^5*x + 40*a^4*b*x - 25*a^3*b^2*x - 16*a^2*b^3*x + 8*a*b^4*x - 40*a^4*b*x^(3/2) + 84*a^3*b^2*x^(3/2) - 56*a^2*b^3*x^(3/2) + 16*a*b^4*x^(3/2) + 16*a^4*b*x^2 - 54*a^3*b^2*x^2 + 25*a^2*b^3*x^2 + 16*a*b^4*x^2 - 8*b^5*x^2 + 28*a^3*b^2*x^(5/2) - 28*a^2*b^3*x^(5/2) - 9*a^3*b^2*x^3 + 14*a^2*b^3*x^3 - 4*a^2*b^3*x^(7/2) + a^2*b^3*x^4 - 16*a^4*Sqrt[a - b]*Sqrt[x]*Sqrt[a - b*x] + 48*a^3*Sqrt[a - b]*b*Sqrt[x]*Sqrt[a - b*x] - 34*a^2*Sqrt[a - b]*b^2*Sqrt[x]*Sqrt[a - b*x] + 4*a*Sqrt[a - b]*b^3*Sqrt[x]*Sqrt[a - b*x] + 8*a^4*Sqrt[a - b]*x*Sqrt[a - b*x] - 36*a^3*Sqrt[a - b]*b*x*Sqrt[a - b*x] + 8*a^2*Sqrt[a - b]*b^2*x*Sqrt[a - b*x] + 16*a*Sqrt[a - b]*b^3*x*Sqrt[a - b*x] + 32*a^3*Sqrt[a - b]*b*x^(3/2)*Sqrt[a - b*x] - 40*a^2*Sqrt[a - b]*b^2*x^(3/2)*Sqrt[a - b*x] + 12*a*Sqrt[a - b]*b^3*x^(3/2)*Sqrt[a - b*x] - 8*Sqrt[a - b]*b^4*x^(3/2)*Sqrt[a - b*x] - 12*a^3*Sqrt[a - b]*b*x^2*Sqrt[a - b*x] + 28*a^2*Sqrt[a - b]*b^2*x^2*Sqrt[a - b*x] - 14*a^2*Sqrt[a - b]*b^2*x^(5/2)*Sqrt[a - b*x] + 4*a^2*Sqrt[a - b]*b^2*x^3*Sqrt[a - b*x]))","B",1
601,1,4850,66,49.5629856,"\int \frac{1}{x^{5/2} (a-b x)^{3/2}} \, dx","IntegrateAlgebraic[1/(x^(5/2)*(a - b*x)^(3/2)),x]","\text{Result too large to show}","-\frac{16 b \sqrt{a-b x}}{3 a^3 \sqrt{x}}-\frac{8 \sqrt{a-b x}}{3 a^2 x^{3/2}}+\frac{2}{a x^{3/2} \sqrt{a-b x}}",1,"((-1/192*1/(a - b) + Sqrt[x]/(192*(a - b)))*(Sqrt[a - b] - Sqrt[a - b*x])^16*((128*a^3*Sqrt[a - b]*(-1 + Sqrt[x])^5*(-a + b - b*Sqrt[x] + b*x + Sqrt[a - b]*Sqrt[a - b*x])^2)/(Sqrt[a - b] - Sqrt[a - b*x])^9 + (128*b*(-a + b*Sqrt[x] + Sqrt[a - b]*Sqrt[a - b*x])^2*(6*a^2 - 11*a*b + 4*b^2 + 10*a*b*Sqrt[x] - 8*b^2*Sqrt[x] - 11*a*b*x + 14*b^2*x - 8*b^2*x^(3/2) + 4*b^2*x^2 - 6*a*Sqrt[a - b]*Sqrt[a - b*x] + 8*Sqrt[a - b]*b*Sqrt[a - b*x] - 10*Sqrt[a - b]*b*Sqrt[x]*Sqrt[a - b*x] + 8*Sqrt[a - b]*b*x*Sqrt[a - b*x])*(16*a^3 - 52*a^2*b + 44*a*b^2 - 8*b^3 - 12*a^3*Sqrt[x] + 81*a^2*b*Sqrt[x] - 96*a*b^2*Sqrt[x] + 24*b^3*Sqrt[x] - 66*a^2*b*x + 135*a*b^2*x - 60*b^3*x + 25*a^2*b*x^(3/2) - 110*a*b^2*x^(3/2) + 80*b^3*x^(3/2) + 51*a*b^2*x^2 - 60*b^3*x^2 - 12*a*b^2*x^(5/2) + 24*b^3*x^(5/2) - 4*b^3*x^3 - 16*a^2*Sqrt[a - b]*Sqrt[a - b*x] + 44*a*Sqrt[a - b]*b*Sqrt[a - b*x] - 24*Sqrt[a - b]*b^2*Sqrt[a - b*x] + 12*a^2*Sqrt[a - b]*Sqrt[x]*Sqrt[a - b*x] - 75*a*Sqrt[a - b]*b*Sqrt[x]*Sqrt[a - b*x] + 60*Sqrt[a - b]*b^2*Sqrt[x]*Sqrt[a - b*x] + 58*a*Sqrt[a - b]*b*x*Sqrt[a - b*x] - 80*Sqrt[a - b]*b^2*x*Sqrt[a - b*x] - 19*a*Sqrt[a - b]*b*x^(3/2)*Sqrt[a - b*x] + 60*Sqrt[a - b]*b^2*x^(3/2)*Sqrt[a - b*x] - 24*Sqrt[a - b]*b^2*x^2*Sqrt[a - b*x] + 4*Sqrt[a - b]*b^2*x^(5/2)*Sqrt[a - b*x]))/(Sqrt[a - b] - Sqrt[a - b*x])^14 + (128*a^2*(-1 + Sqrt[x])^2*(32*a^5 - 216*a^4*b + 498*a^3*b^2 - 468*a^2*b^3 + 166*a*b^4 - 12*b^5 - 48*a^5*Sqrt[x] + 428*a^4*b*Sqrt[x] - 1367*a^3*b^2*Sqrt[x] + 1620*a^2*b^3*Sqrt[x] - 690*a*b^4*Sqrt[x] + 60*b^5*Sqrt[x] - 288*a^4*b*x + 1892*a^3*b^2*x - 3193*a^2*b^3*x + 1842*a*b^4*x - 268*b^5*x + 156*a^4*b*x^(3/2) - 1714*a^3*b^2*x^(3/2) + 4126*a^2*b^3*x^(3/2) - 3270*a*b^4*x^(3/2) + 720*b^5*x^(3/2) + 730*a^3*b^2*x^2 - 3410*a^2*b^3*x^2 + 3970*a*b^4*x^2 - 1260*b^5*x^2 - 199*a^3*b^2*x^(5/2) + 2032*a^2*b^3*x^(5/2) - 3442*a*b^4*x^(5/2) + 1512*b^5*x^(5/2) - 657*a^2*b^3*x^3 + 1978*a*b^4*x^3 - 1244*b^5*x^3 + 110*a^2*b^3*x^(7/2) - 810*a*b^4*x^(7/2) + 720*b^5*x^(7/2) + 196*a*b^4*x^4 - 264*b^5*x^4 - 20*a*b^4*x^(9/2) + 60*b^5*x^(9/2) - 8*b^5*x^5 - 32*a^4*Sqrt[a - b]*Sqrt[a - b*x] + 200*a^3*Sqrt[a - b]*b*Sqrt[a - b*x] - 402*a^2*Sqrt[a - b]*b^2*Sqrt[a - b*x] + 290*a*Sqrt[a - b]*b^3*Sqrt[a - b*x] - 60*Sqrt[a - b]*b^4*Sqrt[a - b*x] + 48*a^4*Sqrt[a - b]*Sqrt[x]*Sqrt[a - b*x] - 404*a^3*Sqrt[a - b]*b*Sqrt[x]*Sqrt[a - b*x] + 1171*a^2*Sqrt[a - b]*b^2*Sqrt[x]*Sqrt[a - b*x] - 1082*a*Sqrt[a - b]*b^3*Sqrt[x]*Sqrt[a - b*x] + 272*Sqrt[a - b]*b^4*Sqrt[x]*Sqrt[a - b*x] + 272*a^3*Sqrt[a - b]*b*x*Sqrt[a - b*x] - 1648*a^2*Sqrt[a - b]*b^2*x*Sqrt[a - b*x] + 2154*a*Sqrt[a - b]*b^3*x*Sqrt[a - b*x] - 720*Sqrt[a - b]*b^4*x*Sqrt[a - b*x] - 132*a^3*Sqrt[a - b]*b*x^(3/2)*Sqrt[a - b*x] + 1434*a^2*Sqrt[a - b]*b^2*x^(3/2)*Sqrt[a - b*x] - 2742*a*Sqrt[a - b]*b^3*x^(3/2)*Sqrt[a - b*x] + 1260*Sqrt[a - b]*b^4*x^(3/2)*Sqrt[a - b*x] - 598*a^2*Sqrt[a - b]*b^2*x^2*Sqrt[a - b*x] + 2246*a*Sqrt[a - b]*b^3*x^2*Sqrt[a - b*x] - 1512*Sqrt[a - b]*b^4*x^2*Sqrt[a - b*x] + 139*a^2*Sqrt[a - b]*b^2*x^(5/2)*Sqrt[a - b*x] - 1266*a*Sqrt[a - b]*b^3*x^(5/2)*Sqrt[a - b*x] + 1276*Sqrt[a - b]*b^4*x^(5/2)*Sqrt[a - b*x] + 390*a*Sqrt[a - b]*b^3*x^3*Sqrt[a - b*x] - 720*Sqrt[a - b]*b^4*x^3*Sqrt[a - b*x] - 54*a*Sqrt[a - b]*b^3*x^(7/2)*Sqrt[a - b*x] + 276*Sqrt[a - b]*b^4*x^(7/2)*Sqrt[a - b*x] - 60*Sqrt[a - b]*b^4*x^4*Sqrt[a - b*x] + 4*Sqrt[a - b]*b^4*x^(9/2)*Sqrt[a - b*x]))/(Sqrt[a - b] - Sqrt[a - b*x])^12 - (128*a*(576*a^7 - 3152*a^6*b + 5880*a^5*b^2 - 3945*a^4*b^3 - 322*a^3*b^4 + 1335*a^2*b^5 - 388*a*b^6 + 16*b^7 - 384*a^7*Sqrt[x] + 3712*a^6*b*Sqrt[x] - 7296*a^5*b^2*Sqrt[x] - 1304*a^4*b^3*Sqrt[x] + 13867*a^3*b^4*Sqrt[x] - 11305*a^2*b^5*Sqrt[x] + 2828*a*b^6*Sqrt[x] - 112*b^7*Sqrt[x] - 3344*a^6*b*x + 10320*a^5*b^2*x + 4653*a^4*b^3*x - 35556*a^3*b^4*x + 33333*a^2*b^5*x - 10104*a*b^6*x + 656*b^7*x + 1440*a^6*b*x^(3/2) - 7824*a^5*b^2*x^(3/2) - 12870*a^4*b^3*x^(3/2) + 68909*a^3*b^4*x^(3/2) - 75544*a^2*b^5*x^(3/2) + 28896*a*b^6*x^(3/2) - 2912*b^7*x^(3/2) + 4632*a^5*b^2*x^2 + 11665*a^4*b^3*x^2 - 85294*a^3*b^4*x^2 + 118880*a^2*b^5*x^2 - 57844*a*b^6*x^2 + 7968*b^7*x^2 - 1680*a^5*b^2*x^(5/2) - 6540*a^4*b^3*x^(5/2) + 78625*a^3*b^4*x^(5/2) - 143134*a^2*b^5*x^(5/2) + 88340*a*b^6*x^(5/2) - 16016*b^7*x^(5/2) + 1419*a^4*b^3*x^3 - 51344*a^3*b^4*x^3 + 128648*a^2*b^5*x^3 - 101968*a*b^6*x^3 + 23952*b^7*x^3 + 202*a^4*b^3*x^(7/2) + 23419*a^3*b^4*x^(7/2) - 87352*a^2*b^5*x^(7/2) + 90892*a*b^6*x^(7/2) - 27456*b^7*x^(7/2) - 6396*a^3*b^4*x^4 + 43865*a^2*b^5*x^4 - 62068*a*b^6*x^4 + 24040*b^7*x^4 + 812*a^3*b^4*x^(9/2) - 16009*a^2*b^5*x^(9/2) + 32088*a*b^6*x^(9/2) - 16016*b^7*x^(9/2) + 3699*a^2*b^5*x^5 - 12136*a*b^6*x^5 + 7992*b^7*x^5 - 448*a^2*b^5*x^(11/2) + 3332*a*b^6*x^(11/2) - 2912*b^7*x^(11/2) - 580*a*b^6*x^6 + 712*b^7*x^6 + 56*a*b^6*x^(13/2) - 112*b^7*x^(13/2) + 8*b^7*x^7 - 576*a^6*Sqrt[a - b]*Sqrt[a - b*x] + 2864*a^5*Sqrt[a - b]*b*Sqrt[a - b*x] - 4520*a^4*Sqrt[a - b]*b^2*Sqrt[a - b*x] + 2007*a^3*Sqrt[a - b]*b^3*Sqrt[a - b*x] + 917*a^2*Sqrt[a - b]*b^4*Sqrt[a - b*x] - 812*a*Sqrt[a - b]*b^5*Sqrt[a - b*x] + 112*Sqrt[a - b]*b^6*Sqrt[a - b*x] + 384*a^6*Sqrt[a - b]*Sqrt[x]*Sqrt[a - b*x] - 3520*a^5*Sqrt[a - b]*b*Sqrt[x]*Sqrt[a - b*x] + 5584*a^4*Sqrt[a - b]*b^2*Sqrt[x]*Sqrt[a - b*x] + 3680*a^3*Sqrt[a - b]*b^3*Sqrt[x]*Sqrt[a - b*x] - 11534*a^2*Sqrt[a - b]*b^4*Sqrt[x]*Sqrt[a - b*x] + 6220*a*Sqrt[a - b]*b^5*Sqrt[x]*Sqrt[a - b*x] - 800*Sqrt[a - b]*b^6*Sqrt[x]*Sqrt[a - b*x] + 3056*a^5*Sqrt[a - b]*b*x*Sqrt[a - b*x] - 7216*a^4*Sqrt[a - b]*b^2*x*Sqrt[a - b*x] - 10819*a^3*Sqrt[a - b]*b^3*x*Sqrt[a - b*x] + 31408*a^2*Sqrt[a - b]*b^4*x*Sqrt[a - b*x] - 19152*a*Sqrt[a - b]*b^5*x*Sqrt[a - b*x] + 2912*Sqrt[a - b]*b^6*x*Sqrt[a - b*x] - 1248*a^5*Sqrt[a - b]*b*x^(3/2)*Sqrt[a - b*x] + 5344*a^4*Sqrt[a - b]*b^2*x^(3/2)*Sqrt[a - b*x] + 19034*a^3*Sqrt[a - b]*b^3*x^(3/2)*Sqrt[a - b*x] - 58150*a^2*Sqrt[a - b]*b^4*x^(3/2)*Sqrt[a - b*x] + 42200*a*Sqrt[a - b]*b^5*x^(3/2)*Sqrt[a - b*x] - 8048*Sqrt[a - b]*b^6*x^(3/2)*Sqrt[a - b*x] - 3176*a^4*Sqrt[a - b]*b^2*x^2*Sqrt[a - b*x] - 17231*a^3*Sqrt[a - b]*b^3*x^2*Sqrt[a - b*x] + 71750*a^2*Sqrt[a - b]*b^4*x^2*Sqrt[a - b*x] - 66100*a*Sqrt[a - b]*b^5*x^2*Sqrt[a - b*x] + 16016*Sqrt[a - b]*b^6*x^2*Sqrt[a - b*x] + 1104*a^4*Sqrt[a - b]*b^2*x^(5/2)*Sqrt[a - b*x] + 9612*a^3*Sqrt[a - b]*b^3*x^(5/2)*Sqrt[a - b*x] - 64510*a^2*Sqrt[a - b]*b^4*x^(5/2)*Sqrt[a - b*x] + 78184*a*Sqrt[a - b]*b^5*x^(5/2)*Sqrt[a - b*x] - 24096*Sqrt[a - b]*b^6*x^(5/2)*Sqrt[a - b*x] - 2661*a^3*Sqrt[a - b]*b^3*x^3*Sqrt[a - b*x] + 41296*a^2*Sqrt[a - b]*b^4*x^3*Sqrt[a - b*x] - 69268*a*Sqrt[a - b]*b^5*x^3*Sqrt[a - b*x] + 27456*Sqrt[a - b]*b^6*x^3*Sqrt[a - b*x] + 218*a^3*Sqrt[a - b]*b^3*x^(7/2)*Sqrt[a - b*x] - 18266*a^2*Sqrt[a - b]*b^4*x^(7/2)*Sqrt[a - b*x] + 46040*a*Sqrt[a - b]*b^5*x^(7/2)*Sqrt[a - b*x] - 24008*Sqrt[a - b]*b^6*x^(7/2)*Sqrt[a - b*x] + 4837*a^2*Sqrt[a - b]*b^4*x^4*Sqrt[a - b*x] - 22512*a*Sqrt[a - b]*b^5*x^4*Sqrt[a - b*x] + 16016*Sqrt[a - b]*b^6*x^4*Sqrt[a - b*x] - 628*a^2*Sqrt[a - b]*b^4*x^(9/2)*Sqrt[a - b*x] + 7868*a*Sqrt[a - b]*b^5*x^(9/2)*Sqrt[a - b*x] - 8024*Sqrt[a - b]*b^6*x^(9/2)*Sqrt[a - b*x] - 1708*a*Sqrt[a - b]*b^5*x^5*Sqrt[a - b*x] + 2912*Sqrt[a - b]*b^6*x^5*Sqrt[a - b*x] + 192*a*Sqrt[a - b]*b^5*x^(11/2)*Sqrt[a - b*x] - 744*Sqrt[a - b]*b^6*x^(11/2)*Sqrt[a - b*x] + 112*Sqrt[a - b]*b^6*x^6*Sqrt[a - b*x] - 8*Sqrt[a - b]*b^6*x^(13/2)*Sqrt[a - b*x]))/(Sqrt[a - b] - Sqrt[a - b*x])^14))/((-Sqrt[a - b] + Sqrt[a - b*x])*(4*a^2*Sqrt[x] - 4*a*b*Sqrt[x] - 2*a^2*x + a*b*x + 2*b^2*x - 2*a*b*x^(3/2) + a*b*x^2 - 4*a*Sqrt[a - b]*Sqrt[x]*Sqrt[a - b*x] + 2*Sqrt[a - b]*b*Sqrt[x]*Sqrt[a - b*x] + 2*a*Sqrt[a - b]*x*Sqrt[a - b*x])^3*(-2*a^3 + 5*a^2*b - 2*a*b^2 - 2*a^2*b*Sqrt[x] + 3*a^2*b*x - 5*a*b^2*x + 2*b^3*x + 2*a*b^2*x^(3/2) - a*b^2*x^2 + 2*a^2*Sqrt[a - b]*Sqrt[a - b*x] - 4*a*Sqrt[a - b]*b*Sqrt[a - b*x] + 2*a*Sqrt[a - b]*b*Sqrt[x]*Sqrt[a - b*x] + 2*Sqrt[a - b]*b^2*Sqrt[x]*Sqrt[a - b*x] - 2*a*Sqrt[a - b]*b*x*Sqrt[a - b*x]))","B",1
602,1,2858,95,47.5798045,"\int \frac{x^{5/2}}{(a-b x)^{5/2}} \, dx","IntegrateAlgebraic[x^(5/2)/(a - b*x)^(5/2),x]","\text{Result too large to show}","\frac{5 a \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)}{b^{7/2}}-\frac{5 \sqrt{x} \sqrt{a-b x}}{b^3}-\frac{10 x^{3/2}}{3 b^2 \sqrt{a-b x}}+\frac{2 x^{5/2}}{3 b (a-b x)^{3/2}}",1,"((-3*a + 2*b - a*Sqrt[x] + 2*b*Sqrt[x] + 4*Sqrt[a - b]*Sqrt[a - b*x])*(-(Sqrt[a - b]/b^3) + Sqrt[a - b*x]/b^3))/(-a + b*Sqrt[x] + Sqrt[a - b]*Sqrt[a - b*x]) + ((Sqrt[a - b] - Sqrt[a - b*x])^3*(a/b^3 + (a*Sqrt[x])/b^3 - (2*Sqrt[x])/b^2 - (2*Sqrt[a - b]*Sqrt[a - b*x])/b^3))/(-a + b*Sqrt[x] + Sqrt[a - b]*Sqrt[a - b*x])^2 + ((Sqrt[a - b] - Sqrt[a - b*x])^9*((184*a^6)/(3*(a - b)^4) - (24*a^8)/((a - b)^4*b^2) + (104*a^7)/(3*(a - b)^4*b) - (200*a^5*b)/(3*(a - b)^4) - (16*a^4*b^2)/(3*(a - b)^4) - (88*a^6*Sqrt[x])/(a - b)^4 + (8*a^8*Sqrt[x])/(3*(a - b)^4*b^2) - (56*a^7*Sqrt[x])/(3*(a - b)^4*b) + (72*a^5*b*Sqrt[x])/(a - b)^4 + (32*a^4*b^2*Sqrt[x])/(a - b)^4 + (40*a^6*x)/(a - b)^4 + (88*a^7*x)/(3*(a - b)^4*b) - (184*a^5*b*x)/(3*(a - b)^4) - (8*a^4*b^2*x)/(a - b)^4 - (40*a^6*x^(3/2))/(3*(a - b)^4) - (8*a^7*x^(3/2))/(3*(a - b)^4*b) + (40*a^5*b*x^(3/2))/(3*(a - b)^4) + (8*a^4*b^2*x^(3/2))/(3*(a - b)^4) - (184*a^5*Sqrt[a - b*x])/(3*(a - b)^(7/2)) + (24*a^7*Sqrt[a - b*x])/((a - b)^(7/2)*b^2) - (64*a^6*Sqrt[a - b*x])/(3*(a - b)^(7/2)*b) + (16*a^4*b*Sqrt[a - b*x])/(a - b)^(7/2) + (200*a^5*Sqrt[x]*Sqrt[a - b*x])/(3*(a - b)^(7/2)) - (8*a^7*Sqrt[x]*Sqrt[a - b*x])/(3*(a - b)^(7/2)*b^2) + (40*a^6*Sqrt[x]*Sqrt[a - b*x])/(3*(a - b)^(7/2)*b) + (8*a^4*b*Sqrt[x]*Sqrt[a - b*x])/(a - b)^(7/2) - (80*a^5*x*Sqrt[a - b*x])/(3*(a - b)^(7/2)) - (40*a^6*x*Sqrt[a - b*x])/(3*(a - b)^(7/2)*b) - (8*a^4*b*x*Sqrt[a - b*x])/(3*(a - b)^(7/2))))/(-2*a^3 + 5*a^2*b - 2*a*b^2 - 2*a^2*b*Sqrt[x] + 3*a^2*b*x - 5*a*b^2*x + 2*b^3*x + 2*a*b^2*x^(3/2) - a*b^2*x^2 + 2*a^2*Sqrt[a - b]*Sqrt[a - b*x] - 4*a*Sqrt[a - b]*b*Sqrt[a - b*x] + 2*a*Sqrt[a - b]*b*Sqrt[x]*Sqrt[a - b*x] + 2*Sqrt[a - b]*b^2*Sqrt[x]*Sqrt[a - b*x] - 2*a*Sqrt[a - b]*b*x*Sqrt[a - b*x])^3 + ((Sqrt[a - b] - Sqrt[a - b*x])^5*((234*a^5)/(a - b)^4 + (26*a^8)/(3*(a - b)^4*b^3) - (326*a^7)/(3*(a - b)^4*b^2) - (50*a^6)/((a - b)^4*b) - (76*a^4*b)/(a - b)^4 - (8*a^3*b^2)/(a - b)^4 - (470*a^5*Sqrt[x])/(3*(a - b)^4) - (2*a^8*Sqrt[x])/(3*(a - b)^4*b^3) + (18*a^7*Sqrt[x])/((a - b)^4*b^2) + (238*a^6*Sqrt[x])/(3*(a - b)^4*b) + (28*a^4*b*Sqrt[x])/(a - b)^4 + (32*a^3*b^2*Sqrt[x])/(a - b)^4 + (98*a^5*x)/(a - b)^4 - (34*a^7*x)/(3*(a - b)^4*b^2) + (110*a^6*x)/(3*(a - b)^4*b) - (334*a^4*b*x)/(3*(a - b)^4) - (12*a^3*b^2*x)/(a - b)^4 - (26*a^5*x^(3/2))/(a - b)^4 + (2*a^7*x^(3/2))/(3*(a - b)^4*b^2) + (10*a^6*x^(3/2))/(3*(a - b)^4*b) + (18*a^4*b*x^(3/2))/(a - b)^4 + (4*a^3*b^2*x^(3/2))/(a - b)^4 - (156*a^4*Sqrt[a - b*x])/(a - b)^(7/2) - (26*a^7*Sqrt[a - b*x])/(3*(a - b)^(7/2)*b^3) + (104*a^6*Sqrt[a - b*x])/((a - b)^(7/2)*b^2) + (286*a^5*Sqrt[a - b*x])/(3*(a - b)^(7/2)*b) + (8*a^3*b*Sqrt[a - b*x])/(a - b)^(7/2) + (218*a^4*Sqrt[x]*Sqrt[a - b*x])/(3*(a - b)^(7/2)) + (2*a^7*Sqrt[x]*Sqrt[a - b*x])/(3*(a - b)^(7/2)*b^3) - (50*a^6*Sqrt[x]*Sqrt[a - b*x])/(3*(a - b)^(7/2)*b^2) - (206*a^5*Sqrt[x]*Sqrt[a - b*x])/(3*(a - b)^(7/2)*b) + (12*a^3*b*Sqrt[x]*Sqrt[a - b*x])/(a - b)^(7/2) - (42*a^4*x*Sqrt[a - b*x])/(a - b)^(7/2) + (6*a^6*x*Sqrt[a - b*x])/((a - b)^(7/2)*b^2) - (8*a^5*x*Sqrt[a - b*x])/(3*(a - b)^(7/2)*b) - (4*a^3*b*x*Sqrt[a - b*x])/(a - b)^(7/2)))/(-2*a^3 + 5*a^2*b - 2*a*b^2 - 2*a^2*b*Sqrt[x] + 3*a^2*b*x - 5*a*b^2*x + 2*b^3*x + 2*a*b^2*x^(3/2) - a*b^2*x^2 + 2*a^2*Sqrt[a - b]*Sqrt[a - b*x] - 4*a*Sqrt[a - b]*b*Sqrt[a - b*x] + 2*a*Sqrt[a - b]*b*Sqrt[x]*Sqrt[a - b*x] + 2*Sqrt[a - b]*b^2*Sqrt[x]*Sqrt[a - b*x] - 2*a*Sqrt[a - b]*b*x*Sqrt[a - b*x])^2 + (((2*a^2)/(3*(a - b)^(5/2)*b^3) - (2*a^2*Sqrt[a - b*x])/(3*(a - b)^3*b^3))*(58*a^4 + 24*a^3*b - 82*a^2*b^2 - 18*a*b^3 + 18*b^4 - 10*a^4*Sqrt[x] + 21*a^3*b*Sqrt[x] - 62*a^2*b^2*Sqrt[x] + 87*a*b^3*Sqrt[x] - 36*b^4*Sqrt[x] - 53*a^3*b*x + 11*a^2*b^2*x + 15*a*b^3*x + 27*b^4*x + 8*a^3*b*x^(3/2) - 11*a^2*b^2*x^(3/2) + 12*a*b^3*x^(3/2) - 9*b^4*x^(3/2) - 58*a^3*Sqrt[a - b]*Sqrt[a - b*x] - 56*a^2*Sqrt[a - b]*b*Sqrt[a - b*x] + 60*a*Sqrt[a - b]*b^2*Sqrt[a - b*x] + 18*Sqrt[a - b]*b^3*Sqrt[a - b*x] + 10*a^3*Sqrt[a - b]*Sqrt[x]*Sqrt[a - b*x] - 7*a^2*Sqrt[a - b]*b*Sqrt[x]*Sqrt[a - b*x] + 24*a*Sqrt[a - b]*b^2*Sqrt[x]*Sqrt[a - b*x] - 27*Sqrt[a - b]*b^3*Sqrt[x]*Sqrt[a - b*x] + 15*a^2*Sqrt[a - b]*b*x*Sqrt[a - b*x] + 12*a*Sqrt[a - b]*b^2*x*Sqrt[a - b*x] + 9*Sqrt[a - b]*b^3*x*Sqrt[a - b*x]))/(-2*a^3 + 5*a^2*b - 2*a*b^2 - 2*a^2*b*Sqrt[x] + 3*a^2*b*x - 5*a*b^2*x + 2*b^3*x + 2*a*b^2*x^(3/2) - a*b^2*x^2 + 2*a^2*Sqrt[a - b]*Sqrt[a - b*x] - 4*a*Sqrt[a - b]*b*Sqrt[a - b*x] + 2*a*Sqrt[a - b]*b*Sqrt[x]*Sqrt[a - b*x] + 2*Sqrt[a - b]*b^2*Sqrt[x]*Sqrt[a - b*x] - 2*a*Sqrt[a - b]*b*x*Sqrt[a - b*x]) + (10*a*ArcTan[(Sqrt[a - b]/Sqrt[b] - Sqrt[a - b*x]/Sqrt[b])/(-1 + Sqrt[x])])/b^(7/2)","B",1
603,1,2627,72,13.5636755,"\int \frac{x^{3/2}}{(a-b x)^{5/2}} \, dx","IntegrateAlgebraic[x^(3/2)/(a - b*x)^(5/2),x]","\text{Result too large to show}","\frac{2 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)}{b^{5/2}}-\frac{2 \sqrt{x}}{b^2 \sqrt{a-b x}}+\frac{2 x^{3/2}}{3 b (a-b x)^{3/2}}",1,"((Sqrt[a - b] - Sqrt[a - b*x])^5*((-50*a^5)/(a - b)^4 + (26*a^7)/(3*(a - b)^4*b^2) - (326*a^6)/(3*(a - b)^4*b) + (234*a^4*b)/(a - b)^4 - (76*a^3*b^2)/(a - b)^4 - (8*a^2*b^3)/(a - b)^4 + (238*a^5*Sqrt[x])/(3*(a - b)^4) - (2*a^7*Sqrt[x])/(3*(a - b)^4*b^2) + (18*a^6*Sqrt[x])/((a - b)^4*b) - (470*a^4*b*Sqrt[x])/(3*(a - b)^4) + (28*a^3*b^2*Sqrt[x])/(a - b)^4 + (32*a^2*b^3*Sqrt[x])/(a - b)^4 + (110*a^5*x)/(3*(a - b)^4) - (34*a^6*x)/(3*(a - b)^4*b) + (98*a^4*b*x)/(a - b)^4 - (334*a^3*b^2*x)/(3*(a - b)^4) - (12*a^2*b^3*x)/(a - b)^4 + (10*a^5*x^(3/2))/(3*(a - b)^4) + (2*a^6*x^(3/2))/(3*(a - b)^4*b) - (26*a^4*b*x^(3/2))/(a - b)^4 + (18*a^3*b^2*x^(3/2))/(a - b)^4 + (4*a^2*b^3*x^(3/2))/(a - b)^4 + (286*a^4*Sqrt[a - b*x])/(3*(a - b)^(7/2)) - (26*a^6*Sqrt[a - b*x])/(3*(a - b)^(7/2)*b^2) + (104*a^5*Sqrt[a - b*x])/((a - b)^(7/2)*b) - (156*a^3*b*Sqrt[a - b*x])/(a - b)^(7/2) + (8*a^2*b^2*Sqrt[a - b*x])/(a - b)^(7/2) - (206*a^4*Sqrt[x]*Sqrt[a - b*x])/(3*(a - b)^(7/2)) + (2*a^6*Sqrt[x]*Sqrt[a - b*x])/(3*(a - b)^(7/2)*b^2) - (50*a^5*Sqrt[x]*Sqrt[a - b*x])/(3*(a - b)^(7/2)*b) + (218*a^3*b*Sqrt[x]*Sqrt[a - b*x])/(3*(a - b)^(7/2)) + (12*a^2*b^2*Sqrt[x]*Sqrt[a - b*x])/(a - b)^(7/2) - (8*a^4*x*Sqrt[a - b*x])/(3*(a - b)^(7/2)) + (6*a^5*x*Sqrt[a - b*x])/((a - b)^(7/2)*b) - (42*a^3*b*x*Sqrt[a - b*x])/(a - b)^(7/2) - (4*a^2*b^2*x*Sqrt[a - b*x])/(a - b)^(7/2)))/(-2*a^3 + 5*a^2*b - 2*a*b^2 - 2*a^2*b*Sqrt[x] + 3*a^2*b*x - 5*a*b^2*x + 2*b^3*x + 2*a*b^2*x^(3/2) - a*b^2*x^2 + 2*a^2*Sqrt[a - b]*Sqrt[a - b*x] - 4*a*Sqrt[a - b]*b*Sqrt[a - b*x] + 2*a*Sqrt[a - b]*b*Sqrt[x]*Sqrt[a - b*x] + 2*Sqrt[a - b]*b^2*Sqrt[x]*Sqrt[a - b*x] - 2*a*Sqrt[a - b]*b*x*Sqrt[a - b*x])^2 + ((Sqrt[a - b] - Sqrt[a - b*x])^9*((104*a^6)/(3*(a - b)^4) - (24*a^7)/((a - b)^4*b) + (184*a^5*b)/(3*(a - b)^4) - (200*a^4*b^2)/(3*(a - b)^4) - (16*a^3*b^3)/(3*(a - b)^4) - (56*a^6*Sqrt[x])/(3*(a - b)^4) + (8*a^7*Sqrt[x])/(3*(a - b)^4*b) - (88*a^5*b*Sqrt[x])/(a - b)^4 + (72*a^4*b^2*Sqrt[x])/(a - b)^4 + (32*a^3*b^3*Sqrt[x])/(a - b)^4 + (88*a^6*x)/(3*(a - b)^4) + (40*a^5*b*x)/(a - b)^4 - (184*a^4*b^2*x)/(3*(a - b)^4) - (8*a^3*b^3*x)/(a - b)^4 - (8*a^6*x^(3/2))/(3*(a - b)^4) - (40*a^5*b*x^(3/2))/(3*(a - b)^4) + (40*a^4*b^2*x^(3/2))/(3*(a - b)^4) + (8*a^3*b^3*x^(3/2))/(3*(a - b)^4) - (64*a^5*Sqrt[a - b*x])/(3*(a - b)^(7/2)) + (24*a^6*Sqrt[a - b*x])/((a - b)^(7/2)*b) - (184*a^4*b*Sqrt[a - b*x])/(3*(a - b)^(7/2)) + (16*a^3*b^2*Sqrt[a - b*x])/(a - b)^(7/2) + (40*a^5*Sqrt[x]*Sqrt[a - b*x])/(3*(a - b)^(7/2)) - (8*a^6*Sqrt[x]*Sqrt[a - b*x])/(3*(a - b)^(7/2)*b) + (200*a^4*b*Sqrt[x]*Sqrt[a - b*x])/(3*(a - b)^(7/2)) + (8*a^3*b^2*Sqrt[x]*Sqrt[a - b*x])/(a - b)^(7/2) - (40*a^5*x*Sqrt[a - b*x])/(3*(a - b)^(7/2)) - (80*a^4*b*x*Sqrt[a - b*x])/(3*(a - b)^(7/2)) - (8*a^3*b^2*x*Sqrt[a - b*x])/(3*(a - b)^(7/2))))/(-2*a^3 + 5*a^2*b - 2*a*b^2 - 2*a^2*b*Sqrt[x] + 3*a^2*b*x - 5*a*b^2*x + 2*b^3*x + 2*a*b^2*x^(3/2) - a*b^2*x^2 + 2*a^2*Sqrt[a - b]*Sqrt[a - b*x] - 4*a*Sqrt[a - b]*b*Sqrt[a - b*x] + 2*a*Sqrt[a - b]*b*Sqrt[x]*Sqrt[a - b*x] + 2*Sqrt[a - b]*b^2*Sqrt[x]*Sqrt[a - b*x] - 2*a*Sqrt[a - b]*b*x*Sqrt[a - b*x])^3 + (((2*a)/(3*(a - b)^(5/2)*b^2) - (2*a*Sqrt[a - b*x])/(3*(a - b)^3*b^2))*(55*a^4 + 39*a^3*b - 109*a^2*b^2 + 3*a*b^3 + 12*b^4 - 7*a^4*Sqrt[x] - 17*a^2*b^2*Sqrt[x] + 48*a*b^3*Sqrt[x] - 24*b^4*Sqrt[x] - 44*a^3*b*x - 16*a^2*b^2*x + 42*a*b^3*x + 18*b^4*x + 5*a^3*b*x^(3/2) - 2*a^2*b^2*x^(3/2) + 3*a*b^3*x^(3/2) - 6*b^4*x^(3/2) - 55*a^3*Sqrt[a - b]*Sqrt[a - b*x] - 68*a^2*Sqrt[a - b]*b*Sqrt[a - b*x] + 75*a*Sqrt[a - b]*b^2*Sqrt[a - b*x] + 12*Sqrt[a - b]*b^3*Sqrt[a - b*x] + 7*a^3*Sqrt[a - b]*Sqrt[x]*Sqrt[a - b*x] + 8*a^2*Sqrt[a - b]*b*Sqrt[x]*Sqrt[a - b*x] + 3*a*Sqrt[a - b]*b^2*Sqrt[x]*Sqrt[a - b*x] - 18*Sqrt[a - b]*b^3*Sqrt[x]*Sqrt[a - b*x] + 12*a^2*Sqrt[a - b]*b*x*Sqrt[a - b*x] + 18*a*Sqrt[a - b]*b^2*x*Sqrt[a - b*x] + 6*Sqrt[a - b]*b^3*x*Sqrt[a - b*x]))/(-2*a^3 + 5*a^2*b - 2*a*b^2 - 2*a^2*b*Sqrt[x] + 3*a^2*b*x - 5*a*b^2*x + 2*b^3*x + 2*a*b^2*x^(3/2) - a*b^2*x^2 + 2*a^2*Sqrt[a - b]*Sqrt[a - b*x] - 4*a*Sqrt[a - b]*b*Sqrt[a - b*x] + 2*a*Sqrt[a - b]*b*Sqrt[x]*Sqrt[a - b*x] + 2*Sqrt[a - b]*b^2*Sqrt[x]*Sqrt[a - b*x] - 2*a*Sqrt[a - b]*b*x*Sqrt[a - b*x]) + (4*ArcTan[(Sqrt[a - b]/Sqrt[b] - Sqrt[a - b*x]/Sqrt[b])/(-1 + Sqrt[x])])/b^(5/2)","B",1
604,1,3101,22,9.353393,"\int \frac{\sqrt{x}}{(a-b x)^{5/2}} \, dx","IntegrateAlgebraic[Sqrt[x]/(a - b*x)^(5/2),x]","\text{Result too large to show}","\frac{2 x^{3/2}}{3 a (a-b x)^{3/2}}",1,"((1/(48*(a - b)^2) - Sqrt[x]/(48*(a - b)^2))*(Sqrt[a - b] - Sqrt[a - b*x])^12*((-32*a^4*(-1 + Sqrt[x])^2*(-a + b - b*Sqrt[x] + b*x + Sqrt[a - b]*Sqrt[a - b*x])^3)/(Sqrt[a - b] - Sqrt[a - b*x])^8 + (96*a*b^2*(-a + b*Sqrt[x] + Sqrt[a - b]*Sqrt[a - b*x])^4*(4*a - 4*b - a*Sqrt[x] + 4*b*Sqrt[x] - 3*b*x - 4*Sqrt[a - b]*Sqrt[a - b*x] + Sqrt[a - b]*Sqrt[x]*Sqrt[a - b*x]))/(Sqrt[a - b] - Sqrt[a - b*x])^10 - (96*b^3*(-a + b*Sqrt[x] + Sqrt[a - b]*Sqrt[a - b*x])^4*(2*a - 2*b - a*Sqrt[x] + 2*b*Sqrt[x] - b*x - 2*Sqrt[a - b]*Sqrt[a - b*x] + Sqrt[a - b]*Sqrt[x]*Sqrt[a - b*x]))/(Sqrt[a - b] - Sqrt[a - b*x])^10 - (32*a^3*(-16*a^4*b - 4*a^3*b^2 + 43*a^2*b^3 - 25*a*b^4 + 2*b^5 - 48*a^5*Sqrt[x] + 140*a^4*b*Sqrt[x] + 5*a^3*b^2*Sqrt[x] - 215*a^2*b^3*Sqrt[x] + 125*a*b^4*Sqrt[x] - 10*b^5*Sqrt[x] + 8*a^4*b*x - 224*a^3*b^2*x + 494*a^2*b^3*x - 303*a*b^4*x + 40*b^5*x + 108*a^4*b*x^(3/2) - 106*a^3*b^2*x^(3/2) - 395*a^2*b^3*x^(3/2) + 485*a*b^4*x^(3/2) - 120*b^5*x^(3/2) - 76*a^3*b^2*x^2 + 563*a^2*b^3*x^2 - 693*a*b^4*x^2 + 226*b^5*x^2 - 75*a^3*b^2*x^(5/2) - 125*a^2*b^3*x^(5/2) + 455*a*b^4*x^(5/2) - 252*b^5*x^(5/2) + 100*a^2*b^3*x^3 - 345*a*b^4*x^3 + 238*b^5*x^3 + 15*a^2*b^3*x^(7/2) + 95*a*b^4*x^(7/2) - 120*b^5*x^(7/2) - 34*a*b^4*x^4 + 52*b^5*x^4 - 10*b^5*x^(9/2) + 2*b^5*x^5 + 16*a^3*Sqrt[a - b]*b*Sqrt[a - b*x] + 12*a^2*Sqrt[a - b]*b^2*Sqrt[a - b*x] - 35*a*Sqrt[a - b]*b^3*Sqrt[a - b*x] + 10*Sqrt[a - b]*b^4*Sqrt[a - b*x] + 48*a^4*Sqrt[a - b]*Sqrt[x]*Sqrt[a - b*x] - 116*a^3*Sqrt[a - b]*b*Sqrt[x]*Sqrt[a - b*x] - 57*a^2*Sqrt[a - b]*b^2*Sqrt[x]*Sqrt[a - b*x] + 175*a*Sqrt[a - b]*b^3*Sqrt[x]*Sqrt[a - b*x] - 50*Sqrt[a - b]*b^4*Sqrt[x]*Sqrt[a - b*x] - 8*a^3*Sqrt[a - b]*b*x*Sqrt[a - b*x] + 228*a^2*Sqrt[a - b]*b^2*x*Sqrt[a - b*x] - 379*a*Sqrt[a - b]*b^3*x*Sqrt[a - b*x] + 120*Sqrt[a - b]*b^4*x*Sqrt[a - b*x] - 84*a^3*Sqrt[a - b]*b*x^(3/2)*Sqrt[a - b*x] - 6*a^2*Sqrt[a - b]*b^2*x^(3/2)*Sqrt[a - b*x] + 379*a*Sqrt[a - b]*b^3*x^(3/2)*Sqrt[a - b*x] - 194*Sqrt[a - b]*b^4*x^(3/2)*Sqrt[a - b*x] + 72*a^2*Sqrt[a - b]*b^2*x^2*Sqrt[a - b*x] - 409*a*Sqrt[a - b]*b^3*x^2*Sqrt[a - b*x] + 252*Sqrt[a - b]*b^4*x^2*Sqrt[a - b*x] + 39*a^2*Sqrt[a - b]*b^2*x^(5/2)*Sqrt[a - b*x] + 145*a*Sqrt[a - b]*b^3*x^(5/2)*Sqrt[a - b*x] - 182*Sqrt[a - b]*b^4*x^(5/2)*Sqrt[a - b*x] - 65*a*Sqrt[a - b]*b^3*x^3*Sqrt[a - b*x] + 120*Sqrt[a - b]*b^4*x^3*Sqrt[a - b*x] - 3*a*Sqrt[a - b]*b^3*x^(7/2)*Sqrt[a - b*x] - 38*Sqrt[a - b]*b^4*x^(7/2)*Sqrt[a - b*x] + 10*Sqrt[a - b]*b^4*x^4*Sqrt[a - b*x]))/(Sqrt[a - b] - Sqrt[a - b*x])^10 + (32*a^2*b*(-96*a^5 + 136*a^4*b - 54*a^3*b^2 + 36*a^2*b^3 - 24*a*b^4 + 2*b^5 - 48*a^5*Sqrt[x] + 316*a^4*b*Sqrt[x] - 267*a^3*b^2*Sqrt[x] - 135*a^2*b^3*Sqrt[x] + 135*a*b^4*Sqrt[x] - 10*b^5*Sqrt[x] + 160*a^4*b*x - 572*a^3*b^2*x + 781*a^2*b^3*x - 361*a*b^4*x + 37*b^5*x + 108*a^4*b*x^(3/2) - 298*a^3*b^2*x^(3/2) - 159*a^2*b^3*x^(3/2) + 380*a*b^4*x^(3/2) - 120*b^5*x^(3/2) - 190*a^3*b^2*x^2 + 890*a^2*b^3*x^2 - 895*a*b^4*x^2 + 280*b^5*x^2 - 59*a^3*b^2*x^(5/2) - 133*a^2*b^3*x^(5/2) + 408*a*b^4*x^(5/2) - 252*b^5*x^(5/2) + 165*a^2*b^3*x^3 - 443*a*b^4*x^3 + 282*b^5*x^3 - 5*a^2*b^3*x^(7/2) + 120*a*b^4*x^(7/2) - 120*b^5*x^(7/2) - 45*a*b^4*x^4 + 54*b^5*x^4 + 5*a*b^4*x^(9/2) - 10*b^5*x^(9/2) + b^5*x^5 + 96*a^4*Sqrt[a - b]*Sqrt[a - b*x] - 88*a^3*Sqrt[a - b]*b*Sqrt[a - b*x] + 22*a^2*Sqrt[a - b]*b^2*Sqrt[a - b*x] - 30*a*Sqrt[a - b]*b^3*Sqrt[a - b*x] + 10*Sqrt[a - b]*b^4*Sqrt[a - b*x] + 48*a^4*Sqrt[a - b]*Sqrt[x]*Sqrt[a - b*x] - 292*a^3*Sqrt[a - b]*b*Sqrt[x]*Sqrt[a - b*x] + 127*a^2*Sqrt[a - b]*b^2*Sqrt[x]*Sqrt[a - b*x] + 165*a*Sqrt[a - b]*b^3*Sqrt[x]*Sqrt[a - b*x] - 53*Sqrt[a - b]*b^4*Sqrt[x]*Sqrt[a - b*x] - 112*a^3*Sqrt[a - b]*b*x*Sqrt[a - b*x] + 448*a^2*Sqrt[a - b]*b^2*x*Sqrt[a - b*x] - 544*a*Sqrt[a - b]*b^3*x*Sqrt[a - b*x] + 120*Sqrt[a - b]*b^4*x*Sqrt[a - b*x] - 84*a^3*Sqrt[a - b]*b*x^(3/2)*Sqrt[a - b*x] + 98*a^2*Sqrt[a - b]*b^2*x^(3/2)*Sqrt[a - b*x] + 331*a*Sqrt[a - b]*b^3*x^(3/2)*Sqrt[a - b*x] - 140*Sqrt[a - b]*b^4*x^(3/2)*Sqrt[a - b*x] + 146*a^2*Sqrt[a - b]*b^2*x^2*Sqrt[a - b*x] - 582*a*Sqrt[a - b]*b^3*x^2*Sqrt[a - b*x] + 252*Sqrt[a - b]*b^4*x^2*Sqrt[a - b*x] + 23*a^2*Sqrt[a - b]*b^2*x^(5/2)*Sqrt[a - b*x] + 175*a*Sqrt[a - b]*b^3*x^(5/2)*Sqrt[a - b*x] - 138*Sqrt[a - b]*b^4*x^(5/2)*Sqrt[a - b*x] - 100*a*Sqrt[a - b]*b^3*x^3*Sqrt[a - b*x] + 120*Sqrt[a - b]*b^4*x^3*Sqrt[a - b*x] + 9*a*Sqrt[a - b]*b^3*x^(7/2)*Sqrt[a - b*x] - 36*Sqrt[a - b]*b^4*x^(7/2)*Sqrt[a - b*x] + 10*Sqrt[a - b]*b^4*x^4*Sqrt[a - b*x] - Sqrt[a - b]*b^4*x^(9/2)*Sqrt[a - b*x]))/(Sqrt[a - b] - Sqrt[a - b*x])^10))/((-Sqrt[a - b] + Sqrt[a - b*x])*(-2*a^3 + 5*a^2*b - 2*a*b^2 - 2*a^2*b*Sqrt[x] + 3*a^2*b*x - 5*a*b^2*x + 2*b^3*x + 2*a*b^2*x^(3/2) - a*b^2*x^2 + 2*a^2*Sqrt[a - b]*Sqrt[a - b*x] - 4*a*Sqrt[a - b]*b*Sqrt[a - b*x] + 2*a*Sqrt[a - b]*b*Sqrt[x]*Sqrt[a - b*x] + 2*Sqrt[a - b]*b^2*Sqrt[x]*Sqrt[a - b*x] - 2*a*Sqrt[a - b]*b*x*Sqrt[a - b*x])^3)","B",1
605,1,2989,45,8.5171457,"\int \frac{1}{\sqrt{x} (a-b x)^{5/2}} \, dx","IntegrateAlgebraic[1/(Sqrt[x]*(a - b*x)^(5/2)),x]","\text{Result too large to show}","\frac{4 \sqrt{x}}{3 a^2 \sqrt{a-b x}}+\frac{2 \sqrt{x}}{3 a (a-b x)^{3/2}}",1,"((-1/48*1/(a - b)^2 + Sqrt[x]/(48*(a - b)^2))*(Sqrt[a - b] - Sqrt[a - b*x])^12*((-32*a^3*(-a + b - b*Sqrt[x] + b*x + Sqrt[a - b]*Sqrt[a - b*x])^3*(-6*a^2 + 7*a*b - 2*b^2 - 2*a*b*Sqrt[x] + 4*b^2*Sqrt[x] + 7*a*b*x - 10*b^2*x + 4*b^2*x^(3/2) - 2*b^2*x^2 + 6*a*Sqrt[a - b]*Sqrt[a - b*x] - 4*Sqrt[a - b]*b*Sqrt[a - b*x] + 2*Sqrt[a - b]*b*Sqrt[x]*Sqrt[a - b*x] - 4*Sqrt[a - b]*b*x*Sqrt[a - b*x]))/(Sqrt[a - b] - Sqrt[a - b*x])^10 + (96*b^3*(-a + b*Sqrt[x] + Sqrt[a - b]*Sqrt[a - b*x])^2*(-a + b - b*Sqrt[x] + b*x + Sqrt[a - b]*Sqrt[a - b*x])*(-6*a^2 + 11*a*b - 4*b^2 + 4*a^2*Sqrt[x] - 14*a*b*Sqrt[x] + 8*b^2*Sqrt[x] + 11*a*b*x - 12*b^2*x - 4*a*b*x^(3/2) + 8*b^2*x^(3/2) - 2*b^2*x^2 + 6*a*Sqrt[a - b]*Sqrt[a - b*x] - 8*Sqrt[a - b]*b*Sqrt[a - b*x] - 4*a*Sqrt[a - b]*Sqrt[x]*Sqrt[a - b*x] + 12*Sqrt[a - b]*b*Sqrt[x]*Sqrt[a - b*x] - 8*Sqrt[a - b]*b*x*Sqrt[a - b*x] + 2*Sqrt[a - b]*b*x^(3/2)*Sqrt[a - b*x]))/(Sqrt[a - b] - Sqrt[a - b*x])^10 - (32*a^2*b*(-a + b - b*Sqrt[x] + b*x + Sqrt[a - b]*Sqrt[a - b*x])*(120*a^4 - 320*a^3*b + 271*a^2*b^2 - 81*a*b^3 + 7*b^4 - 48*a^4*Sqrt[x] + 256*a^3*b*Sqrt[x] - 304*a^2*b^2*Sqrt[x] + 136*a*b^3*Sqrt[x] - 28*b^4*Sqrt[x] - 320*a^3*b*x + 666*a^2*b^2*x - 487*a*b^3*x + 131*b^4*x + 96*a^3*b*x^(3/2) - 412*a^2*b^2*x^(3/2) + 492*a*b^3*x^(3/2) - 196*b^4*x^(3/2) + 271*a^2*b^2*x^2 - 487*a*b^3*x^2 + 265*b^4*x^2 - 60*a^2*b^2*x^(5/2) + 208*a*b^3*x^(5/2) - 196*b^4*x^(5/2) - 81*a*b^3*x^3 + 113*b^4*x^3 + 12*a*b^3*x^(7/2) - 28*b^4*x^(7/2) + 4*b^4*x^4 - 120*a^3*Sqrt[a - b]*Sqrt[a - b*x] + 260*a^2*Sqrt[a - b]*b*Sqrt[a - b*x] - 156*a*Sqrt[a - b]*b^2*Sqrt[a - b*x] + 28*Sqrt[a - b]*b^3*Sqrt[a - b*x] + 48*a^3*Sqrt[a - b]*Sqrt[x]*Sqrt[a - b*x] - 232*a^2*Sqrt[a - b]*b*Sqrt[x]*Sqrt[a - b*x] + 194*a*Sqrt[a - b]*b^2*Sqrt[x]*Sqrt[a - b*x] - 65*Sqrt[a - b]*b^3*Sqrt[x]*Sqrt[a - b*x] + 260*a^2*Sqrt[a - b]*b*x*Sqrt[a - b*x] - 376*a*Sqrt[a - b]*b^2*x*Sqrt[a - b*x] + 196*Sqrt[a - b]*b^3*x*Sqrt[a - b*x] - 72*a^2*Sqrt[a - b]*b*x^(3/2)*Sqrt[a - b*x] + 248*a*Sqrt[a - b]*b^2*x^(3/2)*Sqrt[a - b*x] - 225*Sqrt[a - b]*b^3*x^(3/2)*Sqrt[a - b*x] - 156*a*Sqrt[a - b]*b^2*x^2*Sqrt[a - b*x] + 196*Sqrt[a - b]*b^3*x^2*Sqrt[a - b*x] + 30*a*Sqrt[a - b]*b^2*x^(5/2)*Sqrt[a - b*x] - 83*Sqrt[a - b]*b^3*x^(5/2)*Sqrt[a - b*x] + 28*Sqrt[a - b]*b^3*x^3*Sqrt[a - b*x] - 3*Sqrt[a - b]*b^3*x^(7/2)*Sqrt[a - b*x]))/(Sqrt[a - b] - Sqrt[a - b*x])^10 - (32*a*b^2*(336*a^5 - 1100*a^4*b + 1233*a^3*b^2 - 549*a^2*b^3 + 84*a*b^4 - 4*b^5 - 192*a^5*Sqrt[x] + 1000*a^4*b*Sqrt[x] - 1344*a^3*b^2*Sqrt[x] + 600*a^2*b^3*Sqrt[x] - 90*a*b^4*Sqrt[x] + 20*b^5*Sqrt[x] - 1100*a^4*b*x + 2686*a^3*b^2*x - 2213*a^2*b^3*x + 803*a*b^4*x - 146*b^5*x + 480*a^4*b*x^(3/2) - 1864*a^3*b^2*x^(3/2) + 2067*a^2*b^3*x^(3/2) - 970*a*b^4*x^(3/2) + 240*b^5*x^(3/2) + 1121*a^3*b^2*x^2 - 2143*a^2*b^3*x^2 + 1493*a*b^4*x^2 - 476*b^5*x^2 - 392*a^3*b^2*x^(5/2) + 1106*a^2*b^3*x^(5/2) - 1116*a*b^4*x^(5/2) + 504*b^5*x^(5/2) - 423*a^2*b^3*x^3 + 733*a*b^4*x^3 - 444*b^5*x^3 + 115*a^2*b^3*x^(7/2) - 270*a*b^4*x^(7/2) + 240*b^5*x^(7/2) + 63*a*b^4*x^4 - 96*b^5*x^4 - 10*a*b^4*x^(9/2) + 20*b^5*x^(9/2) - 2*b^5*x^5 - 336*a^4*Sqrt[a - b]*Sqrt[a - b*x] + 932*a^3*Sqrt[a - b]*b*Sqrt[a - b*x] - 809*a^2*Sqrt[a - b]*b^2*Sqrt[a - b*x] + 240*a*Sqrt[a - b]*b^3*Sqrt[a - b*x] - 20*Sqrt[a - b]*b^4*Sqrt[a - b*x] + 192*a^4*Sqrt[a - b]*Sqrt[x]*Sqrt[a - b*x] - 904*a^3*Sqrt[a - b]*b*Sqrt[x]*Sqrt[a - b*x] + 916*a^2*Sqrt[a - b]*b^2*Sqrt[x]*Sqrt[a - b*x] - 243*a*Sqrt[a - b]*b^3*Sqrt[x]*Sqrt[a - b*x] + 34*Sqrt[a - b]*b^4*Sqrt[x]*Sqrt[a - b*x] + 932*a^3*Sqrt[a - b]*b*x*Sqrt[a - b*x] - 1670*a^2*Sqrt[a - b]*b^2*x*Sqrt[a - b*x] + 878*a*Sqrt[a - b]*b^3*x*Sqrt[a - b*x] - 240*Sqrt[a - b]*b^4*x*Sqrt[a - b*x] - 384*a^3*Sqrt[a - b]*b*x^(3/2)*Sqrt[a - b*x] + 1172*a^2*Sqrt[a - b]*b^2*x^(3/2)*Sqrt[a - b*x] - 857*a*Sqrt[a - b]*b^3*x^(3/2)*Sqrt[a - b*x] + 364*Sqrt[a - b]*b^4*x^(3/2)*Sqrt[a - b*x] - 697*a^2*Sqrt[a - b]*b^2*x^2*Sqrt[a - b*x] + 864*a*Sqrt[a - b]*b^3*x^2*Sqrt[a - b*x] - 504*Sqrt[a - b]*b^4*x^2*Sqrt[a - b*x] + 224*a^2*Sqrt[a - b]*b^2*x^(5/2)*Sqrt[a - b*x] - 437*a*Sqrt[a - b]*b^3*x^(5/2)*Sqrt[a - b*x] + 396*Sqrt[a - b]*b^4*x^(5/2)*Sqrt[a - b*x] + 170*a*Sqrt[a - b]*b^3*x^3*Sqrt[a - b*x] - 240*Sqrt[a - b]*b^4*x^3*Sqrt[a - b*x] - 39*a*Sqrt[a - b]*b^3*x^(7/2)*Sqrt[a - b*x] + 84*Sqrt[a - b]*b^4*x^(7/2)*Sqrt[a - b*x] - 20*Sqrt[a - b]*b^4*x^4*Sqrt[a - b*x] + 2*Sqrt[a - b]*b^4*x^(9/2)*Sqrt[a - b*x]))/(Sqrt[a - b] - Sqrt[a - b*x])^10))/((-Sqrt[a - b] + Sqrt[a - b*x])*(-2*a^3 + 5*a^2*b - 2*a*b^2 - 2*a^2*b*Sqrt[x] + 3*a^2*b*x - 5*a*b^2*x + 2*b^3*x + 2*a*b^2*x^(3/2) - a*b^2*x^2 + 2*a^2*Sqrt[a - b]*Sqrt[a - b*x] - 4*a*Sqrt[a - b]*b*Sqrt[a - b*x] + 2*a*Sqrt[a - b]*b*Sqrt[x]*Sqrt[a - b*x] + 2*Sqrt[a - b]*b^2*Sqrt[x]*Sqrt[a - b*x] - 2*a*Sqrt[a - b]*b*x*Sqrt[a - b*x])^3)","B",1
606,1,6195,67,43.4103241,"\int \frac{1}{x^{3/2} (a-b x)^{5/2}} \, dx","IntegrateAlgebraic[1/(x^(3/2)*(a - b*x)^(5/2)),x]","\text{Result too large to show}","-\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,"Result too large to show","B",1
607,-1,0,88,180.4020558,"\int \frac{1}{x^{5/2} (a-b x)^{5/2}} \, dx","IntegrateAlgebraic[1/(x^(5/2)*(a - b*x)^(5/2)),x]","\text{\$Aborted}","-\frac{32 b \sqrt{a-b x}}{3 a^4 \sqrt{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{2}{3 a x^{3/2} (a-b x)^{3/2}}",1,"$Aborted","F",-1
608,1,1294,88,1.598976,"\int \frac{x^{5/2}}{\sqrt{2+b x}} \, dx","IntegrateAlgebraic[x^(5/2)/Sqrt[2 + b*x],x]","\frac{4 \left(8 b^8+24 b^7+18 b^6+2 b^5\right) \sqrt{b x+2} x^{11/2}+4 \left(48 b^7+120 b^6+60 b^5\right) \sqrt{b x+2} x^5+4 \left(4 b^7+144 b^6+273 b^5+67 b^4\right) \sqrt{b x+2} x^{9/2}+4 \left(220 b^5+330 b^4\right) \sqrt{b x+2} x^4+4 \left(18 b^6-12 b^5+156 b^4+219 b^3\right) \sqrt{b x+2} x^{7/2}+4 \left(120 b^5+80 b^4+18 b^3\right) \sqrt{b x+2} x^3+4 \left(-8 b^8-12 b^7-18 b^6-20 b^5+552 b^4+639 b^3+92 b^2\right) \sqrt{b x+2} x^{5/2}+4 \left(-48 b^7-48 b^6-96 b^5-144 b^4+1590 b^3+1500 b^2\right) \sqrt{b x+2} x^2+4 \left(-16 b^7-156 b^6-102 b^5-448 b^4-615 b^3+3000 b^2+1600 b\right) \sqrt{b x+2} x^{3/2}+4 \left(-72 b^6-292 b^5-144 b^4-1386 b^3-1640 b^2+3840 b\right) \sqrt{b x+2} x+4 \left(-6 b^6-141 b^5-327 b^4-243 b^3-2580 b^2-2880 b+3840\right) \sqrt{b x+2} \sqrt{x}+\sqrt{b+2} \left(4 \left(-8 b^8-16 b^7-6 b^6\right) x^6+4 \left(-48 b^7-72 b^6-12 b^5\right) x^{11/2}+4 \left(-12 b^7-156 b^6-141 b^5\right) x^5+4 \left(-48 b^6-292 b^5-122 b^4\right) x^{9/2}+4 \left(-18 b^6-102 b^5-327 b^4\right) x^4+4 \left(-96 b^5-144 b^4-222 b^3\right) x^{7/2}+4 \left(8 b^8+4 b^7+18 b^6-20 b^5-448 b^4-243 b^3\right) x^3+4 \left(48 b^7+120 b^5-144 b^4-1386 b^3-372 b^2\right) x^{5/2}+4 \left(24 b^7+144 b^6-12 b^5+552 b^4-615 b^3-2580 b^2\right) x^2+4 \left(120 b^6+220 b^5+80 b^4+1590 b^3-1640 b^2-2560 b\right) x^{3/2}+4 \left(18 b^6+273 b^5+156 b^4+639 b^3+3000 b^2-2880 b\right) x+4 \left(60 b^5+330 b^4+18 b^3+1500 b^2+3840 b-3840\right) \sqrt{x}+4 \left(2 b^5+67 b^4+219 b^3+92 b^2+1600 b+3840\right)\right)+4 \left(-12 b^5-122 b^4-222 b^3-372 b^2-2560 b-3840\right) \sqrt{b x+2}}{3 \left(32 b^6+96 b^5+72 b^4+8 b^3\right) x^3 b^3+3 \left(8 b^3+288 b^2+1536 b+2048\right) b^3+3 \sqrt{b+2} \left(-48 b^2-512 b-1024\right) \sqrt{b x+2} b^3+x \left(3 \left(72 b^4+1272 b^3+3264 b^2+1536 b\right) b^3+3 \sqrt{b+2} \left(-288 b^3-1312 b^2-512 b\right) \sqrt{b x+2} b^3\right)+\sqrt{x} \left(3 \left(240 b^3+1920 b^2+3072 b\right) b^3+3 \sqrt{b+2} \left(-24 b^3-576 b^2-1536 b\right) \sqrt{b x+2} b^3\right)+x^2 \left(3 \left(96 b^5+816 b^4+1272 b^3+288 b^2\right) b^3+3 \sqrt{b+2} \left(-192 b^4-288 b^3-48 b^2\right) \sqrt{b x+2} b^3\right)+x^{3/2} \left(3 \left(480 b^4+2080 b^3+1920 b^2\right) b^3+3 \sqrt{b+2} \left(-64 b^4-656 b^3-576 b^2\right) \sqrt{b x+2} b^3\right)+x^{5/2} \left(3 \left(192 b^5+480 b^4+240 b^3\right) b^3+3 \sqrt{b+2} \left(-32 b^5-64 b^4-24 b^3\right) \sqrt{b x+2} b^3\right)}+\frac{10 \tanh ^{-1}\left(\frac{\frac{\sqrt{b+2}}{\sqrt{b}}-\frac{\sqrt{b x+2}}{\sqrt{b}}}{\sqrt{x}-1}\right)}{b^{7/2}}","-\frac{5 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{7/2}}+\frac{5 \sqrt{x} \sqrt{b x+2}}{2 b^3}-\frac{5 x^{3/2} \sqrt{b x+2}}{6 b^2}+\frac{x^{5/2} \sqrt{b x+2}}{3 b}",1,"(4*(-3840 - 2560*b - 372*b^2 - 222*b^3 - 122*b^4 - 12*b^5)*Sqrt[2 + b*x] + 4*(3840 - 2880*b - 2580*b^2 - 243*b^3 - 327*b^4 - 141*b^5 - 6*b^6)*Sqrt[x]*Sqrt[2 + b*x] + 4*(3840*b - 1640*b^2 - 1386*b^3 - 144*b^4 - 292*b^5 - 72*b^6)*x*Sqrt[2 + b*x] + 4*(1600*b + 3000*b^2 - 615*b^3 - 448*b^4 - 102*b^5 - 156*b^6 - 16*b^7)*x^(3/2)*Sqrt[2 + b*x] + 4*(1500*b^2 + 1590*b^3 - 144*b^4 - 96*b^5 - 48*b^6 - 48*b^7)*x^2*Sqrt[2 + b*x] + 4*(92*b^2 + 639*b^3 + 552*b^4 - 20*b^5 - 18*b^6 - 12*b^7 - 8*b^8)*x^(5/2)*Sqrt[2 + b*x] + 4*(18*b^3 + 80*b^4 + 120*b^5)*x^3*Sqrt[2 + b*x] + 4*(219*b^3 + 156*b^4 - 12*b^5 + 18*b^6)*x^(7/2)*Sqrt[2 + b*x] + 4*(330*b^4 + 220*b^5)*x^4*Sqrt[2 + b*x] + 4*(67*b^4 + 273*b^5 + 144*b^6 + 4*b^7)*x^(9/2)*Sqrt[2 + b*x] + 4*(60*b^5 + 120*b^6 + 48*b^7)*x^5*Sqrt[2 + b*x] + 4*(2*b^5 + 18*b^6 + 24*b^7 + 8*b^8)*x^(11/2)*Sqrt[2 + b*x] + Sqrt[2 + b]*(4*(3840 + 1600*b + 92*b^2 + 219*b^3 + 67*b^4 + 2*b^5) + 4*(-3840 + 3840*b + 1500*b^2 + 18*b^3 + 330*b^4 + 60*b^5)*Sqrt[x] + 4*(-2880*b + 3000*b^2 + 639*b^3 + 156*b^4 + 273*b^5 + 18*b^6)*x + 4*(-2560*b - 1640*b^2 + 1590*b^3 + 80*b^4 + 220*b^5 + 120*b^6)*x^(3/2) + 4*(-2580*b^2 - 615*b^3 + 552*b^4 - 12*b^5 + 144*b^6 + 24*b^7)*x^2 + 4*(-372*b^2 - 1386*b^3 - 144*b^4 + 120*b^5 + 48*b^7)*x^(5/2) + 4*(-243*b^3 - 448*b^4 - 20*b^5 + 18*b^6 + 4*b^7 + 8*b^8)*x^3 + 4*(-222*b^3 - 144*b^4 - 96*b^5)*x^(7/2) + 4*(-327*b^4 - 102*b^5 - 18*b^6)*x^4 + 4*(-122*b^4 - 292*b^5 - 48*b^6)*x^(9/2) + 4*(-141*b^5 - 156*b^6 - 12*b^7)*x^5 + 4*(-12*b^5 - 72*b^6 - 48*b^7)*x^(11/2) + 4*(-6*b^6 - 16*b^7 - 8*b^8)*x^6))/(3*b^3*(2048 + 1536*b + 288*b^2 + 8*b^3) + 3*b^3*(8*b^3 + 72*b^4 + 96*b^5 + 32*b^6)*x^3 + 3*b^3*Sqrt[2 + b]*(-1024 - 512*b - 48*b^2)*Sqrt[2 + b*x] + x*(3*b^3*(1536*b + 3264*b^2 + 1272*b^3 + 72*b^4) + 3*b^3*Sqrt[2 + b]*(-512*b - 1312*b^2 - 288*b^3)*Sqrt[2 + b*x]) + Sqrt[x]*(3*b^3*(3072*b + 1920*b^2 + 240*b^3) + 3*b^3*Sqrt[2 + b]*(-1536*b - 576*b^2 - 24*b^3)*Sqrt[2 + b*x]) + x^2*(3*b^3*(288*b^2 + 1272*b^3 + 816*b^4 + 96*b^5) + 3*b^3*Sqrt[2 + b]*(-48*b^2 - 288*b^3 - 192*b^4)*Sqrt[2 + b*x]) + x^(3/2)*(3*b^3*(1920*b^2 + 2080*b^3 + 480*b^4) + 3*b^3*Sqrt[2 + b]*(-576*b^2 - 656*b^3 - 64*b^4)*Sqrt[2 + b*x]) + x^(5/2)*(3*b^3*(240*b^3 + 480*b^4 + 192*b^5) + 3*b^3*Sqrt[2 + b]*(-24*b^3 - 64*b^4 - 32*b^5)*Sqrt[2 + b*x])) + (10*ArcTanh[(Sqrt[2 + b]/Sqrt[b] - Sqrt[2 + b*x]/Sqrt[b])/(-1 + Sqrt[x])])/b^(7/2)","B",1
609,1,633,67,0.6720998,"\int \frac{x^{3/2}}{\sqrt{2+b x}} \, dx","IntegrateAlgebraic[x^(3/2)/Sqrt[2 + b*x],x]","\frac{\left(\frac{2 \sqrt{x}}{b^2}-\frac{2}{b^2}\right) \left(\sqrt{b+2}-\sqrt{b x+2}\right) \left(-2 b^5 x^3-2 b^5 x^2-6 b^4 x^{5/2}-6 b^4 x^{3/2}+2 \sqrt{b+2} b^4 x^{5/2} \sqrt{b x+2}+2 \sqrt{b+2} b^4 x^{3/2} \sqrt{b x+2}-4 b^4 x^3-4 b^4 x^2-4 b^4 x-9 b^3 x^{5/2}-6 b^3 x^{3/2}+2 \sqrt{b+2} b^3 x^{5/2} \sqrt{b x+2}-b^3 x^3-8 b^3 x^2+6 \sqrt{b+2} b^3 x^2 \sqrt{b x+2}-8 b^3 x-9 b^3 \sqrt{x}+6 \sqrt{b+2} b^3 x \sqrt{b x+2}+2 \sqrt{b+2} b^3 \sqrt{x} \sqrt{b x+2}-b^3+b^2 x^{3/2}+5 \sqrt{b+2} b^2 x^{3/2} \sqrt{b x+2}-7 b^2 x^2+3 \sqrt{b+2} b^2 x^2 \sqrt{b x+2}+16 b^2 x+b^2 \sqrt{x}-6 \sqrt{b+2} b^2 x \sqrt{b x+2}+3 \sqrt{b+2} b^2 \sqrt{b x+2}+5 \sqrt{b+2} b^2 \sqrt{x} \sqrt{b x+2}-7 b^2+14 b x+44 b \sqrt{x}-\sqrt{b+2} b x \sqrt{b x+2}-\sqrt{b+2} b \sqrt{b x+2}-22 \sqrt{b+2} b \sqrt{x} \sqrt{b x+2}-24 \sqrt{b+2} \sqrt{b x+2}+14 b+48\right)}{\left(b \left(-\sqrt{x}\right)+\sqrt{b+2} \sqrt{b x+2}-2\right)^4}-\frac{6 \tanh ^{-1}\left(\frac{\frac{\sqrt{b+2}}{\sqrt{b}}-\frac{\sqrt{b x+2}}{\sqrt{b}}}{\sqrt{x}-1}\right)}{b^{5/2}}","\frac{3 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{5/2}}-\frac{3 \sqrt{x} \sqrt{b x+2}}{2 b^2}+\frac{x^{3/2} \sqrt{b x+2}}{2 b}",1,"((-2/b^2 + (2*Sqrt[x])/b^2)*(Sqrt[2 + b] - Sqrt[2 + b*x])*(48 + 14*b - 7*b^2 - b^3 + 44*b*Sqrt[x] + b^2*Sqrt[x] - 9*b^3*Sqrt[x] + 14*b*x + 16*b^2*x - 8*b^3*x - 4*b^4*x + b^2*x^(3/2) - 6*b^3*x^(3/2) - 6*b^4*x^(3/2) - 7*b^2*x^2 - 8*b^3*x^2 - 4*b^4*x^2 - 2*b^5*x^2 - 9*b^3*x^(5/2) - 6*b^4*x^(5/2) - b^3*x^3 - 4*b^4*x^3 - 2*b^5*x^3 - 24*Sqrt[2 + b]*Sqrt[2 + b*x] - b*Sqrt[2 + b]*Sqrt[2 + b*x] + 3*b^2*Sqrt[2 + b]*Sqrt[2 + b*x] - 22*b*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] + 5*b^2*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] + 2*b^3*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] - b*Sqrt[2 + b]*x*Sqrt[2 + b*x] - 6*b^2*Sqrt[2 + b]*x*Sqrt[2 + b*x] + 6*b^3*Sqrt[2 + b]*x*Sqrt[2 + b*x] + 5*b^2*Sqrt[2 + b]*x^(3/2)*Sqrt[2 + b*x] + 2*b^4*Sqrt[2 + b]*x^(3/2)*Sqrt[2 + b*x] + 3*b^2*Sqrt[2 + b]*x^2*Sqrt[2 + b*x] + 6*b^3*Sqrt[2 + b]*x^2*Sqrt[2 + b*x] + 2*b^3*Sqrt[2 + b]*x^(5/2)*Sqrt[2 + b*x] + 2*b^4*Sqrt[2 + b]*x^(5/2)*Sqrt[2 + b*x]))/(-2 - b*Sqrt[x] + Sqrt[2 + b]*Sqrt[2 + b*x])^4 - (6*ArcTanh[(Sqrt[2 + b]/Sqrt[b] - Sqrt[2 + b*x]/Sqrt[b])/(-1 + Sqrt[x])])/b^(5/2)","B",1
610,1,174,43,0.2291097,"\int \frac{\sqrt{x}}{\sqrt{2+b x}} \, dx","IntegrateAlgebraic[Sqrt[x]/Sqrt[2 + b*x],x]","\frac{4 \tanh ^{-1}\left(\frac{\frac{\sqrt{b+2}}{\sqrt{b}}-\frac{\sqrt{b x+2}}{\sqrt{b}}}{\sqrt{x}-1}\right)}{b^{3/2}}+\frac{\left(\frac{2}{b}-\frac{2 \sqrt{x}}{b}\right) \left(\sqrt{b+2}-\sqrt{b x+2}\right) \left(b^2 x+b x+b \sqrt{x}-\sqrt{b+2} b \sqrt{x} \sqrt{b x+2}-\sqrt{b+2} \sqrt{b x+2}+b+2\right)}{\left(b \left(-\sqrt{x}\right)+\sqrt{b+2} \sqrt{b x+2}-2\right)^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,"((2/b - (2*Sqrt[x])/b)*(Sqrt[2 + b] - Sqrt[2 + b*x])*(2 + b + b*Sqrt[x] + b*x + b^2*x - Sqrt[2 + b]*Sqrt[2 + b*x] - b*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x]))/(-2 - b*Sqrt[x] + Sqrt[2 + b]*Sqrt[2 + b*x])^2 + (4*ArcTanh[(Sqrt[2 + b]/Sqrt[b] - Sqrt[2 + b*x]/Sqrt[b])/(-1 + Sqrt[x])])/b^(3/2)","B",1
611,1,48,24,0.1112534,"\int \frac{1}{\sqrt{x} \sqrt{2+b x}} \, dx","IntegrateAlgebraic[1/(Sqrt[x]*Sqrt[2 + b*x]),x]","\frac{4 \tanh ^{-1}\left(\frac{\frac{\sqrt{b x+2}}{\sqrt{b}}-\frac{\sqrt{b+2}}{\sqrt{b}}}{\sqrt{x}-1}\right)}{\sqrt{b}}","\frac{2 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{\sqrt{b}}",1,"(4*ArcTanh[(-(Sqrt[2 + b]/Sqrt[b]) + Sqrt[2 + b*x]/Sqrt[b])/(-1 + Sqrt[x])])/Sqrt[b]","A",1
612,1,235,16,0.202148,"\int \frac{1}{x^{3/2} \sqrt{2+b x}} \, dx","IntegrateAlgebraic[1/(x^(3/2)*Sqrt[2 + b*x]),x]","\frac{\left(\frac{1}{2}-\frac{\sqrt{x}}{2}\right) \left(\sqrt{b+2}-\sqrt{b x+2}\right)^4 \left(\frac{b \left(\sqrt{x}-1\right)^2}{\left(\sqrt{b+2}-\sqrt{b x+2}\right)^2}-\frac{2 \sqrt{b+2} \left(\sqrt{x}-1\right)}{\sqrt{b+2}-\sqrt{b x+2}}+1\right)}{\left(\sqrt{b x+2}-\sqrt{b+2}\right) \left(b^2 (-x)-2 b x^{3/2}+b x^2+b x-4 b \sqrt{x}+\sqrt{b+2} b \sqrt{x} \sqrt{b x+2}-2 \sqrt{b+2} x \sqrt{b x+2}+4 \sqrt{b+2} \sqrt{x} \sqrt{b x+2}+4 x-8 \sqrt{x}\right)}","-\frac{\sqrt{b x+2}}{\sqrt{x}}",1,"((1/2 - Sqrt[x]/2)*(Sqrt[2 + b] - Sqrt[2 + b*x])^4*(1 + (b*(-1 + Sqrt[x])^2)/(Sqrt[2 + b] - Sqrt[2 + b*x])^2 - (2*Sqrt[2 + b]*(-1 + Sqrt[x]))/(Sqrt[2 + b] - Sqrt[2 + b*x])))/((-Sqrt[2 + b] + Sqrt[2 + b*x])*(-8*Sqrt[x] - 4*b*Sqrt[x] + 4*x + b*x - b^2*x - 2*b*x^(3/2) + b*x^2 + 4*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] + b*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] - 2*Sqrt[2 + b]*x*Sqrt[2 + b*x]))","B",1
613,1,559,38,3.9389775,"\int \frac{1}{x^{5/2} \sqrt{2+b x}} \, dx","IntegrateAlgebraic[1/(x^(5/2)*Sqrt[2 + b*x]),x]","\frac{\left(\frac{1}{384}-\frac{\sqrt{x}}{384}\right) \left(\sqrt{b+2}-\sqrt{b x+2}\right)^{12} \left(\frac{3 b^5 \left(\sqrt{x}-1\right)^{10}}{\left(\sqrt{b+2}-\sqrt{b x+2}\right)^{10}}-\frac{12 b^4 \sqrt{b+2} \left(\sqrt{x}-1\right)^9}{\left(\sqrt{b+2}-\sqrt{b x+2}\right)^9}+\frac{b^3 (15 b+8) \left(\sqrt{x}-1\right)^8}{\left(\sqrt{b+2}-\sqrt{b x+2}\right)^8}+\frac{48 b^2 \sqrt{b+2} \left(\sqrt{x}-1\right)^7}{\left(\sqrt{b+2}-\sqrt{b x+2}\right)^7}-\frac{18 b^2 (b+4) \left(\sqrt{x}-1\right)^6}{\left(\sqrt{b+2}-\sqrt{b x+2}\right)^6}+\frac{8 \sqrt{b+2} \left(3 b^2+4 b-16\right) \left(\sqrt{x}-1\right)^5}{\left(\sqrt{b+2}-\sqrt{b x+2}\right)^5}-\frac{18 b (b+4) \left(\sqrt{x}-1\right)^4}{\left(\sqrt{b+2}-\sqrt{b x+2}\right)^4}+\frac{48 \sqrt{b+2} \left(\sqrt{x}-1\right)^3}{\left(\sqrt{b+2}-\sqrt{b x+2}\right)^3}+\frac{(15 b+8) \left(\sqrt{x}-1\right)^2}{\left(\sqrt{b+2}-\sqrt{b x+2}\right)^2}-\frac{12 \sqrt{b+2} \left(\sqrt{x}-1\right)}{\sqrt{b+2}-\sqrt{b x+2}}+3\right)}{\left(\sqrt{b x+2}-\sqrt{b+2}\right) \left(b^2 (-x)-2 b x^{3/2}+b x^2+b x-4 b \sqrt{x}+\sqrt{b+2} b \sqrt{x} \sqrt{b x+2}-2 \sqrt{b+2} x \sqrt{b x+2}+4 \sqrt{b+2} \sqrt{x} \sqrt{b x+2}+4 x-8 \sqrt{x}\right)^3}","\frac{b \sqrt{b x+2}}{3 \sqrt{x}}-\frac{\sqrt{b x+2}}{3 x^{3/2}}",1,"((1/384 - Sqrt[x]/384)*(Sqrt[2 + b] - Sqrt[2 + b*x])^12*(3 + (3*b^5*(-1 + Sqrt[x])^10)/(Sqrt[2 + b] - Sqrt[2 + b*x])^10 - (12*b^4*Sqrt[2 + b]*(-1 + Sqrt[x])^9)/(Sqrt[2 + b] - Sqrt[2 + b*x])^9 + (b^3*(8 + 15*b)*(-1 + Sqrt[x])^8)/(Sqrt[2 + b] - Sqrt[2 + b*x])^8 + (48*b^2*Sqrt[2 + b]*(-1 + Sqrt[x])^7)/(Sqrt[2 + b] - Sqrt[2 + b*x])^7 - (18*b^2*(4 + b)*(-1 + Sqrt[x])^6)/(Sqrt[2 + b] - Sqrt[2 + b*x])^6 + (8*Sqrt[2 + b]*(-16 + 4*b + 3*b^2)*(-1 + Sqrt[x])^5)/(Sqrt[2 + b] - Sqrt[2 + b*x])^5 - (18*b*(4 + b)*(-1 + Sqrt[x])^4)/(Sqrt[2 + b] - Sqrt[2 + b*x])^4 + (48*Sqrt[2 + b]*(-1 + Sqrt[x])^3)/(Sqrt[2 + b] - Sqrt[2 + b*x])^3 + ((8 + 15*b)*(-1 + Sqrt[x])^2)/(Sqrt[2 + b] - Sqrt[2 + b*x])^2 - (12*Sqrt[2 + b]*(-1 + Sqrt[x]))/(Sqrt[2 + b] - Sqrt[2 + b*x])))/((-Sqrt[2 + b] + Sqrt[2 + b*x])*(-8*Sqrt[x] - 4*b*Sqrt[x] + 4*x + b*x - b^2*x - 2*b*x^(3/2) + b*x^2 + 4*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] + b*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] - 2*Sqrt[2 + b]*x*Sqrt[2 + b*x])^3)","B",1
614,1,980,59,46.9758871,"\int \frac{1}{x^{7/2} \sqrt{2+b x}} \, dx","IntegrateAlgebraic[1/(x^(7/2)*Sqrt[2 + b*x]),x]","\frac{\left(\frac{1}{122880}-\frac{\sqrt{x}}{122880}\right) \left(\sqrt{b+2}-\sqrt{b x+2}\right)^{20} \left(\frac{15 b^9 \left(\sqrt{x}-1\right)^{18}}{\left(\sqrt{b+2}-\sqrt{b x+2}\right)^{18}}-\frac{90 b^8 \sqrt{b+2} \left(\sqrt{x}-1\right)^{17}}{\left(\sqrt{b+2}-\sqrt{b x+2}\right)^{17}}+\frac{5 b^7 (43 b+48) \left(\sqrt{x}-1\right)^{16}}{\left(\sqrt{b+2}-\sqrt{b x+2}\right)^{16}}-\frac{240 (b-1) b^6 \sqrt{b+2} \left(\sqrt{x}-1\right)^{15}}{\left(\sqrt{b+2}-\sqrt{b x+2}\right)^{15}}-\frac{4 b^5 \left(5 b^2+140 b-48\right) \left(\sqrt{x}-1\right)^{14}}{\left(\sqrt{b+2}-\sqrt{b x+2}\right)^{14}}+\frac{40 b^4 \sqrt{b+2} \left(17 b^2+28 b-96\right) \left(\sqrt{x}-1\right)^{13}}{\left(\sqrt{b+2}-\sqrt{b x+2}\right)^{13}}-\frac{20 b^4 \left(69 b^2+244 b+80\right) \left(\sqrt{x}-1\right)^{12}}{\left(\sqrt{b+2}-\sqrt{b x+2}\right)^{12}}+\frac{80 b^2 \sqrt{b+2} \left(11 b^3+45 b^2+64 b+192\right) \left(\sqrt{x}-1\right)^{11}}{\left(\sqrt{b+2}-\sqrt{b x+2}\right)^{11}}+\frac{10 b^3 \left(117 b^2+520 b+960\right) \left(\sqrt{x}-1\right)^{10}}{\left(\sqrt{b+2}-\sqrt{b x+2}\right)^{10}}-\frac{4 \sqrt{b+2} \left(615 b^4+2480 b^3+4736 b^2+3584 b+6144\right) \left(\sqrt{x}-1\right)^9}{\left(\sqrt{b+2}-\sqrt{b x+2}\right)^9}+\frac{10 b^2 \left(117 b^2+520 b+960\right) \left(\sqrt{x}-1\right)^8}{\left(\sqrt{b+2}-\sqrt{b x+2}\right)^8}+\frac{80 \sqrt{b+2} \left(11 b^3+45 b^2+64 b+192\right) \left(\sqrt{x}-1\right)^7}{\left(\sqrt{b+2}-\sqrt{b x+2}\right)^7}-\frac{20 b \left(69 b^2+244 b+80\right) \left(\sqrt{x}-1\right)^6}{\left(\sqrt{b+2}-\sqrt{b x+2}\right)^6}+\frac{40 \sqrt{b+2} \left(17 b^2+28 b-96\right) \left(\sqrt{x}-1\right)^5}{\left(\sqrt{b+2}-\sqrt{b x+2}\right)^5}-\frac{4 \left(5 b^2+140 b-48\right) \left(\sqrt{x}-1\right)^4}{\left(\sqrt{b+2}-\sqrt{b x+2}\right)^4}-\frac{240 (b-1) \sqrt{b+2} \left(\sqrt{x}-1\right)^3}{\left(\sqrt{b+2}-\sqrt{b x+2}\right)^3}+\frac{5 (43 b+48) \left(\sqrt{x}-1\right)^2}{\left(\sqrt{b+2}-\sqrt{b x+2}\right)^2}-\frac{90 \sqrt{b+2} \left(\sqrt{x}-1\right)}{\sqrt{b+2}-\sqrt{b x+2}}+15\right)}{\left(\sqrt{b x+2}-\sqrt{b+2}\right) \left(-x b^2+x^2 b-2 x^{3/2} b+x b-4 \sqrt{x} b+\sqrt{b+2} \sqrt{x} \sqrt{b x+2} b+4 x-8 \sqrt{x}-2 \sqrt{b+2} x \sqrt{b x+2}+4 \sqrt{b+2} \sqrt{x} \sqrt{b x+2}\right)^5}","-\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,"((1/122880 - Sqrt[x]/122880)*(Sqrt[2 + b] - Sqrt[2 + b*x])^20*(15 + (15*b^9*(-1 + Sqrt[x])^18)/(Sqrt[2 + b] - Sqrt[2 + b*x])^18 - (90*b^8*Sqrt[2 + b]*(-1 + Sqrt[x])^17)/(Sqrt[2 + b] - Sqrt[2 + b*x])^17 + (5*b^7*(48 + 43*b)*(-1 + Sqrt[x])^16)/(Sqrt[2 + b] - Sqrt[2 + b*x])^16 - (240*(-1 + b)*b^6*Sqrt[2 + b]*(-1 + Sqrt[x])^15)/(Sqrt[2 + b] - Sqrt[2 + b*x])^15 - (4*b^5*(-48 + 140*b + 5*b^2)*(-1 + Sqrt[x])^14)/(Sqrt[2 + b] - Sqrt[2 + b*x])^14 + (40*b^4*Sqrt[2 + b]*(-96 + 28*b + 17*b^2)*(-1 + Sqrt[x])^13)/(Sqrt[2 + b] - Sqrt[2 + b*x])^13 - (20*b^4*(80 + 244*b + 69*b^2)*(-1 + Sqrt[x])^12)/(Sqrt[2 + b] - Sqrt[2 + b*x])^12 + (80*b^2*Sqrt[2 + b]*(192 + 64*b + 45*b^2 + 11*b^3)*(-1 + Sqrt[x])^11)/(Sqrt[2 + b] - Sqrt[2 + b*x])^11 + (10*b^3*(960 + 520*b + 117*b^2)*(-1 + Sqrt[x])^10)/(Sqrt[2 + b] - Sqrt[2 + b*x])^10 - (4*Sqrt[2 + b]*(6144 + 3584*b + 4736*b^2 + 2480*b^3 + 615*b^4)*(-1 + Sqrt[x])^9)/(Sqrt[2 + b] - Sqrt[2 + b*x])^9 + (10*b^2*(960 + 520*b + 117*b^2)*(-1 + Sqrt[x])^8)/(Sqrt[2 + b] - Sqrt[2 + b*x])^8 + (80*Sqrt[2 + b]*(192 + 64*b + 45*b^2 + 11*b^3)*(-1 + Sqrt[x])^7)/(Sqrt[2 + b] - Sqrt[2 + b*x])^7 - (20*b*(80 + 244*b + 69*b^2)*(-1 + Sqrt[x])^6)/(Sqrt[2 + b] - Sqrt[2 + b*x])^6 + (40*Sqrt[2 + b]*(-96 + 28*b + 17*b^2)*(-1 + Sqrt[x])^5)/(Sqrt[2 + b] - Sqrt[2 + b*x])^5 - (4*(-48 + 140*b + 5*b^2)*(-1 + Sqrt[x])^4)/(Sqrt[2 + b] - Sqrt[2 + b*x])^4 - (240*(-1 + b)*Sqrt[2 + b]*(-1 + Sqrt[x])^3)/(Sqrt[2 + b] - Sqrt[2 + b*x])^3 + (5*(48 + 43*b)*(-1 + Sqrt[x])^2)/(Sqrt[2 + b] - Sqrt[2 + b*x])^2 - (90*Sqrt[2 + b]*(-1 + Sqrt[x]))/(Sqrt[2 + b] - Sqrt[2 + b*x])))/((-Sqrt[2 + b] + Sqrt[2 + b*x])*(-8*Sqrt[x] - 4*b*Sqrt[x] + 4*x + b*x - b^2*x - 2*b*x^(3/2) + b*x^2 + 4*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] + b*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] - 2*Sqrt[2 + b]*x*Sqrt[2 + b*x])^5)","B",0
615,-1,0,80,180.1067999,"\int \frac{1}{x^{9/2} \sqrt{2+b x}} \, dx","IntegrateAlgebraic[1/(x^(9/2)*Sqrt[2 + b*x]),x]","\text{\$Aborted}","\frac{2 b^3 \sqrt{b x+2}}{35 \sqrt{x}}-\frac{2 b^2 \sqrt{b x+2}}{35 x^{3/2}}+\frac{3 b \sqrt{b x+2}}{35 x^{5/2}}-\frac{\sqrt{b x+2}}{7 x^{7/2}}",1,"$Aborted","F",-1
616,1,892,86,3.1775291,"\int \frac{x^{5/2}}{(2+b x)^{3/2}} \, dx","IntegrateAlgebraic[x^(5/2)/(2 + b*x)^(3/2),x]","\frac{\left(-\frac{4 \sqrt{x}}{b}-\frac{8 \sqrt{x}}{b^2}-\frac{2 \sqrt{x}}{b^3}+\frac{4 \sqrt{b+2} \sqrt{b x+2}}{b^2}+\frac{4 \sqrt{b+2} \sqrt{b x+2}}{b^3}-\frac{4}{b^2}-\frac{6}{b^3}\right) \left(\sqrt{b+2}-\sqrt{b x+2}\right)^7}{\left(-\sqrt{x} b+\sqrt{b+2} \sqrt{b x+2}-2\right)^4}+\frac{\left(-\frac{12 \sqrt{x}}{b}-\frac{24 \sqrt{x}}{b^2}-\frac{6 \sqrt{x}}{b^3}+\frac{16 \sqrt{b+2} \sqrt{b x+2}}{b^2}+\frac{16 \sqrt{b+2} \sqrt{b x+2}}{b^3}-\frac{4}{b}-\frac{24}{b^2}-\frac{26}{b^3}\right) \left(\sqrt{b+2}-\sqrt{b x+2}\right)^5}{\left(-\sqrt{x} b+\sqrt{b+2} \sqrt{b x+2}-2\right)^3}+\frac{\left(-\frac{10 \sqrt{x}}{b}-\frac{12 \sqrt{x}}{b^2}+\frac{3 \sqrt{x}}{b^3}+\frac{20 \sqrt{b+2} \sqrt{b x+2}}{b^2}+\frac{12 \sqrt{b+2} \sqrt{b x+2}}{b^3}-\frac{10}{b}-\frac{40}{b^2}-\frac{27}{b^3}\right) \left(\sqrt{b+2}-\sqrt{b x+2}\right)^3}{\left(-\sqrt{x} b+\sqrt{b+2} \sqrt{b x+2}-2\right)^2}+\frac{\left(\frac{8}{b^3 (b+2)}-\frac{8 \sqrt{x}}{b^3 (b+2)}\right) \left(x b^2-2 \sqrt{x} b^2+2 b^2+2 x b-4 \sqrt{x} b-2 \sqrt{b+2} \sqrt{b x+2} b+\sqrt{b+2} \sqrt{x} \sqrt{b x+2} b+6 b-2 \sqrt{b+2} \sqrt{b x+2}+4\right) \left(\sqrt{b+2}-\sqrt{b x+2}\right)}{-x b^3-x^2 b^2+2 x^{3/2} b^2-5 x b^2+\sqrt{b+2} \sqrt{x} \sqrt{b x+2} b^2-2 b^2-6 x b+4 \sqrt{x} b+2 \sqrt{b+2} x \sqrt{b x+2} b+4 \sqrt{b+2} \sqrt{b x+2} b-2 \sqrt{b+2} \sqrt{x} \sqrt{b x+2} b-10 b+4 \sqrt{b+2} \sqrt{b x+2}-8}+\frac{\left(\frac{\sqrt{b+2}}{b^3}-\frac{\sqrt{b x+2}}{b^3}\right) \left(-2 \sqrt{x} b^2-6 b^2+4 \sqrt{x} b+8 \sqrt{b+2} \sqrt{b x+2} b-12 b+7 \sqrt{x}-8 \sqrt{b+2} \sqrt{b x+2}+9\right)}{-\sqrt{x} b+\sqrt{b+2} \sqrt{b x+2}-2}-\frac{30 \tanh ^{-1}\left(\frac{\frac{\sqrt{b+2}}{\sqrt{b}}-\frac{\sqrt{b x+2}}{\sqrt{b}}}{\sqrt{x}-1}\right)}{b^{7/2}}","\frac{15 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{7/2}}-\frac{15 \sqrt{x} \sqrt{b x+2}}{2 b^3}+\frac{5 x^{3/2} \sqrt{b x+2}}{2 b^2}-\frac{2 x^{5/2}}{b \sqrt{b x+2}}",1,"((Sqrt[2 + b] - Sqrt[2 + b*x])^7*(-6/b^3 - 4/b^2 - (2*Sqrt[x])/b^3 - (8*Sqrt[x])/b^2 - (4*Sqrt[x])/b + (4*Sqrt[2 + b]*Sqrt[2 + b*x])/b^3 + (4*Sqrt[2 + b]*Sqrt[2 + b*x])/b^2))/(-2 - b*Sqrt[x] + Sqrt[2 + b]*Sqrt[2 + b*x])^4 + ((Sqrt[2 + b] - Sqrt[2 + b*x])^5*(-26/b^3 - 24/b^2 - 4/b - (6*Sqrt[x])/b^3 - (24*Sqrt[x])/b^2 - (12*Sqrt[x])/b + (16*Sqrt[2 + b]*Sqrt[2 + b*x])/b^3 + (16*Sqrt[2 + b]*Sqrt[2 + b*x])/b^2))/(-2 - b*Sqrt[x] + Sqrt[2 + b]*Sqrt[2 + b*x])^3 + ((Sqrt[2 + b] - Sqrt[2 + b*x])^3*(-27/b^3 - 40/b^2 - 10/b + (3*Sqrt[x])/b^3 - (12*Sqrt[x])/b^2 - (10*Sqrt[x])/b + (12*Sqrt[2 + b]*Sqrt[2 + b*x])/b^3 + (20*Sqrt[2 + b]*Sqrt[2 + b*x])/b^2))/(-2 - b*Sqrt[x] + Sqrt[2 + b]*Sqrt[2 + b*x])^2 + ((Sqrt[2 + b]/b^3 - Sqrt[2 + b*x]/b^3)*(9 - 12*b - 6*b^2 + 7*Sqrt[x] + 4*b*Sqrt[x] - 2*b^2*Sqrt[x] - 8*Sqrt[2 + b]*Sqrt[2 + b*x] + 8*b*Sqrt[2 + b]*Sqrt[2 + b*x]))/(-2 - b*Sqrt[x] + Sqrt[2 + b]*Sqrt[2 + b*x]) + ((8/(b^3*(2 + b)) - (8*Sqrt[x])/(b^3*(2 + b)))*(Sqrt[2 + b] - Sqrt[2 + b*x])*(4 + 6*b + 2*b^2 - 4*b*Sqrt[x] - 2*b^2*Sqrt[x] + 2*b*x + b^2*x - 2*Sqrt[2 + b]*Sqrt[2 + b*x] - 2*b*Sqrt[2 + b]*Sqrt[2 + b*x] + b*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x]))/(-8 - 10*b - 2*b^2 + 4*b*Sqrt[x] - 6*b*x - 5*b^2*x - b^3*x + 2*b^2*x^(3/2) - b^2*x^2 + 4*Sqrt[2 + b]*Sqrt[2 + b*x] + 4*b*Sqrt[2 + b]*Sqrt[2 + b*x] - 2*b*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] + b^2*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] + 2*b*Sqrt[2 + b]*x*Sqrt[2 + b*x]) - (30*ArcTanh[(Sqrt[2 + b]/Sqrt[b] - Sqrt[2 + b*x]/Sqrt[b])/(-1 + Sqrt[x])])/b^(7/2)","B",1
617,1,545,63,1.0571883,"\int \frac{x^{3/2}}{(2+b x)^{3/2}} \, dx","IntegrateAlgebraic[x^(3/2)/(2 + b*x)^(3/2),x]","\frac{12 \tanh ^{-1}\left(\frac{\frac{\sqrt{b+2}}{\sqrt{b}}-\frac{\sqrt{b x+2}}{\sqrt{b}}}{\sqrt{x}-1}\right)}{b^{5/2}}+\frac{\left(-\frac{2 \sqrt{x}}{b^2}+\frac{2 \sqrt{b+2} \sqrt{b x+2}}{b^2}-\frac{2}{b^2}-\frac{2 \sqrt{x}}{b}\right) \left(\sqrt{b+2}-\sqrt{b x+2}\right)^3}{\left(b \left(-\sqrt{x}\right)+\sqrt{b+2} \sqrt{b x+2}-2\right)^2}+\frac{\left(\frac{2 \sqrt{b+2}}{b^2}-\frac{2 \sqrt{b x+2}}{b^2}\right) \left(b \left(-\sqrt{x}\right)+2 \sqrt{b+2} \sqrt{b x+2}-b-\sqrt{x}-3\right)}{b \left(-\sqrt{x}\right)+\sqrt{b+2} \sqrt{b x+2}-2}+\frac{\left(\frac{4 \sqrt{x}}{b^2 (b+2)}-\frac{4}{b^2 (b+2)}\right) \left(b^2 x-2 b^2 \sqrt{x}+2 b^2+2 b x-4 b \sqrt{x}-2 \sqrt{b+2} b \sqrt{b x+2}+\sqrt{b+2} b \sqrt{x} \sqrt{b x+2}-2 \sqrt{b+2} \sqrt{b x+2}+6 b+4\right) \left(\sqrt{b+2}-\sqrt{b x+2}\right)}{b^3 (-x)+2 b^2 x^{3/2}-b^2 x^2-5 b^2 x+\sqrt{b+2} b^2 \sqrt{x} \sqrt{b x+2}-2 b^2-6 b x+4 b \sqrt{x}+2 \sqrt{b+2} b x \sqrt{b x+2}+4 \sqrt{b+2} b \sqrt{b x+2}-2 \sqrt{b+2} b \sqrt{x} \sqrt{b x+2}+4 \sqrt{b+2} \sqrt{b x+2}-10 b-8}","-\frac{6 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{5/2}}+\frac{3 \sqrt{x} \sqrt{b x+2}}{b^2}-\frac{2 x^{3/2}}{b \sqrt{b x+2}}",1,"(((2*Sqrt[2 + b])/b^2 - (2*Sqrt[2 + b*x])/b^2)*(-3 - b - Sqrt[x] - b*Sqrt[x] + 2*Sqrt[2 + b]*Sqrt[2 + b*x]))/(-2 - b*Sqrt[x] + Sqrt[2 + b]*Sqrt[2 + b*x]) + ((Sqrt[2 + b] - Sqrt[2 + b*x])^3*(-2/b^2 - (2*Sqrt[x])/b^2 - (2*Sqrt[x])/b + (2*Sqrt[2 + b]*Sqrt[2 + b*x])/b^2))/(-2 - b*Sqrt[x] + Sqrt[2 + b]*Sqrt[2 + b*x])^2 + ((-4/(b^2*(2 + b)) + (4*Sqrt[x])/(b^2*(2 + b)))*(Sqrt[2 + b] - Sqrt[2 + b*x])*(4 + 6*b + 2*b^2 - 4*b*Sqrt[x] - 2*b^2*Sqrt[x] + 2*b*x + b^2*x - 2*Sqrt[2 + b]*Sqrt[2 + b*x] - 2*b*Sqrt[2 + b]*Sqrt[2 + b*x] + b*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x]))/(-8 - 10*b - 2*b^2 + 4*b*Sqrt[x] - 6*b*x - 5*b^2*x - b^3*x + 2*b^2*x^(3/2) - b^2*x^2 + 4*Sqrt[2 + b]*Sqrt[2 + b*x] + 4*b*Sqrt[2 + b]*Sqrt[2 + b*x] - 2*b*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] + b^2*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] + 2*b*Sqrt[2 + b]*x*Sqrt[2 + b*x]) + (12*ArcTanh[(Sqrt[2 + b]/Sqrt[b] - Sqrt[2 + b*x]/Sqrt[b])/(-1 + Sqrt[x])])/b^(5/2)","B",1
618,1,352,44,0.3539213,"\int \frac{\sqrt{x}}{(2+b x)^{3/2}} \, dx","IntegrateAlgebraic[Sqrt[x]/(2 + b*x)^(3/2),x]","\frac{\left(\frac{2}{b (b+2)}-\frac{2 \sqrt{x}}{b (b+2)}\right) \left(\sqrt{b+2}-\sqrt{b x+2}\right) \left(b^2 x-2 b^2 \sqrt{x}+2 b^2+2 b x-4 b \sqrt{x}-2 \sqrt{b+2} b \sqrt{b x+2}+\sqrt{b+2} b \sqrt{x} \sqrt{b x+2}-2 \sqrt{b+2} \sqrt{b x+2}+6 b+4\right)}{b^3 (-x)+2 b^2 x^{3/2}-b^2 x^2-5 b^2 x+\sqrt{b+2} b^2 \sqrt{x} \sqrt{b x+2}-2 b^2-6 b x+4 b \sqrt{x}+2 \sqrt{b+2} b x \sqrt{b x+2}+4 \sqrt{b+2} b \sqrt{b x+2}-2 \sqrt{b+2} b \sqrt{x} \sqrt{b x+2}+4 \sqrt{b+2} \sqrt{b x+2}-10 b-8}-\frac{4 \tanh ^{-1}\left(\frac{\frac{\sqrt{b+2}}{\sqrt{b}}-\frac{\sqrt{b x+2}}{\sqrt{b}}}{\sqrt{x}-1}\right)}{b^{3/2}}","\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/(b*(2 + b)) - (2*Sqrt[x])/(b*(2 + b)))*(Sqrt[2 + b] - Sqrt[2 + b*x])*(4 + 6*b + 2*b^2 - 4*b*Sqrt[x] - 2*b^2*Sqrt[x] + 2*b*x + b^2*x - 2*Sqrt[2 + b]*Sqrt[2 + b*x] - 2*b*Sqrt[2 + b]*Sqrt[2 + b*x] + b*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x]))/(-8 - 10*b - 2*b^2 + 4*b*Sqrt[x] - 6*b*x - 5*b^2*x - b^3*x + 2*b^2*x^(3/2) - b^2*x^2 + 4*Sqrt[2 + b]*Sqrt[2 + b*x] + 4*b*Sqrt[2 + b]*Sqrt[2 + b*x] - 2*b*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] + b^2*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] + 2*b*Sqrt[2 + b]*x*Sqrt[2 + b*x]) - (4*ArcTanh[(Sqrt[2 + b]/Sqrt[b] - Sqrt[2 + b*x]/Sqrt[b])/(-1 + Sqrt[x])])/b^(3/2)","B",1
619,1,334,15,0.3037809,"\int \frac{1}{\sqrt{x} (2+b x)^{3/2}} \, dx","IntegrateAlgebraic[1/(Sqrt[x]*(2 + b*x)^(3/2)),x]","\frac{\left(\frac{\sqrt{x}}{2 (b+2)}-\frac{1}{2 (b+2)}\right) \left(\sqrt{b+2}-\sqrt{b x+2}\right)^4 \left(\frac{b^2 \left(\sqrt{x}-1\right)^2}{\left(\sqrt{b+2}-\sqrt{b x+2}\right)^2}+\frac{2 b \left(\sqrt{x}-1\right)^2}{\left(\sqrt{b+2}-\sqrt{b x+2}\right)^2}-\frac{2 b \sqrt{b+2} \left(\sqrt{x}-1\right)}{\sqrt{b+2}-\sqrt{b x+2}}+b+2\right)}{\left(\sqrt{b x+2}-\sqrt{b+2}\right) \left(b^3 x-2 b^2 x^{3/2}+b^2 x^2+5 b^2 x-\sqrt{b+2} b^2 \sqrt{x} \sqrt{b x+2}+2 b^2+6 b x-4 b \sqrt{x}-2 \sqrt{b+2} b x \sqrt{b x+2}-4 \sqrt{b+2} b \sqrt{b x+2}+2 \sqrt{b+2} b \sqrt{x} \sqrt{b x+2}-4 \sqrt{b+2} \sqrt{b x+2}+10 b+8\right)}","\frac{\sqrt{x}}{\sqrt{b x+2}}",1,"((-1/2*1/(2 + b) + Sqrt[x]/(2*(2 + b)))*(Sqrt[2 + b] - Sqrt[2 + b*x])^4*(2 + b + (2*b*(-1 + Sqrt[x])^2)/(Sqrt[2 + b] - Sqrt[2 + b*x])^2 + (b^2*(-1 + Sqrt[x])^2)/(Sqrt[2 + b] - Sqrt[2 + b*x])^2 - (2*b*Sqrt[2 + b]*(-1 + Sqrt[x]))/(Sqrt[2 + b] - Sqrt[2 + b*x])))/((-Sqrt[2 + b] + Sqrt[2 + b*x])*(8 + 10*b + 2*b^2 - 4*b*Sqrt[x] + 6*b*x + 5*b^2*x + b^3*x - 2*b^2*x^(3/2) + b^2*x^2 - 4*Sqrt[2 + b]*Sqrt[2 + b*x] - 4*b*Sqrt[2 + b]*Sqrt[2 + b*x] + 2*b*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] - b^2*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] - 2*b*Sqrt[2 + b]*x*Sqrt[2 + b*x]))","B",1
620,1,1050,32,4.1461963,"\int \frac{1}{x^{3/2} (2+b x)^{3/2}} \, dx","IntegrateAlgebraic[1/(x^(3/2)*(2 + b*x)^(3/2)),x]","\frac{\left(\frac{1}{16 (b+2)}-\frac{\sqrt{x}}{16 (b+2)}\right) \left(\sqrt{b+2}-\sqrt{b x+2}\right)^8 \left(\frac{b \left(\sqrt{x}-1\right)^2}{\left(\sqrt{b+2}-\sqrt{b x+2}\right)^2}+1\right) \left(\frac{b^3 \left(\sqrt{x}-1\right)^4}{\left(\sqrt{b+2}-\sqrt{b x+2}\right)^4}+\frac{2 b^2 \left(3 x b-2 \sqrt{x} b+5 b+x-6 \sqrt{x}-8 \sqrt{b+2} \sqrt{b x+2}+2 \sqrt{b+2} \sqrt{x} \sqrt{b x+2}+17\right) \left(\sqrt{x}-1\right)^2}{\left(\sqrt{b+2}-\sqrt{b x+2}\right)^4}-\frac{4 \sqrt{b+2} \left(\sqrt{x}-1\right)}{\sqrt{b+2}-\sqrt{b x+2}}-\frac{b \left(4 b \sqrt{b+2} x^{3/2}+4 \sqrt{b+2} x^{3/2}-7 b \sqrt{b+2} x-24 \sqrt{b+2} x+b \sqrt{b x+2} x+12 \sqrt{b x+2} x+4 b \sqrt{b+2} \sqrt{x}+52 \sqrt{b+2} \sqrt{x}-8 b \sqrt{b x+2} \sqrt{x}-40 \sqrt{b x+2} \sqrt{x}-5 b \sqrt{b+2}-40 \sqrt{b+2}+11 b \sqrt{b x+2}+36 \sqrt{b x+2}\right)}{\left(\sqrt{b+2}-\sqrt{b x+2}\right)^3}+2\right)}{\left(\sqrt{b x+2}-\sqrt{b+2}\right) \left(-2 x^2 b^5-8 x^2 b^4-8 x^{3/2} b^4-4 x b^4+2 \sqrt{b+2} x^{3/2} \sqrt{b x+2} b^4+x^4 b^3-4 x^{7/2} b^3+14 x^3 b^3-28 x^{5/2} b^3+25 x^2 b^3-56 x^{3/2} b^3-16 x b^3-16 \sqrt{x} b^3+6 \sqrt{b+2} x^{3/2} \sqrt{b x+2} b^3+8 \sqrt{b+2} x \sqrt{b x+2} b^3+2 \sqrt{b+2} \sqrt{x} \sqrt{b x+2} b^3+18 x^3 b^2-56 x^{5/2} b^2+108 x^2 b^2-168 x^{3/2} b^2+50 x b^2-112 \sqrt{x} b^2-4 \sqrt{b+2} x^3 \sqrt{b x+2} b^2+14 \sqrt{b+2} x^{5/2} \sqrt{b x+2} b^2-28 \sqrt{b+2} x^2 \sqrt{b x+2} b^2+40 \sqrt{b+2} x^{3/2} \sqrt{b x+2} b^2-8 \sqrt{b+2} x \sqrt{b x+2} b^2+34 \sqrt{b+2} \sqrt{x} \sqrt{b x+2} b^2+64 x^2 b-160 x^{3/2} b+160 x b-224 \sqrt{x} b-24 \sqrt{b+2} x^2 \sqrt{b x+2} b+64 \sqrt{b+2} x^{3/2} \sqrt{b x+2} b-72 \sqrt{b+2} x \sqrt{b x+2} b+96 \sqrt{b+2} \sqrt{x} \sqrt{b x+2} b+64 x-128 \sqrt{x}-32 \sqrt{b+2} x \sqrt{b x+2}+64 \sqrt{b+2} \sqrt{x} \sqrt{b x+2}\right)}","\frac{1}{\sqrt{x} \sqrt{b x+2}}-\frac{\sqrt{b x+2}}{\sqrt{x}}",1,"((1/(16*(2 + b)) - Sqrt[x]/(16*(2 + b)))*(Sqrt[2 + b] - Sqrt[2 + b*x])^8*(1 + (b*(-1 + Sqrt[x])^2)/(Sqrt[2 + b] - Sqrt[2 + b*x])^2)*(2 + (b^3*(-1 + Sqrt[x])^4)/(Sqrt[2 + b] - Sqrt[2 + b*x])^4 - (4*Sqrt[2 + b]*(-1 + Sqrt[x]))/(Sqrt[2 + b] - Sqrt[2 + b*x]) + (2*b^2*(-1 + Sqrt[x])^2*(17 + 5*b - 6*Sqrt[x] - 2*b*Sqrt[x] + x + 3*b*x - 8*Sqrt[2 + b]*Sqrt[2 + b*x] + 2*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x]))/(Sqrt[2 + b] - Sqrt[2 + b*x])^4 - (b*(-40*Sqrt[2 + b] - 5*b*Sqrt[2 + b] + 52*Sqrt[2 + b]*Sqrt[x] + 4*b*Sqrt[2 + b]*Sqrt[x] - 24*Sqrt[2 + b]*x - 7*b*Sqrt[2 + b]*x + 4*Sqrt[2 + b]*x^(3/2) + 4*b*Sqrt[2 + b]*x^(3/2) + 36*Sqrt[2 + b*x] + 11*b*Sqrt[2 + b*x] - 40*Sqrt[x]*Sqrt[2 + b*x] - 8*b*Sqrt[x]*Sqrt[2 + b*x] + 12*x*Sqrt[2 + b*x] + b*x*Sqrt[2 + b*x]))/(Sqrt[2 + b] - Sqrt[2 + b*x])^3))/((-Sqrt[2 + b] + Sqrt[2 + b*x])*(-128*Sqrt[x] - 224*b*Sqrt[x] - 112*b^2*Sqrt[x] - 16*b^3*Sqrt[x] + 64*x + 160*b*x + 50*b^2*x - 16*b^3*x - 4*b^4*x - 160*b*x^(3/2) - 168*b^2*x^(3/2) - 56*b^3*x^(3/2) - 8*b^4*x^(3/2) + 64*b*x^2 + 108*b^2*x^2 + 25*b^3*x^2 - 8*b^4*x^2 - 2*b^5*x^2 - 56*b^2*x^(5/2) - 28*b^3*x^(5/2) + 18*b^2*x^3 + 14*b^3*x^3 - 4*b^3*x^(7/2) + b^3*x^4 + 64*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] + 96*b*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] + 34*b^2*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] + 2*b^3*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] - 32*Sqrt[2 + b]*x*Sqrt[2 + b*x] - 72*b*Sqrt[2 + b]*x*Sqrt[2 + b*x] - 8*b^2*Sqrt[2 + b]*x*Sqrt[2 + b*x] + 8*b^3*Sqrt[2 + b]*x*Sqrt[2 + b*x] + 64*b*Sqrt[2 + b]*x^(3/2)*Sqrt[2 + b*x] + 40*b^2*Sqrt[2 + b]*x^(3/2)*Sqrt[2 + b*x] + 6*b^3*Sqrt[2 + b]*x^(3/2)*Sqrt[2 + b*x] + 2*b^4*Sqrt[2 + b]*x^(3/2)*Sqrt[2 + b*x] - 24*b*Sqrt[2 + b]*x^2*Sqrt[2 + b*x] - 28*b^2*Sqrt[2 + b]*x^2*Sqrt[2 + b*x] + 14*b^2*Sqrt[2 + b]*x^(5/2)*Sqrt[2 + b*x] - 4*b^2*Sqrt[2 + b]*x^3*Sqrt[2 + b*x]))","B",1
621,1,3969,53,29.9916707,"\int \frac{1}{x^{5/2} (2+b x)^{3/2}} \, dx","IntegrateAlgebraic[1/(x^(5/2)*(2 + b*x)^(3/2)),x]","\text{Result too large to show}","-\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/(3072*(2 + b)) - Sqrt[x]/(3072*(2 + b)))*(Sqrt[2 + b] - Sqrt[2 + b*x])^16*(6 + (3*b^8*(-1 + Sqrt[x])^14)/(Sqrt[2 + b] - Sqrt[2 + b*x])^14 - (256*Sqrt[2 + b]*(-1 + Sqrt[x])^5)/(Sqrt[2 + b] - Sqrt[2 + b*x])^5 + (96*Sqrt[2 + b]*(-1 + Sqrt[x])^3)/(Sqrt[2 + b] - Sqrt[2 + b*x])^3 + (16*(-1 + Sqrt[x])^2)/(Sqrt[2 + b] - Sqrt[2 + b*x])^2 - (24*Sqrt[2 + b]*(-1 + Sqrt[x]))/(Sqrt[2 + b] - Sqrt[2 + b*x]) + (b^7*(-1 + Sqrt[x])^12*(238 + 67*b - 48*Sqrt[x] - 18*b*Sqrt[x] + 6*x + 49*b*x - 116*Sqrt[2 + b]*Sqrt[2 + b*x] + 18*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x]))/(Sqrt[2 + b] - Sqrt[2 + b*x])^14 - (b^6*(-1 + Sqrt[x])^10*(-1194*Sqrt[2 + b] - 175*b*Sqrt[2 + b] + 620*Sqrt[2 + b]*Sqrt[x] + 84*b*Sqrt[2 + b]*Sqrt[x] - 178*Sqrt[2 + b]*x - 357*b*Sqrt[2 + b]*x + 24*Sqrt[2 + b]*x^(3/2) + 84*b*Sqrt[2 + b]*x^(3/2) + 1170*Sqrt[2 + b*x] + 441*b*Sqrt[2 + b*x] - 548*Sqrt[x]*Sqrt[2 + b*x] - 168*b*Sqrt[x]*Sqrt[2 + b*x] + 106*x*Sqrt[2 + b*x] + 91*b*x*Sqrt[2 + b*x]))/(Sqrt[2 + b] - Sqrt[2 + b*x])^13 + (b^5*(-1 + Sqrt[x])^8*(-4120 - 2070*b - 129*b^2 - 816*Sqrt[x] - 344*b*Sqrt[x] - 14*b^2*Sqrt[x] + 504*x - 2000*b*x - 816*b^2*x - 160*x^(3/2) - 192*b*x^(3/2) - 42*b^2*x^(3/2) + 16*x^2 + 30*b*x^2 - 143*b^2*x^2 + 2068*Sqrt[2 + b]*Sqrt[2 + b*x] + 530*b*Sqrt[2 + b]*Sqrt[2 + b*x] + 376*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] + 42*b*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] - 204*Sqrt[2 + b]*x*Sqrt[2 + b*x] + 558*b*Sqrt[2 + b]*x*Sqrt[2 + b*x] + 48*Sqrt[2 + b]*x^(3/2)*Sqrt[2 + b*x] + 14*b*Sqrt[2 + b]*x^(3/2)*Sqrt[2 + b*x]))/(Sqrt[2 + b] - Sqrt[2 + b*x])^12 - (b^3*(-1 + Sqrt[x])^4*(10704*Sqrt[2 + b] + 134*b*Sqrt[2 + b] - 105*b^2*Sqrt[2 + b] - 43680*Sqrt[2 + b]*Sqrt[x] - 6236*b*Sqrt[2 + b]*Sqrt[x] + 14*b^2*Sqrt[2 + b]*Sqrt[x] + 40240*Sqrt[2 + b]*x + 6304*b*Sqrt[2 + b]*x - 994*b^2*Sqrt[2 + b]*x - 16384*Sqrt[2 + b]*x^(3/2) - 12276*b*Sqrt[2 + b]*x^(3/2) + 84*b^2*Sqrt[2 + b]*x^(3/2) + 3680*Sqrt[2 + b]*x^2 + 7626*b*Sqrt[2 + b]*x^2 - 469*b^2*Sqrt[2 + b]*x^2 - 384*Sqrt[2 + b]*x^(5/2) - 1376*b*Sqrt[2 + b]*x^(5/2) + 14*b^2*Sqrt[2 + b]*x^(5/2) - 10320*Sqrt[2 + b*x] - 2274*b*Sqrt[2 + b*x] + 511*b^2*Sqrt[2 + b*x] + 41760*Sqrt[x]*Sqrt[2 + b*x] + 14916*b*Sqrt[x]*Sqrt[2 + b*x] - 56*b^2*Sqrt[x]*Sqrt[2 + b*x] - 36400*x*Sqrt[2 + b*x] - 10624*b*x*Sqrt[2 + b*x] + 966*b^2*x*Sqrt[2 + b*x] + 12544*x^(3/2)*Sqrt[2 + b*x] + 4972*b*x^(3/2)*Sqrt[2 + b*x] - 56*b^2*x^(3/2)*Sqrt[2 + b*x] - 1760*x^2*Sqrt[2 + b*x] - 1166*b*x^2*Sqrt[2 + b*x] + 91*b^2*x^2*Sqrt[2 + b*x]))/(Sqrt[2 + b] - Sqrt[2 + b*x])^9 + (b^4*(-1 + Sqrt[x])^6*(-27936*Sqrt[2 + b] - 8718*b*Sqrt[2 + b] - 375*b^2*Sqrt[2 + b] + 32672*Sqrt[2 + b]*Sqrt[x] + 7268*b*Sqrt[2 + b]*Sqrt[x] + 232*b^2*Sqrt[2 + b]*Sqrt[x] - 17008*Sqrt[2 + b]*x - 15728*b*Sqrt[2 + b]*x - 2822*b^2*Sqrt[2 + b]*x + 3808*Sqrt[2 + b]*x^(3/2) + 12340*b*Sqrt[2 + b]*x^(3/2) + 1392*b^2*Sqrt[2 + b]*x^(3/2) - 784*Sqrt[2 + b]*x^2 - 4722*b*Sqrt[2 + b]*x^2 - 947*b^2*Sqrt[2 + b]*x^2 + 96*Sqrt[2 + b]*x^(5/2) + 408*b*Sqrt[2 + b]*x^(5/2) + 232*b^2*Sqrt[2 + b]*x^(5/2) + 27840*Sqrt[2 + b*x] + 15602*b*Sqrt[2 + b*x] + 1643*b^2*Sqrt[2 + b*x] - 32192*Sqrt[x]*Sqrt[2 + b*x] - 15012*b*Sqrt[x]*Sqrt[2 + b*x] - 928*b^2*Sqrt[x]*Sqrt[2 + b*x] + 16048*x*Sqrt[2 + b*x] + 12400*b*x*Sqrt[2 + b*x] + 2358*b^2*x*Sqrt[2 + b*x] - 2848*x^(3/2)*Sqrt[2 + b*x] - 5004*b*x^(3/2)*Sqrt[2 + b*x] - 928*b^2*x^(3/2)*Sqrt[2 + b*x] + 304*x^2*Sqrt[2 + b*x] + 1166*b*x^2*Sqrt[2 + b*x] + 143*b^2*x^2*Sqrt[2 + b*x]))/(Sqrt[2 + b] - Sqrt[2 + b*x])^11 - (b*(-11008*Sqrt[2 + b] - 7040*b*Sqrt[2 + b] - 946*b^2*Sqrt[2 + b] - 21*b^3*Sqrt[2 + b] + 8960*Sqrt[2 + b]*Sqrt[x] + 7712*b*Sqrt[2 + b]*Sqrt[x] + 1004*b^2*Sqrt[2 + b]*Sqrt[x] + 18*b^3*Sqrt[2 + b]*Sqrt[x] + 7808*Sqrt[2 + b]*x - 7696*b*Sqrt[2 + b]*x - 4430*b^2*Sqrt[2 + b]*x - 333*b^3*Sqrt[2 + b]*x - 5632*Sqrt[2 + b]*x^(3/2) + 4384*b*Sqrt[2 + b]*x^(3/2) + 5192*b^2*Sqrt[2 + b]*x^(3/2) + 270*b^3*Sqrt[2 + b]*x^(3/2) - 7808*Sqrt[2 + b]*x^2 + 4992*b*Sqrt[2 + b]*x^2 - 3486*b^2*Sqrt[2 + b]*x^2 - 375*b^3*Sqrt[2 + b]*x^2 + 9216*Sqrt[2 + b]*x^(5/2) - 7104*b*Sqrt[2 + b]*x^(5/2) + 2140*b^2*Sqrt[2 + b]*x^(5/2) + 270*b^3*Sqrt[2 + b]*x^(5/2) - 3584*Sqrt[2 + b]*x^3 + 2832*b*Sqrt[2 + b]*x^3 - 674*b^2*Sqrt[2 + b]*x^3 - 39*b^3*Sqrt[2 + b]*x^3 + 512*Sqrt[2 + b]*x^(7/2) - 384*b*Sqrt[2 + b]*x^(7/2) + 48*b^2*Sqrt[2 + b]*x^(7/2) + 18*b^3*Sqrt[2 + b]*x^(7/2) + 10496*Sqrt[2 + b*x] + 9664*b*Sqrt[2 + b*x] + 2426*b^2*Sqrt[2 + b*x] + 129*b^3*Sqrt[2 + b*x] - 5376*Sqrt[x]*Sqrt[2 + b*x] - 9056*b*Sqrt[x]*Sqrt[2 + b*x] - 3004*b^2*Sqrt[x]*Sqrt[2 + b*x] - 108*b^3*Sqrt[x]*Sqrt[2 + b*x] - 18560*x*Sqrt[2 + b*x] + 432*b*x*Sqrt[2 + b*x] + 4902*b^2*x*Sqrt[2 + b*x] + 465*b^3*x*Sqrt[2 + b*x] + 23552*x^(3/2)*Sqrt[2 + b*x] + 2848*b*x^(3/2)*Sqrt[2 + b*x] - 4760*b^2*x^(3/2)*Sqrt[2 + b*x] - 360*b^3*x^(3/2)*Sqrt[2 + b*x] - 10112*x^2*Sqrt[2 + b*x] - 2880*b*x^2*Sqrt[2 + b*x] + 2102*b^2*x^2*Sqrt[2 + b*x] + 171*b^3*x^2*Sqrt[2 + b*x] + 1536*x^(5/2)*Sqrt[2 + b*x] + 1600*b*x^(5/2)*Sqrt[2 + b*x] - 620*b^2*x^(5/2)*Sqrt[2 + b*x] - 108*b^3*x^(5/2)*Sqrt[2 + b*x] - 304*b*x^3*Sqrt[2 + b*x] + 106*b^2*x^3*Sqrt[2 + b*x] + 3*b^3*x^3*Sqrt[2 + b*x]))/(Sqrt[2 + b] - Sqrt[2 + b*x])^7 - (b^2*(-1 + Sqrt[x])^2*(-17280*Sqrt[2 + b] - 23152*b*Sqrt[2 + b] - 4998*b^2*Sqrt[2 + b] - 133*b^3*Sqrt[2 + b] - 90112*Sqrt[2 + b]*Sqrt[x] - 14496*b*Sqrt[2 + b]*Sqrt[x] + 1860*b^2*Sqrt[2 + b]*Sqrt[x] + 84*b^3*Sqrt[2 + b]*Sqrt[x] + 159872*Sqrt[2 + b]*x + 13920*b*Sqrt[2 + b]*x - 17714*b^2*Sqrt[2 + b]*x - 2289*b^3*Sqrt[2 + b]*x - 103936*Sqrt[2 + b]*x^(3/2) - 52064*b*Sqrt[2 + b]*x^(3/2) + 2928*b^2*Sqrt[2 + b]*x^(3/2) + 1260*b^3*Sqrt[2 + b]*x^(3/2) + 26880*Sqrt[2 + b]*x^2 + 68144*b*Sqrt[2 + b]*x^2 - 1210*b^2*Sqrt[2 + b]*x^2 - 2975*b^3*Sqrt[2 + b]*x^2 + 1024*Sqrt[2 + b]*x^(5/2) - 39616*b*Sqrt[2 + b]*x^(5/2) - 348*b^2*Sqrt[2 + b]*x^(5/2) + 1260*b^3*Sqrt[2 + b]*x^(5/2) - 1792*Sqrt[2 + b]*x^3 + 10720*b*Sqrt[2 + b]*x^3 + 1074*b^2*Sqrt[2 + b]*x^3 - 427*b^3*Sqrt[2 + b]*x^3 + 256*Sqrt[2 + b]*x^(7/2) - 1088*b*Sqrt[2 + b]*x^(7/2) - 408*b^2*Sqrt[2 + b]*x^(7/2) + 84*b^3*Sqrt[2 + b]*x^(7/2) + 17024*Sqrt[2 + b*x] + 27408*b*Sqrt[2 + b*x] + 10390*b^2*Sqrt[2 + b*x] + 847*b^3*Sqrt[2 + b*x] + 91904*Sqrt[x]*Sqrt[2 + b*x] + 37472*b*Sqrt[x]*Sqrt[2 + b*x] - 1788*b^2*Sqrt[x]*Sqrt[2 + b*x] - 504*b^3*Sqrt[x]*Sqrt[2 + b*x] - 165248*x*Sqrt[2 + b*x] - 59488*b*x*Sqrt[2 + b*x] + 13634*b^2*x*Sqrt[2 + b*x] + 3395*b^3*x*Sqrt[2 + b*x] + 112896*x^(3/2)*Sqrt[2 + b*x] + 57312*b*x^(3/2)*Sqrt[2 + b*x] - 2808*b^2*x^(3/2)*Sqrt[2 + b*x] - 1680*b^3*x^(3/2)*Sqrt[2 + b*x] - 35840*x^2*Sqrt[2 + b*x] - 35792*b*x^2*Sqrt[2 + b*x] - 1206*b^2*x^2*Sqrt[2 + b*x] + 1533*b^3*x^2*Sqrt[2 + b*x] + 4352*x^(5/2)*Sqrt[2 + b*x] + 12480*b*x^(5/2)*Sqrt[2 + b*x] + 564*b^2*x^(5/2)*Sqrt[2 + b*x] - 504*b^3*x^(5/2)*Sqrt[2 + b*x] - 1760*b*x^3*Sqrt[2 + b*x] + 30*b^2*x^3*Sqrt[2 + b*x] + 49*b^3*x^3*Sqrt[2 + b*x]))/(Sqrt[2 + b] - Sqrt[2 + b*x])^9))/((-Sqrt[2 + b] + Sqrt[2 + b*x])*(-8*Sqrt[x] - 4*b*Sqrt[x] + 4*x + b*x - b^2*x - 2*b*x^(3/2) + b*x^2 + 4*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] + b*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] - 2*Sqrt[2 + b]*x*Sqrt[2 + b*x])^3*(8 + 10*b + 2*b^2 - 4*b*Sqrt[x] + 6*b*x + 5*b^2*x + b^3*x - 2*b^2*x^(3/2) + b^2*x^2 - 4*Sqrt[2 + b]*Sqrt[2 + b*x] - 4*b*Sqrt[2 + b]*Sqrt[2 + b*x] + 2*b*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] - b^2*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] - 2*b*Sqrt[2 + b]*x*Sqrt[2 + b*x]))","B",1
622,-1,0,74,180.0994714,"\int \frac{1}{x^{7/2} (2+b x)^{3/2}} \, dx","IntegrateAlgebraic[1/(x^(7/2)*(2 + b*x)^(3/2)),x]","\text{\$Aborted}","-\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,"$Aborted","F",-1
623,1,2262,86,35.523639,"\int \frac{x^{5/2}}{(2+b x)^{5/2}} \, dx","IntegrateAlgebraic[x^(5/2)/(2 + b*x)^(5/2),x]","\text{Result too large to show}","-\frac{10 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{7/2}}+\frac{5 \sqrt{x} \sqrt{b x+2}}{b^3}-\frac{10 x^{3/2}}{3 b^2 \sqrt{b x+2}}-\frac{2 x^{5/2}}{3 b (b x+2)^{3/2}}",1,"(((2*Sqrt[2 + b])/b^3 - (2*Sqrt[2 + b*x])/b^3)*(-3 - b - Sqrt[x] - b*Sqrt[x] + 2*Sqrt[2 + b]*Sqrt[2 + b*x]))/(-2 - b*Sqrt[x] + Sqrt[2 + b]*Sqrt[2 + b*x]) + ((Sqrt[2 + b] - Sqrt[2 + b*x])^3*(-2/b^3 - (2*Sqrt[x])/b^3 - (2*Sqrt[x])/b^2 + (2*Sqrt[2 + b]*Sqrt[2 + b*x])/b^3))/(-2 - b*Sqrt[x] + Sqrt[2 + b]*Sqrt[2 + b*x])^2 + ((Sqrt[2 + b] - Sqrt[2 + b*x])^9*(1472/(3*(2 + b)^4) - 768/(b^2*(2 + b)^4) - 1664/(3*b*(2 + b)^4) + (800*b)/(3*(2 + b)^4) - (32*b^2)/(3*(2 + b)^4) - (704*Sqrt[x])/(2 + b)^4 + (256*Sqrt[x])/(3*b^2*(2 + b)^4) + (896*Sqrt[x])/(3*b*(2 + b)^4) - (288*b*Sqrt[x])/(2 + b)^4 + (64*b^2*Sqrt[x])/(2 + b)^4 + (320*x)/(2 + b)^4 - (1408*x)/(3*b*(2 + b)^4) + (736*b*x)/(3*(2 + b)^4) - (16*b^2*x)/(2 + b)^4 - (320*x^(3/2))/(3*(2 + b)^4) + (128*x^(3/2))/(3*b*(2 + b)^4) - (160*b*x^(3/2))/(3*(2 + b)^4) + (16*b^2*x^(3/2))/(3*(2 + b)^4) - (736*Sqrt[2 + b*x])/(3*(2 + b)^(7/2)) + (384*Sqrt[2 + b*x])/(b^2*(2 + b)^(7/2)) + (512*Sqrt[2 + b*x])/(3*b*(2 + b)^(7/2)) - (32*b*Sqrt[2 + b*x])/(2 + b)^(7/2) + (800*Sqrt[x]*Sqrt[2 + b*x])/(3*(2 + b)^(7/2)) - (128*Sqrt[x]*Sqrt[2 + b*x])/(3*b^2*(2 + b)^(7/2)) - (320*Sqrt[x]*Sqrt[2 + b*x])/(3*b*(2 + b)^(7/2)) - (16*b*Sqrt[x]*Sqrt[2 + b*x])/(2 + b)^(7/2) - (320*x*Sqrt[2 + b*x])/(3*(2 + b)^(7/2)) + (320*x*Sqrt[2 + b*x])/(3*b*(2 + b)^(7/2)) + (16*b*x*Sqrt[2 + b*x])/(3*(2 + b)^(7/2))))/(-8 - 10*b - 2*b^2 + 4*b*Sqrt[x] - 6*b*x - 5*b^2*x - b^3*x + 2*b^2*x^(3/2) - b^2*x^2 + 4*Sqrt[2 + b]*Sqrt[2 + b*x] + 4*b*Sqrt[2 + b]*Sqrt[2 + b*x] - 2*b*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] + b^2*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] + 2*b*Sqrt[2 + b]*x*Sqrt[2 + b*x])^3 + ((Sqrt[2 + b] - Sqrt[2 + b*x])^5*(1872/(2 + b)^4 - 1664/(3*b^3*(2 + b)^4) - 10432/(3*b^2*(2 + b)^4) + 800/(b*(2 + b)^4) + (304*b)/(2 + b)^4 - (16*b^2)/(2 + b)^4 - (3760*Sqrt[x])/(3*(2 + b)^4) + (128*Sqrt[x])/(3*b^3*(2 + b)^4) + (576*Sqrt[x])/(b^2*(2 + b)^4) - (3808*Sqrt[x])/(3*b*(2 + b)^4) - (112*b*Sqrt[x])/(2 + b)^4 + (64*b^2*Sqrt[x])/(2 + b)^4 + (784*x)/(2 + b)^4 - (1088*x)/(3*b^2*(2 + b)^4) - (1760*x)/(3*b*(2 + b)^4) + (1336*b*x)/(3*(2 + b)^4) - (24*b^2*x)/(2 + b)^4 - (208*x^(3/2))/(2 + b)^4 + (64*x^(3/2))/(3*b^2*(2 + b)^4) - (160*x^(3/2))/(3*b*(2 + b)^4) - (72*b*x^(3/2))/(2 + b)^4 + (8*b^2*x^(3/2))/(2 + b)^4 - (624*Sqrt[2 + b*x])/(2 + b)^(7/2) + (832*Sqrt[2 + b*x])/(3*b^3*(2 + b)^(7/2)) + (1664*Sqrt[2 + b*x])/(b^2*(2 + b)^(7/2)) - (2288*Sqrt[2 + b*x])/(3*b*(2 + b)^(7/2)) - (16*b*Sqrt[2 + b*x])/(2 + b)^(7/2) + (872*Sqrt[x]*Sqrt[2 + b*x])/(3*(2 + b)^(7/2)) - (64*Sqrt[x]*Sqrt[2 + b*x])/(3*b^3*(2 + b)^(7/2)) - (800*Sqrt[x]*Sqrt[2 + b*x])/(3*b^2*(2 + b)^(7/2)) + (1648*Sqrt[x]*Sqrt[2 + b*x])/(3*b*(2 + b)^(7/2)) - (24*b*Sqrt[x]*Sqrt[2 + b*x])/(2 + b)^(7/2) - (168*x*Sqrt[2 + b*x])/(2 + b)^(7/2) + (96*x*Sqrt[2 + b*x])/(b^2*(2 + b)^(7/2)) + (64*x*Sqrt[2 + b*x])/(3*b*(2 + b)^(7/2)) + (8*b*x*Sqrt[2 + b*x])/(2 + b)^(7/2)))/(-8 - 10*b - 2*b^2 + 4*b*Sqrt[x] - 6*b*x - 5*b^2*x - b^3*x + 2*b^2*x^(3/2) - b^2*x^2 + 4*Sqrt[2 + b]*Sqrt[2 + b*x] + 4*b*Sqrt[2 + b]*Sqrt[2 + b*x] - 2*b*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] + b^2*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] + 2*b*Sqrt[2 + b]*x*Sqrt[2 + b*x])^2 + ((4/(3*b^3*(2 + b)^(5/2)) - (4*Sqrt[2 + b*x])/(3*b^3*(2 + b)^3))*(-928 + 192*b + 328*b^2 - 36*b^3 - 18*b^4 + 160*Sqrt[x] + 168*b*Sqrt[x] + 248*b^2*Sqrt[x] + 174*b^3*Sqrt[x] + 36*b^4*Sqrt[x] - 424*b*x - 44*b^2*x + 30*b^3*x - 27*b^4*x + 64*b*x^(3/2) + 44*b^2*x^(3/2) + 24*b^3*x^(3/2) + 9*b^4*x^(3/2) + 464*Sqrt[2 + b]*Sqrt[2 + b*x] - 224*b*Sqrt[2 + b]*Sqrt[2 + b*x] - 120*b^2*Sqrt[2 + b]*Sqrt[2 + b*x] + 18*b^3*Sqrt[2 + b]*Sqrt[2 + b*x] - 80*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] - 28*b*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] - 48*b^2*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] - 27*b^3*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] + 60*b*Sqrt[2 + b]*x*Sqrt[2 + b*x] - 24*b^2*Sqrt[2 + b]*x*Sqrt[2 + b*x] + 9*b^3*Sqrt[2 + b]*x*Sqrt[2 + b*x]))/(-8 - 10*b - 2*b^2 + 4*b*Sqrt[x] - 6*b*x - 5*b^2*x - b^3*x + 2*b^2*x^(3/2) - b^2*x^2 + 4*Sqrt[2 + b]*Sqrt[2 + b*x] + 4*b*Sqrt[2 + b]*Sqrt[2 + b*x] - 2*b*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] + b^2*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] + 2*b*Sqrt[2 + b]*x*Sqrt[2 + b*x]) + (20*ArcTanh[(Sqrt[2 + b]/Sqrt[b] - Sqrt[2 + b*x]/Sqrt[b])/(-1 + Sqrt[x])])/b^(7/2)","B",0
624,1,2061,65,10.044512,"\int \frac{x^{3/2}}{(2+b x)^{5/2}} \, dx","IntegrateAlgebraic[x^(3/2)/(2 + b*x)^(5/2),x]","\text{Result too large to show}","\frac{2 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{5/2}}-\frac{2 \sqrt{x}}{b^2 \sqrt{b x+2}}-\frac{2 x^{3/2}}{3 b (b x+2)^{3/2}}",1,"((Sqrt[2 + b] - Sqrt[2 + b*x])^9*(832/(3*(2 + b)^4) + 384/(b*(2 + b)^4) - (736*b)/(3*(2 + b)^4) - (400*b^2)/(3*(2 + b)^4) + (16*b^3)/(3*(2 + b)^4) - (448*Sqrt[x])/(3*(2 + b)^4) - (128*Sqrt[x])/(3*b*(2 + b)^4) + (352*b*Sqrt[x])/(2 + b)^4 + (144*b^2*Sqrt[x])/(2 + b)^4 - (32*b^3*Sqrt[x])/(2 + b)^4 + (704*x)/(3*(2 + b)^4) - (160*b*x)/(2 + b)^4 - (368*b^2*x)/(3*(2 + b)^4) + (8*b^3*x)/(2 + b)^4 - (64*x^(3/2))/(3*(2 + b)^4) + (160*b*x^(3/2))/(3*(2 + b)^4) + (80*b^2*x^(3/2))/(3*(2 + b)^4) - (8*b^3*x^(3/2))/(3*(2 + b)^4) - (256*Sqrt[2 + b*x])/(3*(2 + b)^(7/2)) - (192*Sqrt[2 + b*x])/(b*(2 + b)^(7/2)) + (368*b*Sqrt[2 + b*x])/(3*(2 + b)^(7/2)) + (16*b^2*Sqrt[2 + b*x])/(2 + b)^(7/2) + (160*Sqrt[x]*Sqrt[2 + b*x])/(3*(2 + b)^(7/2)) + (64*Sqrt[x]*Sqrt[2 + b*x])/(3*b*(2 + b)^(7/2)) - (400*b*Sqrt[x]*Sqrt[2 + b*x])/(3*(2 + b)^(7/2)) + (8*b^2*Sqrt[x]*Sqrt[2 + b*x])/(2 + b)^(7/2) - (160*x*Sqrt[2 + b*x])/(3*(2 + b)^(7/2)) + (160*b*x*Sqrt[2 + b*x])/(3*(2 + b)^(7/2)) - (8*b^2*x*Sqrt[2 + b*x])/(3*(2 + b)^(7/2))))/(-8 - 10*b - 2*b^2 + 4*b*Sqrt[x] - 6*b*x - 5*b^2*x - b^3*x + 2*b^2*x^(3/2) - b^2*x^2 + 4*Sqrt[2 + b]*Sqrt[2 + b*x] + 4*b*Sqrt[2 + b]*Sqrt[2 + b*x] - 2*b*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] + b^2*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] + 2*b*Sqrt[2 + b]*x*Sqrt[2 + b*x])^3 + ((Sqrt[2 + b] - Sqrt[2 + b*x])^5*(-400/(2 + b)^4 + 832/(3*b^2*(2 + b)^4) + 5216/(3*b*(2 + b)^4) - (936*b)/(2 + b)^4 - (152*b^2)/(2 + b)^4 + (8*b^3)/(2 + b)^4 + (1904*Sqrt[x])/(3*(2 + b)^4) - (64*Sqrt[x])/(3*b^2*(2 + b)^4) - (288*Sqrt[x])/(b*(2 + b)^4) + (1880*b*Sqrt[x])/(3*(2 + b)^4) + (56*b^2*Sqrt[x])/(2 + b)^4 - (32*b^3*Sqrt[x])/(2 + b)^4 + (880*x)/(3*(2 + b)^4) + (544*x)/(3*b*(2 + b)^4) - (392*b*x)/(2 + b)^4 - (668*b^2*x)/(3*(2 + b)^4) + (12*b^3*x)/(2 + b)^4 + (80*x^(3/2))/(3*(2 + b)^4) - (32*x^(3/2))/(3*b*(2 + b)^4) + (104*b*x^(3/2))/(2 + b)^4 + (36*b^2*x^(3/2))/(2 + b)^4 - (4*b^3*x^(3/2))/(2 + b)^4 + (1144*Sqrt[2 + b*x])/(3*(2 + b)^(7/2)) - (416*Sqrt[2 + b*x])/(3*b^2*(2 + b)^(7/2)) - (832*Sqrt[2 + b*x])/(b*(2 + b)^(7/2)) + (312*b*Sqrt[2 + b*x])/(2 + b)^(7/2) + (8*b^2*Sqrt[2 + b*x])/(2 + b)^(7/2) - (824*Sqrt[x]*Sqrt[2 + b*x])/(3*(2 + b)^(7/2)) + (32*Sqrt[x]*Sqrt[2 + b*x])/(3*b^2*(2 + b)^(7/2)) + (400*Sqrt[x]*Sqrt[2 + b*x])/(3*b*(2 + b)^(7/2)) - (436*b*Sqrt[x]*Sqrt[2 + b*x])/(3*(2 + b)^(7/2)) + (12*b^2*Sqrt[x]*Sqrt[2 + b*x])/(2 + b)^(7/2) - (32*x*Sqrt[2 + b*x])/(3*(2 + b)^(7/2)) - (48*x*Sqrt[2 + b*x])/(b*(2 + b)^(7/2)) + (84*b*x*Sqrt[2 + b*x])/(2 + b)^(7/2) - (4*b^2*x*Sqrt[2 + b*x])/(2 + b)^(7/2)))/(-8 - 10*b - 2*b^2 + 4*b*Sqrt[x] - 6*b*x - 5*b^2*x - b^3*x + 2*b^2*x^(3/2) - b^2*x^2 + 4*Sqrt[2 + b]*Sqrt[2 + b*x] + 4*b*Sqrt[2 + b]*Sqrt[2 + b*x] - 2*b*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] + b^2*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] + 2*b*Sqrt[2 + b]*x*Sqrt[2 + b*x])^2 + ((-4/(3*b^2*(2 + b)^(5/2)) + (4*Sqrt[2 + b*x])/(3*b^2*(2 + b)^3))*(-440 + 156*b + 218*b^2 + 3*b^3 - 6*b^4 + 56*Sqrt[x] + 34*b^2*Sqrt[x] + 48*b^3*Sqrt[x] + 12*b^4*Sqrt[x] - 176*b*x + 32*b^2*x + 42*b^3*x - 9*b^4*x + 20*b*x^(3/2) + 4*b^2*x^(3/2) + 3*b^3*x^(3/2) + 3*b^4*x^(3/2) + 220*Sqrt[2 + b]*Sqrt[2 + b*x] - 136*b*Sqrt[2 + b]*Sqrt[2 + b*x] - 75*b^2*Sqrt[2 + b]*Sqrt[2 + b*x] + 6*b^3*Sqrt[2 + b]*Sqrt[2 + b*x] - 28*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] + 16*b*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] - 3*b^2*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] - 9*b^3*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] + 24*b*Sqrt[2 + b]*x*Sqrt[2 + b*x] - 18*b^2*Sqrt[2 + b]*x*Sqrt[2 + b*x] + 3*b^3*Sqrt[2 + b]*x*Sqrt[2 + b*x]))/(-8 - 10*b - 2*b^2 + 4*b*Sqrt[x] - 6*b*x - 5*b^2*x - b^3*x + 2*b^2*x^(3/2) - b^2*x^2 + 4*Sqrt[2 + b]*Sqrt[2 + b*x] + 4*b*Sqrt[2 + b]*Sqrt[2 + b*x] - 2*b*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] + b^2*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] + 2*b*Sqrt[2 + b]*x*Sqrt[2 + b*x]) - (4*ArcTanh[(Sqrt[2 + b]/Sqrt[b] - Sqrt[2 + b*x]/Sqrt[b])/(-1 + Sqrt[x])])/b^(5/2)","B",1
625,1,4177,18,9.1004005,"\int \frac{\sqrt{x}}{(2+b x)^{5/2}} \, dx","IntegrateAlgebraic[Sqrt[x]/(2 + b*x)^(5/2),x]","\text{Result too large to show}","\frac{x^{3/2}}{3 (b x+2)^{3/2}}",1,"((-1/384*1/(2 + b)^2 + Sqrt[x]/(384*(2 + b)^2))*(Sqrt[2 + b] - Sqrt[2 + b*x])^12*((3*b^8*(-1 + Sqrt[x])^10)/(Sqrt[2 + b] - Sqrt[2 + b*x])^10 + (3*b^7*(-1 + Sqrt[x])^8*(-2 - b - 16*Sqrt[x] - 2*b*Sqrt[x] + 6*x - 3*b*x + 4*Sqrt[2 + b]*Sqrt[2 + b*x] + 2*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x]))/(Sqrt[2 + b] - Sqrt[2 + b*x])^10 - (8*(-8 + 3*b + 4*Sqrt[x] - 6*b*Sqrt[x] - 8*x - 3*b*x + 6*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x]))/(Sqrt[2 + b] - Sqrt[2 + b*x])^2 - (6*b^6*(-1 + Sqrt[x])^6*(58 + 31*b + 3*b^2 - 100*Sqrt[x] - 52*b*Sqrt[x] - 4*b^2*Sqrt[x] - 12*x + 20*b*x + 6*b^2*x + 28*x^(3/2) - 40*b*x^(3/2) - 12*b^2*x^(3/2) - 6*x^2 + 9*b*x^2 - b^2*x^2 - 32*Sqrt[2 + b]*Sqrt[2 + b*x] - 8*b*Sqrt[2 + b]*Sqrt[2 + b*x] + 62*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] + 12*b*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] - 12*Sqrt[2 + b]*x*Sqrt[2 + b*x] - 2*Sqrt[2 + b]*x^(3/2)*Sqrt[2 + b*x] + 4*b*Sqrt[2 + b]*x^(3/2)*Sqrt[2 + b*x]))/(Sqrt[2 + b] - Sqrt[2 + b*x])^10 - (4*b*(-232 - 82*b - 3*b^2 + 80*Sqrt[x] - 64*b*Sqrt[x] - 6*b^2*Sqrt[x] - 280*x - 104*b*x - 36*b^2*x + 192*x^(3/2) - 40*b*x^(3/2) - 18*b^2*x^(3/2) - 48*x^2 + 2*b*x^2 - 9*b^2*x^2 + 92*Sqrt[2 + b]*Sqrt[2 + b*x] + 18*b*Sqrt[2 + b]*Sqrt[2 + b*x] + 56*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] + 18*b*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] - 4*Sqrt[2 + b]*x*Sqrt[2 + b*x] + 30*b*Sqrt[2 + b]*x*Sqrt[2 + b*x] + 6*b*Sqrt[2 + b]*x^(3/2)*Sqrt[2 + b*x]))/(Sqrt[2 + b] - Sqrt[2 + b*x])^4 + (2*b^2*(2272 + 1832*b + 434*b^2 + 15*b^3 - 800*Sqrt[x] + 80*b*Sqrt[x] - 64*b^2*Sqrt[x] - 6*b^3*Sqrt[x] + 3808*x + 2056*b*x + 1118*b^2*x + 195*b^3*x - 4800*x^(3/2) - 448*b*x^(3/2) + 192*b^2*x^(3/2) - 60*b^3*x^(3/2) + 2400*x^2 + 344*b*x^2 + 62*b^2*x^2 + 165*b^3*x^2 - 672*x^(5/2) - 528*b*x^(5/2) + 32*b^2*x^(5/2) - 30*b^3*x^(5/2) + 96*x^3 + 120*b*x^3 - 46*b^2*x^3 + 9*b^3*x^3 - 1088*Sqrt[2 + b]*Sqrt[2 + b*x] - 632*b*Sqrt[2 + b]*Sqrt[2 + b*x] - 84*b^2*Sqrt[2 + b]*Sqrt[2 + b*x] + 112*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] - 128*b*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] + 30*b^2*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] - 1184*Sqrt[2 + b]*x*Sqrt[2 + b*x] - 352*b*Sqrt[2 + b]*x*Sqrt[2 + b*x] - 240*b^2*Sqrt[2 + b]*x*Sqrt[2 + b*x] + 1440*Sqrt[2 + b]*x^(3/2)*Sqrt[2 + b*x] - 224*b*Sqrt[2 + b]*x^(3/2)*Sqrt[2 + b*x] + 60*b^2*Sqrt[2 + b]*x^(3/2)*Sqrt[2 + b*x] - 480*Sqrt[2 + b]*x^2*Sqrt[2 + b*x] + 184*b*Sqrt[2 + b]*x^2*Sqrt[2 + b*x] - 60*b^2*Sqrt[2 + b]*x^2*Sqrt[2 + b*x] + 48*Sqrt[2 + b]*x^(5/2)*Sqrt[2 + b*x] + 6*b^2*Sqrt[2 + b]*x^(5/2)*Sqrt[2 + b*x]))/(Sqrt[2 + b] - Sqrt[2 + b*x])^6 + (2*b^5*(-1 + Sqrt[x])^4*(3068 + 2582*b + 570*b^2 + 21*b^3 - 1520*Sqrt[x] - 1628*b*Sqrt[x] - 432*b^2*Sqrt[x] - 18*b^3*Sqrt[x] - 1740*x + 1286*b*x + 1422*b^2*x + 225*b^3*x + 1120*x^(3/2) - 856*b*x^(3/2) - 1056*b^2*x^(3/2) - 180*b^3*x^(3/2) - 124*x^2 - 526*b*x^2 + 198*b^2*x^2 + 135*b^3*x^2 - 48*x^(5/2) + 340*b*x^(5/2) - 144*b^2*x^(5/2) - 90*b^3*x^(5/2) + 12*x^3 - 46*b*x^3 + 18*b^2*x^3 + 3*b^3*x^3 - 1528*Sqrt[2 + b]*Sqrt[2 + b*x] - 912*b*Sqrt[2 + b]*Sqrt[2 + b*x] - 108*b^2*Sqrt[2 + b]*Sqrt[2 + b*x] + 724*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] + 648*b*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] + 90*b^2*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] + 960*Sqrt[2 + b]*x*Sqrt[2 + b*x] - 528*b*Sqrt[2 + b]*x*Sqrt[2 + b*x] - 240*b^2*Sqrt[2 + b]*x*Sqrt[2 + b*x] - 680*Sqrt[2 + b]*x^(3/2)*Sqrt[2 + b*x] + 432*b*Sqrt[2 + b]*x^(3/2)*Sqrt[2 + b*x] + 180*b^2*Sqrt[2 + b]*x^(3/2)*Sqrt[2 + b*x] + 152*Sqrt[2 + b]*x^2*Sqrt[2 + b*x] - 36*b^2*Sqrt[2 + b]*x^2*Sqrt[2 + b*x] - 12*Sqrt[2 + b]*x^(5/2)*Sqrt[2 + b*x] - 24*b*Sqrt[2 + b]*x^(5/2)*Sqrt[2 + b*x] + 18*b^2*Sqrt[2 + b]*x^(5/2)*Sqrt[2 + b*x]))/(Sqrt[2 + b] - Sqrt[2 + b*x])^10 + (b^4*(-1 + Sqrt[x])^2*(-5240*Sqrt[2 + b] - 5352*b*Sqrt[2 + b] - 1188*b^2*Sqrt[2 + b] - 33*b^3*Sqrt[2 + b] - 8832*Sqrt[2 + b]*Sqrt[x] - 1056*b*Sqrt[2 + b]*Sqrt[x] + 576*b^2*Sqrt[2 + b]*Sqrt[x] + 24*b^3*Sqrt[2 + b]*Sqrt[x] + 13848*Sqrt[2 + b]*x - 648*b*Sqrt[2 + b]*x - 3852*b^2*Sqrt[2 + b]*x - 549*b^3*Sqrt[2 + b]*x - 4304*Sqrt[2 + b]*x^(3/2) - 4800*b*Sqrt[2 + b]*x^(3/2) + 792*b^2*Sqrt[2 + b]*x^(3/2) + 360*b^3*Sqrt[2 + b]*x^(3/2) - 840*Sqrt[2 + b]*x^2 + 7176*b*Sqrt[2 + b]*x^2 + 36*b^2*Sqrt[2 + b]*x^2 - 675*b^3*Sqrt[2 + b]*x^2 + 1056*Sqrt[2 + b]*x^(5/2) - 2592*b*Sqrt[2 + b]*x^(5/2) - 144*b^2*Sqrt[2 + b]*x^(5/2) + 360*b^3*Sqrt[2 + b]*x^(5/2) - 344*Sqrt[2 + b]*x^3 + 360*b*Sqrt[2 + b]*x^3 + 396*b^2*Sqrt[2 + b]*x^3 - 87*b^3*Sqrt[2 + b]*x^3 + 48*Sqrt[2 + b]*x^(7/2) - 72*b^2*Sqrt[2 + b]*x^(7/2) + 24*b^3*Sqrt[2 + b]*x^(7/2) + 5192*Sqrt[2 + b*x] + 6648*b*Sqrt[2 + b*x] + 2364*b^2*Sqrt[2 + b*x] + 207*b^3*Sqrt[2 + b*x] + 9168*Sqrt[x]*Sqrt[2 + b*x] + 3360*b*Sqrt[x]*Sqrt[2 + b*x] - 600*b^2*Sqrt[x]*Sqrt[2 + b*x] - 144*b^3*Sqrt[x]*Sqrt[2 + b*x] - 14856*x*Sqrt[2 + b*x] - 4392*b*x*Sqrt[2 + b*x] + 2820*b^2*x*Sqrt[2 + b*x] + 795*b^3*x*Sqrt[2 + b*x] + 5984*x^(3/2)*Sqrt[2 + b*x] + 4032*b*x^(3/2)*Sqrt[2 + b*x] - 624*b^2*x^(3/2)*Sqrt[2 + b*x] - 480*b^3*x^(3/2)*Sqrt[2 + b*x] - 840*x^2*Sqrt[2 + b*x] - 3672*b*x^2*Sqrt[2 + b*x] - 540*b^2*x^2*Sqrt[2 + b*x] + 333*b^3*x^2*Sqrt[2 + b*x] - 48*x^(5/2)*Sqrt[2 + b*x] + 1056*b*x^(5/2)*Sqrt[2 + b*x] + 72*b^2*x^(5/2)*Sqrt[2 + b*x] - 144*b^3*x^(5/2)*Sqrt[2 + b*x] + 8*x^3*Sqrt[2 + b*x] - 120*b*x^3*Sqrt[2 + b*x] - 36*b^2*x^3*Sqrt[2 + b*x] + 9*b^3*x^3*Sqrt[2 + b*x]))/(Sqrt[2 + b] - Sqrt[2 + b*x])^9 + (b^3*(1232*b + 1520*b^2 + 390*b^3 + 9*b^4 + 4224*Sqrt[x] + 12032*b*Sqrt[x] + 3776*b^2*Sqrt[x] - 48*b^3*Sqrt[x] - 6*b^4*Sqrt[x] + 35136*x + 6752*b*x - 568*b^2*x + 1452*b^3*x + 210*b^4*x - 60160*x^(3/2) - 12224*b*x^(3/2) + 9712*b^2*x^(3/2) + 1512*b^3*x^(3/2) - 126*b^4*x^(3/2) + 36800*x^2 + 18112*b*x^2 - 3560*b^2*x^2 - 864*b^3*x^2 + 420*b^4*x^2 - 12160*x^(5/2) - 22400*b*x^(5/2) - 1952*b^2*x^(5/2) + 1728*b^3*x^(5/2) - 210*b^4*x^(5/2) + 2752*x^3 + 11040*b*x^3 + 696*b^2*x^3 - 1308*b^3*x^3 + 126*b^4*x^3 - 512*x^(7/2) - 2496*b*x^(7/2) - 528*b^2*x^(7/2) + 264*b^3*x^(7/2) - 42*b^4*x^(7/2) + 64*x^4 + 240*b*x^4 + 120*b^2*x^4 - 54*b^3*x^4 + 3*b^4*x^4 + 32*Sqrt[2 + b]*Sqrt[2 + b*x] - 624*b*Sqrt[2 + b]*Sqrt[2 + b*x] - 588*b^2*Sqrt[2 + b]*Sqrt[2 + b*x] - 66*b^3*Sqrt[2 + b]*Sqrt[2 + b*x] - 2368*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] - 5424*b*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] - 696*b^2*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] + 42*b^3*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] - 16672*Sqrt[2 + b]*x*Sqrt[2 + b*x] + 784*b*Sqrt[2 + b]*x*Sqrt[2 + b*x] - 84*b^2*Sqrt[2 + b]*x*Sqrt[2 + b*x] - 378*b^3*Sqrt[2 + b]*x*Sqrt[2 + b*x] + 28288*Sqrt[2 + b]*x^(3/2)*Sqrt[2 + b*x] - 368*b*Sqrt[2 + b]*x^(3/2)*Sqrt[2 + b*x] - 2496*b^2*Sqrt[2 + b]*x^(3/2)*Sqrt[2 + b*x] + 210*b^3*Sqrt[2 + b]*x^(3/2)*Sqrt[2 + b*x] - 16160*Sqrt[2 + b]*x^2*Sqrt[2 + b*x] - 848*b*Sqrt[2 + b]*x^2*Sqrt[2 + b*x] + 2124*b^2*Sqrt[2 + b]*x^2*Sqrt[2 + b*x] - 294*b^3*Sqrt[2 + b]*x^2*Sqrt[2 + b*x] + 4288*Sqrt[2 + b]*x^(5/2)*Sqrt[2 + b*x] + 3056*b*Sqrt[2 + b]*x^(5/2)*Sqrt[2 + b*x] - 984*b^2*Sqrt[2 + b]*x^(5/2)*Sqrt[2 + b*x] + 126*b^3*Sqrt[2 + b]*x^(5/2)*Sqrt[2 + b*x] - 480*Sqrt[2 + b]*x^3*Sqrt[2 + b*x] - 1360*b*Sqrt[2 + b]*x^3*Sqrt[2 + b*x] + 468*b^2*Sqrt[2 + b]*x^3*Sqrt[2 + b*x] - 30*b^3*Sqrt[2 + b]*x^3*Sqrt[2 + b*x] + 176*b*Sqrt[2 + b]*x^(7/2)*Sqrt[2 + b*x] - 48*b^2*Sqrt[2 + b]*x^(7/2)*Sqrt[2 + b*x] + 6*b^3*Sqrt[2 + b]*x^(7/2)*Sqrt[2 + b*x]))/(Sqrt[2 + b] - Sqrt[2 + b*x])^8))/((-Sqrt[2 + b] + Sqrt[2 + b*x])*(8 + 10*b + 2*b^2 - 4*b*Sqrt[x] + 6*b*x + 5*b^2*x + b^3*x - 2*b^2*x^(3/2) + b^2*x^2 - 4*Sqrt[2 + b]*Sqrt[2 + b*x] - 4*b*Sqrt[2 + b]*Sqrt[2 + b*x] + 2*b*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] - b^2*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] - 2*b*Sqrt[2 + b]*x*Sqrt[2 + b*x])^3)","B",1
626,1,2726,37,7.0849524,"\int \frac{1}{\sqrt{x} (2+b x)^{5/2}} \, dx","IntegrateAlgebraic[1/(Sqrt[x]*(2 + b*x)^(5/2)),x]","\text{Result too large to show}","\frac{\sqrt{x}}{3 \sqrt{b x+2}}+\frac{\sqrt{x}}{3 (b x+2)^{3/2}}",1,"((-1/384*1/(2 + b)^2 + Sqrt[x]/(384*(2 + b)^2))*(Sqrt[2 + b] - Sqrt[2 + b*x])^12*(24 + (3*b^8*(-1 + Sqrt[x])^10)/(Sqrt[2 + b] - Sqrt[2 + b*x])^10 + (3*b^7*(-1 + Sqrt[x])^8*(34 + 9*b - 20*Sqrt[x] - 4*b*Sqrt[x] + 6*x + 5*b*x - 14*Sqrt[2 + b]*Sqrt[2 + b*x] + 4*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x]))/(Sqrt[2 + b] - Sqrt[2 + b*x])^10 + (4*b*(82 + 21*b - 68*Sqrt[x] - 12*b*Sqrt[x] + 22*x + 9*b*x - 30*Sqrt[2 + b]*Sqrt[2 + b*x] + 12*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x]))/(Sqrt[2 + b] - Sqrt[2 + b*x])^2 + (2*b^6*(-1 + Sqrt[x])^6*(-58 - 79*b - 9*b^2 - 544*Sqrt[x] - 154*b*Sqrt[x] + 416*x + 10*b*x - 54*b^2*x - 120*x^(3/2) - 106*b*x^(3/2) + 18*x^2 + 41*b*x^2 - 9*b^2*x^2 + 38*Sqrt[2 + b]*Sqrt[2 + b*x] + 36*b*Sqrt[2 + b]*Sqrt[2 + b*x] + 236*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] - 154*Sqrt[2 + b]*x*Sqrt[2 + b*x] + 36*b*Sqrt[2 + b]*x*Sqrt[2 + b*x] + 24*Sqrt[2 + b]*x^(3/2)*Sqrt[2 + b*x]))/(Sqrt[2 + b] - Sqrt[2 + b*x])^10 + (2*b^2*(1136 + 506*b + 33*b^2 - 1552*Sqrt[x] - 532*b*Sqrt[x] - 24*b^2*Sqrt[x] + 1016*x + 580*b*x + 126*b^2*x - 384*x^(3/2) - 340*b*x^(3/2) - 72*b^2*x^(3/2) + 72*x^2 + 74*b*x^2 + 9*b^2*x^2 - 532*Sqrt[2 + b]*Sqrt[2 + b*x] - 108*b*Sqrt[2 + b]*Sqrt[2 + b*x] + 632*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] + 72*b*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] - 292*Sqrt[2 + b]*x*Sqrt[2 + b*x] - 60*b*Sqrt[2 + b]*x*Sqrt[2 + b*x] + 48*Sqrt[2 + b]*x^(3/2)*Sqrt[2 + b*x] + 24*b*Sqrt[2 + b]*x^(3/2)*Sqrt[2 + b*x]))/(Sqrt[2 + b] - Sqrt[2 + b*x])^4 - (b^4*(-1 + Sqrt[x])^2*(-2232 - 1832*b - 440*b^2 - 15*b^3 - 2736*Sqrt[x] - 2304*b*Sqrt[x] - 264*b^2*Sqrt[x] - 744*x - 888*b*x - 1164*b^2*x - 225*b^3*x + 3808*x^(3/2) - 1408*b*x^(3/2) - 1072*b^2*x^(3/2) - 2568*x^2 + 744*b*x^2 + 288*b^2*x^2 - 225*b^3*x^2 + 720*x^(5/2) - 264*b^2*x^(5/2) - 88*x^3 - 72*b*x^3 + 36*b^2*x^3 - 15*b^3*x^3 + 1072*Sqrt[2 + b]*Sqrt[2 + b*x] + 624*b*Sqrt[2 + b]*Sqrt[2 + b*x] + 90*b^2*Sqrt[2 + b]*Sqrt[2 + b*x] + 1632*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] + 864*b*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] - 288*Sqrt[2 + b]*x*Sqrt[2 + b*x] + 32*b*Sqrt[2 + b]*x*Sqrt[2 + b*x] + 300*b^2*Sqrt[2 + b]*x*Sqrt[2 + b*x] - 1024*Sqrt[2 + b]*x^(3/2)*Sqrt[2 + b*x] + 672*b*Sqrt[2 + b]*x^(3/2)*Sqrt[2 + b*x] + 624*Sqrt[2 + b]*x^2*Sqrt[2 + b*x] - 336*b*Sqrt[2 + b]*x^2*Sqrt[2 + b*x] + 90*b^2*Sqrt[2 + b]*x^2*Sqrt[2 + b*x] - 96*Sqrt[2 + b]*x^(5/2)*Sqrt[2 + b*x] + 64*b*Sqrt[2 + b]*x^(5/2)*Sqrt[2 + b*x]))/(Sqrt[2 + b] - Sqrt[2 + b*x])^8 - (2*b^5*(-1 + Sqrt[x])^4*(3676 + 3022*b + 630*b^2 + 21*b^3 - 40*Sqrt[x] - 784*b*Sqrt[x] - 276*b^2*Sqrt[x] - 12*b^3*Sqrt[x] - 3012*x + 1642*b*x + 1782*b^2*x + 255*b^3*x + 2288*x^(3/2) - 32*b*x^(3/2) - 696*b^2*x^(3/2) - 120*b^3*x^(3/2) - 716*x^2 - 782*b*x^2 + 354*b^2*x^2 + 195*b^3*x^2 + 120*x^(5/2) + 464*b*x^(5/2) - 84*b^2*x^(5/2) - 60*b^3*x^(5/2) - 12*x^3 - 74*b*x^3 + 18*b^2*x^3 + 9*b^3*x^3 - 1844*Sqrt[2 + b]*Sqrt[2 + b*x] - 1056*b*Sqrt[2 + b]*Sqrt[2 + b*x] - 114*b^2*Sqrt[2 + b]*Sqrt[2 + b*x] + 56*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] + 408*b*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] + 60*b^2*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] + 1416*Sqrt[2 + b]*x*Sqrt[2 + b*x] - 768*b*Sqrt[2 + b]*x*Sqrt[2 + b*x] - 300*b^2*Sqrt[2 + b]*x*Sqrt[2 + b*x] - 1024*Sqrt[2 + b]*x^(3/2)*Sqrt[2 + b*x] + 288*b*Sqrt[2 + b]*x^(3/2)*Sqrt[2 + b*x] + 120*b^2*Sqrt[2 + b]*x^(3/2)*Sqrt[2 + b*x] + 268*Sqrt[2 + b]*x^2*Sqrt[2 + b*x] - 66*b^2*Sqrt[2 + b]*x^2*Sqrt[2 + b*x] - 24*Sqrt[2 + b]*x^(5/2)*Sqrt[2 + b*x] - 24*b*Sqrt[2 + b]*x^(5/2)*Sqrt[2 + b*x] + 12*b^2*Sqrt[2 + b]*x^(5/2)*Sqrt[2 + b*x]))/(Sqrt[2 + b] - Sqrt[2 + b*x])^10 + (b^3*(6320 + 3880*b + 550*b^2 + 15*b^3 - 12064*Sqrt[x] - 6176*b*Sqrt[x] - 620*b^2*Sqrt[x] - 12*b^3*Sqrt[x] + 10736*x + 7352*b*x + 1942*b^2*x + 165*b^3*x - 6720*x^(3/2) - 6464*b*x^(3/2) - 2184*b^2*x^(3/2) - 120*b^3*x^(3/2) + 3408*x^2 + 3160*b*x^2 + 1234*b^2*x^2 + 105*b^3*x^2 - 1056*x^(5/2) - 672*b*x^(5/2) - 428*b^2*x^(5/2) - 60*b^3*x^(5/2) + 144*x^3 + 72*b*x^3 + 82*b^2*x^3 + 3*b^3*x^3 - 3088*Sqrt[2 + b]*Sqrt[2 + b*x] - 1144*b*Sqrt[2 + b]*Sqrt[2 + b*x] - 78*b^2*Sqrt[2 + b]*Sqrt[2 + b*x] + 5600*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] + 1568*b*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] + 60*b^2*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] - 4288*Sqrt[2 + b]*x*Sqrt[2 + b*x] - 1616*b*Sqrt[2 + b]*x*Sqrt[2 + b*x] - 180*b^2*Sqrt[2 + b]*x*Sqrt[2 + b*x] + 1920*Sqrt[2 + b]*x^(3/2)*Sqrt[2 + b*x] + 1232*b*Sqrt[2 + b]*x^(3/2)*Sqrt[2 + b*x] + 120*b^2*Sqrt[2 + b]*x^(3/2)*Sqrt[2 + b*x] - 624*Sqrt[2 + b]*x^2*Sqrt[2 + b*x] - 472*b*Sqrt[2 + b]*x^2*Sqrt[2 + b*x] - 30*b^2*Sqrt[2 + b]*x^2*Sqrt[2 + b*x] + 96*Sqrt[2 + b]*x^(5/2)*Sqrt[2 + b*x] + 48*b*Sqrt[2 + b]*x^(5/2)*Sqrt[2 + b*x] + 12*b^2*Sqrt[2 + b]*x^(5/2)*Sqrt[2 + b*x]))/(Sqrt[2 + b] - Sqrt[2 + b*x])^6))/((-Sqrt[2 + b] + Sqrt[2 + b*x])*(8 + 10*b + 2*b^2 - 4*b*Sqrt[x] + 6*b*x + 5*b^2*x + b^3*x - 2*b^2*x^(3/2) + b^2*x^2 - 4*Sqrt[2 + b]*Sqrt[2 + b*x] - 4*b*Sqrt[2 + b]*Sqrt[2 + b*x] + 2*b*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] - b^2*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] - 2*b*Sqrt[2 + b]*x*Sqrt[2 + b*x])^3)","B",1
627,1,2293,55,26.2412135,"\int \frac{1}{x^{3/2} (2+b x)^{5/2}} \, dx","IntegrateAlgebraic[1/(x^(3/2)*(2 + b*x)^(5/2)),x]","\text{Result too large to show}","-\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,"((-1/4 + Sqrt[x]/4)*(Sqrt[2 + b] - Sqrt[2 + b*x])*(4 + 2*b - 2*Sqrt[x] - 2*b*Sqrt[x] + b*x - 2*Sqrt[2 + b]*Sqrt[2 + b*x] + Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x]))/(Sqrt[x]*(-8 - 4*b + 4*Sqrt[x] + b*Sqrt[x] - b^2*Sqrt[x] - 2*b*x + b*x^(3/2) + 4*Sqrt[2 + b]*Sqrt[2 + b*x] + b*Sqrt[2 + b]*Sqrt[2 + b*x] - 2*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x])) + ((Sqrt[2 + b] - Sqrt[2 + b*x])^9*((-48*b^2)/(2 + b)^4 - (104*b^3)/(3*(2 + b)^4) + (92*b^4)/(3*(2 + b)^4) + (50*b^5)/(3*(2 + b)^4) - (2*b^6)/(3*(2 + b)^4) + (16*b^2*Sqrt[x])/(3*(2 + b)^4) + (56*b^3*Sqrt[x])/(3*(2 + b)^4) - (44*b^4*Sqrt[x])/(2 + b)^4 - (18*b^5*Sqrt[x])/(2 + b)^4 + (4*b^6*Sqrt[x])/(2 + b)^4 - (88*b^3*x)/(3*(2 + b)^4) + (20*b^4*x)/(2 + b)^4 + (46*b^5*x)/(3*(2 + b)^4) - (b^6*x)/(2 + b)^4 + (8*b^3*x^(3/2))/(3*(2 + b)^4) - (20*b^4*x^(3/2))/(3*(2 + b)^4) - (10*b^5*x^(3/2))/(3*(2 + b)^4) + (b^6*x^(3/2))/(3*(2 + b)^4) + (24*b^2*Sqrt[2 + b*x])/(2 + b)^(7/2) + (32*b^3*Sqrt[2 + b*x])/(3*(2 + b)^(7/2)) - (46*b^4*Sqrt[2 + b*x])/(3*(2 + b)^(7/2)) - (2*b^5*Sqrt[2 + b*x])/(2 + b)^(7/2) - (8*b^2*Sqrt[x]*Sqrt[2 + b*x])/(3*(2 + b)^(7/2)) - (20*b^3*Sqrt[x]*Sqrt[2 + b*x])/(3*(2 + b)^(7/2)) + (50*b^4*Sqrt[x]*Sqrt[2 + b*x])/(3*(2 + b)^(7/2)) - (b^5*Sqrt[x]*Sqrt[2 + b*x])/(2 + b)^(7/2) + (20*b^3*x*Sqrt[2 + b*x])/(3*(2 + b)^(7/2)) - (20*b^4*x*Sqrt[2 + b*x])/(3*(2 + b)^(7/2)) + (b^5*x*Sqrt[2 + b*x])/(3*(2 + b)^(7/2))))/(-8 - 10*b - 2*b^2 + 4*b*Sqrt[x] - 6*b*x - 5*b^2*x - b^3*x + 2*b^2*x^(3/2) - b^2*x^2 + 4*Sqrt[2 + b]*Sqrt[2 + b*x] + 4*b*Sqrt[2 + b]*Sqrt[2 + b*x] - 2*b*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] + b^2*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] + 2*b*Sqrt[2 + b]*x*Sqrt[2 + b*x])^3 + ((Sqrt[2 + b] - Sqrt[2 + b*x])^5*((-104*b)/(3*(2 + b)^4) - (652*b^2)/(3*(2 + b)^4) + (50*b^3)/(2 + b)^4 + (117*b^4)/(2 + b)^4 + (19*b^5)/(2 + b)^4 - b^6/(2 + b)^4 + (8*b*Sqrt[x])/(3*(2 + b)^4) + (36*b^2*Sqrt[x])/(2 + b)^4 - (238*b^3*Sqrt[x])/(3*(2 + b)^4) - (235*b^4*Sqrt[x])/(3*(2 + b)^4) - (7*b^5*Sqrt[x])/(2 + b)^4 + (4*b^6*Sqrt[x])/(2 + b)^4 - (68*b^2*x)/(3*(2 + b)^4) - (110*b^3*x)/(3*(2 + b)^4) + (49*b^4*x)/(2 + b)^4 + (167*b^5*x)/(6*(2 + b)^4) - (3*b^6*x)/(2*(2 + b)^4) + (4*b^2*x^(3/2))/(3*(2 + b)^4) - (10*b^3*x^(3/2))/(3*(2 + b)^4) - (13*b^4*x^(3/2))/(2 + b)^4 - (9*b^5*x^(3/2))/(2*(2 + b)^4) + (b^6*x^(3/2))/(2*(2 + b)^4) + (52*b*Sqrt[2 + b*x])/(3*(2 + b)^(7/2)) + (104*b^2*Sqrt[2 + b*x])/(2 + b)^(7/2) - (143*b^3*Sqrt[2 + b*x])/(3*(2 + b)^(7/2)) - (39*b^4*Sqrt[2 + b*x])/(2 + b)^(7/2) - (b^5*Sqrt[2 + b*x])/(2 + b)^(7/2) - (4*b*Sqrt[x]*Sqrt[2 + b*x])/(3*(2 + b)^(7/2)) - (50*b^2*Sqrt[x]*Sqrt[2 + b*x])/(3*(2 + b)^(7/2)) + (103*b^3*Sqrt[x]*Sqrt[2 + b*x])/(3*(2 + b)^(7/2)) + (109*b^4*Sqrt[x]*Sqrt[2 + b*x])/(6*(2 + b)^(7/2)) - (3*b^5*Sqrt[x]*Sqrt[2 + b*x])/(2*(2 + b)^(7/2)) + (6*b^2*x*Sqrt[2 + b*x])/(2 + b)^(7/2) + (4*b^3*x*Sqrt[2 + b*x])/(3*(2 + b)^(7/2)) - (21*b^4*x*Sqrt[2 + b*x])/(2*(2 + b)^(7/2)) + (b^5*x*Sqrt[2 + b*x])/(2*(2 + b)^(7/2))))/(-8 - 10*b - 2*b^2 + 4*b*Sqrt[x] - 6*b*x - 5*b^2*x - b^3*x + 2*b^2*x^(3/2) - b^2*x^2 + 4*Sqrt[2 + b]*Sqrt[2 + b*x] + 4*b*Sqrt[2 + b]*Sqrt[2 + b*x] - 2*b*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] + b^2*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] + 2*b*Sqrt[2 + b]*x*Sqrt[2 + b*x])^2 + ((-1/12*b/(2 + b)^(5/2) + (b*Sqrt[2 + b*x])/(12*(2 + b)^3))*(736 - 672*b - 760*b^2 - 132*b^3 - 6*b^4 + 32*Sqrt[x] + 504*b*Sqrt[x] + 472*b^2*Sqrt[x] + 138*b^3*Sqrt[x] + 12*b^4*Sqrt[x] + 136*b*x - 388*b^2*x - 246*b^3*x - 9*b^4*x + 32*b*x^(3/2) + 100*b^2*x^(3/2) + 48*b^3*x^(3/2) + 3*b^4*x^(3/2) - 368*Sqrt[2 + b]*Sqrt[2 + b*x] + 416*b*Sqrt[2 + b]*Sqrt[2 + b*x] + 240*b^2*Sqrt[2 + b]*Sqrt[2 + b*x] + 6*b^3*Sqrt[2 + b]*Sqrt[2 + b*x] - 16*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] - 212*b*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] - 120*b^2*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] - 9*b^3*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] - 12*b*Sqrt[2 + b]*x*Sqrt[2 + b*x] + 72*b^2*Sqrt[2 + b]*x*Sqrt[2 + b*x] + 3*b^3*Sqrt[2 + b]*x*Sqrt[2 + b*x]))/(-8 - 10*b - 2*b^2 + 4*b*Sqrt[x] - 6*b*x - 5*b^2*x - b^3*x + 2*b^2*x^(3/2) - b^2*x^2 + 4*Sqrt[2 + b]*Sqrt[2 + b*x] + 4*b*Sqrt[2 + b]*Sqrt[2 + b*x] - 2*b*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] + b^2*Sqrt[2 + b]*Sqrt[x]*Sqrt[2 + b*x] + 2*b*Sqrt[2 + b]*x*Sqrt[2 + b*x])","B",1
628,-1,0,71,180.1853157,"\int \frac{1}{x^{5/2} (2+b x)^{5/2}} \, dx","IntegrateAlgebraic[1/(x^(5/2)*(2 + b*x)^(5/2)),x]","\text{\$Aborted}","-\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,"$Aborted","F",-1
629,1,1329,91,1.7145714,"\int \frac{x^{5/2}}{\sqrt{2-b x}} \, dx","IntegrateAlgebraic[x^(5/2)/Sqrt[2 - b*x],x]","\frac{4 \left(-8 b^8+24 b^7-18 b^6+2 b^5\right) \sqrt{2-b x} x^{11/2}+4 \left(48 b^7-120 b^6+60 b^5\right) \sqrt{2-b x} x^5+4 \left(4 b^7-144 b^6+273 b^5-67 b^4\right) \sqrt{2-b x} x^{9/2}+4 \left(220 b^5-330 b^4\right) \sqrt{2-b x} x^4+4 \left(-18 b^6-12 b^5-156 b^4+219 b^3\right) \sqrt{2-b x} x^{7/2}+4 \left(120 b^5-80 b^4+18 b^3\right) \sqrt{2-b x} x^3+4 \left(8 b^8-12 b^7+18 b^6-20 b^5-552 b^4+639 b^3-92 b^2\right) \sqrt{2-b x} x^{5/2}+4 \left(-48 b^7+48 b^6-96 b^5+144 b^4+1590 b^3-1500 b^2\right) \sqrt{2-b x} x^2+4 \left(-16 b^7+156 b^6-102 b^5+448 b^4-615 b^3-3000 b^2+1600 b\right) \sqrt{2-b x} x^{3/2}+4 \left(72 b^6-292 b^5+144 b^4-1386 b^3+1640 b^2+3840 b\right) \sqrt{2-b x} x+4 \left(6 b^6-141 b^5+327 b^4-243 b^3+2580 b^2-2880 b-3840\right) \sqrt{2-b x} \sqrt{x}+\sqrt{2-b} \left(4 \left(8 b^8-16 b^7+6 b^6\right) x^6+4 \left(-48 b^7+72 b^6-12 b^5\right) x^{11/2}+4 \left(-12 b^7+156 b^6-141 b^5\right) x^5+4 \left(48 b^6-292 b^5+122 b^4\right) x^{9/2}+4 \left(18 b^6-102 b^5+327 b^4\right) x^4+4 \left(-96 b^5+144 b^4-222 b^3\right) x^{7/2}+4 \left(-8 b^8+4 b^7-18 b^6-20 b^5+448 b^4-243 b^3\right) x^3+4 \left(48 b^7+120 b^5+144 b^4-1386 b^3+372 b^2\right) x^{5/2}+4 \left(24 b^7-144 b^6-12 b^5-552 b^4-615 b^3+2580 b^2\right) x^2+4 \left(-120 b^6+220 b^5-80 b^4+1590 b^3+1640 b^2-2560 b\right) x^{3/2}+4 \left(-18 b^6+273 b^5-156 b^4+639 b^3-3000 b^2-2880 b\right) x+4 \left(60 b^5-330 b^4+18 b^3-1500 b^2+3840 b+3840\right) \sqrt{x}+4 \left(2 b^5-67 b^4+219 b^3-92 b^2+1600 b-3840\right)\right)+4 \left(-12 b^5+122 b^4-222 b^3+372 b^2-2560 b+3840\right) \sqrt{2-b x}}{3 \left(32 b^6-96 b^5+72 b^4-8 b^3\right) x^3 b^3+3 \left(-8 b^3+288 b^2-1536 b+2048\right) b^3+3 \sqrt{2-b} \left(-48 b^2+512 b-1024\right) \sqrt{2-b x} b^3+\sqrt{x} \left(3 \left(-240 b^3+1920 b^2-3072 b\right) b^3+3 \sqrt{2-b} \left(24 b^3-576 b^2+1536 b\right) \sqrt{2-b x} b^3\right)+x \left(3 \left(72 b^4-1272 b^3+3264 b^2-1536 b\right) b^3+3 \sqrt{2-b} \left(288 b^3-1312 b^2+512 b\right) \sqrt{2-b x} b^3\right)+x^2 \left(3 \left(-96 b^5+816 b^4-1272 b^3+288 b^2\right) b^3+3 \sqrt{2-b} \left(-192 b^4+288 b^3-48 b^2\right) \sqrt{2-b x} b^3\right)+x^{3/2} \left(3 \left(480 b^4-2080 b^3+1920 b^2\right) b^3+3 \sqrt{2-b} \left(-64 b^4+656 b^3-576 b^2\right) \sqrt{2-b x} b^3\right)+x^{5/2} \left(3 \left(-192 b^5+480 b^4-240 b^3\right) b^3+3 \sqrt{2-b} \left(32 b^5-64 b^4+24 b^3\right) \sqrt{2-b x} b^3\right)}+\frac{10 \tan ^{-1}\left(\frac{\frac{\sqrt{2-b}}{\sqrt{b}}-\frac{\sqrt{2-b x}}{\sqrt{b}}}{\sqrt{x}-1}\right)}{b^{7/2}}","\frac{5 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{7/2}}-\frac{5 \sqrt{x} \sqrt{2-b x}}{2 b^3}-\frac{5 x^{3/2} \sqrt{2-b x}}{6 b^2}-\frac{x^{5/2} \sqrt{2-b x}}{3 b}",1,"(4*(3840 - 2560*b + 372*b^2 - 222*b^3 + 122*b^4 - 12*b^5)*Sqrt[2 - b*x] + 4*(-3840 - 2880*b + 2580*b^2 - 243*b^3 + 327*b^4 - 141*b^5 + 6*b^6)*Sqrt[x]*Sqrt[2 - b*x] + 4*(3840*b + 1640*b^2 - 1386*b^3 + 144*b^4 - 292*b^5 + 72*b^6)*x*Sqrt[2 - b*x] + 4*(1600*b - 3000*b^2 - 615*b^3 + 448*b^4 - 102*b^5 + 156*b^6 - 16*b^7)*x^(3/2)*Sqrt[2 - b*x] + 4*(-1500*b^2 + 1590*b^3 + 144*b^4 - 96*b^5 + 48*b^6 - 48*b^7)*x^2*Sqrt[2 - b*x] + 4*(-92*b^2 + 639*b^3 - 552*b^4 - 20*b^5 + 18*b^6 - 12*b^7 + 8*b^8)*x^(5/2)*Sqrt[2 - b*x] + 4*(18*b^3 - 80*b^4 + 120*b^5)*x^3*Sqrt[2 - b*x] + 4*(219*b^3 - 156*b^4 - 12*b^5 - 18*b^6)*x^(7/2)*Sqrt[2 - b*x] + 4*(-330*b^4 + 220*b^5)*x^4*Sqrt[2 - b*x] + 4*(-67*b^4 + 273*b^5 - 144*b^6 + 4*b^7)*x^(9/2)*Sqrt[2 - b*x] + 4*(60*b^5 - 120*b^6 + 48*b^7)*x^5*Sqrt[2 - b*x] + 4*(2*b^5 - 18*b^6 + 24*b^7 - 8*b^8)*x^(11/2)*Sqrt[2 - b*x] + Sqrt[2 - b]*(4*(-3840 + 1600*b - 92*b^2 + 219*b^3 - 67*b^4 + 2*b^5) + 4*(3840 + 3840*b - 1500*b^2 + 18*b^3 - 330*b^4 + 60*b^5)*Sqrt[x] + 4*(-2880*b - 3000*b^2 + 639*b^3 - 156*b^4 + 273*b^5 - 18*b^6)*x + 4*(-2560*b + 1640*b^2 + 1590*b^3 - 80*b^4 + 220*b^5 - 120*b^6)*x^(3/2) + 4*(2580*b^2 - 615*b^3 - 552*b^4 - 12*b^5 - 144*b^6 + 24*b^7)*x^2 + 4*(372*b^2 - 1386*b^3 + 144*b^4 + 120*b^5 + 48*b^7)*x^(5/2) + 4*(-243*b^3 + 448*b^4 - 20*b^5 - 18*b^6 + 4*b^7 - 8*b^8)*x^3 + 4*(-222*b^3 + 144*b^4 - 96*b^5)*x^(7/2) + 4*(327*b^4 - 102*b^5 + 18*b^6)*x^4 + 4*(122*b^4 - 292*b^5 + 48*b^6)*x^(9/2) + 4*(-141*b^5 + 156*b^6 - 12*b^7)*x^5 + 4*(-12*b^5 + 72*b^6 - 48*b^7)*x^(11/2) + 4*(6*b^6 - 16*b^7 + 8*b^8)*x^6))/(3*b^3*(2048 - 1536*b + 288*b^2 - 8*b^3) + 3*b^3*(-8*b^3 + 72*b^4 - 96*b^5 + 32*b^6)*x^3 + 3*Sqrt[2 - b]*b^3*(-1024 + 512*b - 48*b^2)*Sqrt[2 - b*x] + Sqrt[x]*(3*b^3*(-3072*b + 1920*b^2 - 240*b^3) + 3*Sqrt[2 - b]*b^3*(1536*b - 576*b^2 + 24*b^3)*Sqrt[2 - b*x]) + x*(3*b^3*(-1536*b + 3264*b^2 - 1272*b^3 + 72*b^4) + 3*Sqrt[2 - b]*b^3*(512*b - 1312*b^2 + 288*b^3)*Sqrt[2 - b*x]) + x^2*(3*b^3*(288*b^2 - 1272*b^3 + 816*b^4 - 96*b^5) + 3*Sqrt[2 - b]*b^3*(-48*b^2 + 288*b^3 - 192*b^4)*Sqrt[2 - b*x]) + x^(3/2)*(3*b^3*(1920*b^2 - 2080*b^3 + 480*b^4) + 3*Sqrt[2 - b]*b^3*(-576*b^2 + 656*b^3 - 64*b^4)*Sqrt[2 - b*x]) + x^(5/2)*(3*b^3*(-240*b^3 + 480*b^4 - 192*b^5) + 3*Sqrt[2 - b]*b^3*(24*b^3 - 64*b^4 + 32*b^5)*Sqrt[2 - b*x])) + (10*ArcTan[(Sqrt[2 - b]/Sqrt[b] - Sqrt[2 - b*x]/Sqrt[b])/(-1 + Sqrt[x])])/b^(7/2)","B",1
630,1,681,69,0.6802669,"\int \frac{x^{3/2}}{\sqrt{2-b x}} \, dx","IntegrateAlgebraic[x^(3/2)/Sqrt[2 - b*x],x]","\frac{6 \tan ^{-1}\left(\frac{\frac{\sqrt{2-b}}{\sqrt{b}}-\frac{\sqrt{2-b x}}{\sqrt{b}}}{\sqrt{x}-1}\right)}{b^{5/2}}+\frac{\left(\frac{2 \sqrt{x}}{b^2}-\frac{2}{b^2}\right) \left(\sqrt{2-b}-\sqrt{2-b x}\right) \left(2 b^5 x^3+2 b^5 x^2-6 b^4 x^{5/2}-6 b^4 x^{3/2}+2 \sqrt{2-b} b^4 x^{5/2} \sqrt{2-b x}+2 \sqrt{2-b} b^4 x^{3/2} \sqrt{2-b x}-4 b^4 x^3-4 b^4 x^2-4 b^4 x+9 b^3 x^{5/2}+6 b^3 x^{3/2}-2 \sqrt{2-b} b^3 x^{5/2} \sqrt{2-b x}+b^3 x^3+8 b^3 x^2-6 \sqrt{2-b} b^3 x^2 \sqrt{2-b x}+8 b^3 x+9 b^3 \sqrt{x}-6 \sqrt{2-b} b^3 x \sqrt{2-b x}-2 \sqrt{2-b} b^3 \sqrt{x} \sqrt{2-b x}+b^3+b^2 x^{3/2}+5 \sqrt{2-b} b^2 x^{3/2} \sqrt{2-b x}-7 b^2 x^2+3 \sqrt{2-b} b^2 x^2 \sqrt{2-b x}+16 b^2 x+b^2 \sqrt{x}-6 \sqrt{2-b} b^2 x \sqrt{2-b x}+3 \sqrt{2-b} b^2 \sqrt{2-b x}+5 \sqrt{2-b} b^2 \sqrt{x} \sqrt{2-b x}-7 b^2-14 b x-44 b \sqrt{x}+\sqrt{2-b} b x \sqrt{2-b x}+\sqrt{2-b} b \sqrt{2-b x}+22 \sqrt{2-b} b \sqrt{x} \sqrt{2-b x}-24 \sqrt{2-b} \sqrt{2-b x}-14 b+48\right)}{\left(b \sqrt{x}+\sqrt{2-b} \sqrt{2-b x}-2\right)^4}","\frac{3 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{5/2}}-\frac{3 \sqrt{x} \sqrt{2-b x}}{2 b^2}-\frac{x^{3/2} \sqrt{2-b x}}{2 b}",1,"((-2/b^2 + (2*Sqrt[x])/b^2)*(Sqrt[2 - b] - Sqrt[2 - b*x])*(48 - 14*b - 7*b^2 + b^3 - 44*b*Sqrt[x] + b^2*Sqrt[x] + 9*b^3*Sqrt[x] - 14*b*x + 16*b^2*x + 8*b^3*x - 4*b^4*x + b^2*x^(3/2) + 6*b^3*x^(3/2) - 6*b^4*x^(3/2) - 7*b^2*x^2 + 8*b^3*x^2 - 4*b^4*x^2 + 2*b^5*x^2 + 9*b^3*x^(5/2) - 6*b^4*x^(5/2) + b^3*x^3 - 4*b^4*x^3 + 2*b^5*x^3 - 24*Sqrt[2 - b]*Sqrt[2 - b*x] + Sqrt[2 - b]*b*Sqrt[2 - b*x] + 3*Sqrt[2 - b]*b^2*Sqrt[2 - b*x] + 22*Sqrt[2 - b]*b*Sqrt[x]*Sqrt[2 - b*x] + 5*Sqrt[2 - b]*b^2*Sqrt[x]*Sqrt[2 - b*x] - 2*Sqrt[2 - b]*b^3*Sqrt[x]*Sqrt[2 - b*x] + Sqrt[2 - b]*b*x*Sqrt[2 - b*x] - 6*Sqrt[2 - b]*b^2*x*Sqrt[2 - b*x] - 6*Sqrt[2 - b]*b^3*x*Sqrt[2 - b*x] + 5*Sqrt[2 - b]*b^2*x^(3/2)*Sqrt[2 - b*x] + 2*Sqrt[2 - b]*b^4*x^(3/2)*Sqrt[2 - b*x] + 3*Sqrt[2 - b]*b^2*x^2*Sqrt[2 - b*x] - 6*Sqrt[2 - b]*b^3*x^2*Sqrt[2 - b*x] - 2*Sqrt[2 - b]*b^3*x^(5/2)*Sqrt[2 - b*x] + 2*Sqrt[2 - b]*b^4*x^(5/2)*Sqrt[2 - b*x]))/(-2 + b*Sqrt[x] + Sqrt[2 - b]*Sqrt[2 - b*x])^4 + (6*ArcTan[(Sqrt[2 - b]/Sqrt[b] - Sqrt[2 - b*x]/Sqrt[b])/(-1 + Sqrt[x])])/b^(5/2)","B",1
631,1,191,45,0.2409135,"\int \frac{\sqrt{x}}{\sqrt{2-b x}} \, dx","IntegrateAlgebraic[Sqrt[x]/Sqrt[2 - b*x],x]","\frac{4 \tan ^{-1}\left(\frac{\frac{\sqrt{2-b}}{\sqrt{b}}-\frac{\sqrt{2-b x}}{\sqrt{b}}}{\sqrt{x}-1}\right)}{b^{3/2}}+\frac{\left(\frac{2 \sqrt{x}}{b}-\frac{2}{b}\right) \left(\sqrt{2-b}-\sqrt{2-b x}\right) \left(b^2 x-b x-b \sqrt{x}+\sqrt{2-b} b \sqrt{x} \sqrt{2-b x}-\sqrt{2-b} \sqrt{2-b x}-b+2\right)}{\left(b \sqrt{x}+\sqrt{2-b} \sqrt{2-b x}-2\right)^2}","\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,"((-2/b + (2*Sqrt[x])/b)*(Sqrt[2 - b] - Sqrt[2 - b*x])*(2 - b - b*Sqrt[x] - b*x + b^2*x - Sqrt[2 - b]*Sqrt[2 - b*x] + Sqrt[2 - b]*b*Sqrt[x]*Sqrt[2 - b*x]))/(-2 + b*Sqrt[x] + Sqrt[2 - b]*Sqrt[2 - b*x])^2 + (4*ArcTan[(Sqrt[2 - b]/Sqrt[b] - Sqrt[2 - b*x]/Sqrt[b])/(-1 + Sqrt[x])])/b^(3/2)","B",1
632,1,51,24,0.1196267,"\int \frac{1}{\sqrt{x} \sqrt{2-b x}} \, dx","IntegrateAlgebraic[1/(Sqrt[x]*Sqrt[2 - b*x]),x]","-\frac{4 \tan ^{-1}\left(\frac{\frac{\sqrt{2-b x}}{\sqrt{b}}-\frac{\sqrt{2-b}}{\sqrt{b}}}{\sqrt{x}-1}\right)}{\sqrt{b}}","\frac{2 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{\sqrt{b}}",1,"(-4*ArcTan[(-(Sqrt[2 - b]/Sqrt[b]) + Sqrt[2 - b*x]/Sqrt[b])/(-1 + Sqrt[x])])/Sqrt[b]","B",1
633,1,258,17,0.1989294,"\int \frac{1}{x^{3/2} \sqrt{2-b x}} \, dx","IntegrateAlgebraic[1/(x^(3/2)*Sqrt[2 - b*x]),x]","\frac{\left(\sqrt{2-b}-\sqrt{2-b x}\right)^4 \left(\frac{b \left(\sqrt{x}-1\right)^3}{2 \left(\sqrt{2-b}-\sqrt{2-b x}\right)^3}+\frac{\sqrt{2-b} \left(\sqrt{x}-1\right)^2}{\left(\sqrt{2-b}-\sqrt{2-b x}\right)^2}-\frac{\sqrt{x}-1}{2 \left(\sqrt{2-b}-\sqrt{2-b x}\right)}\right)}{b^2 x-2 b x^{3/2}+b x^2+b x-4 b \sqrt{x}+\sqrt{2-b} b \sqrt{x} \sqrt{2-b x}+2 \sqrt{2-b} x \sqrt{2-b x}-4 \sqrt{2-b} \sqrt{x} \sqrt{2-b x}-4 x+8 \sqrt{x}}","-\frac{\sqrt{2-b x}}{\sqrt{x}}",1,"((Sqrt[2 - b] - Sqrt[2 - b*x])^4*((b*(-1 + Sqrt[x])^3)/(2*(Sqrt[2 - b] - Sqrt[2 - b*x])^3) + (Sqrt[2 - b]*(-1 + Sqrt[x])^2)/(Sqrt[2 - b] - Sqrt[2 - b*x])^2 - (-1 + Sqrt[x])/(2*(Sqrt[2 - b] - Sqrt[2 - b*x]))))/(8*Sqrt[x] - 4*b*Sqrt[x] - 4*x + b*x + b^2*x - 2*b*x^(3/2) + b*x^2 - 4*Sqrt[2 - b]*Sqrt[x]*Sqrt[2 - b*x] + Sqrt[2 - b]*b*Sqrt[x]*Sqrt[2 - b*x] + 2*Sqrt[2 - b]*x*Sqrt[2 - b*x])","B",1
634,1,614,40,3.8990479,"\int \frac{1}{x^{5/2} \sqrt{2-b x}} \, dx","IntegrateAlgebraic[1/(x^(5/2)*Sqrt[2 - b*x]),x]","\frac{\left(\frac{\sqrt{x}}{384}-\frac{1}{384}\right) \left(\sqrt{2-b}-\sqrt{2-b x}\right)^{12} \left(-\frac{3 b^5 \left(\sqrt{x}-1\right)^{10}}{\left(\sqrt{2-b}-\sqrt{2-b x}\right)^{10}}-\frac{12 \sqrt{2-b} b^4 \left(\sqrt{x}-1\right)^9}{\left(\sqrt{2-b}-\sqrt{2-b x}\right)^9}+\frac{b^3 (15 b-8) \left(\sqrt{x}-1\right)^8}{\left(\sqrt{2-b}-\sqrt{2-b x}\right)^8}+\frac{48 \sqrt{2-b} b^2 \left(\sqrt{x}-1\right)^7}{\left(\sqrt{2-b}-\sqrt{2-b x}\right)^7}+\frac{18 (b-4) b^2 \left(\sqrt{x}-1\right)^6}{\left(\sqrt{2-b}-\sqrt{2-b x}\right)^6}+\frac{8 \sqrt{2-b} \left(3 b^2-4 b-16\right) \left(\sqrt{x}-1\right)^5}{\left(\sqrt{2-b}-\sqrt{2-b x}\right)^5}-\frac{18 (b-4) b \left(\sqrt{x}-1\right)^4}{\left(\sqrt{2-b}-\sqrt{2-b x}\right)^4}+\frac{48 \sqrt{2-b} \left(\sqrt{x}-1\right)^3}{\left(\sqrt{2-b}-\sqrt{2-b x}\right)^3}-\frac{(15 b-8) \left(\sqrt{x}-1\right)^2}{\left(\sqrt{2-b}-\sqrt{2-b x}\right)^2}-\frac{12 \sqrt{2-b} \left(\sqrt{x}-1\right)}{\sqrt{2-b}-\sqrt{2-b x}}+3\right)}{\left(\sqrt{2-b x}-\sqrt{2-b}\right) \left(b^2 x-2 b x^{3/2}+b x^2+b x-4 b \sqrt{x}+\sqrt{2-b} b \sqrt{x} \sqrt{2-b x}+2 \sqrt{2-b} x \sqrt{2-b x}-4 \sqrt{2-b} \sqrt{x} \sqrt{2-b x}-4 x+8 \sqrt{x}\right)^3}","-\frac{\sqrt{2-b x}}{3 x^{3/2}}-\frac{b \sqrt{2-b x}}{3 \sqrt{x}}",1,"((-1/384 + Sqrt[x]/384)*(Sqrt[2 - b] - Sqrt[2 - b*x])^12*(3 - (3*b^5*(-1 + Sqrt[x])^10)/(Sqrt[2 - b] - Sqrt[2 - b*x])^10 - (12*Sqrt[2 - b]*b^4*(-1 + Sqrt[x])^9)/(Sqrt[2 - b] - Sqrt[2 - b*x])^9 + (b^3*(-8 + 15*b)*(-1 + Sqrt[x])^8)/(Sqrt[2 - b] - Sqrt[2 - b*x])^8 + (48*Sqrt[2 - b]*b^2*(-1 + Sqrt[x])^7)/(Sqrt[2 - b] - Sqrt[2 - b*x])^7 + (18*(-4 + b)*b^2*(-1 + Sqrt[x])^6)/(Sqrt[2 - b] - Sqrt[2 - b*x])^6 + (8*Sqrt[2 - b]*(-16 - 4*b + 3*b^2)*(-1 + Sqrt[x])^5)/(Sqrt[2 - b] - Sqrt[2 - b*x])^5 - (18*(-4 + b)*b*(-1 + Sqrt[x])^4)/(Sqrt[2 - b] - Sqrt[2 - b*x])^4 + (48*Sqrt[2 - b]*(-1 + Sqrt[x])^3)/(Sqrt[2 - b] - Sqrt[2 - b*x])^3 - ((-8 + 15*b)*(-1 + Sqrt[x])^2)/(Sqrt[2 - b] - Sqrt[2 - b*x])^2 - (12*Sqrt[2 - b]*(-1 + Sqrt[x]))/(Sqrt[2 - b] - Sqrt[2 - b*x])))/((-Sqrt[2 - b] + Sqrt[2 - b*x])*(8*Sqrt[x] - 4*b*Sqrt[x] - 4*x + b*x + b^2*x - 2*b*x^(3/2) + b*x^2 - 4*Sqrt[2 - b]*Sqrt[x]*Sqrt[2 - b*x] + Sqrt[2 - b]*b*Sqrt[x]*Sqrt[2 - b*x] + 2*Sqrt[2 - b]*x*Sqrt[2 - b*x])^3)","B",1
635,1,966,89,2.7945784,"\int \frac{x^{5/2}}{(2-b x)^{3/2}} \, dx","IntegrateAlgebraic[x^(5/2)/(2 - b*x)^(3/2),x]","\frac{\left(\frac{4 \sqrt{x}}{b}-\frac{8 \sqrt{x}}{b^2}+\frac{2 \sqrt{x}}{b^3}+\frac{4 \sqrt{2-b} \sqrt{2-b x}}{b^2}-\frac{4 \sqrt{2-b} \sqrt{2-b x}}{b^3}-\frac{4}{b^2}+\frac{6}{b^3}\right) \left(\sqrt{2-b}-\sqrt{2-b x}\right)^7}{\left(\sqrt{x} b+\sqrt{2-b} \sqrt{2-b x}-2\right)^4}+\frac{\left(\frac{12 \sqrt{x}}{b}-\frac{24 \sqrt{x}}{b^2}+\frac{6 \sqrt{x}}{b^3}+\frac{16 \sqrt{2-b} \sqrt{2-b x}}{b^2}-\frac{16 \sqrt{2-b} \sqrt{2-b x}}{b^3}+\frac{4}{b}-\frac{24}{b^2}+\frac{26}{b^3}\right) \left(\sqrt{2-b}-\sqrt{2-b x}\right)^5}{\left(\sqrt{x} b+\sqrt{2-b} \sqrt{2-b x}-2\right)^3}+\frac{\left(\frac{10 \sqrt{x}}{b}-\frac{12 \sqrt{x}}{b^2}-\frac{3 \sqrt{x}}{b^3}+\frac{20 \sqrt{2-b} \sqrt{2-b x}}{b^2}-\frac{12 \sqrt{2-b} \sqrt{2-b x}}{b^3}+\frac{10}{b}-\frac{40}{b^2}+\frac{27}{b^3}\right) \left(\sqrt{2-b}-\sqrt{2-b x}\right)^3}{\left(\sqrt{x} b+\sqrt{2-b} \sqrt{2-b x}-2\right)^2}+\frac{\left(\frac{8 \sqrt{x}}{(b-2) b^3}-\frac{8}{(b-2) b^3}\right) \left(-x b^2+2 \sqrt{x} b^2-2 b^2+2 x b-4 \sqrt{x} b-2 \sqrt{2-b} \sqrt{2-b x} b+\sqrt{2-b} \sqrt{x} \sqrt{2-b x} b+6 b+2 \sqrt{2-b} \sqrt{2-b x}-4\right) \left(\sqrt{2-b}-\sqrt{2-b x}\right)}{x b^3-x^2 b^2+2 x^{3/2} b^2-5 x b^2+\sqrt{2-b} \sqrt{x} \sqrt{2-b x} b^2-2 b^2+6 x b-4 \sqrt{x} b-2 \sqrt{2-b} x \sqrt{2-b x} b-4 \sqrt{2-b} \sqrt{2-b x} b+2 \sqrt{2-b} \sqrt{x} \sqrt{2-b x} b+10 b+4 \sqrt{2-b} \sqrt{2-b x}-8}+\frac{\left(\frac{\sqrt{2-b x}}{b^3}-\frac{\sqrt{2-b}}{b^3}\right) \left(-2 \sqrt{x} b^2-6 b^2-4 \sqrt{x} b-8 \sqrt{2-b} \sqrt{2-b x} b+12 b+7 \sqrt{x}-8 \sqrt{2-b} \sqrt{2-b x}+9\right)}{\sqrt{x} b+\sqrt{2-b} \sqrt{2-b x}-2}-\frac{30 \tan ^{-1}\left(\frac{\frac{\sqrt{2-b}}{\sqrt{b}}-\frac{\sqrt{2-b x}}{\sqrt{b}}}{\sqrt{x}-1}\right)}{b^{7/2}}","-\frac{15 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{7/2}}+\frac{15 \sqrt{x} \sqrt{2-b x}}{2 b^3}+\frac{5 x^{3/2} \sqrt{2-b x}}{2 b^2}+\frac{2 x^{5/2}}{b \sqrt{2-b x}}",1,"((Sqrt[2 - b] - Sqrt[2 - b*x])^7*(6/b^3 - 4/b^2 + (2*Sqrt[x])/b^3 - (8*Sqrt[x])/b^2 + (4*Sqrt[x])/b - (4*Sqrt[2 - b]*Sqrt[2 - b*x])/b^3 + (4*Sqrt[2 - b]*Sqrt[2 - b*x])/b^2))/(-2 + b*Sqrt[x] + Sqrt[2 - b]*Sqrt[2 - b*x])^4 + ((Sqrt[2 - b] - Sqrt[2 - b*x])^5*(26/b^3 - 24/b^2 + 4/b + (6*Sqrt[x])/b^3 - (24*Sqrt[x])/b^2 + (12*Sqrt[x])/b - (16*Sqrt[2 - b]*Sqrt[2 - b*x])/b^3 + (16*Sqrt[2 - b]*Sqrt[2 - b*x])/b^2))/(-2 + b*Sqrt[x] + Sqrt[2 - b]*Sqrt[2 - b*x])^3 + ((Sqrt[2 - b] - Sqrt[2 - b*x])^3*(27/b^3 - 40/b^2 + 10/b - (3*Sqrt[x])/b^3 - (12*Sqrt[x])/b^2 + (10*Sqrt[x])/b - (12*Sqrt[2 - b]*Sqrt[2 - b*x])/b^3 + (20*Sqrt[2 - b]*Sqrt[2 - b*x])/b^2))/(-2 + b*Sqrt[x] + Sqrt[2 - b]*Sqrt[2 - b*x])^2 + ((-(Sqrt[2 - b]/b^3) + Sqrt[2 - b*x]/b^3)*(9 + 12*b - 6*b^2 + 7*Sqrt[x] - 4*b*Sqrt[x] - 2*b^2*Sqrt[x] - 8*Sqrt[2 - b]*Sqrt[2 - b*x] - 8*Sqrt[2 - b]*b*Sqrt[2 - b*x]))/(-2 + b*Sqrt[x] + Sqrt[2 - b]*Sqrt[2 - b*x]) + ((-8/((-2 + b)*b^3) + (8*Sqrt[x])/((-2 + b)*b^3))*(Sqrt[2 - b] - Sqrt[2 - b*x])*(-4 + 6*b - 2*b^2 - 4*b*Sqrt[x] + 2*b^2*Sqrt[x] + 2*b*x - b^2*x + 2*Sqrt[2 - b]*Sqrt[2 - b*x] - 2*Sqrt[2 - b]*b*Sqrt[2 - b*x] + Sqrt[2 - b]*b*Sqrt[x]*Sqrt[2 - b*x]))/(-8 + 10*b - 2*b^2 - 4*b*Sqrt[x] + 6*b*x - 5*b^2*x + b^3*x + 2*b^2*x^(3/2) - b^2*x^2 + 4*Sqrt[2 - b]*Sqrt[2 - b*x] - 4*Sqrt[2 - b]*b*Sqrt[2 - b*x] + 2*Sqrt[2 - b]*b*Sqrt[x]*Sqrt[2 - b*x] + Sqrt[2 - b]*b^2*Sqrt[x]*Sqrt[2 - b*x] - 2*Sqrt[2 - b]*b*x*Sqrt[2 - b*x]) - (30*ArcTan[(Sqrt[2 - b]/Sqrt[b] - Sqrt[2 - b*x]/Sqrt[b])/(-1 + Sqrt[x])])/b^(7/2)","B",1
636,1,589,65,1.0552339,"\int \frac{x^{3/2}}{(2-b x)^{3/2}} \, dx","IntegrateAlgebraic[x^(3/2)/(2 - b*x)^(3/2),x]","-\frac{12 \tan ^{-1}\left(\frac{\frac{\sqrt{2-b}}{\sqrt{b}}-\frac{\sqrt{2-b x}}{\sqrt{b}}}{\sqrt{x}-1}\right)}{b^{5/2}}+\frac{\left(-\frac{2 \sqrt{x}}{b^2}+\frac{2 \sqrt{2-b} \sqrt{2-b x}}{b^2}-\frac{2}{b^2}+\frac{2 \sqrt{x}}{b}\right) \left(\sqrt{2-b}-\sqrt{2-b x}\right)^3}{\left(b \sqrt{x}+\sqrt{2-b} \sqrt{2-b x}-2\right)^2}+\frac{\left(b \left(-\sqrt{x}\right)-2 \sqrt{2-b} \sqrt{2-b x}-b+\sqrt{x}+3\right) \left(\frac{2 \sqrt{2-b x}}{b^2}-\frac{2 \sqrt{2-b}}{b^2}\right)}{b \sqrt{x}+\sqrt{2-b} \sqrt{2-b x}-2}+\frac{\left(\frac{4 \sqrt{x}}{(b-2) b^2}-\frac{4}{(b-2) b^2}\right) \left(b^2 (-x)+2 b^2 \sqrt{x}-2 b^2+2 b x-4 b \sqrt{x}-2 \sqrt{2-b} b \sqrt{2-b x}+\sqrt{2-b} b \sqrt{x} \sqrt{2-b x}+2 \sqrt{2-b} \sqrt{2-b x}+6 b-4\right) \left(\sqrt{2-b}-\sqrt{2-b x}\right)}{b^3 x+2 b^2 x^{3/2}-b^2 x^2-5 b^2 x+\sqrt{2-b} b^2 \sqrt{x} \sqrt{2-b x}-2 b^2+6 b x-4 b \sqrt{x}-2 \sqrt{2-b} b x \sqrt{2-b x}-4 \sqrt{2-b} b \sqrt{2-b x}+2 \sqrt{2-b} b \sqrt{x} \sqrt{2-b x}+4 \sqrt{2-b} \sqrt{2-b x}+10 b-8}","-\frac{6 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{5/2}}+\frac{3 \sqrt{x} \sqrt{2-b x}}{b^2}+\frac{2 x^{3/2}}{b \sqrt{2-b x}}",1,"((3 - b + Sqrt[x] - b*Sqrt[x] - 2*Sqrt[2 - b]*Sqrt[2 - b*x])*((-2*Sqrt[2 - b])/b^2 + (2*Sqrt[2 - b*x])/b^2))/(-2 + b*Sqrt[x] + Sqrt[2 - b]*Sqrt[2 - b*x]) + ((Sqrt[2 - b] - Sqrt[2 - b*x])^3*(-2/b^2 - (2*Sqrt[x])/b^2 + (2*Sqrt[x])/b + (2*Sqrt[2 - b]*Sqrt[2 - b*x])/b^2))/(-2 + b*Sqrt[x] + Sqrt[2 - b]*Sqrt[2 - b*x])^2 + ((-4/((-2 + b)*b^2) + (4*Sqrt[x])/((-2 + b)*b^2))*(Sqrt[2 - b] - Sqrt[2 - b*x])*(-4 + 6*b - 2*b^2 - 4*b*Sqrt[x] + 2*b^2*Sqrt[x] + 2*b*x - b^2*x + 2*Sqrt[2 - b]*Sqrt[2 - b*x] - 2*Sqrt[2 - b]*b*Sqrt[2 - b*x] + Sqrt[2 - b]*b*Sqrt[x]*Sqrt[2 - b*x]))/(-8 + 10*b - 2*b^2 - 4*b*Sqrt[x] + 6*b*x - 5*b^2*x + b^3*x + 2*b^2*x^(3/2) - b^2*x^2 + 4*Sqrt[2 - b]*Sqrt[2 - b*x] - 4*Sqrt[2 - b]*b*Sqrt[2 - b*x] + 2*Sqrt[2 - b]*b*Sqrt[x]*Sqrt[2 - b*x] + Sqrt[2 - b]*b^2*Sqrt[x]*Sqrt[2 - b*x] - 2*Sqrt[2 - b]*b*x*Sqrt[2 - b*x]) - (12*ArcTan[(Sqrt[2 - b]/Sqrt[b] - Sqrt[2 - b*x]/Sqrt[b])/(-1 + Sqrt[x])])/b^(5/2)","B",1
637,1,382,45,0.3572129,"\int \frac{\sqrt{x}}{(2-b x)^{3/2}} \, dx","IntegrateAlgebraic[Sqrt[x]/(2 - b*x)^(3/2),x]","\frac{\left(\frac{2 \sqrt{x}}{(b-2) b}-\frac{2}{(b-2) b}\right) \left(\sqrt{2-b}-\sqrt{2-b x}\right) \left(b^2 (-x)+2 b^2 \sqrt{x}-2 b^2+2 b x-4 b \sqrt{x}-2 \sqrt{2-b} b \sqrt{2-b x}+\sqrt{2-b} b \sqrt{x} \sqrt{2-b x}+2 \sqrt{2-b} \sqrt{2-b x}+6 b-4\right)}{b^3 x+2 b^2 x^{3/2}-b^2 x^2-5 b^2 x+\sqrt{2-b} b^2 \sqrt{x} \sqrt{2-b x}-2 b^2+6 b x-4 b \sqrt{x}-2 \sqrt{2-b} b x \sqrt{2-b x}-4 \sqrt{2-b} b \sqrt{2-b x}+2 \sqrt{2-b} b \sqrt{x} \sqrt{2-b x}+4 \sqrt{2-b} \sqrt{2-b x}+10 b-8}-\frac{4 \tan ^{-1}\left(\frac{\frac{\sqrt{2-b}}{\sqrt{b}}-\frac{\sqrt{2-b x}}{\sqrt{b}}}{\sqrt{x}-1}\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/((-2 + b)*b) + (2*Sqrt[x])/((-2 + b)*b))*(Sqrt[2 - b] - Sqrt[2 - b*x])*(-4 + 6*b - 2*b^2 - 4*b*Sqrt[x] + 2*b^2*Sqrt[x] + 2*b*x - b^2*x + 2*Sqrt[2 - b]*Sqrt[2 - b*x] - 2*Sqrt[2 - b]*b*Sqrt[2 - b*x] + Sqrt[2 - b]*b*Sqrt[x]*Sqrt[2 - b*x]))/(-8 + 10*b - 2*b^2 - 4*b*Sqrt[x] + 6*b*x - 5*b^2*x + b^3*x + 2*b^2*x^(3/2) - b^2*x^2 + 4*Sqrt[2 - b]*Sqrt[2 - b*x] - 4*Sqrt[2 - b]*b*Sqrt[2 - b*x] + 2*Sqrt[2 - b]*b*Sqrt[x]*Sqrt[2 - b*x] + Sqrt[2 - b]*b^2*Sqrt[x]*Sqrt[2 - b*x] - 2*Sqrt[2 - b]*b*x*Sqrt[2 - b*x]) - (4*ArcTan[(Sqrt[2 - b]/Sqrt[b] - Sqrt[2 - b*x]/Sqrt[b])/(-1 + Sqrt[x])])/b^(3/2)","B",1
638,1,387,16,0.294484,"\int \frac{1}{\sqrt{x} (2-b x)^{3/2}} \, dx","IntegrateAlgebraic[1/(Sqrt[x]*(2 - b*x)^(3/2)),x]","\frac{\left(\frac{\sqrt{x}}{2 (b-2)}-\frac{1}{2 (b-2)}\right) \left(\sqrt{2-b}-\sqrt{2-b x}\right)^4 \left(\frac{b^2 \left(\sqrt{x}-1\right)^2}{\left(\sqrt{2-b}-\sqrt{2-b x}\right)^2}-\frac{b \left(b (-x)+2 b \sqrt{x}-4 \sqrt{2-b} \sqrt{2-b x}+2 \sqrt{2-b} \sqrt{x} \sqrt{2-b x}-3 b+2 x-8 \sqrt{x}+10\right)}{\left(\sqrt{2-b}-\sqrt{2-b x}\right)^2}+2\right)}{\left(\sqrt{2-b x}-\sqrt{2-b}\right) \left(b^3 x+2 b^2 x^{3/2}-b^2 x^2-5 b^2 x+\sqrt{2-b} b^2 \sqrt{x} \sqrt{2-b x}-2 b^2+6 b x-4 b \sqrt{x}-2 \sqrt{2-b} b x \sqrt{2-b x}-4 \sqrt{2-b} b \sqrt{2-b x}+2 \sqrt{2-b} b \sqrt{x} \sqrt{2-b x}+4 \sqrt{2-b} \sqrt{2-b x}+10 b-8\right)}","\frac{\sqrt{x}}{\sqrt{2-b x}}",1,"((-1/2*1/(-2 + b) + Sqrt[x]/(2*(-2 + b)))*(Sqrt[2 - b] - Sqrt[2 - b*x])^4*(2 + (b^2*(-1 + Sqrt[x])^2)/(Sqrt[2 - b] - Sqrt[2 - b*x])^2 - (b*(10 - 3*b - 8*Sqrt[x] + 2*b*Sqrt[x] + 2*x - b*x - 4*Sqrt[2 - b]*Sqrt[2 - b*x] + 2*Sqrt[2 - b]*Sqrt[x]*Sqrt[2 - b*x]))/(Sqrt[2 - b] - Sqrt[2 - b*x])^2))/((-Sqrt[2 - b] + Sqrt[2 - b*x])*(-8 + 10*b - 2*b^2 - 4*b*Sqrt[x] + 6*b*x - 5*b^2*x + b^3*x + 2*b^2*x^(3/2) - b^2*x^2 + 4*Sqrt[2 - b]*Sqrt[2 - b*x] - 4*Sqrt[2 - b]*b*Sqrt[2 - b*x] + 2*Sqrt[2 - b]*b*Sqrt[x]*Sqrt[2 - b*x] + Sqrt[2 - b]*b^2*Sqrt[x]*Sqrt[2 - b*x] - 2*Sqrt[2 - b]*b*x*Sqrt[2 - b*x]))","B",1
639,1,1149,34,4.3162388,"\int \frac{1}{x^{3/2} (2-b x)^{3/2}} \, dx","IntegrateAlgebraic[1/(x^(3/2)*(2 - b*x)^(3/2)),x]","\frac{\left(\frac{\sqrt{x}}{16 (b-2)}-\frac{1}{16 (b-2)}\right) \left(\sqrt{2-b}-\sqrt{2-b x}\right)^8 \left(\frac{b \left(\sqrt{x}-1\right)^2}{\left(\sqrt{2-b}-\sqrt{2-b x}\right)^2}-1\right) \left(\frac{b^3 \left(\sqrt{x}-1\right)^4}{\left(\sqrt{2-b}-\sqrt{2-b x}\right)^4}-\frac{2 b^2 \left(-3 x b+2 \sqrt{x} b-5 b+x-6 \sqrt{x}-8 \sqrt{2-b} \sqrt{2-b x}+2 \sqrt{2-b} \sqrt{x} \sqrt{2-b x}+17\right) \left(\sqrt{x}-1\right)^2}{\left(\sqrt{2-b}-\sqrt{2-b x}\right)^4}+\frac{4 \sqrt{2-b} \left(\sqrt{x}-1\right)}{\sqrt{2-b}-\sqrt{2-b x}}+\frac{b \left(4 \sqrt{2-b} b x^{3/2}-4 \sqrt{2-b} x^{3/2}-7 \sqrt{2-b} b x+24 \sqrt{2-b} x+b \sqrt{2-b x} x-12 \sqrt{2-b x} x+4 \sqrt{2-b} b \sqrt{x}-52 \sqrt{2-b} \sqrt{x}-8 b \sqrt{2-b x} \sqrt{x}+40 \sqrt{2-b x} \sqrt{x}-5 \sqrt{2-b} b+40 \sqrt{2-b}+11 b \sqrt{2-b x}-36 \sqrt{2-b x}\right)}{\left(\sqrt{2-b}-\sqrt{2-b x}\right)^3}-2\right)}{\left(\sqrt{2-b x}-\sqrt{2-b}\right) \left(2 x^2 b^5-8 x^2 b^4-8 x^{3/2} b^4-4 x b^4+2 \sqrt{2-b} x^{3/2} \sqrt{2-b x} b^4-x^4 b^3+4 x^{7/2} b^3-14 x^3 b^3+28 x^{5/2} b^3-25 x^2 b^3+56 x^{3/2} b^3+16 x b^3+16 \sqrt{x} b^3-6 \sqrt{2-b} x^{3/2} \sqrt{2-b x} b^3-8 \sqrt{2-b} x \sqrt{2-b x} b^3-2 \sqrt{2-b} \sqrt{x} \sqrt{2-b x} b^3+18 x^3 b^2-56 x^{5/2} b^2+108 x^2 b^2-168 x^{3/2} b^2+50 x b^2-112 \sqrt{x} b^2-4 \sqrt{2-b} x^3 \sqrt{2-b x} b^2+14 \sqrt{2-b} x^{5/2} \sqrt{2-b x} b^2-28 \sqrt{2-b} x^2 \sqrt{2-b x} b^2+40 \sqrt{2-b} x^{3/2} \sqrt{2-b x} b^2-8 \sqrt{2-b} x \sqrt{2-b x} b^2+34 \sqrt{2-b} \sqrt{x} \sqrt{2-b x} b^2-64 x^2 b+160 x^{3/2} b-160 x b+224 \sqrt{x} b+24 \sqrt{2-b} x^2 \sqrt{2-b x} b-64 \sqrt{2-b} x^{3/2} \sqrt{2-b x} b+72 \sqrt{2-b} x \sqrt{2-b x} b-96 \sqrt{2-b} \sqrt{x} \sqrt{2-b x} b+64 x-128 \sqrt{x}-32 \sqrt{2-b} x \sqrt{2-b x}+64 \sqrt{2-b} \sqrt{x} \sqrt{2-b x}\right)}","\frac{1}{\sqrt{x} \sqrt{2-b x}}-\frac{\sqrt{2-b x}}{\sqrt{x}}",1,"((-1/16*1/(-2 + b) + Sqrt[x]/(16*(-2 + b)))*(Sqrt[2 - b] - Sqrt[2 - b*x])^8*(-1 + (b*(-1 + Sqrt[x])^2)/(Sqrt[2 - b] - Sqrt[2 - b*x])^2)*(-2 + (b^3*(-1 + Sqrt[x])^4)/(Sqrt[2 - b] - Sqrt[2 - b*x])^4 + (4*Sqrt[2 - b]*(-1 + Sqrt[x]))/(Sqrt[2 - b] - Sqrt[2 - b*x]) - (2*b^2*(-1 + Sqrt[x])^2*(17 - 5*b - 6*Sqrt[x] + 2*b*Sqrt[x] + x - 3*b*x - 8*Sqrt[2 - b]*Sqrt[2 - b*x] + 2*Sqrt[2 - b]*Sqrt[x]*Sqrt[2 - b*x]))/(Sqrt[2 - b] - Sqrt[2 - b*x])^4 + (b*(40*Sqrt[2 - b] - 5*Sqrt[2 - b]*b - 52*Sqrt[2 - b]*Sqrt[x] + 4*Sqrt[2 - b]*b*Sqrt[x] + 24*Sqrt[2 - b]*x - 7*Sqrt[2 - b]*b*x - 4*Sqrt[2 - b]*x^(3/2) + 4*Sqrt[2 - b]*b*x^(3/2) - 36*Sqrt[2 - b*x] + 11*b*Sqrt[2 - b*x] + 40*Sqrt[x]*Sqrt[2 - b*x] - 8*b*Sqrt[x]*Sqrt[2 - b*x] - 12*x*Sqrt[2 - b*x] + b*x*Sqrt[2 - b*x]))/(Sqrt[2 - b] - Sqrt[2 - b*x])^3))/((-Sqrt[2 - b] + Sqrt[2 - b*x])*(-128*Sqrt[x] + 224*b*Sqrt[x] - 112*b^2*Sqrt[x] + 16*b^3*Sqrt[x] + 64*x - 160*b*x + 50*b^2*x + 16*b^3*x - 4*b^4*x + 160*b*x^(3/2) - 168*b^2*x^(3/2) + 56*b^3*x^(3/2) - 8*b^4*x^(3/2) - 64*b*x^2 + 108*b^2*x^2 - 25*b^3*x^2 - 8*b^4*x^2 + 2*b^5*x^2 - 56*b^2*x^(5/2) + 28*b^3*x^(5/2) + 18*b^2*x^3 - 14*b^3*x^3 + 4*b^3*x^(7/2) - b^3*x^4 + 64*Sqrt[2 - b]*Sqrt[x]*Sqrt[2 - b*x] - 96*Sqrt[2 - b]*b*Sqrt[x]*Sqrt[2 - b*x] + 34*Sqrt[2 - b]*b^2*Sqrt[x]*Sqrt[2 - b*x] - 2*Sqrt[2 - b]*b^3*Sqrt[x]*Sqrt[2 - b*x] - 32*Sqrt[2 - b]*x*Sqrt[2 - b*x] + 72*Sqrt[2 - b]*b*x*Sqrt[2 - b*x] - 8*Sqrt[2 - b]*b^2*x*Sqrt[2 - b*x] - 8*Sqrt[2 - b]*b^3*x*Sqrt[2 - b*x] - 64*Sqrt[2 - b]*b*x^(3/2)*Sqrt[2 - b*x] + 40*Sqrt[2 - b]*b^2*x^(3/2)*Sqrt[2 - b*x] - 6*Sqrt[2 - b]*b^3*x^(3/2)*Sqrt[2 - b*x] + 2*Sqrt[2 - b]*b^4*x^(3/2)*Sqrt[2 - b*x] + 24*Sqrt[2 - b]*b*x^2*Sqrt[2 - b*x] - 28*Sqrt[2 - b]*b^2*x^2*Sqrt[2 - b*x] + 14*Sqrt[2 - b]*b^2*x^(5/2)*Sqrt[2 - b*x] - 4*Sqrt[2 - b]*b^2*x^3*Sqrt[2 - b*x]))","B",1
640,1,4374,56,31.6264965,"\int \frac{1}{x^{5/2} (2-b x)^{3/2}} \, dx","IntegrateAlgebraic[1/(x^(5/2)*(2 - b*x)^(3/2)),x]","\text{Result too large to show}","-\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,"((-1/3072*1/(-2 + b) + Sqrt[x]/(3072*(-2 + b)))*(Sqrt[2 - b] - Sqrt[2 - b*x])^16*(6 + (3*b^8*(-1 + Sqrt[x])^14)/(Sqrt[2 - b] - Sqrt[2 - b*x])^14 - (256*Sqrt[2 - b]*(-1 + Sqrt[x])^5)/(Sqrt[2 - b] - Sqrt[2 - b*x])^5 + (96*Sqrt[2 - b]*(-1 + Sqrt[x])^3)/(Sqrt[2 - b] - Sqrt[2 - b*x])^3 + (16*(-1 + Sqrt[x])^2)/(Sqrt[2 - b] - Sqrt[2 - b*x])^2 - (24*Sqrt[2 - b]*(-1 + Sqrt[x]))/(Sqrt[2 - b] - Sqrt[2 - b*x]) - (b^7*(-1 + Sqrt[x])^12*(238 - 67*b - 48*Sqrt[x] + 18*b*Sqrt[x] + 6*x - 49*b*x - 116*Sqrt[2 - b]*Sqrt[2 - b*x] + 18*Sqrt[2 - b]*Sqrt[x]*Sqrt[2 - b*x]))/(Sqrt[2 - b] - Sqrt[2 - b*x])^14 + (b^6*(-1 + Sqrt[x])^10*(1194*Sqrt[2 - b] - 175*Sqrt[2 - b]*b - 620*Sqrt[2 - b]*Sqrt[x] + 84*Sqrt[2 - b]*b*Sqrt[x] + 178*Sqrt[2 - b]*x - 357*Sqrt[2 - b]*b*x - 24*Sqrt[2 - b]*x^(3/2) + 84*Sqrt[2 - b]*b*x^(3/2) - 1170*Sqrt[2 - b*x] + 441*b*Sqrt[2 - b*x] + 548*Sqrt[x]*Sqrt[2 - b*x] - 168*b*Sqrt[x]*Sqrt[2 - b*x] - 106*x*Sqrt[2 - b*x] + 91*b*x*Sqrt[2 - b*x]))/(Sqrt[2 - b] - Sqrt[2 - b*x])^13 + (b^5*(-1 + Sqrt[x])^8*(4120 - 2070*b + 129*b^2 + 816*Sqrt[x] - 344*b*Sqrt[x] + 14*b^2*Sqrt[x] - 504*x - 2000*b*x + 816*b^2*x + 160*x^(3/2) - 192*b*x^(3/2) + 42*b^2*x^(3/2) - 16*x^2 + 30*b*x^2 + 143*b^2*x^2 - 2068*Sqrt[2 - b]*Sqrt[2 - b*x] + 530*Sqrt[2 - b]*b*Sqrt[2 - b*x] - 376*Sqrt[2 - b]*Sqrt[x]*Sqrt[2 - b*x] + 42*Sqrt[2 - b]*b*Sqrt[x]*Sqrt[2 - b*x] + 204*Sqrt[2 - b]*x*Sqrt[2 - b*x] + 558*Sqrt[2 - b]*b*x*Sqrt[2 - b*x] - 48*Sqrt[2 - b]*x^(3/2)*Sqrt[2 - b*x] + 14*Sqrt[2 - b]*b*x^(3/2)*Sqrt[2 - b*x]))/(Sqrt[2 - b] - Sqrt[2 - b*x])^12 + (b^3*(-1 + Sqrt[x])^4*(10704*Sqrt[2 - b] - 134*Sqrt[2 - b]*b - 105*Sqrt[2 - b]*b^2 - 43680*Sqrt[2 - b]*Sqrt[x] + 6236*Sqrt[2 - b]*b*Sqrt[x] + 14*Sqrt[2 - b]*b^2*Sqrt[x] + 40240*Sqrt[2 - b]*x - 6304*Sqrt[2 - b]*b*x - 994*Sqrt[2 - b]*b^2*x - 16384*Sqrt[2 - b]*x^(3/2) + 12276*Sqrt[2 - b]*b*x^(3/2) + 84*Sqrt[2 - b]*b^2*x^(3/2) + 3680*Sqrt[2 - b]*x^2 - 7626*Sqrt[2 - b]*b*x^2 - 469*Sqrt[2 - b]*b^2*x^2 - 384*Sqrt[2 - b]*x^(5/2) + 1376*Sqrt[2 - b]*b*x^(5/2) + 14*Sqrt[2 - b]*b^2*x^(5/2) - 10320*Sqrt[2 - b*x] + 2274*b*Sqrt[2 - b*x] + 511*b^2*Sqrt[2 - b*x] + 41760*Sqrt[x]*Sqrt[2 - b*x] - 14916*b*Sqrt[x]*Sqrt[2 - b*x] - 56*b^2*Sqrt[x]*Sqrt[2 - b*x] - 36400*x*Sqrt[2 - b*x] + 10624*b*x*Sqrt[2 - b*x] + 966*b^2*x*Sqrt[2 - b*x] + 12544*x^(3/2)*Sqrt[2 - b*x] - 4972*b*x^(3/2)*Sqrt[2 - b*x] - 56*b^2*x^(3/2)*Sqrt[2 - b*x] - 1760*x^2*Sqrt[2 - b*x] + 1166*b*x^2*Sqrt[2 - b*x] + 91*b^2*x^2*Sqrt[2 - b*x]))/(Sqrt[2 - b] - Sqrt[2 - b*x])^9 + (b^4*(-1 + Sqrt[x])^6*(-27936*Sqrt[2 - b] + 8718*Sqrt[2 - b]*b - 375*Sqrt[2 - b]*b^2 + 32672*Sqrt[2 - b]*Sqrt[x] - 7268*Sqrt[2 - b]*b*Sqrt[x] + 232*Sqrt[2 - b]*b^2*Sqrt[x] - 17008*Sqrt[2 - b]*x + 15728*Sqrt[2 - b]*b*x - 2822*Sqrt[2 - b]*b^2*x + 3808*Sqrt[2 - b]*x^(3/2) - 12340*Sqrt[2 - b]*b*x^(3/2) + 1392*Sqrt[2 - b]*b^2*x^(3/2) - 784*Sqrt[2 - b]*x^2 + 4722*Sqrt[2 - b]*b*x^2 - 947*Sqrt[2 - b]*b^2*x^2 + 96*Sqrt[2 - b]*x^(5/2) - 408*Sqrt[2 - b]*b*x^(5/2) + 232*Sqrt[2 - b]*b^2*x^(5/2) + 27840*Sqrt[2 - b*x] - 15602*b*Sqrt[2 - b*x] + 1643*b^2*Sqrt[2 - b*x] - 32192*Sqrt[x]*Sqrt[2 - b*x] + 15012*b*Sqrt[x]*Sqrt[2 - b*x] - 928*b^2*Sqrt[x]*Sqrt[2 - b*x] + 16048*x*Sqrt[2 - b*x] - 12400*b*x*Sqrt[2 - b*x] + 2358*b^2*x*Sqrt[2 - b*x] - 2848*x^(3/2)*Sqrt[2 - b*x] + 5004*b*x^(3/2)*Sqrt[2 - b*x] - 928*b^2*x^(3/2)*Sqrt[2 - b*x] + 304*x^2*Sqrt[2 - b*x] - 1166*b*x^2*Sqrt[2 - b*x] + 143*b^2*x^2*Sqrt[2 - b*x]))/(Sqrt[2 - b] - Sqrt[2 - b*x])^11 - (b*(11008*Sqrt[2 - b] - 7040*Sqrt[2 - b]*b + 946*Sqrt[2 - b]*b^2 - 21*Sqrt[2 - b]*b^3 - 8960*Sqrt[2 - b]*Sqrt[x] + 7712*Sqrt[2 - b]*b*Sqrt[x] - 1004*Sqrt[2 - b]*b^2*Sqrt[x] + 18*Sqrt[2 - b]*b^3*Sqrt[x] - 7808*Sqrt[2 - b]*x - 7696*Sqrt[2 - b]*b*x + 4430*Sqrt[2 - b]*b^2*x - 333*Sqrt[2 - b]*b^3*x + 5632*Sqrt[2 - b]*x^(3/2) + 4384*Sqrt[2 - b]*b*x^(3/2) - 5192*Sqrt[2 - b]*b^2*x^(3/2) + 270*Sqrt[2 - b]*b^3*x^(3/2) + 7808*Sqrt[2 - b]*x^2 + 4992*Sqrt[2 - b]*b*x^2 + 3486*Sqrt[2 - b]*b^2*x^2 - 375*Sqrt[2 - b]*b^3*x^2 - 9216*Sqrt[2 - b]*x^(5/2) - 7104*Sqrt[2 - b]*b*x^(5/2) - 2140*Sqrt[2 - b]*b^2*x^(5/2) + 270*Sqrt[2 - b]*b^3*x^(5/2) + 3584*Sqrt[2 - b]*x^3 + 2832*Sqrt[2 - b]*b*x^3 + 674*Sqrt[2 - b]*b^2*x^3 - 39*Sqrt[2 - b]*b^3*x^3 - 512*Sqrt[2 - b]*x^(7/2) - 384*Sqrt[2 - b]*b*x^(7/2) - 48*Sqrt[2 - b]*b^2*x^(7/2) + 18*Sqrt[2 - b]*b^3*x^(7/2) - 10496*Sqrt[2 - b*x] + 9664*b*Sqrt[2 - b*x] - 2426*b^2*Sqrt[2 - b*x] + 129*b^3*Sqrt[2 - b*x] + 5376*Sqrt[x]*Sqrt[2 - b*x] - 9056*b*Sqrt[x]*Sqrt[2 - b*x] + 3004*b^2*Sqrt[x]*Sqrt[2 - b*x] - 108*b^3*Sqrt[x]*Sqrt[2 - b*x] + 18560*x*Sqrt[2 - b*x] + 432*b*x*Sqrt[2 - b*x] - 4902*b^2*x*Sqrt[2 - b*x] + 465*b^3*x*Sqrt[2 - b*x] - 23552*x^(3/2)*Sqrt[2 - b*x] + 2848*b*x^(3/2)*Sqrt[2 - b*x] + 4760*b^2*x^(3/2)*Sqrt[2 - b*x] - 360*b^3*x^(3/2)*Sqrt[2 - b*x] + 10112*x^2*Sqrt[2 - b*x] - 2880*b*x^2*Sqrt[2 - b*x] - 2102*b^2*x^2*Sqrt[2 - b*x] + 171*b^3*x^2*Sqrt[2 - b*x] - 1536*x^(5/2)*Sqrt[2 - b*x] + 1600*b*x^(5/2)*Sqrt[2 - b*x] + 620*b^2*x^(5/2)*Sqrt[2 - b*x] - 108*b^3*x^(5/2)*Sqrt[2 - b*x] - 304*b*x^3*Sqrt[2 - b*x] - 106*b^2*x^3*Sqrt[2 - b*x] + 3*b^3*x^3*Sqrt[2 - b*x]))/(Sqrt[2 - b] - Sqrt[2 - b*x])^7 + (b^2*(-1 + Sqrt[x])^2*(17280*Sqrt[2 - b] - 23152*Sqrt[2 - b]*b + 4998*Sqrt[2 - b]*b^2 - 133*Sqrt[2 - b]*b^3 + 90112*Sqrt[2 - b]*Sqrt[x] - 14496*Sqrt[2 - b]*b*Sqrt[x] - 1860*Sqrt[2 - b]*b^2*Sqrt[x] + 84*Sqrt[2 - b]*b^3*Sqrt[x] - 159872*Sqrt[2 - b]*x + 13920*Sqrt[2 - b]*b*x + 17714*Sqrt[2 - b]*b^2*x - 2289*Sqrt[2 - b]*b^3*x + 103936*Sqrt[2 - b]*x^(3/2) - 52064*Sqrt[2 - b]*b*x^(3/2) - 2928*Sqrt[2 - b]*b^2*x^(3/2) + 1260*Sqrt[2 - b]*b^3*x^(3/2) - 26880*Sqrt[2 - b]*x^2 + 68144*Sqrt[2 - b]*b*x^2 + 1210*Sqrt[2 - b]*b^2*x^2 - 2975*Sqrt[2 - b]*b^3*x^2 - 1024*Sqrt[2 - b]*x^(5/2) - 39616*Sqrt[2 - b]*b*x^(5/2) + 348*Sqrt[2 - b]*b^2*x^(5/2) + 1260*Sqrt[2 - b]*b^3*x^(5/2) + 1792*Sqrt[2 - b]*x^3 + 10720*Sqrt[2 - b]*b*x^3 - 1074*Sqrt[2 - b]*b^2*x^3 - 427*Sqrt[2 - b]*b^3*x^3 - 256*Sqrt[2 - b]*x^(7/2) - 1088*Sqrt[2 - b]*b*x^(7/2) + 408*Sqrt[2 - b]*b^2*x^(7/2) + 84*Sqrt[2 - b]*b^3*x^(7/2) - 17024*Sqrt[2 - b*x] + 27408*b*Sqrt[2 - b*x] - 10390*b^2*Sqrt[2 - b*x] + 847*b^3*Sqrt[2 - b*x] - 91904*Sqrt[x]*Sqrt[2 - b*x] + 37472*b*Sqrt[x]*Sqrt[2 - b*x] + 1788*b^2*Sqrt[x]*Sqrt[2 - b*x] - 504*b^3*Sqrt[x]*Sqrt[2 - b*x] + 165248*x*Sqrt[2 - b*x] - 59488*b*x*Sqrt[2 - b*x] - 13634*b^2*x*Sqrt[2 - b*x] + 3395*b^3*x*Sqrt[2 - b*x] - 112896*x^(3/2)*Sqrt[2 - b*x] + 57312*b*x^(3/2)*Sqrt[2 - b*x] + 2808*b^2*x^(3/2)*Sqrt[2 - b*x] - 1680*b^3*x^(3/2)*Sqrt[2 - b*x] + 35840*x^2*Sqrt[2 - b*x] - 35792*b*x^2*Sqrt[2 - b*x] + 1206*b^2*x^2*Sqrt[2 - b*x] + 1533*b^3*x^2*Sqrt[2 - b*x] - 4352*x^(5/2)*Sqrt[2 - b*x] + 12480*b*x^(5/2)*Sqrt[2 - b*x] - 564*b^2*x^(5/2)*Sqrt[2 - b*x] - 504*b^3*x^(5/2)*Sqrt[2 - b*x] - 1760*b*x^3*Sqrt[2 - b*x] - 30*b^2*x^3*Sqrt[2 - b*x] + 49*b^3*x^3*Sqrt[2 - b*x]))/(Sqrt[2 - b] - Sqrt[2 - b*x])^9))/((-Sqrt[2 - b] + Sqrt[2 - b*x])*(8*Sqrt[x] - 4*b*Sqrt[x] - 4*x + b*x + b^2*x - 2*b*x^(3/2) + b*x^2 - 4*Sqrt[2 - b]*Sqrt[x]*Sqrt[2 - b*x] + Sqrt[2 - b]*b*Sqrt[x]*Sqrt[2 - b*x] + 2*Sqrt[2 - b]*x*Sqrt[2 - b*x])^3*(-8 + 10*b - 2*b^2 - 4*b*Sqrt[x] + 6*b*x - 5*b^2*x + b^3*x + 2*b^2*x^(3/2) - b^2*x^2 + 4*Sqrt[2 - b]*Sqrt[2 - b*x] - 4*Sqrt[2 - b]*b*Sqrt[2 - b*x] + 2*Sqrt[2 - b]*b*Sqrt[x]*Sqrt[2 - b*x] + Sqrt[2 - b]*b^2*Sqrt[x]*Sqrt[2 - b*x] - 2*Sqrt[2 - b]*b*x*Sqrt[2 - b*x]))","B",1
641,1,2567,89,16.7174034,"\int \frac{x^{5/2}}{(2-b x)^{5/2}} \, dx","IntegrateAlgebraic[x^(5/2)/(2 - b*x)^(5/2),x]","\text{Result too large to show}","\frac{10 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{7/2}}-\frac{5 \sqrt{x} \sqrt{2-b x}}{b^3}-\frac{10 x^{3/2}}{3 b^2 \sqrt{2-b x}}+\frac{2 x^{5/2}}{3 b (2-b x)^{3/2}}",1,"((-3 + b - Sqrt[x] + b*Sqrt[x] + 2*Sqrt[2 - b]*Sqrt[2 - b*x])*((-2*Sqrt[2 - b])/b^3 + (2*Sqrt[2 - b*x])/b^3))/(-2 + b*Sqrt[x] + Sqrt[2 - b]*Sqrt[2 - b*x]) + ((Sqrt[2 - b] - Sqrt[2 - b*x])^3*(2/b^3 + (2*Sqrt[x])/b^3 - (2*Sqrt[x])/b^2 - (2*Sqrt[2 - b]*Sqrt[2 - b*x])/b^3))/(-2 + b*Sqrt[x] + Sqrt[2 - b]*Sqrt[2 - b*x])^2 + ((Sqrt[2 - b] - Sqrt[2 - b*x])^5*(1872/(-2 + b)^4 + 1664/(3*(-2 + b)^4*b^3) - 10432/(3*(-2 + b)^4*b^2) - 800/((-2 + b)^4*b) - (304*b)/(-2 + b)^4 - (16*b^2)/(-2 + b)^4 - (3760*Sqrt[x])/(3*(-2 + b)^4) - (128*Sqrt[x])/(3*(-2 + b)^4*b^3) + (576*Sqrt[x])/((-2 + b)^4*b^2) + (3808*Sqrt[x])/(3*(-2 + b)^4*b) + (112*b*Sqrt[x])/(-2 + b)^4 + (64*b^2*Sqrt[x])/(-2 + b)^4 + (784*x)/(-2 + b)^4 - (1088*x)/(3*(-2 + b)^4*b^2) + (1760*x)/(3*(-2 + b)^4*b) - (1336*b*x)/(3*(-2 + b)^4) - (24*b^2*x)/(-2 + b)^4 - (208*x^(3/2))/(-2 + b)^4 + (64*x^(3/2))/(3*(-2 + b)^4*b^2) + (160*x^(3/2))/(3*(-2 + b)^4*b) + (72*b*x^(3/2))/(-2 + b)^4 + (8*b^2*x^(3/2))/(-2 + b)^4 - (624*Sqrt[2 - b]*Sqrt[2 - b*x])/(-2 + b)^4 - (832*Sqrt[2 - b]*Sqrt[2 - b*x])/(3*(-2 + b)^4*b^3) + (1664*Sqrt[2 - b]*Sqrt[2 - b*x])/((-2 + b)^4*b^2) + (2288*Sqrt[2 - b]*Sqrt[2 - b*x])/(3*(-2 + b)^4*b) + (16*Sqrt[2 - b]*b*Sqrt[2 - b*x])/(-2 + b)^4 + (872*Sqrt[2 - b]*Sqrt[x]*Sqrt[2 - b*x])/(3*(-2 + b)^4) + (64*Sqrt[2 - b]*Sqrt[x]*Sqrt[2 - b*x])/(3*(-2 + b)^4*b^3) - (800*Sqrt[2 - b]*Sqrt[x]*Sqrt[2 - b*x])/(3*(-2 + b)^4*b^2) - (1648*Sqrt[2 - b]*Sqrt[x]*Sqrt[2 - b*x])/(3*(-2 + b)^4*b) + (24*Sqrt[2 - b]*b*Sqrt[x]*Sqrt[2 - b*x])/(-2 + b)^4 - (168*Sqrt[2 - b]*x*Sqrt[2 - b*x])/(-2 + b)^4 + (96*Sqrt[2 - b]*x*Sqrt[2 - b*x])/((-2 + b)^4*b^2) - (64*Sqrt[2 - b]*x*Sqrt[2 - b*x])/(3*(-2 + b)^4*b) - (8*Sqrt[2 - b]*b*x*Sqrt[2 - b*x])/(-2 + b)^4))/(-8 + 10*b - 2*b^2 - 4*b*Sqrt[x] + 6*b*x - 5*b^2*x + b^3*x + 2*b^2*x^(3/2) - b^2*x^2 + 4*Sqrt[2 - b]*Sqrt[2 - b*x] - 4*Sqrt[2 - b]*b*Sqrt[2 - b*x] + 2*Sqrt[2 - b]*b*Sqrt[x]*Sqrt[2 - b*x] + Sqrt[2 - b]*b^2*Sqrt[x]*Sqrt[2 - b*x] - 2*Sqrt[2 - b]*b*x*Sqrt[2 - b*x])^2 + ((Sqrt[2 - b] - Sqrt[2 - b*x])^9*(1472/(3*(-2 + b)^4) - 768/((-2 + b)^4*b^2) + 1664/(3*(-2 + b)^4*b) - (800*b)/(3*(-2 + b)^4) - (32*b^2)/(3*(-2 + b)^4) - (704*Sqrt[x])/(-2 + b)^4 + (256*Sqrt[x])/(3*(-2 + b)^4*b^2) - (896*Sqrt[x])/(3*(-2 + b)^4*b) + (288*b*Sqrt[x])/(-2 + b)^4 + (64*b^2*Sqrt[x])/(-2 + b)^4 + (320*x)/(-2 + b)^4 + (1408*x)/(3*(-2 + b)^4*b) - (736*b*x)/(3*(-2 + b)^4) - (16*b^2*x)/(-2 + b)^4 - (320*x^(3/2))/(3*(-2 + b)^4) - (128*x^(3/2))/(3*(-2 + b)^4*b) + (160*b*x^(3/2))/(3*(-2 + b)^4) + (16*b^2*x^(3/2))/(3*(-2 + b)^4) - (736*Sqrt[2 - b]*Sqrt[2 - b*x])/(3*(-2 + b)^4) + (384*Sqrt[2 - b]*Sqrt[2 - b*x])/((-2 + b)^4*b^2) - (512*Sqrt[2 - b]*Sqrt[2 - b*x])/(3*(-2 + b)^4*b) + (32*Sqrt[2 - b]*b*Sqrt[2 - b*x])/(-2 + b)^4 + (800*Sqrt[2 - b]*Sqrt[x]*Sqrt[2 - b*x])/(3*(-2 + b)^4) - (128*Sqrt[2 - b]*Sqrt[x]*Sqrt[2 - b*x])/(3*(-2 + b)^4*b^2) + (320*Sqrt[2 - b]*Sqrt[x]*Sqrt[2 - b*x])/(3*(-2 + b)^4*b) + (16*Sqrt[2 - b]*b*Sqrt[x]*Sqrt[2 - b*x])/(-2 + b)^4 - (320*Sqrt[2 - b]*x*Sqrt[2 - b*x])/(3*(-2 + b)^4) - (320*Sqrt[2 - b]*x*Sqrt[2 - b*x])/(3*(-2 + b)^4*b) - (16*Sqrt[2 - b]*b*x*Sqrt[2 - b*x])/(3*(-2 + b)^4)))/(-8 + 10*b - 2*b^2 - 4*b*Sqrt[x] + 6*b*x - 5*b^2*x + b^3*x + 2*b^2*x^(3/2) - b^2*x^2 + 4*Sqrt[2 - b]*Sqrt[2 - b*x] - 4*Sqrt[2 - b]*b*Sqrt[2 - b*x] + 2*Sqrt[2 - b]*b*Sqrt[x]*Sqrt[2 - b*x] + Sqrt[2 - b]*b^2*Sqrt[x]*Sqrt[2 - b*x] - 2*Sqrt[2 - b]*b*x*Sqrt[2 - b*x])^3 + (((-4*Sqrt[2 - b])/(3*(-2 + b)^3*b^3) + (4*Sqrt[2 - b*x])/(3*(-2 + b)^3*b^3))*(928 + 192*b - 328*b^2 - 36*b^3 + 18*b^4 - 160*Sqrt[x] + 168*b*Sqrt[x] - 248*b^2*Sqrt[x] + 174*b^3*Sqrt[x] - 36*b^4*Sqrt[x] - 424*b*x + 44*b^2*x + 30*b^3*x + 27*b^4*x + 64*b*x^(3/2) - 44*b^2*x^(3/2) + 24*b^3*x^(3/2) - 9*b^4*x^(3/2) - 464*Sqrt[2 - b]*Sqrt[2 - b*x] - 224*Sqrt[2 - b]*b*Sqrt[2 - b*x] + 120*Sqrt[2 - b]*b^2*Sqrt[2 - b*x] + 18*Sqrt[2 - b]*b^3*Sqrt[2 - b*x] + 80*Sqrt[2 - b]*Sqrt[x]*Sqrt[2 - b*x] - 28*Sqrt[2 - b]*b*Sqrt[x]*Sqrt[2 - b*x] + 48*Sqrt[2 - b]*b^2*Sqrt[x]*Sqrt[2 - b*x] - 27*Sqrt[2 - b]*b^3*Sqrt[x]*Sqrt[2 - b*x] + 60*Sqrt[2 - b]*b*x*Sqrt[2 - b*x] + 24*Sqrt[2 - b]*b^2*x*Sqrt[2 - b*x] + 9*Sqrt[2 - b]*b^3*x*Sqrt[2 - b*x]))/(-8 + 10*b - 2*b^2 - 4*b*Sqrt[x] + 6*b*x - 5*b^2*x + b^3*x + 2*b^2*x^(3/2) - b^2*x^2 + 4*Sqrt[2 - b]*Sqrt[2 - b*x] - 4*Sqrt[2 - b]*b*Sqrt[2 - b*x] + 2*Sqrt[2 - b]*b*Sqrt[x]*Sqrt[2 - b*x] + Sqrt[2 - b]*b^2*Sqrt[x]*Sqrt[2 - b*x] - 2*Sqrt[2 - b]*b*x*Sqrt[2 - b*x]) + (20*ArcTan[(Sqrt[2 - b]/Sqrt[b] - Sqrt[2 - b*x]/Sqrt[b])/(-1 + Sqrt[x])])/b^(7/2)","B",1
642,1,2126,67,4.1398051,"\int \frac{x^{3/2}}{(2-b x)^{5/2}} \, dx","IntegrateAlgebraic[x^(3/2)/(2 - b*x)^(5/2),x]","\text{Result too large to show}","\frac{2 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{5/2}}-\frac{2 \sqrt{x}}{b^2 \sqrt{2-b x}}+\frac{2 x^{3/2}}{3 b (2-b x)^{3/2}}",1,"(4*(-6144 + 28672*b - 55072*b^2 + 55984*b^3 - 32176*b^4 + 10288*b^5 - 1648*b^6 + 96*b^7)*Sqrt[2 - b*x] + 4*(6144 - 38400*b + 88032*b^2 - 97896*b^3 + 55992*b^4 - 15114*b^5 + 1050*b^6 + 210*b^7 - 18*b^8)*Sqrt[x]*Sqrt[2 - b*x] + 4*(21504*b - 85568*b^2 + 130976*b^3 - 98408*b^4 + 38564*b^5 - 7904*b^6 + 908*b^7 - 72*b^8)*x*Sqrt[2 - b*x] + 4*(-11776*b + 68032*b^2 - 134584*b^3 + 124036*b^4 - 57934*b^5 + 13075*b^6 - 981*b^7 - 78*b^8 + 12*b^9)*x^(3/2)*Sqrt[2 - b*x] + 4*(-23712*b^2 + 79536*b^3 - 98016*b^4 + 56148*b^5 - 14622*b^6 + 1152*b^7 + 72*b^8)*x^2*Sqrt[2 - b*x] + 4*(8288*b^2 - 42200*b^3 + 68300*b^4 - 48830*b^5 + 16067*b^6 - 2093*b^7 + 78*b^8 - 12*b^9)*x^(5/2)*Sqrt[2 - b*x] + 4*(10752*b^3 - 28552*b^4 + 26560*b^5 - 10438*b^6 + 1476*b^7)*x^3*Sqrt[2 - b*x] + 4*(-2568*b^3 + 10428*b^4 - 12474*b^5 + 6057*b^6 - 1089*b^7 + 18*b^8)*x^(7/2)*Sqrt[2 - b*x] + 4*(-1920*b^4 + 3524*b^5 - 2162*b^6 + 440*b^7)*x^4*Sqrt[2 - b*x] + 4*(316*b^4 - 808*b^5 + 607*b^6 - 141*b^7)*x^(9/2)*Sqrt[2 - b*x] + 4*(84*b^5 - 90*b^6 + 24*b^7)*x^5*Sqrt[2 - b*x] + 4*(-8*b^5 + 8*b^6 - 2*b^7)*x^(11/2)*Sqrt[2 - b*x] + Sqrt[2 - b]*(4*(6144 - 27136*b + 48480*b^2 - 44664*b^3 + 22328*b^4 - 5784*b^5 + 648*b^6 - 16*b^7) + 4*(-6144 + 36864*b - 79008*b^2 + 79248*b^3 - 38376*b^4 + 7464*b^5 + 72*b^6 - 120*b^7)*Sqrt[x] + 4*(-23040*b + 86976*b^2 - 123720*b^3 + 84012*b^4 - 28848*b^5 + 5118*b^6 - 528*b^7 + 30*b^8)*x + 4*(13312*b - 74304*b^2 + 138432*b^3 - 116120*b^4 + 46680*b^5 - 7908*b^6 + 116*b^7 + 72*b^8)*x^(3/2) + 4*(28896*b^2 - 92808*b^3 + 106740*b^4 - 54990*b^5 + 12204*b^6 - 873*b^7 + 54*b^8 - 12*b^9)*x^2 + 4*(-11040*b^2 + 55248*b^3 - 85728*b^4 + 56988*b^5 - 16842*b^6 + 1944*b^7 - 72*b^8)*x^(5/2) + 4*(-16056*b^3 + 41972*b^4 - 37410*b^5 + 13677*b^6 - 1645*b^7 - 66*b^8 + 12*b^9)*x^3 + 4*(4320*b^3 - 18072*b^4 + 21648*b^5 - 10266*b^6 + 1692*b^7)*x^(7/2) + 4*(4020*b^4 - 7770*b^5 + 4797*b^6 - 909*b^7 - 18*b^8)*x^4 + 4*(-776*b^4 + 2340*b^5 - 1854*b^6 + 440*b^7)*x^(9/2) + 4*(-366*b^5 + 417*b^6 - 123*b^7)*x^5 + 4*(48*b^5 - 66*b^6 + 24*b^7)*x^(11/2) + 4*(3*b^6 - 2*b^7)*x^6))/(3*(-2 + b)^2*b^2*(-2048 + 7680*b - 11040*b^2 + 7528*b^3 - 2424*b^4 + 312*b^5 - 8*b^6) + 18*(-2 + b)^2*b^8*x^(11/2) - 3*(-2 + b)^2*b^8*x^6 + 3*Sqrt[2 - b]*(-2 + b)^2*b^2*(1024 - 3584*b + 4656*b^2 - 2704*b^3 + 656*b^4 - 48*b^5)*Sqrt[2 - b*x] + x^5*(3*(-2 + b)^2*b^2*(42*b^5 - 39*b^6 + 3*b^7) - 18*Sqrt[2 - b]*(-2 + b)^2*b^7*Sqrt[2 - b*x]) + x^4*(3*(-2 + b)^2*b^2*(-420*b^4 + 810*b^5 - 297*b^6 + 24*b^7 - 6*b^8) + 3*Sqrt[2 - b]*(-2 + b)^2*b^2*(100*b^4 - 128*b^5)*Sqrt[2 - b*x]) + x^(9/2)*(3*(-2 + b)^2*b^2*(-180*b^5 + 92*b^6) + 3*Sqrt[2 - b]*(-2 + b)^2*b^2*(30*b^5 + 3*b^6)*Sqrt[2 - b*x]) + Sqrt[x]*(3*(-2 + b)^2*b^2*(-3072*b + 7296*b^2 - 5040*b^3 + 384*b^4 + 528*b^5 - 96*b^6) + 3*Sqrt[2 - b]*(-2 + b)^2*b^2*(1536*b - 3264*b^2 + 1752*b^3 + 156*b^4 - 192*b^5 + 12*b^6)*Sqrt[2 - b*x]) + x^3*(3*(-2 + b)^2*b^2*(1848*b^3 - 4932*b^4 + 3282*b^5 - 749*b^6 + 87*b^7 - 24*b^8 + 4*b^9) + 3*Sqrt[2 - b]*(-2 + b)^2*b^2*(-584*b^3 + 1288*b^4 - 486*b^5 + 36*b^6)*Sqrt[2 - b*x]) + x*(3*(-2 + b)^2*b^2*(4608*b - 16320*b^2 + 19560*b^3 - 10140*b^4 + 2676*b^5 - 408*b^6 + 24*b^7) + 3*Sqrt[2 - b]*(-2 + b)^2*b^2*(-2048*b + 6688*b^2 - 6792*b^3 + 2624*b^4 - 544*b^5 + 72*b^6)*Sqrt[2 - b*x]) + x^2*(3*(-2 + b)^2*b^2*(-4128*b^2 + 13176*b^3 - 12420*b^4 + 4590*b^5 - 882*b^6 + 174*b^7 - 18*b^8) + 3*Sqrt[2 - b]*(-2 + b)^2*b^2*(1584*b^2 - 4512*b^3 + 3204*b^4 - 708*b^5 + 108*b^6 - 24*b^7)*Sqrt[2 - b*x]) + x^(3/2)*(3*(-2 + b)^2*b^2*(5760*b^2 - 11488*b^3 + 6120*b^4 - 240*b^5 - 528*b^6 + 96*b^7) + 3*Sqrt[2 - b]*(-2 + b)^2*b^2*(-2496*b^2 + 4208*b^3 - 1456*b^4 - 180*b^5 + 136*b^6 - 14*b^7)*Sqrt[2 - b*x]) + x^(7/2)*(3*(-2 + b)^2*b^2*(1320*b^4 - 1416*b^5 + 270*b^6 + 36*b^7) + 3*Sqrt[2 - b]*(-2 + b)^2*b^2*(-360*b^4 + 216*b^5 + 18*b^6 - 6*b^7)*Sqrt[2 - b*x]) + x^(5/2)*(3*(-2 + b)^2*b^2*(-4080*b^3 + 6384*b^4 - 2340*b^5 - 48*b^6 + 132*b^7 - 24*b^8) + 3*Sqrt[2 - b]*(-2 + b)^2*b^2*(1464*b^3 - 1732*b^4 + 254*b^5 + 63*b^6 - 20*b^7 + 4*b^8)*Sqrt[2 - b*x])) + (4*ArcTan[(Sqrt[2 - b]/Sqrt[b] - Sqrt[2 - b*x]/Sqrt[b])/(-1 + Sqrt[x])])/b^(5/2)","B",1
643,1,4559,19,11.8911767,"\int \frac{\sqrt{x}}{(2-b x)^{5/2}} \, dx","IntegrateAlgebraic[Sqrt[x]/(2 - b*x)^(5/2),x]","\text{Result too large to show}","\frac{x^{3/2}}{3 (2-b x)^{3/2}}",1,"((-1/384*1/(-2 + b)^2 + Sqrt[x]/(384*(-2 + b)^2))*(Sqrt[2 - b] - Sqrt[2 - b*x])^12*((-3*b^8*(-1 + Sqrt[x])^10)/(Sqrt[2 - b] - Sqrt[2 - b*x])^10 + (3*b^7*(-1 + Sqrt[x])^8*(-2 + b - 16*Sqrt[x] + 2*b*Sqrt[x] + 6*x + 3*b*x + 4*Sqrt[2 - b]*Sqrt[2 - b*x] + 2*Sqrt[2 - b]*Sqrt[x]*Sqrt[2 - b*x]))/(Sqrt[2 - b] - Sqrt[2 - b*x])^10 + (8*(-8 - 3*b + 4*Sqrt[x] + 6*b*Sqrt[x] - 8*x + 3*b*x + 6*Sqrt[2 - b]*Sqrt[x]*Sqrt[2 - b*x]))/(Sqrt[2 - b] - Sqrt[2 - b*x])^2 - (6*b^6*(-1 + Sqrt[x])^6*(-58 + 31*b - 3*b^2 + 100*Sqrt[x] - 52*b*Sqrt[x] + 4*b^2*Sqrt[x] + 12*x + 20*b*x - 6*b^2*x - 28*x^(3/2) - 40*b*x^(3/2) + 12*b^2*x^(3/2) + 6*x^2 + 9*b*x^2 + b^2*x^2 + 32*Sqrt[2 - b]*Sqrt[2 - b*x] - 8*Sqrt[2 - b]*b*Sqrt[2 - b*x] - 62*Sqrt[2 - b]*Sqrt[x]*Sqrt[2 - b*x] + 12*Sqrt[2 - b]*b*Sqrt[x]*Sqrt[2 - b*x] + 12*Sqrt[2 - b]*x*Sqrt[2 - b*x] + 2*Sqrt[2 - b]*x^(3/2)*Sqrt[2 - b*x] + 4*Sqrt[2 - b]*b*x^(3/2)*Sqrt[2 - b*x]))/(Sqrt[2 - b] - Sqrt[2 - b*x])^10 + (4*b*(232 - 82*b + 3*b^2 - 80*Sqrt[x] - 64*b*Sqrt[x] + 6*b^2*Sqrt[x] + 280*x - 104*b*x + 36*b^2*x - 192*x^(3/2) - 40*b*x^(3/2) + 18*b^2*x^(3/2) + 48*x^2 + 2*b*x^2 + 9*b^2*x^2 - 92*Sqrt[2 - b]*Sqrt[2 - b*x] + 18*Sqrt[2 - b]*b*Sqrt[2 - b*x] - 56*Sqrt[2 - b]*Sqrt[x]*Sqrt[2 - b*x] + 18*Sqrt[2 - b]*b*Sqrt[x]*Sqrt[2 - b*x] + 4*Sqrt[2 - b]*x*Sqrt[2 - b*x] + 30*Sqrt[2 - b]*b*x*Sqrt[2 - b*x] + 6*Sqrt[2 - b]*b*x^(3/2)*Sqrt[2 - b*x]))/(Sqrt[2 - b] - Sqrt[2 - b*x])^4 - (2*b^2*(2272 - 1832*b + 434*b^2 - 15*b^3 - 800*Sqrt[x] - 80*b*Sqrt[x] - 64*b^2*Sqrt[x] + 6*b^3*Sqrt[x] + 3808*x - 2056*b*x + 1118*b^2*x - 195*b^3*x - 4800*x^(3/2) + 448*b*x^(3/2) + 192*b^2*x^(3/2) + 60*b^3*x^(3/2) + 2400*x^2 - 344*b*x^2 + 62*b^2*x^2 - 165*b^3*x^2 - 672*x^(5/2) + 528*b*x^(5/2) + 32*b^2*x^(5/2) + 30*b^3*x^(5/2) + 96*x^3 - 120*b*x^3 - 46*b^2*x^3 - 9*b^3*x^3 - 1088*Sqrt[2 - b]*Sqrt[2 - b*x] + 632*Sqrt[2 - b]*b*Sqrt[2 - b*x] - 84*Sqrt[2 - b]*b^2*Sqrt[2 - b*x] + 112*Sqrt[2 - b]*Sqrt[x]*Sqrt[2 - b*x] + 128*Sqrt[2 - b]*b*Sqrt[x]*Sqrt[2 - b*x] + 30*Sqrt[2 - b]*b^2*Sqrt[x]*Sqrt[2 - b*x] - 1184*Sqrt[2 - b]*x*Sqrt[2 - b*x] + 352*Sqrt[2 - b]*b*x*Sqrt[2 - b*x] - 240*Sqrt[2 - b]*b^2*x*Sqrt[2 - b*x] + 1440*Sqrt[2 - b]*x^(3/2)*Sqrt[2 - b*x] + 224*Sqrt[2 - b]*b*x^(3/2)*Sqrt[2 - b*x] + 60*Sqrt[2 - b]*b^2*x^(3/2)*Sqrt[2 - b*x] - 480*Sqrt[2 - b]*x^2*Sqrt[2 - b*x] - 184*Sqrt[2 - b]*b*x^2*Sqrt[2 - b*x] - 60*Sqrt[2 - b]*b^2*x^2*Sqrt[2 - b*x] + 48*Sqrt[2 - b]*x^(5/2)*Sqrt[2 - b*x] + 6*Sqrt[2 - b]*b^2*x^(5/2)*Sqrt[2 - b*x]))/(Sqrt[2 - b] - Sqrt[2 - b*x])^6 + (2*b^5*(-1 + Sqrt[x])^4*(3068 - 2582*b + 570*b^2 - 21*b^3 - 1520*Sqrt[x] + 1628*b*Sqrt[x] - 432*b^2*Sqrt[x] + 18*b^3*Sqrt[x] - 1740*x - 1286*b*x + 1422*b^2*x - 225*b^3*x + 1120*x^(3/2) + 856*b*x^(3/2) - 1056*b^2*x^(3/2) + 180*b^3*x^(3/2) - 124*x^2 + 526*b*x^2 + 198*b^2*x^2 - 135*b^3*x^2 - 48*x^(5/2) - 340*b*x^(5/2) - 144*b^2*x^(5/2) + 90*b^3*x^(5/2) + 12*x^3 + 46*b*x^3 + 18*b^2*x^3 - 3*b^3*x^3 - 1528*Sqrt[2 - b]*Sqrt[2 - b*x] + 912*Sqrt[2 - b]*b*Sqrt[2 - b*x] - 108*Sqrt[2 - b]*b^2*Sqrt[2 - b*x] + 724*Sqrt[2 - b]*Sqrt[x]*Sqrt[2 - b*x] - 648*Sqrt[2 - b]*b*Sqrt[x]*Sqrt[2 - b*x] + 90*Sqrt[2 - b]*b^2*Sqrt[x]*Sqrt[2 - b*x] + 960*Sqrt[2 - b]*x*Sqrt[2 - b*x] + 528*Sqrt[2 - b]*b*x*Sqrt[2 - b*x] - 240*Sqrt[2 - b]*b^2*x*Sqrt[2 - b*x] - 680*Sqrt[2 - b]*x^(3/2)*Sqrt[2 - b*x] - 432*Sqrt[2 - b]*b*x^(3/2)*Sqrt[2 - b*x] + 180*Sqrt[2 - b]*b^2*x^(3/2)*Sqrt[2 - b*x] + 152*Sqrt[2 - b]*x^2*Sqrt[2 - b*x] - 36*Sqrt[2 - b]*b^2*x^2*Sqrt[2 - b*x] - 12*Sqrt[2 - b]*x^(5/2)*Sqrt[2 - b*x] + 24*Sqrt[2 - b]*b*x^(5/2)*Sqrt[2 - b*x] + 18*Sqrt[2 - b]*b^2*x^(5/2)*Sqrt[2 - b*x]))/(Sqrt[2 - b] - Sqrt[2 - b*x])^10 + (b^4*(-1 + Sqrt[x])^2*(5240*Sqrt[2 - b] - 5352*Sqrt[2 - b]*b + 1188*Sqrt[2 - b]*b^2 - 33*Sqrt[2 - b]*b^3 + 8832*Sqrt[2 - b]*Sqrt[x] - 1056*Sqrt[2 - b]*b*Sqrt[x] - 576*Sqrt[2 - b]*b^2*Sqrt[x] + 24*Sqrt[2 - b]*b^3*Sqrt[x] - 13848*Sqrt[2 - b]*x - 648*Sqrt[2 - b]*b*x + 3852*Sqrt[2 - b]*b^2*x - 549*Sqrt[2 - b]*b^3*x + 4304*Sqrt[2 - b]*x^(3/2) - 4800*Sqrt[2 - b]*b*x^(3/2) - 792*Sqrt[2 - b]*b^2*x^(3/2) + 360*Sqrt[2 - b]*b^3*x^(3/2) + 840*Sqrt[2 - b]*x^2 + 7176*Sqrt[2 - b]*b*x^2 - 36*Sqrt[2 - b]*b^2*x^2 - 675*Sqrt[2 - b]*b^3*x^2 - 1056*Sqrt[2 - b]*x^(5/2) - 2592*Sqrt[2 - b]*b*x^(5/2) + 144*Sqrt[2 - b]*b^2*x^(5/2) + 360*Sqrt[2 - b]*b^3*x^(5/2) + 344*Sqrt[2 - b]*x^3 + 360*Sqrt[2 - b]*b*x^3 - 396*Sqrt[2 - b]*b^2*x^3 - 87*Sqrt[2 - b]*b^3*x^3 - 48*Sqrt[2 - b]*x^(7/2) + 72*Sqrt[2 - b]*b^2*x^(7/2) + 24*Sqrt[2 - b]*b^3*x^(7/2) - 5192*Sqrt[2 - b*x] + 6648*b*Sqrt[2 - b*x] - 2364*b^2*Sqrt[2 - b*x] + 207*b^3*Sqrt[2 - b*x] - 9168*Sqrt[x]*Sqrt[2 - b*x] + 3360*b*Sqrt[x]*Sqrt[2 - b*x] + 600*b^2*Sqrt[x]*Sqrt[2 - b*x] - 144*b^3*Sqrt[x]*Sqrt[2 - b*x] + 14856*x*Sqrt[2 - b*x] - 4392*b*x*Sqrt[2 - b*x] - 2820*b^2*x*Sqrt[2 - b*x] + 795*b^3*x*Sqrt[2 - b*x] - 5984*x^(3/2)*Sqrt[2 - b*x] + 4032*b*x^(3/2)*Sqrt[2 - b*x] + 624*b^2*x^(3/2)*Sqrt[2 - b*x] - 480*b^3*x^(3/2)*Sqrt[2 - b*x] + 840*x^2*Sqrt[2 - b*x] - 3672*b*x^2*Sqrt[2 - b*x] + 540*b^2*x^2*Sqrt[2 - b*x] + 333*b^3*x^2*Sqrt[2 - b*x] + 48*x^(5/2)*Sqrt[2 - b*x] + 1056*b*x^(5/2)*Sqrt[2 - b*x] - 72*b^2*x^(5/2)*Sqrt[2 - b*x] - 144*b^3*x^(5/2)*Sqrt[2 - b*x] - 8*x^3*Sqrt[2 - b*x] - 120*b*x^3*Sqrt[2 - b*x] + 36*b^2*x^3*Sqrt[2 - b*x] + 9*b^3*x^3*Sqrt[2 - b*x]))/(Sqrt[2 - b] - Sqrt[2 - b*x])^9 - (b^3*(1232*b - 1520*b^2 + 390*b^3 - 9*b^4 - 4224*Sqrt[x] + 12032*b*Sqrt[x] - 3776*b^2*Sqrt[x] - 48*b^3*Sqrt[x] + 6*b^4*Sqrt[x] - 35136*x + 6752*b*x + 568*b^2*x + 1452*b^3*x - 210*b^4*x + 60160*x^(3/2) - 12224*b*x^(3/2) - 9712*b^2*x^(3/2) + 1512*b^3*x^(3/2) + 126*b^4*x^(3/2) - 36800*x^2 + 18112*b*x^2 + 3560*b^2*x^2 - 864*b^3*x^2 - 420*b^4*x^2 + 12160*x^(5/2) - 22400*b*x^(5/2) + 1952*b^2*x^(5/2) + 1728*b^3*x^(5/2) + 210*b^4*x^(5/2) - 2752*x^3 + 11040*b*x^3 - 696*b^2*x^3 - 1308*b^3*x^3 - 126*b^4*x^3 + 512*x^(7/2) - 2496*b*x^(7/2) + 528*b^2*x^(7/2) + 264*b^3*x^(7/2) + 42*b^4*x^(7/2) - 64*x^4 + 240*b*x^4 - 120*b^2*x^4 - 54*b^3*x^4 - 3*b^4*x^4 - 32*Sqrt[2 - b]*Sqrt[2 - b*x] - 624*Sqrt[2 - b]*b*Sqrt[2 - b*x] + 588*Sqrt[2 - b]*b^2*Sqrt[2 - b*x] - 66*Sqrt[2 - b]*b^3*Sqrt[2 - b*x] + 2368*Sqrt[2 - b]*Sqrt[x]*Sqrt[2 - b*x] - 5424*Sqrt[2 - b]*b*Sqrt[x]*Sqrt[2 - b*x] + 696*Sqrt[2 - b]*b^2*Sqrt[x]*Sqrt[2 - b*x] + 42*Sqrt[2 - b]*b^3*Sqrt[x]*Sqrt[2 - b*x] + 16672*Sqrt[2 - b]*x*Sqrt[2 - b*x] + 784*Sqrt[2 - b]*b*x*Sqrt[2 - b*x] + 84*Sqrt[2 - b]*b^2*x*Sqrt[2 - b*x] - 378*Sqrt[2 - b]*b^3*x*Sqrt[2 - b*x] - 28288*Sqrt[2 - b]*x^(3/2)*Sqrt[2 - b*x] - 368*Sqrt[2 - b]*b*x^(3/2)*Sqrt[2 - b*x] + 2496*Sqrt[2 - b]*b^2*x^(3/2)*Sqrt[2 - b*x] + 210*Sqrt[2 - b]*b^3*x^(3/2)*Sqrt[2 - b*x] + 16160*Sqrt[2 - b]*x^2*Sqrt[2 - b*x] - 848*Sqrt[2 - b]*b*x^2*Sqrt[2 - b*x] - 2124*Sqrt[2 - b]*b^2*x^2*Sqrt[2 - b*x] - 294*Sqrt[2 - b]*b^3*x^2*Sqrt[2 - b*x] - 4288*Sqrt[2 - b]*x^(5/2)*Sqrt[2 - b*x] + 3056*Sqrt[2 - b]*b*x^(5/2)*Sqrt[2 - b*x] + 984*Sqrt[2 - b]*b^2*x^(5/2)*Sqrt[2 - b*x] + 126*Sqrt[2 - b]*b^3*x^(5/2)*Sqrt[2 - b*x] + 480*Sqrt[2 - b]*x^3*Sqrt[2 - b*x] - 1360*Sqrt[2 - b]*b*x^3*Sqrt[2 - b*x] - 468*Sqrt[2 - b]*b^2*x^3*Sqrt[2 - b*x] - 30*Sqrt[2 - b]*b^3*x^3*Sqrt[2 - b*x] + 176*Sqrt[2 - b]*b*x^(7/2)*Sqrt[2 - b*x] + 48*Sqrt[2 - b]*b^2*x^(7/2)*Sqrt[2 - b*x] + 6*Sqrt[2 - b]*b^3*x^(7/2)*Sqrt[2 - b*x]))/(Sqrt[2 - b] - Sqrt[2 - b*x])^8))/((-Sqrt[2 - b] + Sqrt[2 - b*x])*(-8 + 10*b - 2*b^2 - 4*b*Sqrt[x] + 6*b*x - 5*b^2*x + b^3*x + 2*b^2*x^(3/2) - b^2*x^2 + 4*Sqrt[2 - b]*Sqrt[2 - b*x] - 4*Sqrt[2 - b]*b*Sqrt[2 - b*x] + 2*Sqrt[2 - b]*b*Sqrt[x]*Sqrt[2 - b*x] + Sqrt[2 - b]*b^2*Sqrt[x]*Sqrt[2 - b*x] - 2*Sqrt[2 - b]*b*x*Sqrt[2 - b*x])^3)","B",1
644,1,2974,39,9.3344914,"\int \frac{1}{\sqrt{x} (2-b x)^{5/2}} \, dx","IntegrateAlgebraic[1/(Sqrt[x]*(2 - b*x)^(5/2)),x]","\text{Result too large to show}","\frac{\sqrt{x}}{3 \sqrt{2-b x}}+\frac{\sqrt{x}}{3 (2-b x)^{3/2}}",1,"((-1/384*1/(-2 + b)^2 + Sqrt[x]/(384*(-2 + b)^2))*(Sqrt[2 - b] - Sqrt[2 - b*x])^12*(-24 - (3*b^8*(-1 + Sqrt[x])^10)/(Sqrt[2 - b] - Sqrt[2 - b*x])^10 + (3*b^7*(-1 + Sqrt[x])^8*(34 - 9*b - 20*Sqrt[x] + 4*b*Sqrt[x] + 6*x - 5*b*x - 14*Sqrt[2 - b]*Sqrt[2 - b*x] + 4*Sqrt[2 - b]*Sqrt[x]*Sqrt[2 - b*x]))/(Sqrt[2 - b] - Sqrt[2 - b*x])^10 + (4*b*(82 - 21*b - 68*Sqrt[x] + 12*b*Sqrt[x] + 22*x - 9*b*x - 30*Sqrt[2 - b]*Sqrt[2 - b*x] + 12*Sqrt[2 - b]*Sqrt[x]*Sqrt[2 - b*x]))/(Sqrt[2 - b] - Sqrt[2 - b*x])^2 + (2*b^6*(-1 + Sqrt[x])^6*(58 - 79*b + 9*b^2 + 544*Sqrt[x] - 154*b*Sqrt[x] - 416*x + 10*b*x + 54*b^2*x + 120*x^(3/2) - 106*b*x^(3/2) - 18*x^2 + 41*b*x^2 + 9*b^2*x^2 - 38*Sqrt[2 - b]*Sqrt[2 - b*x] + 36*Sqrt[2 - b]*b*Sqrt[2 - b*x] - 236*Sqrt[2 - b]*Sqrt[x]*Sqrt[2 - b*x] + 154*Sqrt[2 - b]*x*Sqrt[2 - b*x] + 36*Sqrt[2 - b]*b*x*Sqrt[2 - b*x] - 24*Sqrt[2 - b]*x^(3/2)*Sqrt[2 - b*x]))/(Sqrt[2 - b] - Sqrt[2 - b*x])^10 + (2*b^2*(-1136 + 506*b - 33*b^2 + 1552*Sqrt[x] - 532*b*Sqrt[x] + 24*b^2*Sqrt[x] - 1016*x + 580*b*x - 126*b^2*x + 384*x^(3/2) - 340*b*x^(3/2) + 72*b^2*x^(3/2) - 72*x^2 + 74*b*x^2 - 9*b^2*x^2 + 532*Sqrt[2 - b]*Sqrt[2 - b*x] - 108*Sqrt[2 - b]*b*Sqrt[2 - b*x] - 632*Sqrt[2 - b]*Sqrt[x]*Sqrt[2 - b*x] + 72*Sqrt[2 - b]*b*Sqrt[x]*Sqrt[2 - b*x] + 292*Sqrt[2 - b]*x*Sqrt[2 - b*x] - 60*Sqrt[2 - b]*b*x*Sqrt[2 - b*x] - 48*Sqrt[2 - b]*x^(3/2)*Sqrt[2 - b*x] + 24*Sqrt[2 - b]*b*x^(3/2)*Sqrt[2 - b*x]))/(Sqrt[2 - b] - Sqrt[2 - b*x])^4 + (b^4*(-1 + Sqrt[x])^2*(-2232 + 1832*b - 440*b^2 + 15*b^3 - 2736*Sqrt[x] + 2304*b*Sqrt[x] - 264*b^2*Sqrt[x] - 744*x + 888*b*x - 1164*b^2*x + 225*b^3*x + 3808*x^(3/2) + 1408*b*x^(3/2) - 1072*b^2*x^(3/2) - 2568*x^2 - 744*b*x^2 + 288*b^2*x^2 + 225*b^3*x^2 + 720*x^(5/2) - 264*b^2*x^(5/2) - 88*x^3 + 72*b*x^3 + 36*b^2*x^3 + 15*b^3*x^3 + 1072*Sqrt[2 - b]*Sqrt[2 - b*x] - 624*Sqrt[2 - b]*b*Sqrt[2 - b*x] + 90*Sqrt[2 - b]*b^2*Sqrt[2 - b*x] + 1632*Sqrt[2 - b]*Sqrt[x]*Sqrt[2 - b*x] - 864*Sqrt[2 - b]*b*Sqrt[x]*Sqrt[2 - b*x] - 288*Sqrt[2 - b]*x*Sqrt[2 - b*x] - 32*Sqrt[2 - b]*b*x*Sqrt[2 - b*x] + 300*Sqrt[2 - b]*b^2*x*Sqrt[2 - b*x] - 1024*Sqrt[2 - b]*x^(3/2)*Sqrt[2 - b*x] - 672*Sqrt[2 - b]*b*x^(3/2)*Sqrt[2 - b*x] + 624*Sqrt[2 - b]*x^2*Sqrt[2 - b*x] + 336*Sqrt[2 - b]*b*x^2*Sqrt[2 - b*x] + 90*Sqrt[2 - b]*b^2*x^2*Sqrt[2 - b*x] - 96*Sqrt[2 - b]*x^(5/2)*Sqrt[2 - b*x] - 64*Sqrt[2 - b]*b*x^(5/2)*Sqrt[2 - b*x]))/(Sqrt[2 - b] - Sqrt[2 - b*x])^8 + (b^3*(6320 - 3880*b + 550*b^2 - 15*b^3 - 12064*Sqrt[x] + 6176*b*Sqrt[x] - 620*b^2*Sqrt[x] + 12*b^3*Sqrt[x] + 10736*x - 7352*b*x + 1942*b^2*x - 165*b^3*x - 6720*x^(3/2) + 6464*b*x^(3/2) - 2184*b^2*x^(3/2) + 120*b^3*x^(3/2) + 3408*x^2 - 3160*b*x^2 + 1234*b^2*x^2 - 105*b^3*x^2 - 1056*x^(5/2) + 672*b*x^(5/2) - 428*b^2*x^(5/2) + 60*b^3*x^(5/2) + 144*x^3 - 72*b*x^3 + 82*b^2*x^3 - 3*b^3*x^3 - 3088*Sqrt[2 - b]*Sqrt[2 - b*x] + 1144*Sqrt[2 - b]*b*Sqrt[2 - b*x] - 78*Sqrt[2 - b]*b^2*Sqrt[2 - b*x] + 5600*Sqrt[2 - b]*Sqrt[x]*Sqrt[2 - b*x] - 1568*Sqrt[2 - b]*b*Sqrt[x]*Sqrt[2 - b*x] + 60*Sqrt[2 - b]*b^2*Sqrt[x]*Sqrt[2 - b*x] - 4288*Sqrt[2 - b]*x*Sqrt[2 - b*x] + 1616*Sqrt[2 - b]*b*x*Sqrt[2 - b*x] - 180*Sqrt[2 - b]*b^2*x*Sqrt[2 - b*x] + 1920*Sqrt[2 - b]*x^(3/2)*Sqrt[2 - b*x] - 1232*Sqrt[2 - b]*b*x^(3/2)*Sqrt[2 - b*x] + 120*Sqrt[2 - b]*b^2*x^(3/2)*Sqrt[2 - b*x] - 624*Sqrt[2 - b]*x^2*Sqrt[2 - b*x] + 472*Sqrt[2 - b]*b*x^2*Sqrt[2 - b*x] - 30*Sqrt[2 - b]*b^2*x^2*Sqrt[2 - b*x] + 96*Sqrt[2 - b]*x^(5/2)*Sqrt[2 - b*x] - 48*Sqrt[2 - b]*b*x^(5/2)*Sqrt[2 - b*x] + 12*Sqrt[2 - b]*b^2*x^(5/2)*Sqrt[2 - b*x]))/(Sqrt[2 - b] - Sqrt[2 - b*x])^6 - (2*b^5*(-1 + Sqrt[x])^4*(3676 - 3022*b + 630*b^2 - 21*b^3 - 40*Sqrt[x] + 784*b*Sqrt[x] - 276*b^2*Sqrt[x] + 12*b^3*Sqrt[x] - 3012*x - 1642*b*x + 1782*b^2*x - 255*b^3*x + 2288*x^(3/2) + 32*b*x^(3/2) - 696*b^2*x^(3/2) + 120*b^3*x^(3/2) - 716*x^2 + 782*b*x^2 + 354*b^2*x^2 - 195*b^3*x^2 + 120*x^(5/2) - 464*b*x^(5/2) - 84*b^2*x^(5/2) + 60*b^3*x^(5/2) - 12*x^3 + 74*b*x^3 + 18*b^2*x^3 - 9*b^3*x^3 - 1844*Sqrt[2 - b]*Sqrt[2 - b*x] + 1056*Sqrt[2 - b]*b*Sqrt[2 - b*x] - 114*Sqrt[2 - b]*b^2*Sqrt[2 - b*x] + 56*Sqrt[2 - b]*Sqrt[x]*Sqrt[2 - b*x] - 408*Sqrt[2 - b]*b*Sqrt[x]*Sqrt[2 - b*x] + 60*Sqrt[2 - b]*b^2*Sqrt[x]*Sqrt[2 - b*x] + 1416*Sqrt[2 - b]*x*Sqrt[2 - b*x] + 768*Sqrt[2 - b]*b*x*Sqrt[2 - b*x] - 300*Sqrt[2 - b]*b^2*x*Sqrt[2 - b*x] - 1024*Sqrt[2 - b]*x^(3/2)*Sqrt[2 - b*x] - 288*Sqrt[2 - b]*b*x^(3/2)*Sqrt[2 - b*x] + 120*Sqrt[2 - b]*b^2*x^(3/2)*Sqrt[2 - b*x] + 268*Sqrt[2 - b]*x^2*Sqrt[2 - b*x] - 66*Sqrt[2 - b]*b^2*x^2*Sqrt[2 - b*x] - 24*Sqrt[2 - b]*x^(5/2)*Sqrt[2 - b*x] + 24*Sqrt[2 - b]*b*x^(5/2)*Sqrt[2 - b*x] + 12*Sqrt[2 - b]*b^2*x^(5/2)*Sqrt[2 - b*x]))/(Sqrt[2 - b] - Sqrt[2 - b*x])^10))/((-Sqrt[2 - b] + Sqrt[2 - b*x])*(-8 + 10*b - 2*b^2 - 4*b*Sqrt[x] + 6*b*x - 5*b^2*x + b^3*x + 2*b^2*x^(3/2) - b^2*x^2 + 4*Sqrt[2 - b]*Sqrt[2 - b*x] - 4*Sqrt[2 - b]*b*Sqrt[2 - b*x] + 2*Sqrt[2 - b]*b*Sqrt[x]*Sqrt[2 - b*x] + Sqrt[2 - b]*b^2*Sqrt[x]*Sqrt[2 - b*x] - 2*Sqrt[2 - b]*b*x*Sqrt[2 - b*x])^3)","B",1
645,1,2598,58,15.2009741,"\int \frac{1}{x^{3/2} (2-b x)^{5/2}} \, dx","IntegrateAlgebraic[1/(x^(3/2)*(2 - b*x)^(5/2)),x]","\text{Result too large to show}","-\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,"((1/4 - Sqrt[x]/4)*(Sqrt[2 - b] - Sqrt[2 - b*x])*(4 - 2*b - 2*Sqrt[x] + 2*b*Sqrt[x] - b*x - 2*Sqrt[2 - b]*Sqrt[2 - b*x] + Sqrt[2 - b]*Sqrt[x]*Sqrt[2 - b*x]))/(Sqrt[x]*(8 - 4*b - 4*Sqrt[x] + b*Sqrt[x] + b^2*Sqrt[x] - 2*b*x + b*x^(3/2) - 4*Sqrt[2 - b]*Sqrt[2 - b*x] + Sqrt[2 - b]*b*Sqrt[2 - b*x] + 2*Sqrt[2 - b]*Sqrt[x]*Sqrt[2 - b*x])) + (((Sqrt[2 - b]*b)/(12*(-2 + b)^3) - (b*Sqrt[2 - b*x])/(12*(-2 + b)^3))*(-736 - 672*b + 760*b^2 - 132*b^3 + 6*b^4 - 32*Sqrt[x] + 504*b*Sqrt[x] - 472*b^2*Sqrt[x] + 138*b^3*Sqrt[x] - 12*b^4*Sqrt[x] + 136*b*x + 388*b^2*x - 246*b^3*x + 9*b^4*x + 32*b*x^(3/2) - 100*b^2*x^(3/2) + 48*b^3*x^(3/2) - 3*b^4*x^(3/2) + 368*Sqrt[2 - b]*Sqrt[2 - b*x] + 416*Sqrt[2 - b]*b*Sqrt[2 - b*x] - 240*Sqrt[2 - b]*b^2*Sqrt[2 - b*x] + 6*Sqrt[2 - b]*b^3*Sqrt[2 - b*x] + 16*Sqrt[2 - b]*Sqrt[x]*Sqrt[2 - b*x] - 212*Sqrt[2 - b]*b*Sqrt[x]*Sqrt[2 - b*x] + 120*Sqrt[2 - b]*b^2*Sqrt[x]*Sqrt[2 - b*x] - 9*Sqrt[2 - b]*b^3*Sqrt[x]*Sqrt[2 - b*x] - 12*Sqrt[2 - b]*b*x*Sqrt[2 - b*x] - 72*Sqrt[2 - b]*b^2*x*Sqrt[2 - b*x] + 3*Sqrt[2 - b]*b^3*x*Sqrt[2 - b*x]))/(-8 + 10*b - 2*b^2 - 4*b*Sqrt[x] + 6*b*x - 5*b^2*x + b^3*x + 2*b^2*x^(3/2) - b^2*x^2 + 4*Sqrt[2 - b]*Sqrt[2 - b*x] - 4*Sqrt[2 - b]*b*Sqrt[2 - b*x] + 2*Sqrt[2 - b]*b*Sqrt[x]*Sqrt[2 - b*x] + Sqrt[2 - b]*b^2*Sqrt[x]*Sqrt[2 - b*x] - 2*Sqrt[2 - b]*b*x*Sqrt[2 - b*x]) + ((Sqrt[2 - b] - Sqrt[2 - b*x])^5*((104*b)/(3*(-2 + b)^4) - (652*b^2)/(3*(-2 + b)^4) - (50*b^3)/(-2 + b)^4 + (117*b^4)/(-2 + b)^4 - (19*b^5)/(-2 + b)^4 - b^6/(-2 + b)^4 - (8*b*Sqrt[x])/(3*(-2 + b)^4) + (36*b^2*Sqrt[x])/(-2 + b)^4 + (238*b^3*Sqrt[x])/(3*(-2 + b)^4) - (235*b^4*Sqrt[x])/(3*(-2 + b)^4) + (7*b^5*Sqrt[x])/(-2 + b)^4 + (4*b^6*Sqrt[x])/(-2 + b)^4 - (68*b^2*x)/(3*(-2 + b)^4) + (110*b^3*x)/(3*(-2 + b)^4) + (49*b^4*x)/(-2 + b)^4 - (167*b^5*x)/(6*(-2 + b)^4) - (3*b^6*x)/(2*(-2 + b)^4) + (4*b^2*x^(3/2))/(3*(-2 + b)^4) + (10*b^3*x^(3/2))/(3*(-2 + b)^4) - (13*b^4*x^(3/2))/(-2 + b)^4 + (9*b^5*x^(3/2))/(2*(-2 + b)^4) + (b^6*x^(3/2))/(2*(-2 + b)^4) - (52*Sqrt[2 - b]*b*Sqrt[2 - b*x])/(3*(-2 + b)^4) + (104*Sqrt[2 - b]*b^2*Sqrt[2 - b*x])/(-2 + b)^4 + (143*Sqrt[2 - b]*b^3*Sqrt[2 - b*x])/(3*(-2 + b)^4) - (39*Sqrt[2 - b]*b^4*Sqrt[2 - b*x])/(-2 + b)^4 + (Sqrt[2 - b]*b^5*Sqrt[2 - b*x])/(-2 + b)^4 + (4*Sqrt[2 - b]*b*Sqrt[x]*Sqrt[2 - b*x])/(3*(-2 + b)^4) - (50*Sqrt[2 - b]*b^2*Sqrt[x]*Sqrt[2 - b*x])/(3*(-2 + b)^4) - (103*Sqrt[2 - b]*b^3*Sqrt[x]*Sqrt[2 - b*x])/(3*(-2 + b)^4) + (109*Sqrt[2 - b]*b^4*Sqrt[x]*Sqrt[2 - b*x])/(6*(-2 + b)^4) + (3*Sqrt[2 - b]*b^5*Sqrt[x]*Sqrt[2 - b*x])/(2*(-2 + b)^4) + (6*Sqrt[2 - b]*b^2*x*Sqrt[2 - b*x])/(-2 + b)^4 - (4*Sqrt[2 - b]*b^3*x*Sqrt[2 - b*x])/(3*(-2 + b)^4) - (21*Sqrt[2 - b]*b^4*x*Sqrt[2 - b*x])/(2*(-2 + b)^4) - (Sqrt[2 - b]*b^5*x*Sqrt[2 - b*x])/(2*(-2 + b)^4)))/(-8 + 10*b - 2*b^2 - 4*b*Sqrt[x] + 6*b*x - 5*b^2*x + b^3*x + 2*b^2*x^(3/2) - b^2*x^2 + 4*Sqrt[2 - b]*Sqrt[2 - b*x] - 4*Sqrt[2 - b]*b*Sqrt[2 - b*x] + 2*Sqrt[2 - b]*b*Sqrt[x]*Sqrt[2 - b*x] + Sqrt[2 - b]*b^2*Sqrt[x]*Sqrt[2 - b*x] - 2*Sqrt[2 - b]*b*x*Sqrt[2 - b*x])^2 + ((Sqrt[2 - b] - Sqrt[2 - b*x])^9*((-48*b^2)/(-2 + b)^4 + (104*b^3)/(3*(-2 + b)^4) + (92*b^4)/(3*(-2 + b)^4) - (50*b^5)/(3*(-2 + b)^4) - (2*b^6)/(3*(-2 + b)^4) + (16*b^2*Sqrt[x])/(3*(-2 + b)^4) - (56*b^3*Sqrt[x])/(3*(-2 + b)^4) - (44*b^4*Sqrt[x])/(-2 + b)^4 + (18*b^5*Sqrt[x])/(-2 + b)^4 + (4*b^6*Sqrt[x])/(-2 + b)^4 + (88*b^3*x)/(3*(-2 + b)^4) + (20*b^4*x)/(-2 + b)^4 - (46*b^5*x)/(3*(-2 + b)^4) - (b^6*x)/(-2 + b)^4 - (8*b^3*x^(3/2))/(3*(-2 + b)^4) - (20*b^4*x^(3/2))/(3*(-2 + b)^4) + (10*b^5*x^(3/2))/(3*(-2 + b)^4) + (b^6*x^(3/2))/(3*(-2 + b)^4) + (24*Sqrt[2 - b]*b^2*Sqrt[2 - b*x])/(-2 + b)^4 - (32*Sqrt[2 - b]*b^3*Sqrt[2 - b*x])/(3*(-2 + b)^4) - (46*Sqrt[2 - b]*b^4*Sqrt[2 - b*x])/(3*(-2 + b)^4) + (2*Sqrt[2 - b]*b^5*Sqrt[2 - b*x])/(-2 + b)^4 - (8*Sqrt[2 - b]*b^2*Sqrt[x]*Sqrt[2 - b*x])/(3*(-2 + b)^4) + (20*Sqrt[2 - b]*b^3*Sqrt[x]*Sqrt[2 - b*x])/(3*(-2 + b)^4) + (50*Sqrt[2 - b]*b^4*Sqrt[x]*Sqrt[2 - b*x])/(3*(-2 + b)^4) + (Sqrt[2 - b]*b^5*Sqrt[x]*Sqrt[2 - b*x])/(-2 + b)^4 - (20*Sqrt[2 - b]*b^3*x*Sqrt[2 - b*x])/(3*(-2 + b)^4) - (20*Sqrt[2 - b]*b^4*x*Sqrt[2 - b*x])/(3*(-2 + b)^4) - (Sqrt[2 - b]*b^5*x*Sqrt[2 - b*x])/(3*(-2 + b)^4)))/(-8 + 10*b - 2*b^2 - 4*b*Sqrt[x] + 6*b*x - 5*b^2*x + b^3*x + 2*b^2*x^(3/2) - b^2*x^2 + 4*Sqrt[2 - b]*Sqrt[2 - b*x] - 4*Sqrt[2 - b]*b*Sqrt[2 - b*x] + 2*Sqrt[2 - b]*b*Sqrt[x]*Sqrt[2 - b*x] + Sqrt[2 - b]*b^2*Sqrt[x]*Sqrt[2 - b*x] - 2*Sqrt[2 - b]*b*x*Sqrt[2 - b*x])^3","B",1
646,-1,0,75,180.0477484,"\int \frac{1}{x^{5/2} (2-b x)^{5/2}} \, dx","IntegrateAlgebraic[1/(x^(5/2)*(2 - b*x)^(5/2)),x]","\text{\$Aborted}","-\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,"$Aborted","F",-1
647,1,36,27,0.0898086,"\int \frac{\sqrt{x}}{\sqrt{1-x}} \, dx","IntegrateAlgebraic[Sqrt[x]/Sqrt[1 - x],x]","-\sqrt{x-x^2}-2 \tan ^{-1}\left(\frac{\sqrt{1-x}}{\sqrt{x}+1}\right)","-\sqrt{1-x} \sqrt{x}-\frac{1}{2} \sin ^{-1}(1-2 x)",1,"-Sqrt[x - x^2] - 2*ArcTan[Sqrt[1 - x]/(1 + Sqrt[x])]","A",1
648,1,22,8,0.016369,"\int \frac{1}{\sqrt{1-x} \sqrt{x}} \, dx","IntegrateAlgebraic[1/(Sqrt[1 - x]*Sqrt[x]),x]","-4 \tan ^{-1}\left(\frac{\sqrt{1-x}}{\sqrt{x}+1}\right)","-\sin ^{-1}(1-2 x)",1,"-4*ArcTan[Sqrt[1 - x]/(1 + Sqrt[x])]","B",1
649,1,51,19,0.1209553,"\int \frac{1}{\sqrt{x} \sqrt{1-b x}} \, dx","IntegrateAlgebraic[1/(Sqrt[x]*Sqrt[1 - b*x]),x]","-\frac{4 \tan ^{-1}\left(\frac{\frac{\sqrt{1-b x}}{\sqrt{b}}-\frac{\sqrt{1-b}}{\sqrt{b}}}{\sqrt{x}-1}\right)}{\sqrt{b}}","\frac{2 \sin ^{-1}\left(\sqrt{b} \sqrt{x}\right)}{\sqrt{b}}",1,"(-4*ArcTan[(-(Sqrt[1 - b]/Sqrt[b]) + Sqrt[1 - b*x]/Sqrt[b])/(-1 + Sqrt[x])])/Sqrt[b]","B",1
650,1,21,21,0.0077788,"\int x^{5/3} (a+b x) \, dx","IntegrateAlgebraic[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",1
651,1,21,21,0.007501,"\int x^{4/3} (a+b x) \, dx","IntegrateAlgebraic[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",1
652,1,21,21,0.0074901,"\int x^{2/3} (a+b x) \, dx","IntegrateAlgebraic[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",1
653,1,21,21,0.0069355,"\int \sqrt[3]{x} (a+b x) \, dx","IntegrateAlgebraic[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",1
654,1,21,21,0.0074369,"\int \frac{a+b x}{\sqrt[3]{x}} \, dx","IntegrateAlgebraic[(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",1
655,1,19,19,0.0064344,"\int \frac{a+b x}{x^{2/3}} \, dx","IntegrateAlgebraic[(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",1
656,1,19,19,0.0089943,"\int \frac{a+b x}{x^{4/3}} \, dx","IntegrateAlgebraic[(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",1
657,1,19,19,0.0085987,"\int \frac{a+b x}{x^{5/3}} \, dx","IntegrateAlgebraic[(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",1
658,1,36,36,0.0099082,"\int x^{5/3} (a+b x)^2 \, dx","IntegrateAlgebraic[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",1
659,1,36,36,0.0094835,"\int x^{4/3} (a+b x)^2 \, dx","IntegrateAlgebraic[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",1
660,1,36,36,0.0104011,"\int x^{2/3} (a+b x)^2 \, dx","IntegrateAlgebraic[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",1
661,1,36,36,0.0098877,"\int \sqrt[3]{x} (a+b x)^2 \, dx","IntegrateAlgebraic[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",1
662,1,36,36,0.0104169,"\int \frac{(a+b x)^2}{\sqrt[3]{x}} \, dx","IntegrateAlgebraic[(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",1
663,1,34,34,0.0097906,"\int \frac{(a+b x)^2}{x^{2/3}} \, dx","IntegrateAlgebraic[(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",1
664,1,32,32,0.0109191,"\int \frac{(a+b x)^2}{x^{4/3}} \, dx","IntegrateAlgebraic[(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",1
665,1,34,34,0.0115597,"\int \frac{(a+b x)^2}{x^{5/3}} \, dx","IntegrateAlgebraic[(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",1
666,1,51,51,0.01332,"\int x^{5/3} (a+b x)^3 \, dx","IntegrateAlgebraic[x^(5/3)*(a + b*x)^3,x]","\frac{3}{8} a^3 x^{8/3}+\frac{9}{11} a^2 b x^{11/3}+\frac{9}{14} a b^2 x^{14/3}+\frac{3}{17} b^3 x^{17/3}","\frac{3}{8} a^3 x^{8/3}+\frac{9}{11} a^2 b x^{11/3}+\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",1
667,1,51,51,0.0132206,"\int x^{4/3} (a+b x)^3 \, dx","IntegrateAlgebraic[x^(4/3)*(a + b*x)^3,x]","\frac{3}{7} a^3 x^{7/3}+\frac{9}{10} a^2 b x^{10/3}+\frac{9}{13} a b^2 x^{13/3}+\frac{3}{16} b^3 x^{16/3}","\frac{3}{7} a^3 x^{7/3}+\frac{9}{10} a^2 b x^{10/3}+\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",1
668,1,51,51,0.0132306,"\int x^{2/3} (a+b x)^3 \, dx","IntegrateAlgebraic[x^(2/3)*(a + b*x)^3,x]","\frac{3}{5} a^3 x^{5/3}+\frac{9}{8} a^2 b x^{8/3}+\frac{9}{11} a b^2 x^{11/3}+\frac{3}{14} b^3 x^{14/3}","\frac{3}{5} a^3 x^{5/3}+\frac{9}{8} a^2 b x^{8/3}+\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",1
669,1,51,51,0.0131214,"\int \sqrt[3]{x} (a+b x)^3 \, dx","IntegrateAlgebraic[x^(1/3)*(a + b*x)^3,x]","\frac{3}{4} a^3 x^{4/3}+\frac{9}{7} a^2 b x^{7/3}+\frac{9}{10} a b^2 x^{10/3}+\frac{3}{13} b^3 x^{13/3}","\frac{3}{4} a^3 x^{4/3}+\frac{9}{7} a^2 b x^{7/3}+\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",1
670,1,51,51,0.0131529,"\int \frac{(a+b x)^3}{\sqrt[3]{x}} \, dx","IntegrateAlgebraic[(a + b*x)^3/x^(1/3),x]","\frac{3}{2} a^3 x^{2/3}+\frac{9}{5} a^2 b x^{5/3}+\frac{9}{8} a b^2 x^{8/3}+\frac{3}{11} b^3 x^{11/3}","\frac{3}{2} a^3 x^{2/3}+\frac{9}{5} a^2 b x^{5/3}+\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",1
671,1,49,49,0.0132074,"\int \frac{(a+b x)^3}{x^{2/3}} \, dx","IntegrateAlgebraic[(a + b*x)^3/x^(2/3),x]","3 a^3 \sqrt[3]{x}+\frac{9}{4} a^2 b x^{4/3}+\frac{9}{7} a b^2 x^{7/3}+\frac{3}{10} b^3 x^{10/3}","3 a^3 \sqrt[3]{x}+\frac{9}{4} a^2 b x^{4/3}+\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",1
672,1,49,49,0.0162711,"\int \frac{(a+b x)^3}{x^{4/3}} \, dx","IntegrateAlgebraic[(a + b*x)^3/x^(4/3),x]","-\frac{3 a^3}{\sqrt[3]{x}}+\frac{9}{2} a^2 b x^{2/3}+\frac{9}{5} a b^2 x^{5/3}+\frac{3}{8} b^3 x^{8/3}","-\frac{3 a^3}{\sqrt[3]{x}}+\frac{9}{2} a^2 b x^{2/3}+\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",1
673,1,49,49,0.0190881,"\int \frac{(a+b x)^3}{x^{5/3}} \, dx","IntegrateAlgebraic[(a + b*x)^3/x^(5/3),x]","-\frac{3 a^3}{2 x^{2/3}}+9 a^2 b \sqrt[3]{x}+\frac{9}{4} a b^2 x^{4/3}+\frac{3}{7} b^3 x^{7/3}","-\frac{3 a^3}{2 x^{2/3}}+9 a^2 b \sqrt[3]{x}+\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",1
674,1,151,125,0.073031,"\int \frac{x^{5/3}}{a+b x} \, dx","IntegrateAlgebraic[x^(5/3)/(a + b*x),x]","\frac{a^{5/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \sqrt[3]{x}+b^{2/3} x^{2/3}\right)}{2 b^{8/3}}-\frac{a^{5/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{b^{8/3}}-\frac{\sqrt{3} a^{5/3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{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[1/Sqrt[3] - (2*b^(1/3)*x^(1/3))/(Sqrt[3]*a^(1/3))])/b^(8/3) - (a^(5/3)*Log[a^(1/3) + b^(1/3)*x^(1/3)])/b^(8/3) + (a^(5/3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x^(1/3) + b^(2/3)*x^(2/3)])/(2*b^(8/3))","A",1
675,1,148,123,0.0492817,"\int \frac{x^{4/3}}{a+b x} \, dx","IntegrateAlgebraic[x^(4/3)/(a + b*x),x]","-\frac{a^{4/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \sqrt[3]{x}+b^{2/3} x^{2/3}\right)}{2 b^{7/3}}+\frac{a^{4/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{b^{7/3}}-\frac{\sqrt{3} a^{4/3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{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[1/Sqrt[3] - (2*b^(1/3)*x^(1/3))/(Sqrt[3]*a^(1/3))])/b^(7/3) + (a^(4/3)*Log[a^(1/3) + b^(1/3)*x^(1/3)])/b^(7/3) - (a^(4/3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x^(1/3) + b^(2/3)*x^(2/3)])/(2*b^(7/3))","A",1
676,1,136,111,0.043826,"\int \frac{x^{2/3}}{a+b x} \, dx","IntegrateAlgebraic[x^(2/3)/(a + b*x),x]","-\frac{a^{2/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \sqrt[3]{x}+b^{2/3} x^{2/3}\right)}{2 b^{5/3}}+\frac{a^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{b^{5/3}}+\frac{\sqrt{3} a^{2/3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{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[1/Sqrt[3] - (2*b^(1/3)*x^(1/3))/(Sqrt[3]*a^(1/3))])/b^(5/3) + (a^(2/3)*Log[a^(1/3) + b^(1/3)*x^(1/3)])/b^(5/3) - (a^(2/3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x^(1/3) + b^(2/3)*x^(2/3)])/(2*b^(5/3))","A",1
677,1,135,109,0.0397837,"\int \frac{\sqrt[3]{x}}{a+b x} \, dx","IntegrateAlgebraic[x^(1/3)/(a + b*x),x]","\frac{\sqrt[3]{a} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \sqrt[3]{x}+b^{2/3} x^{2/3}\right)}{2 b^{4/3}}-\frac{\sqrt[3]{a} \log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{b^{4/3}}+\frac{\sqrt{3} \sqrt[3]{a} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{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[1/Sqrt[3] - (2*b^(1/3)*x^(1/3))/(Sqrt[3]*a^(1/3))])/b^(4/3) - (a^(1/3)*Log[a^(1/3) + b^(1/3)*x^(1/3)])/b^(4/3) + (a^(1/3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x^(1/3) + b^(2/3)*x^(2/3)])/(2*b^(4/3))","A",1
678,1,126,100,0.0316054,"\int \frac{1}{\sqrt[3]{x} (a+b x)} \, dx","IntegrateAlgebraic[1/(x^(1/3)*(a + b*x)),x]","\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \sqrt[3]{x}+b^{2/3} x^{2/3}\right)}{2 \sqrt[3]{a} b^{2/3}}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{\sqrt[3]{a} b^{2/3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{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[1/Sqrt[3] - (2*b^(1/3)*x^(1/3))/(Sqrt[3]*a^(1/3))])/(a^(1/3)*b^(2/3))) - Log[a^(1/3) + b^(1/3)*x^(1/3)]/(a^(1/3)*b^(2/3)) + Log[a^(2/3) - a^(1/3)*b^(1/3)*x^(1/3) + b^(2/3)*x^(2/3)]/(2*a^(1/3)*b^(2/3))","A",1
679,1,125,100,0.0339825,"\int \frac{1}{x^{2/3} (a+b x)} \, dx","IntegrateAlgebraic[1/(x^(2/3)*(a + b*x)),x]","-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \sqrt[3]{x}+b^{2/3} x^{2/3}\right)}{2 a^{2/3} \sqrt[3]{b}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{a^{2/3} \sqrt[3]{b}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{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[1/Sqrt[3] - (2*b^(1/3)*x^(1/3))/(Sqrt[3]*a^(1/3))])/(a^(2/3)*b^(1/3))) + Log[a^(1/3) + b^(1/3)*x^(1/3)]/(a^(2/3)*b^(1/3)) - Log[a^(2/3) - a^(1/3)*b^(1/3)*x^(1/3) + b^(2/3)*x^(2/3)]/(2*a^(2/3)*b^(1/3))","A",1
680,1,134,109,0.0428524,"\int \frac{1}{x^{4/3} (a+b x)} \, dx","IntegrateAlgebraic[1/(x^(4/3)*(a + b*x)),x]","-\frac{\sqrt[3]{b} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \sqrt[3]{x}+b^{2/3} x^{2/3}\right)}{2 a^{4/3}}+\frac{\sqrt[3]{b} \log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{a^{4/3}}+\frac{\sqrt{3} \sqrt[3]{b} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{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[1/Sqrt[3] - (2*b^(1/3)*x^(1/3))/(Sqrt[3]*a^(1/3))])/a^(4/3) + (b^(1/3)*Log[a^(1/3) + b^(1/3)*x^(1/3)])/a^(4/3) - (b^(1/3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x^(1/3) + b^(2/3)*x^(2/3)])/(2*a^(4/3))","A",1
681,1,137,111,0.0497174,"\int \frac{1}{x^{5/3} (a+b x)} \, dx","IntegrateAlgebraic[1/(x^(5/3)*(a + b*x)),x]","\frac{b^{2/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \sqrt[3]{x}+b^{2/3} x^{2/3}\right)}{2 a^{5/3}}-\frac{b^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{a^{5/3}}+\frac{\sqrt{3} b^{2/3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{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[1/Sqrt[3] - (2*b^(1/3)*x^(1/3))/(Sqrt[3]*a^(1/3))])/a^(5/3) - (b^(2/3)*Log[a^(1/3) + b^(1/3)*x^(1/3)])/a^(5/3) + (b^(2/3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x^(1/3) + b^(2/3)*x^(2/3)])/(2*a^(5/3))","A",1
682,1,157,129,0.1080646,"\int \frac{x^{5/3}}{(a+b x)^2} \, dx","IntegrateAlgebraic[x^(5/3)/(a + b*x)^2,x]","-\frac{5 a^{2/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \sqrt[3]{x}+b^{2/3} x^{2/3}\right)}{6 b^{8/3}}+\frac{5 a^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{3 b^{8/3}}+\frac{5 a^{2/3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{b} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} b^{8/3}}+\frac{a x^{2/3}}{b^2 (a+b x)}+\frac{3 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,"(3*x^(2/3))/(2*b^2) + (a*x^(2/3))/(b^2*(a + b*x)) + (5*a^(2/3)*ArcTan[1/Sqrt[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)])/(3*b^(8/3)) - (5*a^(2/3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x^(1/3) + b^(2/3)*x^(2/3)])/(6*b^(8/3))","A",1
683,1,155,125,0.0991479,"\int \frac{x^{4/3}}{(a+b x)^2} \, dx","IntegrateAlgebraic[x^(4/3)/(a + b*x)^2,x]","\frac{2 \sqrt[3]{a} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \sqrt[3]{x}+b^{2/3} x^{2/3}\right)}{3 b^{7/3}}-\frac{4 \sqrt[3]{a} \log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{3 b^{7/3}}+\frac{4 \sqrt[3]{a} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{b} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} b^{7/3}}+\frac{a \sqrt[3]{x}}{b^2 (a+b x)}+\frac{3 \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,"(3*x^(1/3))/b^2 + (a*x^(1/3))/(b^2*(a + b*x)) + (4*a^(1/3)*ArcTan[1/Sqrt[3] - (2*b^(1/3)*x^(1/3))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*b^(7/3)) - (4*a^(1/3)*Log[a^(1/3) + b^(1/3)*x^(1/3)])/(3*b^(7/3)) + (2*a^(1/3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x^(1/3) + b^(2/3)*x^(2/3)])/(3*b^(7/3))","A",1
684,1,145,115,0.0974516,"\int \frac{x^{2/3}}{(a+b x)^2} \, dx","IntegrateAlgebraic[x^(2/3)/(a + b*x)^2,x]","\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \sqrt[3]{x}+b^{2/3} x^{2/3}\right)}{3 \sqrt[3]{a} b^{5/3}}-\frac{2 \log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{3 \sqrt[3]{a} b^{5/3}}-\frac{2 \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{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[1/Sqrt[3] - (2*b^(1/3)*x^(1/3))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(1/3)*b^(5/3)) - (2*Log[a^(1/3) + b^(1/3)*x^(1/3)])/(3*a^(1/3)*b^(5/3)) + Log[a^(2/3) - a^(1/3)*b^(1/3)*x^(1/3) + b^(2/3)*x^(2/3)]/(3*a^(1/3)*b^(5/3))","A",1
685,1,145,117,0.0848747,"\int \frac{\sqrt[3]{x}}{(a+b x)^2} \, dx","IntegrateAlgebraic[x^(1/3)/(a + b*x)^2,x]","-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \sqrt[3]{x}+b^{2/3} x^{2/3}\right)}{6 a^{2/3} b^{4/3}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{3 a^{2/3} b^{4/3}}-\frac{\tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{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[1/Sqrt[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)]/(3*a^(2/3)*b^(4/3)) - Log[a^(2/3) - a^(1/3)*b^(1/3)*x^(1/3) + b^(2/3)*x^(2/3)]/(6*a^(2/3)*b^(4/3))","A",1
686,1,144,116,0.0843029,"\int \frac{1}{\sqrt[3]{x} (a+b x)^2} \, dx","IntegrateAlgebraic[1/(x^(1/3)*(a + b*x)^2),x]","\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \sqrt[3]{x}+b^{2/3} x^{2/3}\right)}{6 a^{4/3} b^{2/3}}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{3 a^{4/3} b^{2/3}}-\frac{\tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{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[1/Sqrt[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)]/(3*a^(4/3)*b^(2/3)) + Log[a^(2/3) - a^(1/3)*b^(1/3)*x^(1/3) + b^(2/3)*x^(2/3)]/(6*a^(4/3)*b^(2/3))","A",1
687,1,144,113,0.0809445,"\int \frac{1}{x^{2/3} (a+b x)^2} \, dx","IntegrateAlgebraic[1/(x^(2/3)*(a + b*x)^2),x]","-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \sqrt[3]{x}+b^{2/3} x^{2/3}\right)}{3 a^{5/3} \sqrt[3]{b}}+\frac{2 \log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{3 a^{5/3} \sqrt[3]{b}}-\frac{2 \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{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[1/Sqrt[3] - (2*b^(1/3)*x^(1/3))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(5/3)*b^(1/3)) + (2*Log[a^(1/3) + b^(1/3)*x^(1/3)])/(3*a^(5/3)*b^(1/3)) - Log[a^(2/3) - a^(1/3)*b^(1/3)*x^(1/3) + b^(2/3)*x^(2/3)]/(3*a^(5/3)*b^(1/3))","A",1
688,1,156,124,0.1112662,"\int \frac{1}{x^{4/3} (a+b x)^2} \, dx","IntegrateAlgebraic[1/(x^(4/3)*(a + b*x)^2),x]","-\frac{2 \sqrt[3]{b} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \sqrt[3]{x}+b^{2/3} x^{2/3}\right)}{3 a^{7/3}}+\frac{4 \sqrt[3]{b} \log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{3 a^{7/3}}+\frac{4 \sqrt[3]{b} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{b} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{7/3}}-\frac{b x^{2/3}}{a^2 (a+b x)}-\frac{3}{a^2 \sqrt[3]{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,"-3/(a^2*x^(1/3)) - (b*x^(2/3))/(a^2*(a + b*x)) + (4*b^(1/3)*ArcTan[1/Sqrt[3] - (2*b^(1/3)*x^(1/3))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(7/3)) + (4*b^(1/3)*Log[a^(1/3) + b^(1/3)*x^(1/3)])/(3*a^(7/3)) - (2*b^(1/3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x^(1/3) + b^(2/3)*x^(2/3)])/(3*a^(7/3))","A",1
689,1,158,128,0.112152,"\int \frac{1}{x^{5/3} (a+b x)^2} \, dx","IntegrateAlgebraic[1/(x^(5/3)*(a + b*x)^2),x]","\frac{5 b^{2/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \sqrt[3]{x}+b^{2/3} x^{2/3}\right)}{6 a^{8/3}}-\frac{5 b^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{3 a^{8/3}}+\frac{5 b^{2/3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{b} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{8/3}}-\frac{b \sqrt[3]{x}}{a^2 (a+b x)}-\frac{3}{2 a^2 x^{2/3}}","-\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,"-3/(2*a^2*x^(2/3)) - (b*x^(1/3))/(a^2*(a + b*x)) + (5*b^(2/3)*ArcTan[1/Sqrt[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)])/(3*a^(8/3)) + (5*b^(2/3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x^(1/3) + b^(2/3)*x^(2/3)])/(6*a^(8/3))","A",1
690,1,161,140,0.0964478,"\int \frac{x^{5/3}}{(a+b x)^3} \, dx","IntegrateAlgebraic[x^(5/3)/(a + b*x)^3,x]","\frac{5 \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \sqrt[3]{x}+b^{2/3} x^{2/3}\right)}{18 \sqrt[3]{a} b^{8/3}}-\frac{5 \log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{9 \sqrt[3]{a} b^{8/3}}-\frac{5 \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{b} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} \sqrt[3]{a} b^{8/3}}+\frac{-5 a x^{2/3}-8 b x^{5/3}}{6 b^2 (a+b x)^2}","-\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{5 x^{2/3}}{6 b^2 (a+b x)}-\frac{x^{5/3}}{2 b (a+b x)^2}",1,"(-5*a*x^(2/3) - 8*b*x^(5/3))/(6*b^2*(a + b*x)^2) - (5*ArcTan[1/Sqrt[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)])/(9*a^(1/3)*b^(8/3)) + (5*Log[a^(2/3) - a^(1/3)*b^(1/3)*x^(1/3) + b^(2/3)*x^(2/3)])/(18*a^(1/3)*b^(8/3))","A",1
691,1,161,140,0.0943431,"\int \frac{x^{4/3}}{(a+b x)^3} \, dx","IntegrateAlgebraic[x^(4/3)/(a + b*x)^3,x]","-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \sqrt[3]{x}+b^{2/3} x^{2/3}\right)}{9 a^{2/3} b^{7/3}}+\frac{2 \log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{9 a^{2/3} b^{7/3}}-\frac{2 \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{b} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{2/3} b^{7/3}}+\frac{-4 a \sqrt[3]{x}-7 b x^{4/3}}{6 b^2 (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,"(-4*a*x^(1/3) - 7*b*x^(4/3))/(6*b^2*(a + b*x)^2) - (2*ArcTan[1/Sqrt[3] - (2*b^(1/3)*x^(1/3))/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(2/3)*b^(7/3)) + (2*Log[a^(1/3) + b^(1/3)*x^(1/3)])/(9*a^(2/3)*b^(7/3)) - Log[a^(2/3) - a^(1/3)*b^(1/3)*x^(1/3) + b^(2/3)*x^(2/3)]/(9*a^(2/3)*b^(7/3))","A",1
692,1,164,143,0.1264157,"\int \frac{x^{2/3}}{(a+b x)^3} \, dx","IntegrateAlgebraic[x^(2/3)/(a + b*x)^3,x]","\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \sqrt[3]{x}+b^{2/3} x^{2/3}\right)}{18 a^{4/3} b^{5/3}}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{9 a^{4/3} b^{5/3}}-\frac{\tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{b} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{4/3} b^{5/3}}+\frac{2 b x^{5/3}-a x^{2/3}}{6 a 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,"(-(a*x^(2/3)) + 2*b*x^(5/3))/(6*a*b*(a + b*x)^2) - ArcTan[1/Sqrt[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)]/(9*a^(4/3)*b^(5/3)) + Log[a^(2/3) - a^(1/3)*b^(1/3)*x^(1/3) + b^(2/3)*x^(2/3)]/(18*a^(4/3)*b^(5/3))","A",1
693,1,163,143,0.0978415,"\int \frac{\sqrt[3]{x}}{(a+b x)^3} \, dx","IntegrateAlgebraic[x^(1/3)/(a + b*x)^3,x]","-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \sqrt[3]{x}+b^{2/3} x^{2/3}\right)}{18 a^{5/3} b^{4/3}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{9 a^{5/3} b^{4/3}}-\frac{\tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{b} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{5/3} b^{4/3}}+\frac{b x^{4/3}-2 a \sqrt[3]{x}}{6 a 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,"(-2*a*x^(1/3) + b*x^(4/3))/(6*a*b*(a + b*x)^2) - ArcTan[1/Sqrt[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)]/(9*a^(5/3)*b^(4/3)) - Log[a^(2/3) - a^(1/3)*b^(1/3)*x^(1/3) + b^(2/3)*x^(2/3)]/(18*a^(5/3)*b^(4/3))","A",1
694,1,161,140,0.092277,"\int \frac{1}{\sqrt[3]{x} (a+b x)^3} \, dx","IntegrateAlgebraic[1/(x^(1/3)*(a + b*x)^3),x]","\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \sqrt[3]{x}+b^{2/3} x^{2/3}\right)}{9 a^{7/3} b^{2/3}}-\frac{2 \log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{9 a^{7/3} b^{2/3}}-\frac{2 \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{b} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{7/3} b^{2/3}}+\frac{7 a x^{2/3}+4 b x^{5/3}}{6 a^2 (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,"(7*a*x^(2/3) + 4*b*x^(5/3))/(6*a^2*(a + b*x)^2) - (2*ArcTan[1/Sqrt[3] - (2*b^(1/3)*x^(1/3))/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(7/3)*b^(2/3)) - (2*Log[a^(1/3) + b^(1/3)*x^(1/3)])/(9*a^(7/3)*b^(2/3)) + Log[a^(2/3) - a^(1/3)*b^(1/3)*x^(1/3) + b^(2/3)*x^(2/3)]/(9*a^(7/3)*b^(2/3))","A",1
695,1,161,140,0.0846959,"\int \frac{1}{x^{2/3} (a+b x)^3} \, dx","IntegrateAlgebraic[1/(x^(2/3)*(a + b*x)^3),x]","-\frac{5 \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \sqrt[3]{x}+b^{2/3} x^{2/3}\right)}{18 a^{8/3} \sqrt[3]{b}}+\frac{5 \log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{9 a^{8/3} \sqrt[3]{b}}-\frac{5 \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{b} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{8/3} \sqrt[3]{b}}+\frac{8 a \sqrt[3]{x}+5 b x^{4/3}}{6 a^2 (a+b x)^2}","\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{5 \sqrt[3]{x}}{6 a^2 (a+b x)}+\frac{\sqrt[3]{x}}{2 a (a+b x)^2}",1,"(8*a*x^(1/3) + 5*b*x^(4/3))/(6*a^2*(a + b*x)^2) - (5*ArcTan[1/Sqrt[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)])/(9*a^(8/3)*b^(1/3)) - (5*Log[a^(2/3) - a^(1/3)*b^(1/3)*x^(1/3) + b^(2/3)*x^(2/3)])/(18*a^(8/3)*b^(1/3))","A",1
696,1,180,152,0.1007824,"\int \frac{1}{x^{4/3} (a+b x)^3} \, dx","IntegrateAlgebraic[1/(x^(4/3)*(a + b*x)^3),x]","-\frac{7 \sqrt[3]{b} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \sqrt[3]{x}+b^{2/3} x^{2/3}\right)}{9 a^{10/3}}+\frac{14 \sqrt[3]{b} \log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{9 a^{10/3}}+\frac{14 \sqrt[3]{b} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{b} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{10/3}}-\frac{5 b x^{2/3}}{3 a^3 (a+b x)}-\frac{3}{a^3 \sqrt[3]{x}}-\frac{b x^{2/3}}{2 a^2 (a+b x)^2}","\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{7}{6 a^2 \sqrt[3]{x} (a+b x)}+\frac{1}{2 a \sqrt[3]{x} (a+b x)^2}",1,"-3/(a^3*x^(1/3)) - (b*x^(2/3))/(2*a^2*(a + b*x)^2) - (5*b*x^(2/3))/(3*a^3*(a + b*x)) + (14*b^(1/3)*ArcTan[1/Sqrt[3] - (2*b^(1/3)*x^(1/3))/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(10/3)) + (14*b^(1/3)*Log[a^(1/3) + b^(1/3)*x^(1/3)])/(9*a^(10/3)) - (7*b^(1/3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x^(1/3) + b^(2/3)*x^(2/3)])/(9*a^(10/3))","A",1
697,1,182,152,0.1070907,"\int \frac{1}{x^{5/3} (a+b x)^3} \, dx","IntegrateAlgebraic[1/(x^(5/3)*(a + b*x)^3),x]","\frac{10 b^{2/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \sqrt[3]{x}+b^{2/3} x^{2/3}\right)}{9 a^{11/3}}-\frac{20 b^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{9 a^{11/3}}+\frac{20 b^{2/3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{b} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{11/3}}-\frac{11 b \sqrt[3]{x}}{6 a^3 (a+b x)}-\frac{3}{2 a^3 x^{2/3}}-\frac{b \sqrt[3]{x}}{2 a^2 (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{10}{3 a^3 x^{2/3}}+\frac{4}{3 a^2 x^{2/3} (a+b x)}+\frac{1}{2 a x^{2/3} (a+b x)^2}",1,"-3/(2*a^3*x^(2/3)) - (b*x^(1/3))/(2*a^2*(a + b*x)^2) - (11*b*x^(1/3))/(6*a^3*(a + b*x)) + (20*b^(2/3)*ArcTan[1/Sqrt[3] - (2*b^(1/3)*x^(1/3))/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(11/3)) - (20*b^(2/3)*Log[a^(1/3) + b^(1/3)*x^(1/3)])/(9*a^(11/3)) + (10*b^(2/3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x^(1/3) + b^(2/3)*x^(2/3)])/(9*a^(11/3))","A",1
698,1,58,58,0.068064,"\int \frac{\sqrt[4]{1-x}}{1+x} \, dx","IntegrateAlgebraic[(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",1
699,0,0,187,0.0000945,"\int x^m (a+b x)^{10} \, dx","IntegrateAlgebraic[x^m*(a + b*x)^10,x]","\int x^m (a+b x)^{10} \, dx","\frac{a^{10} x^{m+1}}{m+1}+\frac{10 a^9 b x^{m+2}}{m+2}+\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 b^9 x^{m+10}}{m+10}+\frac{b^{10} x^{m+11}}{m+11}",1,"Could not integrate","F",-1
700,0,0,133,0.0000558,"\int x^m (a+b x)^7 \, dx","IntegrateAlgebraic[x^m*(a + b*x)^7,x]","\int x^m (a+b x)^7 \, dx","\frac{a^7 x^{m+1}}{m+1}+\frac{7 a^6 b x^{m+2}}{m+2}+\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 b^6 x^{m+7}}{m+7}+\frac{b^7 x^{m+8}}{m+8}",1,"Could not integrate","F",-1
701,0,0,61,0.0000555,"\int x^m (a+b x)^3 \, dx","IntegrateAlgebraic[x^m*(a + b*x)^3,x]","\int x^m (a+b x)^3 \, dx","\frac{a^3 x^{m+1}}{m+1}+\frac{3 a^2 b x^{m+2}}{m+2}+\frac{3 a b^2 x^{m+3}}{m+3}+\frac{b^3 x^{m+4}}{m+4}",1,"Could not integrate","F",-1
702,0,0,43,0.0000554,"\int x^m (a+b x)^2 \, dx","IntegrateAlgebraic[x^m*(a + b*x)^2,x]","\int x^m (a+b x)^2 \, dx","\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,"Could not integrate","F",-1
703,0,0,25,0.000048,"\int x^m (a+b x) \, dx","IntegrateAlgebraic[x^m*(a + b*x),x]","\int x^m (a+b x) \, dx","\frac{a x^{m+1}}{m+1}+\frac{b x^{m+2}}{m+2}",1,"Could not integrate","F",-1
704,0,0,29,0.0000524,"\int \frac{x^m}{a+b x} \, dx","IntegrateAlgebraic[x^m/(a + b*x),x]","\int \frac{x^m}{a+b x} \, dx","\frac{x^{m+1} \, _2F_1\left(1,m+1;m+2;-\frac{b x}{a}\right)}{a (m+1)}",1,"Could not integrate","F",-1
705,0,0,29,0.0000567,"\int \frac{x^m}{(a+b x)^2} \, dx","IntegrateAlgebraic[x^m/(a + b*x)^2,x]","\int \frac{x^m}{(a+b x)^2} \, dx","\frac{x^{m+1} \, _2F_1\left(2,m+1;m+2;-\frac{b x}{a}\right)}{a^2 (m+1)}",1,"Could not integrate","F",-1
706,0,0,29,0.0000564,"\int \frac{x^m}{(a+b x)^3} \, dx","IntegrateAlgebraic[x^m/(a + b*x)^3,x]","\int \frac{x^m}{(a+b x)^3} \, dx","\frac{x^{m+1} \, _2F_1\left(3,m+1;m+2;-\frac{b x}{a}\right)}{a^3 (m+1)}",1,"Could not integrate","F",-1
707,0,0,48,0.0000574,"\int x^m (a+b x)^{5/2} \, dx","IntegrateAlgebraic[x^m*(a + b*x)^(5/2),x]","\int x^m (a+b x)^{5/2} \, dx","\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,"Could not integrate","F",-1
708,0,0,48,0.0000559,"\int x^m (a+b x)^{3/2} \, dx","IntegrateAlgebraic[x^m*(a + b*x)^(3/2),x]","\int x^m (a+b x)^{3/2} \, dx","\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,"Could not integrate","F",-1
709,0,0,48,0.0000569,"\int x^m \sqrt{a+b x} \, dx","IntegrateAlgebraic[x^m*Sqrt[a + b*x],x]","\int x^m \sqrt{a+b x} \, dx","\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,"Could not integrate","F",-1
710,0,0,46,0.0000562,"\int \frac{x^m}{\sqrt{a+b x}} \, dx","IntegrateAlgebraic[x^m/Sqrt[a + b*x],x]","\int \frac{x^m}{\sqrt{a+b x}} \, dx","\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,"Could not integrate","F",-1
711,0,0,46,0.0000566,"\int \frac{x^m}{(a+b x)^{3/2}} \, dx","IntegrateAlgebraic[x^m/(a + b*x)^(3/2),x]","\int \frac{x^m}{(a+b x)^{3/2}} \, dx","-\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,"Could not integrate","F",-1
712,0,0,48,0.0000582,"\int \frac{x^m}{(a+b x)^{5/2}} \, dx","IntegrateAlgebraic[x^m/(a + b*x)^(5/2),x]","\int \frac{x^m}{(a+b x)^{5/2}} \, dx","-\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,"Could not integrate","F",-1
713,0,0,51,0.0000818,"\int \frac{x^{2+m}}{\sqrt{a+b x}} \, dx","IntegrateAlgebraic[x^(2 + m)/Sqrt[a + b*x],x]","\int \frac{x^{2+m}}{\sqrt{a+b x}} \, dx","\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,"Could not integrate","F",-1
714,0,0,49,0.0000583,"\int \frac{x^{1+m}}{\sqrt{a+b x}} \, dx","IntegrateAlgebraic[x^(1 + m)/Sqrt[a + b*x],x]","\int \frac{x^{1+m}}{\sqrt{a+b x}} \, dx","-\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,"Could not integrate","F",-1
715,0,0,46,0.0000548,"\int \frac{x^m}{\sqrt{a+b x}} \, dx","IntegrateAlgebraic[x^m/Sqrt[a + b*x],x]","\int \frac{x^m}{\sqrt{a+b x}} \, dx","\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,"Could not integrate","F",-1
716,0,0,48,0.0000585,"\int \frac{x^{-1+m}}{\sqrt{a+b x}} \, dx","IntegrateAlgebraic[x^(-1 + m)/Sqrt[a + b*x],x]","\int \frac{x^{-1+m}}{\sqrt{a+b x}} \, dx","-\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,"Could not integrate","F",-1
717,0,0,49,0.0000591,"\int \frac{x^{-2+m}}{\sqrt{a+b x}} \, dx","IntegrateAlgebraic[x^(-2 + m)/Sqrt[a + b*x],x]","\int \frac{x^{-2+m}}{\sqrt{a+b x}} \, dx","\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,"Could not integrate","F",-1
718,0,0,51,0.0000594,"\int \frac{x^{-3+m}}{\sqrt{a+b x}} \, dx","IntegrateAlgebraic[x^(-3 + m)/Sqrt[a + b*x],x]","\int \frac{x^{-3+m}}{\sqrt{a+b x}} \, dx","-\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,"Could not integrate","F",-1
719,0,0,31,0.0000546,"\int \frac{x^m}{\sqrt{2+3 x}} \, dx","IntegrateAlgebraic[x^m/Sqrt[2 + 3*x],x]","\int \frac{x^m}{\sqrt{2+3 x}} \, dx","\frac{x^{m+1} \, _2F_1\left(\frac{1}{2},m+1;m+2;-\frac{3 x}{2}\right)}{\sqrt{2} (m+1)}",1,"Could not integrate","F",-1
720,0,0,31,0.0000547,"\int \frac{x^m}{\sqrt{2-3 x}} \, dx","IntegrateAlgebraic[x^m/Sqrt[2 - 3*x],x]","\int \frac{x^m}{\sqrt{2-3 x}} \, dx","\frac{x^{m+1} \, _2F_1\left(\frac{1}{2},m+1;m+2;\frac{3 x}{2}\right)}{\sqrt{2} (m+1)}",1,"Could not integrate","F",-1
721,0,0,36,0.0000534,"\int \frac{x^m}{\sqrt{-2+3 x}} \, dx","IntegrateAlgebraic[x^m/Sqrt[-2 + 3*x],x]","\int \frac{x^m}{\sqrt{-2+3 x}} \, dx","\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,"Could not integrate","F",-1
722,0,0,50,0.0000542,"\int \frac{x^m}{\sqrt{-2-3 x}} \, dx","IntegrateAlgebraic[x^m/Sqrt[-2 - 3*x],x]","\int \frac{x^m}{\sqrt{-2-3 x}} \, dx","-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,"Could not integrate","F",-1
723,0,0,48,0.0000563,"\int \frac{(-x)^m}{\sqrt{a+b x}} \, dx","IntegrateAlgebraic[(-x)^m/Sqrt[a + b*x],x]","\int \frac{(-x)^m}{\sqrt{a+b x}} \, dx","\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,"Could not integrate","F",-1
724,0,0,34,0.0000942,"\int \frac{(-x)^m}{\sqrt{2+3 x}} \, dx","IntegrateAlgebraic[(-x)^m/Sqrt[2 + 3*x],x]","\int \frac{(-x)^m}{\sqrt{2+3 x}} \, dx","-\frac{(-x)^{m+1} \, _2F_1\left(\frac{1}{2},m+1;m+2;-\frac{3 x}{2}\right)}{\sqrt{2} (m+1)}",1,"Could not integrate","F",-1
725,0,0,34,0.0000567,"\int \frac{(-x)^m}{\sqrt{2-3 x}} \, dx","IntegrateAlgebraic[(-x)^m/Sqrt[2 - 3*x],x]","\int \frac{(-x)^m}{\sqrt{2-3 x}} \, dx","-\frac{(-x)^{m+1} \, _2F_1\left(\frac{1}{2},m+1;m+2;\frac{3 x}{2}\right)}{\sqrt{2} (m+1)}",1,"Could not integrate","F",-1
726,0,0,49,0.0000547,"\int \frac{(-x)^m}{\sqrt{-2+3 x}} \, dx","IntegrateAlgebraic[(-x)^m/Sqrt[-2 + 3*x],x]","\int \frac{(-x)^m}{\sqrt{-2+3 x}} \, dx","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,"Could not integrate","F",-1
727,0,0,37,0.0001868,"\int \frac{(-x)^m}{\sqrt{-2-3 x}} \, dx","IntegrateAlgebraic[(-x)^m/Sqrt[-2 - 3*x],x]","\int \frac{(-x)^m}{\sqrt{-2-3 x}} \, dx","-\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,"Could not integrate","F",-1
728,0,0,26,0.000053,"\int \frac{x^n}{\sqrt{1-x}} \, dx","IntegrateAlgebraic[x^n/Sqrt[1 - x],x]","\int \frac{x^n}{\sqrt{1-x}} \, dx","-2 \sqrt{1-x} \, _2F_1\left(\frac{1}{2},-n;\frac{3}{2};1-x\right)",1,"Could not integrate","F",-1
729,0,0,30,0.0000546,"\int \frac{x^n}{\sqrt{a-a x}} \, dx","IntegrateAlgebraic[x^n/Sqrt[a - a*x],x]","\int \frac{x^n}{\sqrt{a-a x}} \, dx","-\frac{2 \sqrt{a-a x} \, _2F_1\left(\frac{1}{2},-n;\frac{3}{2};1-x\right)}{a}",1,"Could not integrate","F",-1
730,0,0,47,0.0000545,"\int x^m (a+b x)^n \, dx","IntegrateAlgebraic[x^m*(a + b*x)^n,x]","\int x^m (a+b x)^n \, dx","\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,"Could not integrate","F",-1
731,0,0,52,0.0000591,"\int (c x)^m (a+b x)^n \, dx","IntegrateAlgebraic[(c*x)^m*(a + b*x)^n,x]","\int (c x)^m (a+b x)^n \, dx","\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,"Could not integrate","F",-1
732,0,0,83,0.0000536,"\int x^3 (a+b x)^n \, dx","IntegrateAlgebraic[x^3*(a + b*x)^n,x]","\int x^3 (a+b x)^n \, dx","-\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,"Could not integrate","F",-1
733,0,0,60,0.0000491,"\int x^2 (a+b x)^n \, dx","IntegrateAlgebraic[x^2*(a + b*x)^n,x]","\int x^2 (a+b x)^n \, dx","\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,"Could not integrate","F",-1
734,0,0,39,0.0000538,"\int x (a+b x)^n \, dx","IntegrateAlgebraic[x*(a + b*x)^n,x]","\int x (a+b x)^n \, dx","\frac{(a+b x)^{n+2}}{b^2 (n+2)}-\frac{a (a+b x)^{n+1}}{b^2 (n+1)}",1,"Could not integrate","F",-1
735,0,0,18,0.0000427,"\int (a+b x)^n \, dx","IntegrateAlgebraic[(a + b*x)^n,x]","\int (a+b x)^n \, dx","\frac{(a+b x)^{n+1}}{b (n+1)}",1,"Could not integrate","F",-1
736,0,0,35,0.0000925,"\int \frac{(a+b x)^n}{x} \, dx","IntegrateAlgebraic[(a + b*x)^n/x,x]","\int \frac{(a+b x)^n}{x} \, dx","-\frac{(a+b x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b x}{a}+1\right)}{a (n+1)}",1,"Could not integrate","F",-1
737,0,0,35,0.0000536,"\int \frac{(a+b x)^n}{x^2} \, dx","IntegrateAlgebraic[(a + b*x)^n/x^2,x]","\int \frac{(a+b x)^n}{x^2} \, dx","\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,"Could not integrate","F",-1
738,0,0,38,0.0000541,"\int \frac{(a+b x)^n}{x^3} \, dx","IntegrateAlgebraic[(a + b*x)^n/x^3,x]","\int \frac{(a+b x)^n}{x^3} \, dx","-\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,"Could not integrate","F",-1
739,0,0,110,0.0000803,"\int x^{-4+n} (a+b x)^{-n} \, dx","IntegrateAlgebraic[x^(-4 + n)/(a + b*x)^n,x]","\int x^{-4+n} (a+b x)^{-n} \, dx","-\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,"Could not integrate","F",-1
740,0,0,64,0.0000582,"\int x^{-3+n} (a+b x)^{-n} \, dx","IntegrateAlgebraic[x^(-3 + n)/(a + b*x)^n,x]","\int x^{-3+n} (a+b x)^{-n} \, dx","\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,"Could not integrate","F",-1
741,0,0,28,0.0000586,"\int x^{-2+n} (a+b x)^{-n} \, dx","IntegrateAlgebraic[x^(-2 + n)/(a + b*x)^n,x]","\int x^{-2+n} (a+b x)^{-n} \, dx","-\frac{x^{n-1} (a+b x)^{1-n}}{a (1-n)}",1,"Could not integrate","F",-1
742,0,0,39,0.0000521,"\int x^{-1+n} (a+b x)^{-n} \, dx","IntegrateAlgebraic[x^(-1 + n)/(a + b*x)^n,x]","\int x^{-1+n} (a+b x)^{-n} \, dx","\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,"Could not integrate","F",-1
743,0,0,45,0.0000596,"\int x^n (a+b x)^{-n} \, dx","IntegrateAlgebraic[x^n/(a + b*x)^n,x]","\int x^n (a+b x)^{-n} \, dx","\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,"Could not integrate","F",-1
744,0,0,45,0.0000606,"\int x^{1+n} (a+b x)^{-n} \, dx","IntegrateAlgebraic[x^(1 + n)/(a + b*x)^n,x]","\int x^{1+n} (a+b x)^{-n} \, dx","\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,"Could not integrate","F",-1
745,0,0,45,0.0000549,"\int x^{3/2} (a+b x)^n \, dx","IntegrateAlgebraic[x^(3/2)*(a + b*x)^n,x]","\int x^{3/2} (a+b x)^n \, dx","\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,"Could not integrate","F",-1
746,0,0,45,0.0000538,"\int \sqrt{x} (a+b x)^n \, dx","IntegrateAlgebraic[Sqrt[x]*(a + b*x)^n,x]","\int \sqrt{x} (a+b x)^n \, dx","\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,"Could not integrate","F",-1
747,0,0,43,0.0000594,"\int \frac{(a+b x)^n}{\sqrt{x}} \, dx","IntegrateAlgebraic[(a + b*x)^n/Sqrt[x],x]","\int \frac{(a+b x)^n}{\sqrt{x}} \, dx","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,"Could not integrate","F",-1
748,0,0,43,0.0000541,"\int \frac{(a+b x)^n}{x^{3/2}} \, dx","IntegrateAlgebraic[(a + b*x)^n/x^(3/2),x]","\int \frac{(a+b x)^n}{x^{3/2}} \, dx","-\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,"Could not integrate","F",-1
749,0,0,45,0.0000544,"\int \frac{(a+b x)^n}{x^{5/2}} \, dx","IntegrateAlgebraic[(a + b*x)^n/x^(5/2),x]","\int \frac{(a+b x)^n}{x^{5/2}} \, dx","-\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,"Could not integrate","F",-1
750,0,0,35,0.0000821,"\int (b x)^m (2+d x)^n \, dx","IntegrateAlgebraic[(b*x)^m*(2 + d*x)^n,x]","\int (b x)^m (2+d x)^n \, dx","\frac{2^n (b x)^{m+1} \, _2F_1\left(m+1,-n;m+2;-\frac{d x}{2}\right)}{b (m+1)}",1,"Could not integrate","F",-1
751,0,0,40,0.0000601,"\int (b x)^m (c-b c x)^n \, dx","IntegrateAlgebraic[(b*x)^m*(c - b*c*x)^n,x]","\int (b x)^m (c-b c x)^n \, dx","-\frac{(c-b c x)^{n+1} \, _2F_1(-m,n+1;n+2;1-b x)}{b c (n+1)}",1,"Could not integrate","F",-1
752,0,0,52,0.000057,"\int (b x)^m (c+d x)^n \, dx","IntegrateAlgebraic[(b*x)^m*(c + d*x)^n,x]","\int (b x)^m (c+d x)^n \, dx","\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,"Could not integrate","F",-1
753,0,0,19,0.0000608,"\int x^{-1+n} (a+b x)^{-1-n} \, dx","IntegrateAlgebraic[x^(-1 + n)*(a + b*x)^(-1 - n),x]","\int x^{-1+n} (a+b x)^{-1-n} \, dx","\frac{x^n (a+b x)^{-n}}{a n}",1,"Could not integrate","F",-1
754,0,0,58,0.0000498,"\int x^{-3-n} (a+b x)^n \, dx","IntegrateAlgebraic[x^(-3 - n)*(a + b*x)^n,x]","\int x^{-3-n} (a+b x)^n \, dx","\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,"Could not integrate","F",-1
755,0,0,58,0.0000546,"\int x^{2 n-3 (1+n)} (a+b x)^n \, dx","IntegrateAlgebraic[x^(2*n - 3*(1 + n))*(a + b*x)^n,x]","\int x^{2 n-3 (1+n)} (a+b x)^n \, dx","\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,"Could not integrate","F",-1
756,0,0,35,0.1919803,"\int x^3 \sqrt{c x^2} (a+b x) \, dx","IntegrateAlgebraic[x^3*Sqrt[c*x^2]*(a + b*x),x]","\int x^3 \sqrt{c x^2} (a+b x) \, dx","\frac{1}{5} a x^4 \sqrt{c x^2}+\frac{1}{6} b x^5 \sqrt{c x^2}",1,"Could not integrate","F",-1
757,0,0,35,0.1664117,"\int x^2 \sqrt{c x^2} (a+b x) \, dx","IntegrateAlgebraic[x^2*Sqrt[c*x^2]*(a + b*x),x]","\int x^2 \sqrt{c x^2} (a+b x) \, dx","\frac{1}{4} a x^3 \sqrt{c x^2}+\frac{1}{5} b x^4 \sqrt{c x^2}",1,"Could not integrate","F",-1
758,0,0,35,0.1606683,"\int x \sqrt{c x^2} (a+b x) \, dx","IntegrateAlgebraic[x*Sqrt[c*x^2]*(a + b*x),x]","\int x \sqrt{c x^2} (a+b x) \, dx","\frac{1}{3} a x^2 \sqrt{c x^2}+\frac{1}{4} b x^3 \sqrt{c x^2}",1,"Could not integrate","F",-1
759,0,0,33,0.1446345,"\int \sqrt{c x^2} (a+b x) \, dx","IntegrateAlgebraic[Sqrt[c*x^2]*(a + b*x),x]","\int \sqrt{c x^2} (a+b x) \, dx","\frac{1}{2} a x \sqrt{c x^2}+\frac{1}{3} b x^2 \sqrt{c x^2}",1,"Could not integrate","F",-1
760,0,0,27,0.1581344,"\int \frac{\sqrt{c x^2} (a+b x)}{x} \, dx","IntegrateAlgebraic[(Sqrt[c*x^2]*(a + b*x))/x,x]","\int \frac{\sqrt{c x^2} (a+b x)}{x} \, dx","a \sqrt{c x^2}+\frac{1}{2} b x \sqrt{c x^2}",1,"Could not integrate","F",-1
761,1,53,28,0.1390323,"\int \frac{\sqrt{c x^2} (a+b x)}{x^2} \, dx","IntegrateAlgebraic[(Sqrt[c*x^2]*(a + b*x))/x^2,x]","-a \sqrt{c} \log \left(\sqrt{c x^2}-\sqrt{c} x\right)+\frac{1}{2} b \sqrt{c x^2}-\frac{1}{2} b \sqrt{c} x","\frac{a \sqrt{c x^2} \log (x)}{x}+b \sqrt{c x^2}",1,"-1/2*(b*Sqrt[c]*x) + (b*Sqrt[c*x^2])/2 - a*Sqrt[c]*Log[-(Sqrt[c]*x) + Sqrt[c*x^2]]","A",0
762,1,52,32,0.1598778,"\int \frac{\sqrt{c x^2} (a+b x)}{x^3} \, dx","IntegrateAlgebraic[(Sqrt[c*x^2]*(a + b*x))/x^3,x]","-\frac{2 a c}{\sqrt{c x^2}-\sqrt{c} x}-b \sqrt{c} \log \left(\sqrt{c x^2}-\sqrt{c} x\right)","\frac{b \sqrt{c x^2} \log (x)}{x}-\frac{a \sqrt{c x^2}}{x^2}",1,"(-2*a*c)/(-(Sqrt[c]*x) + Sqrt[c*x^2]) - b*Sqrt[c]*Log[-(Sqrt[c]*x) + Sqrt[c*x^2]]","A",0
763,0,0,26,0.1471738,"\int \frac{\sqrt{c x^2} (a+b x)}{x^4} \, dx","IntegrateAlgebraic[(Sqrt[c*x^2]*(a + b*x))/x^4,x]","\int \frac{\sqrt{c x^2} (a+b x)}{x^4} \, dx","-\frac{\sqrt{c x^2} (a+b x)^2}{2 a x^3}",1,"Could not integrate","F",-1
764,0,0,37,0.1796529,"\int x^3 \left(c x^2\right)^{3/2} (a+b x) \, dx","IntegrateAlgebraic[x^3*(c*x^2)^(3/2)*(a + b*x),x]","\int x^3 \left(c x^2\right)^{3/2} (a+b x) \, dx","\frac{1}{7} a c x^6 \sqrt{c x^2}+\frac{1}{8} b c x^7 \sqrt{c x^2}",1,"Could not integrate","F",-1
765,0,0,37,0.1810209,"\int x^2 \left(c x^2\right)^{3/2} (a+b x) \, dx","IntegrateAlgebraic[x^2*(c*x^2)^(3/2)*(a + b*x),x]","\int x^2 \left(c x^2\right)^{3/2} (a+b x) \, dx","\frac{1}{6} a c x^5 \sqrt{c x^2}+\frac{1}{7} b c x^6 \sqrt{c x^2}",1,"Could not integrate","F",-1
766,0,0,37,0.1792496,"\int x \left(c x^2\right)^{3/2} (a+b x) \, dx","IntegrateAlgebraic[x*(c*x^2)^(3/2)*(a + b*x),x]","\int x \left(c x^2\right)^{3/2} (a+b x) \, dx","\frac{1}{5} a c x^4 \sqrt{c x^2}+\frac{1}{6} b c x^5 \sqrt{c x^2}",1,"Could not integrate","F",-1
767,0,0,37,0.1715094,"\int \left(c x^2\right)^{3/2} (a+b x) \, dx","IntegrateAlgebraic[(c*x^2)^(3/2)*(a + b*x),x]","\int \left(c x^2\right)^{3/2} (a+b x) \, dx","\frac{1}{4} a c x^3 \sqrt{c x^2}+\frac{1}{5} b c x^4 \sqrt{c x^2}",1,"Could not integrate","F",-1
768,0,0,37,0.1745794,"\int \frac{\left(c x^2\right)^{3/2} (a+b x)}{x} \, dx","IntegrateAlgebraic[((c*x^2)^(3/2)*(a + b*x))/x,x]","\int \frac{\left(c x^2\right)^{3/2} (a+b x)}{x} \, dx","\frac{1}{3} a c x^2 \sqrt{c x^2}+\frac{1}{4} b c x^3 \sqrt{c x^2}",1,"Could not integrate","F",-1
769,0,0,35,0.148861,"\int \frac{\left(c x^2\right)^{3/2} (a+b x)}{x^2} \, dx","IntegrateAlgebraic[((c*x^2)^(3/2)*(a + b*x))/x^2,x]","\int \frac{\left(c x^2\right)^{3/2} (a+b x)}{x^2} \, dx","\frac{1}{2} a c x \sqrt{c x^2}+\frac{1}{3} b c x^2 \sqrt{c x^2}",1,"Could not integrate","F",-1
770,0,0,29,0.1671406,"\int \frac{\left(c x^2\right)^{3/2} (a+b x)}{x^3} \, dx","IntegrateAlgebraic[((c*x^2)^(3/2)*(a + b*x))/x^3,x]","\int \frac{\left(c x^2\right)^{3/2} (a+b x)}{x^3} \, dx","a c \sqrt{c x^2}+\frac{1}{2} b c x \sqrt{c x^2}",1,"Could not integrate","F",-1
771,1,54,30,0.1424072,"\int \frac{\left(c x^2\right)^{3/2} (a+b x)}{x^4} \, dx","IntegrateAlgebraic[((c*x^2)^(3/2)*(a + b*x))/x^4,x]","-a c^{3/2} \log \left(\sqrt{c x^2}-\sqrt{c} x\right)-\frac{1}{2} b c^{3/2} x+\frac{1}{2} b c \sqrt{c x^2}","\frac{a c \sqrt{c x^2} \log (x)}{x}+b c \sqrt{c x^2}",1,"-1/2*(b*c^(3/2)*x) + (b*c*Sqrt[c*x^2])/2 - a*c^(3/2)*Log[-(Sqrt[c]*x) + Sqrt[c*x^2]]","A",0
772,0,0,41,0.1849559,"\int x^3 \left(c x^2\right)^{5/2} (a+b x) \, dx","IntegrateAlgebraic[x^3*(c*x^2)^(5/2)*(a + b*x),x]","\int x^3 \left(c x^2\right)^{5/2} (a+b x) \, dx","\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,"Could not integrate","F",-1
773,0,0,41,0.180335,"\int x^2 \left(c x^2\right)^{5/2} (a+b x) \, dx","IntegrateAlgebraic[x^2*(c*x^2)^(5/2)*(a + b*x),x]","\int x^2 \left(c x^2\right)^{5/2} (a+b x) \, dx","\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,"Could not integrate","F",-1
774,0,0,41,0.1797847,"\int x \left(c x^2\right)^{5/2} (a+b x) \, dx","IntegrateAlgebraic[x*(c*x^2)^(5/2)*(a + b*x),x]","\int x \left(c x^2\right)^{5/2} (a+b x) \, dx","\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,"Could not integrate","F",-1
775,0,0,41,0.180791,"\int \left(c x^2\right)^{5/2} (a+b x) \, dx","IntegrateAlgebraic[(c*x^2)^(5/2)*(a + b*x),x]","\int \left(c x^2\right)^{5/2} (a+b x) \, dx","\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,"Could not integrate","F",-1
776,0,0,41,0.1844753,"\int \frac{\left(c x^2\right)^{5/2} (a+b x)}{x} \, dx","IntegrateAlgebraic[((c*x^2)^(5/2)*(a + b*x))/x,x]","\int \frac{\left(c x^2\right)^{5/2} (a+b x)}{x} \, dx","\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,"Could not integrate","F",-1
777,0,0,41,0.1682347,"\int \frac{\left(c x^2\right)^{5/2} (a+b x)}{x^2} \, dx","IntegrateAlgebraic[((c*x^2)^(5/2)*(a + b*x))/x^2,x]","\int \frac{\left(c x^2\right)^{5/2} (a+b x)}{x^2} \, dx","\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,"Could not integrate","F",-1
778,0,0,41,0.1680758,"\int \frac{\left(c x^2\right)^{5/2} (a+b x)}{x^3} \, dx","IntegrateAlgebraic[((c*x^2)^(5/2)*(a + b*x))/x^3,x]","\int \frac{\left(c x^2\right)^{5/2} (a+b x)}{x^3} \, dx","\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,"Could not integrate","F",-1
779,0,0,39,0.1560878,"\int \frac{\left(c x^2\right)^{5/2} (a+b x)}{x^4} \, dx","IntegrateAlgebraic[((c*x^2)^(5/2)*(a + b*x))/x^4,x]","\int \frac{\left(c x^2\right)^{5/2} (a+b x)}{x^4} \, dx","\frac{1}{2} a c^2 x \sqrt{c x^2}+\frac{1}{3} b c^2 x^2 \sqrt{c x^2}",1,"Could not integrate","F",-1
780,0,0,35,0.191293,"\int \frac{x^3 (a+b x)}{\sqrt{c x^2}} \, dx","IntegrateAlgebraic[(x^3*(a + b*x))/Sqrt[c*x^2],x]","\int \frac{x^3 (a+b x)}{\sqrt{c x^2}} \, dx","\frac{a x^4}{3 \sqrt{c x^2}}+\frac{b x^5}{4 \sqrt{c x^2}}",1,"Could not integrate","F",-1
781,0,0,35,0.1749025,"\int \frac{x^2 (a+b x)}{\sqrt{c x^2}} \, dx","IntegrateAlgebraic[(x^2*(a + b*x))/Sqrt[c*x^2],x]","\int \frac{x^2 (a+b x)}{\sqrt{c x^2}} \, dx","\frac{a x^3}{2 \sqrt{c x^2}}+\frac{b x^4}{3 \sqrt{c x^2}}",1,"Could not integrate","F",-1
782,0,0,32,0.1731857,"\int \frac{x (a+b x)}{\sqrt{c x^2}} \, dx","IntegrateAlgebraic[(x*(a + b*x))/Sqrt[c*x^2],x]","\int \frac{x (a+b x)}{\sqrt{c x^2}} \, dx","\frac{a x^2}{\sqrt{c x^2}}+\frac{b x^3}{2 \sqrt{c x^2}}",1,"Could not integrate","F",-1
783,1,56,29,0.1314323,"\int \frac{a+b x}{\sqrt{c x^2}} \, dx","IntegrateAlgebraic[(a + b*x)/Sqrt[c*x^2],x]","-\frac{a \log \left(\sqrt{c x^2}-\sqrt{c} x\right)}{\sqrt{c}}+\frac{b \sqrt{c x^2}}{2 c}-\frac{b x}{2 \sqrt{c}}","\frac{a x \log (x)}{\sqrt{c x^2}}+\frac{b x^2}{\sqrt{c x^2}}",1,"-1/2*(b*x)/Sqrt[c] + (b*Sqrt[c*x^2])/(2*c) - (a*Log[-(Sqrt[c]*x) + Sqrt[c*x^2]])/Sqrt[c]","A",0
784,1,51,27,0.1448914,"\int \frac{a+b x}{x \sqrt{c x^2}} \, dx","IntegrateAlgebraic[(a + b*x)/(x*Sqrt[c*x^2]),x]","-\frac{2 a}{\sqrt{c x^2}-\sqrt{c} x}-\frac{b \log \left(\sqrt{c x^2}-\sqrt{c} x\right)}{\sqrt{c}}","\frac{b x \log (x)}{\sqrt{c x^2}}-\frac{a}{\sqrt{c x^2}}",1,"(-2*a)/(-(Sqrt[c]*x) + Sqrt[c*x^2]) - (b*Log[-(Sqrt[c]*x) + Sqrt[c*x^2]])/Sqrt[c]","A",0
785,0,0,26,0.1497035,"\int \frac{a+b x}{x^2 \sqrt{c x^2}} \, dx","IntegrateAlgebraic[(a + b*x)/(x^2*Sqrt[c*x^2]),x]","\int \frac{a+b x}{x^2 \sqrt{c x^2}} \, dx","-\frac{(a+b x)^2}{2 a x \sqrt{c x^2}}",1,"Could not integrate","F",-1
786,1,55,35,0.1660509,"\int \frac{a+b x}{x^3 \sqrt{c x^2}} \, dx","IntegrateAlgebraic[(a + b*x)/(x^3*Sqrt[c*x^2]),x]","\frac{2 b \sqrt{c}}{\left(\sqrt{c x^2}-\sqrt{c} x\right)^2}-\frac{8 a c}{3 \left(\sqrt{c x^2}-\sqrt{c} x\right)^3}","-\frac{a}{3 x^2 \sqrt{c x^2}}-\frac{b}{2 x \sqrt{c x^2}}",1,"(-8*a*c)/(3*(-(Sqrt[c]*x) + Sqrt[c*x^2])^3) + (2*b*Sqrt[c])/(-(Sqrt[c]*x) + Sqrt[c*x^2])^2","A",0
787,1,55,35,0.1774063,"\int \frac{a+b x}{x^4 \sqrt{c x^2}} \, dx","IntegrateAlgebraic[(a + b*x)/(x^4*Sqrt[c*x^2]),x]","\frac{4 a c^{3/2}}{\left(\sqrt{c x^2}-\sqrt{c} x\right)^4}-\frac{8 b c}{3 \left(\sqrt{c x^2}-\sqrt{c} x\right)^3}","-\frac{a}{4 x^3 \sqrt{c x^2}}-\frac{b}{3 x^2 \sqrt{c x^2}}",1,"(4*a*c^(3/2))/(-(Sqrt[c]*x) + Sqrt[c*x^2])^4 - (8*b*c)/(3*(-(Sqrt[c]*x) + Sqrt[c*x^2])^3)","A",0
788,0,0,38,0.1729865,"\int \frac{x^3 (a+b x)}{\left(c x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[(x^3*(a + b*x))/(c*x^2)^(3/2),x]","\int \frac{x^3 (a+b x)}{\left(c x^2\right)^{3/2}} \, dx","\frac{a x^2}{c \sqrt{c x^2}}+\frac{b x^3}{2 c \sqrt{c x^2}}",1,"Could not integrate","F",-1
789,1,56,35,0.1365132,"\int \frac{x^2 (a+b x)}{\left(c x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[(x^2*(a + b*x))/(c*x^2)^(3/2),x]","-\frac{a \log \left(\sqrt{c x^2}-\sqrt{c} x\right)}{c^{3/2}}-\frac{b x}{2 c^{3/2}}+\frac{b \sqrt{c x^2}}{2 c^2}","\frac{a x \log (x)}{c \sqrt{c x^2}}+\frac{b x^2}{c \sqrt{c x^2}}",1,"-1/2*(b*x)/c^(3/2) + (b*Sqrt[c*x^2])/(2*c^2) - (a*Log[-(Sqrt[c]*x) + Sqrt[c*x^2]])/c^(3/2)","A",0
790,1,53,33,0.1560481,"\int \frac{x (a+b x)}{\left(c x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[(x*(a + b*x))/(c*x^2)^(3/2),x]","-\frac{2 a}{c \sqrt{c x^2}-c^{3/2} x}-\frac{b \log \left(\sqrt{c x^2}-\sqrt{c} x\right)}{c^{3/2}}","\frac{b x \log (x)}{c \sqrt{c x^2}}-\frac{a}{c \sqrt{c x^2}}",1,"(-2*a)/(-(c^(3/2)*x) + c*Sqrt[c*x^2]) - (b*Log[-(Sqrt[c]*x) + Sqrt[c*x^2]])/c^(3/2)","A",0
791,0,0,29,0.2071483,"\int \frac{a+b x}{\left(c x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[(a + b*x)/(c*x^2)^(3/2),x]","\int \frac{a+b x}{\left(c x^2\right)^{3/2}} \, dx","-\frac{(a+b x)^2}{2 a c x \sqrt{c x^2}}",1,"Could not integrate","F",-1
792,1,54,41,0.1787663,"\int \frac{a+b x}{x \left(c x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[(a + b*x)/(x*(c*x^2)^(3/2)),x]","\frac{2 b}{\sqrt{c} \left(\sqrt{c x^2}-\sqrt{c} x\right)^2}-\frac{8 a}{3 \left(\sqrt{c x^2}-\sqrt{c} x\right)^3}","-\frac{a}{3 c x^2 \sqrt{c x^2}}-\frac{b}{2 c x \sqrt{c x^2}}",1,"(-8*a)/(3*(-(Sqrt[c]*x) + Sqrt[c*x^2])^3) + (2*b)/(Sqrt[c]*(-(Sqrt[c]*x) + Sqrt[c*x^2])^2)","A",0
793,1,54,41,0.1543234,"\int \frac{a+b x}{x^2 \left(c x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[(a + b*x)/(x^2*(c*x^2)^(3/2)),x]","\frac{4 a \sqrt{c}}{\left(\sqrt{c x^2}-\sqrt{c} x\right)^4}-\frac{8 b}{3 \left(\sqrt{c x^2}-\sqrt{c} x\right)^3}","-\frac{a}{4 c x^3 \sqrt{c x^2}}-\frac{b}{3 c x^2 \sqrt{c x^2}}",1,"(4*a*Sqrt[c])/(-(Sqrt[c]*x) + Sqrt[c*x^2])^4 - (8*b)/(3*(-(Sqrt[c]*x) + Sqrt[c*x^2])^3)","A",0
794,1,55,41,0.1740608,"\int \frac{a+b x}{x^3 \left(c x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[(a + b*x)/(x^3*(c*x^2)^(3/2)),x]","\frac{4 b \sqrt{c}}{\left(\sqrt{c x^2}-\sqrt{c} x\right)^4}-\frac{32 a c}{5 \left(\sqrt{c x^2}-\sqrt{c} x\right)^5}","-\frac{a}{5 c x^4 \sqrt{c x^2}}-\frac{b}{4 c x^3 \sqrt{c x^2}}",1,"(-32*a*c)/(5*(-(Sqrt[c]*x) + Sqrt[c*x^2])^5) + (4*b*Sqrt[c])/(-(Sqrt[c]*x) + Sqrt[c*x^2])^4","A",0
795,1,57,41,0.1634249,"\int \frac{a+b x}{x^4 \left(c x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[(a + b*x)/(x^4*(c*x^2)^(3/2)),x]","\frac{32 a c^{3/2}}{3 \left(\sqrt{c x^2}-\sqrt{c} x\right)^6}-\frac{32 b c}{5 \left(\sqrt{c x^2}-\sqrt{c} x\right)^5}","-\frac{a}{6 c x^5 \sqrt{c x^2}}-\frac{b}{5 c x^4 \sqrt{c x^2}}",1,"(32*a*c^(3/2))/(3*(-(Sqrt[c]*x) + Sqrt[c*x^2])^6) - (32*b*c)/(5*(-(Sqrt[c]*x) + Sqrt[c*x^2])^5)","A",0
796,1,54,33,0.1618175,"\int \frac{x^3 (a+b x)}{\left(c x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[(x^3*(a + b*x))/(c*x^2)^(5/2),x]","-\frac{2 a}{c^2 \left(\sqrt{c x^2}-\sqrt{c} x\right)}-\frac{b \log \left(\sqrt{c x^2}-\sqrt{c} x\right)}{c^{5/2}}","\frac{b x \log (x)}{c^2 \sqrt{c x^2}}-\frac{a}{c^2 \sqrt{c x^2}}",1,"(-2*a)/(c^2*(-(Sqrt[c]*x) + Sqrt[c*x^2])) - (b*Log[-(Sqrt[c]*x) + Sqrt[c*x^2]])/c^(5/2)","A",0
797,0,0,29,0.2046032,"\int \frac{x^2 (a+b x)}{\left(c x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[(x^2*(a + b*x))/(c*x^2)^(5/2),x]","\int \frac{x^2 (a+b x)}{\left(c x^2\right)^{5/2}} \, dx","-\frac{(a+b x)^2}{2 a c^2 x \sqrt{c x^2}}",1,"Could not integrate","F",-1
798,1,57,41,0.1680154,"\int \frac{x (a+b x)}{\left(c x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[(x*(a + b*x))/(c*x^2)^(5/2),x]","\frac{2 b}{c^{3/2} \left(\sqrt{c x^2}-\sqrt{c} x\right)^2}-\frac{8 a}{3 c \left(\sqrt{c x^2}-\sqrt{c} x\right)^3}","-\frac{a}{3 c^2 x^2 \sqrt{c x^2}}-\frac{b}{2 c^2 x \sqrt{c x^2}}",1,"(-8*a)/(3*c*(-(Sqrt[c]*x) + Sqrt[c*x^2])^3) + (2*b)/(c^(3/2)*(-(Sqrt[c]*x) + Sqrt[c*x^2])^2)","A",0
799,1,61,41,0.1921451,"\int \frac{a+b x}{\left(c x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[(a + b*x)/(c*x^2)^(5/2),x]","\frac{\sqrt{c x^2} (3 a+2 b x)-2 b \sqrt{c} x^2}{6 c^{5/2} x^4 \sqrt{c x^2}-6 c^3 x^5}","-\frac{a}{4 c^2 x^3 \sqrt{c x^2}}-\frac{b}{3 c^2 x^2 \sqrt{c x^2}}",1,"(-2*b*Sqrt[c]*x^2 + Sqrt[c*x^2]*(3*a + 2*b*x))/(-6*c^3*x^5 + 6*c^(5/2)*x^4*Sqrt[c*x^2])","A",0
800,1,54,41,0.1815708,"\int \frac{a+b x}{x \left(c x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[(a + b*x)/(x*(c*x^2)^(5/2)),x]","\frac{4 b}{\sqrt{c} \left(\sqrt{c x^2}-\sqrt{c} x\right)^4}-\frac{32 a}{5 \left(\sqrt{c x^2}-\sqrt{c} x\right)^5}","-\frac{a}{5 c^2 x^4 \sqrt{c x^2}}-\frac{b}{4 c^2 x^3 \sqrt{c x^2}}",1,"(-32*a)/(5*(-(Sqrt[c]*x) + Sqrt[c*x^2])^5) + (4*b)/(Sqrt[c]*(-(Sqrt[c]*x) + Sqrt[c*x^2])^4)","A",0
801,1,56,41,0.1533869,"\int \frac{a+b x}{x^2 \left(c x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[(a + b*x)/(x^2*(c*x^2)^(5/2)),x]","\frac{32 a \sqrt{c}}{3 \left(\sqrt{c x^2}-\sqrt{c} x\right)^6}-\frac{32 b}{5 \left(\sqrt{c x^2}-\sqrt{c} x\right)^5}","-\frac{a}{6 c^2 x^5 \sqrt{c x^2}}-\frac{b}{5 c^2 x^4 \sqrt{c x^2}}",1,"(32*a*Sqrt[c])/(3*(-(Sqrt[c]*x) + Sqrt[c*x^2])^6) - (32*b)/(5*(-(Sqrt[c]*x) + Sqrt[c*x^2])^5)","A",0
802,1,57,41,0.172731,"\int \frac{a+b x}{x^3 \left(c x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[(a + b*x)/(x^3*(c*x^2)^(5/2)),x]","\frac{32 b \sqrt{c}}{3 \left(\sqrt{c x^2}-\sqrt{c} x\right)^6}-\frac{128 a c}{7 \left(\sqrt{c x^2}-\sqrt{c} x\right)^7}","-\frac{a}{7 c^2 x^6 \sqrt{c x^2}}-\frac{b}{6 c^2 x^5 \sqrt{c x^2}}",1,"(-128*a*c)/(7*(-(Sqrt[c]*x) + Sqrt[c*x^2])^7) + (32*b*Sqrt[c])/(3*(-(Sqrt[c]*x) + Sqrt[c*x^2])^6)","A",0
803,1,60,41,0.1793141,"\int \frac{a+b x}{x^4 \left(c x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[(a + b*x)/(x^4*(c*x^2)^(5/2)),x]","\frac{-32 c^{3/2} (-7 a-4 b x)-128 b c \sqrt{c x^2}}{896 c^4 x^8-896 c^{7/2} x^7 \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,"(-128*b*c*Sqrt[c*x^2] - 32*c^(3/2)*(-7*a - 4*b*x))/(896*c^4*x^8 - 896*c^(7/2)*x^7*Sqrt[c*x^2])","A",0
804,0,0,57,0.2945097,"\int x^3 \sqrt{c x^2} (a+b x)^2 \, dx","IntegrateAlgebraic[x^3*Sqrt[c*x^2]*(a + b*x)^2,x]","\int x^3 \sqrt{c x^2} (a+b x)^2 \, dx","\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,"Could not integrate","F",-1
805,0,0,57,0.2874253,"\int x^2 \sqrt{c x^2} (a+b x)^2 \, dx","IntegrateAlgebraic[x^2*Sqrt[c*x^2]*(a + b*x)^2,x]","\int x^2 \sqrt{c x^2} (a+b x)^2 \, dx","\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,"Could not integrate","F",-1
806,0,0,57,0.2867421,"\int x \sqrt{c x^2} (a+b x)^2 \, dx","IntegrateAlgebraic[x*Sqrt[c*x^2]*(a + b*x)^2,x]","\int x \sqrt{c x^2} (a+b x)^2 \, dx","\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,"Could not integrate","F",-1
807,0,0,55,0.2688422,"\int \sqrt{c x^2} (a+b x)^2 \, dx","IntegrateAlgebraic[Sqrt[c*x^2]*(a + b*x)^2,x]","\int \sqrt{c x^2} (a+b x)^2 \, dx","\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,"Could not integrate","F",-1
808,0,0,26,0.30735,"\int \frac{\sqrt{c x^2} (a+b x)^2}{x} \, dx","IntegrateAlgebraic[(Sqrt[c*x^2]*(a + b*x)^2)/x,x]","\int \frac{\sqrt{c x^2} (a+b x)^2}{x} \, dx","\frac{\sqrt{c x^2} (a+b x)^3}{3 b x}",1,"Could not integrate","F",-1
809,0,0,49,0.2978558,"\int \frac{\sqrt{c x^2} (a+b x)^2}{x^2} \, dx","IntegrateAlgebraic[(Sqrt[c*x^2]*(a + b*x)^2)/x^2,x]","\int \frac{\sqrt{c x^2} (a+b x)^2}{x^2} \, dx","\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,"Could not integrate","F",-1
810,1,84,49,0.2863876,"\int \frac{\sqrt{c x^2} (a+b x)^2}{x^3} \, dx","IntegrateAlgebraic[(Sqrt[c*x^2]*(a + b*x)^2)/x^3,x]","-\frac{2 a^2 c}{\sqrt{c x^2}-\sqrt{c} x}-2 a b \sqrt{c} \log \left(\sqrt{c x^2}-\sqrt{c} x\right)+\frac{1}{2} b^2 \sqrt{c x^2}-\frac{1}{2} b^2 \sqrt{c} 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}",1,"-1/2*(b^2*Sqrt[c]*x) + (b^2*Sqrt[c*x^2])/2 - (2*a^2*c)/(-(Sqrt[c]*x) + Sqrt[c*x^2]) - 2*a*b*Sqrt[c]*Log[-(Sqrt[c]*x) + Sqrt[c*x^2]]","A",0
811,0,0,54,0.3097257,"\int \frac{\sqrt{c x^2} (a+b x)^2}{x^4} \, dx","IntegrateAlgebraic[(Sqrt[c*x^2]*(a + b*x)^2)/x^4,x]","\int \frac{\sqrt{c x^2} (a+b x)^2}{x^4} \, dx","-\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,"Could not integrate","F",-1
812,0,0,60,0.3004586,"\int x^3 \left(c x^2\right)^{3/2} (a+b x)^2 \, dx","IntegrateAlgebraic[x^3*(c*x^2)^(3/2)*(a + b*x)^2,x]","\int x^3 \left(c x^2\right)^{3/2} (a+b x)^2 \, dx","\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,"Could not integrate","F",-1
813,0,0,60,0.3069575,"\int x^2 \left(c x^2\right)^{3/2} (a+b x)^2 \, dx","IntegrateAlgebraic[x^2*(c*x^2)^(3/2)*(a + b*x)^2,x]","\int x^2 \left(c x^2\right)^{3/2} (a+b x)^2 \, dx","\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,"Could not integrate","F",-1
814,0,0,60,0.3024141,"\int x \left(c x^2\right)^{3/2} (a+b x)^2 \, dx","IntegrateAlgebraic[x*(c*x^2)^(3/2)*(a + b*x)^2,x]","\int x \left(c x^2\right)^{3/2} (a+b x)^2 \, dx","\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,"Could not integrate","F",-1
815,0,0,60,0.2990748,"\int \left(c x^2\right)^{3/2} (a+b x)^2 \, dx","IntegrateAlgebraic[(c*x^2)^(3/2)*(a + b*x)^2,x]","\int \left(c x^2\right)^{3/2} (a+b x)^2 \, dx","\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,"Could not integrate","F",-1
816,0,0,60,0.2935163,"\int \frac{\left(c x^2\right)^{3/2} (a+b x)^2}{x} \, dx","IntegrateAlgebraic[((c*x^2)^(3/2)*(a + b*x)^2)/x,x]","\int \frac{\left(c x^2\right)^{3/2} (a+b x)^2}{x} \, dx","\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,"Could not integrate","F",-1
817,0,0,58,0.2742574,"\int \frac{\left(c x^2\right)^{3/2} (a+b x)^2}{x^2} \, dx","IntegrateAlgebraic[((c*x^2)^(3/2)*(a + b*x)^2)/x^2,x]","\int \frac{\left(c x^2\right)^{3/2} (a+b x)^2}{x^2} \, dx","\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,"Could not integrate","F",-1
818,0,0,27,0.3202592,"\int \frac{\left(c x^2\right)^{3/2} (a+b x)^2}{x^3} \, dx","IntegrateAlgebraic[((c*x^2)^(3/2)*(a + b*x)^2)/x^3,x]","\int \frac{\left(c x^2\right)^{3/2} (a+b x)^2}{x^3} \, dx","\frac{c \sqrt{c x^2} (a+b x)^3}{3 b x}",1,"Could not integrate","F",-1
819,0,0,52,0.3014553,"\int \frac{\left(c x^2\right)^{3/2} (a+b x)^2}{x^4} \, dx","IntegrateAlgebraic[((c*x^2)^(3/2)*(a + b*x)^2)/x^4,x]","\int \frac{\left(c x^2\right)^{3/2} (a+b x)^2}{x^4} \, dx","\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,"Could not integrate","F",-1
820,0,0,66,0.3021886,"\int x \left(c x^2\right)^{5/2} (a+b x)^2 \, dx","IntegrateAlgebraic[x*(c*x^2)^(5/2)*(a + b*x)^2,x]","\int x \left(c x^2\right)^{5/2} (a+b x)^2 \, dx","\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,"Could not integrate","F",-1
821,0,0,66,0.307304,"\int \left(c x^2\right)^{5/2} (a+b x)^2 \, dx","IntegrateAlgebraic[(c*x^2)^(5/2)*(a + b*x)^2,x]","\int \left(c x^2\right)^{5/2} (a+b x)^2 \, dx","\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,"Could not integrate","F",-1
822,0,0,66,0.3020197,"\int \frac{\left(c x^2\right)^{5/2} (a+b x)^2}{x} \, dx","IntegrateAlgebraic[((c*x^2)^(5/2)*(a + b*x)^2)/x,x]","\int \frac{\left(c x^2\right)^{5/2} (a+b x)^2}{x} \, dx","\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,"Could not integrate","F",-1
823,0,0,66,0.2921471,"\int \frac{\left(c x^2\right)^{5/2} (a+b x)^2}{x^2} \, dx","IntegrateAlgebraic[((c*x^2)^(5/2)*(a + b*x)^2)/x^2,x]","\int \frac{\left(c x^2\right)^{5/2} (a+b x)^2}{x^2} \, dx","\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,"Could not integrate","F",-1
824,0,0,66,0.2880124,"\int \frac{\left(c x^2\right)^{5/2} (a+b x)^2}{x^3} \, dx","IntegrateAlgebraic[((c*x^2)^(5/2)*(a + b*x)^2)/x^3,x]","\int \frac{\left(c x^2\right)^{5/2} (a+b x)^2}{x^3} \, dx","\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,"Could not integrate","F",-1
825,0,0,64,0.2762466,"\int \frac{\left(c x^2\right)^{5/2} (a+b x)^2}{x^4} \, dx","IntegrateAlgebraic[((c*x^2)^(5/2)*(a + b*x)^2)/x^4,x]","\int \frac{\left(c x^2\right)^{5/2} (a+b x)^2}{x^4} \, dx","\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,"Could not integrate","F",-1
826,0,0,29,0.3217934,"\int \frac{\left(c x^2\right)^{5/2} (a+b x)^2}{x^5} \, dx","IntegrateAlgebraic[((c*x^2)^(5/2)*(a + b*x)^2)/x^5,x]","\int \frac{\left(c x^2\right)^{5/2} (a+b x)^2}{x^5} \, dx","\frac{c^2 \sqrt{c x^2} (a+b x)^3}{3 b x}",1,"Could not integrate","F",-1
827,0,0,58,0.311809,"\int \frac{\left(c x^2\right)^{5/2} (a+b x)^2}{x^6} \, dx","IntegrateAlgebraic[((c*x^2)^(5/2)*(a + b*x)^2)/x^6,x]","\int \frac{\left(c x^2\right)^{5/2} (a+b x)^2}{x^6} \, dx","\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,"Could not integrate","F",-1
828,0,0,57,0.3392083,"\int \frac{x^3 (a+b x)^2}{\sqrt{c x^2}} \, dx","IntegrateAlgebraic[(x^3*(a + b*x)^2)/Sqrt[c*x^2],x]","\int \frac{x^3 (a+b x)^2}{\sqrt{c x^2}} \, dx","\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,"Could not integrate","F",-1
829,0,0,57,0.3224569,"\int \frac{x^2 (a+b x)^2}{\sqrt{c x^2}} \, dx","IntegrateAlgebraic[(x^2*(a + b*x)^2)/Sqrt[c*x^2],x]","\int \frac{x^2 (a+b x)^2}{\sqrt{c x^2}} \, dx","\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,"Could not integrate","F",-1
830,0,0,24,0.3106333,"\int \frac{x (a+b x)^2}{\sqrt{c x^2}} \, dx","IntegrateAlgebraic[(x*(a + b*x)^2)/Sqrt[c*x^2],x]","\int \frac{x (a+b x)^2}{\sqrt{c x^2}} \, dx","\frac{x (a+b x)^3}{3 b \sqrt{c x^2}}",1,"Could not integrate","F",-1
831,0,0,52,0.3057296,"\int \frac{(a+b x)^2}{\sqrt{c x^2}} \, dx","IntegrateAlgebraic[(a + b*x)^2/Sqrt[c*x^2],x]","\int \frac{(a+b x)^2}{\sqrt{c x^2}} \, dx","\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,"Could not integrate","F",-1
832,1,86,47,0.2943031,"\int \frac{(a+b x)^2}{x \sqrt{c x^2}} \, dx","IntegrateAlgebraic[(a + b*x)^2/(x*Sqrt[c*x^2]),x]","-\frac{2 a^2}{\sqrt{c x^2}-\sqrt{c} x}-\frac{2 a b \log \left(\sqrt{c x^2}-\sqrt{c} x\right)}{\sqrt{c}}+\frac{b^2 \sqrt{c x^2}}{2 c}-\frac{b^2 x}{2 \sqrt{c}}","-\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,"-1/2*(b^2*x)/Sqrt[c] + (b^2*Sqrt[c*x^2])/(2*c) - (2*a^2)/(-(Sqrt[c]*x) + Sqrt[c*x^2]) - (2*a*b*Log[-(Sqrt[c]*x) + Sqrt[c*x^2]])/Sqrt[c]","A",0
833,0,0,49,0.2964808,"\int \frac{(a+b x)^2}{x^2 \sqrt{c x^2}} \, dx","IntegrateAlgebraic[(a + b*x)^2/(x^2*Sqrt[c*x^2]),x]","\int \frac{(a+b x)^2}{x^2 \sqrt{c x^2}} \, dx","-\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,"Could not integrate","F",-1
834,1,79,26,0.2975077,"\int \frac{(a+b x)^2}{x^3 \sqrt{c x^2}} \, dx","IntegrateAlgebraic[(a + b*x)^2/(x^3*Sqrt[c*x^2]),x]","\frac{4 c \left(-2 a^2-3 a b x-3 b^2 x^2\right)+4 \sqrt{c} \sqrt{c x^2} \left(3 a b+3 b^2 x\right)}{12 c x^2 \sqrt{c x^2}-12 c^{3/2} x^3}","-\frac{(a+b x)^3}{3 a x^2 \sqrt{c x^2}}",1,"(4*Sqrt[c]*Sqrt[c*x^2]*(3*a*b + 3*b^2*x) + 4*c*(-2*a^2 - 3*a*b*x - 3*b^2*x^2))/(-12*c^(3/2)*x^3 + 12*c*x^2*Sqrt[c*x^2])","B",0
835,1,81,57,0.3066453,"\int \frac{(a+b x)^2}{x^4 \sqrt{c x^2}} \, dx","IntegrateAlgebraic[(a + b*x)^2/(x^4*Sqrt[c*x^2]),x]","\frac{4 c^{3/2} \left(3 a^2+4 a b x+3 b^2 x^2\right)+4 c \sqrt{c x^2} \left(-4 a b-3 b^2 x\right)}{24 c^2 x^4-24 c^{3/2} x^3 \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,"(4*c*Sqrt[c*x^2]*(-4*a*b - 3*b^2*x) + 4*c^(3/2)*(3*a^2 + 4*a*b*x + 3*b^2*x^2))/(24*c^2*x^4 - 24*c^(3/2)*x^3*Sqrt[c*x^2])","A",0
836,0,0,27,0.3185175,"\int \frac{x^3 (a+b x)^2}{\left(c x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[(x^3*(a + b*x)^2)/(c*x^2)^(3/2),x]","\int \frac{x^3 (a+b x)^2}{\left(c x^2\right)^{3/2}} \, dx","\frac{x (a+b x)^3}{3 b c \sqrt{c x^2}}",1,"Could not integrate","F",-1
837,0,0,61,0.3094106,"\int \frac{x^2 (a+b x)^2}{\left(c x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[(x^2*(a + b*x)^2)/(c*x^2)^(3/2),x]","\int \frac{x^2 (a+b x)^2}{\left(c x^2\right)^{3/2}} \, dx","\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,"Could not integrate","F",-1
838,1,94,56,0.2948395,"\int \frac{x (a+b x)^2}{\left(c x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[(x*(a + b*x)^2)/(c*x^2)^(3/2),x]","\frac{\sqrt{c x^2} \left(2 a^2-b^2 x^2\right)+b^2 \sqrt{c} x^3}{c^{3/2} x \sqrt{c x^2}-c^2 x^2}-\frac{2 a b \log \left(\sqrt{c x^2}-\sqrt{c} x\right)}{c^{3/2}}","-\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,"(b^2*Sqrt[c]*x^3 + Sqrt[c*x^2]*(2*a^2 - b^2*x^2))/(-(c^2*x^2) + c^(3/2)*x*Sqrt[c*x^2]) - (2*a*b*Log[-(Sqrt[c]*x) + Sqrt[c*x^2]])/c^(3/2)","A",0
839,0,0,58,0.3426496,"\int \frac{(a+b x)^2}{\left(c x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[(a + b*x)^2/(c*x^2)^(3/2),x]","\int \frac{(a+b x)^2}{\left(c x^2\right)^{3/2}} \, dx","-\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,"Could not integrate","F",-1
840,1,83,29,0.3207592,"\int \frac{(a+b x)^2}{x \left(c x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[(a + b*x)^2/(x*(c*x^2)^(3/2)),x]","\frac{\sqrt{c x^2} \left(2 a^2+3 a b x+3 b^2 x^2\right)+\sqrt{c} \left(-3 a b x^2-3 b^2 x^3\right)}{3 c^{3/2} x^3 \sqrt{c x^2}-3 c^2 x^4}","-\frac{(a+b x)^3}{3 a c x^2 \sqrt{c x^2}}",1,"(Sqrt[c*x^2]*(2*a^2 + 3*a*b*x + 3*b^2*x^2) + Sqrt[c]*(-3*a*b*x^2 - 3*b^2*x^3))/(-3*c^2*x^4 + 3*c^(3/2)*x^3*Sqrt[c*x^2])","B",0
841,1,83,66,0.3266416,"\int \frac{(a+b x)^2}{x^2 \left(c x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[(a + b*x)^2/(x^2*(c*x^2)^(3/2)),x]","\frac{\sqrt{c x^2} \left(-3 a^2-4 a b x-3 b^2 x^2\right)+\sqrt{c} \left(4 a b x^2+3 b^2 x^3\right)}{6 c^2 x^5-6 c^{3/2} x^4 \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,"(Sqrt[c*x^2]*(-3*a^2 - 4*a*b*x - 3*b^2*x^2) + Sqrt[c]*(4*a*b*x^2 + 3*b^2*x^3))/(6*c^2*x^5 - 6*c^(3/2)*x^4*Sqrt[c*x^2])","A",0
842,1,81,66,0.3285189,"\int \frac{(a+b x)^2}{x^3 \left(c x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[(a + b*x)^2/(x^3*(c*x^2)^(3/2)),x]","\frac{8 c \left(-12 a^2-15 a b x-10 b^2 x^2\right)+8 \sqrt{c} \sqrt{c x^2} \left(15 a b+10 b^2 x\right)}{240 c^2 x^4 \sqrt{c x^2}-240 c^{5/2} x^5}","-\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,"(8*Sqrt[c]*Sqrt[c*x^2]*(15*a*b + 10*b^2*x) + 8*c*(-12*a^2 - 15*a*b*x - 10*b^2*x^2))/(-240*c^(5/2)*x^5 + 240*c^2*x^4*Sqrt[c*x^2])","A",0
843,1,81,66,0.3309447,"\int \frac{(a+b x)^2}{x^4 \left(c x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[(a + b*x)^2/(x^4*(c*x^2)^(3/2)),x]","\frac{8 c^{3/2} \left(20 a^2+24 a b x+15 b^2 x^2\right)+8 c \sqrt{c x^2} \left(-24 a b-15 b^2 x\right)}{480 c^3 x^6-480 c^{5/2} x^5 \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,"(8*c*Sqrt[c*x^2]*(-24*a*b - 15*b^2*x) + 8*c^(3/2)*(20*a^2 + 24*a*b*x + 15*b^2*x^2))/(480*c^3*x^6 - 480*c^(5/2)*x^5*Sqrt[c*x^2])","A",0
844,1,94,56,0.2916661,"\int \frac{x^3 (a+b x)^2}{\left(c x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[(x^3*(a + b*x)^2)/(c*x^2)^(5/2),x]","\frac{\sqrt{c x^2} \left(2 a^2-b^2 x^2\right)+b^2 \sqrt{c} x^3}{c^{5/2} x \sqrt{c x^2}-c^3 x^2}-\frac{2 a b \log \left(\sqrt{c x^2}-\sqrt{c} x\right)}{c^{5/2}}","-\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,"(b^2*Sqrt[c]*x^3 + Sqrt[c*x^2]*(2*a^2 - b^2*x^2))/(-(c^3*x^2) + c^(5/2)*x*Sqrt[c*x^2]) - (2*a*b*Log[-(Sqrt[c]*x) + Sqrt[c*x^2]])/c^(5/2)","A",0
845,0,0,58,0.3480846,"\int \frac{x^2 (a+b x)^2}{\left(c x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[(x^2*(a + b*x)^2)/(c*x^2)^(5/2),x]","\int \frac{x^2 (a+b x)^2}{\left(c x^2\right)^{5/2}} \, dx","-\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,"Could not integrate","F",-1
846,1,83,29,0.3181868,"\int \frac{x (a+b x)^2}{\left(c x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[(x*(a + b*x)^2)/(c*x^2)^(5/2),x]","\frac{\sqrt{c x^2} \left(2 a^2+3 a b x+3 b^2 x^2\right)+\sqrt{c} \left(-3 a b x^2-3 b^2 x^3\right)}{3 c^{5/2} x^3 \sqrt{c x^2}-3 c^3 x^4}","-\frac{(a+b x)^3}{3 a c^2 x^2 \sqrt{c x^2}}",1,"(Sqrt[c*x^2]*(2*a^2 + 3*a*b*x + 3*b^2*x^2) + Sqrt[c]*(-3*a*b*x^2 - 3*b^2*x^3))/(-3*c^3*x^4 + 3*c^(5/2)*x^3*Sqrt[c*x^2])","B",0
847,1,83,66,0.3378264,"\int \frac{(a+b x)^2}{\left(c x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[(a + b*x)^2/(c*x^2)^(5/2),x]","\frac{\sqrt{c x^2} \left(-3 a^2-4 a b x-3 b^2 x^2\right)+\sqrt{c} \left(4 a b x^2+3 b^2 x^3\right)}{6 c^3 x^5-6 c^{5/2} x^4 \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,"(Sqrt[c*x^2]*(-3*a^2 - 4*a*b*x - 3*b^2*x^2) + Sqrt[c]*(4*a*b*x^2 + 3*b^2*x^3))/(6*c^3*x^5 - 6*c^(5/2)*x^4*Sqrt[c*x^2])","A",0
848,1,85,66,0.3305908,"\int \frac{(a+b x)^2}{x \left(c x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[(a + b*x)^2/(x*(c*x^2)^(5/2)),x]","\frac{-8 \sqrt{c x^2} \left(12 a^2+15 a b x+10 b^2 x^2\right)-8 \sqrt{c} \left(-15 a b x^2-10 b^2 x^3\right)}{240 c^3 x^6-240 c^{5/2} x^5 \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,"(-8*Sqrt[c*x^2]*(12*a^2 + 15*a*b*x + 10*b^2*x^2) - 8*Sqrt[c]*(-15*a*b*x^2 - 10*b^2*x^3))/(240*c^3*x^6 - 240*c^(5/2)*x^5*Sqrt[c*x^2])","A",0
849,1,86,66,0.3384878,"\int \frac{(a+b x)^2}{x^2 \left(c x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[(a + b*x)^2/(x^2*(c*x^2)^(5/2)),x]","\frac{8 \sqrt{c} \sqrt{c x^2} \left(20 a^2+24 a b x+15 b^2 x^2\right)+8 c \left(-24 a b x^2-15 b^2 x^3\right)}{480 c^3 x^6 \sqrt{c x^2}-480 c^{7/2} x^7}","-\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,"(8*Sqrt[c]*Sqrt[c*x^2]*(20*a^2 + 24*a*b*x + 15*b^2*x^2) + 8*c*(-24*a*b*x^2 - 15*b^2*x^3))/(-480*c^(7/2)*x^7 + 480*c^3*x^6*Sqrt[c*x^2])","A",0
850,1,81,66,0.3311912,"\int \frac{(a+b x)^2}{x^3 \left(c x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[(a + b*x)^2/(x^3*(c*x^2)^(5/2)),x]","\frac{64 c \left(-30 a^2-35 a b x-21 b^2 x^2\right)+64 \sqrt{c} \sqrt{c x^2} \left(35 a b+21 b^2 x\right)}{6720 c^3 x^6 \sqrt{c x^2}-6720 c^{7/2} x^7}","-\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,"(64*Sqrt[c]*Sqrt[c*x^2]*(35*a*b + 21*b^2*x) + 64*c*(-30*a^2 - 35*a*b*x - 21*b^2*x^2))/(-6720*c^(7/2)*x^7 + 6720*c^3*x^6*Sqrt[c*x^2])","A",0
851,1,81,66,0.337828,"\int \frac{(a+b x)^2}{x^4 \left(c x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[(a + b*x)^2/(x^4*(c*x^2)^(5/2)),x]","\frac{32 c^{3/2} \left(21 a^2+24 a b x+14 b^2 x^2\right)+32 c \sqrt{c x^2} \left(-24 a b-14 b^2 x\right)}{2688 c^4 x^8-2688 c^{7/2} x^7 \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,"(32*c*Sqrt[c*x^2]*(-24*a*b - 14*b^2*x) + 32*c^(3/2)*(21*a^2 + 24*a*b*x + 14*b^2*x^2))/(2688*c^4*x^8 - 2688*c^(7/2)*x^7*Sqrt[c*x^2])","A",0
852,0,0,102,0.2816057,"\int \frac{x^3 \sqrt{c x^2}}{a+b x} \, dx","IntegrateAlgebraic[(x^3*Sqrt[c*x^2])/(a + b*x),x]","\int \frac{x^3 \sqrt{c x^2}}{a+b x} \, dx","\frac{a^4 \sqrt{c x^2} \log (a+b x)}{b^5 x}-\frac{a^3 \sqrt{c x^2}}{b^4}+\frac{a^2 x \sqrt{c x^2}}{2 b^3}-\frac{a x^2 \sqrt{c x^2}}{3 b^2}+\frac{x^3 \sqrt{c x^2}}{4 b}",1,"Could not integrate","F",-1
853,0,0,80,0.2522514,"\int \frac{x^2 \sqrt{c x^2}}{a+b x} \, dx","IntegrateAlgebraic[(x^2*Sqrt[c*x^2])/(a + b*x),x]","\int \frac{x^2 \sqrt{c x^2}}{a+b x} \, dx","-\frac{a^3 \sqrt{c x^2} \log (a+b x)}{b^4 x}+\frac{a^2 \sqrt{c x^2}}{b^3}-\frac{a x \sqrt{c x^2}}{2 b^2}+\frac{x^2 \sqrt{c x^2}}{3 b}",1,"Could not integrate","F",-1
854,0,0,58,0.2391802,"\int \frac{x \sqrt{c x^2}}{a+b x} \, dx","IntegrateAlgebraic[(x*Sqrt[c*x^2])/(a + b*x),x]","\int \frac{x \sqrt{c x^2}}{a+b x} \, dx","\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,"Could not integrate","F",-1
855,0,0,38,0.1971763,"\int \frac{\sqrt{c x^2}}{a+b x} \, dx","IntegrateAlgebraic[Sqrt[c*x^2]/(a + b*x),x]","\int \frac{\sqrt{c x^2}}{a+b x} \, dx","\frac{\sqrt{c x^2}}{b}-\frac{a \sqrt{c x^2} \log (a+b x)}{b^2 x}",1,"Could not integrate","F",-1
856,0,0,22,0.1906324,"\int \frac{\sqrt{c x^2}}{x (a+b x)} \, dx","IntegrateAlgebraic[Sqrt[c*x^2]/(x*(a + b*x)),x]","\int \frac{\sqrt{c x^2}}{x (a+b x)} \, dx","\frac{\sqrt{c x^2} \log (a+b x)}{b x}",1,"Could not integrate","F",-1
857,0,0,42,0.2229028,"\int \frac{\sqrt{c x^2}}{x^2 (a+b x)} \, dx","IntegrateAlgebraic[Sqrt[c*x^2]/(x^2*(a + b*x)),x]","\int \frac{\sqrt{c x^2}}{x^2 (a+b x)} \, dx","\frac{\sqrt{c x^2} \log (x)}{a x}-\frac{\sqrt{c x^2} \log (a+b x)}{a x}",1,"Could not integrate","F",-1
858,1,97,61,0.2184147,"\int \frac{\sqrt{c x^2}}{x^3 (a+b x)} \, dx","IntegrateAlgebraic[Sqrt[c*x^2]/(x^3*(a + b*x)),x]","\frac{b \sqrt{c} \log \left(\sqrt{c x^2}-\sqrt{c} x\right)}{a^2}-\frac{b \sqrt{c} \log \left(2 a \sqrt{c}-b \sqrt{c x^2}+b \sqrt{c} x\right)}{a^2}-\frac{2 c}{a \left(\sqrt{c x^2}-\sqrt{c} x\right)}","-\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,"(-2*c)/(a*(-(Sqrt[c]*x) + Sqrt[c*x^2])) + (b*Sqrt[c]*Log[-(Sqrt[c]*x) + Sqrt[c*x^2]])/a^2 - (b*Sqrt[c]*Log[2*a*Sqrt[c] + b*Sqrt[c]*x - b*Sqrt[c*x^2]])/a^2","A",0
859,1,132,84,0.2264007,"\int \frac{\sqrt{c x^2}}{x^4 (a+b x)} \, dx","IntegrateAlgebraic[Sqrt[c*x^2]/(x^4*(a + b*x)),x]","-\frac{b^2 \sqrt{c} \log \left(\sqrt{c x^2}-\sqrt{c} x\right)}{a^3}+\frac{b^2 \sqrt{c} \log \left(2 a \sqrt{c}-b \sqrt{c x^2}+b \sqrt{c} x\right)}{a^3}+\frac{2 b c}{a^2 \left(\sqrt{c x^2}-\sqrt{c} x\right)}+\frac{2 c^{3/2}}{a \left(\sqrt{c x^2}-\sqrt{c} x\right)^2}","\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,"(2*c^(3/2))/(a*(-(Sqrt[c]*x) + Sqrt[c*x^2])^2) + (2*b*c)/(a^2*(-(Sqrt[c]*x) + Sqrt[c*x^2])) - (b^2*Sqrt[c]*Log[-(Sqrt[c]*x) + Sqrt[c*x^2]])/a^3 + (b^2*Sqrt[c]*Log[2*a*Sqrt[c] + b*Sqrt[c]*x - b*Sqrt[c*x^2]])/a^3","A",0
860,0,0,107,0.3053903,"\int \frac{x \left(c x^2\right)^{3/2}}{a+b x} \, dx","IntegrateAlgebraic[(x*(c*x^2)^(3/2))/(a + b*x),x]","\int \frac{x \left(c x^2\right)^{3/2}}{a+b x} \, dx","\frac{a^4 c \sqrt{c x^2} \log (a+b x)}{b^5 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 c x^2 \sqrt{c x^2}}{3 b^2}+\frac{c x^3 \sqrt{c x^2}}{4 b}",1,"Could not integrate","F",-1
861,0,0,84,0.260091,"\int \frac{\left(c x^2\right)^{3/2}}{a+b x} \, dx","IntegrateAlgebraic[(c*x^2)^(3/2)/(a + b*x),x]","\int \frac{\left(c x^2\right)^{3/2}}{a+b x} \, dx","-\frac{a^3 c \sqrt{c x^2} \log (a+b x)}{b^4 x}+\frac{a^2 c \sqrt{c x^2}}{b^3}-\frac{a c x \sqrt{c x^2}}{2 b^2}+\frac{c x^2 \sqrt{c x^2}}{3 b}",1,"Could not integrate","F",-1
862,0,0,61,0.2407261,"\int \frac{\left(c x^2\right)^{3/2}}{x (a+b x)} \, dx","IntegrateAlgebraic[(c*x^2)^(3/2)/(x*(a + b*x)),x]","\int \frac{\left(c x^2\right)^{3/2}}{x (a+b x)} \, dx","\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,"Could not integrate","F",-1
863,0,0,40,0.2123948,"\int \frac{\left(c x^2\right)^{3/2}}{x^2 (a+b x)} \, dx","IntegrateAlgebraic[(c*x^2)^(3/2)/(x^2*(a + b*x)),x]","\int \frac{\left(c x^2\right)^{3/2}}{x^2 (a+b x)} \, dx","\frac{c \sqrt{c x^2}}{b}-\frac{a c \sqrt{c x^2} \log (a+b x)}{b^2 x}",1,"Could not integrate","F",-1
864,0,0,23,0.2009298,"\int \frac{\left(c x^2\right)^{3/2}}{x^3 (a+b x)} \, dx","IntegrateAlgebraic[(c*x^2)^(3/2)/(x^3*(a + b*x)),x]","\int \frac{\left(c x^2\right)^{3/2}}{x^3 (a+b x)} \, dx","\frac{c \sqrt{c x^2} \log (a+b x)}{b x}",1,"Could not integrate","F",-1
865,0,0,44,0.22564,"\int \frac{\left(c x^2\right)^{3/2}}{x^4 (a+b x)} \, dx","IntegrateAlgebraic[(c*x^2)^(3/2)/(x^4*(a + b*x)),x]","\int \frac{\left(c x^2\right)^{3/2}}{x^4 (a+b x)} \, dx","\frac{c \sqrt{c x^2} \log (x)}{a x}-\frac{c \sqrt{c x^2} \log (a+b x)}{a x}",1,"Could not integrate","F",-1
866,1,99,64,0.2228351,"\int \frac{\left(c x^2\right)^{3/2}}{x^5 (a+b x)} \, dx","IntegrateAlgebraic[(c*x^2)^(3/2)/(x^5*(a + b*x)),x]","\frac{b c^{3/2} \log \left(\sqrt{c x^2}-\sqrt{c} x\right)}{a^2}-\frac{b c^{3/2} \log \left(2 a \sqrt{c}-b \sqrt{c x^2}+b \sqrt{c} x\right)}{a^2}-\frac{2 c^2}{a \left(\sqrt{c x^2}-\sqrt{c} x\right)}","-\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,"(-2*c^2)/(a*(-(Sqrt[c]*x) + Sqrt[c*x^2])) + (b*c^(3/2)*Log[-(Sqrt[c]*x) + Sqrt[c*x^2]])/a^2 - (b*c^(3/2)*Log[2*a*Sqrt[c] + b*Sqrt[c]*x - b*Sqrt[c*x^2]])/a^2","A",0
867,1,134,88,0.233767,"\int \frac{\left(c x^2\right)^{3/2}}{x^6 (a+b x)} \, dx","IntegrateAlgebraic[(c*x^2)^(3/2)/(x^6*(a + b*x)),x]","-\frac{b^2 c^{3/2} \log \left(\sqrt{c x^2}-\sqrt{c} x\right)}{a^3}+\frac{b^2 c^{3/2} \log \left(2 a \sqrt{c}-b \sqrt{c x^2}+b \sqrt{c} x\right)}{a^3}+\frac{2 b c^2}{a^2 \left(\sqrt{c x^2}-\sqrt{c} x\right)}+\frac{2 c^{5/2}}{a \left(\sqrt{c x^2}-\sqrt{c} x\right)^2}","\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,"(2*c^(5/2))/(a*(-(Sqrt[c]*x) + Sqrt[c*x^2])^2) + (2*b*c^2)/(a^2*(-(Sqrt[c]*x) + Sqrt[c*x^2])) - (b^2*c^(3/2)*Log[-(Sqrt[c]*x) + Sqrt[c*x^2]])/a^3 + (b^2*c^(3/2)*Log[2*a*Sqrt[c] + b*Sqrt[c]*x - b*Sqrt[c*x^2]])/a^3","A",0
868,1,162,112,0.2728268,"\int \frac{\left(c x^2\right)^{3/2}}{x^7 (a+b x)} \, dx","IntegrateAlgebraic[(c*x^2)^(3/2)/(x^7*(a + b*x)),x]","\frac{b^3 c^{3/2} \log \left(\sqrt{c x^2}-\sqrt{c} x\right)}{a^4}-\frac{b^3 c^{3/2} \log \left(2 a \sqrt{c}-b \sqrt{c x^2}+b \sqrt{c} x\right)}{a^4}+\frac{-2 c^3 \left(4 a^2-3 a b x+6 b^2 x^2\right)-2 c^{5/2} \sqrt{c x^2} \left(3 a b-6 b^2 x\right)}{12 a^3 c x^2 \sqrt{c x^2}-12 a^3 c^{3/2} x^3}","-\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^2 c \sqrt{c x^2}}{a^3 x^2}+\frac{b c \sqrt{c x^2}}{2 a^2 x^3}-\frac{c \sqrt{c x^2}}{3 a x^4}",1,"(-2*c^(5/2)*Sqrt[c*x^2]*(3*a*b - 6*b^2*x) - 2*c^3*(4*a^2 - 3*a*b*x + 6*b^2*x^2))/(-12*a^3*c^(3/2)*x^3 + 12*a^3*c*x^2*Sqrt[c*x^2]) + (b^3*c^(3/2)*Log[-(Sqrt[c]*x) + Sqrt[c*x^2]])/a^4 - (b^3*c^(3/2)*Log[2*a*Sqrt[c] + b*Sqrt[c]*x - b*Sqrt[c*x^2]])/a^4","A",0
869,0,0,142,0.287814,"\int \frac{\left(c x^2\right)^{5/2}}{a+b x} \, dx","IntegrateAlgebraic[(c*x^2)^(5/2)/(a + b*x),x]","\int \frac{\left(c x^2\right)^{5/2}}{a+b x} \, dx","-\frac{a^5 c^2 \sqrt{c x^2} \log (a+b x)}{b^6 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 c^2 x^3 \sqrt{c x^2}}{4 b^2}+\frac{c^2 x^4 \sqrt{c x^2}}{5 b}",1,"Could not integrate","F",-1
870,0,0,117,0.2919985,"\int \frac{\left(c x^2\right)^{5/2}}{x (a+b x)} \, dx","IntegrateAlgebraic[(c*x^2)^(5/2)/(x*(a + b*x)),x]","\int \frac{\left(c x^2\right)^{5/2}}{x (a+b x)} \, dx","\frac{a^4 c^2 \sqrt{c x^2} \log (a+b x)}{b^5 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 c^2 x^2 \sqrt{c x^2}}{3 b^2}+\frac{c^2 x^3 \sqrt{c x^2}}{4 b}",1,"Could not integrate","F",-1
871,0,0,92,0.2678091,"\int \frac{\left(c x^2\right)^{5/2}}{x^2 (a+b x)} \, dx","IntegrateAlgebraic[(c*x^2)^(5/2)/(x^2*(a + b*x)),x]","\int \frac{\left(c x^2\right)^{5/2}}{x^2 (a+b x)} \, dx","-\frac{a^3 c^2 \sqrt{c x^2} \log (a+b x)}{b^4 x}+\frac{a^2 c^2 \sqrt{c x^2}}{b^3}-\frac{a c^2 x \sqrt{c x^2}}{2 b^2}+\frac{c^2 x^2 \sqrt{c x^2}}{3 b}",1,"Could not integrate","F",-1
872,0,0,67,0.2497515,"\int \frac{\left(c x^2\right)^{5/2}}{x^3 (a+b x)} \, dx","IntegrateAlgebraic[(c*x^2)^(5/2)/(x^3*(a + b*x)),x]","\int \frac{\left(c x^2\right)^{5/2}}{x^3 (a+b x)} \, dx","\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,"Could not integrate","F",-1
873,0,0,44,0.2128019,"\int \frac{\left(c x^2\right)^{5/2}}{x^4 (a+b x)} \, dx","IntegrateAlgebraic[(c*x^2)^(5/2)/(x^4*(a + b*x)),x]","\int \frac{\left(c x^2\right)^{5/2}}{x^4 (a+b x)} \, dx","\frac{c^2 \sqrt{c x^2}}{b}-\frac{a c^2 \sqrt{c x^2} \log (a+b x)}{b^2 x}",1,"Could not integrate","F",-1
874,0,0,25,0.2047029,"\int \frac{\left(c x^2\right)^{5/2}}{x^5 (a+b x)} \, dx","IntegrateAlgebraic[(c*x^2)^(5/2)/(x^5*(a + b*x)),x]","\int \frac{\left(c x^2\right)^{5/2}}{x^5 (a+b x)} \, dx","\frac{c^2 \sqrt{c x^2} \log (a+b x)}{b x}",1,"Could not integrate","F",-1
875,0,0,48,0.2203995,"\int \frac{\left(c x^2\right)^{5/2}}{x^6 (a+b x)} \, dx","IntegrateAlgebraic[(c*x^2)^(5/2)/(x^6*(a + b*x)),x]","\int \frac{\left(c x^2\right)^{5/2}}{x^6 (a+b x)} \, dx","\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,"Could not integrate","F",-1
876,1,99,70,0.2255619,"\int \frac{\left(c x^2\right)^{5/2}}{x^7 (a+b x)} \, dx","IntegrateAlgebraic[(c*x^2)^(5/2)/(x^7*(a + b*x)),x]","\frac{b c^{5/2} \log \left(\sqrt{c x^2}-\sqrt{c} x\right)}{a^2}-\frac{b c^{5/2} \log \left(2 a \sqrt{c}-b \sqrt{c x^2}+b \sqrt{c} x\right)}{a^2}-\frac{2 c^3}{a \left(\sqrt{c x^2}-\sqrt{c} x\right)}","-\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,"(-2*c^3)/(a*(-(Sqrt[c]*x) + Sqrt[c*x^2])) + (b*c^(5/2)*Log[-(Sqrt[c]*x) + Sqrt[c*x^2]])/a^2 - (b*c^(5/2)*Log[2*a*Sqrt[c] + b*Sqrt[c]*x - b*Sqrt[c*x^2]])/a^2","A",0
877,0,0,83,0.2676121,"\int \frac{x^4}{\sqrt{c x^2} (a+b x)} \, dx","IntegrateAlgebraic[x^4/(Sqrt[c*x^2]*(a + b*x)),x]","\int \frac{x^4}{\sqrt{c x^2} (a+b x)} \, dx","-\frac{a^3 x \log (a+b x)}{b^4 \sqrt{c x^2}}+\frac{a^2 x^2}{b^3 \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,"Could not integrate","F",-1
878,0,0,61,0.2399383,"\int \frac{x^3}{\sqrt{c x^2} (a+b x)} \, dx","IntegrateAlgebraic[x^3/(Sqrt[c*x^2]*(a + b*x)),x]","\int \frac{x^3}{\sqrt{c x^2} (a+b x)} \, dx","\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,"Could not integrate","F",-1
879,0,0,39,0.2096831,"\int \frac{x^2}{\sqrt{c x^2} (a+b x)} \, dx","IntegrateAlgebraic[x^2/(Sqrt[c*x^2]*(a + b*x)),x]","\int \frac{x^2}{\sqrt{c x^2} (a+b x)} \, dx","\frac{x^2}{b \sqrt{c x^2}}-\frac{a x \log (a+b x)}{b^2 \sqrt{c x^2}}",1,"Could not integrate","F",-1
880,0,0,20,0.1941551,"\int \frac{x}{\sqrt{c x^2} (a+b x)} \, dx","IntegrateAlgebraic[x/(Sqrt[c*x^2]*(a + b*x)),x]","\int \frac{x}{\sqrt{c x^2} (a+b x)} \, dx","\frac{x \log (a+b x)}{b \sqrt{c x^2}}",1,"Could not integrate","F",-1
881,0,0,38,0.2046988,"\int \frac{1}{\sqrt{c x^2} (a+b x)} \, dx","IntegrateAlgebraic[1/(Sqrt[c*x^2]*(a + b*x)),x]","\int \frac{1}{\sqrt{c x^2} (a+b x)} \, dx","\frac{x \log (x)}{a \sqrt{c x^2}}-\frac{x \log (a+b x)}{a \sqrt{c x^2}}",1,"Could not integrate","F",-1
882,1,96,54,0.2257195,"\int \frac{1}{x \sqrt{c x^2} (a+b x)} \, dx","IntegrateAlgebraic[1/(x*Sqrt[c*x^2]*(a + b*x)),x]","\frac{b \log \left(\sqrt{c x^2}-\sqrt{c} x\right)}{a^2 \sqrt{c}}-\frac{b \log \left(2 a \sqrt{c}-b \sqrt{c x^2}+b \sqrt{c} x\right)}{a^2 \sqrt{c}}-\frac{2}{a \left(\sqrt{c x^2}-\sqrt{c} x\right)}","-\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,"-2/(a*(-(Sqrt[c]*x) + Sqrt[c*x^2])) + (b*Log[-(Sqrt[c]*x) + Sqrt[c*x^2]])/(a^2*Sqrt[c]) - (b*Log[2*a*Sqrt[c] + b*Sqrt[c]*x - b*Sqrt[c*x^2]])/(a^2*Sqrt[c])","A",0
883,0,0,77,0.3377309,"\int \frac{1}{x^2 \sqrt{c x^2} (a+b x)} \, dx","IntegrateAlgebraic[1/(x^2*Sqrt[c*x^2]*(a + b*x)),x]","\int \frac{1}{x^2 \sqrt{c x^2} (a+b x)} \, dx","\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,"Could not integrate","F",-1
884,1,160,100,0.2552909,"\int \frac{1}{x^3 \sqrt{c x^2} (a+b x)} \, dx","IntegrateAlgebraic[1/(x^3*Sqrt[c*x^2]*(a + b*x)),x]","\frac{b^3 \log \left(\sqrt{c x^2}-\sqrt{c} x\right)}{a^4 \sqrt{c}}-\frac{b^3 \log \left(2 a \sqrt{c}-b \sqrt{c x^2}+b \sqrt{c} x\right)}{a^4 \sqrt{c}}+\frac{-2 c \left(4 a^2-3 a b x+6 b^2 x^2\right)-2 \sqrt{c} \sqrt{c x^2} \left(3 a b-6 b^2 x\right)}{12 a^3 c x^2 \sqrt{c x^2}-12 a^3 c^{3/2} x^3}","-\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^3 \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,"(-2*Sqrt[c]*Sqrt[c*x^2]*(3*a*b - 6*b^2*x) - 2*c*(4*a^2 - 3*a*b*x + 6*b^2*x^2))/(-12*a^3*c^(3/2)*x^3 + 12*a^3*c*x^2*Sqrt[c*x^2]) + (b^3*Log[-(Sqrt[c]*x) + Sqrt[c*x^2]])/(a^4*Sqrt[c]) - (b^3*Log[2*a*Sqrt[c] + b*Sqrt[c]*x - b*Sqrt[c*x^2]])/(a^4*Sqrt[c])","A",0
885,0,0,95,0.2758386,"\int \frac{x^6}{\left(c x^2\right)^{3/2} (a+b x)} \, dx","IntegrateAlgebraic[x^6/((c*x^2)^(3/2)*(a + b*x)),x]","\int \frac{x^6}{\left(c x^2\right)^{3/2} (a+b x)} \, dx","-\frac{a^3 x \log (a+b x)}{b^4 c \sqrt{c x^2}}+\frac{a^2 x^2}{b^3 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,"Could not integrate","F",-1
886,0,0,70,0.2450791,"\int \frac{x^5}{\left(c x^2\right)^{3/2} (a+b x)} \, dx","IntegrateAlgebraic[x^5/((c*x^2)^(3/2)*(a + b*x)),x]","\int \frac{x^5}{\left(c x^2\right)^{3/2} (a+b x)} \, dx","\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,"Could not integrate","F",-1
887,0,0,45,0.216112,"\int \frac{x^4}{\left(c x^2\right)^{3/2} (a+b x)} \, dx","IntegrateAlgebraic[x^4/((c*x^2)^(3/2)*(a + b*x)),x]","\int \frac{x^4}{\left(c x^2\right)^{3/2} (a+b x)} \, dx","\frac{x^2}{b c \sqrt{c x^2}}-\frac{a x \log (a+b x)}{b^2 c \sqrt{c x^2}}",1,"Could not integrate","F",-1
888,0,0,23,0.2049558,"\int \frac{x^3}{\left(c x^2\right)^{3/2} (a+b x)} \, dx","IntegrateAlgebraic[x^3/((c*x^2)^(3/2)*(a + b*x)),x]","\int \frac{x^3}{\left(c x^2\right)^{3/2} (a+b x)} \, dx","\frac{x \log (a+b x)}{b c \sqrt{c x^2}}",1,"Could not integrate","F",-1
889,0,0,44,0.2195611,"\int \frac{x^2}{\left(c x^2\right)^{3/2} (a+b x)} \, dx","IntegrateAlgebraic[x^2/((c*x^2)^(3/2)*(a + b*x)),x]","\int \frac{x^2}{\left(c x^2\right)^{3/2} (a+b x)} \, dx","\frac{x \log (x)}{a c \sqrt{c x^2}}-\frac{x \log (a+b x)}{a c \sqrt{c x^2}}",1,"Could not integrate","F",-1
890,1,97,63,0.2314617,"\int \frac{x}{\left(c x^2\right)^{3/2} (a+b x)} \, dx","IntegrateAlgebraic[x/((c*x^2)^(3/2)*(a + b*x)),x]","\frac{b \log \left(\sqrt{c x^2}-\sqrt{c} x\right)}{a^2 c^{3/2}}-\frac{b \log \left(2 a \sqrt{c}-b \sqrt{c x^2}+b \sqrt{c} x\right)}{a^2 c^{3/2}}-\frac{2}{a c \sqrt{c x^2}-a c^{3/2} 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}}",1,"-2/(-(a*c^(3/2)*x) + a*c*Sqrt[c*x^2]) + (b*Log[-(Sqrt[c]*x) + Sqrt[c*x^2]])/(a^2*c^(3/2)) - (b*Log[2*a*Sqrt[c] + b*Sqrt[c]*x - b*Sqrt[c*x^2]])/(a^2*c^(3/2))","A",0
891,1,134,89,0.2249787,"\int \frac{1}{\left(c x^2\right)^{3/2} (a+b x)} \, dx","IntegrateAlgebraic[1/((c*x^2)^(3/2)*(a + b*x)),x]","-\frac{b^2 \log \left(\sqrt{c x^2}-\sqrt{c} x\right)}{a^3 c^{3/2}}+\frac{b^2 \log \left(2 a \sqrt{c}-b \sqrt{c x^2}+b \sqrt{c} x\right)}{a^3 c^{3/2}}+\frac{2 b}{a^2 c \left(\sqrt{c x^2}-\sqrt{c} x\right)}+\frac{2}{a \sqrt{c} \left(\sqrt{c x^2}-\sqrt{c} x\right)^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,"2/(a*Sqrt[c]*(-(Sqrt[c]*x) + Sqrt[c*x^2])^2) + (2*b)/(a^2*c*(-(Sqrt[c]*x) + Sqrt[c*x^2])) - (b^2*Log[-(Sqrt[c]*x) + Sqrt[c*x^2]])/(a^3*c^(3/2)) + (b^2*Log[2*a*Sqrt[c] + b*Sqrt[c]*x - b*Sqrt[c*x^2]])/(a^3*c^(3/2))","A",0
892,1,161,115,0.2643516,"\int \frac{1}{x \left(c x^2\right)^{3/2} (a+b x)} \, dx","IntegrateAlgebraic[1/(x*(c*x^2)^(3/2)*(a + b*x)),x]","\frac{b^3 \log \left(\sqrt{c x^2}-\sqrt{c} x\right)}{a^4 c^{3/2}}-\frac{b^3 \log \left(2 a \sqrt{c}-b \sqrt{c x^2}+b \sqrt{c} x\right)}{a^4 c^{3/2}}+\frac{2 \sqrt{c} \left(4 a^2-3 a b x+6 b^2 x^2\right)+2 \sqrt{c x^2} \left(3 a b-6 b^2 x\right)}{12 a^3 c^2 x^3-12 a^3 c^{3/2} x^2 \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^3 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,"(2*Sqrt[c*x^2]*(3*a*b - 6*b^2*x) + 2*Sqrt[c]*(4*a^2 - 3*a*b*x + 6*b^2*x^2))/(12*a^3*c^2*x^3 - 12*a^3*c^(3/2)*x^2*Sqrt[c*x^2]) + (b^3*Log[-(Sqrt[c]*x) + Sqrt[c*x^2]])/(a^4*c^(3/2)) - (b^3*Log[2*a*Sqrt[c] + b*Sqrt[c]*x - b*Sqrt[c*x^2]])/(a^4*c^(3/2))","A",0
893,0,0,106,0.4474839,"\int \frac{x^3 \sqrt{c x^2}}{(a+b x)^2} \, dx","IntegrateAlgebraic[(x^3*Sqrt[c*x^2])/(a + b*x)^2,x]","\int \frac{x^3 \sqrt{c x^2}}{(a+b x)^2} \, dx","-\frac{a^4 \sqrt{c x^2}}{b^5 x (a+b x)}-\frac{4 a^3 \sqrt{c x^2} \log (a+b x)}{b^5 x}+\frac{3 a^2 \sqrt{c x^2}}{b^4}-\frac{a x \sqrt{c x^2}}{b^3}+\frac{x^2 \sqrt{c x^2}}{3 b^2}",1,"Could not integrate","F",-1
894,0,0,85,0.4179211,"\int \frac{x^2 \sqrt{c x^2}}{(a+b x)^2} \, dx","IntegrateAlgebraic[(x^2*Sqrt[c*x^2])/(a + b*x)^2,x]","\int \frac{x^2 \sqrt{c x^2}}{(a+b x)^2} \, dx","\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,"Could not integrate","F",-1
895,0,0,65,0.4031466,"\int \frac{x \sqrt{c x^2}}{(a+b x)^2} \, dx","IntegrateAlgebraic[(x*Sqrt[c*x^2])/(a + b*x)^2,x]","\int \frac{x \sqrt{c x^2}}{(a+b x)^2} \, dx","-\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,"Could not integrate","F",-1
896,0,0,47,0.3587745,"\int \frac{\sqrt{c x^2}}{(a+b x)^2} \, dx","IntegrateAlgebraic[Sqrt[c*x^2]/(a + b*x)^2,x]","\int \frac{\sqrt{c x^2}}{(a+b x)^2} \, dx","\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,"Could not integrate","F",-1
897,0,0,24,0.3326057,"\int \frac{\sqrt{c x^2}}{x (a+b x)^2} \, dx","IntegrateAlgebraic[Sqrt[c*x^2]/(x*(a + b*x)^2),x]","\int \frac{\sqrt{c x^2}}{x (a+b x)^2} \, dx","-\frac{\sqrt{c x^2}}{b x (a+b x)}",1,"Could not integrate","F",-1
898,0,0,65,0.4576901,"\int \frac{\sqrt{c x^2}}{x^2 (a+b x)^2} \, dx","IntegrateAlgebraic[Sqrt[c*x^2]/(x^2*(a + b*x)^2),x]","\int \frac{\sqrt{c x^2}}{x^2 (a+b x)^2} \, dx","-\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,"Could not integrate","F",-1
899,1,144,87,0.4540641,"\int \frac{\sqrt{c x^2}}{x^3 (a+b x)^2} \, dx","IntegrateAlgebraic[Sqrt[c*x^2]/(x^3*(a + b*x)^2),x]","\frac{2 b \sqrt{c} \log \left(\sqrt{c x^2}-\sqrt{c} x\right)}{a^3}-\frac{2 b \sqrt{c} \log \left(2 a \sqrt{c}-b \sqrt{c x^2}+b \sqrt{c} x\right)}{a^3}+\frac{4 b c \sqrt{c x^2}-4 c^{3/2} (a+b x)}{a^2 \sqrt{c} \sqrt{c x^2} (2 a+2 b x)+a^2 c \left(-2 a x-2 b x^2\right)}","-\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{b \sqrt{c x^2}}{a^2 x (a+b x)}-\frac{\sqrt{c x^2}}{a^2 x^2}",1,"(4*b*c*Sqrt[c*x^2] - 4*c^(3/2)*(a + b*x))/(a^2*Sqrt[c]*Sqrt[c*x^2]*(2*a + 2*b*x) + a^2*c*(-2*a*x - 2*b*x^2)) + (2*b*Sqrt[c]*Log[-(Sqrt[c]*x) + Sqrt[c*x^2]])/a^3 - (2*b*Sqrt[c]*Log[2*a*Sqrt[c] + b*Sqrt[c]*x - b*Sqrt[c*x^2]])/a^3","A",0
900,1,179,112,0.5307194,"\int \frac{\sqrt{c x^2}}{x^4 (a+b x)^2} \, dx","IntegrateAlgebraic[Sqrt[c*x^2]/(x^4*(a + b*x)^2),x]","-\frac{3 b^2 \sqrt{c} \log \left(\sqrt{c x^2}-\sqrt{c} x\right)}{a^4}+\frac{3 b^2 \sqrt{c} \log \left(2 a \sqrt{c}-b \sqrt{c x^2}+b \sqrt{c} x\right)}{a^4}+\frac{2 c^2 \left(2 a^2-3 a b x-6 b^2 x^2\right)+2 c^{3/2} \sqrt{c x^2} \left(3 a b+6 b^2 x\right)}{a^3 c^{3/2} \left(4 a x^2+4 b x^3\right)+a^3 c \sqrt{c x^2} \left(-4 a x-4 b x^2\right)}","\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{b^2 \sqrt{c x^2}}{a^3 x (a+b x)}+\frac{2 b \sqrt{c x^2}}{a^3 x^2}-\frac{\sqrt{c x^2}}{2 a^2 x^3}",1,"(2*c^(3/2)*Sqrt[c*x^2]*(3*a*b + 6*b^2*x) + 2*c^2*(2*a^2 - 3*a*b*x - 6*b^2*x^2))/(a^3*c*Sqrt[c*x^2]*(-4*a*x - 4*b*x^2) + a^3*c^(3/2)*(4*a*x^2 + 4*b*x^3)) - (3*b^2*Sqrt[c]*Log[-(Sqrt[c]*x) + Sqrt[c*x^2]])/a^4 + (3*b^2*Sqrt[c]*Log[2*a*Sqrt[c] + b*Sqrt[c]*x - b*Sqrt[c*x^2]])/a^4","A",0
901,0,0,111,0.45785,"\int \frac{x \left(c x^2\right)^{3/2}}{(a+b x)^2} \, dx","IntegrateAlgebraic[(x*(c*x^2)^(3/2))/(a + b*x)^2,x]","\int \frac{x \left(c x^2\right)^{3/2}}{(a+b x)^2} \, dx","-\frac{a^4 c \sqrt{c x^2}}{b^5 x (a+b x)}-\frac{4 a^3 c \sqrt{c x^2} \log (a+b x)}{b^5 x}+\frac{3 a^2 c \sqrt{c x^2}}{b^4}-\frac{a c x \sqrt{c x^2}}{b^3}+\frac{c x^2 \sqrt{c x^2}}{3 b^2}",1,"Could not integrate","F",-1
902,0,0,89,0.4264526,"\int \frac{\left(c x^2\right)^{3/2}}{(a+b x)^2} \, dx","IntegrateAlgebraic[(c*x^2)^(3/2)/(a + b*x)^2,x]","\int \frac{\left(c x^2\right)^{3/2}}{(a+b x)^2} \, dx","\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,"Could not integrate","F",-1
903,0,0,68,0.4195262,"\int \frac{\left(c x^2\right)^{3/2}}{x (a+b x)^2} \, dx","IntegrateAlgebraic[(c*x^2)^(3/2)/(x*(a + b*x)^2),x]","\int \frac{\left(c x^2\right)^{3/2}}{x (a+b x)^2} \, dx","-\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,"Could not integrate","F",-1
904,0,0,49,0.3719377,"\int \frac{\left(c x^2\right)^{3/2}}{x^2 (a+b x)^2} \, dx","IntegrateAlgebraic[(c*x^2)^(3/2)/(x^2*(a + b*x)^2),x]","\int \frac{\left(c x^2\right)^{3/2}}{x^2 (a+b x)^2} \, dx","\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,"Could not integrate","F",-1
905,0,0,25,0.3451785,"\int \frac{\left(c x^2\right)^{3/2}}{x^3 (a+b x)^2} \, dx","IntegrateAlgebraic[(c*x^2)^(3/2)/(x^3*(a + b*x)^2),x]","\int \frac{\left(c x^2\right)^{3/2}}{x^3 (a+b x)^2} \, dx","-\frac{c \sqrt{c x^2}}{b x (a+b x)}",1,"Could not integrate","F",-1
906,0,0,68,0.4602278,"\int \frac{\left(c x^2\right)^{3/2}}{x^4 (a+b x)^2} \, dx","IntegrateAlgebraic[(c*x^2)^(3/2)/(x^4*(a + b*x)^2),x]","\int \frac{\left(c x^2\right)^{3/2}}{x^4 (a+b x)^2} \, dx","-\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,"Could not integrate","F",-1
907,1,146,91,0.4604164,"\int \frac{\left(c x^2\right)^{3/2}}{x^5 (a+b x)^2} \, dx","IntegrateAlgebraic[(c*x^2)^(3/2)/(x^5*(a + b*x)^2),x]","\frac{2 b c^{3/2} \log \left(\sqrt{c x^2}-\sqrt{c} x\right)}{a^3}-\frac{2 b c^{3/2} \log \left(2 a \sqrt{c}-b \sqrt{c x^2}+b \sqrt{c} x\right)}{a^3}+\frac{4 b c^2 \sqrt{c x^2}-4 c^{5/2} (a+b x)}{a^2 \sqrt{c} \sqrt{c x^2} (2 a+2 b x)+a^2 c \left(-2 a x-2 b x^2\right)}","-\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{b c \sqrt{c x^2}}{a^2 x (a+b x)}-\frac{c \sqrt{c x^2}}{a^2 x^2}",1,"(4*b*c^2*Sqrt[c*x^2] - 4*c^(5/2)*(a + b*x))/(a^2*Sqrt[c]*Sqrt[c*x^2]*(2*a + 2*b*x) + a^2*c*(-2*a*x - 2*b*x^2)) + (2*b*c^(3/2)*Log[-(Sqrt[c]*x) + Sqrt[c*x^2]])/a^3 - (2*b*c^(3/2)*Log[2*a*Sqrt[c] + b*Sqrt[c]*x - b*Sqrt[c*x^2]])/a^3","A",0
908,1,179,117,0.540079,"\int \frac{\left(c x^2\right)^{3/2}}{x^6 (a+b x)^2} \, dx","IntegrateAlgebraic[(c*x^2)^(3/2)/(x^6*(a + b*x)^2),x]","-\frac{3 b^2 c^{3/2} \log \left(\sqrt{c x^2}-\sqrt{c} x\right)}{a^4}+\frac{3 b^2 c^{3/2} \log \left(2 a \sqrt{c}-b \sqrt{c x^2}+b \sqrt{c} x\right)}{a^4}+\frac{2 c^3 \left(2 a^2-3 a b x-6 b^2 x^2\right)+2 c^{5/2} \sqrt{c x^2} \left(3 a b+6 b^2 x\right)}{a^3 c^{3/2} \left(4 a x^2+4 b x^3\right)+a^3 c \sqrt{c x^2} \left(-4 a x-4 b x^2\right)}","\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{b^2 c \sqrt{c x^2}}{a^3 x (a+b 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,"(2*c^(5/2)*Sqrt[c*x^2]*(3*a*b + 6*b^2*x) + 2*c^3*(2*a^2 - 3*a*b*x - 6*b^2*x^2))/(a^3*c*Sqrt[c*x^2]*(-4*a*x - 4*b*x^2) + a^3*c^(3/2)*(4*a*x^2 + 4*b*x^3)) - (3*b^2*c^(3/2)*Log[-(Sqrt[c]*x) + Sqrt[c*x^2]])/a^4 + (3*b^2*c^(3/2)*Log[2*a*Sqrt[c] + b*Sqrt[c]*x - b*Sqrt[c*x^2]])/a^4","A",0
909,0,0,107,0.4845653,"\int \frac{x^5}{\sqrt{c x^2} (a+b x)^2} \, dx","IntegrateAlgebraic[x^5/(Sqrt[c*x^2]*(a + b*x)^2),x]","\int \frac{x^5}{\sqrt{c x^2} (a+b x)^2} \, dx","-\frac{a^4 x}{b^5 \sqrt{c x^2} (a+b x)}-\frac{4 a^3 x \log (a+b x)}{b^5 \sqrt{c x^2}}+\frac{3 a^2 x^2}{b^4 \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,"Could not integrate","F",-1
910,0,0,86,0.44083,"\int \frac{x^4}{\sqrt{c x^2} (a+b x)^2} \, dx","IntegrateAlgebraic[x^4/(Sqrt[c*x^2]*(a + b*x)^2),x]","\int \frac{x^4}{\sqrt{c x^2} (a+b x)^2} \, dx","\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,"Could not integrate","F",-1
911,0,0,64,0.4202805,"\int \frac{x^3}{\sqrt{c x^2} (a+b x)^2} \, dx","IntegrateAlgebraic[x^3/(Sqrt[c*x^2]*(a + b*x)^2),x]","\int \frac{x^3}{\sqrt{c x^2} (a+b x)^2} \, dx","-\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,"Could not integrate","F",-1
912,0,0,43,0.3767254,"\int \frac{x^2}{\sqrt{c x^2} (a+b x)^2} \, dx","IntegrateAlgebraic[x^2/(Sqrt[c*x^2]*(a + b*x)^2),x]","\int \frac{x^2}{\sqrt{c x^2} (a+b x)^2} \, dx","\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,"Could not integrate","F",-1
913,0,0,22,0.347054,"\int \frac{x}{\sqrt{c x^2} (a+b x)^2} \, dx","IntegrateAlgebraic[x/(Sqrt[c*x^2]*(a + b*x)^2),x]","\int \frac{x}{\sqrt{c x^2} (a+b x)^2} \, dx","-\frac{x}{b \sqrt{c x^2} (a+b x)}",1,"Could not integrate","F",-1
914,0,0,59,0.4435064,"\int \frac{1}{\sqrt{c x^2} (a+b x)^2} \, dx","IntegrateAlgebraic[1/(Sqrt[c*x^2]*(a + b*x)^2),x]","\int \frac{1}{\sqrt{c x^2} (a+b x)^2} \, dx","-\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,"Could not integrate","F",-1
915,1,143,78,0.4564399,"\int \frac{1}{x \sqrt{c x^2} (a+b x)^2} \, dx","IntegrateAlgebraic[1/(x*Sqrt[c*x^2]*(a + b*x)^2),x]","\frac{2 b \log \left(\sqrt{c x^2}-\sqrt{c} x\right)}{a^3 \sqrt{c}}-\frac{2 b \log \left(2 a \sqrt{c}-b \sqrt{c x^2}+b \sqrt{c} x\right)}{a^3 \sqrt{c}}+\frac{4 b \sqrt{c x^2}-4 \sqrt{c} (a+b x)}{a^2 \sqrt{c} \sqrt{c x^2} (2 a+2 b x)+a^2 c \left(-2 a x-2 b x^2\right)}","-\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{b x}{a^2 \sqrt{c x^2} (a+b x)}-\frac{1}{a^2 \sqrt{c x^2}}",1,"(4*b*Sqrt[c*x^2] - 4*Sqrt[c]*(a + b*x))/(a^2*Sqrt[c]*Sqrt[c*x^2]*(2*a + 2*b*x) + a^2*c*(-2*a*x - 2*b*x^2)) + (2*b*Log[-(Sqrt[c]*x) + Sqrt[c*x^2]])/(a^3*Sqrt[c]) - (2*b*Log[2*a*Sqrt[c] + b*Sqrt[c]*x - b*Sqrt[c*x^2]])/(a^3*Sqrt[c])","A",0
916,1,177,103,0.5303804,"\int \frac{1}{x^2 \sqrt{c x^2} (a+b x)^2} \, dx","IntegrateAlgebraic[1/(x^2*Sqrt[c*x^2]*(a + b*x)^2),x]","-\frac{3 b^2 \log \left(\sqrt{c x^2}-\sqrt{c} x\right)}{a^4 \sqrt{c}}+\frac{3 b^2 \log \left(2 a \sqrt{c}-b \sqrt{c x^2}+b \sqrt{c} x\right)}{a^4 \sqrt{c}}+\frac{2 c \left(2 a^2-3 a b x-6 b^2 x^2\right)+2 \sqrt{c} \sqrt{c x^2} \left(3 a b+6 b^2 x\right)}{a^3 c^{3/2} \left(4 a x^2+4 b x^3\right)+a^3 c \sqrt{c x^2} \left(-4 a x-4 b x^2\right)}","\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{b^2 x}{a^3 \sqrt{c x^2} (a+b x)}+\frac{2 b}{a^3 \sqrt{c x^2}}-\frac{1}{2 a^2 x \sqrt{c x^2}}",1,"(2*Sqrt[c]*Sqrt[c*x^2]*(3*a*b + 6*b^2*x) + 2*c*(2*a^2 - 3*a*b*x - 6*b^2*x^2))/(a^3*c*Sqrt[c*x^2]*(-4*a*x - 4*b*x^2) + a^3*c^(3/2)*(4*a*x^2 + 4*b*x^3)) - (3*b^2*Log[-(Sqrt[c]*x) + Sqrt[c*x^2]])/(a^4*Sqrt[c]) + (3*b^2*Log[2*a*Sqrt[c] + b*Sqrt[c]*x - b*Sqrt[c*x^2]])/(a^4*Sqrt[c])","A",0
917,0,0,73,0.453873,"\int \frac{x^5}{\left(c x^2\right)^{3/2} (a+b x)^2} \, dx","IntegrateAlgebraic[x^5/((c*x^2)^(3/2)*(a + b*x)^2),x]","\int \frac{x^5}{\left(c x^2\right)^{3/2} (a+b x)^2} \, dx","-\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,"Could not integrate","F",-1
918,0,0,49,0.3877981,"\int \frac{x^4}{\left(c x^2\right)^{3/2} (a+b x)^2} \, dx","IntegrateAlgebraic[x^4/((c*x^2)^(3/2)*(a + b*x)^2),x]","\int \frac{x^4}{\left(c x^2\right)^{3/2} (a+b x)^2} \, dx","\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,"Could not integrate","F",-1
919,0,0,25,0.3596574,"\int \frac{x^3}{\left(c x^2\right)^{3/2} (a+b x)^2} \, dx","IntegrateAlgebraic[x^3/((c*x^2)^(3/2)*(a + b*x)^2),x]","\int \frac{x^3}{\left(c x^2\right)^{3/2} (a+b x)^2} \, dx","-\frac{x}{b c \sqrt{c x^2} (a+b x)}",1,"Could not integrate","F",-1
920,0,0,68,0.4658046,"\int \frac{x^2}{\left(c x^2\right)^{3/2} (a+b x)^2} \, dx","IntegrateAlgebraic[x^2/((c*x^2)^(3/2)*(a + b*x)^2),x]","\int \frac{x^2}{\left(c x^2\right)^{3/2} (a+b x)^2} \, dx","-\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,"Could not integrate","F",-1
921,1,145,90,0.4614832,"\int \frac{x}{\left(c x^2\right)^{3/2} (a+b x)^2} \, dx","IntegrateAlgebraic[x/((c*x^2)^(3/2)*(a + b*x)^2),x]","\frac{2 b \log \left(\sqrt{c x^2}-\sqrt{c} x\right)}{a^3 c^{3/2}}-\frac{2 b \log \left(2 a \sqrt{c}-b \sqrt{c x^2}+b \sqrt{c} x\right)}{a^3 c^{3/2}}+\frac{4 \sqrt{c} (a+b x)-4 b \sqrt{c x^2}}{a^2 c^{3/2} \sqrt{c x^2} (-2 a-2 b x)+a^2 c^2 \left(2 a x+2 b x^2\right)}","-\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{b x}{a^2 c \sqrt{c x^2} (a+b x)}-\frac{1}{a^2 c \sqrt{c x^2}}",1,"(-4*b*Sqrt[c*x^2] + 4*Sqrt[c]*(a + b*x))/(a^2*c^(3/2)*Sqrt[c*x^2]*(-2*a - 2*b*x) + a^2*c^2*(2*a*x + 2*b*x^2)) + (2*b*Log[-(Sqrt[c]*x) + Sqrt[c*x^2]])/(a^3*c^(3/2)) - (2*b*Log[2*a*Sqrt[c] + b*Sqrt[c]*x - b*Sqrt[c*x^2]])/(a^3*c^(3/2))","A",0
922,1,178,118,0.5311121,"\int \frac{1}{\left(c x^2\right)^{3/2} (a+b x)^2} \, dx","IntegrateAlgebraic[1/((c*x^2)^(3/2)*(a + b*x)^2),x]","-\frac{3 b^2 \log \left(\sqrt{c x^2}-\sqrt{c} x\right)}{a^4 c^{3/2}}+\frac{3 b^2 \log \left(2 a \sqrt{c}-b \sqrt{c x^2}+b \sqrt{c} x\right)}{a^4 c^{3/2}}+\frac{2 \sqrt{c} \left(2 a^2-3 a b x-6 b^2 x^2\right)+2 \sqrt{c x^2} \left(3 a b+6 b^2 x\right)}{a^3 c^{3/2} \sqrt{c x^2} \left(-4 a x-4 b x^2\right)+a^3 c^2 \left(4 a x^2+4 b x^3\right)}","\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{b^2 x}{a^3 c \sqrt{c x^2} (a+b x)}+\frac{2 b}{a^3 c \sqrt{c x^2}}-\frac{1}{2 a^2 c x \sqrt{c x^2}}",1,"(2*Sqrt[c*x^2]*(3*a*b + 6*b^2*x) + 2*Sqrt[c]*(2*a^2 - 3*a*b*x - 6*b^2*x^2))/(a^3*c^(3/2)*Sqrt[c*x^2]*(-4*a*x - 4*b*x^2) + a^3*c^2*(4*a*x^2 + 4*b*x^3)) - (3*b^2*Log[-(Sqrt[c]*x) + Sqrt[c*x^2]])/(a^4*c^(3/2)) + (3*b^2*Log[2*a*Sqrt[c] + b*Sqrt[c]*x - b*Sqrt[c*x^2]])/(a^4*c^(3/2))","A",0
923,0,0,131,0.0000611,"\int x^2 \sqrt{c x^2} (a+b x)^n \, dx","IntegrateAlgebraic[x^2*Sqrt[c*x^2]*(a + b*x)^n,x]","\int x^2 \sqrt{c x^2} (a+b x)^n \, dx","-\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,"Could not integrate","F",-1
924,0,0,96,0.0001134,"\int x \sqrt{c x^2} (a+b x)^n \, dx","IntegrateAlgebraic[x*Sqrt[c*x^2]*(a + b*x)^n,x]","\int x \sqrt{c x^2} (a+b x)^n \, dx","\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,"Could not integrate","F",-1
925,0,0,63,0.0000645,"\int \sqrt{c x^2} (a+b x)^n \, dx","IntegrateAlgebraic[Sqrt[c*x^2]*(a + b*x)^n,x]","\int \sqrt{c x^2} (a+b x)^n \, dx","\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,"Could not integrate","F",-1
926,0,0,30,0.0000656,"\int \frac{\sqrt{c x^2} (a+b x)^n}{x} \, dx","IntegrateAlgebraic[(Sqrt[c*x^2]*(a + b*x)^n)/x,x]","\int \frac{\sqrt{c x^2} (a+b x)^n}{x} \, dx","\frac{\sqrt{c x^2} (a+b x)^{n+1}}{b (n+1) x}",1,"Could not integrate","F",-1
927,0,0,47,0.0000611,"\int \frac{\sqrt{c x^2} (a+b x)^n}{x^2} \, dx","IntegrateAlgebraic[(Sqrt[c*x^2]*(a + b*x)^n)/x^2,x]","\int \frac{\sqrt{c x^2} (a+b x)^n}{x^2} \, dx","-\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,"Could not integrate","F",-1
928,0,0,47,0.000067,"\int \frac{\sqrt{c x^2} (a+b x)^n}{x^3} \, dx","IntegrateAlgebraic[(Sqrt[c*x^2]*(a + b*x)^n)/x^3,x]","\int \frac{\sqrt{c x^2} (a+b x)^n}{x^3} \, dx","\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,"Could not integrate","F",-1
929,0,0,50,0.0000671,"\int \frac{\sqrt{c x^2} (a+b x)^n}{x^4} \, dx","IntegrateAlgebraic[(Sqrt[c*x^2]*(a + b*x)^n)/x^4,x]","\int \frac{\sqrt{c x^2} (a+b x)^n}{x^4} \, dx","-\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,"Could not integrate","F",-1
930,0,0,169,0.0000644,"\int x \left(c x^2\right)^{3/2} (a+b x)^n \, dx","IntegrateAlgebraic[x*(c*x^2)^(3/2)*(a + b*x)^n,x]","\int x \left(c x^2\right)^{3/2} (a+b x)^n \, dx","\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,"Could not integrate","F",-1
931,0,0,135,0.0000632,"\int \left(c x^2\right)^{3/2} (a+b x)^n \, dx","IntegrateAlgebraic[(c*x^2)^(3/2)*(a + b*x)^n,x]","\int \left(c x^2\right)^{3/2} (a+b x)^n \, dx","-\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,"Could not integrate","F",-1
932,0,0,99,0.0000664,"\int \frac{\left(c x^2\right)^{3/2} (a+b x)^n}{x} \, dx","IntegrateAlgebraic[((c*x^2)^(3/2)*(a + b*x)^n)/x,x]","\int \frac{\left(c x^2\right)^{3/2} (a+b x)^n}{x} \, dx","\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,"Could not integrate","F",-1
933,0,0,65,0.0000667,"\int \frac{\left(c x^2\right)^{3/2} (a+b x)^n}{x^2} \, dx","IntegrateAlgebraic[((c*x^2)^(3/2)*(a + b*x)^n)/x^2,x]","\int \frac{\left(c x^2\right)^{3/2} (a+b x)^n}{x^2} \, dx","\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,"Could not integrate","F",-1
934,0,0,31,0.0000647,"\int \frac{\left(c x^2\right)^{3/2} (a+b x)^n}{x^3} \, dx","IntegrateAlgebraic[((c*x^2)^(3/2)*(a + b*x)^n)/x^3,x]","\int \frac{\left(c x^2\right)^{3/2} (a+b x)^n}{x^3} \, dx","\frac{c \sqrt{c x^2} (a+b x)^{n+1}}{b (n+1) x}",1,"Could not integrate","F",-1
935,0,0,48,0.0000628,"\int \frac{\left(c x^2\right)^{3/2} (a+b x)^n}{x^4} \, dx","IntegrateAlgebraic[((c*x^2)^(3/2)*(a + b*x)^n)/x^4,x]","\int \frac{\left(c x^2\right)^{3/2} (a+b x)^n}{x^4} \, dx","-\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,"Could not integrate","F",-1
936,0,0,48,0.0000666,"\int \frac{\left(c x^2\right)^{3/2} (a+b x)^n}{x^5} \, dx","IntegrateAlgebraic[((c*x^2)^(3/2)*(a + b*x)^n)/x^5,x]","\int \frac{\left(c x^2\right)^{3/2} (a+b x)^n}{x^5} \, dx","\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,"Could not integrate","F",-1
937,0,0,51,0.0000665,"\int \frac{\left(c x^2\right)^{3/2} (a+b x)^n}{x^6} \, dx","IntegrateAlgebraic[((c*x^2)^(3/2)*(a + b*x)^n)/x^6,x]","\int \frac{\left(c x^2\right)^{3/2} (a+b x)^n}{x^6} \, dx","-\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,"Could not integrate","F",-1
938,0,0,217,0.0001005,"\int \left(c x^2\right)^{5/2} (a+b x)^n \, dx","IntegrateAlgebraic[(c*x^2)^(5/2)*(a + b*x)^n,x]","\int \left(c x^2\right)^{5/2} (a+b x)^n \, dx","-\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,"Could not integrate","F",-1
939,0,0,179,0.0000661,"\int \frac{\left(c x^2\right)^{5/2} (a+b x)^n}{x} \, dx","IntegrateAlgebraic[((c*x^2)^(5/2)*(a + b*x)^n)/x,x]","\int \frac{\left(c x^2\right)^{5/2} (a+b x)^n}{x} \, dx","\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,"Could not integrate","F",-1
940,0,0,143,0.0000675,"\int \frac{\left(c x^2\right)^{5/2} (a+b x)^n}{x^2} \, dx","IntegrateAlgebraic[((c*x^2)^(5/2)*(a + b*x)^n)/x^2,x]","\int \frac{\left(c x^2\right)^{5/2} (a+b x)^n}{x^2} \, dx","-\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,"Could not integrate","F",-1
941,0,0,105,0.0001123,"\int \frac{\left(c x^2\right)^{5/2} (a+b x)^n}{x^3} \, dx","IntegrateAlgebraic[((c*x^2)^(5/2)*(a + b*x)^n)/x^3,x]","\int \frac{\left(c x^2\right)^{5/2} (a+b x)^n}{x^3} \, dx","\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,"Could not integrate","F",-1
942,0,0,69,0.0000905,"\int \frac{\left(c x^2\right)^{5/2} (a+b x)^n}{x^4} \, dx","IntegrateAlgebraic[((c*x^2)^(5/2)*(a + b*x)^n)/x^4,x]","\int \frac{\left(c x^2\right)^{5/2} (a+b x)^n}{x^4} \, dx","\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,"Could not integrate","F",-1
943,0,0,33,0.0000633,"\int \frac{\left(c x^2\right)^{5/2} (a+b x)^n}{x^5} \, dx","IntegrateAlgebraic[((c*x^2)^(5/2)*(a + b*x)^n)/x^5,x]","\int \frac{\left(c x^2\right)^{5/2} (a+b x)^n}{x^5} \, dx","\frac{c^2 \sqrt{c x^2} (a+b x)^{n+1}}{b (n+1) x}",1,"Could not integrate","F",-1
944,0,0,50,0.0000634,"\int \frac{\left(c x^2\right)^{5/2} (a+b x)^n}{x^6} \, dx","IntegrateAlgebraic[((c*x^2)^(5/2)*(a + b*x)^n)/x^6,x]","\int \frac{\left(c x^2\right)^{5/2} (a+b x)^n}{x^6} \, dx","-\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,"Could not integrate","F",-1
945,0,0,50,0.0000662,"\int \frac{\left(c x^2\right)^{5/2} (a+b x)^n}{x^7} \, dx","IntegrateAlgebraic[((c*x^2)^(5/2)*(a + b*x)^n)/x^7,x]","\int \frac{\left(c x^2\right)^{5/2} (a+b x)^n}{x^7} \, dx","\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,"Could not integrate","F",-1
946,0,0,123,0.000066,"\int \frac{x^4 (a+b x)^n}{\sqrt{c x^2}} \, dx","IntegrateAlgebraic[(x^4*(a + b*x)^n)/Sqrt[c*x^2],x]","\int \frac{x^4 (a+b x)^n}{\sqrt{c x^2}} \, dx","-\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,"Could not integrate","F",-1
947,0,0,90,0.0000658,"\int \frac{x^3 (a+b x)^n}{\sqrt{c x^2}} \, dx","IntegrateAlgebraic[(x^3*(a + b*x)^n)/Sqrt[c*x^2],x]","\int \frac{x^3 (a+b x)^n}{\sqrt{c x^2}} \, dx","\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,"Could not integrate","F",-1
948,0,0,59,0.0000662,"\int \frac{x^2 (a+b x)^n}{\sqrt{c x^2}} \, dx","IntegrateAlgebraic[(x^2*(a + b*x)^n)/Sqrt[c*x^2],x]","\int \frac{x^2 (a+b x)^n}{\sqrt{c x^2}} \, dx","\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,"Could not integrate","F",-1
949,0,0,28,0.0000612,"\int \frac{x (a+b x)^n}{\sqrt{c x^2}} \, dx","IntegrateAlgebraic[(x*(a + b*x)^n)/Sqrt[c*x^2],x]","\int \frac{x (a+b x)^n}{\sqrt{c x^2}} \, dx","\frac{x (a+b x)^{n+1}}{b (n+1) \sqrt{c x^2}}",1,"Could not integrate","F",-1
950,0,0,45,0.000058,"\int \frac{(a+b x)^n}{\sqrt{c x^2}} \, dx","IntegrateAlgebraic[(a + b*x)^n/Sqrt[c*x^2],x]","\int \frac{(a+b x)^n}{\sqrt{c x^2}} \, dx","-\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,"Could not integrate","F",-1
951,0,0,45,0.0000993,"\int \frac{(a+b x)^n}{x \sqrt{c x^2}} \, dx","IntegrateAlgebraic[(a + b*x)^n/(x*Sqrt[c*x^2]),x]","\int \frac{(a+b x)^n}{x \sqrt{c x^2}} \, dx","\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,"Could not integrate","F",-1
952,0,0,48,0.0000669,"\int \frac{(a+b x)^n}{x^2 \sqrt{c x^2}} \, dx","IntegrateAlgebraic[(a + b*x)^n/(x^2*Sqrt[c*x^2]),x]","\int \frac{(a+b x)^n}{x^2 \sqrt{c x^2}} \, dx","-\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,"Could not integrate","F",-1
953,0,0,135,0.0000671,"\int \frac{x^6 (a+b x)^n}{\left(c x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[(x^6*(a + b*x)^n)/(c*x^2)^(3/2),x]","\int \frac{x^6 (a+b x)^n}{\left(c x^2\right)^{3/2}} \, dx","-\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,"Could not integrate","F",-1
954,0,0,99,0.0000666,"\int \frac{x^5 (a+b x)^n}{\left(c x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[(x^5*(a + b*x)^n)/(c*x^2)^(3/2),x]","\int \frac{x^5 (a+b x)^n}{\left(c x^2\right)^{3/2}} \, dx","\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,"Could not integrate","F",-1
955,0,0,65,0.0000838,"\int \frac{x^4 (a+b x)^n}{\left(c x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[(x^4*(a + b*x)^n)/(c*x^2)^(3/2),x]","\int \frac{x^4 (a+b x)^n}{\left(c x^2\right)^{3/2}} \, dx","\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,"Could not integrate","F",-1
956,0,0,31,0.0000662,"\int \frac{x^3 (a+b x)^n}{\left(c x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[(x^3*(a + b*x)^n)/(c*x^2)^(3/2),x]","\int \frac{x^3 (a+b x)^n}{\left(c x^2\right)^{3/2}} \, dx","\frac{x (a+b x)^{n+1}}{b c (n+1) \sqrt{c x^2}}",1,"Could not integrate","F",-1
957,0,0,48,0.0000583,"\int \frac{x^2 (a+b x)^n}{\left(c x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[(x^2*(a + b*x)^n)/(c*x^2)^(3/2),x]","\int \frac{x^2 (a+b x)^n}{\left(c x^2\right)^{3/2}} \, dx","-\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,"Could not integrate","F",-1
958,0,0,48,0.0000644,"\int \frac{x (a+b x)^n}{\left(c x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[(x*(a + b*x)^n)/(c*x^2)^(3/2),x]","\int \frac{x (a+b x)^n}{\left(c x^2\right)^{3/2}} \, dx","\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,"Could not integrate","F",-1
959,0,0,51,0.0000756,"\int \frac{(a+b x)^n}{\left(c x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[(a + b*x)^n/(c*x^2)^(3/2),x]","\int \frac{(a+b x)^n}{\left(c x^2\right)^{3/2}} \, dx","-\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,"Could not integrate","F",-1
960,0,0,50,0.0000668,"\int \frac{(a+b x)^n}{x \left(c x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[(a + b*x)^n/(x*(c*x^2)^(3/2)),x]","\int \frac{(a+b x)^n}{x \left(c x^2\right)^{3/2}} \, dx","\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,"Could not integrate","F",-1
961,0,0,135,0.0001096,"\int \frac{x^8 (a+b x)^n}{\left(c x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[(x^8*(a + b*x)^n)/(c*x^2)^(5/2),x]","\int \frac{x^8 (a+b x)^n}{\left(c x^2\right)^{5/2}} \, dx","-\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,"Could not integrate","F",-1
962,0,0,99,0.0000649,"\int \frac{x^7 (a+b x)^n}{\left(c x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[(x^7*(a + b*x)^n)/(c*x^2)^(5/2),x]","\int \frac{x^7 (a+b x)^n}{\left(c x^2\right)^{5/2}} \, dx","\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,"Could not integrate","F",-1
963,0,0,65,0.0000629,"\int \frac{x^6 (a+b x)^n}{\left(c x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[(x^6*(a + b*x)^n)/(c*x^2)^(5/2),x]","\int \frac{x^6 (a+b x)^n}{\left(c x^2\right)^{5/2}} \, dx","\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,"Could not integrate","F",-1
964,0,0,31,0.0000679,"\int \frac{x^5 (a+b x)^n}{\left(c x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[(x^5*(a + b*x)^n)/(c*x^2)^(5/2),x]","\int \frac{x^5 (a+b x)^n}{\left(c x^2\right)^{5/2}} \, dx","\frac{x (a+b x)^{n+1}}{b c^2 (n+1) \sqrt{c x^2}}",1,"Could not integrate","F",-1
965,0,0,48,0.0000618,"\int \frac{x^4 (a+b x)^n}{\left(c x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[(x^4*(a + b*x)^n)/(c*x^2)^(5/2),x]","\int \frac{x^4 (a+b x)^n}{\left(c x^2\right)^{5/2}} \, dx","-\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,"Could not integrate","F",-1
966,0,0,48,0.0000649,"\int \frac{x^3 (a+b x)^n}{\left(c x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[(x^3*(a + b*x)^n)/(c*x^2)^(5/2),x]","\int \frac{x^3 (a+b x)^n}{\left(c x^2\right)^{5/2}} \, dx","\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,"Could not integrate","F",-1
967,0,0,51,0.0000648,"\int \frac{x^2 (a+b x)^n}{\left(c x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[(x^2*(a + b*x)^n)/(c*x^2)^(5/2),x]","\int \frac{x^2 (a+b x)^n}{\left(c x^2\right)^{5/2}} \, dx","-\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,"Could not integrate","F",-1
968,0,0,50,0.0000621,"\int \frac{x (a+b x)^n}{\left(c x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[(x*(a + b*x)^n)/(c*x^2)^(5/2),x]","\int \frac{x (a+b x)^n}{\left(c x^2\right)^{5/2}} \, dx","\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,"Could not integrate","F",-1
969,0,0,65,0.0000647,"\int (d x)^m \left(c x^2\right)^{5/2} (a+b x) \, dx","IntegrateAlgebraic[(d*x)^m*(c*x^2)^(5/2)*(a + b*x),x]","\int (d x)^m \left(c x^2\right)^{5/2} (a+b x) \, dx","\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,"Could not integrate","F",-1
970,0,0,61,0.00006,"\int (d x)^m \left(c x^2\right)^{3/2} (a+b x) \, dx","IntegrateAlgebraic[(d*x)^m*(c*x^2)^(3/2)*(a + b*x),x]","\int (d x)^m \left(c x^2\right)^{3/2} (a+b x) \, dx","\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,"Could not integrate","F",-1
971,0,0,59,0.0000613,"\int (d x)^m \sqrt{c x^2} (a+b x) \, dx","IntegrateAlgebraic[(d*x)^m*Sqrt[c*x^2]*(a + b*x),x]","\int (d x)^m \sqrt{c x^2} (a+b x) \, dx","\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,"Could not integrate","F",-1
972,0,0,48,0.0000589,"\int \frac{(d x)^m (a+b x)}{\sqrt{c x^2}} \, dx","IntegrateAlgebraic[((d*x)^m*(a + b*x))/Sqrt[c*x^2],x]","\int \frac{(d x)^m (a+b x)}{\sqrt{c x^2}} \, dx","\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,"Could not integrate","F",-1
973,0,0,65,0.0000604,"\int \frac{(d x)^m (a+b x)}{\left(c x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[((d*x)^m*(a + b*x))/(c*x^2)^(3/2),x]","\int \frac{(d x)^m (a+b x)}{\left(c x^2\right)^{3/2}} \, dx","-\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,"Could not integrate","F",-1
974,0,0,67,0.0000616,"\int \frac{(d x)^m (a+b x)}{\left(c x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[((d*x)^m*(a + b*x))/(c*x^2)^(5/2),x]","\int \frac{(d x)^m (a+b x)}{\left(c x^2\right)^{5/2}} \, dx","-\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,"Could not integrate","F",-1
975,0,0,103,0.0000648,"\int (d x)^m \left(c x^2\right)^{5/2} (a+b x)^2 \, dx","IntegrateAlgebraic[(d*x)^m*(c*x^2)^(5/2)*(a + b*x)^2,x]","\int (d x)^m \left(c x^2\right)^{5/2} (a+b x)^2 \, dx","\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,"Could not integrate","F",-1
976,0,0,97,0.0001048,"\int (d x)^m \left(c x^2\right)^{3/2} (a+b x)^2 \, dx","IntegrateAlgebraic[(d*x)^m*(c*x^2)^(3/2)*(a + b*x)^2,x]","\int (d x)^m \left(c x^2\right)^{3/2} (a+b x)^2 \, dx","\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,"Could not integrate","F",-1
977,0,0,94,0.0000654,"\int (d x)^m \sqrt{c x^2} (a+b x)^2 \, dx","IntegrateAlgebraic[(d*x)^m*Sqrt[c*x^2]*(a + b*x)^2,x]","\int (d x)^m \sqrt{c x^2} (a+b x)^2 \, dx","\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,"Could not integrate","F",-1
978,0,0,81,0.0000657,"\int \frac{(d x)^m (a+b x)^2}{\sqrt{c x^2}} \, dx","IntegrateAlgebraic[((d*x)^m*(a + b*x)^2)/Sqrt[c*x^2],x]","\int \frac{(d x)^m (a+b x)^2}{\sqrt{c x^2}} \, dx","\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,"Could not integrate","F",-1
979,0,0,93,0.0000681,"\int \frac{(d x)^m (a+b x)^2}{\left(c x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[((d*x)^m*(a + b*x)^2)/(c*x^2)^(3/2),x]","\int \frac{(d x)^m (a+b x)^2}{\left(c x^2\right)^{3/2}} \, dx","-\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,"Could not integrate","F",-1
980,0,0,105,0.0000647,"\int \frac{(d x)^m (a+b x)^2}{\left(c x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[((d*x)^m*(a + b*x)^2)/(c*x^2)^(5/2),x]","\int \frac{(d x)^m (a+b x)^2}{\left(c x^2\right)^{5/2}} \, dx","-\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,"Could not integrate","F",-1
981,0,0,67,0.0000679,"\int (d x)^m \left(c x^2\right)^{5/2} (a+b x)^n \, dx","IntegrateAlgebraic[(d*x)^m*(c*x^2)^(5/2)*(a + b*x)^n,x]","\int (d x)^m \left(c x^2\right)^{5/2} (a+b x)^n \, dx","\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,"Could not integrate","F",-1
982,0,0,65,0.0000679,"\int (d x)^m \left(c x^2\right)^{3/2} (a+b x)^n \, dx","IntegrateAlgebraic[(d*x)^m*(c*x^2)^(3/2)*(a + b*x)^n,x]","\int (d x)^m \left(c x^2\right)^{3/2} (a+b x)^n \, dx","\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,"Could not integrate","F",-1
983,0,0,64,0.0001054,"\int (d x)^m \sqrt{c x^2} (a+b x)^n \, dx","IntegrateAlgebraic[(d*x)^m*Sqrt[c*x^2]*(a + b*x)^n,x]","\int (d x)^m \sqrt{c x^2} (a+b x)^n \, dx","\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,"Could not integrate","F",-1
984,0,0,53,0.0000668,"\int \frac{(d x)^m (a+b x)^n}{\sqrt{c x^2}} \, dx","IntegrateAlgebraic[((d*x)^m*(a + b*x)^n)/Sqrt[c*x^2],x]","\int \frac{(d x)^m (a+b x)^n}{\sqrt{c x^2}} \, dx","\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,"Could not integrate","F",-1
985,0,0,68,0.0001572,"\int \frac{(d x)^m (a+b x)^n}{\left(c x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[((d*x)^m*(a + b*x)^n)/(c*x^2)^(3/2),x]","\int \frac{(d x)^m (a+b x)^n}{\left(c x^2\right)^{3/2}} \, dx","-\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,"Could not integrate","F",-1
986,0,0,68,0.0000708,"\int \frac{(d x)^m (a+b x)^n}{\left(c x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[((d*x)^m*(a + b*x)^n)/(c*x^2)^(5/2),x]","\int \frac{(d x)^m (a+b x)^n}{\left(c x^2\right)^{5/2}} \, dx","-\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,"Could not integrate","F",-1
987,0,0,33,0.0000698,"\int x^3 \left(c x^2\right)^p (a+b x)^{-5-2 p} \, dx","IntegrateAlgebraic[x^3*(c*x^2)^p*(a + b*x)^(-5 - 2*p),x]","\int x^3 \left(c x^2\right)^p (a+b x)^{-5-2 p} \, dx","\frac{x^4 \left(c x^2\right)^p (a+b x)^{-2 (p+2)}}{2 a (p+2)}",1,"Could not integrate","F",-1
988,0,0,32,0.0000632,"\int x^2 \left(c x^2\right)^p (a+b x)^{-4-2 p} \, dx","IntegrateAlgebraic[x^2*(c*x^2)^p*(a + b*x)^(-4 - 2*p),x]","\int x^2 \left(c x^2\right)^p (a+b x)^{-4-2 p} \, dx","\frac{x^3 \left(c x^2\right)^p (a+b x)^{-2 p-3}}{a (2 p+3)}",1,"Could not integrate","F",-1
989,0,0,33,0.0000587,"\int x \left(c x^2\right)^p (a+b x)^{-3-2 p} \, dx","IntegrateAlgebraic[x*(c*x^2)^p*(a + b*x)^(-3 - 2*p),x]","\int x \left(c x^2\right)^p (a+b x)^{-3-2 p} \, dx","\frac{x^2 \left(c x^2\right)^p (a+b x)^{-2 (p+1)}}{2 a (p+1)}",1,"Could not integrate","F",-1
990,0,0,30,0.0000613,"\int \left(c x^2\right)^p (a+b x)^{-2-2 p} \, dx","IntegrateAlgebraic[(c*x^2)^p*(a + b*x)^(-2 - 2*p),x]","\int \left(c x^2\right)^p (a+b x)^{-2-2 p} \, dx","\frac{x \left(c x^2\right)^p (a+b x)^{-2 p-1}}{a (2 p+1)}",1,"Could not integrate","F",-1
991,0,0,26,0.0000651,"\int \frac{\left(c x^2\right)^p (a+b x)^{-1-2 p}}{x} \, dx","IntegrateAlgebraic[((c*x^2)^p*(a + b*x)^(-1 - 2*p))/x,x]","\int \frac{\left(c x^2\right)^p (a+b x)^{-1-2 p}}{x} \, dx","\frac{\left(c x^2\right)^p (a+b x)^{-2 p}}{2 a p}",1,"Could not integrate","F",-1
992,0,0,33,0.0000591,"\int \frac{\left(c x^2\right)^p (a+b x)^{-2 p}}{x^2} \, dx","IntegrateAlgebraic[(c*x^2)^p/(x^2*(a + b*x)^(2*p)),x]","\int \frac{\left(c x^2\right)^p (a+b x)^{-2 p}}{x^2} \, dx","-\frac{\left(c x^2\right)^p (a+b x)^{1-2 p}}{a (1-2 p) x}",1,"Could not integrate","F",-1
993,0,0,35,0.000063,"\int \frac{\left(c x^2\right)^p (a+b x)^{1-2 p}}{x^3} \, dx","IntegrateAlgebraic[((c*x^2)^p*(a + b*x)^(1 - 2*p))/x^3,x]","\int \frac{\left(c x^2\right)^p (a+b x)^{1-2 p}}{x^3} \, dx","-\frac{\left(c x^2\right)^p (a+b x)^{2-2 p}}{2 a (1-p) x^2}",1,"Could not integrate","F",-1
994,0,0,33,0.0000648,"\int \frac{\left(c x^2\right)^p (a+b x)^{2-2 p}}{x^4} \, dx","IntegrateAlgebraic[((c*x^2)^p*(a + b*x)^(2 - 2*p))/x^4,x]","\int \frac{\left(c x^2\right)^p (a+b x)^{2-2 p}}{x^4} \, dx","-\frac{\left(c x^2\right)^p (a+b x)^{3-2 p}}{a (3-2 p) x^3}",1,"Could not integrate","F",-1
995,0,0,38,0.0000647,"\int x^m \left(c x^2\right)^p (a+b x)^{-2-m-2 p} \, dx","IntegrateAlgebraic[x^m*(c*x^2)^p*(a + b*x)^(-2 - m - 2*p),x]","\int x^m \left(c x^2\right)^p (a+b x)^{-2-m-2 p} \, dx","\frac{x^{m+1} \left(c x^2\right)^p (a+b x)^{-m-2 p-1}}{a (m+2 p+1)}",1,"Could not integrate","F",-1
996,0,0,39,0.0000758,"\int (d x)^m \left(c x^2\right)^p (a+b x)^{-2-m-2 p} \, dx","IntegrateAlgebraic[(d*x)^m*(c*x^2)^p*(a + b*x)^(-2 - m - 2*p),x]","\int (d x)^m \left(c x^2\right)^p (a+b x)^{-2-m-2 p} \, dx","\frac{x \left(c x^2\right)^p (d x)^m (a+b x)^{-m-2 p-1}}{a (m+2 p+1)}",1,"Could not integrate","F",-1
997,0,0,63,0.0000612,"\int x^m \left(c x^2\right)^p (a+b x)^n \, dx","IntegrateAlgebraic[x^m*(c*x^2)^p*(a + b*x)^n,x]","\int x^m \left(c x^2\right)^p (a+b x)^n \, dx","\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,"Could not integrate","F",-1
998,0,0,68,0.0000693,"\int (d x)^m \left(c x^2\right)^p (a+b x)^n \, dx","IntegrateAlgebraic[(d*x)^m*(c*x^2)^p*(a + b*x)^n,x]","\int (d x)^m \left(c x^2\right)^p (a+b x)^n \, dx","\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,"Could not integrate","F",-1
999,1,17,17,0.0074186,"\int \frac{(a+b x)^5}{\left(\frac{a d}{b}+d x\right)^3} \, dx","IntegrateAlgebraic[(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",1
1000,1,18,23,0.0070106,"\int \frac{(a+b x)^4}{\left(\frac{a d}{b}+d x\right)^3} \, dx","IntegrateAlgebraic[(a + b*x)^4/((a*d)/b + d*x)^3,x]","\frac{b^3 x (2 a+b x)}{2 d^3}","\frac{a b^3 x}{d^3}+\frac{b^4 x^2}{2 d^3}",1,"(b^3*x*(2*a + b*x))/(2*d^3)","A",1
1001,1,8,8,0.0019749,"\int \frac{(a+b x)^3}{\left(\frac{a d}{b}+d x\right)^3} \, dx","IntegrateAlgebraic[(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",1
1002,1,13,13,0.0048304,"\int \frac{(a+b x)^2}{\left(\frac{a d}{b}+d x\right)^3} \, dx","IntegrateAlgebraic[(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",1
1003,1,15,15,0.0074549,"\int \frac{a+b x}{\left(\frac{a d}{b}+d x\right)^3} \, dx","IntegrateAlgebraic[(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",1
1004,1,17,17,0.0082026,"\int \frac{1}{(a+b x) \left(\frac{a d}{b}+d x\right)^3} \, dx","IntegrateAlgebraic[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,"-1/3*b^2/(d^3*(a + b*x)^3)","A",1
1005,1,17,17,0.0095577,"\int \frac{1}{(a+b x)^2 \left(\frac{a d}{b}+d x\right)^3} \, dx","IntegrateAlgebraic[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,"-1/4*b^2/(d^3*(a + b*x)^4)","A",1
1006,1,17,17,0.0098352,"\int \frac{1}{(a+b x)^3 \left(\frac{a d}{b}+d x\right)^3} \, dx","IntegrateAlgebraic[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,"-1/5*b^2/(d^3*(a + b*x)^5)","A",1
1007,1,17,17,0.0087825,"\int \frac{\left(\frac{b c}{d}+b x\right)^5}{(c+d x)^3} \, dx","IntegrateAlgebraic[((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",1
1008,1,18,23,0.0068135,"\int \frac{\left(\frac{b c}{d}+b x\right)^4}{(c+d x)^3} \, dx","IntegrateAlgebraic[((b*c)/d + b*x)^4/(c + d*x)^3,x]","\frac{b^4 x (2 c+d x)}{2 d^4}","\frac{b^4 c x}{d^4}+\frac{b^4 x^2}{2 d^3}",1,"(b^4*x*(2*c + d*x))/(2*d^4)","A",1
1009,1,8,8,0.0022454,"\int \frac{\left(\frac{b c}{d}+b x\right)^3}{(c+d x)^3} \, dx","IntegrateAlgebraic[((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",1
1010,1,13,13,0.0050273,"\int \frac{\left(\frac{b c}{d}+b x\right)^2}{(c+d x)^3} \, dx","IntegrateAlgebraic[((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",1
1011,1,13,13,0.0075225,"\int \frac{\frac{b c}{d}+b x}{(c+d x)^3} \, dx","IntegrateAlgebraic[((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",1
1012,1,14,14,0.0090094,"\int \frac{1}{\left(\frac{b c}{d}+b x\right) (c+d x)^3} \, dx","IntegrateAlgebraic[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*1/(b*(c + d*x)^3)","A",1
1013,1,15,15,0.0094367,"\int \frac{1}{\left(\frac{b c}{d}+b x\right)^2 (c+d x)^3} \, dx","IntegrateAlgebraic[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,"-1/4*d/(b^2*(c + d*x)^4)","A",1
1014,1,17,17,0.0098921,"\int \frac{1}{\left(\frac{b c}{d}+b x\right)^3 (c+d x)^3} \, dx","IntegrateAlgebraic[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,"-1/5*d^2/(b^3*(c + d*x)^5)","A",1
1015,0,0,24,0.0000592,"\int (a+b x)^5 (a c+b c x)^n \, dx","IntegrateAlgebraic[(a + b*x)^5*(a*c + b*c*x)^n,x]","\int (a+b x)^5 (a c+b c x)^n \, dx","\frac{(a c+b c x)^{n+6}}{b c^6 (n+6)}",1,"Could not integrate","F",-1
1016,1,17,17,0.0083438,"\int (a+b x)^5 (a c+b c x)^3 \, dx","IntegrateAlgebraic[(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",1
1017,1,17,17,0.0081818,"\int (a+b x)^5 (a c+b c x)^2 \, dx","IntegrateAlgebraic[(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",1
1018,1,15,15,0.0071496,"\int (a+b x)^5 (a c+b c x) \, dx","IntegrateAlgebraic[(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",1
1019,1,17,17,0.0061837,"\int \frac{(a+b x)^5}{a c+b c x} \, dx","IntegrateAlgebraic[(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",1
1020,1,17,17,0.0060027,"\int \frac{(a+b x)^5}{(a c+b c x)^2} \, dx","IntegrateAlgebraic[(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",1
1021,1,17,17,0.0048733,"\int \frac{(a+b x)^5}{(a c+b c x)^3} \, dx","IntegrateAlgebraic[(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",1
1022,1,15,18,0.0048826,"\int \frac{(a+b x)^5}{(a c+b c x)^4} \, dx","IntegrateAlgebraic[(a + b*x)^5/(a*c + b*c*x)^4,x]","\frac{x (2 a+b x)}{2 c^4}","\frac{a x}{c^4}+\frac{b x^2}{2 c^4}",1,"(x*(2*a + b*x))/(2*c^4)","A",1
1023,1,5,5,0.0019458,"\int \frac{(a+b x)^5}{(a c+b c x)^5} \, dx","IntegrateAlgebraic[(a + b*x)^5/(a*c + b*c*x)^5,x]","\frac{x}{c^5}","\frac{x}{c^5}",1,"x/c^5","A",1
1024,1,13,13,0.0044369,"\int \frac{(a+b x)^5}{(a c+b c x)^6} \, dx","IntegrateAlgebraic[(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",1
1025,1,15,15,0.0065145,"\int \frac{(a+b x)^5}{(a c+b c x)^7} \, dx","IntegrateAlgebraic[(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",1
1026,1,17,17,0.0079858,"\int \frac{(a+b x)^5}{(a c+b c x)^8} \, dx","IntegrateAlgebraic[(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*1/(b*c^8*(a + b*x)^2)","A",1
1027,0,0,28,1.8489778,"\int \frac{1}{\sqrt{-2-3 x} \sqrt{2+3 x}} \, dx","IntegrateAlgebraic[1/(Sqrt[-2 - 3*x]*Sqrt[2 + 3*x]),x]","\int \frac{1}{\sqrt{-2-3 x} \sqrt{2+3 x}} \, dx","\frac{\sqrt{3 x+2} \log (3 x+2)}{3 \sqrt{-3 x-2}}",1,"Could not integrate","F",-1
1028,1,38,38,0.013042,"\int (a+b x) (a c-b c x)^3 \, dx","IntegrateAlgebraic[(a + b*x)*(a*c - b*c*x)^3,x]","-\frac{1}{10} c^3 x \left(-10 a^4+10 a^3 b x-5 a b^3 x^3+2 b^4 x^4\right)","\frac{c^3 (a-b x)^5}{5 b}-\frac{a c^3 (a-b x)^4}{2 b}",1,"-1/10*(c^3*x*(-10*a^4 + 10*a^3*b*x - 5*a*b^3*x^3 + 2*b^4*x^4))","A",1
1029,1,38,38,0.0093082,"\int (a+b x) (a c-b c x)^2 \, dx","IntegrateAlgebraic[(a + b*x)*(a*c - b*c*x)^2,x]","\frac{1}{12} c^2 x \left(12 a^3-6 a^2 b x-4 a b^2 x^2+3 b^3 x^3\right)","\frac{c^2 (a-b x)^4}{4 b}-\frac{2 a c^2 (a-b x)^3}{3 b}",1,"(c^2*x*(12*a^3 - 6*a^2*b*x - 4*a*b^2*x^2 + 3*b^3*x^3))/12","A",1
1030,1,21,18,0.0050084,"\int (a+b x) (a c-b c x) \, dx","IntegrateAlgebraic[(a + b*x)*(a*c - b*c*x),x]","\frac{1}{3} \left(3 a^2 c x-b^2 c x^3\right)","a^2 c x-\frac{1}{3} b^2 c x^3",1,"(3*a^2*c*x - b^2*c*x^3)/3","A",1
1031,1,14,12,0.0000826,"\int (a+b x) \, dx","IntegrateAlgebraic[a + b*x,x]","\frac{1}{2} \left(2 a x+b x^2\right)","a x+\frac{b x^2}{2}",1,"(2*a*x + b*x^2)/2","A",1
1032,1,23,23,0.0087921,"\int \frac{a+b x}{a c-b c x} \, dx","IntegrateAlgebraic[(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",1
1033,1,36,32,0.0282925,"\int \frac{a+b x}{(a c-b c x)^2} \, dx","IntegrateAlgebraic[(a + b*x)/(a*c - b*c*x)^2,x]","\frac{\log (a c-b c x)}{b c^2}-\frac{2 a}{b c^2 (b x-a)}","\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*c - b*c*x]/(b*c^2)","A",1
1034,1,13,13,0.0111005,"\int \frac{a+b x}{(a c-b c x)^3} \, dx","IntegrateAlgebraic[(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
1035,1,25,38,0.0165708,"\int \frac{a+b x}{(a c-b c x)^4} \, dx","IntegrateAlgebraic[(a + b*x)/(a*c - b*c*x)^4,x]","-\frac{a+3 b x}{6 b c^4 (b x-a)^3}","\frac{2 a}{3 b c^4 (a-b x)^3}-\frac{1}{2 b c^4 (a-b x)^2}",1,"-1/6*(a + 3*b*x)/(b*c^4*(-a + b*x)^3)","A",1
1036,1,25,38,0.0157285,"\int \frac{a+b x}{(a c-b c x)^5} \, dx","IntegrateAlgebraic[(a + b*x)/(a*c - b*c*x)^5,x]","\frac{a+2 b x}{6 b c^5 (b x-a)^4}","\frac{a}{2 b c^5 (a-b x)^4}-\frac{1}{3 b c^5 (a-b x)^3}",1,"(a + 2*b*x)/(6*b*c^5*(-a + b*x)^4)","A",1
1037,1,27,38,0.0183017,"\int \frac{a+b x}{(a c-b c x)^6} \, dx","IntegrateAlgebraic[(a + b*x)/(a*c - b*c*x)^6,x]","-\frac{3 a+5 b x}{20 b c^6 (b x-a)^5}","\frac{2 a}{5 b c^6 (a-b x)^5}-\frac{1}{4 b c^6 (a-b x)^4}",1,"-1/20*(3*a + 5*b*x)/(b*c^6*(-a + b*x)^5)","A",1
1038,1,60,57,0.0154341,"\int (a+b x)^2 (a c-b c x)^3 \, dx","IntegrateAlgebraic[(a + b*x)^2*(a*c - b*c*x)^3,x]","-\frac{1}{30} c^3 x \left(-30 a^5+15 a^4 b x+20 a^3 b^2 x^2-15 a^2 b^3 x^3-6 a b^4 x^4+5 b^5 x^5\right)","-\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,"-1/30*(c^3*x*(-30*a^5 + 15*a^4*b*x + 20*a^3*b^2*x^2 - 15*a^2*b^3*x^3 - 6*a*b^4*x^4 + 5*b^5*x^5))","A",1
1039,1,33,38,0.0077264,"\int (a+b x)^2 (a c-b c x)^2 \, dx","IntegrateAlgebraic[(a + b*x)^2*(a*c - b*c*x)^2,x]","\frac{1}{15} c^2 x \left(15 a^4-10 a^2 b^2 x^2+3 b^4 x^4\right)","a^4 c^2 x-\frac{2}{3} a^2 b^2 c^2 x^3+\frac{1}{5} b^4 c^2 x^5",1,"(c^2*x*(15*a^4 - 10*a^2*b^2*x^2 + 3*b^4*x^4))/15","A",1
1040,1,36,32,0.0087644,"\int (a+b x)^2 (a c-b c x) \, dx","IntegrateAlgebraic[(a + b*x)^2*(a*c - b*c*x),x]","-\frac{1}{12} c x \left(-12 a^3-6 a^2 b x+4 a b^2 x^2+3 b^3 x^3\right)","\frac{2 a c (a+b x)^3}{3 b}-\frac{c (a+b x)^4}{4 b}",1,"-1/12*(c*x*(-12*a^3 - 6*a^2*b*x + 4*a*b^2*x^2 + 3*b^3*x^3))","A",1
1041,1,14,14,0.000093,"\int (a+b x)^2 \, dx","IntegrateAlgebraic[(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
1042,1,34,43,0.0140932,"\int \frac{(a+b x)^2}{a c-b c x} \, dx","IntegrateAlgebraic[(a + b*x)^2/(a*c - b*c*x),x]","-\frac{4 a^2 \log (a-b x)}{b c}-\frac{x (6 a+b x)}{2 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,"-1/2*(x*(6*a + b*x))/c - (4*a^2*Log[a - b*x])/(b*c)","A",1
1043,1,51,41,0.0421381,"\int \frac{(a+b x)^2}{(a c-b c x)^2} \, dx","IntegrateAlgebraic[(a + b*x)^2/(a*c - b*c*x)^2,x]","\frac{-4 a^2-a b x+b^2 x^2}{b c^2 (b x-a)}+\frac{4 a \log (a-b x)}{b 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,"(-4*a^2 - a*b*x + b^2*x^2)/(b*c^2*(-a + b*x)) + (4*a*Log[a - b*x])/(b*c^2)","A",1
1044,1,40,52,0.035088,"\int \frac{(a+b x)^2}{(a c-b c x)^3} \, dx","IntegrateAlgebraic[(a + b*x)^2/(a*c - b*c*x)^3,x]","-\frac{2 a (a-2 b x)}{b c^3 (b x-a)^2}-\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*(a - 2*b*x))/(b*c^3*(-a + b*x)^2) - Log[a - b*x]/(b*c^3)","A",1
1045,1,31,28,0.0237771,"\int \frac{(a+b x)^2}{(a c-b c x)^4} \, dx","IntegrateAlgebraic[(a + b*x)^2/(a*c - b*c*x)^4,x]","-\frac{a^2+3 b^2 x^2}{3 b c^4 (b x-a)^3}","\frac{(a+b x)^3}{6 a b c^4 (a-b x)^3}",1,"-1/3*(a^2 + 3*b^2*x^2)/(b*c^4*(-a + b*x)^3)","A",1
1046,1,36,56,0.0181141,"\int \frac{(a+b x)^2}{(a c-b c x)^5} \, dx","IntegrateAlgebraic[(a + b*x)^2/(a*c - b*c*x)^5,x]","\frac{a^2+2 a b x+3 b^2 x^2}{6 b c^5 (b x-a)^4}","\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 + 2*a*b*x + 3*b^2*x^2)/(6*b*c^5*(-a + b*x)^4)","A",1
1047,1,38,57,0.0244435,"\int \frac{(a+b x)^2}{(a c-b c x)^6} \, dx","IntegrateAlgebraic[(a + b*x)^2/(a*c - b*c*x)^6,x]","-\frac{2 a^2+5 a b x+5 b^2 x^2}{15 b c^6 (b x-a)^5}","\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,"-1/15*(2*a^2 + 5*a*b*x + 5*b^2*x^2)/(b*c^6*(-a + b*x)^5)","A",1
1048,1,38,59,0.020947,"\int \frac{(a+b x)^2}{(a c-b c x)^7} \, dx","IntegrateAlgebraic[(a + b*x)^2/(a*c - b*c*x)^7,x]","\frac{7 a^2+18 a b x+15 b^2 x^2}{60 b c^7 (b x-a)^6}","\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,"(7*a^2 + 18*a*b*x + 15*b^2*x^2)/(60*b*c^7*(-a + b*x)^6)","A",1
1049,1,44,61,0.0146734,"\int \frac{(a c-b c x)^3}{a+b x} \, dx","IntegrateAlgebraic[(a*c - b*c*x)^3/(a + b*x),x]","\frac{8 a^3 c^3 \log (a+b x)}{b}-\frac{1}{3} c^3 x \left(21 a^2-6 a b x+b^2 x^2\right)","\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,"-1/3*(c^3*x*(21*a^2 - 6*a*b*x + b^2*x^2)) + (8*a^3*c^3*Log[a + b*x])/b","A",1
1050,1,33,43,0.0113702,"\int \frac{(a c-b c x)^2}{a+b x} \, dx","IntegrateAlgebraic[(a*c - b*c*x)^2/(a + b*x),x]","\frac{4 a^2 c^2 \log (a+b x)}{b}+\frac{1}{2} c^2 x (b x-6 a)","\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,"(c^2*x*(-6*a + b*x))/2 + (4*a^2*c^2*Log[a + b*x])/b","A",1
1051,1,18,18,0.0069029,"\int \frac{a c-b c x}{a+b x} \, dx","IntegrateAlgebraic[(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",1
1052,1,10,10,0.0000993,"\int \frac{1}{a+b x} \, dx","IntegrateAlgebraic[(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
1053,1,17,17,0.0094831,"\int \frac{1}{(a+b x) (a c-b c x)} \, dx","IntegrateAlgebraic[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",1
1054,1,42,42,0.0283655,"\int \frac{1}{(a+b x) (a c-b c x)^2} \, dx","IntegrateAlgebraic[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",1
1055,1,50,63,0.0369595,"\int \frac{1}{(a+b x) (a c-b c x)^3} \, dx","IntegrateAlgebraic[1/((a + b*x)*(a*c - b*c*x)^3),x]","\frac{\tanh ^{-1}\left(\frac{b x}{a}\right)}{4 a^3 b c^3}+\frac{2 a-b x}{4 a^2 b c^3 (a-b x)^2}","\frac{\tanh ^{-1}\left(\frac{b x}{a}\right)}{4 a^3 b c^3}+\frac{1}{4 a^2 b c^3 (a-b x)}+\frac{1}{4 a b c^3 (a-b x)^2}",1,"(2*a - b*x)/(4*a^2*b*c^3*(a - b*x)^2) + ArcTanh[(b*x)/a]/(4*a^3*b*c^3)","A",1
1056,1,64,54,0.0326581,"\int \frac{(a c-b c x)^3}{(a+b x)^2} \, dx","IntegrateAlgebraic[(a*c - b*c*x)^3/(a + b*x)^2,x]","-\frac{12 a^2 c^3 \log (a+b x)}{b}-\frac{c^3 \left(16 a^3-10 a^2 b x-9 a b^2 x^2+b^3 x^3\right)}{2 b (a+b 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",1,"-1/2*(c^3*(16*a^3 - 10*a^2*b*x - 9*a*b^2*x^2 + b^3*x^3))/(b*(a + b*x)) - (12*a^2*c^3*Log[a + b*x])/b","A",1
1057,1,47,39,0.0265997,"\int \frac{(a c-b c x)^2}{(a+b x)^2} \, dx","IntegrateAlgebraic[(a*c - b*c*x)^2/(a + b*x)^2,x]","\frac{c^2 \left(-4 a^2+a b x+b^2 x^2\right)}{b (a+b x)}-\frac{4 a c^2 \log (a+b x)}{b}","-\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*(-4*a^2 + a*b*x + b^2*x^2))/(b*(a + b*x)) - (4*a*c^2*Log[a + b*x])/b","A",1
1058,1,27,27,0.0164098,"\int \frac{a c-b c x}{(a+b x)^2} \, dx","IntegrateAlgebraic[(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",1
1059,1,12,12,0.0000895,"\int \frac{1}{(a+b x)^2} \, dx","IntegrateAlgebraic[(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
1060,1,41,41,0.0288159,"\int \frac{1}{(a+b x)^2 (a c-b c x)} \, dx","IntegrateAlgebraic[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*1/(a*b*c*(a + b*x)) + ArcTanh[(b*x)/a]/(2*a^2*b*c)","A",1
1061,1,46,46,0.042238,"\int \frac{1}{(a+b x)^2 (a c-b c x)^2} \, dx","IntegrateAlgebraic[1/((a + b*x)^2*(a*c - b*c*x)^2),x]","\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}+\frac{x}{2 a^2 c^2 \left(a^2-b^2 x^2\right)}",1,"x/(2*a^2*c^2*(a^2 - b^2*x^2)) + ArcTanh[(b*x)/a]/(2*a^3*b*c^2)","A",1
1062,1,68,83,0.0587897,"\int \frac{1}{(a+b x)^2 (a c-b c x)^3} \, dx","IntegrateAlgebraic[1/((a + b*x)^2*(a*c - b*c*x)^3),x]","\frac{3 \tanh ^{-1}\left(\frac{b x}{a}\right)}{8 a^4 b c^3}+\frac{2 a^2+3 a b x-3 b^2 x^2}{8 a^3 b c^3 (a-b x)^2 (a+b x)}","\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}",1,"(2*a^2 + 3*a*b*x - 3*b^2*x^2)/(8*a^3*b*c^3*(a - b*x)^2*(a + b*x)) + (3*ArcTanh[(b*x)/a])/(8*a^4*b*c^3)","A",1
1063,1,612,108,0.4570744,"\int (1-x)^{9/2} \sqrt{1+x} \, dx","IntegrateAlgebraic[(1 - x)^(9/2)*Sqrt[1 + x],x]","\frac{21}{4} \tan ^{-1}\left(\frac{\sqrt{x+1}-1}{\sqrt{1-x}-1}\right)+\frac{\left(\frac{4}{15}-\frac{4 \sqrt{1-x}}{15}\right) \left(\sqrt{x+1}-1\right) \left(40 x^{11}+440 \sqrt{1-x} x^{10}-440 \sqrt{x+1} x^{10}-192 x^{10}+13288 \sqrt{1-x} x^9-4600 \sqrt{1-x} \sqrt{x+1} x^9+17512 \sqrt{x+1} x^9-70570 x^9-187110 \sqrt{1-x} x^8+22080 \sqrt{1-x} \sqrt{x+1} x^8+39270 \sqrt{x+1} x^8+340160 x^8+251966 \sqrt{1-x} x^7+301990 \sqrt{1-x} \sqrt{x+1} x^7-865986 \sqrt{x+1} x^7+98575 x^7+1341923 \sqrt{1-x} x^6-1613312 \sqrt{1-x} \sqrt{x+1} x^6+2701853 \sqrt{x+1} x^6-2997824 x^6-4140099 \sqrt{1-x} x^5+2340825 \sqrt{1-x} \sqrt{x+1} x^5-2336451 \sqrt{x+1} x^5+5777655 x^5+3095002 \sqrt{1-x} x^4+937216 \sqrt{1-x} \sqrt{x+1} x^4-3383258 \sqrt{x+1} x^4-2336768 x^4+2876012 \sqrt{1-x} x^3-6437700 \sqrt{1-x} \sqrt{x+1} x^3+10260588 \sqrt{x+1} x^3-7021300 x^3-11260112 \sqrt{1-x} x^2+8866304 \sqrt{1-x} \sqrt{x+1} x^2-9988912 \sqrt{x+1} x^2+16037376 x^2+6094672 \sqrt{1-x} x+1242000 \sqrt{1-x} \sqrt{x+1} x-8554672 \sqrt{x+1} x+1215600 x+14677664 \sqrt{1-x}-14680064 \sqrt{1-x} \sqrt{x+1}+14682464 \sqrt{x+1}-14680064\right)}{\left(\sqrt{1-x}+\sqrt{x+1}-2\right)^{12}}","\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,"((4/15 - (4*Sqrt[1 - x])/15)*(-1 + Sqrt[1 + x])*(-14680064 + 14677664*Sqrt[1 - x] + 1215600*x + 6094672*Sqrt[1 - x]*x + 16037376*x^2 - 11260112*Sqrt[1 - x]*x^2 - 7021300*x^3 + 2876012*Sqrt[1 - x]*x^3 - 2336768*x^4 + 3095002*Sqrt[1 - x]*x^4 + 5777655*x^5 - 4140099*Sqrt[1 - x]*x^5 - 2997824*x^6 + 1341923*Sqrt[1 - x]*x^6 + 98575*x^7 + 251966*Sqrt[1 - x]*x^7 + 340160*x^8 - 187110*Sqrt[1 - x]*x^8 - 70570*x^9 + 13288*Sqrt[1 - x]*x^9 - 192*x^10 + 440*Sqrt[1 - x]*x^10 + 40*x^11 + 14682464*Sqrt[1 + x] - 14680064*Sqrt[1 - x]*Sqrt[1 + x] - 8554672*x*Sqrt[1 + x] + 1242000*Sqrt[1 - x]*x*Sqrt[1 + x] - 9988912*x^2*Sqrt[1 + x] + 8866304*Sqrt[1 - x]*x^2*Sqrt[1 + x] + 10260588*x^3*Sqrt[1 + x] - 6437700*Sqrt[1 - x]*x^3*Sqrt[1 + x] - 3383258*x^4*Sqrt[1 + x] + 937216*Sqrt[1 - x]*x^4*Sqrt[1 + x] - 2336451*x^5*Sqrt[1 + x] + 2340825*Sqrt[1 - x]*x^5*Sqrt[1 + x] + 2701853*x^6*Sqrt[1 + x] - 1613312*Sqrt[1 - x]*x^6*Sqrt[1 + x] - 865986*x^7*Sqrt[1 + x] + 301990*Sqrt[1 - x]*x^7*Sqrt[1 + x] + 39270*x^8*Sqrt[1 + x] + 22080*Sqrt[1 - x]*x^8*Sqrt[1 + x] + 17512*x^9*Sqrt[1 + x] - 4600*Sqrt[1 - x]*x^9*Sqrt[1 + x] - 440*x^10*Sqrt[1 + x]))/(-2 + Sqrt[1 - x] + Sqrt[1 + x])^12 + (21*ArcTan[(-1 + Sqrt[1 + x])/(-1 + Sqrt[1 - x])])/4","B",1
1064,1,524,88,0.4136141,"\int (1-x)^{7/2} \sqrt{1+x} \, dx","IntegrateAlgebraic[(1 - x)^(7/2)*Sqrt[1 + x],x]","\frac{\left(\frac{4}{15}-\frac{4 \sqrt{1-x}}{15}\right) \left(\sqrt{x+1}-1\right) \left(-216 \sqrt{1-x} x^8+24 \sqrt{1-x} \sqrt{x+1} x^8-216 \sqrt{x+1} x^8+1824 x^8+5490 \sqrt{1-x} x^7-90 \sqrt{1-x} \sqrt{x+1} x^7-3870 \sqrt{x+1} x^7-6840 x^7+7362 \sqrt{1-x} x^6-17360 \sqrt{1-x} \sqrt{x+1} x^6+42462 \sqrt{x+1} x^6-40736 x^6-103161 \sqrt{1-x} x^5+65505 \sqrt{1-x} \sqrt{x+1} x^5-90969 \sqrt{x+1} x^5+183540 x^5+174675 \sqrt{1-x} x^4-30792 \sqrt{1-x} \sqrt{x+1} x^4-28995 \sqrt{x+1} x^4-192872 x^4+10344 \sqrt{1-x} x^3-179880 \sqrt{1-x} \sqrt{x+1} x^3+327336 \sqrt{x+1} x^3-147060 x^3-385996 \sqrt{1-x} x^2+346784 \sqrt{1-x} \sqrt{x+1} x^2-423796 \sqrt{x+1} x^2+599392 x^2+306488 \sqrt{1-x} x-31800 \sqrt{1-x} \sqrt{x+1} x-244808 \sqrt{x+1} x-29640 x+557296 \sqrt{1-x}-557056 \sqrt{1-x} \sqrt{x+1}+556816 \sqrt{x+1}-557056\right)}{\left(\sqrt{1-x}+\sqrt{x+1}-2\right)^{10}}+\frac{7}{2} \tan ^{-1}\left(\frac{\sqrt{x+1}-1}{\sqrt{1-x}-1}\right)","\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,"((4/15 - (4*Sqrt[1 - x])/15)*(-1 + Sqrt[1 + x])*(-557056 + 557296*Sqrt[1 - x] - 29640*x + 306488*Sqrt[1 - x]*x + 599392*x^2 - 385996*Sqrt[1 - x]*x^2 - 147060*x^3 + 10344*Sqrt[1 - x]*x^3 - 192872*x^4 + 174675*Sqrt[1 - x]*x^4 + 183540*x^5 - 103161*Sqrt[1 - x]*x^5 - 40736*x^6 + 7362*Sqrt[1 - x]*x^6 - 6840*x^7 + 5490*Sqrt[1 - x]*x^7 + 1824*x^8 - 216*Sqrt[1 - x]*x^8 + 556816*Sqrt[1 + x] - 557056*Sqrt[1 - x]*Sqrt[1 + x] - 244808*x*Sqrt[1 + x] - 31800*Sqrt[1 - x]*x*Sqrt[1 + x] - 423796*x^2*Sqrt[1 + x] + 346784*Sqrt[1 - x]*x^2*Sqrt[1 + x] + 327336*x^3*Sqrt[1 + x] - 179880*Sqrt[1 - x]*x^3*Sqrt[1 + x] - 28995*x^4*Sqrt[1 + x] - 30792*Sqrt[1 - x]*x^4*Sqrt[1 + x] - 90969*x^5*Sqrt[1 + x] + 65505*Sqrt[1 - x]*x^5*Sqrt[1 + x] + 42462*x^6*Sqrt[1 + x] - 17360*Sqrt[1 - x]*x^6*Sqrt[1 + x] - 3870*x^7*Sqrt[1 + x] - 90*Sqrt[1 - x]*x^7*Sqrt[1 + x] - 216*x^8*Sqrt[1 + x] + 24*Sqrt[1 - x]*x^8*Sqrt[1 + x]))/(-2 + Sqrt[1 - x] + Sqrt[1 + x])^10 + (7*ArcTan[(-1 + Sqrt[1 + x])/(-1 + Sqrt[1 - x])])/2","B",1
1065,1,404,68,0.2679555,"\int (1-x)^{5/2} \sqrt{1+x} \, dx","IntegrateAlgebraic[(1 - x)^(5/2)*Sqrt[1 + x],x]","\frac{\left(\frac{2 \sqrt{1-x}}{3}-\frac{2}{3}\right) \left(\sqrt{x+1}-1\right) \left(6 x^7+42 \sqrt{1-x} x^6-42 \sqrt{x+1} x^6-16 x^6+434 \sqrt{1-x} x^5-270 \sqrt{1-x} \sqrt{x+1} x^5+658 \sqrt{x+1} x^5-1365 x^5-2401 \sqrt{1-x} x^4+720 \sqrt{1-x} \sqrt{x+1} x^4-511 \sqrt{x+1} x^4+3680 x^4+2059 \sqrt{1-x} x^3+1299 \sqrt{1-x} \sqrt{x+1} x^3-3541 \sqrt{x+1} x^3-693 x^3+4168 \sqrt{1-x} x^2-5280 \sqrt{1-x} \sqrt{x+1} x^2+7288 \sqrt{x+1} x^2-8032 x^2-6244 \sqrt{1-x} x+2556 \sqrt{1-x} \sqrt{x+1} x+1564 \sqrt{x+1} x+2052 x-8264 \sqrt{1-x}+8192 \sqrt{1-x} \sqrt{x+1}-8120 \sqrt{x+1}+8192\right)}{\left(\sqrt{1-x}+\sqrt{x+1}-2\right)^8}+\frac{5}{2} \tan ^{-1}\left(\frac{\sqrt{x+1}-1}{\sqrt{1-x}-1}\right)","\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,"((-2/3 + (2*Sqrt[1 - x])/3)*(-1 + Sqrt[1 + x])*(8192 - 8264*Sqrt[1 - x] + 2052*x - 6244*Sqrt[1 - x]*x - 8032*x^2 + 4168*Sqrt[1 - x]*x^2 - 693*x^3 + 2059*Sqrt[1 - x]*x^3 + 3680*x^4 - 2401*Sqrt[1 - x]*x^4 - 1365*x^5 + 434*Sqrt[1 - x]*x^5 - 16*x^6 + 42*Sqrt[1 - x]*x^6 + 6*x^7 - 8120*Sqrt[1 + x] + 8192*Sqrt[1 - x]*Sqrt[1 + x] + 1564*x*Sqrt[1 + x] + 2556*Sqrt[1 - x]*x*Sqrt[1 + x] + 7288*x^2*Sqrt[1 + x] - 5280*Sqrt[1 - x]*x^2*Sqrt[1 + x] - 3541*x^3*Sqrt[1 + x] + 1299*Sqrt[1 - x]*x^3*Sqrt[1 + x] - 511*x^4*Sqrt[1 + x] + 720*Sqrt[1 - x]*x^4*Sqrt[1 + x] + 658*x^5*Sqrt[1 + x] - 270*Sqrt[1 - x]*x^5*Sqrt[1 + x] - 42*x^6*Sqrt[1 + x]))/(-2 + Sqrt[1 - x] + Sqrt[1 + x])^8 + (5*ArcTan[(-1 + Sqrt[1 + x])/(-1 + Sqrt[1 - x])])/2","B",1
1066,1,314,48,0.2440717,"\int (1-x)^{3/2} \sqrt{1+x} \, dx","IntegrateAlgebraic[(1 - x)^(3/2)*Sqrt[1 + x],x]","\frac{\left(\frac{4 \sqrt{1-x}}{3}-\frac{4}{3}\right) \left(\sqrt{x+1}-1\right) \left(-10 \sqrt{1-x} x^4+2 \sqrt{1-x} \sqrt{x+1} x^4-10 \sqrt{x+1} x^4+44 x^4+65 \sqrt{1-x} x^3-3 \sqrt{1-x} \sqrt{x+1} x^3-35 \sqrt{x+1} x^3-66 x^3+3 \sqrt{1-x} x^2-86 \sqrt{1-x} \sqrt{x+1} x^2+153 \sqrt{x+1} x^2-90 x^2-154 \sqrt{1-x} x+126 \sqrt{1-x} \sqrt{x+1} x-50 \sqrt{x+1} x+66 x-140 \sqrt{1-x}+128 \sqrt{1-x} \sqrt{x+1}-116 \sqrt{x+1}+128\right)}{\left(\sqrt{1-x}+\sqrt{x+1}-2\right)^6}+2 \tan ^{-1}\left(\frac{\sqrt{x+1}-1}{\sqrt{1-x}-1}\right)","\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,"((-4/3 + (4*Sqrt[1 - x])/3)*(-1 + Sqrt[1 + x])*(128 - 140*Sqrt[1 - x] + 66*x - 154*Sqrt[1 - x]*x - 90*x^2 + 3*Sqrt[1 - x]*x^2 - 66*x^3 + 65*Sqrt[1 - x]*x^3 + 44*x^4 - 10*Sqrt[1 - x]*x^4 - 116*Sqrt[1 + x] + 128*Sqrt[1 - x]*Sqrt[1 + x] - 50*x*Sqrt[1 + x] + 126*Sqrt[1 - x]*x*Sqrt[1 + x] + 153*x^2*Sqrt[1 + x] - 86*Sqrt[1 - x]*x^2*Sqrt[1 + x] - 35*x^3*Sqrt[1 + x] - 3*Sqrt[1 - x]*x^3*Sqrt[1 + x] - 10*x^4*Sqrt[1 + x] + 2*Sqrt[1 - x]*x^4*Sqrt[1 + x]))/(-2 + Sqrt[1 - x] + Sqrt[1 + x])^6 + 2*ArcTan[(-1 + Sqrt[1 + x])/(-1 + Sqrt[1 - x])]","B",1
1067,1,200,28,0.1419292,"\int \sqrt{1-x} \sqrt{1+x} \, dx","IntegrateAlgebraic[Sqrt[1 - x]*Sqrt[1 + x],x]","\frac{\left(\sqrt{x+1}-1\right)^8 \left(\frac{\left(\sqrt{1-x}-1\right)^7}{8 \left(\sqrt{x+1}-1\right)^7}-\frac{7 \left(\sqrt{1-x}-1\right)^5}{8 \left(\sqrt{x+1}-1\right)^5}+\frac{7 \left(\sqrt{1-x}-1\right)^3}{8 \left(\sqrt{x+1}-1\right)^3}-\frac{\sqrt{1-x}-1}{8 \left(\sqrt{x+1}-1\right)}+\frac{2 \left(\sqrt{1-x}+\sqrt{x+1}-2\right)^4 \tan ^{-1}\left(\frac{\sqrt{x+1}-1}{\sqrt{1-x}-1}\right)}{\left(\sqrt{x+1}-1\right)^8}\right)}{\left(\sqrt{1-x}+\sqrt{x+1}-2\right)^4}","\frac{1}{2} \sqrt{1-x} \sqrt{x+1} x+\frac{1}{2} \sin ^{-1}(x)",1,"((-1 + Sqrt[1 + x])^8*((-1 + Sqrt[1 - x])^7/(8*(-1 + Sqrt[1 + x])^7) - (7*(-1 + Sqrt[1 - x])^5)/(8*(-1 + Sqrt[1 + x])^5) + (7*(-1 + Sqrt[1 - x])^3)/(8*(-1 + Sqrt[1 + x])^3) - (-1 + Sqrt[1 - x])/(8*(-1 + Sqrt[1 + x])) + (2*(-2 + Sqrt[1 - x] + Sqrt[1 + x])^4*ArcTan[(-1 + Sqrt[1 + x])/(-1 + Sqrt[1 - x])])/(-1 + Sqrt[1 + x])^8))/(-2 + Sqrt[1 - x] + Sqrt[1 + x])^4","B",1
1068,1,73,21,0.0517729,"\int \frac{\sqrt{1+x}}{\sqrt{1-x}} \, dx","IntegrateAlgebraic[Sqrt[1 + x]/Sqrt[1 - x],x]","4 \tan ^{-1}\left(\frac{\sqrt{x+1}-1}{\sqrt{1-x}-1}\right)-\frac{2 \left(\sqrt{1-x}-1\right)^2 \left(\sqrt{x+1}-1\right)^2}{\left(\sqrt{1-x}+\sqrt{x+1}-2\right)^2}","\sin ^{-1}(x)-\sqrt{1-x} \sqrt{x+1}",1,"(-2*(-1 + Sqrt[1 - x])^2*(-1 + Sqrt[1 + x])^2)/(-2 + Sqrt[1 - x] + Sqrt[1 + x])^2 + 4*ArcTan[(-1 + Sqrt[1 + x])/(-1 + Sqrt[1 - x])]","B",1
1069,1,85,23,0.0623561,"\int \frac{\sqrt{1+x}}{(1-x)^{3/2}} \, dx","IntegrateAlgebraic[Sqrt[1 + x]/(1 - x)^(3/2),x]","\frac{\left(4 \sqrt{1-x}-4\right) \left(\sqrt{x+1}-1\right)}{-x-2 \sqrt{1-x}+\sqrt{1-x} \sqrt{x+1}+1}-4 \tan ^{-1}\left(\frac{\sqrt{x+1}-1}{\sqrt{1-x}-1}\right)","\frac{2 \sqrt{x+1}}{\sqrt{1-x}}-\sin ^{-1}(x)",1,"((-4 + 4*Sqrt[1 - x])*(-1 + Sqrt[1 + x]))/(1 - 2*Sqrt[1 - x] - x + Sqrt[1 - x]*Sqrt[1 + x]) - 4*ArcTan[(-1 + Sqrt[1 + x])/(-1 + Sqrt[1 - x])]","B",1
1070,1,130,20,0.0725194,"\int \frac{\sqrt{1+x}}{(1-x)^{5/2}} \, dx","IntegrateAlgebraic[Sqrt[1 + x]/(1 - x)^(5/2),x]","\frac{\left(\sqrt{x+1}-1\right)^6 \left(\frac{\left(\sqrt{1-x}-1\right)^5}{2 \left(\sqrt{x+1}-1\right)^5}-\frac{\left(\sqrt{1-x}-1\right)^3}{3 \left(\sqrt{x+1}-1\right)^3}+\frac{\sqrt{1-x}-1}{2 \left(\sqrt{x+1}-1\right)}\right)}{\left(-x-2 \sqrt{1-x}+\sqrt{1-x} \sqrt{x+1}+1\right)^3}","\frac{(x+1)^{3/2}}{3 (1-x)^{3/2}}",1,"((-1 + Sqrt[1 + x])^6*((-1 + Sqrt[1 - x])^5/(2*(-1 + Sqrt[1 + x])^5) - (-1 + Sqrt[1 - x])^3/(3*(-1 + Sqrt[1 + x])^3) + (-1 + Sqrt[1 - x])/(2*(-1 + Sqrt[1 + x]))))/(1 - 2*Sqrt[1 - x] - x + Sqrt[1 - x]*Sqrt[1 + x])^3","B",1
1071,1,272,41,0.2911133,"\int \frac{\sqrt{1+x}}{(1-x)^{7/2}} \, dx","IntegrateAlgebraic[Sqrt[1 + x]/(1 - x)^(7/2),x]","\frac{\left(\frac{\sqrt{1-x}}{120}-\frac{1}{120}\right) \left(\sqrt{x+1}-1\right)^9 \left(\frac{15 \left(\sqrt{1-x}-1\right)^8}{\left(\sqrt{x+1}-1\right)^8}+\frac{30 \left(\sqrt{1-x}-1\right)^7}{\left(\sqrt{x+1}-1\right)^7}+\frac{40 \left(\sqrt{1-x}-1\right)^6}{\left(\sqrt{x+1}-1\right)^6}-\frac{50 \left(\sqrt{1-x}-1\right)^5}{\left(\sqrt{x+1}-1\right)^5}-\frac{46 \left(\sqrt{1-x}-1\right)^4}{\left(\sqrt{x+1}-1\right)^4}+\frac{50 \left(\sqrt{1-x}-1\right)^3}{\left(\sqrt{x+1}-1\right)^3}+\frac{40 \left(\sqrt{1-x}-1\right)^2}{\left(\sqrt{x+1}-1\right)^2}-\frac{30 \left(\sqrt{1-x}-1\right)}{\sqrt{x+1}-1}+15\right)}{\left(-x-2 \sqrt{1-x}+\sqrt{1-x} \sqrt{x+1}+1\right)^5}","\frac{(x+1)^{3/2}}{15 (1-x)^{3/2}}+\frac{(x+1)^{3/2}}{5 (1-x)^{5/2}}",1,"((-1/120 + Sqrt[1 - x]/120)*(-1 + Sqrt[1 + x])^9*(15 + (15*(-1 + Sqrt[1 - x])^8)/(-1 + Sqrt[1 + x])^8 + (30*(-1 + Sqrt[1 - x])^7)/(-1 + Sqrt[1 + x])^7 + (40*(-1 + Sqrt[1 - x])^6)/(-1 + Sqrt[1 + x])^6 - (50*(-1 + Sqrt[1 - x])^5)/(-1 + Sqrt[1 + x])^5 - (46*(-1 + Sqrt[1 - x])^4)/(-1 + Sqrt[1 + x])^4 + (50*(-1 + Sqrt[1 - x])^3)/(-1 + Sqrt[1 + x])^3 + (40*(-1 + Sqrt[1 - x])^2)/(-1 + Sqrt[1 + x])^2 - (30*(-1 + Sqrt[1 - x]))/(-1 + Sqrt[1 + x])))/(1 - 2*Sqrt[1 - x] - x + Sqrt[1 - x]*Sqrt[1 + x])^5","B",1
1072,1,376,61,0.8166279,"\int \frac{\sqrt{1+x}}{(1-x)^{9/2}} \, dx","IntegrateAlgebraic[Sqrt[1 + x]/(1 - x)^(9/2),x]","\frac{\left(\frac{\sqrt{1-x}}{3360}-\frac{1}{3360}\right) \left(\sqrt{x+1}-1\right)^{13} \left(\frac{105 \left(\sqrt{1-x}-1\right)^{12}}{\left(\sqrt{x+1}-1\right)^{12}}+\frac{420 \left(\sqrt{1-x}-1\right)^{11}}{\left(\sqrt{x+1}-1\right)^{11}}+\frac{1190 \left(\sqrt{1-x}-1\right)^{10}}{\left(\sqrt{x+1}-1\right)^{10}}+\frac{700 \left(\sqrt{1-x}-1\right)^9}{\left(\sqrt{x+1}-1\right)^9}-\frac{1337 \left(\sqrt{1-x}-1\right)^8}{\left(\sqrt{x+1}-1\right)^8}-\frac{2408 \left(\sqrt{1-x}-1\right)^7}{\left(\sqrt{x+1}-1\right)^7}+\frac{1556 \left(\sqrt{1-x}-1\right)^6}{\left(\sqrt{x+1}-1\right)^6}+\frac{2408 \left(\sqrt{1-x}-1\right)^5}{\left(\sqrt{x+1}-1\right)^5}-\frac{1337 \left(\sqrt{1-x}-1\right)^4}{\left(\sqrt{x+1}-1\right)^4}-\frac{700 \left(\sqrt{1-x}-1\right)^3}{\left(\sqrt{x+1}-1\right)^3}+\frac{1190 \left(\sqrt{1-x}-1\right)^2}{\left(\sqrt{x+1}-1\right)^2}-\frac{420 \left(\sqrt{1-x}-1\right)}{\sqrt{x+1}-1}+105\right)}{\left(-x-2 \sqrt{1-x}+\sqrt{1-x} \sqrt{x+1}+1\right)^7}","\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,"((-1/3360 + Sqrt[1 - x]/3360)*(-1 + Sqrt[1 + x])^13*(105 + (105*(-1 + Sqrt[1 - x])^12)/(-1 + Sqrt[1 + x])^12 + (420*(-1 + Sqrt[1 - x])^11)/(-1 + Sqrt[1 + x])^11 + (1190*(-1 + Sqrt[1 - x])^10)/(-1 + Sqrt[1 + x])^10 + (700*(-1 + Sqrt[1 - x])^9)/(-1 + Sqrt[1 + x])^9 - (1337*(-1 + Sqrt[1 - x])^8)/(-1 + Sqrt[1 + x])^8 - (2408*(-1 + Sqrt[1 - x])^7)/(-1 + Sqrt[1 + x])^7 + (1556*(-1 + Sqrt[1 - x])^6)/(-1 + Sqrt[1 + x])^6 + (2408*(-1 + Sqrt[1 - x])^5)/(-1 + Sqrt[1 + x])^5 - (1337*(-1 + Sqrt[1 - x])^4)/(-1 + Sqrt[1 + x])^4 - (700*(-1 + Sqrt[1 - x])^3)/(-1 + Sqrt[1 + x])^3 + (1190*(-1 + Sqrt[1 - x])^2)/(-1 + Sqrt[1 + x])^2 - (420*(-1 + Sqrt[1 - x]))/(-1 + Sqrt[1 + x])))/(1 - 2*Sqrt[1 - x] - x + Sqrt[1 - x]*Sqrt[1 + x])^7","B",1
1073,1,480,81,1.962643,"\int \frac{\sqrt{1+x}}{(1-x)^{11/2}} \, dx","IntegrateAlgebraic[Sqrt[1 + x]/(1 - x)^(11/2),x]","\frac{\left(\frac{\sqrt{1-x}}{40320}-\frac{1}{40320}\right) \left(\sqrt{x+1}-1\right)^{17} \left(\frac{315 \left(\sqrt{1-x}-1\right)^{16}}{\left(\sqrt{x+1}-1\right)^{16}}+\frac{1890 \left(\sqrt{1-x}-1\right)^{15}}{\left(\sqrt{x+1}-1\right)^{15}}+\frac{7980 \left(\sqrt{1-x}-1\right)^{14}}{\left(\sqrt{x+1}-1\right)^{14}}+\frac{14490 \left(\sqrt{1-x}-1\right)^{13}}{\left(\sqrt{x+1}-1\right)^{13}}+\frac{7308 \left(\sqrt{1-x}-1\right)^{12}}{\left(\sqrt{x+1}-1\right)^{12}}-\frac{27006 \left(\sqrt{1-x}-1\right)^{11}}{\left(\sqrt{x+1}-1\right)^{11}}-\frac{32940 \left(\sqrt{1-x}-1\right)^{10}}{\left(\sqrt{x+1}-1\right)^{10}}+\frac{21834 \left(\sqrt{1-x}-1\right)^9}{\left(\sqrt{x+1}-1\right)^9}+\frac{49522 \left(\sqrt{1-x}-1\right)^8}{\left(\sqrt{x+1}-1\right)^8}-\frac{21834 \left(\sqrt{1-x}-1\right)^7}{\left(\sqrt{x+1}-1\right)^7}-\frac{32940 \left(\sqrt{1-x}-1\right)^6}{\left(\sqrt{x+1}-1\right)^6}+\frac{27006 \left(\sqrt{1-x}-1\right)^5}{\left(\sqrt{x+1}-1\right)^5}+\frac{7308 \left(\sqrt{1-x}-1\right)^4}{\left(\sqrt{x+1}-1\right)^4}-\frac{14490 \left(\sqrt{1-x}-1\right)^3}{\left(\sqrt{x+1}-1\right)^3}+\frac{7980 \left(\sqrt{1-x}-1\right)^2}{\left(\sqrt{x+1}-1\right)^2}-\frac{1890 \left(\sqrt{1-x}-1\right)}{\sqrt{x+1}-1}+315\right)}{\left(-x-2 \sqrt{1-x}+\sqrt{1-x} \sqrt{x+1}+1\right)^9}","\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,"((-1/40320 + Sqrt[1 - x]/40320)*(-1 + Sqrt[1 + x])^17*(315 + (315*(-1 + Sqrt[1 - x])^16)/(-1 + Sqrt[1 + x])^16 + (1890*(-1 + Sqrt[1 - x])^15)/(-1 + Sqrt[1 + x])^15 + (7980*(-1 + Sqrt[1 - x])^14)/(-1 + Sqrt[1 + x])^14 + (14490*(-1 + Sqrt[1 - x])^13)/(-1 + Sqrt[1 + x])^13 + (7308*(-1 + Sqrt[1 - x])^12)/(-1 + Sqrt[1 + x])^12 - (27006*(-1 + Sqrt[1 - x])^11)/(-1 + Sqrt[1 + x])^11 - (32940*(-1 + Sqrt[1 - x])^10)/(-1 + Sqrt[1 + x])^10 + (21834*(-1 + Sqrt[1 - x])^9)/(-1 + Sqrt[1 + x])^9 + (49522*(-1 + Sqrt[1 - x])^8)/(-1 + Sqrt[1 + x])^8 - (21834*(-1 + Sqrt[1 - x])^7)/(-1 + Sqrt[1 + x])^7 - (32940*(-1 + Sqrt[1 - x])^6)/(-1 + Sqrt[1 + x])^6 + (27006*(-1 + Sqrt[1 - x])^5)/(-1 + Sqrt[1 + x])^5 + (7308*(-1 + Sqrt[1 - x])^4)/(-1 + Sqrt[1 + x])^4 - (14490*(-1 + Sqrt[1 - x])^3)/(-1 + Sqrt[1 + x])^3 + (7980*(-1 + Sqrt[1 - x])^2)/(-1 + Sqrt[1 + x])^2 - (1890*(-1 + Sqrt[1 - x]))/(-1 + Sqrt[1 + x])))/(1 - 2*Sqrt[1 - x] - x + Sqrt[1 - x]*Sqrt[1 + x])^9","B",1
1074,1,584,101,4.1105735,"\int \frac{\sqrt{1+x}}{(1-x)^{13/2}} \, dx","IntegrateAlgebraic[Sqrt[1 + x]/(1 - x)^(13/2),x]","\frac{\left(\frac{\sqrt{1-x}}{1774080}-\frac{1}{1774080}\right) \left(\sqrt{x+1}-1\right)^{21} \left(\frac{3465 \left(\sqrt{1-x}-1\right)^{20}}{\left(\sqrt{x+1}-1\right)^{20}}+\frac{27720 \left(\sqrt{1-x}-1\right)^{19}}{\left(\sqrt{x+1}-1\right)^{19}}+\frac{154770 \left(\sqrt{1-x}-1\right)^{18}}{\left(\sqrt{x+1}-1\right)^{18}}+\frac{452760 \left(\sqrt{1-x}-1\right)^{17}}{\left(\sqrt{x+1}-1\right)^{17}}+\frac{717717 \left(\sqrt{1-x}-1\right)^{16}}{\left(\sqrt{x+1}-1\right)^{16}}+\frac{14784 \left(\sqrt{1-x}-1\right)^{15}}{\left(\sqrt{x+1}-1\right)^{15}}-\frac{1640232 \left(\sqrt{1-x}-1\right)^{14}}{\left(\sqrt{x+1}-1\right)^{14}}-\frac{1752960 \left(\sqrt{1-x}-1\right)^{13}}{\left(\sqrt{x+1}-1\right)^{13}}+\frac{1692130 \left(\sqrt{1-x}-1\right)^{12}}{\left(\sqrt{x+1}-1\right)^{12}}+\frac{3072784 \left(\sqrt{1-x}-1\right)^{11}}{\left(\sqrt{x+1}-1\right)^{11}}-\frac{1295572 \left(\sqrt{1-x}-1\right)^{10}}{\left(\sqrt{x+1}-1\right)^{10}}-\frac{3072784 \left(\sqrt{1-x}-1\right)^9}{\left(\sqrt{x+1}-1\right)^9}+\frac{1692130 \left(\sqrt{1-x}-1\right)^8}{\left(\sqrt{x+1}-1\right)^8}+\frac{1752960 \left(\sqrt{1-x}-1\right)^7}{\left(\sqrt{x+1}-1\right)^7}-\frac{1640232 \left(\sqrt{1-x}-1\right)^6}{\left(\sqrt{x+1}-1\right)^6}-\frac{14784 \left(\sqrt{1-x}-1\right)^5}{\left(\sqrt{x+1}-1\right)^5}+\frac{717717 \left(\sqrt{1-x}-1\right)^4}{\left(\sqrt{x+1}-1\right)^4}-\frac{452760 \left(\sqrt{1-x}-1\right)^3}{\left(\sqrt{x+1}-1\right)^3}+\frac{154770 \left(\sqrt{1-x}-1\right)^2}{\left(\sqrt{x+1}-1\right)^2}-\frac{27720 \left(\sqrt{1-x}-1\right)}{\sqrt{x+1}-1}+3465\right)}{\left(-x-2 \sqrt{1-x}+\sqrt{1-x} \sqrt{x+1}+1\right)^{11}}","\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,"((-1/1774080 + Sqrt[1 - x]/1774080)*(-1 + Sqrt[1 + x])^21*(3465 + (3465*(-1 + Sqrt[1 - x])^20)/(-1 + Sqrt[1 + x])^20 + (27720*(-1 + Sqrt[1 - x])^19)/(-1 + Sqrt[1 + x])^19 + (154770*(-1 + Sqrt[1 - x])^18)/(-1 + Sqrt[1 + x])^18 + (452760*(-1 + Sqrt[1 - x])^17)/(-1 + Sqrt[1 + x])^17 + (717717*(-1 + Sqrt[1 - x])^16)/(-1 + Sqrt[1 + x])^16 + (14784*(-1 + Sqrt[1 - x])^15)/(-1 + Sqrt[1 + x])^15 - (1640232*(-1 + Sqrt[1 - x])^14)/(-1 + Sqrt[1 + x])^14 - (1752960*(-1 + Sqrt[1 - x])^13)/(-1 + Sqrt[1 + x])^13 + (1692130*(-1 + Sqrt[1 - x])^12)/(-1 + Sqrt[1 + x])^12 + (3072784*(-1 + Sqrt[1 - x])^11)/(-1 + Sqrt[1 + x])^11 - (1295572*(-1 + Sqrt[1 - x])^10)/(-1 + Sqrt[1 + x])^10 - (3072784*(-1 + Sqrt[1 - x])^9)/(-1 + Sqrt[1 + x])^9 + (1692130*(-1 + Sqrt[1 - x])^8)/(-1 + Sqrt[1 + x])^8 + (1752960*(-1 + Sqrt[1 - x])^7)/(-1 + Sqrt[1 + x])^7 - (1640232*(-1 + Sqrt[1 - x])^6)/(-1 + Sqrt[1 + x])^6 - (14784*(-1 + Sqrt[1 - x])^5)/(-1 + Sqrt[1 + x])^5 + (717717*(-1 + Sqrt[1 - x])^4)/(-1 + Sqrt[1 + x])^4 - (452760*(-1 + Sqrt[1 - x])^3)/(-1 + Sqrt[1 + x])^3 + (154770*(-1 + Sqrt[1 - x])^2)/(-1 + Sqrt[1 + x])^2 - (27720*(-1 + Sqrt[1 - x]))/(-1 + Sqrt[1 + x])))/(1 - 2*Sqrt[1 - x] - x + Sqrt[1 - x]*Sqrt[1 + x])^11","B",1
1075,1,732,109,0.6544301,"\int (1-x)^{9/2} (1+x)^{3/2} \, dx","IntegrateAlgebraic[(1 - x)^(9/2)*(1 + x)^(3/2),x]","\frac{9}{4} \tan ^{-1}\left(\frac{\sqrt{x+1}-1}{\sqrt{1-x}-1}\right)+\frac{\left(\frac{8}{35}-\frac{8 \sqrt{1-x}}{35}\right) \left(\sqrt{x+1}-1\right) \left(-1040 \sqrt{1-x} x^{12}+80 \sqrt{1-x} \sqrt{x+1} x^{12}-1040 \sqrt{x+1} x^{12}+12960 x^{12}+54600 \sqrt{1-x} x^{11}-280 \sqrt{1-x} \sqrt{x+1} x^{11}-47320 \sqrt{x+1} x^{11}-45360 x^{11}+478296 \sqrt{1-x} x^{10}-292432 \sqrt{1-x} \sqrt{x+1} x^{10}+835016 \sqrt{x+1} x^{10}-2145024 x^{10}-4900454 \sqrt{1-x} x^9+1024590 \sqrt{1-x} \sqrt{x+1} x^9+275834 \sqrt{x+1} x^9+7682220 x^9+2998294 \sqrt{1-x} x^8+6264400 \sqrt{1-x} \sqrt{x+1} x^8-16492086 \sqrt{x+1} x^8+6847296 x^8+30375579 \sqrt{1-x} x^7-25870775 \sqrt{1-x} \sqrt{x+1} x^7+34675771 \sqrt{x+1} x^7-53656050 x^7-47386367 \sqrt{1-x} x^6+10148368 \sqrt{1-x} \sqrt{x+1} x^6+13497183 \sqrt{x+1} x^6+40280432 x^6-35303718 \sqrt{1-x} x^5+66658830 \sqrt{1-x} \sqrt{x+1} x^5-108186342 \sqrt{x+1} x^5+85116150 x^5+115012840 \sqrt{1-x} x^4-86367808 \sqrt{1-x} \sqrt{x+1} x^4+84975000 \sqrt{x+1} x^4-142014272 x^4-39147536 \sqrt{1-x} x^3-24503920 \sqrt{1-x} \sqrt{x+1} x^3+79043056 \sqrt{x+1} x^3-7086240 x^3-123893360 \sqrt{1-x} x^2+128537856 \sqrt{1-x} \sqrt{x+1} x^2-156654480 \sqrt{x+1} x^2+176073472 x^2+80301216 \sqrt{1-x} x-32214560 \sqrt{1-x} \sqrt{x+1} x-16060256 \sqrt{x+1} x-32010720 x+96484672 \sqrt{1-x}-96468992 \sqrt{1-x} \sqrt{x+1}+96453312 \sqrt{x+1}-96468992\right)}{\left(\sqrt{1-x}+\sqrt{x+1}-2\right)^{14}}","\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,"((8/35 - (8*Sqrt[1 - x])/35)*(-1 + Sqrt[1 + x])*(-96468992 + 96484672*Sqrt[1 - x] - 32010720*x + 80301216*Sqrt[1 - x]*x + 176073472*x^2 - 123893360*Sqrt[1 - x]*x^2 - 7086240*x^3 - 39147536*Sqrt[1 - x]*x^3 - 142014272*x^4 + 115012840*Sqrt[1 - x]*x^4 + 85116150*x^5 - 35303718*Sqrt[1 - x]*x^5 + 40280432*x^6 - 47386367*Sqrt[1 - x]*x^6 - 53656050*x^7 + 30375579*Sqrt[1 - x]*x^7 + 6847296*x^8 + 2998294*Sqrt[1 - x]*x^8 + 7682220*x^9 - 4900454*Sqrt[1 - x]*x^9 - 2145024*x^10 + 478296*Sqrt[1 - x]*x^10 - 45360*x^11 + 54600*Sqrt[1 - x]*x^11 + 12960*x^12 - 1040*Sqrt[1 - x]*x^12 + 96453312*Sqrt[1 + x] - 96468992*Sqrt[1 - x]*Sqrt[1 + x] - 16060256*x*Sqrt[1 + x] - 32214560*Sqrt[1 - x]*x*Sqrt[1 + x] - 156654480*x^2*Sqrt[1 + x] + 128537856*Sqrt[1 - x]*x^2*Sqrt[1 + x] + 79043056*x^3*Sqrt[1 + x] - 24503920*Sqrt[1 - x]*x^3*Sqrt[1 + x] + 84975000*x^4*Sqrt[1 + x] - 86367808*Sqrt[1 - x]*x^4*Sqrt[1 + x] - 108186342*x^5*Sqrt[1 + x] + 66658830*Sqrt[1 - x]*x^5*Sqrt[1 + x] + 13497183*x^6*Sqrt[1 + x] + 10148368*Sqrt[1 - x]*x^6*Sqrt[1 + x] + 34675771*x^7*Sqrt[1 + x] - 25870775*Sqrt[1 - x]*x^7*Sqrt[1 + x] - 16492086*x^8*Sqrt[1 + x] + 6264400*Sqrt[1 - x]*x^8*Sqrt[1 + x] + 275834*x^9*Sqrt[1 + x] + 1024590*Sqrt[1 - x]*x^9*Sqrt[1 + x] + 835016*x^10*Sqrt[1 + x] - 292432*Sqrt[1 - x]*x^10*Sqrt[1 + x] - 47320*x^11*Sqrt[1 + x] - 280*Sqrt[1 - x]*x^11*Sqrt[1 + x] - 1040*x^12*Sqrt[1 + x] + 80*Sqrt[1 - x]*x^12*Sqrt[1 + x]))/(-2 + Sqrt[1 - x] + Sqrt[1 + x])^14 + (9*ArcTan[(-1 + Sqrt[1 + x])/(-1 + Sqrt[1 - x])])/4","B",1
1076,1,612,89,0.4348884,"\int (1-x)^{7/2} (1+x)^{3/2} \, dx","IntegrateAlgebraic[(1 - x)^(7/2)*(1 + x)^(3/2),x]","\frac{7}{4} \tan ^{-1}\left(\frac{\sqrt{x+1}-1}{\sqrt{1-x}-1}\right)+\frac{\left(\frac{4 \sqrt{1-x}}{15}-\frac{4}{15}\right) \left(\sqrt{x+1}-1\right) \left(40 x^{11}+440 \sqrt{1-x} x^{10}-440 \sqrt{x+1} x^{10}-96 x^{10}+14344 \sqrt{1-x} x^9-4600 \sqrt{1-x} \sqrt{x+1} x^9+16456 \sqrt{x+1} x^9-70930 x^9-154110 \sqrt{1-x} x^8+11040 \sqrt{1-x} \sqrt{x+1} x^8+80190 \sqrt{x+1} x^8+170400 x^8-162602 \sqrt{1-x} x^7+343390 \sqrt{1-x} \sqrt{x+1} x^7-728618 \sqrt{x+1} x^7+736795 x^7+1506879 \sqrt{1-x} x^6-843456 \sqrt{1-x} \sqrt{x+1} x^6+761409 \sqrt{x+1} x^6-2066592 x^6-676287 \sqrt{1-x} x^5-732435 \sqrt{1-x} \sqrt{x+1} x^5+2105217 \sqrt{x+1} x^5-588765 x^5-3422814 \sqrt{1-x} x^4+3243648 \sqrt{1-x} \sqrt{x+1} x^4-4042914 \sqrt{x+1} x^4+5189376 x^4+3296476 \sqrt{1-x} x^3-989460 \sqrt{1-x} \sqrt{x+1} x^3-642596 \sqrt{x+1} x^3-2265220 x^3+3361264 \sqrt{1-x} x^2-4171008 \sqrt{1-x} \sqrt{x+1} x^2+5690384 \sqrt{x+1} x^2-5659392 x^2-3779184 \sqrt{1-x} x+2235600 \sqrt{1-x} \sqrt{x+1} x-648816 \sqrt{x+1} x+2188080 x-3150048 \sqrt{1-x}+3145728 \sqrt{1-x} \sqrt{x+1}-3141408 \sqrt{x+1}+3145728\right)}{\left(\sqrt{1-x}+\sqrt{x+1}-2\right)^{12}}","\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,"((-4/15 + (4*Sqrt[1 - x])/15)*(-1 + Sqrt[1 + x])*(3145728 - 3150048*Sqrt[1 - x] + 2188080*x - 3779184*Sqrt[1 - x]*x - 5659392*x^2 + 3361264*Sqrt[1 - x]*x^2 - 2265220*x^3 + 3296476*Sqrt[1 - x]*x^3 + 5189376*x^4 - 3422814*Sqrt[1 - x]*x^4 - 588765*x^5 - 676287*Sqrt[1 - x]*x^5 - 2066592*x^6 + 1506879*Sqrt[1 - x]*x^6 + 736795*x^7 - 162602*Sqrt[1 - x]*x^7 + 170400*x^8 - 154110*Sqrt[1 - x]*x^8 - 70930*x^9 + 14344*Sqrt[1 - x]*x^9 - 96*x^10 + 440*Sqrt[1 - x]*x^10 + 40*x^11 - 3141408*Sqrt[1 + x] + 3145728*Sqrt[1 - x]*Sqrt[1 + x] - 648816*x*Sqrt[1 + x] + 2235600*Sqrt[1 - x]*x*Sqrt[1 + x] + 5690384*x^2*Sqrt[1 + x] - 4171008*Sqrt[1 - x]*x^2*Sqrt[1 + x] - 642596*x^3*Sqrt[1 + x] - 989460*Sqrt[1 - x]*x^3*Sqrt[1 + x] - 4042914*x^4*Sqrt[1 + x] + 3243648*Sqrt[1 - x]*x^4*Sqrt[1 + x] + 2105217*x^5*Sqrt[1 + x] - 732435*Sqrt[1 - x]*x^5*Sqrt[1 + x] + 761409*x^6*Sqrt[1 + x] - 843456*Sqrt[1 - x]*x^6*Sqrt[1 + x] - 728618*x^7*Sqrt[1 + x] + 343390*Sqrt[1 - x]*x^7*Sqrt[1 + x] + 80190*x^8*Sqrt[1 + x] + 11040*Sqrt[1 - x]*x^8*Sqrt[1 + x] + 16456*x^9*Sqrt[1 + x] - 4600*Sqrt[1 - x]*x^9*Sqrt[1 + x] - 440*x^10*Sqrt[1 + x]))/(-2 + Sqrt[1 - x] + Sqrt[1 + x])^12 + (7*ArcTan[(-1 + Sqrt[1 + x])/(-1 + Sqrt[1 - x])])/4","B",1
1077,1,524,69,0.4148871,"\int (1-x)^{5/2} (1+x)^{3/2} \, dx","IntegrateAlgebraic[(1 - x)^(5/2)*(1 + x)^(3/2),x]","\frac{\left(\frac{4 \sqrt{1-x}}{5}-\frac{4}{5}\right) \left(\sqrt{x+1}-1\right) \left(-72 \sqrt{1-x} x^8+8 \sqrt{1-x} \sqrt{x+1} x^8-72 \sqrt{x+1} x^8+608 x^8+1650 \sqrt{1-x} x^7-10 \sqrt{1-x} \sqrt{x+1} x^7-1470 \sqrt{x+1} x^7-760 x^7+6834 \sqrt{1-x} x^6-5840 \sqrt{1-x} \sqrt{x+1} x^6+10734 \sqrt{x+1} x^6-17632 x^6-23457 \sqrt{1-x} x^5+7305 \sqrt{1-x} \sqrt{x+1} x^5+1407 \sqrt{x+1} x^5+22420 x^5-17285 \sqrt{1-x} x^4+28616 \sqrt{1-x} \sqrt{x+1} x^4-50315 \sqrt{x+1} x^4+49256 x^4+67688 \sqrt{1-x} x^3-39400 \sqrt{1-x} \sqrt{x+1} x^3+27432 \sqrt{x+1} x^3-71060 x^3+14228 \sqrt{1-x} x^2-40352 \sqrt{1-x} \sqrt{x+1} x^2+72108 \sqrt{x+1} x^2-53856 x^2-67464 \sqrt{1-x} x+53000 \sqrt{1-x} \sqrt{x+1} x-35336 \sqrt{x+1} x+49400 x-33168 \sqrt{1-x}+32768 \sqrt{1-x} \sqrt{x+1}-32368 \sqrt{x+1}+32768\right)}{\left(\sqrt{1-x}+\sqrt{x+1}-2\right)^{10}}+\frac{3}{2} \tan ^{-1}\left(\frac{\sqrt{x+1}-1}{\sqrt{1-x}-1}\right)","\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,"((-4/5 + (4*Sqrt[1 - x])/5)*(-1 + Sqrt[1 + x])*(32768 - 33168*Sqrt[1 - x] + 49400*x - 67464*Sqrt[1 - x]*x - 53856*x^2 + 14228*Sqrt[1 - x]*x^2 - 71060*x^3 + 67688*Sqrt[1 - x]*x^3 + 49256*x^4 - 17285*Sqrt[1 - x]*x^4 + 22420*x^5 - 23457*Sqrt[1 - x]*x^5 - 17632*x^6 + 6834*Sqrt[1 - x]*x^6 - 760*x^7 + 1650*Sqrt[1 - x]*x^7 + 608*x^8 - 72*Sqrt[1 - x]*x^8 - 32368*Sqrt[1 + x] + 32768*Sqrt[1 - x]*Sqrt[1 + x] - 35336*x*Sqrt[1 + x] + 53000*Sqrt[1 - x]*x*Sqrt[1 + x] + 72108*x^2*Sqrt[1 + x] - 40352*Sqrt[1 - x]*x^2*Sqrt[1 + x] + 27432*x^3*Sqrt[1 + x] - 39400*Sqrt[1 - x]*x^3*Sqrt[1 + x] - 50315*x^4*Sqrt[1 + x] + 28616*Sqrt[1 - x]*x^4*Sqrt[1 + x] + 1407*x^5*Sqrt[1 + x] + 7305*Sqrt[1 - x]*x^5*Sqrt[1 + x] + 10734*x^6*Sqrt[1 + x] - 5840*Sqrt[1 - x]*x^6*Sqrt[1 + x] - 1470*x^7*Sqrt[1 + x] - 10*Sqrt[1 - x]*x^7*Sqrt[1 + x] - 72*x^8*Sqrt[1 + x] + 8*Sqrt[1 - x]*x^8*Sqrt[1 + x]))/(-2 + Sqrt[1 - x] + Sqrt[1 + x])^10 + (3*ArcTan[(-1 + Sqrt[1 + x])/(-1 + Sqrt[1 - x])])/2","B",1
1078,1,314,49,0.7272119,"\int (1-x)^{3/2} (1+x)^{3/2} \, dx","IntegrateAlgebraic[(1 - x)^(3/2)*(1 + x)^(3/2),x]","\frac{\left(\sqrt{x+1}-1\right)^{16} \left(\frac{5 \left(\sqrt{1-x}-1\right)^{15}}{512 \left(\sqrt{x+1}-1\right)^{15}}-\frac{47 \left(\sqrt{1-x}-1\right)^{13}}{512 \left(\sqrt{x+1}-1\right)^{13}}+\frac{213 \left(\sqrt{1-x}-1\right)^{11}}{512 \left(\sqrt{x+1}-1\right)^{11}}-\frac{759 \left(\sqrt{1-x}-1\right)^9}{512 \left(\sqrt{x+1}-1\right)^9}+\frac{759 \left(\sqrt{1-x}-1\right)^7}{512 \left(\sqrt{x+1}-1\right)^7}-\frac{213 \left(\sqrt{1-x}-1\right)^5}{512 \left(\sqrt{x+1}-1\right)^5}+\frac{47 \left(\sqrt{1-x}-1\right)^3}{512 \left(\sqrt{x+1}-1\right)^3}-\frac{5 \left(\sqrt{1-x}-1\right)}{512 \left(\sqrt{x+1}-1\right)}+\frac{3 \left(\sqrt{1-x}+\sqrt{x+1}-2\right)^8 \tan ^{-1}\left(\frac{\sqrt{x+1}-1}{\sqrt{1-x}-1}\right)}{2 \left(\sqrt{x+1}-1\right)^{16}}\right)}{\left(\sqrt{1-x}+\sqrt{x+1}-2\right)^8}","\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,"((-1 + Sqrt[1 + x])^16*((5*(-1 + Sqrt[1 - x])^15)/(512*(-1 + Sqrt[1 + x])^15) - (47*(-1 + Sqrt[1 - x])^13)/(512*(-1 + Sqrt[1 + x])^13) + (213*(-1 + Sqrt[1 - x])^11)/(512*(-1 + Sqrt[1 + x])^11) - (759*(-1 + Sqrt[1 - x])^9)/(512*(-1 + Sqrt[1 + x])^9) + (759*(-1 + Sqrt[1 - x])^7)/(512*(-1 + Sqrt[1 + x])^7) - (213*(-1 + Sqrt[1 - x])^5)/(512*(-1 + Sqrt[1 + x])^5) + (47*(-1 + Sqrt[1 - x])^3)/(512*(-1 + Sqrt[1 + x])^3) - (5*(-1 + Sqrt[1 - x]))/(512*(-1 + Sqrt[1 + x])) + (3*(-2 + Sqrt[1 - x] + Sqrt[1 + x])^8*ArcTan[(-1 + Sqrt[1 + x])/(-1 + Sqrt[1 - x])])/(2*(-1 + Sqrt[1 + x])^16)))/(-2 + Sqrt[1 - x] + Sqrt[1 + x])^8","B",1
1079,1,314,48,0.2340013,"\int \sqrt{1-x} (1+x)^{3/2} \, dx","IntegrateAlgebraic[Sqrt[1 - x]*(1 + x)^(3/2),x]","\frac{\left(\frac{4}{3}-\frac{4 \sqrt{1-x}}{3}\right) \left(\sqrt{x+1}-1\right) \left(-10 \sqrt{1-x} x^4+2 \sqrt{1-x} \sqrt{x+1} x^4-10 \sqrt{x+1} x^4+44 x^4+35 \sqrt{1-x} x^3+3 \sqrt{1-x} \sqrt{x+1} x^3-65 \sqrt{x+1} x^3+66 x^3+153 \sqrt{1-x} x^2-86 \sqrt{1-x} \sqrt{x+1} x^2+3 \sqrt{x+1} x^2-90 x^2+50 \sqrt{1-x} x-126 \sqrt{1-x} \sqrt{x+1} x+154 \sqrt{x+1} x-66 x-116 \sqrt{1-x}+128 \sqrt{1-x} \sqrt{x+1}-140 \sqrt{x+1}+128\right)}{\left(\sqrt{1-x}+\sqrt{x+1}-2\right)^6}+2 \tan ^{-1}\left(\frac{\sqrt{x+1}-1}{\sqrt{1-x}-1}\right)","-\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,"((4/3 - (4*Sqrt[1 - x])/3)*(-1 + Sqrt[1 + x])*(128 - 116*Sqrt[1 - x] - 66*x + 50*Sqrt[1 - x]*x - 90*x^2 + 153*Sqrt[1 - x]*x^2 + 66*x^3 + 35*Sqrt[1 - x]*x^3 + 44*x^4 - 10*Sqrt[1 - x]*x^4 - 140*Sqrt[1 + x] + 128*Sqrt[1 - x]*Sqrt[1 + x] + 154*x*Sqrt[1 + x] - 126*Sqrt[1 - x]*x*Sqrt[1 + x] + 3*x^2*Sqrt[1 + x] - 86*Sqrt[1 - x]*x^2*Sqrt[1 + x] - 65*x^3*Sqrt[1 + x] + 3*Sqrt[1 - x]*x^3*Sqrt[1 + x] - 10*x^4*Sqrt[1 + x] + 2*Sqrt[1 - x]*x^4*Sqrt[1 + x]))/(-2 + Sqrt[1 - x] + Sqrt[1 + x])^6 + 2*ArcTan[(-1 + Sqrt[1 + x])/(-1 + Sqrt[1 - x])]","B",1
1080,1,188,47,0.1237733,"\int \frac{(1+x)^{3/2}}{\sqrt{1-x}} \, dx","IntegrateAlgebraic[(1 + x)^(3/2)/Sqrt[1 - x],x]","\frac{\left(2 \sqrt{1-x}-2\right) \left(\sqrt{x+1}-1\right) \left(x^3+3 \sqrt{1-x} x^2-3 \sqrt{x+1} x^2+4 x^2+17 \sqrt{1-x} x-7 \sqrt{1-x} \sqrt{x+1} x-7 \sqrt{x+1} x-x+34 \sqrt{1-x}-32 \sqrt{1-x} \sqrt{x+1}+30 \sqrt{x+1}-32\right)}{\left(\sqrt{1-x}+\sqrt{x+1}-2\right)^4}+6 \tan ^{-1}\left(\frac{\sqrt{x+1}-1}{\sqrt{1-x}-1}\right)","-\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,"((-2 + 2*Sqrt[1 - x])*(-1 + Sqrt[1 + x])*(-32 + 34*Sqrt[1 - x] - x + 17*Sqrt[1 - x]*x + 4*x^2 + 3*Sqrt[1 - x]*x^2 + x^3 + 30*Sqrt[1 + x] - 32*Sqrt[1 - x]*Sqrt[1 + x] - 7*x*Sqrt[1 + x] - 7*Sqrt[1 - x]*x*Sqrt[1 + x] - 3*x^2*Sqrt[1 + x]))/(-2 + Sqrt[1 - x] + Sqrt[1 + x])^4 + 6*ArcTan[(-1 + Sqrt[1 + x])/(-1 + Sqrt[1 - x])]","B",1
1081,1,131,41,0.1849919,"\int \frac{(1+x)^{3/2}}{(1-x)^{3/2}} \, dx","IntegrateAlgebraic[(1 + x)^(3/2)/(1 - x)^(3/2),x]","\frac{2 \left(\sqrt{1-x}-1\right)^2 \left(\sqrt{x+1}-1\right)^2}{\left(\sqrt{1-x}+\sqrt{x+1}-2\right)^2}+\frac{\left(8 \sqrt{1-x}-8\right) \left(\sqrt{x+1}-1\right)}{-x-2 \sqrt{1-x}+\sqrt{1-x} \sqrt{x+1}+1}-12 \tan ^{-1}\left(\frac{\sqrt{x+1}-1}{\sqrt{1-x}-1}\right)","\frac{2 (x+1)^{3/2}}{\sqrt{1-x}}+3 \sqrt{1-x} \sqrt{x+1}-3 \sin ^{-1}(x)",1,"(2*(-1 + Sqrt[1 - x])^2*(-1 + Sqrt[1 + x])^2)/(-2 + Sqrt[1 - x] + Sqrt[1 + x])^2 + ((-8 + 8*Sqrt[1 - x])*(-1 + Sqrt[1 + x]))/(1 - 2*Sqrt[1 - x] - x + Sqrt[1 - x]*Sqrt[1 + x]) - 12*ArcTan[(-1 + Sqrt[1 + x])/(-1 + Sqrt[1 - x])]","B",1
1082,1,138,41,0.1147874,"\int \frac{(1+x)^{3/2}}{(1-x)^{5/2}} \, dx","IntegrateAlgebraic[(1 + x)^(3/2)/(1 - x)^(5/2),x]","\frac{\left(\sqrt{1-x}-1\right)^2 \left(8 x+\frac{32 \sqrt{1-x}}{3}-\frac{8}{3} \sqrt{1-x} \sqrt{x+1}-\frac{16 \sqrt{x+1}}{3}-\frac{8}{3}\right) \left(\sqrt{x+1}-1\right)^2}{\left(-x-2 \sqrt{1-x}+\sqrt{1-x} \sqrt{x+1}+1\right)^3}+4 \tan ^{-1}\left(\frac{\sqrt{x+1}-1}{\sqrt{1-x}-1}\right)","\frac{2 (x+1)^{3/2}}{3 (1-x)^{3/2}}-\frac{2 \sqrt{x+1}}{\sqrt{1-x}}+\sin ^{-1}(x)",1,"((-1 + Sqrt[1 - x])^2*(-1 + Sqrt[1 + x])^2*(-8/3 + (32*Sqrt[1 - x])/3 + 8*x - (16*Sqrt[1 + x])/3 - (8*Sqrt[1 - x]*Sqrt[1 + x])/3))/(1 - 2*Sqrt[1 - x] - x + Sqrt[1 - x]*Sqrt[1 + x])^3 + 4*ArcTan[(-1 + Sqrt[1 + x])/(-1 + Sqrt[1 - x])]","B",1
1083,1,170,20,0.1828255,"\int \frac{(1+x)^{3/2}}{(1-x)^{7/2}} \, dx","IntegrateAlgebraic[(1 + x)^(3/2)/(1 - x)^(7/2),x]","\frac{\left(\frac{\sqrt{1-x}}{40}-\frac{1}{40}\right) \left(\sqrt{x+1}-1\right)^9 \left(\frac{5 \left(\sqrt{1-x}-1\right)^8}{\left(\sqrt{x+1}-1\right)^8}+\frac{20 \left(\sqrt{1-x}-1\right)^6}{\left(\sqrt{x+1}-1\right)^6}-\frac{34 \left(\sqrt{1-x}-1\right)^4}{\left(\sqrt{x+1}-1\right)^4}+\frac{20 \left(\sqrt{1-x}-1\right)^2}{\left(\sqrt{x+1}-1\right)^2}+5\right)}{\left(-x-2 \sqrt{1-x}+\sqrt{1-x} \sqrt{x+1}+1\right)^5}","\frac{(x+1)^{5/2}}{5 (1-x)^{5/2}}",1,"((-1/40 + Sqrt[1 - x]/40)*(-1 + Sqrt[1 + x])^9*(5 + (5*(-1 + Sqrt[1 - x])^8)/(-1 + Sqrt[1 + x])^8 + (20*(-1 + Sqrt[1 - x])^6)/(-1 + Sqrt[1 + x])^6 - (34*(-1 + Sqrt[1 - x])^4)/(-1 + Sqrt[1 + x])^4 + (20*(-1 + Sqrt[1 - x])^2)/(-1 + Sqrt[1 + x])^2))/(1 - 2*Sqrt[1 - x] - x + Sqrt[1 - x]*Sqrt[1 + x])^5","B",1
1084,1,376,41,0.805932,"\int \frac{(1+x)^{3/2}}{(1-x)^{9/2}} \, dx","IntegrateAlgebraic[(1 + x)^(3/2)/(1 - x)^(9/2),x]","\frac{\left(\frac{\sqrt{1-x}}{1120}-\frac{1}{1120}\right) \left(\sqrt{x+1}-1\right)^{13} \left(\frac{35 \left(\sqrt{1-x}-1\right)^{12}}{\left(\sqrt{x+1}-1\right)^{12}}+\frac{70 \left(\sqrt{1-x}-1\right)^{11}}{\left(\sqrt{x+1}-1\right)^{11}}+\frac{350 \left(\sqrt{1-x}-1\right)^{10}}{\left(\sqrt{x+1}-1\right)^{10}}+\frac{210 \left(\sqrt{1-x}-1\right)^9}{\left(\sqrt{x+1}-1\right)^9}-\frac{259 \left(\sqrt{1-x}-1\right)^8}{\left(\sqrt{x+1}-1\right)^8}-\frac{756 \left(\sqrt{1-x}-1\right)^7}{\left(\sqrt{x+1}-1\right)^7}+\frac{132 \left(\sqrt{1-x}-1\right)^6}{\left(\sqrt{x+1}-1\right)^6}+\frac{756 \left(\sqrt{1-x}-1\right)^5}{\left(\sqrt{x+1}-1\right)^5}-\frac{259 \left(\sqrt{1-x}-1\right)^4}{\left(\sqrt{x+1}-1\right)^4}-\frac{210 \left(\sqrt{1-x}-1\right)^3}{\left(\sqrt{x+1}-1\right)^3}+\frac{350 \left(\sqrt{1-x}-1\right)^2}{\left(\sqrt{x+1}-1\right)^2}-\frac{70 \left(\sqrt{1-x}-1\right)}{\sqrt{x+1}-1}+35\right)}{\left(-x-2 \sqrt{1-x}+\sqrt{1-x} \sqrt{x+1}+1\right)^7}","\frac{(x+1)^{5/2}}{35 (1-x)^{5/2}}+\frac{(x+1)^{5/2}}{7 (1-x)^{7/2}}",1,"((-1/1120 + Sqrt[1 - x]/1120)*(-1 + Sqrt[1 + x])^13*(35 + (35*(-1 + Sqrt[1 - x])^12)/(-1 + Sqrt[1 + x])^12 + (70*(-1 + Sqrt[1 - x])^11)/(-1 + Sqrt[1 + x])^11 + (350*(-1 + Sqrt[1 - x])^10)/(-1 + Sqrt[1 + x])^10 + (210*(-1 + Sqrt[1 - x])^9)/(-1 + Sqrt[1 + x])^9 - (259*(-1 + Sqrt[1 - x])^8)/(-1 + Sqrt[1 + x])^8 - (756*(-1 + Sqrt[1 - x])^7)/(-1 + Sqrt[1 + x])^7 + (132*(-1 + Sqrt[1 - x])^6)/(-1 + Sqrt[1 + x])^6 + (756*(-1 + Sqrt[1 - x])^5)/(-1 + Sqrt[1 + x])^5 - (259*(-1 + Sqrt[1 - x])^4)/(-1 + Sqrt[1 + x])^4 - (210*(-1 + Sqrt[1 - x])^3)/(-1 + Sqrt[1 + x])^3 + (350*(-1 + Sqrt[1 - x])^2)/(-1 + Sqrt[1 + x])^2 - (70*(-1 + Sqrt[1 - x]))/(-1 + Sqrt[1 + x])))/(1 - 2*Sqrt[1 - x] - x + Sqrt[1 - x]*Sqrt[1 + x])^7","B",1
1085,1,480,61,1.9617807,"\int \frac{(1+x)^{3/2}}{(1-x)^{11/2}} \, dx","IntegrateAlgebraic[(1 + x)^(3/2)/(1 - x)^(11/2),x]","\frac{\left(\frac{\sqrt{1-x}}{40320}-\frac{1}{40320}\right) \left(\sqrt{x+1}-1\right)^{17} \left(\frac{315 \left(\sqrt{1-x}-1\right)^{16}}{\left(\sqrt{x+1}-1\right)^{16}}+\frac{1260 \left(\sqrt{1-x}-1\right)^{15}}{\left(\sqrt{x+1}-1\right)^{15}}+\frac{6720 \left(\sqrt{1-x}-1\right)^{14}}{\left(\sqrt{x+1}-1\right)^{14}}+\frac{11340 \left(\sqrt{1-x}-1\right)^{13}}{\left(\sqrt{x+1}-1\right)^{13}}+\frac{7812 \left(\sqrt{1-x}-1\right)^{12}}{\left(\sqrt{x+1}-1\right)^{12}}-\frac{21924 \left(\sqrt{1-x}-1\right)^{11}}{\left(\sqrt{x+1}-1\right)^{11}}-\frac{28800 \left(\sqrt{1-x}-1\right)^{10}}{\left(\sqrt{x+1}-1\right)^{10}}+\frac{14076 \left(\sqrt{1-x}-1\right)^9}{\left(\sqrt{x+1}-1\right)^9}+\frac{39938 \left(\sqrt{1-x}-1\right)^8}{\left(\sqrt{x+1}-1\right)^8}-\frac{14076 \left(\sqrt{1-x}-1\right)^7}{\left(\sqrt{x+1}-1\right)^7}-\frac{28800 \left(\sqrt{1-x}-1\right)^6}{\left(\sqrt{x+1}-1\right)^6}+\frac{21924 \left(\sqrt{1-x}-1\right)^5}{\left(\sqrt{x+1}-1\right)^5}+\frac{7812 \left(\sqrt{1-x}-1\right)^4}{\left(\sqrt{x+1}-1\right)^4}-\frac{11340 \left(\sqrt{1-x}-1\right)^3}{\left(\sqrt{x+1}-1\right)^3}+\frac{6720 \left(\sqrt{1-x}-1\right)^2}{\left(\sqrt{x+1}-1\right)^2}-\frac{1260 \left(\sqrt{1-x}-1\right)}{\sqrt{x+1}-1}+315\right)}{\left(-x-2 \sqrt{1-x}+\sqrt{1-x} \sqrt{x+1}+1\right)^9}","\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,"((-1/40320 + Sqrt[1 - x]/40320)*(-1 + Sqrt[1 + x])^17*(315 + (315*(-1 + Sqrt[1 - x])^16)/(-1 + Sqrt[1 + x])^16 + (1260*(-1 + Sqrt[1 - x])^15)/(-1 + Sqrt[1 + x])^15 + (6720*(-1 + Sqrt[1 - x])^14)/(-1 + Sqrt[1 + x])^14 + (11340*(-1 + Sqrt[1 - x])^13)/(-1 + Sqrt[1 + x])^13 + (7812*(-1 + Sqrt[1 - x])^12)/(-1 + Sqrt[1 + x])^12 - (21924*(-1 + Sqrt[1 - x])^11)/(-1 + Sqrt[1 + x])^11 - (28800*(-1 + Sqrt[1 - x])^10)/(-1 + Sqrt[1 + x])^10 + (14076*(-1 + Sqrt[1 - x])^9)/(-1 + Sqrt[1 + x])^9 + (39938*(-1 + Sqrt[1 - x])^8)/(-1 + Sqrt[1 + x])^8 - (14076*(-1 + Sqrt[1 - x])^7)/(-1 + Sqrt[1 + x])^7 - (28800*(-1 + Sqrt[1 - x])^6)/(-1 + Sqrt[1 + x])^6 + (21924*(-1 + Sqrt[1 - x])^5)/(-1 + Sqrt[1 + x])^5 + (7812*(-1 + Sqrt[1 - x])^4)/(-1 + Sqrt[1 + x])^4 - (11340*(-1 + Sqrt[1 - x])^3)/(-1 + Sqrt[1 + x])^3 + (6720*(-1 + Sqrt[1 - x])^2)/(-1 + Sqrt[1 + x])^2 - (1260*(-1 + Sqrt[1 - x]))/(-1 + Sqrt[1 + x])))/(1 - 2*Sqrt[1 - x] - x + Sqrt[1 - x]*Sqrt[1 + x])^9","B",1
1086,1,584,81,4.1132477,"\int \frac{(1+x)^{3/2}}{(1-x)^{13/2}} \, dx","IntegrateAlgebraic[(1 + x)^(3/2)/(1 - x)^(13/2),x]","\frac{\left(\frac{\sqrt{1-x}}{591360}-\frac{1}{591360}\right) \left(\sqrt{x+1}-1\right)^{21} \left(\frac{1155 \left(\sqrt{1-x}-1\right)^{20}}{\left(\sqrt{x+1}-1\right)^{20}}+\frac{6930 \left(\sqrt{1-x}-1\right)^{19}}{\left(\sqrt{x+1}-1\right)^{19}}+\frac{43890 \left(\sqrt{1-x}-1\right)^{18}}{\left(\sqrt{x+1}-1\right)^{18}}+\frac{122430 \left(\sqrt{1-x}-1\right)^{17}}{\left(\sqrt{x+1}-1\right)^{17}}+\frac{207207 \left(\sqrt{1-x}-1\right)^{16}}{\left(\sqrt{x+1}-1\right)^{16}}+\frac{5544 \left(\sqrt{1-x}-1\right)^{15}}{\left(\sqrt{x+1}-1\right)^{15}}-\frac{446952 \left(\sqrt{1-x}-1\right)^{14}}{\left(\sqrt{x+1}-1\right)^{14}}-\frac{513480 \left(\sqrt{1-x}-1\right)^{13}}{\left(\sqrt{x+1}-1\right)^{13}}+\frac{444950 \left(\sqrt{1-x}-1\right)^{12}}{\left(\sqrt{x+1}-1\right)^{12}}+\frac{858044 \left(\sqrt{1-x}-1\right)^{11}}{\left(\sqrt{x+1}-1\right)^{11}}-\frac{344852 \left(\sqrt{1-x}-1\right)^{10}}{\left(\sqrt{x+1}-1\right)^{10}}-\frac{858044 \left(\sqrt{1-x}-1\right)^9}{\left(\sqrt{x+1}-1\right)^9}+\frac{444950 \left(\sqrt{1-x}-1\right)^8}{\left(\sqrt{x+1}-1\right)^8}+\frac{513480 \left(\sqrt{1-x}-1\right)^7}{\left(\sqrt{x+1}-1\right)^7}-\frac{446952 \left(\sqrt{1-x}-1\right)^6}{\left(\sqrt{x+1}-1\right)^6}-\frac{5544 \left(\sqrt{1-x}-1\right)^5}{\left(\sqrt{x+1}-1\right)^5}+\frac{207207 \left(\sqrt{1-x}-1\right)^4}{\left(\sqrt{x+1}-1\right)^4}-\frac{122430 \left(\sqrt{1-x}-1\right)^3}{\left(\sqrt{x+1}-1\right)^3}+\frac{43890 \left(\sqrt{1-x}-1\right)^2}{\left(\sqrt{x+1}-1\right)^2}-\frac{6930 \left(\sqrt{1-x}-1\right)}{\sqrt{x+1}-1}+1155\right)}{\left(-x-2 \sqrt{1-x}+\sqrt{1-x} \sqrt{x+1}+1\right)^{11}}","\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,"((-1/591360 + Sqrt[1 - x]/591360)*(-1 + Sqrt[1 + x])^21*(1155 + (1155*(-1 + Sqrt[1 - x])^20)/(-1 + Sqrt[1 + x])^20 + (6930*(-1 + Sqrt[1 - x])^19)/(-1 + Sqrt[1 + x])^19 + (43890*(-1 + Sqrt[1 - x])^18)/(-1 + Sqrt[1 + x])^18 + (122430*(-1 + Sqrt[1 - x])^17)/(-1 + Sqrt[1 + x])^17 + (207207*(-1 + Sqrt[1 - x])^16)/(-1 + Sqrt[1 + x])^16 + (5544*(-1 + Sqrt[1 - x])^15)/(-1 + Sqrt[1 + x])^15 - (446952*(-1 + Sqrt[1 - x])^14)/(-1 + Sqrt[1 + x])^14 - (513480*(-1 + Sqrt[1 - x])^13)/(-1 + Sqrt[1 + x])^13 + (444950*(-1 + Sqrt[1 - x])^12)/(-1 + Sqrt[1 + x])^12 + (858044*(-1 + Sqrt[1 - x])^11)/(-1 + Sqrt[1 + x])^11 - (344852*(-1 + Sqrt[1 - x])^10)/(-1 + Sqrt[1 + x])^10 - (858044*(-1 + Sqrt[1 - x])^9)/(-1 + Sqrt[1 + x])^9 + (444950*(-1 + Sqrt[1 - x])^8)/(-1 + Sqrt[1 + x])^8 + (513480*(-1 + Sqrt[1 - x])^7)/(-1 + Sqrt[1 + x])^7 - (446952*(-1 + Sqrt[1 - x])^6)/(-1 + Sqrt[1 + x])^6 - (5544*(-1 + Sqrt[1 - x])^5)/(-1 + Sqrt[1 + x])^5 + (207207*(-1 + Sqrt[1 - x])^4)/(-1 + Sqrt[1 + x])^4 - (122430*(-1 + Sqrt[1 - x])^3)/(-1 + Sqrt[1 + x])^3 + (43890*(-1 + Sqrt[1 - x])^2)/(-1 + Sqrt[1 + x])^2 - (6930*(-1 + Sqrt[1 - x]))/(-1 + Sqrt[1 + x])))/(1 - 2*Sqrt[1 - x] - x + Sqrt[1 - x]*Sqrt[1 + x])^11","B",1
1087,1,688,101,7.9152565,"\int \frac{(1+x)^{3/2}}{(1-x)^{15/2}} \, dx","IntegrateAlgebraic[(1 + x)^(3/2)/(1 - x)^(15/2),x]","\frac{\left(\frac{\sqrt{1-x}}{30750720}-\frac{1}{30750720}\right) \left(\sqrt{x+1}-1\right)^{25} \left(\frac{15015 \left(\sqrt{1-x}-1\right)^{24}}{\left(\sqrt{x+1}-1\right)^{24}}+\frac{120120 \left(\sqrt{1-x}-1\right)^{23}}{\left(\sqrt{x+1}-1\right)^{23}}+\frac{900900 \left(\sqrt{1-x}-1\right)^{22}}{\left(\sqrt{x+1}-1\right)^{22}}+\frac{3483480 \left(\sqrt{1-x}-1\right)^{21}}{\left(\sqrt{x+1}-1\right)^{21}}+\frac{8966958 \left(\sqrt{1-x}-1\right)^{20}}{\left(\sqrt{x+1}-1\right)^{20}}+\frac{10258248 \left(\sqrt{1-x}-1\right)^{19}}{\left(\sqrt{x+1}-1\right)^{19}}-\frac{5118828 \left(\sqrt{1-x}-1\right)^{18}}{\left(\sqrt{x+1}-1\right)^{18}}-\frac{34975512 \left(\sqrt{1-x}-1\right)^{17}}{\left(\sqrt{x+1}-1\right)^{17}}-\frac{26301847 \left(\sqrt{1-x}-1\right)^{16}}{\left(\sqrt{x+1}-1\right)^{16}}+\frac{39932464 \left(\sqrt{1-x}-1\right)^{15}}{\left(\sqrt{x+1}-1\right)^{15}}+\frac{64055368 \left(\sqrt{1-x}-1\right)^{14}}{\left(\sqrt{x+1}-1\right)^{14}}-\frac{33212816 \left(\sqrt{1-x}-1\right)^{13}}{\left(\sqrt{x+1}-1\right)^{13}}-\frac{77813884 \left(\sqrt{1-x}-1\right)^{12}}{\left(\sqrt{x+1}-1\right)^{12}}+\frac{33212816 \left(\sqrt{1-x}-1\right)^{11}}{\left(\sqrt{x+1}-1\right)^{11}}+\frac{64055368 \left(\sqrt{1-x}-1\right)^{10}}{\left(\sqrt{x+1}-1\right)^{10}}-\frac{39932464 \left(\sqrt{1-x}-1\right)^9}{\left(\sqrt{x+1}-1\right)^9}-\frac{26301847 \left(\sqrt{1-x}-1\right)^8}{\left(\sqrt{x+1}-1\right)^8}+\frac{34975512 \left(\sqrt{1-x}-1\right)^7}{\left(\sqrt{x+1}-1\right)^7}-\frac{5118828 \left(\sqrt{1-x}-1\right)^6}{\left(\sqrt{x+1}-1\right)^6}-\frac{10258248 \left(\sqrt{1-x}-1\right)^5}{\left(\sqrt{x+1}-1\right)^5}+\frac{8966958 \left(\sqrt{1-x}-1\right)^4}{\left(\sqrt{x+1}-1\right)^4}-\frac{3483480 \left(\sqrt{1-x}-1\right)^3}{\left(\sqrt{x+1}-1\right)^3}+\frac{900900 \left(\sqrt{1-x}-1\right)^2}{\left(\sqrt{x+1}-1\right)^2}-\frac{120120 \left(\sqrt{1-x}-1\right)}{\sqrt{x+1}-1}+15015\right)}{\left(-x-2 \sqrt{1-x}+\sqrt{1-x} \sqrt{x+1}+1\right)^{13}}","\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,"((-1/30750720 + Sqrt[1 - x]/30750720)*(-1 + Sqrt[1 + x])^25*(15015 + (15015*(-1 + Sqrt[1 - x])^24)/(-1 + Sqrt[1 + x])^24 + (120120*(-1 + Sqrt[1 - x])^23)/(-1 + Sqrt[1 + x])^23 + (900900*(-1 + Sqrt[1 - x])^22)/(-1 + Sqrt[1 + x])^22 + (3483480*(-1 + Sqrt[1 - x])^21)/(-1 + Sqrt[1 + x])^21 + (8966958*(-1 + Sqrt[1 - x])^20)/(-1 + Sqrt[1 + x])^20 + (10258248*(-1 + Sqrt[1 - x])^19)/(-1 + Sqrt[1 + x])^19 - (5118828*(-1 + Sqrt[1 - x])^18)/(-1 + Sqrt[1 + x])^18 - (34975512*(-1 + Sqrt[1 - x])^17)/(-1 + Sqrt[1 + x])^17 - (26301847*(-1 + Sqrt[1 - x])^16)/(-1 + Sqrt[1 + x])^16 + (39932464*(-1 + Sqrt[1 - x])^15)/(-1 + Sqrt[1 + x])^15 + (64055368*(-1 + Sqrt[1 - x])^14)/(-1 + Sqrt[1 + x])^14 - (33212816*(-1 + Sqrt[1 - x])^13)/(-1 + Sqrt[1 + x])^13 - (77813884*(-1 + Sqrt[1 - x])^12)/(-1 + Sqrt[1 + x])^12 + (33212816*(-1 + Sqrt[1 - x])^11)/(-1 + Sqrt[1 + x])^11 + (64055368*(-1 + Sqrt[1 - x])^10)/(-1 + Sqrt[1 + x])^10 - (39932464*(-1 + Sqrt[1 - x])^9)/(-1 + Sqrt[1 + x])^9 - (26301847*(-1 + Sqrt[1 - x])^8)/(-1 + Sqrt[1 + x])^8 + (34975512*(-1 + Sqrt[1 - x])^7)/(-1 + Sqrt[1 + x])^7 - (5118828*(-1 + Sqrt[1 - x])^6)/(-1 + Sqrt[1 + x])^6 - (10258248*(-1 + Sqrt[1 - x])^5)/(-1 + Sqrt[1 + x])^5 + (8966958*(-1 + Sqrt[1 - x])^4)/(-1 + Sqrt[1 + x])^4 - (3483480*(-1 + Sqrt[1 - x])^3)/(-1 + Sqrt[1 + x])^3 + (900900*(-1 + Sqrt[1 - x])^2)/(-1 + Sqrt[1 + x])^2 - (120120*(-1 + Sqrt[1 - x]))/(-1 + Sqrt[1 + x])))/(1 - 2*Sqrt[1 - x] - x + Sqrt[1 - x]*Sqrt[1 + x])^13","B",1
1088,0,0,130,4.2666967,"\int (1-x)^{11/2} (1+x)^{5/2} \, dx","IntegrateAlgebraic[(1 - x)^(11/2)*(1 + x)^(5/2),x]","\int (1-x)^{11/2} (1+x)^{5/2} \, dx","\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,"Could not integrate","F",-1
1089,1,820,110,0.6632631,"\int (1-x)^{9/2} (1+x)^{5/2} \, dx","IntegrateAlgebraic[(1 - x)^(9/2)*(1 + x)^(5/2),x]","\frac{\left(\frac{2 \sqrt{1-x}}{7}-\frac{2}{7}\right) \left(\sqrt{x+1}-1\right) \left(112 x^{15}+1680 \sqrt{1-x} x^{14}-1680 \sqrt{x+1} x^{14}-256 x^{14}+109840 \sqrt{1-x} x^{13}-24304 \sqrt{1-x} \sqrt{x+1} x^{13}+117520 \sqrt{x+1} x^{13}-755608 x^{13}-2147544 \sqrt{1-x} x^{12}+55552 \sqrt{1-x} \sqrt{x+1} x^{12}+1627864 \sqrt{x+1} x^{12}+1727488 x^{12}-10271128 \sqrt{1-x} x^{11}+8008168 \sqrt{1-x} \sqrt{x+1} x^{11}-18912152 \sqrt{x+1} x^{11}+39457558 x^{11}+75714738 \sqrt{1-x} x^{10}-18387712 \sqrt{1-x} \sqrt{x+1} x^{10}-8230578 \sqrt{x+1} x^{10}-92780032 x^{10}+28911138 \sqrt{1-x} x^9-106517054 \sqrt{1-x} \sqrt{x+1} x^9+233750562 \sqrt{x+1} x^9-210972153 x^9-465166965 \sqrt{1-x} x^8+271069952 \sqrt{1-x} \sqrt{x+1} x^8-236623755 \sqrt{x+1} x^8+622040064 x^8+161757315 \sqrt{1-x} x^7+244382579 \sqrt{1-x} \sqrt{x+1} x^7-671131005 \sqrt{x+1} x^7+273908915 x^7+1126730880 \sqrt{1-x} x^6-972120576 \sqrt{1-x} \sqrt{x+1} x^6+1115844480 \sqrt{x+1} x^6-1594956288 x^6-782908600 \sqrt{1-x} x^5+42415688 \sqrt{1-x} \sqrt{x+1} x^5+573461320 \sqrt{x+1} x^5+313251176 x^5-1282666272 \sqrt{1-x} x^4+1474711552 \sqrt{1-x} \sqrt{x+1} x^4-1910468832 \sqrt{x+1} x^4+1972576256 x^4+1313374128 \sqrt{1-x} x^3-711166288 \sqrt{1-x} \sqrt{x+1} x^3+267394992 \sqrt{x+1} x^3-1023554896 x^3+867944448 \sqrt{1-x} x^2-1108156416 \sqrt{1-x} \sqrt{x+1} x^2+1480980480 \sqrt{x+1} x^2-1374871552 x^2-877580608 \sqrt{1-x} x+609780416 \sqrt{1-x} \sqrt{x+1} x-340939072 \sqrt{x+1} x+608664896 x-536945280 \sqrt{1-x}+536870912 \sqrt{1-x} \sqrt{x+1}-536796544 \sqrt{x+1}+536870912\right)}{\left(\sqrt{1-x}+\sqrt{x+1}-2\right)^{16}}+\frac{45}{32} \tan ^{-1}\left(\frac{\sqrt{x+1}-1}{\sqrt{1-x}-1}\right)","\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,"((-2/7 + (2*Sqrt[1 - x])/7)*(-1 + Sqrt[1 + x])*(536870912 - 536945280*Sqrt[1 - x] + 608664896*x - 877580608*Sqrt[1 - x]*x - 1374871552*x^2 + 867944448*Sqrt[1 - x]*x^2 - 1023554896*x^3 + 1313374128*Sqrt[1 - x]*x^3 + 1972576256*x^4 - 1282666272*Sqrt[1 - x]*x^4 + 313251176*x^5 - 782908600*Sqrt[1 - x]*x^5 - 1594956288*x^6 + 1126730880*Sqrt[1 - x]*x^6 + 273908915*x^7 + 161757315*Sqrt[1 - x]*x^7 + 622040064*x^8 - 465166965*Sqrt[1 - x]*x^8 - 210972153*x^9 + 28911138*Sqrt[1 - x]*x^9 - 92780032*x^10 + 75714738*Sqrt[1 - x]*x^10 + 39457558*x^11 - 10271128*Sqrt[1 - x]*x^11 + 1727488*x^12 - 2147544*Sqrt[1 - x]*x^12 - 755608*x^13 + 109840*Sqrt[1 - x]*x^13 - 256*x^14 + 1680*Sqrt[1 - x]*x^14 + 112*x^15 - 536796544*Sqrt[1 + x] + 536870912*Sqrt[1 - x]*Sqrt[1 + x] - 340939072*x*Sqrt[1 + x] + 609780416*Sqrt[1 - x]*x*Sqrt[1 + x] + 1480980480*x^2*Sqrt[1 + x] - 1108156416*Sqrt[1 - x]*x^2*Sqrt[1 + x] + 267394992*x^3*Sqrt[1 + x] - 711166288*Sqrt[1 - x]*x^3*Sqrt[1 + x] - 1910468832*x^4*Sqrt[1 + x] + 1474711552*Sqrt[1 - x]*x^4*Sqrt[1 + x] + 573461320*x^5*Sqrt[1 + x] + 42415688*Sqrt[1 - x]*x^5*Sqrt[1 + x] + 1115844480*x^6*Sqrt[1 + x] - 972120576*Sqrt[1 - x]*x^6*Sqrt[1 + x] - 671131005*x^7*Sqrt[1 + x] + 244382579*Sqrt[1 - x]*x^7*Sqrt[1 + x] - 236623755*x^8*Sqrt[1 + x] + 271069952*Sqrt[1 - x]*x^8*Sqrt[1 + x] + 233750562*x^9*Sqrt[1 + x] - 106517054*Sqrt[1 - x]*x^9*Sqrt[1 + x] - 8230578*x^10*Sqrt[1 + x] - 18387712*Sqrt[1 - x]*x^10*Sqrt[1 + x] - 18912152*x^11*Sqrt[1 + x] + 8008168*Sqrt[1 - x]*x^11*Sqrt[1 + x] + 1627864*x^12*Sqrt[1 + x] + 55552*Sqrt[1 - x]*x^12*Sqrt[1 + x] + 117520*x^13*Sqrt[1 + x] - 24304*Sqrt[1 - x]*x^13*Sqrt[1 + x] - 1680*x^14*Sqrt[1 + x]))/(-2 + Sqrt[1 - x] + Sqrt[1 + x])^16 + (45*ArcTan[(-1 + Sqrt[1 + x])/(-1 + Sqrt[1 - x])])/32","B",1
1090,1,732,90,0.6248511,"\int (1-x)^{7/2} (1+x)^{5/2} \, dx","IntegrateAlgebraic[(1 - x)^(7/2)*(1 + x)^(5/2),x]","\frac{5}{4} \tan ^{-1}\left(\frac{\sqrt{x+1}-1}{\sqrt{1-x}-1}\right)+\frac{\left(\frac{8 \sqrt{1-x}}{21}-\frac{8}{21}\right) \left(\sqrt{x+1}-1\right) \left(-624 \sqrt{1-x} x^{12}+48 \sqrt{1-x} \sqrt{x+1} x^{12}-624 \sqrt{x+1} x^{12}+7776 x^{12}+31304 \sqrt{1-x} x^{11}-56 \sqrt{1-x} \sqrt{x+1} x^{11}-29848 \sqrt{x+1} x^{11}-9072 x^{11}+361816 \sqrt{1-x} x^{10}-175728 \sqrt{1-x} \sqrt{x+1} x^{10}+433160 \sqrt{x+1} x^{10}-1330560 x^{10}-2188030 \sqrt{1-x} x^9+205030 \sqrt{1-x} \sqrt{x+1} x^9+1260194 \sqrt{x+1} x^9+1554588 x^9-4250194 \sqrt{1-x} x^8+4742448 \sqrt{1-x} \sqrt{x+1} x^8-8290958 \sqrt{x+1} x^8+11515968 x^8+15625623 \sqrt{1-x} x^7-5584131 \sqrt{1-x} \sqrt{x+1} x^7-761865 \sqrt{x+1} x^7-13826778 x^7+12650421 \sqrt{1-x} x^6-19484880 \sqrt{1-x} \sqrt{x+1} x^6+32801643 \sqrt{x+1} x^6-32913840 x^6-43054302 \sqrt{1-x} x^5+24192294 \sqrt{1-x} \sqrt{x+1} x^5-13974558 \sqrt{x+1} x^5+42314286 x^5-14547320 \sqrt{1-x} x^4+31764288 \sqrt{1-x} \sqrt{x+1} x^4-54555400 \sqrt{x+1} x^4+43010112 x^4+59919536 \sqrt{1-x} x^3-44218160 \sqrt{1-x} \sqrt{x+1} x^3+36715184 \sqrt{x+1} x^3-60214560 x^3+10545872 \sqrt{1-x} x^2-24449280 \sqrt{1-x} \sqrt{x+1} x^2+41369392 \sqrt{x+1} x^2-30600960 x^2-36565728 \sqrt{1-x} x+30373728 \sqrt{1-x} \sqrt{x+1} x-24004320 \sqrt{x+1} x+30181536 x-12597696 \sqrt{1-x}+12582912 \sqrt{1-x} \sqrt{x+1}-12568128 \sqrt{x+1}+12582912\right)}{\left(\sqrt{1-x}+\sqrt{x+1}-2\right)^{14}}","\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,"((-8/21 + (8*Sqrt[1 - x])/21)*(-1 + Sqrt[1 + x])*(12582912 - 12597696*Sqrt[1 - x] + 30181536*x - 36565728*Sqrt[1 - x]*x - 30600960*x^2 + 10545872*Sqrt[1 - x]*x^2 - 60214560*x^3 + 59919536*Sqrt[1 - x]*x^3 + 43010112*x^4 - 14547320*Sqrt[1 - x]*x^4 + 42314286*x^5 - 43054302*Sqrt[1 - x]*x^5 - 32913840*x^6 + 12650421*Sqrt[1 - x]*x^6 - 13826778*x^7 + 15625623*Sqrt[1 - x]*x^7 + 11515968*x^8 - 4250194*Sqrt[1 - x]*x^8 + 1554588*x^9 - 2188030*Sqrt[1 - x]*x^9 - 1330560*x^10 + 361816*Sqrt[1 - x]*x^10 - 9072*x^11 + 31304*Sqrt[1 - x]*x^11 + 7776*x^12 - 624*Sqrt[1 - x]*x^12 - 12568128*Sqrt[1 + x] + 12582912*Sqrt[1 - x]*Sqrt[1 + x] - 24004320*x*Sqrt[1 + x] + 30373728*Sqrt[1 - x]*x*Sqrt[1 + x] + 41369392*x^2*Sqrt[1 + x] - 24449280*Sqrt[1 - x]*x^2*Sqrt[1 + x] + 36715184*x^3*Sqrt[1 + x] - 44218160*Sqrt[1 - x]*x^3*Sqrt[1 + x] - 54555400*x^4*Sqrt[1 + x] + 31764288*Sqrt[1 - x]*x^4*Sqrt[1 + x] - 13974558*x^5*Sqrt[1 + x] + 24192294*Sqrt[1 - x]*x^5*Sqrt[1 + x] + 32801643*x^6*Sqrt[1 + x] - 19484880*Sqrt[1 - x]*x^6*Sqrt[1 + x] - 761865*x^7*Sqrt[1 + x] - 5584131*Sqrt[1 - x]*x^7*Sqrt[1 + x] - 8290958*x^8*Sqrt[1 + x] + 4742448*Sqrt[1 - x]*x^8*Sqrt[1 + x] + 1260194*x^9*Sqrt[1 + x] + 205030*Sqrt[1 - x]*x^9*Sqrt[1 + x] + 433160*x^10*Sqrt[1 + x] - 175728*Sqrt[1 - x]*x^10*Sqrt[1 + x] - 29848*x^11*Sqrt[1 + x] - 56*Sqrt[1 - x]*x^11*Sqrt[1 + x] - 624*x^12*Sqrt[1 + x] + 48*Sqrt[1 - x]*x^12*Sqrt[1 + x]))/(-2 + Sqrt[1 - x] + Sqrt[1 + x])^14 + (5*ArcTan[(-1 + Sqrt[1 + x])/(-1 + Sqrt[1 - x])])/4","B",1
1091,1,426,70,2.8816073,"\int (1-x)^{5/2} (1+x)^{5/2} \, dx","IntegrateAlgebraic[(1 - x)^(5/2)*(1 + x)^(5/2),x]","\frac{\left(\sqrt{x+1}-1\right)^{24} \left(\frac{11 \left(\sqrt{1-x}-1\right)^{23}}{16384 \left(\sqrt{x+1}-1\right)^{23}}-\frac{383 \left(\sqrt{1-x}-1\right)^{21}}{49152 \left(\sqrt{x+1}-1\right)^{21}}+\frac{1145 \left(\sqrt{1-x}-1\right)^{19}}{16384 \left(\sqrt{x+1}-1\right)^{19}}-\frac{7335 \left(\sqrt{1-x}-1\right)^{17}}{16384 \left(\sqrt{x+1}-1\right)^{17}}+\frac{36445 \left(\sqrt{1-x}-1\right)^{15}}{24576 \left(\sqrt{x+1}-1\right)^{15}}-\frac{27233 \left(\sqrt{1-x}-1\right)^{13}}{8192 \left(\sqrt{x+1}-1\right)^{13}}+\frac{27233 \left(\sqrt{1-x}-1\right)^{11}}{8192 \left(\sqrt{x+1}-1\right)^{11}}-\frac{36445 \left(\sqrt{1-x}-1\right)^9}{24576 \left(\sqrt{x+1}-1\right)^9}+\frac{7335 \left(\sqrt{1-x}-1\right)^7}{16384 \left(\sqrt{x+1}-1\right)^7}-\frac{1145 \left(\sqrt{1-x}-1\right)^5}{16384 \left(\sqrt{x+1}-1\right)^5}+\frac{383 \left(\sqrt{1-x}-1\right)^3}{49152 \left(\sqrt{x+1}-1\right)^3}-\frac{11 \left(\sqrt{1-x}-1\right)}{16384 \left(\sqrt{x+1}-1\right)}+\frac{5 \left(\sqrt{1-x}+\sqrt{x+1}-2\right)^{12} \tan ^{-1}\left(\frac{\sqrt{x+1}-1}{\sqrt{1-x}-1}\right)}{4 \left(\sqrt{x+1}-1\right)^{24}}\right)}{\left(\sqrt{1-x}+\sqrt{x+1}-2\right)^{12}}","\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,"((-1 + Sqrt[1 + x])^24*((11*(-1 + Sqrt[1 - x])^23)/(16384*(-1 + Sqrt[1 + x])^23) - (383*(-1 + Sqrt[1 - x])^21)/(49152*(-1 + Sqrt[1 + x])^21) + (1145*(-1 + Sqrt[1 - x])^19)/(16384*(-1 + Sqrt[1 + x])^19) - (7335*(-1 + Sqrt[1 - x])^17)/(16384*(-1 + Sqrt[1 + x])^17) + (36445*(-1 + Sqrt[1 - x])^15)/(24576*(-1 + Sqrt[1 + x])^15) - (27233*(-1 + Sqrt[1 - x])^13)/(8192*(-1 + Sqrt[1 + x])^13) + (27233*(-1 + Sqrt[1 - x])^11)/(8192*(-1 + Sqrt[1 + x])^11) - (36445*(-1 + Sqrt[1 - x])^9)/(24576*(-1 + Sqrt[1 + x])^9) + (7335*(-1 + Sqrt[1 - x])^7)/(16384*(-1 + Sqrt[1 + x])^7) - (1145*(-1 + Sqrt[1 - x])^5)/(16384*(-1 + Sqrt[1 + x])^5) + (383*(-1 + Sqrt[1 - x])^3)/(49152*(-1 + Sqrt[1 + x])^3) - (11*(-1 + Sqrt[1 - x]))/(16384*(-1 + Sqrt[1 + x])) + (5*(-2 + Sqrt[1 - x] + Sqrt[1 + x])^12*ArcTan[(-1 + Sqrt[1 + x])/(-1 + Sqrt[1 - x])])/(4*(-1 + Sqrt[1 + x])^24)))/(-2 + Sqrt[1 - x] + Sqrt[1 + x])^12","B",1
1092,1,524,69,0.4126049,"\int (1-x)^{3/2} (1+x)^{5/2} \, dx","IntegrateAlgebraic[(1 - x)^(3/2)*(1 + x)^(5/2),x]","\frac{\left(\frac{4}{5}-\frac{4 \sqrt{1-x}}{5}\right) \left(\sqrt{x+1}-1\right) \left(-72 \sqrt{1-x} x^8+8 \sqrt{1-x} \sqrt{x+1} x^8-72 \sqrt{x+1} x^8+608 x^8+1470 \sqrt{1-x} x^7+10 \sqrt{1-x} \sqrt{x+1} x^7-1650 \sqrt{x+1} x^7+760 x^7+10734 \sqrt{1-x} x^6-5840 \sqrt{1-x} \sqrt{x+1} x^6+6834 \sqrt{x+1} x^6-17632 x^6-1407 \sqrt{1-x} x^5-7305 \sqrt{1-x} \sqrt{x+1} x^5+23457 \sqrt{x+1} x^5-22420 x^5-50315 \sqrt{1-x} x^4+28616 \sqrt{1-x} \sqrt{x+1} x^4-17285 \sqrt{x+1} x^4+49256 x^4-27432 \sqrt{1-x} x^3+39400 \sqrt{1-x} \sqrt{x+1} x^3-67688 \sqrt{x+1} x^3+71060 x^3+72108 \sqrt{1-x} x^2-40352 \sqrt{1-x} \sqrt{x+1} x^2+14228 \sqrt{x+1} x^2-53856 x^2+35336 \sqrt{1-x} x-53000 \sqrt{1-x} \sqrt{x+1} x+67464 \sqrt{x+1} x-49400 x-32368 \sqrt{1-x}+32768 \sqrt{1-x} \sqrt{x+1}-33168 \sqrt{x+1}+32768\right)}{\left(\sqrt{1-x}+\sqrt{x+1}-2\right)^{10}}+\frac{3}{2} \tan ^{-1}\left(\frac{\sqrt{x+1}-1}{\sqrt{1-x}-1}\right)","-\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,"((4/5 - (4*Sqrt[1 - x])/5)*(-1 + Sqrt[1 + x])*(32768 - 32368*Sqrt[1 - x] - 49400*x + 35336*Sqrt[1 - x]*x - 53856*x^2 + 72108*Sqrt[1 - x]*x^2 + 71060*x^3 - 27432*Sqrt[1 - x]*x^3 + 49256*x^4 - 50315*Sqrt[1 - x]*x^4 - 22420*x^5 - 1407*Sqrt[1 - x]*x^5 - 17632*x^6 + 10734*Sqrt[1 - x]*x^6 + 760*x^7 + 1470*Sqrt[1 - x]*x^7 + 608*x^8 - 72*Sqrt[1 - x]*x^8 - 33168*Sqrt[1 + x] + 32768*Sqrt[1 - x]*Sqrt[1 + x] + 67464*x*Sqrt[1 + x] - 53000*Sqrt[1 - x]*x*Sqrt[1 + x] + 14228*x^2*Sqrt[1 + x] - 40352*Sqrt[1 - x]*x^2*Sqrt[1 + x] - 67688*x^3*Sqrt[1 + x] + 39400*Sqrt[1 - x]*x^3*Sqrt[1 + x] - 17285*x^4*Sqrt[1 + x] + 28616*Sqrt[1 - x]*x^4*Sqrt[1 + x] + 23457*x^5*Sqrt[1 + x] - 7305*Sqrt[1 - x]*x^5*Sqrt[1 + x] + 6834*x^6*Sqrt[1 + x] - 5840*Sqrt[1 - x]*x^6*Sqrt[1 + x] - 1650*x^7*Sqrt[1 + x] + 10*Sqrt[1 - x]*x^7*Sqrt[1 + x] - 72*x^8*Sqrt[1 + x] + 8*Sqrt[1 - x]*x^8*Sqrt[1 + x]))/(-2 + Sqrt[1 - x] + Sqrt[1 + x])^10 + (3*ArcTan[(-1 + Sqrt[1 + x])/(-1 + Sqrt[1 - x])])/2","B",1
1093,1,404,68,0.2791814,"\int \sqrt{1-x} (1+x)^{5/2} \, dx","IntegrateAlgebraic[Sqrt[1 - x]*(1 + x)^(5/2),x]","\frac{\left(\frac{2 \sqrt{1-x}}{3}-\frac{2}{3}\right) \left(\sqrt{x+1}-1\right) \left(6 x^7+42 \sqrt{1-x} x^6-42 \sqrt{x+1} x^6+16 x^6+658 \sqrt{1-x} x^5-270 \sqrt{1-x} \sqrt{x+1} x^5+434 \sqrt{x+1} x^5-1365 x^5+511 \sqrt{1-x} x^4-720 \sqrt{1-x} \sqrt{x+1} x^4+2401 \sqrt{x+1} x^4-3680 x^4-3541 \sqrt{1-x} x^3+1299 \sqrt{1-x} \sqrt{x+1} x^3+2059 \sqrt{x+1} x^3-693 x^3-7288 \sqrt{1-x} x^2+5280 \sqrt{1-x} \sqrt{x+1} x^2-4168 \sqrt{x+1} x^2+8032 x^2+1564 \sqrt{1-x} x+2556 \sqrt{1-x} \sqrt{x+1} x-6244 \sqrt{x+1} x+2052 x+8120 \sqrt{1-x}-8192 \sqrt{1-x} \sqrt{x+1}+8264 \sqrt{x+1}-8192\right)}{\left(\sqrt{1-x}+\sqrt{x+1}-2\right)^8}+\frac{5}{2} \tan ^{-1}\left(\frac{\sqrt{x+1}-1}{\sqrt{1-x}-1}\right)","-\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,"((-2/3 + (2*Sqrt[1 - x])/3)*(-1 + Sqrt[1 + x])*(-8192 + 8120*Sqrt[1 - x] + 2052*x + 1564*Sqrt[1 - x]*x + 8032*x^2 - 7288*Sqrt[1 - x]*x^2 - 693*x^3 - 3541*Sqrt[1 - x]*x^3 - 3680*x^4 + 511*Sqrt[1 - x]*x^4 - 1365*x^5 + 658*Sqrt[1 - x]*x^5 + 16*x^6 + 42*Sqrt[1 - x]*x^6 + 6*x^7 + 8264*Sqrt[1 + x] - 8192*Sqrt[1 - x]*Sqrt[1 + x] - 6244*x*Sqrt[1 + x] + 2556*Sqrt[1 - x]*x*Sqrt[1 + x] - 4168*x^2*Sqrt[1 + x] + 5280*Sqrt[1 - x]*x^2*Sqrt[1 + x] + 2059*x^3*Sqrt[1 + x] + 1299*Sqrt[1 - x]*x^3*Sqrt[1 + x] + 2401*x^4*Sqrt[1 + x] - 720*Sqrt[1 - x]*x^4*Sqrt[1 + x] + 434*x^5*Sqrt[1 + x] - 270*Sqrt[1 - x]*x^5*Sqrt[1 + x] - 42*x^6*Sqrt[1 + x]))/(-2 + Sqrt[1 - x] + Sqrt[1 + x])^8 + (5*ArcTan[(-1 + Sqrt[1 + x])/(-1 + Sqrt[1 - x])])/2","B",1
1094,1,314,67,0.2234023,"\int \frac{(1+x)^{5/2}}{\sqrt{1-x}} \, dx","IntegrateAlgebraic[(1 + x)^(5/2)/Sqrt[1 - x],x]","\frac{\left(\frac{4 \sqrt{1-x}}{3}-\frac{4}{3}\right) \left(\sqrt{x+1}-1\right) \left(-10 \sqrt{1-x} x^4+2 \sqrt{1-x} \sqrt{x+1} x^4-10 \sqrt{x+1} x^4+44 x^4+5 \sqrt{1-x} x^3+9 \sqrt{1-x} \sqrt{x+1} x^3-95 \sqrt{x+1} x^3+198 x^3+183 \sqrt{1-x} x^2-62 \sqrt{1-x} \sqrt{x+1} x^2-267 \sqrt{x+1} x^2+462 x^2+974 \sqrt{1-x} x-378 \sqrt{1-x} \sqrt{x+1} x-362 \sqrt{x+1} x-198 x+1444 \sqrt{1-x}-1408 \sqrt{1-x} \sqrt{x+1}+1372 \sqrt{x+1}-1408\right)}{\left(\sqrt{1-x}+\sqrt{x+1}-2\right)^6}+10 \tan ^{-1}\left(\frac{\sqrt{x+1}-1}{\sqrt{1-x}-1}\right)","-\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,"((-4/3 + (4*Sqrt[1 - x])/3)*(-1 + Sqrt[1 + x])*(-1408 + 1444*Sqrt[1 - x] - 198*x + 974*Sqrt[1 - x]*x + 462*x^2 + 183*Sqrt[1 - x]*x^2 + 198*x^3 + 5*Sqrt[1 - x]*x^3 + 44*x^4 - 10*Sqrt[1 - x]*x^4 + 1372*Sqrt[1 + x] - 1408*Sqrt[1 - x]*Sqrt[1 + x] - 362*x*Sqrt[1 + x] - 378*Sqrt[1 - x]*x*Sqrt[1 + x] - 267*x^2*Sqrt[1 + x] - 62*Sqrt[1 - x]*x^2*Sqrt[1 + x] - 95*x^3*Sqrt[1 + x] + 9*Sqrt[1 - x]*x^3*Sqrt[1 + x] - 10*x^4*Sqrt[1 + x] + 2*Sqrt[1 - x]*x^4*Sqrt[1 + x]))/(-2 + Sqrt[1 - x] + Sqrt[1 + x])^6 + 10*ArcTan[(-1 + Sqrt[1 + x])/(-1 + Sqrt[1 - x])]","B",1
1095,1,281,65,0.2264264,"\int \frac{(1+x)^{5/2}}{(1-x)^{3/2}} \, dx","IntegrateAlgebraic[(1 + x)^(5/2)/(1 - x)^(3/2),x]","\frac{\left(2-2 \sqrt{1-x}\right) \left(\sqrt{x+1}-1\right)^7}{\left(\sqrt{1-x}+\sqrt{x+1}-2\right)^4}+\frac{\left(6-6 \sqrt{1-x}\right) \left(\sqrt{x+1}-1\right)^5}{\left(\sqrt{1-x}+\sqrt{x+1}-2\right)^3}+\frac{\left(-5 \sqrt{1-x}-8 \sqrt{x+1}+13\right) \left(\sqrt{x+1}-1\right)^3}{\left(\sqrt{1-x}+\sqrt{x+1}-2\right)^2}+\frac{\left(-\sqrt{1-x}-16 \sqrt{x+1}+17\right) \left(\sqrt{x+1}-1\right)}{\sqrt{1-x}+\sqrt{x+1}-2}+\frac{\left(16 \sqrt{1-x}-16\right) \left(\sqrt{x+1}-1\right)}{-x-2 \sqrt{1-x}+\sqrt{1-x} \sqrt{x+1}+1}-30 \tan ^{-1}\left(\frac{\sqrt{x+1}-1}{\sqrt{1-x}-1}\right)","\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,"((2 - 2*Sqrt[1 - x])*(-1 + Sqrt[1 + x])^7)/(-2 + Sqrt[1 - x] + Sqrt[1 + x])^4 + ((6 - 6*Sqrt[1 - x])*(-1 + Sqrt[1 + x])^5)/(-2 + Sqrt[1 - x] + Sqrt[1 + x])^3 + ((13 - 5*Sqrt[1 - x] - 8*Sqrt[1 + x])*(-1 + Sqrt[1 + x])^3)/(-2 + Sqrt[1 - x] + Sqrt[1 + x])^2 + ((17 - Sqrt[1 - x] - 16*Sqrt[1 + x])*(-1 + Sqrt[1 + x]))/(-2 + Sqrt[1 - x] + Sqrt[1 + x]) + ((-16 + 16*Sqrt[1 - x])*(-1 + Sqrt[1 + x]))/(1 - 2*Sqrt[1 - x] - x + Sqrt[1 - x]*Sqrt[1 + x]) - 30*ArcTan[(-1 + Sqrt[1 + x])/(-1 + Sqrt[1 - x])]","B",1
1096,1,290,63,0.3025299,"\int \frac{(1+x)^{5/2}}{(1-x)^{5/2}} \, dx","IntegrateAlgebraic[(1 + x)^(5/2)/(1 - x)^(5/2),x]","\frac{\left(\frac{4}{3}-\frac{4 \sqrt{1-x}}{3}\right) \left(\sqrt{x+1}-1\right) \left(-3 x^4-24 \sqrt{1-x} x^3+3 \sqrt{1-x} \sqrt{x+1} x^3+96 x^3+248 \sqrt{1-x} x^2+31 \sqrt{1-x} \sqrt{x+1} x^2-256 \sqrt{x+1} x^2-135 x^2+640 \sqrt{1-x} x-810 \sqrt{1-x} \sqrt{x+1} x+1184 \sqrt{x+1} x-1014 x-736 \sqrt{1-x}+688 \sqrt{1-x} \sqrt{x+1}-736 \sqrt{x+1}+784\right)}{\left(\sqrt{1-x}+\sqrt{x+1}-2\right)^2 \left(-x-2 \sqrt{1-x}+\sqrt{1-x} \sqrt{x+1}+1\right)^3}+20 \tan ^{-1}\left(\frac{\sqrt{x+1}-1}{\sqrt{1-x}-1}\right)","\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,"((4/3 - (4*Sqrt[1 - x])/3)*(-1 + Sqrt[1 + x])*(784 - 736*Sqrt[1 - x] - 1014*x + 640*Sqrt[1 - x]*x - 135*x^2 + 248*Sqrt[1 - x]*x^2 + 96*x^3 - 24*Sqrt[1 - x]*x^3 - 3*x^4 - 736*Sqrt[1 + x] + 688*Sqrt[1 - x]*Sqrt[1 + x] + 1184*x*Sqrt[1 + x] - 810*Sqrt[1 - x]*x*Sqrt[1 + x] - 256*x^2*Sqrt[1 + x] + 31*Sqrt[1 - x]*x^2*Sqrt[1 + x] + 3*Sqrt[1 - x]*x^3*Sqrt[1 + x]))/((-2 + Sqrt[1 - x] + Sqrt[1 + x])^2*(1 - 2*Sqrt[1 - x] - x + Sqrt[1 - x]*Sqrt[1 + x])^3) + 20*ArcTan[(-1 + Sqrt[1 + x])/(-1 + Sqrt[1 - x])]","B",1
1097,1,282,63,0.2557869,"\int \frac{(1+x)^{5/2}}{(1-x)^{7/2}} \, dx","IntegrateAlgebraic[(1 + x)^(5/2)/(1 - x)^(7/2),x]","\frac{\left(\frac{16 \sqrt{1-x}}{15}-\frac{16}{15}\right) \left(\sqrt{x+1}-1\right) \left(-18 x^4-92 \sqrt{1-x} x^3+5 \sqrt{1-x} \sqrt{x+1} x^3+52 \sqrt{x+1} x^3+90 x^3-152 \sqrt{1-x} x^2+253 \sqrt{1-x} \sqrt{x+1} x^2-432 \sqrt{x+1} x^2+324 x^2+356 \sqrt{1-x} x-370 \sqrt{1-x} \sqrt{x+1} x+444 \sqrt{x+1} x-430 x-208 \sqrt{1-x}+178 \sqrt{1-x} \sqrt{x+1}-208 \sqrt{x+1}+238\right)}{\left(-x-2 \sqrt{1-x}+\sqrt{1-x} \sqrt{x+1}+1\right)^5}-4 \tan ^{-1}\left(\frac{\sqrt{x+1}-1}{\sqrt{1-x}-1}\right)","\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,"((-16/15 + (16*Sqrt[1 - x])/15)*(-1 + Sqrt[1 + x])*(238 - 208*Sqrt[1 - x] - 430*x + 356*Sqrt[1 - x]*x + 324*x^2 - 152*Sqrt[1 - x]*x^2 + 90*x^3 - 92*Sqrt[1 - x]*x^3 - 18*x^4 - 208*Sqrt[1 + x] + 178*Sqrt[1 - x]*Sqrt[1 + x] + 444*x*Sqrt[1 + x] - 370*Sqrt[1 - x]*x*Sqrt[1 + x] - 432*x^2*Sqrt[1 + x] + 253*Sqrt[1 - x]*x^2*Sqrt[1 + x] + 52*x^3*Sqrt[1 + x] + 5*Sqrt[1 - x]*x^3*Sqrt[1 + x]))/(1 - 2*Sqrt[1 - x] - x + Sqrt[1 - x]*Sqrt[1 + x])^5 - 4*ArcTan[(-1 + Sqrt[1 + x])/(-1 + Sqrt[1 - x])]","B",1
1098,1,222,20,0.480793,"\int \frac{(1+x)^{5/2}}{(1-x)^{9/2}} \, dx","IntegrateAlgebraic[(1 + x)^(5/2)/(1 - x)^(9/2),x]","\frac{\left(\frac{\sqrt{1-x}}{224}-\frac{1}{224}\right) \left(\sqrt{x+1}-1\right)^{13} \left(\frac{7 \left(\sqrt{1-x}-1\right)^{12}}{\left(\sqrt{x+1}-1\right)^{12}}+\frac{98 \left(\sqrt{1-x}-1\right)^{10}}{\left(\sqrt{x+1}-1\right)^{10}}-\frac{119 \left(\sqrt{1-x}-1\right)^8}{\left(\sqrt{x+1}-1\right)^8}+\frac{92 \left(\sqrt{1-x}-1\right)^6}{\left(\sqrt{x+1}-1\right)^6}-\frac{119 \left(\sqrt{1-x}-1\right)^4}{\left(\sqrt{x+1}-1\right)^4}+\frac{98 \left(\sqrt{1-x}-1\right)^2}{\left(\sqrt{x+1}-1\right)^2}+7\right)}{\left(-x-2 \sqrt{1-x}+\sqrt{1-x} \sqrt{x+1}+1\right)^7}","\frac{(x+1)^{7/2}}{7 (1-x)^{7/2}}",1,"((-1/224 + Sqrt[1 - x]/224)*(-1 + Sqrt[1 + x])^13*(7 + (7*(-1 + Sqrt[1 - x])^12)/(-1 + Sqrt[1 + x])^12 + (98*(-1 + Sqrt[1 - x])^10)/(-1 + Sqrt[1 + x])^10 - (119*(-1 + Sqrt[1 - x])^8)/(-1 + Sqrt[1 + x])^8 + (92*(-1 + Sqrt[1 - x])^6)/(-1 + Sqrt[1 + x])^6 - (119*(-1 + Sqrt[1 - x])^4)/(-1 + Sqrt[1 + x])^4 + (98*(-1 + Sqrt[1 - x])^2)/(-1 + Sqrt[1 + x])^2))/(1 - 2*Sqrt[1 - x] - x + Sqrt[1 - x]*Sqrt[1 + x])^7","B",1
1099,1,480,41,1.9650952,"\int \frac{(1+x)^{5/2}}{(1-x)^{11/2}} \, dx","IntegrateAlgebraic[(1 + x)^(5/2)/(1 - x)^(11/2),x]","\frac{\left(\frac{\sqrt{1-x}}{8064}-\frac{1}{8064}\right) \left(\sqrt{x+1}-1\right)^{17} \left(\frac{63 \left(\sqrt{1-x}-1\right)^{16}}{\left(\sqrt{x+1}-1\right)^{16}}+\frac{126 \left(\sqrt{1-x}-1\right)^{15}}{\left(\sqrt{x+1}-1\right)^{15}}+\frac{1428 \left(\sqrt{1-x}-1\right)^{14}}{\left(\sqrt{x+1}-1\right)^{14}}+\frac{1638 \left(\sqrt{1-x}-1\right)^{13}}{\left(\sqrt{x+1}-1\right)^{13}}+\frac{1260 \left(\sqrt{1-x}-1\right)^{12}}{\left(\sqrt{x+1}-1\right)^{12}}-\frac{3906 \left(\sqrt{1-x}-1\right)^{11}}{\left(\sqrt{x+1}-1\right)^{11}}-\frac{4500 \left(\sqrt{1-x}-1\right)^{10}}{\left(\sqrt{x+1}-1\right)^{10}}+\frac{3798 \left(\sqrt{1-x}-1\right)^9}{\left(\sqrt{x+1}-1\right)^9}+\frac{5546 \left(\sqrt{1-x}-1\right)^8}{\left(\sqrt{x+1}-1\right)^8}-\frac{3798 \left(\sqrt{1-x}-1\right)^7}{\left(\sqrt{x+1}-1\right)^7}-\frac{4500 \left(\sqrt{1-x}-1\right)^6}{\left(\sqrt{x+1}-1\right)^6}+\frac{3906 \left(\sqrt{1-x}-1\right)^5}{\left(\sqrt{x+1}-1\right)^5}+\frac{1260 \left(\sqrt{1-x}-1\right)^4}{\left(\sqrt{x+1}-1\right)^4}-\frac{1638 \left(\sqrt{1-x}-1\right)^3}{\left(\sqrt{x+1}-1\right)^3}+\frac{1428 \left(\sqrt{1-x}-1\right)^2}{\left(\sqrt{x+1}-1\right)^2}-\frac{126 \left(\sqrt{1-x}-1\right)}{\sqrt{x+1}-1}+63\right)}{\left(-x-2 \sqrt{1-x}+\sqrt{1-x} \sqrt{x+1}+1\right)^9}","\frac{(x+1)^{7/2}}{63 (1-x)^{7/2}}+\frac{(x+1)^{7/2}}{9 (1-x)^{9/2}}",1,"((-1/8064 + Sqrt[1 - x]/8064)*(-1 + Sqrt[1 + x])^17*(63 + (63*(-1 + Sqrt[1 - x])^16)/(-1 + Sqrt[1 + x])^16 + (126*(-1 + Sqrt[1 - x])^15)/(-1 + Sqrt[1 + x])^15 + (1428*(-1 + Sqrt[1 - x])^14)/(-1 + Sqrt[1 + x])^14 + (1638*(-1 + Sqrt[1 - x])^13)/(-1 + Sqrt[1 + x])^13 + (1260*(-1 + Sqrt[1 - x])^12)/(-1 + Sqrt[1 + x])^12 - (3906*(-1 + Sqrt[1 - x])^11)/(-1 + Sqrt[1 + x])^11 - (4500*(-1 + Sqrt[1 - x])^10)/(-1 + Sqrt[1 + x])^10 + (3798*(-1 + Sqrt[1 - x])^9)/(-1 + Sqrt[1 + x])^9 + (5546*(-1 + Sqrt[1 - x])^8)/(-1 + Sqrt[1 + x])^8 - (3798*(-1 + Sqrt[1 - x])^7)/(-1 + Sqrt[1 + x])^7 - (4500*(-1 + Sqrt[1 - x])^6)/(-1 + Sqrt[1 + x])^6 + (3906*(-1 + Sqrt[1 - x])^5)/(-1 + Sqrt[1 + x])^5 + (1260*(-1 + Sqrt[1 - x])^4)/(-1 + Sqrt[1 + x])^4 - (1638*(-1 + Sqrt[1 - x])^3)/(-1 + Sqrt[1 + x])^3 + (1428*(-1 + Sqrt[1 - x])^2)/(-1 + Sqrt[1 + x])^2 - (126*(-1 + Sqrt[1 - x]))/(-1 + Sqrt[1 + x])))/(1 - 2*Sqrt[1 - x] - x + Sqrt[1 - x]*Sqrt[1 + x])^9","B",1
1100,1,584,61,4.1550564,"\int \frac{(1+x)^{5/2}}{(1-x)^{13/2}} \, dx","IntegrateAlgebraic[(1 + x)^(5/2)/(1 - x)^(13/2),x]","\frac{\left(\frac{\sqrt{1-x}}{354816}-\frac{1}{354816}\right) \left(\sqrt{x+1}-1\right)^{21} \left(\frac{693 \left(\sqrt{1-x}-1\right)^{20}}{\left(\sqrt{x+1}-1\right)^{20}}+\frac{2772 \left(\sqrt{1-x}-1\right)^{19}}{\left(\sqrt{x+1}-1\right)^{19}}+\frac{25410 \left(\sqrt{1-x}-1\right)^{18}}{\left(\sqrt{x+1}-1\right)^{18}}+\frac{60060 \left(\sqrt{1-x}-1\right)^{17}}{\left(\sqrt{x+1}-1\right)^{17}}+\frac{112497 \left(\sqrt{1-x}-1\right)^{16}}{\left(\sqrt{x+1}-1\right)^{16}}-\frac{7392 \left(\sqrt{1-x}-1\right)^{15}}{\left(\sqrt{x+1}-1\right)^{15}}-\frac{229416 \left(\sqrt{1-x}-1\right)^{14}}{\left(\sqrt{x+1}-1\right)^{14}}-\frac{253440 \left(\sqrt{1-x}-1\right)^{13}}{\left(\sqrt{x+1}-1\right)^{13}}+\frac{238810 \left(\sqrt{1-x}-1\right)^{12}}{\left(\sqrt{x+1}-1\right)^{12}}+\frac{442024 \left(\sqrt{1-x}-1\right)^{11}}{\left(\sqrt{x+1}-1\right)^{11}}-\frac{215092 \left(\sqrt{1-x}-1\right)^{10}}{\left(\sqrt{x+1}-1\right)^{10}}-\frac{442024 \left(\sqrt{1-x}-1\right)^9}{\left(\sqrt{x+1}-1\right)^9}+\frac{238810 \left(\sqrt{1-x}-1\right)^8}{\left(\sqrt{x+1}-1\right)^8}+\frac{253440 \left(\sqrt{1-x}-1\right)^7}{\left(\sqrt{x+1}-1\right)^7}-\frac{229416 \left(\sqrt{1-x}-1\right)^6}{\left(\sqrt{x+1}-1\right)^6}+\frac{7392 \left(\sqrt{1-x}-1\right)^5}{\left(\sqrt{x+1}-1\right)^5}+\frac{112497 \left(\sqrt{1-x}-1\right)^4}{\left(\sqrt{x+1}-1\right)^4}-\frac{60060 \left(\sqrt{1-x}-1\right)^3}{\left(\sqrt{x+1}-1\right)^3}+\frac{25410 \left(\sqrt{1-x}-1\right)^2}{\left(\sqrt{x+1}-1\right)^2}-\frac{2772 \left(\sqrt{1-x}-1\right)}{\sqrt{x+1}-1}+693\right)}{\left(-x-2 \sqrt{1-x}+\sqrt{1-x} \sqrt{x+1}+1\right)^{11}}","\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,"((-1/354816 + Sqrt[1 - x]/354816)*(-1 + Sqrt[1 + x])^21*(693 + (693*(-1 + Sqrt[1 - x])^20)/(-1 + Sqrt[1 + x])^20 + (2772*(-1 + Sqrt[1 - x])^19)/(-1 + Sqrt[1 + x])^19 + (25410*(-1 + Sqrt[1 - x])^18)/(-1 + Sqrt[1 + x])^18 + (60060*(-1 + Sqrt[1 - x])^17)/(-1 + Sqrt[1 + x])^17 + (112497*(-1 + Sqrt[1 - x])^16)/(-1 + Sqrt[1 + x])^16 - (7392*(-1 + Sqrt[1 - x])^15)/(-1 + Sqrt[1 + x])^15 - (229416*(-1 + Sqrt[1 - x])^14)/(-1 + Sqrt[1 + x])^14 - (253440*(-1 + Sqrt[1 - x])^13)/(-1 + Sqrt[1 + x])^13 + (238810*(-1 + Sqrt[1 - x])^12)/(-1 + Sqrt[1 + x])^12 + (442024*(-1 + Sqrt[1 - x])^11)/(-1 + Sqrt[1 + x])^11 - (215092*(-1 + Sqrt[1 - x])^10)/(-1 + Sqrt[1 + x])^10 - (442024*(-1 + Sqrt[1 - x])^9)/(-1 + Sqrt[1 + x])^9 + (238810*(-1 + Sqrt[1 - x])^8)/(-1 + Sqrt[1 + x])^8 + (253440*(-1 + Sqrt[1 - x])^7)/(-1 + Sqrt[1 + x])^7 - (229416*(-1 + Sqrt[1 - x])^6)/(-1 + Sqrt[1 + x])^6 + (7392*(-1 + Sqrt[1 - x])^5)/(-1 + Sqrt[1 + x])^5 + (112497*(-1 + Sqrt[1 - x])^4)/(-1 + Sqrt[1 + x])^4 - (60060*(-1 + Sqrt[1 - x])^3)/(-1 + Sqrt[1 + x])^3 + (25410*(-1 + Sqrt[1 - x])^2)/(-1 + Sqrt[1 + x])^2 - (2772*(-1 + Sqrt[1 - x]))/(-1 + Sqrt[1 + x])))/(1 - 2*Sqrt[1 - x] - x + Sqrt[1 - x]*Sqrt[1 + x])^11","B",1
1101,1,688,81,7.9435347,"\int \frac{(1+x)^{5/2}}{(1-x)^{15/2}} \, dx","IntegrateAlgebraic[(1 + x)^(5/2)/(1 - x)^(15/2),x]","\frac{\left(\frac{\sqrt{1-x}}{6150144}-\frac{1}{6150144}\right) \left(\sqrt{x+1}-1\right)^{25} \left(\frac{3003 \left(\sqrt{1-x}-1\right)^{24}}{\left(\sqrt{x+1}-1\right)^{24}}+\frac{18018 \left(\sqrt{1-x}-1\right)^{23}}{\left(\sqrt{x+1}-1\right)^{23}}+\frac{168168 \left(\sqrt{1-x}-1\right)^{22}}{\left(\sqrt{x+1}-1\right)^{22}}+\frac{594594 \left(\sqrt{1-x}-1\right)^{21}}{\left(\sqrt{x+1}-1\right)^{21}}+\frac{1615614 \left(\sqrt{1-x}-1\right)^{20}}{\left(\sqrt{x+1}-1\right)^{20}}+\frac{1735734 \left(\sqrt{1-x}-1\right)^{19}}{\left(\sqrt{x+1}-1\right)^{19}}-\frac{861432 \left(\sqrt{1-x}-1\right)^{18}}{\left(\sqrt{x+1}-1\right)^{18}}-\frac{6199050 \left(\sqrt{1-x}-1\right)^{17}}{\left(\sqrt{x+1}-1\right)^{17}}-\frac{4494347 \left(\sqrt{1-x}-1\right)^{16}}{\left(\sqrt{x+1}-1\right)^{16}}+\frac{7121972 \left(\sqrt{1-x}-1\right)^{15}}{\left(\sqrt{x+1}-1\right)^{15}}+\frac{11103248 \left(\sqrt{1-x}-1\right)^{14}}{\left(\sqrt{x+1}-1\right)^{14}}-\frac{5967052 \left(\sqrt{1-x}-1\right)^{13}}{\left(\sqrt{x+1}-1\right)^{13}}-\frac{13798748 \left(\sqrt{1-x}-1\right)^{12}}{\left(\sqrt{x+1}-1\right)^{12}}+\frac{5967052 \left(\sqrt{1-x}-1\right)^{11}}{\left(\sqrt{x+1}-1\right)^{11}}+\frac{11103248 \left(\sqrt{1-x}-1\right)^{10}}{\left(\sqrt{x+1}-1\right)^{10}}-\frac{7121972 \left(\sqrt{1-x}-1\right)^9}{\left(\sqrt{x+1}-1\right)^9}-\frac{4494347 \left(\sqrt{1-x}-1\right)^8}{\left(\sqrt{x+1}-1\right)^8}+\frac{6199050 \left(\sqrt{1-x}-1\right)^7}{\left(\sqrt{x+1}-1\right)^7}-\frac{861432 \left(\sqrt{1-x}-1\right)^6}{\left(\sqrt{x+1}-1\right)^6}-\frac{1735734 \left(\sqrt{1-x}-1\right)^5}{\left(\sqrt{x+1}-1\right)^5}+\frac{1615614 \left(\sqrt{1-x}-1\right)^4}{\left(\sqrt{x+1}-1\right)^4}-\frac{594594 \left(\sqrt{1-x}-1\right)^3}{\left(\sqrt{x+1}-1\right)^3}+\frac{168168 \left(\sqrt{1-x}-1\right)^2}{\left(\sqrt{x+1}-1\right)^2}-\frac{18018 \left(\sqrt{1-x}-1\right)}{\sqrt{x+1}-1}+3003\right)}{\left(-x-2 \sqrt{1-x}+\sqrt{1-x} \sqrt{x+1}+1\right)^{13}}","\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,"((-1/6150144 + Sqrt[1 - x]/6150144)*(-1 + Sqrt[1 + x])^25*(3003 + (3003*(-1 + Sqrt[1 - x])^24)/(-1 + Sqrt[1 + x])^24 + (18018*(-1 + Sqrt[1 - x])^23)/(-1 + Sqrt[1 + x])^23 + (168168*(-1 + Sqrt[1 - x])^22)/(-1 + Sqrt[1 + x])^22 + (594594*(-1 + Sqrt[1 - x])^21)/(-1 + Sqrt[1 + x])^21 + (1615614*(-1 + Sqrt[1 - x])^20)/(-1 + Sqrt[1 + x])^20 + (1735734*(-1 + Sqrt[1 - x])^19)/(-1 + Sqrt[1 + x])^19 - (861432*(-1 + Sqrt[1 - x])^18)/(-1 + Sqrt[1 + x])^18 - (6199050*(-1 + Sqrt[1 - x])^17)/(-1 + Sqrt[1 + x])^17 - (4494347*(-1 + Sqrt[1 - x])^16)/(-1 + Sqrt[1 + x])^16 + (7121972*(-1 + Sqrt[1 - x])^15)/(-1 + Sqrt[1 + x])^15 + (11103248*(-1 + Sqrt[1 - x])^14)/(-1 + Sqrt[1 + x])^14 - (5967052*(-1 + Sqrt[1 - x])^13)/(-1 + Sqrt[1 + x])^13 - (13798748*(-1 + Sqrt[1 - x])^12)/(-1 + Sqrt[1 + x])^12 + (5967052*(-1 + Sqrt[1 - x])^11)/(-1 + Sqrt[1 + x])^11 + (11103248*(-1 + Sqrt[1 - x])^10)/(-1 + Sqrt[1 + x])^10 - (7121972*(-1 + Sqrt[1 - x])^9)/(-1 + Sqrt[1 + x])^9 - (4494347*(-1 + Sqrt[1 - x])^8)/(-1 + Sqrt[1 + x])^8 + (6199050*(-1 + Sqrt[1 - x])^7)/(-1 + Sqrt[1 + x])^7 - (861432*(-1 + Sqrt[1 - x])^6)/(-1 + Sqrt[1 + x])^6 - (1735734*(-1 + Sqrt[1 - x])^5)/(-1 + Sqrt[1 + x])^5 + (1615614*(-1 + Sqrt[1 - x])^4)/(-1 + Sqrt[1 + x])^4 - (594594*(-1 + Sqrt[1 - x])^3)/(-1 + Sqrt[1 + x])^3 + (168168*(-1 + Sqrt[1 - x])^2)/(-1 + Sqrt[1 + x])^2 - (18018*(-1 + Sqrt[1 - x]))/(-1 + Sqrt[1 + x])))/(1 - 2*Sqrt[1 - x] - x + Sqrt[1 - x]*Sqrt[1 + x])^13","B",1
1102,1,792,101,14.7563709,"\int \frac{(1+x)^{5/2}}{(1-x)^{17/2}} \, dx","IntegrateAlgebraic[(1 + x)^(5/2)/(1 - x)^(17/2),x]","\frac{\left(\frac{\sqrt{1-x}}{369008640}-\frac{1}{369008640}\right) \left(\sqrt{x+1}-1\right)^{29} \left(\frac{45045 \left(\sqrt{1-x}-1\right)^{28}}{\left(\sqrt{x+1}-1\right)^{28}}+\frac{360360 \left(\sqrt{1-x}-1\right)^{27}}{\left(\sqrt{x+1}-1\right)^{27}}+\frac{3633630 \left(\sqrt{1-x}-1\right)^{26}}{\left(\sqrt{x+1}-1\right)^{26}}+\frac{16936920 \left(\sqrt{1-x}-1\right)^{25}}{\left(\sqrt{x+1}-1\right)^{25}}+\frac{59738679 \left(\sqrt{1-x}-1\right)^{24}}{\left(\sqrt{x+1}-1\right)^{24}}+\frac{116996880 \left(\sqrt{1-x}-1\right)^{23}}{\left(\sqrt{x+1}-1\right)^{23}}+\frac{100926540 \left(\sqrt{1-x}-1\right)^{22}}{\left(\sqrt{x+1}-1\right)^{22}}-\frac{167515920 \left(\sqrt{1-x}-1\right)^{21}}{\left(\sqrt{x+1}-1\right)^{21}}-\frac{495816035 \left(\sqrt{1-x}-1\right)^{20}}{\left(\sqrt{x+1}-1\right)^{20}}-\frac{250209960 \left(\sqrt{1-x}-1\right)^{19}}{\left(\sqrt{x+1}-1\right)^{19}}+\frac{742202370 \left(\sqrt{1-x}-1\right)^{18}}{\left(\sqrt{x+1}-1\right)^{18}}+\frac{892538920 \left(\sqrt{1-x}-1\right)^{17}}{\left(\sqrt{x+1}-1\right)^{17}}-\frac{660962505 \left(\sqrt{1-x}-1\right)^{16}}{\left(\sqrt{x+1}-1\right)^{16}}-\frac{1345547040 \left(\sqrt{1-x}-1\right)^{15}}{\left(\sqrt{x+1}-1\right)^{15}}+\frac{569981864 \left(\sqrt{1-x}-1\right)^{14}}{\left(\sqrt{x+1}-1\right)^{14}}+\frac{1345547040 \left(\sqrt{1-x}-1\right)^{13}}{\left(\sqrt{x+1}-1\right)^{13}}-\frac{660962505 \left(\sqrt{1-x}-1\right)^{12}}{\left(\sqrt{x+1}-1\right)^{12}}-\frac{892538920 \left(\sqrt{1-x}-1\right)^{11}}{\left(\sqrt{x+1}-1\right)^{11}}+\frac{742202370 \left(\sqrt{1-x}-1\right)^{10}}{\left(\sqrt{x+1}-1\right)^{10}}+\frac{250209960 \left(\sqrt{1-x}-1\right)^9}{\left(\sqrt{x+1}-1\right)^9}-\frac{495816035 \left(\sqrt{1-x}-1\right)^8}{\left(\sqrt{x+1}-1\right)^8}+\frac{167515920 \left(\sqrt{1-x}-1\right)^7}{\left(\sqrt{x+1}-1\right)^7}+\frac{100926540 \left(\sqrt{1-x}-1\right)^6}{\left(\sqrt{x+1}-1\right)^6}-\frac{116996880 \left(\sqrt{1-x}-1\right)^5}{\left(\sqrt{x+1}-1\right)^5}+\frac{59738679 \left(\sqrt{1-x}-1\right)^4}{\left(\sqrt{x+1}-1\right)^4}-\frac{16936920 \left(\sqrt{1-x}-1\right)^3}{\left(\sqrt{x+1}-1\right)^3}+\frac{3633630 \left(\sqrt{1-x}-1\right)^2}{\left(\sqrt{x+1}-1\right)^2}-\frac{360360 \left(\sqrt{1-x}-1\right)}{\sqrt{x+1}-1}+45045\right)}{\left(-x-2 \sqrt{1-x}+\sqrt{1-x} \sqrt{x+1}+1\right)^{15}}","\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,"((-1/369008640 + Sqrt[1 - x]/369008640)*(-1 + Sqrt[1 + x])^29*(45045 + (45045*(-1 + Sqrt[1 - x])^28)/(-1 + Sqrt[1 + x])^28 + (360360*(-1 + Sqrt[1 - x])^27)/(-1 + Sqrt[1 + x])^27 + (3633630*(-1 + Sqrt[1 - x])^26)/(-1 + Sqrt[1 + x])^26 + (16936920*(-1 + Sqrt[1 - x])^25)/(-1 + Sqrt[1 + x])^25 + (59738679*(-1 + Sqrt[1 - x])^24)/(-1 + Sqrt[1 + x])^24 + (116996880*(-1 + Sqrt[1 - x])^23)/(-1 + Sqrt[1 + x])^23 + (100926540*(-1 + Sqrt[1 - x])^22)/(-1 + Sqrt[1 + x])^22 - (167515920*(-1 + Sqrt[1 - x])^21)/(-1 + Sqrt[1 + x])^21 - (495816035*(-1 + Sqrt[1 - x])^20)/(-1 + Sqrt[1 + x])^20 - (250209960*(-1 + Sqrt[1 - x])^19)/(-1 + Sqrt[1 + x])^19 + (742202370*(-1 + Sqrt[1 - x])^18)/(-1 + Sqrt[1 + x])^18 + (892538920*(-1 + Sqrt[1 - x])^17)/(-1 + Sqrt[1 + x])^17 - (660962505*(-1 + Sqrt[1 - x])^16)/(-1 + Sqrt[1 + x])^16 - (1345547040*(-1 + Sqrt[1 - x])^15)/(-1 + Sqrt[1 + x])^15 + (569981864*(-1 + Sqrt[1 - x])^14)/(-1 + Sqrt[1 + x])^14 + (1345547040*(-1 + Sqrt[1 - x])^13)/(-1 + Sqrt[1 + x])^13 - (660962505*(-1 + Sqrt[1 - x])^12)/(-1 + Sqrt[1 + x])^12 - (892538920*(-1 + Sqrt[1 - x])^11)/(-1 + Sqrt[1 + x])^11 + (742202370*(-1 + Sqrt[1 - x])^10)/(-1 + Sqrt[1 + x])^10 + (250209960*(-1 + Sqrt[1 - x])^9)/(-1 + Sqrt[1 + x])^9 - (495816035*(-1 + Sqrt[1 - x])^8)/(-1 + Sqrt[1 + x])^8 + (167515920*(-1 + Sqrt[1 - x])^7)/(-1 + Sqrt[1 + x])^7 + (100926540*(-1 + Sqrt[1 - x])^6)/(-1 + Sqrt[1 + x])^6 - (116996880*(-1 + Sqrt[1 - x])^5)/(-1 + Sqrt[1 + x])^5 + (59738679*(-1 + Sqrt[1 - x])^4)/(-1 + Sqrt[1 + x])^4 - (16936920*(-1 + Sqrt[1 - x])^3)/(-1 + Sqrt[1 + x])^3 + (3633630*(-1 + Sqrt[1 - x])^2)/(-1 + Sqrt[1 + x])^2 - (360360*(-1 + Sqrt[1 - x]))/(-1 + Sqrt[1 + x])))/(1 - 2*Sqrt[1 - x] - x + Sqrt[1 - x]*Sqrt[1 + x])^15","B",1
1103,1,896,121,27.0619305,"\int \frac{(1+x)^{5/2}}{(1-x)^{19/2}} \, dx","IntegrateAlgebraic[(1 + x)^(5/2)/(1 - x)^(19/2),x]","\frac{\left(\frac{\sqrt{1-x}}{5018517504}-\frac{1}{5018517504}\right) \left(\sqrt{x+1}-1\right)^{33} \left(\frac{153153 \left(\sqrt{1-x}-1\right)^{32}}{\left(\sqrt{x+1}-1\right)^{32}}+\frac{1531530 \left(\sqrt{1-x}-1\right)^{31}}{\left(\sqrt{x+1}-1\right)^{31}}+\frac{16948932 \left(\sqrt{1-x}-1\right)^{30}}{\left(\sqrt{x+1}-1\right)^{30}}+\frac{97507410 \left(\sqrt{1-x}-1\right)^{29}}{\left(\sqrt{x+1}-1\right)^{29}}+\frac{422293872 \left(\sqrt{1-x}-1\right)^{28}}{\left(\sqrt{x+1}-1\right)^{28}}+\frac{1161001842 \left(\sqrt{1-x}-1\right)^{27}}{\left(\sqrt{x+1}-1\right)^{27}}+\frac{1969897644 \left(\sqrt{1-x}-1\right)^{26}}{\left(\sqrt{x+1}-1\right)^{26}}+\frac{750201738 \left(\sqrt{1-x}-1\right)^{25}}{\left(\sqrt{x+1}-1\right)^{25}}-\frac{4251984308 \left(\sqrt{1-x}-1\right)^{24}}{\left(\sqrt{x+1}-1\right)^{24}}-\frac{8952308222 \left(\sqrt{1-x}-1\right)^{23}}{\left(\sqrt{x+1}-1\right)^{23}}-\frac{1496395420 \left(\sqrt{1-x}-1\right)^{22}}{\left(\sqrt{x+1}-1\right)^{22}}+\frac{16166341386 \left(\sqrt{1-x}-1\right)^{21}}{\left(\sqrt{x+1}-1\right)^{21}}+\frac{15309782480 \left(\sqrt{1-x}-1\right)^{20}}{\left(\sqrt{x+1}-1\right)^{20}}-\frac{16857002902 \left(\sqrt{1-x}-1\right)^{19}}{\left(\sqrt{x+1}-1\right)^{19}}-\frac{28048011476 \left(\sqrt{1-x}-1\right)^{18}}{\left(\sqrt{x+1}-1\right)^{18}}+\frac{13955642754 \left(\sqrt{1-x}-1\right)^{17}}{\left(\sqrt{x+1}-1\right)^{17}}+\frac{33023113318 \left(\sqrt{1-x}-1\right)^{16}}{\left(\sqrt{x+1}-1\right)^{16}}-\frac{13955642754 \left(\sqrt{1-x}-1\right)^{15}}{\left(\sqrt{x+1}-1\right)^{15}}-\frac{28048011476 \left(\sqrt{1-x}-1\right)^{14}}{\left(\sqrt{x+1}-1\right)^{14}}+\frac{16857002902 \left(\sqrt{1-x}-1\right)^{13}}{\left(\sqrt{x+1}-1\right)^{13}}+\frac{15309782480 \left(\sqrt{1-x}-1\right)^{12}}{\left(\sqrt{x+1}-1\right)^{12}}-\frac{16166341386 \left(\sqrt{1-x}-1\right)^{11}}{\left(\sqrt{x+1}-1\right)^{11}}-\frac{1496395420 \left(\sqrt{1-x}-1\right)^{10}}{\left(\sqrt{x+1}-1\right)^{10}}+\frac{8952308222 \left(\sqrt{1-x}-1\right)^9}{\left(\sqrt{x+1}-1\right)^9}-\frac{4251984308 \left(\sqrt{1-x}-1\right)^8}{\left(\sqrt{x+1}-1\right)^8}-\frac{750201738 \left(\sqrt{1-x}-1\right)^7}{\left(\sqrt{x+1}-1\right)^7}+\frac{1969897644 \left(\sqrt{1-x}-1\right)^6}{\left(\sqrt{x+1}-1\right)^6}-\frac{1161001842 \left(\sqrt{1-x}-1\right)^5}{\left(\sqrt{x+1}-1\right)^5}+\frac{422293872 \left(\sqrt{1-x}-1\right)^4}{\left(\sqrt{x+1}-1\right)^4}-\frac{97507410 \left(\sqrt{1-x}-1\right)^3}{\left(\sqrt{x+1}-1\right)^3}+\frac{16948932 \left(\sqrt{1-x}-1\right)^2}{\left(\sqrt{x+1}-1\right)^2}-\frac{1531530 \left(\sqrt{1-x}-1\right)}{\sqrt{x+1}-1}+153153\right)}{\left(-x-2 \sqrt{1-x}+\sqrt{1-x} \sqrt{x+1}+1\right)^{17}}","\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,"((-1/5018517504 + Sqrt[1 - x]/5018517504)*(-1 + Sqrt[1 + x])^33*(153153 + (153153*(-1 + Sqrt[1 - x])^32)/(-1 + Sqrt[1 + x])^32 + (1531530*(-1 + Sqrt[1 - x])^31)/(-1 + Sqrt[1 + x])^31 + (16948932*(-1 + Sqrt[1 - x])^30)/(-1 + Sqrt[1 + x])^30 + (97507410*(-1 + Sqrt[1 - x])^29)/(-1 + Sqrt[1 + x])^29 + (422293872*(-1 + Sqrt[1 - x])^28)/(-1 + Sqrt[1 + x])^28 + (1161001842*(-1 + Sqrt[1 - x])^27)/(-1 + Sqrt[1 + x])^27 + (1969897644*(-1 + Sqrt[1 - x])^26)/(-1 + Sqrt[1 + x])^26 + (750201738*(-1 + Sqrt[1 - x])^25)/(-1 + Sqrt[1 + x])^25 - (4251984308*(-1 + Sqrt[1 - x])^24)/(-1 + Sqrt[1 + x])^24 - (8952308222*(-1 + Sqrt[1 - x])^23)/(-1 + Sqrt[1 + x])^23 - (1496395420*(-1 + Sqrt[1 - x])^22)/(-1 + Sqrt[1 + x])^22 + (16166341386*(-1 + Sqrt[1 - x])^21)/(-1 + Sqrt[1 + x])^21 + (15309782480*(-1 + Sqrt[1 - x])^20)/(-1 + Sqrt[1 + x])^20 - (16857002902*(-1 + Sqrt[1 - x])^19)/(-1 + Sqrt[1 + x])^19 - (28048011476*(-1 + Sqrt[1 - x])^18)/(-1 + Sqrt[1 + x])^18 + (13955642754*(-1 + Sqrt[1 - x])^17)/(-1 + Sqrt[1 + x])^17 + (33023113318*(-1 + Sqrt[1 - x])^16)/(-1 + Sqrt[1 + x])^16 - (13955642754*(-1 + Sqrt[1 - x])^15)/(-1 + Sqrt[1 + x])^15 - (28048011476*(-1 + Sqrt[1 - x])^14)/(-1 + Sqrt[1 + x])^14 + (16857002902*(-1 + Sqrt[1 - x])^13)/(-1 + Sqrt[1 + x])^13 + (15309782480*(-1 + Sqrt[1 - x])^12)/(-1 + Sqrt[1 + x])^12 - (16166341386*(-1 + Sqrt[1 - x])^11)/(-1 + Sqrt[1 + x])^11 - (1496395420*(-1 + Sqrt[1 - x])^10)/(-1 + Sqrt[1 + x])^10 + (8952308222*(-1 + Sqrt[1 - x])^9)/(-1 + Sqrt[1 + x])^9 - (4251984308*(-1 + Sqrt[1 - x])^8)/(-1 + Sqrt[1 + x])^8 - (750201738*(-1 + Sqrt[1 - x])^7)/(-1 + Sqrt[1 + x])^7 + (1969897644*(-1 + Sqrt[1 - x])^6)/(-1 + Sqrt[1 + x])^6 - (1161001842*(-1 + Sqrt[1 - x])^5)/(-1 + Sqrt[1 + x])^5 + (422293872*(-1 + Sqrt[1 - x])^4)/(-1 + Sqrt[1 + x])^4 - (97507410*(-1 + Sqrt[1 - x])^3)/(-1 + Sqrt[1 + x])^3 + (16948932*(-1 + Sqrt[1 - x])^2)/(-1 + Sqrt[1 + x])^2 - (1531530*(-1 + Sqrt[1 - x]))/(-1 + Sqrt[1 + x])))/(1 - 2*Sqrt[1 - x] - x + Sqrt[1 - x]*Sqrt[1 + x])^17","B",1
1104,-1,0,64,180.3082382,"\int \frac{(1+a x)^{3/2}}{\sqrt{1-a x}} \, dx","IntegrateAlgebraic[(1 + a*x)^(3/2)/Sqrt[1 - a*x],x]","\text{\$Aborted}","-\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,"$Aborted","F",-1
1105,1,72,62,0.3216238,"\int \frac{(1+a x) \sqrt{1-a^2 x^2}}{1-a x} \, dx","IntegrateAlgebraic[((1 + a*x)*Sqrt[1 - a^2*x^2])/(1 - a*x),x]","\frac{\sqrt{1-a^2 x^2} (-a x-4)}{2 a}+\frac{3 \sqrt{-a^2} \log \left(\sqrt{1-a^2 x^2}-\sqrt{-a^2} x\right)}{2 a^2}","-\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,"((-4 - a*x)*Sqrt[1 - a^2*x^2])/(2*a) + (3*Sqrt[-a^2]*Log[-(Sqrt[-a^2]*x) + Sqrt[1 - a^2*x^2]])/(2*a^2)","A",1
1106,1,404,87,0.2680451,"\int \frac{(1-x)^{7/2}}{\sqrt{1+x}} \, dx","IntegrateAlgebraic[(1 - x)^(7/2)/Sqrt[1 + x],x]","\frac{\left(\frac{2}{3}-\frac{2 \sqrt{1-x}}{3}\right) \left(\sqrt{x+1}-1\right) \left(6 x^7+42 \sqrt{1-x} x^6-42 \sqrt{x+1} x^6-32 x^6+322 \sqrt{1-x} x^5-270 \sqrt{1-x} \sqrt{x+1} x^5+770 \sqrt{x+1} x^5-1293 x^5-3353 \sqrt{1-x} x^4+1440 \sqrt{1-x} \sqrt{x+1} x^4-2471 \sqrt{x+1} x^4+7168 x^4+10067 \sqrt{1-x} x^3-1941 \sqrt{1-x} \sqrt{x+1} x^3+1555 \sqrt{x+1} x^3-17181 x^3-21016 \sqrt{1-x} x^2-1728 \sqrt{1-x} \sqrt{x+1} x^2+6296 \sqrt{x+1} x^2+36544 x^2+19516 \sqrt{1-x} x+23004 \sqrt{1-x} \sqrt{x+1} x-61636 \sqrt{x+1} x+18468 x+81272 \sqrt{1-x}-81920 \sqrt{1-x} \sqrt{x+1}+82568 \sqrt{x+1}-81920\right)}{\left(\sqrt{1-x}+\sqrt{x+1}-2\right)^8}+\frac{35}{2} \tan ^{-1}\left(\frac{\sqrt{x+1}-1}{\sqrt{1-x}-1}\right)","\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,"((2/3 - (2*Sqrt[1 - x])/3)*(-1 + Sqrt[1 + x])*(-81920 + 81272*Sqrt[1 - x] + 18468*x + 19516*Sqrt[1 - x]*x + 36544*x^2 - 21016*Sqrt[1 - x]*x^2 - 17181*x^3 + 10067*Sqrt[1 - x]*x^3 + 7168*x^4 - 3353*Sqrt[1 - x]*x^4 - 1293*x^5 + 322*Sqrt[1 - x]*x^5 - 32*x^6 + 42*Sqrt[1 - x]*x^6 + 6*x^7 + 82568*Sqrt[1 + x] - 81920*Sqrt[1 - x]*Sqrt[1 + x] - 61636*x*Sqrt[1 + x] + 23004*Sqrt[1 - x]*x*Sqrt[1 + x] + 6296*x^2*Sqrt[1 + x] - 1728*Sqrt[1 - x]*x^2*Sqrt[1 + x] + 1555*x^3*Sqrt[1 + x] - 1941*Sqrt[1 - x]*x^3*Sqrt[1 + x] - 2471*x^4*Sqrt[1 + x] + 1440*Sqrt[1 - x]*x^4*Sqrt[1 + x] + 770*x^5*Sqrt[1 + x] - 270*Sqrt[1 - x]*x^5*Sqrt[1 + x] - 42*x^6*Sqrt[1 + x]))/(-2 + Sqrt[1 - x] + Sqrt[1 + x])^8 + (35*ArcTan[(-1 + Sqrt[1 + x])/(-1 + Sqrt[1 - x])])/2","B",1
1107,1,314,67,0.2219455,"\int \frac{(1-x)^{5/2}}{\sqrt{1+x}} \, dx","IntegrateAlgebraic[(1 - x)^(5/2)/Sqrt[1 + x],x]","\frac{\left(\frac{4}{3}-\frac{4 \sqrt{1-x}}{3}\right) \left(\sqrt{x+1}-1\right) \left(-10 \sqrt{1-x} x^4+2 \sqrt{1-x} \sqrt{x+1} x^4-10 \sqrt{x+1} x^4+44 x^4+95 \sqrt{1-x} x^3-9 \sqrt{1-x} \sqrt{x+1} x^3-5 \sqrt{x+1} x^3-198 x^3-267 \sqrt{1-x} x^2-62 \sqrt{1-x} \sqrt{x+1} x^2+183 \sqrt{x+1} x^2+462 x^2+362 \sqrt{1-x} x+378 \sqrt{1-x} \sqrt{x+1} x-974 \sqrt{x+1} x+198 x+1372 \sqrt{1-x}-1408 \sqrt{1-x} \sqrt{x+1}+1444 \sqrt{x+1}-1408\right)}{\left(\sqrt{1-x}+\sqrt{x+1}-2\right)^6}+10 \tan ^{-1}\left(\frac{\sqrt{x+1}-1}{\sqrt{1-x}-1}\right)","\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,"((4/3 - (4*Sqrt[1 - x])/3)*(-1 + Sqrt[1 + x])*(-1408 + 1372*Sqrt[1 - x] + 198*x + 362*Sqrt[1 - x]*x + 462*x^2 - 267*Sqrt[1 - x]*x^2 - 198*x^3 + 95*Sqrt[1 - x]*x^3 + 44*x^4 - 10*Sqrt[1 - x]*x^4 + 1444*Sqrt[1 + x] - 1408*Sqrt[1 - x]*Sqrt[1 + x] - 974*x*Sqrt[1 + x] + 378*Sqrt[1 - x]*x*Sqrt[1 + x] + 183*x^2*Sqrt[1 + x] - 62*Sqrt[1 - x]*x^2*Sqrt[1 + x] - 5*x^3*Sqrt[1 + x] - 9*Sqrt[1 - x]*x^3*Sqrt[1 + x] - 10*x^4*Sqrt[1 + x] + 2*Sqrt[1 - x]*x^4*Sqrt[1 + x]))/(-2 + Sqrt[1 - x] + Sqrt[1 + x])^6 + 10*ArcTan[(-1 + Sqrt[1 + x])/(-1 + Sqrt[1 - x])]","B",1
1108,1,188,47,0.1249747,"\int \frac{(1-x)^{3/2}}{\sqrt{1+x}} \, dx","IntegrateAlgebraic[(1 - x)^(3/2)/Sqrt[1 + x],x]","\frac{\left(2 \sqrt{1-x}-2\right) \left(\sqrt{x+1}-1\right) \left(x^3+3 \sqrt{1-x} x^2-3 \sqrt{x+1} x^2-4 x^2-7 \sqrt{1-x} x-7 \sqrt{1-x} \sqrt{x+1} x+17 \sqrt{x+1} x-x-30 \sqrt{1-x}+32 \sqrt{1-x} \sqrt{x+1}-34 \sqrt{x+1}+32\right)}{\left(\sqrt{1-x}+\sqrt{x+1}-2\right)^4}+6 \tan ^{-1}\left(\frac{\sqrt{x+1}-1}{\sqrt{1-x}-1}\right)","\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,"((-2 + 2*Sqrt[1 - x])*(-1 + Sqrt[1 + x])*(32 - 30*Sqrt[1 - x] - x - 7*Sqrt[1 - x]*x - 4*x^2 + 3*Sqrt[1 - x]*x^2 + x^3 - 34*Sqrt[1 + x] + 32*Sqrt[1 - x]*Sqrt[1 + x] + 17*x*Sqrt[1 + x] - 7*Sqrt[1 - x]*x*Sqrt[1 + x] - 3*x^2*Sqrt[1 + x]))/(-2 + Sqrt[1 - x] + Sqrt[1 + x])^4 + 6*ArcTan[(-1 + Sqrt[1 + x])/(-1 + Sqrt[1 - x])]","B",1
1109,1,73,20,0.0486755,"\int \frac{\sqrt{1-x}}{\sqrt{1+x}} \, dx","IntegrateAlgebraic[Sqrt[1 - x]/Sqrt[1 + x],x]","\frac{2 \left(\sqrt{1-x}-1\right)^2 \left(\sqrt{x+1}-1\right)^2}{\left(\sqrt{1-x}+\sqrt{x+1}-2\right)^2}+4 \tan ^{-1}\left(\frac{\sqrt{x+1}-1}{\sqrt{1-x}-1}\right)","\sqrt{1-x} \sqrt{x+1}+\sin ^{-1}(x)",1,"(2*(-1 + Sqrt[1 - x])^2*(-1 + Sqrt[1 + x])^2)/(-2 + Sqrt[1 - x] + Sqrt[1 + x])^2 + 4*ArcTan[(-1 + Sqrt[1 + x])/(-1 + Sqrt[1 - x])]","B",1
1110,1,26,2,0.0221924,"\int \frac{1}{\sqrt{1-x} \sqrt{1+x}} \, dx","IntegrateAlgebraic[1/(Sqrt[1 - x]*Sqrt[1 + x]),x]","4 \tan ^{-1}\left(\frac{\sqrt{x+1}-1}{\sqrt{1-x}-1}\right)","\sin ^{-1}(x)",1,"4*ArcTan[(-1 + Sqrt[1 + x])/(-1 + Sqrt[1 - x])]","B",1
1111,1,58,17,0.0245829,"\int \frac{1}{(1-x)^{3/2} \sqrt{1+x}} \, dx","IntegrateAlgebraic[1/((1 - x)^(3/2)*Sqrt[1 + x]),x]","\frac{\left(2 \sqrt{1-x}-2\right) \left(\sqrt{x+1}-1\right)}{-x-2 \sqrt{1-x}+\sqrt{1-x} \sqrt{x+1}+1}","\frac{\sqrt{x+1}}{\sqrt{1-x}}",1,"((-2 + 2*Sqrt[1 - x])*(-1 + Sqrt[1 + x]))/(1 - 2*Sqrt[1 - x] - x + Sqrt[1 - x]*Sqrt[1 + x])","B",1
1112,1,168,41,0.0896776,"\int \frac{1}{(1-x)^{5/2} \sqrt{1+x}} \, dx","IntegrateAlgebraic[1/((1 - x)^(5/2)*Sqrt[1 + x]),x]","\frac{\left(\frac{\sqrt{1-x}}{6}-\frac{1}{6}\right) \left(\sqrt{x+1}-1\right)^5 \left(\frac{3 \left(\sqrt{1-x}-1\right)^4}{\left(\sqrt{x+1}-1\right)^4}+\frac{6 \left(\sqrt{1-x}-1\right)^3}{\left(\sqrt{x+1}-1\right)^3}+\frac{2 \left(\sqrt{1-x}-1\right)^2}{\left(\sqrt{x+1}-1\right)^2}-\frac{6 \left(\sqrt{1-x}-1\right)}{\sqrt{x+1}-1}+3\right)}{\left(-x-2 \sqrt{1-x}+\sqrt{1-x} \sqrt{x+1}+1\right)^3}","\frac{\sqrt{x+1}}{3 \sqrt{1-x}}+\frac{\sqrt{x+1}}{3 (1-x)^{3/2}}",1,"((-1/6 + Sqrt[1 - x]/6)*(-1 + Sqrt[1 + x])^5*(3 + (3*(-1 + Sqrt[1 - x])^4)/(-1 + Sqrt[1 + x])^4 + (6*(-1 + Sqrt[1 - x])^3)/(-1 + Sqrt[1 + x])^3 + (2*(-1 + Sqrt[1 - x])^2)/(-1 + Sqrt[1 + x])^2 - (6*(-1 + Sqrt[1 - x]))/(-1 + Sqrt[1 + x])))/(1 - 2*Sqrt[1 - x] - x + Sqrt[1 - x]*Sqrt[1 + x])^3","B",1
1113,1,272,61,0.2748777,"\int \frac{1}{(1-x)^{7/2} \sqrt{1+x}} \, dx","IntegrateAlgebraic[1/((1 - x)^(7/2)*Sqrt[1 + x]),x]","\frac{\left(\frac{\sqrt{1-x}}{120}-\frac{1}{120}\right) \left(\sqrt{x+1}-1\right)^9 \left(\frac{15 \left(\sqrt{1-x}-1\right)^8}{\left(\sqrt{x+1}-1\right)^8}+\frac{60 \left(\sqrt{1-x}-1\right)^7}{\left(\sqrt{x+1}-1\right)^7}+\frac{100 \left(\sqrt{1-x}-1\right)^6}{\left(\sqrt{x+1}-1\right)^6}-\frac{20 \left(\sqrt{1-x}-1\right)^5}{\left(\sqrt{x+1}-1\right)^5}-\frac{118 \left(\sqrt{1-x}-1\right)^4}{\left(\sqrt{x+1}-1\right)^4}+\frac{20 \left(\sqrt{1-x}-1\right)^3}{\left(\sqrt{x+1}-1\right)^3}+\frac{100 \left(\sqrt{1-x}-1\right)^2}{\left(\sqrt{x+1}-1\right)^2}-\frac{60 \left(\sqrt{1-x}-1\right)}{\sqrt{x+1}-1}+15\right)}{\left(-x-2 \sqrt{1-x}+\sqrt{1-x} \sqrt{x+1}+1\right)^5}","\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,"((-1/120 + Sqrt[1 - x]/120)*(-1 + Sqrt[1 + x])^9*(15 + (15*(-1 + Sqrt[1 - x])^8)/(-1 + Sqrt[1 + x])^8 + (60*(-1 + Sqrt[1 - x])^7)/(-1 + Sqrt[1 + x])^7 + (100*(-1 + Sqrt[1 - x])^6)/(-1 + Sqrt[1 + x])^6 - (20*(-1 + Sqrt[1 - x])^5)/(-1 + Sqrt[1 + x])^5 - (118*(-1 + Sqrt[1 - x])^4)/(-1 + Sqrt[1 + x])^4 + (20*(-1 + Sqrt[1 - x])^3)/(-1 + Sqrt[1 + x])^3 + (100*(-1 + Sqrt[1 - x])^2)/(-1 + Sqrt[1 + x])^2 - (60*(-1 + Sqrt[1 - x]))/(-1 + Sqrt[1 + x])))/(1 - 2*Sqrt[1 - x] - x + Sqrt[1 - x]*Sqrt[1 + x])^5","B",1
1114,1,376,81,0.7939312,"\int \frac{1}{(1-x)^{9/2} \sqrt{1+x}} \, dx","IntegrateAlgebraic[1/((1 - x)^(9/2)*Sqrt[1 + x]),x]","\frac{\left(\frac{\sqrt{1-x}}{1120}-\frac{1}{1120}\right) \left(\sqrt{x+1}-1\right)^{13} \left(\frac{35 \left(\sqrt{1-x}-1\right)^{12}}{\left(\sqrt{x+1}-1\right)^{12}}+\frac{210 \left(\sqrt{1-x}-1\right)^{11}}{\left(\sqrt{x+1}-1\right)^{11}}+\frac{630 \left(\sqrt{1-x}-1\right)^{10}}{\left(\sqrt{x+1}-1\right)^{10}}+\frac{630 \left(\sqrt{1-x}-1\right)^9}{\left(\sqrt{x+1}-1\right)^9}-\frac{483 \left(\sqrt{1-x}-1\right)^8}{\left(\sqrt{x+1}-1\right)^8}-\frac{1372 \left(\sqrt{1-x}-1\right)^7}{\left(\sqrt{x+1}-1\right)^7}+\frac{404 \left(\sqrt{1-x}-1\right)^6}{\left(\sqrt{x+1}-1\right)^6}+\frac{1372 \left(\sqrt{1-x}-1\right)^5}{\left(\sqrt{x+1}-1\right)^5}-\frac{483 \left(\sqrt{1-x}-1\right)^4}{\left(\sqrt{x+1}-1\right)^4}-\frac{630 \left(\sqrt{1-x}-1\right)^3}{\left(\sqrt{x+1}-1\right)^3}+\frac{630 \left(\sqrt{1-x}-1\right)^2}{\left(\sqrt{x+1}-1\right)^2}-\frac{210 \left(\sqrt{1-x}-1\right)}{\sqrt{x+1}-1}+35\right)}{\left(-x-2 \sqrt{1-x}+\sqrt{1-x} \sqrt{x+1}+1\right)^7}","\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,"((-1/1120 + Sqrt[1 - x]/1120)*(-1 + Sqrt[1 + x])^13*(35 + (35*(-1 + Sqrt[1 - x])^12)/(-1 + Sqrt[1 + x])^12 + (210*(-1 + Sqrt[1 - x])^11)/(-1 + Sqrt[1 + x])^11 + (630*(-1 + Sqrt[1 - x])^10)/(-1 + Sqrt[1 + x])^10 + (630*(-1 + Sqrt[1 - x])^9)/(-1 + Sqrt[1 + x])^9 - (483*(-1 + Sqrt[1 - x])^8)/(-1 + Sqrt[1 + x])^8 - (1372*(-1 + Sqrt[1 - x])^7)/(-1 + Sqrt[1 + x])^7 + (404*(-1 + Sqrt[1 - x])^6)/(-1 + Sqrt[1 + x])^6 + (1372*(-1 + Sqrt[1 - x])^5)/(-1 + Sqrt[1 + x])^5 - (483*(-1 + Sqrt[1 - x])^4)/(-1 + Sqrt[1 + x])^4 - (630*(-1 + Sqrt[1 - x])^3)/(-1 + Sqrt[1 + x])^3 + (630*(-1 + Sqrt[1 - x])^2)/(-1 + Sqrt[1 + x])^2 - (210*(-1 + Sqrt[1 - x]))/(-1 + Sqrt[1 + x])))/(1 - 2*Sqrt[1 - x] - x + Sqrt[1 - x]*Sqrt[1 + x])^7","B",1
1115,1,480,101,1.9696364,"\int \frac{1}{(1-x)^{11/2} \sqrt{1+x}} \, dx","IntegrateAlgebraic[1/((1 - x)^(11/2)*Sqrt[1 + x]),x]","\frac{\left(\frac{\sqrt{1-x}}{40320}-\frac{1}{40320}\right) \left(\sqrt{x+1}-1\right)^{17} \left(\frac{315 \left(\sqrt{1-x}-1\right)^{16}}{\left(\sqrt{x+1}-1\right)^{16}}+\frac{2520 \left(\sqrt{1-x}-1\right)^{15}}{\left(\sqrt{x+1}-1\right)^{15}}+\frac{10920 \left(\sqrt{1-x}-1\right)^{14}}{\left(\sqrt{x+1}-1\right)^{14}}+\frac{22680 \left(\sqrt{1-x}-1\right)^{13}}{\left(\sqrt{x+1}-1\right)^{13}}+\frac{14868 \left(\sqrt{1-x}-1\right)^{12}}{\left(\sqrt{x+1}-1\right)^{12}}-\frac{33096 \left(\sqrt{1-x}-1\right)^{11}}{\left(\sqrt{x+1}-1\right)^{11}}-\frac{52200 \left(\sqrt{1-x}-1\right)^{10}}{\left(\sqrt{x+1}-1\right)^{10}}+\frac{23544 \left(\sqrt{1-x}-1\right)^9}{\left(\sqrt{x+1}-1\right)^9}+\frac{73442 \left(\sqrt{1-x}-1\right)^8}{\left(\sqrt{x+1}-1\right)^8}-\frac{23544 \left(\sqrt{1-x}-1\right)^7}{\left(\sqrt{x+1}-1\right)^7}-\frac{52200 \left(\sqrt{1-x}-1\right)^6}{\left(\sqrt{x+1}-1\right)^6}+\frac{33096 \left(\sqrt{1-x}-1\right)^5}{\left(\sqrt{x+1}-1\right)^5}+\frac{14868 \left(\sqrt{1-x}-1\right)^4}{\left(\sqrt{x+1}-1\right)^4}-\frac{22680 \left(\sqrt{1-x}-1\right)^3}{\left(\sqrt{x+1}-1\right)^3}+\frac{10920 \left(\sqrt{1-x}-1\right)^2}{\left(\sqrt{x+1}-1\right)^2}-\frac{2520 \left(\sqrt{1-x}-1\right)}{\sqrt{x+1}-1}+315\right)}{\left(-x-2 \sqrt{1-x}+\sqrt{1-x} \sqrt{x+1}+1\right)^9}","\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,"((-1/40320 + Sqrt[1 - x]/40320)*(-1 + Sqrt[1 + x])^17*(315 + (315*(-1 + Sqrt[1 - x])^16)/(-1 + Sqrt[1 + x])^16 + (2520*(-1 + Sqrt[1 - x])^15)/(-1 + Sqrt[1 + x])^15 + (10920*(-1 + Sqrt[1 - x])^14)/(-1 + Sqrt[1 + x])^14 + (22680*(-1 + Sqrt[1 - x])^13)/(-1 + Sqrt[1 + x])^13 + (14868*(-1 + Sqrt[1 - x])^12)/(-1 + Sqrt[1 + x])^12 - (33096*(-1 + Sqrt[1 - x])^11)/(-1 + Sqrt[1 + x])^11 - (52200*(-1 + Sqrt[1 - x])^10)/(-1 + Sqrt[1 + x])^10 + (23544*(-1 + Sqrt[1 - x])^9)/(-1 + Sqrt[1 + x])^9 + (73442*(-1 + Sqrt[1 - x])^8)/(-1 + Sqrt[1 + x])^8 - (23544*(-1 + Sqrt[1 - x])^7)/(-1 + Sqrt[1 + x])^7 - (52200*(-1 + Sqrt[1 - x])^6)/(-1 + Sqrt[1 + x])^6 + (33096*(-1 + Sqrt[1 - x])^5)/(-1 + Sqrt[1 + x])^5 + (14868*(-1 + Sqrt[1 - x])^4)/(-1 + Sqrt[1 + x])^4 - (22680*(-1 + Sqrt[1 - x])^3)/(-1 + Sqrt[1 + x])^3 + (10920*(-1 + Sqrt[1 - x])^2)/(-1 + Sqrt[1 + x])^2 - (2520*(-1 + Sqrt[1 - x]))/(-1 + Sqrt[1 + x])))/(1 - 2*Sqrt[1 - x] - x + Sqrt[1 - x]*Sqrt[1 + x])^9","B",1
1116,1,367,85,0.6420056,"\int \frac{(1-x)^{7/2}}{(1+x)^{3/2}} \, dx","IntegrateAlgebraic[(1 - x)^(7/2)/(1 + x)^(3/2),x]","-\frac{8 \left(\sqrt{x+1}-1\right)^{12}}{3 \left(\sqrt{1-x}+\sqrt{x+1}-2\right)^6}-\frac{16 \left(\sqrt{x+1}-1\right)^{10}}{\left(\sqrt{1-x}+\sqrt{x+1}-2\right)^5}+\frac{\left(-10 \sqrt{1-x}-36 \sqrt{x+1}+46\right) \left(\sqrt{x+1}-1\right)^7}{\left(\sqrt{1-x}+\sqrt{x+1}-2\right)^4}+\frac{\left(-30 \sqrt{1-x}-\frac{112 \sqrt{x+1}}{3}+\frac{202}{3}\right) \left(\sqrt{x+1}-1\right)^5}{\left(\sqrt{1-x}+\sqrt{x+1}-2\right)^3}+\frac{\left(-25 \sqrt{1-x}+6 \sqrt{x+1}+19\right) \left(\sqrt{x+1}-1\right)^3}{\left(\sqrt{1-x}+\sqrt{x+1}-2\right)^2}+\frac{\left(-5 \sqrt{1-x}+44 \sqrt{x+1}-39\right) \left(\sqrt{x+1}-1\right)}{\sqrt{1-x}+\sqrt{x+1}-2}+\frac{\left(32-32 \sqrt{1-x}\right) \left(\sqrt{x+1}-1\right)}{x+\sqrt{1-x} \sqrt{x+1}-2 \sqrt{x+1}+1}-70 \tan ^{-1}\left(\frac{\sqrt{x+1}-1}{\sqrt{1-x}-1}\right)","-\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,"(-8*(-1 + Sqrt[1 + x])^12)/(3*(-2 + Sqrt[1 - x] + Sqrt[1 + x])^6) - (16*(-1 + Sqrt[1 + x])^10)/(-2 + Sqrt[1 - x] + Sqrt[1 + x])^5 + ((46 - 10*Sqrt[1 - x] - 36*Sqrt[1 + x])*(-1 + Sqrt[1 + x])^7)/(-2 + Sqrt[1 - x] + Sqrt[1 + x])^4 + ((202/3 - 30*Sqrt[1 - x] - (112*Sqrt[1 + x])/3)*(-1 + Sqrt[1 + x])^5)/(-2 + Sqrt[1 - x] + Sqrt[1 + x])^3 + ((-1 + Sqrt[1 + x])^3*(19 - 25*Sqrt[1 - x] + 6*Sqrt[1 + x]))/(-2 + Sqrt[1 - x] + Sqrt[1 + x])^2 + ((-1 + Sqrt[1 + x])*(-39 - 5*Sqrt[1 - x] + 44*Sqrt[1 + x]))/(-2 + Sqrt[1 - x] + Sqrt[1 + x]) + ((32 - 32*Sqrt[1 - x])*(-1 + Sqrt[1 + x]))/(1 + x - 2*Sqrt[1 + x] + Sqrt[1 - x]*Sqrt[1 + x]) - 70*ArcTan[(-1 + Sqrt[1 + x])/(-1 + Sqrt[1 - x])]","B",1
1117,1,277,65,0.225409,"\int \frac{(1-x)^{5/2}}{(1+x)^{3/2}} \, dx","IntegrateAlgebraic[(1 - x)^(5/2)/(1 + x)^(3/2),x]","\frac{\left(2-2 \sqrt{1-x}\right) \left(\sqrt{x+1}-1\right)^7}{\left(\sqrt{1-x}+\sqrt{x+1}-2\right)^4}+\frac{\left(6-6 \sqrt{1-x}\right) \left(\sqrt{x+1}-1\right)^5}{\left(\sqrt{1-x}+\sqrt{x+1}-2\right)^3}+\frac{\left(-5 \sqrt{1-x}+8 \sqrt{x+1}-3\right) \left(\sqrt{x+1}-1\right)^3}{\left(\sqrt{1-x}+\sqrt{x+1}-2\right)^2}+\frac{\left(-\sqrt{1-x}+16 \sqrt{x+1}-15\right) \left(\sqrt{x+1}-1\right)}{\sqrt{1-x}+\sqrt{x+1}-2}+\frac{\left(16-16 \sqrt{1-x}\right) \left(\sqrt{x+1}-1\right)}{x+\sqrt{1-x} \sqrt{x+1}-2 \sqrt{x+1}+1}-30 \tan ^{-1}\left(\frac{\sqrt{x+1}-1}{\sqrt{1-x}-1}\right)","-\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 - 2*Sqrt[1 - x])*(-1 + Sqrt[1 + x])^7)/(-2 + Sqrt[1 - x] + Sqrt[1 + x])^4 + ((6 - 6*Sqrt[1 - x])*(-1 + Sqrt[1 + x])^5)/(-2 + Sqrt[1 - x] + Sqrt[1 + x])^3 + ((-1 + Sqrt[1 + x])^3*(-3 - 5*Sqrt[1 - x] + 8*Sqrt[1 + x]))/(-2 + Sqrt[1 - x] + Sqrt[1 + x])^2 + ((-1 + Sqrt[1 + x])*(-15 - Sqrt[1 - x] + 16*Sqrt[1 + x]))/(-2 + Sqrt[1 - x] + Sqrt[1 + x]) + ((16 - 16*Sqrt[1 - x])*(-1 + Sqrt[1 + x]))/(1 + x - 2*Sqrt[1 + x] + Sqrt[1 - x]*Sqrt[1 + x]) - 30*ArcTan[(-1 + Sqrt[1 + x])/(-1 + Sqrt[1 - x])]","B",1
1118,1,179,41,0.1568808,"\int \frac{(1-x)^{3/2}}{(1+x)^{3/2}} \, dx","IntegrateAlgebraic[(1 - x)^(3/2)/(1 + x)^(3/2),x]","\frac{\left(2-2 \sqrt{1-x}\right) \left(\sqrt{x+1}-1\right) \left(-x^2-4 \sqrt{1-x} x+\sqrt{1-x} \sqrt{x+1} x+3 x-20 \sqrt{1-x}+12 \sqrt{1-x} \sqrt{x+1}-20 \sqrt{x+1}+28\right)}{\left(\sqrt{1-x}+\sqrt{x+1}-2\right)^2 \left(x+\sqrt{1-x} \sqrt{x+1}-2 \sqrt{x+1}+1\right)}-12 \tan ^{-1}\left(\frac{\sqrt{x+1}-1}{\sqrt{1-x}-1}\right)","-\frac{2 (1-x)^{3/2}}{\sqrt{x+1}}-3 \sqrt{x+1} \sqrt{1-x}-3 \sin ^{-1}(x)",1,"((2 - 2*Sqrt[1 - x])*(-1 + Sqrt[1 + x])*(28 - 20*Sqrt[1 - x] + 3*x - 4*Sqrt[1 - x]*x - x^2 - 20*Sqrt[1 + x] + 12*Sqrt[1 - x]*Sqrt[1 + x] + Sqrt[1 - x]*x*Sqrt[1 + x]))/((-2 + Sqrt[1 - x] + Sqrt[1 + x])^2*(1 + x - 2*Sqrt[1 + x] + Sqrt[1 - x]*Sqrt[1 + x])) - 12*ArcTan[(-1 + Sqrt[1 + x])/(-1 + Sqrt[1 - x])]","B",1
1119,1,81,23,0.0564349,"\int \frac{\sqrt{1-x}}{(1+x)^{3/2}} \, dx","IntegrateAlgebraic[Sqrt[1 - x]/(1 + x)^(3/2),x]","\frac{\left(4-4 \sqrt{1-x}\right) \left(\sqrt{x+1}-1\right)}{x+\sqrt{1-x} \sqrt{x+1}-2 \sqrt{x+1}+1}-4 \tan ^{-1}\left(\frac{\sqrt{x+1}-1}{\sqrt{1-x}-1}\right)","-\frac{2 \sqrt{1-x}}{\sqrt{x+1}}-\sin ^{-1}(x)",1,"((4 - 4*Sqrt[1 - x])*(-1 + Sqrt[1 + x]))/(1 + x - 2*Sqrt[1 + x] + Sqrt[1 - x]*Sqrt[1 + x]) - 4*ArcTan[(-1 + Sqrt[1 + x])/(-1 + Sqrt[1 - x])]","B",1
1120,1,54,18,0.0250595,"\int \frac{1}{\sqrt{1-x} (1+x)^{3/2}} \, dx","IntegrateAlgebraic[1/(Sqrt[1 - x]*(1 + x)^(3/2)),x]","\frac{\left(2-2 \sqrt{1-x}\right) \left(\sqrt{x+1}-1\right)}{x+\sqrt{1-x} \sqrt{x+1}-2 \sqrt{x+1}+1}","-\frac{\sqrt{1-x}}{\sqrt{x+1}}",1,"((2 - 2*Sqrt[1 - x])*(-1 + Sqrt[1 + x]))/(1 + x - 2*Sqrt[1 + x] + Sqrt[1 - x]*Sqrt[1 + x])","B",1
1121,1,134,18,0.0606012,"\int \frac{1}{(1-x)^{3/2} (1+x)^{3/2}} \, dx","IntegrateAlgebraic[1/((1 - x)^(3/2)*(1 + x)^(3/2)),x]","\frac{\left(\sqrt{x+1}-1\right)^4 \left(\frac{\left(\sqrt{1-x}-1\right)^3}{2 \left(\sqrt{x+1}-1\right)^3}-\frac{\sqrt{1-x}-1}{2 \left(\sqrt{x+1}-1\right)}\right)}{x^2+2 \sqrt{1-x} x-2 \sqrt{x+1} x+2 \sqrt{1-x}-3 \sqrt{1-x} \sqrt{x+1}+2 \sqrt{x+1}-1}","\frac{x}{\sqrt{1-x} \sqrt{x+1}}",1,"((-1 + Sqrt[1 + x])^4*((-1 + Sqrt[1 - x])^3/(2*(-1 + Sqrt[1 + x])^3) - (-1 + Sqrt[1 - x])/(2*(-1 + Sqrt[1 + x]))))/(-1 + 2*Sqrt[1 - x] + 2*Sqrt[1 - x]*x + x^2 + 2*Sqrt[1 + x] - 3*Sqrt[1 - x]*Sqrt[1 + x] - 2*x*Sqrt[1 + x])","B",1
1122,1,251,42,0.2176385,"\int \frac{1}{(1-x)^{5/2} (1+x)^{3/2}} \, dx","IntegrateAlgebraic[1/((1 - x)^(5/2)*(1 + x)^(3/2)),x]","\frac{\left(\frac{1}{12}-\frac{\sqrt{1-x}}{12}\right) \left(\sqrt{x+1}-1\right)^7 \left(\frac{3 \left(\sqrt{1-x}-1\right)^6}{\left(\sqrt{x+1}-1\right)^6}+\frac{6 \left(\sqrt{1-x}-1\right)^5}{\left(\sqrt{x+1}-1\right)^5}-\frac{5 \left(\sqrt{1-x}-1\right)^4}{\left(\sqrt{x+1}-1\right)^4}-\frac{20 \left(\sqrt{1-x}-1\right)^3}{\left(\sqrt{x+1}-1\right)^3}+\frac{5 \left(\sqrt{1-x}-1\right)^2}{\left(\sqrt{x+1}-1\right)^2}+\frac{6 \left(\sqrt{1-x}-1\right)}{\sqrt{x+1}-1}-3\right)}{\left(-x-2 \sqrt{1-x}+\sqrt{1-x} \sqrt{x+1}+1\right)^3 \left(x+\sqrt{1-x} \sqrt{x+1}-2 \sqrt{x+1}+1\right)}","\frac{2 x}{3 \sqrt{1-x} \sqrt{x+1}}+\frac{1}{3 (1-x)^{3/2} \sqrt{x+1}}",1,"((1/12 - Sqrt[1 - x]/12)*(-1 + Sqrt[1 + x])^7*(-3 + (3*(-1 + Sqrt[1 - x])^6)/(-1 + Sqrt[1 + x])^6 + (6*(-1 + Sqrt[1 - x])^5)/(-1 + Sqrt[1 + x])^5 - (5*(-1 + Sqrt[1 - x])^4)/(-1 + Sqrt[1 + x])^4 - (20*(-1 + Sqrt[1 - x])^3)/(-1 + Sqrt[1 + x])^3 + (5*(-1 + Sqrt[1 - x])^2)/(-1 + Sqrt[1 + x])^2 + (6*(-1 + Sqrt[1 - x]))/(-1 + Sqrt[1 + x])))/((1 - 2*Sqrt[1 - x] - x + Sqrt[1 - x]*Sqrt[1 + x])^3*(1 + x - 2*Sqrt[1 + x] + Sqrt[1 - x]*Sqrt[1 + x]))","B",1
1123,1,355,62,0.6389022,"\int \frac{1}{(1-x)^{7/2} (1+x)^{3/2}} \, dx","IntegrateAlgebraic[1/((1 - x)^(7/2)*(1 + x)^(3/2)),x]","\frac{\left(\frac{1}{80}-\frac{\sqrt{1-x}}{80}\right) \left(\sqrt{x+1}-1\right)^{11} \left(\frac{5 \left(\sqrt{1-x}-1\right)^{10}}{\left(\sqrt{x+1}-1\right)^{10}}+\frac{20 \left(\sqrt{1-x}-1\right)^9}{\left(\sqrt{x+1}-1\right)^9}+\frac{15 \left(\sqrt{1-x}-1\right)^8}{\left(\sqrt{x+1}-1\right)^8}-\frac{80 \left(\sqrt{1-x}-1\right)^7}{\left(\sqrt{x+1}-1\right)^7}-\frac{118 \left(\sqrt{1-x}-1\right)^6}{\left(\sqrt{x+1}-1\right)^6}+\frac{56 \left(\sqrt{1-x}-1\right)^5}{\left(\sqrt{x+1}-1\right)^5}+\frac{118 \left(\sqrt{1-x}-1\right)^4}{\left(\sqrt{x+1}-1\right)^4}-\frac{80 \left(\sqrt{1-x}-1\right)^3}{\left(\sqrt{x+1}-1\right)^3}-\frac{15 \left(\sqrt{1-x}-1\right)^2}{\left(\sqrt{x+1}-1\right)^2}+\frac{20 \left(\sqrt{1-x}-1\right)}{\sqrt{x+1}-1}-5\right)}{\left(-x-2 \sqrt{1-x}+\sqrt{1-x} \sqrt{x+1}+1\right)^5 \left(x+\sqrt{1-x} \sqrt{x+1}-2 \sqrt{x+1}+1\right)}","\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,"((1/80 - Sqrt[1 - x]/80)*(-1 + Sqrt[1 + x])^11*(-5 + (5*(-1 + Sqrt[1 - x])^10)/(-1 + Sqrt[1 + x])^10 + (20*(-1 + Sqrt[1 - x])^9)/(-1 + Sqrt[1 + x])^9 + (15*(-1 + Sqrt[1 - x])^8)/(-1 + Sqrt[1 + x])^8 - (80*(-1 + Sqrt[1 - x])^7)/(-1 + Sqrt[1 + x])^7 - (118*(-1 + Sqrt[1 - x])^6)/(-1 + Sqrt[1 + x])^6 + (56*(-1 + Sqrt[1 - x])^5)/(-1 + Sqrt[1 + x])^5 + (118*(-1 + Sqrt[1 - x])^4)/(-1 + Sqrt[1 + x])^4 - (80*(-1 + Sqrt[1 - x])^3)/(-1 + Sqrt[1 + x])^3 - (15*(-1 + Sqrt[1 - x])^2)/(-1 + Sqrt[1 + x])^2 + (20*(-1 + Sqrt[1 - x]))/(-1 + Sqrt[1 + x])))/((1 - 2*Sqrt[1 - x] - x + Sqrt[1 - x]*Sqrt[1 + x])^5*(1 + x - 2*Sqrt[1 + x] + Sqrt[1 - x]*Sqrt[1 + x]))","B",1
1124,1,459,82,1.6658991,"\int \frac{1}{(1-x)^{9/2} (1+x)^{3/2}} \, dx","IntegrateAlgebraic[1/((1 - x)^(9/2)*(1 + x)^(3/2)),x]","\frac{\left(\frac{\sqrt{1-x}}{2240}-\frac{1}{2240}\right) \left(\sqrt{x+1}-1\right)^{15} \left(-\frac{35 \left(\sqrt{1-x}-1\right)^{14}}{\left(\sqrt{x+1}-1\right)^{14}}-\frac{210 \left(\sqrt{1-x}-1\right)^{13}}{\left(\sqrt{x+1}-1\right)^{13}}-\frac{455 \left(\sqrt{1-x}-1\right)^{12}}{\left(\sqrt{x+1}-1\right)^{12}}+\frac{420 \left(\sqrt{1-x}-1\right)^{11}}{\left(\sqrt{x+1}-1\right)^{11}}+\frac{2877 \left(\sqrt{1-x}-1\right)^{10}}{\left(\sqrt{x+1}-1\right)^{10}}+\frac{2674 \left(\sqrt{1-x}-1\right)^9}{\left(\sqrt{x+1}-1\right)^9}-\frac{3359 \left(\sqrt{1-x}-1\right)^8}{\left(\sqrt{x+1}-1\right)^8}-\frac{4104 \left(\sqrt{1-x}-1\right)^7}{\left(\sqrt{x+1}-1\right)^7}+\frac{3359 \left(\sqrt{1-x}-1\right)^6}{\left(\sqrt{x+1}-1\right)^6}+\frac{2674 \left(\sqrt{1-x}-1\right)^5}{\left(\sqrt{x+1}-1\right)^5}-\frac{2877 \left(\sqrt{1-x}-1\right)^4}{\left(\sqrt{x+1}-1\right)^4}+\frac{420 \left(\sqrt{1-x}-1\right)^3}{\left(\sqrt{x+1}-1\right)^3}+\frac{455 \left(\sqrt{1-x}-1\right)^2}{\left(\sqrt{x+1}-1\right)^2}-\frac{210 \left(\sqrt{1-x}-1\right)}{\sqrt{x+1}-1}+35\right)}{\left(-x-2 \sqrt{1-x}+\sqrt{1-x} \sqrt{x+1}+1\right)^7 \left(x+\sqrt{1-x} \sqrt{x+1}-2 \sqrt{x+1}+1\right)}","\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,"((-1/2240 + Sqrt[1 - x]/2240)*(-1 + Sqrt[1 + x])^15*(35 - (35*(-1 + Sqrt[1 - x])^14)/(-1 + Sqrt[1 + x])^14 - (210*(-1 + Sqrt[1 - x])^13)/(-1 + Sqrt[1 + x])^13 - (455*(-1 + Sqrt[1 - x])^12)/(-1 + Sqrt[1 + x])^12 + (420*(-1 + Sqrt[1 - x])^11)/(-1 + Sqrt[1 + x])^11 + (2877*(-1 + Sqrt[1 - x])^10)/(-1 + Sqrt[1 + x])^10 + (2674*(-1 + Sqrt[1 - x])^9)/(-1 + Sqrt[1 + x])^9 - (3359*(-1 + Sqrt[1 - x])^8)/(-1 + Sqrt[1 + x])^8 - (4104*(-1 + Sqrt[1 - x])^7)/(-1 + Sqrt[1 + x])^7 + (3359*(-1 + Sqrt[1 - x])^6)/(-1 + Sqrt[1 + x])^6 + (2674*(-1 + Sqrt[1 - x])^5)/(-1 + Sqrt[1 + x])^5 - (2877*(-1 + Sqrt[1 - x])^4)/(-1 + Sqrt[1 + x])^4 + (420*(-1 + Sqrt[1 - x])^3)/(-1 + Sqrt[1 + x])^3 + (455*(-1 + Sqrt[1 - x])^2)/(-1 + Sqrt[1 + x])^2 - (210*(-1 + Sqrt[1 - x]))/(-1 + Sqrt[1 + x])))/((1 - 2*Sqrt[1 - x] - x + Sqrt[1 - x]*Sqrt[1 + x])^7*(1 + x - 2*Sqrt[1 + x] + Sqrt[1 - x]*Sqrt[1 + x]))","B",1
1125,1,563,102,3.750404,"\int \frac{1}{(1-x)^{11/2} (1+x)^{3/2}} \, dx","IntegrateAlgebraic[1/((1 - x)^(11/2)*(1 + x)^(3/2)),x]","\frac{\left(\frac{1}{16128}-\frac{\sqrt{1-x}}{16128}\right) \left(\sqrt{x+1}-1\right)^{19} \left(\frac{63 \left(\sqrt{1-x}-1\right)^{18}}{\left(\sqrt{x+1}-1\right)^{18}}+\frac{504 \left(\sqrt{1-x}-1\right)^{17}}{\left(\sqrt{x+1}-1\right)^{17}}+\frac{1785 \left(\sqrt{1-x}-1\right)^{16}}{\left(\sqrt{x+1}-1\right)^{16}}+\frac{1344 \left(\sqrt{1-x}-1\right)^{15}}{\left(\sqrt{x+1}-1\right)^{15}}-\frac{8148 \left(\sqrt{1-x}-1\right)^{14}}{\left(\sqrt{x+1}-1\right)^{14}}-\frac{23520 \left(\sqrt{1-x}-1\right)^{13}}{\left(\sqrt{x+1}-1\right)^{13}}-\frac{9948 \left(\sqrt{1-x}-1\right)^{12}}{\left(\sqrt{x+1}-1\right)^{12}}+\frac{37056 \left(\sqrt{1-x}-1\right)^{11}}{\left(\sqrt{x+1}-1\right)^{11}}+\frac{32690 \left(\sqrt{1-x}-1\right)^{10}}{\left(\sqrt{x+1}-1\right)^{10}}-\frac{41008 \left(\sqrt{1-x}-1\right)^9}{\left(\sqrt{x+1}-1\right)^9}-\frac{32690 \left(\sqrt{1-x}-1\right)^8}{\left(\sqrt{x+1}-1\right)^8}+\frac{37056 \left(\sqrt{1-x}-1\right)^7}{\left(\sqrt{x+1}-1\right)^7}+\frac{9948 \left(\sqrt{1-x}-1\right)^6}{\left(\sqrt{x+1}-1\right)^6}-\frac{23520 \left(\sqrt{1-x}-1\right)^5}{\left(\sqrt{x+1}-1\right)^5}+\frac{8148 \left(\sqrt{1-x}-1\right)^4}{\left(\sqrt{x+1}-1\right)^4}+\frac{1344 \left(\sqrt{1-x}-1\right)^3}{\left(\sqrt{x+1}-1\right)^3}-\frac{1785 \left(\sqrt{1-x}-1\right)^2}{\left(\sqrt{x+1}-1\right)^2}+\frac{504 \left(\sqrt{1-x}-1\right)}{\sqrt{x+1}-1}-63\right)}{\left(-x-2 \sqrt{1-x}+\sqrt{1-x} \sqrt{x+1}+1\right)^9 \left(x+\sqrt{1-x} \sqrt{x+1}-2 \sqrt{x+1}+1\right)}","\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,"((1/16128 - Sqrt[1 - x]/16128)*(-1 + Sqrt[1 + x])^19*(-63 + (63*(-1 + Sqrt[1 - x])^18)/(-1 + Sqrt[1 + x])^18 + (504*(-1 + Sqrt[1 - x])^17)/(-1 + Sqrt[1 + x])^17 + (1785*(-1 + Sqrt[1 - x])^16)/(-1 + Sqrt[1 + x])^16 + (1344*(-1 + Sqrt[1 - x])^15)/(-1 + Sqrt[1 + x])^15 - (8148*(-1 + Sqrt[1 - x])^14)/(-1 + Sqrt[1 + x])^14 - (23520*(-1 + Sqrt[1 - x])^13)/(-1 + Sqrt[1 + x])^13 - (9948*(-1 + Sqrt[1 - x])^12)/(-1 + Sqrt[1 + x])^12 + (37056*(-1 + Sqrt[1 - x])^11)/(-1 + Sqrt[1 + x])^11 + (32690*(-1 + Sqrt[1 - x])^10)/(-1 + Sqrt[1 + x])^10 - (41008*(-1 + Sqrt[1 - x])^9)/(-1 + Sqrt[1 + x])^9 - (32690*(-1 + Sqrt[1 - x])^8)/(-1 + Sqrt[1 + x])^8 + (37056*(-1 + Sqrt[1 - x])^7)/(-1 + Sqrt[1 + x])^7 + (9948*(-1 + Sqrt[1 - x])^6)/(-1 + Sqrt[1 + x])^6 - (23520*(-1 + Sqrt[1 - x])^5)/(-1 + Sqrt[1 + x])^5 + (8148*(-1 + Sqrt[1 - x])^4)/(-1 + Sqrt[1 + x])^4 + (1344*(-1 + Sqrt[1 - x])^3)/(-1 + Sqrt[1 + x])^3 - (1785*(-1 + Sqrt[1 - x])^2)/(-1 + Sqrt[1 + x])^2 + (504*(-1 + Sqrt[1 - x]))/(-1 + Sqrt[1 + x])))/((1 - 2*Sqrt[1 - x] - x + Sqrt[1 - x]*Sqrt[1 + x])^9*(1 + x - 2*Sqrt[1 + x] + Sqrt[1 - x]*Sqrt[1 + x]))","B",1
1126,1,516,103,0.538655,"\int \frac{(1-x)^{9/2}}{(1+x)^{5/2}} \, dx","IntegrateAlgebraic[(1 - x)^(9/2)/(1 + x)^(5/2),x]","\frac{8 \left(\sqrt{x+1}-1\right)^{12}}{3 \left(\sqrt{1-x}+\sqrt{x+1}-2\right)^6}+\frac{16 \left(\sqrt{x+1}-1\right)^{10}}{\left(\sqrt{1-x}+\sqrt{x+1}-2\right)^5}+\frac{\left(14 \sqrt{1-x}+36 \sqrt{x+1}-50\right) \left(\sqrt{x+1}-1\right)^7}{\left(\sqrt{1-x}+\sqrt{x+1}-2\right)^4}+\frac{\left(42 \sqrt{1-x}+\frac{112 \sqrt{x+1}}{3}-\frac{238}{3}\right) \left(\sqrt{x+1}-1\right)^5}{\left(\sqrt{1-x}+\sqrt{x+1}-2\right)^3}+\frac{\left(-\frac{640 \sqrt{1-x}}{3}-\frac{256 \sqrt{x+1}}{3}+\frac{896}{3}\right) \left(\sqrt{x+1}-1\right)^5}{\left(x+\sqrt{1-x} \sqrt{x+1}-2 \sqrt{x+1}+1\right)^3}+\frac{\left(35 \sqrt{1-x}-30 \sqrt{x+1}-5\right) \left(\sqrt{x+1}-1\right)^3}{\left(\sqrt{1-x}+\sqrt{x+1}-2\right)^2}+\frac{\left(\frac{640 \sqrt{1-x}}{3}+\frac{704 \sqrt{x+1}}{3}-448\right) \left(\sqrt{x+1}-1\right)^3}{\left(x+\sqrt{1-x} \sqrt{x+1}-2 \sqrt{x+1}+1\right)^2}+\frac{\left(7 \sqrt{1-x}-92 \sqrt{x+1}+85\right) \left(\sqrt{x+1}-1\right)}{\sqrt{1-x}+\sqrt{x+1}-2}+\frac{\left(96 \sqrt{1-x}-128 \sqrt{x+1}+32\right) \left(\sqrt{x+1}-1\right)}{x+\sqrt{1-x} \sqrt{x+1}-2 \sqrt{x+1}+1}+210 \tan ^{-1}\left(\frac{\sqrt{x+1}-1}{\sqrt{1-x}-1}\right)","-\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,"(8*(-1 + Sqrt[1 + x])^12)/(3*(-2 + Sqrt[1 - x] + Sqrt[1 + x])^6) + (16*(-1 + Sqrt[1 + x])^10)/(-2 + Sqrt[1 - x] + Sqrt[1 + x])^5 + ((-5 + 35*Sqrt[1 - x] - 30*Sqrt[1 + x])*(-1 + Sqrt[1 + x])^3)/(-2 + Sqrt[1 - x] + Sqrt[1 + x])^2 + ((85 + 7*Sqrt[1 - x] - 92*Sqrt[1 + x])*(-1 + Sqrt[1 + x]))/(-2 + Sqrt[1 - x] + Sqrt[1 + x]) + ((-1 + Sqrt[1 + x])^7*(-50 + 14*Sqrt[1 - x] + 36*Sqrt[1 + x]))/(-2 + Sqrt[1 - x] + Sqrt[1 + x])^4 + ((-1 + Sqrt[1 + x])^5*(-238/3 + 42*Sqrt[1 - x] + (112*Sqrt[1 + x])/3))/(-2 + Sqrt[1 - x] + Sqrt[1 + x])^3 + ((896/3 - (640*Sqrt[1 - x])/3 - (256*Sqrt[1 + x])/3)*(-1 + Sqrt[1 + x])^5)/(1 + x - 2*Sqrt[1 + x] + Sqrt[1 - x]*Sqrt[1 + x])^3 + ((-1 + Sqrt[1 + x])^3*(-448 + (640*Sqrt[1 - x])/3 + (704*Sqrt[1 + x])/3))/(1 + x - 2*Sqrt[1 + x] + Sqrt[1 - x]*Sqrt[1 + x])^2 + ((32 + 96*Sqrt[1 - x] - 128*Sqrt[1 + x])*(-1 + Sqrt[1 + x]))/(1 + x - 2*Sqrt[1 + x] + Sqrt[1 - x]*Sqrt[1 + x]) + 210*ArcTan[(-1 + Sqrt[1 + x])/(-1 + Sqrt[1 - x])]","B",1
1127,1,390,87,0.3812943,"\int \frac{(1-x)^{7/2}}{(1+x)^{5/2}} \, dx","IntegrateAlgebraic[(1 - x)^(7/2)/(1 + x)^(5/2),x]","\frac{\left(\frac{4 \sqrt{1-x}}{3}-\frac{4}{3}\right) \left(\sqrt{x+1}-1\right) \left(-3 x^6-36 \sqrt{1-x} x^5+3 \sqrt{1-x} \sqrt{x+1} x^5+129 x^5+360 \sqrt{1-x} x^4+66 \sqrt{1-x} \sqrt{x+1} x^4-312 \sqrt{x+1} x^4-649 x^4+3204 \sqrt{1-x} x^3-1725 \sqrt{1-x} \sqrt{x+1} x^3+5400 \sqrt{x+1} x^3-16125 x^3-19648 \sqrt{1-x} x^2+1288 \sqrt{1-x} \sqrt{x+1} x^2+22664 \sqrt{x+1} x^2-12820 x^2-68920 \sqrt{1-x} x+48972 \sqrt{1-x} \sqrt{x+1} x-31688 \sqrt{x+1} x+51636 x-41984 \sqrt{1-x}+41192 \sqrt{1-x} \sqrt{x+1}-41984 \sqrt{x+1}+42776\right)}{\left(\sqrt{1-x}+\sqrt{x+1}-2\right)^4 \left(x+\sqrt{1-x} \sqrt{x+1}-2 \sqrt{x+1}+1\right)^3}+70 \tan ^{-1}\left(\frac{\sqrt{x+1}-1}{\sqrt{1-x}-1}\right)","-\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,"((-4/3 + (4*Sqrt[1 - x])/3)*(-1 + Sqrt[1 + x])*(42776 - 41984*Sqrt[1 - x] + 51636*x - 68920*Sqrt[1 - x]*x - 12820*x^2 - 19648*Sqrt[1 - x]*x^2 - 16125*x^3 + 3204*Sqrt[1 - x]*x^3 - 649*x^4 + 360*Sqrt[1 - x]*x^4 + 129*x^5 - 36*Sqrt[1 - x]*x^5 - 3*x^6 - 41984*Sqrt[1 + x] + 41192*Sqrt[1 - x]*Sqrt[1 + x] - 31688*x*Sqrt[1 + x] + 48972*Sqrt[1 - x]*x*Sqrt[1 + x] + 22664*x^2*Sqrt[1 + x] + 1288*Sqrt[1 - x]*x^2*Sqrt[1 + x] + 5400*x^3*Sqrt[1 + x] - 1725*Sqrt[1 - x]*x^3*Sqrt[1 + x] - 312*x^4*Sqrt[1 + x] + 66*Sqrt[1 - x]*x^4*Sqrt[1 + x] + 3*Sqrt[1 - x]*x^5*Sqrt[1 + x]))/((-2 + Sqrt[1 - x] + Sqrt[1 + x])^4*(1 + x - 2*Sqrt[1 + x] + Sqrt[1 - x]*Sqrt[1 + x])^3) + 70*ArcTan[(-1 + Sqrt[1 + x])/(-1 + Sqrt[1 - x])]","B",1
1128,1,284,63,0.2560217,"\int \frac{(1-x)^{5/2}}{(1+x)^{5/2}} \, dx","IntegrateAlgebraic[(1 - x)^(5/2)/(1 + x)^(5/2),x]","\frac{\left(\frac{4}{3}-\frac{4 \sqrt{1-x}}{3}\right) \left(\sqrt{x+1}-1\right) \left(3 x^4+3 \sqrt{1-x} \sqrt{x+1} x^3-24 \sqrt{x+1} x^3+96 x^3+256 \sqrt{1-x} x^2-31 \sqrt{1-x} \sqrt{x+1} x^2-248 \sqrt{x+1} x^2+135 x^2+1184 \sqrt{1-x} x-810 \sqrt{1-x} \sqrt{x+1} x+640 \sqrt{x+1} x-1014 x+736 \sqrt{1-x}-688 \sqrt{1-x} \sqrt{x+1}+736 \sqrt{x+1}-784\right)}{\left(\sqrt{1-x}+\sqrt{x+1}-2\right)^2 \left(x+\sqrt{1-x} \sqrt{x+1}-2 \sqrt{x+1}+1\right)^3}+20 \tan ^{-1}\left(\frac{\sqrt{x+1}-1}{\sqrt{1-x}-1}\right)","-\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,"((4/3 - (4*Sqrt[1 - x])/3)*(-1 + Sqrt[1 + x])*(-784 + 736*Sqrt[1 - x] - 1014*x + 1184*Sqrt[1 - x]*x + 135*x^2 + 256*Sqrt[1 - x]*x^2 + 96*x^3 + 3*x^4 + 736*Sqrt[1 + x] - 688*Sqrt[1 - x]*Sqrt[1 + x] + 640*x*Sqrt[1 + x] - 810*Sqrt[1 - x]*x*Sqrt[1 + x] - 248*x^2*Sqrt[1 + x] - 31*Sqrt[1 - x]*x^2*Sqrt[1 + x] - 24*x^3*Sqrt[1 + x] + 3*Sqrt[1 - x]*x^3*Sqrt[1 + x]))/((-2 + Sqrt[1 - x] + Sqrt[1 + x])^2*(1 + x - 2*Sqrt[1 + x] + Sqrt[1 - x]*Sqrt[1 + x])^3) + 20*ArcTan[(-1 + Sqrt[1 + x])/(-1 + Sqrt[1 - x])]","B",1
1129,1,134,41,0.1125217,"\int \frac{(1-x)^{3/2}}{(1+x)^{5/2}} \, dx","IntegrateAlgebraic[(1 - x)^(3/2)/(1 + x)^(5/2),x]","\frac{\left(\sqrt{1-x}-1\right)^2 \left(8 x+\frac{16 \sqrt{1-x}}{3}+\frac{8}{3} \sqrt{1-x} \sqrt{x+1}-\frac{32 \sqrt{x+1}}{3}+\frac{8}{3}\right) \left(\sqrt{x+1}-1\right)^2}{\left(x+\sqrt{1-x} \sqrt{x+1}-2 \sqrt{x+1}+1\right)^3}+4 \tan ^{-1}\left(\frac{\sqrt{x+1}-1}{\sqrt{1-x}-1}\right)","-\frac{2 (1-x)^{3/2}}{3 (x+1)^{3/2}}+\frac{2 \sqrt{1-x}}{\sqrt{x+1}}+\sin ^{-1}(x)",1,"((-1 + Sqrt[1 - x])^2*(-1 + Sqrt[1 + x])^2*(8/3 + (16*Sqrt[1 - x])/3 + 8*x - (32*Sqrt[1 + x])/3 + (8*Sqrt[1 - x]*Sqrt[1 + x])/3))/(1 + x - 2*Sqrt[1 + x] + Sqrt[1 - x]*Sqrt[1 + x])^3 + 4*ArcTan[(-1 + Sqrt[1 + x])/(-1 + Sqrt[1 - x])]","B",1
1130,1,126,20,0.0715362,"\int \frac{\sqrt{1-x}}{(1+x)^{5/2}} \, dx","IntegrateAlgebraic[Sqrt[1 - x]/(1 + x)^(5/2),x]","\frac{\left(\sqrt{x+1}-1\right)^6 \left(-\frac{\left(\sqrt{1-x}-1\right)^5}{2 \left(\sqrt{x+1}-1\right)^5}+\frac{\left(\sqrt{1-x}-1\right)^3}{3 \left(\sqrt{x+1}-1\right)^3}-\frac{\sqrt{1-x}-1}{2 \left(\sqrt{x+1}-1\right)}\right)}{\left(x+\sqrt{1-x} \sqrt{x+1}-2 \sqrt{x+1}+1\right)^3}","-\frac{(1-x)^{3/2}}{3 (x+1)^{3/2}}",1,"((-1 + Sqrt[1 + x])^6*(-1/2*(-1 + Sqrt[1 - x])^5/(-1 + Sqrt[1 + x])^5 + (-1 + Sqrt[1 - x])^3/(3*(-1 + Sqrt[1 + x])^3) - (-1 + Sqrt[1 - x])/(2*(-1 + Sqrt[1 + x]))))/(1 + x - 2*Sqrt[1 + x] + Sqrt[1 - x]*Sqrt[1 + x])^3","B",1
1131,1,164,41,0.0821404,"\int \frac{1}{\sqrt{1-x} (1+x)^{5/2}} \, dx","IntegrateAlgebraic[1/(Sqrt[1 - x]*(1 + x)^(5/2)),x]","\frac{\left(\frac{1}{6}-\frac{\sqrt{1-x}}{6}\right) \left(\sqrt{x+1}-1\right)^5 \left(\frac{3 \left(\sqrt{1-x}-1\right)^4}{\left(\sqrt{x+1}-1\right)^4}-\frac{6 \left(\sqrt{1-x}-1\right)^3}{\left(\sqrt{x+1}-1\right)^3}+\frac{2 \left(\sqrt{1-x}-1\right)^2}{\left(\sqrt{x+1}-1\right)^2}+\frac{6 \left(\sqrt{1-x}-1\right)}{\sqrt{x+1}-1}+3\right)}{\left(x+\sqrt{1-x} \sqrt{x+1}-2 \sqrt{x+1}+1\right)^3}","-\frac{\sqrt{1-x}}{3 \sqrt{x+1}}-\frac{\sqrt{1-x}}{3 (x+1)^{3/2}}",1,"((1/6 - Sqrt[1 - x]/6)*(-1 + Sqrt[1 + x])^5*(3 + (3*(-1 + Sqrt[1 - x])^4)/(-1 + Sqrt[1 + x])^4 - (6*(-1 + Sqrt[1 - x])^3)/(-1 + Sqrt[1 + x])^3 + (2*(-1 + Sqrt[1 - x])^2)/(-1 + Sqrt[1 + x])^2 + (6*(-1 + Sqrt[1 - x]))/(-1 + Sqrt[1 + x])))/(1 + x - 2*Sqrt[1 + x] + Sqrt[1 - x]*Sqrt[1 + x])^3","B",1
1132,1,251,58,0.2166387,"\int \frac{1}{(1-x)^{3/2} (1+x)^{5/2}} \, dx","IntegrateAlgebraic[1/((1 - x)^(3/2)*(1 + x)^(5/2)),x]","\frac{\left(\frac{\sqrt{1-x}}{12}-\frac{1}{12}\right) \left(\sqrt{x+1}-1\right)^7 \left(-\frac{3 \left(\sqrt{1-x}-1\right)^6}{\left(\sqrt{x+1}-1\right)^6}+\frac{6 \left(\sqrt{1-x}-1\right)^5}{\left(\sqrt{x+1}-1\right)^5}+\frac{5 \left(\sqrt{1-x}-1\right)^4}{\left(\sqrt{x+1}-1\right)^4}-\frac{20 \left(\sqrt{1-x}-1\right)^3}{\left(\sqrt{x+1}-1\right)^3}-\frac{5 \left(\sqrt{1-x}-1\right)^2}{\left(\sqrt{x+1}-1\right)^2}+\frac{6 \left(\sqrt{1-x}-1\right)}{\sqrt{x+1}-1}+3\right)}{\left(-x-2 \sqrt{1-x}+\sqrt{1-x} \sqrt{x+1}+1\right) \left(x+\sqrt{1-x} \sqrt{x+1}-2 \sqrt{x+1}+1\right)^3}","-\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,"((-1/12 + Sqrt[1 - x]/12)*(-1 + Sqrt[1 + x])^7*(3 - (3*(-1 + Sqrt[1 - x])^6)/(-1 + Sqrt[1 + x])^6 + (6*(-1 + Sqrt[1 - x])^5)/(-1 + Sqrt[1 + x])^5 + (5*(-1 + Sqrt[1 - x])^4)/(-1 + Sqrt[1 + x])^4 - (20*(-1 + Sqrt[1 - x])^3)/(-1 + Sqrt[1 + x])^3 - (5*(-1 + Sqrt[1 - x])^2)/(-1 + Sqrt[1 + x])^2 + (6*(-1 + Sqrt[1 - x]))/(-1 + Sqrt[1 + x])))/((1 - 2*Sqrt[1 - x] - x + Sqrt[1 - x]*Sqrt[1 + x])*(1 + x - 2*Sqrt[1 + x] + Sqrt[1 - x]*Sqrt[1 + x])^3)","B",1
1133,1,246,43,0.3586367,"\int \frac{1}{(1-x)^{5/2} (1+x)^{5/2}} \, dx","IntegrateAlgebraic[1/((1 - x)^(5/2)*(1 + x)^(5/2)),x]","\frac{\left(\sqrt{x+1}-1\right)^{12} \left(\frac{\left(\sqrt{1-x}-1\right)^{11}}{128 \left(\sqrt{x+1}-1\right)^{11}}-\frac{23 \left(\sqrt{1-x}-1\right)^9}{384 \left(\sqrt{x+1}-1\right)^9}+\frac{17 \left(\sqrt{1-x}-1\right)^7}{64 \left(\sqrt{x+1}-1\right)^7}-\frac{17 \left(\sqrt{1-x}-1\right)^5}{64 \left(\sqrt{x+1}-1\right)^5}+\frac{23 \left(\sqrt{1-x}-1\right)^3}{384 \left(\sqrt{x+1}-1\right)^3}-\frac{\sqrt{1-x}-1}{128 \left(\sqrt{x+1}-1\right)}\right)}{\left(x^2+2 \sqrt{1-x} x-2 \sqrt{x+1} x+2 \sqrt{1-x}-3 \sqrt{1-x} \sqrt{x+1}+2 \sqrt{x+1}-1\right)^3}","\frac{2 x}{3 \sqrt{1-x} \sqrt{x+1}}+\frac{x}{3 (1-x)^{3/2} (x+1)^{3/2}}",1,"((-1 + Sqrt[1 + x])^12*((-1 + Sqrt[1 - x])^11/(128*(-1 + Sqrt[1 + x])^11) - (23*(-1 + Sqrt[1 - x])^9)/(384*(-1 + Sqrt[1 + x])^9) + (17*(-1 + Sqrt[1 - x])^7)/(64*(-1 + Sqrt[1 + x])^7) - (17*(-1 + Sqrt[1 - x])^5)/(64*(-1 + Sqrt[1 + x])^5) + (23*(-1 + Sqrt[1 - x])^3)/(384*(-1 + Sqrt[1 + x])^3) - (-1 + Sqrt[1 - x])/(128*(-1 + Sqrt[1 + x]))))/(-1 + 2*Sqrt[1 - x] + 2*Sqrt[1 - x]*x + x^2 + 2*Sqrt[1 + x] - 3*Sqrt[1 - x]*Sqrt[1 + x] - 2*x*Sqrt[1 + x])^3","B",1
1134,1,459,63,1.6770226,"\int \frac{1}{(1-x)^{7/2} (1+x)^{5/2}} \, dx","IntegrateAlgebraic[1/((1 - x)^(7/2)*(1 + x)^(5/2)),x]","\frac{\left(\frac{1}{960}-\frac{\sqrt{1-x}}{960}\right) \left(\sqrt{x+1}-1\right)^{15} \left(\frac{15 \left(\sqrt{1-x}-1\right)^{14}}{\left(\sqrt{x+1}-1\right)^{14}}+\frac{30 \left(\sqrt{1-x}-1\right)^{13}}{\left(\sqrt{x+1}-1\right)^{13}}-\frac{125 \left(\sqrt{1-x}-1\right)^{12}}{\left(\sqrt{x+1}-1\right)^{12}}-\frac{380 \left(\sqrt{1-x}-1\right)^{11}}{\left(\sqrt{x+1}-1\right)^{11}}+\frac{623 \left(\sqrt{1-x}-1\right)^{10}}{\left(\sqrt{x+1}-1\right)^{10}}+\frac{1922 \left(\sqrt{1-x}-1\right)^9}{\left(\sqrt{x+1}-1\right)^9}-\frac{773 \left(\sqrt{1-x}-1\right)^8}{\left(\sqrt{x+1}-1\right)^8}-\frac{3528 \left(\sqrt{1-x}-1\right)^7}{\left(\sqrt{x+1}-1\right)^7}+\frac{773 \left(\sqrt{1-x}-1\right)^6}{\left(\sqrt{x+1}-1\right)^6}+\frac{1922 \left(\sqrt{1-x}-1\right)^5}{\left(\sqrt{x+1}-1\right)^5}-\frac{623 \left(\sqrt{1-x}-1\right)^4}{\left(\sqrt{x+1}-1\right)^4}-\frac{380 \left(\sqrt{1-x}-1\right)^3}{\left(\sqrt{x+1}-1\right)^3}+\frac{125 \left(\sqrt{1-x}-1\right)^2}{\left(\sqrt{x+1}-1\right)^2}+\frac{30 \left(\sqrt{1-x}-1\right)}{\sqrt{x+1}-1}-15\right)}{\left(-x-2 \sqrt{1-x}+\sqrt{1-x} \sqrt{x+1}+1\right)^5 \left(x+\sqrt{1-x} \sqrt{x+1}-2 \sqrt{x+1}+1\right)^3}","\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,"((1/960 - Sqrt[1 - x]/960)*(-1 + Sqrt[1 + x])^15*(-15 + (15*(-1 + Sqrt[1 - x])^14)/(-1 + Sqrt[1 + x])^14 + (30*(-1 + Sqrt[1 - x])^13)/(-1 + Sqrt[1 + x])^13 - (125*(-1 + Sqrt[1 - x])^12)/(-1 + Sqrt[1 + x])^12 - (380*(-1 + Sqrt[1 - x])^11)/(-1 + Sqrt[1 + x])^11 + (623*(-1 + Sqrt[1 - x])^10)/(-1 + Sqrt[1 + x])^10 + (1922*(-1 + Sqrt[1 - x])^9)/(-1 + Sqrt[1 + x])^9 - (773*(-1 + Sqrt[1 - x])^8)/(-1 + Sqrt[1 + x])^8 - (3528*(-1 + Sqrt[1 - x])^7)/(-1 + Sqrt[1 + x])^7 + (773*(-1 + Sqrt[1 - x])^6)/(-1 + Sqrt[1 + x])^6 + (1922*(-1 + Sqrt[1 - x])^5)/(-1 + Sqrt[1 + x])^5 - (623*(-1 + Sqrt[1 - x])^4)/(-1 + Sqrt[1 + x])^4 - (380*(-1 + Sqrt[1 - x])^3)/(-1 + Sqrt[1 + x])^3 + (125*(-1 + Sqrt[1 - x])^2)/(-1 + Sqrt[1 + x])^2 + (30*(-1 + Sqrt[1 - x]))/(-1 + Sqrt[1 + x])))/((1 - 2*Sqrt[1 - x] - x + Sqrt[1 - x]*Sqrt[1 + x])^5*(1 + x - 2*Sqrt[1 + x] + Sqrt[1 - x]*Sqrt[1 + x])^3)","B",1
1135,1,563,83,3.76432,"\int \frac{1}{(1-x)^{9/2} (1+x)^{5/2}} \, dx","IntegrateAlgebraic[1/((1 - x)^(9/2)*(1 + x)^(5/2)),x]","\frac{\left(\frac{1}{5376}-\frac{\sqrt{1-x}}{5376}\right) \left(\sqrt{x+1}-1\right)^{19} \left(\frac{21 \left(\sqrt{1-x}-1\right)^{18}}{\left(\sqrt{x+1}-1\right)^{18}}+\frac{84 \left(\sqrt{1-x}-1\right)^{17}}{\left(\sqrt{x+1}-1\right)^{17}}-\frac{77 \left(\sqrt{1-x}-1\right)^{16}}{\left(\sqrt{x+1}-1\right)^{16}}-\frac{1120 \left(\sqrt{1-x}-1\right)^{15}}{\left(\sqrt{x+1}-1\right)^{15}}-\frac{700 \left(\sqrt{1-x}-1\right)^{14}}{\left(\sqrt{x+1}-1\right)^{14}}+\frac{5936 \left(\sqrt{1-x}-1\right)^{13}}{\left(\sqrt{x+1}-1\right)^{13}}+\frac{8812 \left(\sqrt{1-x}-1\right)^{12}}{\left(\sqrt{x+1}-1\right)^{12}}-\frac{11936 \left(\sqrt{1-x}-1\right)^{11}}{\left(\sqrt{x+1}-1\right)^{11}}-\frac{23354 \left(\sqrt{1-x}-1\right)^{10}}{\left(\sqrt{x+1}-1\right)^{10}}+\frac{11000 \left(\sqrt{1-x}-1\right)^9}{\left(\sqrt{x+1}-1\right)^9}+\frac{23354 \left(\sqrt{1-x}-1\right)^8}{\left(\sqrt{x+1}-1\right)^8}-\frac{11936 \left(\sqrt{1-x}-1\right)^7}{\left(\sqrt{x+1}-1\right)^7}-\frac{8812 \left(\sqrt{1-x}-1\right)^6}{\left(\sqrt{x+1}-1\right)^6}+\frac{5936 \left(\sqrt{1-x}-1\right)^5}{\left(\sqrt{x+1}-1\right)^5}+\frac{700 \left(\sqrt{1-x}-1\right)^4}{\left(\sqrt{x+1}-1\right)^4}-\frac{1120 \left(\sqrt{1-x}-1\right)^3}{\left(\sqrt{x+1}-1\right)^3}+\frac{77 \left(\sqrt{1-x}-1\right)^2}{\left(\sqrt{x+1}-1\right)^2}+\frac{84 \left(\sqrt{1-x}-1\right)}{\sqrt{x+1}-1}-21\right)}{\left(-x-2 \sqrt{1-x}+\sqrt{1-x} \sqrt{x+1}+1\right)^7 \left(x+\sqrt{1-x} \sqrt{x+1}-2 \sqrt{x+1}+1\right)^3}","\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,"((1/5376 - Sqrt[1 - x]/5376)*(-1 + Sqrt[1 + x])^19*(-21 + (21*(-1 + Sqrt[1 - x])^18)/(-1 + Sqrt[1 + x])^18 + (84*(-1 + Sqrt[1 - x])^17)/(-1 + Sqrt[1 + x])^17 - (77*(-1 + Sqrt[1 - x])^16)/(-1 + Sqrt[1 + x])^16 - (1120*(-1 + Sqrt[1 - x])^15)/(-1 + Sqrt[1 + x])^15 - (700*(-1 + Sqrt[1 - x])^14)/(-1 + Sqrt[1 + x])^14 + (5936*(-1 + Sqrt[1 - x])^13)/(-1 + Sqrt[1 + x])^13 + (8812*(-1 + Sqrt[1 - x])^12)/(-1 + Sqrt[1 + x])^12 - (11936*(-1 + Sqrt[1 - x])^11)/(-1 + Sqrt[1 + x])^11 - (23354*(-1 + Sqrt[1 - x])^10)/(-1 + Sqrt[1 + x])^10 + (11000*(-1 + Sqrt[1 - x])^9)/(-1 + Sqrt[1 + x])^9 + (23354*(-1 + Sqrt[1 - x])^8)/(-1 + Sqrt[1 + x])^8 - (11936*(-1 + Sqrt[1 - x])^7)/(-1 + Sqrt[1 + x])^7 - (8812*(-1 + Sqrt[1 - x])^6)/(-1 + Sqrt[1 + x])^6 + (5936*(-1 + Sqrt[1 - x])^5)/(-1 + Sqrt[1 + x])^5 + (700*(-1 + Sqrt[1 - x])^4)/(-1 + Sqrt[1 + x])^4 - (1120*(-1 + Sqrt[1 - x])^3)/(-1 + Sqrt[1 + x])^3 + (77*(-1 + Sqrt[1 - x])^2)/(-1 + Sqrt[1 + x])^2 + (84*(-1 + Sqrt[1 - x]))/(-1 + Sqrt[1 + x])))/((1 - 2*Sqrt[1 - x] - x + Sqrt[1 - x]*Sqrt[1 + x])^7*(1 + x - 2*Sqrt[1 + x] + Sqrt[1 - x]*Sqrt[1 + x])^3)","B",1
1136,1,667,103,7.4867676,"\int \frac{1}{(1-x)^{11/2} (1+x)^{5/2}} \, dx","IntegrateAlgebraic[1/((1 - x)^(11/2)*(1 + x)^(5/2)),x]","\frac{\left(\frac{1}{64512}-\frac{\sqrt{1-x}}{64512}\right) \left(\sqrt{x+1}-1\right)^{23} \left(\frac{63 \left(\sqrt{1-x}-1\right)^{22}}{\left(\sqrt{x+1}-1\right)^{22}}+\frac{378 \left(\sqrt{1-x}-1\right)^{21}}{\left(\sqrt{x+1}-1\right)^{21}}+\frac{399 \left(\sqrt{1-x}-1\right)^{20}}{\left(\sqrt{x+1}-1\right)^{20}}-\frac{4284 \left(\sqrt{1-x}-1\right)^{19}}{\left(\sqrt{x+1}-1\right)^{19}}-\frac{12411 \left(\sqrt{1-x}-1\right)^{18}}{\left(\sqrt{x+1}-1\right)^{18}}+\frac{11634 \left(\sqrt{1-x}-1\right)^{17}}{\left(\sqrt{x+1}-1\right)^{17}}+\frac{90837 \left(\sqrt{1-x}-1\right)^{16}}{\left(\sqrt{x+1}-1\right)^{16}}+\frac{54576 \left(\sqrt{1-x}-1\right)^{15}}{\left(\sqrt{x+1}-1\right)^{15}}-\frac{235706 \left(\sqrt{1-x}-1\right)^{14}}{\left(\sqrt{x+1}-1\right)^{14}}-\frac{283884 \left(\sqrt{1-x}-1\right)^{13}}{\left(\sqrt{x+1}-1\right)^{13}}+\frac{283302 \left(\sqrt{1-x}-1\right)^{12}}{\left(\sqrt{x+1}-1\right)^{12}}+\frac{404248 \left(\sqrt{1-x}-1\right)^{11}}{\left(\sqrt{x+1}-1\right)^{11}}-\frac{283302 \left(\sqrt{1-x}-1\right)^{10}}{\left(\sqrt{x+1}-1\right)^{10}}-\frac{283884 \left(\sqrt{1-x}-1\right)^9}{\left(\sqrt{x+1}-1\right)^9}+\frac{235706 \left(\sqrt{1-x}-1\right)^8}{\left(\sqrt{x+1}-1\right)^8}+\frac{54576 \left(\sqrt{1-x}-1\right)^7}{\left(\sqrt{x+1}-1\right)^7}-\frac{90837 \left(\sqrt{1-x}-1\right)^6}{\left(\sqrt{x+1}-1\right)^6}+\frac{11634 \left(\sqrt{1-x}-1\right)^5}{\left(\sqrt{x+1}-1\right)^5}+\frac{12411 \left(\sqrt{1-x}-1\right)^4}{\left(\sqrt{x+1}-1\right)^4}-\frac{4284 \left(\sqrt{1-x}-1\right)^3}{\left(\sqrt{x+1}-1\right)^3}-\frac{399 \left(\sqrt{1-x}-1\right)^2}{\left(\sqrt{x+1}-1\right)^2}+\frac{378 \left(\sqrt{1-x}-1\right)}{\sqrt{x+1}-1}-63\right)}{\left(-x-2 \sqrt{1-x}+\sqrt{1-x} \sqrt{x+1}+1\right)^9 \left(x+\sqrt{1-x} \sqrt{x+1}-2 \sqrt{x+1}+1\right)^3}","\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,"((1/64512 - Sqrt[1 - x]/64512)*(-1 + Sqrt[1 + x])^23*(-63 + (63*(-1 + Sqrt[1 - x])^22)/(-1 + Sqrt[1 + x])^22 + (378*(-1 + Sqrt[1 - x])^21)/(-1 + Sqrt[1 + x])^21 + (399*(-1 + Sqrt[1 - x])^20)/(-1 + Sqrt[1 + x])^20 - (4284*(-1 + Sqrt[1 - x])^19)/(-1 + Sqrt[1 + x])^19 - (12411*(-1 + Sqrt[1 - x])^18)/(-1 + Sqrt[1 + x])^18 + (11634*(-1 + Sqrt[1 - x])^17)/(-1 + Sqrt[1 + x])^17 + (90837*(-1 + Sqrt[1 - x])^16)/(-1 + Sqrt[1 + x])^16 + (54576*(-1 + Sqrt[1 - x])^15)/(-1 + Sqrt[1 + x])^15 - (235706*(-1 + Sqrt[1 - x])^14)/(-1 + Sqrt[1 + x])^14 - (283884*(-1 + Sqrt[1 - x])^13)/(-1 + Sqrt[1 + x])^13 + (283302*(-1 + Sqrt[1 - x])^12)/(-1 + Sqrt[1 + x])^12 + (404248*(-1 + Sqrt[1 - x])^11)/(-1 + Sqrt[1 + x])^11 - (283302*(-1 + Sqrt[1 - x])^10)/(-1 + Sqrt[1 + x])^10 - (283884*(-1 + Sqrt[1 - x])^9)/(-1 + Sqrt[1 + x])^9 + (235706*(-1 + Sqrt[1 - x])^8)/(-1 + Sqrt[1 + x])^8 + (54576*(-1 + Sqrt[1 - x])^7)/(-1 + Sqrt[1 + x])^7 - (90837*(-1 + Sqrt[1 - x])^6)/(-1 + Sqrt[1 + x])^6 + (11634*(-1 + Sqrt[1 - x])^5)/(-1 + Sqrt[1 + x])^5 + (12411*(-1 + Sqrt[1 - x])^4)/(-1 + Sqrt[1 + x])^4 - (4284*(-1 + Sqrt[1 - x])^3)/(-1 + Sqrt[1 + x])^3 - (399*(-1 + Sqrt[1 - x])^2)/(-1 + Sqrt[1 + x])^2 + (378*(-1 + Sqrt[1 - x]))/(-1 + Sqrt[1 + x])))/((1 - 2*Sqrt[1 - x] - x + Sqrt[1 - x]*Sqrt[1 + x])^9*(1 + x - 2*Sqrt[1 + x] + Sqrt[1 - x]*Sqrt[1 + x])^3)","B",1
1137,1,287,126,0.4614992,"\int (a+a x)^{5/2} (c-c x)^{5/2} \, dx","IntegrateAlgebraic[(a + a*x)^(5/2)*(c - c*x)^(5/2),x]","\frac{4 \sqrt{2} a^{17/2} c^3 (x-1) x \left(8 x^4-26 x^2+33\right) \left(12 x^6+512 x^5+5548 x^4+23648 x^3+46116 x^2+41376 x+13860\right)+4 a^8 c^3 (x-1) x \left(8 x^4-26 x^2+33\right) \left(-x^6-138 x^5-2655 x^4-16652 x^3-43311 x^2-48714 x-19601\right) \sqrt{a x+a}}{\left(3 \sqrt{2} a^{11/2} \left(-768 x^5-32000 x^4-323072 x^3-1190400 x^2-1761024 x-887040\right) \sqrt{a x+a}+3 a^6 \left(64 x^6+8832 x^5+169920 x^4+1065728 x^3+2771904 x^2+3117696 x+1254464\right)\right) \sqrt{c-c x}}-\frac{5}{4} a^{5/2} c^{5/2} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{c-c x}}{\sqrt{c} \sqrt{a x+a}-\sqrt{2} \sqrt{a} \sqrt{c}}\right)","\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}{16} a^2 c^2 x \sqrt{a x+a} \sqrt{c-c x}+\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,"(4*a^8*c^3*(-1 + x)*x*Sqrt[a + a*x]*(33 - 26*x^2 + 8*x^4)*(-19601 - 48714*x - 43311*x^2 - 16652*x^3 - 2655*x^4 - 138*x^5 - x^6) + 4*Sqrt[2]*a^(17/2)*c^3*(-1 + x)*x*(33 - 26*x^2 + 8*x^4)*(13860 + 41376*x + 46116*x^2 + 23648*x^3 + 5548*x^4 + 512*x^5 + 12*x^6))/(Sqrt[c - c*x]*(3*Sqrt[2]*a^(11/2)*Sqrt[a + a*x]*(-887040 - 1761024*x - 1190400*x^2 - 323072*x^3 - 32000*x^4 - 768*x^5) + 3*a^6*(1254464 + 3117696*x + 2771904*x^2 + 1065728*x^3 + 169920*x^4 + 8832*x^5 + 64*x^6))) - (5*a^(5/2)*c^(5/2)*ArcTan[(Sqrt[a]*Sqrt[c - c*x])/(-(Sqrt[2]*Sqrt[a]*Sqrt[c]) + Sqrt[c]*Sqrt[a + a*x])])/4","B",1
1138,1,235,96,0.3231987,"\int (a+a x)^{3/2} (c-c x)^{3/2} \, dx","IntegrateAlgebraic[(a + a*x)^(3/2)*(c - c*x)^(3/2),x]","\frac{-2 \sqrt{2} a^{11/2} c^2 (x-1) x \left(2 x^2-5\right) \left(8 x^4+144 x^3+608 x^2+880 x+408\right)-2 a^5 c^2 (x-1) x \left(2 x^2-5\right) \left(-x^4-60 x^3-454 x^2-956 x-577\right) \sqrt{a x+a}}{\left(\sqrt{2} a^{7/2} \left(-128 x^3-2176 x^2-7552 x-6528\right) \sqrt{a x+a}+a^4 \left(16 x^4+960 x^3+7264 x^2+15296 x+9232\right)\right) \sqrt{c-c x}}-\frac{3}{2} a^{3/2} c^{3/2} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{c-c x}}{\sqrt{c} \sqrt{a x+a}-\sqrt{2} \sqrt{a} \sqrt{c}}\right)","\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,"(-2*a^5*c^2*(-1 + x)*x*Sqrt[a + a*x]*(-5 + 2*x^2)*(-577 - 956*x - 454*x^2 - 60*x^3 - x^4) - 2*Sqrt[2]*a^(11/2)*c^2*(-1 + x)*x*(-5 + 2*x^2)*(408 + 880*x + 608*x^2 + 144*x^3 + 8*x^4))/(Sqrt[c - c*x]*(Sqrt[2]*a^(7/2)*Sqrt[a + a*x]*(-6528 - 7552*x - 2176*x^2 - 128*x^3) + a^4*(9232 + 15296*x + 7264*x^2 + 960*x^3 + 16*x^4))) - (3*a^(3/2)*c^(3/2)*ArcTan[(Sqrt[a]*Sqrt[c - c*x])/(-(Sqrt[2]*Sqrt[a]*Sqrt[c]) + Sqrt[c]*Sqrt[a + a*x])])/2","B",1
1139,1,175,67,0.213067,"\int \sqrt{a+a x} \sqrt{c-c x} \, dx","IntegrateAlgebraic[Sqrt[a + a*x]*Sqrt[c - c*x],x]","\frac{2 \sqrt{2} a^{5/2} c (x-1) x \left(4 x^2+16 x+12\right)+2 a^2 c (x-1) x \left(-x^2-14 x-17\right) \sqrt{a x+a}}{\left(\sqrt{2} a^{3/2} (-16 x-48) \sqrt{a x+a}+a^2 \left(4 x^2+56 x+68\right)\right) \sqrt{c-c x}}-2 \sqrt{a} \sqrt{c} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{c-c x}}{\sqrt{c} \sqrt{a x+a}-\sqrt{2} \sqrt{a} \sqrt{c}}\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,"(2*a^2*c*(-1 + x)*x*Sqrt[a + a*x]*(-17 - 14*x - x^2) + 2*Sqrt[2]*a^(5/2)*c*(-1 + x)*x*(12 + 16*x + 4*x^2))/(Sqrt[c - c*x]*(Sqrt[2]*a^(3/2)*(-48 - 16*x)*Sqrt[a + a*x] + a^2*(68 + 56*x + 4*x^2))) - 2*Sqrt[a]*Sqrt[c]*ArcTan[(Sqrt[a]*Sqrt[c - c*x])/(-(Sqrt[2]*Sqrt[a]*Sqrt[c]) + Sqrt[c]*Sqrt[a + a*x])]","B",1
1140,1,64,43,0.0687235,"\int \frac{1}{\sqrt{a+a x} \sqrt{c-c x}} \, dx","IntegrateAlgebraic[1/(Sqrt[a + a*x]*Sqrt[c - c*x]),x]","-\frac{4 \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{c-c x}}{\sqrt{c} \sqrt{a x+a}-\sqrt{2} \sqrt{a} \sqrt{c}}\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,"(-4*ArcTan[(Sqrt[a]*Sqrt[c - c*x])/(-(Sqrt[2]*Sqrt[a]*Sqrt[c]) + Sqrt[c]*Sqrt[a + a*x])])/(Sqrt[a]*Sqrt[c])","A",1
1141,1,93,27,0.1280298,"\int \frac{1}{(a+a x)^{3/2} (c-c x)^{3/2}} \, dx","IntegrateAlgebraic[1/((a + a*x)^(3/2)*(c - c*x)^(3/2)),x]","\frac{\sqrt{a} \left(-x^2-3 x\right)+2 \sqrt{2} x \sqrt{a x+a}}{a^{3/2} c (-x-3) \sqrt{a x+a} \sqrt{c-c x}+\sqrt{2} a^2 c (2 x+2) \sqrt{c-c x}}","\frac{x}{a c \sqrt{a x+a} \sqrt{c-c x}}",1,"(2*Sqrt[2]*x*Sqrt[a + a*x] + Sqrt[a]*(-3*x - x^2))/(Sqrt[2]*a^2*c*(2 + 2*x)*Sqrt[c - c*x] + a^(3/2)*c*(-3 - x)*Sqrt[a + a*x]*Sqrt[c - c*x])","B",1
1142,1,332,61,0.2120928,"\int \frac{1}{(a+a x)^{5/2} (c-c x)^{5/2}} \, dx","IntegrateAlgebraic[1/((a + a*x)^(5/2)*(c - c*x)^(5/2)),x]","\frac{\left(\frac{x^3}{8}-\frac{3 x^2}{8}+\frac{3 x}{8}-\frac{1}{8}\right) (c-c x)^{3/2} \left(\frac{\left(\sqrt{2} \sqrt{a}-\sqrt{a x+a}\right)^{12}}{192 a^4 c^4 (x-1)^6}-\frac{5 \left(\sqrt{2} \sqrt{a}-\sqrt{a x+a}\right)^{10}}{32 a^3 c^4 (x-1)^5}-\frac{91 \left(\sqrt{2} \sqrt{a}-\sqrt{a x+a}\right)^8}{64 a^2 c^4 (x-1)^4}+\frac{a^2}{192 c^4}-\frac{35 \left(\sqrt{2} \sqrt{a}-\sqrt{a x+a}\right)^6}{16 a c^4 (x-1)^3}-\frac{5 a \left(\sqrt{2} \sqrt{a}-\sqrt{a x+a}\right)^2}{32 c^4 (x-1)}-\frac{91 \left(\sqrt{a x+a}-\sqrt{2} \sqrt{a}\right)^4}{64 c^4 (x-1)^2}\right)}{\left(\sqrt{2} \sqrt{a}-\sqrt{a x+a}\right)^3 \left(a x-\sqrt{2} \sqrt{a} \sqrt{a x+a}+a\right)^3}","\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,"((c - c*x)^(3/2)*(-1/8 + (3*x)/8 - (3*x^2)/8 + x^3/8)*(a^2/(192*c^4) - (5*a*(Sqrt[2]*Sqrt[a] - Sqrt[a + a*x])^2)/(32*c^4*(-1 + x)) - (35*(Sqrt[2]*Sqrt[a] - Sqrt[a + a*x])^6)/(16*a*c^4*(-1 + x)^3) - (91*(Sqrt[2]*Sqrt[a] - Sqrt[a + a*x])^8)/(64*a^2*c^4*(-1 + x)^4) - (5*(Sqrt[2]*Sqrt[a] - Sqrt[a + a*x])^10)/(32*a^3*c^4*(-1 + x)^5) + (Sqrt[2]*Sqrt[a] - Sqrt[a + a*x])^12/(192*a^4*c^4*(-1 + x)^6) - (91*(-(Sqrt[2]*Sqrt[a]) + Sqrt[a + a*x])^4)/(64*c^4*(-1 + x)^2)))/((Sqrt[2]*Sqrt[a] - Sqrt[a + a*x])^3*(a + a*x - Sqrt[2]*Sqrt[a]*Sqrt[a + a*x])^3)","B",1
1143,1,506,91,0.4550819,"\int \frac{1}{(a+a x)^{7/2} (c-c x)^{7/2}} \, dx","IntegrateAlgebraic[1/((a + a*x)^(7/2)*(c - c*x)^(7/2)),x]","\frac{\left(\frac{x^5}{32}-\frac{5 x^4}{32}+\frac{5 x^3}{16}-\frac{5 x^2}{16}+\frac{5 x}{32}-\frac{1}{32}\right) (c-c x)^{5/2} \left(\frac{\left(\sqrt{2} \sqrt{a}-\sqrt{a x+a}\right)^{20}}{5120 a^6 c^6 (x-1)^{10}}-\frac{7 \left(\sqrt{2} \sqrt{a}-\sqrt{a x+a}\right)^{18}}{1536 a^5 c^6 (x-1)^9}+\frac{347 \left(\sqrt{2} \sqrt{a}-\sqrt{a x+a}\right)^{16}}{3072 a^4 c^6 (x-1)^8}+\frac{a^4}{5120 c^6}+\frac{539 \left(\sqrt{2} \sqrt{a}-\sqrt{a x+a}\right)^{14}}{384 a^3 c^6 (x-1)^7}-\frac{7 a^3 \left(\sqrt{2} \sqrt{a}-\sqrt{a x+a}\right)^2}{1536 c^6 (x-1)}+\frac{2101 \left(\sqrt{2} \sqrt{a}-\sqrt{a x+a}\right)^{12}}{512 a^2 c^6 (x-1)^6}+\frac{347 a^2 \left(\sqrt{2} \sqrt{a}-\sqrt{a x+a}\right)^4}{3072 c^6 (x-1)^2}+\frac{7469 \left(\sqrt{2} \sqrt{a}-\sqrt{a x+a}\right)^{10}}{1280 a c^6 (x-1)^5}+\frac{539 a \left(\sqrt{2} \sqrt{a}-\sqrt{a x+a}\right)^6}{384 c^6 (x-1)^3}+\frac{2101 \left(\sqrt{a x+a}-\sqrt{2} \sqrt{a}\right)^8}{512 c^6 (x-1)^4}\right)}{\left(\sqrt{2} \sqrt{a}-\sqrt{a x+a}\right)^5 \left(a x-\sqrt{2} \sqrt{a} \sqrt{a x+a}+a\right)^5}","\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,"((c - c*x)^(5/2)*(-1/32 + (5*x)/32 - (5*x^2)/16 + (5*x^3)/16 - (5*x^4)/32 + x^5/32)*(a^4/(5120*c^6) - (7*a^3*(Sqrt[2]*Sqrt[a] - Sqrt[a + a*x])^2)/(1536*c^6*(-1 + x)) + (347*a^2*(Sqrt[2]*Sqrt[a] - Sqrt[a + a*x])^4)/(3072*c^6*(-1 + x)^2) + (539*a*(Sqrt[2]*Sqrt[a] - Sqrt[a + a*x])^6)/(384*c^6*(-1 + x)^3) + (7469*(Sqrt[2]*Sqrt[a] - Sqrt[a + a*x])^10)/(1280*a*c^6*(-1 + x)^5) + (2101*(Sqrt[2]*Sqrt[a] - Sqrt[a + a*x])^12)/(512*a^2*c^6*(-1 + x)^6) + (539*(Sqrt[2]*Sqrt[a] - Sqrt[a + a*x])^14)/(384*a^3*c^6*(-1 + x)^7) + (347*(Sqrt[2]*Sqrt[a] - Sqrt[a + a*x])^16)/(3072*a^4*c^6*(-1 + x)^8) - (7*(Sqrt[2]*Sqrt[a] - Sqrt[a + a*x])^18)/(1536*a^5*c^6*(-1 + x)^9) + (Sqrt[2]*Sqrt[a] - Sqrt[a + a*x])^20/(5120*a^6*c^6*(-1 + x)^10) + (2101*(-(Sqrt[2]*Sqrt[a]) + Sqrt[a + a*x])^8)/(512*c^6*(-1 + x)^4)))/((Sqrt[2]*Sqrt[a] - Sqrt[a + a*x])^5*(a + a*x - Sqrt[2]*Sqrt[a]*Sqrt[a + a*x])^5)","B",1
1144,1,680,121,0.8562362,"\int \frac{1}{(a+a x)^{9/2} (c-c x)^{9/2}} \, dx","IntegrateAlgebraic[1/((a + a*x)^(9/2)*(c - c*x)^(9/2)),x]","\frac{\left(\frac{x^7}{128}-\frac{7 x^6}{128}+\frac{21 x^5}{128}-\frac{35 x^4}{128}+\frac{35 x^3}{128}-\frac{21 x^2}{128}+\frac{7 x}{128}-\frac{1}{128}\right) (c-c x)^{7/2} \left(\frac{\left(\sqrt{2} \sqrt{a}-\sqrt{a x+a}\right)^{28}}{114688 a^8 c^8 (x-1)^{14}}-\frac{9 \left(\sqrt{2} \sqrt{a}-\sqrt{a x+a}\right)^{26}}{40960 a^7 c^8 (x-1)^{13}}+\frac{289 \left(\sqrt{2} \sqrt{a}-\sqrt{a x+a}\right)^{24}}{81920 a^6 c^8 (x-1)^{12}}+\frac{a^6}{114688 c^8}-\frac{1797 \left(\sqrt{2} \sqrt{a}-\sqrt{a x+a}\right)^{22}}{20480 a^5 c^8 (x-1)^{11}}-\frac{9 a^5 \left(\sqrt{2} \sqrt{a}-\sqrt{a x+a}\right)^2}{40960 c^8 (x-1)}-\frac{22929 \left(\sqrt{2} \sqrt{a}-\sqrt{a x+a}\right)^{20}}{16384 a^4 c^8 (x-1)^{10}}+\frac{289 a^4 \left(\sqrt{2} \sqrt{a}-\sqrt{a x+a}\right)^4}{81920 c^8 (x-1)^2}-\frac{49179 \left(\sqrt{2} \sqrt{a}-\sqrt{a x+a}\right)^{18}}{8192 a^3 c^8 (x-1)^9}-\frac{1797 a^3 \left(\sqrt{2} \sqrt{a}-\sqrt{a x+a}\right)^6}{20480 c^8 (x-1)^3}-\frac{1086943 \left(\sqrt{2} \sqrt{a}-\sqrt{a x+a}\right)^{16}}{81920 a^2 c^8 (x-1)^8}-\frac{22929 a^2 \left(\sqrt{2} \sqrt{a}-\sqrt{a x+a}\right)^8}{16384 c^8 (x-1)^4}-\frac{1218789 \left(\sqrt{2} \sqrt{a}-\sqrt{a x+a}\right)^{14}}{71680 a c^8 (x-1)^7}-\frac{49179 a \left(\sqrt{2} \sqrt{a}-\sqrt{a x+a}\right)^{10}}{8192 c^8 (x-1)^5}-\frac{1086943 \left(\sqrt{a x+a}-\sqrt{2} \sqrt{a}\right)^{12}}{81920 c^8 (x-1)^6}\right)}{\left(\sqrt{2} \sqrt{a}-\sqrt{a x+a}\right)^7 \left(a x-\sqrt{2} \sqrt{a} \sqrt{a x+a}+a\right)^7}","\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,"((c - c*x)^(7/2)*(-1/128 + (7*x)/128 - (21*x^2)/128 + (35*x^3)/128 - (35*x^4)/128 + (21*x^5)/128 - (7*x^6)/128 + x^7/128)*(a^6/(114688*c^8) - (9*a^5*(Sqrt[2]*Sqrt[a] - Sqrt[a + a*x])^2)/(40960*c^8*(-1 + x)) + (289*a^4*(Sqrt[2]*Sqrt[a] - Sqrt[a + a*x])^4)/(81920*c^8*(-1 + x)^2) - (1797*a^3*(Sqrt[2]*Sqrt[a] - Sqrt[a + a*x])^6)/(20480*c^8*(-1 + x)^3) - (22929*a^2*(Sqrt[2]*Sqrt[a] - Sqrt[a + a*x])^8)/(16384*c^8*(-1 + x)^4) - (49179*a*(Sqrt[2]*Sqrt[a] - Sqrt[a + a*x])^10)/(8192*c^8*(-1 + x)^5) - (1218789*(Sqrt[2]*Sqrt[a] - Sqrt[a + a*x])^14)/(71680*a*c^8*(-1 + x)^7) - (1086943*(Sqrt[2]*Sqrt[a] - Sqrt[a + a*x])^16)/(81920*a^2*c^8*(-1 + x)^8) - (49179*(Sqrt[2]*Sqrt[a] - Sqrt[a + a*x])^18)/(8192*a^3*c^8*(-1 + x)^9) - (22929*(Sqrt[2]*Sqrt[a] - Sqrt[a + a*x])^20)/(16384*a^4*c^8*(-1 + x)^10) - (1797*(Sqrt[2]*Sqrt[a] - Sqrt[a + a*x])^22)/(20480*a^5*c^8*(-1 + x)^11) + (289*(Sqrt[2]*Sqrt[a] - Sqrt[a + a*x])^24)/(81920*a^6*c^8*(-1 + x)^12) - (9*(Sqrt[2]*Sqrt[a] - Sqrt[a + a*x])^26)/(40960*a^7*c^8*(-1 + x)^13) + (Sqrt[2]*Sqrt[a] - Sqrt[a + a*x])^28/(114688*a^8*c^8*(-1 + x)^14) - (1086943*(-(Sqrt[2]*Sqrt[a]) + Sqrt[a + a*x])^12)/(81920*c^8*(-1 + x)^6)))/((Sqrt[2]*Sqrt[a] - Sqrt[a + a*x])^7*(a + a*x - Sqrt[2]*Sqrt[a]*Sqrt[a + a*x])^7)","B",1
1145,1,6074,135,34.2461036,"\int (a+b x)^{5/2} (a c-b c x)^{5/2} \, dx","IntegrateAlgebraic[(a + b*x)^(5/2)*(a*c - b*c*x)^(5/2),x]","\text{Result too large to show}","\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}{16} a^4 c^2 x \sqrt{a+b x} \sqrt{a c-b c x}+\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,"Result too large to show","B",1
1146,1,2772,102,9.6014596,"\int (a+b x)^{3/2} (a c-b c x)^{3/2} \, dx","IntegrateAlgebraic[(a + b*x)^(3/2)*(a*c - b*c*x)^(3/2),x]","\text{Result too large to show}","\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,"(2*c^7*Sqrt[a*c - b*c]*Sqrt[a + b*x]*(-5120*a^10*b*c^2 - 2720*a^9*b^2*c^2 + 5168*a^8*b^3*c^2 + 1768*a^7*b^4*c^2 - 1288*a^6*b^5*c^2 - 272*a^5*b^6*c^2 + 16*a^4*b^7*c^2 - 5120*a^10*b*c^2*x - 3120*a^8*b^3*c^2*x - 5840*a^7*b^4*c^2*x + 3016*a^6*b^5*c^2*x + 2128*a^5*b^6*c^2*x - 592*a^4*b^7*c^2*x - 64*a^3*b^8*c^2*x + 2720*a^9*b^2*c^2*x^2 - 3120*a^8*b^3*c^2*x^2 - 1728*a^6*b^5*c^2*x^2 - 3536*a^5*b^6*c^2*x^2 + 784*a^4*b^7*c^2*x^2 + 1088*a^3*b^8*c^2*x^2 - 64*a^2*b^9*c^2*x^2 + 5168*a^8*b^3*c^2*x^3 + 5840*a^7*b^4*c^2*x^3 - 1728*a^6*b^5*c^2*x^3 - 208*a^4*b^7*c^2*x^3 - 448*a^3*b^8*c^2*x^3 + 64*a^2*b^9*c^2*x^3 + 128*a*b^10*c^2*x^3 - 1768*a^7*b^4*c^2*x^4 + 3016*a^6*b^5*c^2*x^4 + 3536*a^5*b^6*c^2*x^4 - 208*a^4*b^7*c^2*x^4 - 1288*a^6*b^5*c^2*x^5 - 2128*a^5*b^6*c^2*x^5 + 784*a^4*b^7*c^2*x^5 + 448*a^3*b^8*c^2*x^5 + 272*a^5*b^6*c^2*x^6 - 592*a^4*b^7*c^2*x^6 - 1088*a^3*b^8*c^2*x^6 + 64*a^2*b^9*c^2*x^6 + 16*a^4*b^7*c^2*x^7 + 64*a^3*b^8*c^2*x^7 - 64*a^2*b^9*c^2*x^7 - 128*a*b^10*c^2*x^7) + 2*c^7*Sqrt[a + b*x]*Sqrt[a*c - b*c*x]*(5080*a^10*b*c^2 - 7412*a^8*b^3*c^2 + 2452*a^6*b^5*c^2 - 120*a^4*b^7*c^2 + 5160*a^10*b*c^2*x + 2280*a^8*b^3*c^2*x - 6399*a^6*b^5*c^2*x + 1852*a^4*b^7*c^2*x - 8*a^2*b^9*c^2*x + 5380*a^8*b^3*c^2*x^2 + 720*a^6*b^5*c^2*x^2 - 1800*a^4*b^7*c^2*x^2 + 480*a^2*b^9*c^2*x^2 - 4344*a^8*b^3*c^2*x^3 + 5482*a^6*b^5*c^2*x^3 + 26*a^4*b^7*c^2*x^3 - 64*a^2*b^9*c^2*x^3 + 16*b^11*c^2*x^3 - 3172*a^6*b^5*c^2*x^4 + 1560*a^4*b^7*c^2*x^4 + 917*a^6*b^5*c^2*x^5 - 1876*a^4*b^7*c^2*x^5 + 56*a^2*b^9*c^2*x^5 + 360*a^4*b^7*c^2*x^6 - 480*a^2*b^9*c^2*x^6 - 2*a^4*b^7*c^2*x^7 + 16*a^2*b^9*c^2*x^7 - 16*b^11*c^2*x^7) + Sqrt[a + b]*(2*c^7*Sqrt[a*c - b*c*x]*(-5120*a^10*b*c^2 + 2720*a^9*b^2*c^2 + 5168*a^8*b^3*c^2 - 1768*a^7*b^4*c^2 - 1288*a^6*b^5*c^2 + 272*a^5*b^6*c^2 + 16*a^4*b^7*c^2 - 5120*a^10*b*c^2*x - 3120*a^8*b^3*c^2*x + 5840*a^7*b^4*c^2*x + 3016*a^6*b^5*c^2*x - 2128*a^5*b^6*c^2*x - 592*a^4*b^7*c^2*x + 64*a^3*b^8*c^2*x - 2720*a^9*b^2*c^2*x^2 - 3120*a^8*b^3*c^2*x^2 - 1728*a^6*b^5*c^2*x^2 + 3536*a^5*b^6*c^2*x^2 + 784*a^4*b^7*c^2*x^2 - 1088*a^3*b^8*c^2*x^2 - 64*a^2*b^9*c^2*x^2 + 5168*a^8*b^3*c^2*x^3 - 5840*a^7*b^4*c^2*x^3 - 1728*a^6*b^5*c^2*x^3 - 208*a^4*b^7*c^2*x^3 + 448*a^3*b^8*c^2*x^3 + 64*a^2*b^9*c^2*x^3 - 128*a*b^10*c^2*x^3 + 1768*a^7*b^4*c^2*x^4 + 3016*a^6*b^5*c^2*x^4 - 3536*a^5*b^6*c^2*x^4 - 208*a^4*b^7*c^2*x^4 - 1288*a^6*b^5*c^2*x^5 + 2128*a^5*b^6*c^2*x^5 + 784*a^4*b^7*c^2*x^5 - 448*a^3*b^8*c^2*x^5 - 272*a^5*b^6*c^2*x^6 - 592*a^4*b^7*c^2*x^6 + 1088*a^3*b^8*c^2*x^6 + 64*a^2*b^9*c^2*x^6 + 16*a^4*b^7*c^2*x^7 - 64*a^3*b^8*c^2*x^7 - 64*a^2*b^9*c^2*x^7 + 128*a*b^10*c^2*x^7) + 2*c^7*Sqrt[a*c - b*c]*(5160*a^10*b*c^2 - 4344*a^8*b^3*c^2 + 917*a^6*b^5*c^2 - 2*a^4*b^7*c^2 + 5080*a^10*b*c^2*x + 5380*a^8*b^3*c^2*x - 3172*a^6*b^5*c^2*x + 360*a^4*b^7*c^2*x + 2280*a^8*b^3*c^2*x^2 + 5482*a^6*b^5*c^2*x^2 - 1876*a^4*b^7*c^2*x^2 + 16*a^2*b^9*c^2*x^2 - 7412*a^8*b^3*c^2*x^3 + 720*a^6*b^5*c^2*x^3 + 1560*a^4*b^7*c^2*x^3 - 480*a^2*b^9*c^2*x^3 - 6399*a^6*b^5*c^2*x^4 + 26*a^4*b^7*c^2*x^4 + 56*a^2*b^9*c^2*x^4 - 16*b^11*c^2*x^4 + 2452*a^6*b^5*c^2*x^5 - 1800*a^4*b^7*c^2*x^5 + 1852*a^4*b^7*c^2*x^6 - 64*a^2*b^9*c^2*x^6 - 120*a^4*b^7*c^2*x^7 + 480*a^2*b^9*c^2*x^7 - 8*a^2*b^9*c^2*x^8 + 16*b^11*c^2*x^8)))/(b*Sqrt[a + b]*Sqrt[a + b*x]*(-16384*a^7*c^8 + 7680*a^6*b*c^8 + 2304*a^5*b^2*c^8 - 128*a^4*b^3*c^8 + 7680*a^6*b*c^8*x - 19968*a^5*b^2*c^8*x + 4224*a^4*b^3*c^8*x + 512*a^3*b^4*c^8*x + 2304*a^5*b^2*c^8*x^2 + 4224*a^4*b^3*c^8*x^2 - 9216*a^3*b^4*c^8*x^2 + 512*a^2*b^5*c^8*x^2 - 128*a^4*b^3*c^8*x^3 + 512*a^3*b^4*c^8*x^3 + 512*a^2*b^5*c^8*x^3 - 1024*a*b^6*c^8*x^3) + b*(16512*a^8*c^8 - 7296*a^6*b^2*c^8 + 16*a^4*b^4*c^8 + 18176*a^6*b^2*c^8*x - 2880*a^4*b^4*c^8*x - 7296*a^6*b^2*c^8*x^2 + 14688*a^4*b^4*c^8*x^2 - 128*a^2*b^6*c^8*x^2 - 2880*a^4*b^4*c^8*x^3 + 3840*a^2*b^6*c^8*x^3 + 16*a^4*b^4*c^8*x^4 - 128*a^2*b^6*c^8*x^4 + 128*b^8*c^8*x^4) + Sqrt[a*c - b*c]*Sqrt[a*c - b*c*x]*(b*Sqrt[a + b]*Sqrt[a + b*x]*(16256*a^6*c^7 - 960*a^4*b^2*c^7 + 14592*a^4*b^2*c^7*x - 64*a^2*b^4*c^7*x - 960*a^4*b^2*c^7*x^2 + 3840*a^2*b^4*c^7*x^2 - 64*a^2*b^4*c^7*x^3 + 128*b^6*c^7*x^3) + b*(-16384*a^7*c^7 - 7680*a^6*b*c^7 + 2304*a^5*b^2*c^7 + 128*a^4*b^3*c^7 - 7680*a^6*b*c^7*x - 19968*a^5*b^2*c^7*x - 4224*a^4*b^3*c^7*x + 512*a^3*b^4*c^7*x + 2304*a^5*b^2*c^7*x^2 - 4224*a^4*b^3*c^7*x^2 - 9216*a^3*b^4*c^7*x^2 - 512*a^2*b^5*c^7*x^2 + 128*a^4*b^3*c^7*x^3 + 512*a^3*b^4*c^7*x^3 - 512*a^2*b^5*c^7*x^3 - 1024*a*b^6*c^7*x^3))) - (3*a^4*c^(3/2)*ArcTan[(Sqrt[a*c - b*c] - Sqrt[a*c - b*c*x])/(Sqrt[a + b]*Sqrt[c] - Sqrt[c]*Sqrt[a + b*x])])/(2*b)","B",1
1147,1,618,68,1.4644093,"\int \sqrt{a+b x} \sqrt{a c-b c x} \, dx","IntegrateAlgebraic[Sqrt[a + b*x]*Sqrt[a*c - b*c*x],x]","\frac{\left(\frac{2 c \sqrt{a+b x}}{b}-\frac{2 c \sqrt{a+b}}{b}\right) \left(\sqrt{a c-b c}-\sqrt{a c-b c x}\right) \left(-c \sqrt{a+b} \sqrt{a+b x}+\sqrt{a c-b c} \sqrt{a c-b c x}+b c x+b c\right) \left(a^4 \left(-c^2\right)+2 a^3 c^2 \sqrt{a+b} \sqrt{a+b x}+2 a^3 c \sqrt{a c-b c} \sqrt{a c-b c x}+a^2 b^2 c^2 x^2-3 a^2 b^2 c^2 x+a^2 b^2 c^2-2 a^2 b c^2 \sqrt{a+b} \sqrt{a+b x}-2 a^2 b c^2 x \sqrt{a+b} \sqrt{a+b x}+2 a^2 b c x \sqrt{a c-b c} \sqrt{a c-b c x}+2 a^2 b c \sqrt{a c-b c} \sqrt{a c-b c x}-3 a^2 c \sqrt{a+b} \sqrt{a c-b c} \sqrt{a+b x} \sqrt{a c-b c x}+4 a b^2 c^2 x \sqrt{a+b} \sqrt{a+b x}+4 a b^2 c x \sqrt{a c-b c} \sqrt{a c-b c x}-2 b^2 c x \sqrt{a+b} \sqrt{a c-b c} \sqrt{a+b x} \sqrt{a c-b c x}-2 b^4 c^2 x^2\right)}{\left(c \sqrt{a+b} \sqrt{a+b x}+\sqrt{a c-b c} \sqrt{a c-b c x}-2 a c\right)^4}-\frac{2 a^2 \sqrt{c} \tan ^{-1}\left(\frac{\sqrt{a c-b c}-\sqrt{a c-b c x}}{\sqrt{c} \sqrt{a+b}-\sqrt{c} \sqrt{a+b x}}\right)}{b}","\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,"(((-2*Sqrt[a + b]*c)/b + (2*c*Sqrt[a + b*x])/b)*(Sqrt[a*c - b*c] - Sqrt[a*c - b*c*x])*(b*c + b*c*x - Sqrt[a + b]*c*Sqrt[a + b*x] + Sqrt[a*c - b*c]*Sqrt[a*c - b*c*x])*(-(a^4*c^2) + a^2*b^2*c^2 - 3*a^2*b^2*c^2*x + a^2*b^2*c^2*x^2 - 2*b^4*c^2*x^2 + 2*a^3*Sqrt[a + b]*c^2*Sqrt[a + b*x] - 2*a^2*b*Sqrt[a + b]*c^2*Sqrt[a + b*x] - 2*a^2*b*Sqrt[a + b]*c^2*x*Sqrt[a + b*x] + 4*a*b^2*Sqrt[a + b]*c^2*x*Sqrt[a + b*x] + 2*a^3*c*Sqrt[a*c - b*c]*Sqrt[a*c - b*c*x] + 2*a^2*b*c*Sqrt[a*c - b*c]*Sqrt[a*c - b*c*x] + 2*a^2*b*c*Sqrt[a*c - b*c]*x*Sqrt[a*c - b*c*x] + 4*a*b^2*c*Sqrt[a*c - b*c]*x*Sqrt[a*c - b*c*x] - 3*a^2*Sqrt[a + b]*c*Sqrt[a*c - b*c]*Sqrt[a + b*x]*Sqrt[a*c - b*c*x] - 2*b^2*Sqrt[a + b]*c*Sqrt[a*c - b*c]*x*Sqrt[a + b*x]*Sqrt[a*c - b*c*x]))/(-2*a*c + Sqrt[a + b]*c*Sqrt[a + b*x] + Sqrt[a*c - b*c]*Sqrt[a*c - b*c*x])^4 - (2*a^2*Sqrt[c]*ArcTan[(Sqrt[a*c - b*c] - Sqrt[a*c - b*c*x])/(Sqrt[a + b]*Sqrt[c] - Sqrt[c]*Sqrt[a + b*x])])/b","B",1
1148,1,72,38,0.2878715,"\int \frac{1}{\sqrt{a+b x} \sqrt{a c-b c x}} \, dx","IntegrateAlgebraic[1/(Sqrt[a + b*x]*Sqrt[a*c - b*c*x]),x]","-\frac{4 \tan ^{-1}\left(\frac{\sqrt{a c-b c}-\sqrt{a c-b c x}}{\sqrt{c} \sqrt{a+b}-\sqrt{c} \sqrt{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,"(-4*ArcTan[(Sqrt[a*c - b*c] - Sqrt[a*c - b*c*x])/(Sqrt[a + b]*Sqrt[c] - Sqrt[c]*Sqrt[a + b*x])])/(b*Sqrt[c])","A",1
1149,1,1911,30,20.605348,"\int \frac{1}{(a+b x)^{3/2} (a c-b c x)^{3/2}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(3/2)*(a*c - b*c*x)^(3/2)),x]","\frac{\left(\frac{\sqrt{a+b x}}{16 b \left(b^2-a^2\right) c}-\frac{\sqrt{a+b}}{16 b \left(b^2-a^2\right) c}\right) \left(\sqrt{a c-b c}-\sqrt{a c-b c x}\right)^8 \left(\frac{c \left(\sqrt{a+b}-\sqrt{a+b x}\right)^2}{\left(\sqrt{a c-b c}-\sqrt{a c-b c x}\right)^2}-1\right) \left(\frac{8 \left(-a^2 c^2+b^2 c^2+b^2 x^2 c^2+3 b^2 x c^2-2 b \sqrt{a+b} x \sqrt{a+b x} c^2+2 a \sqrt{a+b} \sqrt{a+b x} c^2-2 b \sqrt{a+b} \sqrt{a+b x} c^2+2 b \sqrt{a c-b c} x \sqrt{a c-b c x} c+2 a \sqrt{a c-b c} \sqrt{a c-b c x} c+2 b \sqrt{a c-b c} \sqrt{a c-b c x} c-3 \sqrt{a+b} \sqrt{a c-b c} \sqrt{a+b x} \sqrt{a c-b c x} c\right) a^2}{\left(\sqrt{a c-b c}-\sqrt{a c-b c x}\right)^4}-\frac{8 b \sqrt{a+b} \sqrt{a c-b c} \left(\sqrt{a+b}-\sqrt{a+b x}\right) \left(-b c-b x c+\sqrt{a+b} \sqrt{a+b x} c-\sqrt{a c-b c} \sqrt{a c-b c x}\right)}{\left(\sqrt{a c-b c}-\sqrt{a c-b c x}\right)^3}-\frac{8 b^2 \left(-a^2 c^2+b^2 c^2+b^2 x^2 c^2+3 b^2 x c^2-2 b \sqrt{a+b} x \sqrt{a+b x} c^2+2 a \sqrt{a+b} \sqrt{a+b x} c^2-2 b \sqrt{a+b} \sqrt{a+b x} c^2+2 b \sqrt{a c-b c} x \sqrt{a c-b c x} c+2 a \sqrt{a c-b c} \sqrt{a c-b c x} c+2 b \sqrt{a c-b c} \sqrt{a c-b c x} c-3 \sqrt{a+b} \sqrt{a c-b c} \sqrt{a+b x} \sqrt{a c-b c x} c\right)}{\left(\sqrt{a c-b c}-\sqrt{a c-b c x}\right)^4}\right)}{\left(\sqrt{a c-b c x}-\sqrt{a c-b c}\right) \left(18 c^4 a^6-16 \sqrt{a+b} c^4 \sqrt{a+b x} a^5-16 c^3 \sqrt{a c-b c} \sqrt{a c-b c x} a^5-37 b^2 c^4 a^4-19 b^2 c^4 x^2 a^4-14 b^2 c^4 x a^4+4 b \sqrt{a+b} c^4 \sqrt{a+b x} a^4+4 b \sqrt{a+b} c^4 x \sqrt{a+b x} a^4-4 b c^3 \sqrt{a c-b c} x \sqrt{a c-b c x} a^4-4 b c^3 \sqrt{a c-b c} \sqrt{a c-b c x} a^4+14 \sqrt{a+b} c^3 \sqrt{a c-b c} \sqrt{a+b x} \sqrt{a c-b c x} a^4+32 b^2 \sqrt{a+b} c^4 \sqrt{a+b x} a^3+16 b^2 \sqrt{a+b} c^4 x^2 \sqrt{a+b x} a^3+24 b^2 \sqrt{a+b} c^4 x \sqrt{a+b x} a^3+16 b^2 c^3 \sqrt{a c-b c} x^2 \sqrt{a c-b c x} a^3+24 b^2 c^3 \sqrt{a c-b c} x \sqrt{a c-b c x} a^3+32 b^2 c^3 \sqrt{a c-b c} \sqrt{a c-b c x} a^3+2 b^4 c^4 a^2+b^4 c^4 x^4 a^2+14 b^4 c^4 x^3 a^2+37 b^4 c^4 x^2 a^2-8 b^3 \sqrt{a+b} c^4 \sqrt{a+b x} a^2-4 b^3 \sqrt{a+b} c^4 x^3 \sqrt{a+b x} a^2-28 b^3 \sqrt{a+b} c^4 x^2 \sqrt{a+b x} a^2-32 b^3 \sqrt{a+b} c^4 x \sqrt{a+b x} a^2+4 b^3 c^3 \sqrt{a c-b c} x^3 \sqrt{a c-b c x} a^2+28 b^3 c^3 \sqrt{a c-b c} x^2 \sqrt{a c-b c x} a^2+32 b^3 c^3 \sqrt{a c-b c} x \sqrt{a c-b c x} a^2+8 b^3 c^3 \sqrt{a c-b c} \sqrt{a c-b c x} a^2-14 b^2 \sqrt{a+b} c^3 \sqrt{a c-b c} x^2 \sqrt{a+b x} \sqrt{a c-b c x} a^2-34 b^2 \sqrt{a+b} c^3 \sqrt{a c-b c} x \sqrt{a+b x} \sqrt{a c-b c x} a^2-28 b^2 \sqrt{a+b} c^3 \sqrt{a c-b c} \sqrt{a+b x} \sqrt{a c-b c x} a^2+8 b^4 \sqrt{a+b} c^4 x \sqrt{a+b x} a+8 b^4 c^3 \sqrt{a c-b c} x \sqrt{a c-b c x} a-2 b^6 c^4 x^2-2 b^4 \sqrt{a+b} c^3 \sqrt{a c-b c} x \sqrt{a+b x} \sqrt{a c-b c x}\right)}","\frac{x}{a^2 c \sqrt{a+b x} \sqrt{a c-b c x}}",1,"((-1/16*Sqrt[a + b]/(b*(-a^2 + b^2)*c) + Sqrt[a + b*x]/(16*b*(-a^2 + b^2)*c))*(Sqrt[a*c - b*c] - Sqrt[a*c - b*c*x])^8*(-1 + (c*(Sqrt[a + b] - Sqrt[a + b*x])^2)/(Sqrt[a*c - b*c] - Sqrt[a*c - b*c*x])^2)*((-8*b*Sqrt[a + b]*Sqrt[a*c - b*c]*(Sqrt[a + b] - Sqrt[a + b*x])*(-(b*c) - b*c*x + Sqrt[a + b]*c*Sqrt[a + b*x] - Sqrt[a*c - b*c]*Sqrt[a*c - b*c*x]))/(Sqrt[a*c - b*c] - Sqrt[a*c - b*c*x])^3 + (8*a^2*(-(a^2*c^2) + b^2*c^2 + 3*b^2*c^2*x + b^2*c^2*x^2 + 2*a*Sqrt[a + b]*c^2*Sqrt[a + b*x] - 2*b*Sqrt[a + b]*c^2*Sqrt[a + b*x] - 2*b*Sqrt[a + b]*c^2*x*Sqrt[a + b*x] + 2*a*c*Sqrt[a*c - b*c]*Sqrt[a*c - b*c*x] + 2*b*c*Sqrt[a*c - b*c]*Sqrt[a*c - b*c*x] + 2*b*c*Sqrt[a*c - b*c]*x*Sqrt[a*c - b*c*x] - 3*Sqrt[a + b]*c*Sqrt[a*c - b*c]*Sqrt[a + b*x]*Sqrt[a*c - b*c*x]))/(Sqrt[a*c - b*c] - Sqrt[a*c - b*c*x])^4 - (8*b^2*(-(a^2*c^2) + b^2*c^2 + 3*b^2*c^2*x + b^2*c^2*x^2 + 2*a*Sqrt[a + b]*c^2*Sqrt[a + b*x] - 2*b*Sqrt[a + b]*c^2*Sqrt[a + b*x] - 2*b*Sqrt[a + b]*c^2*x*Sqrt[a + b*x] + 2*a*c*Sqrt[a*c - b*c]*Sqrt[a*c - b*c*x] + 2*b*c*Sqrt[a*c - b*c]*Sqrt[a*c - b*c*x] + 2*b*c*Sqrt[a*c - b*c]*x*Sqrt[a*c - b*c*x] - 3*Sqrt[a + b]*c*Sqrt[a*c - b*c]*Sqrt[a + b*x]*Sqrt[a*c - b*c*x]))/(Sqrt[a*c - b*c] - Sqrt[a*c - b*c*x])^4))/((-Sqrt[a*c - b*c] + Sqrt[a*c - b*c*x])*(18*a^6*c^4 - 37*a^4*b^2*c^4 + 2*a^2*b^4*c^4 - 14*a^4*b^2*c^4*x - 19*a^4*b^2*c^4*x^2 + 37*a^2*b^4*c^4*x^2 - 2*b^6*c^4*x^2 + 14*a^2*b^4*c^4*x^3 + a^2*b^4*c^4*x^4 - 16*a^5*Sqrt[a + b]*c^4*Sqrt[a + b*x] + 4*a^4*b*Sqrt[a + b]*c^4*Sqrt[a + b*x] + 32*a^3*b^2*Sqrt[a + b]*c^4*Sqrt[a + b*x] - 8*a^2*b^3*Sqrt[a + b]*c^4*Sqrt[a + b*x] + 4*a^4*b*Sqrt[a + b]*c^4*x*Sqrt[a + b*x] + 24*a^3*b^2*Sqrt[a + b]*c^4*x*Sqrt[a + b*x] - 32*a^2*b^3*Sqrt[a + b]*c^4*x*Sqrt[a + b*x] + 8*a*b^4*Sqrt[a + b]*c^4*x*Sqrt[a + b*x] + 16*a^3*b^2*Sqrt[a + b]*c^4*x^2*Sqrt[a + b*x] - 28*a^2*b^3*Sqrt[a + b]*c^4*x^2*Sqrt[a + b*x] - 4*a^2*b^3*Sqrt[a + b]*c^4*x^3*Sqrt[a + b*x] - 16*a^5*c^3*Sqrt[a*c - b*c]*Sqrt[a*c - b*c*x] - 4*a^4*b*c^3*Sqrt[a*c - b*c]*Sqrt[a*c - b*c*x] + 32*a^3*b^2*c^3*Sqrt[a*c - b*c]*Sqrt[a*c - b*c*x] + 8*a^2*b^3*c^3*Sqrt[a*c - b*c]*Sqrt[a*c - b*c*x] - 4*a^4*b*c^3*Sqrt[a*c - b*c]*x*Sqrt[a*c - b*c*x] + 24*a^3*b^2*c^3*Sqrt[a*c - b*c]*x*Sqrt[a*c - b*c*x] + 32*a^2*b^3*c^3*Sqrt[a*c - b*c]*x*Sqrt[a*c - b*c*x] + 8*a*b^4*c^3*Sqrt[a*c - b*c]*x*Sqrt[a*c - b*c*x] + 16*a^3*b^2*c^3*Sqrt[a*c - b*c]*x^2*Sqrt[a*c - b*c*x] + 28*a^2*b^3*c^3*Sqrt[a*c - b*c]*x^2*Sqrt[a*c - b*c*x] + 4*a^2*b^3*c^3*Sqrt[a*c - b*c]*x^3*Sqrt[a*c - b*c*x] + 14*a^4*Sqrt[a + b]*c^3*Sqrt[a*c - b*c]*Sqrt[a + b*x]*Sqrt[a*c - b*c*x] - 28*a^2*b^2*Sqrt[a + b]*c^3*Sqrt[a*c - b*c]*Sqrt[a + b*x]*Sqrt[a*c - b*c*x] - 34*a^2*b^2*Sqrt[a + b]*c^3*Sqrt[a*c - b*c]*x*Sqrt[a + b*x]*Sqrt[a*c - b*c*x] - 2*b^4*Sqrt[a + b]*c^3*Sqrt[a*c - b*c]*x*Sqrt[a + b*x]*Sqrt[a*c - b*c*x] - 14*a^2*b^2*Sqrt[a + b]*c^3*Sqrt[a*c - b*c]*x^2*Sqrt[a + b*x]*Sqrt[a*c - b*c*x]))","B",1
1150,1,1634,67,40.3599285,"\int \frac{1}{(a+b x)^{5/2} (a c-b c x)^{5/2}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(5/2)*(a*c - b*c*x)^(5/2)),x]","\frac{\left(\frac{c}{48 b (a+b) (a c-b c)^{3/2}}-\frac{c \sqrt{a+b x}}{48 b (a+b)^{3/2} (a c-b c)^{3/2}}\right) \left(\sqrt{a c-b c}-\sqrt{a c-b c x}\right)^{12} \left(\frac{c \left(\sqrt{a+b}-\sqrt{a+b x}\right)^2}{\left(\sqrt{a c-b c}-\sqrt{a c-b c x}\right)^2}-1\right) \left(\frac{64 a^2 \left(-54 a^4 c^4-2 b^4 c^4-2 b^4 x^4 c^4-28 b^4 x^3 c^4+39 a^2 b^2 c^4-74 b^4 x^2 c^4+39 a^2 b^2 x^2 c^4-28 b^4 x c^4+14 a^2 b^2 x c^4+8 b^3 \sqrt{a+b} x^3 \sqrt{a+b x} c^4+56 b^3 \sqrt{a+b} x^2 \sqrt{a+b x} c^4-32 a b^2 \sqrt{a+b} x^2 \sqrt{a+b x} c^4+56 b^3 \sqrt{a+b} x \sqrt{a+b x} c^4-40 a b^2 \sqrt{a+b} x \sqrt{a+b x} c^4-12 a^2 b \sqrt{a+b} x \sqrt{a+b x} c^4+48 a^3 \sqrt{a+b} \sqrt{a+b x} c^4+8 b^3 \sqrt{a+b} \sqrt{a+b x} c^4-32 a b^2 \sqrt{a+b} \sqrt{a+b x} c^4-12 a^2 b \sqrt{a+b} \sqrt{a+b x} c^4-8 b^3 \sqrt{a c-b c} x^3 \sqrt{a c-b c x} c^3-56 b^3 \sqrt{a c-b c} x^2 \sqrt{a c-b c x} c^3-32 a b^2 \sqrt{a c-b c} x^2 \sqrt{a c-b c x} c^3-56 b^3 \sqrt{a c-b c} x \sqrt{a c-b c x} c^3-40 a b^2 \sqrt{a c-b c} x \sqrt{a c-b c x} c^3+12 a^2 b \sqrt{a c-b c} x \sqrt{a c-b c x} c^3+48 a^3 \sqrt{a c-b c} \sqrt{a c-b c x} c^3-8 b^3 \sqrt{a c-b c} \sqrt{a c-b c x} c^3-32 a b^2 \sqrt{a c-b c} \sqrt{a c-b c x} c^3+12 a^2 b \sqrt{a c-b c} \sqrt{a c-b c x} c^3+28 b^2 \sqrt{a+b} \sqrt{a c-b c} x^2 \sqrt{a+b x} \sqrt{a c-b c x} c^3+66 b^2 \sqrt{a+b} \sqrt{a c-b c} x \sqrt{a+b x} \sqrt{a c-b c x} c^3-42 a^2 \sqrt{a+b} \sqrt{a c-b c} \sqrt{a+b x} \sqrt{a c-b c x} c^3+28 b^2 \sqrt{a+b} \sqrt{a c-b c} \sqrt{a+b x} \sqrt{a c-b c x} c^3\right)}{\left(\sqrt{a c-b c}-\sqrt{a c-b c x}\right)^8}-\frac{192 b^2 c^2 \left(-c a^2+2 \sqrt{a+b} c \sqrt{a+b x} a+2 \sqrt{a c-b c} \sqrt{a c-b c x} a+b^2 c x^2+b^2 c+3 b^2 c x-2 b \sqrt{a+b} c \sqrt{a+b x}-2 b \sqrt{a+b} c x \sqrt{a+b x}+2 b \sqrt{a c-b c} x \sqrt{a c-b c x}+2 b \sqrt{a c-b c} \sqrt{a c-b c x}-3 \sqrt{a+b} \sqrt{a c-b c} \sqrt{a+b x} \sqrt{a c-b c x}\right) \left(-3 c x a^2+2 \sqrt{a+b} c x \sqrt{a+b x} a+2 \sqrt{a c-b c} x \sqrt{a c-b c x} a-b^2 c x^2-\sqrt{a+b} \sqrt{a c-b c} x \sqrt{a+b x} \sqrt{a c-b c x}\right)}{\left(\sqrt{a c-b c}-\sqrt{a c-b c x}\right)^8}\right)}{\left(\sqrt{a c-b c x}-\sqrt{a c-b c}\right) \left(-b \sqrt{a c-b c} x c+a \sqrt{a c-b c} c-2 a \sqrt{a c-b c x} c+\sqrt{a+b} \sqrt{a+b x} \sqrt{a c-b c x} c\right)^3 \left(b \sqrt{a+b} x c+a \sqrt{a+b} c-2 a \sqrt{a+b x} c+\sqrt{a c-b c} \sqrt{a+b x} \sqrt{a c-b c x}\right)^3}","\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,"((c/(48*b*(a + b)*(a*c - b*c)^(3/2)) - (c*Sqrt[a + b*x])/(48*b*(a + b)^(3/2)*(a*c - b*c)^(3/2)))*(Sqrt[a*c - b*c] - Sqrt[a*c - b*c*x])^12*(-1 + (c*(Sqrt[a + b] - Sqrt[a + b*x])^2)/(Sqrt[a*c - b*c] - Sqrt[a*c - b*c*x])^2)*((-192*b^2*c^2*(-(a^2*c) + b^2*c + 3*b^2*c*x + b^2*c*x^2 + 2*a*Sqrt[a + b]*c*Sqrt[a + b*x] - 2*b*Sqrt[a + b]*c*Sqrt[a + b*x] - 2*b*Sqrt[a + b]*c*x*Sqrt[a + b*x] + 2*a*Sqrt[a*c - b*c]*Sqrt[a*c - b*c*x] + 2*b*Sqrt[a*c - b*c]*Sqrt[a*c - b*c*x] + 2*b*Sqrt[a*c - b*c]*x*Sqrt[a*c - b*c*x] - 3*Sqrt[a + b]*Sqrt[a*c - b*c]*Sqrt[a + b*x]*Sqrt[a*c - b*c*x])*(-3*a^2*c*x - b^2*c*x^2 + 2*a*Sqrt[a + b]*c*x*Sqrt[a + b*x] + 2*a*Sqrt[a*c - b*c]*x*Sqrt[a*c - b*c*x] - Sqrt[a + b]*Sqrt[a*c - b*c]*x*Sqrt[a + b*x]*Sqrt[a*c - b*c*x]))/(Sqrt[a*c - b*c] - Sqrt[a*c - b*c*x])^8 + (64*a^2*(-54*a^4*c^4 + 39*a^2*b^2*c^4 - 2*b^4*c^4 + 14*a^2*b^2*c^4*x - 28*b^4*c^4*x + 39*a^2*b^2*c^4*x^2 - 74*b^4*c^4*x^2 - 28*b^4*c^4*x^3 - 2*b^4*c^4*x^4 + 48*a^3*Sqrt[a + b]*c^4*Sqrt[a + b*x] - 12*a^2*b*Sqrt[a + b]*c^4*Sqrt[a + b*x] - 32*a*b^2*Sqrt[a + b]*c^4*Sqrt[a + b*x] + 8*b^3*Sqrt[a + b]*c^4*Sqrt[a + b*x] - 12*a^2*b*Sqrt[a + b]*c^4*x*Sqrt[a + b*x] - 40*a*b^2*Sqrt[a + b]*c^4*x*Sqrt[a + b*x] + 56*b^3*Sqrt[a + b]*c^4*x*Sqrt[a + b*x] - 32*a*b^2*Sqrt[a + b]*c^4*x^2*Sqrt[a + b*x] + 56*b^3*Sqrt[a + b]*c^4*x^2*Sqrt[a + b*x] + 8*b^3*Sqrt[a + b]*c^4*x^3*Sqrt[a + b*x] + 48*a^3*c^3*Sqrt[a*c - b*c]*Sqrt[a*c - b*c*x] + 12*a^2*b*c^3*Sqrt[a*c - b*c]*Sqrt[a*c - b*c*x] - 32*a*b^2*c^3*Sqrt[a*c - b*c]*Sqrt[a*c - b*c*x] - 8*b^3*c^3*Sqrt[a*c - b*c]*Sqrt[a*c - b*c*x] + 12*a^2*b*c^3*Sqrt[a*c - b*c]*x*Sqrt[a*c - b*c*x] - 40*a*b^2*c^3*Sqrt[a*c - b*c]*x*Sqrt[a*c - b*c*x] - 56*b^3*c^3*Sqrt[a*c - b*c]*x*Sqrt[a*c - b*c*x] - 32*a*b^2*c^3*Sqrt[a*c - b*c]*x^2*Sqrt[a*c - b*c*x] - 56*b^3*c^3*Sqrt[a*c - b*c]*x^2*Sqrt[a*c - b*c*x] - 8*b^3*c^3*Sqrt[a*c - b*c]*x^3*Sqrt[a*c - b*c*x] - 42*a^2*Sqrt[a + b]*c^3*Sqrt[a*c - b*c]*Sqrt[a + b*x]*Sqrt[a*c - b*c*x] + 28*b^2*Sqrt[a + b]*c^3*Sqrt[a*c - b*c]*Sqrt[a + b*x]*Sqrt[a*c - b*c*x] + 66*b^2*Sqrt[a + b]*c^3*Sqrt[a*c - b*c]*x*Sqrt[a + b*x]*Sqrt[a*c - b*c*x] + 28*b^2*Sqrt[a + b]*c^3*Sqrt[a*c - b*c]*x^2*Sqrt[a + b*x]*Sqrt[a*c - b*c*x]))/(Sqrt[a*c - b*c] - Sqrt[a*c - b*c*x])^8))/((-Sqrt[a*c - b*c] + Sqrt[a*c - b*c*x])*(a*c*Sqrt[a*c - b*c] - b*c*Sqrt[a*c - b*c]*x - 2*a*c*Sqrt[a*c - b*c*x] + Sqrt[a + b]*c*Sqrt[a + b*x]*Sqrt[a*c - b*c*x])^3*(a*Sqrt[a + b]*c + b*Sqrt[a + b]*c*x - 2*a*c*Sqrt[a + b*x] + Sqrt[a*c - b*c]*Sqrt[a + b*x]*Sqrt[a*c - b*c*x])^3)","B",1
1151,-1,0,100,181.5414898,"\int \frac{1}{(a+b x)^{7/2} (a c-b c x)^{7/2}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(7/2)*(a*c - b*c*x)^(7/2)),x]","\text{\$Aborted}","\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,"$Aborted","F",-1
1152,-1,0,133,180.0591841,"\int \frac{1}{(a+b x)^{9/2} (a c-b c x)^{9/2}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(9/2)*(a*c - b*c*x)^(9/2)),x]","\text{\$Aborted}","\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,"$Aborted","F",-1
1153,1,229,100,0.8125874,"\int (3-6 x)^{5/2} (2+4 x)^{5/2} \, dx","IntegrateAlgebraic[(3 - 6*x)^(5/2)*(2 + 4*x)^(5/2),x]","\frac{48 \sqrt{6} \sqrt{1-2 x} x \sqrt{2 x+1} \left(128 x^4-104 x^2+33\right) \left(-352 x^5-6160 x^4-26224 x^3-41096 x^2-26158 x-5741\right)+48 \sqrt{3} \sqrt{1-2 x} x \left(128 x^4-104 x^2+33\right) \left(64 x^6+3712 x^5+30160 x^4+80768 x^3+91052 x^2+45112 x+8119\right)}{-22528 x^5-394240 x^4-1678336 x^3-2630144 x^2+\sqrt{2} \sqrt{2 x+1} \left(1024 x^5+58880 x^4+453120 x^3+1065728 x^2+923968 x+259808\right)-1674112 x-367424}+45 \sqrt{\frac{3}{2}} \tan ^{-1}\left(\frac{\sqrt{2 x+1}-\sqrt{2}}{\sqrt{1-2 x}}\right)","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,"(48*Sqrt[6]*Sqrt[1 - 2*x]*x*Sqrt[1 + 2*x]*(33 - 104*x^2 + 128*x^4)*(-5741 - 26158*x - 41096*x^2 - 26224*x^3 - 6160*x^4 - 352*x^5) + 48*Sqrt[3]*Sqrt[1 - 2*x]*x*(33 - 104*x^2 + 128*x^4)*(8119 + 45112*x + 91052*x^2 + 80768*x^3 + 30160*x^4 + 3712*x^5 + 64*x^6))/(-367424 - 1674112*x - 2630144*x^2 - 1678336*x^3 - 394240*x^4 - 22528*x^5 + Sqrt[2]*Sqrt[1 + 2*x]*(259808 + 923968*x + 1065728*x^2 + 453120*x^3 + 58880*x^4 + 1024*x^5)) + 45*Sqrt[3/2]*ArcTan[(-Sqrt[2] + Sqrt[1 + 2*x])/Sqrt[1 - 2*x]]","B",1
1154,1,179,74,1.1423999,"\int (3-6 x)^{3/2} (2+4 x)^{3/2} \, dx","IntegrateAlgebraic[(3 - 6*x)^(3/2)*(2 + 4*x)^(3/2),x]","\frac{-12 \sqrt{6} \sqrt{1-2 x} x \sqrt{2 x+1} \left(8 x^2-5\right) \left(-56 x^3-364 x^2-490 x-169\right)-12 \sqrt{3} \sqrt{1-2 x} x \left(8 x^2-5\right) \left(16 x^4+368 x^3+1088 x^2+932 x+239\right)}{-896 x^3-5824 x^2+\sqrt{2} \sqrt{2 x+1} \left(64 x^3+1440 x^2+3632 x+1912\right)-7840 x-2704}+9 \sqrt{\frac{3}{2}} \tan ^{-1}\left(\frac{\sqrt{2 x+1}-\sqrt{2}}{\sqrt{1-2 x}}\right)","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,"(-12*Sqrt[6]*Sqrt[1 - 2*x]*x*Sqrt[1 + 2*x]*(-5 + 8*x^2)*(-169 - 490*x - 364*x^2 - 56*x^3) - 12*Sqrt[3]*Sqrt[1 - 2*x]*x*(-5 + 8*x^2)*(239 + 932*x + 1088*x^2 + 368*x^3 + 16*x^4))/(-2704 - 7840*x - 5824*x^2 - 896*x^3 + Sqrt[2]*Sqrt[1 + 2*x]*(1912 + 3632*x + 1440*x^2 + 64*x^3)) + 9*Sqrt[3/2]*ArcTan[(-Sqrt[2] + Sqrt[1 + 2*x])/Sqrt[1 - 2*x]]","B",1
1155,1,122,43,0.6317468,"\int \sqrt{3-6 x} \sqrt{2+4 x} \, dx","IntegrateAlgebraic[Sqrt[3 - 6*x]*Sqrt[2 + 4*x],x]","\frac{2 \sqrt{3} \sqrt{1-2 x} \left(4 x^2+16 x+7\right) x+2 \sqrt{6} (-6 x-5) \sqrt{1-2 x} \sqrt{2 x+1} x}{-24 x+\sqrt{2} \sqrt{2 x+1} (4 x+14)-20}+\sqrt{6} \tan ^{-1}\left(\frac{\sqrt{2 x+1}-\sqrt{2}}{\sqrt{1-2 x}}\right)","\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,"(2*Sqrt[6]*(-5 - 6*x)*Sqrt[1 - 2*x]*x*Sqrt[1 + 2*x] + 2*Sqrt[3]*Sqrt[1 - 2*x]*x*(7 + 16*x + 4*x^2))/(-20 - 24*x + Sqrt[2]*Sqrt[1 + 2*x]*(14 + 4*x)) + Sqrt[6]*ArcTan[(-Sqrt[2] + Sqrt[1 + 2*x])/Sqrt[1 - 2*x]]","B",1
1156,1,36,13,0.5760381,"\int \frac{1}{\sqrt{3-6 x} \sqrt{2+4 x}} \, dx","IntegrateAlgebraic[1/(Sqrt[3 - 6*x]*Sqrt[2 + 4*x]),x]","\sqrt{\frac{2}{3}} \tan ^{-1}\left(\frac{\sqrt{2 x+1}-\sqrt{2}}{\sqrt{1-2 x}}\right)","\frac{\sin ^{-1}(2 x)}{2 \sqrt{6}}",1,"Sqrt[2/3]*ArcTan[(-Sqrt[2] + Sqrt[1 + 2*x])/Sqrt[1 - 2*x]]","B",1
1157,1,80,28,0.6168618,"\int \frac{1}{(3-6 x)^{3/2} (2+4 x)^{3/2}} \, dx","IntegrateAlgebraic[1/((3 - 6*x)^(3/2)*(2 + 4*x)^(3/2)),x]","\frac{x (2 x+3)-2 \sqrt{2} x \sqrt{2 x+1}}{6 \sqrt{3} \sqrt{1-2 x} (-8 x-4)+6 \sqrt{6} \sqrt{1-2 x} \sqrt{2 x+1} (2 x+3)}","\frac{x}{6 \sqrt{6} \sqrt{1-2 x} \sqrt{2 x+1}}",1,"(-2*Sqrt[2]*x*Sqrt[1 + 2*x] + x*(3 + 2*x))/(6*Sqrt[3]*(-4 - 8*x)*Sqrt[1 - 2*x] + 6*Sqrt[6]*Sqrt[1 - 2*x]*Sqrt[1 + 2*x]*(3 + 2*x))","B",1
1158,1,334,57,0.7026251,"\int \frac{1}{(3-6 x)^{5/2} (2+4 x)^{5/2}} \, dx","IntegrateAlgebraic[1/((3 - 6*x)^(5/2)*(2 + 4*x)^(5/2)),x]","\frac{\left(\sqrt{2} \sqrt{2 x+1}-2\right)^9 \left(\frac{91 \left(4 x^2-4 x+1\right)}{294912 \sqrt{3} \left(\sqrt{2} \sqrt{2 x+1}-2\right)^4}+\frac{35 \left(8 x^3-12 x^2+6 x-1\right)}{36864 \sqrt{3} \left(\sqrt{2} \sqrt{2 x+1}-2\right)^6}+\frac{91 \left(16 x^4-32 x^3+24 x^2-8 x+1\right)}{73728 \sqrt{3} \left(\sqrt{2} \sqrt{2 x+1}-2\right)^8}+\frac{5 \left(32 x^5-80 x^4+80 x^3-40 x^2+10 x-1\right)}{18432 \sqrt{3} \left(\sqrt{2} \sqrt{2 x+1}-2\right)^{10}}-\frac{64 x^6-192 x^5+240 x^4-160 x^3+60 x^2-12 x+1}{55296 \sqrt{3} \left(\sqrt{2} \sqrt{2 x+1}-2\right)^{12}}+\frac{5 (2 x-1)}{294912 \sqrt{3} \left(\sqrt{2} \sqrt{2 x+1}-2\right)^2}-\frac{1}{3538944 \sqrt{3}}\right)}{(1-2 x)^{3/2} \left(-2 x+\sqrt{2} \sqrt{2 x+1}-1\right)^3}","\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,"((-2 + Sqrt[2]*Sqrt[1 + 2*x])^9*(-1/3538944*1/Sqrt[3] - (1 - 12*x + 60*x^2 - 160*x^3 + 240*x^4 - 192*x^5 + 64*x^6)/(55296*Sqrt[3]*(-2 + Sqrt[2]*Sqrt[1 + 2*x])^12) + (5*(-1 + 10*x - 40*x^2 + 80*x^3 - 80*x^4 + 32*x^5))/(18432*Sqrt[3]*(-2 + Sqrt[2]*Sqrt[1 + 2*x])^10) + (91*(1 - 8*x + 24*x^2 - 32*x^3 + 16*x^4))/(73728*Sqrt[3]*(-2 + Sqrt[2]*Sqrt[1 + 2*x])^8) + (35*(-1 + 6*x - 12*x^2 + 8*x^3))/(36864*Sqrt[3]*(-2 + Sqrt[2]*Sqrt[1 + 2*x])^6) + (91*(1 - 4*x + 4*x^2))/(294912*Sqrt[3]*(-2 + Sqrt[2]*Sqrt[1 + 2*x])^4) + (5*(-1 + 2*x))/(294912*Sqrt[3]*(-2 + Sqrt[2]*Sqrt[1 + 2*x])^2)))/((1 - 2*x)^(3/2)*(-1 - 2*x + Sqrt[2]*Sqrt[1 + 2*x])^3)","B",1
1159,1,616,85,1.0600866,"\int \frac{1}{(3-6 x)^{7/2} (2+4 x)^{7/2}} \, dx","IntegrateAlgebraic[1/((3 - 6*x)^(7/2)*(2 + 4*x)^(7/2)),x]","\frac{\left(\sqrt{2} \sqrt{2 x+1}-2\right)^{15} \left(-\frac{347 \left(4 x^2-4 x+1\right)}{2717908992 \sqrt{3} \left(\sqrt{2} \sqrt{2 x+1}-2\right)^4}-\frac{539 \left(8 x^3-12 x^2+6 x-1\right)}{169869312 \sqrt{3} \left(\sqrt{2} \sqrt{2 x+1}-2\right)^6}-\frac{2101 \left(16 x^4-32 x^3+24 x^2-8 x+1\right)}{113246208 \sqrt{3} \left(\sqrt{2} \sqrt{2 x+1}-2\right)^8}-\frac{7469 \left(32 x^5-80 x^4+80 x^3-40 x^2+10 x-1\right)}{141557760 \sqrt{3} \left(\sqrt{2} \sqrt{2 x+1}-2\right)^{10}}-\frac{2101 \left(64 x^6-192 x^5+240 x^4-160 x^3+60 x^2-12 x+1\right)}{28311552 \sqrt{3} \left(\sqrt{2} \sqrt{2 x+1}-2\right)^{12}}-\frac{539 \left(128 x^7-448 x^6+672 x^5-560 x^4+280 x^3-84 x^2+14 x-1\right)}{10616832 \sqrt{3} \left(\sqrt{2} \sqrt{2 x+1}-2\right)^{14}}-\frac{347 \left(256 x^8-1024 x^7+1792 x^6-1792 x^5+1120 x^4-448 x^3+112 x^2-16 x+1\right)}{42467328 \sqrt{3} \left(\sqrt{2} \sqrt{2 x+1}-2\right)^{16}}+\frac{7 \left(512 x^9-2304 x^8+4608 x^7-5376 x^6+4032 x^5-2016 x^4+672 x^3-144 x^2+18 x-1\right)}{10616832 \sqrt{3} \left(\sqrt{2} \sqrt{2 x+1}-2\right)^{18}}-\frac{1024 x^{10}-5120 x^9+11520 x^8-15360 x^7+13440 x^6-8064 x^5+3360 x^4-960 x^3+180 x^2-20 x+1}{17694720 \sqrt{3} \left(\sqrt{2} \sqrt{2 x+1}-2\right)^{20}}+\frac{7 (2 x-1)}{2717908992 \sqrt{3} \left(\sqrt{2} \sqrt{2 x+1}-2\right)^2}-\frac{1}{18119393280 \sqrt{3}}\right)}{(1-2 x)^{5/2} \left(-2 x+\sqrt{2} \sqrt{2 x+1}-1\right)^5}","\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,"((-2 + Sqrt[2]*Sqrt[1 + 2*x])^15*(-1/18119393280*1/Sqrt[3] - (1 - 20*x + 180*x^2 - 960*x^3 + 3360*x^4 - 8064*x^5 + 13440*x^6 - 15360*x^7 + 11520*x^8 - 5120*x^9 + 1024*x^10)/(17694720*Sqrt[3]*(-2 + Sqrt[2]*Sqrt[1 + 2*x])^20) + (7*(-1 + 18*x - 144*x^2 + 672*x^3 - 2016*x^4 + 4032*x^5 - 5376*x^6 + 4608*x^7 - 2304*x^8 + 512*x^9))/(10616832*Sqrt[3]*(-2 + Sqrt[2]*Sqrt[1 + 2*x])^18) - (347*(1 - 16*x + 112*x^2 - 448*x^3 + 1120*x^4 - 1792*x^5 + 1792*x^6 - 1024*x^7 + 256*x^8))/(42467328*Sqrt[3]*(-2 + Sqrt[2]*Sqrt[1 + 2*x])^16) - (539*(-1 + 14*x - 84*x^2 + 280*x^3 - 560*x^4 + 672*x^5 - 448*x^6 + 128*x^7))/(10616832*Sqrt[3]*(-2 + Sqrt[2]*Sqrt[1 + 2*x])^14) - (2101*(1 - 12*x + 60*x^2 - 160*x^3 + 240*x^4 - 192*x^5 + 64*x^6))/(28311552*Sqrt[3]*(-2 + Sqrt[2]*Sqrt[1 + 2*x])^12) - (7469*(-1 + 10*x - 40*x^2 + 80*x^3 - 80*x^4 + 32*x^5))/(141557760*Sqrt[3]*(-2 + Sqrt[2]*Sqrt[1 + 2*x])^10) - (2101*(1 - 8*x + 24*x^2 - 32*x^3 + 16*x^4))/(113246208*Sqrt[3]*(-2 + Sqrt[2]*Sqrt[1 + 2*x])^8) - (539*(-1 + 6*x - 12*x^2 + 8*x^3))/(169869312*Sqrt[3]*(-2 + Sqrt[2]*Sqrt[1 + 2*x])^6) - (347*(1 - 4*x + 4*x^2))/(2717908992*Sqrt[3]*(-2 + Sqrt[2]*Sqrt[1 + 2*x])^4) + (7*(-1 + 2*x))/(2717908992*Sqrt[3]*(-2 + Sqrt[2]*Sqrt[1 + 2*x])^2)))/((1 - 2*x)^(5/2)*(-1 - 2*x + Sqrt[2]*Sqrt[1 + 2*x])^5)","B",1
1160,1,158,91,0.1118777,"\int (3-x)^{3/2} (-2+x)^{3/2} \, dx","IntegrateAlgebraic[(3 - x)^(3/2)*(-2 + x)^(3/2),x]","\frac{\sqrt{x-2} \left(-\sqrt{3-x} \left(7 x^3-98 x^2+420 x-568\right) \left(16 x^3-120 x^2+290 x-225\right)-\left(x^4-33 x^3+278 x^2-892 x+984\right) \left(16 x^3-120 x^2+290 x-225\right)\right)}{64 \sqrt{3-x} \left(-x^3+30 x^2-188 x+328\right)+64 \left(7 x^3-98 x^2+420 x-568\right)}+\frac{3}{32} \tan ^{-1}\left(\frac{\sqrt{x-2}}{\sqrt{3-x}-1}\right)","-\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,"(Sqrt[-2 + x]*(-(Sqrt[3 - x]*(-568 + 420*x - 98*x^2 + 7*x^3)*(-225 + 290*x - 120*x^2 + 16*x^3)) - (-225 + 290*x - 120*x^2 + 16*x^3)*(984 - 892*x + 278*x^2 - 33*x^3 + x^4)))/(64*Sqrt[3 - x]*(328 - 188*x + 30*x^2 - x^3) + 64*(-568 + 420*x - 98*x^2 + 7*x^3)) + (3*ArcTan[Sqrt[-2 + x]/(-1 + Sqrt[3 - x])])/32","A",1
1161,1,96,51,0.0744312,"\int \sqrt{3-x} \sqrt{-2+x} \, dx","IntegrateAlgebraic[Sqrt[3 - x]*Sqrt[-2 + x],x]","\frac{\sqrt{x-2} \left((2 x-5) \left(x^2-9 x+18\right)+\sqrt{3-x} (2 x-5) (3 x-10)\right)}{4 \sqrt{3-x} (6-x)+4 (3 x-10)}+\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{x-2}}{\sqrt{3-x}-1}\right)","-\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[-2 + x]*(Sqrt[3 - x]*(-5 + 2*x)*(-10 + 3*x) + (-5 + 2*x)*(18 - 9*x + x^2)))/(4*Sqrt[3 - x]*(6 - x) + 4*(-10 + 3*x)) + ArcTan[Sqrt[-2 + x]/(-1 + Sqrt[3 - x])]/2","A",1
1162,1,24,8,0.020908,"\int \frac{1}{\sqrt{3-x} \sqrt{-2+x}} \, dx","IntegrateAlgebraic[1/(Sqrt[3 - x]*Sqrt[-2 + x]),x]","4 \tan ^{-1}\left(\frac{\sqrt{x-2}}{\sqrt{3-x}-1}\right)","-\sin ^{-1}(5-2 x)",1,"4*ArcTan[Sqrt[-2 + x]/(-1 + Sqrt[3 - x])]","B",1
1163,1,55,37,0.0518485,"\int \frac{1}{(3-x)^{3/2} (-2+x)^{3/2}} \, dx","IntegrateAlgebraic[1/((3 - x)^(3/2)*(-2 + x)^(3/2)),x]","\frac{2 (x-4) (2 x-5)+4 \sqrt{3-x} (2 x-5)}{\left(\sqrt{3-x} (x-4)-2 x+6\right) \sqrt{x-2}}","\frac{2}{\sqrt{3-x} \sqrt{x-2}}-\frac{4 \sqrt{3-x}}{\sqrt{x-2}}",1,"(4*Sqrt[3 - x]*(-5 + 2*x) + 2*(-4 + x)*(-5 + 2*x))/((6 + Sqrt[3 - x]*(-4 + x) - 2*x)*Sqrt[-2 + x])","A",1
1164,1,171,79,0.0911414,"\int \frac{1}{(3-x)^{5/2} (-2+x)^{5/2}} \, dx","IntegrateAlgebraic[1/((3 - x)^(5/2)*(-2 + x)^(5/2)),x]","\frac{\left(\frac{\left(\sqrt{3-x}-1\right)^{12}}{96 (x-2)^6}+\frac{5 \left(\sqrt{3-x}-1\right)^{10}}{16 (x-2)^5}-\frac{91 \left(\sqrt{3-x}-1\right)^8}{32 (x-2)^4}+\frac{35 \left(\sqrt{3-x}-1\right)^6}{8 (x-2)^3}-\frac{91 \left(\sqrt{3-x}-1\right)^4}{32 (x-2)^2}+\frac{5 \left(\sqrt{3-x}-1\right)^2}{16 (x-2)}+\frac{1}{96}\right) (x-2)^{9/2}}{\left(\sqrt{3-x}-1\right)^3 \left(x+\sqrt{3-x}-3\right)^3}","-\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,"((1/96 + (-1 + Sqrt[3 - x])^12/(96*(-2 + x)^6) + (5*(-1 + Sqrt[3 - x])^10)/(16*(-2 + x)^5) - (91*(-1 + Sqrt[3 - x])^8)/(32*(-2 + x)^4) + (35*(-1 + Sqrt[3 - x])^6)/(8*(-2 + x)^3) - (91*(-1 + Sqrt[3 - x])^4)/(32*(-2 + x)^2) + (5*(-1 + Sqrt[3 - x])^2)/(16*(-2 + x)))*(-2 + x)^(9/2))/((-1 + Sqrt[3 - x])^3*(-3 + Sqrt[3 - x] + x)^3)","B",1
1165,1,192,21,1.1315486,"\int \frac{1}{(3-x)^{3/2} (3+x)^{3/2}} \, dx","IntegrateAlgebraic[1/((3 - x)^(3/2)*(3 + x)^(3/2)),x]","\frac{\left(\sqrt{2}-\sqrt{x+3}\right)^4 \left(\frac{\sqrt{3-x}-2}{4 \left(\sqrt{2}-\sqrt{x+3}\right)}-\frac{\left(\sqrt{3-x}-2\right)^3}{4 \left(\sqrt{2}-\sqrt{x+3}\right)^3}\right)}{4 x^2+12 \sqrt{3-x} x+\sqrt{2} \sqrt{3-x} \sqrt{x+3} x-12 \sqrt{2} \sqrt{x+3} x+36 \sqrt{3-x}-27 \sqrt{2} \sqrt{3-x} \sqrt{x+3}+36 \sqrt{2} \sqrt{x+3}-36}","\frac{x}{9 \sqrt{3-x} \sqrt{x+3}}",1,"((Sqrt[2] - Sqrt[3 + x])^4*(-1/4*(-2 + Sqrt[3 - x])^3/(Sqrt[2] - Sqrt[3 + x])^3 + (-2 + Sqrt[3 - x])/(4*(Sqrt[2] - Sqrt[3 + x]))))/(-36 + 36*Sqrt[3 - x] + 12*Sqrt[3 - x]*x + 4*x^2 + 36*Sqrt[2]*Sqrt[3 + x] - 27*Sqrt[2]*Sqrt[3 - x]*Sqrt[3 + x] - 12*Sqrt[2]*x*Sqrt[3 + x] + Sqrt[2]*Sqrt[3 - x]*x*Sqrt[3 + x])","B",1
1166,1,1420,24,14.9766439,"\int \frac{1}{(3-b x)^{3/2} (3+b x)^{3/2}} \, dx","IntegrateAlgebraic[1/((3 - b*x)^(3/2)*(3 + b*x)^(3/2)),x]","\frac{\left(\frac{\sqrt{3-b}}{16 b \left(b^2-9\right)}-\frac{\sqrt{3-b x}}{16 b \left(b^2-9\right)}\right) \left(\sqrt{b+3}-\sqrt{b x+3}\right)^8 \left(\frac{\left(\sqrt{3-b}-\sqrt{3-b x}\right)^2}{\left(\sqrt{b+3}-\sqrt{b x+3}\right)^2}-1\right) \left(-\frac{8 \left(-x^2 b^2-3 x b^2-b^2-2 \sqrt{3-b} x \sqrt{3-b x} b-2 \sqrt{3-b} \sqrt{3-b x} b+2 \sqrt{b+3} x \sqrt{b x+3} b+2 \sqrt{b+3} \sqrt{b x+3} b-6 \sqrt{3-b} \sqrt{3-b x}-6 \sqrt{b+3} \sqrt{b x+3}+3 \sqrt{3-b} \sqrt{b+3} \sqrt{3-b x} \sqrt{b x+3}+9\right) b^2}{\left(\sqrt{b+3}-\sqrt{b x+3}\right)^4}-\frac{8 \sqrt{9-b^2} \left(\sqrt{3-b}-\sqrt{3-b x}\right) \left(x b+b+\sqrt{3-b} \sqrt{3-b x}-\sqrt{b+3} \sqrt{b x+3}\right) b}{\left(\sqrt{b+3}-\sqrt{b x+3}\right)^3}+\frac{72 \left(-x^2 b^2-3 x b^2-b^2-2 \sqrt{3-b} x \sqrt{3-b x} b-2 \sqrt{3-b} \sqrt{3-b x} b+2 \sqrt{b+3} x \sqrt{b x+3} b+2 \sqrt{b+3} \sqrt{b x+3} b-6 \sqrt{3-b} \sqrt{3-b x}-6 \sqrt{b+3} \sqrt{b x+3}+3 \sqrt{3-b} \sqrt{b+3} \sqrt{3-b x} \sqrt{b x+3}+9\right)}{\left(\sqrt{b+3}-\sqrt{b x+3}\right)^4}\right)}{\left(\sqrt{b x+3}-\sqrt{b+3}\right) \left(2 x^2 b^6-9 x^4 b^4-126 x^3 b^4-333 x^2 b^4-24 \sqrt{3-b} x \sqrt{3-b x} b^4-24 \sqrt{b+3} x \sqrt{b x+3} b^4+2 \sqrt{3-b} \sqrt{b+3} x \sqrt{3-b x} \sqrt{b x+3} b^4-18 b^4-36 \sqrt{3-b} x^3 \sqrt{3-b x} b^3-252 \sqrt{3-b} x^2 \sqrt{3-b x} b^3-288 \sqrt{3-b} x \sqrt{3-b x} b^3-72 \sqrt{3-b} \sqrt{3-b x} b^3+36 \sqrt{b+3} x^3 \sqrt{b x+3} b^3+252 \sqrt{b+3} x^2 \sqrt{b x+3} b^3+288 \sqrt{b+3} x \sqrt{b x+3} b^3+72 \sqrt{b+3} \sqrt{b x+3} b^3+1539 x^2 b^2+1134 x b^2-432 \sqrt{3-b} x^2 \sqrt{3-b x} b^2-648 \sqrt{3-b} x \sqrt{3-b x} b^2-864 \sqrt{3-b} \sqrt{3-b x} b^2-432 \sqrt{b+3} x^2 \sqrt{b x+3} b^2-648 \sqrt{b+3} x \sqrt{b x+3} b^2-864 \sqrt{b+3} \sqrt{b x+3} b^2+126 \sqrt{3-b} \sqrt{b+3} x^2 \sqrt{3-b x} \sqrt{b x+3} b^2+306 \sqrt{3-b} \sqrt{b+3} x \sqrt{3-b x} \sqrt{b x+3} b^2+252 \sqrt{3-b} \sqrt{b+3} \sqrt{3-b x} \sqrt{b x+3} b^2+2997 b^2+324 \sqrt{3-b} x \sqrt{3-b x} b+324 \sqrt{3-b} \sqrt{3-b x} b-324 \sqrt{b+3} x \sqrt{b x+3} b-324 \sqrt{b+3} \sqrt{b x+3} b+3888 \sqrt{3-b} \sqrt{3-b x}+3888 \sqrt{b+3} \sqrt{b x+3}-1134 \sqrt{3-b} \sqrt{b+3} \sqrt{3-b x} \sqrt{b x+3}-13122\right)}","\frac{x}{9 \sqrt{3-b x} \sqrt{b x+3}}",1,"((Sqrt[3 - b]/(16*b*(-9 + b^2)) - Sqrt[3 - b*x]/(16*b*(-9 + b^2)))*(Sqrt[3 + b] - Sqrt[3 + b*x])^8*(-1 + (Sqrt[3 - b] - Sqrt[3 - b*x])^2/(Sqrt[3 + b] - Sqrt[3 + b*x])^2)*((-8*b*Sqrt[9 - b^2]*(Sqrt[3 - b] - Sqrt[3 - b*x])*(b + b*x + Sqrt[3 - b]*Sqrt[3 - b*x] - Sqrt[3 + b]*Sqrt[3 + b*x]))/(Sqrt[3 + b] - Sqrt[3 + b*x])^3 + (72*(9 - b^2 - 3*b^2*x - b^2*x^2 - 6*Sqrt[3 - b]*Sqrt[3 - b*x] - 2*Sqrt[3 - b]*b*Sqrt[3 - b*x] - 2*Sqrt[3 - b]*b*x*Sqrt[3 - b*x] - 6*Sqrt[3 + b]*Sqrt[3 + b*x] + 2*b*Sqrt[3 + b]*Sqrt[3 + b*x] + 2*b*Sqrt[3 + b]*x*Sqrt[3 + b*x] + 3*Sqrt[3 - b]*Sqrt[3 + b]*Sqrt[3 - b*x]*Sqrt[3 + b*x]))/(Sqrt[3 + b] - Sqrt[3 + b*x])^4 - (8*b^2*(9 - b^2 - 3*b^2*x - b^2*x^2 - 6*Sqrt[3 - b]*Sqrt[3 - b*x] - 2*Sqrt[3 - b]*b*Sqrt[3 - b*x] - 2*Sqrt[3 - b]*b*x*Sqrt[3 - b*x] - 6*Sqrt[3 + b]*Sqrt[3 + b*x] + 2*b*Sqrt[3 + b]*Sqrt[3 + b*x] + 2*b*Sqrt[3 + b]*x*Sqrt[3 + b*x] + 3*Sqrt[3 - b]*Sqrt[3 + b]*Sqrt[3 - b*x]*Sqrt[3 + b*x]))/(Sqrt[3 + b] - Sqrt[3 + b*x])^4))/((-Sqrt[3 + b] + Sqrt[3 + b*x])*(-13122 + 2997*b^2 - 18*b^4 + 1134*b^2*x + 1539*b^2*x^2 - 333*b^4*x^2 + 2*b^6*x^2 - 126*b^4*x^3 - 9*b^4*x^4 + 3888*Sqrt[3 - b]*Sqrt[3 - b*x] + 324*Sqrt[3 - b]*b*Sqrt[3 - b*x] - 864*Sqrt[3 - b]*b^2*Sqrt[3 - b*x] - 72*Sqrt[3 - b]*b^3*Sqrt[3 - b*x] + 324*Sqrt[3 - b]*b*x*Sqrt[3 - b*x] - 648*Sqrt[3 - b]*b^2*x*Sqrt[3 - b*x] - 288*Sqrt[3 - b]*b^3*x*Sqrt[3 - b*x] - 24*Sqrt[3 - b]*b^4*x*Sqrt[3 - b*x] - 432*Sqrt[3 - b]*b^2*x^2*Sqrt[3 - b*x] - 252*Sqrt[3 - b]*b^3*x^2*Sqrt[3 - b*x] - 36*Sqrt[3 - b]*b^3*x^3*Sqrt[3 - b*x] + 3888*Sqrt[3 + b]*Sqrt[3 + b*x] - 324*b*Sqrt[3 + b]*Sqrt[3 + b*x] - 864*b^2*Sqrt[3 + b]*Sqrt[3 + b*x] + 72*b^3*Sqrt[3 + b]*Sqrt[3 + b*x] - 324*b*Sqrt[3 + b]*x*Sqrt[3 + b*x] - 648*b^2*Sqrt[3 + b]*x*Sqrt[3 + b*x] + 288*b^3*Sqrt[3 + b]*x*Sqrt[3 + b*x] - 24*b^4*Sqrt[3 + b]*x*Sqrt[3 + b*x] - 432*b^2*Sqrt[3 + b]*x^2*Sqrt[3 + b*x] + 252*b^3*Sqrt[3 + b]*x^2*Sqrt[3 + b*x] + 36*b^3*Sqrt[3 + b]*x^3*Sqrt[3 + b*x] - 1134*Sqrt[3 - b]*Sqrt[3 + b]*Sqrt[3 - b*x]*Sqrt[3 + b*x] + 252*Sqrt[3 - b]*b^2*Sqrt[3 + b]*Sqrt[3 - b*x]*Sqrt[3 + b*x] + 306*Sqrt[3 - b]*b^2*Sqrt[3 + b]*x*Sqrt[3 - b*x]*Sqrt[3 + b*x] + 2*Sqrt[3 - b]*b^4*Sqrt[3 + b]*x*Sqrt[3 - b*x]*Sqrt[3 + b*x] + 126*Sqrt[3 - b]*b^2*Sqrt[3 + b]*x^2*Sqrt[3 - b*x]*Sqrt[3 + b*x]))","B",0
1167,1,174,26,0.1058022,"\int \frac{1}{(6-2 x)^{3/2} (3+x)^{3/2}} \, dx","IntegrateAlgebraic[1/((6 - 2*x)^(3/2)*(3 + x)^(3/2)),x]","\frac{\left(\frac{1}{16}-\frac{\sqrt{3-x}}{16 \sqrt{2}}\right) \left(\sqrt{x+3}-2\right)^3 \left(\frac{\left(\sqrt{2} \sqrt{3-x}-2\right)^2}{\left(\sqrt{x+3}-2\right)^2}-2\right)}{-4 x^2-12 \sqrt{2} \sqrt{3-x} x+\sqrt{2} \sqrt{3-x} \sqrt{x+3} x+12 \sqrt{x+3} x-36 \sqrt{2} \sqrt{3-x}+27 \sqrt{2} \sqrt{3-x} \sqrt{x+3}-36 \sqrt{x+3}+36}","\frac{x}{18 \sqrt{2} \sqrt{3-x} \sqrt{x+3}}",1,"((1/16 - Sqrt[3 - x]/(16*Sqrt[2]))*(-2 + Sqrt[3 + x])^3*(-2 + (-2 + Sqrt[2]*Sqrt[3 - x])^2/(-2 + Sqrt[3 + x])^2))/(36 - 36*Sqrt[2]*Sqrt[3 - x] - 12*Sqrt[2]*Sqrt[3 - x]*x - 4*x^2 - 36*Sqrt[3 + x] + 27*Sqrt[2]*Sqrt[3 - x]*Sqrt[3 + x] + 12*x*Sqrt[3 + x] + Sqrt[2]*Sqrt[3 - x]*x*Sqrt[3 + x])","B",1
1168,1,624,29,4.6481115,"\int \frac{1}{(6-2 b x)^{3/2} (3+b x)^{3/2}} \, dx","IntegrateAlgebraic[1/((6 - 2*b*x)^(3/2)*(3 + b*x)^(3/2)),x]","\frac{\left(\frac{\sqrt{3-b x}}{64 b \sqrt{9-b^2}}-\frac{\sqrt{3-b}}{64 b \sqrt{9-b^2}}\right) \left(\sqrt{b+3}-\sqrt{b x+3}\right)^8 \left(\frac{\left(\sqrt{2} \sqrt{3-b}-\sqrt{2} \sqrt{3-b x}\right)^2}{\left(\sqrt{b+3}-\sqrt{b x+3}\right)^2}-2\right) \left(\frac{32 \sqrt{2} \sqrt{9-b^2} \left(b^2 x^2+3 b^2 x+b^2+2 \sqrt{3-b} b x \sqrt{3-b x}+2 \sqrt{3-b} b \sqrt{3-b x}-2 \sqrt{b+3} b x \sqrt{b x+3}-2 \sqrt{b+3} b \sqrt{b x+3}+6 \sqrt{3-b} \sqrt{3-b x}+6 \sqrt{b+3} \sqrt{b x+3}-3 \sqrt{3-b} \sqrt{b+3} \sqrt{3-b x} \sqrt{b x+3}-9\right)}{\left(\sqrt{b+3}-\sqrt{b x+3}\right)^4}-\frac{32 b \left(\sqrt{2} \sqrt{3-b}-\sqrt{2} \sqrt{3-b x}\right) \left(b x+\sqrt{3-b} \sqrt{3-b x}-\sqrt{b+3} \sqrt{b x+3}+b\right)}{\left(\sqrt{b+3}-\sqrt{b x+3}\right)^3}\right)}{\left(\sqrt{b x+3}-\sqrt{b+3}\right) \left(b \sqrt{b+3} x+\sqrt{3-b} \sqrt{3-b x} \sqrt{b x+3}-6 \sqrt{b x+3}+3 \sqrt{b+3}\right)^2 \left(\sqrt{2} \sqrt{3-b} b x+6 \sqrt{2} \sqrt{3-b x}-\sqrt{2} \sqrt{b+3} \sqrt{3-b x} \sqrt{b x+3}-3 \sqrt{2} \sqrt{3-b}\right)^2}","\frac{x}{18 \sqrt{2} \sqrt{3-b x} \sqrt{b x+3}}",1,"((-1/64*Sqrt[3 - b]/(b*Sqrt[9 - b^2]) + Sqrt[3 - b*x]/(64*b*Sqrt[9 - b^2]))*(Sqrt[3 + b] - Sqrt[3 + b*x])^8*(-2 + (Sqrt[2]*Sqrt[3 - b] - Sqrt[2]*Sqrt[3 - b*x])^2/(Sqrt[3 + b] - Sqrt[3 + b*x])^2)*((-32*b*(Sqrt[2]*Sqrt[3 - b] - Sqrt[2]*Sqrt[3 - b*x])*(b + b*x + Sqrt[3 - b]*Sqrt[3 - b*x] - Sqrt[3 + b]*Sqrt[3 + b*x]))/(Sqrt[3 + b] - Sqrt[3 + b*x])^3 + (32*Sqrt[2]*Sqrt[9 - b^2]*(-9 + b^2 + 3*b^2*x + b^2*x^2 + 6*Sqrt[3 - b]*Sqrt[3 - b*x] + 2*Sqrt[3 - b]*b*Sqrt[3 - b*x] + 2*Sqrt[3 - b]*b*x*Sqrt[3 - b*x] + 6*Sqrt[3 + b]*Sqrt[3 + b*x] - 2*b*Sqrt[3 + b]*Sqrt[3 + b*x] - 2*b*Sqrt[3 + b]*x*Sqrt[3 + b*x] - 3*Sqrt[3 - b]*Sqrt[3 + b]*Sqrt[3 - b*x]*Sqrt[3 + b*x]))/(Sqrt[3 + b] - Sqrt[3 + b*x])^4))/((-Sqrt[3 + b] + Sqrt[3 + b*x])*(3*Sqrt[3 + b] + b*Sqrt[3 + b]*x - 6*Sqrt[3 + b*x] + Sqrt[3 - b]*Sqrt[3 - b*x]*Sqrt[3 + b*x])^2*(-3*Sqrt[2]*Sqrt[3 - b] + Sqrt[2]*Sqrt[3 - b]*b*x + 6*Sqrt[2]*Sqrt[3 - b*x] - Sqrt[2]*Sqrt[3 + b]*Sqrt[3 - b*x]*Sqrt[3 + b*x])^2)","B",0
1169,1,72,39,0.3077698,"\int \frac{1}{\sqrt{a+b x} \sqrt{-a d+b d x}} \, dx","IntegrateAlgebraic[1/(Sqrt[a + b*x]*Sqrt[-(a*d) + b*d*x]),x]","\frac{4 \tanh ^{-1}\left(\frac{\sqrt{b d-a d}-\sqrt{b d x-a d}}{\sqrt{d} \sqrt{a+b}-\sqrt{d} \sqrt{a+b x}}\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,"(4*ArcTanh[(Sqrt[-(a*d) + b*d] - Sqrt[-(a*d) + b*d*x])/(Sqrt[a + b]*Sqrt[d] - Sqrt[d]*Sqrt[a + b*x])])/(b*Sqrt[d])","A",1
1170,1,127,241,0.5335182,"\int \frac{1}{\sqrt[4]{6-3 e x} (2+e x)^{3/4}} \, dx","IntegrateAlgebraic[1/((6 - 3*e*x)^(1/4)*(2 + e*x)^(3/4)),x]","\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{2-e x} \sqrt[4]{e x+2}}{\sqrt{2-e x}-\sqrt{e x+2}}\right)}{\sqrt[4]{3} e}+\frac{\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{2-e x} \sqrt[4]{e x+2}}{\sqrt{2-e x}+\sqrt{e x+2}}\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[(Sqrt[2]*(2 - e*x)^(1/4)*(2 + e*x)^(1/4))/(Sqrt[2 - e*x] - Sqrt[2 + e*x])])/(3^(1/4)*e) + (Sqrt[2]*ArcTanh[(Sqrt[2]*(2 - e*x)^(1/4)*(2 + e*x)^(1/4))/(Sqrt[2 - e*x] + Sqrt[2 + e*x])])/(3^(1/4)*e)","A",1
1171,0,0,144,11.7398619,"\int \frac{(a-i a x)^{7/4}}{\sqrt[4]{a+i a x}} \, dx","IntegrateAlgebraic[(a - I*a*x)^(7/4)/(a + I*a*x)^(1/4),x]","\int \frac{(a-i a x)^{7/4}}{\sqrt[4]{a+i a x}} \, dx","-\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,"Could not integrate","F",-1
1172,0,0,106,10.8697786,"\int \frac{(a-i a x)^{3/4}}{\sqrt[4]{a+i a x}} \, dx","IntegrateAlgebraic[(a - I*a*x)^(3/4)/(a + I*a*x)^(1/4),x]","\int \frac{(a-i a x)^{3/4}}{\sqrt[4]{a+i a x}} \, dx","-\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,"Could not integrate","F",-1
1173,0,0,71,10.1943449,"\int \frac{1}{\sqrt[4]{a-i a x} \sqrt[4]{a+i a x}} \, dx","IntegrateAlgebraic[1/((a - I*a*x)^(1/4)*(a + I*a*x)^(1/4)),x]","\int \frac{1}{\sqrt[4]{a-i a x} \sqrt[4]{a+i a x}} \, dx","\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,"Could not integrate","F",-1
1174,0,0,78,16.9828454,"\int \frac{1}{(a-i a x)^{5/4} \sqrt[4]{a+i a x}} \, dx","IntegrateAlgebraic[1/((a - I*a*x)^(5/4)*(a + I*a*x)^(1/4)),x]","\int \frac{1}{(a-i a x)^{5/4} \sqrt[4]{a+i a x}} \, dx","\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,"Could not integrate","F",-1
1175,0,0,82,29.1548536,"\int \frac{1}{(a-i a x)^{9/4} \sqrt[4]{a+i a x}} \, dx","IntegrateAlgebraic[1/((a - I*a*x)^(9/4)*(a + I*a*x)^(1/4)),x]","\int \frac{1}{(a-i a x)^{9/4} \sqrt[4]{a+i a x}} \, dx","\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,"Could not integrate","F",-1
1176,0,0,115,31.6549095,"\int \frac{1}{(a-i a x)^{13/4} \sqrt[4]{a+i a x}} \, dx","IntegrateAlgebraic[1/((a - I*a*x)^(13/4)*(a + I*a*x)^(1/4)),x]","\int \frac{1}{(a-i a x)^{13/4} \sqrt[4]{a+i a x}} \, dx","\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,"Could not integrate","F",-1
1177,0,0,148,19.3991307,"\int \frac{1}{(a-i a x)^{17/4} \sqrt[4]{a+i a x}} \, dx","IntegrateAlgebraic[1/((a - I*a*x)^(17/4)*(a + I*a*x)^(1/4)),x]","\int \frac{1}{(a-i a x)^{17/4} \sqrt[4]{a+i a x}} \, dx","\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{4 i}{39 a^3 (a-i a x)^{5/4} \sqrt[4]{a+i a x}}-\frac{2 i (a+i a x)^{3/4}}{13 a^2 (a-i a x)^{13/4}}",1,"Could not integrate","F",-1
1178,1,126,256,0.3063628,"\int \frac{\sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}} \, dx","IntegrateAlgebraic[(a - I*a*x)^(1/4)/(a + I*a*x)^(1/4),x]","\frac{\sqrt[4]{-1} \sqrt[4]{x-i} \sqrt[4]{a-i a x} \left(-(-1)^{3/4} (x-i)^{3/4} \sqrt[4]{x+i}+\sqrt[4]{-1} \tan ^{-1}\left(\frac{\sqrt[4]{x+i}}{\sqrt[4]{x-i}}\right)+\sqrt[4]{-1} \tanh ^{-1}\left(\frac{\sqrt[4]{x+i}}{\sqrt[4]{x-i}}\right)\right)}{\sqrt[4]{x+i} \sqrt[4]{a+i a 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}}",1,"((-1)^(1/4)*(-I + x)^(1/4)*(a - I*a*x)^(1/4)*(-((-1)^(3/4)*(-I + x)^(3/4)*(I + x)^(1/4)) + (-1)^(1/4)*ArcTan[(I + x)^(1/4)/(-I + x)^(1/4)] + (-1)^(1/4)*ArcTanh[(I + x)^(1/4)/(-I + x)^(1/4)]))/((I + x)^(1/4)*(a + I*a*x)^(1/4))","A",1
1179,1,111,233,0.3391125,"\int \frac{1}{(a-i a x)^{3/4} \sqrt[4]{a+i a x}} \, dx","IntegrateAlgebraic[1/((a - I*a*x)^(3/4)*(a + I*a*x)^(1/4)),x]","-\frac{(-1)^{3/4} a \sqrt[4]{x-i} (x+i)^{3/4} \left(\frac{2 \sqrt[4]{-1} \tan ^{-1}\left(\frac{\sqrt[4]{x+i}}{\sqrt[4]{x-i}}\right)}{a}+\frac{2 \sqrt[4]{-1} \tanh ^{-1}\left(\frac{\sqrt[4]{x+i}}{\sqrt[4]{x-i}}\right)}{a}\right)}{(a-i a x)^{3/4} \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,"-(((-1)^(3/4)*a*(-I + x)^(1/4)*(I + x)^(3/4)*((2*(-1)^(1/4)*ArcTan[(I + x)^(1/4)/(-I + x)^(1/4)])/a + (2*(-1)^(1/4)*ArcTanh[(I + x)^(1/4)/(-I + x)^(1/4)])/a))/((a - I*a*x)^(3/4)*(a + I*a*x)^(1/4)))","A",1
1180,1,40,33,0.2938694,"\int \frac{1}{(a-i a x)^{7/4} \sqrt[4]{a+i a x}} \, dx","IntegrateAlgebraic[1/((a - I*a*x)^(7/4)*(a + I*a*x)^(1/4)),x]","-\frac{2 i (x-i) (x+i)}{3 (a-i a x)^{7/4} \sqrt[4]{a+i a x}}","-\frac{2 i (a+i a x)^{3/4}}{3 a^2 (a-i a x)^{3/4}}",1,"(((-2*I)/3)*(-I + x)*(I + x))/((a - I*a*x)^(7/4)*(a + I*a*x)^(1/4))","A",1
1181,1,63,67,0.3579173,"\int \frac{1}{(a-i a x)^{11/4} \sqrt[4]{a+i a x}} \, dx","IntegrateAlgebraic[1/((a - I*a*x)^(11/4)*(a + I*a*x)^(1/4)),x]","\frac{2 (-1)^{3/4} (x-i) (x+i) \left(3 (-1)^{3/4}+2 \sqrt[4]{-1} (x+i)\right)}{21 (a-i a x)^{11/4} \sqrt[4]{a+i a 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}}",1,"(2*(-1)^(3/4)*(-I + x)*(I + x)*(3*(-1)^(3/4) + 2*(-1)^(1/4)*(I + x)))/(21*(a - I*a*x)^(11/4)*(a + I*a*x)^(1/4))","A",1
1182,1,77,100,0.4269812,"\int \frac{1}{(a-i a x)^{15/4} \sqrt[4]{a+i a x}} \, dx","IntegrateAlgebraic[1/((a - I*a*x)^(15/4)*(a + I*a*x)^(1/4)),x]","\frac{2 \sqrt[4]{-1} (x-i) (x+i) \left(8 \sqrt[4]{-1} (x+i)^2+12 (-1)^{3/4} (x+i)-21 \sqrt[4]{-1}\right)}{231 (a-i a x)^{15/4} \sqrt[4]{a+i a 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}}",1,"(2*(-1)^(1/4)*(-I + x)*(I + x)*(-21*(-1)^(1/4) + 12*(-1)^(3/4)*(I + x) + 8*(-1)^(1/4)*(I + x)^2))/(231*(a - I*a*x)^(15/4)*(a + I*a*x)^(1/4))","A",1
1183,1,117,133,1.4260338,"\int \frac{1}{(a-i a x)^{19/4} \sqrt[4]{a+i a x}} \, dx","IntegrateAlgebraic[1/((a - I*a*x)^(19/4)*(a + I*a*x)^(1/4)),x]","-\frac{2 (-1)^{3/4} \left(16 \sqrt[4]{-1} (x-i)^{15/4}+120 (-1)^{3/4} (x-i)^{11/4}-330 \sqrt[4]{-1} (x-i)^{7/4}-385 (-1)^{3/4} (x-i)^{3/4}\right) \sqrt[4]{a-i a x} (a+i a x)^{3/4}}{1155 a^6 (x-i)^{3/4} (x+i)^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*(-1)^(3/4)*(a - I*a*x)^(1/4)*(a + I*a*x)^(3/4)*(-385*(-1)^(3/4)*(-I + x)^(3/4) - 330*(-1)^(1/4)*(-I + x)^(7/4) + 120*(-1)^(3/4)*(-I + x)^(11/4) + 16*(-1)^(1/4)*(-I + x)^(15/4)))/(1155*a^6*(-I + x)^(3/4)*(I + x)^4)","A",1
1184,1,128,256,0.3269519,"\int \frac{(a-i a x)^{3/4}}{(a+i a x)^{3/4}} \, dx","IntegrateAlgebraic[(a - I*a*x)^(3/4)/(a + I*a*x)^(3/4),x]","\frac{(-1)^{3/4} (x-i)^{3/4} (a-i a x)^{3/4} \left(-\sqrt[4]{-1} \sqrt[4]{x-i} (x+i)^{3/4}+3 (-1)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{x+i}}{\sqrt[4]{x-i}}\right)-3 (-1)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{x+i}}{\sqrt[4]{x-i}}\right)\right)}{(x+i)^{3/4} (a+i a x)^{3/4}}","-\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,"((-1)^(3/4)*(-I + x)^(3/4)*(a - I*a*x)^(3/4)*(-((-1)^(1/4)*(-I + x)^(1/4)*(I + x)^(3/4)) + 3*(-1)^(3/4)*ArcTan[(I + x)^(1/4)/(-I + x)^(1/4)] - 3*(-1)^(3/4)*ArcTanh[(I + x)^(1/4)/(-I + x)^(1/4)]))/((I + x)^(3/4)*(a + I*a*x)^(3/4))","A",1
1185,1,110,233,0.3851507,"\int \frac{1}{\sqrt[4]{a-i a x} (a+i a x)^{3/4}} \, dx","IntegrateAlgebraic[1/((a - I*a*x)^(1/4)*(a + I*a*x)^(3/4)),x]","\frac{\sqrt[4]{-1} a (x-i)^{3/4} \sqrt[4]{x+i} \left(\frac{2 (-1)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{x+i}}{\sqrt[4]{x-i}}\right)}{a}-\frac{2 (-1)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{x+i}}{\sqrt[4]{x-i}}\right)}{a}\right)}{\sqrt[4]{a-i a x} (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,"((-1)^(1/4)*a*(-I + x)^(3/4)*(I + x)^(1/4)*((2*(-1)^(3/4)*ArcTan[(I + x)^(1/4)/(-I + x)^(1/4)])/a - (2*(-1)^(3/4)*ArcTanh[(I + x)^(1/4)/(-I + x)^(1/4)])/a))/((a - I*a*x)^(1/4)*(a + I*a*x)^(3/4))","A",1
1186,1,36,31,0.3883033,"\int \frac{1}{(a-i a x)^{5/4} (a+i a x)^{3/4}} \, dx","IntegrateAlgebraic[1/((a - I*a*x)^(5/4)*(a + I*a*x)^(3/4)),x]","\frac{2 (a-i a x)^{3/4} \sqrt[4]{a+i a x}}{a^3 (x+i)}","-\frac{2 i \sqrt[4]{a+i a x}}{a^2 \sqrt[4]{a-i a x}}",1,"(2*(a - I*a*x)^(3/4)*(a + I*a*x)^(1/4))/(a^3*(I + x))","A",1
1187,1,63,67,0.41928,"\int \frac{1}{(a-i a x)^{9/4} (a+i a x)^{3/4}} \, dx","IntegrateAlgebraic[1/((a - I*a*x)^(9/4)*(a + I*a*x)^(3/4)),x]","-\frac{2 \sqrt[4]{-1} \left(-\sqrt[4]{-1}+2 (-1)^{3/4} (x+i)\right) (a-i a x)^{3/4} \sqrt[4]{a+i a x}}{5 a^4 (x+i)^2}","-\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*(-1)^(1/4)*(a - I*a*x)^(3/4)*(a + I*a*x)^(1/4)*(-(-1)^(1/4) + 2*(-1)^(3/4)*(I + x)))/(5*a^4*(I + x)^2)","A",1
1188,1,77,100,0.5727596,"\int \frac{1}{(a-i a x)^{13/4} (a+i a x)^{3/4}} \, dx","IntegrateAlgebraic[1/((a - I*a*x)^(13/4)*(a + I*a*x)^(3/4)),x]","-\frac{2 \sqrt[4]{-1} \left(8 (-1)^{3/4} (x+i)^2-4 \sqrt[4]{-1} (x+i)-5 (-1)^{3/4}\right) (a-i a x)^{3/4} \sqrt[4]{a+i a x}}{45 a^5 (x+i)^3}","-\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*(-1)^(1/4)*(a - I*a*x)^(3/4)*(a + I*a*x)^(1/4)*(-5*(-1)^(3/4) - 4*(-1)^(1/4)*(I + x) + 8*(-1)^(3/4)*(I + x)^2))/(45*a^5*(I + x)^3)","A",1
1189,0,0,112,11.6057666,"\int \frac{(a-i a x)^{5/4}}{(a+i a x)^{3/4}} \, dx","IntegrateAlgebraic[(a - I*a*x)^(5/4)/(a + I*a*x)^(3/4),x]","\int \frac{(a-i a x)^{5/4}}{(a+i a x)^{3/4}} \, dx","\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,"Could not integrate","F",-1
1190,0,0,76,10.4648042,"\int \frac{\sqrt[4]{a-i a x}}{(a+i a x)^{3/4}} \, dx","IntegrateAlgebraic[(a - I*a*x)^(1/4)/(a + I*a*x)^(3/4),x]","\int \frac{\sqrt[4]{a-i a x}}{(a+i a x)^{3/4}} \, dx","\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,"Could not integrate","F",-1
1191,0,0,43,11.0231456,"\int \frac{1}{(a-i a x)^{3/4} (a+i a x)^{3/4}} \, dx","IntegrateAlgebraic[1/((a - I*a*x)^(3/4)*(a + I*a*x)^(3/4)),x]","\int \frac{1}{(a-i a x)^{3/4} (a+i a x)^{3/4}} \, dx","\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,"Could not integrate","F",-1
1192,0,0,82,25.8547114,"\int \frac{1}{(a-i a x)^{7/4} (a+i a x)^{3/4}} \, dx","IntegrateAlgebraic[1/((a - I*a*x)^(7/4)*(a + I*a*x)^(3/4)),x]","\int \frac{1}{(a-i a x)^{7/4} (a+i a x)^{3/4}} \, dx","\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,"Could not integrate","F",-1
1193,0,0,115,31.7610659,"\int \frac{1}{(a-i a x)^{11/4} (a+i a x)^{3/4}} \, dx","IntegrateAlgebraic[1/((a - I*a*x)^(11/4)*(a + I*a*x)^(3/4)),x]","\int \frac{1}{(a-i a x)^{11/4} (a+i a x)^{3/4}} \, dx","-\frac{2 i \sqrt[4]{a+i a x}}{7 a^3 (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)}{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^2 (a-i a x)^{7/4}}",1,"Could not integrate","F",-1
1194,1,150,291,0.6782704,"\int \frac{(a-i a x)^{7/4}}{(a+i a x)^{7/4}} \, dx","IntegrateAlgebraic[(a - I*a*x)^(7/4)/(a + I*a*x)^(7/4),x]","-\frac{(-1)^{3/4} (x-i)^{7/4} (a-i a x)^{7/4} \left(\frac{3 \sqrt[4]{-1} (x+i)^{7/4}-14 (-1)^{3/4} (x+i)^{3/4}}{3 (x-i)^{3/4}}-7 (-1)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{x+i}}{\sqrt[4]{x-i}}\right)+7 (-1)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{x+i}}{\sqrt[4]{x-i}}\right)\right)}{(x+i)^{7/4} (a+i a x)^{7/4}}","\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,"-(((-1)^(3/4)*(-I + x)^(7/4)*(a - I*a*x)^(7/4)*((-14*(-1)^(3/4)*(I + x)^(3/4) + 3*(-1)^(1/4)*(I + x)^(7/4))/(3*(-I + x)^(3/4)) - 7*(-1)^(3/4)*ArcTan[(I + x)^(1/4)/(-I + x)^(1/4)] + 7*(-1)^(3/4)*ArcTanh[(I + x)^(1/4)/(-I + x)^(1/4)]))/((I + x)^(7/4)*(a + I*a*x)^(7/4)))","A",1
1195,1,141,266,0.7693607,"\int \frac{(a-i a x)^{3/4}}{(a+i a x)^{7/4}} \, dx","IntegrateAlgebraic[(a - I*a*x)^(3/4)/(a + I*a*x)^(7/4),x]","-\frac{\sqrt[4]{-1} a (x-i)^{7/4} (a-i a x)^{3/4} \left(-\frac{4 (-1)^{3/4} (x+i)^{3/4}}{3 a (x-i)^{3/4}}-\frac{2 (-1)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{x+i}}{\sqrt[4]{x-i}}\right)}{a}+\frac{2 (-1)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{x+i}}{\sqrt[4]{x-i}}\right)}{a}\right)}{(x+i)^{3/4} (a+i a x)^{7/4}}","\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,"-(((-1)^(1/4)*a*(-I + x)^(7/4)*(a - I*a*x)^(3/4)*((-4*(-1)^(3/4)*(I + x)^(3/4))/(3*a*(-I + x)^(3/4)) - (2*(-1)^(3/4)*ArcTan[(I + x)^(1/4)/(-I + x)^(1/4)])/a + (2*(-1)^(3/4)*ArcTanh[(I + x)^(1/4)/(-I + x)^(1/4)])/a))/((I + x)^(3/4)*(a + I*a*x)^(7/4)))","A",1
1196,1,40,33,0.6365951,"\int \frac{1}{\sqrt[4]{a-i a x} (a+i a x)^{7/4}} \, dx","IntegrateAlgebraic[1/((a - I*a*x)^(1/4)*(a + I*a*x)^(7/4)),x]","\frac{2 i (x-i) (x+i)}{3 \sqrt[4]{a-i a x} (a+i a x)^{7/4}}","\frac{2 i (a-i a x)^{3/4}}{3 a^2 (a+i a x)^{3/4}}",1,"(((2*I)/3)*(-I + x)*(I + x))/((a - I*a*x)^(1/4)*(a + I*a*x)^(7/4))","A",1
1197,1,56,65,0.6337654,"\int \frac{1}{(a-i a x)^{5/4} (a+i a x)^{7/4}} \, dx","IntegrateAlgebraic[1/((a - I*a*x)^(5/4)*(a + I*a*x)^(7/4)),x]","-\frac{2 \sqrt[4]{-1} \left(3 \sqrt[4]{-1}+2 (-1)^{3/4} (x+i)\right)}{3 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*(-1)^(1/4)*(3*(-1)^(1/4) + 2*(-1)^(3/4)*(I + x)))/(3*a^2*(a - I*a*x)^(1/4)*(a + I*a*x)^(3/4))","A",1
1198,1,84,100,0.8218973,"\int \frac{1}{(a-i a x)^{9/4} (a+i a x)^{7/4}} \, dx","IntegrateAlgebraic[1/((a - I*a*x)^(9/4)*(a + I*a*x)^(7/4)),x]","-\frac{2 \sqrt[4]{-1} \left(8 (-1)^{3/4} (x+i)^2+12 \sqrt[4]{-1} (x+i)+3 (-1)^{3/4}\right) (a-i a x)^{3/4} \sqrt[4]{a+i a x}}{15 a^5 (x-i) (x+i)^2}","\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*(-1)^(1/4)*(a - I*a*x)^(3/4)*(a + I*a*x)^(1/4)*(3*(-1)^(3/4) + 12*(-1)^(1/4)*(I + x) + 8*(-1)^(3/4)*(I + x)^2))/(15*a^5*(-I + x)*(I + x)^2)","A",1
1199,0,0,139,25.1656794,"\int \frac{(a-i a x)^{9/4}}{(a+i a x)^{7/4}} \, dx","IntegrateAlgebraic[(a - I*a*x)^(9/4)/(a + I*a*x)^(7/4),x]","\int \frac{(a-i a x)^{9/4}}{(a+i a x)^{7/4}} \, dx","-\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,"Could not integrate","F",-1
1200,0,0,113,24.4396777,"\int \frac{(a-i a x)^{5/4}}{(a+i a x)^{7/4}} \, dx","IntegrateAlgebraic[(a - I*a*x)^(5/4)/(a + I*a*x)^(7/4),x]","\int \frac{(a-i a x)^{5/4}}{(a+i a x)^{7/4}} \, dx","-\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,"Could not integrate","F",-1
1201,0,0,79,23.1467026,"\int \frac{\sqrt[4]{a-i a x}}{(a+i a x)^{7/4}} \, dx","IntegrateAlgebraic[(a - I*a*x)^(1/4)/(a + I*a*x)^(7/4),x]","\int \frac{\sqrt[4]{a-i a x}}{(a+i a x)^{7/4}} \, dx","\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,"Could not integrate","F",-1
1202,0,0,82,24.2767464,"\int \frac{1}{(a-i a x)^{3/4} (a+i a x)^{7/4}} \, dx","IntegrateAlgebraic[1/((a - I*a*x)^(3/4)*(a + I*a*x)^(7/4)),x]","\int \frac{1}{(a-i a x)^{3/4} (a+i a x)^{7/4}} \, dx","\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,"Could not integrate","F",-1
1203,0,0,81,37.6618362,"\int \frac{1}{(a-i a x)^{7/4} (a+i a x)^{7/4}} \, dx","IntegrateAlgebraic[1/((a - I*a*x)^(7/4)*(a + I*a*x)^(7/4)),x]","\int \frac{1}{(a-i a x)^{7/4} (a+i a x)^{7/4}} \, dx","\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,"Could not integrate","F",-1
1204,0,0,114,44.302519,"\int \frac{1}{(a-i a x)^{11/4} (a+i a x)^{7/4}} \, dx","IntegrateAlgebraic[1/((a - I*a*x)^(11/4)*(a + I*a*x)^(7/4)),x]","\int \frac{1}{(a-i a x)^{11/4} (a+i a x)^{7/4}} \, dx","\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,"Could not integrate","F",-1
1205,0,0,147,46.1202805,"\int \frac{1}{(a-i a x)^{15/4} (a+i a x)^{7/4}} \, dx","IntegrateAlgebraic[1/((a - I*a*x)^(15/4)*(a + I*a*x)^(7/4)),x]","\int \frac{1}{(a-i a x)^{15/4} (a+i a x)^{7/4}} \, dx","\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,"Could not integrate","F",-1
1206,0,0,137,17.7426655,"\int \frac{(a-i a x)^{7/4}}{(a+i a x)^{5/4}} \, dx","IntegrateAlgebraic[(a - I*a*x)^(7/4)/(a + I*a*x)^(5/4),x]","\int \frac{(a-i a x)^{7/4}}{(a+i a x)^{5/4}} \, dx","\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,"Could not integrate","F",-1
1207,0,0,102,17.2059932,"\int \frac{(a-i a x)^{3/4}}{(a+i a x)^{5/4}} \, dx","IntegrateAlgebraic[(a - I*a*x)^(3/4)/(a + I*a*x)^(5/4),x]","\int \frac{(a-i a x)^{3/4}}{(a+i a x)^{5/4}} \, dx","\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,"Could not integrate","F",-1
1208,0,0,78,16.956845,"\int \frac{1}{\sqrt[4]{a-i a x} (a+i a x)^{5/4}} \, dx","IntegrateAlgebraic[1/((a - I*a*x)^(1/4)*(a + I*a*x)^(5/4)),x]","\int \frac{1}{\sqrt[4]{a-i a x} (a+i a x)^{5/4}} \, dx","\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,"Could not integrate","F",-1
1209,0,0,46,24.0353439,"\int \frac{1}{(a-i a x)^{5/4} (a+i a x)^{5/4}} \, dx","IntegrateAlgebraic[1/((a - I*a*x)^(5/4)*(a + I*a*x)^(5/4)),x]","\int \frac{1}{(a-i a x)^{5/4} (a+i a x)^{5/4}} \, dx","\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,"Could not integrate","F",-1
1210,0,0,82,36.5099756,"\int \frac{1}{(a-i a x)^{9/4} (a+i a x)^{5/4}} \, dx","IntegrateAlgebraic[1/((a - I*a*x)^(9/4)*(a + I*a*x)^(5/4)),x]","\int \frac{1}{(a-i a x)^{9/4} (a+i a x)^{5/4}} \, dx","\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,"Could not integrate","F",-1
1211,0,0,115,37.4414004,"\int \frac{1}{(a-i a x)^{13/4} (a+i a x)^{5/4}} \, dx","IntegrateAlgebraic[1/((a - I*a*x)^(13/4)*(a + I*a*x)^(5/4)),x]","\int \frac{1}{(a-i a x)^{13/4} (a+i a x)^{5/4}} \, dx","\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,"Could not integrate","F",-1
1212,1,146,287,0.4909721,"\int \frac{(a-i a x)^{5/4}}{(a+i a x)^{5/4}} \, dx","IntegrateAlgebraic[(a - I*a*x)^(5/4)/(a + I*a*x)^(5/4),x]","-\frac{\sqrt[4]{-1} (x-i)^{5/4} (a-i a x)^{5/4} \left(\frac{(-1)^{3/4} (x+i)^{5/4}+10 \sqrt[4]{-1} \sqrt[4]{x+i}}{\sqrt[4]{x-i}}-5 \sqrt[4]{-1} \tan ^{-1}\left(\frac{\sqrt[4]{x+i}}{\sqrt[4]{x-i}}\right)-5 \sqrt[4]{-1} \tanh ^{-1}\left(\frac{\sqrt[4]{x+i}}{\sqrt[4]{x-i}}\right)\right)}{(x+i)^{5/4} (a+i a x)^{5/4}}","\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,"-(((-1)^(1/4)*(-I + x)^(5/4)*(a - I*a*x)^(5/4)*((10*(-1)^(1/4)*(I + x)^(1/4) + (-1)^(3/4)*(I + x)^(5/4))/(-I + x)^(1/4) - 5*(-1)^(1/4)*ArcTan[(I + x)^(1/4)/(-I + x)^(1/4)] - 5*(-1)^(1/4)*ArcTanh[(I + x)^(1/4)/(-I + x)^(1/4)]))/((I + x)^(5/4)*(a + I*a*x)^(5/4)))","A",1
1213,1,138,264,0.5339552,"\int \frac{\sqrt[4]{a-i a x}}{(a+i a x)^{5/4}} \, dx","IntegrateAlgebraic[(a - I*a*x)^(1/4)/(a + I*a*x)^(5/4),x]","\frac{(-1)^{3/4} a (x-i)^{5/4} \sqrt[4]{a-i a x} \left(\frac{4 \sqrt[4]{-1} \sqrt[4]{x+i}}{a \sqrt[4]{x-i}}-\frac{2 \sqrt[4]{-1} \tan ^{-1}\left(\frac{\sqrt[4]{x+i}}{\sqrt[4]{x-i}}\right)}{a}-\frac{2 \sqrt[4]{-1} \tanh ^{-1}\left(\frac{\sqrt[4]{x+i}}{\sqrt[4]{x-i}}\right)}{a}\right)}{\sqrt[4]{x+i} (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,"((-1)^(3/4)*a*(-I + x)^(5/4)*(a - I*a*x)^(1/4)*((4*(-1)^(1/4)*(I + x)^(1/4))/(a*(-I + x)^(1/4)) - (2*(-1)^(1/4)*ArcTan[(I + x)^(1/4)/(-I + x)^(1/4)])/a - (2*(-1)^(1/4)*ArcTanh[(I + x)^(1/4)/(-I + x)^(1/4)])/a))/((I + x)^(1/4)*(a + I*a*x)^(5/4))","A",1
1214,1,38,31,0.4356539,"\int \frac{1}{(a-i a x)^{3/4} (a+i a x)^{5/4}} \, dx","IntegrateAlgebraic[1/((a - I*a*x)^(3/4)*(a + I*a*x)^(5/4)),x]","\frac{2 i (x-i) (x+i)}{(a-i a x)^{3/4} (a+i a x)^{5/4}}","\frac{2 i \sqrt[4]{a-i a x}}{a^2 \sqrt[4]{a+i a x}}",1,"((2*I)*(-I + x)*(I + x))/((a - I*a*x)^(3/4)*(a + I*a*x)^(5/4))","A",1
1215,1,63,67,0.5119074,"\int \frac{1}{(a-i a x)^{7/4} (a+i a x)^{5/4}} \, dx","IntegrateAlgebraic[1/((a - I*a*x)^(7/4)*(a + I*a*x)^(5/4)),x]","-\frac{2 (-1)^{3/4} (x-i) (x+i) \left(-(-1)^{3/4}+2 \sqrt[4]{-1} (x+i)\right)}{3 (a-i a x)^{7/4} (a+i a x)^{5/4}}","\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*(-1)^(3/4)*(-I + x)*(I + x)*(-(-1)^(3/4) + 2*(-1)^(1/4)*(I + x)))/(3*(a - I*a*x)^(7/4)*(a + I*a*x)^(5/4))","A",1
1216,1,84,100,0.5666304,"\int \frac{1}{(a-i a x)^{11/4} (a+i a x)^{5/4}} \, dx","IntegrateAlgebraic[1/((a - I*a*x)^(11/4)*(a + I*a*x)^(5/4)),x]","-\frac{2 (-1)^{3/4} \left(8 \sqrt[4]{-1} (x+i)^2-4 (-1)^{3/4} (x+i)+3 \sqrt[4]{-1}\right) \sqrt[4]{a-i a x} (a+i a x)^{3/4}}{21 a^5 (x-i) (x+i)^2}","\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*(-1)^(3/4)*(a - I*a*x)^(1/4)*(a + I*a*x)^(3/4)*(3*(-1)^(1/4) - 4*(-1)^(3/4)*(I + x) + 8*(-1)^(1/4)*(I + x)^2))/(21*a^5*(-I + x)*(I + x)^2)","A",1
1217,0,0,141,28.9252287,"\int \frac{(a-i a x)^{7/4}}{(a+i a x)^{9/4}} \, dx","IntegrateAlgebraic[(a - I*a*x)^(7/4)/(a + I*a*x)^(9/4),x]","\int \frac{(a-i a x)^{7/4}}{(a+i a x)^{9/4}} \, dx","-\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,"Could not integrate","F",-1
1218,0,0,115,28.1506234,"\int \frac{(a-i a x)^{3/4}}{(a+i a x)^{9/4}} \, dx","IntegrateAlgebraic[(a - I*a*x)^(3/4)/(a + I*a*x)^(9/4),x]","\int \frac{(a-i a x)^{3/4}}{(a+i a x)^{9/4}} \, dx","-\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,"Could not integrate","F",-1
1219,0,0,82,27.7723704,"\int \frac{1}{\sqrt[4]{a-i a x} (a+i a x)^{9/4}} \, dx","IntegrateAlgebraic[1/((a - I*a*x)^(1/4)*(a + I*a*x)^(9/4)),x]","\int \frac{1}{\sqrt[4]{a-i a x} (a+i a x)^{9/4}} \, dx","\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,"Could not integrate","F",-1
1220,0,0,82,35.680763,"\int \frac{1}{(a-i a x)^{5/4} (a+i a x)^{9/4}} \, dx","IntegrateAlgebraic[1/((a - I*a*x)^(5/4)*(a + I*a*x)^(9/4)),x]","\int \frac{1}{(a-i a x)^{5/4} (a+i a x)^{9/4}} \, dx","\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,"Could not integrate","F",-1
1221,0,0,88,46.3665394,"\int \frac{1}{(a-i a x)^{9/4} (a+i a x)^{9/4}} \, dx","IntegrateAlgebraic[1/((a - I*a*x)^(9/4)*(a + I*a*x)^(9/4)),x]","\int \frac{1}{(a-i a x)^{9/4} (a+i a x)^{9/4}} \, dx","\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,"Could not integrate","F",-1
1222,0,0,121,48.1435023,"\int \frac{1}{(a-i a x)^{13/4} (a+i a x)^{9/4}} \, dx","IntegrateAlgebraic[1/((a - I*a*x)^(13/4)*(a + I*a*x)^(9/4)),x]","\int \frac{1}{(a-i a x)^{13/4} (a+i a x)^{9/4}} \, dx","\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,"Could not integrate","F",-1
1223,0,0,154,53.0629829,"\int \frac{1}{(a-i a x)^{17/4} (a+i a x)^{9/4}} \, dx","IntegrateAlgebraic[1/((a - I*a*x)^(17/4)*(a + I*a*x)^(9/4)),x]","\int \frac{1}{(a-i a x)^{17/4} (a+i a x)^{9/4}} \, dx","\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,"Could not integrate","F",-1
1224,1,160,297,1.1111039,"\int \frac{(a-i a x)^{5/4}}{(a+i a x)^{9/4}} \, dx","IntegrateAlgebraic[(a - I*a*x)^(5/4)/(a + I*a*x)^(9/4),x]","-\frac{(-1)^{3/4} a (x-i)^{9/4} (a-i a x)^{5/4} \left(\frac{8 \left(5 (-1)^{3/4} \sqrt[4]{x+i}-3 \sqrt[4]{-1} (x+i)^{5/4}\right)}{5 a (x-i)^{5/4}}+\frac{2 \sqrt[4]{-1} \tan ^{-1}\left(\frac{\sqrt[4]{x+i}}{\sqrt[4]{x-i}}\right)}{a}+\frac{2 \sqrt[4]{-1} \tanh ^{-1}\left(\frac{\sqrt[4]{x+i}}{\sqrt[4]{x-i}}\right)}{a}\right)}{(x+i)^{5/4} (a+i a x)^{9/4}}","\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,"-(((-1)^(3/4)*a*(-I + x)^(9/4)*(a - I*a*x)^(5/4)*((8*(5*(-1)^(3/4)*(I + x)^(1/4) - 3*(-1)^(1/4)*(I + x)^(5/4)))/(5*a*(-I + x)^(5/4)) + (2*(-1)^(1/4)*ArcTan[(I + x)^(1/4)/(-I + x)^(1/4)])/a + (2*(-1)^(1/4)*ArcTanh[(I + x)^(1/4)/(-I + x)^(1/4)])/a))/((I + x)^(5/4)*(a + I*a*x)^(9/4)))","A",1
1225,1,40,33,0.8746801,"\int \frac{\sqrt[4]{a-i a x}}{(a+i a x)^{9/4}} \, dx","IntegrateAlgebraic[(a - I*a*x)^(1/4)/(a + I*a*x)^(9/4),x]","\frac{2 i (x-i) (x+i) \sqrt[4]{a-i a x}}{5 (a+i a x)^{9/4}}","\frac{2 i (a-i a x)^{5/4}}{5 a^2 (a+i a x)^{5/4}}",1,"(((2*I)/5)*(-I + x)*(I + x)*(a - I*a*x)^(1/4))/(a + I*a*x)^(9/4)","A",1
1226,1,80,67,0.8409693,"\int \frac{1}{(a-i a x)^{3/4} (a+i a x)^{9/4}} \, dx","IntegrateAlgebraic[1/((a - I*a*x)^(3/4)*(a + I*a*x)^(9/4)),x]","-\frac{2 (-1)^{3/4} (x-i) (x+i)^{3/4} \left(5 (-1)^{3/4} \sqrt[4]{x+i}-2 \sqrt[4]{-1} (x+i)^{5/4}\right)}{5 (a-i a x)^{3/4} (a+i a x)^{9/4}}","\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*(-1)^(3/4)*(-I + x)*(I + x)^(3/4)*(5*(-1)^(3/4)*(I + x)^(1/4) - 2*(-1)^(1/4)*(I + x)^(5/4)))/(5*(a - I*a*x)^(3/4)*(a + I*a*x)^(9/4))","A",1
1227,1,77,100,0.9114356,"\int \frac{1}{(a-i a x)^{7/4} (a+i a x)^{9/4}} \, dx","IntegrateAlgebraic[1/((a - I*a*x)^(7/4)*(a + I*a*x)^(9/4)),x]","\frac{2 \sqrt[4]{-1} (x-i) (x+i) \left(8 \sqrt[4]{-1} (x+i)^2-20 (-1)^{3/4} (x+i)-5 \sqrt[4]{-1}\right)}{15 (a-i a x)^{7/4} (a+i a x)^{9/4}}","\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*(-1)^(1/4)*(-I + x)*(I + x)*(-5*(-1)^(1/4) - 20*(-1)^(3/4)*(I + x) + 8*(-1)^(1/4)*(I + x)^2))/(15*(a - I*a*x)^(7/4)*(a + I*a*x)^(9/4))","A",1
1228,1,98,133,1.0884636,"\int \frac{1}{(a-i a x)^{11/4} (a+i a x)^{9/4}} \, dx","IntegrateAlgebraic[1/((a - I*a*x)^(11/4)*(a + I*a*x)^(9/4)),x]","-\frac{2 (-1)^{3/4} \left(16 \sqrt[4]{-1} (x+i)^3-40 (-1)^{3/4} (x+i)^2-10 \sqrt[4]{-1} (x+i)-5 (-1)^{3/4}\right) \sqrt[4]{a-i a x} (a+i a x)^{3/4}}{35 a^6 (x-i)^2 (x+i)^2}","\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*(-1)^(3/4)*(a - I*a*x)^(1/4)*(a + I*a*x)^(3/4)*(-5*(-1)^(3/4) - 10*(-1)^(1/4)*(I + x) - 40*(-1)^(3/4)*(I + x)^2 + 16*(-1)^(1/4)*(I + x)^3))/(35*a^6*(-I + x)^2*(I + x)^2)","A",1
1229,0,0,83,0.0000645,"\int (a+b x)^2 (a c-b c x)^n \, dx","IntegrateAlgebraic[(a + b*x)^2*(a*c - b*c*x)^n,x]","\int (a+b x)^2 (a c-b c x)^n \, dx","-\frac{4 a^2 (a c-b c x)^{n+1}}{b c (n+1)}-\frac{(a c-b c x)^{n+3}}{b c^3 (n+3)}+\frac{4 a (a c-b c x)^{n+2}}{b c^2 (n+2)}",1,"Could not integrate","F",-1
1230,0,0,53,0.0000606,"\int (a+b x) (a c-b c x)^n \, dx","IntegrateAlgebraic[(a + b*x)*(a*c - b*c*x)^n,x]","\int (a+b x) (a c-b c x)^n \, dx","\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,"Could not integrate","F",-1
1231,0,0,52,0.0001195,"\int \frac{(a c-b c x)^n}{a+b x} \, dx","IntegrateAlgebraic[(a*c - b*c*x)^n/(a + b*x),x]","\int \frac{(a c-b c x)^n}{a+b x} \, dx","-\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,"Could not integrate","F",-1
1232,0,0,52,0.0000654,"\int \frac{(a c-b c x)^n}{(a+b x)^2} \, dx","IntegrateAlgebraic[(a*c - b*c*x)^n/(a + b*x)^2,x]","\int \frac{(a c-b c x)^n}{(a+b x)^2} \, dx","-\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,"Could not integrate","F",-1
1233,0,0,41,0.0000633,"\int (a+a x)^m (c-c x)^m \, dx","IntegrateAlgebraic[(a + a*x)^m*(c - c*x)^m,x]","\int (a+a x)^m (c-c x)^m \, dx","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,"Could not integrate","F",-1
1234,0,0,57,0.000067,"\int (a+b x)^m (a c-b c x)^m \, dx","IntegrateAlgebraic[(a + b*x)^m*(a*c - b*c*x)^m,x]","\int (a+b x)^m (a c-b c x)^m \, dx","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,"Could not integrate","F",-1
1235,0,0,20,0.00008,"\int (3-6 x)^m (2+4 x)^m \, dx","IntegrateAlgebraic[(3 - 6*x)^m*(2 + 4*x)^m,x]","\int (3-6 x)^m (2+4 x)^m \, dx","6^m x \, _2F_1\left(\frac{1}{2},-m;\frac{3}{2};4 x^2\right)",1,"Could not integrate","F",-1
1236,1,99,38,0.0463285,"\int (a+b x)^4 (c+d x) \, dx","IntegrateAlgebraic[(a + b*x)^4*(c + d*x),x]","\frac{1}{30} x \left(30 a^4 c+15 a^4 d x+60 a^3 b c x+40 a^3 b d x^2+60 a^2 b^2 c x^2+45 a^2 b^2 d x^3+30 a b^3 c x^3+24 a b^3 d x^4+6 b^4 c x^4+5 b^4 d x^5\right)","\frac{(a+b x)^5 (b c-a d)}{5 b^2}+\frac{d (a+b x)^6}{6 b^2}",1,"(x*(30*a^4*c + 60*a^3*b*c*x + 15*a^4*d*x + 60*a^2*b^2*c*x^2 + 40*a^3*b*d*x^2 + 30*a*b^3*c*x^3 + 45*a^2*b^2*d*x^3 + 6*b^4*c*x^4 + 24*a*b^3*d*x^4 + 5*b^4*d*x^5))/30","B",1
1237,1,79,38,0.0276905,"\int (a+b x)^3 (c+d x) \, dx","IntegrateAlgebraic[(a + b*x)^3*(c + d*x),x]","\frac{1}{20} \left(20 a^3 c x+10 a^3 d x^2+30 a^2 b c x^2+20 a^2 b d x^3+20 a b^2 c x^3+15 a b^2 d x^4+5 b^3 c x^4+4 b^3 d x^5\right)","\frac{(a+b x)^4 (b c-a d)}{4 b^2}+\frac{d (a+b x)^5}{5 b^2}",1,"(20*a^3*c*x + 30*a^2*b*c*x^2 + 10*a^3*d*x^2 + 20*a*b^2*c*x^3 + 20*a^2*b*d*x^3 + 5*b^3*c*x^4 + 15*a*b^2*d*x^4 + 4*b^3*d*x^5)/20","B",1
1238,1,51,38,0.0205723,"\int (a+b x)^2 (c+d x) \, dx","IntegrateAlgebraic[(a + b*x)^2*(c + d*x),x]","\frac{1}{12} x \left(12 a^2 c+6 a^2 d x+12 a b c x+8 a b d x^2+4 b^2 c x^2+3 b^2 d x^3\right)","\frac{(a+b x)^3 (b c-a d)}{3 b^2}+\frac{d (a+b x)^4}{4 b^2}",1,"(x*(12*a^2*c + 12*a*b*c*x + 6*a^2*d*x + 4*b^2*c*x^2 + 8*a*b*d*x^2 + 3*b^2*d*x^3))/12","A",1
1239,1,27,28,0.0104269,"\int (a+b x) (c+d x) \, dx","IntegrateAlgebraic[(a + b*x)*(c + d*x),x]","\frac{1}{6} x \left(6 a c+3 a d x+3 b c x+2 b d x^2\right)","\frac{1}{2} x^2 (a d+b c)+a c x+\frac{1}{3} b d x^3",1,"(x*(6*a*c + 3*b*c*x + 3*a*d*x + 2*b*d*x^2))/6","A",1
1240,1,14,12,0.0026882,"\int (c+d x) \, dx","IntegrateAlgebraic[c + d*x,x]","\frac{1}{2} \left(2 c x+d x^2\right)","c x+\frac{d x^2}{2}",1,"(2*c*x + d*x^2)/2","A",1
1241,1,25,25,0.0129907,"\int \frac{c+d x}{a+b x} \, dx","IntegrateAlgebraic[(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",1
1242,1,31,32,0.0188525,"\int \frac{c+d x}{(a+b x)^2} \, dx","IntegrateAlgebraic[(c + d*x)/(a + b*x)^2,x]","\frac{a d-b c}{b^2 (a+b x)}+\frac{d \log (a+b x)}{b^2}","\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",1
1243,1,28,28,0.0149321,"\int \frac{c+d x}{(a+b x)^3} \, dx","IntegrateAlgebraic[(c + d*x)/(a + b*x)^3,x]","\frac{-a d-b c-2 b d x}{2 b^2 (a+b x)^2}","-\frac{(c+d x)^2}{2 (a+b x)^2 (b c-a d)}",1,"(-(b*c) - a*d - 2*b*d*x)/(2*b^2*(a + b*x)^2)","A",1
1244,1,28,38,0.0144969,"\int \frac{c+d x}{(a+b x)^4} \, dx","IntegrateAlgebraic[(c + d*x)/(a + b*x)^4,x]","\frac{-a d-2 b c-3 b d x}{6 b^2 (a+b x)^3}","-\frac{b c-a d}{3 b^2 (a+b x)^3}-\frac{d}{2 b^2 (a+b x)^2}",1,"(-2*b*c - a*d - 3*b*d*x)/(6*b^2*(a + b*x)^3)","A",1
1245,1,28,38,0.0146417,"\int \frac{c+d x}{(a+b x)^5} \, dx","IntegrateAlgebraic[(c + d*x)/(a + b*x)^5,x]","\frac{-a d-3 b c-4 b d x}{12 b^2 (a+b x)^4}","-\frac{b c-a d}{4 b^2 (a+b x)^4}-\frac{d}{3 b^2 (a+b x)^3}",1,"(-3*b*c - a*d - 4*b*d*x)/(12*b^2*(a + b*x)^4)","A",1
1246,1,178,65,0.0643966,"\int (a+b x)^4 (c+d x)^2 \, dx","IntegrateAlgebraic[(a + b*x)^4*(c + d*x)^2,x]","\frac{1}{105} \left(105 a^4 c^2 x+105 a^4 c d x^2+35 a^4 d^2 x^3+210 a^3 b c^2 x^2+280 a^3 b c d x^3+105 a^3 b d^2 x^4+210 a^2 b^2 c^2 x^3+315 a^2 b^2 c d x^4+126 a^2 b^2 d^2 x^5+105 a b^3 c^2 x^4+168 a b^3 c d x^5+70 a b^3 d^2 x^6+21 b^4 c^2 x^5+35 b^4 c d x^6+15 b^4 d^2 x^7\right)","\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,"(105*a^4*c^2*x + 210*a^3*b*c^2*x^2 + 105*a^4*c*d*x^2 + 210*a^2*b^2*c^2*x^3 + 280*a^3*b*c*d*x^3 + 35*a^4*d^2*x^3 + 105*a*b^3*c^2*x^4 + 315*a^2*b^2*c*d*x^4 + 105*a^3*b*d^2*x^4 + 21*b^4*c^2*x^5 + 168*a*b^3*c*d*x^5 + 126*a^2*b^2*d^2*x^5 + 35*b^4*c*d*x^6 + 70*a*b^3*d^2*x^6 + 15*b^4*d^2*x^7)/105","B",1
1247,1,137,65,0.041747,"\int (a+b x)^3 (c+d x)^2 \, dx","IntegrateAlgebraic[(a + b*x)^3*(c + d*x)^2,x]","\frac{1}{60} \left(60 a^3 c^2 x+60 a^3 c d x^2+20 a^3 d^2 x^3+90 a^2 b c^2 x^2+120 a^2 b c d x^3+45 a^2 b d^2 x^4+60 a b^2 c^2 x^3+90 a b^2 c d x^4+36 a b^2 d^2 x^5+15 b^3 c^2 x^4+24 b^3 c d x^5+10 b^3 d^2 x^6\right)","\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,"(60*a^3*c^2*x + 90*a^2*b*c^2*x^2 + 60*a^3*c*d*x^2 + 60*a*b^2*c^2*x^3 + 120*a^2*b*c*d*x^3 + 20*a^3*d^2*x^3 + 15*b^3*c^2*x^4 + 90*a*b^2*c*d*x^4 + 45*a^2*b*d^2*x^4 + 24*b^3*c*d*x^5 + 36*a*b^2*d^2*x^5 + 10*b^3*d^2*x^6)/60","B",1
1248,1,96,65,0.0287335,"\int (a+b x)^2 (c+d x)^2 \, dx","IntegrateAlgebraic[(a + b*x)^2*(c + d*x)^2,x]","\frac{1}{30} \left(30 a^2 c^2 x+30 a^2 c d x^2+10 a^2 d^2 x^3+30 a b c^2 x^2+40 a b c d x^3+15 a b d^2 x^4+10 b^2 c^2 x^3+15 b^2 c d x^4+6 b^2 d^2 x^5\right)","\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,"(30*a^2*c^2*x + 30*a*b*c^2*x^2 + 30*a^2*c*d*x^2 + 10*b^2*c^2*x^3 + 40*a*b*c*d*x^3 + 10*a^2*d^2*x^3 + 15*b^2*c*d*x^4 + 15*a*b*d^2*x^4 + 6*b^2*d^2*x^5)/30","A",1
1249,1,51,38,0.0215767,"\int (a+b x) (c+d x)^2 \, dx","IntegrateAlgebraic[(a + b*x)*(c + d*x)^2,x]","\frac{1}{12} x \left(12 a c^2+12 a c d x+4 a d^2 x^2+6 b c^2 x+8 b c d x^2+3 b d^2 x^3\right)","\frac{b (c+d x)^4}{4 d^2}-\frac{(c+d x)^3 (b c-a d)}{3 d^2}",1,"(x*(12*a*c^2 + 6*b*c^2*x + 12*a*c*d*x + 8*b*c*d*x^2 + 4*a*d^2*x^2 + 3*b*d^2*x^3))/12","A",1
1250,1,14,14,0.0046602,"\int (c+d x)^2 \, dx","IntegrateAlgebraic[(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
1251,1,43,49,0.0280311,"\int \frac{(c+d x)^2}{a+b x} \, dx","IntegrateAlgebraic[(c + d*x)^2/(a + b*x),x]","\frac{(b c-a d)^2 \log (a+b x)}{b^3}+\frac{d x (-2 a d+4 b c+b d x)}{2 b^2}","\frac{(b c-a d)^2 \log (a+b x)}{b^3}+\frac{d x (b c-a d)}{b^2}+\frac{(c+d x)^2}{2 b}",1,"(d*x*(4*b*c - 2*a*d + b*d*x))/(2*b^2) + ((b*c - a*d)^2*Log[a + b*x])/b^3","A",1
1252,1,74,51,0.0549958,"\int \frac{(c+d x)^2}{(a+b x)^2} \, dx","IntegrateAlgebraic[(c + d*x)^2/(a + b*x)^2,x]","\frac{-a^2 d^2+2 a b c d+a b d^2 x-b^2 c^2+b^2 d^2 x^2}{b^3 (a+b x)}+\frac{2 \left(b c d-a d^2\right) \log (a+b x)}{b^3}","-\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,"(-(b^2*c^2) + 2*a*b*c*d - a^2*d^2 + a*b*d^2*x + b^2*d^2*x^2)/(b^3*(a + b*x)) + (2*(b*c*d - a*d^2)*Log[a + b*x])/b^3","A",1
1253,1,49,59,0.03803,"\int \frac{(c+d x)^2}{(a+b x)^3} \, dx","IntegrateAlgebraic[(c + d*x)^2/(a + b*x)^3,x]","\frac{d^2 \log (a+b x)}{b^3}-\frac{(b c-a d) (3 a d+b c+4 b d x)}{2 b^3 (a+b x)^2}","-\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,"-1/2*((b*c - a*d)*(b*c + 3*a*d + 4*b*d*x))/(b^3*(a + b*x)^2) + (d^2*Log[a + b*x])/b^3","A",1
1254,1,64,28,0.0318661,"\int \frac{(c+d x)^2}{(a+b x)^4} \, dx","IntegrateAlgebraic[(c + d*x)^2/(a + b*x)^4,x]","\frac{-a^2 d^2-a b c d-3 a b d^2 x+b^2 \left(-c^2\right)-3 b^2 c d x-3 b^2 d^2 x^2}{3 b^3 (a+b x)^3}","-\frac{(c+d x)^3}{3 (a+b x)^3 (b c-a d)}",1,"(-(b^2*c^2) - a*b*c*d - a^2*d^2 - 3*b^2*c*d*x - 3*a*b*d^2*x - 3*b^2*d^2*x^2)/(3*b^3*(a + b*x)^3)","B",1
1255,1,64,65,0.029074,"\int \frac{(c+d x)^2}{(a+b x)^5} \, dx","IntegrateAlgebraic[(c + d*x)^2/(a + b*x)^5,x]","\frac{-a^2 d^2-2 a b c d-4 a b d^2 x-3 b^2 c^2-8 b^2 c d x-6 b^2 d^2 x^2}{12 b^3 (a+b x)^4}","-\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,"(-3*b^2*c^2 - 2*a*b*c*d - a^2*d^2 - 8*b^2*c*d*x - 4*a*b*d^2*x - 6*b^2*d^2*x^2)/(12*b^3*(a + b*x)^4)","A",1
1256,1,64,65,0.0337369,"\int \frac{(c+d x)^2}{(a+b x)^6} \, dx","IntegrateAlgebraic[(c + d*x)^2/(a + b*x)^6,x]","\frac{-a^2 d^2-3 a b c d-5 a b d^2 x-6 b^2 c^2-15 b^2 c d x-10 b^2 d^2 x^2}{30 b^3 (a+b x)^5}","-\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,"(-6*b^2*c^2 - 3*a*b*c*d - a^2*d^2 - 15*b^2*c*d*x - 5*a*b*d^2*x - 10*b^2*d^2*x^2)/(30*b^3*(a + b*x)^5)","A",1
1257,1,64,65,0.029326,"\int \frac{(c+d x)^2}{(a+b x)^7} \, dx","IntegrateAlgebraic[(c + d*x)^2/(a + b*x)^7,x]","\frac{-a^2 d^2-4 a b c d-6 a b d^2 x-10 b^2 c^2-24 b^2 c d x-15 b^2 d^2 x^2}{60 b^3 (a+b x)^6}","-\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,"(-10*b^2*c^2 - 4*a*b*c*d - a^2*d^2 - 24*b^2*c*d*x - 6*a*b*d^2*x - 15*b^2*d^2*x^2)/(60*b^3*(a + b*x)^6)","A",1
1258,1,311,92,0.1663322,"\int (a+b x)^5 (c+d x)^3 \, dx","IntegrateAlgebraic[(a + b*x)^5*(c + d*x)^3,x]","\frac{1}{504} \left(504 a^5 c^3 x+756 a^5 c^2 d x^2+504 a^5 c d^2 x^3+126 a^5 d^3 x^4+1260 a^4 b c^3 x^2+2520 a^4 b c^2 d x^3+1890 a^4 b c d^2 x^4+504 a^4 b d^3 x^5+1680 a^3 b^2 c^3 x^3+3780 a^3 b^2 c^2 d x^4+3024 a^3 b^2 c d^2 x^5+840 a^3 b^2 d^3 x^6+1260 a^2 b^3 c^3 x^4+3024 a^2 b^3 c^2 d x^5+2520 a^2 b^3 c d^2 x^6+720 a^2 b^3 d^3 x^7+504 a b^4 c^3 x^5+1260 a b^4 c^2 d x^6+1080 a b^4 c d^2 x^7+315 a b^4 d^3 x^8+84 b^5 c^3 x^6+216 b^5 c^2 d x^7+189 b^5 c d^2 x^8+56 b^5 d^3 x^9\right)","\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,"(504*a^5*c^3*x + 1260*a^4*b*c^3*x^2 + 756*a^5*c^2*d*x^2 + 1680*a^3*b^2*c^3*x^3 + 2520*a^4*b*c^2*d*x^3 + 504*a^5*c*d^2*x^3 + 1260*a^2*b^3*c^3*x^4 + 3780*a^3*b^2*c^2*d*x^4 + 1890*a^4*b*c*d^2*x^4 + 126*a^5*d^3*x^4 + 504*a*b^4*c^3*x^5 + 3024*a^2*b^3*c^2*d*x^5 + 3024*a^3*b^2*c*d^2*x^5 + 504*a^4*b*d^3*x^5 + 84*b^5*c^3*x^6 + 1260*a*b^4*c^2*d*x^6 + 2520*a^2*b^3*c*d^2*x^6 + 840*a^3*b^2*d^3*x^6 + 216*b^5*c^2*d*x^7 + 1080*a*b^4*c*d^2*x^7 + 720*a^2*b^3*d^3*x^7 + 189*b^5*c*d^2*x^8 + 315*a*b^4*d^3*x^8 + 56*b^5*d^3*x^9)/504","B",1
1259,1,253,92,0.0773235,"\int (a+b x)^4 (c+d x)^3 \, dx","IntegrateAlgebraic[(a + b*x)^4*(c + d*x)^3,x]","\frac{1}{280} \left(280 a^4 c^3 x+420 a^4 c^2 d x^2+280 a^4 c d^2 x^3+70 a^4 d^3 x^4+560 a^3 b c^3 x^2+1120 a^3 b c^2 d x^3+840 a^3 b c d^2 x^4+224 a^3 b d^3 x^5+560 a^2 b^2 c^3 x^3+1260 a^2 b^2 c^2 d x^4+1008 a^2 b^2 c d^2 x^5+280 a^2 b^2 d^3 x^6+280 a b^3 c^3 x^4+672 a b^3 c^2 d x^5+560 a b^3 c d^2 x^6+160 a b^3 d^3 x^7+56 b^4 c^3 x^5+140 b^4 c^2 d x^6+120 b^4 c d^2 x^7+35 b^4 d^3 x^8\right)","\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,"(280*a^4*c^3*x + 560*a^3*b*c^3*x^2 + 420*a^4*c^2*d*x^2 + 560*a^2*b^2*c^3*x^3 + 1120*a^3*b*c^2*d*x^3 + 280*a^4*c*d^2*x^3 + 280*a*b^3*c^3*x^4 + 1260*a^2*b^2*c^2*d*x^4 + 840*a^3*b*c*d^2*x^4 + 70*a^4*d^3*x^4 + 56*b^4*c^3*x^5 + 672*a*b^3*c^2*d*x^5 + 1008*a^2*b^2*c*d^2*x^5 + 224*a^3*b*d^3*x^5 + 140*b^4*c^2*d*x^6 + 560*a*b^3*c*d^2*x^6 + 280*a^2*b^2*d^3*x^6 + 120*b^4*c*d^2*x^7 + 160*a*b^3*d^3*x^7 + 35*b^4*d^3*x^8)/280","B",1
1260,1,195,92,0.0518458,"\int (a+b x)^3 (c+d x)^3 \, dx","IntegrateAlgebraic[(a + b*x)^3*(c + d*x)^3,x]","\frac{1}{140} \left(140 a^3 c^3 x+210 a^3 c^2 d x^2+140 a^3 c d^2 x^3+35 a^3 d^3 x^4+210 a^2 b c^3 x^2+420 a^2 b c^2 d x^3+315 a^2 b c d^2 x^4+84 a^2 b d^3 x^5+140 a b^2 c^3 x^3+315 a b^2 c^2 d x^4+252 a b^2 c d^2 x^5+70 a b^2 d^3 x^6+35 b^3 c^3 x^4+84 b^3 c^2 d x^5+70 b^3 c d^2 x^6+20 b^3 d^3 x^7\right)","\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,"(140*a^3*c^3*x + 210*a^2*b*c^3*x^2 + 210*a^3*c^2*d*x^2 + 140*a*b^2*c^3*x^3 + 420*a^2*b*c^2*d*x^3 + 140*a^3*c*d^2*x^3 + 35*b^3*c^3*x^4 + 315*a*b^2*c^2*d*x^4 + 315*a^2*b*c*d^2*x^4 + 35*a^3*d^3*x^4 + 84*b^3*c^2*d*x^5 + 252*a*b^2*c*d^2*x^5 + 84*a^2*b*d^3*x^5 + 70*b^3*c*d^2*x^6 + 70*a*b^2*d^3*x^6 + 20*b^3*d^3*x^7)/140","B",1
1261,1,137,65,0.0406745,"\int (a+b x)^2 (c+d x)^3 \, dx","IntegrateAlgebraic[(a + b*x)^2*(c + d*x)^3,x]","\frac{1}{60} \left(60 a^2 c^3 x+90 a^2 c^2 d x^2+60 a^2 c d^2 x^3+15 a^2 d^3 x^4+60 a b c^3 x^2+120 a b c^2 d x^3+90 a b c d^2 x^4+24 a b d^3 x^5+20 b^2 c^3 x^3+45 b^2 c^2 d x^4+36 b^2 c d^2 x^5+10 b^2 d^3 x^6\right)","-\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,"(60*a^2*c^3*x + 60*a*b*c^3*x^2 + 90*a^2*c^2*d*x^2 + 20*b^2*c^3*x^3 + 120*a*b*c^2*d*x^3 + 60*a^2*c*d^2*x^3 + 45*b^2*c^2*d*x^4 + 90*a*b*c*d^2*x^4 + 15*a^2*d^3*x^4 + 36*b^2*c*d^2*x^5 + 24*a*b*d^3*x^5 + 10*b^2*d^3*x^6)/60","B",1
1262,1,79,38,0.0218402,"\int (a+b x) (c+d x)^3 \, dx","IntegrateAlgebraic[(a + b*x)*(c + d*x)^3,x]","\frac{1}{20} \left(20 a c^3 x+30 a c^2 d x^2+20 a c d^2 x^3+5 a d^3 x^4+10 b c^3 x^2+20 b c^2 d x^3+15 b c d^2 x^4+4 b d^3 x^5\right)","\frac{b (c+d x)^5}{5 d^2}-\frac{(c+d x)^4 (b c-a d)}{4 d^2}",1,"(20*a*c^3*x + 10*b*c^3*x^2 + 30*a*c^2*d*x^2 + 20*b*c^2*d*x^3 + 20*a*c*d^2*x^3 + 15*b*c*d^2*x^4 + 5*a*d^3*x^4 + 4*b*d^3*x^5)/20","B",1
1263,1,14,14,0.0052998,"\int (c+d x)^3 \, dx","IntegrateAlgebraic[(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
1264,1,80,73,0.0505588,"\int \frac{(c+d x)^3}{a+b x} \, dx","IntegrateAlgebraic[(c + d*x)^3/(a + b*x),x]","\frac{d x \left(6 a^2 d^2-18 a b c d-3 a b d^2 x+18 b^2 c^2+9 b^2 c d x+2 b^2 d^2 x^2\right)}{6 b^3}+\frac{(b c-a d)^3 \log (a+b x)}{b^4}","\frac{(b c-a d)^3 \log (a+b x)}{b^4}+\frac{d x (b c-a d)^2}{b^3}+\frac{(c+d x)^2 (b c-a d)}{2 b^2}+\frac{(c+d x)^3}{3 b}",1,"(d*x*(18*b^2*c^2 - 18*a*b*c*d + 6*a^2*d^2 + 9*b^2*c*d*x - 3*a*b*d^2*x + 2*b^2*d^2*x^2))/(6*b^3) + ((b*c - a*d)^3*Log[a + b*x])/b^4","A",1
1265,1,129,75,0.0778479,"\int \frac{(c+d x)^3}{(a+b x)^2} \, dx","IntegrateAlgebraic[(c + d*x)^3/(a + b*x)^2,x]","\frac{2 a^3 d^3-6 a^2 b c d^2-4 a^2 b d^3 x+6 a b^2 c^2 d+6 a b^2 c d^2 x-3 a b^2 d^3 x^2-2 b^3 c^3+6 b^3 c d^2 x^2+b^3 d^3 x^3}{2 b^4 (a+b x)}+\frac{3 d (b c-a d)^2 \log (a+b x)}{b^4}","-\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^2 x (3 b c-2 a d)}{b^3}+\frac{d^3 x^2}{2 b^2}",1,"(-2*b^3*c^3 + 6*a*b^2*c^2*d - 6*a^2*b*c*d^2 + 2*a^3*d^3 + 6*a*b^2*c*d^2*x - 4*a^2*b*d^3*x + 6*b^3*c*d^2*x^2 - 3*a*b^2*d^3*x^2 + b^3*d^3*x^3)/(2*b^4*(a + b*x)) + (3*d*(b*c - a*d)^2*Log[a + b*x])/b^4","A",1
1266,1,130,78,0.0735881,"\int \frac{(c+d x)^3}{(a+b x)^3} \, dx","IntegrateAlgebraic[(c + d*x)^3/(a + b*x)^3,x]","\frac{-5 a^3 d^3+9 a^2 b c d^2-4 a^2 b d^3 x-3 a b^2 c^2 d+12 a b^2 c d^2 x+4 a b^2 d^3 x^2+b^3 \left(-c^3\right)-6 b^3 c^2 d x+2 b^3 d^3 x^3}{2 b^4 (a+b x)^2}+\frac{3 \left(b c d^2-a d^3\right) \log (a+b x)}{b^4}","\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,"(-(b^3*c^3) - 3*a*b^2*c^2*d + 9*a^2*b*c*d^2 - 5*a^3*d^3 - 6*b^3*c^2*d*x + 12*a*b^2*c*d^2*x - 4*a^2*b*d^3*x + 4*a*b^2*d^3*x^2 + 2*b^3*d^3*x^3)/(2*b^4*(a + b*x)^2) + (3*(b*c*d^2 - a*d^3)*Log[a + b*x])/b^4","A",1
1267,1,86,86,0.0628101,"\int \frac{(c+d x)^3}{(a+b x)^4} \, dx","IntegrateAlgebraic[(c + d*x)^3/(a + b*x)^4,x]","\frac{d^3 \log (a+b x)}{b^4}-\frac{(b c-a d) \left(11 a^2 d^2+5 a b c d+27 a b d^2 x+2 b^2 c^2+9 b^2 c d x+18 b^2 d^2 x^2\right)}{6 b^4 (a+b x)^3}","-\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,"-1/6*((b*c - a*d)*(2*b^2*c^2 + 5*a*b*c*d + 11*a^2*d^2 + 9*b^2*c*d*x + 27*a*b*d^2*x + 18*b^2*d^2*x^2))/(b^4*(a + b*x)^3) + (d^3*Log[a + b*x])/b^4","A",1
1268,1,117,28,0.0437984,"\int \frac{(c+d x)^3}{(a+b x)^5} \, dx","IntegrateAlgebraic[(c + d*x)^3/(a + b*x)^5,x]","\frac{-a^3 d^3-a^2 b c d^2-4 a^2 b d^3 x-a b^2 c^2 d-4 a b^2 c d^2 x-6 a b^2 d^3 x^2+b^3 \left(-c^3\right)-4 b^3 c^2 d x-6 b^3 c d^2 x^2-4 b^3 d^3 x^3}{4 b^4 (a+b x)^4}","-\frac{(c+d x)^4}{4 (a+b x)^4 (b c-a d)}",1,"(-(b^3*c^3) - a*b^2*c^2*d - a^2*b*c*d^2 - a^3*d^3 - 4*b^3*c^2*d*x - 4*a*b^2*c*d^2*x - 4*a^2*b*d^3*x - 6*b^3*c*d^2*x^2 - 6*a*b^2*d^3*x^2 - 4*b^3*d^3*x^3)/(4*b^4*(a + b*x)^4)","B",1
1269,1,117,58,0.0479623,"\int \frac{(c+d x)^3}{(a+b x)^6} \, dx","IntegrateAlgebraic[(c + d*x)^3/(a + b*x)^6,x]","\frac{-a^3 d^3-2 a^2 b c d^2-5 a^2 b d^3 x-3 a b^2 c^2 d-10 a b^2 c d^2 x-10 a b^2 d^3 x^2-4 b^3 c^3-15 b^3 c^2 d x-20 b^3 c d^2 x^2-10 b^3 d^3 x^3}{20 b^4 (a+b x)^5}","\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,"(-4*b^3*c^3 - 3*a*b^2*c^2*d - 2*a^2*b*c*d^2 - a^3*d^3 - 15*b^3*c^2*d*x - 10*a*b^2*c*d^2*x - 5*a^2*b*d^3*x - 20*b^3*c*d^2*x^2 - 10*a*b^2*d^3*x^2 - 10*b^3*d^3*x^3)/(20*b^4*(a + b*x)^5)","B",1
1270,1,117,92,0.0442252,"\int \frac{(c+d x)^3}{(a+b x)^7} \, dx","IntegrateAlgebraic[(c + d*x)^3/(a + b*x)^7,x]","\frac{-a^3 d^3-3 a^2 b c d^2-6 a^2 b d^3 x-6 a b^2 c^2 d-18 a b^2 c d^2 x-15 a b^2 d^3 x^2-10 b^3 c^3-36 b^3 c^2 d x-45 b^3 c d^2 x^2-20 b^3 d^3 x^3}{60 b^4 (a+b x)^6}","-\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,"(-10*b^3*c^3 - 6*a*b^2*c^2*d - 3*a^2*b*c*d^2 - a^3*d^3 - 36*b^3*c^2*d*x - 18*a*b^2*c*d^2*x - 6*a^2*b*d^3*x - 45*b^3*c*d^2*x^2 - 15*a*b^2*d^3*x^2 - 20*b^3*d^3*x^3)/(60*b^4*(a + b*x)^6)","A",1
1271,1,117,92,0.0448269,"\int \frac{(c+d x)^3}{(a+b x)^8} \, dx","IntegrateAlgebraic[(c + d*x)^3/(a + b*x)^8,x]","\frac{-a^3 d^3-4 a^2 b c d^2-7 a^2 b d^3 x-10 a b^2 c^2 d-28 a b^2 c d^2 x-21 a b^2 d^3 x^2-20 b^3 c^3-70 b^3 c^2 d x-84 b^3 c d^2 x^2-35 b^3 d^3 x^3}{140 b^4 (a+b x)^7}","-\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,"(-20*b^3*c^3 - 10*a*b^2*c^2*d - 4*a^2*b*c*d^2 - a^3*d^3 - 70*b^3*c^2*d*x - 28*a*b^2*c*d^2*x - 7*a^2*b*d^3*x - 84*b^3*c*d^2*x^2 - 21*a*b^2*d^3*x^2 - 35*b^3*d^3*x^3)/(140*b^4*(a + b*x)^7)","A",1
1272,1,117,92,0.0490989,"\int \frac{(c+d x)^3}{(a+b x)^9} \, dx","IntegrateAlgebraic[(c + d*x)^3/(a + b*x)^9,x]","\frac{-a^3 d^3-5 a^2 b c d^2-8 a^2 b d^3 x-15 a b^2 c^2 d-40 a b^2 c d^2 x-28 a b^2 d^3 x^2-35 b^3 c^3-120 b^3 c^2 d x-140 b^3 c d^2 x^2-56 b^3 d^3 x^3}{280 b^4 (a+b x)^8}","-\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,"(-35*b^3*c^3 - 15*a*b^2*c^2*d - 5*a^2*b*c*d^2 - a^3*d^3 - 120*b^3*c^2*d*x - 40*a*b^2*c*d^2*x - 8*a^2*b*d^3*x - 140*b^3*c*d^2*x^2 - 28*a*b^2*d^3*x^2 - 56*b^3*d^3*x^3)/(280*b^4*(a + b*x)^8)","A",1
1273,1,1183,200,0.3697,"\int (a+b x)^9 (c+d x)^7 \, dx","IntegrateAlgebraic[(a + b*x)^9*(c + d*x)^7,x]","\frac{11440 b^9 d^7 x^{17}+109395 a b^8 d^7 x^{16}+85085 b^9 c d^6 x^{16}+466752 a^2 b^7 d^7 x^{15}+816816 a b^8 c d^6 x^{15}+272272 b^9 c^2 d^5 x^{15}+1166880 a^3 b^6 d^7 x^{14}+3500640 a^2 b^7 c d^6 x^{14}+2625480 a b^8 c^2 d^5 x^{14}+486200 b^9 c^3 d^4 x^{14}+1884960 a^4 b^5 d^7 x^{13}+8796480 a^3 b^6 c d^6 x^{13}+11309760 a^2 b^7 c^2 d^5 x^{13}+4712400 a b^8 c^3 d^4 x^{13}+523600 b^9 c^4 d^3 x^{13}+2042040 a^5 b^4 d^7 x^{12}+14294280 a^4 b^5 c d^6 x^{12}+28588560 a^3 b^6 c^2 d^5 x^{12}+20420400 a^2 b^7 c^3 d^4 x^{12}+5105100 a b^8 c^4 d^3 x^{12}+340340 b^9 c^5 d^2 x^{12}+1485120 a^6 b^3 d^7 x^{11}+15593760 a^5 b^4 c d^6 x^{11}+46781280 a^4 b^5 c^2 d^5 x^{11}+51979200 a^3 b^6 c^3 d^4 x^{11}+22276800 a^2 b^7 c^4 d^3 x^{11}+3341520 a b^8 c^5 d^2 x^{11}+123760 b^9 c^6 d x^{11}+19448 b^9 c^7 x^{10}+700128 a^7 b^2 d^7 x^{10}+11435424 a^6 b^3 c d^6 x^{10}+51459408 a^5 b^4 c^2 d^5 x^{10}+85765680 a^4 b^5 c^3 d^4 x^{10}+57177120 a^3 b^6 c^4 d^3 x^{10}+14702688 a^2 b^7 c^5 d^2 x^{10}+1225224 a b^8 c^6 d x^{10}+194480 a b^8 c^7 x^9+194480 a^8 b d^7 x^9+5445440 a^7 b^2 c d^6 x^9+38118080 a^6 b^3 c^2 d^5 x^9+95295200 a^5 b^4 c^3 d^4 x^9+95295200 a^4 b^5 c^4 d^3 x^9+38118080 a^3 b^6 c^5 d^2 x^9+5445440 a^2 b^7 c^6 d x^9+875160 a^2 b^7 c^7 x^8+24310 a^9 d^7 x^8+1531530 a^8 b c d^6 x^8+18378360 a^7 b^2 c^2 d^5 x^8+71471400 a^6 b^3 c^3 d^4 x^8+107207100 a^5 b^4 c^4 d^3 x^8+64324260 a^4 b^5 c^5 d^2 x^8+14294280 a^3 b^6 c^6 d x^8+2333760 a^3 b^6 c^7 x^7+194480 a^9 c d^6 x^7+5250960 a^8 b c^2 d^5 x^7+35006400 a^7 b^2 c^3 d^4 x^7+81681600 a^6 b^3 c^4 d^3 x^7+73513440 a^5 b^4 c^5 d^2 x^7+24504480 a^4 b^5 c^6 d x^7+4084080 a^4 b^5 c^7 x^6+680680 a^9 c^2 d^5 x^6+10210200 a^8 b c^3 d^4 x^6+40840800 a^7 b^2 c^4 d^3 x^6+57177120 a^6 b^3 c^5 d^2 x^6+28588560 a^5 b^4 c^6 d x^6+4900896 a^5 b^4 c^7 x^5+1361360 a^9 c^3 d^4 x^5+12252240 a^8 b c^4 d^3 x^5+29405376 a^7 b^2 c^5 d^2 x^5+22870848 a^6 b^3 c^6 d x^5+4084080 a^6 b^3 c^7 x^4+1701700 a^9 c^4 d^3 x^4+9189180 a^8 b c^5 d^2 x^4+12252240 a^7 b^2 c^6 d x^4+2333760 a^7 b^2 c^7 x^3+1361360 a^9 c^5 d^2 x^3+4084080 a^8 b c^6 d x^3+875160 a^8 b c^7 x^2+680680 a^9 c^6 d x^2+194480 a^9 c^7 x}{194480}","\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,"(194480*a^9*c^7*x + 875160*a^8*b*c^7*x^2 + 680680*a^9*c^6*d*x^2 + 2333760*a^7*b^2*c^7*x^3 + 4084080*a^8*b*c^6*d*x^3 + 1361360*a^9*c^5*d^2*x^3 + 4084080*a^6*b^3*c^7*x^4 + 12252240*a^7*b^2*c^6*d*x^4 + 9189180*a^8*b*c^5*d^2*x^4 + 1701700*a^9*c^4*d^3*x^4 + 4900896*a^5*b^4*c^7*x^5 + 22870848*a^6*b^3*c^6*d*x^5 + 29405376*a^7*b^2*c^5*d^2*x^5 + 12252240*a^8*b*c^4*d^3*x^5 + 1361360*a^9*c^3*d^4*x^5 + 4084080*a^4*b^5*c^7*x^6 + 28588560*a^5*b^4*c^6*d*x^6 + 57177120*a^6*b^3*c^5*d^2*x^6 + 40840800*a^7*b^2*c^4*d^3*x^6 + 10210200*a^8*b*c^3*d^4*x^6 + 680680*a^9*c^2*d^5*x^6 + 2333760*a^3*b^6*c^7*x^7 + 24504480*a^4*b^5*c^6*d*x^7 + 73513440*a^5*b^4*c^5*d^2*x^7 + 81681600*a^6*b^3*c^4*d^3*x^7 + 35006400*a^7*b^2*c^3*d^4*x^7 + 5250960*a^8*b*c^2*d^5*x^7 + 194480*a^9*c*d^6*x^7 + 875160*a^2*b^7*c^7*x^8 + 14294280*a^3*b^6*c^6*d*x^8 + 64324260*a^4*b^5*c^5*d^2*x^8 + 107207100*a^5*b^4*c^4*d^3*x^8 + 71471400*a^6*b^3*c^3*d^4*x^8 + 18378360*a^7*b^2*c^2*d^5*x^8 + 1531530*a^8*b*c*d^6*x^8 + 24310*a^9*d^7*x^8 + 194480*a*b^8*c^7*x^9 + 5445440*a^2*b^7*c^6*d*x^9 + 38118080*a^3*b^6*c^5*d^2*x^9 + 95295200*a^4*b^5*c^4*d^3*x^9 + 95295200*a^5*b^4*c^3*d^4*x^9 + 38118080*a^6*b^3*c^2*d^5*x^9 + 5445440*a^7*b^2*c*d^6*x^9 + 194480*a^8*b*d^7*x^9 + 19448*b^9*c^7*x^10 + 1225224*a*b^8*c^6*d*x^10 + 14702688*a^2*b^7*c^5*d^2*x^10 + 57177120*a^3*b^6*c^4*d^3*x^10 + 85765680*a^4*b^5*c^3*d^4*x^10 + 51459408*a^5*b^4*c^2*d^5*x^10 + 11435424*a^6*b^3*c*d^6*x^10 + 700128*a^7*b^2*d^7*x^10 + 123760*b^9*c^6*d*x^11 + 3341520*a*b^8*c^5*d^2*x^11 + 22276800*a^2*b^7*c^4*d^3*x^11 + 51979200*a^3*b^6*c^3*d^4*x^11 + 46781280*a^4*b^5*c^2*d^5*x^11 + 15593760*a^5*b^4*c*d^6*x^11 + 1485120*a^6*b^3*d^7*x^11 + 340340*b^9*c^5*d^2*x^12 + 5105100*a*b^8*c^4*d^3*x^12 + 20420400*a^2*b^7*c^3*d^4*x^12 + 28588560*a^3*b^6*c^2*d^5*x^12 + 14294280*a^4*b^5*c*d^6*x^12 + 2042040*a^5*b^4*d^7*x^12 + 523600*b^9*c^4*d^3*x^13 + 4712400*a*b^8*c^3*d^4*x^13 + 11309760*a^2*b^7*c^2*d^5*x^13 + 8796480*a^3*b^6*c*d^6*x^13 + 1884960*a^4*b^5*d^7*x^13 + 486200*b^9*c^3*d^4*x^14 + 2625480*a*b^8*c^2*d^5*x^14 + 3500640*a^2*b^7*c*d^6*x^14 + 1166880*a^3*b^6*d^7*x^14 + 272272*b^9*c^2*d^5*x^15 + 816816*a*b^8*c*d^6*x^15 + 466752*a^2*b^7*d^7*x^15 + 85085*b^9*c*d^6*x^16 + 109395*a*b^8*d^7*x^16 + 11440*b^9*d^7*x^17)/194480","B",1
1274,1,1057,200,0.3013761,"\int (a+b x)^8 (c+d x)^7 \, dx","IntegrateAlgebraic[(a + b*x)^8*(c + d*x)^7,x]","\frac{6435 b^8 d^7 x^{16}+54912 a b^7 d^7 x^{15}+48048 b^8 c d^6 x^{15}+205920 a^2 b^6 d^7 x^{14}+411840 a b^7 c d^6 x^{14}+154440 b^8 c^2 d^5 x^{14}+443520 a^3 b^5 d^7 x^{13}+1552320 a^2 b^6 c d^6 x^{13}+1330560 a b^7 c^2 d^5 x^{13}+277200 b^8 c^3 d^4 x^{13}+600600 a^4 b^4 d^7 x^{12}+3363360 a^3 b^5 c d^6 x^{12}+5045040 a^2 b^6 c^2 d^5 x^{12}+2402400 a b^7 c^3 d^4 x^{12}+300300 b^8 c^4 d^3 x^{12}+524160 a^5 b^3 d^7 x^{11}+4586400 a^4 b^4 c d^6 x^{11}+11007360 a^3 b^5 c^2 d^5 x^{11}+9172800 a^2 b^6 c^3 d^4 x^{11}+2620800 a b^7 c^4 d^3 x^{11}+196560 b^8 c^5 d^2 x^{11}+288288 a^6 b^2 d^7 x^{10}+4036032 a^5 b^3 c d^6 x^{10}+15135120 a^4 b^4 c^2 d^5 x^{10}+20180160 a^3 b^5 c^3 d^4 x^{10}+10090080 a^2 b^6 c^4 d^3 x^{10}+1729728 a b^7 c^5 d^2 x^{10}+72072 b^8 c^6 d x^{10}+11440 b^8 c^7 x^9+91520 a^7 b d^7 x^9+2242240 a^6 b^2 c d^6 x^9+13453440 a^5 b^3 c^2 d^5 x^9+28028000 a^4 b^4 c^3 d^4 x^9+22422400 a^3 b^5 c^4 d^3 x^9+6726720 a^2 b^6 c^5 d^2 x^9+640640 a b^7 c^6 d x^9+102960 a b^7 c^7 x^8+12870 a^8 d^7 x^8+720720 a^7 b c d^6 x^8+7567560 a^6 b^2 c^2 d^5 x^8+25225200 a^5 b^3 c^3 d^4 x^8+31531500 a^4 b^4 c^4 d^3 x^8+15135120 a^3 b^5 c^5 d^2 x^8+2522520 a^2 b^6 c^6 d x^8+411840 a^2 b^6 c^7 x^7+102960 a^8 c d^6 x^7+2471040 a^7 b c^2 d^5 x^7+14414400 a^6 b^2 c^3 d^4 x^7+28828800 a^5 b^3 c^4 d^3 x^7+21621600 a^4 b^4 c^5 d^2 x^7+5765760 a^3 b^5 c^6 d x^7+960960 a^3 b^5 c^7 x^6+360360 a^8 c^2 d^5 x^6+4804800 a^7 b c^3 d^4 x^6+16816800 a^6 b^2 c^4 d^3 x^6+20180160 a^5 b^3 c^5 d^2 x^6+8408400 a^4 b^4 c^6 d x^6+1441440 a^4 b^4 c^7 x^5+720720 a^8 c^3 d^4 x^5+5765760 a^7 b c^4 d^3 x^5+12108096 a^6 b^2 c^5 d^2 x^5+8072064 a^5 b^3 c^6 d x^5+1441440 a^5 b^3 c^7 x^4+900900 a^8 c^4 d^3 x^4+4324320 a^7 b c^5 d^2 x^4+5045040 a^6 b^2 c^6 d x^4+960960 a^6 b^2 c^7 x^3+720720 a^8 c^5 d^2 x^3+1921920 a^7 b c^6 d x^3+411840 a^7 b c^7 x^2+360360 a^8 c^6 d x^2+102960 a^8 c^7 x}{102960}","\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,"(102960*a^8*c^7*x + 411840*a^7*b*c^7*x^2 + 360360*a^8*c^6*d*x^2 + 960960*a^6*b^2*c^7*x^3 + 1921920*a^7*b*c^6*d*x^3 + 720720*a^8*c^5*d^2*x^3 + 1441440*a^5*b^3*c^7*x^4 + 5045040*a^6*b^2*c^6*d*x^4 + 4324320*a^7*b*c^5*d^2*x^4 + 900900*a^8*c^4*d^3*x^4 + 1441440*a^4*b^4*c^7*x^5 + 8072064*a^5*b^3*c^6*d*x^5 + 12108096*a^6*b^2*c^5*d^2*x^5 + 5765760*a^7*b*c^4*d^3*x^5 + 720720*a^8*c^3*d^4*x^5 + 960960*a^3*b^5*c^7*x^6 + 8408400*a^4*b^4*c^6*d*x^6 + 20180160*a^5*b^3*c^5*d^2*x^6 + 16816800*a^6*b^2*c^4*d^3*x^6 + 4804800*a^7*b*c^3*d^4*x^6 + 360360*a^8*c^2*d^5*x^6 + 411840*a^2*b^6*c^7*x^7 + 5765760*a^3*b^5*c^6*d*x^7 + 21621600*a^4*b^4*c^5*d^2*x^7 + 28828800*a^5*b^3*c^4*d^3*x^7 + 14414400*a^6*b^2*c^3*d^4*x^7 + 2471040*a^7*b*c^2*d^5*x^7 + 102960*a^8*c*d^6*x^7 + 102960*a*b^7*c^7*x^8 + 2522520*a^2*b^6*c^6*d*x^8 + 15135120*a^3*b^5*c^5*d^2*x^8 + 31531500*a^4*b^4*c^4*d^3*x^8 + 25225200*a^5*b^3*c^3*d^4*x^8 + 7567560*a^6*b^2*c^2*d^5*x^8 + 720720*a^7*b*c*d^6*x^8 + 12870*a^8*d^7*x^8 + 11440*b^8*c^7*x^9 + 640640*a*b^7*c^6*d*x^9 + 6726720*a^2*b^6*c^5*d^2*x^9 + 22422400*a^3*b^5*c^4*d^3*x^9 + 28028000*a^4*b^4*c^3*d^4*x^9 + 13453440*a^5*b^3*c^2*d^5*x^9 + 2242240*a^6*b^2*c*d^6*x^9 + 91520*a^7*b*d^7*x^9 + 72072*b^8*c^6*d*x^10 + 1729728*a*b^7*c^5*d^2*x^10 + 10090080*a^2*b^6*c^4*d^3*x^10 + 20180160*a^3*b^5*c^3*d^4*x^10 + 15135120*a^4*b^4*c^2*d^5*x^10 + 4036032*a^5*b^3*c*d^6*x^10 + 288288*a^6*b^2*d^7*x^10 + 196560*b^8*c^5*d^2*x^11 + 2620800*a*b^7*c^4*d^3*x^11 + 9172800*a^2*b^6*c^3*d^4*x^11 + 11007360*a^3*b^5*c^2*d^5*x^11 + 4586400*a^4*b^4*c*d^6*x^11 + 524160*a^5*b^3*d^7*x^11 + 300300*b^8*c^4*d^3*x^12 + 2402400*a*b^7*c^3*d^4*x^12 + 5045040*a^2*b^6*c^2*d^5*x^12 + 3363360*a^3*b^5*c*d^6*x^12 + 600600*a^4*b^4*d^7*x^12 + 277200*b^8*c^3*d^4*x^13 + 1330560*a*b^7*c^2*d^5*x^13 + 1552320*a^2*b^6*c*d^6*x^13 + 443520*a^3*b^5*d^7*x^13 + 154440*b^8*c^2*d^5*x^14 + 411840*a*b^7*c*d^6*x^14 + 205920*a^2*b^6*d^7*x^14 + 48048*b^8*c*d^6*x^15 + 54912*a*b^7*d^7*x^15 + 6435*b^8*d^7*x^16)/102960","B",1
1275,1,931,200,0.227186,"\int (a+b x)^7 (c+d x)^7 \, dx","IntegrateAlgebraic[(a + b*x)^7*(c + d*x)^7,x]","\frac{3432 b^7 d^7 x^{15}+25740 a b^6 d^7 x^{14}+25740 b^7 c d^6 x^{14}+83160 a^2 b^5 d^7 x^{13}+194040 a b^6 c d^6 x^{13}+83160 b^7 c^2 d^5 x^{13}+150150 a^3 b^4 d^7 x^{12}+630630 a^2 b^5 c d^6 x^{12}+630630 a b^6 c^2 d^5 x^{12}+150150 b^7 c^3 d^4 x^{12}+163800 a^4 b^3 d^7 x^{11}+1146600 a^3 b^4 c d^6 x^{11}+2063880 a^2 b^5 c^2 d^5 x^{11}+1146600 a b^6 c^3 d^4 x^{11}+163800 b^7 c^4 d^3 x^{11}+108108 a^5 b^2 d^7 x^{10}+1261260 a^4 b^3 c d^6 x^{10}+3783780 a^3 b^4 c^2 d^5 x^{10}+3783780 a^2 b^5 c^3 d^4 x^{10}+1261260 a b^6 c^4 d^3 x^{10}+108108 b^7 c^5 d^2 x^{10}+40040 a^6 b d^7 x^9+840840 a^5 b^2 c d^6 x^9+4204200 a^4 b^3 c^2 d^5 x^9+7007000 a^3 b^4 c^3 d^4 x^9+4204200 a^2 b^5 c^4 d^3 x^9+840840 a b^6 c^5 d^2 x^9+40040 b^7 c^6 d x^9+6435 b^7 c^7 x^8+6435 a^7 d^7 x^8+315315 a^6 b c d^6 x^8+2837835 a^5 b^2 c^2 d^5 x^8+7882875 a^4 b^3 c^3 d^4 x^8+7882875 a^3 b^4 c^4 d^3 x^8+2837835 a^2 b^5 c^5 d^2 x^8+315315 a b^6 c^6 d x^8+51480 a b^6 c^7 x^7+51480 a^7 c d^6 x^7+1081080 a^6 b c^2 d^5 x^7+5405400 a^5 b^2 c^3 d^4 x^7+9009000 a^4 b^3 c^4 d^3 x^7+5405400 a^3 b^4 c^5 d^2 x^7+1081080 a^2 b^5 c^6 d x^7+180180 a^2 b^5 c^7 x^6+180180 a^7 c^2 d^5 x^6+2102100 a^6 b c^3 d^4 x^6+6306300 a^5 b^2 c^4 d^3 x^6+6306300 a^4 b^3 c^5 d^2 x^6+2102100 a^3 b^4 c^6 d x^6+360360 a^3 b^4 c^7 x^5+360360 a^7 c^3 d^4 x^5+2522520 a^6 b c^4 d^3 x^5+4540536 a^5 b^2 c^5 d^2 x^5+2522520 a^4 b^3 c^6 d x^5+450450 a^4 b^3 c^7 x^4+450450 a^7 c^4 d^3 x^4+1891890 a^6 b c^5 d^2 x^4+1891890 a^5 b^2 c^6 d x^4+360360 a^5 b^2 c^7 x^3+360360 a^7 c^5 d^2 x^3+840840 a^6 b c^6 d x^3+180180 a^6 b c^7 x^2+180180 a^7 c^6 d x^2+51480 a^7 c^7 x}{51480}","\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,"(51480*a^7*c^7*x + 180180*a^6*b*c^7*x^2 + 180180*a^7*c^6*d*x^2 + 360360*a^5*b^2*c^7*x^3 + 840840*a^6*b*c^6*d*x^3 + 360360*a^7*c^5*d^2*x^3 + 450450*a^4*b^3*c^7*x^4 + 1891890*a^5*b^2*c^6*d*x^4 + 1891890*a^6*b*c^5*d^2*x^4 + 450450*a^7*c^4*d^3*x^4 + 360360*a^3*b^4*c^7*x^5 + 2522520*a^4*b^3*c^6*d*x^5 + 4540536*a^5*b^2*c^5*d^2*x^5 + 2522520*a^6*b*c^4*d^3*x^5 + 360360*a^7*c^3*d^4*x^5 + 180180*a^2*b^5*c^7*x^6 + 2102100*a^3*b^4*c^6*d*x^6 + 6306300*a^4*b^3*c^5*d^2*x^6 + 6306300*a^5*b^2*c^4*d^3*x^6 + 2102100*a^6*b*c^3*d^4*x^6 + 180180*a^7*c^2*d^5*x^6 + 51480*a*b^6*c^7*x^7 + 1081080*a^2*b^5*c^6*d*x^7 + 5405400*a^3*b^4*c^5*d^2*x^7 + 9009000*a^4*b^3*c^4*d^3*x^7 + 5405400*a^5*b^2*c^3*d^4*x^7 + 1081080*a^6*b*c^2*d^5*x^7 + 51480*a^7*c*d^6*x^7 + 6435*b^7*c^7*x^8 + 315315*a*b^6*c^6*d*x^8 + 2837835*a^2*b^5*c^5*d^2*x^8 + 7882875*a^3*b^4*c^4*d^3*x^8 + 7882875*a^4*b^3*c^3*d^4*x^8 + 2837835*a^5*b^2*c^2*d^5*x^8 + 315315*a^6*b*c*d^6*x^8 + 6435*a^7*d^7*x^8 + 40040*b^7*c^6*d*x^9 + 840840*a*b^6*c^5*d^2*x^9 + 4204200*a^2*b^5*c^4*d^3*x^9 + 7007000*a^3*b^4*c^3*d^4*x^9 + 4204200*a^4*b^3*c^2*d^5*x^9 + 840840*a^5*b^2*c*d^6*x^9 + 40040*a^6*b*d^7*x^9 + 108108*b^7*c^5*d^2*x^10 + 1261260*a*b^6*c^4*d^3*x^10 + 3783780*a^2*b^5*c^3*d^4*x^10 + 3783780*a^3*b^4*c^2*d^5*x^10 + 1261260*a^4*b^3*c*d^6*x^10 + 108108*a^5*b^2*d^7*x^10 + 163800*b^7*c^4*d^3*x^11 + 1146600*a*b^6*c^3*d^4*x^11 + 2063880*a^2*b^5*c^2*d^5*x^11 + 1146600*a^3*b^4*c*d^6*x^11 + 163800*a^4*b^3*d^7*x^11 + 150150*b^7*c^3*d^4*x^12 + 630630*a*b^6*c^2*d^5*x^12 + 630630*a^2*b^5*c*d^6*x^12 + 150150*a^3*b^4*d^7*x^12 + 83160*b^7*c^2*d^5*x^13 + 194040*a*b^6*c*d^6*x^13 + 83160*a^2*b^5*d^7*x^13 + 25740*b^7*c*d^6*x^14 + 25740*a*b^6*d^7*x^14 + 3432*b^7*d^7*x^15)/51480","B",1
1276,1,805,173,0.2210497,"\int (a+b x)^6 (c+d x)^7 \, dx","IntegrateAlgebraic[(a + b*x)^6*(c + d*x)^7,x]","\frac{1716 b^6 d^7 x^{14}+11088 a b^5 d^7 x^{13}+12936 b^6 c d^6 x^{13}+30030 a^2 b^4 d^7 x^{12}+84084 a b^5 c d^6 x^{12}+42042 b^6 c^2 d^5 x^{12}+43680 a^3 b^3 d^7 x^{11}+229320 a^2 b^4 c d^6 x^{11}+275184 a b^5 c^2 d^5 x^{11}+76440 b^6 c^3 d^4 x^{11}+36036 a^4 b^2 d^7 x^{10}+336336 a^3 b^3 c d^6 x^{10}+756756 a^2 b^4 c^2 d^5 x^{10}+504504 a b^5 c^3 d^4 x^{10}+84084 b^6 c^4 d^3 x^{10}+16016 a^5 b d^7 x^9+280280 a^4 b^2 c d^6 x^9+1121120 a^3 b^3 c^2 d^5 x^9+1401400 a^2 b^4 c^3 d^4 x^9+560560 a b^5 c^4 d^3 x^9+56056 b^6 c^5 d^2 x^9+3003 a^6 d^7 x^8+126126 a^5 b c d^6 x^8+945945 a^4 b^2 c^2 d^5 x^8+2102100 a^3 b^3 c^3 d^4 x^8+1576575 a^2 b^4 c^4 d^3 x^8+378378 a b^5 c^5 d^2 x^8+21021 b^6 c^6 d x^8+3432 b^6 c^7 x^7+24024 a^6 c d^6 x^7+432432 a^5 b c^2 d^5 x^7+1801800 a^4 b^2 c^3 d^4 x^7+2402400 a^3 b^3 c^4 d^3 x^7+1081080 a^2 b^4 c^5 d^2 x^7+144144 a b^5 c^6 d x^7+24024 a b^5 c^7 x^6+84084 a^6 c^2 d^5 x^6+840840 a^5 b c^3 d^4 x^6+2102100 a^4 b^2 c^4 d^3 x^6+1681680 a^3 b^3 c^5 d^2 x^6+420420 a^2 b^4 c^6 d x^6+72072 a^2 b^4 c^7 x^5+168168 a^6 c^3 d^4 x^5+1009008 a^5 b c^4 d^3 x^5+1513512 a^4 b^2 c^5 d^2 x^5+672672 a^3 b^3 c^6 d x^5+120120 a^3 b^3 c^7 x^4+210210 a^6 c^4 d^3 x^4+756756 a^5 b c^5 d^2 x^4+630630 a^4 b^2 c^6 d x^4+120120 a^4 b^2 c^7 x^3+168168 a^6 c^5 d^2 x^3+336336 a^5 b c^6 d x^3+72072 a^5 b c^7 x^2+84084 a^6 c^6 d x^2+24024 a^6 c^7 x}{24024}","-\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,"(24024*a^6*c^7*x + 72072*a^5*b*c^7*x^2 + 84084*a^6*c^6*d*x^2 + 120120*a^4*b^2*c^7*x^3 + 336336*a^5*b*c^6*d*x^3 + 168168*a^6*c^5*d^2*x^3 + 120120*a^3*b^3*c^7*x^4 + 630630*a^4*b^2*c^6*d*x^4 + 756756*a^5*b*c^5*d^2*x^4 + 210210*a^6*c^4*d^3*x^4 + 72072*a^2*b^4*c^7*x^5 + 672672*a^3*b^3*c^6*d*x^5 + 1513512*a^4*b^2*c^5*d^2*x^5 + 1009008*a^5*b*c^4*d^3*x^5 + 168168*a^6*c^3*d^4*x^5 + 24024*a*b^5*c^7*x^6 + 420420*a^2*b^4*c^6*d*x^6 + 1681680*a^3*b^3*c^5*d^2*x^6 + 2102100*a^4*b^2*c^4*d^3*x^6 + 840840*a^5*b*c^3*d^4*x^6 + 84084*a^6*c^2*d^5*x^6 + 3432*b^6*c^7*x^7 + 144144*a*b^5*c^6*d*x^7 + 1081080*a^2*b^4*c^5*d^2*x^7 + 2402400*a^3*b^3*c^4*d^3*x^7 + 1801800*a^4*b^2*c^3*d^4*x^7 + 432432*a^5*b*c^2*d^5*x^7 + 24024*a^6*c*d^6*x^7 + 21021*b^6*c^6*d*x^8 + 378378*a*b^5*c^5*d^2*x^8 + 1576575*a^2*b^4*c^4*d^3*x^8 + 2102100*a^3*b^3*c^3*d^4*x^8 + 945945*a^4*b^2*c^2*d^5*x^8 + 126126*a^5*b*c*d^6*x^8 + 3003*a^6*d^7*x^8 + 56056*b^6*c^5*d^2*x^9 + 560560*a*b^5*c^4*d^3*x^9 + 1401400*a^2*b^4*c^3*d^4*x^9 + 1121120*a^3*b^3*c^2*d^5*x^9 + 280280*a^4*b^2*c*d^6*x^9 + 16016*a^5*b*d^7*x^9 + 84084*b^6*c^4*d^3*x^10 + 504504*a*b^5*c^3*d^4*x^10 + 756756*a^2*b^4*c^2*d^5*x^10 + 336336*a^3*b^3*c*d^6*x^10 + 36036*a^4*b^2*d^7*x^10 + 76440*b^6*c^3*d^4*x^11 + 275184*a*b^5*c^2*d^5*x^11 + 229320*a^2*b^4*c*d^6*x^11 + 43680*a^3*b^3*d^7*x^11 + 42042*b^6*c^2*d^5*x^12 + 84084*a*b^5*c*d^6*x^12 + 30030*a^2*b^4*d^7*x^12 + 12936*b^6*c*d^6*x^13 + 11088*a*b^5*d^7*x^13 + 1716*b^6*d^7*x^14)/24024","B",1
1277,1,679,144,0.186127,"\int (a+b x)^5 (c+d x)^7 \, dx","IntegrateAlgebraic[(a + b*x)^5*(c + d*x)^7,x]","\frac{10296 a^5 c^7 x+36036 a^5 c^6 d x^2+72072 a^5 c^5 d^2 x^3+90090 a^5 c^4 d^3 x^4+72072 a^5 c^3 d^4 x^5+36036 a^5 c^2 d^5 x^6+10296 a^5 c d^6 x^7+1287 a^5 d^7 x^8+25740 a^4 b c^7 x^2+120120 a^4 b c^6 d x^3+270270 a^4 b c^5 d^2 x^4+360360 a^4 b c^4 d^3 x^5+300300 a^4 b c^3 d^4 x^6+154440 a^4 b c^2 d^5 x^7+45045 a^4 b c d^6 x^8+5720 a^4 b d^7 x^9+34320 a^3 b^2 c^7 x^3+180180 a^3 b^2 c^6 d x^4+432432 a^3 b^2 c^5 d^2 x^5+600600 a^3 b^2 c^4 d^3 x^6+514800 a^3 b^2 c^3 d^4 x^7+270270 a^3 b^2 c^2 d^5 x^8+80080 a^3 b^2 c d^6 x^9+10296 a^3 b^2 d^7 x^{10}+25740 a^2 b^3 c^7 x^4+144144 a^2 b^3 c^6 d x^5+360360 a^2 b^3 c^5 d^2 x^6+514800 a^2 b^3 c^4 d^3 x^7+450450 a^2 b^3 c^3 d^4 x^8+240240 a^2 b^3 c^2 d^5 x^9+72072 a^2 b^3 c d^6 x^{10}+9360 a^2 b^3 d^7 x^{11}+10296 a b^4 c^7 x^5+60060 a b^4 c^6 d x^6+154440 a b^4 c^5 d^2 x^7+225225 a b^4 c^4 d^3 x^8+200200 a b^4 c^3 d^4 x^9+108108 a b^4 c^2 d^5 x^{10}+32760 a b^4 c d^6 x^{11}+4290 a b^4 d^7 x^{12}+1716 b^5 c^7 x^6+10296 b^5 c^6 d x^7+27027 b^5 c^5 d^2 x^8+40040 b^5 c^4 d^3 x^9+36036 b^5 c^3 d^4 x^{10}+19656 b^5 c^2 d^5 x^{11}+6006 b^5 c d^6 x^{12}+792 b^5 d^7 x^{13}}{10296}","-\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,"(10296*a^5*c^7*x + 25740*a^4*b*c^7*x^2 + 36036*a^5*c^6*d*x^2 + 34320*a^3*b^2*c^7*x^3 + 120120*a^4*b*c^6*d*x^3 + 72072*a^5*c^5*d^2*x^3 + 25740*a^2*b^3*c^7*x^4 + 180180*a^3*b^2*c^6*d*x^4 + 270270*a^4*b*c^5*d^2*x^4 + 90090*a^5*c^4*d^3*x^4 + 10296*a*b^4*c^7*x^5 + 144144*a^2*b^3*c^6*d*x^5 + 432432*a^3*b^2*c^5*d^2*x^5 + 360360*a^4*b*c^4*d^3*x^5 + 72072*a^5*c^3*d^4*x^5 + 1716*b^5*c^7*x^6 + 60060*a*b^4*c^6*d*x^6 + 360360*a^2*b^3*c^5*d^2*x^6 + 600600*a^3*b^2*c^4*d^3*x^6 + 300300*a^4*b*c^3*d^4*x^6 + 36036*a^5*c^2*d^5*x^6 + 10296*b^5*c^6*d*x^7 + 154440*a*b^4*c^5*d^2*x^7 + 514800*a^2*b^3*c^4*d^3*x^7 + 514800*a^3*b^2*c^3*d^4*x^7 + 154440*a^4*b*c^2*d^5*x^7 + 10296*a^5*c*d^6*x^7 + 27027*b^5*c^5*d^2*x^8 + 225225*a*b^4*c^4*d^3*x^8 + 450450*a^2*b^3*c^3*d^4*x^8 + 270270*a^3*b^2*c^2*d^5*x^8 + 45045*a^4*b*c*d^6*x^8 + 1287*a^5*d^7*x^8 + 40040*b^5*c^4*d^3*x^9 + 200200*a*b^4*c^3*d^4*x^9 + 240240*a^2*b^3*c^2*d^5*x^9 + 80080*a^3*b^2*c*d^6*x^9 + 5720*a^4*b*d^7*x^9 + 36036*b^5*c^3*d^4*x^10 + 108108*a*b^4*c^2*d^5*x^10 + 72072*a^2*b^3*c*d^6*x^10 + 10296*a^3*b^2*d^7*x^10 + 19656*b^5*c^2*d^5*x^11 + 32760*a*b^4*c*d^6*x^11 + 9360*a^2*b^3*d^7*x^11 + 6006*b^5*c*d^6*x^12 + 4290*a*b^4*d^7*x^12 + 792*b^5*d^7*x^13)/10296","B",1
1278,1,553,119,0.1442923,"\int (a+b x)^4 (c+d x)^7 \, dx","IntegrateAlgebraic[(a + b*x)^4*(c + d*x)^7,x]","\frac{3960 a^4 c^7 x+13860 a^4 c^6 d x^2+27720 a^4 c^5 d^2 x^3+34650 a^4 c^4 d^3 x^4+27720 a^4 c^3 d^4 x^5+13860 a^4 c^2 d^5 x^6+3960 a^4 c d^6 x^7+495 a^4 d^7 x^8+7920 a^3 b c^7 x^2+36960 a^3 b c^6 d x^3+83160 a^3 b c^5 d^2 x^4+110880 a^3 b c^4 d^3 x^5+92400 a^3 b c^3 d^4 x^6+47520 a^3 b c^2 d^5 x^7+13860 a^3 b c d^6 x^8+1760 a^3 b d^7 x^9+7920 a^2 b^2 c^7 x^3+41580 a^2 b^2 c^6 d x^4+99792 a^2 b^2 c^5 d^2 x^5+138600 a^2 b^2 c^4 d^3 x^6+118800 a^2 b^2 c^3 d^4 x^7+62370 a^2 b^2 c^2 d^5 x^8+18480 a^2 b^2 c d^6 x^9+2376 a^2 b^2 d^7 x^{10}+3960 a b^3 c^7 x^4+22176 a b^3 c^6 d x^5+55440 a b^3 c^5 d^2 x^6+79200 a b^3 c^4 d^3 x^7+69300 a b^3 c^3 d^4 x^8+36960 a b^3 c^2 d^5 x^9+11088 a b^3 c d^6 x^{10}+1440 a b^3 d^7 x^{11}+792 b^4 c^7 x^5+4620 b^4 c^6 d x^6+11880 b^4 c^5 d^2 x^7+17325 b^4 c^4 d^3 x^8+15400 b^4 c^3 d^4 x^9+8316 b^4 c^2 d^5 x^{10}+2520 b^4 c d^6 x^{11}+330 b^4 d^7 x^{12}}{3960}","-\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,"(3960*a^4*c^7*x + 7920*a^3*b*c^7*x^2 + 13860*a^4*c^6*d*x^2 + 7920*a^2*b^2*c^7*x^3 + 36960*a^3*b*c^6*d*x^3 + 27720*a^4*c^5*d^2*x^3 + 3960*a*b^3*c^7*x^4 + 41580*a^2*b^2*c^6*d*x^4 + 83160*a^3*b*c^5*d^2*x^4 + 34650*a^4*c^4*d^3*x^4 + 792*b^4*c^7*x^5 + 22176*a*b^3*c^6*d*x^5 + 99792*a^2*b^2*c^5*d^2*x^5 + 110880*a^3*b*c^4*d^3*x^5 + 27720*a^4*c^3*d^4*x^5 + 4620*b^4*c^6*d*x^6 + 55440*a*b^3*c^5*d^2*x^6 + 138600*a^2*b^2*c^4*d^3*x^6 + 92400*a^3*b*c^3*d^4*x^6 + 13860*a^4*c^2*d^5*x^6 + 11880*b^4*c^5*d^2*x^7 + 79200*a*b^3*c^4*d^3*x^7 + 118800*a^2*b^2*c^3*d^4*x^7 + 47520*a^3*b*c^2*d^5*x^7 + 3960*a^4*c*d^6*x^7 + 17325*b^4*c^4*d^3*x^8 + 69300*a*b^3*c^3*d^4*x^8 + 62370*a^2*b^2*c^2*d^5*x^8 + 13860*a^3*b*c*d^6*x^8 + 495*a^4*d^7*x^8 + 15400*b^4*c^3*d^4*x^9 + 36960*a*b^3*c^2*d^5*x^9 + 18480*a^2*b^2*c*d^6*x^9 + 1760*a^3*b*d^7*x^9 + 8316*b^4*c^2*d^5*x^10 + 11088*a*b^3*c*d^6*x^10 + 2376*a^2*b^2*d^7*x^10 + 2520*b^4*c*d^6*x^11 + 1440*a*b^3*d^7*x^11 + 330*b^4*d^7*x^12)/3960","B",1
1279,1,427,92,0.1140294,"\int (a+b x)^3 (c+d x)^7 \, dx","IntegrateAlgebraic[(a + b*x)^3*(c + d*x)^7,x]","\frac{1320 a^3 c^7 x+4620 a^3 c^6 d x^2+9240 a^3 c^5 d^2 x^3+11550 a^3 c^4 d^3 x^4+9240 a^3 c^3 d^4 x^5+4620 a^3 c^2 d^5 x^6+1320 a^3 c d^6 x^7+165 a^3 d^7 x^8+1980 a^2 b c^7 x^2+9240 a^2 b c^6 d x^3+20790 a^2 b c^5 d^2 x^4+27720 a^2 b c^4 d^3 x^5+23100 a^2 b c^3 d^4 x^6+11880 a^2 b c^2 d^5 x^7+3465 a^2 b c d^6 x^8+440 a^2 b d^7 x^9+1320 a b^2 c^7 x^3+6930 a b^2 c^6 d x^4+16632 a b^2 c^5 d^2 x^5+23100 a b^2 c^4 d^3 x^6+19800 a b^2 c^3 d^4 x^7+10395 a b^2 c^2 d^5 x^8+3080 a b^2 c d^6 x^9+396 a b^2 d^7 x^{10}+330 b^3 c^7 x^4+1848 b^3 c^6 d x^5+4620 b^3 c^5 d^2 x^6+6600 b^3 c^4 d^3 x^7+5775 b^3 c^3 d^4 x^8+3080 b^3 c^2 d^5 x^9+924 b^3 c d^6 x^{10}+120 b^3 d^7 x^{11}}{1320}","-\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,"(1320*a^3*c^7*x + 1980*a^2*b*c^7*x^2 + 4620*a^3*c^6*d*x^2 + 1320*a*b^2*c^7*x^3 + 9240*a^2*b*c^6*d*x^3 + 9240*a^3*c^5*d^2*x^3 + 330*b^3*c^7*x^4 + 6930*a*b^2*c^6*d*x^4 + 20790*a^2*b*c^5*d^2*x^4 + 11550*a^3*c^4*d^3*x^4 + 1848*b^3*c^6*d*x^5 + 16632*a*b^2*c^5*d^2*x^5 + 27720*a^2*b*c^4*d^3*x^5 + 9240*a^3*c^3*d^4*x^5 + 4620*b^3*c^5*d^2*x^6 + 23100*a*b^2*c^4*d^3*x^6 + 23100*a^2*b*c^3*d^4*x^6 + 4620*a^3*c^2*d^5*x^6 + 6600*b^3*c^4*d^3*x^7 + 19800*a*b^2*c^3*d^4*x^7 + 11880*a^2*b*c^2*d^5*x^7 + 1320*a^3*c*d^6*x^7 + 5775*b^3*c^3*d^4*x^8 + 10395*a*b^2*c^2*d^5*x^8 + 3465*a^2*b*c*d^6*x^8 + 165*a^3*d^7*x^8 + 3080*b^3*c^2*d^5*x^9 + 3080*a*b^2*c*d^6*x^9 + 440*a^2*b*d^7*x^9 + 924*b^3*c*d^6*x^10 + 396*a*b^2*d^7*x^10 + 120*b^3*d^7*x^11)/1320","B",1
1280,1,301,65,0.0813204,"\int (a+b x)^2 (c+d x)^7 \, dx","IntegrateAlgebraic[(a + b*x)^2*(c + d*x)^7,x]","\frac{1}{360} \left(360 a^2 c^7 x+1260 a^2 c^6 d x^2+2520 a^2 c^5 d^2 x^3+3150 a^2 c^4 d^3 x^4+2520 a^2 c^3 d^4 x^5+1260 a^2 c^2 d^5 x^6+360 a^2 c d^6 x^7+45 a^2 d^7 x^8+360 a b c^7 x^2+1680 a b c^6 d x^3+3780 a b c^5 d^2 x^4+5040 a b c^4 d^3 x^5+4200 a b c^3 d^4 x^6+2160 a b c^2 d^5 x^7+630 a b c d^6 x^8+80 a b d^7 x^9+120 b^2 c^7 x^3+630 b^2 c^6 d x^4+1512 b^2 c^5 d^2 x^5+2100 b^2 c^4 d^3 x^6+1800 b^2 c^3 d^4 x^7+945 b^2 c^2 d^5 x^8+280 b^2 c d^6 x^9+36 b^2 d^7 x^{10}\right)","-\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,"(360*a^2*c^7*x + 360*a*b*c^7*x^2 + 1260*a^2*c^6*d*x^2 + 120*b^2*c^7*x^3 + 1680*a*b*c^6*d*x^3 + 2520*a^2*c^5*d^2*x^3 + 630*b^2*c^6*d*x^4 + 3780*a*b*c^5*d^2*x^4 + 3150*a^2*c^4*d^3*x^4 + 1512*b^2*c^5*d^2*x^5 + 5040*a*b*c^4*d^3*x^5 + 2520*a^2*c^3*d^4*x^5 + 2100*b^2*c^4*d^3*x^6 + 4200*a*b*c^3*d^4*x^6 + 1260*a^2*c^2*d^5*x^6 + 1800*b^2*c^3*d^4*x^7 + 2160*a*b*c^2*d^5*x^7 + 360*a^2*c*d^6*x^7 + 945*b^2*c^2*d^5*x^8 + 630*a*b*c*d^6*x^8 + 45*a^2*d^7*x^8 + 280*b^2*c*d^6*x^9 + 80*a*b*d^7*x^9 + 36*b^2*d^7*x^10)/360","B",1
1281,1,175,38,0.0473616,"\int (a+b x) (c+d x)^7 \, dx","IntegrateAlgebraic[(a + b*x)*(c + d*x)^7,x]","\frac{1}{72} \left(72 a c^7 x+252 a c^6 d x^2+504 a c^5 d^2 x^3+630 a c^4 d^3 x^4+504 a c^3 d^4 x^5+252 a c^2 d^5 x^6+72 a c d^6 x^7+9 a d^7 x^8+36 b c^7 x^2+168 b c^6 d x^3+378 b c^5 d^2 x^4+504 b c^4 d^3 x^5+420 b c^3 d^4 x^6+216 b c^2 d^5 x^7+63 b c d^6 x^8+8 b d^7 x^9\right)","\frac{b (c+d x)^9}{9 d^2}-\frac{(c+d x)^8 (b c-a d)}{8 d^2}",1,"(72*a*c^7*x + 36*b*c^7*x^2 + 252*a*c^6*d*x^2 + 168*b*c^6*d*x^3 + 504*a*c^5*d^2*x^3 + 378*b*c^5*d^2*x^4 + 630*a*c^4*d^3*x^4 + 504*b*c^4*d^3*x^5 + 504*a*c^3*d^4*x^5 + 420*b*c^3*d^4*x^6 + 252*a*c^2*d^5*x^6 + 216*b*c^2*d^5*x^7 + 72*a*c*d^6*x^7 + 63*b*c*d^6*x^8 + 9*a*d^7*x^8 + 8*b*d^7*x^9)/72","B",1
1282,1,14,14,0.0051254,"\int (c+d x)^7 \, dx","IntegrateAlgebraic[(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
1283,1,394,169,0.2288242,"\int \frac{(c+d x)^7}{a+b x} \, dx","IntegrateAlgebraic[(c + d*x)^7/(a + b*x),x]","\frac{d x \left(420 a^6 d^6-2940 a^5 b c d^5-210 a^5 b d^6 x+8820 a^4 b^2 c^2 d^4+1470 a^4 b^2 c d^5 x+140 a^4 b^2 d^6 x^2-14700 a^3 b^3 c^3 d^3-4410 a^3 b^3 c^2 d^4 x-980 a^3 b^3 c d^5 x^2-105 a^3 b^3 d^6 x^3+14700 a^2 b^4 c^4 d^2+7350 a^2 b^4 c^3 d^3 x+2940 a^2 b^4 c^2 d^4 x^2+735 a^2 b^4 c d^5 x^3+84 a^2 b^4 d^6 x^4-8820 a b^5 c^5 d-7350 a b^5 c^4 d^2 x-4900 a b^5 c^3 d^3 x^2-2205 a b^5 c^2 d^4 x^3-588 a b^5 c d^5 x^4-70 a b^5 d^6 x^5+2940 b^6 c^6+4410 b^6 c^5 d x+4900 b^6 c^4 d^2 x^2+3675 b^6 c^3 d^3 x^3+1764 b^6 c^2 d^4 x^4+490 b^6 c d^5 x^5+60 b^6 d^6 x^6\right)}{420 b^7}+\frac{(b c-a d)^7 \log (a+b x)}{b^8}","\frac{(b c-a d)^7 \log (a+b x)}{b^8}+\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{(c+d x)^7}{7 b}",1,"(d*x*(2940*b^6*c^6 - 8820*a*b^5*c^5*d + 14700*a^2*b^4*c^4*d^2 - 14700*a^3*b^3*c^3*d^3 + 8820*a^4*b^2*c^2*d^4 - 2940*a^5*b*c*d^5 + 420*a^6*d^6 + 4410*b^6*c^5*d*x - 7350*a*b^5*c^4*d^2*x + 7350*a^2*b^4*c^3*d^3*x - 4410*a^3*b^3*c^2*d^4*x + 1470*a^4*b^2*c*d^5*x - 210*a^5*b*d^6*x + 4900*b^6*c^4*d^2*x^2 - 4900*a*b^5*c^3*d^3*x^2 + 2940*a^2*b^4*c^2*d^4*x^2 - 980*a^3*b^3*c*d^5*x^2 + 140*a^4*b^2*d^6*x^2 + 3675*b^6*c^3*d^3*x^3 - 2205*a*b^5*c^2*d^4*x^3 + 735*a^2*b^4*c*d^5*x^3 - 105*a^3*b^3*d^6*x^3 + 1764*b^6*c^2*d^4*x^4 - 588*a*b^5*c*d^5*x^4 + 84*a^2*b^4*d^6*x^4 + 490*b^6*c*d^5*x^5 - 70*a*b^5*d^6*x^5 + 60*b^6*d^6*x^6))/(420*b^7) + ((b*c - a*d)^7*Log[a + b*x])/b^8","B",1
1284,1,512,187,0.2134044,"\int \frac{(c+d x)^7}{(a+b x)^2} \, dx","IntegrateAlgebraic[(c + d*x)^7/(a + b*x)^2,x]","\frac{60 a^7 d^7-420 a^6 b c d^6-360 a^6 b d^7 x+1260 a^5 b^2 c^2 d^5+2100 a^5 b^2 c d^6 x-210 a^5 b^2 d^7 x^2-2100 a^4 b^3 c^3 d^4-5040 a^4 b^3 c^2 d^5 x+1260 a^4 b^3 c d^6 x^2+70 a^4 b^3 d^7 x^3+2100 a^3 b^4 c^4 d^3+6300 a^3 b^4 c^3 d^4 x-3150 a^3 b^4 c^2 d^5 x^2-420 a^3 b^4 c d^6 x^3-35 a^3 b^4 d^7 x^4-1260 a^2 b^5 c^5 d^2-4200 a^2 b^5 c^4 d^3 x+4200 a^2 b^5 c^3 d^4 x^2+1050 a^2 b^5 c^2 d^5 x^3+210 a^2 b^5 c d^6 x^4+21 a^2 b^5 d^7 x^5+420 a b^6 c^6 d+1260 a b^6 c^5 d^2 x-3150 a b^6 c^4 d^3 x^2-1400 a b^6 c^3 d^4 x^3-525 a b^6 c^2 d^5 x^4-126 a b^6 c d^6 x^5-14 a b^6 d^7 x^6-60 b^7 c^7+1260 b^7 c^5 d^2 x^2+1050 b^7 c^4 d^3 x^3+700 b^7 c^3 d^4 x^4+315 b^7 c^2 d^5 x^5+84 b^7 c d^6 x^6+10 b^7 d^7 x^7}{60 b^8 (a+b x)}+\frac{7 d (b c-a d)^6 \log (a+b x)}{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{(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{21 d^2 x (b c-a d)^5}{b^7}",1,"(-60*b^7*c^7 + 420*a*b^6*c^6*d - 1260*a^2*b^5*c^5*d^2 + 2100*a^3*b^4*c^4*d^3 - 2100*a^4*b^3*c^3*d^4 + 1260*a^5*b^2*c^2*d^5 - 420*a^6*b*c*d^6 + 60*a^7*d^7 + 1260*a*b^6*c^5*d^2*x - 4200*a^2*b^5*c^4*d^3*x + 6300*a^3*b^4*c^3*d^4*x - 5040*a^4*b^3*c^2*d^5*x + 2100*a^5*b^2*c*d^6*x - 360*a^6*b*d^7*x + 1260*b^7*c^5*d^2*x^2 - 3150*a*b^6*c^4*d^3*x^2 + 4200*a^2*b^5*c^3*d^4*x^2 - 3150*a^3*b^4*c^2*d^5*x^2 + 1260*a^4*b^3*c*d^6*x^2 - 210*a^5*b^2*d^7*x^2 + 1050*b^7*c^4*d^3*x^3 - 1400*a*b^6*c^3*d^4*x^3 + 1050*a^2*b^5*c^2*d^5*x^3 - 420*a^3*b^4*c*d^6*x^3 + 70*a^4*b^3*d^7*x^3 + 700*b^7*c^3*d^4*x^4 - 525*a*b^6*c^2*d^5*x^4 + 210*a^2*b^5*c*d^6*x^4 - 35*a^3*b^4*d^7*x^4 + 315*b^7*c^2*d^5*x^5 - 126*a*b^6*c*d^6*x^5 + 21*a^2*b^5*d^7*x^5 + 84*b^7*c*d^6*x^6 - 14*a*b^6*d^7*x^6 + 10*b^7*d^7*x^7)/(60*b^8*(a + b*x)) + (7*d*(b*c - a*d)^6*Log[a + b*x])/b^8","B",1
1285,1,510,185,0.2221396,"\int \frac{(c+d x)^7}{(a+b x)^3} \, dx","IntegrateAlgebraic[(c + d*x)^7/(a + b*x)^3,x]","\frac{-130 a^7 d^7+770 a^6 b c d^6+160 a^6 b d^7 x-1890 a^5 b^2 c^2 d^5-560 a^5 b^2 c d^6 x+500 a^5 b^2 d^7 x^2+2450 a^4 b^3 c^3 d^4+420 a^4 b^3 c^2 d^5 x-2380 a^4 b^3 c d^6 x^2+140 a^4 b^3 d^7 x^3-1750 a^3 b^4 c^4 d^3+700 a^3 b^4 c^3 d^4 x+4410 a^3 b^4 c^2 d^5 x^2-700 a^3 b^4 c d^6 x^3-35 a^3 b^4 d^7 x^4+630 a^2 b^5 c^5 d^2-1400 a^2 b^5 c^4 d^3 x-3850 a^2 b^5 c^3 d^4 x^2+1400 a^2 b^5 c^2 d^5 x^3+175 a^2 b^5 c d^6 x^4+14 a^2 b^5 d^7 x^5-70 a b^6 c^6 d+840 a b^6 c^5 d^2 x+1400 a b^6 c^4 d^3 x^2-1400 a b^6 c^3 d^4 x^3-350 a b^6 c^2 d^5 x^4-70 a b^6 c d^6 x^5-7 a b^6 d^7 x^6-10 b^7 c^7-140 b^7 c^6 d x+700 b^7 c^4 d^3 x^3+350 b^7 c^3 d^4 x^4+140 b^7 c^2 d^5 x^5+35 b^7 c d^6 x^6+4 b^7 d^7 x^7}{20 b^8 (a+b x)^2}+\frac{21 d^2 (b c-a d)^5 \log (a+b x)}{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{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{35 d^3 x (b c-a d)^4}{b^7}",1,"(-10*b^7*c^7 - 70*a*b^6*c^6*d + 630*a^2*b^5*c^5*d^2 - 1750*a^3*b^4*c^4*d^3 + 2450*a^4*b^3*c^3*d^4 - 1890*a^5*b^2*c^2*d^5 + 770*a^6*b*c*d^6 - 130*a^7*d^7 - 140*b^7*c^6*d*x + 840*a*b^6*c^5*d^2*x - 1400*a^2*b^5*c^4*d^3*x + 700*a^3*b^4*c^3*d^4*x + 420*a^4*b^3*c^2*d^5*x - 560*a^5*b^2*c*d^6*x + 160*a^6*b*d^7*x + 1400*a*b^6*c^4*d^3*x^2 - 3850*a^2*b^5*c^3*d^4*x^2 + 4410*a^3*b^4*c^2*d^5*x^2 - 2380*a^4*b^3*c*d^6*x^2 + 500*a^5*b^2*d^7*x^2 + 700*b^7*c^4*d^3*x^3 - 1400*a*b^6*c^3*d^4*x^3 + 1400*a^2*b^5*c^2*d^5*x^3 - 700*a^3*b^4*c*d^6*x^3 + 140*a^4*b^3*d^7*x^3 + 350*b^7*c^3*d^4*x^4 - 350*a*b^6*c^2*d^5*x^4 + 175*a^2*b^5*c*d^6*x^4 - 35*a^3*b^4*d^7*x^4 + 140*b^7*c^2*d^5*x^5 - 70*a*b^6*c*d^6*x^5 + 14*a^2*b^5*d^7*x^5 + 35*b^7*c*d^6*x^6 - 7*a*b^6*d^7*x^6 + 4*b^7*d^7*x^7)/(20*b^8*(a + b*x)^2) + (21*d^2*(b*c - a*d)^5*Log[a + b*x])/b^8","B",1
1286,1,510,187,0.191663,"\int \frac{(c+d x)^7}{(a+b x)^4} \, dx","IntegrateAlgebraic[(c + d*x)^7/(a + b*x)^4,x]","\frac{214 a^7 d^7-1036 a^6 b c d^6+222 a^6 b d^7 x+1974 a^5 b^2 c^2 d^5-1428 a^5 b^2 c d^6 x-408 a^5 b^2 d^7 x^2-1820 a^4 b^3 c^3 d^4+3402 a^4 b^3 c^2 d^5 x+1092 a^4 b^3 c d^6 x^2-556 a^4 b^3 d^7 x^3+770 a^3 b^4 c^4 d^3-3780 a^3 b^4 c^3 d^4 x-378 a^3 b^4 c^2 d^5 x^2+2044 a^3 b^4 c d^6 x^3-105 a^3 b^4 d^7 x^4-84 a^2 b^5 c^5 d^2+1890 a^2 b^5 c^4 d^3 x-1260 a^2 b^5 c^3 d^4 x^2-2646 a^2 b^5 c^2 d^5 x^3+420 a^2 b^5 c d^6 x^4+21 a^2 b^5 d^7 x^5-14 a b^6 c^6 d-252 a b^6 c^5 d^2 x+1260 a b^6 c^4 d^3 x^2+1260 a b^6 c^3 d^4 x^3-630 a b^6 c^2 d^5 x^4-84 a b^6 c d^6 x^5-7 a b^6 d^7 x^6-4 b^7 c^7-42 b^7 c^6 d x-252 b^7 c^5 d^2 x^2+420 b^7 c^3 d^4 x^4+126 b^7 c^2 d^5 x^5+28 b^7 c d^6 x^6+3 b^7 d^7 x^7}{12 b^8 (a+b x)^3}+\frac{35 d^3 (b c-a d)^4 \log (a+b x)}{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^3 (b c-a d)^4 \log (a+b x)}{b^8}-\frac{21 d^2 (b c-a d)^5}{b^8 (a+b x)}-\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{35 d^4 x (b c-a d)^3}{b^7}",1,"(-4*b^7*c^7 - 14*a*b^6*c^6*d - 84*a^2*b^5*c^5*d^2 + 770*a^3*b^4*c^4*d^3 - 1820*a^4*b^3*c^3*d^4 + 1974*a^5*b^2*c^2*d^5 - 1036*a^6*b*c*d^6 + 214*a^7*d^7 - 42*b^7*c^6*d*x - 252*a*b^6*c^5*d^2*x + 1890*a^2*b^5*c^4*d^3*x - 3780*a^3*b^4*c^3*d^4*x + 3402*a^4*b^3*c^2*d^5*x - 1428*a^5*b^2*c*d^6*x + 222*a^6*b*d^7*x - 252*b^7*c^5*d^2*x^2 + 1260*a*b^6*c^4*d^3*x^2 - 1260*a^2*b^5*c^3*d^4*x^2 - 378*a^3*b^4*c^2*d^5*x^2 + 1092*a^4*b^3*c*d^6*x^2 - 408*a^5*b^2*d^7*x^2 + 1260*a*b^6*c^3*d^4*x^3 - 2646*a^2*b^5*c^2*d^5*x^3 + 2044*a^3*b^4*c*d^6*x^3 - 556*a^4*b^3*d^7*x^3 + 420*b^7*c^3*d^4*x^4 - 630*a*b^6*c^2*d^5*x^4 + 420*a^2*b^5*c*d^6*x^4 - 105*a^3*b^4*d^7*x^4 + 126*b^7*c^2*d^5*x^5 - 84*a*b^6*c*d^6*x^5 + 21*a^2*b^5*d^7*x^5 + 28*b^7*c*d^6*x^6 - 7*a*b^6*d^7*x^6 + 3*b^7*d^7*x^7)/(12*b^8*(a + b*x)^3) + (35*d^3*(b*c - a*d)^4*Log[a + b*x])/b^8","B",1
1287,1,510,187,0.1909307,"\int \frac{(c+d x)^7}{(a+b x)^5} \, dx","IntegrateAlgebraic[(c + d*x)^7/(a + b*x)^5,x]","\frac{-319 a^7 d^7+1197 a^6 b c d^6-856 a^6 b d^7 x-1617 a^5 b^2 c^2 d^5+3528 a^5 b^2 c d^6 x-444 a^5 b^2 d^7 x^2+875 a^4 b^3 c^3 d^4-5208 a^4 b^3 c^2 d^5 x+2772 a^4 b^3 c d^6 x^2+544 a^4 b^3 d^7 x^3-105 a^3 b^4 c^4 d^3+3080 a^3 b^4 c^3 d^4 x-5292 a^3 b^4 c^2 d^5 x^2-672 a^3 b^4 c d^6 x^3+556 a^3 b^4 d^7 x^4-21 a^2 b^5 c^5 d^2-420 a^2 b^5 c^4 d^3 x+3780 a^2 b^5 c^3 d^4 x^2-1008 a^2 b^5 c^2 d^5 x^3-1428 a^2 b^5 c d^6 x^4+84 a^2 b^5 d^7 x^5-7 a b^6 c^6 d-84 a b^6 c^5 d^2 x-630 a b^6 c^4 d^3 x^2+1680 a b^6 c^3 d^4 x^3+1008 a b^6 c^2 d^5 x^4-252 a b^6 c d^6 x^5-14 a b^6 d^7 x^6-3 b^7 c^7-28 b^7 c^6 d x-126 b^7 c^5 d^2 x^2-420 b^7 c^4 d^3 x^3+252 b^7 c^2 d^5 x^5+42 b^7 c d^6 x^6+4 b^7 d^7 x^7}{12 b^8 (a+b x)^4}+\frac{35 d^4 (b c-a d)^3 \log (a+b x)}{b^8}","\frac{7 d^6 (a+b x)^2 (b c-a d)}{2 b^8}+\frac{35 d^4 (b c-a d)^3 \log (a+b x)}{b^8}-\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{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{21 d^5 x (b c-a d)^2}{b^7}",1,"(-3*b^7*c^7 - 7*a*b^6*c^6*d - 21*a^2*b^5*c^5*d^2 - 105*a^3*b^4*c^4*d^3 + 875*a^4*b^3*c^3*d^4 - 1617*a^5*b^2*c^2*d^5 + 1197*a^6*b*c*d^6 - 319*a^7*d^7 - 28*b^7*c^6*d*x - 84*a*b^6*c^5*d^2*x - 420*a^2*b^5*c^4*d^3*x + 3080*a^3*b^4*c^3*d^4*x - 5208*a^4*b^3*c^2*d^5*x + 3528*a^5*b^2*c*d^6*x - 856*a^6*b*d^7*x - 126*b^7*c^5*d^2*x^2 - 630*a*b^6*c^4*d^3*x^2 + 3780*a^2*b^5*c^3*d^4*x^2 - 5292*a^3*b^4*c^2*d^5*x^2 + 2772*a^4*b^3*c*d^6*x^2 - 444*a^5*b^2*d^7*x^2 - 420*b^7*c^4*d^3*x^3 + 1680*a*b^6*c^3*d^4*x^3 - 1008*a^2*b^5*c^2*d^5*x^3 - 672*a^3*b^4*c*d^6*x^3 + 544*a^4*b^3*d^7*x^3 + 1008*a*b^6*c^2*d^5*x^4 - 1428*a^2*b^5*c*d^6*x^4 + 556*a^3*b^4*d^7*x^4 + 252*b^7*c^2*d^5*x^5 - 252*a*b^6*c*d^6*x^5 + 84*a^2*b^5*d^7*x^5 + 42*b^7*c*d^6*x^6 - 14*a*b^6*d^7*x^6 + 4*b^7*d^7*x^7)/(12*b^8*(a + b*x)^4) + (35*d^4*(b*c - a*d)^3*Log[a + b*x])/b^8","B",1
1288,1,510,181,0.2394337,"\int \frac{(c+d x)^7}{(a+b x)^6} \, dx","IntegrateAlgebraic[(c + d*x)^7/(a + b*x)^6,x]","\frac{459 a^7 d^7-1218 a^6 b c d^6+1875 a^6 b d^7 x+959 a^5 b^2 c^2 d^5-5250 a^5 b^2 c d^6 x+2700 a^5 b^2 d^7 x^2-140 a^4 b^3 c^3 d^4+4375 a^4 b^3 c^2 d^5 x-8400 a^4 b^3 c d^6 x^2+1300 a^4 b^3 d^7 x^3-35 a^3 b^4 c^4 d^3-700 a^3 b^4 c^3 d^4 x+7700 a^3 b^4 c^2 d^5 x^2-5600 a^3 b^4 c d^6 x^3-400 a^3 b^4 d^7 x^4-14 a^2 b^5 c^5 d^2-175 a^2 b^5 c^4 d^3 x-1400 a^2 b^5 c^3 d^4 x^2+6300 a^2 b^5 c^2 d^5 x^3-700 a^2 b^5 c d^6 x^4-500 a^2 b^5 d^7 x^5-7 a b^6 c^6 d-70 a b^6 c^5 d^2 x-350 a b^6 c^4 d^3 x^2-1400 a b^6 c^3 d^4 x^3+2100 a b^6 c^2 d^5 x^4+700 a b^6 c d^6 x^5-70 a b^6 d^7 x^6-4 b^7 c^7-35 b^7 c^6 d x-140 b^7 c^5 d^2 x^2-350 b^7 c^4 d^3 x^3-700 b^7 c^3 d^4 x^4+140 b^7 c d^6 x^6+10 b^7 d^7 x^7}{20 b^8 (a+b x)^5}+\frac{21 d^5 (b c-a d)^2 \log (a+b x)}{b^8}","\frac{21 d^5 (b c-a d)^2 \log (a+b x)}{b^8}-\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{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^6 x (7 b c-6 a d)}{b^7}+\frac{d^7 x^2}{2 b^6}",1,"(-4*b^7*c^7 - 7*a*b^6*c^6*d - 14*a^2*b^5*c^5*d^2 - 35*a^3*b^4*c^4*d^3 - 140*a^4*b^3*c^3*d^4 + 959*a^5*b^2*c^2*d^5 - 1218*a^6*b*c*d^6 + 459*a^7*d^7 - 35*b^7*c^6*d*x - 70*a*b^6*c^5*d^2*x - 175*a^2*b^5*c^4*d^3*x - 700*a^3*b^4*c^3*d^4*x + 4375*a^4*b^3*c^2*d^5*x - 5250*a^5*b^2*c*d^6*x + 1875*a^6*b*d^7*x - 140*b^7*c^5*d^2*x^2 - 350*a*b^6*c^4*d^3*x^2 - 1400*a^2*b^5*c^3*d^4*x^2 + 7700*a^3*b^4*c^2*d^5*x^2 - 8400*a^4*b^3*c*d^6*x^2 + 2700*a^5*b^2*d^7*x^2 - 350*b^7*c^4*d^3*x^3 - 1400*a*b^6*c^3*d^4*x^3 + 6300*a^2*b^5*c^2*d^5*x^3 - 5600*a^3*b^4*c*d^6*x^3 + 1300*a^4*b^3*d^7*x^3 - 700*b^7*c^3*d^4*x^4 + 2100*a*b^6*c^2*d^5*x^4 - 700*a^2*b^5*c*d^6*x^4 - 400*a^3*b^4*d^7*x^4 + 700*a*b^6*c*d^6*x^5 - 500*a^2*b^5*d^7*x^5 + 140*b^7*c*d^6*x^6 - 70*a*b^6*d^7*x^6 + 10*b^7*d^7*x^7)/(20*b^8*(a + b*x)^5) + (21*d^5*(b*c - a*d)^2*Log[a + b*x])/b^8","B",1
1289,1,512,186,0.31058,"\int \frac{(c+d x)^7}{(a+b x)^7} \, dx","IntegrateAlgebraic[(c + d*x)^7/(a + b*x)^7,x]","\frac{-669 a^7 d^7+1029 a^6 b c d^6-3594 a^6 b d^7 x-210 a^5 b^2 c^2 d^5+5754 a^5 b^2 c d^6 x-7725 a^5 b^2 d^7 x^2-70 a^4 b^3 c^3 d^4-1260 a^4 b^3 c^2 d^5 x+13125 a^4 b^3 c d^6 x^2-8200 a^4 b^3 d^7 x^3-35 a^3 b^4 c^4 d^3-420 a^3 b^4 c^3 d^4 x-3150 a^3 b^4 c^2 d^5 x^2+15400 a^3 b^4 c d^6 x^3-4050 a^3 b^4 d^7 x^4-21 a^2 b^5 c^5 d^2-210 a^2 b^5 c^4 d^3 x-1050 a^2 b^5 c^3 d^4 x^2-4200 a^2 b^5 c^2 d^5 x^3+9450 a^2 b^5 c d^6 x^4-360 a^2 b^5 d^7 x^5-14 a b^6 c^6 d-126 a b^6 c^5 d^2 x-525 a b^6 c^4 d^3 x^2-1400 a b^6 c^3 d^4 x^3-3150 a b^6 c^2 d^5 x^4+2520 a b^6 c d^6 x^5+360 a b^6 d^7 x^6-10 b^7 c^7-84 b^7 c^6 d x-315 b^7 c^5 d^2 x^2-700 b^7 c^4 d^3 x^3-1050 b^7 c^3 d^4 x^4-1260 b^7 c^2 d^5 x^5+60 b^7 d^7 x^7}{60 b^8 (a+b x)^6}+\frac{7 \left(b c d^6-a d^7\right) \log (a+b x)}{b^8}","\frac{7 d^6 (b c-a d) \log (a+b x)}{b^8}-\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 (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,"(-10*b^7*c^7 - 14*a*b^6*c^6*d - 21*a^2*b^5*c^5*d^2 - 35*a^3*b^4*c^4*d^3 - 70*a^4*b^3*c^3*d^4 - 210*a^5*b^2*c^2*d^5 + 1029*a^6*b*c*d^6 - 669*a^7*d^7 - 84*b^7*c^6*d*x - 126*a*b^6*c^5*d^2*x - 210*a^2*b^5*c^4*d^3*x - 420*a^3*b^4*c^3*d^4*x - 1260*a^4*b^3*c^2*d^5*x + 5754*a^5*b^2*c*d^6*x - 3594*a^6*b*d^7*x - 315*b^7*c^5*d^2*x^2 - 525*a*b^6*c^4*d^3*x^2 - 1050*a^2*b^5*c^3*d^4*x^2 - 3150*a^3*b^4*c^2*d^5*x^2 + 13125*a^4*b^3*c*d^6*x^2 - 7725*a^5*b^2*d^7*x^2 - 700*b^7*c^4*d^3*x^3 - 1400*a*b^6*c^3*d^4*x^3 - 4200*a^2*b^5*c^2*d^5*x^3 + 15400*a^3*b^4*c*d^6*x^3 - 8200*a^4*b^3*d^7*x^3 - 1050*b^7*c^3*d^4*x^4 - 3150*a*b^6*c^2*d^5*x^4 + 9450*a^2*b^5*c*d^6*x^4 - 4050*a^3*b^4*d^7*x^4 - 1260*b^7*c^2*d^5*x^5 + 2520*a*b^6*c*d^6*x^5 - 360*a^2*b^5*d^7*x^5 + 360*a*b^6*d^7*x^6 + 60*b^7*d^7*x^7)/(60*b^8*(a + b*x)^6) + (7*(b*c*d^6 - a*d^7)*Log[a + b*x])/b^8","B",1
1290,1,400,194,0.2455558,"\int \frac{(c+d x)^7}{(a+b x)^8} \, dx","IntegrateAlgebraic[(c + d*x)^7/(a + b*x)^8,x]","\frac{d^7 \log (a+b x)}{b^8}-\frac{(b c-a d) \left(1089 a^6 d^6+669 a^5 b c d^5+7203 a^5 b d^6 x+459 a^4 b^2 c^2 d^4+4263 a^4 b^2 c d^5 x+20139 a^4 b^2 d^6 x^2+319 a^3 b^3 c^3 d^3+2793 a^3 b^3 c^2 d^4 x+11319 a^3 b^3 c d^5 x^2+30625 a^3 b^3 d^6 x^3+214 a^2 b^4 c^4 d^2+1813 a^2 b^4 c^3 d^3 x+6909 a^2 b^4 c^2 d^4 x^2+15925 a^2 b^4 c d^5 x^3+26950 a^2 b^4 d^6 x^4+130 a b^5 c^5 d+1078 a b^5 c^4 d^2 x+3969 a b^5 c^3 d^3 x^2+8575 a b^5 c^2 d^4 x^3+12250 a b^5 c d^5 x^4+13230 a b^5 d^6 x^5+60 b^6 c^6+490 b^6 c^5 d x+1764 b^6 c^4 d^2 x^2+3675 b^6 c^3 d^3 x^3+4900 b^6 c^2 d^4 x^4+4410 b^6 c d^5 x^5+2940 b^6 d^6 x^6\right)}{420 b^8 (a+b x)^7}","-\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,"-1/420*((b*c - a*d)*(60*b^6*c^6 + 130*a*b^5*c^5*d + 214*a^2*b^4*c^4*d^2 + 319*a^3*b^3*c^3*d^3 + 459*a^4*b^2*c^2*d^4 + 669*a^5*b*c*d^5 + 1089*a^6*d^6 + 490*b^6*c^5*d*x + 1078*a*b^5*c^4*d^2*x + 1813*a^2*b^4*c^3*d^3*x + 2793*a^3*b^3*c^2*d^4*x + 4263*a^4*b^2*c*d^5*x + 7203*a^5*b*d^6*x + 1764*b^6*c^4*d^2*x^2 + 3969*a*b^5*c^3*d^3*x^2 + 6909*a^2*b^4*c^2*d^4*x^2 + 11319*a^3*b^3*c*d^5*x^2 + 20139*a^4*b^2*d^6*x^2 + 3675*b^6*c^3*d^3*x^3 + 8575*a*b^5*c^2*d^4*x^3 + 15925*a^2*b^4*c*d^5*x^3 + 30625*a^3*b^3*d^6*x^3 + 4900*b^6*c^2*d^4*x^4 + 12250*a*b^5*c*d^5*x^4 + 26950*a^2*b^4*d^6*x^4 + 4410*b^6*c*d^5*x^5 + 13230*a*b^5*d^6*x^5 + 2940*b^6*d^6*x^6))/(b^8*(a + b*x)^7) + (d^7*Log[a + b*x])/b^8","B",1
1291,1,499,28,0.15483,"\int \frac{(c+d x)^7}{(a+b x)^9} \, dx","IntegrateAlgebraic[(c + d*x)^7/(a + b*x)^9,x]","\frac{-a^7 d^7-a^6 b c d^6-8 a^6 b d^7 x-a^5 b^2 c^2 d^5-8 a^5 b^2 c d^6 x-28 a^5 b^2 d^7 x^2-a^4 b^3 c^3 d^4-8 a^4 b^3 c^2 d^5 x-28 a^4 b^3 c d^6 x^2-56 a^4 b^3 d^7 x^3-a^3 b^4 c^4 d^3-8 a^3 b^4 c^3 d^4 x-28 a^3 b^4 c^2 d^5 x^2-56 a^3 b^4 c d^6 x^3-70 a^3 b^4 d^7 x^4-a^2 b^5 c^5 d^2-8 a^2 b^5 c^4 d^3 x-28 a^2 b^5 c^3 d^4 x^2-56 a^2 b^5 c^2 d^5 x^3-70 a^2 b^5 c d^6 x^4-56 a^2 b^5 d^7 x^5-a b^6 c^6 d-8 a b^6 c^5 d^2 x-28 a b^6 c^4 d^3 x^2-56 a b^6 c^3 d^4 x^3-70 a b^6 c^2 d^5 x^4-56 a b^6 c d^6 x^5-28 a b^6 d^7 x^6+b^7 \left(-c^7\right)-8 b^7 c^6 d x-28 b^7 c^5 d^2 x^2-56 b^7 c^4 d^3 x^3-70 b^7 c^3 d^4 x^4-56 b^7 c^2 d^5 x^5-28 b^7 c d^6 x^6-8 b^7 d^7 x^7}{8 b^8 (a+b x)^8}","-\frac{(c+d x)^8}{8 (a+b x)^8 (b c-a d)}",1,"(-(b^7*c^7) - a*b^6*c^6*d - a^2*b^5*c^5*d^2 - a^3*b^4*c^4*d^3 - a^4*b^3*c^3*d^4 - a^5*b^2*c^2*d^5 - a^6*b*c*d^6 - a^7*d^7 - 8*b^7*c^6*d*x - 8*a*b^6*c^5*d^2*x - 8*a^2*b^5*c^4*d^3*x - 8*a^3*b^4*c^3*d^4*x - 8*a^4*b^3*c^2*d^5*x - 8*a^5*b^2*c*d^6*x - 8*a^6*b*d^7*x - 28*b^7*c^5*d^2*x^2 - 28*a*b^6*c^4*d^3*x^2 - 28*a^2*b^5*c^3*d^4*x^2 - 28*a^3*b^4*c^2*d^5*x^2 - 28*a^4*b^3*c*d^6*x^2 - 28*a^5*b^2*d^7*x^2 - 56*b^7*c^4*d^3*x^3 - 56*a*b^6*c^3*d^4*x^3 - 56*a^2*b^5*c^2*d^5*x^3 - 56*a^3*b^4*c*d^6*x^3 - 56*a^4*b^3*d^7*x^3 - 70*b^7*c^3*d^4*x^4 - 70*a*b^6*c^2*d^5*x^4 - 70*a^2*b^5*c*d^6*x^4 - 70*a^3*b^4*d^7*x^4 - 56*b^7*c^2*d^5*x^5 - 56*a*b^6*c*d^6*x^5 - 56*a^2*b^5*d^7*x^5 - 28*b^7*c*d^6*x^6 - 28*a*b^6*d^7*x^6 - 8*b^7*d^7*x^7)/(8*b^8*(a + b*x)^8)","B",1
1292,1,499,58,0.15926,"\int \frac{(c+d x)^7}{(a+b x)^{10}} \, dx","IntegrateAlgebraic[(c + d*x)^7/(a + b*x)^10,x]","\frac{-a^7 d^7-2 a^6 b c d^6-9 a^6 b d^7 x-3 a^5 b^2 c^2 d^5-18 a^5 b^2 c d^6 x-36 a^5 b^2 d^7 x^2-4 a^4 b^3 c^3 d^4-27 a^4 b^3 c^2 d^5 x-72 a^4 b^3 c d^6 x^2-84 a^4 b^3 d^7 x^3-5 a^3 b^4 c^4 d^3-36 a^3 b^4 c^3 d^4 x-108 a^3 b^4 c^2 d^5 x^2-168 a^3 b^4 c d^6 x^3-126 a^3 b^4 d^7 x^4-6 a^2 b^5 c^5 d^2-45 a^2 b^5 c^4 d^3 x-144 a^2 b^5 c^3 d^4 x^2-252 a^2 b^5 c^2 d^5 x^3-252 a^2 b^5 c d^6 x^4-126 a^2 b^5 d^7 x^5-7 a b^6 c^6 d-54 a b^6 c^5 d^2 x-180 a b^6 c^4 d^3 x^2-336 a b^6 c^3 d^4 x^3-378 a b^6 c^2 d^5 x^4-252 a b^6 c d^6 x^5-84 a b^6 d^7 x^6-8 b^7 c^7-63 b^7 c^6 d x-216 b^7 c^5 d^2 x^2-420 b^7 c^4 d^3 x^3-504 b^7 c^3 d^4 x^4-378 b^7 c^2 d^5 x^5-168 b^7 c d^6 x^6-36 b^7 d^7 x^7}{72 b^8 (a+b x)^9}","\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,"(-8*b^7*c^7 - 7*a*b^6*c^6*d - 6*a^2*b^5*c^5*d^2 - 5*a^3*b^4*c^4*d^3 - 4*a^4*b^3*c^3*d^4 - 3*a^5*b^2*c^2*d^5 - 2*a^6*b*c*d^6 - a^7*d^7 - 63*b^7*c^6*d*x - 54*a*b^6*c^5*d^2*x - 45*a^2*b^5*c^4*d^3*x - 36*a^3*b^4*c^3*d^4*x - 27*a^4*b^3*c^2*d^5*x - 18*a^5*b^2*c*d^6*x - 9*a^6*b*d^7*x - 216*b^7*c^5*d^2*x^2 - 180*a*b^6*c^4*d^3*x^2 - 144*a^2*b^5*c^3*d^4*x^2 - 108*a^3*b^4*c^2*d^5*x^2 - 72*a^4*b^3*c*d^6*x^2 - 36*a^5*b^2*d^7*x^2 - 420*b^7*c^4*d^3*x^3 - 336*a*b^6*c^3*d^4*x^3 - 252*a^2*b^5*c^2*d^5*x^3 - 168*a^3*b^4*c*d^6*x^3 - 84*a^4*b^3*d^7*x^3 - 504*b^7*c^3*d^4*x^4 - 378*a*b^6*c^2*d^5*x^4 - 252*a^2*b^5*c*d^6*x^4 - 126*a^3*b^4*d^7*x^4 - 378*b^7*c^2*d^5*x^5 - 252*a*b^6*c*d^6*x^5 - 126*a^2*b^5*d^7*x^5 - 168*b^7*c*d^6*x^6 - 84*a*b^6*d^7*x^6 - 36*b^7*d^7*x^7)/(72*b^8*(a + b*x)^9)","B",1
1293,1,499,89,0.1604626,"\int \frac{(c+d x)^7}{(a+b x)^{11}} \, dx","IntegrateAlgebraic[(c + d*x)^7/(a + b*x)^11,x]","\frac{-a^7 d^7-3 a^6 b c d^6-10 a^6 b d^7 x-6 a^5 b^2 c^2 d^5-30 a^5 b^2 c d^6 x-45 a^5 b^2 d^7 x^2-10 a^4 b^3 c^3 d^4-60 a^4 b^3 c^2 d^5 x-135 a^4 b^3 c d^6 x^2-120 a^4 b^3 d^7 x^3-15 a^3 b^4 c^4 d^3-100 a^3 b^4 c^3 d^4 x-270 a^3 b^4 c^2 d^5 x^2-360 a^3 b^4 c d^6 x^3-210 a^3 b^4 d^7 x^4-21 a^2 b^5 c^5 d^2-150 a^2 b^5 c^4 d^3 x-450 a^2 b^5 c^3 d^4 x^2-720 a^2 b^5 c^2 d^5 x^3-630 a^2 b^5 c d^6 x^4-252 a^2 b^5 d^7 x^5-28 a b^6 c^6 d-210 a b^6 c^5 d^2 x-675 a b^6 c^4 d^3 x^2-1200 a b^6 c^3 d^4 x^3-1260 a b^6 c^2 d^5 x^4-756 a b^6 c d^6 x^5-210 a b^6 d^7 x^6-36 b^7 c^7-280 b^7 c^6 d x-945 b^7 c^5 d^2 x^2-1800 b^7 c^4 d^3 x^3-2100 b^7 c^3 d^4 x^4-1512 b^7 c^2 d^5 x^5-630 b^7 c d^6 x^6-120 b^7 d^7 x^7}{360 b^8 (a+b x)^{10}}","-\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,"(-36*b^7*c^7 - 28*a*b^6*c^6*d - 21*a^2*b^5*c^5*d^2 - 15*a^3*b^4*c^4*d^3 - 10*a^4*b^3*c^3*d^4 - 6*a^5*b^2*c^2*d^5 - 3*a^6*b*c*d^6 - a^7*d^7 - 280*b^7*c^6*d*x - 210*a*b^6*c^5*d^2*x - 150*a^2*b^5*c^4*d^3*x - 100*a^3*b^4*c^3*d^4*x - 60*a^4*b^3*c^2*d^5*x - 30*a^5*b^2*c*d^6*x - 10*a^6*b*d^7*x - 945*b^7*c^5*d^2*x^2 - 675*a*b^6*c^4*d^3*x^2 - 450*a^2*b^5*c^3*d^4*x^2 - 270*a^3*b^4*c^2*d^5*x^2 - 135*a^4*b^3*c*d^6*x^2 - 45*a^5*b^2*d^7*x^2 - 1800*b^7*c^4*d^3*x^3 - 1200*a*b^6*c^3*d^4*x^3 - 720*a^2*b^5*c^2*d^5*x^3 - 360*a^3*b^4*c*d^6*x^3 - 120*a^4*b^3*d^7*x^3 - 2100*b^7*c^3*d^4*x^4 - 1260*a*b^6*c^2*d^5*x^4 - 630*a^2*b^5*c*d^6*x^4 - 210*a^3*b^4*d^7*x^4 - 1512*b^7*c^2*d^5*x^5 - 756*a*b^6*c*d^6*x^5 - 252*a^2*b^5*d^7*x^5 - 630*b^7*c*d^6*x^6 - 210*a*b^6*d^7*x^6 - 120*b^7*d^7*x^7)/(360*b^8*(a + b*x)^10)","B",1
1294,1,499,120,0.1555752,"\int \frac{(c+d x)^7}{(a+b x)^{12}} \, dx","IntegrateAlgebraic[(c + d*x)^7/(a + b*x)^12,x]","\frac{-a^7 d^7-4 a^6 b c d^6-11 a^6 b d^7 x-10 a^5 b^2 c^2 d^5-44 a^5 b^2 c d^6 x-55 a^5 b^2 d^7 x^2-20 a^4 b^3 c^3 d^4-110 a^4 b^3 c^2 d^5 x-220 a^4 b^3 c d^6 x^2-165 a^4 b^3 d^7 x^3-35 a^3 b^4 c^4 d^3-220 a^3 b^4 c^3 d^4 x-550 a^3 b^4 c^2 d^5 x^2-660 a^3 b^4 c d^6 x^3-330 a^3 b^4 d^7 x^4-56 a^2 b^5 c^5 d^2-385 a^2 b^5 c^4 d^3 x-1100 a^2 b^5 c^3 d^4 x^2-1650 a^2 b^5 c^2 d^5 x^3-1320 a^2 b^5 c d^6 x^4-462 a^2 b^5 d^7 x^5-84 a b^6 c^6 d-616 a b^6 c^5 d^2 x-1925 a b^6 c^4 d^3 x^2-3300 a b^6 c^3 d^4 x^3-3300 a b^6 c^2 d^5 x^4-1848 a b^6 c d^6 x^5-462 a b^6 d^7 x^6-120 b^7 c^7-924 b^7 c^6 d x-3080 b^7 c^5 d^2 x^2-5775 b^7 c^4 d^3 x^3-6600 b^7 c^3 d^4 x^4-4620 b^7 c^2 d^5 x^5-1848 b^7 c d^6 x^6-330 b^7 d^7 x^7}{1320 b^8 (a+b x)^{11}}","\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,"(-120*b^7*c^7 - 84*a*b^6*c^6*d - 56*a^2*b^5*c^5*d^2 - 35*a^3*b^4*c^4*d^3 - 20*a^4*b^3*c^3*d^4 - 10*a^5*b^2*c^2*d^5 - 4*a^6*b*c*d^6 - a^7*d^7 - 924*b^7*c^6*d*x - 616*a*b^6*c^5*d^2*x - 385*a^2*b^5*c^4*d^3*x - 220*a^3*b^4*c^3*d^4*x - 110*a^4*b^3*c^2*d^5*x - 44*a^5*b^2*c*d^6*x - 11*a^6*b*d^7*x - 3080*b^7*c^5*d^2*x^2 - 1925*a*b^6*c^4*d^3*x^2 - 1100*a^2*b^5*c^3*d^4*x^2 - 550*a^3*b^4*c^2*d^5*x^2 - 220*a^4*b^3*c*d^6*x^2 - 55*a^5*b^2*d^7*x^2 - 5775*b^7*c^4*d^3*x^3 - 3300*a*b^6*c^3*d^4*x^3 - 1650*a^2*b^5*c^2*d^5*x^3 - 660*a^3*b^4*c*d^6*x^3 - 165*a^4*b^3*d^7*x^3 - 6600*b^7*c^3*d^4*x^4 - 3300*a*b^6*c^2*d^5*x^4 - 1320*a^2*b^5*c*d^6*x^4 - 330*a^3*b^4*d^7*x^4 - 4620*b^7*c^2*d^5*x^5 - 1848*a*b^6*c*d^6*x^5 - 462*a^2*b^5*d^7*x^5 - 1848*b^7*c*d^6*x^6 - 462*a*b^6*d^7*x^6 - 330*b^7*d^7*x^7)/(1320*b^8*(a + b*x)^11)","B",1
1295,1,499,151,0.1616618,"\int \frac{(c+d x)^7}{(a+b x)^{13}} \, dx","IntegrateAlgebraic[(c + d*x)^7/(a + b*x)^13,x]","\frac{-a^7 d^7-5 a^6 b c d^6-12 a^6 b d^7 x-15 a^5 b^2 c^2 d^5-60 a^5 b^2 c d^6 x-66 a^5 b^2 d^7 x^2-35 a^4 b^3 c^3 d^4-180 a^4 b^3 c^2 d^5 x-330 a^4 b^3 c d^6 x^2-220 a^4 b^3 d^7 x^3-70 a^3 b^4 c^4 d^3-420 a^3 b^4 c^3 d^4 x-990 a^3 b^4 c^2 d^5 x^2-1100 a^3 b^4 c d^6 x^3-495 a^3 b^4 d^7 x^4-126 a^2 b^5 c^5 d^2-840 a^2 b^5 c^4 d^3 x-2310 a^2 b^5 c^3 d^4 x^2-3300 a^2 b^5 c^2 d^5 x^3-2475 a^2 b^5 c d^6 x^4-792 a^2 b^5 d^7 x^5-210 a b^6 c^6 d-1512 a b^6 c^5 d^2 x-4620 a b^6 c^4 d^3 x^2-7700 a b^6 c^3 d^4 x^3-7425 a b^6 c^2 d^5 x^4-3960 a b^6 c d^6 x^5-924 a b^6 d^7 x^6-330 b^7 c^7-2520 b^7 c^6 d x-8316 b^7 c^5 d^2 x^2-15400 b^7 c^4 d^3 x^3-17325 b^7 c^3 d^4 x^4-11880 b^7 c^2 d^5 x^5-4620 b^7 c d^6 x^6-792 b^7 d^7 x^7}{3960 b^8 (a+b x)^{12}}","-\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,"(-330*b^7*c^7 - 210*a*b^6*c^6*d - 126*a^2*b^5*c^5*d^2 - 70*a^3*b^4*c^4*d^3 - 35*a^4*b^3*c^3*d^4 - 15*a^5*b^2*c^2*d^5 - 5*a^6*b*c*d^6 - a^7*d^7 - 2520*b^7*c^6*d*x - 1512*a*b^6*c^5*d^2*x - 840*a^2*b^5*c^4*d^3*x - 420*a^3*b^4*c^3*d^4*x - 180*a^4*b^3*c^2*d^5*x - 60*a^5*b^2*c*d^6*x - 12*a^6*b*d^7*x - 8316*b^7*c^5*d^2*x^2 - 4620*a*b^6*c^4*d^3*x^2 - 2310*a^2*b^5*c^3*d^4*x^2 - 990*a^3*b^4*c^2*d^5*x^2 - 330*a^4*b^3*c*d^6*x^2 - 66*a^5*b^2*d^7*x^2 - 15400*b^7*c^4*d^3*x^3 - 7700*a*b^6*c^3*d^4*x^3 - 3300*a^2*b^5*c^2*d^5*x^3 - 1100*a^3*b^4*c*d^6*x^3 - 220*a^4*b^3*d^7*x^3 - 17325*b^7*c^3*d^4*x^4 - 7425*a*b^6*c^2*d^5*x^4 - 2475*a^2*b^5*c*d^6*x^4 - 495*a^3*b^4*d^7*x^4 - 11880*b^7*c^2*d^5*x^5 - 3960*a*b^6*c*d^6*x^5 - 792*a^2*b^5*d^7*x^5 - 4620*b^7*c*d^6*x^6 - 924*a*b^6*d^7*x^6 - 792*b^7*d^7*x^7)/(3960*b^8*(a + b*x)^12)","B",1
1296,1,499,198,0.1618663,"\int \frac{(c+d x)^7}{(a+b x)^{14}} \, dx","IntegrateAlgebraic[(c + d*x)^7/(a + b*x)^14,x]","\frac{-a^7 d^7-6 a^6 b c d^6-13 a^6 b d^7 x-21 a^5 b^2 c^2 d^5-78 a^5 b^2 c d^6 x-78 a^5 b^2 d^7 x^2-56 a^4 b^3 c^3 d^4-273 a^4 b^3 c^2 d^5 x-468 a^4 b^3 c d^6 x^2-286 a^4 b^3 d^7 x^3-126 a^3 b^4 c^4 d^3-728 a^3 b^4 c^3 d^4 x-1638 a^3 b^4 c^2 d^5 x^2-1716 a^3 b^4 c d^6 x^3-715 a^3 b^4 d^7 x^4-252 a^2 b^5 c^5 d^2-1638 a^2 b^5 c^4 d^3 x-4368 a^2 b^5 c^3 d^4 x^2-6006 a^2 b^5 c^2 d^5 x^3-4290 a^2 b^5 c d^6 x^4-1287 a^2 b^5 d^7 x^5-462 a b^6 c^6 d-3276 a b^6 c^5 d^2 x-9828 a b^6 c^4 d^3 x^2-16016 a b^6 c^3 d^4 x^3-15015 a b^6 c^2 d^5 x^4-7722 a b^6 c d^6 x^5-1716 a b^6 d^7 x^6-792 b^7 c^7-6006 b^7 c^6 d x-19656 b^7 c^5 d^2 x^2-36036 b^7 c^4 d^3 x^3-40040 b^7 c^3 d^4 x^4-27027 b^7 c^2 d^5 x^5-10296 b^7 c d^6 x^6-1716 b^7 d^7 x^7}{10296 b^8 (a+b x)^{13}}","-\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,"(-792*b^7*c^7 - 462*a*b^6*c^6*d - 252*a^2*b^5*c^5*d^2 - 126*a^3*b^4*c^4*d^3 - 56*a^4*b^3*c^3*d^4 - 21*a^5*b^2*c^2*d^5 - 6*a^6*b*c*d^6 - a^7*d^7 - 6006*b^7*c^6*d*x - 3276*a*b^6*c^5*d^2*x - 1638*a^2*b^5*c^4*d^3*x - 728*a^3*b^4*c^3*d^4*x - 273*a^4*b^3*c^2*d^5*x - 78*a^5*b^2*c*d^6*x - 13*a^6*b*d^7*x - 19656*b^7*c^5*d^2*x^2 - 9828*a*b^6*c^4*d^3*x^2 - 4368*a^2*b^5*c^3*d^4*x^2 - 1638*a^3*b^4*c^2*d^5*x^2 - 468*a^4*b^3*c*d^6*x^2 - 78*a^5*b^2*d^7*x^2 - 36036*b^7*c^4*d^3*x^3 - 16016*a*b^6*c^3*d^4*x^3 - 6006*a^2*b^5*c^2*d^5*x^3 - 1716*a^3*b^4*c*d^6*x^3 - 286*a^4*b^3*d^7*x^3 - 40040*b^7*c^3*d^4*x^4 - 15015*a*b^6*c^2*d^5*x^4 - 4290*a^2*b^5*c*d^6*x^4 - 715*a^3*b^4*d^7*x^4 - 27027*b^7*c^2*d^5*x^5 - 7722*a*b^6*c*d^6*x^5 - 1287*a^2*b^5*d^7*x^5 - 10296*b^7*c*d^6*x^6 - 1716*a*b^6*d^7*x^6 - 1716*b^7*d^7*x^7)/(10296*b^8*(a + b*x)^13)","B",1
1297,1,499,200,0.1611293,"\int \frac{(c+d x)^7}{(a+b x)^{15}} \, dx","IntegrateAlgebraic[(c + d*x)^7/(a + b*x)^15,x]","\frac{-a^7 d^7-7 a^6 b c d^6-14 a^6 b d^7 x-28 a^5 b^2 c^2 d^5-98 a^5 b^2 c d^6 x-91 a^5 b^2 d^7 x^2-84 a^4 b^3 c^3 d^4-392 a^4 b^3 c^2 d^5 x-637 a^4 b^3 c d^6 x^2-364 a^4 b^3 d^7 x^3-210 a^3 b^4 c^4 d^3-1176 a^3 b^4 c^3 d^4 x-2548 a^3 b^4 c^2 d^5 x^2-2548 a^3 b^4 c d^6 x^3-1001 a^3 b^4 d^7 x^4-462 a^2 b^5 c^5 d^2-2940 a^2 b^5 c^4 d^3 x-7644 a^2 b^5 c^3 d^4 x^2-10192 a^2 b^5 c^2 d^5 x^3-7007 a^2 b^5 c d^6 x^4-2002 a^2 b^5 d^7 x^5-924 a b^6 c^6 d-6468 a b^6 c^5 d^2 x-19110 a b^6 c^4 d^3 x^2-30576 a b^6 c^3 d^4 x^3-28028 a b^6 c^2 d^5 x^4-14014 a b^6 c d^6 x^5-3003 a b^6 d^7 x^6-1716 b^7 c^7-12936 b^7 c^6 d x-42042 b^7 c^5 d^2 x^2-76440 b^7 c^4 d^3 x^3-84084 b^7 c^3 d^4 x^4-56056 b^7 c^2 d^5 x^5-21021 b^7 c d^6 x^6-3432 b^7 d^7 x^7}{24024 b^8 (a+b x)^{14}}","-\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,"(-1716*b^7*c^7 - 924*a*b^6*c^6*d - 462*a^2*b^5*c^5*d^2 - 210*a^3*b^4*c^4*d^3 - 84*a^4*b^3*c^3*d^4 - 28*a^5*b^2*c^2*d^5 - 7*a^6*b*c*d^6 - a^7*d^7 - 12936*b^7*c^6*d*x - 6468*a*b^6*c^5*d^2*x - 2940*a^2*b^5*c^4*d^3*x - 1176*a^3*b^4*c^3*d^4*x - 392*a^4*b^3*c^2*d^5*x - 98*a^5*b^2*c*d^6*x - 14*a^6*b*d^7*x - 42042*b^7*c^5*d^2*x^2 - 19110*a*b^6*c^4*d^3*x^2 - 7644*a^2*b^5*c^3*d^4*x^2 - 2548*a^3*b^4*c^2*d^5*x^2 - 637*a^4*b^3*c*d^6*x^2 - 91*a^5*b^2*d^7*x^2 - 76440*b^7*c^4*d^3*x^3 - 30576*a*b^6*c^3*d^4*x^3 - 10192*a^2*b^5*c^2*d^5*x^3 - 2548*a^3*b^4*c*d^6*x^3 - 364*a^4*b^3*d^7*x^3 - 84084*b^7*c^3*d^4*x^4 - 28028*a*b^6*c^2*d^5*x^4 - 7007*a^2*b^5*c*d^6*x^4 - 1001*a^3*b^4*d^7*x^4 - 56056*b^7*c^2*d^5*x^5 - 14014*a*b^6*c*d^6*x^5 - 2002*a^2*b^5*d^7*x^5 - 21021*b^7*c*d^6*x^6 - 3003*a*b^6*d^7*x^6 - 3432*b^7*d^7*x^7)/(24024*b^8*(a + b*x)^14)","B",1
1298,1,499,200,0.1593976,"\int \frac{(c+d x)^7}{(a+b x)^{16}} \, dx","IntegrateAlgebraic[(c + d*x)^7/(a + b*x)^16,x]","\frac{-a^7 d^7-8 a^6 b c d^6-15 a^6 b d^7 x-36 a^5 b^2 c^2 d^5-120 a^5 b^2 c d^6 x-105 a^5 b^2 d^7 x^2-120 a^4 b^3 c^3 d^4-540 a^4 b^3 c^2 d^5 x-840 a^4 b^3 c d^6 x^2-455 a^4 b^3 d^7 x^3-330 a^3 b^4 c^4 d^3-1800 a^3 b^4 c^3 d^4 x-3780 a^3 b^4 c^2 d^5 x^2-3640 a^3 b^4 c d^6 x^3-1365 a^3 b^4 d^7 x^4-792 a^2 b^5 c^5 d^2-4950 a^2 b^5 c^4 d^3 x-12600 a^2 b^5 c^3 d^4 x^2-16380 a^2 b^5 c^2 d^5 x^3-10920 a^2 b^5 c d^6 x^4-3003 a^2 b^5 d^7 x^5-1716 a b^6 c^6 d-11880 a b^6 c^5 d^2 x-34650 a b^6 c^4 d^3 x^2-54600 a b^6 c^3 d^4 x^3-49140 a b^6 c^2 d^5 x^4-24024 a b^6 c d^6 x^5-5005 a b^6 d^7 x^6-3432 b^7 c^7-25740 b^7 c^6 d x-83160 b^7 c^5 d^2 x^2-150150 b^7 c^4 d^3 x^3-163800 b^7 c^3 d^4 x^4-108108 b^7 c^2 d^5 x^5-40040 b^7 c d^6 x^6-6435 b^7 d^7 x^7}{51480 b^8 (a+b x)^{15}}","-\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,"(-3432*b^7*c^7 - 1716*a*b^6*c^6*d - 792*a^2*b^5*c^5*d^2 - 330*a^3*b^4*c^4*d^3 - 120*a^4*b^3*c^3*d^4 - 36*a^5*b^2*c^2*d^5 - 8*a^6*b*c*d^6 - a^7*d^7 - 25740*b^7*c^6*d*x - 11880*a*b^6*c^5*d^2*x - 4950*a^2*b^5*c^4*d^3*x - 1800*a^3*b^4*c^3*d^4*x - 540*a^4*b^3*c^2*d^5*x - 120*a^5*b^2*c*d^6*x - 15*a^6*b*d^7*x - 83160*b^7*c^5*d^2*x^2 - 34650*a*b^6*c^4*d^3*x^2 - 12600*a^2*b^5*c^3*d^4*x^2 - 3780*a^3*b^4*c^2*d^5*x^2 - 840*a^4*b^3*c*d^6*x^2 - 105*a^5*b^2*d^7*x^2 - 150150*b^7*c^4*d^3*x^3 - 54600*a*b^6*c^3*d^4*x^3 - 16380*a^2*b^5*c^2*d^5*x^3 - 3640*a^3*b^4*c*d^6*x^3 - 455*a^4*b^3*d^7*x^3 - 163800*b^7*c^3*d^4*x^4 - 49140*a*b^6*c^2*d^5*x^4 - 10920*a^2*b^5*c*d^6*x^4 - 1365*a^3*b^4*d^7*x^4 - 108108*b^7*c^2*d^5*x^5 - 24024*a*b^6*c*d^6*x^5 - 3003*a^2*b^5*d^7*x^5 - 40040*b^7*c*d^6*x^6 - 5005*a*b^6*d^7*x^6 - 6435*b^7*d^7*x^7)/(51480*b^8*(a + b*x)^15)","B",1
1299,1,2194,275,0.7094083,"\int (a+b x)^{12} (c+d x)^{10} \, dx","IntegrateAlgebraic[(a + b*x)^12*(c + d*x)^10,x]","\text{Result too large to show}","\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,"(14872858*a^12*c^10*x + 89237148*a^11*b*c^10*x^2 + 74364290*a^12*c^9*d*x^2 + 327202876*a^10*b^2*c^10*x^3 + 594914320*a^11*b*c^9*d*x^3 + 223092870*a^12*c^8*d^2*x^3 + 818007190*a^9*b^3*c^10*x^4 + 2454021570*a^10*b^2*c^9*d*x^4 + 2007835830*a^11*b*c^8*d^2*x^4 + 446185740*a^12*c^7*d^3*x^4 + 1472412942*a^8*b^4*c^10*x^5 + 6544057520*a^9*b^3*c^9*d*x^5 + 8834477652*a^10*b^2*c^8*d^2*x^5 + 4283383104*a^11*b*c^7*d^3*x^5 + 624660036*a^12*c^6*d^4*x^5 + 1963217256*a^7*b^5*c^10*x^6 + 12270107850*a^8*b^4*c^9*d*x^6 + 24540215700*a^9*b^3*c^8*d^2*x^6 + 19632172560*a^10*b^2*c^7*d^3*x^6 + 6246600360*a^11*b*c^6*d^4*x^6 + 624660036*a^12*c^5*d^5*x^6 + 1963217256*a^6*b^6*c^10*x^7 + 16827576480*a^7*b^5*c^9*d*x^7 + 47327558850*a^8*b^4*c^8*d^2*x^7 + 56091921600*a^9*b^3*c^7*d^3*x^7 + 29448258840*a^10*b^2*c^6*d^4*x^7 + 6425074656*a^11*b*c^5*d^5*x^7 + 446185740*a^12*c^4*d^6*x^7 + 1472412942*a^5*b^7*c^10*x^8 + 17178150990*a^6*b^6*c^9*d*x^8 + 66258582390*a^7*b^5*c^8*d^2*x^8 + 110430970650*a^8*b^4*c^7*d^3*x^8 + 85890754950*a^9*b^3*c^6*d^4*x^8 + 30920671782*a^10*b^2*c^5*d^5*x^8 + 4684950270*a^11*b*c^4*d^6*x^8 + 223092870*a^12*c^3*d^7*x^8 + 818007190*a^4*b^8*c^10*x^9 + 13088115040*a^5*b^7*c^9*d*x^9 + 68712603960*a^6*b^6*c^8*d^2*x^9 + 157057380480*a^7*b^5*c^7*d^3*x^9 + 171781509900*a^8*b^4*c^6*d^4*x^9 + 91616805280*a^9*b^3*c^5*d^5*x^9 + 22904201320*a^10*b^2*c^4*d^6*x^9 + 2379657280*a^11*b*c^3*d^7*x^9 + 74364290*a^12*c^2*d^8*x^9 + 327202876*a^3*b^9*c^10*x^10 + 7362064710*a^4*b^8*c^9*d*x^10 + 53006865912*a^5*b^7*c^8*d^2*x^10 + 164910249504*a^6*b^6*c^7*d^3*x^10 + 247365374256*a^7*b^5*c^6*d^4*x^10 + 185524030692*a^8*b^4*c^5*d^5*x^10 + 68712603960*a^9*b^3*c^4*d^6*x^10 + 11779303536*a^10*b^2*c^3*d^7*x^10 + 803134332*a^11*b*c^2*d^8*x^10 + 14872858*a^12*c*d^9*x^10 + 89237148*a^2*b^10*c^10*x^11 + 2974571600*a^3*b^9*c^9*d*x^11 + 30117537450*a^4*b^8*c^8*d^2*x^11 + 128501493120*a^5*b^7*c^7*d^3*x^11 + 262357215120*a^6*b^6*c^6*d^4*x^11 + 269853135552*a^7*b^5*c^5*d^5*x^11 + 140548508100*a^8*b^4*c^4*d^6*x^11 + 35694859200*a^9*b^3*c^3*d^7*x^11 + 4015671660*a^10*b^2*c^2*d^8*x^11 + 162249360*a^11*b*c*d^9*x^11 + 1352078*a^12*d^10*x^11 + 14872858*a*b^11*c^10*x^12 + 818007190*a^2*b^10*c^9*d*x^12 + 12270107850*a^3*b^9*c^8*d^2*x^12 + 73620647100*a^4*b^8*c^7*d^3*x^12 + 206137811880*a^5*b^7*c^6*d^4*x^12 + 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54970083168*a^3*b^9*c^5*d^5*x^15 + 103068905940*a^4*b^8*c^4*d^6*x^15 + 94234428288*a^5*b^7*c^3*d^7*x^15 + 41227562376*a^6*b^6*c^2*d^8*x^15 + 7852869024*a^7*b^5*c*d^9*x^15 + 490804314*a^8*b^4*d^10*x^15 + 111546435*b^12*c^7*d^3*x^16 + 2342475135*a*b^11*c^6*d^4*x^16 + 15460335891*a^2*b^10*c^5*d^5*x^16 + 42945377475*a^3*b^9*c^4*d^6*x^16 + 55215485325*a^4*b^8*c^3*d^7*x^16 + 33129291195*a^5*b^7*c^2*d^8*x^16 + 8589075495*a^6*b^6*c*d^9*x^16 + 736206471*a^7*b^5*d^10*x^16 + 183723540*b^12*c^6*d^4*x^17 + 2645618976*a*b^11*c^5*d^5*x^17 + 12125753640*a^2*b^10*c^4*d^6*x^17 + 23096673600*a^3*b^9*c^3*d^7*x^17 + 19487818350*a^4*b^8*c^2*d^8*x^17 + 6929002080*a^5*b^7*c*d^9*x^17 + 808383576*a^6*b^6*d^10*x^17 + 208220012*b^12*c^5*d^5*x^18 + 2082200120*a*b^11*c^4*d^6*x^18 + 6544057520*a^2*b^10*c^3*d^7*x^18 + 8180071900*a^3*b^9*c^2*d^8*x^18 + 4090035950*a^4*b^8*c*d^9*x^18 + 654405752*a^5*b^7*d^10*x^18 + 164384220*b^12*c^4*d^6*x^19 + 1127206080*a*b^11*c^3*d^7*x^19 + 2324862540*a^2*b^10*c^2*d^8*x^19 + 1722120400*a^3*b^9*c*d^9*x^19 + 387477090*a^4*b^8*d^10*x^19 + 89237148*b^12*c^3*d^7*x^20 + 401567166*a*b^11*c^2*d^8*x^20 + 490804314*a^2*b^10*c*d^9*x^20 + 163601438*a^3*b^9*d^10*x^20 + 31870410*b^12*c^2*d^8*x^21 + 84987760*a*b^11*c*d^9*x^21 + 46743268*a^2*b^10*d^10*x^21 + 6760390*b^12*c*d^9*x^22 + 8112468*a*b^11*d^10*x^22 + 646646*b^12*d^10*x^23)/14872858","B",1
1300,1,2017,279,0.6188252,"\int (a+b x)^{11} (c+d x)^{10} \, dx","IntegrateAlgebraic[(a + b*x)^11*(c + d*x)^10,x]","\text{Result too large to show}","\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,"(7759752*a^11*c^10*x + 42678636*a^10*b*c^10*x^2 + 38798760*a^11*c^9*d*x^2 + 142262120*a^9*b^2*c^10*x^3 + 284524240*a^10*b*c^9*d*x^3 + 116396280*a^11*c^8*d^2*x^3 + 320089770*a^8*b^3*c^10*x^4 + 1066965900*a^9*b^2*c^9*d*x^4 + 960269310*a^10*b*c^8*d^2*x^4 + 232792560*a^11*c^7*d^3*x^4 + 512143632*a^7*b^4*c^10*x^5 + 2560718160*a^8*b^3*c^9*d*x^5 + 3841077240*a^9*b^2*c^8*d^2*x^5 + 2048574528*a^10*b*c^7*d^3*x^5 + 325909584*a^11*c^6*d^4*x^5 + 597500904*a^6*b^5*c^10*x^6 + 4267863600*a^7*b^4*c^9*d*x^6 + 9602693100*a^8*b^3*c^8*d^2*x^6 + 8535727200*a^9*b^2*c^7*d^3*x^6 + 2987504520*a^10*b*c^6*d^4*x^6 + 325909584*a^11*c^5*d^5*x^6 + 512143632*a^5*b^6*c^10*x^7 + 5121436320*a^6*b^5*c^9*d*x^7 + 16461759600*a^7*b^4*c^8*d^2*x^7 + 21949012800*a^8*b^3*c^7*d^3*x^7 + 12803590800*a^9*b^2*c^6*d^4*x^7 + 3072861792*a^10*b*c^5*d^5*x^7 + 232792560*a^11*c^4*d^6*x^7 + 320089770*a^4*b^7*c^10*x^8 + 4481256780*a^5*b^6*c^9*d*x^8 + 20165655510*a^6*b^5*c^8*d^2*x^8 + 38410772400*a^7*b^4*c^7*d^3*x^8 + 33609425850*a^8*b^3*c^6*d^4*x^8 + 13443770340*a^9*b^2*c^5*d^5*x^8 + 2240628390*a^10*b*c^4*d^6*x^8 + 116396280*a^11*c^3*d^7*x^8 + 142262120*a^3*b^8*c^10*x^9 + 2845242400*a^4*b^7*c^9*d*x^9 + 17925027120*a^5*b^6*c^8*d^2*x^9 + 47800072320*a^6*b^5*c^7*d^3*x^9 + 59750090400*a^7*b^4*c^6*d^4*x^9 + 35850054240*a^8*b^3*c^5*d^5*x^9 + 9958348400*a^9*b^2*c^4*d^6*x^9 + 1138096960*a^10*b*c^3*d^7*x^9 + 38798760*a^11*c^2*d^8*x^9 + 42678636*a^2*b^9*c^10*x^10 + 1280359080*a^3*b^8*c^9*d*x^10 + 11523231720*a^4*b^7*c^8*d^2*x^10 + 43020065088*a^5*b^6*c^7*d^3*x^10 + 75285113904*a^6*b^5*c^6*d^4*x^10 + 64530097632*a^7*b^4*c^5*d^5*x^10 + 26887540680*a^8*b^3*c^4*d^6*x^10 + 5121436320*a^9*b^2*c^3*d^7*x^10 + 384107724*a^10*b*c^2*d^8*x^10 + 7759752*a^11*c*d^9*x^10 + 7759752*a*b^10*c^10*x^11 + 387987600*a^2*b^9*c^9*d*x^11 + 5237832600*a^3*b^8*c^8*d^2*x^11 + 27935107200*a^4*b^7*c^7*d^3*x^11 + 68441012640*a^5*b^6*c^6*d^4*x^11 + 82129215168*a^6*b^5*c^5*d^5*x^11 + 48886437600*a^7*b^4*c^4*d^6*x^11 + 13967553600*a^8*b^3*c^3*d^7*x^11 + 1745944200*a^9*b^2*c^2*d^8*x^11 + 77597520*a^10*b*c*d^9*x^11 + 705432*a^11*d^10*x^11 + 646646*b^11*c^10*x^12 + 71131060*a*b^10*c^9*d*x^12 + 1600448850*a^2*b^9*c^8*d^2*x^12 + 12803590800*a^3*b^8*c^7*d^3*x^12 + 44812567800*a^4*b^7*c^6*d^4*x^12 + 75285113904*a^5*b^6*c^5*d^5*x^12 + 62737594920*a^6*b^5*c^4*d^6*x^12 + 25607181600*a^7*b^4*c^3*d^7*x^12 + 4801346550*a^8*b^3*c^2*d^8*x^12 + 355655300*a^9*b^2*c*d^9*x^12 + 7113106*a^10*b*d^10*x^12 + 5969040*b^11*c^9*d*x^13 + 295467480*a*b^10*c^8*d^2*x^13 + 3939566400*a^2*b^9*c^7*d^3*x^13 + 20682723600*a^3*b^8*c^6*d^4*x^13 + 49638536640*a^4*b^7*c^5*d^5*x^13 + 57911626080*a^5*b^6*c^4*d^6*x^13 + 33092357760*a^6*b^5*c^3*d^7*x^13 + 8864024400*a^7*b^4*c^2*d^8*x^13 + 984891600*a^8*b^3*c*d^9*x^13 + 32829720*a^9*b^2*d^10*x^13 + 24942060*b^11*c^8*d^2*x^14 + 731633760*a*b^10*c^7*d^3*x^14 + 6401795400*a^2*b^9*c^6*d^4*x^14 + 23046463440*a^3*b^8*c^5*d^5*x^14 + 38410772400*a^4*b^7*c^4*d^6*x^14 + 30728617920*a^5*b^6*c^3*d^7*x^14 + 11523231720*a^6*b^5*c^2*d^8*x^14 + 1829084400*a^7*b^4*c*d^9*x^14 + 91454220*a^8*b^3*d^10*x^14 + 62078016*b^11*c^7*d^3*x^15 + 1195001808*a*b^10*c^6*d^4*x^15 + 7170010848*a^2*b^9*c^5*d^5*x^15 + 17925027120*a^3*b^8*c^4*d^6*x^15 + 20485745280*a^4*b^7*c^3*d^7*x^15 + 10755016272*a^5*b^6*c^2*d^8*x^15 + 2390003616*a^6*b^5*c*d^9*x^15 + 170714544*a^7*b^4*d^10*x^15 + 101846745*b^11*c^6*d^4*x^16 + 1344377034*a*b^10*c^5*d^5*x^16 + 5601570975*a^2*b^9*c^4*d^6*x^16 + 9602693100*a^3*b^8*c^3*d^7*x^16 + 7202019825*a^4*b^7*c^2*d^8*x^16 + 2240628390*a^5*b^6*c*d^9*x^16 + 224062839*a^6*b^5*d^10*x^16 + 115026912*b^11*c^5*d^5*x^17 + 1054413360*a*b^10*c^4*d^6*x^17 + 3012609600*a^2*b^9*c^3*d^7*x^17 + 3389185800*a^3*b^8*c^2*d^8*x^17 + 1506304800*a^4*b^7*c*d^9*x^17 + 210882672*a^5*b^6*d^10*x^17 + 90530440*b^11*c^4*d^6*x^18 + 569048480*a*b^10*c^3*d^7*x^18 + 1066965900*a^2*b^9*c^2*d^8*x^18 + 711310600*a^3*b^8*c*d^9*x^18 + 142262120*a^4*b^7*d^10*x^18 + 49008960*b^11*c^3*d^7*x^19 + 202161960*a*b^10*c^2*d^8*x^19 + 224624400*a^2*b^9*c*d^9*x^19 + 67387320*a^3*b^8*d^10*x^19 + 17459442*b^11*c^2*d^8*x^20 + 42678636*a*b^10*c*d^9*x^20 + 21339318*a^2*b^9*d^10*x^20 + 3695120*b^11*c*d^9*x^21 + 4064632*a*b^10*d^10*x^21 + 352716*b^11*d^10*x^22)/7759752","B",1
1301,1,1840,279,0.4951721,"\int (a+b x)^{10} (c+d x)^{10} \, dx","IntegrateAlgebraic[(a + b*x)^10*(c + d*x)^10,x]","\frac{184756 b^{10} d^{10} x^{21}+1939938 a b^9 d^{10} x^{20}+1939938 b^{10} c d^9 x^{20}+9189180 a^2 b^8 d^{10} x^{19}+20420400 a b^9 c d^9 x^{19}+9189180 b^{10} c^2 d^8 x^{19}+25865840 a^3 b^7 d^{10} x^{18}+96996900 a^2 b^8 c d^9 x^{18}+96996900 a b^9 c^2 d^8 x^{18}+25865840 b^{10} c^3 d^7 x^{18}+47927880 a^4 b^6 d^{10} x^{17}+273873600 a^3 b^7 c d^9 x^{17}+462161700 a^2 b^8 c^2 d^8 x^{17}+273873600 a b^9 c^3 d^7 x^{17}+47927880 b^{10} c^4 d^6 x^{17}+61108047 a^5 b^5 d^{10} x^{16}+509233725 a^4 b^6 c d^9 x^{16}+1309458150 a^3 b^7 c^2 d^8 x^{16}+1309458150 a^2 b^8 c^3 d^7 x^{16}+509233725 a b^9 c^4 d^6 x^{16}+61108047 b^{10} c^5 d^5 x^{16}+54318264 a^6 b^4 d^{10} x^{15}+651819168 a^5 b^5 c d^9 x^{15}+2444321880 a^4 b^6 c^2 d^8 x^{15}+3724680960 a^3 b^7 c^3 d^7 x^{15}+2444321880 a^2 b^8 c^4 d^6 x^{15}+651819168 a b^9 c^5 d^5 x^{15}+54318264 b^{10} c^6 d^4 x^{15}+33256080 a^7 b^3 d^{10} x^{14}+581981400 a^6 b^4 c d^9 x^{14}+3142699560 a^5 b^5 c^2 d^8 x^{14}+6983776800 a^4 b^6 c^3 d^7 x^{14}+6983776800 a^3 b^7 c^4 d^6 x^{14}+3142699560 a^2 b^8 c^5 d^5 x^{14}+581981400 a b^9 c^6 d^4 x^{14}+33256080 b^{10} c^7 d^3 x^{14}+13430340 a^8 b^2 d^{10} x^{13}+358142400 a^7 b^3 c d^9 x^{13}+2820371400 a^6 b^4 c^2 d^8 x^{13}+9025188480 a^5 b^5 c^3 d^7 x^{13}+13161733200 a^4 b^6 c^4 d^6 x^{13}+9025188480 a^3 b^7 c^5 d^5 x^{13}+2820371400 a^2 b^8 c^6 d^4 x^{13}+358142400 a b^9 c^7 d^3 x^{13}+13430340 b^{10} c^8 d^2 x^{13}+3233230 a^9 b d^{10} x^{12}+145495350 a^8 b^2 c d^9 x^{12}+1745944200 a^7 b^3 c^2 d^8 x^{12}+8147739600 a^6 b^4 c^3 d^7 x^{12}+17110253160 a^5 b^5 c^4 d^6 x^{12}+17110253160 a^4 b^6 c^5 d^5 x^{12}+8147739600 a^3 b^7 c^6 d^4 x^{12}+1745944200 a^2 b^8 c^7 d^3 x^{12}+145495350 a b^9 c^8 d^2 x^{12}+3233230 b^{10} c^9 d x^{12}+352716 b^{10} c^{10} x^{11}+352716 a^{10} d^{10} x^{11}+35271600 a^9 b c d^9 x^{11}+714249900 a^8 b^2 c^2 d^8 x^{11}+5079110400 a^7 b^3 c^3 d^7 x^{11}+15554775600 a^6 b^4 c^4 d^6 x^{11}+22398876864 a^5 b^5 c^5 d^5 x^{11}+15554775600 a^4 b^6 c^6 d^4 x^{11}+5079110400 a^3 b^7 c^7 d^3 x^{11}+714249900 a^2 b^8 c^8 d^2 x^{11}+35271600 a b^9 c^9 d x^{11}+3879876 a b^9 c^{10} x^{10}+3879876 a^{10} c d^9 x^{10}+174594420 a^9 b c^2 d^8 x^{10}+2095133040 a^8 b^2 c^3 d^7 x^{10}+9777287520 a^7 b^3 c^4 d^6 x^{10}+20532303792 a^6 b^4 c^5 d^5 x^{10}+20532303792 a^5 b^5 c^6 d^4 x^{10}+9777287520 a^4 b^6 c^7 d^3 x^{10}+2095133040 a^3 b^7 c^8 d^2 x^{10}+174594420 a^2 b^8 c^9 d x^{10}+19399380 a^2 b^8 c^{10} x^9+19399380 a^{10} c^2 d^8 x^9+517316800 a^9 b c^3 d^7 x^9+4073869800 a^8 b^2 c^4 d^6 x^9+13036383360 a^7 b^3 c^5 d^5 x^9+19011392400 a^6 b^4 c^6 d^4 x^9+13036383360 a^5 b^5 c^7 d^3 x^9+4073869800 a^4 b^6 c^8 d^2 x^9+517316800 a^3 b^7 c^9 d x^9+58198140 a^3 b^7 c^{10} x^8+58198140 a^{10} c^3 d^7 x^8+1018467450 a^9 b c^4 d^6 x^8+5499724230 a^8 b^2 c^5 d^5 x^8+12221609400 a^7 b^3 c^6 d^4 x^8+12221609400 a^6 b^4 c^7 d^3 x^8+5499724230 a^5 b^5 c^8 d^2 x^8+1018467450 a^4 b^6 c^9 d x^8+116396280 a^4 b^6 c^{10} x^7+116396280 a^{10} c^4 d^6 x^7+1396755360 a^9 b c^5 d^5 x^7+5237832600 a^8 b^2 c^6 d^4 x^7+7981459200 a^7 b^3 c^7 d^3 x^7+5237832600 a^6 b^4 c^8 d^2 x^7+1396755360 a^5 b^5 c^9 d x^7+162954792 a^5 b^5 c^{10} x^6+162954792 a^{10} c^5 d^5 x^6+1357956600 a^9 b c^6 d^4 x^6+3491888400 a^8 b^2 c^7 d^3 x^6+3491888400 a^7 b^3 c^8 d^2 x^6+1357956600 a^6 b^4 c^9 d x^6+162954792 a^6 b^4 c^{10} x^5+162954792 a^{10} c^6 d^4 x^5+931170240 a^9 b c^7 d^3 x^5+1571349780 a^8 b^2 c^8 d^2 x^5+931170240 a^7 b^3 c^9 d x^5+116396280 a^7 b^3 c^{10} x^4+116396280 a^{10} c^7 d^3 x^4+436486050 a^9 b c^8 d^2 x^4+436486050 a^8 b^2 c^9 d x^4+58198140 a^8 b^2 c^{10} x^3+58198140 a^{10} c^8 d^2 x^3+129329200 a^9 b c^9 d x^3+19399380 a^9 b c^{10} x^2+19399380 a^{10} c^9 d x^2+3879876 a^{10} c^{10} x}{3879876}","\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,"(3879876*a^10*c^10*x + 19399380*a^9*b*c^10*x^2 + 19399380*a^10*c^9*d*x^2 + 58198140*a^8*b^2*c^10*x^3 + 129329200*a^9*b*c^9*d*x^3 + 58198140*a^10*c^8*d^2*x^3 + 116396280*a^7*b^3*c^10*x^4 + 436486050*a^8*b^2*c^9*d*x^4 + 436486050*a^9*b*c^8*d^2*x^4 + 116396280*a^10*c^7*d^3*x^4 + 162954792*a^6*b^4*c^10*x^5 + 931170240*a^7*b^3*c^9*d*x^5 + 1571349780*a^8*b^2*c^8*d^2*x^5 + 931170240*a^9*b*c^7*d^3*x^5 + 162954792*a^10*c^6*d^4*x^5 + 162954792*a^5*b^5*c^10*x^6 + 1357956600*a^6*b^4*c^9*d*x^6 + 3491888400*a^7*b^3*c^8*d^2*x^6 + 3491888400*a^8*b^2*c^7*d^3*x^6 + 1357956600*a^9*b*c^6*d^4*x^6 + 162954792*a^10*c^5*d^5*x^6 + 116396280*a^4*b^6*c^10*x^7 + 1396755360*a^5*b^5*c^9*d*x^7 + 5237832600*a^6*b^4*c^8*d^2*x^7 + 7981459200*a^7*b^3*c^7*d^3*x^7 + 5237832600*a^8*b^2*c^6*d^4*x^7 + 1396755360*a^9*b*c^5*d^5*x^7 + 116396280*a^10*c^4*d^6*x^7 + 58198140*a^3*b^7*c^10*x^8 + 1018467450*a^4*b^6*c^9*d*x^8 + 5499724230*a^5*b^5*c^8*d^2*x^8 + 12221609400*a^6*b^4*c^7*d^3*x^8 + 12221609400*a^7*b^3*c^6*d^4*x^8 + 5499724230*a^8*b^2*c^5*d^5*x^8 + 1018467450*a^9*b*c^4*d^6*x^8 + 58198140*a^10*c^3*d^7*x^8 + 19399380*a^2*b^8*c^10*x^9 + 517316800*a^3*b^7*c^9*d*x^9 + 4073869800*a^4*b^6*c^8*d^2*x^9 + 13036383360*a^5*b^5*c^7*d^3*x^9 + 19011392400*a^6*b^4*c^6*d^4*x^9 + 13036383360*a^7*b^3*c^5*d^5*x^9 + 4073869800*a^8*b^2*c^4*d^6*x^9 + 517316800*a^9*b*c^3*d^7*x^9 + 19399380*a^10*c^2*d^8*x^9 + 3879876*a*b^9*c^10*x^10 + 174594420*a^2*b^8*c^9*d*x^10 + 2095133040*a^3*b^7*c^8*d^2*x^10 + 9777287520*a^4*b^6*c^7*d^3*x^10 + 20532303792*a^5*b^5*c^6*d^4*x^10 + 20532303792*a^6*b^4*c^5*d^5*x^10 + 9777287520*a^7*b^3*c^4*d^6*x^10 + 2095133040*a^8*b^2*c^3*d^7*x^10 + 174594420*a^9*b*c^2*d^8*x^10 + 3879876*a^10*c*d^9*x^10 + 352716*b^10*c^10*x^11 + 35271600*a*b^9*c^9*d*x^11 + 714249900*a^2*b^8*c^8*d^2*x^11 + 5079110400*a^3*b^7*c^7*d^3*x^11 + 15554775600*a^4*b^6*c^6*d^4*x^11 + 22398876864*a^5*b^5*c^5*d^5*x^11 + 15554775600*a^6*b^4*c^4*d^6*x^11 + 5079110400*a^7*b^3*c^3*d^7*x^11 + 714249900*a^8*b^2*c^2*d^8*x^11 + 35271600*a^9*b*c*d^9*x^11 + 352716*a^10*d^10*x^11 + 3233230*b^10*c^9*d*x^12 + 145495350*a*b^9*c^8*d^2*x^12 + 1745944200*a^2*b^8*c^7*d^3*x^12 + 8147739600*a^3*b^7*c^6*d^4*x^12 + 17110253160*a^4*b^6*c^5*d^5*x^12 + 17110253160*a^5*b^5*c^4*d^6*x^12 + 8147739600*a^6*b^4*c^3*d^7*x^12 + 1745944200*a^7*b^3*c^2*d^8*x^12 + 145495350*a^8*b^2*c*d^9*x^12 + 3233230*a^9*b*d^10*x^12 + 13430340*b^10*c^8*d^2*x^13 + 358142400*a*b^9*c^7*d^3*x^13 + 2820371400*a^2*b^8*c^6*d^4*x^13 + 9025188480*a^3*b^7*c^5*d^5*x^13 + 13161733200*a^4*b^6*c^4*d^6*x^13 + 9025188480*a^5*b^5*c^3*d^7*x^13 + 2820371400*a^6*b^4*c^2*d^8*x^13 + 358142400*a^7*b^3*c*d^9*x^13 + 13430340*a^8*b^2*d^10*x^13 + 33256080*b^10*c^7*d^3*x^14 + 581981400*a*b^9*c^6*d^4*x^14 + 3142699560*a^2*b^8*c^5*d^5*x^14 + 6983776800*a^3*b^7*c^4*d^6*x^14 + 6983776800*a^4*b^6*c^3*d^7*x^14 + 3142699560*a^5*b^5*c^2*d^8*x^14 + 581981400*a^6*b^4*c*d^9*x^14 + 33256080*a^7*b^3*d^10*x^14 + 54318264*b^10*c^6*d^4*x^15 + 651819168*a*b^9*c^5*d^5*x^15 + 2444321880*a^2*b^8*c^4*d^6*x^15 + 3724680960*a^3*b^7*c^3*d^7*x^15 + 2444321880*a^4*b^6*c^2*d^8*x^15 + 651819168*a^5*b^5*c*d^9*x^15 + 54318264*a^6*b^4*d^10*x^15 + 61108047*b^10*c^5*d^5*x^16 + 509233725*a*b^9*c^4*d^6*x^16 + 1309458150*a^2*b^8*c^3*d^7*x^16 + 1309458150*a^3*b^7*c^2*d^8*x^16 + 509233725*a^4*b^6*c*d^9*x^16 + 61108047*a^5*b^5*d^10*x^16 + 47927880*b^10*c^4*d^6*x^17 + 273873600*a*b^9*c^3*d^7*x^17 + 462161700*a^2*b^8*c^2*d^8*x^17 + 273873600*a^3*b^7*c*d^9*x^17 + 47927880*a^4*b^6*d^10*x^17 + 25865840*b^10*c^3*d^7*x^18 + 96996900*a*b^9*c^2*d^8*x^18 + 96996900*a^2*b^8*c*d^9*x^18 + 25865840*a^3*b^7*d^10*x^18 + 9189180*b^10*c^2*d^8*x^19 + 20420400*a*b^9*c*d^9*x^19 + 9189180*a^2*b^8*d^10*x^19 + 1939938*b^10*c*d^9*x^20 + 1939938*a*b^9*d^10*x^20 + 184756*b^10*d^10*x^21)/3879876","B",1
1302,1,1663,250,0.5221801,"\int (a+b x)^9 (c+d x)^{10} \, dx","IntegrateAlgebraic[(a + b*x)^9*(c + d*x)^10,x]","\frac{92378 b^9 d^{10} x^{20}+875160 a b^8 d^{10} x^{19}+972400 b^9 c d^9 x^{19}+3695120 a^2 b^7 d^{10} x^{18}+9237800 a b^8 c d^9 x^{18}+4618900 b^9 c^2 d^8 x^{18}+9129120 a^3 b^6 d^{10} x^{17}+39124800 a^2 b^7 c d^9 x^{17}+44015400 a b^8 c^2 d^8 x^{17}+13041600 b^9 c^3 d^7 x^{17}+14549535 a^4 b^5 d^{10} x^{16}+96996900 a^3 b^6 c d^9 x^{16}+187065450 a^2 b^7 c^2 d^8 x^{16}+124710300 a b^8 c^3 d^7 x^{16}+24249225 b^9 c^4 d^6 x^{16}+15519504 a^5 b^4 d^{10} x^{15}+155195040 a^4 b^5 c d^9 x^{15}+465585120 a^3 b^6 c^2 d^8 x^{15}+532097280 a^2 b^7 c^3 d^7 x^{15}+232792560 a b^8 c^4 d^6 x^{15}+31039008 b^9 c^5 d^5 x^{15}+11085360 a^6 b^3 d^{10} x^{14}+166280400 a^5 b^4 c d^9 x^{14}+748261800 a^4 b^5 c^2 d^8 x^{14}+1330243200 a^3 b^6 c^3 d^7 x^{14}+997682400 a^2 b^7 c^4 d^6 x^{14}+299304720 a b^8 c^5 d^5 x^{14}+27713400 b^9 c^6 d^4 x^{14}+5116320 a^7 b^2 d^{10} x^{13}+119380800 a^6 b^3 c d^9 x^{13}+805820400 a^5 b^4 c^2 d^8 x^{13}+2148854400 a^4 b^5 c^3 d^7 x^{13}+2506996800 a^3 b^6 c^4 d^6 x^{13}+1289312640 a^2 b^7 c^5 d^5 x^{13}+268606800 a b^8 c^6 d^4 x^{13}+17054400 b^9 c^7 d^3 x^{13}+1385670 a^8 b d^{10} x^{12}+55426800 a^7 b^2 c d^9 x^{12}+581981400 a^6 b^3 c^2 d^8 x^{12}+2327925600 a^5 b^4 c^3 d^7 x^{12}+4073869800 a^4 b^5 c^4 d^6 x^{12}+3259095840 a^3 b^6 c^5 d^5 x^{12}+1163962800 a^2 b^7 c^6 d^4 x^{12}+166280400 a b^8 c^7 d^3 x^{12}+6928350 b^9 c^8 d^2 x^{12}+167960 a^9 d^{10} x^{11}+15116400 a^8 b c d^9 x^{11}+272095200 a^7 b^2 c^2 d^8 x^{11}+1693036800 a^6 b^3 c^3 d^7 x^{11}+4444221600 a^5 b^4 c^4 d^6 x^{11}+5333065920 a^4 b^5 c^5 d^5 x^{11}+2962814400 a^3 b^6 c^6 d^4 x^{11}+725587200 a^2 b^7 c^7 d^3 x^{11}+68023800 a b^8 c^8 d^2 x^{11}+1679600 b^9 c^9 d x^{11}+184756 b^9 c^{10} x^{10}+1847560 a^9 c d^9 x^{10}+74826180 a^8 b c^2 d^8 x^{10}+798145920 a^7 b^2 c^3 d^7 x^{10}+3259095840 a^6 b^3 c^4 d^6 x^{10}+5866372512 a^5 b^4 c^5 d^5 x^{10}+4888643760 a^4 b^5 c^6 d^4 x^{10}+1862340480 a^3 b^6 c^7 d^3 x^{10}+299304720 a^2 b^7 c^8 d^2 x^{10}+16628040 a b^8 c^9 d x^{10}+1847560 a b^8 c^{10} x^9+9237800 a^9 c^2 d^8 x^9+221707200 a^8 b c^3 d^7 x^9+1551950400 a^7 b^2 c^4 d^6 x^9+4345461120 a^6 b^3 c^5 d^5 x^9+5431826400 a^5 b^4 c^6 d^4 x^9+3103900800 a^4 b^5 c^7 d^3 x^9+775975200 a^3 b^6 c^8 d^2 x^9+73902400 a^2 b^7 c^9 d x^9+8314020 a^2 b^7 c^{10} x^8+27713400 a^9 c^3 d^7 x^8+436486050 a^8 b c^4 d^6 x^8+2095133040 a^7 b^2 c^5 d^5 x^8+4073869800 a^6 b^3 c^6 d^4 x^8+3491888400 a^5 b^4 c^7 d^3 x^8+1309458150 a^4 b^5 c^8 d^2 x^8+193993800 a^3 b^6 c^9 d x^8+22170720 a^3 b^6 c^{10} x^7+55426800 a^9 c^4 d^6 x^7+598609440 a^8 b c^5 d^5 x^7+1995364800 a^7 b^2 c^6 d^4 x^7+2660486400 a^6 b^3 c^7 d^3 x^7+1496523600 a^5 b^4 c^8 d^2 x^7+332560800 a^4 b^5 c^9 d x^7+38798760 a^4 b^5 c^{10} x^6+77597520 a^9 c^5 d^5 x^6+581981400 a^8 b c^6 d^4 x^6+1330243200 a^7 b^2 c^7 d^3 x^6+1163962800 a^6 b^3 c^8 d^2 x^6+387987600 a^5 b^4 c^9 d x^6+46558512 a^5 b^4 c^{10} x^5+77597520 a^9 c^6 d^4 x^5+399072960 a^8 b c^7 d^3 x^5+598609440 a^7 b^2 c^8 d^2 x^5+310390080 a^6 b^3 c^9 d x^5+38798760 a^6 b^3 c^{10} x^4+55426800 a^9 c^7 d^3 x^4+187065450 a^8 b c^8 d^2 x^4+166280400 a^7 b^2 c^9 d x^4+22170720 a^7 b^2 c^{10} x^3+27713400 a^9 c^8 d^2 x^3+55426800 a^8 b c^9 d x^3+8314020 a^8 b c^{10} x^2+9237800 a^9 c^9 d x^2+1847560 a^9 c^{10} x}{1847560}","-\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,"(1847560*a^9*c^10*x + 8314020*a^8*b*c^10*x^2 + 9237800*a^9*c^9*d*x^2 + 22170720*a^7*b^2*c^10*x^3 + 55426800*a^8*b*c^9*d*x^3 + 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1303,1,1486,225,0.4581604,"\int (a+b x)^8 (c+d x)^{10} \, dx","IntegrateAlgebraic[(a + b*x)^8*(c + d*x)^10,x]","\frac{43758 b^8 d^{10} x^{19}+369512 a b^7 d^{10} x^{18}+461890 b^8 c d^9 x^{18}+1369368 a^2 b^6 d^{10} x^{17}+3912480 a b^7 c d^9 x^{17}+2200770 b^8 c^2 d^8 x^{17}+2909907 a^3 b^5 d^{10} x^{16}+14549535 a^2 b^6 c d^9 x^{16}+18706545 a b^7 c^2 d^8 x^{16}+6235515 b^8 c^3 d^7 x^{16}+3879876 a^4 b^4 d^{10} x^{15}+31039008 a^3 b^5 c d^9 x^{15}+69837768 a^2 b^6 c^2 d^8 x^{15}+53209728 a b^7 c^3 d^7 x^{15}+11639628 b^8 c^4 d^6 x^{15}+3325608 a^5 b^3 d^{10} x^{14}+41570100 a^4 b^4 c d^9 x^{14}+149652360 a^3 b^5 c^2 d^8 x^{14}+199536480 a^2 b^6 c^3 d^7 x^{14}+99768240 a b^7 c^4 d^6 x^{14}+14965236 b^8 c^5 d^5 x^{14}+1790712 a^6 b^2 d^{10} x^{13}+35814240 a^5 b^3 c d^9 x^{13}+201455100 a^4 b^4 c^2 d^8 x^{13}+429770880 a^3 b^5 c^3 d^7 x^{13}+376049520 a^2 b^6 c^4 d^6 x^{13}+128931264 a b^7 c^5 d^5 x^{13}+13430340 b^8 c^6 d^4 x^{13}+554268 a^7 b d^{10} x^{12}+19399380 a^6 b^2 c d^9 x^{12}+174594420 a^5 b^3 c^2 d^8 x^{12}+581981400 a^4 b^4 c^3 d^7 x^{12}+814773960 a^3 b^5 c^4 d^6 x^{12}+488864376 a^2 b^6 c^5 d^5 x^{12}+116396280 a b^7 c^6 d^4 x^{12}+8314020 b^8 c^7 d^3 x^{12}+75582 a^8 d^{10} x^{11}+6046560 a^7 b c d^9 x^{11}+95233320 a^6 b^2 c^2 d^8 x^{11}+507911040 a^5 b^3 c^3 d^7 x^{11}+1111055400 a^4 b^4 c^4 d^6 x^{11}+1066613184 a^3 b^5 c^5 d^5 x^{11}+444422160 a^2 b^6 c^6 d^4 x^{11}+72558720 a b^7 c^7 d^3 x^{11}+3401190 b^8 c^8 d^2 x^{11}+831402 a^8 c d^9 x^{10}+29930472 a^7 b c^2 d^8 x^{10}+279351072 a^6 b^2 c^3 d^7 x^{10}+977728752 a^5 b^3 c^4 d^6 x^{10}+1466593128 a^4 b^4 c^5 d^5 x^{10}+977728752 a^3 b^5 c^6 d^4 x^{10}+279351072 a^2 b^6 c^7 d^3 x^{10}+29930472 a b^7 c^8 d^2 x^{10}+831402 b^8 c^9 d x^{10}+92378 b^8 c^{10} x^9+4157010 a^8 c^2 d^8 x^9+88682880 a^7 b c^3 d^7 x^9+543182640 a^6 b^2 c^4 d^6 x^9+1303638336 a^5 b^3 c^5 d^5 x^9+1357956600 a^4 b^4 c^6 d^4 x^9+620780160 a^3 b^5 c^7 d^3 x^9+116396280 a^2 b^6 c^8 d^2 x^9+7390240 a b^7 c^9 d x^9+831402 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31039008*a^3*b^5*c*d^9*x^15 + 3879876*a^4*b^4*d^10*x^15 + 6235515*b^8*c^3*d^7*x^16 + 18706545*a*b^7*c^2*d^8*x^16 + 14549535*a^2*b^6*c*d^9*x^16 + 2909907*a^3*b^5*d^10*x^16 + 2200770*b^8*c^2*d^8*x^17 + 3912480*a*b^7*c*d^9*x^17 + 1369368*a^2*b^6*d^10*x^17 + 461890*b^8*c*d^9*x^18 + 369512*a*b^7*d^10*x^18 + 43758*b^8*d^10*x^19)/831402","B",1
1304,1,1309,200,0.377005,"\int (a+b x)^7 (c+d x)^{10} \, dx","IntegrateAlgebraic[(a + b*x)^7*(c + d*x)^10,x]","\frac{19448 b^7 d^{10} x^{18}+144144 a b^6 d^{10} x^{17}+205920 b^7 c d^9 x^{17}+459459 a^2 b^5 d^{10} x^{16}+1531530 a b^6 c d^9 x^{16}+984555 b^7 c^2 d^8 x^{16}+816816 a^3 b^4 d^{10} x^{15}+4900896 a^2 b^5 c d^9 x^{15}+7351344 a b^6 c^2 d^8 x^{15}+2800512 b^7 c^3 d^7 x^{15}+875160 a^4 b^3 d^{10} x^{14}+8751600 a^3 b^4 c d^9 x^{14}+23629320 a^2 b^5 c^2 d^8 x^{14}+21003840 a b^6 c^3 d^7 x^{14}+5250960 b^7 c^4 d^6 x^{14}+565488 a^5 b^2 d^{10} x^{13}+9424800 a^4 b^3 c d^9 x^{13}+42411600 a^3 b^4 c^2 d^8 x^{13}+67858560 a^2 b^5 c^3 d^7 x^{13}+39584160 a b^6 c^4 d^6 x^{13}+6785856 b^7 c^5 d^5 x^{13}+204204 a^6 b d^{10} x^{12}+6126120 a^5 b^2 c d^9 x^{12}+45945900 a^4 b^3 c^2 d^8 x^{12}+122522400 a^3 b^4 c^3 d^7 x^{12}+128648520 a^2 b^5 c^4 d^6 x^{12}+51459408 a b^6 c^5 d^5 x^{12}+6126120 b^7 c^6 d^4 x^{12}+31824 a^7 d^{10} x^{11}+2227680 a^6 b c d^9 x^{11}+30073680 a^5 b^2 c^2 d^8 x^{11}+133660800 a^4 b^3 c^3 d^7 x^{11}+233906400 a^3 b^4 c^4 d^6 x^{11}+168412608 a^2 b^5 c^5 d^5 x^{11}+46781280 a b^6 c^6 d^4 x^{11}+3818880 b^7 c^7 d^3 x^{11}+350064 a^7 c d^9 x^{10}+11027016 a^6 b c^2 d^8 x^{10}+88216128 a^5 b^2 c^3 d^7 x^{10}+257297040 a^4 b^3 c^4 d^6 x^{10}+308756448 a^3 b^4 c^5 d^5 x^{10}+154378224 a^2 b^5 c^6 d^4 x^{10}+29405376 a b^6 c^7 d^3 x^{10}+1575288 b^7 c^8 d^2 x^{10}+1750320 a^7 c^2 d^8 x^9+32672640 a^6 b c^3 d^7 x^9+171531360 a^5 b^2 c^4 d^6 x^9+343062720 a^4 b^3 c^5 d^5 x^9+285885600 a^3 b^4 c^6 d^4 x^9+98017920 a^2 b^5 c^7 d^3 x^9+12252240 a b^6 c^8 d^2 x^9+388960 b^7 c^9 d x^9+43758 b^7 c^{10} x^8+5250960 a^7 c^3 d^7 x^8+64324260 a^6 b c^4 d^6 x^8+231567336 a^5 b^2 c^5 d^5 x^8+321621300 a^4 b^3 c^6 d^4 x^8+183783600 a^3 b^4 c^7 d^3 x^8+41351310 a^2 b^5 c^8 d^2 x^8+3063060 a b^6 c^9 d x^8+350064 a b^6 c^{10} x^7+10501920 a^7 c^4 d^6 x^7+88216128 a^6 b c^5 d^5 x^7+220540320 a^5 b^2 c^6 d^4 x^7+210038400 a^4 b^3 c^7 d^3 x^7+78764400 a^3 b^4 c^8 d^2 x^7+10501920 a^2 b^5 c^9 d x^7+1225224 a^2 b^5 c^{10} x^6+14702688 a^7 c^5 d^5 x^6+85765680 a^6 b c^6 d^4 x^6+147026880 a^5 b^2 c^7 d^3 x^6+91891800 a^4 b^3 c^8 d^2 x^6+20420400 a^3 b^4 c^9 d x^6+2450448 a^3 b^4 c^{10} x^5+14702688 a^7 c^6 d^4 x^5+58810752 a^6 b c^7 d^3 x^5+66162096 a^5 b^2 c^8 d^2 x^5+24504480 a^4 b^3 c^9 d x^5+3063060 a^4 b^3 c^{10} x^4+10501920 a^7 c^7 d^3 x^4+27567540 a^6 b c^8 d^2 x^4+18378360 a^5 b^2 c^9 d x^4+2450448 a^5 b^2 c^{10} x^3+5250960 a^7 c^8 d^2 x^3+8168160 a^6 b c^9 d x^3+1225224 a^6 b c^{10} x^2+1750320 a^7 c^9 d x^2+350064 a^7 c^{10} x}{350064}","-\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,"(350064*a^7*c^10*x + 1225224*a^6*b*c^10*x^2 + 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12252240*a*b^6*c^8*d^2*x^9 + 98017920*a^2*b^5*c^7*d^3*x^9 + 285885600*a^3*b^4*c^6*d^4*x^9 + 343062720*a^4*b^3*c^5*d^5*x^9 + 171531360*a^5*b^2*c^4*d^6*x^9 + 32672640*a^6*b*c^3*d^7*x^9 + 1750320*a^7*c^2*d^8*x^9 + 1575288*b^7*c^8*d^2*x^10 + 29405376*a*b^6*c^7*d^3*x^10 + 154378224*a^2*b^5*c^6*d^4*x^10 + 308756448*a^3*b^4*c^5*d^5*x^10 + 257297040*a^4*b^3*c^4*d^6*x^10 + 88216128*a^5*b^2*c^3*d^7*x^10 + 11027016*a^6*b*c^2*d^8*x^10 + 350064*a^7*c*d^9*x^10 + 3818880*b^7*c^7*d^3*x^11 + 46781280*a*b^6*c^6*d^4*x^11 + 168412608*a^2*b^5*c^5*d^5*x^11 + 233906400*a^3*b^4*c^4*d^6*x^11 + 133660800*a^4*b^3*c^3*d^7*x^11 + 30073680*a^5*b^2*c^2*d^8*x^11 + 2227680*a^6*b*c*d^9*x^11 + 31824*a^7*d^10*x^11 + 6126120*b^7*c^6*d^4*x^12 + 51459408*a*b^6*c^5*d^5*x^12 + 128648520*a^2*b^5*c^4*d^6*x^12 + 122522400*a^3*b^4*c^3*d^7*x^12 + 45945900*a^4*b^3*c^2*d^8*x^12 + 6126120*a^5*b^2*c*d^9*x^12 + 204204*a^6*b*d^10*x^12 + 6785856*b^7*c^5*d^5*x^13 + 39584160*a*b^6*c^4*d^6*x^13 + 67858560*a^2*b^5*c^3*d^7*x^13 + 42411600*a^3*b^4*c^2*d^8*x^13 + 9424800*a^4*b^3*c*d^9*x^13 + 565488*a^5*b^2*d^10*x^13 + 5250960*b^7*c^4*d^6*x^14 + 21003840*a*b^6*c^3*d^7*x^14 + 23629320*a^2*b^5*c^2*d^8*x^14 + 8751600*a^3*b^4*c*d^9*x^14 + 875160*a^4*b^3*d^10*x^14 + 2800512*b^7*c^3*d^7*x^15 + 7351344*a*b^6*c^2*d^8*x^15 + 4900896*a^2*b^5*c*d^9*x^15 + 816816*a^3*b^4*d^10*x^15 + 984555*b^7*c^2*d^8*x^16 + 1531530*a*b^6*c*d^9*x^16 + 459459*a^2*b^5*d^10*x^16 + 205920*b^7*c*d^9*x^17 + 144144*a*b^6*d^10*x^17 + 19448*b^7*d^10*x^18)/350064","B",1
1305,1,1132,170,0.3241485,"\int (a+b x)^6 (c+d x)^{10} \, dx","IntegrateAlgebraic[(a + b*x)^6*(c + d*x)^10,x]","\frac{8008 b^6 d^{10} x^{17}+51051 a b^5 d^{10} x^{16}+85085 b^6 c d^9 x^{16}+136136 a^2 b^4 d^{10} x^{15}+544544 a b^5 c d^9 x^{15}+408408 b^6 c^2 d^8 x^{15}+194480 a^3 b^3 d^{10} x^{14}+1458600 a^2 b^4 c d^9 x^{14}+2625480 a b^5 c^2 d^8 x^{14}+1166880 b^6 c^3 d^7 x^{14}+157080 a^4 b^2 d^{10} x^{13}+2094400 a^3 b^3 c d^9 x^{13}+7068600 a^2 b^4 c^2 d^8 x^{13}+7539840 a b^5 c^3 d^7 x^{13}+2199120 b^6 c^4 d^6 x^{13}+68068 a^5 b d^{10} x^{12}+1701700 a^4 b^2 c d^9 x^{12}+10210200 a^3 b^3 c^2 d^8 x^{12}+20420400 a^2 b^4 c^3 d^7 x^{12}+14294280 a b^5 c^4 d^6 x^{12}+2858856 b^6 c^5 d^5 x^{12}+12376 a^6 d^{10} x^{11}+742560 a^5 b c d^9 x^{11}+8353800 a^4 b^2 c^2 d^8 x^{11}+29702400 a^3 b^3 c^3 d^7 x^{11}+38984400 a^2 b^4 c^4 d^6 x^{11}+18712512 a b^5 c^5 d^5 x^{11}+2598960 b^6 c^6 d^4 x^{11}+136136 a^6 c d^9 x^{10}+3675672 a^5 b c^2 d^8 x^{10}+24504480 a^4 b^2 c^3 d^7 x^{10}+57177120 a^3 b^3 c^4 d^6 x^{10}+51459408 a^2 b^4 c^5 d^5 x^{10}+17153136 a b^5 c^6 d^4 x^{10}+1633632 b^6 c^7 d^3 x^{10}+680680 a^6 c^2 d^8 x^9+10890880 a^5 b c^3 d^7 x^9+47647600 a^4 b^2 c^4 d^6 x^9+76236160 a^3 b^3 c^5 d^5 x^9+47647600 a^2 b^4 c^6 d^4 x^9+10890880 a b^5 c^7 d^3 x^9+680680 b^6 c^8 d^2 x^9+2042040 a^6 c^3 d^7 x^8+21441420 a^5 b c^4 d^6 x^8+64324260 a^4 b^2 c^5 d^5 x^8+71471400 a^3 b^3 c^6 d^4 x^8+30630600 a^2 b^4 c^7 d^3 x^8+4594590 a b^5 c^8 d^2 x^8+170170 b^6 c^9 d x^8+19448 b^6 c^{10} x^7+4084080 a^6 c^4 d^6 x^7+29405376 a^5 b c^5 d^5 x^7+61261200 a^4 b^2 c^6 d^4 x^7+46675200 a^3 b^3 c^7 d^3 x^7+13127400 a^2 b^4 c^8 d^2 x^7+1166880 a b^5 c^9 d x^7+136136 a b^5 c^{10} x^6+5717712 a^6 c^5 d^5 x^6+28588560 a^5 b c^6 d^4 x^6+40840800 a^4 b^2 c^7 d^3 x^6+20420400 a^3 b^3 c^8 d^2 x^6+3403400 a^2 b^4 c^9 d x^6+408408 a^2 b^4 c^{10} x^5+5717712 a^6 c^6 d^4 x^5+19603584 a^5 b c^7 d^3 x^5+18378360 a^4 b^2 c^8 d^2 x^5+5445440 a^3 b^3 c^9 d x^5+680680 a^3 b^3 c^{10} x^4+4084080 a^6 c^7 d^3 x^4+9189180 a^5 b c^8 d^2 x^4+5105100 a^4 b^2 c^9 d x^4+680680 a^4 b^2 c^{10} x^3+2042040 a^6 c^8 d^2 x^3+2722720 a^5 b c^9 d x^3+408408 a^5 b c^{10} x^2+680680 a^6 c^9 d x^2+136136 a^6 c^{10} x}{136136}","-\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,"(136136*a^6*c^10*x + 408408*a^5*b*c^10*x^2 + 680680*a^6*c^9*d*x^2 + 680680*a^4*b^2*c^10*x^3 + 2722720*a^5*b*c^9*d*x^3 + 2042040*a^6*c^8*d^2*x^3 + 680680*a^3*b^3*c^10*x^4 + 5105100*a^4*b^2*c^9*d*x^4 + 9189180*a^5*b*c^8*d^2*x^4 + 4084080*a^6*c^7*d^3*x^4 + 408408*a^2*b^4*c^10*x^5 + 5445440*a^3*b^3*c^9*d*x^5 + 18378360*a^4*b^2*c^8*d^2*x^5 + 19603584*a^5*b*c^7*d^3*x^5 + 5717712*a^6*c^6*d^4*x^5 + 136136*a*b^5*c^10*x^6 + 3403400*a^2*b^4*c^9*d*x^6 + 20420400*a^3*b^3*c^8*d^2*x^6 + 40840800*a^4*b^2*c^7*d^3*x^6 + 28588560*a^5*b*c^6*d^4*x^6 + 5717712*a^6*c^5*d^5*x^6 + 19448*b^6*c^10*x^7 + 1166880*a*b^5*c^9*d*x^7 + 13127400*a^2*b^4*c^8*d^2*x^7 + 46675200*a^3*b^3*c^7*d^3*x^7 + 61261200*a^4*b^2*c^6*d^4*x^7 + 29405376*a^5*b*c^5*d^5*x^7 + 4084080*a^6*c^4*d^6*x^7 + 170170*b^6*c^9*d*x^8 + 4594590*a*b^5*c^8*d^2*x^8 + 30630600*a^2*b^4*c^7*d^3*x^8 + 71471400*a^3*b^3*c^6*d^4*x^8 + 64324260*a^4*b^2*c^5*d^5*x^8 + 21441420*a^5*b*c^4*d^6*x^8 + 2042040*a^6*c^3*d^7*x^8 + 680680*b^6*c^8*d^2*x^9 + 10890880*a*b^5*c^7*d^3*x^9 + 47647600*a^2*b^4*c^6*d^4*x^9 + 76236160*a^3*b^3*c^5*d^5*x^9 + 47647600*a^4*b^2*c^4*d^6*x^9 + 10890880*a^5*b*c^3*d^7*x^9 + 680680*a^6*c^2*d^8*x^9 + 1633632*b^6*c^7*d^3*x^10 + 17153136*a*b^5*c^6*d^4*x^10 + 51459408*a^2*b^4*c^5*d^5*x^10 + 57177120*a^3*b^3*c^4*d^6*x^10 + 24504480*a^4*b^2*c^3*d^7*x^10 + 3675672*a^5*b*c^2*d^8*x^10 + 136136*a^6*c*d^9*x^10 + 2598960*b^6*c^6*d^4*x^11 + 18712512*a*b^5*c^5*d^5*x^11 + 38984400*a^2*b^4*c^4*d^6*x^11 + 29702400*a^3*b^3*c^3*d^7*x^11 + 8353800*a^4*b^2*c^2*d^8*x^11 + 742560*a^5*b*c*d^9*x^11 + 12376*a^6*d^10*x^11 + 2858856*b^6*c^5*d^5*x^12 + 14294280*a*b^5*c^4*d^6*x^12 + 20420400*a^2*b^4*c^3*d^7*x^12 + 10210200*a^3*b^3*c^2*d^8*x^12 + 1701700*a^4*b^2*c*d^9*x^12 + 68068*a^5*b*d^10*x^12 + 2199120*b^6*c^4*d^6*x^13 + 7539840*a*b^5*c^3*d^7*x^13 + 7068600*a^2*b^4*c^2*d^8*x^13 + 2094400*a^3*b^3*c*d^9*x^13 + 157080*a^4*b^2*d^10*x^13 + 1166880*b^6*c^3*d^7*x^14 + 2625480*a*b^5*c^2*d^8*x^14 + 1458600*a^2*b^4*c*d^9*x^14 + 194480*a^3*b^3*d^10*x^14 + 408408*b^6*c^2*d^8*x^15 + 544544*a*b^5*c*d^9*x^15 + 136136*a^2*b^4*d^10*x^15 + 85085*b^6*c*d^9*x^16 + 51051*a*b^5*d^10*x^16 + 8008*b^6*d^10*x^17)/136136","B",1
1306,1,955,146,0.2661787,"\int (a+b x)^5 (c+d x)^{10} \, dx","IntegrateAlgebraic[(a + b*x)^5*(c + d*x)^10,x]","\frac{3003 b^5 d^{10} x^{16}+16016 a b^4 d^{10} x^{15}+32032 b^5 c d^9 x^{15}+34320 a^2 b^3 d^{10} x^{14}+171600 a b^4 c d^9 x^{14}+154440 b^5 c^2 d^8 x^{14}+36960 a^3 b^2 d^{10} x^{13}+369600 a^2 b^3 c d^9 x^{13}+831600 a b^4 c^2 d^8 x^{13}+443520 b^5 c^3 d^7 x^{13}+20020 a^4 b d^{10} x^{12}+400400 a^3 b^2 c d^9 x^{12}+1801800 a^2 b^3 c^2 d^8 x^{12}+2402400 a b^4 c^3 d^7 x^{12}+840840 b^5 c^4 d^6 x^{12}+4368 a^5 d^{10} x^{11}+218400 a^4 b c d^9 x^{11}+1965600 a^3 b^2 c^2 d^8 x^{11}+5241600 a^2 b^3 c^3 d^7 x^{11}+4586400 a b^4 c^4 d^6 x^{11}+1100736 b^5 c^5 d^5 x^{11}+48048 a^5 c d^9 x^{10}+1081080 a^4 b c^2 d^8 x^{10}+5765760 a^3 b^2 c^3 d^7 x^{10}+10090080 a^2 b^3 c^4 d^6 x^{10}+6054048 a b^4 c^5 d^5 x^{10}+1009008 b^5 c^6 d^4 x^{10}+240240 a^5 c^2 d^8 x^9+3203200 a^4 b c^3 d^7 x^9+11211200 a^3 b^2 c^4 d^6 x^9+13453440 a^2 b^3 c^5 d^5 x^9+5605600 a b^4 c^6 d^4 x^9+640640 b^5 c^7 d^3 x^9+720720 a^5 c^3 d^7 x^8+6306300 a^4 b c^4 d^6 x^8+15135120 a^3 b^2 c^5 d^5 x^8+12612600 a^2 b^3 c^6 d^4 x^8+3603600 a b^4 c^7 d^3 x^8+270270 b^5 c^8 d^2 x^8+1441440 a^5 c^4 d^6 x^7+8648640 a^4 b c^5 d^5 x^7+14414400 a^3 b^2 c^6 d^4 x^7+8236800 a^2 b^3 c^7 d^3 x^7+1544400 a b^4 c^8 d^2 x^7+68640 b^5 c^9 d x^7+8008 b^5 c^{10} x^6+2018016 a^5 c^5 d^5 x^6+8408400 a^4 b c^6 d^4 x^6+9609600 a^3 b^2 c^7 d^3 x^6+3603600 a^2 b^3 c^8 d^2 x^6+400400 a b^4 c^9 d x^6+48048 a b^4 c^{10} x^5+2018016 a^5 c^6 d^4 x^5+5765760 a^4 b c^7 d^3 x^5+4324320 a^3 b^2 c^8 d^2 x^5+960960 a^2 b^3 c^9 d x^5+120120 a^2 b^3 c^{10} x^4+1441440 a^5 c^7 d^3 x^4+2702700 a^4 b c^8 d^2 x^4+1201200 a^3 b^2 c^9 d x^4+160160 a^3 b^2 c^{10} x^3+720720 a^5 c^8 d^2 x^3+800800 a^4 b c^9 d x^3+120120 a^4 b c^{10} x^2+240240 a^5 c^9 d x^2+48048 a^5 c^{10} x}{48048}","-\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,"(48048*a^5*c^10*x + 120120*a^4*b*c^10*x^2 + 240240*a^5*c^9*d*x^2 + 160160*a^3*b^2*c^10*x^3 + 800800*a^4*b*c^9*d*x^3 + 720720*a^5*c^8*d^2*x^3 + 120120*a^2*b^3*c^10*x^4 + 1201200*a^3*b^2*c^9*d*x^4 + 2702700*a^4*b*c^8*d^2*x^4 + 1441440*a^5*c^7*d^3*x^4 + 48048*a*b^4*c^10*x^5 + 960960*a^2*b^3*c^9*d*x^5 + 4324320*a^3*b^2*c^8*d^2*x^5 + 5765760*a^4*b*c^7*d^3*x^5 + 2018016*a^5*c^6*d^4*x^5 + 8008*b^5*c^10*x^6 + 400400*a*b^4*c^9*d*x^6 + 3603600*a^2*b^3*c^8*d^2*x^6 + 9609600*a^3*b^2*c^7*d^3*x^6 + 8408400*a^4*b*c^6*d^4*x^6 + 2018016*a^5*c^5*d^5*x^6 + 68640*b^5*c^9*d*x^7 + 1544400*a*b^4*c^8*d^2*x^7 + 8236800*a^2*b^3*c^7*d^3*x^7 + 14414400*a^3*b^2*c^6*d^4*x^7 + 8648640*a^4*b*c^5*d^5*x^7 + 1441440*a^5*c^4*d^6*x^7 + 270270*b^5*c^8*d^2*x^8 + 3603600*a*b^4*c^7*d^3*x^8 + 12612600*a^2*b^3*c^6*d^4*x^8 + 15135120*a^3*b^2*c^5*d^5*x^8 + 6306300*a^4*b*c^4*d^6*x^8 + 720720*a^5*c^3*d^7*x^8 + 640640*b^5*c^7*d^3*x^9 + 5605600*a*b^4*c^6*d^4*x^9 + 13453440*a^2*b^3*c^5*d^5*x^9 + 11211200*a^3*b^2*c^4*d^6*x^9 + 3203200*a^4*b*c^3*d^7*x^9 + 240240*a^5*c^2*d^8*x^9 + 1009008*b^5*c^6*d^4*x^10 + 6054048*a*b^4*c^5*d^5*x^10 + 10090080*a^2*b^3*c^4*d^6*x^10 + 5765760*a^3*b^2*c^3*d^7*x^10 + 1081080*a^4*b*c^2*d^8*x^10 + 48048*a^5*c*d^9*x^10 + 1100736*b^5*c^5*d^5*x^11 + 4586400*a*b^4*c^4*d^6*x^11 + 5241600*a^2*b^3*c^3*d^7*x^11 + 1965600*a^3*b^2*c^2*d^8*x^11 + 218400*a^4*b*c*d^9*x^11 + 4368*a^5*d^10*x^11 + 840840*b^5*c^4*d^6*x^12 + 2402400*a*b^4*c^3*d^7*x^12 + 1801800*a^2*b^3*c^2*d^8*x^12 + 400400*a^3*b^2*c*d^9*x^12 + 20020*a^4*b*d^10*x^12 + 443520*b^5*c^3*d^7*x^13 + 831600*a*b^4*c^2*d^8*x^13 + 369600*a^2*b^3*c*d^9*x^13 + 36960*a^3*b^2*d^10*x^13 + 154440*b^5*c^2*d^8*x^14 + 171600*a*b^4*c*d^9*x^14 + 34320*a^2*b^3*d^10*x^14 + 32032*b^5*c*d^9*x^15 + 16016*a*b^4*d^10*x^15 + 3003*b^5*d^10*x^16)/48048","B",1
1307,1,778,119,0.2273152,"\int (a+b x)^4 (c+d x)^{10} \, dx","IntegrateAlgebraic[(a + b*x)^4*(c + d*x)^10,x]","\frac{15015 a^4 c^{10} x+75075 a^4 c^9 d x^2+225225 a^4 c^8 d^2 x^3+450450 a^4 c^7 d^3 x^4+630630 a^4 c^6 d^4 x^5+630630 a^4 c^5 d^5 x^6+450450 a^4 c^4 d^6 x^7+225225 a^4 c^3 d^7 x^8+75075 a^4 c^2 d^8 x^9+15015 a^4 c d^9 x^{10}+1365 a^4 d^{10} x^{11}+30030 a^3 b c^{10} x^2+200200 a^3 b c^9 d x^3+675675 a^3 b c^8 d^2 x^4+1441440 a^3 b c^7 d^3 x^5+2102100 a^3 b c^6 d^4 x^6+2162160 a^3 b c^5 d^5 x^7+1576575 a^3 b c^4 d^6 x^8+800800 a^3 b c^3 d^7 x^9+270270 a^3 b c^2 d^8 x^{10}+54600 a^3 b c d^9 x^{11}+5005 a^3 b d^{10} x^{12}+30030 a^2 b^2 c^{10} x^3+225225 a^2 b^2 c^9 d x^4+810810 a^2 b^2 c^8 d^2 x^5+1801800 a^2 b^2 c^7 d^3 x^6+2702700 a^2 b^2 c^6 d^4 x^7+2837835 a^2 b^2 c^5 d^5 x^8+2102100 a^2 b^2 c^4 d^6 x^9+1081080 a^2 b^2 c^3 d^7 x^{10}+368550 a^2 b^2 c^2 d^8 x^{11}+75075 a^2 b^2 c d^9 x^{12}+6930 a^2 b^2 d^{10} x^{13}+15015 a b^3 c^{10} x^4+120120 a b^3 c^9 d x^5+450450 a b^3 c^8 d^2 x^6+1029600 a b^3 c^7 d^3 x^7+1576575 a b^3 c^6 d^4 x^8+1681680 a b^3 c^5 d^5 x^9+1261260 a b^3 c^4 d^6 x^{10}+655200 a b^3 c^3 d^7 x^{11}+225225 a b^3 c^2 d^8 x^{12}+46200 a b^3 c d^9 x^{13}+4290 a b^3 d^{10} x^{14}+3003 b^4 c^{10} x^5+25025 b^4 c^9 d x^6+96525 b^4 c^8 d^2 x^7+225225 b^4 c^7 d^3 x^8+350350 b^4 c^6 d^4 x^9+378378 b^4 c^5 d^5 x^{10}+286650 b^4 c^4 d^6 x^{11}+150150 b^4 c^3 d^7 x^{12}+51975 b^4 c^2 d^8 x^{13}+10725 b^4 c d^9 x^{14}+1001 b^4 d^{10} x^{15}}{15015}","-\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,"(15015*a^4*c^10*x + 30030*a^3*b*c^10*x^2 + 75075*a^4*c^9*d*x^2 + 30030*a^2*b^2*c^10*x^3 + 200200*a^3*b*c^9*d*x^3 + 225225*a^4*c^8*d^2*x^3 + 15015*a*b^3*c^10*x^4 + 225225*a^2*b^2*c^9*d*x^4 + 675675*a^3*b*c^8*d^2*x^4 + 450450*a^4*c^7*d^3*x^4 + 3003*b^4*c^10*x^5 + 120120*a*b^3*c^9*d*x^5 + 810810*a^2*b^2*c^8*d^2*x^5 + 1441440*a^3*b*c^7*d^3*x^5 + 630630*a^4*c^6*d^4*x^5 + 25025*b^4*c^9*d*x^6 + 450450*a*b^3*c^8*d^2*x^6 + 1801800*a^2*b^2*c^7*d^3*x^6 + 2102100*a^3*b*c^6*d^4*x^6 + 630630*a^4*c^5*d^5*x^6 + 96525*b^4*c^8*d^2*x^7 + 1029600*a*b^3*c^7*d^3*x^7 + 2702700*a^2*b^2*c^6*d^4*x^7 + 2162160*a^3*b*c^5*d^5*x^7 + 450450*a^4*c^4*d^6*x^7 + 225225*b^4*c^7*d^3*x^8 + 1576575*a*b^3*c^6*d^4*x^8 + 2837835*a^2*b^2*c^5*d^5*x^8 + 1576575*a^3*b*c^4*d^6*x^8 + 225225*a^4*c^3*d^7*x^8 + 350350*b^4*c^6*d^4*x^9 + 1681680*a*b^3*c^5*d^5*x^9 + 2102100*a^2*b^2*c^4*d^6*x^9 + 800800*a^3*b*c^3*d^7*x^9 + 75075*a^4*c^2*d^8*x^9 + 378378*b^4*c^5*d^5*x^10 + 1261260*a*b^3*c^4*d^6*x^10 + 1081080*a^2*b^2*c^3*d^7*x^10 + 270270*a^3*b*c^2*d^8*x^10 + 15015*a^4*c*d^9*x^10 + 286650*b^4*c^4*d^6*x^11 + 655200*a*b^3*c^3*d^7*x^11 + 368550*a^2*b^2*c^2*d^8*x^11 + 54600*a^3*b*c*d^9*x^11 + 1365*a^4*d^10*x^11 + 150150*b^4*c^3*d^7*x^12 + 225225*a*b^3*c^2*d^8*x^12 + 75075*a^2*b^2*c*d^9*x^12 + 5005*a^3*b*d^10*x^12 + 51975*b^4*c^2*d^8*x^13 + 46200*a*b^3*c*d^9*x^13 + 6930*a^2*b^2*d^10*x^13 + 10725*b^4*c*d^9*x^14 + 4290*a*b^3*d^10*x^14 + 1001*b^4*d^10*x^15)/15015","B",1
1308,1,601,92,0.1765775,"\int (a+b x)^3 (c+d x)^{10} \, dx","IntegrateAlgebraic[(a + b*x)^3*(c + d*x)^10,x]","\frac{4004 a^3 c^{10} x+20020 a^3 c^9 d x^2+60060 a^3 c^8 d^2 x^3+120120 a^3 c^7 d^3 x^4+168168 a^3 c^6 d^4 x^5+168168 a^3 c^5 d^5 x^6+120120 a^3 c^4 d^6 x^7+60060 a^3 c^3 d^7 x^8+20020 a^3 c^2 d^8 x^9+4004 a^3 c d^9 x^{10}+364 a^3 d^{10} x^{11}+6006 a^2 b c^{10} x^2+40040 a^2 b c^9 d x^3+135135 a^2 b c^8 d^2 x^4+288288 a^2 b c^7 d^3 x^5+420420 a^2 b c^6 d^4 x^6+432432 a^2 b c^5 d^5 x^7+315315 a^2 b c^4 d^6 x^8+160160 a^2 b c^3 d^7 x^9+54054 a^2 b c^2 d^8 x^{10}+10920 a^2 b c d^9 x^{11}+1001 a^2 b d^{10} x^{12}+4004 a b^2 c^{10} x^3+30030 a b^2 c^9 d x^4+108108 a b^2 c^8 d^2 x^5+240240 a b^2 c^7 d^3 x^6+360360 a b^2 c^6 d^4 x^7+378378 a b^2 c^5 d^5 x^8+280280 a b^2 c^4 d^6 x^9+144144 a b^2 c^3 d^7 x^{10}+49140 a b^2 c^2 d^8 x^{11}+10010 a b^2 c d^9 x^{12}+924 a b^2 d^{10} x^{13}+1001 b^3 c^{10} x^4+8008 b^3 c^9 d x^5+30030 b^3 c^8 d^2 x^6+68640 b^3 c^7 d^3 x^7+105105 b^3 c^6 d^4 x^8+112112 b^3 c^5 d^5 x^9+84084 b^3 c^4 d^6 x^{10}+43680 b^3 c^3 d^7 x^{11}+15015 b^3 c^2 d^8 x^{12}+3080 b^3 c d^9 x^{13}+286 b^3 d^{10} x^{14}}{4004}","-\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,"(4004*a^3*c^10*x + 6006*a^2*b*c^10*x^2 + 20020*a^3*c^9*d*x^2 + 4004*a*b^2*c^10*x^3 + 40040*a^2*b*c^9*d*x^3 + 60060*a^3*c^8*d^2*x^3 + 1001*b^3*c^10*x^4 + 30030*a*b^2*c^9*d*x^4 + 135135*a^2*b*c^8*d^2*x^4 + 120120*a^3*c^7*d^3*x^4 + 8008*b^3*c^9*d*x^5 + 108108*a*b^2*c^8*d^2*x^5 + 288288*a^2*b*c^7*d^3*x^5 + 168168*a^3*c^6*d^4*x^5 + 30030*b^3*c^8*d^2*x^6 + 240240*a*b^2*c^7*d^3*x^6 + 420420*a^2*b*c^6*d^4*x^6 + 168168*a^3*c^5*d^5*x^6 + 68640*b^3*c^7*d^3*x^7 + 360360*a*b^2*c^6*d^4*x^7 + 432432*a^2*b*c^5*d^5*x^7 + 120120*a^3*c^4*d^6*x^7 + 105105*b^3*c^6*d^4*x^8 + 378378*a*b^2*c^5*d^5*x^8 + 315315*a^2*b*c^4*d^6*x^8 + 60060*a^3*c^3*d^7*x^8 + 112112*b^3*c^5*d^5*x^9 + 280280*a*b^2*c^4*d^6*x^9 + 160160*a^2*b*c^3*d^7*x^9 + 20020*a^3*c^2*d^8*x^9 + 84084*b^3*c^4*d^6*x^10 + 144144*a*b^2*c^3*d^7*x^10 + 54054*a^2*b*c^2*d^8*x^10 + 4004*a^3*c*d^9*x^10 + 43680*b^3*c^3*d^7*x^11 + 49140*a*b^2*c^2*d^8*x^11 + 10920*a^2*b*c*d^9*x^11 + 364*a^3*d^10*x^11 + 15015*b^3*c^2*d^8*x^12 + 10010*a*b^2*c*d^9*x^12 + 1001*a^2*b*d^10*x^12 + 3080*b^3*c*d^9*x^13 + 924*a*b^2*d^10*x^13 + 286*b^3*d^10*x^14)/4004","B",1
1309,1,424,65,0.1233222,"\int (a+b x)^2 (c+d x)^{10} \, dx","IntegrateAlgebraic[(a + b*x)^2*(c + d*x)^10,x]","\frac{1}{858} \left(858 a^2 c^{10} x+4290 a^2 c^9 d x^2+12870 a^2 c^8 d^2 x^3+25740 a^2 c^7 d^3 x^4+36036 a^2 c^6 d^4 x^5+36036 a^2 c^5 d^5 x^6+25740 a^2 c^4 d^6 x^7+12870 a^2 c^3 d^7 x^8+4290 a^2 c^2 d^8 x^9+858 a^2 c d^9 x^{10}+78 a^2 d^{10} x^{11}+858 a b c^{10} x^2+5720 a b c^9 d x^3+19305 a b c^8 d^2 x^4+41184 a b c^7 d^3 x^5+60060 a b c^6 d^4 x^6+61776 a b c^5 d^5 x^7+45045 a b c^4 d^6 x^8+22880 a b c^3 d^7 x^9+7722 a b c^2 d^8 x^{10}+1560 a b c d^9 x^{11}+143 a b d^{10} x^{12}+286 b^2 c^{10} x^3+2145 b^2 c^9 d x^4+7722 b^2 c^8 d^2 x^5+17160 b^2 c^7 d^3 x^6+25740 b^2 c^6 d^4 x^7+27027 b^2 c^5 d^5 x^8+20020 b^2 c^4 d^6 x^9+10296 b^2 c^3 d^7 x^{10}+3510 b^2 c^2 d^8 x^{11}+715 b^2 c d^9 x^{12}+66 b^2 d^{10} x^{13}\right)","-\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,"(858*a^2*c^10*x + 858*a*b*c^10*x^2 + 4290*a^2*c^9*d*x^2 + 286*b^2*c^10*x^3 + 5720*a*b*c^9*d*x^3 + 12870*a^2*c^8*d^2*x^3 + 2145*b^2*c^9*d*x^4 + 19305*a*b*c^8*d^2*x^4 + 25740*a^2*c^7*d^3*x^4 + 7722*b^2*c^8*d^2*x^5 + 41184*a*b*c^7*d^3*x^5 + 36036*a^2*c^6*d^4*x^5 + 17160*b^2*c^7*d^3*x^6 + 60060*a*b*c^6*d^4*x^6 + 36036*a^2*c^5*d^5*x^6 + 25740*b^2*c^6*d^4*x^7 + 61776*a*b*c^5*d^5*x^7 + 25740*a^2*c^4*d^6*x^7 + 27027*b^2*c^5*d^5*x^8 + 45045*a*b*c^4*d^6*x^8 + 12870*a^2*c^3*d^7*x^8 + 20020*b^2*c^4*d^6*x^9 + 22880*a*b*c^3*d^7*x^9 + 4290*a^2*c^2*d^8*x^9 + 10296*b^2*c^3*d^7*x^10 + 7722*a*b*c^2*d^8*x^10 + 858*a^2*c*d^9*x^10 + 3510*b^2*c^2*d^8*x^11 + 1560*a*b*c*d^9*x^11 + 78*a^2*d^10*x^11 + 715*b^2*c*d^9*x^12 + 143*a*b*d^10*x^12 + 66*b^2*d^10*x^13)/858","B",1
1310,1,247,38,0.0752411,"\int (a+b x) (c+d x)^{10} \, dx","IntegrateAlgebraic[(a + b*x)*(c + d*x)^10,x]","\frac{1}{132} \left(132 a c^{10} x+660 a c^9 d x^2+1980 a c^8 d^2 x^3+3960 a c^7 d^3 x^4+5544 a c^6 d^4 x^5+5544 a c^5 d^5 x^6+3960 a c^4 d^6 x^7+1980 a c^3 d^7 x^8+660 a c^2 d^8 x^9+132 a c d^9 x^{10}+12 a d^{10} x^{11}+66 b c^{10} x^2+440 b c^9 d x^3+1485 b c^8 d^2 x^4+3168 b c^7 d^3 x^5+4620 b c^6 d^4 x^6+4752 b c^5 d^5 x^7+3465 b c^4 d^6 x^8+1760 b c^3 d^7 x^9+594 b c^2 d^8 x^{10}+120 b c d^9 x^{11}+11 b d^{10} x^{12}\right)","\frac{b (c+d x)^{12}}{12 d^2}-\frac{(c+d x)^{11} (b c-a d)}{11 d^2}",1,"(132*a*c^10*x + 66*b*c^10*x^2 + 660*a*c^9*d*x^2 + 440*b*c^9*d*x^3 + 1980*a*c^8*d^2*x^3 + 1485*b*c^8*d^2*x^4 + 3960*a*c^7*d^3*x^4 + 3168*b*c^7*d^3*x^5 + 5544*a*c^6*d^4*x^5 + 4620*b*c^6*d^4*x^6 + 5544*a*c^5*d^5*x^6 + 4752*b*c^5*d^5*x^7 + 3960*a*c^4*d^6*x^7 + 3465*b*c^4*d^6*x^8 + 1980*a*c^3*d^7*x^8 + 1760*b*c^3*d^7*x^9 + 660*a*c^2*d^8*x^9 + 594*b*c^2*d^8*x^10 + 132*a*c*d^9*x^10 + 120*b*c*d^9*x^11 + 12*a*d^10*x^11 + 11*b*d^10*x^12)/132","B",1
1311,1,14,14,0.0056815,"\int (c+d x)^{10} \, dx","IntegrateAlgebraic[(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
1312,1,839,241,0.4646383,"\int \frac{(c+d x)^{10}}{a+b x} \, dx","IntegrateAlgebraic[(c + d*x)^10/(a + b*x),x]","\frac{\log (a+b x) (b c-a d)^{10}}{b^{11}}+\frac{252 b^9 x^{10} d^{10}-280 a b^8 x^9 d^{10}+315 a^2 b^7 x^8 d^{10}-360 a^3 b^6 x^7 d^{10}+420 a^4 b^5 x^6 d^{10}-504 a^5 b^4 x^5 d^{10}+630 a^6 b^3 x^4 d^{10}-840 a^7 b^2 x^3 d^{10}+1260 a^8 b x^2 d^{10}-2520 a^9 x d^{10}+2800 b^9 c x^9 d^9-3150 a b^8 c x^8 d^9+3600 a^2 b^7 c x^7 d^9-4200 a^3 b^6 c x^6 d^9+5040 a^4 b^5 c x^5 d^9-6300 a^5 b^4 c x^4 d^9+8400 a^6 b^3 c x^3 d^9-12600 a^7 b^2 c x^2 d^9+25200 a^8 b c x d^9+14175 b^9 c^2 x^8 d^8-16200 a b^8 c^2 x^7 d^8+18900 a^2 b^7 c^2 x^6 d^8-22680 a^3 b^6 c^2 x^5 d^8+28350 a^4 b^5 c^2 x^4 d^8-37800 a^5 b^4 c^2 x^3 d^8+56700 a^6 b^3 c^2 x^2 d^8-113400 a^7 b^2 c^2 x d^8+43200 b^9 c^3 x^7 d^7-50400 a b^8 c^3 x^6 d^7+60480 a^2 b^7 c^3 x^5 d^7-75600 a^3 b^6 c^3 x^4 d^7+100800 a^4 b^5 c^3 x^3 d^7-151200 a^5 b^4 c^3 x^2 d^7+302400 a^6 b^3 c^3 x d^7+88200 b^9 c^4 x^6 d^6-105840 a b^8 c^4 x^5 d^6+132300 a^2 b^7 c^4 x^4 d^6-176400 a^3 b^6 c^4 x^3 d^6+264600 a^4 b^5 c^4 x^2 d^6-529200 a^5 b^4 c^4 x d^6+127008 b^9 c^5 x^5 d^5-158760 a b^8 c^5 x^4 d^5+211680 a^2 b^7 c^5 x^3 d^5-317520 a^3 b^6 c^5 x^2 d^5+635040 a^4 b^5 c^5 x d^5+132300 b^9 c^6 x^4 d^4-176400 a b^8 c^6 x^3 d^4+264600 a^2 b^7 c^6 x^2 d^4-529200 a^3 b^6 c^6 x d^4+100800 b^9 c^7 x^3 d^3-151200 a b^8 c^7 x^2 d^3+302400 a^2 b^7 c^7 x d^3+56700 b^9 c^8 x^2 d^2-113400 a b^8 c^8 x d^2+25200 b^9 c^9 x d}{2520 b^{10}}","\frac{(b c-a d)^{10} \log (a+b x)}{b^{11}}+\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{(c+d x)^{10}}{10 b}",1,"(25200*b^9*c^9*d*x - 113400*a*b^8*c^8*d^2*x + 302400*a^2*b^7*c^7*d^3*x - 529200*a^3*b^6*c^6*d^4*x + 635040*a^4*b^5*c^5*d^5*x - 529200*a^5*b^4*c^4*d^6*x + 302400*a^6*b^3*c^3*d^7*x - 113400*a^7*b^2*c^2*d^8*x + 25200*a^8*b*c*d^9*x - 2520*a^9*d^10*x + 56700*b^9*c^8*d^2*x^2 - 151200*a*b^8*c^7*d^3*x^2 + 264600*a^2*b^7*c^6*d^4*x^2 - 317520*a^3*b^6*c^5*d^5*x^2 + 264600*a^4*b^5*c^4*d^6*x^2 - 151200*a^5*b^4*c^3*d^7*x^2 + 56700*a^6*b^3*c^2*d^8*x^2 - 12600*a^7*b^2*c*d^9*x^2 + 1260*a^8*b*d^10*x^2 + 100800*b^9*c^7*d^3*x^3 - 176400*a*b^8*c^6*d^4*x^3 + 211680*a^2*b^7*c^5*d^5*x^3 - 176400*a^3*b^6*c^4*d^6*x^3 + 100800*a^4*b^5*c^3*d^7*x^3 - 37800*a^5*b^4*c^2*d^8*x^3 + 8400*a^6*b^3*c*d^9*x^3 - 840*a^7*b^2*d^10*x^3 + 132300*b^9*c^6*d^4*x^4 - 158760*a*b^8*c^5*d^5*x^4 + 132300*a^2*b^7*c^4*d^6*x^4 - 75600*a^3*b^6*c^3*d^7*x^4 + 28350*a^4*b^5*c^2*d^8*x^4 - 6300*a^5*b^4*c*d^9*x^4 + 630*a^6*b^3*d^10*x^4 + 127008*b^9*c^5*d^5*x^5 - 105840*a*b^8*c^4*d^6*x^5 + 60480*a^2*b^7*c^3*d^7*x^5 - 22680*a^3*b^6*c^2*d^8*x^5 + 5040*a^4*b^5*c*d^9*x^5 - 504*a^5*b^4*d^10*x^5 + 88200*b^9*c^4*d^6*x^6 - 50400*a*b^8*c^3*d^7*x^6 + 18900*a^2*b^7*c^2*d^8*x^6 - 4200*a^3*b^6*c*d^9*x^6 + 420*a^4*b^5*d^10*x^6 + 43200*b^9*c^3*d^7*x^7 - 16200*a*b^8*c^2*d^8*x^7 + 3600*a^2*b^7*c*d^9*x^7 - 360*a^3*b^6*d^10*x^7 + 14175*b^9*c^2*d^8*x^8 - 3150*a*b^8*c*d^9*x^8 + 315*a^2*b^7*d^10*x^8 + 2800*b^9*c*d^9*x^9 - 280*a*b^8*d^10*x^9 + 252*b^9*d^10*x^10)/(2520*b^10) + ((b*c - a*d)^10*Log[a + b*x])/b^11","B",1
1313,1,977,258,0.4043257,"\int \frac{(c+d x)^{10}}{(a+b x)^2} \, dx","IntegrateAlgebraic[(c + d*x)^10/(a + b*x)^2,x]","\frac{10 d \log (a+b x) (b c-a d)^9}{b^{11}}+\frac{-252 c^{10} b^{10}+28 d^{10} x^{10} b^{10}+315 c d^9 x^9 b^{10}+1620 c^2 d^8 x^8 b^{10}+5040 c^3 d^7 x^7 b^{10}+10584 c^4 d^6 x^6 b^{10}+15876 c^5 d^5 x^5 b^{10}+17640 c^6 d^4 x^4 b^{10}+15120 c^7 d^3 x^3 b^{10}+11340 c^8 d^2 x^2 b^{10}-35 a d^{10} x^9 b^9-405 a c d^9 x^8 b^9-2160 a c^2 d^8 x^7 b^9-7056 a c^3 d^7 x^6 b^9-15876 a c^4 d^6 x^5 b^9-26460 a c^5 d^5 x^4 b^9-35280 a c^6 d^4 x^3 b^9-45360 a c^7 d^3 x^2 b^9+2520 a c^9 d b^9+11340 a c^8 d^2 x b^9+45 a^2 d^{10} x^8 b^8+540 a^2 c d^9 x^7 b^8+3024 a^2 c^2 d^8 x^6 b^8+10584 a^2 c^3 d^7 x^5 b^8+26460 a^2 c^4 d^6 x^4 b^8+52920 a^2 c^5 d^5 x^3 b^8-11340 a^2 c^8 d^2 b^8+105840 a^2 c^6 d^4 x^2 b^8-60480 a^2 c^7 d^3 x b^8-60 a^3 d^{10} x^7 b^7-756 a^3 c d^9 x^6 b^7-4536 a^3 c^2 d^8 x^5 b^7-17640 a^3 c^3 d^7 x^4 b^7+30240 a^3 c^7 d^3 b^7-52920 a^3 c^4 d^6 x^3 b^7-158760 a^3 c^5 d^5 x^2 b^7+158760 a^3 c^6 d^4 x b^7+84 a^4 d^{10} x^6 b^6+1134 a^4 c d^9 x^5 b^6-52920 a^4 c^6 d^4 b^6+7560 a^4 c^2 d^8 x^4 b^6+35280 a^4 c^3 d^7 x^3 b^6+158760 a^4 c^4 d^6 x^2 b^6-254016 a^4 c^5 d^5 x b^6+63504 a^5 c^5 d^5 b^5-126 a^5 d^{10} x^5 b^5-1890 a^5 c d^9 x^4 b^5-15120 a^5 c^2 d^8 x^3 b^5-105840 a^5 c^3 d^7 x^2 b^5+264600 a^5 c^4 d^6 x b^5-52920 a^6 c^4 d^6 b^4+210 a^6 d^{10} x^4 b^4+3780 a^6 c d^9 x^3 b^4+45360 a^6 c^2 d^8 x^2 b^4-181440 a^6 c^3 d^7 x b^4+30240 a^7 c^3 d^7 b^3-420 a^7 d^{10} x^3 b^3-11340 a^7 c d^9 x^2 b^3+79380 a^7 c^2 d^8 x b^3-11340 a^8 c^2 d^8 b^2+1260 a^8 d^{10} x^2 b^2-20160 a^8 c d^9 x b^2+2520 a^9 c d^9 b+2268 a^9 d^{10} x b-252 a^{10} d^{10}}{252 b^{11} (a+b 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{(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{45 d^2 x (b c-a d)^8}{b^{10}}",1,"(-252*b^10*c^10 + 2520*a*b^9*c^9*d - 11340*a^2*b^8*c^8*d^2 + 30240*a^3*b^7*c^7*d^3 - 52920*a^4*b^6*c^6*d^4 + 63504*a^5*b^5*c^5*d^5 - 52920*a^6*b^4*c^4*d^6 + 30240*a^7*b^3*c^3*d^7 - 11340*a^8*b^2*c^2*d^8 + 2520*a^9*b*c*d^9 - 252*a^10*d^10 + 11340*a*b^9*c^8*d^2*x - 60480*a^2*b^8*c^7*d^3*x + 158760*a^3*b^7*c^6*d^4*x - 254016*a^4*b^6*c^5*d^5*x + 264600*a^5*b^5*c^4*d^6*x - 181440*a^6*b^4*c^3*d^7*x + 79380*a^7*b^3*c^2*d^8*x - 20160*a^8*b^2*c*d^9*x + 2268*a^9*b*d^10*x + 11340*b^10*c^8*d^2*x^2 - 45360*a*b^9*c^7*d^3*x^2 + 105840*a^2*b^8*c^6*d^4*x^2 - 158760*a^3*b^7*c^5*d^5*x^2 + 158760*a^4*b^6*c^4*d^6*x^2 - 105840*a^5*b^5*c^3*d^7*x^2 + 45360*a^6*b^4*c^2*d^8*x^2 - 11340*a^7*b^3*c*d^9*x^2 + 1260*a^8*b^2*d^10*x^2 + 15120*b^10*c^7*d^3*x^3 - 35280*a*b^9*c^6*d^4*x^3 + 52920*a^2*b^8*c^5*d^5*x^3 - 52920*a^3*b^7*c^4*d^6*x^3 + 35280*a^4*b^6*c^3*d^7*x^3 - 15120*a^5*b^5*c^2*d^8*x^3 + 3780*a^6*b^4*c*d^9*x^3 - 420*a^7*b^3*d^10*x^3 + 17640*b^10*c^6*d^4*x^4 - 26460*a*b^9*c^5*d^5*x^4 + 26460*a^2*b^8*c^4*d^6*x^4 - 17640*a^3*b^7*c^3*d^7*x^4 + 7560*a^4*b^6*c^2*d^8*x^4 - 1890*a^5*b^5*c*d^9*x^4 + 210*a^6*b^4*d^10*x^4 + 15876*b^10*c^5*d^5*x^5 - 15876*a*b^9*c^4*d^6*x^5 + 10584*a^2*b^8*c^3*d^7*x^5 - 4536*a^3*b^7*c^2*d^8*x^5 + 1134*a^4*b^6*c*d^9*x^5 - 126*a^5*b^5*d^10*x^5 + 10584*b^10*c^4*d^6*x^6 - 7056*a*b^9*c^3*d^7*x^6 + 3024*a^2*b^8*c^2*d^8*x^6 - 756*a^3*b^7*c*d^9*x^6 + 84*a^4*b^6*d^10*x^6 + 5040*b^10*c^3*d^7*x^7 - 2160*a*b^9*c^2*d^8*x^7 + 540*a^2*b^8*c*d^9*x^7 - 60*a^3*b^7*d^10*x^7 + 1620*b^10*c^2*d^8*x^8 - 405*a*b^9*c*d^9*x^8 + 45*a^2*b^8*d^10*x^8 + 315*b^10*c*d^9*x^9 - 35*a*b^9*d^10*x^9 + 28*b^10*d^10*x^10)/(252*b^11*(a + b*x)) + (10*d*(b*c - a*d)^9*Log[a + b*x])/b^11","B",1
1314,1,975,262,0.4044609,"\int \frac{(c+d x)^{10}}{(a+b x)^3} \, dx","IntegrateAlgebraic[(c + d*x)^10/(a + b*x)^3,x]","\frac{45 d^2 \log (a+b x) (b c-a d)^8}{b^{11}}+\frac{-28 c^{10} b^{10}+7 d^{10} x^{10} b^{10}+80 c d^9 x^9 b^{10}+420 c^2 d^8 x^8 b^{10}+1344 c^3 d^7 x^7 b^{10}+2940 c^4 d^6 x^6 b^{10}+4704 c^5 d^5 x^5 b^{10}+5880 c^6 d^4 x^4 b^{10}+6720 c^7 d^3 x^3 b^{10}-560 c^9 d x b^{10}-10 a d^{10} x^9 b^9-120 a c d^9 x^8 b^9-672 a c^2 d^8 x^7 b^9-2352 a c^3 d^7 x^6 b^9-5880 a c^4 d^6 x^5 b^9-11760 a c^5 d^5 x^4 b^9-23520 a c^6 d^4 x^3 b^9+13440 a c^7 d^3 x^2 b^9-280 a c^9 d b^9+5040 a c^8 d^2 x b^9+15 a^2 d^{10} x^8 b^8+192 a^2 c d^9 x^7 b^8+1176 a^2 c^2 d^8 x^6 b^8+4704 a^2 c^3 d^7 x^5 b^8+14700 a^2 c^4 d^6 x^4 b^8+47040 a^2 c^5 d^5 x^3 b^8+3780 a^2 c^8 d^2 b^8-64680 a^2 c^6 d^4 x^2 b^8-13440 a^2 c^7 d^3 x b^8-24 a^3 d^{10} x^7 b^7-336 a^3 c d^9 x^6 b^7-2352 a^3 c^2 d^8 x^5 b^7-11760 a^3 c^3 d^7 x^4 b^7-16800 a^3 c^7 d^3 b^7-58800 a^3 c^4 d^6 x^3 b^7+148176 a^3 c^5 d^5 x^2 b^7+11760 a^3 c^6 d^4 x b^7+42 a^4 d^{10} x^6 b^6+672 a^4 c d^9 x^5 b^6+41160 a^4 c^6 d^4 b^6+5880 a^4 c^2 d^8 x^4 b^6+47040 a^4 c^3 d^7 x^3 b^6-199920 a^4 c^4 d^6 x^2 b^6+14112 a^4 c^5 d^5 x b^6-63504 a^5 c^5 d^5 b^5-84 a^5 d^{10} x^5 b^5-1680 a^5 c d^9 x^4 b^5-23520 a^5 c^2 d^8 x^3 b^5+168000 a^5 c^3 d^7 x^2 b^5-47040 a^5 c^4 d^6 x b^5+64680 a^6 c^4 d^6 b^4+210 a^6 d^{10} x^4 b^4+6720 a^6 c d^9 x^3 b^4-86940 a^6 c^2 d^8 x^2 b^4+53760 a^6 c^3 d^7 x b^4-43680 a^7 c^3 d^7 b^3-840 a^7 d^{10} x^3 b^3+25480 a^7 c d^9 x^2 b^3-32760 a^7 c^2 d^8 x b^3+18900 a^8 c^2 d^8 b^2-3248 a^8 d^{10} x^2 b^2+10640 a^8 c d^9 x b^2-4760 a^9 c d^9 b-1456 a^9 d^{10} x b+532 a^{10} d^{10}}{56 b^{11} (a+b x)^2}","\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{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{120 d^3 x (b c-a d)^7}{b^{10}}",1,"(-28*b^10*c^10 - 280*a*b^9*c^9*d + 3780*a^2*b^8*c^8*d^2 - 16800*a^3*b^7*c^7*d^3 + 41160*a^4*b^6*c^6*d^4 - 63504*a^5*b^5*c^5*d^5 + 64680*a^6*b^4*c^4*d^6 - 43680*a^7*b^3*c^3*d^7 + 18900*a^8*b^2*c^2*d^8 - 4760*a^9*b*c*d^9 + 532*a^10*d^10 - 560*b^10*c^9*d*x + 5040*a*b^9*c^8*d^2*x - 13440*a^2*b^8*c^7*d^3*x + 11760*a^3*b^7*c^6*d^4*x + 14112*a^4*b^6*c^5*d^5*x - 47040*a^5*b^5*c^4*d^6*x + 53760*a^6*b^4*c^3*d^7*x - 32760*a^7*b^3*c^2*d^8*x + 10640*a^8*b^2*c*d^9*x - 1456*a^9*b*d^10*x + 13440*a*b^9*c^7*d^3*x^2 - 64680*a^2*b^8*c^6*d^4*x^2 + 148176*a^3*b^7*c^5*d^5*x^2 - 199920*a^4*b^6*c^4*d^6*x^2 + 168000*a^5*b^5*c^3*d^7*x^2 - 86940*a^6*b^4*c^2*d^8*x^2 + 25480*a^7*b^3*c*d^9*x^2 - 3248*a^8*b^2*d^10*x^2 + 6720*b^10*c^7*d^3*x^3 - 23520*a*b^9*c^6*d^4*x^3 + 47040*a^2*b^8*c^5*d^5*x^3 - 58800*a^3*b^7*c^4*d^6*x^3 + 47040*a^4*b^6*c^3*d^7*x^3 - 23520*a^5*b^5*c^2*d^8*x^3 + 6720*a^6*b^4*c*d^9*x^3 - 840*a^7*b^3*d^10*x^3 + 5880*b^10*c^6*d^4*x^4 - 11760*a*b^9*c^5*d^5*x^4 + 14700*a^2*b^8*c^4*d^6*x^4 - 11760*a^3*b^7*c^3*d^7*x^4 + 5880*a^4*b^6*c^2*d^8*x^4 - 1680*a^5*b^5*c*d^9*x^4 + 210*a^6*b^4*d^10*x^4 + 4704*b^10*c^5*d^5*x^5 - 5880*a*b^9*c^4*d^6*x^5 + 4704*a^2*b^8*c^3*d^7*x^5 - 2352*a^3*b^7*c^2*d^8*x^5 + 672*a^4*b^6*c*d^9*x^5 - 84*a^5*b^5*d^10*x^5 + 2940*b^10*c^4*d^6*x^6 - 2352*a*b^9*c^3*d^7*x^6 + 1176*a^2*b^8*c^2*d^8*x^6 - 336*a^3*b^7*c*d^9*x^6 + 42*a^4*b^6*d^10*x^6 + 1344*b^10*c^3*d^7*x^7 - 672*a*b^9*c^2*d^8*x^7 + 192*a^2*b^8*c*d^9*x^7 - 24*a^3*b^7*d^10*x^7 + 420*b^10*c^2*d^8*x^8 - 120*a*b^9*c*d^9*x^8 + 15*a^2*b^8*d^10*x^8 + 80*b^10*c*d^9*x^9 - 10*a*b^9*d^10*x^9 + 7*b^10*d^10*x^10)/(56*b^11*(a + b*x)^2) + (45*d^2*(b*c - a*d)^8*Log[a + b*x])/b^11","B",1
1315,1,975,258,0.334616,"\int \frac{(c+d x)^{10}}{(a+b x)^4} \, dx","IntegrateAlgebraic[(c + d*x)^10/(a + b*x)^4,x]","\frac{120 d^3 \log (a+b x) (b c-a d)^7}{b^{11}}+\frac{-7 c^{10} b^{10}+3 d^{10} x^{10} b^{10}+35 c d^9 x^9 b^{10}+189 c^2 d^8 x^8 b^{10}+630 c^3 d^7 x^7 b^{10}+1470 c^4 d^6 x^6 b^{10}+2646 c^5 d^5 x^5 b^{10}+4410 c^6 d^4 x^4 b^{10}-945 c^8 d^2 x^2 b^{10}-105 c^9 d x b^{10}-5 a d^{10} x^9 b^9-63 a c d^9 x^8 b^9-378 a c^2 d^8 x^7 b^9-1470 a c^3 d^7 x^6 b^9-4410 a c^4 d^6 x^5 b^9-13230 a c^5 d^5 x^4 b^9+13230 a c^6 d^4 x^3 b^9+7560 a c^7 d^3 x^2 b^9-35 a c^9 d b^9-945 a c^8 d^2 x b^9+9 a^2 d^{10} x^8 b^8+126 a^2 c d^9 x^7 b^8+882 a^2 c^2 d^8 x^6 b^8+4410 a^2 c^3 d^7 x^5 b^8+22050 a^2 c^4 d^6 x^4 b^8-55566 a^2 c^5 d^5 x^3 b^8-315 a^2 c^8 d^2 b^8-13230 a^2 c^6 d^4 x^2 b^8+11340 a^2 c^7 d^3 x b^8-18 a^3 d^{10} x^7 b^7-294 a^3 c d^9 x^6 b^7-2646 a^3 c^2 d^8 x^5 b^7-22050 a^3 c^3 d^7 x^4 b^7+4620 a^3 c^7 d^3 b^7+107310 a^3 c^4 d^6 x^3 b^7-7938 a^3 c^5 d^5 x^2 b^7-39690 a^3 c^6 d^4 x b^7+42 a^4 d^{10} x^6 b^6+882 a^4 c d^9 x^5 b^6-19110 a^4 c^6 d^4 b^6+13230 a^4 c^2 d^8 x^4 b^6-116760 a^4 c^3 d^7 x^3 b^6+57330 a^4 c^4 d^6 x^2 b^6+71442 a^4 c^5 d^5 x b^6+41454 a^5 c^5 d^5 b^5-126 a^5 d^{10} x^5 b^5-4410 a^5 c d^9 x^4 b^5+74025 a^5 c^2 d^8 x^3 b^5-85680 a^5 c^3 d^7 x^2 b^5-74970 a^5 c^4 d^6 x b^5-54390 a^6 c^4 d^6 b^4+630 a^6 d^{10} x^4 b^4-25655 a^6 c d^9 x^3 b^4+63315 a^6 c^2 d^8 x^2 b^4+46620 a^6 c^3 d^7 x b^4+44940 a^7 c^3 d^7 b^3+3773 a^7 d^{10} x^3 b^3-24045 a^7 c d^9 x^2 b^3-16065 a^7 c^2 d^8 x b^3-22995 a^8 c^2 d^8 b^2+3759 a^8 d^{10} x^2 b^2+2415 a^8 c d^9 x b^2+6685 a^9 c d^9 b-21 a^9 d^{10} x b-847 a^{10} d^{10}}{21 b^{11} (a+b x)^3}","\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{120 d^3 (b c-a d)^7 \log (a+b x)}{b^{11}}-\frac{45 d^2 (b c-a d)^8}{b^{11} (a+b x)}-\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{210 d^4 x (b c-a d)^6}{b^{10}}",1,"(-7*b^10*c^10 - 35*a*b^9*c^9*d - 315*a^2*b^8*c^8*d^2 + 4620*a^3*b^7*c^7*d^3 - 19110*a^4*b^6*c^6*d^4 + 41454*a^5*b^5*c^5*d^5 - 54390*a^6*b^4*c^4*d^6 + 44940*a^7*b^3*c^3*d^7 - 22995*a^8*b^2*c^2*d^8 + 6685*a^9*b*c*d^9 - 847*a^10*d^10 - 105*b^10*c^9*d*x - 945*a*b^9*c^8*d^2*x + 11340*a^2*b^8*c^7*d^3*x - 39690*a^3*b^7*c^6*d^4*x + 71442*a^4*b^6*c^5*d^5*x - 74970*a^5*b^5*c^4*d^6*x + 46620*a^6*b^4*c^3*d^7*x - 16065*a^7*b^3*c^2*d^8*x + 2415*a^8*b^2*c*d^9*x - 21*a^9*b*d^10*x - 945*b^10*c^8*d^2*x^2 + 7560*a*b^9*c^7*d^3*x^2 - 13230*a^2*b^8*c^6*d^4*x^2 - 7938*a^3*b^7*c^5*d^5*x^2 + 57330*a^4*b^6*c^4*d^6*x^2 - 85680*a^5*b^5*c^3*d^7*x^2 + 63315*a^6*b^4*c^2*d^8*x^2 - 24045*a^7*b^3*c*d^9*x^2 + 3759*a^8*b^2*d^10*x^2 + 13230*a*b^9*c^6*d^4*x^3 - 55566*a^2*b^8*c^5*d^5*x^3 + 107310*a^3*b^7*c^4*d^6*x^3 - 116760*a^4*b^6*c^3*d^7*x^3 + 74025*a^5*b^5*c^2*d^8*x^3 - 25655*a^6*b^4*c*d^9*x^3 + 3773*a^7*b^3*d^10*x^3 + 4410*b^10*c^6*d^4*x^4 - 13230*a*b^9*c^5*d^5*x^4 + 22050*a^2*b^8*c^4*d^6*x^4 - 22050*a^3*b^7*c^3*d^7*x^4 + 13230*a^4*b^6*c^2*d^8*x^4 - 4410*a^5*b^5*c*d^9*x^4 + 630*a^6*b^4*d^10*x^4 + 2646*b^10*c^5*d^5*x^5 - 4410*a*b^9*c^4*d^6*x^5 + 4410*a^2*b^8*c^3*d^7*x^5 - 2646*a^3*b^7*c^2*d^8*x^5 + 882*a^4*b^6*c*d^9*x^5 - 126*a^5*b^5*d^10*x^5 + 1470*b^10*c^4*d^6*x^6 - 1470*a*b^9*c^3*d^7*x^6 + 882*a^2*b^8*c^2*d^8*x^6 - 294*a^3*b^7*c*d^9*x^6 + 42*a^4*b^6*d^10*x^6 + 630*b^10*c^3*d^7*x^7 - 378*a*b^9*c^2*d^8*x^7 + 126*a^2*b^8*c*d^9*x^7 - 18*a^3*b^7*d^10*x^7 + 189*b^10*c^2*d^8*x^8 - 63*a*b^9*c*d^9*x^8 + 9*a^2*b^8*d^10*x^8 + 35*b^10*c*d^9*x^9 - 5*a*b^9*d^10*x^9 + 3*b^10*d^10*x^10)/(21*b^11*(a + b*x)^3) + (120*d^3*(b*c - a*d)^7*Log[a + b*x])/b^11","B",1
1316,1,975,262,0.3440774,"\int \frac{(c+d x)^{10}}{(a+b x)^5} \, dx","IntegrateAlgebraic[(c + d*x)^10/(a + b*x)^5,x]","\frac{210 d^4 \log (a+b x) (b c-a d)^6}{b^{11}}+\frac{-3 c^{10} b^{10}+2 d^{10} x^{10} b^{10}+24 c d^9 x^9 b^{10}+135 c^2 d^8 x^8 b^{10}+480 c^3 d^7 x^7 b^{10}+1260 c^4 d^6 x^6 b^{10}+3024 c^5 d^5 x^5 b^{10}-1440 c^7 d^3 x^3 b^{10}-270 c^8 d^2 x^2 b^{10}-40 c^9 d x b^{10}-4 a d^{10} x^9 b^9-54 a c d^9 x^8 b^9-360 a c^2 d^8 x^7 b^9-1680 a c^3 d^7 x^6 b^9-7560 a c^4 d^6 x^5 b^9+12096 a c^5 d^5 x^4 b^9+10080 a c^6 d^4 x^3 b^9-2160 a c^7 d^3 x^2 b^9-10 a c^9 d b^9-180 a c^8 d^2 x b^9+9 a^2 d^{10} x^8 b^8+144 a^2 c d^9 x^7 b^8+1260 a^2 c^2 d^8 x^6 b^8+10080 a^2 c^3 d^7 x^5 b^8-42840 a^2 c^4 d^6 x^4 b^8-12096 a^2 c^5 d^5 x^3 b^8-45 a^2 c^8 d^2 b^8+22680 a^2 c^6 d^4 x^2 b^8-1440 a^2 c^7 d^3 x b^8-24 a^3 d^{10} x^7 b^7-504 a^3 c d^9 x^6 b^7-7560 a^3 c^2 d^8 x^5 b^7+66720 a^3 c^3 d^7 x^4 b^7-360 a^3 c^7 d^3 b^7-20160 a^3 c^4 d^6 x^3 b^7-63504 a^3 c^5 d^5 x^2 b^7+18480 a^3 c^6 d^4 x b^7+84 a^4 d^{10} x^6 b^6+3024 a^4 c d^9 x^5 b^6+5250 a^4 c^6 d^4 b^6-54765 a^4 c^2 d^8 x^4 b^6+65280 a^4 c^3 d^7 x^3 b^6+83160 a^4 c^4 d^6 x^2 b^6-62496 a^4 c^5 d^5 x b^6-19404 a^5 c^5 d^5 b^5-504 a^5 d^{10} x^5 b^5+23250 a^5 c d^9 x^4 b^5-67860 a^5 c^2 d^8 x^3 b^5-53280 a^5 c^3 d^7 x^2 b^5+105840 a^5 c^4 d^6 x b^5+35910 a^6 c^4 d^6 b^4-4043 a^6 d^{10} x^4 b^4+32520 a^6 c d^9 x^3 b^4+11610 a^6 c^2 d^8 x^2 b^4-102720 a^6 c^3 d^7 x b^4-38280 a^7 c^3 d^7 b^3-6092 a^7 d^{10} x^3 b^3+3420 a^7 c d^9 x^2 b^3+58140 a^7 c^2 d^8 x b^3+23985 a^8 c^2 d^8 b^2-1578 a^8 d^{10} x^2 b^2-17880 a^8 c d^9 x b^2-8250 a^9 c d^9 b+2308 a^9 d^{10} x b+1207 a^{10} d^{10}}{12 b^{11} (a+b x)^4}","\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{210 d^4 (b c-a d)^6 \log (a+b x)}{b^{11}}-\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{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{252 d^5 x (b c-a d)^5}{b^{10}}",1,"(-3*b^10*c^10 - 10*a*b^9*c^9*d - 45*a^2*b^8*c^8*d^2 - 360*a^3*b^7*c^7*d^3 + 5250*a^4*b^6*c^6*d^4 - 19404*a^5*b^5*c^5*d^5 + 35910*a^6*b^4*c^4*d^6 - 38280*a^7*b^3*c^3*d^7 + 23985*a^8*b^2*c^2*d^8 - 8250*a^9*b*c*d^9 + 1207*a^10*d^10 - 40*b^10*c^9*d*x - 180*a*b^9*c^8*d^2*x - 1440*a^2*b^8*c^7*d^3*x + 18480*a^3*b^7*c^6*d^4*x - 62496*a^4*b^6*c^5*d^5*x + 105840*a^5*b^5*c^4*d^6*x - 102720*a^6*b^4*c^3*d^7*x + 58140*a^7*b^3*c^2*d^8*x - 17880*a^8*b^2*c*d^9*x + 2308*a^9*b*d^10*x - 270*b^10*c^8*d^2*x^2 - 2160*a*b^9*c^7*d^3*x^2 + 22680*a^2*b^8*c^6*d^4*x^2 - 63504*a^3*b^7*c^5*d^5*x^2 + 83160*a^4*b^6*c^4*d^6*x^2 - 53280*a^5*b^5*c^3*d^7*x^2 + 11610*a^6*b^4*c^2*d^8*x^2 + 3420*a^7*b^3*c*d^9*x^2 - 1578*a^8*b^2*d^10*x^2 - 1440*b^10*c^7*d^3*x^3 + 10080*a*b^9*c^6*d^4*x^3 - 12096*a^2*b^8*c^5*d^5*x^3 - 20160*a^3*b^7*c^4*d^6*x^3 + 65280*a^4*b^6*c^3*d^7*x^3 - 67860*a^5*b^5*c^2*d^8*x^3 + 32520*a^6*b^4*c*d^9*x^3 - 6092*a^7*b^3*d^10*x^3 + 12096*a*b^9*c^5*d^5*x^4 - 42840*a^2*b^8*c^4*d^6*x^4 + 66720*a^3*b^7*c^3*d^7*x^4 - 54765*a^4*b^6*c^2*d^8*x^4 + 23250*a^5*b^5*c*d^9*x^4 - 4043*a^6*b^4*d^10*x^4 + 3024*b^10*c^5*d^5*x^5 - 7560*a*b^9*c^4*d^6*x^5 + 10080*a^2*b^8*c^3*d^7*x^5 - 7560*a^3*b^7*c^2*d^8*x^5 + 3024*a^4*b^6*c*d^9*x^5 - 504*a^5*b^5*d^10*x^5 + 1260*b^10*c^4*d^6*x^6 - 1680*a*b^9*c^3*d^7*x^6 + 1260*a^2*b^8*c^2*d^8*x^6 - 504*a^3*b^7*c*d^9*x^6 + 84*a^4*b^6*d^10*x^6 + 480*b^10*c^3*d^7*x^7 - 360*a*b^9*c^2*d^8*x^7 + 144*a^2*b^8*c*d^9*x^7 - 24*a^3*b^7*d^10*x^7 + 135*b^10*c^2*d^8*x^8 - 54*a*b^9*c*d^9*x^8 + 9*a^2*b^8*d^10*x^8 + 24*b^10*c*d^9*x^9 - 4*a*b^9*d^10*x^9 + 2*b^10*d^10*x^10)/(12*b^11*(a + b*x)^4) + (210*d^4*(b*c - a*d)^6*Log[a + b*x])/b^11","B",1
1317,1,975,260,0.3625857,"\int \frac{(c+d x)^{10}}{(a+b x)^6} \, dx","IntegrateAlgebraic[(c + d*x)^10/(a + b*x)^6,x]","\frac{252 d^5 \log (a+b x) (b c-a d)^5}{b^{11}}+\frac{-2 c^{10} b^{10}+2 d^{10} x^{10} b^{10}+25 c d^9 x^9 b^{10}+150 c^2 d^8 x^8 b^{10}+600 c^3 d^7 x^7 b^{10}+2100 c^4 d^6 x^6 b^{10}-2100 c^6 d^4 x^4 b^{10}-600 c^7 d^3 x^3 b^{10}-150 c^8 d^2 x^2 b^{10}-25 c^9 d x b^{10}-5 a d^{10} x^9 b^9-75 a c d^9 x^8 b^9-600 a c^2 d^8 x^7 b^9-4200 a c^3 d^7 x^6 b^9+10500 a c^4 d^6 x^5 b^9+12600 a c^5 d^5 x^4 b^9-4200 a c^6 d^4 x^3 b^9-600 a c^7 d^3 x^2 b^9-5 a c^9 d b^9-75 a c^8 d^2 x b^9+15 a^2 d^{10} x^8 b^8+300 a^2 c d^9 x^7 b^8+4200 a^2 c^2 d^8 x^6 b^8-30000 a^2 c^3 d^7 x^5 b^8-10500 a^2 c^4 d^6 x^4 b^8+37800 a^2 c^5 d^5 x^3 b^8-15 a^2 c^8 d^2 b^8-4200 a^2 c^6 d^4 x^2 b^8-300 a^2 c^7 d^3 x b^8-60 a^3 d^{10} x^7 b^7-2100 a^3 c d^9 x^6 b^7+35250 a^3 c^2 d^8 x^5 b^7-24000 a^3 c^3 d^7 x^4 b^7-60 a^3 c^7 d^3 b^7-84000 a^3 c^4 d^6 x^3 b^7+46200 a^3 c^5 d^5 x^2 b^7-2100 a^3 c^6 d^4 x b^7+420 a^4 d^{10} x^6 b^6-19375 a^4 c d^9 x^5 b^6-420 a^4 c^6 d^4 b^6+50250 a^4 c^2 d^8 x^4 b^6+78000 a^4 c^3 d^7 x^3 b^6-126000 a^4 c^4 d^6 x^2 b^6+26250 a^4 c^5 d^5 x b^6+5754 a^5 c^5 d^5 b^5+4127 a^5 d^{10} x^5 b^5-33875 a^5 c d^9 x^4 b^5-25500 a^5 c^2 d^8 x^3 b^5+162000 a^5 c^3 d^7 x^2 b^5-78750 a^5 c^4 d^6 x b^5-18270 a^6 c^4 d^6 b^4+8035 a^6 d^{10} x^4 b^4-4750 a^6 c d^9 x^3 b^4-109500 a^6 c^2 d^8 x^2 b^4+112500 a^6 c^3 d^7 x b^4+27540 a^7 c^3 d^7 b^3+3470 a^7 d^{10} x^3 b^3+37250 a^7 c d^9 x^2 b^3-86250 a^7 c^2 d^8 x b^3-22290 a^8 c^2 d^8 b^2-4930 a^8 d^{10} x^2 b^2+34375 a^8 c d^9 x b^2+9395 a^9 c d^9 b-5615 a^9 d^{10} x b-1627 a^{10} d^{10}}{10 b^{11} (a+b x)^5}","\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{252 d^5 (b c-a d)^5 \log (a+b x)}{b^{11}}-\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{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{210 d^6 x (b c-a d)^4}{b^{10}}",1,"(-2*b^10*c^10 - 5*a*b^9*c^9*d - 15*a^2*b^8*c^8*d^2 - 60*a^3*b^7*c^7*d^3 - 420*a^4*b^6*c^6*d^4 + 5754*a^5*b^5*c^5*d^5 - 18270*a^6*b^4*c^4*d^6 + 27540*a^7*b^3*c^3*d^7 - 22290*a^8*b^2*c^2*d^8 + 9395*a^9*b*c*d^9 - 1627*a^10*d^10 - 25*b^10*c^9*d*x - 75*a*b^9*c^8*d^2*x - 300*a^2*b^8*c^7*d^3*x - 2100*a^3*b^7*c^6*d^4*x + 26250*a^4*b^6*c^5*d^5*x - 78750*a^5*b^5*c^4*d^6*x + 112500*a^6*b^4*c^3*d^7*x - 86250*a^7*b^3*c^2*d^8*x + 34375*a^8*b^2*c*d^9*x - 5615*a^9*b*d^10*x - 150*b^10*c^8*d^2*x^2 - 600*a*b^9*c^7*d^3*x^2 - 4200*a^2*b^8*c^6*d^4*x^2 + 46200*a^3*b^7*c^5*d^5*x^2 - 126000*a^4*b^6*c^4*d^6*x^2 + 162000*a^5*b^5*c^3*d^7*x^2 - 109500*a^6*b^4*c^2*d^8*x^2 + 37250*a^7*b^3*c*d^9*x^2 - 4930*a^8*b^2*d^10*x^2 - 600*b^10*c^7*d^3*x^3 - 4200*a*b^9*c^6*d^4*x^3 + 37800*a^2*b^8*c^5*d^5*x^3 - 84000*a^3*b^7*c^4*d^6*x^3 + 78000*a^4*b^6*c^3*d^7*x^3 - 25500*a^5*b^5*c^2*d^8*x^3 - 4750*a^6*b^4*c*d^9*x^3 + 3470*a^7*b^3*d^10*x^3 - 2100*b^10*c^6*d^4*x^4 + 12600*a*b^9*c^5*d^5*x^4 - 10500*a^2*b^8*c^4*d^6*x^4 - 24000*a^3*b^7*c^3*d^7*x^4 + 50250*a^4*b^6*c^2*d^8*x^4 - 33875*a^5*b^5*c*d^9*x^4 + 8035*a^6*b^4*d^10*x^4 + 10500*a*b^9*c^4*d^6*x^5 - 30000*a^2*b^8*c^3*d^7*x^5 + 35250*a^3*b^7*c^2*d^8*x^5 - 19375*a^4*b^6*c*d^9*x^5 + 4127*a^5*b^5*d^10*x^5 + 2100*b^10*c^4*d^6*x^6 - 4200*a*b^9*c^3*d^7*x^6 + 4200*a^2*b^8*c^2*d^8*x^6 - 2100*a^3*b^7*c*d^9*x^6 + 420*a^4*b^6*d^10*x^6 + 600*b^10*c^3*d^7*x^7 - 600*a*b^9*c^2*d^8*x^7 + 300*a^2*b^8*c*d^9*x^7 - 60*a^3*b^7*d^10*x^7 + 150*b^10*c^2*d^8*x^8 - 75*a*b^9*c*d^9*x^8 + 15*a^2*b^8*d^10*x^8 + 25*b^10*c*d^9*x^9 - 5*a*b^9*d^10*x^9 + 2*b^10*d^10*x^10)/(10*b^11*(a + b*x)^5) + (252*d^5*(b*c - a*d)^5*Log[a + b*x])/b^11","B",1
1318,1,975,262,0.3769552,"\int \frac{(c+d x)^{10}}{(a+b x)^7} \, dx","IntegrateAlgebraic[(c + d*x)^10/(a + b*x)^7,x]","\frac{210 (b c-a d)^4 \log (a+b x) d^6}{b^{11}}+\frac{-2 c^{10} b^{10}+3 d^{10} x^{10} b^{10}+40 c d^9 x^9 b^{10}+270 c^2 d^8 x^8 b^{10}+1440 c^3 d^7 x^7 b^{10}-3024 c^5 d^5 x^5 b^{10}-1260 c^6 d^4 x^4 b^{10}-480 c^7 d^3 x^3 b^{10}-135 c^8 d^2 x^2 b^{10}-24 c^9 d x b^{10}-10 a d^{10} x^9 b^9-180 a c d^9 x^8 b^9-2160 a c^2 d^8 x^7 b^9+8640 a c^3 d^7 x^6 b^9+15120 a c^4 d^6 x^5 b^9-7560 a c^5 d^5 x^4 b^9-1680 a c^6 d^4 x^3 b^9-360 a c^7 d^3 x^2 b^9-4 a c^9 d b^9-54 a c^8 d^2 x b^9+45 a^2 d^{10} x^8 b^8+1440 a^2 c d^9 x^7 b^8-18630 a^2 c^2 d^8 x^6 b^8-8640 a^2 c^3 d^7 x^5 b^8+56700 a^2 c^4 d^6 x^4 b^8-10080 a^2 c^5 d^5 x^3 b^8-9 a^2 c^8 d^2 b^8-1260 a^2 c^6 d^4 x^2 b^8-144 a^2 c^7 d^3 x b^8-360 a^3 d^{10} x^7 b^7+14660 a^3 c d^9 x^6 b^7-21060 a^3 c^2 d^8 x^5 b^7-97200 a^3 c^3 d^7 x^4 b^7-24 a^3 c^7 d^3 b^7+92400 a^3 c^4 d^6 x^3 b^7-7560 a^3 c^5 d^5 x^2 b^7-504 a^3 c^6 d^4 x b^7-4043 a^4 d^{10} x^6 b^6+27480 a^4 c d^9 x^5 b^6-84 a^4 c^6 d^4 b^6+60750 a^4 c^2 d^8 x^4 b^6-196800 a^4 c^3 d^7 x^3 b^6+78750 a^4 c^4 d^6 x^2 b^6-3024 a^4 c^5 d^5 x b^6-504 a^5 c^5 d^5 b^5-9138 a^5 d^{10} x^5 b^5-6900 a^5 c d^9 x^4 b^5+181800 a^5 c^2 d^8 x^3 b^5-185400 a^5 c^3 d^7 x^2 b^5+34524 a^5 c^4 d^6 x b^5+6174 a^6 c^4 d^6 b^4-3945 a^6 d^{10} x^4 b^4-76400 a^6 c d^9 x^3 b^4+193050 a^6 c^2 d^8 x^2 b^4-86256 a^6 c^3 d^7 x b^4-16056 a^7 c^3 d^7 b^3+11540 a^7 d^{10} x^3 b^3-95100 a^7 c d^9 x^2 b^3+95364 a^7 c^2 d^8 x b^3+18414 a^8 c^2 d^8 b^2+18105 a^8 d^{10} x^2 b^2-50136 a^8 c d^9 x b^2-10036 a^9 c d^9 b+10266 a^9 d^{10} x b+2131 a^{10} d^{10}}{12 b^{11} (a+b x)^6}","\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{210 d^6 (b c-a d)^4 \log (a+b x)}{b^{11}}-\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{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{120 d^7 x (b c-a d)^3}{b^{10}}",1,"(-2*b^10*c^10 - 4*a*b^9*c^9*d - 9*a^2*b^8*c^8*d^2 - 24*a^3*b^7*c^7*d^3 - 84*a^4*b^6*c^6*d^4 - 504*a^5*b^5*c^5*d^5 + 6174*a^6*b^4*c^4*d^6 - 16056*a^7*b^3*c^3*d^7 + 18414*a^8*b^2*c^2*d^8 - 10036*a^9*b*c*d^9 + 2131*a^10*d^10 - 24*b^10*c^9*d*x - 54*a*b^9*c^8*d^2*x - 144*a^2*b^8*c^7*d^3*x - 504*a^3*b^7*c^6*d^4*x - 3024*a^4*b^6*c^5*d^5*x + 34524*a^5*b^5*c^4*d^6*x - 86256*a^6*b^4*c^3*d^7*x + 95364*a^7*b^3*c^2*d^8*x - 50136*a^8*b^2*c*d^9*x + 10266*a^9*b*d^10*x - 135*b^10*c^8*d^2*x^2 - 360*a*b^9*c^7*d^3*x^2 - 1260*a^2*b^8*c^6*d^4*x^2 - 7560*a^3*b^7*c^5*d^5*x^2 + 78750*a^4*b^6*c^4*d^6*x^2 - 185400*a^5*b^5*c^3*d^7*x^2 + 193050*a^6*b^4*c^2*d^8*x^2 - 95100*a^7*b^3*c*d^9*x^2 + 18105*a^8*b^2*d^10*x^2 - 480*b^10*c^7*d^3*x^3 - 1680*a*b^9*c^6*d^4*x^3 - 10080*a^2*b^8*c^5*d^5*x^3 + 92400*a^3*b^7*c^4*d^6*x^3 - 196800*a^4*b^6*c^3*d^7*x^3 + 181800*a^5*b^5*c^2*d^8*x^3 - 76400*a^6*b^4*c*d^9*x^3 + 11540*a^7*b^3*d^10*x^3 - 1260*b^10*c^6*d^4*x^4 - 7560*a*b^9*c^5*d^5*x^4 + 56700*a^2*b^8*c^4*d^6*x^4 - 97200*a^3*b^7*c^3*d^7*x^4 + 60750*a^4*b^6*c^2*d^8*x^4 - 6900*a^5*b^5*c*d^9*x^4 - 3945*a^6*b^4*d^10*x^4 - 3024*b^10*c^5*d^5*x^5 + 15120*a*b^9*c^4*d^6*x^5 - 8640*a^2*b^8*c^3*d^7*x^5 - 21060*a^3*b^7*c^2*d^8*x^5 + 27480*a^4*b^6*c*d^9*x^5 - 9138*a^5*b^5*d^10*x^5 + 8640*a*b^9*c^3*d^7*x^6 - 18630*a^2*b^8*c^2*d^8*x^6 + 14660*a^3*b^7*c*d^9*x^6 - 4043*a^4*b^6*d^10*x^6 + 1440*b^10*c^3*d^7*x^7 - 2160*a*b^9*c^2*d^8*x^7 + 1440*a^2*b^8*c*d^9*x^7 - 360*a^3*b^7*d^10*x^7 + 270*b^10*c^2*d^8*x^8 - 180*a*b^9*c*d^9*x^8 + 45*a^2*b^8*d^10*x^8 + 40*b^10*c*d^9*x^9 - 10*a*b^9*d^10*x^9 + 3*b^10*d^10*x^10)/(12*b^11*(a + b*x)^6) + (210*d^6*(b*c - a*d)^4*Log[a + b*x])/b^11","B",1
1319,1,975,258,0.4650209,"\int \frac{(c+d x)^{10}}{(a+b x)^8} \, dx","IntegrateAlgebraic[(c + d*x)^10/(a + b*x)^8,x]","\frac{120 (b c-a d)^3 \log (a+b x) d^7}{b^{11}}+\frac{-3 c^{10} b^{10}+7 d^{10} x^{10} b^{10}+105 c d^9 x^9 b^{10}+945 c^2 d^8 x^8 b^{10}-4410 c^4 d^6 x^6 b^{10}-2646 c^5 d^5 x^5 b^{10}-1470 c^6 d^4 x^4 b^{10}-630 c^7 d^3 x^3 b^{10}-189 c^8 d^2 x^2 b^{10}-35 c^9 d x b^{10}-35 a d^{10} x^9 b^9-945 a c d^9 x^8 b^9+6615 a c^2 d^8 x^7 b^9+17640 a c^3 d^7 x^6 b^9-13230 a c^4 d^6 x^5 b^9-4410 a c^5 d^5 x^4 b^9-1470 a c^6 d^4 x^3 b^9-378 a c^7 d^3 x^2 b^9-5 a c^9 d b^9-63 a c^8 d^2 x b^9+315 a^2 d^{10} x^8 b^8-9555 a^2 c d^9 x^7 b^8-6615 a^2 c^2 d^8 x^6 b^8+79380 a^2 c^3 d^7 x^5 b^8-22050 a^2 c^4 d^6 x^4 b^8-4410 a^2 c^5 d^5 x^3 b^8-9 a^2 c^8 d^2 b^8-882 a^2 c^6 d^4 x^2 b^8-126 a^2 c^7 d^3 x b^8+3773 a^3 d^{10} x^7 b^7-13965 a^3 c d^9 x^6 b^7-99225 a^3 c^2 d^8 x^5 b^7+161700 a^3 c^3 d^7 x^4 b^7-18 a^3 c^7 d^3 b^7-22050 a^3 c^4 d^6 x^3 b^7-2646 a^3 c^5 d^5 x^2 b^7-294 a^3 c^6 d^4 x b^7+8771 a^4 d^{10} x^6 b^6+37485 a^4 c d^9 x^5 b^6-42 a^4 c^6 d^4 b^6-253575 a^4 c^2 d^8 x^4 b^6+183750 a^4 c^3 d^7 x^3 b^6-13230 a^4 c^4 d^6 x^2 b^6-882 a^4 c^5 d^5 x b^6-126 a^5 c^5 d^5 b^5-147 a^5 d^{10} x^5 b^5+150675 a^5 c d^9 x^4 b^5-319725 a^5 c^2 d^8 x^3 b^5+120834 a^5 c^3 d^7 x^2 b^5-4410 a^5 c^4 d^6 x b^5-630 a^6 c^4 d^6 b^4-29645 a^6 d^{10} x^4 b^4+216825 a^6 c d^9 x^3 b^4-223587 a^6 c^2 d^8 x^2 b^4+43218 a^6 c^3 d^7 x b^4+6534 a^7 c^3 d^7 b^3-51695 a^7 d^{10} x^3 b^3+161847 a^7 c d^9 x^2 b^3-83349 a^7 c^2 d^8 x b^3-12987 a^8 c^2 d^8 b^2-41601 a^8 d^{10} x^2 b^2+62769 a^8 c d^9 x b^2+10047 a^9 c d^9 b-16807 a^9 d^{10} x b-2761 a^{10} d^{10}}{21 b^{11} (a+b x)^7}","\frac{5 d^9 (a+b x)^2 (b c-a d)}{b^{11}}+\frac{120 d^7 (b c-a d)^3 \log (a+b x)}{b^{11}}-\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{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{45 d^8 x (b c-a d)^2}{b^{10}}",1,"(-3*b^10*c^10 - 5*a*b^9*c^9*d - 9*a^2*b^8*c^8*d^2 - 18*a^3*b^7*c^7*d^3 - 42*a^4*b^6*c^6*d^4 - 126*a^5*b^5*c^5*d^5 - 630*a^6*b^4*c^4*d^6 + 6534*a^7*b^3*c^3*d^7 - 12987*a^8*b^2*c^2*d^8 + 10047*a^9*b*c*d^9 - 2761*a^10*d^10 - 35*b^10*c^9*d*x - 63*a*b^9*c^8*d^2*x - 126*a^2*b^8*c^7*d^3*x - 294*a^3*b^7*c^6*d^4*x - 882*a^4*b^6*c^5*d^5*x - 4410*a^5*b^5*c^4*d^6*x + 43218*a^6*b^4*c^3*d^7*x - 83349*a^7*b^3*c^2*d^8*x + 62769*a^8*b^2*c*d^9*x - 16807*a^9*b*d^10*x - 189*b^10*c^8*d^2*x^2 - 378*a*b^9*c^7*d^3*x^2 - 882*a^2*b^8*c^6*d^4*x^2 - 2646*a^3*b^7*c^5*d^5*x^2 - 13230*a^4*b^6*c^4*d^6*x^2 + 120834*a^5*b^5*c^3*d^7*x^2 - 223587*a^6*b^4*c^2*d^8*x^2 + 161847*a^7*b^3*c*d^9*x^2 - 41601*a^8*b^2*d^10*x^2 - 630*b^10*c^7*d^3*x^3 - 1470*a*b^9*c^6*d^4*x^3 - 4410*a^2*b^8*c^5*d^5*x^3 - 22050*a^3*b^7*c^4*d^6*x^3 + 183750*a^4*b^6*c^3*d^7*x^3 - 319725*a^5*b^5*c^2*d^8*x^3 + 216825*a^6*b^4*c*d^9*x^3 - 51695*a^7*b^3*d^10*x^3 - 1470*b^10*c^6*d^4*x^4 - 4410*a*b^9*c^5*d^5*x^4 - 22050*a^2*b^8*c^4*d^6*x^4 + 161700*a^3*b^7*c^3*d^7*x^4 - 253575*a^4*b^6*c^2*d^8*x^4 + 150675*a^5*b^5*c*d^9*x^4 - 29645*a^6*b^4*d^10*x^4 - 2646*b^10*c^5*d^5*x^5 - 13230*a*b^9*c^4*d^6*x^5 + 79380*a^2*b^8*c^3*d^7*x^5 - 99225*a^3*b^7*c^2*d^8*x^5 + 37485*a^4*b^6*c*d^9*x^5 - 147*a^5*b^5*d^10*x^5 - 4410*b^10*c^4*d^6*x^6 + 17640*a*b^9*c^3*d^7*x^6 - 6615*a^2*b^8*c^2*d^8*x^6 - 13965*a^3*b^7*c*d^9*x^6 + 8771*a^4*b^6*d^10*x^6 + 6615*a*b^9*c^2*d^8*x^7 - 9555*a^2*b^8*c*d^9*x^7 + 3773*a^3*b^7*d^10*x^7 + 945*b^10*c^2*d^8*x^8 - 945*a*b^9*c*d^9*x^8 + 315*a^2*b^8*d^10*x^8 + 105*b^10*c*d^9*x^9 - 35*a*b^9*d^10*x^9 + 7*b^10*d^10*x^10)/(21*b^11*(a + b*x)^7) + (120*d^7*(b*c - a*d)^3*Log[a + b*x])/b^11","B",1
1320,1,975,258,0.5946465,"\int \frac{(c+d x)^{10}}{(a+b x)^9} \, dx","IntegrateAlgebraic[(c + d*x)^10/(a + b*x)^9,x]","\frac{45 (b c-a d)^2 \log (a+b x) d^8}{b^{11}}+\frac{-7 c^{10} b^{10}+28 d^{10} x^{10} b^{10}+560 c d^9 x^9 b^{10}-6720 c^3 d^7 x^7 b^{10}-5880 c^4 d^6 x^6 b^{10}-4704 c^5 d^5 x^5 b^{10}-2940 c^6 d^4 x^4 b^{10}-1344 c^7 d^3 x^3 b^{10}-420 c^8 d^2 x^2 b^{10}-80 c^9 d x b^{10}-280 a d^{10} x^9 b^9+4480 a c d^9 x^8 b^9+20160 a c^2 d^8 x^7 b^9-23520 a c^3 d^7 x^6 b^9-11760 a c^4 d^6 x^5 b^9-5880 a c^5 d^5 x^4 b^9-2352 a c^6 d^4 x^3 b^9-672 a c^7 d^3 x^2 b^9-10 a c^9 d b^9-120 a c^8 d^2 x b^9-3248 a^2 d^{10} x^8 b^8-4480 a^2 c d^9 x^7 b^8+105840 a^2 c^2 d^8 x^6 b^8-47040 a^2 c^3 d^7 x^5 b^8-14700 a^2 c^4 d^6 x^4 b^8-4704 a^2 c^5 d^5 x^3 b^8-15 a^2 c^8 d^2 b^8-1176 a^2 c^6 d^4 x^2 b^8-192 a^2 c^7 d^3 x b^8-5824 a^3 d^{10} x^7 b^7-86240 a^3 c d^9 x^6 b^7+258720 a^3 c^2 d^8 x^5 b^7-58800 a^3 c^3 d^7 x^4 b^7-24 a^3 c^7 d^3 b^7-11760 a^3 c^4 d^6 x^3 b^7-2352 a^3 c^5 d^5 x^2 b^7-336 a^3 c^6 d^4 x b^7+14896 a^4 d^{10} x^6 b^6-266560 a^4 c d^9 x^5 b^6-42 a^4 c^6 d^4 b^6+367500 a^4 c^2 d^8 x^4 b^6-47040 a^4 c^3 d^7 x^3 b^6-5880 a^4 c^4 d^6 x^2 b^6-672 a^4 c^5 d^5 x b^6-84 a^5 c^5 d^5 b^5+76832 a^5 d^{10} x^5 b^5-421400 a^5 c d^9 x^4 b^5+322224 a^5 c^2 d^8 x^3 b^5-23520 a^5 c^3 d^7 x^2 b^5-1680 a^5 c^4 d^6 x b^5-210 a^6 c^4 d^6 b^4+140140 a^6 d^{10} x^4 b^4-393568 a^6 c d^9 x^3 b^4+172872 a^6 c^2 d^8 x^2 b^4-6720 a^6 c^3 d^7 x b^4-840 a^7 c^3 d^7 b^3+140336 a^7 d^{10} x^3 b^3-220304 a^7 c d^9 x^2 b^3+52272 a^7 c^2 d^8 x b^3+6849 a^8 c^2 d^8 b^2+81928 a^8 d^{10} x^2 b^2-68704 a^8 c d^9 x b^2-9218 a^9 c d^9 b+26288 a^9 d^{10} x b+3601 a^{10} d^{10}}{56 b^{11} (a+b x)^8}","\frac{45 d^8 (b c-a d)^2 \log (a+b x)}{b^{11}}-\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{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^9 x (10 b c-9 a d)}{b^{10}}+\frac{d^{10} x^2}{2 b^9}",1,"(-7*b^10*c^10 - 10*a*b^9*c^9*d - 15*a^2*b^8*c^8*d^2 - 24*a^3*b^7*c^7*d^3 - 42*a^4*b^6*c^6*d^4 - 84*a^5*b^5*c^5*d^5 - 210*a^6*b^4*c^4*d^6 - 840*a^7*b^3*c^3*d^7 + 6849*a^8*b^2*c^2*d^8 - 9218*a^9*b*c*d^9 + 3601*a^10*d^10 - 80*b^10*c^9*d*x - 120*a*b^9*c^8*d^2*x - 192*a^2*b^8*c^7*d^3*x - 336*a^3*b^7*c^6*d^4*x - 672*a^4*b^6*c^5*d^5*x - 1680*a^5*b^5*c^4*d^6*x - 6720*a^6*b^4*c^3*d^7*x + 52272*a^7*b^3*c^2*d^8*x - 68704*a^8*b^2*c*d^9*x + 26288*a^9*b*d^10*x - 420*b^10*c^8*d^2*x^2 - 672*a*b^9*c^7*d^3*x^2 - 1176*a^2*b^8*c^6*d^4*x^2 - 2352*a^3*b^7*c^5*d^5*x^2 - 5880*a^4*b^6*c^4*d^6*x^2 - 23520*a^5*b^5*c^3*d^7*x^2 + 172872*a^6*b^4*c^2*d^8*x^2 - 220304*a^7*b^3*c*d^9*x^2 + 81928*a^8*b^2*d^10*x^2 - 1344*b^10*c^7*d^3*x^3 - 2352*a*b^9*c^6*d^4*x^3 - 4704*a^2*b^8*c^5*d^5*x^3 - 11760*a^3*b^7*c^4*d^6*x^3 - 47040*a^4*b^6*c^3*d^7*x^3 + 322224*a^5*b^5*c^2*d^8*x^3 - 393568*a^6*b^4*c*d^9*x^3 + 140336*a^7*b^3*d^10*x^3 - 2940*b^10*c^6*d^4*x^4 - 5880*a*b^9*c^5*d^5*x^4 - 14700*a^2*b^8*c^4*d^6*x^4 - 58800*a^3*b^7*c^3*d^7*x^4 + 367500*a^4*b^6*c^2*d^8*x^4 - 421400*a^5*b^5*c*d^9*x^4 + 140140*a^6*b^4*d^10*x^4 - 4704*b^10*c^5*d^5*x^5 - 11760*a*b^9*c^4*d^6*x^5 - 47040*a^2*b^8*c^3*d^7*x^5 + 258720*a^3*b^7*c^2*d^8*x^5 - 266560*a^4*b^6*c*d^9*x^5 + 76832*a^5*b^5*d^10*x^5 - 5880*b^10*c^4*d^6*x^6 - 23520*a*b^9*c^3*d^7*x^6 + 105840*a^2*b^8*c^2*d^8*x^6 - 86240*a^3*b^7*c*d^9*x^6 + 14896*a^4*b^6*d^10*x^6 - 6720*b^10*c^3*d^7*x^7 + 20160*a*b^9*c^2*d^8*x^7 - 4480*a^2*b^8*c*d^9*x^7 - 5824*a^3*b^7*d^10*x^7 + 4480*a*b^9*c*d^9*x^8 - 3248*a^2*b^8*d^10*x^8 + 560*b^10*c*d^9*x^9 - 280*a*b^9*d^10*x^9 + 28*b^10*d^10*x^10)/(56*b^11*(a + b*x)^8) + (45*d^8*(b*c - a*d)^2*Log[a + b*x])/b^11","B",1
1321,1,977,257,0.65521,"\int \frac{(c+d x)^{10}}{(a+b x)^{10}} \, dx","IntegrateAlgebraic[(c + d*x)^10/(a + b*x)^10,x]","\frac{-28 c^{10} b^{10}+252 d^{10} x^{10} b^{10}-11340 c^2 d^8 x^8 b^{10}-15120 c^3 d^7 x^7 b^{10}-17640 c^4 d^6 x^6 b^{10}-15876 c^5 d^5 x^5 b^{10}-10584 c^6 d^4 x^4 b^{10}-5040 c^7 d^3 x^3 b^{10}-1620 c^8 d^2 x^2 b^{10}-315 c^9 d x b^{10}+2268 a d^{10} x^9 b^9+22680 a c d^9 x^8 b^9-45360 a c^2 d^8 x^7 b^9-35280 a c^3 d^7 x^6 b^9-26460 a c^4 d^6 x^5 b^9-15876 a c^5 d^5 x^4 b^9-7056 a c^6 d^4 x^3 b^9-2160 a c^7 d^3 x^2 b^9-35 a c^9 d b^9-405 a c^8 d^2 x b^9-2268 a^2 d^{10} x^8 b^8+136080 a^2 c d^9 x^7 b^8-105840 a^2 c^2 d^8 x^6 b^8-52920 a^2 c^3 d^7 x^5 b^8-26460 a^2 c^4 d^6 x^4 b^8-10584 a^2 c^5 d^5 x^3 b^8-45 a^2 c^8 d^2 b^8-3024 a^2 c^6 d^4 x^2 b^8-540 a^2 c^7 d^3 x b^8-54432 a^3 d^{10} x^7 b^7+388080 a^3 c d^9 x^6 b^7-158760 a^3 c^2 d^8 x^5 b^7-52920 a^3 c^3 d^7 x^4 b^7-60 a^3 c^7 d^3 b^7-17640 a^3 c^4 d^6 x^3 b^7-4536 a^3 c^5 d^5 x^2 b^7-756 a^3 c^6 d^4 x b^7-197568 a^4 d^{10} x^6 b^6+661500 a^4 c d^9 x^5 b^6-84 a^4 c^6 d^4 b^6-158760 a^4 c^2 d^8 x^4 b^6-35280 a^4 c^3 d^7 x^3 b^6-7560 a^4 c^4 d^6 x^2 b^6-1134 a^4 c^5 d^5 x b^6-126 a^5 c^5 d^5 b^5-375732 a^5 d^{10} x^5 b^5+725004 a^5 c d^9 x^4 b^5-105840 a^5 c^2 d^8 x^3 b^5-15120 a^5 c^3 d^7 x^2 b^5-1890 a^5 c^4 d^6 x b^5-210 a^6 c^4 d^6 b^4-439236 a^6 d^{10} x^4 b^4+518616 a^6 c d^9 x^3 b^4-45360 a^6 c^2 d^8 x^2 b^4-3780 a^6 c^3 d^7 x b^4-420 a^7 c^3 d^7 b^3-328104 a^7 d^{10} x^3 b^3+235224 a^7 c d^9 x^2 b^3-11340 a^7 c^2 d^8 x b^3-1260 a^8 c^2 d^8 b^2-153576 a^8 d^{10} x^2 b^2+61641 a^8 c d^9 x b^2+7129 a^9 c d^9 b-41229 a^9 d^{10} x b-4861 a^{10} d^{10}}{252 b^{11} (a+b x)^9}+\frac{10 \left(b c d^9-a d^{10}\right) \log (a+b x)}{b^{11}}","\frac{10 d^9 (b c-a d) \log (a+b x)}{b^{11}}-\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{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,"(-28*b^10*c^10 - 35*a*b^9*c^9*d - 45*a^2*b^8*c^8*d^2 - 60*a^3*b^7*c^7*d^3 - 84*a^4*b^6*c^6*d^4 - 126*a^5*b^5*c^5*d^5 - 210*a^6*b^4*c^4*d^6 - 420*a^7*b^3*c^3*d^7 - 1260*a^8*b^2*c^2*d^8 + 7129*a^9*b*c*d^9 - 4861*a^10*d^10 - 315*b^10*c^9*d*x - 405*a*b^9*c^8*d^2*x - 540*a^2*b^8*c^7*d^3*x - 756*a^3*b^7*c^6*d^4*x - 1134*a^4*b^6*c^5*d^5*x - 1890*a^5*b^5*c^4*d^6*x - 3780*a^6*b^4*c^3*d^7*x - 11340*a^7*b^3*c^2*d^8*x + 61641*a^8*b^2*c*d^9*x - 41229*a^9*b*d^10*x - 1620*b^10*c^8*d^2*x^2 - 2160*a*b^9*c^7*d^3*x^2 - 3024*a^2*b^8*c^6*d^4*x^2 - 4536*a^3*b^7*c^5*d^5*x^2 - 7560*a^4*b^6*c^4*d^6*x^2 - 15120*a^5*b^5*c^3*d^7*x^2 - 45360*a^6*b^4*c^2*d^8*x^2 + 235224*a^7*b^3*c*d^9*x^2 - 153576*a^8*b^2*d^10*x^2 - 5040*b^10*c^7*d^3*x^3 - 7056*a*b^9*c^6*d^4*x^3 - 10584*a^2*b^8*c^5*d^5*x^3 - 17640*a^3*b^7*c^4*d^6*x^3 - 35280*a^4*b^6*c^3*d^7*x^3 - 105840*a^5*b^5*c^2*d^8*x^3 + 518616*a^6*b^4*c*d^9*x^3 - 328104*a^7*b^3*d^10*x^3 - 10584*b^10*c^6*d^4*x^4 - 15876*a*b^9*c^5*d^5*x^4 - 26460*a^2*b^8*c^4*d^6*x^4 - 52920*a^3*b^7*c^3*d^7*x^4 - 158760*a^4*b^6*c^2*d^8*x^4 + 725004*a^5*b^5*c*d^9*x^4 - 439236*a^6*b^4*d^10*x^4 - 15876*b^10*c^5*d^5*x^5 - 26460*a*b^9*c^4*d^6*x^5 - 52920*a^2*b^8*c^3*d^7*x^5 - 158760*a^3*b^7*c^2*d^8*x^5 + 661500*a^4*b^6*c*d^9*x^5 - 375732*a^5*b^5*d^10*x^5 - 17640*b^10*c^4*d^6*x^6 - 35280*a*b^9*c^3*d^7*x^6 - 105840*a^2*b^8*c^2*d^8*x^6 + 388080*a^3*b^7*c*d^9*x^6 - 197568*a^4*b^6*d^10*x^6 - 15120*b^10*c^3*d^7*x^7 - 45360*a*b^9*c^2*d^8*x^7 + 136080*a^2*b^8*c*d^9*x^7 - 54432*a^3*b^7*d^10*x^7 - 11340*b^10*c^2*d^8*x^8 + 22680*a*b^9*c*d^9*x^8 - 2268*a^2*b^8*d^10*x^8 + 2268*a*b^9*d^10*x^9 + 252*b^10*d^10*x^10)/(252*b^11*(a + b*x)^9) + (10*(b*c*d^9 - a*d^10)*Log[a + b*x])/b^11","B",1
1322,1,814,271,0.5487388,"\int \frac{(c+d x)^{10}}{(a+b x)^{11}} \, dx","IntegrateAlgebraic[(c + d*x)^10/(a + b*x)^11,x]","\frac{d^{10} \log (a+b x)}{b^{11}}-\frac{(b c-a d) \left(252 c^9 b^9+25200 d^9 x^9 b^9+56700 c d^8 x^8 b^9+100800 c^2 d^7 x^7 b^9+132300 c^3 d^6 x^6 b^9+127008 c^4 d^5 x^5 b^9+88200 c^5 d^4 x^4 b^9+43200 c^6 d^3 x^3 b^9+14175 c^7 d^2 x^2 b^9+2800 c^8 d x b^9+170100 a d^9 x^8 b^8+252000 a c d^8 x^7 b^8+308700 a c^2 d^7 x^6 b^8+285768 a c^3 d^6 x^5 b^8+194040 a c^4 d^5 x^4 b^8+93600 a c^5 d^4 x^3 b^8+30375 a c^6 d^3 x^2 b^8+532 a c^8 d b^8+5950 a c^7 d^2 x b^8+554400 a^2 d^9 x^7 b^7+573300 a^2 c d^8 x^6 b^7+497448 a^2 c^2 d^7 x^5 b^7+326340 a^2 c^3 d^6 x^4 b^7+154080 a^2 c^4 d^5 x^3 b^7+847 a^2 c^7 d^2 b^7+49275 a^2 c^5 d^4 x^2 b^7+9550 a^2 c^6 d^3 x b^7+1102500 a^3 d^9 x^6 b^6+814968 a^3 c d^8 x^5 b^6+502740 a^3 c^2 d^7 x^4 b^6+1207 a^3 c^6 d^3 b^6+229680 a^3 c^3 d^6 x^3 b^6+71955 a^3 c^4 d^5 x^2 b^6+13750 a^3 c^5 d^4 x b^6+1450008 a^4 d^9 x^5 b^5+1627 a^4 c^5 d^4 b^5+767340 a^4 c d^8 x^4 b^5+330480 a^4 c^2 d^7 x^3 b^5+100305 a^4 c^3 d^6 x^2 b^5+18790 a^4 c^4 d^5 x b^5+2131 a^5 c^4 d^5 b^4+1296540 a^5 d^9 x^4 b^4+481680 a^5 c d^8 x^3 b^4+138105 a^5 c^2 d^7 x^2 b^4+25090 a^5 c^3 d^6 x b^4+2761 a^6 c^3 d^6 b^3+784080 a^6 d^9 x^3 b^3+194805 a^6 c d^8 x^2 b^3+33490 a^6 c^2 d^7 x b^3+3601 a^7 c^2 d^7 b^2+308205 a^7 d^9 x^2 b^2+46090 a^7 c d^8 x b^2+4861 a^8 c d^8 b+71290 a^8 d^9 x b+7381 a^9 d^9\right)}{2520 b^{11} (a+b x)^{10}}","-\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,"-1/2520*((b*c - a*d)*(252*b^9*c^9 + 532*a*b^8*c^8*d + 847*a^2*b^7*c^7*d^2 + 1207*a^3*b^6*c^6*d^3 + 1627*a^4*b^5*c^5*d^4 + 2131*a^5*b^4*c^4*d^5 + 2761*a^6*b^3*c^3*d^6 + 3601*a^7*b^2*c^2*d^7 + 4861*a^8*b*c*d^8 + 7381*a^9*d^9 + 2800*b^9*c^8*d*x + 5950*a*b^8*c^7*d^2*x + 9550*a^2*b^7*c^6*d^3*x + 13750*a^3*b^6*c^5*d^4*x + 18790*a^4*b^5*c^4*d^5*x + 25090*a^5*b^4*c^3*d^6*x + 33490*a^6*b^3*c^2*d^7*x + 46090*a^7*b^2*c*d^8*x + 71290*a^8*b*d^9*x + 14175*b^9*c^7*d^2*x^2 + 30375*a*b^8*c^6*d^3*x^2 + 49275*a^2*b^7*c^5*d^4*x^2 + 71955*a^3*b^6*c^4*d^5*x^2 + 100305*a^4*b^5*c^3*d^6*x^2 + 138105*a^5*b^4*c^2*d^7*x^2 + 194805*a^6*b^3*c*d^8*x^2 + 308205*a^7*b^2*d^9*x^2 + 43200*b^9*c^6*d^3*x^3 + 93600*a*b^8*c^5*d^4*x^3 + 154080*a^2*b^7*c^4*d^5*x^3 + 229680*a^3*b^6*c^3*d^6*x^3 + 330480*a^4*b^5*c^2*d^7*x^3 + 481680*a^5*b^4*c*d^8*x^3 + 784080*a^6*b^3*d^9*x^3 + 88200*b^9*c^5*d^4*x^4 + 194040*a*b^8*c^4*d^5*x^4 + 326340*a^2*b^7*c^3*d^6*x^4 + 502740*a^3*b^6*c^2*d^7*x^4 + 767340*a^4*b^5*c*d^8*x^4 + 1296540*a^5*b^4*d^9*x^4 + 127008*b^9*c^4*d^5*x^5 + 285768*a*b^8*c^3*d^6*x^5 + 497448*a^2*b^7*c^2*d^7*x^5 + 814968*a^3*b^6*c*d^8*x^5 + 1450008*a^4*b^5*d^9*x^5 + 132300*b^9*c^3*d^6*x^6 + 308700*a*b^8*c^2*d^7*x^6 + 573300*a^2*b^7*c*d^8*x^6 + 1102500*a^3*b^6*d^9*x^6 + 100800*b^9*c^2*d^7*x^7 + 252000*a*b^8*c*d^8*x^7 + 554400*a^2*b^7*d^9*x^7 + 56700*b^9*c*d^8*x^8 + 170100*a*b^8*d^9*x^8 + 25200*b^9*d^9*x^9))/(b^11*(a + b*x)^10) + (d^10*Log[a + b*x])/b^11","B",1
1323,1,964,28,0.3342024,"\int \frac{(c+d x)^{10}}{(a+b x)^{12}} \, dx","IntegrateAlgebraic[(c + d*x)^10/(a + b*x)^12,x]","\frac{-c^{10} b^{10}-11 d^{10} x^{10} b^{10}-55 c d^9 x^9 b^{10}-165 c^2 d^8 x^8 b^{10}-330 c^3 d^7 x^7 b^{10}-462 c^4 d^6 x^6 b^{10}-462 c^5 d^5 x^5 b^{10}-330 c^6 d^4 x^4 b^{10}-165 c^7 d^3 x^3 b^{10}-55 c^8 d^2 x^2 b^{10}-11 c^9 d x b^{10}-55 a d^{10} x^9 b^9-165 a c d^9 x^8 b^9-330 a c^2 d^8 x^7 b^9-462 a c^3 d^7 x^6 b^9-462 a c^4 d^6 x^5 b^9-330 a c^5 d^5 x^4 b^9-165 a c^6 d^4 x^3 b^9-55 a c^7 d^3 x^2 b^9-a c^9 d b^9-11 a c^8 d^2 x b^9-165 a^2 d^{10} x^8 b^8-330 a^2 c d^9 x^7 b^8-462 a^2 c^2 d^8 x^6 b^8-462 a^2 c^3 d^7 x^5 b^8-330 a^2 c^4 d^6 x^4 b^8-165 a^2 c^5 d^5 x^3 b^8-a^2 c^8 d^2 b^8-55 a^2 c^6 d^4 x^2 b^8-11 a^2 c^7 d^3 x b^8-330 a^3 d^{10} x^7 b^7-462 a^3 c d^9 x^6 b^7-462 a^3 c^2 d^8 x^5 b^7-330 a^3 c^3 d^7 x^4 b^7-a^3 c^7 d^3 b^7-165 a^3 c^4 d^6 x^3 b^7-55 a^3 c^5 d^5 x^2 b^7-11 a^3 c^6 d^4 x b^7-462 a^4 d^{10} x^6 b^6-462 a^4 c d^9 x^5 b^6-a^4 c^6 d^4 b^6-330 a^4 c^2 d^8 x^4 b^6-165 a^4 c^3 d^7 x^3 b^6-55 a^4 c^4 d^6 x^2 b^6-11 a^4 c^5 d^5 x b^6-a^5 c^5 d^5 b^5-462 a^5 d^{10} x^5 b^5-330 a^5 c d^9 x^4 b^5-165 a^5 c^2 d^8 x^3 b^5-55 a^5 c^3 d^7 x^2 b^5-11 a^5 c^4 d^6 x b^5-a^6 c^4 d^6 b^4-330 a^6 d^{10} x^4 b^4-165 a^6 c d^9 x^3 b^4-55 a^6 c^2 d^8 x^2 b^4-11 a^6 c^3 d^7 x b^4-a^7 c^3 d^7 b^3-165 a^7 d^{10} x^3 b^3-55 a^7 c d^9 x^2 b^3-11 a^7 c^2 d^8 x b^3-a^8 c^2 d^8 b^2-55 a^8 d^{10} x^2 b^2-11 a^8 c d^9 x b^2-a^9 c d^9 b-11 a^9 d^{10} x b-a^{10} d^{10}}{11 b^{11} (a+b x)^{11}}","-\frac{(c+d x)^{11}}{11 (a+b x)^{11} (b c-a d)}",1,"(-(b^10*c^10) - a*b^9*c^9*d - a^2*b^8*c^8*d^2 - a^3*b^7*c^7*d^3 - a^4*b^6*c^6*d^4 - a^5*b^5*c^5*d^5 - a^6*b^4*c^4*d^6 - a^7*b^3*c^3*d^7 - a^8*b^2*c^2*d^8 - a^9*b*c*d^9 - a^10*d^10 - 11*b^10*c^9*d*x - 11*a*b^9*c^8*d^2*x - 11*a^2*b^8*c^7*d^3*x - 11*a^3*b^7*c^6*d^4*x - 11*a^4*b^6*c^5*d^5*x - 11*a^5*b^5*c^4*d^6*x - 11*a^6*b^4*c^3*d^7*x - 11*a^7*b^3*c^2*d^8*x - 11*a^8*b^2*c*d^9*x - 11*a^9*b*d^10*x - 55*b^10*c^8*d^2*x^2 - 55*a*b^9*c^7*d^3*x^2 - 55*a^2*b^8*c^6*d^4*x^2 - 55*a^3*b^7*c^5*d^5*x^2 - 55*a^4*b^6*c^4*d^6*x^2 - 55*a^5*b^5*c^3*d^7*x^2 - 55*a^6*b^4*c^2*d^8*x^2 - 55*a^7*b^3*c*d^9*x^2 - 55*a^8*b^2*d^10*x^2 - 165*b^10*c^7*d^3*x^3 - 165*a*b^9*c^6*d^4*x^3 - 165*a^2*b^8*c^5*d^5*x^3 - 165*a^3*b^7*c^4*d^6*x^3 - 165*a^4*b^6*c^3*d^7*x^3 - 165*a^5*b^5*c^2*d^8*x^3 - 165*a^6*b^4*c*d^9*x^3 - 165*a^7*b^3*d^10*x^3 - 330*b^10*c^6*d^4*x^4 - 330*a*b^9*c^5*d^5*x^4 - 330*a^2*b^8*c^4*d^6*x^4 - 330*a^3*b^7*c^3*d^7*x^4 - 330*a^4*b^6*c^2*d^8*x^4 - 330*a^5*b^5*c*d^9*x^4 - 330*a^6*b^4*d^10*x^4 - 462*b^10*c^5*d^5*x^5 - 462*a*b^9*c^4*d^6*x^5 - 462*a^2*b^8*c^3*d^7*x^5 - 462*a^3*b^7*c^2*d^8*x^5 - 462*a^4*b^6*c*d^9*x^5 - 462*a^5*b^5*d^10*x^5 - 462*b^10*c^4*d^6*x^6 - 462*a*b^9*c^3*d^7*x^6 - 462*a^2*b^8*c^2*d^8*x^6 - 462*a^3*b^7*c*d^9*x^6 - 462*a^4*b^6*d^10*x^6 - 330*b^10*c^3*d^7*x^7 - 330*a*b^9*c^2*d^8*x^7 - 330*a^2*b^8*c*d^9*x^7 - 330*a^3*b^7*d^10*x^7 - 165*b^10*c^2*d^8*x^8 - 165*a*b^9*c*d^9*x^8 - 165*a^2*b^8*d^10*x^8 - 55*b^10*c*d^9*x^9 - 55*a*b^9*d^10*x^9 - 11*b^10*d^10*x^10)/(11*b^11*(a + b*x)^11)","B",1
1324,1,964,58,0.3331657,"\int \frac{(c+d x)^{10}}{(a+b x)^{13}} \, dx","IntegrateAlgebraic[(c + d*x)^10/(a + b*x)^13,x]","\frac{-11 c^{10} b^{10}-66 d^{10} x^{10} b^{10}-440 c d^9 x^9 b^{10}-1485 c^2 d^8 x^8 b^{10}-3168 c^3 d^7 x^7 b^{10}-4620 c^4 d^6 x^6 b^{10}-4752 c^5 d^5 x^5 b^{10}-3465 c^6 d^4 x^4 b^{10}-1760 c^7 d^3 x^3 b^{10}-594 c^8 d^2 x^2 b^{10}-120 c^9 d x b^{10}-220 a d^{10} x^9 b^9-990 a c d^9 x^8 b^9-2376 a c^2 d^8 x^7 b^9-3696 a c^3 d^7 x^6 b^9-3960 a c^4 d^6 x^5 b^9-2970 a c^5 d^5 x^4 b^9-1540 a c^6 d^4 x^3 b^9-528 a c^7 d^3 x^2 b^9-10 a c^9 d b^9-108 a c^8 d^2 x b^9-495 a^2 d^{10} x^8 b^8-1584 a^2 c d^9 x^7 b^8-2772 a^2 c^2 d^8 x^6 b^8-3168 a^2 c^3 d^7 x^5 b^8-2475 a^2 c^4 d^6 x^4 b^8-1320 a^2 c^5 d^5 x^3 b^8-9 a^2 c^8 d^2 b^8-462 a^2 c^6 d^4 x^2 b^8-96 a^2 c^7 d^3 x b^8-792 a^3 d^{10} x^7 b^7-1848 a^3 c d^9 x^6 b^7-2376 a^3 c^2 d^8 x^5 b^7-1980 a^3 c^3 d^7 x^4 b^7-8 a^3 c^7 d^3 b^7-1100 a^3 c^4 d^6 x^3 b^7-396 a^3 c^5 d^5 x^2 b^7-84 a^3 c^6 d^4 x b^7-924 a^4 d^{10} x^6 b^6-1584 a^4 c d^9 x^5 b^6-7 a^4 c^6 d^4 b^6-1485 a^4 c^2 d^8 x^4 b^6-880 a^4 c^3 d^7 x^3 b^6-330 a^4 c^4 d^6 x^2 b^6-72 a^4 c^5 d^5 x b^6-6 a^5 c^5 d^5 b^5-792 a^5 d^{10} x^5 b^5-990 a^5 c d^9 x^4 b^5-660 a^5 c^2 d^8 x^3 b^5-264 a^5 c^3 d^7 x^2 b^5-60 a^5 c^4 d^6 x b^5-5 a^6 c^4 d^6 b^4-495 a^6 d^{10} x^4 b^4-440 a^6 c d^9 x^3 b^4-198 a^6 c^2 d^8 x^2 b^4-48 a^6 c^3 d^7 x b^4-4 a^7 c^3 d^7 b^3-220 a^7 d^{10} x^3 b^3-132 a^7 c d^9 x^2 b^3-36 a^7 c^2 d^8 x b^3-3 a^8 c^2 d^8 b^2-66 a^8 d^{10} x^2 b^2-24 a^8 c d^9 x b^2-2 a^9 c d^9 b-12 a^9 d^{10} x b-a^{10} d^{10}}{132 b^{11} (a+b x)^{12}}","\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,"(-11*b^10*c^10 - 10*a*b^9*c^9*d - 9*a^2*b^8*c^8*d^2 - 8*a^3*b^7*c^7*d^3 - 7*a^4*b^6*c^6*d^4 - 6*a^5*b^5*c^5*d^5 - 5*a^6*b^4*c^4*d^6 - 4*a^7*b^3*c^3*d^7 - 3*a^8*b^2*c^2*d^8 - 2*a^9*b*c*d^9 - a^10*d^10 - 120*b^10*c^9*d*x - 108*a*b^9*c^8*d^2*x - 96*a^2*b^8*c^7*d^3*x - 84*a^3*b^7*c^6*d^4*x - 72*a^4*b^6*c^5*d^5*x - 60*a^5*b^5*c^4*d^6*x - 48*a^6*b^4*c^3*d^7*x - 36*a^7*b^3*c^2*d^8*x - 24*a^8*b^2*c*d^9*x - 12*a^9*b*d^10*x - 594*b^10*c^8*d^2*x^2 - 528*a*b^9*c^7*d^3*x^2 - 462*a^2*b^8*c^6*d^4*x^2 - 396*a^3*b^7*c^5*d^5*x^2 - 330*a^4*b^6*c^4*d^6*x^2 - 264*a^5*b^5*c^3*d^7*x^2 - 198*a^6*b^4*c^2*d^8*x^2 - 132*a^7*b^3*c*d^9*x^2 - 66*a^8*b^2*d^10*x^2 - 1760*b^10*c^7*d^3*x^3 - 1540*a*b^9*c^6*d^4*x^3 - 1320*a^2*b^8*c^5*d^5*x^3 - 1100*a^3*b^7*c^4*d^6*x^3 - 880*a^4*b^6*c^3*d^7*x^3 - 660*a^5*b^5*c^2*d^8*x^3 - 440*a^6*b^4*c*d^9*x^3 - 220*a^7*b^3*d^10*x^3 - 3465*b^10*c^6*d^4*x^4 - 2970*a*b^9*c^5*d^5*x^4 - 2475*a^2*b^8*c^4*d^6*x^4 - 1980*a^3*b^7*c^3*d^7*x^4 - 1485*a^4*b^6*c^2*d^8*x^4 - 990*a^5*b^5*c*d^9*x^4 - 495*a^6*b^4*d^10*x^4 - 4752*b^10*c^5*d^5*x^5 - 3960*a*b^9*c^4*d^6*x^5 - 3168*a^2*b^8*c^3*d^7*x^5 - 2376*a^3*b^7*c^2*d^8*x^5 - 1584*a^4*b^6*c*d^9*x^5 - 792*a^5*b^5*d^10*x^5 - 4620*b^10*c^4*d^6*x^6 - 3696*a*b^9*c^3*d^7*x^6 - 2772*a^2*b^8*c^2*d^8*x^6 - 1848*a^3*b^7*c*d^9*x^6 - 924*a^4*b^6*d^10*x^6 - 3168*b^10*c^3*d^7*x^7 - 2376*a*b^9*c^2*d^8*x^7 - 1584*a^2*b^8*c*d^9*x^7 - 792*a^3*b^7*d^10*x^7 - 1485*b^10*c^2*d^8*x^8 - 990*a*b^9*c*d^9*x^8 - 495*a^2*b^8*d^10*x^8 - 440*b^10*c*d^9*x^9 - 220*a*b^9*d^10*x^9 - 66*b^10*d^10*x^10)/(132*b^11*(a + b*x)^12)","B",1
1325,1,964,89,0.3472519,"\int \frac{(c+d x)^{10}}{(a+b x)^{14}} \, dx","IntegrateAlgebraic[(c + d*x)^10/(a + b*x)^14,x]","\frac{-66 c^{10} b^{10}-286 d^{10} x^{10} b^{10}-2145 c d^9 x^9 b^{10}-7722 c^2 d^8 x^8 b^{10}-17160 c^3 d^7 x^7 b^{10}-25740 c^4 d^6 x^6 b^{10}-27027 c^5 d^5 x^5 b^{10}-20020 c^6 d^4 x^4 b^{10}-10296 c^7 d^3 x^3 b^{10}-3510 c^8 d^2 x^2 b^{10}-715 c^9 d x b^{10}-715 a d^{10} x^9 b^9-3861 a c d^9 x^8 b^9-10296 a c^2 d^8 x^7 b^9-17160 a c^3 d^7 x^6 b^9-19305 a c^4 d^6 x^5 b^9-15015 a c^5 d^5 x^4 b^9-8008 a c^6 d^4 x^3 b^9-2808 a c^7 d^3 x^2 b^9-55 a c^9 d b^9-585 a c^8 d^2 x b^9-1287 a^2 d^{10} x^8 b^8-5148 a^2 c d^9 x^7 b^8-10296 a^2 c^2 d^8 x^6 b^8-12870 a^2 c^3 d^7 x^5 b^8-10725 a^2 c^4 d^6 x^4 b^8-6006 a^2 c^5 d^5 x^3 b^8-45 a^2 c^8 d^2 b^8-2184 a^2 c^6 d^4 x^2 b^8-468 a^2 c^7 d^3 x b^8-1716 a^3 d^{10} x^7 b^7-5148 a^3 c d^9 x^6 b^7-7722 a^3 c^2 d^8 x^5 b^7-7150 a^3 c^3 d^7 x^4 b^7-36 a^3 c^7 d^3 b^7-4290 a^3 c^4 d^6 x^3 b^7-1638 a^3 c^5 d^5 x^2 b^7-364 a^3 c^6 d^4 x b^7-1716 a^4 d^{10} x^6 b^6-3861 a^4 c d^9 x^5 b^6-28 a^4 c^6 d^4 b^6-4290 a^4 c^2 d^8 x^4 b^6-2860 a^4 c^3 d^7 x^3 b^6-1170 a^4 c^4 d^6 x^2 b^6-273 a^4 c^5 d^5 x b^6-21 a^5 c^5 d^5 b^5-1287 a^5 d^{10} x^5 b^5-2145 a^5 c d^9 x^4 b^5-1716 a^5 c^2 d^8 x^3 b^5-780 a^5 c^3 d^7 x^2 b^5-195 a^5 c^4 d^6 x b^5-15 a^6 c^4 d^6 b^4-715 a^6 d^{10} x^4 b^4-858 a^6 c d^9 x^3 b^4-468 a^6 c^2 d^8 x^2 b^4-130 a^6 c^3 d^7 x b^4-10 a^7 c^3 d^7 b^3-286 a^7 d^{10} x^3 b^3-234 a^7 c d^9 x^2 b^3-78 a^7 c^2 d^8 x b^3-6 a^8 c^2 d^8 b^2-78 a^8 d^{10} x^2 b^2-39 a^8 c d^9 x b^2-3 a^9 c d^9 b-13 a^9 d^{10} x b-a^{10} d^{10}}{858 b^{11} (a+b x)^{13}}","-\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,"(-66*b^10*c^10 - 55*a*b^9*c^9*d - 45*a^2*b^8*c^8*d^2 - 36*a^3*b^7*c^7*d^3 - 28*a^4*b^6*c^6*d^4 - 21*a^5*b^5*c^5*d^5 - 15*a^6*b^4*c^4*d^6 - 10*a^7*b^3*c^3*d^7 - 6*a^8*b^2*c^2*d^8 - 3*a^9*b*c*d^9 - a^10*d^10 - 715*b^10*c^9*d*x - 585*a*b^9*c^8*d^2*x - 468*a^2*b^8*c^7*d^3*x - 364*a^3*b^7*c^6*d^4*x - 273*a^4*b^6*c^5*d^5*x - 195*a^5*b^5*c^4*d^6*x - 130*a^6*b^4*c^3*d^7*x - 78*a^7*b^3*c^2*d^8*x - 39*a^8*b^2*c*d^9*x - 13*a^9*b*d^10*x - 3510*b^10*c^8*d^2*x^2 - 2808*a*b^9*c^7*d^3*x^2 - 2184*a^2*b^8*c^6*d^4*x^2 - 1638*a^3*b^7*c^5*d^5*x^2 - 1170*a^4*b^6*c^4*d^6*x^2 - 780*a^5*b^5*c^3*d^7*x^2 - 468*a^6*b^4*c^2*d^8*x^2 - 234*a^7*b^3*c*d^9*x^2 - 78*a^8*b^2*d^10*x^2 - 10296*b^10*c^7*d^3*x^3 - 8008*a*b^9*c^6*d^4*x^3 - 6006*a^2*b^8*c^5*d^5*x^3 - 4290*a^3*b^7*c^4*d^6*x^3 - 2860*a^4*b^6*c^3*d^7*x^3 - 1716*a^5*b^5*c^2*d^8*x^3 - 858*a^6*b^4*c*d^9*x^3 - 286*a^7*b^3*d^10*x^3 - 20020*b^10*c^6*d^4*x^4 - 15015*a*b^9*c^5*d^5*x^4 - 10725*a^2*b^8*c^4*d^6*x^4 - 7150*a^3*b^7*c^3*d^7*x^4 - 4290*a^4*b^6*c^2*d^8*x^4 - 2145*a^5*b^5*c*d^9*x^4 - 715*a^6*b^4*d^10*x^4 - 27027*b^10*c^5*d^5*x^5 - 19305*a*b^9*c^4*d^6*x^5 - 12870*a^2*b^8*c^3*d^7*x^5 - 7722*a^3*b^7*c^2*d^8*x^5 - 3861*a^4*b^6*c*d^9*x^5 - 1287*a^5*b^5*d^10*x^5 - 25740*b^10*c^4*d^6*x^6 - 17160*a*b^9*c^3*d^7*x^6 - 10296*a^2*b^8*c^2*d^8*x^6 - 5148*a^3*b^7*c*d^9*x^6 - 1716*a^4*b^6*d^10*x^6 - 17160*b^10*c^3*d^7*x^7 - 10296*a*b^9*c^2*d^8*x^7 - 5148*a^2*b^8*c*d^9*x^7 - 1716*a^3*b^7*d^10*x^7 - 7722*b^10*c^2*d^8*x^8 - 3861*a*b^9*c*d^9*x^8 - 1287*a^2*b^8*d^10*x^8 - 2145*b^10*c*d^9*x^9 - 715*a*b^9*d^10*x^9 - 286*b^10*d^10*x^10)/(858*b^11*(a + b*x)^13)","B",1
1326,1,964,120,0.3402288,"\int \frac{(c+d x)^{10}}{(a+b x)^{15}} \, dx","IntegrateAlgebraic[(c + d*x)^10/(a + b*x)^15,x]","\frac{-286 c^{10} b^{10}-1001 d^{10} x^{10} b^{10}-8008 c d^9 x^9 b^{10}-30030 c^2 d^8 x^8 b^{10}-68640 c^3 d^7 x^7 b^{10}-105105 c^4 d^6 x^6 b^{10}-112112 c^5 d^5 x^5 b^{10}-84084 c^6 d^4 x^4 b^{10}-43680 c^7 d^3 x^3 b^{10}-15015 c^8 d^2 x^2 b^{10}-3080 c^9 d x b^{10}-2002 a d^{10} x^9 b^9-12012 a c d^9 x^8 b^9-34320 a c^2 d^8 x^7 b^9-60060 a c^3 d^7 x^6 b^9-70070 a c^4 d^6 x^5 b^9-56056 a c^5 d^5 x^4 b^9-30576 a c^6 d^4 x^3 b^9-10920 a c^7 d^3 x^2 b^9-220 a c^9 d b^9-2310 a c^8 d^2 x b^9-3003 a^2 d^{10} x^8 b^8-13728 a^2 c d^9 x^7 b^8-30030 a^2 c^2 d^8 x^6 b^8-40040 a^2 c^3 d^7 x^5 b^8-35035 a^2 c^4 d^6 x^4 b^8-20384 a^2 c^5 d^5 x^3 b^8-165 a^2 c^8 d^2 b^8-7644 a^2 c^6 d^4 x^2 b^8-1680 a^2 c^7 d^3 x b^8-3432 a^3 d^{10} x^7 b^7-12012 a^3 c d^9 x^6 b^7-20020 a^3 c^2 d^8 x^5 b^7-20020 a^3 c^3 d^7 x^4 b^7-120 a^3 c^7 d^3 b^7-12740 a^3 c^4 d^6 x^3 b^7-5096 a^3 c^5 d^5 x^2 b^7-1176 a^3 c^6 d^4 x b^7-3003 a^4 d^{10} x^6 b^6-8008 a^4 c d^9 x^5 b^6-84 a^4 c^6 d^4 b^6-10010 a^4 c^2 d^8 x^4 b^6-7280 a^4 c^3 d^7 x^3 b^6-3185 a^4 c^4 d^6 x^2 b^6-784 a^4 c^5 d^5 x b^6-56 a^5 c^5 d^5 b^5-2002 a^5 d^{10} x^5 b^5-4004 a^5 c d^9 x^4 b^5-3640 a^5 c^2 d^8 x^3 b^5-1820 a^5 c^3 d^7 x^2 b^5-490 a^5 c^4 d^6 x b^5-35 a^6 c^4 d^6 b^4-1001 a^6 d^{10} x^4 b^4-1456 a^6 c d^9 x^3 b^4-910 a^6 c^2 d^8 x^2 b^4-280 a^6 c^3 d^7 x b^4-20 a^7 c^3 d^7 b^3-364 a^7 d^{10} x^3 b^3-364 a^7 c d^9 x^2 b^3-140 a^7 c^2 d^8 x b^3-10 a^8 c^2 d^8 b^2-91 a^8 d^{10} x^2 b^2-56 a^8 c d^9 x b^2-4 a^9 c d^9 b-14 a^9 d^{10} x b-a^{10} d^{10}}{4004 b^{11} (a+b x)^{14}}","\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,"(-286*b^10*c^10 - 220*a*b^9*c^9*d - 165*a^2*b^8*c^8*d^2 - 120*a^3*b^7*c^7*d^3 - 84*a^4*b^6*c^6*d^4 - 56*a^5*b^5*c^5*d^5 - 35*a^6*b^4*c^4*d^6 - 20*a^7*b^3*c^3*d^7 - 10*a^8*b^2*c^2*d^8 - 4*a^9*b*c*d^9 - a^10*d^10 - 3080*b^10*c^9*d*x - 2310*a*b^9*c^8*d^2*x - 1680*a^2*b^8*c^7*d^3*x - 1176*a^3*b^7*c^6*d^4*x - 784*a^4*b^6*c^5*d^5*x - 490*a^5*b^5*c^4*d^6*x - 280*a^6*b^4*c^3*d^7*x - 140*a^7*b^3*c^2*d^8*x - 56*a^8*b^2*c*d^9*x - 14*a^9*b*d^10*x - 15015*b^10*c^8*d^2*x^2 - 10920*a*b^9*c^7*d^3*x^2 - 7644*a^2*b^8*c^6*d^4*x^2 - 5096*a^3*b^7*c^5*d^5*x^2 - 3185*a^4*b^6*c^4*d^6*x^2 - 1820*a^5*b^5*c^3*d^7*x^2 - 910*a^6*b^4*c^2*d^8*x^2 - 364*a^7*b^3*c*d^9*x^2 - 91*a^8*b^2*d^10*x^2 - 43680*b^10*c^7*d^3*x^3 - 30576*a*b^9*c^6*d^4*x^3 - 20384*a^2*b^8*c^5*d^5*x^3 - 12740*a^3*b^7*c^4*d^6*x^3 - 7280*a^4*b^6*c^3*d^7*x^3 - 3640*a^5*b^5*c^2*d^8*x^3 - 1456*a^6*b^4*c*d^9*x^3 - 364*a^7*b^3*d^10*x^3 - 84084*b^10*c^6*d^4*x^4 - 56056*a*b^9*c^5*d^5*x^4 - 35035*a^2*b^8*c^4*d^6*x^4 - 20020*a^3*b^7*c^3*d^7*x^4 - 10010*a^4*b^6*c^2*d^8*x^4 - 4004*a^5*b^5*c*d^9*x^4 - 1001*a^6*b^4*d^10*x^4 - 112112*b^10*c^5*d^5*x^5 - 70070*a*b^9*c^4*d^6*x^5 - 40040*a^2*b^8*c^3*d^7*x^5 - 20020*a^3*b^7*c^2*d^8*x^5 - 8008*a^4*b^6*c*d^9*x^5 - 2002*a^5*b^5*d^10*x^5 - 105105*b^10*c^4*d^6*x^6 - 60060*a*b^9*c^3*d^7*x^6 - 30030*a^2*b^8*c^2*d^8*x^6 - 12012*a^3*b^7*c*d^9*x^6 - 3003*a^4*b^6*d^10*x^6 - 68640*b^10*c^3*d^7*x^7 - 34320*a*b^9*c^2*d^8*x^7 - 13728*a^2*b^8*c*d^9*x^7 - 3432*a^3*b^7*d^10*x^7 - 30030*b^10*c^2*d^8*x^8 - 12012*a*b^9*c*d^9*x^8 - 3003*a^2*b^8*d^10*x^8 - 8008*b^10*c*d^9*x^9 - 2002*a*b^9*d^10*x^9 - 1001*b^10*d^10*x^10)/(4004*b^11*(a + b*x)^14)","B",1
1327,1,964,151,0.351142,"\int \frac{(c+d x)^{10}}{(a+b x)^{16}} \, dx","IntegrateAlgebraic[(c + d*x)^10/(a + b*x)^16,x]","\frac{-1001 c^{10} b^{10}-3003 d^{10} x^{10} b^{10}-25025 c d^9 x^9 b^{10}-96525 c^2 d^8 x^8 b^{10}-225225 c^3 d^7 x^7 b^{10}-350350 c^4 d^6 x^6 b^{10}-378378 c^5 d^5 x^5 b^{10}-286650 c^6 d^4 x^4 b^{10}-150150 c^7 d^3 x^3 b^{10}-51975 c^8 d^2 x^2 b^{10}-10725 c^9 d x b^{10}-5005 a d^{10} x^9 b^9-32175 a c d^9 x^8 b^9-96525 a c^2 d^8 x^7 b^9-175175 a c^3 d^7 x^6 b^9-210210 a c^4 d^6 x^5 b^9-171990 a c^5 d^5 x^4 b^9-95550 a c^6 d^4 x^3 b^9-34650 a c^7 d^3 x^2 b^9-715 a c^9 d b^9-7425 a c^8 d^2 x b^9-6435 a^2 d^{10} x^8 b^8-32175 a^2 c d^9 x^7 b^8-75075 a^2 c^2 d^8 x^6 b^8-105105 a^2 c^3 d^7 x^5 b^8-95550 a^2 c^4 d^6 x^4 b^8-57330 a^2 c^5 d^5 x^3 b^8-495 a^2 c^8 d^2 b^8-22050 a^2 c^6 d^4 x^2 b^8-4950 a^2 c^7 d^3 x b^8-6435 a^3 d^{10} x^7 b^7-25025 a^3 c d^9 x^6 b^7-45045 a^3 c^2 d^8 x^5 b^7-47775 a^3 c^3 d^7 x^4 b^7-330 a^3 c^7 d^3 b^7-31850 a^3 c^4 d^6 x^3 b^7-13230 a^3 c^5 d^5 x^2 b^7-3150 a^3 c^6 d^4 x b^7-5005 a^4 d^{10} x^6 b^6-15015 a^4 c d^9 x^5 b^6-210 a^4 c^6 d^4 b^6-20475 a^4 c^2 d^8 x^4 b^6-15925 a^4 c^3 d^7 x^3 b^6-7350 a^4 c^4 d^6 x^2 b^6-1890 a^4 c^5 d^5 x b^6-126 a^5 c^5 d^5 b^5-3003 a^5 d^{10} x^5 b^5-6825 a^5 c d^9 x^4 b^5-6825 a^5 c^2 d^8 x^3 b^5-3675 a^5 c^3 d^7 x^2 b^5-1050 a^5 c^4 d^6 x b^5-70 a^6 c^4 d^6 b^4-1365 a^6 d^{10} x^4 b^4-2275 a^6 c d^9 x^3 b^4-1575 a^6 c^2 d^8 x^2 b^4-525 a^6 c^3 d^7 x b^4-35 a^7 c^3 d^7 b^3-455 a^7 d^{10} x^3 b^3-525 a^7 c d^9 x^2 b^3-225 a^7 c^2 d^8 x b^3-15 a^8 c^2 d^8 b^2-105 a^8 d^{10} x^2 b^2-75 a^8 c d^9 x b^2-5 a^9 c d^9 b-15 a^9 d^{10} x b-a^{10} d^{10}}{15015 b^{11} (a+b x)^{15}}","-\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,"(-1001*b^10*c^10 - 715*a*b^9*c^9*d - 495*a^2*b^8*c^8*d^2 - 330*a^3*b^7*c^7*d^3 - 210*a^4*b^6*c^6*d^4 - 126*a^5*b^5*c^5*d^5 - 70*a^6*b^4*c^4*d^6 - 35*a^7*b^3*c^3*d^7 - 15*a^8*b^2*c^2*d^8 - 5*a^9*b*c*d^9 - a^10*d^10 - 10725*b^10*c^9*d*x - 7425*a*b^9*c^8*d^2*x - 4950*a^2*b^8*c^7*d^3*x - 3150*a^3*b^7*c^6*d^4*x - 1890*a^4*b^6*c^5*d^5*x - 1050*a^5*b^5*c^4*d^6*x - 525*a^6*b^4*c^3*d^7*x - 225*a^7*b^3*c^2*d^8*x - 75*a^8*b^2*c*d^9*x - 15*a^9*b*d^10*x - 51975*b^10*c^8*d^2*x^2 - 34650*a*b^9*c^7*d^3*x^2 - 22050*a^2*b^8*c^6*d^4*x^2 - 13230*a^3*b^7*c^5*d^5*x^2 - 7350*a^4*b^6*c^4*d^6*x^2 - 3675*a^5*b^5*c^3*d^7*x^2 - 1575*a^6*b^4*c^2*d^8*x^2 - 525*a^7*b^3*c*d^9*x^2 - 105*a^8*b^2*d^10*x^2 - 150150*b^10*c^7*d^3*x^3 - 95550*a*b^9*c^6*d^4*x^3 - 57330*a^2*b^8*c^5*d^5*x^3 - 31850*a^3*b^7*c^4*d^6*x^3 - 15925*a^4*b^6*c^3*d^7*x^3 - 6825*a^5*b^5*c^2*d^8*x^3 - 2275*a^6*b^4*c*d^9*x^3 - 455*a^7*b^3*d^10*x^3 - 286650*b^10*c^6*d^4*x^4 - 171990*a*b^9*c^5*d^5*x^4 - 95550*a^2*b^8*c^4*d^6*x^4 - 47775*a^3*b^7*c^3*d^7*x^4 - 20475*a^4*b^6*c^2*d^8*x^4 - 6825*a^5*b^5*c*d^9*x^4 - 1365*a^6*b^4*d^10*x^4 - 378378*b^10*c^5*d^5*x^5 - 210210*a*b^9*c^4*d^6*x^5 - 105105*a^2*b^8*c^3*d^7*x^5 - 45045*a^3*b^7*c^2*d^8*x^5 - 15015*a^4*b^6*c*d^9*x^5 - 3003*a^5*b^5*d^10*x^5 - 350350*b^10*c^4*d^6*x^6 - 175175*a*b^9*c^3*d^7*x^6 - 75075*a^2*b^8*c^2*d^8*x^6 - 25025*a^3*b^7*c*d^9*x^6 - 5005*a^4*b^6*d^10*x^6 - 225225*b^10*c^3*d^7*x^7 - 96525*a*b^9*c^2*d^8*x^7 - 32175*a^2*b^8*c*d^9*x^7 - 6435*a^3*b^7*d^10*x^7 - 96525*b^10*c^2*d^8*x^8 - 32175*a*b^9*c*d^9*x^8 - 6435*a^2*b^8*d^10*x^8 - 25025*b^10*c*d^9*x^9 - 5005*a*b^9*d^10*x^9 - 3003*b^10*d^10*x^10)/(15015*b^11*(a + b*x)^15)","B",1
1328,1,964,182,0.3465523,"\int \frac{(c+d x)^{10}}{(a+b x)^{17}} \, dx","IntegrateAlgebraic[(c + d*x)^10/(a + b*x)^17,x]","\frac{-3003 c^{10} b^{10}-8008 d^{10} x^{10} b^{10}-68640 c d^9 x^9 b^{10}-270270 c^2 d^8 x^8 b^{10}-640640 c^3 d^7 x^7 b^{10}-1009008 c^4 d^6 x^6 b^{10}-1100736 c^5 d^5 x^5 b^{10}-840840 c^6 d^4 x^4 b^{10}-443520 c^7 d^3 x^3 b^{10}-154440 c^8 d^2 x^2 b^{10}-32032 c^9 d x b^{10}-11440 a d^{10} x^9 b^9-77220 a c d^9 x^8 b^9-240240 a c^2 d^8 x^7 b^9-448448 a c^3 d^7 x^6 b^9-550368 a c^4 d^6 x^5 b^9-458640 a c^5 d^5 x^4 b^9-258720 a c^6 d^4 x^3 b^9-95040 a c^7 d^3 x^2 b^9-2002 a c^9 d b^9-20592 a c^8 d^2 x b^9-12870 a^2 d^{10} x^8 b^8-68640 a^2 c d^9 x^7 b^8-168168 a^2 c^2 d^8 x^6 b^8-244608 a^2 c^3 d^7 x^5 b^8-229320 a^2 c^4 d^6 x^4 b^8-141120 a^2 c^5 d^5 x^3 b^8-1287 a^2 c^8 d^2 b^8-55440 a^2 c^6 d^4 x^2 b^8-12672 a^2 c^7 d^3 x b^8-11440 a^3 d^{10} x^7 b^7-48048 a^3 c d^9 x^6 b^7-91728 a^3 c^2 d^8 x^5 b^7-101920 a^3 c^3 d^7 x^4 b^7-792 a^3 c^7 d^3 b^7-70560 a^3 c^4 d^6 x^3 b^7-30240 a^3 c^5 d^5 x^2 b^7-7392 a^3 c^6 d^4 x b^7-8008 a^4 d^{10} x^6 b^6-26208 a^4 c d^9 x^5 b^6-462 a^4 c^6 d^4 b^6-38220 a^4 c^2 d^8 x^4 b^6-31360 a^4 c^3 d^7 x^3 b^6-15120 a^4 c^4 d^6 x^2 b^6-4032 a^4 c^5 d^5 x b^6-252 a^5 c^5 d^5 b^5-4368 a^5 d^{10} x^5 b^5-10920 a^5 c d^9 x^4 b^5-11760 a^5 c^2 d^8 x^3 b^5-6720 a^5 c^3 d^7 x^2 b^5-2016 a^5 c^4 d^6 x b^5-126 a^6 c^4 d^6 b^4-1820 a^6 d^{10} x^4 b^4-3360 a^6 c d^9 x^3 b^4-2520 a^6 c^2 d^8 x^2 b^4-896 a^6 c^3 d^7 x b^4-56 a^7 c^3 d^7 b^3-560 a^7 d^{10} x^3 b^3-720 a^7 c d^9 x^2 b^3-336 a^7 c^2 d^8 x b^3-21 a^8 c^2 d^8 b^2-120 a^8 d^{10} x^2 b^2-96 a^8 c d^9 x b^2-6 a^9 c d^9 b-16 a^9 d^{10} x b-a^{10} d^{10}}{48048 b^{11} (a+b x)^{16}}","\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,"(-3003*b^10*c^10 - 2002*a*b^9*c^9*d - 1287*a^2*b^8*c^8*d^2 - 792*a^3*b^7*c^7*d^3 - 462*a^4*b^6*c^6*d^4 - 252*a^5*b^5*c^5*d^5 - 126*a^6*b^4*c^4*d^6 - 56*a^7*b^3*c^3*d^7 - 21*a^8*b^2*c^2*d^8 - 6*a^9*b*c*d^9 - a^10*d^10 - 32032*b^10*c^9*d*x - 20592*a*b^9*c^8*d^2*x - 12672*a^2*b^8*c^7*d^3*x - 7392*a^3*b^7*c^6*d^4*x - 4032*a^4*b^6*c^5*d^5*x - 2016*a^5*b^5*c^4*d^6*x - 896*a^6*b^4*c^3*d^7*x - 336*a^7*b^3*c^2*d^8*x - 96*a^8*b^2*c*d^9*x - 16*a^9*b*d^10*x - 154440*b^10*c^8*d^2*x^2 - 95040*a*b^9*c^7*d^3*x^2 - 55440*a^2*b^8*c^6*d^4*x^2 - 30240*a^3*b^7*c^5*d^5*x^2 - 15120*a^4*b^6*c^4*d^6*x^2 - 6720*a^5*b^5*c^3*d^7*x^2 - 2520*a^6*b^4*c^2*d^8*x^2 - 720*a^7*b^3*c*d^9*x^2 - 120*a^8*b^2*d^10*x^2 - 443520*b^10*c^7*d^3*x^3 - 258720*a*b^9*c^6*d^4*x^3 - 141120*a^2*b^8*c^5*d^5*x^3 - 70560*a^3*b^7*c^4*d^6*x^3 - 31360*a^4*b^6*c^3*d^7*x^3 - 11760*a^5*b^5*c^2*d^8*x^3 - 3360*a^6*b^4*c*d^9*x^3 - 560*a^7*b^3*d^10*x^3 - 840840*b^10*c^6*d^4*x^4 - 458640*a*b^9*c^5*d^5*x^4 - 229320*a^2*b^8*c^4*d^6*x^4 - 101920*a^3*b^7*c^3*d^7*x^4 - 38220*a^4*b^6*c^2*d^8*x^4 - 10920*a^5*b^5*c*d^9*x^4 - 1820*a^6*b^4*d^10*x^4 - 1100736*b^10*c^5*d^5*x^5 - 550368*a*b^9*c^4*d^6*x^5 - 244608*a^2*b^8*c^3*d^7*x^5 - 91728*a^3*b^7*c^2*d^8*x^5 - 26208*a^4*b^6*c*d^9*x^5 - 4368*a^5*b^5*d^10*x^5 - 1009008*b^10*c^4*d^6*x^6 - 448448*a*b^9*c^3*d^7*x^6 - 168168*a^2*b^8*c^2*d^8*x^6 - 48048*a^3*b^7*c*d^9*x^6 - 8008*a^4*b^6*d^10*x^6 - 640640*b^10*c^3*d^7*x^7 - 240240*a*b^9*c^2*d^8*x^7 - 68640*a^2*b^8*c*d^9*x^7 - 11440*a^3*b^7*d^10*x^7 - 270270*b^10*c^2*d^8*x^8 - 77220*a*b^9*c*d^9*x^8 - 12870*a^2*b^8*d^10*x^8 - 68640*b^10*c*d^9*x^9 - 11440*a*b^9*d^10*x^9 - 8008*b^10*d^10*x^10)/(48048*b^11*(a + b*x)^16)","B",1
1329,1,964,213,0.3493486,"\int \frac{(c+d x)^{10}}{(a+b x)^{18}} \, dx","IntegrateAlgebraic[(c + d*x)^10/(a + b*x)^18,x]","\frac{-8008 c^{10} b^{10}-19448 d^{10} x^{10} b^{10}-170170 c d^9 x^9 b^{10}-680680 c^2 d^8 x^8 b^{10}-1633632 c^3 d^7 x^7 b^{10}-2598960 c^4 d^6 x^6 b^{10}-2858856 c^5 d^5 x^5 b^{10}-2199120 c^6 d^4 x^4 b^{10}-1166880 c^7 d^3 x^3 b^{10}-408408 c^8 d^2 x^2 b^{10}-85085 c^9 d x b^{10}-24310 a d^{10} x^9 b^9-170170 a c d^9 x^8 b^9-544544 a c^2 d^8 x^7 b^9-1039584 a c^3 d^7 x^6 b^9-1299480 a c^4 d^6 x^5 b^9-1099560 a c^5 d^5 x^4 b^9-628320 a c^6 d^4 x^3 b^9-233376 a c^7 d^3 x^2 b^9-5005 a c^9 d b^9-51051 a c^8 d^2 x b^9-24310 a^2 d^{10} x^8 b^8-136136 a^2 c d^9 x^7 b^8-346528 a^2 c^2 d^8 x^6 b^8-519792 a^2 c^3 d^7 x^5 b^8-499800 a^2 c^4 d^6 x^4 b^8-314160 a^2 c^5 d^5 x^3 b^8-3003 a^2 c^8 d^2 b^8-125664 a^2 c^6 d^4 x^2 b^8-29172 a^2 c^7 d^3 x b^8-19448 a^3 d^{10} x^7 b^7-86632 a^3 c d^9 x^6 b^7-173264 a^3 c^2 d^8 x^5 b^7-199920 a^3 c^3 d^7 x^4 b^7-1716 a^3 c^7 d^3 b^7-142800 a^3 c^4 d^6 x^3 b^7-62832 a^3 c^5 d^5 x^2 b^7-15708 a^3 c^6 d^4 x b^7-12376 a^4 d^{10} x^6 b^6-43316 a^4 c d^9 x^5 b^6-924 a^4 c^6 d^4 b^6-66640 a^4 c^2 d^8 x^4 b^6-57120 a^4 c^3 d^7 x^3 b^6-28560 a^4 c^4 d^6 x^2 b^6-7854 a^4 c^5 d^5 x b^6-462 a^5 c^5 d^5 b^5-6188 a^5 d^{10} x^5 b^5-16660 a^5 c d^9 x^4 b^5-19040 a^5 c^2 d^8 x^3 b^5-11424 a^5 c^3 d^7 x^2 b^5-3570 a^5 c^4 d^6 x b^5-210 a^6 c^4 d^6 b^4-2380 a^6 d^{10} x^4 b^4-4760 a^6 c d^9 x^3 b^4-3808 a^6 c^2 d^8 x^2 b^4-1428 a^6 c^3 d^7 x b^4-84 a^7 c^3 d^7 b^3-680 a^7 d^{10} x^3 b^3-952 a^7 c d^9 x^2 b^3-476 a^7 c^2 d^8 x b^3-28 a^8 c^2 d^8 b^2-136 a^8 d^{10} x^2 b^2-119 a^8 c d^9 x b^2-7 a^9 c d^9 b-17 a^9 d^{10} x b-a^{10} d^{10}}{136136 b^{11} (a+b x)^{17}}","-\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,"(-8008*b^10*c^10 - 5005*a*b^9*c^9*d - 3003*a^2*b^8*c^8*d^2 - 1716*a^3*b^7*c^7*d^3 - 924*a^4*b^6*c^6*d^4 - 462*a^5*b^5*c^5*d^5 - 210*a^6*b^4*c^4*d^6 - 84*a^7*b^3*c^3*d^7 - 28*a^8*b^2*c^2*d^8 - 7*a^9*b*c*d^9 - a^10*d^10 - 85085*b^10*c^9*d*x - 51051*a*b^9*c^8*d^2*x - 29172*a^2*b^8*c^7*d^3*x - 15708*a^3*b^7*c^6*d^4*x - 7854*a^4*b^6*c^5*d^5*x - 3570*a^5*b^5*c^4*d^6*x - 1428*a^6*b^4*c^3*d^7*x - 476*a^7*b^3*c^2*d^8*x - 119*a^8*b^2*c*d^9*x - 17*a^9*b*d^10*x - 408408*b^10*c^8*d^2*x^2 - 233376*a*b^9*c^7*d^3*x^2 - 125664*a^2*b^8*c^6*d^4*x^2 - 62832*a^3*b^7*c^5*d^5*x^2 - 28560*a^4*b^6*c^4*d^6*x^2 - 11424*a^5*b^5*c^3*d^7*x^2 - 3808*a^6*b^4*c^2*d^8*x^2 - 952*a^7*b^3*c*d^9*x^2 - 136*a^8*b^2*d^10*x^2 - 1166880*b^10*c^7*d^3*x^3 - 628320*a*b^9*c^6*d^4*x^3 - 314160*a^2*b^8*c^5*d^5*x^3 - 142800*a^3*b^7*c^4*d^6*x^3 - 57120*a^4*b^6*c^3*d^7*x^3 - 19040*a^5*b^5*c^2*d^8*x^3 - 4760*a^6*b^4*c*d^9*x^3 - 680*a^7*b^3*d^10*x^3 - 2199120*b^10*c^6*d^4*x^4 - 1099560*a*b^9*c^5*d^5*x^4 - 499800*a^2*b^8*c^4*d^6*x^4 - 199920*a^3*b^7*c^3*d^7*x^4 - 66640*a^4*b^6*c^2*d^8*x^4 - 16660*a^5*b^5*c*d^9*x^4 - 2380*a^6*b^4*d^10*x^4 - 2858856*b^10*c^5*d^5*x^5 - 1299480*a*b^9*c^4*d^6*x^5 - 519792*a^2*b^8*c^3*d^7*x^5 - 173264*a^3*b^7*c^2*d^8*x^5 - 43316*a^4*b^6*c*d^9*x^5 - 6188*a^5*b^5*d^10*x^5 - 2598960*b^10*c^4*d^6*x^6 - 1039584*a*b^9*c^3*d^7*x^6 - 346528*a^2*b^8*c^2*d^8*x^6 - 86632*a^3*b^7*c*d^9*x^6 - 12376*a^4*b^6*d^10*x^6 - 1633632*b^10*c^3*d^7*x^7 - 544544*a*b^9*c^2*d^8*x^7 - 136136*a^2*b^8*c*d^9*x^7 - 19448*a^3*b^7*d^10*x^7 - 680680*b^10*c^2*d^8*x^8 - 170170*a*b^9*c*d^9*x^8 - 24310*a^2*b^8*d^10*x^8 - 170170*b^10*c*d^9*x^9 - 24310*a*b^9*d^10*x^9 - 19448*b^10*d^10*x^10)/(136136*b^11*(a + b*x)^17)","B",1
1330,1,964,244,0.3367317,"\int \frac{(c+d x)^{10}}{(a+b x)^{19}} \, dx","IntegrateAlgebraic[(c + d*x)^10/(a + b*x)^19,x]","\frac{-19448 c^{10} b^{10}-43758 d^{10} x^{10} b^{10}-388960 c d^9 x^9 b^{10}-1575288 c^2 d^8 x^8 b^{10}-3818880 c^3 d^7 x^7 b^{10}-6126120 c^4 d^6 x^6 b^{10}-6785856 c^5 d^5 x^5 b^{10}-5250960 c^6 d^4 x^4 b^{10}-2800512 c^7 d^3 x^3 b^{10}-984555 c^8 d^2 x^2 b^{10}-205920 c^9 d x b^{10}-48620 a d^{10} x^9 b^9-350064 a c d^9 x^8 b^9-1145664 a c^2 d^8 x^7 b^9-2227680 a c^3 d^7 x^6 b^9-2827440 a c^4 d^6 x^5 b^9-2423520 a c^5 d^5 x^4 b^9-1400256 a c^6 d^4 x^3 b^9-525096 a c^7 d^3 x^2 b^9-11440 a c^9 d b^9-115830 a c^8 d^2 x b^9-43758 a^2 d^{10} x^8 b^8-254592 a^2 c d^9 x^7 b^8-668304 a^2 c^2 d^8 x^6 b^8-1028160 a^2 c^3 d^7 x^5 b^8-1009800 a^2 c^4 d^6 x^4 b^8-646272 a^2 c^5 d^5 x^3 b^8-6435 a^2 c^8 d^2 b^8-262548 a^2 c^6 d^4 x^2 b^8-61776 a^2 c^7 d^3 x b^8-31824 a^3 d^{10} x^7 b^7-148512 a^3 c d^9 x^6 b^7-308448 a^3 c^2 d^8 x^5 b^7-367200 a^3 c^3 d^7 x^4 b^7-3432 a^3 c^7 d^3 b^7-269280 a^3 c^4 d^6 x^3 b^7-121176 a^3 c^5 d^5 x^2 b^7-30888 a^3 c^6 d^4 x b^7-18564 a^4 d^{10} x^6 b^6-68544 a^4 c d^9 x^5 b^6-1716 a^4 c^6 d^4 b^6-110160 a^4 c^2 d^8 x^4 b^6-97920 a^4 c^3 d^7 x^3 b^6-50490 a^4 c^4 d^6 x^2 b^6-14256 a^4 c^5 d^5 x b^6-792 a^5 c^5 d^5 b^5-8568 a^5 d^{10} x^5 b^5-24480 a^5 c d^9 x^4 b^5-29376 a^5 c^2 d^8 x^3 b^5-18360 a^5 c^3 d^7 x^2 b^5-5940 a^5 c^4 d^6 x b^5-330 a^6 c^4 d^6 b^4-3060 a^6 d^{10} x^4 b^4-6528 a^6 c d^9 x^3 b^4-5508 a^6 c^2 d^8 x^2 b^4-2160 a^6 c^3 d^7 x b^4-120 a^7 c^3 d^7 b^3-816 a^7 d^{10} x^3 b^3-1224 a^7 c d^9 x^2 b^3-648 a^7 c^2 d^8 x b^3-36 a^8 c^2 d^8 b^2-153 a^8 d^{10} x^2 b^2-144 a^8 c d^9 x b^2-8 a^9 c d^9 b-18 a^9 d^{10} x b-a^{10} d^{10}}{350064 b^{11} (a+b x)^{18}}","\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,"(-19448*b^10*c^10 - 11440*a*b^9*c^9*d - 6435*a^2*b^8*c^8*d^2 - 3432*a^3*b^7*c^7*d^3 - 1716*a^4*b^6*c^6*d^4 - 792*a^5*b^5*c^5*d^5 - 330*a^6*b^4*c^4*d^6 - 120*a^7*b^3*c^3*d^7 - 36*a^8*b^2*c^2*d^8 - 8*a^9*b*c*d^9 - a^10*d^10 - 205920*b^10*c^9*d*x - 115830*a*b^9*c^8*d^2*x - 61776*a^2*b^8*c^7*d^3*x - 30888*a^3*b^7*c^6*d^4*x - 14256*a^4*b^6*c^5*d^5*x - 5940*a^5*b^5*c^4*d^6*x - 2160*a^6*b^4*c^3*d^7*x - 648*a^7*b^3*c^2*d^8*x - 144*a^8*b^2*c*d^9*x - 18*a^9*b*d^10*x - 984555*b^10*c^8*d^2*x^2 - 525096*a*b^9*c^7*d^3*x^2 - 262548*a^2*b^8*c^6*d^4*x^2 - 121176*a^3*b^7*c^5*d^5*x^2 - 50490*a^4*b^6*c^4*d^6*x^2 - 18360*a^5*b^5*c^3*d^7*x^2 - 5508*a^6*b^4*c^2*d^8*x^2 - 1224*a^7*b^3*c*d^9*x^2 - 153*a^8*b^2*d^10*x^2 - 2800512*b^10*c^7*d^3*x^3 - 1400256*a*b^9*c^6*d^4*x^3 - 646272*a^2*b^8*c^5*d^5*x^3 - 269280*a^3*b^7*c^4*d^6*x^3 - 97920*a^4*b^6*c^3*d^7*x^3 - 29376*a^5*b^5*c^2*d^8*x^3 - 6528*a^6*b^4*c*d^9*x^3 - 816*a^7*b^3*d^10*x^3 - 5250960*b^10*c^6*d^4*x^4 - 2423520*a*b^9*c^5*d^5*x^4 - 1009800*a^2*b^8*c^4*d^6*x^4 - 367200*a^3*b^7*c^3*d^7*x^4 - 110160*a^4*b^6*c^2*d^8*x^4 - 24480*a^5*b^5*c*d^9*x^4 - 3060*a^6*b^4*d^10*x^4 - 6785856*b^10*c^5*d^5*x^5 - 2827440*a*b^9*c^4*d^6*x^5 - 1028160*a^2*b^8*c^3*d^7*x^5 - 308448*a^3*b^7*c^2*d^8*x^5 - 68544*a^4*b^6*c*d^9*x^5 - 8568*a^5*b^5*d^10*x^5 - 6126120*b^10*c^4*d^6*x^6 - 2227680*a*b^9*c^3*d^7*x^6 - 668304*a^2*b^8*c^2*d^8*x^6 - 148512*a^3*b^7*c*d^9*x^6 - 18564*a^4*b^6*d^10*x^6 - 3818880*b^10*c^3*d^7*x^7 - 1145664*a*b^9*c^2*d^8*x^7 - 254592*a^2*b^8*c*d^9*x^7 - 31824*a^3*b^7*d^10*x^7 - 1575288*b^10*c^2*d^8*x^8 - 350064*a*b^9*c*d^9*x^8 - 43758*a^2*b^8*d^10*x^8 - 388960*b^10*c*d^9*x^9 - 48620*a*b^9*d^10*x^9 - 43758*b^10*d^10*x^10)/(350064*b^11*(a + b*x)^18)","B",1
1331,1,964,273,0.341897,"\int \frac{(c+d x)^{10}}{(a+b x)^{20}} \, dx","IntegrateAlgebraic[(c + d*x)^10/(a + b*x)^20,x]","\frac{-43758 c^{10} b^{10}-92378 d^{10} x^{10} b^{10}-831402 c d^9 x^9 b^{10}-3401190 c^2 d^8 x^8 b^{10}-8314020 c^3 d^7 x^7 b^{10}-13430340 c^4 d^6 x^6 b^{10}-14965236 c^5 d^5 x^5 b^{10}-11639628 c^6 d^4 x^4 b^{10}-6235515 c^7 d^3 x^3 b^{10}-2200770 c^8 d^2 x^2 b^{10}-461890 c^9 d x b^{10}-92378 a d^{10} x^9 b^9-680238 a c d^9 x^8 b^9-2267460 a c^2 d^8 x^7 b^9-4476780 a c^3 d^7 x^6 b^9-5755860 a c^4 d^6 x^5 b^9-4988412 a c^5 d^5 x^4 b^9-2909907 a c^6 d^4 x^3 b^9-1100385 a c^7 d^3 x^2 b^9-24310 a c^9 d b^9-244530 a c^8 d^2 x b^9-75582 a^2 d^{10} x^8 b^8-453492 a^2 c d^9 x^7 b^8-1220940 a^2 c^2 d^8 x^6 b^8-1918620 a^2 c^3 d^7 x^5 b^8-1918620 a^2 c^4 d^6 x^4 b^8-1247103 a^2 c^5 d^5 x^3 b^8-12870 a^2 c^8 d^2 b^8-513513 a^2 c^6 d^4 x^2 b^8-122265 a^2 c^7 d^3 x b^8-50388 a^3 d^{10} x^7 b^7-244188 a^3 c d^9 x^6 b^7-523260 a^3 c^2 d^8 x^5 b^7-639540 a^3 c^3 d^7 x^4 b^7-6435 a^3 c^7 d^3 b^7-479655 a^3 c^4 d^6 x^3 b^7-220077 a^3 c^5 d^5 x^2 b^7-57057 a^3 c^6 d^4 x b^7-27132 a^4 d^{10} x^6 b^6-104652 a^4 c d^9 x^5 b^6-3003 a^4 c^6 d^4 b^6-174420 a^4 c^2 d^8 x^4 b^6-159885 a^4 c^3 d^7 x^3 b^6-84645 a^4 c^4 d^6 x^2 b^6-24453 a^4 c^5 d^5 x b^6-1287 a^5 c^5 d^5 b^5-11628 a^5 d^{10} x^5 b^5-34884 a^5 c d^9 x^4 b^5-43605 a^5 c^2 d^8 x^3 b^5-28215 a^5 c^3 d^7 x^2 b^5-9405 a^5 c^4 d^6 x b^5-495 a^6 c^4 d^6 b^4-3876 a^6 d^{10} x^4 b^4-8721 a^6 c d^9 x^3 b^4-7695 a^6 c^2 d^8 x^2 b^4-3135 a^6 c^3 d^7 x b^4-165 a^7 c^3 d^7 b^3-969 a^7 d^{10} x^3 b^3-1539 a^7 c d^9 x^2 b^3-855 a^7 c^2 d^8 x b^3-45 a^8 c^2 d^8 b^2-171 a^8 d^{10} x^2 b^2-171 a^8 c d^9 x b^2-9 a^9 c d^9 b-19 a^9 d^{10} x b-a^{10} d^{10}}{831402 b^{11} (a+b x)^{19}}","-\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,"(-43758*b^10*c^10 - 24310*a*b^9*c^9*d - 12870*a^2*b^8*c^8*d^2 - 6435*a^3*b^7*c^7*d^3 - 3003*a^4*b^6*c^6*d^4 - 1287*a^5*b^5*c^5*d^5 - 495*a^6*b^4*c^4*d^6 - 165*a^7*b^3*c^3*d^7 - 45*a^8*b^2*c^2*d^8 - 9*a^9*b*c*d^9 - a^10*d^10 - 461890*b^10*c^9*d*x - 244530*a*b^9*c^8*d^2*x - 122265*a^2*b^8*c^7*d^3*x - 57057*a^3*b^7*c^6*d^4*x - 24453*a^4*b^6*c^5*d^5*x - 9405*a^5*b^5*c^4*d^6*x - 3135*a^6*b^4*c^3*d^7*x - 855*a^7*b^3*c^2*d^8*x - 171*a^8*b^2*c*d^9*x - 19*a^9*b*d^10*x - 2200770*b^10*c^8*d^2*x^2 - 1100385*a*b^9*c^7*d^3*x^2 - 513513*a^2*b^8*c^6*d^4*x^2 - 220077*a^3*b^7*c^5*d^5*x^2 - 84645*a^4*b^6*c^4*d^6*x^2 - 28215*a^5*b^5*c^3*d^7*x^2 - 7695*a^6*b^4*c^2*d^8*x^2 - 1539*a^7*b^3*c*d^9*x^2 - 171*a^8*b^2*d^10*x^2 - 6235515*b^10*c^7*d^3*x^3 - 2909907*a*b^9*c^6*d^4*x^3 - 1247103*a^2*b^8*c^5*d^5*x^3 - 479655*a^3*b^7*c^4*d^6*x^3 - 159885*a^4*b^6*c^3*d^7*x^3 - 43605*a^5*b^5*c^2*d^8*x^3 - 8721*a^6*b^4*c*d^9*x^3 - 969*a^7*b^3*d^10*x^3 - 11639628*b^10*c^6*d^4*x^4 - 4988412*a*b^9*c^5*d^5*x^4 - 1918620*a^2*b^8*c^4*d^6*x^4 - 639540*a^3*b^7*c^3*d^7*x^4 - 174420*a^4*b^6*c^2*d^8*x^4 - 34884*a^5*b^5*c*d^9*x^4 - 3876*a^6*b^4*d^10*x^4 - 14965236*b^10*c^5*d^5*x^5 - 5755860*a*b^9*c^4*d^6*x^5 - 1918620*a^2*b^8*c^3*d^7*x^5 - 523260*a^3*b^7*c^2*d^8*x^5 - 104652*a^4*b^6*c*d^9*x^5 - 11628*a^5*b^5*d^10*x^5 - 13430340*b^10*c^4*d^6*x^6 - 4476780*a*b^9*c^3*d^7*x^6 - 1220940*a^2*b^8*c^2*d^8*x^6 - 244188*a^3*b^7*c*d^9*x^6 - 27132*a^4*b^6*d^10*x^6 - 8314020*b^10*c^3*d^7*x^7 - 2267460*a*b^9*c^2*d^8*x^7 - 453492*a^2*b^8*c*d^9*x^7 - 50388*a^3*b^7*d^10*x^7 - 3401190*b^10*c^2*d^8*x^8 - 680238*a*b^9*c*d^9*x^8 - 75582*a^2*b^8*d^10*x^8 - 831402*b^10*c*d^9*x^9 - 92378*a*b^9*d^10*x^9 - 92378*b^10*d^10*x^10)/(831402*b^11*(a + b*x)^19)","B",1
1332,1,964,279,0.335159,"\int \frac{(c+d x)^{10}}{(a+b x)^{21}} \, dx","IntegrateAlgebraic[(c + d*x)^10/(a + b*x)^21,x]","\frac{-92378 c^{10} b^{10}-184756 d^{10} x^{10} b^{10}-1679600 c d^9 x^9 b^{10}-6928350 c^2 d^8 x^8 b^{10}-17054400 c^3 d^7 x^7 b^{10}-27713400 c^4 d^6 x^6 b^{10}-31039008 c^5 d^5 x^5 b^{10}-24249225 c^6 d^4 x^4 b^{10}-13041600 c^7 d^3 x^3 b^{10}-4618900 c^8 d^2 x^2 b^{10}-972400 c^9 d x b^{10}-167960 a d^{10} x^9 b^9-1259700 a c d^9 x^8 b^9-4263600 a c^2 d^8 x^7 b^9-8527200 a c^3 d^7 x^6 b^9-11085360 a c^4 d^6 x^5 b^9-9699690 a c^5 d^5 x^4 b^9-5705700 a c^6 d^4 x^3 b^9-2173600 a c^7 d^3 x^2 b^9-48620 a c^9 d b^9-486200 a c^8 d^2 x b^9-125970 a^2 d^{10} x^8 b^8-775200 a^2 c d^9 x^7 b^8-2131800 a^2 c^2 d^8 x^6 b^8-3410880 a^2 c^3 d^7 x^5 b^8-3464175 a^2 c^4 d^6 x^4 b^8-2282280 a^2 c^5 d^5 x^3 b^8-24310 a^2 c^8 d^2 b^8-950950 a^2 c^6 d^4 x^2 b^8-228800 a^2 c^7 d^3 x b^8-77520 a^3 d^{10} x^7 b^7-387600 a^3 c d^9 x^6 b^7-852720 a^3 c^2 d^8 x^5 b^7-1065900 a^3 c^3 d^7 x^4 b^7-11440 a^3 c^7 d^3 b^7-815100 a^3 c^4 d^6 x^3 b^7-380380 a^3 c^5 d^5 x^2 b^7-100100 a^3 c^6 d^4 x b^7-38760 a^4 d^{10} x^6 b^6-155040 a^4 c d^9 x^5 b^6-5005 a^4 c^6 d^4 b^6-266475 a^4 c^2 d^8 x^4 b^6-250800 a^4 c^3 d^7 x^3 b^6-135850 a^4 c^4 d^6 x^2 b^6-40040 a^4 c^5 d^5 x b^6-2002 a^5 c^5 d^5 b^5-15504 a^5 d^{10} x^5 b^5-48450 a^5 c d^9 x^4 b^5-62700 a^5 c^2 d^8 x^3 b^5-41800 a^5 c^3 d^7 x^2 b^5-14300 a^5 c^4 d^6 x b^5-715 a^6 c^4 d^6 b^4-4845 a^6 d^{10} x^4 b^4-11400 a^6 c d^9 x^3 b^4-10450 a^6 c^2 d^8 x^2 b^4-4400 a^6 c^3 d^7 x b^4-220 a^7 c^3 d^7 b^3-1140 a^7 d^{10} x^3 b^3-1900 a^7 c d^9 x^2 b^3-1100 a^7 c^2 d^8 x b^3-55 a^8 c^2 d^8 b^2-190 a^8 d^{10} x^2 b^2-200 a^8 c d^9 x b^2-10 a^9 c d^9 b-20 a^9 d^{10} x b-a^{10} d^{10}}{1847560 b^{11} (a+b x)^{20}}","-\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,"(-92378*b^10*c^10 - 48620*a*b^9*c^9*d - 24310*a^2*b^8*c^8*d^2 - 11440*a^3*b^7*c^7*d^3 - 5005*a^4*b^6*c^6*d^4 - 2002*a^5*b^5*c^5*d^5 - 715*a^6*b^4*c^4*d^6 - 220*a^7*b^3*c^3*d^7 - 55*a^8*b^2*c^2*d^8 - 10*a^9*b*c*d^9 - a^10*d^10 - 972400*b^10*c^9*d*x - 486200*a*b^9*c^8*d^2*x - 228800*a^2*b^8*c^7*d^3*x - 100100*a^3*b^7*c^6*d^4*x - 40040*a^4*b^6*c^5*d^5*x - 14300*a^5*b^5*c^4*d^6*x - 4400*a^6*b^4*c^3*d^7*x - 1100*a^7*b^3*c^2*d^8*x - 200*a^8*b^2*c*d^9*x - 20*a^9*b*d^10*x - 4618900*b^10*c^8*d^2*x^2 - 2173600*a*b^9*c^7*d^3*x^2 - 950950*a^2*b^8*c^6*d^4*x^2 - 380380*a^3*b^7*c^5*d^5*x^2 - 135850*a^4*b^6*c^4*d^6*x^2 - 41800*a^5*b^5*c^3*d^7*x^2 - 10450*a^6*b^4*c^2*d^8*x^2 - 1900*a^7*b^3*c*d^9*x^2 - 190*a^8*b^2*d^10*x^2 - 13041600*b^10*c^7*d^3*x^3 - 5705700*a*b^9*c^6*d^4*x^3 - 2282280*a^2*b^8*c^5*d^5*x^3 - 815100*a^3*b^7*c^4*d^6*x^3 - 250800*a^4*b^6*c^3*d^7*x^3 - 62700*a^5*b^5*c^2*d^8*x^3 - 11400*a^6*b^4*c*d^9*x^3 - 1140*a^7*b^3*d^10*x^3 - 24249225*b^10*c^6*d^4*x^4 - 9699690*a*b^9*c^5*d^5*x^4 - 3464175*a^2*b^8*c^4*d^6*x^4 - 1065900*a^3*b^7*c^3*d^7*x^4 - 266475*a^4*b^6*c^2*d^8*x^4 - 48450*a^5*b^5*c*d^9*x^4 - 4845*a^6*b^4*d^10*x^4 - 31039008*b^10*c^5*d^5*x^5 - 11085360*a*b^9*c^4*d^6*x^5 - 3410880*a^2*b^8*c^3*d^7*x^5 - 852720*a^3*b^7*c^2*d^8*x^5 - 155040*a^4*b^6*c*d^9*x^5 - 15504*a^5*b^5*d^10*x^5 - 27713400*b^10*c^4*d^6*x^6 - 8527200*a*b^9*c^3*d^7*x^6 - 2131800*a^2*b^8*c^2*d^8*x^6 - 387600*a^3*b^7*c*d^9*x^6 - 38760*a^4*b^6*d^10*x^6 - 17054400*b^10*c^3*d^7*x^7 - 4263600*a*b^9*c^2*d^8*x^7 - 775200*a^2*b^8*c*d^9*x^7 - 77520*a^3*b^7*d^10*x^7 - 6928350*b^10*c^2*d^8*x^8 - 1259700*a*b^9*c*d^9*x^8 - 125970*a^2*b^8*d^10*x^8 - 1679600*b^10*c*d^9*x^9 - 167960*a*b^9*d^10*x^9 - 184756*b^10*d^10*x^10)/(1847560*b^11*(a + b*x)^20)","B",1
1333,1,964,279,0.3537716,"\int \frac{(c+d x)^{10}}{(a+b x)^{22}} \, dx","IntegrateAlgebraic[(c + d*x)^10/(a + b*x)^22,x]","\frac{-184756 c^{10} b^{10}-352716 d^{10} x^{10} b^{10}-3233230 c d^9 x^9 b^{10}-13430340 c^2 d^8 x^8 b^{10}-33256080 c^3 d^7 x^7 b^{10}-54318264 c^4 d^6 x^6 b^{10}-61108047 c^5 d^5 x^5 b^{10}-47927880 c^6 d^4 x^4 b^{10}-25865840 c^7 d^3 x^3 b^{10}-9189180 c^8 d^2 x^2 b^{10}-1939938 c^9 d x b^{10}-293930 a d^{10} x^9 b^9-2238390 a c d^9 x^8 b^9-7674480 a c^2 d^8 x^7 b^9-15519504 a c^3 d^7 x^6 b^9-20369349 a c^4 d^6 x^5 b^9-17972955 a c^5 d^5 x^4 b^9-10650640 a c^6 d^4 x^3 b^9-4084080 a c^7 d^3 x^2 b^9-92378 a c^9 d b^9-918918 a c^8 d^2 x b^9-203490 a^2 d^{10} x^8 b^8-1279080 a^2 c d^9 x^7 b^8-3581424 a^2 c^2 d^8 x^6 b^8-5819814 a^2 c^3 d^7 x^5 b^8-5990985 a^2 c^4 d^6 x^4 b^8-3993990 a^2 c^5 d^5 x^3 b^8-43758 a^2 c^8 d^2 b^8-1681680 a^2 c^6 d^4 x^2 b^8-408408 a^2 c^7 d^3 x b^8-116280 a^3 d^{10} x^7 b^7-596904 a^3 c d^9 x^6 b^7-1343034 a^3 c^2 d^8 x^5 b^7-1711710 a^3 c^3 d^7 x^4 b^7-19448 a^3 c^7 d^3 b^7-1331330 a^3 c^4 d^6 x^3 b^7-630630 a^3 c^5 d^5 x^2 b^7-168168 a^3 c^6 d^4 x b^7-54264 a^4 d^{10} x^6 b^6-223839 a^4 c d^9 x^5 b^6-8008 a^4 c^6 d^4 b^6-395010 a^4 c^2 d^8 x^4 b^6-380380 a^4 c^3 d^7 x^3 b^6-210210 a^4 c^4 d^6 x^2 b^6-63063 a^4 c^5 d^5 x b^6-3003 a^5 c^5 d^5 b^5-20349 a^5 d^{10} x^5 b^5-65835 a^5 c d^9 x^4 b^5-87780 a^5 c^2 d^8 x^3 b^5-60060 a^5 c^3 d^7 x^2 b^5-21021 a^5 c^4 d^6 x b^5-1001 a^6 c^4 d^6 b^4-5985 a^6 d^{10} x^4 b^4-14630 a^6 c d^9 x^3 b^4-13860 a^6 c^2 d^8 x^2 b^4-6006 a^6 c^3 d^7 x b^4-286 a^7 c^3 d^7 b^3-1330 a^7 d^{10} x^3 b^3-2310 a^7 c d^9 x^2 b^3-1386 a^7 c^2 d^8 x b^3-66 a^8 c^2 d^8 b^2-210 a^8 d^{10} x^2 b^2-231 a^8 c d^9 x b^2-11 a^9 c d^9 b-21 a^9 d^{10} x b-a^{10} d^{10}}{3879876 b^{11} (a+b x)^{21}}","-\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,"(-184756*b^10*c^10 - 92378*a*b^9*c^9*d - 43758*a^2*b^8*c^8*d^2 - 19448*a^3*b^7*c^7*d^3 - 8008*a^4*b^6*c^6*d^4 - 3003*a^5*b^5*c^5*d^5 - 1001*a^6*b^4*c^4*d^6 - 286*a^7*b^3*c^3*d^7 - 66*a^8*b^2*c^2*d^8 - 11*a^9*b*c*d^9 - a^10*d^10 - 1939938*b^10*c^9*d*x - 918918*a*b^9*c^8*d^2*x - 408408*a^2*b^8*c^7*d^3*x - 168168*a^3*b^7*c^6*d^4*x - 63063*a^4*b^6*c^5*d^5*x - 21021*a^5*b^5*c^4*d^6*x - 6006*a^6*b^4*c^3*d^7*x - 1386*a^7*b^3*c^2*d^8*x - 231*a^8*b^2*c*d^9*x - 21*a^9*b*d^10*x - 9189180*b^10*c^8*d^2*x^2 - 4084080*a*b^9*c^7*d^3*x^2 - 1681680*a^2*b^8*c^6*d^4*x^2 - 630630*a^3*b^7*c^5*d^5*x^2 - 210210*a^4*b^6*c^4*d^6*x^2 - 60060*a^5*b^5*c^3*d^7*x^2 - 13860*a^6*b^4*c^2*d^8*x^2 - 2310*a^7*b^3*c*d^9*x^2 - 210*a^8*b^2*d^10*x^2 - 25865840*b^10*c^7*d^3*x^3 - 10650640*a*b^9*c^6*d^4*x^3 - 3993990*a^2*b^8*c^5*d^5*x^3 - 1331330*a^3*b^7*c^4*d^6*x^3 - 380380*a^4*b^6*c^3*d^7*x^3 - 87780*a^5*b^5*c^2*d^8*x^3 - 14630*a^6*b^4*c*d^9*x^3 - 1330*a^7*b^3*d^10*x^3 - 47927880*b^10*c^6*d^4*x^4 - 17972955*a*b^9*c^5*d^5*x^4 - 5990985*a^2*b^8*c^4*d^6*x^4 - 1711710*a^3*b^7*c^3*d^7*x^4 - 395010*a^4*b^6*c^2*d^8*x^4 - 65835*a^5*b^5*c*d^9*x^4 - 5985*a^6*b^4*d^10*x^4 - 61108047*b^10*c^5*d^5*x^5 - 20369349*a*b^9*c^4*d^6*x^5 - 5819814*a^2*b^8*c^3*d^7*x^5 - 1343034*a^3*b^7*c^2*d^8*x^5 - 223839*a^4*b^6*c*d^9*x^5 - 20349*a^5*b^5*d^10*x^5 - 54318264*b^10*c^4*d^6*x^6 - 15519504*a*b^9*c^3*d^7*x^6 - 3581424*a^2*b^8*c^2*d^8*x^6 - 596904*a^3*b^7*c*d^9*x^6 - 54264*a^4*b^6*d^10*x^6 - 33256080*b^10*c^3*d^7*x^7 - 7674480*a*b^9*c^2*d^8*x^7 - 1279080*a^2*b^8*c*d^9*x^7 - 116280*a^3*b^7*d^10*x^7 - 13430340*b^10*c^2*d^8*x^8 - 2238390*a*b^9*c*d^9*x^8 - 203490*a^2*b^8*d^10*x^8 - 3233230*b^10*c*d^9*x^9 - 293930*a*b^9*d^10*x^9 - 352716*b^10*d^10*x^10)/(3879876*b^11*(a + b*x)^21)","B",1
1334,1,203,122,0.1137446,"\int \frac{(a+b x)^5}{c+d x} \, dx","IntegrateAlgebraic[(a + b*x)^5/(c + d*x),x]","\frac{b x \left(300 a^4 d^4-600 a^3 b c d^3+300 a^3 b d^4 x+600 a^2 b^2 c^2 d^2-300 a^2 b^2 c d^3 x+200 a^2 b^2 d^4 x^2-300 a b^3 c^3 d+150 a b^3 c^2 d^2 x-100 a b^3 c d^3 x^2+75 a b^3 d^4 x^3+60 b^4 c^4-30 b^4 c^3 d x+20 b^4 c^2 d^2 x^2-15 b^4 c d^3 x^3+12 b^4 d^4 x^4\right)}{60 d^5}+\frac{(a d-b c)^5 \log (c+d x)}{d^6}","-\frac{(b c-a d)^5 \log (c+d x)}{d^6}+\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{(a+b x)^5}{5 d}",1,"(b*x*(60*b^4*c^4 - 300*a*b^3*c^3*d + 600*a^2*b^2*c^2*d^2 - 600*a^3*b*c*d^3 + 300*a^4*d^4 - 30*b^4*c^3*d*x + 150*a*b^3*c^2*d^2*x - 300*a^2*b^2*c*d^3*x + 300*a^3*b*d^4*x + 20*b^4*c^2*d^2*x^2 - 100*a*b^3*c*d^3*x^2 + 200*a^2*b^2*d^4*x^2 - 15*b^4*c*d^3*x^3 + 75*a*b^3*d^4*x^3 + 12*b^4*d^4*x^4))/(60*d^5) + ((-(b*c) + a*d)^5*Log[c + d*x])/d^6","A",1
1335,1,133,98,0.0739431,"\int \frac{(a+b x)^4}{c+d x} \, dx","IntegrateAlgebraic[(a + b*x)^4/(c + d*x),x]","\frac{b x \left(48 a^3 d^3-72 a^2 b c d^2+36 a^2 b d^3 x+48 a b^2 c^2 d-24 a b^2 c d^2 x+16 a b^2 d^3 x^2-12 b^3 c^3+6 b^3 c^2 d x-4 b^3 c d^2 x^2+3 b^3 d^3 x^3\right)}{12 d^4}+\frac{(a d-b c)^4 \log (c+d x)}{d^5}","\frac{(b c-a d)^4 \log (c+d x)}{d^5}-\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{(a+b x)^4}{4 d}",1,"(b*x*(-12*b^3*c^3 + 48*a*b^2*c^2*d - 72*a^2*b*c*d^2 + 48*a^3*d^3 + 6*b^3*c^2*d*x - 24*a*b^2*c*d^2*x + 36*a^2*b*d^3*x - 4*b^3*c*d^2*x^2 + 16*a*b^2*d^3*x^2 + 3*b^3*d^3*x^3))/(12*d^4) + ((-(b*c) + a*d)^4*Log[c + d*x])/d^5","A",1
1336,1,80,74,0.0495093,"\int \frac{(a+b x)^3}{c+d x} \, dx","IntegrateAlgebraic[(a + b*x)^3/(c + d*x),x]","\frac{b x \left(18 a^2 d^2-18 a b c d+9 a b d^2 x+6 b^2 c^2-3 b^2 c d x+2 b^2 d^2 x^2\right)}{6 d^3}+\frac{(a d-b c)^3 \log (c+d x)}{d^4}","-\frac{(b c-a d)^3 \log (c+d x)}{d^4}+\frac{b x (b c-a d)^2}{d^3}-\frac{(a+b x)^2 (b c-a d)}{2 d^2}+\frac{(a+b x)^3}{3 d}",1,"(b*x*(6*b^2*c^2 - 18*a*b*c*d + 18*a^2*d^2 - 3*b^2*c*d*x + 9*a*b*d^2*x + 2*b^2*d^2*x^2))/(6*d^3) + ((-(b*c) + a*d)^3*Log[c + d*x])/d^4","A",1
1337,1,43,50,0.0269079,"\int \frac{(a+b x)^2}{c+d x} \, dx","IntegrateAlgebraic[(a + b*x)^2/(c + d*x),x]","\frac{(a d-b c)^2 \log (c+d x)}{d^3}+\frac{b x (4 a d-2 b c+b d x)}{2 d^2}","\frac{(b c-a d)^2 \log (c+d x)}{d^3}-\frac{b x (b c-a d)}{d^2}+\frac{(a+b x)^2}{2 d}",1,"(b*x*(-2*b*c + 4*a*d + b*d*x))/(2*d^2) + ((-(b*c) + a*d)^2*Log[c + d*x])/d^3","A",1
1338,1,25,26,0.0128454,"\int \frac{a+b x}{c+d x} \, dx","IntegrateAlgebraic[(a + b*x)/(c + d*x),x]","\frac{(a d-b c) \log (c+d x)}{d^2}+\frac{b x}{d}","\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",1
1339,1,10,10,0.0032164,"\int \frac{1}{c+d x} \, dx","IntegrateAlgebraic[(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
1340,1,35,36,0.0229257,"\int \frac{1}{(a+b x) (c+d x)} \, dx","IntegrateAlgebraic[1/((a + b*x)*(c + d*x)),x]","\frac{\log (a+b x)}{b c-a d}+\frac{\log (c+d x)}{a d-b c}","\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",1
1341,1,57,57,0.0501217,"\int \frac{1}{(a+b x)^2 (c+d x)} \, dx","IntegrateAlgebraic[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",1
1342,1,77,82,0.0860695,"\int \frac{1}{(a+b x)^3 (c+d x)} \, dx","IntegrateAlgebraic[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{3 a d-b c+2 b d x}{2 (a+b x)^2 (b c-a d)^2}","\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,"(-(b*c) + 3*a*d + 2*b*d*x)/(2*(b*c - a*d)^2*(a + b*x)^2) + (d^2*Log[a + b*x])/(b*c - a*d)^3 - (d^2*Log[c + d*x])/(b*c - a*d)^3","A",1
1343,1,287,130,0.1306227,"\int \frac{(a+b x)^5}{(c+d x)^2} \, dx","IntegrateAlgebraic[(a + b*x)^5/(c + d*x)^2,x]","\frac{-12 a^5 d^5+60 a^4 b c d^4-120 a^3 b^2 c^2 d^3+120 a^3 b^2 c d^4 x+120 a^3 b^2 d^5 x^2+120 a^2 b^3 c^3 d^2-240 a^2 b^3 c^2 d^3 x-180 a^2 b^3 c d^4 x^2+60 a^2 b^3 d^5 x^3-60 a b^4 c^4 d+180 a b^4 c^3 d^2 x+120 a b^4 c^2 d^3 x^2-40 a b^4 c d^4 x^3+20 a b^4 d^5 x^4+12 b^5 c^5-48 b^5 c^4 d x-30 b^5 c^3 d^2 x^2+10 b^5 c^2 d^3 x^3-5 b^5 c d^4 x^4+3 b^5 d^5 x^5}{12 d^6 (c+d x)}+\frac{5 b (b c-a d)^4 \log (c+d x)}{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,"(12*b^5*c^5 - 60*a*b^4*c^4*d + 120*a^2*b^3*c^3*d^2 - 120*a^3*b^2*c^2*d^3 + 60*a^4*b*c*d^4 - 12*a^5*d^5 - 48*b^5*c^4*d*x + 180*a*b^4*c^3*d^2*x - 240*a^2*b^3*c^2*d^3*x + 120*a^3*b^2*c*d^4*x - 30*b^5*c^3*d^2*x^2 + 120*a*b^4*c^2*d^3*x^2 - 180*a^2*b^3*c*d^4*x^2 + 120*a^3*b^2*d^5*x^2 + 10*b^5*c^2*d^3*x^3 - 40*a*b^4*c*d^4*x^3 + 60*a^2*b^3*d^5*x^3 - 5*b^5*c*d^4*x^4 + 20*a*b^4*d^5*x^4 + 3*b^5*d^5*x^5)/(12*d^6*(c + d*x)) + (5*b*(b*c - a*d)^4*Log[c + d*x])/d^6","B",1
1344,1,199,104,0.0945103,"\int \frac{(a+b x)^4}{(c+d x)^2} \, dx","IntegrateAlgebraic[(a + b*x)^4/(c + d*x)^2,x]","\frac{-3 a^4 d^4+12 a^3 b c d^3-18 a^2 b^2 c^2 d^2+18 a^2 b^2 c d^3 x+18 a^2 b^2 d^4 x^2+12 a b^3 c^3 d-24 a b^3 c^2 d^2 x-18 a b^3 c d^3 x^2+6 a b^3 d^4 x^3-3 b^4 c^4+9 b^4 c^3 d x+6 b^4 c^2 d^2 x^2-2 b^4 c d^3 x^3+b^4 d^4 x^4}{3 d^5 (c+d x)}-\frac{4 b (b c-a d)^3 \log (c+d x)}{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,"(-3*b^4*c^4 + 12*a*b^3*c^3*d - 18*a^2*b^2*c^2*d^2 + 12*a^3*b*c*d^3 - 3*a^4*d^4 + 9*b^4*c^3*d*x - 24*a*b^3*c^2*d^2*x + 18*a^2*b^2*c*d^3*x + 6*b^4*c^2*d^2*x^2 - 18*a*b^3*c*d^3*x^2 + 18*a^2*b^2*d^4*x^2 - 2*b^4*c*d^3*x^3 + 6*a*b^3*d^4*x^3 + b^4*d^4*x^4)/(3*d^5*(c + d*x)) - (4*b*(b*c - a*d)^3*Log[c + d*x])/d^5","A",1
1345,1,142,75,0.0639365,"\int \frac{(a+b x)^3}{(c+d x)^2} \, dx","IntegrateAlgebraic[(a + b*x)^3/(c + d*x)^2,x]","\frac{3 \left(a^2 b d^2-2 a b^2 c d+b^3 c^2\right) \log (c+d x)}{d^4}+\frac{-2 a^3 d^3+6 a^2 b c d^2-6 a b^2 c^2 d+6 a b^2 c d^2 x+6 a b^2 d^3 x^2+2 b^3 c^3-4 b^3 c^2 d x-3 b^3 c d^2 x^2+b^3 d^3 x^3}{2 d^4 (c+d 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}",1,"(2*b^3*c^3 - 6*a*b^2*c^2*d + 6*a^2*b*c*d^2 - 2*a^3*d^3 - 4*b^3*c^2*d*x + 6*a*b^2*c*d^2*x - 3*b^3*c*d^2*x^2 + 6*a*b^2*d^3*x^2 + b^3*d^3*x^3)/(2*d^4*(c + d*x)) + (3*(b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2)*Log[c + d*x])/d^4","A",1
1346,1,74,51,0.0519138,"\int \frac{(a+b x)^2}{(c+d x)^2} \, dx","IntegrateAlgebraic[(a + b*x)^2/(c + d*x)^2,x]","\frac{-a^2 d^2+2 a b c d+b^2 \left(-c^2\right)+b^2 c d x+b^2 d^2 x^2}{d^3 (c+d x)}-\frac{2 \left(b^2 c-a b d\right) \log (c+d x)}{d^3}","-\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*c^2) + 2*a*b*c*d - a^2*d^2 + b^2*c*d*x + b^2*d^2*x^2)/(d^3*(c + d*x)) - (2*(b^2*c - a*b*d)*Log[c + d*x])/d^3","A",1
1347,1,31,31,0.0195216,"\int \frac{a+b x}{(c+d x)^2} \, dx","IntegrateAlgebraic[(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",1
1348,1,12,12,0.0057083,"\int \frac{1}{(c+d x)^2} \, dx","IntegrateAlgebraic[(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
1349,1,56,56,0.048931,"\int \frac{1}{(a+b x) (c+d x)^2} \, dx","IntegrateAlgebraic[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",1
1350,1,80,81,0.0967136,"\int \frac{1}{(a+b x)^2 (c+d x)^2} \, dx","IntegrateAlgebraic[1/((a + b*x)^2*(c + d*x)^2),x]","\frac{-a d-b c-2 b d x}{(a+b x) (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*c) - a*d - 2*b*d*x)/((b*c - a*d)^2*(a + b*x)*(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",1
1351,1,123,109,0.1129193,"\int \frac{1}{(a+b x)^3 (c+d x)^2} \, dx","IntegrateAlgebraic[1/((a + b*x)^3*(c + d*x)^2),x]","\frac{2 a^2 d^2+5 a b c d+9 a b d^2 x+b^2 \left(-c^2\right)+3 b^2 c d x+6 b^2 d^2 x^2}{2 (a+b x)^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{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*c^2) + 5*a*b*c*d + 2*a^2*d^2 + 3*b^2*c*d*x + 9*a*b*d^2*x + 6*b^2*d^2*x^2)/(2*(b*c - a*d)^3*(a + b*x)^2*(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",1
1352,1,388,158,0.1862135,"\int \frac{(a+b x)^6}{(c+d x)^3} \, dx","IntegrateAlgebraic[(a + b*x)^6/(c + d*x)^3,x]","\frac{-2 a^6 d^6-12 a^5 b c d^5-24 a^5 b d^6 x+90 a^4 b^2 c^2 d^4+120 a^4 b^2 c d^5 x-200 a^3 b^3 c^3 d^3-160 a^3 b^3 c^2 d^4 x+160 a^3 b^3 c d^5 x^2+80 a^3 b^3 d^6 x^3+210 a^2 b^4 c^4 d^2+60 a^2 b^4 c^3 d^3 x-330 a^2 b^4 c^2 d^4 x^2-120 a^2 b^4 c d^5 x^3+30 a^2 b^4 d^6 x^4-108 a b^5 c^5 d+24 a b^5 c^4 d^2 x+252 a b^5 c^3 d^3 x^2+80 a b^5 c^2 d^4 x^3-20 a b^5 c d^5 x^4+8 a b^5 d^6 x^5+22 b^6 c^6-16 b^6 c^5 d x-68 b^6 c^4 d^2 x^2-20 b^6 c^3 d^3 x^3+5 b^6 c^2 d^4 x^4-2 b^6 c d^5 x^5+b^6 d^6 x^6}{4 d^7 (c+d x)^2}+\frac{15 b^2 (b c-a d)^4 \log (c+d x)}{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,"(22*b^6*c^6 - 108*a*b^5*c^5*d + 210*a^2*b^4*c^4*d^2 - 200*a^3*b^3*c^3*d^3 + 90*a^4*b^2*c^2*d^4 - 12*a^5*b*c*d^5 - 2*a^6*d^6 - 16*b^6*c^5*d*x + 24*a*b^5*c^4*d^2*x + 60*a^2*b^4*c^3*d^3*x - 160*a^3*b^3*c^2*d^4*x + 120*a^4*b^2*c*d^5*x - 24*a^5*b*d^6*x - 68*b^6*c^4*d^2*x^2 + 252*a*b^5*c^3*d^3*x^2 - 330*a^2*b^4*c^2*d^4*x^2 + 160*a^3*b^3*c*d^5*x^2 - 20*b^6*c^3*d^3*x^3 + 80*a*b^5*c^2*d^4*x^3 - 120*a^2*b^4*c*d^5*x^3 + 80*a^3*b^3*d^6*x^3 + 5*b^6*c^2*d^4*x^4 - 20*a*b^5*c*d^5*x^4 + 30*a^2*b^4*d^6*x^4 - 2*b^6*c*d^5*x^5 + 8*a*b^5*d^6*x^5 + b^6*d^6*x^6)/(4*d^7*(c + d*x)^2) + (15*b^2*(b*c - a*d)^4*Log[c + d*x])/d^7","B",1
1353,1,285,133,0.123737,"\int \frac{(a+b x)^5}{(c+d x)^3} \, dx","IntegrateAlgebraic[(a + b*x)^5/(c + d*x)^3,x]","\frac{-3 a^5 d^5-15 a^4 b c d^4-30 a^4 b d^5 x+90 a^3 b^2 c^2 d^3+120 a^3 b^2 c d^4 x-150 a^2 b^3 c^3 d^2-120 a^2 b^3 c^2 d^3 x+120 a^2 b^3 c d^4 x^2+60 a^2 b^3 d^5 x^3+105 a b^4 c^4 d+30 a b^4 c^3 d^2 x-165 a b^4 c^2 d^3 x^2-60 a b^4 c d^4 x^3+15 a b^4 d^5 x^4-27 b^5 c^5+6 b^5 c^4 d x+63 b^5 c^3 d^2 x^2+20 b^5 c^2 d^3 x^3-5 b^5 c d^4 x^4+2 b^5 d^5 x^5}{6 d^6 (c+d x)^2}-\frac{10 b^2 (b c-a d)^3 \log (c+d x)}{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,"(-27*b^5*c^5 + 105*a*b^4*c^4*d - 150*a^2*b^3*c^3*d^2 + 90*a^3*b^2*c^2*d^3 - 15*a^4*b*c*d^4 - 3*a^5*d^5 + 6*b^5*c^4*d*x + 30*a*b^4*c^3*d^2*x - 120*a^2*b^3*c^2*d^3*x + 120*a^3*b^2*c*d^4*x - 30*a^4*b*d^5*x + 63*b^5*c^3*d^2*x^2 - 165*a*b^4*c^2*d^3*x^2 + 120*a^2*b^3*c*d^4*x^2 + 20*b^5*c^2*d^3*x^3 - 60*a*b^4*c*d^4*x^3 + 60*a^2*b^3*d^5*x^3 - 5*b^5*c*d^4*x^4 + 15*a*b^4*d^5*x^4 + 2*b^5*d^5*x^5)/(6*d^6*(c + d*x)^2) - (10*b^2*(b*c - a*d)^3*Log[c + d*x])/d^6","B",1
1354,1,197,103,0.0965827,"\int \frac{(a+b x)^4}{(c+d x)^3} \, dx","IntegrateAlgebraic[(a + b*x)^4/(c + d*x)^3,x]","\frac{-a^4 d^4-4 a^3 b c d^3-8 a^3 b d^4 x+18 a^2 b^2 c^2 d^2+24 a^2 b^2 c d^3 x-20 a b^3 c^3 d-16 a b^3 c^2 d^2 x+16 a b^3 c d^3 x^2+8 a b^3 d^4 x^3+7 b^4 c^4+2 b^4 c^3 d x-11 b^4 c^2 d^2 x^2-4 b^4 c d^3 x^3+b^4 d^4 x^4}{2 d^5 (c+d x)^2}+\frac{6 b^2 (b c-a d)^2 \log (c+d x)}{d^5}","-\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,"(7*b^4*c^4 - 20*a*b^3*c^3*d + 18*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 - a^4*d^4 + 2*b^4*c^3*d*x - 16*a*b^3*c^2*d^2*x + 24*a^2*b^2*c*d^3*x - 8*a^3*b*d^4*x - 11*b^4*c^2*d^2*x^2 + 16*a*b^3*c*d^3*x^2 - 4*b^4*c*d^3*x^3 + 8*a*b^3*d^4*x^3 + b^4*d^4*x^4)/(2*d^5*(c + d*x)^2) + (6*b^2*(b*c - a*d)^2*Log[c + d*x])/d^5","A",1
1355,1,130,78,0.069296,"\int \frac{(a+b x)^3}{(c+d x)^3} \, dx","IntegrateAlgebraic[(a + b*x)^3/(c + d*x)^3,x]","\frac{-a^3 d^3-3 a^2 b c d^2-6 a^2 b d^3 x+9 a b^2 c^2 d+12 a b^2 c d^2 x-5 b^3 c^3-4 b^3 c^2 d x+4 b^3 c d^2 x^2+2 b^3 d^3 x^3}{2 d^4 (c+d x)^2}-\frac{3 \left(b^3 c-a b^2 d\right) \log (c+d x)}{d^4}","-\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,"(-5*b^3*c^3 + 9*a*b^2*c^2*d - 3*a^2*b*c*d^2 - a^3*d^3 - 4*b^3*c^2*d*x + 12*a*b^2*c*d^2*x - 6*a^2*b*d^3*x + 4*b^3*c*d^2*x^2 + 2*b^3*d^3*x^3)/(2*d^4*(c + d*x)^2) - (3*(b^3*c - a*b^2*d)*Log[c + d*x])/d^4","A",1
1356,1,49,59,0.0364139,"\int \frac{(a+b x)^2}{(c+d x)^3} \, dx","IntegrateAlgebraic[(a + b*x)^2/(c + d*x)^3,x]","\frac{b^2 \log (c+d x)}{d^3}-\frac{(a d-b c) (a d+3 b c+4 b d x)}{2 d^3 (c+d x)^2}","\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,"-1/2*((-(b*c) + a*d)*(3*b*c + a*d + 4*b*d*x))/(d^3*(c + d*x)^2) + (b^2*Log[c + d*x])/d^3","A",1
1357,1,28,28,0.0149098,"\int \frac{a+b x}{(c+d x)^3} \, dx","IntegrateAlgebraic[(a + b*x)/(c + d*x)^3,x]","\frac{-a d-b c-2 b d x}{2 d^2 (c+d x)^2}","\frac{(a+b x)^2}{2 (c+d x)^2 (b c-a d)}",1,"(-(b*c) - a*d - 2*b*d*x)/(2*d^2*(c + d*x)^2)","A",1
1358,1,14,14,0.0063377,"\int \frac{1}{(c+d x)^3} \, dx","IntegrateAlgebraic[(c + d*x)^(-3),x]","-\frac{1}{2 d (c+d x)^2}","-\frac{1}{2 d (c+d x)^2}",1,"-1/2*1/(d*(c + d*x)^2)","A",1
1359,1,77,82,0.0739088,"\int \frac{1}{(a+b x) (c+d x)^3} \, dx","IntegrateAlgebraic[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{-a d+3 b c+2 b d x}{2 (c+d x)^2 (b c-a d)^2}","\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,"(3*b*c - a*d + 2*b*d*x)/(2*(b*c - a*d)^2*(c + d*x)^2) + (b^2*Log[a + b*x])/(b*c - a*d)^3 - (b^2*Log[c + d*x])/(b*c - a*d)^3","A",1
1360,1,122,110,0.1408731,"\int \frac{1}{(a+b x)^2 (c+d x)^3} \, dx","IntegrateAlgebraic[1/((a + b*x)^2*(c + d*x)^3),x]","\frac{a^2 d^2-5 a b c d-3 a b d^2 x-2 b^2 c^2-9 b^2 c d x-6 b^2 d^2 x^2}{2 (a+b x) (c+d x)^2 (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{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,"(-2*b^2*c^2 - 5*a*b*c*d + a^2*d^2 - 9*b^2*c*d*x - 3*a*b*d^2*x - 6*b^2*d^2*x^2)/(2*(b*c - a*d)^3*(a + b*x)*(c + d*x)^2) - (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",1
1361,1,180,143,0.1553062,"\int \frac{1}{(a+b x)^3 (c+d x)^3} \, dx","IntegrateAlgebraic[1/((a + b*x)^3*(c + d*x)^3),x]","\frac{-a^3 d^3+7 a^2 b c d^2+4 a^2 b d^3 x+7 a b^2 c^2 d+28 a b^2 c d^2 x+18 a b^2 d^3 x^2+b^3 \left(-c^3\right)+4 b^3 c^2 d x+18 b^3 c d^2 x^2+12 b^3 d^3 x^3}{2 (a+b x)^2 (c+d x)^2 (b c-a d)^4}+\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{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^3*c^3) + 7*a*b^2*c^2*d + 7*a^2*b*c*d^2 - a^3*d^3 + 4*b^3*c^2*d*x + 28*a*b^2*c*d^2*x + 4*a^2*b*d^3*x + 18*b^3*c*d^2*x^2 + 18*a*b^2*d^3*x^2 + 12*b^3*d^3*x^3)/(2*(b*c - a*d)^4*(a + b*x)^2*(c + d*x)^2) + (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",1
1362,1,803,232,0.4196211,"\int \frac{(a+b x)^9}{(c+d x)^8} \, dx","IntegrateAlgebraic[(a + b*x)^9/(c + d*x)^8,x]","\frac{36 (b c-a d)^2 \log (c+d x) b^7}{d^{10}}+\frac{3349 c^9 b^9+35 d^9 x^9 b^9-315 c d^8 x^8 b^9-3185 c^2 d^7 x^7 b^9-4655 c^3 d^6 x^6 b^9+12495 c^4 d^5 x^5 b^9+50225 c^5 d^4 x^4 b^9+72275 c^6 d^3 x^3 b^9+53949 c^7 d^2 x^2 b^9+20923 c^8 d x b^9+630 a d^9 x^8 b^8+4410 a c d^8 x^7 b^8-4410 a c^2 d^7 x^6 b^8-66150 a c^3 d^6 x^5 b^8-169050 a c^4 d^5 x^4 b^8-213150 a c^5 d^4 x^3 b^8-149058 a c^6 d^3 x^2 b^8-8658 a c^8 d b^8-55566 a c^7 d^2 x b^8+17640 a^2 c d^8 x^6 b^7+79380 a^2 c^2 d^7 x^5 b^7+161700 a^2 c^3 d^6 x^4 b^7+183750 a^2 c^4 d^5 x^3 b^7+6534 a^2 c^7 d^2 b^7+120834 a^2 c^5 d^4 x^2 b^7+43218 a^2 c^6 d^3 x b^7-5880 a^3 d^9 x^6 b^6-17640 a^3 c d^8 x^5 b^6-29400 a^3 c^2 d^7 x^4 b^6-840 a^3 c^6 d^3 b^6-29400 a^3 c^3 d^6 x^3 b^6-17640 a^3 c^4 d^5 x^2 b^6-5880 a^3 c^5 d^4 x b^6-4410 a^4 d^9 x^5 b^5-210 a^4 c^5 d^4 b^5-7350 a^4 c d^8 x^4 b^5-7350 a^4 c^2 d^7 x^3 b^5-4410 a^4 c^3 d^6 x^2 b^5-1470 a^4 c^4 d^5 x b^5-84 a^5 c^4 d^5 b^4-2940 a^5 d^9 x^4 b^4-2940 a^5 c d^8 x^3 b^4-1764 a^5 c^2 d^7 x^2 b^4-588 a^5 c^3 d^6 x b^4-42 a^6 c^3 d^6 b^3-1470 a^6 d^9 x^3 b^3-882 a^6 c d^8 x^2 b^3-294 a^6 c^2 d^7 x b^3-24 a^7 c^2 d^7 b^2-504 a^7 d^9 x^2 b^2-168 a^7 c d^8 x b^2-15 a^8 c d^8 b-105 a^8 d^9 x b-10 a^9 d^9}{70 d^{10} (c+d x)^7}","-\frac{b^8 x (8 b c-9 a d)}{d^9}+\frac{36 b^7 (b c-a d)^2 \log (c+d x)}{d^{10}}+\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{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,"(3349*b^9*c^9 - 8658*a*b^8*c^8*d + 6534*a^2*b^7*c^7*d^2 - 840*a^3*b^6*c^6*d^3 - 210*a^4*b^5*c^5*d^4 - 84*a^5*b^4*c^4*d^5 - 42*a^6*b^3*c^3*d^6 - 24*a^7*b^2*c^2*d^7 - 15*a^8*b*c*d^8 - 10*a^9*d^9 + 20923*b^9*c^8*d*x - 55566*a*b^8*c^7*d^2*x + 43218*a^2*b^7*c^6*d^3*x - 5880*a^3*b^6*c^5*d^4*x - 1470*a^4*b^5*c^4*d^5*x - 588*a^5*b^4*c^3*d^6*x - 294*a^6*b^3*c^2*d^7*x - 168*a^7*b^2*c*d^8*x - 105*a^8*b*d^9*x + 53949*b^9*c^7*d^2*x^2 - 149058*a*b^8*c^6*d^3*x^2 + 120834*a^2*b^7*c^5*d^4*x^2 - 17640*a^3*b^6*c^4*d^5*x^2 - 4410*a^4*b^5*c^3*d^6*x^2 - 1764*a^5*b^4*c^2*d^7*x^2 - 882*a^6*b^3*c*d^8*x^2 - 504*a^7*b^2*d^9*x^2 + 72275*b^9*c^6*d^3*x^3 - 213150*a*b^8*c^5*d^4*x^3 + 183750*a^2*b^7*c^4*d^5*x^3 - 29400*a^3*b^6*c^3*d^6*x^3 - 7350*a^4*b^5*c^2*d^7*x^3 - 2940*a^5*b^4*c*d^8*x^3 - 1470*a^6*b^3*d^9*x^3 + 50225*b^9*c^5*d^4*x^4 - 169050*a*b^8*c^4*d^5*x^4 + 161700*a^2*b^7*c^3*d^6*x^4 - 29400*a^3*b^6*c^2*d^7*x^4 - 7350*a^4*b^5*c*d^8*x^4 - 2940*a^5*b^4*d^9*x^4 + 12495*b^9*c^4*d^5*x^5 - 66150*a*b^8*c^3*d^6*x^5 + 79380*a^2*b^7*c^2*d^7*x^5 - 17640*a^3*b^6*c*d^8*x^5 - 4410*a^4*b^5*d^9*x^5 - 4655*b^9*c^3*d^6*x^6 - 4410*a*b^8*c^2*d^7*x^6 + 17640*a^2*b^7*c*d^8*x^6 - 5880*a^3*b^6*d^9*x^6 - 3185*b^9*c^2*d^7*x^7 + 4410*a*b^8*c*d^8*x^7 - 315*b^9*c*d^8*x^8 + 630*a*b^8*d^9*x^8 + 35*b^9*d^9*x^9)/(70*d^10*(c + d*x)^7) + (36*b^7*(b*c - a*d)^2*Log[c + d*x])/d^10","B",1
1363,1,650,209,0.3153613,"\int \frac{(a+b x)^8}{(c+d x)^8} \, dx","IntegrateAlgebraic[(a + b*x)^8/(c + d*x)^8,x]","\frac{-15 a^8 d^8-20 a^7 b c d^7-140 a^7 b d^8 x-28 a^6 b^2 c^2 d^6-196 a^6 b^2 c d^7 x-588 a^6 b^2 d^8 x^2-42 a^5 b^3 c^3 d^5-294 a^5 b^3 c^2 d^6 x-882 a^5 b^3 c d^7 x^2-1470 a^5 b^3 d^8 x^3-70 a^4 b^4 c^4 d^4-490 a^4 b^4 c^3 d^5 x-1470 a^4 b^4 c^2 d^6 x^2-2450 a^4 b^4 c d^7 x^3-2450 a^4 b^4 d^8 x^4-140 a^3 b^5 c^5 d^3-980 a^3 b^5 c^4 d^4 x-2940 a^3 b^5 c^3 d^5 x^2-4900 a^3 b^5 c^2 d^6 x^3-4900 a^3 b^5 c d^7 x^4-2940 a^3 b^5 d^8 x^5-420 a^2 b^6 c^6 d^2-2940 a^2 b^6 c^5 d^3 x-8820 a^2 b^6 c^4 d^4 x^2-14700 a^2 b^6 c^3 d^5 x^3-14700 a^2 b^6 c^2 d^6 x^4-8820 a^2 b^6 c d^7 x^5-2940 a^2 b^6 d^8 x^6+2178 a b^7 c^7 d+14406 a b^7 c^6 d^2 x+40278 a b^7 c^5 d^3 x^2+61250 a b^7 c^4 d^4 x^3+53900 a b^7 c^3 d^5 x^4+26460 a b^7 c^2 d^6 x^5+5880 a b^7 c d^7 x^6-1443 b^8 c^8-9261 b^8 c^7 d x-24843 b^8 c^6 d^2 x^2-35525 b^8 c^5 d^3 x^3-28175 b^8 c^4 d^4 x^4-11025 b^8 c^3 d^5 x^5-735 b^8 c^2 d^6 x^6+735 b^8 c d^7 x^7+105 b^8 d^8 x^8}{105 d^9 (c+d x)^7}-\frac{8 \left(b^8 c-a b^7 d\right) \log (c+d x)}{d^9}","-\frac{8 b^7 (b c-a d) \log (c+d x)}{d^9}-\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{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,"(-1443*b^8*c^8 + 2178*a*b^7*c^7*d - 420*a^2*b^6*c^6*d^2 - 140*a^3*b^5*c^5*d^3 - 70*a^4*b^4*c^4*d^4 - 42*a^5*b^3*c^3*d^5 - 28*a^6*b^2*c^2*d^6 - 20*a^7*b*c*d^7 - 15*a^8*d^8 - 9261*b^8*c^7*d*x + 14406*a*b^7*c^6*d^2*x - 2940*a^2*b^6*c^5*d^3*x - 980*a^3*b^5*c^4*d^4*x - 490*a^4*b^4*c^3*d^5*x - 294*a^5*b^3*c^2*d^6*x - 196*a^6*b^2*c*d^7*x - 140*a^7*b*d^8*x - 24843*b^8*c^6*d^2*x^2 + 40278*a*b^7*c^5*d^3*x^2 - 8820*a^2*b^6*c^4*d^4*x^2 - 2940*a^3*b^5*c^3*d^5*x^2 - 1470*a^4*b^4*c^2*d^6*x^2 - 882*a^5*b^3*c*d^7*x^2 - 588*a^6*b^2*d^8*x^2 - 35525*b^8*c^5*d^3*x^3 + 61250*a*b^7*c^4*d^4*x^3 - 14700*a^2*b^6*c^3*d^5*x^3 - 4900*a^3*b^5*c^2*d^6*x^3 - 2450*a^4*b^4*c*d^7*x^3 - 1470*a^5*b^3*d^8*x^3 - 28175*b^8*c^4*d^4*x^4 + 53900*a*b^7*c^3*d^5*x^4 - 14700*a^2*b^6*c^2*d^6*x^4 - 4900*a^3*b^5*c*d^7*x^4 - 2450*a^4*b^4*d^8*x^4 - 11025*b^8*c^3*d^5*x^5 + 26460*a*b^7*c^2*d^6*x^5 - 8820*a^2*b^6*c*d^7*x^5 - 2940*a^3*b^5*d^8*x^5 - 735*b^8*c^2*d^6*x^6 + 5880*a*b^7*c*d^7*x^6 - 2940*a^2*b^6*d^8*x^6 + 735*b^8*c*d^7*x^7 + 105*b^8*d^8*x^8)/(105*d^9*(c + d*x)^7) - (8*(b^8*c - a*b^7*d)*Log[c + d*x])/d^9","B",1
1364,1,400,194,0.2503009,"\int \frac{(a+b x)^7}{(c+d x)^8} \, dx","IntegrateAlgebraic[(a + b*x)^7/(c + d*x)^8,x]","\frac{b^7 \log (c+d x)}{d^8}-\frac{(a d-b c) \left(60 a^6 d^6+130 a^5 b c d^5+490 a^5 b d^6 x+214 a^4 b^2 c^2 d^4+1078 a^4 b^2 c d^5 x+1764 a^4 b^2 d^6 x^2+319 a^3 b^3 c^3 d^3+1813 a^3 b^3 c^2 d^4 x+3969 a^3 b^3 c d^5 x^2+3675 a^3 b^3 d^6 x^3+459 a^2 b^4 c^4 d^2+2793 a^2 b^4 c^3 d^3 x+6909 a^2 b^4 c^2 d^4 x^2+8575 a^2 b^4 c d^5 x^3+4900 a^2 b^4 d^6 x^4+669 a b^5 c^5 d+4263 a b^5 c^4 d^2 x+11319 a b^5 c^3 d^3 x^2+15925 a b^5 c^2 d^4 x^3+12250 a b^5 c d^5 x^4+4410 a b^5 d^6 x^5+1089 b^6 c^6+7203 b^6 c^5 d x+20139 b^6 c^4 d^2 x^2+30625 b^6 c^3 d^3 x^3+26950 b^6 c^2 d^4 x^4+13230 b^6 c d^5 x^5+2940 b^6 d^6 x^6\right)}{420 d^8 (c+d x)^7}","\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,"-1/420*((-(b*c) + a*d)*(1089*b^6*c^6 + 669*a*b^5*c^5*d + 459*a^2*b^4*c^4*d^2 + 319*a^3*b^3*c^3*d^3 + 214*a^4*b^2*c^2*d^4 + 130*a^5*b*c*d^5 + 60*a^6*d^6 + 7203*b^6*c^5*d*x + 4263*a*b^5*c^4*d^2*x + 2793*a^2*b^4*c^3*d^3*x + 1813*a^3*b^3*c^2*d^4*x + 1078*a^4*b^2*c*d^5*x + 490*a^5*b*d^6*x + 20139*b^6*c^4*d^2*x^2 + 11319*a*b^5*c^3*d^3*x^2 + 6909*a^2*b^4*c^2*d^4*x^2 + 3969*a^3*b^3*c*d^5*x^2 + 1764*a^4*b^2*d^6*x^2 + 30625*b^6*c^3*d^3*x^3 + 15925*a*b^5*c^2*d^4*x^3 + 8575*a^2*b^4*c*d^5*x^3 + 3675*a^3*b^3*d^6*x^3 + 26950*b^6*c^2*d^4*x^4 + 12250*a*b^5*c*d^5*x^4 + 4900*a^2*b^4*d^6*x^4 + 13230*b^6*c*d^5*x^5 + 4410*a*b^5*d^6*x^5 + 2940*b^6*d^6*x^6))/(d^8*(c + d*x)^7) + (b^7*Log[c + d*x])/d^8","B",1
1365,1,378,28,0.1236784,"\int \frac{(a+b x)^6}{(c+d x)^8} \, dx","IntegrateAlgebraic[(a + b*x)^6/(c + d*x)^8,x]","\frac{-a^6 d^6-a^5 b c d^5-7 a^5 b d^6 x-a^4 b^2 c^2 d^4-7 a^4 b^2 c d^5 x-21 a^4 b^2 d^6 x^2-a^3 b^3 c^3 d^3-7 a^3 b^3 c^2 d^4 x-21 a^3 b^3 c d^5 x^2-35 a^3 b^3 d^6 x^3-a^2 b^4 c^4 d^2-7 a^2 b^4 c^3 d^3 x-21 a^2 b^4 c^2 d^4 x^2-35 a^2 b^4 c d^5 x^3-35 a^2 b^4 d^6 x^4-a b^5 c^5 d-7 a b^5 c^4 d^2 x-21 a b^5 c^3 d^3 x^2-35 a b^5 c^2 d^4 x^3-35 a b^5 c d^5 x^4-21 a b^5 d^6 x^5+b^6 \left(-c^6\right)-7 b^6 c^5 d x-21 b^6 c^4 d^2 x^2-35 b^6 c^3 d^3 x^3-35 b^6 c^2 d^4 x^4-21 b^6 c d^5 x^5-7 b^6 d^6 x^6}{7 d^7 (c+d x)^7}","\frac{(a+b x)^7}{7 (c+d x)^7 (b c-a d)}",1,"(-(b^6*c^6) - a*b^5*c^5*d - a^2*b^4*c^4*d^2 - a^3*b^3*c^3*d^3 - a^4*b^2*c^2*d^4 - a^5*b*c*d^5 - a^6*d^6 - 7*b^6*c^5*d*x - 7*a*b^5*c^4*d^2*x - 7*a^2*b^4*c^3*d^3*x - 7*a^3*b^3*c^2*d^4*x - 7*a^4*b^2*c*d^5*x - 7*a^5*b*d^6*x - 21*b^6*c^4*d^2*x^2 - 21*a*b^5*c^3*d^3*x^2 - 21*a^2*b^4*c^2*d^4*x^2 - 21*a^3*b^3*c*d^5*x^2 - 21*a^4*b^2*d^6*x^2 - 35*b^6*c^3*d^3*x^3 - 35*a*b^5*c^2*d^4*x^3 - 35*a^2*b^4*c*d^5*x^3 - 35*a^3*b^3*d^6*x^3 - 35*b^6*c^2*d^4*x^4 - 35*a*b^5*c*d^5*x^4 - 35*a^2*b^4*d^6*x^4 - 21*b^6*c*d^5*x^5 - 21*a*b^5*d^6*x^5 - 7*b^6*d^6*x^6)/(7*d^7*(c + d*x)^7)","B",1
1366,1,274,58,0.0814786,"\int \frac{(a+b x)^5}{(c+d x)^8} \, dx","IntegrateAlgebraic[(a + b*x)^5/(c + d*x)^8,x]","\frac{-6 a^5 d^5-5 a^4 b c d^4-35 a^4 b d^5 x-4 a^3 b^2 c^2 d^3-28 a^3 b^2 c d^4 x-84 a^3 b^2 d^5 x^2-3 a^2 b^3 c^3 d^2-21 a^2 b^3 c^2 d^3 x-63 a^2 b^3 c d^4 x^2-105 a^2 b^3 d^5 x^3-2 a b^4 c^4 d-14 a b^4 c^3 d^2 x-42 a b^4 c^2 d^3 x^2-70 a b^4 c d^4 x^3-70 a b^4 d^5 x^4+b^5 \left(-c^5\right)-7 b^5 c^4 d x-21 b^5 c^3 d^2 x^2-35 b^5 c^2 d^3 x^3-35 b^5 c d^4 x^4-21 b^5 d^5 x^5}{42 d^6 (c+d x)^7}","\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,"(-(b^5*c^5) - 2*a*b^4*c^4*d - 3*a^2*b^3*c^3*d^2 - 4*a^3*b^2*c^2*d^3 - 5*a^4*b*c*d^4 - 6*a^5*d^5 - 7*b^5*c^4*d*x - 14*a*b^4*c^3*d^2*x - 21*a^2*b^3*c^2*d^3*x - 28*a^3*b^2*c*d^4*x - 35*a^4*b*d^5*x - 21*b^5*c^3*d^2*x^2 - 42*a*b^4*c^2*d^3*x^2 - 63*a^2*b^3*c*d^4*x^2 - 84*a^3*b^2*d^5*x^2 - 35*b^5*c^2*d^3*x^3 - 70*a*b^4*c*d^4*x^3 - 105*a^2*b^3*d^5*x^3 - 35*b^5*c*d^4*x^4 - 70*a*b^4*d^5*x^4 - 21*b^5*d^5*x^5)/(42*d^6*(c + d*x)^7)","B",1
1367,1,187,89,0.0676417,"\int \frac{(a+b x)^4}{(c+d x)^8} \, dx","IntegrateAlgebraic[(a + b*x)^4/(c + d*x)^8,x]","\frac{-15 a^4 d^4-10 a^3 b c d^3-70 a^3 b d^4 x-6 a^2 b^2 c^2 d^2-42 a^2 b^2 c d^3 x-126 a^2 b^2 d^4 x^2-3 a b^3 c^3 d-21 a b^3 c^2 d^2 x-63 a b^3 c d^3 x^2-105 a b^3 d^4 x^3+b^4 \left(-c^4\right)-7 b^4 c^3 d x-21 b^4 c^2 d^2 x^2-35 b^4 c d^3 x^3-35 b^4 d^4 x^4}{105 d^5 (c+d x)^7}","\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,"(-(b^4*c^4) - 3*a*b^3*c^3*d - 6*a^2*b^2*c^2*d^2 - 10*a^3*b*c*d^3 - 15*a^4*d^4 - 7*b^4*c^3*d*x - 21*a*b^3*c^2*d^2*x - 42*a^2*b^2*c*d^3*x - 70*a^3*b*d^4*x - 21*b^4*c^2*d^2*x^2 - 63*a*b^3*c*d^3*x^2 - 126*a^2*b^2*d^4*x^2 - 35*b^4*c*d^3*x^3 - 105*a*b^3*d^4*x^3 - 35*b^4*d^4*x^4)/(105*d^5*(c + d*x)^7)","B",1
1368,1,117,92,0.0436216,"\int \frac{(a+b x)^3}{(c+d x)^8} \, dx","IntegrateAlgebraic[(a + b*x)^3/(c + d*x)^8,x]","\frac{-20 a^3 d^3-10 a^2 b c d^2-70 a^2 b d^3 x-4 a b^2 c^2 d-28 a b^2 c d^2 x-84 a b^2 d^3 x^2+b^3 \left(-c^3\right)-7 b^3 c^2 d x-21 b^3 c d^2 x^2-35 b^3 d^3 x^3}{140 d^4 (c+d x)^7}","\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^3*c^3) - 4*a*b^2*c^2*d - 10*a^2*b*c*d^2 - 20*a^3*d^3 - 7*b^3*c^2*d*x - 28*a*b^2*c*d^2*x - 70*a^2*b*d^3*x - 21*b^3*c*d^2*x^2 - 84*a*b^2*d^3*x^2 - 35*b^3*d^3*x^3)/(140*d^4*(c + d*x)^7)","A",1
1369,1,64,65,0.0328342,"\int \frac{(a+b x)^2}{(c+d x)^8} \, dx","IntegrateAlgebraic[(a + b*x)^2/(c + d*x)^8,x]","\frac{-15 a^2 d^2-5 a b c d-35 a b d^2 x+b^2 \left(-c^2\right)-7 b^2 c d x-21 b^2 d^2 x^2}{105 d^3 (c+d x)^7}","\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^2*c^2) - 5*a*b*c*d - 15*a^2*d^2 - 7*b^2*c*d*x - 35*a*b*d^2*x - 21*b^2*d^2*x^2)/(105*d^3*(c + d*x)^7)","A",1
1370,1,28,38,0.0155813,"\int \frac{a+b x}{(c+d x)^8} \, dx","IntegrateAlgebraic[(a + b*x)/(c + d*x)^8,x]","\frac{-6 a d-b c-7 b d x}{42 d^2 (c+d x)^7}","\frac{b c-a d}{7 d^2 (c+d x)^7}-\frac{b}{6 d^2 (c+d x)^6}",1,"(-(b*c) - 6*a*d - 7*b*d*x)/(42*d^2*(c + d*x)^7)","A",1
1371,1,14,14,0.0063554,"\int \frac{1}{(c+d x)^8} \, dx","IntegrateAlgebraic[(c + d*x)^(-8),x]","-\frac{1}{7 d (c+d x)^7}","-\frac{1}{7 d (c+d x)^7}",1,"-1/7*1/(d*(c + d*x)^7)","A",1
1372,1,427,202,0.1973247,"\int \frac{1}{(a+b x) (c+d x)^8} \, dx","IntegrateAlgebraic[1/((a + b*x)*(c + d*x)^8),x]","\frac{60 a^6 d^6-430 a^5 b c d^5-70 a^5 b d^6 x+1334 a^4 b^2 c^2 d^4+518 a^4 b^2 c d^5 x+84 a^4 b^2 d^6 x^2-2341 a^3 b^3 c^3 d^3-1687 a^3 b^3 c^2 d^4 x-651 a^3 b^3 c d^5 x^2-105 a^3 b^3 d^6 x^3+2559 a^2 b^4 c^4 d^2+3213 a^2 b^4 c^3 d^3 x+2289 a^2 b^4 c^2 d^4 x^2+875 a^2 b^4 c d^5 x^3+140 a^2 b^4 d^6 x^4-1851 a b^5 c^5 d-4137 a b^5 c^4 d^2 x-5061 a b^5 c^3 d^3 x^2-3535 a b^5 c^2 d^4 x^3-1330 a b^5 c d^5 x^4-210 a b^5 d^6 x^5+1089 b^6 c^6+4683 b^6 c^5 d x+9639 b^6 c^4 d^2 x^2+11165 b^6 c^3 d^3 x^3+7490 b^6 c^2 d^4 x^4+2730 b^6 c d^5 x^5+420 b^6 d^6 x^6}{420 (c+d x)^7 (b c-a d)^7}+\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^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) (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}{6 (c+d x)^6 (b c-a d)^2}+\frac{1}{7 (c+d x)^7 (b c-a d)}",1,"(1089*b^6*c^6 - 1851*a*b^5*c^5*d + 2559*a^2*b^4*c^4*d^2 - 2341*a^3*b^3*c^3*d^3 + 1334*a^4*b^2*c^2*d^4 - 430*a^5*b*c*d^5 + 60*a^6*d^6 + 4683*b^6*c^5*d*x - 4137*a*b^5*c^4*d^2*x + 3213*a^2*b^4*c^3*d^3*x - 1687*a^3*b^3*c^2*d^4*x + 518*a^4*b^2*c*d^5*x - 70*a^5*b*d^6*x + 9639*b^6*c^4*d^2*x^2 - 5061*a*b^5*c^3*d^3*x^2 + 2289*a^2*b^4*c^2*d^4*x^2 - 651*a^3*b^3*c*d^5*x^2 + 84*a^4*b^2*d^6*x^2 + 11165*b^6*c^3*d^3*x^3 - 3535*a*b^5*c^2*d^4*x^3 + 875*a^2*b^4*c*d^5*x^3 - 105*a^3*b^3*d^6*x^3 + 7490*b^6*c^2*d^4*x^4 - 1330*a*b^5*c*d^5*x^4 + 140*a^2*b^4*d^6*x^4 + 2730*b^6*c*d^5*x^5 - 210*a*b^5*d^6*x^5 + 420*b^6*d^6*x^6)/(420*(b*c - a*d)^7*(c + d*x)^7) + (b^7*Log[a + b*x])/(b*c - a*d)^8 - (b^7*Log[c + d*x])/(b*c - a*d)^8","B",1
1373,1,558,231,0.3658762,"\int \frac{1}{(a+b x)^2 (c+d x)^8} \, dx","IntegrateAlgebraic[1/((a + b*x)^2*(c + d*x)^8),x]","\frac{-15 a^7 d^7+125 a^6 b c d^6+20 a^6 b d^7 x-463 a^5 b^2 c^2 d^5-176 a^5 b^2 c d^6 x-28 a^5 b^2 d^7 x^2+1007 a^4 b^3 c^3 d^4+706 a^4 b^3 c^2 d^5 x+266 a^4 b^3 c d^6 x^2+42 a^4 b^3 d^7 x^3-1443 a^3 b^4 c^4 d^3-1744 a^3 b^4 c^3 d^4 x-1204 a^3 b^4 c^2 d^5 x^2-448 a^3 b^4 c d^6 x^3-70 a^3 b^4 d^7 x^4+1497 a^2 b^5 c^5 d^2+3156 a^2 b^5 c^4 d^3 x+3696 a^2 b^5 c^3 d^4 x^2+2492 a^2 b^5 c^2 d^5 x^3+910 a^2 b^5 c d^6 x^4+140 a^2 b^5 d^7 x^5-1443 a b^6 c^6 d-5664 a b^6 c^5 d^2 x-11004 a b^6 c^4 d^3 x^2-12208 a b^6 c^3 d^4 x^3-7910 a b^6 c^2 d^5 x^4-2800 a b^6 c d^6 x^5-420 a b^6 d^7 x^6-105 b^7 c^7-2178 b^7 c^6 d x-9366 b^7 c^5 d^2 x^2-19278 b^7 c^4 d^3 x^3-22330 b^7 c^3 d^4 x^4-14980 b^7 c^2 d^5 x^5-5460 b^7 c d^6 x^6-840 b^7 d^7 x^7}{105 (a+b x) (c+d x)^7 (b c-a d)^8}-\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^7}{(a+b x) (b c-a d)^8}-\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{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{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,"(-105*b^7*c^7 - 1443*a*b^6*c^6*d + 1497*a^2*b^5*c^5*d^2 - 1443*a^3*b^4*c^4*d^3 + 1007*a^4*b^3*c^3*d^4 - 463*a^5*b^2*c^2*d^5 + 125*a^6*b*c*d^6 - 15*a^7*d^7 - 2178*b^7*c^6*d*x - 5664*a*b^6*c^5*d^2*x + 3156*a^2*b^5*c^4*d^3*x - 1744*a^3*b^4*c^3*d^4*x + 706*a^4*b^3*c^2*d^5*x - 176*a^5*b^2*c*d^6*x + 20*a^6*b*d^7*x - 9366*b^7*c^5*d^2*x^2 - 11004*a*b^6*c^4*d^3*x^2 + 3696*a^2*b^5*c^3*d^4*x^2 - 1204*a^3*b^4*c^2*d^5*x^2 + 266*a^4*b^3*c*d^6*x^2 - 28*a^5*b^2*d^7*x^2 - 19278*b^7*c^4*d^3*x^3 - 12208*a*b^6*c^3*d^4*x^3 + 2492*a^2*b^5*c^2*d^5*x^3 - 448*a^3*b^4*c*d^6*x^3 + 42*a^4*b^3*d^7*x^3 - 22330*b^7*c^3*d^4*x^4 - 7910*a*b^6*c^2*d^5*x^4 + 910*a^2*b^5*c*d^6*x^4 - 70*a^3*b^4*d^7*x^4 - 14980*b^7*c^2*d^5*x^5 - 2800*a*b^6*c*d^6*x^5 + 140*a^2*b^5*d^7*x^5 - 5460*b^7*c*d^6*x^6 - 420*a*b^6*d^7*x^6 - 840*b^7*d^7*x^7)/(105*(b*c - a*d)^8*(a + b*x)*(c + d*x)^7) - (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","B",1
1374,1,700,276,0.3389278,"\int \frac{1}{(a+b x)^3 (c+d x)^8} \, dx","IntegrateAlgebraic[1/((a + b*x)^3*(c + d*x)^8),x]","\frac{10 a^8 d^8-95 a^7 b c d^7-15 a^7 b d^8 x+409 a^6 b^2 c^2 d^6+153 a^6 b^2 c d^7 x+24 a^6 b^2 d^8 x^2-1061 a^5 b^3 c^3 d^5-729 a^5 b^3 c^2 d^6 x-270 a^5 b^3 c d^7 x^2-42 a^5 b^3 d^8 x^3+1879 a^4 b^4 c^4 d^4+2211 a^4 b^4 c^3 d^5 x+1494 a^4 b^4 c^2 d^6 x^2+546 a^4 b^4 c d^7 x^3+84 a^4 b^4 d^8 x^4-2531 a^3 b^5 c^5 d^3-5139 a^3 b^5 c^4 d^4 x-5856 a^3 b^5 c^3 d^5 x^2-3864 a^3 b^5 c^2 d^6 x^3-1386 a^3 b^5 c d^7 x^4-210 a^3 b^5 d^8 x^5+3349 a^2 b^6 c^6 d^2+12501 a^2 b^6 c^5 d^3 x+23544 a^2 b^6 c^4 d^4 x^2+25536 a^2 b^6 c^3 d^5 x^3+16254 a^2 b^6 c^2 d^6 x^4+5670 a^2 b^6 c d^7 x^5+840 a^2 b^6 d^8 x^6+595 a b^7 c^7 d+10863 a b^7 c^6 d^2 x+45090 a b^7 c^5 d^3 x^2+90846 a b^7 c^4 d^4 x^3+103614 a b^7 c^3 d^5 x^4+68670 a b^7 c^2 d^6 x^5+24780 a b^7 c d^7 x^6+3780 a b^7 d^8 x^7-35 b^8 c^8+315 b^8 c^7 d x+6534 b^8 c^6 d^2 x^2+28098 b^8 c^5 d^3 x^3+57834 b^8 c^4 d^4 x^4+66990 b^8 c^3 d^5 x^5+44940 b^8 c^2 d^6 x^6+16380 b^8 c d^7 x^7+2520 b^8 d^8 x^8}{70 (a+b x)^2 (c+d x)^7 (b c-a d)^9}+\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{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{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{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,"(-35*b^8*c^8 + 595*a*b^7*c^7*d + 3349*a^2*b^6*c^6*d^2 - 2531*a^3*b^5*c^5*d^3 + 1879*a^4*b^4*c^4*d^4 - 1061*a^5*b^3*c^3*d^5 + 409*a^6*b^2*c^2*d^6 - 95*a^7*b*c*d^7 + 10*a^8*d^8 + 315*b^8*c^7*d*x + 10863*a*b^7*c^6*d^2*x + 12501*a^2*b^6*c^5*d^3*x - 5139*a^3*b^5*c^4*d^4*x + 2211*a^4*b^4*c^3*d^5*x - 729*a^5*b^3*c^2*d^6*x + 153*a^6*b^2*c*d^7*x - 15*a^7*b*d^8*x + 6534*b^8*c^6*d^2*x^2 + 45090*a*b^7*c^5*d^3*x^2 + 23544*a^2*b^6*c^4*d^4*x^2 - 5856*a^3*b^5*c^3*d^5*x^2 + 1494*a^4*b^4*c^2*d^6*x^2 - 270*a^5*b^3*c*d^7*x^2 + 24*a^6*b^2*d^8*x^2 + 28098*b^8*c^5*d^3*x^3 + 90846*a*b^7*c^4*d^4*x^3 + 25536*a^2*b^6*c^3*d^5*x^3 - 3864*a^3*b^5*c^2*d^6*x^3 + 546*a^4*b^4*c*d^7*x^3 - 42*a^5*b^3*d^8*x^3 + 57834*b^8*c^4*d^4*x^4 + 103614*a*b^7*c^3*d^5*x^4 + 16254*a^2*b^6*c^2*d^6*x^4 - 1386*a^3*b^5*c*d^7*x^4 + 84*a^4*b^4*d^8*x^4 + 66990*b^8*c^3*d^5*x^5 + 68670*a*b^7*c^2*d^6*x^5 + 5670*a^2*b^6*c*d^7*x^5 - 210*a^3*b^5*d^8*x^5 + 44940*b^8*c^2*d^6*x^6 + 24780*a*b^7*c*d^7*x^6 + 840*a^2*b^6*d^8*x^6 + 16380*b^8*c*d^7*x^7 + 3780*a*b^7*d^8*x^7 + 2520*b^8*d^8*x^8)/(70*(b*c - a*d)^9*(a + b*x)^2*(c + d*x)^7) + (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","B",1
1375,1,364,156,0.0657673,"\int (a+b x)^5 \sqrt{c+d x} \, dx","IntegrateAlgebraic[(a + b*x)^5*Sqrt[c + d*x],x]","-\frac{2 \sqrt{c+d x} \left(-3003 a^5 c d^5-3003 a^5 d^6 x+6006 a^4 b c^2 d^4-3003 a^4 b c d^5 x-9009 a^4 b d^6 x^2-6864 a^3 b^2 c^3 d^3+3432 a^3 b^2 c^2 d^4 x-2574 a^3 b^2 c d^5 x^2-12870 a^3 b^2 d^6 x^3+4576 a^2 b^3 c^4 d^2-2288 a^2 b^3 c^3 d^3 x+1716 a^2 b^3 c^2 d^4 x^2-1430 a^2 b^3 c d^5 x^3-10010 a^2 b^3 d^6 x^4-1664 a b^4 c^5 d+832 a b^4 c^4 d^2 x-624 a b^4 c^3 d^3 x^2+520 a b^4 c^2 d^4 x^3-455 a b^4 c d^5 x^4-4095 a b^4 d^6 x^5+256 b^5 c^6-128 b^5 c^5 d x+96 b^5 c^4 d^2 x^2-80 b^5 c^3 d^3 x^3+70 b^5 c^2 d^4 x^4-63 b^5 c d^5 x^5-693 b^5 d^6 x^6\right)}{9009 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*Sqrt[c + d*x]*(256*b^5*c^6 - 1664*a*b^4*c^5*d + 4576*a^2*b^3*c^4*d^2 - 6864*a^3*b^2*c^3*d^3 + 6006*a^4*b*c^2*d^4 - 3003*a^5*c*d^5 - 128*b^5*c^5*d*x + 832*a*b^4*c^4*d^2*x - 2288*a^2*b^3*c^3*d^3*x + 3432*a^3*b^2*c^2*d^4*x - 3003*a^4*b*c*d^5*x - 3003*a^5*d^6*x + 96*b^5*c^4*d^2*x^2 - 624*a*b^4*c^3*d^3*x^2 + 1716*a^2*b^3*c^2*d^4*x^2 - 2574*a^3*b^2*c*d^5*x^2 - 9009*a^4*b*d^6*x^2 - 80*b^5*c^3*d^3*x^3 + 520*a*b^4*c^2*d^4*x^3 - 1430*a^2*b^3*c*d^5*x^3 - 12870*a^3*b^2*d^6*x^3 + 70*b^5*c^2*d^4*x^4 - 455*a*b^4*c*d^5*x^4 - 10010*a^2*b^3*d^6*x^4 - 63*b^5*c*d^5*x^5 - 4095*a*b^4*d^6*x^5 - 693*b^5*d^6*x^6))/(9009*d^6)","B",1
1376,1,260,129,0.0527972,"\int (a+b x)^4 \sqrt{c+d x} \, dx","IntegrateAlgebraic[(a + b*x)^4*Sqrt[c + d*x],x]","\frac{2 \sqrt{c+d x} \left(1155 a^4 c d^4+1155 a^4 d^5 x-1848 a^3 b c^2 d^3+924 a^3 b c d^4 x+2772 a^3 b d^5 x^2+1584 a^2 b^2 c^3 d^2-792 a^2 b^2 c^2 d^3 x+594 a^2 b^2 c d^4 x^2+2970 a^2 b^2 d^5 x^3-704 a b^3 c^4 d+352 a b^3 c^3 d^2 x-264 a b^3 c^2 d^3 x^2+220 a b^3 c d^4 x^3+1540 a b^3 d^5 x^4+128 b^4 c^5-64 b^4 c^4 d x+48 b^4 c^3 d^2 x^2-40 b^4 c^2 d^3 x^3+35 b^4 c d^4 x^4+315 b^4 d^5 x^5\right)}{3465 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*Sqrt[c + d*x]*(128*b^4*c^5 - 704*a*b^3*c^4*d + 1584*a^2*b^2*c^3*d^2 - 1848*a^3*b*c^2*d^3 + 1155*a^4*c*d^4 - 64*b^4*c^4*d*x + 352*a*b^3*c^3*d^2*x - 792*a^2*b^2*c^2*d^3*x + 924*a^3*b*c*d^4*x + 1155*a^4*d^5*x + 48*b^4*c^3*d^2*x^2 - 264*a*b^3*c^2*d^3*x^2 + 594*a^2*b^2*c*d^4*x^2 + 2772*a^3*b*d^5*x^2 - 40*b^4*c^2*d^3*x^3 + 220*a*b^3*c*d^4*x^3 + 2970*a^2*b^2*d^5*x^3 + 35*b^4*c*d^4*x^4 + 1540*a*b^3*d^5*x^4 + 315*b^4*d^5*x^5))/(3465*d^5)","B",1
1377,1,173,100,0.0534449,"\int (a+b x)^3 \sqrt{c+d x} \, dx","IntegrateAlgebraic[(a + b*x)^3*Sqrt[c + d*x],x]","-\frac{2 \sqrt{c+d x} \left(-105 a^3 c d^3-105 a^3 d^4 x+126 a^2 b c^2 d^2-63 a^2 b c d^3 x-189 a^2 b d^4 x^2-72 a b^2 c^3 d+36 a b^2 c^2 d^2 x-27 a b^2 c d^3 x^2-135 a b^2 d^4 x^3+16 b^3 c^4-8 b^3 c^3 d x+6 b^3 c^2 d^2 x^2-5 b^3 c d^3 x^3-35 b^3 d^4 x^4\right)}{315 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*Sqrt[c + d*x]*(16*b^3*c^4 - 72*a*b^2*c^3*d + 126*a^2*b*c^2*d^2 - 105*a^3*c*d^3 - 8*b^3*c^3*d*x + 36*a*b^2*c^2*d^2*x - 63*a^2*b*c*d^3*x - 105*a^3*d^4*x + 6*b^3*c^2*d^2*x^2 - 27*a*b^2*c*d^3*x^2 - 189*a^2*b*d^4*x^2 - 5*b^3*c*d^3*x^3 - 135*a*b^2*d^4*x^3 - 35*b^3*d^4*x^4))/(315*d^4)","A",1
1378,1,103,71,0.0357778,"\int (a+b x)^2 \sqrt{c+d x} \, dx","IntegrateAlgebraic[(a + b*x)^2*Sqrt[c + d*x],x]","\frac{2 \sqrt{c+d x} \left(35 a^2 c d^2+35 a^2 d^3 x-28 a b c^2 d+14 a b c d^2 x+42 a b d^3 x^2+8 b^2 c^3-4 b^2 c^2 d x+3 b^2 c d^2 x^2+15 b^2 d^3 x^3\right)}{105 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*Sqrt[c + d*x]*(8*b^2*c^3 - 28*a*b*c^2*d + 35*a^2*c*d^2 - 4*b^2*c^2*d*x + 14*a*b*c*d^2*x + 35*a^2*d^3*x + 3*b^2*c*d^2*x^2 + 42*a*b*d^3*x^2 + 15*b^2*d^3*x^3))/(105*d^3)","A",1
1379,1,50,42,0.0196525,"\int (a+b x) \sqrt{c+d x} \, dx","IntegrateAlgebraic[(a + b*x)*Sqrt[c + d*x],x]","-\frac{2 \sqrt{c+d x} \left(-5 a c d-5 a d^2 x+2 b c^2-b c d x-3 b d^2 x^2\right)}{15 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*Sqrt[c + d*x]*(2*b*c^2 - 5*a*c*d - b*c*d*x - 5*a*d^2*x - 3*b*d^2*x^2))/(15*d^2)","A",1
1380,1,16,16,0.005093,"\int \sqrt{c+d x} \, dx","IntegrateAlgebraic[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
1381,1,72,62,0.0767851,"\int \frac{\sqrt{c+d x}}{a+b x} \, dx","IntegrateAlgebraic[Sqrt[c + d*x]/(a + b*x),x]","\frac{2 \sqrt{a d-b c} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x} \sqrt{a d-b c}}{b c-a d}\right)}{b^{3/2}}+\frac{2 \sqrt{c+d x}}{b}","\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]*ArcTan[(Sqrt[b]*Sqrt[-(b*c) + a*d]*Sqrt[c + d*x])/(b*c - a*d)])/b^(3/2)","A",1
1382,1,80,70,0.0995922,"\int \frac{\sqrt{c+d x}}{(a+b x)^2} \, dx","IntegrateAlgebraic[Sqrt[c + d*x]/(a + b*x)^2,x]","-\frac{d \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x} \sqrt{a d-b c}}{b c-a d}\right)}{b^{3/2} \sqrt{a d-b c}}-\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*ArcTan[(Sqrt[b]*Sqrt[-(b*c) + a*d]*Sqrt[c + d*x])/(b*c - a*d)])/(b^(3/2)*Sqrt[-(b*c) + a*d])","A",1
1383,1,109,110,0.198171,"\int \frac{\sqrt{c+d x}}{(a+b x)^3} \, dx","IntegrateAlgebraic[Sqrt[c + d*x]/(a + b*x)^3,x]","\frac{\sqrt{c+d x} (a d-2 b c-b d x)}{4 b (a+b x)^2 (b c-a d)}-\frac{d^2 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x} \sqrt{a d-b c}}{b c-a d}\right)}{4 b^{3/2} (a d-b c)^{3/2}}","\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*c + a*d - b*d*x))/(4*b*(b*c - a*d)*(a + b*x)^2) - (d^2*ArcTan[(Sqrt[b]*Sqrt[-(b*c) + a*d]*Sqrt[c + d*x])/(b*c - a*d)])/(4*b^(3/2)*(-(b*c) + a*d)^(3/2))","A",1
1384,1,146,146,0.3006097,"\int \frac{\sqrt{c+d x}}{(a+b x)^4} \, dx","IntegrateAlgebraic[Sqrt[c + d*x]/(a + b*x)^4,x]","\frac{\sqrt{c+d x} \left(-3 a^2 d^2+14 a b c d+8 a b d^2 x-8 b^2 c^2-2 b^2 c d x+3 b^2 d^2 x^2\right)}{24 b (a+b x)^3 (b c-a d)^2}-\frac{d^3 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x} \sqrt{a d-b c}}{b c-a d}\right)}{8 b^{3/2} (a d-b c)^{5/2}}","-\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]*(-8*b^2*c^2 + 14*a*b*c*d - 3*a^2*d^2 - 2*b^2*c*d*x + 8*a*b*d^2*x + 3*b^2*d^2*x^2))/(24*b*(b*c - a*d)^2*(a + b*x)^3) - (d^3*ArcTan[(Sqrt[b]*Sqrt[-(b*c) + a*d]*Sqrt[c + d*x])/(b*c - a*d)])/(8*b^(3/2)*(-(b*c) + a*d)^(5/2))","A",1
1385,1,199,182,0.4031261,"\int \frac{\sqrt{c+d x}}{(a+b x)^5} \, dx","IntegrateAlgebraic[Sqrt[c + d*x]/(a + b*x)^5,x]","\frac{\sqrt{c+d x} \left(15 a^3 d^3-118 a^2 b c d^2-73 a^2 b d^3 x+136 a b^2 c^2 d+36 a b^2 c d^2 x-55 a b^2 d^3 x^2-48 b^3 c^3-8 b^3 c^2 d x+10 b^3 c d^2 x^2-15 b^3 d^3 x^3\right)}{192 b (a+b x)^4 (b c-a d)^3}-\frac{5 d^4 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x} \sqrt{a d-b c}}{b c-a d}\right)}{64 b^{3/2} (a d-b c)^{7/2}}","\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]*(-48*b^3*c^3 + 136*a*b^2*c^2*d - 118*a^2*b*c*d^2 + 15*a^3*d^3 - 8*b^3*c^2*d*x + 36*a*b^2*c*d^2*x - 73*a^2*b*d^3*x + 10*b^3*c*d^2*x^2 - 55*a*b^2*d^3*x^2 - 15*b^3*d^3*x^3))/(192*b*(b*c - a*d)^3*(a + b*x)^4) - (5*d^4*ArcTan[(Sqrt[b]*Sqrt[-(b*c) + a*d]*Sqrt[c + d*x])/(b*c - a*d)])/(64*b^(3/2)*(-(b*c) + a*d)^(7/2))","A",1
1386,1,269,218,0.6318363,"\int \frac{\sqrt{c+d x}}{(a+b x)^6} \, dx","IntegrateAlgebraic[Sqrt[c + d*x]/(a + b*x)^6,x]","\frac{\sqrt{c+d x} \left(-105 a^4 d^4+1210 a^3 b c d^3+790 a^3 b d^4 x-2104 a^2 b^2 c^2 d^2-578 a^2 b^2 c d^3 x+896 a^2 b^2 d^4 x^2+1488 a b^3 c^3 d+256 a b^3 c^2 d^2 x-322 a b^3 c d^3 x^2+490 a b^3 d^4 x^3-384 b^4 c^4-48 b^4 c^3 d x+56 b^4 c^2 d^2 x^2-70 b^4 c d^3 x^3+105 b^4 d^4 x^4\right)}{1920 b (a+b x)^5 (b c-a d)^4}-\frac{7 d^5 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x} \sqrt{a d-b c}}{b c-a d}\right)}{128 b^{3/2} (a d-b c)^{9/2}}","-\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]*(-384*b^4*c^4 + 1488*a*b^3*c^3*d - 2104*a^2*b^2*c^2*d^2 + 1210*a^3*b*c*d^3 - 105*a^4*d^4 - 48*b^4*c^3*d*x + 256*a*b^3*c^2*d^2*x - 578*a^2*b^2*c*d^3*x + 790*a^3*b*d^4*x + 56*b^4*c^2*d^2*x^2 - 322*a*b^3*c*d^3*x^2 + 896*a^2*b^2*d^4*x^2 - 70*b^4*c*d^3*x^3 + 490*a*b^3*d^4*x^3 + 105*b^4*d^4*x^4))/(1920*b*(b*c - a*d)^4*(a + b*x)^5) - (7*d^5*ArcTan[(Sqrt[b]*Sqrt[-(b*c) + a*d]*Sqrt[c + d*x])/(b*c - a*d)])/(128*b^(3/2)*(-(b*c) + a*d)^(9/2))","A",1
1387,1,456,158,0.0694509,"\int (a+b x)^5 (c+d x)^{3/2} \, dx","IntegrateAlgebraic[(a + b*x)^5*(c + d*x)^(3/2),x]","-\frac{2 \sqrt{c+d x} \left(-9009 a^5 c^2 d^5-18018 a^5 c d^6 x-9009 a^5 d^7 x^2+12870 a^4 b c^3 d^4-6435 a^4 b c^2 d^5 x-51480 a^4 b c d^6 x^2-32175 a^4 b d^7 x^3-11440 a^3 b^2 c^4 d^3+5720 a^3 b^2 c^3 d^4 x-4290 a^3 b^2 c^2 d^5 x^2-71500 a^3 b^2 c d^6 x^3-50050 a^3 b^2 d^7 x^4+6240 a^2 b^3 c^5 d^2-3120 a^2 b^3 c^4 d^3 x+2340 a^2 b^3 c^3 d^4 x^2-1950 a^2 b^3 c^2 d^5 x^3-54600 a^2 b^3 c d^6 x^4-40950 a^2 b^3 d^7 x^5-1920 a b^4 c^6 d+960 a b^4 c^5 d^2 x-720 a b^4 c^4 d^3 x^2+600 a b^4 c^3 d^4 x^3-525 a b^4 c^2 d^5 x^4-22050 a b^4 c d^6 x^5-17325 a b^4 d^7 x^6+256 b^5 c^7-128 b^5 c^6 d x+96 b^5 c^5 d^2 x^2-80 b^5 c^4 d^3 x^3+70 b^5 c^3 d^4 x^4-63 b^5 c^2 d^5 x^5-3696 b^5 c d^6 x^6-3003 b^5 d^7 x^7\right)}{45045 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*Sqrt[c + d*x]*(256*b^5*c^7 - 1920*a*b^4*c^6*d + 6240*a^2*b^3*c^5*d^2 - 11440*a^3*b^2*c^4*d^3 + 12870*a^4*b*c^3*d^4 - 9009*a^5*c^2*d^5 - 128*b^5*c^6*d*x + 960*a*b^4*c^5*d^2*x - 3120*a^2*b^3*c^4*d^3*x + 5720*a^3*b^2*c^3*d^4*x - 6435*a^4*b*c^2*d^5*x - 18018*a^5*c*d^6*x + 96*b^5*c^5*d^2*x^2 - 720*a*b^4*c^4*d^3*x^2 + 2340*a^2*b^3*c^3*d^4*x^2 - 4290*a^3*b^2*c^2*d^5*x^2 - 51480*a^4*b*c*d^6*x^2 - 9009*a^5*d^7*x^2 - 80*b^5*c^4*d^3*x^3 + 600*a*b^4*c^3*d^4*x^3 - 1950*a^2*b^3*c^2*d^5*x^3 - 71500*a^3*b^2*c*d^6*x^3 - 32175*a^4*b*d^7*x^3 + 70*b^5*c^3*d^4*x^4 - 525*a*b^4*c^2*d^5*x^4 - 54600*a^2*b^3*c*d^6*x^4 - 50050*a^3*b^2*d^7*x^4 - 63*b^5*c^2*d^5*x^5 - 22050*a*b^4*c*d^6*x^5 - 40950*a^2*b^3*d^7*x^5 - 3696*b^5*c*d^6*x^6 - 17325*a*b^4*d^7*x^6 - 3003*b^5*d^7*x^7))/(45045*d^6)","B",1
1388,1,335,129,0.0584639,"\int (a+b x)^4 (c+d x)^{3/2} \, dx","IntegrateAlgebraic[(a + b*x)^4*(c + d*x)^(3/2),x]","\frac{2 \sqrt{c+d x} \left(3003 a^4 c^2 d^4+6006 a^4 c d^5 x+3003 a^4 d^6 x^2-3432 a^3 b c^3 d^3+1716 a^3 b c^2 d^4 x+13728 a^3 b c d^5 x^2+8580 a^3 b d^6 x^3+2288 a^2 b^2 c^4 d^2-1144 a^2 b^2 c^3 d^3 x+858 a^2 b^2 c^2 d^4 x^2+14300 a^2 b^2 c d^5 x^3+10010 a^2 b^2 d^6 x^4-832 a b^3 c^5 d+416 a b^3 c^4 d^2 x-312 a b^3 c^3 d^3 x^2+260 a b^3 c^2 d^4 x^3+7280 a b^3 c d^5 x^4+5460 a b^3 d^6 x^5+128 b^4 c^6-64 b^4 c^5 d x+48 b^4 c^4 d^2 x^2-40 b^4 c^3 d^3 x^3+35 b^4 c^2 d^4 x^4+1470 b^4 c d^5 x^5+1155 b^4 d^6 x^6\right)}{15015 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*Sqrt[c + d*x]*(128*b^4*c^6 - 832*a*b^3*c^5*d + 2288*a^2*b^2*c^4*d^2 - 3432*a^3*b*c^3*d^3 + 3003*a^4*c^2*d^4 - 64*b^4*c^5*d*x + 416*a*b^3*c^4*d^2*x - 1144*a^2*b^2*c^3*d^3*x + 1716*a^3*b*c^2*d^4*x + 6006*a^4*c*d^5*x + 48*b^4*c^4*d^2*x^2 - 312*a*b^3*c^3*d^3*x^2 + 858*a^2*b^2*c^2*d^4*x^2 + 13728*a^3*b*c*d^5*x^2 + 3003*a^4*d^6*x^2 - 40*b^4*c^3*d^3*x^3 + 260*a*b^3*c^2*d^4*x^3 + 14300*a^2*b^2*c*d^5*x^3 + 8580*a^3*b*d^6*x^3 + 35*b^4*c^2*d^4*x^4 + 7280*a*b^3*c*d^5*x^4 + 10010*a^2*b^2*d^6*x^4 + 1470*b^4*c*d^5*x^5 + 5460*a*b^3*d^6*x^5 + 1155*b^4*d^6*x^6))/(15015*d^5)","B",1
1389,1,231,100,0.0545171,"\int (a+b x)^3 (c+d x)^{3/2} \, dx","IntegrateAlgebraic[(a + b*x)^3*(c + d*x)^(3/2),x]","-\frac{2 \sqrt{c+d x} \left(-231 a^3 c^2 d^3-462 a^3 c d^4 x-231 a^3 d^5 x^2+198 a^2 b c^3 d^2-99 a^2 b c^2 d^3 x-792 a^2 b c d^4 x^2-495 a^2 b d^5 x^3-88 a b^2 c^4 d+44 a b^2 c^3 d^2 x-33 a b^2 c^2 d^3 x^2-550 a b^2 c d^4 x^3-385 a b^2 d^5 x^4+16 b^3 c^5-8 b^3 c^4 d x+6 b^3 c^3 d^2 x^2-5 b^3 c^2 d^3 x^3-140 b^3 c d^4 x^4-105 b^3 d^5 x^5\right)}{1155 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*Sqrt[c + d*x]*(16*b^3*c^5 - 88*a*b^2*c^4*d + 198*a^2*b*c^3*d^2 - 231*a^3*c^2*d^3 - 8*b^3*c^4*d*x + 44*a*b^2*c^3*d^2*x - 99*a^2*b*c^2*d^3*x - 462*a^3*c*d^4*x + 6*b^3*c^3*d^2*x^2 - 33*a*b^2*c^2*d^3*x^2 - 792*a^2*b*c*d^4*x^2 - 231*a^3*d^5*x^2 - 5*b^3*c^2*d^3*x^3 - 550*a*b^2*c*d^4*x^3 - 495*a^2*b*d^5*x^3 - 140*b^3*c*d^4*x^4 - 385*a*b^2*d^5*x^4 - 105*b^3*d^5*x^5))/(1155*d^4)","B",1
1390,1,144,71,0.0383663,"\int (a+b x)^2 (c+d x)^{3/2} \, dx","IntegrateAlgebraic[(a + b*x)^2*(c + d*x)^(3/2),x]","\frac{2 \sqrt{c+d x} \left(63 a^2 c^2 d^2+126 a^2 c d^3 x+63 a^2 d^4 x^2-36 a b c^3 d+18 a b c^2 d^2 x+144 a b c d^3 x^2+90 a b d^4 x^3+8 b^2 c^4-4 b^2 c^3 d x+3 b^2 c^2 d^2 x^2+50 b^2 c d^3 x^3+35 b^2 d^4 x^4\right)}{315 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*Sqrt[c + d*x]*(8*b^2*c^4 - 36*a*b*c^3*d + 63*a^2*c^2*d^2 - 4*b^2*c^3*d*x + 18*a*b*c^2*d^2*x + 126*a^2*c*d^3*x + 3*b^2*c^2*d^2*x^2 + 144*a*b*c*d^3*x^2 + 63*a^2*d^4*x^2 + 50*b^2*c*d^3*x^3 + 90*a*b*d^4*x^3 + 35*b^2*d^4*x^4))/(315*d^3)","B",1
1391,1,74,42,0.0223143,"\int (a+b x) (c+d x)^{3/2} \, dx","IntegrateAlgebraic[(a + b*x)*(c + d*x)^(3/2),x]","-\frac{2 \sqrt{c+d x} \left(-7 a c^2 d-14 a c d^2 x-7 a d^3 x^2+2 b c^3-b c^2 d x-8 b c d^2 x^2-5 b d^3 x^3\right)}{35 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*Sqrt[c + d*x]*(2*b*c^3 - 7*a*c^2*d - b*c^2*d*x - 14*a*c*d^2*x - 8*b*c*d^2*x^2 - 7*a*d^3*x^2 - 5*b*d^3*x^3))/(35*d^2)","A",1
1392,1,16,16,0.0052234,"\int (c+d x)^{3/2} \, dx","IntegrateAlgebraic[(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
1393,1,87,86,0.1201906,"\int \frac{(c+d x)^{3/2}}{a+b x} \, dx","IntegrateAlgebraic[(c + d*x)^(3/2)/(a + b*x),x]","\frac{2 \sqrt{c+d x} (-3 a d+4 b c+b d x)}{3 b^2}-\frac{2 (a d-b c)^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x} \sqrt{a d-b c}}{b c-a d}\right)}{b^{5/2}}","-\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 \sqrt{c+d x} (b c-a d)}{b^2}+\frac{2 (c+d x)^{3/2}}{3 b}",1,"(2*Sqrt[c + d*x]*(4*b*c - 3*a*d + b*d*x))/(3*b^2) - (2*(-(b*c) + a*d)^(3/2)*ArcTan[(Sqrt[b]*Sqrt[-(b*c) + a*d]*Sqrt[c + d*x])/(b*c - a*d)])/b^(5/2)","A",1
1394,1,93,85,0.1209802,"\int \frac{(c+d x)^{3/2}}{(a+b x)^2} \, dx","IntegrateAlgebraic[(c + d*x)^(3/2)/(a + b*x)^2,x]","\frac{3 d \sqrt{a d-b c} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x} \sqrt{a d-b c}}{b c-a d}\right)}{b^{5/2}}+\frac{\sqrt{c+d x} (3 a d-b c+2 b d x)}{b^2 (a+b 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}",1,"(Sqrt[c + d*x]*(-(b*c) + 3*a*d + 2*b*d*x))/(b^2*(a + b*x)) + (3*d*Sqrt[-(b*c) + a*d]*ArcTan[(Sqrt[b]*Sqrt[-(b*c) + a*d]*Sqrt[c + d*x])/(b*c - a*d)])/b^(5/2)","A",1
1395,1,100,100,0.1162009,"\int \frac{(c+d x)^{3/2}}{(a+b x)^3} \, dx","IntegrateAlgebraic[(c + d*x)^(3/2)/(a + b*x)^3,x]","\frac{\sqrt{c+d x} (-3 a d-2 b c-5 b d x)}{4 b^2 (a+b x)^2}-\frac{3 d^2 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x} \sqrt{a d-b c}}{b c-a d}\right)}{4 b^{5/2} \sqrt{a d-b c}}","-\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,"(Sqrt[c + d*x]*(-2*b*c - 3*a*d - 5*b*d*x))/(4*b^2*(a + b*x)^2) - (3*d^2*ArcTan[(Sqrt[b]*Sqrt[-(b*c) + a*d]*Sqrt[c + d*x])/(b*c - a*d)])/(4*b^(5/2)*Sqrt[-(b*c) + a*d])","A",1
1396,1,146,136,0.2861745,"\int \frac{(c+d x)^{3/2}}{(a+b x)^4} \, dx","IntegrateAlgebraic[(c + d*x)^(3/2)/(a + b*x)^4,x]","\frac{\sqrt{c+d x} \left(3 a^2 d^2+2 a b c d+8 a b d^2 x-8 b^2 c^2-14 b^2 c d x-3 b^2 d^2 x^2\right)}{24 b^2 (a+b x)^3 (b c-a d)}-\frac{d^3 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x} \sqrt{a d-b c}}{b c-a d}\right)}{8 b^{5/2} (a d-b c)^{3/2}}","\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^2 \sqrt{c+d x}}{8 b^2 (a+b x) (b c-a d)}-\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,"(Sqrt[c + d*x]*(-8*b^2*c^2 + 2*a*b*c*d + 3*a^2*d^2 - 14*b^2*c*d*x + 8*a*b*d^2*x - 3*b^2*d^2*x^2))/(24*b^2*(b*c - a*d)*(a + b*x)^3) - (d^3*ArcTan[(Sqrt[b]*Sqrt[-(b*c) + a*d]*Sqrt[c + d*x])/(b*c - a*d)])/(8*b^(5/2)*(-(b*c) + a*d)^(3/2))","A",1
1397,1,199,172,0.3711823,"\int \frac{(c+d x)^{3/2}}{(a+b x)^5} \, dx","IntegrateAlgebraic[(c + d*x)^(3/2)/(a + b*x)^5,x]","\frac{\sqrt{c+d x} \left(-3 a^3 d^3-2 a^2 b c d^2-11 a^2 b d^3 x+24 a b^2 c^2 d+44 a b^2 c d^2 x+11 a b^2 d^3 x^2-16 b^3 c^3-24 b^3 c^2 d x-2 b^3 c d^2 x^2+3 b^3 d^3 x^3\right)}{64 b^2 (a+b x)^4 (b c-a d)^2}-\frac{3 d^4 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x} \sqrt{a d-b c}}{b c-a d}\right)}{64 b^{5/2} (a d-b c)^{5/2}}","-\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{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{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,"(Sqrt[c + d*x]*(-16*b^3*c^3 + 24*a*b^2*c^2*d - 2*a^2*b*c*d^2 - 3*a^3*d^3 - 24*b^3*c^2*d*x + 44*a*b^2*c*d^2*x - 11*a^2*b*d^3*x - 2*b^3*c*d^2*x^2 + 11*a*b^2*d^3*x^2 + 3*b^3*d^3*x^3))/(64*b^2*(b*c - a*d)^2*(a + b*x)^4) - (3*d^4*ArcTan[(Sqrt[b]*Sqrt[-(b*c) + a*d]*Sqrt[c + d*x])/(b*c - a*d)])/(64*b^(5/2)*(-(b*c) + a*d)^(5/2))","A",1
1398,1,269,208,0.4951394,"\int \frac{(c+d x)^{3/2}}{(a+b x)^6} \, dx","IntegrateAlgebraic[(c + d*x)^(3/2)/(a + b*x)^6,x]","\frac{\sqrt{c+d x} \left(15 a^4 d^4+10 a^3 b c d^3+70 a^3 b d^4 x-248 a^2 b^2 c^2 d^2-466 a^2 b^2 c d^3 x-128 a^2 b^2 d^4 x^2+336 a b^3 c^3 d+512 a b^3 c^2 d^2 x+46 a b^3 c d^3 x^2-70 a b^3 d^4 x^3-128 b^4 c^4-176 b^4 c^3 d x-8 b^4 c^2 d^2 x^2+10 b^4 c d^3 x^3-15 b^4 d^4 x^4\right)}{640 b^2 (a+b x)^5 (b c-a d)^3}-\frac{3 d^5 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x} \sqrt{a d-b c}}{b c-a d}\right)}{128 b^{5/2} (a d-b c)^{7/2}}","\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^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 \sqrt{c+d x}}{40 b^2 (a+b x)^4}-\frac{(c+d x)^{3/2}}{5 b (a+b x)^5}",1,"(Sqrt[c + d*x]*(-128*b^4*c^4 + 336*a*b^3*c^3*d - 248*a^2*b^2*c^2*d^2 + 10*a^3*b*c*d^3 + 15*a^4*d^4 - 176*b^4*c^3*d*x + 512*a*b^3*c^2*d^2*x - 466*a^2*b^2*c*d^3*x + 70*a^3*b*d^4*x - 8*b^4*c^2*d^2*x^2 + 46*a*b^3*c*d^3*x^2 - 128*a^2*b^2*d^4*x^2 + 10*b^4*c*d^3*x^3 - 70*a*b^3*d^4*x^3 - 15*b^4*d^4*x^4))/(640*b^2*(b*c - a*d)^3*(a + b*x)^5) - (3*d^5*ArcTan[(Sqrt[b]*Sqrt[-(b*c) + a*d]*Sqrt[c + d*x])/(b*c - a*d)])/(128*b^(5/2)*(-(b*c) + a*d)^(7/2))","A",1
1399,1,548,158,0.0763402,"\int (a+b x)^5 (c+d x)^{5/2} \, dx","IntegrateAlgebraic[(a + b*x)^5*(c + d*x)^(5/2),x]","-\frac{2 \sqrt{c+d x} \left(-21879 a^5 c^3 d^5-65637 a^5 c^2 d^6 x-65637 a^5 c d^7 x^2-21879 a^5 d^8 x^3+24310 a^4 b c^4 d^4-12155 a^4 b c^3 d^5 x-182325 a^4 b c^2 d^6 x^2-230945 a^4 b c d^7 x^3-85085 a^4 b d^8 x^4-17680 a^3 b^2 c^5 d^3+8840 a^3 b^2 c^4 d^4 x-6630 a^3 b^2 c^3 d^5 x^2-249730 a^3 b^2 c^2 d^6 x^3-355810 a^3 b^2 c d^7 x^4-139230 a^3 b^2 d^8 x^5+8160 a^2 b^3 c^6 d^2-4080 a^2 b^3 c^5 d^3 x+3060 a^2 b^3 c^4 d^4 x^2-2550 a^2 b^3 c^3 d^5 x^3-189210 a^2 b^3 c^2 d^6 x^4-289170 a^2 b^3 c d^7 x^5-117810 a^2 b^3 d^8 x^6-2176 a b^4 c^7 d+1088 a b^4 c^6 d^2 x-816 a b^4 c^5 d^3 x^2+680 a b^4 c^4 d^4 x^3-595 a b^4 c^3 d^5 x^4-76041 a b^4 c^2 d^6 x^5-121737 a b^4 c d^7 x^6-51051 a b^4 d^8 x^7+256 b^5 c^8-128 b^5 c^7 d x+96 b^5 c^6 d^2 x^2-80 b^5 c^5 d^3 x^3+70 b^5 c^4 d^4 x^4-63 b^5 c^3 d^5 x^5-12705 b^5 c^2 d^6 x^6-21021 b^5 c d^7 x^7-9009 b^5 d^8 x^8\right)}{153153 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*Sqrt[c + d*x]*(256*b^5*c^8 - 2176*a*b^4*c^7*d + 8160*a^2*b^3*c^6*d^2 - 17680*a^3*b^2*c^5*d^3 + 24310*a^4*b*c^4*d^4 - 21879*a^5*c^3*d^5 - 128*b^5*c^7*d*x + 1088*a*b^4*c^6*d^2*x - 4080*a^2*b^3*c^5*d^3*x + 8840*a^3*b^2*c^4*d^4*x - 12155*a^4*b*c^3*d^5*x - 65637*a^5*c^2*d^6*x + 96*b^5*c^6*d^2*x^2 - 816*a*b^4*c^5*d^3*x^2 + 3060*a^2*b^3*c^4*d^4*x^2 - 6630*a^3*b^2*c^3*d^5*x^2 - 182325*a^4*b*c^2*d^6*x^2 - 65637*a^5*c*d^7*x^2 - 80*b^5*c^5*d^3*x^3 + 680*a*b^4*c^4*d^4*x^3 - 2550*a^2*b^3*c^3*d^5*x^3 - 249730*a^3*b^2*c^2*d^6*x^3 - 230945*a^4*b*c*d^7*x^3 - 21879*a^5*d^8*x^3 + 70*b^5*c^4*d^4*x^4 - 595*a*b^4*c^3*d^5*x^4 - 189210*a^2*b^3*c^2*d^6*x^4 - 355810*a^3*b^2*c*d^7*x^4 - 85085*a^4*b*d^8*x^4 - 63*b^5*c^3*d^5*x^5 - 76041*a*b^4*c^2*d^6*x^5 - 289170*a^2*b^3*c*d^7*x^5 - 139230*a^3*b^2*d^8*x^5 - 12705*b^5*c^2*d^6*x^6 - 121737*a*b^4*c*d^7*x^6 - 117810*a^2*b^3*d^8*x^6 - 21021*b^5*c*d^7*x^7 - 51051*a*b^4*d^8*x^7 - 9009*b^5*d^8*x^8))/(153153*d^6)","B",1
1400,1,410,129,0.0615029,"\int (a+b x)^4 (c+d x)^{5/2} \, dx","IntegrateAlgebraic[(a + b*x)^4*(c + d*x)^(5/2),x]","\frac{2 \sqrt{c+d x} \left(6435 a^4 c^3 d^4+19305 a^4 c^2 d^5 x+19305 a^4 c d^6 x^2+6435 a^4 d^7 x^3-5720 a^3 b c^4 d^3+2860 a^3 b c^3 d^4 x+42900 a^3 b c^2 d^5 x^2+54340 a^3 b c d^6 x^3+20020 a^3 b d^7 x^4+3120 a^2 b^2 c^5 d^2-1560 a^2 b^2 c^4 d^3 x+1170 a^2 b^2 c^3 d^4 x^2+44070 a^2 b^2 c^2 d^5 x^3+62790 a^2 b^2 c d^6 x^4+24570 a^2 b^2 d^7 x^5-960 a b^3 c^6 d+480 a b^3 c^5 d^2 x-360 a b^3 c^4 d^3 x^2+300 a b^3 c^3 d^4 x^3+22260 a b^3 c^2 d^5 x^4+34020 a b^3 c d^6 x^5+13860 a b^3 d^7 x^6+128 b^4 c^7-64 b^4 c^6 d x+48 b^4 c^5 d^2 x^2-40 b^4 c^4 d^3 x^3+35 b^4 c^3 d^4 x^4+4473 b^4 c^2 d^5 x^5+7161 b^4 c d^6 x^6+3003 b^4 d^7 x^7\right)}{45045 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*Sqrt[c + d*x]*(128*b^4*c^7 - 960*a*b^3*c^6*d + 3120*a^2*b^2*c^5*d^2 - 5720*a^3*b*c^4*d^3 + 6435*a^4*c^3*d^4 - 64*b^4*c^6*d*x + 480*a*b^3*c^5*d^2*x - 1560*a^2*b^2*c^4*d^3*x + 2860*a^3*b*c^3*d^4*x + 19305*a^4*c^2*d^5*x + 48*b^4*c^5*d^2*x^2 - 360*a*b^3*c^4*d^3*x^2 + 1170*a^2*b^2*c^3*d^4*x^2 + 42900*a^3*b*c^2*d^5*x^2 + 19305*a^4*c*d^6*x^2 - 40*b^4*c^4*d^3*x^3 + 300*a*b^3*c^3*d^4*x^3 + 44070*a^2*b^2*c^2*d^5*x^3 + 54340*a^3*b*c*d^6*x^3 + 6435*a^4*d^7*x^3 + 35*b^4*c^3*d^4*x^4 + 22260*a*b^3*c^2*d^5*x^4 + 62790*a^2*b^2*c*d^6*x^4 + 20020*a^3*b*d^7*x^4 + 4473*b^4*c^2*d^5*x^5 + 34020*a*b^3*c*d^6*x^5 + 24570*a^2*b^2*d^7*x^5 + 7161*b^4*c*d^6*x^6 + 13860*a*b^3*d^7*x^6 + 3003*b^4*d^7*x^7))/(45045*d^5)","B",1
1401,1,289,100,0.0573879,"\int (a+b x)^3 (c+d x)^{5/2} \, dx","IntegrateAlgebraic[(a + b*x)^3*(c + d*x)^(5/2),x]","-\frac{2 \sqrt{c+d x} \left(-429 a^3 c^3 d^3-1287 a^3 c^2 d^4 x-1287 a^3 c d^5 x^2-429 a^3 d^6 x^3+286 a^2 b c^4 d^2-143 a^2 b c^3 d^3 x-2145 a^2 b c^2 d^4 x^2-2717 a^2 b c d^5 x^3-1001 a^2 b d^6 x^4-104 a b^2 c^5 d+52 a b^2 c^4 d^2 x-39 a b^2 c^3 d^3 x^2-1469 a b^2 c^2 d^4 x^3-2093 a b^2 c d^5 x^4-819 a b^2 d^6 x^5+16 b^3 c^6-8 b^3 c^5 d x+6 b^3 c^4 d^2 x^2-5 b^3 c^3 d^3 x^3-371 b^3 c^2 d^4 x^4-567 b^3 c d^5 x^5-231 b^3 d^6 x^6\right)}{3003 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*Sqrt[c + d*x]*(16*b^3*c^6 - 104*a*b^2*c^5*d + 286*a^2*b*c^4*d^2 - 429*a^3*c^3*d^3 - 8*b^3*c^5*d*x + 52*a*b^2*c^4*d^2*x - 143*a^2*b*c^3*d^3*x - 1287*a^3*c^2*d^4*x + 6*b^3*c^4*d^2*x^2 - 39*a*b^2*c^3*d^3*x^2 - 2145*a^2*b*c^2*d^4*x^2 - 1287*a^3*c*d^5*x^2 - 5*b^3*c^3*d^3*x^3 - 1469*a*b^2*c^2*d^4*x^3 - 2717*a^2*b*c*d^5*x^3 - 429*a^3*d^6*x^3 - 371*b^3*c^2*d^4*x^4 - 2093*a*b^2*c*d^5*x^4 - 1001*a^2*b*d^6*x^4 - 567*b^3*c*d^5*x^5 - 819*a*b^2*d^6*x^5 - 231*b^3*d^6*x^6))/(3003*d^4)","B",1
1402,1,185,71,0.0422952,"\int (a+b x)^2 (c+d x)^{5/2} \, dx","IntegrateAlgebraic[(a + b*x)^2*(c + d*x)^(5/2),x]","\frac{2 \sqrt{c+d x} \left(99 a^2 c^3 d^2+297 a^2 c^2 d^3 x+297 a^2 c d^4 x^2+99 a^2 d^5 x^3-44 a b c^4 d+22 a b c^3 d^2 x+330 a b c^2 d^3 x^2+418 a b c d^4 x^3+154 a b d^5 x^4+8 b^2 c^5-4 b^2 c^4 d x+3 b^2 c^3 d^2 x^2+113 b^2 c^2 d^3 x^3+161 b^2 c d^4 x^4+63 b^2 d^5 x^5\right)}{693 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*Sqrt[c + d*x]*(8*b^2*c^5 - 44*a*b*c^4*d + 99*a^2*c^3*d^2 - 4*b^2*c^4*d*x + 22*a*b*c^3*d^2*x + 297*a^2*c^2*d^3*x + 3*b^2*c^3*d^2*x^2 + 330*a*b*c^2*d^3*x^2 + 297*a^2*c*d^4*x^2 + 113*b^2*c^2*d^3*x^3 + 418*a*b*c*d^4*x^3 + 99*a^2*d^5*x^3 + 161*b^2*c*d^4*x^4 + 154*a*b*d^5*x^4 + 63*b^2*d^5*x^5))/(693*d^3)","B",1
1403,1,98,42,0.0234591,"\int (a+b x) (c+d x)^{5/2} \, dx","IntegrateAlgebraic[(a + b*x)*(c + d*x)^(5/2),x]","-\frac{2 \sqrt{c+d x} \left(-9 a c^3 d-27 a c^2 d^2 x-27 a c d^3 x^2-9 a d^4 x^3+2 b c^4-b c^3 d x-15 b c^2 d^2 x^2-19 b c d^3 x^3-7 b d^4 x^4\right)}{63 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*Sqrt[c + d*x]*(2*b*c^4 - 9*a*c^3*d - b*c^3*d*x - 27*a*c^2*d^2*x - 15*b*c^2*d^2*x^2 - 27*a*c*d^3*x^2 - 19*b*c*d^3*x^3 - 9*a*d^4*x^3 - 7*b*d^4*x^4))/(63*d^2)","B",1
1404,1,16,16,0.0051939,"\int (c+d x)^{5/2} \, dx","IntegrateAlgebraic[(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
1405,1,124,112,0.1071775,"\int \frac{(c+d x)^{5/2}}{a+b x} \, dx","IntegrateAlgebraic[(c + d*x)^(5/2)/(a + b*x),x]","\frac{2 \sqrt{c+d x} \left(15 a^2 d^2-35 a b c d-5 a b d^2 x+23 b^2 c^2+11 b^2 c d x+3 b^2 d^2 x^2\right)}{15 b^3}+\frac{2 (a d-b c)^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x} \sqrt{a d-b c}}{b c-a d}\right)}{b^{7/2}}","-\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 \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 (c+d x)^{5/2}}{5 b}",1,"(2*Sqrt[c + d*x]*(23*b^2*c^2 - 35*a*b*c*d + 15*a^2*d^2 + 11*b^2*c*d*x - 5*a*b*d^2*x + 3*b^2*d^2*x^2))/(15*b^3) + (2*(-(b*c) + a*d)^(5/2)*ArcTan[(Sqrt[b]*Sqrt[-(b*c) + a*d]*Sqrt[c + d*x])/(b*c - a*d)])/b^(7/2)","A",1
1406,1,132,110,0.1620524,"\int \frac{(c+d x)^{5/2}}{(a+b x)^2} \, dx","IntegrateAlgebraic[(c + d*x)^(5/2)/(a + b*x)^2,x]","\frac{\sqrt{c+d x} \left(-15 a^2 d^2+20 a b c d-10 a b d^2 x-3 b^2 c^2+14 b^2 c d x+2 b^2 d^2 x^2\right)}{3 b^3 (a+b x)}-\frac{5 d (a d-b c)^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x} \sqrt{a d-b c}}{b c-a d}\right)}{b^{7/2}}","-\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{5 d \sqrt{c+d x} (b c-a d)}{b^3}-\frac{(c+d x)^{5/2}}{b (a+b x)}+\frac{5 d (c+d x)^{3/2}}{3 b^2}",1,"(Sqrt[c + d*x]*(-3*b^2*c^2 + 20*a*b*c*d - 15*a^2*d^2 + 14*b^2*c*d*x - 10*a*b*d^2*x + 2*b^2*d^2*x^2))/(3*b^3*(a + b*x)) - (5*d*(-(b*c) + a*d)^(3/2)*ArcTan[(Sqrt[b]*Sqrt[-(b*c) + a*d]*Sqrt[c + d*x])/(b*c - a*d)])/b^(7/2)","A",1
1407,1,136,119,0.1842443,"\int \frac{(c+d x)^{5/2}}{(a+b x)^3} \, dx","IntegrateAlgebraic[(c + d*x)^(5/2)/(a + b*x)^3,x]","\frac{\sqrt{c+d x} \left(15 a^2 d^2-5 a b c d+25 a b d^2 x-2 b^2 c^2-9 b^2 c d x+8 b^2 d^2 x^2\right)}{4 b^3 (a+b x)^2}+\frac{15 d^2 \sqrt{a d-b c} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x} \sqrt{a d-b c}}{b c-a d}\right)}{4 b^{7/2}}","-\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,"(Sqrt[c + d*x]*(-2*b^2*c^2 - 5*a*b*c*d + 15*a^2*d^2 - 9*b^2*c*d*x + 25*a*b*d^2*x + 8*b^2*d^2*x^2))/(4*b^3*(a + b*x)^2) + (15*d^2*Sqrt[-(b*c) + a*d]*ArcTan[(Sqrt[b]*Sqrt[-(b*c) + a*d]*Sqrt[c + d*x])/(b*c - a*d)])/(4*b^(7/2))","A",1
1408,1,136,126,0.2283968,"\int \frac{(c+d x)^{5/2}}{(a+b x)^4} \, dx","IntegrateAlgebraic[(c + d*x)^(5/2)/(a + b*x)^4,x]","\frac{\sqrt{c+d x} \left(-15 a^2 d^2-10 a b c d-40 a b d^2 x-8 b^2 c^2-26 b^2 c d x-33 b^2 d^2 x^2\right)}{24 b^3 (a+b x)^3}-\frac{5 d^3 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x} \sqrt{a d-b c}}{b c-a d}\right)}{8 b^{7/2} \sqrt{a d-b c}}","-\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^2 \sqrt{c+d x}}{8 b^3 (a+b x)}-\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,"(Sqrt[c + d*x]*(-8*b^2*c^2 - 10*a*b*c*d - 15*a^2*d^2 - 26*b^2*c*d*x - 40*a*b*d^2*x - 33*b^2*d^2*x^2))/(24*b^3*(a + b*x)^3) - (5*d^3*ArcTan[(Sqrt[b]*Sqrt[-(b*c) + a*d]*Sqrt[c + d*x])/(b*c - a*d)])/(8*b^(7/2)*Sqrt[-(b*c) + a*d])","A",1
1409,1,199,162,0.3926671,"\int \frac{(c+d x)^{5/2}}{(a+b x)^5} \, dx","IntegrateAlgebraic[(c + d*x)^(5/2)/(a + b*x)^5,x]","\frac{\sqrt{c+d x} \left(15 a^3 d^3+10 a^2 b c d^2+55 a^2 b d^3 x+8 a b^2 c^2 d+36 a b^2 c d^2 x+73 a b^2 d^3 x^2-48 b^3 c^3-136 b^3 c^2 d x-118 b^3 c d^2 x^2-15 b^3 d^3 x^3\right)}{192 b^3 (a+b x)^4 (b c-a d)}-\frac{5 d^4 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x} \sqrt{a d-b c}}{b c-a d}\right)}{64 b^{7/2} (a d-b c)^{3/2}}","\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^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 (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,"(Sqrt[c + d*x]*(-48*b^3*c^3 + 8*a*b^2*c^2*d + 10*a^2*b*c*d^2 + 15*a^3*d^3 - 136*b^3*c^2*d*x + 36*a*b^2*c*d^2*x + 55*a^2*b*d^3*x - 118*b^3*c*d^2*x^2 + 73*a*b^2*d^3*x^2 - 15*b^3*d^3*x^3))/(192*b^3*(b*c - a*d)*(a + b*x)^4) - (5*d^4*ArcTan[(Sqrt[b]*Sqrt[-(b*c) + a*d]*Sqrt[c + d*x])/(b*c - a*d)])/(64*b^(7/2)*(-(b*c) + a*d)^(3/2))","A",1
1410,1,269,198,0.471724,"\int \frac{(c+d x)^{5/2}}{(a+b x)^6} \, dx","IntegrateAlgebraic[(c + d*x)^(5/2)/(a + b*x)^6,x]","\frac{\sqrt{c+d x} \left(-15 a^4 d^4-10 a^3 b c d^3-70 a^3 b d^4 x-8 a^2 b^2 c^2 d^2-46 a^2 b^2 c d^3 x-128 a^2 b^2 d^4 x^2+176 a b^3 c^3 d+512 a b^3 c^2 d^2 x+466 a b^3 c d^3 x^2+70 a b^3 d^4 x^3-128 b^4 c^4-336 b^4 c^3 d x-248 b^4 c^2 d^2 x^2-10 b^4 c d^3 x^3+15 b^4 d^4 x^4\right)}{640 b^3 (a+b x)^5 (b c-a d)^2}-\frac{3 d^5 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x} \sqrt{a d-b c}}{b c-a d}\right)}{128 b^{7/2} (a d-b c)^{5/2}}","-\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{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{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,"(Sqrt[c + d*x]*(-128*b^4*c^4 + 176*a*b^3*c^3*d - 8*a^2*b^2*c^2*d^2 - 10*a^3*b*c*d^3 - 15*a^4*d^4 - 336*b^4*c^3*d*x + 512*a*b^3*c^2*d^2*x - 46*a^2*b^2*c*d^3*x - 70*a^3*b*d^4*x - 248*b^4*c^2*d^2*x^2 + 466*a*b^3*c*d^3*x^2 - 128*a^2*b^2*d^4*x^2 - 10*b^4*c*d^3*x^3 + 70*a*b^3*d^4*x^3 + 15*b^4*d^4*x^4))/(640*b^3*(b*c - a*d)^2*(a + b*x)^5) - (3*d^5*ArcTan[(Sqrt[b]*Sqrt[-(b*c) + a*d]*Sqrt[c + d*x])/(b*c - a*d)])/(128*b^(7/2)*(-(b*c) + a*d)^(5/2))","A",1
1411,1,36,35,0.0348842,"\int \frac{\sqrt{-1+x}}{(1+x)^2} \, dx","IntegrateAlgebraic[Sqrt[-1 + x]/(1 + x)^2,x]","\frac{\sqrt{x-1}}{-x-1}+\frac{\tan ^{-1}\left(\frac{\sqrt{x-1}}{\sqrt{2}}\right)}{\sqrt{2}}","\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",1
1412,1,43,56,0.0375818,"\int \frac{\sqrt{-1+x}}{(1+x)^3} \, dx","IntegrateAlgebraic[Sqrt[-1 + x]/(1 + x)^3,x]","\frac{\sqrt{x-1} (x-3)}{8 (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,"((-3 + x)*Sqrt[-1 + x])/(8*(1 + x)^2) + ArcTan[Sqrt[-1 + x]/Sqrt[2]]/(8*Sqrt[2])","A",1
1413,1,276,154,0.0594691,"\int \frac{(a+b x)^5}{\sqrt{c+d x}} \, dx","IntegrateAlgebraic[(a + b*x)^5/Sqrt[c + d*x],x]","-\frac{2 \sqrt{c+d x} \left(-693 a^5 d^5+2310 a^4 b c d^4-1155 a^4 b d^5 x-3696 a^3 b^2 c^2 d^3+1848 a^3 b^2 c d^4 x-1386 a^3 b^2 d^5 x^2+3168 a^2 b^3 c^3 d^2-1584 a^2 b^3 c^2 d^3 x+1188 a^2 b^3 c d^4 x^2-990 a^2 b^3 d^5 x^3-1408 a b^4 c^4 d+704 a b^4 c^3 d^2 x-528 a b^4 c^2 d^3 x^2+440 a b^4 c d^4 x^3-385 a b^4 d^5 x^4+256 b^5 c^5-128 b^5 c^4 d x+96 b^5 c^3 d^2 x^2-80 b^5 c^2 d^3 x^3+70 b^5 c d^4 x^4-63 b^5 d^5 x^5\right)}{693 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*Sqrt[c + d*x]*(256*b^5*c^5 - 1408*a*b^4*c^4*d + 3168*a^2*b^3*c^3*d^2 - 3696*a^3*b^2*c^2*d^3 + 2310*a^4*b*c*d^4 - 693*a^5*d^5 - 128*b^5*c^4*d*x + 704*a*b^4*c^3*d^2*x - 1584*a^2*b^3*c^2*d^3*x + 1848*a^3*b^2*c*d^4*x - 1155*a^4*b*d^5*x + 96*b^5*c^3*d^2*x^2 - 528*a*b^4*c^2*d^3*x^2 + 1188*a^2*b^3*c*d^4*x^2 - 1386*a^3*b^2*d^5*x^2 - 80*b^5*c^2*d^3*x^3 + 440*a*b^4*c*d^4*x^3 - 990*a^2*b^3*d^5*x^3 + 70*b^5*c*d^4*x^4 - 385*a*b^4*d^5*x^4 - 63*b^5*d^5*x^5))/(693*d^6)","A",1
1414,1,189,127,0.0462544,"\int \frac{(a+b x)^4}{\sqrt{c+d x}} \, dx","IntegrateAlgebraic[(a + b*x)^4/Sqrt[c + d*x],x]","\frac{2 \sqrt{c+d x} \left(315 a^4 d^4-840 a^3 b c d^3+420 a^3 b d^4 x+1008 a^2 b^2 c^2 d^2-504 a^2 b^2 c d^3 x+378 a^2 b^2 d^4 x^2-576 a b^3 c^3 d+288 a b^3 c^2 d^2 x-216 a b^3 c d^3 x^2+180 a b^3 d^4 x^3+128 b^4 c^4-64 b^4 c^3 d x+48 b^4 c^2 d^2 x^2-40 b^4 c d^3 x^3+35 b^4 d^4 x^4\right)}{315 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*Sqrt[c + d*x]*(128*b^4*c^4 - 576*a*b^3*c^3*d + 1008*a^2*b^2*c^2*d^2 - 840*a^3*b*c*d^3 + 315*a^4*d^4 - 64*b^4*c^3*d*x + 288*a*b^3*c^2*d^2*x - 504*a^2*b^2*c*d^3*x + 420*a^3*b*d^4*x + 48*b^4*c^2*d^2*x^2 - 216*a*b^3*c*d^3*x^2 + 378*a^2*b^2*d^4*x^2 - 40*b^4*c*d^3*x^3 + 180*a*b^3*d^4*x^3 + 35*b^4*d^4*x^4))/(315*d^5)","A",1
1415,1,119,96,0.0436333,"\int \frac{(a+b x)^3}{\sqrt{c+d x}} \, dx","IntegrateAlgebraic[(a + b*x)^3/Sqrt[c + d*x],x]","-\frac{2 \sqrt{c+d x} \left(-35 a^3 d^3+70 a^2 b c d^2-35 a^2 b d^3 x-56 a b^2 c^2 d+28 a b^2 c d^2 x-21 a b^2 d^3 x^2+16 b^3 c^3-8 b^3 c^2 d x+6 b^3 c d^2 x^2-5 b^3 d^3 x^3\right)}{35 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*Sqrt[c + d*x]*(16*b^3*c^3 - 56*a*b^2*c^2*d + 70*a^2*b*c*d^2 - 35*a^3*d^3 - 8*b^3*c^2*d*x + 28*a*b^2*c*d^2*x - 35*a^2*b*d^3*x + 6*b^3*c*d^2*x^2 - 21*a*b^2*d^3*x^2 - 5*b^3*d^3*x^3))/(35*d^4)","A",1
1416,1,66,69,0.0332414,"\int \frac{(a+b x)^2}{\sqrt{c+d x}} \, dx","IntegrateAlgebraic[(a + b*x)^2/Sqrt[c + d*x],x]","\frac{2 \sqrt{c+d x} \left(15 a^2 d^2-20 a b c d+10 a b d^2 x+8 b^2 c^2-4 b^2 c d x+3 b^2 d^2 x^2\right)}{15 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*Sqrt[c + d*x]*(8*b^2*c^2 - 20*a*b*c*d + 15*a^2*d^2 - 4*b^2*c*d*x + 10*a*b*d^2*x + 3*b^2*d^2*x^2))/(15*d^3)","A",1
1417,1,30,40,0.0143922,"\int \frac{a+b x}{\sqrt{c+d x}} \, dx","IntegrateAlgebraic[(a + b*x)/Sqrt[c + d*x],x]","-\frac{2 \sqrt{c+d x} (-3 a d+2 b c-b d x)}{3 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*Sqrt[c + d*x]*(2*b*c - 3*a*d - b*d*x))/(3*d^2)","A",1
1418,1,14,14,0.0047706,"\int \frac{1}{\sqrt{c+d x}} \, dx","IntegrateAlgebraic[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
1419,1,57,47,0.0337353,"\int \frac{1}{(a+b x) \sqrt{c+d x}} \, dx","IntegrateAlgebraic[1/((a + b*x)*Sqrt[c + d*x]),x]","-\frac{2 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x} \sqrt{a d-b c}}{b c-a d}\right)}{\sqrt{b} \sqrt{a d-b c}}","-\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*ArcTan[(Sqrt[b]*Sqrt[-(b*c) + a*d]*Sqrt[c + d*x])/(b*c - a*d)])/(Sqrt[b]*Sqrt[-(b*c) + a*d])","A",1
1420,1,87,76,0.1329101,"\int \frac{1}{(a+b x)^2 \sqrt{c+d x}} \, dx","IntegrateAlgebraic[1/((a + b*x)^2*Sqrt[c + d*x]),x]","-\frac{\sqrt{c+d x}}{(a+b x) (b c-a d)}-\frac{d \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x} \sqrt{a d-b c}}{b c-a d}\right)}{\sqrt{b} (a d-b c)^{3/2}}","\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*ArcTan[(Sqrt[b]*Sqrt[-(b*c) + a*d]*Sqrt[c + d*x])/(b*c - a*d)])/(Sqrt[b]*(-(b*c) + a*d)^(3/2))","A",1
1421,1,107,114,0.1838737,"\int \frac{1}{(a+b x)^3 \sqrt{c+d x}} \, dx","IntegrateAlgebraic[1/((a + b*x)^3*Sqrt[c + d*x]),x]","\frac{\sqrt{c+d x} (5 a d-2 b c+3 b d x)}{4 (a+b x)^2 (b c-a d)^2}-\frac{3 d^2 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x} \sqrt{a d-b c}}{b c-a d}\right)}{4 \sqrt{b} (a d-b c)^{5/2}}","-\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 + 5*a*d + 3*b*d*x))/(4*(b*c - a*d)^2*(a + b*x)^2) - (3*d^2*ArcTan[(Sqrt[b]*Sqrt[-(b*c) + a*d]*Sqrt[c + d*x])/(b*c - a*d)])/(4*Sqrt[b]*(-(b*c) + a*d)^(5/2))","A",1
1422,1,153,147,0.2274625,"\int \frac{1}{(a+b x)^4 \sqrt{c+d x}} \, dx","IntegrateAlgebraic[1/((a + b*x)^4*Sqrt[c + d*x]),x]","\frac{\sqrt{c+d x} \left(-33 a^2 d^2+26 a b c d-40 a b d^2 x-8 b^2 c^2+10 b^2 c d x-15 b^2 d^2 x^2\right)}{24 (a+b x)^3 (b c-a d)^3}+\frac{5 d^3 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x} \sqrt{a d-b c}}{b c-a d}\right)}{8 \sqrt{b} (b c-a d)^3 \sqrt{a d-b c}}","\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^2 \sqrt{c+d x}}{8 (a+b x) (b c-a d)^3}+\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]*(-8*b^2*c^2 + 26*a*b*c*d - 33*a^2*d^2 + 10*b^2*c*d*x - 40*a*b*d^2*x - 15*b^2*d^2*x^2))/(24*(b*c - a*d)^3*(a + b*x)^3) + (5*d^3*ArcTan[(Sqrt[b]*Sqrt[-(b*c) + a*d]*Sqrt[c + d*x])/(b*c - a*d)])/(8*Sqrt[b]*(b*c - a*d)^3*Sqrt[-(b*c) + a*d])","A",1
1423,1,196,180,0.4124066,"\int \frac{1}{(a+b x)^5 \sqrt{c+d x}} \, dx","IntegrateAlgebraic[1/((a + b*x)^5*Sqrt[c + d*x]),x]","\frac{\sqrt{c+d x} \left(279 a^3 d^3-326 a^2 b c d^2+511 a^2 b d^3 x+200 a b^2 c^2 d-252 a b^2 c d^2 x+385 a b^2 d^3 x^2-48 b^3 c^3+56 b^3 c^2 d x-70 b^3 c d^2 x^2+105 b^3 d^3 x^3\right)}{192 (a+b x)^4 (b c-a d)^4}-\frac{35 d^4 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x} \sqrt{a d-b c}}{b c-a d}\right)}{64 \sqrt{b} (a d-b c)^{9/2}}","-\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{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{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]*(-48*b^3*c^3 + 200*a*b^2*c^2*d - 326*a^2*b*c*d^2 + 279*a^3*d^3 + 56*b^3*c^2*d*x - 252*a*b^2*c*d^2*x + 511*a^2*b*d^3*x - 70*b^3*c*d^2*x^2 + 385*a*b^2*d^3*x^2 + 105*b^3*d^3*x^3))/(192*(b*c - a*d)^4*(a + b*x)^4) - (35*d^4*ArcTan[(Sqrt[b]*Sqrt[-(b*c) + a*d]*Sqrt[c + d*x])/(b*c - a*d)])/(64*Sqrt[b]*(-(b*c) + a*d)^(9/2))","A",1
1424,1,276,152,0.0868222,"\int \frac{(a+b x)^5}{(c+d x)^{3/2}} \, dx","IntegrateAlgebraic[(a + b*x)^5/(c + d*x)^(3/2),x]","\frac{2 \left(-63 a^5 d^5+630 a^4 b c d^4+315 a^4 b d^5 x-1680 a^3 b^2 c^2 d^3-840 a^3 b^2 c d^4 x+210 a^3 b^2 d^5 x^2+2016 a^2 b^3 c^3 d^2+1008 a^2 b^3 c^2 d^3 x-252 a^2 b^3 c d^4 x^2+126 a^2 b^3 d^5 x^3-1152 a b^4 c^4 d-576 a b^4 c^3 d^2 x+144 a b^4 c^2 d^3 x^2-72 a b^4 c d^4 x^3+45 a b^4 d^5 x^4+256 b^5 c^5+128 b^5 c^4 d x-32 b^5 c^3 d^2 x^2+16 b^5 c^2 d^3 x^3-10 b^5 c d^4 x^4+7 b^5 d^5 x^5\right)}{63 d^6 \sqrt{c+d 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}",1,"(2*(256*b^5*c^5 - 1152*a*b^4*c^4*d + 2016*a^2*b^3*c^3*d^2 - 1680*a^3*b^2*c^2*d^3 + 630*a^4*b*c*d^4 - 63*a^5*d^5 + 128*b^5*c^4*d*x - 576*a*b^4*c^3*d^2*x + 1008*a^2*b^3*c^2*d^3*x - 840*a^3*b^2*c*d^4*x + 315*a^4*b*d^5*x - 32*b^5*c^3*d^2*x^2 + 144*a*b^4*c^2*d^3*x^2 - 252*a^2*b^3*c*d^4*x^2 + 210*a^3*b^2*d^5*x^2 + 16*b^5*c^2*d^3*x^3 - 72*a*b^4*c*d^4*x^3 + 126*a^2*b^3*d^5*x^3 - 10*b^5*c*d^4*x^4 + 45*a*b^4*d^5*x^4 + 7*b^5*d^5*x^5))/(63*d^6*Sqrt[c + d*x])","A",1
1425,1,189,123,0.0758357,"\int \frac{(a+b x)^4}{(c+d x)^{3/2}} \, dx","IntegrateAlgebraic[(a + b*x)^4/(c + d*x)^(3/2),x]","-\frac{2 \left(35 a^4 d^4-280 a^3 b c d^3-140 a^3 b d^4 x+560 a^2 b^2 c^2 d^2+280 a^2 b^2 c d^3 x-70 a^2 b^2 d^4 x^2-448 a b^3 c^3 d-224 a b^3 c^2 d^2 x+56 a b^3 c d^3 x^2-28 a b^3 d^4 x^3+128 b^4 c^4+64 b^4 c^3 d x-16 b^4 c^2 d^2 x^2+8 b^4 c d^3 x^3-5 b^4 d^4 x^4\right)}{35 d^5 \sqrt{c+d 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}",1,"(-2*(128*b^4*c^4 - 448*a*b^3*c^3*d + 560*a^2*b^2*c^2*d^2 - 280*a^3*b*c*d^3 + 35*a^4*d^4 + 64*b^4*c^3*d*x - 224*a*b^3*c^2*d^2*x + 280*a^2*b^2*c*d^3*x - 140*a^3*b*d^4*x - 16*b^4*c^2*d^2*x^2 + 56*a*b^3*c*d^3*x^2 - 70*a^2*b^2*d^4*x^2 + 8*b^4*c*d^3*x^3 - 28*a*b^3*d^4*x^3 - 5*b^4*d^4*x^4))/(35*d^5*Sqrt[c + d*x])","A",1
1426,1,118,94,0.0479408,"\int \frac{(a+b x)^3}{(c+d x)^{3/2}} \, dx","IntegrateAlgebraic[(a + b*x)^3/(c + d*x)^(3/2),x]","\frac{2 \left(-5 a^3 d^3+30 a^2 b c d^2+15 a^2 b d^3 x-40 a b^2 c^2 d-20 a b^2 c d^2 x+5 a b^2 d^3 x^2+16 b^3 c^3+8 b^3 c^2 d x-2 b^3 c d^2 x^2+b^3 d^3 x^3\right)}{5 d^4 \sqrt{c+d 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}",1,"(2*(16*b^3*c^3 - 40*a*b^2*c^2*d + 30*a^2*b*c*d^2 - 5*a^3*d^3 + 8*b^3*c^2*d*x - 20*a*b^2*c*d^2*x + 15*a^2*b*d^3*x - 2*b^3*c*d^2*x^2 + 5*a*b^2*d^3*x^2 + b^3*d^3*x^3))/(5*d^4*Sqrt[c + d*x])","A",1
1427,1,66,67,0.0361676,"\int \frac{(a+b x)^2}{(c+d x)^{3/2}} \, dx","IntegrateAlgebraic[(a + b*x)^2/(c + d*x)^(3/2),x]","-\frac{2 \left(3 a^2 d^2-12 a b c d-6 a b d^2 x+8 b^2 c^2+4 b^2 c d x-b^2 d^2 x^2\right)}{3 d^3 \sqrt{c+d 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}",1,"(-2*(8*b^2*c^2 - 12*a*b*c*d + 3*a^2*d^2 + 4*b^2*c*d*x - 6*a*b*d^2*x - b^2*d^2*x^2))/(3*d^3*Sqrt[c + d*x])","A",1
1428,1,27,38,0.0195378,"\int \frac{a+b x}{(c+d x)^{3/2}} \, dx","IntegrateAlgebraic[(a + b*x)/(c + d*x)^(3/2),x]","\frac{2 (-a d+2 b c+b d x)}{d^2 \sqrt{c+d x}}","\frac{2 (b c-a d)}{d^2 \sqrt{c+d x}}+\frac{2 b \sqrt{c+d x}}{d^2}",1,"(2*(2*b*c - a*d + b*d*x))/(d^2*Sqrt[c + d*x])","A",1
1429,1,14,14,0.0066938,"\int \frac{1}{(c+d x)^{3/2}} \, dx","IntegrateAlgebraic[(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
1430,1,79,69,0.0845453,"\int \frac{1}{(a+b x) (c+d x)^{3/2}} \, dx","IntegrateAlgebraic[1/((a + b*x)*(c + d*x)^(3/2)),x]","\frac{2}{\sqrt{c+d x} (b c-a d)}+\frac{2 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x} \sqrt{a d-b c}}{b c-a d}\right)}{(a d-b c)^{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]*ArcTan[(Sqrt[b]*Sqrt[-(b*c) + a*d]*Sqrt[c + d*x])/(b*c - a*d)])/(-(b*c) + a*d)^(3/2)","A",1
1431,1,100,99,0.1525973,"\int \frac{1}{(a+b x)^2 (c+d x)^{3/2}} \, dx","IntegrateAlgebraic[1/((a + b*x)^2*(c + d*x)^(3/2)),x]","\frac{-2 a d-b c-3 b d x}{(a+b x) \sqrt{c+d x} (b c-a d)^2}+\frac{3 \sqrt{b} d \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x} \sqrt{a d-b c}}{b c-a d}\right)}{(a d-b c)^{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,"(-(b*c) - 2*a*d - 3*b*d*x)/((b*c - a*d)^2*(a + b*x)*Sqrt[c + d*x]) + (3*Sqrt[b]*d*ArcTan[(Sqrt[b]*Sqrt[-(b*c) + a*d]*Sqrt[c + d*x])/(b*c - a*d)])/(-(b*c) + a*d)^(5/2)","A",1
1432,1,143,140,0.2816342,"\int \frac{1}{(a+b x)^3 (c+d x)^{3/2}} \, dx","IntegrateAlgebraic[1/((a + b*x)^3*(c + d*x)^(3/2)),x]","\frac{8 a^2 d^2+9 a b c d+25 a b d^2 x-2 b^2 c^2+5 b^2 c d x+15 b^2 d^2 x^2}{4 (a+b x)^2 \sqrt{c+d x} (b c-a d)^3}+\frac{15 \sqrt{b} d^2 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x} \sqrt{a d-b c}}{b c-a d}\right)}{4 (a d-b c)^{7/2}}","\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,"(-2*b^2*c^2 + 9*a*b*c*d + 8*a^2*d^2 + 5*b^2*c*d*x + 25*a*b*d^2*x + 15*b^2*d^2*x^2)/(4*(b*c - a*d)^3*(a + b*x)^2*Sqrt[c + d*x]) + (15*Sqrt[b]*d^2*ArcTan[(Sqrt[b]*Sqrt[-(b*c) + a*d]*Sqrt[c + d*x])/(b*c - a*d)])/(4*(-(b*c) + a*d)^(7/2))","A",1
1433,1,196,173,0.5310639,"\int \frac{1}{(a+b x)^4 (c+d x)^{3/2}} \, dx","IntegrateAlgebraic[1/((a + b*x)^4*(c + d*x)^(3/2)),x]","\frac{-48 a^3 d^3-87 a^2 b c d^2-231 a^2 b d^3 x+38 a b^2 c^2 d-98 a b^2 c d^2 x-280 a b^2 d^3 x^2-8 b^3 c^3+14 b^3 c^2 d x-35 b^3 c d^2 x^2-105 b^3 d^3 x^3}{24 (a+b x)^3 \sqrt{c+d x} (b c-a d)^4}+\frac{35 \sqrt{b} d^3 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x} \sqrt{a d-b c}}{b c-a d}\right)}{8 (a d-b c)^{9/2}}","-\frac{35 d^3}{8 \sqrt{c+d x} (b c-a d)^4}+\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{35 d^2}{24 (a+b x) \sqrt{c+d x} (b c-a d)^3}+\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,"(-8*b^3*c^3 + 38*a*b^2*c^2*d - 87*a^2*b*c*d^2 - 48*a^3*d^3 + 14*b^3*c^2*d*x - 98*a*b^2*c*d^2*x - 231*a^2*b*d^3*x - 35*b^3*c*d^2*x^2 - 280*a*b^2*d^3*x^2 - 105*b^3*d^3*x^3)/(24*(b*c - a*d)^4*(a + b*x)^3*Sqrt[c + d*x]) + (35*Sqrt[b]*d^3*ArcTan[(Sqrt[b]*Sqrt[-(b*c) + a*d]*Sqrt[c + d*x])/(b*c - a*d)])/(8*(-(b*c) + a*d)^(9/2))","A",1
1434,1,276,152,0.0878181,"\int \frac{(a+b x)^5}{(c+d x)^{5/2}} \, dx","IntegrateAlgebraic[(a + b*x)^5/(c + d*x)^(5/2),x]","-\frac{2 \left(7 a^5 d^5+70 a^4 b c d^4+105 a^4 b d^5 x-560 a^3 b^2 c^2 d^3-840 a^3 b^2 c d^4 x-210 a^3 b^2 d^5 x^2+1120 a^2 b^3 c^3 d^2+1680 a^2 b^3 c^2 d^3 x+420 a^2 b^3 c d^4 x^2-70 a^2 b^3 d^5 x^3-896 a b^4 c^4 d-1344 a b^4 c^3 d^2 x-336 a b^4 c^2 d^3 x^2+56 a b^4 c d^4 x^3-21 a b^4 d^5 x^4+256 b^5 c^5+384 b^5 c^4 d x+96 b^5 c^3 d^2 x^2-16 b^5 c^2 d^3 x^3+6 b^5 c d^4 x^4-3 b^5 d^5 x^5\right)}{21 d^6 (c+d x)^{3/2}}","-\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*(256*b^5*c^5 - 896*a*b^4*c^4*d + 1120*a^2*b^3*c^3*d^2 - 560*a^3*b^2*c^2*d^3 + 70*a^4*b*c*d^4 + 7*a^5*d^5 + 384*b^5*c^4*d*x - 1344*a*b^4*c^3*d^2*x + 1680*a^2*b^3*c^2*d^3*x - 840*a^3*b^2*c*d^4*x + 105*a^4*b*d^5*x + 96*b^5*c^3*d^2*x^2 - 336*a*b^4*c^2*d^3*x^2 + 420*a^2*b^3*c*d^4*x^2 - 210*a^3*b^2*d^5*x^2 - 16*b^5*c^2*d^3*x^3 + 56*a*b^4*c*d^4*x^3 - 70*a^2*b^3*d^5*x^3 + 6*b^5*c*d^4*x^4 - 21*a*b^4*d^5*x^4 - 3*b^5*d^5*x^5))/(21*d^6*(c + d*x)^(3/2))","A",1
1435,1,189,125,0.0623614,"\int \frac{(a+b x)^4}{(c+d x)^{5/2}} \, dx","IntegrateAlgebraic[(a + b*x)^4/(c + d*x)^(5/2),x]","\frac{2 \left(-5 a^4 d^4-40 a^3 b c d^3-60 a^3 b d^4 x+240 a^2 b^2 c^2 d^2+360 a^2 b^2 c d^3 x+90 a^2 b^2 d^4 x^2-320 a b^3 c^3 d-480 a b^3 c^2 d^2 x-120 a b^3 c d^3 x^2+20 a b^3 d^4 x^3+128 b^4 c^4+192 b^4 c^3 d x+48 b^4 c^2 d^2 x^2-8 b^4 c d^3 x^3+3 b^4 d^4 x^4\right)}{15 d^5 (c+d x)^{3/2}}","-\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*(128*b^4*c^4 - 320*a*b^3*c^3*d + 240*a^2*b^2*c^2*d^2 - 40*a^3*b*c*d^3 - 5*a^4*d^4 + 192*b^4*c^3*d*x - 480*a*b^3*c^2*d^2*x + 360*a^2*b^2*c*d^3*x - 60*a^3*b*d^4*x + 48*b^4*c^2*d^2*x^2 - 120*a*b^3*c*d^3*x^2 + 90*a^2*b^2*d^4*x^2 - 8*b^4*c*d^3*x^3 + 20*a*b^3*d^4*x^3 + 3*b^4*d^4*x^4))/(15*d^5*(c + d*x)^(3/2))","A",1
1436,1,118,96,0.0483655,"\int \frac{(a+b x)^3}{(c+d x)^{5/2}} \, dx","IntegrateAlgebraic[(a + b*x)^3/(c + d*x)^(5/2),x]","-\frac{2 \left(a^3 d^3+6 a^2 b c d^2+9 a^2 b d^3 x-24 a b^2 c^2 d-36 a b^2 c d^2 x-9 a b^2 d^3 x^2+16 b^3 c^3+24 b^3 c^2 d x+6 b^3 c d^2 x^2-b^3 d^3 x^3\right)}{3 d^4 (c+d x)^{3/2}}","-\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*(16*b^3*c^3 - 24*a*b^2*c^2*d + 6*a^2*b*c*d^2 + a^3*d^3 + 24*b^3*c^2*d*x - 36*a*b^2*c*d^2*x + 9*a^2*b*d^3*x + 6*b^3*c*d^2*x^2 - 9*a*b^2*d^3*x^2 - b^3*d^3*x^3))/(3*d^4*(c + d*x)^(3/2))","A",1
1437,1,66,67,0.0385875,"\int \frac{(a+b x)^2}{(c+d x)^{5/2}} \, dx","IntegrateAlgebraic[(a + b*x)^2/(c + d*x)^(5/2),x]","\frac{2 \left(-a^2 d^2-4 a b c d-6 a b d^2 x+8 b^2 c^2+12 b^2 c d x+3 b^2 d^2 x^2\right)}{3 d^3 (c+d x)^{3/2}}","\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*(8*b^2*c^2 - 4*a*b*c*d - a^2*d^2 + 12*b^2*c*d*x - 6*a*b*d^2*x + 3*b^2*d^2*x^2))/(3*d^3*(c + d*x)^(3/2))","A",1
1438,1,29,40,0.0213947,"\int \frac{a+b x}{(c+d x)^{5/2}} \, dx","IntegrateAlgebraic[(a + b*x)/(c + d*x)^(5/2),x]","-\frac{2 (a d+2 b c+3 b d x)}{3 d^2 (c+d x)^{3/2}}","\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*(2*b*c + a*d + 3*b*d*x))/(3*d^2*(c + d*x)^(3/2))","A",1
1439,1,16,16,0.0061434,"\int \frac{1}{(c+d x)^{5/2}} \, dx","IntegrateAlgebraic[(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
1440,1,95,93,0.1441271,"\int \frac{1}{(a+b x) (c+d x)^{5/2}} \, dx","IntegrateAlgebraic[1/((a + b*x)*(c + d*x)^(5/2)),x]","\frac{2 (-a d+4 b c+3 b d x)}{3 (c+d x)^{3/2} (b c-a d)^2}-\frac{2 b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x} \sqrt{a d-b c}}{b c-a d}\right)}{(a d-b c)^{5/2}}","-\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*(4*b*c - a*d + 3*b*d*x))/(3*(b*c - a*d)^2*(c + d*x)^(3/2)) - (2*b^(3/2)*ArcTan[(Sqrt[b]*Sqrt[-(b*c) + a*d]*Sqrt[c + d*x])/(b*c - a*d)])/(-(b*c) + a*d)^(5/2)","A",1
1441,1,139,124,0.2547794,"\int \frac{1}{(a+b x)^2 (c+d x)^{5/2}} \, dx","IntegrateAlgebraic[1/((a + b*x)^2*(c + d*x)^(5/2)),x]","\frac{2 a^2 d^2-14 a b c d-10 a b d^2 x-3 b^2 c^2-20 b^2 c d x-15 b^2 d^2 x^2}{3 (a+b x) (c+d x)^{3/2} (b c-a d)^3}-\frac{5 b^{3/2} d \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x} \sqrt{a d-b c}}{b c-a d}\right)}{(a d-b c)^{7/2}}","\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,"(-3*b^2*c^2 - 14*a*b*c*d + 2*a^2*d^2 - 20*b^2*c*d*x - 10*a*b*d^2*x - 15*b^2*d^2*x^2)/(3*(b*c - a*d)^3*(a + b*x)*(c + d*x)^(3/2)) - (5*b^(3/2)*d*ArcTan[(Sqrt[b]*Sqrt[-(b*c) + a*d]*Sqrt[c + d*x])/(b*c - a*d)])/(-(b*c) + a*d)^(7/2)","A",1
1442,1,196,167,0.4275307,"\int \frac{1}{(a+b x)^3 (c+d x)^{5/2}} \, dx","IntegrateAlgebraic[1/((a + b*x)^3*(c + d*x)^(5/2)),x]","\frac{-8 a^3 d^3+80 a^2 b c d^2+56 a^2 b d^3 x+39 a b^2 c^2 d+238 a b^2 c d^2 x+175 a b^2 d^3 x^2-6 b^3 c^3+21 b^3 c^2 d x+140 b^3 c d^2 x^2+105 b^3 d^3 x^3}{12 (a+b x)^2 (c+d x)^{3/2} (b c-a d)^4}-\frac{35 b^{3/2} d^2 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x} \sqrt{a d-b c}}{b c-a d}\right)}{4 (a d-b c)^{9/2}}","-\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,"(-6*b^3*c^3 + 39*a*b^2*c^2*d + 80*a^2*b*c*d^2 - 8*a^3*d^3 + 21*b^3*c^2*d*x + 238*a*b^2*c*d^2*x + 56*a^2*b*d^3*x + 140*b^3*c*d^2*x^2 + 175*a*b^2*d^3*x^2 + 105*b^3*d^3*x^3)/(12*(b*c - a*d)^4*(a + b*x)^2*(c + d*x)^(3/2)) - (35*b^(3/2)*d^2*ArcTan[(Sqrt[b]*Sqrt[-(b*c) + a*d]*Sqrt[c + d*x])/(b*c - a*d)])/(4*(-(b*c) + a*d)^(9/2))","A",1
1443,1,266,200,0.6385834,"\int \frac{1}{(a+b x)^4 (c+d x)^{5/2}} \, dx","IntegrateAlgebraic[1/((a + b*x)^4*(c + d*x)^(5/2)),x]","\frac{16 a^4 d^4-208 a^3 b c d^3-144 a^3 b d^4 x-165 a^2 b^2 c^2 d^2-954 a^2 b^2 c d^3 x-693 a^2 b^2 d^4 x^2+50 a b^3 c^3 d-180 a b^3 c^2 d^2 x-1134 a b^3 c d^3 x^2-840 a b^3 d^4 x^3-8 b^4 c^4+18 b^4 c^3 d x-63 b^4 c^2 d^2 x^2-420 b^4 c d^3 x^3-315 b^4 d^4 x^4}{24 (a+b x)^3 (c+d x)^{3/2} (b c-a d)^5}-\frac{105 b^{3/2} d^3 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x} \sqrt{a d-b c}}{b c-a d}\right)}{8 (a d-b c)^{11/2}}","\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,"(-8*b^4*c^4 + 50*a*b^3*c^3*d - 165*a^2*b^2*c^2*d^2 - 208*a^3*b*c*d^3 + 16*a^4*d^4 + 18*b^4*c^3*d*x - 180*a*b^3*c^2*d^2*x - 954*a^2*b^2*c*d^3*x - 144*a^3*b*d^4*x - 63*b^4*c^2*d^2*x^2 - 1134*a*b^3*c*d^3*x^2 - 693*a^2*b^2*d^4*x^2 - 420*b^4*c*d^3*x^3 - 840*a*b^3*d^4*x^3 - 315*b^4*d^4*x^4)/(24*(b*c - a*d)^5*(a + b*x)^3*(c + d*x)^(3/2)) - (105*b^(3/2)*d^3*ArcTan[(Sqrt[b]*Sqrt[-(b*c) + a*d]*Sqrt[c + d*x])/(b*c - a*d)])/(8*(-(b*c) + a*d)^(11/2))","A",1
1444,1,22,22,0.009417,"\int (a+b x)^5 (a c+b c x)^{3/2} \, dx","IntegrateAlgebraic[(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",1
1445,1,22,22,0.0084005,"\int (a+b x)^5 \sqrt{a c+b c x} \, dx","IntegrateAlgebraic[(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",1
1446,1,22,22,0.0088476,"\int \frac{(a+b x)^5}{\sqrt{a c+b c x}} \, dx","IntegrateAlgebraic[(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",1
1447,1,22,22,0.009062,"\int \frac{(a+b x)^5}{(a c+b c x)^{3/2}} \, dx","IntegrateAlgebraic[(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",1
1448,1,22,22,0.0096562,"\int \frac{(a+b x)^5}{(a c+b c x)^{5/2}} \, dx","IntegrateAlgebraic[(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",1
1449,1,22,22,0.0091773,"\int \frac{(a+b x)^5}{(a c+b c x)^{7/2}} \, dx","IntegrateAlgebraic[(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",1
1450,1,22,22,0.0089196,"\int \frac{(a+b x)^5}{(a c+b c x)^{9/2}} \, dx","IntegrateAlgebraic[(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",1
1451,1,20,20,0.0083441,"\int \frac{(a+b x)^5}{(a c+b c x)^{11/2}} \, dx","IntegrateAlgebraic[(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",1
1452,1,27,20,0.0113442,"\int \frac{(a+b x)^5}{(a c+b c x)^{13/2}} \, dx","IntegrateAlgebraic[(a + b*x)^5/(a*c + b*c*x)^(13/2),x]","-\frac{2 \sqrt{a c+b c x}}{b c^7 (a+b x)}","-\frac{2}{b c^6 \sqrt{a c+b c x}}",1,"(-2*Sqrt[a*c + b*c*x])/(b*c^7*(a + b*x))","A",1
1453,1,14,14,0.0110134,"\int \frac{1}{(-2+x) \sqrt{2+x}} \, dx","IntegrateAlgebraic[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",1
1454,1,25,25,0.0199233,"\int \frac{1}{(2+3 x) \sqrt{1+5 x}} \, dx","IntegrateAlgebraic[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",1
1455,1,115,84,0.1057278,"\int \frac{\sqrt[3]{1-x}}{1+x} \, dx","IntegrateAlgebraic[(1 - x)^(1/3)/(1 + x),x]","3 \sqrt[3]{1-x}+\sqrt[3]{2} \log \left(2^{2/3} \sqrt[3]{1-x}-2\right)-\frac{\log \left(\sqrt[3]{2} (1-x)^{2/3}+2^{2/3} \sqrt[3]{1-x}+2\right)}{2^{2/3}}-\sqrt[3]{2} \sqrt{3} \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{1-x}}{\sqrt{3}}+\frac{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/Sqrt[3] + (2^(2/3)*(1 - x)^(1/3))/Sqrt[3]] + 2^(1/3)*Log[-2 + 2^(2/3)*(1 - x)^(1/3)] - Log[2 + 2^(2/3)*(1 - x)^(1/3) + 2^(1/3)*(1 - x)^(2/3)]/2^(2/3)","A",1
1456,1,23,27,0.0073361,"\int \sqrt[3]{3-2 x} (7+x) \, dx","IntegrateAlgebraic[(3 - 2*x)^(1/3)*(7 + x),x]","\frac{3}{112} \sqrt[3]{3-2 x} \left(16 x^2+190 x-321\right)","\frac{3}{28} (3-2 x)^{7/3}-\frac{51}{16} (3-2 x)^{4/3}",1,"(3*(3 - 2*x)^(1/3)*(-321 + 190*x + 16*x^2))/112","A",1
1457,1,28,38,0.0081122,"\int \sqrt[3]{1-x} (1+x)^2 \, dx","IntegrateAlgebraic[(1 - x)^(1/3)*(1 + x)^2,x]","\frac{3}{70} \sqrt[3]{1-x} \left(7 x^3+19 x^2+11 x-37\right)","-\frac{3}{10} (1-x)^{10/3}+\frac{12}{7} (1-x)^{7/3}-3 (1-x)^{4/3}",1,"(3*(1 - x)^(1/3)*(-37 + 11*x + 19*x^2 + 7*x^3))/70","A",1
1458,1,191,139,0.1956994,"\int \frac{1}{(a+b x) \sqrt[3]{c+d x}} \, dx","IntegrateAlgebraic[1/((a + b*x)*(c + d*x)^(1/3)),x]","-\frac{\log \left(\sqrt[3]{a d-b c}+\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{b^{2/3} \sqrt[3]{a d-b c}}+\frac{\log \left(-\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{a d-b c}+(a d-b c)^{2/3}+b^{2/3} (c+d x)^{2/3}\right)}{2 b^{2/3} \sqrt[3]{a d-b c}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt{3} \sqrt[3]{a d-b c}}\right)}{b^{2/3} \sqrt[3]{a d-b c}}","-\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/Sqrt[3] - (2*b^(1/3)*(c + d*x)^(1/3))/(Sqrt[3]*(-(b*c) + a*d)^(1/3))])/(b^(2/3)*(-(b*c) + a*d)^(1/3))) - Log[(-(b*c) + a*d)^(1/3) + b^(1/3)*(c + d*x)^(1/3)]/(b^(2/3)*(-(b*c) + a*d)^(1/3)) + Log[(-(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)]/(2*b^(2/3)*(-(b*c) + a*d)^(1/3))","A",1
1459,1,190,140,0.1356021,"\int \frac{1}{(a+b x) (c+d x)^{2/3}} \, dx","IntegrateAlgebraic[1/((a + b*x)*(c + d*x)^(2/3)),x]","-\frac{\log \left(-\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{a d-b c}+(a d-b c)^{2/3}+b^{2/3} (c+d x)^{2/3}\right)}{2 \sqrt[3]{b} (a d-b c)^{2/3}}+\frac{\log \left(\sqrt[3]{a d-b c}+\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\sqrt[3]{b} (a d-b c)^{2/3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt{3} \sqrt[3]{a d-b c}}\right)}{\sqrt[3]{b} (a d-b c)^{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/Sqrt[3] - (2*b^(1/3)*(c + d*x)^(1/3))/(Sqrt[3]*(-(b*c) + a*d)^(1/3))])/(b^(1/3)*(-(b*c) + a*d)^(2/3))) + Log[(-(b*c) + a*d)^(1/3) + b^(1/3)*(c + d*x)^(1/3)]/(b^(1/3)*(-(b*c) + a*d)^(2/3)) - Log[(-(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)]/(2*b^(1/3)*(-(b*c) + a*d)^(2/3))","A",1
1460,-1,0,230,180.017265,"\int (a+b x)^{7/2} \sqrt{c+d x} \, dx","IntegrateAlgebraic[(a + b*x)^(7/2)*Sqrt[c + d*x],x]","\text{\$Aborted}","\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,"$Aborted","F",-1
1461,-1,0,192,180.0160254,"\int (a+b x)^{5/2} \sqrt{c+d x} \, dx","IntegrateAlgebraic[(a + b*x)^(5/2)*Sqrt[c + d*x],x]","\text{\$Aborted}","-\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,"$Aborted","F",-1
1462,1,9697,154,117.0678272,"\int (a+b x)^{3/2} \sqrt{c+d x} \, dx","IntegrateAlgebraic[(a + b*x)^(3/2)*Sqrt[c + d*x],x]","\text{Result too large to show}","\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,"Result too large to show","B",0
1463,1,1506,116,5.1990883,"\int \sqrt{a+b x} \sqrt{c+d x} \, dx","IntegrateAlgebraic[Sqrt[a + b*x]*Sqrt[c + d*x],x]","\frac{\left(\frac{\sqrt{a+b}}{4 b d}-\frac{\sqrt{a+b x}}{4 b d}\right) \left(\sqrt{c+d}-\sqrt{c+d x}\right) \left(c b+d b+d x b-\sqrt{c+d} \sqrt{c+d x} b+a d-\sqrt{a+b} d \sqrt{a+b x}\right) \left(2 c^4 b^4+2 c^2 d^2 b^4+16 d^4 x^2 b^4+16 c d^3 x^2 b^4+2 c^2 d^2 x^2 b^4+5 c^3 d b^4+16 c d^3 x b^4+22 c^2 d^2 x b^4+5 c^3 d x b^4-16 c d^2 \sqrt{c+d} x \sqrt{c+d x} b^4-4 c^2 d \sqrt{c+d} x \sqrt{c+d x} b^4-2 c^3 \sqrt{c+d} \sqrt{c+d x} b^4-4 c^2 d \sqrt{c+d} \sqrt{c+d x} b^4+12 a c d^3 b^3+11 a c^2 d^2 b^3+16 a d^4 x^2 b^3+12 a c d^3 x^2 b^3+2 a c^3 d b^3+16 a d^4 x b^3+20 a c d^3 x b^3+11 a c^2 d^2 x b^3+12 \sqrt{a+b} c^2 d^2 \sqrt{a+b x} b^3+10 \sqrt{a+b} c^3 d \sqrt{a+b x} b^3+16 \sqrt{a+b} c d^3 x \sqrt{a+b x} b^3+12 \sqrt{a+b} c^2 d^2 x \sqrt{a+b x} b^3+16 a d^3 \sqrt{c+d} x \sqrt{c+d x} b^3-8 a c d^2 \sqrt{c+d} x \sqrt{c+d x} b^3-8 a c d^2 \sqrt{c+d} \sqrt{c+d x} b^3-2 a c^2 d \sqrt{c+d} \sqrt{c+d x} b^3-16 \sqrt{a+b} d^3 \sqrt{c+d} x \sqrt{a+b x} \sqrt{c+d x} b^3-8 \sqrt{a+b} c d^2 \sqrt{c+d} x \sqrt{a+b x} \sqrt{c+d x} b^3-8 \sqrt{a+b} c d^2 \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x} b^3-10 \sqrt{a+b} c^2 d \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x} b^3+2 a^2 d^4 b^2+11 a^2 c d^3 b^2+8 a^2 c^2 d^2 b^2+2 a^2 d^4 x^2 b^2+22 a^2 d^4 x b^2+11 a^2 c d^3 x b^2-8 a \sqrt{a+b} c d^3 \sqrt{a+b x} b^2-6 a \sqrt{a+b} c^2 d^2 \sqrt{a+b x} b^2-16 a \sqrt{a+b} d^4 x \sqrt{a+b x} b^2-8 a \sqrt{a+b} c d^3 x \sqrt{a+b x} b^2+12 a^2 d^3 \sqrt{c+d} x \sqrt{c+d x} b^2+12 a^2 d^3 \sqrt{c+d} \sqrt{c+d x} b^2-6 a^2 c d^2 \sqrt{c+d} \sqrt{c+d x} b^2-8 a \sqrt{a+b} d^3 \sqrt{c+d} x \sqrt{a+b x} \sqrt{c+d x} b^2-8 a \sqrt{a+b} d^3 \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x} b^2+4 a \sqrt{a+b} c d^2 \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x} b^2+5 a^3 d^4 b+2 a^3 c d^3 b+5 a^3 d^4 x b-4 a^2 \sqrt{a+b} d^4 \sqrt{a+b x} b-2 a^2 \sqrt{a+b} c d^3 \sqrt{a+b x} b-4 a^2 \sqrt{a+b} d^4 x \sqrt{a+b x} b+10 a^3 d^3 \sqrt{c+d} \sqrt{c+d x} b-10 a^2 \sqrt{a+b} d^3 \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x} b+2 a^4 d^4-2 a^3 \sqrt{a+b} d^4 \sqrt{a+b x}\right)}{\left(-c b+\sqrt{c+d} \sqrt{c+d x} b+a d-\sqrt{a+b} d \sqrt{a+b x}\right)^4}-\frac{(b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d}-\sqrt{b} \sqrt{c+d x}}{\sqrt{a+b} \sqrt{d}-\sqrt{d} \sqrt{a+b x}}\right)}{2 b^{3/2} d^{3/2}}","-\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,"((Sqrt[a + b]/(4*b*d) - Sqrt[a + b*x]/(4*b*d))*(Sqrt[c + d] - Sqrt[c + d*x])*(b*c + a*d + b*d + b*d*x - Sqrt[a + b]*d*Sqrt[a + b*x] - b*Sqrt[c + d]*Sqrt[c + d*x])*(2*b^4*c^4 + 2*a*b^3*c^3*d + 5*b^4*c^3*d + 8*a^2*b^2*c^2*d^2 + 11*a*b^3*c^2*d^2 + 2*b^4*c^2*d^2 + 2*a^3*b*c*d^3 + 11*a^2*b^2*c*d^3 + 12*a*b^3*c*d^3 + 2*a^4*d^4 + 5*a^3*b*d^4 + 2*a^2*b^2*d^4 + 5*b^4*c^3*d*x + 11*a*b^3*c^2*d^2*x + 22*b^4*c^2*d^2*x + 11*a^2*b^2*c*d^3*x + 20*a*b^3*c*d^3*x + 16*b^4*c*d^3*x + 5*a^3*b*d^4*x + 22*a^2*b^2*d^4*x + 16*a*b^3*d^4*x + 2*b^4*c^2*d^2*x^2 + 12*a*b^3*c*d^3*x^2 + 16*b^4*c*d^3*x^2 + 2*a^2*b^2*d^4*x^2 + 16*a*b^3*d^4*x^2 + 16*b^4*d^4*x^2 + 10*b^3*Sqrt[a + b]*c^3*d*Sqrt[a + b*x] - 6*a*b^2*Sqrt[a + b]*c^2*d^2*Sqrt[a + b*x] + 12*b^3*Sqrt[a + b]*c^2*d^2*Sqrt[a + b*x] - 2*a^2*b*Sqrt[a + b]*c*d^3*Sqrt[a + b*x] - 8*a*b^2*Sqrt[a + b]*c*d^3*Sqrt[a + b*x] - 2*a^3*Sqrt[a + b]*d^4*Sqrt[a + b*x] - 4*a^2*b*Sqrt[a + b]*d^4*Sqrt[a + b*x] + 12*b^3*Sqrt[a + b]*c^2*d^2*x*Sqrt[a + b*x] - 8*a*b^2*Sqrt[a + b]*c*d^3*x*Sqrt[a + b*x] + 16*b^3*Sqrt[a + b]*c*d^3*x*Sqrt[a + b*x] - 4*a^2*b*Sqrt[a + b]*d^4*x*Sqrt[a + b*x] - 16*a*b^2*Sqrt[a + b]*d^4*x*Sqrt[a + b*x] - 2*b^4*c^3*Sqrt[c + d]*Sqrt[c + d*x] - 2*a*b^3*c^2*d*Sqrt[c + d]*Sqrt[c + d*x] - 4*b^4*c^2*d*Sqrt[c + d]*Sqrt[c + d*x] - 6*a^2*b^2*c*d^2*Sqrt[c + d]*Sqrt[c + d*x] - 8*a*b^3*c*d^2*Sqrt[c + d]*Sqrt[c + d*x] + 10*a^3*b*d^3*Sqrt[c + d]*Sqrt[c + d*x] + 12*a^2*b^2*d^3*Sqrt[c + d]*Sqrt[c + d*x] - 4*b^4*c^2*d*Sqrt[c + d]*x*Sqrt[c + d*x] - 8*a*b^3*c*d^2*Sqrt[c + d]*x*Sqrt[c + d*x] - 16*b^4*c*d^2*Sqrt[c + d]*x*Sqrt[c + d*x] + 12*a^2*b^2*d^3*Sqrt[c + d]*x*Sqrt[c + d*x] + 16*a*b^3*d^3*Sqrt[c + d]*x*Sqrt[c + d*x] - 10*b^3*Sqrt[a + b]*c^2*d*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 4*a*b^2*Sqrt[a + b]*c*d^2*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] - 8*b^3*Sqrt[a + b]*c*d^2*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] - 10*a^2*b*Sqrt[a + b]*d^3*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] - 8*a*b^2*Sqrt[a + b]*d^3*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] - 8*b^3*Sqrt[a + b]*c*d^2*Sqrt[c + d]*x*Sqrt[a + b*x]*Sqrt[c + d*x] - 8*a*b^2*Sqrt[a + b]*d^3*Sqrt[c + d]*x*Sqrt[a + b*x]*Sqrt[c + d*x] - 16*b^3*Sqrt[a + b]*d^3*Sqrt[c + d]*x*Sqrt[a + b*x]*Sqrt[c + d*x]))/(-(b*c) + a*d - Sqrt[a + b]*d*Sqrt[a + b*x] + b*Sqrt[c + d]*Sqrt[c + d*x])^4 - ((b*c - a*d)^2*ArcTanh[(Sqrt[b]*Sqrt[c + d] - Sqrt[b]*Sqrt[c + d*x])/(Sqrt[a + b]*Sqrt[d] - Sqrt[d]*Sqrt[a + b*x])])/(2*b^(3/2)*d^(3/2))","B",1
1464,1,350,72,0.7583262,"\int \frac{\sqrt{c+d x}}{\sqrt{a+b x}} \, dx","IntegrateAlgebraic[Sqrt[c + d*x]/Sqrt[a + b*x],x]","\frac{\left(\frac{\sqrt{a+b}}{b}-\frac{\sqrt{a+b x}}{b}\right) \left(\sqrt{c+d}-\sqrt{c+d x}\right) \left(a^2 d^2+b c d \sqrt{a+b} \sqrt{a+b x}+a b d \sqrt{c+d} \sqrt{c+d x}-2 b d \sqrt{a+b} \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x}+a b d^2 x-a d^2 \sqrt{a+b} \sqrt{a+b x}+a b d^2+b^2 c^2+b^2 c d x-b^2 c \sqrt{c+d} \sqrt{c+d x}+b^2 c d+2 b^2 d^2 x\right)}{\left(-d \sqrt{a+b} \sqrt{a+b x}+a d+b \sqrt{c+d} \sqrt{c+d x}+b (-c)\right)^2}+\left(\frac{2 c}{\sqrt{b} \sqrt{d}}-\frac{2 a \sqrt{d}}{b^{3/2}}\right) \tanh ^{-1}\left(\frac{\sqrt{b} \left(\sqrt{c+d}-\sqrt{c+d x}\right)}{\sqrt{d} \sqrt{a+b}-\sqrt{d} \sqrt{a+b x}}\right)","\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]/b - Sqrt[a + b*x]/b)*(Sqrt[c + d] - Sqrt[c + d*x])*(b^2*c^2 + b^2*c*d + a^2*d^2 + a*b*d^2 + b^2*c*d*x + a*b*d^2*x + 2*b^2*d^2*x + b*Sqrt[a + b]*c*d*Sqrt[a + b*x] - a*Sqrt[a + b]*d^2*Sqrt[a + b*x] - b^2*c*Sqrt[c + d]*Sqrt[c + d*x] + a*b*d*Sqrt[c + d]*Sqrt[c + d*x] - 2*b*Sqrt[a + b]*d*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x]))/(-(b*c) + a*d - Sqrt[a + b]*d*Sqrt[a + b*x] + b*Sqrt[c + d]*Sqrt[c + d*x])^2 + ((2*c)/(Sqrt[b]*Sqrt[d]) - (2*a*Sqrt[d])/b^(3/2))*ArcTanh[(Sqrt[b]*(Sqrt[c + d] - Sqrt[c + d*x]))/(Sqrt[a + b]*Sqrt[d] - Sqrt[d]*Sqrt[a + b*x])]","B",1
1465,1,834,66,8.6912556,"\int \frac{\sqrt{c+d x}}{(a+b x)^{3/2}} \, dx","IntegrateAlgebraic[Sqrt[c + d*x]/(a + b*x)^(3/2),x]","\frac{\left(-\frac{2 \sqrt{a+b x} c}{a+b}+\frac{2 c}{\sqrt{a+b}}-\frac{2 a d}{b \sqrt{a+b}}+\frac{2 a d \sqrt{a+b x}}{b (a+b)}\right) \left(\sqrt{c+d}-\sqrt{c+d x}\right) \left(-d a^2-2 b c a-3 b d a-b d x a+\sqrt{a+b} d \sqrt{a+b x} a+2 b \sqrt{c+d} \sqrt{c+d x} a-2 b^2 c-2 b^2 d-b^2 d x+b \sqrt{a+b} c \sqrt{a+b x}+2 b \sqrt{a+b} d \sqrt{a+b x}+2 b^2 \sqrt{c+d} \sqrt{c+d x}-b \sqrt{a+b} \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x}\right)}{-2 d^2 a^3-5 b d^2 a^2-2 b c d a^2-3 b d^2 x a^2+2 \sqrt{a+b} d^2 \sqrt{a+b x} a^2+2 b d \sqrt{c+d} \sqrt{c+d x} a^2+2 b^2 c^2 a-2 b^2 d^2 a-b^2 d^2 x^2 a+b^2 c d a-5 b^2 d^2 x a-b^2 c d x a+4 b \sqrt{a+b} d^2 \sqrt{a+b x} a+2 b \sqrt{a+b} c d \sqrt{a+b x} a+2 b \sqrt{a+b} d^2 x \sqrt{a+b x} a+2 b^2 d \sqrt{c+d} x \sqrt{c+d x} a-2 b^2 c \sqrt{c+d} \sqrt{c+d x} a-2 b \sqrt{a+b} d \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x} a+b^3 c d x^2+2 b^3 c^2 x-2 b^3 d^2 x+b^3 c d x-4 b^2 \sqrt{a+b} c^2 \sqrt{a+b x}-4 b^2 \sqrt{a+b} c d \sqrt{a+b x}-2 b^2 \sqrt{a+b} c d x \sqrt{a+b x}-2 b^3 c \sqrt{c+d} x \sqrt{c+d x}+4 b^2 \sqrt{a+b} c \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x}+2 b^2 \sqrt{a+b} d \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x}}+\frac{4 \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d}-\sqrt{b} \sqrt{c+d x}}{\sqrt{a+b} \sqrt{d}-\sqrt{d} \sqrt{a+b x}}\right)}{b^{3/2}}","\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*c)/Sqrt[a + b] - (2*a*d)/(b*Sqrt[a + b]) - (2*c*Sqrt[a + b*x])/(a + b) + (2*a*d*Sqrt[a + b*x])/(b*(a + b)))*(Sqrt[c + d] - Sqrt[c + d*x])*(-2*a*b*c - 2*b^2*c - a^2*d - 3*a*b*d - 2*b^2*d - a*b*d*x - b^2*d*x + b*Sqrt[a + b]*c*Sqrt[a + b*x] + a*Sqrt[a + b]*d*Sqrt[a + b*x] + 2*b*Sqrt[a + b]*d*Sqrt[a + b*x] + 2*a*b*Sqrt[c + d]*Sqrt[c + d*x] + 2*b^2*Sqrt[c + d]*Sqrt[c + d*x] - b*Sqrt[a + b]*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x]))/(2*a*b^2*c^2 - 2*a^2*b*c*d + a*b^2*c*d - 2*a^3*d^2 - 5*a^2*b*d^2 - 2*a*b^2*d^2 + 2*b^3*c^2*x - a*b^2*c*d*x + b^3*c*d*x - 3*a^2*b*d^2*x - 5*a*b^2*d^2*x - 2*b^3*d^2*x + b^3*c*d*x^2 - a*b^2*d^2*x^2 - 4*b^2*Sqrt[a + b]*c^2*Sqrt[a + b*x] + 2*a*b*Sqrt[a + b]*c*d*Sqrt[a + b*x] - 4*b^2*Sqrt[a + b]*c*d*Sqrt[a + b*x] + 2*a^2*Sqrt[a + b]*d^2*Sqrt[a + b*x] + 4*a*b*Sqrt[a + b]*d^2*Sqrt[a + b*x] - 2*b^2*Sqrt[a + b]*c*d*x*Sqrt[a + b*x] + 2*a*b*Sqrt[a + b]*d^2*x*Sqrt[a + b*x] - 2*a*b^2*c*Sqrt[c + d]*Sqrt[c + d*x] + 2*a^2*b*d*Sqrt[c + d]*Sqrt[c + d*x] - 2*b^3*c*Sqrt[c + d]*x*Sqrt[c + d*x] + 2*a*b^2*d*Sqrt[c + d]*x*Sqrt[c + d*x] + 4*b^2*Sqrt[a + b]*c*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] - 2*a*b*Sqrt[a + b]*d*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 2*b^2*Sqrt[a + b]*d*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x]) + (4*Sqrt[d]*ArcTanh[(Sqrt[b]*Sqrt[c + d] - Sqrt[b]*Sqrt[c + d*x])/(Sqrt[a + b]*Sqrt[d] - Sqrt[d]*Sqrt[a + b*x])])/b^(3/2)","B",1
1466,1,1644,32,4.1175271,"\int \frac{\sqrt{c+d x}}{(a+b x)^{5/2}} \, dx","IntegrateAlgebraic[Sqrt[c + d*x]/(a + b*x)^(5/2),x]","\frac{\left(\frac{1}{6 (a+b)}-\frac{\sqrt{a+b x}}{6 (a+b)^{3/2}}\right) \left(\sqrt{c+d}-\sqrt{c+d x}\right)^6 \left(\frac{4 a^2 d^2 \left(\sqrt{a+b}-\sqrt{a+b x}\right)^2}{\left(\sqrt{c+d}-\sqrt{c+d x}\right)^2}-\frac{4 a \left(-6 b^2 c^3-11 b^2 d c^2-4 a b d c^2-11 b^2 d x c^2+4 b \sqrt{a+b} d \sqrt{a+b x} c^2+6 b^2 \sqrt{c+d} \sqrt{c+d x} c^2-10 b^2 d^2 c-14 a b d^2 c-4 b^2 d^2 x^2 c-20 b^2 d^2 x c-2 a b d^2 x c+14 b \sqrt{a+b} d^2 \sqrt{a+b x} c+2 b \sqrt{a+b} d^2 x \sqrt{a+b x} c+8 b^2 d \sqrt{c+d} x \sqrt{c+d x} c+8 b^2 d \sqrt{c+d} \sqrt{c+d x} c+4 a b d \sqrt{c+d} \sqrt{c+d x} c-4 b \sqrt{a+b} d \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x} c-3 b^2 d^3-6 a b d^3-6 b^2 d^3 x^2-9 b^2 d^3 x-6 a b d^3 x+6 b \sqrt{a+b} d^3 \sqrt{a+b x}+6 b \sqrt{a+b} d^3 x \sqrt{a+b x}+6 b^2 d^2 \sqrt{c+d} x \sqrt{c+d x}-6 a b d^2 \sqrt{c+d} x \sqrt{c+d x}-6 a^2 d^2 \sqrt{c+d} \sqrt{c+d x}+6 b^2 d^2 \sqrt{c+d} \sqrt{c+d x}+6 a b d^2 \sqrt{c+d} \sqrt{c+d x}+3 b \sqrt{a+b} d^2 \sqrt{c+d} x \sqrt{a+b x} \sqrt{c+d x}+6 a \sqrt{a+b} d^2 \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x}-9 b \sqrt{a+b} d^2 \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x}\right)}{\left(\sqrt{c+d}-\sqrt{c+d x}\right)^4}-\frac{4 b \left(-2 b^2 c^3+2 a b c^3-2 b^2 x c^3-2 b \sqrt{a+b} \sqrt{a+b x} c^3-b^2 d x^2 c^2+6 a^2 d c^2-b^2 d c^2+7 a b d c^2-8 b^2 d x c^2+7 a b d x c^2-6 a \sqrt{a+b} d \sqrt{a+b x} c^2-4 b \sqrt{a+b} d \sqrt{a+b x} c^2-4 b \sqrt{a+b} d x \sqrt{a+b x} c^2+2 b^2 \sqrt{c+d} x \sqrt{c+d x} c^2+2 b^2 \sqrt{c+d} \sqrt{c+d x} c^2-2 a b \sqrt{c+d} \sqrt{c+d x} c^2+2 b \sqrt{a+b} \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x} c^2+12 a^2 d^2 c+6 a b d^2 c-6 b^2 d^2 x^2 c-6 b^2 d^2 x c+12 a b d^2 x c-12 a \sqrt{a+b} d^2 \sqrt{a+b x} c-6 b \sqrt{a+b} d^2 x \sqrt{a+b x} c+6 b^2 d \sqrt{c+d} x \sqrt{c+d x} c-6 a b d \sqrt{c+d} x \sqrt{c+d x} c-6 a^2 d \sqrt{c+d} \sqrt{c+d x} c-6 a b d \sqrt{c+d} \sqrt{c+d x} c+3 b \sqrt{a+b} d \sqrt{c+d} x \sqrt{a+b x} \sqrt{c+d x} c+6 a \sqrt{a+b} d \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x} c+3 b \sqrt{a+b} d \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x} c+6 a^2 d^3+3 a b d^3-6 b^2 d^3 x^2+3 a b d^3 x-6 a \sqrt{a+b} d^3 \sqrt{a+b x}-12 a b d^2 \sqrt{c+d} x \sqrt{c+d x}-12 a^2 d^2 \sqrt{c+d} \sqrt{c+d x}-6 a b d^2 \sqrt{c+d} \sqrt{c+d x}+6 b \sqrt{a+b} d^2 \sqrt{c+d} x \sqrt{a+b x} \sqrt{c+d x}+12 a \sqrt{a+b} d^2 \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x}\right)}{\left(\sqrt{c+d}-\sqrt{c+d x}\right)^4}\right)}{\left(\sqrt{c+d x}-\sqrt{c+d}\right) \left(-\sqrt{a+b} d x b-c \sqrt{a+b x} b+\sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x} b-a \sqrt{a+b} d+a d \sqrt{a+b x}\right)^3}","-\frac{2 (c+d x)^{3/2}}{3 (a+b x)^{3/2} (b c-a d)}",1,"((1/(6*(a + b)) - Sqrt[a + b*x]/(6*(a + b)^(3/2)))*(Sqrt[c + d] - Sqrt[c + d*x])^6*((4*a^2*d^2*(Sqrt[a + b] - Sqrt[a + b*x])^2)/(Sqrt[c + d] - Sqrt[c + d*x])^2 - (4*a*(-6*b^2*c^3 - 4*a*b*c^2*d - 11*b^2*c^2*d - 14*a*b*c*d^2 - 10*b^2*c*d^2 - 6*a*b*d^3 - 3*b^2*d^3 - 11*b^2*c^2*d*x - 2*a*b*c*d^2*x - 20*b^2*c*d^2*x - 6*a*b*d^3*x - 9*b^2*d^3*x - 4*b^2*c*d^2*x^2 - 6*b^2*d^3*x^2 + 4*b*Sqrt[a + b]*c^2*d*Sqrt[a + b*x] + 14*b*Sqrt[a + b]*c*d^2*Sqrt[a + b*x] + 6*b*Sqrt[a + b]*d^3*Sqrt[a + b*x] + 2*b*Sqrt[a + b]*c*d^2*x*Sqrt[a + b*x] + 6*b*Sqrt[a + b]*d^3*x*Sqrt[a + b*x] + 6*b^2*c^2*Sqrt[c + d]*Sqrt[c + d*x] + 4*a*b*c*d*Sqrt[c + d]*Sqrt[c + d*x] + 8*b^2*c*d*Sqrt[c + d]*Sqrt[c + d*x] - 6*a^2*d^2*Sqrt[c + d]*Sqrt[c + d*x] + 6*a*b*d^2*Sqrt[c + d]*Sqrt[c + d*x] + 6*b^2*d^2*Sqrt[c + d]*Sqrt[c + d*x] + 8*b^2*c*d*Sqrt[c + d]*x*Sqrt[c + d*x] - 6*a*b*d^2*Sqrt[c + d]*x*Sqrt[c + d*x] + 6*b^2*d^2*Sqrt[c + d]*x*Sqrt[c + d*x] - 4*b*Sqrt[a + b]*c*d*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 6*a*Sqrt[a + b]*d^2*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] - 9*b*Sqrt[a + b]*d^2*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 3*b*Sqrt[a + b]*d^2*Sqrt[c + d]*x*Sqrt[a + b*x]*Sqrt[c + d*x]))/(Sqrt[c + d] - Sqrt[c + d*x])^4 - (4*b*(2*a*b*c^3 - 2*b^2*c^3 + 6*a^2*c^2*d + 7*a*b*c^2*d - b^2*c^2*d + 12*a^2*c*d^2 + 6*a*b*c*d^2 + 6*a^2*d^3 + 3*a*b*d^3 - 2*b^2*c^3*x + 7*a*b*c^2*d*x - 8*b^2*c^2*d*x + 12*a*b*c*d^2*x - 6*b^2*c*d^2*x + 3*a*b*d^3*x - b^2*c^2*d*x^2 - 6*b^2*c*d^2*x^2 - 6*b^2*d^3*x^2 - 2*b*Sqrt[a + b]*c^3*Sqrt[a + b*x] - 6*a*Sqrt[a + b]*c^2*d*Sqrt[a + b*x] - 4*b*Sqrt[a + b]*c^2*d*Sqrt[a + b*x] - 12*a*Sqrt[a + b]*c*d^2*Sqrt[a + b*x] - 6*a*Sqrt[a + b]*d^3*Sqrt[a + b*x] - 4*b*Sqrt[a + b]*c^2*d*x*Sqrt[a + b*x] - 6*b*Sqrt[a + b]*c*d^2*x*Sqrt[a + b*x] - 2*a*b*c^2*Sqrt[c + d]*Sqrt[c + d*x] + 2*b^2*c^2*Sqrt[c + d]*Sqrt[c + d*x] - 6*a^2*c*d*Sqrt[c + d]*Sqrt[c + d*x] - 6*a*b*c*d*Sqrt[c + d]*Sqrt[c + d*x] - 12*a^2*d^2*Sqrt[c + d]*Sqrt[c + d*x] - 6*a*b*d^2*Sqrt[c + d]*Sqrt[c + d*x] + 2*b^2*c^2*Sqrt[c + d]*x*Sqrt[c + d*x] - 6*a*b*c*d*Sqrt[c + d]*x*Sqrt[c + d*x] + 6*b^2*c*d*Sqrt[c + d]*x*Sqrt[c + d*x] - 12*a*b*d^2*Sqrt[c + d]*x*Sqrt[c + d*x] + 2*b*Sqrt[a + b]*c^2*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 6*a*Sqrt[a + b]*c*d*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 3*b*Sqrt[a + b]*c*d*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 12*a*Sqrt[a + b]*d^2*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 3*b*Sqrt[a + b]*c*d*Sqrt[c + d]*x*Sqrt[a + b*x]*Sqrt[c + d*x] + 6*b*Sqrt[a + b]*d^2*Sqrt[c + d]*x*Sqrt[a + b*x]*Sqrt[c + d*x]))/(Sqrt[c + d] - Sqrt[c + d*x])^4))/((-Sqrt[c + d] + Sqrt[c + d*x])*(-(a*Sqrt[a + b]*d) - b*Sqrt[a + b]*d*x - b*c*Sqrt[a + b*x] + a*d*Sqrt[a + b*x] + b*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x])^3)","B",1
1467,1,12875,66,55.7103903,"\int \frac{\sqrt{c+d x}}{(a+b x)^{7/2}} \, dx","IntegrateAlgebraic[Sqrt[c + d*x]/(a + b*x)^(7/2),x]","\text{Result too large to show}","\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,"Result too large to show","B",1
1468,-1,0,101,180.0581911,"\int \frac{\sqrt{c+d x}}{(a+b x)^{9/2}} \, dx","IntegrateAlgebraic[Sqrt[c + d*x]/(a + b*x)^(9/2),x]","\text{\$Aborted}","-\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,"$Aborted","F",-1
1469,-1,0,136,180.1226724,"\int \frac{\sqrt{c+d x}}{(a+b x)^{11/2}} \, dx","IntegrateAlgebraic[Sqrt[c + d*x]/(a + b*x)^(11/2),x]","\text{\$Aborted}","\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,"$Aborted","F",-1
1470,-1,0,171,180.3763242,"\int \frac{\sqrt{c+d x}}{(a+b x)^{13/2}} \, dx","IntegrateAlgebraic[Sqrt[c + d*x]/(a + b*x)^(13/2),x]","\text{\$Aborted}","-\frac{256 d^4 (c+d x)^{3/2}}{3465 (a+b x)^{3/2} (b c-a d)^5}+\frac{128 d^3 (c+d x)^{3/2}}{1155 (a+b x)^{5/2} (b c-a d)^4}-\frac{32 d^2 (c+d x)^{3/2}}{231 (a+b x)^{7/2} (b c-a d)^3}+\frac{16 d (c+d x)^{3/2}}{99 (a+b x)^{9/2} (b c-a d)^2}-\frac{2 (c+d x)^{3/2}}{11 (a+b x)^{11/2} (b c-a d)}",1,"$Aborted","F",-1
1471,-1,0,227,180.03213,"\int (a+b x)^{5/2} (c+d x)^{3/2} \, dx","IntegrateAlgebraic[(a + b*x)^(5/2)*(c + d*x)^(3/2),x]","\text{\$Aborted}","-\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{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{(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,"$Aborted","F",-1
1472,-1,0,189,180.022127,"\int (a+b x)^{3/2} (c+d x)^{3/2} \, dx","IntegrateAlgebraic[(a + b*x)^(3/2)*(c + d*x)^(3/2),x]","\text{\$Aborted}","\frac{3 (b c-a d)^4 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{64 b^{5/2} d^{5/2}}-\frac{3 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^3}{64 b^2 d^2}+\frac{(a+b x)^{3/2} \sqrt{c+d x} (b c-a d)^2}{32 b^2 d}+\frac{(a+b x)^{5/2} \sqrt{c+d x} (b c-a d)}{8 b^2}+\frac{(a+b x)^{5/2} (c+d x)^{3/2}}{4 b}",1,"$Aborted","F",-1
1473,1,9697,151,109.87412,"\int \sqrt{a+b x} (c+d x)^{3/2} \, dx","IntegrateAlgebraic[Sqrt[a + b*x]*(c + d*x)^(3/2),x]","\text{Result too large to show}","-\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,"Result too large to show","B",0
1474,1,2909,113,6.5358445,"\int \frac{(c+d x)^{3/2}}{\sqrt{a+b x}} \, dx","IntegrateAlgebraic[(c + d*x)^(3/2)/Sqrt[a + b*x],x]","\text{Result too large to show}","\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{3 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)}{4 b^2}+\frac{\sqrt{a+b x} (c+d x)^{3/2}}{2 b}",1,"((Sqrt[a + b]/(4*b^2) - Sqrt[a + b*x]/(4*b^2))*(Sqrt[c + d] - Sqrt[c + d*x])*(20*b^5*c^5 - 34*a*b^4*c^4*d + 33*b^5*c^4*d + 78*a^2*b^3*c^3*d^2 + 10*a*b^4*c^3*d^2 + 15*b^5*c^3*d^2 - 66*a^3*b^2*c^2*d^3 + 18*a^2*b^3*c^2*d^3 + 41*a*b^4*c^2*d^3 + 2*b^5*c^2*d^3 + 46*a^4*b*c*d^4 + 26*a^3*b^2*c*d^4 + a^2*b^3*c*d^4 + 12*a*b^4*c*d^4 - 12*a^5*d^5 - 7*a^4*b*d^5 + 7*a^3*b^2*d^5 + 2*a^2*b^3*d^5 + 33*b^5*c^4*d*x + 10*a*b^4*c^3*d^2*x + 112*b^5*c^3*d^2*x + 18*a^2*b^3*c^2*d^3*x - 16*a*b^4*c^2*d^3*x + 80*b^5*c^2*d^3*x + 26*a^3*b^2*c*d^4*x + 112*a^2*b^3*c*d^4*x + 48*a*b^4*c*d^4*x + 16*b^5*c*d^4*x - 7*a^4*b*d^5*x - 16*a^3*b^2*d^5*x + 16*a^2*b^3*d^5*x + 16*a*b^4*d^5*x + 15*b^5*c^3*d^2*x^2 + 41*a*b^4*c^2*d^3*x^2 + 80*b^5*c^2*d^3*x^2 + a^2*b^3*c*d^4*x^2 + 48*a*b^4*c*d^4*x^2 + 80*b^5*c*d^4*x^2 + 7*a^3*b^2*d^5*x^2 + 16*a^2*b^3*d^5*x^2 + 16*a*b^4*d^5*x^2 + 16*b^5*d^5*x^2 + 2*b^5*c^2*d^3*x^3 + 12*a*b^4*c*d^4*x^3 + 16*b^5*c*d^4*x^3 + 2*a^2*b^3*d^5*x^3 + 16*a*b^4*d^5*x^3 + 16*b^5*d^5*x^3 + 58*b^4*Sqrt[a + b]*c^4*d*Sqrt[a + b*x] - 90*a*b^3*Sqrt[a + b]*c^3*d^2*Sqrt[a + b*x] + 71*b^4*Sqrt[a + b]*c^3*d^2*Sqrt[a + b*x] + 66*a^2*b^2*Sqrt[a + b]*c^2*d^3*Sqrt[a + b*x] - 69*a*b^3*Sqrt[a + b]*c^2*d^3*Sqrt[a + b*x] + 18*b^4*Sqrt[a + b]*c^2*d^3*Sqrt[a + b*x] - 46*a^3*b*Sqrt[a + b]*c*d^4*Sqrt[a + b*x] - 3*a^2*b^2*Sqrt[a + b]*c*d^4*Sqrt[a + b*x] - 12*a*b^3*Sqrt[a + b]*c*d^4*Sqrt[a + b*x] + 12*a^4*Sqrt[a + b]*d^5*Sqrt[a + b*x] + a^3*b*Sqrt[a + b]*d^5*Sqrt[a + b*x] - 6*a^2*b^2*Sqrt[a + b]*d^5*Sqrt[a + b*x] + 71*b^4*Sqrt[a + b]*c^3*d^2*x*Sqrt[a + b*x] - 69*a*b^3*Sqrt[a + b]*c^2*d^3*x*Sqrt[a + b*x] + 108*b^4*Sqrt[a + b]*c^2*d^3*x*Sqrt[a + b*x] - 3*a^2*b^2*Sqrt[a + b]*c*d^4*x*Sqrt[a + b*x] - 120*a*b^3*Sqrt[a + b]*c*d^4*x*Sqrt[a + b*x] + 24*b^4*Sqrt[a + b]*c*d^4*x*Sqrt[a + b*x] + a^3*b*Sqrt[a + b]*d^5*x*Sqrt[a + b*x] + 12*a^2*b^2*Sqrt[a + b]*d^5*x*Sqrt[a + b*x] - 24*a*b^3*Sqrt[a + b]*d^5*x*Sqrt[a + b*x] + 18*b^4*Sqrt[a + b]*c^2*d^3*x^2*Sqrt[a + b*x] - 12*a*b^3*Sqrt[a + b]*c*d^4*x^2*Sqrt[a + b*x] + 24*b^4*Sqrt[a + b]*c*d^4*x^2*Sqrt[a + b*x] - 6*a^2*b^2*Sqrt[a + b]*d^5*x^2*Sqrt[a + b*x] - 24*a*b^3*Sqrt[a + b]*d^5*x^2*Sqrt[a + b*x] - 20*b^5*c^4*Sqrt[c + d]*Sqrt[c + d*x] + 34*a*b^4*c^3*d*Sqrt[c + d]*Sqrt[c + d*x] - 23*b^5*c^3*d*Sqrt[c + d]*Sqrt[c + d*x] - 78*a^2*b^3*c^2*d^2*Sqrt[c + d]*Sqrt[c + d*x] - 27*a*b^4*c^2*d^2*Sqrt[c + d]*Sqrt[c + d*x] - 6*b^5*c^2*d^2*Sqrt[c + d]*Sqrt[c + d*x] + 86*a^3*b^2*c*d^3*Sqrt[c + d]*Sqrt[c + d*x] + 51*a^2*b^3*c*d^3*Sqrt[c + d]*Sqrt[c + d*x] - 12*a*b^4*c*d^3*Sqrt[c + d]*Sqrt[c + d*x] - 22*a^4*b*d^4*Sqrt[c + d]*Sqrt[c + d*x] - a^3*b^2*d^4*Sqrt[c + d]*Sqrt[c + d*x] + 18*a^2*b^3*d^4*Sqrt[c + d]*Sqrt[c + d*x] - 23*b^5*c^3*d*Sqrt[c + d]*x*Sqrt[c + d*x] - 27*a*b^4*c^2*d^2*Sqrt[c + d]*x*Sqrt[c + d*x] - 84*b^5*c^2*d^2*Sqrt[c + d]*x*Sqrt[c + d*x] + 51*a^2*b^3*c*d^3*Sqrt[c + d]*x*Sqrt[c + d*x] + 72*a*b^4*c*d^3*Sqrt[c + d]*x*Sqrt[c + d*x] - 24*b^5*c*d^3*Sqrt[c + d]*x*Sqrt[c + d*x] - a^3*b^2*d^4*Sqrt[c + d]*x*Sqrt[c + d*x] + 12*a^2*b^3*d^4*Sqrt[c + d]*x*Sqrt[c + d*x] + 24*a*b^4*d^4*Sqrt[c + d]*x*Sqrt[c + d*x] - 6*b^5*c^2*d^2*Sqrt[c + d]*x^2*Sqrt[c + d*x] - 12*a*b^4*c*d^3*Sqrt[c + d]*x^2*Sqrt[c + d*x] - 24*b^5*c*d^3*Sqrt[c + d]*x^2*Sqrt[c + d*x] + 18*a^2*b^3*d^4*Sqrt[c + d]*x^2*Sqrt[c + d*x] + 24*a*b^4*d^4*Sqrt[c + d]*x^2*Sqrt[c + d*x] - 58*b^4*Sqrt[a + b]*c^3*d*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 90*a*b^3*Sqrt[a + b]*c^2*d^2*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] - 42*b^4*Sqrt[a + b]*c^2*d^2*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] - 86*a^2*b^2*Sqrt[a + b]*c*d^3*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 4*a*b^3*Sqrt[a + b]*c*d^3*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] - 8*b^4*Sqrt[a + b]*c*d^3*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 22*a^3*b*Sqrt[a + b]*d^4*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] - 10*a^2*b^2*Sqrt[a + b]*d^4*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] - 8*a*b^3*Sqrt[a + b]*d^4*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] - 42*b^4*Sqrt[a + b]*c^2*d^2*Sqrt[c + d]*x*Sqrt[a + b*x]*Sqrt[c + d*x] + 4*a*b^3*Sqrt[a + b]*c*d^3*Sqrt[c + d]*x*Sqrt[a + b*x]*Sqrt[c + d*x] - 64*b^4*Sqrt[a + b]*c*d^3*Sqrt[c + d]*x*Sqrt[a + b*x]*Sqrt[c + d*x] - 10*a^2*b^2*Sqrt[a + b]*d^4*Sqrt[c + d]*x*Sqrt[a + b*x]*Sqrt[c + d*x] - 16*b^4*Sqrt[a + b]*d^4*Sqrt[c + d]*x*Sqrt[a + b*x]*Sqrt[c + d*x] - 8*b^4*Sqrt[a + b]*c*d^3*Sqrt[c + d]*x^2*Sqrt[a + b*x]*Sqrt[c + d*x] - 8*a*b^3*Sqrt[a + b]*d^4*Sqrt[c + d]*x^2*Sqrt[a + b*x]*Sqrt[c + d*x] - 16*b^4*Sqrt[a + b]*d^4*Sqrt[c + d]*x^2*Sqrt[a + b*x]*Sqrt[c + d*x]))/(-(b*c) + a*d - Sqrt[a + b]*d*Sqrt[a + b*x] + b*Sqrt[c + d]*Sqrt[c + d*x])^4 + (3*(b*c - a*d)^2*ArcTanh[(Sqrt[b]*Sqrt[c + d] - Sqrt[b]*Sqrt[c + d*x])/(Sqrt[a + b]*Sqrt[d] - Sqrt[d]*Sqrt[a + b*x])])/(2*b^(5/2)*Sqrt[d])","B",1
1475,-1,0,98,180.0291452,"\int \frac{(c+d x)^{3/2}}{(a+b x)^{3/2}} \, dx","IntegrateAlgebraic[(c + d*x)^(3/2)/(a + b*x)^(3/2),x]","\text{\$Aborted}","\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{3 d \sqrt{a+b x} \sqrt{c+d x}}{b^2}-\frac{2 (c+d x)^{3/2}}{b \sqrt{a+b x}}",1,"$Aborted","F",-1
1476,-1,0,92,180.1861255,"\int \frac{(c+d x)^{3/2}}{(a+b x)^{5/2}} \, dx","IntegrateAlgebraic[(c + d*x)^(3/2)/(a + b*x)^(5/2),x]","\text{\$Aborted}","\frac{2 d^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{b^{5/2}}-\frac{2 d \sqrt{c+d x}}{b^2 \sqrt{a+b x}}-\frac{2 (c+d x)^{3/2}}{3 b (a+b x)^{3/2}}",1,"$Aborted","F",-1
1477,1,17029,32,103.4719156,"\int \frac{(c+d x)^{3/2}}{(a+b x)^{7/2}} \, dx","IntegrateAlgebraic[(c + d*x)^(3/2)/(a + b*x)^(7/2),x]","\text{Result too large to show}","-\frac{2 (c+d x)^{5/2}}{5 (a+b x)^{5/2} (b c-a d)}",1,"Result too large to show","B",1
1478,-1,0,66,180.0687115,"\int \frac{(c+d x)^{3/2}}{(a+b x)^{9/2}} \, dx","IntegrateAlgebraic[(c + d*x)^(3/2)/(a + b*x)^(9/2),x]","\text{\$Aborted}","\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,"$Aborted","F",-1
1479,-1,0,101,180.157628,"\int \frac{(c+d x)^{3/2}}{(a+b x)^{11/2}} \, dx","IntegrateAlgebraic[(c + d*x)^(3/2)/(a + b*x)^(11/2),x]","\text{\$Aborted}","-\frac{16 d^2 (c+d x)^{5/2}}{315 (a+b x)^{5/2} (b c-a d)^3}+\frac{8 d (c+d x)^{5/2}}{63 (a+b x)^{7/2} (b c-a d)^2}-\frac{2 (c+d x)^{5/2}}{9 (a+b x)^{9/2} (b c-a d)}",1,"$Aborted","F",-1
1480,-1,0,136,180.4508748,"\int \frac{(c+d x)^{3/2}}{(a+b x)^{13/2}} \, dx","IntegrateAlgebraic[(c + d*x)^(3/2)/(a + b*x)^(13/2),x]","\text{\$Aborted}","\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,"$Aborted","F",-1
1481,-1,0,262,180.045824,"\int (a+b x)^{5/2} (c+d x)^{5/2} \, dx","IntegrateAlgebraic[(a + b*x)^(5/2)*(c + d*x)^(5/2),x]","\text{\$Aborted}","-\frac{5 (b c-a d)^6 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{512 b^{7/2} d^{7/2}}+\frac{5 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^5}{512 b^3 d^3}-\frac{5 (a+b x)^{3/2} \sqrt{c+d x} (b c-a d)^4}{768 b^3 d^2}+\frac{(a+b x)^{5/2} \sqrt{c+d x} (b c-a d)^3}{192 b^3 d}+\frac{(a+b x)^{7/2} \sqrt{c+d x} (b c-a d)^2}{32 b^3}+\frac{(a+b x)^{7/2} (c+d x)^{3/2} (b c-a d)}{12 b^2}+\frac{(a+b x)^{7/2} (c+d x)^{5/2}}{6 b}",1,"$Aborted","F",-1
1482,-1,0,224,180.033592,"\int (a+b x)^{3/2} (c+d x)^{5/2} \, dx","IntegrateAlgebraic[(a + b*x)^(3/2)*(c + d*x)^(5/2),x]","\text{\$Aborted}","\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{3 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^4}{128 b^3 d^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,"$Aborted","F",-1
1483,-1,0,186,180.0239267,"\int \sqrt{a+b x} (c+d x)^{5/2} \, dx","IntegrateAlgebraic[Sqrt[a + b*x]*(c + d*x)^(5/2),x]","\text{\$Aborted}","-\frac{5 (b c-a d)^4 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{64 b^{7/2} d^{3/2}}+\frac{5 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^3}{64 b^3 d}+\frac{5 (a+b x)^{3/2} \sqrt{c+d x} (b c-a d)^2}{32 b^3}+\frac{5 (a+b x)^{3/2} (c+d x)^{3/2} (b c-a d)}{24 b^2}+\frac{(a+b x)^{3/2} (c+d x)^{5/2}}{4 b}",1,"$Aborted","F",-1
1484,1,9693,148,123.7875608,"\int \frac{(c+d x)^{5/2}}{\sqrt{a+b x}} \, dx","IntegrateAlgebraic[(c + d*x)^(5/2)/Sqrt[a + b*x],x]","\text{Result too large to show}","\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{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{\sqrt{a+b x} (c+d x)^{5/2}}{3 b}",1,"Result too large to show","B",0
1485,-1,0,138,180.0398939,"\int \frac{(c+d x)^{5/2}}{(a+b x)^{3/2}} \, dx","IntegrateAlgebraic[(c + d*x)^(5/2)/(a + b*x)^(3/2),x]","\text{\$Aborted}","\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{15 d \sqrt{a+b x} \sqrt{c+d x} (b c-a d)}{4 b^3}+\frac{5 d \sqrt{a+b x} (c+d x)^{3/2}}{2 b^2}-\frac{2 (c+d x)^{5/2}}{b \sqrt{a+b x}}",1,"$Aborted","F",-1
1486,-1,0,128,180.1901588,"\int \frac{(c+d x)^{5/2}}{(a+b x)^{5/2}} \, dx","IntegrateAlgebraic[(c + d*x)^(5/2)/(a + b*x)^(5/2),x]","\text{\$Aborted}","\frac{5 d^{3/2} (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{b^{7/2}}+\frac{5 d^2 \sqrt{a+b x} \sqrt{c+d x}}{b^3}-\frac{10 d (c+d x)^{3/2}}{3 b^2 \sqrt{a+b x}}-\frac{2 (c+d x)^{5/2}}{3 b (a+b x)^{3/2}}",1,"$Aborted","F",-1
1487,-1,0,120,180.1929584,"\int \frac{(c+d x)^{5/2}}{(a+b x)^{7/2}} \, dx","IntegrateAlgebraic[(c + d*x)^(5/2)/(a + b*x)^(7/2),x]","\text{\$Aborted}","\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^2 \sqrt{c+d x}}{b^3 \sqrt{a+b x}}-\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,"$Aborted","F",-1
1488,-1,0,32,180.0607688,"\int \frac{(c+d x)^{5/2}}{(a+b x)^{9/2}} \, dx","IntegrateAlgebraic[(c + d*x)^(5/2)/(a + b*x)^(9/2),x]","\text{\$Aborted}","-\frac{2 (c+d x)^{7/2}}{7 (a+b x)^{7/2} (b c-a d)}",1,"$Aborted","F",-1
1489,-1,0,66,180.1681941,"\int \frac{(c+d x)^{5/2}}{(a+b x)^{11/2}} \, dx","IntegrateAlgebraic[(c + d*x)^(5/2)/(a + b*x)^(11/2),x]","\text{\$Aborted}","\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,"$Aborted","F",-1
1490,-1,0,101,181.8423917,"\int \frac{(c+d x)^{5/2}}{(a+b x)^{13/2}} \, dx","IntegrateAlgebraic[(c + d*x)^(5/2)/(a + b*x)^(13/2),x]","\text{\$Aborted}","-\frac{16 d^2 (c+d x)^{7/2}}{693 (a+b x)^{7/2} (b c-a d)^3}+\frac{8 d (c+d x)^{7/2}}{99 (a+b x)^{9/2} (b c-a d)^2}-\frac{2 (c+d x)^{7/2}}{11 (a+b x)^{11/2} (b c-a d)}",1,"$Aborted","F",-1
1491,-1,0,136,181.696895,"\int \frac{(c+d x)^{5/2}}{(a+b x)^{15/2}} \, dx","IntegrateAlgebraic[(c + d*x)^(5/2)/(a + b*x)^(15/2),x]","\text{\$Aborted}","\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,"$Aborted","F",-1
1492,-1,0,183,180.0285826,"\int \frac{(a+b x)^{7/2}}{\sqrt{c+d x}} \, dx","IntegrateAlgebraic[(a + b*x)^(7/2)/Sqrt[c + d*x],x]","\text{\$Aborted}","\frac{35 (b c-a d)^4 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{64 \sqrt{b} d^{9/2}}-\frac{35 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^3}{64 d^4}+\frac{35 (a+b x)^{3/2} \sqrt{c+d x} (b c-a d)^2}{96 d^3}-\frac{7 (a+b x)^{5/2} \sqrt{c+d x} (b c-a d)}{24 d^2}+\frac{(a+b x)^{7/2} \sqrt{c+d x}}{4 d}",1,"$Aborted","F",-1
1493,1,9693,148,112.2745343,"\int \frac{(a+b x)^{5/2}}{\sqrt{c+d x}} \, dx","IntegrateAlgebraic[(a + b*x)^(5/2)/Sqrt[c + d*x],x]","\text{Result too large to show}","-\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{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{(a+b x)^{5/2} \sqrt{c+d x}}{3 d}",1,"Result too large to show","B",0
1494,1,2911,113,6.7660955,"\int \frac{(a+b x)^{3/2}}{\sqrt{c+d x}} \, dx","IntegrateAlgebraic[(a + b*x)^(3/2)/Sqrt[c + d*x],x]","\text{Result too large to show}","\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{3 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)}{4 d^2}+\frac{(a+b x)^{3/2} \sqrt{c+d x}}{2 d}",1,"((-1/4*Sqrt[a + b]/d^2 + Sqrt[a + b*x]/(4*d^2))*(Sqrt[c + d] - Sqrt[c + d*x])*(12*b^5*c^5 - 46*a*b^4*c^4*d + 7*b^5*c^4*d + 66*a^2*b^3*c^3*d^2 - 26*a*b^4*c^3*d^2 - 7*b^5*c^3*d^2 - 78*a^3*b^2*c^2*d^3 - 18*a^2*b^3*c^2*d^3 - a*b^4*c^2*d^3 - 2*b^5*c^2*d^3 + 34*a^4*b*c*d^4 - 10*a^3*b^2*c*d^4 - 41*a^2*b^3*c*d^4 - 12*a*b^4*c*d^4 - 20*a^5*d^5 - 33*a^4*b*d^5 - 15*a^3*b^2*d^5 - 2*a^2*b^3*d^5 + 7*b^5*c^4*d*x - 26*a*b^4*c^3*d^2*x + 16*b^5*c^3*d^2*x - 18*a^2*b^3*c^2*d^3*x - 112*a*b^4*c^2*d^3*x - 16*b^5*c^2*d^3*x - 10*a^3*b^2*c*d^4*x + 16*a^2*b^3*c*d^4*x - 48*a*b^4*c*d^4*x - 16*b^5*c*d^4*x - 33*a^4*b*d^5*x - 112*a^3*b^2*d^5*x - 80*a^2*b^3*d^5*x - 16*a*b^4*d^5*x - 7*b^5*c^3*d^2*x^2 - a*b^4*c^2*d^3*x^2 - 16*b^5*c^2*d^3*x^2 - 41*a^2*b^3*c*d^4*x^2 - 48*a*b^4*c*d^4*x^2 - 16*b^5*c*d^4*x^2 - 15*a^3*b^2*d^5*x^2 - 80*a^2*b^3*d^5*x^2 - 80*a*b^4*d^5*x^2 - 16*b^5*d^5*x^2 - 2*b^5*c^2*d^3*x^3 - 12*a*b^4*c*d^4*x^3 - 16*b^5*c*d^4*x^3 - 2*a^2*b^3*d^5*x^3 - 16*a*b^4*d^5*x^3 - 16*b^5*d^5*x^3 + 22*b^4*Sqrt[a + b]*c^4*d*Sqrt[a + b*x] - 86*a*b^3*Sqrt[a + b]*c^3*d^2*Sqrt[a + b*x] + b^4*Sqrt[a + b]*c^3*d^2*Sqrt[a + b*x] + 78*a^2*b^2*Sqrt[a + b]*c^2*d^3*Sqrt[a + b*x] - 51*a*b^3*Sqrt[a + b]*c^2*d^3*Sqrt[a + b*x] - 18*b^4*Sqrt[a + b]*c^2*d^3*Sqrt[a + b*x] - 34*a^3*b*Sqrt[a + b]*c*d^4*Sqrt[a + b*x] + 27*a^2*b^2*Sqrt[a + b]*c*d^4*Sqrt[a + b*x] + 12*a*b^3*Sqrt[a + b]*c*d^4*Sqrt[a + b*x] + 20*a^4*Sqrt[a + b]*d^5*Sqrt[a + b*x] + 23*a^3*b*Sqrt[a + b]*d^5*Sqrt[a + b*x] + 6*a^2*b^2*Sqrt[a + b]*d^5*Sqrt[a + b*x] + b^4*Sqrt[a + b]*c^3*d^2*x*Sqrt[a + b*x] - 51*a*b^3*Sqrt[a + b]*c^2*d^3*x*Sqrt[a + b*x] - 12*b^4*Sqrt[a + b]*c^2*d^3*x*Sqrt[a + b*x] + 27*a^2*b^2*Sqrt[a + b]*c*d^4*x*Sqrt[a + b*x] - 72*a*b^3*Sqrt[a + b]*c*d^4*x*Sqrt[a + b*x] - 24*b^4*Sqrt[a + b]*c*d^4*x*Sqrt[a + b*x] + 23*a^3*b*Sqrt[a + b]*d^5*x*Sqrt[a + b*x] + 84*a^2*b^2*Sqrt[a + b]*d^5*x*Sqrt[a + b*x] + 24*a*b^3*Sqrt[a + b]*d^5*x*Sqrt[a + b*x] - 18*b^4*Sqrt[a + b]*c^2*d^3*x^2*Sqrt[a + b*x] + 12*a*b^3*Sqrt[a + b]*c*d^4*x^2*Sqrt[a + b*x] - 24*b^4*Sqrt[a + b]*c*d^4*x^2*Sqrt[a + b*x] + 6*a^2*b^2*Sqrt[a + b]*d^5*x^2*Sqrt[a + b*x] + 24*a*b^3*Sqrt[a + b]*d^5*x^2*Sqrt[a + b*x] - 12*b^5*c^4*Sqrt[c + d]*Sqrt[c + d*x] + 46*a*b^4*c^3*d*Sqrt[c + d]*Sqrt[c + d*x] - b^5*c^3*d*Sqrt[c + d]*Sqrt[c + d*x] - 66*a^2*b^3*c^2*d^2*Sqrt[c + d]*Sqrt[c + d*x] + 3*a*b^4*c^2*d^2*Sqrt[c + d]*Sqrt[c + d*x] + 6*b^5*c^2*d^2*Sqrt[c + d]*Sqrt[c + d*x] + 90*a^3*b^2*c*d^3*Sqrt[c + d]*Sqrt[c + d*x] + 69*a^2*b^3*c*d^3*Sqrt[c + d]*Sqrt[c + d*x] + 12*a*b^4*c*d^3*Sqrt[c + d]*Sqrt[c + d*x] - 58*a^4*b*d^4*Sqrt[c + d]*Sqrt[c + d*x] - 71*a^3*b^2*d^4*Sqrt[c + d]*Sqrt[c + d*x] - 18*a^2*b^3*d^4*Sqrt[c + d]*Sqrt[c + d*x] - b^5*c^3*d*Sqrt[c + d]*x*Sqrt[c + d*x] + 3*a*b^4*c^2*d^2*Sqrt[c + d]*x*Sqrt[c + d*x] - 12*b^5*c^2*d^2*Sqrt[c + d]*x*Sqrt[c + d*x] + 69*a^2*b^3*c*d^3*Sqrt[c + d]*x*Sqrt[c + d*x] + 120*a*b^4*c*d^3*Sqrt[c + d]*x*Sqrt[c + d*x] + 24*b^5*c*d^3*Sqrt[c + d]*x*Sqrt[c + d*x] - 71*a^3*b^2*d^4*Sqrt[c + d]*x*Sqrt[c + d*x] - 108*a^2*b^3*d^4*Sqrt[c + d]*x*Sqrt[c + d*x] - 24*a*b^4*d^4*Sqrt[c + d]*x*Sqrt[c + d*x] + 6*b^5*c^2*d^2*Sqrt[c + d]*x^2*Sqrt[c + d*x] + 12*a*b^4*c*d^3*Sqrt[c + d]*x^2*Sqrt[c + d*x] + 24*b^5*c*d^3*Sqrt[c + d]*x^2*Sqrt[c + d*x] - 18*a^2*b^3*d^4*Sqrt[c + d]*x^2*Sqrt[c + d*x] - 24*a*b^4*d^4*Sqrt[c + d]*x^2*Sqrt[c + d*x] - 22*b^4*Sqrt[a + b]*c^3*d*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 86*a*b^3*Sqrt[a + b]*c^2*d^2*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 10*b^4*Sqrt[a + b]*c^2*d^2*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] - 90*a^2*b^2*Sqrt[a + b]*c*d^3*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] - 4*a*b^3*Sqrt[a + b]*c*d^3*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 8*b^4*Sqrt[a + b]*c*d^3*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 58*a^3*b*Sqrt[a + b]*d^4*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 42*a^2*b^2*Sqrt[a + b]*d^4*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 8*a*b^3*Sqrt[a + b]*d^4*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 10*b^4*Sqrt[a + b]*c^2*d^2*Sqrt[c + d]*x*Sqrt[a + b*x]*Sqrt[c + d*x] - 4*a*b^3*Sqrt[a + b]*c*d^3*Sqrt[c + d]*x*Sqrt[a + b*x]*Sqrt[c + d*x] + 42*a^2*b^2*Sqrt[a + b]*d^4*Sqrt[c + d]*x*Sqrt[a + b*x]*Sqrt[c + d*x] + 64*a*b^3*Sqrt[a + b]*d^4*Sqrt[c + d]*x*Sqrt[a + b*x]*Sqrt[c + d*x] + 16*b^4*Sqrt[a + b]*d^4*Sqrt[c + d]*x*Sqrt[a + b*x]*Sqrt[c + d*x] + 8*b^4*Sqrt[a + b]*c*d^3*Sqrt[c + d]*x^2*Sqrt[a + b*x]*Sqrt[c + d*x] + 8*a*b^3*Sqrt[a + b]*d^4*Sqrt[c + d]*x^2*Sqrt[a + b*x]*Sqrt[c + d*x] + 16*b^4*Sqrt[a + b]*d^4*Sqrt[c + d]*x^2*Sqrt[a + b*x]*Sqrt[c + d*x]))/(-(b*c) + a*d - Sqrt[a + b]*d*Sqrt[a + b*x] + b*Sqrt[c + d]*Sqrt[c + d*x])^4 + (3*(b*c - a*d)^2*ArcTanh[(Sqrt[b]*Sqrt[c + d] - Sqrt[b]*Sqrt[c + d*x])/(Sqrt[a + b]*Sqrt[d] - Sqrt[d]*Sqrt[a + b*x])])/(2*Sqrt[b]*d^(5/2))","B",1
1495,1,350,73,0.7611962,"\int \frac{\sqrt{a+b x}}{\sqrt{c+d x}} \, dx","IntegrateAlgebraic[Sqrt[a + b*x]/Sqrt[c + d*x],x]","\frac{\left(\sqrt{c+d}-\sqrt{c+d x}\right) \left(\frac{\sqrt{a+b}}{d}-\frac{\sqrt{a+b x}}{d}\right) \left(a^2 d^2+b c d \sqrt{a+b} \sqrt{a+b x}+a b d \sqrt{c+d} \sqrt{c+d x}-2 b d \sqrt{a+b} \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x}+a b d^2 x-a d^2 \sqrt{a+b} \sqrt{a+b x}+a b d^2+b^2 c^2+b^2 c d x-b^2 c \sqrt{c+d} \sqrt{c+d x}+b^2 c d+2 b^2 d^2 x\right)}{\left(-d \sqrt{a+b} \sqrt{a+b x}+a d+b \sqrt{c+d} \sqrt{c+d x}+b (-c)\right)^2}+\left(\frac{2 a}{\sqrt{b} \sqrt{d}}-\frac{2 \sqrt{b} c}{d^{3/2}}\right) \tanh ^{-1}\left(\frac{\sqrt{b} \left(\sqrt{c+d}-\sqrt{c+d x}\right)}{\sqrt{d} \sqrt{a+b}-\sqrt{d} \sqrt{a+b x}}\right)","\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]/d - Sqrt[a + b*x]/d)*(Sqrt[c + d] - Sqrt[c + d*x])*(b^2*c^2 + b^2*c*d + a^2*d^2 + a*b*d^2 + b^2*c*d*x + a*b*d^2*x + 2*b^2*d^2*x + b*Sqrt[a + b]*c*d*Sqrt[a + b*x] - a*Sqrt[a + b]*d^2*Sqrt[a + b*x] - b^2*c*Sqrt[c + d]*Sqrt[c + d*x] + a*b*d*Sqrt[c + d]*Sqrt[c + d*x] - 2*b*Sqrt[a + b]*d*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x]))/(-(b*c) + a*d - Sqrt[a + b]*d*Sqrt[a + b*x] + b*Sqrt[c + d]*Sqrt[c + d*x])^2 + ((-2*Sqrt[b]*c)/d^(3/2) + (2*a)/(Sqrt[b]*Sqrt[d]))*ArcTanh[(Sqrt[b]*(Sqrt[c + d] - Sqrt[c + d*x]))/(Sqrt[a + b]*Sqrt[d] - Sqrt[d]*Sqrt[a + b*x])]","B",1
1496,1,76,42,0.3283046,"\int \frac{1}{\sqrt{a+b x} \sqrt{c+d x}} \, dx","IntegrateAlgebraic[1/(Sqrt[a + b*x]*Sqrt[c + d*x]),x]","\frac{4 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d}-\sqrt{b} \sqrt{c+d x}}{\sqrt{d} \sqrt{a+b}-\sqrt{d} \sqrt{a+b 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,"(4*ArcTanh[(Sqrt[b]*Sqrt[c + d] - Sqrt[b]*Sqrt[c + d*x])/(Sqrt[a + b]*Sqrt[d] - Sqrt[d]*Sqrt[a + b*x])])/(Sqrt[b]*Sqrt[d])","A",1
1497,1,800,30,1.5382721,"\int \frac{1}{(a+b x)^{3/2} \sqrt{c+d x}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(3/2)*Sqrt[c + d*x]),x]","\frac{\left(\frac{\sqrt{a+b x}}{a+b}-\frac{1}{\sqrt{a+b}}\right) \left(\sqrt{c+d}-\sqrt{c+d x}\right)^4 \left(-\frac{2 a \left(-c b-d b-d x b+\sqrt{c+d} \sqrt{c+d x} b-a d+\sqrt{a+b} d \sqrt{a+b x}\right)}{\left(\sqrt{c+d}-\sqrt{c+d x}\right)^2}-\frac{2 b \left(-c a-2 d a+\sqrt{c+d} \sqrt{c+d x} a-2 b c-2 b d-b d x+\sqrt{a+b} c \sqrt{a+b x}+2 \sqrt{a+b} d \sqrt{a+b x}+2 b \sqrt{c+d} \sqrt{c+d x}-\sqrt{a+b} \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x}\right)}{\left(\sqrt{c+d}-\sqrt{c+d x}\right)^2}\right)}{\left(\sqrt{c+d x}-\sqrt{c+d}\right) \left(2 d^2 a^3+5 b d^2 a^2+2 b c d a^2+3 b d^2 x a^2-2 \sqrt{a+b} d^2 \sqrt{a+b x} a^2-2 b d \sqrt{c+d} \sqrt{c+d x} a^2-2 b^2 c^2 a+2 b^2 d^2 a+b^2 d^2 x^2 a-b^2 c d a+5 b^2 d^2 x a+b^2 c d x a-4 b \sqrt{a+b} d^2 \sqrt{a+b x} a-2 b \sqrt{a+b} c d \sqrt{a+b x} a-2 b \sqrt{a+b} d^2 x \sqrt{a+b x} a-2 b^2 d \sqrt{c+d} x \sqrt{c+d x} a+2 b^2 c \sqrt{c+d} \sqrt{c+d x} a+2 b \sqrt{a+b} d \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x} a-b^3 c d x^2-2 b^3 c^2 x+2 b^3 d^2 x-b^3 c d x+4 b^2 \sqrt{a+b} c^2 \sqrt{a+b x}+4 b^2 \sqrt{a+b} c d \sqrt{a+b x}+2 b^2 \sqrt{a+b} c d x \sqrt{a+b x}+2 b^3 c \sqrt{c+d} x \sqrt{c+d x}-4 b^2 \sqrt{a+b} c \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x}-2 b^2 \sqrt{a+b} d \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x}\right)}","-\frac{2 \sqrt{c+d x}}{\sqrt{a+b x} (b c-a d)}",1,"((-(1/Sqrt[a + b]) + Sqrt[a + b*x]/(a + b))*(Sqrt[c + d] - Sqrt[c + d*x])^4*((-2*a*(-(b*c) - a*d - b*d - b*d*x + Sqrt[a + b]*d*Sqrt[a + b*x] + b*Sqrt[c + d]*Sqrt[c + d*x]))/(Sqrt[c + d] - Sqrt[c + d*x])^2 - (2*b*(-(a*c) - 2*b*c - 2*a*d - 2*b*d - b*d*x + Sqrt[a + b]*c*Sqrt[a + b*x] + 2*Sqrt[a + b]*d*Sqrt[a + b*x] + a*Sqrt[c + d]*Sqrt[c + d*x] + 2*b*Sqrt[c + d]*Sqrt[c + d*x] - Sqrt[a + b]*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x]))/(Sqrt[c + d] - Sqrt[c + d*x])^2))/((-Sqrt[c + d] + Sqrt[c + d*x])*(-2*a*b^2*c^2 + 2*a^2*b*c*d - a*b^2*c*d + 2*a^3*d^2 + 5*a^2*b*d^2 + 2*a*b^2*d^2 - 2*b^3*c^2*x + a*b^2*c*d*x - b^3*c*d*x + 3*a^2*b*d^2*x + 5*a*b^2*d^2*x + 2*b^3*d^2*x - b^3*c*d*x^2 + a*b^2*d^2*x^2 + 4*b^2*Sqrt[a + b]*c^2*Sqrt[a + b*x] - 2*a*b*Sqrt[a + b]*c*d*Sqrt[a + b*x] + 4*b^2*Sqrt[a + b]*c*d*Sqrt[a + b*x] - 2*a^2*Sqrt[a + b]*d^2*Sqrt[a + b*x] - 4*a*b*Sqrt[a + b]*d^2*Sqrt[a + b*x] + 2*b^2*Sqrt[a + b]*c*d*x*Sqrt[a + b*x] - 2*a*b*Sqrt[a + b]*d^2*x*Sqrt[a + b*x] + 2*a*b^2*c*Sqrt[c + d]*Sqrt[c + d*x] - 2*a^2*b*d*Sqrt[c + d]*Sqrt[c + d*x] + 2*b^3*c*Sqrt[c + d]*x*Sqrt[c + d*x] - 2*a*b^2*d*Sqrt[c + d]*x*Sqrt[c + d*x] - 4*b^2*Sqrt[a + b]*c*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 2*a*b*Sqrt[a + b]*d*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] - 2*b^2*Sqrt[a + b]*d*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x]))","B",1
1498,1,1190,66,3.4219301,"\int \frac{1}{(a+b x)^{5/2} \sqrt{c+d x}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(5/2)*Sqrt[c + d*x]),x]","\frac{\left(\frac{1}{6 (a+b) \sqrt{c+d}}-\frac{\sqrt{a+b x}}{6 (a+b)^{3/2} \sqrt{c+d}}\right) \left(\sqrt{c+d}-\sqrt{c+d x}\right)^6 \left(\frac{4 b \left(-6 c d \sqrt{c+d} a^2+6 d^2 \sqrt{c+d x} a^2+6 c d \sqrt{c+d x} a^2-7 b c d \sqrt{c+d} x a-2 b c^2 \sqrt{c+d} a-7 b c d \sqrt{c+d} a+6 \sqrt{a+b} c d \sqrt{c+d} \sqrt{a+b x} a+2 b c^2 \sqrt{c+d x} a+6 b d^2 \sqrt{c+d x} a+8 b c d \sqrt{c+d x} a+6 b d^2 x \sqrt{c+d x} a+6 b c d x \sqrt{c+d x} a-6 \sqrt{a+b} d^2 \sqrt{a+b x} \sqrt{c+d x} a-6 \sqrt{a+b} c d \sqrt{a+b x} \sqrt{c+d x} a+3 b^2 d^2 \sqrt{c+d} x^2+b^2 c d \sqrt{c+d} x^2+2 b^2 c^2 \sqrt{c+d} x+3 b^2 d^2 \sqrt{c+d} x+2 b^2 c d \sqrt{c+d} x+2 b^2 c^2 \sqrt{c+d}+b^2 c d \sqrt{c+d}+4 b \sqrt{a+b} c d \sqrt{c+d} x \sqrt{a+b x}+2 b \sqrt{a+b} c^2 \sqrt{c+d} \sqrt{a+b x}+4 b \sqrt{a+b} c d \sqrt{c+d} \sqrt{a+b x}-2 b^2 c^2 \sqrt{c+d x}-2 b^2 c d \sqrt{c+d x}-2 b^2 c^2 x \sqrt{c+d x}-2 b^2 c d x \sqrt{c+d x}-2 b \sqrt{a+b} c^2 \sqrt{a+b x} \sqrt{c+d x}-3 b \sqrt{a+b} d^2 \sqrt{a+b x} \sqrt{c+d x}-5 b \sqrt{a+b} c d \sqrt{a+b x} \sqrt{c+d x}-3 b \sqrt{a+b} d^2 x \sqrt{a+b x} \sqrt{c+d x}-3 b \sqrt{a+b} c d x \sqrt{a+b x} \sqrt{c+d x}\right)}{\left(\sqrt{c+d}-\sqrt{c+d x}\right)^4}-\frac{4 a \sqrt{c+d} \left(-6 c^2 b^2-2 d^2 b^2-2 d^2 x^2 b^2-7 c d b^2-10 d^2 x b^2-7 c d x b^2+4 d \sqrt{c+d} x \sqrt{c+d x} b^2+6 c \sqrt{c+d} \sqrt{c+d x} b^2+4 d \sqrt{c+d} \sqrt{c+d x} b^2-7 a d^2 b-2 a c d b-7 a d^2 x b+4 \sqrt{a+b} d^2 \sqrt{a+b x} b+2 \sqrt{a+b} c d \sqrt{a+b x} b+4 \sqrt{a+b} d^2 x \sqrt{a+b x} b+2 a d \sqrt{c+d} \sqrt{c+d x} b-2 \sqrt{a+b} d \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x} b-6 a^2 d^2+6 a \sqrt{a+b} d^2 \sqrt{a+b x}\right)}{\left(\sqrt{c+d}-\sqrt{c+d x}\right)^4}\right)}{\left(\sqrt{c+d x}-\sqrt{c+d}\right) \left(-\sqrt{a+b} d x b-c \sqrt{a+b x} b+\sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x} b-a \sqrt{a+b} d+a d \sqrt{a+b x}\right)^3}","\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,"((1/(6*(a + b)*Sqrt[c + d]) - Sqrt[a + b*x]/(6*(a + b)^(3/2)*Sqrt[c + d]))*(Sqrt[c + d] - Sqrt[c + d*x])^6*((-4*a*Sqrt[c + d]*(-6*b^2*c^2 - 2*a*b*c*d - 7*b^2*c*d - 6*a^2*d^2 - 7*a*b*d^2 - 2*b^2*d^2 - 7*b^2*c*d*x - 7*a*b*d^2*x - 10*b^2*d^2*x - 2*b^2*d^2*x^2 + 2*b*Sqrt[a + b]*c*d*Sqrt[a + b*x] + 6*a*Sqrt[a + b]*d^2*Sqrt[a + b*x] + 4*b*Sqrt[a + b]*d^2*Sqrt[a + b*x] + 4*b*Sqrt[a + b]*d^2*x*Sqrt[a + b*x] + 6*b^2*c*Sqrt[c + d]*Sqrt[c + d*x] + 2*a*b*d*Sqrt[c + d]*Sqrt[c + d*x] + 4*b^2*d*Sqrt[c + d]*Sqrt[c + d*x] + 4*b^2*d*Sqrt[c + d]*x*Sqrt[c + d*x] - 2*b*Sqrt[a + b]*d*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x]))/(Sqrt[c + d] - Sqrt[c + d*x])^4 + (4*b*(-2*a*b*c^2*Sqrt[c + d] + 2*b^2*c^2*Sqrt[c + d] - 6*a^2*c*d*Sqrt[c + d] - 7*a*b*c*d*Sqrt[c + d] + b^2*c*d*Sqrt[c + d] + 2*b^2*c^2*Sqrt[c + d]*x - 7*a*b*c*d*Sqrt[c + d]*x + 2*b^2*c*d*Sqrt[c + d]*x + 3*b^2*d^2*Sqrt[c + d]*x + b^2*c*d*Sqrt[c + d]*x^2 + 3*b^2*d^2*Sqrt[c + d]*x^2 + 2*b*Sqrt[a + b]*c^2*Sqrt[c + d]*Sqrt[a + b*x] + 6*a*Sqrt[a + b]*c*d*Sqrt[c + d]*Sqrt[a + b*x] + 4*b*Sqrt[a + b]*c*d*Sqrt[c + d]*Sqrt[a + b*x] + 4*b*Sqrt[a + b]*c*d*Sqrt[c + d]*x*Sqrt[a + b*x] + 2*a*b*c^2*Sqrt[c + d*x] - 2*b^2*c^2*Sqrt[c + d*x] + 6*a^2*c*d*Sqrt[c + d*x] + 8*a*b*c*d*Sqrt[c + d*x] - 2*b^2*c*d*Sqrt[c + d*x] + 6*a^2*d^2*Sqrt[c + d*x] + 6*a*b*d^2*Sqrt[c + d*x] - 2*b^2*c^2*x*Sqrt[c + d*x] + 6*a*b*c*d*x*Sqrt[c + d*x] - 2*b^2*c*d*x*Sqrt[c + d*x] + 6*a*b*d^2*x*Sqrt[c + d*x] - 2*b*Sqrt[a + b]*c^2*Sqrt[a + b*x]*Sqrt[c + d*x] - 6*a*Sqrt[a + b]*c*d*Sqrt[a + b*x]*Sqrt[c + d*x] - 5*b*Sqrt[a + b]*c*d*Sqrt[a + b*x]*Sqrt[c + d*x] - 6*a*Sqrt[a + b]*d^2*Sqrt[a + b*x]*Sqrt[c + d*x] - 3*b*Sqrt[a + b]*d^2*Sqrt[a + b*x]*Sqrt[c + d*x] - 3*b*Sqrt[a + b]*c*d*x*Sqrt[a + b*x]*Sqrt[c + d*x] - 3*b*Sqrt[a + b]*d^2*x*Sqrt[a + b*x]*Sqrt[c + d*x]))/(Sqrt[c + d] - Sqrt[c + d*x])^4))/((-Sqrt[c + d] + Sqrt[c + d*x])*(-(a*Sqrt[a + b]*d) - b*Sqrt[a + b]*d*x - b*c*Sqrt[a + b*x] + a*d*Sqrt[a + b*x] + b*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x])^3)","B",1
1499,1,10544,101,31.9834501,"\int \frac{1}{(a+b x)^{7/2} \sqrt{c+d x}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(7/2)*Sqrt[c + d*x]),x]","\text{Result too large to show}","-\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,"Result too large to show","B",1
1500,-1,0,136,180.0239365,"\int \frac{1}{(a+b x)^{9/2} \sqrt{c+d x}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(9/2)*Sqrt[c + d*x]),x]","\text{\$Aborted}","\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,"$Aborted","F",-1
1501,-1,0,171,180.0920556,"\int \frac{1}{(a+b x)^{11/2} \sqrt{c+d x}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(11/2)*Sqrt[c + d*x]),x]","\text{\$Aborted}","-\frac{256 d^4 \sqrt{c+d x}}{315 \sqrt{a+b x} (b c-a d)^5}+\frac{128 d^3 \sqrt{c+d x}}{315 (a+b x)^{3/2} (b c-a d)^4}-\frac{32 d^2 \sqrt{c+d x}}{105 (a+b x)^{5/2} (b c-a d)^3}+\frac{16 d \sqrt{c+d x}}{63 (a+b x)^{7/2} (b c-a d)^2}-\frac{2 \sqrt{c+d x}}{9 (a+b x)^{9/2} (b c-a d)}",1,"$Aborted","F",-1
1502,-1,0,174,180.0193231,"\int \frac{(a+b x)^{7/2}}{(c+d x)^{3/2}} \, dx","IntegrateAlgebraic[(a + b*x)^(7/2)/(c + d*x)^(3/2),x]","\text{\$Aborted}","-\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{35 b \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^2}{8 d^4}-\frac{35 b (a+b x)^{3/2} \sqrt{c+d x} (b c-a d)}{12 d^3}+\frac{7 b (a+b x)^{5/2} \sqrt{c+d x}}{3 d^2}-\frac{2 (a+b x)^{7/2}}{d \sqrt{c+d x}}",1,"$Aborted","F",-1
1503,1,2049,138,161.7079351,"\int \frac{(a+b x)^{5/2}}{(c+d x)^{3/2}} \, dx","IntegrateAlgebraic[(a + b*x)^(5/2)/(c + d*x)^(3/2),x]","\text{Result too large to show}","\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{15 b \sqrt{a+b x} \sqrt{c+d x} (b c-a d)}{4 d^3}+\frac{5 b (a+b x)^{3/2} \sqrt{c+d x}}{2 d^2}-\frac{2 (a+b x)^{5/2}}{d \sqrt{c+d x}}",1,"((Sqrt[c + d] - Sqrt[c + d*x])^7*((-3*b^6*Sqrt[a + b]*c^2)/(2*d^3) + (a*b^5*Sqrt[a + b]*c)/d^2 - (2*b^6*Sqrt[a + b]*c)/d^2 + (a^2*b^4*Sqrt[a + b])/(2*d) + (2*a*b^5*Sqrt[a + b])/d - (b^6*c^2*Sqrt[a + b*x])/(2*d^3) - (3*a*b^5*c*Sqrt[a + b*x])/d^2 - (4*b^6*c*Sqrt[a + b*x])/d^2 - (a^2*b^4*Sqrt[a + b*x])/(2*d) - (4*a*b^5*Sqrt[a + b*x])/d - (4*b^6*Sqrt[a + b*x])/d + (2*b^6*Sqrt[a + b]*c^2*Sqrt[c + d*x])/(d^3*Sqrt[c + d]) + (2*a*b^5*Sqrt[a + b]*c*Sqrt[c + d*x])/(d^2*Sqrt[c + d]) + (6*b^6*Sqrt[a + b]*c*Sqrt[c + d*x])/(d^2*Sqrt[c + d]) + (2*a*b^5*Sqrt[a + b]*Sqrt[c + d*x])/(d*Sqrt[c + d]) + (4*b^6*Sqrt[a + b]*Sqrt[c + d*x])/(d*Sqrt[c + d])))/(-(b*c) + a*d - Sqrt[a + b]*d*Sqrt[a + b*x] + b*Sqrt[c + d]*Sqrt[c + d*x])^4 + ((Sqrt[c + d] - Sqrt[c + d*x])^5*((-13*b^5*Sqrt[a + b]*c^2)/(2*d^3) + (a*b^4*Sqrt[a + b]*c)/d^2 - (12*b^5*Sqrt[a + b]*c)/d^2 + (3*a^2*b^3*Sqrt[a + b])/(2*d) + (4*a*b^4*Sqrt[a + b])/d - (4*b^5*Sqrt[a + b])/d - (3*b^5*c^2*Sqrt[a + b*x])/(2*d^3) - (9*a*b^4*c*Sqrt[a + b*x])/d^2 - (12*b^5*c*Sqrt[a + b*x])/d^2 - (3*a^2*b^3*Sqrt[a + b*x])/(2*d) - (12*a*b^4*Sqrt[a + b*x])/d - (12*b^5*Sqrt[a + b*x])/d + (8*b^5*Sqrt[a + b]*c^2*Sqrt[c + d*x])/(d^3*Sqrt[c + d]) + (8*a*b^4*Sqrt[a + b]*c*Sqrt[c + d*x])/(d^2*Sqrt[c + d]) + (24*b^5*Sqrt[a + b]*c*Sqrt[c + d*x])/(d^2*Sqrt[c + d]) + (8*a*b^4*Sqrt[a + b]*Sqrt[c + d*x])/(d*Sqrt[c + d]) + (16*b^5*Sqrt[a + b]*Sqrt[c + d*x])/(d*Sqrt[c + d])))/(-(b*c) + a*d - Sqrt[a + b]*d*Sqrt[a + b*x] + b*Sqrt[c + d]*Sqrt[c + d*x])^3 + ((Sqrt[c + d] - Sqrt[c + d*x])^3*((-27*b^4*Sqrt[a + b]*c^2)/(4*d^3) - (13*a*b^3*Sqrt[a + b]*c)/(2*d^2) - (20*b^4*Sqrt[a + b]*c)/d^2 + (13*a^2*b^2*Sqrt[a + b])/(4*d) - (10*b^4*Sqrt[a + b])/d + (3*b^4*c^2*Sqrt[a + b*x])/(4*d^3) - (15*a*b^3*c*Sqrt[a + b*x])/(2*d^2) - (6*b^4*c*Sqrt[a + b*x])/d^2 - (13*a^2*b^2*Sqrt[a + b*x])/(4*d) - (14*a*b^3*Sqrt[a + b*x])/d - (10*b^4*Sqrt[a + b*x])/d + (6*b^4*Sqrt[a + b]*c^2*Sqrt[c + d*x])/(d^3*Sqrt[c + d]) + (14*a*b^3*Sqrt[a + b]*c*Sqrt[c + d*x])/(d^2*Sqrt[c + d]) + (26*b^4*Sqrt[a + b]*c*Sqrt[c + d*x])/(d^2*Sqrt[c + d]) + (14*a*b^3*Sqrt[a + b]*Sqrt[c + d*x])/(d*Sqrt[c + d]) + (20*b^4*Sqrt[a + b]*Sqrt[c + d*x])/(d*Sqrt[c + d])))/(-(b*c) + a*d - Sqrt[a + b]*d*Sqrt[a + b*x] + b*Sqrt[c + d]*Sqrt[c + d*x])^2 + ((9*b^2*Sqrt[a + b]*c^2*Sqrt[c + d] - 42*a*b*Sqrt[a + b]*c*d*Sqrt[c + d] - 24*b^2*Sqrt[a + b]*c*d*Sqrt[c + d] + 9*a^2*Sqrt[a + b]*d^2*Sqrt[c + d] - 24*a*b*Sqrt[a + b]*d^2*Sqrt[c + d] - 24*b^2*Sqrt[a + b]*d^2*Sqrt[c + d] + 7*b^2*c^2*Sqrt[c + d]*Sqrt[a + b*x] - 6*a*b*c*d*Sqrt[c + d]*Sqrt[a + b*x] + 8*b^2*c*d*Sqrt[c + d]*Sqrt[a + b*x] - 9*a^2*d^2*Sqrt[c + d]*Sqrt[a + b*x] - 24*a*b*d^2*Sqrt[c + d]*Sqrt[a + b*x] - 8*b^2*d^2*Sqrt[c + d]*Sqrt[a + b*x] - 16*b^2*Sqrt[a + b]*c^2*Sqrt[c + d*x] + 48*a*b*Sqrt[a + b]*c*d*Sqrt[c + d*x] + 16*b^2*Sqrt[a + b]*c*d*Sqrt[c + d*x] + 48*a*b*Sqrt[a + b]*d^2*Sqrt[c + d*x] + 32*b^2*Sqrt[a + b]*d^2*Sqrt[c + d*x])*(b/(4*d^3) - (b*Sqrt[c + d*x])/(4*d^3*Sqrt[c + d])))/(-(b*c) + a*d - Sqrt[a + b]*d*Sqrt[a + b*x] + b*Sqrt[c + d]*Sqrt[c + d*x]) + (((2*Sqrt[a + b]*(b*c - a*d)^3)/d^3 - (2*(b*c - a*d)^3*Sqrt[a + b*x])/d^3)*(Sqrt[c + d] - Sqrt[c + d*x]))/(-(b*c^2) - b*c*d - b*c*d*x - b*d^2*x + b*c*Sqrt[c + d]*Sqrt[c + d*x] - a*d*Sqrt[c + d]*Sqrt[c + d*x] + Sqrt[a + b]*d*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x]) + (15*Sqrt[b]*(b*c - a*d)^2*ArcTanh[(Sqrt[b]*Sqrt[c + d] - Sqrt[b]*Sqrt[c + d*x])/(Sqrt[a + b]*Sqrt[d] - Sqrt[d]*Sqrt[a + b*x])])/(2*d^(7/2))","B",0
1504,1,1195,98,84.8010099,"\int \frac{(a+b x)^{3/2}}{(c+d x)^{3/2}} \, dx","IntegrateAlgebraic[(a + b*x)^(3/2)/(c + d*x)^(3/2),x]","\frac{\left(-\frac{2 \sqrt{a+b x} b^3}{d}-\frac{c \sqrt{a+b x} b^3}{d^2}+\frac{2 \sqrt{a+b} \sqrt{c+d} \sqrt{c+d x} b^3}{d^2}-\frac{\sqrt{a+b} c b^3}{d^2}-\frac{a \sqrt{a+b x} b^2}{d}+\frac{a \sqrt{a+b} b^2}{d}\right) \left(\sqrt{c+d}-\sqrt{c+d x}\right)^3}{\left(-c b+\sqrt{c+d} \sqrt{c+d x} b+a d-\sqrt{a+b} d \sqrt{a+b x}\right)^2}+\frac{\left(\frac{2 (b c-a d)^2 \sqrt{a+b x}}{d^2 (c+d)}-\frac{2 \sqrt{a+b} (b c-a d)^2}{d^2 (c+d)}\right) \left(b c^2+2 a d c+3 b d c+b d x c-2 \sqrt{a+b} d \sqrt{a+b x} c-b \sqrt{c+d} \sqrt{c+d x} c+2 a d^2+2 b d^2+b d^2 x-2 \sqrt{a+b} d^2 \sqrt{a+b x}-a d \sqrt{c+d} \sqrt{c+d x}-2 b d \sqrt{c+d} \sqrt{c+d x}+\sqrt{a+b} d \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x}\right) \left(\sqrt{c+d}-\sqrt{c+d x}\right)}{-2 b^2 c^3-5 b^2 d c^2-2 a b d c^2-3 b^2 d x c^2+2 b \sqrt{a+b} d \sqrt{a+b x} c^2+2 b^2 \sqrt{c+d} \sqrt{c+d x} c^2+2 a^2 d^2 c-2 b^2 d^2 c+a b d^2 c-b^2 d^2 x^2 c-5 b^2 d^2 x c-a b d^2 x c-2 a \sqrt{a+b} d^2 \sqrt{a+b x} c+2 b \sqrt{a+b} d^2 x \sqrt{a+b x} c+2 b^2 d \sqrt{c+d} x \sqrt{c+d x} c+4 b^2 d \sqrt{c+d} \sqrt{c+d x} c+2 a b d \sqrt{c+d} \sqrt{c+d x} c-2 b \sqrt{a+b} d \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x} c+a b d^3 x^2+2 a^2 d^3 x-2 b^2 d^3 x+a b d^3 x-2 a \sqrt{a+b} d^3 x \sqrt{a+b x}-2 a b d^2 \sqrt{c+d} x \sqrt{c+d x}-4 a^2 d^2 \sqrt{c+d} \sqrt{c+d x}-4 a b d^2 \sqrt{c+d} \sqrt{c+d x}+4 a \sqrt{a+b} d^2 \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x}+2 b \sqrt{a+b} d^2 \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x}}+\frac{\left(\frac{b \sqrt{c+d}}{d^2}-\frac{b \sqrt{c+d x}}{d^2}\right) \left(-3 \sqrt{a+b} c b-2 \sqrt{a+b} d b-c \sqrt{a+b x} b-2 d \sqrt{a+b x} b+4 \sqrt{a+b} \sqrt{c+d} \sqrt{c+d x} b+a \sqrt{a+b} d-a d \sqrt{a+b x}\right)}{-c b+\sqrt{c+d} \sqrt{c+d x} b+a d-\sqrt{a+b} d \sqrt{a+b x}}+\left(\frac{6 a \sqrt{b}}{d^{3/2}}-\frac{6 b^{3/2} c}{d^{5/2}}\right) \tanh ^{-1}\left(\frac{\sqrt{b} \left(\sqrt{c+d}-\sqrt{c+d x}\right)}{\sqrt{a+b} \sqrt{d}-\sqrt{d} \sqrt{a+b x}}\right)","-\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{3 b \sqrt{a+b x} \sqrt{c+d x}}{d^2}-\frac{2 (a+b x)^{3/2}}{d \sqrt{c+d x}}",1,"(((b*Sqrt[c + d])/d^2 - (b*Sqrt[c + d*x])/d^2)*(-3*b*Sqrt[a + b]*c + a*Sqrt[a + b]*d - 2*b*Sqrt[a + b]*d - b*c*Sqrt[a + b*x] - a*d*Sqrt[a + b*x] - 2*b*d*Sqrt[a + b*x] + 4*b*Sqrt[a + b]*Sqrt[c + d]*Sqrt[c + d*x]))/(-(b*c) + a*d - Sqrt[a + b]*d*Sqrt[a + b*x] + b*Sqrt[c + d]*Sqrt[c + d*x]) + ((Sqrt[c + d] - Sqrt[c + d*x])^3*(-((b^3*Sqrt[a + b]*c)/d^2) + (a*b^2*Sqrt[a + b])/d - (b^3*c*Sqrt[a + b*x])/d^2 - (a*b^2*Sqrt[a + b*x])/d - (2*b^3*Sqrt[a + b*x])/d + (2*b^3*Sqrt[a + b]*Sqrt[c + d]*Sqrt[c + d*x])/d^2))/(-(b*c) + a*d - Sqrt[a + b]*d*Sqrt[a + b*x] + b*Sqrt[c + d]*Sqrt[c + d*x])^2 + (((-2*Sqrt[a + b]*(b*c - a*d)^2)/(d^2*(c + d)) + (2*(b*c - a*d)^2*Sqrt[a + b*x])/(d^2*(c + d)))*(Sqrt[c + d] - Sqrt[c + d*x])*(b*c^2 + 2*a*c*d + 3*b*c*d + 2*a*d^2 + 2*b*d^2 + b*c*d*x + b*d^2*x - 2*Sqrt[a + b]*c*d*Sqrt[a + b*x] - 2*Sqrt[a + b]*d^2*Sqrt[a + b*x] - b*c*Sqrt[c + d]*Sqrt[c + d*x] - a*d*Sqrt[c + d]*Sqrt[c + d*x] - 2*b*d*Sqrt[c + d]*Sqrt[c + d*x] + Sqrt[a + b]*d*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x]))/(-2*b^2*c^3 - 2*a*b*c^2*d - 5*b^2*c^2*d + 2*a^2*c*d^2 + a*b*c*d^2 - 2*b^2*c*d^2 - 3*b^2*c^2*d*x - a*b*c*d^2*x - 5*b^2*c*d^2*x + 2*a^2*d^3*x + a*b*d^3*x - 2*b^2*d^3*x - b^2*c*d^2*x^2 + a*b*d^3*x^2 + 2*b*Sqrt[a + b]*c^2*d*Sqrt[a + b*x] - 2*a*Sqrt[a + b]*c*d^2*Sqrt[a + b*x] + 2*b*Sqrt[a + b]*c*d^2*x*Sqrt[a + b*x] - 2*a*Sqrt[a + b]*d^3*x*Sqrt[a + b*x] + 2*b^2*c^2*Sqrt[c + d]*Sqrt[c + d*x] + 2*a*b*c*d*Sqrt[c + d]*Sqrt[c + d*x] + 4*b^2*c*d*Sqrt[c + d]*Sqrt[c + d*x] - 4*a^2*d^2*Sqrt[c + d]*Sqrt[c + d*x] - 4*a*b*d^2*Sqrt[c + d]*Sqrt[c + d*x] + 2*b^2*c*d*Sqrt[c + d]*x*Sqrt[c + d*x] - 2*a*b*d^2*Sqrt[c + d]*x*Sqrt[c + d*x] - 2*b*Sqrt[a + b]*c*d*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 4*a*Sqrt[a + b]*d^2*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 2*b*Sqrt[a + b]*d^2*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x]) + ((-6*b^(3/2)*c)/d^(5/2) + (6*a*Sqrt[b])/d^(3/2))*ArcTanh[(Sqrt[b]*(Sqrt[c + d] - Sqrt[c + d*x]))/(Sqrt[a + b]*Sqrt[d] - Sqrt[d]*Sqrt[a + b*x])]","B",1
1505,1,661,66,5.2317786,"\int \frac{\sqrt{a+b x}}{(c+d x)^{3/2}} \, dx","IntegrateAlgebraic[Sqrt[a + b*x]/(c + d*x)^(3/2),x]","\frac{\sqrt{a+b} \left(-2 \sqrt{c+d} (b c-a d) \left(6 a c d+2 a d^2 x+4 a d^2+2 b c^2+5 b c d x+5 b c d+b d^2 x^2+5 b d^2 x+2 b d^2\right)-2 \sqrt{c+d x} (b c-a d) \left(-6 a c d-6 a d^2-2 b c^2-4 b c d x-6 b c d-4 b d^2 x-4 b d^2\right)\right)-2 \sqrt{c+d} \sqrt{a+b x} (b c-a d) \left(-6 a c d-2 a d^2 x-4 a d^2-2 b c^2-2 b c d x-8 b c d-4 b d^2 x-4 b d^2\right)-2 \sqrt{a+b x} \sqrt{c+d x} (b c-a d) \left(6 a c d+6 a d^2+2 b c^2+b c d x+9 b c d+b d^2 x+7 b d^2\right)}{d (c+d)^{3/2} \sqrt{c+d x} \left(4 a^2 d^2-2 a b c d+2 a b d^2 x+4 a b d^2-2 b^2 c^2-2 b^2 c d x-4 b^2 c d\right)+d (c+d) \left(-2 a^2 c d^2-2 a^2 d^3 x+2 a b c^2 d+a b c d^2 x-a b c d^2-a b d^3 x^2-a b d^3 x+2 b^2 c^3+3 b^2 c^2 d x+5 b^2 c^2 d+b^2 c d^2 x^2+5 b^2 c d^2 x+2 b^2 c d^2+2 b^2 d^3 x\right)+\sqrt{a+b} \sqrt{a+b x} \left(d (c+d) \left(2 a c d^2+2 a d^3 x-2 b c^2 d-2 b c d^2 x\right)+d (c+d)^{3/2} \sqrt{c+d x} \left(-4 a d^2+2 b c d-2 b d^2\right)\right)}+\frac{4 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d}-\sqrt{b} \sqrt{c+d x}}{\sqrt{d} \sqrt{a+b}-\sqrt{d} \sqrt{a+b x}}\right)}{d^{3/2}}","\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[c + d]*(b*c - a*d)*Sqrt[a + b*x]*(-2*b*c^2 - 6*a*c*d - 8*b*c*d - 4*a*d^2 - 4*b*d^2 - 2*b*c*d*x - 2*a*d^2*x - 4*b*d^2*x) - 2*(b*c - a*d)*Sqrt[a + b*x]*Sqrt[c + d*x]*(2*b*c^2 + 6*a*c*d + 9*b*c*d + 6*a*d^2 + 7*b*d^2 + b*c*d*x + b*d^2*x) + Sqrt[a + b]*(-2*(b*c - a*d)*Sqrt[c + d*x]*(-2*b*c^2 - 6*a*c*d - 6*b*c*d - 6*a*d^2 - 4*b*d^2 - 4*b*c*d*x - 4*b*d^2*x) - 2*Sqrt[c + d]*(b*c - a*d)*(2*b*c^2 + 6*a*c*d + 5*b*c*d + 4*a*d^2 + 2*b*d^2 + 5*b*c*d*x + 2*a*d^2*x + 5*b*d^2*x + b*d^2*x^2)))/(d*(c + d)^(3/2)*Sqrt[c + d*x]*(-2*b^2*c^2 - 2*a*b*c*d - 4*b^2*c*d + 4*a^2*d^2 + 4*a*b*d^2 - 2*b^2*c*d*x + 2*a*b*d^2*x) + d*(c + d)*(2*b^2*c^3 + 2*a*b*c^2*d + 5*b^2*c^2*d - 2*a^2*c*d^2 - a*b*c*d^2 + 2*b^2*c*d^2 + 3*b^2*c^2*d*x + a*b*c*d^2*x + 5*b^2*c*d^2*x - 2*a^2*d^3*x - a*b*d^3*x + 2*b^2*d^3*x + b^2*c*d^2*x^2 - a*b*d^3*x^2) + Sqrt[a + b]*Sqrt[a + b*x]*(d*(c + d)^(3/2)*(2*b*c*d - 4*a*d^2 - 2*b*d^2)*Sqrt[c + d*x] + d*(c + d)*(-2*b*c^2*d + 2*a*c*d^2 - 2*b*c*d^2*x + 2*a*d^3*x))) + (4*Sqrt[b]*ArcTanh[(Sqrt[b]*Sqrt[c + d] - Sqrt[b]*Sqrt[c + d*x])/(Sqrt[a + b]*Sqrt[d] - Sqrt[d]*Sqrt[a + b*x])])/d^(3/2)","B",1
1506,1,688,30,1.2910782,"\int \frac{1}{\sqrt{a+b x} (c+d x)^{3/2}} \, dx","IntegrateAlgebraic[1/(Sqrt[a + b*x]*(c + d*x)^(3/2)),x]","\frac{\left(\sqrt{c+d}-\sqrt{c+d x}\right)^4 \left(\frac{\sqrt{a+b}}{c+d}-\frac{\sqrt{a+b x}}{c+d}\right) \left(b (c+d)-\frac{d \left(\sqrt{a+b}-\sqrt{a+b x}\right) \left(2 \sqrt{a+b} \sqrt{c+d} \sqrt{c+d x}+c \sqrt{a+b x}-3 c \sqrt{a+b}+d \sqrt{a+b x}-3 d \sqrt{a+b}\right)}{\left(\sqrt{c+d}-\sqrt{c+d x}\right)^2}\right)}{\left(\sqrt{c+d x}-\sqrt{c+d}\right) \left(-4 a^2 d^2 \sqrt{c+d} \sqrt{c+d x}+2 a^2 c d^2+2 a^2 d^3 x+2 b c^2 d \sqrt{a+b} \sqrt{a+b x}-2 a b c^2 d-a b c d^2 x-2 a c d^2 \sqrt{a+b} \sqrt{a+b x}+2 b c d^2 x \sqrt{a+b} \sqrt{a+b x}-2 a b d^2 x \sqrt{c+d} \sqrt{c+d x}-4 a b d^2 \sqrt{c+d} \sqrt{c+d x}+4 a d^2 \sqrt{a+b} \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x}+2 b d^2 \sqrt{a+b} \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x}+a b c d^2+2 a b c d \sqrt{c+d} \sqrt{c+d x}-2 b c d \sqrt{a+b} \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x}+a b d^3 x^2+a b d^3 x-2 a d^3 x \sqrt{a+b} \sqrt{a+b x}-2 b^2 c^3-3 b^2 c^2 d x+2 b^2 c^2 \sqrt{c+d} \sqrt{c+d x}-5 b^2 c^2 d-b^2 c d^2 x^2-5 b^2 c d^2 x-2 b^2 c d^2+2 b^2 c d x \sqrt{c+d} \sqrt{c+d x}+4 b^2 c d \sqrt{c+d} \sqrt{c+d x}-2 b^2 d^3 x\right)}","\frac{2 \sqrt{a+b x}}{\sqrt{c+d x} (b c-a d)}",1,"((Sqrt[a + b]/(c + d) - Sqrt[a + b*x]/(c + d))*(Sqrt[c + d] - Sqrt[c + d*x])^4*(b*(c + d) - (d*(Sqrt[a + b] - Sqrt[a + b*x])*(-3*Sqrt[a + b]*c - 3*Sqrt[a + b]*d + c*Sqrt[a + b*x] + d*Sqrt[a + b*x] + 2*Sqrt[a + b]*Sqrt[c + d]*Sqrt[c + d*x]))/(Sqrt[c + d] - Sqrt[c + d*x])^2))/((-Sqrt[c + d] + Sqrt[c + d*x])*(-2*b^2*c^3 - 2*a*b*c^2*d - 5*b^2*c^2*d + 2*a^2*c*d^2 + a*b*c*d^2 - 2*b^2*c*d^2 - 3*b^2*c^2*d*x - a*b*c*d^2*x - 5*b^2*c*d^2*x + 2*a^2*d^3*x + a*b*d^3*x - 2*b^2*d^3*x - b^2*c*d^2*x^2 + a*b*d^3*x^2 + 2*b*Sqrt[a + b]*c^2*d*Sqrt[a + b*x] - 2*a*Sqrt[a + b]*c*d^2*Sqrt[a + b*x] + 2*b*Sqrt[a + b]*c*d^2*x*Sqrt[a + b*x] - 2*a*Sqrt[a + b]*d^3*x*Sqrt[a + b*x] + 2*b^2*c^2*Sqrt[c + d]*Sqrt[c + d*x] + 2*a*b*c*d*Sqrt[c + d]*Sqrt[c + d*x] + 4*b^2*c*d*Sqrt[c + d]*Sqrt[c + d*x] - 4*a^2*d^2*Sqrt[c + d]*Sqrt[c + d*x] - 4*a*b*d^2*Sqrt[c + d]*Sqrt[c + d*x] + 2*b^2*c*d*Sqrt[c + d]*x*Sqrt[c + d*x] - 2*a*b*d^2*Sqrt[c + d]*x*Sqrt[c + d*x] - 2*b*Sqrt[a + b]*c*d*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 4*a*Sqrt[a + b]*d^2*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 2*b*Sqrt[a + b]*d^2*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x]))","B",1
1507,1,277,62,1.7121014,"\int \frac{1}{(a+b x)^{3/2} (c+d x)^{3/2}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(3/2)*(c + d*x)^(3/2)),x]","\frac{\left(\sqrt{c+d}-\sqrt{c+d x}\right)^4 \left(\frac{1}{\sqrt{c+d}}-\frac{\sqrt{a+b x}}{\sqrt{a+b} \sqrt{c+d}}\right) \left(\frac{d \left(\sqrt{a+b}-\sqrt{a+b x}\right)^2}{\left(\sqrt{c+d}-\sqrt{c+d x}\right)^2}+b\right)}{\left(\sqrt{c+d x}-\sqrt{c+d}\right) \left(-d \sqrt{a+b} \sqrt{a+b x} \sqrt{c+d x}+a d \sqrt{c+d x}-b c \sqrt{c+d x}+b d x \sqrt{c+d}+b c \sqrt{c+d}\right) \left(b \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x}-b c \sqrt{a+b x}+b d x \left(-\sqrt{a+b}\right)+a d \sqrt{a+b x}-a d \sqrt{a+b}\right)}","-\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,"((1/Sqrt[c + d] - Sqrt[a + b*x]/(Sqrt[a + b]*Sqrt[c + d]))*(Sqrt[c + d] - Sqrt[c + d*x])^4*(b + (d*(Sqrt[a + b] - Sqrt[a + b*x])^2)/(Sqrt[c + d] - Sqrt[c + d*x])^2))/((-Sqrt[c + d] + Sqrt[c + d*x])*(b*c*Sqrt[c + d] + b*d*Sqrt[c + d]*x - b*c*Sqrt[c + d*x] + a*d*Sqrt[c + d*x] - Sqrt[a + b]*d*Sqrt[a + b*x]*Sqrt[c + d*x])*(-(a*Sqrt[a + b]*d) - b*Sqrt[a + b]*d*x - b*c*Sqrt[a + b*x] + a*d*Sqrt[a + b*x] + b*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x]))","B",1
1508,1,1624,101,22.2796025,"\int \frac{1}{(a+b x)^{5/2} (c+d x)^{3/2}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(5/2)*(c + d*x)^(3/2)),x]","\frac{\left(\frac{1}{12 (a+b) \sqrt{c+d}}-\frac{\sqrt{a+b x}}{12 (a+b)^{3/2} \sqrt{c+d}}\right) \left(\sqrt{c+d}-\sqrt{c+d x}\right)^8 \left(-\frac{24 a \left(-c b-d b-d x b+\sqrt{c+d} \sqrt{c+d x} b-a d+\sqrt{a+b} d \sqrt{a+b x}\right)^3}{\left(\sqrt{c+d}-\sqrt{c+d x}\right)^6}-\frac{8 b \left(12 c d^2 a^3-12 d^2 \sqrt{c+d} \sqrt{c+d x} a^3+41 b c d^2 a^2+32 b c^2 d a^2+14 b d^3 x a^2+41 b c d^2 x a^2-12 \sqrt{a+b} c d^2 \sqrt{a+b x} a^2-25 b d^2 \sqrt{c+d} x \sqrt{c+d x} a^2-25 b d^2 \sqrt{c+d} \sqrt{c+d x} a^2-32 b c d \sqrt{c+d} \sqrt{c+d x} a^2+12 \sqrt{a+b} d^2 \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x} a^2+4 b^2 c^3 a+25 b^2 c d^2 a+7 b^2 d^3 x^2 a+25 b^2 c d^2 x^2 a+29 b^2 c^2 d a+7 b^2 d^3 x a+54 b^2 c d^2 x a+29 b^2 c^2 d x a-35 b \sqrt{a+b} c d^2 \sqrt{a+b x} a-32 b \sqrt{a+b} c^2 d \sqrt{a+b x} a-14 b \sqrt{a+b} d^3 x \sqrt{a+b x} a-35 b \sqrt{a+b} c d^2 x \sqrt{a+b x} a-12 b^2 d^2 \sqrt{c+d} x^2 \sqrt{c+d x} a-26 b^2 d^2 \sqrt{c+d} x \sqrt{c+d x} a-27 b^2 c d \sqrt{c+d} x \sqrt{c+d x} a-4 b^2 c^2 \sqrt{c+d} \sqrt{c+d x} a-12 b^2 d^2 \sqrt{c+d} \sqrt{c+d x} a-27 b^2 c d \sqrt{c+d} \sqrt{c+d x} a+19 b \sqrt{a+b} d^2 \sqrt{c+d} x \sqrt{a+b x} \sqrt{c+d x} a+19 b \sqrt{a+b} d^2 \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x} a+32 b \sqrt{a+b} c d \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x} a-4 b^3 c^3-4 b^3 d^3 x^3-b^3 c d^2 x^3-b^3 c d^2-4 b^3 d^3 x^2-5 b^3 c^2 d x^2-5 b^3 c^2 d-4 b^3 c^3 x-4 b^3 d^3 x-4 b^2 \sqrt{a+b} c^3 \sqrt{a+b x}-9 b^2 \sqrt{a+b} c d^2 \sqrt{a+b x}-9 b^2 \sqrt{a+b} c d^2 x^2 \sqrt{a+b x}-13 b^2 \sqrt{a+b} c^2 d \sqrt{a+b x}-16 b^2 \sqrt{a+b} c d^2 x \sqrt{a+b x}-13 b^2 \sqrt{a+b} c^2 d x \sqrt{a+b x}+3 b^3 c d \sqrt{c+d} x^2 \sqrt{c+d x}+4 b^3 c^2 \sqrt{c+d} x \sqrt{c+d x}-4 b^3 c d \sqrt{c+d} x \sqrt{c+d x}+4 b^3 c^2 \sqrt{c+d} \sqrt{c+d x}+3 b^3 c d \sqrt{c+d} \sqrt{c+d x}+4 b^2 \sqrt{a+b} d^2 \sqrt{c+d} x^2 \sqrt{a+b x} \sqrt{c+d x}+4 b^2 \sqrt{a+b} d^2 \sqrt{c+d} x \sqrt{a+b x} \sqrt{c+d x}+11 b^2 \sqrt{a+b} c d \sqrt{c+d} x \sqrt{a+b x} \sqrt{c+d x}+4 b^2 \sqrt{a+b} c^2 \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x}+4 b^2 \sqrt{a+b} d^2 \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x}+11 b^2 \sqrt{a+b} c d \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x}\right)}{\left(\sqrt{c+d}-\sqrt{c+d x}\right)^6}\right)}{\left(\sqrt{c+d x}-\sqrt{c+d}\right) \left(b \sqrt{c+d} c-b \sqrt{c+d x} c+b d \sqrt{c+d} x+a d \sqrt{c+d x}-\sqrt{a+b} d \sqrt{a+b x} \sqrt{c+d x}\right) \left(-\sqrt{a+b} d x b-c \sqrt{a+b x} b+\sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x} b-a \sqrt{a+b} d+a d \sqrt{a+b x}\right)^3}","\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,"((1/(12*(a + b)*Sqrt[c + d]) - Sqrt[a + b*x]/(12*(a + b)^(3/2)*Sqrt[c + d]))*(Sqrt[c + d] - Sqrt[c + d*x])^8*((-24*a*(-(b*c) - a*d - b*d - b*d*x + Sqrt[a + b]*d*Sqrt[a + b*x] + b*Sqrt[c + d]*Sqrt[c + d*x])^3)/(Sqrt[c + d] - Sqrt[c + d*x])^6 - (8*b*(4*a*b^2*c^3 - 4*b^3*c^3 + 32*a^2*b*c^2*d + 29*a*b^2*c^2*d - 5*b^3*c^2*d + 12*a^3*c*d^2 + 41*a^2*b*c*d^2 + 25*a*b^2*c*d^2 - b^3*c*d^2 - 4*b^3*c^3*x + 29*a*b^2*c^2*d*x + 41*a^2*b*c*d^2*x + 54*a*b^2*c*d^2*x + 14*a^2*b*d^3*x + 7*a*b^2*d^3*x - 4*b^3*d^3*x - 5*b^3*c^2*d*x^2 + 25*a*b^2*c*d^2*x^2 + 7*a*b^2*d^3*x^2 - 4*b^3*d^3*x^2 - b^3*c*d^2*x^3 - 4*b^3*d^3*x^3 - 4*b^2*Sqrt[a + b]*c^3*Sqrt[a + b*x] - 32*a*b*Sqrt[a + b]*c^2*d*Sqrt[a + b*x] - 13*b^2*Sqrt[a + b]*c^2*d*Sqrt[a + b*x] - 12*a^2*Sqrt[a + b]*c*d^2*Sqrt[a + b*x] - 35*a*b*Sqrt[a + b]*c*d^2*Sqrt[a + b*x] - 9*b^2*Sqrt[a + b]*c*d^2*Sqrt[a + b*x] - 13*b^2*Sqrt[a + b]*c^2*d*x*Sqrt[a + b*x] - 35*a*b*Sqrt[a + b]*c*d^2*x*Sqrt[a + b*x] - 16*b^2*Sqrt[a + b]*c*d^2*x*Sqrt[a + b*x] - 14*a*b*Sqrt[a + b]*d^3*x*Sqrt[a + b*x] - 9*b^2*Sqrt[a + b]*c*d^2*x^2*Sqrt[a + b*x] - 4*a*b^2*c^2*Sqrt[c + d]*Sqrt[c + d*x] + 4*b^3*c^2*Sqrt[c + d]*Sqrt[c + d*x] - 32*a^2*b*c*d*Sqrt[c + d]*Sqrt[c + d*x] - 27*a*b^2*c*d*Sqrt[c + d]*Sqrt[c + d*x] + 3*b^3*c*d*Sqrt[c + d]*Sqrt[c + d*x] - 12*a^3*d^2*Sqrt[c + d]*Sqrt[c + d*x] - 25*a^2*b*d^2*Sqrt[c + d]*Sqrt[c + d*x] - 12*a*b^2*d^2*Sqrt[c + d]*Sqrt[c + d*x] + 4*b^3*c^2*Sqrt[c + d]*x*Sqrt[c + d*x] - 27*a*b^2*c*d*Sqrt[c + d]*x*Sqrt[c + d*x] - 4*b^3*c*d*Sqrt[c + d]*x*Sqrt[c + d*x] - 25*a^2*b*d^2*Sqrt[c + d]*x*Sqrt[c + d*x] - 26*a*b^2*d^2*Sqrt[c + d]*x*Sqrt[c + d*x] + 3*b^3*c*d*Sqrt[c + d]*x^2*Sqrt[c + d*x] - 12*a*b^2*d^2*Sqrt[c + d]*x^2*Sqrt[c + d*x] + 4*b^2*Sqrt[a + b]*c^2*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 32*a*b*Sqrt[a + b]*c*d*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 11*b^2*Sqrt[a + b]*c*d*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 12*a^2*Sqrt[a + b]*d^2*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 19*a*b*Sqrt[a + b]*d^2*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 4*b^2*Sqrt[a + b]*d^2*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 11*b^2*Sqrt[a + b]*c*d*Sqrt[c + d]*x*Sqrt[a + b*x]*Sqrt[c + d*x] + 19*a*b*Sqrt[a + b]*d^2*Sqrt[c + d]*x*Sqrt[a + b*x]*Sqrt[c + d*x] + 4*b^2*Sqrt[a + b]*d^2*Sqrt[c + d]*x*Sqrt[a + b*x]*Sqrt[c + d*x] + 4*b^2*Sqrt[a + b]*d^2*Sqrt[c + d]*x^2*Sqrt[a + b*x]*Sqrt[c + d*x]))/(Sqrt[c + d] - Sqrt[c + d*x])^6))/((-Sqrt[c + d] + Sqrt[c + d*x])*(b*c*Sqrt[c + d] + b*d*Sqrt[c + d]*x - b*c*Sqrt[c + d*x] + a*d*Sqrt[c + d*x] - Sqrt[a + b]*d*Sqrt[a + b*x]*Sqrt[c + d*x])*(-(a*Sqrt[a + b]*d) - b*Sqrt[a + b]*d*x - b*c*Sqrt[a + b*x] + a*d*Sqrt[a + b*x] + b*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x])^3)","B",1
1509,-1,0,136,180.0354921,"\int \frac{1}{(a+b x)^{7/2} (c+d x)^{3/2}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(7/2)*(c + d*x)^(3/2)),x]","\text{\$Aborted}","-\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,"$Aborted","F",-1
1510,-1,0,171,180.0945224,"\int \frac{1}{(a+b x)^{9/2} (c+d x)^{3/2}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(9/2)*(c + d*x)^(3/2)),x]","\text{\$Aborted}","\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,"$Aborted","F",-1
1511,-1,0,206,180.1677702,"\int \frac{1}{(a+b x)^{11/2} (c+d x)^{3/2}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(11/2)*(c + d*x)^(3/2)),x]","\text{\$Aborted}","-\frac{512 d^5 \sqrt{a+b x}}{63 \sqrt{c+d x} (b c-a d)^6}-\frac{256 d^4}{63 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^5}+\frac{64 d^3}{63 (a+b x)^{3/2} \sqrt{c+d x} (b c-a d)^4}-\frac{32 d^2}{63 (a+b x)^{5/2} \sqrt{c+d x} (b c-a d)^3}+\frac{20 d}{63 (a+b x)^{7/2} \sqrt{c+d x} (b c-a d)^2}-\frac{2}{9 (a+b x)^{9/2} \sqrt{c+d x} (b c-a d)}",1,"$Aborted","F",-1
1512,-1,0,204,180.0658638,"\int \frac{(a+b x)^{9/2}}{(c+d x)^{5/2}} \, dx","IntegrateAlgebraic[(a + b*x)^(9/2)/(c + d*x)^(5/2),x]","\text{\$Aborted}","-\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{105 b^2 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^2}{8 d^5}-\frac{35 b^2 (a+b x)^{3/2} \sqrt{c+d x} (b c-a d)}{4 d^4}+\frac{7 b^2 (a+b x)^{5/2} \sqrt{c+d x}}{d^3}-\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,"$Aborted","F",-1
1513,-1,0,170,180.0509083,"\int \frac{(a+b x)^{7/2}}{(c+d x)^{5/2}} \, dx","IntegrateAlgebraic[(a + b*x)^(7/2)/(c + d*x)^(5/2),x]","\text{\$Aborted}","\frac{35 b^{3/2} (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{4 d^{9/2}}-\frac{35 b^2 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)}{4 d^4}+\frac{35 b^2 (a+b x)^{3/2} \sqrt{c+d x}}{6 d^3}-\frac{14 b (a+b x)^{5/2}}{3 d^2 \sqrt{c+d x}}-\frac{2 (a+b x)^{7/2}}{3 d (c+d x)^{3/2}}",1,"$Aborted","F",-1
1514,-1,0,128,180.5300421,"\int \frac{(a+b x)^{5/2}}{(c+d x)^{5/2}} \, dx","IntegrateAlgebraic[(a + b*x)^(5/2)/(c + d*x)^(5/2),x]","\text{\$Aborted}","-\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{5 b^2 \sqrt{a+b x} \sqrt{c+d x}}{d^3}-\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,"$Aborted","F",-1
1515,-1,0,92,180.0555873,"\int \frac{(a+b x)^{3/2}}{(c+d x)^{5/2}} \, dx","IntegrateAlgebraic[(a + b*x)^(3/2)/(c + d*x)^(5/2),x]","\text{\$Aborted}","\frac{2 b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{d^{5/2}}-\frac{2 b \sqrt{a+b x}}{d^2 \sqrt{c+d x}}-\frac{2 (a+b x)^{3/2}}{3 d (c+d x)^{3/2}}",1,"$Aborted","F",-1
1516,1,1652,32,2.3699918,"\int \frac{\sqrt{a+b x}}{(c+d x)^{5/2}} \, dx","IntegrateAlgebraic[Sqrt[a + b*x]/(c + d*x)^(5/2),x]","\frac{\left(\frac{\sqrt{a+b x}}{6 (c+d)^{3/2}}-\frac{\sqrt{a+b}}{6 (c+d)^{3/2}}\right) \left(\sqrt{c+d}-\sqrt{c+d x}\right)^6 \left(\frac{4 a^2 d^2 \left(\sqrt{a+b}-\sqrt{a+b x}\right)^2}{\left(\sqrt{c+d}-\sqrt{c+d x}\right)^2}-\frac{4 a \left(-6 b^2 c^3-11 b^2 d c^2-4 a b d c^2-11 b^2 d x c^2+4 b \sqrt{a+b} d \sqrt{a+b x} c^2+6 b^2 \sqrt{c+d} \sqrt{c+d x} c^2-10 b^2 d^2 c-14 a b d^2 c-4 b^2 d^2 x^2 c-20 b^2 d^2 x c-2 a b d^2 x c+14 b \sqrt{a+b} d^2 \sqrt{a+b x} c+2 b \sqrt{a+b} d^2 x \sqrt{a+b x} c+8 b^2 d \sqrt{c+d} x \sqrt{c+d x} c+8 b^2 d \sqrt{c+d} \sqrt{c+d x} c+4 a b d \sqrt{c+d} \sqrt{c+d x} c-4 b \sqrt{a+b} d \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x} c-3 b^2 d^3-6 a b d^3-6 b^2 d^3 x^2-9 b^2 d^3 x-6 a b d^3 x+6 b \sqrt{a+b} d^3 \sqrt{a+b x}+6 b \sqrt{a+b} d^3 x \sqrt{a+b x}+6 b^2 d^2 \sqrt{c+d} x \sqrt{c+d x}-6 a b d^2 \sqrt{c+d} x \sqrt{c+d x}-6 a^2 d^2 \sqrt{c+d} \sqrt{c+d x}+6 b^2 d^2 \sqrt{c+d} \sqrt{c+d x}+6 a b d^2 \sqrt{c+d} \sqrt{c+d x}+3 b \sqrt{a+b} d^2 \sqrt{c+d} x \sqrt{a+b x} \sqrt{c+d x}+6 a \sqrt{a+b} d^2 \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x}-9 b \sqrt{a+b} d^2 \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x}\right)}{\left(\sqrt{c+d}-\sqrt{c+d x}\right)^4}-\frac{4 b \left(-2 b^2 c^3+2 a b c^3-2 b^2 x c^3-2 b \sqrt{a+b} \sqrt{a+b x} c^3-b^2 d x^2 c^2+6 a^2 d c^2-b^2 d c^2+7 a b d c^2-8 b^2 d x c^2+7 a b d x c^2-6 a \sqrt{a+b} d \sqrt{a+b x} c^2-4 b \sqrt{a+b} d \sqrt{a+b x} c^2-4 b \sqrt{a+b} d x \sqrt{a+b x} c^2+2 b^2 \sqrt{c+d} x \sqrt{c+d x} c^2+2 b^2 \sqrt{c+d} \sqrt{c+d x} c^2-2 a b \sqrt{c+d} \sqrt{c+d x} c^2+2 b \sqrt{a+b} \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x} c^2+12 a^2 d^2 c+6 a b d^2 c-6 b^2 d^2 x^2 c-6 b^2 d^2 x c+12 a b d^2 x c-12 a \sqrt{a+b} d^2 \sqrt{a+b x} c-6 b \sqrt{a+b} d^2 x \sqrt{a+b x} c+6 b^2 d \sqrt{c+d} x \sqrt{c+d x} c-6 a b d \sqrt{c+d} x \sqrt{c+d x} c-6 a^2 d \sqrt{c+d} \sqrt{c+d x} c-6 a b d \sqrt{c+d} \sqrt{c+d x} c+3 b \sqrt{a+b} d \sqrt{c+d} x \sqrt{a+b x} \sqrt{c+d x} c+6 a \sqrt{a+b} d \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x} c+3 b \sqrt{a+b} d \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x} c+6 a^2 d^3+3 a b d^3-6 b^2 d^3 x^2+3 a b d^3 x-6 a \sqrt{a+b} d^3 \sqrt{a+b x}-12 a b d^2 \sqrt{c+d} x \sqrt{c+d x}-12 a^2 d^2 \sqrt{c+d} \sqrt{c+d x}-6 a b d^2 \sqrt{c+d} \sqrt{c+d x}+6 b \sqrt{a+b} d^2 \sqrt{c+d} x \sqrt{a+b x} \sqrt{c+d x}+12 a \sqrt{a+b} d^2 \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x}\right)}{\left(\sqrt{c+d}-\sqrt{c+d x}\right)^4}\right)}{\left(\sqrt{c+d x}-\sqrt{c+d}\right) \left(b \sqrt{c+d} c-b \sqrt{c+d x} c+b d \sqrt{c+d} x+a d \sqrt{c+d x}-\sqrt{a+b} d \sqrt{a+b x} \sqrt{c+d x}\right)^3}","\frac{2 (a+b x)^{3/2}}{3 (c+d x)^{3/2} (b c-a d)}",1,"((-1/6*Sqrt[a + b]/(c + d)^(3/2) + Sqrt[a + b*x]/(6*(c + d)^(3/2)))*(Sqrt[c + d] - Sqrt[c + d*x])^6*((4*a^2*d^2*(Sqrt[a + b] - Sqrt[a + b*x])^2)/(Sqrt[c + d] - Sqrt[c + d*x])^2 - (4*a*(-6*b^2*c^3 - 4*a*b*c^2*d - 11*b^2*c^2*d - 14*a*b*c*d^2 - 10*b^2*c*d^2 - 6*a*b*d^3 - 3*b^2*d^3 - 11*b^2*c^2*d*x - 2*a*b*c*d^2*x - 20*b^2*c*d^2*x - 6*a*b*d^3*x - 9*b^2*d^3*x - 4*b^2*c*d^2*x^2 - 6*b^2*d^3*x^2 + 4*b*Sqrt[a + b]*c^2*d*Sqrt[a + b*x] + 14*b*Sqrt[a + b]*c*d^2*Sqrt[a + b*x] + 6*b*Sqrt[a + b]*d^3*Sqrt[a + b*x] + 2*b*Sqrt[a + b]*c*d^2*x*Sqrt[a + b*x] + 6*b*Sqrt[a + b]*d^3*x*Sqrt[a + b*x] + 6*b^2*c^2*Sqrt[c + d]*Sqrt[c + d*x] + 4*a*b*c*d*Sqrt[c + d]*Sqrt[c + d*x] + 8*b^2*c*d*Sqrt[c + d]*Sqrt[c + d*x] - 6*a^2*d^2*Sqrt[c + d]*Sqrt[c + d*x] + 6*a*b*d^2*Sqrt[c + d]*Sqrt[c + d*x] + 6*b^2*d^2*Sqrt[c + d]*Sqrt[c + d*x] + 8*b^2*c*d*Sqrt[c + d]*x*Sqrt[c + d*x] - 6*a*b*d^2*Sqrt[c + d]*x*Sqrt[c + d*x] + 6*b^2*d^2*Sqrt[c + d]*x*Sqrt[c + d*x] - 4*b*Sqrt[a + b]*c*d*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 6*a*Sqrt[a + b]*d^2*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] - 9*b*Sqrt[a + b]*d^2*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 3*b*Sqrt[a + b]*d^2*Sqrt[c + d]*x*Sqrt[a + b*x]*Sqrt[c + d*x]))/(Sqrt[c + d] - Sqrt[c + d*x])^4 - (4*b*(2*a*b*c^3 - 2*b^2*c^3 + 6*a^2*c^2*d + 7*a*b*c^2*d - b^2*c^2*d + 12*a^2*c*d^2 + 6*a*b*c*d^2 + 6*a^2*d^3 + 3*a*b*d^3 - 2*b^2*c^3*x + 7*a*b*c^2*d*x - 8*b^2*c^2*d*x + 12*a*b*c*d^2*x - 6*b^2*c*d^2*x + 3*a*b*d^3*x - b^2*c^2*d*x^2 - 6*b^2*c*d^2*x^2 - 6*b^2*d^3*x^2 - 2*b*Sqrt[a + b]*c^3*Sqrt[a + b*x] - 6*a*Sqrt[a + b]*c^2*d*Sqrt[a + b*x] - 4*b*Sqrt[a + b]*c^2*d*Sqrt[a + b*x] - 12*a*Sqrt[a + b]*c*d^2*Sqrt[a + b*x] - 6*a*Sqrt[a + b]*d^3*Sqrt[a + b*x] - 4*b*Sqrt[a + b]*c^2*d*x*Sqrt[a + b*x] - 6*b*Sqrt[a + b]*c*d^2*x*Sqrt[a + b*x] - 2*a*b*c^2*Sqrt[c + d]*Sqrt[c + d*x] + 2*b^2*c^2*Sqrt[c + d]*Sqrt[c + d*x] - 6*a^2*c*d*Sqrt[c + d]*Sqrt[c + d*x] - 6*a*b*c*d*Sqrt[c + d]*Sqrt[c + d*x] - 12*a^2*d^2*Sqrt[c + d]*Sqrt[c + d*x] - 6*a*b*d^2*Sqrt[c + d]*Sqrt[c + d*x] + 2*b^2*c^2*Sqrt[c + d]*x*Sqrt[c + d*x] - 6*a*b*c*d*Sqrt[c + d]*x*Sqrt[c + d*x] + 6*b^2*c*d*Sqrt[c + d]*x*Sqrt[c + d*x] - 12*a*b*d^2*Sqrt[c + d]*x*Sqrt[c + d*x] + 2*b*Sqrt[a + b]*c^2*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 6*a*Sqrt[a + b]*c*d*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 3*b*Sqrt[a + b]*c*d*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 12*a*Sqrt[a + b]*d^2*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 3*b*Sqrt[a + b]*c*d*Sqrt[c + d]*x*Sqrt[a + b*x]*Sqrt[c + d*x] + 6*b*Sqrt[a + b]*d^2*Sqrt[c + d]*x*Sqrt[a + b*x]*Sqrt[c + d*x]))/(Sqrt[c + d] - Sqrt[c + d*x])^4))/((-Sqrt[c + d] + Sqrt[c + d*x])*(b*c*Sqrt[c + d] + b*d*Sqrt[c + d]*x - b*c*Sqrt[c + d*x] + a*d*Sqrt[c + d*x] - Sqrt[a + b]*d*Sqrt[a + b*x]*Sqrt[c + d*x])^3)","B",1
1517,1,744,66,2.9450105,"\int \frac{1}{\sqrt{a+b x} (c+d x)^{5/2}} \, dx","IntegrateAlgebraic[1/(Sqrt[a + b*x]*(c + d*x)^(5/2)),x]","\frac{\left(\sqrt{c+d}-\sqrt{c+d x}\right)^6 \left(\frac{\sqrt{a+b x}}{6 \sqrt{a+b} (c+d)^{3/2}}-\frac{1}{6 (c+d)^{3/2}}\right) \left(\frac{3 b^2 \left(-c \sqrt{a+b} \sqrt{c+d x}+2 d \sqrt{c+d} \sqrt{a+b x}-d \sqrt{a+b} \sqrt{c+d x}+c \sqrt{a+b} \sqrt{c+d}-d \sqrt{a+b} \sqrt{c+d}\right)}{\sqrt{c+d}-\sqrt{c+d x}}+\frac{d^2 \left(\sqrt{a+b}-\sqrt{a+b x}\right)^2 \left(-2 a \sqrt{a+b} \sqrt{c+d} \sqrt{c+d x}-6 a \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x}+3 b c x \sqrt{a+b}-6 b c \sqrt{a+b x}+8 a c \sqrt{a+b}+3 b c \sqrt{a+b}+4 a d x \sqrt{a+b}+3 b d x \sqrt{a+b}-6 b d \sqrt{a+b x}+4 a d \sqrt{a+b}+3 b d \sqrt{a+b}\right)}{\left(\sqrt{c+d}-\sqrt{c+d x}\right)^4}+\frac{2 b d \left(\sqrt{a+b}-\sqrt{a+b x}\right) \left(-c \sqrt{a+b} \sqrt{c+d} \sqrt{a+b x}+c \sqrt{a+b} \sqrt{a+b x} \sqrt{c+d x}+3 d \sqrt{a+b} \sqrt{c+d} \sqrt{a+b x}+3 d \sqrt{a+b} \sqrt{a+b x} \sqrt{c+d x}+5 a c \sqrt{c+d x}-3 a d x \sqrt{c+d}+3 a d \sqrt{c+d x}-5 a c \sqrt{c+d}-6 a d \sqrt{c+d}-b c \sqrt{c+d x}-3 b d x \sqrt{c+d}-3 b d \sqrt{c+d x}+b c \sqrt{c+d}\right)}{\left(\sqrt{c+d}-\sqrt{c+d x}\right)^3}\right)}{\left(\sqrt{c+d x}-\sqrt{c+d}\right) \left(-d \sqrt{a+b} \sqrt{a+b x} \sqrt{c+d x}+a d \sqrt{c+d x}-b c \sqrt{c+d x}+b d x \sqrt{c+d}+b c \sqrt{c+d}\right)^3}","\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,"((-1/6*1/(c + d)^(3/2) + Sqrt[a + b*x]/(6*Sqrt[a + b]*(c + d)^(3/2)))*(Sqrt[c + d] - Sqrt[c + d*x])^6*((3*b^2*(Sqrt[a + b]*c*Sqrt[c + d] - Sqrt[a + b]*d*Sqrt[c + d] + 2*d*Sqrt[c + d]*Sqrt[a + b*x] - Sqrt[a + b]*c*Sqrt[c + d*x] - Sqrt[a + b]*d*Sqrt[c + d*x]))/(Sqrt[c + d] - Sqrt[c + d*x]) + (2*b*d*(Sqrt[a + b] - Sqrt[a + b*x])*(-5*a*c*Sqrt[c + d] + b*c*Sqrt[c + d] - 6*a*d*Sqrt[c + d] - 3*a*d*Sqrt[c + d]*x - 3*b*d*Sqrt[c + d]*x - Sqrt[a + b]*c*Sqrt[c + d]*Sqrt[a + b*x] + 3*Sqrt[a + b]*d*Sqrt[c + d]*Sqrt[a + b*x] + 5*a*c*Sqrt[c + d*x] - b*c*Sqrt[c + d*x] + 3*a*d*Sqrt[c + d*x] - 3*b*d*Sqrt[c + d*x] + Sqrt[a + b]*c*Sqrt[a + b*x]*Sqrt[c + d*x] + 3*Sqrt[a + b]*d*Sqrt[a + b*x]*Sqrt[c + d*x]))/(Sqrt[c + d] - Sqrt[c + d*x])^3 + (d^2*(Sqrt[a + b] - Sqrt[a + b*x])^2*(8*a*Sqrt[a + b]*c + 3*b*Sqrt[a + b]*c + 4*a*Sqrt[a + b]*d + 3*b*Sqrt[a + b]*d + 3*b*Sqrt[a + b]*c*x + 4*a*Sqrt[a + b]*d*x + 3*b*Sqrt[a + b]*d*x - 6*b*c*Sqrt[a + b*x] - 6*b*d*Sqrt[a + b*x] - 2*a*Sqrt[a + b]*Sqrt[c + d]*Sqrt[c + d*x] - 6*a*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x]))/(Sqrt[c + d] - Sqrt[c + d*x])^4))/((-Sqrt[c + d] + Sqrt[c + d*x])*(b*c*Sqrt[c + d] + b*d*Sqrt[c + d]*x - b*c*Sqrt[c + d*x] + a*d*Sqrt[c + d*x] - Sqrt[a + b]*d*Sqrt[a + b*x]*Sqrt[c + d*x])^3)","B",1
1518,1,702,98,13.5602633,"\int \frac{1}{(a+b x)^{3/2} (c+d x)^{5/2}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(3/2)*(c + d*x)^(5/2)),x]","\frac{\left(\sqrt{c+d}-\sqrt{c+d x}\right)^8 \left(\frac{1}{12 (c+d)^{3/2}}-\frac{\sqrt{a+b x}}{12 \sqrt{a+b} (c+d)^{3/2}}\right) \left(\frac{b^2 d \left(\sqrt{a+b}-\sqrt{a+b x}\right) \left(6 \sqrt{a+b} \sqrt{c+d} \sqrt{c+d x}-9 c \sqrt{a+b x}+3 c \sqrt{a+b}-13 d \sqrt{a+b x}+7 d \sqrt{a+b}\right)}{\left(\sqrt{c+d}-\sqrt{c+d x}\right)^2}-\frac{d^3 \left(\sqrt{a+b}-\sqrt{a+b x}\right)^4 \left(6 \sqrt{a+b} \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x}+2 a \sqrt{c+d} \sqrt{c+d x}-8 a c-4 a d x-4 a d-6 b \sqrt{c+d} \sqrt{c+d x}-3 b c x+3 b c-3 b d x+3 b d\right)}{\left(\sqrt{c+d}-\sqrt{c+d x}\right)^6}-\frac{b d^2 \left(\sqrt{a+b}-\sqrt{a+b x}\right)^2 \left(20 \sqrt{a+b} \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x}-2 c \sqrt{a+b} \sqrt{a+b x}+6 d \sqrt{a+b} \sqrt{a+b x}-12 a \sqrt{c+d} \sqrt{c+d x}-6 a c-4 a d x-10 a d-20 b \sqrt{c+d} \sqrt{c+d x}-9 b c x+11 b c-13 b d x+7 b d\right)}{\left(\sqrt{c+d}-\sqrt{c+d x}\right)^4}+3 b^3 (c+d)\right)}{\left(\sqrt{c+d x}-\sqrt{c+d}\right) \left(-d \sqrt{a+b} \sqrt{a+b x} \sqrt{c+d x}+a d \sqrt{c+d x}-b c \sqrt{c+d x}+b d x \sqrt{c+d}+b c \sqrt{c+d}\right)^3 \left(b \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x}-b c \sqrt{a+b x}+b d x \left(-\sqrt{a+b}\right)+a d \sqrt{a+b x}-a d \sqrt{a+b}\right)}","-\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,"((1/(12*(c + d)^(3/2)) - Sqrt[a + b*x]/(12*Sqrt[a + b]*(c + d)^(3/2)))*(Sqrt[c + d] - Sqrt[c + d*x])^8*(3*b^3*(c + d) + (b^2*d*(Sqrt[a + b] - Sqrt[a + b*x])*(3*Sqrt[a + b]*c + 7*Sqrt[a + b]*d - 9*c*Sqrt[a + b*x] - 13*d*Sqrt[a + b*x] + 6*Sqrt[a + b]*Sqrt[c + d]*Sqrt[c + d*x]))/(Sqrt[c + d] - Sqrt[c + d*x])^2 - (d^3*(Sqrt[a + b] - Sqrt[a + b*x])^4*(-8*a*c + 3*b*c - 4*a*d + 3*b*d - 3*b*c*x - 4*a*d*x - 3*b*d*x + 2*a*Sqrt[c + d]*Sqrt[c + d*x] - 6*b*Sqrt[c + d]*Sqrt[c + d*x] + 6*Sqrt[a + b]*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x]))/(Sqrt[c + d] - Sqrt[c + d*x])^6 - (b*d^2*(Sqrt[a + b] - Sqrt[a + b*x])^2*(-6*a*c + 11*b*c - 10*a*d + 7*b*d - 9*b*c*x - 4*a*d*x - 13*b*d*x - 2*Sqrt[a + b]*c*Sqrt[a + b*x] + 6*Sqrt[a + b]*d*Sqrt[a + b*x] - 12*a*Sqrt[c + d]*Sqrt[c + d*x] - 20*b*Sqrt[c + d]*Sqrt[c + d*x] + 20*Sqrt[a + b]*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x]))/(Sqrt[c + d] - Sqrt[c + d*x])^4))/((-Sqrt[c + d] + Sqrt[c + d*x])*(b*c*Sqrt[c + d] + b*d*Sqrt[c + d]*x - b*c*Sqrt[c + d*x] + a*d*Sqrt[c + d*x] - Sqrt[a + b]*d*Sqrt[a + b*x]*Sqrt[c + d*x])^3*(-(a*Sqrt[a + b]*d) - b*Sqrt[a + b]*d*x - b*c*Sqrt[a + b*x] + a*d*Sqrt[a + b*x] + b*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x]))","B",1
1519,-1,0,135,180.0337694,"\int \frac{1}{(a+b x)^{5/2} (c+d x)^{5/2}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(5/2)*(c + d*x)^(5/2)),x]","\text{\$Aborted}","\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,"$Aborted","F",-1
1520,-1,0,172,180.1103867,"\int \frac{1}{(a+b x)^{7/2} (c+d x)^{5/2}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(7/2)*(c + d*x)^(5/2)),x]","\text{\$Aborted}","-\frac{256 b d^3 \sqrt{a+b x}}{15 \sqrt{c+d x} (b c-a d)^5}-\frac{128 d^3 \sqrt{a+b x}}{15 (c+d x)^{3/2} (b c-a d)^4}-\frac{32 d^2}{5 \sqrt{a+b x} (c+d x)^{3/2} (b c-a d)^3}+\frac{16 d}{15 (a+b x)^{3/2} (c+d x)^{3/2} (b c-a d)^2}-\frac{2}{5 (a+b x)^{5/2} (c+d x)^{3/2} (b c-a d)}",1,"$Aborted","F",-1
1521,-1,0,207,180.1876822,"\int \frac{1}{(a+b x)^{9/2} (c+d x)^{5/2}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(9/2)*(c + d*x)^(5/2)),x]","\text{\$Aborted}","\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,"$Aborted","F",-1
1522,1,49,19,0.2295963,"\int \frac{1}{\sqrt{a+b x} \sqrt{4+a+b x}} \, dx","IntegrateAlgebraic[1/(Sqrt[a + b*x]*Sqrt[4 + a + b*x]),x]","-\frac{4 \tanh ^{-1}\left(\frac{\sqrt{a+b x+4}-\sqrt{a+b+4}}{\sqrt{a+b}-\sqrt{a+b x}}\right)}{b}","\frac{2 \sinh ^{-1}\left(\frac{1}{2} \sqrt{a+b x}\right)}{b}",1,"(-4*ArcTanh[(-Sqrt[4 + a + b] + Sqrt[4 + a + b*x])/(Sqrt[a + b] - Sqrt[a + b*x])])/b","B",1
1523,1,47,19,0.1541119,"\int \frac{1}{\sqrt{2+b x} \sqrt{6+b x}} \, dx","IntegrateAlgebraic[1/(Sqrt[2 + b*x]*Sqrt[6 + b*x]),x]","-\frac{4 \tanh ^{-1}\left(\frac{\sqrt{b x+6}-\sqrt{b+6}}{\sqrt{b+2}-\sqrt{b x+2}}\right)}{b}","\frac{2 \sinh ^{-1}\left(\frac{1}{2} \sqrt{b x+2}\right)}{b}",1,"(-4*ArcTanh[(-Sqrt[6 + b] + Sqrt[6 + b*x])/(Sqrt[2 + b] - Sqrt[2 + b*x])])/b","B",1
1524,1,47,19,0.1542779,"\int \frac{1}{\sqrt{1+b x} \sqrt{5+b x}} \, dx","IntegrateAlgebraic[1/(Sqrt[1 + b*x]*Sqrt[5 + b*x]),x]","-\frac{4 \tanh ^{-1}\left(\frac{\sqrt{b x+5}-\sqrt{b+5}}{\sqrt{b+1}-\sqrt{b x+1}}\right)}{b}","\frac{2 \sinh ^{-1}\left(\frac{1}{2} \sqrt{b x+1}\right)}{b}",1,"(-4*ArcTanh[(-Sqrt[5 + b] + Sqrt[5 + b*x])/(Sqrt[1 + b] - Sqrt[1 + b*x])])/b","B",1
1525,1,43,17,0.1546956,"\int \frac{1}{\sqrt{b x} \sqrt{4+b x}} \, dx","IntegrateAlgebraic[1/(Sqrt[b*x]*Sqrt[4 + b*x]),x]","-\frac{4 \tanh ^{-1}\left(\frac{\sqrt{b x}-\sqrt{b}}{\sqrt{b+4}-\sqrt{b x+4}}\right)}{b}","\frac{2 \sinh ^{-1}\left(\frac{\sqrt{b x}}{2}\right)}{b}",1,"(-4*ArcTanh[(-Sqrt[b] + Sqrt[b*x])/(Sqrt[4 + b] - Sqrt[4 + b*x])])/b","B",1
1526,1,47,19,0.1533664,"\int \frac{1}{\sqrt{-1+b x} \sqrt{3+b x}} \, dx","IntegrateAlgebraic[1/(Sqrt[-1 + b*x]*Sqrt[3 + b*x]),x]","-\frac{4 \tanh ^{-1}\left(\frac{\sqrt{b x+3}-\sqrt{b+3}}{\sqrt{b-1}-\sqrt{b x-1}}\right)}{b}","\frac{2 \sinh ^{-1}\left(\frac{1}{2} \sqrt{b x-1}\right)}{b}",1,"(-4*ArcTanh[(-Sqrt[3 + b] + Sqrt[3 + b*x])/(Sqrt[-1 + b] - Sqrt[-1 + b*x])])/b","B",1
1527,1,47,11,0.1509465,"\int \frac{1}{\sqrt{-2+b x} \sqrt{2+b x}} \, dx","IntegrateAlgebraic[1/(Sqrt[-2 + b*x]*Sqrt[2 + b*x]),x]","-\frac{4 \tanh ^{-1}\left(\frac{\sqrt{b x+2}-\sqrt{b+2}}{\sqrt{b-2}-\sqrt{b x-2}}\right)}{b}","\frac{\cosh ^{-1}\left(\frac{b x}{2}\right)}{b}",1,"(-4*ArcTanh[(-Sqrt[2 + b] + Sqrt[2 + b*x])/(Sqrt[-2 + b] - Sqrt[-2 + b*x])])/b","B",1
1528,1,47,19,0.1510389,"\int \frac{1}{\sqrt{-3+b x} \sqrt{1+b x}} \, dx","IntegrateAlgebraic[1/(Sqrt[-3 + b*x]*Sqrt[1 + b*x]),x]","-\frac{4 \tanh ^{-1}\left(\frac{\sqrt{b x+1}-\sqrt{b+1}}{\sqrt{b-3}-\sqrt{b x-3}}\right)}{b}","\frac{2 \sinh ^{-1}\left(\frac{1}{2} \sqrt{b x-3}\right)}{b}",1,"(-4*ArcTanh[(-Sqrt[1 + b] + Sqrt[1 + b*x])/(Sqrt[-3 + b] - Sqrt[-3 + b*x])])/b","B",1
1529,1,47,15,0.1481983,"\int \frac{1}{\sqrt{2+b x} \sqrt{3+b x}} \, dx","IntegrateAlgebraic[1/(Sqrt[2 + b*x]*Sqrt[3 + b*x]),x]","-\frac{4 \tanh ^{-1}\left(\frac{\sqrt{b x+3}-\sqrt{b+3}}{\sqrt{b+2}-\sqrt{b x+2}}\right)}{b}","\frac{2 \sinh ^{-1}\left(\sqrt{b x+2}\right)}{b}",1,"(-4*ArcTanh[(-Sqrt[3 + b] + Sqrt[3 + b*x])/(Sqrt[2 + b] - Sqrt[2 + b*x])])/b","B",1
1530,1,10,10,0.0033855,"\int \frac{1}{2+b x} \, dx","IntegrateAlgebraic[(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
1531,1,47,15,0.1497569,"\int \frac{1}{\sqrt{1+b x} \sqrt{2+b x}} \, dx","IntegrateAlgebraic[1/(Sqrt[1 + b*x]*Sqrt[2 + b*x]),x]","-\frac{4 \tanh ^{-1}\left(\frac{\sqrt{b x+2}-\sqrt{b+2}}{\sqrt{b+1}-\sqrt{b x+1}}\right)}{b}","\frac{2 \sinh ^{-1}\left(\sqrt{b x+1}\right)}{b}",1,"(-4*ArcTanh[(-Sqrt[2 + b] + Sqrt[2 + b*x])/(Sqrt[1 + b] - Sqrt[1 + b*x])])/b","B",1
1532,1,43,19,0.1489991,"\int \frac{1}{\sqrt{b x} \sqrt{2+b x}} \, dx","IntegrateAlgebraic[1/(Sqrt[b*x]*Sqrt[2 + b*x]),x]","-\frac{4 \tanh ^{-1}\left(\frac{\sqrt{b x}-\sqrt{b}}{\sqrt{b+2}-\sqrt{b x+2}}\right)}{b}","\frac{2 \sinh ^{-1}\left(\frac{\sqrt{b x}}{\sqrt{2}}\right)}{b}",1,"(-4*ArcTanh[(-Sqrt[b] + Sqrt[b*x])/(Sqrt[2 + b] - Sqrt[2 + b*x])])/b","B",1
1533,1,47,21,0.1506506,"\int \frac{1}{\sqrt{-1+b x} \sqrt{2+b x}} \, dx","IntegrateAlgebraic[1/(Sqrt[-1 + b*x]*Sqrt[2 + b*x]),x]","-\frac{4 \tanh ^{-1}\left(\frac{\sqrt{b x+2}-\sqrt{b+2}}{\sqrt{b-1}-\sqrt{b x-1}}\right)}{b}","\frac{2 \sinh ^{-1}\left(\frac{\sqrt{b x-1}}{\sqrt{3}}\right)}{b}",1,"(-4*ArcTanh[(-Sqrt[2 + b] + Sqrt[2 + b*x])/(Sqrt[-1 + b] - Sqrt[-1 + b*x])])/b","B",1
1534,1,47,11,0.0001261,"\int \frac{1}{\sqrt{-2+b x} \sqrt{2+b x}} \, dx","IntegrateAlgebraic[1/(Sqrt[-2 + b*x]*Sqrt[2 + b*x]),x]","-\frac{4 \tanh ^{-1}\left(\frac{\sqrt{b x+2}-\sqrt{b+2}}{\sqrt{b-2}-\sqrt{b x-2}}\right)}{b}","\frac{\cosh ^{-1}\left(\frac{b x}{2}\right)}{b}",1,"(-4*ArcTanh[(-Sqrt[2 + b] + Sqrt[2 + b*x])/(Sqrt[-2 + b] - Sqrt[-2 + b*x])])/b","B",1
1535,1,47,21,0.1499735,"\int \frac{1}{\sqrt{-3+b x} \sqrt{2+b x}} \, dx","IntegrateAlgebraic[1/(Sqrt[-3 + b*x]*Sqrt[2 + b*x]),x]","-\frac{4 \tanh ^{-1}\left(\frac{\sqrt{b x+2}-\sqrt{b+2}}{\sqrt{b-3}-\sqrt{b x-3}}\right)}{b}","\frac{2 \sinh ^{-1}\left(\frac{\sqrt{b x-3}}{\sqrt{5}}\right)}{b}",1,"(-4*ArcTanh[(-Sqrt[2 + b] + Sqrt[2 + b*x])/(Sqrt[-3 + b] - Sqrt[-3 + b*x])])/b","B",1
1536,1,50,16,0.3269789,"\int \frac{1}{\sqrt{3-b x} \sqrt{2+b x}} \, dx","IntegrateAlgebraic[1/(Sqrt[3 - b*x]*Sqrt[2 + b*x]),x]","\frac{4 \tan ^{-1}\left(\frac{\sqrt{b+2}-\sqrt{b x+2}}{\sqrt{3-b}-\sqrt{3-b x}}\right)}{b}","-\frac{\sin ^{-1}\left(\frac{1}{5} (1-2 b x)\right)}{b}",1,"(4*ArcTan[(Sqrt[2 + b] - Sqrt[2 + b*x])/(Sqrt[3 - b] - Sqrt[3 - b*x])])/b","B",1
1537,1,50,11,0.2561228,"\int \frac{1}{\sqrt{2-b x} \sqrt{2+b x}} \, dx","IntegrateAlgebraic[1/(Sqrt[2 - b*x]*Sqrt[2 + b*x]),x]","\frac{4 \tan ^{-1}\left(\frac{\sqrt{b+2}-\sqrt{b x+2}}{\sqrt{2-b}-\sqrt{2-b x}}\right)}{b}","\frac{\sin ^{-1}\left(\frac{b x}{2}\right)}{b}",1,"(4*ArcTan[(Sqrt[2 + b] - Sqrt[2 + b*x])/(Sqrt[2 - b] - Sqrt[2 - b*x])])/b","B",1
1538,1,50,16,0.3768258,"\int \frac{1}{\sqrt{1-b x} \sqrt{2+b x}} \, dx","IntegrateAlgebraic[1/(Sqrt[1 - b*x]*Sqrt[2 + b*x]),x]","\frac{4 \tan ^{-1}\left(\frac{\sqrt{b+2}-\sqrt{b x+2}}{\sqrt{1-b}-\sqrt{1-b x}}\right)}{b}","-\frac{\sin ^{-1}\left(\frac{1}{3} (-2 b x-1)\right)}{b}",1,"(4*ArcTan[(Sqrt[2 + b] - Sqrt[2 + b*x])/(Sqrt[1 - b] - Sqrt[1 - b*x])])/b","B",1
1539,1,46,10,0.2713325,"\int \frac{1}{\sqrt{-b x} \sqrt{2+b x}} \, dx","IntegrateAlgebraic[1/(Sqrt[-(b*x)]*Sqrt[2 + b*x]),x]","\frac{4 \tan ^{-1}\left(\frac{\sqrt{b+2}-\sqrt{b x+2}}{\sqrt{-b}-\sqrt{-b x}}\right)}{b}","\frac{\sin ^{-1}(b x+1)}{b}",1,"(4*ArcTan[(Sqrt[2 + b] - Sqrt[2 + b*x])/(Sqrt[-b] - Sqrt[-(b*x)])])/b","B",1
1540,1,50,11,0.3228374,"\int \frac{1}{\sqrt{-1-b x} \sqrt{2+b x}} \, dx","IntegrateAlgebraic[1/(Sqrt[-1 - b*x]*Sqrt[2 + b*x]),x]","\frac{4 \tan ^{-1}\left(\frac{\sqrt{b+2}-\sqrt{b x+2}}{\sqrt{-b-1}-\sqrt{-b x-1}}\right)}{b}","\frac{\sin ^{-1}(2 b x+3)}{b}",1,"(4*ArcTan[(Sqrt[2 + b] - Sqrt[2 + b*x])/(Sqrt[-1 - b] - Sqrt[-1 - b*x])])/b","B",1
1541,1,50,29,0.3045421,"\int \frac{1}{\sqrt{-2-b x} \sqrt{2+b x}} \, dx","IntegrateAlgebraic[1/(Sqrt[-2 - b*x]*Sqrt[2 + b*x]),x]","\frac{4 \tan ^{-1}\left(\frac{\sqrt{b+2}-\sqrt{b x+2}}{\sqrt{-b-2}-\sqrt{-b x-2}}\right)}{b}","\frac{\sqrt{b x+2} \log (b x+2)}{b \sqrt{-b x-2}}",1,"(4*ArcTan[(Sqrt[2 + b] - Sqrt[2 + b*x])/(Sqrt[-2 - b] - Sqrt[-2 - b*x])])/b","A",1
1542,1,50,26,0.1359914,"\int \frac{1}{\sqrt{-3-b x} \sqrt{2+b x}} \, dx","IntegrateAlgebraic[1/(Sqrt[-3 - b*x]*Sqrt[2 + b*x]),x]","\frac{4 \tan ^{-1}\left(\frac{\sqrt{b+2}-\sqrt{b x+2}}{\sqrt{-b-3}-\sqrt{-b x-3}}\right)}{b}","-\frac{2 \tan ^{-1}\left(\frac{\sqrt{-b x-3}}{\sqrt{b x+2}}\right)}{b}",1,"(4*ArcTan[(Sqrt[2 + b] - Sqrt[2 + b*x])/(Sqrt[-3 - b] - Sqrt[-3 - b*x])])/b","A",1
1543,1,53,16,0.1702704,"\int \frac{1}{\sqrt{2-b x} \sqrt{3-b x}} \, dx","IntegrateAlgebraic[1/(Sqrt[2 - b*x]*Sqrt[3 - b*x]),x]","\frac{4 \tanh ^{-1}\left(\frac{\sqrt{3-b x}-\sqrt{3-b}}{\sqrt{2-b}-\sqrt{2-b x}}\right)}{b}","-\frac{2 \sinh ^{-1}\left(\sqrt{2-b x}\right)}{b}",1,"(4*ArcTanh[(-Sqrt[3 - b] + Sqrt[3 - b*x])/(Sqrt[2 - b] - Sqrt[2 - b*x])])/b","B",1
1544,1,11,12,0.0037561,"\int \frac{1}{2-b x} \, dx","IntegrateAlgebraic[(2 - b*x)^(-1),x]","-\frac{\log (b x-2)}{b}","-\frac{\log (2-b x)}{b}",1,"-(Log[-2 + b*x]/b)","A",1
1545,1,53,16,0.1694948,"\int \frac{1}{\sqrt{1-b x} \sqrt{2-b x}} \, dx","IntegrateAlgebraic[1/(Sqrt[1 - b*x]*Sqrt[2 - b*x]),x]","\frac{4 \tanh ^{-1}\left(\frac{\sqrt{2-b x}-\sqrt{2-b}}{\sqrt{1-b}-\sqrt{1-b x}}\right)}{b}","-\frac{2 \sinh ^{-1}\left(\sqrt{1-b x}\right)}{b}",1,"(4*ArcTanh[(-Sqrt[2 - b] + Sqrt[2 - b*x])/(Sqrt[1 - b] - Sqrt[1 - b*x])])/b","B",1
1546,1,49,20,0.1583233,"\int \frac{1}{\sqrt{-b x} \sqrt{2-b x}} \, dx","IntegrateAlgebraic[1/(Sqrt[-(b*x)]*Sqrt[2 - b*x]),x]","\frac{4 \tanh ^{-1}\left(\frac{\sqrt{-b x}-\sqrt{-b}}{\sqrt{2-b}-\sqrt{2-b x}}\right)}{b}","-\frac{2 \sinh ^{-1}\left(\frac{\sqrt{-b x}}{\sqrt{2}}\right)}{b}",1,"(4*ArcTanh[(-Sqrt[-b] + Sqrt[-(b*x)])/(Sqrt[2 - b] - Sqrt[2 - b*x])])/b","B",1
1547,1,53,22,0.1627737,"\int \frac{1}{\sqrt{-1-b x} \sqrt{2-b x}} \, dx","IntegrateAlgebraic[1/(Sqrt[-1 - b*x]*Sqrt[2 - b*x]),x]","\frac{4 \tanh ^{-1}\left(\frac{\sqrt{2-b x}-\sqrt{2-b}}{\sqrt{-b-1}-\sqrt{-b x-1}}\right)}{b}","-\frac{2 \sinh ^{-1}\left(\frac{\sqrt{-b x-1}}{\sqrt{3}}\right)}{b}",1,"(4*ArcTanh[(-Sqrt[2 - b] + Sqrt[2 - b*x])/(Sqrt[-1 - b] - Sqrt[-1 - b*x])])/b","B",1
1548,1,53,12,0.1553165,"\int \frac{1}{\sqrt{-2-b x} \sqrt{2-b x}} \, dx","IntegrateAlgebraic[1/(Sqrt[-2 - b*x]*Sqrt[2 - b*x]),x]","\frac{4 \tanh ^{-1}\left(\frac{\sqrt{2-b x}-\sqrt{2-b}}{\sqrt{-b-2}-\sqrt{-b x-2}}\right)}{b}","-\frac{\cosh ^{-1}\left(-\frac{b x}{2}\right)}{b}",1,"(4*ArcTanh[(-Sqrt[2 - b] + Sqrt[2 - b*x])/(Sqrt[-2 - b] - Sqrt[-2 - b*x])])/b","B",1
1549,1,53,22,0.1585467,"\int \frac{1}{\sqrt{-3-b x} \sqrt{2-b x}} \, dx","IntegrateAlgebraic[1/(Sqrt[-3 - b*x]*Sqrt[2 - b*x]),x]","\frac{4 \tanh ^{-1}\left(\frac{\sqrt{2-b x}-\sqrt{2-b}}{\sqrt{-b-3}-\sqrt{-b x-3}}\right)}{b}","-\frac{2 \sinh ^{-1}\left(\frac{\sqrt{-b x-3}}{\sqrt{5}}\right)}{b}",1,"(4*ArcTanh[(-Sqrt[2 - b] + Sqrt[2 - b*x])/(Sqrt[-3 - b] - Sqrt[-3 - b*x])])/b","B",1
1550,1,47,11,0.1560353,"\int \frac{1}{\sqrt{-4+b x} \sqrt{4+b x}} \, dx","IntegrateAlgebraic[1/(Sqrt[-4 + b*x]*Sqrt[4 + b*x]),x]","-\frac{4 \tanh ^{-1}\left(\frac{\sqrt{b x+4}-\sqrt{b+4}}{\sqrt{b-4}-\sqrt{b x-4}}\right)}{b}","\frac{\cosh ^{-1}\left(\frac{b x}{4}\right)}{b}",1,"(-4*ArcTanh[(-Sqrt[4 + b] + Sqrt[4 + b*x])/(Sqrt[-4 + b] - Sqrt[-4 + b*x])])/b","B",1
1551,1,97,43,0.5156431,"\int \frac{1}{\sqrt{\frac{-b+b c}{d}+b x} \sqrt{c+d x}} \, dx","IntegrateAlgebraic[1/(Sqrt[(-b + b*c)/d + b*x]*Sqrt[c + d*x]),x]","\frac{4 \tanh ^{-1}\left(\frac{\frac{\sqrt{b} \sqrt{c+d}}{\sqrt{d}}-\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{d}}}{\sqrt{\frac{b c}{d}-\frac{b}{d}+b}-\sqrt{\frac{b c}{d}-\frac{b}{d}+b x}}\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,"(4*ArcTanh[((Sqrt[b]*Sqrt[c + d])/Sqrt[d] - (Sqrt[b]*Sqrt[c + d*x])/Sqrt[d])/(Sqrt[b - b/d + (b*c)/d] - Sqrt[-(b/d) + (b*c)/d + b*x])])/(Sqrt[b]*Sqrt[d])","B",1
1552,1,47,22,2.0422797,"\int \frac{1}{\sqrt{x} \sqrt{-3+2 x}} \, dx","IntegrateAlgebraic[1/(Sqrt[x]*Sqrt[-3 + 2*x]),x]","-2 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{x}-2 \sqrt{2}}{\sqrt{5}-\sqrt{2 x-3}}\right)","\sqrt{2} \sinh ^{-1}\left(\frac{\sqrt{2 x-3}}{\sqrt{3}}\right)",1,"-2*Sqrt[2]*ArcTanh[(-2*Sqrt[2] + Sqrt[2]*Sqrt[x])/(Sqrt[5] - Sqrt[-3 + 2*x])]","B",1
1553,1,53,26,1.4170995,"\int \frac{1}{\sqrt{-3+2 x} \sqrt{2+3 x}} \, dx","IntegrateAlgebraic[1/(Sqrt[-3 + 2*x]*Sqrt[2 + 3*x]),x]","2 \sqrt{\frac{2}{3}} \tanh ^{-1}\left(\frac{\sqrt{3} \sqrt{2 x-3}-\sqrt{3}}{\sqrt{2} \sqrt{3 x+2}-4}\right)","\sqrt{\frac{2}{3}} \sinh ^{-1}\left(\sqrt{\frac{3}{13}} \sqrt{2 x-3}\right)",1,"2*Sqrt[2/3]*ArcTanh[(-Sqrt[3] + Sqrt[3]*Sqrt[-3 + 2*x])/(-4 + Sqrt[2]*Sqrt[2 + 3*x])]","B",1
1554,1,100,42,0.5413444,"\int \frac{1}{\sqrt{\frac{b-b c}{d}+b x} \sqrt{c-d x}} \, dx","IntegrateAlgebraic[1/(Sqrt[(b - b*c)/d + b*x]*Sqrt[c - d*x]),x]","-\frac{4 \tan ^{-1}\left(\frac{\frac{\sqrt{b} \sqrt{c-d}}{\sqrt{d}}-\frac{\sqrt{b} \sqrt{c-d x}}{\sqrt{d}}}{\sqrt{-\frac{b c}{d}+\frac{b}{d}+b}-\sqrt{-\frac{b c}{d}+\frac{b}{d}+b x}}\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,"(-4*ArcTan[((Sqrt[b]*Sqrt[c - d])/Sqrt[d] - (Sqrt[b]*Sqrt[c - d*x])/Sqrt[d])/(Sqrt[b + b/d - (b*c)/d] - Sqrt[b/d - (b*c)/d + b*x])])/(Sqrt[b]*Sqrt[d])","B",1
1555,1,22,10,0.0202371,"\int \frac{1}{\sqrt{4-x} \sqrt{x}} \, dx","IntegrateAlgebraic[1/(Sqrt[4 - x]*Sqrt[x]),x]","4 \tan ^{-1}\left(\frac{\sqrt{x}}{\sqrt{4-x}-2}\right)","-\sin ^{-1}\left(1-\frac{x}{2}\right)",1,"4*ArcTan[Sqrt[x]/(-2 + Sqrt[4 - x])]","B",1
1556,1,41,20,0.0307221,"\int \frac{1}{\sqrt{3-2 x} \sqrt{x}} \, dx","IntegrateAlgebraic[1/(Sqrt[3 - 2*x]*Sqrt[x]),x]","2 \sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{x}-\sqrt{2}}{\sqrt{3-2 x}-1}\right)","\sqrt{2} \sin ^{-1}\left(\sqrt{\frac{2}{3}} \sqrt{x}\right)",1,"2*Sqrt[2]*ArcTan[(-Sqrt[2] + Sqrt[2]*Sqrt[x])/(-1 + Sqrt[3 - 2*x])]","B",1
1557,1,49,26,1.3832374,"\int \frac{1}{\sqrt{3-2 x} \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[1/(Sqrt[3 - 2*x]*Sqrt[3 + 5*x]),x]","2 \sqrt{\frac{2}{5}} \tan ^{-1}\left(\frac{\sqrt{\frac{2}{5}} \sqrt{5 x+3}-\frac{4}{\sqrt{5}}}{\sqrt{3-2 x}-1}\right)","\sqrt{\frac{2}{5}} \sin ^{-1}\left(\sqrt{\frac{2}{21}} \sqrt{5 x+3}\right)",1,"2*Sqrt[2/5]*ArcTan[(-4/Sqrt[5] + Sqrt[2/5]*Sqrt[3 + 5*x])/(-1 + Sqrt[3 - 2*x])]","A",1
1558,1,79,43,0.3146417,"\int \frac{1}{\sqrt{a-b x} \sqrt{c+d x}} \, dx","IntegrateAlgebraic[1/(Sqrt[a - b*x]*Sqrt[c + d*x]),x]","\frac{4 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d}-\sqrt{b} \sqrt{c+d x}}{\sqrt{d} \sqrt{a-b}-\sqrt{d} \sqrt{a-b 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,"(4*ArcTan[(Sqrt[b]*Sqrt[c + d] - Sqrt[b]*Sqrt[c + d*x])/(Sqrt[a - b]*Sqrt[d] - Sqrt[d]*Sqrt[a - b*x])])/(Sqrt[b]*Sqrt[d])","A",1
1559,0,0,457,19.62833,"\int (a+b x)^{3/2} \sqrt[3]{c+d x} \, dx","IntegrateAlgebraic[(a + b*x)^(3/2)*(c + d*x)^(1/3),x]","\int (a+b x)^{3/2} \sqrt[3]{c+d x} \, dx","-\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,"Could not integrate","F",-1
1560,0,0,419,12.0992792,"\int \sqrt{a+b x} \sqrt[3]{c+d x} \, dx","IntegrateAlgebraic[Sqrt[a + b*x]*(c + d*x)^(1/3),x]","\int \sqrt{a+b x} \sqrt[3]{c+d x} \, dx","\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,"Could not integrate","F",-1
1561,0,0,381,12.3626657,"\int \frac{\sqrt[3]{c+d x}}{\sqrt{a+b x}} \, dx","IntegrateAlgebraic[(c + d*x)^(1/3)/Sqrt[a + b*x],x]","\int \frac{\sqrt[3]{c+d x}}{\sqrt{a+b x}} \, dx","\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,"Could not integrate","F",-1
1562,0,0,366,13.5574408,"\int \frac{\sqrt[3]{c+d x}}{(a+b x)^{3/2}} \, dx","IntegrateAlgebraic[(c + d*x)^(1/3)/(a + b*x)^(3/2),x]","\int \frac{\sqrt[3]{c+d x}}{(a+b x)^{3/2}} \, dx","-\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,"Could not integrate","F",-1
1563,0,0,417,17.0168049,"\int \frac{\sqrt[3]{c+d x}}{(a+b x)^{5/2}} \, dx","IntegrateAlgebraic[(c + d*x)^(1/3)/(a + b*x)^(5/2),x]","\int \frac{\sqrt[3]{c+d x}}{(a+b x)^{5/2}} \, dx","\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,"Could not integrate","F",-1
1564,0,0,457,20.1880877,"\int \frac{\sqrt[3]{c+d x}}{(a+b x)^{7/2}} \, dx","IntegrateAlgebraic[(c + d*x)^(1/3)/(a + b*x)^(7/2),x]","\int \frac{\sqrt[3]{c+d x}}{(a+b x)^{7/2}} \, dx","-\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,"Could not integrate","F",-1
1565,0,0,839,16.6311983,"\int \frac{(a+b x)^{3/2}}{\sqrt[3]{c+d x}} \, dx","IntegrateAlgebraic[(a + b*x)^(3/2)/(c + d*x)^(1/3),x]","\int \frac{(a+b x)^{3/2}}{\sqrt[3]{c+d x}} \, dx","\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,"Could not integrate","F",-1
1566,0,0,804,11.1958829,"\int \frac{\sqrt{a+b x}}{\sqrt[3]{c+d x}} \, dx","IntegrateAlgebraic[Sqrt[a + b*x]/(c + d*x)^(1/3),x]","\int \frac{\sqrt{a+b x}}{\sqrt[3]{c+d x}} \, dx","-\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,"Could not integrate","F",-1
1567,0,0,762,11.2611439,"\int \frac{1}{\sqrt{a+b x} \sqrt[3]{c+d x}} \, dx","IntegrateAlgebraic[1/(Sqrt[a + b*x]*(c + d*x)^(1/3)),x]","\int \frac{1}{\sqrt{a+b x} \sqrt[3]{c+d x}} \, dx","-\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,"Could not integrate","F",-1
1568,0,0,796,13.724967,"\int \frac{1}{(a+b x)^{3/2} \sqrt[3]{c+d x}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(3/2)*(c + d*x)^(1/3)),x]","\int \frac{1}{(a+b x)^{3/2} \sqrt[3]{c+d x}} \, dx","-\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,"Could not integrate","F",-1
1569,0,0,842,16.8157481,"\int \frac{1}{(a+b x)^{5/2} \sqrt[3]{c+d x}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(5/2)*(c + d*x)^(1/3)),x]","\int \frac{1}{(a+b x)^{5/2} \sqrt[3]{c+d x}} \, dx","\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,"Could not integrate","F",-1
1570,0,0,416,15.544943,"\int \frac{(a+b x)^{3/2}}{(c+d x)^{2/3}} \, dx","IntegrateAlgebraic[(a + b*x)^(3/2)/(c + d*x)^(2/3),x]","\int \frac{(a+b x)^{3/2}}{(c+d x)^{2/3}} \, dx","-\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,"Could not integrate","F",-1
1571,0,0,381,11.5137079,"\int \frac{\sqrt{a+b x}}{(c+d x)^{2/3}} \, dx","IntegrateAlgebraic[Sqrt[a + b*x]/(c + d*x)^(2/3),x]","\int \frac{\sqrt{a+b x}}{(c+d x)^{2/3}} \, dx","\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,"Could not integrate","F",-1
1572,0,0,345,32.0453389,"\int \frac{1}{\sqrt{a+b x} (c+d x)^{2/3}} \, dx","IntegrateAlgebraic[1/(Sqrt[a + b*x]*(c + d*x)^(2/3)),x]","\int \frac{1}{\sqrt{a+b x} (c+d x)^{2/3}} \, dx","-\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,"Could not integrate","F",-1
1573,0,0,383,13.2666063,"\int \frac{1}{(a+b x)^{3/2} (c+d x)^{2/3}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(3/2)*(c + d*x)^(2/3)),x]","\int \frac{1}{(a+b x)^{3/2} (c+d x)^{2/3}} \, dx","\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,"Could not integrate","F",-1
1574,0,0,421,17.2622464,"\int \frac{1}{(a+b x)^{5/2} (c+d x)^{2/3}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(5/2)*(c + d*x)^(2/3)),x]","\int \frac{1}{(a+b x)^{5/2} (c+d x)^{2/3}} \, dx","-\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,"Could not integrate","F",-1
1575,1,397,219,7.8252099,"\int (a+b x)^{2/3} \sqrt[3]{c+d x} \, dx","IntegrateAlgebraic[(a + b*x)^(2/3)*(c + d*x)^(1/3),x]","\frac{\sqrt[3]{b} \sqrt[3]{\frac{d (a+b x)-a d+b c}{b}} \left(\frac{\left(a^2 d^2-2 a b c d+b^2 c^2\right) \log \left(\sqrt[3]{d (a+b x)-a d+b c}-\sqrt[3]{d} \sqrt[3]{a+b x}\right)}{9 b^{4/3} d^{5/3}}+\frac{\left(-a^2 d^2+2 a b c d-b^2 c^2\right) \log \left(\sqrt[3]{d} \sqrt[3]{a+b x} \sqrt[3]{d (a+b x)-a d+b c}+(d (a+b x)-a d+b c)^{2/3}+d^{2/3} (a+b x)^{2/3}\right)}{18 b^{4/3} d^{5/3}}+\frac{\left(a^2 d^2-2 a b c d+b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{d} \sqrt[3]{a+b x}}{2 \sqrt[3]{d (a+b x)-a d+b c}+\sqrt[3]{d} \sqrt[3]{a+b x}}\right)}{3 \sqrt{3} b^{4/3} d^{5/3}}+\frac{\sqrt[3]{d (a+b x)-a d+b c} \left(b c (a+b x)^{2/3}+3 d (a+b x)^{5/3}-a d (a+b x)^{2/3}\right)}{6 b^{4/3} d}\right)}{\sqrt[3]{d (a+b x)-a d+b c}}","\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^(1/3)*((b*c - a*d + d*(a + b*x))/b)^(1/3)*(((b*c - a*d + d*(a + b*x))^(1/3)*(b*c*(a + b*x)^(2/3) - a*d*(a + b*x)^(2/3) + 3*d*(a + b*x)^(5/3)))/(6*b^(4/3)*d) + ((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*ArcTan[(Sqrt[3]*d^(1/3)*(a + b*x)^(1/3))/(d^(1/3)*(a + b*x)^(1/3) + 2*(b*c - a*d + d*(a + b*x))^(1/3))])/(3*Sqrt[3]*b^(4/3)*d^(5/3)) + ((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*Log[-(d^(1/3)*(a + b*x)^(1/3)) + (b*c - a*d + d*(a + b*x))^(1/3)])/(9*b^(4/3)*d^(5/3)) + ((-(b^2*c^2) + 2*a*b*c*d - a^2*d^2)*Log[d^(2/3)*(a + b*x)^(2/3) + d^(1/3)*(a + b*x)^(1/3)*(b*c - a*d + d*(a + b*x))^(1/3) + (b*c - a*d + d*(a + b*x))^(2/3)])/(18*b^(4/3)*d^(5/3))))/(b*c - a*d + d*(a + b*x))^(1/3)","A",1
1576,1,300,172,7.4392419,"\int \frac{\sqrt[3]{c+d x}}{\sqrt[3]{a+b x}} \, dx","IntegrateAlgebraic[(c + d*x)^(1/3)/(a + b*x)^(1/3),x]","\frac{\sqrt[3]{a d+b d x} \left(\frac{(a d-b c) \log \left(\sqrt[3]{a d+b (c+d x)-b c}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{3 b^{4/3} d^{2/3}}+\frac{(b c-a d) \log \left(\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{a d+b (c+d x)-b c}+(a d+b (c+d x)-b c)^{2/3}+b^{2/3} (c+d x)^{2/3}\right)}{6 b^{4/3} d^{2/3}}+\frac{(b c-a d) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{b} \sqrt[3]{c+d x}}{2 \sqrt[3]{a d+b (c+d x)-b c}+\sqrt[3]{b} \sqrt[3]{c+d x}}\right)}{\sqrt{3} b^{4/3} d^{2/3}}+\frac{\sqrt[3]{c+d x} (a d+b (c+d x)-b c)^{2/3}}{b d^{2/3}}\right)}{\sqrt[3]{d} \sqrt[3]{a+b 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}",1,"((a*d + b*d*x)^(1/3)*(((c + d*x)^(1/3)*(-(b*c) + a*d + b*(c + d*x))^(2/3))/(b*d^(2/3)) + ((b*c - a*d)*ArcTan[(Sqrt[3]*b^(1/3)*(c + d*x)^(1/3))/(b^(1/3)*(c + d*x)^(1/3) + 2*(-(b*c) + a*d + b*(c + d*x))^(1/3))])/(Sqrt[3]*b^(4/3)*d^(2/3)) + ((-(b*c) + a*d)*Log[-(b^(1/3)*(c + d*x)^(1/3)) + (-(b*c) + a*d + b*(c + d*x))^(1/3)])/(3*b^(4/3)*d^(2/3)) + ((b*c - a*d)*Log[b^(2/3)*(c + d*x)^(2/3) + b^(1/3)*(c + d*x)^(1/3)*(-(b*c) + a*d + b*(c + d*x))^(1/3) + (-(b*c) + a*d + b*(c + d*x))^(2/3)])/(6*b^(4/3)*d^(2/3))))/(d^(1/3)*(a + b*x)^(1/3))","A",1
1577,1,318,149,5.9009574,"\int \frac{\sqrt[3]{c+d x}}{(a+b x)^{4/3}} \, dx","IntegrateAlgebraic[(c + d*x)^(1/3)/(a + b*x)^(4/3),x]","\frac{\sqrt[3]{d} \log \left(d^{2/3} \left(a+\frac{b (c+d x)}{d}-\frac{b c}{d}\right)^{2/3}+\sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{c+d x} \sqrt[3]{a+\frac{b (c+d x)}{d}-\frac{b c}{d}}+b^{2/3} (c+d x)^{2/3}\right)}{2 b^{4/3}}-\frac{\sqrt[3]{d} \log \left(\sqrt[3]{b} \sqrt[3]{c+d x}-\sqrt[3]{d} \sqrt[3]{a+\frac{b (c+d x)}{d}-\frac{b c}{d}}\right)}{b^{4/3}}-\frac{\sqrt{3} \sqrt[3]{d} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{d} \sqrt[3]{a+\frac{b (c+d x)}{d}-\frac{b c}{d}}}{\sqrt[3]{d} \sqrt[3]{a+\frac{b (c+d x)}{d}-\frac{b c}{d}}+2 \sqrt[3]{b} \sqrt[3]{c+d x}}\right)}{b^{4/3}}-\frac{3 d \sqrt[3]{c+d x} \left(a+\frac{b (c+d x)}{d}-\frac{b c}{d}\right)^{2/3}}{b (a d+b (c+d x)-b c)}","-\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*d*(c + d*x)^(1/3)*(a - (b*c)/d + (b*(c + d*x))/d)^(2/3))/(b*(-(b*c) + a*d + b*(c + d*x))) - (Sqrt[3]*d^(1/3)*ArcTan[(Sqrt[3]*d^(1/3)*(a - (b*c)/d + (b*(c + d*x))/d)^(1/3))/(2*b^(1/3)*(c + d*x)^(1/3) + d^(1/3)*(a - (b*c)/d + (b*(c + d*x))/d)^(1/3))])/b^(4/3) - (d^(1/3)*Log[b^(1/3)*(c + d*x)^(1/3) - d^(1/3)*(a - (b*c)/d + (b*(c + d*x))/d)^(1/3)])/b^(4/3) + (d^(1/3)*Log[b^(2/3)*(c + d*x)^(2/3) + b^(1/3)*d^(1/3)*(c + d*x)^(1/3)*(a - (b*c)/d + (b*(c + d*x))/d)^(1/3) + d^(2/3)*(a - (b*c)/d + (b*(c + d*x))/d)^(2/3)])/(2*b^(4/3))","B",1
1578,1,66,32,11.1645116,"\int \frac{\sqrt[3]{c+d x}}{(a+b x)^{7/3}} \, dx","IntegrateAlgebraic[(c + d*x)^(1/3)/(a + b*x)^(7/3),x]","\frac{3 (c+d x)^{4/3} (a d+b d x)^{7/3}}{4 d (a+b x)^{7/3} (a d-b c) (a d+b (c+d x)-b c)^{4/3}}","-\frac{3 (c+d x)^{4/3}}{4 (a+b x)^{4/3} (b c-a d)}",1,"(3*(c + d*x)^(4/3)*(a*d + b*d*x)^(7/3))/(4*d*(-(b*c) + a*d)*(a + b*x)^(7/3)*(-(b*c) + a*d + b*(c + d*x))^(4/3))","B",1
1579,1,83,66,17.00547,"\int \frac{\sqrt[3]{c+d x}}{(a+b x)^{10/3}} \, dx","IntegrateAlgebraic[(c + d*x)^(1/3)/(a + b*x)^(10/3),x]","\frac{3 d^3 (a+b x)^{2/3} (c+d x)^{4/3} (7 a d+3 b (c+d x)-7 b c)}{28 (b c-a d)^2 (a d+b d x)^{2/3} (a d+b (c+d x)-b c)^{7/3}}","\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*d^3*(a + b*x)^(2/3)*(c + d*x)^(4/3)*(-7*b*c + 7*a*d + 3*b*(c + d*x)))/(28*(b*c - a*d)^2*(a*d + b*d*x)^(2/3)*(-(b*c) + a*d + b*(c + d*x))^(7/3))","A",1
1580,1,149,101,19.5331653,"\int \frac{\sqrt[3]{c+d x}}{(a+b x)^{13/3}} \, dx","IntegrateAlgebraic[(c + d*x)^(1/3)/(a + b*x)^(13/3),x]","-\frac{3 d^{2/3} (a+b x)^{2/3} (c+d x)^{4/3} \left(35 a^2 d^{16/3}+30 a b d^{13/3} (c+d x)-70 a b c d^{13/3}+35 b^2 c^2 d^{10/3}+9 b^2 d^{10/3} (c+d x)^2-30 b^2 c d^{10/3} (c+d x)\right)}{140 (b c-a d)^3 (a d+b d x)^{2/3} (a d+b (c+d x)-b c)^{10/3}}","-\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*d^(2/3)*(a + b*x)^(2/3)*(c + d*x)^(4/3)*(35*b^2*c^2*d^(10/3) - 70*a*b*c*d^(13/3) + 35*a^2*d^(16/3) - 30*b^2*c*d^(10/3)*(c + d*x) + 30*a*b*d^(13/3)*(c + d*x) + 9*b^2*d^(10/3)*(c + d*x)^2))/(140*(b*c - a*d)^3*(a*d + b*d*x)^(2/3)*(-(b*c) + a*d + b*(c + d*x))^(10/3))","A",1
1581,0,0,136,33.240781,"\int \frac{\sqrt[3]{c+d x}}{(a+b x)^{16/3}} \, dx","IntegrateAlgebraic[(c + d*x)^(1/3)/(a + b*x)^(16/3),x]","\int \frac{\sqrt[3]{c+d x}}{(a+b x)^{16/3}} \, dx","\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,"Could not integrate","F",-1
1582,0,0,655,16.5003978,"\int (a+b x)^{4/3} \sqrt[3]{c+d x} \, dx","IntegrateAlgebraic[(a + b*x)^(4/3)*(c + d*x)^(1/3),x]","\int (a+b x)^{4/3} \sqrt[3]{c+d x} \, dx","\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,"Could not integrate","F",-1
1583,0,0,617,12.631545,"\int \sqrt[3]{a+b x} \sqrt[3]{c+d x} \, dx","IntegrateAlgebraic[(a + b*x)^(1/3)*(c + d*x)^(1/3),x]","\int \sqrt[3]{a+b x} \sqrt[3]{c+d x} \, dx","-\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,"Could not integrate","F",-1
1584,0,0,576,12.241768,"\int \frac{\sqrt[3]{c+d x}}{(a+b x)^{2/3}} \, dx","IntegrateAlgebraic[(c + d*x)^(1/3)/(a + b*x)^(2/3),x]","\int \frac{\sqrt[3]{c+d x}}{(a+b x)^{2/3}} \, dx","\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,"Could not integrate","F",-1
1585,0,0,568,17.4045924,"\int \frac{\sqrt[3]{c+d x}}{(a+b x)^{5/3}} \, dx","IntegrateAlgebraic[(c + d*x)^(1/3)/(a + b*x)^(5/3),x]","\int \frac{\sqrt[3]{c+d x}}{(a+b x)^{5/3}} \, dx","\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,"Could not integrate","F",-1
1586,0,0,617,26.5385442,"\int \frac{\sqrt[3]{c+d x}}{(a+b x)^{8/3}} \, dx","IntegrateAlgebraic[(c + d*x)^(1/3)/(a + b*x)^(8/3),x]","\int \frac{\sqrt[3]{c+d x}}{(a+b x)^{8/3}} \, dx","-\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,"Could not integrate","F",-1
1587,1,372,216,9.4549732,"\int \frac{(a+b x)^{4/3}}{\sqrt[3]{c+d x}} \, dx","IntegrateAlgebraic[(a + b*x)^(4/3)/(c + d*x)^(1/3),x]","\frac{d^{4/3} (a+b x)^{4/3} \left(-\frac{2 \left(a^2 d^2-2 a b c d+b^2 c^2\right) \log \left(\sqrt[3]{a d+b (c+d x)-b c}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{9 b^{2/3} d^{7/3}}+\frac{\left(a^2 d^2-2 a b c d+b^2 c^2\right) \log \left(\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{a d+b (c+d x)-b c}+(a d+b (c+d x)-b c)^{2/3}+b^{2/3} (c+d x)^{2/3}\right)}{9 b^{2/3} d^{7/3}}-\frac{2 \left(a^2 d^2-2 a b c d+b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{b} \sqrt[3]{c+d x}}{2 \sqrt[3]{a d+b (c+d x)-b c}+\sqrt[3]{b} \sqrt[3]{c+d x}}\right)}{3 \sqrt{3} b^{2/3} d^{7/3}}+\frac{\sqrt[3]{a d+b (c+d x)-b c} \left(7 a d (c+d x)^{2/3}+3 b (c+d x)^{5/3}-7 b c (c+d x)^{2/3}\right)}{6 d^{7/3}}\right)}{(a d+b d x)^{4/3}}","-\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,"(d^(4/3)*(a + b*x)^(4/3)*(((-(b*c) + a*d + b*(c + d*x))^(1/3)*(-7*b*c*(c + d*x)^(2/3) + 7*a*d*(c + d*x)^(2/3) + 3*b*(c + d*x)^(5/3)))/(6*d^(7/3)) - (2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*ArcTan[(Sqrt[3]*b^(1/3)*(c + d*x)^(1/3))/(b^(1/3)*(c + d*x)^(1/3) + 2*(-(b*c) + a*d + b*(c + d*x))^(1/3))])/(3*Sqrt[3]*b^(2/3)*d^(7/3)) - (2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*Log[-(b^(1/3)*(c + d*x)^(1/3)) + (-(b*c) + a*d + b*(c + d*x))^(1/3)])/(9*b^(2/3)*d^(7/3)) + ((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*Log[b^(2/3)*(c + d*x)^(2/3) + b^(1/3)*(c + d*x)^(1/3)*(-(b*c) + a*d + b*(c + d*x))^(1/3) + (-(b*c) + a*d + b*(c + d*x))^(2/3)])/(9*b^(2/3)*d^(7/3))))/(a*d + b*d*x)^(4/3)","A",1
1588,1,297,171,7.6548196,"\int \frac{\sqrt[3]{a+b x}}{\sqrt[3]{c+d x}} \, dx","IntegrateAlgebraic[(a + b*x)^(1/3)/(c + d*x)^(1/3),x]","\frac{\sqrt[3]{d} \sqrt[3]{a+b x} \left(\frac{(b c-a d) \log \left(\sqrt[3]{a d+b (c+d x)-b c}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{3 b^{2/3} d^{4/3}}+\frac{(a d-b c) \log \left(\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{a d+b (c+d x)-b c}+(a d+b (c+d x)-b c)^{2/3}+b^{2/3} (c+d x)^{2/3}\right)}{6 b^{2/3} d^{4/3}}+\frac{(b c-a d) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{b} \sqrt[3]{c+d x}}{2 \sqrt[3]{a d+b (c+d x)-b c}+\sqrt[3]{b} \sqrt[3]{c+d x}}\right)}{\sqrt{3} b^{2/3} d^{4/3}}+\frac{(c+d x)^{2/3} \sqrt[3]{a d+b (c+d x)-b c}}{d^{4/3}}\right)}{\sqrt[3]{a d+b d 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}",1,"(d^(1/3)*(a + b*x)^(1/3)*(((c + d*x)^(2/3)*(-(b*c) + a*d + b*(c + d*x))^(1/3))/d^(4/3) + ((b*c - a*d)*ArcTan[(Sqrt[3]*b^(1/3)*(c + d*x)^(1/3))/(b^(1/3)*(c + d*x)^(1/3) + 2*(-(b*c) + a*d + b*(c + d*x))^(1/3))])/(Sqrt[3]*b^(2/3)*d^(4/3)) + ((b*c - a*d)*Log[-(b^(1/3)*(c + d*x)^(1/3)) + (-(b*c) + a*d + b*(c + d*x))^(1/3)])/(3*b^(2/3)*d^(4/3)) + ((-(b*c) + a*d)*Log[b^(2/3)*(c + d*x)^(2/3) + b^(1/3)*(c + d*x)^(1/3)*(-(b*c) + a*d + b*(c + d*x))^(1/3) + (-(b*c) + a*d + b*(c + d*x))^(2/3)])/(6*b^(2/3)*d^(4/3))))/(a*d + b*d*x)^(1/3)","A",1
1589,1,263,126,1.4207776,"\int \frac{1}{(a+b x)^{2/3} \sqrt[3]{c+d x}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(2/3)*(c + d*x)^(1/3)),x]","\frac{\log \left(b^{2/3} \left(\frac{d (a+b x)}{b}-\frac{a d}{b}+c\right)^{2/3}+\sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{a+b x} \sqrt[3]{\frac{d (a+b x)}{b}-\frac{a d}{b}+c}+d^{2/3} (a+b x)^{2/3}\right)}{2 b^{2/3} \sqrt[3]{d}}-\frac{\log \left(\sqrt[3]{d} \sqrt[3]{a+b x}-\sqrt[3]{b} \sqrt[3]{\frac{d (a+b x)}{b}-\frac{a d}{b}+c}\right)}{b^{2/3} \sqrt[3]{d}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{b} \sqrt[3]{\frac{d (a+b x)}{b}-\frac{a d}{b}+c}}{\sqrt[3]{b} \sqrt[3]{\frac{d (a+b x)}{b}-\frac{a d}{b}+c}+2 \sqrt[3]{d} \sqrt[3]{a+b x}}\right)}{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[(Sqrt[3]*b^(1/3)*(c - (a*d)/b + (d*(a + b*x))/b)^(1/3))/(2*d^(1/3)*(a + b*x)^(1/3) + b^(1/3)*(c - (a*d)/b + (d*(a + b*x))/b)^(1/3))])/(b^(2/3)*d^(1/3))) - Log[d^(1/3)*(a + b*x)^(1/3) - b^(1/3)*(c - (a*d)/b + (d*(a + b*x))/b)^(1/3)]/(b^(2/3)*d^(1/3)) + Log[d^(2/3)*(a + b*x)^(2/3) + b^(1/3)*d^(1/3)*(a + b*x)^(1/3)*(c - (a*d)/b + (d*(a + b*x))/b)^(1/3) + b^(2/3)*(c - (a*d)/b + (d*(a + b*x))/b)^(2/3)]/(2*b^(2/3)*d^(1/3))","B",1
1590,1,66,32,8.9437159,"\int \frac{1}{(a+b x)^{5/3} \sqrt[3]{c+d x}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(5/3)*(c + d*x)^(1/3)),x]","\frac{3 (c+d x)^{2/3} (a d+b d x)^{5/3}}{2 d (a+b x)^{5/3} (a d-b c) (a d+b (c+d x)-b c)^{2/3}}","-\frac{3 (c+d x)^{2/3}}{2 (a+b x)^{2/3} (b c-a d)}",1,"(3*(c + d*x)^(2/3)*(a*d + b*d*x)^(5/3))/(2*d*(-(b*c) + a*d)*(a + b*x)^(5/3)*(-(b*c) + a*d + b*(c + d*x))^(2/3))","B",1
1591,1,83,66,11.65941,"\int \frac{1}{(a+b x)^{8/3} \sqrt[3]{c+d x}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(8/3)*(c + d*x)^(1/3)),x]","\frac{3 (c+d x)^{2/3} (a d+b d x)^{8/3} (5 a d+3 b (c+d x)-5 b c)}{10 d (a+b x)^{8/3} (b c-a d)^2 (a d+b (c+d x)-b c)^{5/3}}","\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)*(a*d + b*d*x)^(8/3)*(-5*b*c + 5*a*d + 3*b*(c + d*x)))/(10*d*(b*c - a*d)^2*(a + b*x)^(8/3)*(-(b*c) + a*d + b*(c + d*x))^(5/3))","A",1
1592,0,0,101,28.4743387,"\int \frac{1}{(a+b x)^{11/3} \sqrt[3]{c+d x}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(11/3)*(c + d*x)^(1/3)),x]","\int \frac{1}{(a+b x)^{11/3} \sqrt[3]{c+d x}} \, dx","-\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,"Could not integrate","F",-1
1593,0,0,136,34.8770486,"\int \frac{1}{(a+b x)^{14/3} \sqrt[3]{c+d x}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(14/3)*(c + d*x)^(1/3)),x]","\int \frac{1}{(a+b x)^{14/3} \sqrt[3]{c+d x}} \, dx","\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,"Could not integrate","F",-1
1594,0,0,1365,20.0745871,"\int \frac{(a+b x)^{8/3}}{\sqrt[3]{c+d x}} \, dx","IntegrateAlgebraic[(a + b*x)^(8/3)/(c + d*x)^(1/3),x]","\int \frac{(a+b x)^{8/3}}{\sqrt[3]{c+d x}} \, dx","\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,"Could not integrate","F",-1
1595,0,0,1330,17.9442982,"\int \frac{(a+b x)^{5/3}}{\sqrt[3]{c+d x}} \, dx","IntegrateAlgebraic[(a + b*x)^(5/3)/(c + d*x)^(1/3),x]","\int \frac{(a+b x)^{5/3}}{\sqrt[3]{c+d x}} \, dx","-\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,"Could not integrate","F",-1
1596,0,0,1293,12.4717462,"\int \frac{(a+b x)^{2/3}}{\sqrt[3]{c+d x}} \, dx","IntegrateAlgebraic[(a + b*x)^(2/3)/(c + d*x)^(1/3),x]","\int \frac{(a+b x)^{2/3}}{\sqrt[3]{c+d x}} \, dx","\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,"Could not integrate","F",-1
1597,0,0,1257,12.0633938,"\int \frac{1}{\sqrt[3]{a+b x} \sqrt[3]{c+d x}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(1/3)*(c + d*x)^(1/3)),x]","\int \frac{1}{\sqrt[3]{a+b x} \sqrt[3]{c+d x}} \, dx","-\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,"Could not integrate","F",-1
1598,0,0,1297,15.8961899,"\int \frac{1}{(a+b x)^{4/3} \sqrt[3]{c+d x}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(4/3)*(c + d*x)^(1/3)),x]","\int \frac{1}{(a+b x)^{4/3} \sqrt[3]{c+d x}} \, dx","-\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,"Could not integrate","F",-1
1599,0,0,1335,23.8884403,"\int \frac{1}{(a+b x)^{7/3} \sqrt[3]{c+d x}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(7/3)*(c + d*x)^(1/3)),x]","\int \frac{1}{(a+b x)^{7/3} \sqrt[3]{c+d x}} \, dx","\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,"Could not integrate","F",-1
1600,0,0,1372,27.3887986,"\int \frac{1}{(a+b x)^{10/3} \sqrt[3]{c+d x}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(10/3)*(c + d*x)^(1/3)),x]","\int \frac{1}{(a+b x)^{10/3} \sqrt[3]{c+d x}} \, dx","-\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,"Could not integrate","F",-1
1601,1,372,216,9.7102496,"\int \frac{(a+b x)^{5/3}}{(c+d x)^{2/3}} \, dx","IntegrateAlgebraic[(a + b*x)^(5/3)/(c + d*x)^(2/3),x]","\frac{d^{2/3} (a+b x)^{2/3} \left(-\frac{5 \left(a^2 d^2-2 a b c d+b^2 c^2\right) \log \left(\sqrt[3]{a d+b (c+d x)-b c}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{9 \sqrt[3]{b} d^{8/3}}+\frac{5 \left(a^2 d^2-2 a b c d+b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{b} \sqrt[3]{c+d x}}{2 \sqrt[3]{a d+b (c+d x)-b c}+\sqrt[3]{b} \sqrt[3]{c+d x}}\right)}{3 \sqrt{3} \sqrt[3]{b} d^{8/3}}+\frac{5 \left(a^2 d^2-2 a b c d+b^2 c^2\right) \log \left(\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{a d+b (c+d x)-b c}+(a d+b (c+d x)-b c)^{2/3}+b^{2/3} (c+d x)^{2/3}\right)}{18 \sqrt[3]{b} d^{8/3}}+\frac{(a d+b (c+d x)-b c)^{2/3} \left(8 a d \sqrt[3]{c+d x}+3 b (c+d x)^{4/3}-8 b c \sqrt[3]{c+d x}\right)}{6 d^{8/3}}\right)}{(a d+b d x)^{2/3}}","-\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{5 (a+b x)^{2/3} \sqrt[3]{c+d x} (b c-a d)}{6 d^2}+\frac{(a+b x)^{5/3} \sqrt[3]{c+d x}}{2 d}",1,"(d^(2/3)*(a + b*x)^(2/3)*(((-(b*c) + a*d + b*(c + d*x))^(2/3)*(-8*b*c*(c + d*x)^(1/3) + 8*a*d*(c + d*x)^(1/3) + 3*b*(c + d*x)^(4/3)))/(6*d^(8/3)) + (5*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*ArcTan[(Sqrt[3]*b^(1/3)*(c + d*x)^(1/3))/(b^(1/3)*(c + d*x)^(1/3) + 2*(-(b*c) + a*d + b*(c + d*x))^(1/3))])/(3*Sqrt[3]*b^(1/3)*d^(8/3)) - (5*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*Log[-(b^(1/3)*(c + d*x)^(1/3)) + (-(b*c) + a*d + b*(c + d*x))^(1/3)])/(9*b^(1/3)*d^(8/3)) + (5*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*Log[b^(2/3)*(c + d*x)^(2/3) + b^(1/3)*(c + d*x)^(1/3)*(-(b*c) + a*d + b*(c + d*x))^(1/3) + (-(b*c) + a*d + b*(c + d*x))^(2/3)])/(18*b^(1/3)*d^(8/3))))/(a*d + b*d*x)^(2/3)","A",1
1602,1,298,169,8.2046272,"\int \frac{(a+b x)^{2/3}}{(c+d x)^{2/3}} \, dx","IntegrateAlgebraic[(a + b*x)^(2/3)/(c + d*x)^(2/3),x]","\frac{d^{2/3} (a+b x)^{2/3} \left(\frac{(a d-b c) \log \left(\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{a d+b (c+d x)-b c}+(a d+b (c+d x)-b c)^{2/3}+b^{2/3} (c+d x)^{2/3}\right)}{3 \sqrt[3]{b} d^{5/3}}+\frac{\sqrt[3]{c+d x} (a d+b (c+d x)-b c)^{2/3}}{d^{5/3}}+\frac{2 (b c-a d) \log \left(\sqrt[3]{a d+b (c+d x)-b c}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{3 \sqrt[3]{b} d^{5/3}}-\frac{2 (b c-a d) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{b} \sqrt[3]{c+d x}}{2 \sqrt[3]{a d+b (c+d x)-b c}+\sqrt[3]{b} \sqrt[3]{c+d x}}\right)}{\sqrt{3} \sqrt[3]{b} d^{5/3}}\right)}{(a d+b d x)^{2/3}}","\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,"(d^(2/3)*(a + b*x)^(2/3)*(((c + d*x)^(1/3)*(-(b*c) + a*d + b*(c + d*x))^(2/3))/d^(5/3) - (2*(b*c - a*d)*ArcTan[(Sqrt[3]*b^(1/3)*(c + d*x)^(1/3))/(b^(1/3)*(c + d*x)^(1/3) + 2*(-(b*c) + a*d + b*(c + d*x))^(1/3))])/(Sqrt[3]*b^(1/3)*d^(5/3)) + (2*(b*c - a*d)*Log[-(b^(1/3)*(c + d*x)^(1/3)) + (-(b*c) + a*d + b*(c + d*x))^(1/3)])/(3*b^(1/3)*d^(5/3)) + ((-(b*c) + a*d)*Log[b^(2/3)*(c + d*x)^(2/3) + b^(1/3)*(c + d*x)^(1/3)*(-(b*c) + a*d + b*(c + d*x))^(1/3) + (-(b*c) + a*d + b*(c + d*x))^(2/3)])/(3*b^(1/3)*d^(5/3))))/(a*d + b*d*x)^(2/3)","A",1
1603,1,263,126,1.4841211,"\int \frac{1}{\sqrt[3]{a+b x} (c+d x)^{2/3}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(1/3)*(c + d*x)^(2/3)),x]","\frac{\log \left(d^{2/3} \left(a+\frac{b (c+d x)}{d}-\frac{b c}{d}\right)^{2/3}+\sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{c+d x} \sqrt[3]{a+\frac{b (c+d x)}{d}-\frac{b c}{d}}+b^{2/3} (c+d x)^{2/3}\right)}{2 \sqrt[3]{b} d^{2/3}}-\frac{\log \left(\sqrt[3]{b} \sqrt[3]{c+d x}-\sqrt[3]{d} \sqrt[3]{a+\frac{b (c+d x)}{d}-\frac{b c}{d}}\right)}{\sqrt[3]{b} d^{2/3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{d} \sqrt[3]{a+\frac{b (c+d x)}{d}-\frac{b c}{d}}}{\sqrt[3]{d} \sqrt[3]{a+\frac{b (c+d x)}{d}-\frac{b c}{d}}+2 \sqrt[3]{b} \sqrt[3]{c+d x}}\right)}{\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[(Sqrt[3]*d^(1/3)*(a - (b*c)/d + (b*(c + d*x))/d)^(1/3))/(2*b^(1/3)*(c + d*x)^(1/3) + d^(1/3)*(a - (b*c)/d + (b*(c + d*x))/d)^(1/3))])/(b^(1/3)*d^(2/3))) - Log[b^(1/3)*(c + d*x)^(1/3) - d^(1/3)*(a - (b*c)/d + (b*(c + d*x))/d)^(1/3)]/(b^(1/3)*d^(2/3)) + Log[b^(2/3)*(c + d*x)^(2/3) + b^(1/3)*d^(1/3)*(c + d*x)^(1/3)*(a - (b*c)/d + (b*(c + d*x))/d)^(1/3) + d^(2/3)*(a - (b*c)/d + (b*(c + d*x))/d)^(2/3)]/(2*b^(1/3)*d^(2/3))","B",1
1604,1,63,30,4.9364922,"\int \frac{1}{(a+b x)^{4/3} (c+d x)^{2/3}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(4/3)*(c + d*x)^(2/3)),x]","\frac{3 d \sqrt[3]{c+d x} \left(a+\frac{b (c+d x)}{d}-\frac{b c}{d}\right)^{2/3}}{(b c-a d) (-a d-b (c+d x)+b c)}","-\frac{3 \sqrt[3]{c+d x}}{\sqrt[3]{a+b x} (b c-a d)}",1,"(3*d*(c + d*x)^(1/3)*(a - (b*c)/d + (b*(c + d*x))/d)^(2/3))/((b*c - a*d)*(b*c - a*d - b*(c + d*x)))","B",1
1605,1,83,66,10.4875758,"\int \frac{1}{(a+b x)^{7/3} (c+d x)^{2/3}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(7/3)*(c + d*x)^(2/3)),x]","\frac{3 \sqrt[3]{c+d x} (a d+b d x)^{7/3} (4 a d+3 b (c+d x)-4 b c)}{4 d (a+b x)^{7/3} (b c-a d)^2 (a d+b (c+d x)-b c)^{4/3}}","\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)*(a*d + b*d*x)^(7/3)*(-4*b*c + 4*a*d + 3*b*(c + d*x)))/(4*d*(b*c - a*d)^2*(a + b*x)^(7/3)*(-(b*c) + a*d + b*(c + d*x))^(4/3))","A",1
1606,1,149,101,15.0082025,"\int \frac{1}{(a+b x)^{10/3} (c+d x)^{2/3}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(10/3)*(c + d*x)^(2/3)),x]","-\frac{3 d^{2/3} (a+b x)^{2/3} \sqrt[3]{c+d x} \left(14 a^2 d^{13/3}+21 a b d^{10/3} (c+d x)-28 a b c d^{10/3}+14 b^2 c^2 d^{7/3}+9 b^2 d^{7/3} (c+d x)^2-21 b^2 c d^{7/3} (c+d x)\right)}{14 (b c-a d)^3 (a d+b d x)^{2/3} (a d+b (c+d x)-b c)^{7/3}}","-\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*d^(2/3)*(a + b*x)^(2/3)*(c + d*x)^(1/3)*(14*b^2*c^2*d^(7/3) - 28*a*b*c*d^(10/3) + 14*a^2*d^(13/3) - 21*b^2*c*d^(7/3)*(c + d*x) + 21*a*b*d^(10/3)*(c + d*x) + 9*b^2*d^(7/3)*(c + d*x)^2))/(14*(b*c - a*d)^3*(a*d + b*d*x)^(2/3)*(-(b*c) + a*d + b*(c + d*x))^(7/3))","A",1
1607,0,0,136,33.2189995,"\int \frac{1}{(a+b x)^{13/3} (c+d x)^{2/3}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(13/3)*(c + d*x)^(2/3)),x]","\int \frac{1}{(a+b x)^{13/3} (c+d x)^{2/3}} \, dx","\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,"Could not integrate","F",-1
1608,0,0,649,18.4317354,"\int \frac{(a+b x)^{7/3}}{(c+d x)^{2/3}} \, dx","IntegrateAlgebraic[(a + b*x)^(7/3)/(c + d*x)^(2/3),x]","\int \frac{(a+b x)^{7/3}}{(c+d x)^{2/3}} \, dx","-\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,"Could not integrate","F",-1
1609,0,0,614,15.8911029,"\int \frac{(a+b x)^{4/3}}{(c+d x)^{2/3}} \, dx","IntegrateAlgebraic[(a + b*x)^(4/3)/(c + d*x)^(2/3),x]","\int \frac{(a+b x)^{4/3}}{(c+d x)^{2/3}} \, dx","\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,"Could not integrate","F",-1
1610,0,0,577,12.2967432,"\int \frac{\sqrt[3]{a+b x}}{(c+d x)^{2/3}} \, dx","IntegrateAlgebraic[(a + b*x)^(1/3)/(c + d*x)^(2/3),x]","\int \frac{\sqrt[3]{a+b x}}{(c+d x)^{2/3}} \, dx","\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,"Could not integrate","F",-1
1611,0,0,542,12.3782032,"\int \frac{1}{(a+b x)^{2/3} (c+d x)^{2/3}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(2/3)*(c + d*x)^(2/3)),x]","\int \frac{1}{(a+b x)^{2/3} (c+d x)^{2/3}} \, dx","\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,"Could not integrate","F",-1
1612,0,0,586,19.9673206,"\int \frac{1}{(a+b x)^{5/3} (c+d x)^{2/3}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(5/3)*(c + d*x)^(2/3)),x]","\int \frac{1}{(a+b x)^{5/3} (c+d x)^{2/3}} \, dx","-\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,"Could not integrate","F",-1
1613,0,0,621,24.4665516,"\int \frac{1}{(a+b x)^{8/3} (c+d x)^{2/3}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(8/3)*(c + d*x)^(2/3)),x]","\int \frac{1}{(a+b x)^{8/3} (c+d x)^{2/3}} \, dx","\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,"Could not integrate","F",-1
1614,0,0,656,29.4200814,"\int \frac{1}{(a+b x)^{11/3} (c+d x)^{2/3}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(11/3)*(c + d*x)^(2/3)),x]","\int \frac{1}{(a+b x)^{11/3} (c+d x)^{2/3}} \, dx","-\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,"Could not integrate","F",-1
1615,1,416,241,13.465068,"\int \frac{(a+b x)^{7/3}}{(c+d x)^{4/3}} \, dx","IntegrateAlgebraic[(a + b*x)^(7/3)/(c + d*x)^(4/3),x]","\frac{d^{7/3} (a+b x)^{7/3} \left(-\frac{14 \left(a^2 \sqrt[3]{b} d^2-2 a b^{4/3} c d+b^{7/3} c^2\right) \log \left(\sqrt[3]{a d+b (c+d x)-b c}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{9 d^{10/3}}+\frac{7 \left(a^2 \sqrt[3]{b} d^2-2 a b^{4/3} c d+b^{7/3} c^2\right) \log \left(\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{a d+b (c+d x)-b c}+(a d+b (c+d x)-b c)^{2/3}+b^{2/3} (c+d x)^{2/3}\right)}{9 d^{10/3}}-\frac{14 \left(a^2 \sqrt[3]{b} d^2-2 a b^{4/3} c d+b^{7/3} c^2\right) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{b} \sqrt[3]{c+d x}}{2 \sqrt[3]{a d+b (c+d x)-b c}+\sqrt[3]{b} \sqrt[3]{c+d x}}\right)}{3 \sqrt{3} d^{10/3}}+\frac{\sqrt[3]{a d+b (c+d x)-b c} \left(-18 a^2 d^2+13 a b d (c+d x)+36 a b c d-18 b^2 c^2+3 b^2 (c+d x)^2-13 b^2 c (c+d x)\right)}{6 d^{10/3} \sqrt[3]{c+d x}}\right)}{(a d+b d x)^{7/3}}","-\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{14 b \sqrt[3]{a+b x} (c+d x)^{2/3} (b c-a d)}{3 d^3}+\frac{7 b (a+b x)^{4/3} (c+d x)^{2/3}}{2 d^2}-\frac{3 (a+b x)^{7/3}}{d \sqrt[3]{c+d x}}",1,"(d^(7/3)*(a + b*x)^(7/3)*(((-(b*c) + a*d + b*(c + d*x))^(1/3)*(-18*b^2*c^2 + 36*a*b*c*d - 18*a^2*d^2 - 13*b^2*c*(c + d*x) + 13*a*b*d*(c + d*x) + 3*b^2*(c + d*x)^2))/(6*d^(10/3)*(c + d*x)^(1/3)) - (14*(b^(7/3)*c^2 - 2*a*b^(4/3)*c*d + a^2*b^(1/3)*d^2)*ArcTan[(Sqrt[3]*b^(1/3)*(c + d*x)^(1/3))/(b^(1/3)*(c + d*x)^(1/3) + 2*(-(b*c) + a*d + b*(c + d*x))^(1/3))])/(3*Sqrt[3]*d^(10/3)) - (14*(b^(7/3)*c^2 - 2*a*b^(4/3)*c*d + a^2*b^(1/3)*d^2)*Log[-(b^(1/3)*(c + d*x)^(1/3)) + (-(b*c) + a*d + b*(c + d*x))^(1/3)])/(9*d^(10/3)) + (7*(b^(7/3)*c^2 - 2*a*b^(4/3)*c*d + a^2*b^(1/3)*d^2)*Log[b^(2/3)*(c + d*x)^(2/3) + b^(1/3)*(c + d*x)^(1/3)*(-(b*c) + a*d + b*(c + d*x))^(1/3) + (-(b*c) + a*d + b*(c + d*x))^(2/3)])/(9*d^(10/3))))/(a*d + b*d*x)^(7/3)","A",1
1616,1,326,195,12.2587566,"\int \frac{(a+b x)^{4/3}}{(c+d x)^{4/3}} \, dx","IntegrateAlgebraic[(a + b*x)^(4/3)/(c + d*x)^(4/3),x]","\frac{d^{4/3} (a+b x)^{4/3} \left(\frac{4 \left(b^{4/3} c-a \sqrt[3]{b} d\right) \log \left(\sqrt[3]{a d+b (c+d x)-b c}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{3 d^{7/3}}-\frac{2 \left(b^{4/3} c-a \sqrt[3]{b} d\right) \log \left(\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{a d+b (c+d x)-b c}+(a d+b (c+d x)-b c)^{2/3}+b^{2/3} (c+d x)^{2/3}\right)}{3 d^{7/3}}+\frac{4 \left(b^{4/3} c-a \sqrt[3]{b} d\right) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{b} \sqrt[3]{c+d x}}{2 \sqrt[3]{a d+b (c+d x)-b c}+\sqrt[3]{b} \sqrt[3]{c+d x}}\right)}{\sqrt{3} d^{7/3}}+\frac{\sqrt[3]{a d+b (c+d x)-b c} (-3 a d+b (c+d x)+3 b c)}{d^{7/3} \sqrt[3]{c+d x}}\right)}{(a d+b d x)^{4/3}}","\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{4 b \sqrt[3]{a+b x} (c+d x)^{2/3}}{d^2}-\frac{3 (a+b x)^{4/3}}{d \sqrt[3]{c+d x}}",1,"(d^(4/3)*(a + b*x)^(4/3)*(((3*b*c - 3*a*d + b*(c + d*x))*(-(b*c) + a*d + b*(c + d*x))^(1/3))/(d^(7/3)*(c + d*x)^(1/3)) + (4*(b^(4/3)*c - a*b^(1/3)*d)*ArcTan[(Sqrt[3]*b^(1/3)*(c + d*x)^(1/3))/(b^(1/3)*(c + d*x)^(1/3) + 2*(-(b*c) + a*d + b*(c + d*x))^(1/3))])/(Sqrt[3]*d^(7/3)) + (4*(b^(4/3)*c - a*b^(1/3)*d)*Log[-(b^(1/3)*(c + d*x)^(1/3)) + (-(b*c) + a*d + b*(c + d*x))^(1/3)])/(3*d^(7/3)) - (2*(b^(4/3)*c - a*b^(1/3)*d)*Log[b^(2/3)*(c + d*x)^(2/3) + b^(1/3)*(c + d*x)^(1/3)*(-(b*c) + a*d + b*(c + d*x))^(1/3) + (-(b*c) + a*d + b*(c + d*x))^(2/3)])/(3*d^(7/3))))/(a*d + b*d*x)^(4/3)","A",1
1617,1,299,149,3.6695349,"\int \frac{\sqrt[3]{a+b x}}{(c+d x)^{4/3}} \, dx","IntegrateAlgebraic[(a + b*x)^(1/3)/(c + d*x)^(4/3),x]","\frac{\sqrt[3]{b} \log \left(d^{2/3} \left(a+\frac{b (c+d x)}{d}-\frac{b c}{d}\right)^{2/3}+\sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{c+d x} \sqrt[3]{a+\frac{b (c+d x)}{d}-\frac{b c}{d}}+b^{2/3} (c+d x)^{2/3}\right)}{2 d^{4/3}}-\frac{\sqrt[3]{b} \log \left(\sqrt[3]{b} \sqrt[3]{c+d x}-\sqrt[3]{d} \sqrt[3]{a+\frac{b (c+d x)}{d}-\frac{b c}{d}}\right)}{d^{4/3}}+\frac{\sqrt{3} \sqrt[3]{b} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{d} \sqrt[3]{a+\frac{b (c+d x)}{d}-\frac{b c}{d}}}{\sqrt[3]{d} \sqrt[3]{a+\frac{b (c+d x)}{d}-\frac{b c}{d}}+2 \sqrt[3]{b} \sqrt[3]{c+d x}}\right)}{d^{4/3}}-\frac{3 \sqrt[3]{a+\frac{b (c+d x)}{d}-\frac{b c}{d}}}{d \sqrt[3]{c+d 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}}",1,"(-3*(a - (b*c)/d + (b*(c + d*x))/d)^(1/3))/(d*(c + d*x)^(1/3)) + (Sqrt[3]*b^(1/3)*ArcTan[(Sqrt[3]*d^(1/3)*(a - (b*c)/d + (b*(c + d*x))/d)^(1/3))/(2*b^(1/3)*(c + d*x)^(1/3) + d^(1/3)*(a - (b*c)/d + (b*(c + d*x))/d)^(1/3))])/d^(4/3) - (b^(1/3)*Log[b^(1/3)*(c + d*x)^(1/3) - d^(1/3)*(a - (b*c)/d + (b*(c + d*x))/d)^(1/3)])/d^(4/3) + (b^(1/3)*Log[b^(2/3)*(c + d*x)^(2/3) + b^(1/3)*d^(1/3)*(c + d*x)^(1/3)*(a - (b*c)/d + (b*(c + d*x))/d)^(1/3) + d^(2/3)*(a - (b*c)/d + (b*(c + d*x))/d)^(2/3)])/(2*d^(4/3))","B",1
1618,1,62,30,5.2938139,"\int \frac{1}{(a+b x)^{2/3} (c+d x)^{4/3}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(2/3)*(c + d*x)^(4/3)),x]","\frac{3 b \sqrt[3]{a+b x} \left(\frac{d (a+b x)}{b}-\frac{a d}{b}+c\right)^{2/3}}{(b c-a d) (d (a+b x)-a d+b c)}","\frac{3 \sqrt[3]{a+b x}}{\sqrt[3]{c+d x} (b c-a d)}",1,"(3*b*(a + b*x)^(1/3)*(c - (a*d)/b + (d*(a + b*x))/b)^(2/3))/((b*c - a*d)*(b*c - a*d + d*(a + b*x)))","B",1
1619,1,83,66,12.0471713,"\int \frac{1}{(a+b x)^{5/3} (c+d x)^{4/3}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(5/3)*(c + d*x)^(4/3)),x]","-\frac{3 (a d+b d x)^{5/3} (2 a d+3 b (c+d x)-2 b c)}{2 d (a+b x)^{5/3} \sqrt[3]{c+d x} (b c-a d)^2 (a d+b (c+d x)-b c)^{2/3}}","-\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*(a*d + b*d*x)^(5/3)*(-2*b*c + 2*a*d + 3*b*(c + d*x)))/(2*d*(b*c - a*d)^2*(a + b*x)^(5/3)*(c + d*x)^(1/3)*(-(b*c) + a*d + b*(c + d*x))^(2/3))","A",1
1620,1,149,101,15.2355354,"\int \frac{1}{(a+b x)^{8/3} (c+d x)^{4/3}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(8/3)*(c + d*x)^(4/3)),x]","\frac{3 (a d+b d x)^{8/3} \left(5 a^2 d^{11/3}+15 a b d^{8/3} (c+d x)-10 a b c d^{8/3}+5 b^2 c^2 d^{5/3}+9 b^2 d^{5/3} (c+d x)^2-15 b^2 c d^{5/3} (c+d x)\right)}{5 d^{8/3} (a+b x)^{8/3} \sqrt[3]{c+d x} (b c-a d)^3 (a d+b (c+d x)-b c)^{5/3}}","\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*(a*d + b*d*x)^(8/3)*(5*b^2*c^2*d^(5/3) - 10*a*b*c*d^(8/3) + 5*a^2*d^(11/3) - 15*b^2*c*d^(5/3)*(c + d*x) + 15*a*b*d^(8/3)*(c + d*x) + 9*b^2*d^(5/3)*(c + d*x)^2))/(5*d^(8/3)*(b*c - a*d)^3*(a + b*x)^(8/3)*(c + d*x)^(1/3)*(-(b*c) + a*d + b*(c + d*x))^(5/3))","A",1
1621,0,0,136,37.2629465,"\int \frac{1}{(a+b x)^{11/3} (c+d x)^{4/3}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(11/3)*(c + d*x)^(4/3)),x]","\int \frac{1}{(a+b x)^{11/3} (c+d x)^{4/3}} \, dx","-\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,"Could not integrate","F",-1
1622,0,0,1355,26.0436808,"\int \frac{(a+b x)^{8/3}}{(c+d x)^{4/3}} \, dx","IntegrateAlgebraic[(a + b*x)^(8/3)/(c + d*x)^(4/3),x]","\int \frac{(a+b x)^{8/3}}{(c+d x)^{4/3}} \, dx","-\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,"Could not integrate","F",-1
1623,0,0,1317,23.4790366,"\int \frac{(a+b x)^{5/3}}{(c+d x)^{4/3}} \, dx","IntegrateAlgebraic[(a + b*x)^(5/3)/(c + d*x)^(4/3),x]","\int \frac{(a+b x)^{5/3}}{(c+d x)^{4/3}} \, dx","\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,"Could not integrate","F",-1
1624,0,0,1279,15.5237846,"\int \frac{(a+b x)^{2/3}}{(c+d x)^{4/3}} \, dx","IntegrateAlgebraic[(a + b*x)^(2/3)/(c + d*x)^(4/3),x]","\int \frac{(a+b x)^{2/3}}{(c+d x)^{4/3}} \, dx","-\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,"Could not integrate","F",-1
1625,0,0,1298,19.9213544,"\int \frac{1}{\sqrt[3]{a+b x} (c+d x)^{4/3}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(1/3)*(c + d*x)^(4/3)),x]","\int \frac{1}{\sqrt[3]{a+b x} (c+d x)^{4/3}} \, dx","\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,"Could not integrate","F",-1
1626,0,0,1327,25.5697176,"\int \frac{1}{(a+b x)^{4/3} (c+d x)^{4/3}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(4/3)*(c + d*x)^(4/3)),x]","\int \frac{1}{(a+b x)^{4/3} (c+d x)^{4/3}} \, dx","-\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,"Could not integrate","F",-1
1627,0,0,1370,29.7535728,"\int \frac{1}{(a+b x)^{7/3} (c+d x)^{4/3}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(7/3)*(c + d*x)^(4/3)),x]","\int \frac{1}{(a+b x)^{7/3} (c+d x)^{4/3}} \, dx","\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,"Could not integrate","F",-1
1628,1,113,77,0.175198,"\int \frac{\sqrt[3]{-1+x}}{\sqrt[3]{1+x}} \, dx","IntegrateAlgebraic[(-1 + x)^(1/3)/(1 + x)^(1/3),x]","\sqrt[3]{x-1} (x+1)^{2/3}+\frac{2}{3} \log \left(\sqrt[3]{x-1}-\sqrt[3]{x+1}\right)-\frac{1}{3} \log \left((x-1)^{2/3}+\sqrt[3]{x+1} \sqrt[3]{x-1}+(x+1)^{2/3}\right)+\frac{2 \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x+1}}{2 \sqrt[3]{x-1}+\sqrt[3]{x+1}}\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[(Sqrt[3]*(1 + x)^(1/3))/(2*(-1 + x)^(1/3) + (1 + x)^(1/3))])/Sqrt[3] + (2*Log[(-1 + x)^(1/3) - (1 + x)^(1/3)])/3 - Log[(-1 + x)^(2/3) + (-1 + x)^(1/3)*(1 + x)^(1/3) + (1 + x)^(2/3)]/3","A",1
1629,0,0,185,35.4487812,"\int (a+b x)^{3/2} \sqrt[4]{c+d x} \, dx","IntegrateAlgebraic[(a + b*x)^(3/2)*(c + d*x)^(1/4),x]","\int (a+b x)^{3/2} \sqrt[4]{c+d x} \, dx","\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,"Could not integrate","F",-1
1630,0,0,147,13.9920056,"\int \sqrt{a+b x} \sqrt[4]{c+d x} \, dx","IntegrateAlgebraic[Sqrt[a + b*x]*(c + d*x)^(1/4),x]","\int \sqrt{a+b x} \sqrt[4]{c+d x} \, dx","-\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,"Could not integrate","F",-1
1631,0,0,111,13.7434964,"\int \frac{\sqrt[4]{c+d x}}{\sqrt{a+b x}} \, dx","IntegrateAlgebraic[(c + d*x)^(1/4)/Sqrt[a + b*x],x]","\int \frac{\sqrt[4]{c+d x}}{\sqrt{a+b x}} \, dx","\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,"Could not integrate","F",-1
1632,0,0,104,35.1769477,"\int \frac{\sqrt[4]{c+d x}}{(a+b x)^{3/2}} \, dx","IntegrateAlgebraic[(c + d*x)^(1/4)/(a + b*x)^(3/2),x]","\int \frac{\sqrt[4]{c+d x}}{(a+b x)^{3/2}} \, dx","\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,"Could not integrate","F",-1
1633,0,0,145,52.4310316,"\int \frac{\sqrt[4]{c+d x}}{(a+b x)^{5/2}} \, dx","IntegrateAlgebraic[(c + d*x)^(1/4)/(a + b*x)^(5/2),x]","\int \frac{\sqrt[4]{c+d x}}{(a+b x)^{5/2}} \, dx","-\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,"Could not integrate","F",-1
1634,0,0,185,60.4516691,"\int \frac{\sqrt[4]{c+d x}}{(a+b x)^{7/2}} \, dx","IntegrateAlgebraic[(c + d*x)^(1/4)/(a + b*x)^(7/2),x]","\int \frac{\sqrt[4]{c+d x}}{(a+b x)^{7/2}} \, dx","\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,"Could not integrate","F",-1
1635,0,0,270,37.0779016,"\int (a+b x)^{3/2} (c+d x)^{3/4} \, dx","IntegrateAlgebraic[(a + b*x)^(3/2)*(c + d*x)^(3/4),x]","\int (a+b x)^{3/2} (c+d x)^{3/4} \, dx","-\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,"Could not integrate","F",-1
1636,0,0,232,29.9933673,"\int \sqrt{a+b x} (c+d x)^{3/4} \, dx","IntegrateAlgebraic[Sqrt[a + b*x]*(c + d*x)^(3/4),x]","\int \sqrt{a+b x} (c+d x)^{3/4} \, dx","\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,"Could not integrate","F",-1
1637,0,0,196,55.1178585,"\int \frac{(c+d x)^{3/4}}{\sqrt{a+b x}} \, dx","IntegrateAlgebraic[(c + d*x)^(3/4)/Sqrt[a + b*x],x]","\int \frac{(c+d x)^{3/4}}{\sqrt{a+b x}} \, dx","-\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,"Could not integrate","F",-1
1638,0,0,184,35.6192463,"\int \frac{(c+d x)^{3/4}}{(a+b x)^{3/2}} \, dx","IntegrateAlgebraic[(c + d*x)^(3/4)/(a + b*x)^(3/2),x]","\int \frac{(c+d x)^{3/4}}{(a+b x)^{3/2}} \, dx","-\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,"Could not integrate","F",-1
1639,0,0,221,51.1197576,"\int \frac{(c+d x)^{3/4}}{(a+b x)^{5/2}} \, dx","IntegrateAlgebraic[(c + d*x)^(3/4)/(a + b*x)^(5/2),x]","\int \frac{(c+d x)^{3/4}}{(a+b x)^{5/2}} \, dx","-\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,"Could not integrate","F",-1
1640,0,0,270,58.673509,"\int \frac{(c+d x)^{3/4}}{(a+b x)^{7/2}} \, dx","IntegrateAlgebraic[(c + d*x)^(3/4)/(a + b*x)^(7/2),x]","\int \frac{(c+d x)^{3/4}}{(a+b x)^{7/2}} \, dx","\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,"Could not integrate","F",-1
1641,0,0,220,40.6936315,"\int (a+b x)^{3/2} (c+d x)^{5/4} \, dx","IntegrateAlgebraic[(a + b*x)^(3/2)*(c + d*x)^(5/4),x]","\int (a+b x)^{3/2} (c+d x)^{5/4} \, dx","\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{8 \sqrt{a+b x} \sqrt[4]{c+d x} (b c-a d)^3}{231 b^2 d^2}+\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,"Could not integrate","F",-1
1642,0,0,182,18.6910048,"\int \sqrt{a+b x} (c+d x)^{5/4} \, dx","IntegrateAlgebraic[Sqrt[a + b*x]*(c + d*x)^(5/4),x]","\int \sqrt{a+b x} (c+d x)^{5/4} \, dx","-\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,"Could not integrate","F",-1
1643,0,0,144,18.0449229,"\int \frac{(c+d x)^{5/4}}{\sqrt{a+b x}} \, dx","IntegrateAlgebraic[(c + d*x)^(5/4)/Sqrt[a + b*x],x]","\int \frac{(c+d x)^{5/4}}{\sqrt{a+b x}} \, dx","\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{20 \sqrt{a+b x} \sqrt[4]{c+d x} (b c-a d)}{21 b^2}+\frac{4 \sqrt{a+b x} (c+d x)^{5/4}}{7 b}",1,"Could not integrate","F",-1
1644,0,0,132,39.5984153,"\int \frac{(c+d x)^{5/4}}{(a+b x)^{3/2}} \, dx","IntegrateAlgebraic[(c + d*x)^(5/4)/(a + b*x)^(3/2),x]","\int \frac{(c+d x)^{5/4}}{(a+b x)^{3/2}} \, dx","\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{10 d \sqrt{a+b x} \sqrt[4]{c+d x}}{3 b^2}-\frac{2 (c+d x)^{5/4}}{b \sqrt{a+b x}}",1,"Could not integrate","F",-1
1645,0,0,135,51.4572323,"\int \frac{(c+d x)^{5/4}}{(a+b x)^{5/2}} \, dx","IntegrateAlgebraic[(c + d*x)^(5/4)/(a + b*x)^(5/2),x]","\int \frac{(c+d x)^{5/4}}{(a+b x)^{5/2}} \, dx","\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{5 d \sqrt[4]{c+d x}}{3 b^2 \sqrt{a+b x}}-\frac{2 (c+d x)^{5/4}}{3 b (a+b x)^{3/2}}",1,"Could not integrate","F",-1
1646,0,0,175,62.394672,"\int \frac{(c+d x)^{5/4}}{(a+b x)^{7/2}} \, dx","IntegrateAlgebraic[(c + d*x)^(5/4)/(a + b*x)^(7/2),x]","\int \frac{(c+d x)^{5/4}}{(a+b x)^{7/2}} \, dx","-\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^2 \sqrt[4]{c+d x}}{6 b^2 \sqrt{a+b x} (b c-a d)}-\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,"Could not integrate","F",-1
1647,0,0,213,66.036091,"\int \frac{(c+d x)^{5/4}}{(a+b x)^{9/2}} \, dx","IntegrateAlgebraic[(c + d*x)^(5/4)/(a + b*x)^(9/2),x]","\int \frac{(c+d x)^{5/4}}{(a+b x)^{9/2}} \, dx","\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{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{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,"Could not integrate","F",-1
1648,0,0,264,39.2050021,"\int \frac{(a+b x)^{5/2}}{\sqrt[4]{c+d x}} \, dx","IntegrateAlgebraic[(a + b*x)^(5/2)/(c + d*x)^(1/4),x]","\int \frac{(a+b x)^{5/2}}{\sqrt[4]{c+d x}} \, dx","\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,"Could not integrate","F",-1
1649,0,0,229,33.4717598,"\int \frac{(a+b x)^{3/2}}{\sqrt[4]{c+d x}} \, dx","IntegrateAlgebraic[(a + b*x)^(3/2)/(c + d*x)^(1/4),x]","\int \frac{(a+b x)^{3/2}}{\sqrt[4]{c+d x}} \, dx","-\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,"Could not integrate","F",-1
1650,0,0,196,13.1545299,"\int \frac{\sqrt{a+b x}}{\sqrt[4]{c+d x}} \, dx","IntegrateAlgebraic[Sqrt[a + b*x]/(c + d*x)^(1/4),x]","\int \frac{\sqrt{a+b x}}{\sqrt[4]{c+d x}} \, dx","\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,"Could not integrate","F",-1
1651,0,0,167,12.8504342,"\int \frac{1}{\sqrt{a+b x} \sqrt[4]{c+d x}} \, dx","IntegrateAlgebraic[1/(Sqrt[a + b*x]*(c + d*x)^(1/4)),x]","\int \frac{1}{\sqrt{a+b x} \sqrt[4]{c+d x}} \, dx","\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,"Could not integrate","F",-1
1652,0,0,191,39.3038847,"\int \frac{1}{(a+b x)^{3/2} \sqrt[4]{c+d x}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(3/2)*(c + d*x)^(1/4)),x]","\int \frac{1}{(a+b x)^{3/2} \sqrt[4]{c+d x}} \, dx","-\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,"Could not integrate","F",-1
1653,0,0,224,52.0130201,"\int \frac{1}{(a+b x)^{5/2} \sqrt[4]{c+d x}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(5/2)*(c + d*x)^(1/4)),x]","\int \frac{1}{(a+b x)^{5/2} \sqrt[4]{c+d x}} \, dx","\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,"Could not integrate","F",-1
1654,0,0,144,25.0323097,"\int \frac{(a+b x)^{3/2}}{(c+d x)^{3/4}} \, dx","IntegrateAlgebraic[(a + b*x)^(3/2)/(c + d*x)^(3/4),x]","\int \frac{(a+b x)^{3/2}}{(c+d x)^{3/4}} \, dx","\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{8 \sqrt{a+b x} \sqrt[4]{c+d x} (b c-a d)}{7 d^2}+\frac{4 (a+b x)^{3/2} \sqrt[4]{c+d x}}{7 d}",1,"Could not integrate","F",-1
1655,0,0,111,13.4178685,"\int \frac{\sqrt{a+b x}}{(c+d x)^{3/4}} \, dx","IntegrateAlgebraic[Sqrt[a + b*x]/(c + d*x)^(3/4),x]","\int \frac{\sqrt{a+b x}}{(c+d x)^{3/4}} \, dx","\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,"Could not integrate","F",-1
1656,0,0,83,30.2105855,"\int \frac{1}{\sqrt{a+b x} (c+d x)^{3/4}} \, dx","IntegrateAlgebraic[1/(Sqrt[a + b*x]*(c + d*x)^(3/4)),x]","\int \frac{1}{\sqrt{a+b x} (c+d x)^{3/4}} \, dx","\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,"Could not integrate","F",-1
1657,0,0,111,38.2299935,"\int \frac{1}{(a+b x)^{3/2} (c+d x)^{3/4}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(3/2)*(c + d*x)^(3/4)),x]","\int \frac{1}{(a+b x)^{3/2} (c+d x)^{3/4}} \, dx","-\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,"Could not integrate","F",-1
1658,0,0,149,52.191174,"\int \frac{1}{(a+b x)^{5/2} (c+d x)^{3/4}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(5/2)*(c + d*x)^(3/4)),x]","\int \frac{1}{(a+b x)^{5/2} (c+d x)^{3/4}} \, dx","\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,"Could not integrate","F",-1
1659,0,0,254,41.1452403,"\int \frac{(a+b x)^{5/2}}{(c+d x)^{5/4}} \, dx","IntegrateAlgebraic[(a + b*x)^(5/2)/(c + d*x)^(5/4),x]","\int \frac{(a+b x)^{5/2}}{(c+d x)^{5/4}} \, dx","-\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{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{4 (a+b x)^{5/2}}{d \sqrt[4]{c+d x}}",1,"Could not integrate","F",-1
1660,0,0,220,29.8779174,"\int \frac{(a+b x)^{3/2}}{(c+d x)^{5/4}} \, dx","IntegrateAlgebraic[(a + b*x)^(3/2)/(c + d*x)^(5/4),x]","\int \frac{(a+b x)^{3/2}}{(c+d x)^{5/4}} \, dx","\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{24 b \sqrt{a+b x} (c+d x)^{3/4}}{5 d^2}-\frac{4 (a+b x)^{3/2}}{d \sqrt[4]{c+d x}}",1,"Could not integrate","F",-1
1661,0,0,190,15.3566828,"\int \frac{\sqrt{a+b x}}{(c+d x)^{5/4}} \, dx","IntegrateAlgebraic[Sqrt[a + b*x]/(c + d*x)^(5/4),x]","\int \frac{\sqrt{a+b x}}{(c+d x)^{5/4}} \, dx","-\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,"Could not integrate","F",-1
1662,0,0,197,14.3702085,"\int \frac{1}{\sqrt{a+b x} (c+d x)^{5/4}} \, dx","IntegrateAlgebraic[1/(Sqrt[a + b*x]*(c + d*x)^(5/4)),x]","\int \frac{1}{\sqrt{a+b x} (c+d x)^{5/4}} \, dx","\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,"Could not integrate","F",-1
1663,0,0,222,54.5393618,"\int \frac{1}{(a+b x)^{3/2} (c+d x)^{5/4}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(3/2)*(c + d*x)^(5/4)),x]","\int \frac{1}{(a+b x)^{3/2} (c+d x)^{5/4}} \, dx","-\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,"Could not integrate","F",-1
1664,0,0,261,62.7373028,"\int \frac{1}{(a+b x)^{5/2} (c+d x)^{5/4}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(5/2)*(c + d*x)^(5/4)),x]","\int \frac{1}{(a+b x)^{5/2} (c+d x)^{5/4}} \, dx","\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,"Could not integrate","F",-1
1665,0,0,207,56.7289015,"\int \frac{(a+b x)^{7/2}}{(c+d x)^{7/4}} \, dx","IntegrateAlgebraic[(a + b*x)^(7/2)/(c + d*x)^(7/4),x]","\int \frac{(a+b x)^{7/2}}{(c+d x)^{7/4}} \, dx","-\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{160 b \sqrt{a+b x} \sqrt[4]{c+d x} (b c-a d)^2}{33 d^4}-\frac{80 b (a+b x)^{3/2} \sqrt[4]{c+d x} (b c-a d)}{33 d^3}+\frac{56 b (a+b x)^{5/2} \sqrt[4]{c+d x}}{33 d^2}-\frac{4 (a+b x)^{7/2}}{3 d (c+d x)^{3/4}}",1,"Could not integrate","F",-1
1666,0,0,137,39.5123204,"\int \frac{(a+b x)^{3/2}}{(c+d x)^{7/4}} \, dx","IntegrateAlgebraic[(a + b*x)^(3/2)/(c + d*x)^(7/4),x]","\int \frac{(a+b x)^{3/2}}{(c+d x)^{7/4}} \, dx","-\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,"Could not integrate","F",-1
1667,0,0,111,19.1352367,"\int \frac{\sqrt{a+b x}}{(c+d x)^{7/4}} \, dx","IntegrateAlgebraic[Sqrt[a + b*x]/(c + d*x)^(7/4),x]","\int \frac{\sqrt{a+b x}}{(c+d x)^{7/4}} \, dx","\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,"Could not integrate","F",-1
1668,0,0,118,17.643427,"\int \frac{1}{\sqrt{a+b x} (c+d x)^{7/4}} \, dx","IntegrateAlgebraic[1/(Sqrt[a + b*x]*(c + d*x)^(7/4)),x]","\int \frac{1}{\sqrt{a+b x} (c+d x)^{7/4}} \, dx","\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,"Could not integrate","F",-1
1669,0,0,146,75.5761635,"\int \frac{1}{(a+b x)^{3/2} (c+d x)^{7/4}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(3/2)*(c + d*x)^(7/4)),x]","\int \frac{1}{(a+b x)^{3/2} (c+d x)^{7/4}} \, dx","-\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,"Could not integrate","F",-1
1670,0,0,178,77.7180366,"\int \frac{1}{(a+b x)^{5/2} (c+d x)^{7/4}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(5/2)*(c + d*x)^(7/4)),x]","\int \frac{1}{(a+b x)^{5/2} (c+d x)^{7/4}} \, dx","\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,"Could not integrate","F",-1
1671,0,0,286,58.7563647,"\int \frac{(a+b x)^{7/2}}{(c+d x)^{9/4}} \, dx","IntegrateAlgebraic[(a + b*x)^(7/2)/(c + d*x)^(9/4),x]","\int \frac{(a+b x)^{7/2}}{(c+d x)^{9/4}} \, dx","-\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{224 b^2 \sqrt{a+b x} (c+d x)^{3/4} (b c-a d)}{15 d^4}+\frac{112 b^2 (a+b x)^{3/2} (c+d x)^{3/4}}{9 d^3}-\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,"Could not integrate","F",-1
1672,0,0,248,49.6192464,"\int \frac{(a+b x)^{5/2}}{(c+d x)^{9/4}} \, dx","IntegrateAlgebraic[(a + b*x)^(5/2)/(c + d*x)^(9/4),x]","\int \frac{(a+b x)^{5/2}}{(c+d x)^{9/4}} \, dx","\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{48 b^2 \sqrt{a+b x} (c+d x)^{3/4}}{5 d^3}-\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,"Could not integrate","F",-1
1673,0,0,222,51.0874832,"\int \frac{(a+b x)^{3/2}}{(c+d x)^{9/4}} \, dx","IntegrateAlgebraic[(a + b*x)^(3/2)/(c + d*x)^(9/4),x]","\int \frac{(a+b x)^{3/2}}{(c+d x)^{9/4}} \, dx","-\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,"Could not integrate","F",-1
1674,0,0,232,20.9735666,"\int \frac{\sqrt{a+b x}}{(c+d x)^{9/4}} \, dx","IntegrateAlgebraic[Sqrt[a + b*x]/(c + d*x)^(9/4),x]","\int \frac{\sqrt{a+b x}}{(c+d x)^{9/4}} \, dx","\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,"Could not integrate","F",-1
1675,0,0,236,20.1082745,"\int \frac{1}{\sqrt{a+b x} (c+d x)^{9/4}} \, dx","IntegrateAlgebraic[1/(Sqrt[a + b*x]*(c + d*x)^(9/4)),x]","\int \frac{1}{\sqrt{a+b x} (c+d x)^{9/4}} \, dx","\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,"Could not integrate","F",-1
1676,0,0,262,85.0230384,"\int \frac{1}{(a+b x)^{3/2} (c+d x)^{9/4}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(3/2)*(c + d*x)^(9/4)),x]","\int \frac{1}{(a+b x)^{3/2} (c+d x)^{9/4}} \, dx","-\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,"Could not integrate","F",-1
1677,0,0,303,88.4077345,"\int \frac{1}{(a+b x)^{5/2} (c+d x)^{9/4}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(5/2)*(c + d*x)^(9/4)),x]","\int \frac{1}{(a+b x)^{5/2} (c+d x)^{9/4}} \, dx","\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,"Could not integrate","F",-1
1678,0,0,205,25.5832073,"\int (a+b x)^{3/4} (c+d x)^{5/4} \, dx","IntegrateAlgebraic[(a + b*x)^(3/4)*(c + d*x)^(5/4),x]","\int (a+b x)^{3/4} (c+d x)^{5/4} \, dx","\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,"Could not integrate","F",-1
1679,0,0,167,21.8141094,"\int \frac{(c+d x)^{5/4}}{\sqrt[4]{a+b x}} \, dx","IntegrateAlgebraic[(c + d*x)^(5/4)/(a + b*x)^(1/4),x]","\int \frac{(c+d x)^{5/4}}{\sqrt[4]{a+b x}} \, dx","-\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,"Could not integrate","F",-1
1680,1,244,152,14.4696741,"\int \frac{(c+d x)^{5/4}}{(a+b x)^{5/4}} \, dx","IntegrateAlgebraic[(c + d*x)^(5/4)/(a + b*x)^(5/4),x]","\frac{(a d+b d x)^{5/4} \left(\frac{5 \left(b c \sqrt[4]{d}-a d^{5/4}\right) \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{a d+b (c+d x)-b c}}\right)}{2 b^{9/4}}+\frac{5 \left(b c \sqrt[4]{d}-a d^{5/4}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{a d+b (c+d x)-b c}}\right)}{2 b^{9/4}}+\frac{(a d+b (c+d x)-b c)^{3/4} \left(-5 a d^{5/4} \sqrt[4]{c+d x}-b \sqrt[4]{d} (c+d x)^{5/4}+5 b c \sqrt[4]{d} \sqrt[4]{c+d x}\right)}{b^2 (-a d-b (c+d x)+b c)}\right)}{d^{5/4} (a+b x)^{5/4}}","-\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{5 d (a+b x)^{3/4} \sqrt[4]{c+d x}}{b^2}-\frac{4 (c+d x)^{5/4}}{b \sqrt[4]{a+b x}}",1,"((a*d + b*d*x)^(5/4)*(((-(b*c) + a*d + b*(c + d*x))^(3/4)*(5*b*c*d^(1/4)*(c + d*x)^(1/4) - 5*a*d^(5/4)*(c + d*x)^(1/4) - b*d^(1/4)*(c + d*x)^(5/4)))/(b^2*(b*c - a*d - b*(c + d*x))) + (5*(b*c*d^(1/4) - a*d^(5/4))*ArcTan[(b^(1/4)*(c + d*x)^(1/4))/(-(b*c) + a*d + b*(c + d*x))^(1/4)])/(2*b^(9/4)) + (5*(b*c*d^(1/4) - a*d^(5/4))*ArcTanh[(b^(1/4)*(c + d*x)^(1/4))/(-(b*c) + a*d + b*(c + d*x))^(1/4)])/(2*b^(9/4))))/(d^(5/4)*(a + b*x)^(5/4))","A",1
1681,1,219,134,20.9286489,"\int \frac{(c+d x)^{5/4}}{(a+b x)^{9/4}} \, dx","IntegrateAlgebraic[(c + d*x)^(5/4)/(a + b*x)^(9/4),x]","\frac{(a d+b d x)^{9/4} \left(\frac{2 d^{5/4} \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{a d+b (c+d x)-b c}}\right)}{b^{9/4}}+\frac{2 d^{5/4} \tanh ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{a d+b (c+d x)-b c}}\right)}{b^{9/4}}+\frac{4 (a d+b (c+d x)-b c)^{3/4} \left(-5 a d^{9/4} \sqrt[4]{c+d x}-6 b d^{5/4} (c+d x)^{5/4}+5 b c d^{5/4} \sqrt[4]{c+d x}\right)}{5 b^2 (-a d-b (c+d x)+b c)^2}\right)}{d^{9/4} (a+b x)^{9/4}}","-\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,"((a*d + b*d*x)^(9/4)*((4*(-(b*c) + a*d + b*(c + d*x))^(3/4)*(5*b*c*d^(5/4)*(c + d*x)^(1/4) - 5*a*d^(9/4)*(c + d*x)^(1/4) - 6*b*d^(5/4)*(c + d*x)^(5/4)))/(5*b^2*(b*c - a*d - b*(c + d*x))^2) + (2*d^(5/4)*ArcTan[(b^(1/4)*(c + d*x)^(1/4))/(-(b*c) + a*d + b*(c + d*x))^(1/4)])/b^(9/4) + (2*d^(5/4)*ArcTanh[(b^(1/4)*(c + d*x)^(1/4))/(-(b*c) + a*d + b*(c + d*x))^(1/4)])/b^(9/4)))/(d^(9/4)*(a + b*x)^(9/4))","A",1
1682,1,66,32,23.0596897,"\int \frac{(c+d x)^{5/4}}{(a+b x)^{13/4}} \, dx","IntegrateAlgebraic[(c + d*x)^(5/4)/(a + b*x)^(13/4),x]","\frac{4 d^3 (a+b x)^{3/4} (c+d x)^{9/4}}{9 (a d-b c) (a d+b d x)^{3/4} (a d+b (c+d x)-b c)^{9/4}}","-\frac{4 (c+d x)^{9/4}}{9 (a+b x)^{9/4} (b c-a d)}",1,"(4*d^3*(a + b*x)^(3/4)*(c + d*x)^(9/4))/(9*(-(b*c) + a*d)*(a*d + b*d*x)^(3/4)*(-(b*c) + a*d + b*(c + d*x))^(9/4))","B",1
1683,0,0,66,39.086508,"\int \frac{(c+d x)^{5/4}}{(a+b x)^{17/4}} \, dx","IntegrateAlgebraic[(c + d*x)^(5/4)/(a + b*x)^(17/4),x]","\int \frac{(c+d x)^{5/4}}{(a+b x)^{17/4}} \, dx","\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,"Could not integrate","F",-1
1684,0,0,101,39.5642758,"\int \frac{(c+d x)^{5/4}}{(a+b x)^{21/4}} \, dx","IntegrateAlgebraic[(c + d*x)^(5/4)/(a + b*x)^(21/4),x]","\int \frac{(c+d x)^{5/4}}{(a+b x)^{21/4}} \, dx","-\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,"Could not integrate","F",-1
1685,0,0,136,39.8645609,"\int \frac{(c+d x)^{5/4}}{(a+b x)^{25/4}} \, dx","IntegrateAlgebraic[(c + d*x)^(5/4)/(a + b*x)^(25/4),x]","\int \frac{(c+d x)^{5/4}}{(a+b x)^{25/4}} \, dx","\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,"Could not integrate","F",-1
1686,0,0,408,20.3702888,"\int (a+b x)^{5/4} (c+d x)^{5/4} \, dx","IntegrateAlgebraic[(a + b*x)^(5/4)*(c + d*x)^(5/4),x]","\int (a+b x)^{5/4} (c+d x)^{5/4} \, dx","\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{5 \sqrt[4]{a+b x} \sqrt[4]{c+d x} (b c-a d)^3}{84 b^2 d^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,"Could not integrate","F",-1
1687,0,0,370,16.38719,"\int \sqrt[4]{a+b x} (c+d x)^{5/4} \, dx","IntegrateAlgebraic[(a + b*x)^(1/4)*(c + d*x)^(5/4),x]","\int \sqrt[4]{a+b x} (c+d x)^{5/4} \, dx","-\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,"Could not integrate","F",-1
1688,0,0,332,18.9568446,"\int \frac{(c+d x)^{5/4}}{(a+b x)^{3/4}} \, dx","IntegrateAlgebraic[(c + d*x)^(5/4)/(a + b*x)^(3/4),x]","\int \frac{(c+d x)^{5/4}}{(a+b x)^{3/4}} \, dx","\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{5 \sqrt[4]{a+b x} \sqrt[4]{c+d x} (b c-a d)}{3 b^2}+\frac{2 \sqrt[4]{a+b x} (c+d x)^{5/4}}{3 b}",1,"Could not integrate","F",-1
1689,0,0,325,32.2355712,"\int \frac{(c+d x)^{5/4}}{(a+b x)^{7/4}} \, dx","IntegrateAlgebraic[(c + d*x)^(5/4)/(a + b*x)^(7/4),x]","\int \frac{(c+d x)^{5/4}}{(a+b x)^{7/4}} \, dx","\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,"Could not integrate","F",-1
1690,0,0,325,36.9841141,"\int \frac{(c+d x)^{5/4}}{(a+b x)^{11/4}} \, dx","IntegrateAlgebraic[(c + d*x)^(5/4)/(a + b*x)^(11/4),x]","\int \frac{(c+d x)^{5/4}}{(a+b x)^{11/4}} \, dx","\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,"Could not integrate","F",-1
1691,0,0,363,38.5918565,"\int \frac{(c+d x)^{5/4}}{(a+b x)^{15/4}} \, dx","IntegrateAlgebraic[(c + d*x)^(5/4)/(a + b*x)^(15/4),x]","\int \frac{(c+d x)^{5/4}}{(a+b x)^{15/4}} \, dx","-\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^2 \sqrt[4]{c+d x}}{231 b^2 (a+b x)^{3/4} (b c-a d)}-\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,"Could not integrate","F",-1
1692,0,0,401,39.4422008,"\int \frac{(c+d x)^{5/4}}{(a+b x)^{19/4}} \, dx","IntegrateAlgebraic[(c + d*x)^(5/4)/(a + b*x)^(19/4),x]","\int \frac{(c+d x)^{5/4}}{(a+b x)^{19/4}} \, dx","\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{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 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,"Could not integrate","F",-1
1693,1,235,167,10.64337,"\int \frac{(a+b x)^{5/4}}{\sqrt[4]{c+d x}} \, dx","IntegrateAlgebraic[(a + b*x)^(5/4)/(c + d*x)^(1/4),x]","\frac{d^{5/4} (a+b x)^{5/4} \left(-\frac{5 \left(a^2 d^2-2 a b c d+b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{a d+b (c+d x)-b c}}\right)}{16 b^{3/4} d^{9/4}}+\frac{5 \left(a^2 d^2-2 a b c d+b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{a d+b (c+d x)-b c}}\right)}{16 b^{3/4} d^{9/4}}+\frac{\sqrt[4]{a d+b (c+d x)-b c} \left(9 a d (c+d x)^{3/4}+4 b (c+d x)^{7/4}-9 b c (c+d x)^{3/4}\right)}{8 d^{9/4}}\right)}{(a d+b d x)^{5/4}}","\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,"(d^(5/4)*(a + b*x)^(5/4)*(((-(b*c) + a*d + b*(c + d*x))^(1/4)*(-9*b*c*(c + d*x)^(3/4) + 9*a*d*(c + d*x)^(3/4) + 4*b*(c + d*x)^(7/4)))/(8*d^(9/4)) - (5*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*ArcTan[(b^(1/4)*(c + d*x)^(1/4))/(-(b*c) + a*d + b*(c + d*x))^(1/4)])/(16*b^(3/4)*d^(9/4)) + (5*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*ArcTanh[(b^(1/4)*(c + d*x)^(1/4))/(-(b*c) + a*d + b*(c + d*x))^(1/4)])/(16*b^(3/4)*d^(9/4))))/(a*d + b*d*x)^(5/4)","A",1
1694,1,176,127,8.6645325,"\int \frac{\sqrt[4]{a+b x}}{\sqrt[4]{c+d x}} \, dx","IntegrateAlgebraic[(a + b*x)^(1/4)/(c + d*x)^(1/4),x]","\frac{\sqrt[4]{d} \sqrt[4]{a+b x} \left(\frac{(b c-a d) \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{a d+b (c+d x)-b c}}\right)}{2 b^{3/4} d^{5/4}}+\frac{(a d-b c) \tanh ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{a d+b (c+d x)-b c}}\right)}{2 b^{3/4} d^{5/4}}+\frac{(c+d x)^{3/4} \sqrt[4]{a d+b (c+d x)-b c}}{d^{5/4}}\right)}{\sqrt[4]{a d+b d 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}",1,"(d^(1/4)*(a + b*x)^(1/4)*(((c + d*x)^(3/4)*(-(b*c) + a*d + b*(c + d*x))^(1/4))/d^(5/4) + ((b*c - a*d)*ArcTan[(b^(1/4)*(c + d*x)^(1/4))/(-(b*c) + a*d + b*(c + d*x))^(1/4)])/(2*b^(3/4)*d^(5/4)) + ((-(b*c) + a*d)*ArcTanh[(b^(1/4)*(c + d*x)^(1/4))/(-(b*c) + a*d + b*(c + d*x))^(1/4)])/(2*b^(3/4)*d^(5/4))))/(a*d + b*d*x)^(1/4)","A",1
1695,1,113,85,1.5649837,"\int \frac{1}{(a+b x)^{3/4} \sqrt[4]{c+d x}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(3/4)*(c + d*x)^(1/4)),x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{\frac{d (a+b x)}{b}-\frac{a d}{b}+c}}{\sqrt[4]{d} \sqrt[4]{a+b x}}\right)}{b^{3/4} \sqrt[4]{d}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{\frac{d (a+b x)}{b}-\frac{a d}{b}+c}}{\sqrt[4]{d} \sqrt[4]{a+b 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[(b^(1/4)*(c - (a*d)/b + (d*(a + b*x))/b)^(1/4))/(d^(1/4)*(a + b*x)^(1/4))])/(b^(3/4)*d^(1/4)) + (2*ArcTanh[(b^(1/4)*(c - (a*d)/b + (d*(a + b*x))/b)^(1/4))/(d^(1/4)*(a + b*x)^(1/4))])/(b^(3/4)*d^(1/4))","A",1
1696,1,66,32,13.2840223,"\int \frac{1}{(a+b x)^{7/4} \sqrt[4]{c+d x}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(7/4)*(c + d*x)^(1/4)),x]","\frac{4 (c+d x)^{3/4} (a d+b d x)^{7/4}}{3 d (a+b x)^{7/4} (a d-b c) (a d+b (c+d x)-b c)^{3/4}}","-\frac{4 (c+d x)^{3/4}}{3 (a+b x)^{3/4} (b c-a d)}",1,"(4*(c + d*x)^(3/4)*(a*d + b*d*x)^(7/4))/(3*d*(-(b*c) + a*d)*(a + b*x)^(7/4)*(-(b*c) + a*d + b*(c + d*x))^(3/4))","B",1
1697,0,0,66,36.3353838,"\int \frac{1}{(a+b x)^{11/4} \sqrt[4]{c+d x}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(11/4)*(c + d*x)^(1/4)),x]","\int \frac{1}{(a+b x)^{11/4} \sqrt[4]{c+d x}} \, dx","\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,"Could not integrate","F",-1
1698,0,0,101,38.3517237,"\int \frac{1}{(a+b x)^{15/4} \sqrt[4]{c+d x}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(15/4)*(c + d*x)^(1/4)),x]","\int \frac{1}{(a+b x)^{15/4} \sqrt[4]{c+d x}} \, dx","-\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,"Could not integrate","F",-1
1699,0,0,136,39.2157918,"\int \frac{1}{(a+b x)^{19/4} \sqrt[4]{c+d x}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(19/4)*(c + d*x)^(1/4)),x]","\int \frac{1}{(a+b x)^{19/4} \sqrt[4]{c+d x}} \, dx","\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,"Could not integrate","F",-1
1700,0,0,751,20.6050544,"\int \frac{(a+b x)^{7/4}}{\sqrt[4]{c+d x}} \, dx","IntegrateAlgebraic[(a + b*x)^(7/4)/(c + d*x)^(1/4),x]","\int \frac{(a+b x)^{7/4}}{\sqrt[4]{c+d x}} \, dx","\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 (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{7 (a+b x)^{3/4} (c+d x)^{3/4} (b c-a d)}{15 d^2}+\frac{2 (a+b x)^{7/4} (c+d x)^{3/4}}{5 d}",1,"Could not integrate","F",-1
1701,0,0,705,19.0792658,"\int \frac{(a+b x)^{3/4}}{\sqrt[4]{c+d x}} \, dx","IntegrateAlgebraic[(a + b*x)^(3/4)/(c + d*x)^(1/4),x]","\int \frac{(a+b x)^{3/4}}{\sqrt[4]{c+d x}} \, dx","-\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,"Could not integrate","F",-1
1702,0,0,688,14.6239514,"\int \frac{1}{\sqrt[4]{a+b x} \sqrt[4]{c+d x}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(1/4)*(c + d*x)^(1/4)),x]","\int \frac{1}{\sqrt[4]{a+b x} \sqrt[4]{c+d x}} \, dx","\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,"Could not integrate","F",-1
1703,0,0,718,19.2866356,"\int \frac{1}{(a+b x)^{5/4} \sqrt[4]{c+d x}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(5/4)*(c + d*x)^(1/4)),x]","\int \frac{1}{(a+b x)^{5/4} \sqrt[4]{c+d x}} \, dx","\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,"Could not integrate","F",-1
1704,0,0,760,30.2579509,"\int \frac{1}{(a+b x)^{9/4} \sqrt[4]{c+d x}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(9/4)*(c + d*x)^(1/4)),x]","\int \frac{1}{(a+b x)^{9/4} \sqrt[4]{c+d x}} \, dx","-\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,"Could not integrate","F",-1
1705,1,235,167,10.4640341,"\int \frac{(a+b x)^{7/4}}{(c+d x)^{3/4}} \, dx","IntegrateAlgebraic[(a + b*x)^(7/4)/(c + d*x)^(3/4),x]","\frac{d^{3/4} (a+b x)^{3/4} \left(\frac{21 \left(a^2 d^2-2 a b c d+b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{a d+b (c+d x)-b c}}\right)}{16 \sqrt[4]{b} d^{11/4}}+\frac{21 \left(a^2 d^2-2 a b c d+b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{a d+b (c+d x)-b c}}\right)}{16 \sqrt[4]{b} d^{11/4}}+\frac{(a d+b (c+d x)-b c)^{3/4} \left(11 a d \sqrt[4]{c+d x}+4 b (c+d x)^{5/4}-11 b c \sqrt[4]{c+d x}\right)}{8 d^{11/4}}\right)}{(a d+b d x)^{3/4}}","-\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{7 (a+b x)^{3/4} \sqrt[4]{c+d x} (b c-a d)}{8 d^2}+\frac{(a+b x)^{7/4} \sqrt[4]{c+d x}}{2 d}",1,"(d^(3/4)*(a + b*x)^(3/4)*(((-(b*c) + a*d + b*(c + d*x))^(3/4)*(-11*b*c*(c + d*x)^(1/4) + 11*a*d*(c + d*x)^(1/4) + 4*b*(c + d*x)^(5/4)))/(8*d^(11/4)) + (21*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*ArcTan[(b^(1/4)*(c + d*x)^(1/4))/(-(b*c) + a*d + b*(c + d*x))^(1/4)])/(16*b^(1/4)*d^(11/4)) + (21*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*ArcTanh[(b^(1/4)*(c + d*x)^(1/4))/(-(b*c) + a*d + b*(c + d*x))^(1/4)])/(16*b^(1/4)*d^(11/4))))/(a*d + b*d*x)^(3/4)","A",1
1706,1,176,127,8.8765375,"\int \frac{(a+b x)^{3/4}}{(c+d x)^{3/4}} \, dx","IntegrateAlgebraic[(a + b*x)^(3/4)/(c + d*x)^(3/4),x]","\frac{d^{3/4} (a+b x)^{3/4} \left(\frac{\sqrt[4]{c+d x} (a d+b (c+d x)-b c)^{3/4}}{d^{7/4}}-\frac{3 (b c-a d) \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{a d+b (c+d x)-b c}}\right)}{2 \sqrt[4]{b} d^{7/4}}-\frac{3 (b c-a d) \tanh ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{a d+b (c+d x)-b c}}\right)}{2 \sqrt[4]{b} d^{7/4}}\right)}{(a d+b d x)^{3/4}}","\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,"(d^(3/4)*(a + b*x)^(3/4)*(((c + d*x)^(1/4)*(-(b*c) + a*d + b*(c + d*x))^(3/4))/d^(7/4) - (3*(b*c - a*d)*ArcTan[(b^(1/4)*(c + d*x)^(1/4))/(-(b*c) + a*d + b*(c + d*x))^(1/4)])/(2*b^(1/4)*d^(7/4)) - (3*(b*c - a*d)*ArcTanh[(b^(1/4)*(c + d*x)^(1/4))/(-(b*c) + a*d + b*(c + d*x))^(1/4)])/(2*b^(1/4)*d^(7/4))))/(a*d + b*d*x)^(3/4)","A",1
1707,1,113,85,1.5202157,"\int \frac{1}{\sqrt[4]{a+b x} (c+d x)^{3/4}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(1/4)*(c + d*x)^(3/4)),x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+\frac{b (c+d x)}{d}-\frac{b c}{d}}}{\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+\frac{b (c+d x)}{d}-\frac{b c}{d}}}{\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*c)/d + (b*(c + d*x))/d)^(1/4))/(b^(1/4)*(c + d*x)^(1/4))])/(b^(1/4)*d^(3/4)) + (2*ArcTanh[(d^(1/4)*(a - (b*c)/d + (b*(c + d*x))/d)^(1/4))/(b^(1/4)*(c + d*x)^(1/4))])/(b^(1/4)*d^(3/4))","A",1
1708,1,63,30,6.2047038,"\int \frac{1}{(a+b x)^{5/4} (c+d x)^{3/4}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(5/4)*(c + d*x)^(3/4)),x]","\frac{4 d \sqrt[4]{c+d x} \left(a+\frac{b (c+d x)}{d}-\frac{b c}{d}\right)^{3/4}}{(b c-a d) (-a d-b (c+d x)+b c)}","-\frac{4 \sqrt[4]{c+d x}}{\sqrt[4]{a+b x} (b c-a d)}",1,"(4*d*(c + d*x)^(1/4)*(a - (b*c)/d + (b*(c + d*x))/d)^(3/4))/((b*c - a*d)*(b*c - a*d - b*(c + d*x)))","B",1
1709,1,83,66,16.5526672,"\int \frac{1}{(a+b x)^{9/4} (c+d x)^{3/4}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(9/4)*(c + d*x)^(3/4)),x]","\frac{4 \sqrt[4]{c+d x} (a d+b d x)^{9/4} (5 a d+4 b (c+d x)-5 b c)}{5 d (a+b x)^{9/4} (b c-a d)^2 (a d+b (c+d x)-b c)^{5/4}}","\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)*(a*d + b*d*x)^(9/4)*(-5*b*c + 5*a*d + 4*b*(c + d*x)))/(5*d*(b*c - a*d)^2*(a + b*x)^(9/4)*(-(b*c) + a*d + b*(c + d*x))^(5/4))","A",1
1710,1,149,101,23.8269642,"\int \frac{1}{(a+b x)^{13/4} (c+d x)^{3/4}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(13/4)*(c + d*x)^(3/4)),x]","-\frac{4 d^{3/4} (a+b x)^{3/4} \sqrt[4]{c+d x} \left(45 a^2 d^{17/4}+72 a b d^{13/4} (c+d x)-90 a b c d^{13/4}+45 b^2 c^2 d^{9/4}+32 b^2 d^{9/4} (c+d x)^2-72 b^2 c d^{9/4} (c+d x)\right)}{45 (b c-a d)^3 (a d+b d x)^{3/4} (a d+b (c+d x)-b c)^{9/4}}","-\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*d^(3/4)*(a + b*x)^(3/4)*(c + d*x)^(1/4)*(45*b^2*c^2*d^(9/4) - 90*a*b*c*d^(13/4) + 45*a^2*d^(17/4) - 72*b^2*c*d^(9/4)*(c + d*x) + 72*a*b*d^(13/4)*(c + d*x) + 32*b^2*d^(9/4)*(c + d*x)^2))/(45*(b*c - a*d)^3*(a*d + b*d*x)^(3/4)*(-(b*c) + a*d + b*(c + d*x))^(9/4))","A",1
1711,0,0,136,35.4864037,"\int \frac{1}{(a+b x)^{17/4} (c+d x)^{3/4}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(17/4)*(c + d*x)^(3/4)),x]","\int \frac{1}{(a+b x)^{17/4} (c+d x)^{3/4}} \, dx","\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,"Could not integrate","F",-1
1712,0,0,332,17.905085,"\int \frac{(a+b x)^{5/4}}{(c+d x)^{3/4}} \, dx","IntegrateAlgebraic[(a + b*x)^(5/4)/(c + d*x)^(3/4),x]","\int \frac{(a+b x)^{5/4}}{(c+d x)^{3/4}} \, dx","\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{5 \sqrt[4]{a+b x} \sqrt[4]{c+d x} (b c-a d)}{3 d^2}+\frac{2 (a+b x)^{5/4} \sqrt[4]{c+d x}}{3 d}",1,"Could not integrate","F",-1
1713,0,0,295,13.82099,"\int \frac{\sqrt[4]{a+b x}}{(c+d x)^{3/4}} \, dx","IntegrateAlgebraic[(a + b*x)^(1/4)/(c + d*x)^(3/4),x]","\int \frac{\sqrt[4]{a+b x}}{(c+d x)^{3/4}} \, dx","\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,"Could not integrate","F",-1
1714,0,0,270,14.72097,"\int \frac{1}{(a+b x)^{3/4} (c+d x)^{3/4}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(3/4)*(c + d*x)^(3/4)),x]","\int \frac{1}{(a+b x)^{3/4} (c+d x)^{3/4}} \, dx","\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,"Could not integrate","F",-1
1715,0,0,306,24.1758723,"\int \frac{1}{(a+b x)^{7/4} (c+d x)^{3/4}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(7/4)*(c + d*x)^(3/4)),x]","\int \frac{1}{(a+b x)^{7/4} (c+d x)^{3/4}} \, dx","-\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,"Could not integrate","F",-1
1716,0,0,339,34.6668398,"\int \frac{1}{(a+b x)^{11/4} (c+d x)^{3/4}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(11/4)*(c + d*x)^(3/4)),x]","\int \frac{1}{(a+b x)^{11/4} (c+d x)^{3/4}} \, dx","\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,"Could not integrate","F",-1
1717,1,200,152,16.1931044,"\int \frac{(a+b x)^{5/4}}{(c+d x)^{5/4}} \, dx","IntegrateAlgebraic[(a + b*x)^(5/4)/(c + d*x)^(5/4),x]","\frac{d^{5/4} (a+b x)^{5/4} \left(\frac{5 \left(b^{5/4} c-a \sqrt[4]{b} d\right) \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{a d+b (c+d x)-b c}}\right)}{2 d^{9/4}}-\frac{5 \left(b^{5/4} c-a \sqrt[4]{b} d\right) \tanh ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{a d+b (c+d x)-b c}}\right)}{2 d^{9/4}}+\frac{\sqrt[4]{a d+b (c+d x)-b c} (-4 a d+b (c+d x)+4 b c)}{d^{9/4} \sqrt[4]{c+d x}}\right)}{(a d+b d x)^{5/4}}","-\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{5 b \sqrt[4]{a+b x} (c+d x)^{3/4}}{d^2}-\frac{4 (a+b x)^{5/4}}{d \sqrt[4]{c+d x}}",1,"(d^(5/4)*(a + b*x)^(5/4)*(((4*b*c - 4*a*d + b*(c + d*x))*(-(b*c) + a*d + b*(c + d*x))^(1/4))/(d^(9/4)*(c + d*x)^(1/4)) + (5*(b^(5/4)*c - a*b^(1/4)*d)*ArcTan[(b^(1/4)*(c + d*x)^(1/4))/(-(b*c) + a*d + b*(c + d*x))^(1/4)])/(2*d^(9/4)) - (5*(b^(5/4)*c - a*b^(1/4)*d)*ArcTanh[(b^(1/4)*(c + d*x)^(1/4))/(-(b*c) + a*d + b*(c + d*x))^(1/4)])/(2*d^(9/4))))/(a*d + b*d*x)^(5/4)","A",1
1718,1,157,108,13.8341987,"\int \frac{\sqrt[4]{a+b x}}{(c+d x)^{5/4}} \, dx","IntegrateAlgebraic[(a + b*x)^(1/4)/(c + d*x)^(5/4),x]","\frac{\sqrt[4]{d} \sqrt[4]{a+b x} \left(-\frac{4 \sqrt[4]{a d+b (c+d x)-b c}}{d^{5/4} \sqrt[4]{c+d x}}-\frac{2 \sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{a d+b (c+d x)-b c}}\right)}{d^{5/4}}+\frac{2 \sqrt[4]{b} \tanh ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{a d+b (c+d x)-b c}}\right)}{d^{5/4}}\right)}{\sqrt[4]{a d+b 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,"(d^(1/4)*(a + b*x)^(1/4)*((-4*(-(b*c) + a*d + b*(c + d*x))^(1/4))/(d^(5/4)*(c + d*x)^(1/4)) - (2*b^(1/4)*ArcTan[(b^(1/4)*(c + d*x)^(1/4))/(-(b*c) + a*d + b*(c + d*x))^(1/4)])/d^(5/4) + (2*b^(1/4)*ArcTanh[(b^(1/4)*(c + d*x)^(1/4))/(-(b*c) + a*d + b*(c + d*x))^(1/4)])/d^(5/4)))/(a*d + b*d*x)^(1/4)","A",1
1719,1,62,30,8.1845886,"\int \frac{1}{(a+b x)^{3/4} (c+d x)^{5/4}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(3/4)*(c + d*x)^(5/4)),x]","\frac{4 b \sqrt[4]{a+b x} \left(\frac{d (a+b x)}{b}-\frac{a d}{b}+c\right)^{3/4}}{(b c-a d) (d (a+b x)-a d+b c)}","\frac{4 \sqrt[4]{a+b x}}{\sqrt[4]{c+d x} (b c-a d)}",1,"(4*b*(a + b*x)^(1/4)*(c - (a*d)/b + (d*(a + b*x))/b)^(3/4))/((b*c - a*d)*(b*c - a*d + d*(a + b*x)))","B",1
1720,1,83,66,20.8144043,"\int \frac{1}{(a+b x)^{7/4} (c+d x)^{5/4}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(7/4)*(c + d*x)^(5/4)),x]","-\frac{4 (a d+b d x)^{7/4} (3 a d+4 b (c+d x)-3 b c)}{3 d (a+b x)^{7/4} \sqrt[4]{c+d x} (b c-a d)^2 (a d+b (c+d x)-b c)^{3/4}}","-\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*(a*d + b*d*x)^(7/4)*(-3*b*c + 3*a*d + 4*b*(c + d*x)))/(3*d*(b*c - a*d)^2*(a + b*x)^(7/4)*(c + d*x)^(1/4)*(-(b*c) + a*d + b*(c + d*x))^(3/4))","A",1
1721,0,0,101,48.0922261,"\int \frac{1}{(a+b x)^{11/4} (c+d x)^{5/4}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(11/4)*(c + d*x)^(5/4)),x]","\int \frac{1}{(a+b x)^{11/4} (c+d x)^{5/4}} \, dx","\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,"Could not integrate","F",-1
1722,0,0,136,48.4657172,"\int \frac{1}{(a+b x)^{15/4} (c+d x)^{5/4}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(15/4)*(c + d*x)^(5/4)),x]","\int \frac{1}{(a+b x)^{15/4} (c+d x)^{5/4}} \, dx","-\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,"Could not integrate","F",-1
1723,0,0,776,32.2556514,"\int \frac{(a+b x)^{11/4}}{(c+d x)^{5/4}} \, dx","IntegrateAlgebraic[(a + b*x)^(11/4)/(c + d*x)^(5/4),x]","\int \frac{(a+b x)^{11/4}}{(c+d x)^{5/4}} \, dx","\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{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{77 b (a+b x)^{3/4} (c+d x)^{3/4} (b c-a d)}{15 d^3}+\frac{22 b (a+b x)^{7/4} (c+d x)^{3/4}}{5 d^2}-\frac{4 (a+b x)^{11/4}}{d \sqrt[4]{c+d x}}",1,"Could not integrate","F",-1
1724,0,0,730,31.9405633,"\int \frac{(a+b x)^{7/4}}{(c+d x)^{5/4}} \, dx","IntegrateAlgebraic[(a + b*x)^(7/4)/(c + d*x)^(5/4),x]","\int \frac{(a+b x)^{7/4}}{(c+d x)^{5/4}} \, dx","-\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{14 b (a+b x)^{3/4} (c+d x)^{3/4}}{3 d^2}-\frac{4 (a+b x)^{7/4}}{d \sqrt[4]{c+d x}}",1,"Could not integrate","F",-1
1725,0,0,712,22.6589328,"\int \frac{(a+b x)^{3/4}}{(c+d x)^{5/4}} \, dx","IntegrateAlgebraic[(a + b*x)^(3/4)/(c + d*x)^(5/4),x]","\int \frac{(a+b x)^{3/4}}{(c+d x)^{5/4}} \, dx","\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,"Could not integrate","F",-1
1726,0,0,719,25.0610019,"\int \frac{1}{\sqrt[4]{a+b x} (c+d x)^{5/4}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(1/4)*(c + d*x)^(5/4)),x]","\int \frac{1}{\sqrt[4]{a+b x} (c+d x)^{5/4}} \, dx","-\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,"Could not integrate","F",-1
1727,0,0,750,31.3480162,"\int \frac{1}{(a+b x)^{5/4} (c+d x)^{5/4}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(5/4)*(c + d*x)^(5/4)),x]","\int \frac{1}{(a+b x)^{5/4} (c+d x)^{5/4}} \, dx","-\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,"Could not integrate","F",-1
1728,0,0,795,46.5934913,"\int \frac{1}{(a+b x)^{9/4} (c+d x)^{5/4}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(9/4)*(c + d*x)^(5/4)),x]","\int \frac{1}{(a+b x)^{9/4} (c+d x)^{5/4}} \, dx","\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,"Could not integrate","F",-1
1729,1,226,279,1.6366339,"\int \frac{1}{\sqrt[4]{1-a x} (1+b x)^{3/4}} \, dx","IntegrateAlgebraic[1/((1 - a*x)^(1/4)*(1 + b*x)^(3/4)),x]","\frac{\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt[4]{b x+1} \sqrt[4]{-\frac{a (b x+1)}{b}+\frac{a}{b}+1}}{\sqrt{a} \sqrt{b x+1}+\sqrt{b} \sqrt{-\frac{a (b x+1)}{b}+\frac{a}{b}+1}}\right)}{\sqrt[4]{a} b^{3/4}}-\frac{\sqrt{2} \tan ^{-1}\left(\frac{\frac{\sqrt[4]{b} \sqrt{-\frac{a (b x+1)}{b}+\frac{a}{b}+1}}{\sqrt{2} \sqrt[4]{a}}-\frac{\sqrt[4]{a} \sqrt{b x+1}}{\sqrt{2} \sqrt[4]{b}}}{\sqrt[4]{b x+1} \sqrt[4]{-\frac{a (b x+1)}{b}+\frac{a}{b}+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[(-((a^(1/4)*Sqrt[1 + b*x])/(Sqrt[2]*b^(1/4))) + (b^(1/4)*Sqrt[1 + a/b - (a*(1 + b*x))/b])/(Sqrt[2]*a^(1/4)))/((1 + b*x)^(1/4)*(1 + a/b - (a*(1 + b*x))/b)^(1/4))])/(a^(1/4)*b^(3/4))) + (Sqrt[2]*ArcTanh[(Sqrt[2]*a^(1/4)*b^(1/4)*(1 + b*x)^(1/4)*(1 + a/b - (a*(1 + b*x))/b)^(1/4))/(Sqrt[a]*Sqrt[1 + b*x] + Sqrt[b]*Sqrt[1 + a/b - (a*(1 + b*x))/b])])/(a^(1/4)*b^(3/4))","A",1
1730,1,117,193,0.3079882,"\int \frac{1}{\sqrt[4]{1-a x} (1+a x)^{3/4}} \, dx","IntegrateAlgebraic[1/((1 - a*x)^(1/4)*(1 + a*x)^(3/4)),x]","\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-a x} \sqrt[4]{a x+1}}{\sqrt{1-a x}-\sqrt{a x+1}}\right)}{a}+\frac{\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-a x} \sqrt[4]{a x+1}}{\sqrt{1-a x}+\sqrt{a x+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[(Sqrt[2]*(1 - a*x)^(1/4)*(1 + a*x)^(1/4))/(Sqrt[1 - a*x] - Sqrt[1 + a*x])])/a + (Sqrt[2]*ArcTanh[(Sqrt[2]*(1 - a*x)^(1/4)*(1 + a*x)^(1/4))/(Sqrt[1 - a*x] + Sqrt[1 + a*x])])/a","A",1
1731,0,0,74,33.2500381,"\int \frac{(a+b x)^{3/2}}{\sqrt[5]{c+d x}} \, dx","IntegrateAlgebraic[(a + b*x)^(3/2)/(c + d*x)^(1/5),x]","\int \frac{(a+b x)^{3/2}}{\sqrt[5]{c+d x}} \, dx","\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,"Could not integrate","F",-1
1732,0,0,74,13.9914752,"\int \frac{\sqrt{a+b x}}{\sqrt[5]{c+d x}} \, dx","IntegrateAlgebraic[Sqrt[a + b*x]/(c + d*x)^(1/5),x]","\int \frac{\sqrt{a+b x}}{\sqrt[5]{c+d x}} \, dx","\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,"Could not integrate","F",-1
1733,0,0,72,13.8377732,"\int \frac{1}{\sqrt{a+b x} \sqrt[5]{c+d x}} \, dx","IntegrateAlgebraic[1/(Sqrt[a + b*x]*(c + d*x)^(1/5)),x]","\int \frac{1}{\sqrt{a+b x} \sqrt[5]{c+d x}} \, dx","\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,"Could not integrate","F",-1
1734,0,0,72,15.5321284,"\int \frac{1}{(a+b x)^{3/2} \sqrt[5]{c+d x}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(3/2)*(c + d*x)^(1/5)),x]","\int \frac{1}{(a+b x)^{3/2} \sqrt[5]{c+d x}} \, dx","-\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,"Could not integrate","F",-1
1735,0,0,74,23.6223323,"\int \frac{1}{(a+b x)^{5/2} \sqrt[5]{c+d x}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(5/2)*(c + d*x)^(1/5)),x]","\int \frac{1}{(a+b x)^{5/2} \sqrt[5]{c+d x}} \, dx","-\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,"Could not integrate","F",-1
1736,0,0,487,46.3762251,"\int (a+b x)^{5/2} \sqrt[6]{c+d x} \, dx","IntegrateAlgebraic[(a + b*x)^(5/2)*(c + d*x)^(1/6),x]","\int (a+b x)^{5/2} \sqrt[6]{c+d x} \, dx","-\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,"Could not integrate","F",-1
1737,0,0,449,38.3362837,"\int (a+b x)^{3/2} \sqrt[6]{c+d x} \, dx","IntegrateAlgebraic[(a + b*x)^(3/2)*(c + d*x)^(1/6),x]","\int (a+b x)^{3/2} \sqrt[6]{c+d x} \, dx","\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,"Could not integrate","F",-1
1738,0,0,411,15.6611488,"\int \sqrt{a+b x} \sqrt[6]{c+d x} \, dx","IntegrateAlgebraic[Sqrt[a + b*x]*(c + d*x)^(1/6),x]","\int \sqrt{a+b x} \sqrt[6]{c+d x} \, dx","-\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,"Could not integrate","F",-1
1739,0,0,375,15.4319096,"\int \frac{\sqrt[6]{c+d x}}{\sqrt{a+b x}} \, dx","IntegrateAlgebraic[(c + d*x)^(1/6)/Sqrt[a + b*x],x]","\int \frac{\sqrt[6]{c+d x}}{\sqrt{a+b x}} \, dx","\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,"Could not integrate","F",-1
1740,0,0,367,37.8359219,"\int \frac{\sqrt[6]{c+d x}}{(a+b x)^{3/2}} \, dx","IntegrateAlgebraic[(c + d*x)^(1/6)/(a + b*x)^(3/2),x]","\int \frac{\sqrt[6]{c+d x}}{(a+b x)^{3/2}} \, dx","\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,"Could not integrate","F",-1
1741,0,0,409,60.2737324,"\int \frac{\sqrt[6]{c+d x}}{(a+b x)^{5/2}} \, dx","IntegrateAlgebraic[(c + d*x)^(1/6)/(a + b*x)^(5/2),x]","\int \frac{\sqrt[6]{c+d x}}{(a+b x)^{5/2}} \, dx","-\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,"Could not integrate","F",-1
1742,0,0,896,45.6400546,"\int (a+b x)^{3/2} (c+d x)^{5/6} \, dx","IntegrateAlgebraic[(a + b*x)^(3/2)*(c + d*x)^(5/6),x]","\int (a+b x)^{3/2} (c+d x)^{5/6} \, dx","-\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,"Could not integrate","F",-1
1743,0,0,858,35.47128,"\int \sqrt{a+b x} (c+d x)^{5/6} \, dx","IntegrateAlgebraic[Sqrt[a + b*x]*(c + d*x)^(5/6),x]","\int \sqrt{a+b x} (c+d x)^{5/6} \, dx","\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,"Could not integrate","F",-1
1744,0,0,817,78.6216306,"\int \frac{(c+d x)^{5/6}}{\sqrt{a+b x}} \, dx","IntegrateAlgebraic[(c + d*x)^(5/6)/Sqrt[a + b*x],x]","\int \frac{(c+d x)^{5/6}}{\sqrt{a+b x}} \, dx","-\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,"Could not integrate","F",-1
1745,0,0,798,40.8287618,"\int \frac{(c+d x)^{5/6}}{(a+b x)^{3/2}} \, dx","IntegrateAlgebraic[(c + d*x)^(5/6)/(a + b*x)^(3/2),x]","\int \frac{(c+d x)^{5/6}}{(a+b x)^{3/2}} \, dx","-\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,"Could not integrate","F",-1
1746,0,0,854,52.1588133,"\int \frac{(c+d x)^{5/6}}{(a+b x)^{5/2}} \, dx","IntegrateAlgebraic[(c + d*x)^(5/6)/(a + b*x)^(5/2),x]","\int \frac{(c+d x)^{5/6}}{(a+b x)^{5/2}} \, dx","-\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,"Could not integrate","F",-1
1747,0,0,896,67.2834267,"\int \frac{(c+d x)^{5/6}}{(a+b x)^{7/2}} \, dx","IntegrateAlgebraic[(c + d*x)^(5/6)/(a + b*x)^(7/2),x]","\int \frac{(c+d x)^{5/6}}{(a+b x)^{7/2}} \, dx","\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,"Could not integrate","F",-1
1748,0,0,890,43.820472,"\int \frac{(a+b x)^{5/2}}{\sqrt[6]{c+d x}} \, dx","IntegrateAlgebraic[(a + b*x)^(5/2)/(c + d*x)^(1/6),x]","\int \frac{(a+b x)^{5/2}}{\sqrt[6]{c+d x}} \, dx","\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,"Could not integrate","F",-1
1749,0,0,855,36.0518816,"\int \frac{(a+b x)^{3/2}}{\sqrt[6]{c+d x}} \, dx","IntegrateAlgebraic[(a + b*x)^(3/2)/(c + d*x)^(1/6),x]","\int \frac{(a+b x)^{3/2}}{\sqrt[6]{c+d x}} \, dx","-\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,"Could not integrate","F",-1
1750,0,0,820,15.284529,"\int \frac{\sqrt{a+b x}}{\sqrt[6]{c+d x}} \, dx","IntegrateAlgebraic[Sqrt[a + b*x]/(c + d*x)^(1/6),x]","\int \frac{\sqrt{a+b x}}{\sqrt[6]{c+d x}} \, dx","\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,"Could not integrate","F",-1
1751,0,0,780,14.7570247,"\int \frac{1}{\sqrt{a+b x} \sqrt[6]{c+d x}} \, dx","IntegrateAlgebraic[1/(Sqrt[a + b*x]*(c + d*x)^(1/6)),x]","\int \frac{1}{\sqrt{a+b x} \sqrt[6]{c+d x}} \, dx","-\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,"Could not integrate","F",-1
1752,0,0,813,36.9099647,"\int \frac{1}{(a+b x)^{3/2} \sqrt[6]{c+d x}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(3/2)*(c + d*x)^(1/6)),x]","\int \frac{1}{(a+b x)^{3/2} \sqrt[6]{c+d x}} \, dx","-\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,"Could not integrate","F",-1
1753,0,0,858,54.8397755,"\int \frac{1}{(a+b x)^{5/2} \sqrt[6]{c+d x}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(5/2)*(c + d*x)^(1/6)),x]","\int \frac{1}{(a+b x)^{5/2} \sqrt[6]{c+d x}} \, dx","\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,"Could not integrate","F",-1
1754,0,0,440,48.7381659,"\int \frac{(a+b x)^{5/2}}{(c+d x)^{5/6}} \, dx","IntegrateAlgebraic[(a + b*x)^(5/2)/(c + d*x)^(5/6),x]","\int \frac{(a+b x)^{5/2}}{(c+d x)^{5/6}} \, dx","-\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,"Could not integrate","F",-1
1755,0,0,405,41.342907,"\int \frac{(a+b x)^{3/2}}{(c+d x)^{5/6}} \, dx","IntegrateAlgebraic[(a + b*x)^(3/2)/(c + d*x)^(5/6),x]","\int \frac{(a+b x)^{3/2}}{(c+d x)^{5/6}} \, dx","\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,"Could not integrate","F",-1
1756,0,0,372,25.2211274,"\int \frac{\sqrt{a+b x}}{(c+d x)^{5/6}} \, dx","IntegrateAlgebraic[Sqrt[a + b*x]/(c + d*x)^(5/6),x]","\int \frac{\sqrt{a+b x}}{(c+d x)^{5/6}} \, dx","\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,"Could not integrate","F",-1
1757,0,0,343,44.3546888,"\int \frac{1}{\sqrt{a+b x} (c+d x)^{5/6}} \, dx","IntegrateAlgebraic[1/(Sqrt[a + b*x]*(c + d*x)^(5/6)),x]","\int \frac{1}{\sqrt{a+b x} (c+d x)^{5/6}} \, dx","\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,"Could not integrate","F",-1
1758,0,0,372,47.7324497,"\int \frac{1}{(a+b x)^{3/2} (c+d x)^{5/6}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(3/2)*(c + d*x)^(5/6)),x]","\int \frac{1}{(a+b x)^{3/2} (c+d x)^{5/6}} \, dx","-\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,"Could not integrate","F",-1
1759,0,0,410,70.3923215,"\int \frac{1}{(a+b x)^{5/2} (c+d x)^{5/6}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(5/2)*(c + d*x)^(5/6)),x]","\int \frac{1}{(a+b x)^{5/2} (c+d x)^{5/6}} \, dx","\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,"Could not integrate","F",-1
1760,0,0,880,60.3522575,"\int \frac{(a+b x)^{5/2}}{(c+d x)^{7/6}} \, dx","IntegrateAlgebraic[(a + b*x)^(5/2)/(c + d*x)^(7/6),x]","\int \frac{(a+b x)^{5/2}}{(c+d x)^{7/6}} \, dx","-\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,"Could not integrate","F",-1
1761,0,0,844,44.6125848,"\int \frac{(a+b x)^{3/2}}{(c+d x)^{7/6}} \, dx","IntegrateAlgebraic[(a + b*x)^(3/2)/(c + d*x)^(7/6),x]","\int \frac{(a+b x)^{3/2}}{(c+d x)^{7/6}} \, dx","-\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,"Could not integrate","F",-1
1762,0,0,806,18.6177391,"\int \frac{\sqrt{a+b x}}{(c+d x)^{7/6}} \, dx","IntegrateAlgebraic[Sqrt[a + b*x]/(c + d*x)^(7/6),x]","\int \frac{\sqrt{a+b x}}{(c+d x)^{7/6}} \, dx","-\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,"Could not integrate","F",-1
1763,0,0,817,17.0538688,"\int \frac{1}{\sqrt{a+b x} (c+d x)^{7/6}} \, dx","IntegrateAlgebraic[1/(Sqrt[a + b*x]*(c + d*x)^(7/6)),x]","\int \frac{1}{\sqrt{a+b x} (c+d x)^{7/6}} \, dx","\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,"Could not integrate","F",-1
1764,0,0,844,65.8467777,"\int \frac{1}{(a+b x)^{3/2} (c+d x)^{7/6}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(3/2)*(c + d*x)^(7/6)),x]","\int \frac{1}{(a+b x)^{3/2} (c+d x)^{7/6}} \, dx","-\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,"Could not integrate","F",-1
1765,0,0,893,88.1686002,"\int \frac{1}{(a+b x)^{5/2} (c+d x)^{7/6}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(5/2)*(c + d*x)^(7/6)),x]","\int \frac{1}{(a+b x)^{5/2} (c+d x)^{7/6}} \, dx","\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,"Could not integrate","F",-1
1766,0,0,84,18.6134013,"\int \sqrt[6]{a+b x} (c+d x)^{13/6} \, dx","IntegrateAlgebraic[(a + b*x)^(1/6)*(c + d*x)^(13/6),x]","\int \sqrt[6]{a+b x} (c+d x)^{13/6} \, dx","\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,"Could not integrate","F",-1
1767,0,0,82,18.6083914,"\int \sqrt[6]{a+b x} (c+d x)^{7/6} \, dx","IntegrateAlgebraic[(a + b*x)^(1/6)*(c + d*x)^(7/6),x]","\int \sqrt[6]{a+b x} (c+d x)^{7/6} \, dx","\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,"Could not integrate","F",-1
1768,0,0,74,17.5320303,"\int \sqrt[6]{a+b x} \sqrt[6]{c+d x} \, dx","IntegrateAlgebraic[(a + b*x)^(1/6)*(c + d*x)^(1/6),x]","\int \sqrt[6]{a+b x} \sqrt[6]{c+d x} \, dx","\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,"Could not integrate","F",-1
1769,0,0,74,29.0495707,"\int \frac{\sqrt[6]{a+b x}}{(c+d x)^{5/6}} \, dx","IntegrateAlgebraic[(a + b*x)^(1/6)/(c + d*x)^(5/6),x]","\int \frac{\sqrt[6]{a+b x}}{(c+d x)^{5/6}} \, dx","\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,"Could not integrate","F",-1
1770,0,0,81,50.0349002,"\int \frac{\sqrt[6]{a+b x}}{(c+d x)^{11/6}} \, dx","IntegrateAlgebraic[(a + b*x)^(1/6)/(c + d*x)^(11/6),x]","\int \frac{\sqrt[6]{a+b x}}{(c+d x)^{11/6}} \, dx","\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,"Could not integrate","F",-1
1771,0,0,82,45.9653813,"\int \frac{\sqrt[6]{a+b x}}{(c+d x)^{17/6}} \, dx","IntegrateAlgebraic[(a + b*x)^(1/6)/(c + d*x)^(17/6),x]","\int \frac{\sqrt[6]{a+b x}}{(c+d x)^{17/6}} \, dx","\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,"Could not integrate","F",-1
1772,0,0,427,27.4458059,"\int \sqrt[6]{a+b x} (c+d x)^{5/6} \, dx","IntegrateAlgebraic[(a + b*x)^(1/6)*(c + d*x)^(5/6),x]","\int \sqrt[6]{a+b x} (c+d x)^{5/6} \, dx","\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,"Could not integrate","F",-1
1773,1,385,378,12.7786463,"\int \frac{\sqrt[6]{a+b x}}{\sqrt[6]{c+d x}} \, dx","IntegrateAlgebraic[(a + b*x)^(1/6)/(c + d*x)^(1/6),x]","\frac{\sqrt[6]{d} \sqrt[6]{a+b x} \left(-\frac{(b c-a d) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}{\sqrt[6]{b} \sqrt[6]{c+d x}-2 \sqrt[6]{a d+b (c+d x)-b c}}\right)}{2 \sqrt{3} b^{5/6} d^{7/6}}+\frac{(b c-a d) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}{2 \sqrt[6]{a d+b (c+d x)-b c}+\sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{2 \sqrt{3} b^{5/6} d^{7/6}}+\frac{(a d-b c) \tanh ^{-1}\left(\frac{\sqrt[6]{b} \sqrt[6]{c+d x}}{\sqrt[6]{a d+b (c+d x)-b c}}\right)}{3 b^{5/6} d^{7/6}}+\frac{(a d-b c) \tanh ^{-1}\left(\frac{\sqrt[3]{a d+b (c+d x)-b c}+\sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[6]{b} \sqrt[6]{c+d x} \sqrt[6]{a d+b (c+d x)-b c}}\right)}{6 b^{5/6} d^{7/6}}+\frac{(c+d x)^{5/6} \sqrt[6]{a d+b (c+d x)-b c}}{d^{7/6}}\right)}{\sqrt[6]{a d+b d 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}",1,"(d^(1/6)*(a + b*x)^(1/6)*(((c + d*x)^(5/6)*(-(b*c) + a*d + b*(c + d*x))^(1/6))/d^(7/6) - ((b*c - a*d)*ArcTan[(Sqrt[3]*b^(1/6)*(c + d*x)^(1/6))/(b^(1/6)*(c + d*x)^(1/6) - 2*(-(b*c) + a*d + b*(c + d*x))^(1/6))])/(2*Sqrt[3]*b^(5/6)*d^(7/6)) + ((b*c - a*d)*ArcTan[(Sqrt[3]*b^(1/6)*(c + d*x)^(1/6))/(b^(1/6)*(c + d*x)^(1/6) + 2*(-(b*c) + a*d + b*(c + d*x))^(1/6))])/(2*Sqrt[3]*b^(5/6)*d^(7/6)) + ((-(b*c) + a*d)*ArcTanh[(b^(1/6)*(c + d*x)^(1/6))/(-(b*c) + a*d + b*(c + d*x))^(1/6)])/(3*b^(5/6)*d^(7/6)) + ((-(b*c) + a*d)*ArcTanh[(b^(1/3)*(c + d*x)^(1/3) + (-(b*c) + a*d + b*(c + d*x))^(1/3))/(b^(1/6)*(c + d*x)^(1/6)*(-(b*c) + a*d + b*(c + d*x))^(1/6))])/(6*b^(5/6)*d^(7/6))))/(a*d + b*d*x)^(1/6)","A",1
1774,1,345,332,25.1524966,"\int \frac{\sqrt[6]{a+b x}}{(c+d x)^{7/6}} \, dx","IntegrateAlgebraic[(a + b*x)^(1/6)/(c + d*x)^(7/6),x]","\frac{\sqrt[6]{d} \sqrt[6]{a+b x} \left(-\frac{6 \sqrt[6]{a d+b (c+d x)-b c}}{d^{7/6} \sqrt[6]{c+d x}}+\frac{\sqrt{3} \sqrt[6]{b} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}{\sqrt[6]{b} \sqrt[6]{c+d x}-2 \sqrt[6]{a d+b (c+d x)-b c}}\right)}{d^{7/6}}-\frac{\sqrt{3} \sqrt[6]{b} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}{2 \sqrt[6]{a d+b (c+d x)-b c}+\sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{d^{7/6}}+\frac{2 \sqrt[6]{b} \tanh ^{-1}\left(\frac{\sqrt[6]{b} \sqrt[6]{c+d x}}{\sqrt[6]{a d+b (c+d x)-b c}}\right)}{d^{7/6}}+\frac{\sqrt[6]{b} \tanh ^{-1}\left(\frac{\frac{\sqrt[3]{a d+b (c+d x)-b c}}{\sqrt[6]{b}}+\sqrt[6]{b} \sqrt[3]{c+d x}}{\sqrt[6]{c+d x} \sqrt[6]{a d+b (c+d x)-b c}}\right)}{d^{7/6}}\right)}{\sqrt[6]{a d+b 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,"(d^(1/6)*(a + b*x)^(1/6)*((-6*(-(b*c) + a*d + b*(c + d*x))^(1/6))/(d^(7/6)*(c + d*x)^(1/6)) + (Sqrt[3]*b^(1/6)*ArcTan[(Sqrt[3]*b^(1/6)*(c + d*x)^(1/6))/(b^(1/6)*(c + d*x)^(1/6) - 2*(-(b*c) + a*d + b*(c + d*x))^(1/6))])/d^(7/6) - (Sqrt[3]*b^(1/6)*ArcTan[(Sqrt[3]*b^(1/6)*(c + d*x)^(1/6))/(b^(1/6)*(c + d*x)^(1/6) + 2*(-(b*c) + a*d + b*(c + d*x))^(1/6))])/d^(7/6) + (2*b^(1/6)*ArcTanh[(b^(1/6)*(c + d*x)^(1/6))/(-(b*c) + a*d + b*(c + d*x))^(1/6)])/d^(7/6) + (b^(1/6)*ArcTanh[(b^(1/6)*(c + d*x)^(1/3) + (-(b*c) + a*d + b*(c + d*x))^(1/3)/b^(1/6))/((c + d*x)^(1/6)*(-(b*c) + a*d + b*(c + d*x))^(1/6))])/d^(7/6)))/(a*d + b*d*x)^(1/6)","A",1
1775,1,66,32,24.9389091,"\int \frac{\sqrt[6]{a+b x}}{(c+d x)^{13/6}} \, dx","IntegrateAlgebraic[(a + b*x)^(1/6)/(c + d*x)^(13/6),x]","-\frac{6 \sqrt[6]{a+b x} (a d+b (c+d x)-b c)^{7/6}}{7 d (c+d x)^{7/6} (a d-b c) \sqrt[6]{a d+b d x}}","\frac{6 (a+b x)^{7/6}}{7 (c+d x)^{7/6} (b c-a d)}",1,"(-6*(a + b*x)^(1/6)*(-(b*c) + a*d + b*(c + d*x))^(7/6))/(7*d*(-(b*c) + a*d)*(c + d*x)^(7/6)*(a*d + b*d*x)^(1/6))","B",1
1776,0,0,66,45.8646209,"\int \frac{\sqrt[6]{a+b x}}{(c+d x)^{19/6}} \, dx","IntegrateAlgebraic[(a + b*x)^(1/6)/(c + d*x)^(19/6),x]","\int \frac{\sqrt[6]{a+b x}}{(c+d x)^{19/6}} \, dx","\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,"Could not integrate","F",-1
1777,0,0,101,45.9382241,"\int \frac{\sqrt[6]{a+b x}}{(c+d x)^{25/6}} \, dx","IntegrateAlgebraic[(a + b*x)^(1/6)/(c + d*x)^(25/6),x]","\int \frac{\sqrt[6]{a+b x}}{(c+d x)^{25/6}} \, dx","\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,"Could not integrate","F",-1
1778,0,0,136,44.9320875,"\int \frac{\sqrt[6]{a+b x}}{(c+d x)^{31/6}} \, dx","IntegrateAlgebraic[(a + b*x)^(1/6)/(c + d*x)^(31/6),x]","\int \frac{\sqrt[6]{a+b x}}{(c+d x)^{31/6}} \, dx","\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,"Could not integrate","F",-1
1779,0,0,427,27.3088122,"\int (a+b x)^{5/6} \sqrt[6]{c+d x} \, dx","IntegrateAlgebraic[(a + b*x)^(5/6)*(c + d*x)^(1/6),x]","\int (a+b x)^{5/6} \sqrt[6]{c+d x} \, dx","\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,"Could not integrate","F",-1
1780,1,385,378,20.1679911,"\int \frac{(a+b x)^{5/6}}{(c+d x)^{5/6}} \, dx","IntegrateAlgebraic[(a + b*x)^(5/6)/(c + d*x)^(5/6),x]","\frac{d^{5/6} (a+b x)^{5/6} \left(\frac{\sqrt[6]{c+d x} (a d+b (c+d x)-b c)^{5/6}}{d^{11/6}}+\frac{5 (b c-a d) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}{\sqrt[6]{b} \sqrt[6]{c+d x}-2 \sqrt[6]{a d+b (c+d x)-b c}}\right)}{2 \sqrt{3} \sqrt[6]{b} d^{11/6}}-\frac{5 (b c-a d) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}{2 \sqrt[6]{a d+b (c+d x)-b c}+\sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{2 \sqrt{3} \sqrt[6]{b} d^{11/6}}-\frac{5 (b c-a d) \tanh ^{-1}\left(\frac{\sqrt[6]{b} \sqrt[6]{c+d x}}{\sqrt[6]{a d+b (c+d x)-b c}}\right)}{3 \sqrt[6]{b} d^{11/6}}-\frac{5 (b c-a d) \tanh ^{-1}\left(\frac{\sqrt[3]{a d+b (c+d x)-b c}+\sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[6]{b} \sqrt[6]{c+d x} \sqrt[6]{a d+b (c+d x)-b c}}\right)}{6 \sqrt[6]{b} d^{11/6}}\right)}{(a d+b d x)^{5/6}}","\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) \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,"(d^(5/6)*(a + b*x)^(5/6)*(((c + d*x)^(1/6)*(-(b*c) + a*d + b*(c + d*x))^(5/6))/d^(11/6) + (5*(b*c - a*d)*ArcTan[(Sqrt[3]*b^(1/6)*(c + d*x)^(1/6))/(b^(1/6)*(c + d*x)^(1/6) - 2*(-(b*c) + a*d + b*(c + d*x))^(1/6))])/(2*Sqrt[3]*b^(1/6)*d^(11/6)) - (5*(b*c - a*d)*ArcTan[(Sqrt[3]*b^(1/6)*(c + d*x)^(1/6))/(b^(1/6)*(c + d*x)^(1/6) + 2*(-(b*c) + a*d + b*(c + d*x))^(1/6))])/(2*Sqrt[3]*b^(1/6)*d^(11/6)) - (5*(b*c - a*d)*ArcTanh[(b^(1/6)*(c + d*x)^(1/6))/(-(b*c) + a*d + b*(c + d*x))^(1/6)])/(3*b^(1/6)*d^(11/6)) - (5*(b*c - a*d)*ArcTanh[(b^(1/3)*(c + d*x)^(1/3) + (-(b*c) + a*d + b*(c + d*x))^(1/3))/(b^(1/6)*(c + d*x)^(1/6)*(-(b*c) + a*d + b*(c + d*x))^(1/6))])/(6*b^(1/6)*d^(11/6))))/(a*d + b*d*x)^(5/6)","A",1
1781,0,0,334,45.1095646,"\int \frac{(a+b x)^{5/6}}{(c+d x)^{11/6}} \, dx","IntegrateAlgebraic[(a + b*x)^(5/6)/(c + d*x)^(11/6),x]","\int \frac{(a+b x)^{5/6}}{(c+d x)^{11/6}} \, dx","-\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,"Could not integrate","F",-1
1782,0,0,32,46.5905703,"\int \frac{(a+b x)^{5/6}}{(c+d x)^{17/6}} \, dx","IntegrateAlgebraic[(a + b*x)^(5/6)/(c + d*x)^(17/6),x]","\int \frac{(a+b x)^{5/6}}{(c+d x)^{17/6}} \, dx","\frac{6 (a+b x)^{11/6}}{11 (c+d x)^{11/6} (b c-a d)}",1,"Could not integrate","F",-1
1783,0,0,66,46.6757659,"\int \frac{(a+b x)^{5/6}}{(c+d x)^{23/6}} \, dx","IntegrateAlgebraic[(a + b*x)^(5/6)/(c + d*x)^(23/6),x]","\int \frac{(a+b x)^{5/6}}{(c+d x)^{23/6}} \, dx","\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,"Could not integrate","F",-1
1784,0,0,101,45.0944282,"\int \frac{(a+b x)^{5/6}}{(c+d x)^{29/6}} \, dx","IntegrateAlgebraic[(a + b*x)^(5/6)/(c + d*x)^(29/6),x]","\int \frac{(a+b x)^{5/6}}{(c+d x)^{29/6}} \, dx","\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,"Could not integrate","F",-1
1785,0,0,136,43.9666289,"\int \frac{(a+b x)^{5/6}}{(c+d x)^{35/6}} \, dx","IntegrateAlgebraic[(a + b*x)^(5/6)/(c + d*x)^(35/6),x]","\int \frac{(a+b x)^{5/6}}{(c+d x)^{35/6}} \, dx","\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,"Could not integrate","F",-1
1786,0,0,82,23.3757944,"\int (a+b x)^{5/6} (c+d x)^{11/6} \, dx","IntegrateAlgebraic[(a + b*x)^(5/6)*(c + d*x)^(11/6),x]","\int (a+b x)^{5/6} (c+d x)^{11/6} \, dx","\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,"Could not integrate","F",-1
1787,0,0,74,20.8067532,"\int (a+b x)^{5/6} (c+d x)^{5/6} \, dx","IntegrateAlgebraic[(a + b*x)^(5/6)*(c + d*x)^(5/6),x]","\int (a+b x)^{5/6} (c+d x)^{5/6} \, dx","\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,"Could not integrate","F",-1
1788,0,0,74,24.8980126,"\int \frac{(a+b x)^{5/6}}{\sqrt[6]{c+d x}} \, dx","IntegrateAlgebraic[(a + b*x)^(5/6)/(c + d*x)^(1/6),x]","\int \frac{(a+b x)^{5/6}}{\sqrt[6]{c+d x}} \, dx","\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,"Could not integrate","F",-1
1789,0,0,81,42.6428779,"\int \frac{(a+b x)^{5/6}}{(c+d x)^{7/6}} \, dx","IntegrateAlgebraic[(a + b*x)^(5/6)/(c + d*x)^(7/6),x]","\int \frac{(a+b x)^{5/6}}{(c+d x)^{7/6}} \, dx","\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,"Could not integrate","F",-1
1790,0,0,82,45.8925279,"\int \frac{(a+b x)^{5/6}}{(c+d x)^{13/6}} \, dx","IntegrateAlgebraic[(a + b*x)^(5/6)/(c + d*x)^(13/6),x]","\int \frac{(a+b x)^{5/6}}{(c+d x)^{13/6}} \, dx","\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,"Could not integrate","F",-1
1791,0,0,84,46.3697094,"\int \frac{(a+b x)^{5/6}}{(c+d x)^{19/6}} \, dx","IntegrateAlgebraic[(a + b*x)^(5/6)/(c + d*x)^(19/6),x]","\int \frac{(a+b x)^{5/6}}{(c+d x)^{19/6}} \, dx","\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,"Could not integrate","F",-1
1792,0,0,84,24.2383692,"\int (a+b x)^{7/6} (c+d x)^{13/6} \, dx","IntegrateAlgebraic[(a + b*x)^(7/6)*(c + d*x)^(13/6),x]","\int (a+b x)^{7/6} (c+d x)^{13/6} \, dx","\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,"Could not integrate","F",-1
1793,0,0,82,23.8770676,"\int (a+b x)^{7/6} (c+d x)^{7/6} \, dx","IntegrateAlgebraic[(a + b*x)^(7/6)*(c + d*x)^(7/6),x]","\int (a+b x)^{7/6} (c+d x)^{7/6} \, dx","\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,"Could not integrate","F",-1
1794,0,0,74,21.7702447,"\int (a+b x)^{7/6} \sqrt[6]{c+d x} \, dx","IntegrateAlgebraic[(a + b*x)^(7/6)*(c + d*x)^(1/6),x]","\int (a+b x)^{7/6} \sqrt[6]{c+d x} \, dx","\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,"Could not integrate","F",-1
1795,0,0,74,32.4542557,"\int \frac{(a+b x)^{7/6}}{(c+d x)^{5/6}} \, dx","IntegrateAlgebraic[(a + b*x)^(7/6)/(c + d*x)^(5/6),x]","\int \frac{(a+b x)^{7/6}}{(c+d x)^{5/6}} \, dx","\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,"Could not integrate","F",-1
1796,0,0,81,53.5468162,"\int \frac{(a+b x)^{7/6}}{(c+d x)^{11/6}} \, dx","IntegrateAlgebraic[(a + b*x)^(7/6)/(c + d*x)^(11/6),x]","\int \frac{(a+b x)^{7/6}}{(c+d x)^{11/6}} \, dx","\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,"Could not integrate","F",-1
1797,0,0,82,46.5984388,"\int \frac{(a+b x)^{7/6}}{(c+d x)^{17/6}} \, dx","IntegrateAlgebraic[(a + b*x)^(7/6)/(c + d*x)^(17/6),x]","\int \frac{(a+b x)^{7/6}}{(c+d x)^{17/6}} \, dx","\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,"Could not integrate","F",-1
1798,1,470,424,14.9320765,"\int \frac{(a+b x)^{7/6}}{\sqrt[6]{c+d x}} \, dx","IntegrateAlgebraic[(a + b*x)^(7/6)/(c + d*x)^(1/6),x]","\frac{d^{7/6} (a+b x)^{7/6} \left(\frac{7 \left(a^2 d^2-2 a b c d+b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}{\sqrt[6]{b} \sqrt[6]{c+d x}-2 \sqrt[6]{a d+b (c+d x)-b c}}\right)}{24 \sqrt{3} b^{5/6} d^{13/6}}-\frac{7 \left(a^2 d^2-2 a b c d+b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}{2 \sqrt[6]{a d+b (c+d x)-b c}+\sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{24 \sqrt{3} b^{5/6} d^{13/6}}+\frac{7 \left(a^2 d^2-2 a b c d+b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt[6]{b} \sqrt[6]{c+d x}}{\sqrt[6]{a d+b (c+d x)-b c}}\right)}{36 b^{5/6} d^{13/6}}+\frac{7 \left(a^2 d^2-2 a b c d+b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt[3]{a d+b (c+d x)-b c}+\sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[6]{b} \sqrt[6]{c+d x} \sqrt[6]{a d+b (c+d x)-b c}}\right)}{72 b^{5/6} d^{13/6}}+\frac{\sqrt[6]{a d+b (c+d x)-b c} \left(13 a d (c+d x)^{5/6}+6 b (c+d x)^{11/6}-13 b c (c+d x)^{5/6}\right)}{12 d^{13/6}}\right)}{(a d+b d x)^{7/6}}","-\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 \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,"(d^(7/6)*(a + b*x)^(7/6)*(((-(b*c) + a*d + b*(c + d*x))^(1/6)*(-13*b*c*(c + d*x)^(5/6) + 13*a*d*(c + d*x)^(5/6) + 6*b*(c + d*x)^(11/6)))/(12*d^(13/6)) + (7*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*ArcTan[(Sqrt[3]*b^(1/6)*(c + d*x)^(1/6))/(b^(1/6)*(c + d*x)^(1/6) - 2*(-(b*c) + a*d + b*(c + d*x))^(1/6))])/(24*Sqrt[3]*b^(5/6)*d^(13/6)) - (7*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*ArcTan[(Sqrt[3]*b^(1/6)*(c + d*x)^(1/6))/(b^(1/6)*(c + d*x)^(1/6) + 2*(-(b*c) + a*d + b*(c + d*x))^(1/6))])/(24*Sqrt[3]*b^(5/6)*d^(13/6)) + (7*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*ArcTanh[(b^(1/6)*(c + d*x)^(1/6))/(-(b*c) + a*d + b*(c + d*x))^(1/6)])/(36*b^(5/6)*d^(13/6)) + (7*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*ArcTanh[(b^(1/3)*(c + d*x)^(1/3) + (-(b*c) + a*d + b*(c + d*x))^(1/3))/(b^(1/6)*(c + d*x)^(1/6)*(-(b*c) + a*d + b*(c + d*x))^(1/6))])/(72*b^(5/6)*d^(13/6))))/(a*d + b*d*x)^(7/6)","A",1
1799,1,417,403,27.4686301,"\int \frac{(a+b x)^{7/6}}{(c+d x)^{7/6}} \, dx","IntegrateAlgebraic[(a + b*x)^(7/6)/(c + d*x)^(7/6),x]","\frac{d^{7/6} (a+b x)^{7/6} \left(-\frac{7 \left(b^{7/6} c-a \sqrt[6]{b} d\right) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}{\sqrt[6]{b} \sqrt[6]{c+d x}-2 \sqrt[6]{a d+b (c+d x)-b c}}\right)}{2 \sqrt{3} d^{13/6}}+\frac{7 \left(b^{7/6} c-a \sqrt[6]{b} d\right) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}{2 \sqrt[6]{a d+b (c+d x)-b c}+\sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{2 \sqrt{3} d^{13/6}}-\frac{7 \left(b^{7/6} c-a \sqrt[6]{b} d\right) \tanh ^{-1}\left(\frac{\sqrt[6]{b} \sqrt[6]{c+d x}}{\sqrt[6]{a d+b (c+d x)-b c}}\right)}{3 d^{13/6}}-\frac{7 \left(b^{7/6} c-a \sqrt[6]{b} d\right) \tanh ^{-1}\left(\frac{\sqrt[3]{a d+b (c+d x)-b c}+\sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[6]{b} \sqrt[6]{c+d x} \sqrt[6]{a d+b (c+d x)-b c}}\right)}{6 d^{13/6}}+\frac{\sqrt[6]{a d+b (c+d x)-b c} (-6 a d+b (c+d x)+6 b c)}{d^{13/6} \sqrt[6]{c+d x}}\right)}{(a d+b d x)^{7/6}}","\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) \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{7 b \sqrt[6]{a+b x} (c+d x)^{5/6}}{d^2}-\frac{6 (a+b x)^{7/6}}{d \sqrt[6]{c+d x}}",1,"(d^(7/6)*(a + b*x)^(7/6)*(((6*b*c - 6*a*d + b*(c + d*x))*(-(b*c) + a*d + b*(c + d*x))^(1/6))/(d^(13/6)*(c + d*x)^(1/6)) - (7*(b^(7/6)*c - a*b^(1/6)*d)*ArcTan[(Sqrt[3]*b^(1/6)*(c + d*x)^(1/6))/(b^(1/6)*(c + d*x)^(1/6) - 2*(-(b*c) + a*d + b*(c + d*x))^(1/6))])/(2*Sqrt[3]*d^(13/6)) + (7*(b^(7/6)*c - a*b^(1/6)*d)*ArcTan[(Sqrt[3]*b^(1/6)*(c + d*x)^(1/6))/(b^(1/6)*(c + d*x)^(1/6) + 2*(-(b*c) + a*d + b*(c + d*x))^(1/6))])/(2*Sqrt[3]*d^(13/6)) - (7*(b^(7/6)*c - a*b^(1/6)*d)*ArcTanh[(b^(1/6)*(c + d*x)^(1/6))/(-(b*c) + a*d + b*(c + d*x))^(1/6)])/(3*d^(13/6)) - (7*(b^(7/6)*c - a*b^(1/6)*d)*ArcTanh[(b^(1/3)*(c + d*x)^(1/3) + (-(b*c) + a*d + b*(c + d*x))^(1/3))/(b^(1/6)*(c + d*x)^(1/6)*(-(b*c) + a*d + b*(c + d*x))^(1/6))])/(6*d^(13/6))))/(a*d + b*d*x)^(7/6)","A",1
1800,1,363,358,30.6541734,"\int \frac{(a+b x)^{7/6}}{(c+d x)^{13/6}} \, dx","IntegrateAlgebraic[(a + b*x)^(7/6)/(c + d*x)^(13/6),x]","\frac{d^{7/6} (a+b x)^{7/6} \left(\frac{\sqrt{3} b^{7/6} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}{\sqrt[6]{b} \sqrt[6]{c+d x}-2 \sqrt[6]{a d+b (c+d x)-b c}}\right)}{d^{13/6}}-\frac{\sqrt{3} b^{7/6} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}{2 \sqrt[6]{a d+b (c+d x)-b c}+\sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{d^{13/6}}+\frac{2 b^{7/6} \tanh ^{-1}\left(\frac{\sqrt[6]{b} \sqrt[6]{c+d x}}{\sqrt[6]{a d+b (c+d x)-b c}}\right)}{d^{13/6}}+\frac{b^{7/6} \tanh ^{-1}\left(\frac{\frac{\sqrt[3]{a d+b (c+d x)-b c}}{\sqrt[6]{b}}+\sqrt[6]{b} \sqrt[3]{c+d x}}{\sqrt[6]{c+d x} \sqrt[6]{a d+b (c+d x)-b c}}\right)}{d^{13/6}}+\frac{6 (-a d-8 b (c+d x)+b c) \sqrt[6]{a d+b (c+d x)-b c}}{7 d^{13/6} (c+d x)^{7/6}}\right)}{(a d+b 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,"(d^(7/6)*(a + b*x)^(7/6)*((6*(b*c - a*d - 8*b*(c + d*x))*(-(b*c) + a*d + b*(c + d*x))^(1/6))/(7*d^(13/6)*(c + d*x)^(7/6)) + (Sqrt[3]*b^(7/6)*ArcTan[(Sqrt[3]*b^(1/6)*(c + d*x)^(1/6))/(b^(1/6)*(c + d*x)^(1/6) - 2*(-(b*c) + a*d + b*(c + d*x))^(1/6))])/d^(13/6) - (Sqrt[3]*b^(7/6)*ArcTan[(Sqrt[3]*b^(1/6)*(c + d*x)^(1/6))/(b^(1/6)*(c + d*x)^(1/6) + 2*(-(b*c) + a*d + b*(c + d*x))^(1/6))])/d^(13/6) + (2*b^(7/6)*ArcTanh[(b^(1/6)*(c + d*x)^(1/6))/(-(b*c) + a*d + b*(c + d*x))^(1/6)])/d^(13/6) + (b^(7/6)*ArcTanh[(b^(1/6)*(c + d*x)^(1/3) + (-(b*c) + a*d + b*(c + d*x))^(1/3)/b^(1/6))/((c + d*x)^(1/6)*(-(b*c) + a*d + b*(c + d*x))^(1/6))])/d^(13/6)))/(a*d + b*d*x)^(7/6)","A",1
1801,0,0,32,46.0926062,"\int \frac{(a+b x)^{7/6}}{(c+d x)^{19/6}} \, dx","IntegrateAlgebraic[(a + b*x)^(7/6)/(c + d*x)^(19/6),x]","\int \frac{(a+b x)^{7/6}}{(c+d x)^{19/6}} \, dx","\frac{6 (a+b x)^{13/6}}{13 (c+d x)^{13/6} (b c-a d)}",1,"Could not integrate","F",-1
1802,0,0,66,46.479039,"\int \frac{(a+b x)^{7/6}}{(c+d x)^{25/6}} \, dx","IntegrateAlgebraic[(a + b*x)^(7/6)/(c + d*x)^(25/6),x]","\int \frac{(a+b x)^{7/6}}{(c+d x)^{25/6}} \, dx","\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,"Could not integrate","F",-1
1803,0,0,101,45.7438339,"\int \frac{(a+b x)^{7/6}}{(c+d x)^{31/6}} \, dx","IntegrateAlgebraic[(a + b*x)^(7/6)/(c + d*x)^(31/6),x]","\int \frac{(a+b x)^{7/6}}{(c+d x)^{31/6}} \, dx","\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,"Could not integrate","F",-1
1804,0,0,136,44.2634952,"\int \frac{(a+b x)^{7/6}}{(c+d x)^{37/6}} \, dx","IntegrateAlgebraic[(a + b*x)^(7/6)/(c + d*x)^(37/6),x]","\int \frac{(a+b x)^{7/6}}{(c+d x)^{37/6}} \, dx","\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,"Could not integrate","F",-1
1805,0,0,424,34.9011731,"\int \frac{(c+d x)^{7/6}}{\sqrt[6]{a+b x}} \, dx","IntegrateAlgebraic[(c + d*x)^(7/6)/(a + b*x)^(1/6),x]","\int \frac{(c+d x)^{7/6}}{\sqrt[6]{a+b x}} \, dx","-\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,"Could not integrate","F",-1
1806,1,388,378,16.9950276,"\int \frac{\sqrt[6]{c+d x}}{\sqrt[6]{a+b x}} \, dx","IntegrateAlgebraic[(c + d*x)^(1/6)/(a + b*x)^(1/6),x]","\frac{\sqrt[6]{a d+b d x} \left(-\frac{(b c-a d) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}{\sqrt[6]{b} \sqrt[6]{c+d x}-2 \sqrt[6]{a d+b (c+d x)-b c}}\right)}{2 \sqrt{3} b^{7/6} d^{5/6}}+\frac{(b c-a d) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}{2 \sqrt[6]{a d+b (c+d x)-b c}+\sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{2 \sqrt{3} b^{7/6} d^{5/6}}+\frac{(b c-a d) \tanh ^{-1}\left(\frac{\sqrt[6]{b} \sqrt[6]{c+d x}}{\sqrt[6]{a d+b (c+d x)-b c}}\right)}{3 b^{7/6} d^{5/6}}+\frac{(b c-a d) \tanh ^{-1}\left(\frac{\sqrt[3]{a d+b (c+d x)-b c}+\sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[6]{b} \sqrt[6]{c+d x} \sqrt[6]{a d+b (c+d x)-b c}}\right)}{6 b^{7/6} d^{5/6}}+\frac{\sqrt[6]{c+d x} (a d+b (c+d x)-b c)^{5/6}}{b d^{5/6}}\right)}{\sqrt[6]{d} \sqrt[6]{a+b 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}",1,"((a*d + b*d*x)^(1/6)*(((c + d*x)^(1/6)*(-(b*c) + a*d + b*(c + d*x))^(5/6))/(b*d^(5/6)) - ((b*c - a*d)*ArcTan[(Sqrt[3]*b^(1/6)*(c + d*x)^(1/6))/(b^(1/6)*(c + d*x)^(1/6) - 2*(-(b*c) + a*d + b*(c + d*x))^(1/6))])/(2*Sqrt[3]*b^(7/6)*d^(5/6)) + ((b*c - a*d)*ArcTan[(Sqrt[3]*b^(1/6)*(c + d*x)^(1/6))/(b^(1/6)*(c + d*x)^(1/6) + 2*(-(b*c) + a*d + b*(c + d*x))^(1/6))])/(2*Sqrt[3]*b^(7/6)*d^(5/6)) + ((b*c - a*d)*ArcTanh[(b^(1/6)*(c + d*x)^(1/6))/(-(b*c) + a*d + b*(c + d*x))^(1/6)])/(3*b^(7/6)*d^(5/6)) + ((b*c - a*d)*ArcTanh[(b^(1/3)*(c + d*x)^(1/3) + (-(b*c) + a*d + b*(c + d*x))^(1/3))/(b^(1/6)*(c + d*x)^(1/6)*(-(b*c) + a*d + b*(c + d*x))^(1/6))])/(6*b^(7/6)*d^(5/6))))/(d^(1/6)*(a + b*x)^(1/6))","A",1
1807,1,310,309,19.6520348,"\int \frac{1}{\sqrt[6]{a+b x} (c+d x)^{5/6}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(1/6)*(c + d*x)^(5/6)),x]","\frac{\sqrt[6]{a d+b d x} \left(-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}{\sqrt[6]{b} \sqrt[6]{c+d x}-2 \sqrt[6]{a d+b (c+d x)-b c}}\right)}{\sqrt[6]{b} d^{5/6}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}{2 \sqrt[6]{a d+b (c+d x)-b c}+\sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{\sqrt[6]{b} d^{5/6}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt[6]{b} \sqrt[6]{c+d x}}{\sqrt[6]{a d+b (c+d x)-b c}}\right)}{\sqrt[6]{b} d^{5/6}}+\frac{\tanh ^{-1}\left(\frac{\frac{\sqrt[3]{a d+b (c+d x)-b c}}{\sqrt[6]{b}}+\sqrt[6]{b} \sqrt[3]{c+d x}}{\sqrt[6]{c+d x} \sqrt[6]{a d+b (c+d x)-b c}}\right)}{\sqrt[6]{b} d^{5/6}}\right)}{\sqrt[6]{d} \sqrt[6]{a+b 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}}",1,"((a*d + b*d*x)^(1/6)*(-((Sqrt[3]*ArcTan[(Sqrt[3]*b^(1/6)*(c + d*x)^(1/6))/(b^(1/6)*(c + d*x)^(1/6) - 2*(-(b*c) + a*d + b*(c + d*x))^(1/6))])/(b^(1/6)*d^(5/6))) + (Sqrt[3]*ArcTan[(Sqrt[3]*b^(1/6)*(c + d*x)^(1/6))/(b^(1/6)*(c + d*x)^(1/6) + 2*(-(b*c) + a*d + b*(c + d*x))^(1/6))])/(b^(1/6)*d^(5/6)) + (2*ArcTanh[(b^(1/6)*(c + d*x)^(1/6))/(-(b*c) + a*d + b*(c + d*x))^(1/6)])/(b^(1/6)*d^(5/6)) + ArcTanh[(b^(1/6)*(c + d*x)^(1/3) + (-(b*c) + a*d + b*(c + d*x))^(1/3)/b^(1/6))/((c + d*x)^(1/6)*(-(b*c) + a*d + b*(c + d*x))^(1/6))]/(b^(1/6)*d^(5/6))))/(d^(1/6)*(a + b*x)^(1/6))","A",1
1808,1,46,32,1.8367153,"\int \frac{1}{\sqrt[6]{a+b x} (c+d x)^{11/6}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(1/6)*(c + d*x)^(11/6)),x]","\frac{6 \left(a+\frac{b (c+d x)}{d}-\frac{b c}{d}\right)^{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*c)/d + (b*(c + d*x))/d)^(5/6))/(5*(b*c - a*d)*(c + d*x)^(5/6))","A",1
1809,0,0,66,46.8878238,"\int \frac{1}{\sqrt[6]{a+b x} (c+d x)^{17/6}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(1/6)*(c + d*x)^(17/6)),x]","\int \frac{1}{\sqrt[6]{a+b x} (c+d x)^{17/6}} \, dx","\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,"Could not integrate","F",-1
1810,0,0,101,47.6800101,"\int \frac{1}{\sqrt[6]{a+b x} (c+d x)^{23/6}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(1/6)*(c + d*x)^(23/6)),x]","\int \frac{1}{\sqrt[6]{a+b x} (c+d x)^{23/6}} \, dx","\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,"Could not integrate","F",-1
1811,0,0,136,46.3202665,"\int \frac{1}{\sqrt[6]{a+b x} (c+d x)^{29/6}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(1/6)*(c + d*x)^(29/6)),x]","\int \frac{1}{\sqrt[6]{a+b x} (c+d x)^{29/6}} \, dx","\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,"Could not integrate","F",-1
1812,0,0,82,35.7042067,"\int \frac{(c+d x)^{11/6}}{\sqrt[6]{a+b x}} \, dx","IntegrateAlgebraic[(c + d*x)^(11/6)/(a + b*x)^(1/6),x]","\int \frac{(c+d x)^{11/6}}{\sqrt[6]{a+b x}} \, dx","\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,"Could not integrate","F",-1
1813,0,0,74,26.8107813,"\int \frac{(c+d x)^{5/6}}{\sqrt[6]{a+b x}} \, dx","IntegrateAlgebraic[(c + d*x)^(5/6)/(a + b*x)^(1/6),x]","\int \frac{(c+d x)^{5/6}}{\sqrt[6]{a+b x}} \, dx","\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,"Could not integrate","F",-1
1814,0,0,74,20.8336255,"\int \frac{1}{\sqrt[6]{a+b x} \sqrt[6]{c+d x}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(1/6)*(c + d*x)^(1/6)),x]","\int \frac{1}{\sqrt[6]{a+b x} \sqrt[6]{c+d x}} \, dx","\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,"Could not integrate","F",-1
1815,0,0,81,44.8284895,"\int \frac{1}{\sqrt[6]{a+b x} (c+d x)^{7/6}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(1/6)*(c + d*x)^(7/6)),x]","\int \frac{1}{\sqrt[6]{a+b x} (c+d x)^{7/6}} \, dx","\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,"Could not integrate","F",-1
1816,0,0,82,58.6193417,"\int \frac{1}{\sqrt[6]{a+b x} (c+d x)^{13/6}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(1/6)*(c + d*x)^(13/6)),x]","\int \frac{1}{\sqrt[6]{a+b x} (c+d x)^{13/6}} \, dx","\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,"Could not integrate","F",-1
1817,0,0,84,47.3012354,"\int \frac{1}{\sqrt[6]{a+b x} (c+d x)^{19/6}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(1/6)*(c + d*x)^(19/6)),x]","\int \frac{1}{\sqrt[6]{a+b x} (c+d x)^{19/6}} \, dx","\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,"Could not integrate","F",-1
1818,0,0,82,35.6273781,"\int \frac{(c+d x)^{13/6}}{(a+b x)^{5/6}} \, dx","IntegrateAlgebraic[(c + d*x)^(13/6)/(a + b*x)^(5/6),x]","\int \frac{(c+d x)^{13/6}}{(a+b x)^{5/6}} \, dx","\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,"Could not integrate","F",-1
1819,0,0,80,33.6214053,"\int \frac{(c+d x)^{7/6}}{(a+b x)^{5/6}} \, dx","IntegrateAlgebraic[(c + d*x)^(7/6)/(a + b*x)^(5/6),x]","\int \frac{(c+d x)^{7/6}}{(a+b x)^{5/6}} \, dx","\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,"Could not integrate","F",-1
1820,0,0,72,29.6469816,"\int \frac{\sqrt[6]{c+d x}}{(a+b x)^{5/6}} \, dx","IntegrateAlgebraic[(c + d*x)^(1/6)/(a + b*x)^(5/6),x]","\int \frac{\sqrt[6]{c+d x}}{(a+b x)^{5/6}} \, dx","\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,"Could not integrate","F",-1
1821,0,0,72,41.6775579,"\int \frac{1}{(a+b x)^{5/6} (c+d x)^{5/6}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(5/6)*(c + d*x)^(5/6)),x]","\int \frac{1}{(a+b x)^{5/6} (c+d x)^{5/6}} \, dx","\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,"Could not integrate","F",-1
1822,0,0,79,56.9755771,"\int \frac{1}{(a+b x)^{5/6} (c+d x)^{11/6}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(5/6)*(c + d*x)^(11/6)),x]","\int \frac{1}{(a+b x)^{5/6} (c+d x)^{11/6}} \, dx","\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,"Could not integrate","F",-1
1823,0,0,80,58.9256055,"\int \frac{1}{(a+b x)^{5/6} (c+d x)^{17/6}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(5/6)*(c + d*x)^(17/6)),x]","\int \frac{1}{(a+b x)^{5/6} (c+d x)^{17/6}} \, dx","\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,"Could not integrate","F",-1
1824,1,491,424,22.1889895,"\int \frac{(c+d x)^{11/6}}{(a+b x)^{5/6}} \, dx","IntegrateAlgebraic[(c + d*x)^(11/6)/(a + b*x)^(5/6),x]","\frac{b^{5/6} \left(\frac{d (a+b x)-a d+b c}{b}\right)^{5/6} \left(-\frac{55 \left(a^2 d^2-2 a b c d+b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{d} \sqrt[6]{a+b x}-2 \sqrt[6]{d (a+b x)-a d+b c}}\right)}{24 \sqrt{3} b^{17/6} \sqrt[6]{d}}+\frac{55 \left(a^2 d^2-2 a b c d+b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{d} \sqrt[6]{a+b x}}{2 \sqrt[6]{d (a+b x)-a d+b c}+\sqrt[6]{d} \sqrt[6]{a+b x}}\right)}{24 \sqrt{3} b^{17/6} \sqrt[6]{d}}+\frac{55 \left(a^2 d^2-2 a b c d+b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{d (a+b x)-a d+b c}}\right)}{36 b^{17/6} \sqrt[6]{d}}+\frac{55 \left(a^2 d^2-2 a b c d+b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt[3]{d (a+b x)-a d+b c}+\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[6]{d} \sqrt[6]{a+b x} \sqrt[6]{d (a+b x)-a d+b c}}\right)}{72 b^{17/6} \sqrt[6]{d}}+\frac{(d (a+b x)-a d+b c)^{5/6} \left(17 b c \sqrt[6]{a+b x}+6 d (a+b x)^{7/6}-17 a d \sqrt[6]{a+b x}\right)}{12 b^{17/6}}\right)}{(d (a+b x)-a d+b c)^{5/6}}","-\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{11 \sqrt[6]{a+b x} (c+d x)^{5/6} (b c-a d)}{12 b^2}+\frac{\sqrt[6]{a+b x} (c+d x)^{11/6}}{2 b}",1,"(b^(5/6)*((b*c - a*d + d*(a + b*x))/b)^(5/6)*(((b*c - a*d + d*(a + b*x))^(5/6)*(17*b*c*(a + b*x)^(1/6) - 17*a*d*(a + b*x)^(1/6) + 6*d*(a + b*x)^(7/6)))/(12*b^(17/6)) - (55*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*ArcTan[(Sqrt[3]*d^(1/6)*(a + b*x)^(1/6))/(d^(1/6)*(a + b*x)^(1/6) - 2*(b*c - a*d + d*(a + b*x))^(1/6))])/(24*Sqrt[3]*b^(17/6)*d^(1/6)) + (55*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*ArcTan[(Sqrt[3]*d^(1/6)*(a + b*x)^(1/6))/(d^(1/6)*(a + b*x)^(1/6) + 2*(b*c - a*d + d*(a + b*x))^(1/6))])/(24*Sqrt[3]*b^(17/6)*d^(1/6)) + (55*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*ArcTanh[(d^(1/6)*(a + b*x)^(1/6))/(b*c - a*d + d*(a + b*x))^(1/6)])/(36*b^(17/6)*d^(1/6)) + (55*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*ArcTanh[(d^(1/3)*(a + b*x)^(1/3) + (b*c - a*d + d*(a + b*x))^(1/3))/(d^(1/6)*(a + b*x)^(1/6)*(b*c - a*d + d*(a + b*x))^(1/6))])/(72*b^(17/6)*d^(1/6))))/(b*c - a*d + d*(a + b*x))^(5/6)","A",1
1825,0,0,378,35.6621943,"\int \frac{(c+d x)^{5/6}}{(a+b x)^{5/6}} \, dx","IntegrateAlgebraic[(c + d*x)^(5/6)/(a + b*x)^(5/6),x]","\int \frac{(c+d x)^{5/6}}{(a+b x)^{5/6}} \, dx","-\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,"Could not integrate","F",-1
1826,1,331,309,20.267753,"\int \frac{1}{(a+b x)^{5/6} \sqrt[6]{c+d x}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(5/6)*(c + d*x)^(1/6)),x]","\frac{b^{5/6} \left(\frac{d (a+b x)-a d+b c}{b}\right)^{5/6} \left(-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{d} \sqrt[6]{a+b x}-2 \sqrt[6]{d (a+b x)-a d+b c}}\right)}{b^{5/6} \sqrt[6]{d}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{d} \sqrt[6]{a+b x}}{2 \sqrt[6]{d (a+b x)-a d+b c}+\sqrt[6]{d} \sqrt[6]{a+b x}}\right)}{b^{5/6} \sqrt[6]{d}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{d (a+b x)-a d+b c}}\right)}{b^{5/6} \sqrt[6]{d}}+\frac{\tanh ^{-1}\left(\frac{\frac{\sqrt[3]{d (a+b x)-a d+b c}}{\sqrt[6]{d}}+\sqrt[6]{d} \sqrt[3]{a+b x}}{\sqrt[6]{a+b x} \sqrt[6]{d (a+b x)-a d+b c}}\right)}{b^{5/6} \sqrt[6]{d}}\right)}{(d (a+b x)-a d+b c)^{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 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,"(b^(5/6)*((b*c - a*d + d*(a + b*x))/b)^(5/6)*(-((Sqrt[3]*ArcTan[(Sqrt[3]*d^(1/6)*(a + b*x)^(1/6))/(d^(1/6)*(a + b*x)^(1/6) - 2*(b*c - a*d + d*(a + b*x))^(1/6))])/(b^(5/6)*d^(1/6))) + (Sqrt[3]*ArcTan[(Sqrt[3]*d^(1/6)*(a + b*x)^(1/6))/(d^(1/6)*(a + b*x)^(1/6) + 2*(b*c - a*d + d*(a + b*x))^(1/6))])/(b^(5/6)*d^(1/6)) + (2*ArcTanh[(d^(1/6)*(a + b*x)^(1/6))/(b*c - a*d + d*(a + b*x))^(1/6)])/(b^(5/6)*d^(1/6)) + ArcTanh[(d^(1/6)*(a + b*x)^(1/3) + (b*c - a*d + d*(a + b*x))^(1/3)/d^(1/6))/((a + b*x)^(1/6)*(b*c - a*d + d*(a + b*x))^(1/6))]/(b^(5/6)*d^(1/6))))/(b*c - a*d + d*(a + b*x))^(5/6)","A",1
1827,1,62,30,30.4405626,"\int \frac{1}{(a+b x)^{5/6} (c+d x)^{7/6}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(5/6)*(c + d*x)^(7/6)),x]","\frac{6 b \sqrt[6]{a+b x} \left(\frac{d (a+b x)-a d+b c}{b}\right)^{5/6}}{(b c-a d) (d (a+b x)-a d+b c)}","\frac{6 \sqrt[6]{a+b x}}{\sqrt[6]{c+d x} (b c-a d)}",1,"(6*b*(a + b*x)^(1/6)*((b*c - a*d + d*(a + b*x))/b)^(5/6))/((b*c - a*d)*(b*c - a*d + d*(a + b*x)))","B",1
1828,0,0,66,56.436001,"\int \frac{1}{(a+b x)^{5/6} (c+d x)^{13/6}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(5/6)*(c + d*x)^(13/6)),x]","\int \frac{1}{(a+b x)^{5/6} (c+d x)^{13/6}} \, dx","\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,"Could not integrate","F",-1
1829,0,0,101,56.8233799,"\int \frac{1}{(a+b x)^{5/6} (c+d x)^{19/6}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(5/6)*(c + d*x)^(19/6)),x]","\int \frac{1}{(a+b x)^{5/6} (c+d x)^{19/6}} \, dx","\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,"Could not integrate","F",-1
1830,0,0,136,57.1011882,"\int \frac{1}{(a+b x)^{5/6} (c+d x)^{25/6}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(5/6)*(c + d*x)^(25/6)),x]","\int \frac{1}{(a+b x)^{5/6} (c+d x)^{25/6}} \, dx","\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,"Could not integrate","F",-1
1831,0,0,449,42.8438586,"\int \frac{(c+d x)^{13/6}}{(a+b x)^{7/6}} \, dx","IntegrateAlgebraic[(c + d*x)^(13/6)/(a + b*x)^(7/6),x]","\int \frac{(c+d x)^{13/6}}{(a+b x)^{7/6}} \, dx","-\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{91 d (a+b x)^{5/6} \sqrt[6]{c+d x} (b c-a d)}{12 b^3}+\frac{13 d (a+b x)^{5/6} (c+d x)^{7/6}}{2 b^2}-\frac{6 (c+d x)^{13/6}}{b \sqrt[6]{a+b x}}",1,"Could not integrate","F",-1
1832,0,0,403,42.8833443,"\int \frac{(c+d x)^{7/6}}{(a+b x)^{7/6}} \, dx","IntegrateAlgebraic[(c + d*x)^(7/6)/(a + b*x)^(7/6),x]","\int \frac{(c+d x)^{7/6}}{(a+b x)^{7/6}} \, dx","-\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{7 d (a+b x)^{5/6} \sqrt[6]{c+d x}}{b^2}-\frac{6 (c+d x)^{7/6}}{b \sqrt[6]{a+b x}}",1,"Could not integrate","F",-1
1833,1,348,332,28.4361121,"\int \frac{\sqrt[6]{c+d x}}{(a+b x)^{7/6}} \, dx","IntegrateAlgebraic[(c + d*x)^(1/6)/(a + b*x)^(7/6),x]","\frac{(a d+b d x)^{7/6} \left(-\frac{\sqrt{3} \sqrt[6]{d} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}{\sqrt[6]{b} \sqrt[6]{c+d x}-2 \sqrt[6]{a d+b (c+d x)-b c}}\right)}{b^{7/6}}+\frac{\sqrt{3} \sqrt[6]{d} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}{2 \sqrt[6]{a d+b (c+d x)-b c}+\sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{b^{7/6}}+\frac{2 \sqrt[6]{d} \tanh ^{-1}\left(\frac{\sqrt[6]{b} \sqrt[6]{c+d x}}{\sqrt[6]{a d+b (c+d x)-b c}}\right)}{b^{7/6}}+\frac{\sqrt[6]{d} \tanh ^{-1}\left(\frac{\frac{\sqrt[3]{a d+b (c+d x)-b c}}{\sqrt[6]{b}}+\sqrt[6]{b} \sqrt[3]{c+d x}}{\sqrt[6]{c+d x} \sqrt[6]{a d+b (c+d x)-b c}}\right)}{b^{7/6}}-\frac{6 \sqrt[6]{d} \sqrt[6]{c+d x}}{b \sqrt[6]{a d+b (c+d x)-b c}}\right)}{d^{7/6} (a+b x)^{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[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,"((a*d + b*d*x)^(7/6)*((-6*d^(1/6)*(c + d*x)^(1/6))/(b*(-(b*c) + a*d + b*(c + d*x))^(1/6)) - (Sqrt[3]*d^(1/6)*ArcTan[(Sqrt[3]*b^(1/6)*(c + d*x)^(1/6))/(b^(1/6)*(c + d*x)^(1/6) - 2*(-(b*c) + a*d + b*(c + d*x))^(1/6))])/b^(7/6) + (Sqrt[3]*d^(1/6)*ArcTan[(Sqrt[3]*b^(1/6)*(c + d*x)^(1/6))/(b^(1/6)*(c + d*x)^(1/6) + 2*(-(b*c) + a*d + b*(c + d*x))^(1/6))])/b^(7/6) + (2*d^(1/6)*ArcTanh[(b^(1/6)*(c + d*x)^(1/6))/(-(b*c) + a*d + b*(c + d*x))^(1/6)])/b^(7/6) + (d^(1/6)*ArcTanh[(b^(1/6)*(c + d*x)^(1/3) + (-(b*c) + a*d + b*(c + d*x))^(1/3)/b^(1/6))/((c + d*x)^(1/6)*(-(b*c) + a*d + b*(c + d*x))^(1/6))])/b^(7/6)))/(d^(7/6)*(a + b*x)^(7/6))","A",1
1834,1,82,30,27.9351087,"\int \frac{1}{(a+b x)^{7/6} (c+d x)^{5/6}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(7/6)*(c + d*x)^(5/6)),x]","\frac{6 \sqrt[6]{c+d x} (a d+b d x)^{7/6} (a d+b (c+d x)-b c)^{5/6}}{d (a+b x)^{7/6} (b c-a d) (-a d-b (c+d x)+b c)}","-\frac{6 \sqrt[6]{c+d x}}{\sqrt[6]{a+b x} (b c-a d)}",1,"(6*(c + d*x)^(1/6)*(a*d + b*d*x)^(7/6)*(-(b*c) + a*d + b*(c + d*x))^(5/6))/(d*(b*c - a*d)*(a + b*x)^(7/6)*(b*c - a*d - b*(c + d*x)))","B",1
1835,1,83,64,23.47843,"\int \frac{1}{(a+b x)^{7/6} (c+d x)^{11/6}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(7/6)*(c + d*x)^(11/6)),x]","-\frac{6 \left(a+\frac{b (c+d x)}{d}-\frac{b c}{d}\right)^{5/6} \left(a d^2+6 b d (c+d x)-b c d\right)}{5 (c+d x)^{5/6} (b c-a d)^2 (a d+b (c+d x)-b c)}","-\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*(a - (b*c)/d + (b*(c + d*x))/d)^(5/6)*(-(b*c*d) + a*d^2 + 6*b*d*(c + d*x)))/(5*(b*c - a*d)^2*(c + d*x)^(5/6)*(-(b*c) + a*d + b*(c + d*x)))","A",1
1836,0,0,98,71.9564282,"\int \frac{1}{(a+b x)^{7/6} (c+d x)^{17/6}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(7/6)*(c + d*x)^(17/6)),x]","\int \frac{1}{(a+b x)^{7/6} (c+d x)^{17/6}} \, dx","-\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,"Could not integrate","F",-1
1837,0,0,134,71.0078205,"\int \frac{1}{(a+b x)^{7/6} (c+d x)^{23/6}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(7/6)*(c + d*x)^(23/6)),x]","\int \frac{1}{(a+b x)^{7/6} (c+d x)^{23/6}} \, dx","-\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,"Could not integrate","F",-1
1838,0,0,80,43.2565446,"\int \frac{(c+d x)^{11/6}}{(a+b x)^{7/6}} \, dx","IntegrateAlgebraic[(c + d*x)^(11/6)/(a + b*x)^(7/6),x]","\int \frac{(c+d x)^{11/6}}{(a+b x)^{7/6}} \, dx","-\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,"Could not integrate","F",-1
1839,0,0,72,42.2947312,"\int \frac{(c+d x)^{5/6}}{(a+b x)^{7/6}} \, dx","IntegrateAlgebraic[(c + d*x)^(5/6)/(a + b*x)^(7/6),x]","\int \frac{(c+d x)^{5/6}}{(a+b x)^{7/6}} \, dx","-\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,"Could not integrate","F",-1
1840,0,0,72,41.8537041,"\int \frac{1}{(a+b x)^{7/6} \sqrt[6]{c+d x}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(7/6)*(c + d*x)^(1/6)),x]","\int \frac{1}{(a+b x)^{7/6} \sqrt[6]{c+d x}} \, dx","-\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,"Could not integrate","F",-1
1841,0,0,79,68.0594126,"\int \frac{1}{(a+b x)^{7/6} (c+d x)^{7/6}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(7/6)*(c + d*x)^(7/6)),x]","\int \frac{1}{(a+b x)^{7/6} (c+d x)^{7/6}} \, dx","-\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,"Could not integrate","F",-1
1842,0,0,80,76.2192087,"\int \frac{1}{(a+b x)^{7/6} (c+d x)^{13/6}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(7/6)*(c + d*x)^(13/6)),x]","\int \frac{1}{(a+b x)^{7/6} (c+d x)^{13/6}} \, dx","-\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,"Could not integrate","F",-1
1843,0,0,82,71.3489138,"\int \frac{1}{(a+b x)^{7/6} (c+d x)^{19/6}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(7/6)*(c + d*x)^(19/6)),x]","\int \frac{1}{(a+b x)^{7/6} (c+d x)^{19/6}} \, dx","-\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,"Could not integrate","F",-1
1844,0,0,11,0.00006,"\int (a+b x)^m (a+b (2+m) x) \, dx","IntegrateAlgebraic[(a + b*x)^m*(a + b*(2 + m)*x),x]","\int (a+b x)^m (a+b (2+m) x) \, dx","x (a+b x)^{m+1}",1,"Could not integrate","F",-1
1845,0,0,61,0.0000555,"\int (a+b x)^m (c+d x)^n \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)^n,x]","\int (a+b x)^m (c+d x)^n \, dx","-\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,"Could not integrate","F",-1
1846,0,0,110,0.0000842,"\int (a+b x)^m (c+d x)^3 \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)^3,x]","\int (a+b x)^m (c+d x)^3 \, dx","\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,"Could not integrate","F",-1
1847,0,0,78,0.0000615,"\int (a+b x)^m (c+d x)^2 \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)^2,x]","\int (a+b x)^m (c+d x)^2 \, dx","\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,"Could not integrate","F",-1
1848,0,0,46,0.0000612,"\int (a+b x)^m (c+d x) \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x),x]","\int (a+b x)^m (c+d x) \, dx","\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,"Could not integrate","F",-1
1849,0,0,51,0.0000614,"\int \frac{(a+b x)^m}{c+d x} \, dx","IntegrateAlgebraic[(a + b*x)^m/(c + d*x),x]","\int \frac{(a+b x)^m}{c+d x} \, dx","\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,"Could not integrate","F",-1
1850,0,0,52,0.0000619,"\int \frac{(a+b x)^m}{(c+d x)^2} \, dx","IntegrateAlgebraic[(a + b*x)^m/(c + d*x)^2,x]","\int \frac{(a+b x)^m}{(c+d x)^2} \, dx","\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,"Could not integrate","F",-1
1851,0,0,54,0.0000633,"\int \frac{(a+b x)^m}{(c+d x)^3} \, dx","IntegrateAlgebraic[(a + b*x)^m/(c + d*x)^3,x]","\int \frac{(a+b x)^m}{(c+d x)^3} \, dx","\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,"Could not integrate","F",-1
1852,0,0,111,0.0000627,"\int (a+b x)^3 (c+d x)^n \, dx","IntegrateAlgebraic[(a + b*x)^3*(c + d*x)^n,x]","\int (a+b x)^3 (c+d x)^n \, dx","-\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,"Could not integrate","F",-1
1853,0,0,78,0.0000664,"\int (a+b x)^2 (c+d x)^n \, dx","IntegrateAlgebraic[(a + b*x)^2*(c + d*x)^n,x]","\int (a+b x)^2 (c+d x)^n \, dx","\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,"Could not integrate","F",-1
1854,0,0,47,0.0000608,"\int (a+b x) (c+d x)^n \, dx","IntegrateAlgebraic[(a + b*x)*(c + d*x)^n,x]","\int (a+b x) (c+d x)^n \, dx","\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,"Could not integrate","F",-1
1855,0,0,18,0.000051,"\int (c+d x)^n \, dx","IntegrateAlgebraic[(c + d*x)^n,x]","\int (c+d x)^n \, dx","\frac{(c+d x)^{n+1}}{d (n+1)}",1,"Could not integrate","F",-1
1856,0,0,51,0.000175,"\int \frac{(c+d x)^n}{a+b x} \, dx","IntegrateAlgebraic[(c + d*x)^n/(a + b*x),x]","\int \frac{(c+d x)^n}{a+b x} \, dx","-\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,"Could not integrate","F",-1
1857,0,0,51,0.0000619,"\int \frac{(c+d x)^n}{(a+b x)^2} \, dx","IntegrateAlgebraic[(c + d*x)^n/(a + b*x)^2,x]","\int \frac{(c+d x)^n}{(a+b x)^2} \, dx","\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,"Could not integrate","F",-1
1858,0,0,54,0.0000646,"\int \frac{(c+d x)^n}{(a+b x)^3} \, dx","IntegrateAlgebraic[(c + d*x)^n/(a + b*x)^3,x]","\int \frac{(c+d x)^n}{(a+b x)^3} \, dx","-\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,"Could not integrate","F",-1
1859,0,0,143,0.0000683,"\int (a+b x)^{-4+n} (c+d x)^{-n} \, dx","IntegrateAlgebraic[(a + b*x)^(-4 + n)/(c + d*x)^n,x]","\int (a+b x)^{-4+n} (c+d x)^{-n} \, dx","-\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,"Could not integrate","F",-1
1860,0,0,86,0.0000694,"\int (a+b x)^{-3+n} (c+d x)^{-n} \, dx","IntegrateAlgebraic[(a + b*x)^(-3 + n)/(c + d*x)^n,x]","\int (a+b x)^{-3+n} (c+d x)^{-n} \, dx","\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,"Could not integrate","F",-1
1861,0,0,39,0.0000859,"\int (a+b x)^{-2+n} (c+d x)^{-n} \, dx","IntegrateAlgebraic[(a + b*x)^(-2 + n)/(c + d*x)^n,x]","\int (a+b x)^{-2+n} (c+d x)^{-n} \, dx","-\frac{(a+b x)^{n-1} (c+d x)^{1-n}}{(1-n) (b c-a d)}",1,"Could not integrate","F",-1
1862,0,0,66,0.0000694,"\int (a+b x)^{-1+n} (c+d x)^{-n} \, dx","IntegrateAlgebraic[(a + b*x)^(-1 + n)/(c + d*x)^n,x]","\int (a+b x)^{-1+n} (c+d x)^{-n} \, dx","\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,"Could not integrate","F",-1
1863,0,0,72,0.0000659,"\int (a+b x)^n (c+d x)^{-n} \, dx","IntegrateAlgebraic[(a + b*x)^n/(c + d*x)^n,x]","\int (a+b x)^n (c+d x)^{-n} \, dx","\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,"Could not integrate","F",-1
1864,0,0,72,0.0000733,"\int (a+b x)^{1+n} (c+d x)^{-n} \, dx","IntegrateAlgebraic[(a + b*x)^(1 + n)/(c + d*x)^n,x]","\int (a+b x)^{1+n} (c+d x)^{-n} \, dx","\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,"Could not integrate","F",-1
1865,0,0,72,0.0000688,"\int (a+b x)^{2+n} (c+d x)^{-n} \, dx","IntegrateAlgebraic[(a + b*x)^(2 + n)/(c + d*x)^n,x]","\int (a+b x)^{2+n} (c+d x)^{-n} \, dx","\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,"Could not integrate","F",-1
1866,0,0,72,0.0000662,"\int (a+b x)^{-n} (c+d x)^n \, dx","IntegrateAlgebraic[(c + d*x)^n/(a + b*x)^n,x]","\int (a+b x)^{-n} (c+d x)^n \, dx","\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,"Could not integrate","F",-1
1867,0,0,75,0.0000669,"\int (a+b x)^{-1-n} (c+d x)^n \, dx","IntegrateAlgebraic[(a + b*x)^(-1 - n)*(c + d*x)^n,x]","\int (a+b x)^{-1-n} (c+d x)^n \, dx","-\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,"Could not integrate","F",-1
1868,0,0,37,0.0000739,"\int (a+b x)^{-2-n} (c+d x)^n \, dx","IntegrateAlgebraic[(a + b*x)^(-2 - n)*(c + d*x)^n,x]","\int (a+b x)^{-2-n} (c+d x)^n \, dx","-\frac{(a+b x)^{-n-1} (c+d x)^{n+1}}{(n+1) (b c-a d)}",1,"Could not integrate","F",-1
1869,0,0,80,0.0000646,"\int (a+b x)^{-3-n} (c+d x)^n \, dx","IntegrateAlgebraic[(a + b*x)^(-3 - n)*(c + d*x)^n,x]","\int (a+b x)^{-3-n} (c+d x)^n \, dx","\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,"Could not integrate","F",-1
1870,0,0,131,0.0000671,"\int (a+b x)^{-4-n} (c+d x)^n \, dx","IntegrateAlgebraic[(a + b*x)^(-4 - n)*(c + d*x)^n,x]","\int (a+b x)^{-4-n} (c+d x)^n \, dx","-\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,"Could not integrate","F",-1
1871,0,0,186,0.000067,"\int (a+b x)^{-5-n} (c+d x)^n \, dx","IntegrateAlgebraic[(a + b*x)^(-5 - n)*(c + d*x)^n,x]","\int (a+b x)^{-5-n} (c+d x)^n \, dx","\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{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{(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,"Could not integrate","F",-1
1872,0,0,72,0.0000671,"\int (a+b x)^n (c+d x)^{-n} \, dx","IntegrateAlgebraic[(a + b*x)^n/(c + d*x)^n,x]","\int (a+b x)^n (c+d x)^{-n} \, dx","\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,"Could not integrate","F",-1
1873,0,0,75,0.0000662,"\int (a+b x)^n (c+d x)^{-1-n} \, dx","IntegrateAlgebraic[(a + b*x)^n*(c + d*x)^(-1 - n),x]","\int (a+b x)^n (c+d x)^{-1-n} \, dx","-\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,"Could not integrate","F",-1
1874,0,0,36,0.0000678,"\int (a+b x)^n (c+d x)^{-2-n} \, dx","IntegrateAlgebraic[(a + b*x)^n*(c + d*x)^(-2 - n),x]","\int (a+b x)^n (c+d x)^{-2-n} \, dx","\frac{(a+b x)^{n+1} (c+d x)^{-n-1}}{(n+1) (b c-a d)}",1,"Could not integrate","F",-1
1875,0,0,79,0.0001023,"\int (a+b x)^n (c+d x)^{-3-n} \, dx","IntegrateAlgebraic[(a + b*x)^n*(c + d*x)^(-3 - n),x]","\int (a+b x)^n (c+d x)^{-3-n} \, dx","\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,"Could not integrate","F",-1
1876,0,0,130,0.0000659,"\int (a+b x)^n (c+d x)^{-4-n} \, dx","IntegrateAlgebraic[(a + b*x)^n*(c + d*x)^(-4 - n),x]","\int (a+b x)^n (c+d x)^{-4-n} \, dx","\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,"Could not integrate","F",-1
1877,0,0,185,0.0000659,"\int (a+b x)^n (c+d x)^{-5-n} \, dx","IntegrateAlgebraic[(a + b*x)^n*(c + d*x)^(-5 - n),x]","\int (a+b x)^n (c+d x)^{-5-n} \, dx","\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{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{(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,"Could not integrate","F",-1
1878,0,0,83,0.0000708,"\int (a+b x)^{-2+n} (c+d x)^{1-n} \, dx","IntegrateAlgebraic[(a + b*x)^(-2 + n)*(c + d*x)^(1 - n),x]","\int (a+b x)^{-2+n} (c+d x)^{1-n} \, dx","-\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,"Could not integrate","F",-1
1879,0,0,84,0.000071,"\int (a+b x)^{1+n} (c+d x)^{-1-n} \, dx","IntegrateAlgebraic[(a + b*x)^(1 + n)*(c + d*x)^(-1 - n),x]","\int (a+b x)^{1+n} (c+d x)^{-1-n} \, dx","\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,"Could not integrate","F",-1
1880,0,0,51,0.0000695,"\int (a+b x)^m (c+d x)^{1+2 n-2 (1+n)} \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)^(1 + 2*n - 2*(1 + n)),x]","\int (a+b x)^m (c+d x)^{1+2 n-2 (1+n)} \, dx","\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,"Could not integrate","F",-1
1881,0,0,57,0.0000714,"\int \frac{(c+d x)^{1+2 n-2 (1+n)}}{(a+b x)^2} \, dx","IntegrateAlgebraic[(c + d*x)^(1 + 2*n - 2*(1 + n))/(a + b*x)^2,x]","\int \frac{(c+d x)^{1+2 n-2 (1+n)}}{(a+b x)^2} \, dx","-\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,"Could not integrate","F",-1
1882,0,0,95,0.0000744,"\int (a+b x)^m (a c (1+m)+b c (2+m) x)^{-3-m} \, dx","IntegrateAlgebraic[(a + b*x)^m*(a*c*(1 + m) + b*c*(2 + m)*x)^(-3 - m),x]","\int (a+b x)^m (a c (1+m)+b c (2+m) x)^{-3-m} \, dx","\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,"Could not integrate","F",-1
1883,0,0,97,0.0000959,"\int (a+b x)^{-1-\frac{b c}{b c-a d}} (c+d x)^{-1+\frac{a d}{b c-a d}} \, dx","IntegrateAlgebraic[(a + b*x)^(-1 - (b*c)/(b*c - a*d))*(c + d*x)^(-1 + (a*d)/(b*c - a*d)),x]","\int (a+b x)^{-1-\frac{b c}{b c-a d}} (c+d x)^{-1+\frac{a d}{b c-a d}} \, dx","\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,"Could not integrate","F",-1
1884,0,0,97,0.0000984,"\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","IntegrateAlgebraic[(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]","\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","\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,"Could not integrate","F",-1
1885,0,0,30,0.0000578,"\int \frac{(1-x)^n}{\sqrt{1+x}} \, dx","IntegrateAlgebraic[(1 - x)^n/Sqrt[1 + x],x]","\int \frac{(1-x)^n}{\sqrt{1+x}} \, dx","2^{n+1} \sqrt{x+1} \, _2F_1\left(\frac{1}{2},-n;\frac{3}{2};\frac{x+1}{2}\right)",1,"Could not integrate","F",-1
1886,0,0,35,0.0000739,"\int \frac{(1+x)^n}{\sqrt{1-x}} \, dx","IntegrateAlgebraic[(1 + x)^n/Sqrt[1 - x],x]","\int \frac{(1+x)^n}{\sqrt{1-x}} \, dx","-2^{n+1} \sqrt{1-x} \, _2F_1\left(\frac{1}{2},-n;\frac{3}{2};\frac{1-x}{2}\right)",1,"Could not integrate","F",-1
1887,0,0,33,0.000058,"\int (1-x)^n (1+x)^{7/3} \, dx","IntegrateAlgebraic[(1 - x)^n*(1 + x)^(7/3),x]","\int (1-x)^n (1+x)^{7/3} \, dx","\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,"Could not integrate","F",-1
1888,0,0,37,0.0000587,"\int (1-x)^{7/3} (1+x)^n \, dx","IntegrateAlgebraic[(1 - x)^(7/3)*(1 + x)^n,x]","\int (1-x)^{7/3} (1+x)^n \, dx","-\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,"Could not integrate","F",-1
1889,0,0,47,0.0000616,"\int (1+2 x)^{-m} (2+3 x)^m \, dx","IntegrateAlgebraic[(2 + 3*x)^m/(1 + 2*x)^m,x]","\int (1+2 x)^{-m} (2+3 x)^m \, dx","\frac{2^{-m-1} (2 x+1)^{1-m} \, _2F_1(1-m,-m;2-m;-3 (2 x+1))}{1-m}",1,"Could not integrate","F",-1
1890,0,0,45,0.0000955,"\int \left(\frac{d (a+b x)}{-b c+a d}\right)^m (c+d x)^n \, dx","IntegrateAlgebraic[((d*(a + b*x))/(-(b*c) + a*d))^m*(c + d*x)^n,x]","\int \left(\frac{d (a+b x)}{-b c+a d}\right)^m (c+d x)^n \, dx","\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,"Could not integrate","F",-1
1891,1,27,28,0.009804,"\int \left(a+b x+c x^2+d x^3\right) \, dx","IntegrateAlgebraic[a + b*x + c*x^2 + d*x^3,x]","\frac{1}{12} \left(12 a x+6 b x^2+4 c x^3+3 d x^4\right)","a x+\frac{b x^2}{2}+\frac{c x^3}{3}+\frac{d x^4}{4}",1,"(12*a*x + 6*b*x^2 + 4*c*x^3 + 3*d*x^4)/12","A",1
1892,1,12,15,0.0028054,"\int \left(-x^3+x^4\right) \, dx","IntegrateAlgebraic[-x^3 + x^4,x]","\frac{1}{20} x^4 (4 x-5)","\frac{x^5}{5}-\frac{x^4}{4}",1,"(x^4*(-5 + 4*x))/20","A",1
1893,1,10,11,0.0022058,"\int \left(-1+x^5\right) \, dx","IntegrateAlgebraic[-1 + x^5,x]","\frac{1}{6} x \left(x^5-6\right)","\frac{x^6}{6}-x",1,"(x*(-6 + x^5))/6","A",1
1894,1,7,9,0.002129,"\int (7+4 x) \, dx","IntegrateAlgebraic[7 + 4*x,x]","x (2 x+7)","2 x^2+7 x",1,"x*(7 + 2*x)","A",1
1895,1,15,14,0.0029726,"\int \left(4 x+\pi  x^3\right) \, dx","IntegrateAlgebraic[4*x + Pi*x^3,x]","\frac{1}{4} \left(\pi  x^4+8 x^2\right)","\frac{\pi  x^4}{4}+2 x^2",1,"(8*x^2 + Pi*x^4)/4","A",1
1896,1,15,11,0.0027472,"\int \left(2 x+5 x^2\right) \, dx","IntegrateAlgebraic[2*x + 5*x^2,x]","\frac{1}{3} \left(5 x^3+3 x^2\right)","\frac{5 x^3}{3}+x^2",1,"(3*x^2 + 5*x^3)/3","A",1
1897,1,10,15,0.0028428,"\int \left(\frac{x^2}{2}+\frac{x^3}{3}\right) \, dx","IntegrateAlgebraic[x^2/2 + x^3/3,x]","\frac{1}{12} x^3 (x+2)","\frac{x^4}{12}+\frac{x^3}{6}",1,"(x^3*(2 + x))/12","A",1
1898,1,15,18,0.0030375,"\int \left(3-5 x+2 x^2\right) \, dx","IntegrateAlgebraic[3 - 5*x + 2*x^2,x]","\frac{1}{6} x \left(4 x^2-15 x+18\right)","\frac{2 x^3}{3}-\frac{5 x^2}{2}+3 x",1,"(x*(18 - 15*x + 4*x^2))/6","A",1
1899,1,17,20,0.0032977,"\int \left(-2 x+x^2+x^3\right) \, dx","IntegrateAlgebraic[-2*x + x^2 + x^3,x]","\frac{1}{12} x^2 \left(3 x^2+4 x-12\right)","\frac{x^4}{4}+\frac{x^3}{3}-x^2",1,"(x^2*(-12 + 4*x + 3*x^2))/12","A",1
1900,1,18,16,0.0030009,"\int \left(1-x^2-3 x^5\right) \, dx","IntegrateAlgebraic[1 - x^2 - 3*x^5,x]","\frac{1}{6} \left(-3 x^6-2 x^3+6 x\right)","-\frac{x^6}{2}-\frac{x^3}{3}+x",1,"(6*x - 2*x^3 - 3*x^6)/6","A",1
1901,1,11,13,0.0023121,"\int \left(5+2 x+3 x^2+4 x^3\right) \, dx","IntegrateAlgebraic[5 + 2*x + 3*x^2 + 4*x^3,x]","x \left(x^3+x^2+x+5\right)","x^4+x^3+x^2+5 x",1,"x*(5 + x + x^2 + x^3)","A",1
1902,1,26,22,0.0156831,"\int \left(a+\frac{d}{x^3}+\frac{c}{x^2}+\frac{b}{x}\right) \, dx","IntegrateAlgebraic[a + d/x^3 + c/x^2 + b/x,x]","\frac{2 a x^3-2 c x-d}{2 x^2}+b \log (x)","a x+b \log (x)-\frac{c}{x}-\frac{d}{2 x^2}",1,"(-d - 2*c*x + 2*a*x^3)/(2*x^2) + b*Log[x]","A",1
1903,1,19,22,0.0044507,"\int \left(\frac{1}{x^5}+x+x^5\right) \, dx","IntegrateAlgebraic[x^(-5) + x + x^5,x]","\frac{2 x^{10}+6 x^6-3}{12 x^4}","\frac{x^6}{6}-\frac{1}{4 x^4}+\frac{x^2}{2}",1,"(-3 + 6*x^6 + 2*x^10)/(12*x^4)","A",1
1904,1,15,15,0.0057398,"\int \left(\frac{1}{x^3}+\frac{1}{x^2}+\frac{1}{x}\right) \, dx","IntegrateAlgebraic[x^(-3) + x^(-2) + x^(-1),x]","\frac{-2 x-1}{2 x^2}+\log (x)","-\frac{1}{2 x^2}-\frac{1}{x}+\log (x)",1,"(-1 - 2*x)/(2*x^2) + Log[x]","A",1
1905,1,10,10,0.0039301,"\int \left(-\frac{2}{x^2}+\frac{3}{x}\right) \, dx","IntegrateAlgebraic[-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
1906,1,14,15,0.0034525,"\int \left(-\frac{1}{7 x^6}+x^6\right) \, dx","IntegrateAlgebraic[-1/7*1/x^6 + x^6,x]","\frac{5 x^{12}+1}{35 x^5}","\frac{x^7}{7}+\frac{1}{35 x^5}",1,"(1 + 5*x^12)/(35*x^5)","A",1
1907,1,11,11,0.0031818,"\int \left(1+\frac{1}{x}+x\right) \, dx","IntegrateAlgebraic[1 + x^(-1) + x,x]","\frac{1}{2} x (x+2)+\log (x)","\frac{x^2}{2}+x+\log (x)",1,"(x*(2 + x))/2 + Log[x]","A",1
1908,1,12,13,0.003441,"\int \left(-\frac{3}{x^3}+\frac{4}{x^2}\right) \, dx","IntegrateAlgebraic[-3/x^3 + 4/x^2,x]","\frac{3-8 x}{2 x^2}","\frac{3}{2 x^2}-\frac{4}{x}",1,"(3 - 8*x)/(2*x^2)","A",1
1909,1,13,13,0.0038913,"\int \left(\frac{1}{x}+2 x+x^2\right) \, dx","IntegrateAlgebraic[x^(-1) + 2*x + x^2,x]","\frac{1}{3} (x+3) x^2+\log (x)","\frac{x^3}{3}+x^2+\log (x)",1,"(x^2*(3 + x))/3 + Log[x]","A",1
1910,1,17,17,0.0063038,"\int \left(x^{5/6}-x^3\right) \, dx","IntegrateAlgebraic[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
1911,1,13,13,0.005287,"\int \left(33+\sqrt[33]{x}\right) \, dx","IntegrateAlgebraic[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
1912,1,15,15,0.004711,"\int \left(\frac{1}{2 \sqrt{x}}+2 \sqrt{x}\right) \, dx","IntegrateAlgebraic[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
1913,1,15,15,0.0105892,"\int \left(-\frac{1}{x^2}+\frac{10}{x}+6 \sqrt{x}\right) \, dx","IntegrateAlgebraic[-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
1914,1,17,17,0.0073606,"\int \left(\frac{1}{x^{3/2}}+x^{3/2}\right) \, dx","IntegrateAlgebraic[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
1915,1,15,15,0.0062091,"\int \left(-5 x^{3/2}+7 x^{5/2}\right) \, dx","IntegrateAlgebraic[-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
1916,1,24,24,0.007724,"\int \left(\frac{2}{\sqrt{x}}+\sqrt{x}-\frac{x}{2}\right) \, dx","IntegrateAlgebraic[2/Sqrt[x] + Sqrt[x] - x/2,x]","\frac{2 x^{3/2}}{3}-\frac{x^2}{4}+4 \sqrt{x}","\frac{2 x^{3/2}}{3}-\frac{x^2}{4}+4 \sqrt{x}",1,"4*Sqrt[x] + (2*x^(3/2))/3 - x^2/4","A",1
1917,1,23,23,0.0104189,"\int \left(-\frac{2}{x}+\frac{\sqrt{x}}{5}+x^{3/2}\right) \, dx","IntegrateAlgebraic[-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