1,1,1,1,0.0000598,"\int 0 \, dx","Integrate[0,x]","0","0",1,"0","A",1
2,1,1,1,0.0000497,"\int 1 \, dx","Integrate[1,x]","x","x",1,"x","A",1
3,1,3,3,0.0000788,"\int 5 \, dx","Integrate[5,x]","5 x","5 x",1,"5*x","A",1
4,1,3,3,0.0000468,"\int -2 \, dx","Integrate[-2,x]","-2 x","-2 x",1,"-2*x","A",1
5,1,5,5,0.0000497,"\int -\frac{3}{2} \, dx","Integrate[-3/2,x]","-\frac{3 x}{2}","-\frac{3 x}{2}",1,"(-3*x)/2","A",1
6,1,3,3,0.0000507,"\int \pi  \, dx","Integrate[Pi,x]","\pi  x","\pi  x",1,"Pi*x","A",1
7,1,3,3,0.0000562,"\int a \, dx","Integrate[a,x]","a x","a x",1,"a*x","A",1
8,1,4,4,0.0000695,"\int 3 a \, dx","Integrate[3*a,x]","3 a x","3 a x",1,"3*a*x","A",1
9,1,14,14,0.0001208,"\int \frac{\pi }{\sqrt{16-e^2}} \, dx","Integrate[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
10,1,7,7,0.0000645,"\int x^{100} \, dx","Integrate[x^100,x]","\frac{x^{101}}{101}","\frac{x^{101}}{101}",1,"x^101/101","A",1
11,1,7,7,0.000064,"\int x^3 \, dx","Integrate[x^3,x]","\frac{x^4}{4}","\frac{x^4}{4}",1,"x^4/4","A",1
12,1,7,7,0.0000512,"\int x^2 \, dx","Integrate[x^2,x]","\frac{x^3}{3}","\frac{x^3}{3}",1,"x^3/3","A",1
13,1,7,7,0.0000482,"\int x \, dx","Integrate[x,x]","\frac{x^2}{2}","\frac{x^2}{2}",1,"x^2/2","A",1
14,1,1,1,0.000047,"\int 1 \, dx","Integrate[1,x]","x","x",1,"x","A",1
15,1,2,2,0.0001397,"\int \frac{1}{x} \, dx","Integrate[x^(-1),x]","\log (x)","\log (x)",1,"Log[x]","A",1
16,1,5,5,0.0002078,"\int \frac{1}{x^2} \, dx","Integrate[x^(-2),x]","-\frac{1}{x}","-\frac{1}{x}",1,"-x^(-1)","A",1
17,1,7,7,0.0001979,"\int \frac{1}{x^3} \, dx","Integrate[x^(-3),x]","-\frac{1}{2 x^2}","-\frac{1}{2 x^2}",1,"-1/2*1/x^2","A",1
18,1,7,7,0.0001892,"\int \frac{1}{x^4} \, dx","Integrate[x^(-4),x]","-\frac{1}{3 x^3}","-\frac{1}{3 x^3}",1,"-1/3*1/x^3","A",1
19,1,7,7,0.0001798,"\int \frac{1}{x^{100}} \, dx","Integrate[x^(-100),x]","-\frac{1}{99 x^{99}}","-\frac{1}{99 x^{99}}",1,"-1/99*1/x^99","A",1
20,1,9,9,0.0006478,"\int x^{5/2} \, dx","Integrate[x^(5/2),x]","\frac{2 x^{7/2}}{7}","\frac{2 x^{7/2}}{7}",1,"(2*x^(7/2))/7","A",1
21,1,9,9,0.0006654,"\int x^{3/2} \, dx","Integrate[x^(3/2),x]","\frac{2 x^{5/2}}{5}","\frac{2 x^{5/2}}{5}",1,"(2*x^(5/2))/5","A",1
22,1,9,9,0.0006003,"\int \sqrt{x} \, dx","Integrate[Sqrt[x],x]","\frac{2 x^{3/2}}{3}","\frac{2 x^{3/2}}{3}",1,"(2*x^(3/2))/3","A",1
23,1,7,7,0.0005382,"\int \frac{1}{\sqrt{x}} \, dx","Integrate[1/Sqrt[x],x]","2 \sqrt{x}","2 \sqrt{x}",1,"2*Sqrt[x]","A",1
24,1,7,7,0.0006598,"\int \frac{1}{x^{3/2}} \, dx","Integrate[x^(-3/2),x]","-\frac{2}{\sqrt{x}}","-\frac{2}{\sqrt{x}}",1,"-2/Sqrt[x]","A",1
25,1,9,9,0.0006208,"\int \frac{1}{x^{5/2}} \, dx","Integrate[x^(-5/2),x]","-\frac{2}{3 x^{3/2}}","-\frac{2}{3 x^{3/2}}",1,"-2/(3*x^(3/2))","A",1
26,1,9,9,0.0007692,"\int x^{5/3} \, dx","Integrate[x^(5/3),x]","\frac{3 x^{8/3}}{8}","\frac{3 x^{8/3}}{8}",1,"(3*x^(8/3))/8","A",1
27,1,9,9,0.0006794,"\int x^{4/3} \, dx","Integrate[x^(4/3),x]","\frac{3 x^{7/3}}{7}","\frac{3 x^{7/3}}{7}",1,"(3*x^(7/3))/7","A",1
28,1,9,9,0.0006146,"\int x^{2/3} \, dx","Integrate[x^(2/3),x]","\frac{3 x^{5/3}}{5}","\frac{3 x^{5/3}}{5}",1,"(3*x^(5/3))/5","A",1
29,1,9,9,0.0006131,"\int \sqrt[3]{x} \, dx","Integrate[x^(1/3),x]","\frac{3 x^{4/3}}{4}","\frac{3 x^{4/3}}{4}",1,"(3*x^(4/3))/4","A",1
30,1,9,9,0.0007956,"\int \frac{1}{\sqrt[3]{x}} \, dx","Integrate[x^(-1/3),x]","\frac{3 x^{2/3}}{2}","\frac{3 x^{2/3}}{2}",1,"(3*x^(2/3))/2","A",1
31,1,7,7,0.0006584,"\int \frac{1}{x^{2/3}} \, dx","Integrate[x^(-2/3),x]","3 \sqrt[3]{x}","3 \sqrt[3]{x}",1,"3*x^(1/3)","A",1
32,1,7,7,0.0006599,"\int \frac{1}{x^{4/3}} \, dx","Integrate[x^(-4/3),x]","-\frac{3}{\sqrt[3]{x}}","-\frac{3}{\sqrt[3]{x}}",1,"-3/x^(1/3)","A",1
33,1,9,9,0.0006447,"\int \frac{1}{x^{5/3}} \, dx","Integrate[x^(-5/3),x]","-\frac{3}{2 x^{2/3}}","-\frac{3}{2 x^{2/3}}",1,"-3/(2*x^(2/3))","A",1
34,1,11,11,0.001248,"\int x^n \, dx","Integrate[x^n,x]","\frac{x^{n+1}}{n+1}","\frac{x^{n+1}}{n+1}",1,"x^(1 + n)/(1 + n)","A",1
35,1,12,16,0.0017472,"\int (b x)^n \, dx","Integrate[(b*x)^n,x]","\frac{x (b x)^n}{n+1}","\frac{(b x)^{n+1}}{b (n+1)}",1,"(x*(b*x)^n)/(1 + n)","A",1
36,1,23,23,0.0043201,"\int \frac{1}{\sqrt{-a}+e (c+d x)} \, dx","Integrate[(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
37,1,23,23,0.020252,"\int (c+d (a+b x))^{5/2} \, dx","Integrate[(c + d*(a + b*x))^(5/2),x]","\frac{2 (d (a+b x)+c)^{7/2}}{7 b d}","\frac{2 (d (a+b x)+c)^{7/2}}{7 b d}",1,"(2*(c + d*(a + b*x))^(7/2))/(7*b*d)","A",1
38,1,23,23,0.013582,"\int (c+d (a+b x))^{3/2} \, dx","Integrate[(c + d*(a + b*x))^(3/2),x]","\frac{2 (d (a+b x)+c)^{5/2}}{5 b d}","\frac{2 (d (a+b x)+c)^{5/2}}{5 b d}",1,"(2*(c + d*(a + b*x))^(5/2))/(5*b*d)","A",1
39,1,23,23,0.0097292,"\int \sqrt{c+d (a+b x)} \, dx","Integrate[Sqrt[c + d*(a + b*x)],x]","\frac{2 (d (a+b x)+c)^{3/2}}{3 b d}","\frac{2 (d (a+b x)+c)^{3/2}}{3 b d}",1,"(2*(c + d*(a + b*x))^(3/2))/(3*b*d)","A",1
40,1,21,21,0.0077785,"\int \frac{1}{\sqrt{c+d (a+b x)}} \, dx","Integrate[1/Sqrt[c + d*(a + b*x)],x]","\frac{2 \sqrt{d (a+b x)+c}}{b d}","\frac{2 \sqrt{d (a+b x)+c}}{b d}",1,"(2*Sqrt[c + d*(a + b*x)])/(b*d)","A",1
41,1,21,21,0.0084147,"\int \frac{1}{(c+d (a+b x))^{3/2}} \, dx","Integrate[(c + d*(a + b*x))^(-3/2),x]","-\frac{2}{b d \sqrt{d (a+b x)+c}}","-\frac{2}{b d \sqrt{d (a+b x)+c}}",1,"-2/(b*d*Sqrt[c + d*(a + b*x)])","A",1
42,1,23,23,0.0105841,"\int \frac{1}{(c+d (a+b x))^{5/2}} \, dx","Integrate[(c + d*(a + b*x))^(-5/2),x]","-\frac{2}{3 b d (d (a+b x)+c)^{3/2}}","-\frac{2}{3 b d (d (a+b x)+c)^{3/2}}",1,"-2/(3*b*d*(c + d*(a + b*x))^(3/2))","A",1
43,1,17,17,0.0012471,"\int x^3 (a+b x) \, dx","Integrate[x^3*(a + b*x),x]","\frac{a x^4}{4}+\frac{b x^5}{5}","\frac{a x^4}{4}+\frac{b x^5}{5}",1,"(a*x^4)/4 + (b*x^5)/5","A",1
44,1,17,17,0.0011066,"\int x^2 (a+b x) \, dx","Integrate[x^2*(a + b*x),x]","\frac{a x^3}{3}+\frac{b x^4}{4}","\frac{a x^3}{3}+\frac{b x^4}{4}",1,"(a*x^3)/3 + (b*x^4)/4","A",1
45,1,17,17,0.0008777,"\int x (a+b x) \, dx","Integrate[x*(a + b*x),x]","\frac{a x^2}{2}+\frac{b x^3}{3}","\frac{a x^2}{2}+\frac{b x^3}{3}",1,"(a*x^2)/2 + (b*x^3)/3","A",1
46,1,12,12,0.0000682,"\int (a+b x) \, dx","Integrate[a + b*x,x]","a x+\frac{b x^2}{2}","a x+\frac{b x^2}{2}",1,"a*x + (b*x^2)/2","A",1
47,1,8,8,0.0007818,"\int \frac{a+b x}{x} \, dx","Integrate[(a + b*x)/x,x]","a \log (x)+b x","a \log (x)+b x",1,"b*x + a*Log[x]","A",1
48,1,11,11,0.0017709,"\int \frac{a+b x}{x^2} \, dx","Integrate[(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
49,1,15,17,0.0014806,"\int \frac{a+b x}{x^3} \, dx","Integrate[(a + b*x)/x^3,x]","-\frac{a}{2 x^2}-\frac{b}{x}","-\frac{(a+b x)^2}{2 a x^2}",1,"-1/2*a/x^2 - b/x","A",1
50,1,17,17,0.0018557,"\int \frac{a+b x}{x^4} \, dx","Integrate[(a + b*x)/x^4,x]","-\frac{a}{3 x^3}-\frac{b}{2 x^2}","-\frac{a}{3 x^3}-\frac{b}{2 x^2}",1,"-1/3*a/x^3 - b/(2*x^2)","A",1
51,1,17,17,0.0015396,"\int \frac{a+b x}{x^5} \, dx","Integrate[(a + b*x)/x^5,x]","-\frac{a}{4 x^4}-\frac{b}{3 x^3}","-\frac{a}{4 x^4}-\frac{b}{3 x^3}",1,"-1/4*a/x^4 - b/(3*x^3)","A",1
52,1,30,30,0.0019495,"\int x^3 (a+b x)^2 \, dx","Integrate[x^3*(a + b*x)^2,x]","\frac{a^2 x^4}{4}+\frac{2}{5} a b x^5+\frac{b^2 x^6}{6}","\frac{a^2 x^4}{4}+\frac{2}{5} a b x^5+\frac{b^2 x^6}{6}",1,"(a^2*x^4)/4 + (2*a*b*x^5)/5 + (b^2*x^6)/6","A",1
53,1,30,30,0.0015389,"\int x^2 (a+b x)^2 \, dx","Integrate[x^2*(a + b*x)^2,x]","\frac{a^2 x^3}{3}+\frac{1}{2} a b x^4+\frac{b^2 x^5}{5}","\frac{a^2 x^3}{3}+\frac{1}{2} a b x^4+\frac{b^2 x^5}{5}",1,"(a^2*x^3)/3 + (a*b*x^4)/2 + (b^2*x^5)/5","A",1
54,1,30,30,0.0013295,"\int x (a+b x)^2 \, dx","Integrate[x*(a + b*x)^2,x]","\frac{a^2 x^2}{2}+\frac{2}{3} a b x^3+\frac{b^2 x^4}{4}","\frac{a^2 x^2}{2}+\frac{2}{3} a b x^3+\frac{b^2 x^4}{4}",1,"(a^2*x^2)/2 + (2*a*b*x^3)/3 + (b^2*x^4)/4","A",1
55,1,14,14,0.0011342,"\int (a+b x)^2 \, dx","Integrate[(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
56,1,22,22,0.0007847,"\int \frac{(a+b x)^2}{x} \, dx","Integrate[(a + b*x)^2/x,x]","a^2 \log (x)+2 a b x+\frac{b^2 x^2}{2}","a^2 \log (x)+2 a b x+\frac{b^2 x^2}{2}",1,"2*a*b*x + (b^2*x^2)/2 + a^2*Log[x]","A",1
57,1,20,20,0.0007207,"\int \frac{(a+b x)^2}{x^2} \, dx","Integrate[(a + b*x)^2/x^2,x]","-\frac{a^2}{x}+2 a b \log (x)+b^2 x","-\frac{a^2}{x}+2 a b \log (x)+b^2 x",1,"-(a^2/x) + b^2*x + 2*a*b*Log[x]","A",1
58,1,24,24,0.0034777,"\int \frac{(a+b x)^2}{x^3} \, dx","Integrate[(a + b*x)^2/x^3,x]","-\frac{a^2}{2 x^2}-\frac{2 a b}{x}+b^2 \log (x)","-\frac{a^2}{2 x^2}-\frac{2 a b}{x}+b^2 \log (x)",1,"-1/2*a^2/x^2 - (2*a*b)/x + b^2*Log[x]","A",1
59,1,26,17,0.006192,"\int \frac{(a+b x)^2}{x^4} \, dx","Integrate[(a + b*x)^2/x^4,x]","-\frac{a^2}{3 x^3}-\frac{a b}{x^2}-\frac{b^2}{x}","-\frac{(a+b x)^3}{3 a x^3}",1,"-1/3*a^2/x^3 - (a*b)/x^2 - b^2/x","A",1
60,1,30,30,0.0031762,"\int \frac{(a+b x)^2}{x^5} \, dx","Integrate[(a + b*x)^2/x^5,x]","-\frac{a^2}{4 x^4}-\frac{2 a b}{3 x^3}-\frac{b^2}{2 x^2}","-\frac{a^2}{4 x^4}-\frac{2 a b}{3 x^3}-\frac{b^2}{2 x^2}",1,"-1/4*a^2/x^4 - (2*a*b)/(3*x^3) - b^2/(2*x^2)","A",1
61,1,30,30,0.0067437,"\int \frac{(a+b x)^2}{x^6} \, dx","Integrate[(a + b*x)^2/x^6,x]","-\frac{a^2}{5 x^5}-\frac{a b}{2 x^4}-\frac{b^2}{3 x^3}","-\frac{a^2}{5 x^5}-\frac{a b}{2 x^4}-\frac{b^2}{3 x^3}",1,"-1/5*a^2/x^5 - (a*b)/(2*x^4) - b^2/(3*x^3)","A",1
62,1,30,30,0.0034158,"\int \frac{(a+b x)^2}{x^7} \, dx","Integrate[(a + b*x)^2/x^7,x]","-\frac{a^2}{6 x^6}-\frac{2 a b}{5 x^5}-\frac{b^2}{4 x^4}","-\frac{a^2}{6 x^6}-\frac{2 a b}{5 x^5}-\frac{b^2}{4 x^4}",1,"-1/6*a^2/x^6 - (2*a*b)/(5*x^5) - b^2/(4*x^4)","A",1
63,1,30,30,0.0064098,"\int \frac{(a+b x)^2}{x^8} \, dx","Integrate[(a + b*x)^2/x^8,x]","-\frac{a^2}{7 x^7}-\frac{a b}{3 x^6}-\frac{b^2}{5 x^5}","-\frac{a^2}{7 x^7}-\frac{a b}{3 x^6}-\frac{b^2}{5 x^5}",1,"-1/7*a^2/x^7 - (a*b)/(3*x^6) - b^2/(5*x^5)","A",1
64,1,43,43,0.0019322,"\int x^4 (a+b x)^3 \, dx","Integrate[x^4*(a + b*x)^3,x]","\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}","\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,"(a^3*x^5)/5 + (a^2*b*x^6)/2 + (3*a*b^2*x^7)/7 + (b^3*x^8)/8","A",1
65,1,43,43,0.0019648,"\int x^3 (a+b x)^3 \, dx","Integrate[x^3*(a + b*x)^3,x]","\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}","\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,"(a^3*x^4)/4 + (3*a^2*b*x^5)/5 + (a*b^2*x^6)/2 + (b^3*x^7)/7","A",1
66,1,43,43,0.0018301,"\int x^2 (a+b x)^3 \, dx","Integrate[x^2*(a + b*x)^3,x]","\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}","\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,"(a^3*x^3)/3 + (3*a^2*b*x^4)/4 + (3*a*b^2*x^5)/5 + (b^3*x^6)/6","A",1
67,1,40,30,0.0015405,"\int x (a+b x)^3 \, dx","Integrate[x*(a + b*x)^3,x]","\frac{a^3 x^2}{2}+a^2 b x^3+\frac{3}{4} a b^2 x^4+\frac{b^3 x^5}{5}","\frac{(a+b x)^5}{5 b^2}-\frac{a (a+b x)^4}{4 b^2}",1,"(a^3*x^2)/2 + a^2*b*x^3 + (3*a*b^2*x^4)/4 + (b^3*x^5)/5","A",1
68,1,14,14,0.0015462,"\int (a+b x)^3 \, dx","Integrate[(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
69,1,35,35,0.0029333,"\int \frac{(a+b x)^3}{x} \, dx","Integrate[(a + b*x)^3/x,x]","a^3 \log (x)+3 a^2 b x+\frac{3}{2} a b^2 x^2+\frac{b^3 x^3}{3}","a^3 \log (x)+3 a^2 b x+\frac{3}{2} a b^2 x^2+\frac{b^3 x^3}{3}",1,"3*a^2*b*x + (3*a*b^2*x^2)/2 + (b^3*x^3)/3 + a^3*Log[x]","A",1
70,1,34,34,0.0038641,"\int \frac{(a+b x)^3}{x^2} \, dx","Integrate[(a + b*x)^3/x^2,x]","-\frac{a^3}{x}+3 a^2 b \log (x)+3 a b^2 x+\frac{b^3 x^2}{2}","-\frac{a^3}{x}+3 a^2 b \log (x)+3 a b^2 x+\frac{b^3 x^2}{2}",1,"-(a^3/x) + 3*a*b^2*x + (b^3*x^2)/2 + 3*a^2*b*Log[x]","A",1
71,1,33,33,0.0050044,"\int \frac{(a+b x)^3}{x^3} \, dx","Integrate[(a + b*x)^3/x^3,x]","-\frac{a^3}{2 x^2}-\frac{3 a^2 b}{x}+3 a b^2 \log (x)+b^3 x","-\frac{a^3}{2 x^2}-\frac{3 a^2 b}{x}+3 a b^2 \log (x)+b^3 x",1,"-1/2*a^3/x^2 - (3*a^2*b)/x + b^3*x + 3*a*b^2*Log[x]","A",1
72,1,37,37,0.003784,"\int \frac{(a+b x)^3}{x^4} \, dx","Integrate[(a + b*x)^3/x^4,x]","-\frac{a^3}{3 x^3}-\frac{3 a^2 b}{2 x^2}-\frac{3 a b^2}{x}+b^3 \log (x)","-\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,"-1/3*a^3/x^3 - (3*a^2*b)/(2*x^2) - (3*a*b^2)/x + b^3*Log[x]","A",1
73,1,39,17,0.0034026,"\int \frac{(a+b x)^3}{x^5} \, dx","Integrate[(a + b*x)^3/x^5,x]","-\frac{a^3}{4 x^4}-\frac{a^2 b}{x^3}-\frac{3 a b^2}{2 x^2}-\frac{b^3}{x}","-\frac{(a+b x)^4}{4 a x^4}",1,"-1/4*a^3/x^4 - (a^2*b)/x^3 - (3*a*b^2)/(2*x^2) - b^3/x","B",1
74,1,41,36,0.0059323,"\int \frac{(a+b x)^3}{x^6} \, dx","Integrate[(a + b*x)^3/x^6,x]","-\frac{a^3}{5 x^5}-\frac{3 a^2 b}{4 x^4}-\frac{a b^2}{x^3}-\frac{b^3}{2 x^2}","\frac{b (a+b x)^4}{20 a^2 x^4}-\frac{(a+b x)^4}{5 a x^5}",1,"-1/5*a^3/x^5 - (3*a^2*b)/(4*x^4) - (a*b^2)/x^3 - b^3/(2*x^2)","A",1
75,1,43,43,0.0035853,"\int \frac{(a+b x)^3}{x^7} \, dx","Integrate[(a + b*x)^3/x^7,x]","-\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}","-\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,"-1/6*a^3/x^6 - (3*a^2*b)/(5*x^5) - (3*a*b^2)/(4*x^4) - b^3/(3*x^3)","A",1
76,1,43,43,0.0033806,"\int \frac{(a+b x)^3}{x^8} \, dx","Integrate[(a + b*x)^3/x^8,x]","-\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}","-\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,"-1/7*a^3/x^7 - (a^2*b)/(2*x^6) - (3*a*b^2)/(5*x^5) - b^3/(4*x^4)","A",1
77,1,66,66,0.0027041,"\int x^6 (a+b x)^5 \, dx","Integrate[x^6*(a + b*x)^5,x]","\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}","\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,"(a^5*x^7)/7 + (5*a^4*b*x^8)/8 + (10*a^3*b^2*x^9)/9 + a^2*b^3*x^10 + (5*a*b^4*x^11)/11 + (b^5*x^12)/12","A",1
78,1,69,69,0.0022777,"\int x^5 (a+b x)^5 \, dx","Integrate[x^5*(a + b*x)^5,x]","\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}","\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,"(a^5*x^6)/6 + (5*a^4*b*x^7)/7 + (5*a^3*b^2*x^8)/4 + (10*a^2*b^3*x^9)/9 + (a*b^4*x^10)/2 + (b^5*x^11)/11","A",1
79,1,69,69,0.0021443,"\int x^4 (a+b x)^5 \, dx","Integrate[x^4*(a + b*x)^5,x]","\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}","\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,"(a^5*x^5)/5 + (5*a^4*b*x^6)/6 + (10*a^3*b^2*x^7)/7 + (5*a^2*b^3*x^8)/4 + (5*a*b^4*x^9)/9 + (b^5*x^10)/10","A",1
80,1,66,64,0.0021692,"\int x^3 (a+b x)^5 \, dx","Integrate[x^3*(a + b*x)^5,x]","\frac{a^5 x^4}{4}+a^4 b x^5+\frac{5}{3} a^3 b^2 x^6+\frac{10}{7} a^2 b^3 x^7+\frac{5}{8} a b^4 x^8+\frac{b^5 x^9}{9}","-\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,"(a^5*x^4)/4 + a^4*b*x^5 + (5*a^3*b^2*x^6)/3 + (10*a^2*b^3*x^7)/7 + (5*a*b^4*x^8)/8 + (b^5*x^9)/9","A",1
81,1,67,47,0.0022882,"\int x^2 (a+b x)^5 \, dx","Integrate[x^2*(a + b*x)^5,x]","\frac{a^5 x^3}{3}+\frac{5}{4} a^4 b x^4+2 a^3 b^2 x^5+\frac{5}{3} a^2 b^3 x^6+\frac{5}{7} a b^4 x^7+\frac{b^5 x^8}{8}","\frac{a^2 (a+b x)^6}{6 b^3}+\frac{(a+b x)^8}{8 b^3}-\frac{2 a (a+b x)^7}{7 b^3}",1,"(a^5*x^3)/3 + (5*a^4*b*x^4)/4 + 2*a^3*b^2*x^5 + (5*a^2*b^3*x^6)/3 + (5*a*b^4*x^7)/7 + (b^5*x^8)/8","A",1
82,1,67,30,0.0018779,"\int x (a+b x)^5 \, dx","Integrate[x*(a + b*x)^5,x]","\frac{a^5 x^2}{2}+\frac{5}{3} a^4 b x^3+\frac{5}{2} a^3 b^2 x^4+2 a^2 b^3 x^5+\frac{5}{6} a b^4 x^6+\frac{b^5 x^7}{7}","\frac{(a+b x)^7}{7 b^2}-\frac{a (a+b x)^6}{6 b^2}",1,"(a^5*x^2)/2 + (5*a^4*b*x^3)/3 + (5*a^3*b^2*x^4)/2 + 2*a^2*b^3*x^5 + (5*a*b^4*x^6)/6 + (b^5*x^7)/7","B",1
83,1,14,14,0.0015075,"\int (a+b x)^5 \, dx","Integrate[(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
84,1,59,59,0.0032275,"\int \frac{(a+b x)^5}{x} \, dx","Integrate[(a + b*x)^5/x,x]","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}","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,"5*a^4*b*x + 5*a^3*b^2*x^2 + (10*a^2*b^3*x^3)/3 + (5*a*b^4*x^4)/4 + (b^5*x^5)/5 + a^5*Log[x]","A",1
85,1,58,58,0.0045497,"\int \frac{(a+b x)^5}{x^2} \, dx","Integrate[(a + b*x)^5/x^2,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}","-\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,"-(a^5/x) + 10*a^3*b^2*x + 5*a^2*b^3*x^2 + (5*a*b^4*x^3)/3 + (b^5*x^4)/4 + 5*a^4*b*Log[x]","A",1
86,1,60,60,0.0047666,"\int \frac{(a+b x)^5}{x^3} \, dx","Integrate[(a + b*x)^5/x^3,x]","-\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}","-\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,"-1/2*a^5/x^2 - (5*a^4*b)/x + 10*a^2*b^3*x + (5*a*b^4*x^2)/2 + (b^5*x^3)/3 + 10*a^3*b^2*Log[x]","A",1
87,1,60,60,0.004335,"\int \frac{(a+b x)^5}{x^4} \, dx","Integrate[(a + b*x)^5/x^4,x]","-\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}","-\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,"-1/3*a^5/x^3 - (5*a^4*b)/(2*x^2) - (10*a^3*b^2)/x + 5*a*b^4*x + (b^5*x^2)/2 + 10*a^2*b^3*Log[x]","A",1
88,1,57,57,0.0053782,"\int \frac{(a+b x)^5}{x^5} \, dx","Integrate[(a + b*x)^5/x^5,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","-\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,"-1/4*a^5/x^4 - (5*a^4*b)/(3*x^3) - (5*a^3*b^2)/x^2 - (10*a^2*b^3)/x + b^5*x + 5*a*b^4*Log[x]","A",1
89,1,61,61,0.0041841,"\int \frac{(a+b x)^5}{x^6} \, dx","Integrate[(a + b*x)^5/x^6,x]","-\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)","-\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,"-1/5*a^5/x^5 - (5*a^4*b)/(4*x^4) - (10*a^3*b^2)/(3*x^3) - (5*a^2*b^3)/x^2 - (5*a*b^4)/x + b^5*Log[x]","A",1
90,1,65,17,0.0037066,"\int \frac{(a+b x)^5}{x^7} \, dx","Integrate[(a + b*x)^5/x^7,x]","-\frac{a^5}{6 x^6}-\frac{a^4 b}{x^5}-\frac{5 a^3 b^2}{2 x^4}-\frac{10 a^2 b^3}{3 x^3}-\frac{5 a b^4}{2 x^2}-\frac{b^5}{x}","-\frac{(a+b x)^6}{6 a x^6}",1,"-1/6*a^5/x^6 - (a^4*b)/x^5 - (5*a^3*b^2)/(2*x^4) - (10*a^2*b^3)/(3*x^3) - (5*a*b^4)/(2*x^2) - b^5/x","B",1
91,1,67,36,0.0037069,"\int \frac{(a+b x)^5}{x^8} \, dx","Integrate[(a + b*x)^5/x^8,x]","-\frac{a^5}{7 x^7}-\frac{5 a^4 b}{6 x^6}-\frac{2 a^3 b^2}{x^5}-\frac{5 a^2 b^3}{2 x^4}-\frac{5 a b^4}{3 x^3}-\frac{b^5}{2 x^2}","\frac{b (a+b x)^6}{42 a^2 x^6}-\frac{(a+b x)^6}{7 a x^7}",1,"-1/7*a^5/x^7 - (5*a^4*b)/(6*x^6) - (2*a^3*b^2)/x^5 - (5*a^2*b^3)/(2*x^4) - (5*a*b^4)/(3*x^3) - b^5/(2*x^2)","A",1
92,1,67,56,0.0037905,"\int \frac{(a+b x)^5}{x^9} \, dx","Integrate[(a + b*x)^5/x^9,x]","-\frac{a^5}{8 x^8}-\frac{5 a^4 b}{7 x^7}-\frac{5 a^3 b^2}{3 x^6}-\frac{2 a^2 b^3}{x^5}-\frac{5 a b^4}{4 x^4}-\frac{b^5}{3 x^3}","-\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,"-1/8*a^5/x^8 - (5*a^4*b)/(7*x^7) - (5*a^3*b^2)/(3*x^6) - (2*a^2*b^3)/x^5 - (5*a*b^4)/(4*x^4) - b^5/(3*x^3)","A",1
93,1,67,67,0.0063463,"\int \frac{(a+b x)^5}{x^{10}} \, dx","Integrate[(a + b*x)^5/x^10,x]","-\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}","-\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,"-1/9*a^5/x^9 - (5*a^4*b)/(8*x^8) - (10*a^3*b^2)/(7*x^7) - (5*a^2*b^3)/(3*x^6) - (a*b^4)/x^5 - b^5/(4*x^4)","A",1
94,1,69,69,0.0039592,"\int \frac{(a+b x)^5}{x^{11}} \, dx","Integrate[(a + b*x)^5/x^11,x]","-\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}","-\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,"-1/10*a^5/x^10 - (5*a^4*b)/(9*x^9) - (5*a^3*b^2)/(4*x^8) - (10*a^2*b^3)/(7*x^7) - (5*a*b^4)/(6*x^6) - b^5/(5*x^5)","A",1
95,1,69,69,0.0038929,"\int \frac{(a+b x)^5}{x^{12}} \, dx","Integrate[(a + b*x)^5/x^12,x]","-\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}","-\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,"-1/11*a^5/x^11 - (a^4*b)/(2*x^10) - (10*a^3*b^2)/(9*x^9) - (5*a^2*b^3)/(4*x^8) - (5*a*b^4)/(7*x^7) - b^5/(6*x^6)","A",1
96,1,67,67,0.0040157,"\int \frac{(a+b x)^5}{x^{13}} \, dx","Integrate[(a + b*x)^5/x^13,x]","-\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}","-\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,"-1/12*a^5/x^12 - (5*a^4*b)/(11*x^11) - (a^3*b^2)/x^10 - (10*a^2*b^3)/(9*x^9) - (5*a*b^4)/(8*x^8) - b^5/(7*x^7)","A",1
97,1,67,67,0.0039321,"\int \frac{(a+b x)^5}{x^{14}} \, dx","Integrate[(a + b*x)^5/x^14,x]","-\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}","-\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,"-1/13*a^5/x^13 - (5*a^4*b)/(12*x^12) - (10*a^3*b^2)/(11*x^11) - (a^2*b^3)/x^10 - (5*a*b^4)/(9*x^9) - b^5/(8*x^8)","A",1
98,1,95,95,0.0026263,"\int x^8 (a+b x)^7 \, dx","Integrate[x^8*(a + b*x)^7,x]","\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}","\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,"(a^7*x^9)/9 + (7*a^6*b*x^10)/10 + (21*a^5*b^2*x^11)/11 + (35*a^4*b^3*x^12)/12 + (35*a^3*b^4*x^13)/13 + (3*a^2*b^5*x^14)/2 + (7*a*b^6*x^15)/15 + (b^7*x^16)/16","A",1
99,1,95,95,0.002473,"\int x^7 (a+b x)^7 \, dx","Integrate[x^7*(a + b*x)^7,x]","\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}","\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,"(a^7*x^8)/8 + (7*a^6*b*x^9)/9 + (21*a^5*b^2*x^10)/10 + (35*a^4*b^3*x^11)/11 + (35*a^3*b^4*x^12)/12 + (21*a^2*b^5*x^13)/13 + (a*b^6*x^14)/2 + (b^7*x^15)/15","A",1
100,1,95,95,0.0024102,"\int x^6 (a+b x)^7 \, dx","Integrate[x^6*(a + b*x)^7,x]","\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}","\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,"(a^7*x^7)/7 + (7*a^6*b*x^8)/8 + (7*a^5*b^2*x^9)/3 + (7*a^4*b^3*x^10)/2 + (35*a^3*b^4*x^11)/11 + (7*a^2*b^5*x^12)/4 + (7*a*b^6*x^13)/13 + (b^7*x^14)/14","A",1
101,1,92,96,0.0024043,"\int x^5 (a+b x)^7 \, dx","Integrate[x^5*(a + b*x)^7,x]","\frac{a^7 x^6}{6}+a^6 b x^7+\frac{21}{8} a^5 b^2 x^8+\frac{35}{9} a^4 b^3 x^9+\frac{7}{2} a^3 b^4 x^{10}+\frac{21}{11} a^2 b^5 x^{11}+\frac{7}{12} a b^6 x^{12}+\frac{b^7 x^{13}}{13}","-\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,"(a^7*x^6)/6 + a^6*b*x^7 + (21*a^5*b^2*x^8)/8 + (35*a^4*b^3*x^9)/9 + (7*a^3*b^4*x^10)/2 + (21*a^2*b^5*x^11)/11 + (7*a*b^6*x^12)/12 + (b^7*x^13)/13","A",1
102,1,93,81,0.0024198,"\int x^4 (a+b x)^7 \, dx","Integrate[x^4*(a + b*x)^7,x]","\frac{a^7 x^5}{5}+\frac{7}{6} a^6 b x^6+3 a^5 b^2 x^7+\frac{35}{8} a^4 b^3 x^8+\frac{35}{9} a^3 b^4 x^9+\frac{21}{10} a^2 b^5 x^{10}+\frac{7}{11} a b^6 x^{11}+\frac{b^7 x^{12}}{12}","\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,"(a^7*x^5)/5 + (7*a^6*b*x^6)/6 + 3*a^5*b^2*x^7 + (35*a^4*b^3*x^8)/8 + (35*a^3*b^4*x^9)/9 + (21*a^2*b^5*x^10)/10 + (7*a*b^6*x^11)/11 + (b^7*x^12)/12","A",1
103,1,93,64,0.0024999,"\int x^3 (a+b x)^7 \, dx","Integrate[x^3*(a + b*x)^7,x]","\frac{a^7 x^4}{4}+\frac{7}{5} a^6 b x^5+\frac{7}{2} a^5 b^2 x^6+5 a^4 b^3 x^7+\frac{35}{8} a^3 b^4 x^8+\frac{7}{3} a^2 b^5 x^9+\frac{7}{10} a b^6 x^{10}+\frac{b^7 x^{11}}{11}","-\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,"(a^7*x^4)/4 + (7*a^6*b*x^5)/5 + (7*a^5*b^2*x^6)/2 + 5*a^4*b^3*x^7 + (35*a^3*b^4*x^8)/8 + (7*a^2*b^5*x^9)/3 + (7*a*b^6*x^10)/10 + (b^7*x^11)/11","A",1
104,1,93,47,0.0023813,"\int x^2 (a+b x)^7 \, dx","Integrate[x^2*(a + b*x)^7,x]","\frac{a^7 x^3}{3}+\frac{7}{4} a^6 b x^4+\frac{21}{5} a^5 b^2 x^5+\frac{35}{6} a^4 b^3 x^6+5 a^3 b^4 x^7+\frac{21}{8} a^2 b^5 x^8+\frac{7}{9} a b^6 x^9+\frac{b^7 x^{10}}{10}","\frac{a^2 (a+b x)^8}{8 b^3}+\frac{(a+b x)^{10}}{10 b^3}-\frac{2 a (a+b x)^9}{9 b^3}",1,"(a^7*x^3)/3 + (7*a^6*b*x^4)/4 + (21*a^5*b^2*x^5)/5 + (35*a^4*b^3*x^6)/6 + 5*a^3*b^4*x^7 + (21*a^2*b^5*x^8)/8 + (7*a*b^6*x^9)/9 + (b^7*x^10)/10","A",1
105,1,91,30,0.0021026,"\int x (a+b x)^7 \, dx","Integrate[x*(a + b*x)^7,x]","\frac{a^7 x^2}{2}+\frac{7}{3} a^6 b x^3+\frac{21}{4} a^5 b^2 x^4+7 a^4 b^3 x^5+\frac{35}{6} a^3 b^4 x^6+3 a^2 b^5 x^7+\frac{7}{8} a b^6 x^8+\frac{b^7 x^9}{9}","\frac{(a+b x)^9}{9 b^2}-\frac{a (a+b x)^8}{8 b^2}",1,"(a^7*x^2)/2 + (7*a^6*b*x^3)/3 + (21*a^5*b^2*x^4)/4 + 7*a^4*b^3*x^5 + (35*a^3*b^4*x^6)/6 + 3*a^2*b^5*x^7 + (7*a*b^6*x^8)/8 + (b^7*x^9)/9","B",1
106,1,14,14,0.0008814,"\int (a+b x)^7 \, dx","Integrate[(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
107,1,87,87,0.0032938,"\int \frac{(a+b x)^7}{x} \, dx","Integrate[(a + b*x)^7/x,x]","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}","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,"7*a^6*b*x + (21*a^5*b^2*x^2)/2 + (35*a^4*b^3*x^3)/3 + (35*a^3*b^4*x^4)/4 + (21*a^2*b^5*x^5)/5 + (7*a*b^6*x^6)/6 + (b^7*x^7)/7 + a^7*Log[x]","A",1
108,1,86,86,0.00424,"\int \frac{(a+b x)^7}{x^2} \, dx","Integrate[(a + b*x)^7/x^2,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}","-\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,"-(a^7/x) + 21*a^5*b^2*x + (35*a^4*b^3*x^2)/2 + (35*a^3*b^4*x^3)/3 + (21*a^2*b^5*x^4)/4 + (7*a*b^6*x^5)/5 + (b^7*x^6)/6 + 7*a^6*b*Log[x]","A",1
109,1,84,84,0.0044236,"\int \frac{(a+b x)^7}{x^3} \, dx","Integrate[(a + b*x)^7/x^3,x]","-\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}","-\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,"-1/2*a^7/x^2 - (7*a^6*b)/x + 35*a^4*b^3*x + (35*a^3*b^4*x^2)/2 + 7*a^2*b^5*x^3 + (7*a*b^6*x^4)/4 + (b^7*x^5)/5 + 21*a^5*b^2*Log[x]","A",1
110,1,86,86,0.0044707,"\int \frac{(a+b x)^7}{x^4} \, dx","Integrate[(a + b*x)^7/x^4,x]","-\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}","-\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,"-1/3*a^7/x^3 - (7*a^6*b)/(2*x^2) - (21*a^5*b^2)/x + 35*a^3*b^4*x + (21*a^2*b^5*x^2)/2 + (7*a*b^6*x^3)/3 + (b^7*x^4)/4 + 35*a^4*b^3*Log[x]","A",1
111,1,86,86,0.0042678,"\int \frac{(a+b x)^7}{x^5} \, dx","Integrate[(a + b*x)^7/x^5,x]","-\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}","-\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,"-1/4*a^7/x^4 - (7*a^6*b)/(3*x^3) - (21*a^5*b^2)/(2*x^2) - (35*a^4*b^3)/x + 21*a^2*b^5*x + (7*a*b^6*x^2)/2 + (b^7*x^3)/3 + 35*a^3*b^4*Log[x]","A",1
112,1,84,84,0.0043989,"\int \frac{(a+b x)^7}{x^6} \, dx","Integrate[(a + b*x)^7/x^6,x]","-\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}","-\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,"-1/5*a^7/x^5 - (7*a^6*b)/(4*x^4) - (7*a^5*b^2)/x^3 - (35*a^4*b^3)/(2*x^2) - (35*a^3*b^4)/x + 7*a*b^6*x + (b^7*x^2)/2 + 21*a^2*b^5*Log[x]","A",1
113,1,85,85,0.0053325,"\int \frac{(a+b x)^7}{x^7} \, dx","Integrate[(a + b*x)^7/x^7,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","-\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,"-1/6*a^7/x^6 - (7*a^6*b)/(5*x^5) - (21*a^5*b^2)/(4*x^4) - (35*a^4*b^3)/(3*x^3) - (35*a^3*b^4)/(2*x^2) - (21*a^2*b^5)/x + b^7*x + 7*a*b^6*Log[x]","A",1
114,1,89,89,0.0042773,"\int \frac{(a+b x)^7}{x^8} \, dx","Integrate[(a + b*x)^7/x^8,x]","-\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)","-\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,"-1/7*a^7/x^7 - (7*a^6*b)/(6*x^6) - (21*a^5*b^2)/(5*x^5) - (35*a^4*b^3)/(4*x^4) - (35*a^3*b^4)/(3*x^3) - (21*a^2*b^5)/(2*x^2) - (7*a*b^6)/x + b^7*Log[x]","A",1
115,1,87,17,0.0040217,"\int \frac{(a+b x)^7}{x^9} \, dx","Integrate[(a + b*x)^7/x^9,x]","-\frac{a^7}{8 x^8}-\frac{a^6 b}{x^7}-\frac{7 a^5 b^2}{2 x^6}-\frac{7 a^4 b^3}{x^5}-\frac{35 a^3 b^4}{4 x^4}-\frac{7 a^2 b^5}{x^3}-\frac{7 a b^6}{2 x^2}-\frac{b^7}{x}","-\frac{(a+b x)^8}{8 a x^8}",1,"-1/8*a^7/x^8 - (a^6*b)/x^7 - (7*a^5*b^2)/(2*x^6) - (7*a^4*b^3)/x^5 - (35*a^3*b^4)/(4*x^4) - (7*a^2*b^5)/x^3 - (7*a*b^6)/(2*x^2) - b^7/x","B",1
116,1,91,36,0.0041163,"\int \frac{(a+b x)^7}{x^{10}} \, dx","Integrate[(a + b*x)^7/x^10,x]","-\frac{a^7}{9 x^9}-\frac{7 a^6 b}{8 x^8}-\frac{3 a^5 b^2}{x^7}-\frac{35 a^4 b^3}{6 x^6}-\frac{7 a^3 b^4}{x^5}-\frac{21 a^2 b^5}{4 x^4}-\frac{7 a b^6}{3 x^3}-\frac{b^7}{2 x^2}","\frac{b (a+b x)^8}{72 a^2 x^8}-\frac{(a+b x)^8}{9 a x^9}",1,"-1/9*a^7/x^9 - (7*a^6*b)/(8*x^8) - (3*a^5*b^2)/x^7 - (35*a^4*b^3)/(6*x^6) - (7*a^3*b^4)/x^5 - (21*a^2*b^5)/(4*x^4) - (7*a*b^6)/(3*x^3) - b^7/(2*x^2)","B",1
117,1,93,56,0.0039127,"\int \frac{(a+b x)^7}{x^{11}} \, dx","Integrate[(a + b*x)^7/x^11,x]","-\frac{a^7}{10 x^{10}}-\frac{7 a^6 b}{9 x^9}-\frac{21 a^5 b^2}{8 x^8}-\frac{5 a^4 b^3}{x^7}-\frac{35 a^3 b^4}{6 x^6}-\frac{21 a^2 b^5}{5 x^5}-\frac{7 a b^6}{4 x^4}-\frac{b^7}{3 x^3}","-\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,"-1/10*a^7/x^10 - (7*a^6*b)/(9*x^9) - (21*a^5*b^2)/(8*x^8) - (5*a^4*b^3)/x^7 - (35*a^3*b^4)/(6*x^6) - (21*a^2*b^5)/(5*x^5) - (7*a*b^6)/(4*x^4) - b^7/(3*x^3)","A",1
118,1,93,76,0.0038204,"\int \frac{(a+b x)^7}{x^{12}} \, dx","Integrate[(a + b*x)^7/x^12,x]","-\frac{a^7}{11 x^{11}}-\frac{7 a^6 b}{10 x^{10}}-\frac{7 a^5 b^2}{3 x^9}-\frac{35 a^4 b^3}{8 x^8}-\frac{5 a^3 b^4}{x^7}-\frac{7 a^2 b^5}{2 x^6}-\frac{7 a b^6}{5 x^5}-\frac{b^7}{4 x^4}","\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,"-1/11*a^7/x^11 - (7*a^6*b)/(10*x^10) - (7*a^5*b^2)/(3*x^9) - (35*a^4*b^3)/(8*x^8) - (5*a^3*b^4)/x^7 - (7*a^2*b^5)/(2*x^6) - (7*a*b^6)/(5*x^5) - b^7/(4*x^4)","A",1
119,1,93,96,0.0040571,"\int \frac{(a+b x)^7}{x^{13}} \, dx","Integrate[(a + b*x)^7/x^13,x]","-\frac{a^7}{12 x^{12}}-\frac{7 a^6 b}{11 x^{11}}-\frac{21 a^5 b^2}{10 x^{10}}-\frac{35 a^4 b^3}{9 x^9}-\frac{35 a^3 b^4}{8 x^8}-\frac{3 a^2 b^5}{x^7}-\frac{7 a b^6}{6 x^6}-\frac{b^7}{5 x^5}","-\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,"-1/12*a^7/x^12 - (7*a^6*b)/(11*x^11) - (21*a^5*b^2)/(10*x^10) - (35*a^4*b^3)/(9*x^9) - (35*a^3*b^4)/(8*x^8) - (3*a^2*b^5)/x^7 - (7*a*b^6)/(6*x^6) - b^7/(5*x^5)","A",1
120,1,93,93,0.0064378,"\int \frac{(a+b x)^7}{x^{14}} \, dx","Integrate[(a + b*x)^7/x^14,x]","-\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}","-\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,"-1/13*a^7/x^13 - (7*a^6*b)/(12*x^12) - (21*a^5*b^2)/(11*x^11) - (7*a^4*b^3)/(2*x^10) - (35*a^3*b^4)/(9*x^9) - (21*a^2*b^5)/(8*x^8) - (a*b^6)/x^7 - b^7/(6*x^6)","A",1
121,1,95,95,0.0038241,"\int \frac{(a+b x)^7}{x^{15}} \, dx","Integrate[(a + b*x)^7/x^15,x]","-\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}","-\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,"-1/14*a^7/x^14 - (7*a^6*b)/(13*x^13) - (7*a^5*b^2)/(4*x^12) - (35*a^4*b^3)/(11*x^11) - (7*a^3*b^4)/(2*x^10) - (7*a^2*b^5)/(3*x^9) - (7*a*b^6)/(8*x^8) - b^7/(7*x^7)","A",1
122,1,95,95,0.0037755,"\int \frac{(a+b x)^7}{x^{16}} \, dx","Integrate[(a + b*x)^7/x^16,x]","-\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}","-\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,"-1/15*a^7/x^15 - (a^6*b)/(2*x^14) - (21*a^5*b^2)/(13*x^13) - (35*a^4*b^3)/(12*x^12) - (35*a^3*b^4)/(11*x^11) - (21*a^2*b^5)/(10*x^10) - (7*a*b^6)/(9*x^9) - b^7/(8*x^8)","A",1
123,1,132,132,0.0031872,"\int x^{11} (a+b x)^{10} \, dx","Integrate[x^11*(a + b*x)^10,x]","\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}","\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,"(a^10*x^12)/12 + (10*a^9*b*x^13)/13 + (45*a^8*b^2*x^14)/14 + 8*a^7*b^3*x^15 + (105*a^6*b^4*x^16)/8 + (252*a^5*b^5*x^17)/17 + (35*a^4*b^6*x^18)/3 + (120*a^3*b^7*x^19)/19 + (9*a^2*b^8*x^20)/4 + (10*a*b^9*x^21)/21 + (b^10*x^22)/22","A",1
124,1,132,132,0.0037271,"\int x^{10} (a+b x)^{10} \, dx","Integrate[x^10*(a + b*x)^10,x]","\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}","\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,"(a^10*x^11)/11 + (5*a^9*b*x^12)/6 + (45*a^8*b^2*x^13)/13 + (60*a^7*b^3*x^14)/7 + 14*a^6*b^4*x^15 + (63*a^5*b^5*x^16)/4 + (210*a^4*b^6*x^17)/17 + (20*a^3*b^7*x^18)/3 + (45*a^2*b^8*x^19)/19 + (a*b^9*x^20)/2 + (b^10*x^21)/21","A",1
125,1,132,132,0.0029975,"\int x^9 (a+b x)^{10} \, dx","Integrate[x^9*(a + b*x)^10,x]","\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}","\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,"(a^10*x^10)/10 + (10*a^9*b*x^11)/11 + (15*a^8*b^2*x^12)/4 + (120*a^7*b^3*x^13)/13 + 15*a^6*b^4*x^14 + (84*a^5*b^5*x^15)/5 + (105*a^4*b^6*x^16)/8 + (120*a^3*b^7*x^17)/17 + (5*a^2*b^8*x^18)/2 + (10*a*b^9*x^19)/19 + (b^10*x^20)/20","A",1
126,1,125,147,0.0032298,"\int x^8 (a+b x)^{10} \, dx","Integrate[x^8*(a + b*x)^10,x]","\frac{a^{10} x^9}{9}+a^9 b x^{10}+\frac{45}{11} a^8 b^2 x^{11}+10 a^7 b^3 x^{12}+\frac{210}{13} a^6 b^4 x^{13}+18 a^5 b^5 x^{14}+14 a^4 b^6 x^{15}+\frac{15}{2} a^3 b^7 x^{16}+\frac{45}{17} a^2 b^8 x^{17}+\frac{5}{9} a b^9 x^{18}+\frac{b^{10} x^{19}}{19}","\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,"(a^10*x^9)/9 + a^9*b*x^10 + (45*a^8*b^2*x^11)/11 + 10*a^7*b^3*x^12 + (210*a^6*b^4*x^13)/13 + 18*a^5*b^5*x^14 + 14*a^4*b^6*x^15 + (15*a^3*b^7*x^16)/2 + (45*a^2*b^8*x^17)/17 + (5*a*b^9*x^18)/9 + (b^10*x^19)/19","A",1
127,1,130,132,0.0033008,"\int x^7 (a+b x)^{10} \, dx","Integrate[x^7*(a + b*x)^10,x]","\frac{a^{10} x^8}{8}+\frac{10}{9} a^9 b x^9+\frac{9}{2} a^8 b^2 x^{10}+\frac{120}{11} a^7 b^3 x^{11}+\frac{35}{2} a^6 b^4 x^{12}+\frac{252}{13} a^5 b^5 x^{13}+15 a^4 b^6 x^{14}+8 a^3 b^7 x^{15}+\frac{45}{16} a^2 b^8 x^{16}+\frac{10}{17} a b^9 x^{17}+\frac{b^{10} x^{18}}{18}","-\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,"(a^10*x^8)/8 + (10*a^9*b*x^9)/9 + (9*a^8*b^2*x^10)/2 + (120*a^7*b^3*x^11)/11 + (35*a^6*b^4*x^12)/2 + (252*a^5*b^5*x^13)/13 + 15*a^4*b^6*x^14 + 8*a^3*b^7*x^15 + (45*a^2*b^8*x^16)/16 + (10*a*b^9*x^17)/17 + (b^10*x^18)/18","A",1
128,1,126,112,0.0030233,"\int x^6 (a+b x)^{10} \, dx","Integrate[x^6*(a + b*x)^10,x]","\frac{a^{10} x^7}{7}+\frac{5}{4} a^9 b x^8+5 a^8 b^2 x^9+12 a^7 b^3 x^{10}+\frac{210}{11} a^6 b^4 x^{11}+21 a^5 b^5 x^{12}+\frac{210}{13} a^4 b^6 x^{13}+\frac{60}{7} a^3 b^7 x^{14}+3 a^2 b^8 x^{15}+\frac{5}{8} a b^9 x^{16}+\frac{b^{10} x^{17}}{17}","\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,"(a^10*x^7)/7 + (5*a^9*b*x^8)/4 + 5*a^8*b^2*x^9 + 12*a^7*b^3*x^10 + (210*a^6*b^4*x^11)/11 + 21*a^5*b^5*x^12 + (210*a^4*b^6*x^13)/13 + (60*a^3*b^7*x^14)/7 + 3*a^2*b^8*x^15 + (5*a*b^9*x^16)/8 + (b^10*x^17)/17","A",1
129,1,132,98,0.00331,"\int x^5 (a+b x)^{10} \, dx","Integrate[x^5*(a + b*x)^10,x]","\frac{a^{10} x^6}{6}+\frac{10}{7} a^9 b x^7+\frac{45}{8} a^8 b^2 x^8+\frac{40}{3} a^7 b^3 x^9+21 a^6 b^4 x^{10}+\frac{252}{11} a^5 b^5 x^{11}+\frac{35}{2} a^4 b^6 x^{12}+\frac{120}{13} a^3 b^7 x^{13}+\frac{45}{14} a^2 b^8 x^{14}+\frac{2}{3} a b^9 x^{15}+\frac{b^{10} x^{16}}{16}","-\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,"(a^10*x^6)/6 + (10*a^9*b*x^7)/7 + (45*a^8*b^2*x^8)/8 + (40*a^7*b^3*x^9)/3 + 21*a^6*b^4*x^10 + (252*a^5*b^5*x^11)/11 + (35*a^4*b^6*x^12)/2 + (120*a^3*b^7*x^13)/13 + (45*a^2*b^8*x^14)/14 + (2*a*b^9*x^15)/3 + (b^10*x^16)/16","A",1
130,1,130,81,0.0030173,"\int x^4 (a+b x)^{10} \, dx","Integrate[x^4*(a + b*x)^10,x]","\frac{a^{10} x^5}{5}+\frac{5}{3} a^9 b x^6+\frac{45}{7} a^8 b^2 x^7+15 a^7 b^3 x^8+\frac{70}{3} a^6 b^4 x^9+\frac{126}{5} a^5 b^5 x^{10}+\frac{210}{11} a^4 b^6 x^{11}+10 a^3 b^7 x^{12}+\frac{45}{13} a^2 b^8 x^{13}+\frac{5}{7} a b^9 x^{14}+\frac{b^{10} x^{15}}{15}","\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,"(a^10*x^5)/5 + (5*a^9*b*x^6)/3 + (45*a^8*b^2*x^7)/7 + 15*a^7*b^3*x^8 + (70*a^6*b^4*x^9)/3 + (126*a^5*b^5*x^10)/5 + (210*a^4*b^6*x^11)/11 + 10*a^3*b^7*x^12 + (45*a^2*b^8*x^13)/13 + (5*a*b^9*x^14)/7 + (b^10*x^15)/15","A",1
131,1,128,64,0.003037,"\int x^3 (a+b x)^{10} \, dx","Integrate[x^3*(a + b*x)^10,x]","\frac{a^{10} x^4}{4}+2 a^9 b x^5+\frac{15}{2} a^8 b^2 x^6+\frac{120}{7} a^7 b^3 x^7+\frac{105}{4} a^6 b^4 x^8+28 a^5 b^5 x^9+21 a^4 b^6 x^{10}+\frac{120}{11} a^3 b^7 x^{11}+\frac{15}{4} a^2 b^8 x^{12}+\frac{10}{13} a b^9 x^{13}+\frac{b^{10} x^{14}}{14}","-\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,"(a^10*x^4)/4 + 2*a^9*b*x^5 + (15*a^8*b^2*x^6)/2 + (120*a^7*b^3*x^7)/7 + (105*a^6*b^4*x^8)/4 + 28*a^5*b^5*x^9 + 21*a^4*b^6*x^10 + (120*a^3*b^7*x^11)/11 + (15*a^2*b^8*x^12)/4 + (10*a*b^9*x^13)/13 + (b^10*x^14)/14","A",1
132,1,126,47,0.0032858,"\int x^2 (a+b x)^{10} \, dx","Integrate[x^2*(a + b*x)^10,x]","\frac{a^{10} x^3}{3}+\frac{5}{2} a^9 b x^4+9 a^8 b^2 x^5+20 a^7 b^3 x^6+30 a^6 b^4 x^7+\frac{63}{2} a^5 b^5 x^8+\frac{70}{3} a^4 b^6 x^9+12 a^3 b^7 x^{10}+\frac{45}{11} a^2 b^8 x^{11}+\frac{5}{6} a b^9 x^{12}+\frac{b^{10} x^{13}}{13}","\frac{a^2 (a+b x)^{11}}{11 b^3}+\frac{(a+b x)^{13}}{13 b^3}-\frac{a (a+b x)^{12}}{6 b^3}",1,"(a^10*x^3)/3 + (5*a^9*b*x^4)/2 + 9*a^8*b^2*x^5 + 20*a^7*b^3*x^6 + 30*a^6*b^4*x^7 + (63*a^5*b^5*x^8)/2 + (70*a^4*b^6*x^9)/3 + 12*a^3*b^7*x^10 + (45*a^2*b^8*x^11)/11 + (5*a*b^9*x^12)/6 + (b^10*x^13)/13","B",1
133,1,128,30,0.0027016,"\int x (a+b x)^{10} \, dx","Integrate[x*(a + b*x)^10,x]","\frac{a^{10} x^2}{2}+\frac{10}{3} a^9 b x^3+\frac{45}{4} a^8 b^2 x^4+24 a^7 b^3 x^5+35 a^6 b^4 x^6+36 a^5 b^5 x^7+\frac{105}{4} a^4 b^6 x^8+\frac{40}{3} a^3 b^7 x^9+\frac{9}{2} a^2 b^8 x^{10}+\frac{10}{11} a b^9 x^{11}+\frac{b^{10} x^{12}}{12}","\frac{(a+b x)^{12}}{12 b^2}-\frac{a (a+b x)^{11}}{11 b^2}",1,"(a^10*x^2)/2 + (10*a^9*b*x^3)/3 + (45*a^8*b^2*x^4)/4 + 24*a^7*b^3*x^5 + 35*a^6*b^4*x^6 + 36*a^5*b^5*x^7 + (105*a^4*b^6*x^8)/4 + (40*a^3*b^7*x^9)/3 + (9*a^2*b^8*x^10)/2 + (10*a*b^9*x^11)/11 + (b^10*x^12)/12","B",1
134,1,14,14,0.0009416,"\int (a+b x)^{10} \, dx","Integrate[(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
135,1,122,122,0.0039324,"\int \frac{(a+b x)^{10}}{x} \, dx","Integrate[(a + b*x)^10/x,x]","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}","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,"10*a^9*b*x + (45*a^8*b^2*x^2)/2 + 40*a^7*b^3*x^3 + (105*a^6*b^4*x^4)/2 + (252*a^5*b^5*x^5)/5 + 35*a^4*b^6*x^6 + (120*a^3*b^7*x^7)/7 + (45*a^2*b^8*x^8)/8 + (10*a*b^9*x^9)/9 + (b^10*x^10)/10 + a^10*Log[x]","A",1
136,1,115,115,0.0095043,"\int \frac{(a+b x)^{10}}{x^2} \, dx","Integrate[(a + b*x)^10/x^2,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}","-\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,"-(a^10/x) + 45*a^8*b^2*x + 60*a^7*b^3*x^2 + 70*a^6*b^4*x^3 + 63*a^5*b^5*x^4 + 42*a^4*b^6*x^5 + 20*a^3*b^7*x^6 + (45*a^2*b^8*x^7)/7 + (5*a*b^9*x^8)/4 + (b^10*x^9)/9 + 10*a^9*b*Log[x]","A",1
137,1,119,119,0.0051468,"\int \frac{(a+b x)^{10}}{x^3} \, dx","Integrate[(a + b*x)^10/x^3,x]","-\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}","-\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,"-1/2*a^10/x^2 - (10*a^9*b)/x + 120*a^7*b^3*x + 105*a^6*b^4*x^2 + 84*a^5*b^5*x^3 + (105*a^4*b^6*x^4)/2 + 24*a^3*b^7*x^5 + (15*a^2*b^8*x^6)/2 + (10*a*b^9*x^7)/7 + (b^10*x^8)/8 + 45*a^8*b^2*Log[x]","A",1
138,1,115,115,0.0098697,"\int \frac{(a+b x)^{10}}{x^4} \, dx","Integrate[(a + b*x)^10/x^4,x]","-\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}","-\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,"-1/3*a^10/x^3 - (5*a^9*b)/x^2 - (45*a^8*b^2)/x + 210*a^6*b^4*x + 126*a^5*b^5*x^2 + 70*a^4*b^6*x^3 + 30*a^3*b^7*x^4 + 9*a^2*b^8*x^5 + (5*a*b^9*x^6)/3 + (b^10*x^7)/7 + 120*a^7*b^3*Log[x]","A",1
139,1,119,119,0.0083487,"\int \frac{(a+b x)^{10}}{x^5} \, dx","Integrate[(a + b*x)^10/x^5,x]","-\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}","-\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,"-1/4*a^10/x^4 - (10*a^9*b)/(3*x^3) - (45*a^8*b^2)/(2*x^2) - (120*a^7*b^3)/x + 252*a^5*b^5*x + 105*a^4*b^6*x^2 + 40*a^3*b^7*x^3 + (45*a^2*b^8*x^4)/4 + 2*a*b^9*x^5 + (b^10*x^6)/6 + 210*a^6*b^4*Log[x]","A",1
140,1,117,117,0.0099262,"\int \frac{(a+b x)^{10}}{x^6} \, dx","Integrate[(a + b*x)^10/x^6,x]","-\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}","-\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,"-1/5*a^10/x^5 - (5*a^9*b)/(2*x^4) - (15*a^8*b^2)/x^3 - (60*a^7*b^3)/x^2 - (210*a^6*b^4)/x + 210*a^4*b^6*x + 60*a^3*b^7*x^2 + 15*a^2*b^8*x^3 + (5*a*b^9*x^4)/2 + (b^10*x^5)/5 + 252*a^5*b^5*Log[x]","A",1
141,1,119,119,0.0052971,"\int \frac{(a+b x)^{10}}{x^7} \, dx","Integrate[(a + b*x)^10/x^7,x]","-\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}","-\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,"-1/6*a^10/x^6 - (2*a^9*b)/x^5 - (45*a^8*b^2)/(4*x^4) - (40*a^7*b^3)/x^3 - (105*a^6*b^4)/x^2 - (252*a^5*b^5)/x + 120*a^3*b^7*x + (45*a^2*b^8*x^2)/2 + (10*a*b^9*x^3)/3 + (b^10*x^4)/4 + 210*a^4*b^6*Log[x]","A",1
142,1,115,115,0.0102208,"\int \frac{(a+b x)^{10}}{x^8} \, dx","Integrate[(a + b*x)^10/x^8,x]","-\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}","-\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,"-1/7*a^10/x^7 - (5*a^9*b)/(3*x^6) - (9*a^8*b^2)/x^5 - (30*a^7*b^3)/x^4 - (70*a^6*b^4)/x^3 - (126*a^5*b^5)/x^2 - (210*a^4*b^6)/x + 45*a^2*b^8*x + 5*a*b^9*x^2 + (b^10*x^3)/3 + 120*a^3*b^7*Log[x]","A",1
143,1,119,119,0.0052345,"\int \frac{(a+b x)^{10}}{x^9} \, dx","Integrate[(a + b*x)^10/x^9,x]","-\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}","-\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,"-1/8*a^10/x^8 - (10*a^9*b)/(7*x^7) - (15*a^8*b^2)/(2*x^6) - (24*a^7*b^3)/x^5 - (105*a^6*b^4)/(2*x^4) - (84*a^5*b^5)/x^3 - (105*a^4*b^6)/x^2 - (120*a^3*b^7)/x + 10*a*b^9*x + (b^10*x^2)/2 + 45*a^2*b^8*Log[x]","A",1
144,1,114,114,0.0061895,"\int \frac{(a+b x)^{10}}{x^{10}} \, dx","Integrate[(a + b*x)^10/x^10,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","-\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,"-1/9*a^10/x^9 - (5*a^9*b)/(4*x^8) - (45*a^8*b^2)/(7*x^7) - (20*a^7*b^3)/x^6 - (42*a^6*b^4)/x^5 - (63*a^5*b^5)/x^4 - (70*a^4*b^6)/x^3 - (60*a^3*b^7)/x^2 - (45*a^2*b^8)/x + b^10*x + 10*a*b^9*Log[x]","A",1
145,1,124,124,0.0049952,"\int \frac{(a+b x)^{10}}{x^{11}} \, dx","Integrate[(a + b*x)^10/x^11,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)","-\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,"-1/10*a^10/x^10 - (10*a^9*b)/(9*x^9) - (45*a^8*b^2)/(8*x^8) - (120*a^7*b^3)/(7*x^7) - (35*a^6*b^4)/x^6 - (252*a^5*b^5)/(5*x^5) - (105*a^4*b^6)/(2*x^4) - (40*a^3*b^7)/x^3 - (45*a^2*b^8)/(2*x^2) - (10*a*b^9)/x + b^10*Log[x]","A",1
146,1,114,17,0.0096249,"\int \frac{(a+b x)^{10}}{x^{12}} \, dx","Integrate[(a + b*x)^10/x^12,x]","-\frac{a^{10}}{11 x^{11}}-\frac{a^9 b}{x^{10}}-\frac{5 a^8 b^2}{x^9}-\frac{15 a^7 b^3}{x^8}-\frac{30 a^6 b^4}{x^7}-\frac{42 a^5 b^5}{x^6}-\frac{42 a^4 b^6}{x^5}-\frac{30 a^3 b^7}{x^4}-\frac{15 a^2 b^8}{x^3}-\frac{5 a b^9}{x^2}-\frac{b^{10}}{x}","-\frac{(a+b x)^{11}}{11 a x^{11}}",1,"-1/11*a^10/x^11 - (a^9*b)/x^10 - (5*a^8*b^2)/x^9 - (15*a^7*b^3)/x^8 - (30*a^6*b^4)/x^7 - (42*a^5*b^5)/x^6 - (42*a^4*b^6)/x^5 - (30*a^3*b^7)/x^4 - (15*a^2*b^8)/x^3 - (5*a*b^9)/x^2 - b^10/x","B",1
147,1,128,36,0.0044641,"\int \frac{(a+b x)^{10}}{x^{13}} \, dx","Integrate[(a + b*x)^10/x^13,x]","-\frac{a^{10}}{12 x^{12}}-\frac{10 a^9 b}{11 x^{11}}-\frac{9 a^8 b^2}{2 x^{10}}-\frac{40 a^7 b^3}{3 x^9}-\frac{105 a^6 b^4}{4 x^8}-\frac{36 a^5 b^5}{x^7}-\frac{35 a^4 b^6}{x^6}-\frac{24 a^3 b^7}{x^5}-\frac{45 a^2 b^8}{4 x^4}-\frac{10 a b^9}{3 x^3}-\frac{b^{10}}{2 x^2}","\frac{b (a+b x)^{11}}{132 a^2 x^{11}}-\frac{(a+b x)^{11}}{12 a x^{12}}",1,"-1/12*a^10/x^12 - (10*a^9*b)/(11*x^11) - (9*a^8*b^2)/(2*x^10) - (40*a^7*b^3)/(3*x^9) - (105*a^6*b^4)/(4*x^8) - (36*a^5*b^5)/x^7 - (35*a^4*b^6)/x^6 - (24*a^3*b^7)/x^5 - (45*a^2*b^8)/(4*x^4) - (10*a*b^9)/(3*x^3) - b^10/(2*x^2)","B",1
148,1,126,56,0.0092367,"\int \frac{(a+b x)^{10}}{x^{14}} \, dx","Integrate[(a + b*x)^10/x^14,x]","-\frac{a^{10}}{13 x^{13}}-\frac{5 a^9 b}{6 x^{12}}-\frac{45 a^8 b^2}{11 x^{11}}-\frac{12 a^7 b^3}{x^{10}}-\frac{70 a^6 b^4}{3 x^9}-\frac{63 a^5 b^5}{2 x^8}-\frac{30 a^4 b^6}{x^7}-\frac{20 a^3 b^7}{x^6}-\frac{9 a^2 b^8}{x^5}-\frac{5 a b^9}{2 x^4}-\frac{b^{10}}{3 x^3}","-\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,"-1/13*a^10/x^13 - (5*a^9*b)/(6*x^12) - (45*a^8*b^2)/(11*x^11) - (12*a^7*b^3)/x^10 - (70*a^6*b^4)/(3*x^9) - (63*a^5*b^5)/(2*x^8) - (30*a^4*b^6)/x^7 - (20*a^3*b^7)/x^6 - (9*a^2*b^8)/x^5 - (5*a*b^9)/(2*x^4) - b^10/(3*x^3)","B",1
149,1,128,76,0.0082989,"\int \frac{(a+b x)^{10}}{x^{15}} \, dx","Integrate[(a + b*x)^10/x^15,x]","-\frac{a^{10}}{14 x^{14}}-\frac{10 a^9 b}{13 x^{13}}-\frac{15 a^8 b^2}{4 x^{12}}-\frac{120 a^7 b^3}{11 x^{11}}-\frac{21 a^6 b^4}{x^{10}}-\frac{28 a^5 b^5}{x^9}-\frac{105 a^4 b^6}{4 x^8}-\frac{120 a^3 b^7}{7 x^7}-\frac{15 a^2 b^8}{2 x^6}-\frac{2 a b^9}{x^5}-\frac{b^{10}}{4 x^4}","\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,"-1/14*a^10/x^14 - (10*a^9*b)/(13*x^13) - (15*a^8*b^2)/(4*x^12) - (120*a^7*b^3)/(11*x^11) - (21*a^6*b^4)/x^10 - (28*a^5*b^5)/x^9 - (105*a^4*b^6)/(4*x^8) - (120*a^3*b^7)/(7*x^7) - (15*a^2*b^8)/(2*x^6) - (2*a*b^9)/x^5 - b^10/(4*x^4)","A",1
150,1,130,96,0.009736,"\int \frac{(a+b x)^{10}}{x^{16}} \, dx","Integrate[(a + b*x)^10/x^16,x]","-\frac{a^{10}}{15 x^{15}}-\frac{5 a^9 b}{7 x^{14}}-\frac{45 a^8 b^2}{13 x^{13}}-\frac{10 a^7 b^3}{x^{12}}-\frac{210 a^6 b^4}{11 x^{11}}-\frac{126 a^5 b^5}{5 x^{10}}-\frac{70 a^4 b^6}{3 x^9}-\frac{15 a^3 b^7}{x^8}-\frac{45 a^2 b^8}{7 x^7}-\frac{5 a b^9}{3 x^6}-\frac{b^{10}}{5 x^5}","-\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,"-1/15*a^10/x^15 - (5*a^9*b)/(7*x^14) - (45*a^8*b^2)/(13*x^13) - (10*a^7*b^3)/x^12 - (210*a^6*b^4)/(11*x^11) - (126*a^5*b^5)/(5*x^10) - (70*a^4*b^6)/(3*x^9) - (15*a^3*b^7)/x^8 - (45*a^2*b^8)/(7*x^7) - (5*a*b^9)/(3*x^6) - b^10/(5*x^5)","A",1
151,1,132,116,0.0049845,"\int \frac{(a+b x)^{10}}{x^{17}} \, dx","Integrate[(a + b*x)^10/x^17,x]","-\frac{a^{10}}{16 x^{16}}-\frac{2 a^9 b}{3 x^{15}}-\frac{45 a^8 b^2}{14 x^{14}}-\frac{120 a^7 b^3}{13 x^{13}}-\frac{35 a^6 b^4}{2 x^{12}}-\frac{252 a^5 b^5}{11 x^{11}}-\frac{21 a^4 b^6}{x^{10}}-\frac{40 a^3 b^7}{3 x^9}-\frac{45 a^2 b^8}{8 x^8}-\frac{10 a b^9}{7 x^7}-\frac{b^{10}}{6 x^6}","\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,"-1/16*a^10/x^16 - (2*a^9*b)/(3*x^15) - (45*a^8*b^2)/(14*x^14) - (120*a^7*b^3)/(13*x^13) - (35*a^6*b^4)/(2*x^12) - (252*a^5*b^5)/(11*x^11) - (21*a^4*b^6)/x^10 - (40*a^3*b^7)/(3*x^9) - (45*a^2*b^8)/(8*x^8) - (10*a*b^9)/(7*x^7) - b^10/(6*x^6)","A",1
152,1,126,136,0.0096938,"\int \frac{(a+b x)^{10}}{x^{18}} \, dx","Integrate[(a + b*x)^10/x^18,x]","-\frac{a^{10}}{17 x^{17}}-\frac{5 a^9 b}{8 x^{16}}-\frac{3 a^8 b^2}{x^{15}}-\frac{60 a^7 b^3}{7 x^{14}}-\frac{210 a^6 b^4}{13 x^{13}}-\frac{21 a^5 b^5}{x^{12}}-\frac{210 a^4 b^6}{11 x^{11}}-\frac{12 a^3 b^7}{x^{10}}-\frac{5 a^2 b^8}{x^9}-\frac{5 a b^9}{4 x^8}-\frac{b^{10}}{7 x^7}","-\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,"-1/17*a^10/x^17 - (5*a^9*b)/(8*x^16) - (3*a^8*b^2)/x^15 - (60*a^7*b^3)/(7*x^14) - (210*a^6*b^4)/(13*x^13) - (21*a^5*b^5)/x^12 - (210*a^4*b^6)/(11*x^11) - (12*a^3*b^7)/x^10 - (5*a^2*b^8)/x^9 - (5*a*b^9)/(4*x^8) - b^10/(7*x^7)","A",1
153,1,130,130,0.0044661,"\int \frac{(a+b x)^{10}}{x^{19}} \, dx","Integrate[(a + b*x)^10/x^19,x]","-\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}","-\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,"-1/18*a^10/x^18 - (10*a^9*b)/(17*x^17) - (45*a^8*b^2)/(16*x^16) - (8*a^7*b^3)/x^15 - (15*a^6*b^4)/x^14 - (252*a^5*b^5)/(13*x^13) - (35*a^4*b^6)/(2*x^12) - (120*a^3*b^7)/(11*x^11) - (9*a^2*b^8)/(2*x^10) - (10*a*b^9)/(9*x^9) - b^10/(8*x^8)","A",1
154,1,126,126,0.0073119,"\int \frac{(a+b x)^{10}}{x^{20}} \, dx","Integrate[(a + b*x)^10/x^20,x]","-\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}","-\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,"-1/19*a^10/x^19 - (5*a^9*b)/(9*x^18) - (45*a^8*b^2)/(17*x^17) - (15*a^7*b^3)/(2*x^16) - (14*a^6*b^4)/x^15 - (18*a^5*b^5)/x^14 - (210*a^4*b^6)/(13*x^13) - (10*a^3*b^7)/x^12 - (45*a^2*b^8)/(11*x^11) - (a*b^9)/x^10 - b^10/(9*x^9)","A",1
155,1,14,15,0.0005293,"\int c (a+b x) \, dx","Integrate[c*(a + b*x),x]","c \left(a x+\frac{b x^2}{2}\right)","\frac{c (a+b x)^2}{2 b}",1,"c*(a*x + (b*x^2)/2)","A",1
156,1,19,20,0.0008865,"\int \frac{(c+d) (a+b x)}{e} \, dx","Integrate[((c + d)*(a + b*x))/e,x]","\frac{(c+d) \left(a x+\frac{b x^2}{2}\right)}{e}","\frac{(c+d) (a+b x)^2}{2 b e}",1,"((c + d)*(a*x + (b*x^2)/2))/e","A",1
157,1,70,70,0.0041649,"\int \frac{x^5}{a+b x} \, dx","Integrate[x^5/(a + b*x),x]","-\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}","-\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,"(a^4*x)/b^5 - (a^3*x^2)/(2*b^4) + (a^2*x^3)/(3*b^3) - (a*x^4)/(4*b^2) + x^5/(5*b) - (a^5*Log[a + b*x])/b^6","A",1
158,1,57,57,0.0041913,"\int \frac{x^4}{a+b x} \, dx","Integrate[x^4/(a + b*x),x]","\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}","\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,"-((a^3*x)/b^4) + (a^2*x^2)/(2*b^3) - (a*x^3)/(3*b^2) + x^4/(4*b) + (a^4*Log[a + b*x])/b^5","A",1
159,1,44,44,0.0035998,"\int \frac{x^3}{a+b x} \, dx","Integrate[x^3/(a + b*x),x]","-\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}","-\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,"(a^2*x)/b^3 - (a*x^2)/(2*b^2) + x^3/(3*b) - (a^3*Log[a + b*x])/b^4","A",1
160,1,31,31,0.0034152,"\int \frac{x^2}{a+b x} \, dx","Integrate[x^2/(a + b*x),x]","\frac{a^2 \log (a+b x)}{b^3}-\frac{a x}{b^2}+\frac{x^2}{2 b}","\frac{a^2 \log (a+b x)}{b^3}-\frac{a x}{b^2}+\frac{x^2}{2 b}",1,"-((a*x)/b^2) + x^2/(2*b) + (a^2*Log[a + b*x])/b^3","A",1
161,1,18,18,0.0026159,"\int \frac{x}{a+b x} \, dx","Integrate[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
162,1,10,10,0.0008375,"\int \frac{1}{a+b x} \, dx","Integrate[(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
163,1,18,18,0.0036886,"\int \frac{1}{x (a+b x)} \, dx","Integrate[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
164,1,28,28,0.004506,"\int \frac{1}{x^2 (a+b x)} \, dx","Integrate[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
165,1,42,42,0.0047011,"\int \frac{1}{x^3 (a+b x)} \, dx","Integrate[1/(x^3*(a + b*x)),x]","\frac{b^2 \log (x)}{a^3}-\frac{b^2 \log (a+b x)}{a^3}+\frac{b}{a^2 x}-\frac{1}{2 a x^2}","\frac{b^2 \log (x)}{a^3}-\frac{b^2 \log (a+b x)}{a^3}+\frac{b}{a^2 x}-\frac{1}{2 a x^2}",1,"-1/2*1/(a*x^2) + b/(a^2*x) + (b^2*Log[x])/a^3 - (b^2*Log[a + b*x])/a^3","A",1
166,1,56,56,0.0051251,"\int \frac{1}{x^4 (a+b x)} \, dx","Integrate[1/(x^4*(a + b*x)),x]","-\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}","-\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,"-1/3*1/(a*x^3) + b/(2*a^2*x^2) - b^2/(a^3*x) - (b^3*Log[x])/a^4 + (b^3*Log[a + b*x])/a^4","A",1
167,1,68,68,0.004784,"\int \frac{1}{x^5 (a+b x)} \, dx","Integrate[1/(x^5*(a + b*x)),x]","\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}","\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,"-1/4*1/(a*x^4) + b/(3*a^2*x^3) - b^2/(2*a^3*x^2) + b^3/(a^4*x) + (b^4*Log[x])/a^5 - (b^4*Log[a + b*x])/a^5","A",1
168,1,77,81,0.0239415,"\int \frac{x^6}{(a+b x)^2} \, dx","Integrate[x^6/(a + b*x)^2,x]","\frac{-\frac{10 a^6}{a+b x}-60 a^5 \log (a+b x)+50 a^4 b x-20 a^3 b^2 x^2+10 a^2 b^3 x^3-5 a b^4 x^4+2 b^5 x^5}{10 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,"(50*a^4*b*x - 20*a^3*b^2*x^2 + 10*a^2*b^3*x^3 - 5*a*b^4*x^4 + 2*b^5*x^5 - (10*a^6)/(a + b*x) - 60*a^5*Log[a + b*x])/(10*b^7)","A",1
169,1,66,72,0.0171044,"\int \frac{x^5}{(a+b x)^2} \, dx","Integrate[x^5/(a + b*x)^2,x]","\frac{\frac{12 a^5}{a+b x}+60 a^4 \log (a+b x)-48 a^3 b x+18 a^2 b^2 x^2-8 a b^3 x^3+3 b^4 x^4}{12 b^6}","\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,"(-48*a^3*b*x + 18*a^2*b^2*x^2 - 8*a*b^3*x^3 + 3*b^4*x^4 + (12*a^5)/(a + b*x) + 60*a^4*Log[a + b*x])/(12*b^6)","A",1
170,1,54,58,0.019075,"\int \frac{x^4}{(a+b x)^2} \, dx","Integrate[x^4/(a + b*x)^2,x]","\frac{-\frac{3 a^4}{a+b x}-12 a^3 \log (a+b x)+9 a^2 b x-3 a b^2 x^2+b^3 x^3}{3 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,"(9*a^2*b*x - 3*a*b^2*x^2 + b^3*x^3 - (3*a^4)/(a + b*x) - 12*a^3*Log[a + b*x])/(3*b^5)","A",1
171,1,43,46,0.0134885,"\int \frac{x^3}{(a+b x)^2} \, dx","Integrate[x^3/(a + b*x)^2,x]","\frac{\frac{2 a^3}{a+b x}+6 a^2 \log (a+b x)-4 a b x+b^2 x^2}{2 b^4}","\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,"(-4*a*b*x + b^2*x^2 + (2*a^3)/(a + b*x) + 6*a^2*Log[a + b*x])/(2*b^4)","A",1
172,1,29,33,0.0127894,"\int \frac{x^2}{(a+b x)^2} \, dx","Integrate[x^2/(a + b*x)^2,x]","\frac{-\frac{a^2}{a+b x}-2 a \log (a+b x)+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,"(b*x - a^2/(a + b*x) - 2*a*Log[a + b*x])/b^3","A",1
173,1,20,23,0.0066922,"\int \frac{x}{(a+b x)^2} \, dx","Integrate[x/(a + b*x)^2,x]","\frac{\frac{a}{a+b x}+\log (a+b x)}{b^2}","\frac{a}{b^2 (a+b x)}+\frac{\log (a+b x)}{b^2}",1,"(a/(a + b*x) + Log[a + b*x])/b^2","A",1
174,1,12,12,0.0024213,"\int \frac{1}{(a+b x)^2} \, dx","Integrate[(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
175,1,24,29,0.0119196,"\int \frac{1}{x (a+b x)^2} \, dx","Integrate[1/(x*(a + b*x)^2),x]","\frac{\frac{a}{a+b x}-\log (a+b x)+\log (x)}{a^2}","-\frac{\log (a+b x)}{a^2}+\frac{\log (x)}{a^2}+\frac{1}{a (a+b x)}",1,"(a/(a + b*x) + Log[x] - Log[a + b*x])/a^2","A",1
176,1,35,42,0.0393212,"\int \frac{1}{x^2 (a+b x)^2} \, dx","Integrate[1/(x^2*(a + b*x)^2),x]","-\frac{a \left(\frac{b}{a+b x}+\frac{1}{x}\right)-2 b \log (a+b x)+2 b \log (x)}{a^3}","-\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*(x^(-1) + b/(a + b*x)) + 2*b*Log[x] - 2*b*Log[a + b*x])/a^3)","A",1
177,1,53,58,0.0500213,"\int \frac{1}{x^3 (a+b x)^2} \, dx","Integrate[1/(x^3*(a + b*x)^2),x]","\frac{a \left(\frac{2 b^2}{a+b x}-\frac{a}{x^2}+\frac{4 b}{x}\right)-6 b^2 \log (a+b x)+6 b^2 \log (x)}{2 a^4}","\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*(-(a/x^2) + (4*b)/x + (2*b^2)/(a + b*x)) + 6*b^2*Log[x] - 6*b^2*Log[a + b*x])/(2*a^4)","A",1
178,1,66,69,0.0557787,"\int \frac{1}{x^4 (a+b x)^2} \, dx","Integrate[1/(x^4*(a + b*x)^2),x]","-\frac{\frac{a \left(a^3-2 a^2 b x+6 a b^2 x^2+12 b^3 x^3\right)}{x^3 (a+b x)}-12 b^3 \log (a+b x)+12 b^3 \log (x)}{3 a^5}","-\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,"-1/3*((a*(a^3 - 2*a^2*b*x + 6*a*b^2*x^2 + 12*b^3*x^3))/(x^3*(a + b*x)) + 12*b^3*Log[x] - 12*b^3*Log[a + b*x])/a^5","A",1
179,1,79,84,0.0425987,"\int \frac{1}{x^5 (a+b x)^2} \, dx","Integrate[1/(x^5*(a + b*x)^2),x]","\frac{\frac{a \left(-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\right)}{x^4 (a+b x)}-60 b^4 \log (a+b x)+60 b^4 \log (x)}{12 a^6}","\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,"((a*(-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))/(x^4*(a + b*x)) + 60*b^4*Log[x] - 60*b^4*Log[a + b*x])/(12*a^6)","A",1
180,1,89,99,0.0271072,"\int \frac{x^7}{(a+b x)^3} \, dx","Integrate[x^7/(a + b*x)^3,x]","\frac{\frac{10 a^7}{(a+b x)^2}-\frac{140 a^6}{a+b x}-420 a^5 \log (a+b x)+300 a^4 b x-100 a^3 b^2 x^2+40 a^2 b^3 x^3-15 a b^4 x^4+4 b^5 x^5}{20 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,"(300*a^4*b*x - 100*a^3*b^2*x^2 + 40*a^2*b^3*x^3 - 15*a*b^4*x^4 + 4*b^5*x^5 + (10*a^7)/(a + b*x)^2 - (140*a^6)/(a + b*x) - 420*a^5*Log[a + b*x])/(20*b^8)","A",1
181,1,77,86,0.0248623,"\int \frac{x^6}{(a+b x)^3} \, dx","Integrate[x^6/(a + b*x)^3,x]","\frac{-\frac{2 a^6}{(a+b x)^2}+\frac{24 a^5}{a+b x}+60 a^4 \log (a+b x)-40 a^3 b x+12 a^2 b^2 x^2-4 a b^3 x^3+b^4 x^4}{4 b^7}","-\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,"(-40*a^3*b*x + 12*a^2*b^2*x^2 - 4*a*b^3*x^3 + b^4*x^4 - (2*a^6)/(a + b*x)^2 + (24*a^5)/(a + b*x) + 60*a^4*Log[a + b*x])/(4*b^7)","A",1
182,1,67,77,0.0227647,"\int \frac{x^5}{(a+b x)^3} \, dx","Integrate[x^5/(a + b*x)^3,x]","\frac{\frac{3 a^5}{(a+b x)^2}-\frac{30 a^4}{a+b x}-60 a^3 \log (a+b x)+36 a^2 b x-9 a b^2 x^2+2 b^3 x^3}{6 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,"(36*a^2*b*x - 9*a*b^2*x^2 + 2*b^3*x^3 + (3*a^5)/(a + b*x)^2 - (30*a^4)/(a + b*x) - 60*a^3*Log[a + b*x])/(6*b^6)","A",1
183,1,55,64,0.0182302,"\int \frac{x^4}{(a+b x)^3} \, dx","Integrate[x^4/(a + b*x)^3,x]","\frac{-\frac{a^4}{(a+b x)^2}+\frac{8 a^3}{a+b x}+12 a^2 \log (a+b x)-6 a b x+b^2 x^2}{2 b^5}","-\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,"(-6*a*b*x + b^2*x^2 - a^4/(a + b*x)^2 + (8*a^3)/(a + b*x) + 12*a^2*Log[a + b*x])/(2*b^5)","A",1
184,1,40,50,0.0398677,"\int \frac{x^3}{(a+b x)^3} \, dx","Integrate[x^3/(a + b*x)^3,x]","-\frac{\frac{a^2 (5 a+6 b x)}{(a+b x)^2}+6 a \log (a+b x)-2 b x}{2 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,"-1/2*(-2*b*x + (a^2*(5*a + 6*b*x))/(a + b*x)^2 + 6*a*Log[a + b*x])/b^4","A",1
185,1,33,41,0.0129064,"\int \frac{x^2}{(a+b x)^3} \, dx","Integrate[x^2/(a + b*x)^3,x]","\frac{\frac{a (3 a+4 b x)}{(a+b x)^2}+2 \log (a+b x)}{2 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))/(a + b*x)^2 + 2*Log[a + b*x])/(2*b^3)","A",1
186,1,20,17,0.0051311,"\int \frac{x}{(a+b x)^3} \, dx","Integrate[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,"-1/2*(a + 2*b*x)/(b^2*(a + b*x)^2)","A",1
187,1,14,14,0.0023744,"\int \frac{1}{(a+b x)^3} \, dx","Integrate[(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
188,1,37,43,0.0291278,"\int \frac{1}{x (a+b x)^3} \, dx","Integrate[1/(x*(a + b*x)^3),x]","\frac{\frac{a (3 a+2 b x)}{(a+b x)^2}-2 \log (a+b x)+2 \log (x)}{2 a^3}","-\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,"((a*(3*a + 2*b*x))/(a + b*x)^2 + 2*Log[x] - 2*Log[a + b*x])/(2*a^3)","A",1
189,1,53,57,0.0492933,"\int \frac{1}{x^2 (a+b x)^3} \, dx","Integrate[1/(x^2*(a + b*x)^3),x]","-\frac{\frac{a \left(2 a^2+9 a b x+6 b^2 x^2\right)}{x (a+b x)^2}-6 b \log (a+b x)+6 b \log (x)}{2 a^4}","-\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,"-1/2*((a*(2*a^2 + 9*a*b*x + 6*b^2*x^2))/(x*(a + b*x)^2) + 6*b*Log[x] - 6*b*Log[a + b*x])/a^4","A",1
190,1,68,76,0.0520541,"\int \frac{1}{x^3 (a+b x)^3} \, dx","Integrate[1/(x^3*(a + b*x)^3),x]","\frac{\frac{a \left(-a^3+4 a^2 b x+18 a b^2 x^2+12 b^3 x^3\right)}{x^2 (a+b x)^2}-12 b^2 \log (a+b x)+12 b^2 \log (x)}{2 a^5}","\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*(-a^3 + 4*a^2*b*x + 18*a*b^2*x^2 + 12*b^3*x^3))/(x^2*(a + b*x)^2) + 12*b^2*Log[x] - 12*b^2*Log[a + b*x])/(2*a^5)","A",1
191,1,79,89,0.0679354,"\int \frac{1}{x^4 (a+b x)^3} \, dx","Integrate[1/(x^4*(a + b*x)^3),x]","-\frac{\frac{a \left(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\right)}{x^3 (a+b x)^2}-60 b^3 \log (a+b x)+60 b^3 \log (x)}{6 a^6}","-\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,"-1/6*((a*(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))/(x^3*(a + b*x)^2) + 60*b^3*Log[x] - 60*b^3*Log[a + b*x])/a^6","A",1
192,1,90,97,0.0566541,"\int \frac{1}{x^5 (a+b x)^3} \, dx","Integrate[1/(x^5*(a + b*x)^3),x]","\frac{\frac{a \left(-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\right)}{x^4 (a+b x)^2}-60 b^4 \log (a+b x)+60 b^4 \log (x)}{4 a^7}","\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*(-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))/(x^4*(a + b*x)^2) + 60*b^4*Log[x] - 60*b^4*Log[a + b*x])/(4*a^7)","A",1
193,1,101,114,0.0356672,"\int \frac{x^8}{(a+b x)^4} \, dx","Integrate[x^8/(a + b*x)^4,x]","\frac{-\frac{5 a^8}{(a+b x)^3}+\frac{60 a^7}{(a+b x)^2}-\frac{420 a^6}{a+b x}-840 a^5 \log (a+b x)+525 a^4 b x-150 a^3 b^2 x^2+50 a^2 b^3 x^3-15 a b^4 x^4+3 b^5 x^5}{15 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,"(525*a^4*b*x - 150*a^3*b^2*x^2 + 50*a^2*b^3*x^3 - 15*a*b^4*x^4 + 3*b^5*x^5 - (5*a^8)/(a + b*x)^3 + (60*a^7)/(a + b*x)^2 - (420*a^6)/(a + b*x) - 840*a^5*Log[a + b*x])/(15*b^9)","A",1
194,1,90,105,0.0284524,"\int \frac{x^7}{(a+b x)^4} \, dx","Integrate[x^7/(a + b*x)^4,x]","\frac{\frac{4 a^7}{(a+b x)^3}-\frac{42 a^6}{(a+b x)^2}+\frac{252 a^5}{a+b x}+420 a^4 \log (a+b x)-240 a^3 b x+60 a^2 b^2 x^2-16 a b^3 x^3+3 b^4 x^4}{12 b^8}","\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,"(-240*a^3*b*x + 60*a^2*b^2*x^2 - 16*a*b^3*x^3 + 3*b^4*x^4 + (4*a^7)/(a + b*x)^3 - (42*a^6)/(a + b*x)^2 + (252*a^5)/(a + b*x) + 420*a^4*Log[a + b*x])/(12*b^8)","A",1
195,1,90,90,0.0221666,"\int \frac{x^6}{(a+b x)^4} \, dx","Integrate[x^6/(a + b*x)^4,x]","-\frac{a^6}{3 b^7 (a+b x)^3}+\frac{3 a^5}{b^7 (a+b x)^2}-\frac{15 a^4}{b^7 (a+b x)}-\frac{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}","-\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,"(10*a^2*x)/b^6 - (2*a*x^2)/b^5 + x^3/(3*b^4) - a^6/(3*b^7*(a + b*x)^3) + (3*a^5)/(b^7*(a + b*x)^2) - (15*a^4)/(b^7*(a + b*x)) - (20*a^3*Log[a + b*x])/b^7","A",1
196,1,68,81,0.0243495,"\int \frac{x^5}{(a+b x)^4} \, dx","Integrate[x^5/(a + b*x)^4,x]","\frac{\frac{2 a^5}{(a+b x)^3}-\frac{15 a^4}{(a+b x)^2}+\frac{60 a^3}{a+b x}+60 a^2 \log (a+b x)-24 a b x+3 b^2 x^2}{6 b^6}","\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,"(-24*a*b*x + 3*b^2*x^2 + (2*a^5)/(a + b*x)^3 - (15*a^4)/(a + b*x)^2 + (60*a^3)/(a + b*x) + 60*a^2*Log[a + b*x])/(6*b^6)","A",1
197,1,51,65,0.045383,"\int \frac{x^4}{(a+b x)^4} \, dx","Integrate[x^4/(a + b*x)^4,x]","-\frac{\frac{a^2 \left(13 a^2+30 a b x+18 b^2 x^2\right)}{(a+b x)^3}+12 a \log (a+b x)-3 b x}{3 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,"-1/3*(-3*b*x + (a^2*(13*a^2 + 30*a*b*x + 18*b^2*x^2))/(a + b*x)^3 + 12*a*Log[a + b*x])/b^5","A",1
198,1,44,58,0.0156978,"\int \frac{x^3}{(a+b x)^4} \, dx","Integrate[x^3/(a + b*x)^4,x]","\frac{\frac{a \left(11 a^2+27 a b x+18 b^2 x^2\right)}{(a+b x)^3}+6 \log (a+b x)}{6 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))/(a + b*x)^3 + 6*Log[a + b*x])/(6*b^4)","A",1
199,1,31,17,0.0107383,"\int \frac{x^2}{(a+b x)^4} \, dx","Integrate[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,"-1/3*(a^2 + 3*a*b*x + 3*b^2*x^2)/(b^3*(a + b*x)^3)","A",1
200,1,20,30,0.0051489,"\int \frac{x}{(a+b x)^4} \, dx","Integrate[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,"-1/6*(a + 3*b*x)/(b^2*(a + b*x)^3)","A",1
201,1,14,14,0.0026704,"\int \frac{1}{(a+b x)^4} \, dx","Integrate[(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
202,1,48,57,0.0335966,"\int \frac{1}{x (a+b x)^4} \, dx","Integrate[1/(x*(a + b*x)^4),x]","\frac{\frac{a \left(11 a^2+15 a b x+6 b^2 x^2\right)}{(a+b x)^3}-6 \log (a+b x)+6 \log (x)}{6 a^4}","-\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,"((a*(11*a^2 + 15*a*b*x + 6*b^2*x^2))/(a + b*x)^3 + 6*Log[x] - 6*Log[a + b*x])/(6*a^4)","A",1
203,1,64,70,0.0594616,"\int \frac{1}{x^2 (a+b x)^4} \, dx","Integrate[1/(x^2*(a + b*x)^4),x]","-\frac{\frac{a \left(3 a^3+22 a^2 b x+30 a b^2 x^2+12 b^3 x^3\right)}{x (a+b x)^3}-12 b \log (a+b x)+12 b \log (x)}{3 a^5}","-\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,"-1/3*((a*(3*a^3 + 22*a^2*b*x + 30*a*b^2*x^2 + 12*b^3*x^3))/(x*(a + b*x)^3) + 12*b*Log[x] - 12*b*Log[a + b*x])/a^5","A",1
204,1,79,93,0.0566851,"\int \frac{1}{x^3 (a+b x)^4} \, dx","Integrate[1/(x^3*(a + b*x)^4),x]","\frac{\frac{a \left(-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\right)}{x^2 (a+b x)^3}-60 b^2 \log (a+b x)+60 b^2 \log (x)}{6 a^6}","\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,"((a*(-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))/(x^2*(a + b*x)^3) + 60*b^2*Log[x] - 60*b^2*Log[a + b*x])/(6*a^6)","A",1
205,1,88,102,0.0554039,"\int \frac{1}{x^4 (a+b x)^4} \, dx","Integrate[1/(x^4*(a + b*x)^4),x]","-\frac{\frac{a \left(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\right)}{x^3 (a+b x)^3}-60 b^3 \log (a+b x)+60 b^3 \log (x)}{3 a^7}","-\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,"-1/3*((a*(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))/(x^3*(a + b*x)^3) + 60*b^3*Log[x] - 60*b^3*Log[a + b*x])/a^7","A",1
206,1,101,117,0.0675303,"\int \frac{1}{x^5 (a+b x)^4} \, dx","Integrate[1/(x^5*(a + b*x)^4),x]","\frac{\frac{a \left(-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\right)}{x^4 (a+b x)^3}-420 b^4 \log (a+b x)+420 b^4 \log (x)}{12 a^8}","\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,"((a*(-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))/(x^4*(a + b*x)^3) + 420*b^4*Log[x] - 420*b^4*Log[a + b*x])/(12*a^8)","A",1
207,1,139,150,0.0271521,"\int \frac{x^{10}}{(a+b x)^7} \, dx","Integrate[x^10/(a + b*x)^7,x]","\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+2520 a^4 (a+b x)^6 \log (a+b x)-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 + 2520*a^4*(a + b*x)^6*Log[a + b*x])/(12*b^11*(a + b*x)^6)","A",1
208,1,128,139,0.0316717,"\int \frac{x^9}{(a+b x)^7} \, dx","Integrate[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+2520 a^3 (a+b x)^6 \log (a+b x)-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{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,"-1/30*(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 + 2520*a^3*(a + b*x)^6*Log[a + b*x])/(b^10*(a + b*x)^6)","A",1
209,1,104,128,0.0477831,"\int \frac{x^8}{(a+b x)^7} \, dx","Integrate[x^8/(a + b*x)^7,x]","\frac{-\frac{5 a^8}{(a+b x)^6}+\frac{48 a^7}{(a+b x)^5}-\frac{210 a^6}{(a+b x)^4}+\frac{560 a^5}{(a+b x)^3}-\frac{1050 a^4}{(a+b x)^2}+\frac{1680 a^3}{a+b x}+840 a^2 \log (a+b x)-210 a b x+15 b^2 x^2}{30 b^9}","-\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,"(-210*a*b*x + 15*b^2*x^2 - (5*a^8)/(a + b*x)^6 + (48*a^7)/(a + b*x)^5 - (210*a^6)/(a + b*x)^4 + (560*a^5)/(a + b*x)^3 - (1050*a^4)/(a + b*x)^2 + (1680*a^3)/(a + b*x) + 840*a^2*Log[a + b*x])/(30*b^9)","A",1
210,1,104,118,0.0287051,"\int \frac{x^7}{(a+b x)^7} \, dx","Integrate[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+420 a (a+b x)^6 \log (a+b x)-60 b^7 x^7}{60 b^8 (a+b x)^6}","\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,"-1/60*(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 + 420*a*(a + b*x)^6*Log[a + b*x])/(b^8*(a + b*x)^6)","A",1
211,1,77,109,0.0237485,"\int \frac{x^6}{(a+b x)^7} \, dx","Integrate[x^6/(a + b*x)^7,x]","\frac{\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)}{(a+b x)^6}+60 \log (a+b x)}{60 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))/(a + b*x)^6 + 60*Log[a + b*x])/(60*b^7)","A",1
212,1,64,17,0.0112423,"\int \frac{x^5}{(a+b x)^7} \, dx","Integrate[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,"-1/6*(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)/(b^6*(a + b*x)^6)","B",1
213,1,53,35,0.0099913,"\int \frac{x^4}{(a+b x)^7} \, dx","Integrate[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,"-1/30*(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)/(b^5*(a + b*x)^6)","A",1
214,1,42,52,0.0097022,"\int \frac{x^3}{(a+b x)^7} \, dx","Integrate[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,"-1/60*(a^3 + 6*a^2*b*x + 15*a*b^2*x^2 + 20*b^3*x^3)/(b^4*(a + b*x)^6)","A",1
215,1,31,47,0.0082222,"\int \frac{x^2}{(a+b x)^7} \, dx","Integrate[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,"-1/60*(a^2 + 6*a*b*x + 15*b^2*x^2)/(b^3*(a + b*x)^6)","A",1
216,1,20,30,0.0058989,"\int \frac{x}{(a+b x)^7} \, dx","Integrate[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,"-1/30*(a + 6*b*x)/(b^2*(a + b*x)^6)","A",1
217,1,14,14,0.0034647,"\int \frac{1}{(a+b x)^7} \, dx","Integrate[(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
218,1,81,99,0.0630532,"\int \frac{1}{x (a+b x)^7} \, dx","Integrate[1/(x*(a + b*x)^7),x]","\frac{\frac{a \left(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\right)}{(a+b x)^6}-60 \log (a+b x)+60 \log (x)}{60 a^7}","-\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,"((a*(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))/(a + b*x)^6 + 60*Log[x] - 60*Log[a + b*x])/(60*a^7)","A",1
219,1,97,117,0.093673,"\int \frac{1}{x^2 (a+b x)^7} \, dx","Integrate[1/(x^2*(a + b*x)^7),x]","-\frac{\frac{a \left(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\right)}{x (a+b x)^6}-420 b \log (a+b x)+420 b \log (x)}{60 a^8}","-\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,"-1/60*((a*(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))/(x*(a + b*x)^6) + 420*b*Log[x] - 420*b*Log[a + b*x])/a^8","A",1
220,1,112,144,0.0731245,"\int \frac{1}{x^3 (a+b x)^7} \, dx","Integrate[1/(x^3*(a + b*x)^7),x]","\frac{\frac{a \left(-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\right)}{x^2 (a+b x)^6}-840 b^2 \log (a+b x)+840 b^2 \log (x)}{30 a^9}","\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,"((a*(-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))/(x^2*(a + b*x)^6) + 840*b^2*Log[x] - 840*b^2*Log[a + b*x])/(30*a^9)","A",1
221,1,123,157,0.0920202,"\int \frac{1}{x^4 (a+b x)^7} \, dx","Integrate[1/(x^4*(a + b*x)^7),x]","-\frac{\frac{a \left(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\right)}{x^3 (a+b x)^6}-2520 b^3 \log (a+b x)+2520 b^3 \log (x)}{30 a^{10}}","-\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,"-1/30*((a*(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))/(x^3*(a + b*x)^6) + 2520*b^3*Log[x] - 2520*b^3*Log[a + b*x])/a^10","A",1
222,1,161,186,0.0466669,"\int \frac{x^{12}}{(a+b x)^{10}} \, dx","Integrate[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+27720 a^3 (a+b x)^9 \log (a+b x)-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{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,"-1/126*(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 + 27720*a^3*(a + b*x)^9*Log[a + b*x])/(b^13*(a + b*x)^9)","A",1
223,1,150,177,0.0286129,"\int \frac{x^{11}}{(a+b x)^{10}} \, dx","Integrate[x^11/(a + b*x)^10,x]","\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+27720 a^2 (a+b x)^9 \log (a+b x)-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 + 27720*a^2*(a + b*x)^9*Log[a + b*x])/(504*b^12*(a + b*x)^9)","A",1
224,1,137,159,0.0330487,"\int \frac{x^{10}}{(a+b x)^{10}} \, dx","Integrate[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+2520 a (a+b x)^9 \log (a+b x)-252 b^{10} x^{10}}{252 b^{11} (a+b x)^9}","-\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,"-1/252*(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 + 2520*a*(a + b*x)^9*Log[a + b*x])/(b^11*(a + b*x)^9)","A",1
225,1,111,154,0.0339059,"\int \frac{x^9}{(a+b x)^{10}} \, dx","Integrate[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
226,1,97,17,0.0182656,"\int \frac{x^8}{(a+b x)^{10}} \, dx","Integrate[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,"-1/9*(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)/(b^9*(a + b*x)^9)","B",1
227,1,86,35,0.0144581,"\int \frac{x^7}{(a+b x)^{10}} \, dx","Integrate[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,"-1/72*(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)/(b^8*(a + b*x)^9)","B",1
228,1,75,52,0.0158255,"\int \frac{x^6}{(a+b x)^{10}} \, dx","Integrate[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,"-1/252*(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)/(b^7*(a + b*x)^9)","A",1
229,1,64,69,0.0146855,"\int \frac{x^5}{(a+b x)^{10}} \, dx","Integrate[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,"-1/504*(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)/(b^6*(a + b*x)^9)","A",1
230,1,53,81,0.0149552,"\int \frac{x^4}{(a+b x)^{10}} \, dx","Integrate[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,"-1/630*(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)/(b^5*(a + b*x)^9)","A",1
231,1,42,64,0.0097979,"\int \frac{x^3}{(a+b x)^{10}} \, dx","Integrate[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,"-1/504*(a^3 + 9*a^2*b*x + 36*a*b^2*x^2 + 84*b^3*x^3)/(b^4*(a + b*x)^9)","A",1
232,1,31,47,0.011133,"\int \frac{x^2}{(a+b x)^{10}} \, dx","Integrate[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,"-1/252*(a^2 + 9*a*b*x + 36*b^2*x^2)/(b^3*(a + b*x)^9)","A",1
233,1,20,30,0.0056399,"\int \frac{x}{(a+b x)^{10}} \, dx","Integrate[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,"-1/72*(a + 9*b*x)/(b^2*(a + b*x)^9)","A",1
234,1,14,14,0.0029859,"\int \frac{1}{(a+b x)^{10}} \, dx","Integrate[(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
235,1,127,141,0.1020792,"\int \frac{1}{x (a+b x)^{10}} \, dx","Integrate[1/(x*(a + b*x)^10),x]","-\frac{\log (a+b x)}{a^{10}}+\frac{\log (x)}{a^{10}}+\frac{280 a^8+315 a^7 (a+b x)+360 a^6 (a+b x)^2+420 a^5 (a+b x)^3+504 a^4 (a+b x)^4+630 a^3 (a+b x)^5+840 a^2 (a+b x)^6+1260 a (a+b x)^7+2520 (a+b 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,"(280*a^8 + 315*a^7*(a + b*x) + 360*a^6*(a + b*x)^2 + 420*a^5*(a + b*x)^3 + 504*a^4*(a + b*x)^4 + 630*a^3*(a + b*x)^5 + 840*a^2*(a + b*x)^6 + 1260*a*(a + b*x)^7 + 2520*(a + b*x)^8)/(2520*a^9*(a + b*x)^9) + Log[x]/a^10 - Log[a + b*x]/a^10","A",1
236,1,130,158,0.1266303,"\int \frac{1}{x^2 (a+b x)^{10}} \, dx","Integrate[1/(x^2*(a + b*x)^10),x]","-\frac{\frac{a \left(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\right)}{x (a+b x)^9}-2520 b \log (a+b x)+2520 b \log (x)}{252 a^{11}}","-\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,"-1/252*((a*(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))/(x*(a + b*x)^9) + 2520*b*Log[x] - 2520*b*Log[a + b*x])/a^11","A",1
237,1,145,191,0.1109928,"\int \frac{1}{x^3 (a+b x)^{10}} \, dx","Integrate[1/(x^3*(a + b*x)^10),x]","\frac{\frac{a \left(-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}\right)}{x^2 (a+b x)^9}-27720 b^2 \log (a+b x)+27720 b^2 \log (x)}{504 a^{12}}","\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,"((a*(-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))/(x^2*(a + b*x)^9) + 27720*b^2*Log[x] - 27720*b^2*Log[a + b*x])/(504*a^12)","A",1
238,1,156,198,0.1244298,"\int \frac{1}{x^4 (a+b x)^{10}} \, dx","Integrate[1/(x^4*(a + b*x)^10),x]","-\frac{-27720 b^3 \log (a+b x)+\frac{a \left(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}\right)}{x^3 (a+b x)^9}+27720 b^3 \log (x)}{126 a^{13}}","-\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,"-1/126*((a*(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))/(x^3*(a + b*x)^9) + 27720*b^3*Log[x] - 27720*b^3*Log[a + b*x])/a^13","A",1
239,1,141,141,0.0107342,"\int \frac{(a+b x)^{12}}{x^{10}} \, dx","Integrate[(a + b*x)^12/x^10,x]","-\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}","-\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,"-1/9*a^12/x^9 - (3*a^11*b)/(2*x^8) - (66*a^10*b^2)/(7*x^7) - (110*a^9*b^3)/(3*x^6) - (99*a^8*b^4)/x^5 - (198*a^7*b^5)/x^4 - (308*a^6*b^6)/x^3 - (396*a^5*b^7)/x^2 - (495*a^4*b^8)/x + 66*a^2*b^10*x + 6*a*b^11*x^2 + (b^12*x^3)/3 + 220*a^3*b^9*Log[x]","A",1
240,1,132,132,0.0053605,"\int \frac{(a+b x)^{11}}{x^{10}} \, dx","Integrate[(a + b*x)^11/x^10,x]","-\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}","-\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,"-1/9*a^11/x^9 - (11*a^10*b)/(8*x^8) - (55*a^9*b^2)/(7*x^7) - (55*a^8*b^3)/(2*x^6) - (66*a^7*b^4)/x^5 - (231*a^6*b^5)/(2*x^4) - (154*a^5*b^6)/x^3 - (165*a^4*b^7)/x^2 - (165*a^3*b^8)/x + 11*a*b^10*x + (b^11*x^2)/2 + 55*a^2*b^9*Log[x]","A",1
241,1,114,114,0.006265,"\int \frac{(a+b x)^{10}}{x^{10}} \, dx","Integrate[(a + b*x)^10/x^10,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","-\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,"-1/9*a^10/x^9 - (5*a^9*b)/(4*x^8) - (45*a^8*b^2)/(7*x^7) - (20*a^7*b^3)/x^6 - (42*a^6*b^4)/x^5 - (63*a^5*b^5)/x^4 - (70*a^4*b^6)/x^3 - (60*a^3*b^7)/x^2 - (45*a^2*b^8)/x + b^10*x + 10*a*b^9*Log[x]","A",1
242,1,109,109,0.0047701,"\int \frac{(a+b x)^9}{x^{10}} \, dx","Integrate[(a + b*x)^9/x^10,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)","-\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,"-1/9*a^9/x^9 - (9*a^8*b)/(8*x^8) - (36*a^7*b^2)/(7*x^7) - (14*a^6*b^3)/x^6 - (126*a^5*b^4)/(5*x^5) - (63*a^4*b^5)/(2*x^4) - (28*a^3*b^6)/x^3 - (18*a^2*b^7)/x^2 - (9*a*b^8)/x + b^9*Log[x]","A",1
243,1,96,17,0.009148,"\int \frac{(a+b x)^8}{x^{10}} \, dx","Integrate[(a + b*x)^8/x^10,x]","-\frac{a^8}{9 x^9}-\frac{a^7 b}{x^8}-\frac{4 a^6 b^2}{x^7}-\frac{28 a^5 b^3}{3 x^6}-\frac{14 a^4 b^4}{x^5}-\frac{14 a^3 b^5}{x^4}-\frac{28 a^2 b^6}{3 x^3}-\frac{4 a b^7}{x^2}-\frac{b^8}{x}","-\frac{(a+b x)^9}{9 a x^9}",1,"-1/9*a^8/x^9 - (a^7*b)/x^8 - (4*a^6*b^2)/x^7 - (28*a^5*b^3)/(3*x^6) - (14*a^4*b^4)/x^5 - (14*a^3*b^5)/x^4 - (28*a^2*b^6)/(3*x^3) - (4*a*b^7)/x^2 - b^8/x","B",1
244,1,91,36,0.0041427,"\int \frac{(a+b x)^7}{x^{10}} \, dx","Integrate[(a + b*x)^7/x^10,x]","-\frac{a^7}{9 x^9}-\frac{7 a^6 b}{8 x^8}-\frac{3 a^5 b^2}{x^7}-\frac{35 a^4 b^3}{6 x^6}-\frac{7 a^3 b^4}{x^5}-\frac{21 a^2 b^5}{4 x^4}-\frac{7 a b^6}{3 x^3}-\frac{b^7}{2 x^2}","\frac{b (a+b x)^8}{72 a^2 x^8}-\frac{(a+b x)^8}{9 a x^9}",1,"-1/9*a^7/x^9 - (7*a^6*b)/(8*x^8) - (3*a^5*b^2)/x^7 - (35*a^4*b^3)/(6*x^6) - (7*a^3*b^4)/x^5 - (21*a^2*b^5)/(4*x^4) - (7*a*b^6)/(3*x^3) - b^7/(2*x^2)","B",1
245,1,80,56,0.0088948,"\int \frac{(a+b x)^6}{x^{10}} \, dx","Integrate[(a + b*x)^6/x^10,x]","-\frac{a^6}{9 x^9}-\frac{3 a^5 b}{4 x^8}-\frac{15 a^4 b^2}{7 x^7}-\frac{10 a^3 b^3}{3 x^6}-\frac{3 a^2 b^4}{x^5}-\frac{3 a b^5}{2 x^4}-\frac{b^6}{3 x^3}","-\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,"-1/9*a^6/x^9 - (3*a^5*b)/(4*x^8) - (15*a^4*b^2)/(7*x^7) - (10*a^3*b^3)/(3*x^6) - (3*a^2*b^4)/x^5 - (3*a*b^5)/(2*x^4) - b^6/(3*x^3)","A",1
246,1,67,67,0.0068936,"\int \frac{(a+b x)^5}{x^{10}} \, dx","Integrate[(a + b*x)^5/x^10,x]","-\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}","-\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,"-1/9*a^5/x^9 - (5*a^4*b)/(8*x^8) - (10*a^3*b^2)/(7*x^7) - (5*a^2*b^3)/(3*x^6) - (a*b^4)/x^5 - b^5/(4*x^4)","A",1
247,1,56,56,0.0078869,"\int \frac{(a+b x)^4}{x^{10}} \, dx","Integrate[(a + b*x)^4/x^10,x]","-\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}","-\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,"-1/9*a^4/x^9 - (a^3*b)/(2*x^8) - (6*a^2*b^2)/(7*x^7) - (2*a*b^3)/(3*x^6) - b^4/(5*x^5)","A",1
248,1,43,43,0.0035632,"\int \frac{(a+b x)^3}{x^{10}} \, dx","Integrate[(a + b*x)^3/x^10,x]","-\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}","-\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,"-1/9*a^3/x^9 - (3*a^2*b)/(8*x^8) - (3*a*b^2)/(7*x^7) - b^3/(6*x^6)","A",1
249,1,30,30,0.0069914,"\int \frac{(a+b x)^2}{x^{10}} \, dx","Integrate[(a + b*x)^2/x^10,x]","-\frac{a^2}{9 x^9}-\frac{a b}{4 x^8}-\frac{b^2}{7 x^7}","-\frac{a^2}{9 x^9}-\frac{a b}{4 x^8}-\frac{b^2}{7 x^7}",1,"-1/9*a^2/x^9 - (a*b)/(4*x^8) - b^2/(7*x^7)","A",1
250,1,17,17,0.0019244,"\int \frac{a+b x}{x^{10}} \, dx","Integrate[(a + b*x)/x^10,x]","-\frac{a}{9 x^9}-\frac{b}{8 x^8}","-\frac{a}{9 x^9}-\frac{b}{8 x^8}",1,"-1/9*a/x^9 - b/(8*x^8)","A",1
251,1,7,7,0.0001508,"\int \frac{1}{x^{10}} \, dx","Integrate[x^(-10),x]","-\frac{1}{9 x^9}","-\frac{1}{9 x^9}",1,"-1/9*1/x^9","A",1
252,1,134,134,0.0062465,"\int \frac{1}{x^{10} (a+b x)} \, dx","Integrate[1/(x^10*(a + b*x)),x]","-\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}","-\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,"-1/9*1/(a*x^9) + b/(8*a^2*x^8) - b^2/(7*a^3*x^7) + b^3/(6*a^4*x^6) - b^4/(5*a^5*x^5) + b^5/(4*a^6*x^4) - b^6/(3*a^7*x^3) + b^7/(2*a^8*x^2) - b^8/(a^9*x) - (b^9*Log[x])/a^10 + (b^9*Log[a + b*x])/a^10","A",1
253,1,134,146,0.0943084,"\int \frac{1}{x^{10} (a+b x)^2} \, dx","Integrate[1/(x^10*(a + b*x)^2),x]","-\frac{\frac{a \left(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\right)}{x^9 (a+b x)}-2520 b^9 \log (a+b x)+2520 b^9 \log (x)}{252 a^{11}}","-\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,"-1/252*((a*(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))/(x^9*(a + b*x)) + 2520*b^9*Log[x] - 2520*b^9*Log[a + b*x])/a^11","A",1
254,1,145,163,0.1076934,"\int \frac{1}{x^{10} (a+b x)^3} \, dx","Integrate[1/(x^10*(a + b*x)^3),x]","-\frac{\frac{a \left(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}\right)}{x^9 (a+b x)^2}-27720 b^9 \log (a+b x)+27720 b^9 \log (x)}{504 a^{12}}","-\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,"-1/504*((a*(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))/(x^9*(a + b*x)^2) + 27720*b^9*Log[x] - 27720*b^9*Log[a + b*x])/a^12","A",1
255,1,17,17,0.0027151,"\int \frac{1}{x (2+3 x)} \, dx","Integrate[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
256,1,17,17,0.0028101,"\int \frac{1}{x (4+6 x)} \, dx","Integrate[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
257,1,24,24,0.0028081,"\int \frac{1}{x^2 (4+6 x)} \, dx","Integrate[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
258,1,31,31,0.0026587,"\int \frac{1}{x^3 (4+6 x)} \, dx","Integrate[1/(x^3*(4 + 6*x)),x]","-\frac{1}{8 x^2}+\frac{3}{8 x}+\frac{9 \log (x)}{16}-\frac{9}{16} \log (3 x+2)","-\frac{1}{8 x^2}+\frac{3}{8 x}+\frac{9 \log (x)}{16}-\frac{9}{16} \log (3 x+2)",1,"-1/8*1/x^2 + 3/(8*x) + (9*Log[x])/16 - (9*Log[2 + 3*x])/16","A",1
259,1,38,38,0.0029649,"\int \frac{1}{x^4 (4+6 x)} \, dx","Integrate[1/(x^4*(4 + 6*x)),x]","-\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)","-\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,"-1/12*1/x^3 + 3/(16*x^2) - 9/(16*x) - (27*Log[x])/32 + (27*Log[2 + 3*x])/32","A",1
260,1,45,45,0.0026972,"\int \frac{1}{x^5 (4+6 x)} \, dx","Integrate[1/(x^5*(4 + 6*x)),x]","-\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)","-\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,"-1/16*1/x^4 + 1/(8*x^3) - 9/(32*x^2) + 27/(32*x) + (81*Log[x])/64 - (81*Log[2 + 3*x])/64","A",1
261,1,26,28,0.0133536,"\int \frac{1}{x (4+6 x)^2} \, dx","Integrate[1/(x*(4 + 6*x)^2),x]","\frac{1}{16} \left(\frac{2}{3 x+2}+\log (-6 x)-\log (6 x+4)\right)","\frac{1}{8 (3 x+2)}+\frac{\log (x)}{16}-\frac{1}{16} \log (3 x+2)",1,"(2/(2 + 3*x) + Log[-6*x] - Log[4 + 6*x])/16","A",1
262,1,31,35,0.0134865,"\int \frac{1}{x^2 (4+6 x)^2} \, dx","Integrate[1/(x^2*(4 + 6*x)^2),x]","\frac{1}{16} \left(-\frac{1}{x}-\frac{3}{3 x+2}-3 \log (x)+3 \log (3 x+2)\right)","-\frac{1}{16 x}-\frac{3}{16 (3 x+2)}-\frac{3 \log (x)}{16}+\frac{3}{16} \log (3 x+2)",1,"(-x^(-1) - 3/(2 + 3*x) - 3*Log[x] + 3*Log[2 + 3*x])/16","A",1
263,1,36,42,0.0130353,"\int \frac{1}{x^3 (4+6 x)^2} \, dx","Integrate[1/(x^3*(4 + 6*x)^2),x]","\frac{1}{64} \left(-\frac{2}{x^2}+\frac{12}{x}+\frac{18}{3 x+2}+27 \log (x)-27 \log (3 x+2)\right)","-\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/x^2 + 12/x + 18/(2 + 3*x) + 27*Log[x] - 27*Log[2 + 3*x])/64","A",1
264,1,44,49,0.0302089,"\int \frac{1}{x^4 (4+6 x)^2} \, dx","Integrate[1/(x^4*(4 + 6*x)^2),x]","\frac{1}{192} \left(-\frac{4 \left(81 x^3+27 x^2-6 x+2\right)}{x^3 (3 x+2)}-162 \log (x)+162 \log (3 x+2)\right)","-\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,"((-4*(2 - 6*x + 27*x^2 + 81*x^3))/(x^3*(2 + 3*x)) - 162*Log[x] + 162*Log[2 + 3*x])/192","A",1
265,1,56,56,0.0099605,"\int \frac{1}{x^5 (4+6 x)^2} \, dx","Integrate[1/(x^5*(4 + 6*x)^2),x]","-\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)","-\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,"-1/64*1/x^4 + 1/(16*x^3) - 27/(128*x^2) + 27/(32*x) + 81/(128*(2 + 3*x)) + (405*Log[x])/256 - (405*Log[2 + 3*x])/256","A",1
266,1,29,39,0.0199476,"\int \frac{1}{x (4+6 x)^3} \, dx","Integrate[1/(x*(4 + 6*x)^3),x]","\frac{1}{64} \left(\frac{6 (x+1)}{(3 x+2)^2}+\log (-6 x)-\log (6 x+4)\right)","\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,"((6*(1 + x))/(2 + 3*x)^2 + Log[-6*x] - Log[4 + 6*x])/64","A",1
267,1,39,46,0.0206838,"\int \frac{1}{x^2 (4+6 x)^3} \, dx","Integrate[1/(x^2*(4 + 6*x)^3),x]","\frac{1}{128} \left(-\frac{2 \left(27 x^2+27 x+4\right)}{x (3 x+2)^2}-9 \log (x)+9 \log (3 x+2)\right)","-\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,"((-2*(4 + 27*x + 27*x^2))/(x*(2 + 3*x)^2) - 9*Log[x] + 9*Log[2 + 3*x])/128","A",1
268,1,44,53,0.024557,"\int \frac{1}{x^3 (4+6 x)^3} \, dx","Integrate[1/(x^3*(4 + 6*x)^3),x]","\frac{1}{128} \left(\frac{2 \left(81 x^3+81 x^2+12 x-2\right)}{x^2 (3 x+2)^2}+27 \log (x)-27 \log (3 x+2)\right)","-\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*(-2 + 12*x + 81*x^2 + 81*x^3))/(x^2*(2 + 3*x)^2) + 27*Log[x] - 27*Log[2 + 3*x])/128","A",1
269,1,49,60,0.0189869,"\int \frac{1}{x^4 (4+6 x)^3} \, dx","Integrate[1/(x^4*(4 + 6*x)^3),x]","\frac{1}{768} \left(-\frac{2 \left(1215 x^4+1215 x^3+180 x^2-30 x+8\right)}{x^3 (3 x+2)^2}-405 \log (x)+405 \log (3 x+2)\right)","-\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,"((-2*(8 - 30*x + 180*x^2 + 1215*x^3 + 1215*x^4))/(x^3*(2 + 3*x)^2) - 405*Log[x] + 405*Log[2 + 3*x])/768","A",1
270,1,54,67,0.0219574,"\int \frac{1}{x^5 (4+6 x)^3} \, dx","Integrate[1/(x^5*(4 + 6*x)^3),x]","\frac{\frac{2 \left(3645 x^5+3645 x^4+540 x^3-90 x^2+24 x-8\right)}{x^4 (3 x+2)^2}+1215 \log (x)-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,"((2*(-8 + 24*x - 90*x^2 + 540*x^3 + 3645*x^4 + 3645*x^5))/(x^4*(2 + 3*x)^2) + 1215*Log[x] - 1215*Log[2 + 3*x])/1024","A",1
271,1,10,8,0.0010962,"\int \frac{1}{2+2 x} \, dx","Integrate[(2 + 2*x)^(-1),x]","\frac{1}{2} \log (2 x+2)","\frac{1}{2} \log (x+1)",1,"Log[2 + 2*x]/2","A",1
272,1,10,10,0.0011854,"\int \frac{1}{4-6 x} \, dx","Integrate[(4 - 6*x)^(-1),x]","-\frac{1}{6} \log (4-6 x)","-\frac{1}{6} \log (2-3 x)",1,"-1/6*Log[4 - 6*x]","A",1
273,1,16,14,0.0036073,"\int \frac{1}{a+\sqrt{a} x} \, dx","Integrate[(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
274,1,20,20,0.0047353,"\int \frac{1}{a+\sqrt{-a} x} \, dx","Integrate[(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
275,1,22,22,0.0035853,"\int \frac{1}{a^2+\sqrt{-a} x} \, dx","Integrate[(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
276,1,22,22,0.0036227,"\int \frac{1}{a^3+\sqrt{-a} x} \, dx","Integrate[(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
277,1,21,21,0.0070873,"\int \frac{1}{\frac{1}{a}+\sqrt{-a} x} \, dx","Integrate[(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
278,1,22,20,0.0088652,"\int \frac{1}{\frac{1}{a^2}+\sqrt{-a} x} \, dx","Integrate[(a^(-2) + Sqrt[-a]*x)^(-1),x]","\frac{\log \left(\frac{1}{a^2}+\sqrt{-a} x\right)}{\sqrt{-a}}","\frac{\log \left((-a)^{5/2} x+1\right)}{\sqrt{-a}}",1,"Log[a^(-2) + Sqrt[-a]*x]/Sqrt[-a]","A",1
279,1,11,11,0.0031951,"\int \frac{1}{x (1+b x)} \, dx","Integrate[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
280,1,12,12,0.0027231,"\int \frac{1}{x (-1+b x)} \, dx","Integrate[1/(x*(-1 + b*x)),x]","\log (1-b x)-\log (x)","\log (1-b x)-\log (x)",1,"-Log[x] + Log[1 - b*x]","A",1
281,1,19,19,0.0038966,"\int \frac{1}{x^2 (1+b x)} \, dx","Integrate[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
282,1,18,18,0.0031329,"\int \frac{1}{x^2 (-1+b x)} \, dx","Integrate[1/(x^2*(-1 + b*x)),x]","-b \log (x)+b \log (1-b x)+\frac{1}{x}","-b \log (x)+b \log (1-b x)+\frac{1}{x}",1,"x^(-1) - b*Log[x] + b*Log[1 - b*x]","A",1
283,1,14,14,0.0049272,"\int \left(\frac{b}{x}+\frac{1}{x^2 (1+b x)}\right) \, dx","Integrate[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
284,1,46,72,0.023328,"\int x^3 \sqrt{a+b x} \, dx","Integrate[x^3*Sqrt[a + b*x],x]","\frac{2 (a+b x)^{3/2} \left(-16 a^3+24 a^2 b x-30 a b^2 x^2+35 b^3 x^3\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*(a + b*x)^(3/2)*(-16*a^3 + 24*a^2*b*x - 30*a*b^2*x^2 + 35*b^3*x^3))/(315*b^4)","A",1
285,1,35,53,0.0160818,"\int x^2 \sqrt{a+b x} \, dx","Integrate[x^2*Sqrt[a + b*x],x]","\frac{2 (a+b x)^{3/2} \left(8 a^2-12 a b x+15 b^2 x^2\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*(a + b*x)^(3/2)*(8*a^2 - 12*a*b*x + 15*b^2*x^2))/(105*b^3)","A",1
286,1,24,34,0.011451,"\int x \sqrt{a+b x} \, dx","Integrate[x*Sqrt[a + b*x],x]","\frac{2 (a+b x)^{3/2} (3 b x-2 a)}{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*(a + b*x)^(3/2)*(-2*a + 3*b*x))/(15*b^2)","A",1
287,1,16,16,0.0040864,"\int \sqrt{a+b x} \, dx","Integrate[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
288,1,35,35,0.0087759,"\int \frac{\sqrt{a+b x}}{x} \, dx","Integrate[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
289,1,47,39,0.0271755,"\int \frac{\sqrt{a+b x}}{x^2} \, dx","Integrate[Sqrt[a + b*x]/x^2,x]","-\frac{b x \sqrt{\frac{b x}{a}+1} \tanh ^{-1}\left(\sqrt{\frac{b x}{a}+1}\right)+a+b x}{x \sqrt{a+b x}}","-\frac{\sqrt{a+b x}}{x}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{\sqrt{a}}",1,"-((a + b*x + b*x*Sqrt[1 + (b*x)/a]*ArcTanh[Sqrt[1 + (b*x)/a]])/(x*Sqrt[a + b*x]))","A",1
290,1,35,65,0.00678,"\int \frac{\sqrt{a+b x}}{x^3} \, dx","Integrate[Sqrt[a + b*x]/x^3,x]","-\frac{2 b^2 (a+b x)^{3/2} \, _2F_1\left(\frac{3}{2},3;\frac{5}{2};\frac{b x}{a}+1\right)}{3 a^3}","\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*b^2*(a + b*x)^(3/2)*Hypergeometric2F1[3/2, 3, 5/2, 1 + (b*x)/a])/(3*a^3)","C",1
291,1,35,87,0.0067626,"\int \frac{\sqrt{a+b x}}{x^4} \, dx","Integrate[Sqrt[a + b*x]/x^4,x]","\frac{2 b^3 (a+b x)^{3/2} \, _2F_1\left(\frac{3}{2},4;\frac{5}{2};\frac{b x}{a}+1\right)}{3 a^4}","-\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,"(2*b^3*(a + b*x)^(3/2)*Hypergeometric2F1[3/2, 4, 5/2, 1 + (b*x)/a])/(3*a^4)","C",1
292,1,46,72,0.0241665,"\int x^3 (a+b x)^{3/2} \, dx","Integrate[x^3*(a + b*x)^(3/2),x]","\frac{2 (a+b x)^{5/2} \left(-16 a^3+40 a^2 b x-70 a b^2 x^2+105 b^3 x^3\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*(a + b*x)^(5/2)*(-16*a^3 + 40*a^2*b*x - 70*a*b^2*x^2 + 105*b^3*x^3))/(1155*b^4)","A",1
293,1,35,53,0.0168037,"\int x^2 (a+b x)^{3/2} \, dx","Integrate[x^2*(a + b*x)^(3/2),x]","\frac{2 (a+b x)^{5/2} \left(8 a^2-20 a b x+35 b^2 x^2\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*(a + b*x)^(5/2)*(8*a^2 - 20*a*b*x + 35*b^2*x^2))/(315*b^3)","A",1
294,1,24,34,0.0127811,"\int x (a+b x)^{3/2} \, dx","Integrate[x*(a + b*x)^(3/2),x]","\frac{2 (a+b x)^{5/2} (5 b x-2 a)}{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*(a + b*x)^(5/2)*(-2*a + 5*b*x))/(35*b^2)","A",1
295,1,16,16,0.0050975,"\int (a+b x)^{3/2} \, dx","Integrate[(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
296,1,44,49,0.0212037,"\int \frac{(a+b x)^{3/2}}{x} \, dx","Integrate[(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
297,1,33,51,0.0071301,"\int \frac{(a+b x)^{3/2}}{x^2} \, dx","Integrate[(a + b*x)^(3/2)/x^2,x]","\frac{2 b (a+b x)^{5/2} \, _2F_1\left(2,\frac{5}{2};\frac{7}{2};\frac{b x}{a}+1\right)}{5 a^2}","-\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,"(2*b*(a + b*x)^(5/2)*Hypergeometric2F1[2, 5/2, 7/2, 1 + (b*x)/a])/(5*a^2)","C",1
298,1,68,62,0.0337133,"\int \frac{(a+b x)^{3/2}}{x^3} \, dx","Integrate[(a + b*x)^(3/2)/x^3,x]","-\frac{2 a^2+3 b^2 x^2 \sqrt{\frac{b x}{a}+1} \tanh ^{-1}\left(\sqrt{\frac{b x}{a}+1}\right)+7 a b x+5 b^2 x^2}{4 x^2 \sqrt{a+b x}}","-\frac{3 b^2 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{4 \sqrt{a}}-\frac{(a+b x)^{3/2}}{2 x^2}-\frac{3 b \sqrt{a+b x}}{4 x}",1,"-1/4*(2*a^2 + 7*a*b*x + 5*b^2*x^2 + 3*b^2*x^2*Sqrt[1 + (b*x)/a]*ArcTanh[Sqrt[1 + (b*x)/a]])/(x^2*Sqrt[a + b*x])","A",1
299,1,35,84,0.0085447,"\int \frac{(a+b x)^{3/2}}{x^4} \, dx","Integrate[(a + b*x)^(3/2)/x^4,x]","\frac{2 b^3 (a+b x)^{5/2} \, _2F_1\left(\frac{5}{2},4;\frac{7}{2};\frac{b x}{a}+1\right)}{5 a^4}","\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,"(2*b^3*(a + b*x)^(5/2)*Hypergeometric2F1[5/2, 4, 7/2, 1 + (b*x)/a])/(5*a^4)","C",1
300,1,46,72,0.0267999,"\int x^3 (a+b x)^{5/2} \, dx","Integrate[x^3*(a + b*x)^(5/2),x]","\frac{2 (a+b x)^{7/2} \left(-16 a^3+56 a^2 b x-126 a b^2 x^2+231 b^3 x^3\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*(a + b*x)^(7/2)*(-16*a^3 + 56*a^2*b*x - 126*a*b^2*x^2 + 231*b^3*x^3))/(3003*b^4)","A",1
301,1,35,53,0.0200542,"\int x^2 (a+b x)^{5/2} \, dx","Integrate[x^2*(a + b*x)^(5/2),x]","\frac{2 (a+b x)^{7/2} \left(8 a^2-28 a b x+63 b^2 x^2\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*(a + b*x)^(7/2)*(8*a^2 - 28*a*b*x + 63*b^2*x^2))/(693*b^3)","A",1
302,1,24,34,0.0156923,"\int x (a+b x)^{5/2} \, dx","Integrate[x*(a + b*x)^(5/2),x]","\frac{2 (a+b x)^{7/2} (7 b x-2 a)}{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*(a + b*x)^(7/2)*(-2*a + 7*b*x))/(63*b^2)","A",1
303,1,16,16,0.0061121,"\int (a+b x)^{5/2} \, dx","Integrate[(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
304,1,58,65,0.0479797,"\int \frac{(a+b x)^{5/2}}{x} \, dx","Integrate[(a + b*x)^(5/2)/x,x]","-2 a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)+\frac{2}{3} a \sqrt{a+b x} (4 a+b x)+\frac{2}{5} (a+b x)^{5/2}","-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*(a + b*x)^(5/2))/5 + (2*a*Sqrt[a + b*x]*(4*a + b*x))/3 - 2*a^(5/2)*ArcTanh[Sqrt[a + b*x]/Sqrt[a]]","A",1
305,1,33,66,0.0091312,"\int \frac{(a+b x)^{5/2}}{x^2} \, dx","Integrate[(a + b*x)^(5/2)/x^2,x]","\frac{2 b (a+b x)^{7/2} \, _2F_1\left(2,\frac{7}{2};\frac{9}{2};\frac{b x}{a}+1\right)}{7 a^2}","-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,"(2*b*(a + b*x)^(7/2)*Hypergeometric2F1[2, 7/2, 9/2, 1 + (b*x)/a])/(7*a^2)","C",1
306,1,35,78,0.0086814,"\int \frac{(a+b x)^{5/2}}{x^3} \, dx","Integrate[(a + b*x)^(5/2)/x^3,x]","-\frac{2 b^2 (a+b x)^{7/2} \, _2F_1\left(3,\frac{7}{2};\frac{9}{2};\frac{b x}{a}+1\right)}{7 a^3}","\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,"(-2*b^2*(a + b*x)^(7/2)*Hypergeometric2F1[3, 7/2, 9/2, 1 + (b*x)/a])/(7*a^3)","C",1
307,1,79,81,0.0379456,"\int \frac{(a+b x)^{5/2}}{x^4} \, dx","Integrate[(a + b*x)^(5/2)/x^4,x]","-\frac{8 a^3+34 a^2 b x+15 b^3 x^3 \sqrt{\frac{b x}{a}+1} \tanh ^{-1}\left(\sqrt{\frac{b x}{a}+1}\right)+59 a b^2 x^2+33 b^3 x^3}{24 x^3 \sqrt{a+b x}}","-\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,"-1/24*(8*a^3 + 34*a^2*b*x + 59*a*b^2*x^2 + 33*b^3*x^3 + 15*b^3*x^3*Sqrt[1 + (b*x)/a]*ArcTanh[Sqrt[1 + (b*x)/a]])/(x^3*Sqrt[a + b*x])","A",1
308,1,35,103,0.0088975,"\int \frac{(a+b x)^{5/2}}{x^5} \, dx","Integrate[(a + b*x)^(5/2)/x^5,x]","-\frac{2 b^4 (a+b x)^{7/2} \, _2F_1\left(\frac{7}{2},5;\frac{9}{2};\frac{b x}{a}+1\right)}{7 a^5}","\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,"(-2*b^4*(a + b*x)^(7/2)*Hypergeometric2F1[7/2, 5, 9/2, 1 + (b*x)/a])/(7*a^5)","C",1
309,1,90,146,0.0547553,"\int x^7 (a+b x)^{9/2} \, dx","Integrate[x^7*(a + b*x)^(9/2),x]","\frac{2 (a+b x)^{11/2} \left(-2048 a^7+11264 a^6 b x-36608 a^5 b^2 x^2+91520 a^4 b^3 x^3-194480 a^3 b^4 x^4+369512 a^2 b^5 x^5-646646 a b^6 x^6+1062347 b^7 x^7\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*(a + b*x)^(11/2)*(-2048*a^7 + 11264*a^6*b*x - 36608*a^5*b^2*x^2 + 91520*a^4*b^3*x^3 - 194480*a^3*b^4*x^4 + 369512*a^2*b^5*x^5 - 646646*a*b^6*x^6 + 1062347*b^7*x^7))/(26558675*b^8)","A",1
310,1,79,127,0.0423829,"\int x^6 (a+b x)^{9/2} \, dx","Integrate[x^6*(a + b*x)^(9/2),x]","\frac{2 (a+b x)^{11/2} \left(1024 a^6-5632 a^5 b x+18304 a^4 b^2 x^2-45760 a^3 b^3 x^3+97240 a^2 b^4 x^4-184756 a b^5 x^5+323323 b^6 x^6\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*(a + b*x)^(11/2)*(1024*a^6 - 5632*a^5*b*x + 18304*a^4*b^2*x^2 - 45760*a^3*b^3*x^3 + 97240*a^2*b^4*x^4 - 184756*a*b^5*x^5 + 323323*b^6*x^6))/(7436429*b^7)","A",1
311,1,68,110,0.0381913,"\int x^5 (a+b x)^{9/2} \, dx","Integrate[x^5*(a + b*x)^(9/2),x]","\frac{2 (a+b x)^{11/2} \left(-256 a^5+1408 a^4 b x-4576 a^3 b^2 x^2+11440 a^2 b^3 x^3-24310 a b^4 x^4+46189 b^5 x^5\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*(a + b*x)^(11/2)*(-256*a^5 + 1408*a^4*b*x - 4576*a^3*b^2*x^2 + 11440*a^2*b^3*x^3 - 24310*a*b^4*x^4 + 46189*b^5*x^5))/(969969*b^6)","A",1
312,1,57,91,0.0318435,"\int x^4 (a+b x)^{9/2} \, dx","Integrate[x^4*(a + b*x)^(9/2),x]","\frac{2 (a+b x)^{11/2} \left(128 a^4-704 a^3 b x+2288 a^2 b^2 x^2-5720 a b^3 x^3+12155 b^4 x^4\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*(a + b*x)^(11/2)*(128*a^4 - 704*a^3*b*x + 2288*a^2*b^2*x^2 - 5720*a*b^3*x^3 + 12155*b^4*x^4))/(230945*b^5)","A",1
313,1,46,72,0.0298593,"\int x^3 (a+b x)^{9/2} \, dx","Integrate[x^3*(a + b*x)^(9/2),x]","\frac{2 (a+b x)^{11/2} \left(-16 a^3+88 a^2 b x-286 a b^2 x^2+715 b^3 x^3\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*(a + b*x)^(11/2)*(-16*a^3 + 88*a^2*b*x - 286*a*b^2*x^2 + 715*b^3*x^3))/(12155*b^4)","A",1
314,1,35,53,0.0217874,"\int x^2 (a+b x)^{9/2} \, dx","Integrate[x^2*(a + b*x)^(9/2),x]","\frac{2 (a+b x)^{11/2} \left(8 a^2-44 a b x+143 b^2 x^2\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*(a + b*x)^(11/2)*(8*a^2 - 44*a*b*x + 143*b^2*x^2))/(2145*b^3)","A",1
315,1,24,34,0.016762,"\int x (a+b x)^{9/2} \, dx","Integrate[x*(a + b*x)^(9/2),x]","\frac{2 (a+b x)^{11/2} (11 b x-2 a)}{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*(a + b*x)^(11/2)*(-2*a + 11*b*x))/(143*b^2)","A",1
316,1,16,16,0.0074688,"\int (a+b x)^{9/2} \, dx","Integrate[(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
317,1,78,97,0.0850211,"\int \frac{(a+b x)^{9/2}}{x} \, dx","Integrate[(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
318,1,33,98,0.0108309,"\int \frac{(a+b x)^{9/2}}{x^2} \, dx","Integrate[(a + b*x)^(9/2)/x^2,x]","\frac{2 b (a+b x)^{11/2} \, _2F_1\left(2,\frac{11}{2};\frac{13}{2};\frac{b x}{a}+1\right)}{11 a^2}","-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,"(2*b*(a + b*x)^(11/2)*Hypergeometric2F1[2, 11/2, 13/2, 1 + (b*x)/a])/(11*a^2)","C",1
319,1,35,114,0.0105236,"\int \frac{(a+b x)^{9/2}}{x^3} \, dx","Integrate[(a + b*x)^(9/2)/x^3,x]","-\frac{2 b^2 (a+b x)^{11/2} \, _2F_1\left(3,\frac{11}{2};\frac{13}{2};\frac{b x}{a}+1\right)}{11 a^3}","-\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,"(-2*b^2*(a + b*x)^(11/2)*Hypergeometric2F1[3, 11/2, 13/2, 1 + (b*x)/a])/(11*a^3)","C",1
320,1,35,114,0.0106098,"\int \frac{(a+b x)^{9/2}}{x^4} \, dx","Integrate[(a + b*x)^(9/2)/x^4,x]","\frac{2 b^3 (a+b x)^{11/2} \, _2F_1\left(4,\frac{11}{2};\frac{13}{2};\frac{b x}{a}+1\right)}{11 a^4}","-\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,"(2*b^3*(a + b*x)^(11/2)*Hypergeometric2F1[4, 11/2, 13/2, 1 + (b*x)/a])/(11*a^4)","C",1
321,1,35,116,0.0106389,"\int \frac{(a+b x)^{9/2}}{x^5} \, dx","Integrate[(a + b*x)^(9/2)/x^5,x]","-\frac{2 b^4 (a+b x)^{11/2} \, _2F_1\left(5,\frac{11}{2};\frac{13}{2};\frac{b x}{a}+1\right)}{11 a^5}","\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,"(-2*b^4*(a + b*x)^(11/2)*Hypergeometric2F1[5, 11/2, 13/2, 1 + (b*x)/a])/(11*a^5)","C",1
322,1,101,119,0.0441695,"\int \frac{(a+b x)^{9/2}}{x^6} \, dx","Integrate[(a + b*x)^(9/2)/x^6,x]","-\frac{128 a^5+784 a^4 b x+2024 a^3 b^2 x^2+2858 a^2 b^3 x^3+315 b^5 x^5 \sqrt{\frac{b x}{a}+1} \tanh ^{-1}\left(\sqrt{\frac{b x}{a}+1}\right)+2455 a b^4 x^4+965 b^5 x^5}{640 x^5 \sqrt{a+b x}}","-\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,"-1/640*(128*a^5 + 784*a^4*b*x + 2024*a^3*b^2*x^2 + 2858*a^2*b^3*x^3 + 2455*a*b^4*x^4 + 965*b^5*x^5 + 315*b^5*x^5*Sqrt[1 + (b*x)/a]*ArcTanh[Sqrt[1 + (b*x)/a]])/(x^5*Sqrt[a + b*x])","A",1
323,1,35,141,0.0109339,"\int \frac{(a+b x)^{9/2}}{x^7} \, dx","Integrate[(a + b*x)^(9/2)/x^7,x]","-\frac{2 b^6 (a+b x)^{11/2} \, _2F_1\left(\frac{11}{2},7;\frac{13}{2};\frac{b x}{a}+1\right)}{11 a^7}","\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,"(-2*b^6*(a + b*x)^(11/2)*Hypergeometric2F1[11/2, 7, 13/2, 1 + (b*x)/a])/(11*a^7)","C",1
324,1,35,163,0.0109711,"\int \frac{(a+b x)^{9/2}}{x^8} \, dx","Integrate[(a + b*x)^(9/2)/x^8,x]","\frac{2 b^7 (a+b x)^{11/2} \, _2F_1\left(\frac{11}{2},8;\frac{13}{2};\frac{b x}{a}+1\right)}{11 a^8}","-\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,"(2*b^7*(a + b*x)^(11/2)*Hypergeometric2F1[11/2, 8, 13/2, 1 + (b*x)/a])/(11*a^8)","C",1
325,1,39,39,0.011237,"\int \frac{\sqrt{-a+b x}}{x} \, dx","Integrate[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
326,1,52,42,0.0235671,"\int \frac{\sqrt{-a+b x}}{x^2} \, dx","Integrate[Sqrt[-a + b*x]/x^2,x]","\frac{-b x \sqrt{1-\frac{b x}{a}} \tanh ^{-1}\left(\sqrt{1-\frac{b x}{a}}\right)+a-b x}{x \sqrt{b x-a}}","\frac{b \tan ^{-1}\left(\frac{\sqrt{b x-a}}{\sqrt{a}}\right)}{\sqrt{a}}-\frac{\sqrt{b x-a}}{x}",1,"(a - b*x - b*x*Sqrt[1 - (b*x)/a]*ArcTanh[Sqrt[1 - (b*x)/a]])/(x*Sqrt[-a + b*x])","A",1
327,1,38,71,0.0085563,"\int \frac{\sqrt{-a+b x}}{x^3} \, dx","Integrate[Sqrt[-a + b*x]/x^3,x]","\frac{2 b^2 (b x-a)^{3/2} \, _2F_1\left(\frac{3}{2},3;\frac{5}{2};1-\frac{b x}{a}\right)}{3 a^3}","\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*b^2*(-a + b*x)^(3/2)*Hypergeometric2F1[3/2, 3, 5/2, 1 - (b*x)/a])/(3*a^3)","C",1
328,1,48,55,0.0236463,"\int \frac{(-a+b x)^{3/2}}{x} \, dx","Integrate[(-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} (b x-4 a) \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
329,1,36,57,0.0092252,"\int \frac{(-a+b x)^{3/2}}{x^2} \, dx","Integrate[(-a + b*x)^(3/2)/x^2,x]","\frac{2 b (b x-a)^{5/2} \, _2F_1\left(2,\frac{5}{2};\frac{7}{2};1-\frac{b x}{a}\right)}{5 a^2}","-\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,"(2*b*(-a + b*x)^(5/2)*Hypergeometric2F1[2, 5/2, 7/2, 1 - (b*x)/a])/(5*a^2)","C",1
330,1,72,68,0.0349764,"\int \frac{(-a+b x)^{3/2}}{x^3} \, dx","Integrate[(-a + b*x)^(3/2)/x^3,x]","-\frac{2 a^2+3 b^2 x^2 \sqrt{1-\frac{b x}{a}} \tanh ^{-1}\left(\sqrt{1-\frac{b x}{a}}\right)-7 a b x+5 b^2 x^2}{4 x^2 \sqrt{b x-a}}","\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,"-1/4*(2*a^2 - 7*a*b*x + 5*b^2*x^2 + 3*b^2*x^2*Sqrt[1 - (b*x)/a]*ArcTanh[Sqrt[1 - (b*x)/a]])/(x^2*Sqrt[-a + b*x])","A",1
331,1,60,73,0.0325539,"\int \frac{(-a+b x)^{5/2}}{x} \, dx","Integrate[(-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
332,1,36,74,0.0114463,"\int \frac{(-a+b x)^{5/2}}{x^2} \, dx","Integrate[(-a + b*x)^(5/2)/x^2,x]","\frac{2 b (b x-a)^{7/2} \, _2F_1\left(2,\frac{7}{2};\frac{9}{2};1-\frac{b x}{a}\right)}{7 a^2}","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,"(2*b*(-a + b*x)^(7/2)*Hypergeometric2F1[2, 7/2, 9/2, 1 - (b*x)/a])/(7*a^2)","C",1
333,1,38,86,0.0097385,"\int \frac{(-a+b x)^{5/2}}{x^3} \, dx","Integrate[(-a + b*x)^(5/2)/x^3,x]","\frac{2 b^2 (b x-a)^{7/2} \, _2F_1\left(3,\frac{7}{2};\frac{9}{2};1-\frac{b x}{a}\right)}{7 a^3}","\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,"(2*b^2*(-a + b*x)^(7/2)*Hypergeometric2F1[3, 7/2, 9/2, 1 - (b*x)/a])/(7*a^3)","C",1
334,1,57,89,0.0281008,"\int \frac{x^4}{\sqrt{a+b x}} \, dx","Integrate[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
335,1,46,68,0.0261373,"\int \frac{x^3}{\sqrt{a+b x}} \, dx","Integrate[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
336,1,35,51,0.0162894,"\int \frac{x^2}{\sqrt{a+b x}} \, dx","Integrate[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
337,1,23,32,0.011219,"\int \frac{x}{\sqrt{a+b x}} \, dx","Integrate[x/Sqrt[a + b*x],x]","\frac{2 (b x-2 a) \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
338,1,14,14,0.0031658,"\int \frac{1}{\sqrt{a+b x}} \, dx","Integrate[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
339,1,23,23,0.0041368,"\int \frac{1}{x \sqrt{a+b x}} \, dx","Integrate[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
340,1,47,41,0.0648812,"\int \frac{1}{x^2 \sqrt{a+b x}} \, dx","Integrate[1/(x^2*Sqrt[a + b*x]),x]","\frac{\sqrt{a+b x} \left(\frac{b \tanh ^{-1}\left(\sqrt{\frac{b x}{a}+1}\right)}{\sqrt{\frac{b x}{a}+1}}-\frac{a}{x}\right)}{a^2}","\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[1 + (b*x)/a]])/Sqrt[1 + (b*x)/a]))/a^2","A",1
341,1,33,68,0.0057,"\int \frac{1}{x^3 \sqrt{a+b x}} \, dx","Integrate[1/(x^3*Sqrt[a + b*x]),x]","-\frac{2 b^2 \sqrt{a+b x} \, _2F_1\left(\frac{1}{2},3;\frac{3}{2};\frac{b x}{a}+1\right)}{a^3}","-\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,"(-2*b^2*Sqrt[a + b*x]*Hypergeometric2F1[1/2, 3, 3/2, 1 + (b*x)/a])/a^3","C",1
342,1,33,90,0.0059586,"\int \frac{1}{x^4 \sqrt{a+b x}} \, dx","Integrate[1/(x^4*Sqrt[a + b*x]),x]","\frac{2 b^3 \sqrt{a+b x} \, _2F_1\left(\frac{1}{2},4;\frac{3}{2};\frac{b x}{a}+1\right)}{a^4}","\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,"(2*b^3*Sqrt[a + b*x]*Hypergeometric2F1[1/2, 4, 3/2, 1 + (b*x)/a])/a^4","C",1
343,1,57,85,0.0279761,"\int \frac{x^4}{(a+b x)^{3/2}} \, dx","Integrate[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
344,1,45,66,0.0202049,"\int \frac{x^3}{(a+b x)^{3/2}} \, dx","Integrate[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
345,1,34,49,0.0158801,"\int \frac{x^2}{(a+b x)^{3/2}} \, dx","Integrate[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
346,1,21,30,0.0101547,"\int \frac{x}{(a+b x)^{3/2}} \, dx","Integrate[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
347,1,14,14,0.0036058,"\int \frac{1}{(a+b x)^{3/2}} \, dx","Integrate[(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
348,1,30,38,0.0051543,"\int \frac{1}{x (a+b x)^{3/2}} \, dx","Integrate[1/(x*(a + b*x)^(3/2)),x]","\frac{2 \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{b x}{a}+1\right)}{a \sqrt{a+b x}}","\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*Hypergeometric2F1[-1/2, 1, 1/2, 1 + (b*x)/a])/(a*Sqrt[a + b*x])","C",1
349,1,31,57,0.0066077,"\int \frac{1}{x^2 (a+b x)^{3/2}} \, dx","Integrate[1/(x^2*(a + b*x)^(3/2)),x]","-\frac{2 b \, _2F_1\left(-\frac{1}{2},2;\frac{1}{2};\frac{b x}{a}+1\right)}{a^2 \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,"(-2*b*Hypergeometric2F1[-1/2, 2, 1/2, 1 + (b*x)/a])/(a^2*Sqrt[a + b*x])","C",1
350,1,33,87,0.0061618,"\int \frac{1}{x^3 (a+b x)^{3/2}} \, dx","Integrate[1/(x^3*(a + b*x)^(3/2)),x]","\frac{2 b^2 \, _2F_1\left(-\frac{1}{2},3;\frac{1}{2};\frac{b x}{a}+1\right)}{a^3 \sqrt{a+b x}}","-\frac{15 b^2 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{4 a^{7/2}}+\frac{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*b^2*Hypergeometric2F1[-1/2, 3, 1/2, 1 + (b*x)/a])/(a^3*Sqrt[a + b*x])","C",1
351,1,57,87,0.0280861,"\int \frac{x^4}{(a+b x)^{5/2}} \, dx","Integrate[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
352,1,45,68,0.0244658,"\int \frac{x^3}{(a+b x)^{5/2}} \, dx","Integrate[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
353,1,35,49,0.0166546,"\int \frac{x^2}{(a+b x)^{5/2}} \, dx","Integrate[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
354,1,24,32,0.0120774,"\int \frac{x}{(a+b x)^{5/2}} \, dx","Integrate[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
355,1,16,16,0.0047223,"\int \frac{1}{(a+b x)^{5/2}} \, dx","Integrate[(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
356,1,32,54,0.0061047,"\int \frac{1}{x (a+b x)^{5/2}} \, dx","Integrate[1/(x*(a + b*x)^(5/2)),x]","\frac{2 \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};\frac{b x}{a}+1\right)}{3 a (a+b x)^{3/2}}","-\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*Hypergeometric2F1[-3/2, 1, -1/2, 1 + (b*x)/a])/(3*a*(a + b*x)^(3/2))","C",1
357,1,33,74,0.0060753,"\int \frac{1}{x^2 (a+b x)^{5/2}} \, dx","Integrate[1/(x^2*(a + b*x)^(5/2)),x]","-\frac{2 b \, _2F_1\left(-\frac{3}{2},2;-\frac{1}{2};\frac{b x}{a}+1\right)}{3 a^2 (a+b x)^{3/2}}","\frac{5 b \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{a^{7/2}}-\frac{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,"(-2*b*Hypergeometric2F1[-3/2, 2, -1/2, 1 + (b*x)/a])/(3*a^2*(a + b*x)^(3/2))","C",1
358,1,35,106,0.0067158,"\int \frac{1}{x^3 (a+b x)^{5/2}} \, dx","Integrate[1/(x^3*(a + b*x)^(5/2)),x]","\frac{2 b^2 \, _2F_1\left(-\frac{3}{2},3;-\frac{1}{2};\frac{b x}{a}+1\right)}{3 a^3 (a+b x)^{3/2}}","-\frac{35 b^2 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{4 a^{9/2}}+\frac{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,"(2*b^2*Hypergeometric2F1[-3/2, 3, -1/2, 1 + (b*x)/a])/(3*a^3*(a + b*x)^(3/2))","C",1
359,1,25,25,0.005069,"\int \frac{1}{x \sqrt{-a+b x}} \, dx","Integrate[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
360,1,53,44,0.064564,"\int \frac{1}{x^2 \sqrt{-a+b x}} \, dx","Integrate[1/(x^2*Sqrt[-a + b*x]),x]","\frac{b \sqrt{b x-a} \left(\frac{a}{b x}+\frac{\tanh ^{-1}\left(\sqrt{1-\frac{b x}{a}}\right)}{\sqrt{1-\frac{b x}{a}}}\right)}{a^2}","\frac{b \tan ^{-1}\left(\frac{\sqrt{b x-a}}{\sqrt{a}}\right)}{a^{3/2}}+\frac{\sqrt{b x-a}}{a x}",1,"(b*Sqrt[-a + b*x]*(a/(b*x) + ArcTanh[Sqrt[1 - (b*x)/a]]/Sqrt[1 - (b*x)/a]))/a^2","A",1
361,1,36,74,0.0060841,"\int \frac{1}{x^3 \sqrt{-a+b x}} \, dx","Integrate[1/(x^3*Sqrt[-a + b*x]),x]","\frac{2 b^2 \sqrt{b x-a} \, _2F_1\left(\frac{1}{2},3;\frac{3}{2};1-\frac{b x}{a}\right)}{a^3}","\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,"(2*b^2*Sqrt[-a + b*x]*Hypergeometric2F1[1/2, 3, 3/2, 1 - (b*x)/a])/a^3","C",1
362,1,33,42,0.0074803,"\int \frac{1}{x (-a+b x)^{3/2}} \, dx","Integrate[1/(x*(-a + b*x)^(3/2)),x]","-\frac{2 \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};1-\frac{b x}{a}\right)}{a \sqrt{b x-a}}","-\frac{2 \tan ^{-1}\left(\frac{\sqrt{b x-a}}{\sqrt{a}}\right)}{a^{3/2}}-\frac{2}{a \sqrt{b x-a}}",1,"(-2*Hypergeometric2F1[-1/2, 1, 1/2, 1 - (b*x)/a])/(a*Sqrt[-a + b*x])","C",1
363,1,34,62,0.0067326,"\int \frac{1}{x^2 (-a+b x)^{3/2}} \, dx","Integrate[1/(x^2*(-a + b*x)^(3/2)),x]","-\frac{2 b \, _2F_1\left(-\frac{1}{2},2;\frac{1}{2};1-\frac{b x}{a}\right)}{a^2 \sqrt{b x-a}}","-\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,"(-2*b*Hypergeometric2F1[-1/2, 2, 1/2, 1 - (b*x)/a])/(a^2*Sqrt[-a + b*x])","C",1
364,1,36,95,0.0065855,"\int \frac{1}{x^3 (-a+b x)^{3/2}} \, dx","Integrate[1/(x^3*(-a + b*x)^(3/2)),x]","-\frac{2 b^2 \, _2F_1\left(-\frac{1}{2},3;\frac{1}{2};1-\frac{b x}{a}\right)}{a^3 \sqrt{b x-a}}","-\frac{15 b^2 \tan ^{-1}\left(\frac{\sqrt{b x-a}}{\sqrt{a}}\right)}{4 a^{7/2}}-\frac{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,"(-2*b^2*Hypergeometric2F1[-1/2, 3, 1/2, 1 - (b*x)/a])/(a^3*Sqrt[-a + b*x])","C",1
365,1,35,60,0.0081339,"\int \frac{1}{x (-a+b x)^{5/2}} \, dx","Integrate[1/(x*(-a + b*x)^(5/2)),x]","-\frac{2 \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};1-\frac{b x}{a}\right)}{3 a (b x-a)^{3/2}}","\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*Hypergeometric2F1[-3/2, 1, -1/2, 1 - (b*x)/a])/(3*a*(-a + b*x)^(3/2))","C",1
366,1,36,81,0.0087649,"\int \frac{1}{x^2 (-a+b x)^{5/2}} \, dx","Integrate[1/(x^2*(-a + b*x)^(5/2)),x]","-\frac{2 b \, _2F_1\left(-\frac{3}{2},2;-\frac{1}{2};1-\frac{b x}{a}\right)}{3 a^2 (b x-a)^{3/2}}","\frac{5 b \tan ^{-1}\left(\frac{\sqrt{b x-a}}{\sqrt{a}}\right)}{a^{7/2}}+\frac{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,"(-2*b*Hypergeometric2F1[-3/2, 2, -1/2, 1 - (b*x)/a])/(3*a^2*(-a + b*x)^(3/2))","C",1
367,1,38,116,0.0072215,"\int \frac{1}{x^3 (-a+b x)^{5/2}} \, dx","Integrate[1/(x^3*(-a + b*x)^(5/2)),x]","-\frac{2 b^2 \, _2F_1\left(-\frac{3}{2},3;-\frac{1}{2};1-\frac{b x}{a}\right)}{3 a^3 (b x-a)^{3/2}}","\frac{35 b^2 \tan ^{-1}\left(\frac{\sqrt{b x-a}}{\sqrt{a}}\right)}{4 a^{9/2}}+\frac{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,"(-2*b^2*Hypergeometric2F1[-3/2, 3, -1/2, 1 - (b*x)/a])/(3*a^3*(-a + b*x)^(3/2))","C",1
368,1,13,13,0.0410039,"\int \frac{x^{-1+m} (2 a m+b (-1+2 m) x)}{2 (a+b x)^{3/2}} \, dx","Integrate[(x^(-1 + m)*(2*a*m + b*(-1 + 2*m)*x))/(2*(a + b*x)^(3/2)),x]","\frac{x^m}{\sqrt{a+b x}}","\frac{x^m}{\sqrt{a+b x}}",1,"x^m/Sqrt[a + b*x]","A",1
369,1,13,13,0.0153636,"\int \left(-\frac{b x^m}{2 (a+b x)^{3/2}}+\frac{m x^{-1+m}}{\sqrt{a+b x}}\right) \, dx","Integrate[-1/2*(b*x^m)/(a + b*x)^(3/2) + (m*x^(-1 + m))/Sqrt[a + b*x],x]","\frac{x^m}{\sqrt{a+b x}}","\frac{x^m}{\sqrt{a+b x}}",1,"x^m/Sqrt[a + b*x]","A",1
370,1,23,23,0.0035454,"\int \frac{x^{\frac{1-n}{2}+\frac{1}{2} (-3+n)}}{\sqrt{a+b x}} \, dx","Integrate[x^((1 - n)/2 + (-3 + n)/2)/Sqrt[a + b*x],x]","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{\sqrt{a}}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{\sqrt{a}}",1,"(-2*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/Sqrt[a]","A",1
371,1,46,72,0.0236912,"\int x^3 \sqrt[3]{a+b x} \, dx","Integrate[x^3*(a + b*x)^(1/3),x]","\frac{3 (a+b x)^{4/3} \left(-81 a^3+108 a^2 b x-126 a b^2 x^2+140 b^3 x^3\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)^(4/3)*(-81*a^3 + 108*a^2*b*x - 126*a*b^2*x^2 + 140*b^3*x^3))/(1820*b^4)","A",1
372,1,35,53,0.0168106,"\int x^2 \sqrt[3]{a+b x} \, dx","Integrate[x^2*(a + b*x)^(1/3),x]","\frac{3 (a+b x)^{4/3} \left(9 a^2-12 a b x+14 b^2 x^2\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)^(4/3)*(9*a^2 - 12*a*b*x + 14*b^2*x^2))/(140*b^3)","A",1
373,1,24,34,0.0118599,"\int x \sqrt[3]{a+b x} \, dx","Integrate[x*(a + b*x)^(1/3),x]","\frac{3 (a+b x)^{4/3} (4 b x-3 a)}{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)^(4/3)*(-3*a + 4*b*x))/(28*b^2)","A",1
374,1,16,16,0.0044068,"\int \sqrt[3]{a+b x} \, dx","Integrate[(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
375,1,113,91,0.0474249,"\int \frac{\sqrt[3]{a+b x}}{x} \, dx","Integrate[(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}-\sqrt[3]{a+b x}\right)-\sqrt{3} \sqrt[3]{a} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{a+b x}}{\sqrt[3]{a}}+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 + (2*(a + b*x)^(1/3))/a^(1/3))/Sqrt[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
376,1,33,97,0.0064724,"\int \frac{\sqrt[3]{a+b x}}{x^2} \, dx","Integrate[(a + b*x)^(1/3)/x^2,x]","\frac{3 b (a+b x)^{4/3} \, _2F_1\left(\frac{4}{3},2;\frac{7}{3};\frac{b x}{a}+1\right)}{4 a^2}","-\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,"(3*b*(a + b*x)^(4/3)*Hypergeometric2F1[4/3, 2, 7/3, 1 + (b*x)/a])/(4*a^2)","C",1
377,1,35,127,0.007066,"\int \frac{\sqrt[3]{a+b x}}{x^3} \, dx","Integrate[(a + b*x)^(1/3)/x^3,x]","-\frac{3 b^2 (a+b x)^{4/3} \, _2F_1\left(\frac{4}{3},3;\frac{7}{3};\frac{b x}{a}+1\right)}{4 a^3}","\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*b^2*(a + b*x)^(4/3)*Hypergeometric2F1[4/3, 3, 7/3, 1 + (b*x)/a])/(4*a^3)","C",1
378,1,46,72,0.0249781,"\int x^3 (a+b x)^{2/3} \, dx","Integrate[x^3*(a + b*x)^(2/3),x]","\frac{3 (a+b x)^{5/3} \left(-81 a^3+135 a^2 b x-180 a b^2 x^2+220 b^3 x^3\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)^(5/3)*(-81*a^3 + 135*a^2*b*x - 180*a*b^2*x^2 + 220*b^3*x^3))/(3080*b^4)","A",1
379,1,35,53,0.0167247,"\int x^2 (a+b x)^{2/3} \, dx","Integrate[x^2*(a + b*x)^(2/3),x]","\frac{3 (a+b x)^{5/3} \left(9 a^2-15 a b x+20 b^2 x^2\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)^(5/3)*(9*a^2 - 15*a*b*x + 20*b^2*x^2))/(220*b^3)","A",1
380,1,24,34,0.0123212,"\int x (a+b x)^{2/3} \, dx","Integrate[x*(a + b*x)^(2/3),x]","\frac{3 (a+b x)^{5/3} (5 b x-3 a)}{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)^(5/3)*(-3*a + 5*b*x))/(40*b^2)","A",1
381,1,16,16,0.0043128,"\int (a+b x)^{2/3} \, dx","Integrate[(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
382,1,86,92,0.0393914,"\int \frac{(a+b x)^{2/3}}{x} \, dx","Integrate[(a + b*x)^(2/3)/x,x]","\frac{3}{2} \left(a^{2/3} \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x}\right)+(a+b x)^{2/3}\right)+\sqrt{3} a^{2/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{a+b x}}{\sqrt[3]{a}}+1}{\sqrt{3}}\right)-\frac{1}{2} a^{2/3} \log (x)","\frac{3}{2} a^{2/3} \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x}\right)+\sqrt{3} a^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)-\frac{1}{2} a^{2/3} \log (x)+\frac{3}{2} (a+b x)^{2/3}",1,"Sqrt[3]*a^(2/3)*ArcTan[(1 + (2*(a + b*x)^(1/3))/a^(1/3))/Sqrt[3]] - (a^(2/3)*Log[x])/2 + (3*((a + b*x)^(2/3) + a^(2/3)*Log[a^(1/3) - (a + b*x)^(1/3)]))/2","A",1
383,1,33,94,0.006667,"\int \frac{(a+b x)^{2/3}}{x^2} \, dx","Integrate[(a + b*x)^(2/3)/x^2,x]","\frac{3 b (a+b x)^{5/3} \, _2F_1\left(\frac{5}{3},2;\frac{8}{3};\frac{b x}{a}+1\right)}{5 a^2}","-\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,"(3*b*(a + b*x)^(5/3)*Hypergeometric2F1[5/3, 2, 8/3, 1 + (b*x)/a])/(5*a^2)","C",1
384,1,35,127,0.0075921,"\int \frac{(a+b x)^{2/3}}{x^3} \, dx","Integrate[(a + b*x)^(2/3)/x^3,x]","-\frac{3 b^2 (a+b x)^{5/3} \, _2F_1\left(\frac{5}{3},3;\frac{8}{3};\frac{b x}{a}+1\right)}{5 a^3}","\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*b^2*(a + b*x)^(5/3)*Hypergeometric2F1[5/3, 3, 8/3, 1 + (b*x)/a])/(5*a^3)","C",1
385,1,46,72,0.0248347,"\int x^3 (a+b x)^{4/3} \, dx","Integrate[x^3*(a + b*x)^(4/3),x]","\frac{3 (a+b x)^{7/3} \left(-81 a^3+189 a^2 b x-315 a b^2 x^2+455 b^3 x^3\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)^(7/3)*(-81*a^3 + 189*a^2*b*x - 315*a*b^2*x^2 + 455*b^3*x^3))/(7280*b^4)","A",1
386,1,35,53,0.0176783,"\int x^2 (a+b x)^{4/3} \, dx","Integrate[x^2*(a + b*x)^(4/3),x]","\frac{3 (a+b x)^{7/3} \left(9 a^2-21 a b x+35 b^2 x^2\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)^(7/3)*(9*a^2 - 21*a*b*x + 35*b^2*x^2))/(455*b^3)","A",1
387,1,24,34,0.0133517,"\int x (a+b x)^{4/3} \, dx","Integrate[x*(a + b*x)^(4/3),x]","\frac{3 (a+b x)^{7/3} (7 b x-3 a)}{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)^(7/3)*(-3*a + 7*b*x))/(70*b^2)","A",1
388,1,16,16,0.0053646,"\int (a+b x)^{4/3} \, dx","Integrate[(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
389,1,130,105,0.0324597,"\int \frac{(a+b x)^{4/3}}{x} \, dx","Integrate[(a + b*x)^(4/3)/x,x]","\frac{1}{4} \left(4 a^{4/3} \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x}\right)-2 a^{4/3} \log \left(a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x}+(a+b x)^{2/3}\right)-4 \sqrt{3} a^{4/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{a+b x}}{\sqrt[3]{a}}+1}{\sqrt{3}}\right)+15 a \sqrt[3]{a+b x}+3 b x \sqrt[3]{a+b x}\right)","\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,"(15*a*(a + b*x)^(1/3) + 3*b*x*(a + b*x)^(1/3) - 4*Sqrt[3]*a^(4/3)*ArcTan[(1 + (2*(a + b*x)^(1/3))/a^(1/3))/Sqrt[3]] + 4*a^(4/3)*Log[a^(1/3) - (a + b*x)^(1/3)] - 2*a^(4/3)*Log[a^(2/3) + a^(1/3)*(a + b*x)^(1/3) + (a + b*x)^(2/3)])/4","A",1
390,1,33,107,0.0071264,"\int \frac{(a+b x)^{4/3}}{x^2} \, dx","Integrate[(a + b*x)^(4/3)/x^2,x]","\frac{3 b (a+b x)^{7/3} \, _2F_1\left(2,\frac{7}{3};\frac{10}{3};\frac{b x}{a}+1\right)}{7 a^2}","-\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,"(3*b*(a + b*x)^(7/3)*Hypergeometric2F1[2, 7/3, 10/3, 1 + (b*x)/a])/(7*a^2)","C",1
391,1,35,124,0.0080575,"\int \frac{(a+b x)^{4/3}}{x^3} \, dx","Integrate[(a + b*x)^(4/3)/x^3,x]","-\frac{3 b^2 (a+b x)^{7/3} \, _2F_1\left(\frac{7}{3},3;\frac{10}{3};\frac{b x}{a}+1\right)}{7 a^3}","-\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*b^2*(a + b*x)^(7/3)*Hypergeometric2F1[7/3, 3, 10/3, 1 + (b*x)/a])/(7*a^3)","C",1
392,1,46,72,0.027503,"\int \frac{x^3}{\sqrt[3]{a+b x}} \, dx","Integrate[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
393,1,35,53,0.020137,"\int \frac{x^2}{\sqrt[3]{a+b x}} \, dx","Integrate[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
394,1,24,34,0.0123909,"\int \frac{x}{\sqrt[3]{a+b x}} \, dx","Integrate[x/(a + b*x)^(1/3),x]","\frac{3 (a+b x)^{2/3} (2 b x-3 a)}{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*(a + b*x)^(2/3)*(-3*a + 2*b*x))/(10*b^2)","A",1
395,1,16,16,0.0034648,"\int \frac{1}{\sqrt[3]{a+b x}} \, dx","Integrate[(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
396,1,66,79,0.012736,"\int \frac{1}{x \sqrt[3]{a+b x}} \, dx","Integrate[1/(x*(a + b*x)^(1/3)),x]","\frac{3 \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x}\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{a+b x}}{\sqrt[3]{a}}+1}{\sqrt{3}}\right)-\log (x)}{2 \sqrt[3]{a}}","\frac{3 \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x}\right)}{2 \sqrt[3]{a}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt[3]{a}}-\frac{\log (x)}{2 \sqrt[3]{a}}",1,"(2*Sqrt[3]*ArcTan[(1 + (2*(a + b*x)^(1/3))/a^(1/3))/Sqrt[3]] - Log[x] + 3*Log[a^(1/3) - (a + b*x)^(1/3)])/(2*a^(1/3))","A",1
397,1,33,100,0.0055732,"\int \frac{1}{x^2 \sqrt[3]{a+b x}} \, dx","Integrate[1/(x^2*(a + b*x)^(1/3)),x]","\frac{3 b (a+b x)^{2/3} \, _2F_1\left(\frac{2}{3},2;\frac{5}{3};\frac{b x}{a}+1\right)}{2 a^2}","\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,"(3*b*(a + b*x)^(2/3)*Hypergeometric2F1[2/3, 2, 5/3, 1 + (b*x)/a])/(2*a^2)","C",1
398,1,35,130,0.006521,"\int \frac{1}{x^3 \sqrt[3]{a+b x}} \, dx","Integrate[1/(x^3*(a + b*x)^(1/3)),x]","-\frac{3 b^2 (a+b x)^{2/3} \, _2F_1\left(\frac{2}{3},3;\frac{5}{3};\frac{b x}{a}+1\right)}{2 a^3}","-\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,"(-3*b^2*(a + b*x)^(2/3)*Hypergeometric2F1[2/3, 3, 5/3, 1 + (b*x)/a])/(2*a^3)","C",1
399,1,48,80,0.0272788,"\int \frac{x^3}{\sqrt[3]{-a+b x}} \, dx","Integrate[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
400,1,37,59,0.0205044,"\int \frac{x^2}{\sqrt[3]{-a+b x}} \, dx","Integrate[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
401,1,26,38,0.0123641,"\int \frac{x}{\sqrt[3]{-a+b x}} \, dx","Integrate[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
402,1,18,18,0.0038099,"\int \frac{1}{\sqrt[3]{-a+b x}} \, dx","Integrate[(-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
403,1,35,82,0.0105373,"\int \frac{1}{x \sqrt[3]{-a+b x}} \, dx","Integrate[1/(x*(-a + b*x)^(1/3)),x]","\frac{3 (b x-a)^{2/3} \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};1-\frac{b x}{a}\right)}{2 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,"(3*(-a + b*x)^(2/3)*Hypergeometric2F1[2/3, 1, 5/3, 1 - (b*x)/a])/(2*a)","C",1
404,1,36,103,0.0061045,"\int \frac{1}{x^2 \sqrt[3]{-a+b x}} \, dx","Integrate[1/(x^2*(-a + b*x)^(1/3)),x]","\frac{3 b (b x-a)^{2/3} \, _2F_1\left(\frac{2}{3},2;\frac{5}{3};1-\frac{b x}{a}\right)}{2 a^2}","\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,"(3*b*(-a + b*x)^(2/3)*Hypergeometric2F1[2/3, 2, 5/3, 1 - (b*x)/a])/(2*a^2)","C",1
405,1,38,136,0.0061942,"\int \frac{1}{x^3 \sqrt[3]{-a+b x}} \, dx","Integrate[1/(x^3*(-a + b*x)^(1/3)),x]","\frac{3 b^2 (b x-a)^{2/3} \, _2F_1\left(\frac{2}{3},3;\frac{5}{3};1-\frac{b x}{a}\right)}{2 a^3}","\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,"(3*b^2*(-a + b*x)^(2/3)*Hypergeometric2F1[2/3, 3, 5/3, 1 - (b*x)/a])/(2*a^3)","C",1
406,1,46,70,0.0235283,"\int \frac{x^3}{(a+b x)^{2/3}} \, dx","Integrate[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
407,1,35,51,0.0172407,"\int \frac{x^2}{(a+b x)^{2/3}} \, dx","Integrate[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
408,1,23,32,0.0111002,"\int \frac{x}{(a+b x)^{2/3}} \, dx","Integrate[x/(a + b*x)^(2/3),x]","\frac{3 (b x-3 a) \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
409,1,14,14,0.0032657,"\int \frac{1}{(a+b x)^{2/3}} \, dx","Integrate[(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
410,1,93,80,0.0258516,"\int \frac{1}{x (a+b x)^{2/3}} \, dx","Integrate[1/(x*(a + b*x)^(2/3)),x]","-\frac{\log \left(a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x}+(a+b x)^{2/3}\right)-2 \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x}\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{a+b x}}{\sqrt[3]{a}}+1}{\sqrt{3}}\right)}{2 a^{2/3}}","\frac{3 \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x}\right)}{2 a^{2/3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{a^{2/3}}-\frac{\log (x)}{2 a^{2/3}}",1,"-1/2*(2*Sqrt[3]*ArcTan[(1 + (2*(a + b*x)^(1/3))/a^(1/3))/Sqrt[3]] - 2*Log[a^(1/3) - (a + b*x)^(1/3)] + Log[a^(2/3) + a^(1/3)*(a + b*x)^(1/3) + (a + b*x)^(2/3)])/a^(2/3)","A",1
411,1,31,98,0.0054238,"\int \frac{1}{x^2 (a+b x)^{2/3}} \, dx","Integrate[1/(x^2*(a + b*x)^(2/3)),x]","\frac{3 b \sqrt[3]{a+b x} \, _2F_1\left(\frac{1}{3},2;\frac{4}{3};\frac{b x}{a}+1\right)}{a^2}","\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,"(3*b*(a + b*x)^(1/3)*Hypergeometric2F1[1/3, 2, 4/3, 1 + (b*x)/a])/a^2","C",1
412,1,33,130,0.0064612,"\int \frac{1}{x^3 (a+b x)^{2/3}} \, dx","Integrate[1/(x^3*(a + b*x)^(2/3)),x]","-\frac{3 b^2 \sqrt[3]{a+b x} \, _2F_1\left(\frac{1}{3},3;\frac{4}{3};\frac{b x}{a}+1\right)}{a^3}","-\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,"(-3*b^2*(a + b*x)^(1/3)*Hypergeometric2F1[1/3, 3, 4/3, 1 + (b*x)/a])/a^3","C",1
413,1,46,70,0.0217725,"\int \frac{x^3}{(a+b x)^{4/3}} \, dx","Integrate[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
414,1,34,49,0.0163134,"\int \frac{x^2}{(a+b x)^{4/3}} \, dx","Integrate[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
415,1,23,32,0.0112471,"\int \frac{x}{(a+b x)^{4/3}} \, dx","Integrate[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
416,1,14,14,0.0040549,"\int \frac{1}{(a+b x)^{4/3}} \, dx","Integrate[(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
417,1,30,93,0.0054237,"\int \frac{1}{x (a+b x)^{4/3}} \, dx","Integrate[1/(x*(a + b*x)^(4/3)),x]","\frac{3 \, _2F_1\left(-\frac{1}{3},1;\frac{2}{3};\frac{b x}{a}+1\right)}{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*Hypergeometric2F1[-1/3, 1, 2/3, 1 + (b*x)/a])/(a*(a + b*x)^(1/3))","C",1
418,1,31,113,0.0059194,"\int \frac{1}{x^2 (a+b x)^{4/3}} \, dx","Integrate[1/(x^2*(a + b*x)^(4/3)),x]","-\frac{3 b \, _2F_1\left(-\frac{1}{3},2;\frac{2}{3};\frac{b x}{a}+1\right)}{a^2 \sqrt[3]{a+b x}}","\frac{2 b \log (x)}{3 a^{7/3}}-\frac{2 b \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x}\right)}{a^{7/3}}-\frac{4 b \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{7/3}}-\frac{4 b}{a^2 \sqrt[3]{a+b x}}-\frac{1}{a x \sqrt[3]{a+b x}}",1,"(-3*b*Hypergeometric2F1[-1/3, 2, 2/3, 1 + (b*x)/a])/(a^2*(a + b*x)^(1/3))","C",1
419,1,33,149,0.0063166,"\int \frac{1}{x^3 (a+b x)^{4/3}} \, dx","Integrate[1/(x^3*(a + b*x)^(4/3)),x]","\frac{3 b^2 \, _2F_1\left(-\frac{1}{3},3;\frac{2}{3};\frac{b x}{a}+1\right)}{a^3 \sqrt[3]{a+b x}}","-\frac{7 b^2 \log (x)}{9 a^{10/3}}+\frac{7 b^2 \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x}\right)}{3 a^{10/3}}+\frac{14 b^2 \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{10/3}}+\frac{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*b^2*Hypergeometric2F1[-1/3, 3, 2/3, 1 + (b*x)/a])/(a^3*(a + b*x)^(1/3))","C",1
420,1,66,71,0.0214067,"\int \frac{1}{x \sqrt[3]{a^3+b^3 x}} \, dx","Integrate[1/(x*(a^3 + b^3*x)^(1/3)),x]","\frac{3 \log \left(a-\sqrt[3]{a^3+b^3 x}\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3+b^3 x}+a}{\sqrt{3} a}\right)-\log (x)}{2 a}","\frac{3 \log \left(a-\sqrt[3]{a^3+b^3 x}\right)}{2 a}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3+b^3 x}+a}{\sqrt{3} a}\right)}{a}-\frac{\log (x)}{2 a}",1,"(2*Sqrt[3]*ArcTan[(a + 2*(a^3 + b^3*x)^(1/3))/(Sqrt[3]*a)] - Log[x] + 3*Log[a - (a^3 + b^3*x)^(1/3)])/(2*a)","A",1
421,1,68,73,0.0220572,"\int \frac{1}{x \sqrt[3]{a^3-b^3 x}} \, dx","Integrate[1/(x*(a^3 - b^3*x)^(1/3)),x]","\frac{3 \log \left(a-\sqrt[3]{a^3-b^3 x}\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3-b^3 x}+a}{\sqrt{3} a}\right)-\log (x)}{2 a}","\frac{3 \log \left(a-\sqrt[3]{a^3-b^3 x}\right)}{2 a}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3-b^3 x}+a}{\sqrt{3} a}\right)}{a}-\frac{\log (x)}{2 a}",1,"(2*Sqrt[3]*ArcTan[(a + 2*(a^3 - b^3*x)^(1/3))/(Sqrt[3]*a)] - Log[x] + 3*Log[a - (a^3 - b^3*x)^(1/3)])/(2*a)","A",1
422,1,41,74,0.0131392,"\int \frac{1}{x \sqrt[3]{-a^3+b^3 x}} \, dx","Integrate[1/(x*(-a^3 + b^3*x)^(1/3)),x]","\frac{3 \left(b^3 x-a^3\right)^{2/3} \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};1-\frac{b^3 x}{a^3}\right)}{2 a^3}","-\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,"(3*(-a^3 + b^3*x)^(2/3)*Hypergeometric2F1[2/3, 1, 5/3, 1 - (b^3*x)/a^3])/(2*a^3)","C",1
423,1,41,76,0.012273,"\int \frac{1}{x \sqrt[3]{-a^3-b^3 x}} \, dx","Integrate[1/(x*(-a^3 - b^3*x)^(1/3)),x]","\frac{3 \left(-a^3-b^3 x\right)^{2/3} \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{x b^3}{a^3}+1\right)}{2 a^3}","-\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,"(3*(-a^3 - b^3*x)^(2/3)*Hypergeometric2F1[2/3, 1, 5/3, 1 + (b^3*x)/a^3])/(2*a^3)","C",1
424,1,95,72,0.0254313,"\int \frac{1}{x \left(a^3+b^3 x\right)^{2/3}} \, dx","Integrate[1/(x*(a^3 + b^3*x)^(2/3)),x]","-\frac{-2 \log \left(a-\sqrt[3]{a^3+b^3 x}\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3+b^3 x}+a}{\sqrt{3} a}\right)+\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{\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,"-1/2*(2*Sqrt[3]*ArcTan[(a + 2*(a^3 + b^3*x)^(1/3))/(Sqrt[3]*a)] - 2*Log[a - (a^3 + b^3*x)^(1/3)] + Log[a^2 + a*(a^3 + b^3*x)^(1/3) + (a^3 + b^3*x)^(2/3)])/a^2","A",1
425,1,99,74,0.0248928,"\int \frac{1}{x \left(a^3-b^3 x\right)^{2/3}} \, dx","Integrate[1/(x*(a^3 - b^3*x)^(2/3)),x]","-\frac{-2 \log \left(a-\sqrt[3]{a^3-b^3 x}\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3-b^3 x}+a}{\sqrt{3} a}\right)+\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{\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,"-1/2*(2*Sqrt[3]*ArcTan[(a + 2*(a^3 - b^3*x)^(1/3))/(Sqrt[3]*a)] - 2*Log[a - (a^3 - b^3*x)^(1/3)] + Log[a^2 + a*(a^3 - b^3*x)^(1/3) + (a^3 - b^3*x)^(2/3)])/a^2","A",1
426,1,108,74,0.0324528,"\int \frac{1}{x \left(-a^3+b^3 x\right)^{2/3}} \, dx","Integrate[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{2 \sqrt[3]{b^3 x-a^3}-a}{\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[(-a + 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
427,1,112,76,0.0306849,"\int \frac{1}{x \left(-a^3-b^3 x\right)^{2/3}} \, dx","Integrate[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}-a}{\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[(-a + 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
428,1,22,25,0.0151835,"\int x^m (a+b x) \, dx","Integrate[x^m*(a + b*x),x]","x^{m+1} \left(\frac{a}{m+1}+\frac{b x}{m+2}\right)","\frac{a x^{m+1}}{m+1}+\frac{b x^{m+2}}{m+2}",1,"x^(1 + m)*(a/(1 + m) + (b*x)/(2 + m))","A",1
429,1,17,21,0.0046362,"\int x^{5/2} (a+b x) \, dx","Integrate[x^(5/2)*(a + b*x),x]","\frac{2}{63} x^{7/2} (9 a+7 b x)","\frac{2}{7} a x^{7/2}+\frac{2}{9} b x^{9/2}",1,"(2*x^(7/2)*(9*a + 7*b*x))/63","A",1
430,1,17,21,0.00459,"\int x^{3/2} (a+b x) \, dx","Integrate[x^(3/2)*(a + b*x),x]","\frac{2}{35} x^{5/2} (7 a+5 b x)","\frac{2}{5} a x^{5/2}+\frac{2}{7} b x^{7/2}",1,"(2*x^(5/2)*(7*a + 5*b*x))/35","A",1
431,1,17,21,0.0046207,"\int \sqrt{x} (a+b x) \, dx","Integrate[Sqrt[x]*(a + b*x),x]","\frac{2}{15} x^{3/2} (5 a+3 b x)","\frac{2}{3} a x^{3/2}+\frac{2}{5} b x^{5/2}",1,"(2*x^(3/2)*(5*a + 3*b*x))/15","A",1
432,1,16,19,0.0046211,"\int \frac{a+b x}{\sqrt{x}} \, dx","Integrate[(a + b*x)/Sqrt[x],x]","\frac{2}{3} \sqrt{x} (3 a+b x)","2 a \sqrt{x}+\frac{2}{3} b x^{3/2}",1,"(2*Sqrt[x]*(3*a + b*x))/3","A",1
433,1,14,17,0.0051047,"\int \frac{a+b x}{x^{3/2}} \, dx","Integrate[(a + b*x)/x^(3/2),x]","\frac{2 (b x-a)}{\sqrt{x}}","2 b \sqrt{x}-\frac{2 a}{\sqrt{x}}",1,"(2*(-a + b*x))/Sqrt[x]","A",1
434,1,15,19,0.0052555,"\int \frac{a+b x}{x^{5/2}} \, dx","Integrate[(a + b*x)/x^(5/2),x]","-\frac{2 (a+3 b x)}{3 x^{3/2}}","-\frac{2 a}{3 x^{3/2}}-\frac{2 b}{\sqrt{x}}",1,"(-2*(a + 3*b*x))/(3*x^(3/2))","A",1
435,1,38,43,0.033015,"\int x^m (a+b x)^2 \, dx","Integrate[x^m*(a + b*x)^2,x]","x^{m+1} \left(\frac{a^2}{m+1}+\frac{2 a b x}{m+2}+\frac{b^2 x^2}{m+3}\right)","\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,"x^(1 + m)*(a^2/(1 + m) + (2*a*b*x)/(2 + m) + (b^2*x^2)/(3 + m))","A",1
436,1,28,36,0.007748,"\int x^{5/2} (a+b x)^2 \, dx","Integrate[x^(5/2)*(a + b*x)^2,x]","\frac{2}{693} x^{7/2} \left(99 a^2+154 a b x+63 b^2 x^2\right)","\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*x^(7/2)*(99*a^2 + 154*a*b*x + 63*b^2*x^2))/693","A",1
437,1,28,36,0.007479,"\int x^{3/2} (a+b x)^2 \, dx","Integrate[x^(3/2)*(a + b*x)^2,x]","\frac{2}{315} x^{5/2} \left(63 a^2+90 a b x+35 b^2 x^2\right)","\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*x^(5/2)*(63*a^2 + 90*a*b*x + 35*b^2*x^2))/315","A",1
438,1,28,36,0.0073366,"\int \sqrt{x} (a+b x)^2 \, dx","Integrate[Sqrt[x]*(a + b*x)^2,x]","\frac{2}{105} x^{3/2} \left(35 a^2+42 a b x+15 b^2 x^2\right)","\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*x^(3/2)*(35*a^2 + 42*a*b*x + 15*b^2*x^2))/105","A",1
439,1,28,34,0.0074954,"\int \frac{(a+b x)^2}{\sqrt{x}} \, dx","Integrate[(a + b*x)^2/Sqrt[x],x]","\frac{2}{15} \sqrt{x} \left(15 a^2+10 a b x+3 b^2 x^2\right)","2 a^2 \sqrt{x}+\frac{4}{3} a b x^{3/2}+\frac{2}{5} b^2 x^{5/2}",1,"(2*Sqrt[x]*(15*a^2 + 10*a*b*x + 3*b^2*x^2))/15","A",1
440,1,27,32,0.0077925,"\int \frac{(a+b x)^2}{x^{3/2}} \, dx","Integrate[(a + b*x)^2/x^(3/2),x]","\frac{2 \left(-3 a^2+6 a b x+b^2 x^2\right)}{3 \sqrt{x}}","-\frac{2 a^2}{\sqrt{x}}+4 a b \sqrt{x}+\frac{2}{3} b^2 x^{3/2}",1,"(2*(-3*a^2 + 6*a*b*x + b^2*x^2))/(3*Sqrt[x])","A",1
441,1,26,32,0.0086293,"\int \frac{(a+b x)^2}{x^{5/2}} \, dx","Integrate[(a + b*x)^2/x^(5/2),x]","-\frac{2 \left(a^2+6 a b x-3 b^2 x^2\right)}{3 x^{3/2}}","-\frac{2 a^2}{3 x^{3/2}}-\frac{4 a b}{\sqrt{x}}+2 b^2 \sqrt{x}",1,"(-2*(a^2 + 6*a*b*x - 3*b^2*x^2))/(3*x^(3/2))","A",1
442,1,54,61,0.0319516,"\int x^m (a+b x)^3 \, dx","Integrate[x^m*(a + b*x)^3,x]","x^{m+1} \left(\frac{a^3}{m+1}+\frac{3 a^2 b x}{m+2}+\frac{3 a b^2 x^2}{m+3}+\frac{b^3 x^3}{m+4}\right)","\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,"x^(1 + m)*(a^3/(1 + m) + (3*a^2*b*x)/(2 + m) + (3*a*b^2*x^2)/(3 + m) + (b^3*x^3)/(4 + m))","A",1
443,1,39,51,0.0104644,"\int x^{5/2} (a+b x)^3 \, dx","Integrate[x^(5/2)*(a + b*x)^3,x]","\frac{2 x^{7/2} \left(429 a^3+1001 a^2 b x+819 a b^2 x^2+231 b^3 x^3\right)}{3003}","\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*x^(7/2)*(429*a^3 + 1001*a^2*b*x + 819*a*b^2*x^2 + 231*b^3*x^3))/3003","A",1
444,1,39,51,0.0104358,"\int x^{3/2} (a+b x)^3 \, dx","Integrate[x^(3/2)*(a + b*x)^3,x]","\frac{2 x^{5/2} \left(231 a^3+495 a^2 b x+385 a b^2 x^2+105 b^3 x^3\right)}{1155}","\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*x^(5/2)*(231*a^3 + 495*a^2*b*x + 385*a*b^2*x^2 + 105*b^3*x^3))/1155","A",1
445,1,39,51,0.0102487,"\int \sqrt{x} (a+b x)^3 \, dx","Integrate[Sqrt[x]*(a + b*x)^3,x]","\frac{2}{315} x^{3/2} \left(105 a^3+189 a^2 b x+135 a b^2 x^2+35 b^3 x^3\right)","\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*x^(3/2)*(105*a^3 + 189*a^2*b*x + 135*a*b^2*x^2 + 35*b^3*x^3))/315","A",1
446,1,39,47,0.0100772,"\int \frac{(a+b x)^3}{\sqrt{x}} \, dx","Integrate[(a + b*x)^3/Sqrt[x],x]","\frac{2}{35} \sqrt{x} \left(35 a^3+35 a^2 b x+21 a b^2 x^2+5 b^3 x^3\right)","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*Sqrt[x]*(35*a^3 + 35*a^2*b*x + 21*a*b^2*x^2 + 5*b^3*x^3))/35","A",1
447,1,38,45,0.0110814,"\int \frac{(a+b x)^3}{x^{3/2}} \, dx","Integrate[(a + b*x)^3/x^(3/2),x]","\frac{2 \left(-5 a^3+15 a^2 b x+5 a b^2 x^2+b^3 x^3\right)}{5 \sqrt{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}",1,"(2*(-5*a^3 + 15*a^2*b*x + 5*a*b^2*x^2 + b^3*x^3))/(5*Sqrt[x])","A",1
448,1,38,47,0.0117494,"\int \frac{(a+b x)^3}{x^{5/2}} \, dx","Integrate[(a + b*x)^3/x^(5/2),x]","\frac{2 \left(-a^3-9 a^2 b x+9 a b^2 x^2+b^3 x^3\right)}{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 - 9*a^2*b*x + 9*a*b^2*x^2 + b^3*x^3))/(3*x^(3/2))","A",1
449,1,61,68,0.0263561,"\int \frac{x^{5/2}}{a+b x} \, dx","Integrate[x^(5/2)/(a + b*x),x]","\frac{2 \sqrt{x} \left(15 a^2-5 a b x+3 b^2 x^2\right)}{15 b^3}-\frac{2 a^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{7/2}}","-\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*Sqrt[x]*(15*a^2 - 5*a*b*x + 3*b^2*x^2))/(15*b^3) - (2*a^(5/2)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/b^(7/2)","A",1
450,1,49,53,0.0185687,"\int \frac{x^{3/2}}{a+b x} \, dx","Integrate[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 \sqrt{x} (b x-3 a)}{3 b^2}","\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*Sqrt[x]*(-3*a + b*x))/(3*b^2) + (2*a^(3/2)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/b^(5/2)","A",1
451,1,40,40,0.0097571,"\int \frac{\sqrt{x}}{a+b x} \, dx","Integrate[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
452,1,29,29,0.0051826,"\int \frac{1}{\sqrt{x} (a+b x)} \, dx","Integrate[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
453,1,25,40,0.0046025,"\int \frac{1}{x^{3/2} (a+b x)} \, dx","Integrate[1/(x^(3/2)*(a + b*x)),x]","-\frac{2 \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};-\frac{b x}{a}\right)}{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*Hypergeometric2F1[-1/2, 1, 1/2, -((b*x)/a)])/(a*Sqrt[x])","C",1
454,1,27,53,0.005149,"\int \frac{1}{x^{5/2} (a+b x)} \, dx","Integrate[1/(x^(5/2)*(a + b*x)),x]","-\frac{2 \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};-\frac{b x}{a}\right)}{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*Hypergeometric2F1[-3/2, 1, -1/2, -((b*x)/a)])/(3*a*x^(3/2))","C",1
455,1,27,68,0.0055069,"\int \frac{1}{x^{7/2} (a+b x)} \, dx","Integrate[1/(x^(7/2)*(a + b*x)),x]","-\frac{2 \, _2F_1\left(-\frac{5}{2},1;-\frac{3}{2};-\frac{b x}{a}\right)}{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*Hypergeometric2F1[-5/2, 1, -3/2, -((b*x)/a)])/(5*a*x^(5/2))","C",1
456,1,27,70,0.0048013,"\int \frac{x^{5/2}}{(a+b x)^2} \, dx","Integrate[x^(5/2)/(a + b*x)^2,x]","\frac{2 x^{7/2} \, _2F_1\left(2,\frac{7}{2};\frac{9}{2};-\frac{b x}{a}\right)}{7 a^2}","\frac{5 a^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{7/2}}-\frac{5 a \sqrt{x}}{b^3}-\frac{x^{5/2}}{b (a+b x)}+\frac{5 x^{3/2}}{3 b^2}",1,"(2*x^(7/2)*Hypergeometric2F1[2, 7/2, 9/2, -((b*x)/a)])/(7*a^2)","C",1
457,1,27,57,0.0037484,"\int \frac{x^{3/2}}{(a+b x)^2} \, dx","Integrate[x^(3/2)/(a + b*x)^2,x]","\frac{2 x^{5/2} \, _2F_1\left(2,\frac{5}{2};\frac{7}{2};-\frac{b x}{a}\right)}{5 a^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*x^(5/2)*Hypergeometric2F1[2, 5/2, 7/2, -((b*x)/a)])/(5*a^2)","C",1
458,1,46,46,0.0201005,"\int \frac{\sqrt{x}}{(a+b x)^2} \, dx","Integrate[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
459,1,45,45,0.0174929,"\int \frac{1}{\sqrt{x} (a+b x)^2} \, dx","Integrate[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^2+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^2 + a*b*x) + ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]]/(a^(3/2)*Sqrt[b])","A",1
460,1,25,56,0.0048452,"\int \frac{1}{x^{3/2} (a+b x)^2} \, dx","Integrate[1/(x^(3/2)*(a + b*x)^2),x]","-\frac{2 \, _2F_1\left(-\frac{1}{2},2;\frac{1}{2};-\frac{b x}{a}\right)}{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*Hypergeometric2F1[-1/2, 2, 1/2, -((b*x)/a)])/(a^2*Sqrt[x])","C",1
461,1,27,69,0.0052704,"\int \frac{1}{x^{5/2} (a+b x)^2} \, dx","Integrate[1/(x^(5/2)*(a + b*x)^2),x]","-\frac{2 \, _2F_1\left(-\frac{3}{2},2;-\frac{1}{2};-\frac{b x}{a}\right)}{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*Hypergeometric2F1[-3/2, 2, -1/2, -((b*x)/a)])/(3*a^2*x^(3/2))","C",1
462,1,27,95,0.004829,"\int \frac{x^{7/2}}{(a+b x)^3} \, dx","Integrate[x^(7/2)/(a + b*x)^3,x]","\frac{2 x^{9/2} \, _2F_1\left(3,\frac{9}{2};\frac{11}{2};-\frac{b x}{a}\right)}{9 a^3}","\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,"(2*x^(9/2)*Hypergeometric2F1[3, 9/2, 11/2, -((b*x)/a)])/(9*a^3)","C",1
463,1,27,82,0.0049109,"\int \frac{x^{5/2}}{(a+b x)^3} \, dx","Integrate[x^(5/2)/(a + b*x)^3,x]","\frac{2 x^{7/2} \, _2F_1\left(3,\frac{7}{2};\frac{9}{2};-\frac{b x}{a}\right)}{7 a^3}","-\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,"(2*x^(7/2)*Hypergeometric2F1[3, 7/2, 9/2, -((b*x)/a)])/(7*a^3)","C",1
464,1,59,70,0.0348109,"\int \frac{x^{3/2}}{(a+b x)^3} \, dx","Integrate[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{\sqrt{x} (3 a+5 b x)}{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,"-1/4*(Sqrt[x]*(3*a + 5*b*x))/(b^2*(a + b*x)^2) + (3*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(4*Sqrt[a]*b^(5/2))","A",1
465,1,27,73,0.0054129,"\int \frac{\sqrt{x}}{(a+b x)^3} \, dx","Integrate[Sqrt[x]/(a + b*x)^3,x]","\frac{2 x^{3/2} \, _2F_1\left(\frac{3}{2},3;\frac{5}{2};-\frac{b x}{a}\right)}{3 a^3}","\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,"(2*x^(3/2)*Hypergeometric2F1[3/2, 3, 5/2, -((b*x)/a)])/(3*a^3)","C",1
466,1,25,70,0.0047166,"\int \frac{1}{\sqrt{x} (a+b x)^3} \, dx","Integrate[1/(Sqrt[x]*(a + b*x)^3),x]","\frac{2 \sqrt{x} \, _2F_1\left(\frac{1}{2},3;\frac{3}{2};-\frac{b x}{a}\right)}{a^3}","\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,"(2*Sqrt[x]*Hypergeometric2F1[1/2, 3, 3/2, -((b*x)/a)])/a^3","C",1
467,1,25,82,0.005113,"\int \frac{1}{x^{3/2} (a+b x)^3} \, dx","Integrate[1/(x^(3/2)*(a + b*x)^3),x]","-\frac{2 \, _2F_1\left(-\frac{1}{2},3;\frac{1}{2};-\frac{b x}{a}\right)}{a^3 \sqrt{x}}","-\frac{15 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 a^{7/2}}-\frac{15}{4 a^3 \sqrt{x}}+\frac{5}{4 a^2 \sqrt{x} (a+b x)}+\frac{1}{2 a \sqrt{x} (a+b x)^2}",1,"(-2*Hypergeometric2F1[-1/2, 3, 1/2, -((b*x)/a)])/(a^3*Sqrt[x])","C",1
468,1,27,95,0.0051368,"\int \frac{1}{x^{5/2} (a+b x)^3} \, dx","Integrate[1/(x^(5/2)*(a + b*x)^3),x]","-\frac{2 \, _2F_1\left(-\frac{3}{2},3;-\frac{1}{2};-\frac{b x}{a}\right)}{3 a^3 x^{3/2}}","\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*Hypergeometric2F1[-3/2, 3, -1/2, -((b*x)/a)])/(3*a^3*x^(3/2))","C",1
469,1,61,68,0.0257123,"\int \frac{x^{5/2}}{-a+b x} \, dx","Integrate[x^(5/2)/(-a + b*x),x]","\frac{2 \sqrt{x} \left(15 a^2+5 a b x+3 b^2 x^2\right)}{15 b^3}-\frac{2 a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{7/2}}","-\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*Sqrt[x]*(15*a^2 + 5*a*b*x + 3*b^2*x^2))/(15*b^3) - (2*a^(5/2)*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/b^(7/2)","A",1
470,1,49,53,0.0186383,"\int \frac{x^{3/2}}{-a+b x} \, dx","Integrate[x^(3/2)/(-a + b*x),x]","\frac{2 \sqrt{x} (3 a+b x)}{3 b^2}-\frac{2 a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{5/2}}","-\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*Sqrt[x]*(3*a + b*x))/(3*b^2) - (2*a^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/b^(5/2)","A",1
471,1,40,40,0.0103782,"\int \frac{\sqrt{x}}{-a+b x} \, dx","Integrate[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
472,1,29,29,0.0055435,"\int \frac{1}{\sqrt{x} (-a+b x)} \, dx","Integrate[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
473,1,24,40,0.0043166,"\int \frac{1}{x^{3/2} (-a+b x)} \, dx","Integrate[1/(x^(3/2)*(-a + b*x)),x]","\frac{2 \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{b x}{a}\right)}{a \sqrt{x}}","\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*Hypergeometric2F1[-1/2, 1, 1/2, (b*x)/a])/(a*Sqrt[x])","C",1
474,1,26,53,0.0049514,"\int \frac{1}{x^{5/2} (-a+b x)} \, dx","Integrate[1/(x^(5/2)*(-a + b*x)),x]","\frac{2 \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};\frac{b x}{a}\right)}{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*Hypergeometric2F1[-3/2, 1, -1/2, (b*x)/a])/(3*a*x^(3/2))","C",1
475,1,26,68,0.0051375,"\int \frac{1}{x^{7/2} (-a+b x)} \, dx","Integrate[1/(x^(7/2)*(-a + b*x)),x]","\frac{2 \, _2F_1\left(-\frac{5}{2},1;-\frac{3}{2};\frac{b x}{a}\right)}{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*Hypergeometric2F1[-5/2, 1, -3/2, (b*x)/a])/(5*a*x^(5/2))","C",1
476,1,26,70,0.0054244,"\int \frac{x^{5/2}}{(-a+b x)^2} \, dx","Integrate[x^(5/2)/(-a + b*x)^2,x]","\frac{2 x^{7/2} \, _2F_1\left(2,\frac{7}{2};\frac{9}{2};\frac{b x}{a}\right)}{7 a^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,"(2*x^(7/2)*Hypergeometric2F1[2, 7/2, 9/2, (b*x)/a])/(7*a^2)","C",1
477,1,26,57,0.0049577,"\int \frac{x^{3/2}}{(-a+b x)^2} \, dx","Integrate[x^(3/2)/(-a + b*x)^2,x]","\frac{2 x^{5/2} \, _2F_1\left(2,\frac{5}{2};\frac{7}{2};\frac{b x}{a}\right)}{5 a^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,"(2*x^(5/2)*Hypergeometric2F1[2, 5/2, 7/2, (b*x)/a])/(5*a^2)","C",1
478,1,61,47,0.0160166,"\int \frac{\sqrt{x}}{(-a+b x)^2} \, dx","Integrate[Sqrt[x]/(-a + b*x)^2,x]","\frac{\sqrt{a} \sqrt{b} \sqrt{x}+(b x-a) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{\sqrt{a} b^{3/2} (a-b x)}","\frac{\sqrt{x}}{b (a-b x)}-\frac{\tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{\sqrt{a} b^{3/2}}",1,"(Sqrt[a]*Sqrt[b]*Sqrt[x] + (-a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(Sqrt[a]*b^(3/2)*(a - b*x))","A",1
479,1,46,46,0.0203879,"\int \frac{1}{\sqrt{x} (-a+b x)^2} \, dx","Integrate[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^2-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^2 - a*b*x) + ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a]]/(a^(3/2)*Sqrt[b])","A",1
480,1,24,57,0.006395,"\int \frac{1}{x^{3/2} (-a+b x)^2} \, dx","Integrate[1/(x^(3/2)*(-a + b*x)^2),x]","-\frac{2 \, _2F_1\left(-\frac{1}{2},2;\frac{1}{2};\frac{b x}{a}\right)}{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*Hypergeometric2F1[-1/2, 2, 1/2, (b*x)/a])/(a^2*Sqrt[x])","C",1
481,1,26,70,0.0061609,"\int \frac{1}{x^{5/2} (-a+b x)^2} \, dx","Integrate[1/(x^(5/2)*(-a + b*x)^2),x]","-\frac{2 \, _2F_1\left(-\frac{3}{2},2;-\frac{1}{2};\frac{b x}{a}\right)}{3 a^2 x^{3/2}}","\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*Hypergeometric2F1[-3/2, 2, -1/2, (b*x)/a])/(3*a^2*x^(3/2))","C",1
482,1,26,97,0.0056493,"\int \frac{x^{7/2}}{(-a+b x)^3} \, dx","Integrate[x^(7/2)/(-a + b*x)^3,x]","-\frac{2 x^{9/2} \, _2F_1\left(3,\frac{9}{2};\frac{11}{2};\frac{b x}{a}\right)}{9 a^3}","-\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,"(-2*x^(9/2)*Hypergeometric2F1[3, 9/2, 11/2, (b*x)/a])/(9*a^3)","C",1
483,1,26,84,0.0046673,"\int \frac{x^{5/2}}{(-a+b x)^3} \, dx","Integrate[x^(5/2)/(-a + b*x)^3,x]","-\frac{2 x^{7/2} \, _2F_1\left(3,\frac{7}{2};\frac{9}{2};\frac{b x}{a}\right)}{7 a^3}","-\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,"(-2*x^(7/2)*Hypergeometric2F1[3, 7/2, 9/2, (b*x)/a])/(7*a^3)","C",1
484,1,60,72,0.0363111,"\int \frac{x^{3/2}}{(-a+b x)^3} \, dx","Integrate[x^(3/2)/(-a + b*x)^3,x]","\frac{\sqrt{x} (3 a-5 b x)}{4 b^2 (a-b x)^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,"(Sqrt[x]*(3*a - 5*b*x))/(4*b^2*(a - b*x)^2) - (3*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(4*Sqrt[a]*b^(5/2))","A",1
485,1,26,75,0.0052344,"\int \frac{\sqrt{x}}{(-a+b x)^3} \, dx","Integrate[Sqrt[x]/(-a + b*x)^3,x]","-\frac{2 x^{3/2} \, _2F_1\left(\frac{3}{2},3;\frac{5}{2};\frac{b x}{a}\right)}{3 a^3}","\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,"(-2*x^(3/2)*Hypergeometric2F1[3/2, 3, 5/2, (b*x)/a])/(3*a^3)","C",1
486,1,24,72,0.0050601,"\int \frac{1}{\sqrt{x} (-a+b x)^3} \, dx","Integrate[1/(Sqrt[x]*(-a + b*x)^3),x]","-\frac{2 \sqrt{x} \, _2F_1\left(\frac{1}{2},3;\frac{3}{2};\frac{b x}{a}\right)}{a^3}","-\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,"(-2*Sqrt[x]*Hypergeometric2F1[1/2, 3, 3/2, (b*x)/a])/a^3","C",1
487,1,24,84,0.0050524,"\int \frac{1}{x^{3/2} (-a+b x)^3} \, dx","Integrate[1/(x^(3/2)*(-a + b*x)^3),x]","\frac{2 \, _2F_1\left(-\frac{1}{2},3;\frac{1}{2};\frac{b x}{a}\right)}{a^3 \sqrt{x}}","-\frac{15 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 a^{7/2}}+\frac{15}{4 a^3 \sqrt{x}}-\frac{5}{4 a^2 \sqrt{x} (a-b x)}-\frac{1}{2 a \sqrt{x} (a-b x)^2}",1,"(2*Hypergeometric2F1[-1/2, 3, 1/2, (b*x)/a])/(a^3*Sqrt[x])","C",1
488,1,26,97,0.0041784,"\int \frac{1}{x^{5/2} (-a+b x)^3} \, dx","Integrate[1/(x^(5/2)*(-a + b*x)^3),x]","\frac{2 \, _2F_1\left(-\frac{3}{2},3;-\frac{1}{2};\frac{b x}{a}\right)}{3 a^3 x^{3/2}}","-\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*Hypergeometric2F1[-3/2, 3, -1/2, (b*x)/a])/(3*a^3*x^(3/2))","C",1
489,1,96,122,0.1846846,"\int x^{5/2} \sqrt{a+b x} \, dx","Integrate[x^(5/2)*Sqrt[a + b*x],x]","\frac{\sqrt{a+b x} \left(\sqrt{b} \sqrt{x} \left(15 a^3-10 a^2 b x+8 a b^2 x^2+48 b^3 x^3\right)-\frac{15 a^{7/2} \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{\sqrt{\frac{b x}{a}+1}}\right)}{192 b^{7/2}}","-\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,"(Sqrt[a + b*x]*(Sqrt[b]*Sqrt[x]*(15*a^3 - 10*a^2*b*x + 8*a*b^2*x^2 + 48*b^3*x^3) - (15*a^(7/2)*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/Sqrt[1 + (b*x)/a]))/(192*b^(7/2))","A",1
490,1,85,98,0.1073777,"\int x^{3/2} \sqrt{a+b x} \, dx","Integrate[x^(3/2)*Sqrt[a + b*x],x]","\frac{\sqrt{a+b x} \left(\frac{3 a^{5/2} \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{\sqrt{\frac{b x}{a}+1}}+\sqrt{b} \sqrt{x} \left(-3 a^2+2 a b x+8 b^2 x^2\right)\right)}{24 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,"(Sqrt[a + b*x]*(Sqrt[b]*Sqrt[x]*(-3*a^2 + 2*a*b*x + 8*b^2*x^2) + (3*a^(5/2)*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/Sqrt[1 + (b*x)/a]))/(24*b^(5/2))","A",1
491,1,72,74,0.1098694,"\int \sqrt{x} \sqrt{a+b x} \, dx","Integrate[Sqrt[x]*Sqrt[a + b*x],x]","\frac{\sqrt{a+b x} \left(\sqrt{b} \sqrt{x} (a+2 b x)-\frac{a^{3/2} \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{\sqrt{\frac{b x}{a}+1}}\right)}{4 b^{3/2}}","-\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,"(Sqrt[a + b*x]*(Sqrt[b]*Sqrt[x]*(a + 2*b*x) - (a^(3/2)*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/Sqrt[1 + (b*x)/a]))/(4*b^(3/2))","A",1
492,1,62,44,0.085798,"\int \frac{\sqrt{a+b x}}{\sqrt{x}} \, dx","Integrate[Sqrt[a + b*x]/Sqrt[x],x]","\frac{\frac{a^{3/2} \sqrt{\frac{b x}{a}+1} \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{\sqrt{b}}+\sqrt{x} (a+b x)}{\sqrt{a+b x}}","\sqrt{x} \sqrt{a+b x}+\frac{a \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{\sqrt{b}}",1,"(Sqrt[x]*(a + b*x) + (a^(3/2)*Sqrt[1 + (b*x)/a]*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/Sqrt[b])/Sqrt[a + b*x]","A",1
493,1,64,45,0.095093,"\int \frac{\sqrt{a+b x}}{x^{3/2}} \, dx","Integrate[Sqrt[a + b*x]/x^(3/2),x]","\frac{2 \left(\sqrt{a} \sqrt{b} \sqrt{\frac{b x}{a}+1} \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)-\frac{a+b x}{\sqrt{x}}\right)}{\sqrt{a+b x}}","2 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)-\frac{2 \sqrt{a+b x}}{\sqrt{x}}",1,"(2*(-((a + b*x)/Sqrt[x]) + Sqrt[a]*Sqrt[b]*Sqrt[1 + (b*x)/a]*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[a]]))/Sqrt[a + b*x]","A",1
494,1,21,21,0.0068899,"\int \frac{\sqrt{a+b x}}{x^{5/2}} \, dx","Integrate[Sqrt[a + b*x]/x^(5/2),x]","-\frac{2 (a+b x)^{3/2}}{3 a x^{3/2}}","-\frac{2 (a+b x)^{3/2}}{3 a x^{3/2}}",1,"(-2*(a + b*x)^(3/2))/(3*a*x^(3/2))","A",1
495,1,29,44,0.00865,"\int \frac{\sqrt{a+b x}}{x^{7/2}} \, dx","Integrate[Sqrt[a + b*x]/x^(7/2),x]","-\frac{2 (3 a-2 b x) (a+b x)^{3/2}}{15 a^2 x^{5/2}}","\frac{4 b (a+b x)^{3/2}}{15 a^2 x^{3/2}}-\frac{2 (a+b x)^{3/2}}{5 a x^{5/2}}",1,"(-2*(3*a - 2*b*x)*(a + b*x)^(3/2))/(15*a^2*x^(5/2))","A",1
496,1,40,68,0.010898,"\int \frac{\sqrt{a+b x}}{x^{9/2}} \, dx","Integrate[Sqrt[a + b*x]/x^(9/2),x]","-\frac{2 (a+b x)^{3/2} \left(15 a^2-12 a b x+8 b^2 x^2\right)}{105 a^3 x^{7/2}}","-\frac{16 b^2 (a+b x)^{3/2}}{105 a^3 x^{3/2}}+\frac{8 b (a+b x)^{3/2}}{35 a^2 x^{5/2}}-\frac{2 (a+b x)^{3/2}}{7 a x^{7/2}}",1,"(-2*(a + b*x)^(3/2)*(15*a^2 - 12*a*b*x + 8*b^2*x^2))/(105*a^3*x^(7/2))","A",1
497,1,98,127,0.1407319,"\int x^{5/2} \sqrt{a-b x} \, dx","Integrate[x^(5/2)*Sqrt[a - b*x],x]","\frac{\sqrt{a-b x} \left(\frac{15 a^{7/2} \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{\sqrt{1-\frac{b x}{a}}}+\sqrt{b} \sqrt{x} \left(-15 a^3-10 a^2 b x-8 a b^2 x^2+48 b^3 x^3\right)\right)}{192 b^{7/2}}","\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,"(Sqrt[a - b*x]*(Sqrt[b]*Sqrt[x]*(-15*a^3 - 10*a^2*b*x - 8*a*b^2*x^2 + 48*b^3*x^3) + (15*a^(7/2)*ArcSin[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/Sqrt[1 - (b*x)/a]))/(192*b^(7/2))","A",1
498,1,87,102,0.1173172,"\int x^{3/2} \sqrt{a-b x} \, dx","Integrate[x^(3/2)*Sqrt[a - b*x],x]","\frac{\sqrt{a-b x} \left(\frac{3 a^{5/2} \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{\sqrt{1-\frac{b x}{a}}}+\sqrt{b} \sqrt{x} \left(-3 a^2-2 a b x+8 b^2 x^2\right)\right)}{24 b^{5/2}}","\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,"(Sqrt[a - b*x]*(Sqrt[b]*Sqrt[x]*(-3*a^2 - 2*a*b*x + 8*b^2*x^2) + (3*a^(5/2)*ArcSin[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/Sqrt[1 - (b*x)/a]))/(24*b^(5/2))","A",1
499,1,75,77,0.0972044,"\int \sqrt{x} \sqrt{a-b x} \, dx","Integrate[Sqrt[x]*Sqrt[a - b*x],x]","\frac{\sqrt{a-b x} \left(\frac{a^{3/2} \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{\sqrt{1-\frac{b x}{a}}}+\sqrt{b} \sqrt{x} (2 b x-a)\right)}{4 b^{3/2}}","\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,"(Sqrt[a - b*x]*(Sqrt[b]*Sqrt[x]*(-a + 2*b*x) + (a^(3/2)*ArcSin[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/Sqrt[1 - (b*x)/a]))/(4*b^(3/2))","A",1
500,1,65,46,0.0901566,"\int \frac{\sqrt{a-b x}}{\sqrt{x}} \, dx","Integrate[Sqrt[a - b*x]/Sqrt[x],x]","\frac{\frac{a^{3/2} \sqrt{1-\frac{b x}{a}} \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{\sqrt{b}}+\sqrt{x} (a-b x)}{\sqrt{a-b x}}","\sqrt{x} \sqrt{a-b x}+\frac{a \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)}{\sqrt{b}}",1,"(Sqrt[x]*(a - b*x) + (a^(3/2)*Sqrt[1 - (b*x)/a]*ArcSin[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/Sqrt[b])/Sqrt[a - b*x]","A",1
501,1,69,47,0.0604543,"\int \frac{\sqrt{a-b x}}{x^{3/2}} \, dx","Integrate[Sqrt[a - b*x]/x^(3/2),x]","-\frac{2 \left(\sqrt{a} \sqrt{b} \sqrt{x} \sqrt{1-\frac{b x}{a}} \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)+a-b x\right)}{\sqrt{x} \sqrt{a-b x}}","-\frac{2 \sqrt{a-b x}}{\sqrt{x}}-2 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)",1,"(-2*(a - b*x + Sqrt[a]*Sqrt[b]*Sqrt[x]*Sqrt[1 - (b*x)/a]*ArcSin[(Sqrt[b]*Sqrt[x])/Sqrt[a]]))/(Sqrt[x]*Sqrt[a - b*x])","A",1
502,1,22,22,0.0065847,"\int \frac{\sqrt{a-b x}}{x^{5/2}} \, dx","Integrate[Sqrt[a - b*x]/x^(5/2),x]","-\frac{2 (a-b x)^{3/2}}{3 a x^{3/2}}","-\frac{2 (a-b x)^{3/2}}{3 a x^{3/2}}",1,"(-2*(a - b*x)^(3/2))/(3*a*x^(3/2))","A",1
503,1,30,46,0.0088441,"\int \frac{\sqrt{a-b x}}{x^{7/2}} \, dx","Integrate[Sqrt[a - b*x]/x^(7/2),x]","-\frac{2 (a-b x)^{3/2} (3 a+2 b x)}{15 a^2 x^{5/2}}","-\frac{4 b (a-b x)^{3/2}}{15 a^2 x^{3/2}}-\frac{2 (a-b x)^{3/2}}{5 a x^{5/2}}",1,"(-2*(a - b*x)^(3/2)*(3*a + 2*b*x))/(15*a^2*x^(5/2))","A",1
504,1,41,71,0.0107535,"\int \frac{\sqrt{a-b x}}{x^{9/2}} \, dx","Integrate[Sqrt[a - b*x]/x^(9/2),x]","-\frac{2 (a-b x)^{3/2} \left(15 a^2+12 a b x+8 b^2 x^2\right)}{105 a^3 x^{7/2}}","-\frac{16 b^2 (a-b x)^{3/2}}{105 a^3 x^{3/2}}-\frac{8 b (a-b x)^{3/2}}{35 a^2 x^{5/2}}-\frac{2 (a-b x)^{3/2}}{7 a x^{7/2}}",1,"(-2*(a - b*x)^(3/2)*(15*a^2 + 12*a*b*x + 8*b^2*x^2))/(105*a^3*x^(7/2))","A",1
505,1,70,108,0.0466196,"\int x^{5/2} \sqrt{2+b x} \, dx","Integrate[x^(5/2)*Sqrt[2 + b*x],x]","\frac{\sqrt{x} \sqrt{b x+2} \left(6 b^3 x^3+2 b^2 x^2-5 b x+15\right)}{24 b^3}-\frac{5 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{4 b^{7/2}}","-\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,"(Sqrt[x]*Sqrt[2 + b*x]*(15 - 5*b*x + 2*b^2*x^2 + 6*b^3*x^3))/(24*b^3) - (5*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/(4*b^(7/2))","A",1
506,1,58,84,0.033547,"\int x^{3/2} \sqrt{2+b x} \, dx","Integrate[x^(3/2)*Sqrt[2 + b*x],x]","\frac{\sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{5/2}}+\frac{\sqrt{x} \sqrt{b x+2} \left(2 b^2 x^2+b x-3\right)}{6 b^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,"(Sqrt[x]*Sqrt[2 + b*x]*(-3 + b*x + 2*b^2*x^2))/(6*b^2) + ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[2]]/b^(5/2)","A",1
507,1,51,64,0.027044,"\int \sqrt{x} \sqrt{2+b x} \, dx","Integrate[Sqrt[x]*Sqrt[2 + b*x],x]","\frac{\sqrt{x} (b x+1) \sqrt{b x+2}}{2 b}-\frac{\sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{3/2}}","-\frac{\sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{3/2}}+\frac{1}{2} x^{3/2} \sqrt{b x+2}+\frac{\sqrt{x} \sqrt{b x+2}}{2 b}",1,"(Sqrt[x]*(1 + b*x)*Sqrt[2 + b*x])/(2*b) - ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[2]]/b^(3/2)","A",1
508,1,40,40,0.0130339,"\int \frac{\sqrt{2+b x}}{\sqrt{x}} \, dx","Integrate[Sqrt[2 + b*x]/Sqrt[x],x]","\sqrt{x} \sqrt{b x+2}+\frac{2 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{\sqrt{b}}","\sqrt{x} \sqrt{b x+2}+\frac{2 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{\sqrt{b}}",1,"Sqrt[x]*Sqrt[2 + b*x] + (2*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/Sqrt[b]","A",1
509,1,41,41,0.0123694,"\int \frac{\sqrt{2+b x}}{x^{3/2}} \, dx","Integrate[Sqrt[2 + b*x]/x^(3/2),x]","2 \sqrt{b} \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)-\frac{2 \sqrt{b x+2}}{\sqrt{x}}","2 \sqrt{b} \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)-\frac{2 \sqrt{b x+2}}{\sqrt{x}}",1,"(-2*Sqrt[2 + b*x])/Sqrt[x] + 2*Sqrt[b]*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[2]]","A",1
510,1,18,18,0.005218,"\int \frac{\sqrt{2+b x}}{x^{5/2}} \, dx","Integrate[Sqrt[2 + b*x]/x^(5/2),x]","-\frac{(b x+2)^{3/2}}{3 x^{3/2}}","-\frac{(b x+2)^{3/2}}{3 x^{3/2}}",1,"-1/3*(2 + b*x)^(3/2)/x^(3/2)","A",1
511,1,23,38,0.0070574,"\int \frac{\sqrt{2+b x}}{x^{7/2}} \, dx","Integrate[Sqrt[2 + b*x]/x^(7/2),x]","\frac{(b x-3) (b x+2)^{3/2}}{15 x^{5/2}}","\frac{b (b x+2)^{3/2}}{15 x^{3/2}}-\frac{(b x+2)^{3/2}}{5 x^{5/2}}",1,"((-3 + b*x)*(2 + b*x)^(3/2))/(15*x^(5/2))","A",1
512,1,32,59,0.0099482,"\int \frac{\sqrt{2+b x}}{x^{9/2}} \, dx","Integrate[Sqrt[2 + b*x]/x^(9/2),x]","-\frac{(b x+2)^{3/2} \left(2 b^2 x^2-6 b x+15\right)}{105 x^{7/2}}","-\frac{2 b^2 (b x+2)^{3/2}}{105 x^{3/2}}+\frac{2 b (b x+2)^{3/2}}{35 x^{5/2}}-\frac{(b x+2)^{3/2}}{7 x^{7/2}}",1,"-1/105*((2 + b*x)^(3/2)*(15 - 6*b*x + 2*b^2*x^2))/x^(7/2)","A",1
513,1,71,112,0.0442597,"\int x^{5/2} \sqrt{2-b x} \, dx","Integrate[x^(5/2)*Sqrt[2 - b*x],x]","\frac{5 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{4 b^{7/2}}+\frac{\sqrt{x} \sqrt{2-b x} \left(6 b^3 x^3-2 b^2 x^2-5 b x-15\right)}{24 b^3}","\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,"(Sqrt[x]*Sqrt[2 - b*x]*(-15 - 5*b*x - 2*b^2*x^2 + 6*b^3*x^3))/(24*b^3) + (5*ArcSin[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/(4*b^(7/2))","A",1
514,1,60,87,0.0352322,"\int x^{3/2} \sqrt{2-b x} \, dx","Integrate[x^(3/2)*Sqrt[2 - b*x],x]","\frac{\sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{5/2}}+\frac{\sqrt{x} \sqrt{2-b x} \left(2 b^2 x^2-b x-3\right)}{6 b^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,"(Sqrt[x]*Sqrt[2 - b*x]*(-3 - b*x + 2*b^2*x^2))/(6*b^2) + ArcSin[(Sqrt[b]*Sqrt[x])/Sqrt[2]]/b^(5/2)","A",1
515,1,51,65,0.0290942,"\int \sqrt{x} \sqrt{2-b x} \, dx","Integrate[Sqrt[x]*Sqrt[2 - b*x],x]","\frac{\sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{3/2}}+\frac{\sqrt{x} \sqrt{2-b x} (b x-1)}{2 b}","\frac{\sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{3/2}}+\frac{1}{2} x^{3/2} \sqrt{2-b x}-\frac{\sqrt{x} \sqrt{2-b x}}{2 b}",1,"(Sqrt[x]*Sqrt[2 - b*x]*(-1 + b*x))/(2*b) + ArcSin[(Sqrt[b]*Sqrt[x])/Sqrt[2]]/b^(3/2)","A",1
516,1,41,41,0.0140263,"\int \frac{\sqrt{2-b x}}{\sqrt{x}} \, dx","Integrate[Sqrt[2 - b*x]/Sqrt[x],x]","\sqrt{x} \sqrt{2-b x}+\frac{2 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{\sqrt{b}}","\sqrt{x} \sqrt{2-b x}+\frac{2 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{\sqrt{b}}",1,"Sqrt[x]*Sqrt[2 - b*x] + (2*ArcSin[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/Sqrt[b]","A",1
517,1,42,42,0.0136549,"\int \frac{\sqrt{2-b x}}{x^{3/2}} \, dx","Integrate[Sqrt[2 - b*x]/x^(3/2),x]","-\frac{2 \sqrt{2-b x}}{\sqrt{x}}-2 \sqrt{b} \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)","-\frac{2 \sqrt{2-b x}}{\sqrt{x}}-2 \sqrt{b} \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)",1,"(-2*Sqrt[2 - b*x])/Sqrt[x] - 2*Sqrt[b]*ArcSin[(Sqrt[b]*Sqrt[x])/Sqrt[2]]","A",1
518,1,19,19,0.0053299,"\int \frac{\sqrt{2-b x}}{x^{5/2}} \, dx","Integrate[Sqrt[2 - b*x]/x^(5/2),x]","-\frac{(2-b x)^{3/2}}{3 x^{3/2}}","-\frac{(2-b x)^{3/2}}{3 x^{3/2}}",1,"-1/3*(2 - b*x)^(3/2)/x^(3/2)","A",1
519,1,24,40,0.0082414,"\int \frac{\sqrt{2-b x}}{x^{7/2}} \, dx","Integrate[Sqrt[2 - b*x]/x^(7/2),x]","-\frac{(2-b x)^{3/2} (b x+3)}{15 x^{5/2}}","-\frac{b (2-b x)^{3/2}}{15 x^{3/2}}-\frac{(2-b x)^{3/2}}{5 x^{5/2}}",1,"-1/15*((2 - b*x)^(3/2)*(3 + b*x))/x^(5/2)","A",1
520,1,33,62,0.0095789,"\int \frac{\sqrt{2-b x}}{x^{9/2}} \, dx","Integrate[Sqrt[2 - b*x]/x^(9/2),x]","-\frac{(2-b x)^{3/2} \left(2 b^2 x^2+6 b x+15\right)}{105 x^{7/2}}","-\frac{2 b^2 (2-b x)^{3/2}}{105 x^{3/2}}-\frac{2 b (2-b x)^{3/2}}{35 x^{5/2}}-\frac{(2-b x)^{3/2}}{7 x^{7/2}}",1,"-1/105*((2 - b*x)^(3/2)*(15 + 6*b*x + 2*b^2*x^2))/x^(7/2)","A",1
521,1,107,143,0.2075345,"\int x^{5/2} (a+b x)^{3/2} \, dx","Integrate[x^(5/2)*(a + b*x)^(3/2),x]","\frac{\sqrt{a+b x} \left(\sqrt{b} \sqrt{x} \left(15 a^4-10 a^3 b x+8 a^2 b^2 x^2+176 a b^3 x^3+128 b^4 x^4\right)-\frac{15 a^{9/2} \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{\sqrt{\frac{b x}{a}+1}}\right)}{640 b^{7/2}}","-\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,"(Sqrt[a + b*x]*(Sqrt[b]*Sqrt[x]*(15*a^4 - 10*a^3*b*x + 8*a^2*b^2*x^2 + 176*a*b^3*x^3 + 128*b^4*x^4) - (15*a^(9/2)*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/Sqrt[1 + (b*x)/a]))/(640*b^(7/2))","A",1
522,1,96,119,0.1253846,"\int x^{3/2} (a+b x)^{3/2} \, dx","Integrate[x^(3/2)*(a + b*x)^(3/2),x]","\frac{\sqrt{a+b x} \left(\frac{3 a^{7/2} \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{\sqrt{\frac{b x}{a}+1}}+\sqrt{b} \sqrt{x} \left(-3 a^3+2 a^2 b x+24 a b^2 x^2+16 b^3 x^3\right)\right)}{64 b^{5/2}}","\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,"(Sqrt[a + b*x]*(Sqrt[b]*Sqrt[x]*(-3*a^3 + 2*a^2*b*x + 24*a*b^2*x^2 + 16*b^3*x^3) + (3*a^(7/2)*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/Sqrt[1 + (b*x)/a]))/(64*b^(5/2))","A",1
523,1,85,95,0.1147262,"\int \sqrt{x} (a+b x)^{3/2} \, dx","Integrate[Sqrt[x]*(a + b*x)^(3/2),x]","\frac{\sqrt{a+b x} \left(\sqrt{b} \sqrt{x} \left(3 a^2+14 a b x+8 b^2 x^2\right)-\frac{3 a^{5/2} \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{\sqrt{\frac{b x}{a}+1}}\right)}{24 b^{3/2}}","-\frac{a^3 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{8 b^{3/2}}+\frac{a^2 \sqrt{x} \sqrt{a+b x}}{8 b}+\frac{1}{4} a x^{3/2} \sqrt{a+b x}+\frac{1}{3} x^{3/2} (a+b x)^{3/2}",1,"(Sqrt[a + b*x]*(Sqrt[b]*Sqrt[x]*(3*a^2 + 14*a*b*x + 8*b^2*x^2) - (3*a^(5/2)*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/Sqrt[1 + (b*x)/a]))/(24*b^(3/2))","A",1
524,1,69,71,0.0983108,"\int \frac{(a+b x)^{3/2}}{\sqrt{x}} \, dx","Integrate[(a + b*x)^(3/2)/Sqrt[x],x]","\frac{1}{4} \sqrt{a+b x} \left(\frac{3 a^{3/2} \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{\sqrt{b} \sqrt{\frac{b x}{a}+1}}+\sqrt{x} (5 a+2 b x)\right)","\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,"(Sqrt[a + b*x]*(Sqrt[x]*(5*a + 2*b*x) + (3*a^(3/2)*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(Sqrt[b]*Sqrt[1 + (b*x)/a])))/4","A",1
525,1,46,63,0.0106988,"\int \frac{(a+b x)^{3/2}}{x^{3/2}} \, dx","Integrate[(a + b*x)^(3/2)/x^(3/2),x]","-\frac{2 a \sqrt{a+b x} \, _2F_1\left(-\frac{3}{2},-\frac{1}{2};\frac{1}{2};-\frac{b x}{a}\right)}{\sqrt{x} \sqrt{\frac{b x}{a}+1}}","-\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,"(-2*a*Sqrt[a + b*x]*Hypergeometric2F1[-3/2, -1/2, 1/2, -((b*x)/a)])/(Sqrt[x]*Sqrt[1 + (b*x)/a])","C",1
526,1,48,64,0.010202,"\int \frac{(a+b x)^{3/2}}{x^{5/2}} \, dx","Integrate[(a + b*x)^(3/2)/x^(5/2),x]","-\frac{2 a \sqrt{a+b x} \, _2F_1\left(-\frac{3}{2},-\frac{3}{2};-\frac{1}{2};-\frac{b x}{a}\right)}{3 x^{3/2} \sqrt{\frac{b x}{a}+1}}","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*Sqrt[a + b*x]*Hypergeometric2F1[-3/2, -3/2, -1/2, -((b*x)/a)])/(3*x^(3/2)*Sqrt[1 + (b*x)/a])","C",1
527,1,110,149,0.1712376,"\int x^{5/2} (a-b x)^{3/2} \, dx","Integrate[x^(5/2)*(a - b*x)^(3/2),x]","\frac{\sqrt{a-b x} \left(\frac{15 a^{9/2} \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{\sqrt{1-\frac{b x}{a}}}-\sqrt{b} \sqrt{x} \left(15 a^4+10 a^3 b x+8 a^2 b^2 x^2-176 a b^3 x^3+128 b^4 x^4\right)\right)}{640 b^{7/2}}","\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,"(Sqrt[a - b*x]*(-(Sqrt[b]*Sqrt[x]*(15*a^4 + 10*a^3*b*x + 8*a^2*b^2*x^2 - 176*a*b^3*x^3 + 128*b^4*x^4)) + (15*a^(9/2)*ArcSin[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/Sqrt[1 - (b*x)/a]))/(640*b^(7/2))","A",1
528,1,99,124,0.1452691,"\int x^{3/2} (a-b x)^{3/2} \, dx","Integrate[x^(3/2)*(a - b*x)^(3/2),x]","\frac{\sqrt{a-b x} \left(\frac{3 a^{7/2} \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{\sqrt{1-\frac{b x}{a}}}-\sqrt{b} \sqrt{x} \left(3 a^3+2 a^2 b x-24 a b^2 x^2+16 b^3 x^3\right)\right)}{64 b^{5/2}}","\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,"(Sqrt[a - b*x]*(-(Sqrt[b]*Sqrt[x]*(3*a^3 + 2*a^2*b*x - 24*a*b^2*x^2 + 16*b^3*x^3)) + (3*a^(7/2)*ArcSin[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/Sqrt[1 - (b*x)/a]))/(64*b^(5/2))","A",1
529,1,87,99,0.1212988,"\int \sqrt{x} (a-b x)^{3/2} \, dx","Integrate[Sqrt[x]*(a - b*x)^(3/2),x]","\frac{\sqrt{a-b x} \left(\frac{3 a^{5/2} \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{\sqrt{1-\frac{b x}{a}}}+\sqrt{b} \sqrt{x} \left(-3 a^2+14 a b x-8 b^2 x^2\right)\right)}{24 b^{3/2}}","\frac{a^3 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)}{8 b^{3/2}}-\frac{a^2 \sqrt{x} \sqrt{a-b x}}{8 b}+\frac{1}{4} a x^{3/2} \sqrt{a-b x}+\frac{1}{3} x^{3/2} (a-b x)^{3/2}",1,"(Sqrt[a - b*x]*(Sqrt[b]*Sqrt[x]*(-3*a^2 + 14*a*b*x - 8*b^2*x^2) + (3*a^(5/2)*ArcSin[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/Sqrt[1 - (b*x)/a]))/(24*b^(3/2))","A",1
530,1,71,74,0.1155745,"\int \frac{(a-b x)^{3/2}}{\sqrt{x}} \, dx","Integrate[(a - b*x)^(3/2)/Sqrt[x],x]","\frac{1}{4} \sqrt{a-b x} \left(\frac{3 a^{3/2} \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{\sqrt{b} \sqrt{1-\frac{b x}{a}}}+\sqrt{x} (5 a-2 b x)\right)","\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,"(Sqrt[a - b*x]*(Sqrt[x]*(5*a - 2*b*x) + (3*a^(3/2)*ArcSin[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(Sqrt[b]*Sqrt[1 - (b*x)/a])))/4","A",1
531,1,47,66,0.0113616,"\int \frac{(a-b x)^{3/2}}{x^{3/2}} \, dx","Integrate[(a - b*x)^(3/2)/x^(3/2),x]","-\frac{2 a \sqrt{a-b x} \, _2F_1\left(-\frac{3}{2},-\frac{1}{2};\frac{1}{2};\frac{b x}{a}\right)}{\sqrt{x} \sqrt{1-\frac{b x}{a}}}","-\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,"(-2*a*Sqrt[a - b*x]*Hypergeometric2F1[-3/2, -1/2, 1/2, (b*x)/a])/(Sqrt[x]*Sqrt[1 - (b*x)/a])","C",1
532,1,49,67,0.011383,"\int \frac{(a-b x)^{3/2}}{x^{5/2}} \, dx","Integrate[(a - b*x)^(3/2)/x^(5/2),x]","-\frac{2 a \sqrt{a-b x} \, _2F_1\left(-\frac{3}{2},-\frac{3}{2};-\frac{1}{2};\frac{b x}{a}\right)}{3 x^{3/2} \sqrt{1-\frac{b x}{a}}}","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*Sqrt[a - b*x]*Hypergeometric2F1[-3/2, -3/2, -1/2, (b*x)/a])/(3*x^(3/2)*Sqrt[1 - (b*x)/a])","C",1
533,1,78,126,0.0501421,"\int x^{5/2} (2+b x)^{3/2} \, dx","Integrate[x^(5/2)*(2 + b*x)^(3/2),x]","\frac{\sqrt{x} \sqrt{b x+2} \left(8 b^4 x^4+22 b^3 x^3+2 b^2 x^2-5 b x+15\right)}{40 b^3}-\frac{3 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{4 b^{7/2}}","-\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,"(Sqrt[x]*Sqrt[2 + b*x]*(15 - 5*b*x + 2*b^2*x^2 + 22*b^3*x^3 + 8*b^4*x^4))/(40*b^3) - (3*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/(4*b^(7/2))","A",1
534,1,70,105,0.0322328,"\int x^{3/2} (2+b x)^{3/2} \, dx","Integrate[x^(3/2)*(2 + b*x)^(3/2),x]","\frac{\sqrt{b} \sqrt{x} \sqrt{b x+2} \left(2 b^3 x^3+6 b^2 x^2+b x-3\right)+6 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{8 b^{5/2}}","\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,"(Sqrt[b]*Sqrt[x]*Sqrt[2 + b*x]*(-3 + b*x + 6*b^2*x^2 + 2*b^3*x^3) + 6*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/(8*b^(5/2))","A",1
535,1,60,82,0.0332903,"\int \sqrt{x} (2+b x)^{3/2} \, dx","Integrate[Sqrt[x]*(2 + b*x)^(3/2),x]","\frac{\sqrt{x} \sqrt{b x+2} \left(2 b^2 x^2+7 b x+3\right)}{6 b}-\frac{\sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\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,"(Sqrt[x]*Sqrt[2 + b*x]*(3 + 7*b*x + 2*b^2*x^2))/(6*b) - ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[2]]/b^(3/2)","A",1
536,1,48,61,0.0257512,"\int \frac{(2+b x)^{3/2}}{\sqrt{x}} \, dx","Integrate[(2 + b*x)^(3/2)/Sqrt[x],x]","\frac{1}{2} \sqrt{x} \sqrt{b x+2} (b x+5)+\frac{3 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{\sqrt{b}}","\frac{1}{2} \sqrt{x} (b x+2)^{3/2}+\frac{3}{2} \sqrt{x} \sqrt{b x+2}+\frac{3 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{\sqrt{b}}",1,"(Sqrt[x]*Sqrt[2 + b*x]*(5 + b*x))/2 + (3*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/Sqrt[b]","A",1
537,1,28,58,0.0047125,"\int \frac{(2+b x)^{3/2}}{x^{3/2}} \, dx","Integrate[(2 + b*x)^(3/2)/x^(3/2),x]","-\frac{4 \sqrt{2} \, _2F_1\left(-\frac{3}{2},-\frac{1}{2};\frac{1}{2};-\frac{b x}{2}\right)}{\sqrt{x}}","-\frac{2 (b x+2)^{3/2}}{\sqrt{x}}+3 b \sqrt{x} \sqrt{b x+2}+6 \sqrt{b} \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)",1,"(-4*Sqrt[2]*Hypergeometric2F1[-3/2, -1/2, 1/2, -1/2*(b*x)])/Sqrt[x]","C",1
538,1,30,60,0.0056504,"\int \frac{(2+b x)^{3/2}}{x^{5/2}} \, dx","Integrate[(2 + b*x)^(3/2)/x^(5/2),x]","-\frac{4 \sqrt{2} \, _2F_1\left(-\frac{3}{2},-\frac{3}{2};-\frac{1}{2};-\frac{b x}{2}\right)}{3 x^{3/2}}","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*Sqrt[2]*Hypergeometric2F1[-3/2, -3/2, -1/2, -1/2*(b*x)])/(3*x^(3/2))","C",1
539,1,79,131,0.0518426,"\int x^{5/2} (2-b x)^{3/2} \, dx","Integrate[x^(5/2)*(2 - b*x)^(3/2),x]","\frac{3 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{4 b^{7/2}}-\frac{\sqrt{x} \sqrt{2-b x} \left(8 b^4 x^4-22 b^3 x^3+2 b^2 x^2+5 b x+15\right)}{40 b^3}","\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,"-1/40*(Sqrt[x]*Sqrt[2 - b*x]*(15 + 5*b*x + 2*b^2*x^2 - 22*b^3*x^3 + 8*b^4*x^4))/b^3 + (3*ArcSin[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/(4*b^(7/2))","A",1
540,1,70,109,0.0448901,"\int x^{3/2} (2-b x)^{3/2} \, dx","Integrate[x^(3/2)*(2 - b*x)^(3/2),x]","\frac{3 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{4 b^{5/2}}-\frac{\sqrt{x} \sqrt{2-b x} \left(2 b^3 x^3-6 b^2 x^2+b x+3\right)}{8 b^2}","\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,"-1/8*(Sqrt[x]*Sqrt[2 - b*x]*(3 + b*x - 6*b^2*x^2 + 2*b^3*x^3))/b^2 + (3*ArcSin[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/(4*b^(5/2))","A",1
541,1,60,84,0.0417369,"\int \sqrt{x} (2-b x)^{3/2} \, dx","Integrate[Sqrt[x]*(2 - b*x)^(3/2),x]","\frac{\sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{3/2}}-\frac{\sqrt{x} \sqrt{2-b x} \left(2 b^2 x^2-7 b x+3\right)}{6 b}","\frac{\sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{3/2}}+\frac{1}{3} x^{3/2} (2-b x)^{3/2}+\frac{1}{2} x^{3/2} \sqrt{2-b x}-\frac{\sqrt{x} \sqrt{2-b x}}{2 b}",1,"-1/6*(Sqrt[x]*Sqrt[2 - b*x]*(3 - 7*b*x + 2*b^2*x^2))/b + ArcSin[(Sqrt[b]*Sqrt[x])/Sqrt[2]]/b^(3/2)","A",1
542,1,49,63,0.0288641,"\int \frac{(2-b x)^{3/2}}{\sqrt{x}} \, dx","Integrate[(2 - b*x)^(3/2)/Sqrt[x],x]","\frac{3 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{\sqrt{b}}-\frac{1}{2} \sqrt{x} \sqrt{2-b x} (b x-5)","\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,"-1/2*(Sqrt[x]*Sqrt[2 - b*x]*(-5 + b*x)) + (3*ArcSin[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/Sqrt[b]","A",1
543,1,28,60,0.0050227,"\int \frac{(2-b x)^{3/2}}{x^{3/2}} \, dx","Integrate[(2 - b*x)^(3/2)/x^(3/2),x]","-\frac{4 \sqrt{2} \, _2F_1\left(-\frac{3}{2},-\frac{1}{2};\frac{1}{2};\frac{b x}{2}\right)}{\sqrt{x}}","-\frac{2 (2-b x)^{3/2}}{\sqrt{x}}-3 b \sqrt{x} \sqrt{2-b x}-6 \sqrt{b} \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)",1,"(-4*Sqrt[2]*Hypergeometric2F1[-3/2, -1/2, 1/2, (b*x)/2])/Sqrt[x]","C",1
544,1,30,62,0.0058688,"\int \frac{(2-b x)^{3/2}}{x^{5/2}} \, dx","Integrate[(2 - b*x)^(3/2)/x^(5/2),x]","-\frac{4 \sqrt{2} \, _2F_1\left(-\frac{3}{2},-\frac{3}{2};-\frac{1}{2};\frac{b x}{2}\right)}{3 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*Sqrt[2]*Hypergeometric2F1[-3/2, -3/2, -1/2, (b*x)/2])/(3*x^(3/2))","C",1
545,1,118,164,0.2438898,"\int x^{5/2} (a+b x)^{5/2} \, dx","Integrate[x^(5/2)*(a + b*x)^(5/2),x]","\frac{\sqrt{a+b x} \left(\sqrt{b} \sqrt{x} \left(15 a^5-10 a^4 b x+8 a^3 b^2 x^2+432 a^2 b^3 x^3+640 a b^4 x^4+256 b^5 x^5\right)-\frac{15 a^{11/2} \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{\sqrt{\frac{b x}{a}+1}}\right)}{1536 b^{7/2}}","-\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,"(Sqrt[a + b*x]*(Sqrt[b]*Sqrt[x]*(15*a^5 - 10*a^4*b*x + 8*a^3*b^2*x^2 + 432*a^2*b^3*x^3 + 640*a*b^4*x^4 + 256*b^5*x^5) - (15*a^(11/2)*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/Sqrt[1 + (b*x)/a]))/(1536*b^(7/2))","A",1
546,1,107,140,0.1384521,"\int x^{3/2} (a+b x)^{5/2} \, dx","Integrate[x^(3/2)*(a + b*x)^(5/2),x]","\frac{\sqrt{a+b x} \left(\frac{15 a^{9/2} \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{\sqrt{\frac{b x}{a}+1}}+\sqrt{b} \sqrt{x} \left(-15 a^4+10 a^3 b x+248 a^2 b^2 x^2+336 a b^3 x^3+128 b^4 x^4\right)\right)}{640 b^{5/2}}","\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,"(Sqrt[a + b*x]*(Sqrt[b]*Sqrt[x]*(-15*a^4 + 10*a^3*b*x + 248*a^2*b^2*x^2 + 336*a*b^3*x^3 + 128*b^4*x^4) + (15*a^(9/2)*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/Sqrt[1 + (b*x)/a]))/(640*b^(5/2))","A",1
547,1,96,116,0.1989889,"\int \sqrt{x} (a+b x)^{5/2} \, dx","Integrate[Sqrt[x]*(a + b*x)^(5/2),x]","\frac{\sqrt{a+b x} \left(\sqrt{b} \sqrt{x} \left(15 a^3+118 a^2 b x+136 a b^2 x^2+48 b^3 x^3\right)-\frac{15 a^{7/2} \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{\sqrt{\frac{b x}{a}+1}}\right)}{192 b^{3/2}}","-\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,"(Sqrt[a + b*x]*(Sqrt[b]*Sqrt[x]*(15*a^3 + 118*a^2*b*x + 136*a*b^2*x^2 + 48*b^3*x^3) - (15*a^(7/2)*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/Sqrt[1 + (b*x)/a]))/(192*b^(3/2))","A",1
548,1,80,92,0.1105346,"\int \frac{(a+b x)^{5/2}}{\sqrt{x}} \, dx","Integrate[(a + b*x)^(5/2)/Sqrt[x],x]","\frac{1}{24} \sqrt{a+b x} \left(\frac{15 a^{5/2} \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{\sqrt{b} \sqrt{\frac{b x}{a}+1}}+\sqrt{x} \left(33 a^2+26 a b x+8 b^2 x^2\right)\right)","\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,"(Sqrt[a + b*x]*(Sqrt[x]*(33*a^2 + 26*a*b*x + 8*b^2*x^2) + (15*a^(5/2)*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(Sqrt[b]*Sqrt[1 + (b*x)/a])))/24","A",1
549,1,48,89,0.0115277,"\int \frac{(a+b x)^{5/2}}{x^{3/2}} \, dx","Integrate[(a + b*x)^(5/2)/x^(3/2),x]","-\frac{2 a^2 \sqrt{a+b x} \, _2F_1\left(-\frac{5}{2},-\frac{1}{2};\frac{1}{2};-\frac{b x}{a}\right)}{\sqrt{x} \sqrt{\frac{b x}{a}+1}}","\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,"(-2*a^2*Sqrt[a + b*x]*Hypergeometric2F1[-5/2, -1/2, 1/2, -((b*x)/a)])/(Sqrt[x]*Sqrt[1 + (b*x)/a])","C",1
550,1,50,86,0.0112147,"\int \frac{(a+b x)^{5/2}}{x^{5/2}} \, dx","Integrate[(a + b*x)^(5/2)/x^(5/2),x]","-\frac{2 a^2 \sqrt{a+b x} \, _2F_1\left(-\frac{5}{2},-\frac{3}{2};-\frac{1}{2};-\frac{b x}{a}\right)}{3 x^{3/2} \sqrt{\frac{b x}{a}+1}}","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,"(-2*a^2*Sqrt[a + b*x]*Hypergeometric2F1[-5/2, -3/2, -1/2, -((b*x)/a)])/(3*x^(3/2)*Sqrt[1 + (b*x)/a])","C",1
551,1,120,171,0.1913636,"\int x^{5/2} (a-b x)^{5/2} \, dx","Integrate[x^(5/2)*(a - b*x)^(5/2),x]","\frac{\sqrt{a-b x} \left(\frac{15 a^{11/2} \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{\sqrt{1-\frac{b x}{a}}}+\sqrt{b} \sqrt{x} \left(-15 a^5-10 a^4 b x-8 a^3 b^2 x^2+432 a^2 b^3 x^3-640 a b^4 x^4+256 b^5 x^5\right)\right)}{1536 b^{7/2}}","\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,"(Sqrt[a - b*x]*(Sqrt[b]*Sqrt[x]*(-15*a^5 - 10*a^4*b*x - 8*a^3*b^2*x^2 + 432*a^2*b^3*x^3 - 640*a*b^4*x^4 + 256*b^5*x^5) + (15*a^(11/2)*ArcSin[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/Sqrt[1 - (b*x)/a]))/(1536*b^(7/2))","A",1
552,1,109,146,0.1489912,"\int x^{3/2} (a-b x)^{5/2} \, dx","Integrate[x^(3/2)*(a - b*x)^(5/2),x]","\frac{\sqrt{a-b x} \left(\frac{15 a^{9/2} \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{\sqrt{1-\frac{b x}{a}}}+\sqrt{b} \sqrt{x} \left(-15 a^4-10 a^3 b x+248 a^2 b^2 x^2-336 a b^3 x^3+128 b^4 x^4\right)\right)}{640 b^{5/2}}","\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,"(Sqrt[a - b*x]*(Sqrt[b]*Sqrt[x]*(-15*a^4 - 10*a^3*b*x + 248*a^2*b^2*x^2 - 336*a*b^3*x^3 + 128*b^4*x^4) + (15*a^(9/2)*ArcSin[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/Sqrt[1 - (b*x)/a]))/(640*b^(5/2))","A",1
553,1,98,121,0.1323909,"\int \sqrt{x} (a-b x)^{5/2} \, dx","Integrate[Sqrt[x]*(a - b*x)^(5/2),x]","\frac{\sqrt{a-b x} \left(\frac{15 a^{7/2} \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{\sqrt{1-\frac{b x}{a}}}+\sqrt{b} \sqrt{x} \left(-15 a^3+118 a^2 b x-136 a b^2 x^2+48 b^3 x^3\right)\right)}{192 b^{3/2}}","\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,"(Sqrt[a - b*x]*(Sqrt[b]*Sqrt[x]*(-15*a^3 + 118*a^2*b*x - 136*a*b^2*x^2 + 48*b^3*x^3) + (15*a^(7/2)*ArcSin[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/Sqrt[1 - (b*x)/a]))/(192*b^(3/2))","A",1
554,1,82,96,0.1229573,"\int \frac{(a-b x)^{5/2}}{\sqrt{x}} \, dx","Integrate[(a - b*x)^(5/2)/Sqrt[x],x]","\frac{1}{24} \sqrt{a-b x} \left(\frac{15 a^{5/2} \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{\sqrt{b} \sqrt{1-\frac{b x}{a}}}+\sqrt{x} \left(33 a^2-26 a b x+8 b^2 x^2\right)\right)","\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,"(Sqrt[a - b*x]*(Sqrt[x]*(33*a^2 - 26*a*b*x + 8*b^2*x^2) + (15*a^(5/2)*ArcSin[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(Sqrt[b]*Sqrt[1 - (b*x)/a])))/24","A",1
555,1,49,93,0.0120784,"\int \frac{(a-b x)^{5/2}}{x^{3/2}} \, dx","Integrate[(a - b*x)^(5/2)/x^(3/2),x]","-\frac{2 a^2 \sqrt{a-b x} \, _2F_1\left(-\frac{5}{2},-\frac{1}{2};\frac{1}{2};\frac{b x}{a}\right)}{\sqrt{x} \sqrt{1-\frac{b x}{a}}}","-\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,"(-2*a^2*Sqrt[a - b*x]*Hypergeometric2F1[-5/2, -1/2, 1/2, (b*x)/a])/(Sqrt[x]*Sqrt[1 - (b*x)/a])","C",1
556,1,51,90,0.0120859,"\int \frac{(a-b x)^{5/2}}{x^{5/2}} \, dx","Integrate[(a - b*x)^(5/2)/x^(5/2),x]","-\frac{2 a^2 \sqrt{a-b x} \, _2F_1\left(-\frac{5}{2},-\frac{3}{2};-\frac{1}{2};\frac{b x}{a}\right)}{3 x^{3/2} \sqrt{1-\frac{b x}{a}}}","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,"(-2*a^2*Sqrt[a - b*x]*Hypergeometric2F1[-5/2, -3/2, -1/2, (b*x)/a])/(3*x^(3/2)*Sqrt[1 - (b*x)/a])","C",1
557,1,86,144,0.0587737,"\int x^{5/2} (2+b x)^{5/2} \, dx","Integrate[x^(5/2)*(2 + b*x)^(5/2),x]","\frac{\sqrt{x} \sqrt{b x+2} \left(8 b^5 x^5+40 b^4 x^4+54 b^3 x^3+2 b^2 x^2-5 b x+15\right)}{48 b^3}-\frac{5 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{8 b^{7/2}}","-\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,"(Sqrt[x]*Sqrt[2 + b*x]*(15 - 5*b*x + 2*b^2*x^2 + 54*b^3*x^3 + 40*b^4*x^4 + 8*b^5*x^5))/(48*b^3) - (5*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/(8*b^(7/2))","A",1
558,1,78,123,0.0481298,"\int x^{3/2} (2+b x)^{5/2} \, dx","Integrate[x^(3/2)*(2 + b*x)^(5/2),x]","\frac{3 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{4 b^{5/2}}+\frac{\sqrt{x} \sqrt{b x+2} \left(8 b^4 x^4+42 b^3 x^3+62 b^2 x^2+5 b x-15\right)}{40 b^2}","\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,"(Sqrt[x]*Sqrt[2 + b*x]*(-15 + 5*b*x + 62*b^2*x^2 + 42*b^3*x^3 + 8*b^4*x^4))/(40*b^2) + (3*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/(4*b^(5/2))","A",1
559,1,70,102,0.0407463,"\int \sqrt{x} (2+b x)^{5/2} \, dx","Integrate[Sqrt[x]*(2 + b*x)^(5/2),x]","\frac{\sqrt{x} \sqrt{b x+2} \left(6 b^3 x^3+34 b^2 x^2+59 b x+15\right)}{24 b}-\frac{5 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{4 b^{3/2}}","-\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,"(Sqrt[x]*Sqrt[2 + b*x]*(15 + 59*b*x + 34*b^2*x^2 + 6*b^3*x^3))/(24*b) - (5*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/(4*b^(3/2))","A",1
560,1,57,79,0.0323395,"\int \frac{(2+b x)^{5/2}}{\sqrt{x}} \, dx","Integrate[(2 + b*x)^(5/2)/Sqrt[x],x]","\frac{1}{6} \sqrt{x} \sqrt{b x+2} \left(2 b^2 x^2+13 b x+33\right)+\frac{5 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{\sqrt{b}}","\frac{1}{3} \sqrt{x} (b x+2)^{5/2}+\frac{5}{6} \sqrt{x} (b x+2)^{3/2}+\frac{5}{2} \sqrt{x} \sqrt{b x+2}+\frac{5 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{\sqrt{b}}",1,"(Sqrt[x]*Sqrt[2 + b*x]*(33 + 13*b*x + 2*b^2*x^2))/6 + (5*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/Sqrt[b]","A",1
561,1,28,79,0.0066545,"\int \frac{(2+b x)^{5/2}}{x^{3/2}} \, dx","Integrate[(2 + b*x)^(5/2)/x^(3/2),x]","-\frac{8 \sqrt{2} \, _2F_1\left(-\frac{5}{2},-\frac{1}{2};\frac{1}{2};-\frac{b x}{2}\right)}{\sqrt{x}}","-\frac{2 (b x+2)^{5/2}}{\sqrt{x}}+\frac{5}{2} b \sqrt{x} (b x+2)^{3/2}+\frac{15}{2} b \sqrt{x} \sqrt{b x+2}+15 \sqrt{b} \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)",1,"(-8*Sqrt[2]*Hypergeometric2F1[-5/2, -1/2, 1/2, -1/2*(b*x)])/Sqrt[x]","C",1
562,1,30,81,0.0064212,"\int \frac{(2+b x)^{5/2}}{x^{5/2}} \, dx","Integrate[(2 + b*x)^(5/2)/x^(5/2),x]","-\frac{8 \sqrt{2} \, _2F_1\left(-\frac{5}{2},-\frac{3}{2};-\frac{1}{2};-\frac{b x}{2}\right)}{3 x^{3/2}}","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,"(-8*Sqrt[2]*Hypergeometric2F1[-5/2, -3/2, -1/2, -1/2*(b*x)])/(3*x^(3/2))","C",1
563,1,87,150,0.0592281,"\int x^{5/2} (2-b x)^{5/2} \, dx","Integrate[x^(5/2)*(2 - b*x)^(5/2),x]","\frac{5 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{8 b^{7/2}}+\frac{\sqrt{x} \sqrt{2-b x} \left(8 b^5 x^5-40 b^4 x^4+54 b^3 x^3-2 b^2 x^2-5 b x-15\right)}{48 b^3}","\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,"(Sqrt[x]*Sqrt[2 - b*x]*(-15 - 5*b*x - 2*b^2*x^2 + 54*b^3*x^3 - 40*b^4*x^4 + 8*b^5*x^5))/(48*b^3) + (5*ArcSin[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/(8*b^(7/2))","A",1
564,1,79,128,0.0460114,"\int x^{3/2} (2-b x)^{5/2} \, dx","Integrate[x^(3/2)*(2 - b*x)^(5/2),x]","\frac{3 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{4 b^{5/2}}+\frac{\sqrt{x} \sqrt{2-b x} \left(8 b^4 x^4-42 b^3 x^3+62 b^2 x^2-5 b x-15\right)}{40 b^2}","\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,"(Sqrt[x]*Sqrt[2 - b*x]*(-15 - 5*b*x + 62*b^2*x^2 - 42*b^3*x^3 + 8*b^4*x^4))/(40*b^2) + (3*ArcSin[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/(4*b^(5/2))","A",1
565,1,71,106,0.040644,"\int \sqrt{x} (2-b x)^{5/2} \, dx","Integrate[Sqrt[x]*(2 - b*x)^(5/2),x]","\frac{5 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{4 b^{3/2}}+\frac{\sqrt{x} \sqrt{2-b x} \left(6 b^3 x^3-34 b^2 x^2+59 b x-15\right)}{24 b}","\frac{5 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{4 b^{3/2}}+\frac{1}{4} x^{3/2} (2-b x)^{5/2}+\frac{5}{12} x^{3/2} (2-b x)^{3/2}+\frac{5}{8} x^{3/2} \sqrt{2-b x}-\frac{5 \sqrt{x} \sqrt{2-b x}}{8 b}",1,"(Sqrt[x]*Sqrt[2 - b*x]*(-15 + 59*b*x - 34*b^2*x^2 + 6*b^3*x^3))/(24*b) + (5*ArcSin[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/(4*b^(3/2))","A",1
566,1,58,82,0.0337949,"\int \frac{(2-b x)^{5/2}}{\sqrt{x}} \, dx","Integrate[(2 - b*x)^(5/2)/Sqrt[x],x]","\frac{1}{6} \sqrt{x} \sqrt{2-b x} \left(2 b^2 x^2-13 b x+33\right)+\frac{5 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{\sqrt{b}}","\frac{1}{3} \sqrt{x} (2-b x)^{5/2}+\frac{5}{6} \sqrt{x} (2-b x)^{3/2}+\frac{5}{2} \sqrt{x} \sqrt{2-b x}+\frac{5 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{\sqrt{b}}",1,"(Sqrt[x]*Sqrt[2 - b*x]*(33 - 13*b*x + 2*b^2*x^2))/6 + (5*ArcSin[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/Sqrt[b]","A",1
567,1,28,82,0.0056617,"\int \frac{(2-b x)^{5/2}}{x^{3/2}} \, dx","Integrate[(2 - b*x)^(5/2)/x^(3/2),x]","-\frac{8 \sqrt{2} \, _2F_1\left(-\frac{5}{2},-\frac{1}{2};\frac{1}{2};\frac{b x}{2}\right)}{\sqrt{x}}","-\frac{2 (2-b x)^{5/2}}{\sqrt{x}}-\frac{5}{2} b \sqrt{x} (2-b x)^{3/2}-\frac{15}{2} b \sqrt{x} \sqrt{2-b x}-15 \sqrt{b} \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)",1,"(-8*Sqrt[2]*Hypergeometric2F1[-5/2, -1/2, 1/2, (b*x)/2])/Sqrt[x]","C",1
568,1,30,84,0.0069634,"\int \frac{(2-b x)^{5/2}}{x^{5/2}} \, dx","Integrate[(2 - b*x)^(5/2)/x^(5/2),x]","-\frac{8 \sqrt{2} \, _2F_1\left(-\frac{5}{2},-\frac{3}{2};-\frac{1}{2};\frac{b x}{2}\right)}{3 x^{3/2}}","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,"(-8*Sqrt[2]*Hypergeometric2F1[-5/2, -3/2, -1/2, (b*x)/2])/(3*x^(3/2))","C",1
569,1,85,101,0.1607838,"\int \frac{x^{5/2}}{\sqrt{a+b x}} \, dx","Integrate[x^(5/2)/Sqrt[a + b*x],x]","\frac{\sqrt{a+b x} \left(\sqrt{b} \sqrt{x} \left(15 a^2-10 a b x+8 b^2 x^2\right)-\frac{15 a^{5/2} \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{\sqrt{\frac{b x}{a}+1}}\right)}{24 b^{7/2}}","-\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,"(Sqrt[a + b*x]*(Sqrt[b]*Sqrt[x]*(15*a^2 - 10*a*b*x + 8*b^2*x^2) - (15*a^(5/2)*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/Sqrt[1 + (b*x)/a]))/(24*b^(7/2))","A",1
570,1,85,77,0.0496995,"\int \frac{x^{3/2}}{\sqrt{a+b x}} \, dx","Integrate[x^(3/2)/Sqrt[a + b*x],x]","\frac{3 a^{5/2} \sqrt{\frac{b x}{a}+1} \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)+\sqrt{b} \sqrt{x} \left(-3 a^2-a b x+2 b^2 x^2\right)}{4 b^{5/2} \sqrt{a+b x}}","\frac{3 a^2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{4 b^{5/2}}-\frac{3 a \sqrt{x} \sqrt{a+b x}}{4 b^2}+\frac{x^{3/2} \sqrt{a+b x}}{2 b}",1,"(Sqrt[b]*Sqrt[x]*(-3*a^2 - a*b*x + 2*b^2*x^2) + 3*a^(5/2)*Sqrt[1 + (b*x)/a]*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(4*b^(5/2)*Sqrt[a + b*x])","A",1
571,1,68,48,0.0386933,"\int \frac{\sqrt{x}}{\sqrt{a+b x}} \, dx","Integrate[Sqrt[x]/Sqrt[a + b*x],x]","\frac{\sqrt{b} \sqrt{x} (a+b x)-a^{3/2} \sqrt{\frac{b x}{a}+1} \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{3/2} \sqrt{a+b x}}","\frac{\sqrt{x} \sqrt{a+b x}}{b}-\frac{a \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{b^{3/2}}",1,"(Sqrt[b]*Sqrt[x]*(a + b*x) - a^(3/2)*Sqrt[1 + (b*x)/a]*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(b^(3/2)*Sqrt[a + b*x])","A",1
572,1,50,28,0.0129978,"\int \frac{1}{\sqrt{x} \sqrt{a+b x}} \, dx","Integrate[1/(Sqrt[x]*Sqrt[a + b*x]),x]","\frac{2 \sqrt{a} \sqrt{\frac{b x}{a}+1} \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{\sqrt{b} \sqrt{a+b x}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{\sqrt{b}}",1,"(2*Sqrt[a]*Sqrt[1 + (b*x)/a]*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(Sqrt[b]*Sqrt[a + b*x])","A",1
573,1,19,19,0.0042378,"\int \frac{1}{x^{3/2} \sqrt{a+b x}} \, dx","Integrate[1/(x^(3/2)*Sqrt[a + b*x]),x]","-\frac{2 \sqrt{a+b x}}{a \sqrt{x}}","-\frac{2 \sqrt{a+b x}}{a \sqrt{x}}",1,"(-2*Sqrt[a + b*x])/(a*Sqrt[x])","A",1
574,1,27,44,0.0071183,"\int \frac{1}{x^{5/2} \sqrt{a+b x}} \, dx","Integrate[1/(x^(5/2)*Sqrt[a + b*x]),x]","-\frac{2 (a-2 b x) \sqrt{a+b x}}{3 a^2 x^{3/2}}","\frac{4 b \sqrt{a+b x}}{3 a^2 \sqrt{x}}-\frac{2 \sqrt{a+b x}}{3 a x^{3/2}}",1,"(-2*(a - 2*b*x)*Sqrt[a + b*x])/(3*a^2*x^(3/2))","A",1
575,1,40,68,0.0091358,"\int \frac{1}{x^{7/2} \sqrt{a+b x}} \, dx","Integrate[1/(x^(7/2)*Sqrt[a + b*x]),x]","-\frac{2 \sqrt{a+b x} \left(3 a^2-4 a b x+8 b^2 x^2\right)}{15 a^3 x^{5/2}}","-\frac{16 b^2 \sqrt{a+b x}}{15 a^3 \sqrt{x}}+\frac{8 b \sqrt{a+b x}}{15 a^2 x^{3/2}}-\frac{2 \sqrt{a+b x}}{5 a x^{5/2}}",1,"(-2*Sqrt[a + b*x]*(3*a^2 - 4*a*b*x + 8*b^2*x^2))/(15*a^3*x^(5/2))","A",1
576,1,51,92,0.0116534,"\int \frac{1}{x^{9/2} \sqrt{a+b x}} \, dx","Integrate[1/(x^(9/2)*Sqrt[a + b*x]),x]","-\frac{2 \sqrt{a+b x} \left(5 a^3-6 a^2 b x+8 a b^2 x^2-16 b^3 x^3\right)}{35 a^4 x^{7/2}}","\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,"(-2*Sqrt[a + b*x]*(5*a^3 - 6*a^2*b*x + 8*a*b^2*x^2 - 16*b^3*x^3))/(35*a^4*x^(7/2))","A",1
577,1,50,96,0.0099363,"\int \frac{x^{5/2}}{(a+b x)^{3/2}} \, dx","Integrate[x^(5/2)/(a + b*x)^(3/2),x]","\frac{2 x^{7/2} \sqrt{\frac{b x}{a}+1} \, _2F_1\left(\frac{3}{2},\frac{7}{2};\frac{9}{2};-\frac{b x}{a}\right)}{7 a \sqrt{a+b x}}","\frac{15 a^2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{4 b^{7/2}}-\frac{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,"(2*x^(7/2)*Sqrt[1 + (b*x)/a]*Hypergeometric2F1[3/2, 7/2, 9/2, -((b*x)/a)])/(7*a*Sqrt[a + b*x])","C",1
578,1,50,68,0.0097788,"\int \frac{x^{3/2}}{(a+b x)^{3/2}} \, dx","Integrate[x^(3/2)/(a + b*x)^(3/2),x]","\frac{2 x^{5/2} \sqrt{\frac{b x}{a}+1} \, _2F_1\left(\frac{3}{2},\frac{5}{2};\frac{7}{2};-\frac{b x}{a}\right)}{5 a \sqrt{a+b 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,"(2*x^(5/2)*Sqrt[1 + (b*x)/a]*Hypergeometric2F1[3/2, 5/2, 7/2, -((b*x)/a)])/(5*a*Sqrt[a + b*x])","C",1
579,1,64,48,0.0690492,"\int \frac{\sqrt{x}}{(a+b x)^{3/2}} \, dx","Integrate[Sqrt[x]/(a + b*x)^(3/2),x]","\frac{2 \left(\sqrt{a} \sqrt{\frac{b x}{a}+1} \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)-\sqrt{b} \sqrt{x}\right)}{b^{3/2} \sqrt{a+b x}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{b^{3/2}}-\frac{2 \sqrt{x}}{b \sqrt{a+b x}}",1,"(2*(-(Sqrt[b]*Sqrt[x]) + Sqrt[a]*Sqrt[1 + (b*x)/a]*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[a]]))/(b^(3/2)*Sqrt[a + b*x])","A",1
580,1,19,19,0.0045309,"\int \frac{1}{\sqrt{x} (a+b x)^{3/2}} \, dx","Integrate[1/(Sqrt[x]*(a + b*x)^(3/2)),x]","\frac{2 \sqrt{x}}{a \sqrt{a+b x}}","\frac{2 \sqrt{x}}{a \sqrt{a+b x}}",1,"(2*Sqrt[x])/(a*Sqrt[a + b*x])","A",1
581,1,25,39,0.008207,"\int \frac{1}{x^{3/2} (a+b x)^{3/2}} \, dx","Integrate[1/(x^(3/2)*(a + b*x)^(3/2)),x]","-\frac{2 (a+2 b x)}{a^2 \sqrt{x} \sqrt{a+b x}}","\frac{2}{a \sqrt{x} \sqrt{a+b x}}-\frac{4 \sqrt{a+b x}}{a^2 \sqrt{x}}",1,"(-2*(a + 2*b*x))/(a^2*Sqrt[x]*Sqrt[a + b*x])","A",1
582,1,38,63,0.0093255,"\int \frac{1}{x^{5/2} (a+b x)^{3/2}} \, dx","Integrate[1/(x^(5/2)*(a + b*x)^(3/2)),x]","-\frac{2 \left(a^2-4 a b x-8 b^2 x^2\right)}{3 a^3 x^{3/2} \sqrt{a+b x}}","\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,"(-2*(a^2 - 4*a*b*x - 8*b^2*x^2))/(3*a^3*x^(3/2)*Sqrt[a + b*x])","A",1
583,1,49,87,0.0103161,"\int \frac{1}{x^{7/2} (a+b x)^{3/2}} \, dx","Integrate[1/(x^(7/2)*(a + b*x)^(3/2)),x]","-\frac{2 \left(a^3-2 a^2 b x+8 a b^2 x^2+16 b^3 x^3\right)}{5 a^4 x^{5/2} \sqrt{a+b x}}","-\frac{32 b^2 \sqrt{a+b x}}{5 a^4 \sqrt{x}}+\frac{16 b \sqrt{a+b x}}{5 a^3 x^{3/2}}-\frac{12 \sqrt{a+b x}}{5 a^2 x^{5/2}}+\frac{2}{a x^{5/2} \sqrt{a+b x}}",1,"(-2*(a^3 - 2*a^2*b*x + 8*a*b^2*x^2 + 16*b^3*x^3))/(5*a^4*x^(5/2)*Sqrt[a + b*x])","A",1
584,1,50,91,0.0101705,"\int \frac{x^{5/2}}{(a+b x)^{5/2}} \, dx","Integrate[x^(5/2)/(a + b*x)^(5/2),x]","\frac{2 x^{7/2} \sqrt{\frac{b x}{a}+1} \, _2F_1\left(\frac{5}{2},\frac{7}{2};\frac{9}{2};-\frac{b x}{a}\right)}{7 a^2 \sqrt{a+b x}}","-\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,"(2*x^(7/2)*Sqrt[1 + (b*x)/a]*Hypergeometric2F1[5/2, 7/2, 9/2, -((b*x)/a)])/(7*a^2*Sqrt[a + b*x])","C",1
585,1,80,69,0.1210384,"\int \frac{x^{3/2}}{(a+b x)^{5/2}} \, dx","Integrate[x^(3/2)/(a + b*x)^(5/2),x]","\frac{6 \sqrt{a} (a+b x) \sqrt{\frac{b x}{a}+1} \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)-2 \sqrt{b} \sqrt{x} (3 a+4 b x)}{3 b^{5/2} (a+b x)^{3/2}}","\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,"(-2*Sqrt[b]*Sqrt[x]*(3*a + 4*b*x) + 6*Sqrt[a]*(a + b*x)*Sqrt[1 + (b*x)/a]*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(3*b^(5/2)*(a + b*x)^(3/2))","A",1
586,1,21,21,0.004999,"\int \frac{\sqrt{x}}{(a+b x)^{5/2}} \, dx","Integrate[Sqrt[x]/(a + b*x)^(5/2),x]","\frac{2 x^{3/2}}{3 a (a+b x)^{3/2}}","\frac{2 x^{3/2}}{3 a (a+b x)^{3/2}}",1,"(2*x^(3/2))/(3*a*(a + b*x)^(3/2))","A",1
587,1,29,43,0.0086154,"\int \frac{1}{\sqrt{x} (a+b x)^{5/2}} \, dx","Integrate[1/(Sqrt[x]*(a + b*x)^(5/2)),x]","\frac{2 \sqrt{x} (3 a+2 b x)}{3 a^2 (a+b x)^{3/2}}","\frac{4 \sqrt{x}}{3 a^2 \sqrt{a+b x}}+\frac{2 \sqrt{x}}{3 a (a+b x)^{3/2}}",1,"(2*Sqrt[x]*(3*a + 2*b*x))/(3*a^2*(a + b*x)^(3/2))","A",1
588,1,40,64,0.0114695,"\int \frac{1}{x^{3/2} (a+b x)^{5/2}} \, dx","Integrate[1/(x^(3/2)*(a + b*x)^(5/2)),x]","-\frac{2 \left(3 a^2+12 a b x+8 b^2 x^2\right)}{3 a^3 \sqrt{x} (a+b x)^{3/2}}","-\frac{16 \sqrt{a+b x}}{3 a^3 \sqrt{x}}+\frac{8}{3 a^2 \sqrt{x} \sqrt{a+b x}}+\frac{2}{3 a \sqrt{x} (a+b x)^{3/2}}",1,"(-2*(3*a^2 + 12*a*b*x + 8*b^2*x^2))/(3*a^3*Sqrt[x]*(a + b*x)^(3/2))","A",1
589,1,49,84,0.0135075,"\int \frac{1}{x^{5/2} (a+b x)^{5/2}} \, dx","Integrate[1/(x^(5/2)*(a + b*x)^(5/2)),x]","-\frac{2 \left(a^3-6 a^2 b x-24 a b^2 x^2-16 b^3 x^3\right)}{3 a^4 x^{3/2} (a+b x)^{3/2}}","\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,"(-2*(a^3 - 6*a^2*b*x - 24*a*b^2*x^2 - 16*b^3*x^3))/(3*a^4*x^(3/2)*(a + b*x)^(3/2))","A",1
590,1,88,105,0.1455441,"\int \frac{x^{5/2}}{\sqrt{a-b x}} \, dx","Integrate[x^(5/2)/Sqrt[a - b*x],x]","\frac{\sqrt{a-b x} \left(\frac{15 a^{5/2} \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{\sqrt{1-\frac{b x}{a}}}-\sqrt{b} \sqrt{x} \left(15 a^2+10 a b x+8 b^2 x^2\right)\right)}{24 b^{7/2}}","\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,"(Sqrt[a - b*x]*(-(Sqrt[b]*Sqrt[x]*(15*a^2 + 10*a*b*x + 8*b^2*x^2)) + (15*a^(5/2)*ArcSin[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/Sqrt[1 - (b*x)/a]))/(24*b^(7/2))","A",1
591,1,86,80,0.0479286,"\int \frac{x^{3/2}}{\sqrt{a-b x}} \, dx","Integrate[x^(3/2)/Sqrt[a - b*x],x]","\frac{3 a^{5/2} \sqrt{1-\frac{b x}{a}} \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)+\sqrt{b} \sqrt{x} \left(-3 a^2+a b x+2 b^2 x^2\right)}{4 b^{5/2} \sqrt{a-b x}}","\frac{3 a^2 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)}{4 b^{5/2}}-\frac{3 a \sqrt{x} \sqrt{a-b x}}{4 b^2}-\frac{x^{3/2} \sqrt{a-b x}}{2 b}",1,"(Sqrt[b]*Sqrt[x]*(-3*a^2 + a*b*x + 2*b^2*x^2) + 3*a^(5/2)*Sqrt[1 - (b*x)/a]*ArcSin[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(4*b^(5/2)*Sqrt[a - b*x])","A",1
592,1,71,50,0.0416779,"\int \frac{\sqrt{x}}{\sqrt{a-b x}} \, dx","Integrate[Sqrt[x]/Sqrt[a - b*x],x]","\frac{a^{3/2} \sqrt{1-\frac{b x}{a}} \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)+\sqrt{b} \sqrt{x} (b x-a)}{b^{3/2} \sqrt{a-b x}}","\frac{a \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)}{b^{3/2}}-\frac{\sqrt{x} \sqrt{a-b x}}{b}",1,"(Sqrt[b]*Sqrt[x]*(-a + b*x) + a^(3/2)*Sqrt[1 - (b*x)/a]*ArcSin[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(b^(3/2)*Sqrt[a - b*x])","A",1
593,1,52,29,0.0139882,"\int \frac{1}{\sqrt{x} \sqrt{a-b x}} \, dx","Integrate[1/(Sqrt[x]*Sqrt[a - b*x]),x]","\frac{2 \sqrt{a} \sqrt{1-\frac{b x}{a}} \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{\sqrt{b} \sqrt{a-b x}}","\frac{2 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)}{\sqrt{b}}",1,"(2*Sqrt[a]*Sqrt[1 - (b*x)/a]*ArcSin[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(Sqrt[b]*Sqrt[a - b*x])","A",1
594,1,20,20,0.0044718,"\int \frac{1}{x^{3/2} \sqrt{a-b x}} \, dx","Integrate[1/(x^(3/2)*Sqrt[a - b*x]),x]","-\frac{2 \sqrt{a-b x}}{a \sqrt{x}}","-\frac{2 \sqrt{a-b x}}{a \sqrt{x}}",1,"(-2*Sqrt[a - b*x])/(a*Sqrt[x])","A",1
595,1,28,46,0.0066513,"\int \frac{1}{x^{5/2} \sqrt{a-b x}} \, dx","Integrate[1/(x^(5/2)*Sqrt[a - b*x]),x]","-\frac{2 \sqrt{a-b x} (a+2 b x)}{3 a^2 x^{3/2}}","-\frac{4 b \sqrt{a-b x}}{3 a^2 \sqrt{x}}-\frac{2 \sqrt{a-b x}}{3 a x^{3/2}}",1,"(-2*Sqrt[a - b*x]*(a + 2*b*x))/(3*a^2*x^(3/2))","A",1
596,1,51,100,0.0100723,"\int \frac{x^{5/2}}{(a-b x)^{3/2}} \, dx","Integrate[x^(5/2)/(a - b*x)^(3/2),x]","\frac{2 x^{7/2} \sqrt{1-\frac{b x}{a}} \, _2F_1\left(\frac{3}{2},\frac{7}{2};\frac{9}{2};\frac{b x}{a}\right)}{7 a \sqrt{a-b x}}","-\frac{15 a^2 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)}{4 b^{7/2}}+\frac{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,"(2*x^(7/2)*Sqrt[1 - (b*x)/a]*Hypergeometric2F1[3/2, 7/2, 9/2, (b*x)/a])/(7*a*Sqrt[a - b*x])","C",1
597,1,51,71,0.010316,"\int \frac{x^{3/2}}{(a-b x)^{3/2}} \, dx","Integrate[x^(3/2)/(a - b*x)^(3/2),x]","\frac{2 x^{5/2} \sqrt{1-\frac{b x}{a}} \, _2F_1\left(\frac{3}{2},\frac{5}{2};\frac{7}{2};\frac{b x}{a}\right)}{5 a \sqrt{a-b 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,"(2*x^(5/2)*Sqrt[1 - (b*x)/a]*Hypergeometric2F1[3/2, 5/2, 7/2, (b*x)/a])/(5*a*Sqrt[a - b*x])","C",1
598,1,66,50,0.0753248,"\int \frac{\sqrt{x}}{(a-b x)^{3/2}} \, dx","Integrate[Sqrt[x]/(a - b*x)^(3/2),x]","\frac{2 \sqrt{b} \sqrt{x}-2 \sqrt{a} \sqrt{1-\frac{b x}{a}} \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{3/2} \sqrt{a-b x}}","\frac{2 \sqrt{x}}{b \sqrt{a-b x}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a-b x}}\right)}{b^{3/2}}",1,"(2*Sqrt[b]*Sqrt[x] - 2*Sqrt[a]*Sqrt[1 - (b*x)/a]*ArcSin[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(b^(3/2)*Sqrt[a - b*x])","A",1
599,1,20,20,0.0047568,"\int \frac{1}{\sqrt{x} (a-b x)^{3/2}} \, dx","Integrate[1/(Sqrt[x]*(a - b*x)^(3/2)),x]","\frac{2 \sqrt{x}}{a \sqrt{a-b x}}","\frac{2 \sqrt{x}}{a \sqrt{a-b x}}",1,"(2*Sqrt[x])/(a*Sqrt[a - b*x])","A",1
600,1,26,41,0.0082508,"\int \frac{1}{x^{3/2} (a-b x)^{3/2}} \, dx","Integrate[1/(x^(3/2)*(a - b*x)^(3/2)),x]","-\frac{2 (a-2 b x)}{a^2 \sqrt{x} \sqrt{a-b x}}","\frac{2}{a \sqrt{x} \sqrt{a-b x}}-\frac{4 \sqrt{a-b x}}{a^2 \sqrt{x}}",1,"(-2*(a - 2*b*x))/(a^2*Sqrt[x]*Sqrt[a - b*x])","A",1
601,1,39,66,0.0093453,"\int \frac{1}{x^{5/2} (a-b x)^{3/2}} \, dx","Integrate[1/(x^(5/2)*(a - b*x)^(3/2)),x]","-\frac{2 \left(a^2+4 a b x-8 b^2 x^2\right)}{3 a^3 x^{3/2} \sqrt{a-b x}}","-\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,"(-2*(a^2 + 4*a*b*x - 8*b^2*x^2))/(3*a^3*x^(3/2)*Sqrt[a - b*x])","A",1
602,1,51,95,0.0115994,"\int \frac{x^{5/2}}{(a-b x)^{5/2}} \, dx","Integrate[x^(5/2)/(a - b*x)^(5/2),x]","\frac{2 x^{7/2} \sqrt{1-\frac{b x}{a}} \, _2F_1\left(\frac{5}{2},\frac{7}{2};\frac{9}{2};\frac{b x}{a}\right)}{7 a^2 \sqrt{a-b x}}","\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,"(2*x^(7/2)*Sqrt[1 - (b*x)/a]*Hypergeometric2F1[5/2, 7/2, 9/2, (b*x)/a])/(7*a^2*Sqrt[a - b*x])","C",1
603,1,82,72,0.1709977,"\int \frac{x^{3/2}}{(a-b x)^{5/2}} \, dx","Integrate[x^(3/2)/(a - b*x)^(5/2),x]","\frac{2 \left(\sqrt{b} \sqrt{x} (4 b x-3 a)+3 \sqrt{a} (a-b x) \sqrt{1-\frac{b x}{a}} \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)\right)}{3 b^{5/2} (a-b x)^{3/2}}","\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,"(2*(Sqrt[b]*Sqrt[x]*(-3*a + 4*b*x) + 3*Sqrt[a]*(a - b*x)*Sqrt[1 - (b*x)/a]*ArcSin[(Sqrt[b]*Sqrt[x])/Sqrt[a]]))/(3*b^(5/2)*(a - b*x)^(3/2))","A",1
604,1,22,22,0.0054752,"\int \frac{\sqrt{x}}{(a-b x)^{5/2}} \, dx","Integrate[Sqrt[x]/(a - b*x)^(5/2),x]","\frac{2 x^{3/2}}{3 a (a-b x)^{3/2}}","\frac{2 x^{3/2}}{3 a (a-b x)^{3/2}}",1,"(2*x^(3/2))/(3*a*(a - b*x)^(3/2))","A",1
605,1,30,45,0.0090999,"\int \frac{1}{\sqrt{x} (a-b x)^{5/2}} \, dx","Integrate[1/(Sqrt[x]*(a - b*x)^(5/2)),x]","\frac{2 \sqrt{x} (3 a-2 b x)}{3 a^2 (a-b x)^{3/2}}","\frac{4 \sqrt{x}}{3 a^2 \sqrt{a-b x}}+\frac{2 \sqrt{x}}{3 a (a-b x)^{3/2}}",1,"(2*Sqrt[x]*(3*a - 2*b*x))/(3*a^2*(a - b*x)^(3/2))","A",1
606,1,41,67,0.0119569,"\int \frac{1}{x^{3/2} (a-b x)^{5/2}} \, dx","Integrate[1/(x^(3/2)*(a - b*x)^(5/2)),x]","-\frac{2 \left(3 a^2-12 a b x+8 b^2 x^2\right)}{3 a^3 \sqrt{x} (a-b x)^{3/2}}","-\frac{16 \sqrt{a-b x}}{3 a^3 \sqrt{x}}+\frac{8}{3 a^2 \sqrt{x} \sqrt{a-b x}}+\frac{2}{3 a \sqrt{x} (a-b x)^{3/2}}",1,"(-2*(3*a^2 - 12*a*b*x + 8*b^2*x^2))/(3*a^3*Sqrt[x]*(a - b*x)^(3/2))","A",1
607,1,50,88,0.0140629,"\int \frac{1}{x^{5/2} (a-b x)^{5/2}} \, dx","Integrate[1/(x^(5/2)*(a - b*x)^(5/2)),x]","-\frac{2 \left(a^3+6 a^2 b x-24 a b^2 x^2+16 b^3 x^3\right)}{3 a^4 x^{3/2} (a-b x)^{3/2}}","-\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,"(-2*(a^3 + 6*a^2*b*x - 24*a*b^2*x^2 + 16*b^3*x^3))/(3*a^4*x^(3/2)*(a - b*x)^(3/2))","A",1
608,1,60,88,0.0401603,"\int \frac{x^{5/2}}{\sqrt{2+b x}} \, dx","Integrate[x^(5/2)/Sqrt[2 + b*x],x]","\frac{\sqrt{x} \sqrt{b x+2} \left(2 b^2 x^2-5 b x+15\right)}{6 b^3}-\frac{5 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\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,"(Sqrt[x]*Sqrt[2 + b*x]*(15 - 5*b*x + 2*b^2*x^2))/(6*b^3) - (5*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/b^(7/2)","A",1
609,1,51,67,0.0277563,"\int \frac{x^{3/2}}{\sqrt{2+b x}} \, dx","Integrate[x^(3/2)/Sqrt[2 + b*x],x]","\frac{3 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{5/2}}+\frac{\sqrt{x} \sqrt{b x+2} (b x-3)}{2 b^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,"(Sqrt[x]*(-3 + b*x)*Sqrt[2 + b*x])/(2*b^2) + (3*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/b^(5/2)","A",1
610,1,43,43,0.0160176,"\int \frac{\sqrt{x}}{\sqrt{2+b x}} \, dx","Integrate[Sqrt[x]/Sqrt[2 + b*x],x]","\frac{\sqrt{x} \sqrt{b x+2}}{b}-\frac{2 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{3/2}}","\frac{\sqrt{x} \sqrt{b x+2}}{b}-\frac{2 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{3/2}}",1,"(Sqrt[x]*Sqrt[2 + b*x])/b - (2*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/b^(3/2)","A",1
611,1,24,24,0.0040861,"\int \frac{1}{\sqrt{x} \sqrt{2+b x}} \, dx","Integrate[1/(Sqrt[x]*Sqrt[2 + b*x]),x]","\frac{2 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{\sqrt{b}}","\frac{2 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{\sqrt{b}}",1,"(2*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/Sqrt[b]","A",1
612,1,16,16,0.0038518,"\int \frac{1}{x^{3/2} \sqrt{2+b x}} \, dx","Integrate[1/(x^(3/2)*Sqrt[2 + b*x]),x]","-\frac{\sqrt{b x+2}}{\sqrt{x}}","-\frac{\sqrt{b x+2}}{\sqrt{x}}",1,"-(Sqrt[2 + b*x]/Sqrt[x])","A",1
613,1,23,38,0.0058959,"\int \frac{1}{x^{5/2} \sqrt{2+b x}} \, dx","Integrate[1/(x^(5/2)*Sqrt[2 + b*x]),x]","\frac{(b x-1) \sqrt{b x+2}}{3 x^{3/2}}","\frac{b \sqrt{b x+2}}{3 \sqrt{x}}-\frac{\sqrt{b x+2}}{3 x^{3/2}}",1,"((-1 + b*x)*Sqrt[2 + b*x])/(3*x^(3/2))","A",1
614,1,32,59,0.0083064,"\int \frac{1}{x^{7/2} \sqrt{2+b x}} \, dx","Integrate[1/(x^(7/2)*Sqrt[2 + b*x]),x]","-\frac{\sqrt{b x+2} \left(2 b^2 x^2-2 b x+3\right)}{15 x^{5/2}}","-\frac{2 b^2 \sqrt{b x+2}}{15 \sqrt{x}}+\frac{2 b \sqrt{b x+2}}{15 x^{3/2}}-\frac{\sqrt{b x+2}}{5 x^{5/2}}",1,"-1/15*(Sqrt[2 + b*x]*(3 - 2*b*x + 2*b^2*x^2))/x^(5/2)","A",1
615,1,40,80,0.0093073,"\int \frac{1}{x^{9/2} \sqrt{2+b x}} \, dx","Integrate[1/(x^(9/2)*Sqrt[2 + b*x]),x]","\frac{\sqrt{b x+2} \left(2 b^3 x^3-2 b^2 x^2+3 b x-5\right)}{35 x^{7/2}}","\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,"(Sqrt[2 + b*x]*(-5 + 3*b*x - 2*b^2*x^2 + 2*b^3*x^3))/(35*x^(7/2))","A",1
616,1,30,86,0.0058537,"\int \frac{x^{5/2}}{(2+b x)^{3/2}} \, dx","Integrate[x^(5/2)/(2 + b*x)^(3/2),x]","\frac{x^{7/2} \, _2F_1\left(\frac{3}{2},\frac{7}{2};\frac{9}{2};-\frac{b x}{2}\right)}{7 \sqrt{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,"(x^(7/2)*Hypergeometric2F1[3/2, 7/2, 9/2, -1/2*(b*x)])/(7*Sqrt[2])","C",1
617,1,30,63,0.0061315,"\int \frac{x^{3/2}}{(2+b x)^{3/2}} \, dx","Integrate[x^(3/2)/(2 + b*x)^(3/2),x]","\frac{x^{5/2} \, _2F_1\left(\frac{3}{2},\frac{5}{2};\frac{7}{2};-\frac{b x}{2}\right)}{5 \sqrt{2}}","-\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,"(x^(5/2)*Hypergeometric2F1[3/2, 5/2, 7/2, -1/2*(b*x)])/(5*Sqrt[2])","C",1
618,1,44,44,0.028638,"\int \frac{\sqrt{x}}{(2+b x)^{3/2}} \, dx","Integrate[Sqrt[x]/(2 + b*x)^(3/2),x]","\frac{2 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{3/2}}-\frac{2 \sqrt{x}}{b \sqrt{b x+2}}","\frac{2 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{3/2}}-\frac{2 \sqrt{x}}{b \sqrt{b x+2}}",1,"(-2*Sqrt[x])/(b*Sqrt[2 + b*x]) + (2*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/b^(3/2)","A",1
619,1,15,15,0.0034718,"\int \frac{1}{\sqrt{x} (2+b x)^{3/2}} \, dx","Integrate[1/(Sqrt[x]*(2 + b*x)^(3/2)),x]","\frac{\sqrt{x}}{\sqrt{b x+2}}","\frac{\sqrt{x}}{\sqrt{b x+2}}",1,"Sqrt[x]/Sqrt[2 + b*x]","A",1
620,1,21,32,0.0066353,"\int \frac{1}{x^{3/2} (2+b x)^{3/2}} \, dx","Integrate[1/(x^(3/2)*(2 + b*x)^(3/2)),x]","\frac{-b x-1}{\sqrt{x} \sqrt{b x+2}}","\frac{1}{\sqrt{x} \sqrt{b x+2}}-\frac{\sqrt{b x+2}}{\sqrt{x}}",1,"(-1 - b*x)/(Sqrt[x]*Sqrt[2 + b*x])","A",1
621,1,32,53,0.0075315,"\int \frac{1}{x^{5/2} (2+b x)^{3/2}} \, dx","Integrate[1/(x^(5/2)*(2 + b*x)^(3/2)),x]","\frac{2 b^2 x^2+2 b x-1}{3 x^{3/2} \sqrt{b x+2}}","-\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 + 2*b*x + 2*b^2*x^2)/(3*x^(3/2)*Sqrt[2 + b*x])","A",1
622,1,39,74,0.008496,"\int \frac{1}{x^{7/2} (2+b x)^{3/2}} \, dx","Integrate[1/(x^(7/2)*(2 + b*x)^(3/2)),x]","\frac{-2 b^3 x^3-2 b^2 x^2+b x-1}{5 x^{5/2} \sqrt{b x+2}}","-\frac{2 b^2 \sqrt{b x+2}}{5 \sqrt{x}}+\frac{2 b \sqrt{b x+2}}{5 x^{3/2}}-\frac{3 \sqrt{b x+2}}{5 x^{5/2}}+\frac{1}{x^{5/2} \sqrt{b x+2}}",1,"(-1 + b*x - 2*b^2*x^2 - 2*b^3*x^3)/(5*x^(5/2)*Sqrt[2 + b*x])","A",1
623,1,30,86,0.0066454,"\int \frac{x^{5/2}}{(2+b x)^{5/2}} \, dx","Integrate[x^(5/2)/(2 + b*x)^(5/2),x]","\frac{x^{7/2} \, _2F_1\left(\frac{5}{2},\frac{7}{2};\frac{9}{2};-\frac{b x}{2}\right)}{14 \sqrt{2}}","-\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,"(x^(7/2)*Hypergeometric2F1[5/2, 7/2, 9/2, -1/2*(b*x)])/(14*Sqrt[2])","C",1
624,1,52,65,0.0690163,"\int \frac{x^{3/2}}{(2+b x)^{5/2}} \, dx","Integrate[x^(3/2)/(2 + b*x)^(5/2),x]","\frac{2 \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{5/2}}-\frac{4 \sqrt{x} (2 b x+3)}{3 b^2 (b x+2)^{3/2}}","\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,"(-4*Sqrt[x]*(3 + 2*b*x))/(3*b^2*(2 + b*x)^(3/2)) + (2*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/b^(5/2)","A",1
625,1,18,18,0.0041326,"\int \frac{\sqrt{x}}{(2+b x)^{5/2}} \, dx","Integrate[Sqrt[x]/(2 + b*x)^(5/2),x]","\frac{x^{3/2}}{3 (b x+2)^{3/2}}","\frac{x^{3/2}}{3 (b x+2)^{3/2}}",1,"x^(3/2)/(3*(2 + b*x)^(3/2))","A",1
626,1,23,37,0.0058035,"\int \frac{1}{\sqrt{x} (2+b x)^{5/2}} \, dx","Integrate[1/(Sqrt[x]*(2 + b*x)^(5/2)),x]","\frac{\sqrt{x} (b x+3)}{3 (b x+2)^{3/2}}","\frac{\sqrt{x}}{3 \sqrt{b x+2}}+\frac{\sqrt{x}}{3 (b x+2)^{3/2}}",1,"(Sqrt[x]*(3 + b*x))/(3*(2 + b*x)^(3/2))","A",1
627,1,32,55,0.0082734,"\int \frac{1}{x^{3/2} (2+b x)^{5/2}} \, dx","Integrate[1/(x^(3/2)*(2 + b*x)^(5/2)),x]","\frac{-2 b^2 x^2-6 b x-3}{3 \sqrt{x} (b x+2)^{3/2}}","-\frac{2 \sqrt{b x+2}}{3 \sqrt{x}}+\frac{2}{3 \sqrt{x} \sqrt{b x+2}}+\frac{1}{3 \sqrt{x} (b x+2)^{3/2}}",1,"(-3 - 6*b*x - 2*b^2*x^2)/(3*Sqrt[x]*(2 + b*x)^(3/2))","A",1
628,1,40,71,0.010199,"\int \frac{1}{x^{5/2} (2+b x)^{5/2}} \, dx","Integrate[1/(x^(5/2)*(2 + b*x)^(5/2)),x]","\frac{2 b^3 x^3+6 b^2 x^2+3 b x-1}{3 x^{3/2} (b x+2)^{3/2}}","-\frac{2 \sqrt{b x+2}}{3 x^{3/2}}+\frac{1}{x^{3/2} \sqrt{b x+2}}+\frac{1}{3 x^{3/2} (b x+2)^{3/2}}+\frac{2 b \sqrt{b x+2}}{3 \sqrt{x}}",1,"(-1 + 3*b*x + 6*b^2*x^2 + 2*b^3*x^3)/(3*x^(3/2)*(2 + b*x)^(3/2))","A",1
629,1,61,91,0.0408683,"\int \frac{x^{5/2}}{\sqrt{2-b x}} \, dx","Integrate[x^(5/2)/Sqrt[2 - b*x],x]","\frac{5 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{7/2}}-\frac{\sqrt{x} \sqrt{2-b x} \left(2 b^2 x^2+5 b x+15\right)}{6 b^3}","\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,"-1/6*(Sqrt[x]*Sqrt[2 - b*x]*(15 + 5*b*x + 2*b^2*x^2))/b^3 + (5*ArcSin[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/b^(7/2)","A",1
630,1,52,69,0.0293689,"\int \frac{x^{3/2}}{\sqrt{2-b x}} \, dx","Integrate[x^(3/2)/Sqrt[2 - b*x],x]","\frac{3 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{5/2}}-\frac{\sqrt{x} \sqrt{2-b x} (b x+3)}{2 b^2}","\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,"-1/2*(Sqrt[x]*Sqrt[2 - b*x]*(3 + b*x))/b^2 + (3*ArcSin[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/b^(5/2)","A",1
631,1,45,45,0.0159462,"\int \frac{\sqrt{x}}{\sqrt{2-b x}} \, dx","Integrate[Sqrt[x]/Sqrt[2 - b*x],x]","\frac{2 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{3/2}}-\frac{\sqrt{x} \sqrt{2-b x}}{b}","\frac{2 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{3/2}}-\frac{\sqrt{x} \sqrt{2-b x}}{b}",1,"-((Sqrt[x]*Sqrt[2 - b*x])/b) + (2*ArcSin[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/b^(3/2)","A",1
632,1,24,24,0.0039745,"\int \frac{1}{\sqrt{x} \sqrt{2-b x}} \, dx","Integrate[1/(Sqrt[x]*Sqrt[2 - b*x]),x]","\frac{2 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{\sqrt{b}}","\frac{2 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{\sqrt{b}}",1,"(2*ArcSin[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/Sqrt[b]","A",1
633,1,17,17,0.0038294,"\int \frac{1}{x^{3/2} \sqrt{2-b x}} \, dx","Integrate[1/(x^(3/2)*Sqrt[2 - b*x]),x]","-\frac{\sqrt{2-b x}}{\sqrt{x}}","-\frac{\sqrt{2-b x}}{\sqrt{x}}",1,"-(Sqrt[2 - b*x]/Sqrt[x])","A",1
634,1,24,40,0.0062125,"\int \frac{1}{x^{5/2} \sqrt{2-b x}} \, dx","Integrate[1/(x^(5/2)*Sqrt[2 - b*x]),x]","-\frac{\sqrt{2-b x} (b x+1)}{3 x^{3/2}}","-\frac{\sqrt{2-b x}}{3 x^{3/2}}-\frac{b \sqrt{2-b x}}{3 \sqrt{x}}",1,"-1/3*(Sqrt[2 - b*x]*(1 + b*x))/x^(3/2)","A",1
635,1,30,89,0.0058148,"\int \frac{x^{5/2}}{(2-b x)^{3/2}} \, dx","Integrate[x^(5/2)/(2 - b*x)^(3/2),x]","\frac{x^{7/2} \, _2F_1\left(\frac{3}{2},\frac{7}{2};\frac{9}{2};\frac{b x}{2}\right)}{7 \sqrt{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,"(x^(7/2)*Hypergeometric2F1[3/2, 7/2, 9/2, (b*x)/2])/(7*Sqrt[2])","C",1
636,1,30,65,0.0063167,"\int \frac{x^{3/2}}{(2-b x)^{3/2}} \, dx","Integrate[x^(3/2)/(2 - b*x)^(3/2),x]","\frac{x^{5/2} \, _2F_1\left(\frac{3}{2},\frac{5}{2};\frac{7}{2};\frac{b x}{2}\right)}{5 \sqrt{2}}","-\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,"(x^(5/2)*Hypergeometric2F1[3/2, 5/2, 7/2, (b*x)/2])/(5*Sqrt[2])","C",1
637,1,45,45,0.0382887,"\int \frac{\sqrt{x}}{(2-b x)^{3/2}} \, dx","Integrate[Sqrt[x]/(2 - b*x)^(3/2),x]","\frac{2 \sqrt{x}}{b \sqrt{2-b x}}-\frac{2 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{3/2}}","\frac{2 \sqrt{x}}{b \sqrt{2-b x}}-\frac{2 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{3/2}}",1,"(2*Sqrt[x])/(b*Sqrt[2 - b*x]) - (2*ArcSin[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/b^(3/2)","A",1
638,1,16,16,0.0036308,"\int \frac{1}{\sqrt{x} (2-b x)^{3/2}} \, dx","Integrate[1/(Sqrt[x]*(2 - b*x)^(3/2)),x]","\frac{\sqrt{x}}{\sqrt{2-b x}}","\frac{\sqrt{x}}{\sqrt{2-b x}}",1,"Sqrt[x]/Sqrt[2 - b*x]","A",1
639,1,21,34,0.0071817,"\int \frac{1}{x^{3/2} (2-b x)^{3/2}} \, dx","Integrate[1/(x^(3/2)*(2 - b*x)^(3/2)),x]","\frac{b x-1}{\sqrt{x} \sqrt{2-b x}}","\frac{1}{\sqrt{x} \sqrt{2-b x}}-\frac{\sqrt{2-b x}}{\sqrt{x}}",1,"(-1 + b*x)/(Sqrt[x]*Sqrt[2 - b*x])","A",1
640,1,33,56,0.0076218,"\int \frac{1}{x^{5/2} (2-b x)^{3/2}} \, dx","Integrate[1/(x^(5/2)*(2 - b*x)^(3/2)),x]","\frac{2 b^2 x^2-2 b x-1}{3 x^{3/2} \sqrt{2-b x}}","-\frac{2 \sqrt{2-b x}}{3 x^{3/2}}+\frac{1}{x^{3/2} \sqrt{2-b x}}-\frac{2 b \sqrt{2-b x}}{3 \sqrt{x}}",1,"(-1 - 2*b*x + 2*b^2*x^2)/(3*x^(3/2)*Sqrt[2 - b*x])","A",1
641,1,30,89,0.0065907,"\int \frac{x^{5/2}}{(2-b x)^{5/2}} \, dx","Integrate[x^(5/2)/(2 - b*x)^(5/2),x]","\frac{x^{7/2} \, _2F_1\left(\frac{5}{2},\frac{7}{2};\frac{9}{2};\frac{b x}{2}\right)}{14 \sqrt{2}}","\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,"(x^(7/2)*Hypergeometric2F1[5/2, 7/2, 9/2, (b*x)/2])/(14*Sqrt[2])","C",1
642,1,53,67,0.0557914,"\int \frac{x^{3/2}}{(2-b x)^{5/2}} \, dx","Integrate[x^(3/2)/(2 - b*x)^(5/2),x]","\frac{2 \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{5/2}}+\frac{4 \sqrt{x} (2 b x-3)}{3 b^2 (2-b x)^{3/2}}","\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*Sqrt[x]*(-3 + 2*b*x))/(3*b^2*(2 - b*x)^(3/2)) + (2*ArcSin[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/b^(5/2)","A",1
643,1,19,19,0.0051115,"\int \frac{\sqrt{x}}{(2-b x)^{5/2}} \, dx","Integrate[Sqrt[x]/(2 - b*x)^(5/2),x]","\frac{x^{3/2}}{3 (2-b x)^{3/2}}","\frac{x^{3/2}}{3 (2-b x)^{3/2}}",1,"x^(3/2)/(3*(2 - b*x)^(3/2))","A",1
644,1,24,39,0.0077118,"\int \frac{1}{\sqrt{x} (2-b x)^{5/2}} \, dx","Integrate[1/(Sqrt[x]*(2 - b*x)^(5/2)),x]","-\frac{\sqrt{x} (b x-3)}{3 (2-b x)^{3/2}}","\frac{\sqrt{x}}{3 \sqrt{2-b x}}+\frac{\sqrt{x}}{3 (2-b x)^{3/2}}",1,"-1/3*(Sqrt[x]*(-3 + b*x))/(2 - b*x)^(3/2)","A",1
645,1,33,58,0.0103837,"\int \frac{1}{x^{3/2} (2-b x)^{5/2}} \, dx","Integrate[1/(x^(3/2)*(2 - b*x)^(5/2)),x]","-\frac{2 b^2 x^2-6 b x+3}{3 \sqrt{x} (2-b x)^{3/2}}","-\frac{2 \sqrt{2-b x}}{3 \sqrt{x}}+\frac{2}{3 \sqrt{x} \sqrt{2-b x}}+\frac{1}{3 \sqrt{x} (2-b x)^{3/2}}",1,"-1/3*(3 - 6*b*x + 2*b^2*x^2)/(Sqrt[x]*(2 - b*x)^(3/2))","A",1
646,1,41,75,0.0125414,"\int \frac{1}{x^{5/2} (2-b x)^{5/2}} \, dx","Integrate[1/(x^(5/2)*(2 - b*x)^(5/2)),x]","-\frac{2 b^3 x^3-6 b^2 x^2+3 b x+1}{3 x^{3/2} (2-b x)^{3/2}}","-\frac{2 \sqrt{2-b x}}{3 x^{3/2}}+\frac{1}{x^{3/2} \sqrt{2-b x}}+\frac{1}{3 x^{3/2} (2-b x)^{3/2}}-\frac{2 b \sqrt{2-b x}}{3 \sqrt{x}}",1,"-1/3*(1 + 3*b*x - 6*b^2*x^2 + 2*b^3*x^3)/(x^(3/2)*(2 - b*x)^(3/2))","A",1
647,1,25,27,0.0090009,"\int \frac{\sqrt{x}}{\sqrt{1-x}} \, dx","Integrate[Sqrt[x]/Sqrt[1 - x],x]","-\sqrt{-((x-1) x)}-\sin ^{-1}\left(\sqrt{1-x}\right)","-\sqrt{1-x} \sqrt{x}-\frac{1}{2} \sin ^{-1}(1-2 x)",1,"-Sqrt[-((-1 + x)*x)] - ArcSin[Sqrt[1 - x]]","A",1
648,1,12,8,0.0082153,"\int \frac{1}{\sqrt{1-x} \sqrt{x}} \, dx","Integrate[1/(Sqrt[1 - x]*Sqrt[x]),x]","-2 \sin ^{-1}\left(\sqrt{1-x}\right)","-\sin ^{-1}(1-2 x)",1,"-2*ArcSin[Sqrt[1 - x]]","A",1
649,1,19,19,0.0050557,"\int \frac{1}{\sqrt{x} \sqrt{1-b x}} \, dx","Integrate[1/(Sqrt[x]*Sqrt[1 - b*x]),x]","\frac{2 \sin ^{-1}\left(\sqrt{b} \sqrt{x}\right)}{\sqrt{b}}","\frac{2 \sin ^{-1}\left(\sqrt{b} \sqrt{x}\right)}{\sqrt{b}}",1,"(2*ArcSin[Sqrt[b]*Sqrt[x]])/Sqrt[b]","A",1
650,1,17,21,0.0051337,"\int x^{5/3} (a+b x) \, dx","Integrate[x^(5/3)*(a + b*x),x]","\frac{3}{88} x^{8/3} (11 a+8 b x)","\frac{3}{8} a x^{8/3}+\frac{3}{11} b x^{11/3}",1,"(3*x^(8/3)*(11*a + 8*b*x))/88","A",1
651,1,17,21,0.0047645,"\int x^{4/3} (a+b x) \, dx","Integrate[x^(4/3)*(a + b*x),x]","\frac{3}{70} x^{7/3} (10 a+7 b x)","\frac{3}{7} a x^{7/3}+\frac{3}{10} b x^{10/3}",1,"(3*x^(7/3)*(10*a + 7*b*x))/70","A",1
652,1,17,21,0.004615,"\int x^{2/3} (a+b x) \, dx","Integrate[x^(2/3)*(a + b*x),x]","\frac{3}{40} x^{5/3} (8 a+5 b x)","\frac{3}{5} a x^{5/3}+\frac{3}{8} b x^{8/3}",1,"(3*x^(5/3)*(8*a + 5*b*x))/40","A",1
653,1,17,21,0.0045333,"\int \sqrt[3]{x} (a+b x) \, dx","Integrate[x^(1/3)*(a + b*x),x]","\frac{3}{28} x^{4/3} (7 a+4 b x)","\frac{3}{4} a x^{4/3}+\frac{3}{7} b x^{7/3}",1,"(3*x^(4/3)*(7*a + 4*b*x))/28","A",1
654,1,17,21,0.0046107,"\int \frac{a+b x}{\sqrt[3]{x}} \, dx","Integrate[(a + b*x)/x^(1/3),x]","\frac{3}{10} x^{2/3} (5 a+2 b x)","\frac{3}{2} a x^{2/3}+\frac{3}{5} b x^{5/3}",1,"(3*x^(2/3)*(5*a + 2*b*x))/10","A",1
655,1,16,19,0.0046442,"\int \frac{a+b x}{x^{2/3}} \, dx","Integrate[(a + b*x)/x^(2/3),x]","\frac{3}{4} \sqrt[3]{x} (4 a+b x)","3 a \sqrt[3]{x}+\frac{3}{4} b x^{4/3}",1,"(3*x^(1/3)*(4*a + b*x))/4","A",1
656,1,16,19,0.0053145,"\int \frac{a+b x}{x^{4/3}} \, dx","Integrate[(a + b*x)/x^(4/3),x]","\frac{3 (b x-2 a)}{2 \sqrt[3]{x}}","\frac{3}{2} b x^{2/3}-\frac{3 a}{\sqrt[3]{x}}",1,"(3*(-2*a + b*x))/(2*x^(1/3))","A",1
657,1,19,19,0.005435,"\int \frac{a+b x}{x^{5/3}} \, dx","Integrate[(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
658,1,28,36,0.0078544,"\int x^{5/3} (a+b x)^2 \, dx","Integrate[x^(5/3)*(a + b*x)^2,x]","\frac{3}{616} x^{8/3} \left(77 a^2+112 a b x+44 b^2 x^2\right)","\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*x^(8/3)*(77*a^2 + 112*a*b*x + 44*b^2*x^2))/616","A",1
659,1,28,36,0.0076104,"\int x^{4/3} (a+b x)^2 \, dx","Integrate[x^(4/3)*(a + b*x)^2,x]","\frac{3}{455} x^{7/3} \left(65 a^2+91 a b x+35 b^2 x^2\right)","\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*x^(7/3)*(65*a^2 + 91*a*b*x + 35*b^2*x^2))/455","A",1
660,1,28,36,0.0074328,"\int x^{2/3} (a+b x)^2 \, dx","Integrate[x^(2/3)*(a + b*x)^2,x]","\frac{3}{220} x^{5/3} \left(44 a^2+55 a b x+20 b^2 x^2\right)","\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*x^(5/3)*(44*a^2 + 55*a*b*x + 20*b^2*x^2))/220","A",1
661,1,28,36,0.0073263,"\int \sqrt[3]{x} (a+b x)^2 \, dx","Integrate[x^(1/3)*(a + b*x)^2,x]","\frac{3}{140} x^{4/3} \left(35 a^2+40 a b x+14 b^2 x^2\right)","\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*x^(4/3)*(35*a^2 + 40*a*b*x + 14*b^2*x^2))/140","A",1
662,1,28,36,0.0075121,"\int \frac{(a+b x)^2}{\sqrt[3]{x}} \, dx","Integrate[(a + b*x)^2/x^(1/3),x]","\frac{3}{40} x^{2/3} \left(20 a^2+16 a b x+5 b^2 x^2\right)","\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*x^(2/3)*(20*a^2 + 16*a*b*x + 5*b^2*x^2))/40","A",1
663,1,28,34,0.0075279,"\int \frac{(a+b x)^2}{x^{2/3}} \, dx","Integrate[(a + b*x)^2/x^(2/3),x]","\frac{3}{14} \sqrt[3]{x} \left(14 a^2+7 a b x+2 b^2 x^2\right)","3 a^2 \sqrt[3]{x}+\frac{3}{2} a b x^{4/3}+\frac{3}{7} b^2 x^{7/3}",1,"(3*x^(1/3)*(14*a^2 + 7*a*b*x + 2*b^2*x^2))/14","A",1
664,1,27,32,0.008095,"\int \frac{(a+b x)^2}{x^{4/3}} \, dx","Integrate[(a + b*x)^2/x^(4/3),x]","\frac{3 \left(-5 a^2+5 a b x+b^2 x^2\right)}{5 \sqrt[3]{x}}","-\frac{3 a^2}{\sqrt[3]{x}}+3 a b x^{2/3}+\frac{3}{5} b^2 x^{5/3}",1,"(3*(-5*a^2 + 5*a*b*x + b^2*x^2))/(5*x^(1/3))","A",1
665,1,27,34,0.007947,"\int \frac{(a+b x)^2}{x^{5/3}} \, dx","Integrate[(a + b*x)^2/x^(5/3),x]","\frac{3 \left(-2 a^2+8 a b x+b^2 x^2\right)}{4 x^{2/3}}","-\frac{3 a^2}{2 x^{2/3}}+6 a b \sqrt[3]{x}+\frac{3}{4} b^2 x^{4/3}",1,"(3*(-2*a^2 + 8*a*b*x + b^2*x^2))/(4*x^(2/3))","A",1
666,1,39,51,0.0110823,"\int x^{5/3} (a+b x)^3 \, dx","Integrate[x^(5/3)*(a + b*x)^3,x]","\frac{3 x^{8/3} \left(1309 a^3+2856 a^2 b x+2244 a b^2 x^2+616 b^3 x^3\right)}{10472}","\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*x^(8/3)*(1309*a^3 + 2856*a^2*b*x + 2244*a*b^2*x^2 + 616*b^3*x^3))/10472","A",1
667,1,39,51,0.0099238,"\int x^{4/3} (a+b x)^3 \, dx","Integrate[x^(4/3)*(a + b*x)^3,x]","\frac{3 x^{7/3} \left(1040 a^3+2184 a^2 b x+1680 a b^2 x^2+455 b^3 x^3\right)}{7280}","\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*x^(7/3)*(1040*a^3 + 2184*a^2*b*x + 1680*a*b^2*x^2 + 455*b^3*x^3))/7280","A",1
668,1,39,51,0.0098001,"\int x^{2/3} (a+b x)^3 \, dx","Integrate[x^(2/3)*(a + b*x)^3,x]","\frac{3 x^{5/3} \left(616 a^3+1155 a^2 b x+840 a b^2 x^2+220 b^3 x^3\right)}{3080}","\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*x^(5/3)*(616*a^3 + 1155*a^2*b*x + 840*a*b^2*x^2 + 220*b^3*x^3))/3080","A",1
669,1,39,51,0.0096954,"\int \sqrt[3]{x} (a+b x)^3 \, dx","Integrate[x^(1/3)*(a + b*x)^3,x]","\frac{3 x^{4/3} \left(455 a^3+780 a^2 b x+546 a b^2 x^2+140 b^3 x^3\right)}{1820}","\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*x^(4/3)*(455*a^3 + 780*a^2*b*x + 546*a*b^2*x^2 + 140*b^3*x^3))/1820","A",1
670,1,39,51,0.0098984,"\int \frac{(a+b x)^3}{\sqrt[3]{x}} \, dx","Integrate[(a + b*x)^3/x^(1/3),x]","\frac{3}{440} x^{2/3} \left(220 a^3+264 a^2 b x+165 a b^2 x^2+40 b^3 x^3\right)","\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*x^(2/3)*(220*a^3 + 264*a^2*b*x + 165*a*b^2*x^2 + 40*b^3*x^3))/440","A",1
671,1,39,49,0.010021,"\int \frac{(a+b x)^3}{x^{2/3}} \, dx","Integrate[(a + b*x)^3/x^(2/3),x]","\frac{3}{140} \sqrt[3]{x} \left(140 a^3+105 a^2 b x+60 a b^2 x^2+14 b^3 x^3\right)","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*x^(1/3)*(140*a^3 + 105*a^2*b*x + 60*a*b^2*x^2 + 14*b^3*x^3))/140","A",1
672,1,39,49,0.010687,"\int \frac{(a+b x)^3}{x^{4/3}} \, dx","Integrate[(a + b*x)^3/x^(4/3),x]","\frac{3 \left(-40 a^3+60 a^2 b x+24 a b^2 x^2+5 b^3 x^3\right)}{40 \sqrt[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}",1,"(3*(-40*a^3 + 60*a^2*b*x + 24*a*b^2*x^2 + 5*b^3*x^3))/(40*x^(1/3))","A",1
673,1,39,49,0.0109785,"\int \frac{(a+b x)^3}{x^{5/3}} \, dx","Integrate[(a + b*x)^3/x^(5/3),x]","\frac{3 \left(-14 a^3+84 a^2 b x+21 a b^2 x^2+4 b^3 x^3\right)}{28 x^{2/3}}","-\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*(-14*a^3 + 84*a^2*b*x + 21*a*b^2*x^2 + 4*b^3*x^3))/(28*x^(2/3))","A",1
674,1,38,125,0.0099167,"\int \frac{x^{5/3}}{a+b x} \, dx","Integrate[x^(5/3)/(a + b*x),x]","\frac{3 x^{2/3} \left(5 a \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};-\frac{b x}{a}\right)-5 a+2 b x\right)}{10 b^2}","-\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*x^(2/3)*(-5*a + 2*b*x + 5*a*Hypergeometric2F1[2/3, 1, 5/3, -((b*x)/a)]))/(10*b^2)","C",1
675,1,140,123,0.0577887,"\int \frac{x^{4/3}}{a+b x} \, dx","Integrate[x^(4/3)/(a + b*x),x]","\frac{-2 a^{4/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \sqrt[3]{x}+b^{2/3} x^{2/3}\right)+4 a^{4/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)-4 \sqrt{3} a^{4/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b} \sqrt[3]{x}}{\sqrt[3]{a}}}{\sqrt{3}}\right)-12 a \sqrt[3]{b} \sqrt[3]{x}+3 b^{4/3} x^{4/3}}{4 b^{7/3}}","\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,"(-12*a*b^(1/3)*x^(1/3) + 3*b^(4/3)*x^(4/3) - 4*Sqrt[3]*a^(4/3)*ArcTan[(1 - (2*b^(1/3)*x^(1/3))/a^(1/3))/Sqrt[3]] + 4*a^(4/3)*Log[a^(1/3) + b^(1/3)*x^(1/3)] - 2*a^(4/3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x^(1/3) + b^(2/3)*x^(2/3)])/(4*b^(7/3))","A",1
676,1,29,111,0.0086877,"\int \frac{x^{2/3}}{a+b x} \, dx","Integrate[x^(2/3)/(a + b*x),x]","-\frac{3 x^{2/3} \left(\, _2F_1\left(\frac{2}{3},1;\frac{5}{3};-\frac{b x}{a}\right)-1\right)}{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)*(-1 + Hypergeometric2F1[2/3, 1, 5/3, -((b*x)/a)]))/(2*b)","C",1
677,1,126,109,0.0263627,"\int \frac{\sqrt[3]{x}}{a+b x} \, dx","Integrate[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 \sqrt[3]{a} \log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)+2 \sqrt{3} \sqrt[3]{a} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b} \sqrt[3]{x}}{\sqrt[3]{a}}}{\sqrt{3}}\right)+6 \sqrt[3]{b} \sqrt[3]{x}}{2 b^{4/3}}","-\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,"(6*b^(1/3)*x^(1/3) + 2*Sqrt[3]*a^(1/3)*ArcTan[(1 - (2*b^(1/3)*x^(1/3))/a^(1/3))/Sqrt[3]] - 2*a^(1/3)*Log[a^(1/3) + b^(1/3)*x^(1/3)] + 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
678,1,27,100,0.006531,"\int \frac{1}{\sqrt[3]{x} (a+b x)} \, dx","Integrate[1/(x^(1/3)*(a + b*x)),x]","\frac{3 x^{2/3} \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};-\frac{b x}{a}\right)}{2 a}","-\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,"(3*x^(2/3)*Hypergeometric2F1[2/3, 1, 5/3, -((b*x)/a)])/(2*a)","C",1
679,1,103,100,0.0244052,"\int \frac{1}{x^{2/3} (a+b x)} \, dx","Integrate[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 \log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b} \sqrt[3]{x}}{\sqrt[3]{a}}}{\sqrt{3}}\right)}{2 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,"-1/2*(2*Sqrt[3]*ArcTan[(1 - (2*b^(1/3)*x^(1/3))/a^(1/3))/Sqrt[3]] - 2*Log[a^(1/3) + b^(1/3)*x^(1/3)] + Log[a^(2/3) - a^(1/3)*b^(1/3)*x^(1/3) + b^(2/3)*x^(2/3)])/(a^(2/3)*b^(1/3))","A",1
680,1,25,109,0.0052152,"\int \frac{1}{x^{4/3} (a+b x)} \, dx","Integrate[1/(x^(4/3)*(a + b*x)),x]","-\frac{3 \, _2F_1\left(-\frac{1}{3},1;\frac{2}{3};-\frac{b x}{a}\right)}{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*Hypergeometric2F1[-1/3, 1, 2/3, -((b*x)/a)])/(a*x^(1/3))","C",1
681,1,27,111,0.005449,"\int \frac{1}{x^{5/3} (a+b x)} \, dx","Integrate[1/(x^(5/3)*(a + b*x)),x]","-\frac{3 \, _2F_1\left(-\frac{2}{3},1;\frac{1}{3};-\frac{b x}{a}\right)}{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*Hypergeometric2F1[-2/3, 1, 1/3, -((b*x)/a)])/(2*a*x^(2/3))","C",1
682,1,27,129,0.0048251,"\int \frac{x^{5/3}}{(a+b x)^2} \, dx","Integrate[x^(5/3)/(a + b*x)^2,x]","\frac{3 x^{8/3} \, _2F_1\left(2,\frac{8}{3};\frac{11}{3};-\frac{b x}{a}\right)}{8 a^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^(8/3)*Hypergeometric2F1[2, 8/3, 11/3, -((b*x)/a)])/(8*a^2)","C",1
683,1,27,125,0.0046062,"\int \frac{x^{4/3}}{(a+b x)^2} \, dx","Integrate[x^(4/3)/(a + b*x)^2,x]","\frac{3 x^{7/3} \, _2F_1\left(2,\frac{7}{3};\frac{10}{3};-\frac{b x}{a}\right)}{7 a^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^(7/3)*Hypergeometric2F1[2, 7/3, 10/3, -((b*x)/a)])/(7*a^2)","C",1
684,1,27,115,0.0041938,"\int \frac{x^{2/3}}{(a+b x)^2} \, dx","Integrate[x^(2/3)/(a + b*x)^2,x]","\frac{3 x^{5/3} \, _2F_1\left(\frac{5}{3},2;\frac{8}{3};-\frac{b x}{a}\right)}{5 a^2}","-\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,"(3*x^(5/3)*Hypergeometric2F1[5/3, 2, 8/3, -((b*x)/a)])/(5*a^2)","C",1
685,1,27,117,0.0048257,"\int \frac{\sqrt[3]{x}}{(a+b x)^2} \, dx","Integrate[x^(1/3)/(a + b*x)^2,x]","\frac{3 x^{4/3} \, _2F_1\left(\frac{4}{3},2;\frac{7}{3};-\frac{b x}{a}\right)}{4 a^2}","\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,"(3*x^(4/3)*Hypergeometric2F1[4/3, 2, 7/3, -((b*x)/a)])/(4*a^2)","C",1
686,1,27,116,0.0049545,"\int \frac{1}{\sqrt[3]{x} (a+b x)^2} \, dx","Integrate[1/(x^(1/3)*(a + b*x)^2),x]","\frac{3 x^{2/3} \, _2F_1\left(\frac{2}{3},2;\frac{5}{3};-\frac{b x}{a}\right)}{2 a^2}","-\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,"(3*x^(2/3)*Hypergeometric2F1[2/3, 2, 5/3, -((b*x)/a)])/(2*a^2)","C",1
687,1,25,113,0.0048777,"\int \frac{1}{x^{2/3} (a+b x)^2} \, dx","Integrate[1/(x^(2/3)*(a + b*x)^2),x]","\frac{3 \sqrt[3]{x} \, _2F_1\left(\frac{1}{3},2;\frac{4}{3};-\frac{b x}{a}\right)}{a^2}","\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,"(3*x^(1/3)*Hypergeometric2F1[1/3, 2, 4/3, -((b*x)/a)])/a^2","C",1
688,1,25,124,0.0052866,"\int \frac{1}{x^{4/3} (a+b x)^2} \, dx","Integrate[1/(x^(4/3)*(a + b*x)^2),x]","-\frac{3 \, _2F_1\left(-\frac{1}{3},2;\frac{2}{3};-\frac{b x}{a}\right)}{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*Hypergeometric2F1[-1/3, 2, 2/3, -((b*x)/a)])/(a^2*x^(1/3))","C",1
689,1,27,128,0.0052421,"\int \frac{1}{x^{5/3} (a+b x)^2} \, dx","Integrate[1/(x^(5/3)*(a + b*x)^2),x]","-\frac{3 \, _2F_1\left(-\frac{2}{3},2;\frac{1}{3};-\frac{b x}{a}\right)}{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*Hypergeometric2F1[-2/3, 2, 1/3, -((b*x)/a)])/(2*a^2*x^(2/3))","C",1
690,1,27,140,0.0047883,"\int \frac{x^{5/3}}{(a+b x)^3} \, dx","Integrate[x^(5/3)/(a + b*x)^3,x]","\frac{3 x^{8/3} \, _2F_1\left(\frac{8}{3},3;\frac{11}{3};-\frac{b x}{a}\right)}{8 a^3}","-\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,"(3*x^(8/3)*Hypergeometric2F1[8/3, 3, 11/3, -((b*x)/a)])/(8*a^3)","C",1
691,1,27,140,0.0043884,"\int \frac{x^{4/3}}{(a+b x)^3} \, dx","Integrate[x^(4/3)/(a + b*x)^3,x]","\frac{3 x^{7/3} \, _2F_1\left(\frac{7}{3},3;\frac{10}{3};-\frac{b x}{a}\right)}{7 a^3}","\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,"(3*x^(7/3)*Hypergeometric2F1[7/3, 3, 10/3, -((b*x)/a)])/(7*a^3)","C",1
692,1,27,143,0.0051262,"\int \frac{x^{2/3}}{(a+b x)^3} \, dx","Integrate[x^(2/3)/(a + b*x)^3,x]","\frac{3 x^{5/3} \, _2F_1\left(\frac{5}{3},3;\frac{8}{3};-\frac{b x}{a}\right)}{5 a^3}","-\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,"(3*x^(5/3)*Hypergeometric2F1[5/3, 3, 8/3, -((b*x)/a)])/(5*a^3)","C",1
693,1,27,143,0.0048983,"\int \frac{\sqrt[3]{x}}{(a+b x)^3} \, dx","Integrate[x^(1/3)/(a + b*x)^3,x]","\frac{3 x^{4/3} \, _2F_1\left(\frac{4}{3},3;\frac{7}{3};-\frac{b x}{a}\right)}{4 a^3}","\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,"(3*x^(4/3)*Hypergeometric2F1[4/3, 3, 7/3, -((b*x)/a)])/(4*a^3)","C",1
694,1,27,140,0.0049055,"\int \frac{1}{\sqrt[3]{x} (a+b x)^3} \, dx","Integrate[1/(x^(1/3)*(a + b*x)^3),x]","\frac{3 x^{2/3} \, _2F_1\left(\frac{2}{3},3;\frac{5}{3};-\frac{b x}{a}\right)}{2 a^3}","-\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,"(3*x^(2/3)*Hypergeometric2F1[2/3, 3, 5/3, -((b*x)/a)])/(2*a^3)","C",1
695,1,25,140,0.0042001,"\int \frac{1}{x^{2/3} (a+b x)^3} \, dx","Integrate[1/(x^(2/3)*(a + b*x)^3),x]","\frac{3 \sqrt[3]{x} \, _2F_1\left(\frac{1}{3},3;\frac{4}{3};-\frac{b x}{a}\right)}{a^3}","\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,"(3*x^(1/3)*Hypergeometric2F1[1/3, 3, 4/3, -((b*x)/a)])/a^3","C",1
696,1,25,152,0.0052189,"\int \frac{1}{x^{4/3} (a+b x)^3} \, dx","Integrate[1/(x^(4/3)*(a + b*x)^3),x]","-\frac{3 \, _2F_1\left(-\frac{1}{3},3;\frac{2}{3};-\frac{b x}{a}\right)}{a^3 \sqrt[3]{x}}","\frac{7 \sqrt[3]{b} \log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{x}\right)}{3 a^{10/3}}-\frac{7 \sqrt[3]{b} \log (a+b x)}{9 a^{10/3}}+\frac{14 \sqrt[3]{b} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{10/3}}-\frac{14}{3 a^3 \sqrt[3]{x}}+\frac{7}{6 a^2 \sqrt[3]{x} (a+b x)}+\frac{1}{2 a \sqrt[3]{x} (a+b x)^2}",1,"(-3*Hypergeometric2F1[-1/3, 3, 2/3, -((b*x)/a)])/(a^3*x^(1/3))","C",1
697,1,27,152,0.0054787,"\int \frac{1}{x^{5/3} (a+b x)^3} \, dx","Integrate[1/(x^(5/3)*(a + b*x)^3),x]","-\frac{3 \, _2F_1\left(-\frac{2}{3},3;\frac{1}{3};-\frac{b x}{a}\right)}{2 a^3 x^{2/3}}","-\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*Hypergeometric2F1[-2/3, 3, 1/3, -((b*x)/a)])/(2*a^3*x^(2/3))","C",1
698,1,58,58,0.0167588,"\int \frac{\sqrt[4]{1-x}}{1+x} \, dx","Integrate[(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
699,1,166,187,0.1107714,"\int x^m (a+b x)^{10} \, dx","Integrate[x^m*(a + b*x)^10,x]","x^{m+1} \left(\frac{a^{10}}{m+1}+\frac{10 a^9 b x}{m+2}+\frac{45 a^8 b^2 x^2}{m+3}+\frac{120 a^7 b^3 x^3}{m+4}+\frac{210 a^6 b^4 x^4}{m+5}+\frac{252 a^5 b^5 x^5}{m+6}+\frac{210 a^4 b^6 x^6}{m+7}+\frac{120 a^3 b^7 x^7}{m+8}+\frac{45 a^2 b^8 x^8}{m+9}+\frac{10 a b^9 x^9}{m+10}+\frac{b^{10} x^{10}}{m+11}\right)","\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,"x^(1 + m)*(a^10/(1 + m) + (10*a^9*b*x)/(2 + m) + (45*a^8*b^2*x^2)/(3 + m) + (120*a^7*b^3*x^3)/(4 + m) + (210*a^6*b^4*x^4)/(5 + m) + (252*a^5*b^5*x^5)/(6 + m) + (210*a^4*b^6*x^6)/(7 + m) + (120*a^3*b^7*x^7)/(8 + m) + (45*a^2*b^8*x^8)/(9 + m) + (10*a*b^9*x^9)/(10 + m) + (b^10*x^10)/(11 + m))","A",1
700,1,118,133,0.0679978,"\int x^m (a+b x)^7 \, dx","Integrate[x^m*(a + b*x)^7,x]","x^{m+1} \left(\frac{a^7}{m+1}+\frac{7 a^6 b x}{m+2}+\frac{21 a^5 b^2 x^2}{m+3}+\frac{35 a^4 b^3 x^3}{m+4}+\frac{35 a^3 b^4 x^4}{m+5}+\frac{21 a^2 b^5 x^5}{m+6}+\frac{7 a b^6 x^6}{m+7}+\frac{b^7 x^7}{m+8}\right)","\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,"x^(1 + m)*(a^7/(1 + m) + (7*a^6*b*x)/(2 + m) + (21*a^5*b^2*x^2)/(3 + m) + (35*a^4*b^3*x^3)/(4 + m) + (35*a^3*b^4*x^4)/(5 + m) + (21*a^2*b^5*x^5)/(6 + m) + (7*a*b^6*x^6)/(7 + m) + (b^7*x^7)/(8 + m))","A",1
701,1,54,61,0.0311562,"\int x^m (a+b x)^3 \, dx","Integrate[x^m*(a + b*x)^3,x]","x^{m+1} \left(\frac{a^3}{m+1}+\frac{3 a^2 b x}{m+2}+\frac{3 a b^2 x^2}{m+3}+\frac{b^3 x^3}{m+4}\right)","\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,"x^(1 + m)*(a^3/(1 + m) + (3*a^2*b*x)/(2 + m) + (3*a*b^2*x^2)/(3 + m) + (b^3*x^3)/(4 + m))","A",1
702,1,38,43,0.0312106,"\int x^m (a+b x)^2 \, dx","Integrate[x^m*(a + b*x)^2,x]","x^{m+1} \left(\frac{a^2}{m+1}+\frac{2 a b x}{m+2}+\frac{b^2 x^2}{m+3}\right)","\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,"x^(1 + m)*(a^2/(1 + m) + (2*a*b*x)/(2 + m) + (b^2*x^2)/(3 + m))","A",1
703,1,22,25,0.0140587,"\int x^m (a+b x) \, dx","Integrate[x^m*(a + b*x),x]","x^{m+1} \left(\frac{a}{m+1}+\frac{b x}{m+2}\right)","\frac{a x^{m+1}}{m+1}+\frac{b x^{m+2}}{m+2}",1,"x^(1 + m)*(a/(1 + m) + (b*x)/(2 + m))","A",1
704,1,29,29,0.0068164,"\int \frac{x^m}{a+b x} \, dx","Integrate[x^m/(a + b*x),x]","\frac{x^{m+1} \, _2F_1\left(1,m+1;m+2;-\frac{b x}{a}\right)}{a (m+1)}","\frac{x^{m+1} \, _2F_1\left(1,m+1;m+2;-\frac{b x}{a}\right)}{a (m+1)}",1,"(x^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, -((b*x)/a)])/(a*(1 + m))","A",1
705,1,29,29,0.005691,"\int \frac{x^m}{(a+b x)^2} \, dx","Integrate[x^m/(a + b*x)^2,x]","\frac{x^{m+1} \, _2F_1\left(2,m+1;m+2;-\frac{b x}{a}\right)}{a^2 (m+1)}","\frac{x^{m+1} \, _2F_1\left(2,m+1;m+2;-\frac{b x}{a}\right)}{a^2 (m+1)}",1,"(x^(1 + m)*Hypergeometric2F1[2, 1 + m, 2 + m, -((b*x)/a)])/(a^2*(1 + m))","A",1
706,1,29,29,0.0055311,"\int \frac{x^m}{(a+b x)^3} \, dx","Integrate[x^m/(a + b*x)^3,x]","\frac{x^{m+1} \, _2F_1\left(3,m+1;m+2;-\frac{b x}{a}\right)}{a^3 (m+1)}","\frac{x^{m+1} \, _2F_1\left(3,m+1;m+2;-\frac{b x}{a}\right)}{a^3 (m+1)}",1,"(x^(1 + m)*Hypergeometric2F1[3, 1 + m, 2 + m, -((b*x)/a)])/(a^3*(1 + m))","A",1
707,1,48,48,0.0640848,"\int x^m (a+b x)^{5/2} \, dx","Integrate[x^m*(a + b*x)^(5/2),x]","\frac{2 x^m (a+b x)^{7/2} \left(-\frac{b x}{a}\right)^{-m} \, _2F_1\left(\frac{7}{2},-m;\frac{9}{2};\frac{b x}{a}+1\right)}{7 b}","\frac{2 x^m (a+b x)^{7/2} \left(-\frac{b x}{a}\right)^{-m} \, _2F_1\left(\frac{7}{2},-m;\frac{9}{2};\frac{b x}{a}+1\right)}{7 b}",1,"(2*x^m*(a + b*x)^(7/2)*Hypergeometric2F1[7/2, -m, 9/2, 1 + (b*x)/a])/(7*b*(-((b*x)/a))^m)","A",1
708,1,48,48,0.03967,"\int x^m (a+b x)^{3/2} \, dx","Integrate[x^m*(a + b*x)^(3/2),x]","\frac{2 x^m (a+b x)^{5/2} \left(-\frac{b x}{a}\right)^{-m} \, _2F_1\left(\frac{5}{2},-m;\frac{7}{2};\frac{b x}{a}+1\right)}{5 b}","\frac{2 x^m (a+b x)^{5/2} \left(-\frac{b x}{a}\right)^{-m} \, _2F_1\left(\frac{5}{2},-m;\frac{7}{2};\frac{b x}{a}+1\right)}{5 b}",1,"(2*x^m*(a + b*x)^(5/2)*Hypergeometric2F1[5/2, -m, 7/2, 1 + (b*x)/a])/(5*b*(-((b*x)/a))^m)","A",1
709,1,48,48,0.0308303,"\int x^m \sqrt{a+b x} \, dx","Integrate[x^m*Sqrt[a + b*x],x]","\frac{2 x^m (a+b x)^{3/2} \left(-\frac{b x}{a}\right)^{-m} \, _2F_1\left(\frac{3}{2},-m;\frac{5}{2};\frac{b x}{a}+1\right)}{3 b}","\frac{2 x^m (a+b x)^{3/2} \left(-\frac{b x}{a}\right)^{-m} \, _2F_1\left(\frac{3}{2},-m;\frac{5}{2};\frac{b x}{a}+1\right)}{3 b}",1,"(2*x^m*(a + b*x)^(3/2)*Hypergeometric2F1[3/2, -m, 5/2, 1 + (b*x)/a])/(3*b*(-((b*x)/a))^m)","A",1
710,1,46,46,0.023609,"\int \frac{x^m}{\sqrt{a+b x}} \, dx","Integrate[x^m/Sqrt[a + b*x],x]","\frac{2 x^m \sqrt{a+b x} \left(-\frac{b x}{a}\right)^{-m} \, _2F_1\left(\frac{1}{2},-m;\frac{3}{2};\frac{b x}{a}+1\right)}{b}","\frac{2 x^m \sqrt{a+b x} \left(-\frac{b x}{a}\right)^{-m} \, _2F_1\left(\frac{1}{2},-m;\frac{3}{2};\frac{b x}{a}+1\right)}{b}",1,"(2*x^m*Sqrt[a + b*x]*Hypergeometric2F1[1/2, -m, 3/2, 1 + (b*x)/a])/(b*(-((b*x)/a))^m)","A",1
711,1,46,46,0.0360214,"\int \frac{x^m}{(a+b x)^{3/2}} \, dx","Integrate[x^m/(a + b*x)^(3/2),x]","-\frac{2 x^m \left(-\frac{b x}{a}\right)^{-m} \, _2F_1\left(-\frac{1}{2},-m;\frac{1}{2};\frac{b x}{a}+1\right)}{b \sqrt{a+b x}}","-\frac{2 x^m \left(-\frac{b x}{a}\right)^{-m} \, _2F_1\left(-\frac{1}{2},-m;\frac{1}{2};\frac{b x}{a}+1\right)}{b \sqrt{a+b x}}",1,"(-2*x^m*Hypergeometric2F1[-1/2, -m, 1/2, 1 + (b*x)/a])/(b*(-((b*x)/a))^m*Sqrt[a + b*x])","A",1
712,1,48,48,0.0387983,"\int \frac{x^m}{(a+b x)^{5/2}} \, dx","Integrate[x^m/(a + b*x)^(5/2),x]","-\frac{2 x^m \left(-\frac{b x}{a}\right)^{-m} \, _2F_1\left(-\frac{3}{2},-m;-\frac{1}{2};\frac{b x}{a}+1\right)}{3 b (a+b x)^{3/2}}","-\frac{2 x^m \left(-\frac{b x}{a}\right)^{-m} \, _2F_1\left(-\frac{3}{2},-m;-\frac{1}{2};\frac{b x}{a}+1\right)}{3 b (a+b x)^{3/2}}",1,"(-2*x^m*Hypergeometric2F1[-3/2, -m, -1/2, 1 + (b*x)/a])/(3*b*(-((b*x)/a))^m*(a + b*x)^(3/2))","A",1
713,1,51,51,0.0360313,"\int \frac{x^{2+m}}{\sqrt{a+b x}} \, dx","Integrate[x^(2 + m)/Sqrt[a + b*x],x]","\frac{2 a^2 x^m \sqrt{a+b x} \left(-\frac{b x}{a}\right)^{-m} \, _2F_1\left(\frac{1}{2},-m-2;\frac{3}{2};\frac{b x}{a}+1\right)}{b^3}","\frac{2 a^2 x^m \sqrt{a+b x} \left(-\frac{b x}{a}\right)^{-m} \, _2F_1\left(\frac{1}{2},-m-2;\frac{3}{2};\frac{b x}{a}+1\right)}{b^3}",1,"(2*a^2*x^m*Sqrt[a + b*x]*Hypergeometric2F1[1/2, -2 - m, 3/2, 1 + (b*x)/a])/(b^3*(-((b*x)/a))^m)","A",1
714,1,49,49,0.034543,"\int \frac{x^{1+m}}{\sqrt{a+b x}} \, dx","Integrate[x^(1 + m)/Sqrt[a + b*x],x]","-\frac{2 a x^m \sqrt{a+b x} \left(-\frac{b x}{a}\right)^{-m} \, _2F_1\left(\frac{1}{2},-m-1;\frac{3}{2};\frac{b x}{a}+1\right)}{b^2}","-\frac{2 a x^m \sqrt{a+b x} \left(-\frac{b x}{a}\right)^{-m} \, _2F_1\left(\frac{1}{2},-m-1;\frac{3}{2};\frac{b x}{a}+1\right)}{b^2}",1,"(-2*a*x^m*Sqrt[a + b*x]*Hypergeometric2F1[1/2, -1 - m, 3/2, 1 + (b*x)/a])/(b^2*(-((b*x)/a))^m)","A",1
715,1,46,46,0.0152696,"\int \frac{x^m}{\sqrt{a+b x}} \, dx","Integrate[x^m/Sqrt[a + b*x],x]","\frac{2 x^m \sqrt{a+b x} \left(-\frac{b x}{a}\right)^{-m} \, _2F_1\left(\frac{1}{2},-m;\frac{3}{2};\frac{b x}{a}+1\right)}{b}","\frac{2 x^m \sqrt{a+b x} \left(-\frac{b x}{a}\right)^{-m} \, _2F_1\left(\frac{1}{2},-m;\frac{3}{2};\frac{b x}{a}+1\right)}{b}",1,"(2*x^m*Sqrt[a + b*x]*Hypergeometric2F1[1/2, -m, 3/2, 1 + (b*x)/a])/(b*(-((b*x)/a))^m)","A",1
716,1,48,48,0.0288994,"\int \frac{x^{-1+m}}{\sqrt{a+b x}} \, dx","Integrate[x^(-1 + m)/Sqrt[a + b*x],x]","-\frac{2 x^m \sqrt{a+b x} \left(-\frac{b x}{a}\right)^{-m} \, _2F_1\left(\frac{1}{2},1-m;\frac{3}{2};\frac{b x}{a}+1\right)}{a}","-\frac{2 x^m \sqrt{a+b x} \left(-\frac{b x}{a}\right)^{-m} \, _2F_1\left(\frac{1}{2},1-m;\frac{3}{2};\frac{b x}{a}+1\right)}{a}",1,"(-2*x^m*Sqrt[a + b*x]*Hypergeometric2F1[1/2, 1 - m, 3/2, 1 + (b*x)/a])/(a*(-((b*x)/a))^m)","A",1
717,1,49,49,0.0312906,"\int \frac{x^{-2+m}}{\sqrt{a+b x}} \, dx","Integrate[x^(-2 + m)/Sqrt[a + b*x],x]","\frac{2 b x^m \sqrt{a+b x} \left(-\frac{b x}{a}\right)^{-m} \, _2F_1\left(\frac{1}{2},2-m;\frac{3}{2};\frac{b x}{a}+1\right)}{a^2}","\frac{2 b x^m \sqrt{a+b x} \left(-\frac{b x}{a}\right)^{-m} \, _2F_1\left(\frac{1}{2},2-m;\frac{3}{2};\frac{b x}{a}+1\right)}{a^2}",1,"(2*b*x^m*Sqrt[a + b*x]*Hypergeometric2F1[1/2, 2 - m, 3/2, 1 + (b*x)/a])/(a^2*(-((b*x)/a))^m)","A",1
718,1,51,51,0.0318825,"\int \frac{x^{-3+m}}{\sqrt{a+b x}} \, dx","Integrate[x^(-3 + m)/Sqrt[a + b*x],x]","-\frac{2 b^2 x^m \sqrt{a+b x} \left(-\frac{b x}{a}\right)^{-m} \, _2F_1\left(\frac{1}{2},3-m;\frac{3}{2};\frac{b x}{a}+1\right)}{a^3}","-\frac{2 b^2 x^m \sqrt{a+b x} \left(-\frac{b x}{a}\right)^{-m} \, _2F_1\left(\frac{1}{2},3-m;\frac{3}{2};\frac{b x}{a}+1\right)}{a^3}",1,"(-2*b^2*x^m*Sqrt[a + b*x]*Hypergeometric2F1[1/2, 3 - m, 3/2, 1 + (b*x)/a])/(a^3*(-((b*x)/a))^m)","A",1
719,1,31,31,0.0056703,"\int \frac{x^m}{\sqrt{2+3 x}} \, dx","Integrate[x^m/Sqrt[2 + 3*x],x]","\frac{x^{m+1} \, _2F_1\left(\frac{1}{2},m+1;m+2;-\frac{3 x}{2}\right)}{\sqrt{2} (m+1)}","\frac{x^{m+1} \, _2F_1\left(\frac{1}{2},m+1;m+2;-\frac{3 x}{2}\right)}{\sqrt{2} (m+1)}",1,"(x^(1 + m)*Hypergeometric2F1[1/2, 1 + m, 2 + m, (-3*x)/2])/(Sqrt[2]*(1 + m))","A",1
720,1,31,31,0.0061276,"\int \frac{x^m}{\sqrt{2-3 x}} \, dx","Integrate[x^m/Sqrt[2 - 3*x],x]","\frac{x^{m+1} \, _2F_1\left(\frac{1}{2},m+1;m+2;\frac{3 x}{2}\right)}{\sqrt{2} (m+1)}","\frac{x^{m+1} \, _2F_1\left(\frac{1}{2},m+1;m+2;\frac{3 x}{2}\right)}{\sqrt{2} (m+1)}",1,"(x^(1 + m)*Hypergeometric2F1[1/2, 1 + m, 2 + m, (3*x)/2])/(Sqrt[2]*(1 + m))","A",1
721,1,36,36,0.0068032,"\int \frac{x^m}{\sqrt{-2+3 x}} \, dx","Integrate[x^m/Sqrt[-2 + 3*x],x]","\left(\frac{3}{2}\right)^{-m-1} \sqrt{3 x-2} \, _2F_1\left(\frac{1}{2},-m;\frac{3}{2};1-\frac{3 x}{2}\right)","\left(\frac{3}{2}\right)^{-m-1} \sqrt{3 x-2} \, _2F_1\left(\frac{1}{2},-m;\frac{3}{2};1-\frac{3 x}{2}\right)",1,"(3/2)^(-1 - m)*Sqrt[-2 + 3*x]*Hypergeometric2F1[1/2, -m, 3/2, 1 - (3*x)/2]","A",1
722,1,48,50,0.0265192,"\int \frac{x^m}{\sqrt{-2-3 x}} \, dx","Integrate[x^m/Sqrt[-2 - 3*x],x]","-\frac{2}{3} \sqrt{-3 x-2} \left(\frac{1}{2} (-3 x-2)+1\right)^{-m} x^m \, _2F_1\left(\frac{1}{2},-m;\frac{3}{2};\frac{3 x}{2}+1\right)","-2^{m+1} 3^{-m-1} \sqrt{-3 x-2} (-x)^{-m} x^m \, _2F_1\left(\frac{1}{2},-m;\frac{3}{2};\frac{3 x}{2}+1\right)",1,"(-2*Sqrt[-2 - 3*x]*x^m*Hypergeometric2F1[1/2, -m, 3/2, 1 + (3*x)/2])/(3*(1 + (-2 - 3*x)/2)^m)","A",1
723,1,48,48,0.0166674,"\int \frac{(-x)^m}{\sqrt{a+b x}} \, dx","Integrate[(-x)^m/Sqrt[a + b*x],x]","\frac{2 (-x)^m \sqrt{a+b x} \left(-\frac{b x}{a}\right)^{-m} \, _2F_1\left(\frac{1}{2},-m;\frac{3}{2};\frac{b x}{a}+1\right)}{b}","\frac{2 (-x)^m \sqrt{a+b x} \left(-\frac{b x}{a}\right)^{-m} \, _2F_1\left(\frac{1}{2},-m;\frac{3}{2};\frac{b x}{a}+1\right)}{b}",1,"(2*(-x)^m*Sqrt[a + b*x]*Hypergeometric2F1[1/2, -m, 3/2, 1 + (b*x)/a])/(b*(-((b*x)/a))^m)","A",1
724,1,32,34,0.0062054,"\int \frac{(-x)^m}{\sqrt{2+3 x}} \, dx","Integrate[(-x)^m/Sqrt[2 + 3*x],x]","\frac{x (-x)^m \, _2F_1\left(\frac{1}{2},m+1;m+2;-\frac{3 x}{2}\right)}{\sqrt{2} (m+1)}","-\frac{(-x)^{m+1} \, _2F_1\left(\frac{1}{2},m+1;m+2;-\frac{3 x}{2}\right)}{\sqrt{2} (m+1)}",1,"((-x)^m*x*Hypergeometric2F1[1/2, 1 + m, 2 + m, (-3*x)/2])/(Sqrt[2]*(1 + m))","A",1
725,1,32,34,0.006334,"\int \frac{(-x)^m}{\sqrt{2-3 x}} \, dx","Integrate[(-x)^m/Sqrt[2 - 3*x],x]","\frac{x (-x)^m \, _2F_1\left(\frac{1}{2},m+1;m+2;\frac{3 x}{2}\right)}{\sqrt{2} (m+1)}","-\frac{(-x)^{m+1} \, _2F_1\left(\frac{1}{2},m+1;m+2;\frac{3 x}{2}\right)}{\sqrt{2} (m+1)}",1,"((-x)^m*x*Hypergeometric2F1[1/2, 1 + m, 2 + m, (3*x)/2])/(Sqrt[2]*(1 + m))","A",1
726,1,49,49,0.0086459,"\int \frac{(-x)^m}{\sqrt{-2+3 x}} \, dx","Integrate[(-x)^m/Sqrt[-2 + 3*x],x]","2^{m+1} 3^{-m-1} \sqrt{3 x-2} (-x)^m x^{-m} \, _2F_1\left(\frac{1}{2},-m;\frac{3}{2};1-\frac{3 x}{2}\right)","2^{m+1} 3^{-m-1} \sqrt{3 x-2} (-x)^m x^{-m} \, _2F_1\left(\frac{1}{2},-m;\frac{3}{2};1-\frac{3 x}{2}\right)",1,"(2^(1 + m)*3^(-1 - m)*(-x)^m*Sqrt[-2 + 3*x]*Hypergeometric2F1[1/2, -m, 3/2, 1 - (3*x)/2])/x^m","A",1
727,1,57,37,0.0158421,"\int \frac{(-x)^m}{\sqrt{-2-3 x}} \, dx","Integrate[(-x)^m/Sqrt[-2 - 3*x],x]","-\frac{2}{3} \sqrt{-3 x-2} \left(\frac{1}{2} (-3 x-2)+1\right)^{-m} x^{-m} \left(-x^2\right)^m \, _2F_1\left(\frac{1}{2},-m;\frac{3}{2};\frac{3 x}{2}+1\right)","-\left(\frac{3}{2}\right)^{-m-1} \sqrt{-3 x-2} \, _2F_1\left(\frac{1}{2},-m;\frac{3}{2};\frac{3 x}{2}+1\right)",1,"(-2*Sqrt[-2 - 3*x]*(-x^2)^m*Hypergeometric2F1[1/2, -m, 3/2, 1 + (3*x)/2])/(3*(1 + (-2 - 3*x)/2)^m*x^m)","A",1
728,1,26,26,0.0043532,"\int \frac{x^n}{\sqrt{1-x}} \, dx","Integrate[x^n/Sqrt[1 - x],x]","-2 \sqrt{1-x} \, _2F_1\left(\frac{1}{2},-n;\frac{3}{2};1-x\right)","-2 \sqrt{1-x} \, _2F_1\left(\frac{1}{2},-n;\frac{3}{2};1-x\right)",1,"-2*Sqrt[1 - x]*Hypergeometric2F1[1/2, -n, 3/2, 1 - x]","A",1
729,1,30,30,0.008105,"\int \frac{x^n}{\sqrt{a-a x}} \, dx","Integrate[x^n/Sqrt[a - a*x],x]","-\frac{2 \sqrt{a-a x} \, _2F_1\left(\frac{1}{2},-n;\frac{3}{2};1-x\right)}{a}","-\frac{2 \sqrt{a-a x} \, _2F_1\left(\frac{1}{2},-n;\frac{3}{2};1-x\right)}{a}",1,"(-2*Sqrt[a - a*x]*Hypergeometric2F1[1/2, -n, 3/2, 1 - x])/a","A",1
730,1,47,47,0.0101385,"\int x^m (a+b x)^n \, dx","Integrate[x^m*(a + b*x)^n,x]","\frac{x^{m+1} (a+b x)^n \left(\frac{b x}{a}+1\right)^{-n} \, _2F_1\left(m+1,-n;m+2;-\frac{b x}{a}\right)}{m+1}","\frac{x^{m+1} (a+b x)^n \left(\frac{b x}{a}+1\right)^{-n} \, _2F_1\left(m+1,-n;m+2;-\frac{b x}{a}\right)}{m+1}",1,"(x^(1 + m)*(a + b*x)^n*Hypergeometric2F1[1 + m, -n, 2 + m, -((b*x)/a)])/((1 + m)*(1 + (b*x)/a)^n)","A",1
731,1,48,52,0.007772,"\int (c x)^m (a+b x)^n \, dx","Integrate[(c*x)^m*(a + b*x)^n,x]","\frac{x (c x)^m (a+b x)^n \left(\frac{b x}{a}+1\right)^{-n} \, _2F_1\left(m+1,-n;m+2;-\frac{b x}{a}\right)}{m+1}","\frac{(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,"(x*(c*x)^m*(a + b*x)^n*Hypergeometric2F1[1 + m, -n, 2 + m, -((b*x)/a)])/((1 + m)*(1 + (b*x)/a)^n)","A",1
732,1,67,83,0.0536056,"\int x^3 (a+b x)^n \, dx","Integrate[x^3*(a + b*x)^n,x]","\frac{(a+b x)^{n+1} \left(-\frac{a^3}{n+1}+\frac{3 a^2 (a+b x)}{n+2}-\frac{3 a (a+b x)^2}{n+3}+\frac{(a+b x)^3}{n+4}\right)}{b^4}","-\frac{a^3 (a+b x)^{n+1}}{b^4 (n+1)}+\frac{3 a^2 (a+b x)^{n+2}}{b^4 (n+2)}-\frac{3 a (a+b x)^{n+3}}{b^4 (n+3)}+\frac{(a+b x)^{n+4}}{b^4 (n+4)}",1,"((a + b*x)^(1 + n)*(-(a^3/(1 + n)) + (3*a^2*(a + b*x))/(2 + n) - (3*a*(a + b*x)^2)/(3 + n) + (a + b*x)^3/(4 + n)))/b^4","A",1
733,1,57,60,0.0276327,"\int x^2 (a+b x)^n \, dx","Integrate[x^2*(a + b*x)^n,x]","\frac{(a+b x)^{n+1} \left(2 a^2-2 a b (n+1) x+b^2 \left(n^2+3 n+2\right) x^2\right)}{b^3 (n+1) (n+2) (n+3)}","\frac{a^2 (a+b x)^{n+1}}{b^3 (n+1)}-\frac{2 a (a+b x)^{n+2}}{b^3 (n+2)}+\frac{(a+b x)^{n+3}}{b^3 (n+3)}",1,"((a + b*x)^(1 + n)*(2*a^2 - 2*a*b*(1 + n)*x + b^2*(2 + 3*n + n^2)*x^2))/(b^3*(1 + n)*(2 + n)*(3 + n))","A",1
734,1,33,39,0.0169494,"\int x (a+b x)^n \, dx","Integrate[x*(a + b*x)^n,x]","\frac{(a+b x)^{n+1} (b (n+1) x-a)}{b^2 (n+1) (n+2)}","\frac{(a+b x)^{n+2}}{b^2 (n+2)}-\frac{a (a+b x)^{n+1}}{b^2 (n+1)}",1,"((a + b*x)^(1 + n)*(-a + b*(1 + n)*x))/(b^2*(1 + n)*(2 + n))","A",1
735,1,17,18,0.0086241,"\int (a+b x)^n \, dx","Integrate[(a + b*x)^n,x]","\frac{(a+b x)^{n+1}}{b n+b}","\frac{(a+b x)^{n+1}}{b (n+1)}",1,"(a + b*x)^(1 + n)/(b + b*n)","A",1
736,1,35,35,0.0092137,"\int \frac{(a+b x)^n}{x} \, dx","Integrate[(a + b*x)^n/x,x]","-\frac{(a+b x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b x}{a}+1\right)}{a (n+1)}","-\frac{(a+b x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b x}{a}+1\right)}{a (n+1)}",1,"-(((a + b*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, 1 + (b*x)/a])/(a*(1 + n)))","A",1
737,1,35,35,0.0058232,"\int \frac{(a+b x)^n}{x^2} \, dx","Integrate[(a + b*x)^n/x^2,x]","\frac{b (a+b x)^{n+1} \, _2F_1\left(2,n+1;n+2;\frac{b x}{a}+1\right)}{a^2 (n+1)}","\frac{b (a+b x)^{n+1} \, _2F_1\left(2,n+1;n+2;\frac{b x}{a}+1\right)}{a^2 (n+1)}",1,"(b*(a + b*x)^(1 + n)*Hypergeometric2F1[2, 1 + n, 2 + n, 1 + (b*x)/a])/(a^2*(1 + n))","A",1
738,1,38,38,0.0064637,"\int \frac{(a+b x)^n}{x^3} \, dx","Integrate[(a + b*x)^n/x^3,x]","-\frac{b^2 (a+b x)^{n+1} \, _2F_1\left(3,n+1;n+2;\frac{b x}{a}+1\right)}{a^3 (n+1)}","-\frac{b^2 (a+b x)^{n+1} \, _2F_1\left(3,n+1;n+2;\frac{b x}{a}+1\right)}{a^3 (n+1)}",1,"-((b^2*(a + b*x)^(1 + n)*Hypergeometric2F1[3, 1 + n, 2 + n, 1 + (b*x)/a])/(a^3*(1 + n)))","A",1
739,1,64,110,0.0261081,"\int x^{-4+n} (a+b x)^{-n} \, dx","Integrate[x^(-4 + n)/(a + b*x)^n,x]","\frac{x^{n-3} (a+b x)^{1-n} \left(a^2 \left(n^2-3 n+2\right)+2 a b (n-1) x+2 b^2 x^2\right)}{a^3 (n-3) (n-2) (n-1)}","-\frac{2 b^2 x^{n-1} (a+b x)^{1-n}}{a^3 (1-n) (2-n) (3-n)}+\frac{2 b x^{n-2} (a+b x)^{1-n}}{a^2 (2-n) (3-n)}-\frac{x^{n-3} (a+b x)^{1-n}}{a (3-n)}",1,"(x^(-3 + n)*(a + b*x)^(1 - n)*(a^2*(2 - 3*n + n^2) + 2*a*b*(-1 + n)*x + 2*b^2*x^2))/(a^3*(-3 + n)*(-2 + n)*(-1 + n))","A",1
740,1,39,64,0.0156883,"\int x^{-3+n} (a+b x)^{-n} \, dx","Integrate[x^(-3 + n)/(a + b*x)^n,x]","\frac{x^{n-2} (a+b x)^{1-n} (a (n-1)+b x)}{a^2 (n-2) (n-1)}","\frac{b x^{n-1} (a+b x)^{1-n}}{a^2 (1-n) (2-n)}-\frac{x^{n-2} (a+b x)^{1-n}}{a (2-n)}",1,"(x^(-2 + n)*(a + b*x)^(1 - n)*(a*(-1 + n) + b*x))/(a^2*(-2 + n)*(-1 + n))","A",1
741,1,25,28,0.0057541,"\int x^{-2+n} (a+b x)^{-n} \, dx","Integrate[x^(-2 + n)/(a + b*x)^n,x]","\frac{x^{n-1} (a+b x)^{1-n}}{a (n-1)}","-\frac{x^{n-1} (a+b x)^{1-n}}{a (1-n)}",1,"(x^(-1 + n)*(a + b*x)^(1 - n))/(a*(-1 + n))","A",1
742,1,39,39,0.0071803,"\int x^{-1+n} (a+b x)^{-n} \, dx","Integrate[x^(-1 + n)/(a + b*x)^n,x]","\frac{x^n (a+b x)^{-n} \left(\frac{b x}{a}+1\right)^n \, _2F_1\left(n,n;n+1;-\frac{b x}{a}\right)}{n}","\frac{x^n (a+b x)^{-n} \left(\frac{b x}{a}+1\right)^n \, _2F_1\left(n,n;n+1;-\frac{b x}{a}\right)}{n}",1,"(x^n*(1 + (b*x)/a)^n*Hypergeometric2F1[n, n, 1 + n, -((b*x)/a)])/(n*(a + b*x)^n)","A",1
743,1,45,45,0.0072686,"\int x^n (a+b x)^{-n} \, dx","Integrate[x^n/(a + b*x)^n,x]","\frac{x^{n+1} (a+b x)^{-n} \left(\frac{b x}{a}+1\right)^n \, _2F_1\left(n,n+1;n+2;-\frac{b x}{a}\right)}{n+1}","\frac{x^{n+1} (a+b x)^{-n} \left(\frac{b x}{a}+1\right)^n \, _2F_1\left(n,n+1;n+2;-\frac{b x}{a}\right)}{n+1}",1,"(x^(1 + n)*(1 + (b*x)/a)^n*Hypergeometric2F1[n, 1 + n, 2 + n, -((b*x)/a)])/((1 + n)*(a + b*x)^n)","A",1
744,1,45,45,0.0078066,"\int x^{1+n} (a+b x)^{-n} \, dx","Integrate[x^(1 + n)/(a + b*x)^n,x]","\frac{x^{n+2} (a+b x)^{-n} \left(\frac{b x}{a}+1\right)^n \, _2F_1\left(n,n+2;n+3;-\frac{b x}{a}\right)}{n+2}","\frac{x^{n+2} (a+b x)^{-n} \left(\frac{b x}{a}+1\right)^n \, _2F_1\left(n,n+2;n+3;-\frac{b x}{a}\right)}{n+2}",1,"(x^(2 + n)*(1 + (b*x)/a)^n*Hypergeometric2F1[n, 2 + n, 3 + n, -((b*x)/a)])/((2 + n)*(a + b*x)^n)","A",1
745,1,45,45,0.0077802,"\int x^{3/2} (a+b x)^n \, dx","Integrate[x^(3/2)*(a + b*x)^n,x]","\frac{2}{5} x^{5/2} (a+b x)^n \left(\frac{b x}{a}+1\right)^{-n} \, _2F_1\left(\frac{5}{2},-n;\frac{7}{2};-\frac{b x}{a}\right)","\frac{2}{5} x^{5/2} (a+b x)^n \left(\frac{b x}{a}+1\right)^{-n} \, _2F_1\left(\frac{5}{2},-n;\frac{7}{2};-\frac{b x}{a}\right)",1,"(2*x^(5/2)*(a + b*x)^n*Hypergeometric2F1[5/2, -n, 7/2, -((b*x)/a)])/(5*(1 + (b*x)/a)^n)","A",1
746,1,45,45,0.0069086,"\int \sqrt{x} (a+b x)^n \, dx","Integrate[Sqrt[x]*(a + b*x)^n,x]","\frac{2}{3} x^{3/2} (a+b x)^n \left(\frac{b x}{a}+1\right)^{-n} \, _2F_1\left(\frac{3}{2},-n;\frac{5}{2};-\frac{b x}{a}\right)","\frac{2}{3} x^{3/2} (a+b x)^n \left(\frac{b x}{a}+1\right)^{-n} \, _2F_1\left(\frac{3}{2},-n;\frac{5}{2};-\frac{b x}{a}\right)",1,"(2*x^(3/2)*(a + b*x)^n*Hypergeometric2F1[3/2, -n, 5/2, -((b*x)/a)])/(3*(1 + (b*x)/a)^n)","A",1
747,1,43,43,0.0062647,"\int \frac{(a+b x)^n}{\sqrt{x}} \, dx","Integrate[(a + b*x)^n/Sqrt[x],x]","2 \sqrt{x} (a+b x)^n \left(\frac{b x}{a}+1\right)^{-n} \, _2F_1\left(\frac{1}{2},-n;\frac{3}{2};-\frac{b x}{a}\right)","2 \sqrt{x} (a+b x)^n \left(\frac{b x}{a}+1\right)^{-n} \, _2F_1\left(\frac{1}{2},-n;\frac{3}{2};-\frac{b x}{a}\right)",1,"(2*Sqrt[x]*(a + b*x)^n*Hypergeometric2F1[1/2, -n, 3/2, -((b*x)/a)])/(1 + (b*x)/a)^n","A",1
748,1,43,43,0.0077778,"\int \frac{(a+b x)^n}{x^{3/2}} \, dx","Integrate[(a + b*x)^n/x^(3/2),x]","-\frac{2 (a+b x)^n \left(\frac{b x}{a}+1\right)^{-n} \, _2F_1\left(-\frac{1}{2},-n;\frac{1}{2};-\frac{b x}{a}\right)}{\sqrt{x}}","-\frac{2 (a+b x)^n \left(\frac{b x}{a}+1\right)^{-n} \, _2F_1\left(-\frac{1}{2},-n;\frac{1}{2};-\frac{b x}{a}\right)}{\sqrt{x}}",1,"(-2*(a + b*x)^n*Hypergeometric2F1[-1/2, -n, 1/2, -((b*x)/a)])/(Sqrt[x]*(1 + (b*x)/a)^n)","A",1
749,1,45,45,0.0072133,"\int \frac{(a+b x)^n}{x^{5/2}} \, dx","Integrate[(a + b*x)^n/x^(5/2),x]","-\frac{2 (a+b x)^n \left(\frac{b x}{a}+1\right)^{-n} \, _2F_1\left(-\frac{3}{2},-n;-\frac{1}{2};-\frac{b x}{a}\right)}{3 x^{3/2}}","-\frac{2 (a+b x)^n \left(\frac{b x}{a}+1\right)^{-n} \, _2F_1\left(-\frac{3}{2},-n;-\frac{1}{2};-\frac{b x}{a}\right)}{3 x^{3/2}}",1,"(-2*(a + b*x)^n*Hypergeometric2F1[-3/2, -n, -1/2, -((b*x)/a)])/(3*x^(3/2)*(1 + (b*x)/a)^n)","A",1
750,1,31,35,0.0065332,"\int (b x)^m (2+d x)^n \, dx","Integrate[(b*x)^m*(2 + d*x)^n,x]","\frac{2^n x (b x)^m \, _2F_1\left(m+1,-n;m+2;-\frac{d x}{2}\right)}{m+1}","\frac{2^n (b x)^{m+1} \, _2F_1\left(m+1,-n;m+2;-\frac{d x}{2}\right)}{b (m+1)}",1,"(2^n*x*(b*x)^m*Hypergeometric2F1[1 + m, -n, 2 + m, -1/2*(d*x)])/(1 + m)","A",1
751,1,44,40,0.0099826,"\int (b x)^m (c-b c x)^n \, dx","Integrate[(b*x)^m*(c - b*c*x)^n,x]","\frac{x (b x)^m (1-b x)^{-n} (c-b c x)^n \, _2F_1(m+1,-n;m+2;b x)}{m+1}","-\frac{(c-b c x)^{n+1} \, _2F_1(-m,n+1;n+2;1-b x)}{b c (n+1)}",1,"(x*(b*x)^m*(c - b*c*x)^n*Hypergeometric2F1[1 + m, -n, 2 + m, b*x])/((1 + m)*(1 - b*x)^n)","A",1
752,1,48,52,0.0124042,"\int (b x)^m (c+d x)^n \, dx","Integrate[(b*x)^m*(c + d*x)^n,x]","\frac{x (b x)^m (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)}{m+1}","\frac{(b x)^{m+1} (c+d x)^n \left(\frac{d x}{c}+1\right)^{-n} \, _2F_1\left(m+1,-n;m+2;-\frac{d x}{c}\right)}{b (m+1)}",1,"(x*(b*x)^m*(c + d*x)^n*Hypergeometric2F1[1 + m, -n, 2 + m, -((d*x)/c)])/((1 + m)*(1 + (d*x)/c)^n)","A",1
753,1,19,19,0.0049194,"\int x^{-1+n} (a+b x)^{-1-n} \, dx","Integrate[x^(-1 + n)*(a + b*x)^(-1 - n),x]","\frac{x^n (a+b x)^{-n}}{a n}","\frac{x^n (a+b x)^{-n}}{a n}",1,"x^n/(a*n*(a + b*x)^n)","A",1
754,1,40,58,0.0143433,"\int x^{-3-n} (a+b x)^n \, dx","Integrate[x^(-3 - n)*(a + b*x)^n,x]","-\frac{x^{-n-2} (a n+a-b x) (a+b x)^{n+1}}{a^2 (n+1) (n+2)}","\frac{b x^{-n-1} (a+b x)^{n+1}}{a^2 (n+1) (n+2)}-\frac{x^{-n-2} (a+b x)^{n+1}}{a (n+2)}",1,"-((x^(-2 - n)*(a + a*n - b*x)*(a + b*x)^(1 + n))/(a^2*(1 + n)*(2 + n)))","A",1
755,1,40,58,0.0023197,"\int x^{2 n-3 (1+n)} (a+b x)^n \, dx","Integrate[x^(2*n - 3*(1 + n))*(a + b*x)^n,x]","-\frac{x^{-n-2} (a n+a-b x) (a+b x)^{n+1}}{a^2 (n+1) (n+2)}","\frac{b x^{-n-1} (a+b x)^{n+1}}{a^2 (n+1) (n+2)}-\frac{x^{-n-2} (a+b x)^{n+1}}{a (n+2)}",1,"-((x^(-2 - n)*(a + a*n - b*x)*(a + b*x)^(1 + n))/(a^2*(1 + n)*(2 + n)))","A",1
756,1,24,35,0.0045646,"\int x^3 \sqrt{c x^2} (a+b x) \, dx","Integrate[x^3*Sqrt[c*x^2]*(a + b*x),x]","\frac{1}{30} x^4 \sqrt{c x^2} (6 a+5 b x)","\frac{1}{5} a x^4 \sqrt{c x^2}+\frac{1}{6} b x^5 \sqrt{c x^2}",1,"(x^4*Sqrt[c*x^2]*(6*a + 5*b*x))/30","A",1
757,1,24,35,0.0042408,"\int x^2 \sqrt{c x^2} (a+b x) \, dx","Integrate[x^2*Sqrt[c*x^2]*(a + b*x),x]","\frac{1}{20} x^3 \sqrt{c x^2} (5 a+4 b x)","\frac{1}{4} a x^3 \sqrt{c x^2}+\frac{1}{5} b x^4 \sqrt{c x^2}",1,"(x^3*Sqrt[c*x^2]*(5*a + 4*b*x))/20","A",1
758,1,24,35,0.0039143,"\int x \sqrt{c x^2} (a+b x) \, dx","Integrate[x*Sqrt[c*x^2]*(a + b*x),x]","\frac{1}{12} x^2 \sqrt{c x^2} (4 a+3 b x)","\frac{1}{3} a x^2 \sqrt{c x^2}+\frac{1}{4} b x^3 \sqrt{c x^2}",1,"(x^2*Sqrt[c*x^2]*(4*a + 3*b*x))/12","A",1
759,1,22,33,0.0032976,"\int \sqrt{c x^2} (a+b x) \, dx","Integrate[Sqrt[c*x^2]*(a + b*x),x]","\frac{1}{6} x \sqrt{c x^2} (3 a+2 b x)","\frac{1}{2} a x \sqrt{c x^2}+\frac{1}{3} b x^2 \sqrt{c x^2}",1,"(x*Sqrt[c*x^2]*(3*a + 2*b*x))/6","A",1
760,1,24,27,0.0048281,"\int \frac{\sqrt{c x^2} (a+b x)}{x} \, dx","Integrate[(Sqrt[c*x^2]*(a + b*x))/x,x]","\frac{c x^2 (2 a+b x)}{2 \sqrt{c x^2}}","a \sqrt{c x^2}+\frac{1}{2} b x \sqrt{c x^2}",1,"(c*x^2*(2*a + b*x))/(2*Sqrt[c*x^2])","A",1
761,1,20,28,0.0050446,"\int \frac{\sqrt{c x^2} (a+b x)}{x^2} \, dx","Integrate[(Sqrt[c*x^2]*(a + b*x))/x^2,x]","\frac{c x (a \log (x)+b x)}{\sqrt{c x^2}}","\frac{a \sqrt{c x^2} \log (x)}{x}+b \sqrt{c x^2}",1,"(c*x*(b*x + a*Log[x]))/Sqrt[c*x^2]","A",1
762,1,20,32,0.0055272,"\int \frac{\sqrt{c x^2} (a+b x)}{x^3} \, dx","Integrate[(Sqrt[c*x^2]*(a + b*x))/x^3,x]","\frac{c (b x \log (x)-a)}{\sqrt{c x^2}}","\frac{b \sqrt{c x^2} \log (x)}{x}-\frac{a \sqrt{c x^2}}{x^2}",1,"(c*(-a + b*x*Log[x]))/Sqrt[c*x^2]","A",1
763,1,22,26,0.0041775,"\int \frac{\sqrt{c x^2} (a+b x)}{x^4} \, dx","Integrate[(Sqrt[c*x^2]*(a + b*x))/x^4,x]","-\frac{\sqrt{c x^2} (a+2 b x)}{2 x^3}","-\frac{\sqrt{c x^2} (a+b x)^2}{2 a x^3}",1,"-1/2*(Sqrt[c*x^2]*(a + 2*b*x))/x^3","A",1
764,1,24,37,0.006156,"\int x^3 \left(c x^2\right)^{3/2} (a+b x) \, dx","Integrate[x^3*(c*x^2)^(3/2)*(a + b*x),x]","\frac{1}{56} x^4 \left(c x^2\right)^{3/2} (8 a+7 b x)","\frac{1}{7} a c x^6 \sqrt{c x^2}+\frac{1}{8} b c x^7 \sqrt{c x^2}",1,"(x^4*(c*x^2)^(3/2)*(8*a + 7*b*x))/56","A",1
765,1,24,37,0.0060546,"\int x^2 \left(c x^2\right)^{3/2} (a+b x) \, dx","Integrate[x^2*(c*x^2)^(3/2)*(a + b*x),x]","\frac{1}{42} x^3 \left(c x^2\right)^{3/2} (7 a+6 b x)","\frac{1}{6} a c x^5 \sqrt{c x^2}+\frac{1}{7} b c x^6 \sqrt{c x^2}",1,"(x^3*(c*x^2)^(3/2)*(7*a + 6*b*x))/42","A",1
766,1,24,37,0.0052687,"\int x \left(c x^2\right)^{3/2} (a+b x) \, dx","Integrate[x*(c*x^2)^(3/2)*(a + b*x),x]","\frac{1}{30} x^2 \left(c x^2\right)^{3/2} (6 a+5 b x)","\frac{1}{5} a c x^4 \sqrt{c x^2}+\frac{1}{6} b c x^5 \sqrt{c x^2}",1,"(x^2*(c*x^2)^(3/2)*(6*a + 5*b*x))/30","A",1
767,1,22,37,0.0051738,"\int \left(c x^2\right)^{3/2} (a+b x) \, dx","Integrate[(c*x^2)^(3/2)*(a + b*x),x]","\frac{1}{20} x \left(c x^2\right)^{3/2} (5 a+4 b x)","\frac{1}{4} a c x^3 \sqrt{c x^2}+\frac{1}{5} b c x^4 \sqrt{c x^2}",1,"(x*(c*x^2)^(3/2)*(5*a + 4*b*x))/20","A",1
768,1,25,37,0.0023441,"\int \frac{\left(c x^2\right)^{3/2} (a+b x)}{x} \, dx","Integrate[((c*x^2)^(3/2)*(a + b*x))/x,x]","\frac{1}{12} c x^2 \sqrt{c x^2} (4 a+3 b x)","\frac{1}{3} a c x^2 \sqrt{c x^2}+\frac{1}{4} b c x^3 \sqrt{c x^2}",1,"(c*x^2*Sqrt[c*x^2]*(4*a + 3*b*x))/12","A",1
769,1,23,35,0.0020347,"\int \frac{\left(c x^2\right)^{3/2} (a+b x)}{x^2} \, dx","Integrate[((c*x^2)^(3/2)*(a + b*x))/x^2,x]","\frac{1}{6} c x \sqrt{c x^2} (3 a+2 b x)","\frac{1}{2} a c x \sqrt{c x^2}+\frac{1}{3} b c x^2 \sqrt{c x^2}",1,"(c*x*Sqrt[c*x^2]*(3*a + 2*b*x))/6","A",1
770,1,21,29,0.0031826,"\int \frac{\left(c x^2\right)^{3/2} (a+b x)}{x^3} \, dx","Integrate[((c*x^2)^(3/2)*(a + b*x))/x^3,x]","\frac{1}{2} c \sqrt{c x^2} (2 a+b x)","a c \sqrt{c x^2}+\frac{1}{2} b c x \sqrt{c x^2}",1,"(c*Sqrt[c*x^2]*(2*a + b*x))/2","A",1
771,1,21,30,0.0047837,"\int \frac{\left(c x^2\right)^{3/2} (a+b x)}{x^4} \, dx","Integrate[((c*x^2)^(3/2)*(a + b*x))/x^4,x]","\frac{\left(c x^2\right)^{3/2} (a \log (x)+b x)}{x^3}","\frac{a c \sqrt{c x^2} \log (x)}{x}+b c \sqrt{c x^2}",1,"((c*x^2)^(3/2)*(b*x + a*Log[x]))/x^3","A",1
772,1,24,41,0.0071691,"\int x^3 \left(c x^2\right)^{5/2} (a+b x) \, dx","Integrate[x^3*(c*x^2)^(5/2)*(a + b*x),x]","\frac{1}{90} x^4 \left(c x^2\right)^{5/2} (10 a+9 b x)","\frac{1}{9} a c^2 x^8 \sqrt{c x^2}+\frac{1}{10} b c^2 x^9 \sqrt{c x^2}",1,"(x^4*(c*x^2)^(5/2)*(10*a + 9*b*x))/90","A",1
773,1,24,41,0.0067532,"\int x^2 \left(c x^2\right)^{5/2} (a+b x) \, dx","Integrate[x^2*(c*x^2)^(5/2)*(a + b*x),x]","\frac{1}{72} x^3 \left(c x^2\right)^{5/2} (9 a+8 b x)","\frac{1}{8} a c^2 x^7 \sqrt{c x^2}+\frac{1}{9} b c^2 x^8 \sqrt{c x^2}",1,"(x^3*(c*x^2)^(5/2)*(9*a + 8*b*x))/72","A",1
774,1,24,41,0.0065271,"\int x \left(c x^2\right)^{5/2} (a+b x) \, dx","Integrate[x*(c*x^2)^(5/2)*(a + b*x),x]","\frac{1}{56} x^2 \left(c x^2\right)^{5/2} (8 a+7 b x)","\frac{1}{7} a c^2 x^6 \sqrt{c x^2}+\frac{1}{8} b c^2 x^7 \sqrt{c x^2}",1,"(x^2*(c*x^2)^(5/2)*(8*a + 7*b*x))/56","A",1
775,1,22,41,0.0061556,"\int \left(c x^2\right)^{5/2} (a+b x) \, dx","Integrate[(c*x^2)^(5/2)*(a + b*x),x]","\frac{1}{42} x \left(c x^2\right)^{5/2} (7 a+6 b x)","\frac{1}{6} a c^2 x^5 \sqrt{c x^2}+\frac{1}{7} b c^2 x^6 \sqrt{c x^2}",1,"(x*(c*x^2)^(5/2)*(7*a + 6*b*x))/42","A",1
776,1,25,41,0.0028677,"\int \frac{\left(c x^2\right)^{5/2} (a+b x)}{x} \, dx","Integrate[((c*x^2)^(5/2)*(a + b*x))/x,x]","\frac{1}{30} c x^2 \left(c x^2\right)^{3/2} (6 a+5 b x)","\frac{1}{5} a c^2 x^4 \sqrt{c x^2}+\frac{1}{6} b c^2 x^5 \sqrt{c x^2}",1,"(c*x^2*(c*x^2)^(3/2)*(6*a + 5*b*x))/30","A",1
777,1,23,41,0.0027372,"\int \frac{\left(c x^2\right)^{5/2} (a+b x)}{x^2} \, dx","Integrate[((c*x^2)^(5/2)*(a + b*x))/x^2,x]","\frac{1}{20} c x \left(c x^2\right)^{3/2} (5 a+4 b x)","\frac{1}{4} a c^2 x^3 \sqrt{c x^2}+\frac{1}{5} b c^2 x^4 \sqrt{c x^2}",1,"(c*x*(c*x^2)^(3/2)*(5*a + 4*b*x))/20","A",1
778,1,27,41,0.0028219,"\int \frac{\left(c x^2\right)^{5/2} (a+b x)}{x^3} \, dx","Integrate[((c*x^2)^(5/2)*(a + b*x))/x^3,x]","\frac{1}{12} c^2 x^2 \sqrt{c x^2} (4 a+3 b x)","\frac{1}{3} a c^2 x^2 \sqrt{c x^2}+\frac{1}{4} b c^2 x^3 \sqrt{c x^2}",1,"(c^2*x^2*Sqrt[c*x^2]*(4*a + 3*b*x))/12","A",1
779,1,25,39,0.0023641,"\int \frac{\left(c x^2\right)^{5/2} (a+b x)}{x^4} \, dx","Integrate[((c*x^2)^(5/2)*(a + b*x))/x^4,x]","\frac{1}{6} c^2 x \sqrt{c x^2} (3 a+2 b x)","\frac{1}{2} a c^2 x \sqrt{c x^2}+\frac{1}{3} b c^2 x^2 \sqrt{c x^2}",1,"(c^2*x*Sqrt[c*x^2]*(3*a + 2*b*x))/6","A",1
780,1,24,35,0.0048449,"\int \frac{x^3 (a+b x)}{\sqrt{c x^2}} \, dx","Integrate[(x^3*(a + b*x))/Sqrt[c*x^2],x]","\frac{x^4 (4 a+3 b x)}{12 \sqrt{c x^2}}","\frac{a x^4}{3 \sqrt{c x^2}}+\frac{b x^5}{4 \sqrt{c x^2}}",1,"(x^4*(4*a + 3*b*x))/(12*Sqrt[c*x^2])","A",1
781,1,24,35,0.0044193,"\int \frac{x^2 (a+b x)}{\sqrt{c x^2}} \, dx","Integrate[(x^2*(a + b*x))/Sqrt[c*x^2],x]","\frac{x^3 (3 a+2 b x)}{6 \sqrt{c x^2}}","\frac{a x^3}{2 \sqrt{c x^2}}+\frac{b x^4}{3 \sqrt{c x^2}}",1,"(x^3*(3*a + 2*b*x))/(6*Sqrt[c*x^2])","A",1
782,1,23,32,0.0015077,"\int \frac{x (a+b x)}{\sqrt{c x^2}} \, dx","Integrate[(x*(a + b*x))/Sqrt[c*x^2],x]","\frac{x^2 (2 a+b x)}{2 \sqrt{c x^2}}","\frac{a x^2}{\sqrt{c x^2}}+\frac{b x^3}{2 \sqrt{c x^2}}",1,"(x^2*(2*a + b*x))/(2*Sqrt[c*x^2])","A",1
783,1,19,29,0.0019069,"\int \frac{a+b x}{\sqrt{c x^2}} \, dx","Integrate[(a + b*x)/Sqrt[c*x^2],x]","\frac{x (a \log (x)+b x)}{\sqrt{c x^2}}","\frac{a x \log (x)}{\sqrt{c x^2}}+\frac{b x^2}{\sqrt{c x^2}}",1,"(x*(b*x + a*Log[x]))/Sqrt[c*x^2]","A",1
784,1,23,27,0.0063797,"\int \frac{a+b x}{x \sqrt{c x^2}} \, dx","Integrate[(a + b*x)/(x*Sqrt[c*x^2]),x]","\frac{c x^2 (b x \log (x)-a)}{\left(c x^2\right)^{3/2}}","\frac{b x \log (x)}{\sqrt{c x^2}}-\frac{a}{\sqrt{c x^2}}",1,"(c*x^2*(-a + b*x*Log[x]))/(c*x^2)^(3/2)","A",1
785,1,23,26,0.0056088,"\int \frac{a+b x}{x^2 \sqrt{c x^2}} \, dx","Integrate[(a + b*x)/(x^2*Sqrt[c*x^2]),x]","\frac{c x (-a-2 b x)}{2 \left(c x^2\right)^{3/2}}","-\frac{(a+b x)^2}{2 a x \sqrt{c x^2}}",1,"(c*x*(-a - 2*b*x))/(2*(c*x^2)^(3/2))","A",1
786,1,22,35,0.0059559,"\int \frac{a+b x}{x^3 \sqrt{c x^2}} \, dx","Integrate[(a + b*x)/(x^3*Sqrt[c*x^2]),x]","\frac{c (-2 a-3 b x)}{6 \left(c x^2\right)^{3/2}}","-\frac{a}{3 x^2 \sqrt{c x^2}}-\frac{b}{2 x \sqrt{c x^2}}",1,"(c*(-2*a - 3*b*x))/(6*(c*x^2)^(3/2))","A",1
787,1,24,35,0.0051604,"\int \frac{a+b x}{x^4 \sqrt{c x^2}} \, dx","Integrate[(a + b*x)/(x^4*Sqrt[c*x^2]),x]","\frac{-3 a-4 b x}{12 x^3 \sqrt{c x^2}}","-\frac{a}{4 x^3 \sqrt{c x^2}}-\frac{b}{3 x^2 \sqrt{c x^2}}",1,"(-3*a - 4*b*x)/(12*x^3*Sqrt[c*x^2])","A",1
788,1,23,38,0.0039317,"\int \frac{x^3 (a+b x)}{\left(c x^2\right)^{3/2}} \, dx","Integrate[(x^3*(a + b*x))/(c*x^2)^(3/2),x]","\frac{x^4 (2 a+b x)}{2 \left(c x^2\right)^{3/2}}","\frac{a x^2}{c \sqrt{c x^2}}+\frac{b x^3}{2 c \sqrt{c x^2}}",1,"(x^4*(2*a + b*x))/(2*(c*x^2)^(3/2))","A",1
789,1,21,35,0.0042545,"\int \frac{x^2 (a+b x)}{\left(c x^2\right)^{3/2}} \, dx","Integrate[(x^2*(a + b*x))/(c*x^2)^(3/2),x]","\frac{x^3 (a \log (x)+b x)}{\left(c x^2\right)^{3/2}}","\frac{a x \log (x)}{c \sqrt{c x^2}}+\frac{b x^2}{c \sqrt{c x^2}}",1,"(x^3*(b*x + a*Log[x]))/(c*x^2)^(3/2)","A",1
790,1,22,33,0.0029808,"\int \frac{x (a+b x)}{\left(c x^2\right)^{3/2}} \, dx","Integrate[(x*(a + b*x))/(c*x^2)^(3/2),x]","\frac{x^2 (b x \log (x)-a)}{\left(c x^2\right)^{3/2}}","\frac{b x \log (x)}{c \sqrt{c x^2}}-\frac{a}{c \sqrt{c x^2}}",1,"(x^2*(-a + b*x*Log[x]))/(c*x^2)^(3/2)","A",1
791,1,22,29,0.0027399,"\int \frac{a+b x}{\left(c x^2\right)^{3/2}} \, dx","Integrate[(a + b*x)/(c*x^2)^(3/2),x]","\frac{x (-a-2 b x)}{2 \left(c x^2\right)^{3/2}}","-\frac{(a+b x)^2}{2 a c x \sqrt{c x^2}}",1,"(x*(-a - 2*b*x))/(2*(c*x^2)^(3/2))","A",1
792,1,25,41,0.0077828,"\int \frac{a+b x}{x \left(c x^2\right)^{3/2}} \, dx","Integrate[(a + b*x)/(x*(c*x^2)^(3/2)),x]","\frac{c x^2 (-2 a-3 b x)}{6 \left(c x^2\right)^{5/2}}","-\frac{a}{3 c x^2 \sqrt{c x^2}}-\frac{b}{2 c x \sqrt{c x^2}}",1,"(c*x^2*(-2*a - 3*b*x))/(6*(c*x^2)^(5/2))","A",1
793,1,27,41,0.0075755,"\int \frac{a+b x}{x^2 \left(c x^2\right)^{3/2}} \, dx","Integrate[(a + b*x)/(x^2*(c*x^2)^(3/2)),x]","-\frac{\sqrt{c x^2} (3 a+4 b x)}{12 c^2 x^5}","-\frac{a}{4 c x^3 \sqrt{c x^2}}-\frac{b}{3 c x^2 \sqrt{c x^2}}",1,"-1/12*(Sqrt[c*x^2]*(3*a + 4*b*x))/(c^2*x^5)","A",1
794,1,22,41,0.0074037,"\int \frac{a+b x}{x^3 \left(c x^2\right)^{3/2}} \, dx","Integrate[(a + b*x)/(x^3*(c*x^2)^(3/2)),x]","\frac{c (-4 a-5 b x)}{20 \left(c x^2\right)^{5/2}}","-\frac{a}{5 c x^4 \sqrt{c x^2}}-\frac{b}{4 c x^3 \sqrt{c x^2}}",1,"(c*(-4*a - 5*b*x))/(20*(c*x^2)^(5/2))","A",1
795,1,24,41,0.0063689,"\int \frac{a+b x}{x^4 \left(c x^2\right)^{3/2}} \, dx","Integrate[(a + b*x)/(x^4*(c*x^2)^(3/2)),x]","\frac{-5 a-6 b x}{30 x^3 \left(c x^2\right)^{3/2}}","-\frac{a}{6 c x^5 \sqrt{c x^2}}-\frac{b}{5 c x^4 \sqrt{c x^2}}",1,"(-5*a - 6*b*x)/(30*x^3*(c*x^2)^(3/2))","A",1
796,1,22,33,0.0051611,"\int \frac{x^3 (a+b x)}{\left(c x^2\right)^{5/2}} \, dx","Integrate[(x^3*(a + b*x))/(c*x^2)^(5/2),x]","\frac{b x \log (x)-a}{c^2 \sqrt{c x^2}}","\frac{b x \log (x)}{c^2 \sqrt{c x^2}}-\frac{a}{c^2 \sqrt{c x^2}}",1,"(-a + b*x*Log[x])/(c^2*Sqrt[c*x^2])","A",1
797,1,24,29,0.0063561,"\int \frac{x^2 (a+b x)}{\left(c x^2\right)^{5/2}} \, dx","Integrate[(x^2*(a + b*x))/(c*x^2)^(5/2),x]","\frac{x^3 (-a-2 b x)}{2 \left(c x^2\right)^{5/2}}","-\frac{(a+b x)^2}{2 a c^2 x \sqrt{c x^2}}",1,"(x^3*(-a - 2*b*x))/(2*(c*x^2)^(5/2))","A",1
798,1,24,41,0.0038219,"\int \frac{x (a+b x)}{\left(c x^2\right)^{5/2}} \, dx","Integrate[(x*(a + b*x))/(c*x^2)^(5/2),x]","\frac{x^2 (-2 a-3 b x)}{6 \left(c x^2\right)^{5/2}}","-\frac{a}{3 c^2 x^2 \sqrt{c x^2}}-\frac{b}{2 c^2 x \sqrt{c x^2}}",1,"(x^2*(-2*a - 3*b*x))/(6*(c*x^2)^(5/2))","A",1
799,1,27,41,0.002851,"\int \frac{a+b x}{\left(c x^2\right)^{5/2}} \, dx","Integrate[(a + b*x)/(c*x^2)^(5/2),x]","-\frac{\sqrt{c x^2} (3 a+4 b x)}{12 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,"-1/12*(Sqrt[c*x^2]*(3*a + 4*b*x))/(c^3*x^5)","A",1
800,1,27,41,0.008355,"\int \frac{a+b x}{x \left(c x^2\right)^{5/2}} \, dx","Integrate[(a + b*x)/(x*(c*x^2)^(5/2)),x]","-\frac{\sqrt{c x^2} (4 a+5 b x)}{20 c^3 x^6}","-\frac{a}{5 c^2 x^4 \sqrt{c x^2}}-\frac{b}{4 c^2 x^3 \sqrt{c x^2}}",1,"-1/20*(Sqrt[c*x^2]*(4*a + 5*b*x))/(c^3*x^6)","A",1
801,1,27,41,0.0073478,"\int \frac{a+b x}{x^2 \left(c x^2\right)^{5/2}} \, dx","Integrate[(a + b*x)/(x^2*(c*x^2)^(5/2)),x]","-\frac{\sqrt{c x^2} (5 a+6 b x)}{30 c^3 x^7}","-\frac{a}{6 c^2 x^5 \sqrt{c x^2}}-\frac{b}{5 c^2 x^4 \sqrt{c x^2}}",1,"-1/30*(Sqrt[c*x^2]*(5*a + 6*b*x))/(c^3*x^7)","A",1
802,1,22,41,0.0079917,"\int \frac{a+b x}{x^3 \left(c x^2\right)^{5/2}} \, dx","Integrate[(a + b*x)/(x^3*(c*x^2)^(5/2)),x]","\frac{c (-6 a-7 b x)}{42 \left(c x^2\right)^{7/2}}","-\frac{a}{7 c^2 x^6 \sqrt{c x^2}}-\frac{b}{6 c^2 x^5 \sqrt{c x^2}}",1,"(c*(-6*a - 7*b*x))/(42*(c*x^2)^(7/2))","A",1
803,1,24,41,0.0069064,"\int \frac{a+b x}{x^4 \left(c x^2\right)^{5/2}} \, dx","Integrate[(a + b*x)/(x^4*(c*x^2)^(5/2)),x]","\frac{-7 a-8 b x}{56 x^3 \left(c x^2\right)^{5/2}}","-\frac{a}{8 c^2 x^7 \sqrt{c x^2}}-\frac{b}{7 c^2 x^6 \sqrt{c x^2}}",1,"(-7*a - 8*b*x)/(56*x^3*(c*x^2)^(5/2))","A",1
804,1,35,57,0.0057313,"\int x^3 \sqrt{c x^2} (a+b x)^2 \, dx","Integrate[x^3*Sqrt[c*x^2]*(a + b*x)^2,x]","\frac{1}{105} x^4 \sqrt{c x^2} \left(21 a^2+35 a b x+15 b^2 x^2\right)","\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,"(x^4*Sqrt[c*x^2]*(21*a^2 + 35*a*b*x + 15*b^2*x^2))/105","A",1
805,1,35,57,0.0060691,"\int x^2 \sqrt{c x^2} (a+b x)^2 \, dx","Integrate[x^2*Sqrt[c*x^2]*(a + b*x)^2,x]","\frac{1}{60} x^3 \sqrt{c x^2} \left(15 a^2+24 a b x+10 b^2 x^2\right)","\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,"(x^3*Sqrt[c*x^2]*(15*a^2 + 24*a*b*x + 10*b^2*x^2))/60","A",1
806,1,35,57,0.0059706,"\int x \sqrt{c x^2} (a+b x)^2 \, dx","Integrate[x*Sqrt[c*x^2]*(a + b*x)^2,x]","\frac{1}{30} x^2 \sqrt{c x^2} \left(10 a^2+15 a b x+6 b^2 x^2\right)","\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,"(x^2*Sqrt[c*x^2]*(10*a^2 + 15*a*b*x + 6*b^2*x^2))/30","A",1
807,1,33,55,0.006692,"\int \sqrt{c x^2} (a+b x)^2 \, dx","Integrate[Sqrt[c*x^2]*(a + b*x)^2,x]","\frac{1}{12} x \sqrt{c x^2} \left(6 a^2+8 a b x+3 b^2 x^2\right)","\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,"(x*Sqrt[c*x^2]*(6*a^2 + 8*a*b*x + 3*b^2*x^2))/12","A",1
808,1,25,26,0.0052034,"\int \frac{\sqrt{c x^2} (a+b x)^2}{x} \, dx","Integrate[(Sqrt[c*x^2]*(a + b*x)^2)/x,x]","\frac{c x (a+b x)^3}{3 b \sqrt{c x^2}}","\frac{\sqrt{c x^2} (a+b x)^3}{3 b x}",1,"(c*x*(a + b*x)^3)/(3*b*Sqrt[c*x^2])","A",1
809,1,33,49,0.0089654,"\int \frac{\sqrt{c x^2} (a+b x)^2}{x^2} \, dx","Integrate[(Sqrt[c*x^2]*(a + b*x)^2)/x^2,x]","\frac{c x \left(2 a^2 \log (x)+b x (4 a+b x)\right)}{2 \sqrt{c x^2}}","\frac{a^2 \sqrt{c x^2} \log (x)}{x}+2 a b \sqrt{c x^2}+\frac{1}{2} b^2 x \sqrt{c x^2}",1,"(c*x*(b*x*(4*a + b*x) + 2*a^2*Log[x]))/(2*Sqrt[c*x^2])","A",1
810,1,31,49,0.0113559,"\int \frac{\sqrt{c x^2} (a+b x)^2}{x^3} \, dx","Integrate[(Sqrt[c*x^2]*(a + b*x)^2)/x^3,x]","\frac{c \left(-a^2+2 a b x \log (x)+b^2 x^2\right)}{\sqrt{c x^2}}","-\frac{a^2 \sqrt{c x^2}}{x^2}+\frac{2 a b \sqrt{c x^2} \log (x)}{x}+b^2 \sqrt{c x^2}",1,"(c*(-a^2 + b^2*x^2 + 2*a*b*x*Log[x]))/Sqrt[c*x^2]","A",1
811,1,36,54,0.0097693,"\int \frac{\sqrt{c x^2} (a+b x)^2}{x^4} \, dx","Integrate[(Sqrt[c*x^2]*(a + b*x)^2)/x^4,x]","\frac{\sqrt{c x^2} \left(2 b^2 x^2 \log (x)-a (a+4 b x)\right)}{2 x^3}","-\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,"(Sqrt[c*x^2]*(-(a*(a + 4*b*x)) + 2*b^2*x^2*Log[x]))/(2*x^3)","A",1
812,1,35,60,0.0083704,"\int x^3 \left(c x^2\right)^{3/2} (a+b x)^2 \, dx","Integrate[x^3*(c*x^2)^(3/2)*(a + b*x)^2,x]","\frac{1}{252} x^4 \left(c x^2\right)^{3/2} \left(36 a^2+63 a b x+28 b^2 x^2\right)","\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,"(x^4*(c*x^2)^(3/2)*(36*a^2 + 63*a*b*x + 28*b^2*x^2))/252","A",1
813,1,35,60,0.0080258,"\int x^2 \left(c x^2\right)^{3/2} (a+b x)^2 \, dx","Integrate[x^2*(c*x^2)^(3/2)*(a + b*x)^2,x]","\frac{1}{168} x^3 \left(c x^2\right)^{3/2} \left(28 a^2+48 a b x+21 b^2 x^2\right)","\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,"(x^3*(c*x^2)^(3/2)*(28*a^2 + 48*a*b*x + 21*b^2*x^2))/168","A",1
814,1,35,60,0.0073955,"\int x \left(c x^2\right)^{3/2} (a+b x)^2 \, dx","Integrate[x*(c*x^2)^(3/2)*(a + b*x)^2,x]","\frac{1}{105} x^2 \left(c x^2\right)^{3/2} \left(21 a^2+35 a b x+15 b^2 x^2\right)","\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,"(x^2*(c*x^2)^(3/2)*(21*a^2 + 35*a*b*x + 15*b^2*x^2))/105","A",1
815,1,33,60,0.006823,"\int \left(c x^2\right)^{3/2} (a+b x)^2 \, dx","Integrate[(c*x^2)^(3/2)*(a + b*x)^2,x]","\frac{1}{60} x \left(c x^2\right)^{3/2} \left(15 a^2+24 a b x+10 b^2 x^2\right)","\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,"(x*(c*x^2)^(3/2)*(15*a^2 + 24*a*b*x + 10*b^2*x^2))/60","A",1
816,1,36,60,0.0042539,"\int \frac{\left(c x^2\right)^{3/2} (a+b x)^2}{x} \, dx","Integrate[((c*x^2)^(3/2)*(a + b*x)^2)/x,x]","\frac{1}{30} c x^2 \sqrt{c x^2} \left(10 a^2+15 a b x+6 b^2 x^2\right)","\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,"(c*x^2*Sqrt[c*x^2]*(10*a^2 + 15*a*b*x + 6*b^2*x^2))/30","A",1
817,1,34,58,0.0038935,"\int \frac{\left(c x^2\right)^{3/2} (a+b x)^2}{x^2} \, dx","Integrate[((c*x^2)^(3/2)*(a + b*x)^2)/x^2,x]","\frac{1}{12} c x \sqrt{c x^2} \left(6 a^2+8 a b x+3 b^2 x^2\right)","\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,"(c*x*Sqrt[c*x^2]*(6*a^2 + 8*a*b*x + 3*b^2*x^2))/12","A",1
818,1,26,27,0.0050492,"\int \frac{\left(c x^2\right)^{3/2} (a+b x)^2}{x^3} \, dx","Integrate[((c*x^2)^(3/2)*(a + b*x)^2)/x^3,x]","\frac{\left(c x^2\right)^{3/2} (a+b x)^3}{3 b x^3}","\frac{c \sqrt{c x^2} (a+b x)^3}{3 b x}",1,"((c*x^2)^(3/2)*(a + b*x)^3)/(3*b*x^3)","A",1
819,1,34,52,0.0088037,"\int \frac{\left(c x^2\right)^{3/2} (a+b x)^2}{x^4} \, dx","Integrate[((c*x^2)^(3/2)*(a + b*x)^2)/x^4,x]","\frac{\left(c x^2\right)^{3/2} \left(2 a^2 \log (x)+b x (4 a+b x)\right)}{2 x^3}","\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,"((c*x^2)^(3/2)*(b*x*(4*a + b*x) + 2*a^2*Log[x]))/(2*x^3)","A",1
820,1,35,66,0.0083465,"\int x \left(c x^2\right)^{5/2} (a+b x)^2 \, dx","Integrate[x*(c*x^2)^(5/2)*(a + b*x)^2,x]","\frac{1}{252} x^2 \left(c x^2\right)^{5/2} \left(36 a^2+63 a b x+28 b^2 x^2\right)","\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,"(x^2*(c*x^2)^(5/2)*(36*a^2 + 63*a*b*x + 28*b^2*x^2))/252","A",1
821,1,33,66,0.008128,"\int \left(c x^2\right)^{5/2} (a+b x)^2 \, dx","Integrate[(c*x^2)^(5/2)*(a + b*x)^2,x]","\frac{1}{168} x \left(c x^2\right)^{5/2} \left(28 a^2+48 a b x+21 b^2 x^2\right)","\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,"(x*(c*x^2)^(5/2)*(28*a^2 + 48*a*b*x + 21*b^2*x^2))/168","A",1
822,1,36,66,0.0037804,"\int \frac{\left(c x^2\right)^{5/2} (a+b x)^2}{x} \, dx","Integrate[((c*x^2)^(5/2)*(a + b*x)^2)/x,x]","\frac{1}{105} c x^2 \left(c x^2\right)^{3/2} \left(21 a^2+35 a b x+15 b^2 x^2\right)","\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,"(c*x^2*(c*x^2)^(3/2)*(21*a^2 + 35*a*b*x + 15*b^2*x^2))/105","A",1
823,1,34,66,0.0053484,"\int \frac{\left(c x^2\right)^{5/2} (a+b x)^2}{x^2} \, dx","Integrate[((c*x^2)^(5/2)*(a + b*x)^2)/x^2,x]","\frac{1}{60} c x \left(c x^2\right)^{3/2} \left(15 a^2+24 a b x+10 b^2 x^2\right)","\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,"(c*x*(c*x^2)^(3/2)*(15*a^2 + 24*a*b*x + 10*b^2*x^2))/60","A",1
824,1,38,66,0.0038465,"\int \frac{\left(c x^2\right)^{5/2} (a+b x)^2}{x^3} \, dx","Integrate[((c*x^2)^(5/2)*(a + b*x)^2)/x^3,x]","\frac{1}{30} c^2 x^2 \sqrt{c x^2} \left(10 a^2+15 a b x+6 b^2 x^2\right)","\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,"(c^2*x^2*Sqrt[c*x^2]*(10*a^2 + 15*a*b*x + 6*b^2*x^2))/30","A",1
825,1,36,64,0.0029984,"\int \frac{\left(c x^2\right)^{5/2} (a+b x)^2}{x^4} \, dx","Integrate[((c*x^2)^(5/2)*(a + b*x)^2)/x^4,x]","\frac{1}{12} c^2 x \sqrt{c x^2} \left(6 a^2+8 a b x+3 b^2 x^2\right)","\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,"(c^2*x*Sqrt[c*x^2]*(6*a^2 + 8*a*b*x + 3*b^2*x^2))/12","A",1
826,1,26,29,0.0056683,"\int \frac{\left(c x^2\right)^{5/2} (a+b x)^2}{x^5} \, dx","Integrate[((c*x^2)^(5/2)*(a + b*x)^2)/x^5,x]","\frac{\left(c x^2\right)^{5/2} (a+b x)^3}{3 b x^5}","\frac{c^2 \sqrt{c x^2} (a+b x)^3}{3 b x}",1,"((c*x^2)^(5/2)*(a + b*x)^3)/(3*b*x^5)","A",1
827,1,35,58,0.0100258,"\int \frac{\left(c x^2\right)^{5/2} (a+b x)^2}{x^6} \, dx","Integrate[((c*x^2)^(5/2)*(a + b*x)^2)/x^6,x]","\frac{c^3 x \left(2 a^2 \log (x)+b x (4 a+b x)\right)}{2 \sqrt{c x^2}}","\frac{a^2 c^2 \sqrt{c x^2} \log (x)}{x}+2 a b c^2 \sqrt{c x^2}+\frac{1}{2} b^2 c^2 x \sqrt{c x^2}",1,"(c^3*x*(b*x*(4*a + b*x) + 2*a^2*Log[x]))/(2*Sqrt[c*x^2])","A",1
828,1,35,57,0.0060309,"\int \frac{x^3 (a+b x)^2}{\sqrt{c x^2}} \, dx","Integrate[(x^3*(a + b*x)^2)/Sqrt[c*x^2],x]","\frac{x^4 \left(10 a^2+15 a b x+6 b^2 x^2\right)}{30 \sqrt{c x^2}}","\frac{a^2 x^4}{3 \sqrt{c x^2}}+\frac{a b x^5}{2 \sqrt{c x^2}}+\frac{b^2 x^6}{5 \sqrt{c x^2}}",1,"(x^4*(10*a^2 + 15*a*b*x + 6*b^2*x^2))/(30*Sqrt[c*x^2])","A",1
829,1,35,57,0.0050195,"\int \frac{x^2 (a+b x)^2}{\sqrt{c x^2}} \, dx","Integrate[(x^2*(a + b*x)^2)/Sqrt[c*x^2],x]","\frac{x^3 \left(6 a^2+8 a b x+3 b^2 x^2\right)}{12 \sqrt{c x^2}}","\frac{a^2 x^3}{2 \sqrt{c x^2}}+\frac{2 a b x^4}{3 \sqrt{c x^2}}+\frac{b^2 x^5}{4 \sqrt{c x^2}}",1,"(x^3*(6*a^2 + 8*a*b*x + 3*b^2*x^2))/(12*Sqrt[c*x^2])","A",1
830,1,24,24,0.0019706,"\int \frac{x (a+b x)^2}{\sqrt{c x^2}} \, dx","Integrate[(x*(a + b*x)^2)/Sqrt[c*x^2],x]","\frac{x (a+b x)^3}{3 b \sqrt{c x^2}}","\frac{x (a+b x)^3}{3 b \sqrt{c x^2}}",1,"(x*(a + b*x)^3)/(3*b*Sqrt[c*x^2])","A",1
831,1,32,52,0.0033589,"\int \frac{(a+b x)^2}{\sqrt{c x^2}} \, dx","Integrate[(a + b*x)^2/Sqrt[c*x^2],x]","\frac{x \left(2 a^2 \log (x)+b x (4 a+b x)\right)}{2 \sqrt{c x^2}}","\frac{a^2 x \log (x)}{\sqrt{c x^2}}+\frac{2 a b x^2}{\sqrt{c x^2}}+\frac{b^2 x^3}{2 \sqrt{c x^2}}",1,"(x*(b*x*(4*a + b*x) + 2*a^2*Log[x]))/(2*Sqrt[c*x^2])","A",1
832,1,34,47,0.0089427,"\int \frac{(a+b x)^2}{x \sqrt{c x^2}} \, dx","Integrate[(a + b*x)^2/(x*Sqrt[c*x^2]),x]","\frac{c x^2 \left(-a^2+2 a b x \log (x)+b^2 x^2\right)}{\left(c x^2\right)^{3/2}}","-\frac{a^2}{\sqrt{c x^2}}+\frac{2 a b x \log (x)}{\sqrt{c x^2}}+\frac{b^2 x^2}{\sqrt{c x^2}}",1,"(c*x^2*(-a^2 + b^2*x^2 + 2*a*b*x*Log[x]))/(c*x^2)^(3/2)","A",1
833,1,35,49,0.0079176,"\int \frac{(a+b x)^2}{x^2 \sqrt{c x^2}} \, dx","Integrate[(a + b*x)^2/(x^2*Sqrt[c*x^2]),x]","\frac{c x \left(2 b^2 x^2 \log (x)-a (a+4 b x)\right)}{2 \left(c x^2\right)^{3/2}}","-\frac{a^2}{2 x \sqrt{c x^2}}-\frac{2 a b}{\sqrt{c x^2}}+\frac{b^2 x \log (x)}{\sqrt{c x^2}}",1,"(c*x*(-(a*(a + 4*b*x)) + 2*b^2*x^2*Log[x]))/(2*(c*x^2)^(3/2))","A",1
834,1,33,26,0.0101348,"\int \frac{(a+b x)^2}{x^3 \sqrt{c x^2}} \, dx","Integrate[(a + b*x)^2/(x^3*Sqrt[c*x^2]),x]","\frac{c \left(-a^2-3 a b x-3 b^2 x^2\right)}{3 \left(c x^2\right)^{3/2}}","-\frac{(a+b x)^3}{3 a x^2 \sqrt{c x^2}}",1,"(c*(-a^2 - 3*a*b*x - 3*b^2*x^2))/(3*(c*x^2)^(3/2))","A",1
835,1,35,57,0.007419,"\int \frac{(a+b x)^2}{x^4 \sqrt{c x^2}} \, dx","Integrate[(a + b*x)^2/(x^4*Sqrt[c*x^2]),x]","\frac{-3 a^2-8 a b x-6 b^2 x^2}{12 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,"(-3*a^2 - 8*a*b*x - 6*b^2*x^2)/(12*x^3*Sqrt[c*x^2])","A",1
836,1,26,27,0.0043555,"\int \frac{x^3 (a+b x)^2}{\left(c x^2\right)^{3/2}} \, dx","Integrate[(x^3*(a + b*x)^2)/(c*x^2)^(3/2),x]","\frac{x^3 (a+b x)^3}{3 b \left(c x^2\right)^{3/2}}","\frac{x (a+b x)^3}{3 b c \sqrt{c x^2}}",1,"(x^3*(a + b*x)^3)/(3*b*(c*x^2)^(3/2))","A",1
837,1,34,61,0.0071022,"\int \frac{x^2 (a+b x)^2}{\left(c x^2\right)^{3/2}} \, dx","Integrate[(x^2*(a + b*x)^2)/(c*x^2)^(3/2),x]","\frac{x^3 \left(2 a^2 \log (x)+b x (4 a+b x)\right)}{2 \left(c x^2\right)^{3/2}}","\frac{a^2 x \log (x)}{c \sqrt{c x^2}}+\frac{2 a b x^2}{c \sqrt{c x^2}}+\frac{b^2 x^3}{2 c \sqrt{c x^2}}",1,"(x^3*(b*x*(4*a + b*x) + 2*a^2*Log[x]))/(2*(c*x^2)^(3/2))","A",1
838,1,33,56,0.0053745,"\int \frac{x (a+b x)^2}{\left(c x^2\right)^{3/2}} \, dx","Integrate[(x*(a + b*x)^2)/(c*x^2)^(3/2),x]","\frac{x^2 \left(-a^2+2 a b x \log (x)+b^2 x^2\right)}{\left(c x^2\right)^{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,"(x^2*(-a^2 + b^2*x^2 + 2*a*b*x*Log[x]))/(c*x^2)^(3/2)","A",1
839,1,34,58,0.0040734,"\int \frac{(a+b x)^2}{\left(c x^2\right)^{3/2}} \, dx","Integrate[(a + b*x)^2/(c*x^2)^(3/2),x]","\frac{x \left(2 b^2 x^2 \log (x)-a (a+4 b x)\right)}{2 \left(c x^2\right)^{3/2}}","-\frac{a^2}{2 c x \sqrt{c x^2}}-\frac{2 a b}{c \sqrt{c x^2}}+\frac{b^2 x \log (x)}{c \sqrt{c x^2}}",1,"(x*(-(a*(a + 4*b*x)) + 2*b^2*x^2*Log[x]))/(2*(c*x^2)^(3/2))","A",1
840,1,36,29,0.0120374,"\int \frac{(a+b x)^2}{x \left(c x^2\right)^{3/2}} \, dx","Integrate[(a + b*x)^2/(x*(c*x^2)^(3/2)),x]","\frac{c x^2 \left(-a^2-3 a b x-3 b^2 x^2\right)}{3 \left(c x^2\right)^{5/2}}","-\frac{(a+b x)^3}{3 a c x^2 \sqrt{c x^2}}",1,"(c*x^2*(-a^2 - 3*a*b*x - 3*b^2*x^2))/(3*(c*x^2)^(5/2))","A",1
841,1,38,66,0.0091708,"\int \frac{(a+b x)^2}{x^2 \left(c x^2\right)^{3/2}} \, dx","Integrate[(a + b*x)^2/(x^2*(c*x^2)^(3/2)),x]","-\frac{\sqrt{c x^2} \left(3 a^2+8 a b x+6 b^2 x^2\right)}{12 c^2 x^5}","-\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,"-1/12*(Sqrt[c*x^2]*(3*a^2 + 8*a*b*x + 6*b^2*x^2))/(c^2*x^5)","A",1
842,1,33,66,0.0117073,"\int \frac{(a+b x)^2}{x^3 \left(c x^2\right)^{3/2}} \, dx","Integrate[(a + b*x)^2/(x^3*(c*x^2)^(3/2)),x]","\frac{c \left(-6 a^2-15 a b x-10 b^2 x^2\right)}{30 \left(c x^2\right)^{5/2}}","-\frac{a^2}{5 c x^4 \sqrt{c x^2}}-\frac{a b}{2 c x^3 \sqrt{c x^2}}-\frac{b^2}{3 c x^2 \sqrt{c x^2}}",1,"(c*(-6*a^2 - 15*a*b*x - 10*b^2*x^2))/(30*(c*x^2)^(5/2))","A",1
843,1,35,66,0.0085909,"\int \frac{(a+b x)^2}{x^4 \left(c x^2\right)^{3/2}} \, dx","Integrate[(a + b*x)^2/(x^4*(c*x^2)^(3/2)),x]","\frac{-10 a^2-24 a b x-15 b^2 x^2}{60 x^3 \left(c x^2\right)^{3/2}}","-\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,"(-10*a^2 - 24*a*b*x - 15*b^2*x^2)/(60*x^3*(c*x^2)^(3/2))","A",1
844,1,33,56,0.008254,"\int \frac{x^3 (a+b x)^2}{\left(c x^2\right)^{5/2}} \, dx","Integrate[(x^3*(a + b*x)^2)/(c*x^2)^(5/2),x]","\frac{-a^2+2 a b x \log (x)+b^2 x^2}{c^2 \sqrt{c x^2}}","-\frac{a^2}{c^2 \sqrt{c x^2}}+\frac{2 a b x \log (x)}{c^2 \sqrt{c x^2}}+\frac{b^2 x^2}{c^2 \sqrt{c x^2}}",1,"(-a^2 + b^2*x^2 + 2*a*b*x*Log[x])/(c^2*Sqrt[c*x^2])","A",1
845,1,36,58,0.009467,"\int \frac{x^2 (a+b x)^2}{\left(c x^2\right)^{5/2}} \, dx","Integrate[(x^2*(a + b*x)^2)/(c*x^2)^(5/2),x]","\frac{x^3 \left(2 b^2 x^2 \log (x)-a (a+4 b x)\right)}{2 \left(c x^2\right)^{5/2}}","-\frac{a^2}{2 c^2 x \sqrt{c x^2}}-\frac{2 a b}{c^2 \sqrt{c x^2}}+\frac{b^2 x \log (x)}{c^2 \sqrt{c x^2}}",1,"(x^3*(-(a*(a + 4*b*x)) + 2*b^2*x^2*Log[x]))/(2*(c*x^2)^(5/2))","A",1
846,1,35,29,0.0070875,"\int \frac{x (a+b x)^2}{\left(c x^2\right)^{5/2}} \, dx","Integrate[(x*(a + b*x)^2)/(c*x^2)^(5/2),x]","\frac{x^2 \left(-a^2-3 a b x-3 b^2 x^2\right)}{3 \left(c x^2\right)^{5/2}}","-\frac{(a+b x)^3}{3 a c^2 x^2 \sqrt{c x^2}}",1,"(x^2*(-a^2 - 3*a*b*x - 3*b^2*x^2))/(3*(c*x^2)^(5/2))","A",1
847,1,38,66,0.0038898,"\int \frac{(a+b x)^2}{\left(c x^2\right)^{5/2}} \, dx","Integrate[(a + b*x)^2/(c*x^2)^(5/2),x]","-\frac{\sqrt{c x^2} \left(3 a^2+8 a b x+6 b^2 x^2\right)}{12 c^3 x^5}","-\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,"-1/12*(Sqrt[c*x^2]*(3*a^2 + 8*a*b*x + 6*b^2*x^2))/(c^3*x^5)","A",1
848,1,38,66,0.0116029,"\int \frac{(a+b x)^2}{x \left(c x^2\right)^{5/2}} \, dx","Integrate[(a + b*x)^2/(x*(c*x^2)^(5/2)),x]","-\frac{\sqrt{c x^2} \left(6 a^2+15 a b x+10 b^2 x^2\right)}{30 c^3 x^6}","-\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,"-1/30*(Sqrt[c*x^2]*(6*a^2 + 15*a*b*x + 10*b^2*x^2))/(c^3*x^6)","A",1
849,1,38,66,0.0087776,"\int \frac{(a+b x)^2}{x^2 \left(c x^2\right)^{5/2}} \, dx","Integrate[(a + b*x)^2/(x^2*(c*x^2)^(5/2)),x]","-\frac{\sqrt{c x^2} \left(10 a^2+24 a b x+15 b^2 x^2\right)}{60 c^3 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,"-1/60*(Sqrt[c*x^2]*(10*a^2 + 24*a*b*x + 15*b^2*x^2))/(c^3*x^7)","A",1
850,1,33,66,0.0142994,"\int \frac{(a+b x)^2}{x^3 \left(c x^2\right)^{5/2}} \, dx","Integrate[(a + b*x)^2/(x^3*(c*x^2)^(5/2)),x]","\frac{c \left(-15 a^2-35 a b x-21 b^2 x^2\right)}{105 \left(c x^2\right)^{7/2}}","-\frac{a^2}{7 c^2 x^6 \sqrt{c x^2}}-\frac{a b}{3 c^2 x^5 \sqrt{c x^2}}-\frac{b^2}{5 c^2 x^4 \sqrt{c x^2}}",1,"(c*(-15*a^2 - 35*a*b*x - 21*b^2*x^2))/(105*(c*x^2)^(7/2))","A",1
851,1,35,66,0.0092148,"\int \frac{(a+b x)^2}{x^4 \left(c x^2\right)^{5/2}} \, dx","Integrate[(a + b*x)^2/(x^4*(c*x^2)^(5/2)),x]","\frac{-21 a^2-48 a b x-28 b^2 x^2}{168 x^3 \left(c x^2\right)^{5/2}}","-\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,"(-21*a^2 - 48*a*b*x - 28*b^2*x^2)/(168*x^3*(c*x^2)^(5/2))","A",1
852,1,63,102,0.0179126,"\int \frac{x^3 \sqrt{c x^2}}{a+b x} \, dx","Integrate[(x^3*Sqrt[c*x^2])/(a + b*x),x]","\frac{c x \left(12 a^4 \log (a+b x)+b x \left(-12 a^3+6 a^2 b x-4 a b^2 x^2+3 b^3 x^3\right)\right)}{12 b^5 \sqrt{c x^2}}","\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,"(c*x*(b*x*(-12*a^3 + 6*a^2*b*x - 4*a*b^2*x^2 + 3*b^3*x^3) + 12*a^4*Log[a + b*x]))/(12*b^5*Sqrt[c*x^2])","A",1
853,1,52,80,0.0150217,"\int \frac{x^2 \sqrt{c x^2}}{a+b x} \, dx","Integrate[(x^2*Sqrt[c*x^2])/(a + b*x),x]","\frac{c x \left(b x \left(6 a^2-3 a b x+2 b^2 x^2\right)-6 a^3 \log (a+b x)\right)}{6 b^4 \sqrt{c x^2}}","-\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,"(c*x*(b*x*(6*a^2 - 3*a*b*x + 2*b^2*x^2) - 6*a^3*Log[a + b*x]))/(6*b^4*Sqrt[c*x^2])","A",1
854,1,40,58,0.0114481,"\int \frac{x \sqrt{c x^2}}{a+b x} \, dx","Integrate[(x*Sqrt[c*x^2])/(a + b*x),x]","\frac{c x \left(2 a^2 \log (a+b x)+b x (b x-2 a)\right)}{2 b^3 \sqrt{c x^2}}","\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,"(c*x*(b*x*(-2*a + b*x) + 2*a^2*Log[a + b*x]))/(2*b^3*Sqrt[c*x^2])","A",1
855,1,28,38,0.0069363,"\int \frac{\sqrt{c x^2}}{a+b x} \, dx","Integrate[Sqrt[c*x^2]/(a + b*x),x]","\frac{c x (b x-a \log (a+b x))}{b^2 \sqrt{c x^2}}","\frac{\sqrt{c x^2}}{b}-\frac{a \sqrt{c x^2} \log (a+b x)}{b^2 x}",1,"(c*x*(b*x - a*Log[a + b*x]))/(b^2*Sqrt[c*x^2])","A",1
856,1,21,22,0.0044367,"\int \frac{\sqrt{c x^2}}{x (a+b x)} \, dx","Integrate[Sqrt[c*x^2]/(x*(a + b*x)),x]","\frac{c x \log (a+b x)}{b \sqrt{c x^2}}","\frac{\sqrt{c x^2} \log (a+b x)}{b x}",1,"(c*x*Log[a + b*x])/(b*Sqrt[c*x^2])","A",1
857,1,26,42,0.0069562,"\int \frac{\sqrt{c x^2}}{x^2 (a+b x)} \, dx","Integrate[Sqrt[c*x^2]/(x^2*(a + b*x)),x]","\frac{c x (\log (x)-\log (a+b x))}{a \sqrt{c x^2}}","\frac{\sqrt{c x^2} \log (x)}{a x}-\frac{\sqrt{c x^2} \log (a+b x)}{a x}",1,"(c*x*(Log[x] - Log[a + b*x]))/(a*Sqrt[c*x^2])","A",1
858,1,32,61,0.0112544,"\int \frac{\sqrt{c x^2}}{x^3 (a+b x)} \, dx","Integrate[Sqrt[c*x^2]/(x^3*(a + b*x)),x]","-\frac{c (-b x \log (a+b x)+a+b x \log (x))}{a^2 \sqrt{c x^2}}","-\frac{b \sqrt{c x^2} \log (x)}{a^2 x}+\frac{b \sqrt{c x^2} \log (a+b x)}{a^2 x}-\frac{\sqrt{c x^2}}{a x^2}",1,"-((c*(a + b*x*Log[x] - b*x*Log[a + b*x]))/(a^2*Sqrt[c*x^2]))","A",1
859,1,53,84,0.0152068,"\int \frac{\sqrt{c x^2}}{x^4 (a+b x)} \, dx","Integrate[Sqrt[c*x^2]/(x^4*(a + b*x)),x]","\frac{\sqrt{c x^2} \left(-2 b^2 x^2 \log (a+b x)-a (a-2 b x)+2 b^2 x^2 \log (x)\right)}{2 a^3 x^3}","\frac{b^2 \sqrt{c x^2} \log (x)}{a^3 x}-\frac{b^2 \sqrt{c x^2} \log (a+b x)}{a^3 x}+\frac{b \sqrt{c x^2}}{a^2 x^2}-\frac{\sqrt{c x^2}}{2 a x^3}",1,"(Sqrt[c*x^2]*(-(a*(a - 2*b*x)) + 2*b^2*x^2*Log[x] - 2*b^2*x^2*Log[a + b*x]))/(2*a^3*x^3)","A",1
860,1,64,107,0.0129859,"\int \frac{x \left(c x^2\right)^{3/2}}{a+b x} \, dx","Integrate[(x*(c*x^2)^(3/2))/(a + b*x),x]","\frac{\left(c x^2\right)^{3/2} \left(12 a^4 \log (a+b x)+b x \left(-12 a^3+6 a^2 b x-4 a b^2 x^2+3 b^3 x^3\right)\right)}{12 b^5 x^3}","\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,"((c*x^2)^(3/2)*(b*x*(-12*a^3 + 6*a^2*b*x - 4*a*b^2*x^2 + 3*b^3*x^3) + 12*a^4*Log[a + b*x]))/(12*b^5*x^3)","A",1
861,1,53,84,0.0114986,"\int \frac{\left(c x^2\right)^{3/2}}{a+b x} \, dx","Integrate[(c*x^2)^(3/2)/(a + b*x),x]","\frac{\left(c x^2\right)^{3/2} \left(b x \left(6 a^2-3 a b x+2 b^2 x^2\right)-6 a^3 \log (a+b x)\right)}{6 b^4 x^3}","-\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,"((c*x^2)^(3/2)*(b*x*(6*a^2 - 3*a*b*x + 2*b^2*x^2) - 6*a^3*Log[a + b*x]))/(6*b^4*x^3)","A",1
862,1,42,61,0.0047249,"\int \frac{\left(c x^2\right)^{3/2}}{x (a+b x)} \, dx","Integrate[(c*x^2)^(3/2)/(x*(a + b*x)),x]","\frac{c^2 x \left(2 a^2 \log (a+b x)+b x (b x-2 a)\right)}{2 b^3 \sqrt{c x^2}}","\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,"(c^2*x*(b*x*(-2*a + b*x) + 2*a^2*Log[a + b*x]))/(2*b^3*Sqrt[c*x^2])","A",1
863,1,30,40,0.0038258,"\int \frac{\left(c x^2\right)^{3/2}}{x^2 (a+b x)} \, dx","Integrate[(c*x^2)^(3/2)/(x^2*(a + b*x)),x]","\frac{c^2 x (b x-a \log (a+b x))}{b^2 \sqrt{c x^2}}","\frac{c \sqrt{c x^2}}{b}-\frac{a c \sqrt{c x^2} \log (a+b x)}{b^2 x}",1,"(c^2*x*(b*x - a*Log[a + b*x]))/(b^2*Sqrt[c*x^2])","A",1
864,1,22,23,0.0033881,"\int \frac{\left(c x^2\right)^{3/2}}{x^3 (a+b x)} \, dx","Integrate[(c*x^2)^(3/2)/(x^3*(a + b*x)),x]","\frac{\left(c x^2\right)^{3/2} \log (a+b x)}{b x^3}","\frac{c \sqrt{c x^2} \log (a+b x)}{b x}",1,"((c*x^2)^(3/2)*Log[a + b*x])/(b*x^3)","A",1
865,1,27,44,0.0075878,"\int \frac{\left(c x^2\right)^{3/2}}{x^4 (a+b x)} \, dx","Integrate[(c*x^2)^(3/2)/(x^4*(a + b*x)),x]","\frac{\left(c x^2\right)^{3/2} (\log (x)-\log (a+b x))}{a x^3}","\frac{c \sqrt{c x^2} \log (x)}{a x}-\frac{c \sqrt{c x^2} \log (a+b x)}{a x}",1,"((c*x^2)^(3/2)*(Log[x] - Log[a + b*x]))/(a*x^3)","A",1
866,1,34,64,0.0108381,"\int \frac{\left(c x^2\right)^{3/2}}{x^5 (a+b x)} \, dx","Integrate[(c*x^2)^(3/2)/(x^5*(a + b*x)),x]","-\frac{c^2 (-b x \log (a+b x)+a+b x \log (x))}{a^2 \sqrt{c x^2}}","-\frac{b c \sqrt{c x^2} \log (x)}{a^2 x}+\frac{b c \sqrt{c x^2} \log (a+b x)}{a^2 x}-\frac{c \sqrt{c x^2}}{a x^2}",1,"-((c^2*(a + b*x*Log[x] - b*x*Log[a + b*x]))/(a^2*Sqrt[c*x^2]))","A",1
867,1,53,88,0.0145472,"\int \frac{\left(c x^2\right)^{3/2}}{x^6 (a+b x)} \, dx","Integrate[(c*x^2)^(3/2)/(x^6*(a + b*x)),x]","\frac{\left(c x^2\right)^{3/2} \left(-2 b^2 x^2 \log (a+b x)-a (a-2 b x)+2 b^2 x^2 \log (x)\right)}{2 a^3 x^5}","\frac{b^2 c \sqrt{c x^2} \log (x)}{a^3 x}-\frac{b^2 c \sqrt{c x^2} \log (a+b x)}{a^3 x}+\frac{b c \sqrt{c x^2}}{a^2 x^2}-\frac{c \sqrt{c x^2}}{2 a x^3}",1,"((c*x^2)^(3/2)*(-(a*(a - 2*b*x)) + 2*b^2*x^2*Log[x] - 2*b^2*x^2*Log[a + b*x]))/(2*a^3*x^5)","A",1
868,1,65,112,0.0258587,"\int \frac{\left(c x^2\right)^{3/2}}{x^7 (a+b x)} \, dx","Integrate[(c*x^2)^(3/2)/(x^7*(a + b*x)),x]","-\frac{\left(c x^2\right)^{3/2} \left(a \left(2 a^2-3 a b x+6 b^2 x^2\right)-6 b^3 x^3 \log (a+b x)+6 b^3 x^3 \log (x)\right)}{6 a^4 x^6}","-\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,"-1/6*((c*x^2)^(3/2)*(a*(2*a^2 - 3*a*b*x + 6*b^2*x^2) + 6*b^3*x^3*Log[x] - 6*b^3*x^3*Log[a + b*x]))/(a^4*x^6)","A",1
869,1,76,142,0.0215822,"\int \frac{\left(c x^2\right)^{5/2}}{a+b x} \, dx","Integrate[(c*x^2)^(5/2)/(a + b*x),x]","\frac{c^3 x \left(b 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 a^5 \log (a+b x)\right)}{60 b^6 \sqrt{c x^2}}","-\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,"(c^3*x*(b*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*a^5*Log[a + b*x]))/(60*b^6*Sqrt[c*x^2])","A",1
870,1,65,117,0.0057224,"\int \frac{\left(c x^2\right)^{5/2}}{x (a+b x)} \, dx","Integrate[(c*x^2)^(5/2)/(x*(a + b*x)),x]","\frac{c \left(c x^2\right)^{3/2} \left(12 a^4 \log (a+b x)+b x \left(-12 a^3+6 a^2 b x-4 a b^2 x^2+3 b^3 x^3\right)\right)}{12 b^5 x^3}","\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,"(c*(c*x^2)^(3/2)*(b*x*(-12*a^3 + 6*a^2*b*x - 4*a*b^2*x^2 + 3*b^3*x^3) + 12*a^4*Log[a + b*x]))/(12*b^5*x^3)","A",1
871,1,54,92,0.0054067,"\int \frac{\left(c x^2\right)^{5/2}}{x^2 (a+b x)} \, dx","Integrate[(c*x^2)^(5/2)/(x^2*(a + b*x)),x]","\frac{c \left(c x^2\right)^{3/2} \left(b x \left(6 a^2-3 a b x+2 b^2 x^2\right)-6 a^3 \log (a+b x)\right)}{6 b^4 x^3}","-\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,"(c*(c*x^2)^(3/2)*(b*x*(6*a^2 - 3*a*b*x + 2*b^2*x^2) - 6*a^3*Log[a + b*x]))/(6*b^4*x^3)","A",1
872,1,42,67,0.0054156,"\int \frac{\left(c x^2\right)^{5/2}}{x^3 (a+b x)} \, dx","Integrate[(c*x^2)^(5/2)/(x^3*(a + b*x)),x]","\frac{c^3 x \left(2 a^2 \log (a+b x)+b x (b x-2 a)\right)}{2 b^3 \sqrt{c x^2}}","\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,"(c^3*x*(b*x*(-2*a + b*x) + 2*a^2*Log[a + b*x]))/(2*b^3*Sqrt[c*x^2])","A",1
873,1,30,44,0.004154,"\int \frac{\left(c x^2\right)^{5/2}}{x^4 (a+b x)} \, dx","Integrate[(c*x^2)^(5/2)/(x^4*(a + b*x)),x]","\frac{c^3 x (b x-a \log (a+b x))}{b^2 \sqrt{c x^2}}","\frac{c^2 \sqrt{c x^2}}{b}-\frac{a c^2 \sqrt{c x^2} \log (a+b x)}{b^2 x}",1,"(c^3*x*(b*x - a*Log[a + b*x]))/(b^2*Sqrt[c*x^2])","A",1
874,1,22,25,0.0037144,"\int \frac{\left(c x^2\right)^{5/2}}{x^5 (a+b x)} \, dx","Integrate[(c*x^2)^(5/2)/(x^5*(a + b*x)),x]","\frac{\left(c x^2\right)^{5/2} \log (a+b x)}{b x^5}","\frac{c^2 \sqrt{c x^2} \log (a+b x)}{b x}",1,"((c*x^2)^(5/2)*Log[a + b*x])/(b*x^5)","A",1
875,1,28,48,0.0090338,"\int \frac{\left(c x^2\right)^{5/2}}{x^6 (a+b x)} \, dx","Integrate[(c*x^2)^(5/2)/(x^6*(a + b*x)),x]","\frac{c^3 x (\log (x)-\log (a+b x))}{a \sqrt{c x^2}}","\frac{c^2 \sqrt{c x^2} \log (x)}{a x}-\frac{c^2 \sqrt{c x^2} \log (a+b x)}{a x}",1,"(c^3*x*(Log[x] - Log[a + b*x]))/(a*Sqrt[c*x^2])","A",1
876,1,34,70,0.0118463,"\int \frac{\left(c x^2\right)^{5/2}}{x^7 (a+b x)} \, dx","Integrate[(c*x^2)^(5/2)/(x^7*(a + b*x)),x]","-\frac{c^3 (-b x \log (a+b x)+a+b x \log (x))}{a^2 \sqrt{c x^2}}","-\frac{b c^2 \sqrt{c x^2} \log (x)}{a^2 x}+\frac{b c^2 \sqrt{c x^2} \log (a+b x)}{a^2 x}-\frac{c^2 \sqrt{c x^2}}{a x^2}",1,"-((c^3*(a + b*x*Log[x] - b*x*Log[a + b*x]))/(a^2*Sqrt[c*x^2]))","A",1
877,1,51,83,0.0112868,"\int \frac{x^4}{\sqrt{c x^2} (a+b x)} \, dx","Integrate[x^4/(Sqrt[c*x^2]*(a + b*x)),x]","\frac{x \left(b x \left(6 a^2-3 a b x+2 b^2 x^2\right)-6 a^3 \log (a+b x)\right)}{6 b^4 \sqrt{c x^2}}","-\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,"(x*(b*x*(6*a^2 - 3*a*b*x + 2*b^2*x^2) - 6*a^3*Log[a + b*x]))/(6*b^4*Sqrt[c*x^2])","A",1
878,1,39,61,0.0115353,"\int \frac{x^3}{\sqrt{c x^2} (a+b x)} \, dx","Integrate[x^3/(Sqrt[c*x^2]*(a + b*x)),x]","\frac{x \left(2 a^2 \log (a+b x)+b x (b x-2 a)\right)}{2 b^3 \sqrt{c x^2}}","\frac{a^2 x \log (a+b x)}{b^3 \sqrt{c x^2}}-\frac{a x^2}{b^2 \sqrt{c x^2}}+\frac{x^3}{2 b \sqrt{c x^2}}",1,"(x*(b*x*(-2*a + b*x) + 2*a^2*Log[a + b*x]))/(2*b^3*Sqrt[c*x^2])","A",1
879,1,27,39,0.0074017,"\int \frac{x^2}{\sqrt{c x^2} (a+b x)} \, dx","Integrate[x^2/(Sqrt[c*x^2]*(a + b*x)),x]","\frac{x (b x-a \log (a+b x))}{b^2 \sqrt{c x^2}}","\frac{x^2}{b \sqrt{c x^2}}-\frac{a x \log (a+b x)}{b^2 \sqrt{c x^2}}",1,"(x*(b*x - a*Log[a + b*x]))/(b^2*Sqrt[c*x^2])","A",1
880,1,20,20,0.0021562,"\int \frac{x}{\sqrt{c x^2} (a+b x)} \, dx","Integrate[x/(Sqrt[c*x^2]*(a + b*x)),x]","\frac{x \log (a+b x)}{b \sqrt{c x^2}}","\frac{x \log (a+b x)}{b \sqrt{c x^2}}",1,"(x*Log[a + b*x])/(b*Sqrt[c*x^2])","A",1
881,1,25,38,0.003813,"\int \frac{1}{\sqrt{c x^2} (a+b x)} \, dx","Integrate[1/(Sqrt[c*x^2]*(a + b*x)),x]","\frac{x (\log (x)-\log (a+b x))}{a \sqrt{c x^2}}","\frac{x \log (x)}{a \sqrt{c x^2}}-\frac{x \log (a+b x)}{a \sqrt{c x^2}}",1,"(x*(Log[x] - Log[a + b*x]))/(a*Sqrt[c*x^2])","A",1
882,1,36,54,0.0111007,"\int \frac{1}{x \sqrt{c x^2} (a+b x)} \, dx","Integrate[1/(x*Sqrt[c*x^2]*(a + b*x)),x]","\frac{c x^2 (b x \log (a+b x)-a-b x \log (x))}{a^2 \left(c x^2\right)^{3/2}}","-\frac{b x \log (x)}{a^2 \sqrt{c x^2}}+\frac{b x \log (a+b x)}{a^2 \sqrt{c x^2}}-\frac{1}{a \sqrt{c x^2}}",1,"(c*x^2*(-a - b*x*Log[x] + b*x*Log[a + b*x]))/(a^2*(c*x^2)^(3/2))","A",1
883,1,52,77,0.0116231,"\int \frac{1}{x^2 \sqrt{c x^2} (a+b x)} \, dx","Integrate[1/(x^2*Sqrt[c*x^2]*(a + b*x)),x]","\frac{c x \left(-2 b^2 x^2 \log (a+b x)-a (a-2 b x)+2 b^2 x^2 \log (x)\right)}{2 a^3 \left(c x^2\right)^{3/2}}","\frac{b^2 x \log (x)}{a^3 \sqrt{c x^2}}-\frac{b^2 x \log (a+b x)}{a^3 \sqrt{c x^2}}+\frac{b}{a^2 \sqrt{c x^2}}-\frac{1}{2 a x \sqrt{c x^2}}",1,"(c*x*(-(a*(a - 2*b*x)) + 2*b^2*x^2*Log[x] - 2*b^2*x^2*Log[a + b*x]))/(2*a^3*(c*x^2)^(3/2))","A",1
884,1,63,100,0.0123993,"\int \frac{1}{x^3 \sqrt{c x^2} (a+b x)} \, dx","Integrate[1/(x^3*Sqrt[c*x^2]*(a + b*x)),x]","\frac{c \left(a \left(-2 a^2+3 a b x-6 b^2 x^2\right)+6 b^3 x^3 \log (a+b x)-6 b^3 x^3 \log (x)\right)}{6 a^4 \left(c x^2\right)^{3/2}}","-\frac{b^3 x \log (x)}{a^4 \sqrt{c x^2}}+\frac{b^3 x \log (a+b x)}{a^4 \sqrt{c x^2}}-\frac{b^2}{a^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,"(c*(a*(-2*a^2 + 3*a*b*x - 6*b^2*x^2) - 6*b^3*x^3*Log[x] + 6*b^3*x^3*Log[a + b*x]))/(6*a^4*(c*x^2)^(3/2))","A",1
885,1,53,95,0.0105705,"\int \frac{x^6}{\left(c x^2\right)^{3/2} (a+b x)} \, dx","Integrate[x^6/((c*x^2)^(3/2)*(a + b*x)),x]","\frac{x^3 \left(b x \left(6 a^2-3 a b x+2 b^2 x^2\right)-6 a^3 \log (a+b x)\right)}{6 b^4 \left(c x^2\right)^{3/2}}","-\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,"(x^3*(b*x*(6*a^2 - 3*a*b*x + 2*b^2*x^2) - 6*a^3*Log[a + b*x]))/(6*b^4*(c*x^2)^(3/2))","A",1
886,1,41,70,0.0082387,"\int \frac{x^5}{\left(c x^2\right)^{3/2} (a+b x)} \, dx","Integrate[x^5/((c*x^2)^(3/2)*(a + b*x)),x]","\frac{x^3 \left(2 a^2 \log (a+b x)+b x (b x-2 a)\right)}{2 b^3 \left(c x^2\right)^{3/2}}","\frac{a^2 x \log (a+b x)}{b^3 c \sqrt{c x^2}}-\frac{a x^2}{b^2 c \sqrt{c x^2}}+\frac{x^3}{2 b c \sqrt{c x^2}}",1,"(x^3*(b*x*(-2*a + b*x) + 2*a^2*Log[a + b*x]))/(2*b^3*(c*x^2)^(3/2))","A",1
887,1,29,45,0.0065669,"\int \frac{x^4}{\left(c x^2\right)^{3/2} (a+b x)} \, dx","Integrate[x^4/((c*x^2)^(3/2)*(a + b*x)),x]","\frac{x^3 (b x-a \log (a+b x))}{b^2 \left(c x^2\right)^{3/2}}","\frac{x^2}{b c \sqrt{c x^2}}-\frac{a x \log (a+b x)}{b^2 c \sqrt{c x^2}}",1,"(x^3*(b*x - a*Log[a + b*x]))/(b^2*(c*x^2)^(3/2))","A",1
888,1,22,23,0.0037909,"\int \frac{x^3}{\left(c x^2\right)^{3/2} (a+b x)} \, dx","Integrate[x^3/((c*x^2)^(3/2)*(a + b*x)),x]","\frac{x^3 \log (a+b x)}{b \left(c x^2\right)^{3/2}}","\frac{x \log (a+b x)}{b c \sqrt{c x^2}}",1,"(x^3*Log[a + b*x])/(b*(c*x^2)^(3/2))","A",1
889,1,27,44,0.0066223,"\int \frac{x^2}{\left(c x^2\right)^{3/2} (a+b x)} \, dx","Integrate[x^2/((c*x^2)^(3/2)*(a + b*x)),x]","\frac{x^3 (\log (x)-\log (a+b x))}{a \left(c x^2\right)^{3/2}}","\frac{x \log (x)}{a c \sqrt{c x^2}}-\frac{x \log (a+b x)}{a c \sqrt{c x^2}}",1,"(x^3*(Log[x] - Log[a + b*x]))/(a*(c*x^2)^(3/2))","A",1
890,1,35,63,0.0062495,"\int \frac{x}{\left(c x^2\right)^{3/2} (a+b x)} \, dx","Integrate[x/((c*x^2)^(3/2)*(a + b*x)),x]","\frac{x^2 (b x \log (a+b x)-a-b x \log (x))}{a^2 \left(c x^2\right)^{3/2}}","-\frac{b x \log (x)}{a^2 c \sqrt{c x^2}}+\frac{b x \log (a+b x)}{a^2 c \sqrt{c x^2}}-\frac{1}{a c \sqrt{c x^2}}",1,"(x^2*(-a - b*x*Log[x] + b*x*Log[a + b*x]))/(a^2*(c*x^2)^(3/2))","A",1
891,1,51,89,0.0068105,"\int \frac{1}{\left(c x^2\right)^{3/2} (a+b x)} \, dx","Integrate[1/((c*x^2)^(3/2)*(a + b*x)),x]","\frac{x \left(-2 b^2 x^2 \log (a+b x)-a (a-2 b x)+2 b^2 x^2 \log (x)\right)}{2 a^3 \left(c x^2\right)^{3/2}}","\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,"(x*(-(a*(a - 2*b*x)) + 2*b^2*x^2*Log[x] - 2*b^2*x^2*Log[a + b*x]))/(2*a^3*(c*x^2)^(3/2))","A",1
892,1,66,115,0.0145225,"\int \frac{1}{x \left(c x^2\right)^{3/2} (a+b x)} \, dx","Integrate[1/(x*(c*x^2)^(3/2)*(a + b*x)),x]","\frac{c x^2 \left(a \left(-2 a^2+3 a b x-6 b^2 x^2\right)+6 b^3 x^3 \log (a+b x)-6 b^3 x^3 \log (x)\right)}{6 a^4 \left(c x^2\right)^{5/2}}","-\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,"(c*x^2*(a*(-2*a^2 + 3*a*b*x - 6*b^2*x^2) - 6*b^3*x^3*Log[x] + 6*b^3*x^3*Log[a + b*x]))/(6*a^4*(c*x^2)^(5/2))","A",1
893,1,81,106,0.0277807,"\int \frac{x^3 \sqrt{c x^2}}{(a+b x)^2} \, dx","Integrate[(x^3*Sqrt[c*x^2])/(a + b*x)^2,x]","\frac{c x \left(-3 a^4+9 a^3 b x-12 a^3 (a+b x) \log (a+b x)+6 a^2 b^2 x^2-2 a b^3 x^3+b^4 x^4\right)}{3 b^5 \sqrt{c x^2} (a+b x)}","-\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,"(c*x*(-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 - 12*a^3*(a + b*x)*Log[a + b*x]))/(3*b^5*Sqrt[c*x^2]*(a + b*x))","A",1
894,1,70,85,0.0214853,"\int \frac{x^2 \sqrt{c x^2}}{(a+b x)^2} \, dx","Integrate[(x^2*Sqrt[c*x^2])/(a + b*x)^2,x]","\frac{c x \left(2 a^3-4 a^2 b x+6 a^2 (a+b x) \log (a+b x)-3 a b^2 x^2+b^3 x^3\right)}{2 b^4 \sqrt{c x^2} (a+b x)}","\frac{a^3 \sqrt{c x^2}}{b^4 x (a+b x)}+\frac{3 a^2 \sqrt{c x^2} \log (a+b x)}{b^4 x}-\frac{2 a \sqrt{c x^2}}{b^3}+\frac{x \sqrt{c x^2}}{2 b^2}",1,"(c*x*(2*a^3 - 4*a^2*b*x - 3*a*b^2*x^2 + b^3*x^3 + 6*a^2*(a + b*x)*Log[a + b*x]))/(2*b^4*Sqrt[c*x^2]*(a + b*x))","A",1
895,1,53,65,0.0198706,"\int \frac{x \sqrt{c x^2}}{(a+b x)^2} \, dx","Integrate[(x*Sqrt[c*x^2])/(a + b*x)^2,x]","\frac{c x \left(-a^2+a b x-2 a (a+b x) \log (a+b x)+b^2 x^2\right)}{b^3 \sqrt{c x^2} (a+b x)}","-\frac{a^2 \sqrt{c x^2}}{b^3 x (a+b x)}-\frac{2 a \sqrt{c x^2} \log (a+b x)}{b^3 x}+\frac{\sqrt{c x^2}}{b^2}",1,"(c*x*(-a^2 + a*b*x + b^2*x^2 - 2*a*(a + b*x)*Log[a + b*x]))/(b^3*Sqrt[c*x^2]*(a + b*x))","A",1
896,1,36,47,0.011971,"\int \frac{\sqrt{c x^2}}{(a+b x)^2} \, dx","Integrate[Sqrt[c*x^2]/(a + b*x)^2,x]","\frac{c x ((a+b x) \log (a+b x)+a)}{b^2 \sqrt{c x^2} (a+b x)}","\frac{a \sqrt{c x^2}}{b^2 x (a+b x)}+\frac{\sqrt{c x^2} \log (a+b x)}{b^2 x}",1,"(c*x*(a + (a + b*x)*Log[a + b*x]))/(b^2*Sqrt[c*x^2]*(a + b*x))","A",1
897,1,23,24,0.0065608,"\int \frac{\sqrt{c x^2}}{x (a+b x)^2} \, dx","Integrate[Sqrt[c*x^2]/(x*(a + b*x)^2),x]","-\frac{c x}{b \sqrt{c x^2} (a+b x)}","-\frac{\sqrt{c x^2}}{b x (a+b x)}",1,"-((c*x)/(b*Sqrt[c*x^2]*(a + b*x)))","A",1
898,1,45,65,0.01669,"\int \frac{\sqrt{c x^2}}{x^2 (a+b x)^2} \, dx","Integrate[Sqrt[c*x^2]/(x^2*(a + b*x)^2),x]","\frac{c x (\log (x) (a+b x)-(a+b x) \log (a+b x)+a)}{a^2 \sqrt{c x^2} (a+b x)}","-\frac{\sqrt{c x^2} \log (a+b x)}{a^2 x}+\frac{\sqrt{c x^2} \log (x)}{a^2 x}+\frac{\sqrt{c x^2}}{a x (a+b x)}",1,"(c*x*(a + (a + b*x)*Log[x] - (a + b*x)*Log[a + b*x]))/(a^2*Sqrt[c*x^2]*(a + b*x))","A",1
899,1,57,87,0.029814,"\int \frac{\sqrt{c x^2}}{x^3 (a+b x)^2} \, dx","Integrate[Sqrt[c*x^2]/(x^3*(a + b*x)^2),x]","-\frac{c (a (a+2 b x)+2 b x \log (x) (a+b x)-2 b x (a+b x) \log (a+b x))}{a^3 \sqrt{c x^2} (a+b x)}","-\frac{2 b \sqrt{c x^2} \log (x)}{a^3 x}+\frac{2 b \sqrt{c x^2} \log (a+b x)}{a^3 x}-\frac{b \sqrt{c x^2}}{a^2 x (a+b x)}-\frac{\sqrt{c x^2}}{a^2 x^2}",1,"-((c*(a*(a + 2*b*x) + 2*b*x*(a + b*x)*Log[x] - 2*b*x*(a + b*x)*Log[a + b*x]))/(a^3*Sqrt[c*x^2]*(a + b*x)))","A",1
900,1,82,112,0.0239846,"\int \frac{\sqrt{c x^2}}{x^4 (a+b x)^2} \, dx","Integrate[Sqrt[c*x^2]/(x^4*(a + b*x)^2),x]","\frac{\sqrt{c x^2} \left(a \left(-a^2+3 a b x+6 b^2 x^2\right)+6 b^2 x^2 \log (x) (a+b x)-6 b^2 x^2 (a+b x) \log (a+b x)\right)}{2 a^4 x^3 (a+b x)}","\frac{3 b^2 \sqrt{c x^2} \log (x)}{a^4 x}-\frac{3 b^2 \sqrt{c x^2} \log (a+b x)}{a^4 x}+\frac{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,"(Sqrt[c*x^2]*(a*(-a^2 + 3*a*b*x + 6*b^2*x^2) + 6*b^2*x^2*(a + b*x)*Log[x] - 6*b^2*x^2*(a + b*x)*Log[a + b*x]))/(2*a^4*x^3*(a + b*x))","A",1
901,1,82,111,0.0198274,"\int \frac{x \left(c x^2\right)^{3/2}}{(a+b x)^2} \, dx","Integrate[(x*(c*x^2)^(3/2))/(a + b*x)^2,x]","\frac{\left(c x^2\right)^{3/2} \left(-3 a^4+9 a^3 b x-12 a^3 (a+b x) \log (a+b x)+6 a^2 b^2 x^2-2 a b^3 x^3+b^4 x^4\right)}{3 b^5 x^3 (a+b x)}","-\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,"((c*x^2)^(3/2)*(-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 - 12*a^3*(a + b*x)*Log[a + b*x]))/(3*b^5*x^3*(a + b*x))","A",1
902,1,71,89,0.0166351,"\int \frac{\left(c x^2\right)^{3/2}}{(a+b x)^2} \, dx","Integrate[(c*x^2)^(3/2)/(a + b*x)^2,x]","\frac{\left(c x^2\right)^{3/2} \left(2 a^3-4 a^2 b x+6 a^2 (a+b x) \log (a+b x)-3 a b^2 x^2+b^3 x^3\right)}{2 b^4 x^3 (a+b x)}","\frac{a^3 c \sqrt{c x^2}}{b^4 x (a+b x)}+\frac{3 a^2 c \sqrt{c x^2} \log (a+b x)}{b^4 x}-\frac{2 a c \sqrt{c x^2}}{b^3}+\frac{c x \sqrt{c x^2}}{2 b^2}",1,"((c*x^2)^(3/2)*(2*a^3 - 4*a^2*b*x - 3*a*b^2*x^2 + b^3*x^3 + 6*a^2*(a + b*x)*Log[a + b*x]))/(2*b^4*x^3*(a + b*x))","A",1
903,1,55,68,0.0072976,"\int \frac{\left(c x^2\right)^{3/2}}{x (a+b x)^2} \, dx","Integrate[(c*x^2)^(3/2)/(x*(a + b*x)^2),x]","\frac{c^2 x \left(-a^2+a b x-2 a (a+b x) \log (a+b x)+b^2 x^2\right)}{b^3 \sqrt{c x^2} (a+b x)}","-\frac{a^2 c \sqrt{c x^2}}{b^3 x (a+b x)}-\frac{2 a c \sqrt{c x^2} \log (a+b x)}{b^3 x}+\frac{c \sqrt{c x^2}}{b^2}",1,"(c^2*x*(-a^2 + a*b*x + b^2*x^2 - 2*a*(a + b*x)*Log[a + b*x]))/(b^3*Sqrt[c*x^2]*(a + b*x))","A",1
904,1,38,49,0.0090373,"\int \frac{\left(c x^2\right)^{3/2}}{x^2 (a+b x)^2} \, dx","Integrate[(c*x^2)^(3/2)/(x^2*(a + b*x)^2),x]","\frac{c^2 x ((a+b x) \log (a+b x)+a)}{b^2 \sqrt{c x^2} (a+b x)}","\frac{a c \sqrt{c x^2}}{b^2 x (a+b x)}+\frac{c \sqrt{c x^2} \log (a+b x)}{b^2 x}",1,"(c^2*x*(a + (a + b*x)*Log[a + b*x]))/(b^2*Sqrt[c*x^2]*(a + b*x))","A",1
905,1,24,25,0.005671,"\int \frac{\left(c x^2\right)^{3/2}}{x^3 (a+b x)^2} \, dx","Integrate[(c*x^2)^(3/2)/(x^3*(a + b*x)^2),x]","-\frac{\left(c x^2\right)^{3/2}}{b x^3 (a+b x)}","-\frac{c \sqrt{c x^2}}{b x (a+b x)}",1,"-((c*x^2)^(3/2)/(b*x^3*(a + b*x)))","A",1
906,1,46,68,0.0166283,"\int \frac{\left(c x^2\right)^{3/2}}{x^4 (a+b x)^2} \, dx","Integrate[(c*x^2)^(3/2)/(x^4*(a + b*x)^2),x]","\frac{\left(c x^2\right)^{3/2} (\log (x) (a+b x)-(a+b x) \log (a+b x)+a)}{a^2 x^3 (a+b x)}","-\frac{c \sqrt{c x^2} \log (a+b x)}{a^2 x}+\frac{c \sqrt{c x^2} \log (x)}{a^2 x}+\frac{c \sqrt{c x^2}}{a x (a+b x)}",1,"((c*x^2)^(3/2)*(a + (a + b*x)*Log[x] - (a + b*x)*Log[a + b*x]))/(a^2*x^3*(a + b*x))","A",1
907,1,59,91,0.0221475,"\int \frac{\left(c x^2\right)^{3/2}}{x^5 (a+b x)^2} \, dx","Integrate[(c*x^2)^(3/2)/(x^5*(a + b*x)^2),x]","-\frac{c^2 (a (a+2 b x)+2 b x \log (x) (a+b x)-2 b x (a+b x) \log (a+b x))}{a^3 \sqrt{c x^2} (a+b x)}","-\frac{2 b c \sqrt{c x^2} \log (x)}{a^3 x}+\frac{2 b c \sqrt{c x^2} \log (a+b x)}{a^3 x}-\frac{b c \sqrt{c x^2}}{a^2 x (a+b x)}-\frac{c \sqrt{c x^2}}{a^2 x^2}",1,"-((c^2*(a*(a + 2*b*x) + 2*b*x*(a + b*x)*Log[x] - 2*b*x*(a + b*x)*Log[a + b*x]))/(a^3*Sqrt[c*x^2]*(a + b*x)))","A",1
908,1,82,117,0.0221123,"\int \frac{\left(c x^2\right)^{3/2}}{x^6 (a+b x)^2} \, dx","Integrate[(c*x^2)^(3/2)/(x^6*(a + b*x)^2),x]","\frac{\left(c x^2\right)^{3/2} \left(a \left(-a^2+3 a b x+6 b^2 x^2\right)+6 b^2 x^2 \log (x) (a+b x)-6 b^2 x^2 (a+b x) \log (a+b x)\right)}{2 a^4 x^5 (a+b x)}","\frac{3 b^2 c \sqrt{c x^2} \log (x)}{a^4 x}-\frac{3 b^2 c \sqrt{c x^2} \log (a+b x)}{a^4 x}+\frac{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,"((c*x^2)^(3/2)*(a*(-a^2 + 3*a*b*x + 6*b^2*x^2) + 6*b^2*x^2*(a + b*x)*Log[x] - 6*b^2*x^2*(a + b*x)*Log[a + b*x]))/(2*a^4*x^5*(a + b*x))","A",1
909,1,80,107,0.0153918,"\int \frac{x^5}{\sqrt{c x^2} (a+b x)^2} \, dx","Integrate[x^5/(Sqrt[c*x^2]*(a + b*x)^2),x]","\frac{x \left(-3 a^4+9 a^3 b x-12 a^3 (a+b x) \log (a+b x)+6 a^2 b^2 x^2-2 a b^3 x^3+b^4 x^4\right)}{3 b^5 \sqrt{c x^2} (a+b x)}","-\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,"(x*(-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 - 12*a^3*(a + b*x)*Log[a + b*x]))/(3*b^5*Sqrt[c*x^2]*(a + b*x))","A",1
910,1,69,86,0.01243,"\int \frac{x^4}{\sqrt{c x^2} (a+b x)^2} \, dx","Integrate[x^4/(Sqrt[c*x^2]*(a + b*x)^2),x]","\frac{x \left(2 a^3-4 a^2 b x+6 a^2 (a+b x) \log (a+b x)-3 a b^2 x^2+b^3 x^3\right)}{2 b^4 \sqrt{c x^2} (a+b x)}","\frac{a^3 x}{b^4 \sqrt{c x^2} (a+b x)}+\frac{3 a^2 x \log (a+b x)}{b^4 \sqrt{c x^2}}-\frac{2 a x^2}{b^3 \sqrt{c x^2}}+\frac{x^3}{2 b^2 \sqrt{c x^2}}",1,"(x*(2*a^3 - 4*a^2*b*x - 3*a*b^2*x^2 + b^3*x^3 + 6*a^2*(a + b*x)*Log[a + b*x]))/(2*b^4*Sqrt[c*x^2]*(a + b*x))","A",1
911,1,52,64,0.0122001,"\int \frac{x^3}{\sqrt{c x^2} (a+b x)^2} \, dx","Integrate[x^3/(Sqrt[c*x^2]*(a + b*x)^2),x]","\frac{x \left(-a^2+a b x-2 a (a+b x) \log (a+b x)+b^2 x^2\right)}{b^3 \sqrt{c x^2} (a+b x)}","-\frac{a^2 x}{b^3 \sqrt{c x^2} (a+b x)}-\frac{2 a x \log (a+b x)}{b^3 \sqrt{c x^2}}+\frac{x^2}{b^2 \sqrt{c x^2}}",1,"(x*(-a^2 + a*b*x + b^2*x^2 - 2*a*(a + b*x)*Log[a + b*x]))/(b^3*Sqrt[c*x^2]*(a + b*x))","A",1
912,1,35,43,0.009166,"\int \frac{x^2}{\sqrt{c x^2} (a+b x)^2} \, dx","Integrate[x^2/(Sqrt[c*x^2]*(a + b*x)^2),x]","\frac{x ((a+b x) \log (a+b x)+a)}{b^2 \sqrt{c x^2} (a+b x)}","\frac{a x}{b^2 \sqrt{c x^2} (a+b x)}+\frac{x \log (a+b x)}{b^2 \sqrt{c x^2}}",1,"(x*(a + (a + b*x)*Log[a + b*x]))/(b^2*Sqrt[c*x^2]*(a + b*x))","A",1
913,1,22,22,0.0028838,"\int \frac{x}{\sqrt{c x^2} (a+b x)^2} \, dx","Integrate[x/(Sqrt[c*x^2]*(a + b*x)^2),x]","-\frac{x}{b \sqrt{c x^2} (a+b x)}","-\frac{x}{b \sqrt{c x^2} (a+b x)}",1,"-(x/(b*Sqrt[c*x^2]*(a + b*x)))","A",1
914,1,44,59,0.0053535,"\int \frac{1}{\sqrt{c x^2} (a+b x)^2} \, dx","Integrate[1/(Sqrt[c*x^2]*(a + b*x)^2),x]","\frac{x (\log (x) (a+b x)-(a+b x) \log (a+b x)+a)}{a^2 \sqrt{c x^2} (a+b x)}","-\frac{x \log (a+b x)}{a^2 \sqrt{c x^2}}+\frac{x \log (x)}{a^2 \sqrt{c x^2}}+\frac{x}{a \sqrt{c x^2} (a+b x)}",1,"(x*(a + (a + b*x)*Log[x] - (a + b*x)*Log[a + b*x]))/(a^2*Sqrt[c*x^2]*(a + b*x))","A",1
915,1,60,78,0.0261354,"\int \frac{1}{x \sqrt{c x^2} (a+b x)^2} \, dx","Integrate[1/(x*Sqrt[c*x^2]*(a + b*x)^2),x]","\frac{c x^2 (-a (a+2 b x)-2 b x \log (x) (a+b x)+2 b x (a+b x) \log (a+b x))}{a^3 \left(c x^2\right)^{3/2} (a+b x)}","-\frac{2 b x \log (x)}{a^3 \sqrt{c x^2}}+\frac{2 b x \log (a+b x)}{a^3 \sqrt{c x^2}}-\frac{b x}{a^2 \sqrt{c x^2} (a+b x)}-\frac{1}{a^2 \sqrt{c x^2}}",1,"(c*x^2*(-(a*(a + 2*b*x)) - 2*b*x*(a + b*x)*Log[x] + 2*b*x*(a + b*x)*Log[a + b*x]))/(a^3*(c*x^2)^(3/2)*(a + b*x))","A",1
916,1,81,103,0.0177378,"\int \frac{1}{x^2 \sqrt{c x^2} (a+b x)^2} \, dx","Integrate[1/(x^2*Sqrt[c*x^2]*(a + b*x)^2),x]","\frac{c x \left(a \left(-a^2+3 a b x+6 b^2 x^2\right)+6 b^2 x^2 \log (x) (a+b x)-6 b^2 x^2 (a+b x) \log (a+b x)\right)}{2 a^4 \left(c x^2\right)^{3/2} (a+b x)}","\frac{3 b^2 x \log (x)}{a^4 \sqrt{c x^2}}-\frac{3 b^2 x \log (a+b x)}{a^4 \sqrt{c x^2}}+\frac{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,"(c*x*(a*(-a^2 + 3*a*b*x + 6*b^2*x^2) + 6*b^2*x^2*(a + b*x)*Log[x] - 6*b^2*x^2*(a + b*x)*Log[a + b*x]))/(2*a^4*(c*x^2)^(3/2)*(a + b*x))","A",1
917,1,54,73,0.014733,"\int \frac{x^5}{\left(c x^2\right)^{3/2} (a+b x)^2} \, dx","Integrate[x^5/((c*x^2)^(3/2)*(a + b*x)^2),x]","\frac{x^3 \left(-a^2+a b x-2 a (a+b x) \log (a+b x)+b^2 x^2\right)}{b^3 \left(c x^2\right)^{3/2} (a+b x)}","-\frac{a^2 x}{b^3 c \sqrt{c x^2} (a+b x)}-\frac{2 a x \log (a+b x)}{b^3 c \sqrt{c x^2}}+\frac{x^2}{b^2 c \sqrt{c x^2}}",1,"(x^3*(-a^2 + a*b*x + b^2*x^2 - 2*a*(a + b*x)*Log[a + b*x]))/(b^3*(c*x^2)^(3/2)*(a + b*x))","A",1
918,1,37,49,0.0110339,"\int \frac{x^4}{\left(c x^2\right)^{3/2} (a+b x)^2} \, dx","Integrate[x^4/((c*x^2)^(3/2)*(a + b*x)^2),x]","\frac{x^3 ((a+b x) \log (a+b x)+a)}{b^2 \left(c x^2\right)^{3/2} (a+b x)}","\frac{a x}{b^2 c \sqrt{c x^2} (a+b x)}+\frac{x \log (a+b x)}{b^2 c \sqrt{c x^2}}",1,"(x^3*(a + (a + b*x)*Log[a + b*x]))/(b^2*(c*x^2)^(3/2)*(a + b*x))","A",1
919,1,24,25,0.0059661,"\int \frac{x^3}{\left(c x^2\right)^{3/2} (a+b x)^2} \, dx","Integrate[x^3/((c*x^2)^(3/2)*(a + b*x)^2),x]","-\frac{x^3}{b \left(c x^2\right)^{3/2} (a+b x)}","-\frac{x}{b c \sqrt{c x^2} (a+b x)}",1,"-(x^3/(b*(c*x^2)^(3/2)*(a + b*x)))","A",1
920,1,46,68,0.0138505,"\int \frac{x^2}{\left(c x^2\right)^{3/2} (a+b x)^2} \, dx","Integrate[x^2/((c*x^2)^(3/2)*(a + b*x)^2),x]","\frac{x^3 (\log (x) (a+b x)-(a+b x) \log (a+b x)+a)}{a^2 \left(c x^2\right)^{3/2} (a+b x)}","-\frac{x \log (a+b x)}{a^2 c \sqrt{c x^2}}+\frac{x \log (x)}{a^2 c \sqrt{c x^2}}+\frac{x}{a c \sqrt{c x^2} (a+b x)}",1,"(x^3*(a + (a + b*x)*Log[x] - (a + b*x)*Log[a + b*x]))/(a^2*(c*x^2)^(3/2)*(a + b*x))","A",1
921,1,59,90,0.0107474,"\int \frac{x}{\left(c x^2\right)^{3/2} (a+b x)^2} \, dx","Integrate[x/((c*x^2)^(3/2)*(a + b*x)^2),x]","\frac{x^2 (-a (a+2 b x)-2 b x \log (x) (a+b x)+2 b x (a+b x) \log (a+b x))}{a^3 \left(c x^2\right)^{3/2} (a+b x)}","-\frac{2 b x \log (x)}{a^3 c \sqrt{c x^2}}+\frac{2 b x \log (a+b x)}{a^3 c \sqrt{c x^2}}-\frac{b x}{a^2 c \sqrt{c x^2} (a+b x)}-\frac{1}{a^2 c \sqrt{c x^2}}",1,"(x^2*(-(a*(a + 2*b*x)) - 2*b*x*(a + b*x)*Log[x] + 2*b*x*(a + b*x)*Log[a + b*x]))/(a^3*(c*x^2)^(3/2)*(a + b*x))","A",1
922,1,80,118,0.0093379,"\int \frac{1}{\left(c x^2\right)^{3/2} (a+b x)^2} \, dx","Integrate[1/((c*x^2)^(3/2)*(a + b*x)^2),x]","\frac{x \left(a \left(-a^2+3 a b x+6 b^2 x^2\right)+6 b^2 x^2 \log (x) (a+b x)-6 b^2 x^2 (a+b x) \log (a+b x)\right)}{2 a^4 \left(c x^2\right)^{3/2} (a+b x)}","\frac{3 b^2 x \log (x)}{a^4 c \sqrt{c x^2}}-\frac{3 b^2 x \log (a+b x)}{a^4 c \sqrt{c x^2}}+\frac{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,"(x*(a*(-a^2 + 3*a*b*x + 6*b^2*x^2) + 6*b^2*x^2*(a + b*x)*Log[x] - 6*b^2*x^2*(a + b*x)*Log[a + b*x]))/(2*a^4*(c*x^2)^(3/2)*(a + b*x))","A",1
923,1,97,131,0.0684053,"\int x^2 \sqrt{c x^2} (a+b x)^n \, dx","Integrate[x^2*Sqrt[c*x^2]*(a + b*x)^n,x]","\frac{c x (a+b x)^{n+1} \left(-6 a^3+6 a^2 b (n+1) x-3 a b^2 \left(n^2+3 n+2\right) x^2+b^3 \left(n^3+6 n^2+11 n+6\right) x^3\right)}{b^4 (n+1) (n+2) (n+3) (n+4) \sqrt{c x^2}}","-\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,"(c*x*(a + b*x)^(1 + n)*(-6*a^3 + 6*a^2*b*(1 + n)*x - 3*a*b^2*(2 + 3*n + n^2)*x^2 + b^3*(6 + 11*n + 6*n^2 + n^3)*x^3))/(b^4*(1 + n)*(2 + n)*(3 + n)*(4 + n)*Sqrt[c*x^2])","A",1
924,1,68,96,0.0465556,"\int x \sqrt{c x^2} (a+b x)^n \, dx","Integrate[x*Sqrt[c*x^2]*(a + b*x)^n,x]","\frac{c x (a+b x)^{n+1} \left(2 a^2-2 a b (n+1) x+b^2 \left(n^2+3 n+2\right) x^2\right)}{b^3 (n+1) (n+2) (n+3) \sqrt{c x^2}}","\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,"(c*x*(a + b*x)^(1 + n)*(2*a^2 - 2*a*b*(1 + n)*x + b^2*(2 + 3*n + n^2)*x^2))/(b^3*(1 + n)*(2 + n)*(3 + n)*Sqrt[c*x^2])","A",1
925,1,44,63,0.03038,"\int \sqrt{c x^2} (a+b x)^n \, dx","Integrate[Sqrt[c*x^2]*(a + b*x)^n,x]","\frac{c x (a+b x)^{n+1} (b (n+1) x-a)}{b^2 (n+1) (n+2) \sqrt{c x^2}}","\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,"(c*x*(a + b*x)^(1 + n)*(-a + b*(1 + n)*x))/(b^2*(1 + n)*(2 + n)*Sqrt[c*x^2])","A",1
926,1,29,30,0.0135958,"\int \frac{\sqrt{c x^2} (a+b x)^n}{x} \, dx","Integrate[(Sqrt[c*x^2]*(a + b*x)^n)/x,x]","\frac{c x (a+b x)^{n+1}}{b (n+1) \sqrt{c x^2}}","\frac{\sqrt{c x^2} (a+b x)^{n+1}}{b (n+1) x}",1,"(c*x*(a + b*x)^(1 + n))/(b*(1 + n)*Sqrt[c*x^2])","A",1
927,1,46,47,0.0105563,"\int \frac{\sqrt{c x^2} (a+b x)^n}{x^2} \, dx","Integrate[(Sqrt[c*x^2]*(a + b*x)^n)/x^2,x]","-\frac{c x (a+b x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b x}{a}+1\right)}{a (n+1) \sqrt{c x^2}}","-\frac{\sqrt{c x^2} (a+b x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b x}{a}+1\right)}{a (n+1) x}",1,"-((c*x*(a + b*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, 1 + (b*x)/a])/(a*(1 + n)*Sqrt[c*x^2]))","A",1
928,1,47,47,0.0145364,"\int \frac{\sqrt{c x^2} (a+b x)^n}{x^3} \, dx","Integrate[(Sqrt[c*x^2]*(a + b*x)^n)/x^3,x]","\frac{b \sqrt{c x^2} (a+b x)^{n+1} \, _2F_1\left(2,n+1;n+2;\frac{b x}{a}+1\right)}{a^2 (n+1) x}","\frac{b \sqrt{c x^2} (a+b x)^{n+1} \, _2F_1\left(2,n+1;n+2;\frac{b x}{a}+1\right)}{a^2 (n+1) x}",1,"(b*Sqrt[c*x^2]*(a + b*x)^(1 + n)*Hypergeometric2F1[2, 1 + n, 2 + n, 1 + (b*x)/a])/(a^2*(1 + n)*x)","A",1
929,1,50,50,0.0158601,"\int \frac{\sqrt{c x^2} (a+b x)^n}{x^4} \, dx","Integrate[(Sqrt[c*x^2]*(a + b*x)^n)/x^4,x]","-\frac{b^2 \sqrt{c x^2} (a+b x)^{n+1} \, _2F_1\left(3,n+1;n+2;\frac{b x}{a}+1\right)}{a^3 (n+1) x}","-\frac{b^2 \sqrt{c x^2} (a+b x)^{n+1} \, _2F_1\left(3,n+1;n+2;\frac{b x}{a}+1\right)}{a^3 (n+1) x}",1,"-((b^2*Sqrt[c*x^2]*(a + b*x)^(1 + n)*Hypergeometric2F1[3, 1 + n, 2 + n, 1 + (b*x)/a])/(a^3*(1 + n)*x))","A",1
930,1,132,169,0.0767299,"\int x \left(c x^2\right)^{3/2} (a+b x)^n \, dx","Integrate[x*(c*x^2)^(3/2)*(a + b*x)^n,x]","\frac{\left(c x^2\right)^{3/2} (a+b x)^{n+1} \left(24 a^4-24 a^3 b (n+1) x+12 a^2 b^2 \left(n^2+3 n+2\right) x^2-4 a b^3 \left(n^3+6 n^2+11 n+6\right) x^3+b^4 \left(n^4+10 n^3+35 n^2+50 n+24\right) x^4\right)}{b^5 (n+1) (n+2) (n+3) (n+4) (n+5) x^3}","\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,"((c*x^2)^(3/2)*(a + b*x)^(1 + n)*(24*a^4 - 24*a^3*b*(1 + n)*x + 12*a^2*b^2*(2 + 3*n + n^2)*x^2 - 4*a*b^3*(6 + 11*n + 6*n^2 + n^3)*x^3 + b^4*(24 + 50*n + 35*n^2 + 10*n^3 + n^4)*x^4))/(b^5*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)*x^3)","A",1
931,1,98,135,0.0546763,"\int \left(c x^2\right)^{3/2} (a+b x)^n \, dx","Integrate[(c*x^2)^(3/2)*(a + b*x)^n,x]","\frac{\left(c x^2\right)^{3/2} (a+b x)^{n+1} \left(-6 a^3+6 a^2 b (n+1) x-3 a b^2 \left(n^2+3 n+2\right) x^2+b^3 \left(n^3+6 n^2+11 n+6\right) x^3\right)}{b^4 (n+1) (n+2) (n+3) (n+4) x^3}","-\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,"((c*x^2)^(3/2)*(a + b*x)^(1 + n)*(-6*a^3 + 6*a^2*b*(1 + n)*x - 3*a*b^2*(2 + 3*n + n^2)*x^2 + b^3*(6 + 11*n + 6*n^2 + n^3)*x^3))/(b^4*(1 + n)*(2 + n)*(3 + n)*(4 + n)*x^3)","A",1
932,1,70,99,0.0313039,"\int \frac{\left(c x^2\right)^{3/2} (a+b x)^n}{x} \, dx","Integrate[((c*x^2)^(3/2)*(a + b*x)^n)/x,x]","\frac{c^2 x (a+b x)^{n+1} \left(2 a^2-2 a b (n+1) x+b^2 \left(n^2+3 n+2\right) x^2\right)}{b^3 (n+1) (n+2) (n+3) \sqrt{c x^2}}","\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,"(c^2*x*(a + b*x)^(1 + n)*(2*a^2 - 2*a*b*(1 + n)*x + b^2*(2 + 3*n + n^2)*x^2))/(b^3*(1 + n)*(2 + n)*(3 + n)*Sqrt[c*x^2])","A",1
933,1,46,65,0.008492,"\int \frac{\left(c x^2\right)^{3/2} (a+b x)^n}{x^2} \, dx","Integrate[((c*x^2)^(3/2)*(a + b*x)^n)/x^2,x]","\frac{c^2 x (a+b x)^{n+1} (b (n+1) x-a)}{b^2 (n+1) (n+2) \sqrt{c x^2}}","\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,"(c^2*x*(a + b*x)^(1 + n)*(-a + b*(1 + n)*x))/(b^2*(1 + n)*(2 + n)*Sqrt[c*x^2])","A",1
934,1,30,31,0.0147783,"\int \frac{\left(c x^2\right)^{3/2} (a+b x)^n}{x^3} \, dx","Integrate[((c*x^2)^(3/2)*(a + b*x)^n)/x^3,x]","\frac{\left(c x^2\right)^{3/2} (a+b x)^{n+1}}{b (n+1) x^3}","\frac{c \sqrt{c x^2} (a+b x)^{n+1}}{b (n+1) x}",1,"((c*x^2)^(3/2)*(a + b*x)^(1 + n))/(b*(1 + n)*x^3)","A",1
935,1,47,48,0.0102922,"\int \frac{\left(c x^2\right)^{3/2} (a+b x)^n}{x^4} \, dx","Integrate[((c*x^2)^(3/2)*(a + b*x)^n)/x^4,x]","-\frac{\left(c x^2\right)^{3/2} (a+b x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b x}{a}+1\right)}{a (n+1) x^3}","-\frac{c \sqrt{c x^2} (a+b x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b x}{a}+1\right)}{a (n+1) x}",1,"-(((c*x^2)^(3/2)*(a + b*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, 1 + (b*x)/a])/(a*(1 + n)*x^3))","A",1
936,1,47,48,0.0111624,"\int \frac{\left(c x^2\right)^{3/2} (a+b x)^n}{x^5} \, dx","Integrate[((c*x^2)^(3/2)*(a + b*x)^n)/x^5,x]","\frac{b \left(c x^2\right)^{3/2} (a+b x)^{n+1} \, _2F_1\left(2,n+1;n+2;\frac{b x}{a}+1\right)}{a^2 (n+1) x^3}","\frac{b c \sqrt{c x^2} (a+b x)^{n+1} \, _2F_1\left(2,n+1;n+2;\frac{b x}{a}+1\right)}{a^2 (n+1) x}",1,"(b*(c*x^2)^(3/2)*(a + b*x)^(1 + n)*Hypergeometric2F1[2, 1 + n, 2 + n, 1 + (b*x)/a])/(a^2*(1 + n)*x^3)","A",1
937,1,50,51,0.0126461,"\int \frac{\left(c x^2\right)^{3/2} (a+b x)^n}{x^6} \, dx","Integrate[((c*x^2)^(3/2)*(a + b*x)^n)/x^6,x]","-\frac{b^2 \left(c x^2\right)^{3/2} (a+b x)^{n+1} \, _2F_1\left(3,n+1;n+2;\frac{b x}{a}+1\right)}{a^3 (n+1) x^3}","-\frac{b^2 c \sqrt{c x^2} (a+b x)^{n+1} \, _2F_1\left(3,n+1;n+2;\frac{b x}{a}+1\right)}{a^3 (n+1) x}",1,"-((b^2*(c*x^2)^(3/2)*(a + b*x)^(1 + n)*Hypergeometric2F1[3, 1 + n, 2 + n, 1 + (b*x)/a])/(a^3*(1 + n)*x^3))","A",1
938,1,172,217,0.1075059,"\int \left(c x^2\right)^{5/2} (a+b x)^n \, dx","Integrate[(c*x^2)^(5/2)*(a + b*x)^n,x]","\frac{c^3 x (a+b x)^{n+1} \left(-120 a^5+120 a^4 b (n+1) x-60 a^3 b^2 \left(n^2+3 n+2\right) x^2+20 a^2 b^3 \left(n^3+6 n^2+11 n+6\right) x^3-5 a b^4 \left(n^4+10 n^3+35 n^2+50 n+24\right) x^4+b^5 \left(n^5+15 n^4+85 n^3+225 n^2+274 n+120\right) x^5\right)}{b^6 (n+1) (n+2) (n+3) (n+4) (n+5) (n+6) \sqrt{c x^2}}","-\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,"(c^3*x*(a + b*x)^(1 + n)*(-120*a^5 + 120*a^4*b*(1 + n)*x - 60*a^3*b^2*(2 + 3*n + n^2)*x^2 + 20*a^2*b^3*(6 + 11*n + 6*n^2 + n^3)*x^3 - 5*a*b^4*(24 + 50*n + 35*n^2 + 10*n^3 + n^4)*x^4 + b^5*(120 + 274*n + 225*n^2 + 85*n^3 + 15*n^4 + n^5)*x^5))/(b^6*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)*(6 + n)*Sqrt[c*x^2])","A",1
939,1,133,179,0.0222988,"\int \frac{\left(c x^2\right)^{5/2} (a+b x)^n}{x} \, dx","Integrate[((c*x^2)^(5/2)*(a + b*x)^n)/x,x]","\frac{c \left(c x^2\right)^{3/2} (a+b x)^{n+1} \left(24 a^4-24 a^3 b (n+1) x+12 a^2 b^2 \left(n^2+3 n+2\right) x^2-4 a b^3 \left(n^3+6 n^2+11 n+6\right) x^3+b^4 \left(n^4+10 n^3+35 n^2+50 n+24\right) x^4\right)}{b^5 (n+1) (n+2) (n+3) (n+4) (n+5) x^3}","\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,"(c*(c*x^2)^(3/2)*(a + b*x)^(1 + n)*(24*a^4 - 24*a^3*b*(1 + n)*x + 12*a^2*b^2*(2 + 3*n + n^2)*x^2 - 4*a*b^3*(6 + 11*n + 6*n^2 + n^3)*x^3 + b^4*(24 + 50*n + 35*n^2 + 10*n^3 + n^4)*x^4))/(b^5*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)*x^3)","A",1
940,1,99,143,0.0180066,"\int \frac{\left(c x^2\right)^{5/2} (a+b x)^n}{x^2} \, dx","Integrate[((c*x^2)^(5/2)*(a + b*x)^n)/x^2,x]","\frac{c \left(c x^2\right)^{3/2} (a+b x)^{n+1} \left(-6 a^3+6 a^2 b (n+1) x-3 a b^2 \left(n^2+3 n+2\right) x^2+b^3 \left(n^3+6 n^2+11 n+6\right) x^3\right)}{b^4 (n+1) (n+2) (n+3) (n+4) x^3}","-\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,"(c*(c*x^2)^(3/2)*(a + b*x)^(1 + n)*(-6*a^3 + 6*a^2*b*(1 + n)*x - 3*a*b^2*(2 + 3*n + n^2)*x^2 + b^3*(6 + 11*n + 6*n^2 + n^3)*x^3))/(b^4*(1 + n)*(2 + n)*(3 + n)*(4 + n)*x^3)","A",1
941,1,70,105,0.0453559,"\int \frac{\left(c x^2\right)^{5/2} (a+b x)^n}{x^3} \, dx","Integrate[((c*x^2)^(5/2)*(a + b*x)^n)/x^3,x]","\frac{c^3 x (a+b x)^{n+1} \left(2 a^2-2 a b (n+1) x+b^2 \left(n^2+3 n+2\right) x^2\right)}{b^3 (n+1) (n+2) (n+3) \sqrt{c x^2}}","\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,"(c^3*x*(a + b*x)^(1 + n)*(2*a^2 - 2*a*b*(1 + n)*x + b^2*(2 + 3*n + n^2)*x^2))/(b^3*(1 + n)*(2 + n)*(3 + n)*Sqrt[c*x^2])","A",1
942,1,46,69,0.0086959,"\int \frac{\left(c x^2\right)^{5/2} (a+b x)^n}{x^4} \, dx","Integrate[((c*x^2)^(5/2)*(a + b*x)^n)/x^4,x]","\frac{c^3 x (a+b x)^{n+1} (b (n+1) x-a)}{b^2 (n+1) (n+2) \sqrt{c x^2}}","\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,"(c^3*x*(a + b*x)^(1 + n)*(-a + b*(1 + n)*x))/(b^2*(1 + n)*(2 + n)*Sqrt[c*x^2])","A",1
943,1,31,33,0.0166988,"\int \frac{\left(c x^2\right)^{5/2} (a+b x)^n}{x^5} \, dx","Integrate[((c*x^2)^(5/2)*(a + b*x)^n)/x^5,x]","\frac{c^3 x (a+b x)^{n+1}}{b (n+1) \sqrt{c x^2}}","\frac{c^2 \sqrt{c x^2} (a+b x)^{n+1}}{b (n+1) x}",1,"(c^3*x*(a + b*x)^(1 + n))/(b*(1 + n)*Sqrt[c*x^2])","A",1
944,1,47,50,0.0113579,"\int \frac{\left(c x^2\right)^{5/2} (a+b x)^n}{x^6} \, dx","Integrate[((c*x^2)^(5/2)*(a + b*x)^n)/x^6,x]","-\frac{\left(c x^2\right)^{5/2} (a+b x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b x}{a}+1\right)}{a (n+1) x^5}","-\frac{c^2 \sqrt{c x^2} (a+b x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b x}{a}+1\right)}{a (n+1) x}",1,"-(((c*x^2)^(5/2)*(a + b*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, 1 + (b*x)/a])/(a*(1 + n)*x^5))","A",1
945,1,47,50,0.0119768,"\int \frac{\left(c x^2\right)^{5/2} (a+b x)^n}{x^7} \, dx","Integrate[((c*x^2)^(5/2)*(a + b*x)^n)/x^7,x]","\frac{b \left(c x^2\right)^{5/2} (a+b x)^{n+1} \, _2F_1\left(2,n+1;n+2;\frac{b x}{a}+1\right)}{a^2 (n+1) x^5}","\frac{b c^2 \sqrt{c x^2} (a+b x)^{n+1} \, _2F_1\left(2,n+1;n+2;\frac{b x}{a}+1\right)}{a^2 (n+1) x}",1,"(b*(c*x^2)^(5/2)*(a + b*x)^(1 + n)*Hypergeometric2F1[2, 1 + n, 2 + n, 1 + (b*x)/a])/(a^2*(1 + n)*x^5)","A",1
946,1,96,123,0.0398454,"\int \frac{x^4 (a+b x)^n}{\sqrt{c x^2}} \, dx","Integrate[(x^4*(a + b*x)^n)/Sqrt[c*x^2],x]","\frac{x (a+b x)^{n+1} \left(-6 a^3+6 a^2 b (n+1) x-3 a b^2 \left(n^2+3 n+2\right) x^2+b^3 \left(n^3+6 n^2+11 n+6\right) x^3\right)}{b^4 (n+1) (n+2) (n+3) (n+4) \sqrt{c x^2}}","-\frac{a^3 x (a+b x)^{n+1}}{b^4 (n+1) \sqrt{c x^2}}+\frac{3 a^2 x (a+b x)^{n+2}}{b^4 (n+2) \sqrt{c x^2}}-\frac{3 a x (a+b x)^{n+3}}{b^4 (n+3) \sqrt{c x^2}}+\frac{x (a+b x)^{n+4}}{b^4 (n+4) \sqrt{c x^2}}",1,"(x*(a + b*x)^(1 + n)*(-6*a^3 + 6*a^2*b*(1 + n)*x - 3*a*b^2*(2 + 3*n + n^2)*x^2 + b^3*(6 + 11*n + 6*n^2 + n^3)*x^3))/(b^4*(1 + n)*(2 + n)*(3 + n)*(4 + n)*Sqrt[c*x^2])","A",1
947,1,67,90,0.0286132,"\int \frac{x^3 (a+b x)^n}{\sqrt{c x^2}} \, dx","Integrate[(x^3*(a + b*x)^n)/Sqrt[c*x^2],x]","\frac{x (a+b x)^{n+1} \left(2 a^2-2 a b (n+1) x+b^2 \left(n^2+3 n+2\right) x^2\right)}{b^3 (n+1) (n+2) (n+3) \sqrt{c x^2}}","\frac{a^2 x (a+b x)^{n+1}}{b^3 (n+1) \sqrt{c x^2}}-\frac{2 a x (a+b x)^{n+2}}{b^3 (n+2) \sqrt{c x^2}}+\frac{x (a+b x)^{n+3}}{b^3 (n+3) \sqrt{c x^2}}",1,"(x*(a + b*x)^(1 + n)*(2*a^2 - 2*a*b*(1 + n)*x + b^2*(2 + 3*n + n^2)*x^2))/(b^3*(1 + n)*(2 + n)*(3 + n)*Sqrt[c*x^2])","A",1
948,1,43,59,0.0206075,"\int \frac{x^2 (a+b x)^n}{\sqrt{c x^2}} \, dx","Integrate[(x^2*(a + b*x)^n)/Sqrt[c*x^2],x]","\frac{x (a+b x)^{n+1} (b (n+1) x-a)}{b^2 (n+1) (n+2) \sqrt{c x^2}}","\frac{x (a+b x)^{n+2}}{b^2 (n+2) \sqrt{c x^2}}-\frac{a x (a+b x)^{n+1}}{b^2 (n+1) \sqrt{c x^2}}",1,"(x*(a + b*x)^(1 + n)*(-a + b*(1 + n)*x))/(b^2*(1 + n)*(2 + n)*Sqrt[c*x^2])","A",1
949,1,28,28,0.0111342,"\int \frac{x (a+b x)^n}{\sqrt{c x^2}} \, dx","Integrate[(x*(a + b*x)^n)/Sqrt[c*x^2],x]","\frac{x (a+b x)^{n+1}}{b (n+1) \sqrt{c x^2}}","\frac{x (a+b x)^{n+1}}{b (n+1) \sqrt{c x^2}}",1,"(x*(a + b*x)^(1 + n))/(b*(1 + n)*Sqrt[c*x^2])","A",1
950,1,45,45,0.0085148,"\int \frac{(a+b x)^n}{\sqrt{c x^2}} \, dx","Integrate[(a + b*x)^n/Sqrt[c*x^2],x]","-\frac{x (a+b x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b x}{a}+1\right)}{a (n+1) \sqrt{c x^2}}","-\frac{x (a+b x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b x}{a}+1\right)}{a (n+1) \sqrt{c x^2}}",1,"-((x*(a + b*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, 1 + (b*x)/a])/(a*(1 + n)*Sqrt[c*x^2]))","A",1
951,1,48,45,0.0123303,"\int \frac{(a+b x)^n}{x \sqrt{c x^2}} \, dx","Integrate[(a + b*x)^n/(x*Sqrt[c*x^2]),x]","\frac{b c x^3 (a+b x)^{n+1} \, _2F_1\left(2,n+1;n+2;\frac{b x}{a}+1\right)}{a^2 (n+1) \left(c x^2\right)^{3/2}}","\frac{b x (a+b x)^{n+1} \, _2F_1\left(2,n+1;n+2;\frac{b x}{a}+1\right)}{a^2 (n+1) \sqrt{c x^2}}",1,"(b*c*x^3*(a + b*x)^(1 + n)*Hypergeometric2F1[2, 1 + n, 2 + n, 1 + (b*x)/a])/(a^2*(1 + n)*(c*x^2)^(3/2))","A",1
952,1,51,48,0.013275,"\int \frac{(a+b x)^n}{x^2 \sqrt{c x^2}} \, dx","Integrate[(a + b*x)^n/(x^2*Sqrt[c*x^2]),x]","-\frac{b^2 c x^3 (a+b x)^{n+1} \, _2F_1\left(3,n+1;n+2;\frac{b x}{a}+1\right)}{a^3 (n+1) \left(c x^2\right)^{3/2}}","-\frac{b^2 x (a+b x)^{n+1} \, _2F_1\left(3,n+1;n+2;\frac{b x}{a}+1\right)}{a^3 (n+1) \sqrt{c x^2}}",1,"-((b^2*c*x^3*(a + b*x)^(1 + n)*Hypergeometric2F1[3, 1 + n, 2 + n, 1 + (b*x)/a])/(a^3*(1 + n)*(c*x^2)^(3/2)))","A",1
953,1,98,135,0.0408585,"\int \frac{x^6 (a+b x)^n}{\left(c x^2\right)^{3/2}} \, dx","Integrate[(x^6*(a + b*x)^n)/(c*x^2)^(3/2),x]","\frac{x^3 (a+b x)^{n+1} \left(-6 a^3+6 a^2 b (n+1) x-3 a b^2 \left(n^2+3 n+2\right) x^2+b^3 \left(n^3+6 n^2+11 n+6\right) x^3\right)}{b^4 (n+1) (n+2) (n+3) (n+4) \left(c x^2\right)^{3/2}}","-\frac{a^3 x (a+b x)^{n+1}}{b^4 c (n+1) \sqrt{c x^2}}+\frac{3 a^2 x (a+b x)^{n+2}}{b^4 c (n+2) \sqrt{c x^2}}-\frac{3 a x (a+b x)^{n+3}}{b^4 c (n+3) \sqrt{c x^2}}+\frac{x (a+b x)^{n+4}}{b^4 c (n+4) \sqrt{c x^2}}",1,"(x^3*(a + b*x)^(1 + n)*(-6*a^3 + 6*a^2*b*(1 + n)*x - 3*a*b^2*(2 + 3*n + n^2)*x^2 + b^3*(6 + 11*n + 6*n^2 + n^3)*x^3))/(b^4*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(c*x^2)^(3/2))","A",1
954,1,69,99,0.0336117,"\int \frac{x^5 (a+b x)^n}{\left(c x^2\right)^{3/2}} \, dx","Integrate[(x^5*(a + b*x)^n)/(c*x^2)^(3/2),x]","\frac{x^3 (a+b x)^{n+1} \left(2 a^2-2 a b (n+1) x+b^2 \left(n^2+3 n+2\right) x^2\right)}{b^3 (n+1) (n+2) (n+3) \left(c x^2\right)^{3/2}}","\frac{a^2 x (a+b x)^{n+1}}{b^3 c (n+1) \sqrt{c x^2}}-\frac{2 a x (a+b x)^{n+2}}{b^3 c (n+2) \sqrt{c x^2}}+\frac{x (a+b x)^{n+3}}{b^3 c (n+3) \sqrt{c x^2}}",1,"(x^3*(a + b*x)^(1 + n)*(2*a^2 - 2*a*b*(1 + n)*x + b^2*(2 + 3*n + n^2)*x^2))/(b^3*(1 + n)*(2 + n)*(3 + n)*(c*x^2)^(3/2))","A",1
955,1,45,65,0.0231191,"\int \frac{x^4 (a+b x)^n}{\left(c x^2\right)^{3/2}} \, dx","Integrate[(x^4*(a + b*x)^n)/(c*x^2)^(3/2),x]","\frac{x^3 (a+b x)^{n+1} (b (n+1) x-a)}{b^2 (n+1) (n+2) \left(c x^2\right)^{3/2}}","\frac{x (a+b x)^{n+2}}{b^2 c (n+2) \sqrt{c x^2}}-\frac{a x (a+b x)^{n+1}}{b^2 c (n+1) \sqrt{c x^2}}",1,"(x^3*(a + b*x)^(1 + n)*(-a + b*(1 + n)*x))/(b^2*(1 + n)*(2 + n)*(c*x^2)^(3/2))","A",1
956,1,30,31,0.014488,"\int \frac{x^3 (a+b x)^n}{\left(c x^2\right)^{3/2}} \, dx","Integrate[(x^3*(a + b*x)^n)/(c*x^2)^(3/2),x]","\frac{x^3 (a+b x)^{n+1}}{b (n+1) \left(c x^2\right)^{3/2}}","\frac{x (a+b x)^{n+1}}{b c (n+1) \sqrt{c x^2}}",1,"(x^3*(a + b*x)^(1 + n))/(b*(1 + n)*(c*x^2)^(3/2))","A",1
957,1,47,48,0.0104004,"\int \frac{x^2 (a+b x)^n}{\left(c x^2\right)^{3/2}} \, dx","Integrate[(x^2*(a + b*x)^n)/(c*x^2)^(3/2),x]","-\frac{x^3 (a+b x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b x}{a}+1\right)}{a (n+1) \left(c x^2\right)^{3/2}}","-\frac{x (a+b x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b x}{a}+1\right)}{a c (n+1) \sqrt{c x^2}}",1,"-((x^3*(a + b*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, 1 + (b*x)/a])/(a*(1 + n)*(c*x^2)^(3/2)))","A",1
958,1,47,48,0.0104665,"\int \frac{x (a+b x)^n}{\left(c x^2\right)^{3/2}} \, dx","Integrate[(x*(a + b*x)^n)/(c*x^2)^(3/2),x]","\frac{b x^3 (a+b x)^{n+1} \, _2F_1\left(2,n+1;n+2;\frac{b x}{a}+1\right)}{a^2 (n+1) \left(c x^2\right)^{3/2}}","\frac{b x (a+b x)^{n+1} \, _2F_1\left(2,n+1;n+2;\frac{b x}{a}+1\right)}{a^2 c (n+1) \sqrt{c x^2}}",1,"(b*x^3*(a + b*x)^(1 + n)*Hypergeometric2F1[2, 1 + n, 2 + n, 1 + (b*x)/a])/(a^2*(1 + n)*(c*x^2)^(3/2))","A",1
959,1,50,51,0.0112322,"\int \frac{(a+b x)^n}{\left(c x^2\right)^{3/2}} \, dx","Integrate[(a + b*x)^n/(c*x^2)^(3/2),x]","-\frac{b^2 x^3 (a+b x)^{n+1} \, _2F_1\left(3,n+1;n+2;\frac{b x}{a}+1\right)}{a^3 (n+1) \left(c x^2\right)^{3/2}}","-\frac{b^2 x (a+b x)^{n+1} \, _2F_1\left(3,n+1;n+2;\frac{b x}{a}+1\right)}{a^3 c (n+1) \sqrt{c x^2}}",1,"-((b^2*x^3*(a + b*x)^(1 + n)*Hypergeometric2F1[3, 1 + n, 2 + n, 1 + (b*x)/a])/(a^3*(1 + n)*(c*x^2)^(3/2)))","A",1
960,1,50,50,0.0141962,"\int \frac{(a+b x)^n}{x \left(c x^2\right)^{3/2}} \, dx","Integrate[(a + b*x)^n/(x*(c*x^2)^(3/2)),x]","\frac{b^3 c x^5 (a+b x)^{n+1} \, _2F_1\left(4,n+1;n+2;\frac{b x}{a}+1\right)}{a^4 (n+1) \left(c x^2\right)^{5/2}}","\frac{b^3 x (a+b x)^{n+1} \, _2F_1\left(4,n+1;n+2;\frac{b x}{a}+1\right)}{a^4 c (n+1) \sqrt{c x^2}}",1,"(b^3*c*x^5*(a + b*x)^(1 + n)*Hypergeometric2F1[4, 1 + n, 2 + n, 1 + (b*x)/a])/(a^4*(1 + n)*(c*x^2)^(5/2))","A",1
961,1,99,135,0.0370532,"\int \frac{x^8 (a+b x)^n}{\left(c x^2\right)^{5/2}} \, dx","Integrate[(x^8*(a + b*x)^n)/(c*x^2)^(5/2),x]","\frac{x (a+b x)^{n+1} \left(-6 a^3+6 a^2 b (n+1) x-3 a b^2 \left(n^2+3 n+2\right) x^2+b^3 \left(n^3+6 n^2+11 n+6\right) x^3\right)}{b^4 c^2 (n+1) (n+2) (n+3) (n+4) \sqrt{c x^2}}","-\frac{a^3 x (a+b x)^{n+1}}{b^4 c^2 (n+1) \sqrt{c x^2}}+\frac{3 a^2 x (a+b x)^{n+2}}{b^4 c^2 (n+2) \sqrt{c x^2}}-\frac{3 a x (a+b x)^{n+3}}{b^4 c^2 (n+3) \sqrt{c x^2}}+\frac{x (a+b x)^{n+4}}{b^4 c^2 (n+4) \sqrt{c x^2}}",1,"(x*(a + b*x)^(1 + n)*(-6*a^3 + 6*a^2*b*(1 + n)*x - 3*a*b^2*(2 + 3*n + n^2)*x^2 + b^3*(6 + 11*n + 6*n^2 + n^3)*x^3))/(b^4*c^2*(1 + n)*(2 + n)*(3 + n)*(4 + n)*Sqrt[c*x^2])","A",1
962,1,70,99,0.0303622,"\int \frac{x^7 (a+b x)^n}{\left(c x^2\right)^{5/2}} \, dx","Integrate[(x^7*(a + b*x)^n)/(c*x^2)^(5/2),x]","\frac{x (a+b x)^{n+1} \left(2 a^2-2 a b (n+1) x+b^2 \left(n^2+3 n+2\right) x^2\right)}{b^3 c^2 (n+1) (n+2) (n+3) \sqrt{c x^2}}","\frac{a^2 x (a+b x)^{n+1}}{b^3 c^2 (n+1) \sqrt{c x^2}}-\frac{2 a x (a+b x)^{n+2}}{b^3 c^2 (n+2) \sqrt{c x^2}}+\frac{x (a+b x)^{n+3}}{b^3 c^2 (n+3) \sqrt{c x^2}}",1,"(x*(a + b*x)^(1 + n)*(2*a^2 - 2*a*b*(1 + n)*x + b^2*(2 + 3*n + n^2)*x^2))/(b^3*c^2*(1 + n)*(2 + n)*(3 + n)*Sqrt[c*x^2])","A",1
963,1,46,65,0.0197238,"\int \frac{x^6 (a+b x)^n}{\left(c x^2\right)^{5/2}} \, dx","Integrate[(x^6*(a + b*x)^n)/(c*x^2)^(5/2),x]","\frac{x (a+b x)^{n+1} (b (n+1) x-a)}{b^2 c^2 (n+1) (n+2) \sqrt{c x^2}}","\frac{x (a+b x)^{n+2}}{b^2 c^2 (n+2) \sqrt{c x^2}}-\frac{a x (a+b x)^{n+1}}{b^2 c^2 (n+1) \sqrt{c x^2}}",1,"(x*(a + b*x)^(1 + n)*(-a + b*(1 + n)*x))/(b^2*c^2*(1 + n)*(2 + n)*Sqrt[c*x^2])","A",1
964,1,31,31,0.0120044,"\int \frac{x^5 (a+b x)^n}{\left(c x^2\right)^{5/2}} \, dx","Integrate[(x^5*(a + b*x)^n)/(c*x^2)^(5/2),x]","\frac{x (a+b x)^{n+1}}{b c^2 (n+1) \sqrt{c x^2}}","\frac{x (a+b x)^{n+1}}{b c^2 (n+1) \sqrt{c x^2}}",1,"(x*(a + b*x)^(1 + n))/(b*c^2*(1 + n)*Sqrt[c*x^2])","A",1
965,1,47,48,0.0103587,"\int \frac{x^4 (a+b x)^n}{\left(c x^2\right)^{5/2}} \, dx","Integrate[(x^4*(a + b*x)^n)/(c*x^2)^(5/2),x]","-\frac{x^5 (a+b x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b x}{a}+1\right)}{a (n+1) \left(c x^2\right)^{5/2}}","-\frac{x (a+b x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b x}{a}+1\right)}{a c^2 (n+1) \sqrt{c x^2}}",1,"-((x^5*(a + b*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, 1 + (b*x)/a])/(a*(1 + n)*(c*x^2)^(5/2)))","A",1
966,1,47,48,0.0119503,"\int \frac{x^3 (a+b x)^n}{\left(c x^2\right)^{5/2}} \, dx","Integrate[(x^3*(a + b*x)^n)/(c*x^2)^(5/2),x]","\frac{b x^5 (a+b x)^{n+1} \, _2F_1\left(2,n+1;n+2;\frac{b x}{a}+1\right)}{a^2 (n+1) \left(c x^2\right)^{5/2}}","\frac{b x (a+b x)^{n+1} \, _2F_1\left(2,n+1;n+2;\frac{b x}{a}+1\right)}{a^2 c^2 (n+1) \sqrt{c x^2}}",1,"(b*x^5*(a + b*x)^(1 + n)*Hypergeometric2F1[2, 1 + n, 2 + n, 1 + (b*x)/a])/(a^2*(1 + n)*(c*x^2)^(5/2))","A",1
967,1,50,51,0.012501,"\int \frac{x^2 (a+b x)^n}{\left(c x^2\right)^{5/2}} \, dx","Integrate[(x^2*(a + b*x)^n)/(c*x^2)^(5/2),x]","-\frac{b^2 x^5 (a+b x)^{n+1} \, _2F_1\left(3,n+1;n+2;\frac{b x}{a}+1\right)}{a^3 (n+1) \left(c x^2\right)^{5/2}}","-\frac{b^2 x (a+b x)^{n+1} \, _2F_1\left(3,n+1;n+2;\frac{b x}{a}+1\right)}{a^3 c^2 (n+1) \sqrt{c x^2}}",1,"-((b^2*x^5*(a + b*x)^(1 + n)*Hypergeometric2F1[3, 1 + n, 2 + n, 1 + (b*x)/a])/(a^3*(1 + n)*(c*x^2)^(5/2)))","A",1
968,1,49,50,0.0110145,"\int \frac{x (a+b x)^n}{\left(c x^2\right)^{5/2}} \, dx","Integrate[(x*(a + b*x)^n)/(c*x^2)^(5/2),x]","\frac{b^3 x^5 (a+b x)^{n+1} \, _2F_1\left(4,n+1;n+2;\frac{b x}{a}+1\right)}{a^4 (n+1) \left(c x^2\right)^{5/2}}","\frac{b^3 x (a+b x)^{n+1} \, _2F_1\left(4,n+1;n+2;\frac{b x}{a}+1\right)}{a^4 c^2 (n+1) \sqrt{c x^2}}",1,"(b^3*x^5*(a + b*x)^(1 + n)*Hypergeometric2F1[4, 1 + n, 2 + n, 1 + (b*x)/a])/(a^4*(1 + n)*(c*x^2)^(5/2))","A",1
969,1,38,65,0.027316,"\int (d x)^m \left(c x^2\right)^{5/2} (a+b x) \, dx","Integrate[(d*x)^m*(c*x^2)^(5/2)*(a + b*x),x]","\frac{x \left(c x^2\right)^{5/2} (d x)^m (a (m+7)+b (m+6) x)}{(m+6) (m+7)}","\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,"(x*(d*x)^m*(c*x^2)^(5/2)*(a*(7 + m) + b*(6 + m)*x))/((6 + m)*(7 + m))","A",1
970,1,38,61,0.0244603,"\int (d x)^m \left(c x^2\right)^{3/2} (a+b x) \, dx","Integrate[(d*x)^m*(c*x^2)^(3/2)*(a + b*x),x]","\frac{x \left(c x^2\right)^{3/2} (d x)^m (a (m+5)+b (m+4) x)}{(m+4) (m+5)}","\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,"(x*(d*x)^m*(c*x^2)^(3/2)*(a*(5 + m) + b*(4 + m)*x))/((4 + m)*(5 + m))","A",1
971,1,38,59,0.0200376,"\int (d x)^m \sqrt{c x^2} (a+b x) \, dx","Integrate[(d*x)^m*Sqrt[c*x^2]*(a + b*x),x]","\frac{x \sqrt{c x^2} (d x)^m (a (m+3)+b (m+2) x)}{(m+2) (m+3)}","\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,"(x*(d*x)^m*Sqrt[c*x^2]*(a*(3 + m) + b*(2 + m)*x))/((2 + m)*(3 + m))","A",1
972,1,33,48,0.0153376,"\int \frac{(d x)^m (a+b x)}{\sqrt{c x^2}} \, dx","Integrate[((d*x)^m*(a + b*x))/Sqrt[c*x^2],x]","\frac{x (d x)^m (a m+a+b m x)}{m (m+1) \sqrt{c x^2}}","\frac{a x (d x)^m}{m \sqrt{c x^2}}+\frac{b x (d x)^{m+1}}{d (m+1) \sqrt{c x^2}}",1,"(x*(d*x)^m*(a + a*m + b*m*x))/(m*(1 + m)*Sqrt[c*x^2])","A",1
973,1,38,65,0.025165,"\int \frac{(d x)^m (a+b x)}{\left(c x^2\right)^{3/2}} \, dx","Integrate[((d*x)^m*(a + b*x))/(c*x^2)^(3/2),x]","\frac{x (d x)^m (a (m-1)+b (m-2) x)}{(m-2) (m-1) \left(c x^2\right)^{3/2}}","-\frac{a d^2 x (d x)^{m-2}}{c (2-m) \sqrt{c x^2}}-\frac{b d x (d x)^{m-1}}{c (1-m) \sqrt{c x^2}}",1,"(x*(d*x)^m*(a*(-1 + m) + b*(-2 + m)*x))/((-2 + m)*(-1 + m)*(c*x^2)^(3/2))","A",1
974,1,38,67,0.0270355,"\int \frac{(d x)^m (a+b x)}{\left(c x^2\right)^{5/2}} \, dx","Integrate[((d*x)^m*(a + b*x))/(c*x^2)^(5/2),x]","\frac{x (d x)^m (a (m-3)+b (m-4) x)}{(m-4) (m-3) \left(c x^2\right)^{5/2}}","-\frac{a d^4 x (d x)^{m-4}}{c^2 (4-m) \sqrt{c x^2}}-\frac{b d^3 x (d x)^{m-3}}{c^2 (3-m) \sqrt{c x^2}}",1,"(x*(d*x)^m*(a*(-3 + m) + b*(-4 + m)*x))/((-4 + m)*(-3 + m)*(c*x^2)^(5/2))","A",1
975,1,48,103,0.0509161,"\int (d x)^m \left(c x^2\right)^{5/2} (a+b x)^2 \, dx","Integrate[(d*x)^m*(c*x^2)^(5/2)*(a + b*x)^2,x]","x \left(c x^2\right)^{5/2} (d x)^m \left(\frac{a^2}{m+6}+\frac{2 a b x}{m+7}+\frac{b^2 x^2}{m+8}\right)","\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,"x*(d*x)^m*(c*x^2)^(5/2)*(a^2/(6 + m) + (2*a*b*x)/(7 + m) + (b^2*x^2)/(8 + m))","A",1
976,1,48,97,0.0449605,"\int (d x)^m \left(c x^2\right)^{3/2} (a+b x)^2 \, dx","Integrate[(d*x)^m*(c*x^2)^(3/2)*(a + b*x)^2,x]","x \left(c x^2\right)^{3/2} (d x)^m \left(\frac{a^2}{m+4}+\frac{2 a b x}{m+5}+\frac{b^2 x^2}{m+6}\right)","\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,"x*(d*x)^m*(c*x^2)^(3/2)*(a^2/(4 + m) + (2*a*b*x)/(5 + m) + (b^2*x^2)/(6 + m))","A",1
977,1,72,94,0.0429139,"\int (d x)^m \sqrt{c x^2} (a+b x)^2 \, dx","Integrate[(d*x)^m*Sqrt[c*x^2]*(a + b*x)^2,x]","\frac{x \sqrt{c x^2} (d x)^m \left(a^2 \left(m^2+7 m+12\right)+2 a b \left(m^2+6 m+8\right) x+b^2 \left(m^2+5 m+6\right) x^2\right)}{(m+2) (m+3) (m+4)}","\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,"(x*(d*x)^m*Sqrt[c*x^2]*(a^2*(12 + 7*m + m^2) + 2*a*b*(8 + 6*m + m^2)*x + b^2*(6 + 5*m + m^2)*x^2))/((2 + m)*(3 + m)*(4 + m))","A",1
978,1,62,81,0.0335893,"\int \frac{(d x)^m (a+b x)^2}{\sqrt{c x^2}} \, dx","Integrate[((d*x)^m*(a + b*x)^2)/Sqrt[c*x^2],x]","\frac{x (d x)^m \left(a^2 \left(m^2+3 m+2\right)+2 a b m (m+2) x+b^2 m (m+1) x^2\right)}{m (m+1) (m+2) \sqrt{c x^2}}","\frac{a^2 x (d x)^m}{m \sqrt{c x^2}}+\frac{2 a b x (d x)^{m+1}}{d (m+1) \sqrt{c x^2}}+\frac{b^2 x (d x)^{m+2}}{d^2 (m+2) \sqrt{c x^2}}",1,"(x*(d*x)^m*(a^2*(2 + 3*m + m^2) + 2*a*b*m*(2 + m)*x + b^2*m*(1 + m)*x^2))/(m*(1 + m)*(2 + m)*Sqrt[c*x^2])","A",1
979,1,62,93,0.0388514,"\int \frac{(d x)^m (a+b x)^2}{\left(c x^2\right)^{3/2}} \, dx","Integrate[((d*x)^m*(a + b*x)^2)/(c*x^2)^(3/2),x]","\frac{x (d x)^m \left(a^2 (m-1) m+2 a b (m-2) m x+b^2 \left(m^2-3 m+2\right) x^2\right)}{(m-2) (m-1) m \left(c x^2\right)^{3/2}}","-\frac{a^2 d^2 x (d x)^{m-2}}{c (2-m) \sqrt{c x^2}}-\frac{2 a b d x (d x)^{m-1}}{c (1-m) \sqrt{c x^2}}+\frac{b^2 x (d x)^m}{c m \sqrt{c x^2}}",1,"(x*(d*x)^m*(a^2*(-1 + m)*m + 2*a*b*(-2 + m)*m*x + b^2*(2 - 3*m + m^2)*x^2))/((-2 + m)*(-1 + m)*m*(c*x^2)^(3/2))","A",1
980,1,72,105,0.0457151,"\int \frac{(d x)^m (a+b x)^2}{\left(c x^2\right)^{5/2}} \, dx","Integrate[((d*x)^m*(a + b*x)^2)/(c*x^2)^(5/2),x]","\frac{x (d x)^m \left(a^2 \left(m^2-5 m+6\right)+2 a b \left(m^2-6 m+8\right) x+b^2 \left(m^2-7 m+12\right) x^2\right)}{(m-4) (m-3) (m-2) \left(c x^2\right)^{5/2}}","-\frac{a^2 d^4 x (d x)^{m-4}}{c^2 (4-m) \sqrt{c x^2}}-\frac{2 a b d^3 x (d x)^{m-3}}{c^2 (3-m) \sqrt{c x^2}}-\frac{b^2 d^2 x (d x)^{m-2}}{c^2 (2-m) \sqrt{c x^2}}",1,"(x*(d*x)^m*(a^2*(6 - 5*m + m^2) + 2*a*b*(8 - 6*m + m^2)*x + b^2*(12 - 7*m + m^2)*x^2))/((-4 + m)*(-3 + m)*(-2 + m)*(c*x^2)^(5/2))","A",1
981,1,57,67,0.0174669,"\int (d x)^m \left(c x^2\right)^{5/2} (a+b x)^n \, dx","Integrate[(d*x)^m*(c*x^2)^(5/2)*(a + b*x)^n,x]","\frac{x \left(c x^2\right)^{5/2} (d x)^m (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)}{m+6}","\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,"(x*(d*x)^m*(c*x^2)^(5/2)*(a + b*x)^n*Hypergeometric2F1[6 + m, -n, 7 + m, -((b*x)/a)])/((6 + m)*(1 + (b*x)/a)^n)","A",1
982,1,57,65,0.01394,"\int (d x)^m \left(c x^2\right)^{3/2} (a+b x)^n \, dx","Integrate[(d*x)^m*(c*x^2)^(3/2)*(a + b*x)^n,x]","\frac{x \left(c x^2\right)^{3/2} (d x)^m (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)}{m+4}","\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,"(x*(d*x)^m*(c*x^2)^(3/2)*(a + b*x)^n*Hypergeometric2F1[4 + m, -n, 5 + m, -((b*x)/a)])/((4 + m)*(1 + (b*x)/a)^n)","A",1
983,1,57,64,0.0113609,"\int (d x)^m \sqrt{c x^2} (a+b x)^n \, dx","Integrate[(d*x)^m*Sqrt[c*x^2]*(a + b*x)^n,x]","\frac{x \sqrt{c x^2} (d x)^m (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)}{m+2}","\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,"(x*(d*x)^m*Sqrt[c*x^2]*(a + b*x)^n*Hypergeometric2F1[2 + m, -n, 3 + m, -((b*x)/a)])/((2 + m)*(1 + (b*x)/a)^n)","A",1
984,1,53,53,0.0097685,"\int \frac{(d x)^m (a+b x)^n}{\sqrt{c x^2}} \, dx","Integrate[((d*x)^m*(a + b*x)^n)/Sqrt[c*x^2],x]","\frac{x (d x)^m (a+b x)^n \left(\frac{b x}{a}+1\right)^{-n} \, _2F_1\left(m,-n;m+1;-\frac{b x}{a}\right)}{m \sqrt{c x^2}}","\frac{x (d x)^m (a+b x)^n \left(\frac{b x}{a}+1\right)^{-n} \, _2F_1\left(m,-n;m+1;-\frac{b x}{a}\right)}{m \sqrt{c x^2}}",1,"(x*(d*x)^m*(a + b*x)^n*Hypergeometric2F1[m, -n, 1 + m, -((b*x)/a)])/(m*Sqrt[c*x^2]*(1 + (b*x)/a)^n)","A",1
985,1,57,68,0.0135177,"\int \frac{(d x)^m (a+b x)^n}{\left(c x^2\right)^{3/2}} \, dx","Integrate[((d*x)^m*(a + b*x)^n)/(c*x^2)^(3/2),x]","\frac{x (d x)^m (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)}{(m-2) \left(c x^2\right)^{3/2}}","-\frac{d^2 x (d x)^{m-2} (a+b x)^n \left(\frac{b x}{a}+1\right)^{-n} \, _2F_1\left(m-2,-n;m-1;-\frac{b x}{a}\right)}{c (2-m) \sqrt{c x^2}}",1,"(x*(d*x)^m*(a + b*x)^n*Hypergeometric2F1[-2 + m, -n, -1 + m, -((b*x)/a)])/((-2 + m)*(c*x^2)^(3/2)*(1 + (b*x)/a)^n)","A",1
986,1,57,68,0.0159227,"\int \frac{(d x)^m (a+b x)^n}{\left(c x^2\right)^{5/2}} \, dx","Integrate[((d*x)^m*(a + b*x)^n)/(c*x^2)^(5/2),x]","\frac{x (d x)^m (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)}{(m-4) \left(c x^2\right)^{5/2}}","-\frac{d^4 x (d x)^{m-4} (a+b x)^n \left(\frac{b x}{a}+1\right)^{-n} \, _2F_1\left(m-4,-n;m-3;-\frac{b x}{a}\right)}{c^2 (4-m) \sqrt{c x^2}}",1,"(x*(d*x)^m*(a + b*x)^n*Hypergeometric2F1[-4 + m, -n, -3 + m, -((b*x)/a)])/((-4 + m)*(c*x^2)^(5/2)*(1 + (b*x)/a)^n)","A",1
987,1,32,33,0.0173619,"\int x^3 \left(c x^2\right)^p (a+b x)^{-5-2 p} \, dx","Integrate[x^3*(c*x^2)^p*(a + b*x)^(-5 - 2*p),x]","\frac{x^4 \left(c x^2\right)^p (a+b x)^{-2 p-4}}{a (2 p+4)}","\frac{x^4 \left(c x^2\right)^p (a+b x)^{-2 (p+2)}}{2 a (p+2)}",1,"(x^4*(c*x^2)^p*(a + b*x)^(-4 - 2*p))/(a*(4 + 2*p))","A",1
988,1,34,32,0.0188626,"\int x^2 \left(c x^2\right)^p (a+b x)^{-4-2 p} \, dx","Integrate[x^2*(c*x^2)^p*(a + b*x)^(-4 - 2*p),x]","\frac{x^3 \left(c x^2\right)^p (a+b x)^{1-2 (p+2)}}{a (2 p+3)}","\frac{x^3 \left(c x^2\right)^p (a+b x)^{-2 p-3}}{a (2 p+3)}",1,"(x^3*(c*x^2)^p*(a + b*x)^(1 - 2*(2 + p)))/(a*(3 + 2*p))","A",1
989,1,32,33,0.0151922,"\int x \left(c x^2\right)^p (a+b x)^{-3-2 p} \, dx","Integrate[x*(c*x^2)^p*(a + b*x)^(-3 - 2*p),x]","\frac{x^2 \left(c x^2\right)^p (a+b x)^{-2 p-2}}{a (2 p+2)}","\frac{x^2 \left(c x^2\right)^p (a+b x)^{-2 (p+1)}}{2 a (p+1)}",1,"(x^2*(c*x^2)^p*(a + b*x)^(-2 - 2*p))/(a*(2 + 2*p))","A",1
990,1,28,30,0.0153984,"\int \left(c x^2\right)^p (a+b x)^{-2-2 p} \, dx","Integrate[(c*x^2)^p*(a + b*x)^(-2 - 2*p),x]","\frac{x \left(c x^2\right)^p (a+b x)^{-2 p-1}}{2 a p+a}","\frac{x \left(c x^2\right)^p (a+b x)^{-2 p-1}}{a (2 p+1)}",1,"(x*(c*x^2)^p*(a + b*x)^(-1 - 2*p))/(a + 2*a*p)","A",1
991,1,26,26,0.0073505,"\int \frac{\left(c x^2\right)^p (a+b x)^{-1-2 p}}{x} \, dx","Integrate[((c*x^2)^p*(a + b*x)^(-1 - 2*p))/x,x]","\frac{\left(c x^2\right)^p (a+b x)^{-2 p}}{2 a p}","\frac{\left(c x^2\right)^p (a+b x)^{-2 p}}{2 a p}",1,"(c*x^2)^p/(2*a*p*(a + b*x)^(2*p))","A",1
992,1,32,33,0.0104248,"\int \frac{\left(c x^2\right)^p (a+b x)^{-2 p}}{x^2} \, dx","Integrate[(c*x^2)^p/(x^2*(a + b*x)^(2*p)),x]","\frac{\left(c x^2\right)^p (a+b x)^{1-2 p}}{a (2 p-1) x}","-\frac{\left(c x^2\right)^p (a+b x)^{1-2 p}}{a (1-2 p) x}",1,"((c*x^2)^p*(a + b*x)^(1 - 2*p))/(a*(-1 + 2*p)*x)","A",1
993,1,32,35,0.0098582,"\int \frac{\left(c x^2\right)^p (a+b x)^{1-2 p}}{x^3} \, dx","Integrate[((c*x^2)^p*(a + b*x)^(1 - 2*p))/x^3,x]","\frac{\left(c x^2\right)^p (a+b x)^{2-2 p}}{a (2 p-2) x^2}","-\frac{\left(c x^2\right)^p (a+b x)^{2-2 p}}{2 a (1-p) x^2}",1,"((c*x^2)^p*(a + b*x)^(2 - 2*p))/(a*(-2 + 2*p)*x^2)","A",1
994,1,32,33,0.0102042,"\int \frac{\left(c x^2\right)^p (a+b x)^{2-2 p}}{x^4} \, dx","Integrate[((c*x^2)^p*(a + b*x)^(2 - 2*p))/x^4,x]","\frac{\left(c x^2\right)^p (a+b x)^{3-2 p}}{a (2 p-3) x^3}","-\frac{\left(c x^2\right)^p (a+b x)^{3-2 p}}{a (3-2 p) x^3}",1,"((c*x^2)^p*(a + b*x)^(3 - 2*p))/(a*(-3 + 2*p)*x^3)","A",1
995,1,38,38,0.0286515,"\int x^m \left(c x^2\right)^p (a+b x)^{-2-m-2 p} \, dx","Integrate[x^m*(c*x^2)^p*(a + b*x)^(-2 - m - 2*p),x]","\frac{x^{m+1} \left(c x^2\right)^p (a+b x)^{-m-2 p-1}}{a (m+2 p+1)}","\frac{x^{m+1} \left(c x^2\right)^p (a+b x)^{-m-2 p-1}}{a (m+2 p+1)}",1,"(x^(1 + m)*(c*x^2)^p*(a + b*x)^(-1 - m - 2*p))/(a*(1 + m + 2*p))","A",1
996,1,39,39,0.0154987,"\int (d x)^m \left(c x^2\right)^p (a+b x)^{-2-m-2 p} \, dx","Integrate[(d*x)^m*(c*x^2)^p*(a + b*x)^(-2 - m - 2*p),x]","\frac{x \left(c x^2\right)^p (d x)^m (a+b x)^{-m-2 p-1}}{a (m+2 p+1)}","\frac{x \left(c x^2\right)^p (d x)^m (a+b x)^{-m-2 p-1}}{a (m+2 p+1)}",1,"(x*(d*x)^m*(c*x^2)^p*(a + b*x)^(-1 - m - 2*p))/(a*(1 + m + 2*p))","A",1
997,1,63,63,0.0106183,"\int x^m \left(c x^2\right)^p (a+b x)^n \, dx","Integrate[x^m*(c*x^2)^p*(a + b*x)^n,x]","\frac{x^{m+1} \left(c x^2\right)^p (a+b x)^n \left(\frac{b x}{a}+1\right)^{-n} \, _2F_1\left(-n,m+2 p+1;m+2 p+2;-\frac{b x}{a}\right)}{m+2 p+1}","\frac{x^{m+1} \left(c x^2\right)^p (a+b x)^n \left(\frac{b x}{a}+1\right)^{-n} \, _2F_1\left(-n,m+2 p+1;m+2 p+2;-\frac{b x}{a}\right)}{m+2 p+1}",1,"(x^(1 + m)*(c*x^2)^p*(a + b*x)^n*Hypergeometric2F1[-n, 1 + m + 2*p, 2 + m + 2*p, -((b*x)/a)])/((1 + m + 2*p)*(1 + (b*x)/a)^n)","A",1
998,1,64,68,0.0093847,"\int (d x)^m \left(c x^2\right)^p (a+b x)^n \, dx","Integrate[(d*x)^m*(c*x^2)^p*(a + b*x)^n,x]","\frac{x \left(c x^2\right)^p (d x)^m (a+b x)^n \left(\frac{b x}{a}+1\right)^{-n} \, _2F_1\left(-n,m+2 p+1;m+2 p+2;-\frac{b x}{a}\right)}{m+2 p+1}","\frac{\left(c x^2\right)^p (d x)^{m+1} (a+b x)^n \left(\frac{b x}{a}+1\right)^{-n} \, _2F_1\left(-n,m+2 p+1;m+2 p+2;-\frac{b x}{a}\right)}{d (m+2 p+1)}",1,"(x*(d*x)^m*(c*x^2)^p*(a + b*x)^n*Hypergeometric2F1[-n, 1 + m + 2*p, 2 + m + 2*p, -((b*x)/a)])/((1 + m + 2*p)*(1 + (b*x)/a)^n)","A",1
999,1,17,17,0.0024343,"\int \frac{(a+b x)^5}{\left(\frac{a d}{b}+d x\right)^3} \, dx","Integrate[(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
1000,1,19,23,0.0011382,"\int \frac{(a+b x)^4}{\left(\frac{a d}{b}+d x\right)^3} \, dx","Integrate[(a + b*x)^4/((a*d)/b + d*x)^3,x]","\frac{b^3 \left(a x+\frac{b x^2}{2}\right)}{d^3}","\frac{a b^3 x}{d^3}+\frac{b^4 x^2}{2 d^3}",1,"(b^3*(a*x + (b*x^2)/2))/d^3","A",1
1001,1,8,8,0.000425,"\int \frac{(a+b x)^3}{\left(\frac{a d}{b}+d x\right)^3} \, dx","Integrate[(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
1002,1,13,13,0.0020282,"\int \frac{(a+b x)^2}{\left(\frac{a d}{b}+d x\right)^3} \, dx","Integrate[(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
1003,1,15,15,0.0039909,"\int \frac{a+b x}{\left(\frac{a d}{b}+d x\right)^3} \, dx","Integrate[(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
1004,1,17,17,0.0051092,"\int \frac{1}{(a+b x) \left(\frac{a d}{b}+d x\right)^3} \, dx","Integrate[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
1005,1,17,17,0.0058449,"\int \frac{1}{(a+b x)^2 \left(\frac{a d}{b}+d x\right)^3} \, dx","Integrate[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
1006,1,17,17,0.0064603,"\int \frac{1}{(a+b x)^3 \left(\frac{a d}{b}+d x\right)^3} \, dx","Integrate[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
1007,1,17,17,0.002707,"\int \frac{\left(\frac{b c}{d}+b x\right)^5}{(c+d x)^3} \, dx","Integrate[((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
1008,1,19,23,0.0011531,"\int \frac{\left(\frac{b c}{d}+b x\right)^4}{(c+d x)^3} \, dx","Integrate[((b*c)/d + b*x)^4/(c + d*x)^3,x]","\frac{b^4 \left(c x+\frac{d x^2}{2}\right)}{d^4}","\frac{b^4 c x}{d^4}+\frac{b^4 x^2}{2 d^3}",1,"(b^4*(c*x + (d*x^2)/2))/d^4","A",1
1009,1,8,8,0.0004447,"\int \frac{\left(\frac{b c}{d}+b x\right)^3}{(c+d x)^3} \, dx","Integrate[((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
1010,1,13,13,0.0021656,"\int \frac{\left(\frac{b c}{d}+b x\right)^2}{(c+d x)^3} \, dx","Integrate[((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
1011,1,13,13,0.0041636,"\int \frac{\frac{b c}{d}+b x}{(c+d x)^3} \, dx","Integrate[((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
1012,1,14,14,0.0049923,"\int \frac{1}{\left(\frac{b c}{d}+b x\right) (c+d x)^3} \, dx","Integrate[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
1013,1,15,15,0.0056948,"\int \frac{1}{\left(\frac{b c}{d}+b x\right)^2 (c+d x)^3} \, dx","Integrate[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
1014,1,17,17,0.0060931,"\int \frac{1}{\left(\frac{b c}{d}+b x\right)^3 (c+d x)^3} \, dx","Integrate[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
1015,1,25,24,0.0201535,"\int (a+b x)^5 (a c+b c x)^n \, dx","Integrate[(a + b*x)^5*(a*c + b*c*x)^n,x]","\frac{(a+b x)^6 (c (a+b x))^n}{b (n+6)}","\frac{(a c+b c x)^{n+6}}{b c^6 (n+6)}",1,"((a + b*x)^6*(c*(a + b*x))^n)/(b*(6 + n))","A",1
1016,1,17,17,0.0022197,"\int (a+b x)^5 (a c+b c x)^3 \, dx","Integrate[(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
1017,1,17,17,0.0020756,"\int (a+b x)^5 (a c+b c x)^2 \, dx","Integrate[(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
1018,1,15,15,0.0017587,"\int (a+b x)^5 (a c+b c x) \, dx","Integrate[(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
1019,1,17,17,0.001584,"\int \frac{(a+b x)^5}{a c+b c x} \, dx","Integrate[(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
1020,1,17,17,0.0014373,"\int \frac{(a+b x)^5}{(a c+b c x)^2} \, dx","Integrate[(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
1021,1,17,17,0.000977,"\int \frac{(a+b x)^5}{(a c+b c x)^3} \, dx","Integrate[(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
1022,1,16,18,0.0007734,"\int \frac{(a+b x)^5}{(a c+b c x)^4} \, dx","Integrate[(a + b*x)^5/(a*c + b*c*x)^4,x]","\frac{a x+\frac{b x^2}{2}}{c^4}","\frac{a x}{c^4}+\frac{b x^2}{2 c^4}",1,"(a*x + (b*x^2)/2)/c^4","A",1
1023,1,5,5,0.0003563,"\int \frac{(a+b x)^5}{(a c+b c x)^5} \, dx","Integrate[(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
1024,1,13,13,0.0017203,"\int \frac{(a+b x)^5}{(a c+b c x)^6} \, dx","Integrate[(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
1025,1,15,15,0.0023402,"\int \frac{(a+b x)^5}{(a c+b c x)^7} \, dx","Integrate[(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
1026,1,17,17,0.0040538,"\int \frac{(a+b x)^5}{(a c+b c x)^8} \, dx","Integrate[(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
1027,1,28,28,0.0062593,"\int \frac{1}{\sqrt{-2-3 x} \sqrt{2+3 x}} \, dx","Integrate[1/(Sqrt[-2 - 3*x]*Sqrt[2 + 3*x]),x]","\frac{(3 x+2) \log (3 x+2)}{3 \sqrt{-(3 x+2)^2}}","\frac{\sqrt{3 x+2} \log (3 x+2)}{3 \sqrt{-3 x-2}}",1,"((2 + 3*x)*Log[2 + 3*x])/(3*Sqrt[-(2 + 3*x)^2])","A",1
1028,1,40,38,0.0031778,"\int (a+b x) (a c-b c x)^3 \, dx","Integrate[(a + b*x)*(a*c - b*c*x)^3,x]","c^3 \left(a^4 x-a^3 b x^2+\frac{1}{2} a b^3 x^4-\frac{1}{5} b^4 x^5\right)","\frac{c^3 (a-b x)^5}{5 b}-\frac{a c^3 (a-b x)^4}{2 b}",1,"c^3*(a^4*x - a^3*b*x^2 + (a*b^3*x^4)/2 - (b^4*x^5)/5)","A",1
1029,1,42,38,0.002311,"\int (a+b x) (a c-b c x)^2 \, dx","Integrate[(a + b*x)*(a*c - b*c*x)^2,x]","c^2 \left(a^3 x-\frac{1}{2} a^2 b x^2-\frac{1}{3} a b^2 x^3+\frac{b^3 x^4}{4}\right)","\frac{c^2 (a-b x)^4}{4 b}-\frac{2 a c^2 (a-b x)^3}{3 b}",1,"c^2*(a^3*x - (a^2*b*x^2)/2 - (a*b^2*x^3)/3 + (b^3*x^4)/4)","A",1
1030,1,18,18,0.0013554,"\int (a+b x) (a c-b c x) \, dx","Integrate[(a + b*x)*(a*c - b*c*x),x]","c \left(a^2 x-\frac{b^2 x^3}{3}\right)","a^2 c x-\frac{1}{3} b^2 c x^3",1,"c*(a^2*x - (b^2*x^3)/3)","A",1
1031,1,12,12,0.0000718,"\int (a+b x) \, dx","Integrate[a + b*x,x]","a x+\frac{b x^2}{2}","a x+\frac{b x^2}{2}",1,"a*x + (b*x^2)/2","A",1
1032,1,23,23,0.0046178,"\int \frac{a+b x}{a c-b c x} \, dx","Integrate[(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
1033,1,28,32,0.0171155,"\int \frac{a+b x}{(a c-b c x)^2} \, dx","Integrate[(a + b*x)/(a*c - b*c*x)^2,x]","\frac{\log (c (a-b x))+\frac{2 a}{a-b x}}{b c^2}","\frac{2 a}{b c^2 (a-b x)}+\frac{\log (a-b x)}{b c^2}",1,"((2*a)/(a - b*x) + Log[c*(a - b*x)])/(b*c^2)","A",1
1034,1,13,13,0.0075837,"\int \frac{a+b x}{(a c-b c x)^3} \, dx","Integrate[(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
1035,1,25,38,0.0110459,"\int \frac{a+b x}{(a c-b c x)^4} \, dx","Integrate[(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
1036,1,24,38,0.010367,"\int \frac{a+b x}{(a c-b c x)^5} \, dx","Integrate[(a + b*x)/(a*c - b*c*x)^5,x]","\frac{a+2 b x}{6 b c^5 (a-b x)^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
1037,1,27,38,0.0126408,"\int \frac{a+b x}{(a c-b c x)^6} \, dx","Integrate[(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
1038,1,68,57,0.0031884,"\int (a+b x)^2 (a c-b c x)^3 \, dx","Integrate[(a + b*x)^2*(a*c - b*c*x)^3,x]","c^3 \left(a^5 x-\frac{1}{2} a^4 b x^2-\frac{2}{3} a^3 b^2 x^3+\frac{1}{2} a^2 b^3 x^4+\frac{1}{5} a b^4 x^5-\frac{1}{6} b^5 x^6\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,"c^3*(a^5*x - (a^4*b*x^2)/2 - (2*a^3*b^2*x^3)/3 + (a^2*b^3*x^4)/2 + (a*b^4*x^5)/5 - (b^5*x^6)/6)","A",1
1039,1,38,38,0.0018287,"\int (a+b x)^2 (a c-b c x)^2 \, dx","Integrate[(a + b*x)^2*(a*c - b*c*x)^2,x]","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","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,"a^4*c^2*x - (2*a^2*b^2*c^2*x^3)/3 + (b^4*c^2*x^5)/5","A",1
1040,1,40,32,0.0017869,"\int (a+b x)^2 (a c-b c x) \, dx","Integrate[(a + b*x)^2*(a*c - b*c*x),x]","c \left(a^3 x+\frac{1}{2} a^2 b x^2-\frac{1}{3} a b^2 x^3-\frac{1}{4} b^3 x^4\right)","\frac{2 a c (a+b x)^3}{3 b}-\frac{c (a+b x)^4}{4 b}",1,"c*(a^3*x + (a^2*b*x^2)/2 - (a*b^2*x^3)/3 - (b^3*x^4)/4)","A",1
1041,1,14,14,0.0010012,"\int (a+b x)^2 \, dx","Integrate[(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
1042,1,37,43,0.0071562,"\int \frac{(a+b x)^2}{a c-b c x} \, dx","Integrate[(a + b*x)^2/(a*c - b*c*x),x]","-\frac{4 a^2 \log (a-b x)}{b c}-\frac{3 a x}{c}-\frac{b x^2}{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,"(-3*a*x)/c - (b*x^2)/(2*c) - (4*a^2*Log[a - b*x])/(b*c)","A",1
1043,1,35,41,0.029233,"\int \frac{(a+b x)^2}{(a c-b c x)^2} \, dx","Integrate[(a + b*x)^2/(a*c - b*c*x)^2,x]","\frac{\frac{4 a^2}{b (a-b x)}+\frac{4 a \log (a-b x)}{b}+x}{c^2}","\frac{4 a^2}{b c^2 (a-b x)}+\frac{4 a \log (a-b x)}{b c^2}+\frac{x}{c^2}",1,"(x + (4*a^2)/(b*(a - b*x)) + (4*a*Log[a - b*x])/b)/c^2","A",1
1044,1,33,52,0.0235388,"\int \frac{(a+b x)^2}{(a c-b c x)^3} \, dx","Integrate[(a + b*x)^2/(a*c - b*c*x)^3,x]","-\frac{\frac{2 a (a-2 b x)}{(a-b x)^2}+\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))/(a - b*x)^2 + Log[a - b*x])/(b*c^3))","A",1
1045,1,31,28,0.017807,"\int \frac{(a+b x)^2}{(a c-b c x)^4} \, dx","Integrate[(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
1046,1,35,56,0.0121917,"\int \frac{(a+b x)^2}{(a c-b c x)^5} \, dx","Integrate[(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 (a-b x)^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
1047,1,38,57,0.0183451,"\int \frac{(a+b x)^2}{(a c-b c x)^6} \, dx","Integrate[(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
1048,1,37,59,0.0150097,"\int \frac{(a+b x)^2}{(a c-b c x)^7} \, dx","Integrate[(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 (a-b x)^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
1049,1,42,61,0.006291,"\int \frac{(a c-b c x)^3}{a+b x} \, dx","Integrate[(a*c - b*c*x)^3/(a + b*x),x]","c^3 \left(\frac{8 a^3 \log (a+b x)}{b}-7 a^2 x+2 a b x^2-\frac{b^2 x^3}{3}\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,"c^3*(-7*a^2*x + 2*a*b*x^2 - (b^2*x^3)/3 + (8*a^3*Log[a + b*x])/b)","A",1
1050,1,31,43,0.0054879,"\int \frac{(a c-b c x)^2}{a+b x} \, dx","Integrate[(a*c - b*c*x)^2/(a + b*x),x]","c^2 \left(\frac{4 a^2 \log (a+b x)}{b}-3 a x+\frac{b x^2}{2}\right)","\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*(-3*a*x + (b*x^2)/2 + (4*a^2*Log[a + b*x])/b)","A",1
1051,1,18,18,0.0030541,"\int \frac{a c-b c x}{a+b x} \, dx","Integrate[(a*c - b*c*x)/(a + b*x),x]","c \left(\frac{2 a \log (a+b x)}{b}-x\right)","\frac{2 a c \log (a+b x)}{b}-c x",1,"c*(-x + (2*a*Log[a + b*x])/b)","A",1
1052,1,10,10,0.0008759,"\int \frac{1}{a+b x} \, dx","Integrate[(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
1053,1,17,17,0.0064865,"\int \frac{1}{(a+b x) (a c-b c x)} \, dx","Integrate[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
1054,1,53,42,0.0154232,"\int \frac{1}{(a+b x) (a c-b c x)^2} \, dx","Integrate[1/((a + b*x)*(a*c - b*c*x)^2),x]","\frac{(b x-a) \log (a-b x)+(a-b x) \log (a+b x)+2 a}{4 a^2 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,"(2*a + (-a + b*x)*Log[a - b*x] + (a - b*x)*Log[a + b*x])/(4*a^2*b*c^2*(a - b*x))","A",1
1055,1,65,63,0.0218089,"\int \frac{1}{(a+b x) (a c-b c x)^3} \, dx","Integrate[1/((a + b*x)*(a*c - b*c*x)^3),x]","\frac{2 a (2 a-b x)+(a-b x)^2 (-\log (a-b x))+(a-b x)^2 \log (a+b x)}{8 a^3 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*(2*a - b*x) - (a - b*x)^2*Log[a - b*x] + (a - b*x)^2*Log[a + b*x])/(8*a^3*b*c^3*(a - b*x)^2)","A",1
1056,1,46,54,0.0195552,"\int \frac{(a c-b c x)^3}{(a+b x)^2} \, dx","Integrate[(a*c - b*c*x)^3/(a + b*x)^2,x]","c^3 \left(-\frac{8 a^3}{b (a+b x)}-\frac{12 a^2 \log (a+b x)}{b}+5 a x-\frac{b x^2}{2}\right)","-\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,"c^3*(5*a*x - (b*x^2)/2 - (8*a^3)/(b*(a + b*x)) - (12*a^2*Log[a + b*x])/b)","A",1
1057,1,33,39,0.0169996,"\int \frac{(a c-b c x)^2}{(a+b x)^2} \, dx","Integrate[(a*c - b*c*x)^2/(a + b*x)^2,x]","c^2 \left(-\frac{4 a^2}{b (a+b x)}-\frac{4 a \log (a+b x)}{b}+x\right)","-\frac{4 a^2 c^2}{b (a+b x)}-\frac{4 a c^2 \log (a+b x)}{b}+c^2 x",1,"c^2*(x - (4*a^2)/(b*(a + b*x)) - (4*a*Log[a + b*x])/b)","A",1
1058,1,23,27,0.0092767,"\int \frac{a c-b c x}{(a+b x)^2} \, dx","Integrate[(a*c - b*c*x)/(a + b*x)^2,x]","-\frac{c \left(\frac{2 a}{a+b x}+\log (a+b x)\right)}{b}","-\frac{2 a c}{b (a+b x)}-\frac{c \log (a+b x)}{b}",1,"-((c*((2*a)/(a + b*x) + Log[a + b*x]))/b)","A",1
1059,1,12,12,0.001876,"\int \frac{1}{(a+b x)^2} \, dx","Integrate[(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
1060,1,50,41,0.0157826,"\int \frac{1}{(a+b x)^2 (a c-b c x)} \, dx","Integrate[1/((a + b*x)^2*(a*c - b*c*x)),x]","\frac{-(a+b x) \log (a-b x)+(a+b x) \log (a+b x)-2 a}{4 a^2 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,"(-2*a - (a + b*x)*Log[a - b*x] + (a + b*x)*Log[a + b*x])/(4*a^2*b*c*(a + b*x))","A",1
1061,1,74,46,0.0238765,"\int \frac{1}{(a+b x)^2 (a c-b c x)^2} \, dx","Integrate[1/((a + b*x)^2*(a*c - b*c*x)^2),x]","\frac{\left(b^2 x^2-a^2\right) \log (a-b x)+\left(a^2-b^2 x^2\right) \log (a+b x)+2 a b x}{4 a^3 b c^2 (a-b x) (a+b 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)}",1,"(2*a*b*x + (-a^2 + b^2*x^2)*Log[a - b*x] + (a^2 - b^2*x^2)*Log[a + b*x])/(4*a^3*b*c^2*(a - b*x)*(a + b*x))","A",1
1062,1,68,83,0.0430706,"\int \frac{1}{(a+b x)^2 (a c-b c x)^3} \, dx","Integrate[1/((a + b*x)^2*(a*c - b*c*x)^3),x]","\frac{\frac{2 a \left(2 a^2+3 a b x-3 b^2 x^2\right)}{(a-b x)^2 (a+b x)}-3 \log (a-b x)+3 \log (a+b x)}{16 a^4 b c^3}","\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*a^2 + 3*a*b*x - 3*b^2*x^2))/((a - b*x)^2*(a + b*x)) - 3*Log[a - b*x] + 3*Log[a + b*x])/(16*a^4*b*c^3)","A",1
1063,1,60,108,0.0519177,"\int (1-x)^{9/2} \sqrt{1+x} \, dx","Integrate[(1 - x)^(9/2)*Sqrt[1 + x],x]","\frac{1}{240} \left(\sqrt{1-x^2} \left(40 x^5-192 x^4+350 x^3-256 x^2-75 x+448\right)-630 \sin ^{-1}\left(\frac{\sqrt{1-x}}{\sqrt{2}}\right)\right)","\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,"(Sqrt[1 - x^2]*(448 - 75*x - 256*x^2 + 350*x^3 - 192*x^4 + 40*x^5) - 630*ArcSin[Sqrt[1 - x]/Sqrt[2]])/240","A",1
1064,1,56,88,0.0508137,"\int (1-x)^{7/2} \sqrt{1+x} \, dx","Integrate[(1 - x)^(7/2)*Sqrt[1 + x],x]","\frac{1}{120} \sqrt{1-x^2} \left(-24 x^4+90 x^3-112 x^2+15 x+136\right)-\frac{7}{4} \sin ^{-1}\left(\frac{\sqrt{1-x}}{\sqrt{2}}\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,"(Sqrt[1 - x^2]*(136 + 15*x - 112*x^2 + 90*x^3 - 24*x^4))/120 - (7*ArcSin[Sqrt[1 - x]/Sqrt[2]])/4","A",1
1065,1,50,68,0.0408082,"\int (1-x)^{5/2} \sqrt{1+x} \, dx","Integrate[(1 - x)^(5/2)*Sqrt[1 + x],x]","\frac{1}{24} \left(\sqrt{1-x^2} \left(6 x^3-16 x^2+9 x+16\right)-30 \sin ^{-1}\left(\frac{\sqrt{1-x}}{\sqrt{2}}\right)\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,"(Sqrt[1 - x^2]*(16 + 9*x - 16*x^2 + 6*x^3) - 30*ArcSin[Sqrt[1 - x]/Sqrt[2]])/24","A",1
1066,1,44,48,0.038367,"\int (1-x)^{3/2} \sqrt{1+x} \, dx","Integrate[(1 - x)^(3/2)*Sqrt[1 + x],x]","\frac{1}{6} \left(-2 x^2+3 x+2\right) \sqrt{1-x^2}-\sin ^{-1}\left(\frac{\sqrt{1-x}}{\sqrt{2}}\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,"((2 + 3*x - 2*x^2)*Sqrt[1 - x^2])/6 - ArcSin[Sqrt[1 - x]/Sqrt[2]]","A",1
1067,1,20,28,0.0064185,"\int \sqrt{1-x} \sqrt{1+x} \, dx","Integrate[Sqrt[1 - x]*Sqrt[1 + x],x]","\frac{1}{2} \left(\sqrt{1-x^2} x+\sin ^{-1}(x)\right)","\frac{1}{2} \sqrt{1-x} \sqrt{x+1} x+\frac{1}{2} \sin ^{-1}(x)",1,"(x*Sqrt[1 - x^2] + ArcSin[x])/2","A",1
1068,1,32,21,0.0065726,"\int \frac{\sqrt{1+x}}{\sqrt{1-x}} \, dx","Integrate[Sqrt[1 + x]/Sqrt[1 - x],x]","-\sqrt{1-x^2}-2 \sin ^{-1}\left(\frac{\sqrt{1-x}}{\sqrt{2}}\right)","\sin ^{-1}(x)-\sqrt{1-x} \sqrt{x+1}",1,"-Sqrt[1 - x^2] - 2*ArcSin[Sqrt[1 - x]/Sqrt[2]]","A",1
1069,1,36,23,0.0126271,"\int \frac{\sqrt{1+x}}{(1-x)^{3/2}} \, dx","Integrate[Sqrt[1 + x]/(1 - x)^(3/2),x]","2 \left(\frac{\sqrt{x+1}}{\sqrt{1-x}}+\sin ^{-1}\left(\frac{\sqrt{1-x}}{\sqrt{2}}\right)\right)","\frac{2 \sqrt{x+1}}{\sqrt{1-x}}-\sin ^{-1}(x)",1,"2*(Sqrt[1 + x]/Sqrt[1 - x] + ArcSin[Sqrt[1 - x]/Sqrt[2]])","A",1
1070,1,20,20,0.0054016,"\int \frac{\sqrt{1+x}}{(1-x)^{5/2}} \, dx","Integrate[Sqrt[1 + x]/(1 - x)^(5/2),x]","\frac{(x+1)^{3/2}}{3 (1-x)^{3/2}}","\frac{(x+1)^{3/2}}{3 (1-x)^{3/2}}",1,"(1 + x)^(3/2)/(3*(1 - x)^(3/2))","A",1
1071,1,23,41,0.0085833,"\int \frac{\sqrt{1+x}}{(1-x)^{7/2}} \, dx","Integrate[Sqrt[1 + x]/(1 - x)^(7/2),x]","-\frac{(x-4) (x+1)^{3/2}}{15 (1-x)^{5/2}}","\frac{(x+1)^{3/2}}{15 (1-x)^{3/2}}+\frac{(x+1)^{3/2}}{5 (1-x)^{5/2}}",1,"-1/15*((-4 + x)*(1 + x)^(3/2))/(1 - x)^(5/2)","A",1
1072,1,30,61,0.0120303,"\int \frac{\sqrt{1+x}}{(1-x)^{9/2}} \, dx","Integrate[Sqrt[1 + x]/(1 - x)^(9/2),x]","\frac{(x+1)^{3/2} \left(2 x^2-10 x+23\right)}{105 (1-x)^{7/2}}","\frac{2 (x+1)^{3/2}}{105 (1-x)^{3/2}}+\frac{2 (x+1)^{3/2}}{35 (1-x)^{5/2}}+\frac{(x+1)^{3/2}}{7 (1-x)^{7/2}}",1,"((1 + x)^(3/2)*(23 - 10*x + 2*x^2))/(105*(1 - x)^(7/2))","A",1
1073,1,35,81,0.0135223,"\int \frac{\sqrt{1+x}}{(1-x)^{11/2}} \, dx","Integrate[Sqrt[1 + x]/(1 - x)^(11/2),x]","\frac{(x+1)^{3/2} \left(-2 x^3+12 x^2-33 x+58\right)}{315 (1-x)^{9/2}}","\frac{2 (x+1)^{3/2}}{315 (1-x)^{3/2}}+\frac{2 (x+1)^{3/2}}{105 (1-x)^{5/2}}+\frac{(x+1)^{3/2}}{21 (1-x)^{7/2}}+\frac{(x+1)^{3/2}}{9 (1-x)^{9/2}}",1,"((1 + x)^(3/2)*(58 - 33*x + 12*x^2 - 2*x^3))/(315*(1 - x)^(9/2))","A",1
1074,1,40,101,0.0173611,"\int \frac{\sqrt{1+x}}{(1-x)^{13/2}} \, dx","Integrate[Sqrt[1 + x]/(1 - x)^(13/2),x]","\frac{(x+1)^{3/2} \left(8 x^4-56 x^3+180 x^2-364 x+547\right)}{3465 (1-x)^{11/2}}","\frac{8 (x+1)^{3/2}}{3465 (1-x)^{3/2}}+\frac{8 (x+1)^{3/2}}{1155 (1-x)^{5/2}}+\frac{4 (x+1)^{3/2}}{231 (1-x)^{7/2}}+\frac{4 (x+1)^{3/2}}{99 (1-x)^{9/2}}+\frac{(x+1)^{3/2}}{11 (1-x)^{11/2}}",1,"((1 + x)^(3/2)*(547 - 364*x + 180*x^2 - 56*x^3 + 8*x^4))/(3465*(1 - x)^(11/2))","A",1
1075,1,66,109,0.057767,"\int (1-x)^{9/2} (1+x)^{3/2} \, dx","Integrate[(1 - x)^(9/2)*(1 + x)^(3/2),x]","\frac{1}{560} \sqrt{1-x^2} \left(80 x^6-280 x^5+208 x^4+350 x^3-656 x^2+245 x+368\right)-\frac{9}{8} \sin ^{-1}\left(\frac{\sqrt{1-x}}{\sqrt{2}}\right)","\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,"(Sqrt[1 - x^2]*(368 + 245*x - 656*x^2 + 350*x^3 + 208*x^4 - 280*x^5 + 80*x^6))/560 - (9*ArcSin[Sqrt[1 - x]/Sqrt[2]])/8","A",1
1076,1,61,89,0.0550053,"\int (1-x)^{7/2} (1+x)^{3/2} \, dx","Integrate[(1 - x)^(7/2)*(1 + x)^(3/2),x]","\frac{1}{240} \sqrt{1-x^2} \left(-40 x^5+96 x^4+10 x^3-192 x^2+135 x+96\right)-\frac{7}{8} \sin ^{-1}\left(\frac{\sqrt{1-x}}{\sqrt{2}}\right)","\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,"(Sqrt[1 - x^2]*(96 + 135*x - 192*x^2 + 10*x^3 + 96*x^4 - 40*x^5))/240 - (7*ArcSin[Sqrt[1 - x]/Sqrt[2]])/8","A",1
1077,1,55,69,0.0432651,"\int (1-x)^{5/2} (1+x)^{3/2} \, dx","Integrate[(1 - x)^(5/2)*(1 + x)^(3/2),x]","\frac{1}{40} \left(\sqrt{1-x^2} \left(8 x^4-10 x^3-16 x^2+25 x+8\right)-30 \sin ^{-1}\left(\frac{\sqrt{1-x}}{\sqrt{2}}\right)\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,"(Sqrt[1 - x^2]*(8 + 25*x - 16*x^2 - 10*x^3 + 8*x^4) - 30*ArcSin[Sqrt[1 - x]/Sqrt[2]])/40","A",1
1078,1,29,49,0.0114174,"\int (1-x)^{3/2} (1+x)^{3/2} \, dx","Integrate[(1 - x)^(3/2)*(1 + x)^(3/2),x]","\frac{1}{8} \left(x \sqrt{1-x^2} \left(5-2 x^2\right)+3 \sin ^{-1}(x)\right)","\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,"(x*(5 - 2*x^2)*Sqrt[1 - x^2] + 3*ArcSin[x])/8","A",1
1079,1,44,48,0.0330245,"\int \sqrt{1-x} (1+x)^{3/2} \, dx","Integrate[Sqrt[1 - x]*(1 + x)^(3/2),x]","\frac{1}{6} \sqrt{1-x^2} \left(2 x^2+3 x-2\right)-\sin ^{-1}\left(\frac{\sqrt{1-x}}{\sqrt{2}}\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,"(Sqrt[1 - x^2]*(-2 + 3*x + 2*x^2))/6 - ArcSin[Sqrt[1 - x]/Sqrt[2]]","A",1
1080,1,37,47,0.0121862,"\int \frac{(1+x)^{3/2}}{\sqrt{1-x}} \, dx","Integrate[(1 + x)^(3/2)/Sqrt[1 - x],x]","-\frac{1}{2} \sqrt{1-x^2} (x+4)-3 \sin ^{-1}\left(\frac{\sqrt{1-x}}{\sqrt{2}}\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,"-1/2*((4 + x)*Sqrt[1 - x^2]) - 3*ArcSin[Sqrt[1 - x]/Sqrt[2]]","A",1
1081,1,35,41,0.0063477,"\int \frac{(1+x)^{3/2}}{(1-x)^{3/2}} \, dx","Integrate[(1 + x)^(3/2)/(1 - x)^(3/2),x]","\frac{4 \sqrt{2} \, _2F_1\left(-\frac{3}{2},-\frac{1}{2};\frac{1}{2};\frac{1-x}{2}\right)}{\sqrt{1-x}}","\frac{2 (x+1)^{3/2}}{\sqrt{1-x}}+3 \sqrt{1-x} \sqrt{x+1}-3 \sin ^{-1}(x)",1,"(4*Sqrt[2]*Hypergeometric2F1[-3/2, -1/2, 1/2, (1 - x)/2])/Sqrt[1 - x]","C",1
1082,1,37,41,0.0060739,"\int \frac{(1+x)^{3/2}}{(1-x)^{5/2}} \, dx","Integrate[(1 + x)^(3/2)/(1 - x)^(5/2),x]","\frac{4 \sqrt{2} \, _2F_1\left(-\frac{3}{2},-\frac{3}{2};-\frac{1}{2};\frac{1-x}{2}\right)}{3 (1-x)^{3/2}}","\frac{2 (x+1)^{3/2}}{3 (1-x)^{3/2}}-\frac{2 \sqrt{x+1}}{\sqrt{1-x}}+\sin ^{-1}(x)",1,"(4*Sqrt[2]*Hypergeometric2F1[-3/2, -3/2, -1/2, (1 - x)/2])/(3*(1 - x)^(3/2))","C",1
1083,1,20,20,0.0064335,"\int \frac{(1+x)^{3/2}}{(1-x)^{7/2}} \, dx","Integrate[(1 + x)^(3/2)/(1 - x)^(7/2),x]","\frac{(x+1)^{5/2}}{5 (1-x)^{5/2}}","\frac{(x+1)^{5/2}}{5 (1-x)^{5/2}}",1,"(1 + x)^(5/2)/(5*(1 - x)^(5/2))","A",1
1084,1,23,41,0.0102282,"\int \frac{(1+x)^{3/2}}{(1-x)^{9/2}} \, dx","Integrate[(1 + x)^(3/2)/(1 - x)^(9/2),x]","-\frac{(x-6) (x+1)^{5/2}}{35 (1-x)^{7/2}}","\frac{(x+1)^{5/2}}{35 (1-x)^{5/2}}+\frac{(x+1)^{5/2}}{7 (1-x)^{7/2}}",1,"-1/35*((-6 + x)*(1 + x)^(5/2))/(1 - x)^(7/2)","A",1
1085,1,30,61,0.0118912,"\int \frac{(1+x)^{3/2}}{(1-x)^{11/2}} \, dx","Integrate[(1 + x)^(3/2)/(1 - x)^(11/2),x]","\frac{(x+1)^{5/2} \left(2 x^2-14 x+47\right)}{315 (1-x)^{9/2}}","\frac{2 (x+1)^{5/2}}{315 (1-x)^{5/2}}+\frac{2 (x+1)^{5/2}}{63 (1-x)^{7/2}}+\frac{(x+1)^{5/2}}{9 (1-x)^{9/2}}",1,"((1 + x)^(5/2)*(47 - 14*x + 2*x^2))/(315*(1 - x)^(9/2))","A",1
1086,1,35,81,0.0150299,"\int \frac{(1+x)^{3/2}}{(1-x)^{13/2}} \, dx","Integrate[(1 + x)^(3/2)/(1 - x)^(13/2),x]","\frac{(x+1)^{5/2} \left(-2 x^3+16 x^2-61 x+152\right)}{1155 (1-x)^{11/2}}","\frac{2 (x+1)^{5/2}}{1155 (1-x)^{5/2}}+\frac{2 (x+1)^{5/2}}{231 (1-x)^{7/2}}+\frac{(x+1)^{5/2}}{33 (1-x)^{9/2}}+\frac{(x+1)^{5/2}}{11 (1-x)^{11/2}}",1,"((1 + x)^(5/2)*(152 - 61*x + 16*x^2 - 2*x^3))/(1155*(1 - x)^(11/2))","A",1
1087,1,40,101,0.0168413,"\int \frac{(1+x)^{3/2}}{(1-x)^{15/2}} \, dx","Integrate[(1 + x)^(3/2)/(1 - x)^(15/2),x]","\frac{(x+1)^{5/2} \left(8 x^4-72 x^3+308 x^2-852 x+1763\right)}{15015 (1-x)^{13/2}}","\frac{8 (x+1)^{5/2}}{15015 (1-x)^{5/2}}+\frac{8 (x+1)^{5/2}}{3003 (1-x)^{7/2}}+\frac{4 (x+1)^{5/2}}{429 (1-x)^{9/2}}+\frac{4 (x+1)^{5/2}}{143 (1-x)^{11/2}}+\frac{(x+1)^{5/2}}{13 (1-x)^{13/2}}",1,"((1 + x)^(5/2)*(1763 - 852*x + 308*x^2 - 72*x^3 + 8*x^4))/(15015*(1 - x)^(13/2))","A",1
1088,1,75,130,0.0688223,"\int (1-x)^{11/2} (1+x)^{5/2} \, dx","Integrate[(1 - x)^(11/2)*(1 + x)^(5/2),x]","\frac{\sqrt{1-x^2} \left(-896 x^8+3024 x^7-1024 x^6-7224 x^5+8448 x^4+3066 x^3-10240 x^2+4599 x+3712\right)-6930 \sin ^{-1}\left(\frac{\sqrt{1-x}}{\sqrt{2}}\right)}{8064}","\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,"(Sqrt[1 - x^2]*(3712 + 4599*x - 10240*x^2 + 3066*x^3 + 8448*x^4 - 7224*x^5 - 1024*x^6 + 3024*x^7 - 896*x^8) - 6930*ArcSin[Sqrt[1 - x]/Sqrt[2]])/8064","A",1
1089,1,70,110,0.0613448,"\int (1-x)^{9/2} (1+x)^{5/2} \, dx","Integrate[(1 - x)^(9/2)*(1 + x)^(5/2),x]","\frac{1}{896} \left(\sqrt{1-x^2} \left(112 x^7-256 x^6-168 x^5+768 x^4-210 x^3-768 x^2+581 x+256\right)-630 \sin ^{-1}\left(\frac{\sqrt{1-x}}{\sqrt{2}}\right)\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,"(Sqrt[1 - x^2]*(256 + 581*x - 768*x^2 - 210*x^3 + 768*x^4 - 168*x^5 - 256*x^6 + 112*x^7) - 630*ArcSin[Sqrt[1 - x]/Sqrt[2]])/896","A",1
1090,1,66,90,0.0627294,"\int (1-x)^{7/2} (1+x)^{5/2} \, dx","Integrate[(1 - x)^(7/2)*(1 + x)^(5/2),x]","\frac{1}{336} \sqrt{1-x^2} \left(-48 x^6+56 x^5+144 x^4-182 x^3-144 x^2+231 x+48\right)-\frac{5}{8} \sin ^{-1}\left(\frac{\sqrt{1-x}}{\sqrt{2}}\right)","\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,"(Sqrt[1 - x^2]*(48 + 231*x - 144*x^2 - 182*x^3 + 144*x^4 + 56*x^5 - 48*x^6))/336 - (5*ArcSin[Sqrt[1 - x]/Sqrt[2]])/8","A",1
1091,1,34,70,0.0143328,"\int (1-x)^{5/2} (1+x)^{5/2} \, dx","Integrate[(1 - x)^(5/2)*(1 + x)^(5/2),x]","\frac{1}{48} \left(x \sqrt{1-x^2} \left(8 x^4-26 x^2+33\right)+15 \sin ^{-1}(x)\right)","\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,"(x*Sqrt[1 - x^2]*(33 - 26*x^2 + 8*x^4) + 15*ArcSin[x])/48","A",1
1092,1,55,69,0.0448903,"\int (1-x)^{3/2} (1+x)^{5/2} \, dx","Integrate[(1 - x)^(3/2)*(1 + x)^(5/2),x]","\frac{1}{40} \left(\sqrt{1-x^2} \left(-8 x^4-10 x^3+16 x^2+25 x-8\right)-30 \sin ^{-1}\left(\frac{\sqrt{1-x}}{\sqrt{2}}\right)\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,"(Sqrt[1 - x^2]*(-8 + 25*x + 16*x^2 - 10*x^3 - 8*x^4) - 30*ArcSin[Sqrt[1 - x]/Sqrt[2]])/40","A",1
1093,1,50,68,0.0367878,"\int \sqrt{1-x} (1+x)^{5/2} \, dx","Integrate[Sqrt[1 - x]*(1 + x)^(5/2),x]","\frac{1}{24} \left(\sqrt{1-x^2} \left(6 x^3+16 x^2+9 x-16\right)-30 \sin ^{-1}\left(\frac{\sqrt{1-x}}{\sqrt{2}}\right)\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,"(Sqrt[1 - x^2]*(-16 + 9*x + 16*x^2 + 6*x^3) - 30*ArcSin[Sqrt[1 - x]/Sqrt[2]])/24","A",1
1094,1,44,67,0.0230662,"\int \frac{(1+x)^{5/2}}{\sqrt{1-x}} \, dx","Integrate[(1 + x)^(5/2)/Sqrt[1 - x],x]","-\frac{1}{6} \sqrt{1-x^2} \left(2 x^2+9 x+22\right)-5 \sin ^{-1}\left(\frac{\sqrt{1-x}}{\sqrt{2}}\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,"-1/6*(Sqrt[1 - x^2]*(22 + 9*x + 2*x^2)) - 5*ArcSin[Sqrt[1 - x]/Sqrt[2]]","A",1
1095,1,35,65,0.0067917,"\int \frac{(1+x)^{5/2}}{(1-x)^{3/2}} \, dx","Integrate[(1 + x)^(5/2)/(1 - x)^(3/2),x]","\frac{8 \sqrt{2} \, _2F_1\left(-\frac{5}{2},-\frac{1}{2};\frac{1}{2};\frac{1-x}{2}\right)}{\sqrt{1-x}}","\frac{2 (x+1)^{5/2}}{\sqrt{1-x}}+\frac{5}{2} \sqrt{1-x} (x+1)^{3/2}+\frac{15}{2} \sqrt{1-x} \sqrt{x+1}-\frac{15}{2} \sin ^{-1}(x)",1,"(8*Sqrt[2]*Hypergeometric2F1[-5/2, -1/2, 1/2, (1 - x)/2])/Sqrt[1 - x]","C",1
1096,1,37,63,0.0081407,"\int \frac{(1+x)^{5/2}}{(1-x)^{5/2}} \, dx","Integrate[(1 + x)^(5/2)/(1 - x)^(5/2),x]","\frac{8 \sqrt{2} \, _2F_1\left(-\frac{5}{2},-\frac{3}{2};-\frac{1}{2};\frac{1-x}{2}\right)}{3 (1-x)^{3/2}}","\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,"(8*Sqrt[2]*Hypergeometric2F1[-5/2, -3/2, -1/2, (1 - x)/2])/(3*(1 - x)^(3/2))","C",1
1097,1,37,63,0.0088725,"\int \frac{(1+x)^{5/2}}{(1-x)^{7/2}} \, dx","Integrate[(1 + x)^(5/2)/(1 - x)^(7/2),x]","\frac{8 \sqrt{2} \, _2F_1\left(-\frac{5}{2},-\frac{5}{2};-\frac{3}{2};\frac{1-x}{2}\right)}{5 (1-x)^{5/2}}","\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,"(8*Sqrt[2]*Hypergeometric2F1[-5/2, -5/2, -3/2, (1 - x)/2])/(5*(1 - x)^(5/2))","C",1
1098,1,20,20,0.0080032,"\int \frac{(1+x)^{5/2}}{(1-x)^{9/2}} \, dx","Integrate[(1 + x)^(5/2)/(1 - x)^(9/2),x]","\frac{(x+1)^{7/2}}{7 (1-x)^{7/2}}","\frac{(x+1)^{7/2}}{7 (1-x)^{7/2}}",1,"(1 + x)^(7/2)/(7*(1 - x)^(7/2))","A",1
1099,1,23,41,0.0111517,"\int \frac{(1+x)^{5/2}}{(1-x)^{11/2}} \, dx","Integrate[(1 + x)^(5/2)/(1 - x)^(11/2),x]","-\frac{(x-8) (x+1)^{7/2}}{63 (1-x)^{9/2}}","\frac{(x+1)^{7/2}}{63 (1-x)^{7/2}}+\frac{(x+1)^{7/2}}{9 (1-x)^{9/2}}",1,"-1/63*((-8 + x)*(1 + x)^(7/2))/(1 - x)^(9/2)","A",1
1100,1,30,61,0.0158736,"\int \frac{(1+x)^{5/2}}{(1-x)^{13/2}} \, dx","Integrate[(1 + x)^(5/2)/(1 - x)^(13/2),x]","\frac{(x+1)^{7/2} \left(2 x^2-18 x+79\right)}{693 (1-x)^{11/2}}","\frac{2 (x+1)^{7/2}}{693 (1-x)^{7/2}}+\frac{2 (x+1)^{7/2}}{99 (1-x)^{9/2}}+\frac{(x+1)^{7/2}}{11 (1-x)^{11/2}}",1,"((1 + x)^(7/2)*(79 - 18*x + 2*x^2))/(693*(1 - x)^(11/2))","A",1
1101,1,35,81,0.017354,"\int \frac{(1+x)^{5/2}}{(1-x)^{15/2}} \, dx","Integrate[(1 + x)^(5/2)/(1 - x)^(15/2),x]","\frac{(x+1)^{7/2} \left(-2 x^3+20 x^2-97 x+310\right)}{3003 (1-x)^{13/2}}","\frac{2 (x+1)^{7/2}}{3003 (1-x)^{7/2}}+\frac{2 (x+1)^{7/2}}{429 (1-x)^{9/2}}+\frac{3 (x+1)^{7/2}}{143 (1-x)^{11/2}}+\frac{(x+1)^{7/2}}{13 (1-x)^{13/2}}",1,"((1 + x)^(7/2)*(310 - 97*x + 20*x^2 - 2*x^3))/(3003*(1 - x)^(13/2))","A",1
1102,1,40,101,0.0211972,"\int \frac{(1+x)^{5/2}}{(1-x)^{17/2}} \, dx","Integrate[(1 + x)^(5/2)/(1 - x)^(17/2),x]","\frac{(x+1)^{7/2} \left(8 x^4-88 x^3+468 x^2-1628 x+4243\right)}{45045 (1-x)^{15/2}}","\frac{8 (x+1)^{7/2}}{45045 (1-x)^{7/2}}+\frac{8 (x+1)^{7/2}}{6435 (1-x)^{9/2}}+\frac{4 (x+1)^{7/2}}{715 (1-x)^{11/2}}+\frac{4 (x+1)^{7/2}}{195 (1-x)^{13/2}}+\frac{(x+1)^{7/2}}{15 (1-x)^{15/2}}",1,"((1 + x)^(7/2)*(4243 - 1628*x + 468*x^2 - 88*x^3 + 8*x^4))/(45045*(1 - x)^(15/2))","A",1
1103,1,45,121,0.0216723,"\int \frac{(1+x)^{5/2}}{(1-x)^{19/2}} \, dx","Integrate[(1 + x)^(5/2)/(1 - x)^(19/2),x]","\frac{(x+1)^{7/2} \left(-8 x^5+96 x^4-556 x^3+2096 x^2-5871 x+13252\right)}{153153 (1-x)^{17/2}}","\frac{8 (x+1)^{7/2}}{153153 (1-x)^{7/2}}+\frac{8 (x+1)^{7/2}}{21879 (1-x)^{9/2}}+\frac{4 (x+1)^{7/2}}{2431 (1-x)^{11/2}}+\frac{4 (x+1)^{7/2}}{663 (1-x)^{13/2}}+\frac{(x+1)^{7/2}}{51 (1-x)^{15/2}}+\frac{(x+1)^{7/2}}{17 (1-x)^{17/2}}",1,"((1 + x)^(7/2)*(13252 - 5871*x + 2096*x^2 - 556*x^3 + 96*x^4 - 8*x^5))/(153153*(1 - x)^(17/2))","A",1
1104,1,47,64,0.0393387,"\int \frac{(1+a x)^{3/2}}{\sqrt{1-a x}} \, dx","Integrate[(1 + a*x)^(3/2)/Sqrt[1 - a*x],x]","-\frac{\sqrt{1-a^2 x^2} (a x+4)+6 \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)}{2 a}","-\frac{\sqrt{1-a x} (a x+1)^{3/2}}{2 a}-\frac{3 \sqrt{1-a x} \sqrt{a x+1}}{2 a}+\frac{3 \sin ^{-1}(a x)}{2 a}",1,"-1/2*((4 + a*x)*Sqrt[1 - a^2*x^2] + 6*ArcSin[Sqrt[1 - a*x]/Sqrt[2]])/a","A",1
1105,1,91,62,0.1017826,"\int \frac{(1+a x) \sqrt{1-a^2 x^2}}{1-a x} \, dx","Integrate[((1 + a*x)*Sqrt[1 - a^2*x^2])/(1 - a*x),x]","\frac{\sqrt{1-a^2 x^2} \left(6 \sqrt{a x+1} \sin ^{-1}\left(\frac{\sqrt{a x+1}}{\sqrt{2}}\right)-\sqrt{1-a x} \left(a^2 x^2+5 a x+4\right)\right)}{2 a \sqrt{1-a x} (a x+1)}","-\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,"(Sqrt[1 - a^2*x^2]*(-(Sqrt[1 - a*x]*(4 + 5*a*x + a^2*x^2)) + 6*Sqrt[1 + a*x]*ArcSin[Sqrt[1 + a*x]/Sqrt[2]]))/(2*a*Sqrt[1 - a*x]*(1 + a*x))","A",1
1106,1,61,87,0.0247878,"\int \frac{(1-x)^{7/2}}{\sqrt{1+x}} \, dx","Integrate[(1 - x)^(7/2)/Sqrt[1 + x],x]","\frac{\sqrt{x+1} \left(6 x^4-38 x^3+113 x^2-241 x+160\right)}{24 \sqrt{1-x}}-\frac{35}{4} \sin ^{-1}\left(\frac{\sqrt{1-x}}{\sqrt{2}}\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,"(Sqrt[1 + x]*(160 - 241*x + 113*x^2 - 38*x^3 + 6*x^4))/(24*Sqrt[1 - x]) - (35*ArcSin[Sqrt[1 - x]/Sqrt[2]])/4","A",1
1107,1,54,67,0.0261233,"\int \frac{(1-x)^{5/2}}{\sqrt{1+x}} \, dx","Integrate[(1 - x)^(5/2)/Sqrt[1 + x],x]","\frac{\sqrt{x+1} \left(-2 x^3+11 x^2-31 x+22\right)}{6 \sqrt{1-x}}-5 \sin ^{-1}\left(\frac{\sqrt{1-x}}{\sqrt{2}}\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,"(Sqrt[1 + x]*(22 - 31*x + 11*x^2 - 2*x^3))/(6*Sqrt[1 - x]) - 5*ArcSin[Sqrt[1 - x]/Sqrt[2]]","A",1
1108,1,47,47,0.0201956,"\int \frac{(1-x)^{3/2}}{\sqrt{1+x}} \, dx","Integrate[(1 - x)^(3/2)/Sqrt[1 + x],x]","\frac{\sqrt{x+1} \left(x^2-5 x+4\right)}{2 \sqrt{1-x}}-3 \sin ^{-1}\left(\frac{\sqrt{1-x}}{\sqrt{2}}\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,"(Sqrt[1 + x]*(4 - 5*x + x^2))/(2*Sqrt[1 - x]) - 3*ArcSin[Sqrt[1 - x]/Sqrt[2]]","A",1
1109,1,30,20,0.0133072,"\int \frac{\sqrt{1-x}}{\sqrt{1+x}} \, dx","Integrate[Sqrt[1 - x]/Sqrt[1 + x],x]","\sqrt{1-x^2}-2 \sin ^{-1}\left(\frac{\sqrt{1-x}}{\sqrt{2}}\right)","\sqrt{1-x} \sqrt{x+1}+\sin ^{-1}(x)",1,"Sqrt[1 - x^2] - 2*ArcSin[Sqrt[1 - x]/Sqrt[2]]","A",1
1110,1,2,2,0.0049096,"\int \frac{1}{\sqrt{1-x} \sqrt{1+x}} \, dx","Integrate[1/(Sqrt[1 - x]*Sqrt[1 + x]),x]","\sin ^{-1}(x)","\sin ^{-1}(x)",1,"ArcSin[x]","A",1
1111,1,17,17,0.0033599,"\int \frac{1}{(1-x)^{3/2} \sqrt{1+x}} \, dx","Integrate[1/((1 - x)^(3/2)*Sqrt[1 + x]),x]","\frac{\sqrt{x+1}}{\sqrt{1-x}}","\frac{\sqrt{x+1}}{\sqrt{1-x}}",1,"Sqrt[1 + x]/Sqrt[1 - x]","A",1
1112,1,23,41,0.0066441,"\int \frac{1}{(1-x)^{5/2} \sqrt{1+x}} \, dx","Integrate[1/((1 - x)^(5/2)*Sqrt[1 + x]),x]","-\frac{(x-2) \sqrt{x+1}}{3 (1-x)^{3/2}}","\frac{\sqrt{x+1}}{3 \sqrt{1-x}}+\frac{\sqrt{x+1}}{3 (1-x)^{3/2}}",1,"-1/3*((-2 + x)*Sqrt[1 + x])/(1 - x)^(3/2)","A",1
1113,1,30,61,0.0088837,"\int \frac{1}{(1-x)^{7/2} \sqrt{1+x}} \, dx","Integrate[1/((1 - x)^(7/2)*Sqrt[1 + x]),x]","\frac{\sqrt{x+1} \left(2 x^2-6 x+7\right)}{15 (1-x)^{5/2}}","\frac{2 \sqrt{x+1}}{15 \sqrt{1-x}}+\frac{2 \sqrt{x+1}}{15 (1-x)^{3/2}}+\frac{\sqrt{x+1}}{5 (1-x)^{5/2}}",1,"(Sqrt[1 + x]*(7 - 6*x + 2*x^2))/(15*(1 - x)^(5/2))","A",1
1114,1,35,81,0.0112483,"\int \frac{1}{(1-x)^{9/2} \sqrt{1+x}} \, dx","Integrate[1/((1 - x)^(9/2)*Sqrt[1 + x]),x]","\frac{\sqrt{x+1} \left(-2 x^3+8 x^2-13 x+12\right)}{35 (1-x)^{7/2}}","\frac{2 \sqrt{x+1}}{35 \sqrt{1-x}}+\frac{2 \sqrt{x+1}}{35 (1-x)^{3/2}}+\frac{3 \sqrt{x+1}}{35 (1-x)^{5/2}}+\frac{\sqrt{x+1}}{7 (1-x)^{7/2}}",1,"(Sqrt[1 + x]*(12 - 13*x + 8*x^2 - 2*x^3))/(35*(1 - x)^(7/2))","A",1
1115,1,40,101,0.0115288,"\int \frac{1}{(1-x)^{11/2} \sqrt{1+x}} \, dx","Integrate[1/((1 - x)^(11/2)*Sqrt[1 + x]),x]","\frac{\sqrt{x+1} \left(8 x^4-40 x^3+84 x^2-100 x+83\right)}{315 (1-x)^{9/2}}","\frac{8 \sqrt{x+1}}{315 \sqrt{1-x}}+\frac{8 \sqrt{x+1}}{315 (1-x)^{3/2}}+\frac{4 \sqrt{x+1}}{105 (1-x)^{5/2}}+\frac{4 \sqrt{x+1}}{63 (1-x)^{7/2}}+\frac{\sqrt{x+1}}{9 (1-x)^{9/2}}",1,"(Sqrt[1 + x]*(83 - 100*x + 84*x^2 - 40*x^3 + 8*x^4))/(315*(1 - x)^(9/2))","A",1
1116,1,37,85,0.0130958,"\int \frac{(1-x)^{7/2}}{(1+x)^{3/2}} \, dx","Integrate[(1 - x)^(7/2)/(1 + x)^(3/2),x]","-\frac{(1-x)^{9/2} \, _2F_1\left(\frac{3}{2},\frac{9}{2};\frac{11}{2};\frac{1-x}{2}\right)}{9 \sqrt{2}}","-\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,"-1/9*((1 - x)^(9/2)*Hypergeometric2F1[3/2, 9/2, 11/2, (1 - x)/2])/Sqrt[2]","C",1
1117,1,37,65,0.0111281,"\int \frac{(1-x)^{5/2}}{(1+x)^{3/2}} \, dx","Integrate[(1 - x)^(5/2)/(1 + x)^(3/2),x]","-\frac{(1-x)^{7/2} \, _2F_1\left(\frac{3}{2},\frac{7}{2};\frac{9}{2};\frac{1-x}{2}\right)}{7 \sqrt{2}}","-\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,"-1/7*((1 - x)^(7/2)*Hypergeometric2F1[3/2, 7/2, 9/2, (1 - x)/2])/Sqrt[2]","C",1
1118,1,37,41,0.0098756,"\int \frac{(1-x)^{3/2}}{(1+x)^{3/2}} \, dx","Integrate[(1 - x)^(3/2)/(1 + x)^(3/2),x]","-\frac{(1-x)^{5/2} \, _2F_1\left(\frac{3}{2},\frac{5}{2};\frac{7}{2};\frac{1-x}{2}\right)}{5 \sqrt{2}}","-\frac{2 (1-x)^{3/2}}{\sqrt{x+1}}-3 \sqrt{x+1} \sqrt{1-x}-3 \sin ^{-1}(x)",1,"-1/5*((1 - x)^(5/2)*Hypergeometric2F1[3/2, 5/2, 7/2, (1 - x)/2])/Sqrt[2]","C",1
1119,1,34,23,0.0363008,"\int \frac{\sqrt{1-x}}{(1+x)^{3/2}} \, dx","Integrate[Sqrt[1 - x]/(1 + x)^(3/2),x]","2 \left(\frac{x-1}{\sqrt{1-x^2}}+\sin ^{-1}\left(\frac{\sqrt{1-x}}{\sqrt{2}}\right)\right)","-\frac{2 \sqrt{1-x}}{\sqrt{x+1}}-\sin ^{-1}(x)",1,"2*((-1 + x)/Sqrt[1 - x^2] + ArcSin[Sqrt[1 - x]/Sqrt[2]])","A",1
1120,1,18,18,0.0035465,"\int \frac{1}{\sqrt{1-x} (1+x)^{3/2}} \, dx","Integrate[1/(Sqrt[1 - x]*(1 + x)^(3/2)),x]","-\frac{\sqrt{1-x}}{\sqrt{x+1}}","-\frac{\sqrt{1-x}}{\sqrt{x+1}}",1,"-(Sqrt[1 - x]/Sqrt[1 + x])","A",1
1121,1,13,18,0.0030855,"\int \frac{1}{(1-x)^{3/2} (1+x)^{3/2}} \, dx","Integrate[1/((1 - x)^(3/2)*(1 + x)^(3/2)),x]","\frac{x}{\sqrt{1-x^2}}","\frac{x}{\sqrt{1-x} \sqrt{x+1}}",1,"x/Sqrt[1 - x^2]","A",1
1122,1,30,42,0.0073331,"\int \frac{1}{(1-x)^{5/2} (1+x)^{3/2}} \, dx","Integrate[1/((1 - x)^(5/2)*(1 + x)^(3/2)),x]","\frac{2 x^2-2 x-1}{3 (x-1) \sqrt{1-x^2}}","\frac{2 x}{3 \sqrt{1-x} \sqrt{x+1}}+\frac{1}{3 (1-x)^{3/2} \sqrt{x+1}}",1,"(-1 - 2*x + 2*x^2)/(3*(-1 + x)*Sqrt[1 - x^2])","A",1
1123,1,33,62,0.0086229,"\int \frac{1}{(1-x)^{7/2} (1+x)^{3/2}} \, dx","Integrate[1/((1 - x)^(7/2)*(1 + x)^(3/2)),x]","\frac{2 x^3-4 x^2+x+2}{5 (x-1)^2 \sqrt{1-x^2}}","\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,"(2 + x - 4*x^2 + 2*x^3)/(5*(-1 + x)^2*Sqrt[1 - x^2])","A",1
1124,1,40,82,0.0101201,"\int \frac{1}{(1-x)^{9/2} (1+x)^{3/2}} \, dx","Integrate[1/((1 - x)^(9/2)*(1 + x)^(3/2)),x]","\frac{8 x^4-24 x^3+20 x^2+4 x-13}{35 (x-1)^3 \sqrt{1-x^2}}","\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,"(-13 + 4*x + 20*x^2 - 24*x^3 + 8*x^4)/(35*(-1 + x)^3*Sqrt[1 - x^2])","A",1
1125,1,45,102,0.0121602,"\int \frac{1}{(1-x)^{11/2} (1+x)^{3/2}} \, dx","Integrate[1/((1 - x)^(11/2)*(1 + x)^(3/2)),x]","\frac{8 x^5-32 x^4+44 x^3-16 x^2-17 x+20}{63 (x-1)^4 \sqrt{1-x^2}}","\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,"(20 - 17*x - 16*x^2 + 44*x^3 - 32*x^4 + 8*x^5)/(63*(-1 + x)^4*Sqrt[1 - x^2])","A",1
1126,1,37,103,0.0149219,"\int \frac{(1-x)^{9/2}}{(1+x)^{5/2}} \, dx","Integrate[(1 - x)^(9/2)/(1 + x)^(5/2),x]","-\frac{(1-x)^{11/2} \, _2F_1\left(\frac{5}{2},\frac{11}{2};\frac{13}{2};\frac{1-x}{2}\right)}{22 \sqrt{2}}","-\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,"-1/22*((1 - x)^(11/2)*Hypergeometric2F1[5/2, 11/2, 13/2, (1 - x)/2])/Sqrt[2]","C",1
1127,1,37,87,0.0122538,"\int \frac{(1-x)^{7/2}}{(1+x)^{5/2}} \, dx","Integrate[(1 - x)^(7/2)/(1 + x)^(5/2),x]","-\frac{(1-x)^{9/2} \, _2F_1\left(\frac{5}{2},\frac{9}{2};\frac{11}{2};\frac{1-x}{2}\right)}{18 \sqrt{2}}","-\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,"-1/18*((1 - x)^(9/2)*Hypergeometric2F1[5/2, 9/2, 11/2, (1 - x)/2])/Sqrt[2]","C",1
1128,1,37,63,0.0109045,"\int \frac{(1-x)^{5/2}}{(1+x)^{5/2}} \, dx","Integrate[(1 - x)^(5/2)/(1 + x)^(5/2),x]","-\frac{(1-x)^{7/2} \, _2F_1\left(\frac{5}{2},\frac{7}{2};\frac{9}{2};\frac{1-x}{2}\right)}{14 \sqrt{2}}","-\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,"-1/14*((1 - x)^(7/2)*Hypergeometric2F1[5/2, 7/2, 9/2, (1 - x)/2])/Sqrt[2]","C",1
1129,1,49,41,0.0568197,"\int \frac{(1-x)^{3/2}}{(1+x)^{5/2}} \, dx","Integrate[(1 - x)^(3/2)/(1 + x)^(5/2),x]","\frac{-8 x^2+4 x+4}{3 \sqrt{1-x} (x+1)^{3/2}}-2 \sin ^{-1}\left(\frac{\sqrt{1-x}}{\sqrt{2}}\right)","-\frac{2 (1-x)^{3/2}}{3 (x+1)^{3/2}}+\frac{2 \sqrt{1-x}}{\sqrt{x+1}}+\sin ^{-1}(x)",1,"(4 + 4*x - 8*x^2)/(3*Sqrt[1 - x]*(1 + x)^(3/2)) - 2*ArcSin[Sqrt[1 - x]/Sqrt[2]]","A",1
1130,1,20,20,0.0043577,"\int \frac{\sqrt{1-x}}{(1+x)^{5/2}} \, dx","Integrate[Sqrt[1 - x]/(1 + x)^(5/2),x]","-\frac{(1-x)^{3/2}}{3 (x+1)^{3/2}}","-\frac{(1-x)^{3/2}}{3 (x+1)^{3/2}}",1,"-1/3*(1 - x)^(3/2)/(1 + x)^(3/2)","A",1
1131,1,23,41,0.0053228,"\int \frac{1}{\sqrt{1-x} (1+x)^{5/2}} \, dx","Integrate[1/(Sqrt[1 - x]*(1 + x)^(5/2)),x]","-\frac{\sqrt{1-x} (x+2)}{3 (x+1)^{3/2}}","-\frac{\sqrt{1-x}}{3 \sqrt{x+1}}-\frac{\sqrt{1-x}}{3 (x+1)^{3/2}}",1,"-1/3*(Sqrt[1 - x]*(2 + x))/(1 + x)^(3/2)","A",1
1132,1,30,58,0.0063247,"\int \frac{1}{(1-x)^{3/2} (1+x)^{5/2}} \, dx","Integrate[1/((1 - x)^(3/2)*(1 + x)^(5/2)),x]","\frac{2 x^2+2 x-1}{3 \sqrt{1-x} (x+1)^{3/2}}","-\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 + 2*x + 2*x^2)/(3*Sqrt[1 - x]*(1 + x)^(3/2))","A",1
1133,1,23,43,0.0073649,"\int \frac{1}{(1-x)^{5/2} (1+x)^{5/2}} \, dx","Integrate[1/((1 - x)^(5/2)*(1 + x)^(5/2)),x]","-\frac{x \left(2 x^2-3\right)}{3 \left(1-x^2\right)^{3/2}}","\frac{2 x}{3 \sqrt{1-x} \sqrt{x+1}}+\frac{x}{3 (1-x)^{3/2} (x+1)^{3/2}}",1,"-1/3*(x*(-3 + 2*x^2))/(1 - x^2)^(3/2)","A",1
1134,1,40,63,0.0111352,"\int \frac{1}{(1-x)^{7/2} (1+x)^{5/2}} \, dx","Integrate[1/((1 - x)^(7/2)*(1 + x)^(5/2)),x]","\frac{8 x^4-8 x^3-12 x^2+12 x+3}{15 (1-x)^{5/2} (x+1)^{3/2}}","\frac{8 x}{15 \sqrt{1-x} \sqrt{x+1}}+\frac{4 x}{15 (1-x)^{3/2} (x+1)^{3/2}}+\frac{1}{5 (1-x)^{5/2} (x+1)^{3/2}}",1,"(3 + 12*x - 12*x^2 - 8*x^3 + 8*x^4)/(15*(1 - x)^(5/2)*(1 + x)^(3/2))","A",1
1135,1,45,83,0.0134642,"\int \frac{1}{(1-x)^{9/2} (1+x)^{5/2}} \, dx","Integrate[1/((1 - x)^(9/2)*(1 + x)^(5/2)),x]","\frac{-8 x^5+16 x^4+4 x^3-24 x^2+9 x+6}{21 (1-x)^{7/2} (x+1)^{3/2}}","\frac{8 x}{21 \sqrt{1-x} \sqrt{x+1}}+\frac{4 x}{21 (1-x)^{3/2} (x+1)^{3/2}}+\frac{1}{7 (1-x)^{5/2} (x+1)^{3/2}}+\frac{1}{7 (1-x)^{7/2} (x+1)^{3/2}}",1,"(6 + 9*x - 24*x^2 + 4*x^3 + 16*x^4 - 8*x^5)/(21*(1 - x)^(7/2)*(1 + x)^(3/2))","A",1
1136,1,50,103,0.0137542,"\int \frac{1}{(1-x)^{11/2} (1+x)^{5/2}} \, dx","Integrate[1/((1 - x)^(11/2)*(1 + x)^(5/2)),x]","\frac{16 x^6-48 x^5+24 x^4+56 x^3-66 x^2+6 x+19}{63 (1-x)^{9/2} (x+1)^{3/2}}","\frac{16 x}{63 \sqrt{1-x} \sqrt{x+1}}+\frac{8 x}{63 (1-x)^{3/2} (x+1)^{3/2}}+\frac{2}{21 (1-x)^{5/2} (x+1)^{3/2}}+\frac{2}{21 (1-x)^{7/2} (x+1)^{3/2}}+\frac{1}{9 (1-x)^{9/2} (x+1)^{3/2}}",1,"(19 + 6*x - 66*x^2 + 56*x^3 + 24*x^4 - 48*x^5 + 16*x^6)/(63*(1 - x)^(9/2)*(1 + x)^(3/2))","A",1
1137,1,114,126,0.0996732,"\int (a+a x)^{5/2} (c-c x)^{5/2} \, dx","Integrate[(a + a*x)^(5/2)*(c - c*x)^(5/2),x]","\frac{c^{3/2} (a (x+1))^{5/2} \sqrt{c-c x} \left(\sqrt{c} x \sqrt{x+1} \left(8 x^5-8 x^4-26 x^3+26 x^2+33 x-33\right)+30 \sqrt{c-c x} \sin ^{-1}\left(\frac{\sqrt{c-c x}}{\sqrt{2} \sqrt{c}}\right)\right)}{48 (x-1) (x+1)^{5/2}}","\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,"(c^(3/2)*(a*(1 + x))^(5/2)*Sqrt[c - c*x]*(Sqrt[c]*x*Sqrt[1 + x]*(-33 + 33*x + 26*x^2 - 26*x^3 - 8*x^4 + 8*x^5) + 30*Sqrt[c - c*x]*ArcSin[Sqrt[c - c*x]/(Sqrt[2]*Sqrt[c])]))/(48*(-1 + x)*(1 + x)^(5/2))","A",1
1138,1,104,96,0.0824736,"\int (a+a x)^{3/2} (c-c x)^{3/2} \, dx","Integrate[(a + a*x)^(3/2)*(c - c*x)^(3/2),x]","\frac{\sqrt{c} (a (x+1))^{3/2} \sqrt{c-c x} \left(\sqrt{c} x \sqrt{x+1} \left(-2 x^3+2 x^2+5 x-5\right)+6 \sqrt{c-c x} \sin ^{-1}\left(\frac{\sqrt{c-c x}}{\sqrt{2} \sqrt{c}}\right)\right)}{8 (x-1) (x+1)^{3/2}}","\frac{3}{4} a^{3/2} c^{3/2} \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a x+a}}{\sqrt{a} \sqrt{c-c x}}\right)+\frac{3}{8} a c x \sqrt{a x+a} \sqrt{c-c x}+\frac{1}{4} x (a x+a)^{3/2} (c-c x)^{3/2}",1,"(Sqrt[c]*(a*(1 + x))^(3/2)*Sqrt[c - c*x]*(Sqrt[c]*x*Sqrt[1 + x]*(-5 + 5*x + 2*x^2 - 2*x^3) + 6*Sqrt[c - c*x]*ArcSin[Sqrt[c - c*x]/(Sqrt[2]*Sqrt[c])]))/(8*(-1 + x)*(1 + x)^(3/2))","A",1
1139,1,69,67,0.060896,"\int \sqrt{a+a x} \sqrt{c-c x} \, dx","Integrate[Sqrt[a + a*x]*Sqrt[c - c*x],x]","\frac{\sqrt{a (x+1)} \left(x \sqrt{x+1} \sqrt{c-c x}-2 \sqrt{c} \sin ^{-1}\left(\frac{\sqrt{c-c x}}{\sqrt{2} \sqrt{c}}\right)\right)}{2 \sqrt{x+1}}","\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,"(Sqrt[a*(1 + x)]*(x*Sqrt[1 + x]*Sqrt[c - c*x] - 2*Sqrt[c]*ArcSin[Sqrt[c - c*x]/(Sqrt[2]*Sqrt[c])]))/(2*Sqrt[1 + x])","A",1
1140,1,47,43,0.0171763,"\int \frac{1}{\sqrt{a+a x} \sqrt{c-c x}} \, dx","Integrate[1/(Sqrt[a + a*x]*Sqrt[c - c*x]),x]","\frac{2 \sqrt{x+1} \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{x+1}}{\sqrt{c-c x}}\right)}{\sqrt{c} \sqrt{a (x+1)}}","\frac{2 \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a x+a}}{\sqrt{a} \sqrt{c-c x}}\right)}{\sqrt{a} \sqrt{c}}",1,"(2*Sqrt[1 + x]*ArcTan[(Sqrt[c]*Sqrt[1 + x])/Sqrt[c - c*x]])/(Sqrt[c]*Sqrt[a*(1 + x)])","A",1
1141,1,27,27,0.0174802,"\int \frac{1}{(a+a x)^{3/2} (c-c x)^{3/2}} \, dx","Integrate[1/((a + a*x)^(3/2)*(c - c*x)^(3/2)),x]","\frac{x (x+1)}{c (a (x+1))^{3/2} \sqrt{c-c x}}","\frac{x}{a c \sqrt{a x+a} \sqrt{c-c x}}",1,"(x*(1 + x))/(c*(a*(1 + x))^(3/2)*Sqrt[c - c*x])","A",1
1142,1,42,61,0.027998,"\int \frac{1}{(a+a x)^{5/2} (c-c x)^{5/2}} \, dx","Integrate[1/((a + a*x)^(5/2)*(c - c*x)^(5/2)),x]","\frac{x (x+1) \left(2 x^2-3\right)}{3 c^2 (x-1) (a (x+1))^{5/2} \sqrt{c-c x}}","\frac{2 x}{3 a^2 c^2 \sqrt{a x+a} \sqrt{c-c x}}+\frac{x}{3 a c (a x+a)^{3/2} (c-c x)^{3/2}}",1,"(x*(1 + x)*(-3 + 2*x^2))/(3*c^2*(-1 + x)*(a*(1 + x))^(5/2)*Sqrt[c - c*x])","A",1
1143,1,49,91,0.0358069,"\int \frac{1}{(a+a x)^{7/2} (c-c x)^{7/2}} \, dx","Integrate[1/((a + a*x)^(7/2)*(c - c*x)^(7/2)),x]","\frac{x \left(8 x^4-20 x^2+15\right)}{15 a^3 c^3 \left(x^2-1\right)^2 \sqrt{a (x+1)} \sqrt{c-c x}}","\frac{8 x}{15 a^3 c^3 \sqrt{a x+a} \sqrt{c-c x}}+\frac{4 x}{15 a^2 c^2 (a x+a)^{3/2} (c-c x)^{3/2}}+\frac{x}{5 a c (a x+a)^{5/2} (c-c x)^{5/2}}",1,"(x*(15 - 20*x^2 + 8*x^4))/(15*a^3*c^3*Sqrt[a*(1 + x)]*Sqrt[c - c*x]*(-1 + x^2)^2)","A",1
1144,1,54,121,0.0400001,"\int \frac{1}{(a+a x)^{9/2} (c-c x)^{9/2}} \, dx","Integrate[1/((a + a*x)^(9/2)*(c - c*x)^(9/2)),x]","\frac{x \left(16 x^6-56 x^4+70 x^2-35\right)}{35 a^4 c^4 \left(x^2-1\right)^3 \sqrt{a (x+1)} \sqrt{c-c x}}","\frac{16 x}{35 a^4 c^4 \sqrt{a x+a} \sqrt{c-c x}}+\frac{8 x}{35 a^3 c^3 (a x+a)^{3/2} (c-c x)^{3/2}}+\frac{6 x}{35 a^2 c^2 (a x+a)^{5/2} (c-c x)^{5/2}}+\frac{x}{7 a c (a x+a)^{7/2} (c-c x)^{7/2}}",1,"(x*(-35 + 70*x^2 - 56*x^4 + 16*x^6))/(35*a^4*c^4*Sqrt[a*(1 + x)]*Sqrt[c - c*x]*(-1 + x^2)^3)","A",1
1145,1,120,135,0.1501096,"\int (a+b x)^{5/2} (a c-b c x)^{5/2} \, dx","Integrate[(a + b*x)^(5/2)*(a*c - b*c*x)^(5/2),x]","\frac{c^3 \left(-30 a^{13/2} \sqrt{a-b x} \sqrt{\frac{b x}{a}+1} \sin ^{-1}\left(\frac{\sqrt{a-b x}}{\sqrt{2} \sqrt{a}}\right)+33 a^6 b x-59 a^4 b^3 x^3+34 a^2 b^5 x^5-8 b^7 x^7\right)}{48 b \sqrt{a+b x} \sqrt{c (a-b x)}}","\frac{5 a^6 c^{5/2} \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{c (a-b x)}}\right)}{8 b}+\frac{5}{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,"(c^3*(33*a^6*b*x - 59*a^4*b^3*x^3 + 34*a^2*b^5*x^5 - 8*b^7*x^7 - 30*a^(13/2)*Sqrt[a - b*x]*Sqrt[1 + (b*x)/a]*ArcSin[Sqrt[a - b*x]/(Sqrt[2]*Sqrt[a])]))/(48*b*Sqrt[c*(a - b*x)]*Sqrt[a + b*x])","A",1
1146,1,109,102,0.1266576,"\int (a+b x)^{3/2} (a c-b c x)^{3/2} \, dx","Integrate[(a + b*x)^(3/2)*(a*c - b*c*x)^(3/2),x]","\frac{c^2 \left(-6 a^{9/2} \sqrt{a-b x} \sqrt{\frac{b x}{a}+1} \sin ^{-1}\left(\frac{\sqrt{a-b x}}{\sqrt{2} \sqrt{a}}\right)+5 a^4 b x-7 a^2 b^3 x^3+2 b^5 x^5\right)}{8 b \sqrt{a+b x} \sqrt{c (a-b x)}}","\frac{3 a^4 c^{3/2} \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{c (a-b x)}}\right)}{4 b}+\frac{3}{8} a^2 c x \sqrt{a+b x} \sqrt{a c-b c x}+\frac{1}{4} x (a+b x)^{3/2} (a c-b c x)^{3/2}",1,"(c^2*(5*a^4*b*x - 7*a^2*b^3*x^3 + 2*b^5*x^5 - 6*a^(9/2)*Sqrt[a - b*x]*Sqrt[1 + (b*x)/a]*ArcSin[Sqrt[a - b*x]/(Sqrt[2]*Sqrt[a])]))/(8*b*Sqrt[c*(a - b*x)]*Sqrt[a + b*x])","A",1
1147,1,95,68,0.1234205,"\int \sqrt{a+b x} \sqrt{a c-b c x} \, dx","Integrate[Sqrt[a + b*x]*Sqrt[a*c - b*c*x],x]","\frac{c \left(-2 a^{5/2} \sqrt{a-b x} \sqrt{\frac{b x}{a}+1} \sin ^{-1}\left(\frac{\sqrt{a-b x}}{\sqrt{2} \sqrt{a}}\right)+a^2 b x-b^3 x^3\right)}{2 b \sqrt{a+b x} \sqrt{c (a-b x)}}","\frac{a^2 \sqrt{c} \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{c (a-b x)}}\right)}{b}+\frac{1}{2} x \sqrt{a+b x} \sqrt{a c-b c x}",1,"(c*(a^2*b*x - b^3*x^3 - 2*a^(5/2)*Sqrt[a - b*x]*Sqrt[1 + (b*x)/a]*ArcSin[Sqrt[a - b*x]/(Sqrt[2]*Sqrt[a])]))/(2*b*Sqrt[c*(a - b*x)]*Sqrt[a + b*x])","A",1
1148,1,48,38,0.0144264,"\int \frac{1}{\sqrt{a+b x} \sqrt{a c-b c x}} \, dx","Integrate[1/(Sqrt[a + b*x]*Sqrt[a*c - b*c*x]),x]","-\frac{2 \sqrt{a-b x} \tan ^{-1}\left(\frac{\sqrt{a-b x}}{\sqrt{a+b x}}\right)}{b \sqrt{c (a-b x)}}","\frac{2 \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{c (a-b x)}}\right)}{b \sqrt{c}}",1,"(-2*Sqrt[a - b*x]*ArcTan[Sqrt[a - b*x]/Sqrt[a + b*x]])/(b*Sqrt[c*(a - b*x)])","A",1
1149,1,29,30,0.0137852,"\int \frac{1}{(a+b x)^{3/2} (a c-b c x)^{3/2}} \, dx","Integrate[1/((a + b*x)^(3/2)*(a*c - b*c*x)^(3/2)),x]","\frac{x}{a^2 c \sqrt{a+b x} \sqrt{c (a-b x)}}","\frac{x}{a^2 c \sqrt{a+b x} \sqrt{a c-b c x}}",1,"x/(a^2*c*Sqrt[c*(a - b*x)]*Sqrt[a + b*x])","A",1
1150,1,46,67,0.0251795,"\int \frac{1}{(a+b x)^{5/2} (a c-b c x)^{5/2}} \, dx","Integrate[1/((a + b*x)^(5/2)*(a*c - b*c*x)^(5/2)),x]","\frac{3 a^2 x-2 b^2 x^3}{3 a^4 c (a+b x)^{3/2} (c (a-b x))^{3/2}}","\frac{2 x}{3 a^4 c^2 \sqrt{a+b x} \sqrt{a c-b c x}}+\frac{x}{3 a^2 c (a+b x)^{3/2} (a c-b c x)^{3/2}}",1,"(3*a^2*x - 2*b^2*x^3)/(3*a^4*c*(c*(a - b*x))^(3/2)*(a + b*x)^(3/2))","A",1
1151,1,57,100,0.0313639,"\int \frac{1}{(a+b x)^{7/2} (a c-b c x)^{7/2}} \, dx","Integrate[1/((a + b*x)^(7/2)*(a*c - b*c*x)^(7/2)),x]","\frac{15 a^4 x-20 a^2 b^2 x^3+8 b^4 x^5}{15 a^6 c (a+b x)^{5/2} (c (a-b x))^{5/2}}","\frac{8 x}{15 a^6 c^3 \sqrt{a+b x} \sqrt{a c-b c x}}+\frac{4 x}{15 a^4 c^2 (a+b x)^{3/2} (a c-b c x)^{3/2}}+\frac{x}{5 a^2 c (a+b x)^{5/2} (a c-b c x)^{5/2}}",1,"(15*a^4*x - 20*a^2*b^2*x^3 + 8*b^4*x^5)/(15*a^6*c*(c*(a - b*x))^(5/2)*(a + b*x)^(5/2))","A",1
1152,1,76,133,0.0410221,"\int \frac{1}{(a+b x)^{9/2} (a c-b c x)^{9/2}} \, dx","Integrate[1/((a + b*x)^(9/2)*(a*c - b*c*x)^(9/2)),x]","\frac{x \left(35 a^6-70 a^4 b^2 x^2+56 a^2 b^4 x^4-16 b^6 x^6\right) \sqrt{c (a-b x)}}{35 a^8 c^5 (a-b x)^4 (a+b x)^{7/2}}","\frac{16 x}{35 a^8 c^4 \sqrt{a+b x} \sqrt{a c-b c x}}+\frac{8 x}{35 a^6 c^3 (a+b x)^{3/2} (a c-b c x)^{3/2}}+\frac{6 x}{35 a^4 c^2 (a+b x)^{5/2} (a c-b c x)^{5/2}}+\frac{x}{7 a^2 c (a+b x)^{7/2} (a c-b c x)^{7/2}}",1,"(x*Sqrt[c*(a - b*x)]*(35*a^6 - 70*a^4*b^2*x^2 + 56*a^2*b^4*x^4 - 16*b^6*x^6))/(35*a^8*c^5*(a - b*x)^4*(a + b*x)^(7/2))","A",1
1153,1,44,100,0.0335539,"\int (3-6 x)^{5/2} (2+4 x)^{5/2} \, dx","Integrate[(3 - 6*x)^(5/2)*(2 + 4*x)^(5/2),x]","\frac{3}{4} \sqrt{\frac{3}{2}} \left(2 x \sqrt{1-4 x^2} \left(128 x^4-104 x^2+33\right)+15 \sin ^{-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,"(3*Sqrt[3/2]*(2*x*Sqrt[1 - 4*x^2]*(33 - 104*x^2 + 128*x^4) + 15*ArcSin[2*x]))/4","A",1
1154,1,39,74,0.0350006,"\int (3-6 x)^{3/2} (2+4 x)^{3/2} \, dx","Integrate[(3 - 6*x)^(3/2)*(2 + 4*x)^(3/2),x]","\frac{3}{4} \sqrt{\frac{3}{2}} \left(2 x \sqrt{1-4 x^2} \left(5-8 x^2\right)+3 \sin ^{-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,"(3*Sqrt[3/2]*(2*x*(5 - 8*x^2)*Sqrt[1 - 4*x^2] + 3*ArcSin[2*x]))/4","A",1
1155,1,30,43,0.0099046,"\int \sqrt{3-6 x} \sqrt{2+4 x} \, dx","Integrate[Sqrt[3 - 6*x]*Sqrt[2 + 4*x],x]","\frac{1}{2} \sqrt{\frac{3}{2}} \left(2 \sqrt{1-4 x^2} x+\sin ^{-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,"(Sqrt[3/2]*(2*x*Sqrt[1 - 4*x^2] + ArcSin[2*x]))/2","A",1
1156,1,13,13,0.0159446,"\int \frac{1}{\sqrt{3-6 x} \sqrt{2+4 x}} \, dx","Integrate[1/(Sqrt[3 - 6*x]*Sqrt[2 + 4*x]),x]","\frac{\sin ^{-1}(2 x)}{2 \sqrt{6}}","\frac{\sin ^{-1}(2 x)}{2 \sqrt{6}}",1,"ArcSin[2*x]/(2*Sqrt[6])","A",1
1157,1,16,28,0.0178434,"\int \frac{1}{(3-6 x)^{3/2} (2+4 x)^{3/2}} \, dx","Integrate[1/((3 - 6*x)^(3/2)*(2 + 4*x)^(3/2)),x]","\frac{x}{6 \sqrt{6-24 x^2}}","\frac{x}{6 \sqrt{6} \sqrt{1-2 x} \sqrt{2 x+1}}",1,"x/(6*Sqrt[6 - 24*x^2])","A",1
1158,1,37,57,0.0249007,"\int \frac{1}{(3-6 x)^{5/2} (2+4 x)^{5/2}} \, dx","Integrate[1/((3 - 6*x)^(5/2)*(2 + 4*x)^(5/2)),x]","\frac{x \left(8 x^2-3\right)}{108 \sqrt{6-12 x} (2 x-1) (2 x+1)^{3/2}}","\frac{x}{54 \sqrt{6} \sqrt{1-2 x} \sqrt{2 x+1}}+\frac{x}{108 \sqrt{6} (1-2 x)^{3/2} (2 x+1)^{3/2}}",1,"(x*(-3 + 8*x^2))/(108*Sqrt[6 - 12*x]*(-1 + 2*x)*(1 + 2*x)^(3/2))","A",1
1159,1,42,85,0.0315642,"\int \frac{1}{(3-6 x)^{7/2} (2+4 x)^{7/2}} \, dx","Integrate[1/((3 - 6*x)^(7/2)*(2 + 4*x)^(7/2)),x]","\frac{x \left(128 x^4-80 x^2+15\right)}{3240 \sqrt{6-12 x} (1-2 x)^2 (2 x+1)^{5/2}}","\frac{x}{405 \sqrt{6} \sqrt{1-2 x} \sqrt{2 x+1}}+\frac{x}{810 \sqrt{6} (1-2 x)^{3/2} (2 x+1)^{3/2}}+\frac{x}{1080 \sqrt{6} (1-2 x)^{5/2} (2 x+1)^{5/2}}",1,"(x*(15 - 80*x^2 + 128*x^4))/(3240*Sqrt[6 - 12*x]*(1 - 2*x)^2*(1 + 2*x)^(5/2))","A",1
1160,1,80,91,0.0474227,"\int (3-x)^{3/2} (-2+x)^{3/2} \, dx","Integrate[(3 - x)^(3/2)*(-2 + x)^(3/2),x]","\frac{\sqrt{-x^2+5 x-6} \left(\sqrt{x-2} \left(-16 x^4+168 x^3-650 x^2+1095 x-675\right)+3 \sqrt{3-x} \sin ^{-1}\left(\sqrt{3-x}\right)\right)}{64 (x-3) \sqrt{x-2}}","-\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[-6 + 5*x - x^2]*(Sqrt[-2 + x]*(-675 + 1095*x - 650*x^2 + 168*x^3 - 16*x^4) + 3*Sqrt[3 - x]*ArcSin[Sqrt[3 - x]]))/(64*(-3 + x)*Sqrt[-2 + x])","A",1
1161,1,69,51,0.0229604,"\int \sqrt{3-x} \sqrt{-2+x} \, dx","Integrate[Sqrt[3 - x]*Sqrt[-2 + x],x]","\frac{\sqrt{-x^2+5 x-6} \left(\sqrt{x-2} \left(2 x^2-11 x+15\right)+\sqrt{3-x} \sin ^{-1}\left(\sqrt{3-x}\right)\right)}{4 (x-3) \sqrt{x-2}}","-\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[-6 + 5*x - x^2]*(Sqrt[-2 + x]*(15 - 11*x + 2*x^2) + Sqrt[3 - x]*ArcSin[Sqrt[3 - x]]))/(4*(-3 + x)*Sqrt[-2 + x])","A",1
1162,1,12,8,0.0102608,"\int \frac{1}{\sqrt{3-x} \sqrt{-2+x}} \, dx","Integrate[1/(Sqrt[3 - x]*Sqrt[-2 + x]),x]","-2 \sin ^{-1}\left(\sqrt{3-x}\right)","-\sin ^{-1}(5-2 x)",1,"-2*ArcSin[Sqrt[3 - x]]","A",1
1163,1,21,37,0.0057612,"\int \frac{1}{(3-x)^{3/2} (-2+x)^{3/2}} \, dx","Integrate[1/((3 - x)^(3/2)*(-2 + x)^(3/2)),x]","\frac{2 (2 x-5)}{\sqrt{-x^2+5 x-6}}","\frac{2}{\sqrt{3-x} \sqrt{x-2}}-\frac{4 \sqrt{3-x}}{\sqrt{x-2}}",1,"(2*(-5 + 2*x))/Sqrt[-6 + 5*x - x^2]","A",1
1164,1,33,79,0.0133683,"\int \frac{1}{(3-x)^{5/2} (-2+x)^{5/2}} \, dx","Integrate[1/((3 - x)^(5/2)*(-2 + x)^(5/2)),x]","\frac{-32 x^3+240 x^2-588 x+470}{3 \left(-x^2+5 x-6\right)^{3/2}}","-\frac{32 \sqrt{3-x}}{3 \sqrt{x-2}}-\frac{16 \sqrt{3-x}}{3 (x-2)^{3/2}}+\frac{4}{(x-2)^{3/2} \sqrt{3-x}}+\frac{2}{3 (x-2)^{3/2} (3-x)^{3/2}}",1,"(470 - 588*x + 240*x^2 - 32*x^3)/(3*(-6 + 5*x - x^2)^(3/2))","A",1
1165,1,16,21,0.0046258,"\int \frac{1}{(3-x)^{3/2} (3+x)^{3/2}} \, dx","Integrate[1/((3 - x)^(3/2)*(3 + x)^(3/2)),x]","\frac{x}{9 \sqrt{9-x^2}}","\frac{x}{9 \sqrt{3-x} \sqrt{x+3}}",1,"x/(9*Sqrt[9 - x^2])","A",1
1166,1,19,24,0.00699,"\int \frac{1}{(3-b x)^{3/2} (3+b x)^{3/2}} \, dx","Integrate[1/((3 - b*x)^(3/2)*(3 + b*x)^(3/2)),x]","\frac{x}{9 \sqrt{9-b^2 x^2}}","\frac{x}{9 \sqrt{3-b x} \sqrt{b x+3}}",1,"x/(9*Sqrt[9 - b^2*x^2])","A",1
1167,1,21,26,0.0127698,"\int \frac{1}{(6-2 x)^{3/2} (3+x)^{3/2}} \, dx","Integrate[1/((6 - 2*x)^(3/2)*(3 + x)^(3/2)),x]","\frac{x}{18 \sqrt{6-2 x} \sqrt{x+3}}","\frac{x}{18 \sqrt{2} \sqrt{3-x} \sqrt{x+3}}",1,"x/(18*Sqrt[6 - 2*x]*Sqrt[3 + x])","A",1
1168,1,19,29,0.0175781,"\int \frac{1}{(6-2 b x)^{3/2} (3+b x)^{3/2}} \, dx","Integrate[1/((6 - 2*b*x)^(3/2)*(3 + b*x)^(3/2)),x]","\frac{x}{18 \sqrt{18-2 b^2 x^2}}","\frac{x}{18 \sqrt{2} \sqrt{3-b x} \sqrt{b x+3}}",1,"x/(18*Sqrt[18 - 2*b^2*x^2])","A",1
1169,1,39,39,0.0197701,"\int \frac{1}{\sqrt{a+b x} \sqrt{-a d+b d x}} \, dx","Integrate[1/(Sqrt[a + b*x]*Sqrt[-(a*d) + b*d*x]),x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b d x-a d}}\right)}{b \sqrt{d}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b d x-a d}}\right)}{b \sqrt{d}}",1,"(2*ArcTanh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[-(a*d) + b*d*x]])/(b*Sqrt[d])","A",1
1170,1,42,241,0.0209228,"\int \frac{1}{\sqrt[4]{6-3 e x} (2+e x)^{3/4}} \, dx","Integrate[1/((6 - 3*e*x)^(1/4)*(2 + e*x)^(3/4)),x]","-\frac{\sqrt{2} (6-3 e x)^{3/4} \, _2F_1\left(\frac{3}{4},\frac{3}{4};\frac{7}{4};\frac{1}{12} (6-3 e x)\right)}{9 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,"-1/9*(Sqrt[2]*(6 - 3*e*x)^(3/4)*Hypergeometric2F1[3/4, 3/4, 7/4, (6 - 3*e*x)/12])/e","C",1
1171,1,70,144,0.0356558,"\int \frac{(a-i a x)^{7/4}}{\sqrt[4]{a+i a x}} \, dx","Integrate[(a - I*a*x)^(7/4)/(a + I*a*x)^(1/4),x]","\frac{2 i 2^{3/4} \sqrt[4]{1+i x} (a-i a x)^{11/4} \, _2F_1\left(\frac{1}{4},\frac{11}{4};\frac{15}{4};\frac{1}{2}-\frac{i x}{2}\right)}{11 a \sqrt[4]{a+i a x}}","-\frac{14 a^2 \sqrt[4]{x^2+1} E\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{5 \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}+\frac{14 a^2 x}{5 \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}-\frac{14}{15} i (a-i a x)^{3/4} (a+i a x)^{3/4}-\frac{2 i (a-i a x)^{7/4} (a+i a x)^{3/4}}{5 a}",1,"(((2*I)/11)*2^(3/4)*(1 + I*x)^(1/4)*(a - I*a*x)^(11/4)*Hypergeometric2F1[1/4, 11/4, 15/4, 1/2 - (I/2)*x])/(a*(a + I*a*x)^(1/4))","C",1
1172,1,70,106,0.0232249,"\int \frac{(a-i a x)^{3/4}}{\sqrt[4]{a+i a x}} \, dx","Integrate[(a - I*a*x)^(3/4)/(a + I*a*x)^(1/4),x]","\frac{2 i 2^{3/4} \sqrt[4]{1+i x} (a-i a x)^{7/4} \, _2F_1\left(\frac{1}{4},\frac{7}{4};\frac{11}{4};\frac{1}{2}-\frac{i x}{2}\right)}{7 a \sqrt[4]{a+i a x}}","-\frac{2 a \sqrt[4]{x^2+1} E\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{\sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}+\frac{2 a x}{\sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}-\frac{2 i (a-i a x)^{3/4} (a+i a x)^{3/4}}{3 a}",1,"(((2*I)/7)*2^(3/4)*(1 + I*x)^(1/4)*(a - I*a*x)^(7/4)*Hypergeometric2F1[1/4, 7/4, 11/4, 1/2 - (I/2)*x])/(a*(a + I*a*x)^(1/4))","C",1
1173,1,70,71,0.0228341,"\int \frac{1}{\sqrt[4]{a-i a x} \sqrt[4]{a+i a x}} \, dx","Integrate[1/((a - I*a*x)^(1/4)*(a + I*a*x)^(1/4)),x]","\frac{2 i 2^{3/4} \sqrt[4]{1+i x} (a-i a x)^{3/4} \, _2F_1\left(\frac{1}{4},\frac{3}{4};\frac{7}{4};\frac{1}{2}-\frac{i x}{2}\right)}{3 a \sqrt[4]{a+i a x}}","\frac{2 x}{\sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}-\frac{2 \sqrt[4]{x^2+1} E\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{\sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}",1,"(((2*I)/3)*2^(3/4)*(1 + I*x)^(1/4)*(a - I*a*x)^(3/4)*Hypergeometric2F1[1/4, 3/4, 7/4, 1/2 - (I/2)*x])/(a*(a + I*a*x)^(1/4))","C",1
1174,1,68,78,0.0233199,"\int \frac{1}{(a-i a x)^{5/4} \sqrt[4]{a+i a x}} \, dx","Integrate[1/((a - I*a*x)^(5/4)*(a + I*a*x)^(1/4)),x]","-\frac{2 i 2^{3/4} \sqrt[4]{1+i x} \, _2F_1\left(-\frac{1}{4},\frac{1}{4};\frac{3}{4};\frac{1}{2}-\frac{i x}{2}\right)}{a \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}","\frac{2 \sqrt[4]{x^2+1} E\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{a \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}-\frac{2 i}{a \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}",1,"((-2*I)*2^(3/4)*(1 + I*x)^(1/4)*Hypergeometric2F1[-1/4, 1/4, 3/4, 1/2 - (I/2)*x])/(a*(a - I*a*x)^(1/4)*(a + I*a*x)^(1/4))","C",1
1175,1,70,82,0.0262293,"\int \frac{1}{(a-i a x)^{9/4} \sqrt[4]{a+i a x}} \, dx","Integrate[1/((a - I*a*x)^(9/4)*(a + I*a*x)^(1/4)),x]","-\frac{2 i 2^{3/4} \sqrt[4]{1+i x} \, _2F_1\left(-\frac{5}{4},\frac{1}{4};-\frac{1}{4};\frac{1}{2}-\frac{i x}{2}\right)}{5 a (a-i a x)^{5/4} \sqrt[4]{a+i a x}}","\frac{2 \sqrt[4]{x^2+1} E\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{5 a^2 \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}-\frac{4 i}{5 a (a-i a x)^{5/4} \sqrt[4]{a+i a x}}",1,"(((-2*I)/5)*2^(3/4)*(1 + I*x)^(1/4)*Hypergeometric2F1[-5/4, 1/4, -1/4, 1/2 - (I/2)*x])/(a*(a - I*a*x)^(5/4)*(a + I*a*x)^(1/4))","C",1
1176,1,70,115,0.0282342,"\int \frac{1}{(a-i a x)^{13/4} \sqrt[4]{a+i a x}} \, dx","Integrate[1/((a - I*a*x)^(13/4)*(a + I*a*x)^(1/4)),x]","-\frac{2 i 2^{3/4} \sqrt[4]{1+i x} \, _2F_1\left(-\frac{9}{4},\frac{1}{4};-\frac{5}{4};\frac{1}{2}-\frac{i x}{2}\right)}{9 a (a-i a x)^{9/4} \sqrt[4]{a+i a x}}","\frac{2 \sqrt[4]{x^2+1} E\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{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,"(((-2*I)/9)*2^(3/4)*(1 + I*x)^(1/4)*Hypergeometric2F1[-9/4, 1/4, -5/4, 1/2 - (I/2)*x])/(a*(a - I*a*x)^(9/4)*(a + I*a*x)^(1/4))","C",1
1177,1,70,148,0.0298331,"\int \frac{1}{(a-i a x)^{17/4} \sqrt[4]{a+i a x}} \, dx","Integrate[1/((a - I*a*x)^(17/4)*(a + I*a*x)^(1/4)),x]","-\frac{2 i 2^{3/4} \sqrt[4]{1+i x} \, _2F_1\left(-\frac{13}{4},\frac{1}{4};-\frac{9}{4};\frac{1}{2}-\frac{i x}{2}\right)}{13 a (a-i a x)^{13/4} \sqrt[4]{a+i a x}}","\frac{2 \sqrt[4]{x^2+1} E\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{39 a^4 \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}-\frac{10 i (a+i a x)^{3/4}}{117 a^3 (a-i a x)^{9/4}}-\frac{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,"(((-2*I)/13)*2^(3/4)*(1 + I*x)^(1/4)*Hypergeometric2F1[-13/4, 1/4, -9/4, 1/2 - (I/2)*x])/(a*(a - I*a*x)^(13/4)*(a + I*a*x)^(1/4))","C",1
1178,1,70,256,0.0212422,"\int \frac{\sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}} \, dx","Integrate[(a - I*a*x)^(1/4)/(a + I*a*x)^(1/4),x]","\frac{2 i 2^{3/4} \sqrt[4]{1+i x} (a-i a x)^{5/4} \, _2F_1\left(\frac{1}{4},\frac{5}{4};\frac{9}{4};\frac{1}{2}-\frac{i x}{2}\right)}{5 a \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,"(((2*I)/5)*2^(3/4)*(1 + I*x)^(1/4)*(a - I*a*x)^(5/4)*Hypergeometric2F1[1/4, 5/4, 9/4, 1/2 - (I/2)*x])/(a*(a + I*a*x)^(1/4))","C",1
1179,1,68,233,0.0232936,"\int \frac{1}{(a-i a x)^{3/4} \sqrt[4]{a+i a x}} \, dx","Integrate[1/((a - I*a*x)^(3/4)*(a + I*a*x)^(1/4)),x]","\frac{2 i 2^{3/4} \sqrt[4]{1+i x} \sqrt[4]{a-i a x} \, _2F_1\left(\frac{1}{4},\frac{1}{4};\frac{5}{4};\frac{1}{2}-\frac{i x}{2}\right)}{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,"((2*I)*2^(3/4)*(1 + I*x)^(1/4)*(a - I*a*x)^(1/4)*Hypergeometric2F1[1/4, 1/4, 5/4, 1/2 - (I/2)*x])/(a*(a + I*a*x)^(1/4))","C",1
1180,1,33,33,0.0143101,"\int \frac{1}{(a-i a x)^{7/4} \sqrt[4]{a+i a x}} \, dx","Integrate[1/((a - I*a*x)^(7/4)*(a + I*a*x)^(1/4)),x]","-\frac{2 i (a+i a x)^{3/4}}{3 a^2 (a-i a x)^{3/4}}","-\frac{2 i (a+i a x)^{3/4}}{3 a^2 (a-i a x)^{3/4}}",1,"(((-2*I)/3)*(a + I*a*x)^(3/4))/(a^2*(a - I*a*x)^(3/4))","A",1
1181,1,45,67,0.0210518,"\int \frac{1}{(a-i a x)^{11/4} \sqrt[4]{a+i a x}} \, dx","Integrate[1/((a - I*a*x)^(11/4)*(a + I*a*x)^(1/4)),x]","\frac{2 (5-2 i x) (a+i a x)^{3/4}}{21 a^3 (x+i) (a-i a x)^{3/4}}","-\frac{4 i (a+i a x)^{3/4}}{21 a^3 (a-i a x)^{3/4}}-\frac{2 i (a+i a x)^{3/4}}{7 a^2 (a-i a x)^{7/4}}",1,"(2*(5 - (2*I)*x)*(a + I*a*x)^(3/4))/(21*a^3*(I + x)*(a - I*a*x)^(3/4))","A",1
1182,1,52,100,0.0249602,"\int \frac{1}{(a-i a x)^{15/4} \sqrt[4]{a+i a x}} \, dx","Integrate[1/((a - I*a*x)^(15/4)*(a + I*a*x)^(1/4)),x]","\frac{2 \left(-8 i x^2+28 x+41 i\right) (a+i a x)^{3/4}}{231 a^4 (x+i)^2 (a-i a x)^{3/4}}","-\frac{16 i (a+i a x)^{3/4}}{231 a^4 (a-i a x)^{3/4}}-\frac{8 i (a+i a x)^{3/4}}{77 a^3 (a-i a x)^{7/4}}-\frac{2 i (a+i a x)^{3/4}}{11 a^2 (a-i a x)^{11/4}}",1,"(2*(a + I*a*x)^(3/4)*(41*I + 28*x - (8*I)*x^2))/(231*a^4*(I + x)^2*(a - I*a*x)^(3/4))","A",1
1183,1,57,133,0.0291329,"\int \frac{1}{(a-i a x)^{19/4} \sqrt[4]{a+i a x}} \, dx","Integrate[1/((a - I*a*x)^(19/4)*(a + I*a*x)^(1/4)),x]","\frac{2 \left(-16 i x^3+72 x^2+138 i x-159\right) (a+i a x)^{3/4}}{1155 a^5 (x+i)^3 (a-i a x)^{3/4}}","-\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*(a + I*a*x)^(3/4)*(-159 + (138*I)*x + 72*x^2 - (16*I)*x^3))/(1155*a^5*(I + x)^3*(a - I*a*x)^(3/4))","A",1
1184,1,70,256,0.0254999,"\int \frac{(a-i a x)^{3/4}}{(a+i a x)^{3/4}} \, dx","Integrate[(a - I*a*x)^(3/4)/(a + I*a*x)^(3/4),x]","\frac{2 i \sqrt[4]{2} (1+i x)^{3/4} (a-i a x)^{7/4} \, _2F_1\left(\frac{3}{4},\frac{7}{4};\frac{11}{4};\frac{1}{2}-\frac{i x}{2}\right)}{7 a (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,"(((2*I)/7)*2^(1/4)*(1 + I*x)^(3/4)*(a - I*a*x)^(7/4)*Hypergeometric2F1[3/4, 7/4, 11/4, 1/2 - (I/2)*x])/(a*(a + I*a*x)^(3/4))","C",1
1185,1,70,233,0.0233237,"\int \frac{1}{\sqrt[4]{a-i a x} (a+i a x)^{3/4}} \, dx","Integrate[1/((a - I*a*x)^(1/4)*(a + I*a*x)^(3/4)),x]","\frac{2 i \sqrt[4]{2} (1+i x)^{3/4} (a-i a x)^{3/4} \, _2F_1\left(\frac{3}{4},\frac{3}{4};\frac{7}{4};\frac{1}{2}-\frac{i x}{2}\right)}{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,"(((2*I)/3)*2^(1/4)*(1 + I*x)^(3/4)*(a - I*a*x)^(3/4)*Hypergeometric2F1[3/4, 3/4, 7/4, 1/2 - (I/2)*x])/(a*(a + I*a*x)^(3/4))","C",1
1186,1,31,31,0.0135117,"\int \frac{1}{(a-i a x)^{5/4} (a+i a x)^{3/4}} \, dx","Integrate[1/((a - I*a*x)^(5/4)*(a + I*a*x)^(3/4)),x]","-\frac{2 i \sqrt[4]{a+i a x}}{a^2 \sqrt[4]{a-i a x}}","-\frac{2 i \sqrt[4]{a+i a x}}{a^2 \sqrt[4]{a-i a x}}",1,"((-2*I)*(a + I*a*x)^(1/4))/(a^2*(a - I*a*x)^(1/4))","A",1
1187,1,45,67,0.0197274,"\int \frac{1}{(a-i a x)^{9/4} (a+i a x)^{3/4}} \, dx","Integrate[1/((a - I*a*x)^(9/4)*(a + I*a*x)^(3/4)),x]","\frac{2 (3-2 i x) \sqrt[4]{a+i a x}}{5 a^3 (x+i) \sqrt[4]{a-i a x}}","-\frac{4 i \sqrt[4]{a+i a x}}{5 a^3 \sqrt[4]{a-i a x}}-\frac{2 i \sqrt[4]{a+i a x}}{5 a^2 (a-i a x)^{5/4}}",1,"(2*(3 - (2*I)*x)*(a + I*a*x)^(1/4))/(5*a^3*(I + x)*(a - I*a*x)^(1/4))","A",1
1188,1,52,100,0.0240202,"\int \frac{1}{(a-i a x)^{13/4} (a+i a x)^{3/4}} \, dx","Integrate[1/((a - I*a*x)^(13/4)*(a + I*a*x)^(3/4)),x]","\frac{2 \left(-8 i x^2+20 x+17 i\right) \sqrt[4]{a+i a x}}{45 a^4 (x+i)^2 \sqrt[4]{a-i a x}}","-\frac{16 i \sqrt[4]{a+i a x}}{45 a^4 \sqrt[4]{a-i a x}}-\frac{8 i \sqrt[4]{a+i a x}}{45 a^3 (a-i a x)^{5/4}}-\frac{2 i \sqrt[4]{a+i a x}}{9 a^2 (a-i a x)^{9/4}}",1,"(2*(a + I*a*x)^(1/4)*(17*I + 20*x - (8*I)*x^2))/(45*a^4*(I + x)^2*(a - I*a*x)^(1/4))","A",1
1189,1,70,112,0.0265138,"\int \frac{(a-i a x)^{5/4}}{(a+i a x)^{3/4}} \, dx","Integrate[(a - I*a*x)^(5/4)/(a + I*a*x)^(3/4),x]","\frac{2 i \sqrt[4]{2} (1+i x)^{3/4} (a-i a x)^{9/4} \, _2F_1\left(\frac{3}{4},\frac{9}{4};\frac{13}{4};\frac{1}{2}-\frac{i x}{2}\right)}{9 a (a+i a x)^{3/4}}","\frac{10 a^2 \left(x^2+1\right)^{3/4} \operatorname{EllipticF}\left(\frac{1}{2} \tan ^{-1}(x),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,"(((2*I)/9)*2^(1/4)*(1 + I*x)^(3/4)*(a - I*a*x)^(9/4)*Hypergeometric2F1[3/4, 9/4, 13/4, 1/2 - (I/2)*x])/(a*(a + I*a*x)^(3/4))","C",1
1190,1,70,76,0.0220031,"\int \frac{\sqrt[4]{a-i a x}}{(a+i a x)^{3/4}} \, dx","Integrate[(a - I*a*x)^(1/4)/(a + I*a*x)^(3/4),x]","\frac{2 i \sqrt[4]{2} (1+i x)^{3/4} (a-i a x)^{5/4} \, _2F_1\left(\frac{3}{4},\frac{5}{4};\frac{9}{4};\frac{1}{2}-\frac{i x}{2}\right)}{5 a (a+i a x)^{3/4}}","\frac{2 a \left(x^2+1\right)^{3/4} \operatorname{EllipticF}\left(\frac{1}{2} \tan ^{-1}(x),2\right)}{(a-i a x)^{3/4} (a+i a x)^{3/4}}-\frac{2 i \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}{a}",1,"(((2*I)/5)*2^(1/4)*(1 + I*x)^(3/4)*(a - I*a*x)^(5/4)*Hypergeometric2F1[3/4, 5/4, 9/4, 1/2 - (I/2)*x])/(a*(a + I*a*x)^(3/4))","C",1
1191,1,68,43,0.0208269,"\int \frac{1}{(a-i a x)^{3/4} (a+i a x)^{3/4}} \, dx","Integrate[1/((a - I*a*x)^(3/4)*(a + I*a*x)^(3/4)),x]","\frac{2 i \sqrt[4]{2} (1+i x)^{3/4} \sqrt[4]{a-i a x} \, _2F_1\left(\frac{1}{4},\frac{3}{4};\frac{5}{4};\frac{1}{2}-\frac{i x}{2}\right)}{a (a+i a x)^{3/4}}","\frac{2 \left(x^2+1\right)^{3/4} \operatorname{EllipticF}\left(\frac{1}{2} \tan ^{-1}(x),2\right)}{(a-i a x)^{3/4} (a+i a x)^{3/4}}",1,"((2*I)*2^(1/4)*(1 + I*x)^(3/4)*(a - I*a*x)^(1/4)*Hypergeometric2F1[1/4, 3/4, 5/4, 1/2 - (I/2)*x])/(a*(a + I*a*x)^(3/4))","C",1
1192,1,70,82,0.0219917,"\int \frac{1}{(a-i a x)^{7/4} (a+i a x)^{3/4}} \, dx","Integrate[1/((a - I*a*x)^(7/4)*(a + I*a*x)^(3/4)),x]","-\frac{2 i \sqrt[4]{2} (1+i x)^{3/4} \, _2F_1\left(-\frac{3}{4},\frac{3}{4};\frac{1}{4};\frac{1}{2}-\frac{i x}{2}\right)}{3 a (a-i a x)^{3/4} (a+i a x)^{3/4}}","\frac{2 \left(x^2+1\right)^{3/4} \operatorname{EllipticF}\left(\frac{1}{2} \tan ^{-1}(x),2\right)}{3 a (a-i a x)^{3/4} (a+i a x)^{3/4}}-\frac{2 i \sqrt[4]{a+i a x}}{3 a^2 (a-i a x)^{3/4}}",1,"(((-2*I)/3)*2^(1/4)*(1 + I*x)^(3/4)*Hypergeometric2F1[-3/4, 3/4, 1/4, 1/2 - (I/2)*x])/(a*(a - I*a*x)^(3/4)*(a + I*a*x)^(3/4))","C",1
1193,1,70,115,0.0245985,"\int \frac{1}{(a-i a x)^{11/4} (a+i a x)^{3/4}} \, dx","Integrate[1/((a - I*a*x)^(11/4)*(a + I*a*x)^(3/4)),x]","-\frac{2 i \sqrt[4]{2} (1+i x)^{3/4} \, _2F_1\left(-\frac{7}{4},\frac{3}{4};-\frac{3}{4};\frac{1}{2}-\frac{i x}{2}\right)}{7 a (a-i a x)^{7/4} (a+i a x)^{3/4}}","\frac{2 \left(x^2+1\right)^{3/4} \operatorname{EllipticF}\left(\frac{1}{2} \tan ^{-1}(x),2\right)}{7 a^2 (a-i a x)^{3/4} (a+i a x)^{3/4}}-\frac{2 i \sqrt[4]{a+i a x}}{7 a^3 (a-i a x)^{3/4}}-\frac{2 i \sqrt[4]{a+i a x}}{7 a^2 (a-i a x)^{7/4}}",1,"(((-2*I)/7)*2^(1/4)*(1 + I*x)^(3/4)*Hypergeometric2F1[-7/4, 3/4, -3/4, 1/2 - (I/2)*x])/(a*(a - I*a*x)^(7/4)*(a + I*a*x)^(3/4))","C",1
1194,1,70,291,0.0284708,"\int \frac{(a-i a x)^{7/4}}{(a+i a x)^{7/4}} \, dx","Integrate[(a - I*a*x)^(7/4)/(a + I*a*x)^(7/4),x]","\frac{i \sqrt[4]{2} (1+i x)^{3/4} (a-i a x)^{11/4} \, _2F_1\left(\frac{7}{4},\frac{11}{4};\frac{15}{4};\frac{1}{2}-\frac{i x}{2}\right)}{11 a^2 (a+i a x)^{3/4}}","\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,"((I/11)*2^(1/4)*(1 + I*x)^(3/4)*(a - I*a*x)^(11/4)*Hypergeometric2F1[7/4, 11/4, 15/4, 1/2 - (I/2)*x])/(a^2*(a + I*a*x)^(3/4))","C",1
1195,1,70,266,0.0221782,"\int \frac{(a-i a x)^{3/4}}{(a+i a x)^{7/4}} \, dx","Integrate[(a - I*a*x)^(3/4)/(a + I*a*x)^(7/4),x]","\frac{i \sqrt[4]{2} (1+i x)^{3/4} (a-i a x)^{7/4} \, _2F_1\left(\frac{7}{4},\frac{7}{4};\frac{11}{4};\frac{1}{2}-\frac{i x}{2}\right)}{7 a^2 (a+i a x)^{3/4}}","\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,"((I/7)*2^(1/4)*(1 + I*x)^(3/4)*(a - I*a*x)^(7/4)*Hypergeometric2F1[7/4, 7/4, 11/4, 1/2 - (I/2)*x])/(a^2*(a + I*a*x)^(3/4))","C",1
1196,1,33,33,0.0115437,"\int \frac{1}{\sqrt[4]{a-i a x} (a+i a x)^{7/4}} \, dx","Integrate[1/((a - I*a*x)^(1/4)*(a + I*a*x)^(7/4)),x]","\frac{2 i (a-i a x)^{3/4}}{3 a^2 (a+i a x)^{3/4}}","\frac{2 i (a-i a x)^{3/4}}{3 a^2 (a+i a x)^{3/4}}",1,"(((2*I)/3)*(a - I*a*x)^(3/4))/(a^2*(a + I*a*x)^(3/4))","A",1
1197,1,38,65,0.0169913,"\int \frac{1}{(a-i a x)^{5/4} (a+i a x)^{7/4}} \, dx","Integrate[1/((a - I*a*x)^(5/4)*(a + I*a*x)^(7/4)),x]","\frac{4 x-2 i}{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*I + 4*x)/(3*a^2*(a - I*a*x)^(1/4)*(a + I*a*x)^(3/4))","A",1
1198,1,50,100,0.0228659,"\int \frac{1}{(a-i a x)^{9/4} (a+i a x)^{7/4}} \, dx","Integrate[1/((a - I*a*x)^(9/4)*(a + I*a*x)^(7/4)),x]","\frac{2 \left(8 x^2+4 i x+7\right)}{15 a^3 (x+i) \sqrt[4]{a-i a x} (a+i a x)^{3/4}}","\frac{16 i (a-i a x)^{3/4}}{15 a^4 (a+i a x)^{3/4}}-\frac{8 i}{5 a^3 (a+i a x)^{3/4} \sqrt[4]{a-i a x}}-\frac{2 i}{5 a^2 (a+i a x)^{3/4} (a-i a x)^{5/4}}",1,"(2*(7 + (4*I)*x + 8*x^2))/(15*a^3*(I + x)*(a - I*a*x)^(1/4)*(a + I*a*x)^(3/4))","A",1
1199,1,70,139,0.0305395,"\int \frac{(a-i a x)^{9/4}}{(a+i a x)^{7/4}} \, dx","Integrate[(a - I*a*x)^(9/4)/(a + I*a*x)^(7/4),x]","\frac{i \sqrt[4]{2} (1+i x)^{3/4} (a-i a x)^{13/4} \, _2F_1\left(\frac{7}{4},\frac{13}{4};\frac{17}{4};\frac{1}{2}-\frac{i x}{2}\right)}{13 a^2 (a+i a x)^{3/4}}","-\frac{10 a^2 \left(x^2+1\right)^{3/4} \operatorname{EllipticF}\left(\frac{1}{2} \tan ^{-1}(x),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,"((I/13)*2^(1/4)*(1 + I*x)^(3/4)*(a - I*a*x)^(13/4)*Hypergeometric2F1[7/4, 13/4, 17/4, 1/2 - (I/2)*x])/(a^2*(a + I*a*x)^(3/4))","C",1
1200,1,70,113,0.0264827,"\int \frac{(a-i a x)^{5/4}}{(a+i a x)^{7/4}} \, dx","Integrate[(a - I*a*x)^(5/4)/(a + I*a*x)^(7/4),x]","\frac{i \sqrt[4]{2} (1+i x)^{3/4} (a-i a x)^{9/4} \, _2F_1\left(\frac{7}{4},\frac{9}{4};\frac{13}{4};\frac{1}{2}-\frac{i x}{2}\right)}{9 a^2 (a+i a x)^{3/4}}","-\frac{10 a \left(x^2+1\right)^{3/4} \operatorname{EllipticF}\left(\frac{1}{2} \tan ^{-1}(x),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,"((I/9)*2^(1/4)*(1 + I*x)^(3/4)*(a - I*a*x)^(9/4)*Hypergeometric2F1[7/4, 9/4, 13/4, 1/2 - (I/2)*x])/(a^2*(a + I*a*x)^(3/4))","C",1
1201,1,70,79,0.0225394,"\int \frac{\sqrt[4]{a-i a x}}{(a+i a x)^{7/4}} \, dx","Integrate[(a - I*a*x)^(1/4)/(a + I*a*x)^(7/4),x]","\frac{i \sqrt[4]{2} (1+i x)^{3/4} (a-i a x)^{5/4} \, _2F_1\left(\frac{5}{4},\frac{7}{4};\frac{9}{4};\frac{1}{2}-\frac{i x}{2}\right)}{5 a^2 (a+i a x)^{3/4}}","\frac{4 i \sqrt[4]{a-i a x}}{3 a (a+i a x)^{3/4}}-\frac{2 \left(x^2+1\right)^{3/4} \operatorname{EllipticF}\left(\frac{1}{2} \tan ^{-1}(x),2\right)}{3 (a-i a x)^{3/4} (a+i a x)^{3/4}}",1,"((I/5)*2^(1/4)*(1 + I*x)^(3/4)*(a - I*a*x)^(5/4)*Hypergeometric2F1[5/4, 7/4, 9/4, 1/2 - (I/2)*x])/(a^2*(a + I*a*x)^(3/4))","C",1
1202,1,68,82,0.021288,"\int \frac{1}{(a-i a x)^{3/4} (a+i a x)^{7/4}} \, dx","Integrate[1/((a - I*a*x)^(3/4)*(a + I*a*x)^(7/4)),x]","\frac{i \sqrt[4]{2} (1+i x)^{3/4} \sqrt[4]{a-i a x} \, _2F_1\left(\frac{1}{4},\frac{7}{4};\frac{5}{4};\frac{1}{2}-\frac{i x}{2}\right)}{a^2 (a+i a x)^{3/4}}","\frac{2 \left(x^2+1\right)^{3/4} \operatorname{EllipticF}\left(\frac{1}{2} \tan ^{-1}(x),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,"(I*2^(1/4)*(1 + I*x)^(3/4)*(a - I*a*x)^(1/4)*Hypergeometric2F1[1/4, 7/4, 5/4, 1/2 - (I/2)*x])/(a^2*(a + I*a*x)^(3/4))","C",1
1203,1,70,81,0.0251312,"\int \frac{1}{(a-i a x)^{7/4} (a+i a x)^{7/4}} \, dx","Integrate[1/((a - I*a*x)^(7/4)*(a + I*a*x)^(7/4)),x]","-\frac{i \sqrt[4]{2} (1+i x)^{3/4} \, _2F_1\left(-\frac{3}{4},\frac{7}{4};\frac{1}{4};\frac{1}{2}-\frac{i x}{2}\right)}{3 a^2 (a-i a x)^{3/4} (a+i a x)^{3/4}}","\frac{2 \left(x^2+1\right)^{3/4} \operatorname{EllipticF}\left(\frac{1}{2} \tan ^{-1}(x),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,"((-1/3*I)*2^(1/4)*(1 + I*x)^(3/4)*Hypergeometric2F1[-3/4, 7/4, 1/4, 1/2 - (I/2)*x])/(a^2*(a - I*a*x)^(3/4)*(a + I*a*x)^(3/4))","C",1
1204,1,70,114,0.0236791,"\int \frac{1}{(a-i a x)^{11/4} (a+i a x)^{7/4}} \, dx","Integrate[1/((a - I*a*x)^(11/4)*(a + I*a*x)^(7/4)),x]","-\frac{i \sqrt[4]{2} (1+i x)^{3/4} \, _2F_1\left(-\frac{7}{4},\frac{7}{4};-\frac{3}{4};\frac{1}{2}-\frac{i x}{2}\right)}{7 a^2 (a-i a x)^{7/4} (a+i a x)^{3/4}}","\frac{10 \left(x^2+1\right)^{3/4} \operatorname{EllipticF}\left(\frac{1}{2} \tan ^{-1}(x),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,"((-1/7*I)*2^(1/4)*(1 + I*x)^(3/4)*Hypergeometric2F1[-7/4, 7/4, -3/4, 1/2 - (I/2)*x])/(a^2*(a - I*a*x)^(7/4)*(a + I*a*x)^(3/4))","C",1
1205,1,70,147,0.0278618,"\int \frac{1}{(a-i a x)^{15/4} (a+i a x)^{7/4}} \, dx","Integrate[1/((a - I*a*x)^(15/4)*(a + I*a*x)^(7/4)),x]","-\frac{i \sqrt[4]{2} (1+i x)^{3/4} \, _2F_1\left(-\frac{11}{4},\frac{7}{4};-\frac{7}{4};\frac{1}{2}-\frac{i x}{2}\right)}{11 a^2 (a-i a x)^{11/4} (a+i a x)^{3/4}}","\frac{10 \left(x^2+1\right)^{3/4} \operatorname{EllipticF}\left(\frac{1}{2} \tan ^{-1}(x),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,"((-1/11*I)*2^(1/4)*(1 + I*x)^(3/4)*Hypergeometric2F1[-11/4, 7/4, -7/4, 1/2 - (I/2)*x])/(a^2*(a - I*a*x)^(11/4)*(a + I*a*x)^(3/4))","C",1
1206,1,70,137,0.0304297,"\int \frac{(a-i a x)^{7/4}}{(a+i a x)^{5/4}} \, dx","Integrate[(a - I*a*x)^(7/4)/(a + I*a*x)^(5/4),x]","\frac{i 2^{3/4} \sqrt[4]{1+i x} (a-i a x)^{11/4} \, _2F_1\left(\frac{5}{4},\frac{11}{4};\frac{15}{4};\frac{1}{2}-\frac{i x}{2}\right)}{11 a^2 \sqrt[4]{a+i a x}}","\frac{14 a \sqrt[4]{x^2+1} E\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{\sqrt[4]{a+i a x} \sqrt[4]{a-i a x}}+\frac{4 i (a-i a x)^{7/4}}{a \sqrt[4]{a+i a x}}+\frac{14 i (a+i a x)^{3/4} (a-i a x)^{3/4}}{3 a}-\frac{14 a x}{\sqrt[4]{a+i a x} \sqrt[4]{a-i a x}}",1,"((I/11)*2^(3/4)*(1 + I*x)^(1/4)*(a - I*a*x)^(11/4)*Hypergeometric2F1[5/4, 11/4, 15/4, 1/2 - (I/2)*x])/(a^2*(a + I*a*x)^(1/4))","C",1
1207,1,70,102,0.0228756,"\int \frac{(a-i a x)^{3/4}}{(a+i a x)^{5/4}} \, dx","Integrate[(a - I*a*x)^(3/4)/(a + I*a*x)^(5/4),x]","\frac{i 2^{3/4} \sqrt[4]{1+i x} (a-i a x)^{7/4} \, _2F_1\left(\frac{5}{4},\frac{7}{4};\frac{11}{4};\frac{1}{2}-\frac{i x}{2}\right)}{7 a^2 \sqrt[4]{a+i a x}}","\frac{6 \sqrt[4]{x^2+1} E\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{\sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}-\frac{6 x}{\sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}+\frac{4 i (a-i a x)^{3/4}}{a \sqrt[4]{a+i a x}}",1,"((I/7)*2^(3/4)*(1 + I*x)^(1/4)*(a - I*a*x)^(7/4)*Hypergeometric2F1[5/4, 7/4, 11/4, 1/2 - (I/2)*x])/(a^2*(a + I*a*x)^(1/4))","C",1
1208,1,70,78,0.0222471,"\int \frac{1}{\sqrt[4]{a-i a x} (a+i a x)^{5/4}} \, dx","Integrate[1/((a - I*a*x)^(1/4)*(a + I*a*x)^(5/4)),x]","\frac{i 2^{3/4} \sqrt[4]{1+i x} (a-i a x)^{3/4} \, _2F_1\left(\frac{3}{4},\frac{5}{4};\frac{7}{4};\frac{1}{2}-\frac{i x}{2}\right)}{3 a^2 \sqrt[4]{a+i a x}}","\frac{2 \sqrt[4]{x^2+1} E\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{a \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}+\frac{2 i}{a \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}",1,"((I/3)*2^(3/4)*(1 + I*x)^(1/4)*(a - I*a*x)^(3/4)*Hypergeometric2F1[3/4, 5/4, 7/4, 1/2 - (I/2)*x])/(a^2*(a + I*a*x)^(1/4))","C",1
1209,1,68,46,0.0236328,"\int \frac{1}{(a-i a x)^{5/4} (a+i a x)^{5/4}} \, dx","Integrate[1/((a - I*a*x)^(5/4)*(a + I*a*x)^(5/4)),x]","-\frac{i 2^{3/4} \sqrt[4]{1+i x} \, _2F_1\left(-\frac{1}{4},\frac{5}{4};\frac{3}{4};\frac{1}{2}-\frac{i x}{2}\right)}{a^2 \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}","\frac{2 \sqrt[4]{x^2+1} E\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{a^2 \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}",1,"((-I)*2^(3/4)*(1 + I*x)^(1/4)*Hypergeometric2F1[-1/4, 5/4, 3/4, 1/2 - (I/2)*x])/(a^2*(a - I*a*x)^(1/4)*(a + I*a*x)^(1/4))","C",1
1210,1,70,82,0.0245577,"\int \frac{1}{(a-i a x)^{9/4} (a+i a x)^{5/4}} \, dx","Integrate[1/((a - I*a*x)^(9/4)*(a + I*a*x)^(5/4)),x]","-\frac{i 2^{3/4} \sqrt[4]{1+i x} \, _2F_1\left(-\frac{5}{4},\frac{5}{4};-\frac{1}{4};\frac{1}{2}-\frac{i x}{2}\right)}{5 a^2 (a-i a x)^{5/4} \sqrt[4]{a+i a x}}","\frac{6 \sqrt[4]{x^2+1} E\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{5 a^3 \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}-\frac{2 i}{5 a^2 (a-i a x)^{5/4} \sqrt[4]{a+i a x}}",1,"((-1/5*I)*2^(3/4)*(1 + I*x)^(1/4)*Hypergeometric2F1[-5/4, 5/4, -1/4, 1/2 - (I/2)*x])/(a^2*(a - I*a*x)^(5/4)*(a + I*a*x)^(1/4))","C",1
1211,1,70,115,0.0288824,"\int \frac{1}{(a-i a x)^{13/4} (a+i a x)^{5/4}} \, dx","Integrate[1/((a - I*a*x)^(13/4)*(a + I*a*x)^(5/4)),x]","-\frac{i 2^{3/4} \sqrt[4]{1+i x} \, _2F_1\left(-\frac{9}{4},\frac{5}{4};-\frac{5}{4};\frac{1}{2}-\frac{i x}{2}\right)}{9 a^2 (a-i a x)^{9/4} \sqrt[4]{a+i a x}}","\frac{2 \sqrt[4]{x^2+1} E\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{3 a^4 \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}-\frac{2 i}{9 a^3 (a-i a x)^{5/4} \sqrt[4]{a+i a x}}-\frac{2 i}{9 a^2 (a-i a x)^{9/4} \sqrt[4]{a+i a x}}",1,"((-1/9*I)*2^(3/4)*(1 + I*x)^(1/4)*Hypergeometric2F1[-9/4, 5/4, -5/4, 1/2 - (I/2)*x])/(a^2*(a - I*a*x)^(9/4)*(a + I*a*x)^(1/4))","C",1
1212,1,70,287,0.0290095,"\int \frac{(a-i a x)^{5/4}}{(a+i a x)^{5/4}} \, dx","Integrate[(a - I*a*x)^(5/4)/(a + I*a*x)^(5/4),x]","\frac{i 2^{3/4} \sqrt[4]{1+i x} (a-i a x)^{9/4} \, _2F_1\left(\frac{5}{4},\frac{9}{4};\frac{13}{4};\frac{1}{2}-\frac{i x}{2}\right)}{9 a^2 \sqrt[4]{a+i a x}}","\frac{4 i (a-i a x)^{5/4}}{a \sqrt[4]{a+i a x}}+\frac{5 i (a+i a x)^{3/4} \sqrt[4]{a-i a x}}{a}+\frac{5 i \log \left(\frac{\sqrt{a-i a x}}{\sqrt{a+i a x}}-\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}+1\right)}{2 \sqrt{2}}-\frac{5 i \log \left(\frac{\sqrt{a-i a x}}{\sqrt{a+i a x}}+\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}+1\right)}{2 \sqrt{2}}+\frac{5 i \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}\right)}{\sqrt{2}}-\frac{5 i \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}\right)}{\sqrt{2}}",1,"((I/9)*2^(3/4)*(1 + I*x)^(1/4)*(a - I*a*x)^(9/4)*Hypergeometric2F1[5/4, 9/4, 13/4, 1/2 - (I/2)*x])/(a^2*(a + I*a*x)^(1/4))","C",1
1213,1,70,264,0.0236803,"\int \frac{\sqrt[4]{a-i a x}}{(a+i a x)^{5/4}} \, dx","Integrate[(a - I*a*x)^(1/4)/(a + I*a*x)^(5/4),x]","\frac{i 2^{3/4} \sqrt[4]{1+i x} (a-i a x)^{5/4} \, _2F_1\left(\frac{5}{4},\frac{5}{4};\frac{9}{4};\frac{1}{2}-\frac{i x}{2}\right)}{5 a^2 \sqrt[4]{a+i a x}}","\frac{4 i \sqrt[4]{a-i a x}}{a \sqrt[4]{a+i a x}}+\frac{i \log \left(\frac{\sqrt{a-i a x}}{\sqrt{a+i a x}}-\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}+1\right)}{\sqrt{2} a}-\frac{i \log \left(\frac{\sqrt{a-i a x}}{\sqrt{a+i a x}}+\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}+1\right)}{\sqrt{2} a}+\frac{i \sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}\right)}{a}-\frac{i \sqrt{2} \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}\right)}{a}",1,"((I/5)*2^(3/4)*(1 + I*x)^(1/4)*(a - I*a*x)^(5/4)*Hypergeometric2F1[5/4, 5/4, 9/4, 1/2 - (I/2)*x])/(a^2*(a + I*a*x)^(1/4))","C",1
1214,1,31,31,0.0115742,"\int \frac{1}{(a-i a x)^{3/4} (a+i a x)^{5/4}} \, dx","Integrate[1/((a - I*a*x)^(3/4)*(a + I*a*x)^(5/4)),x]","\frac{2 i \sqrt[4]{a-i a x}}{a^2 \sqrt[4]{a+i a x}}","\frac{2 i \sqrt[4]{a-i a x}}{a^2 \sqrt[4]{a+i a x}}",1,"((2*I)*(a - I*a*x)^(1/4))/(a^2*(a + I*a*x)^(1/4))","A",1
1215,1,38,67,0.0175245,"\int \frac{1}{(a-i a x)^{7/4} (a+i a x)^{5/4}} \, dx","Integrate[1/((a - I*a*x)^(7/4)*(a + I*a*x)^(5/4)),x]","\frac{4 x+2 i}{3 a^2 (a-i a x)^{3/4} \sqrt[4]{a+i a x}}","\frac{4 i \sqrt[4]{a-i a x}}{3 a^3 \sqrt[4]{a+i a x}}-\frac{2 i}{3 a^2 (a-i a x)^{3/4} \sqrt[4]{a+i a x}}",1,"(2*I + 4*x)/(3*a^2*(a - I*a*x)^(3/4)*(a + I*a*x)^(1/4))","A",1
1216,1,50,100,0.0220779,"\int \frac{1}{(a-i a x)^{11/4} (a+i a x)^{5/4}} \, dx","Integrate[1/((a - I*a*x)^(11/4)*(a + I*a*x)^(5/4)),x]","\frac{16 x^2+24 i x-2}{21 a^3 (x+i) (a-i a x)^{3/4} \sqrt[4]{a+i a x}}","\frac{16 i \sqrt[4]{a-i a x}}{21 a^4 \sqrt[4]{a+i a x}}-\frac{8 i}{21 a^3 \sqrt[4]{a+i a x} (a-i a x)^{3/4}}-\frac{2 i}{7 a^2 \sqrt[4]{a+i a x} (a-i a x)^{7/4}}",1,"(-2 + (24*I)*x + 16*x^2)/(21*a^3*(I + x)*(a - I*a*x)^(3/4)*(a + I*a*x)^(1/4))","A",1
1217,1,70,141,0.0305564,"\int \frac{(a-i a x)^{7/4}}{(a+i a x)^{9/4}} \, dx","Integrate[(a - I*a*x)^(7/4)/(a + I*a*x)^(9/4),x]","\frac{i \sqrt[4]{1+i x} (a-i a x)^{11/4} \, _2F_1\left(\frac{9}{4},\frac{11}{4};\frac{15}{4};\frac{1}{2}-\frac{i x}{2}\right)}{11 \sqrt[4]{2} a^3 \sqrt[4]{a+i a x}}","-\frac{42 \sqrt[4]{x^2+1} E\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{5 \sqrt[4]{a+i a x} \sqrt[4]{a-i a x}}+\frac{4 i (a-i a x)^{7/4}}{5 a (a+i a x)^{5/4}}-\frac{28 i (a-i a x)^{3/4}}{5 a \sqrt[4]{a+i a x}}+\frac{42 x}{5 \sqrt[4]{a+i a x} \sqrt[4]{a-i a x}}",1,"((I/11)*(1 + I*x)^(1/4)*(a - I*a*x)^(11/4)*Hypergeometric2F1[9/4, 11/4, 15/4, 1/2 - (I/2)*x])/(2^(1/4)*a^3*(a + I*a*x)^(1/4))","C",1
1218,1,70,115,0.0236925,"\int \frac{(a-i a x)^{3/4}}{(a+i a x)^{9/4}} \, dx","Integrate[(a - I*a*x)^(3/4)/(a + I*a*x)^(9/4),x]","\frac{i \sqrt[4]{1+i x} (a-i a x)^{7/4} \, _2F_1\left(\frac{7}{4},\frac{9}{4};\frac{11}{4};\frac{1}{2}-\frac{i x}{2}\right)}{7 \sqrt[4]{2} a^3 \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 \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,"((I/7)*(1 + I*x)^(1/4)*(a - I*a*x)^(7/4)*Hypergeometric2F1[7/4, 9/4, 11/4, 1/2 - (I/2)*x])/(2^(1/4)*a^3*(a + I*a*x)^(1/4))","C",1
1219,1,70,82,0.0248297,"\int \frac{1}{\sqrt[4]{a-i a x} (a+i a x)^{9/4}} \, dx","Integrate[1/((a - I*a*x)^(1/4)*(a + I*a*x)^(9/4)),x]","\frac{i \sqrt[4]{1+i x} (a-i a x)^{3/4} \, _2F_1\left(\frac{3}{4},\frac{9}{4};\frac{7}{4};\frac{1}{2}-\frac{i x}{2}\right)}{3 \sqrt[4]{2} a^3 \sqrt[4]{a+i a x}}","\frac{2 \sqrt[4]{x^2+1} E\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{5 a^2 \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}+\frac{4 i}{5 a \sqrt[4]{a-i a x} (a+i a x)^{5/4}}",1,"((I/3)*(1 + I*x)^(1/4)*(a - I*a*x)^(3/4)*Hypergeometric2F1[3/4, 9/4, 7/4, 1/2 - (I/2)*x])/(2^(1/4)*a^3*(a + I*a*x)^(1/4))","C",1
1220,1,68,82,0.0266976,"\int \frac{1}{(a-i a x)^{5/4} (a+i a x)^{9/4}} \, dx","Integrate[1/((a - I*a*x)^(5/4)*(a + I*a*x)^(9/4)),x]","-\frac{i \sqrt[4]{1+i x} \, _2F_1\left(-\frac{1}{4},\frac{9}{4};\frac{3}{4};\frac{1}{2}-\frac{i x}{2}\right)}{\sqrt[4]{2} a^3 \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^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,"((-I)*(1 + I*x)^(1/4)*Hypergeometric2F1[-1/4, 9/4, 3/4, 1/2 - (I/2)*x])/(2^(1/4)*a^3*(a - I*a*x)^(1/4)*(a + I*a*x)^(1/4))","C",1
1221,1,70,88,0.0297497,"\int \frac{1}{(a-i a x)^{9/4} (a+i a x)^{9/4}} \, dx","Integrate[1/((a - I*a*x)^(9/4)*(a + I*a*x)^(9/4)),x]","-\frac{i \sqrt[4]{1+i x} \, _2F_1\left(-\frac{5}{4},\frac{9}{4};-\frac{1}{4};\frac{1}{2}-\frac{i x}{2}\right)}{5 \sqrt[4]{2} a^3 (a-i a x)^{5/4} \sqrt[4]{a+i a x}}","\frac{2 x}{5 a^4 \left(x^2+1\right) \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}+\frac{6 \sqrt[4]{x^2+1} E\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{5 a^4 \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}",1,"((-1/5*I)*(1 + I*x)^(1/4)*Hypergeometric2F1[-5/4, 9/4, -1/4, 1/2 - (I/2)*x])/(2^(1/4)*a^3*(a - I*a*x)^(5/4)*(a + I*a*x)^(1/4))","C",1
1222,1,70,121,0.0290397,"\int \frac{1}{(a-i a x)^{13/4} (a+i a x)^{9/4}} \, dx","Integrate[1/((a - I*a*x)^(13/4)*(a + I*a*x)^(9/4)),x]","-\frac{i \sqrt[4]{1+i x} \, _2F_1\left(-\frac{9}{4},\frac{9}{4};-\frac{5}{4};\frac{1}{2}-\frac{i x}{2}\right)}{9 \sqrt[4]{2} a^3 (a-i a x)^{9/4} \sqrt[4]{a+i a x}}","\frac{14 x}{45 a^5 \left(x^2+1\right) \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}+\frac{14 \sqrt[4]{x^2+1} E\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{15 a^5 \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}-\frac{2 i}{9 a^2 (a-i a x)^{9/4} (a+i a x)^{5/4}}",1,"((-1/9*I)*(1 + I*x)^(1/4)*Hypergeometric2F1[-9/4, 9/4, -5/4, 1/2 - (I/2)*x])/(2^(1/4)*a^3*(a - I*a*x)^(9/4)*(a + I*a*x)^(1/4))","C",1
1223,1,70,154,0.0360229,"\int \frac{1}{(a-i a x)^{17/4} (a+i a x)^{9/4}} \, dx","Integrate[1/((a - I*a*x)^(17/4)*(a + I*a*x)^(9/4)),x]","-\frac{i \sqrt[4]{1+i x} \, _2F_1\left(-\frac{13}{4},\frac{9}{4};-\frac{9}{4};\frac{1}{2}-\frac{i x}{2}\right)}{13 \sqrt[4]{2} a^3 (a-i a x)^{13/4} \sqrt[4]{a+i a x}}","\frac{14 x}{65 a^6 \left(x^2+1\right) \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}+\frac{42 \sqrt[4]{x^2+1} E\left(\left.\frac{1}{2} \tan ^{-1}(x)\right|2\right)}{65 a^6 \sqrt[4]{a-i a x} \sqrt[4]{a+i a x}}-\frac{2 i}{13 a^3 (a-i a x)^{9/4} (a+i a x)^{5/4}}-\frac{2 i}{13 a^2 (a-i a x)^{13/4} (a+i a x)^{5/4}}",1,"((-1/13*I)*(1 + I*x)^(1/4)*Hypergeometric2F1[-13/4, 9/4, -9/4, 1/2 - (I/2)*x])/(2^(1/4)*a^3*(a - I*a*x)^(13/4)*(a + I*a*x)^(1/4))","C",1
1224,1,70,297,0.0254254,"\int \frac{(a-i a x)^{5/4}}{(a+i a x)^{9/4}} \, dx","Integrate[(a - I*a*x)^(5/4)/(a + I*a*x)^(9/4),x]","\frac{i \sqrt[4]{1+i x} (a-i a x)^{9/4} \, _2F_1\left(\frac{9}{4},\frac{9}{4};\frac{13}{4};\frac{1}{2}-\frac{i x}{2}\right)}{9 \sqrt[4]{2} a^3 \sqrt[4]{a+i a x}}","\frac{4 i (a-i a x)^{5/4}}{5 a (a+i a x)^{5/4}}-\frac{4 i \sqrt[4]{a-i a x}}{a \sqrt[4]{a+i a x}}-\frac{i \log \left(\frac{\sqrt{a-i a x}}{\sqrt{a+i a x}}-\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}+1\right)}{\sqrt{2} a}+\frac{i \log \left(\frac{\sqrt{a-i a x}}{\sqrt{a+i a x}}+\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}+1\right)}{\sqrt{2} a}-\frac{i \sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}\right)}{a}+\frac{i \sqrt{2} \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{a-i a x}}{\sqrt[4]{a+i a x}}\right)}{a}",1,"((I/9)*(1 + I*x)^(1/4)*(a - I*a*x)^(9/4)*Hypergeometric2F1[9/4, 9/4, 13/4, 1/2 - (I/2)*x])/(2^(1/4)*a^3*(a + I*a*x)^(1/4))","C",1
1225,1,33,33,0.0124524,"\int \frac{\sqrt[4]{a-i a x}}{(a+i a x)^{9/4}} \, dx","Integrate[(a - I*a*x)^(1/4)/(a + I*a*x)^(9/4),x]","\frac{2 i (a-i a x)^{5/4}}{5 a^2 (a+i a x)^{5/4}}","\frac{2 i (a-i a x)^{5/4}}{5 a^2 (a+i a x)^{5/4}}",1,"(((2*I)/5)*(a - I*a*x)^(5/4))/(a^2*(a + I*a*x)^(5/4))","A",1
1226,1,45,67,0.0201271,"\int \frac{1}{(a-i a x)^{3/4} (a+i a x)^{9/4}} \, dx","Integrate[1/((a - I*a*x)^(3/4)*(a + I*a*x)^(9/4)),x]","\frac{2 (3+2 i x) \sqrt[4]{a-i a x}}{5 a^3 (x-i) \sqrt[4]{a+i a x}}","\frac{4 i \sqrt[4]{a-i a x}}{5 a^3 \sqrt[4]{a+i a x}}+\frac{2 i \sqrt[4]{a-i a x}}{5 a^2 (a+i a x)^{5/4}}",1,"(2*(3 + (2*I)*x)*(a - I*a*x)^(1/4))/(5*a^3*(-I + x)*(a + I*a*x)^(1/4))","A",1
1227,1,50,100,0.0228732,"\int \frac{1}{(a-i a x)^{7/4} (a+i a x)^{9/4}} \, dx","Integrate[1/((a - I*a*x)^(7/4)*(a + I*a*x)^(9/4)),x]","\frac{2 \left(8 x^2-4 i x+7\right)}{15 a^3 (x-i) (a-i a x)^{3/4} \sqrt[4]{a+i a x}}","\frac{16 i \sqrt[4]{a-i a x}}{15 a^4 \sqrt[4]{a+i a x}}+\frac{8 i \sqrt[4]{a-i a x}}{15 a^3 (a+i a x)^{5/4}}-\frac{2 i}{3 a^2 (a+i a x)^{5/4} (a-i a x)^{3/4}}",1,"(2*(7 - (4*I)*x + 8*x^2))/(15*a^3*(-I + x)*(a - I*a*x)^(3/4)*(a + I*a*x)^(1/4))","A",1
1228,1,57,133,0.0304559,"\int \frac{1}{(a-i a x)^{11/4} (a+i a x)^{9/4}} \, dx","Integrate[1/((a - I*a*x)^(11/4)*(a + I*a*x)^(9/4)),x]","\frac{2 \left(16 x^3+8 i x^2+22 x+9 i\right)}{35 a^4 \left(x^2+1\right) (a-i a x)^{3/4} \sqrt[4]{a+i a x}}","\frac{32 i \sqrt[4]{a-i a x}}{35 a^5 \sqrt[4]{a+i a x}}+\frac{16 i \sqrt[4]{a-i a x}}{35 a^4 (a+i a x)^{5/4}}-\frac{4 i}{7 a^3 (a+i a x)^{5/4} (a-i a x)^{3/4}}-\frac{2 i}{7 a^2 (a+i a x)^{5/4} (a-i a x)^{7/4}}",1,"(2*(9*I + 22*x + (8*I)*x^2 + 16*x^3))/(35*a^4*(a - I*a*x)^(3/4)*(a + I*a*x)^(1/4)*(1 + x^2))","A",1
1229,1,77,83,0.0432147,"\int (a+b x)^2 (a c-b c x)^n \, dx","Integrate[(a + b*x)^2*(a*c - b*c*x)^n,x]","\frac{(b x-a) \left(a^2 \left(n^2+7 n+14\right)+2 a b \left(n^2+5 n+4\right) x+b^2 \left(n^2+3 n+2\right) x^2\right) (c (a-b x))^n}{b (n+1) (n+2) (n+3)}","-\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,"((c*(a - b*x))^n*(-a + b*x)*(a^2*(14 + 7*n + n^2) + 2*a*b*(4 + 5*n + n^2)*x + b^2*(2 + 3*n + n^2)*x^2))/(b*(1 + n)*(2 + n)*(3 + n))","A",1
1230,1,43,53,0.02069,"\int (a+b x) (a c-b c x)^n \, dx","Integrate[(a + b*x)*(a*c - b*c*x)^n,x]","\frac{(b x-a) (a (n+3)+b (n+1) x) (c (a-b x))^n}{b (n+1) (n+2)}","\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,"((c*(a - b*x))^n*(-a + b*x)*(a*(3 + n) + b*(1 + n)*x))/(b*(1 + n)*(2 + n))","A",1
1231,1,52,52,0.0124015,"\int \frac{(a c-b c x)^n}{a+b x} \, dx","Integrate[(a*c - b*c*x)^n/(a + b*x),x]","-\frac{(a-b x) (c (a-b x))^n \, _2F_1\left(1,n+1;n+2;\frac{a-b x}{2 a}\right)}{2 a b (n+1)}","-\frac{(a c-b c x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{a-b x}{2 a}\right)}{2 a b c (n+1)}",1,"-1/2*((a - b*x)*(c*(a - b*x))^n*Hypergeometric2F1[1, 1 + n, 2 + n, (a - b*x)/(2*a)])/(a*b*(1 + n))","A",1
1232,1,52,52,0.0105049,"\int \frac{(a c-b c x)^n}{(a+b x)^2} \, dx","Integrate[(a*c - b*c*x)^n/(a + b*x)^2,x]","-\frac{(a-b x) (c (a-b x))^n \, _2F_1\left(2,n+1;n+2;\frac{a-b x}{2 a}\right)}{4 a^2 b (n+1)}","-\frac{(a c-b c x)^{n+1} \, _2F_1\left(2,n+1;n+2;\frac{a-b x}{2 a}\right)}{4 a^2 b c (n+1)}",1,"-1/4*((a - b*x)*(c*(a - b*x))^n*Hypergeometric2F1[2, 1 + n, 2 + n, (a - b*x)/(2*a)])/(a^2*b*(1 + n))","A",1
1233,1,53,41,0.0222853,"\int (a+a x)^m (c-c x)^m \, dx","Integrate[(a + a*x)^m*(c - c*x)^m,x]","\frac{2^m (x-1) (x+1)^{-m} (a (x+1))^m (c-c x)^m \, _2F_1\left(-m,m+1;m+2;\frac{1}{2}-\frac{x}{2}\right)}{m+1}","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,"(2^m*(-1 + x)*(a*(1 + x))^m*(c - c*x)^m*Hypergeometric2F1[-m, 1 + m, 2 + m, 1/2 - x/2])/((1 + m)*(1 + x)^m)","A",1
1234,1,72,57,0.0261818,"\int (a+b x)^m (a c-b c x)^m \, dx","Integrate[(a + b*x)^m*(a*c - b*c*x)^m,x]","-\frac{2^m (a-b x) (a+b x)^m \left(\frac{a+b x}{a}\right)^{-m} (c (a-b x))^m \, _2F_1\left(-m,m+1;m+2;\frac{a-b x}{2 a}\right)}{b (m+1)}","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,"-((2^m*(a - b*x)*(c*(a - b*x))^m*(a + b*x)^m*Hypergeometric2F1[-m, 1 + m, 2 + m, (a - b*x)/(2*a)])/(b*(1 + m)*((a + b*x)/a)^m))","A",1
1235,1,20,20,0.0055132,"\int (3-6 x)^m (2+4 x)^m \, dx","Integrate[(3 - 6*x)^m*(2 + 4*x)^m,x]","6^m x \, _2F_1\left(\frac{1}{2},-m;\frac{3}{2};4 x^2\right)","6^m x \, _2F_1\left(\frac{1}{2},-m;\frac{3}{2};4 x^2\right)",1,"6^m*x*Hypergeometric2F1[1/2, -m, 3/2, 4*x^2]","A",1
1236,1,84,38,0.0193969,"\int (a+b x)^4 (c+d x) \, dx","Integrate[(a + b*x)^4*(c + d*x),x]","\frac{1}{30} x \left(15 a^4 (2 c+d x)+20 a^3 b x (3 c+2 d x)+15 a^2 b^2 x^2 (4 c+3 d x)+6 a b^3 x^3 (5 c+4 d x)+b^4 x^4 (6 c+5 d x)\right)","\frac{(a+b x)^5 (b c-a d)}{5 b^2}+\frac{d (a+b x)^6}{6 b^2}",1,"(x*(15*a^4*(2*c + d*x) + 20*a^3*b*x*(3*c + 2*d*x) + 15*a^2*b^2*x^2*(4*c + 3*d*x) + 6*a*b^3*x^3*(5*c + 4*d*x) + b^4*x^4*(6*c + 5*d*x)))/30","B",1
1237,1,67,38,0.0108068,"\int (a+b x)^3 (c+d x) \, dx","Integrate[(a + b*x)^3*(c + d*x),x]","a^3 c x+\frac{1}{2} a^2 x^2 (a d+3 b c)+\frac{1}{4} b^2 x^4 (3 a d+b c)+a b x^3 (a d+b c)+\frac{1}{5} b^3 d x^5","\frac{(a+b x)^4 (b c-a d)}{4 b^2}+\frac{d (a+b x)^5}{5 b^2}",1,"a^3*c*x + (a^2*(3*b*c + a*d)*x^2)/2 + a*b*(b*c + a*d)*x^3 + (b^2*(b*c + 3*a*d)*x^4)/4 + (b^3*d*x^5)/5","A",1
1238,1,46,38,0.0080548,"\int (a+b x)^2 (c+d x) \, dx","Integrate[(a + b*x)^2*(c + d*x),x]","\frac{1}{12} x \left(6 a^2 (2 c+d x)+4 a b x (3 c+2 d x)+b^2 x^2 (4 c+3 d x)\right)","\frac{(a+b x)^3 (b c-a d)}{3 b^2}+\frac{d (a+b x)^4}{4 b^2}",1,"(x*(6*a^2*(2*c + d*x) + 4*a*b*x*(3*c + 2*d*x) + b^2*x^2*(4*c + 3*d*x)))/12","A",1
1239,1,28,28,0.0046335,"\int (a+b x) (c+d x) \, dx","Integrate[(a + b*x)*(c + d*x),x]","\frac{1}{2} x^2 (a d+b c)+a c x+\frac{1}{3} b d x^3","\frac{1}{2} x^2 (a d+b c)+a c x+\frac{1}{3} b d x^3",1,"a*c*x + ((b*c + a*d)*x^2)/2 + (b*d*x^3)/3","A",1
1240,1,12,12,0.0000767,"\int (c+d x) \, dx","Integrate[c + d*x,x]","c x+\frac{d x^2}{2}","c x+\frac{d x^2}{2}",1,"c*x + (d*x^2)/2","A",1
1241,1,25,25,0.0081967,"\int \frac{c+d x}{a+b x} \, dx","Integrate[(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
1242,1,31,32,0.011527,"\int \frac{c+d x}{(a+b x)^2} \, dx","Integrate[(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
1243,1,26,28,0.009441,"\int \frac{c+d x}{(a+b x)^3} \, dx","Integrate[(c + d*x)/(a + b*x)^3,x]","-\frac{a d+b (c+2 d x)}{2 b^2 (a+b x)^2}","-\frac{(c+d x)^2}{2 (a+b x)^2 (b c-a d)}",1,"-1/2*(a*d + b*(c + 2*d*x))/(b^2*(a + b*x)^2)","A",1
1244,1,27,38,0.008759,"\int \frac{c+d x}{(a+b x)^4} \, dx","Integrate[(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,"-1/6*(2*b*c + a*d + 3*b*d*x)/(b^2*(a + b*x)^3)","A",1
1245,1,27,38,0.0096284,"\int \frac{c+d x}{(a+b x)^5} \, dx","Integrate[(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,"-1/12*(3*b*c + a*d + 4*b*d*x)/(b^2*(a + b*x)^4)","A",1
1246,1,148,65,0.0274003,"\int (a+b x)^4 (c+d x)^2 \, dx","Integrate[(a + b*x)^4*(c + d*x)^2,x]","a^4 c^2 x+a^3 c x^2 (a d+2 b c)+\frac{1}{5} b^2 x^5 \left(6 a^2 d^2+8 a b c d+b^2 c^2\right)+a b x^4 \left(a^2 d^2+3 a b c d+b^2 c^2\right)+\frac{1}{3} a^2 x^3 \left(a^2 d^2+8 a b c d+6 b^2 c^2\right)+\frac{1}{3} b^3 d x^6 (2 a d+b c)+\frac{1}{7} b^4 d^2 x^7","\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,"a^4*c^2*x + a^3*c*(2*b*c + a*d)*x^2 + (a^2*(6*b^2*c^2 + 8*a*b*c*d + a^2*d^2)*x^3)/3 + a*b*(b^2*c^2 + 3*a*b*c*d + a^2*d^2)*x^4 + (b^2*(b^2*c^2 + 8*a*b*c*d + 6*a^2*d^2)*x^5)/5 + (b^3*d*(b*c + 2*a*d)*x^6)/3 + (b^4*d^2*x^7)/7","B",1
1247,1,122,65,0.0154948,"\int (a+b x)^3 (c+d x)^2 \, dx","Integrate[(a + b*x)^3*(c + d*x)^2,x]","a^3 c^2 x+\frac{1}{4} b x^4 \left(3 a^2 d^2+6 a b c d+b^2 c^2\right)+\frac{1}{3} a x^3 \left(a^2 d^2+6 a b c d+3 b^2 c^2\right)+\frac{1}{2} a^2 c x^2 (2 a d+3 b c)+\frac{1}{5} b^2 d x^5 (3 a d+2 b c)+\frac{1}{6} b^3 d^2 x^6","\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,"a^3*c^2*x + (a^2*c*(3*b*c + 2*a*d)*x^2)/2 + (a*(3*b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^3)/3 + (b*(b^2*c^2 + 6*a*b*c*d + 3*a^2*d^2)*x^4)/4 + (b^2*d*(2*b*c + 3*a*d)*x^5)/5 + (b^3*d^2*x^6)/6","A",1
1248,1,79,65,0.0112132,"\int (a+b x)^2 (c+d x)^2 \, dx","Integrate[(a + b*x)^2*(c + d*x)^2,x]","\frac{1}{3} x^3 \left(a^2 d^2+4 a b c d+b^2 c^2\right)+a^2 c^2 x+\frac{1}{2} b d x^4 (a d+b c)+a c x^2 (a d+b c)+\frac{1}{5} b^2 d^2 x^5","\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,"a^2*c^2*x + a*c*(b*c + a*d)*x^2 + ((b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^3)/3 + (b*d*(b*c + a*d)*x^4)/2 + (b^2*d^2*x^5)/5","A",1
1249,1,47,38,0.0101916,"\int (a+b x) (c+d x)^2 \, dx","Integrate[(a + b*x)*(c + d*x)^2,x]","\frac{1}{12} x \left(4 d x^2 (a d+2 b c)+6 c x (2 a d+b c)+12 a c^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*c*(b*c + 2*a*d)*x + 4*d*(2*b*c + a*d)*x^2 + 3*b*d^2*x^3))/12","A",1
1250,1,14,14,0.0015072,"\int (c+d x)^2 \, dx","Integrate[(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
1251,1,43,49,0.0179053,"\int \frac{(c+d x)^2}{a+b x} \, dx","Integrate[(c + d*x)^2/(a + b*x),x]","\frac{b d x (-2 a d+4 b c+b d x)+2 (b c-a d)^2 \log (a+b x)}{2 b^3}","\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,"(b*d*x*(4*b*c - 2*a*d + b*d*x) + 2*(b*c - a*d)^2*Log[a + b*x])/(2*b^3)","A",1
1252,1,47,51,0.037008,"\int \frac{(c+d x)^2}{(a+b x)^2} \, dx","Integrate[(c + d*x)^2/(a + b*x)^2,x]","\frac{-\frac{(b c-a d)^2}{a+b x}+2 d (b c-a d) \log (a+b x)+b d^2 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*d^2*x - (b*c - a*d)^2/(a + b*x) + 2*d*(b*c - a*d)*Log[a + b*x])/b^3","A",1
1253,1,49,59,0.0245228,"\int \frac{(c+d x)^2}{(a+b x)^3} \, dx","Integrate[(c + d*x)^2/(a + b*x)^3,x]","\frac{2 d^2 \log (a+b x)-\frac{(b c-a d) (3 a d+b (c+4 d x))}{(a+b x)^2}}{2 b^3}","-\frac{2 d (b c-a d)}{b^3 (a+b x)}-\frac{(b c-a d)^2}{2 b^3 (a+b x)^2}+\frac{d^2 \log (a+b x)}{b^3}",1,"(-(((b*c - a*d)*(3*a*d + b*(c + 4*d*x)))/(a + b*x)^2) + 2*d^2*Log[a + b*x])/(2*b^3)","A",1
1254,1,53,28,0.0222773,"\int \frac{(c+d x)^2}{(a+b x)^4} \, dx","Integrate[(c + d*x)^2/(a + b*x)^4,x]","-\frac{a^2 d^2+a b d (c+3 d x)+b^2 \left(c^2+3 c d x+3 d^2 x^2\right)}{3 b^3 (a+b x)^3}","-\frac{(c+d x)^3}{3 (a+b x)^3 (b c-a d)}",1,"-1/3*(a^2*d^2 + a*b*d*(c + 3*d*x) + b^2*(c^2 + 3*c*d*x + 3*d^2*x^2))/(b^3*(a + b*x)^3)","A",1
1255,1,56,65,0.0187018,"\int \frac{(c+d x)^2}{(a+b x)^5} \, dx","Integrate[(c + d*x)^2/(a + b*x)^5,x]","-\frac{a^2 d^2+2 a b d (c+2 d x)+b^2 \left(3 c^2+8 c d x+6 d^2 x^2\right)}{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,"-1/12*(a^2*d^2 + 2*a*b*d*(c + 2*d*x) + b^2*(3*c^2 + 8*c*d*x + 6*d^2*x^2))/(b^3*(a + b*x)^4)","A",1
1256,1,57,65,0.0244699,"\int \frac{(c+d x)^2}{(a+b x)^6} \, dx","Integrate[(c + d*x)^2/(a + b*x)^6,x]","-\frac{a^2 d^2+a b d (3 c+5 d x)+b^2 \left(6 c^2+15 c d x+10 d^2 x^2\right)}{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,"-1/30*(a^2*d^2 + a*b*d*(3*c + 5*d*x) + b^2*(6*c^2 + 15*c*d*x + 10*d^2*x^2))/(b^3*(a + b*x)^5)","A",1
1257,1,58,65,0.0203785,"\int \frac{(c+d x)^2}{(a+b x)^7} \, dx","Integrate[(c + d*x)^2/(a + b*x)^7,x]","-\frac{a^2 d^2+2 a b d (2 c+3 d x)+b^2 \left(10 c^2+24 c d x+15 d^2 x^2\right)}{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,"-1/60*(a^2*d^2 + 2*a*b*d*(2*c + 3*d*x) + b^2*(10*c^2 + 24*c*d*x + 15*d^2*x^2))/(b^3*(a + b*x)^6)","A",1
1258,1,235,92,0.0753344,"\int (a+b x)^5 (c+d x)^3 \, dx","Integrate[(a + b*x)^5*(c + d*x)^3,x]","\frac{1}{504} x \left(126 a^5 \left(4 c^3+6 c^2 d x+4 c d^2 x^2+d^3 x^3\right)+126 a^4 b x \left(10 c^3+20 c^2 d x+15 c d^2 x^2+4 d^3 x^3\right)+84 a^3 b^2 x^2 \left(20 c^3+45 c^2 d x+36 c d^2 x^2+10 d^3 x^3\right)+36 a^2 b^3 x^3 \left(35 c^3+84 c^2 d x+70 c d^2 x^2+20 d^3 x^3\right)+9 a b^4 x^4 \left(56 c^3+140 c^2 d x+120 c d^2 x^2+35 d^3 x^3\right)+b^5 x^5 \left(84 c^3+216 c^2 d x+189 c d^2 x^2+56 d^3 x^3\right)\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,"(x*(126*a^5*(4*c^3 + 6*c^2*d*x + 4*c*d^2*x^2 + d^3*x^3) + 126*a^4*b*x*(10*c^3 + 20*c^2*d*x + 15*c*d^2*x^2 + 4*d^3*x^3) + 84*a^3*b^2*x^2*(20*c^3 + 45*c^2*d*x + 36*c*d^2*x^2 + 10*d^3*x^3) + 36*a^2*b^3*x^3*(35*c^3 + 84*c^2*d*x + 70*c*d^2*x^2 + 20*d^3*x^3) + 9*a*b^4*x^4*(56*c^3 + 140*c^2*d*x + 120*c*d^2*x^2 + 35*d^3*x^3) + b^5*x^5*(84*c^3 + 216*c^2*d*x + 189*c*d^2*x^2 + 56*d^3*x^3)))/504","B",1
1259,1,217,92,0.0286618,"\int (a+b x)^4 (c+d x)^3 \, dx","Integrate[(a + b*x)^4*(c + d*x)^3,x]","a^4 c^3 x+\frac{1}{2} a^3 c^2 x^2 (3 a d+4 b c)+\frac{1}{2} b^2 d x^6 \left(2 a^2 d^2+4 a b c d+b^2 c^2\right)+a^2 c x^3 \left(a^2 d^2+4 a b c d+2 b^2 c^2\right)+\frac{1}{5} b x^5 \left(4 a^3 d^3+18 a^2 b c d^2+12 a b^2 c^2 d+b^3 c^3\right)+\frac{1}{4} a x^4 \left(a^3 d^3+12 a^2 b c d^2+18 a b^2 c^2 d+4 b^3 c^3\right)+\frac{1}{7} b^3 d^2 x^7 (4 a d+3 b c)+\frac{1}{8} b^4 d^3 x^8","\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,"a^4*c^3*x + (a^3*c^2*(4*b*c + 3*a*d)*x^2)/2 + a^2*c*(2*b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^3 + (a*(4*b^3*c^3 + 18*a*b^2*c^2*d + 12*a^2*b*c*d^2 + a^3*d^3)*x^4)/4 + (b*(b^3*c^3 + 12*a*b^2*c^2*d + 18*a^2*b*c*d^2 + 4*a^3*d^3)*x^5)/5 + (b^2*d*(b^2*c^2 + 4*a*b*c*d + 2*a^2*d^2)*x^6)/2 + (b^3*d^2*(3*b*c + 4*a*d)*x^7)/7 + (b^4*d^3*x^8)/8","B",1
1260,1,161,92,0.0191721,"\int (a+b x)^3 (c+d x)^3 \, dx","Integrate[(a + b*x)^3*(c + d*x)^3,x]","a^3 c^3 x+\frac{3}{5} b d x^5 \left(a^2 d^2+3 a b c d+b^2 c^2\right)+a c x^3 \left(a^2 d^2+3 a b c d+b^2 c^2\right)+\frac{3}{2} a^2 c^2 x^2 (a d+b c)+\frac{1}{4} x^4 \left(a^3 d^3+9 a^2 b c d^2+9 a b^2 c^2 d+b^3 c^3\right)+\frac{1}{2} b^2 d^2 x^6 (a d+b c)+\frac{1}{7} b^3 d^3 x^7","\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,"a^3*c^3*x + (3*a^2*c^2*(b*c + a*d)*x^2)/2 + a*c*(b^2*c^2 + 3*a*b*c*d + a^2*d^2)*x^3 + ((b^3*c^3 + 9*a*b^2*c^2*d + 9*a^2*b*c*d^2 + a^3*d^3)*x^4)/4 + (3*b*d*(b^2*c^2 + 3*a*b*c*d + a^2*d^2)*x^5)/5 + (b^2*d^2*(b*c + a*d)*x^6)/2 + (b^3*d^3*x^7)/7","A",1
1261,1,122,65,0.0135985,"\int (a+b x)^2 (c+d x)^3 \, dx","Integrate[(a + b*x)^2*(c + d*x)^3,x]","\frac{1}{4} d x^4 \left(a^2 d^2+6 a b c d+3 b^2 c^2\right)+\frac{1}{3} c x^3 \left(3 a^2 d^2+6 a b c d+b^2 c^2\right)+a^2 c^3 x+\frac{1}{2} a c^2 x^2 (3 a d+2 b c)+\frac{1}{5} b d^2 x^5 (2 a d+3 b c)+\frac{1}{6} b^2 d^3 x^6","-\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,"a^2*c^3*x + (a*c^2*(2*b*c + 3*a*d)*x^2)/2 + (c*(b^2*c^2 + 6*a*b*c*d + 3*a^2*d^2)*x^3)/3 + (d*(3*b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^4)/4 + (b*d^2*(3*b*c + 2*a*d)*x^5)/5 + (b^2*d^3*x^6)/6","A",1
1262,1,67,38,0.0083951,"\int (a+b x) (c+d x)^3 \, dx","Integrate[(a + b*x)*(c + d*x)^3,x]","\frac{1}{2} c^2 x^2 (3 a d+b c)+\frac{1}{4} d^2 x^4 (a d+3 b c)+c d x^3 (a d+b c)+a c^3 x+\frac{1}{5} b d^3 x^5","\frac{b (c+d x)^5}{5 d^2}-\frac{(c+d x)^4 (b c-a d)}{4 d^2}",1,"a*c^3*x + (c^2*(b*c + 3*a*d)*x^2)/2 + c*d*(b*c + a*d)*x^3 + (d^2*(3*b*c + a*d)*x^4)/4 + (b*d^3*x^5)/5","A",1
1263,1,14,14,0.0014537,"\int (c+d x)^3 \, dx","Integrate[(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
1264,1,74,73,0.0308353,"\int \frac{(c+d x)^3}{a+b x} \, dx","Integrate[(c + d*x)^3/(a + b*x),x]","\frac{b d x \left(6 a^2 d^2-3 a b d (6 c+d x)+b^2 \left(18 c^2+9 c d x+2 d^2 x^2\right)\right)+6 (b c-a d)^3 \log (a+b x)}{6 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,"(b*d*x*(6*a^2*d^2 - 3*a*b*d*(6*c + d*x) + b^2*(18*c^2 + 9*c*d*x + 2*d^2*x^2)) + 6*(b*c - a*d)^3*Log[a + b*x])/(6*b^4)","A",1
1265,1,72,75,0.0513357,"\int \frac{(c+d x)^3}{(a+b x)^2} \, dx","Integrate[(c + d*x)^3/(a + b*x)^2,x]","\frac{2 b d^2 x (3 b c-2 a d)-\frac{2 (b c-a d)^3}{a+b x}+6 d (b c-a d)^2 \log (a+b x)+b^2 d^3 x^2}{2 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*d^2*(3*b*c - 2*a*d)*x + b^2*d^3*x^2 - (2*(b*c - a*d)^3)/(a + b*x) + 6*d*(b*c - a*d)^2*Log[a + b*x])/(2*b^4)","A",1
1266,1,114,78,0.0424881,"\int \frac{(c+d x)^3}{(a+b x)^3} \, dx","Integrate[(c + d*x)^3/(a + b*x)^3,x]","\frac{-5 a^3 d^3+a^2 b d^2 (9 c-4 d x)+a b^2 d \left(-3 c^2+12 c d x+4 d^2 x^2\right)-6 d^2 (a+b x)^2 (a d-b c) \log (a+b x)-\left(b^3 \left(c^3+6 c^2 d x-2 d^3 x^3\right)\right)}{2 b^4 (a+b x)^2}","\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,"(-5*a^3*d^3 + a^2*b*d^2*(9*c - 4*d*x) + a*b^2*d*(-3*c^2 + 12*c*d*x + 4*d^2*x^2) - b^3*(c^3 + 6*c^2*d*x - 2*d^3*x^3) - 6*d^2*(-(b*c) + a*d)*(a + b*x)^2*Log[a + b*x])/(2*b^4*(a + b*x)^2)","A",1
1267,1,80,86,0.0410862,"\int \frac{(c+d x)^3}{(a+b x)^4} \, dx","Integrate[(c + d*x)^3/(a + b*x)^4,x]","\frac{6 d^3 \log (a+b x)-\frac{(b c-a d) \left(11 a^2 d^2+a b d (5 c+27 d x)+b^2 \left(2 c^2+9 c d x+18 d^2 x^2\right)\right)}{(a+b x)^3}}{6 b^4}","-\frac{3 d^2 (b c-a d)}{b^4 (a+b x)}-\frac{3 d (b c-a d)^2}{2 b^4 (a+b x)^2}-\frac{(b c-a d)^3}{3 b^4 (a+b x)^3}+\frac{d^3 \log (a+b x)}{b^4}",1,"(-(((b*c - a*d)*(11*a^2*d^2 + a*b*d*(5*c + 27*d*x) + b^2*(2*c^2 + 9*c*d*x + 18*d^2*x^2)))/(a + b*x)^3) + 6*d^3*Log[a + b*x])/(6*b^4)","A",1
1268,1,91,28,0.0307926,"\int \frac{(c+d x)^3}{(a+b x)^5} \, dx","Integrate[(c + d*x)^3/(a + b*x)^5,x]","-\frac{a^3 d^3+a^2 b d^2 (c+4 d x)+a b^2 d \left(c^2+4 c d x+6 d^2 x^2\right)+b^3 \left(c^3+4 c^2 d x+6 c d^2 x^2+4 d^3 x^3\right)}{4 b^4 (a+b x)^4}","-\frac{(c+d x)^4}{4 (a+b x)^4 (b c-a d)}",1,"-1/4*(a^3*d^3 + a^2*b*d^2*(c + 4*d*x) + a*b^2*d*(c^2 + 4*c*d*x + 6*d^2*x^2) + b^3*(c^3 + 4*c^2*d*x + 6*c*d^2*x^2 + 4*d^3*x^3))/(b^4*(a + b*x)^4)","B",1
1269,1,97,58,0.0348887,"\int \frac{(c+d x)^3}{(a+b x)^6} \, dx","Integrate[(c + d*x)^3/(a + b*x)^6,x]","-\frac{a^3 d^3+a^2 b d^2 (2 c+5 d x)+a b^2 d \left(3 c^2+10 c d x+10 d^2 x^2\right)+b^3 \left(4 c^3+15 c^2 d x+20 c d^2 x^2+10 d^3 x^3\right)}{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,"-1/20*(a^3*d^3 + a^2*b*d^2*(2*c + 5*d*x) + a*b^2*d*(3*c^2 + 10*c*d*x + 10*d^2*x^2) + b^3*(4*c^3 + 15*c^2*d*x + 20*c*d^2*x^2 + 10*d^3*x^3))/(b^4*(a + b*x)^5)","A",1
1270,1,97,92,0.0310836,"\int \frac{(c+d x)^3}{(a+b x)^7} \, dx","Integrate[(c + d*x)^3/(a + b*x)^7,x]","-\frac{a^3 d^3+3 a^2 b d^2 (c+2 d x)+3 a b^2 d \left(2 c^2+6 c d x+5 d^2 x^2\right)+b^3 \left(10 c^3+36 c^2 d x+45 c d^2 x^2+20 d^3 x^3\right)}{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,"-1/60*(a^3*d^3 + 3*a^2*b*d^2*(c + 2*d*x) + 3*a*b^2*d*(2*c^2 + 6*c*d*x + 5*d^2*x^2) + b^3*(10*c^3 + 36*c^2*d*x + 45*c*d^2*x^2 + 20*d^3*x^3))/(b^4*(a + b*x)^6)","A",1
1271,1,97,92,0.0318147,"\int \frac{(c+d x)^3}{(a+b x)^8} \, dx","Integrate[(c + d*x)^3/(a + b*x)^8,x]","-\frac{a^3 d^3+a^2 b d^2 (4 c+7 d x)+a b^2 d \left(10 c^2+28 c d x+21 d^2 x^2\right)+b^3 \left(20 c^3+70 c^2 d x+84 c d^2 x^2+35 d^3 x^3\right)}{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,"-1/140*(a^3*d^3 + a^2*b*d^2*(4*c + 7*d*x) + a*b^2*d*(10*c^2 + 28*c*d*x + 21*d^2*x^2) + b^3*(20*c^3 + 70*c^2*d*x + 84*c*d^2*x^2 + 35*d^3*x^3))/(b^4*(a + b*x)^7)","A",1
1272,1,97,92,0.0358601,"\int \frac{(c+d x)^3}{(a+b x)^9} \, dx","Integrate[(c + d*x)^3/(a + b*x)^9,x]","-\frac{a^3 d^3+a^2 b d^2 (5 c+8 d x)+a b^2 d \left(15 c^2+40 c d x+28 d^2 x^2\right)+b^3 \left(35 c^3+120 c^2 d x+140 c d^2 x^2+56 d^3 x^3\right)}{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,"-1/280*(a^3*d^3 + a^2*b*d^2*(5*c + 8*d*x) + a*b^2*d*(15*c^2 + 40*c*d*x + 28*d^2*x^2) + b^3*(35*c^3 + 120*c^2*d*x + 140*c*d^2*x^2 + 56*d^3*x^3))/(b^4*(a + b*x)^8)","A",1
1273,1,993,200,0.1470856,"\int (a+b x)^9 (c+d x)^7 \, dx","Integrate[(a + b*x)^9*(c + d*x)^7,x]","\frac{1}{17} b^9 d^7 x^{17}+\frac{1}{16} b^8 d^6 (7 b c+9 a d) x^{16}+\frac{1}{5} b^7 d^5 \left(7 b^2 c^2+21 a b d c+12 a^2 d^2\right) x^{15}+\frac{1}{2} b^6 d^4 \left(5 b^3 c^3+27 a b^2 d c^2+36 a^2 b d^2 c+12 a^3 d^3\right) x^{14}+\frac{7}{13} b^5 d^3 \left(5 b^4 c^4+45 a b^3 d c^3+108 a^2 b^2 d^2 c^2+84 a^3 b d^3 c+18 a^4 d^4\right) x^{13}+\frac{7}{4} b^4 d^2 \left(b^5 c^5+15 a b^4 d c^4+60 a^2 b^3 d^2 c^3+84 a^3 b^2 d^3 c^2+42 a^4 b d^4 c+6 a^5 d^5\right) x^{12}+\frac{7}{11} b^3 d \left(b^6 c^6+27 a b^5 d c^5+180 a^2 b^4 d^2 c^4+420 a^3 b^3 d^3 c^3+378 a^4 b^2 d^4 c^2+126 a^5 b d^5 c+12 a^6 d^6\right) x^{11}+\frac{1}{10} b^2 \left(b^7 c^7+63 a b^6 d c^6+756 a^2 b^5 d^2 c^5+2940 a^3 b^4 d^3 c^4+4410 a^4 b^3 d^4 c^3+2646 a^5 b^2 d^5 c^2+588 a^6 b d^6 c+36 a^7 d^7\right) x^{10}+a b \left(b^7 c^7+28 a b^6 d c^6+196 a^2 b^5 d^2 c^5+490 a^3 b^4 d^3 c^4+490 a^4 b^3 d^4 c^3+196 a^5 b^2 d^5 c^2+28 a^6 b d^6 c+a^7 d^7\right) x^9+\frac{1}{8} a^2 \left(36 b^7 c^7+588 a b^6 d c^6+2646 a^2 b^5 d^2 c^5+4410 a^3 b^4 d^3 c^4+2940 a^4 b^3 d^4 c^3+756 a^5 b^2 d^5 c^2+63 a^6 b d^6 c+a^7 d^7\right) x^8+a^3 c \left(12 b^6 c^6+126 a b^5 d c^5+378 a^2 b^4 d^2 c^4+420 a^3 b^3 d^3 c^3+180 a^4 b^2 d^4 c^2+27 a^5 b d^5 c+a^6 d^6\right) x^7+\frac{7}{2} a^4 c^2 \left(6 b^5 c^5+42 a b^4 d c^4+84 a^2 b^3 d^2 c^3+60 a^3 b^2 d^3 c^2+15 a^4 b d^4 c+a^5 d^5\right) x^6+\frac{7}{5} a^5 c^3 \left(18 b^4 c^4+84 a b^3 d c^3+108 a^2 b^2 d^2 c^2+45 a^3 b d^3 c+5 a^4 d^4\right) x^5+\frac{7}{4} a^6 c^4 \left(12 b^3 c^3+36 a b^2 d c^2+27 a^2 b d^2 c+5 a^3 d^3\right) x^4+a^7 c^5 \left(12 b^2 c^2+21 a b d c+7 a^2 d^2\right) x^3+\frac{1}{2} a^8 c^6 (9 b c+7 a d) x^2+a^9 c^7 x","\frac{7 d^6 (a+b x)^{16} (b c-a d)}{16 b^8}+\frac{7 d^5 (a+b x)^{15} (b c-a d)^2}{5 b^8}+\frac{5 d^4 (a+b x)^{14} (b c-a d)^3}{2 b^8}+\frac{35 d^3 (a+b x)^{13} (b c-a d)^4}{13 b^8}+\frac{7 d^2 (a+b x)^{12} (b c-a d)^5}{4 b^8}+\frac{7 d (a+b x)^{11} (b c-a d)^6}{11 b^8}+\frac{(a+b x)^{10} (b c-a d)^7}{10 b^8}+\frac{d^7 (a+b x)^{17}}{17 b^8}",1,"a^9*c^7*x + (a^8*c^6*(9*b*c + 7*a*d)*x^2)/2 + a^7*c^5*(12*b^2*c^2 + 21*a*b*c*d + 7*a^2*d^2)*x^3 + (7*a^6*c^4*(12*b^3*c^3 + 36*a*b^2*c^2*d + 27*a^2*b*c*d^2 + 5*a^3*d^3)*x^4)/4 + (7*a^5*c^3*(18*b^4*c^4 + 84*a*b^3*c^3*d + 108*a^2*b^2*c^2*d^2 + 45*a^3*b*c*d^3 + 5*a^4*d^4)*x^5)/5 + (7*a^4*c^2*(6*b^5*c^5 + 42*a*b^4*c^4*d + 84*a^2*b^3*c^3*d^2 + 60*a^3*b^2*c^2*d^3 + 15*a^4*b*c*d^4 + a^5*d^5)*x^6)/2 + a^3*c*(12*b^6*c^6 + 126*a*b^5*c^5*d + 378*a^2*b^4*c^4*d^2 + 420*a^3*b^3*c^3*d^3 + 180*a^4*b^2*c^2*d^4 + 27*a^5*b*c*d^5 + a^6*d^6)*x^7 + (a^2*(36*b^7*c^7 + 588*a*b^6*c^6*d + 2646*a^2*b^5*c^5*d^2 + 4410*a^3*b^4*c^4*d^3 + 2940*a^4*b^3*c^3*d^4 + 756*a^5*b^2*c^2*d^5 + 63*a^6*b*c*d^6 + a^7*d^7)*x^8)/8 + a*b*(b^7*c^7 + 28*a*b^6*c^6*d + 196*a^2*b^5*c^5*d^2 + 490*a^3*b^4*c^4*d^3 + 490*a^4*b^3*c^3*d^4 + 196*a^5*b^2*c^2*d^5 + 28*a^6*b*c*d^6 + a^7*d^7)*x^9 + (b^2*(b^7*c^7 + 63*a*b^6*c^6*d + 756*a^2*b^5*c^5*d^2 + 2940*a^3*b^4*c^4*d^3 + 4410*a^4*b^3*c^3*d^4 + 2646*a^5*b^2*c^2*d^5 + 588*a^6*b*c*d^6 + 36*a^7*d^7)*x^10)/10 + (7*b^3*d*(b^6*c^6 + 27*a*b^5*c^5*d + 180*a^2*b^4*c^4*d^2 + 420*a^3*b^3*c^3*d^3 + 378*a^4*b^2*c^2*d^4 + 126*a^5*b*c*d^5 + 12*a^6*d^6)*x^11)/11 + (7*b^4*d^2*(b^5*c^5 + 15*a*b^4*c^4*d + 60*a^2*b^3*c^3*d^2 + 84*a^3*b^2*c^2*d^3 + 42*a^4*b*c*d^4 + 6*a^5*d^5)*x^12)/4 + (7*b^5*d^3*(5*b^4*c^4 + 45*a*b^3*c^3*d + 108*a^2*b^2*c^2*d^2 + 84*a^3*b*c*d^3 + 18*a^4*d^4)*x^13)/13 + (b^6*d^4*(5*b^3*c^3 + 27*a*b^2*c^2*d + 36*a^2*b*c*d^2 + 12*a^3*d^3)*x^14)/2 + (b^7*d^5*(7*b^2*c^2 + 21*a*b*c*d + 12*a^2*d^2)*x^15)/5 + (b^8*d^6*(7*b*c + 9*a*d)*x^16)/16 + (b^9*d^7*x^17)/17","B",1
1274,1,897,200,0.1110202,"\int (a+b x)^8 (c+d x)^7 \, dx","Integrate[(a + b*x)^8*(c + d*x)^7,x]","\frac{1}{16} b^8 d^7 x^{16}+\frac{1}{15} b^7 d^6 (7 b c+8 a d) x^{15}+\frac{1}{2} b^6 d^5 \left(3 b^2 c^2+8 a b d c+4 a^2 d^2\right) x^{14}+\frac{7}{13} b^5 d^4 \left(5 b^3 c^3+24 a b^2 d c^2+28 a^2 b d^2 c+8 a^3 d^3\right) x^{13}+\frac{7}{12} b^4 d^3 \left(5 b^4 c^4+40 a b^3 d c^3+84 a^2 b^2 d^2 c^2+56 a^3 b d^3 c+10 a^4 d^4\right) x^{12}+\frac{7}{11} b^3 d^2 \left(3 b^5 c^5+40 a b^4 d c^4+140 a^2 b^3 d^2 c^3+168 a^3 b^2 d^3 c^2+70 a^4 b d^4 c+8 a^5 d^5\right) x^{11}+\frac{7}{10} b^2 d \left(b^6 c^6+24 a b^5 d c^5+140 a^2 b^4 d^2 c^4+280 a^3 b^3 d^3 c^3+210 a^4 b^2 d^4 c^2+56 a^5 b d^5 c+4 a^6 d^6\right) x^{10}+\frac{1}{9} b \left(b^7 c^7+56 a b^6 d c^6+588 a^2 b^5 d^2 c^5+1960 a^3 b^4 d^3 c^4+2450 a^4 b^3 d^4 c^3+1176 a^5 b^2 d^5 c^2+196 a^6 b d^6 c+8 a^7 d^7\right) x^9+\frac{1}{8} a \left(8 b^7 c^7+196 a b^6 d c^6+1176 a^2 b^5 d^2 c^5+2450 a^3 b^4 d^3 c^4+1960 a^4 b^3 d^4 c^3+588 a^5 b^2 d^5 c^2+56 a^6 b d^6 c+a^7 d^7\right) x^8+a^2 c \left(4 b^6 c^6+56 a b^5 d c^5+210 a^2 b^4 d^2 c^4+280 a^3 b^3 d^3 c^3+140 a^4 b^2 d^4 c^2+24 a^5 b d^5 c+a^6 d^6\right) x^7+\frac{7}{6} a^3 c^2 \left(8 b^5 c^5+70 a b^4 d c^4+168 a^2 b^3 d^2 c^3+140 a^3 b^2 d^3 c^2+40 a^4 b d^4 c+3 a^5 d^5\right) x^6+\frac{7}{5} a^4 c^3 \left(10 b^4 c^4+56 a b^3 d c^3+84 a^2 b^2 d^2 c^2+40 a^3 b d^3 c+5 a^4 d^4\right) x^5+\frac{7}{4} a^5 c^4 \left(8 b^3 c^3+28 a b^2 d c^2+24 a^2 b d^2 c+5 a^3 d^3\right) x^4+\frac{7}{3} a^6 c^5 \left(4 b^2 c^2+8 a b d c+3 a^2 d^2\right) x^3+\frac{1}{2} a^7 c^6 (8 b c+7 a d) x^2+a^8 c^7 x","\frac{7 d^6 (a+b x)^{15} (b c-a d)}{15 b^8}+\frac{3 d^5 (a+b x)^{14} (b c-a d)^2}{2 b^8}+\frac{35 d^4 (a+b x)^{13} (b c-a d)^3}{13 b^8}+\frac{35 d^3 (a+b x)^{12} (b c-a d)^4}{12 b^8}+\frac{21 d^2 (a+b x)^{11} (b c-a d)^5}{11 b^8}+\frac{7 d (a+b x)^{10} (b c-a d)^6}{10 b^8}+\frac{(a+b x)^9 (b c-a d)^7}{9 b^8}+\frac{d^7 (a+b x)^{16}}{16 b^8}",1,"a^8*c^7*x + (a^7*c^6*(8*b*c + 7*a*d)*x^2)/2 + (7*a^6*c^5*(4*b^2*c^2 + 8*a*b*c*d + 3*a^2*d^2)*x^3)/3 + (7*a^5*c^4*(8*b^3*c^3 + 28*a*b^2*c^2*d + 24*a^2*b*c*d^2 + 5*a^3*d^3)*x^4)/4 + (7*a^4*c^3*(10*b^4*c^4 + 56*a*b^3*c^3*d + 84*a^2*b^2*c^2*d^2 + 40*a^3*b*c*d^3 + 5*a^4*d^4)*x^5)/5 + (7*a^3*c^2*(8*b^5*c^5 + 70*a*b^4*c^4*d + 168*a^2*b^3*c^3*d^2 + 140*a^3*b^2*c^2*d^3 + 40*a^4*b*c*d^4 + 3*a^5*d^5)*x^6)/6 + a^2*c*(4*b^6*c^6 + 56*a*b^5*c^5*d + 210*a^2*b^4*c^4*d^2 + 280*a^3*b^3*c^3*d^3 + 140*a^4*b^2*c^2*d^4 + 24*a^5*b*c*d^5 + a^6*d^6)*x^7 + (a*(8*b^7*c^7 + 196*a*b^6*c^6*d + 1176*a^2*b^5*c^5*d^2 + 2450*a^3*b^4*c^4*d^3 + 1960*a^4*b^3*c^3*d^4 + 588*a^5*b^2*c^2*d^5 + 56*a^6*b*c*d^6 + a^7*d^7)*x^8)/8 + (b*(b^7*c^7 + 56*a*b^6*c^6*d + 588*a^2*b^5*c^5*d^2 + 1960*a^3*b^4*c^4*d^3 + 2450*a^4*b^3*c^3*d^4 + 1176*a^5*b^2*c^2*d^5 + 196*a^6*b*c*d^6 + 8*a^7*d^7)*x^9)/9 + (7*b^2*d*(b^6*c^6 + 24*a*b^5*c^5*d + 140*a^2*b^4*c^4*d^2 + 280*a^3*b^3*c^3*d^3 + 210*a^4*b^2*c^2*d^4 + 56*a^5*b*c*d^5 + 4*a^6*d^6)*x^10)/10 + (7*b^3*d^2*(3*b^5*c^5 + 40*a*b^4*c^4*d + 140*a^2*b^3*c^3*d^2 + 168*a^3*b^2*c^2*d^3 + 70*a^4*b*c*d^4 + 8*a^5*d^5)*x^11)/11 + (7*b^4*d^3*(5*b^4*c^4 + 40*a*b^3*c^3*d + 84*a^2*b^2*c^2*d^2 + 56*a^3*b*c*d^3 + 10*a^4*d^4)*x^12)/12 + (7*b^5*d^4*(5*b^3*c^3 + 24*a*b^2*c^2*d + 28*a^2*b*c*d^2 + 8*a^3*d^3)*x^13)/13 + (b^6*d^5*(3*b^2*c^2 + 8*a*b*c*d + 4*a^2*d^2)*x^14)/2 + (b^7*d^6*(7*b*c + 8*a*d)*x^15)/15 + (b^8*d^7*x^16)/16","B",1
1275,1,785,200,0.0863719,"\int (a+b x)^7 (c+d x)^7 \, dx","Integrate[(a + b*x)^7*(c + d*x)^7,x]","a^7 c^7 x+\frac{7}{2} a^6 c^6 x^2 (a d+b c)+\frac{7}{13} b^5 d^5 x^{13} \left(3 a^2 d^2+7 a b c d+3 b^2 c^2\right)+\frac{7}{3} a^5 c^5 x^3 \left(3 a^2 d^2+7 a b c d+3 b^2 c^2\right)+\frac{7}{12} b^4 d^4 x^{12} \left(5 a^3 d^3+21 a^2 b c d^2+21 a b^2 c^2 d+5 b^3 c^3\right)+\frac{7}{4} a^4 c^4 x^4 \left(5 a^3 d^3+21 a^2 b c d^2+21 a b^2 c^2 d+5 b^3 c^3\right)+\frac{7}{11} b^3 d^3 x^{11} \left(5 a^4 d^4+35 a^3 b c d^3+63 a^2 b^2 c^2 d^2+35 a b^3 c^3 d+5 b^4 c^4\right)+\frac{7}{5} a^3 c^3 x^5 \left(5 a^4 d^4+35 a^3 b c d^3+63 a^2 b^2 c^2 d^2+35 a b^3 c^3 d+5 b^4 c^4\right)+\frac{7}{10} b^2 d^2 x^{10} \left(3 a^5 d^5+35 a^4 b c d^4+105 a^3 b^2 c^2 d^3+105 a^2 b^3 c^3 d^2+35 a b^4 c^4 d+3 b^5 c^5\right)+\frac{7}{6} a^2 c^2 x^6 \left(3 a^5 d^5+35 a^4 b c d^4+105 a^3 b^2 c^2 d^3+105 a^2 b^3 c^3 d^2+35 a b^4 c^4 d+3 b^5 c^5\right)+\frac{7}{9} b d x^9 \left(a^6 d^6+21 a^5 b c d^5+105 a^4 b^2 c^2 d^4+175 a^3 b^3 c^3 d^3+105 a^2 b^4 c^4 d^2+21 a b^5 c^5 d+b^6 c^6\right)+a c x^7 \left(a^6 d^6+21 a^5 b c d^5+105 a^4 b^2 c^2 d^4+175 a^3 b^3 c^3 d^3+105 a^2 b^4 c^4 d^2+21 a b^5 c^5 d+b^6 c^6\right)+\frac{1}{8} x^8 \left(a^7 d^7+49 a^6 b c d^6+441 a^5 b^2 c^2 d^5+1225 a^4 b^3 c^3 d^4+1225 a^3 b^4 c^4 d^3+441 a^2 b^5 c^5 d^2+49 a b^6 c^6 d+b^7 c^7\right)+\frac{1}{2} b^6 d^6 x^{14} (a d+b c)+\frac{1}{15} b^7 d^7 x^{15}","\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,"a^7*c^7*x + (7*a^6*c^6*(b*c + a*d)*x^2)/2 + (7*a^5*c^5*(3*b^2*c^2 + 7*a*b*c*d + 3*a^2*d^2)*x^3)/3 + (7*a^4*c^4*(5*b^3*c^3 + 21*a*b^2*c^2*d + 21*a^2*b*c*d^2 + 5*a^3*d^3)*x^4)/4 + (7*a^3*c^3*(5*b^4*c^4 + 35*a*b^3*c^3*d + 63*a^2*b^2*c^2*d^2 + 35*a^3*b*c*d^3 + 5*a^4*d^4)*x^5)/5 + (7*a^2*c^2*(3*b^5*c^5 + 35*a*b^4*c^4*d + 105*a^2*b^3*c^3*d^2 + 105*a^3*b^2*c^2*d^3 + 35*a^4*b*c*d^4 + 3*a^5*d^5)*x^6)/6 + a*c*(b^6*c^6 + 21*a*b^5*c^5*d + 105*a^2*b^4*c^4*d^2 + 175*a^3*b^3*c^3*d^3 + 105*a^4*b^2*c^2*d^4 + 21*a^5*b*c*d^5 + a^6*d^6)*x^7 + ((b^7*c^7 + 49*a*b^6*c^6*d + 441*a^2*b^5*c^5*d^2 + 1225*a^3*b^4*c^4*d^3 + 1225*a^4*b^3*c^3*d^4 + 441*a^5*b^2*c^2*d^5 + 49*a^6*b*c*d^6 + a^7*d^7)*x^8)/8 + (7*b*d*(b^6*c^6 + 21*a*b^5*c^5*d + 105*a^2*b^4*c^4*d^2 + 175*a^3*b^3*c^3*d^3 + 105*a^4*b^2*c^2*d^4 + 21*a^5*b*c*d^5 + a^6*d^6)*x^9)/9 + (7*b^2*d^2*(3*b^5*c^5 + 35*a*b^4*c^4*d + 105*a^2*b^3*c^3*d^2 + 105*a^3*b^2*c^2*d^3 + 35*a^4*b*c*d^4 + 3*a^5*d^5)*x^10)/10 + (7*b^3*d^3*(5*b^4*c^4 + 35*a*b^3*c^3*d + 63*a^2*b^2*c^2*d^2 + 35*a^3*b*c*d^3 + 5*a^4*d^4)*x^11)/11 + (7*b^4*d^4*(5*b^3*c^3 + 21*a*b^2*c^2*d + 21*a^2*b*c*d^2 + 5*a^3*d^3)*x^12)/12 + (7*b^5*d^5*(3*b^2*c^2 + 7*a*b*c*d + 3*a^2*d^2)*x^13)/13 + (b^6*d^6*(b*c + a*d)*x^14)/2 + (b^7*d^7*x^15)/15","B",1
1276,1,684,173,0.0813324,"\int (a+b x)^6 (c+d x)^7 \, dx","Integrate[(a + b*x)^6*(c + d*x)^7,x]","a^6 c^7 x+\frac{1}{2} a^5 c^6 x^2 (7 a d+6 b c)+\frac{1}{4} b^4 d^5 x^{12} \left(5 a^2 d^2+14 a b c d+7 b^2 c^2\right)+a^4 c^5 x^3 \left(7 a^2 d^2+14 a b c d+5 b^2 c^2\right)+\frac{1}{11} b^3 d^4 x^{11} \left(20 a^3 d^3+105 a^2 b c d^2+126 a b^2 c^2 d+35 b^3 c^3\right)+\frac{1}{4} a^3 c^4 x^4 \left(35 a^3 d^3+126 a^2 b c d^2+105 a b^2 c^2 d+20 b^3 c^3\right)+\frac{1}{2} b^2 d^3 x^{10} \left(3 a^4 d^4+28 a^3 b c d^3+63 a^2 b^2 c^2 d^2+42 a b^3 c^3 d+7 b^4 c^4\right)+a^2 c^3 x^5 \left(7 a^4 d^4+42 a^3 b c d^3+63 a^2 b^2 c^2 d^2+28 a b^3 c^3 d+3 b^4 c^4\right)+\frac{1}{3} b d^2 x^9 \left(2 a^5 d^5+35 a^4 b c d^4+140 a^3 b^2 c^2 d^3+175 a^2 b^3 c^3 d^2+70 a b^4 c^4 d+7 b^5 c^5\right)+\frac{1}{2} a c^2 x^6 \left(7 a^5 d^5+70 a^4 b c d^4+175 a^3 b^2 c^2 d^3+140 a^2 b^3 c^3 d^2+35 a b^4 c^4 d+2 b^5 c^5\right)+\frac{1}{8} d x^8 \left(a^6 d^6+42 a^5 b c d^5+315 a^4 b^2 c^2 d^4+700 a^3 b^3 c^3 d^3+525 a^2 b^4 c^4 d^2+126 a b^5 c^5 d+7 b^6 c^6\right)+\frac{1}{7} c x^7 \left(7 a^6 d^6+126 a^5 b c d^5+525 a^4 b^2 c^2 d^4+700 a^3 b^3 c^3 d^3+315 a^2 b^4 c^4 d^2+42 a b^5 c^5 d+b^6 c^6\right)+\frac{1}{13} b^5 d^6 x^{13} (6 a d+7 b c)+\frac{1}{14} b^6 d^7 x^{14}","-\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,"a^6*c^7*x + (a^5*c^6*(6*b*c + 7*a*d)*x^2)/2 + a^4*c^5*(5*b^2*c^2 + 14*a*b*c*d + 7*a^2*d^2)*x^3 + (a^3*c^4*(20*b^3*c^3 + 105*a*b^2*c^2*d + 126*a^2*b*c*d^2 + 35*a^3*d^3)*x^4)/4 + a^2*c^3*(3*b^4*c^4 + 28*a*b^3*c^3*d + 63*a^2*b^2*c^2*d^2 + 42*a^3*b*c*d^3 + 7*a^4*d^4)*x^5 + (a*c^2*(2*b^5*c^5 + 35*a*b^4*c^4*d + 140*a^2*b^3*c^3*d^2 + 175*a^3*b^2*c^2*d^3 + 70*a^4*b*c*d^4 + 7*a^5*d^5)*x^6)/2 + (c*(b^6*c^6 + 42*a*b^5*c^5*d + 315*a^2*b^4*c^4*d^2 + 700*a^3*b^3*c^3*d^3 + 525*a^4*b^2*c^2*d^4 + 126*a^5*b*c*d^5 + 7*a^6*d^6)*x^7)/7 + (d*(7*b^6*c^6 + 126*a*b^5*c^5*d + 525*a^2*b^4*c^4*d^2 + 700*a^3*b^3*c^3*d^3 + 315*a^4*b^2*c^2*d^4 + 42*a^5*b*c*d^5 + a^6*d^6)*x^8)/8 + (b*d^2*(7*b^5*c^5 + 70*a*b^4*c^4*d + 175*a^2*b^3*c^3*d^2 + 140*a^3*b^2*c^2*d^3 + 35*a^4*b*c*d^4 + 2*a^5*d^5)*x^9)/3 + (b^2*d^3*(7*b^4*c^4 + 42*a*b^3*c^3*d + 63*a^2*b^2*c^2*d^2 + 28*a^3*b*c*d^3 + 3*a^4*d^4)*x^10)/2 + (b^3*d^4*(35*b^3*c^3 + 126*a*b^2*c^2*d + 105*a^2*b*c*d^2 + 20*a^3*d^3)*x^11)/11 + (b^4*d^5*(7*b^2*c^2 + 14*a*b*c*d + 5*a^2*d^2)*x^12)/4 + (b^5*d^6*(7*b*c + 6*a*d)*x^13)/13 + (b^6*d^7*x^14)/14","B",1
1277,1,574,144,0.0755492,"\int (a+b x)^5 (c+d x)^7 \, dx","Integrate[(a + b*x)^5*(c + d*x)^7,x]","a^5 c^7 x+\frac{1}{2} a^4 c^6 x^2 (7 a d+5 b c)+\frac{1}{11} b^3 d^5 x^{11} \left(10 a^2 d^2+35 a b c d+21 b^2 c^2\right)+\frac{1}{3} a^3 c^5 x^3 \left(21 a^2 d^2+35 a b c d+10 b^2 c^2\right)+\frac{1}{2} b^2 d^4 x^{10} \left(2 a^3 d^3+14 a^2 b c d^2+21 a b^2 c^2 d+7 b^3 c^3\right)+\frac{5}{4} a^2 c^4 x^4 \left(7 a^3 d^3+21 a^2 b c d^2+14 a b^2 c^2 d+2 b^3 c^3\right)+\frac{5}{9} b d^3 x^9 \left(a^4 d^4+14 a^3 b c d^3+42 a^2 b^2 c^2 d^2+35 a b^3 c^3 d+7 b^4 c^4\right)+a c^3 x^5 \left(7 a^4 d^4+35 a^3 b c d^3+42 a^2 b^2 c^2 d^2+14 a b^3 c^3 d+b^4 c^4\right)+\frac{1}{8} d^2 x^8 \left(a^5 d^5+35 a^4 b c d^4+210 a^3 b^2 c^2 d^3+350 a^2 b^3 c^3 d^2+175 a b^4 c^4 d+21 b^5 c^5\right)+c d x^7 \left(a^5 d^5+15 a^4 b c d^4+50 a^3 b^2 c^2 d^3+50 a^2 b^3 c^3 d^2+15 a b^4 c^4 d+b^5 c^5\right)+\frac{1}{6} c^2 x^6 \left(21 a^5 d^5+175 a^4 b c d^4+350 a^3 b^2 c^2 d^3+210 a^2 b^3 c^3 d^2+35 a b^4 c^4 d+b^5 c^5\right)+\frac{1}{12} b^4 d^6 x^{12} (5 a d+7 b c)+\frac{1}{13} b^5 d^7 x^{13}","-\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,"a^5*c^7*x + (a^4*c^6*(5*b*c + 7*a*d)*x^2)/2 + (a^3*c^5*(10*b^2*c^2 + 35*a*b*c*d + 21*a^2*d^2)*x^3)/3 + (5*a^2*c^4*(2*b^3*c^3 + 14*a*b^2*c^2*d + 21*a^2*b*c*d^2 + 7*a^3*d^3)*x^4)/4 + a*c^3*(b^4*c^4 + 14*a*b^3*c^3*d + 42*a^2*b^2*c^2*d^2 + 35*a^3*b*c*d^3 + 7*a^4*d^4)*x^5 + (c^2*(b^5*c^5 + 35*a*b^4*c^4*d + 210*a^2*b^3*c^3*d^2 + 350*a^3*b^2*c^2*d^3 + 175*a^4*b*c*d^4 + 21*a^5*d^5)*x^6)/6 + c*d*(b^5*c^5 + 15*a*b^4*c^4*d + 50*a^2*b^3*c^3*d^2 + 50*a^3*b^2*c^2*d^3 + 15*a^4*b*c*d^4 + a^5*d^5)*x^7 + (d^2*(21*b^5*c^5 + 175*a*b^4*c^4*d + 350*a^2*b^3*c^3*d^2 + 210*a^3*b^2*c^2*d^3 + 35*a^4*b*c*d^4 + a^5*d^5)*x^8)/8 + (5*b*d^3*(7*b^4*c^4 + 35*a*b^3*c^3*d + 42*a^2*b^2*c^2*d^2 + 14*a^3*b*c*d^3 + a^4*d^4)*x^9)/9 + (b^2*d^4*(7*b^3*c^3 + 21*a*b^2*c^2*d + 14*a^2*b*c*d^2 + 2*a^3*d^3)*x^10)/2 + (b^3*d^5*(21*b^2*c^2 + 35*a*b*c*d + 10*a^2*d^2)*x^11)/11 + (b^4*d^6*(7*b*c + 5*a*d)*x^12)/12 + (b^5*d^7*x^13)/13","B",1
1278,1,473,119,0.0544161,"\int (a+b x)^4 (c+d x)^7 \, dx","Integrate[(a + b*x)^4*(c + d*x)^7,x]","a^4 c^7 x+\frac{1}{2} a^3 c^6 x^2 (7 a d+4 b c)+\frac{1}{10} b^2 d^5 x^{10} \left(6 a^2 d^2+28 a b c d+21 b^2 c^2\right)+\frac{1}{3} a^2 c^5 x^3 \left(21 a^2 d^2+28 a b c d+6 b^2 c^2\right)+\frac{1}{9} b d^4 x^9 \left(4 a^3 d^3+42 a^2 b c d^2+84 a b^2 c^2 d+35 b^3 c^3\right)+\frac{1}{4} a c^4 x^4 \left(35 a^3 d^3+84 a^2 b c d^2+42 a b^2 c^2 d+4 b^3 c^3\right)+\frac{1}{8} d^3 x^8 \left(a^4 d^4+28 a^3 b c d^3+126 a^2 b^2 c^2 d^2+140 a b^3 c^3 d+35 b^4 c^4\right)+c d^2 x^7 \left(a^4 d^4+12 a^3 b c d^3+30 a^2 b^2 c^2 d^2+20 a b^3 c^3 d+3 b^4 c^4\right)+\frac{7}{6} c^2 d x^6 \left(3 a^4 d^4+20 a^3 b c d^3+30 a^2 b^2 c^2 d^2+12 a b^3 c^3 d+b^4 c^4\right)+\frac{1}{5} c^3 x^5 \left(35 a^4 d^4+140 a^3 b c d^3+126 a^2 b^2 c^2 d^2+28 a b^3 c^3 d+b^4 c^4\right)+\frac{1}{11} b^3 d^6 x^{11} (4 a d+7 b c)+\frac{1}{12} b^4 d^7 x^{12}","-\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,"a^4*c^7*x + (a^3*c^6*(4*b*c + 7*a*d)*x^2)/2 + (a^2*c^5*(6*b^2*c^2 + 28*a*b*c*d + 21*a^2*d^2)*x^3)/3 + (a*c^4*(4*b^3*c^3 + 42*a*b^2*c^2*d + 84*a^2*b*c*d^2 + 35*a^3*d^3)*x^4)/4 + (c^3*(b^4*c^4 + 28*a*b^3*c^3*d + 126*a^2*b^2*c^2*d^2 + 140*a^3*b*c*d^3 + 35*a^4*d^4)*x^5)/5 + (7*c^2*d*(b^4*c^4 + 12*a*b^3*c^3*d + 30*a^2*b^2*c^2*d^2 + 20*a^3*b*c*d^3 + 3*a^4*d^4)*x^6)/6 + c*d^2*(3*b^4*c^4 + 20*a*b^3*c^3*d + 30*a^2*b^2*c^2*d^2 + 12*a^3*b*c*d^3 + a^4*d^4)*x^7 + (d^3*(35*b^4*c^4 + 140*a*b^3*c^3*d + 126*a^2*b^2*c^2*d^2 + 28*a^3*b*c*d^3 + a^4*d^4)*x^8)/8 + (b*d^4*(35*b^3*c^3 + 84*a*b^2*c^2*d + 42*a^2*b*c*d^2 + 4*a^3*d^3)*x^9)/9 + (b^2*d^5*(21*b^2*c^2 + 28*a*b*c*d + 6*a^2*d^2)*x^10)/10 + (b^3*d^6*(7*b*c + 4*a*d)*x^11)/11 + (b^4*d^7*x^12)/12","B",1
1279,1,360,92,0.0423444,"\int (a+b x)^3 (c+d x)^7 \, dx","Integrate[(a + b*x)^3*(c + d*x)^7,x]","a^3 c^7 x+\frac{1}{3} b d^5 x^9 \left(a^2 d^2+7 a b c d+7 b^2 c^2\right)+a c^5 x^3 \left(7 a^2 d^2+7 a b c d+b^2 c^2\right)+\frac{1}{2} a^2 c^6 x^2 (7 a d+3 b c)+c d^3 x^7 \left(a^3 d^3+9 a^2 b c d^2+15 a b^2 c^2 d+5 b^3 c^3\right)+\frac{7}{2} c^2 d^2 x^6 \left(a^3 d^3+5 a^2 b c d^2+5 a b^2 c^2 d+b^3 c^3\right)+\frac{7}{5} c^3 d x^5 \left(5 a^3 d^3+15 a^2 b c d^2+9 a b^2 c^2 d+b^3 c^3\right)+\frac{1}{8} d^4 x^8 \left(a^3 d^3+21 a^2 b c d^2+63 a b^2 c^2 d+35 b^3 c^3\right)+\frac{1}{4} c^4 x^4 \left(35 a^3 d^3+63 a^2 b c d^2+21 a b^2 c^2 d+b^3 c^3\right)+\frac{1}{10} b^2 d^6 x^{10} (3 a d+7 b c)+\frac{1}{11} b^3 d^7 x^{11}","-\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,"a^3*c^7*x + (a^2*c^6*(3*b*c + 7*a*d)*x^2)/2 + a*c^5*(b^2*c^2 + 7*a*b*c*d + 7*a^2*d^2)*x^3 + (c^4*(b^3*c^3 + 21*a*b^2*c^2*d + 63*a^2*b*c*d^2 + 35*a^3*d^3)*x^4)/4 + (7*c^3*d*(b^3*c^3 + 9*a*b^2*c^2*d + 15*a^2*b*c*d^2 + 5*a^3*d^3)*x^5)/5 + (7*c^2*d^2*(b^3*c^3 + 5*a*b^2*c^2*d + 5*a^2*b*c*d^2 + a^3*d^3)*x^6)/2 + c*d^3*(5*b^3*c^3 + 15*a*b^2*c^2*d + 9*a^2*b*c*d^2 + a^3*d^3)*x^7 + (d^4*(35*b^3*c^3 + 63*a*b^2*c^2*d + 21*a^2*b*c*d^2 + a^3*d^3)*x^8)/8 + (b*d^5*(7*b^2*c^2 + 7*a*b*c*d + a^2*d^2)*x^9)/3 + (b^2*d^6*(7*b*c + 3*a*d)*x^10)/10 + (b^3*d^7*x^11)/11","B",1
1280,1,261,65,0.0299837,"\int (a+b x)^2 (c+d x)^7 \, dx","Integrate[(a + b*x)^2*(c + d*x)^7,x]","\frac{1}{8} d^5 x^8 \left(a^2 d^2+14 a b c d+21 b^2 c^2\right)+c d^4 x^7 \left(a^2 d^2+6 a b c d+5 b^2 c^2\right)+\frac{7}{6} c^2 d^3 x^6 \left(3 a^2 d^2+10 a b c d+5 b^2 c^2\right)+\frac{1}{3} c^5 x^3 \left(21 a^2 d^2+14 a b c d+b^2 c^2\right)+\frac{7}{4} c^4 d x^4 \left(5 a^2 d^2+6 a b c d+b^2 c^2\right)+\frac{7}{5} c^3 d^2 x^5 \left(5 a^2 d^2+10 a b c d+3 b^2 c^2\right)+a^2 c^7 x+\frac{1}{2} a c^6 x^2 (7 a d+2 b c)+\frac{1}{9} b d^6 x^9 (2 a d+7 b c)+\frac{1}{10} b^2 d^7 x^{10}","-\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,"a^2*c^7*x + (a*c^6*(2*b*c + 7*a*d)*x^2)/2 + (c^5*(b^2*c^2 + 14*a*b*c*d + 21*a^2*d^2)*x^3)/3 + (7*c^4*d*(b^2*c^2 + 6*a*b*c*d + 5*a^2*d^2)*x^4)/4 + (7*c^3*d^2*(3*b^2*c^2 + 10*a*b*c*d + 5*a^2*d^2)*x^5)/5 + (7*c^2*d^3*(5*b^2*c^2 + 10*a*b*c*d + 3*a^2*d^2)*x^6)/6 + c*d^4*(5*b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^7 + (d^5*(21*b^2*c^2 + 14*a*b*c*d + a^2*d^2)*x^8)/8 + (b*d^6*(7*b*c + 2*a*d)*x^9)/9 + (b^2*d^7*x^10)/10","B",1
1281,1,151,38,0.0153743,"\int (a+b x) (c+d x)^7 \, dx","Integrate[(a + b*x)*(c + d*x)^7,x]","\frac{1}{2} c^6 x^2 (7 a d+b c)+\frac{7}{3} c^5 d x^3 (3 a d+b c)+\frac{7}{4} c^4 d^2 x^4 (5 a d+3 b c)+7 c^3 d^3 x^5 (a d+b c)+\frac{7}{6} c^2 d^4 x^6 (3 a d+5 b c)+\frac{1}{8} d^6 x^8 (a d+7 b c)+c d^5 x^7 (a d+3 b c)+a c^7 x+\frac{1}{9} b d^7 x^9","\frac{b (c+d x)^9}{9 d^2}-\frac{(c+d x)^8 (b c-a d)}{8 d^2}",1,"a*c^7*x + (c^6*(b*c + 7*a*d)*x^2)/2 + (7*c^5*d*(b*c + 3*a*d)*x^3)/3 + (7*c^4*d^2*(3*b*c + 5*a*d)*x^4)/4 + 7*c^3*d^3*(b*c + a*d)*x^5 + (7*c^2*d^4*(5*b*c + 3*a*d)*x^6)/6 + c*d^5*(3*b*c + a*d)*x^7 + (d^6*(7*b*c + a*d)*x^8)/8 + (b*d^7*x^9)/9","B",1
1282,1,14,14,0.0013302,"\int (c+d x)^7 \, dx","Integrate[(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
1283,1,304,169,0.1477401,"\int \frac{(c+d x)^7}{a+b x} \, dx","Integrate[(c + d*x)^7/(a + b*x),x]","\frac{d x \left(420 a^6 d^6-210 a^5 b d^5 (14 c+d x)+70 a^4 b^2 d^4 \left(126 c^2+21 c d x+2 d^2 x^2\right)-35 a^3 b^3 d^3 \left(420 c^3+126 c^2 d x+28 c d^2 x^2+3 d^3 x^3\right)+21 a^2 b^4 d^2 \left(700 c^4+350 c^3 d x+140 c^2 d^2 x^2+35 c d^3 x^3+4 d^4 x^4\right)-7 a b^5 d \left(1260 c^5+1050 c^4 d x+700 c^3 d^2 x^2+315 c^2 d^3 x^3+84 c d^4 x^4+10 d^5 x^5\right)+b^6 \left(2940 c^6+4410 c^5 d x+4900 c^4 d^2 x^2+3675 c^3 d^3 x^3+1764 c^2 d^4 x^4+490 c d^5 x^5+60 d^6 x^6\right)\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*(420*a^6*d^6 - 210*a^5*b*d^5*(14*c + d*x) + 70*a^4*b^2*d^4*(126*c^2 + 21*c*d*x + 2*d^2*x^2) - 35*a^3*b^3*d^3*(420*c^3 + 126*c^2*d*x + 28*c*d^2*x^2 + 3*d^3*x^3) + 21*a^2*b^4*d^2*(700*c^4 + 350*c^3*d*x + 140*c^2*d^2*x^2 + 35*c*d^3*x^3 + 4*d^4*x^4) - 7*a*b^5*d*(1260*c^5 + 1050*c^4*d*x + 700*c^3*d^2*x^2 + 315*c^2*d^3*x^3 + 84*c*d^4*x^4 + 10*d^5*x^5) + b^6*(2940*c^6 + 4410*c^5*d*x + 4900*c^4*d^2*x^2 + 3675*c^3*d^3*x^3 + 1764*c^2*d^4*x^4 + 490*c*d^5*x^5 + 60*d^6*x^6)))/(420*b^7) + ((b*c - a*d)^7*Log[a + b*x])/b^8","A",1
1284,1,388,187,0.1229797,"\int \frac{(c+d x)^7}{(a+b x)^2} \, dx","Integrate[(c + d*x)^7/(a + b*x)^2,x]","\frac{60 a^7 d^7-60 a^6 b d^6 (7 c+6 d x)+210 a^5 b^2 d^5 \left(6 c^2+10 c d x-d^2 x^2\right)+70 a^4 b^3 d^4 \left(-30 c^3-72 c^2 d x+18 c d^2 x^2+d^3 x^3\right)-35 a^3 b^4 d^3 \left(-60 c^4-180 c^3 d x+90 c^2 d^2 x^2+12 c d^3 x^3+d^4 x^4\right)+21 a^2 b^5 d^2 \left(-60 c^5-200 c^4 d x+200 c^3 d^2 x^2+50 c^2 d^3 x^3+10 c d^4 x^4+d^5 x^5\right)-7 a b^6 d \left(-60 c^6-180 c^5 d x+450 c^4 d^2 x^2+200 c^3 d^3 x^3+75 c^2 d^4 x^4+18 c d^5 x^5+2 d^6 x^6\right)+420 d (a+b x) (b c-a d)^6 \log (a+b x)+b^7 \left(-60 c^7+1260 c^5 d^2 x^2+1050 c^4 d^3 x^3+700 c^3 d^4 x^4+315 c^2 d^5 x^5+84 c d^6 x^6+10 d^7 x^7\right)}{60 b^8 (a+b x)}","\frac{7 d^6 (a+b x)^5 (b c-a d)}{5 b^8}+\frac{21 d^5 (a+b x)^4 (b c-a d)^2}{4 b^8}+\frac{35 d^4 (a+b x)^3 (b c-a d)^3}{3 b^8}+\frac{35 d^3 (a+b x)^2 (b c-a d)^4}{2 b^8}-\frac{(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*a^7*d^7 - 60*a^6*b*d^6*(7*c + 6*d*x) + 210*a^5*b^2*d^5*(6*c^2 + 10*c*d*x - d^2*x^2) + 70*a^4*b^3*d^4*(-30*c^3 - 72*c^2*d*x + 18*c*d^2*x^2 + d^3*x^3) - 35*a^3*b^4*d^3*(-60*c^4 - 180*c^3*d*x + 90*c^2*d^2*x^2 + 12*c*d^3*x^3 + d^4*x^4) + 21*a^2*b^5*d^2*(-60*c^5 - 200*c^4*d*x + 200*c^3*d^2*x^2 + 50*c^2*d^3*x^3 + 10*c*d^4*x^4 + d^5*x^5) - 7*a*b^6*d*(-60*c^6 - 180*c^5*d*x + 450*c^4*d^2*x^2 + 200*c^3*d^3*x^3 + 75*c^2*d^4*x^4 + 18*c*d^5*x^5 + 2*d^6*x^6) + b^7*(-60*c^7 + 1260*c^5*d^2*x^2 + 1050*c^4*d^3*x^3 + 700*c^3*d^4*x^4 + 315*c^2*d^5*x^5 + 84*c*d^6*x^6 + 10*d^7*x^7) + 420*d*(b*c - a*d)^6*(a + b*x)*Log[a + b*x])/(60*b^8*(a + b*x))","B",1
1285,1,389,185,0.1324559,"\int \frac{(c+d x)^7}{(a+b x)^3} \, dx","Integrate[(c + d*x)^7/(a + b*x)^3,x]","\frac{-130 a^7 d^7+10 a^6 b d^6 (77 c+16 d x)+10 a^5 b^2 d^5 \left(-189 c^2-56 c d x+50 d^2 x^2\right)+70 a^4 b^3 d^4 \left(35 c^3+6 c^2 d x-34 c d^2 x^2+2 d^3 x^3\right)-35 a^3 b^4 d^3 \left(50 c^4-20 c^3 d x-126 c^2 d^2 x^2+20 c d^3 x^3+d^4 x^4\right)+7 a^2 b^5 d^2 \left(90 c^5-200 c^4 d x-550 c^3 d^2 x^2+200 c^2 d^3 x^3+25 c d^4 x^4+2 d^5 x^5\right)-7 a b^6 d \left(10 c^6-120 c^5 d x-200 c^4 d^2 x^2+200 c^3 d^3 x^3+50 c^2 d^4 x^4+10 c d^5 x^5+d^6 x^6\right)-420 d^2 (a+b x)^2 (a d-b c)^5 \log (a+b x)+b^7 \left(-10 c^7-140 c^6 d x+700 c^4 d^3 x^3+350 c^3 d^4 x^4+140 c^2 d^5 x^5+35 c d^6 x^6+4 d^7 x^7\right)}{20 b^8 (a+b x)^2}","\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,"(-130*a^7*d^7 + 10*a^6*b*d^6*(77*c + 16*d*x) + 10*a^5*b^2*d^5*(-189*c^2 - 56*c*d*x + 50*d^2*x^2) + 70*a^4*b^3*d^4*(35*c^3 + 6*c^2*d*x - 34*c*d^2*x^2 + 2*d^3*x^3) - 35*a^3*b^4*d^3*(50*c^4 - 20*c^3*d*x - 126*c^2*d^2*x^2 + 20*c*d^3*x^3 + d^4*x^4) + 7*a^2*b^5*d^2*(90*c^5 - 200*c^4*d*x - 550*c^3*d^2*x^2 + 200*c^2*d^3*x^3 + 25*c*d^4*x^4 + 2*d^5*x^5) - 7*a*b^6*d*(10*c^6 - 120*c^5*d*x - 200*c^4*d^2*x^2 + 200*c^3*d^3*x^3 + 50*c^2*d^4*x^4 + 10*c*d^5*x^5 + d^6*x^6) + b^7*(-10*c^7 - 140*c^6*d*x + 700*c^4*d^3*x^3 + 350*c^3*d^4*x^4 + 140*c^2*d^5*x^5 + 35*c*d^6*x^6 + 4*d^7*x^7) - 420*d^2*(-(b*c) + a*d)^5*(a + b*x)^2*Log[a + b*x])/(20*b^8*(a + b*x)^2)","B",1
1286,1,199,187,0.1085894,"\int \frac{(c+d x)^7}{(a+b x)^4} \, dx","Integrate[(c + d*x)^7/(a + b*x)^4,x]","\frac{6 b^2 d^5 x^2 \left(10 a^2 d^2-28 a b c d+21 b^2 c^2\right)+12 b d^4 x \left(-20 a^3 d^3+70 a^2 b c d^2-84 a b^2 c^2 d+35 b^3 c^3\right)+4 b^3 d^6 x^3 (7 b c-4 a d)+420 d^3 (b c-a d)^4 \log (a+b x)+\frac{252 d^2 (a d-b c)^5}{a+b x}-\frac{42 d (b c-a d)^6}{(a+b x)^2}-\frac{4 (b c-a d)^7}{(a+b x)^3}+3 b^4 d^7 x^4}{12 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,"(12*b*d^4*(35*b^3*c^3 - 84*a*b^2*c^2*d + 70*a^2*b*c*d^2 - 20*a^3*d^3)*x + 6*b^2*d^5*(21*b^2*c^2 - 28*a*b*c*d + 10*a^2*d^2)*x^2 + 4*b^3*d^6*(7*b*c - 4*a*d)*x^3 + 3*b^4*d^7*x^4 - (4*(b*c - a*d)^7)/(a + b*x)^3 - (42*d*(b*c - a*d)^6)/(a + b*x)^2 + (252*d^2*(-(b*c) + a*d)^5)/(a + b*x) + 420*d^3*(b*c - a*d)^4*Log[a + b*x])/(12*b^8)","A",1
1287,1,173,187,0.1115031,"\int \frac{(c+d x)^7}{(a+b x)^5} \, dx","Integrate[(c + d*x)^7/(a + b*x)^5,x]","\frac{12 b d^5 x \left(15 a^2 d^2-35 a b c d+21 b^2 c^2\right)+6 b^2 d^6 x^2 (7 b c-5 a d)+420 d^4 (b c-a d)^3 \log (a+b x)-\frac{420 d^3 (b c-a d)^4}{a+b x}+\frac{126 d^2 (a d-b c)^5}{(a+b x)^2}-\frac{28 d (b c-a d)^6}{(a+b x)^3}-\frac{3 (b c-a d)^7}{(a+b x)^4}+4 b^3 d^7 x^3}{12 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,"(12*b*d^5*(21*b^2*c^2 - 35*a*b*c*d + 15*a^2*d^2)*x + 6*b^2*d^6*(7*b*c - 5*a*d)*x^2 + 4*b^3*d^7*x^3 - (3*(b*c - a*d)^7)/(a + b*x)^4 - (28*d*(b*c - a*d)^6)/(a + b*x)^3 + (126*d^2*(-(b*c) + a*d)^5)/(a + b*x)^2 - (420*d^3*(b*c - a*d)^4)/(a + b*x) + 420*d^4*(b*c - a*d)^3*Log[a + b*x])/(12*b^8)","A",1
1288,1,389,181,0.1533643,"\int \frac{(c+d x)^7}{(a+b x)^6} \, dx","Integrate[(c + d*x)^7/(a + b*x)^6,x]","\frac{459 a^7 d^7+3 a^6 b d^6 (625 d x-406 c)+a^5 b^2 d^5 \left(959 c^2-5250 c d x+2700 d^2 x^2\right)+5 a^4 b^3 d^4 \left(-28 c^3+875 c^2 d x-1680 c d^2 x^2+260 d^3 x^3\right)-5 a^3 b^4 d^3 \left(7 c^4+140 c^3 d x-1540 c^2 d^2 x^2+1120 c d^3 x^3+80 d^4 x^4\right)-a^2 b^5 d^2 \left(14 c^5+175 c^4 d x+1400 c^3 d^2 x^2-6300 c^2 d^3 x^3+700 c d^4 x^4+500 d^5 x^5\right)-7 a b^6 d \left(c^6+10 c^5 d x+50 c^4 d^2 x^2+200 c^3 d^3 x^3-300 c^2 d^4 x^4-100 c d^5 x^5+10 d^6 x^6\right)+420 d^5 (a+b x)^5 (b c-a d)^2 \log (a+b x)-\left(b^7 \left(4 c^7+35 c^6 d x+140 c^5 d^2 x^2+350 c^4 d^3 x^3+700 c^3 d^4 x^4-140 c d^6 x^6-10 d^7 x^7\right)\right)}{20 b^8 (a+b x)^5}","\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,"(459*a^7*d^7 + 3*a^6*b*d^6*(-406*c + 625*d*x) + a^5*b^2*d^5*(959*c^2 - 5250*c*d*x + 2700*d^2*x^2) + 5*a^4*b^3*d^4*(-28*c^3 + 875*c^2*d*x - 1680*c*d^2*x^2 + 260*d^3*x^3) - 5*a^3*b^4*d^3*(7*c^4 + 140*c^3*d*x - 1540*c^2*d^2*x^2 + 1120*c*d^3*x^3 + 80*d^4*x^4) - a^2*b^5*d^2*(14*c^5 + 175*c^4*d*x + 1400*c^3*d^2*x^2 - 6300*c^2*d^3*x^3 + 700*c*d^4*x^4 + 500*d^5*x^5) - 7*a*b^6*d*(c^6 + 10*c^5*d*x + 50*c^4*d^2*x^2 + 200*c^3*d^3*x^3 - 300*c^2*d^4*x^4 - 100*c*d^5*x^5 + 10*d^6*x^6) - b^7*(4*c^7 + 35*c^6*d*x + 140*c^5*d^2*x^2 + 350*c^4*d^3*x^3 + 700*c^3*d^4*x^4 - 140*c*d^6*x^6 - 10*d^7*x^7) + 420*d^5*(b*c - a*d)^2*(a + b*x)^5*Log[a + b*x])/(20*b^8*(a + b*x)^5)","B",1
1289,1,390,186,0.2043499,"\int \frac{(c+d x)^7}{(a+b x)^7} \, dx","Integrate[(c + d*x)^7/(a + b*x)^7,x]","-\frac{669 a^7 d^7+3 a^6 b d^6 (1198 d x-343 c)+3 a^5 b^2 d^5 \left(70 c^2-1918 c d x+2575 d^2 x^2\right)+5 a^4 b^3 d^4 \left(14 c^3+252 c^2 d x-2625 c d^2 x^2+1640 d^3 x^3\right)+5 a^3 b^4 d^3 \left(7 c^4+84 c^3 d x+630 c^2 d^2 x^2-3080 c d^3 x^3+810 d^4 x^4\right)+3 a^2 b^5 d^2 \left(7 c^5+70 c^4 d x+350 c^3 d^2 x^2+1400 c^2 d^3 x^3-3150 c d^4 x^4+120 d^5 x^5\right)+a b^6 d \left(14 c^6+126 c^5 d x+525 c^4 d^2 x^2+1400 c^3 d^3 x^3+3150 c^2 d^4 x^4-2520 c d^5 x^5-360 d^6 x^6\right)+420 d^6 (a+b x)^6 (a d-b c) \log (a+b x)+b^7 \left(10 c^7+84 c^6 d x+315 c^5 d^2 x^2+700 c^4 d^3 x^3+1050 c^3 d^4 x^4+1260 c^2 d^5 x^5-60 d^7 x^7\right)}{60 b^8 (a+b x)^6}","\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,"-1/60*(669*a^7*d^7 + 3*a^6*b*d^6*(-343*c + 1198*d*x) + 3*a^5*b^2*d^5*(70*c^2 - 1918*c*d*x + 2575*d^2*x^2) + 5*a^4*b^3*d^4*(14*c^3 + 252*c^2*d*x - 2625*c*d^2*x^2 + 1640*d^3*x^3) + 5*a^3*b^4*d^3*(7*c^4 + 84*c^3*d*x + 630*c^2*d^2*x^2 - 3080*c*d^3*x^3 + 810*d^4*x^4) + 3*a^2*b^5*d^2*(7*c^5 + 70*c^4*d*x + 350*c^3*d^2*x^2 + 1400*c^2*d^3*x^3 - 3150*c*d^4*x^4 + 120*d^5*x^5) + a*b^6*d*(14*c^6 + 126*c^5*d*x + 525*c^4*d^2*x^2 + 1400*c^3*d^3*x^3 + 3150*c^2*d^4*x^4 - 2520*c*d^5*x^5 - 360*d^6*x^6) + b^7*(10*c^7 + 84*c^6*d*x + 315*c^5*d^2*x^2 + 700*c^4*d^3*x^3 + 1050*c^3*d^4*x^4 + 1260*c^2*d^5*x^5 - 60*d^7*x^7) + 420*d^6*(-(b*c) + a*d)*(a + b*x)^6*Log[a + b*x])/(b^8*(a + b*x)^6)","B",1
1290,1,308,194,0.1631186,"\int \frac{(c+d x)^7}{(a+b x)^8} \, dx","Integrate[(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+3 a^5 b d^5 (223 c+2401 d x)+3 a^4 b^2 d^4 \left(153 c^2+1421 c d x+6713 d^2 x^2\right)+a^3 b^3 d^3 \left(319 c^3+2793 c^2 d x+11319 c d^2 x^2+30625 d^3 x^3\right)+a^2 b^4 d^2 \left(214 c^4+1813 c^3 d x+6909 c^2 d^2 x^2+15925 c d^3 x^3+26950 d^4 x^4\right)+a b^5 d \left(130 c^5+1078 c^4 d x+3969 c^3 d^2 x^2+8575 c^2 d^3 x^3+12250 c d^4 x^4+13230 d^5 x^5\right)+b^6 \left(60 c^6+490 c^5 d x+1764 c^4 d^2 x^2+3675 c^3 d^3 x^3+4900 c^2 d^4 x^4+4410 c d^5 x^5+2940 d^6 x^6\right)\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)*(1089*a^6*d^6 + 3*a^5*b*d^5*(223*c + 2401*d*x) + 3*a^4*b^2*d^4*(153*c^2 + 1421*c*d*x + 6713*d^2*x^2) + a^3*b^3*d^3*(319*c^3 + 2793*c^2*d*x + 11319*c*d^2*x^2 + 30625*d^3*x^3) + a^2*b^4*d^2*(214*c^4 + 1813*c^3*d*x + 6909*c^2*d^2*x^2 + 15925*c*d^3*x^3 + 26950*d^4*x^4) + a*b^5*d*(130*c^5 + 1078*c^4*d*x + 3969*c^3*d^2*x^2 + 8575*c^2*d^3*x^3 + 12250*c*d^4*x^4 + 13230*d^5*x^5) + b^6*(60*c^6 + 490*c^5*d*x + 1764*c^4*d^2*x^2 + 3675*c^3*d^3*x^3 + 4900*c^2*d^4*x^4 + 4410*c*d^5*x^5 + 2940*d^6*x^6)))/(b^8*(a + b*x)^7) + (d^7*Log[a + b*x])/b^8","A",1
1291,1,353,28,0.1254217,"\int \frac{(c+d x)^7}{(a+b x)^9} \, dx","Integrate[(c + d*x)^7/(a + b*x)^9,x]","-\frac{a^7 d^7+a^6 b d^6 (c+8 d x)+a^5 b^2 d^5 \left(c^2+8 c d x+28 d^2 x^2\right)+a^4 b^3 d^4 \left(c^3+8 c^2 d x+28 c d^2 x^2+56 d^3 x^3\right)+a^3 b^4 d^3 \left(c^4+8 c^3 d x+28 c^2 d^2 x^2+56 c d^3 x^3+70 d^4 x^4\right)+a^2 b^5 d^2 \left(c^5+8 c^4 d x+28 c^3 d^2 x^2+56 c^2 d^3 x^3+70 c d^4 x^4+56 d^5 x^5\right)+a b^6 d \left(c^6+8 c^5 d x+28 c^4 d^2 x^2+56 c^3 d^3 x^3+70 c^2 d^4 x^4+56 c d^5 x^5+28 d^6 x^6\right)+b^7 \left(c^7+8 c^6 d x+28 c^5 d^2 x^2+56 c^4 d^3 x^3+70 c^3 d^4 x^4+56 c^2 d^5 x^5+28 c d^6 x^6+8 d^7 x^7\right)}{8 b^8 (a+b x)^8}","-\frac{(c+d x)^8}{8 (a+b x)^8 (b c-a d)}",1,"-1/8*(a^7*d^7 + a^6*b*d^6*(c + 8*d*x) + a^5*b^2*d^5*(c^2 + 8*c*d*x + 28*d^2*x^2) + a^4*b^3*d^4*(c^3 + 8*c^2*d*x + 28*c*d^2*x^2 + 56*d^3*x^3) + a^3*b^4*d^3*(c^4 + 8*c^3*d*x + 28*c^2*d^2*x^2 + 56*c*d^3*x^3 + 70*d^4*x^4) + a^2*b^5*d^2*(c^5 + 8*c^4*d*x + 28*c^3*d^2*x^2 + 56*c^2*d^3*x^3 + 70*c*d^4*x^4 + 56*d^5*x^5) + a*b^6*d*(c^6 + 8*c^5*d*x + 28*c^4*d^2*x^2 + 56*c^3*d^3*x^3 + 70*c^2*d^4*x^4 + 56*c*d^5*x^5 + 28*d^6*x^6) + b^7*(c^7 + 8*c^6*d*x + 28*c^5*d^2*x^2 + 56*c^4*d^3*x^3 + 70*c^3*d^4*x^4 + 56*c^2*d^5*x^5 + 28*c*d^6*x^6 + 8*d^7*x^7))/(b^8*(a + b*x)^8)","B",1
1292,1,367,58,0.1262224,"\int \frac{(c+d x)^7}{(a+b x)^{10}} \, dx","Integrate[(c + d*x)^7/(a + b*x)^10,x]","-\frac{a^7 d^7+a^6 b d^6 (2 c+9 d x)+3 a^5 b^2 d^5 \left(c^2+6 c d x+12 d^2 x^2\right)+a^4 b^3 d^4 \left(4 c^3+27 c^2 d x+72 c d^2 x^2+84 d^3 x^3\right)+a^3 b^4 d^3 \left(5 c^4+36 c^3 d x+108 c^2 d^2 x^2+168 c d^3 x^3+126 d^4 x^4\right)+3 a^2 b^5 d^2 \left(2 c^5+15 c^4 d x+48 c^3 d^2 x^2+84 c^2 d^3 x^3+84 c d^4 x^4+42 d^5 x^5\right)+a b^6 d \left(7 c^6+54 c^5 d x+180 c^4 d^2 x^2+336 c^3 d^3 x^3+378 c^2 d^4 x^4+252 c d^5 x^5+84 d^6 x^6\right)+b^7 \left(8 c^7+63 c^6 d x+216 c^5 d^2 x^2+420 c^4 d^3 x^3+504 c^3 d^4 x^4+378 c^2 d^5 x^5+168 c d^6 x^6+36 d^7 x^7\right)}{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,"-1/72*(a^7*d^7 + a^6*b*d^6*(2*c + 9*d*x) + 3*a^5*b^2*d^5*(c^2 + 6*c*d*x + 12*d^2*x^2) + a^4*b^3*d^4*(4*c^3 + 27*c^2*d*x + 72*c*d^2*x^2 + 84*d^3*x^3) + a^3*b^4*d^3*(5*c^4 + 36*c^3*d*x + 108*c^2*d^2*x^2 + 168*c*d^3*x^3 + 126*d^4*x^4) + 3*a^2*b^5*d^2*(2*c^5 + 15*c^4*d*x + 48*c^3*d^2*x^2 + 84*c^2*d^3*x^3 + 84*c*d^4*x^4 + 42*d^5*x^5) + a*b^6*d*(7*c^6 + 54*c^5*d*x + 180*c^4*d^2*x^2 + 336*c^3*d^3*x^3 + 378*c^2*d^4*x^4 + 252*c*d^5*x^5 + 84*d^6*x^6) + b^7*(8*c^7 + 63*c^6*d*x + 216*c^5*d^2*x^2 + 420*c^4*d^3*x^3 + 504*c^3*d^4*x^4 + 378*c^2*d^5*x^5 + 168*c*d^6*x^6 + 36*d^7*x^7))/(b^8*(a + b*x)^9)","B",1
1293,1,371,89,0.1227734,"\int \frac{(c+d x)^7}{(a+b x)^{11}} \, dx","Integrate[(c + d*x)^7/(a + b*x)^11,x]","-\frac{a^7 d^7+a^6 b d^6 (3 c+10 d x)+3 a^5 b^2 d^5 \left(2 c^2+10 c d x+15 d^2 x^2\right)+5 a^4 b^3 d^4 \left(2 c^3+12 c^2 d x+27 c d^2 x^2+24 d^3 x^3\right)+5 a^3 b^4 d^3 \left(3 c^4+20 c^3 d x+54 c^2 d^2 x^2+72 c d^3 x^3+42 d^4 x^4\right)+3 a^2 b^5 d^2 \left(7 c^5+50 c^4 d x+150 c^3 d^2 x^2+240 c^2 d^3 x^3+210 c d^4 x^4+84 d^5 x^5\right)+a b^6 d \left(28 c^6+210 c^5 d x+675 c^4 d^2 x^2+1200 c^3 d^3 x^3+1260 c^2 d^4 x^4+756 c d^5 x^5+210 d^6 x^6\right)+b^7 \left(36 c^7+280 c^6 d x+945 c^5 d^2 x^2+1800 c^4 d^3 x^3+2100 c^3 d^4 x^4+1512 c^2 d^5 x^5+630 c d^6 x^6+120 d^7 x^7\right)}{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,"-1/360*(a^7*d^7 + a^6*b*d^6*(3*c + 10*d*x) + 3*a^5*b^2*d^5*(2*c^2 + 10*c*d*x + 15*d^2*x^2) + 5*a^4*b^3*d^4*(2*c^3 + 12*c^2*d*x + 27*c*d^2*x^2 + 24*d^3*x^3) + 5*a^3*b^4*d^3*(3*c^4 + 20*c^3*d*x + 54*c^2*d^2*x^2 + 72*c*d^3*x^3 + 42*d^4*x^4) + 3*a^2*b^5*d^2*(7*c^5 + 50*c^4*d*x + 150*c^3*d^2*x^2 + 240*c^2*d^3*x^3 + 210*c*d^4*x^4 + 84*d^5*x^5) + a*b^6*d*(28*c^6 + 210*c^5*d*x + 675*c^4*d^2*x^2 + 1200*c^3*d^3*x^3 + 1260*c^2*d^4*x^4 + 756*c*d^5*x^5 + 210*d^6*x^6) + b^7*(36*c^7 + 280*c^6*d*x + 945*c^5*d^2*x^2 + 1800*c^4*d^3*x^3 + 2100*c^3*d^4*x^4 + 1512*c^2*d^5*x^5 + 630*c*d^6*x^6 + 120*d^7*x^7))/(b^8*(a + b*x)^10)","B",1
1294,1,369,120,0.1218378,"\int \frac{(c+d x)^7}{(a+b x)^{12}} \, dx","Integrate[(c + d*x)^7/(a + b*x)^12,x]","-\frac{a^7 d^7+a^6 b d^6 (4 c+11 d x)+a^5 b^2 d^5 \left(10 c^2+44 c d x+55 d^2 x^2\right)+5 a^4 b^3 d^4 \left(4 c^3+22 c^2 d x+44 c d^2 x^2+33 d^3 x^3\right)+5 a^3 b^4 d^3 \left(7 c^4+44 c^3 d x+110 c^2 d^2 x^2+132 c d^3 x^3+66 d^4 x^4\right)+a^2 b^5 d^2 \left(56 c^5+385 c^4 d x+1100 c^3 d^2 x^2+1650 c^2 d^3 x^3+1320 c d^4 x^4+462 d^5 x^5\right)+a b^6 d \left(84 c^6+616 c^5 d x+1925 c^4 d^2 x^2+3300 c^3 d^3 x^3+3300 c^2 d^4 x^4+1848 c d^5 x^5+462 d^6 x^6\right)+b^7 \left(120 c^7+924 c^6 d x+3080 c^5 d^2 x^2+5775 c^4 d^3 x^3+6600 c^3 d^4 x^4+4620 c^2 d^5 x^5+1848 c d^6 x^6+330 d^7 x^7\right)}{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,"-1/1320*(a^7*d^7 + a^6*b*d^6*(4*c + 11*d*x) + a^5*b^2*d^5*(10*c^2 + 44*c*d*x + 55*d^2*x^2) + 5*a^4*b^3*d^4*(4*c^3 + 22*c^2*d*x + 44*c*d^2*x^2 + 33*d^3*x^3) + 5*a^3*b^4*d^3*(7*c^4 + 44*c^3*d*x + 110*c^2*d^2*x^2 + 132*c*d^3*x^3 + 66*d^4*x^4) + a^2*b^5*d^2*(56*c^5 + 385*c^4*d*x + 1100*c^3*d^2*x^2 + 1650*c^2*d^3*x^3 + 1320*c*d^4*x^4 + 462*d^5*x^5) + a*b^6*d*(84*c^6 + 616*c^5*d*x + 1925*c^4*d^2*x^2 + 3300*c^3*d^3*x^3 + 3300*c^2*d^4*x^4 + 1848*c*d^5*x^5 + 462*d^6*x^6) + b^7*(120*c^7 + 924*c^6*d*x + 3080*c^5*d^2*x^2 + 5775*c^4*d^3*x^3 + 6600*c^3*d^4*x^4 + 4620*c^2*d^5*x^5 + 1848*c*d^6*x^6 + 330*d^7*x^7))/(b^8*(a + b*x)^11)","B",1
1295,1,371,151,0.1287392,"\int \frac{(c+d x)^7}{(a+b x)^{13}} \, dx","Integrate[(c + d*x)^7/(a + b*x)^13,x]","-\frac{a^7 d^7+a^6 b d^6 (5 c+12 d x)+3 a^5 b^2 d^5 \left(5 c^2+20 c d x+22 d^2 x^2\right)+5 a^4 b^3 d^4 \left(7 c^3+36 c^2 d x+66 c d^2 x^2+44 d^3 x^3\right)+5 a^3 b^4 d^3 \left(14 c^4+84 c^3 d x+198 c^2 d^2 x^2+220 c d^3 x^3+99 d^4 x^4\right)+3 a^2 b^5 d^2 \left(42 c^5+280 c^4 d x+770 c^3 d^2 x^2+1100 c^2 d^3 x^3+825 c d^4 x^4+264 d^5 x^5\right)+a b^6 d \left(210 c^6+1512 c^5 d x+4620 c^4 d^2 x^2+7700 c^3 d^3 x^3+7425 c^2 d^4 x^4+3960 c d^5 x^5+924 d^6 x^6\right)+b^7 \left(330 c^7+2520 c^6 d x+8316 c^5 d^2 x^2+15400 c^4 d^3 x^3+17325 c^3 d^4 x^4+11880 c^2 d^5 x^5+4620 c d^6 x^6+792 d^7 x^7\right)}{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,"-1/3960*(a^7*d^7 + a^6*b*d^6*(5*c + 12*d*x) + 3*a^5*b^2*d^5*(5*c^2 + 20*c*d*x + 22*d^2*x^2) + 5*a^4*b^3*d^4*(7*c^3 + 36*c^2*d*x + 66*c*d^2*x^2 + 44*d^3*x^3) + 5*a^3*b^4*d^3*(14*c^4 + 84*c^3*d*x + 198*c^2*d^2*x^2 + 220*c*d^3*x^3 + 99*d^4*x^4) + 3*a^2*b^5*d^2*(42*c^5 + 280*c^4*d*x + 770*c^3*d^2*x^2 + 1100*c^2*d^3*x^3 + 825*c*d^4*x^4 + 264*d^5*x^5) + a*b^6*d*(210*c^6 + 1512*c^5*d*x + 4620*c^4*d^2*x^2 + 7700*c^3*d^3*x^3 + 7425*c^2*d^4*x^4 + 3960*c*d^5*x^5 + 924*d^6*x^6) + b^7*(330*c^7 + 2520*c^6*d*x + 8316*c^5*d^2*x^2 + 15400*c^4*d^3*x^3 + 17325*c^3*d^4*x^4 + 11880*c^2*d^5*x^5 + 4620*c*d^6*x^6 + 792*d^7*x^7))/(b^8*(a + b*x)^12)","B",1
1296,1,369,198,0.1272177,"\int \frac{(c+d x)^7}{(a+b x)^{14}} \, dx","Integrate[(c + d*x)^7/(a + b*x)^14,x]","-\frac{a^7 d^7+a^6 b d^6 (6 c+13 d x)+3 a^5 b^2 d^5 \left(7 c^2+26 c d x+26 d^2 x^2\right)+a^4 b^3 d^4 \left(56 c^3+273 c^2 d x+468 c d^2 x^2+286 d^3 x^3\right)+a^3 b^4 d^3 \left(126 c^4+728 c^3 d x+1638 c^2 d^2 x^2+1716 c d^3 x^3+715 d^4 x^4\right)+3 a^2 b^5 d^2 \left(84 c^5+546 c^4 d x+1456 c^3 d^2 x^2+2002 c^2 d^3 x^3+1430 c d^4 x^4+429 d^5 x^5\right)+a b^6 d \left(462 c^6+3276 c^5 d x+9828 c^4 d^2 x^2+16016 c^3 d^3 x^3+15015 c^2 d^4 x^4+7722 c d^5 x^5+1716 d^6 x^6\right)+b^7 \left(792 c^7+6006 c^6 d x+19656 c^5 d^2 x^2+36036 c^4 d^3 x^3+40040 c^3 d^4 x^4+27027 c^2 d^5 x^5+10296 c d^6 x^6+1716 d^7 x^7\right)}{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,"-1/10296*(a^7*d^7 + a^6*b*d^6*(6*c + 13*d*x) + 3*a^5*b^2*d^5*(7*c^2 + 26*c*d*x + 26*d^2*x^2) + a^4*b^3*d^4*(56*c^3 + 273*c^2*d*x + 468*c*d^2*x^2 + 286*d^3*x^3) + a^3*b^4*d^3*(126*c^4 + 728*c^3*d*x + 1638*c^2*d^2*x^2 + 1716*c*d^3*x^3 + 715*d^4*x^4) + 3*a^2*b^5*d^2*(84*c^5 + 546*c^4*d*x + 1456*c^3*d^2*x^2 + 2002*c^2*d^3*x^3 + 1430*c*d^4*x^4 + 429*d^5*x^5) + a*b^6*d*(462*c^6 + 3276*c^5*d*x + 9828*c^4*d^2*x^2 + 16016*c^3*d^3*x^3 + 15015*c^2*d^4*x^4 + 7722*c*d^5*x^5 + 1716*d^6*x^6) + b^7*(792*c^7 + 6006*c^6*d*x + 19656*c^5*d^2*x^2 + 36036*c^4*d^3*x^3 + 40040*c^3*d^4*x^4 + 27027*c^2*d^5*x^5 + 10296*c*d^6*x^6 + 1716*d^7*x^7))/(b^8*(a + b*x)^13)","A",1
1297,1,371,200,0.1265731,"\int \frac{(c+d x)^7}{(a+b x)^{15}} \, dx","Integrate[(c + d*x)^7/(a + b*x)^15,x]","-\frac{a^7 d^7+7 a^6 b d^6 (c+2 d x)+7 a^5 b^2 d^5 \left(4 c^2+14 c d x+13 d^2 x^2\right)+7 a^4 b^3 d^4 \left(12 c^3+56 c^2 d x+91 c d^2 x^2+52 d^3 x^3\right)+7 a^3 b^4 d^3 \left(30 c^4+168 c^3 d x+364 c^2 d^2 x^2+364 c d^3 x^3+143 d^4 x^4\right)+7 a^2 b^5 d^2 \left(66 c^5+420 c^4 d x+1092 c^3 d^2 x^2+1456 c^2 d^3 x^3+1001 c d^4 x^4+286 d^5 x^5\right)+7 a b^6 d \left(132 c^6+924 c^5 d x+2730 c^4 d^2 x^2+4368 c^3 d^3 x^3+4004 c^2 d^4 x^4+2002 c d^5 x^5+429 d^6 x^6\right)+b^7 \left(1716 c^7+12936 c^6 d x+42042 c^5 d^2 x^2+76440 c^4 d^3 x^3+84084 c^3 d^4 x^4+56056 c^2 d^5 x^5+21021 c d^6 x^6+3432 d^7 x^7\right)}{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,"-1/24024*(a^7*d^7 + 7*a^6*b*d^6*(c + 2*d*x) + 7*a^5*b^2*d^5*(4*c^2 + 14*c*d*x + 13*d^2*x^2) + 7*a^4*b^3*d^4*(12*c^3 + 56*c^2*d*x + 91*c*d^2*x^2 + 52*d^3*x^3) + 7*a^3*b^4*d^3*(30*c^4 + 168*c^3*d*x + 364*c^2*d^2*x^2 + 364*c*d^3*x^3 + 143*d^4*x^4) + 7*a^2*b^5*d^2*(66*c^5 + 420*c^4*d*x + 1092*c^3*d^2*x^2 + 1456*c^2*d^3*x^3 + 1001*c*d^4*x^4 + 286*d^5*x^5) + 7*a*b^6*d*(132*c^6 + 924*c^5*d*x + 2730*c^4*d^2*x^2 + 4368*c^3*d^3*x^3 + 4004*c^2*d^4*x^4 + 2002*c*d^5*x^5 + 429*d^6*x^6) + b^7*(1716*c^7 + 12936*c^6*d*x + 42042*c^5*d^2*x^2 + 76440*c^4*d^3*x^3 + 84084*c^3*d^4*x^4 + 56056*c^2*d^5*x^5 + 21021*c*d^6*x^6 + 3432*d^7*x^7))/(b^8*(a + b*x)^14)","A",1
1298,1,371,200,0.1280972,"\int \frac{(c+d x)^7}{(a+b x)^{16}} \, dx","Integrate[(c + d*x)^7/(a + b*x)^16,x]","-\frac{a^7 d^7+a^6 b d^6 (8 c+15 d x)+3 a^5 b^2 d^5 \left(12 c^2+40 c d x+35 d^2 x^2\right)+5 a^4 b^3 d^4 \left(24 c^3+108 c^2 d x+168 c d^2 x^2+91 d^3 x^3\right)+5 a^3 b^4 d^3 \left(66 c^4+360 c^3 d x+756 c^2 d^2 x^2+728 c d^3 x^3+273 d^4 x^4\right)+3 a^2 b^5 d^2 \left(264 c^5+1650 c^4 d x+4200 c^3 d^2 x^2+5460 c^2 d^3 x^3+3640 c d^4 x^4+1001 d^5 x^5\right)+a b^6 d \left(1716 c^6+11880 c^5 d x+34650 c^4 d^2 x^2+54600 c^3 d^3 x^3+49140 c^2 d^4 x^4+24024 c d^5 x^5+5005 d^6 x^6\right)+b^7 \left(3432 c^7+25740 c^6 d x+83160 c^5 d^2 x^2+150150 c^4 d^3 x^3+163800 c^3 d^4 x^4+108108 c^2 d^5 x^5+40040 c d^6 x^6+6435 d^7 x^7\right)}{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,"-1/51480*(a^7*d^7 + a^6*b*d^6*(8*c + 15*d*x) + 3*a^5*b^2*d^5*(12*c^2 + 40*c*d*x + 35*d^2*x^2) + 5*a^4*b^3*d^4*(24*c^3 + 108*c^2*d*x + 168*c*d^2*x^2 + 91*d^3*x^3) + 5*a^3*b^4*d^3*(66*c^4 + 360*c^3*d*x + 756*c^2*d^2*x^2 + 728*c*d^3*x^3 + 273*d^4*x^4) + 3*a^2*b^5*d^2*(264*c^5 + 1650*c^4*d*x + 4200*c^3*d^2*x^2 + 5460*c^2*d^3*x^3 + 3640*c*d^4*x^4 + 1001*d^5*x^5) + a*b^6*d*(1716*c^6 + 11880*c^5*d*x + 34650*c^4*d^2*x^2 + 54600*c^3*d^3*x^3 + 49140*c^2*d^4*x^4 + 24024*c*d^5*x^5 + 5005*d^6*x^6) + b^7*(3432*c^7 + 25740*c^6*d*x + 83160*c^5*d^2*x^2 + 150150*c^4*d^3*x^3 + 163800*c^3*d^4*x^4 + 108108*c^2*d^5*x^5 + 40040*c*d^6*x^6 + 6435*d^7*x^7))/(b^8*(a + b*x)^15)","A",1
1299,1,1817,275,0.2899543,"\int (a+b x)^{12} (c+d x)^{10} \, dx","Integrate[(a + b*x)^12*(c + d*x)^10,x]","\frac{1}{23} b^{12} d^{10} x^{23}+\frac{1}{11} b^{11} d^9 (5 b c+6 a d) x^{22}+\frac{1}{7} b^{10} d^8 \left(15 b^2 c^2+40 a b d c+22 a^2 d^2\right) x^{21}+b^9 d^7 \left(6 b^3 c^3+27 a b^2 d c^2+33 a^2 b d^2 c+11 a^3 d^3\right) x^{20}+\frac{5}{19} b^8 d^6 \left(42 b^4 c^4+288 a b^3 d c^3+594 a^2 b^2 d^2 c^2+440 a^3 b d^3 c+99 a^4 d^4\right) x^{19}+b^7 d^5 \left(14 b^5 c^5+140 a b^4 d c^4+440 a^2 b^3 d^2 c^3+550 a^3 b^2 d^3 c^2+275 a^4 b d^4 c+44 a^5 d^5\right) x^{18}+\frac{3}{17} b^6 d^4 \left(70 b^6 c^6+1008 a b^5 d c^5+4620 a^2 b^4 d^2 c^4+8800 a^3 b^3 d^3 c^3+7425 a^4 b^2 d^4 c^2+2640 a^5 b d^5 c+308 a^6 d^6\right) x^{17}+\frac{3}{2} b^5 d^3 \left(5 b^7 c^7+105 a b^6 d c^6+693 a^2 b^5 d^2 c^5+1925 a^3 b^4 d^3 c^4+2475 a^4 b^3 d^4 c^3+1485 a^5 b^2 d^5 c^2+385 a^6 b d^6 c+33 a^7 d^7\right) x^{16}+3 b^4 d^2 \left(b^8 c^8+32 a b^7 d c^7+308 a^2 b^6 d^2 c^6+1232 a^3 b^5 d^3 c^5+2310 a^4 b^4 d^4 c^4+2112 a^5 b^3 d^5 c^3+924 a^6 b^2 d^6 c^2+176 a^7 b d^7 c+11 a^8 d^8\right) x^{15}+\frac{5}{7} b^3 d \left(b^9 c^9+54 a b^8 d c^8+792 a^2 b^7 d^2 c^7+4620 a^3 b^6 d^3 c^6+12474 a^4 b^5 d^4 c^5+16632 a^5 b^4 d^5 c^4+11088 a^6 b^3 d^6 c^3+3564 a^7 b^2 d^7 c^2+495 a^8 b d^8 c+22 a^9 d^9\right) x^{14}+\frac{1}{13} b^2 \left(b^{10} c^{10}+120 a b^9 d c^9+2970 a^2 b^8 d^2 c^8+26400 a^3 b^7 d^3 c^7+103950 a^4 b^6 d^4 c^6+199584 a^5 b^5 d^5 c^5+194040 a^6 b^4 d^6 c^4+95040 a^7 b^3 d^7 c^3+22275 a^8 b^2 d^8 c^2+2200 a^9 b d^9 c+66 a^{10} d^{10}\right) x^{13}+a b \left(b^{10} c^{10}+55 a b^9 d c^9+825 a^2 b^8 d^2 c^8+4950 a^3 b^7 d^3 c^7+13860 a^4 b^6 d^4 c^6+19404 a^5 b^5 d^5 c^5+13860 a^6 b^4 d^6 c^4+4950 a^7 b^3 d^7 c^3+825 a^8 b^2 d^8 c^2+55 a^9 b d^9 c+a^{10} d^{10}\right) x^{12}+\frac{1}{11} a^2 \left(66 b^{10} c^{10}+2200 a b^9 d c^9+22275 a^2 b^8 d^2 c^8+95040 a^3 b^7 d^3 c^7+194040 a^4 b^6 d^4 c^6+199584 a^5 b^5 d^5 c^5+103950 a^6 b^4 d^6 c^4+26400 a^7 b^3 d^7 c^3+2970 a^8 b^2 d^8 c^2+120 a^9 b d^9 c+a^{10} d^{10}\right) x^{11}+a^3 c \left(22 b^9 c^9+495 a b^8 d c^8+3564 a^2 b^7 d^2 c^7+11088 a^3 b^6 d^3 c^6+16632 a^4 b^5 d^4 c^5+12474 a^5 b^4 d^5 c^4+4620 a^6 b^3 d^6 c^3+792 a^7 b^2 d^7 c^2+54 a^8 b d^8 c+a^9 d^9\right) x^{10}+5 a^4 c^2 \left(11 b^8 c^8+176 a b^7 d c^7+924 a^2 b^6 d^2 c^6+2112 a^3 b^5 d^3 c^5+2310 a^4 b^4 d^4 c^4+1232 a^5 b^3 d^5 c^3+308 a^6 b^2 d^6 c^2+32 a^7 b d^7 c+a^8 d^8\right) x^9+3 a^5 c^3 \left(33 b^7 c^7+385 a b^6 d c^6+1485 a^2 b^5 d^2 c^5+2475 a^3 b^4 d^3 c^4+1925 a^4 b^3 d^4 c^3+693 a^5 b^2 d^5 c^2+105 a^6 b d^6 c+5 a^7 d^7\right) x^8+\frac{3}{7} a^6 c^4 \left(308 b^6 c^6+2640 a b^5 d c^5+7425 a^2 b^4 d^2 c^4+8800 a^3 b^3 d^3 c^3+4620 a^4 b^2 d^4 c^2+1008 a^5 b d^5 c+70 a^6 d^6\right) x^7+3 a^7 c^5 \left(44 b^5 c^5+275 a b^4 d c^4+550 a^2 b^3 d^2 c^3+440 a^3 b^2 d^3 c^2+140 a^4 b d^4 c+14 a^5 d^5\right) x^6+a^8 c^6 \left(99 b^4 c^4+440 a b^3 d c^3+594 a^2 b^2 d^2 c^2+288 a^3 b d^3 c+42 a^4 d^4\right) x^5+5 a^9 c^7 \left(11 b^3 c^3+33 a b^2 d c^2+27 a^2 b d^2 c+6 a^3 d^3\right) x^4+a^{10} c^8 \left(22 b^2 c^2+40 a b d c+15 a^2 d^2\right) x^3+a^{11} c^9 (6 b c+5 a d) x^2+a^{12} c^{10} x","\frac{5 d^9 (a+b x)^{22} (b c-a d)}{11 b^{11}}+\frac{15 d^8 (a+b x)^{21} (b c-a d)^2}{7 b^{11}}+\frac{6 d^7 (a+b x)^{20} (b c-a d)^3}{b^{11}}+\frac{210 d^6 (a+b x)^{19} (b c-a d)^4}{19 b^{11}}+\frac{14 d^5 (a+b x)^{18} (b c-a d)^5}{b^{11}}+\frac{210 d^4 (a+b x)^{17} (b c-a d)^6}{17 b^{11}}+\frac{15 d^3 (a+b x)^{16} (b c-a d)^7}{2 b^{11}}+\frac{3 d^2 (a+b x)^{15} (b c-a d)^8}{b^{11}}+\frac{5 d (a+b x)^{14} (b c-a d)^9}{7 b^{11}}+\frac{(a+b x)^{13} (b c-a d)^{10}}{13 b^{11}}+\frac{d^{10} (a+b x)^{23}}{23 b^{11}}",1,"a^12*c^10*x + a^11*c^9*(6*b*c + 5*a*d)*x^2 + a^10*c^8*(22*b^2*c^2 + 40*a*b*c*d + 15*a^2*d^2)*x^3 + 5*a^9*c^7*(11*b^3*c^3 + 33*a*b^2*c^2*d + 27*a^2*b*c*d^2 + 6*a^3*d^3)*x^4 + a^8*c^6*(99*b^4*c^4 + 440*a*b^3*c^3*d + 594*a^2*b^2*c^2*d^2 + 288*a^3*b*c*d^3 + 42*a^4*d^4)*x^5 + 3*a^7*c^5*(44*b^5*c^5 + 275*a*b^4*c^4*d + 550*a^2*b^3*c^3*d^2 + 440*a^3*b^2*c^2*d^3 + 140*a^4*b*c*d^4 + 14*a^5*d^5)*x^6 + (3*a^6*c^4*(308*b^6*c^6 + 2640*a*b^5*c^5*d + 7425*a^2*b^4*c^4*d^2 + 8800*a^3*b^3*c^3*d^3 + 4620*a^4*b^2*c^2*d^4 + 1008*a^5*b*c*d^5 + 70*a^6*d^6)*x^7)/7 + 3*a^5*c^3*(33*b^7*c^7 + 385*a*b^6*c^6*d + 1485*a^2*b^5*c^5*d^2 + 2475*a^3*b^4*c^4*d^3 + 1925*a^4*b^3*c^3*d^4 + 693*a^5*b^2*c^2*d^5 + 105*a^6*b*c*d^6 + 5*a^7*d^7)*x^8 + 5*a^4*c^2*(11*b^8*c^8 + 176*a*b^7*c^7*d + 924*a^2*b^6*c^6*d^2 + 2112*a^3*b^5*c^5*d^3 + 2310*a^4*b^4*c^4*d^4 + 1232*a^5*b^3*c^3*d^5 + 308*a^6*b^2*c^2*d^6 + 32*a^7*b*c*d^7 + a^8*d^8)*x^9 + a^3*c*(22*b^9*c^9 + 495*a*b^8*c^8*d + 3564*a^2*b^7*c^7*d^2 + 11088*a^3*b^6*c^6*d^3 + 16632*a^4*b^5*c^5*d^4 + 12474*a^5*b^4*c^4*d^5 + 4620*a^6*b^3*c^3*d^6 + 792*a^7*b^2*c^2*d^7 + 54*a^8*b*c*d^8 + a^9*d^9)*x^10 + (a^2*(66*b^10*c^10 + 2200*a*b^9*c^9*d + 22275*a^2*b^8*c^8*d^2 + 95040*a^3*b^7*c^7*d^3 + 194040*a^4*b^6*c^6*d^4 + 199584*a^5*b^5*c^5*d^5 + 103950*a^6*b^4*c^4*d^6 + 26400*a^7*b^3*c^3*d^7 + 2970*a^8*b^2*c^2*d^8 + 120*a^9*b*c*d^9 + a^10*d^10)*x^11)/11 + a*b*(b^10*c^10 + 55*a*b^9*c^9*d + 825*a^2*b^8*c^8*d^2 + 4950*a^3*b^7*c^7*d^3 + 13860*a^4*b^6*c^6*d^4 + 19404*a^5*b^5*c^5*d^5 + 13860*a^6*b^4*c^4*d^6 + 4950*a^7*b^3*c^3*d^7 + 825*a^8*b^2*c^2*d^8 + 55*a^9*b*c*d^9 + a^10*d^10)*x^12 + (b^2*(b^10*c^10 + 120*a*b^9*c^9*d + 2970*a^2*b^8*c^8*d^2 + 26400*a^3*b^7*c^7*d^3 + 103950*a^4*b^6*c^6*d^4 + 199584*a^5*b^5*c^5*d^5 + 194040*a^6*b^4*c^4*d^6 + 95040*a^7*b^3*c^3*d^7 + 22275*a^8*b^2*c^2*d^8 + 2200*a^9*b*c*d^9 + 66*a^10*d^10)*x^13)/13 + (5*b^3*d*(b^9*c^9 + 54*a*b^8*c^8*d + 792*a^2*b^7*c^7*d^2 + 4620*a^3*b^6*c^6*d^3 + 12474*a^4*b^5*c^5*d^4 + 16632*a^5*b^4*c^4*d^5 + 11088*a^6*b^3*c^3*d^6 + 3564*a^7*b^2*c^2*d^7 + 495*a^8*b*c*d^8 + 22*a^9*d^9)*x^14)/7 + 3*b^4*d^2*(b^8*c^8 + 32*a*b^7*c^7*d + 308*a^2*b^6*c^6*d^2 + 1232*a^3*b^5*c^5*d^3 + 2310*a^4*b^4*c^4*d^4 + 2112*a^5*b^3*c^3*d^5 + 924*a^6*b^2*c^2*d^6 + 176*a^7*b*c*d^7 + 11*a^8*d^8)*x^15 + (3*b^5*d^3*(5*b^7*c^7 + 105*a*b^6*c^6*d + 693*a^2*b^5*c^5*d^2 + 1925*a^3*b^4*c^4*d^3 + 2475*a^4*b^3*c^3*d^4 + 1485*a^5*b^2*c^2*d^5 + 385*a^6*b*c*d^6 + 33*a^7*d^7)*x^16)/2 + (3*b^6*d^4*(70*b^6*c^6 + 1008*a*b^5*c^5*d + 4620*a^2*b^4*c^4*d^2 + 8800*a^3*b^3*c^3*d^3 + 7425*a^4*b^2*c^2*d^4 + 2640*a^5*b*c*d^5 + 308*a^6*d^6)*x^17)/17 + b^7*d^5*(14*b^5*c^5 + 140*a*b^4*c^4*d + 440*a^2*b^3*c^3*d^2 + 550*a^3*b^2*c^2*d^3 + 275*a^4*b*c*d^4 + 44*a^5*d^5)*x^18 + (5*b^8*d^6*(42*b^4*c^4 + 288*a*b^3*c^3*d + 594*a^2*b^2*c^2*d^2 + 440*a^3*b*c*d^3 + 99*a^4*d^4)*x^19)/19 + b^9*d^7*(6*b^3*c^3 + 27*a*b^2*c^2*d + 33*a^2*b*c*d^2 + 11*a^3*d^3)*x^20 + (b^10*d^8*(15*b^2*c^2 + 40*a*b*c*d + 22*a^2*d^2)*x^21)/7 + (b^11*d^9*(5*b*c + 6*a*d)*x^22)/11 + (b^12*d^10*x^23)/23","B",1
1300,1,1702,279,0.2255248,"\int (a+b x)^{11} (c+d x)^{10} \, dx","Integrate[(a + b*x)^11*(c + d*x)^10,x]","\frac{1}{22} b^{11} d^{10} x^{22}+\frac{1}{21} b^{10} d^9 (10 b c+11 a d) x^{21}+\frac{1}{4} b^9 d^8 \left(9 b^2 c^2+22 a b d c+11 a^2 d^2\right) x^{20}+\frac{5}{19} b^8 d^7 \left(24 b^3 c^3+99 a b^2 d c^2+110 a^2 b d^2 c+33 a^3 d^3\right) x^{19}+\frac{5}{6} b^7 d^6 \left(14 b^4 c^4+88 a b^3 d c^3+165 a^2 b^2 d^2 c^2+110 a^3 b d^3 c+22 a^4 d^4\right) x^{18}+\frac{3}{17} b^6 d^5 \left(84 b^5 c^5+770 a b^4 d c^4+2200 a^2 b^3 d^2 c^3+2475 a^3 b^2 d^3 c^2+1100 a^4 b d^4 c+154 a^5 d^5\right) x^{17}+\frac{3}{8} b^5 d^4 \left(35 b^6 c^6+462 a b^5 d c^5+1925 a^2 b^4 d^2 c^4+3300 a^3 b^3 d^3 c^3+2475 a^4 b^2 d^4 c^2+770 a^5 b d^5 c+77 a^6 d^6\right) x^{16}+2 b^4 d^3 \left(4 b^7 c^7+77 a b^6 d c^6+462 a^2 b^5 d^2 c^5+1155 a^3 b^4 d^3 c^4+1320 a^4 b^3 d^4 c^3+693 a^5 b^2 d^5 c^2+154 a^6 b d^6 c+11 a^7 d^7\right) x^{15}+\frac{15}{14} b^3 d^2 \left(3 b^8 c^8+88 a b^7 d c^7+770 a^2 b^6 d^2 c^6+2772 a^3 b^5 d^3 c^5+4620 a^4 b^4 d^4 c^4+3696 a^5 b^3 d^5 c^3+1386 a^6 b^2 d^6 c^2+220 a^7 b d^7 c+11 a^8 d^8\right) x^{14}+\frac{5}{13} b^2 d \left(2 b^9 c^9+99 a b^8 d c^8+1320 a^2 b^7 d^2 c^7+6930 a^3 b^6 d^3 c^6+16632 a^4 b^5 d^4 c^5+19404 a^5 b^4 d^5 c^4+11088 a^6 b^3 d^6 c^3+2970 a^7 b^2 d^7 c^2+330 a^8 b d^8 c+11 a^9 d^9\right) x^{13}+\frac{1}{12} b \left(b^{10} c^{10}+110 a b^9 d c^9+2475 a^2 b^8 d^2 c^8+19800 a^3 b^7 d^3 c^7+69300 a^4 b^6 d^4 c^6+116424 a^5 b^5 d^5 c^5+97020 a^6 b^4 d^6 c^4+39600 a^7 b^3 d^7 c^3+7425 a^8 b^2 d^8 c^2+550 a^9 b d^9 c+11 a^{10} d^{10}\right) x^{12}+\frac{1}{11} a \left(11 b^{10} c^{10}+550 a b^9 d c^9+7425 a^2 b^8 d^2 c^8+39600 a^3 b^7 d^3 c^7+97020 a^4 b^6 d^4 c^6+116424 a^5 b^5 d^5 c^5+69300 a^6 b^4 d^6 c^4+19800 a^7 b^3 d^7 c^3+2475 a^8 b^2 d^8 c^2+110 a^9 b d^9 c+a^{10} d^{10}\right) x^{11}+\frac{1}{2} a^2 c \left(11 b^9 c^9+330 a b^8 d c^8+2970 a^2 b^7 d^2 c^7+11088 a^3 b^6 d^3 c^6+19404 a^4 b^5 d^4 c^5+16632 a^5 b^4 d^5 c^4+6930 a^6 b^3 d^6 c^3+1320 a^7 b^2 d^7 c^2+99 a^8 b d^8 c+2 a^9 d^9\right) x^{10}+\frac{5}{3} a^3 c^2 \left(11 b^8 c^8+220 a b^7 d c^7+1386 a^2 b^6 d^2 c^6+3696 a^3 b^5 d^3 c^5+4620 a^4 b^4 d^4 c^4+2772 a^5 b^3 d^5 c^3+770 a^6 b^2 d^6 c^2+88 a^7 b d^7 c+3 a^8 d^8\right) x^9+\frac{15}{4} a^4 c^3 \left(11 b^7 c^7+154 a b^6 d c^6+693 a^2 b^5 d^2 c^5+1320 a^3 b^4 d^3 c^4+1155 a^4 b^3 d^4 c^3+462 a^5 b^2 d^5 c^2+77 a^6 b d^6 c+4 a^7 d^7\right) x^8+\frac{6}{7} a^5 c^4 \left(77 b^6 c^6+770 a b^5 d c^5+2475 a^2 b^4 d^2 c^4+3300 a^3 b^3 d^3 c^3+1925 a^4 b^2 d^4 c^2+462 a^5 b d^5 c+35 a^6 d^6\right) x^7+\frac{1}{2} a^6 c^5 \left(154 b^5 c^5+1100 a b^4 d c^4+2475 a^2 b^3 d^2 c^3+2200 a^3 b^2 d^3 c^2+770 a^4 b d^4 c+84 a^5 d^5\right) x^6+3 a^7 c^6 \left(22 b^4 c^4+110 a b^3 d c^3+165 a^2 b^2 d^2 c^2+88 a^3 b d^3 c+14 a^4 d^4\right) x^5+\frac{5}{4} a^8 c^7 \left(33 b^3 c^3+110 a b^2 d c^2+99 a^2 b d^2 c+24 a^3 d^3\right) x^4+\frac{5}{3} a^9 c^8 \left(11 b^2 c^2+22 a b d c+9 a^2 d^2\right) x^3+\frac{1}{2} a^{10} c^9 (11 b c+10 a d) x^2+a^{11} c^{10} x","\frac{10 d^9 (a+b x)^{21} (b c-a d)}{21 b^{11}}+\frac{9 d^8 (a+b x)^{20} (b c-a d)^2}{4 b^{11}}+\frac{120 d^7 (a+b x)^{19} (b c-a d)^3}{19 b^{11}}+\frac{35 d^6 (a+b x)^{18} (b c-a d)^4}{3 b^{11}}+\frac{252 d^5 (a+b x)^{17} (b c-a d)^5}{17 b^{11}}+\frac{105 d^4 (a+b x)^{16} (b c-a d)^6}{8 b^{11}}+\frac{8 d^3 (a+b x)^{15} (b c-a d)^7}{b^{11}}+\frac{45 d^2 (a+b x)^{14} (b c-a d)^8}{14 b^{11}}+\frac{10 d (a+b x)^{13} (b c-a d)^9}{13 b^{11}}+\frac{(a+b x)^{12} (b c-a d)^{10}}{12 b^{11}}+\frac{d^{10} (a+b x)^{22}}{22 b^{11}}",1,"a^11*c^10*x + (a^10*c^9*(11*b*c + 10*a*d)*x^2)/2 + (5*a^9*c^8*(11*b^2*c^2 + 22*a*b*c*d + 9*a^2*d^2)*x^3)/3 + (5*a^8*c^7*(33*b^3*c^3 + 110*a*b^2*c^2*d + 99*a^2*b*c*d^2 + 24*a^3*d^3)*x^4)/4 + 3*a^7*c^6*(22*b^4*c^4 + 110*a*b^3*c^3*d + 165*a^2*b^2*c^2*d^2 + 88*a^3*b*c*d^3 + 14*a^4*d^4)*x^5 + (a^6*c^5*(154*b^5*c^5 + 1100*a*b^4*c^4*d + 2475*a^2*b^3*c^3*d^2 + 2200*a^3*b^2*c^2*d^3 + 770*a^4*b*c*d^4 + 84*a^5*d^5)*x^6)/2 + (6*a^5*c^4*(77*b^6*c^6 + 770*a*b^5*c^5*d + 2475*a^2*b^4*c^4*d^2 + 3300*a^3*b^3*c^3*d^3 + 1925*a^4*b^2*c^2*d^4 + 462*a^5*b*c*d^5 + 35*a^6*d^6)*x^7)/7 + (15*a^4*c^3*(11*b^7*c^7 + 154*a*b^6*c^6*d + 693*a^2*b^5*c^5*d^2 + 1320*a^3*b^4*c^4*d^3 + 1155*a^4*b^3*c^3*d^4 + 462*a^5*b^2*c^2*d^5 + 77*a^6*b*c*d^6 + 4*a^7*d^7)*x^8)/4 + (5*a^3*c^2*(11*b^8*c^8 + 220*a*b^7*c^7*d + 1386*a^2*b^6*c^6*d^2 + 3696*a^3*b^5*c^5*d^3 + 4620*a^4*b^4*c^4*d^4 + 2772*a^5*b^3*c^3*d^5 + 770*a^6*b^2*c^2*d^6 + 88*a^7*b*c*d^7 + 3*a^8*d^8)*x^9)/3 + (a^2*c*(11*b^9*c^9 + 330*a*b^8*c^8*d + 2970*a^2*b^7*c^7*d^2 + 11088*a^3*b^6*c^6*d^3 + 19404*a^4*b^5*c^5*d^4 + 16632*a^5*b^4*c^4*d^5 + 6930*a^6*b^3*c^3*d^6 + 1320*a^7*b^2*c^2*d^7 + 99*a^8*b*c*d^8 + 2*a^9*d^9)*x^10)/2 + (a*(11*b^10*c^10 + 550*a*b^9*c^9*d + 7425*a^2*b^8*c^8*d^2 + 39600*a^3*b^7*c^7*d^3 + 97020*a^4*b^6*c^6*d^4 + 116424*a^5*b^5*c^5*d^5 + 69300*a^6*b^4*c^4*d^6 + 19800*a^7*b^3*c^3*d^7 + 2475*a^8*b^2*c^2*d^8 + 110*a^9*b*c*d^9 + a^10*d^10)*x^11)/11 + (b*(b^10*c^10 + 110*a*b^9*c^9*d + 2475*a^2*b^8*c^8*d^2 + 19800*a^3*b^7*c^7*d^3 + 69300*a^4*b^6*c^6*d^4 + 116424*a^5*b^5*c^5*d^5 + 97020*a^6*b^4*c^4*d^6 + 39600*a^7*b^3*c^3*d^7 + 7425*a^8*b^2*c^2*d^8 + 550*a^9*b*c*d^9 + 11*a^10*d^10)*x^12)/12 + (5*b^2*d*(2*b^9*c^9 + 99*a*b^8*c^8*d + 1320*a^2*b^7*c^7*d^2 + 6930*a^3*b^6*c^6*d^3 + 16632*a^4*b^5*c^5*d^4 + 19404*a^5*b^4*c^4*d^5 + 11088*a^6*b^3*c^3*d^6 + 2970*a^7*b^2*c^2*d^7 + 330*a^8*b*c*d^8 + 11*a^9*d^9)*x^13)/13 + (15*b^3*d^2*(3*b^8*c^8 + 88*a*b^7*c^7*d + 770*a^2*b^6*c^6*d^2 + 2772*a^3*b^5*c^5*d^3 + 4620*a^4*b^4*c^4*d^4 + 3696*a^5*b^3*c^3*d^5 + 1386*a^6*b^2*c^2*d^6 + 220*a^7*b*c*d^7 + 11*a^8*d^8)*x^14)/14 + 2*b^4*d^3*(4*b^7*c^7 + 77*a*b^6*c^6*d + 462*a^2*b^5*c^5*d^2 + 1155*a^3*b^4*c^4*d^3 + 1320*a^4*b^3*c^3*d^4 + 693*a^5*b^2*c^2*d^5 + 154*a^6*b*c*d^6 + 11*a^7*d^7)*x^15 + (3*b^5*d^4*(35*b^6*c^6 + 462*a*b^5*c^5*d + 1925*a^2*b^4*c^4*d^2 + 3300*a^3*b^3*c^3*d^3 + 2475*a^4*b^2*c^2*d^4 + 770*a^5*b*c*d^5 + 77*a^6*d^6)*x^16)/8 + (3*b^6*d^5*(84*b^5*c^5 + 770*a*b^4*c^4*d + 2200*a^2*b^3*c^3*d^2 + 2475*a^3*b^2*c^2*d^3 + 1100*a^4*b*c*d^4 + 154*a^5*d^5)*x^17)/17 + (5*b^7*d^6*(14*b^4*c^4 + 88*a*b^3*c^3*d + 165*a^2*b^2*c^2*d^2 + 110*a^3*b*c*d^3 + 22*a^4*d^4)*x^18)/6 + (5*b^8*d^7*(24*b^3*c^3 + 99*a*b^2*c^2*d + 110*a^2*b*c*d^2 + 33*a^3*d^3)*x^19)/19 + (b^9*d^8*(9*b^2*c^2 + 22*a*b*c*d + 11*a^2*d^2)*x^20)/4 + (b^10*d^9*(10*b*c + 11*a*d)*x^21)/21 + (b^11*d^10*x^22)/22","B",1
1301,1,1539,279,0.1726162,"\int (a+b x)^{10} (c+d x)^{10} \, dx","Integrate[(a + b*x)^10*(c + d*x)^10,x]","\frac{1}{21} b^{10} d^{10} x^{21}+\frac{1}{2} b^9 d^9 (b c+a d) x^{20}+\frac{5}{19} b^8 d^8 \left(9 b^2 c^2+20 a b d c+9 a^2 d^2\right) x^{19}+\frac{5}{3} b^7 d^7 \left(4 b^3 c^3+15 a b^2 d c^2+15 a^2 b d^2 c+4 a^3 d^3\right) x^{18}+\frac{15}{17} b^6 d^6 \left(14 b^4 c^4+80 a b^3 d c^3+135 a^2 b^2 d^2 c^2+80 a^3 b d^3 c+14 a^4 d^4\right) x^{17}+\frac{3}{4} b^5 d^5 \left(21 b^5 c^5+175 a b^4 d c^4+450 a^2 b^3 d^2 c^3+450 a^3 b^2 d^3 c^2+175 a^4 b d^4 c+21 a^5 d^5\right) x^{16}+2 b^4 d^4 \left(7 b^6 c^6+84 a b^5 d c^5+315 a^2 b^4 d^2 c^4+480 a^3 b^3 d^3 c^3+315 a^4 b^2 d^4 c^2+84 a^5 b d^5 c+7 a^6 d^6\right) x^{15}+\frac{30}{7} b^3 d^3 \left(2 b^7 c^7+35 a b^6 d c^6+189 a^2 b^5 d^2 c^5+420 a^3 b^4 d^3 c^4+420 a^4 b^3 d^4 c^3+189 a^5 b^2 d^5 c^2+35 a^6 b d^6 c+2 a^7 d^7\right) x^{14}+\frac{15}{13} b^2 d^2 \left(3 b^8 c^8+80 a b^7 d c^7+630 a^2 b^6 d^2 c^6+2016 a^3 b^5 d^3 c^5+2940 a^4 b^4 d^4 c^4+2016 a^5 b^3 d^5 c^3+630 a^6 b^2 d^6 c^2+80 a^7 b d^7 c+3 a^8 d^8\right) x^{13}+\frac{5}{6} b d \left(b^9 c^9+45 a b^8 d c^8+540 a^2 b^7 d^2 c^7+2520 a^3 b^6 d^3 c^6+5292 a^4 b^5 d^4 c^5+5292 a^5 b^4 d^5 c^4+2520 a^6 b^3 d^6 c^3+540 a^7 b^2 d^7 c^2+45 a^8 b d^8 c+a^9 d^9\right) x^{12}+\frac{1}{11} \left(b^{10} c^{10}+100 a b^9 d c^9+2025 a^2 b^8 d^2 c^8+14400 a^3 b^7 d^3 c^7+44100 a^4 b^6 d^4 c^6+63504 a^5 b^5 d^5 c^5+44100 a^6 b^4 d^6 c^4+14400 a^7 b^3 d^7 c^3+2025 a^8 b^2 d^8 c^2+100 a^9 b d^9 c+a^{10} d^{10}\right) x^{11}+a c \left(b^9 c^9+45 a b^8 d c^8+540 a^2 b^7 d^2 c^7+2520 a^3 b^6 d^3 c^6+5292 a^4 b^5 d^4 c^5+5292 a^5 b^4 d^5 c^4+2520 a^6 b^3 d^6 c^3+540 a^7 b^2 d^7 c^2+45 a^8 b d^8 c+a^9 d^9\right) x^{10}+\frac{5}{3} a^2 c^2 \left(3 b^8 c^8+80 a b^7 d c^7+630 a^2 b^6 d^2 c^6+2016 a^3 b^5 d^3 c^5+2940 a^4 b^4 d^4 c^4+2016 a^5 b^3 d^5 c^3+630 a^6 b^2 d^6 c^2+80 a^7 b d^7 c+3 a^8 d^8\right) x^9+\frac{15}{2} a^3 c^3 \left(2 b^7 c^7+35 a b^6 d c^6+189 a^2 b^5 d^2 c^5+420 a^3 b^4 d^3 c^4+420 a^4 b^3 d^4 c^3+189 a^5 b^2 d^5 c^2+35 a^6 b d^6 c+2 a^7 d^7\right) x^8+\frac{30}{7} a^4 c^4 \left(7 b^6 c^6+84 a b^5 d c^5+315 a^2 b^4 d^2 c^4+480 a^3 b^3 d^3 c^3+315 a^4 b^2 d^4 c^2+84 a^5 b d^5 c+7 a^6 d^6\right) x^7+2 a^5 c^5 \left(21 b^5 c^5+175 a b^4 d c^4+450 a^2 b^3 d^2 c^3+450 a^3 b^2 d^3 c^2+175 a^4 b d^4 c+21 a^5 d^5\right) x^6+3 a^6 c^6 \left(14 b^4 c^4+80 a b^3 d c^3+135 a^2 b^2 d^2 c^2+80 a^3 b d^3 c+14 a^4 d^4\right) x^5+\frac{15}{2} a^7 c^7 \left(4 b^3 c^3+15 a b^2 d c^2+15 a^2 b d^2 c+4 a^3 d^3\right) x^4+\frac{5}{3} a^8 c^8 \left(9 b^2 c^2+20 a b d c+9 a^2 d^2\right) x^3+5 a^9 c^9 (b c+a d) x^2+a^{10} c^{10} x","\frac{d^9 (a+b x)^{20} (b c-a d)}{2 b^{11}}+\frac{45 d^8 (a+b x)^{19} (b c-a d)^2}{19 b^{11}}+\frac{20 d^7 (a+b x)^{18} (b c-a d)^3}{3 b^{11}}+\frac{210 d^6 (a+b x)^{17} (b c-a d)^4}{17 b^{11}}+\frac{63 d^5 (a+b x)^{16} (b c-a d)^5}{4 b^{11}}+\frac{14 d^4 (a+b x)^{15} (b c-a d)^6}{b^{11}}+\frac{60 d^3 (a+b x)^{14} (b c-a d)^7}{7 b^{11}}+\frac{45 d^2 (a+b x)^{13} (b c-a d)^8}{13 b^{11}}+\frac{5 d (a+b x)^{12} (b c-a d)^9}{6 b^{11}}+\frac{(a+b x)^{11} (b c-a d)^{10}}{11 b^{11}}+\frac{d^{10} (a+b x)^{21}}{21 b^{11}}",1,"a^10*c^10*x + 5*a^9*c^9*(b*c + a*d)*x^2 + (5*a^8*c^8*(9*b^2*c^2 + 20*a*b*c*d + 9*a^2*d^2)*x^3)/3 + (15*a^7*c^7*(4*b^3*c^3 + 15*a*b^2*c^2*d + 15*a^2*b*c*d^2 + 4*a^3*d^3)*x^4)/2 + 3*a^6*c^6*(14*b^4*c^4 + 80*a*b^3*c^3*d + 135*a^2*b^2*c^2*d^2 + 80*a^3*b*c*d^3 + 14*a^4*d^4)*x^5 + 2*a^5*c^5*(21*b^5*c^5 + 175*a*b^4*c^4*d + 450*a^2*b^3*c^3*d^2 + 450*a^3*b^2*c^2*d^3 + 175*a^4*b*c*d^4 + 21*a^5*d^5)*x^6 + (30*a^4*c^4*(7*b^6*c^6 + 84*a*b^5*c^5*d + 315*a^2*b^4*c^4*d^2 + 480*a^3*b^3*c^3*d^3 + 315*a^4*b^2*c^2*d^4 + 84*a^5*b*c*d^5 + 7*a^6*d^6)*x^7)/7 + (15*a^3*c^3*(2*b^7*c^7 + 35*a*b^6*c^6*d + 189*a^2*b^5*c^5*d^2 + 420*a^3*b^4*c^4*d^3 + 420*a^4*b^3*c^3*d^4 + 189*a^5*b^2*c^2*d^5 + 35*a^6*b*c*d^6 + 2*a^7*d^7)*x^8)/2 + (5*a^2*c^2*(3*b^8*c^8 + 80*a*b^7*c^7*d + 630*a^2*b^6*c^6*d^2 + 2016*a^3*b^5*c^5*d^3 + 2940*a^4*b^4*c^4*d^4 + 2016*a^5*b^3*c^3*d^5 + 630*a^6*b^2*c^2*d^6 + 80*a^7*b*c*d^7 + 3*a^8*d^8)*x^9)/3 + a*c*(b^9*c^9 + 45*a*b^8*c^8*d + 540*a^2*b^7*c^7*d^2 + 2520*a^3*b^6*c^6*d^3 + 5292*a^4*b^5*c^5*d^4 + 5292*a^5*b^4*c^4*d^5 + 2520*a^6*b^3*c^3*d^6 + 540*a^7*b^2*c^2*d^7 + 45*a^8*b*c*d^8 + a^9*d^9)*x^10 + ((b^10*c^10 + 100*a*b^9*c^9*d + 2025*a^2*b^8*c^8*d^2 + 14400*a^3*b^7*c^7*d^3 + 44100*a^4*b^6*c^6*d^4 + 63504*a^5*b^5*c^5*d^5 + 44100*a^6*b^4*c^4*d^6 + 14400*a^7*b^3*c^3*d^7 + 2025*a^8*b^2*c^2*d^8 + 100*a^9*b*c*d^9 + a^10*d^10)*x^11)/11 + (5*b*d*(b^9*c^9 + 45*a*b^8*c^8*d + 540*a^2*b^7*c^7*d^2 + 2520*a^3*b^6*c^6*d^3 + 5292*a^4*b^5*c^5*d^4 + 5292*a^5*b^4*c^4*d^5 + 2520*a^6*b^3*c^3*d^6 + 540*a^7*b^2*c^2*d^7 + 45*a^8*b*c*d^8 + a^9*d^9)*x^12)/6 + (15*b^2*d^2*(3*b^8*c^8 + 80*a*b^7*c^7*d + 630*a^2*b^6*c^6*d^2 + 2016*a^3*b^5*c^5*d^3 + 2940*a^4*b^4*c^4*d^4 + 2016*a^5*b^3*c^3*d^5 + 630*a^6*b^2*c^2*d^6 + 80*a^7*b*c*d^7 + 3*a^8*d^8)*x^13)/13 + (30*b^3*d^3*(2*b^7*c^7 + 35*a*b^6*c^6*d + 189*a^2*b^5*c^5*d^2 + 420*a^3*b^4*c^4*d^3 + 420*a^4*b^3*c^3*d^4 + 189*a^5*b^2*c^2*d^5 + 35*a^6*b*c*d^6 + 2*a^7*d^7)*x^14)/7 + 2*b^4*d^4*(7*b^6*c^6 + 84*a*b^5*c^5*d + 315*a^2*b^4*c^4*d^2 + 480*a^3*b^3*c^3*d^3 + 315*a^4*b^2*c^2*d^4 + 84*a^5*b*c*d^5 + 7*a^6*d^6)*x^15 + (3*b^5*d^5*(21*b^5*c^5 + 175*a*b^4*c^4*d + 450*a^2*b^3*c^3*d^2 + 450*a^3*b^2*c^2*d^3 + 175*a^4*b*c*d^4 + 21*a^5*d^5)*x^16)/4 + (15*b^6*d^6*(14*b^4*c^4 + 80*a*b^3*c^3*d + 135*a^2*b^2*c^2*d^2 + 80*a^3*b*c*d^3 + 14*a^4*d^4)*x^17)/17 + (5*b^7*d^7*(4*b^3*c^3 + 15*a*b^2*c^2*d + 15*a^2*b*c*d^2 + 4*a^3*d^3)*x^18)/3 + (5*b^8*d^8*(9*b^2*c^2 + 20*a*b*c*d + 9*a^2*d^2)*x^19)/19 + (b^9*d^9*(b*c + a*d)*x^20)/2 + (b^10*d^10*x^21)/21","B",1
1302,1,1397,250,0.1853936,"\int (a+b x)^9 (c+d x)^{10} \, dx","Integrate[(a + b*x)^9*(c + d*x)^10,x]","\frac{1}{20} b^9 d^{10} x^{20}+\frac{1}{19} b^8 d^9 (10 b c+9 a d) x^{19}+\frac{1}{2} b^7 d^8 \left(5 b^2 c^2+10 a b d c+4 a^2 d^2\right) x^{18}+\frac{3}{17} b^6 d^7 \left(40 b^3 c^3+135 a b^2 d c^2+120 a^2 b d^2 c+28 a^3 d^3\right) x^{17}+\frac{3}{8} b^5 d^6 \left(35 b^4 c^4+180 a b^3 d c^3+270 a^2 b^2 d^2 c^2+140 a^3 b d^3 c+21 a^4 d^4\right) x^{16}+\frac{6}{5} b^4 d^5 \left(14 b^5 c^5+105 a b^4 d c^4+240 a^2 b^3 d^2 c^3+210 a^3 b^2 d^3 c^2+70 a^4 b d^4 c+7 a^5 d^5\right) x^{15}+3 b^3 d^4 \left(5 b^6 c^6+54 a b^5 d c^5+180 a^2 b^4 d^2 c^4+240 a^3 b^3 d^3 c^3+135 a^4 b^2 d^4 c^2+30 a^5 b d^5 c+2 a^6 d^6\right) x^{14}+\frac{6}{13} b^2 d^3 \left(20 b^7 c^7+315 a b^6 d c^6+1512 a^2 b^5 d^2 c^5+2940 a^3 b^4 d^3 c^4+2520 a^4 b^3 d^4 c^3+945 a^5 b^2 d^5 c^2+140 a^6 b d^6 c+6 a^7 d^7\right) x^{13}+\frac{3}{4} b d^2 \left(5 b^8 c^8+120 a b^7 d c^7+840 a^2 b^6 d^2 c^6+2352 a^3 b^5 d^3 c^5+2940 a^4 b^4 d^4 c^4+1680 a^5 b^3 d^5 c^3+420 a^6 b^2 d^6 c^2+40 a^7 b d^7 c+a^8 d^8\right) x^{12}+\frac{1}{11} d \left(10 b^9 c^9+405 a b^8 d c^8+4320 a^2 b^7 d^2 c^7+17640 a^3 b^6 d^3 c^6+31752 a^4 b^5 d^4 c^5+26460 a^5 b^4 d^5 c^4+10080 a^6 b^3 d^6 c^3+1620 a^7 b^2 d^7 c^2+90 a^8 b d^8 c+a^9 d^9\right) x^{11}+\frac{1}{10} c \left(b^9 c^9+90 a b^8 d c^8+1620 a^2 b^7 d^2 c^7+10080 a^3 b^6 d^3 c^6+26460 a^4 b^5 d^4 c^5+31752 a^5 b^4 d^5 c^4+17640 a^6 b^3 d^6 c^3+4320 a^7 b^2 d^7 c^2+405 a^8 b d^8 c+10 a^9 d^9\right) x^{10}+a c^2 \left(b^8 c^8+40 a b^7 d c^7+420 a^2 b^6 d^2 c^6+1680 a^3 b^5 d^3 c^5+2940 a^4 b^4 d^4 c^4+2352 a^5 b^3 d^5 c^3+840 a^6 b^2 d^6 c^2+120 a^7 b d^7 c+5 a^8 d^8\right) x^9+\frac{3}{4} a^2 c^3 \left(6 b^7 c^7+140 a b^6 d c^6+945 a^2 b^5 d^2 c^5+2520 a^3 b^4 d^3 c^4+2940 a^4 b^3 d^4 c^3+1512 a^5 b^2 d^5 c^2+315 a^6 b d^6 c+20 a^7 d^7\right) x^8+6 a^3 c^4 \left(2 b^6 c^6+30 a b^5 d c^5+135 a^2 b^4 d^2 c^4+240 a^3 b^3 d^3 c^3+180 a^4 b^2 d^4 c^2+54 a^5 b d^5 c+5 a^6 d^6\right) x^7+3 a^4 c^5 \left(7 b^5 c^5+70 a b^4 d c^4+210 a^2 b^3 d^2 c^3+240 a^3 b^2 d^3 c^2+105 a^4 b d^4 c+14 a^5 d^5\right) x^6+\frac{6}{5} a^5 c^6 \left(21 b^4 c^4+140 a b^3 d c^3+270 a^2 b^2 d^2 c^2+180 a^3 b d^3 c+35 a^4 d^4\right) x^5+\frac{3}{4} a^6 c^7 \left(28 b^3 c^3+120 a b^2 d c^2+135 a^2 b d^2 c+40 a^3 d^3\right) x^4+3 a^7 c^8 \left(4 b^2 c^2+10 a b d c+5 a^2 d^2\right) x^3+\frac{1}{2} a^8 c^9 (9 b c+10 a d) x^2+a^9 c^{10} x","-\frac{9 b^8 (c+d x)^{19} (b c-a d)}{19 d^{10}}+\frac{2 b^7 (c+d x)^{18} (b c-a d)^2}{d^{10}}-\frac{84 b^6 (c+d x)^{17} (b c-a d)^3}{17 d^{10}}+\frac{63 b^5 (c+d x)^{16} (b c-a d)^4}{8 d^{10}}-\frac{42 b^4 (c+d x)^{15} (b c-a d)^5}{5 d^{10}}+\frac{6 b^3 (c+d x)^{14} (b c-a d)^6}{d^{10}}-\frac{36 b^2 (c+d x)^{13} (b c-a d)^7}{13 d^{10}}+\frac{3 b (c+d x)^{12} (b c-a d)^8}{4 d^{10}}-\frac{(c+d x)^{11} (b c-a d)^9}{11 d^{10}}+\frac{b^9 (c+d x)^{20}}{20 d^{10}}",1,"a^9*c^10*x + (a^8*c^9*(9*b*c + 10*a*d)*x^2)/2 + 3*a^7*c^8*(4*b^2*c^2 + 10*a*b*c*d + 5*a^2*d^2)*x^3 + (3*a^6*c^7*(28*b^3*c^3 + 120*a*b^2*c^2*d + 135*a^2*b*c*d^2 + 40*a^3*d^3)*x^4)/4 + (6*a^5*c^6*(21*b^4*c^4 + 140*a*b^3*c^3*d + 270*a^2*b^2*c^2*d^2 + 180*a^3*b*c*d^3 + 35*a^4*d^4)*x^5)/5 + 3*a^4*c^5*(7*b^5*c^5 + 70*a*b^4*c^4*d + 210*a^2*b^3*c^3*d^2 + 240*a^3*b^2*c^2*d^3 + 105*a^4*b*c*d^4 + 14*a^5*d^5)*x^6 + 6*a^3*c^4*(2*b^6*c^6 + 30*a*b^5*c^5*d + 135*a^2*b^4*c^4*d^2 + 240*a^3*b^3*c^3*d^3 + 180*a^4*b^2*c^2*d^4 + 54*a^5*b*c*d^5 + 5*a^6*d^6)*x^7 + (3*a^2*c^3*(6*b^7*c^7 + 140*a*b^6*c^6*d + 945*a^2*b^5*c^5*d^2 + 2520*a^3*b^4*c^4*d^3 + 2940*a^4*b^3*c^3*d^4 + 1512*a^5*b^2*c^2*d^5 + 315*a^6*b*c*d^6 + 20*a^7*d^7)*x^8)/4 + a*c^2*(b^8*c^8 + 40*a*b^7*c^7*d + 420*a^2*b^6*c^6*d^2 + 1680*a^3*b^5*c^5*d^3 + 2940*a^4*b^4*c^4*d^4 + 2352*a^5*b^3*c^3*d^5 + 840*a^6*b^2*c^2*d^6 + 120*a^7*b*c*d^7 + 5*a^8*d^8)*x^9 + (c*(b^9*c^9 + 90*a*b^8*c^8*d + 1620*a^2*b^7*c^7*d^2 + 10080*a^3*b^6*c^6*d^3 + 26460*a^4*b^5*c^5*d^4 + 31752*a^5*b^4*c^4*d^5 + 17640*a^6*b^3*c^3*d^6 + 4320*a^7*b^2*c^2*d^7 + 405*a^8*b*c*d^8 + 10*a^9*d^9)*x^10)/10 + (d*(10*b^9*c^9 + 405*a*b^8*c^8*d + 4320*a^2*b^7*c^7*d^2 + 17640*a^3*b^6*c^6*d^3 + 31752*a^4*b^5*c^5*d^4 + 26460*a^5*b^4*c^4*d^5 + 10080*a^6*b^3*c^3*d^6 + 1620*a^7*b^2*c^2*d^7 + 90*a^8*b*c*d^8 + a^9*d^9)*x^11)/11 + (3*b*d^2*(5*b^8*c^8 + 120*a*b^7*c^7*d + 840*a^2*b^6*c^6*d^2 + 2352*a^3*b^5*c^5*d^3 + 2940*a^4*b^4*c^4*d^4 + 1680*a^5*b^3*c^3*d^5 + 420*a^6*b^2*c^2*d^6 + 40*a^7*b*c*d^7 + a^8*d^8)*x^12)/4 + (6*b^2*d^3*(20*b^7*c^7 + 315*a*b^6*c^6*d + 1512*a^2*b^5*c^5*d^2 + 2940*a^3*b^4*c^4*d^3 + 2520*a^4*b^3*c^3*d^4 + 945*a^5*b^2*c^2*d^5 + 140*a^6*b*c*d^6 + 6*a^7*d^7)*x^13)/13 + 3*b^3*d^4*(5*b^6*c^6 + 54*a*b^5*c^5*d + 180*a^2*b^4*c^4*d^2 + 240*a^3*b^3*c^3*d^3 + 135*a^4*b^2*c^2*d^4 + 30*a^5*b*c*d^5 + 2*a^6*d^6)*x^14 + (6*b^4*d^5*(14*b^5*c^5 + 105*a*b^4*c^4*d + 240*a^2*b^3*c^3*d^2 + 210*a^3*b^2*c^2*d^3 + 70*a^4*b*c*d^4 + 7*a^5*d^5)*x^15)/5 + (3*b^5*d^6*(35*b^4*c^4 + 180*a*b^3*c^3*d + 270*a^2*b^2*c^2*d^2 + 140*a^3*b*c*d^3 + 21*a^4*d^4)*x^16)/8 + (3*b^6*d^7*(40*b^3*c^3 + 135*a*b^2*c^2*d + 120*a^2*b*c*d^2 + 28*a^3*d^3)*x^17)/17 + (b^7*d^8*(5*b^2*c^2 + 10*a*b*c*d + 4*a^2*d^2)*x^18)/2 + (b^8*d^9*(10*b*c + 9*a*d)*x^19)/19 + (b^9*d^10*x^20)/20","B",1
1303,1,1241,225,0.1609418,"\int (a+b x)^8 (c+d x)^{10} \, dx","Integrate[(a + b*x)^8*(c + d*x)^10,x]","\frac{1}{19} b^8 d^{10} x^{19}+\frac{1}{9} b^7 d^9 (5 b c+4 a d) x^{18}+\frac{1}{17} b^6 d^8 \left(45 b^2 c^2+80 a b d c+28 a^2 d^2\right) x^{17}+\frac{1}{2} b^5 d^7 \left(15 b^3 c^3+45 a b^2 d c^2+35 a^2 b d^2 c+7 a^3 d^3\right) x^{16}+\frac{2}{3} b^4 d^6 \left(21 b^4 c^4+96 a b^3 d c^3+126 a^2 b^2 d^2 c^2+56 a^3 b d^3 c+7 a^4 d^4\right) x^{15}+2 b^3 d^5 \left(9 b^5 c^5+60 a b^4 d c^4+120 a^2 b^3 d^2 c^3+90 a^3 b^2 d^3 c^2+25 a^4 b d^4 c+2 a^5 d^5\right) x^{14}+\frac{14}{13} b^2 d^4 \left(15 b^6 c^6+144 a b^5 d c^5+420 a^2 b^4 d^2 c^4+480 a^3 b^3 d^3 c^3+225 a^4 b^2 d^4 c^2+40 a^5 b d^5 c+2 a^6 d^6\right) x^{13}+\frac{2}{3} b d^3 \left(15 b^7 c^7+210 a b^6 d c^6+882 a^2 b^5 d^2 c^5+1470 a^3 b^4 d^3 c^4+1050 a^4 b^3 d^4 c^3+315 a^5 b^2 d^5 c^2+35 a^6 b d^6 c+a^7 d^7\right) x^{12}+\frac{1}{11} d^2 \left(45 b^8 c^8+960 a b^7 d c^7+5880 a^2 b^6 d^2 c^6+14112 a^3 b^5 d^3 c^5+14700 a^4 b^4 d^4 c^4+6720 a^5 b^3 d^5 c^3+1260 a^6 b^2 d^6 c^2+80 a^7 b d^7 c+a^8 d^8\right) x^{11}+c d \left(b^8 c^8+36 a b^7 d c^7+336 a^2 b^6 d^2 c^6+1176 a^3 b^5 d^3 c^5+1764 a^4 b^4 d^4 c^4+1176 a^5 b^3 d^5 c^3+336 a^6 b^2 d^6 c^2+36 a^7 b d^7 c+a^8 d^8\right) x^{10}+\frac{1}{9} c^2 \left(b^8 c^8+80 a b^7 d c^7+1260 a^2 b^6 d^2 c^6+6720 a^3 b^5 d^3 c^5+14700 a^4 b^4 d^4 c^4+14112 a^5 b^3 d^5 c^3+5880 a^6 b^2 d^6 c^2+960 a^7 b d^7 c+45 a^8 d^8\right) x^9+a c^3 \left(b^7 c^7+35 a b^6 d c^6+315 a^2 b^5 d^2 c^5+1050 a^3 b^4 d^3 c^4+1470 a^4 b^3 d^4 c^3+882 a^5 b^2 d^5 c^2+210 a^6 b d^6 c+15 a^7 d^7\right) x^8+2 a^2 c^4 \left(2 b^6 c^6+40 a b^5 d c^5+225 a^2 b^4 d^2 c^4+480 a^3 b^3 d^3 c^3+420 a^4 b^2 d^4 c^2+144 a^5 b d^5 c+15 a^6 d^6\right) x^7+\frac{14}{3} a^3 c^5 \left(2 b^5 c^5+25 a b^4 d c^4+90 a^2 b^3 d^2 c^3+120 a^3 b^2 d^3 c^2+60 a^4 b d^4 c+9 a^5 d^5\right) x^6+2 a^4 c^6 \left(7 b^4 c^4+56 a b^3 d c^3+126 a^2 b^2 d^2 c^2+96 a^3 b d^3 c+21 a^4 d^4\right) x^5+2 a^5 c^7 \left(7 b^3 c^3+35 a b^2 d c^2+45 a^2 b d^2 c+15 a^3 d^3\right) x^4+\frac{1}{3} a^6 c^8 \left(28 b^2 c^2+80 a b d c+45 a^2 d^2\right) x^3+a^7 c^9 (4 b c+5 a d) x^2+a^8 c^{10} x","-\frac{4 b^7 (c+d x)^{18} (b c-a d)}{9 d^9}+\frac{28 b^6 (c+d x)^{17} (b c-a d)^2}{17 d^9}-\frac{7 b^5 (c+d x)^{16} (b c-a d)^3}{2 d^9}+\frac{14 b^4 (c+d x)^{15} (b c-a d)^4}{3 d^9}-\frac{4 b^3 (c+d x)^{14} (b c-a d)^5}{d^9}+\frac{28 b^2 (c+d x)^{13} (b c-a d)^6}{13 d^9}-\frac{2 b (c+d x)^{12} (b c-a d)^7}{3 d^9}+\frac{(c+d x)^{11} (b c-a d)^8}{11 d^9}+\frac{b^8 (c+d x)^{19}}{19 d^9}",1,"a^8*c^10*x + a^7*c^9*(4*b*c + 5*a*d)*x^2 + (a^6*c^8*(28*b^2*c^2 + 80*a*b*c*d + 45*a^2*d^2)*x^3)/3 + 2*a^5*c^7*(7*b^3*c^3 + 35*a*b^2*c^2*d + 45*a^2*b*c*d^2 + 15*a^3*d^3)*x^4 + 2*a^4*c^6*(7*b^4*c^4 + 56*a*b^3*c^3*d + 126*a^2*b^2*c^2*d^2 + 96*a^3*b*c*d^3 + 21*a^4*d^4)*x^5 + (14*a^3*c^5*(2*b^5*c^5 + 25*a*b^4*c^4*d + 90*a^2*b^3*c^3*d^2 + 120*a^3*b^2*c^2*d^3 + 60*a^4*b*c*d^4 + 9*a^5*d^5)*x^6)/3 + 2*a^2*c^4*(2*b^6*c^6 + 40*a*b^5*c^5*d + 225*a^2*b^4*c^4*d^2 + 480*a^3*b^3*c^3*d^3 + 420*a^4*b^2*c^2*d^4 + 144*a^5*b*c*d^5 + 15*a^6*d^6)*x^7 + a*c^3*(b^7*c^7 + 35*a*b^6*c^6*d + 315*a^2*b^5*c^5*d^2 + 1050*a^3*b^4*c^4*d^3 + 1470*a^4*b^3*c^3*d^4 + 882*a^5*b^2*c^2*d^5 + 210*a^6*b*c*d^6 + 15*a^7*d^7)*x^8 + (c^2*(b^8*c^8 + 80*a*b^7*c^7*d + 1260*a^2*b^6*c^6*d^2 + 6720*a^3*b^5*c^5*d^3 + 14700*a^4*b^4*c^4*d^4 + 14112*a^5*b^3*c^3*d^5 + 5880*a^6*b^2*c^2*d^6 + 960*a^7*b*c*d^7 + 45*a^8*d^8)*x^9)/9 + c*d*(b^8*c^8 + 36*a*b^7*c^7*d + 336*a^2*b^6*c^6*d^2 + 1176*a^3*b^5*c^5*d^3 + 1764*a^4*b^4*c^4*d^4 + 1176*a^5*b^3*c^3*d^5 + 336*a^6*b^2*c^2*d^6 + 36*a^7*b*c*d^7 + a^8*d^8)*x^10 + (d^2*(45*b^8*c^8 + 960*a*b^7*c^7*d + 5880*a^2*b^6*c^6*d^2 + 14112*a^3*b^5*c^5*d^3 + 14700*a^4*b^4*c^4*d^4 + 6720*a^5*b^3*c^3*d^5 + 1260*a^6*b^2*c^2*d^6 + 80*a^7*b*c*d^7 + a^8*d^8)*x^11)/11 + (2*b*d^3*(15*b^7*c^7 + 210*a*b^6*c^6*d + 882*a^2*b^5*c^5*d^2 + 1470*a^3*b^4*c^4*d^3 + 1050*a^4*b^3*c^3*d^4 + 315*a^5*b^2*c^2*d^5 + 35*a^6*b*c*d^6 + a^7*d^7)*x^12)/3 + (14*b^2*d^4*(15*b^6*c^6 + 144*a*b^5*c^5*d + 420*a^2*b^4*c^4*d^2 + 480*a^3*b^3*c^3*d^3 + 225*a^4*b^2*c^2*d^4 + 40*a^5*b*c*d^5 + 2*a^6*d^6)*x^13)/13 + 2*b^3*d^5*(9*b^5*c^5 + 60*a*b^4*c^4*d + 120*a^2*b^3*c^3*d^2 + 90*a^3*b^2*c^2*d^3 + 25*a^4*b*c*d^4 + 2*a^5*d^5)*x^14 + (2*b^4*d^6*(21*b^4*c^4 + 96*a*b^3*c^3*d + 126*a^2*b^2*c^2*d^2 + 56*a^3*b*c*d^3 + 7*a^4*d^4)*x^15)/3 + (b^5*d^7*(15*b^3*c^3 + 45*a*b^2*c^2*d + 35*a^2*b*c*d^2 + 7*a^3*d^3)*x^16)/2 + (b^6*d^8*(45*b^2*c^2 + 80*a*b*c*d + 28*a^2*d^2)*x^17)/17 + (b^7*d^9*(5*b*c + 4*a*d)*x^18)/9 + (b^8*d^10*x^19)/19","B",1
1304,1,1105,200,0.1357606,"\int (a+b x)^7 (c+d x)^{10} \, dx","Integrate[(a + b*x)^7*(c + d*x)^10,x]","\frac{1}{18} b^7 d^{10} x^{18}+\frac{1}{17} b^6 d^9 (10 b c+7 a d) x^{17}+\frac{1}{16} b^5 d^8 \left(45 b^2 c^2+70 a b d c+21 a^2 d^2\right) x^{16}+\frac{1}{3} b^4 d^7 \left(24 b^3 c^3+63 a b^2 d c^2+42 a^2 b d^2 c+7 a^3 d^3\right) x^{15}+\frac{5}{2} b^3 d^6 \left(6 b^4 c^4+24 a b^3 d c^3+27 a^2 b^2 d^2 c^2+10 a^3 b d^3 c+a^4 d^4\right) x^{14}+\frac{7}{13} b^2 d^5 \left(36 b^5 c^5+210 a b^4 d c^4+360 a^2 b^3 d^2 c^3+225 a^3 b^2 d^3 c^2+50 a^4 b d^4 c+3 a^5 d^5\right) x^{13}+\frac{7}{12} b d^4 \left(30 b^6 c^6+252 a b^5 d c^5+630 a^2 b^4 d^2 c^4+600 a^3 b^3 d^3 c^3+225 a^4 b^2 d^4 c^2+30 a^5 b d^5 c+a^6 d^6\right) x^{12}+\frac{1}{11} d^3 \left(120 b^7 c^7+1470 a b^6 d c^6+5292 a^2 b^5 d^2 c^5+7350 a^3 b^4 d^3 c^4+4200 a^4 b^3 d^4 c^3+945 a^5 b^2 d^5 c^2+70 a^6 b d^6 c+a^7 d^7\right) x^{11}+\frac{1}{2} c d^2 \left(9 b^7 c^7+168 a b^6 d c^6+882 a^2 b^5 d^2 c^5+1764 a^3 b^4 d^3 c^4+1470 a^4 b^3 d^4 c^3+504 a^5 b^2 d^5 c^2+63 a^6 b d^6 c+2 a^7 d^7\right) x^{10}+\frac{5}{9} c^2 d \left(2 b^7 c^7+63 a b^6 d c^6+504 a^2 b^5 d^2 c^5+1470 a^3 b^4 d^3 c^4+1764 a^4 b^3 d^4 c^3+882 a^5 b^2 d^5 c^2+168 a^6 b d^6 c+9 a^7 d^7\right) x^9+\frac{1}{8} c^3 \left(b^7 c^7+70 a b^6 d c^6+945 a^2 b^5 d^2 c^5+4200 a^3 b^4 d^3 c^4+7350 a^4 b^3 d^4 c^3+5292 a^5 b^2 d^5 c^2+1470 a^6 b d^6 c+120 a^7 d^7\right) x^8+a c^4 \left(b^6 c^6+30 a b^5 d c^5+225 a^2 b^4 d^2 c^4+600 a^3 b^3 d^3 c^3+630 a^4 b^2 d^4 c^2+252 a^5 b d^5 c+30 a^6 d^6\right) x^7+\frac{7}{6} a^2 c^5 \left(3 b^5 c^5+50 a b^4 d c^4+225 a^2 b^3 d^2 c^3+360 a^3 b^2 d^3 c^2+210 a^4 b d^4 c+36 a^5 d^5\right) x^6+7 a^3 c^6 \left(b^4 c^4+10 a b^3 d c^3+27 a^2 b^2 d^2 c^2+24 a^3 b d^3 c+6 a^4 d^4\right) x^5+\frac{5}{4} a^4 c^7 \left(7 b^3 c^3+42 a b^2 d c^2+63 a^2 b d^2 c+24 a^3 d^3\right) x^4+\frac{1}{3} a^5 c^8 \left(21 b^2 c^2+70 a b d c+45 a^2 d^2\right) x^3+\frac{1}{2} a^6 c^9 (7 b c+10 a d) x^2+a^7 c^{10} x","-\frac{7 b^6 (c+d x)^{17} (b c-a d)}{17 d^8}+\frac{21 b^5 (c+d x)^{16} (b c-a d)^2}{16 d^8}-\frac{7 b^4 (c+d x)^{15} (b c-a d)^3}{3 d^8}+\frac{5 b^3 (c+d x)^{14} (b c-a d)^4}{2 d^8}-\frac{21 b^2 (c+d x)^{13} (b c-a d)^5}{13 d^8}+\frac{7 b (c+d x)^{12} (b c-a d)^6}{12 d^8}-\frac{(c+d x)^{11} (b c-a d)^7}{11 d^8}+\frac{b^7 (c+d x)^{18}}{18 d^8}",1,"a^7*c^10*x + (a^6*c^9*(7*b*c + 10*a*d)*x^2)/2 + (a^5*c^8*(21*b^2*c^2 + 70*a*b*c*d + 45*a^2*d^2)*x^3)/3 + (5*a^4*c^7*(7*b^3*c^3 + 42*a*b^2*c^2*d + 63*a^2*b*c*d^2 + 24*a^3*d^3)*x^4)/4 + 7*a^3*c^6*(b^4*c^4 + 10*a*b^3*c^3*d + 27*a^2*b^2*c^2*d^2 + 24*a^3*b*c*d^3 + 6*a^4*d^4)*x^5 + (7*a^2*c^5*(3*b^5*c^5 + 50*a*b^4*c^4*d + 225*a^2*b^3*c^3*d^2 + 360*a^3*b^2*c^2*d^3 + 210*a^4*b*c*d^4 + 36*a^5*d^5)*x^6)/6 + a*c^4*(b^6*c^6 + 30*a*b^5*c^5*d + 225*a^2*b^4*c^4*d^2 + 600*a^3*b^3*c^3*d^3 + 630*a^4*b^2*c^2*d^4 + 252*a^5*b*c*d^5 + 30*a^6*d^6)*x^7 + (c^3*(b^7*c^7 + 70*a*b^6*c^6*d + 945*a^2*b^5*c^5*d^2 + 4200*a^3*b^4*c^4*d^3 + 7350*a^4*b^3*c^3*d^4 + 5292*a^5*b^2*c^2*d^5 + 1470*a^6*b*c*d^6 + 120*a^7*d^7)*x^8)/8 + (5*c^2*d*(2*b^7*c^7 + 63*a*b^6*c^6*d + 504*a^2*b^5*c^5*d^2 + 1470*a^3*b^4*c^4*d^3 + 1764*a^4*b^3*c^3*d^4 + 882*a^5*b^2*c^2*d^5 + 168*a^6*b*c*d^6 + 9*a^7*d^7)*x^9)/9 + (c*d^2*(9*b^7*c^7 + 168*a*b^6*c^6*d + 882*a^2*b^5*c^5*d^2 + 1764*a^3*b^4*c^4*d^3 + 1470*a^4*b^3*c^3*d^4 + 504*a^5*b^2*c^2*d^5 + 63*a^6*b*c*d^6 + 2*a^7*d^7)*x^10)/2 + (d^3*(120*b^7*c^7 + 1470*a*b^6*c^6*d + 5292*a^2*b^5*c^5*d^2 + 7350*a^3*b^4*c^4*d^3 + 4200*a^4*b^3*c^3*d^4 + 945*a^5*b^2*c^2*d^5 + 70*a^6*b*c*d^6 + a^7*d^7)*x^11)/11 + (7*b*d^4*(30*b^6*c^6 + 252*a*b^5*c^5*d + 630*a^2*b^4*c^4*d^2 + 600*a^3*b^3*c^3*d^3 + 225*a^4*b^2*c^2*d^4 + 30*a^5*b*c*d^5 + a^6*d^6)*x^12)/12 + (7*b^2*d^5*(36*b^5*c^5 + 210*a*b^4*c^4*d + 360*a^2*b^3*c^3*d^2 + 225*a^3*b^2*c^2*d^3 + 50*a^4*b*c*d^4 + 3*a^5*d^5)*x^13)/13 + (5*b^3*d^6*(6*b^4*c^4 + 24*a*b^3*c^3*d + 27*a^2*b^2*c^2*d^2 + 10*a^3*b*c*d^3 + a^4*d^4)*x^14)/2 + (b^4*d^7*(24*b^3*c^3 + 63*a*b^2*c^2*d + 42*a^2*b*c*d^2 + 7*a^3*d^3)*x^15)/3 + (b^5*d^8*(45*b^2*c^2 + 70*a*b*c*d + 21*a^2*d^2)*x^16)/16 + (b^6*d^9*(10*b*c + 7*a*d)*x^17)/17 + (b^7*d^10*x^18)/18","B",1
1305,1,939,170,0.1242376,"\int (a+b x)^6 (c+d x)^{10} \, dx","Integrate[(a + b*x)^6*(c + d*x)^10,x]","\frac{1}{17} b^6 d^{10} x^{17}+\frac{1}{8} b^5 d^9 (5 b c+3 a d) x^{16}+b^4 d^8 \left(3 b^2 c^2+4 a b d c+a^2 d^2\right) x^{15}+\frac{5}{7} b^3 d^7 \left(12 b^3 c^3+27 a b^2 d c^2+15 a^2 b d^2 c+2 a^3 d^3\right) x^{14}+\frac{5}{13} b^2 d^6 \left(42 b^4 c^4+144 a b^3 d c^3+135 a^2 b^2 d^2 c^2+40 a^3 b d^3 c+3 a^4 d^4\right) x^{13}+\frac{1}{2} b d^5 \left(42 b^5 c^5+210 a b^4 d c^4+300 a^2 b^3 d^2 c^3+150 a^3 b^2 d^3 c^2+25 a^4 b d^4 c+a^5 d^5\right) x^{12}+\frac{1}{11} d^4 \left(210 b^6 c^6+1512 a b^5 d c^5+3150 a^2 b^4 d^2 c^4+2400 a^3 b^3 d^3 c^3+675 a^4 b^2 d^4 c^2+60 a^5 b d^5 c+a^6 d^6\right) x^{11}+c d^3 \left(12 b^6 c^6+126 a b^5 d c^5+378 a^2 b^4 d^2 c^4+420 a^3 b^3 d^3 c^3+180 a^4 b^2 d^4 c^2+27 a^5 b d^5 c+a^6 d^6\right) x^{10}+5 c^2 d^2 \left(b^6 c^6+16 a b^5 d c^5+70 a^2 b^4 d^2 c^4+112 a^3 b^3 d^3 c^3+70 a^4 b^2 d^4 c^2+16 a^5 b d^5 c+a^6 d^6\right) x^9+\frac{5}{4} c^3 d \left(b^6 c^6+27 a b^5 d c^5+180 a^2 b^4 d^2 c^4+420 a^3 b^3 d^3 c^3+378 a^4 b^2 d^4 c^2+126 a^5 b d^5 c+12 a^6 d^6\right) x^8+\frac{1}{7} c^4 \left(b^6 c^6+60 a b^5 d c^5+675 a^2 b^4 d^2 c^4+2400 a^3 b^3 d^3 c^3+3150 a^4 b^2 d^4 c^2+1512 a^5 b d^5 c+210 a^6 d^6\right) x^7+a c^5 \left(b^5 c^5+25 a b^4 d c^4+150 a^2 b^3 d^2 c^3+300 a^3 b^2 d^3 c^2+210 a^4 b d^4 c+42 a^5 d^5\right) x^6+a^2 c^6 \left(3 b^4 c^4+40 a b^3 d c^3+135 a^2 b^2 d^2 c^2+144 a^3 b d^3 c+42 a^4 d^4\right) x^5+\frac{5}{2} a^3 c^7 \left(2 b^3 c^3+15 a b^2 d c^2+27 a^2 b d^2 c+12 a^3 d^3\right) x^4+5 a^4 c^8 \left(b^2 c^2+4 a b d c+3 a^2 d^2\right) x^3+a^5 c^9 (3 b c+5 a d) x^2+a^6 c^{10} x","-\frac{3 b^5 (c+d x)^{16} (b c-a d)}{8 d^7}+\frac{b^4 (c+d x)^{15} (b c-a d)^2}{d^7}-\frac{10 b^3 (c+d x)^{14} (b c-a d)^3}{7 d^7}+\frac{15 b^2 (c+d x)^{13} (b c-a d)^4}{13 d^7}-\frac{b (c+d x)^{12} (b c-a d)^5}{2 d^7}+\frac{(c+d x)^{11} (b c-a d)^6}{11 d^7}+\frac{b^6 (c+d x)^{17}}{17 d^7}",1,"a^6*c^10*x + a^5*c^9*(3*b*c + 5*a*d)*x^2 + 5*a^4*c^8*(b^2*c^2 + 4*a*b*c*d + 3*a^2*d^2)*x^3 + (5*a^3*c^7*(2*b^3*c^3 + 15*a*b^2*c^2*d + 27*a^2*b*c*d^2 + 12*a^3*d^3)*x^4)/2 + a^2*c^6*(3*b^4*c^4 + 40*a*b^3*c^3*d + 135*a^2*b^2*c^2*d^2 + 144*a^3*b*c*d^3 + 42*a^4*d^4)*x^5 + a*c^5*(b^5*c^5 + 25*a*b^4*c^4*d + 150*a^2*b^3*c^3*d^2 + 300*a^3*b^2*c^2*d^3 + 210*a^4*b*c*d^4 + 42*a^5*d^5)*x^6 + (c^4*(b^6*c^6 + 60*a*b^5*c^5*d + 675*a^2*b^4*c^4*d^2 + 2400*a^3*b^3*c^3*d^3 + 3150*a^4*b^2*c^2*d^4 + 1512*a^5*b*c*d^5 + 210*a^6*d^6)*x^7)/7 + (5*c^3*d*(b^6*c^6 + 27*a*b^5*c^5*d + 180*a^2*b^4*c^4*d^2 + 420*a^3*b^3*c^3*d^3 + 378*a^4*b^2*c^2*d^4 + 126*a^5*b*c*d^5 + 12*a^6*d^6)*x^8)/4 + 5*c^2*d^2*(b^6*c^6 + 16*a*b^5*c^5*d + 70*a^2*b^4*c^4*d^2 + 112*a^3*b^3*c^3*d^3 + 70*a^4*b^2*c^2*d^4 + 16*a^5*b*c*d^5 + a^6*d^6)*x^9 + c*d^3*(12*b^6*c^6 + 126*a*b^5*c^5*d + 378*a^2*b^4*c^4*d^2 + 420*a^3*b^3*c^3*d^3 + 180*a^4*b^2*c^2*d^4 + 27*a^5*b*c*d^5 + a^6*d^6)*x^10 + (d^4*(210*b^6*c^6 + 1512*a*b^5*c^5*d + 3150*a^2*b^4*c^4*d^2 + 2400*a^3*b^3*c^3*d^3 + 675*a^4*b^2*c^2*d^4 + 60*a^5*b*c*d^5 + a^6*d^6)*x^11)/11 + (b*d^5*(42*b^5*c^5 + 210*a*b^4*c^4*d + 300*a^2*b^3*c^3*d^2 + 150*a^3*b^2*c^2*d^3 + 25*a^4*b*c*d^4 + a^5*d^5)*x^12)/2 + (5*b^2*d^6*(42*b^4*c^4 + 144*a*b^3*c^3*d + 135*a^2*b^2*c^2*d^2 + 40*a^3*b*c*d^3 + 3*a^4*d^4)*x^13)/13 + (5*b^3*d^7*(12*b^3*c^3 + 27*a*b^2*c^2*d + 15*a^2*b*c*d^2 + 2*a^3*d^3)*x^14)/7 + b^4*d^8*(3*b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^15 + (b^5*d^9*(5*b*c + 3*a*d)*x^16)/8 + (b^6*d^10*x^17)/17","B",1
1306,1,811,146,0.0880952,"\int (a+b x)^5 (c+d x)^{10} \, dx","Integrate[(a + b*x)^5*(c + d*x)^10,x]","\frac{1}{16} b^5 d^{10} x^{16}+\frac{1}{3} b^4 d^9 (2 b c+a d) x^{15}+\frac{5}{14} b^3 d^8 \left(9 b^2 c^2+10 a b d c+2 a^2 d^2\right) x^{14}+\frac{5}{13} b^2 d^7 \left(24 b^3 c^3+45 a b^2 d c^2+20 a^2 b d^2 c+2 a^3 d^3\right) x^{13}+\frac{5}{12} b d^6 \left(42 b^4 c^4+120 a b^3 d c^3+90 a^2 b^2 d^2 c^2+20 a^3 b d^3 c+a^4 d^4\right) x^{12}+\frac{1}{11} d^5 \left(252 b^5 c^5+1050 a b^4 d c^4+1200 a^2 b^3 d^2 c^3+450 a^3 b^2 d^3 c^2+50 a^4 b d^4 c+a^5 d^5\right) x^{11}+\frac{1}{2} c d^4 \left(42 b^5 c^5+252 a b^4 d c^4+420 a^2 b^3 d^2 c^3+240 a^3 b^2 d^3 c^2+45 a^4 b d^4 c+2 a^5 d^5\right) x^{10}+\frac{5}{3} c^2 d^3 \left(8 b^5 c^5+70 a b^4 d c^4+168 a^2 b^3 d^2 c^3+140 a^3 b^2 d^3 c^2+40 a^4 b d^4 c+3 a^5 d^5\right) x^9+\frac{15}{8} c^3 d^2 \left(3 b^5 c^5+40 a b^4 d c^4+140 a^2 b^3 d^2 c^3+168 a^3 b^2 d^3 c^2+70 a^4 b d^4 c+8 a^5 d^5\right) x^8+\frac{5}{7} c^4 d \left(2 b^5 c^5+45 a b^4 d c^4+240 a^2 b^3 d^2 c^3+420 a^3 b^2 d^3 c^2+252 a^4 b d^4 c+42 a^5 d^5\right) x^7+\frac{1}{6} c^5 \left(b^5 c^5+50 a b^4 d c^4+450 a^2 b^3 d^2 c^3+1200 a^3 b^2 d^3 c^2+1050 a^4 b d^4 c+252 a^5 d^5\right) x^6+a c^6 \left(b^4 c^4+20 a b^3 d c^3+90 a^2 b^2 d^2 c^2+120 a^3 b d^3 c+42 a^4 d^4\right) x^5+\frac{5}{4} a^2 c^7 \left(2 b^3 c^3+20 a b^2 d c^2+45 a^2 b d^2 c+24 a^3 d^3\right) x^4+\frac{5}{3} a^3 c^8 \left(2 b^2 c^2+10 a b d c+9 a^2 d^2\right) x^3+\frac{5}{2} a^4 c^9 (b c+2 a d) x^2+a^5 c^{10} x","-\frac{b^4 (c+d x)^{15} (b c-a d)}{3 d^6}+\frac{5 b^3 (c+d x)^{14} (b c-a d)^2}{7 d^6}-\frac{10 b^2 (c+d x)^{13} (b c-a d)^3}{13 d^6}+\frac{5 b (c+d x)^{12} (b c-a d)^4}{12 d^6}-\frac{(c+d x)^{11} (b c-a d)^5}{11 d^6}+\frac{b^5 (c+d x)^{16}}{16 d^6}",1,"a^5*c^10*x + (5*a^4*c^9*(b*c + 2*a*d)*x^2)/2 + (5*a^3*c^8*(2*b^2*c^2 + 10*a*b*c*d + 9*a^2*d^2)*x^3)/3 + (5*a^2*c^7*(2*b^3*c^3 + 20*a*b^2*c^2*d + 45*a^2*b*c*d^2 + 24*a^3*d^3)*x^4)/4 + a*c^6*(b^4*c^4 + 20*a*b^3*c^3*d + 90*a^2*b^2*c^2*d^2 + 120*a^3*b*c*d^3 + 42*a^4*d^4)*x^5 + (c^5*(b^5*c^5 + 50*a*b^4*c^4*d + 450*a^2*b^3*c^3*d^2 + 1200*a^3*b^2*c^2*d^3 + 1050*a^4*b*c*d^4 + 252*a^5*d^5)*x^6)/6 + (5*c^4*d*(2*b^5*c^5 + 45*a*b^4*c^4*d + 240*a^2*b^3*c^3*d^2 + 420*a^3*b^2*c^2*d^3 + 252*a^4*b*c*d^4 + 42*a^5*d^5)*x^7)/7 + (15*c^3*d^2*(3*b^5*c^5 + 40*a*b^4*c^4*d + 140*a^2*b^3*c^3*d^2 + 168*a^3*b^2*c^2*d^3 + 70*a^4*b*c*d^4 + 8*a^5*d^5)*x^8)/8 + (5*c^2*d^3*(8*b^5*c^5 + 70*a*b^4*c^4*d + 168*a^2*b^3*c^3*d^2 + 140*a^3*b^2*c^2*d^3 + 40*a^4*b*c*d^4 + 3*a^5*d^5)*x^9)/3 + (c*d^4*(42*b^5*c^5 + 252*a*b^4*c^4*d + 420*a^2*b^3*c^3*d^2 + 240*a^3*b^2*c^2*d^3 + 45*a^4*b*c*d^4 + 2*a^5*d^5)*x^10)/2 + (d^5*(252*b^5*c^5 + 1050*a*b^4*c^4*d + 1200*a^2*b^3*c^3*d^2 + 450*a^3*b^2*c^2*d^3 + 50*a^4*b*c*d^4 + a^5*d^5)*x^11)/11 + (5*b*d^6*(42*b^4*c^4 + 120*a*b^3*c^3*d + 90*a^2*b^2*c^2*d^2 + 20*a^3*b*c*d^3 + a^4*d^4)*x^12)/12 + (5*b^2*d^7*(24*b^3*c^3 + 45*a*b^2*c^2*d + 20*a^2*b*c*d^2 + 2*a^3*d^3)*x^13)/13 + (5*b^3*d^8*(9*b^2*c^2 + 10*a*b*c*d + 2*a^2*d^2)*x^14)/14 + (b^4*d^9*(2*b*c + a*d)*x^15)/3 + (b^5*d^10*x^16)/16","B",1
1307,1,660,119,0.0790549,"\int (a+b x)^4 (c+d x)^{10} \, dx","Integrate[(a + b*x)^4*(c + d*x)^10,x]","a^4 c^{10} x+a^3 c^9 x^2 (5 a d+2 b c)+\frac{1}{13} b^2 d^8 x^{13} \left(6 a^2 d^2+40 a b c d+45 b^2 c^2\right)+\frac{1}{3} a^2 c^8 x^3 \left(45 a^2 d^2+40 a b c d+6 b^2 c^2\right)+\frac{1}{3} b d^7 x^{12} \left(a^3 d^3+15 a^2 b c d^2+45 a b^2 c^2 d+30 b^3 c^3\right)+a c^7 x^4 \left(30 a^3 d^3+45 a^2 b c d^2+15 a b^2 c^2 d+b^3 c^3\right)+\frac{1}{3} c^2 d^4 x^9 \left(15 a^4 d^4+160 a^3 b c d^3+420 a^2 b^2 c^2 d^2+336 a b^3 c^3 d+70 b^4 c^4\right)+3 c^3 d^3 x^8 \left(5 a^4 d^4+35 a^3 b c d^3+63 a^2 b^2 c^2 d^2+35 a b^3 c^3 d+5 b^4 c^4\right)+\frac{3}{7} c^4 d^2 x^7 \left(70 a^4 d^4+336 a^3 b c d^3+420 a^2 b^2 c^2 d^2+160 a b^3 c^3 d+15 b^4 c^4\right)+\frac{1}{11} d^6 x^{11} \left(a^4 d^4+40 a^3 b c d^3+270 a^2 b^2 c^2 d^2+480 a b^3 c^3 d+210 b^4 c^4\right)+\frac{1}{5} c d^5 x^{10} \left(5 a^4 d^4+90 a^3 b c d^3+360 a^2 b^2 c^2 d^2+420 a b^3 c^3 d+126 b^4 c^4\right)+\frac{1}{5} c^6 x^5 \left(210 a^4 d^4+480 a^3 b c d^3+270 a^2 b^2 c^2 d^2+40 a b^3 c^3 d+b^4 c^4\right)+\frac{1}{3} c^5 d x^6 \left(126 a^4 d^4+420 a^3 b c d^3+360 a^2 b^2 c^2 d^2+90 a b^3 c^3 d+5 b^4 c^4\right)+\frac{1}{7} b^3 d^9 x^{14} (2 a d+5 b c)+\frac{1}{15} b^4 d^{10} x^{15}","-\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,"a^4*c^10*x + a^3*c^9*(2*b*c + 5*a*d)*x^2 + (a^2*c^8*(6*b^2*c^2 + 40*a*b*c*d + 45*a^2*d^2)*x^3)/3 + a*c^7*(b^3*c^3 + 15*a*b^2*c^2*d + 45*a^2*b*c*d^2 + 30*a^3*d^3)*x^4 + (c^6*(b^4*c^4 + 40*a*b^3*c^3*d + 270*a^2*b^2*c^2*d^2 + 480*a^3*b*c*d^3 + 210*a^4*d^4)*x^5)/5 + (c^5*d*(5*b^4*c^4 + 90*a*b^3*c^3*d + 360*a^2*b^2*c^2*d^2 + 420*a^3*b*c*d^3 + 126*a^4*d^4)*x^6)/3 + (3*c^4*d^2*(15*b^4*c^4 + 160*a*b^3*c^3*d + 420*a^2*b^2*c^2*d^2 + 336*a^3*b*c*d^3 + 70*a^4*d^4)*x^7)/7 + 3*c^3*d^3*(5*b^4*c^4 + 35*a*b^3*c^3*d + 63*a^2*b^2*c^2*d^2 + 35*a^3*b*c*d^3 + 5*a^4*d^4)*x^8 + (c^2*d^4*(70*b^4*c^4 + 336*a*b^3*c^3*d + 420*a^2*b^2*c^2*d^2 + 160*a^3*b*c*d^3 + 15*a^4*d^4)*x^9)/3 + (c*d^5*(126*b^4*c^4 + 420*a*b^3*c^3*d + 360*a^2*b^2*c^2*d^2 + 90*a^3*b*c*d^3 + 5*a^4*d^4)*x^10)/5 + (d^6*(210*b^4*c^4 + 480*a*b^3*c^3*d + 270*a^2*b^2*c^2*d^2 + 40*a^3*b*c*d^3 + a^4*d^4)*x^11)/11 + (b*d^7*(30*b^3*c^3 + 45*a*b^2*c^2*d + 15*a^2*b*c*d^2 + a^3*d^3)*x^12)/3 + (b^2*d^8*(45*b^2*c^2 + 40*a*b*c*d + 6*a^2*d^2)*x^13)/13 + (b^3*d^9*(5*b*c + 2*a*d)*x^14)/7 + (b^4*d^10*x^15)/15","B",1
1308,1,511,92,0.0653488,"\int (a+b x)^3 (c+d x)^{10} \, dx","Integrate[(a + b*x)^3*(c + d*x)^10,x]","a^3 c^{10} x+\frac{1}{4} b d^8 x^{12} \left(a^2 d^2+10 a b c d+15 b^2 c^2\right)+a c^8 x^3 \left(15 a^2 d^2+10 a b c d+b^2 c^2\right)+\frac{1}{2} a^2 c^9 x^2 (10 a d+3 b c)+\frac{1}{11} d^7 x^{11} \left(a^3 d^3+30 a^2 b c d^2+135 a b^2 c^2 d+120 b^3 c^3\right)+\frac{1}{2} c d^6 x^{10} \left(2 a^3 d^3+27 a^2 b c d^2+72 a b^2 c^2 d+42 b^3 c^3\right)+c^2 d^5 x^9 \left(5 a^3 d^3+40 a^2 b c d^2+70 a b^2 c^2 d+28 b^3 c^3\right)+\frac{3}{4} c^3 d^4 x^8 \left(20 a^3 d^3+105 a^2 b c d^2+126 a b^2 c^2 d+35 b^3 c^3\right)+\frac{1}{4} c^7 x^4 \left(120 a^3 d^3+135 a^2 b c d^2+30 a b^2 c^2 d+b^3 c^3\right)+c^6 d x^5 \left(42 a^3 d^3+72 a^2 b c d^2+27 a b^2 c^2 d+2 b^3 c^3\right)+\frac{3}{2} c^5 d^2 x^6 \left(28 a^3 d^3+70 a^2 b c d^2+40 a b^2 c^2 d+5 b^3 c^3\right)+\frac{6}{7} c^4 d^3 x^7 \left(35 a^3 d^3+126 a^2 b c d^2+105 a b^2 c^2 d+20 b^3 c^3\right)+\frac{1}{13} b^2 d^9 x^{13} (3 a d+10 b c)+\frac{1}{14} b^3 d^{10} x^{14}","-\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,"a^3*c^10*x + (a^2*c^9*(3*b*c + 10*a*d)*x^2)/2 + a*c^8*(b^2*c^2 + 10*a*b*c*d + 15*a^2*d^2)*x^3 + (c^7*(b^3*c^3 + 30*a*b^2*c^2*d + 135*a^2*b*c*d^2 + 120*a^3*d^3)*x^4)/4 + c^6*d*(2*b^3*c^3 + 27*a*b^2*c^2*d + 72*a^2*b*c*d^2 + 42*a^3*d^3)*x^5 + (3*c^5*d^2*(5*b^3*c^3 + 40*a*b^2*c^2*d + 70*a^2*b*c*d^2 + 28*a^3*d^3)*x^6)/2 + (6*c^4*d^3*(20*b^3*c^3 + 105*a*b^2*c^2*d + 126*a^2*b*c*d^2 + 35*a^3*d^3)*x^7)/7 + (3*c^3*d^4*(35*b^3*c^3 + 126*a*b^2*c^2*d + 105*a^2*b*c*d^2 + 20*a^3*d^3)*x^8)/4 + c^2*d^5*(28*b^3*c^3 + 70*a*b^2*c^2*d + 40*a^2*b*c*d^2 + 5*a^3*d^3)*x^9 + (c*d^6*(42*b^3*c^3 + 72*a*b^2*c^2*d + 27*a^2*b*c*d^2 + 2*a^3*d^3)*x^10)/2 + (d^7*(120*b^3*c^3 + 135*a*b^2*c^2*d + 30*a^2*b*c*d^2 + a^3*d^3)*x^11)/11 + (b*d^8*(15*b^2*c^2 + 10*a*b*c*d + a^2*d^2)*x^12)/4 + (b^2*d^9*(10*b*c + 3*a*d)*x^13)/13 + (b^3*d^10*x^14)/14","B",1
1309,1,358,65,0.0455539,"\int (a+b x)^2 (c+d x)^{10} \, dx","Integrate[(a + b*x)^2*(c + d*x)^10,x]","\frac{1}{11} d^8 x^{11} \left(a^2 d^2+20 a b c d+45 b^2 c^2\right)+c d^7 x^{10} \left(a^2 d^2+9 a b c d+12 b^2 c^2\right)+\frac{5}{3} c^2 d^6 x^9 \left(3 a^2 d^2+16 a b c d+14 b^2 c^2\right)+\frac{1}{3} c^8 x^3 \left(45 a^2 d^2+20 a b c d+b^2 c^2\right)+\frac{5}{2} c^7 d x^4 \left(12 a^2 d^2+9 a b c d+b^2 c^2\right)+3 c^6 d^2 x^5 \left(14 a^2 d^2+16 a b c d+3 b^2 c^2\right)+2 c^5 d^3 x^6 \left(21 a^2 d^2+35 a b c d+10 b^2 c^2\right)+6 c^4 d^4 x^7 \left(5 a^2 d^2+12 a b c d+5 b^2 c^2\right)+\frac{3}{2} c^3 d^5 x^8 \left(10 a^2 d^2+35 a b c d+21 b^2 c^2\right)+a^2 c^{10} x+a c^9 x^2 (5 a d+b c)+\frac{1}{6} b d^9 x^{12} (a d+5 b c)+\frac{1}{13} b^2 d^{10} x^{13}","-\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,"a^2*c^10*x + a*c^9*(b*c + 5*a*d)*x^2 + (c^8*(b^2*c^2 + 20*a*b*c*d + 45*a^2*d^2)*x^3)/3 + (5*c^7*d*(b^2*c^2 + 9*a*b*c*d + 12*a^2*d^2)*x^4)/2 + 3*c^6*d^2*(3*b^2*c^2 + 16*a*b*c*d + 14*a^2*d^2)*x^5 + 2*c^5*d^3*(10*b^2*c^2 + 35*a*b*c*d + 21*a^2*d^2)*x^6 + 6*c^4*d^4*(5*b^2*c^2 + 12*a*b*c*d + 5*a^2*d^2)*x^7 + (3*c^3*d^5*(21*b^2*c^2 + 35*a*b*c*d + 10*a^2*d^2)*x^8)/2 + (5*c^2*d^6*(14*b^2*c^2 + 16*a*b*c*d + 3*a^2*d^2)*x^9)/3 + c*d^7*(12*b^2*c^2 + 9*a*b*c*d + a^2*d^2)*x^10 + (d^8*(45*b^2*c^2 + 20*a*b*c*d + a^2*d^2)*x^11)/11 + (b*d^9*(5*b*c + a*d)*x^12)/6 + (b^2*d^10*x^13)/13","B",1
1310,1,220,38,0.0287237,"\int (a+b x) (c+d x)^{10} \, dx","Integrate[(a + b*x)*(c + d*x)^10,x]","\frac{1}{2} c^9 x^2 (10 a d+b c)+\frac{5}{3} c^8 d x^3 (9 a d+2 b c)+\frac{15}{4} c^7 d^2 x^4 (8 a d+3 b c)+6 c^6 d^3 x^5 (7 a d+4 b c)+7 c^5 d^4 x^6 (6 a d+5 b c)+6 c^4 d^5 x^7 (5 a d+6 b c)+\frac{15}{4} c^3 d^6 x^8 (4 a d+7 b c)+\frac{5}{3} c^2 d^7 x^9 (3 a d+8 b c)+\frac{1}{11} d^9 x^{11} (a d+10 b c)+\frac{1}{2} c d^8 x^{10} (2 a d+9 b c)+a c^{10} x+\frac{1}{12} b d^{10} x^{12}","\frac{b (c+d x)^{12}}{12 d^2}-\frac{(c+d x)^{11} (b c-a d)}{11 d^2}",1,"a*c^10*x + (c^9*(b*c + 10*a*d)*x^2)/2 + (5*c^8*d*(2*b*c + 9*a*d)*x^3)/3 + (15*c^7*d^2*(3*b*c + 8*a*d)*x^4)/4 + 6*c^6*d^3*(4*b*c + 7*a*d)*x^5 + 7*c^5*d^4*(5*b*c + 6*a*d)*x^6 + 6*c^4*d^5*(6*b*c + 5*a*d)*x^7 + (15*c^3*d^6*(7*b*c + 4*a*d)*x^8)/4 + (5*c^2*d^7*(8*b*c + 3*a*d)*x^9)/3 + (c*d^8*(9*b*c + 2*a*d)*x^10)/2 + (d^9*(10*b*c + a*d)*x^11)/11 + (b*d^10*x^12)/12","B",1
1311,1,14,14,0.0011059,"\int (c+d x)^{10} \, dx","Integrate[(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
1312,1,591,241,0.3390146,"\int \frac{(c+d x)^{10}}{a+b x} \, dx","Integrate[(c + d*x)^10/(a + b*x),x]","\frac{d x \left(-2520 a^9 d^9+1260 a^8 b d^8 (20 c+d x)-840 a^7 b^2 d^7 \left(135 c^2+15 c d x+d^2 x^2\right)+210 a^6 b^3 d^6 \left(1440 c^3+270 c^2 d x+40 c d^2 x^2+3 d^3 x^3\right)-252 a^5 b^4 d^5 \left(2100 c^4+600 c^3 d x+150 c^2 d^2 x^2+25 c d^3 x^3+2 d^4 x^4\right)+210 a^4 b^5 d^4 \left(3024 c^5+1260 c^4 d x+480 c^3 d^2 x^2+135 c^2 d^3 x^3+24 c d^4 x^4+2 d^5 x^5\right)-120 a^3 b^6 d^3 \left(4410 c^6+2646 c^5 d x+1470 c^4 d^2 x^2+630 c^3 d^3 x^3+189 c^2 d^4 x^4+35 c d^5 x^5+3 d^6 x^6\right)+45 a^2 b^7 d^2 \left(6720 c^7+5880 c^6 d x+4704 c^5 d^2 x^2+2940 c^4 d^3 x^3+1344 c^3 d^4 x^4+420 c^2 d^5 x^5+80 c d^6 x^6+7 d^7 x^7\right)-10 a b^8 d \left(11340 c^8+15120 c^7 d x+17640 c^6 d^2 x^2+15876 c^5 d^3 x^3+10584 c^4 d^4 x^4+5040 c^3 d^5 x^5+1620 c^2 d^6 x^6+315 c d^7 x^7+28 d^8 x^8\right)+b^9 \left(25200 c^9+56700 c^8 d x+100800 c^7 d^2 x^2+132300 c^6 d^3 x^3+127008 c^5 d^4 x^4+88200 c^4 d^5 x^5+43200 c^3 d^6 x^6+14175 c^2 d^7 x^7+2800 c d^8 x^8+252 d^9 x^9\right)\right)}{2520 b^{10}}+\frac{(b c-a d)^{10} \log (a+b x)}{b^{11}}","\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,"(d*x*(-2520*a^9*d^9 + 1260*a^8*b*d^8*(20*c + d*x) - 840*a^7*b^2*d^7*(135*c^2 + 15*c*d*x + d^2*x^2) + 210*a^6*b^3*d^6*(1440*c^3 + 270*c^2*d*x + 40*c*d^2*x^2 + 3*d^3*x^3) - 252*a^5*b^4*d^5*(2100*c^4 + 600*c^3*d*x + 150*c^2*d^2*x^2 + 25*c*d^3*x^3 + 2*d^4*x^4) + 210*a^4*b^5*d^4*(3024*c^5 + 1260*c^4*d*x + 480*c^3*d^2*x^2 + 135*c^2*d^3*x^3 + 24*c*d^4*x^4 + 2*d^5*x^5) - 120*a^3*b^6*d^3*(4410*c^6 + 2646*c^5*d*x + 1470*c^4*d^2*x^2 + 630*c^3*d^3*x^3 + 189*c^2*d^4*x^4 + 35*c*d^5*x^5 + 3*d^6*x^6) + 45*a^2*b^7*d^2*(6720*c^7 + 5880*c^6*d*x + 4704*c^5*d^2*x^2 + 2940*c^4*d^3*x^3 + 1344*c^3*d^4*x^4 + 420*c^2*d^5*x^5 + 80*c*d^6*x^6 + 7*d^7*x^7) - 10*a*b^8*d*(11340*c^8 + 15120*c^7*d*x + 17640*c^6*d^2*x^2 + 15876*c^5*d^3*x^3 + 10584*c^4*d^4*x^4 + 5040*c^3*d^5*x^5 + 1620*c^2*d^6*x^6 + 315*c*d^7*x^7 + 28*d^8*x^8) + b^9*(25200*c^9 + 56700*c^8*d*x + 100800*c^7*d^2*x^2 + 132300*c^6*d^3*x^3 + 127008*c^5*d^4*x^4 + 88200*c^4*d^5*x^5 + 43200*c^3*d^6*x^6 + 14175*c^2*d^7*x^7 + 2800*c*d^8*x^8 + 252*d^9*x^9)))/(2520*b^10) + ((b*c - a*d)^10*Log[a + b*x])/b^11","B",1
1313,1,708,258,0.2396016,"\int \frac{(c+d x)^{10}}{(a+b x)^2} \, dx","Integrate[(c + d*x)^10/(a + b*x)^2,x]","\frac{-252 a^{10} d^{10}+252 a^9 b d^9 (10 c+9 d x)+1260 a^8 b^2 d^8 \left(-9 c^2-16 c d x+d^2 x^2\right)-420 a^7 b^3 d^7 \left(-72 c^3-189 c^2 d x+27 c d^2 x^2+d^3 x^3\right)+210 a^6 b^4 d^6 \left(-252 c^4-864 c^3 d x+216 c^2 d^2 x^2+18 c d^3 x^3+d^4 x^4\right)-126 a^5 b^5 d^5 \left(-504 c^5-2100 c^4 d x+840 c^3 d^2 x^2+120 c^2 d^3 x^3+15 c d^4 x^4+d^5 x^5\right)+42 a^4 b^6 d^4 \left(-1260 c^6-6048 c^5 d x+3780 c^4 d^2 x^2+840 c^3 d^3 x^3+180 c^2 d^4 x^4+27 c d^5 x^5+2 d^6 x^6\right)-12 a^3 b^7 d^3 \left(-2520 c^7-13230 c^6 d x+13230 c^5 d^2 x^2+4410 c^4 d^3 x^3+1470 c^3 d^4 x^4+378 c^2 d^5 x^5+63 c d^6 x^6+5 d^7 x^7\right)+9 a^2 b^8 d^2 \left(-1260 c^8-6720 c^7 d x+11760 c^6 d^2 x^2+5880 c^5 d^3 x^3+2940 c^4 d^4 x^4+1176 c^3 d^5 x^5+336 c^2 d^6 x^6+60 c d^7 x^7+5 d^8 x^8\right)-a b^9 d \left(-2520 c^9-11340 c^8 d x+45360 c^7 d^2 x^2+35280 c^6 d^3 x^3+26460 c^5 d^4 x^4+15876 c^4 d^5 x^5+7056 c^3 d^6 x^6+2160 c^2 d^7 x^7+405 c d^8 x^8+35 d^9 x^9\right)-2520 d (a+b x) (a d-b c)^9 \log (a+b x)+b^{10} \left(-252 c^{10}+11340 c^8 d^2 x^2+15120 c^7 d^3 x^3+17640 c^6 d^4 x^4+15876 c^5 d^5 x^5+10584 c^4 d^6 x^6+5040 c^3 d^7 x^7+1620 c^2 d^8 x^8+315 c d^9 x^9+28 d^{10} x^{10}\right)}{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*a^10*d^10 + 252*a^9*b*d^9*(10*c + 9*d*x) + 1260*a^8*b^2*d^8*(-9*c^2 - 16*c*d*x + d^2*x^2) - 420*a^7*b^3*d^7*(-72*c^3 - 189*c^2*d*x + 27*c*d^2*x^2 + d^3*x^3) + 210*a^6*b^4*d^6*(-252*c^4 - 864*c^3*d*x + 216*c^2*d^2*x^2 + 18*c*d^3*x^3 + d^4*x^4) - 126*a^5*b^5*d^5*(-504*c^5 - 2100*c^4*d*x + 840*c^3*d^2*x^2 + 120*c^2*d^3*x^3 + 15*c*d^4*x^4 + d^5*x^5) + 42*a^4*b^6*d^4*(-1260*c^6 - 6048*c^5*d*x + 3780*c^4*d^2*x^2 + 840*c^3*d^3*x^3 + 180*c^2*d^4*x^4 + 27*c*d^5*x^5 + 2*d^6*x^6) - 12*a^3*b^7*d^3*(-2520*c^7 - 13230*c^6*d*x + 13230*c^5*d^2*x^2 + 4410*c^4*d^3*x^3 + 1470*c^3*d^4*x^4 + 378*c^2*d^5*x^5 + 63*c*d^6*x^6 + 5*d^7*x^7) + 9*a^2*b^8*d^2*(-1260*c^8 - 6720*c^7*d*x + 11760*c^6*d^2*x^2 + 5880*c^5*d^3*x^3 + 2940*c^4*d^4*x^4 + 1176*c^3*d^5*x^5 + 336*c^2*d^6*x^6 + 60*c*d^7*x^7 + 5*d^8*x^8) - a*b^9*d*(-2520*c^9 - 11340*c^8*d*x + 45360*c^7*d^2*x^2 + 35280*c^6*d^3*x^3 + 26460*c^5*d^4*x^4 + 15876*c^4*d^5*x^5 + 7056*c^3*d^6*x^6 + 2160*c^2*d^7*x^7 + 405*c*d^8*x^8 + 35*d^9*x^9) + b^10*(-252*c^10 + 11340*c^8*d^2*x^2 + 15120*c^7*d^3*x^3 + 17640*c^6*d^4*x^4 + 15876*c^5*d^5*x^5 + 10584*c^4*d^6*x^6 + 5040*c^3*d^7*x^7 + 1620*c^2*d^8*x^8 + 315*c*d^9*x^9 + 28*d^10*x^10) - 2520*d*(-(b*c) + a*d)^9*(a + b*x)*Log[a + b*x])/(252*b^11*(a + b*x))","B",1
1314,1,708,262,0.2408597,"\int \frac{(c+d x)^{10}}{(a+b x)^3} \, dx","Integrate[(c + d*x)^10/(a + b*x)^3,x]","\frac{532 a^{10} d^{10}-56 a^9 b d^9 (85 c+26 d x)+28 a^8 b^2 d^8 \left(675 c^2+380 c d x-116 d^2 x^2\right)-280 a^7 b^3 d^7 \left(156 c^3+117 c^2 d x-91 c d^2 x^2+3 d^3 x^3\right)+210 a^6 b^4 d^6 \left(308 c^4+256 c^3 d x-414 c^2 d^2 x^2+32 c d^3 x^3+d^4 x^4\right)-84 a^5 b^5 d^5 \left(756 c^5+560 c^4 d x-2000 c^3 d^2 x^2+280 c^2 d^3 x^3+20 c d^4 x^4+d^5 x^5\right)+42 a^4 b^6 d^4 \left(980 c^6+336 c^5 d x-4760 c^4 d^2 x^2+1120 c^3 d^3 x^3+140 c^2 d^4 x^4+16 c d^5 x^5+d^6 x^6\right)-24 a^3 b^7 d^3 \left(700 c^7-490 c^6 d x-6174 c^5 d^2 x^2+2450 c^4 d^3 x^3+490 c^3 d^4 x^4+98 c^2 d^5 x^5+14 c d^6 x^6+d^7 x^7\right)+3 a^2 b^8 d^2 \left(1260 c^8-4480 c^7 d x-21560 c^6 d^2 x^2+15680 c^5 d^3 x^3+4900 c^4 d^4 x^4+1568 c^3 d^5 x^5+392 c^2 d^6 x^6+64 c d^7 x^7+5 d^8 x^8\right)-2 a b^9 d \left(140 c^9-2520 c^8 d x-6720 c^7 d^2 x^2+11760 c^6 d^3 x^3+5880 c^5 d^4 x^4+2940 c^4 d^5 x^5+1176 c^3 d^6 x^6+336 c^2 d^7 x^7+60 c d^8 x^8+5 d^9 x^9\right)+2520 d^2 (a+b x)^2 (b c-a d)^8 \log (a+b x)+b^{10} \left(-28 c^{10}-560 c^9 d x+6720 c^7 d^3 x^3+5880 c^6 d^4 x^4+4704 c^5 d^5 x^5+2940 c^4 d^6 x^6+1344 c^3 d^7 x^7+420 c^2 d^8 x^8+80 c d^9 x^9+7 d^{10} x^{10}\right)}{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,"(532*a^10*d^10 - 56*a^9*b*d^9*(85*c + 26*d*x) + 28*a^8*b^2*d^8*(675*c^2 + 380*c*d*x - 116*d^2*x^2) - 280*a^7*b^3*d^7*(156*c^3 + 117*c^2*d*x - 91*c*d^2*x^2 + 3*d^3*x^3) + 210*a^6*b^4*d^6*(308*c^4 + 256*c^3*d*x - 414*c^2*d^2*x^2 + 32*c*d^3*x^3 + d^4*x^4) - 84*a^5*b^5*d^5*(756*c^5 + 560*c^4*d*x - 2000*c^3*d^2*x^2 + 280*c^2*d^3*x^3 + 20*c*d^4*x^4 + d^5*x^5) + 42*a^4*b^6*d^4*(980*c^6 + 336*c^5*d*x - 4760*c^4*d^2*x^2 + 1120*c^3*d^3*x^3 + 140*c^2*d^4*x^4 + 16*c*d^5*x^5 + d^6*x^6) - 24*a^3*b^7*d^3*(700*c^7 - 490*c^6*d*x - 6174*c^5*d^2*x^2 + 2450*c^4*d^3*x^3 + 490*c^3*d^4*x^4 + 98*c^2*d^5*x^5 + 14*c*d^6*x^6 + d^7*x^7) + 3*a^2*b^8*d^2*(1260*c^8 - 4480*c^7*d*x - 21560*c^6*d^2*x^2 + 15680*c^5*d^3*x^3 + 4900*c^4*d^4*x^4 + 1568*c^3*d^5*x^5 + 392*c^2*d^6*x^6 + 64*c*d^7*x^7 + 5*d^8*x^8) - 2*a*b^9*d*(140*c^9 - 2520*c^8*d*x - 6720*c^7*d^2*x^2 + 11760*c^6*d^3*x^3 + 5880*c^5*d^4*x^4 + 2940*c^4*d^5*x^5 + 1176*c^3*d^6*x^6 + 336*c^2*d^7*x^7 + 60*c*d^8*x^8 + 5*d^9*x^9) + b^10*(-28*c^10 - 560*c^9*d*x + 6720*c^7*d^3*x^3 + 5880*c^6*d^4*x^4 + 4704*c^5*d^5*x^5 + 2940*c^4*d^6*x^6 + 1344*c^3*d^7*x^7 + 420*c^2*d^8*x^8 + 80*c*d^9*x^9 + 7*d^10*x^10) + 2520*d^2*(b*c - a*d)^8*(a + b*x)^2*Log[a + b*x])/(56*b^11*(a + b*x)^2)","B",1
1315,1,427,258,0.179498,"\int \frac{(c+d x)^{10}}{(a+b x)^4} \, dx","Integrate[(c + d*x)^10/(a + b*x)^4,x]","\frac{21 b^5 d^8 x^5 \left(2 a^2 d^2-8 a b c d+9 b^2 c^2\right)+105 b^4 d^7 x^4 \left(-a^3 d^3+5 a^2 b c d^2-9 a b^2 c^2 d+6 b^3 c^3\right)+35 b^3 d^6 x^3 \left(7 a^4 d^4-40 a^3 b c d^3+90 a^2 b^2 c^2 d^2-96 a b^3 c^3 d+42 b^4 c^4\right)+21 b^2 d^5 x^2 \left(-28 a^5 d^5+175 a^4 b c d^4-450 a^3 b^2 c^2 d^3+600 a^2 b^3 c^3 d^2-420 a b^4 c^4 d+126 b^5 c^5\right)+21 b d^4 x \left(84 a^6 d^6-560 a^5 b c d^5+1575 a^4 b^2 c^2 d^4-2400 a^3 b^3 c^3 d^3+2100 a^2 b^4 c^4 d^2-1008 a b^5 c^5 d+210 b^6 c^6\right)+7 b^6 d^9 x^6 (5 b c-2 a d)+2520 d^3 (b c-a d)^7 \log (a+b x)-\frac{945 d^2 (b c-a d)^8}{a+b x}+\frac{105 d (a d-b c)^9}{(a+b x)^2}-\frac{7 (b c-a d)^{10}}{(a+b x)^3}+3 b^7 d^{10} x^7}{21 b^{11}}","\frac{5 d^9 (a+b x)^6 (b c-a d)}{3 b^{11}}+\frac{9 d^8 (a+b x)^5 (b c-a d)^2}{b^{11}}+\frac{30 d^7 (a+b x)^4 (b c-a d)^3}{b^{11}}+\frac{70 d^6 (a+b x)^3 (b c-a d)^4}{b^{11}}+\frac{126 d^5 (a+b x)^2 (b c-a d)^5}{b^{11}}+\frac{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,"(21*b*d^4*(210*b^6*c^6 - 1008*a*b^5*c^5*d + 2100*a^2*b^4*c^4*d^2 - 2400*a^3*b^3*c^3*d^3 + 1575*a^4*b^2*c^2*d^4 - 560*a^5*b*c*d^5 + 84*a^6*d^6)*x + 21*b^2*d^5*(126*b^5*c^5 - 420*a*b^4*c^4*d + 600*a^2*b^3*c^3*d^2 - 450*a^3*b^2*c^2*d^3 + 175*a^4*b*c*d^4 - 28*a^5*d^5)*x^2 + 35*b^3*d^6*(42*b^4*c^4 - 96*a*b^3*c^3*d + 90*a^2*b^2*c^2*d^2 - 40*a^3*b*c*d^3 + 7*a^4*d^4)*x^3 + 105*b^4*d^7*(6*b^3*c^3 - 9*a*b^2*c^2*d + 5*a^2*b*c*d^2 - a^3*d^3)*x^4 + 21*b^5*d^8*(9*b^2*c^2 - 8*a*b*c*d + 2*a^2*d^2)*x^5 + 7*b^6*d^9*(5*b*c - 2*a*d)*x^6 + 3*b^7*d^10*x^7 - (7*(b*c - a*d)^10)/(a + b*x)^3 + (105*d*(-(b*c) + a*d)^9)/(a + b*x)^2 - (945*d^2*(b*c - a*d)^8)/(a + b*x) + 2520*d^3*(b*c - a*d)^7*Log[a + b*x])/(21*b^11)","A",1
1316,1,359,262,0.1963671,"\int \frac{(c+d x)^{10}}{(a+b x)^5} \, dx","Integrate[(c + d*x)^10/(a + b*x)^5,x]","\frac{15 b^4 d^8 x^4 \left(3 a^2 d^2-10 a b c d+9 b^2 c^2\right)+20 b^3 d^7 x^3 \left(-7 a^3 d^3+30 a^2 b c d^2-45 a b^2 c^2 d+24 b^3 c^3\right)+30 b^2 d^6 x^2 \left(14 a^4 d^4-70 a^3 b c d^3+135 a^2 b^2 c^2 d^2-120 a b^3 c^3 d+42 b^4 c^4\right)+12 b d^5 x \left(-126 a^5 d^5+700 a^4 b c d^4-1575 a^3 b^2 c^2 d^3+1800 a^2 b^3 c^3 d^2-1050 a b^4 c^4 d+252 b^5 c^5\right)+12 b^5 d^9 x^5 (2 b c-a d)+2520 d^4 (b c-a d)^6 \log (a+b x)+\frac{1440 d^3 (a d-b c)^7}{a+b x}-\frac{270 d^2 (b c-a d)^8}{(a+b x)^2}+\frac{40 d (a d-b c)^9}{(a+b x)^3}-\frac{3 (b c-a d)^{10}}{(a+b x)^4}+2 b^6 d^{10} x^6}{12 b^{11}}","\frac{2 d^9 (a+b x)^5 (b c-a d)}{b^{11}}+\frac{45 d^8 (a+b x)^4 (b c-a d)^2}{4 b^{11}}+\frac{40 d^7 (a+b x)^3 (b c-a d)^3}{b^{11}}+\frac{105 d^6 (a+b x)^2 (b c-a d)^4}{b^{11}}+\frac{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,"(12*b*d^5*(252*b^5*c^5 - 1050*a*b^4*c^4*d + 1800*a^2*b^3*c^3*d^2 - 1575*a^3*b^2*c^2*d^3 + 700*a^4*b*c*d^4 - 126*a^5*d^5)*x + 30*b^2*d^6*(42*b^4*c^4 - 120*a*b^3*c^3*d + 135*a^2*b^2*c^2*d^2 - 70*a^3*b*c*d^3 + 14*a^4*d^4)*x^2 + 20*b^3*d^7*(24*b^3*c^3 - 45*a*b^2*c^2*d + 30*a^2*b*c*d^2 - 7*a^3*d^3)*x^3 + 15*b^4*d^8*(9*b^2*c^2 - 10*a*b*c*d + 3*a^2*d^2)*x^4 + 12*b^5*d^9*(2*b*c - a*d)*x^5 + 2*b^6*d^10*x^6 - (3*(b*c - a*d)^10)/(a + b*x)^4 + (40*d*(-(b*c) + a*d)^9)/(a + b*x)^3 - (270*d^2*(b*c - a*d)^8)/(a + b*x)^2 + (1440*d^3*(-(b*c) + a*d)^7)/(a + b*x) + 2520*d^4*(b*c - a*d)^6*Log[a + b*x])/(12*b^11)","A",1
1317,1,305,260,0.2140024,"\int \frac{(c+d x)^{10}}{(a+b x)^6} \, dx","Integrate[(c + d*x)^10/(a + b*x)^6,x]","\frac{10 b^3 d^8 x^3 \left(7 a^2 d^2-20 a b c d+15 b^2 c^2\right)+10 b^2 d^7 x^2 \left(-28 a^3 d^3+105 a^2 b c d^2-135 a b^2 c^2 d+60 b^3 c^3\right)+10 b d^6 x \left(126 a^4 d^4-560 a^3 b c d^3+945 a^2 b^2 c^2 d^2-720 a b^3 c^3 d+210 b^4 c^4\right)+5 b^4 d^9 x^4 (5 b c-3 a d)+2520 d^5 (b c-a d)^5 \log (a+b x)-\frac{2100 d^4 (b c-a d)^6}{a+b x}+\frac{600 d^3 (a d-b c)^7}{(a+b x)^2}-\frac{150 d^2 (b c-a d)^8}{(a+b x)^3}+\frac{25 d (a d-b c)^9}{(a+b x)^4}-\frac{2 (b c-a d)^{10}}{(a+b x)^5}+2 b^5 d^{10} x^5}{10 b^{11}}","\frac{5 d^9 (a+b x)^4 (b c-a d)}{2 b^{11}}+\frac{15 d^8 (a+b x)^3 (b c-a d)^2}{b^{11}}+\frac{60 d^7 (a+b x)^2 (b c-a d)^3}{b^{11}}+\frac{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,"(10*b*d^6*(210*b^4*c^4 - 720*a*b^3*c^3*d + 945*a^2*b^2*c^2*d^2 - 560*a^3*b*c*d^3 + 126*a^4*d^4)*x + 10*b^2*d^7*(60*b^3*c^3 - 135*a*b^2*c^2*d + 105*a^2*b*c*d^2 - 28*a^3*d^3)*x^2 + 10*b^3*d^8*(15*b^2*c^2 - 20*a*b*c*d + 7*a^2*d^2)*x^3 + 5*b^4*d^9*(5*b*c - 3*a*d)*x^4 + 2*b^5*d^10*x^5 - (2*(b*c - a*d)^10)/(a + b*x)^5 + (25*d*(-(b*c) + a*d)^9)/(a + b*x)^4 - (150*d^2*(b*c - a*d)^8)/(a + b*x)^3 + (600*d^3*(-(b*c) + a*d)^7)/(a + b*x)^2 - (2100*d^4*(b*c - a*d)^6)/(a + b*x) + 2520*d^5*(b*c - a*d)^5*Log[a + b*x])/(10*b^11)","A",1
1318,1,265,262,0.2185509,"\int \frac{(c+d x)^{10}}{(a+b x)^7} \, dx","Integrate[(c + d*x)^10/(a + b*x)^7,x]","\frac{6 b^2 d^8 x^2 \left(28 a^2 d^2-70 a b c d+45 b^2 c^2\right)+12 b d^7 x \left(-84 a^3 d^3+280 a^2 b c d^2-315 a b^2 c^2 d+120 b^3 c^3\right)+4 b^3 d^9 x^3 (10 b c-7 a d)+2520 d^6 (b c-a d)^4 \log (a+b x)+\frac{3024 d^5 (a d-b c)^5}{a+b x}-\frac{1260 d^4 (b c-a d)^6}{(a+b x)^2}+\frac{480 d^3 (a d-b c)^7}{(a+b x)^3}-\frac{135 d^2 (b c-a d)^8}{(a+b x)^4}+\frac{24 d (a d-b c)^9}{(a+b x)^5}-\frac{2 (b c-a d)^{10}}{(a+b x)^6}+3 b^4 d^{10} x^4}{12 b^{11}}","\frac{10 d^9 (a+b x)^3 (b c-a d)}{3 b^{11}}+\frac{45 d^8 (a+b x)^2 (b c-a d)^2}{2 b^{11}}+\frac{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,"(12*b*d^7*(120*b^3*c^3 - 315*a*b^2*c^2*d + 280*a^2*b*c*d^2 - 84*a^3*d^3)*x + 6*b^2*d^8*(45*b^2*c^2 - 70*a*b*c*d + 28*a^2*d^2)*x^2 + 4*b^3*d^9*(10*b*c - 7*a*d)*x^3 + 3*b^4*d^10*x^4 - (2*(b*c - a*d)^10)/(a + b*x)^6 + (24*d*(-(b*c) + a*d)^9)/(a + b*x)^5 - (135*d^2*(b*c - a*d)^8)/(a + b*x)^4 + (480*d^3*(-(b*c) + a*d)^7)/(a + b*x)^3 - (1260*d^4*(b*c - a*d)^6)/(a + b*x)^2 + (3024*d^5*(-(b*c) + a*d)^5)/(a + b*x) + 2520*d^6*(b*c - a*d)^4*Log[a + b*x])/(12*b^11)","A",1
1319,1,239,258,0.248763,"\int \frac{(c+d x)^{10}}{(a+b x)^8} \, dx","Integrate[(c + d*x)^10/(a + b*x)^8,x]","\frac{21 b d^8 x \left(36 a^2 d^2-80 a b c d+45 b^2 c^2\right)+21 b^2 d^9 x^2 (5 b c-4 a d)+2520 d^7 (b c-a d)^3 \log (a+b x)-\frac{4410 d^6 (b c-a d)^4}{a+b x}+\frac{2646 d^5 (a d-b c)^5}{(a+b x)^2}-\frac{1470 d^4 (b c-a d)^6}{(a+b x)^3}+\frac{630 d^3 (a d-b c)^7}{(a+b x)^4}-\frac{189 d^2 (b c-a d)^8}{(a+b x)^5}+\frac{35 d (a d-b c)^9}{(a+b x)^6}-\frac{3 (b c-a d)^{10}}{(a+b x)^7}+7 b^3 d^{10} x^3}{21 b^{11}}","\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,"(21*b*d^8*(45*b^2*c^2 - 80*a*b*c*d + 36*a^2*d^2)*x + 21*b^2*d^9*(5*b*c - 4*a*d)*x^2 + 7*b^3*d^10*x^3 - (3*(b*c - a*d)^10)/(a + b*x)^7 + (35*d*(-(b*c) + a*d)^9)/(a + b*x)^6 - (189*d^2*(b*c - a*d)^8)/(a + b*x)^5 + (630*d^3*(-(b*c) + a*d)^7)/(a + b*x)^4 - (1470*d^4*(b*c - a*d)^6)/(a + b*x)^3 + (2646*d^5*(-(b*c) + a*d)^5)/(a + b*x)^2 - (4410*d^6*(b*c - a*d)^4)/(a + b*x) + 2520*d^7*(b*c - a*d)^3*Log[a + b*x])/(21*b^11)","A",1
1320,1,712,258,0.3167918,"\int \frac{(c+d x)^{10}}{(a+b x)^9} \, dx","Integrate[(c + d*x)^10/(a + b*x)^9,x]","\frac{3601 a^{10} d^{10}+2 a^9 b d^9 (13144 d x-4609 c)+a^8 b^2 d^8 \left(6849 c^2-68704 c d x+81928 d^2 x^2\right)+8 a^7 b^3 d^7 \left(-105 c^3+6534 c^2 d x-27538 c d^2 x^2+17542 d^3 x^3\right)+14 a^6 b^4 d^6 \left(-15 c^4-480 c^3 d x+12348 c^2 d^2 x^2-28112 c d^3 x^3+10010 d^4 x^4\right)-28 a^5 b^5 d^5 \left(3 c^5+60 c^4 d x+840 c^3 d^2 x^2-11508 c^2 d^3 x^3+15050 c d^4 x^4-2744 d^5 x^5\right)-14 a^4 b^6 d^4 \left(3 c^6+48 c^5 d x+420 c^4 d^2 x^2+3360 c^3 d^3 x^3-26250 c^2 d^4 x^4+19040 c d^5 x^5-1064 d^6 x^6\right)-8 a^3 b^7 d^3 \left(3 c^7+42 c^6 d x+294 c^5 d^2 x^2+1470 c^4 d^3 x^3+7350 c^3 d^4 x^4-32340 c^2 d^5 x^5+10780 c d^6 x^6+728 d^7 x^7\right)-a^2 b^8 d^2 \left(15 c^8+192 c^7 d x+1176 c^6 d^2 x^2+4704 c^5 d^3 x^3+14700 c^4 d^4 x^4+47040 c^3 d^5 x^5-105840 c^2 d^6 x^6+4480 c d^7 x^7+3248 d^8 x^8\right)-2 a b^9 d \left(5 c^9+60 c^8 d x+336 c^7 d^2 x^2+1176 c^6 d^3 x^3+2940 c^5 d^4 x^4+5880 c^4 d^5 x^5+11760 c^3 d^6 x^6-10080 c^2 d^7 x^7-2240 c d^8 x^8+140 d^9 x^9\right)+2520 d^8 (a+b x)^8 (b c-a d)^2 \log (a+b x)-\left(b^{10} \left(7 c^{10}+80 c^9 d x+420 c^8 d^2 x^2+1344 c^7 d^3 x^3+2940 c^6 d^4 x^4+4704 c^5 d^5 x^5+5880 c^4 d^6 x^6+6720 c^3 d^7 x^7-560 c d^9 x^9-28 d^{10} x^{10}\right)\right)}{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,"(3601*a^10*d^10 + 2*a^9*b*d^9*(-4609*c + 13144*d*x) + a^8*b^2*d^8*(6849*c^2 - 68704*c*d*x + 81928*d^2*x^2) + 8*a^7*b^3*d^7*(-105*c^3 + 6534*c^2*d*x - 27538*c*d^2*x^2 + 17542*d^3*x^3) + 14*a^6*b^4*d^6*(-15*c^4 - 480*c^3*d*x + 12348*c^2*d^2*x^2 - 28112*c*d^3*x^3 + 10010*d^4*x^4) - 28*a^5*b^5*d^5*(3*c^5 + 60*c^4*d*x + 840*c^3*d^2*x^2 - 11508*c^2*d^3*x^3 + 15050*c*d^4*x^4 - 2744*d^5*x^5) - 14*a^4*b^6*d^4*(3*c^6 + 48*c^5*d*x + 420*c^4*d^2*x^2 + 3360*c^3*d^3*x^3 - 26250*c^2*d^4*x^4 + 19040*c*d^5*x^5 - 1064*d^6*x^6) - 8*a^3*b^7*d^3*(3*c^7 + 42*c^6*d*x + 294*c^5*d^2*x^2 + 1470*c^4*d^3*x^3 + 7350*c^3*d^4*x^4 - 32340*c^2*d^5*x^5 + 10780*c*d^6*x^6 + 728*d^7*x^7) - a^2*b^8*d^2*(15*c^8 + 192*c^7*d*x + 1176*c^6*d^2*x^2 + 4704*c^5*d^3*x^3 + 14700*c^4*d^4*x^4 + 47040*c^3*d^5*x^5 - 105840*c^2*d^6*x^6 + 4480*c*d^7*x^7 + 3248*d^8*x^8) - 2*a*b^9*d*(5*c^9 + 60*c^8*d*x + 336*c^7*d^2*x^2 + 1176*c^6*d^3*x^3 + 2940*c^5*d^4*x^4 + 5880*c^4*d^5*x^5 + 11760*c^3*d^6*x^6 - 10080*c^2*d^7*x^7 - 2240*c*d^8*x^8 + 140*d^9*x^9) - b^10*(7*c^10 + 80*c^9*d*x + 420*c^8*d^2*x^2 + 1344*c^7*d^3*x^3 + 2940*c^6*d^4*x^4 + 4704*c^5*d^5*x^5 + 5880*c^4*d^6*x^6 + 6720*c^3*d^7*x^7 - 560*c*d^9*x^9 - 28*d^10*x^10) + 2520*d^8*(b*c - a*d)^2*(a + b*x)^8*Log[a + b*x])/(56*b^11*(a + b*x)^8)","B",1
1321,1,708,257,0.4237924,"\int \frac{(c+d x)^{10}}{(a+b x)^{10}} \, dx","Integrate[(c + d*x)^10/(a + b*x)^10,x]","-\frac{4861 a^{10} d^{10}+a^9 b d^9 (41229 d x-7129 c)+9 a^8 b^2 d^8 \left(140 c^2-6849 c d x+17064 d^2 x^2\right)+12 a^7 b^3 d^7 \left(35 c^3+945 c^2 d x-19602 c d^2 x^2+27342 d^3 x^3\right)+42 a^6 b^4 d^6 \left(5 c^4+90 c^3 d x+1080 c^2 d^2 x^2-12348 c d^3 x^3+10458 d^4 x^4\right)+126 a^5 b^5 d^5 \left(c^5+15 c^4 d x+120 c^3 d^2 x^2+840 c^2 d^3 x^3-5754 c d^4 x^4+2982 d^5 x^5\right)+42 a^4 b^6 d^4 \left(2 c^6+27 c^5 d x+180 c^4 d^2 x^2+840 c^3 d^3 x^3+3780 c^2 d^4 x^4-15750 c d^5 x^5+4704 d^6 x^6\right)+12 a^3 b^7 d^3 \left(5 c^7+63 c^6 d x+378 c^5 d^2 x^2+1470 c^4 d^3 x^3+4410 c^3 d^4 x^4+13230 c^2 d^5 x^5-32340 c d^6 x^6+4536 d^7 x^7\right)+9 a^2 b^8 d^2 \left(5 c^8+60 c^7 d x+336 c^6 d^2 x^2+1176 c^5 d^3 x^3+2940 c^4 d^4 x^4+5880 c^3 d^5 x^5+11760 c^2 d^6 x^6-15120 c d^7 x^7+252 d^8 x^8\right)+a b^9 d \left(35 c^9+405 c^8 d x+2160 c^7 d^2 x^2+7056 c^6 d^3 x^3+15876 c^5 d^4 x^4+26460 c^4 d^5 x^5+35280 c^3 d^6 x^6+45360 c^2 d^7 x^7-22680 c d^8 x^8-2268 d^9 x^9\right)+2520 d^9 (a+b x)^9 (a d-b c) \log (a+b x)+b^{10} \left(28 c^{10}+315 c^9 d x+1620 c^8 d^2 x^2+5040 c^7 d^3 x^3+10584 c^6 d^4 x^4+15876 c^5 d^5 x^5+17640 c^4 d^6 x^6+15120 c^3 d^7 x^7+11340 c^2 d^8 x^8-252 d^{10} x^{10}\right)}{252 b^{11} (a+b x)^9}","\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,"-1/252*(4861*a^10*d^10 + a^9*b*d^9*(-7129*c + 41229*d*x) + 9*a^8*b^2*d^8*(140*c^2 - 6849*c*d*x + 17064*d^2*x^2) + 12*a^7*b^3*d^7*(35*c^3 + 945*c^2*d*x - 19602*c*d^2*x^2 + 27342*d^3*x^3) + 42*a^6*b^4*d^6*(5*c^4 + 90*c^3*d*x + 1080*c^2*d^2*x^2 - 12348*c*d^3*x^3 + 10458*d^4*x^4) + 126*a^5*b^5*d^5*(c^5 + 15*c^4*d*x + 120*c^3*d^2*x^2 + 840*c^2*d^3*x^3 - 5754*c*d^4*x^4 + 2982*d^5*x^5) + 42*a^4*b^6*d^4*(2*c^6 + 27*c^5*d*x + 180*c^4*d^2*x^2 + 840*c^3*d^3*x^3 + 3780*c^2*d^4*x^4 - 15750*c*d^5*x^5 + 4704*d^6*x^6) + 12*a^3*b^7*d^3*(5*c^7 + 63*c^6*d*x + 378*c^5*d^2*x^2 + 1470*c^4*d^3*x^3 + 4410*c^3*d^4*x^4 + 13230*c^2*d^5*x^5 - 32340*c*d^6*x^6 + 4536*d^7*x^7) + 9*a^2*b^8*d^2*(5*c^8 + 60*c^7*d*x + 336*c^6*d^2*x^2 + 1176*c^5*d^3*x^3 + 2940*c^4*d^4*x^4 + 5880*c^3*d^5*x^5 + 11760*c^2*d^6*x^6 - 15120*c*d^7*x^7 + 252*d^8*x^8) + a*b^9*d*(35*c^9 + 405*c^8*d*x + 2160*c^7*d^2*x^2 + 7056*c^6*d^3*x^3 + 15876*c^5*d^4*x^4 + 26460*c^4*d^5*x^5 + 35280*c^3*d^6*x^6 + 45360*c^2*d^7*x^7 - 22680*c*d^8*x^8 - 2268*d^9*x^9) + b^10*(28*c^10 + 315*c^9*d*x + 1620*c^8*d^2*x^2 + 5040*c^7*d^3*x^3 + 10584*c^6*d^4*x^4 + 15876*c^5*d^5*x^5 + 17640*c^4*d^6*x^6 + 15120*c^3*d^7*x^7 + 11340*c^2*d^8*x^8 - 252*d^10*x^10) + 2520*d^9*(-(b*c) + a*d)*(a + b*x)^9*Log[a + b*x])/(b^11*(a + b*x)^9)","B",1
1322,1,591,271,0.3612697,"\int \frac{(c+d x)^{10}}{(a+b x)^{11}} \, dx","Integrate[(c + d*x)^10/(a + b*x)^11,x]","\frac{d^{10} \log (a+b x)}{b^{11}}-\frac{(b c-a d) \left(7381 a^9 d^9+a^8 b d^8 (4861 c+71290 d x)+a^7 b^2 d^7 \left(3601 c^2+46090 c d x+308205 d^2 x^2\right)+a^6 b^3 d^6 \left(2761 c^3+33490 c^2 d x+194805 c d^2 x^2+784080 d^3 x^3\right)+a^5 b^4 d^5 \left(2131 c^4+25090 c^3 d x+138105 c^2 d^2 x^2+481680 c d^3 x^3+1296540 d^4 x^4\right)+a^4 b^5 d^4 \left(1627 c^5+18790 c^4 d x+100305 c^3 d^2 x^2+330480 c^2 d^3 x^3+767340 c d^4 x^4+1450008 d^5 x^5\right)+a^3 b^6 d^3 \left(1207 c^6+13750 c^5 d x+71955 c^4 d^2 x^2+229680 c^3 d^3 x^3+502740 c^2 d^4 x^4+814968 c d^5 x^5+1102500 d^6 x^6\right)+a^2 b^7 d^2 \left(847 c^7+9550 c^6 d x+49275 c^5 d^2 x^2+154080 c^4 d^3 x^3+326340 c^3 d^4 x^4+497448 c^2 d^5 x^5+573300 c d^6 x^6+554400 d^7 x^7\right)+a b^8 d \left(532 c^8+5950 c^7 d x+30375 c^6 d^2 x^2+93600 c^5 d^3 x^3+194040 c^4 d^4 x^4+285768 c^3 d^5 x^5+308700 c^2 d^6 x^6+252000 c d^7 x^7+170100 d^8 x^8\right)+b^9 \left(252 c^9+2800 c^8 d x+14175 c^7 d^2 x^2+43200 c^6 d^3 x^3+88200 c^5 d^4 x^4+127008 c^4 d^5 x^5+132300 c^3 d^6 x^6+100800 c^2 d^7 x^7+56700 c d^8 x^8+25200 d^9 x^9\right)\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)*(7381*a^9*d^9 + a^8*b*d^8*(4861*c + 71290*d*x) + a^7*b^2*d^7*(3601*c^2 + 46090*c*d*x + 308205*d^2*x^2) + a^6*b^3*d^6*(2761*c^3 + 33490*c^2*d*x + 194805*c*d^2*x^2 + 784080*d^3*x^3) + a^5*b^4*d^5*(2131*c^4 + 25090*c^3*d*x + 138105*c^2*d^2*x^2 + 481680*c*d^3*x^3 + 1296540*d^4*x^4) + a^4*b^5*d^4*(1627*c^5 + 18790*c^4*d*x + 100305*c^3*d^2*x^2 + 330480*c^2*d^3*x^3 + 767340*c*d^4*x^4 + 1450008*d^5*x^5) + a^3*b^6*d^3*(1207*c^6 + 13750*c^5*d*x + 71955*c^4*d^2*x^2 + 229680*c^3*d^3*x^3 + 502740*c^2*d^4*x^4 + 814968*c*d^5*x^5 + 1102500*d^6*x^6) + a^2*b^7*d^2*(847*c^7 + 9550*c^6*d*x + 49275*c^5*d^2*x^2 + 154080*c^4*d^3*x^3 + 326340*c^3*d^4*x^4 + 497448*c^2*d^5*x^5 + 573300*c*d^6*x^6 + 554400*d^7*x^7) + a*b^8*d*(532*c^8 + 5950*c^7*d*x + 30375*c^6*d^2*x^2 + 93600*c^5*d^3*x^3 + 194040*c^4*d^4*x^4 + 285768*c^3*d^5*x^5 + 308700*c^2*d^6*x^6 + 252000*c*d^7*x^7 + 170100*d^8*x^8) + b^9*(252*c^9 + 2800*c^8*d*x + 14175*c^7*d^2*x^2 + 43200*c^6*d^3*x^3 + 88200*c^5*d^4*x^4 + 127008*c^4*d^5*x^5 + 132300*c^3*d^6*x^6 + 100800*c^2*d^7*x^7 + 56700*c*d^8*x^8 + 25200*d^9*x^9)))/(b^11*(a + b*x)^10) + (d^10*Log[a + b*x])/b^11","B",1
1323,1,665,28,0.2845271,"\int \frac{(c+d x)^{10}}{(a+b x)^{12}} \, dx","Integrate[(c + d*x)^10/(a + b*x)^12,x]","-\frac{a^{10} d^{10}+a^9 b d^9 (c+11 d x)+a^8 b^2 d^8 \left(c^2+11 c d x+55 d^2 x^2\right)+a^7 b^3 d^7 \left(c^3+11 c^2 d x+55 c d^2 x^2+165 d^3 x^3\right)+a^6 b^4 d^6 \left(c^4+11 c^3 d x+55 c^2 d^2 x^2+165 c d^3 x^3+330 d^4 x^4\right)+a^5 b^5 d^5 \left(c^5+11 c^4 d x+55 c^3 d^2 x^2+165 c^2 d^3 x^3+330 c d^4 x^4+462 d^5 x^5\right)+a^4 b^6 d^4 \left(c^6+11 c^5 d x+55 c^4 d^2 x^2+165 c^3 d^3 x^3+330 c^2 d^4 x^4+462 c d^5 x^5+462 d^6 x^6\right)+a^3 b^7 d^3 \left(c^7+11 c^6 d x+55 c^5 d^2 x^2+165 c^4 d^3 x^3+330 c^3 d^4 x^4+462 c^2 d^5 x^5+462 c d^6 x^6+330 d^7 x^7\right)+a^2 b^8 d^2 \left(c^8+11 c^7 d x+55 c^6 d^2 x^2+165 c^5 d^3 x^3+330 c^4 d^4 x^4+462 c^3 d^5 x^5+462 c^2 d^6 x^6+330 c d^7 x^7+165 d^8 x^8\right)+a b^9 d \left(c^9+11 c^8 d x+55 c^7 d^2 x^2+165 c^6 d^3 x^3+330 c^5 d^4 x^4+462 c^4 d^5 x^5+462 c^3 d^6 x^6+330 c^2 d^7 x^7+165 c d^8 x^8+55 d^9 x^9\right)+b^{10} \left(c^{10}+11 c^9 d x+55 c^8 d^2 x^2+165 c^7 d^3 x^3+330 c^6 d^4 x^4+462 c^5 d^5 x^5+462 c^4 d^6 x^6+330 c^3 d^7 x^7+165 c^2 d^8 x^8+55 c d^9 x^9+11 d^{10} x^{10}\right)}{11 b^{11} (a+b x)^{11}}","-\frac{(c+d x)^{11}}{11 (a+b x)^{11} (b c-a d)}",1,"-1/11*(a^10*d^10 + a^9*b*d^9*(c + 11*d*x) + a^8*b^2*d^8*(c^2 + 11*c*d*x + 55*d^2*x^2) + a^7*b^3*d^7*(c^3 + 11*c^2*d*x + 55*c*d^2*x^2 + 165*d^3*x^3) + a^6*b^4*d^6*(c^4 + 11*c^3*d*x + 55*c^2*d^2*x^2 + 165*c*d^3*x^3 + 330*d^4*x^4) + a^5*b^5*d^5*(c^5 + 11*c^4*d*x + 55*c^3*d^2*x^2 + 165*c^2*d^3*x^3 + 330*c*d^4*x^4 + 462*d^5*x^5) + a^4*b^6*d^4*(c^6 + 11*c^5*d*x + 55*c^4*d^2*x^2 + 165*c^3*d^3*x^3 + 330*c^2*d^4*x^4 + 462*c*d^5*x^5 + 462*d^6*x^6) + a^3*b^7*d^3*(c^7 + 11*c^6*d*x + 55*c^5*d^2*x^2 + 165*c^4*d^3*x^3 + 330*c^3*d^4*x^4 + 462*c^2*d^5*x^5 + 462*c*d^6*x^6 + 330*d^7*x^7) + a^2*b^8*d^2*(c^8 + 11*c^7*d*x + 55*c^6*d^2*x^2 + 165*c^5*d^3*x^3 + 330*c^4*d^4*x^4 + 462*c^3*d^5*x^5 + 462*c^2*d^6*x^6 + 330*c*d^7*x^7 + 165*d^8*x^8) + a*b^9*d*(c^9 + 11*c^8*d*x + 55*c^7*d^2*x^2 + 165*c^6*d^3*x^3 + 330*c^5*d^4*x^4 + 462*c^4*d^5*x^5 + 462*c^3*d^6*x^6 + 330*c^2*d^7*x^7 + 165*c*d^8*x^8 + 55*d^9*x^9) + b^10*(c^10 + 11*c^9*d*x + 55*c^8*d^2*x^2 + 165*c^7*d^3*x^3 + 330*c^6*d^4*x^4 + 462*c^5*d^5*x^5 + 462*c^4*d^6*x^6 + 330*c^3*d^7*x^7 + 165*c^2*d^8*x^8 + 55*c*d^9*x^9 + 11*d^10*x^10))/(b^11*(a + b*x)^11)","B",1
1324,1,684,58,0.280602,"\int \frac{(c+d x)^{10}}{(a+b x)^{13}} \, dx","Integrate[(c + d*x)^10/(a + b*x)^13,x]","-\frac{a^{10} d^{10}+2 a^9 b d^9 (c+6 d x)+3 a^8 b^2 d^8 \left(c^2+8 c d x+22 d^2 x^2\right)+4 a^7 b^3 d^7 \left(c^3+9 c^2 d x+33 c d^2 x^2+55 d^3 x^3\right)+a^6 b^4 d^6 \left(5 c^4+48 c^3 d x+198 c^2 d^2 x^2+440 c d^3 x^3+495 d^4 x^4\right)+6 a^5 b^5 d^5 \left(c^5+10 c^4 d x+44 c^3 d^2 x^2+110 c^2 d^3 x^3+165 c d^4 x^4+132 d^5 x^5\right)+a^4 b^6 d^4 \left(7 c^6+72 c^5 d x+330 c^4 d^2 x^2+880 c^3 d^3 x^3+1485 c^2 d^4 x^4+1584 c d^5 x^5+924 d^6 x^6\right)+4 a^3 b^7 d^3 \left(2 c^7+21 c^6 d x+99 c^5 d^2 x^2+275 c^4 d^3 x^3+495 c^3 d^4 x^4+594 c^2 d^5 x^5+462 c d^6 x^6+198 d^7 x^7\right)+3 a^2 b^8 d^2 \left(3 c^8+32 c^7 d x+154 c^6 d^2 x^2+440 c^5 d^3 x^3+825 c^4 d^4 x^4+1056 c^3 d^5 x^5+924 c^2 d^6 x^6+528 c d^7 x^7+165 d^8 x^8\right)+2 a b^9 d \left(5 c^9+54 c^8 d x+264 c^7 d^2 x^2+770 c^6 d^3 x^3+1485 c^5 d^4 x^4+1980 c^4 d^5 x^5+1848 c^3 d^6 x^6+1188 c^2 d^7 x^7+495 c d^8 x^8+110 d^9 x^9\right)+b^{10} \left(11 c^{10}+120 c^9 d x+594 c^8 d^2 x^2+1760 c^7 d^3 x^3+3465 c^6 d^4 x^4+4752 c^5 d^5 x^5+4620 c^4 d^6 x^6+3168 c^3 d^7 x^7+1485 c^2 d^8 x^8+440 c d^9 x^9+66 d^{10} x^{10}\right)}{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,"-1/132*(a^10*d^10 + 2*a^9*b*d^9*(c + 6*d*x) + 3*a^8*b^2*d^8*(c^2 + 8*c*d*x + 22*d^2*x^2) + 4*a^7*b^3*d^7*(c^3 + 9*c^2*d*x + 33*c*d^2*x^2 + 55*d^3*x^3) + a^6*b^4*d^6*(5*c^4 + 48*c^3*d*x + 198*c^2*d^2*x^2 + 440*c*d^3*x^3 + 495*d^4*x^4) + 6*a^5*b^5*d^5*(c^5 + 10*c^4*d*x + 44*c^3*d^2*x^2 + 110*c^2*d^3*x^3 + 165*c*d^4*x^4 + 132*d^5*x^5) + a^4*b^6*d^4*(7*c^6 + 72*c^5*d*x + 330*c^4*d^2*x^2 + 880*c^3*d^3*x^3 + 1485*c^2*d^4*x^4 + 1584*c*d^5*x^5 + 924*d^6*x^6) + 4*a^3*b^7*d^3*(2*c^7 + 21*c^6*d*x + 99*c^5*d^2*x^2 + 275*c^4*d^3*x^3 + 495*c^3*d^4*x^4 + 594*c^2*d^5*x^5 + 462*c*d^6*x^6 + 198*d^7*x^7) + 3*a^2*b^8*d^2*(3*c^8 + 32*c^7*d*x + 154*c^6*d^2*x^2 + 440*c^5*d^3*x^3 + 825*c^4*d^4*x^4 + 1056*c^3*d^5*x^5 + 924*c^2*d^6*x^6 + 528*c*d^7*x^7 + 165*d^8*x^8) + 2*a*b^9*d*(5*c^9 + 54*c^8*d*x + 264*c^7*d^2*x^2 + 770*c^6*d^3*x^3 + 1485*c^5*d^4*x^4 + 1980*c^4*d^5*x^5 + 1848*c^3*d^6*x^6 + 1188*c^2*d^7*x^7 + 495*c*d^8*x^8 + 110*d^9*x^9) + b^10*(11*c^10 + 120*c^9*d*x + 594*c^8*d^2*x^2 + 1760*c^7*d^3*x^3 + 3465*c^6*d^4*x^4 + 4752*c^5*d^5*x^5 + 4620*c^4*d^6*x^6 + 3168*c^3*d^7*x^7 + 1485*c^2*d^8*x^8 + 440*c*d^9*x^9 + 66*d^10*x^10))/(b^11*(a + b*x)^12)","B",1
1325,1,690,89,0.2942899,"\int \frac{(c+d x)^{10}}{(a+b x)^{14}} \, dx","Integrate[(c + d*x)^10/(a + b*x)^14,x]","-\frac{a^{10} d^{10}+a^9 b d^9 (3 c+13 d x)+3 a^8 b^2 d^8 \left(2 c^2+13 c d x+26 d^2 x^2\right)+2 a^7 b^3 d^7 \left(5 c^3+39 c^2 d x+117 c d^2 x^2+143 d^3 x^3\right)+a^6 b^4 d^6 \left(15 c^4+130 c^3 d x+468 c^2 d^2 x^2+858 c d^3 x^3+715 d^4 x^4\right)+3 a^5 b^5 d^5 \left(7 c^5+65 c^4 d x+260 c^3 d^2 x^2+572 c^2 d^3 x^3+715 c d^4 x^4+429 d^5 x^5\right)+a^4 b^6 d^4 \left(28 c^6+273 c^5 d x+1170 c^4 d^2 x^2+2860 c^3 d^3 x^3+4290 c^2 d^4 x^4+3861 c d^5 x^5+1716 d^6 x^6\right)+2 a^3 b^7 d^3 \left(18 c^7+182 c^6 d x+819 c^5 d^2 x^2+2145 c^4 d^3 x^3+3575 c^3 d^4 x^4+3861 c^2 d^5 x^5+2574 c d^6 x^6+858 d^7 x^7\right)+3 a^2 b^8 d^2 \left(15 c^8+156 c^7 d x+728 c^6 d^2 x^2+2002 c^5 d^3 x^3+3575 c^4 d^4 x^4+4290 c^3 d^5 x^5+3432 c^2 d^6 x^6+1716 c d^7 x^7+429 d^8 x^8\right)+a b^9 d \left(55 c^9+585 c^8 d x+2808 c^7 d^2 x^2+8008 c^6 d^3 x^3+15015 c^5 d^4 x^4+19305 c^4 d^5 x^5+17160 c^3 d^6 x^6+10296 c^2 d^7 x^7+3861 c d^8 x^8+715 d^9 x^9\right)+b^{10} \left(66 c^{10}+715 c^9 d x+3510 c^8 d^2 x^2+10296 c^7 d^3 x^3+20020 c^6 d^4 x^4+27027 c^5 d^5 x^5+25740 c^4 d^6 x^6+17160 c^3 d^7 x^7+7722 c^2 d^8 x^8+2145 c d^9 x^9+286 d^{10} x^{10}\right)}{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,"-1/858*(a^10*d^10 + a^9*b*d^9*(3*c + 13*d*x) + 3*a^8*b^2*d^8*(2*c^2 + 13*c*d*x + 26*d^2*x^2) + 2*a^7*b^3*d^7*(5*c^3 + 39*c^2*d*x + 117*c*d^2*x^2 + 143*d^3*x^3) + a^6*b^4*d^6*(15*c^4 + 130*c^3*d*x + 468*c^2*d^2*x^2 + 858*c*d^3*x^3 + 715*d^4*x^4) + 3*a^5*b^5*d^5*(7*c^5 + 65*c^4*d*x + 260*c^3*d^2*x^2 + 572*c^2*d^3*x^3 + 715*c*d^4*x^4 + 429*d^5*x^5) + a^4*b^6*d^4*(28*c^6 + 273*c^5*d*x + 1170*c^4*d^2*x^2 + 2860*c^3*d^3*x^3 + 4290*c^2*d^4*x^4 + 3861*c*d^5*x^5 + 1716*d^6*x^6) + 2*a^3*b^7*d^3*(18*c^7 + 182*c^6*d*x + 819*c^5*d^2*x^2 + 2145*c^4*d^3*x^3 + 3575*c^3*d^4*x^4 + 3861*c^2*d^5*x^5 + 2574*c*d^6*x^6 + 858*d^7*x^7) + 3*a^2*b^8*d^2*(15*c^8 + 156*c^7*d*x + 728*c^6*d^2*x^2 + 2002*c^5*d^3*x^3 + 3575*c^4*d^4*x^4 + 4290*c^3*d^5*x^5 + 3432*c^2*d^6*x^6 + 1716*c*d^7*x^7 + 429*d^8*x^8) + a*b^9*d*(55*c^9 + 585*c^8*d*x + 2808*c^7*d^2*x^2 + 8008*c^6*d^3*x^3 + 15015*c^5*d^4*x^4 + 19305*c^4*d^5*x^5 + 17160*c^3*d^6*x^6 + 10296*c^2*d^7*x^7 + 3861*c*d^8*x^8 + 715*d^9*x^9) + b^10*(66*c^10 + 715*c^9*d*x + 3510*c^8*d^2*x^2 + 10296*c^7*d^3*x^3 + 20020*c^6*d^4*x^4 + 27027*c^5*d^5*x^5 + 25740*c^4*d^6*x^6 + 17160*c^3*d^7*x^7 + 7722*c^2*d^8*x^8 + 2145*c*d^9*x^9 + 286*d^10*x^10))/(b^11*(a + b*x)^13)","B",1
1326,1,692,120,0.2870623,"\int \frac{(c+d x)^{10}}{(a+b x)^{15}} \, dx","Integrate[(c + d*x)^10/(a + b*x)^15,x]","-\frac{a^{10} d^{10}+2 a^9 b d^9 (2 c+7 d x)+a^8 b^2 d^8 \left(10 c^2+56 c d x+91 d^2 x^2\right)+4 a^7 b^3 d^7 \left(5 c^3+35 c^2 d x+91 c d^2 x^2+91 d^3 x^3\right)+7 a^6 b^4 d^6 \left(5 c^4+40 c^3 d x+130 c^2 d^2 x^2+208 c d^3 x^3+143 d^4 x^4\right)+14 a^5 b^5 d^5 \left(4 c^5+35 c^4 d x+130 c^3 d^2 x^2+260 c^2 d^3 x^3+286 c d^4 x^4+143 d^5 x^5\right)+7 a^4 b^6 d^4 \left(12 c^6+112 c^5 d x+455 c^4 d^2 x^2+1040 c^3 d^3 x^3+1430 c^2 d^4 x^4+1144 c d^5 x^5+429 d^6 x^6\right)+4 a^3 b^7 d^3 \left(30 c^7+294 c^6 d x+1274 c^5 d^2 x^2+3185 c^4 d^3 x^3+5005 c^3 d^4 x^4+5005 c^2 d^5 x^5+3003 c d^6 x^6+858 d^7 x^7\right)+a^2 b^8 d^2 \left(165 c^8+1680 c^7 d x+7644 c^6 d^2 x^2+20384 c^5 d^3 x^3+35035 c^4 d^4 x^4+40040 c^3 d^5 x^5+30030 c^2 d^6 x^6+13728 c d^7 x^7+3003 d^8 x^8\right)+2 a b^9 d \left(110 c^9+1155 c^8 d x+5460 c^7 d^2 x^2+15288 c^6 d^3 x^3+28028 c^5 d^4 x^4+35035 c^4 d^5 x^5+30030 c^3 d^6 x^6+17160 c^2 d^7 x^7+6006 c d^8 x^8+1001 d^9 x^9\right)+b^{10} \left(286 c^{10}+3080 c^9 d x+15015 c^8 d^2 x^2+43680 c^7 d^3 x^3+84084 c^6 d^4 x^4+112112 c^5 d^5 x^5+105105 c^4 d^6 x^6+68640 c^3 d^7 x^7+30030 c^2 d^8 x^8+8008 c d^9 x^9+1001 d^{10} x^{10}\right)}{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,"-1/4004*(a^10*d^10 + 2*a^9*b*d^9*(2*c + 7*d*x) + a^8*b^2*d^8*(10*c^2 + 56*c*d*x + 91*d^2*x^2) + 4*a^7*b^3*d^7*(5*c^3 + 35*c^2*d*x + 91*c*d^2*x^2 + 91*d^3*x^3) + 7*a^6*b^4*d^6*(5*c^4 + 40*c^3*d*x + 130*c^2*d^2*x^2 + 208*c*d^3*x^3 + 143*d^4*x^4) + 14*a^5*b^5*d^5*(4*c^5 + 35*c^4*d*x + 130*c^3*d^2*x^2 + 260*c^2*d^3*x^3 + 286*c*d^4*x^4 + 143*d^5*x^5) + 7*a^4*b^6*d^4*(12*c^6 + 112*c^5*d*x + 455*c^4*d^2*x^2 + 1040*c^3*d^3*x^3 + 1430*c^2*d^4*x^4 + 1144*c*d^5*x^5 + 429*d^6*x^6) + 4*a^3*b^7*d^3*(30*c^7 + 294*c^6*d*x + 1274*c^5*d^2*x^2 + 3185*c^4*d^3*x^3 + 5005*c^3*d^4*x^4 + 5005*c^2*d^5*x^5 + 3003*c*d^6*x^6 + 858*d^7*x^7) + a^2*b^8*d^2*(165*c^8 + 1680*c^7*d*x + 7644*c^6*d^2*x^2 + 20384*c^5*d^3*x^3 + 35035*c^4*d^4*x^4 + 40040*c^3*d^5*x^5 + 30030*c^2*d^6*x^6 + 13728*c*d^7*x^7 + 3003*d^8*x^8) + 2*a*b^9*d*(110*c^9 + 1155*c^8*d*x + 5460*c^7*d^2*x^2 + 15288*c^6*d^3*x^3 + 28028*c^5*d^4*x^4 + 35035*c^4*d^5*x^5 + 30030*c^3*d^6*x^6 + 17160*c^2*d^7*x^7 + 6006*c*d^8*x^8 + 1001*d^9*x^9) + b^10*(286*c^10 + 3080*c^9*d*x + 15015*c^8*d^2*x^2 + 43680*c^7*d^3*x^3 + 84084*c^6*d^4*x^4 + 112112*c^5*d^5*x^5 + 105105*c^4*d^6*x^6 + 68640*c^3*d^7*x^7 + 30030*c^2*d^8*x^8 + 8008*c*d^9*x^9 + 1001*d^10*x^10))/(b^11*(a + b*x)^14)","B",1
1327,1,690,151,0.2878859,"\int \frac{(c+d x)^{10}}{(a+b x)^{16}} \, dx","Integrate[(c + d*x)^10/(a + b*x)^16,x]","-\frac{a^{10} d^{10}+5 a^9 b d^9 (c+3 d x)+15 a^8 b^2 d^8 \left(c^2+5 c d x+7 d^2 x^2\right)+5 a^7 b^3 d^7 \left(7 c^3+45 c^2 d x+105 c d^2 x^2+91 d^3 x^3\right)+35 a^6 b^4 d^6 \left(2 c^4+15 c^3 d x+45 c^2 d^2 x^2+65 c d^3 x^3+39 d^4 x^4\right)+21 a^5 b^5 d^5 \left(6 c^5+50 c^4 d x+175 c^3 d^2 x^2+325 c^2 d^3 x^3+325 c d^4 x^4+143 d^5 x^5\right)+35 a^4 b^6 d^4 \left(6 c^6+54 c^5 d x+210 c^4 d^2 x^2+455 c^3 d^3 x^3+585 c^2 d^4 x^4+429 c d^5 x^5+143 d^6 x^6\right)+5 a^3 b^7 d^3 \left(66 c^7+630 c^6 d x+2646 c^5 d^2 x^2+6370 c^4 d^3 x^3+9555 c^3 d^4 x^4+9009 c^2 d^5 x^5+5005 c d^6 x^6+1287 d^7 x^7\right)+15 a^2 b^8 d^2 \left(33 c^8+330 c^7 d x+1470 c^6 d^2 x^2+3822 c^5 d^3 x^3+6370 c^4 d^4 x^4+7007 c^3 d^5 x^5+5005 c^2 d^6 x^6+2145 c d^7 x^7+429 d^8 x^8\right)+5 a b^9 d \left(143 c^9+1485 c^8 d x+6930 c^7 d^2 x^2+19110 c^6 d^3 x^3+34398 c^5 d^4 x^4+42042 c^4 d^5 x^5+35035 c^3 d^6 x^6+19305 c^2 d^7 x^7+6435 c d^8 x^8+1001 d^9 x^9\right)+b^{10} \left(1001 c^{10}+10725 c^9 d x+51975 c^8 d^2 x^2+150150 c^7 d^3 x^3+286650 c^6 d^4 x^4+378378 c^5 d^5 x^5+350350 c^4 d^6 x^6+225225 c^3 d^7 x^7+96525 c^2 d^8 x^8+25025 c d^9 x^9+3003 d^{10} x^{10}\right)}{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,"-1/15015*(a^10*d^10 + 5*a^9*b*d^9*(c + 3*d*x) + 15*a^8*b^2*d^8*(c^2 + 5*c*d*x + 7*d^2*x^2) + 5*a^7*b^3*d^7*(7*c^3 + 45*c^2*d*x + 105*c*d^2*x^2 + 91*d^3*x^3) + 35*a^6*b^4*d^6*(2*c^4 + 15*c^3*d*x + 45*c^2*d^2*x^2 + 65*c*d^3*x^3 + 39*d^4*x^4) + 21*a^5*b^5*d^5*(6*c^5 + 50*c^4*d*x + 175*c^3*d^2*x^2 + 325*c^2*d^3*x^3 + 325*c*d^4*x^4 + 143*d^5*x^5) + 35*a^4*b^6*d^4*(6*c^6 + 54*c^5*d*x + 210*c^4*d^2*x^2 + 455*c^3*d^3*x^3 + 585*c^2*d^4*x^4 + 429*c*d^5*x^5 + 143*d^6*x^6) + 5*a^3*b^7*d^3*(66*c^7 + 630*c^6*d*x + 2646*c^5*d^2*x^2 + 6370*c^4*d^3*x^3 + 9555*c^3*d^4*x^4 + 9009*c^2*d^5*x^5 + 5005*c*d^6*x^6 + 1287*d^7*x^7) + 15*a^2*b^8*d^2*(33*c^8 + 330*c^7*d*x + 1470*c^6*d^2*x^2 + 3822*c^5*d^3*x^3 + 6370*c^4*d^4*x^4 + 7007*c^3*d^5*x^5 + 5005*c^2*d^6*x^6 + 2145*c*d^7*x^7 + 429*d^8*x^8) + 5*a*b^9*d*(143*c^9 + 1485*c^8*d*x + 6930*c^7*d^2*x^2 + 19110*c^6*d^3*x^3 + 34398*c^5*d^4*x^4 + 42042*c^4*d^5*x^5 + 35035*c^3*d^6*x^6 + 19305*c^2*d^7*x^7 + 6435*c*d^8*x^8 + 1001*d^9*x^9) + b^10*(1001*c^10 + 10725*c^9*d*x + 51975*c^8*d^2*x^2 + 150150*c^7*d^3*x^3 + 286650*c^6*d^4*x^4 + 378378*c^5*d^5*x^5 + 350350*c^4*d^6*x^6 + 225225*c^3*d^7*x^7 + 96525*c^2*d^8*x^8 + 25025*c*d^9*x^9 + 3003*d^10*x^10))/(b^11*(a + b*x)^15)","B",1
1328,1,694,182,0.2802876,"\int \frac{(c+d x)^{10}}{(a+b x)^{17}} \, dx","Integrate[(c + d*x)^10/(a + b*x)^17,x]","-\frac{a^{10} d^{10}+2 a^9 b d^9 (3 c+8 d x)+3 a^8 b^2 d^8 \left(7 c^2+32 c d x+40 d^2 x^2\right)+8 a^7 b^3 d^7 \left(7 c^3+42 c^2 d x+90 c d^2 x^2+70 d^3 x^3\right)+14 a^6 b^4 d^6 \left(9 c^4+64 c^3 d x+180 c^2 d^2 x^2+240 c d^3 x^3+130 d^4 x^4\right)+84 a^5 b^5 d^5 \left(3 c^5+24 c^4 d x+80 c^3 d^2 x^2+140 c^2 d^3 x^3+130 c d^4 x^4+52 d^5 x^5\right)+14 a^4 b^6 d^4 \left(33 c^6+288 c^5 d x+1080 c^4 d^2 x^2+2240 c^3 d^3 x^3+2730 c^2 d^4 x^4+1872 c d^5 x^5+572 d^6 x^6\right)+8 a^3 b^7 d^3 \left(99 c^7+924 c^6 d x+3780 c^5 d^2 x^2+8820 c^4 d^3 x^3+12740 c^3 d^4 x^4+11466 c^2 d^5 x^5+6006 c d^6 x^6+1430 d^7 x^7\right)+3 a^2 b^8 d^2 \left(429 c^8+4224 c^7 d x+18480 c^6 d^2 x^2+47040 c^5 d^3 x^3+76440 c^4 d^4 x^4+81536 c^3 d^5 x^5+56056 c^2 d^6 x^6+22880 c d^7 x^7+4290 d^8 x^8\right)+2 a b^9 d \left(1001 c^9+10296 c^8 d x+47520 c^7 d^2 x^2+129360 c^6 d^3 x^3+229320 c^5 d^4 x^4+275184 c^4 d^5 x^5+224224 c^3 d^6 x^6+120120 c^2 d^7 x^7+38610 c d^8 x^8+5720 d^9 x^9\right)+b^{10} \left(3003 c^{10}+32032 c^9 d x+154440 c^8 d^2 x^2+443520 c^7 d^3 x^3+840840 c^6 d^4 x^4+1100736 c^5 d^5 x^5+1009008 c^4 d^6 x^6+640640 c^3 d^7 x^7+270270 c^2 d^8 x^8+68640 c d^9 x^9+8008 d^{10} x^{10}\right)}{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,"-1/48048*(a^10*d^10 + 2*a^9*b*d^9*(3*c + 8*d*x) + 3*a^8*b^2*d^8*(7*c^2 + 32*c*d*x + 40*d^2*x^2) + 8*a^7*b^3*d^7*(7*c^3 + 42*c^2*d*x + 90*c*d^2*x^2 + 70*d^3*x^3) + 14*a^6*b^4*d^6*(9*c^4 + 64*c^3*d*x + 180*c^2*d^2*x^2 + 240*c*d^3*x^3 + 130*d^4*x^4) + 84*a^5*b^5*d^5*(3*c^5 + 24*c^4*d*x + 80*c^3*d^2*x^2 + 140*c^2*d^3*x^3 + 130*c*d^4*x^4 + 52*d^5*x^5) + 14*a^4*b^6*d^4*(33*c^6 + 288*c^5*d*x + 1080*c^4*d^2*x^2 + 2240*c^3*d^3*x^3 + 2730*c^2*d^4*x^4 + 1872*c*d^5*x^5 + 572*d^6*x^6) + 8*a^3*b^7*d^3*(99*c^7 + 924*c^6*d*x + 3780*c^5*d^2*x^2 + 8820*c^4*d^3*x^3 + 12740*c^3*d^4*x^4 + 11466*c^2*d^5*x^5 + 6006*c*d^6*x^6 + 1430*d^7*x^7) + 3*a^2*b^8*d^2*(429*c^8 + 4224*c^7*d*x + 18480*c^6*d^2*x^2 + 47040*c^5*d^3*x^3 + 76440*c^4*d^4*x^4 + 81536*c^3*d^5*x^5 + 56056*c^2*d^6*x^6 + 22880*c*d^7*x^7 + 4290*d^8*x^8) + 2*a*b^9*d*(1001*c^9 + 10296*c^8*d*x + 47520*c^7*d^2*x^2 + 129360*c^6*d^3*x^3 + 229320*c^5*d^4*x^4 + 275184*c^4*d^5*x^5 + 224224*c^3*d^6*x^6 + 120120*c^2*d^7*x^7 + 38610*c*d^8*x^8 + 5720*d^9*x^9) + b^10*(3003*c^10 + 32032*c^9*d*x + 154440*c^8*d^2*x^2 + 443520*c^7*d^3*x^3 + 840840*c^6*d^4*x^4 + 1100736*c^5*d^5*x^5 + 1009008*c^4*d^6*x^6 + 640640*c^3*d^7*x^7 + 270270*c^2*d^8*x^8 + 68640*c*d^9*x^9 + 8008*d^10*x^10))/(b^11*(a + b*x)^16)","B",1
1329,1,690,213,0.3230489,"\int \frac{(c+d x)^{10}}{(a+b x)^{18}} \, dx","Integrate[(c + d*x)^10/(a + b*x)^18,x]","-\frac{a^{10} d^{10}+a^9 b d^9 (7 c+17 d x)+a^8 b^2 d^8 \left(28 c^2+119 c d x+136 d^2 x^2\right)+4 a^7 b^3 d^7 \left(21 c^3+119 c^2 d x+238 c d^2 x^2+170 d^3 x^3\right)+14 a^6 b^4 d^6 \left(15 c^4+102 c^3 d x+272 c^2 d^2 x^2+340 c d^3 x^3+170 d^4 x^4\right)+14 a^5 b^5 d^5 \left(33 c^5+255 c^4 d x+816 c^3 d^2 x^2+1360 c^2 d^3 x^3+1190 c d^4 x^4+442 d^5 x^5\right)+14 a^4 b^6 d^4 \left(66 c^6+561 c^5 d x+2040 c^4 d^2 x^2+4080 c^3 d^3 x^3+4760 c^2 d^4 x^4+3094 c d^5 x^5+884 d^6 x^6\right)+4 a^3 b^7 d^3 \left(429 c^7+3927 c^6 d x+15708 c^5 d^2 x^2+35700 c^4 d^3 x^3+49980 c^3 d^4 x^4+43316 c^2 d^5 x^5+21658 c d^6 x^6+4862 d^7 x^7\right)+a^2 b^8 d^2 \left(3003 c^8+29172 c^7 d x+125664 c^6 d^2 x^2+314160 c^5 d^3 x^3+499800 c^4 d^4 x^4+519792 c^3 d^5 x^5+346528 c^2 d^6 x^6+136136 c d^7 x^7+24310 d^8 x^8\right)+a b^9 d \left(5005 c^9+51051 c^8 d x+233376 c^7 d^2 x^2+628320 c^6 d^3 x^3+1099560 c^5 d^4 x^4+1299480 c^4 d^5 x^5+1039584 c^3 d^6 x^6+544544 c^2 d^7 x^7+170170 c d^8 x^8+24310 d^9 x^9\right)+b^{10} \left(8008 c^{10}+85085 c^9 d x+408408 c^8 d^2 x^2+1166880 c^7 d^3 x^3+2199120 c^6 d^4 x^4+2858856 c^5 d^5 x^5+2598960 c^4 d^6 x^6+1633632 c^3 d^7 x^7+680680 c^2 d^8 x^8+170170 c d^9 x^9+19448 d^{10} x^{10}\right)}{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,"-1/136136*(a^10*d^10 + a^9*b*d^9*(7*c + 17*d*x) + a^8*b^2*d^8*(28*c^2 + 119*c*d*x + 136*d^2*x^2) + 4*a^7*b^3*d^7*(21*c^3 + 119*c^2*d*x + 238*c*d^2*x^2 + 170*d^3*x^3) + 14*a^6*b^4*d^6*(15*c^4 + 102*c^3*d*x + 272*c^2*d^2*x^2 + 340*c*d^3*x^3 + 170*d^4*x^4) + 14*a^5*b^5*d^5*(33*c^5 + 255*c^4*d*x + 816*c^3*d^2*x^2 + 1360*c^2*d^3*x^3 + 1190*c*d^4*x^4 + 442*d^5*x^5) + 14*a^4*b^6*d^4*(66*c^6 + 561*c^5*d*x + 2040*c^4*d^2*x^2 + 4080*c^3*d^3*x^3 + 4760*c^2*d^4*x^4 + 3094*c*d^5*x^5 + 884*d^6*x^6) + 4*a^3*b^7*d^3*(429*c^7 + 3927*c^6*d*x + 15708*c^5*d^2*x^2 + 35700*c^4*d^3*x^3 + 49980*c^3*d^4*x^4 + 43316*c^2*d^5*x^5 + 21658*c*d^6*x^6 + 4862*d^7*x^7) + a^2*b^8*d^2*(3003*c^8 + 29172*c^7*d*x + 125664*c^6*d^2*x^2 + 314160*c^5*d^3*x^3 + 499800*c^4*d^4*x^4 + 519792*c^3*d^5*x^5 + 346528*c^2*d^6*x^6 + 136136*c*d^7*x^7 + 24310*d^8*x^8) + a*b^9*d*(5005*c^9 + 51051*c^8*d*x + 233376*c^7*d^2*x^2 + 628320*c^6*d^3*x^3 + 1099560*c^5*d^4*x^4 + 1299480*c^4*d^5*x^5 + 1039584*c^3*d^6*x^6 + 544544*c^2*d^7*x^7 + 170170*c*d^8*x^8 + 24310*d^9*x^9) + b^10*(8008*c^10 + 85085*c^9*d*x + 408408*c^8*d^2*x^2 + 1166880*c^7*d^3*x^3 + 2199120*c^6*d^4*x^4 + 2858856*c^5*d^5*x^5 + 2598960*c^4*d^6*x^6 + 1633632*c^3*d^7*x^7 + 680680*c^2*d^8*x^8 + 170170*c*d^9*x^9 + 19448*d^10*x^10))/(b^11*(a + b*x)^17)","B",1
1330,1,694,244,0.2785855,"\int \frac{(c+d x)^{10}}{(a+b x)^{19}} \, dx","Integrate[(c + d*x)^10/(a + b*x)^19,x]","-\frac{a^{10} d^{10}+2 a^9 b d^9 (4 c+9 d x)+9 a^8 b^2 d^8 \left(4 c^2+16 c d x+17 d^2 x^2\right)+24 a^7 b^3 d^7 \left(5 c^3+27 c^2 d x+51 c d^2 x^2+34 d^3 x^3\right)+6 a^6 b^4 d^6 \left(55 c^4+360 c^3 d x+918 c^2 d^2 x^2+1088 c d^3 x^3+510 d^4 x^4\right)+36 a^5 b^5 d^5 \left(22 c^5+165 c^4 d x+510 c^3 d^2 x^2+816 c^2 d^3 x^3+680 c d^4 x^4+238 d^5 x^5\right)+6 a^4 b^6 d^4 \left(286 c^6+2376 c^5 d x+8415 c^4 d^2 x^2+16320 c^3 d^3 x^3+18360 c^2 d^4 x^4+11424 c d^5 x^5+3094 d^6 x^6\right)+24 a^3 b^7 d^3 \left(143 c^7+1287 c^6 d x+5049 c^5 d^2 x^2+11220 c^4 d^3 x^3+15300 c^3 d^4 x^4+12852 c^2 d^5 x^5+6188 c d^6 x^6+1326 d^7 x^7\right)+9 a^2 b^8 d^2 \left(715 c^8+6864 c^7 d x+29172 c^6 d^2 x^2+71808 c^5 d^3 x^3+112200 c^4 d^4 x^4+114240 c^3 d^5 x^5+74256 c^2 d^6 x^6+28288 c d^7 x^7+4862 d^8 x^8\right)+2 a b^9 d \left(5720 c^9+57915 c^8 d x+262548 c^7 d^2 x^2+700128 c^6 d^3 x^3+1211760 c^5 d^4 x^4+1413720 c^4 d^5 x^5+1113840 c^3 d^6 x^6+572832 c^2 d^7 x^7+175032 c d^8 x^8+24310 d^9 x^9\right)+b^{10} \left(19448 c^{10}+205920 c^9 d x+984555 c^8 d^2 x^2+2800512 c^7 d^3 x^3+5250960 c^6 d^4 x^4+6785856 c^5 d^5 x^5+6126120 c^4 d^6 x^6+3818880 c^3 d^7 x^7+1575288 c^2 d^8 x^8+388960 c d^9 x^9+43758 d^{10} x^{10}\right)}{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,"-1/350064*(a^10*d^10 + 2*a^9*b*d^9*(4*c + 9*d*x) + 9*a^8*b^2*d^8*(4*c^2 + 16*c*d*x + 17*d^2*x^2) + 24*a^7*b^3*d^7*(5*c^3 + 27*c^2*d*x + 51*c*d^2*x^2 + 34*d^3*x^3) + 6*a^6*b^4*d^6*(55*c^4 + 360*c^3*d*x + 918*c^2*d^2*x^2 + 1088*c*d^3*x^3 + 510*d^4*x^4) + 36*a^5*b^5*d^5*(22*c^5 + 165*c^4*d*x + 510*c^3*d^2*x^2 + 816*c^2*d^3*x^3 + 680*c*d^4*x^4 + 238*d^5*x^5) + 6*a^4*b^6*d^4*(286*c^6 + 2376*c^5*d*x + 8415*c^4*d^2*x^2 + 16320*c^3*d^3*x^3 + 18360*c^2*d^4*x^4 + 11424*c*d^5*x^5 + 3094*d^6*x^6) + 24*a^3*b^7*d^3*(143*c^7 + 1287*c^6*d*x + 5049*c^5*d^2*x^2 + 11220*c^4*d^3*x^3 + 15300*c^3*d^4*x^4 + 12852*c^2*d^5*x^5 + 6188*c*d^6*x^6 + 1326*d^7*x^7) + 9*a^2*b^8*d^2*(715*c^8 + 6864*c^7*d*x + 29172*c^6*d^2*x^2 + 71808*c^5*d^3*x^3 + 112200*c^4*d^4*x^4 + 114240*c^3*d^5*x^5 + 74256*c^2*d^6*x^6 + 28288*c*d^7*x^7 + 4862*d^8*x^8) + 2*a*b^9*d*(5720*c^9 + 57915*c^8*d*x + 262548*c^7*d^2*x^2 + 700128*c^6*d^3*x^3 + 1211760*c^5*d^4*x^4 + 1413720*c^4*d^5*x^5 + 1113840*c^3*d^6*x^6 + 572832*c^2*d^7*x^7 + 175032*c*d^8*x^8 + 24310*d^9*x^9) + b^10*(19448*c^10 + 205920*c^9*d*x + 984555*c^8*d^2*x^2 + 2800512*c^7*d^3*x^3 + 5250960*c^6*d^4*x^4 + 6785856*c^5*d^5*x^5 + 6126120*c^4*d^6*x^6 + 3818880*c^3*d^7*x^7 + 1575288*c^2*d^8*x^8 + 388960*c*d^9*x^9 + 43758*d^10*x^10))/(b^11*(a + b*x)^18)","B",1
1331,1,692,273,0.2824734,"\int \frac{(c+d x)^{10}}{(a+b x)^{20}} \, dx","Integrate[(c + d*x)^10/(a + b*x)^20,x]","-\frac{a^{10} d^{10}+a^9 b d^9 (9 c+19 d x)+9 a^8 b^2 d^8 \left(5 c^2+19 c d x+19 d^2 x^2\right)+3 a^7 b^3 d^7 \left(55 c^3+285 c^2 d x+513 c d^2 x^2+323 d^3 x^3\right)+3 a^6 b^4 d^6 \left(165 c^4+1045 c^3 d x+2565 c^2 d^2 x^2+2907 c d^3 x^3+1292 d^4 x^4\right)+9 a^5 b^5 d^5 \left(143 c^5+1045 c^4 d x+3135 c^3 d^2 x^2+4845 c^2 d^3 x^3+3876 c d^4 x^4+1292 d^5 x^5\right)+3 a^4 b^6 d^4 \left(1001 c^6+8151 c^5 d x+28215 c^4 d^2 x^2+53295 c^3 d^3 x^3+58140 c^2 d^4 x^4+34884 c d^5 x^5+9044 d^6 x^6\right)+3 a^3 b^7 d^3 \left(2145 c^7+19019 c^6 d x+73359 c^5 d^2 x^2+159885 c^4 d^3 x^3+213180 c^3 d^4 x^4+174420 c^2 d^5 x^5+81396 c d^6 x^6+16796 d^7 x^7\right)+9 a^2 b^8 d^2 \left(1430 c^8+13585 c^7 d x+57057 c^6 d^2 x^2+138567 c^5 d^3 x^3+213180 c^4 d^4 x^4+213180 c^3 d^5 x^5+135660 c^2 d^6 x^6+50388 c d^7 x^7+8398 d^8 x^8\right)+a b^9 d \left(24310 c^9+244530 c^8 d x+1100385 c^7 d^2 x^2+2909907 c^6 d^3 x^3+4988412 c^5 d^4 x^4+5755860 c^4 d^5 x^5+4476780 c^3 d^6 x^6+2267460 c^2 d^7 x^7+680238 c d^8 x^8+92378 d^9 x^9\right)+b^{10} \left(43758 c^{10}+461890 c^9 d x+2200770 c^8 d^2 x^2+6235515 c^7 d^3 x^3+11639628 c^6 d^4 x^4+14965236 c^5 d^5 x^5+13430340 c^4 d^6 x^6+8314020 c^3 d^7 x^7+3401190 c^2 d^8 x^8+831402 c d^9 x^9+92378 d^{10} x^{10}\right)}{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,"-1/831402*(a^10*d^10 + a^9*b*d^9*(9*c + 19*d*x) + 9*a^8*b^2*d^8*(5*c^2 + 19*c*d*x + 19*d^2*x^2) + 3*a^7*b^3*d^7*(55*c^3 + 285*c^2*d*x + 513*c*d^2*x^2 + 323*d^3*x^3) + 3*a^6*b^4*d^6*(165*c^4 + 1045*c^3*d*x + 2565*c^2*d^2*x^2 + 2907*c*d^3*x^3 + 1292*d^4*x^4) + 9*a^5*b^5*d^5*(143*c^5 + 1045*c^4*d*x + 3135*c^3*d^2*x^2 + 4845*c^2*d^3*x^3 + 3876*c*d^4*x^4 + 1292*d^5*x^5) + 3*a^4*b^6*d^4*(1001*c^6 + 8151*c^5*d*x + 28215*c^4*d^2*x^2 + 53295*c^3*d^3*x^3 + 58140*c^2*d^4*x^4 + 34884*c*d^5*x^5 + 9044*d^6*x^6) + 3*a^3*b^7*d^3*(2145*c^7 + 19019*c^6*d*x + 73359*c^5*d^2*x^2 + 159885*c^4*d^3*x^3 + 213180*c^3*d^4*x^4 + 174420*c^2*d^5*x^5 + 81396*c*d^6*x^6 + 16796*d^7*x^7) + 9*a^2*b^8*d^2*(1430*c^8 + 13585*c^7*d*x + 57057*c^6*d^2*x^2 + 138567*c^5*d^3*x^3 + 213180*c^4*d^4*x^4 + 213180*c^3*d^5*x^5 + 135660*c^2*d^6*x^6 + 50388*c*d^7*x^7 + 8398*d^8*x^8) + a*b^9*d*(24310*c^9 + 244530*c^8*d*x + 1100385*c^7*d^2*x^2 + 2909907*c^6*d^3*x^3 + 4988412*c^5*d^4*x^4 + 5755860*c^4*d^5*x^5 + 4476780*c^3*d^6*x^6 + 2267460*c^2*d^7*x^7 + 680238*c*d^8*x^8 + 92378*d^9*x^9) + b^10*(43758*c^10 + 461890*c^9*d*x + 2200770*c^8*d^2*x^2 + 6235515*c^7*d^3*x^3 + 11639628*c^6*d^4*x^4 + 14965236*c^5*d^5*x^5 + 13430340*c^4*d^6*x^6 + 8314020*c^3*d^7*x^7 + 3401190*c^2*d^8*x^8 + 831402*c*d^9*x^9 + 92378*d^10*x^10))/(b^11*(a + b*x)^19)","B",1
1332,1,692,279,0.2879095,"\int \frac{(c+d x)^{10}}{(a+b x)^{21}} \, dx","Integrate[(c + d*x)^10/(a + b*x)^21,x]","-\frac{a^{10} d^{10}+10 a^9 b d^9 (c+2 d x)+5 a^8 b^2 d^8 \left(11 c^2+40 c d x+38 d^2 x^2\right)+20 a^7 b^3 d^7 \left(11 c^3+55 c^2 d x+95 c d^2 x^2+57 d^3 x^3\right)+5 a^6 b^4 d^6 \left(143 c^4+880 c^3 d x+2090 c^2 d^2 x^2+2280 c d^3 x^3+969 d^4 x^4\right)+2 a^5 b^5 d^5 \left(1001 c^5+7150 c^4 d x+20900 c^3 d^2 x^2+31350 c^2 d^3 x^3+24225 c d^4 x^4+7752 d^5 x^5\right)+5 a^4 b^6 d^4 \left(1001 c^6+8008 c^5 d x+27170 c^4 d^2 x^2+50160 c^3 d^3 x^3+53295 c^2 d^4 x^4+31008 c d^5 x^5+7752 d^6 x^6\right)+20 a^3 b^7 d^3 \left(572 c^7+5005 c^6 d x+19019 c^5 d^2 x^2+40755 c^4 d^3 x^3+53295 c^3 d^4 x^4+42636 c^2 d^5 x^5+19380 c d^6 x^6+3876 d^7 x^7\right)+5 a^2 b^8 d^2 \left(4862 c^8+45760 c^7 d x+190190 c^6 d^2 x^2+456456 c^5 d^3 x^3+692835 c^4 d^4 x^4+682176 c^3 d^5 x^5+426360 c^2 d^6 x^6+155040 c d^7 x^7+25194 d^8 x^8\right)+10 a b^9 d \left(4862 c^9+48620 c^8 d x+217360 c^7 d^2 x^2+570570 c^6 d^3 x^3+969969 c^5 d^4 x^4+1108536 c^4 d^5 x^5+852720 c^3 d^6 x^6+426360 c^2 d^7 x^7+125970 c d^8 x^8+16796 d^9 x^9\right)+b^{10} \left(92378 c^{10}+972400 c^9 d x+4618900 c^8 d^2 x^2+13041600 c^7 d^3 x^3+24249225 c^6 d^4 x^4+31039008 c^5 d^5 x^5+27713400 c^4 d^6 x^6+17054400 c^3 d^7 x^7+6928350 c^2 d^8 x^8+1679600 c d^9 x^9+184756 d^{10} x^{10}\right)}{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,"-1/1847560*(a^10*d^10 + 10*a^9*b*d^9*(c + 2*d*x) + 5*a^8*b^2*d^8*(11*c^2 + 40*c*d*x + 38*d^2*x^2) + 20*a^7*b^3*d^7*(11*c^3 + 55*c^2*d*x + 95*c*d^2*x^2 + 57*d^3*x^3) + 5*a^6*b^4*d^6*(143*c^4 + 880*c^3*d*x + 2090*c^2*d^2*x^2 + 2280*c*d^3*x^3 + 969*d^4*x^4) + 2*a^5*b^5*d^5*(1001*c^5 + 7150*c^4*d*x + 20900*c^3*d^2*x^2 + 31350*c^2*d^3*x^3 + 24225*c*d^4*x^4 + 7752*d^5*x^5) + 5*a^4*b^6*d^4*(1001*c^6 + 8008*c^5*d*x + 27170*c^4*d^2*x^2 + 50160*c^3*d^3*x^3 + 53295*c^2*d^4*x^4 + 31008*c*d^5*x^5 + 7752*d^6*x^6) + 20*a^3*b^7*d^3*(572*c^7 + 5005*c^6*d*x + 19019*c^5*d^2*x^2 + 40755*c^4*d^3*x^3 + 53295*c^3*d^4*x^4 + 42636*c^2*d^5*x^5 + 19380*c*d^6*x^6 + 3876*d^7*x^7) + 5*a^2*b^8*d^2*(4862*c^8 + 45760*c^7*d*x + 190190*c^6*d^2*x^2 + 456456*c^5*d^3*x^3 + 692835*c^4*d^4*x^4 + 682176*c^3*d^5*x^5 + 426360*c^2*d^6*x^6 + 155040*c*d^7*x^7 + 25194*d^8*x^8) + 10*a*b^9*d*(4862*c^9 + 48620*c^8*d*x + 217360*c^7*d^2*x^2 + 570570*c^6*d^3*x^3 + 969969*c^5*d^4*x^4 + 1108536*c^4*d^5*x^5 + 852720*c^3*d^6*x^6 + 426360*c^2*d^7*x^7 + 125970*c*d^8*x^8 + 16796*d^9*x^9) + b^10*(92378*c^10 + 972400*c^9*d*x + 4618900*c^8*d^2*x^2 + 13041600*c^7*d^3*x^3 + 24249225*c^6*d^4*x^4 + 31039008*c^5*d^5*x^5 + 27713400*c^4*d^6*x^6 + 17054400*c^3*d^7*x^7 + 6928350*c^2*d^8*x^8 + 1679600*c*d^9*x^9 + 184756*d^10*x^10))/(b^11*(a + b*x)^20)","B",1
1333,1,692,279,0.3013854,"\int \frac{(c+d x)^{10}}{(a+b x)^{22}} \, dx","Integrate[(c + d*x)^10/(a + b*x)^22,x]","-\frac{a^{10} d^{10}+a^9 b d^9 (11 c+21 d x)+3 a^8 b^2 d^8 \left(22 c^2+77 c d x+70 d^2 x^2\right)+2 a^7 b^3 d^7 \left(143 c^3+693 c^2 d x+1155 c d^2 x^2+665 d^3 x^3\right)+7 a^6 b^4 d^6 \left(143 c^4+858 c^3 d x+1980 c^2 d^2 x^2+2090 c d^3 x^3+855 d^4 x^4\right)+21 a^5 b^5 d^5 \left(143 c^5+1001 c^4 d x+2860 c^3 d^2 x^2+4180 c^2 d^3 x^3+3135 c d^4 x^4+969 d^5 x^5\right)+7 a^4 b^6 d^4 \left(1144 c^6+9009 c^5 d x+30030 c^4 d^2 x^2+54340 c^3 d^3 x^3+56430 c^2 d^4 x^4+31977 c d^5 x^5+7752 d^6 x^6\right)+2 a^3 b^7 d^3 \left(9724 c^7+84084 c^6 d x+315315 c^5 d^2 x^2+665665 c^4 d^3 x^3+855855 c^3 d^4 x^4+671517 c^2 d^5 x^5+298452 c d^6 x^6+58140 d^7 x^7\right)+3 a^2 b^8 d^2 \left(14586 c^8+136136 c^7 d x+560560 c^6 d^2 x^2+1331330 c^5 d^3 x^3+1996995 c^4 d^4 x^4+1939938 c^3 d^5 x^5+1193808 c^2 d^6 x^6+426360 c d^7 x^7+67830 d^8 x^8\right)+a b^9 d \left(92378 c^9+918918 c^8 d x+4084080 c^7 d^2 x^2+10650640 c^6 d^3 x^3+17972955 c^5 d^4 x^4+20369349 c^4 d^5 x^5+15519504 c^3 d^6 x^6+7674480 c^2 d^7 x^7+2238390 c d^8 x^8+293930 d^9 x^9\right)+b^{10} \left(184756 c^{10}+1939938 c^9 d x+9189180 c^8 d^2 x^2+25865840 c^7 d^3 x^3+47927880 c^6 d^4 x^4+61108047 c^5 d^5 x^5+54318264 c^4 d^6 x^6+33256080 c^3 d^7 x^7+13430340 c^2 d^8 x^8+3233230 c d^9 x^9+352716 d^{10} x^{10}\right)}{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,"-1/3879876*(a^10*d^10 + a^9*b*d^9*(11*c + 21*d*x) + 3*a^8*b^2*d^8*(22*c^2 + 77*c*d*x + 70*d^2*x^2) + 2*a^7*b^3*d^7*(143*c^3 + 693*c^2*d*x + 1155*c*d^2*x^2 + 665*d^3*x^3) + 7*a^6*b^4*d^6*(143*c^4 + 858*c^3*d*x + 1980*c^2*d^2*x^2 + 2090*c*d^3*x^3 + 855*d^4*x^4) + 21*a^5*b^5*d^5*(143*c^5 + 1001*c^4*d*x + 2860*c^3*d^2*x^2 + 4180*c^2*d^3*x^3 + 3135*c*d^4*x^4 + 969*d^5*x^5) + 7*a^4*b^6*d^4*(1144*c^6 + 9009*c^5*d*x + 30030*c^4*d^2*x^2 + 54340*c^3*d^3*x^3 + 56430*c^2*d^4*x^4 + 31977*c*d^5*x^5 + 7752*d^6*x^6) + 2*a^3*b^7*d^3*(9724*c^7 + 84084*c^6*d*x + 315315*c^5*d^2*x^2 + 665665*c^4*d^3*x^3 + 855855*c^3*d^4*x^4 + 671517*c^2*d^5*x^5 + 298452*c*d^6*x^6 + 58140*d^7*x^7) + 3*a^2*b^8*d^2*(14586*c^8 + 136136*c^7*d*x + 560560*c^6*d^2*x^2 + 1331330*c^5*d^3*x^3 + 1996995*c^4*d^4*x^4 + 1939938*c^3*d^5*x^5 + 1193808*c^2*d^6*x^6 + 426360*c*d^7*x^7 + 67830*d^8*x^8) + a*b^9*d*(92378*c^9 + 918918*c^8*d*x + 4084080*c^7*d^2*x^2 + 10650640*c^6*d^3*x^3 + 17972955*c^5*d^4*x^4 + 20369349*c^4*d^5*x^5 + 15519504*c^3*d^6*x^6 + 7674480*c^2*d^7*x^7 + 2238390*c*d^8*x^8 + 293930*d^9*x^9) + b^10*(184756*c^10 + 1939938*c^9*d*x + 9189180*c^8*d^2*x^2 + 25865840*c^7*d^3*x^3 + 47927880*c^6*d^4*x^4 + 61108047*c^5*d^5*x^5 + 54318264*c^4*d^6*x^6 + 33256080*c^3*d^7*x^7 + 13430340*c^2*d^8*x^8 + 3233230*c*d^9*x^9 + 352716*d^10*x^10))/(b^11*(a + b*x)^21)","B",1
1334,1,167,122,0.0717687,"\int \frac{(a+b x)^5}{c+d x} \, dx","Integrate[(a + b*x)^5/(c + d*x),x]","\frac{b d x \left(300 a^4 d^4+300 a^3 b d^3 (d x-2 c)+100 a^2 b^2 d^2 \left(6 c^2-3 c d x+2 d^2 x^2\right)+25 a b^3 d \left(-12 c^3+6 c^2 d x-4 c d^2 x^2+3 d^3 x^3\right)+b^4 \left(60 c^4-30 c^3 d x+20 c^2 d^2 x^2-15 c d^3 x^3+12 d^4 x^4\right)\right)-60 (b c-a d)^5 \log (c+d x)}{60 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*d*x*(300*a^4*d^4 + 300*a^3*b*d^3*(-2*c + d*x) + 100*a^2*b^2*d^2*(6*c^2 - 3*c*d*x + 2*d^2*x^2) + 25*a*b^3*d*(-12*c^3 + 6*c^2*d*x - 4*c*d^2*x^2 + 3*d^3*x^3) + b^4*(60*c^4 - 30*c^3*d*x + 20*c^2*d^2*x^2 - 15*c*d^3*x^3 + 12*d^4*x^4)) - 60*(b*c - a*d)^5*Log[c + d*x])/(60*d^6)","A",1
1335,1,115,98,0.0439253,"\int \frac{(a+b x)^4}{c+d x} \, dx","Integrate[(a + b*x)^4/(c + d*x),x]","\frac{b d x \left(48 a^3 d^3+36 a^2 b d^2 (d x-2 c)+8 a b^2 d \left(6 c^2-3 c d x+2 d^2 x^2\right)+b^3 \left(-12 c^3+6 c^2 d x-4 c d^2 x^2+3 d^3 x^3\right)\right)+12 (b c-a d)^4 \log (c+d x)}{12 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*d*x*(48*a^3*d^3 + 36*a^2*b*d^2*(-2*c + d*x) + 8*a*b^2*d*(6*c^2 - 3*c*d*x + 2*d^2*x^2) + b^3*(-12*c^3 + 6*c^2*d*x - 4*c*d^2*x^2 + 3*d^3*x^3)) + 12*(b*c - a*d)^4*Log[c + d*x])/(12*d^5)","A",1
1336,1,74,74,0.028349,"\int \frac{(a+b x)^3}{c+d x} \, dx","Integrate[(a + b*x)^3/(c + d*x),x]","\frac{b d x \left(18 a^2 d^2+9 a b d (d x-2 c)+b^2 \left(6 c^2-3 c d x+2 d^2 x^2\right)\right)-6 (b c-a d)^3 \log (c+d x)}{6 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*d*x*(18*a^2*d^2 + 9*a*b*d*(-2*c + d*x) + b^2*(6*c^2 - 3*c*d*x + 2*d^2*x^2)) - 6*(b*c - a*d)^3*Log[c + d*x])/(6*d^4)","A",1
1337,1,43,50,0.017334,"\int \frac{(a+b x)^2}{c+d x} \, dx","Integrate[(a + b*x)^2/(c + d*x),x]","\frac{b d x (4 a d-2 b c+b d x)+2 (b c-a d)^2 \log (c+d x)}{2 d^3}","\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*d*x*(-2*b*c + 4*a*d + b*d*x) + 2*(b*c - a*d)^2*Log[c + d*x])/(2*d^3)","A",1
1338,1,25,26,0.0080542,"\int \frac{a+b x}{c+d x} \, dx","Integrate[(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
1339,1,10,10,0.00093,"\int \frac{1}{c+d x} \, dx","Integrate[(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
1340,1,26,36,0.0126573,"\int \frac{1}{(a+b x) (c+d x)} \, dx","Integrate[1/((a + b*x)*(c + d*x)),x]","\frac{\log (a+b x)-\log (c+d x)}{b c-a d}","\frac{\log (a+b x)}{b c-a d}-\frac{\log (c+d x)}{b c-a d}",1,"(Log[a + b*x] - Log[c + d*x])/(b*c - a*d)","A",1
1341,1,53,57,0.0247031,"\int \frac{1}{(a+b x)^2 (c+d x)} \, dx","Integrate[1/((a + b*x)^2*(c + d*x)),x]","\frac{d (a+b x) \log (c+d x)-d (a+b x) \log (a+b x)+a d-b c}{(a+b 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,"(-(b*c) + a*d - d*(a + b*x)*Log[a + b*x] + d*(a + b*x)*Log[c + d*x])/((b*c - a*d)^2*(a + b*x))","A",1
1342,1,67,82,0.0657101,"\int \frac{1}{(a+b x)^3 (c+d x)} \, dx","Integrate[1/((a + b*x)^3*(c + d*x)),x]","\frac{\frac{(b c-a d) (3 a d-b c+2 b d x)}{(a+b x)^2}+2 d^2 \log (a+b x)-2 d^2 \log (c+d x)}{2 (b c-a d)^3}","\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 - a*d)*(-(b*c) + 3*a*d + 2*b*d*x))/(a + b*x)^2 + 2*d^2*Log[a + b*x] - 2*d^2*Log[c + d*x])/(2*(b*c - a*d)^3)","A",1
1343,1,228,130,0.0754708,"\int \frac{(a+b x)^5}{(c+d x)^2} \, dx","Integrate[(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 d^3 \left(-c^2+c d x+d^2 x^2\right)+60 a^2 b^3 d^2 \left(2 c^3-4 c^2 d x-3 c d^2 x^2+d^3 x^3\right)+20 a b^4 d \left(-3 c^4+9 c^3 d x+6 c^2 d^2 x^2-2 c d^3 x^3+d^4 x^4\right)+60 b (c+d x) (b c-a d)^4 \log (c+d x)+b^5 \left(12 c^5-48 c^4 d x-30 c^3 d^2 x^2+10 c^2 d^3 x^3-5 c d^4 x^4+3 d^5 x^5\right)}{12 d^6 (c+d x)}","-\frac{5 b^4 (c+d x)^3 (b c-a d)}{3 d^6}+\frac{5 b^3 (c+d x)^2 (b c-a d)^2}{d^6}-\frac{10 b^2 x (b c-a d)^3}{d^5}+\frac{(b c-a d)^5}{d^6 (c+d x)}+\frac{5 b (b c-a d)^4 \log (c+d x)}{d^6}+\frac{b^5 (c+d x)^4}{4 d^6}",1,"(60*a^4*b*c*d^4 - 12*a^5*d^5 + 120*a^3*b^2*d^3*(-c^2 + c*d*x + d^2*x^2) + 60*a^2*b^3*d^2*(2*c^3 - 4*c^2*d*x - 3*c*d^2*x^2 + d^3*x^3) + 20*a*b^4*d*(-3*c^4 + 9*c^3*d*x + 6*c^2*d^2*x^2 - 2*c*d^3*x^3 + d^4*x^4) + b^5*(12*c^5 - 48*c^4*d*x - 30*c^3*d^2*x^2 + 10*c^2*d^3*x^3 - 5*c*d^4*x^4 + 3*d^5*x^5) + 60*b*(b*c - a*d)^4*(c + d*x)*Log[c + d*x])/(12*d^6*(c + d*x))","A",1
1344,1,165,104,0.0574366,"\int \frac{(a+b x)^4}{(c+d x)^2} \, dx","Integrate[(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 d^2 \left(-c^2+c d x+d^2 x^2\right)+6 a b^3 d \left(2 c^3-4 c^2 d x-3 c d^2 x^2+d^3 x^3\right)-12 b (c+d x) (b c-a d)^3 \log (c+d x)+b^4 \left(-3 c^4+9 c^3 d x+6 c^2 d^2 x^2-2 c d^3 x^3+d^4 x^4\right)}{3 d^5 (c+d x)}","-\frac{2 b^3 (c+d x)^2 (b c-a d)}{d^5}+\frac{6 b^2 x (b c-a d)^2}{d^4}-\frac{(b c-a d)^4}{d^5 (c+d x)}-\frac{4 b (b c-a d)^3 \log (c+d x)}{d^5}+\frac{b^4 (c+d x)^3}{3 d^5}",1,"(12*a^3*b*c*d^3 - 3*a^4*d^4 + 18*a^2*b^2*d^2*(-c^2 + c*d*x + d^2*x^2) + 6*a*b^3*d*(2*c^3 - 4*c^2*d*x - 3*c*d^2*x^2 + d^3*x^3) + b^4*(-3*c^4 + 9*c^3*d*x + 6*c^2*d^2*x^2 - 2*c*d^3*x^3 + d^4*x^4) - 12*b*(b*c - a*d)^3*(c + d*x)*Log[c + d*x])/(3*d^5*(c + d*x))","A",1
1345,1,114,75,0.0355743,"\int \frac{(a+b x)^3}{(c+d x)^2} \, dx","Integrate[(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{-a^3 d^3+3 a^2 b c d^2-3 a b^2 c^2 d+b^3 c^3}{d^4 (c+d x)}-\frac{b^2 x (2 b c-3 a d)}{d^3}+\frac{b^3 x^2}{2 d^2}","-\frac{b^2 x (2 b c-3 a d)}{d^3}+\frac{(b c-a d)^3}{d^4 (c+d x)}+\frac{3 b (b c-a d)^2 \log (c+d x)}{d^4}+\frac{b^3 x^2}{2 d^2}",1,"-((b^2*(2*b*c - 3*a*d)*x)/d^3) + (b^3*x^2)/(2*d^2) + (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)/(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
1346,1,47,51,0.0371549,"\int \frac{(a+b x)^2}{(c+d x)^2} \, dx","Integrate[(a + b*x)^2/(c + d*x)^2,x]","\frac{-\frac{(b c-a d)^2}{c+d x}+2 b (a d-b c) \log (c+d x)+b^2 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*d*x - (b*c - a*d)^2/(c + d*x) + 2*b*(-(b*c) + a*d)*Log[c + d*x])/d^3","A",1
1347,1,31,31,0.010602,"\int \frac{a+b x}{(c+d x)^2} \, dx","Integrate[(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
1348,1,12,12,0.0025601,"\int \frac{1}{(c+d x)^2} \, dx","Integrate[(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
1349,1,53,56,0.028894,"\int \frac{1}{(a+b x) (c+d x)^2} \, dx","Integrate[1/((a + b*x)*(c + d*x)^2),x]","\frac{b (c+d x) \log (a+b x)-a d-b (c+d x) \log (c+d x)+b c}{(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,"(b*c - a*d + b*(c + d*x)*Log[a + b*x] - b*(c + d*x)*Log[c + d*x])/((b*c - a*d)^2*(c + d*x))","A",1
1350,1,66,81,0.0706151,"\int \frac{1}{(a+b x)^2 (c+d x)^2} \, dx","Integrate[1/((a + b*x)^2*(c + d*x)^2),x]","\frac{\frac{b (a d-b c)}{a+b x}+\frac{d (a d-b c)}{c+d x}-2 b d \log (a+b x)+2 b d \log (c+d x)}{(b c-a d)^3}","-\frac{b}{(a+b x) (b c-a d)^2}-\frac{d}{(c+d x) (b c-a d)^2}-\frac{2 b d \log (a+b x)}{(b c-a d)^3}+\frac{2 b d \log (c+d x)}{(b c-a d)^3}",1,"((b*(-(b*c) + a*d))/(a + b*x) + (d*(-(b*c) + a*d))/(c + d*x) - 2*b*d*Log[a + b*x] + 2*b*d*Log[c + d*x])/(b*c - a*d)^3","A",1
1351,1,98,109,0.074494,"\int \frac{1}{(a+b x)^3 (c+d x)^2} \, dx","Integrate[1/((a + b*x)^3*(c + d*x)^2),x]","\frac{\frac{2 d^2 (b c-a d)}{c+d x}+\frac{4 b d (b c-a d)}{a+b x}-\frac{b (b c-a d)^2}{(a+b x)^2}+6 b d^2 \log (a+b x)-6 b d^2 \log (c+d x)}{2 (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*(b*c - a*d)^2)/(a + b*x)^2) + (4*b*d*(b*c - a*d))/(a + b*x) + (2*d^2*(b*c - a*d))/(c + d*x) + 6*b*d^2*Log[a + b*x] - 6*b*d^2*Log[c + d*x])/(2*(b*c - a*d)^4)","A",1
1352,1,303,158,0.1134277,"\int \frac{(a+b x)^6}{(c+d x)^3} \, dx","Integrate[(a + b*x)^6/(c + d*x)^3,x]","\frac{-2 a^6 d^6-12 a^5 b d^5 (c+2 d x)+30 a^4 b^2 c d^4 (3 c+4 d x)+40 a^3 b^3 d^3 \left(-5 c^3-4 c^2 d x+4 c d^2 x^2+2 d^3 x^3\right)+30 a^2 b^4 d^2 \left(7 c^4+2 c^3 d x-11 c^2 d^2 x^2-4 c d^3 x^3+d^4 x^4\right)+4 a b^5 d \left(-27 c^5+6 c^4 d x+63 c^3 d^2 x^2+20 c^2 d^3 x^3-5 c d^4 x^4+2 d^5 x^5\right)+60 b^2 (c+d x)^2 (b c-a d)^4 \log (c+d x)+b^6 \left(22 c^6-16 c^5 d x-68 c^4 d^2 x^2-20 c^3 d^3 x^3+5 c^2 d^4 x^4-2 c d^5 x^5+d^6 x^6\right)}{4 d^7 (c+d x)^2}","-\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,"(-2*a^6*d^6 - 12*a^5*b*d^5*(c + 2*d*x) + 30*a^4*b^2*c*d^4*(3*c + 4*d*x) + 40*a^3*b^3*d^3*(-5*c^3 - 4*c^2*d*x + 4*c*d^2*x^2 + 2*d^3*x^3) + 30*a^2*b^4*d^2*(7*c^4 + 2*c^3*d*x - 11*c^2*d^2*x^2 - 4*c*d^3*x^3 + d^4*x^4) + 4*a*b^5*d*(-27*c^5 + 6*c^4*d*x + 63*c^3*d^2*x^2 + 20*c^2*d^3*x^3 - 5*c*d^4*x^4 + 2*d^5*x^5) + b^6*(22*c^6 - 16*c^5*d*x - 68*c^4*d^2*x^2 - 20*c^3*d^3*x^3 + 5*c^2*d^4*x^4 - 2*c*d^5*x^5 + d^6*x^6) + 60*b^2*(b*c - a*d)^4*(c + d*x)^2*Log[c + d*x])/(4*d^7*(c + d*x)^2)","A",1
1353,1,230,133,0.0730775,"\int \frac{(a+b x)^5}{(c+d x)^3} \, dx","Integrate[(a + b*x)^5/(c + d*x)^3,x]","\frac{-3 a^5 d^5-15 a^4 b d^4 (c+2 d x)+30 a^3 b^2 c d^3 (3 c+4 d x)+30 a^2 b^3 d^2 \left(-5 c^3-4 c^2 d x+4 c d^2 x^2+2 d^3 x^3\right)+15 a b^4 d \left(7 c^4+2 c^3 d x-11 c^2 d^2 x^2-4 c d^3 x^3+d^4 x^4\right)-60 b^2 (c+d x)^2 (b c-a d)^3 \log (c+d x)+b^5 \left(-27 c^5+6 c^4 d x+63 c^3 d^2 x^2+20 c^2 d^3 x^3-5 c d^4 x^4+2 d^5 x^5\right)}{6 d^6 (c+d x)^2}","-\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,"(-3*a^5*d^5 - 15*a^4*b*d^4*(c + 2*d*x) + 30*a^3*b^2*c*d^3*(3*c + 4*d*x) + 30*a^2*b^3*d^2*(-5*c^3 - 4*c^2*d*x + 4*c*d^2*x^2 + 2*d^3*x^3) + 15*a*b^4*d*(7*c^4 + 2*c^3*d*x - 11*c^2*d^2*x^2 - 4*c*d^3*x^3 + d^4*x^4) + b^5*(-27*c^5 + 6*c^4*d*x + 63*c^3*d^2*x^2 + 20*c^2*d^3*x^3 - 5*c*d^4*x^4 + 2*d^5*x^5) - 60*b^2*(b*c - a*d)^3*(c + d*x)^2*Log[c + d*x])/(6*d^6*(c + d*x)^2)","A",1
1354,1,167,103,0.0561148,"\int \frac{(a+b x)^4}{(c+d x)^3} \, dx","Integrate[(a + b*x)^4/(c + d*x)^3,x]","\frac{-a^4 d^4-4 a^3 b d^3 (c+2 d x)+6 a^2 b^2 c d^2 (3 c+4 d x)+4 a b^3 d \left(-5 c^3-4 c^2 d x+4 c d^2 x^2+2 d^3 x^3\right)+12 b^2 (c+d x)^2 (b c-a d)^2 \log (c+d x)+b^4 \left(7 c^4+2 c^3 d x-11 c^2 d^2 x^2-4 c d^3 x^3+d^4 x^4\right)}{2 d^5 (c+d x)^2}","-\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,"(-(a^4*d^4) - 4*a^3*b*d^3*(c + 2*d*x) + 6*a^2*b^2*c*d^2*(3*c + 4*d*x) + 4*a*b^3*d*(-5*c^3 - 4*c^2*d*x + 4*c*d^2*x^2 + 2*d^3*x^3) + b^4*(7*c^4 + 2*c^3*d*x - 11*c^2*d^2*x^2 - 4*c*d^3*x^3 + d^4*x^4) + 12*b^2*(b*c - a*d)^2*(c + d*x)^2*Log[c + d*x])/(2*d^5*(c + d*x)^2)","A",1
1355,1,114,78,0.0390543,"\int \frac{(a+b x)^3}{(c+d x)^3} \, dx","Integrate[(a + b*x)^3/(c + d*x)^3,x]","\frac{-a^3 d^3-3 a^2 b d^2 (c+2 d x)+3 a b^2 c d (3 c+4 d x)-6 b^2 (c+d x)^2 (b c-a d) \log (c+d x)+b^3 \left(-5 c^3-4 c^2 d x+4 c d^2 x^2+2 d^3 x^3\right)}{2 d^4 (c+d x)^2}","-\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,"(-(a^3*d^3) - 3*a^2*b*d^2*(c + 2*d*x) + 3*a*b^2*c*d*(3*c + 4*d*x) + b^3*(-5*c^3 - 4*c^2*d*x + 4*c*d^2*x^2 + 2*d^3*x^3) - 6*b^2*(b*c - a*d)*(c + d*x)^2*Log[c + d*x])/(2*d^4*(c + d*x)^2)","A",1
1356,1,48,59,0.024681,"\int \frac{(a+b x)^2}{(c+d x)^3} \, dx","Integrate[(a + b*x)^2/(c + d*x)^3,x]","\frac{\frac{(b c-a d) (a d+3 b c+4 b d x)}{(c+d x)^2}+2 b^2 \log (c+d x)}{2 d^3}","\frac{2 b (b c-a d)}{d^3 (c+d x)}-\frac{(b c-a d)^2}{2 d^3 (c+d x)^2}+\frac{b^2 \log (c+d x)}{d^3}",1,"(((b*c - a*d)*(3*b*c + a*d + 4*b*d*x))/(c + d*x)^2 + 2*b^2*Log[c + d*x])/(2*d^3)","A",1
1357,1,26,28,0.0091299,"\int \frac{a+b x}{(c+d x)^3} \, dx","Integrate[(a + b*x)/(c + d*x)^3,x]","-\frac{a d+b (c+2 d x)}{2 d^2 (c+d x)^2}","\frac{(a+b x)^2}{2 (c+d x)^2 (b c-a d)}",1,"-1/2*(a*d + b*(c + 2*d*x))/(d^2*(c + d*x)^2)","A",1
1358,1,14,14,0.002594,"\int \frac{1}{(c+d x)^3} \, dx","Integrate[(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
1359,1,67,82,0.0531872,"\int \frac{1}{(a+b x) (c+d x)^3} \, dx","Integrate[1/((a + b*x)*(c + d*x)^3),x]","\frac{2 b^2 \log (a+b x)+\frac{(b c-a d) (-a d+3 b c+2 b d x)}{(c+d x)^2}-2 b^2 \log (c+d x)}{2 (b c-a d)^3}","\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,"(((b*c - a*d)*(3*b*c - a*d + 2*b*d*x))/(c + d*x)^2 + 2*b^2*Log[a + b*x] - 2*b^2*Log[c + d*x])/(2*(b*c - a*d)^3)","A",1
1360,1,97,110,0.1049478,"\int \frac{1}{(a+b x)^2 (c+d x)^3} \, dx","Integrate[1/((a + b*x)^2*(c + d*x)^3),x]","-\frac{\frac{2 b^2 (b c-a d)}{a+b x}+6 b^2 d \log (a+b x)+\frac{4 b d (b c-a d)}{c+d x}+\frac{d (b c-a d)^2}{(c+d x)^2}-6 b^2 d \log (c+d x)}{2 (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,"-1/2*((2*b^2*(b*c - a*d))/(a + b*x) + (d*(b*c - a*d)^2)/(c + d*x)^2 + (4*b*d*(b*c - a*d))/(c + d*x) + 6*b^2*d*Log[a + b*x] - 6*b^2*d*Log[c + d*x])/(b*c - a*d)^4","A",1
1361,1,128,143,0.1159522,"\int \frac{1}{(a+b x)^3 (c+d x)^3} \, dx","Integrate[1/((a + b*x)^3*(c + d*x)^3),x]","\frac{\frac{6 b^2 d (b c-a d)}{a+b x}-\frac{b^2 (b c-a d)^2}{(a+b x)^2}+12 b^2 d^2 \log (a+b x)+\frac{6 b d^2 (b c-a d)}{c+d x}+\frac{d^2 (b c-a d)^2}{(c+d x)^2}-12 b^2 d^2 \log (c+d x)}{2 (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^2*(b*c - a*d)^2)/(a + b*x)^2) + (6*b^2*d*(b*c - a*d))/(a + b*x) + (d^2*(b*c - a*d)^2)/(c + d*x)^2 + (6*b*d^2*(b*c - a*d))/(c + d*x) + 12*b^2*d^2*Log[a + b*x] - 12*b^2*d^2*Log[c + d*x])/(2*(b*c - a*d)^5)","A",1
1362,1,584,232,0.2711905,"\int \frac{(a+b x)^9}{(c+d x)^8} \, dx","Integrate[(a + b*x)^9/(c + d*x)^8,x]","-\frac{10 a^9 d^9+15 a^8 b d^8 (c+7 d x)+24 a^7 b^2 d^7 \left(c^2+7 c d x+21 d^2 x^2\right)+42 a^6 b^3 d^6 \left(c^3+7 c^2 d x+21 c d^2 x^2+35 d^3 x^3\right)+84 a^5 b^4 d^5 \left(c^4+7 c^3 d x+21 c^2 d^2 x^2+35 c d^3 x^3+35 d^4 x^4\right)+210 a^4 b^5 d^4 \left(c^5+7 c^4 d x+21 c^3 d^2 x^2+35 c^2 d^3 x^3+35 c d^4 x^4+21 d^5 x^5\right)+840 a^3 b^6 d^3 \left(c^6+7 c^5 d x+21 c^4 d^2 x^2+35 c^3 d^3 x^3+35 c^2 d^4 x^4+21 c d^5 x^5+7 d^6 x^6\right)-6 a^2 b^7 c d^2 \left(1089 c^6+7203 c^5 d x+20139 c^4 d^2 x^2+30625 c^3 d^3 x^3+26950 c^2 d^4 x^4+13230 c d^5 x^5+2940 d^6 x^6\right)+6 a b^8 d \left(1443 c^8+9261 c^7 d x+24843 c^6 d^2 x^2+35525 c^5 d^3 x^3+28175 c^4 d^4 x^4+11025 c^3 d^5 x^5+735 c^2 d^6 x^6-735 c d^7 x^7-105 d^8 x^8\right)-2520 b^7 (c+d x)^7 (b c-a d)^2 \log (c+d x)-\left(b^9 \left(3349 c^9+20923 c^8 d x+53949 c^7 d^2 x^2+72275 c^6 d^3 x^3+50225 c^5 d^4 x^4+12495 c^4 d^5 x^5-4655 c^3 d^6 x^6-3185 c^2 d^7 x^7-315 c d^8 x^8+35 d^9 x^9\right)\right)}{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,"-1/70*(10*a^9*d^9 + 15*a^8*b*d^8*(c + 7*d*x) + 24*a^7*b^2*d^7*(c^2 + 7*c*d*x + 21*d^2*x^2) + 42*a^6*b^3*d^6*(c^3 + 7*c^2*d*x + 21*c*d^2*x^2 + 35*d^3*x^3) + 84*a^5*b^4*d^5*(c^4 + 7*c^3*d*x + 21*c^2*d^2*x^2 + 35*c*d^3*x^3 + 35*d^4*x^4) + 210*a^4*b^5*d^4*(c^5 + 7*c^4*d*x + 21*c^3*d^2*x^2 + 35*c^2*d^3*x^3 + 35*c*d^4*x^4 + 21*d^5*x^5) + 840*a^3*b^6*d^3*(c^6 + 7*c^5*d*x + 21*c^4*d^2*x^2 + 35*c^3*d^3*x^3 + 35*c^2*d^4*x^4 + 21*c*d^5*x^5 + 7*d^6*x^6) - 6*a^2*b^7*c*d^2*(1089*c^6 + 7203*c^5*d*x + 20139*c^4*d^2*x^2 + 30625*c^3*d^3*x^3 + 26950*c^2*d^4*x^4 + 13230*c*d^5*x^5 + 2940*d^6*x^6) + 6*a*b^8*d*(1443*c^8 + 9261*c^7*d*x + 24843*c^6*d^2*x^2 + 35525*c^5*d^3*x^3 + 28175*c^4*d^4*x^4 + 11025*c^3*d^5*x^5 + 735*c^2*d^6*x^6 - 735*c*d^7*x^7 - 105*d^8*x^8) - b^9*(3349*c^9 + 20923*c^8*d*x + 53949*c^7*d^2*x^2 + 72275*c^6*d^3*x^3 + 50225*c^5*d^4*x^4 + 12495*c^4*d^5*x^5 - 4655*c^3*d^6*x^6 - 3185*c^2*d^7*x^7 - 315*c*d^8*x^8 + 35*d^9*x^9) - 2520*b^7*(b*c - a*d)^2*(c + d*x)^7*Log[c + d*x])/(d^10*(c + d*x)^7)","B",1
1363,1,474,209,0.2038596,"\int \frac{(a+b x)^8}{(c+d x)^8} \, dx","Integrate[(a + b*x)^8/(c + d*x)^8,x]","-\frac{15 a^8 d^8+20 a^7 b d^7 (c+7 d x)+28 a^6 b^2 d^6 \left(c^2+7 c d x+21 d^2 x^2\right)+42 a^5 b^3 d^5 \left(c^3+7 c^2 d x+21 c d^2 x^2+35 d^3 x^3\right)+70 a^4 b^4 d^4 \left(c^4+7 c^3 d x+21 c^2 d^2 x^2+35 c d^3 x^3+35 d^4 x^4\right)+140 a^3 b^5 d^3 \left(c^5+7 c^4 d x+21 c^3 d^2 x^2+35 c^2 d^3 x^3+35 c d^4 x^4+21 d^5 x^5\right)+420 a^2 b^6 d^2 \left(c^6+7 c^5 d x+21 c^4 d^2 x^2+35 c^3 d^3 x^3+35 c^2 d^4 x^4+21 c d^5 x^5+7 d^6 x^6\right)-2 a b^7 c d \left(1089 c^6+7203 c^5 d x+20139 c^4 d^2 x^2+30625 c^3 d^3 x^3+26950 c^2 d^4 x^4+13230 c d^5 x^5+2940 d^6 x^6\right)+840 b^7 (c+d x)^7 (b c-a d) \log (c+d x)+b^8 \left(1443 c^8+9261 c^7 d x+24843 c^6 d^2 x^2+35525 c^5 d^3 x^3+28175 c^4 d^4 x^4+11025 c^3 d^5 x^5+735 c^2 d^6 x^6-735 c d^7 x^7-105 d^8 x^8\right)}{105 d^9 (c+d x)^7}","-\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,"-1/105*(15*a^8*d^8 + 20*a^7*b*d^7*(c + 7*d*x) + 28*a^6*b^2*d^6*(c^2 + 7*c*d*x + 21*d^2*x^2) + 42*a^5*b^3*d^5*(c^3 + 7*c^2*d*x + 21*c*d^2*x^2 + 35*d^3*x^3) + 70*a^4*b^4*d^4*(c^4 + 7*c^3*d*x + 21*c^2*d^2*x^2 + 35*c*d^3*x^3 + 35*d^4*x^4) + 140*a^3*b^5*d^3*(c^5 + 7*c^4*d*x + 21*c^3*d^2*x^2 + 35*c^2*d^3*x^3 + 35*c*d^4*x^4 + 21*d^5*x^5) + 420*a^2*b^6*d^2*(c^6 + 7*c^5*d*x + 21*c^4*d^2*x^2 + 35*c^3*d^3*x^3 + 35*c^2*d^4*x^4 + 21*c*d^5*x^5 + 7*d^6*x^6) - 2*a*b^7*c*d*(1089*c^6 + 7203*c^5*d*x + 20139*c^4*d^2*x^2 + 30625*c^3*d^3*x^3 + 26950*c^2*d^4*x^4 + 13230*c*d^5*x^5 + 2940*d^6*x^6) + b^8*(1443*c^8 + 9261*c^7*d*x + 24843*c^6*d^2*x^2 + 35525*c^5*d^3*x^3 + 28175*c^4*d^4*x^4 + 11025*c^3*d^5*x^5 + 735*c^2*d^6*x^6 - 735*c*d^7*x^7 - 105*d^8*x^8) + 840*b^7*(b*c - a*d)*(c + d*x)^7*Log[c + d*x])/(d^9*(c + d*x)^7)","B",1
1364,1,308,194,0.1616482,"\int \frac{(a+b x)^7}{(c+d x)^8} \, dx","Integrate[(a + b*x)^7/(c + d*x)^8,x]","\frac{(b c-a d) \left(60 a^6 d^6+10 a^5 b d^5 (13 c+49 d x)+2 a^4 b^2 d^4 \left(107 c^2+539 c d x+882 d^2 x^2\right)+a^3 b^3 d^3 \left(319 c^3+1813 c^2 d x+3969 c d^2 x^2+3675 d^3 x^3\right)+a^2 b^4 d^2 \left(459 c^4+2793 c^3 d x+6909 c^2 d^2 x^2+8575 c d^3 x^3+4900 d^4 x^4\right)+a b^5 d \left(669 c^5+4263 c^4 d x+11319 c^3 d^2 x^2+15925 c^2 d^3 x^3+12250 c d^4 x^4+4410 d^5 x^5\right)+b^6 \left(1089 c^6+7203 c^5 d x+20139 c^4 d^2 x^2+30625 c^3 d^3 x^3+26950 c^2 d^4 x^4+13230 c d^5 x^5+2940 d^6 x^6\right)\right)}{420 d^8 (c+d x)^7}+\frac{b^7 \log (c+d x)}{d^8}","\frac{7 b^6 (b c-a d)}{d^8 (c+d x)}-\frac{21 b^5 (b c-a d)^2}{2 d^8 (c+d x)^2}+\frac{35 b^4 (b c-a d)^3}{3 d^8 (c+d x)^3}-\frac{35 b^3 (b c-a d)^4}{4 d^8 (c+d x)^4}+\frac{21 b^2 (b c-a d)^5}{5 d^8 (c+d x)^5}-\frac{7 b (b c-a d)^6}{6 d^8 (c+d x)^6}+\frac{(b c-a d)^7}{7 d^8 (c+d x)^7}+\frac{b^7 \log (c+d x)}{d^8}",1,"((b*c - a*d)*(60*a^6*d^6 + 10*a^5*b*d^5*(13*c + 49*d*x) + 2*a^4*b^2*d^4*(107*c^2 + 539*c*d*x + 882*d^2*x^2) + a^3*b^3*d^3*(319*c^3 + 1813*c^2*d*x + 3969*c*d^2*x^2 + 3675*d^3*x^3) + a^2*b^4*d^2*(459*c^4 + 2793*c^3*d*x + 6909*c^2*d^2*x^2 + 8575*c*d^3*x^3 + 4900*d^4*x^4) + a*b^5*d*(669*c^5 + 4263*c^4*d*x + 11319*c^3*d^2*x^2 + 15925*c^2*d^3*x^3 + 12250*c*d^4*x^4 + 4410*d^5*x^5) + b^6*(1089*c^6 + 7203*c^5*d*x + 20139*c^4*d^2*x^2 + 30625*c^3*d^3*x^3 + 26950*c^2*d^4*x^4 + 13230*c*d^5*x^5 + 2940*d^6*x^6)))/(420*d^8*(c + d*x)^7) + (b^7*Log[c + d*x])/d^8","A",1
1365,1,271,28,0.0895949,"\int \frac{(a+b x)^6}{(c+d x)^8} \, dx","Integrate[(a + b*x)^6/(c + d*x)^8,x]","-\frac{a^6 d^6+a^5 b d^5 (c+7 d x)+a^4 b^2 d^4 \left(c^2+7 c d x+21 d^2 x^2\right)+a^3 b^3 d^3 \left(c^3+7 c^2 d x+21 c d^2 x^2+35 d^3 x^3\right)+a^2 b^4 d^2 \left(c^4+7 c^3 d x+21 c^2 d^2 x^2+35 c d^3 x^3+35 d^4 x^4\right)+a b^5 d \left(c^5+7 c^4 d x+21 c^3 d^2 x^2+35 c^2 d^3 x^3+35 c d^4 x^4+21 d^5 x^5\right)+b^6 \left(c^6+7 c^5 d x+21 c^4 d^2 x^2+35 c^3 d^3 x^3+35 c^2 d^4 x^4+21 c d^5 x^5+7 d^6 x^6\right)}{7 d^7 (c+d x)^7}","\frac{(a+b x)^7}{7 (c+d x)^7 (b c-a d)}",1,"-1/7*(a^6*d^6 + a^5*b*d^5*(c + 7*d*x) + a^4*b^2*d^4*(c^2 + 7*c*d*x + 21*d^2*x^2) + a^3*b^3*d^3*(c^3 + 7*c^2*d*x + 21*c*d^2*x^2 + 35*d^3*x^3) + a^2*b^4*d^2*(c^4 + 7*c^3*d*x + 21*c^2*d^2*x^2 + 35*c*d^3*x^3 + 35*d^4*x^4) + a*b^5*d*(c^5 + 7*c^4*d*x + 21*c^3*d^2*x^2 + 35*c^2*d^3*x^3 + 35*c*d^4*x^4 + 21*d^5*x^5) + b^6*(c^6 + 7*c^5*d*x + 21*c^4*d^2*x^2 + 35*c^3*d^3*x^3 + 35*c^2*d^4*x^4 + 21*c*d^5*x^5 + 7*d^6*x^6))/(d^7*(c + d*x)^7)","B",1
1366,1,205,58,0.0598206,"\int \frac{(a+b x)^5}{(c+d x)^8} \, dx","Integrate[(a + b*x)^5/(c + d*x)^8,x]","-\frac{6 a^5 d^5+5 a^4 b d^4 (c+7 d x)+4 a^3 b^2 d^3 \left(c^2+7 c d x+21 d^2 x^2\right)+3 a^2 b^3 d^2 \left(c^3+7 c^2 d x+21 c d^2 x^2+35 d^3 x^3\right)+2 a b^4 d \left(c^4+7 c^3 d x+21 c^2 d^2 x^2+35 c d^3 x^3+35 d^4 x^4\right)+b^5 \left(c^5+7 c^4 d x+21 c^3 d^2 x^2+35 c^2 d^3 x^3+35 c d^4 x^4+21 d^5 x^5\right)}{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,"-1/42*(6*a^5*d^5 + 5*a^4*b*d^4*(c + 7*d*x) + 4*a^3*b^2*d^3*(c^2 + 7*c*d*x + 21*d^2*x^2) + 3*a^2*b^3*d^2*(c^3 + 7*c^2*d*x + 21*c*d^2*x^2 + 35*d^3*x^3) + 2*a*b^4*d*(c^4 + 7*c^3*d*x + 21*c^2*d^2*x^2 + 35*c*d^3*x^3 + 35*d^4*x^4) + b^5*(c^5 + 7*c^4*d*x + 21*c^3*d^2*x^2 + 35*c^2*d^3*x^3 + 35*c*d^4*x^4 + 21*d^5*x^5))/(d^6*(c + d*x)^7)","B",1
1367,1,144,89,0.0479362,"\int \frac{(a+b x)^4}{(c+d x)^8} \, dx","Integrate[(a + b*x)^4/(c + d*x)^8,x]","-\frac{15 a^4 d^4+10 a^3 b d^3 (c+7 d x)+6 a^2 b^2 d^2 \left(c^2+7 c d x+21 d^2 x^2\right)+3 a b^3 d \left(c^3+7 c^2 d x+21 c d^2 x^2+35 d^3 x^3\right)+b^4 \left(c^4+7 c^3 d x+21 c^2 d^2 x^2+35 c d^3 x^3+35 d^4 x^4\right)}{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,"-1/105*(15*a^4*d^4 + 10*a^3*b*d^3*(c + 7*d*x) + 6*a^2*b^2*d^2*(c^2 + 7*c*d*x + 21*d^2*x^2) + 3*a*b^3*d*(c^3 + 7*c^2*d*x + 21*c*d^2*x^2 + 35*d^3*x^3) + b^4*(c^4 + 7*c^3*d*x + 21*c^2*d^2*x^2 + 35*c*d^3*x^3 + 35*d^4*x^4))/(d^5*(c + d*x)^7)","A",1
1368,1,94,92,0.0293416,"\int \frac{(a+b x)^3}{(c+d x)^8} \, dx","Integrate[(a + b*x)^3/(c + d*x)^8,x]","-\frac{20 a^3 d^3+10 a^2 b d^2 (c+7 d x)+4 a b^2 d \left(c^2+7 c d x+21 d^2 x^2\right)+b^3 \left(c^3+7 c^2 d x+21 c d^2 x^2+35 d^3 x^3\right)}{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,"-1/140*(20*a^3*d^3 + 10*a^2*b*d^2*(c + 7*d*x) + 4*a*b^2*d*(c^2 + 7*c*d*x + 21*d^2*x^2) + b^3*(c^3 + 7*c^2*d*x + 21*c*d^2*x^2 + 35*d^3*x^3))/(d^4*(c + d*x)^7)","A",1
1369,1,55,65,0.0243672,"\int \frac{(a+b x)^2}{(c+d x)^8} \, dx","Integrate[(a + b*x)^2/(c + d*x)^8,x]","-\frac{15 a^2 d^2+5 a b d (c+7 d x)+b^2 \left(c^2+7 c d x+21 d^2 x^2\right)}{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,"-1/105*(15*a^2*d^2 + 5*a*b*d*(c + 7*d*x) + b^2*(c^2 + 7*c*d*x + 21*d^2*x^2))/(d^3*(c + d*x)^7)","A",1
1370,1,27,38,0.0095152,"\int \frac{a+b x}{(c+d x)^8} \, dx","Integrate[(a + b*x)/(c + d*x)^8,x]","-\frac{6 a d+b (c+7 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,"-1/42*(6*a*d + b*(c + 7*d*x))/(d^2*(c + d*x)^7)","A",1
1371,1,14,14,0.0029907,"\int \frac{1}{(c+d x)^8} \, dx","Integrate[(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
1372,1,196,202,0.0973384,"\int \frac{1}{(a+b x) (c+d x)^8} \, dx","Integrate[1/((a + b*x)*(c + d*x)^8),x]","\frac{420 b^7 (c+d x)^7 \log (a+b x)+420 b^6 (c+d x)^6 (b c-a d)+210 b^5 (c+d x)^5 (b c-a d)^2+140 b^4 (c+d x)^4 (b c-a d)^3+105 b^3 (c+d x)^3 (b c-a d)^4+84 b^2 (c+d x)^2 (b c-a d)^5+70 b (c+d x) (b c-a d)^6+60 (b c-a d)^7-420 b^7 (c+d x)^7 \log (c+d x)}{420 (c+d x)^7 (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,"(60*(b*c - a*d)^7 + 70*b*(b*c - a*d)^6*(c + d*x) + 84*b^2*(b*c - a*d)^5*(c + d*x)^2 + 105*b^3*(b*c - a*d)^4*(c + d*x)^3 + 140*b^4*(b*c - a*d)^3*(c + d*x)^4 + 210*b^5*(b*c - a*d)^2*(c + d*x)^5 + 420*b^6*(b*c - a*d)*(c + d*x)^6 + 420*b^7*(c + d*x)^7*Log[a + b*x] - 420*b^7*(c + d*x)^7*Log[c + d*x])/(420*(b*c - a*d)^8*(c + d*x)^7)","A",1
1373,1,213,231,0.2431998,"\int \frac{1}{(a+b x)^2 (c+d x)^8} \, dx","Integrate[1/((a + b*x)^2*(c + d*x)^8),x]","-\frac{\frac{105 b^7 (b c-a d)}{a+b x}+840 b^7 d \log (a+b x)+\frac{735 b^6 d (b c-a d)}{c+d x}+\frac{315 b^5 d (b c-a d)^2}{(c+d x)^2}+\frac{175 b^4 d (b c-a d)^3}{(c+d x)^3}+\frac{105 b^3 d (b c-a d)^4}{(c+d x)^4}+\frac{63 b^2 d (b c-a d)^5}{(c+d x)^5}+\frac{35 b d (b c-a d)^6}{(c+d x)^6}-\frac{15 d (a d-b c)^7}{(c+d x)^7}-840 b^7 d \log (c+d x)}{105 (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,"-1/105*((105*b^7*(b*c - a*d))/(a + b*x) - (15*d*(-(b*c) + a*d)^7)/(c + d*x)^7 + (35*b*d*(b*c - a*d)^6)/(c + d*x)^6 + (63*b^2*d*(b*c - a*d)^5)/(c + d*x)^5 + (105*b^3*d*(b*c - a*d)^4)/(c + d*x)^4 + (175*b^4*d*(b*c - a*d)^3)/(c + d*x)^3 + (315*b^5*d*(b*c - a*d)^2)/(c + d*x)^2 + (735*b^6*d*(b*c - a*d))/(c + d*x) + 840*b^7*d*Log[a + b*x] - 840*b^7*d*Log[c + d*x])/(b*c - a*d)^9","A",1
1374,1,254,276,0.2049729,"\int \frac{1}{(a+b x)^3 (c+d x)^8} \, dx","Integrate[1/((a + b*x)^3*(c + d*x)^8),x]","\frac{\frac{560 b^7 d (b c-a d)}{a+b x}-\frac{35 b^7 (b c-a d)^2}{(a+b x)^2}+2520 b^7 d^2 \log (a+b x)+\frac{1960 b^6 d^2 (b c-a d)}{c+d x}+\frac{735 b^5 d^2 (b c-a d)^2}{(c+d x)^2}+\frac{350 b^4 d^2 (b c-a d)^3}{(c+d x)^3}+\frac{175 b^3 d^2 (b c-a d)^4}{(c+d x)^4}+\frac{84 b^2 d^2 (b c-a d)^5}{(c+d x)^5}+\frac{35 b d^2 (b c-a d)^6}{(c+d x)^6}+\frac{10 d^2 (b c-a d)^7}{(c+d x)^7}-2520 b^7 d^2 \log (c+d x)}{70 (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^7*(b*c - a*d)^2)/(a + b*x)^2 + (560*b^7*d*(b*c - a*d))/(a + b*x) + (10*d^2*(b*c - a*d)^7)/(c + d*x)^7 + (35*b*d^2*(b*c - a*d)^6)/(c + d*x)^6 + (84*b^2*d^2*(b*c - a*d)^5)/(c + d*x)^5 + (175*b^3*d^2*(b*c - a*d)^4)/(c + d*x)^4 + (350*b^4*d^2*(b*c - a*d)^3)/(c + d*x)^3 + (735*b^5*d^2*(b*c - a*d)^2)/(c + d*x)^2 + (1960*b^6*d^2*(b*c - a*d))/(c + d*x) + 2520*b^7*d^2*Log[a + b*x] - 2520*b^7*d^2*Log[c + d*x])/(70*(b*c - a*d)^10)","A",1
1375,1,123,156,0.1452648,"\int (a+b x)^5 \sqrt{c+d x} \, dx","Integrate[(a + b*x)^5*Sqrt[c + d*x],x]","\frac{2 (c+d x)^{3/2} \left(-4095 b^4 (c+d x)^4 (b c-a d)+10010 b^3 (c+d x)^3 (b c-a d)^2-12870 b^2 (c+d x)^2 (b c-a d)^3+9009 b (c+d x) (b c-a d)^4-3003 (b c-a d)^5+693 b^5 (c+d x)^5\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*(c + d*x)^(3/2)*(-3003*(b*c - a*d)^5 + 9009*b*(b*c - a*d)^4*(c + d*x) - 12870*b^2*(b*c - a*d)^3*(c + d*x)^2 + 10010*b^3*(b*c - a*d)^2*(c + d*x)^3 - 4095*b^4*(b*c - a*d)*(c + d*x)^4 + 693*b^5*(c + d*x)^5))/(9009*d^6)","A",1
1376,1,101,129,0.0952863,"\int (a+b x)^4 \sqrt{c+d x} \, dx","Integrate[(a + b*x)^4*Sqrt[c + d*x],x]","\frac{2 (c+d x)^{3/2} \left(-1540 b^3 (c+d x)^3 (b c-a d)+2970 b^2 (c+d x)^2 (b c-a d)^2-2772 b (c+d x) (b c-a d)^3+1155 (b c-a d)^4+315 b^4 (c+d x)^4\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*(c + d*x)^(3/2)*(1155*(b*c - a*d)^4 - 2772*b*(b*c - a*d)^3*(c + d*x) + 2970*b^2*(b*c - a*d)^2*(c + d*x)^2 - 1540*b^3*(b*c - a*d)*(c + d*x)^3 + 315*b^4*(c + d*x)^4))/(3465*d^5)","A",1
1377,1,79,100,0.0629588,"\int (a+b x)^3 \sqrt{c+d x} \, dx","Integrate[(a + b*x)^3*Sqrt[c + d*x],x]","\frac{2 (c+d x)^{3/2} \left(-135 b^2 (c+d x)^2 (b c-a d)+189 b (c+d x) (b c-a d)^2-105 (b c-a d)^3+35 b^3 (c+d x)^3\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*(c + d*x)^(3/2)*(-105*(b*c - a*d)^3 + 189*b*(b*c - a*d)^2*(c + d*x) - 135*b^2*(b*c - a*d)*(c + d*x)^2 + 35*b^3*(c + d*x)^3))/(315*d^4)","A",1
1378,1,61,71,0.0376363,"\int (a+b x)^2 \sqrt{c+d x} \, dx","Integrate[(a + b*x)^2*Sqrt[c + d*x],x]","\frac{2 (c+d x)^{3/2} \left(35 a^2 d^2+14 a b d (3 d x-2 c)+b^2 \left(8 c^2-12 c d x+15 d^2 x^2\right)\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*(c + d*x)^(3/2)*(35*a^2*d^2 + 14*a*b*d*(-2*c + 3*d*x) + b^2*(8*c^2 - 12*c*d*x + 15*d^2*x^2)))/(105*d^3)","A",1
1379,1,30,42,0.0188672,"\int (a+b x) \sqrt{c+d x} \, dx","Integrate[(a + b*x)*Sqrt[c + d*x],x]","\frac{2 (c+d x)^{3/2} (5 a d-2 b c+3 b d x)}{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*(c + d*x)^(3/2)*(-2*b*c + 5*a*d + 3*b*d*x))/(15*d^2)","A",1
1380,1,16,16,0.004083,"\int \sqrt{c+d x} \, dx","Integrate[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
1381,1,62,62,0.0382266,"\int \frac{\sqrt{c+d x}}{a+b x} \, dx","Integrate[Sqrt[c + d*x]/(a + b*x),x]","\frac{2 \sqrt{c+d x}}{b}-\frac{2 \sqrt{b c-a d} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{b^{3/2}}","\frac{2 \sqrt{c+d x}}{b}-\frac{2 \sqrt{b c-a d} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{b^{3/2}}",1,"(2*Sqrt[c + d*x])/b - (2*Sqrt[b*c - a*d]*ArcTanh[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[b*c - a*d]])/b^(3/2)","A",1
1382,1,69,70,0.0805691,"\int \frac{\sqrt{c+d x}}{(a+b x)^2} \, dx","Integrate[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}}\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[c + d*x])/Sqrt[-(b*c) + a*d]])/(b^(3/2)*Sqrt[-(b*c) + a*d])","A",1
1383,1,52,110,0.0158277,"\int \frac{\sqrt{c+d x}}{(a+b x)^3} \, dx","Integrate[Sqrt[c + d*x]/(a + b*x)^3,x]","\frac{2 d^2 (c+d x)^{3/2} \, _2F_1\left(\frac{3}{2},3;\frac{5}{2};-\frac{b (c+d x)}{a d-b c}\right)}{3 (a d-b c)^3}","\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,"(2*d^2*(c + d*x)^(3/2)*Hypergeometric2F1[3/2, 3, 5/2, -((b*(c + d*x))/(-(b*c) + a*d))])/(3*(-(b*c) + a*d)^3)","C",1
1384,1,52,146,0.0144314,"\int \frac{\sqrt{c+d x}}{(a+b x)^4} \, dx","Integrate[Sqrt[c + d*x]/(a + b*x)^4,x]","\frac{2 d^3 (c+d x)^{3/2} \, _2F_1\left(\frac{3}{2},4;\frac{5}{2};-\frac{b (c+d x)}{a d-b c}\right)}{3 (a d-b c)^4}","-\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,"(2*d^3*(c + d*x)^(3/2)*Hypergeometric2F1[3/2, 4, 5/2, -((b*(c + d*x))/(-(b*c) + a*d))])/(3*(-(b*c) + a*d)^4)","C",1
1385,1,52,182,0.0151943,"\int \frac{\sqrt{c+d x}}{(a+b x)^5} \, dx","Integrate[Sqrt[c + d*x]/(a + b*x)^5,x]","\frac{2 d^4 (c+d x)^{3/2} \, _2F_1\left(\frac{3}{2},5;\frac{5}{2};-\frac{b (c+d x)}{a d-b c}\right)}{3 (a d-b c)^5}","\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,"(2*d^4*(c + d*x)^(3/2)*Hypergeometric2F1[3/2, 5, 5/2, -((b*(c + d*x))/(-(b*c) + a*d))])/(3*(-(b*c) + a*d)^5)","C",1
1386,1,52,218,0.0157763,"\int \frac{\sqrt{c+d x}}{(a+b x)^6} \, dx","Integrate[Sqrt[c + d*x]/(a + b*x)^6,x]","\frac{2 d^5 (c+d x)^{3/2} \, _2F_1\left(\frac{3}{2},6;\frac{5}{2};-\frac{b (c+d x)}{a d-b c}\right)}{3 (a d-b c)^6}","-\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,"(2*d^5*(c + d*x)^(3/2)*Hypergeometric2F1[3/2, 6, 5/2, -((b*(c + d*x))/(-(b*c) + a*d))])/(3*(-(b*c) + a*d)^6)","C",1
1387,1,123,158,0.1462491,"\int (a+b x)^5 (c+d x)^{3/2} \, dx","Integrate[(a + b*x)^5*(c + d*x)^(3/2),x]","\frac{2 (c+d x)^{5/2} \left(-17325 b^4 (c+d x)^4 (b c-a d)+40950 b^3 (c+d x)^3 (b c-a d)^2-50050 b^2 (c+d x)^2 (b c-a d)^3+32175 b (c+d x) (b c-a d)^4-9009 (b c-a d)^5+3003 b^5 (c+d x)^5\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*(c + d*x)^(5/2)*(-9009*(b*c - a*d)^5 + 32175*b*(b*c - a*d)^4*(c + d*x) - 50050*b^2*(b*c - a*d)^3*(c + d*x)^2 + 40950*b^3*(b*c - a*d)^2*(c + d*x)^3 - 17325*b^4*(b*c - a*d)*(c + d*x)^4 + 3003*b^5*(c + d*x)^5))/(45045*d^6)","A",1
1388,1,101,129,0.0965769,"\int (a+b x)^4 (c+d x)^{3/2} \, dx","Integrate[(a + b*x)^4*(c + d*x)^(3/2),x]","\frac{2 (c+d x)^{5/2} \left(-5460 b^3 (c+d x)^3 (b c-a d)+10010 b^2 (c+d x)^2 (b c-a d)^2-8580 b (c+d x) (b c-a d)^3+3003 (b c-a d)^4+1155 b^4 (c+d x)^4\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*(c + d*x)^(5/2)*(3003*(b*c - a*d)^4 - 8580*b*(b*c - a*d)^3*(c + d*x) + 10010*b^2*(b*c - a*d)^2*(c + d*x)^2 - 5460*b^3*(b*c - a*d)*(c + d*x)^3 + 1155*b^4*(c + d*x)^4))/(15015*d^5)","A",1
1389,1,79,100,0.0690688,"\int (a+b x)^3 (c+d x)^{3/2} \, dx","Integrate[(a + b*x)^3*(c + d*x)^(3/2),x]","\frac{2 (c+d x)^{5/2} \left(-385 b^2 (c+d x)^2 (b c-a d)+495 b (c+d x) (b c-a d)^2-231 (b c-a d)^3+105 b^3 (c+d x)^3\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*(c + d*x)^(5/2)*(-231*(b*c - a*d)^3 + 495*b*(b*c - a*d)^2*(c + d*x) - 385*b^2*(b*c - a*d)*(c + d*x)^2 + 105*b^3*(c + d*x)^3))/(1155*d^4)","A",1
1390,1,61,71,0.0428428,"\int (a+b x)^2 (c+d x)^{3/2} \, dx","Integrate[(a + b*x)^2*(c + d*x)^(3/2),x]","\frac{2 (c+d x)^{5/2} \left(63 a^2 d^2+18 a b d (5 d x-2 c)+b^2 \left(8 c^2-20 c d x+35 d^2 x^2\right)\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*(c + d*x)^(5/2)*(63*a^2*d^2 + 18*a*b*d*(-2*c + 5*d*x) + b^2*(8*c^2 - 20*c*d*x + 35*d^2*x^2)))/(315*d^3)","A",1
1391,1,30,42,0.0208935,"\int (a+b x) (c+d x)^{3/2} \, dx","Integrate[(a + b*x)*(c + d*x)^(3/2),x]","\frac{2 (c+d x)^{5/2} (7 a d-2 b c+5 b d x)}{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*(c + d*x)^(5/2)*(-2*b*c + 7*a*d + 5*b*d*x))/(35*d^2)","A",1
1392,1,16,16,0.0049459,"\int (c+d x)^{3/2} \, dx","Integrate[(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
1393,1,77,86,0.0732615,"\int \frac{(c+d x)^{3/2}}{a+b x} \, dx","Integrate[(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 (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 (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)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[b*c - a*d]])/b^(5/2)","A",1
1394,1,50,85,0.0137127,"\int \frac{(c+d x)^{3/2}}{(a+b x)^2} \, dx","Integrate[(c + d*x)^(3/2)/(a + b*x)^2,x]","\frac{2 d (c+d x)^{5/2} \, _2F_1\left(2,\frac{5}{2};\frac{7}{2};-\frac{b (c+d x)}{a d-b c}\right)}{5 (a d-b c)^2}","-\frac{3 d \sqrt{b c-a d} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{b^{5/2}}-\frac{(c+d x)^{3/2}}{b (a+b x)}+\frac{3 d \sqrt{c+d x}}{b^2}",1,"(2*d*(c + d*x)^(5/2)*Hypergeometric2F1[2, 5/2, 7/2, -((b*(c + d*x))/(-(b*c) + a*d))])/(5*(-(b*c) + a*d)^2)","C",1
1395,1,90,100,0.1000267,"\int \frac{(c+d x)^{3/2}}{(a+b x)^3} \, dx","Integrate[(c + d*x)^(3/2)/(a + b*x)^3,x]","\frac{3 d^2 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{a d-b c}}\right)}{4 b^{5/2} \sqrt{a d-b c}}-\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 \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,"-1/4*(Sqrt[c + d*x]*(2*b*c + 3*a*d + 5*b*d*x))/(b^2*(a + b*x)^2) + (3*d^2*ArcTan[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[-(b*c) + a*d]])/(4*b^(5/2)*Sqrt[-(b*c) + a*d])","A",1
1396,1,52,136,0.0165368,"\int \frac{(c+d x)^{3/2}}{(a+b x)^4} \, dx","Integrate[(c + d*x)^(3/2)/(a + b*x)^4,x]","\frac{2 d^3 (c+d x)^{5/2} \, _2F_1\left(\frac{5}{2},4;\frac{7}{2};-\frac{b (c+d x)}{a d-b c}\right)}{5 (a d-b c)^4}","\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,"(2*d^3*(c + d*x)^(5/2)*Hypergeometric2F1[5/2, 4, 7/2, -((b*(c + d*x))/(-(b*c) + a*d))])/(5*(-(b*c) + a*d)^4)","C",1
1397,1,52,172,0.0157711,"\int \frac{(c+d x)^{3/2}}{(a+b x)^5} \, dx","Integrate[(c + d*x)^(3/2)/(a + b*x)^5,x]","\frac{2 d^4 (c+d x)^{5/2} \, _2F_1\left(\frac{5}{2},5;\frac{7}{2};-\frac{b (c+d x)}{a d-b c}\right)}{5 (a d-b c)^5}","-\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,"(2*d^4*(c + d*x)^(5/2)*Hypergeometric2F1[5/2, 5, 7/2, -((b*(c + d*x))/(-(b*c) + a*d))])/(5*(-(b*c) + a*d)^5)","C",1
1398,1,52,208,0.0174319,"\int \frac{(c+d x)^{3/2}}{(a+b x)^6} \, dx","Integrate[(c + d*x)^(3/2)/(a + b*x)^6,x]","\frac{2 d^5 (c+d x)^{5/2} \, _2F_1\left(\frac{5}{2},6;\frac{7}{2};-\frac{b (c+d x)}{a d-b c}\right)}{5 (a d-b c)^6}","\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,"(2*d^5*(c + d*x)^(5/2)*Hypergeometric2F1[5/2, 6, 7/2, -((b*(c + d*x))/(-(b*c) + a*d))])/(5*(-(b*c) + a*d)^6)","C",1
1399,1,123,158,0.113956,"\int (a+b x)^5 (c+d x)^{5/2} \, dx","Integrate[(a + b*x)^5*(c + d*x)^(5/2),x]","\frac{2 (c+d x)^{7/2} \left(-51051 b^4 (c+d x)^4 (b c-a d)+117810 b^3 (c+d x)^3 (b c-a d)^2-139230 b^2 (c+d x)^2 (b c-a d)^3+85085 b (c+d x) (b c-a d)^4-21879 (b c-a d)^5+9009 b^5 (c+d x)^5\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*(c + d*x)^(7/2)*(-21879*(b*c - a*d)^5 + 85085*b*(b*c - a*d)^4*(c + d*x) - 139230*b^2*(b*c - a*d)^3*(c + d*x)^2 + 117810*b^3*(b*c - a*d)^2*(c + d*x)^3 - 51051*b^4*(b*c - a*d)*(c + d*x)^4 + 9009*b^5*(c + d*x)^5))/(153153*d^6)","A",1
1400,1,101,129,0.11018,"\int (a+b x)^4 (c+d x)^{5/2} \, dx","Integrate[(a + b*x)^4*(c + d*x)^(5/2),x]","\frac{2 (c+d x)^{7/2} \left(-13860 b^3 (c+d x)^3 (b c-a d)+24570 b^2 (c+d x)^2 (b c-a d)^2-20020 b (c+d x) (b c-a d)^3+6435 (b c-a d)^4+3003 b^4 (c+d x)^4\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*(c + d*x)^(7/2)*(6435*(b*c - a*d)^4 - 20020*b*(b*c - a*d)^3*(c + d*x) + 24570*b^2*(b*c - a*d)^2*(c + d*x)^2 - 13860*b^3*(b*c - a*d)*(c + d*x)^3 + 3003*b^4*(c + d*x)^4))/(45045*d^5)","A",1
1401,1,79,100,0.0723289,"\int (a+b x)^3 (c+d x)^{5/2} \, dx","Integrate[(a + b*x)^3*(c + d*x)^(5/2),x]","\frac{2 (c+d x)^{7/2} \left(-819 b^2 (c+d x)^2 (b c-a d)+1001 b (c+d x) (b c-a d)^2-429 (b c-a d)^3+231 b^3 (c+d x)^3\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*(c + d*x)^(7/2)*(-429*(b*c - a*d)^3 + 1001*b*(b*c - a*d)^2*(c + d*x) - 819*b^2*(b*c - a*d)*(c + d*x)^2 + 231*b^3*(c + d*x)^3))/(3003*d^4)","A",1
1402,1,61,71,0.0456888,"\int (a+b x)^2 (c+d x)^{5/2} \, dx","Integrate[(a + b*x)^2*(c + d*x)^(5/2),x]","\frac{2 (c+d x)^{7/2} \left(99 a^2 d^2+22 a b d (7 d x-2 c)+b^2 \left(8 c^2-28 c d x+63 d^2 x^2\right)\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*(c + d*x)^(7/2)*(99*a^2*d^2 + 22*a*b*d*(-2*c + 7*d*x) + b^2*(8*c^2 - 28*c*d*x + 63*d^2*x^2)))/(693*d^3)","A",1
1403,1,30,42,0.0235301,"\int (a+b x) (c+d x)^{5/2} \, dx","Integrate[(a + b*x)*(c + d*x)^(5/2),x]","\frac{2 (c+d x)^{7/2} (9 a d-2 b c+7 b d x)}{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*(c + d*x)^(7/2)*(-2*b*c + 9*a*d + 7*b*d*x))/(63*d^2)","A",1
1404,1,16,16,0.0058566,"\int (c+d x)^{5/2} \, dx","Integrate[(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
1405,1,105,112,0.1550449,"\int \frac{(c+d x)^{5/2}}{a+b x} \, dx","Integrate[(c + d*x)^(5/2)/(a + b*x),x]","\frac{2 (b c-a d) \left(\sqrt{b} \sqrt{c+d x} (-3 a d+4 b c+b d x)-3 (b c-a d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)\right)}{3 b^{7/2}}+\frac{2 (c+d x)^{5/2}}{5 b}","-\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*(c + d*x)^(5/2))/(5*b) + (2*(b*c - a*d)*(Sqrt[b]*Sqrt[c + d*x]*(4*b*c - 3*a*d + b*d*x) - 3*(b*c - a*d)^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[b*c - a*d]]))/(3*b^(7/2))","A",1
1406,1,50,110,0.0147831,"\int \frac{(c+d x)^{5/2}}{(a+b x)^2} \, dx","Integrate[(c + d*x)^(5/2)/(a + b*x)^2,x]","\frac{2 d (c+d x)^{7/2} \, _2F_1\left(2,\frac{7}{2};\frac{9}{2};-\frac{b (c+d x)}{a d-b c}\right)}{7 (a d-b c)^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,"(2*d*(c + d*x)^(7/2)*Hypergeometric2F1[2, 7/2, 9/2, -((b*(c + d*x))/(-(b*c) + a*d))])/(7*(-(b*c) + a*d)^2)","C",1
1407,1,52,119,0.0182008,"\int \frac{(c+d x)^{5/2}}{(a+b x)^3} \, dx","Integrate[(c + d*x)^(5/2)/(a + b*x)^3,x]","\frac{2 d^2 (c+d x)^{7/2} \, _2F_1\left(3,\frac{7}{2};\frac{9}{2};-\frac{b (c+d x)}{a d-b c}\right)}{7 (a d-b c)^3}","-\frac{15 d^2 \sqrt{b c-a d} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{4 b^{7/2}}-\frac{5 d (c+d x)^{3/2}}{4 b^2 (a+b x)}-\frac{(c+d x)^{5/2}}{2 b (a+b x)^2}+\frac{15 d^2 \sqrt{c+d x}}{4 b^3}",1,"(2*d^2*(c + d*x)^(7/2)*Hypergeometric2F1[3, 7/2, 9/2, -((b*(c + d*x))/(-(b*c) + a*d))])/(7*(-(b*c) + a*d)^3)","C",1
1408,1,119,126,0.1518221,"\int \frac{(c+d x)^{5/2}}{(a+b x)^4} \, dx","Integrate[(c + d*x)^(5/2)/(a + b*x)^4,x]","\frac{5 d^3 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{a d-b c}}\right)}{8 b^{7/2} \sqrt{a d-b c}}-\frac{\sqrt{c+d x} \left(15 a^2 d^2+10 a b d (c+4 d x)+b^2 \left(8 c^2+26 c d x+33 d^2 x^2\right)\right)}{24 b^3 (a+b x)^3}","-\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,"-1/24*(Sqrt[c + d*x]*(15*a^2*d^2 + 10*a*b*d*(c + 4*d*x) + b^2*(8*c^2 + 26*c*d*x + 33*d^2*x^2)))/(b^3*(a + b*x)^3) + (5*d^3*ArcTan[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[-(b*c) + a*d]])/(8*b^(7/2)*Sqrt[-(b*c) + a*d])","A",1
1409,1,52,162,0.0175906,"\int \frac{(c+d x)^{5/2}}{(a+b x)^5} \, dx","Integrate[(c + d*x)^(5/2)/(a + b*x)^5,x]","\frac{2 d^4 (c+d x)^{7/2} \, _2F_1\left(\frac{7}{2},5;\frac{9}{2};-\frac{b (c+d x)}{a d-b c}\right)}{7 (a d-b c)^5}","\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,"(2*d^4*(c + d*x)^(7/2)*Hypergeometric2F1[7/2, 5, 9/2, -((b*(c + d*x))/(-(b*c) + a*d))])/(7*(-(b*c) + a*d)^5)","C",1
1410,1,52,198,0.0183151,"\int \frac{(c+d x)^{5/2}}{(a+b x)^6} \, dx","Integrate[(c + d*x)^(5/2)/(a + b*x)^6,x]","\frac{2 d^5 (c+d x)^{7/2} \, _2F_1\left(\frac{7}{2},6;\frac{9}{2};-\frac{b (c+d x)}{a d-b c}\right)}{7 (a d-b c)^6}","-\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,"(2*d^5*(c + d*x)^(7/2)*Hypergeometric2F1[7/2, 6, 9/2, -((b*(c + d*x))/(-(b*c) + a*d))])/(7*(-(b*c) + a*d)^6)","C",1
1411,1,51,35,0.0301145,"\int \frac{\sqrt{-1+x}}{(1+x)^2} \, dx","Integrate[Sqrt[-1 + x]/(1 + x)^2,x]","\frac{-2 x-\sqrt{2-2 x} (x+1) \tanh ^{-1}\left(\frac{\sqrt{1-x}}{\sqrt{2}}\right)+2}{2 \sqrt{x-1} (x+1)}","\frac{\tan ^{-1}\left(\frac{\sqrt{x-1}}{\sqrt{2}}\right)}{\sqrt{2}}-\frac{\sqrt{x-1}}{x+1}",1,"(2 - 2*x - Sqrt[2 - 2*x]*(1 + x)*ArcTanh[Sqrt[1 - x]/Sqrt[2]])/(2*Sqrt[-1 + x]*(1 + x))","A",1
1412,1,28,56,0.0053878,"\int \frac{\sqrt{-1+x}}{(1+x)^3} \, dx","Integrate[Sqrt[-1 + x]/(1 + x)^3,x]","\frac{1}{12} (x-1)^{3/2} \, _2F_1\left(\frac{3}{2},3;\frac{5}{2};\frac{1-x}{2}\right)","\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,"((-1 + x)^(3/2)*Hypergeometric2F1[3/2, 3, 5/2, (1 - x)/2])/12","C",1
1413,1,123,154,0.088223,"\int \frac{(a+b x)^5}{\sqrt{c+d x}} \, dx","Integrate[(a + b*x)^5/Sqrt[c + d*x],x]","\frac{2 \sqrt{c+d x} \left(-385 b^4 (c+d x)^4 (b c-a d)+990 b^3 (c+d x)^3 (b c-a d)^2-1386 b^2 (c+d x)^2 (b c-a d)^3+1155 b (c+d x) (b c-a d)^4-693 (b c-a d)^5+63 b^5 (c+d 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]*(-693*(b*c - a*d)^5 + 1155*b*(b*c - a*d)^4*(c + d*x) - 1386*b^2*(b*c - a*d)^3*(c + d*x)^2 + 990*b^3*(b*c - a*d)^2*(c + d*x)^3 - 385*b^4*(b*c - a*d)*(c + d*x)^4 + 63*b^5*(c + d*x)^5))/(693*d^6)","A",1
1414,1,101,127,0.087775,"\int \frac{(a+b x)^4}{\sqrt{c+d x}} \, dx","Integrate[(a + b*x)^4/Sqrt[c + d*x],x]","\frac{2 \sqrt{c+d x} \left(-180 b^3 (c+d x)^3 (b c-a d)+378 b^2 (c+d x)^2 (b c-a d)^2-420 b (c+d x) (b c-a d)^3+315 (b c-a d)^4+35 b^4 (c+d 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]*(315*(b*c - a*d)^4 - 420*b*(b*c - a*d)^3*(c + d*x) + 378*b^2*(b*c - a*d)^2*(c + d*x)^2 - 180*b^3*(b*c - a*d)*(c + d*x)^3 + 35*b^4*(c + d*x)^4))/(315*d^5)","A",1
1415,1,79,96,0.0562066,"\int \frac{(a+b x)^3}{\sqrt{c+d x}} \, dx","Integrate[(a + b*x)^3/Sqrt[c + d*x],x]","\frac{2 \sqrt{c+d x} \left(-21 b^2 (c+d x)^2 (b c-a d)+35 b (c+d x) (b c-a d)^2-35 (b c-a d)^3+5 b^3 (c+d 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]*(-35*(b*c - a*d)^3 + 35*b*(b*c - a*d)^2*(c + d*x) - 21*b^2*(b*c - a*d)*(c + d*x)^2 + 5*b^3*(c + d*x)^3))/(35*d^4)","A",1
1416,1,60,69,0.0354984,"\int \frac{(a+b x)^2}{\sqrt{c+d x}} \, dx","Integrate[(a + b*x)^2/Sqrt[c + d*x],x]","\frac{2 \sqrt{c+d x} \left(15 a^2 d^2+10 a b d (d x-2 c)+b^2 \left(8 c^2-4 c d x+3 d^2 x^2\right)\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]*(15*a^2*d^2 + 10*a*b*d*(-2*c + d*x) + b^2*(8*c^2 - 4*c*d*x + 3*d^2*x^2)))/(15*d^3)","A",1
1417,1,29,40,0.0172212,"\int \frac{a+b x}{\sqrt{c+d x}} \, dx","Integrate[(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
1418,1,14,14,0.0033825,"\int \frac{1}{\sqrt{c+d x}} \, dx","Integrate[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
1419,1,47,47,0.015202,"\int \frac{1}{(a+b x) \sqrt{c+d x}} \, dx","Integrate[1/((a + b*x)*Sqrt[c + d*x]),x]","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{\sqrt{b} \sqrt{b c-a d}}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{\sqrt{b} \sqrt{b c-a d}}",1,"(-2*ArcTanh[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[b*c - a*d]])/(Sqrt[b]*Sqrt[b*c - a*d])","A",1
1420,1,76,76,0.0706393,"\int \frac{1}{(a+b x)^2 \sqrt{c+d x}} \, dx","Integrate[1/((a + b*x)^2*Sqrt[c + d*x]),x]","\frac{d \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{a d-b c}}\right)}{\sqrt{b} (a d-b c)^{3/2}}-\frac{\sqrt{c+d x}}{(a+b x) (b c-a d)}","\frac{d \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{\sqrt{b} (b c-a d)^{3/2}}-\frac{\sqrt{c+d x}}{(a+b x) (b c-a d)}",1,"-(Sqrt[c + d*x]/((b*c - a*d)*(a + b*x))) + (d*ArcTan[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[-(b*c) + a*d]])/(Sqrt[b]*(-(b*c) + a*d)^(3/2))","A",1
1421,1,50,114,0.0113935,"\int \frac{1}{(a+b x)^3 \sqrt{c+d x}} \, dx","Integrate[1/((a + b*x)^3*Sqrt[c + d*x]),x]","\frac{2 d^2 \sqrt{c+d x} \, _2F_1\left(\frac{1}{2},3;\frac{3}{2};-\frac{b (c+d x)}{a d-b c}\right)}{(a d-b c)^3}","-\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,"(2*d^2*Sqrt[c + d*x]*Hypergeometric2F1[1/2, 3, 3/2, -((b*(c + d*x))/(-(b*c) + a*d))])/(-(b*c) + a*d)^3","C",1
1422,1,50,147,0.0112465,"\int \frac{1}{(a+b x)^4 \sqrt{c+d x}} \, dx","Integrate[1/((a + b*x)^4*Sqrt[c + d*x]),x]","\frac{2 d^3 \sqrt{c+d x} \, _2F_1\left(\frac{1}{2},4;\frac{3}{2};-\frac{b (c+d x)}{a d-b c}\right)}{(a d-b c)^4}","\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,"(2*d^3*Sqrt[c + d*x]*Hypergeometric2F1[1/2, 4, 3/2, -((b*(c + d*x))/(-(b*c) + a*d))])/(-(b*c) + a*d)^4","C",1
1423,1,50,180,0.011894,"\int \frac{1}{(a+b x)^5 \sqrt{c+d x}} \, dx","Integrate[1/((a + b*x)^5*Sqrt[c + d*x]),x]","\frac{2 d^4 \sqrt{c+d x} \, _2F_1\left(\frac{1}{2},5;\frac{3}{2};-\frac{b (c+d x)}{a d-b c}\right)}{(a d-b c)^5}","-\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,"(2*d^4*Sqrt[c + d*x]*Hypergeometric2F1[1/2, 5, 3/2, -((b*(c + d*x))/(-(b*c) + a*d))])/(-(b*c) + a*d)^5","C",1
1424,1,123,152,0.1204963,"\int \frac{(a+b x)^5}{(c+d x)^{3/2}} \, dx","Integrate[(a + b*x)^5/(c + d*x)^(3/2),x]","\frac{2 \left(-45 b^4 (c+d x)^4 (b c-a d)+126 b^3 (c+d x)^3 (b c-a d)^2-210 b^2 (c+d x)^2 (b c-a d)^3+315 b (c+d x) (b c-a d)^4+63 (b c-a d)^5+7 b^5 (c+d 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*(63*(b*c - a*d)^5 + 315*b*(b*c - a*d)^4*(c + d*x) - 210*b^2*(b*c - a*d)^3*(c + d*x)^2 + 126*b^3*(b*c - a*d)^2*(c + d*x)^3 - 45*b^4*(b*c - a*d)*(c + d*x)^4 + 7*b^5*(c + d*x)^5))/(63*d^6*Sqrt[c + d*x])","A",1
1425,1,101,123,0.0804386,"\int \frac{(a+b x)^4}{(c+d x)^{3/2}} \, dx","Integrate[(a + b*x)^4/(c + d*x)^(3/2),x]","\frac{2 \left(-28 b^3 (c+d x)^3 (b c-a d)+70 b^2 (c+d x)^2 (b c-a d)^2-140 b (c+d x) (b c-a d)^3-35 (b c-a d)^4+5 b^4 (c+d 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*(-35*(b*c - a*d)^4 - 140*b*(b*c - a*d)^3*(c + d*x) + 70*b^2*(b*c - a*d)^2*(c + d*x)^2 - 28*b^3*(b*c - a*d)*(c + d*x)^3 + 5*b^4*(c + d*x)^4))/(35*d^5*Sqrt[c + d*x])","A",1
1426,1,78,94,0.0561235,"\int \frac{(a+b x)^3}{(c+d x)^{3/2}} \, dx","Integrate[(a + b*x)^3/(c + d*x)^(3/2),x]","\frac{2 \left(-5 b^2 (c+d x)^2 (b c-a d)+15 b (c+d x) (b c-a d)^2+5 (b c-a d)^3+b^3 (c+d 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*(5*(b*c - a*d)^3 + 15*b*(b*c - a*d)^2*(c + d*x) - 5*b^2*(b*c - a*d)*(c + d*x)^2 + b^3*(c + d*x)^3))/(5*d^4*Sqrt[c + d*x])","A",1
1427,1,59,67,0.0312535,"\int \frac{(a+b x)^2}{(c+d x)^{3/2}} \, dx","Integrate[(a + b*x)^2/(c + d*x)^(3/2),x]","\frac{2 \left(-3 a^2 d^2+6 a b d (2 c+d x)+b^2 \left(-8 c^2-4 c d x+d^2 x^2\right)\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*(-3*a^2*d^2 + 6*a*b*d*(2*c + d*x) + b^2*(-8*c^2 - 4*c*d*x + d^2*x^2)))/(3*d^3*Sqrt[c + d*x])","A",1
1428,1,27,38,0.0185624,"\int \frac{a+b x}{(c+d x)^{3/2}} \, dx","Integrate[(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
1429,1,14,14,0.0036814,"\int \frac{1}{(c+d x)^{3/2}} \, dx","Integrate[(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
1430,1,46,69,0.0097954,"\int \frac{1}{(a+b x) (c+d x)^{3/2}} \, dx","Integrate[1/((a + b*x)*(c + d*x)^(3/2)),x]","-\frac{2 \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{b (c+d x)}{b c-a d}\right)}{\sqrt{c+d x} (a d-b c)}","\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*Hypergeometric2F1[-1/2, 1, 1/2, (b*(c + d*x))/(b*c - a*d)])/((-(b*c) + a*d)*Sqrt[c + d*x])","C",1
1431,1,48,99,0.0126836,"\int \frac{1}{(a+b x)^2 (c+d x)^{3/2}} \, dx","Integrate[1/((a + b*x)^2*(c + d*x)^(3/2)),x]","-\frac{2 d \, _2F_1\left(-\frac{1}{2},2;\frac{1}{2};-\frac{b (c+d x)}{a d-b c}\right)}{\sqrt{c+d x} (a d-b c)^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,"(-2*d*Hypergeometric2F1[-1/2, 2, 1/2, -((b*(c + d*x))/(-(b*c) + a*d))])/((-(b*c) + a*d)^2*Sqrt[c + d*x])","C",1
1432,1,50,140,0.0127713,"\int \frac{1}{(a+b x)^3 (c+d x)^{3/2}} \, dx","Integrate[1/((a + b*x)^3*(c + d*x)^(3/2)),x]","-\frac{2 d^2 \, _2F_1\left(-\frac{1}{2},3;\frac{1}{2};-\frac{b (c+d x)}{a d-b c}\right)}{\sqrt{c+d x} (a d-b c)^3}","\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*d^2*Hypergeometric2F1[-1/2, 3, 1/2, -((b*(c + d*x))/(-(b*c) + a*d))])/((-(b*c) + a*d)^3*Sqrt[c + d*x])","C",1
1433,1,50,173,0.0154903,"\int \frac{1}{(a+b x)^4 (c+d x)^{3/2}} \, dx","Integrate[1/((a + b*x)^4*(c + d*x)^(3/2)),x]","-\frac{2 d^3 \, _2F_1\left(-\frac{1}{2},4;\frac{1}{2};-\frac{b (c+d x)}{a d-b c}\right)}{\sqrt{c+d x} (a d-b c)^4}","-\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,"(-2*d^3*Hypergeometric2F1[-1/2, 4, 1/2, -((b*(c + d*x))/(-(b*c) + a*d))])/((-(b*c) + a*d)^4*Sqrt[c + d*x])","C",1
1434,1,123,152,0.1187769,"\int \frac{(a+b x)^5}{(c+d x)^{5/2}} \, dx","Integrate[(a + b*x)^5/(c + d*x)^(5/2),x]","\frac{2 \left(-21 b^4 (c+d x)^4 (b c-a d)+70 b^3 (c+d x)^3 (b c-a d)^2-210 b^2 (c+d x)^2 (b c-a d)^3-105 b (c+d x) (b c-a d)^4+7 (b c-a d)^5+3 b^5 (c+d 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*(7*(b*c - a*d)^5 - 105*b*(b*c - a*d)^4*(c + d*x) - 210*b^2*(b*c - a*d)^3*(c + d*x)^2 + 70*b^3*(b*c - a*d)^2*(c + d*x)^3 - 21*b^4*(b*c - a*d)*(c + d*x)^4 + 3*b^5*(c + d*x)^5))/(21*d^6*(c + d*x)^(3/2))","A",1
1435,1,101,125,0.0836246,"\int \frac{(a+b x)^4}{(c+d x)^{5/2}} \, dx","Integrate[(a + b*x)^4/(c + d*x)^(5/2),x]","\frac{2 \left(-20 b^3 (c+d x)^3 (b c-a d)+90 b^2 (c+d x)^2 (b c-a d)^2+60 b (c+d x) (b c-a d)^3-5 (b c-a d)^4+3 b^4 (c+d 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*(-5*(b*c - a*d)^4 + 60*b*(b*c - a*d)^3*(c + d*x) + 90*b^2*(b*c - a*d)^2*(c + d*x)^2 - 20*b^3*(b*c - a*d)*(c + d*x)^3 + 3*b^4*(c + d*x)^4))/(15*d^5*(c + d*x)^(3/2))","A",1
1436,1,76,96,0.0582097,"\int \frac{(a+b x)^3}{(c+d x)^{5/2}} \, dx","Integrate[(a + b*x)^3/(c + d*x)^(5/2),x]","\frac{2 \left(-9 b^2 (c+d x)^2 (b c-a d)-9 b (c+d x) (b c-a d)^2+(b c-a d)^3+b^3 (c+d 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*((b*c - a*d)^3 - 9*b*(b*c - a*d)^2*(c + d*x) - 9*b^2*(b*c - a*d)*(c + d*x)^2 + b^3*(c + d*x)^3))/(3*d^4*(c + d*x)^(3/2))","A",1
1437,1,62,67,0.0350993,"\int \frac{(a+b x)^2}{(c+d x)^{5/2}} \, dx","Integrate[(a + b*x)^2/(c + d*x)^(5/2),x]","\frac{-2 a^2 d^2-4 a b d (2 c+3 d x)+2 b^2 \left(8 c^2+12 c d x+3 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*a^2*d^2 - 4*a*b*d*(2*c + 3*d*x) + 2*b^2*(8*c^2 + 12*c*d*x + 3*d^2*x^2))/(3*d^3*(c + d*x)^(3/2))","A",1
1438,1,29,40,0.0199018,"\int \frac{a+b x}{(c+d x)^{5/2}} \, dx","Integrate[(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
1439,1,16,16,0.004391,"\int \frac{1}{(c+d x)^{5/2}} \, dx","Integrate[(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
1440,1,48,93,0.0101542,"\int \frac{1}{(a+b x) (c+d x)^{5/2}} \, dx","Integrate[1/((a + b*x)*(c + d*x)^(5/2)),x]","\frac{2 \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};\frac{b (c+d x)}{b c-a d}\right)}{3 (c+d x)^{3/2} (b c-a d)}","-\frac{2 b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{(b c-a d)^{5/2}}+\frac{2 b}{\sqrt{c+d x} (b c-a d)^2}+\frac{2}{3 (c+d x)^{3/2} (b c-a d)}",1,"(2*Hypergeometric2F1[-3/2, 1, -1/2, (b*(c + d*x))/(b*c - a*d)])/(3*(b*c - a*d)*(c + d*x)^(3/2))","C",1
1441,1,50,124,0.0147709,"\int \frac{1}{(a+b x)^2 (c+d x)^{5/2}} \, dx","Integrate[1/((a + b*x)^2*(c + d*x)^(5/2)),x]","-\frac{2 d \, _2F_1\left(-\frac{3}{2},2;-\frac{1}{2};-\frac{b (c+d x)}{a d-b c}\right)}{3 (c+d x)^{3/2} (a d-b c)^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,"(-2*d*Hypergeometric2F1[-3/2, 2, -1/2, -((b*(c + d*x))/(-(b*c) + a*d))])/(3*(-(b*c) + a*d)^2*(c + d*x)^(3/2))","C",1
1442,1,52,167,0.0161175,"\int \frac{1}{(a+b x)^3 (c+d x)^{5/2}} \, dx","Integrate[1/((a + b*x)^3*(c + d*x)^(5/2)),x]","-\frac{2 d^2 \, _2F_1\left(-\frac{3}{2},3;-\frac{1}{2};-\frac{b (c+d x)}{a d-b c}\right)}{3 (c+d x)^{3/2} (a d-b c)^3}","-\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,"(-2*d^2*Hypergeometric2F1[-3/2, 3, -1/2, -((b*(c + d*x))/(-(b*c) + a*d))])/(3*(-(b*c) + a*d)^3*(c + d*x)^(3/2))","C",1
1443,1,52,200,0.0190351,"\int \frac{1}{(a+b x)^4 (c+d x)^{5/2}} \, dx","Integrate[1/((a + b*x)^4*(c + d*x)^(5/2)),x]","-\frac{2 d^3 \, _2F_1\left(-\frac{3}{2},4;-\frac{1}{2};-\frac{b (c+d x)}{a d-b c}\right)}{3 (c+d x)^{3/2} (a d-b c)^4}","\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,"(-2*d^3*Hypergeometric2F1[-3/2, 4, -1/2, -((b*(c + d*x))/(-(b*c) + a*d))])/(3*(-(b*c) + a*d)^4*(c + d*x)^(3/2))","C",1
1444,1,25,22,0.0204782,"\int (a+b x)^5 (a c+b c x)^{3/2} \, dx","Integrate[(a + b*x)^5*(a*c + b*c*x)^(3/2),x]","\frac{2 (a+b x)^6 (c (a+b x))^{3/2}}{15 b}","\frac{2 (a c+b c x)^{15/2}}{15 b c^6}",1,"(2*(a + b*x)^6*(c*(a + b*x))^(3/2))/(15*b)","A",1
1445,1,25,22,0.0122116,"\int (a+b x)^5 \sqrt{a c+b c x} \, dx","Integrate[(a + b*x)^5*Sqrt[a*c + b*c*x],x]","\frac{2 (a+b x)^6 \sqrt{c (a+b x)}}{13 b}","\frac{2 (a c+b c x)^{13/2}}{13 b c^6}",1,"(2*(a + b*x)^6*Sqrt[c*(a + b*x)])/(13*b)","A",1
1446,1,25,22,0.0140783,"\int \frac{(a+b x)^5}{\sqrt{a c+b c x}} \, dx","Integrate[(a + b*x)^5/Sqrt[a*c + b*c*x],x]","\frac{2 (a+b x)^6}{11 b \sqrt{c (a+b x)}}","\frac{2 (a c+b c x)^{11/2}}{11 b c^6}",1,"(2*(a + b*x)^6)/(11*b*Sqrt[c*(a + b*x)])","A",1
1447,1,25,22,0.01494,"\int \frac{(a+b x)^5}{(a c+b c x)^{3/2}} \, dx","Integrate[(a + b*x)^5/(a*c + b*c*x)^(3/2),x]","\frac{2 (a+b x)^6}{9 b (c (a+b x))^{3/2}}","\frac{2 (a c+b c x)^{9/2}}{9 b c^6}",1,"(2*(a + b*x)^6)/(9*b*(c*(a + b*x))^(3/2))","A",1
1448,1,25,22,0.0142816,"\int \frac{(a+b x)^5}{(a c+b c x)^{5/2}} \, dx","Integrate[(a + b*x)^5/(a*c + b*c*x)^(5/2),x]","\frac{2 (a+b x)^6}{7 b (c (a+b x))^{5/2}}","\frac{2 (a c+b c x)^{7/2}}{7 b c^6}",1,"(2*(a + b*x)^6)/(7*b*(c*(a + b*x))^(5/2))","A",1
1449,1,25,22,0.0135046,"\int \frac{(a+b x)^5}{(a c+b c x)^{7/2}} \, dx","Integrate[(a + b*x)^5/(a*c + b*c*x)^(7/2),x]","\frac{2 (a+b x)^6}{5 b (c (a+b x))^{7/2}}","\frac{2 (a c+b c x)^{5/2}}{5 b c^6}",1,"(2*(a + b*x)^6)/(5*b*(c*(a + b*x))^(7/2))","A",1
1450,1,26,22,0.0135428,"\int \frac{(a+b x)^5}{(a c+b c x)^{9/2}} \, dx","Integrate[(a + b*x)^5/(a*c + b*c*x)^(9/2),x]","\frac{2 (a+b x) \sqrt{c (a+b x)}}{3 b c^5}","\frac{2 (a c+b c x)^{3/2}}{3 b c^6}",1,"(2*(a + b*x)*Sqrt[c*(a + b*x)])/(3*b*c^5)","A",1
1451,1,24,20,0.0076337,"\int \frac{(a+b x)^5}{(a c+b c x)^{11/2}} \, dx","Integrate[(a + b*x)^5/(a*c + b*c*x)^(11/2),x]","\frac{2 (a+b x)}{b c^5 \sqrt{c (a+b x)}}","\frac{2 \sqrt{a c+b c x}}{b c^6}",1,"(2*(a + b*x))/(b*c^5*Sqrt[c*(a + b*x)])","A",1
1452,1,24,20,0.0097987,"\int \frac{(a+b x)^5}{(a c+b c x)^{13/2}} \, dx","Integrate[(a + b*x)^5/(a*c + b*c*x)^(13/2),x]","-\frac{2 (a+b x)}{b c^5 (c (a+b x))^{3/2}}","-\frac{2}{b c^6 \sqrt{a c+b c x}}",1,"(-2*(a + b*x))/(b*c^5*(c*(a + b*x))^(3/2))","A",1
1453,1,14,14,0.0027866,"\int \frac{1}{(-2+x) \sqrt{2+x}} \, dx","Integrate[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
1454,1,25,25,0.0092482,"\int \frac{1}{(2+3 x) \sqrt{1+5 x}} \, dx","Integrate[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
1455,1,104,84,0.0483383,"\int \frac{\sqrt[3]{1-x}}{1+x} \, dx","Integrate[(1 - x)^(1/3)/(1 + x),x]","3 \sqrt[3]{1-x}+\sqrt[3]{2} \log \left(\sqrt[3]{2}-\sqrt[3]{1-x}\right)-\frac{\log \left((1-x)^{2/3}+\sqrt[3]{2-2 x}+2^{2/3}\right)}{2^{2/3}}-\sqrt[3]{2} \sqrt{3} \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{1-x}+1}{\sqrt{3}}\right)","3 \sqrt[3]{1-x}+\frac{3 \log \left(\sqrt[3]{2}-\sqrt[3]{1-x}\right)}{2^{2/3}}-\frac{\log (x+1)}{2^{2/3}}-\sqrt[3]{2} \sqrt{3} \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{1-x}+1}{\sqrt{3}}\right)",1,"3*(1 - x)^(1/3) - 2^(1/3)*Sqrt[3]*ArcTan[(1 + 2^(2/3)*(1 - x)^(1/3))/Sqrt[3]] + 2^(1/3)*Log[2^(1/3) - (1 - x)^(1/3)] - Log[2^(2/3) + (2 - 2*x)^(1/3) + (1 - x)^(2/3)]/2^(2/3)","A",1
1456,1,18,27,0.0086942,"\int \sqrt[3]{3-2 x} (7+x) \, dx","Integrate[(3 - 2*x)^(1/3)*(7 + x),x]","-\frac{3}{112} (3-2 x)^{4/3} (8 x+107)","\frac{3}{28} (3-2 x)^{7/3}-\frac{51}{16} (3-2 x)^{4/3}",1,"(-3*(3 - 2*x)^(4/3)*(107 + 8*x))/112","A",1
1457,1,23,38,0.0101052,"\int \sqrt[3]{1-x} (1+x)^2 \, dx","Integrate[(1 - x)^(1/3)*(1 + x)^2,x]","-\frac{3}{70} (1-x)^{4/3} \left(7 x^2+26 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)^(4/3)*(37 + 26*x + 7*x^2))/70","A",1
1458,1,106,139,0.0760984,"\int \frac{1}{(a+b x) \sqrt[3]{c+d x}} \, dx","Integrate[1/((a + b*x)*(c + d*x)^(1/3)),x]","\frac{3 \log \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)+2 \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)-\log (a+b x)}{2 b^{2/3} \sqrt[3]{b c-a d}}","-\frac{\log (a+b x)}{2 b^{2/3} \sqrt[3]{b c-a d}}+\frac{3 \log \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{2 b^{2/3} \sqrt[3]{b c-a d}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}}+1}{\sqrt{3}}\right)}{b^{2/3} \sqrt[3]{b c-a d}}",1,"(2*Sqrt[3]*ArcTan[(1 + (2*b^(1/3)*(c + d*x)^(1/3))/(b*c - a*d)^(1/3))/Sqrt[3]] - Log[a + b*x] + 3*Log[(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(1/3)])/(2*b^(2/3)*(b*c - a*d)^(1/3))","A",1
1459,1,154,140,0.074995,"\int \frac{1}{(a+b x) (c+d x)^{2/3}} \, dx","Integrate[1/((a + b*x)*(c + d*x)^(2/3)),x]","-\frac{\log \left(\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}\right)-2 \log \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)+2 \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)}{2 \sqrt[3]{b} (b c-a d)^{2/3}}","-\frac{\log (a+b x)}{2 \sqrt[3]{b} (b c-a d)^{2/3}}+\frac{3 \log \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{2 \sqrt[3]{b} (b c-a d)^{2/3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}}+1}{\sqrt{3}}\right)}{\sqrt[3]{b} (b c-a d)^{2/3}}",1,"-1/2*(2*Sqrt[3]*ArcTan[(1 + (2*b^(1/3)*(c + d*x)^(1/3))/(b*c - a*d)^(1/3))/Sqrt[3]] - 2*Log[(b*c - a*d)^(1/3) - b^(1/3)*(c + d*x)^(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)])/(b^(1/3)*(b*c - a*d)^(2/3))","A",1
1460,1,194,230,1.4654702,"\int (a+b x)^{7/2} \sqrt{c+d x} \, dx","Integrate[(a + b*x)^(7/2)*Sqrt[c + d*x],x]","\frac{(a+b x)^{9/2} \sqrt{c+d x} \left(\frac{70 (b c-a d)^{9/2} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{d^{9/2} (a+b x)^{9/2} \sqrt{\frac{b (c+d x)}{b c-a d}}}-\frac{70 (b c-a d)^4}{d^4 (a+b x)^4}+\frac{140 (b c-a d)^3}{3 d^3 (a+b x)^3}-\frac{112 (b c-a d)^2}{3 d^2 (a+b x)^2}+\frac{32 b c-32 a d}{a d+b d x}+256\right)}{1280 b}","\frac{7 (b c-a d)^5 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{128 b^{3/2} d^{9/2}}-\frac{7 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^4}{128 b d^4}+\frac{7 (a+b x)^{3/2} \sqrt{c+d x} (b c-a d)^3}{192 b d^3}-\frac{7 (a+b x)^{5/2} \sqrt{c+d x} (b c-a d)^2}{240 b d^2}+\frac{(a+b x)^{7/2} \sqrt{c+d x} (b c-a d)}{40 b d}+\frac{(a+b x)^{9/2} \sqrt{c+d x}}{5 b}",1,"((a + b*x)^(9/2)*Sqrt[c + d*x]*(256 - (70*(b*c - a*d)^4)/(d^4*(a + b*x)^4) + (140*(b*c - a*d)^3)/(3*d^3*(a + b*x)^3) - (112*(b*c - a*d)^2)/(3*d^2*(a + b*x)^2) + (32*b*c - 32*a*d)/(a*d + b*d*x) + (70*(b*c - a*d)^(9/2)*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(d^(9/2)*(a + b*x)^(9/2)*Sqrt[(b*(c + d*x))/(b*c - a*d)])))/(1280*b)","A",1
1461,1,190,192,0.5978718,"\int (a+b x)^{5/2} \sqrt{c+d x} \, dx","Integrate[(a + b*x)^(5/2)*Sqrt[c + d*x],x]","\frac{b \sqrt{d} \sqrt{a+b x} (c+d x) \left(15 a^3 d^3+a^2 b d^2 (73 c+118 d x)+a b^2 d \left(-55 c^2+36 c d x+136 d^2 x^2\right)+b^3 \left(15 c^3-10 c^2 d x+8 c d^2 x^2+48 d^3 x^3\right)\right)-15 (b c-a d)^{9/2} \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{192 b^2 d^{7/2} \sqrt{c+d x}}","-\frac{5 (b c-a d)^4 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{64 b^{3/2} d^{7/2}}+\frac{5 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^3}{64 b d^3}-\frac{5 (a+b x)^{3/2} \sqrt{c+d x} (b c-a d)^2}{96 b d^2}+\frac{(a+b x)^{5/2} \sqrt{c+d x} (b c-a d)}{24 b d}+\frac{(a+b x)^{7/2} \sqrt{c+d x}}{4 b}",1,"(b*Sqrt[d]*Sqrt[a + b*x]*(c + d*x)*(15*a^3*d^3 + a^2*b*d^2*(73*c + 118*d*x) + a*b^2*d*(-55*c^2 + 36*c*d*x + 136*d^2*x^2) + b^3*(15*c^3 - 10*c^2*d*x + 8*c*d^2*x^2 + 48*d^3*x^3)) - 15*(b*c - a*d)^(9/2)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(192*b^2*d^(7/2)*Sqrt[c + d*x])","A",1
1462,1,151,154,0.434628,"\int (a+b x)^{3/2} \sqrt{c+d x} \, dx","Integrate[(a + b*x)^(3/2)*Sqrt[c + d*x],x]","\frac{b \sqrt{d} \sqrt{a+b x} (c+d x) \left(3 a^2 d^2+2 a b d (4 c+7 d x)+b^2 \left(-3 c^2+2 c d x+8 d^2 x^2\right)\right)+3 (b c-a d)^{7/2} \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{24 b^2 d^{5/2} \sqrt{c+d x}}","\frac{(b c-a d)^3 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{8 b^{3/2} d^{5/2}}-\frac{\sqrt{a+b x} \sqrt{c+d x} (b c-a d)^2}{8 b d^2}+\frac{(a+b x)^{3/2} \sqrt{c+d x} (b c-a d)}{12 b d}+\frac{(a+b x)^{5/2} \sqrt{c+d x}}{3 b}",1,"(b*Sqrt[d]*Sqrt[a + b*x]*(c + d*x)*(3*a^2*d^2 + 2*a*b*d*(4*c + 7*d*x) + b^2*(-3*c^2 + 2*c*d*x + 8*d^2*x^2)) + 3*(b*c - a*d)^(7/2)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(24*b^2*d^(5/2)*Sqrt[c + d*x])","A",1
1463,1,118,116,0.2772907,"\int \sqrt{a+b x} \sqrt{c+d x} \, dx","Integrate[Sqrt[a + b*x]*Sqrt[c + d*x],x]","\frac{b \sqrt{d} \sqrt{a+b x} (c+d x) (a d+b (c+2 d x))-(b c-a d)^{5/2} \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{4 b^2 d^{3/2} \sqrt{c+d x}}","-\frac{(b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{4 b^{3/2} d^{3/2}}+\frac{\sqrt{a+b x} \sqrt{c+d x} (b c-a d)}{4 b d}+\frac{(a+b x)^{3/2} \sqrt{c+d x}}{2 b}",1,"(b*Sqrt[d]*Sqrt[a + b*x]*(c + d*x)*(a*d + b*(c + 2*d*x)) - (b*c - a*d)^(5/2)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(4*b^2*d^(3/2)*Sqrt[c + d*x])","A",1
1464,1,117,72,0.1042552,"\int \frac{\sqrt{c+d x}}{\sqrt{a+b x}} \, dx","Integrate[Sqrt[c + d*x]/Sqrt[a + b*x],x]","\frac{\sqrt{c+d x} \left(\sqrt{d} \sqrt{a+b x} \sqrt{\frac{b (c+d x)}{b c-a d}}+\sqrt{b c-a d} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)\right)}{b \sqrt{d} \sqrt{\frac{b (c+d x)}{b c-a d}}}","\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[c + d*x]*(Sqrt[d]*Sqrt[a + b*x]*Sqrt[(b*(c + d*x))/(b*c - a*d)] + Sqrt[b*c - a*d]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]]))/(b*Sqrt[d]*Sqrt[(b*(c + d*x))/(b*c - a*d)])","A",1
1465,1,99,66,0.2268748,"\int \frac{\sqrt{c+d x}}{(a+b x)^{3/2}} \, dx","Integrate[Sqrt[c + d*x]/(a + b*x)^(3/2),x]","\frac{2 \left(\sqrt{d} \sqrt{b c-a d} \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)-\frac{b (c+d x)}{\sqrt{a+b x}}\right)}{b^2 \sqrt{c+d x}}","\frac{2 \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{b^{3/2}}-\frac{2 \sqrt{c+d x}}{b \sqrt{a+b x}}",1,"(2*(-((b*(c + d*x))/Sqrt[a + b*x]) + Sqrt[d]*Sqrt[b*c - a*d]*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]]))/(b^2*Sqrt[c + d*x])","A",1
1466,1,32,32,0.0116316,"\int \frac{\sqrt{c+d x}}{(a+b x)^{5/2}} \, dx","Integrate[Sqrt[c + d*x]/(a + b*x)^(5/2),x]","-\frac{2 (c+d x)^{3/2}}{3 (a+b x)^{3/2} (b c-a d)}","-\frac{2 (c+d x)^{3/2}}{3 (a+b x)^{3/2} (b c-a d)}",1,"(-2*(c + d*x)^(3/2))/(3*(b*c - a*d)*(a + b*x)^(3/2))","A",1
1467,1,46,66,0.0204099,"\int \frac{\sqrt{c+d x}}{(a+b x)^{7/2}} \, dx","Integrate[Sqrt[c + d*x]/(a + b*x)^(7/2),x]","\frac{2 (c+d x)^{3/2} (5 a d-3 b c+2 b d x)}{15 (a+b x)^{5/2} (b c-a d)^2}","\frac{4 d (c+d x)^{3/2}}{15 (a+b x)^{3/2} (b c-a d)^2}-\frac{2 (c+d x)^{3/2}}{5 (a+b x)^{5/2} (b c-a d)}",1,"(2*(c + d*x)^(3/2)*(-3*b*c + 5*a*d + 2*b*d*x))/(15*(b*c - a*d)^2*(a + b*x)^(5/2))","A",1
1468,1,77,101,0.039138,"\int \frac{\sqrt{c+d x}}{(a+b x)^{9/2}} \, dx","Integrate[Sqrt[c + d*x]/(a + b*x)^(9/2),x]","-\frac{2 (c+d x)^{3/2} \left(35 a^2 d^2+14 a b d (2 d x-3 c)+b^2 \left(15 c^2-12 c d x+8 d^2 x^2\right)\right)}{105 (a+b x)^{7/2} (b c-a d)^3}","-\frac{16 d^2 (c+d x)^{3/2}}{105 (a+b x)^{3/2} (b c-a d)^3}+\frac{8 d (c+d x)^{3/2}}{35 (a+b x)^{5/2} (b c-a d)^2}-\frac{2 (c+d x)^{3/2}}{7 (a+b x)^{7/2} (b c-a d)}",1,"(-2*(c + d*x)^(3/2)*(35*a^2*d^2 + 14*a*b*d*(-3*c + 2*d*x) + b^2*(15*c^2 - 12*c*d*x + 8*d^2*x^2)))/(105*(b*c - a*d)^3*(a + b*x)^(7/2))","A",1
1469,1,118,136,0.0544998,"\int \frac{\sqrt{c+d x}}{(a+b x)^{11/2}} \, dx","Integrate[Sqrt[c + d*x]/(a + b*x)^(11/2),x]","\frac{2 (c+d x)^{3/2} \left(105 a^3 d^3+63 a^2 b d^2 (2 d x-3 c)+9 a b^2 d \left(15 c^2-12 c d x+8 d^2 x^2\right)+b^3 \left(-35 c^3+30 c^2 d x-24 c d^2 x^2+16 d^3 x^3\right)\right)}{315 (a+b x)^{9/2} (b c-a d)^4}","\frac{32 d^3 (c+d x)^{3/2}}{315 (a+b x)^{3/2} (b c-a d)^4}-\frac{16 d^2 (c+d x)^{3/2}}{105 (a+b x)^{5/2} (b c-a d)^3}+\frac{4 d (c+d x)^{3/2}}{21 (a+b x)^{7/2} (b c-a d)^2}-\frac{2 (c+d x)^{3/2}}{9 (a+b x)^{9/2} (b c-a d)}",1,"(2*(c + d*x)^(3/2)*(105*a^3*d^3 + 63*a^2*b*d^2*(-3*c + 2*d*x) + 9*a*b^2*d*(15*c^2 - 12*c*d*x + 8*d^2*x^2) + b^3*(-35*c^3 + 30*c^2*d*x - 24*c*d^2*x^2 + 16*d^3*x^3)))/(315*(b*c - a*d)^4*(a + b*x)^(9/2))","A",1
1470,1,170,171,0.0774738,"\int \frac{\sqrt{c+d x}}{(a+b x)^{13/2}} \, dx","Integrate[Sqrt[c + d*x]/(a + b*x)^(13/2),x]","-\frac{2 (c+d x)^{3/2} \left(1155 a^4 d^4+924 a^3 b d^3 (2 d x-3 c)+198 a^2 b^2 d^2 \left(15 c^2-12 c d x+8 d^2 x^2\right)+44 a b^3 d \left(-35 c^3+30 c^2 d x-24 c d^2 x^2+16 d^3 x^3\right)+b^4 \left(315 c^4-280 c^3 d x+240 c^2 d^2 x^2-192 c d^3 x^3+128 d^4 x^4\right)\right)}{3465 (a+b x)^{11/2} (b c-a d)^5}","-\frac{256 d^4 (c+d x)^{3/2}}{3465 (a+b x)^{3/2} (b c-a d)^5}+\frac{128 d^3 (c+d x)^{3/2}}{1155 (a+b x)^{5/2} (b c-a d)^4}-\frac{32 d^2 (c+d x)^{3/2}}{231 (a+b x)^{7/2} (b c-a d)^3}+\frac{16 d (c+d x)^{3/2}}{99 (a+b x)^{9/2} (b c-a d)^2}-\frac{2 (c+d x)^{3/2}}{11 (a+b x)^{11/2} (b c-a d)}",1,"(-2*(c + d*x)^(3/2)*(1155*a^4*d^4 + 924*a^3*b*d^3*(-3*c + 2*d*x) + 198*a^2*b^2*d^2*(15*c^2 - 12*c*d*x + 8*d^2*x^2) + 44*a*b^3*d*(-35*c^3 + 30*c^2*d*x - 24*c*d^2*x^2 + 16*d^3*x^3) + b^4*(315*c^4 - 280*c^3*d*x + 240*c^2*d^2*x^2 - 192*c*d^3*x^3 + 128*d^4*x^4)))/(3465*(b*c - a*d)^5*(a + b*x)^(11/2))","A",1
1471,1,187,227,1.7804949,"\int (a+b x)^{5/2} (c+d x)^{3/2} \, dx","Integrate[(a + b*x)^(5/2)*(c + d*x)^(3/2),x]","\frac{(a+b x)^{7/2} \sqrt{c+d x} \left(-\frac{15 (b c-a d)^{9/2} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{d^{7/2} (a+b x)^{7/2} \sqrt{\frac{b (c+d x)}{b c-a d}}}+\frac{15 (b c-a d)^4}{d^3 (a+b x)^3}+\frac{10 (a d-b c)^3}{d^2 (a+b x)^2}+\frac{8 (b c-a d)^2}{d (a+b x)}+48 (b c-a d)+128 b (c+d x)\right)}{640 b^2}","-\frac{3 (b c-a d)^5 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{128 b^{5/2} d^{7/2}}+\frac{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,"((a + b*x)^(7/2)*Sqrt[c + d*x]*(48*(b*c - a*d) + (15*(b*c - a*d)^4)/(d^3*(a + b*x)^3) + (10*(-(b*c) + a*d)^3)/(d^2*(a + b*x)^2) + (8*(b*c - a*d)^2)/(d*(a + b*x)) + 128*b*(c + d*x) - (15*(b*c - a*d)^(9/2)*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(d^(7/2)*(a + b*x)^(7/2)*Sqrt[(b*(c + d*x))/(b*c - a*d)])))/(640*b^2)","A",1
1472,1,193,189,0.5666191,"\int (a+b x)^{3/2} (c+d x)^{3/2} \, dx","Integrate[(a + b*x)^(3/2)*(c + d*x)^(3/2),x]","\frac{3 (b c-a d)^{9/2} \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)-b \sqrt{d} \sqrt{a+b x} (c+d x) \left(3 a^3 d^3-a^2 b d^2 (11 c+2 d x)-a b^2 d \left(11 c^2+44 c d x+24 d^2 x^2\right)+b^3 \left(3 c^3-2 c^2 d x-24 c d^2 x^2-16 d^3 x^3\right)\right)}{64 b^3 d^{5/2} \sqrt{c+d x}}","\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,"(-(b*Sqrt[d]*Sqrt[a + b*x]*(c + d*x)*(3*a^3*d^3 - a^2*b*d^2*(11*c + 2*d*x) - a*b^2*d*(11*c^2 + 44*c*d*x + 24*d^2*x^2) + b^3*(3*c^3 - 2*c^2*d*x - 24*c*d^2*x^2 - 16*d^3*x^3))) + 3*(b*c - a*d)^(9/2)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(64*b^3*d^(5/2)*Sqrt[c + d*x])","A",1
1473,1,152,151,0.4447859,"\int \sqrt{a+b x} (c+d x)^{3/2} \, dx","Integrate[Sqrt[a + b*x]*(c + d*x)^(3/2),x]","\frac{-b \sqrt{d} \sqrt{a+b x} (c+d x) \left(3 a^2 d^2-2 a b d (4 c+d x)-\left(b^2 \left(3 c^2+14 c d x+8 d^2 x^2\right)\right)\right)-3 (b c-a d)^{7/2} \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{24 b^3 d^{3/2} \sqrt{c+d x}}","-\frac{(b c-a d)^3 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{8 b^{5/2} d^{3/2}}+\frac{\sqrt{a+b x} \sqrt{c+d x} (b c-a d)^2}{8 b^2 d}+\frac{(a+b x)^{3/2} \sqrt{c+d x} (b c-a d)}{4 b^2}+\frac{(a+b x)^{3/2} (c+d x)^{3/2}}{3 b}",1,"(-(b*Sqrt[d]*Sqrt[a + b*x]*(c + d*x)*(3*a^2*d^2 - 2*a*b*d*(4*c + d*x) - b^2*(3*c^2 + 14*c*d*x + 8*d^2*x^2))) - 3*(b*c - a*d)^(7/2)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(24*b^3*d^(3/2)*Sqrt[c + d*x])","A",1
1474,1,109,113,0.2911015,"\int \frac{(c+d x)^{3/2}}{\sqrt{a+b x}} \, dx","Integrate[(c + d*x)^(3/2)/Sqrt[a + b*x],x]","\frac{\sqrt{c+d x} \left(\sqrt{a+b x} (-3 a d+5 b c+2 b d x)+\frac{3 (b c-a d)^{3/2} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{\sqrt{d} \sqrt{\frac{b (c+d x)}{b c-a d}}}\right)}{4 b^2}","\frac{3 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{4 b^{5/2} \sqrt{d}}+\frac{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[c + d*x]*(Sqrt[a + b*x]*(5*b*c - 3*a*d + 2*b*d*x) + (3*(b*c - a*d)^(3/2)*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(Sqrt[d]*Sqrt[(b*(c + d*x))/(b*c - a*d)])))/(4*b^2)","A",1
1475,1,71,98,0.0527497,"\int \frac{(c+d x)^{3/2}}{(a+b x)^{3/2}} \, dx","Integrate[(c + d*x)^(3/2)/(a + b*x)^(3/2),x]","-\frac{2 (c+d x)^{3/2} \, _2F_1\left(-\frac{3}{2},-\frac{1}{2};\frac{1}{2};\frac{d (a+b x)}{a d-b c}\right)}{b \sqrt{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{3/2}}","\frac{3 \sqrt{d} (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{b^{5/2}}+\frac{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,"(-2*(c + d*x)^(3/2)*Hypergeometric2F1[-3/2, -1/2, 1/2, (d*(a + b*x))/(-(b*c) + a*d)])/(b*Sqrt[a + b*x]*((b*(c + d*x))/(b*c - a*d))^(3/2))","C",1
1476,1,73,92,0.0498731,"\int \frac{(c+d x)^{3/2}}{(a+b x)^{5/2}} \, dx","Integrate[(c + d*x)^(3/2)/(a + b*x)^(5/2),x]","-\frac{2 (c+d x)^{3/2} \, _2F_1\left(-\frac{3}{2},-\frac{3}{2};-\frac{1}{2};\frac{d (a+b x)}{a d-b c}\right)}{3 b (a+b x)^{3/2} \left(\frac{b (c+d x)}{b c-a d}\right)^{3/2}}","\frac{2 d^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{b^{5/2}}-\frac{2 d \sqrt{c+d x}}{b^2 \sqrt{a+b x}}-\frac{2 (c+d x)^{3/2}}{3 b (a+b x)^{3/2}}",1,"(-2*(c + d*x)^(3/2)*Hypergeometric2F1[-3/2, -3/2, -1/2, (d*(a + b*x))/(-(b*c) + a*d)])/(3*b*(a + b*x)^(3/2)*((b*(c + d*x))/(b*c - a*d))^(3/2))","C",1
1477,1,32,32,0.0153149,"\int \frac{(c+d x)^{3/2}}{(a+b x)^{7/2}} \, dx","Integrate[(c + d*x)^(3/2)/(a + b*x)^(7/2),x]","-\frac{2 (c+d x)^{5/2}}{5 (a+b x)^{5/2} (b c-a d)}","-\frac{2 (c+d x)^{5/2}}{5 (a+b x)^{5/2} (b c-a d)}",1,"(-2*(c + d*x)^(5/2))/(5*(b*c - a*d)*(a + b*x)^(5/2))","A",1
1478,1,46,66,0.0245254,"\int \frac{(c+d x)^{3/2}}{(a+b x)^{9/2}} \, dx","Integrate[(c + d*x)^(3/2)/(a + b*x)^(9/2),x]","\frac{2 (c+d x)^{5/2} (7 a d-5 b c+2 b d x)}{35 (a+b x)^{7/2} (b c-a d)^2}","\frac{4 d (c+d x)^{5/2}}{35 (a+b x)^{5/2} (b c-a d)^2}-\frac{2 (c+d x)^{5/2}}{7 (a+b x)^{7/2} (b c-a d)}",1,"(2*(c + d*x)^(5/2)*(-5*b*c + 7*a*d + 2*b*d*x))/(35*(b*c - a*d)^2*(a + b*x)^(7/2))","A",1
1479,1,77,101,0.0453006,"\int \frac{(c+d x)^{3/2}}{(a+b x)^{11/2}} \, dx","Integrate[(c + d*x)^(3/2)/(a + b*x)^(11/2),x]","-\frac{2 (c+d x)^{5/2} \left(63 a^2 d^2+18 a b d (2 d x-5 c)+b^2 \left(35 c^2-20 c d x+8 d^2 x^2\right)\right)}{315 (a+b x)^{9/2} (b c-a d)^3}","-\frac{16 d^2 (c+d x)^{5/2}}{315 (a+b x)^{5/2} (b c-a d)^3}+\frac{8 d (c+d x)^{5/2}}{63 (a+b x)^{7/2} (b c-a d)^2}-\frac{2 (c+d x)^{5/2}}{9 (a+b x)^{9/2} (b c-a d)}",1,"(-2*(c + d*x)^(5/2)*(63*a^2*d^2 + 18*a*b*d*(-5*c + 2*d*x) + b^2*(35*c^2 - 20*c*d*x + 8*d^2*x^2)))/(315*(b*c - a*d)^3*(a + b*x)^(9/2))","A",1
1480,1,118,136,0.0637749,"\int \frac{(c+d x)^{3/2}}{(a+b x)^{13/2}} \, dx","Integrate[(c + d*x)^(3/2)/(a + b*x)^(13/2),x]","\frac{2 (c+d x)^{5/2} \left(231 a^3 d^3+99 a^2 b d^2 (2 d x-5 c)+11 a b^2 d \left(35 c^2-20 c d x+8 d^2 x^2\right)+b^3 \left(-105 c^3+70 c^2 d x-40 c d^2 x^2+16 d^3 x^3\right)\right)}{1155 (a+b x)^{11/2} (b c-a d)^4}","\frac{32 d^3 (c+d x)^{5/2}}{1155 (a+b x)^{5/2} (b c-a d)^4}-\frac{16 d^2 (c+d x)^{5/2}}{231 (a+b x)^{7/2} (b c-a d)^3}+\frac{4 d (c+d x)^{5/2}}{33 (a+b x)^{9/2} (b c-a d)^2}-\frac{2 (c+d x)^{5/2}}{11 (a+b x)^{11/2} (b c-a d)}",1,"(2*(c + d*x)^(5/2)*(231*a^3*d^3 + 99*a^2*b*d^2*(-5*c + 2*d*x) + 11*a*b^2*d*(35*c^2 - 20*c*d*x + 8*d^2*x^2) + b^3*(-105*c^3 + 70*c^2*d*x - 40*c*d^2*x^2 + 16*d^3*x^3)))/(1155*(b*c - a*d)^4*(a + b*x)^(11/2))","A",1
1481,1,209,262,2.5291551,"\int (a+b x)^{5/2} (c+d x)^{5/2} \, dx","Integrate[(a + b*x)^(5/2)*(c + d*x)^(5/2),x]","\frac{(a+b x)^{7/2} \sqrt{c+d x} \left(-\frac{15 (b c-a d)^{11/2} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{d^{7/2} (a+b x)^{7/2} \sqrt{\frac{b (c+d x)}{b c-a d}}}+\frac{15 (b c-a d)^5}{d^3 (a+b x)^3}-\frac{10 (b c-a d)^4}{d^2 (a+b x)^2}+\frac{8 (b c-a d)^3}{d (a+b x)}+128 b (c+d x) (b c-a d)+48 (b c-a d)^2+256 b^2 (c+d x)^2\right)}{1536 b^3}","-\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,"((a + b*x)^(7/2)*Sqrt[c + d*x]*(48*(b*c - a*d)^2 + (15*(b*c - a*d)^5)/(d^3*(a + b*x)^3) - (10*(b*c - a*d)^4)/(d^2*(a + b*x)^2) + (8*(b*c - a*d)^3)/(d*(a + b*x)) + 128*b*(b*c - a*d)*(c + d*x) + 256*b^2*(c + d*x)^2 - (15*(b*c - a*d)^(11/2)*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(d^(7/2)*(a + b*x)^(7/2)*Sqrt[(b*(c + d*x))/(b*c - a*d)])))/(1536*b^3)","A",1
1482,1,187,224,1.4684085,"\int (a+b x)^{3/2} (c+d x)^{5/2} \, dx","Integrate[(a + b*x)^(3/2)*(c + d*x)^(5/2),x]","\frac{(a+b x)^{5/2} \sqrt{c+d x} \left(\frac{15 (b c-a d)^{9/2} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{d^{5/2} (a+b x)^{5/2} \sqrt{\frac{b (c+d x)}{b c-a d}}}-\frac{15 (b c-a d)^4}{d^2 (a+b x)^2}+\frac{10 (b c-a d)^3}{d (a+b x)}+80 b (c+d x) (b c-a d)+40 (b c-a d)^2+128 b^2 (c+d x)^2\right)}{640 b^3}","\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,"((a + b*x)^(5/2)*Sqrt[c + d*x]*(40*(b*c - a*d)^2 - (15*(b*c - a*d)^4)/(d^2*(a + b*x)^2) + (10*(b*c - a*d)^3)/(d*(a + b*x)) + 80*b*(b*c - a*d)*(c + d*x) + 128*b^2*(c + d*x)^2 + (15*(b*c - a*d)^(9/2)*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(d^(5/2)*(a + b*x)^(5/2)*Sqrt[(b*(c + d*x))/(b*c - a*d)])))/(640*b^3)","A",1
1483,1,191,186,0.5795535,"\int \sqrt{a+b x} (c+d x)^{5/2} \, dx","Integrate[Sqrt[a + b*x]*(c + d*x)^(5/2),x]","\frac{b \sqrt{d} \sqrt{a+b x} (c+d x) \left(15 a^3 d^3-5 a^2 b d^2 (11 c+2 d x)+a b^2 d \left(73 c^2+36 c d x+8 d^2 x^2\right)+b^3 \left(15 c^3+118 c^2 d x+136 c d^2 x^2+48 d^3 x^3\right)\right)-15 (b c-a d)^{9/2} \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{192 b^4 d^{3/2} \sqrt{c+d x}}","-\frac{5 (b c-a d)^4 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{64 b^{7/2} d^{3/2}}+\frac{5 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^3}{64 b^3 d}+\frac{5 (a+b x)^{3/2} \sqrt{c+d x} (b c-a d)^2}{32 b^3}+\frac{5 (a+b x)^{3/2} (c+d x)^{3/2} (b c-a d)}{24 b^2}+\frac{(a+b x)^{3/2} (c+d x)^{5/2}}{4 b}",1,"(b*Sqrt[d]*Sqrt[a + b*x]*(c + d*x)*(15*a^3*d^3 - 5*a^2*b*d^2*(11*c + 2*d*x) + a*b^2*d*(73*c^2 + 36*c*d*x + 8*d^2*x^2) + b^3*(15*c^3 + 118*c^2*d*x + 136*c*d^2*x^2 + 48*d^3*x^3)) - 15*(b*c - a*d)^(9/2)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(192*b^4*d^(3/2)*Sqrt[c + d*x])","A",1
1484,1,139,148,0.406746,"\int \frac{(c+d x)^{5/2}}{\sqrt{a+b x}} \, dx","Integrate[(c + d*x)^(5/2)/Sqrt[a + b*x],x]","\frac{\sqrt{c+d x} \left(\sqrt{a+b x} \left(15 a^2 d^2-10 a b d (4 c+d x)+b^2 \left(33 c^2+26 c d x+8 d^2 x^2\right)\right)+\frac{15 (b c-a d)^{5/2} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{\sqrt{d} \sqrt{\frac{b (c+d x)}{b c-a d}}}\right)}{24 b^3}","\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,"(Sqrt[c + d*x]*(Sqrt[a + b*x]*(15*a^2*d^2 - 10*a*b*d*(4*c + d*x) + b^2*(33*c^2 + 26*c*d*x + 8*d^2*x^2)) + (15*(b*c - a*d)^(5/2)*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(Sqrt[d]*Sqrt[(b*(c + d*x))/(b*c - a*d)])))/(24*b^3)","A",1
1485,1,71,138,0.0679304,"\int \frac{(c+d x)^{5/2}}{(a+b x)^{3/2}} \, dx","Integrate[(c + d*x)^(5/2)/(a + b*x)^(3/2),x]","-\frac{2 (c+d x)^{5/2} \, _2F_1\left(-\frac{5}{2},-\frac{1}{2};\frac{1}{2};\frac{d (a+b x)}{a d-b c}\right)}{b \sqrt{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/2}}","\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,"(-2*(c + d*x)^(5/2)*Hypergeometric2F1[-5/2, -1/2, 1/2, (d*(a + b*x))/(-(b*c) + a*d)])/(b*Sqrt[a + b*x]*((b*(c + d*x))/(b*c - a*d))^(5/2))","C",1
1486,1,73,128,0.0616215,"\int \frac{(c+d x)^{5/2}}{(a+b x)^{5/2}} \, dx","Integrate[(c + d*x)^(5/2)/(a + b*x)^(5/2),x]","-\frac{2 (c+d x)^{5/2} \, _2F_1\left(-\frac{5}{2},-\frac{3}{2};-\frac{1}{2};\frac{d (a+b x)}{a d-b c}\right)}{3 b (a+b x)^{3/2} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/2}}","\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,"(-2*(c + d*x)^(5/2)*Hypergeometric2F1[-5/2, -3/2, -1/2, (d*(a + b*x))/(-(b*c) + a*d)])/(3*b*(a + b*x)^(3/2)*((b*(c + d*x))/(b*c - a*d))^(5/2))","C",1
1487,1,73,120,0.0704562,"\int \frac{(c+d x)^{5/2}}{(a+b x)^{7/2}} \, dx","Integrate[(c + d*x)^(5/2)/(a + b*x)^(7/2),x]","-\frac{2 (c+d x)^{5/2} \, _2F_1\left(-\frac{5}{2},-\frac{5}{2};-\frac{3}{2};\frac{d (a+b x)}{a d-b c}\right)}{5 b (a+b x)^{5/2} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/2}}","\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,"(-2*(c + d*x)^(5/2)*Hypergeometric2F1[-5/2, -5/2, -3/2, (d*(a + b*x))/(-(b*c) + a*d)])/(5*b*(a + b*x)^(5/2)*((b*(c + d*x))/(b*c - a*d))^(5/2))","C",1
1488,1,32,32,0.0184527,"\int \frac{(c+d x)^{5/2}}{(a+b x)^{9/2}} \, dx","Integrate[(c + d*x)^(5/2)/(a + b*x)^(9/2),x]","-\frac{2 (c+d x)^{7/2}}{7 (a+b x)^{7/2} (b c-a d)}","-\frac{2 (c+d x)^{7/2}}{7 (a+b x)^{7/2} (b c-a d)}",1,"(-2*(c + d*x)^(7/2))/(7*(b*c - a*d)*(a + b*x)^(7/2))","A",1
1489,1,46,66,0.0313245,"\int \frac{(c+d x)^{5/2}}{(a+b x)^{11/2}} \, dx","Integrate[(c + d*x)^(5/2)/(a + b*x)^(11/2),x]","\frac{2 (c+d x)^{7/2} (9 a d-7 b c+2 b d x)}{63 (a+b x)^{9/2} (b c-a d)^2}","\frac{4 d (c+d x)^{7/2}}{63 (a+b x)^{7/2} (b c-a d)^2}-\frac{2 (c+d x)^{7/2}}{9 (a+b x)^{9/2} (b c-a d)}",1,"(2*(c + d*x)^(7/2)*(-7*b*c + 9*a*d + 2*b*d*x))/(63*(b*c - a*d)^2*(a + b*x)^(9/2))","A",1
1490,1,77,101,0.0519682,"\int \frac{(c+d x)^{5/2}}{(a+b x)^{13/2}} \, dx","Integrate[(c + d*x)^(5/2)/(a + b*x)^(13/2),x]","-\frac{2 (c+d x)^{7/2} \left(99 a^2 d^2+22 a b d (2 d x-7 c)+b^2 \left(63 c^2-28 c d x+8 d^2 x^2\right)\right)}{693 (a+b x)^{11/2} (b c-a d)^3}","-\frac{16 d^2 (c+d x)^{7/2}}{693 (a+b x)^{7/2} (b c-a d)^3}+\frac{8 d (c+d x)^{7/2}}{99 (a+b x)^{9/2} (b c-a d)^2}-\frac{2 (c+d x)^{7/2}}{11 (a+b x)^{11/2} (b c-a d)}",1,"(-2*(c + d*x)^(7/2)*(99*a^2*d^2 + 22*a*b*d*(-7*c + 2*d*x) + b^2*(63*c^2 - 28*c*d*x + 8*d^2*x^2)))/(693*(b*c - a*d)^3*(a + b*x)^(11/2))","A",1
1491,1,118,136,0.0744638,"\int \frac{(c+d x)^{5/2}}{(a+b x)^{15/2}} \, dx","Integrate[(c + d*x)^(5/2)/(a + b*x)^(15/2),x]","\frac{2 (c+d x)^{7/2} \left(429 a^3 d^3+143 a^2 b d^2 (2 d x-7 c)+13 a b^2 d \left(63 c^2-28 c d x+8 d^2 x^2\right)+b^3 \left(-231 c^3+126 c^2 d x-56 c d^2 x^2+16 d^3 x^3\right)\right)}{3003 (a+b x)^{13/2} (b c-a d)^4}","\frac{32 d^3 (c+d x)^{7/2}}{3003 (a+b x)^{7/2} (b c-a d)^4}-\frac{16 d^2 (c+d x)^{7/2}}{429 (a+b x)^{9/2} (b c-a d)^3}+\frac{12 d (c+d x)^{7/2}}{143 (a+b x)^{11/2} (b c-a d)^2}-\frac{2 (c+d x)^{7/2}}{13 (a+b x)^{13/2} (b c-a d)}",1,"(2*(c + d*x)^(7/2)*(429*a^3*d^3 + 143*a^2*b*d^2*(-7*c + 2*d*x) + 13*a*b^2*d*(63*c^2 - 28*c*d*x + 8*d^2*x^2) + b^3*(-231*c^3 + 126*c^2*d*x - 56*c*d^2*x^2 + 16*d^3*x^3)))/(3003*(b*c - a*d)^4*(a + b*x)^(13/2))","A",1
1492,1,189,183,0.6555087,"\int \frac{(a+b x)^{7/2}}{\sqrt{c+d x}} \, dx","Integrate[(a + b*x)^(7/2)/Sqrt[c + d*x],x]","\frac{\sqrt{d} \sqrt{a+b x} (c+d x) \left(279 a^3 d^3+a^2 b d^2 (326 d x-511 c)+a b^2 d \left(385 c^2-252 c d x+200 d^2 x^2\right)+b^3 \left(-105 c^3+70 c^2 d x-56 c d^2 x^2+48 d^3 x^3\right)\right)+\frac{105 (b c-a d)^{9/2} \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{b}}{192 d^{9/2} \sqrt{c+d x}}","\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,"(Sqrt[d]*Sqrt[a + b*x]*(c + d*x)*(279*a^3*d^3 + a^2*b*d^2*(-511*c + 326*d*x) + a*b^2*d*(385*c^2 - 252*c*d*x + 200*d^2*x^2) + b^3*(-105*c^3 + 70*c^2*d*x - 56*c*d^2*x^2 + 48*d^3*x^3)) + (105*(b*c - a*d)^(9/2)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/b)/(192*d^(9/2)*Sqrt[c + d*x])","A",1
1493,1,150,148,0.5238783,"\int \frac{(a+b x)^{5/2}}{\sqrt{c+d x}} \, dx","Integrate[(a + b*x)^(5/2)/Sqrt[c + d*x],x]","\frac{\sqrt{d} \sqrt{a+b x} (c+d x) \left(33 a^2 d^2+2 a b d (13 d x-20 c)+b^2 \left(15 c^2-10 c d x+8 d^2 x^2\right)\right)-\frac{15 (b c-a d)^{7/2} \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{b}}{24 d^{7/2} \sqrt{c+d x}}","-\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,"(Sqrt[d]*Sqrt[a + b*x]*(c + d*x)*(33*a^2*d^2 + 2*a*b*d*(-20*c + 13*d*x) + b^2*(15*c^2 - 10*c*d*x + 8*d^2*x^2)) - (15*(b*c - a*d)^(7/2)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/b)/(24*d^(7/2)*Sqrt[c + d*x])","A",1
1494,1,119,113,0.3650239,"\int \frac{(a+b x)^{3/2}}{\sqrt{c+d x}} \, dx","Integrate[(a + b*x)^(3/2)/Sqrt[c + d*x],x]","\frac{\sqrt{d} \sqrt{a+b x} (c+d x) (5 a d-3 b c+2 b d x)+\frac{3 (b c-a d)^{5/2} \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{b}}{4 d^{5/2} \sqrt{c+d x}}","\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,"(Sqrt[d]*Sqrt[a + b*x]*(c + d*x)*(-3*b*c + 5*a*d + 2*b*d*x) + (3*(b*c - a*d)^(5/2)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/b)/(4*d^(5/2)*Sqrt[c + d*x])","A",1
1495,1,103,73,0.2678659,"\int \frac{\sqrt{a+b x}}{\sqrt{c+d x}} \, dx","Integrate[Sqrt[a + b*x]/Sqrt[c + d*x],x]","\frac{b \sqrt{d} \sqrt{a+b x} (c+d x)-(b c-a d)^{3/2} \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{b d^{3/2} \sqrt{c+d x}}","\frac{\sqrt{a+b x} \sqrt{c+d x}}{d}-\frac{(b c-a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{\sqrt{b} d^{3/2}}",1,"(b*Sqrt[d]*Sqrt[a + b*x]*(c + d*x) - (b*c - a*d)^(3/2)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(b*d^(3/2)*Sqrt[c + d*x])","A",1
1496,1,77,42,0.0654231,"\int \frac{1}{\sqrt{a+b x} \sqrt{c+d x}} \, dx","Integrate[1/(Sqrt[a + b*x]*Sqrt[c + d*x]),x]","\frac{2 \sqrt{c+d x} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{\sqrt{d} \sqrt{b c-a d} \sqrt{\frac{b (c+d x)}{b c-a d}}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{\sqrt{b} \sqrt{d}}",1,"(2*Sqrt[c + d*x]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(Sqrt[d]*Sqrt[b*c - a*d]*Sqrt[(b*(c + d*x))/(b*c - a*d)])","A",1
1497,1,30,30,0.0090718,"\int \frac{1}{(a+b x)^{3/2} \sqrt{c+d x}} \, dx","Integrate[1/((a + b*x)^(3/2)*Sqrt[c + d*x]),x]","\frac{2 \sqrt{c+d x}}{\sqrt{a+b x} (a d-b c)}","-\frac{2 \sqrt{c+d x}}{\sqrt{a+b x} (b c-a d)}",1,"(2*Sqrt[c + d*x])/((-(b*c) + a*d)*Sqrt[a + b*x])","A",1
1498,1,46,66,0.0165704,"\int \frac{1}{(a+b x)^{5/2} \sqrt{c+d x}} \, dx","Integrate[1/((a + b*x)^(5/2)*Sqrt[c + d*x]),x]","\frac{2 \sqrt{c+d x} (3 a d-b c+2 b d x)}{3 (a+b x)^{3/2} (b c-a d)^2}","\frac{4 d \sqrt{c+d x}}{3 \sqrt{a+b x} (b c-a d)^2}-\frac{2 \sqrt{c+d x}}{3 (a+b x)^{3/2} (b c-a d)}",1,"(2*Sqrt[c + d*x]*(-(b*c) + 3*a*d + 2*b*d*x))/(3*(b*c - a*d)^2*(a + b*x)^(3/2))","A",1
1499,1,75,101,0.031037,"\int \frac{1}{(a+b x)^{7/2} \sqrt{c+d x}} \, dx","Integrate[1/((a + b*x)^(7/2)*Sqrt[c + d*x]),x]","-\frac{2 \sqrt{c+d x} \left(15 a^2 d^2-10 a b d (c-2 d x)+b^2 \left(3 c^2-4 c d x+8 d^2 x^2\right)\right)}{15 (a+b x)^{5/2} (b c-a d)^3}","-\frac{16 d^2 \sqrt{c+d x}}{15 \sqrt{a+b x} (b c-a d)^3}+\frac{8 d \sqrt{c+d x}}{15 (a+b x)^{3/2} (b c-a d)^2}-\frac{2 \sqrt{c+d x}}{5 (a+b x)^{5/2} (b c-a d)}",1,"(-2*Sqrt[c + d*x]*(15*a^2*d^2 - 10*a*b*d*(c - 2*d*x) + b^2*(3*c^2 - 4*c*d*x + 8*d^2*x^2)))/(15*(b*c - a*d)^3*(a + b*x)^(5/2))","A",1
1500,1,116,136,0.0468408,"\int \frac{1}{(a+b x)^{9/2} \sqrt{c+d x}} \, dx","Integrate[1/((a + b*x)^(9/2)*Sqrt[c + d*x]),x]","\frac{2 \sqrt{c+d x} \left(35 a^3 d^3-35 a^2 b d^2 (c-2 d x)+7 a b^2 d \left(3 c^2-4 c d x+8 d^2 x^2\right)+b^3 \left(-5 c^3+6 c^2 d x-8 c d^2 x^2+16 d^3 x^3\right)\right)}{35 (a+b x)^{7/2} (b c-a d)^4}","\frac{32 d^3 \sqrt{c+d x}}{35 \sqrt{a+b x} (b c-a d)^4}-\frac{16 d^2 \sqrt{c+d x}}{35 (a+b x)^{3/2} (b c-a d)^3}+\frac{12 d \sqrt{c+d x}}{35 (a+b x)^{5/2} (b c-a d)^2}-\frac{2 \sqrt{c+d x}}{7 (a+b x)^{7/2} (b c-a d)}",1,"(2*Sqrt[c + d*x]*(35*a^3*d^3 - 35*a^2*b*d^2*(c - 2*d*x) + 7*a*b^2*d*(3*c^2 - 4*c*d*x + 8*d^2*x^2) + b^3*(-5*c^3 + 6*c^2*d*x - 8*c*d^2*x^2 + 16*d^3*x^3)))/(35*(b*c - a*d)^4*(a + b*x)^(7/2))","A",1
1501,1,168,171,0.0657714,"\int \frac{1}{(a+b x)^{11/2} \sqrt{c+d x}} \, dx","Integrate[1/((a + b*x)^(11/2)*Sqrt[c + d*x]),x]","-\frac{2 \sqrt{c+d x} \left(315 a^4 d^4-420 a^3 b d^3 (c-2 d x)+126 a^2 b^2 d^2 \left(3 c^2-4 c d x+8 d^2 x^2\right)+36 a b^3 d \left(-5 c^3+6 c^2 d x-8 c d^2 x^2+16 d^3 x^3\right)+b^4 \left(35 c^4-40 c^3 d x+48 c^2 d^2 x^2-64 c d^3 x^3+128 d^4 x^4\right)\right)}{315 (a+b x)^{9/2} (b c-a d)^5}","-\frac{256 d^4 \sqrt{c+d x}}{315 \sqrt{a+b x} (b c-a d)^5}+\frac{128 d^3 \sqrt{c+d x}}{315 (a+b x)^{3/2} (b c-a d)^4}-\frac{32 d^2 \sqrt{c+d x}}{105 (a+b x)^{5/2} (b c-a d)^3}+\frac{16 d \sqrt{c+d x}}{63 (a+b x)^{7/2} (b c-a d)^2}-\frac{2 \sqrt{c+d x}}{9 (a+b x)^{9/2} (b c-a d)}",1,"(-2*Sqrt[c + d*x]*(315*a^4*d^4 - 420*a^3*b*d^3*(c - 2*d*x) + 126*a^2*b^2*d^2*(3*c^2 - 4*c*d*x + 8*d^2*x^2) + 36*a*b^3*d*(-5*c^3 + 6*c^2*d*x - 8*c*d^2*x^2 + 16*d^3*x^3) + b^4*(35*c^4 - 40*c^3*d*x + 48*c^2*d^2*x^2 - 64*c*d^3*x^3 + 128*d^4*x^4)))/(315*(b*c - a*d)^5*(a + b*x)^(9/2))","A",1
1502,1,73,174,0.0672807,"\int \frac{(a+b x)^{7/2}}{(c+d x)^{3/2}} \, dx","Integrate[(a + b*x)^(7/2)/(c + d*x)^(3/2),x]","\frac{2 (a+b x)^{9/2} \left(\frac{b (c+d x)}{b c-a d}\right)^{3/2} \, _2F_1\left(\frac{3}{2},\frac{9}{2};\frac{11}{2};\frac{d (a+b x)}{a d-b c}\right)}{9 b (c+d x)^{3/2}}","-\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,"(2*(a + b*x)^(9/2)*((b*(c + d*x))/(b*c - a*d))^(3/2)*Hypergeometric2F1[3/2, 9/2, 11/2, (d*(a + b*x))/(-(b*c) + a*d)])/(9*b*(c + d*x)^(3/2))","C",1
1503,1,73,138,0.0550249,"\int \frac{(a+b x)^{5/2}}{(c+d x)^{3/2}} \, dx","Integrate[(a + b*x)^(5/2)/(c + d*x)^(3/2),x]","\frac{2 (a+b x)^{7/2} \left(\frac{b (c+d x)}{b c-a d}\right)^{3/2} \, _2F_1\left(\frac{3}{2},\frac{7}{2};\frac{9}{2};\frac{d (a+b x)}{a d-b c}\right)}{7 b (c+d x)^{3/2}}","\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,"(2*(a + b*x)^(7/2)*((b*(c + d*x))/(b*c - a*d))^(3/2)*Hypergeometric2F1[3/2, 7/2, 9/2, (d*(a + b*x))/(-(b*c) + a*d)])/(7*b*(c + d*x)^(3/2))","C",1
1504,1,73,98,0.0481539,"\int \frac{(a+b x)^{3/2}}{(c+d x)^{3/2}} \, dx","Integrate[(a + b*x)^(3/2)/(c + d*x)^(3/2),x]","\frac{2 (a+b x)^{5/2} \left(\frac{b (c+d x)}{b c-a d}\right)^{3/2} \, _2F_1\left(\frac{3}{2},\frac{5}{2};\frac{7}{2};\frac{d (a+b x)}{a d-b c}\right)}{5 b (c+d x)^{3/2}}","-\frac{3 \sqrt{b} (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{d^{5/2}}+\frac{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,"(2*(a + b*x)^(5/2)*((b*(c + d*x))/(b*c - a*d))^(3/2)*Hypergeometric2F1[3/2, 5/2, 7/2, (d*(a + b*x))/(-(b*c) + a*d)])/(5*b*(c + d*x)^(3/2))","C",1
1505,1,95,66,0.3485525,"\int \frac{\sqrt{a+b x}}{(c+d x)^{3/2}} \, dx","Integrate[Sqrt[a + b*x]/(c + d*x)^(3/2),x]","\frac{2 \sqrt{b c-a d} \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)-2 \sqrt{d} \sqrt{a+b x}}{d^{3/2} \sqrt{c+d x}}","\frac{2 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{d^{3/2}}-\frac{2 \sqrt{a+b x}}{d \sqrt{c+d x}}",1,"(-2*Sqrt[d]*Sqrt[a + b*x] + 2*Sqrt[b*c - a*d]*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(d^(3/2)*Sqrt[c + d*x])","A",1
1506,1,30,30,0.0081098,"\int \frac{1}{\sqrt{a+b x} (c+d x)^{3/2}} \, dx","Integrate[1/(Sqrt[a + b*x]*(c + d*x)^(3/2)),x]","\frac{2 \sqrt{a+b x}}{\sqrt{c+d x} (b c-a d)}","\frac{2 \sqrt{a+b x}}{\sqrt{c+d x} (b c-a d)}",1,"(2*Sqrt[a + b*x])/((b*c - a*d)*Sqrt[c + d*x])","A",1
1507,1,42,62,0.0172404,"\int \frac{1}{(a+b x)^{3/2} (c+d x)^{3/2}} \, dx","Integrate[1/((a + b*x)^(3/2)*(c + d*x)^(3/2)),x]","-\frac{2 (a d+b (c+2 d x))}{\sqrt{a+b x} \sqrt{c+d x} (b c-a d)^2}","-\frac{4 d \sqrt{a+b x}}{\sqrt{c+d x} (b c-a d)^2}-\frac{2}{\sqrt{a+b x} \sqrt{c+d x} (b c-a d)}",1,"(-2*(a*d + b*(c + 2*d*x)))/((b*c - a*d)^2*Sqrt[a + b*x]*Sqrt[c + d*x])","A",1
1508,1,75,101,0.0299282,"\int \frac{1}{(a+b x)^{5/2} (c+d x)^{3/2}} \, dx","Integrate[1/((a + b*x)^(5/2)*(c + d*x)^(3/2)),x]","\frac{2 \left(3 a^2 d^2+6 a b d (c+2 d x)+b^2 \left(-c^2+4 c d x+8 d^2 x^2\right)\right)}{3 (a+b x)^{3/2} \sqrt{c+d x} (b c-a d)^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,"(2*(3*a^2*d^2 + 6*a*b*d*(c + 2*d*x) + b^2*(-c^2 + 4*c*d*x + 8*d^2*x^2)))/(3*(b*c - a*d)^3*(a + b*x)^(3/2)*Sqrt[c + d*x])","A",1
1509,1,114,136,0.0418381,"\int \frac{1}{(a+b x)^{7/2} (c+d x)^{3/2}} \, dx","Integrate[1/((a + b*x)^(7/2)*(c + d*x)^(3/2)),x]","-\frac{2 \left(5 a^3 d^3+15 a^2 b d^2 (c+2 d x)+5 a b^2 d \left(-c^2+4 c d x+8 d^2 x^2\right)+b^3 \left(c^3-2 c^2 d x+8 c d^2 x^2+16 d^3 x^3\right)\right)}{5 (a+b x)^{5/2} \sqrt{c+d x} (b c-a d)^4}","-\frac{32 d^3 \sqrt{a+b x}}{5 \sqrt{c+d x} (b c-a d)^4}-\frac{16 d^2}{5 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^3}+\frac{4 d}{5 (a+b x)^{3/2} \sqrt{c+d x} (b c-a d)^2}-\frac{2}{5 (a+b x)^{5/2} \sqrt{c+d x} (b c-a d)}",1,"(-2*(5*a^3*d^3 + 15*a^2*b*d^2*(c + 2*d*x) + 5*a*b^2*d*(-c^2 + 4*c*d*x + 8*d^2*x^2) + b^3*(c^3 - 2*c^2*d*x + 8*c*d^2*x^2 + 16*d^3*x^3)))/(5*(b*c - a*d)^4*(a + b*x)^(5/2)*Sqrt[c + d*x])","A",1
1510,1,166,171,0.0613959,"\int \frac{1}{(a+b x)^{9/2} (c+d x)^{3/2}} \, dx","Integrate[1/((a + b*x)^(9/2)*(c + d*x)^(3/2)),x]","\frac{2 \left(35 a^4 d^4+140 a^3 b d^3 (c+2 d x)+70 a^2 b^2 d^2 \left(-c^2+4 c d x+8 d^2 x^2\right)+28 a b^3 d \left(c^3-2 c^2 d x+8 c d^2 x^2+16 d^3 x^3\right)+b^4 \left(-5 c^4+8 c^3 d x-16 c^2 d^2 x^2+64 c d^3 x^3+128 d^4 x^4\right)\right)}{35 (a+b x)^{7/2} \sqrt{c+d x} (b c-a d)^5}","\frac{256 d^4 \sqrt{a+b x}}{35 \sqrt{c+d x} (b c-a d)^5}+\frac{128 d^3}{35 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^4}-\frac{32 d^2}{35 (a+b x)^{3/2} \sqrt{c+d x} (b c-a d)^3}+\frac{16 d}{35 (a+b x)^{5/2} \sqrt{c+d x} (b c-a d)^2}-\frac{2}{7 (a+b x)^{7/2} \sqrt{c+d x} (b c-a d)}",1,"(2*(35*a^4*d^4 + 140*a^3*b*d^3*(c + 2*d*x) + 70*a^2*b^2*d^2*(-c^2 + 4*c*d*x + 8*d^2*x^2) + 28*a*b^3*d*(c^3 - 2*c^2*d*x + 8*c*d^2*x^2 + 16*d^3*x^3) + b^4*(-5*c^4 + 8*c^3*d*x - 16*c^2*d^2*x^2 + 64*c*d^3*x^3 + 128*d^4*x^4)))/(35*(b*c - a*d)^5*(a + b*x)^(7/2)*Sqrt[c + d*x])","A",1
1511,1,226,206,0.0804143,"\int \frac{1}{(a+b x)^{11/2} (c+d x)^{3/2}} \, dx","Integrate[1/((a + b*x)^(11/2)*(c + d*x)^(3/2)),x]","\frac{512 d^5 \sqrt{a+b x}}{63 \sqrt{c+d x} (b c-a d)^5 (a d-b c)}+\frac{256 d^4}{63 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^4 (a d-b c)}+\frac{64 d^3}{63 (a+b x)^{3/2} \sqrt{c+d x} (b c-a d)^4}-\frac{32 d^2}{63 (a+b x)^{5/2} \sqrt{c+d x} (b c-a d)^3}+\frac{20 d}{63 (a+b x)^{7/2} \sqrt{c+d x} (b c-a d)^2}-\frac{2}{9 (a+b x)^{9/2} \sqrt{c+d x} (b c-a d)}","-\frac{512 d^5 \sqrt{a+b x}}{63 \sqrt{c+d x} (b c-a d)^6}-\frac{256 d^4}{63 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^5}+\frac{64 d^3}{63 (a+b x)^{3/2} \sqrt{c+d x} (b c-a d)^4}-\frac{32 d^2}{63 (a+b x)^{5/2} \sqrt{c+d x} (b c-a d)^3}+\frac{20 d}{63 (a+b x)^{7/2} \sqrt{c+d x} (b c-a d)^2}-\frac{2}{9 (a+b x)^{9/2} \sqrt{c+d x} (b c-a d)}",1,"-2/(9*(b*c - a*d)*(a + b*x)^(9/2)*Sqrt[c + d*x]) + (20*d)/(63*(b*c - a*d)^2*(a + b*x)^(7/2)*Sqrt[c + d*x]) - (32*d^2)/(63*(b*c - a*d)^3*(a + b*x)^(5/2)*Sqrt[c + d*x]) + (64*d^3)/(63*(b*c - a*d)^4*(a + b*x)^(3/2)*Sqrt[c + d*x]) + (256*d^4)/(63*(b*c - a*d)^4*(-(b*c) + a*d)*Sqrt[a + b*x]*Sqrt[c + d*x]) + (512*d^5*Sqrt[a + b*x])/(63*(b*c - a*d)^5*(-(b*c) + a*d)*Sqrt[c + d*x])","A",1
1512,1,73,204,0.0969534,"\int \frac{(a+b x)^{9/2}}{(c+d x)^{5/2}} \, dx","Integrate[(a + b*x)^(9/2)/(c + d*x)^(5/2),x]","\frac{2 (a+b x)^{11/2} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/2} \, _2F_1\left(\frac{5}{2},\frac{11}{2};\frac{13}{2};\frac{d (a+b x)}{a d-b c}\right)}{11 b (c+d x)^{5/2}}","-\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,"(2*(a + b*x)^(11/2)*((b*(c + d*x))/(b*c - a*d))^(5/2)*Hypergeometric2F1[5/2, 11/2, 13/2, (d*(a + b*x))/(-(b*c) + a*d)])/(11*b*(c + d*x)^(5/2))","C",1
1513,1,73,170,0.0818962,"\int \frac{(a+b x)^{7/2}}{(c+d x)^{5/2}} \, dx","Integrate[(a + b*x)^(7/2)/(c + d*x)^(5/2),x]","\frac{2 (a+b x)^{9/2} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/2} \, _2F_1\left(\frac{5}{2},\frac{9}{2};\frac{11}{2};\frac{d (a+b x)}{a d-b c}\right)}{9 b (c+d x)^{5/2}}","\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,"(2*(a + b*x)^(9/2)*((b*(c + d*x))/(b*c - a*d))^(5/2)*Hypergeometric2F1[5/2, 9/2, 11/2, (d*(a + b*x))/(-(b*c) + a*d)])/(9*b*(c + d*x)^(5/2))","C",1
1514,1,73,128,0.0778492,"\int \frac{(a+b x)^{5/2}}{(c+d x)^{5/2}} \, dx","Integrate[(a + b*x)^(5/2)/(c + d*x)^(5/2),x]","\frac{2 (a+b x)^{7/2} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/2} \, _2F_1\left(\frac{5}{2},\frac{7}{2};\frac{9}{2};\frac{d (a+b x)}{a d-b c}\right)}{7 b (c+d x)^{5/2}}","-\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,"(2*(a + b*x)^(7/2)*((b*(c + d*x))/(b*c - a*d))^(5/2)*Hypergeometric2F1[5/2, 7/2, 9/2, (d*(a + b*x))/(-(b*c) + a*d)])/(7*b*(c + d*x)^(5/2))","C",1
1515,1,111,92,0.5502549,"\int \frac{(a+b x)^{3/2}}{(c+d x)^{5/2}} \, dx","Integrate[(a + b*x)^(3/2)/(c + d*x)^(5/2),x]","\frac{6 (b c-a d)^{3/2} \left(\frac{b (c+d x)}{b c-a d}\right)^{3/2} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)-2 \sqrt{d} \sqrt{a+b x} (a d+3 b c+4 b d x)}{3 d^{5/2} (c+d x)^{3/2}}","\frac{2 b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{d^{5/2}}-\frac{2 b \sqrt{a+b x}}{d^2 \sqrt{c+d x}}-\frac{2 (a+b x)^{3/2}}{3 d (c+d x)^{3/2}}",1,"(-2*Sqrt[d]*Sqrt[a + b*x]*(3*b*c + a*d + 4*b*d*x) + 6*(b*c - a*d)^(3/2)*((b*(c + d*x))/(b*c - a*d))^(3/2)*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(3*d^(5/2)*(c + d*x)^(3/2))","A",1
1516,1,32,32,0.0104712,"\int \frac{\sqrt{a+b x}}{(c+d x)^{5/2}} \, dx","Integrate[Sqrt[a + b*x]/(c + d*x)^(5/2),x]","\frac{2 (a+b x)^{3/2}}{3 (c+d x)^{3/2} (b c-a d)}","\frac{2 (a+b x)^{3/2}}{3 (c+d x)^{3/2} (b c-a d)}",1,"(2*(a + b*x)^(3/2))/(3*(b*c - a*d)*(c + d*x)^(3/2))","A",1
1517,1,46,66,0.015307,"\int \frac{1}{\sqrt{a+b x} (c+d x)^{5/2}} \, dx","Integrate[1/(Sqrt[a + b*x]*(c + d*x)^(5/2)),x]","\frac{2 \sqrt{a+b x} (-a d+3 b c+2 b d x)}{3 (c+d x)^{3/2} (b c-a d)^2}","\frac{4 b \sqrt{a+b x}}{3 \sqrt{c+d x} (b c-a d)^2}+\frac{2 \sqrt{a+b x}}{3 (c+d x)^{3/2} (b c-a d)}",1,"(2*Sqrt[a + b*x]*(3*b*c - a*d + 2*b*d*x))/(3*(b*c - a*d)^2*(c + d*x)^(3/2))","A",1
1518,1,78,98,0.0308774,"\int \frac{1}{(a+b x)^{3/2} (c+d x)^{5/2}} \, dx","Integrate[1/((a + b*x)^(3/2)*(c + d*x)^(5/2)),x]","\frac{2 a^2 d^2-4 a b d (3 c+2 d x)-2 b^2 \left(3 c^2+12 c d x+8 d^2 x^2\right)}{3 \sqrt{a+b x} (c+d x)^{3/2} (b c-a d)^3}","-\frac{16 b d \sqrt{a+b x}}{3 \sqrt{c+d x} (b c-a d)^3}-\frac{8 d \sqrt{a+b x}}{3 (c+d x)^{3/2} (b c-a d)^2}-\frac{2}{\sqrt{a+b x} (c+d x)^{3/2} (b c-a d)}",1,"(2*a^2*d^2 - 4*a*b*d*(3*c + 2*d*x) - 2*b^2*(3*c^2 + 12*c*d*x + 8*d^2*x^2))/(3*(b*c - a*d)^3*Sqrt[a + b*x]*(c + d*x)^(3/2))","A",1
1519,1,118,135,0.051882,"\int \frac{1}{(a+b x)^{5/2} (c+d x)^{5/2}} \, dx","Integrate[1/((a + b*x)^(5/2)*(c + d*x)^(5/2)),x]","\frac{-2 a^3 d^3+6 a^2 b d^2 (3 c+2 d x)+6 a b^2 d \left(3 c^2+12 c d x+8 d^2 x^2\right)+b^3 \left(-2 c^3+12 c^2 d x+48 c d^2 x^2+32 d^3 x^3\right)}{3 (a+b x)^{3/2} (c+d x)^{3/2} (b c-a d)^4}","\frac{32 b d^2 \sqrt{a+b x}}{3 \sqrt{c+d x} (b c-a d)^4}+\frac{16 d^2 \sqrt{a+b x}}{3 (c+d x)^{3/2} (b c-a d)^3}+\frac{4 d}{\sqrt{a+b x} (c+d x)^{3/2} (b c-a d)^2}-\frac{2}{3 (a+b x)^{3/2} (c+d x)^{3/2} (b c-a d)}",1,"(-2*a^3*d^3 + 6*a^2*b*d^2*(3*c + 2*d*x) + 6*a*b^2*d*(3*c^2 + 12*c*d*x + 8*d^2*x^2) + b^3*(-2*c^3 + 12*c^2*d*x + 48*c*d^2*x^2 + 32*d^3*x^3))/(3*(b*c - a*d)^4*(a + b*x)^(3/2)*(c + d*x)^(3/2))","A",1
1520,1,170,172,0.0669927,"\int \frac{1}{(a+b x)^{7/2} (c+d x)^{5/2}} \, dx","Integrate[1/((a + b*x)^(7/2)*(c + d*x)^(5/2)),x]","-\frac{2 \left(-5 a^4 d^4+20 a^3 b d^3 (3 c+2 d x)+30 a^2 b^2 d^2 \left(3 c^2+12 c d x+8 d^2 x^2\right)+20 a b^3 d \left(-c^3+6 c^2 d x+24 c d^2 x^2+16 d^3 x^3\right)+b^4 \left(3 c^4-8 c^3 d x+48 c^2 d^2 x^2+192 c d^3 x^3+128 d^4 x^4\right)\right)}{15 (a+b x)^{5/2} (c+d x)^{3/2} (b c-a d)^5}","-\frac{256 b d^3 \sqrt{a+b x}}{15 \sqrt{c+d x} (b c-a d)^5}-\frac{128 d^3 \sqrt{a+b x}}{15 (c+d x)^{3/2} (b c-a d)^4}-\frac{32 d^2}{5 \sqrt{a+b x} (c+d x)^{3/2} (b c-a d)^3}+\frac{16 d}{15 (a+b x)^{3/2} (c+d x)^{3/2} (b c-a d)^2}-\frac{2}{5 (a+b x)^{5/2} (c+d x)^{3/2} (b c-a d)}",1,"(-2*(-5*a^4*d^4 + 20*a^3*b*d^3*(3*c + 2*d*x) + 30*a^2*b^2*d^2*(3*c^2 + 12*c*d*x + 8*d^2*x^2) + 20*a*b^3*d*(-c^3 + 6*c^2*d*x + 24*c*d^2*x^2 + 16*d^3*x^3) + b^4*(3*c^4 - 8*c^3*d*x + 48*c^2*d^2*x^2 + 192*c*d^3*x^3 + 128*d^4*x^4)))/(15*(b*c - a*d)^5*(a + b*x)^(5/2)*(c + d*x)^(3/2))","A",1
1521,1,233,207,0.0821284,"\int \frac{1}{(a+b x)^{9/2} (c+d x)^{5/2}} \, dx","Integrate[1/((a + b*x)^(9/2)*(c + d*x)^(5/2)),x]","\frac{2 \left(-7 a^5 d^5+35 a^4 b d^4 (3 c+2 d x)+70 a^3 b^2 d^3 \left(3 c^2+12 c d x+8 d^2 x^2\right)+70 a^2 b^3 d^2 \left(-c^3+6 c^2 d x+24 c d^2 x^2+16 d^3 x^3\right)+7 a b^4 d \left(3 c^4-8 c^3 d x+48 c^2 d^2 x^2+192 c d^3 x^3+128 d^4 x^4\right)+b^5 \left(-3 c^5+6 c^4 d x-16 c^3 d^2 x^2+96 c^2 d^3 x^3+384 c d^4 x^4+256 d^5 x^5\right)\right)}{21 (a+b x)^{7/2} (c+d x)^{3/2} (b c-a d)^6}","\frac{512 b d^4 \sqrt{a+b x}}{21 \sqrt{c+d x} (b c-a d)^6}+\frac{256 d^4 \sqrt{a+b x}}{21 (c+d x)^{3/2} (b c-a d)^5}+\frac{64 d^3}{7 \sqrt{a+b x} (c+d x)^{3/2} (b c-a d)^4}-\frac{32 d^2}{21 (a+b x)^{3/2} (c+d x)^{3/2} (b c-a d)^3}+\frac{4 d}{7 (a+b x)^{5/2} (c+d x)^{3/2} (b c-a d)^2}-\frac{2}{7 (a+b x)^{7/2} (c+d x)^{3/2} (b c-a d)}",1,"(2*(-7*a^5*d^5 + 35*a^4*b*d^4*(3*c + 2*d*x) + 70*a^3*b^2*d^3*(3*c^2 + 12*c*d*x + 8*d^2*x^2) + 70*a^2*b^3*d^2*(-c^3 + 6*c^2*d*x + 24*c*d^2*x^2 + 16*d^3*x^3) + 7*a*b^4*d*(3*c^4 - 8*c^3*d*x + 48*c^2*d^2*x^2 + 192*c*d^3*x^3 + 128*d^4*x^4) + b^5*(-3*c^5 + 6*c^4*d*x - 16*c^3*d^2*x^2 + 96*c^2*d^3*x^3 + 384*c*d^4*x^4 + 256*d^5*x^5)))/(21*(b*c - a*d)^6*(a + b*x)^(7/2)*(c + d*x)^(3/2))","A",1
1522,1,19,19,0.0101281,"\int \frac{1}{\sqrt{a+b x} \sqrt{4+a+b x}} \, dx","Integrate[1/(Sqrt[a + b*x]*Sqrt[4 + a + b*x]),x]","\frac{2 \sinh ^{-1}\left(\frac{1}{2} \sqrt{a+b x}\right)}{b}","\frac{2 \sinh ^{-1}\left(\frac{1}{2} \sqrt{a+b x}\right)}{b}",1,"(2*ArcSinh[Sqrt[a + b*x]/2])/b","A",1
1523,1,39,19,0.0119634,"\int \frac{1}{\sqrt{2+b x} \sqrt{6+b x}} \, dx","Integrate[1/(Sqrt[2 + b*x]*Sqrt[6 + b*x]),x]","\frac{2 \sqrt{b x+2} \sin ^{-1}\left(\frac{1}{2} \sqrt{-b x-2}\right)}{b \sqrt{-b x-2}}","\frac{2 \sinh ^{-1}\left(\frac{1}{2} \sqrt{b x+2}\right)}{b}",1,"(2*Sqrt[2 + b*x]*ArcSin[Sqrt[-2 - b*x]/2])/(b*Sqrt[-2 - b*x])","B",1
1524,1,39,19,0.0114068,"\int \frac{1}{\sqrt{1+b x} \sqrt{5+b x}} \, dx","Integrate[1/(Sqrt[1 + b*x]*Sqrt[5 + b*x]),x]","\frac{2 \sqrt{b x+1} \sin ^{-1}\left(\frac{1}{2} \sqrt{-b x-1}\right)}{b \sqrt{-b x-1}}","\frac{2 \sinh ^{-1}\left(\frac{1}{2} \sqrt{b x+1}\right)}{b}",1,"(2*Sqrt[1 + b*x]*ArcSin[Sqrt[-1 - b*x]/2])/(b*Sqrt[-1 - b*x])","B",1
1525,1,34,17,0.010491,"\int \frac{1}{\sqrt{b x} \sqrt{4+b x}} \, dx","Integrate[1/(Sqrt[b*x]*Sqrt[4 + b*x]),x]","\frac{2 \sqrt{x} \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{2}\right)}{\sqrt{b} \sqrt{b x}}","\frac{2 \sinh ^{-1}\left(\frac{\sqrt{b x}}{2}\right)}{b}",1,"(2*Sqrt[x]*ArcSinh[(Sqrt[b]*Sqrt[x])/2])/(Sqrt[b]*Sqrt[b*x])","A",1
1526,1,39,19,0.011198,"\int \frac{1}{\sqrt{-1+b x} \sqrt{3+b x}} \, dx","Integrate[1/(Sqrt[-1 + b*x]*Sqrt[3 + b*x]),x]","\frac{2 \sqrt{b x-1} \sin ^{-1}\left(\frac{1}{2} \sqrt{1-b x}\right)}{b \sqrt{1-b x}}","\frac{2 \sinh ^{-1}\left(\frac{1}{2} \sqrt{b x-1}\right)}{b}",1,"(2*Sqrt[-1 + b*x]*ArcSin[Sqrt[1 - b*x]/2])/(b*Sqrt[1 - b*x])","B",1
1527,1,25,11,0.0046167,"\int \frac{1}{\sqrt{-2+b x} \sqrt{2+b x}} \, dx","Integrate[1/(Sqrt[-2 + b*x]*Sqrt[2 + b*x]),x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b x-2}}{\sqrt{b x+2}}\right)}{b}","\frac{\cosh ^{-1}\left(\frac{b x}{2}\right)}{b}",1,"(2*ArcTanh[Sqrt[-2 + b*x]/Sqrt[2 + b*x]])/b","B",1
1528,1,39,19,0.0108081,"\int \frac{1}{\sqrt{-3+b x} \sqrt{1+b x}} \, dx","Integrate[1/(Sqrt[-3 + b*x]*Sqrt[1 + b*x]),x]","\frac{2 \sqrt{b x-3} \sin ^{-1}\left(\frac{1}{2} \sqrt{3-b x}\right)}{b \sqrt{3-b x}}","\frac{2 \sinh ^{-1}\left(\frac{1}{2} \sqrt{b x-3}\right)}{b}",1,"(2*Sqrt[-3 + b*x]*ArcSin[Sqrt[3 - b*x]/2])/(b*Sqrt[3 - b*x])","B",1
1529,1,15,15,0.004442,"\int \frac{1}{\sqrt{2+b x} \sqrt{3+b x}} \, dx","Integrate[1/(Sqrt[2 + b*x]*Sqrt[3 + b*x]),x]","\frac{2 \sinh ^{-1}\left(\sqrt{b x+2}\right)}{b}","\frac{2 \sinh ^{-1}\left(\sqrt{b x+2}\right)}{b}",1,"(2*ArcSinh[Sqrt[2 + b*x]])/b","A",1
1530,1,10,10,0.0010033,"\int \frac{1}{2+b x} \, dx","Integrate[(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
1531,1,15,15,0.0042496,"\int \frac{1}{\sqrt{1+b x} \sqrt{2+b x}} \, dx","Integrate[1/(Sqrt[1 + b*x]*Sqrt[2 + b*x]),x]","\frac{2 \sinh ^{-1}\left(\sqrt{b x+1}\right)}{b}","\frac{2 \sinh ^{-1}\left(\sqrt{b x+1}\right)}{b}",1,"(2*ArcSinh[Sqrt[1 + b*x]])/b","A",1
1532,1,36,19,0.0093174,"\int \frac{1}{\sqrt{b x} \sqrt{2+b x}} \, dx","Integrate[1/(Sqrt[b*x]*Sqrt[2 + b*x]),x]","\frac{2 \sqrt{x} \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{\sqrt{b} \sqrt{b x}}","\frac{2 \sinh ^{-1}\left(\frac{\sqrt{b x}}{\sqrt{2}}\right)}{b}",1,"(2*Sqrt[x]*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/(Sqrt[b]*Sqrt[b*x])","A",1
1533,1,41,21,0.0088611,"\int \frac{1}{\sqrt{-1+b x} \sqrt{2+b x}} \, dx","Integrate[1/(Sqrt[-1 + b*x]*Sqrt[2 + b*x]),x]","\frac{2 \sqrt{b x-1} \sin ^{-1}\left(\frac{\sqrt{1-b x}}{\sqrt{3}}\right)}{b \sqrt{1-b x}}","\frac{2 \sinh ^{-1}\left(\frac{\sqrt{b x-1}}{\sqrt{3}}\right)}{b}",1,"(2*Sqrt[-1 + b*x]*ArcSin[Sqrt[1 - b*x]/Sqrt[3]])/(b*Sqrt[1 - b*x])","A",1
1534,1,25,11,0.0025922,"\int \frac{1}{\sqrt{-2+b x} \sqrt{2+b x}} \, dx","Integrate[1/(Sqrt[-2 + b*x]*Sqrt[2 + b*x]),x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b x-2}}{\sqrt{b x+2}}\right)}{b}","\frac{\cosh ^{-1}\left(\frac{b x}{2}\right)}{b}",1,"(2*ArcTanh[Sqrt[-2 + b*x]/Sqrt[2 + b*x]])/b","B",1
1535,1,41,21,0.0105052,"\int \frac{1}{\sqrt{-3+b x} \sqrt{2+b x}} \, dx","Integrate[1/(Sqrt[-3 + b*x]*Sqrt[2 + b*x]),x]","\frac{2 \sqrt{b x-3} \sin ^{-1}\left(\frac{\sqrt{3-b x}}{\sqrt{5}}\right)}{b \sqrt{3-b x}}","\frac{2 \sinh ^{-1}\left(\frac{\sqrt{b x-3}}{\sqrt{5}}\right)}{b}",1,"(2*Sqrt[-3 + b*x]*ArcSin[Sqrt[3 - b*x]/Sqrt[5]])/(b*Sqrt[3 - b*x])","A",1
1536,1,22,16,0.0125729,"\int \frac{1}{\sqrt{3-b x} \sqrt{2+b x}} \, dx","Integrate[1/(Sqrt[3 - b*x]*Sqrt[2 + b*x]),x]","-\frac{2 \sin ^{-1}\left(\frac{\sqrt{3-b x}}{\sqrt{5}}\right)}{b}","-\frac{\sin ^{-1}\left(\frac{1}{5} (1-2 b x)\right)}{b}",1,"(-2*ArcSin[Sqrt[3 - b*x]/Sqrt[5]])/b","A",1
1537,1,11,11,0.0093616,"\int \frac{1}{\sqrt{2-b x} \sqrt{2+b x}} \, dx","Integrate[1/(Sqrt[2 - b*x]*Sqrt[2 + b*x]),x]","\frac{\sin ^{-1}\left(\frac{b x}{2}\right)}{b}","\frac{\sin ^{-1}\left(\frac{b x}{2}\right)}{b}",1,"ArcSin[(b*x)/2]/b","A",1
1538,1,22,16,0.0134273,"\int \frac{1}{\sqrt{1-b x} \sqrt{2+b x}} \, dx","Integrate[1/(Sqrt[1 - b*x]*Sqrt[2 + b*x]),x]","-\frac{2 \sin ^{-1}\left(\frac{\sqrt{1-b x}}{\sqrt{3}}\right)}{b}","-\frac{\sin ^{-1}\left(\frac{1}{3} (-2 b x-1)\right)}{b}",1,"(-2*ArcSin[Sqrt[1 - b*x]/Sqrt[3]])/b","A",1
1539,1,51,10,0.0141273,"\int \frac{1}{\sqrt{-b x} \sqrt{2+b x}} \, dx","Integrate[1/(Sqrt[-(b*x)]*Sqrt[2 + b*x]),x]","\frac{2 \sqrt{x} \sqrt{b x+2} \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{\sqrt{b} \sqrt{-b x (b x+2)}}","\frac{\sin ^{-1}(b x+1)}{b}",1,"(2*Sqrt[x]*Sqrt[2 + b*x]*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/(Sqrt[b]*Sqrt[-(b*x*(2 + b*x))])","B",1
1540,1,49,11,0.0147949,"\int \frac{1}{\sqrt{-1-b x} \sqrt{2+b x}} \, dx","Integrate[1/(Sqrt[-1 - b*x]*Sqrt[2 + b*x]),x]","\frac{2 \sqrt{b x+1} \sqrt{b x+2} \sinh ^{-1}\left(\sqrt{b x+1}\right)}{b \sqrt{-((b x+1) (b x+2))}}","\frac{\sin ^{-1}(2 b x+3)}{b}",1,"(2*Sqrt[1 + b*x]*Sqrt[2 + b*x]*ArcSinh[Sqrt[1 + b*x]])/(b*Sqrt[-((1 + b*x)*(2 + b*x))])","B",1
1541,1,28,29,0.0085281,"\int \frac{1}{\sqrt{-2-b x} \sqrt{2+b x}} \, dx","Integrate[1/(Sqrt[-2 - b*x]*Sqrt[2 + b*x]),x]","\frac{(b x+2) \log (b x+2)}{b \sqrt{-(b x+2)^2}}","\frac{\sqrt{b x+2} \log (b x+2)}{b \sqrt{-b x-2}}",1,"((2 + b*x)*Log[2 + b*x])/(b*Sqrt[-(2 + b*x)^2])","A",1
1542,1,53,26,0.0156138,"\int \frac{1}{\sqrt{-3-b x} \sqrt{2+b x}} \, dx","Integrate[1/(Sqrt[-3 - b*x]*Sqrt[2 + b*x]),x]","-\frac{2 \sqrt{-b x-3} \sqrt{-b x-2} \sin ^{-1}\left(\sqrt{b x+3}\right)}{b \sqrt{b x+2} \sqrt{b x+3}}","-\frac{2 \tan ^{-1}\left(\frac{\sqrt{-b x-3}}{\sqrt{b x+2}}\right)}{b}",1,"(-2*Sqrt[-3 - b*x]*Sqrt[-2 - b*x]*ArcSin[Sqrt[3 + b*x]])/(b*Sqrt[2 + b*x]*Sqrt[3 + b*x])","B",1
1543,1,16,16,0.0074373,"\int \frac{1}{\sqrt{2-b x} \sqrt{3-b x}} \, dx","Integrate[1/(Sqrt[2 - b*x]*Sqrt[3 - b*x]),x]","-\frac{2 \sinh ^{-1}\left(\sqrt{2-b x}\right)}{b}","-\frac{2 \sinh ^{-1}\left(\sqrt{2-b x}\right)}{b}",1,"(-2*ArcSinh[Sqrt[2 - b*x]])/b","A",1
1544,1,12,12,0.0010951,"\int \frac{1}{2-b x} \, dx","Integrate[(2 - b*x)^(-1),x]","-\frac{\log (2-b x)}{b}","-\frac{\log (2-b x)}{b}",1,"-(Log[2 - b*x]/b)","A",1
1545,1,16,16,0.0066213,"\int \frac{1}{\sqrt{1-b x} \sqrt{2-b x}} \, dx","Integrate[1/(Sqrt[1 - b*x]*Sqrt[2 - b*x]),x]","-\frac{2 \sinh ^{-1}\left(\sqrt{1-b x}\right)}{b}","-\frac{2 \sinh ^{-1}\left(\sqrt{1-b x}\right)}{b}",1,"(-2*ArcSinh[Sqrt[1 - b*x]])/b","A",1
1546,1,37,20,0.0076272,"\int \frac{1}{\sqrt{-b x} \sqrt{2-b x}} \, dx","Integrate[1/(Sqrt[-(b*x)]*Sqrt[2 - b*x]),x]","\frac{2 \sqrt{x} \sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{\sqrt{b} \sqrt{-b x}}","-\frac{2 \sinh ^{-1}\left(\frac{\sqrt{-b x}}{\sqrt{2}}\right)}{b}",1,"(2*Sqrt[x]*ArcSin[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/(Sqrt[b]*Sqrt[-(b*x)])","A",1
1547,1,40,22,0.0109189,"\int \frac{1}{\sqrt{-1-b x} \sqrt{2-b x}} \, dx","Integrate[1/(Sqrt[-1 - b*x]*Sqrt[2 - b*x]),x]","-\frac{2 \sqrt{-b x-1} \sin ^{-1}\left(\frac{\sqrt{b x+1}}{\sqrt{3}}\right)}{b \sqrt{b x+1}}","-\frac{2 \sinh ^{-1}\left(\frac{\sqrt{-b x-1}}{\sqrt{3}}\right)}{b}",1,"(-2*Sqrt[-1 - b*x]*ArcSin[Sqrt[1 + b*x]/Sqrt[3]])/(b*Sqrt[1 + b*x])","A",1
1548,1,27,12,0.004977,"\int \frac{1}{\sqrt{-2-b x} \sqrt{2-b x}} \, dx","Integrate[1/(Sqrt[-2 - b*x]*Sqrt[2 - b*x]),x]","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{-b x-2}}{\sqrt{2-b x}}\right)}{b}","-\frac{\cosh ^{-1}\left(-\frac{b x}{2}\right)}{b}",1,"(-2*ArcTanh[Sqrt[-2 - b*x]/Sqrt[2 - b*x]])/b","B",1
1549,1,40,22,0.0106118,"\int \frac{1}{\sqrt{-3-b x} \sqrt{2-b x}} \, dx","Integrate[1/(Sqrt[-3 - b*x]*Sqrt[2 - b*x]),x]","-\frac{2 \sqrt{-b x-3} \sin ^{-1}\left(\frac{\sqrt{b x+3}}{\sqrt{5}}\right)}{b \sqrt{b x+3}}","-\frac{2 \sinh ^{-1}\left(\frac{\sqrt{-b x-3}}{\sqrt{5}}\right)}{b}",1,"(-2*Sqrt[-3 - b*x]*ArcSin[Sqrt[3 + b*x]/Sqrt[5]])/(b*Sqrt[3 + b*x])","A",1
1550,1,25,11,0.0048823,"\int \frac{1}{\sqrt{-4+b x} \sqrt{4+b x}} \, dx","Integrate[1/(Sqrt[-4 + b*x]*Sqrt[4 + b*x]),x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b x-4}}{\sqrt{b x+4}}\right)}{b}","\frac{\cosh ^{-1}\left(\frac{b x}{4}\right)}{b}",1,"(2*ArcTanh[Sqrt[-4 + b*x]/Sqrt[4 + b*x]])/b","B",1
1551,1,41,43,0.0253818,"\int \frac{1}{\sqrt{\frac{-b+b c}{d}+b x} \sqrt{c+d x}} \, dx","Integrate[1/(Sqrt[(-b + b*c)/d + b*x]*Sqrt[c + d*x]),x]","\frac{2 \sqrt{c+d x-1} \sinh ^{-1}\left(\sqrt{c+d x-1}\right)}{d \sqrt{\frac{b (c+d x-1)}{d}}}","\frac{2 \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{b x-\frac{b (1-c)}{d}}}{\sqrt{b}}\right)}{\sqrt{b} \sqrt{d}}",1,"(2*Sqrt[-1 + c + d*x]*ArcSinh[Sqrt[-1 + c + d*x]])/(d*Sqrt[(b*(-1 + c + d*x))/d])","A",1
1552,1,31,22,0.0087468,"\int \frac{1}{\sqrt{x} \sqrt{-3+2 x}} \, dx","Integrate[1/(Sqrt[x]*Sqrt[-3 + 2*x]),x]","\frac{\sqrt{4 x-6} \sin ^{-1}\left(\sqrt{1-\frac{2 x}{3}}\right)}{\sqrt{3-2 x}}","\sqrt{2} \sinh ^{-1}\left(\frac{\sqrt{2 x-3}}{\sqrt{3}}\right)",1,"(Sqrt[-6 + 4*x]*ArcSin[Sqrt[1 - (2*x)/3]])/Sqrt[3 - 2*x]","A",1
1553,1,26,26,0.0091349,"\int \frac{1}{\sqrt{-3+2 x} \sqrt{2+3 x}} \, dx","Integrate[1/(Sqrt[-3 + 2*x]*Sqrt[2 + 3*x]),x]","\sqrt{\frac{2}{3}} \sinh ^{-1}\left(\sqrt{\frac{3}{13}} \sqrt{2 x-3}\right)","\sqrt{\frac{2}{3}} \sinh ^{-1}\left(\sqrt{\frac{3}{13}} \sqrt{2 x-3}\right)",1,"Sqrt[2/3]*ArcSinh[Sqrt[3/13]*Sqrt[-3 + 2*x]]","A",1
1554,1,67,42,0.050381,"\int \frac{1}{\sqrt{\frac{b-b c}{d}+b x} \sqrt{c-d x}} \, dx","Integrate[1/(Sqrt[(b - b*c)/d + b*x]*Sqrt[c - d*x]),x]","\frac{2 \sqrt{-d} \sqrt{-c+d x+1} \sinh ^{-1}\left(\frac{\sqrt{-d} \sqrt{c-d x}}{\sqrt{d}}\right)}{d^{3/2} \sqrt{\frac{b (-c+d x+1)}{d}}}","\frac{2 \sin ^{-1}\left(\frac{\sqrt{d} \sqrt{\frac{b (1-c)}{d}+b x}}{\sqrt{b}}\right)}{\sqrt{b} \sqrt{d}}",1,"(2*Sqrt[-d]*Sqrt[1 - c + d*x]*ArcSinh[(Sqrt[-d]*Sqrt[c - d*x])/Sqrt[d]])/(d^(3/2)*Sqrt[(b*(1 - c + d*x))/d])","A",1
1555,1,14,10,0.0102423,"\int \frac{1}{\sqrt{4-x} \sqrt{x}} \, dx","Integrate[1/(Sqrt[4 - x]*Sqrt[x]),x]","-2 \sin ^{-1}\left(\sqrt{1-\frac{x}{4}}\right)","-\sin ^{-1}\left(1-\frac{x}{2}\right)",1,"-2*ArcSin[Sqrt[1 - x/4]]","A",1
1556,1,20,20,0.0044775,"\int \frac{1}{\sqrt{3-2 x} \sqrt{x}} \, dx","Integrate[1/(Sqrt[3 - 2*x]*Sqrt[x]),x]","\sqrt{2} \sin ^{-1}\left(\sqrt{\frac{2}{3}} \sqrt{x}\right)","\sqrt{2} \sin ^{-1}\left(\sqrt{\frac{2}{3}} \sqrt{x}\right)",1,"Sqrt[2]*ArcSin[Sqrt[2/3]*Sqrt[x]]","A",1
1557,1,45,26,0.0123016,"\int \frac{1}{\sqrt{3-2 x} \sqrt{3+5 x}} \, dx","Integrate[1/(Sqrt[3 - 2*x]*Sqrt[3 + 5*x]),x]","-\frac{\sqrt{\frac{2}{5}} \sqrt{3-2 x} \sinh ^{-1}\left(\sqrt{\frac{5}{21}} \sqrt{2 x-3}\right)}{\sqrt{2 x-3}}","\sqrt{\frac{2}{5}} \sin ^{-1}\left(\sqrt{\frac{2}{21}} \sqrt{5 x+3}\right)",1,"-((Sqrt[2/5]*Sqrt[3 - 2*x]*ArcSinh[Sqrt[5/21]*Sqrt[-3 + 2*x]])/Sqrt[-3 + 2*x])","A",1
1558,1,103,43,0.0806088,"\int \frac{1}{\sqrt{a-b x} \sqrt{c+d x}} \, dx","Integrate[1/(Sqrt[a - b*x]*Sqrt[c + d*x]),x]","\frac{2 \sqrt{-b} \sqrt{-a d-b c} \sqrt{\frac{b (c+d x)}{a d+b c}} \sin ^{-1}\left(\frac{\sqrt{-b} \sqrt{d} \sqrt{a-b x}}{\sqrt{b} \sqrt{-a d-b c}}\right)}{b^{3/2} \sqrt{d} \sqrt{c+d x}}","-\frac{2 \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{a-b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{\sqrt{b} \sqrt{d}}",1,"(2*Sqrt[-b]*Sqrt[-(b*c) - a*d]*Sqrt[(b*(c + d*x))/(b*c + a*d)]*ArcSin[(Sqrt[-b]*Sqrt[d]*Sqrt[a - b*x])/(Sqrt[b]*Sqrt[-(b*c) - a*d])])/(b^(3/2)*Sqrt[d]*Sqrt[c + d*x])","B",1
1559,1,73,457,0.0416817,"\int (a+b x)^{3/2} \sqrt[3]{c+d x} \, dx","Integrate[(a + b*x)^(3/2)*(c + d*x)^(1/3),x]","\frac{2 (a+b x)^{5/2} \sqrt[3]{c+d x} \, _2F_1\left(-\frac{1}{3},\frac{5}{2};\frac{7}{2};\frac{d (a+b x)}{a d-b c}\right)}{5 b \sqrt[3]{\frac{b (c+d x)}{b c-a d}}}","-\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}} \operatorname{EllipticF}\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),4 \sqrt{3}-7\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,"(2*(a + b*x)^(5/2)*(c + d*x)^(1/3)*Hypergeometric2F1[-1/3, 5/2, 7/2, (d*(a + b*x))/(-(b*c) + a*d)])/(5*b*((b*(c + d*x))/(b*c - a*d))^(1/3))","C",1
1560,1,73,419,0.0276335,"\int \sqrt{a+b x} \sqrt[3]{c+d x} \, dx","Integrate[Sqrt[a + b*x]*(c + d*x)^(1/3),x]","\frac{2 (a+b x)^{3/2} \sqrt[3]{c+d x} \, _2F_1\left(-\frac{1}{3},\frac{3}{2};\frac{5}{2};\frac{d (a+b x)}{a d-b c}\right)}{3 b \sqrt[3]{\frac{b (c+d x)}{b c-a d}}}","\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}} \operatorname{EllipticF}\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),4 \sqrt{3}-7\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,"(2*(a + b*x)^(3/2)*(c + d*x)^(1/3)*Hypergeometric2F1[-1/3, 3/2, 5/2, (d*(a + b*x))/(-(b*c) + a*d)])/(3*b*((b*(c + d*x))/(b*c - a*d))^(1/3))","C",1
1561,1,71,381,0.0227319,"\int \frac{\sqrt[3]{c+d x}}{\sqrt{a+b x}} \, dx","Integrate[(c + d*x)^(1/3)/Sqrt[a + b*x],x]","\frac{2 \sqrt{a+b x} \sqrt[3]{c+d x} \, _2F_1\left(-\frac{1}{3},\frac{1}{2};\frac{3}{2};\frac{d (a+b x)}{a d-b c}\right)}{b \sqrt[3]{\frac{b (c+d x)}{b c-a d}}}","\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}} \operatorname{EllipticF}\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),4 \sqrt{3}-7\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,"(2*Sqrt[a + b*x]*(c + d*x)^(1/3)*Hypergeometric2F1[-1/3, 1/2, 3/2, (d*(a + b*x))/(-(b*c) + a*d)])/(b*((b*(c + d*x))/(b*c - a*d))^(1/3))","C",1
1562,1,71,366,0.0256474,"\int \frac{\sqrt[3]{c+d x}}{(a+b x)^{3/2}} \, dx","Integrate[(c + d*x)^(1/3)/(a + b*x)^(3/2),x]","-\frac{2 \sqrt[3]{c+d x} \, _2F_1\left(-\frac{1}{2},-\frac{1}{3};\frac{1}{2};\frac{d (a+b x)}{a d-b c}\right)}{b \sqrt{a+b x} \sqrt[3]{\frac{b (c+d x)}{b c-a d}}}","-\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}} \operatorname{EllipticF}\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),4 \sqrt{3}-7\right)}{\sqrt[4]{3} b^{4/3} \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b c-a d} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{2 \sqrt[3]{c+d x}}{b \sqrt{a+b x}}",1,"(-2*(c + d*x)^(1/3)*Hypergeometric2F1[-1/2, -1/3, 1/2, (d*(a + b*x))/(-(b*c) + a*d)])/(b*Sqrt[a + b*x]*((b*(c + d*x))/(b*c - a*d))^(1/3))","C",1
1563,1,73,417,0.0247476,"\int \frac{\sqrt[3]{c+d x}}{(a+b x)^{5/2}} \, dx","Integrate[(c + d*x)^(1/3)/(a + b*x)^(5/2),x]","-\frac{2 \sqrt[3]{c+d x} \, _2F_1\left(-\frac{3}{2},-\frac{1}{3};-\frac{1}{2};\frac{d (a+b x)}{a d-b c}\right)}{3 b (a+b x)^{3/2} \sqrt[3]{\frac{b (c+d x)}{b c-a d}}}","\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}} \operatorname{EllipticF}\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),4 \sqrt{3}-7\right)}{9 \sqrt[4]{3} b^{4/3} \sqrt{a+b x} (b c-a d) \sqrt{-\frac{\sqrt[3]{b c-a d} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{4 d \sqrt[3]{c+d x}}{9 b \sqrt{a+b x} (b c-a d)}-\frac{2 \sqrt[3]{c+d x}}{3 b (a+b x)^{3/2}}",1,"(-2*(c + d*x)^(1/3)*Hypergeometric2F1[-3/2, -1/3, -1/2, (d*(a + b*x))/(-(b*c) + a*d)])/(3*b*(a + b*x)^(3/2)*((b*(c + d*x))/(b*c - a*d))^(1/3))","C",1
1564,1,73,457,0.0255114,"\int \frac{\sqrt[3]{c+d x}}{(a+b x)^{7/2}} \, dx","Integrate[(c + d*x)^(1/3)/(a + b*x)^(7/2),x]","-\frac{2 \sqrt[3]{c+d x} \, _2F_1\left(-\frac{5}{2},-\frac{1}{3};-\frac{3}{2};\frac{d (a+b x)}{a d-b c}\right)}{5 b (a+b x)^{5/2} \sqrt[3]{\frac{b (c+d x)}{b c-a d}}}","-\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}} \operatorname{EllipticF}\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),4 \sqrt{3}-7\right)}{135 \sqrt[4]{3} b^{4/3} \sqrt{a+b x} (b c-a d)^2 \sqrt{-\frac{\sqrt[3]{b c-a d} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{28 d^2 \sqrt[3]{c+d x}}{135 b \sqrt{a+b x} (b c-a d)^2}-\frac{4 d \sqrt[3]{c+d x}}{45 b (a+b x)^{3/2} (b c-a d)}-\frac{2 \sqrt[3]{c+d x}}{5 b (a+b x)^{5/2}}",1,"(-2*(c + d*x)^(1/3)*Hypergeometric2F1[-5/2, -1/3, -3/2, (d*(a + b*x))/(-(b*c) + a*d)])/(5*b*(a + b*x)^(5/2)*((b*(c + d*x))/(b*c - a*d))^(1/3))","C",1
1565,1,73,839,0.0300441,"\int \frac{(a+b x)^{3/2}}{\sqrt[3]{c+d x}} \, dx","Integrate[(a + b*x)^(3/2)/(c + d*x)^(1/3),x]","\frac{2 (a+b x)^{5/2} \sqrt[3]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{1}{3},\frac{5}{2};\frac{7}{2};\frac{d (a+b x)}{a d-b c}\right)}{5 b \sqrt[3]{c+d x}}","\frac{81 \sqrt[4]{3} \sqrt{2+\sqrt{3}} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}{\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}\right)|-7+4 \sqrt{3}\right) (b c-a d)^{7/3}}{91 b^{2/3} d^3 \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b c-a d} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{54 \sqrt{2} 3^{3/4} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} \operatorname{EllipticF}\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,"(2*(a + b*x)^(5/2)*((b*(c + d*x))/(b*c - a*d))^(1/3)*Hypergeometric2F1[1/3, 5/2, 7/2, (d*(a + b*x))/(-(b*c) + a*d)])/(5*b*(c + d*x)^(1/3))","C",1
1566,1,73,804,0.0257555,"\int \frac{\sqrt{a+b x}}{\sqrt[3]{c+d x}} \, dx","Integrate[Sqrt[a + b*x]/(c + d*x)^(1/3),x]","\frac{2 (a+b x)^{3/2} \sqrt[3]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{1}{3},\frac{3}{2};\frac{5}{2};\frac{d (a+b x)}{a d-b c}\right)}{3 b \sqrt[3]{c+d x}}","-\frac{9 \sqrt[4]{3} \sqrt{2+\sqrt{3}} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}{\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}\right)|-7+4 \sqrt{3}\right) (b c-a d)^{4/3}}{7 b^{2/3} d^2 \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b c-a d} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{6 \sqrt{2} 3^{3/4} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} \operatorname{EllipticF}\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,"(2*(a + b*x)^(3/2)*((b*(c + d*x))/(b*c - a*d))^(1/3)*Hypergeometric2F1[1/3, 3/2, 5/2, (d*(a + b*x))/(-(b*c) + a*d)])/(3*b*(c + d*x)^(1/3))","C",1
1567,1,71,762,0.0217775,"\int \frac{1}{\sqrt{a+b x} \sqrt[3]{c+d x}} \, dx","Integrate[1/(Sqrt[a + b*x]*(c + d*x)^(1/3)),x]","\frac{2 \sqrt{a+b x} \sqrt[3]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{3}{2};\frac{d (a+b x)}{a d-b c}\right)}{b \sqrt[3]{c+d x}}","-\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}} \operatorname{EllipticF}\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),4 \sqrt{3}-7\right)}{b^{2/3} d \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b c-a d} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{6 \sqrt{a+b x}}{b^{2/3} \left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}+\frac{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,"(2*Sqrt[a + b*x]*((b*(c + d*x))/(b*c - a*d))^(1/3)*Hypergeometric2F1[1/3, 1/2, 3/2, (d*(a + b*x))/(-(b*c) + a*d)])/(b*(c + d*x)^(1/3))","C",1
1568,1,71,796,0.0226446,"\int \frac{1}{(a+b x)^{3/2} \sqrt[3]{c+d x}} \, dx","Integrate[1/((a + b*x)^(3/2)*(c + d*x)^(1/3)),x]","-\frac{2 \sqrt[3]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(-\frac{1}{2},\frac{1}{3};\frac{1}{2};\frac{d (a+b x)}{a d-b c}\right)}{b \sqrt{a+b x} \sqrt[3]{c+d x}}","-\frac{2 \sqrt{a+b x} d}{b^{2/3} (b c-a d) \left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}+\frac{\sqrt[4]{3} \sqrt{2+\sqrt{3}} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}{\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}\right)|-7+4 \sqrt{3}\right)}{b^{2/3} (b c-a d)^{2/3} \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b c-a d} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{2 \sqrt{2} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}{\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}\right),-7+4 \sqrt{3}\right)}{\sqrt[4]{3} b^{2/3} (b c-a d)^{2/3} \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b c-a d} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{2 (c+d x)^{2/3}}{(b c-a d) \sqrt{a+b x}}",1,"(-2*((b*(c + d*x))/(b*c - a*d))^(1/3)*Hypergeometric2F1[-1/2, 1/3, 1/2, (d*(a + b*x))/(-(b*c) + a*d)])/(b*Sqrt[a + b*x]*(c + d*x)^(1/3))","C",1
1569,1,73,842,0.0221991,"\int \frac{1}{(a+b x)^{5/2} \sqrt[3]{c+d x}} \, dx","Integrate[1/((a + b*x)^(5/2)*(c + d*x)^(1/3)),x]","-\frac{2 \sqrt[3]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(-\frac{3}{2},\frac{1}{3};-\frac{1}{2};\frac{d (a+b x)}{a d-b c}\right)}{3 b (a+b x)^{3/2} \sqrt[3]{c+d x}}","\frac{10 \sqrt{a+b x} d^2}{9 b^{2/3} (b c-a d)^2 \left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}-\frac{5 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}{\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}\right)|-7+4 \sqrt{3}\right) d}{3\ 3^{3/4} b^{2/3} (b c-a d)^{5/3} \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b c-a d} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{10 \sqrt{2} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}{\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}}\right),-7+4 \sqrt{3}\right) d}{9 \sqrt[4]{3} b^{2/3} (b c-a d)^{5/3} \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b c-a d} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{10 (c+d x)^{2/3} d}{9 (b c-a d)^2 \sqrt{a+b x}}-\frac{2 (c+d x)^{2/3}}{3 (b c-a d) (a+b x)^{3/2}}",1,"(-2*((b*(c + d*x))/(b*c - a*d))^(1/3)*Hypergeometric2F1[-3/2, 1/3, -1/2, (d*(a + b*x))/(-(b*c) + a*d)])/(3*b*(a + b*x)^(3/2)*(c + d*x)^(1/3))","C",1
1570,1,73,416,0.0347869,"\int \frac{(a+b x)^{3/2}}{(c+d x)^{2/3}} \, dx","Integrate[(a + b*x)^(3/2)/(c + d*x)^(2/3),x]","\frac{2 (a+b x)^{5/2} \left(\frac{b (c+d x)}{b c-a d}\right)^{2/3} \, _2F_1\left(\frac{2}{3},\frac{5}{2};\frac{7}{2};\frac{d (a+b x)}{a d-b c}\right)}{5 b (c+d x)^{2/3}}","-\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}} \operatorname{EllipticF}\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),4 \sqrt{3}-7\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,"(2*(a + b*x)^(5/2)*((b*(c + d*x))/(b*c - a*d))^(2/3)*Hypergeometric2F1[2/3, 5/2, 7/2, (d*(a + b*x))/(-(b*c) + a*d)])/(5*b*(c + d*x)^(2/3))","C",1
1571,1,73,381,0.026832,"\int \frac{\sqrt{a+b x}}{(c+d x)^{2/3}} \, dx","Integrate[Sqrt[a + b*x]/(c + d*x)^(2/3),x]","\frac{2 (a+b x)^{3/2} \left(\frac{b (c+d x)}{b c-a d}\right)^{2/3} \, _2F_1\left(\frac{2}{3},\frac{3}{2};\frac{5}{2};\frac{d (a+b x)}{a d-b c}\right)}{3 b (c+d x)^{2/3}}","\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}} \operatorname{EllipticF}\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),4 \sqrt{3}-7\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,"(2*(a + b*x)^(3/2)*((b*(c + d*x))/(b*c - a*d))^(2/3)*Hypergeometric2F1[2/3, 3/2, 5/2, (d*(a + b*x))/(-(b*c) + a*d)])/(3*b*(c + d*x)^(2/3))","C",1
1572,1,71,345,0.0227862,"\int \frac{1}{\sqrt{a+b x} (c+d x)^{2/3}} \, dx","Integrate[1/(Sqrt[a + b*x]*(c + d*x)^(2/3)),x]","\frac{2 \sqrt{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{2/3} \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{3}{2};\frac{d (a+b x)}{a d-b c}\right)}{b (c+d x)^{2/3}}","-\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}} \operatorname{EllipticF}\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),4 \sqrt{3}-7\right)}{\sqrt[3]{b} d \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b c-a d} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}",1,"(2*Sqrt[a + b*x]*((b*(c + d*x))/(b*c - a*d))^(2/3)*Hypergeometric2F1[1/2, 2/3, 3/2, (d*(a + b*x))/(-(b*c) + a*d)])/(b*(c + d*x)^(2/3))","C",1
1573,1,71,383,0.0233057,"\int \frac{1}{(a+b x)^{3/2} (c+d x)^{2/3}} \, dx","Integrate[1/((a + b*x)^(3/2)*(c + d*x)^(2/3)),x]","-\frac{2 \left(\frac{b (c+d x)}{b c-a d}\right)^{2/3} \, _2F_1\left(-\frac{1}{2},\frac{2}{3};\frac{1}{2};\frac{d (a+b x)}{a d-b c}\right)}{b \sqrt{a+b x} (c+d x)^{2/3}}","\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}} \operatorname{EllipticF}\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),4 \sqrt{3}-7\right)}{\sqrt[4]{3} \sqrt[3]{b} \sqrt{a+b x} (b c-a d) \sqrt{-\frac{\sqrt[3]{b c-a d} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{2 \sqrt[3]{c+d x}}{\sqrt{a+b x} (b c-a d)}",1,"(-2*((b*(c + d*x))/(b*c - a*d))^(2/3)*Hypergeometric2F1[-1/2, 2/3, 1/2, (d*(a + b*x))/(-(b*c) + a*d)])/(b*Sqrt[a + b*x]*(c + d*x)^(2/3))","C",1
1574,1,73,421,0.0227902,"\int \frac{1}{(a+b x)^{5/2} (c+d x)^{2/3}} \, dx","Integrate[1/((a + b*x)^(5/2)*(c + d*x)^(2/3)),x]","-\frac{2 \left(\frac{b (c+d x)}{b c-a d}\right)^{2/3} \, _2F_1\left(-\frac{3}{2},\frac{2}{3};-\frac{1}{2};\frac{d (a+b x)}{a d-b c}\right)}{3 b (a+b x)^{3/2} (c+d x)^{2/3}}","-\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}} \operatorname{EllipticF}\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),4 \sqrt{3}-7\right)}{9 \sqrt[4]{3} \sqrt[3]{b} \sqrt{a+b x} (b c-a d)^2 \sqrt{-\frac{\sqrt[3]{b c-a d} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{14 d \sqrt[3]{c+d x}}{9 \sqrt{a+b x} (b c-a d)^2}-\frac{2 \sqrt[3]{c+d x}}{3 (a+b x)^{3/2} (b c-a d)}",1,"(-2*((b*(c + d*x))/(b*c - a*d))^(2/3)*Hypergeometric2F1[-3/2, 2/3, -1/2, (d*(a + b*x))/(-(b*c) + a*d)])/(3*b*(a + b*x)^(3/2)*(c + d*x)^(2/3))","C",1
1575,1,73,219,0.0343739,"\int (a+b x)^{2/3} \sqrt[3]{c+d x} \, dx","Integrate[(a + b*x)^(2/3)*(c + d*x)^(1/3),x]","\frac{3 (a+b x)^{5/3} \sqrt[3]{c+d x} \, _2F_1\left(-\frac{1}{3},\frac{5}{3};\frac{8}{3};\frac{d (a+b x)}{a d-b c}\right)}{5 b \sqrt[3]{\frac{b (c+d x)}{b c-a d}}}","\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,"(3*(a + b*x)^(5/3)*(c + d*x)^(1/3)*Hypergeometric2F1[-1/3, 5/3, 8/3, (d*(a + b*x))/(-(b*c) + a*d)])/(5*b*((b*(c + d*x))/(b*c - a*d))^(1/3))","C",1
1576,1,73,172,0.0252238,"\int \frac{\sqrt[3]{c+d x}}{\sqrt[3]{a+b x}} \, dx","Integrate[(c + d*x)^(1/3)/(a + b*x)^(1/3),x]","\frac{3 (a+b x)^{2/3} \sqrt[3]{c+d x} \, _2F_1\left(-\frac{1}{3},\frac{2}{3};\frac{5}{3};\frac{d (a+b x)}{a d-b c}\right)}{2 b \sqrt[3]{\frac{b (c+d x)}{b c-a d}}}","-\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,"(3*(a + b*x)^(2/3)*(c + d*x)^(1/3)*Hypergeometric2F1[-1/3, 2/3, 5/3, (d*(a + b*x))/(-(b*c) + a*d)])/(2*b*((b*(c + d*x))/(b*c - a*d))^(1/3))","C",1
1577,1,71,149,0.0281139,"\int \frac{\sqrt[3]{c+d x}}{(a+b x)^{4/3}} \, dx","Integrate[(c + d*x)^(1/3)/(a + b*x)^(4/3),x]","-\frac{3 \sqrt[3]{c+d x} \, _2F_1\left(-\frac{1}{3},-\frac{1}{3};\frac{2}{3};\frac{d (a+b x)}{a d-b c}\right)}{b \sqrt[3]{a+b x} \sqrt[3]{\frac{b (c+d x)}{b c-a d}}}","-\frac{3 \sqrt[3]{d} \log \left(\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{b} \sqrt[3]{c+d x}}-1\right)}{2 b^{4/3}}-\frac{\sqrt{3} \sqrt[3]{d} \tan ^{-1}\left(\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt{3} \sqrt[3]{b} \sqrt[3]{c+d x}}+\frac{1}{\sqrt{3}}\right)}{b^{4/3}}-\frac{3 \sqrt[3]{c+d x}}{b \sqrt[3]{a+b x}}-\frac{\sqrt[3]{d} \log (c+d x)}{2 b^{4/3}}",1,"(-3*(c + d*x)^(1/3)*Hypergeometric2F1[-1/3, -1/3, 2/3, (d*(a + b*x))/(-(b*c) + a*d)])/(b*(a + b*x)^(1/3)*((b*(c + d*x))/(b*c - a*d))^(1/3))","C",1
1578,1,32,32,0.0125088,"\int \frac{\sqrt[3]{c+d x}}{(a+b x)^{7/3}} \, dx","Integrate[(c + d*x)^(1/3)/(a + b*x)^(7/3),x]","-\frac{3 (c+d x)^{4/3}}{4 (a+b x)^{4/3} (b c-a d)}","-\frac{3 (c+d x)^{4/3}}{4 (a+b x)^{4/3} (b c-a d)}",1,"(-3*(c + d*x)^(4/3))/(4*(b*c - a*d)*(a + b*x)^(4/3))","A",1
1579,1,46,66,0.0232246,"\int \frac{\sqrt[3]{c+d x}}{(a+b x)^{10/3}} \, dx","Integrate[(c + d*x)^(1/3)/(a + b*x)^(10/3),x]","\frac{3 (c+d x)^{4/3} (7 a d-4 b c+3 b d x)}{28 (a+b x)^{7/3} (b c-a d)^2}","\frac{9 d (c+d x)^{4/3}}{28 (a+b x)^{4/3} (b c-a d)^2}-\frac{3 (c+d x)^{4/3}}{7 (a+b x)^{7/3} (b c-a d)}",1,"(3*(c + d*x)^(4/3)*(-4*b*c + 7*a*d + 3*b*d*x))/(28*(b*c - a*d)^2*(a + b*x)^(7/3))","A",1
1580,1,77,101,0.0398404,"\int \frac{\sqrt[3]{c+d x}}{(a+b x)^{13/3}} \, dx","Integrate[(c + d*x)^(1/3)/(a + b*x)^(13/3),x]","-\frac{3 (c+d x)^{4/3} \left(35 a^2 d^2+10 a b d (3 d x-4 c)+b^2 \left(14 c^2-12 c d x+9 d^2 x^2\right)\right)}{140 (a+b x)^{10/3} (b c-a d)^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*(c + d*x)^(4/3)*(35*a^2*d^2 + 10*a*b*d*(-4*c + 3*d*x) + b^2*(14*c^2 - 12*c*d*x + 9*d^2*x^2)))/(140*(b*c - a*d)^3*(a + b*x)^(10/3))","A",1
1581,1,118,136,0.0575939,"\int \frac{\sqrt[3]{c+d x}}{(a+b x)^{16/3}} \, dx","Integrate[(c + d*x)^(1/3)/(a + b*x)^(16/3),x]","\frac{3 (c+d x)^{4/3} \left(455 a^3 d^3+195 a^2 b d^2 (3 d x-4 c)+39 a b^2 d \left(14 c^2-12 c d x+9 d^2 x^2\right)+b^3 \left(-140 c^3+126 c^2 d x-108 c d^2 x^2+81 d^3 x^3\right)\right)}{1820 (a+b x)^{13/3} (b c-a d)^4}","\frac{243 d^3 (c+d x)^{4/3}}{1820 (a+b x)^{4/3} (b c-a d)^4}-\frac{81 d^2 (c+d x)^{4/3}}{455 (a+b x)^{7/3} (b c-a d)^3}+\frac{27 d (c+d x)^{4/3}}{130 (a+b x)^{10/3} (b c-a d)^2}-\frac{3 (c+d x)^{4/3}}{13 (a+b x)^{13/3} (b c-a d)}",1,"(3*(c + d*x)^(4/3)*(455*a^3*d^3 + 195*a^2*b*d^2*(-4*c + 3*d*x) + 39*a*b^2*d*(14*c^2 - 12*c*d*x + 9*d^2*x^2) + b^3*(-140*c^3 + 126*c^2*d*x - 108*c*d^2*x^2 + 81*d^3*x^3)))/(1820*(b*c - a*d)^4*(a + b*x)^(13/3))","A",1
1582,1,73,655,0.0334937,"\int (a+b x)^{4/3} \sqrt[3]{c+d x} \, dx","Integrate[(a + b*x)^(4/3)*(c + d*x)^(1/3),x]","\frac{3 (a+b x)^{7/3} \sqrt[3]{c+d x} \, _2F_1\left(-\frac{1}{3},\frac{7}{3};\frac{10}{3};\frac{d (a+b x)}{a d-b c}\right)}{7 b \sqrt[3]{\frac{b (c+d x)}{b c-a d}}}","\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}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{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)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}}\right),-7-4 \sqrt{3}\right)}{10\ 2^{2/3} b^{4/3} d^{7/3} (a+b x)^{2/3} (c+d x)^{2/3} (a d+b c+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{2/3}\right)}{\left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}-\frac{3 \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c-a d)^2}{20 b d^2}+\frac{3 (a+b x)^{4/3} \sqrt[3]{c+d x} (b c-a d)}{40 b d}+\frac{3 (a+b x)^{7/3} \sqrt[3]{c+d x}}{8 b}",1,"(3*(a + b*x)^(7/3)*(c + d*x)^(1/3)*Hypergeometric2F1[-1/3, 7/3, 10/3, (d*(a + b*x))/(-(b*c) + a*d)])/(7*b*((b*(c + d*x))/(b*c - a*d))^(1/3))","C",1
1583,1,73,617,0.0327062,"\int \sqrt[3]{a+b x} \sqrt[3]{c+d x} \, dx","Integrate[(a + b*x)^(1/3)*(c + d*x)^(1/3),x]","\frac{3 (a+b x)^{4/3} \sqrt[3]{c+d x} \, _2F_1\left(-\frac{1}{3},\frac{4}{3};\frac{7}{3};\frac{d (a+b x)}{a d-b c}\right)}{4 b \sqrt[3]{\frac{b (c+d x)}{b c-a d}}}","-\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}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{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)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}}\right),-7-4 \sqrt{3}\right)}{5\ 2^{2/3} b^{4/3} d^{4/3} (a+b x)^{2/3} (c+d x)^{2/3} (a d+b c+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{2/3}\right)}{\left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}+\frac{3 \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c-a d)}{10 b d}+\frac{3 (a+b x)^{4/3} \sqrt[3]{c+d x}}{5 b}",1,"(3*(a + b*x)^(4/3)*(c + d*x)^(1/3)*Hypergeometric2F1[-1/3, 4/3, 7/3, (d*(a + b*x))/(-(b*c) + a*d)])/(4*b*((b*(c + d*x))/(b*c - a*d))^(1/3))","C",1
1584,1,71,576,0.0284594,"\int \frac{\sqrt[3]{c+d x}}{(a+b x)^{2/3}} \, dx","Integrate[(c + d*x)^(1/3)/(a + b*x)^(2/3),x]","\frac{3 \sqrt[3]{a+b x} \sqrt[3]{c+d x} \, _2F_1\left(-\frac{1}{3},\frac{1}{3};\frac{4}{3};\frac{d (a+b x)}{a d-b c}\right)}{b \sqrt[3]{\frac{b (c+d x)}{b c-a 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}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{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)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}}\right),-7-4 \sqrt{3}\right)}{2^{2/3} b^{4/3} \sqrt[3]{d} (a+b x)^{2/3} (c+d x)^{2/3} (a d+b c+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{2/3}\right)}{\left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}+\frac{3 \sqrt[3]{a+b x} \sqrt[3]{c+d x}}{2 b}",1,"(3*(a + b*x)^(1/3)*(c + d*x)^(1/3)*Hypergeometric2F1[-1/3, 1/3, 4/3, (d*(a + b*x))/(-(b*c) + a*d)])/(b*((b*(c + d*x))/(b*c - a*d))^(1/3))","C",1
1585,1,73,568,0.0234652,"\int \frac{\sqrt[3]{c+d x}}{(a+b x)^{5/3}} \, dx","Integrate[(c + d*x)^(1/3)/(a + b*x)^(5/3),x]","-\frac{3 \sqrt[3]{c+d x} \, _2F_1\left(-\frac{2}{3},-\frac{1}{3};\frac{1}{3};\frac{d (a+b x)}{a d-b c}\right)}{2 b (a+b x)^{2/3} \sqrt[3]{\frac{b (c+d x)}{b c-a d}}}","\frac{3^{3/4} \sqrt{2+\sqrt{3}} d^{2/3} ((a+b x) (c+d x))^{2/3} \sqrt{(a d+b c+2 b d x)^2} \left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{2/3}\right) \sqrt{\frac{2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} (b c-a d)^{2/3} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{4/3}}{\left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}\right)^2}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{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)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}}\right),-7-4 \sqrt{3}\right)}{2^{2/3} b^{4/3} (a+b x)^{2/3} (c+d x)^{2/3} (a d+b c+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{2/3}\right)}{\left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}-\frac{3 \sqrt[3]{c+d x}}{2 b (a+b x)^{2/3}}",1,"(-3*(c + d*x)^(1/3)*Hypergeometric2F1[-2/3, -1/3, 1/3, (d*(a + b*x))/(-(b*c) + a*d)])/(2*b*(a + b*x)^(2/3)*((b*(c + d*x))/(b*c - a*d))^(1/3))","C",1
1586,1,73,617,0.0270454,"\int \frac{\sqrt[3]{c+d x}}{(a+b x)^{8/3}} \, dx","Integrate[(c + d*x)^(1/3)/(a + b*x)^(8/3),x]","-\frac{3 \sqrt[3]{c+d x} \, _2F_1\left(-\frac{5}{3},-\frac{1}{3};-\frac{2}{3};\frac{d (a+b x)}{a d-b c}\right)}{5 b (a+b x)^{5/3} \sqrt[3]{\frac{b (c+d x)}{b c-a d}}}","-\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}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{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)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}}\right),-7-4 \sqrt{3}\right)}{5\ 2^{2/3} b^{4/3} (a+b x)^{2/3} (c+d x)^{2/3} (b c-a d) (a d+b c+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{2/3}\right)}{\left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}-\frac{3 d \sqrt[3]{c+d x}}{10 b (a+b x)^{2/3} (b c-a d)}-\frac{3 \sqrt[3]{c+d x}}{5 b (a+b x)^{5/3}}",1,"(-3*(c + d*x)^(1/3)*Hypergeometric2F1[-5/3, -1/3, -2/3, (d*(a + b*x))/(-(b*c) + a*d)])/(5*b*(a + b*x)^(5/3)*((b*(c + d*x))/(b*c - a*d))^(1/3))","C",1
1587,1,73,216,0.0303987,"\int \frac{(a+b x)^{4/3}}{\sqrt[3]{c+d x}} \, dx","Integrate[(a + b*x)^(4/3)/(c + d*x)^(1/3),x]","\frac{3 (a+b x)^{7/3} \sqrt[3]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{1}{3},\frac{7}{3};\frac{10}{3};\frac{d (a+b x)}{a d-b c}\right)}{7 b \sqrt[3]{c+d x}}","-\frac{(b c-a d)^2 \log (a+b x)}{9 b^{2/3} d^{7/3}}-\frac{(b c-a d)^2 \log \left(\frac{\sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{d} \sqrt[3]{a+b x}}-1\right)}{3 b^{2/3} d^{7/3}}-\frac{2 (b c-a d)^2 \tan ^{-1}\left(\frac{2 \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt{3} \sqrt[3]{d} \sqrt[3]{a+b x}}+\frac{1}{\sqrt{3}}\right)}{3 \sqrt{3} b^{2/3} d^{7/3}}-\frac{2 \sqrt[3]{a+b x} (c+d x)^{2/3} (b c-a d)}{3 d^2}+\frac{(a+b x)^{4/3} (c+d x)^{2/3}}{2 d}",1,"(3*(a + b*x)^(7/3)*((b*(c + d*x))/(b*c - a*d))^(1/3)*Hypergeometric2F1[1/3, 7/3, 10/3, (d*(a + b*x))/(-(b*c) + a*d)])/(7*b*(c + d*x)^(1/3))","C",1
1588,1,73,171,0.0290112,"\int \frac{\sqrt[3]{a+b x}}{\sqrt[3]{c+d x}} \, dx","Integrate[(a + b*x)^(1/3)/(c + d*x)^(1/3),x]","\frac{3 (a+b x)^{4/3} \sqrt[3]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{1}{3},\frac{4}{3};\frac{7}{3};\frac{d (a+b x)}{a d-b c}\right)}{4 b \sqrt[3]{c+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,"(3*(a + b*x)^(4/3)*((b*(c + d*x))/(b*c - a*d))^(1/3)*Hypergeometric2F1[1/3, 4/3, 7/3, (d*(a + b*x))/(-(b*c) + a*d)])/(4*b*(c + d*x)^(1/3))","C",1
1589,1,71,126,0.0285392,"\int \frac{1}{(a+b x)^{2/3} \sqrt[3]{c+d x}} \, dx","Integrate[1/((a + b*x)^(2/3)*(c + d*x)^(1/3)),x]","\frac{3 \sqrt[3]{a+b x} \sqrt[3]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{1}{3},\frac{1}{3};\frac{4}{3};\frac{d (a+b x)}{a d-b c}\right)}{b \sqrt[3]{c+d x}}","-\frac{3 \log \left(\frac{\sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{d} \sqrt[3]{a+b x}}-1\right)}{2 b^{2/3} \sqrt[3]{d}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt{3} \sqrt[3]{d} \sqrt[3]{a+b x}}+\frac{1}{\sqrt{3}}\right)}{b^{2/3} \sqrt[3]{d}}-\frac{\log (a+b x)}{2 b^{2/3} \sqrt[3]{d}}",1,"(3*(a + b*x)^(1/3)*((b*(c + d*x))/(b*c - a*d))^(1/3)*Hypergeometric2F1[1/3, 1/3, 4/3, (d*(a + b*x))/(-(b*c) + a*d)])/(b*(c + d*x)^(1/3))","C",1
1590,1,32,32,0.0119731,"\int \frac{1}{(a+b x)^{5/3} \sqrt[3]{c+d x}} \, dx","Integrate[1/((a + b*x)^(5/3)*(c + d*x)^(1/3)),x]","-\frac{3 (c+d x)^{2/3}}{2 (a+b x)^{2/3} (b c-a d)}","-\frac{3 (c+d x)^{2/3}}{2 (a+b x)^{2/3} (b c-a d)}",1,"(-3*(c + d*x)^(2/3))/(2*(b*c - a*d)*(a + b*x)^(2/3))","A",1
1591,1,46,66,0.0169757,"\int \frac{1}{(a+b x)^{8/3} \sqrt[3]{c+d x}} \, dx","Integrate[1/((a + b*x)^(8/3)*(c + d*x)^(1/3)),x]","\frac{3 (c+d x)^{2/3} (5 a d-2 b c+3 b d x)}{10 (a+b x)^{5/3} (b c-a d)^2}","\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)*(-2*b*c + 5*a*d + 3*b*d*x))/(10*(b*c - a*d)^2*(a + b*x)^(5/3))","A",1
1592,1,77,101,0.0335812,"\int \frac{1}{(a+b x)^{11/3} \sqrt[3]{c+d x}} \, dx","Integrate[1/((a + b*x)^(11/3)*(c + d*x)^(1/3)),x]","-\frac{3 (c+d x)^{2/3} \left(20 a^2 d^2+8 a b d (3 d x-2 c)+b^2 \left(5 c^2-6 c d x+9 d^2 x^2\right)\right)}{40 (a+b x)^{8/3} (b c-a d)^3}","-\frac{27 d^2 (c+d x)^{2/3}}{40 (a+b x)^{2/3} (b c-a d)^3}+\frac{9 d (c+d x)^{2/3}}{20 (a+b x)^{5/3} (b c-a d)^2}-\frac{3 (c+d x)^{2/3}}{8 (a+b x)^{8/3} (b c-a d)}",1,"(-3*(c + d*x)^(2/3)*(20*a^2*d^2 + 8*a*b*d*(-2*c + 3*d*x) + b^2*(5*c^2 - 6*c*d*x + 9*d^2*x^2)))/(40*(b*c - a*d)^3*(a + b*x)^(8/3))","A",1
1593,1,118,136,0.0477465,"\int \frac{1}{(a+b x)^{14/3} \sqrt[3]{c+d x}} \, dx","Integrate[1/((a + b*x)^(14/3)*(c + d*x)^(1/3)),x]","\frac{3 (c+d x)^{2/3} \left(220 a^3 d^3+132 a^2 b d^2 (3 d x-2 c)+33 a b^2 d \left(5 c^2-6 c d x+9 d^2 x^2\right)+b^3 \left(-40 c^3+45 c^2 d x-54 c d^2 x^2+81 d^3 x^3\right)\right)}{440 (a+b x)^{11/3} (b c-a d)^4}","\frac{243 d^3 (c+d x)^{2/3}}{440 (a+b x)^{2/3} (b c-a d)^4}-\frac{81 d^2 (c+d x)^{2/3}}{220 (a+b x)^{5/3} (b c-a d)^3}+\frac{27 d (c+d x)^{2/3}}{88 (a+b x)^{8/3} (b c-a d)^2}-\frac{3 (c+d x)^{2/3}}{11 (a+b x)^{11/3} (b c-a d)}",1,"(3*(c + d*x)^(2/3)*(220*a^3*d^3 + 132*a^2*b*d^2*(-2*c + 3*d*x) + 33*a*b^2*d*(5*c^2 - 6*c*d*x + 9*d^2*x^2) + b^3*(-40*c^3 + 45*c^2*d*x - 54*c*d^2*x^2 + 81*d^3*x^3)))/(440*(b*c - a*d)^4*(a + b*x)^(11/3))","A",1
1594,1,73,1365,0.0343684,"\int \frac{(a+b x)^{8/3}}{\sqrt[3]{c+d x}} \, dx","Integrate[(a + b*x)^(8/3)/(c + d*x)^(1/3),x]","\frac{3 (a+b x)^{11/3} \sqrt[3]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{1}{3},\frac{11}{3};\frac{14}{3};\frac{d (a+b x)}{a d-b c}\right)}{11 b \sqrt[3]{c+d x}}","\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right) (b c-a d)^{11/3}}{7 \sqrt[3]{2} b^{2/3} d^{11/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}-\frac{2 \sqrt[6]{2} 3^{3/4} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right),-7-4 \sqrt{3}\right) (b c-a d)^{11/3}}{7 b^{2/3} d^{11/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}-\frac{3\ 2^{2/3} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \sqrt{(a d+b (c+2 d x))^2} (b c-a d)^3}{7 b^{2/3} d^{11/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}+\frac{3 (a+b x)^{2/3} (c+d x)^{2/3} (b c-a d)^2}{7 d^3}-\frac{12 (a+b x)^{5/3} (c+d x)^{2/3} (b c-a d)}{35 d^2}+\frac{3 (a+b x)^{8/3} (c+d x)^{2/3}}{10 d}",1,"(3*(a + b*x)^(11/3)*((b*(c + d*x))/(b*c - a*d))^(1/3)*Hypergeometric2F1[1/3, 11/3, 14/3, (d*(a + b*x))/(-(b*c) + a*d)])/(11*b*(c + d*x)^(1/3))","C",1
1595,1,73,1330,0.0348549,"\int \frac{(a+b x)^{5/3}}{\sqrt[3]{c+d x}} \, dx","Integrate[(a + b*x)^(5/3)/(c + d*x)^(1/3),x]","\frac{3 (a+b x)^{8/3} \sqrt[3]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{1}{3},\frac{8}{3};\frac{11}{3};\frac{d (a+b x)}{a d-b c}\right)}{8 b \sqrt[3]{c+d x}}","-\frac{15 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right) (b c-a d)^{8/3}}{28 \sqrt[3]{2} b^{2/3} d^{8/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}+\frac{5\ 3^{3/4} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \operatorname{EllipticF}\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,"(3*(a + b*x)^(8/3)*((b*(c + d*x))/(b*c - a*d))^(1/3)*Hypergeometric2F1[1/3, 8/3, 11/3, (d*(a + b*x))/(-(b*c) + a*d)])/(8*b*(c + d*x)^(1/3))","C",1
1596,1,73,1293,0.028965,"\int \frac{(a+b x)^{2/3}}{\sqrt[3]{c+d x}} \, dx","Integrate[(a + b*x)^(2/3)/(c + d*x)^(1/3),x]","\frac{3 (a+b x)^{5/3} \sqrt[3]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{1}{3},\frac{5}{3};\frac{8}{3};\frac{d (a+b x)}{a d-b c}\right)}{5 b \sqrt[3]{c+d x}}","\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right) (b c-a d)^{5/3}}{4 \sqrt[3]{2} b^{2/3} d^{5/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}-\frac{3^{3/4} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right),-7-4 \sqrt{3}\right) (b c-a d)^{5/3}}{2^{5/6} b^{2/3} d^{5/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}-\frac{3 \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \sqrt{(a d+b (c+2 d x))^2} (b c-a d)}{2 \sqrt[3]{2} b^{2/3} d^{5/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}+\frac{3 (a+b x)^{2/3} (c+d x)^{2/3}}{4 d}",1,"(3*(a + b*x)^(5/3)*((b*(c + d*x))/(b*c - a*d))^(1/3)*Hypergeometric2F1[1/3, 5/3, 8/3, (d*(a + b*x))/(-(b*c) + a*d)])/(5*b*(c + d*x)^(1/3))","C",1
1597,1,73,1257,0.0231918,"\int \frac{1}{\sqrt[3]{a+b x} \sqrt[3]{c+d x}} \, dx","Integrate[1/((a + b*x)^(1/3)*(c + d*x)^(1/3)),x]","\frac{3 (a+b x)^{2/3} \sqrt[3]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{5}{3};\frac{d (a+b x)}{a d-b c}\right)}{2 b \sqrt[3]{c+d x}}","-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} (b c-a d)^{2/3} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right)}{2 \sqrt[3]{2} b^{2/3} d^{2/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}+\frac{\sqrt[6]{2} 3^{3/4} (b c-a d)^{2/3} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right),-7-4 \sqrt{3}\right)}{b^{2/3} d^{2/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}+\frac{3 \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \sqrt{(a d+b (c+2 d x))^2}}{\sqrt[3]{2} b^{2/3} d^{2/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}",1,"(3*(a + b*x)^(2/3)*((b*(c + d*x))/(b*c - a*d))^(1/3)*Hypergeometric2F1[1/3, 2/3, 5/3, (d*(a + b*x))/(-(b*c) + a*d)])/(2*b*(c + d*x)^(1/3))","C",1
1598,1,71,1297,0.0238362,"\int \frac{1}{(a+b x)^{4/3} \sqrt[3]{c+d x}} \, dx","Integrate[1/((a + b*x)^(4/3)*(c + d*x)^(1/3)),x]","-\frac{3 \sqrt[3]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(-\frac{1}{3},\frac{1}{3};\frac{2}{3};\frac{d (a+b x)}{a d-b c}\right)}{b \sqrt[3]{a+b x} \sqrt[3]{c+d x}}","-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right)}{2 \sqrt[3]{2} b^{2/3} \sqrt[3]{b c-a d} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}+\frac{\sqrt[6]{2} 3^{3/4} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right),-7-4 \sqrt{3}\right)}{b^{2/3} \sqrt[3]{b c-a d} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}-\frac{3 (c+d x)^{2/3}}{(b c-a d) \sqrt[3]{a+b x}}+\frac{3 \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \sqrt{(a d+b (c+2 d x))^2}}{\sqrt[3]{2} b^{2/3} (b c-a d) \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}",1,"(-3*((b*(c + d*x))/(b*c - a*d))^(1/3)*Hypergeometric2F1[-1/3, 1/3, 2/3, (d*(a + b*x))/(-(b*c) + a*d)])/(b*(a + b*x)^(1/3)*(c + d*x)^(1/3))","C",1
1599,1,73,1335,0.0248664,"\int \frac{1}{(a+b x)^{7/3} \sqrt[3]{c+d x}} \, dx","Integrate[1/((a + b*x)^(7/3)*(c + d*x)^(1/3)),x]","-\frac{3 \sqrt[3]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(-\frac{4}{3},\frac{1}{3};-\frac{1}{3};\frac{d (a+b x)}{a d-b c}\right)}{4 b (a+b x)^{4/3} \sqrt[3]{c+d x}}","\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right) d^{4/3}}{4 \sqrt[3]{2} b^{2/3} (b c-a d)^{4/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}-\frac{3^{3/4} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right),-7-4 \sqrt{3}\right) d^{4/3}}{2^{5/6} b^{2/3} (b c-a d)^{4/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}-\frac{3 \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \sqrt{(a d+b (c+2 d x))^2} d^{4/3}}{2 \sqrt[3]{2} b^{2/3} (b c-a d)^2 \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}+\frac{3 (c+d x)^{2/3} d}{2 (b c-a d)^2 \sqrt[3]{a+b x}}-\frac{3 (c+d x)^{2/3}}{4 (b c-a d) (a+b x)^{4/3}}",1,"(-3*((b*(c + d*x))/(b*c - a*d))^(1/3)*Hypergeometric2F1[-4/3, 1/3, -1/3, (d*(a + b*x))/(-(b*c) + a*d)])/(4*b*(a + b*x)^(4/3)*(c + d*x)^(1/3))","C",1
1600,1,73,1372,0.0250915,"\int \frac{1}{(a+b x)^{10/3} \sqrt[3]{c+d x}} \, dx","Integrate[1/((a + b*x)^(10/3)*(c + d*x)^(1/3)),x]","-\frac{3 \sqrt[3]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(-\frac{7}{3},\frac{1}{3};-\frac{4}{3};\frac{d (a+b x)}{a d-b c}\right)}{7 b (a+b x)^{7/3} \sqrt[3]{c+d x}}","-\frac{15 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right)|-7-4 \sqrt{3}\right) d^{7/3}}{28 \sqrt[3]{2} b^{2/3} (b c-a d)^{7/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}+\frac{5\ 3^{3/4} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right) \sqrt{\frac{(b c-a d)^{4/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)} (b c-a d)^{2/3}+2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right),-7-4 \sqrt{3}\right) d^{7/3}}{7\ 2^{5/6} b^{2/3} (b c-a d)^{7/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}+\frac{15 \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \sqrt{(a d+b (c+2 d x))^2} d^{7/3}}{14 \sqrt[3]{2} b^{2/3} (b c-a d)^3 \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}-\frac{15 (c+d x)^{2/3} d^2}{14 (b c-a d)^3 \sqrt[3]{a+b x}}+\frac{15 (c+d x)^{2/3} d}{28 (b c-a d)^2 (a+b x)^{4/3}}-\frac{3 (c+d x)^{2/3}}{7 (b c-a d) (a+b x)^{7/3}}",1,"(-3*((b*(c + d*x))/(b*c - a*d))^(1/3)*Hypergeometric2F1[-7/3, 1/3, -4/3, (d*(a + b*x))/(-(b*c) + a*d)])/(7*b*(a + b*x)^(7/3)*(c + d*x)^(1/3))","C",1
1601,1,73,216,0.0354639,"\int \frac{(a+b x)^{5/3}}{(c+d x)^{2/3}} \, dx","Integrate[(a + b*x)^(5/3)/(c + d*x)^(2/3),x]","\frac{3 (a+b x)^{8/3} \left(\frac{b (c+d x)}{b c-a d}\right)^{2/3} \, _2F_1\left(\frac{2}{3},\frac{8}{3};\frac{11}{3};\frac{d (a+b x)}{a d-b c}\right)}{8 b (c+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,"(3*(a + b*x)^(8/3)*((b*(c + d*x))/(b*c - a*d))^(2/3)*Hypergeometric2F1[2/3, 8/3, 11/3, (d*(a + b*x))/(-(b*c) + a*d)])/(8*b*(c + d*x)^(2/3))","C",1
1602,1,73,169,0.0266368,"\int \frac{(a+b x)^{2/3}}{(c+d x)^{2/3}} \, dx","Integrate[(a + b*x)^(2/3)/(c + d*x)^(2/3),x]","\frac{3 (a+b x)^{5/3} \left(\frac{b (c+d x)}{b c-a d}\right)^{2/3} \, _2F_1\left(\frac{2}{3},\frac{5}{3};\frac{8}{3};\frac{d (a+b x)}{a d-b c}\right)}{5 b (c+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,"(3*(a + b*x)^(5/3)*((b*(c + d*x))/(b*c - a*d))^(2/3)*Hypergeometric2F1[2/3, 5/3, 8/3, (d*(a + b*x))/(-(b*c) + a*d)])/(5*b*(c + d*x)^(2/3))","C",1
1603,1,73,126,0.0295233,"\int \frac{1}{\sqrt[3]{a+b x} (c+d x)^{2/3}} \, dx","Integrate[1/((a + b*x)^(1/3)*(c + d*x)^(2/3)),x]","\frac{3 (a+b x)^{2/3} \left(\frac{b (c+d x)}{b c-a d}\right)^{2/3} \, _2F_1\left(\frac{2}{3},\frac{2}{3};\frac{5}{3};\frac{d (a+b x)}{a d-b c}\right)}{2 b (c+d x)^{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,"(3*(a + b*x)^(2/3)*((b*(c + d*x))/(b*c - a*d))^(2/3)*Hypergeometric2F1[2/3, 2/3, 5/3, (d*(a + b*x))/(-(b*c) + a*d)])/(2*b*(c + d*x)^(2/3))","C",1
1604,1,30,30,0.008748,"\int \frac{1}{(a+b x)^{4/3} (c+d x)^{2/3}} \, dx","Integrate[1/((a + b*x)^(4/3)*(c + d*x)^(2/3)),x]","\frac{3 \sqrt[3]{c+d x}}{\sqrt[3]{a+b x} (a d-b c)}","-\frac{3 \sqrt[3]{c+d x}}{\sqrt[3]{a+b x} (b c-a d)}",1,"(3*(c + d*x)^(1/3))/((-(b*c) + a*d)*(a + b*x)^(1/3))","A",1
1605,1,46,66,0.0170404,"\int \frac{1}{(a+b x)^{7/3} (c+d x)^{2/3}} \, dx","Integrate[1/((a + b*x)^(7/3)*(c + d*x)^(2/3)),x]","\frac{3 \sqrt[3]{c+d x} (4 a d-b c+3 b d x)}{4 (a+b x)^{4/3} (b c-a d)^2}","\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)*(-(b*c) + 4*a*d + 3*b*d*x))/(4*(b*c - a*d)^2*(a + b*x)^(4/3))","A",1
1606,1,75,101,0.0333148,"\int \frac{1}{(a+b x)^{10/3} (c+d x)^{2/3}} \, dx","Integrate[1/((a + b*x)^(10/3)*(c + d*x)^(2/3)),x]","-\frac{3 \sqrt[3]{c+d x} \left(14 a^2 d^2-7 a b d (c-3 d x)+b^2 \left(2 c^2-3 c d x+9 d^2 x^2\right)\right)}{14 (a+b x)^{7/3} (b c-a d)^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*(c + d*x)^(1/3)*(14*a^2*d^2 - 7*a*b*d*(c - 3*d*x) + b^2*(2*c^2 - 3*c*d*x + 9*d^2*x^2)))/(14*(b*c - a*d)^3*(a + b*x)^(7/3))","A",1
1607,1,116,136,0.0491414,"\int \frac{1}{(a+b x)^{13/3} (c+d x)^{2/3}} \, dx","Integrate[1/((a + b*x)^(13/3)*(c + d*x)^(2/3)),x]","\frac{3 \sqrt[3]{c+d x} \left(140 a^3 d^3-105 a^2 b d^2 (c-3 d x)+30 a b^2 d \left(2 c^2-3 c d x+9 d^2 x^2\right)+b^3 \left(-14 c^3+18 c^2 d x-27 c d^2 x^2+81 d^3 x^3\right)\right)}{140 (a+b x)^{10/3} (b c-a d)^4}","\frac{243 d^3 \sqrt[3]{c+d x}}{140 \sqrt[3]{a+b x} (b c-a d)^4}-\frac{81 d^2 \sqrt[3]{c+d x}}{140 (a+b x)^{4/3} (b c-a d)^3}+\frac{27 d \sqrt[3]{c+d x}}{70 (a+b x)^{7/3} (b c-a d)^2}-\frac{3 \sqrt[3]{c+d x}}{10 (a+b x)^{10/3} (b c-a d)}",1,"(3*(c + d*x)^(1/3)*(140*a^3*d^3 - 105*a^2*b*d^2*(c - 3*d*x) + 30*a*b^2*d*(2*c^2 - 3*c*d*x + 9*d^2*x^2) + b^3*(-14*c^3 + 18*c^2*d*x - 27*c*d^2*x^2 + 81*d^3*x^3)))/(140*(b*c - a*d)^4*(a + b*x)^(10/3))","A",1
1608,1,73,649,0.0338651,"\int \frac{(a+b x)^{7/3}}{(c+d x)^{2/3}} \, dx","Integrate[(a + b*x)^(7/3)/(c + d*x)^(2/3),x]","\frac{3 (a+b x)^{10/3} \left(\frac{b (c+d x)}{b c-a d}\right)^{2/3} \, _2F_1\left(\frac{2}{3},\frac{10}{3};\frac{13}{3};\frac{d (a+b x)}{a d-b c}\right)}{10 b (c+d x)^{2/3}}","-\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}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{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)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}}\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,"(3*(a + b*x)^(10/3)*((b*(c + d*x))/(b*c - a*d))^(2/3)*Hypergeometric2F1[2/3, 10/3, 13/3, (d*(a + b*x))/(-(b*c) + a*d)])/(10*b*(c + d*x)^(2/3))","C",1
1609,1,73,614,0.0299742,"\int \frac{(a+b x)^{4/3}}{(c+d x)^{2/3}} \, dx","Integrate[(a + b*x)^(4/3)/(c + d*x)^(2/3),x]","\frac{3 (a+b x)^{7/3} \left(\frac{b (c+d x)}{b c-a d}\right)^{2/3} \, _2F_1\left(\frac{2}{3},\frac{7}{3};\frac{10}{3};\frac{d (a+b x)}{a d-b c}\right)}{7 b (c+d x)^{2/3}}","\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}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{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)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}}\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,"(3*(a + b*x)^(7/3)*((b*(c + d*x))/(b*c - a*d))^(2/3)*Hypergeometric2F1[2/3, 7/3, 10/3, (d*(a + b*x))/(-(b*c) + a*d)])/(7*b*(c + d*x)^(2/3))","C",1
1610,1,73,577,0.0270241,"\int \frac{\sqrt[3]{a+b x}}{(c+d x)^{2/3}} \, dx","Integrate[(a + b*x)^(1/3)/(c + d*x)^(2/3),x]","\frac{3 (a+b x)^{4/3} \left(\frac{b (c+d x)}{b c-a d}\right)^{2/3} \, _2F_1\left(\frac{2}{3},\frac{4}{3};\frac{7}{3};\frac{d (a+b x)}{a d-b c}\right)}{4 b (c+d x)^{2/3}}","\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}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{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)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}}\right),-7-4 \sqrt{3}\right)}{2^{2/3} \sqrt[3]{b} d^{4/3} (a+b x)^{2/3} (c+d x)^{2/3} (a d+b c+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{2/3}\right)}{\left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}",1,"(3*(a + b*x)^(4/3)*((b*(c + d*x))/(b*c - a*d))^(2/3)*Hypergeometric2F1[2/3, 4/3, 7/3, (d*(a + b*x))/(-(b*c) + a*d)])/(4*b*(c + d*x)^(2/3))","C",1
1611,1,71,542,0.0229152,"\int \frac{1}{(a+b x)^{2/3} (c+d x)^{2/3}} \, dx","Integrate[1/((a + b*x)^(2/3)*(c + d*x)^(2/3)),x]","\frac{3 \sqrt[3]{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{2/3} \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{4}{3};\frac{d (a+b x)}{a d-b c}\right)}{b (c+d x)^{2/3}}","\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}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{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)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}}\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,"(3*(a + b*x)^(1/3)*((b*(c + d*x))/(b*c - a*d))^(2/3)*Hypergeometric2F1[1/3, 2/3, 4/3, (d*(a + b*x))/(-(b*c) + a*d)])/(b*(c + d*x)^(2/3))","C",1
1612,1,73,586,0.0239316,"\int \frac{1}{(a+b x)^{5/3} (c+d x)^{2/3}} \, dx","Integrate[1/((a + b*x)^(5/3)*(c + d*x)^(2/3)),x]","-\frac{3 \left(\frac{b (c+d x)}{b c-a d}\right)^{2/3} \, _2F_1\left(-\frac{2}{3},\frac{2}{3};\frac{1}{3};\frac{d (a+b x)}{a d-b c}\right)}{2 b (a+b x)^{2/3} (c+d x)^{2/3}}","-\frac{3^{3/4} \sqrt{2+\sqrt{3}} d^{2/3} ((a+b x) (c+d x))^{2/3} \sqrt{(a d+b c+2 b d x)^2} \left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{2/3}\right) \sqrt{\frac{2 \sqrt[3]{2} b^{2/3} d^{2/3} ((a+b x) (c+d x))^{2/3}-2^{2/3} \sqrt[3]{b} \sqrt[3]{d} (b c-a d)^{2/3} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{4/3}}{\left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}\right)^2}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{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)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}}\right),-7-4 \sqrt{3}\right)}{2^{2/3} \sqrt[3]{b} (a+b x)^{2/3} (c+d x)^{2/3} (b c-a d) (a d+b c+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{2/3}\right)}{\left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}-\frac{3 \sqrt[3]{c+d x}}{2 (a+b x)^{2/3} (b c-a d)}",1,"(-3*((b*(c + d*x))/(b*c - a*d))^(2/3)*Hypergeometric2F1[-2/3, 2/3, 1/3, (d*(a + b*x))/(-(b*c) + a*d)])/(2*b*(a + b*x)^(2/3)*(c + d*x)^(2/3))","C",1
1613,1,73,621,0.0238815,"\int \frac{1}{(a+b x)^{8/3} (c+d x)^{2/3}} \, dx","Integrate[1/((a + b*x)^(8/3)*(c + d*x)^(2/3)),x]","-\frac{3 \left(\frac{b (c+d x)}{b c-a d}\right)^{2/3} \, _2F_1\left(-\frac{5}{3},\frac{2}{3};-\frac{2}{3};\frac{d (a+b x)}{a d-b c}\right)}{5 b (a+b x)^{5/3} (c+d x)^{2/3}}","\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}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{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)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}}\right),-7-4 \sqrt{3}\right)}{5 \sqrt[3]{b} (a+b x)^{2/3} (c+d x)^{2/3} (b c-a d)^2 (a d+b c+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{2/3}\right)}{\left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}+\frac{6 d \sqrt[3]{c+d x}}{5 (a+b x)^{2/3} (b c-a d)^2}-\frac{3 \sqrt[3]{c+d x}}{5 (a+b x)^{5/3} (b c-a d)}",1,"(-3*((b*(c + d*x))/(b*c - a*d))^(2/3)*Hypergeometric2F1[-5/3, 2/3, -2/3, (d*(a + b*x))/(-(b*c) + a*d)])/(5*b*(a + b*x)^(5/3)*(c + d*x)^(2/3))","C",1
1614,1,73,656,0.0255738,"\int \frac{1}{(a+b x)^{11/3} (c+d x)^{2/3}} \, dx","Integrate[1/((a + b*x)^(11/3)*(c + d*x)^(2/3)),x]","-\frac{3 \left(\frac{b (c+d x)}{b c-a d}\right)^{2/3} \, _2F_1\left(-\frac{8}{3},\frac{2}{3};-\frac{5}{3};\frac{d (a+b x)}{a d-b c}\right)}{8 b (a+b x)^{8/3} (c+d x)^{2/3}}","-\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}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{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)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}}\right),-7-4 \sqrt{3}\right)}{10\ 2^{2/3} \sqrt[3]{b} (a+b x)^{2/3} (c+d x)^{2/3} (b c-a d)^3 (a d+b c+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+(b c-a d)^{2/3}\right)}{\left(2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}+\left(1+\sqrt{3}\right) (b c-a d)^{2/3}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}-\frac{21 d^2 \sqrt[3]{c+d x}}{20 (a+b x)^{2/3} (b c-a d)^3}+\frac{21 d \sqrt[3]{c+d x}}{40 (a+b x)^{5/3} (b c-a d)^2}-\frac{3 \sqrt[3]{c+d x}}{8 (a+b x)^{8/3} (b c-a d)}",1,"(-3*((b*(c + d*x))/(b*c - a*d))^(2/3)*Hypergeometric2F1[-8/3, 2/3, -5/3, (d*(a + b*x))/(-(b*c) + a*d)])/(8*b*(a + b*x)^(8/3)*(c + d*x)^(2/3))","C",1
1615,1,73,241,0.0617649,"\int \frac{(a+b x)^{7/3}}{(c+d x)^{4/3}} \, dx","Integrate[(a + b*x)^(7/3)/(c + d*x)^(4/3),x]","\frac{3 (a+b x)^{10/3} \left(\frac{b (c+d x)}{b c-a d}\right)^{4/3} \, _2F_1\left(\frac{4}{3},\frac{10}{3};\frac{13}{3};\frac{d (a+b x)}{a d-b c}\right)}{10 b (c+d x)^{4/3}}","-\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,"(3*(a + b*x)^(10/3)*((b*(c + d*x))/(b*c - a*d))^(4/3)*Hypergeometric2F1[4/3, 10/3, 13/3, (d*(a + b*x))/(-(b*c) + a*d)])/(10*b*(c + d*x)^(4/3))","C",1
1616,1,73,195,0.0483365,"\int \frac{(a+b x)^{4/3}}{(c+d x)^{4/3}} \, dx","Integrate[(a + b*x)^(4/3)/(c + d*x)^(4/3),x]","\frac{3 (a+b x)^{7/3} \left(\frac{b (c+d x)}{b c-a d}\right)^{4/3} \, _2F_1\left(\frac{4}{3},\frac{7}{3};\frac{10}{3};\frac{d (a+b x)}{a d-b c}\right)}{7 b (c+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,"(3*(a + b*x)^(7/3)*((b*(c + d*x))/(b*c - a*d))^(4/3)*Hypergeometric2F1[4/3, 7/3, 10/3, (d*(a + b*x))/(-(b*c) + a*d)])/(7*b*(c + d*x)^(4/3))","C",1
1617,1,73,149,0.0441278,"\int \frac{\sqrt[3]{a+b x}}{(c+d x)^{4/3}} \, dx","Integrate[(a + b*x)^(1/3)/(c + d*x)^(4/3),x]","\frac{3 (a+b x)^{4/3} \left(\frac{b (c+d x)}{b c-a d}\right)^{4/3} \, _2F_1\left(\frac{4}{3},\frac{4}{3};\frac{7}{3};\frac{d (a+b x)}{a d-b c}\right)}{4 b (c+d x)^{4/3}}","-\frac{3 \sqrt[3]{b} \log \left(\frac{\sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{d} \sqrt[3]{a+b x}}-1\right)}{2 d^{4/3}}-\frac{\sqrt{3} \sqrt[3]{b} \tan ^{-1}\left(\frac{2 \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt{3} \sqrt[3]{d} \sqrt[3]{a+b x}}+\frac{1}{\sqrt{3}}\right)}{d^{4/3}}-\frac{3 \sqrt[3]{a+b x}}{d \sqrt[3]{c+d x}}-\frac{\sqrt[3]{b} \log (a+b x)}{2 d^{4/3}}",1,"(3*(a + b*x)^(4/3)*((b*(c + d*x))/(b*c - a*d))^(4/3)*Hypergeometric2F1[4/3, 4/3, 7/3, (d*(a + b*x))/(-(b*c) + a*d)])/(4*b*(c + d*x)^(4/3))","C",1
1618,1,30,30,0.0070686,"\int \frac{1}{(a+b x)^{2/3} (c+d x)^{4/3}} \, dx","Integrate[1/((a + b*x)^(2/3)*(c + d*x)^(4/3)),x]","\frac{3 \sqrt[3]{a+b x}}{\sqrt[3]{c+d x} (b c-a d)}","\frac{3 \sqrt[3]{a+b x}}{\sqrt[3]{c+d x} (b c-a d)}",1,"(3*(a + b*x)^(1/3))/((b*c - a*d)*(c + d*x)^(1/3))","A",1
1619,1,45,66,0.0195074,"\int \frac{1}{(a+b x)^{5/3} (c+d x)^{4/3}} \, dx","Integrate[1/((a + b*x)^(5/3)*(c + d*x)^(4/3)),x]","-\frac{3 (2 a d+b (c+3 d x))}{2 (a+b x)^{2/3} \sqrt[3]{c+d x} (b c-a d)^2}","-\frac{9 d \sqrt[3]{a+b x}}{2 \sqrt[3]{c+d x} (b c-a d)^2}-\frac{3}{2 (a+b x)^{2/3} \sqrt[3]{c+d x} (b c-a d)}",1,"(-3*(2*a*d + b*(c + 3*d*x)))/(2*(b*c - a*d)^2*(a + b*x)^(2/3)*(c + d*x)^(1/3))","A",1
1620,1,75,101,0.0306453,"\int \frac{1}{(a+b x)^{8/3} (c+d x)^{4/3}} \, dx","Integrate[1/((a + b*x)^(8/3)*(c + d*x)^(4/3)),x]","\frac{3 \left(5 a^2 d^2+5 a b d (c+3 d x)+b^2 \left(-c^2+3 c d x+9 d^2 x^2\right)\right)}{5 (a+b x)^{5/3} \sqrt[3]{c+d x} (b c-a d)^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*(5*a^2*d^2 + 5*a*b*d*(c + 3*d*x) + b^2*(-c^2 + 3*c*d*x + 9*d^2*x^2)))/(5*(b*c - a*d)^3*(a + b*x)^(5/3)*(c + d*x)^(1/3))","A",1
1621,1,116,136,0.04662,"\int \frac{1}{(a+b x)^{11/3} (c+d x)^{4/3}} \, dx","Integrate[1/((a + b*x)^(11/3)*(c + d*x)^(4/3)),x]","-\frac{3 \left(40 a^3 d^3+60 a^2 b d^2 (c+3 d x)+24 a b^2 d \left(-c^2+3 c d x+9 d^2 x^2\right)+b^3 \left(5 c^3-9 c^2 d x+27 c d^2 x^2+81 d^3 x^3\right)\right)}{40 (a+b x)^{8/3} \sqrt[3]{c+d x} (b c-a d)^4}","-\frac{243 d^3 \sqrt[3]{a+b x}}{40 \sqrt[3]{c+d x} (b c-a d)^4}-\frac{81 d^2}{40 (a+b x)^{2/3} \sqrt[3]{c+d x} (b c-a d)^3}+\frac{27 d}{40 (a+b x)^{5/3} \sqrt[3]{c+d x} (b c-a d)^2}-\frac{3}{8 (a+b x)^{8/3} \sqrt[3]{c+d x} (b c-a d)}",1,"(-3*(40*a^3*d^3 + 60*a^2*b*d^2*(c + 3*d*x) + 24*a*b^2*d*(-c^2 + 3*c*d*x + 9*d^2*x^2) + b^3*(5*c^3 - 9*c^2*d*x + 27*c*d^2*x^2 + 81*d^3*x^3)))/(40*(b*c - a*d)^4*(a + b*x)^(8/3)*(c + d*x)^(1/3))","A",1
1622,1,73,1355,0.0603677,"\int \frac{(a+b x)^{8/3}}{(c+d x)^{4/3}} \, dx","Integrate[(a + b*x)^(8/3)/(c + d*x)^(4/3),x]","\frac{3 (a+b x)^{11/3} \left(\frac{b (c+d x)}{b c-a d}\right)^{4/3} \, _2F_1\left(\frac{4}{3},\frac{11}{3};\frac{14}{3};\frac{d (a+b x)}{a d-b c}\right)}{11 b (c+d x)^{4/3}}","-\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}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right),-7-4 \sqrt{3}\right) (b c-a d)^{8/3}}{7 d^{11/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}+\frac{30\ 2^{2/3} \sqrt[3]{b} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \sqrt{(a d+b (c+2 d x))^2} (b c-a d)^2}{7 d^{11/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}-\frac{30 b (a+b x)^{2/3} (c+d x)^{2/3} (b c-a d)}{7 d^3}+\frac{24 b (a+b x)^{5/3} (c+d x)^{2/3}}{7 d^2}-\frac{3 (a+b x)^{8/3}}{d \sqrt[3]{c+d x}}",1,"(3*(a + b*x)^(11/3)*((b*(c + d*x))/(b*c - a*d))^(4/3)*Hypergeometric2F1[4/3, 11/3, 14/3, (d*(a + b*x))/(-(b*c) + a*d)])/(11*b*(c + d*x)^(4/3))","C",1
1623,1,73,1317,0.0510567,"\int \frac{(a+b x)^{5/3}}{(c+d x)^{4/3}} \, dx","Integrate[(a + b*x)^(5/3)/(c + d*x)^(4/3),x]","\frac{3 (a+b x)^{8/3} \left(\frac{b (c+d x)}{b c-a d}\right)^{4/3} \, _2F_1\left(\frac{4}{3},\frac{8}{3};\frac{11}{3};\frac{d (a+b x)}{a d-b c}\right)}{8 b (c+d x)^{4/3}}","\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}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right),-7-4 \sqrt{3}\right) (b c-a d)^{5/3}}{2^{5/6} d^{8/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}-\frac{15 \sqrt[3]{b} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \sqrt{(a d+b (c+2 d x))^2} (b c-a d)}{2 \sqrt[3]{2} d^{8/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}+\frac{15 b (a+b x)^{2/3} (c+d x)^{2/3}}{4 d^2}-\frac{3 (a+b x)^{5/3}}{d \sqrt[3]{c+d x}}",1,"(3*(a + b*x)^(8/3)*((b*(c + d*x))/(b*c - a*d))^(4/3)*Hypergeometric2F1[4/3, 8/3, 11/3, (d*(a + b*x))/(-(b*c) + a*d)])/(8*b*(c + d*x)^(4/3))","C",1
1624,1,73,1279,0.0426894,"\int \frac{(a+b x)^{2/3}}{(c+d x)^{4/3}} \, dx","Integrate[(a + b*x)^(2/3)/(c + d*x)^(4/3),x]","\frac{3 (a+b x)^{5/3} \left(\frac{b (c+d x)}{b c-a d}\right)^{4/3} \, _2F_1\left(\frac{4}{3},\frac{5}{3};\frac{8}{3};\frac{d (a+b x)}{a d-b c}\right)}{5 b (c+d x)^{4/3}}","-\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}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right),-7-4 \sqrt{3}\right)}{d^{5/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}+\frac{3\ 2^{2/3} \sqrt[3]{b} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \sqrt{(a d+b (c+2 d x))^2}}{d^{5/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}-\frac{3 (a+b x)^{2/3}}{d \sqrt[3]{c+d x}}",1,"(3*(a + b*x)^(5/3)*((b*(c + d*x))/(b*c - a*d))^(4/3)*Hypergeometric2F1[4/3, 5/3, 8/3, (d*(a + b*x))/(-(b*c) + a*d)])/(5*b*(c + d*x)^(4/3))","C",1
1625,1,73,1298,0.0372219,"\int \frac{1}{\sqrt[3]{a+b x} (c+d x)^{4/3}} \, dx","Integrate[1/((a + b*x)^(1/3)*(c + d*x)^(4/3)),x]","\frac{3 (a+b x)^{2/3} \left(\frac{b (c+d x)}{b c-a d}\right)^{4/3} \, _2F_1\left(\frac{2}{3},\frac{4}{3};\frac{5}{3};\frac{d (a+b x)}{a d-b c}\right)}{2 b (c+d x)^{4/3}}","\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}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right),-7-4 \sqrt{3}\right)}{d^{2/3} \sqrt[3]{b c-a d} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}-\frac{3 \sqrt[3]{b} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \sqrt{(a d+b (c+2 d x))^2}}{\sqrt[3]{2} d^{2/3} (b c-a d) \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}+\frac{3 (a+b x)^{2/3}}{(b c-a d) \sqrt[3]{c+d x}}",1,"(3*(a + b*x)^(2/3)*((b*(c + d*x))/(b*c - a*d))^(4/3)*Hypergeometric2F1[2/3, 4/3, 5/3, (d*(a + b*x))/(-(b*c) + a*d)])/(2*b*(c + d*x)^(4/3))","C",1
1626,1,71,1327,0.0384553,"\int \frac{1}{(a+b x)^{4/3} (c+d x)^{4/3}} \, dx","Integrate[1/((a + b*x)^(4/3)*(c + d*x)^(4/3)),x]","-\frac{3 \left(\frac{b (c+d x)}{b c-a d}\right)^{4/3} \, _2F_1\left(-\frac{1}{3},\frac{4}{3};\frac{2}{3};\frac{d (a+b x)}{a d-b c}\right)}{b \sqrt[3]{a+b x} (c+d x)^{4/3}}","-\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}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right),-7-4 \sqrt{3}\right) \sqrt[3]{d}}{(b c-a d)^{4/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}+\frac{3\ 2^{2/3} \sqrt[3]{b} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \sqrt{(a d+b (c+2 d x))^2} \sqrt[3]{d}}{(b c-a d)^2 \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}-\frac{3}{(b c-a d) \sqrt[3]{a+b x} \sqrt[3]{c+d x}}",1,"(-3*((b*(c + d*x))/(b*c - a*d))^(4/3)*Hypergeometric2F1[-1/3, 4/3, 2/3, (d*(a + b*x))/(-(b*c) + a*d)])/(b*(a + b*x)^(1/3)*(c + d*x)^(4/3))","C",1
1627,1,73,1370,0.0422232,"\int \frac{1}{(a+b x)^{7/3} (c+d x)^{4/3}} \, dx","Integrate[1/((a + b*x)^(7/3)*(c + d*x)^(4/3)),x]","-\frac{3 \left(\frac{b (c+d x)}{b c-a d}\right)^{4/3} \, _2F_1\left(-\frac{4}{3},\frac{4}{3};-\frac{1}{3};\frac{d (a+b x)}{a d-b c}\right)}{4 b (a+b x)^{4/3} (c+d x)^{4/3}}","\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}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}}\right),-7-4 \sqrt{3}\right) d^{4/3}}{2^{5/6} (b c-a d)^{7/3} \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)^2}} \sqrt{(a d+b (c+2 d x))^2}}-\frac{15 \sqrt[3]{b} \sqrt[3]{(a+b x) (c+d x)} \sqrt{(b c+a d+2 b d x)^2} \sqrt{(a d+b (c+2 d x))^2} d^{4/3}}{2 \sqrt[3]{2} (b c-a d)^3 \sqrt[3]{a+b x} \sqrt[3]{c+d x} (b c+a d+2 b d x) \left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2^{2/3} \sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{(a+b x) (c+d x)}\right)}+\frac{15 d}{4 (b c-a d)^2 \sqrt[3]{a+b x} \sqrt[3]{c+d x}}-\frac{3}{4 (b c-a d) (a+b x)^{4/3} \sqrt[3]{c+d x}}",1,"(-3*((b*(c + d*x))/(b*c - a*d))^(4/3)*Hypergeometric2F1[-4/3, 4/3, -1/3, (d*(a + b*x))/(-(b*c) + a*d)])/(4*b*(a + b*x)^(4/3)*(c + d*x)^(4/3))","C",1
1628,1,48,77,0.0192769,"\int \frac{\sqrt[3]{-1+x}}{\sqrt[3]{1+x}} \, dx","Integrate[(-1 + x)^(1/3)/(1 + x)^(1/3),x]","\frac{3 \left(\frac{x-1}{x+1}\right)^{4/3} (x+1)^{4/3} \, _2F_1\left(\frac{1}{3},\frac{4}{3};\frac{7}{3};\frac{1-x}{2}\right)}{4 \sqrt[3]{2}}","\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,"(3*((-1 + x)/(1 + x))^(4/3)*(1 + x)^(4/3)*Hypergeometric2F1[1/3, 4/3, 7/3, (1 - x)/2])/(4*2^(1/3))","C",1
1629,1,73,185,0.0381802,"\int (a+b x)^{3/2} \sqrt[4]{c+d x} \, dx","Integrate[(a + b*x)^(3/2)*(c + d*x)^(1/4),x]","\frac{2 (a+b x)^{5/2} \sqrt[4]{c+d x} \, _2F_1\left(-\frac{1}{4},\frac{5}{2};\frac{7}{2};\frac{d (a+b x)}{a d-b c}\right)}{5 b \sqrt[4]{\frac{b (c+d x)}{b c-a d}}}","\frac{16 (b c-a d)^{13/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\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,"(2*(a + b*x)^(5/2)*(c + d*x)^(1/4)*Hypergeometric2F1[-1/4, 5/2, 7/2, (d*(a + b*x))/(-(b*c) + a*d)])/(5*b*((b*(c + d*x))/(b*c - a*d))^(1/4))","C",1
1630,1,73,147,0.0297654,"\int \sqrt{a+b x} \sqrt[4]{c+d x} \, dx","Integrate[Sqrt[a + b*x]*(c + d*x)^(1/4),x]","\frac{2 (a+b x)^{3/2} \sqrt[4]{c+d x} \, _2F_1\left(-\frac{1}{4},\frac{3}{2};\frac{5}{2};\frac{d (a+b x)}{a d-b c}\right)}{3 b \sqrt[4]{\frac{b (c+d x)}{b c-a d}}}","-\frac{8 (b c-a d)^{9/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\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,"(2*(a + b*x)^(3/2)*(c + d*x)^(1/4)*Hypergeometric2F1[-1/4, 3/2, 5/2, (d*(a + b*x))/(-(b*c) + a*d)])/(3*b*((b*(c + d*x))/(b*c - a*d))^(1/4))","C",1
1631,1,71,111,0.023814,"\int \frac{\sqrt[4]{c+d x}}{\sqrt{a+b x}} \, dx","Integrate[(c + d*x)^(1/4)/Sqrt[a + b*x],x]","\frac{2 \sqrt{a+b x} \sqrt[4]{c+d x} \, _2F_1\left(-\frac{1}{4},\frac{1}{2};\frac{3}{2};\frac{d (a+b x)}{a d-b c}\right)}{b \sqrt[4]{\frac{b (c+d x)}{b c-a d}}}","\frac{4 (b c-a d)^{5/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\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,"(2*Sqrt[a + b*x]*(c + d*x)^(1/4)*Hypergeometric2F1[-1/4, 1/2, 3/2, (d*(a + b*x))/(-(b*c) + a*d)])/(b*((b*(c + d*x))/(b*c - a*d))^(1/4))","C",1
1632,1,71,104,0.023233,"\int \frac{\sqrt[4]{c+d x}}{(a+b x)^{3/2}} \, dx","Integrate[(c + d*x)^(1/4)/(a + b*x)^(3/2),x]","-\frac{2 \sqrt[4]{c+d x} \, _2F_1\left(-\frac{1}{2},-\frac{1}{4};\frac{1}{2};\frac{d (a+b x)}{a d-b c}\right)}{b \sqrt{a+b x} \sqrt[4]{\frac{b (c+d x)}{b c-a d}}}","\frac{2 \sqrt[4]{b c-a d} \sqrt{-\frac{d (a+b x)}{b c-a d}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right),-1\right)}{b^{5/4} \sqrt{a+b x}}-\frac{2 \sqrt[4]{c+d x}}{b \sqrt{a+b x}}",1,"(-2*(c + d*x)^(1/4)*Hypergeometric2F1[-1/2, -1/4, 1/2, (d*(a + b*x))/(-(b*c) + a*d)])/(b*Sqrt[a + b*x]*((b*(c + d*x))/(b*c - a*d))^(1/4))","C",1
1633,1,73,145,0.0247659,"\int \frac{\sqrt[4]{c+d x}}{(a+b x)^{5/2}} \, dx","Integrate[(c + d*x)^(1/4)/(a + b*x)^(5/2),x]","-\frac{2 \sqrt[4]{c+d x} \, _2F_1\left(-\frac{3}{2},-\frac{1}{4};-\frac{1}{2};\frac{d (a+b x)}{a d-b c}\right)}{3 b (a+b x)^{3/2} \sqrt[4]{\frac{b (c+d x)}{b c-a d}}}","-\frac{d \sqrt{-\frac{d (a+b x)}{b c-a d}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right),-1\right)}{3 b^{5/4} \sqrt{a+b x} (b c-a d)^{3/4}}-\frac{d \sqrt[4]{c+d x}}{3 b \sqrt{a+b x} (b c-a d)}-\frac{2 \sqrt[4]{c+d x}}{3 b (a+b x)^{3/2}}",1,"(-2*(c + d*x)^(1/4)*Hypergeometric2F1[-3/2, -1/4, -1/2, (d*(a + b*x))/(-(b*c) + a*d)])/(3*b*(a + b*x)^(3/2)*((b*(c + d*x))/(b*c - a*d))^(1/4))","C",1
1634,1,73,185,0.0264532,"\int \frac{\sqrt[4]{c+d x}}{(a+b x)^{7/2}} \, dx","Integrate[(c + d*x)^(1/4)/(a + b*x)^(7/2),x]","-\frac{2 \sqrt[4]{c+d x} \, _2F_1\left(-\frac{5}{2},-\frac{1}{4};-\frac{3}{2};\frac{d (a+b x)}{a d-b c}\right)}{5 b (a+b x)^{5/2} \sqrt[4]{\frac{b (c+d x)}{b c-a d}}}","\frac{d^2 \sqrt{-\frac{d (a+b x)}{b c-a d}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right),-1\right)}{6 b^{5/4} \sqrt{a+b x} (b c-a d)^{7/4}}+\frac{d^2 \sqrt[4]{c+d x}}{6 b \sqrt{a+b x} (b c-a d)^2}-\frac{d \sqrt[4]{c+d x}}{15 b (a+b x)^{3/2} (b c-a d)}-\frac{2 \sqrt[4]{c+d x}}{5 b (a+b x)^{5/2}}",1,"(-2*(c + d*x)^(1/4)*Hypergeometric2F1[-5/2, -1/4, -3/2, (d*(a + b*x))/(-(b*c) + a*d)])/(5*b*(a + b*x)^(5/2)*((b*(c + d*x))/(b*c - a*d))^(1/4))","C",1
1635,1,73,270,0.0391281,"\int (a+b x)^{3/2} (c+d x)^{3/4} \, dx","Integrate[(a + b*x)^(3/2)*(c + d*x)^(3/4),x]","\frac{2 (a+b x)^{5/2} (c+d x)^{3/4} \, _2F_1\left(-\frac{3}{4},\frac{5}{2};\frac{7}{2};\frac{d (a+b x)}{a d-b c}\right)}{5 b \left(\frac{b (c+d x)}{b c-a d}\right)^{3/4}}","-\frac{16 (b c-a d)^{15/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\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,"(2*(a + b*x)^(5/2)*(c + d*x)^(3/4)*Hypergeometric2F1[-3/4, 5/2, 7/2, (d*(a + b*x))/(-(b*c) + a*d)])/(5*b*((b*(c + d*x))/(b*c - a*d))^(3/4))","C",1
1636,1,73,232,0.0302063,"\int \sqrt{a+b x} (c+d x)^{3/4} \, dx","Integrate[Sqrt[a + b*x]*(c + d*x)^(3/4),x]","\frac{2 (a+b x)^{3/2} (c+d x)^{3/4} \, _2F_1\left(-\frac{3}{4},\frac{3}{2};\frac{5}{2};\frac{d (a+b x)}{a d-b c}\right)}{3 b \left(\frac{b (c+d x)}{b c-a d}\right)^{3/4}}","\frac{8 (b c-a d)^{11/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\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,"(2*(a + b*x)^(3/2)*(c + d*x)^(3/4)*Hypergeometric2F1[-3/4, 3/2, 5/2, (d*(a + b*x))/(-(b*c) + a*d)])/(3*b*((b*(c + d*x))/(b*c - a*d))^(3/4))","C",1
1637,1,71,196,0.0234946,"\int \frac{(c+d x)^{3/4}}{\sqrt{a+b x}} \, dx","Integrate[(c + d*x)^(3/4)/Sqrt[a + b*x],x]","\frac{2 \sqrt{a+b x} (c+d x)^{3/4} \, _2F_1\left(-\frac{3}{4},\frac{1}{2};\frac{3}{2};\frac{d (a+b x)}{a d-b c}\right)}{b \left(\frac{b (c+d x)}{b c-a d}\right)^{3/4}}","-\frac{12 (b c-a d)^{7/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\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,"(2*Sqrt[a + b*x]*(c + d*x)^(3/4)*Hypergeometric2F1[-3/4, 1/2, 3/2, (d*(a + b*x))/(-(b*c) + a*d)])/(b*((b*(c + d*x))/(b*c - a*d))^(3/4))","C",1
1638,1,71,184,0.0234949,"\int \frac{(c+d x)^{3/4}}{(a+b x)^{3/2}} \, dx","Integrate[(c + d*x)^(3/4)/(a + b*x)^(3/2),x]","-\frac{2 (c+d x)^{3/4} \, _2F_1\left(-\frac{3}{4},-\frac{1}{2};\frac{1}{2};\frac{d (a+b x)}{a d-b c}\right)}{b \sqrt{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{3/4}}","-\frac{6 (b c-a d)^{3/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right),-1\right)}{b^{7/4} \sqrt{a+b x}}+\frac{6 (b c-a d)^{3/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{b^{7/4} \sqrt{a+b x}}-\frac{2 (c+d x)^{3/4}}{b \sqrt{a+b x}}",1,"(-2*(c + d*x)^(3/4)*Hypergeometric2F1[-3/4, -1/2, 1/2, (d*(a + b*x))/(-(b*c) + a*d)])/(b*Sqrt[a + b*x]*((b*(c + d*x))/(b*c - a*d))^(3/4))","C",1
1639,1,73,221,0.0255792,"\int \frac{(c+d x)^{3/4}}{(a+b x)^{5/2}} \, dx","Integrate[(c + d*x)^(3/4)/(a + b*x)^(5/2),x]","-\frac{2 (c+d x)^{3/4} \, _2F_1\left(-\frac{3}{2},-\frac{3}{4};-\frac{1}{2};\frac{d (a+b x)}{a d-b c}\right)}{3 b (a+b x)^{3/2} \left(\frac{b (c+d x)}{b c-a d}\right)^{3/4}}","-\frac{d \sqrt{-\frac{d (a+b x)}{b c-a d}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right),-1\right)}{b^{7/4} \sqrt{a+b x} \sqrt[4]{b c-a d}}+\frac{d \sqrt{-\frac{d (a+b x)}{b c-a d}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{b^{7/4} \sqrt{a+b x} \sqrt[4]{b c-a d}}-\frac{d (c+d x)^{3/4}}{b \sqrt{a+b x} (b c-a d)}-\frac{2 (c+d x)^{3/4}}{3 b (a+b x)^{3/2}}",1,"(-2*(c + d*x)^(3/4)*Hypergeometric2F1[-3/2, -3/4, -1/2, (d*(a + b*x))/(-(b*c) + a*d)])/(3*b*(a + b*x)^(3/2)*((b*(c + d*x))/(b*c - a*d))^(3/4))","C",1
1640,1,73,270,0.0306931,"\int \frac{(c+d x)^{3/4}}{(a+b x)^{7/2}} \, dx","Integrate[(c + d*x)^(3/4)/(a + b*x)^(7/2),x]","-\frac{2 (c+d x)^{3/4} \, _2F_1\left(-\frac{5}{2},-\frac{3}{4};-\frac{3}{2};\frac{d (a+b x)}{a d-b c}\right)}{5 b (a+b x)^{5/2} \left(\frac{b (c+d x)}{b c-a d}\right)^{3/4}}","\frac{3 d^2 \sqrt{-\frac{d (a+b x)}{b c-a d}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right),-1\right)}{10 b^{7/4} \sqrt{a+b x} (b c-a d)^{5/4}}-\frac{3 d^2 \sqrt{-\frac{d (a+b x)}{b c-a d}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{10 b^{7/4} \sqrt{a+b x} (b c-a d)^{5/4}}+\frac{3 d^2 (c+d x)^{3/4}}{10 b \sqrt{a+b x} (b c-a d)^2}-\frac{d (c+d x)^{3/4}}{5 b (a+b x)^{3/2} (b c-a d)}-\frac{2 (c+d x)^{3/4}}{5 b (a+b x)^{5/2}}",1,"(-2*(c + d*x)^(3/4)*Hypergeometric2F1[-5/2, -3/4, -3/2, (d*(a + b*x))/(-(b*c) + a*d)])/(5*b*(a + b*x)^(5/2)*((b*(c + d*x))/(b*c - a*d))^(3/4))","C",1
1641,1,73,220,0.0696144,"\int (a+b x)^{3/2} (c+d x)^{5/4} \, dx","Integrate[(a + b*x)^(3/2)*(c + d*x)^(5/4),x]","\frac{2 (a+b x)^{5/2} (c+d x)^{5/4} \, _2F_1\left(-\frac{5}{4},\frac{5}{2};\frac{7}{2};\frac{d (a+b x)}{a d-b c}\right)}{5 b \left(\frac{b (c+d x)}{b c-a d}\right)^{5/4}}","\frac{16 (b c-a d)^{17/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\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,"(2*(a + b*x)^(5/2)*(c + d*x)^(5/4)*Hypergeometric2F1[-5/4, 5/2, 7/2, (d*(a + b*x))/(-(b*c) + a*d)])/(5*b*((b*(c + d*x))/(b*c - a*d))^(5/4))","C",1
1642,1,73,182,0.0488806,"\int \sqrt{a+b x} (c+d x)^{5/4} \, dx","Integrate[Sqrt[a + b*x]*(c + d*x)^(5/4),x]","\frac{2 (a+b x)^{3/2} (c+d x)^{5/4} \, _2F_1\left(-\frac{5}{4},\frac{3}{2};\frac{5}{2};\frac{d (a+b x)}{a d-b c}\right)}{3 b \left(\frac{b (c+d x)}{b c-a d}\right)^{5/4}}","-\frac{40 (b c-a d)^{13/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\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,"(2*(a + b*x)^(3/2)*(c + d*x)^(5/4)*Hypergeometric2F1[-5/4, 3/2, 5/2, (d*(a + b*x))/(-(b*c) + a*d)])/(3*b*((b*(c + d*x))/(b*c - a*d))^(5/4))","C",1
1643,1,71,144,0.0386016,"\int \frac{(c+d x)^{5/4}}{\sqrt{a+b x}} \, dx","Integrate[(c + d*x)^(5/4)/Sqrt[a + b*x],x]","\frac{2 \sqrt{a+b x} (c+d x)^{5/4} \, _2F_1\left(-\frac{5}{4},\frac{1}{2};\frac{3}{2};\frac{d (a+b x)}{a d-b c}\right)}{b \left(\frac{b (c+d x)}{b c-a d}\right)^{5/4}}","\frac{20 (b c-a d)^{9/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\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,"(2*Sqrt[a + b*x]*(c + d*x)^(5/4)*Hypergeometric2F1[-5/4, 1/2, 3/2, (d*(a + b*x))/(-(b*c) + a*d)])/(b*((b*(c + d*x))/(b*c - a*d))^(5/4))","C",1
1644,1,71,132,0.0385953,"\int \frac{(c+d x)^{5/4}}{(a+b x)^{3/2}} \, dx","Integrate[(c + d*x)^(5/4)/(a + b*x)^(3/2),x]","-\frac{2 (c+d x)^{5/4} \, _2F_1\left(-\frac{5}{4},-\frac{1}{2};\frac{1}{2};\frac{d (a+b x)}{a d-b c}\right)}{b \sqrt{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/4}}","\frac{10 (b c-a d)^{5/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\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,"(-2*(c + d*x)^(5/4)*Hypergeometric2F1[-5/4, -1/2, 1/2, (d*(a + b*x))/(-(b*c) + a*d)])/(b*Sqrt[a + b*x]*((b*(c + d*x))/(b*c - a*d))^(5/4))","C",1
1645,1,73,135,0.0453355,"\int \frac{(c+d x)^{5/4}}{(a+b x)^{5/2}} \, dx","Integrate[(c + d*x)^(5/4)/(a + b*x)^(5/2),x]","-\frac{2 (c+d x)^{5/4} \, _2F_1\left(-\frac{3}{2},-\frac{5}{4};-\frac{1}{2};\frac{d (a+b x)}{a d-b c}\right)}{3 b (a+b x)^{3/2} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/4}}","\frac{5 d \sqrt[4]{b c-a d} \sqrt{-\frac{d (a+b x)}{b c-a d}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\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,"(-2*(c + d*x)^(5/4)*Hypergeometric2F1[-3/2, -5/4, -1/2, (d*(a + b*x))/(-(b*c) + a*d)])/(3*b*(a + b*x)^(3/2)*((b*(c + d*x))/(b*c - a*d))^(5/4))","C",1
1646,1,73,175,0.0484046,"\int \frac{(c+d x)^{5/4}}{(a+b x)^{7/2}} \, dx","Integrate[(c + d*x)^(5/4)/(a + b*x)^(7/2),x]","-\frac{2 (c+d x)^{5/4} \, _2F_1\left(-\frac{5}{2},-\frac{5}{4};-\frac{3}{2};\frac{d (a+b x)}{a d-b c}\right)}{5 b (a+b x)^{5/2} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/4}}","-\frac{d^2 \sqrt{-\frac{d (a+b x)}{b c-a d}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\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,"(-2*(c + d*x)^(5/4)*Hypergeometric2F1[-5/2, -5/4, -3/2, (d*(a + b*x))/(-(b*c) + a*d)])/(5*b*(a + b*x)^(5/2)*((b*(c + d*x))/(b*c - a*d))^(5/4))","C",1
1647,1,73,213,0.0519219,"\int \frac{(c+d x)^{5/4}}{(a+b x)^{9/2}} \, dx","Integrate[(c + d*x)^(5/4)/(a + b*x)^(9/2),x]","-\frac{2 (c+d x)^{5/4} \, _2F_1\left(-\frac{7}{2},-\frac{5}{4};-\frac{5}{2};\frac{d (a+b x)}{a d-b c}\right)}{7 b (a+b x)^{7/2} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/4}}","\frac{5 d^3 \sqrt{-\frac{d (a+b x)}{b c-a d}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\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,"(-2*(c + d*x)^(5/4)*Hypergeometric2F1[-7/2, -5/4, -5/2, (d*(a + b*x))/(-(b*c) + a*d)])/(7*b*(a + b*x)^(7/2)*((b*(c + d*x))/(b*c - a*d))^(5/4))","C",1
1648,1,73,264,0.0348658,"\int \frac{(a+b x)^{5/2}}{\sqrt[4]{c+d x}} \, dx","Integrate[(a + b*x)^(5/2)/(c + d*x)^(1/4),x]","\frac{2 (a+b x)^{7/2} \sqrt[4]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{1}{4},\frac{7}{2};\frac{9}{2};\frac{d (a+b x)}{a d-b c}\right)}{7 b \sqrt[4]{c+d x}}","\frac{32 (b c-a d)^{15/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\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,"(2*(a + b*x)^(7/2)*((b*(c + d*x))/(b*c - a*d))^(1/4)*Hypergeometric2F1[1/4, 7/2, 9/2, (d*(a + b*x))/(-(b*c) + a*d)])/(7*b*(c + d*x)^(1/4))","C",1
1649,1,73,229,0.0307859,"\int \frac{(a+b x)^{3/2}}{\sqrt[4]{c+d x}} \, dx","Integrate[(a + b*x)^(3/2)/(c + d*x)^(1/4),x]","\frac{2 (a+b x)^{5/2} \sqrt[4]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{1}{4},\frac{5}{2};\frac{7}{2};\frac{d (a+b x)}{a d-b c}\right)}{5 b \sqrt[4]{c+d x}}","-\frac{16 (b c-a d)^{11/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\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,"(2*(a + b*x)^(5/2)*((b*(c + d*x))/(b*c - a*d))^(1/4)*Hypergeometric2F1[1/4, 5/2, 7/2, (d*(a + b*x))/(-(b*c) + a*d)])/(5*b*(c + d*x)^(1/4))","C",1
1650,1,73,196,0.026331,"\int \frac{\sqrt{a+b x}}{\sqrt[4]{c+d x}} \, dx","Integrate[Sqrt[a + b*x]/(c + d*x)^(1/4),x]","\frac{2 (a+b x)^{3/2} \sqrt[4]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{1}{4},\frac{3}{2};\frac{5}{2};\frac{d (a+b x)}{a d-b c}\right)}{3 b \sqrt[4]{c+d x}}","\frac{8 (b c-a d)^{7/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\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,"(2*(a + b*x)^(3/2)*((b*(c + d*x))/(b*c - a*d))^(1/4)*Hypergeometric2F1[1/4, 3/2, 5/2, (d*(a + b*x))/(-(b*c) + a*d)])/(3*b*(c + d*x)^(1/4))","C",1
1651,1,71,167,0.0217487,"\int \frac{1}{\sqrt{a+b x} \sqrt[4]{c+d x}} \, dx","Integrate[1/(Sqrt[a + b*x]*(c + d*x)^(1/4)),x]","\frac{2 \sqrt{a+b x} \sqrt[4]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{3}{2};\frac{d (a+b x)}{a d-b c}\right)}{b \sqrt[4]{c+d x}}","\frac{4 (b c-a d)^{3/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{b^{3/4} d \sqrt{a+b x}}-\frac{4 (b c-a d)^{3/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right),-1\right)}{b^{3/4} d \sqrt{a+b x}}",1,"(2*Sqrt[a + b*x]*((b*(c + d*x))/(b*c - a*d))^(1/4)*Hypergeometric2F1[1/4, 1/2, 3/2, (d*(a + b*x))/(-(b*c) + a*d)])/(b*(c + d*x)^(1/4))","C",1
1652,1,71,191,0.0228519,"\int \frac{1}{(a+b x)^{3/2} \sqrt[4]{c+d x}} \, dx","Integrate[1/((a + b*x)^(3/2)*(c + d*x)^(1/4)),x]","-\frac{2 \sqrt[4]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(-\frac{1}{2},\frac{1}{4};\frac{1}{2};\frac{d (a+b x)}{a d-b c}\right)}{b \sqrt{a+b x} \sqrt[4]{c+d x}}","-\frac{2 \sqrt{-\frac{d (a+b x)}{b c-a d}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right),-1\right)}{b^{3/4} \sqrt{a+b x} \sqrt[4]{b c-a d}}+\frac{2 \sqrt{-\frac{d (a+b x)}{b c-a d}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{b^{3/4} \sqrt{a+b x} \sqrt[4]{b c-a d}}-\frac{2 (c+d x)^{3/4}}{\sqrt{a+b x} (b c-a d)}",1,"(-2*((b*(c + d*x))/(b*c - a*d))^(1/4)*Hypergeometric2F1[-1/2, 1/4, 1/2, (d*(a + b*x))/(-(b*c) + a*d)])/(b*Sqrt[a + b*x]*(c + d*x)^(1/4))","C",1
1653,1,73,224,0.024245,"\int \frac{1}{(a+b x)^{5/2} \sqrt[4]{c+d x}} \, dx","Integrate[1/((a + b*x)^(5/2)*(c + d*x)^(1/4)),x]","-\frac{2 \sqrt[4]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(-\frac{3}{2},\frac{1}{4};-\frac{1}{2};\frac{d (a+b x)}{a d-b c}\right)}{3 b (a+b x)^{3/2} \sqrt[4]{c+d x}}","\frac{d \sqrt{-\frac{d (a+b x)}{b c-a d}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right),-1\right)}{b^{3/4} \sqrt{a+b x} (b c-a d)^{5/4}}-\frac{d \sqrt{-\frac{d (a+b x)}{b c-a d}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{b^{3/4} \sqrt{a+b x} (b c-a d)^{5/4}}+\frac{d (c+d x)^{3/4}}{\sqrt{a+b x} (b c-a d)^2}-\frac{2 (c+d x)^{3/4}}{3 (a+b x)^{3/2} (b c-a d)}",1,"(-2*((b*(c + d*x))/(b*c - a*d))^(1/4)*Hypergeometric2F1[-3/2, 1/4, -1/2, (d*(a + b*x))/(-(b*c) + a*d)])/(3*b*(a + b*x)^(3/2)*(c + d*x)^(1/4))","C",1
1654,1,73,144,0.0372979,"\int \frac{(a+b x)^{3/2}}{(c+d x)^{3/4}} \, dx","Integrate[(a + b*x)^(3/2)/(c + d*x)^(3/4),x]","\frac{2 (a+b x)^{5/2} \left(\frac{b (c+d x)}{b c-a d}\right)^{3/4} \, _2F_1\left(\frac{3}{4},\frac{5}{2};\frac{7}{2};\frac{d (a+b x)}{a d-b c}\right)}{5 b (c+d x)^{3/4}}","\frac{16 (b c-a d)^{9/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\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,"(2*(a + b*x)^(5/2)*((b*(c + d*x))/(b*c - a*d))^(3/4)*Hypergeometric2F1[3/4, 5/2, 7/2, (d*(a + b*x))/(-(b*c) + a*d)])/(5*b*(c + d*x)^(3/4))","C",1
1655,1,73,111,0.0292774,"\int \frac{\sqrt{a+b x}}{(c+d x)^{3/4}} \, dx","Integrate[Sqrt[a + b*x]/(c + d*x)^(3/4),x]","\frac{2 (a+b x)^{3/2} \left(\frac{b (c+d x)}{b c-a d}\right)^{3/4} \, _2F_1\left(\frac{3}{4},\frac{3}{2};\frac{5}{2};\frac{d (a+b x)}{a d-b c}\right)}{3 b (c+d x)^{3/4}}","\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}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right),-1\right)}{3 \sqrt[4]{b} d^2 \sqrt{a+b x}}",1,"(2*(a + b*x)^(3/2)*((b*(c + d*x))/(b*c - a*d))^(3/4)*Hypergeometric2F1[3/4, 3/2, 5/2, (d*(a + b*x))/(-(b*c) + a*d)])/(3*b*(c + d*x)^(3/4))","C",1
1656,1,71,83,0.0232077,"\int \frac{1}{\sqrt{a+b x} (c+d x)^{3/4}} \, dx","Integrate[1/(Sqrt[a + b*x]*(c + d*x)^(3/4)),x]","\frac{2 \sqrt{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{3/4} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{3}{2};\frac{d (a+b x)}{a d-b c}\right)}{b (c+d x)^{3/4}}","\frac{4 \sqrt[4]{b c-a d} \sqrt{-\frac{d (a+b x)}{b c-a d}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right),-1\right)}{\sqrt[4]{b} d \sqrt{a+b x}}",1,"(2*Sqrt[a + b*x]*((b*(c + d*x))/(b*c - a*d))^(3/4)*Hypergeometric2F1[1/2, 3/4, 3/2, (d*(a + b*x))/(-(b*c) + a*d)])/(b*(c + d*x)^(3/4))","C",1
1657,1,71,111,0.0233308,"\int \frac{1}{(a+b x)^{3/2} (c+d x)^{3/4}} \, dx","Integrate[1/((a + b*x)^(3/2)*(c + d*x)^(3/4)),x]","-\frac{2 \left(\frac{b (c+d x)}{b c-a d}\right)^{3/4} \, _2F_1\left(-\frac{1}{2},\frac{3}{4};\frac{1}{2};\frac{d (a+b x)}{a d-b c}\right)}{b \sqrt{a+b x} (c+d x)^{3/4}}","-\frac{2 \sqrt{-\frac{d (a+b x)}{b c-a d}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right),-1\right)}{\sqrt[4]{b} \sqrt{a+b x} (b c-a d)^{3/4}}-\frac{2 \sqrt[4]{c+d x}}{\sqrt{a+b x} (b c-a d)}",1,"(-2*((b*(c + d*x))/(b*c - a*d))^(3/4)*Hypergeometric2F1[-1/2, 3/4, 1/2, (d*(a + b*x))/(-(b*c) + a*d)])/(b*Sqrt[a + b*x]*(c + d*x)^(3/4))","C",1
1658,1,73,149,0.0258322,"\int \frac{1}{(a+b x)^{5/2} (c+d x)^{3/4}} \, dx","Integrate[1/((a + b*x)^(5/2)*(c + d*x)^(3/4)),x]","-\frac{2 \left(\frac{b (c+d x)}{b c-a d}\right)^{3/4} \, _2F_1\left(-\frac{3}{2},\frac{3}{4};-\frac{1}{2};\frac{d (a+b x)}{a d-b c}\right)}{3 b (a+b x)^{3/2} (c+d x)^{3/4}}","\frac{5 d \sqrt{-\frac{d (a+b x)}{b c-a d}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right),-1\right)}{3 \sqrt[4]{b} \sqrt{a+b x} (b c-a d)^{7/4}}+\frac{5 d \sqrt[4]{c+d x}}{3 \sqrt{a+b x} (b c-a d)^2}-\frac{2 \sqrt[4]{c+d x}}{3 (a+b x)^{3/2} (b c-a d)}",1,"(-2*((b*(c + d*x))/(b*c - a*d))^(3/4)*Hypergeometric2F1[-3/2, 3/4, -1/2, (d*(a + b*x))/(-(b*c) + a*d)])/(3*b*(a + b*x)^(3/2)*(c + d*x)^(3/4))","C",1
1659,1,73,254,0.0621597,"\int \frac{(a+b x)^{5/2}}{(c+d x)^{5/4}} \, dx","Integrate[(a + b*x)^(5/2)/(c + d*x)^(5/4),x]","\frac{2 (a+b x)^{7/2} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/4} \, _2F_1\left(\frac{5}{4},\frac{7}{2};\frac{9}{2};\frac{d (a+b x)}{a d-b c}\right)}{7 b (c+d x)^{5/4}}","-\frac{32 \sqrt[4]{b} (b c-a d)^{11/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\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,"(2*(a + b*x)^(7/2)*((b*(c + d*x))/(b*c - a*d))^(5/4)*Hypergeometric2F1[5/4, 7/2, 9/2, (d*(a + b*x))/(-(b*c) + a*d)])/(7*b*(c + d*x)^(5/4))","C",1
1660,1,73,220,0.0494517,"\int \frac{(a+b x)^{3/2}}{(c+d x)^{5/4}} \, dx","Integrate[(a + b*x)^(3/2)/(c + d*x)^(5/4),x]","\frac{2 (a+b x)^{5/2} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/4} \, _2F_1\left(\frac{5}{4},\frac{5}{2};\frac{7}{2};\frac{d (a+b x)}{a d-b c}\right)}{5 b (c+d x)^{5/4}}","\frac{48 \sqrt[4]{b} (b c-a d)^{7/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\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,"(2*(a + b*x)^(5/2)*((b*(c + d*x))/(b*c - a*d))^(5/4)*Hypergeometric2F1[5/4, 5/2, 7/2, (d*(a + b*x))/(-(b*c) + a*d)])/(5*b*(c + d*x)^(5/4))","C",1
1661,1,73,190,0.0423353,"\int \frac{\sqrt{a+b x}}{(c+d x)^{5/4}} \, dx","Integrate[Sqrt[a + b*x]/(c + d*x)^(5/4),x]","\frac{2 (a+b x)^{3/2} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/4} \, _2F_1\left(\frac{5}{4},\frac{3}{2};\frac{5}{2};\frac{d (a+b x)}{a d-b c}\right)}{3 b (c+d x)^{5/4}}","-\frac{8 \sqrt[4]{b} (b c-a d)^{3/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\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,"(2*(a + b*x)^(3/2)*((b*(c + d*x))/(b*c - a*d))^(5/4)*Hypergeometric2F1[5/4, 3/2, 5/2, (d*(a + b*x))/(-(b*c) + a*d)])/(3*b*(c + d*x)^(5/4))","C",1
1662,1,71,197,0.0373866,"\int \frac{1}{\sqrt{a+b x} (c+d x)^{5/4}} \, dx","Integrate[1/(Sqrt[a + b*x]*(c + d*x)^(5/4)),x]","\frac{2 \sqrt{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/4} \, _2F_1\left(\frac{1}{2},\frac{5}{4};\frac{3}{2};\frac{d (a+b x)}{a d-b c}\right)}{b (c+d x)^{5/4}}","\frac{4 \sqrt[4]{b} \sqrt{-\frac{d (a+b x)}{b c-a d}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right),-1\right)}{d \sqrt{a+b x} \sqrt[4]{b c-a d}}+\frac{4 \sqrt{a+b x}}{\sqrt[4]{c+d x} (b c-a d)}-\frac{4 \sqrt[4]{b} \sqrt{-\frac{d (a+b x)}{b c-a d}} 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,"(2*Sqrt[a + b*x]*((b*(c + d*x))/(b*c - a*d))^(5/4)*Hypergeometric2F1[1/2, 5/4, 3/2, (d*(a + b*x))/(-(b*c) + a*d)])/(b*(c + d*x)^(5/4))","C",1
1663,1,71,222,0.0358969,"\int \frac{1}{(a+b x)^{3/2} (c+d x)^{5/4}} \, dx","Integrate[1/((a + b*x)^(3/2)*(c + d*x)^(5/4)),x]","-\frac{2 \left(\frac{b (c+d x)}{b c-a d}\right)^{5/4} \, _2F_1\left(-\frac{1}{2},\frac{5}{4};\frac{1}{2};\frac{d (a+b x)}{a d-b c}\right)}{b \sqrt{a+b x} (c+d x)^{5/4}}","-\frac{6 \sqrt[4]{b} \sqrt{-\frac{d (a+b x)}{b c-a d}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right),-1\right)}{\sqrt{a+b x} (b c-a d)^{5/4}}-\frac{6 d \sqrt{a+b x}}{\sqrt[4]{c+d x} (b c-a d)^2}-\frac{2}{\sqrt{a+b x} \sqrt[4]{c+d x} (b c-a d)}+\frac{6 \sqrt[4]{b} \sqrt{-\frac{d (a+b x)}{b c-a d}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{\sqrt{a+b x} (b c-a d)^{5/4}}",1,"(-2*((b*(c + d*x))/(b*c - a*d))^(5/4)*Hypergeometric2F1[-1/2, 5/4, 1/2, (d*(a + b*x))/(-(b*c) + a*d)])/(b*Sqrt[a + b*x]*(c + d*x)^(5/4))","C",1
1664,1,73,261,0.0389788,"\int \frac{1}{(a+b x)^{5/2} (c+d x)^{5/4}} \, dx","Integrate[1/((a + b*x)^(5/2)*(c + d*x)^(5/4)),x]","-\frac{2 \left(\frac{b (c+d x)}{b c-a d}\right)^{5/4} \, _2F_1\left(-\frac{3}{2},\frac{5}{4};-\frac{1}{2};\frac{d (a+b x)}{a d-b c}\right)}{3 b (a+b x)^{3/2} (c+d x)^{5/4}}","\frac{7 \sqrt[4]{b} d \sqrt{-\frac{d (a+b x)}{b c-a d}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right),-1\right)}{\sqrt{a+b x} (b c-a d)^{9/4}}+\frac{7 d^2 \sqrt{a+b x}}{\sqrt[4]{c+d x} (b c-a d)^3}+\frac{7 d}{3 \sqrt{a+b x} \sqrt[4]{c+d x} (b c-a d)^2}-\frac{2}{3 (a+b x)^{3/2} \sqrt[4]{c+d x} (b c-a d)}-\frac{7 \sqrt[4]{b} d \sqrt{-\frac{d (a+b x)}{b c-a d}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{\sqrt{a+b x} (b c-a d)^{9/4}}",1,"(-2*((b*(c + d*x))/(b*c - a*d))^(5/4)*Hypergeometric2F1[-3/2, 5/4, -1/2, (d*(a + b*x))/(-(b*c) + a*d)])/(3*b*(a + b*x)^(3/2)*(c + d*x)^(5/4))","C",1
1665,1,73,207,0.0757544,"\int \frac{(a+b x)^{7/2}}{(c+d x)^{7/4}} \, dx","Integrate[(a + b*x)^(7/2)/(c + d*x)^(7/4),x]","\frac{2 (a+b x)^{9/2} \left(\frac{b (c+d x)}{b c-a d}\right)^{7/4} \, _2F_1\left(\frac{7}{4},\frac{9}{2};\frac{11}{2};\frac{d (a+b x)}{a d-b c}\right)}{9 b (c+d x)^{7/4}}","-\frac{320 b^{3/4} (b c-a d)^{13/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\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,"(2*(a + b*x)^(9/2)*((b*(c + d*x))/(b*c - a*d))^(7/4)*Hypergeometric2F1[7/4, 9/2, 11/2, (d*(a + b*x))/(-(b*c) + a*d)])/(9*b*(c + d*x)^(7/4))","C",1
1666,1,73,137,0.0513777,"\int \frac{(a+b x)^{3/2}}{(c+d x)^{7/4}} \, dx","Integrate[(a + b*x)^(3/2)/(c + d*x)^(7/4),x]","\frac{2 (a+b x)^{5/2} \left(\frac{b (c+d x)}{b c-a d}\right)^{7/4} \, _2F_1\left(\frac{7}{4},\frac{5}{2};\frac{7}{2};\frac{d (a+b x)}{a d-b c}\right)}{5 b (c+d x)^{7/4}}","-\frac{16 b^{3/4} (b c-a d)^{5/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\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,"(2*(a + b*x)^(5/2)*((b*(c + d*x))/(b*c - a*d))^(7/4)*Hypergeometric2F1[7/4, 5/2, 7/2, (d*(a + b*x))/(-(b*c) + a*d)])/(5*b*(c + d*x)^(7/4))","C",1
1667,1,73,111,0.0458239,"\int \frac{\sqrt{a+b x}}{(c+d x)^{7/4}} \, dx","Integrate[Sqrt[a + b*x]/(c + d*x)^(7/4),x]","\frac{2 (a+b x)^{3/2} \left(\frac{b (c+d x)}{b c-a d}\right)^{7/4} \, _2F_1\left(\frac{3}{2},\frac{7}{4};\frac{5}{2};\frac{d (a+b x)}{a d-b c}\right)}{3 b (c+d x)^{7/4}}","\frac{8 b^{3/4} \sqrt[4]{b c-a d} \sqrt{-\frac{d (a+b x)}{b c-a d}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right),-1\right)}{3 d^2 \sqrt{a+b x}}-\frac{4 \sqrt{a+b x}}{3 d (c+d x)^{3/4}}",1,"(2*(a + b*x)^(3/2)*((b*(c + d*x))/(b*c - a*d))^(7/4)*Hypergeometric2F1[3/2, 7/4, 5/2, (d*(a + b*x))/(-(b*c) + a*d)])/(3*b*(c + d*x)^(7/4))","C",1
1668,1,71,118,0.0378021,"\int \frac{1}{\sqrt{a+b x} (c+d x)^{7/4}} \, dx","Integrate[1/(Sqrt[a + b*x]*(c + d*x)^(7/4)),x]","\frac{2 \sqrt{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{7/4} \, _2F_1\left(\frac{1}{2},\frac{7}{4};\frac{3}{2};\frac{d (a+b x)}{a d-b c}\right)}{b (c+d x)^{7/4}}","\frac{4 b^{3/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\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,"(2*Sqrt[a + b*x]*((b*(c + d*x))/(b*c - a*d))^(7/4)*Hypergeometric2F1[1/2, 7/4, 3/2, (d*(a + b*x))/(-(b*c) + a*d)])/(b*(c + d*x)^(7/4))","C",1
1669,1,71,146,0.0364888,"\int \frac{1}{(a+b x)^{3/2} (c+d x)^{7/4}} \, dx","Integrate[1/((a + b*x)^(3/2)*(c + d*x)^(7/4)),x]","-\frac{2 \left(\frac{b (c+d x)}{b c-a d}\right)^{7/4} \, _2F_1\left(-\frac{1}{2},\frac{7}{4};\frac{1}{2};\frac{d (a+b x)}{a d-b c}\right)}{b \sqrt{a+b x} (c+d x)^{7/4}}","-\frac{10 b^{3/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right),-1\right)}{3 \sqrt{a+b x} (b c-a d)^{7/4}}-\frac{10 d \sqrt{a+b x}}{3 (c+d x)^{3/4} (b c-a d)^2}-\frac{2}{\sqrt{a+b x} (c+d x)^{3/4} (b c-a d)}",1,"(-2*((b*(c + d*x))/(b*c - a*d))^(7/4)*Hypergeometric2F1[-1/2, 7/4, 1/2, (d*(a + b*x))/(-(b*c) + a*d)])/(b*Sqrt[a + b*x]*(c + d*x)^(7/4))","C",1
1670,1,73,178,0.0399777,"\int \frac{1}{(a+b x)^{5/2} (c+d x)^{7/4}} \, dx","Integrate[1/((a + b*x)^(5/2)*(c + d*x)^(7/4)),x]","-\frac{2 \left(\frac{b (c+d x)}{b c-a d}\right)^{7/4} \, _2F_1\left(-\frac{3}{2},\frac{7}{4};-\frac{1}{2};\frac{d (a+b x)}{a d-b c}\right)}{3 b (a+b x)^{3/2} (c+d x)^{7/4}}","\frac{5 b^{3/4} d \sqrt{-\frac{d (a+b x)}{b c-a d}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right),-1\right)}{\sqrt{a+b x} (b c-a d)^{11/4}}+\frac{5 d^2 \sqrt{a+b x}}{(c+d x)^{3/4} (b c-a d)^3}+\frac{3 d}{\sqrt{a+b x} (c+d x)^{3/4} (b c-a d)^2}-\frac{2}{3 (a+b x)^{3/2} (c+d x)^{3/4} (b c-a d)}",1,"(-2*((b*(c + d*x))/(b*c - a*d))^(7/4)*Hypergeometric2F1[-3/2, 7/4, -1/2, (d*(a + b*x))/(-(b*c) + a*d)])/(3*b*(a + b*x)^(3/2)*(c + d*x)^(7/4))","C",1
1671,1,73,286,0.0881371,"\int \frac{(a+b x)^{7/2}}{(c+d x)^{9/4}} \, dx","Integrate[(a + b*x)^(7/2)/(c + d*x)^(9/4),x]","\frac{2 (a+b x)^{9/2} \left(\frac{b (c+d x)}{b c-a d}\right)^{9/4} \, _2F_1\left(\frac{9}{4},\frac{9}{2};\frac{11}{2};\frac{d (a+b x)}{a d-b c}\right)}{9 b (c+d x)^{9/4}}","-\frac{448 b^{5/4} (b c-a d)^{11/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\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,"(2*(a + b*x)^(9/2)*((b*(c + d*x))/(b*c - a*d))^(9/4)*Hypergeometric2F1[9/4, 9/2, 11/2, (d*(a + b*x))/(-(b*c) + a*d)])/(9*b*(c + d*x)^(9/4))","C",1
1672,1,73,248,0.0728892,"\int \frac{(a+b x)^{5/2}}{(c+d x)^{9/4}} \, dx","Integrate[(a + b*x)^(5/2)/(c + d*x)^(9/4),x]","\frac{2 (a+b x)^{7/2} \left(\frac{b (c+d x)}{b c-a d}\right)^{9/4} \, _2F_1\left(\frac{9}{4},\frac{7}{2};\frac{9}{2};\frac{d (a+b x)}{a d-b c}\right)}{7 b (c+d x)^{9/4}}","\frac{96 b^{5/4} (b c-a d)^{7/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\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,"(2*(a + b*x)^(7/2)*((b*(c + d*x))/(b*c - a*d))^(9/4)*Hypergeometric2F1[9/4, 7/2, 9/2, (d*(a + b*x))/(-(b*c) + a*d)])/(7*b*(c + d*x)^(9/4))","C",1
1673,1,73,222,0.0634398,"\int \frac{(a+b x)^{3/2}}{(c+d x)^{9/4}} \, dx","Integrate[(a + b*x)^(3/2)/(c + d*x)^(9/4),x]","\frac{2 (a+b x)^{5/2} \left(\frac{b (c+d x)}{b c-a d}\right)^{9/4} \, _2F_1\left(\frac{9}{4},\frac{5}{2};\frac{7}{2};\frac{d (a+b x)}{a d-b c}\right)}{5 b (c+d x)^{9/4}}","-\frac{48 b^{5/4} (b c-a d)^{3/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\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,"(2*(a + b*x)^(5/2)*((b*(c + d*x))/(b*c - a*d))^(9/4)*Hypergeometric2F1[9/4, 5/2, 7/2, (d*(a + b*x))/(-(b*c) + a*d)])/(5*b*(c + d*x)^(9/4))","C",1
1674,1,73,232,0.0549039,"\int \frac{\sqrt{a+b x}}{(c+d x)^{9/4}} \, dx","Integrate[Sqrt[a + b*x]/(c + d*x)^(9/4),x]","\frac{2 (a+b x)^{3/2} \left(\frac{b (c+d x)}{b c-a d}\right)^{9/4} \, _2F_1\left(\frac{3}{2},\frac{9}{4};\frac{5}{2};\frac{d (a+b x)}{a d-b c}\right)}{3 b (c+d x)^{9/4}}","\frac{8 b^{5/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\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,"(2*(a + b*x)^(3/2)*((b*(c + d*x))/(b*c - a*d))^(9/4)*Hypergeometric2F1[3/2, 9/4, 5/2, (d*(a + b*x))/(-(b*c) + a*d)])/(3*b*(c + d*x)^(9/4))","C",1
1675,1,71,236,0.0444094,"\int \frac{1}{\sqrt{a+b x} (c+d x)^{9/4}} \, dx","Integrate[1/(Sqrt[a + b*x]*(c + d*x)^(9/4)),x]","\frac{2 \sqrt{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{9/4} \, _2F_1\left(\frac{1}{2},\frac{9}{4};\frac{3}{2};\frac{d (a+b x)}{a d-b c}\right)}{b (c+d x)^{9/4}}","\frac{12 b^{5/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\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,"(2*Sqrt[a + b*x]*((b*(c + d*x))/(b*c - a*d))^(9/4)*Hypergeometric2F1[1/2, 9/4, 3/2, (d*(a + b*x))/(-(b*c) + a*d)])/(b*(c + d*x)^(9/4))","C",1
1676,1,71,262,0.0451954,"\int \frac{1}{(a+b x)^{3/2} (c+d x)^{9/4}} \, dx","Integrate[1/((a + b*x)^(3/2)*(c + d*x)^(9/4)),x]","-\frac{2 \left(\frac{b (c+d x)}{b c-a d}\right)^{9/4} \, _2F_1\left(-\frac{1}{2},\frac{9}{4};\frac{1}{2};\frac{d (a+b x)}{a d-b c}\right)}{b \sqrt{a+b x} (c+d x)^{9/4}}","-\frac{42 b^{5/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right),-1\right)}{5 \sqrt{a+b x} (b c-a d)^{9/4}}+\frac{42 b^{5/4} \sqrt{-\frac{d (a+b x)}{b c-a d}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{5 \sqrt{a+b x} (b c-a d)^{9/4}}-\frac{42 b d \sqrt{a+b x}}{5 \sqrt[4]{c+d x} (b c-a d)^3}-\frac{14 d \sqrt{a+b x}}{5 (c+d x)^{5/4} (b c-a d)^2}-\frac{2}{\sqrt{a+b x} (c+d x)^{5/4} (b c-a d)}",1,"(-2*((b*(c + d*x))/(b*c - a*d))^(9/4)*Hypergeometric2F1[-1/2, 9/4, 1/2, (d*(a + b*x))/(-(b*c) + a*d)])/(b*Sqrt[a + b*x]*(c + d*x)^(9/4))","C",1
1677,1,73,303,0.0499709,"\int \frac{1}{(a+b x)^{5/2} (c+d x)^{9/4}} \, dx","Integrate[1/((a + b*x)^(5/2)*(c + d*x)^(9/4)),x]","-\frac{2 \left(\frac{b (c+d x)}{b c-a d}\right)^{9/4} \, _2F_1\left(-\frac{3}{2},\frac{9}{4};-\frac{1}{2};\frac{d (a+b x)}{a d-b c}\right)}{3 b (a+b x)^{3/2} (c+d x)^{9/4}}","\frac{77 b^{5/4} d \sqrt{-\frac{d (a+b x)}{b c-a d}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right),-1\right)}{5 \sqrt{a+b x} (b c-a d)^{13/4}}-\frac{77 b^{5/4} d \sqrt{-\frac{d (a+b x)}{b c-a d}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{c+d x}}{\sqrt[4]{b c-a d}}\right)\right|-1\right)}{5 \sqrt{a+b x} (b c-a d)^{13/4}}+\frac{77 b d^2 \sqrt{a+b x}}{5 \sqrt[4]{c+d x} (b c-a d)^4}+\frac{77 d^2 \sqrt{a+b x}}{15 (c+d x)^{5/4} (b c-a d)^3}+\frac{11 d}{3 \sqrt{a+b x} (c+d x)^{5/4} (b c-a d)^2}-\frac{2}{3 (a+b x)^{3/2} (c+d x)^{5/4} (b c-a d)}",1,"(-2*((b*(c + d*x))/(b*c - a*d))^(9/4)*Hypergeometric2F1[-3/2, 9/4, -1/2, (d*(a + b*x))/(-(b*c) + a*d)])/(3*b*(a + b*x)^(3/2)*(c + d*x)^(9/4))","C",1
1678,1,73,205,0.0591488,"\int (a+b x)^{3/4} (c+d x)^{5/4} \, dx","Integrate[(a + b*x)^(3/4)*(c + d*x)^(5/4),x]","\frac{4 (a+b x)^{7/4} (c+d x)^{5/4} \, _2F_1\left(-\frac{5}{4},\frac{7}{4};\frac{11}{4};\frac{d (a+b x)}{a d-b c}\right)}{7 b \left(\frac{b (c+d x)}{b c-a d}\right)^{5/4}}","\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,"(4*(a + b*x)^(7/4)*(c + d*x)^(5/4)*Hypergeometric2F1[-5/4, 7/4, 11/4, (d*(a + b*x))/(-(b*c) + a*d)])/(7*b*((b*(c + d*x))/(b*c - a*d))^(5/4))","C",1
1679,1,73,167,0.042966,"\int \frac{(c+d x)^{5/4}}{\sqrt[4]{a+b x}} \, dx","Integrate[(c + d*x)^(5/4)/(a + b*x)^(1/4),x]","\frac{4 (a+b x)^{3/4} (c+d x)^{5/4} \, _2F_1\left(-\frac{5}{4},\frac{3}{4};\frac{7}{4};\frac{d (a+b x)}{a d-b c}\right)}{3 b \left(\frac{b (c+d x)}{b c-a d}\right)^{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^{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,"(4*(a + b*x)^(3/4)*(c + d*x)^(5/4)*Hypergeometric2F1[-5/4, 3/4, 7/4, (d*(a + b*x))/(-(b*c) + a*d)])/(3*b*((b*(c + d*x))/(b*c - a*d))^(5/4))","C",1
1680,1,71,152,0.0465801,"\int \frac{(c+d x)^{5/4}}{(a+b x)^{5/4}} \, dx","Integrate[(c + d*x)^(5/4)/(a + b*x)^(5/4),x]","-\frac{4 (c+d x)^{5/4} \, _2F_1\left(-\frac{5}{4},-\frac{1}{4};\frac{3}{4};\frac{d (a+b x)}{a d-b c}\right)}{b \sqrt[4]{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{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,"(-4*(c + d*x)^(5/4)*Hypergeometric2F1[-5/4, -1/4, 3/4, (d*(a + b*x))/(-(b*c) + a*d)])/(b*(a + b*x)^(1/4)*((b*(c + d*x))/(b*c - a*d))^(5/4))","C",1
1681,1,73,134,0.0526976,"\int \frac{(c+d x)^{5/4}}{(a+b x)^{9/4}} \, dx","Integrate[(c + d*x)^(5/4)/(a + b*x)^(9/4),x]","-\frac{4 (c+d x)^{5/4} \, _2F_1\left(-\frac{5}{4},-\frac{5}{4};-\frac{1}{4};\frac{d (a+b x)}{a d-b c}\right)}{5 b (a+b x)^{5/4} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/4}}","-\frac{2 d^{5/4} \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{b^{9/4}}+\frac{2 d^{5/4} \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{b^{9/4}}-\frac{4 d \sqrt[4]{c+d x}}{b^2 \sqrt[4]{a+b x}}-\frac{4 (c+d x)^{5/4}}{5 b (a+b x)^{5/4}}",1,"(-4*(c + d*x)^(5/4)*Hypergeometric2F1[-5/4, -5/4, -1/4, (d*(a + b*x))/(-(b*c) + a*d)])/(5*b*(a + b*x)^(5/4)*((b*(c + d*x))/(b*c - a*d))^(5/4))","C",1
1682,1,32,32,0.0154058,"\int \frac{(c+d x)^{5/4}}{(a+b x)^{13/4}} \, dx","Integrate[(c + d*x)^(5/4)/(a + b*x)^(13/4),x]","-\frac{4 (c+d x)^{9/4}}{9 (a+b x)^{9/4} (b c-a d)}","-\frac{4 (c+d x)^{9/4}}{9 (a+b x)^{9/4} (b c-a d)}",1,"(-4*(c + d*x)^(9/4))/(9*(b*c - a*d)*(a + b*x)^(9/4))","A",1
1683,1,46,66,0.0274399,"\int \frac{(c+d x)^{5/4}}{(a+b x)^{17/4}} \, dx","Integrate[(c + d*x)^(5/4)/(a + b*x)^(17/4),x]","\frac{4 (c+d x)^{9/4} (13 a d-9 b c+4 b d x)}{117 (a+b x)^{13/4} (b c-a d)^2}","\frac{16 d (c+d x)^{9/4}}{117 (a+b x)^{9/4} (b c-a d)^2}-\frac{4 (c+d x)^{9/4}}{13 (a+b x)^{13/4} (b c-a d)}",1,"(4*(c + d*x)^(9/4)*(-9*b*c + 13*a*d + 4*b*d*x))/(117*(b*c - a*d)^2*(a + b*x)^(13/4))","A",1
1684,1,77,101,0.0494625,"\int \frac{(c+d x)^{5/4}}{(a+b x)^{21/4}} \, dx","Integrate[(c + d*x)^(5/4)/(a + b*x)^(21/4),x]","-\frac{4 (c+d x)^{9/4} \left(221 a^2 d^2+34 a b d (4 d x-9 c)+b^2 \left(117 c^2-72 c d x+32 d^2 x^2\right)\right)}{1989 (a+b x)^{17/4} (b c-a d)^3}","-\frac{128 d^2 (c+d x)^{9/4}}{1989 (a+b x)^{9/4} (b c-a d)^3}+\frac{32 d (c+d x)^{9/4}}{221 (a+b x)^{13/4} (b c-a d)^2}-\frac{4 (c+d x)^{9/4}}{17 (a+b x)^{17/4} (b c-a d)}",1,"(-4*(c + d*x)^(9/4)*(221*a^2*d^2 + 34*a*b*d*(-9*c + 4*d*x) + b^2*(117*c^2 - 72*c*d*x + 32*d^2*x^2)))/(1989*(b*c - a*d)^3*(a + b*x)^(17/4))","A",1
1685,1,118,136,0.0672921,"\int \frac{(c+d x)^{5/4}}{(a+b x)^{25/4}} \, dx","Integrate[(c + d*x)^(5/4)/(a + b*x)^(25/4),x]","\frac{4 (c+d x)^{9/4} \left(1547 a^3 d^3+357 a^2 b d^2 (4 d x-9 c)+21 a b^2 d \left(117 c^2-72 c d x+32 d^2 x^2\right)+b^3 \left(-663 c^3+468 c^2 d x-288 c d^2 x^2+128 d^3 x^3\right)\right)}{13923 (a+b x)^{21/4} (b c-a d)^4}","\frac{512 d^3 (c+d x)^{9/4}}{13923 (a+b x)^{9/4} (b c-a d)^4}-\frac{128 d^2 (c+d x)^{9/4}}{1547 (a+b x)^{13/4} (b c-a d)^3}+\frac{16 d (c+d x)^{9/4}}{119 (a+b x)^{17/4} (b c-a d)^2}-\frac{4 (c+d x)^{9/4}}{21 (a+b x)^{21/4} (b c-a d)}",1,"(4*(c + d*x)^(9/4)*(1547*a^3*d^3 + 357*a^2*b*d^2*(-9*c + 4*d*x) + 21*a*b^2*d*(117*c^2 - 72*c*d*x + 32*d^2*x^2) + b^3*(-663*c^3 + 468*c^2*d*x - 288*c*d^2*x^2 + 128*d^3*x^3)))/(13923*(b*c - a*d)^4*(a + b*x)^(21/4))","A",1
1686,1,73,408,0.0574811,"\int (a+b x)^{5/4} (c+d x)^{5/4} \, dx","Integrate[(a + b*x)^(5/4)*(c + d*x)^(5/4),x]","\frac{4 (a+b x)^{9/4} (c+d x)^{5/4} \, _2F_1\left(-\frac{5}{4},\frac{9}{4};\frac{13}{4};\frac{d (a+b x)}{a d-b c}\right)}{9 b \left(\frac{b (c+d x)}{b c-a d}\right)^{5/4}}","\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}} \operatorname{EllipticF}\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,"(4*(a + b*x)^(9/4)*(c + d*x)^(5/4)*Hypergeometric2F1[-5/4, 9/4, 13/4, (d*(a + b*x))/(-(b*c) + a*d)])/(9*b*((b*(c + d*x))/(b*c - a*d))^(5/4))","C",1
1687,1,73,370,0.0505565,"\int \sqrt[4]{a+b x} (c+d x)^{5/4} \, dx","Integrate[(a + b*x)^(1/4)*(c + d*x)^(5/4),x]","\frac{4 (a+b x)^{5/4} (c+d x)^{5/4} \, _2F_1\left(-\frac{5}{4},\frac{5}{4};\frac{9}{4};\frac{d (a+b x)}{a d-b c}\right)}{5 b \left(\frac{b (c+d x)}{b c-a d}\right)^{5/4}}","-\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}} \operatorname{EllipticF}\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,"(4*(a + b*x)^(5/4)*(c + d*x)^(5/4)*Hypergeometric2F1[-5/4, 5/4, 9/4, (d*(a + b*x))/(-(b*c) + a*d)])/(5*b*((b*(c + d*x))/(b*c - a*d))^(5/4))","C",1
1688,1,71,332,0.0459498,"\int \frac{(c+d x)^{5/4}}{(a+b x)^{3/4}} \, dx","Integrate[(c + d*x)^(5/4)/(a + b*x)^(3/4),x]","\frac{4 \sqrt[4]{a+b x} (c+d x)^{5/4} \, _2F_1\left(-\frac{5}{4},\frac{1}{4};\frac{5}{4};\frac{d (a+b x)}{a d-b c}\right)}{b \left(\frac{b (c+d x)}{b c-a d}\right)^{5/4}}","\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}} \operatorname{EllipticF}\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,"(4*(a + b*x)^(1/4)*(c + d*x)^(5/4)*Hypergeometric2F1[-5/4, 1/4, 5/4, (d*(a + b*x))/(-(b*c) + a*d)])/(b*((b*(c + d*x))/(b*c - a*d))^(5/4))","C",1
1689,1,73,325,0.0409502,"\int \frac{(c+d x)^{5/4}}{(a+b x)^{7/4}} \, dx","Integrate[(c + d*x)^(5/4)/(a + b*x)^(7/4),x]","-\frac{4 (c+d x)^{5/4} \, _2F_1\left(-\frac{5}{4},-\frac{3}{4};\frac{1}{4};\frac{d (a+b x)}{a d-b c}\right)}{3 b (a+b x)^{3/4} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/4}}","\frac{5 d^{3/4} (b c-a d)^{3/2} ((a+b x) (c+d x))^{3/4} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} \operatorname{EllipticF}\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,"(-4*(c + d*x)^(5/4)*Hypergeometric2F1[-5/4, -3/4, 1/4, (d*(a + b*x))/(-(b*c) + a*d)])/(3*b*(a + b*x)^(3/4)*((b*(c + d*x))/(b*c - a*d))^(5/4))","C",1
1690,1,73,325,0.0471116,"\int \frac{(c+d x)^{5/4}}{(a+b x)^{11/4}} \, dx","Integrate[(c + d*x)^(5/4)/(a + b*x)^(11/4),x]","-\frac{4 (c+d x)^{5/4} \, _2F_1\left(-\frac{7}{4},-\frac{5}{4};-\frac{3}{4};\frac{d (a+b x)}{a d-b c}\right)}{7 b (a+b x)^{7/4} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/4}}","\frac{5 \sqrt{2} d^{7/4} \sqrt{b c-a d} ((a+b x) (c+d x))^{3/4} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} \operatorname{EllipticF}\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,"(-4*(c + d*x)^(5/4)*Hypergeometric2F1[-7/4, -5/4, -3/4, (d*(a + b*x))/(-(b*c) + a*d)])/(7*b*(a + b*x)^(7/4)*((b*(c + d*x))/(b*c - a*d))^(5/4))","C",1
1691,1,73,363,0.0507638,"\int \frac{(c+d x)^{5/4}}{(a+b x)^{15/4}} \, dx","Integrate[(c + d*x)^(5/4)/(a + b*x)^(15/4),x]","-\frac{4 (c+d x)^{5/4} \, _2F_1\left(-\frac{11}{4},-\frac{5}{4};-\frac{7}{4};\frac{d (a+b x)}{a d-b c}\right)}{11 b (a+b x)^{11/4} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/4}}","-\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}} \operatorname{EllipticF}\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,"(-4*(c + d*x)^(5/4)*Hypergeometric2F1[-11/4, -5/4, -7/4, (d*(a + b*x))/(-(b*c) + a*d)])/(11*b*(a + b*x)^(11/4)*((b*(c + d*x))/(b*c - a*d))^(5/4))","C",1
1692,1,73,401,0.0534562,"\int \frac{(c+d x)^{5/4}}{(a+b x)^{19/4}} \, dx","Integrate[(c + d*x)^(5/4)/(a + b*x)^(19/4),x]","-\frac{4 (c+d x)^{5/4} \, _2F_1\left(-\frac{15}{4},-\frac{5}{4};-\frac{11}{4};\frac{d (a+b x)}{a d-b c}\right)}{15 b (a+b x)^{15/4} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/4}}","\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}} \operatorname{EllipticF}\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,"(-4*(c + d*x)^(5/4)*Hypergeometric2F1[-15/4, -5/4, -11/4, (d*(a + b*x))/(-(b*c) + a*d)])/(15*b*(a + b*x)^(15/4)*((b*(c + d*x))/(b*c - a*d))^(5/4))","C",1
1693,1,73,167,0.030867,"\int \frac{(a+b x)^{5/4}}{\sqrt[4]{c+d x}} \, dx","Integrate[(a + b*x)^(5/4)/(c + d*x)^(1/4),x]","\frac{4 (a+b x)^{9/4} \sqrt[4]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{1}{4},\frac{9}{4};\frac{13}{4};\frac{d (a+b x)}{a d-b c}\right)}{9 b \sqrt[4]{c+d x}}","\frac{5 (b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{16 b^{3/4} d^{9/4}}+\frac{5 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{16 b^{3/4} d^{9/4}}-\frac{5 \sqrt[4]{a+b x} (c+d x)^{3/4} (b c-a d)}{8 d^2}+\frac{(a+b x)^{5/4} (c+d x)^{3/4}}{2 d}",1,"(4*(a + b*x)^(9/4)*((b*(c + d*x))/(b*c - a*d))^(1/4)*Hypergeometric2F1[1/4, 9/4, 13/4, (d*(a + b*x))/(-(b*c) + a*d)])/(9*b*(c + d*x)^(1/4))","C",1
1694,1,73,127,0.0258799,"\int \frac{\sqrt[4]{a+b x}}{\sqrt[4]{c+d x}} \, dx","Integrate[(a + b*x)^(1/4)/(c + d*x)^(1/4),x]","\frac{4 (a+b x)^{5/4} \sqrt[4]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{1}{4},\frac{5}{4};\frac{9}{4};\frac{d (a+b x)}{a d-b c}\right)}{5 b \sqrt[4]{c+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,"(4*(a + b*x)^(5/4)*((b*(c + d*x))/(b*c - a*d))^(1/4)*Hypergeometric2F1[1/4, 5/4, 9/4, (d*(a + b*x))/(-(b*c) + a*d)])/(5*b*(c + d*x)^(1/4))","C",1
1695,1,71,85,0.0285746,"\int \frac{1}{(a+b x)^{3/4} \sqrt[4]{c+d x}} \, dx","Integrate[1/((a + b*x)^(3/4)*(c + d*x)^(1/4)),x]","\frac{4 \sqrt[4]{a+b x} \sqrt[4]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{1}{4},\frac{1}{4};\frac{5}{4};\frac{d (a+b x)}{a d-b c}\right)}{b \sqrt[4]{c+d x}}","\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{b^{3/4} \sqrt[4]{d}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{b^{3/4} \sqrt[4]{d}}",1,"(4*(a + b*x)^(1/4)*((b*(c + d*x))/(b*c - a*d))^(1/4)*Hypergeometric2F1[1/4, 1/4, 5/4, (d*(a + b*x))/(-(b*c) + a*d)])/(b*(c + d*x)^(1/4))","C",1
1696,1,32,32,0.0115517,"\int \frac{1}{(a+b x)^{7/4} \sqrt[4]{c+d x}} \, dx","Integrate[1/((a + b*x)^(7/4)*(c + d*x)^(1/4)),x]","-\frac{4 (c+d x)^{3/4}}{3 (a+b x)^{3/4} (b c-a d)}","-\frac{4 (c+d x)^{3/4}}{3 (a+b x)^{3/4} (b c-a d)}",1,"(-4*(c + d*x)^(3/4))/(3*(b*c - a*d)*(a + b*x)^(3/4))","A",1
1697,1,46,66,0.0167369,"\int \frac{1}{(a+b x)^{11/4} \sqrt[4]{c+d x}} \, dx","Integrate[1/((a + b*x)^(11/4)*(c + d*x)^(1/4)),x]","\frac{4 (c+d x)^{3/4} (7 a d-3 b c+4 b d x)}{21 (a+b x)^{7/4} (b c-a d)^2}","\frac{16 d (c+d x)^{3/4}}{21 (a+b x)^{3/4} (b c-a d)^2}-\frac{4 (c+d x)^{3/4}}{7 (a+b x)^{7/4} (b c-a d)}",1,"(4*(c + d*x)^(3/4)*(-3*b*c + 7*a*d + 4*b*d*x))/(21*(b*c - a*d)^2*(a + b*x)^(7/4))","A",1
1698,1,77,101,0.0332565,"\int \frac{1}{(a+b x)^{15/4} \sqrt[4]{c+d x}} \, dx","Integrate[1/((a + b*x)^(15/4)*(c + d*x)^(1/4)),x]","-\frac{4 (c+d x)^{3/4} \left(77 a^2 d^2+22 a b d (4 d x-3 c)+b^2 \left(21 c^2-24 c d x+32 d^2 x^2\right)\right)}{231 (a+b x)^{11/4} (b c-a d)^3}","-\frac{128 d^2 (c+d x)^{3/4}}{231 (a+b x)^{3/4} (b c-a d)^3}+\frac{32 d (c+d x)^{3/4}}{77 (a+b x)^{7/4} (b c-a d)^2}-\frac{4 (c+d x)^{3/4}}{11 (a+b x)^{11/4} (b c-a d)}",1,"(-4*(c + d*x)^(3/4)*(77*a^2*d^2 + 22*a*b*d*(-3*c + 4*d*x) + b^2*(21*c^2 - 24*c*d*x + 32*d^2*x^2)))/(231*(b*c - a*d)^3*(a + b*x)^(11/4))","A",1
1699,1,118,136,0.0494034,"\int \frac{1}{(a+b x)^{19/4} \sqrt[4]{c+d x}} \, dx","Integrate[1/((a + b*x)^(19/4)*(c + d*x)^(1/4)),x]","\frac{4 (c+d x)^{3/4} \left(385 a^3 d^3+165 a^2 b d^2 (4 d x-3 c)+15 a b^2 d \left(21 c^2-24 c d x+32 d^2 x^2\right)+b^3 \left(-77 c^3+84 c^2 d x-96 c d^2 x^2+128 d^3 x^3\right)\right)}{1155 (a+b x)^{15/4} (b c-a d)^4}","\frac{512 d^3 (c+d x)^{3/4}}{1155 (a+b x)^{3/4} (b c-a d)^4}-\frac{128 d^2 (c+d x)^{3/4}}{385 (a+b x)^{7/4} (b c-a d)^3}+\frac{16 d (c+d x)^{3/4}}{55 (a+b x)^{11/4} (b c-a d)^2}-\frac{4 (c+d x)^{3/4}}{15 (a+b x)^{15/4} (b c-a d)}",1,"(4*(c + d*x)^(3/4)*(385*a^3*d^3 + 165*a^2*b*d^2*(-3*c + 4*d*x) + 15*a*b^2*d*(21*c^2 - 24*c*d*x + 32*d^2*x^2) + b^3*(-77*c^3 + 84*c^2*d*x - 96*c*d^2*x^2 + 128*d^3*x^3)))/(1155*(b*c - a*d)^4*(a + b*x)^(15/4))","A",1
1700,1,73,751,0.0315094,"\int \frac{(a+b x)^{7/4}}{\sqrt[4]{c+d x}} \, dx","Integrate[(a + b*x)^(7/4)/(c + d*x)^(1/4),x]","\frac{4 (a+b x)^{11/4} \sqrt[4]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{1}{4},\frac{11}{4};\frac{15}{4};\frac{d (a+b x)}{a d-b c}\right)}{11 b \sqrt[4]{c+d x}}","\frac{7 (b c-a d)^{7/2} \sqrt[4]{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} \operatorname{EllipticF}\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,"(4*(a + b*x)^(11/4)*((b*(c + d*x))/(b*c - a*d))^(1/4)*Hypergeometric2F1[1/4, 11/4, 15/4, (d*(a + b*x))/(-(b*c) + a*d)])/(11*b*(c + d*x)^(1/4))","C",1
1701,1,73,705,0.0269092,"\int \frac{(a+b x)^{3/4}}{\sqrt[4]{c+d x}} \, dx","Integrate[(a + b*x)^(3/4)/(c + d*x)^(1/4),x]","\frac{4 (a+b x)^{7/4} \sqrt[4]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{1}{4},\frac{7}{4};\frac{11}{4};\frac{d (a+b x)}{a d-b c}\right)}{7 b \sqrt[4]{c+d x}}","-\frac{(b c-a d)^{5/2} \sqrt[4]{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} \operatorname{EllipticF}\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,"(4*(a + b*x)^(7/4)*((b*(c + d*x))/(b*c - a*d))^(1/4)*Hypergeometric2F1[1/4, 7/4, 11/4, (d*(a + b*x))/(-(b*c) + a*d)])/(7*b*(c + d*x)^(1/4))","C",1
1702,1,73,688,0.0230113,"\int \frac{1}{\sqrt[4]{a+b x} \sqrt[4]{c+d x}} \, dx","Integrate[1/((a + b*x)^(1/4)*(c + d*x)^(1/4)),x]","\frac{4 (a+b x)^{3/4} \sqrt[4]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{1}{4},\frac{3}{4};\frac{7}{4};\frac{d (a+b x)}{a d-b c}\right)}{3 b \sqrt[4]{c+d x}}","\frac{(b c-a d)^{3/2} \sqrt[4]{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} \operatorname{EllipticF}\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,"(4*(a + b*x)^(3/4)*((b*(c + d*x))/(b*c - a*d))^(1/4)*Hypergeometric2F1[1/4, 3/4, 7/4, (d*(a + b*x))/(-(b*c) + a*d)])/(3*b*(c + d*x)^(1/4))","C",1
1703,1,71,718,0.0242933,"\int \frac{1}{(a+b x)^{5/4} \sqrt[4]{c+d x}} \, dx","Integrate[1/((a + b*x)^(5/4)*(c + d*x)^(1/4)),x]","-\frac{4 \sqrt[4]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(-\frac{1}{4},\frac{1}{4};\frac{3}{4};\frac{d (a+b x)}{a d-b c}\right)}{b \sqrt[4]{a+b x} \sqrt[4]{c+d x}}","\frac{\sqrt{2} \sqrt[4]{d} \sqrt{b c-a d} \sqrt[4]{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} \operatorname{EllipticF}\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right),\frac{1}{2}\right)}{b^{3/4} \sqrt[4]{a+b x} \sqrt[4]{c+d x} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}-\frac{2 \sqrt{2} \sqrt[4]{d} \sqrt{b c-a d} \sqrt[4]{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{b^{3/4} \sqrt[4]{a+b x} \sqrt[4]{c+d x} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}-\frac{4 (c+d x)^{3/4}}{\sqrt[4]{a+b x} (b c-a d)}+\frac{4 \sqrt{d} \sqrt{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \sqrt{(a d+b (c+2 d x))^2}}{\sqrt{b} \sqrt[4]{a+b x} \sqrt[4]{c+d x} (b c-a d)^2 (a d+b c+2 b d x) \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)}",1,"(-4*((b*(c + d*x))/(b*c - a*d))^(1/4)*Hypergeometric2F1[-1/4, 1/4, 3/4, (d*(a + b*x))/(-(b*c) + a*d)])/(b*(a + b*x)^(1/4)*(c + d*x)^(1/4))","C",1
1704,1,73,760,0.0238679,"\int \frac{1}{(a+b x)^{9/4} \sqrt[4]{c+d x}} \, dx","Integrate[1/((a + b*x)^(9/4)*(c + d*x)^(1/4)),x]","-\frac{4 \sqrt[4]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(-\frac{5}{4},\frac{1}{4};-\frac{1}{4};\frac{d (a+b x)}{a d-b c}\right)}{5 b (a+b x)^{5/4} \sqrt[4]{c+d x}}","-\frac{2 \sqrt{2} d^{5/4} \sqrt[4]{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} \operatorname{EllipticF}\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right),\frac{1}{2}\right)}{5 b^{3/4} \sqrt[4]{a+b x} \sqrt[4]{c+d x} \sqrt{b c-a d} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}+\frac{4 \sqrt{2} d^{5/4} \sqrt[4]{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{5 b^{3/4} \sqrt[4]{a+b x} \sqrt[4]{c+d x} \sqrt{b c-a d} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}-\frac{8 d^{3/2} \sqrt{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \sqrt{(a d+b (c+2 d x))^2}}{5 \sqrt{b} \sqrt[4]{a+b x} \sqrt[4]{c+d x} (b c-a d)^3 (a d+b c+2 b d x) \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)}+\frac{8 d (c+d x)^{3/4}}{5 \sqrt[4]{a+b x} (b c-a d)^2}-\frac{4 (c+d x)^{3/4}}{5 (a+b x)^{5/4} (b c-a d)}",1,"(-4*((b*(c + d*x))/(b*c - a*d))^(1/4)*Hypergeometric2F1[-5/4, 1/4, -1/4, (d*(a + b*x))/(-(b*c) + a*d)])/(5*b*(a + b*x)^(5/4)*(c + d*x)^(1/4))","C",1
1705,1,73,167,0.0349079,"\int \frac{(a+b x)^{7/4}}{(c+d x)^{3/4}} \, dx","Integrate[(a + b*x)^(7/4)/(c + d*x)^(3/4),x]","\frac{4 (a+b x)^{11/4} \left(\frac{b (c+d x)}{b c-a d}\right)^{3/4} \, _2F_1\left(\frac{3}{4},\frac{11}{4};\frac{15}{4};\frac{d (a+b x)}{a d-b c}\right)}{11 b (c+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,"(4*(a + b*x)^(11/4)*((b*(c + d*x))/(b*c - a*d))^(3/4)*Hypergeometric2F1[3/4, 11/4, 15/4, (d*(a + b*x))/(-(b*c) + a*d)])/(11*b*(c + d*x)^(3/4))","C",1
1706,1,73,127,0.0284383,"\int \frac{(a+b x)^{3/4}}{(c+d x)^{3/4}} \, dx","Integrate[(a + b*x)^(3/4)/(c + d*x)^(3/4),x]","\frac{4 (a+b x)^{7/4} \left(\frac{b (c+d x)}{b c-a d}\right)^{3/4} \, _2F_1\left(\frac{3}{4},\frac{7}{4};\frac{11}{4};\frac{d (a+b x)}{a d-b c}\right)}{7 b (c+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,"(4*(a + b*x)^(7/4)*((b*(c + d*x))/(b*c - a*d))^(3/4)*Hypergeometric2F1[3/4, 7/4, 11/4, (d*(a + b*x))/(-(b*c) + a*d)])/(7*b*(c + d*x)^(3/4))","C",1
1707,1,73,85,0.0312415,"\int \frac{1}{\sqrt[4]{a+b x} (c+d x)^{3/4}} \, dx","Integrate[1/((a + b*x)^(1/4)*(c + d*x)^(3/4)),x]","\frac{4 (a+b x)^{3/4} \left(\frac{b (c+d x)}{b c-a d}\right)^{3/4} \, _2F_1\left(\frac{3}{4},\frac{3}{4};\frac{7}{4};\frac{d (a+b x)}{a d-b c}\right)}{3 b (c+d x)^{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,"(4*(a + b*x)^(3/4)*((b*(c + d*x))/(b*c - a*d))^(3/4)*Hypergeometric2F1[3/4, 3/4, 7/4, (d*(a + b*x))/(-(b*c) + a*d)])/(3*b*(c + d*x)^(3/4))","C",1
1708,1,30,30,0.0074396,"\int \frac{1}{(a+b x)^{5/4} (c+d x)^{3/4}} \, dx","Integrate[1/((a + b*x)^(5/4)*(c + d*x)^(3/4)),x]","\frac{4 \sqrt[4]{c+d x}}{\sqrt[4]{a+b x} (a d-b c)}","-\frac{4 \sqrt[4]{c+d x}}{\sqrt[4]{a+b x} (b c-a d)}",1,"(4*(c + d*x)^(1/4))/((-(b*c) + a*d)*(a + b*x)^(1/4))","A",1
1709,1,46,66,0.0154183,"\int \frac{1}{(a+b x)^{9/4} (c+d x)^{3/4}} \, dx","Integrate[1/((a + b*x)^(9/4)*(c + d*x)^(3/4)),x]","\frac{4 \sqrt[4]{c+d x} (5 a d-b c+4 b d x)}{5 (a+b x)^{5/4} (b c-a d)^2}","\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)*(-(b*c) + 5*a*d + 4*b*d*x))/(5*(b*c - a*d)^2*(a + b*x)^(5/4))","A",1
1710,1,75,101,0.0332678,"\int \frac{1}{(a+b x)^{13/4} (c+d x)^{3/4}} \, dx","Integrate[1/((a + b*x)^(13/4)*(c + d*x)^(3/4)),x]","-\frac{4 \sqrt[4]{c+d x} \left(45 a^2 d^2-18 a b d (c-4 d x)+b^2 \left(5 c^2-8 c d x+32 d^2 x^2\right)\right)}{45 (a+b x)^{9/4} (b c-a d)^3}","-\frac{128 d^2 \sqrt[4]{c+d x}}{45 \sqrt[4]{a+b x} (b c-a d)^3}+\frac{32 d \sqrt[4]{c+d x}}{45 (a+b x)^{5/4} (b c-a d)^2}-\frac{4 \sqrt[4]{c+d x}}{9 (a+b x)^{9/4} (b c-a d)}",1,"(-4*(c + d*x)^(1/4)*(45*a^2*d^2 - 18*a*b*d*(c - 4*d*x) + b^2*(5*c^2 - 8*c*d*x + 32*d^2*x^2)))/(45*(b*c - a*d)^3*(a + b*x)^(9/4))","A",1
1711,1,116,136,0.0477907,"\int \frac{1}{(a+b x)^{17/4} (c+d x)^{3/4}} \, dx","Integrate[1/((a + b*x)^(17/4)*(c + d*x)^(3/4)),x]","\frac{4 \sqrt[4]{c+d x} \left(195 a^3 d^3-117 a^2 b d^2 (c-4 d x)+13 a b^2 d \left(5 c^2-8 c d x+32 d^2 x^2\right)+b^3 \left(-15 c^3+20 c^2 d x-32 c d^2 x^2+128 d^3 x^3\right)\right)}{195 (a+b x)^{13/4} (b c-a d)^4}","\frac{512 d^3 \sqrt[4]{c+d x}}{195 \sqrt[4]{a+b x} (b c-a d)^4}-\frac{128 d^2 \sqrt[4]{c+d x}}{195 (a+b x)^{5/4} (b c-a d)^3}+\frac{16 d \sqrt[4]{c+d x}}{39 (a+b x)^{9/4} (b c-a d)^2}-\frac{4 \sqrt[4]{c+d x}}{13 (a+b x)^{13/4} (b c-a d)}",1,"(4*(c + d*x)^(1/4)*(195*a^3*d^3 - 117*a^2*b*d^2*(c - 4*d*x) + 13*a*b^2*d*(5*c^2 - 8*c*d*x + 32*d^2*x^2) + b^3*(-15*c^3 + 20*c^2*d*x - 32*c*d^2*x^2 + 128*d^3*x^3)))/(195*(b*c - a*d)^4*(a + b*x)^(13/4))","A",1
1712,1,73,332,0.0312599,"\int \frac{(a+b x)^{5/4}}{(c+d x)^{3/4}} \, dx","Integrate[(a + b*x)^(5/4)/(c + d*x)^(3/4),x]","\frac{4 (a+b x)^{9/4} \left(\frac{b (c+d x)}{b c-a d}\right)^{3/4} \, _2F_1\left(\frac{3}{4},\frac{9}{4};\frac{13}{4};\frac{d (a+b x)}{a d-b c}\right)}{9 b (c+d x)^{3/4}}","\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}} \operatorname{EllipticF}\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,"(4*(a + b*x)^(9/4)*((b*(c + d*x))/(b*c - a*d))^(3/4)*Hypergeometric2F1[3/4, 9/4, 13/4, (d*(a + b*x))/(-(b*c) + a*d)])/(9*b*(c + d*x)^(3/4))","C",1
1713,1,73,295,0.0268754,"\int \frac{\sqrt[4]{a+b x}}{(c+d x)^{3/4}} \, dx","Integrate[(a + b*x)^(1/4)/(c + d*x)^(3/4),x]","\frac{4 (a+b x)^{5/4} \left(\frac{b (c+d x)}{b c-a d}\right)^{3/4} \, _2F_1\left(\frac{3}{4},\frac{5}{4};\frac{9}{4};\frac{d (a+b x)}{a d-b c}\right)}{5 b (c+d x)^{3/4}}","\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}} \operatorname{EllipticF}\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,"(4*(a + b*x)^(5/4)*((b*(c + d*x))/(b*c - a*d))^(3/4)*Hypergeometric2F1[3/4, 5/4, 9/4, (d*(a + b*x))/(-(b*c) + a*d)])/(5*b*(c + d*x)^(3/4))","C",1
1714,1,71,270,0.0246807,"\int \frac{1}{(a+b x)^{3/4} (c+d x)^{3/4}} \, dx","Integrate[1/((a + b*x)^(3/4)*(c + d*x)^(3/4)),x]","\frac{4 \sqrt[4]{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{3/4} \, _2F_1\left(\frac{1}{4},\frac{3}{4};\frac{5}{4};\frac{d (a+b x)}{a d-b c}\right)}{b (c+d x)^{3/4}}","\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}} \operatorname{EllipticF}\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,"(4*(a + b*x)^(1/4)*((b*(c + d*x))/(b*c - a*d))^(3/4)*Hypergeometric2F1[1/4, 3/4, 5/4, (d*(a + b*x))/(-(b*c) + a*d)])/(b*(c + d*x)^(3/4))","C",1
1715,1,73,306,0.0245975,"\int \frac{1}{(a+b x)^{7/4} (c+d x)^{3/4}} \, dx","Integrate[1/((a + b*x)^(7/4)*(c + d*x)^(3/4)),x]","-\frac{4 \left(\frac{b (c+d x)}{b c-a d}\right)^{3/4} \, _2F_1\left(-\frac{3}{4},\frac{3}{4};\frac{1}{4};\frac{d (a+b x)}{a d-b c}\right)}{3 b (a+b x)^{3/4} (c+d x)^{3/4}}","-\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}} \operatorname{EllipticF}\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right),\frac{1}{2}\right)}{3 \sqrt[4]{b} (a+b x)^{3/4} (c+d x)^{3/4} \sqrt{b c-a d} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}-\frac{4 \sqrt[4]{c+d x}}{3 (a+b x)^{3/4} (b c-a d)}",1,"(-4*((b*(c + d*x))/(b*c - a*d))^(3/4)*Hypergeometric2F1[-3/4, 3/4, 1/4, (d*(a + b*x))/(-(b*c) + a*d)])/(3*b*(a + b*x)^(3/4)*(c + d*x)^(3/4))","C",1
1716,1,73,339,0.0245024,"\int \frac{1}{(a+b x)^{11/4} (c+d x)^{3/4}} \, dx","Integrate[1/((a + b*x)^(11/4)*(c + d*x)^(3/4)),x]","-\frac{4 \left(\frac{b (c+d x)}{b c-a d}\right)^{3/4} \, _2F_1\left(-\frac{7}{4},\frac{3}{4};-\frac{3}{4};\frac{d (a+b x)}{a d-b c}\right)}{7 b (a+b x)^{7/4} (c+d x)^{3/4}}","\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}} \operatorname{EllipticF}\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right),\frac{1}{2}\right)}{7 \sqrt[4]{b} (a+b x)^{3/4} (c+d x)^{3/4} (b c-a d)^{3/2} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}+\frac{8 d \sqrt[4]{c+d x}}{7 (a+b x)^{3/4} (b c-a d)^2}-\frac{4 \sqrt[4]{c+d x}}{7 (a+b x)^{7/4} (b c-a d)}",1,"(-4*((b*(c + d*x))/(b*c - a*d))^(3/4)*Hypergeometric2F1[-7/4, 3/4, -3/4, (d*(a + b*x))/(-(b*c) + a*d)])/(7*b*(a + b*x)^(7/4)*(c + d*x)^(3/4))","C",1
1717,1,73,152,0.0500196,"\int \frac{(a+b x)^{5/4}}{(c+d x)^{5/4}} \, dx","Integrate[(a + b*x)^(5/4)/(c + d*x)^(5/4),x]","\frac{4 (a+b x)^{9/4} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/4} \, _2F_1\left(\frac{5}{4},\frac{9}{4};\frac{13}{4};\frac{d (a+b x)}{a d-b c}\right)}{9 b (c+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,"(4*(a + b*x)^(9/4)*((b*(c + d*x))/(b*c - a*d))^(5/4)*Hypergeometric2F1[5/4, 9/4, 13/4, (d*(a + b*x))/(-(b*c) + a*d)])/(9*b*(c + d*x)^(5/4))","C",1
1718,1,73,108,0.0444248,"\int \frac{\sqrt[4]{a+b x}}{(c+d x)^{5/4}} \, dx","Integrate[(a + b*x)^(1/4)/(c + d*x)^(5/4),x]","\frac{4 (a+b x)^{5/4} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/4} \, _2F_1\left(\frac{5}{4},\frac{5}{4};\frac{9}{4};\frac{d (a+b x)}{a d-b c}\right)}{5 b (c+d x)^{5/4}}","\frac{2 \sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{d^{5/4}}+\frac{2 \sqrt[4]{b} \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{d^{5/4}}-\frac{4 \sqrt[4]{a+b x}}{d \sqrt[4]{c+d x}}",1,"(4*(a + b*x)^(5/4)*((b*(c + d*x))/(b*c - a*d))^(5/4)*Hypergeometric2F1[5/4, 5/4, 9/4, (d*(a + b*x))/(-(b*c) + a*d)])/(5*b*(c + d*x)^(5/4))","C",1
1719,1,30,30,0.0077427,"\int \frac{1}{(a+b x)^{3/4} (c+d x)^{5/4}} \, dx","Integrate[1/((a + b*x)^(3/4)*(c + d*x)^(5/4)),x]","\frac{4 \sqrt[4]{a+b x}}{\sqrt[4]{c+d x} (b c-a d)}","\frac{4 \sqrt[4]{a+b x}}{\sqrt[4]{c+d x} (b c-a d)}",1,"(4*(a + b*x)^(1/4))/((b*c - a*d)*(c + d*x)^(1/4))","A",1
1720,1,45,66,0.0168509,"\int \frac{1}{(a+b x)^{7/4} (c+d x)^{5/4}} \, dx","Integrate[1/((a + b*x)^(7/4)*(c + d*x)^(5/4)),x]","-\frac{4 (3 a d+b (c+4 d x))}{3 (a+b x)^{3/4} \sqrt[4]{c+d x} (b c-a d)^2}","-\frac{16 d \sqrt[4]{a+b x}}{3 \sqrt[4]{c+d x} (b c-a d)^2}-\frac{4}{3 (a+b x)^{3/4} \sqrt[4]{c+d x} (b c-a d)}",1,"(-4*(3*a*d + b*(c + 4*d*x)))/(3*(b*c - a*d)^2*(a + b*x)^(3/4)*(c + d*x)^(1/4))","A",1
1721,1,76,101,0.0330664,"\int \frac{1}{(a+b x)^{11/4} (c+d x)^{5/4}} \, dx","Integrate[1/((a + b*x)^(11/4)*(c + d*x)^(5/4)),x]","\frac{84 a^2 d^2+56 a b d (c+4 d x)+4 b^2 \left(-3 c^2+8 c d x+32 d^2 x^2\right)}{21 (a+b x)^{7/4} \sqrt[4]{c+d x} (b c-a d)^3}","\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,"(84*a^2*d^2 + 56*a*b*d*(c + 4*d*x) + 4*b^2*(-3*c^2 + 8*c*d*x + 32*d^2*x^2))/(21*(b*c - a*d)^3*(a + b*x)^(7/4)*(c + d*x)^(1/4))","A",1
1722,1,116,136,0.0431574,"\int \frac{1}{(a+b x)^{15/4} (c+d x)^{5/4}} \, dx","Integrate[1/((a + b*x)^(15/4)*(c + d*x)^(5/4)),x]","-\frac{4 \left(77 a^3 d^3+77 a^2 b d^2 (c+4 d x)+11 a b^2 d \left(-3 c^2+8 c d x+32 d^2 x^2\right)+b^3 \left(7 c^3-12 c^2 d x+32 c d^2 x^2+128 d^3 x^3\right)\right)}{77 (a+b x)^{11/4} \sqrt[4]{c+d x} (b c-a d)^4}","-\frac{512 d^3 \sqrt[4]{a+b x}}{77 \sqrt[4]{c+d x} (b c-a d)^4}-\frac{128 d^2}{77 (a+b x)^{3/4} \sqrt[4]{c+d x} (b c-a d)^3}+\frac{48 d}{77 (a+b x)^{7/4} \sqrt[4]{c+d x} (b c-a d)^2}-\frac{4}{11 (a+b x)^{11/4} \sqrt[4]{c+d x} (b c-a d)}",1,"(-4*(77*a^3*d^3 + 77*a^2*b*d^2*(c + 4*d*x) + 11*a*b^2*d*(-3*c^2 + 8*c*d*x + 32*d^2*x^2) + b^3*(7*c^3 - 12*c^2*d*x + 32*c*d^2*x^2 + 128*d^3*x^3)))/(77*(b*c - a*d)^4*(a + b*x)^(11/4)*(c + d*x)^(1/4))","A",1
1723,1,73,776,0.0602647,"\int \frac{(a+b x)^{11/4}}{(c+d x)^{5/4}} \, dx","Integrate[(a + b*x)^(11/4)/(c + d*x)^(5/4),x]","\frac{4 (a+b x)^{15/4} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/4} \, _2F_1\left(\frac{5}{4},\frac{15}{4};\frac{19}{4};\frac{d (a+b x)}{a d-b c}\right)}{15 b (c+d x)^{5/4}}","\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}} \operatorname{EllipticF}\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{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}} 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,"(4*(a + b*x)^(15/4)*((b*(c + d*x))/(b*c - a*d))^(5/4)*Hypergeometric2F1[5/4, 15/4, 19/4, (d*(a + b*x))/(-(b*c) + a*d)])/(15*b*(c + d*x)^(5/4))","C",1
1724,1,73,730,0.0660978,"\int \frac{(a+b x)^{7/4}}{(c+d x)^{5/4}} \, dx","Integrate[(a + b*x)^(7/4)/(c + d*x)^(5/4),x]","\frac{4 (a+b x)^{11/4} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/4} \, _2F_1\left(\frac{5}{4},\frac{11}{4};\frac{15}{4};\frac{d (a+b x)}{a d-b c}\right)}{11 b (c+d x)^{5/4}}","-\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}} \operatorname{EllipticF}\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{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}} 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,"(4*(a + b*x)^(11/4)*((b*(c + d*x))/(b*c - a*d))^(5/4)*Hypergeometric2F1[5/4, 11/4, 15/4, (d*(a + b*x))/(-(b*c) + a*d)])/(11*b*(c + d*x)^(5/4))","C",1
1725,1,73,712,0.0596457,"\int \frac{(a+b x)^{3/4}}{(c+d x)^{5/4}} \, dx","Integrate[(a + b*x)^(3/4)/(c + d*x)^(5/4),x]","\frac{4 (a+b x)^{7/4} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/4} \, _2F_1\left(\frac{5}{4},\frac{7}{4};\frac{11}{4};\frac{d (a+b x)}{a d-b c}\right)}{7 b (c+d x)^{5/4}}","\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}} \operatorname{EllipticF}\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{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{2} \sqrt[4]{b} (b c-a d)^{3/2} \sqrt[4]{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{d^{7/4} \sqrt[4]{a+b x} \sqrt[4]{c+d x} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}-\frac{4 (a+b x)^{3/4}}{d \sqrt[4]{c+d x}}",1,"(4*(a + b*x)^(7/4)*((b*(c + d*x))/(b*c - a*d))^(5/4)*Hypergeometric2F1[5/4, 7/4, 11/4, (d*(a + b*x))/(-(b*c) + a*d)])/(7*b*(c + d*x)^(5/4))","C",1
1726,1,73,719,0.0507664,"\int \frac{1}{\sqrt[4]{a+b x} (c+d x)^{5/4}} \, dx","Integrate[1/((a + b*x)^(1/4)*(c + d*x)^(5/4)),x]","\frac{4 (a+b x)^{3/4} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/4} \, _2F_1\left(\frac{3}{4},\frac{5}{4};\frac{7}{4};\frac{d (a+b x)}{a d-b c}\right)}{3 b (c+d x)^{5/4}}","-\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}} \operatorname{EllipticF}\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right),\frac{1}{2}\right)}{d^{3/4} \sqrt[4]{a+b x} \sqrt[4]{c+d x} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}+\frac{2 \sqrt{2} \sqrt[4]{b} \sqrt{b c-a d} \sqrt[4]{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{d^{3/4} \sqrt[4]{a+b x} \sqrt[4]{c+d x} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}-\frac{4 \sqrt{b} \sqrt{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \sqrt{(a d+b (c+2 d x))^2}}{\sqrt{d} \sqrt[4]{a+b x} \sqrt[4]{c+d x} (b c-a d)^2 (a d+b c+2 b d x) \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)}+\frac{4 (a+b x)^{3/4}}{\sqrt[4]{c+d x} (b c-a d)}",1,"(4*(a + b*x)^(3/4)*((b*(c + d*x))/(b*c - a*d))^(5/4)*Hypergeometric2F1[3/4, 5/4, 7/4, (d*(a + b*x))/(-(b*c) + a*d)])/(3*b*(c + d*x)^(5/4))","C",1
1727,1,71,750,0.0538082,"\int \frac{1}{(a+b x)^{5/4} (c+d x)^{5/4}} \, dx","Integrate[1/((a + b*x)^(5/4)*(c + d*x)^(5/4)),x]","-\frac{4 \left(\frac{b (c+d x)}{b c-a d}\right)^{5/4} \, _2F_1\left(-\frac{1}{4},\frac{5}{4};\frac{3}{4};\frac{d (a+b x)}{a d-b c}\right)}{b \sqrt[4]{a+b x} (c+d x)^{5/4}}","\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}} \operatorname{EllipticF}\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right),\frac{1}{2}\right)}{\sqrt[4]{a+b x} \sqrt[4]{c+d x} \sqrt{b c-a d} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}-\frac{8 d (a+b x)^{3/4}}{\sqrt[4]{c+d x} (b c-a d)^2}+\frac{8 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \sqrt{(a d+b (c+2 d x))^2}}{\sqrt[4]{a+b x} \sqrt[4]{c+d x} (b c-a d)^3 (a d+b c+2 b d x) \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)}-\frac{4}{\sqrt[4]{a+b x} \sqrt[4]{c+d x} (b c-a d)}-\frac{4 \sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)} \sqrt{(a d+b c+2 b d x)^2} \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right) \sqrt{\frac{(a d+b (c+2 d x))^2}{(b c-a d)^2 \left(\frac{2 \sqrt{b} \sqrt{d} \sqrt{(a+b x) (c+d x)}}{b c-a d}+1\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right)|\frac{1}{2}\right)}{\sqrt[4]{a+b x} \sqrt[4]{c+d x} \sqrt{b c-a d} (a d+b c+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}",1,"(-4*((b*(c + d*x))/(b*c - a*d))^(5/4)*Hypergeometric2F1[-1/4, 5/4, 3/4, (d*(a + b*x))/(-(b*c) + a*d)])/(b*(a + b*x)^(1/4)*(c + d*x)^(5/4))","C",1
1728,1,73,795,0.0532827,"\int \frac{1}{(a+b x)^{9/4} (c+d x)^{5/4}} \, dx","Integrate[1/((a + b*x)^(9/4)*(c + d*x)^(5/4)),x]","-\frac{4 \left(\frac{b (c+d x)}{b c-a d}\right)^{5/4} \, _2F_1\left(-\frac{5}{4},\frac{5}{4};-\frac{1}{4};\frac{d (a+b x)}{a d-b c}\right)}{5 b (a+b x)^{5/4} (c+d x)^{5/4}}","\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}} \operatorname{EllipticF}\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{d} \sqrt[4]{(a+b x) (c+d x)}}{\sqrt{b c-a d}}\right),\frac{1}{2}\right) d^{5/4}}{5 (b c-a d)^{3/2} \sqrt[4]{a+b x} \sqrt[4]{c+d x} (b c+a d+2 b d x) \sqrt{(a d+b (c+2 d x))^2}}+\frac{24 d}{5 (b c-a d)^2 \sqrt[4]{a+b x} \sqrt[4]{c+d x}}-\frac{4}{5 (b c-a d) (a+b x)^{5/4} \sqrt[4]{c+d x}}",1,"(-4*((b*(c + d*x))/(b*c - a*d))^(5/4)*Hypergeometric2F1[-5/4, 5/4, -1/4, (d*(a + b*x))/(-(b*c) + a*d)])/(5*b*(a + b*x)^(5/4)*(c + d*x)^(5/4))","C",1
1729,1,65,279,0.0373662,"\int \frac{1}{\sqrt[4]{1-a x} (1+b x)^{3/4}} \, dx","Integrate[1/((1 - a*x)^(1/4)*(1 + b*x)^(3/4)),x]","-\frac{4 (1-a x)^{3/4} \left(\frac{a b x+a}{a+b}\right)^{3/4} \, _2F_1\left(\frac{3}{4},\frac{3}{4};\frac{7}{4};\frac{b-a b x}{a+b}\right)}{3 a (b x+1)^{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,"(-4*(1 - a*x)^(3/4)*((a + a*b*x)/(a + b))^(3/4)*Hypergeometric2F1[3/4, 3/4, 7/4, (b - a*b*x)/(a + b)])/(3*a*(1 + b*x)^(3/4))","C",1
1730,1,42,193,0.0095021,"\int \frac{1}{\sqrt[4]{1-a x} (1+a x)^{3/4}} \, dx","Integrate[1/((1 - a*x)^(1/4)*(1 + a*x)^(3/4)),x]","-\frac{2 \sqrt[4]{2} (1-a x)^{3/4} \, _2F_1\left(\frac{3}{4},\frac{3}{4};\frac{7}{4};\frac{1}{2} (1-a x)\right)}{3 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,"(-2*2^(1/4)*(1 - a*x)^(3/4)*Hypergeometric2F1[3/4, 3/4, 7/4, (1 - a*x)/2])/(3*a)","C",1
1731,1,73,74,0.0341607,"\int \frac{(a+b x)^{3/2}}{\sqrt[5]{c+d x}} \, dx","Integrate[(a + b*x)^(3/2)/(c + d*x)^(1/5),x]","\frac{2 (a+b x)^{5/2} \sqrt[5]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{1}{5},\frac{5}{2};\frac{7}{2};\frac{d (a+b x)}{a d-b c}\right)}{5 b \sqrt[5]{c+d x}}","\frac{2 (a+b x)^{5/2} \sqrt[5]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{1}{5},\frac{5}{2};\frac{7}{2};-\frac{d (a+b x)}{b c-a d}\right)}{5 b \sqrt[5]{c+d x}}",1,"(2*(a + b*x)^(5/2)*((b*(c + d*x))/(b*c - a*d))^(1/5)*Hypergeometric2F1[1/5, 5/2, 7/2, (d*(a + b*x))/(-(b*c) + a*d)])/(5*b*(c + d*x)^(1/5))","A",1
1732,1,73,74,0.0264991,"\int \frac{\sqrt{a+b x}}{\sqrt[5]{c+d x}} \, dx","Integrate[Sqrt[a + b*x]/(c + d*x)^(1/5),x]","\frac{2 (a+b x)^{3/2} \sqrt[5]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{1}{5},\frac{3}{2};\frac{5}{2};\frac{d (a+b x)}{a d-b c}\right)}{3 b \sqrt[5]{c+d x}}","\frac{2 (a+b x)^{3/2} \sqrt[5]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{1}{5},\frac{3}{2};\frac{5}{2};-\frac{d (a+b x)}{b c-a d}\right)}{3 b \sqrt[5]{c+d x}}",1,"(2*(a + b*x)^(3/2)*((b*(c + d*x))/(b*c - a*d))^(1/5)*Hypergeometric2F1[1/5, 3/2, 5/2, (d*(a + b*x))/(-(b*c) + a*d)])/(3*b*(c + d*x)^(1/5))","A",1
1733,1,71,72,0.0218433,"\int \frac{1}{\sqrt{a+b x} \sqrt[5]{c+d x}} \, dx","Integrate[1/(Sqrt[a + b*x]*(c + d*x)^(1/5)),x]","\frac{2 \sqrt{a+b x} \sqrt[5]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{1}{5},\frac{1}{2};\frac{3}{2};\frac{d (a+b x)}{a d-b c}\right)}{b \sqrt[5]{c+d x}}","\frac{2 \sqrt{a+b x} \sqrt[5]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{1}{5},\frac{1}{2};\frac{3}{2};-\frac{d (a+b x)}{b c-a d}\right)}{b \sqrt[5]{c+d x}}",1,"(2*Sqrt[a + b*x]*((b*(c + d*x))/(b*c - a*d))^(1/5)*Hypergeometric2F1[1/5, 1/2, 3/2, (d*(a + b*x))/(-(b*c) + a*d)])/(b*(c + d*x)^(1/5))","A",1
1734,1,71,72,0.0231912,"\int \frac{1}{(a+b x)^{3/2} \sqrt[5]{c+d x}} \, dx","Integrate[1/((a + b*x)^(3/2)*(c + d*x)^(1/5)),x]","-\frac{2 \sqrt[5]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(-\frac{1}{2},\frac{1}{5};\frac{1}{2};\frac{d (a+b x)}{a d-b c}\right)}{b \sqrt{a+b x} \sqrt[5]{c+d x}}","-\frac{2 \sqrt[5]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(-\frac{1}{2},\frac{1}{5};\frac{1}{2};-\frac{d (a+b x)}{b c-a d}\right)}{b \sqrt{a+b x} \sqrt[5]{c+d x}}",1,"(-2*((b*(c + d*x))/(b*c - a*d))^(1/5)*Hypergeometric2F1[-1/2, 1/5, 1/2, (d*(a + b*x))/(-(b*c) + a*d)])/(b*Sqrt[a + b*x]*(c + d*x)^(1/5))","A",1
1735,1,73,74,0.0228599,"\int \frac{1}{(a+b x)^{5/2} \sqrt[5]{c+d x}} \, dx","Integrate[1/((a + b*x)^(5/2)*(c + d*x)^(1/5)),x]","-\frac{2 \sqrt[5]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(-\frac{3}{2},\frac{1}{5};-\frac{1}{2};\frac{d (a+b x)}{a d-b c}\right)}{3 b (a+b x)^{3/2} \sqrt[5]{c+d x}}","-\frac{2 \sqrt[5]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(-\frac{3}{2},\frac{1}{5};-\frac{1}{2};-\frac{d (a+b x)}{b c-a d}\right)}{3 b (a+b x)^{3/2} \sqrt[5]{c+d x}}",1,"(-2*((b*(c + d*x))/(b*c - a*d))^(1/5)*Hypergeometric2F1[-3/2, 1/5, -1/2, (d*(a + b*x))/(-(b*c) + a*d)])/(3*b*(a + b*x)^(3/2)*(c + d*x)^(1/5))","A",1
1736,1,73,487,0.0433397,"\int (a+b x)^{5/2} \sqrt[6]{c+d x} \, dx","Integrate[(a + b*x)^(5/2)*(c + d*x)^(1/6),x]","\frac{2 (a+b x)^{7/2} \sqrt[6]{c+d x} \, _2F_1\left(-\frac{1}{6},\frac{7}{2};\frac{9}{2};\frac{d (a+b x)}{a d-b c}\right)}{7 b \sqrt[6]{\frac{b (c+d x)}{b c-a d}}}","-\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}} \operatorname{EllipticF}\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,"(2*(a + b*x)^(7/2)*(c + d*x)^(1/6)*Hypergeometric2F1[-1/6, 7/2, 9/2, (d*(a + b*x))/(-(b*c) + a*d)])/(7*b*((b*(c + d*x))/(b*c - a*d))^(1/6))","C",1
1737,1,73,449,0.0315885,"\int (a+b x)^{3/2} \sqrt[6]{c+d x} \, dx","Integrate[(a + b*x)^(3/2)*(c + d*x)^(1/6),x]","\frac{2 (a+b x)^{5/2} \sqrt[6]{c+d x} \, _2F_1\left(-\frac{1}{6},\frac{5}{2};\frac{7}{2};\frac{d (a+b x)}{a d-b c}\right)}{5 b \sqrt[6]{\frac{b (c+d x)}{b c-a d}}}","\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}} \operatorname{EllipticF}\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,"(2*(a + b*x)^(5/2)*(c + d*x)^(1/6)*Hypergeometric2F1[-1/6, 5/2, 7/2, (d*(a + b*x))/(-(b*c) + a*d)])/(5*b*((b*(c + d*x))/(b*c - a*d))^(1/6))","C",1
1738,1,73,411,0.0277523,"\int \sqrt{a+b x} \sqrt[6]{c+d x} \, dx","Integrate[Sqrt[a + b*x]*(c + d*x)^(1/6),x]","\frac{2 (a+b x)^{3/2} \sqrt[6]{c+d x} \, _2F_1\left(-\frac{1}{6},\frac{3}{2};\frac{5}{2};\frac{d (a+b x)}{a d-b c}\right)}{3 b \sqrt[6]{\frac{b (c+d x)}{b c-a d}}}","-\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}} \operatorname{EllipticF}\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,"(2*(a + b*x)^(3/2)*(c + d*x)^(1/6)*Hypergeometric2F1[-1/6, 3/2, 5/2, (d*(a + b*x))/(-(b*c) + a*d)])/(3*b*((b*(c + d*x))/(b*c - a*d))^(1/6))","C",1
1739,1,71,375,0.0239361,"\int \frac{\sqrt[6]{c+d x}}{\sqrt{a+b x}} \, dx","Integrate[(c + d*x)^(1/6)/Sqrt[a + b*x],x]","\frac{2 \sqrt{a+b x} \sqrt[6]{c+d x} \, _2F_1\left(-\frac{1}{6},\frac{1}{2};\frac{3}{2};\frac{d (a+b x)}{a d-b c}\right)}{b \sqrt[6]{\frac{b (c+d x)}{b c-a d}}}","\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}} \operatorname{EllipticF}\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,"(2*Sqrt[a + b*x]*(c + d*x)^(1/6)*Hypergeometric2F1[-1/6, 1/2, 3/2, (d*(a + b*x))/(-(b*c) + a*d)])/(b*((b*(c + d*x))/(b*c - a*d))^(1/6))","C",1
1740,1,71,367,0.0255705,"\int \frac{\sqrt[6]{c+d x}}{(a+b x)^{3/2}} \, dx","Integrate[(c + d*x)^(1/6)/(a + b*x)^(3/2),x]","-\frac{2 \sqrt[6]{c+d x} \, _2F_1\left(-\frac{1}{2},-\frac{1}{6};\frac{1}{2};\frac{d (a+b x)}{a d-b c}\right)}{b \sqrt{a+b x} \sqrt[6]{\frac{b (c+d x)}{b c-a d}}}","\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}} \operatorname{EllipticF}\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right),\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{\sqrt[4]{3} b \sqrt{a+b x} \sqrt[3]{b c-a d} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{2 \sqrt[6]{c+d x}}{b \sqrt{a+b x}}",1,"(-2*(c + d*x)^(1/6)*Hypergeometric2F1[-1/2, -1/6, 1/2, (d*(a + b*x))/(-(b*c) + a*d)])/(b*Sqrt[a + b*x]*((b*(c + d*x))/(b*c - a*d))^(1/6))","C",1
1741,1,73,409,0.0243236,"\int \frac{\sqrt[6]{c+d x}}{(a+b x)^{5/2}} \, dx","Integrate[(c + d*x)^(1/6)/(a + b*x)^(5/2),x]","-\frac{2 \sqrt[6]{c+d x} \, _2F_1\left(-\frac{3}{2},-\frac{1}{6};-\frac{1}{2};\frac{d (a+b x)}{a d-b c}\right)}{3 b (a+b x)^{3/2} \sqrt[6]{\frac{b (c+d x)}{b c-a d}}}","-\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}} \operatorname{EllipticF}\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right),\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{9 \sqrt[4]{3} b \sqrt{a+b x} (b c-a d)^{4/3} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{2 d \sqrt[6]{c+d x}}{9 b \sqrt{a+b x} (b c-a d)}-\frac{2 \sqrt[6]{c+d x}}{3 b (a+b x)^{3/2}}",1,"(-2*(c + d*x)^(1/6)*Hypergeometric2F1[-3/2, -1/6, -1/2, (d*(a + b*x))/(-(b*c) + a*d)])/(3*b*(a + b*x)^(3/2)*((b*(c + d*x))/(b*c - a*d))^(1/6))","C",1
1742,1,73,896,0.0392696,"\int (a+b x)^{3/2} (c+d x)^{5/6} \, dx","Integrate[(a + b*x)^(3/2)*(c + d*x)^(5/6),x]","\frac{2 (a+b x)^{5/2} (c+d x)^{5/6} \, _2F_1\left(-\frac{5}{6},\frac{5}{2};\frac{7}{2};\frac{d (a+b x)}{a d-b c}\right)}{5 b \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6}}","-\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}} \operatorname{EllipticF}\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,"(2*(a + b*x)^(5/2)*(c + d*x)^(5/6)*Hypergeometric2F1[-5/6, 5/2, 7/2, (d*(a + b*x))/(-(b*c) + a*d)])/(5*b*((b*(c + d*x))/(b*c - a*d))^(5/6))","C",1
1743,1,73,858,0.0316729,"\int \sqrt{a+b x} (c+d x)^{5/6} \, dx","Integrate[Sqrt[a + b*x]*(c + d*x)^(5/6),x]","\frac{2 (a+b x)^{3/2} (c+d x)^{5/6} \, _2F_1\left(-\frac{5}{6},\frac{3}{2};\frac{5}{2};\frac{d (a+b x)}{a d-b c}\right)}{3 b \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6}}","\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}} \operatorname{EllipticF}\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,"(2*(a + b*x)^(3/2)*(c + d*x)^(5/6)*Hypergeometric2F1[-5/6, 3/2, 5/2, (d*(a + b*x))/(-(b*c) + a*d)])/(3*b*((b*(c + d*x))/(b*c - a*d))^(5/6))","C",1
1744,1,71,817,0.0228388,"\int \frac{(c+d x)^{5/6}}{\sqrt{a+b x}} \, dx","Integrate[(c + d*x)^(5/6)/Sqrt[a + b*x],x]","\frac{2 \sqrt{a+b x} (c+d x)^{5/6} \, _2F_1\left(-\frac{5}{6},\frac{1}{2};\frac{3}{2};\frac{d (a+b x)}{a d-b c}\right)}{b \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6}}","-\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}} \operatorname{EllipticF}\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,"(2*Sqrt[a + b*x]*(c + d*x)^(5/6)*Hypergeometric2F1[-5/6, 1/2, 3/2, (d*(a + b*x))/(-(b*c) + a*d)])/(b*((b*(c + d*x))/(b*c - a*d))^(5/6))","C",1
1745,1,71,798,0.0232433,"\int \frac{(c+d x)^{5/6}}{(a+b x)^{3/2}} \, dx","Integrate[(c + d*x)^(5/6)/(a + b*x)^(3/2),x]","-\frac{2 (c+d x)^{5/6} \, _2F_1\left(-\frac{5}{6},-\frac{1}{2};\frac{1}{2};\frac{d (a+b x)}{a d-b c}\right)}{b \sqrt{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6}}","-\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}} \operatorname{EllipticF}\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right),\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{2 \sqrt[4]{3} b^{5/3} \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{2 (c+d x)^{5/6}}{b \sqrt{a+b x}}",1,"(-2*(c + d*x)^(5/6)*Hypergeometric2F1[-5/6, -1/2, 1/2, (d*(a + b*x))/(-(b*c) + a*d)])/(b*Sqrt[a + b*x]*((b*(c + d*x))/(b*c - a*d))^(5/6))","C",1
1746,1,73,854,0.0245467,"\int \frac{(c+d x)^{5/6}}{(a+b x)^{5/2}} \, dx","Integrate[(c + d*x)^(5/6)/(a + b*x)^(5/2),x]","-\frac{2 (c+d x)^{5/6} \, _2F_1\left(-\frac{3}{2},-\frac{5}{6};-\frac{1}{2};\frac{d (a+b x)}{a d-b c}\right)}{3 b (a+b x)^{3/2} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6}}","-\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}} \operatorname{EllipticF}\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right),\frac{1}{4} \left(2+\sqrt{3}\right)\right) d}{9 \sqrt[4]{3} b^{5/3} (b c-a d)^{2/3} \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{10 (c+d x)^{5/6} d}{9 b (b c-a d) \sqrt{a+b x}}-\frac{2 (c+d x)^{5/6}}{3 b (a+b x)^{3/2}}",1,"(-2*(c + d*x)^(5/6)*Hypergeometric2F1[-3/2, -5/6, -1/2, (d*(a + b*x))/(-(b*c) + a*d)])/(3*b*(a + b*x)^(3/2)*((b*(c + d*x))/(b*c - a*d))^(5/6))","C",1
1747,1,73,896,0.0258754,"\int \frac{(c+d x)^{5/6}}{(a+b x)^{7/2}} \, dx","Integrate[(c + d*x)^(5/6)/(a + b*x)^(7/2),x]","-\frac{2 (c+d x)^{5/6} \, _2F_1\left(-\frac{5}{2},-\frac{5}{6};-\frac{3}{2};\frac{d (a+b x)}{a d-b c}\right)}{5 b (a+b x)^{5/2} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6}}","\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}} \operatorname{EllipticF}\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right),\frac{1}{4} \left(2+\sqrt{3}\right)\right) d^2}{27 \sqrt[4]{3} b^{5/3} (b c-a d)^{5/3} \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{8 (c+d x)^{5/6} d^2}{27 b (b c-a d)^2 \sqrt{a+b x}}-\frac{2 (c+d x)^{5/6} d}{9 b (b c-a d) (a+b x)^{3/2}}-\frac{2 (c+d x)^{5/6}}{5 b (a+b x)^{5/2}}",1,"(-2*(c + d*x)^(5/6)*Hypergeometric2F1[-5/2, -5/6, -3/2, (d*(a + b*x))/(-(b*c) + a*d)])/(5*b*(a + b*x)^(5/2)*((b*(c + d*x))/(b*c - a*d))^(5/6))","C",1
1748,1,73,890,0.0337716,"\int \frac{(a+b x)^{5/2}}{\sqrt[6]{c+d x}} \, dx","Integrate[(a + b*x)^(5/2)/(c + d*x)^(1/6),x]","\frac{2 (a+b x)^{7/2} \sqrt[6]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{1}{6},\frac{7}{2};\frac{9}{2};\frac{d (a+b x)}{a d-b c}\right)}{7 b \sqrt[6]{c+d x}}","\frac{243 \sqrt[4]{3} \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} E\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right) (b c-a d)^{10/3}}{448 b^{2/3} d^4 \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{81\ 3^{3/4} \left(1-\sqrt{3}\right) \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} \operatorname{EllipticF}\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,"(2*(a + b*x)^(7/2)*((b*(c + d*x))/(b*c - a*d))^(1/6)*Hypergeometric2F1[1/6, 7/2, 9/2, (d*(a + b*x))/(-(b*c) + a*d)])/(7*b*(c + d*x)^(1/6))","C",1
1749,1,73,855,0.0327873,"\int \frac{(a+b x)^{3/2}}{\sqrt[6]{c+d x}} \, dx","Integrate[(a + b*x)^(3/2)/(c + d*x)^(1/6),x]","\frac{2 (a+b x)^{5/2} \sqrt[6]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{1}{6},\frac{5}{2};\frac{7}{2};\frac{d (a+b x)}{a d-b c}\right)}{5 b \sqrt[6]{c+d x}}","-\frac{81 \sqrt[4]{3} \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} E\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right) (b c-a d)^{7/3}}{112 b^{2/3} d^3 \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{27\ 3^{3/4} \left(1-\sqrt{3}\right) \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} \operatorname{EllipticF}\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,"(2*(a + b*x)^(5/2)*((b*(c + d*x))/(b*c - a*d))^(1/6)*Hypergeometric2F1[1/6, 5/2, 7/2, (d*(a + b*x))/(-(b*c) + a*d)])/(5*b*(c + d*x)^(1/6))","C",1
1750,1,73,820,0.0257809,"\int \frac{\sqrt{a+b x}}{\sqrt[6]{c+d x}} \, dx","Integrate[Sqrt[a + b*x]/(c + d*x)^(1/6),x]","\frac{2 (a+b x)^{3/2} \sqrt[6]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{1}{6},\frac{3}{2};\frac{5}{2};\frac{d (a+b x)}{a d-b c}\right)}{3 b \sqrt[6]{c+d x}}","\frac{9 \sqrt[4]{3} \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} E\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right) (b c-a d)^{4/3}}{8 b^{2/3} d^2 \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{3\ 3^{3/4} \left(1-\sqrt{3}\right) \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} \operatorname{EllipticF}\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,"(2*(a + b*x)^(3/2)*((b*(c + d*x))/(b*c - a*d))^(1/6)*Hypergeometric2F1[1/6, 3/2, 5/2, (d*(a + b*x))/(-(b*c) + a*d)])/(3*b*(c + d*x)^(1/6))","C",1
1751,1,71,780,0.0217343,"\int \frac{1}{\sqrt{a+b x} \sqrt[6]{c+d x}} \, dx","Integrate[1/(Sqrt[a + b*x]*(c + d*x)^(1/6)),x]","\frac{2 \sqrt{a+b x} \sqrt[6]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{3}{2};\frac{d (a+b x)}{a d-b c}\right)}{b \sqrt[6]{c+d x}}","-\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}} \operatorname{EllipticF}\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 \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 \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,"(2*Sqrt[a + b*x]*((b*(c + d*x))/(b*c - a*d))^(1/6)*Hypergeometric2F1[1/6, 1/2, 3/2, (d*(a + b*x))/(-(b*c) + a*d)])/(b*(c + d*x)^(1/6))","C",1
1752,1,71,813,0.0232381,"\int \frac{1}{(a+b x)^{3/2} \sqrt[6]{c+d x}} \, dx","Integrate[1/((a + b*x)^(3/2)*(c + d*x)^(1/6)),x]","-\frac{2 \sqrt[6]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(-\frac{1}{2},\frac{1}{6};\frac{1}{2};\frac{d (a+b x)}{a d-b c}\right)}{b \sqrt{a+b x} \sqrt[6]{c+d x}}","-\frac{2 \left(1+\sqrt{3}\right) \sqrt{a+b x} \sqrt[6]{c+d x} d}{b^{2/3} (b c-a d) \left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)}-\frac{2 \sqrt[4]{3} \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} E\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{b^{2/3} (b c-a d)^{2/3} \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{\left(1-\sqrt{3}\right) \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} \operatorname{EllipticF}\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right),\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{\sqrt[4]{3} b^{2/3} (b c-a d)^{2/3} \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{2 (c+d x)^{5/6}}{(b c-a d) \sqrt{a+b x}}",1,"(-2*((b*(c + d*x))/(b*c - a*d))^(1/6)*Hypergeometric2F1[-1/2, 1/6, 1/2, (d*(a + b*x))/(-(b*c) + a*d)])/(b*Sqrt[a + b*x]*(c + d*x)^(1/6))","C",1
1753,1,73,858,0.0240063,"\int \frac{1}{(a+b x)^{5/2} \sqrt[6]{c+d x}} \, dx","Integrate[1/((a + b*x)^(5/2)*(c + d*x)^(1/6)),x]","-\frac{2 \sqrt[6]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(-\frac{3}{2},\frac{1}{6};-\frac{1}{2};\frac{d (a+b x)}{a d-b c}\right)}{3 b (a+b x)^{3/2} \sqrt[6]{c+d x}}","\frac{8 \left(1+\sqrt{3}\right) \sqrt{a+b x} \sqrt[6]{c+d x} d^2}{9 b^{2/3} (b c-a d)^2 \left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)}+\frac{8 \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} E\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right) d}{3\ 3^{3/4} b^{2/3} (b c-a d)^{5/3} \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{4 \left(1-\sqrt{3}\right) \sqrt[6]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right) \sqrt{\frac{(b c-a d)^{2/3}+\sqrt[3]{b} \sqrt[3]{c+d x} \sqrt[3]{b c-a d}+b^{2/3} (c+d x)^{2/3}}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}} \operatorname{EllipticF}\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right),\frac{1}{4} \left(2+\sqrt{3}\right)\right) d}{9 \sqrt[4]{3} b^{2/3} (b c-a d)^{5/3} \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{8 (c+d x)^{5/6} d}{9 (b c-a d)^2 \sqrt{a+b x}}-\frac{2 (c+d x)^{5/6}}{3 (b c-a d) (a+b x)^{3/2}}",1,"(-2*((b*(c + d*x))/(b*c - a*d))^(1/6)*Hypergeometric2F1[-3/2, 1/6, -1/2, (d*(a + b*x))/(-(b*c) + a*d)])/(3*b*(a + b*x)^(3/2)*(c + d*x)^(1/6))","C",1
1754,1,73,440,0.0514304,"\int \frac{(a+b x)^{5/2}}{(c+d x)^{5/6}} \, dx","Integrate[(a + b*x)^(5/2)/(c + d*x)^(5/6),x]","\frac{2 (a+b x)^{7/2} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6} \, _2F_1\left(\frac{5}{6},\frac{7}{2};\frac{9}{2};\frac{d (a+b x)}{a d-b c}\right)}{7 b (c+d x)^{5/6}}","-\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}} \operatorname{EllipticF}\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,"(2*(a + b*x)^(7/2)*((b*(c + d*x))/(b*c - a*d))^(5/6)*Hypergeometric2F1[5/6, 7/2, 9/2, (d*(a + b*x))/(-(b*c) + a*d)])/(7*b*(c + d*x)^(5/6))","C",1
1755,1,73,405,0.0437124,"\int \frac{(a+b x)^{3/2}}{(c+d x)^{5/6}} \, dx","Integrate[(a + b*x)^(3/2)/(c + d*x)^(5/6),x]","\frac{2 (a+b x)^{5/2} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6} \, _2F_1\left(\frac{5}{6},\frac{5}{2};\frac{7}{2};\frac{d (a+b x)}{a d-b c}\right)}{5 b (c+d x)^{5/6}}","\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}} \operatorname{EllipticF}\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,"(2*(a + b*x)^(5/2)*((b*(c + d*x))/(b*c - a*d))^(5/6)*Hypergeometric2F1[5/6, 5/2, 7/2, (d*(a + b*x))/(-(b*c) + a*d)])/(5*b*(c + d*x)^(5/6))","C",1
1756,1,73,372,0.0334927,"\int \frac{\sqrt{a+b x}}{(c+d x)^{5/6}} \, dx","Integrate[Sqrt[a + b*x]/(c + d*x)^(5/6),x]","\frac{2 (a+b x)^{3/2} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6} \, _2F_1\left(\frac{5}{6},\frac{3}{2};\frac{5}{2};\frac{d (a+b x)}{a d-b c}\right)}{3 b (c+d x)^{5/6}}","\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}} \operatorname{EllipticF}\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,"(2*(a + b*x)^(3/2)*((b*(c + d*x))/(b*c - a*d))^(5/6)*Hypergeometric2F1[5/6, 3/2, 5/2, (d*(a + b*x))/(-(b*c) + a*d)])/(3*b*(c + d*x)^(5/6))","C",1
1757,1,71,343,0.0386917,"\int \frac{1}{\sqrt{a+b x} (c+d x)^{5/6}} \, dx","Integrate[1/(Sqrt[a + b*x]*(c + d*x)^(5/6)),x]","\frac{2 \sqrt{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6} \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{3}{2};\frac{d (a+b x)}{a d-b c}\right)}{b (c+d x)^{5/6}}","\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}} \operatorname{EllipticF}\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,"(2*Sqrt[a + b*x]*((b*(c + d*x))/(b*c - a*d))^(5/6)*Hypergeometric2F1[1/2, 5/6, 3/2, (d*(a + b*x))/(-(b*c) + a*d)])/(b*(c + d*x)^(5/6))","C",1
1758,1,71,372,0.0247244,"\int \frac{1}{(a+b x)^{3/2} (c+d x)^{5/6}} \, dx","Integrate[1/((a + b*x)^(3/2)*(c + d*x)^(5/6)),x]","-\frac{2 \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6} \, _2F_1\left(-\frac{1}{2},\frac{5}{6};\frac{1}{2};\frac{d (a+b x)}{a d-b c}\right)}{b \sqrt{a+b x} (c+d x)^{5/6}}","-\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}} \operatorname{EllipticF}\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right),\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{\sqrt[4]{3} \sqrt{a+b x} (b c-a d)^{4/3} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{2 \sqrt[6]{c+d x}}{\sqrt{a+b x} (b c-a d)}",1,"(-2*((b*(c + d*x))/(b*c - a*d))^(5/6)*Hypergeometric2F1[-1/2, 5/6, 1/2, (d*(a + b*x))/(-(b*c) + a*d)])/(b*Sqrt[a + b*x]*(c + d*x)^(5/6))","C",1
1759,1,73,410,0.0320077,"\int \frac{1}{(a+b x)^{5/2} (c+d x)^{5/6}} \, dx","Integrate[1/((a + b*x)^(5/2)*(c + d*x)^(5/6)),x]","-\frac{2 \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6} \, _2F_1\left(-\frac{3}{2},\frac{5}{6};-\frac{1}{2};\frac{d (a+b x)}{a d-b c}\right)}{3 b (a+b x)^{3/2} (c+d x)^{5/6}}","\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}} \operatorname{EllipticF}\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right),\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{9 \sqrt[4]{3} \sqrt{a+b x} (b c-a d)^{7/3} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{16 d \sqrt[6]{c+d x}}{9 \sqrt{a+b x} (b c-a d)^2}-\frac{2 \sqrt[6]{c+d x}}{3 (a+b x)^{3/2} (b c-a d)}",1,"(-2*((b*(c + d*x))/(b*c - a*d))^(5/6)*Hypergeometric2F1[-3/2, 5/6, -1/2, (d*(a + b*x))/(-(b*c) + a*d)])/(3*b*(a + b*x)^(3/2)*(c + d*x)^(5/6))","C",1
1760,1,73,880,0.0768923,"\int \frac{(a+b x)^{5/2}}{(c+d x)^{7/6}} \, dx","Integrate[(a + b*x)^(5/2)/(c + d*x)^(7/6),x]","\frac{2 (a+b x)^{7/2} \left(\frac{b (c+d x)}{b c-a d}\right)^{7/6} \, _2F_1\left(\frac{7}{6},\frac{7}{2};\frac{9}{2};\frac{d (a+b x)}{a d-b c}\right)}{7 b (c+d x)^{7/6}}","-\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}} \operatorname{EllipticF}\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,"(2*(a + b*x)^(7/2)*((b*(c + d*x))/(b*c - a*d))^(7/6)*Hypergeometric2F1[7/6, 7/2, 9/2, (d*(a + b*x))/(-(b*c) + a*d)])/(7*b*(c + d*x)^(7/6))","C",1
1761,1,73,844,0.0678184,"\int \frac{(a+b x)^{3/2}}{(c+d x)^{7/6}} \, dx","Integrate[(a + b*x)^(3/2)/(c + d*x)^(7/6),x]","\frac{2 (a+b x)^{5/2} \left(\frac{b (c+d x)}{b c-a d}\right)^{7/6} \, _2F_1\left(\frac{7}{6},\frac{5}{2};\frac{7}{2};\frac{d (a+b x)}{a d-b c}\right)}{5 b (c+d x)^{7/6}}","-\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}} \operatorname{EllipticF}\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,"(2*(a + b*x)^(5/2)*((b*(c + d*x))/(b*c - a*d))^(7/6)*Hypergeometric2F1[7/6, 5/2, 7/2, (d*(a + b*x))/(-(b*c) + a*d)])/(5*b*(c + d*x)^(7/6))","C",1
1762,1,73,806,0.0488395,"\int \frac{\sqrt{a+b x}}{(c+d x)^{7/6}} \, dx","Integrate[Sqrt[a + b*x]/(c + d*x)^(7/6),x]","\frac{2 (a+b x)^{3/2} \left(\frac{b (c+d x)}{b c-a d}\right)^{7/6} \, _2F_1\left(\frac{7}{6},\frac{3}{2};\frac{5}{2};\frac{d (a+b x)}{a d-b c}\right)}{3 b (c+d x)^{7/6}}","-\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}} \operatorname{EllipticF}\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,"(2*(a + b*x)^(3/2)*((b*(c + d*x))/(b*c - a*d))^(7/6)*Hypergeometric2F1[7/6, 3/2, 5/2, (d*(a + b*x))/(-(b*c) + a*d)])/(3*b*(c + d*x)^(7/6))","C",1
1763,1,71,817,0.0419692,"\int \frac{1}{\sqrt{a+b x} (c+d x)^{7/6}} \, dx","Integrate[1/(Sqrt[a + b*x]*(c + d*x)^(7/6)),x]","\frac{2 \sqrt{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{7/6} \, _2F_1\left(\frac{1}{2},\frac{7}{6};\frac{3}{2};\frac{d (a+b x)}{a d-b c}\right)}{b (c+d x)^{7/6}}","\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}} \operatorname{EllipticF}\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,"(2*Sqrt[a + b*x]*((b*(c + d*x))/(b*c - a*d))^(7/6)*Hypergeometric2F1[1/2, 7/6, 3/2, (d*(a + b*x))/(-(b*c) + a*d)])/(b*(c + d*x)^(7/6))","C",1
1764,1,71,844,0.0416045,"\int \frac{1}{(a+b x)^{3/2} (c+d x)^{7/6}} \, dx","Integrate[1/((a + b*x)^(3/2)*(c + d*x)^(7/6)),x]","-\frac{2 \left(\frac{b (c+d x)}{b c-a d}\right)^{7/6} \, _2F_1\left(-\frac{1}{2},\frac{7}{6};\frac{1}{2};\frac{d (a+b x)}{a d-b c}\right)}{b \sqrt{a+b x} (c+d x)^{7/6}}","-\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}} \operatorname{EllipticF}\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right),\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{\sqrt[4]{3} (b c-a d)^{5/3} \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}-\frac{2}{(b c-a d) \sqrt{a+b x} \sqrt[6]{c+d x}}",1,"(-2*((b*(c + d*x))/(b*c - a*d))^(7/6)*Hypergeometric2F1[-1/2, 7/6, 1/2, (d*(a + b*x))/(-(b*c) + a*d)])/(b*Sqrt[a + b*x]*(c + d*x)^(7/6))","C",1
1765,1,73,893,0.0547703,"\int \frac{1}{(a+b x)^{5/2} (c+d x)^{7/6}} \, dx","Integrate[1/((a + b*x)^(5/2)*(c + d*x)^(7/6)),x]","-\frac{2 \left(\frac{b (c+d x)}{b c-a d}\right)^{7/6} \, _2F_1\left(-\frac{3}{2},\frac{7}{6};-\frac{1}{2};\frac{d (a+b x)}{a d-b c}\right)}{3 b (a+b x)^{3/2} (c+d x)^{7/6}}","\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}} \operatorname{EllipticF}\left(\cos ^{-1}\left(\frac{\sqrt[3]{b c-a d}-\left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}}\right),\frac{1}{4} \left(2+\sqrt{3}\right)\right) d}{9 \sqrt[4]{3} (b c-a d)^{8/3} \sqrt{a+b x} \sqrt{-\frac{\sqrt[3]{b} \sqrt[3]{c+d x} \left(\sqrt[3]{b c-a d}-\sqrt[3]{b} \sqrt[3]{c+d x}\right)}{\left(\sqrt[3]{b c-a d}-\left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt[3]{c+d x}\right)^2}}}+\frac{20 d}{9 (b c-a d)^2 \sqrt{a+b x} \sqrt[6]{c+d x}}-\frac{2}{3 (b c-a d) (a+b x)^{3/2} \sqrt[6]{c+d x}}",1,"(-2*((b*(c + d*x))/(b*c - a*d))^(7/6)*Hypergeometric2F1[-3/2, 7/6, -1/2, (d*(a + b*x))/(-(b*c) + a*d)])/(3*b*(a + b*x)^(3/2)*(c + d*x)^(7/6))","C",1
1766,1,73,84,0.1102779,"\int \sqrt[6]{a+b x} (c+d x)^{13/6} \, dx","Integrate[(a + b*x)^(1/6)*(c + d*x)^(13/6),x]","\frac{6 (a+b x)^{7/6} (c+d x)^{13/6} \, _2F_1\left(-\frac{13}{6},\frac{7}{6};\frac{13}{6};\frac{d (a+b x)}{a d-b c}\right)}{7 b \left(\frac{b (c+d x)}{b c-a d}\right)^{13/6}}","\frac{6 (a+b x)^{7/6} \sqrt[6]{c+d x} (b c-a d)^2 \, _2F_1\left(-\frac{13}{6},\frac{7}{6};\frac{13}{6};-\frac{d (a+b x)}{b c-a d}\right)}{7 b^3 \sqrt[6]{\frac{b (c+d x)}{b c-a d}}}",1,"(6*(a + b*x)^(7/6)*(c + d*x)^(13/6)*Hypergeometric2F1[-13/6, 7/6, 13/6, (d*(a + b*x))/(-(b*c) + a*d)])/(7*b*((b*(c + d*x))/(b*c - a*d))^(13/6))","A",1
1767,1,73,82,0.0641774,"\int \sqrt[6]{a+b x} (c+d x)^{7/6} \, dx","Integrate[(a + b*x)^(1/6)*(c + d*x)^(7/6),x]","\frac{6 (a+b x)^{7/6} (c+d x)^{7/6} \, _2F_1\left(-\frac{7}{6},\frac{7}{6};\frac{13}{6};\frac{d (a+b x)}{a d-b c}\right)}{7 b \left(\frac{b (c+d x)}{b c-a d}\right)^{7/6}}","\frac{6 (a+b x)^{7/6} \sqrt[6]{c+d x} (b c-a d) \, _2F_1\left(-\frac{7}{6},\frac{7}{6};\frac{13}{6};-\frac{d (a+b x)}{b c-a d}\right)}{7 b^2 \sqrt[6]{\frac{b (c+d x)}{b c-a d}}}",1,"(6*(a + b*x)^(7/6)*(c + d*x)^(7/6)*Hypergeometric2F1[-7/6, 7/6, 13/6, (d*(a + b*x))/(-(b*c) + a*d)])/(7*b*((b*(c + d*x))/(b*c - a*d))^(7/6))","A",1
1768,1,73,74,0.0379699,"\int \sqrt[6]{a+b x} \sqrt[6]{c+d x} \, dx","Integrate[(a + b*x)^(1/6)*(c + d*x)^(1/6),x]","\frac{6 (a+b x)^{7/6} \sqrt[6]{c+d x} \, _2F_1\left(-\frac{1}{6},\frac{7}{6};\frac{13}{6};\frac{d (a+b x)}{a d-b c}\right)}{7 b \sqrt[6]{\frac{b (c+d x)}{b c-a d}}}","\frac{6 (a+b x)^{7/6} \sqrt[6]{c+d x} \, _2F_1\left(-\frac{1}{6},\frac{7}{6};\frac{13}{6};-\frac{d (a+b x)}{b c-a d}\right)}{7 b \sqrt[6]{\frac{b (c+d x)}{b c-a d}}}",1,"(6*(a + b*x)^(7/6)*(c + d*x)^(1/6)*Hypergeometric2F1[-1/6, 7/6, 13/6, (d*(a + b*x))/(-(b*c) + a*d)])/(7*b*((b*(c + d*x))/(b*c - a*d))^(1/6))","A",1
1769,1,73,74,0.0401613,"\int \frac{\sqrt[6]{a+b x}}{(c+d x)^{5/6}} \, dx","Integrate[(a + b*x)^(1/6)/(c + d*x)^(5/6),x]","\frac{6 (a+b x)^{7/6} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6} \, _2F_1\left(\frac{5}{6},\frac{7}{6};\frac{13}{6};\frac{d (a+b x)}{a d-b c}\right)}{7 b (c+d x)^{5/6}}","\frac{6 (a+b x)^{7/6} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6} \, _2F_1\left(\frac{5}{6},\frac{7}{6};\frac{13}{6};-\frac{d (a+b x)}{b c-a d}\right)}{7 b (c+d x)^{5/6}}",1,"(6*(a + b*x)^(7/6)*((b*(c + d*x))/(b*c - a*d))^(5/6)*Hypergeometric2F1[5/6, 7/6, 13/6, (d*(a + b*x))/(-(b*c) + a*d)])/(7*b*(c + d*x)^(5/6))","A",1
1770,1,73,81,0.0723021,"\int \frac{\sqrt[6]{a+b x}}{(c+d x)^{11/6}} \, dx","Integrate[(a + b*x)^(1/6)/(c + d*x)^(11/6),x]","\frac{6 (a+b x)^{7/6} \left(\frac{b (c+d x)}{b c-a d}\right)^{11/6} \, _2F_1\left(\frac{7}{6},\frac{11}{6};\frac{13}{6};\frac{d (a+b x)}{a d-b c}\right)}{7 b (c+d x)^{11/6}}","\frac{6 (a+b x)^{7/6} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6} \, _2F_1\left(\frac{7}{6},\frac{11}{6};\frac{13}{6};-\frac{d (a+b x)}{b c-a d}\right)}{7 (c+d x)^{5/6} (b c-a d)}",1,"(6*(a + b*x)^(7/6)*((b*(c + d*x))/(b*c - a*d))^(11/6)*Hypergeometric2F1[7/6, 11/6, 13/6, (d*(a + b*x))/(-(b*c) + a*d)])/(7*b*(c + d*x)^(11/6))","A",1
1771,1,81,82,0.0512363,"\int \frac{\sqrt[6]{a+b x}}{(c+d x)^{17/6}} \, dx","Integrate[(a + b*x)^(1/6)/(c + d*x)^(17/6),x]","\frac{6 b (a+b x)^{7/6} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6} \, _2F_1\left(\frac{7}{6},\frac{17}{6};\frac{13}{6};\frac{d (a+b x)}{a d-b c}\right)}{7 (c+d x)^{5/6} (b c-a d)^2}","\frac{6 b (a+b x)^{7/6} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6} \, _2F_1\left(\frac{7}{6},\frac{17}{6};\frac{13}{6};-\frac{d (a+b x)}{b c-a d}\right)}{7 (c+d x)^{5/6} (b c-a d)^2}",1,"(6*b*(a + b*x)^(7/6)*((b*(c + d*x))/(b*c - a*d))^(5/6)*Hypergeometric2F1[7/6, 17/6, 13/6, (d*(a + b*x))/(-(b*c) + a*d)])/(7*(b*c - a*d)^2*(c + d*x)^(5/6))","A",1
1772,1,73,427,0.0526277,"\int \sqrt[6]{a+b x} (c+d x)^{5/6} \, dx","Integrate[(a + b*x)^(1/6)*(c + d*x)^(5/6),x]","\frac{6 (a+b x)^{7/6} (c+d x)^{5/6} \, _2F_1\left(-\frac{5}{6},\frac{7}{6};\frac{13}{6};\frac{d (a+b x)}{a d-b c}\right)}{7 b \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6}}","\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 \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,"(6*(a + b*x)^(7/6)*(c + d*x)^(5/6)*Hypergeometric2F1[-5/6, 7/6, 13/6, (d*(a + b*x))/(-(b*c) + a*d)])/(7*b*((b*(c + d*x))/(b*c - a*d))^(5/6))","C",1
1773,1,73,378,0.0414903,"\int \frac{\sqrt[6]{a+b x}}{\sqrt[6]{c+d x}} \, dx","Integrate[(a + b*x)^(1/6)/(c + d*x)^(1/6),x]","\frac{6 (a+b x)^{7/6} \sqrt[6]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{1}{6},\frac{7}{6};\frac{13}{6};\frac{d (a+b x)}{a d-b c}\right)}{7 b \sqrt[6]{c+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,"(6*(a + b*x)^(7/6)*((b*(c + d*x))/(b*c - a*d))^(1/6)*Hypergeometric2F1[1/6, 7/6, 13/6, (d*(a + b*x))/(-(b*c) + a*d)])/(7*b*(c + d*x)^(1/6))","C",1
1774,1,73,332,0.056037,"\int \frac{\sqrt[6]{a+b x}}{(c+d x)^{7/6}} \, dx","Integrate[(a + b*x)^(1/6)/(c + d*x)^(7/6),x]","\frac{6 (a+b x)^{7/6} \left(\frac{b (c+d x)}{b c-a d}\right)^{7/6} \, _2F_1\left(\frac{7}{6},\frac{7}{6};\frac{13}{6};\frac{d (a+b x)}{a d-b c}\right)}{7 b (c+d x)^{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[6]{b} \log \left(\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{2 d^{7/6}}-\frac{\sqrt{3} \sqrt[6]{b} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{d^{7/6}}+\frac{\sqrt{3} \sqrt[6]{b} \tan ^{-1}\left(\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}+\frac{1}{\sqrt{3}}\right)}{d^{7/6}}+\frac{2 \sqrt[6]{b} \tanh ^{-1}\left(\frac{\sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{d^{7/6}}-\frac{6 \sqrt[6]{a+b x}}{d \sqrt[6]{c+d x}}",1,"(6*(a + b*x)^(7/6)*((b*(c + d*x))/(b*c - a*d))^(7/6)*Hypergeometric2F1[7/6, 7/6, 13/6, (d*(a + b*x))/(-(b*c) + a*d)])/(7*b*(c + d*x)^(7/6))","C",1
1775,1,32,32,0.0154507,"\int \frac{\sqrt[6]{a+b x}}{(c+d x)^{13/6}} \, dx","Integrate[(a + b*x)^(1/6)/(c + d*x)^(13/6),x]","\frac{6 (a+b x)^{7/6}}{7 (c+d x)^{7/6} (b c-a d)}","\frac{6 (a+b x)^{7/6}}{7 (c+d x)^{7/6} (b c-a d)}",1,"(6*(a + b*x)^(7/6))/(7*(b*c - a*d)*(c + d*x)^(7/6))","A",1
1776,1,46,66,0.0335167,"\int \frac{\sqrt[6]{a+b x}}{(c+d x)^{19/6}} \, dx","Integrate[(a + b*x)^(1/6)/(c + d*x)^(19/6),x]","\frac{6 (a+b x)^{7/6} (-7 a d+13 b c+6 b d x)}{91 (c+d x)^{13/6} (b c-a d)^2}","\frac{36 b (a+b x)^{7/6}}{91 (c+d x)^{7/6} (b c-a d)^2}+\frac{6 (a+b x)^{7/6}}{13 (c+d x)^{13/6} (b c-a d)}",1,"(6*(a + b*x)^(7/6)*(13*b*c - 7*a*d + 6*b*d*x))/(91*(b*c - a*d)^2*(c + d*x)^(13/6))","A",1
1777,1,77,101,0.057224,"\int \frac{\sqrt[6]{a+b x}}{(c+d x)^{25/6}} \, dx","Integrate[(a + b*x)^(1/6)/(c + d*x)^(25/6),x]","\frac{6 (a+b x)^{7/6} \left(91 a^2 d^2-14 a b d (19 c+6 d x)+b^2 \left(247 c^2+228 c d x+72 d^2 x^2\right)\right)}{1729 (c+d x)^{19/6} (b c-a d)^3}","\frac{432 b^2 (a+b x)^{7/6}}{1729 (c+d x)^{7/6} (b c-a d)^3}+\frac{72 b (a+b x)^{7/6}}{247 (c+d x)^{13/6} (b c-a d)^2}+\frac{6 (a+b x)^{7/6}}{19 (c+d x)^{19/6} (b c-a d)}",1,"(6*(a + b*x)^(7/6)*(91*a^2*d^2 - 14*a*b*d*(19*c + 6*d*x) + b^2*(247*c^2 + 228*c*d*x + 72*d^2*x^2)))/(1729*(b*c - a*d)^3*(c + d*x)^(19/6))","A",1
1778,1,118,136,0.0824175,"\int \frac{\sqrt[6]{a+b x}}{(c+d x)^{31/6}} \, dx","Integrate[(a + b*x)^(1/6)/(c + d*x)^(31/6),x]","\frac{6 (a+b x)^{7/6} \left(-1729 a^3 d^3+273 a^2 b d^2 (25 c+6 d x)-21 a b^2 d \left(475 c^2+300 c d x+72 d^2 x^2\right)+b^3 \left(6175 c^3+8550 c^2 d x+5400 c d^2 x^2+1296 d^3 x^3\right)\right)}{43225 (c+d x)^{25/6} (b c-a d)^4}","\frac{7776 b^3 (a+b x)^{7/6}}{43225 (c+d x)^{7/6} (b c-a d)^4}+\frac{1296 b^2 (a+b x)^{7/6}}{6175 (c+d x)^{13/6} (b c-a d)^3}+\frac{108 b (a+b x)^{7/6}}{475 (c+d x)^{19/6} (b c-a d)^2}+\frac{6 (a+b x)^{7/6}}{25 (c+d x)^{25/6} (b c-a d)}",1,"(6*(a + b*x)^(7/6)*(-1729*a^3*d^3 + 273*a^2*b*d^2*(25*c + 6*d*x) - 21*a*b^2*d*(475*c^2 + 300*c*d*x + 72*d^2*x^2) + b^3*(6175*c^3 + 8550*c^2*d*x + 5400*c*d^2*x^2 + 1296*d^3*x^3)))/(43225*(b*c - a*d)^4*(c + d*x)^(25/6))","A",1
1779,1,73,427,0.0470096,"\int (a+b x)^{5/6} \sqrt[6]{c+d x} \, dx","Integrate[(a + b*x)^(5/6)*(c + d*x)^(1/6),x]","\frac{6 (a+b x)^{11/6} \sqrt[6]{c+d x} \, _2F_1\left(-\frac{1}{6},\frac{11}{6};\frac{17}{6};\frac{d (a+b x)}{a d-b c}\right)}{11 b \sqrt[6]{\frac{b (c+d x)}{b c-a d}}}","\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,"(6*(a + b*x)^(11/6)*(c + d*x)^(1/6)*Hypergeometric2F1[-1/6, 11/6, 17/6, (d*(a + b*x))/(-(b*c) + a*d)])/(11*b*((b*(c + d*x))/(b*c - a*d))^(1/6))","C",1
1780,1,73,378,0.03702,"\int \frac{(a+b x)^{5/6}}{(c+d x)^{5/6}} \, dx","Integrate[(a + b*x)^(5/6)/(c + d*x)^(5/6),x]","\frac{6 (a+b x)^{11/6} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6} \, _2F_1\left(\frac{5}{6},\frac{11}{6};\frac{17}{6};\frac{d (a+b x)}{a d-b c}\right)}{11 b (c+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,"(6*(a + b*x)^(11/6)*((b*(c + d*x))/(b*c - a*d))^(5/6)*Hypergeometric2F1[5/6, 11/6, 17/6, (d*(a + b*x))/(-(b*c) + a*d)])/(11*b*(c + d*x)^(5/6))","C",1
1781,1,73,334,0.0715685,"\int \frac{(a+b x)^{5/6}}{(c+d x)^{11/6}} \, dx","Integrate[(a + b*x)^(5/6)/(c + d*x)^(11/6),x]","\frac{6 (a+b x)^{11/6} \left(\frac{b (c+d x)}{b c-a d}\right)^{11/6} \, _2F_1\left(\frac{11}{6},\frac{11}{6};\frac{17}{6};\frac{d (a+b x)}{a d-b c}\right)}{11 b (c+d x)^{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{b^{5/6} \log \left(\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{2 d^{11/6}}+\frac{\sqrt{3} b^{5/6} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{d^{11/6}}-\frac{\sqrt{3} b^{5/6} \tan ^{-1}\left(\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}+\frac{1}{\sqrt{3}}\right)}{d^{11/6}}+\frac{2 b^{5/6} \tanh ^{-1}\left(\frac{\sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{d^{11/6}}-\frac{6 (a+b x)^{5/6}}{5 d (c+d x)^{5/6}}",1,"(6*(a + b*x)^(11/6)*((b*(c + d*x))/(b*c - a*d))^(11/6)*Hypergeometric2F1[11/6, 11/6, 17/6, (d*(a + b*x))/(-(b*c) + a*d)])/(11*b*(c + d*x)^(11/6))","C",1
1782,1,32,32,0.0113741,"\int \frac{(a+b x)^{5/6}}{(c+d x)^{17/6}} \, dx","Integrate[(a + b*x)^(5/6)/(c + d*x)^(17/6),x]","\frac{6 (a+b x)^{11/6}}{11 (c+d x)^{11/6} (b c-a d)}","\frac{6 (a+b x)^{11/6}}{11 (c+d x)^{11/6} (b c-a d)}",1,"(6*(a + b*x)^(11/6))/(11*(b*c - a*d)*(c + d*x)^(11/6))","A",1
1783,1,46,66,0.0322771,"\int \frac{(a+b x)^{5/6}}{(c+d x)^{23/6}} \, dx","Integrate[(a + b*x)^(5/6)/(c + d*x)^(23/6),x]","\frac{6 (a+b x)^{11/6} (-11 a d+17 b c+6 b d x)}{187 (c+d x)^{17/6} (b c-a d)^2}","\frac{36 b (a+b x)^{11/6}}{187 (c+d x)^{11/6} (b c-a d)^2}+\frac{6 (a+b x)^{11/6}}{17 (c+d x)^{17/6} (b c-a d)}",1,"(6*(a + b*x)^(11/6)*(17*b*c - 11*a*d + 6*b*d*x))/(187*(b*c - a*d)^2*(c + d*x)^(17/6))","A",1
1784,1,77,101,0.0553006,"\int \frac{(a+b x)^{5/6}}{(c+d x)^{29/6}} \, dx","Integrate[(a + b*x)^(5/6)/(c + d*x)^(29/6),x]","\frac{6 (a+b x)^{11/6} \left(187 a^2 d^2-22 a b d (23 c+6 d x)+b^2 \left(391 c^2+276 c d x+72 d^2 x^2\right)\right)}{4301 (c+d x)^{23/6} (b c-a d)^3}","\frac{432 b^2 (a+b x)^{11/6}}{4301 (c+d x)^{11/6} (b c-a d)^3}+\frac{72 b (a+b x)^{11/6}}{391 (c+d x)^{17/6} (b c-a d)^2}+\frac{6 (a+b x)^{11/6}}{23 (c+d x)^{23/6} (b c-a d)}",1,"(6*(a + b*x)^(11/6)*(187*a^2*d^2 - 22*a*b*d*(23*c + 6*d*x) + b^2*(391*c^2 + 276*c*d*x + 72*d^2*x^2)))/(4301*(b*c - a*d)^3*(c + d*x)^(23/6))","A",1
1785,1,118,136,0.0888404,"\int \frac{(a+b x)^{5/6}}{(c+d x)^{35/6}} \, dx","Integrate[(a + b*x)^(5/6)/(c + d*x)^(35/6),x]","\frac{6 (a+b x)^{11/6} \left(-4301 a^3 d^3+561 a^2 b d^2 (29 c+6 d x)-33 a b^2 d \left(667 c^2+348 c d x+72 d^2 x^2\right)+b^3 \left(11339 c^3+12006 c^2 d x+6264 c d^2 x^2+1296 d^3 x^3\right)\right)}{124729 (c+d x)^{29/6} (b c-a d)^4}","\frac{7776 b^3 (a+b x)^{11/6}}{124729 (c+d x)^{11/6} (b c-a d)^4}+\frac{1296 b^2 (a+b x)^{11/6}}{11339 (c+d x)^{17/6} (b c-a d)^3}+\frac{108 b (a+b x)^{11/6}}{667 (c+d x)^{23/6} (b c-a d)^2}+\frac{6 (a+b x)^{11/6}}{29 (c+d x)^{29/6} (b c-a d)}",1,"(6*(a + b*x)^(11/6)*(-4301*a^3*d^3 + 561*a^2*b*d^2*(29*c + 6*d*x) - 33*a*b^2*d*(667*c^2 + 348*c*d*x + 72*d^2*x^2) + b^3*(11339*c^3 + 12006*c^2*d*x + 6264*c*d^2*x^2 + 1296*d^3*x^3)))/(124729*(b*c - a*d)^4*(c + d*x)^(29/6))","A",1
1786,1,73,82,0.0831844,"\int (a+b x)^{5/6} (c+d x)^{11/6} \, dx","Integrate[(a + b*x)^(5/6)*(c + d*x)^(11/6),x]","\frac{6 (a+b x)^{11/6} (c+d x)^{11/6} \, _2F_1\left(-\frac{11}{6},\frac{11}{6};\frac{17}{6};\frac{d (a+b x)}{a d-b c}\right)}{11 b \left(\frac{b (c+d x)}{b c-a d}\right)^{11/6}}","\frac{6 (a+b x)^{11/6} (c+d x)^{5/6} (b c-a d) \, _2F_1\left(-\frac{11}{6},\frac{11}{6};\frac{17}{6};-\frac{d (a+b x)}{b c-a d}\right)}{11 b^2 \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6}}",1,"(6*(a + b*x)^(11/6)*(c + d*x)^(11/6)*Hypergeometric2F1[-11/6, 11/6, 17/6, (d*(a + b*x))/(-(b*c) + a*d)])/(11*b*((b*(c + d*x))/(b*c - a*d))^(11/6))","A",1
1787,1,73,74,0.0360053,"\int (a+b x)^{5/6} (c+d x)^{5/6} \, dx","Integrate[(a + b*x)^(5/6)*(c + d*x)^(5/6),x]","\frac{6 (a+b x)^{11/6} (c+d x)^{5/6} \, _2F_1\left(-\frac{5}{6},\frac{11}{6};\frac{17}{6};\frac{d (a+b x)}{a d-b c}\right)}{11 b \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6}}","\frac{6 (a+b x)^{11/6} (c+d x)^{5/6} \, _2F_1\left(-\frac{5}{6},\frac{11}{6};\frac{17}{6};-\frac{d (a+b x)}{b c-a d}\right)}{11 b \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6}}",1,"(6*(a + b*x)^(11/6)*(c + d*x)^(5/6)*Hypergeometric2F1[-5/6, 11/6, 17/6, (d*(a + b*x))/(-(b*c) + a*d)])/(11*b*((b*(c + d*x))/(b*c - a*d))^(5/6))","A",1
1788,1,73,74,0.0428361,"\int \frac{(a+b x)^{5/6}}{\sqrt[6]{c+d x}} \, dx","Integrate[(a + b*x)^(5/6)/(c + d*x)^(1/6),x]","\frac{6 (a+b x)^{11/6} \sqrt[6]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{1}{6},\frac{11}{6};\frac{17}{6};\frac{d (a+b x)}{a d-b c}\right)}{11 b \sqrt[6]{c+d x}}","\frac{6 (a+b x)^{11/6} \sqrt[6]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{1}{6},\frac{11}{6};\frac{17}{6};-\frac{d (a+b x)}{b c-a d}\right)}{11 b \sqrt[6]{c+d x}}",1,"(6*(a + b*x)^(11/6)*((b*(c + d*x))/(b*c - a*d))^(1/6)*Hypergeometric2F1[1/6, 11/6, 17/6, (d*(a + b*x))/(-(b*c) + a*d)])/(11*b*(c + d*x)^(1/6))","A",1
1789,1,73,81,0.0591629,"\int \frac{(a+b x)^{5/6}}{(c+d x)^{7/6}} \, dx","Integrate[(a + b*x)^(5/6)/(c + d*x)^(7/6),x]","\frac{6 (a+b x)^{11/6} \left(\frac{b (c+d x)}{b c-a d}\right)^{7/6} \, _2F_1\left(\frac{7}{6},\frac{11}{6};\frac{17}{6};\frac{d (a+b x)}{a d-b c}\right)}{11 b (c+d x)^{7/6}}","\frac{6 (a+b x)^{11/6} \sqrt[6]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{7}{6},\frac{11}{6};\frac{17}{6};-\frac{d (a+b x)}{b c-a d}\right)}{11 \sqrt[6]{c+d x} (b c-a d)}",1,"(6*(a + b*x)^(11/6)*((b*(c + d*x))/(b*c - a*d))^(7/6)*Hypergeometric2F1[7/6, 11/6, 17/6, (d*(a + b*x))/(-(b*c) + a*d)])/(11*b*(c + d*x)^(7/6))","A",1
1790,1,73,82,0.0775765,"\int \frac{(a+b x)^{5/6}}{(c+d x)^{13/6}} \, dx","Integrate[(a + b*x)^(5/6)/(c + d*x)^(13/6),x]","\frac{6 (a+b x)^{11/6} \left(\frac{b (c+d x)}{b c-a d}\right)^{13/6} \, _2F_1\left(\frac{11}{6},\frac{13}{6};\frac{17}{6};\frac{d (a+b x)}{a d-b c}\right)}{11 b (c+d x)^{13/6}}","\frac{6 b (a+b x)^{11/6} \sqrt[6]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{11}{6},\frac{13}{6};\frac{17}{6};-\frac{d (a+b x)}{b c-a d}\right)}{11 \sqrt[6]{c+d x} (b c-a d)^2}",1,"(6*(a + b*x)^(11/6)*((b*(c + d*x))/(b*c - a*d))^(13/6)*Hypergeometric2F1[11/6, 13/6, 17/6, (d*(a + b*x))/(-(b*c) + a*d)])/(11*b*(c + d*x)^(13/6))","A",1
1791,1,81,84,0.0480456,"\int \frac{(a+b x)^{5/6}}{(c+d x)^{19/6}} \, dx","Integrate[(a + b*x)^(5/6)/(c + d*x)^(19/6),x]","\frac{6 b (a+b x)^{11/6} \left(\frac{b (c+d x)}{b c-a d}\right)^{7/6} \, _2F_1\left(\frac{11}{6},\frac{19}{6};\frac{17}{6};\frac{d (a+b x)}{a d-b c}\right)}{11 (c+d x)^{7/6} (b c-a d)^2}","\frac{6 b^2 (a+b x)^{11/6} \sqrt[6]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{11}{6},\frac{19}{6};\frac{17}{6};-\frac{d (a+b x)}{b c-a d}\right)}{11 \sqrt[6]{c+d x} (b c-a d)^3}",1,"(6*b*(a + b*x)^(11/6)*((b*(c + d*x))/(b*c - a*d))^(7/6)*Hypergeometric2F1[11/6, 19/6, 17/6, (d*(a + b*x))/(-(b*c) + a*d)])/(11*(b*c - a*d)^2*(c + d*x)^(7/6))","A",1
1792,1,73,84,0.1139731,"\int (a+b x)^{7/6} (c+d x)^{13/6} \, dx","Integrate[(a + b*x)^(7/6)*(c + d*x)^(13/6),x]","\frac{6 (a+b x)^{13/6} (c+d x)^{13/6} \, _2F_1\left(-\frac{13}{6},\frac{13}{6};\frac{19}{6};\frac{d (a+b x)}{a d-b c}\right)}{13 b \left(\frac{b (c+d x)}{b c-a d}\right)^{13/6}}","\frac{6 (a+b x)^{13/6} \sqrt[6]{c+d x} (b c-a d)^2 \, _2F_1\left(-\frac{13}{6},\frac{13}{6};\frac{19}{6};-\frac{d (a+b x)}{b c-a d}\right)}{13 b^3 \sqrt[6]{\frac{b (c+d x)}{b c-a d}}}",1,"(6*(a + b*x)^(13/6)*(c + d*x)^(13/6)*Hypergeometric2F1[-13/6, 13/6, 19/6, (d*(a + b*x))/(-(b*c) + a*d)])/(13*b*((b*(c + d*x))/(b*c - a*d))^(13/6))","A",1
1793,1,73,82,0.0738038,"\int (a+b x)^{7/6} (c+d x)^{7/6} \, dx","Integrate[(a + b*x)^(7/6)*(c + d*x)^(7/6),x]","\frac{6 (a+b x)^{13/6} (c+d x)^{7/6} \, _2F_1\left(-\frac{7}{6},\frac{13}{6};\frac{19}{6};\frac{d (a+b x)}{a d-b c}\right)}{13 b \left(\frac{b (c+d x)}{b c-a d}\right)^{7/6}}","\frac{6 (a+b x)^{13/6} \sqrt[6]{c+d x} (b c-a d) \, _2F_1\left(-\frac{7}{6},\frac{13}{6};\frac{19}{6};-\frac{d (a+b x)}{b c-a d}\right)}{13 b^2 \sqrt[6]{\frac{b (c+d x)}{b c-a d}}}",1,"(6*(a + b*x)^(13/6)*(c + d*x)^(7/6)*Hypergeometric2F1[-7/6, 13/6, 19/6, (d*(a + b*x))/(-(b*c) + a*d)])/(13*b*((b*(c + d*x))/(b*c - a*d))^(7/6))","A",1
1794,1,73,74,0.0396267,"\int (a+b x)^{7/6} \sqrt[6]{c+d x} \, dx","Integrate[(a + b*x)^(7/6)*(c + d*x)^(1/6),x]","\frac{6 (a+b x)^{13/6} \sqrt[6]{c+d x} \, _2F_1\left(-\frac{1}{6},\frac{13}{6};\frac{19}{6};\frac{d (a+b x)}{a d-b c}\right)}{13 b \sqrt[6]{\frac{b (c+d x)}{b c-a d}}}","\frac{6 (a+b x)^{13/6} \sqrt[6]{c+d x} \, _2F_1\left(-\frac{1}{6},\frac{13}{6};\frac{19}{6};-\frac{d (a+b x)}{b c-a d}\right)}{13 b \sqrt[6]{\frac{b (c+d x)}{b c-a d}}}",1,"(6*(a + b*x)^(13/6)*(c + d*x)^(1/6)*Hypergeometric2F1[-1/6, 13/6, 19/6, (d*(a + b*x))/(-(b*c) + a*d)])/(13*b*((b*(c + d*x))/(b*c - a*d))^(1/6))","A",1
1795,1,73,74,0.03956,"\int \frac{(a+b x)^{7/6}}{(c+d x)^{5/6}} \, dx","Integrate[(a + b*x)^(7/6)/(c + d*x)^(5/6),x]","\frac{6 (a+b x)^{13/6} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6} \, _2F_1\left(\frac{5}{6},\frac{13}{6};\frac{19}{6};\frac{d (a+b x)}{a d-b c}\right)}{13 b (c+d x)^{5/6}}","\frac{6 (a+b x)^{13/6} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6} \, _2F_1\left(\frac{5}{6},\frac{13}{6};\frac{19}{6};-\frac{d (a+b x)}{b c-a d}\right)}{13 b (c+d x)^{5/6}}",1,"(6*(a + b*x)^(13/6)*((b*(c + d*x))/(b*c - a*d))^(5/6)*Hypergeometric2F1[5/6, 13/6, 19/6, (d*(a + b*x))/(-(b*c) + a*d)])/(13*b*(c + d*x)^(5/6))","A",1
1796,1,73,81,0.0692465,"\int \frac{(a+b x)^{7/6}}{(c+d x)^{11/6}} \, dx","Integrate[(a + b*x)^(7/6)/(c + d*x)^(11/6),x]","\frac{6 (a+b x)^{13/6} \left(\frac{b (c+d x)}{b c-a d}\right)^{11/6} \, _2F_1\left(\frac{11}{6},\frac{13}{6};\frac{19}{6};\frac{d (a+b x)}{a d-b c}\right)}{13 b (c+d x)^{11/6}}","\frac{6 (a+b x)^{13/6} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6} \, _2F_1\left(\frac{11}{6},\frac{13}{6};\frac{19}{6};-\frac{d (a+b x)}{b c-a d}\right)}{13 (c+d x)^{5/6} (b c-a d)}",1,"(6*(a + b*x)^(13/6)*((b*(c + d*x))/(b*c - a*d))^(11/6)*Hypergeometric2F1[11/6, 13/6, 19/6, (d*(a + b*x))/(-(b*c) + a*d)])/(13*b*(c + d*x)^(11/6))","A",1
1797,1,81,82,0.0484406,"\int \frac{(a+b x)^{7/6}}{(c+d x)^{17/6}} \, dx","Integrate[(a + b*x)^(7/6)/(c + d*x)^(17/6),x]","\frac{6 b (a+b x)^{13/6} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6} \, _2F_1\left(\frac{13}{6},\frac{17}{6};\frac{19}{6};\frac{d (a+b x)}{a d-b c}\right)}{13 (c+d x)^{5/6} (b c-a d)^2}","\frac{6 b (a+b x)^{13/6} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6} \, _2F_1\left(\frac{13}{6},\frac{17}{6};\frac{19}{6};-\frac{d (a+b x)}{b c-a d}\right)}{13 (c+d x)^{5/6} (b c-a d)^2}",1,"(6*b*(a + b*x)^(13/6)*((b*(c + d*x))/(b*c - a*d))^(5/6)*Hypergeometric2F1[13/6, 17/6, 19/6, (d*(a + b*x))/(-(b*c) + a*d)])/(13*(b*c - a*d)^2*(c + d*x)^(5/6))","A",1
1798,1,73,424,0.0390126,"\int \frac{(a+b x)^{7/6}}{\sqrt[6]{c+d x}} \, dx","Integrate[(a + b*x)^(7/6)/(c + d*x)^(1/6),x]","\frac{6 (a+b x)^{13/6} \sqrt[6]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{1}{6},\frac{13}{6};\frac{19}{6};\frac{d (a+b x)}{a d-b c}\right)}{13 b \sqrt[6]{c+d x}}","-\frac{7 (b c-a d)^2 \log \left(-\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{144 b^{5/6} d^{13/6}}+\frac{7 (b c-a d)^2 \log \left(\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{144 b^{5/6} d^{13/6}}-\frac{7 (b c-a d)^2 \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{24 \sqrt{3} b^{5/6} d^{13/6}}+\frac{7 (b c-a d)^2 \tan ^{-1}\left(\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}+\frac{1}{\sqrt{3}}\right)}{24 \sqrt{3} b^{5/6} d^{13/6}}+\frac{7 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{36 b^{5/6} d^{13/6}}-\frac{7 \sqrt[6]{a+b x} (c+d x)^{5/6} (b c-a d)}{12 d^2}+\frac{(a+b x)^{7/6} (c+d x)^{5/6}}{2 d}",1,"(6*(a + b*x)^(13/6)*((b*(c + d*x))/(b*c - a*d))^(1/6)*Hypergeometric2F1[1/6, 13/6, 19/6, (d*(a + b*x))/(-(b*c) + a*d)])/(13*b*(c + d*x)^(1/6))","C",1
1799,1,73,403,0.0664254,"\int \frac{(a+b x)^{7/6}}{(c+d x)^{7/6}} \, dx","Integrate[(a + b*x)^(7/6)/(c + d*x)^(7/6),x]","\frac{6 (a+b x)^{13/6} \left(\frac{b (c+d x)}{b c-a d}\right)^{7/6} \, _2F_1\left(\frac{7}{6},\frac{13}{6};\frac{19}{6};\frac{d (a+b x)}{a d-b c}\right)}{13 b (c+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,"(6*(a + b*x)^(13/6)*((b*(c + d*x))/(b*c - a*d))^(7/6)*Hypergeometric2F1[7/6, 13/6, 19/6, (d*(a + b*x))/(-(b*c) + a*d)])/(13*b*(c + d*x)^(7/6))","C",1
1800,1,73,358,0.0850114,"\int \frac{(a+b x)^{7/6}}{(c+d x)^{13/6}} \, dx","Integrate[(a + b*x)^(7/6)/(c + d*x)^(13/6),x]","\frac{6 (a+b x)^{13/6} \left(\frac{b (c+d x)}{b c-a d}\right)^{13/6} \, _2F_1\left(\frac{13}{6},\frac{13}{6};\frac{19}{6};\frac{d (a+b x)}{a d-b c}\right)}{13 b (c+d x)^{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{b^{7/6} \log \left(\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{2 d^{13/6}}-\frac{\sqrt{3} b^{7/6} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{d^{13/6}}+\frac{\sqrt{3} b^{7/6} \tan ^{-1}\left(\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}+\frac{1}{\sqrt{3}}\right)}{d^{13/6}}+\frac{2 b^{7/6} \tanh ^{-1}\left(\frac{\sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{d^{13/6}}-\frac{6 b \sqrt[6]{a+b x}}{d^2 \sqrt[6]{c+d x}}-\frac{6 (a+b x)^{7/6}}{7 d (c+d x)^{7/6}}",1,"(6*(a + b*x)^(13/6)*((b*(c + d*x))/(b*c - a*d))^(13/6)*Hypergeometric2F1[13/6, 13/6, 19/6, (d*(a + b*x))/(-(b*c) + a*d)])/(13*b*(c + d*x)^(13/6))","C",1
1801,1,32,32,0.022838,"\int \frac{(a+b x)^{7/6}}{(c+d x)^{19/6}} \, dx","Integrate[(a + b*x)^(7/6)/(c + d*x)^(19/6),x]","\frac{6 (a+b x)^{13/6}}{13 (c+d x)^{13/6} (b c-a d)}","\frac{6 (a+b x)^{13/6}}{13 (c+d x)^{13/6} (b c-a d)}",1,"(6*(a + b*x)^(13/6))/(13*(b*c - a*d)*(c + d*x)^(13/6))","A",1
1802,1,46,66,0.0362109,"\int \frac{(a+b x)^{7/6}}{(c+d x)^{25/6}} \, dx","Integrate[(a + b*x)^(7/6)/(c + d*x)^(25/6),x]","\frac{6 (a+b x)^{13/6} (-13 a d+19 b c+6 b d x)}{247 (c+d x)^{19/6} (b c-a d)^2}","\frac{36 b (a+b x)^{13/6}}{247 (c+d x)^{13/6} (b c-a d)^2}+\frac{6 (a+b x)^{13/6}}{19 (c+d x)^{19/6} (b c-a d)}",1,"(6*(a + b*x)^(13/6)*(19*b*c - 13*a*d + 6*b*d*x))/(247*(b*c - a*d)^2*(c + d*x)^(19/6))","A",1
1803,1,77,101,0.0598124,"\int \frac{(a+b x)^{7/6}}{(c+d x)^{31/6}} \, dx","Integrate[(a + b*x)^(7/6)/(c + d*x)^(31/6),x]","\frac{6 (a+b x)^{13/6} \left(247 a^2 d^2-26 a b d (25 c+6 d x)+b^2 \left(475 c^2+300 c d x+72 d^2 x^2\right)\right)}{6175 (c+d x)^{25/6} (b c-a d)^3}","\frac{432 b^2 (a+b x)^{13/6}}{6175 (c+d x)^{13/6} (b c-a d)^3}+\frac{72 b (a+b x)^{13/6}}{475 (c+d x)^{19/6} (b c-a d)^2}+\frac{6 (a+b x)^{13/6}}{25 (c+d x)^{25/6} (b c-a d)}",1,"(6*(a + b*x)^(13/6)*(247*a^2*d^2 - 26*a*b*d*(25*c + 6*d*x) + b^2*(475*c^2 + 300*c*d*x + 72*d^2*x^2)))/(6175*(b*c - a*d)^3*(c + d*x)^(25/6))","A",1
1804,1,118,136,0.0936931,"\int \frac{(a+b x)^{7/6}}{(c+d x)^{37/6}} \, dx","Integrate[(a + b*x)^(7/6)/(c + d*x)^(37/6),x]","\frac{6 (a+b x)^{13/6} \left(-6175 a^3 d^3+741 a^2 b d^2 (31 c+6 d x)-39 a b^2 d \left(775 c^2+372 c d x+72 d^2 x^2\right)+b^3 \left(14725 c^3+13950 c^2 d x+6696 c d^2 x^2+1296 d^3 x^3\right)\right)}{191425 (c+d x)^{31/6} (b c-a d)^4}","\frac{7776 b^3 (a+b x)^{13/6}}{191425 (c+d x)^{13/6} (b c-a d)^4}+\frac{1296 b^2 (a+b x)^{13/6}}{14725 (c+d x)^{19/6} (b c-a d)^3}+\frac{108 b (a+b x)^{13/6}}{775 (c+d x)^{25/6} (b c-a d)^2}+\frac{6 (a+b x)^{13/6}}{31 (c+d x)^{31/6} (b c-a d)}",1,"(6*(a + b*x)^(13/6)*(-6175*a^3*d^3 + 741*a^2*b*d^2*(31*c + 6*d*x) - 39*a*b^2*d*(775*c^2 + 372*c*d*x + 72*d^2*x^2) + b^3*(14725*c^3 + 13950*c^2*d*x + 6696*c*d^2*x^2 + 1296*d^3*x^3)))/(191425*(b*c - a*d)^4*(c + d*x)^(31/6))","A",1
1805,1,73,424,0.0540167,"\int \frac{(c+d x)^{7/6}}{\sqrt[6]{a+b x}} \, dx","Integrate[(c + d*x)^(7/6)/(a + b*x)^(1/6),x]","\frac{6 (a+b x)^{5/6} (c+d x)^{7/6} \, _2F_1\left(-\frac{7}{6},\frac{5}{6};\frac{11}{6};\frac{d (a+b x)}{a d-b c}\right)}{5 b \left(\frac{b (c+d x)}{b c-a d}\right)^{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^{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,"(6*(a + b*x)^(5/6)*(c + d*x)^(7/6)*Hypergeometric2F1[-7/6, 5/6, 11/6, (d*(a + b*x))/(-(b*c) + a*d)])/(5*b*((b*(c + d*x))/(b*c - a*d))^(7/6))","C",1
1806,1,73,378,0.035971,"\int \frac{\sqrt[6]{c+d x}}{\sqrt[6]{a+b x}} \, dx","Integrate[(c + d*x)^(1/6)/(a + b*x)^(1/6),x]","\frac{6 (a+b x)^{5/6} \sqrt[6]{c+d x} \, _2F_1\left(-\frac{1}{6},\frac{5}{6};\frac{11}{6};\frac{d (a+b x)}{a d-b c}\right)}{5 b \sqrt[6]{\frac{b (c+d x)}{b c-a d}}}","-\frac{(b c-a d) \log \left(-\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{12 b^{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,"(6*(a + b*x)^(5/6)*(c + d*x)^(1/6)*Hypergeometric2F1[-1/6, 5/6, 11/6, (d*(a + b*x))/(-(b*c) + a*d)])/(5*b*((b*(c + d*x))/(b*c - a*d))^(1/6))","C",1
1807,1,73,309,0.0471991,"\int \frac{1}{\sqrt[6]{a+b x} (c+d x)^{5/6}} \, dx","Integrate[1/((a + b*x)^(1/6)*(c + d*x)^(5/6)),x]","\frac{6 (a+b x)^{5/6} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6} \, _2F_1\left(\frac{5}{6},\frac{5}{6};\frac{11}{6};\frac{d (a+b x)}{a d-b c}\right)}{5 b (c+d x)^{5/6}}","-\frac{\log \left(-\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{2 \sqrt[6]{b} d^{5/6}}+\frac{\log \left(\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{2 \sqrt[6]{b} d^{5/6}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{\sqrt[6]{b} d^{5/6}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt[6]{b} d^{5/6}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{\sqrt[6]{b} d^{5/6}}",1,"(6*(a + b*x)^(5/6)*((b*(c + d*x))/(b*c - a*d))^(5/6)*Hypergeometric2F1[5/6, 5/6, 11/6, (d*(a + b*x))/(-(b*c) + a*d)])/(5*b*(c + d*x)^(5/6))","C",1
1808,1,32,32,0.0127759,"\int \frac{1}{\sqrt[6]{a+b x} (c+d x)^{11/6}} \, dx","Integrate[1/((a + b*x)^(1/6)*(c + d*x)^(11/6)),x]","\frac{6 (a+b x)^{5/6}}{5 (c+d x)^{5/6} (b c-a d)}","\frac{6 (a+b x)^{5/6}}{5 (c+d x)^{5/6} (b c-a d)}",1,"(6*(a + b*x)^(5/6))/(5*(b*c - a*d)*(c + d*x)^(5/6))","A",1
1809,1,46,66,0.0274162,"\int \frac{1}{\sqrt[6]{a+b x} (c+d x)^{17/6}} \, dx","Integrate[1/((a + b*x)^(1/6)*(c + d*x)^(17/6)),x]","\frac{6 (a+b x)^{5/6} (-5 a d+11 b c+6 b d x)}{55 (c+d x)^{11/6} (b c-a d)^2}","\frac{36 b (a+b x)^{5/6}}{55 (c+d x)^{5/6} (b c-a d)^2}+\frac{6 (a+b x)^{5/6}}{11 (c+d x)^{11/6} (b c-a d)}",1,"(6*(a + b*x)^(5/6)*(11*b*c - 5*a*d + 6*b*d*x))/(55*(b*c - a*d)^2*(c + d*x)^(11/6))","A",1
1810,1,77,101,0.0452439,"\int \frac{1}{\sqrt[6]{a+b x} (c+d x)^{23/6}} \, dx","Integrate[1/((a + b*x)^(1/6)*(c + d*x)^(23/6)),x]","\frac{6 (a+b x)^{5/6} \left(55 a^2 d^2-10 a b d (17 c+6 d x)+b^2 \left(187 c^2+204 c d x+72 d^2 x^2\right)\right)}{935 (c+d x)^{17/6} (b c-a d)^3}","\frac{432 b^2 (a+b x)^{5/6}}{935 (c+d x)^{5/6} (b c-a d)^3}+\frac{72 b (a+b x)^{5/6}}{187 (c+d x)^{11/6} (b c-a d)^2}+\frac{6 (a+b x)^{5/6}}{17 (c+d x)^{17/6} (b c-a d)}",1,"(6*(a + b*x)^(5/6)*(55*a^2*d^2 - 10*a*b*d*(17*c + 6*d*x) + b^2*(187*c^2 + 204*c*d*x + 72*d^2*x^2)))/(935*(b*c - a*d)^3*(c + d*x)^(17/6))","A",1
1811,1,118,136,0.0681817,"\int \frac{1}{\sqrt[6]{a+b x} (c+d x)^{29/6}} \, dx","Integrate[1/((a + b*x)^(1/6)*(c + d*x)^(29/6)),x]","\frac{6 (a+b x)^{5/6} \left(-935 a^3 d^3+165 a^2 b d^2 (23 c+6 d x)-15 a b^2 d \left(391 c^2+276 c d x+72 d^2 x^2\right)+b^3 \left(4301 c^3+7038 c^2 d x+4968 c d^2 x^2+1296 d^3 x^3\right)\right)}{21505 (c+d x)^{23/6} (b c-a d)^4}","\frac{7776 b^3 (a+b x)^{5/6}}{21505 (c+d x)^{5/6} (b c-a d)^4}+\frac{1296 b^2 (a+b x)^{5/6}}{4301 (c+d x)^{11/6} (b c-a d)^3}+\frac{108 b (a+b x)^{5/6}}{391 (c+d x)^{17/6} (b c-a d)^2}+\frac{6 (a+b x)^{5/6}}{23 (c+d x)^{23/6} (b c-a d)}",1,"(6*(a + b*x)^(5/6)*(-935*a^3*d^3 + 165*a^2*b*d^2*(23*c + 6*d*x) - 15*a*b^2*d*(391*c^2 + 276*c*d*x + 72*d^2*x^2) + b^3*(4301*c^3 + 7038*c^2*d*x + 4968*c*d^2*x^2 + 1296*d^3*x^3)))/(21505*(b*c - a*d)^4*(c + d*x)^(23/6))","A",1
1812,1,73,82,0.0684436,"\int \frac{(c+d x)^{11/6}}{\sqrt[6]{a+b x}} \, dx","Integrate[(c + d*x)^(11/6)/(a + b*x)^(1/6),x]","\frac{6 (a+b x)^{5/6} (c+d x)^{11/6} \, _2F_1\left(-\frac{11}{6},\frac{5}{6};\frac{11}{6};\frac{d (a+b x)}{a d-b c}\right)}{5 b \left(\frac{b (c+d x)}{b c-a d}\right)^{11/6}}","\frac{6 (a+b x)^{5/6} (c+d x)^{5/6} (b c-a d) \, _2F_1\left(-\frac{11}{6},\frac{5}{6};\frac{11}{6};-\frac{d (a+b x)}{b c-a d}\right)}{5 b^2 \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6}}",1,"(6*(a + b*x)^(5/6)*(c + d*x)^(11/6)*Hypergeometric2F1[-11/6, 5/6, 11/6, (d*(a + b*x))/(-(b*c) + a*d)])/(5*b*((b*(c + d*x))/(b*c - a*d))^(11/6))","A",1
1813,1,73,74,0.0364958,"\int \frac{(c+d x)^{5/6}}{\sqrt[6]{a+b x}} \, dx","Integrate[(c + d*x)^(5/6)/(a + b*x)^(1/6),x]","\frac{6 (a+b x)^{5/6} (c+d x)^{5/6} \, _2F_1\left(-\frac{5}{6},\frac{5}{6};\frac{11}{6};\frac{d (a+b x)}{a d-b c}\right)}{5 b \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6}}","\frac{6 (a+b x)^{5/6} (c+d x)^{5/6} \, _2F_1\left(-\frac{5}{6},\frac{5}{6};\frac{11}{6};-\frac{d (a+b x)}{b c-a d}\right)}{5 b \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6}}",1,"(6*(a + b*x)^(5/6)*(c + d*x)^(5/6)*Hypergeometric2F1[-5/6, 5/6, 11/6, (d*(a + b*x))/(-(b*c) + a*d)])/(5*b*((b*(c + d*x))/(b*c - a*d))^(5/6))","A",1
1814,1,73,74,0.0308355,"\int \frac{1}{\sqrt[6]{a+b x} \sqrt[6]{c+d x}} \, dx","Integrate[1/((a + b*x)^(1/6)*(c + d*x)^(1/6)),x]","\frac{6 (a+b x)^{5/6} \sqrt[6]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{1}{6},\frac{5}{6};\frac{11}{6};\frac{d (a+b x)}{a d-b c}\right)}{5 b \sqrt[6]{c+d x}}","\frac{6 (a+b x)^{5/6} \sqrt[6]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{1}{6},\frac{5}{6};\frac{11}{6};-\frac{d (a+b x)}{b c-a d}\right)}{5 b \sqrt[6]{c+d x}}",1,"(6*(a + b*x)^(5/6)*((b*(c + d*x))/(b*c - a*d))^(1/6)*Hypergeometric2F1[1/6, 5/6, 11/6, (d*(a + b*x))/(-(b*c) + a*d)])/(5*b*(c + d*x)^(1/6))","A",1
1815,1,73,81,0.0458195,"\int \frac{1}{\sqrt[6]{a+b x} (c+d x)^{7/6}} \, dx","Integrate[1/((a + b*x)^(1/6)*(c + d*x)^(7/6)),x]","\frac{6 (a+b x)^{5/6} \left(\frac{b (c+d x)}{b c-a d}\right)^{7/6} \, _2F_1\left(\frac{5}{6},\frac{7}{6};\frac{11}{6};\frac{d (a+b x)}{a d-b c}\right)}{5 b (c+d x)^{7/6}}","\frac{6 (a+b x)^{5/6} \sqrt[6]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{5}{6},\frac{7}{6};\frac{11}{6};-\frac{d (a+b x)}{b c-a d}\right)}{5 \sqrt[6]{c+d x} (b c-a d)}",1,"(6*(a + b*x)^(5/6)*((b*(c + d*x))/(b*c - a*d))^(7/6)*Hypergeometric2F1[5/6, 7/6, 11/6, (d*(a + b*x))/(-(b*c) + a*d)])/(5*b*(c + d*x)^(7/6))","A",1
1816,1,73,82,0.0594513,"\int \frac{1}{\sqrt[6]{a+b x} (c+d x)^{13/6}} \, dx","Integrate[1/((a + b*x)^(1/6)*(c + d*x)^(13/6)),x]","\frac{6 (a+b x)^{5/6} \left(\frac{b (c+d x)}{b c-a d}\right)^{13/6} \, _2F_1\left(\frac{5}{6},\frac{13}{6};\frac{11}{6};\frac{d (a+b x)}{a d-b c}\right)}{5 b (c+d x)^{13/6}}","\frac{6 b (a+b x)^{5/6} \sqrt[6]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{5}{6},\frac{13}{6};\frac{11}{6};-\frac{d (a+b x)}{b c-a d}\right)}{5 \sqrt[6]{c+d x} (b c-a d)^2}",1,"(6*(a + b*x)^(5/6)*((b*(c + d*x))/(b*c - a*d))^(13/6)*Hypergeometric2F1[5/6, 13/6, 11/6, (d*(a + b*x))/(-(b*c) + a*d)])/(5*b*(c + d*x)^(13/6))","A",1
1817,1,81,84,0.0443763,"\int \frac{1}{\sqrt[6]{a+b x} (c+d x)^{19/6}} \, dx","Integrate[1/((a + b*x)^(1/6)*(c + d*x)^(19/6)),x]","\frac{6 b (a+b x)^{5/6} \left(\frac{b (c+d x)}{b c-a d}\right)^{7/6} \, _2F_1\left(\frac{5}{6},\frac{19}{6};\frac{11}{6};\frac{d (a+b x)}{a d-b c}\right)}{5 (c+d x)^{7/6} (b c-a d)^2}","\frac{6 b^2 (a+b x)^{5/6} \sqrt[6]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{5}{6},\frac{19}{6};\frac{11}{6};-\frac{d (a+b x)}{b c-a d}\right)}{5 \sqrt[6]{c+d x} (b c-a d)^3}",1,"(6*b*(a + b*x)^(5/6)*((b*(c + d*x))/(b*c - a*d))^(7/6)*Hypergeometric2F1[5/6, 19/6, 11/6, (d*(a + b*x))/(-(b*c) + a*d)])/(5*(b*c - a*d)^2*(c + d*x)^(7/6))","A",1
1818,1,71,82,0.0876116,"\int \frac{(c+d x)^{13/6}}{(a+b x)^{5/6}} \, dx","Integrate[(c + d*x)^(13/6)/(a + b*x)^(5/6),x]","\frac{6 \sqrt[6]{a+b x} (c+d x)^{13/6} \, _2F_1\left(-\frac{13}{6},\frac{1}{6};\frac{7}{6};\frac{d (a+b x)}{a d-b c}\right)}{b \left(\frac{b (c+d x)}{b c-a d}\right)^{13/6}}","\frac{6 \sqrt[6]{a+b x} \sqrt[6]{c+d x} (b c-a d)^2 \, _2F_1\left(-\frac{13}{6},\frac{1}{6};\frac{7}{6};-\frac{d (a+b x)}{b c-a d}\right)}{b^3 \sqrt[6]{\frac{b (c+d x)}{b c-a d}}}",1,"(6*(a + b*x)^(1/6)*(c + d*x)^(13/6)*Hypergeometric2F1[-13/6, 1/6, 7/6, (d*(a + b*x))/(-(b*c) + a*d)])/(b*((b*(c + d*x))/(b*c - a*d))^(13/6))","A",1
1819,1,71,80,0.0457278,"\int \frac{(c+d x)^{7/6}}{(a+b x)^{5/6}} \, dx","Integrate[(c + d*x)^(7/6)/(a + b*x)^(5/6),x]","\frac{6 \sqrt[6]{a+b x} (c+d x)^{7/6} \, _2F_1\left(-\frac{7}{6},\frac{1}{6};\frac{7}{6};\frac{d (a+b x)}{a d-b c}\right)}{b \left(\frac{b (c+d x)}{b c-a d}\right)^{7/6}}","\frac{6 \sqrt[6]{a+b x} \sqrt[6]{c+d x} (b c-a d) \, _2F_1\left(-\frac{7}{6},\frac{1}{6};\frac{7}{6};-\frac{d (a+b x)}{b c-a d}\right)}{b^2 \sqrt[6]{\frac{b (c+d x)}{b c-a d}}}",1,"(6*(a + b*x)^(1/6)*(c + d*x)^(7/6)*Hypergeometric2F1[-7/6, 1/6, 7/6, (d*(a + b*x))/(-(b*c) + a*d)])/(b*((b*(c + d*x))/(b*c - a*d))^(7/6))","A",1
1820,1,71,72,0.0310635,"\int \frac{\sqrt[6]{c+d x}}{(a+b x)^{5/6}} \, dx","Integrate[(c + d*x)^(1/6)/(a + b*x)^(5/6),x]","\frac{6 \sqrt[6]{a+b x} \sqrt[6]{c+d x} \, _2F_1\left(-\frac{1}{6},\frac{1}{6};\frac{7}{6};\frac{d (a+b x)}{a d-b c}\right)}{b \sqrt[6]{\frac{b (c+d x)}{b c-a d}}}","\frac{6 \sqrt[6]{a+b x} \sqrt[6]{c+d x} \, _2F_1\left(-\frac{1}{6},\frac{1}{6};\frac{7}{6};-\frac{d (a+b x)}{b c-a d}\right)}{b \sqrt[6]{\frac{b (c+d x)}{b c-a d}}}",1,"(6*(a + b*x)^(1/6)*(c + d*x)^(1/6)*Hypergeometric2F1[-1/6, 1/6, 7/6, (d*(a + b*x))/(-(b*c) + a*d)])/(b*((b*(c + d*x))/(b*c - a*d))^(1/6))","A",1
1821,1,71,72,0.0377332,"\int \frac{1}{(a+b x)^{5/6} (c+d x)^{5/6}} \, dx","Integrate[1/((a + b*x)^(5/6)*(c + d*x)^(5/6)),x]","\frac{6 \sqrt[6]{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6} \, _2F_1\left(\frac{1}{6},\frac{5}{6};\frac{7}{6};\frac{d (a+b x)}{a d-b c}\right)}{b (c+d x)^{5/6}}","\frac{6 \sqrt[6]{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6} \, _2F_1\left(\frac{1}{6},\frac{5}{6};\frac{7}{6};-\frac{d (a+b x)}{b c-a d}\right)}{b (c+d x)^{5/6}}",1,"(6*(a + b*x)^(1/6)*((b*(c + d*x))/(b*c - a*d))^(5/6)*Hypergeometric2F1[1/6, 5/6, 7/6, (d*(a + b*x))/(-(b*c) + a*d)])/(b*(c + d*x)^(5/6))","A",1
1822,1,71,79,0.057837,"\int \frac{1}{(a+b x)^{5/6} (c+d x)^{11/6}} \, dx","Integrate[1/((a + b*x)^(5/6)*(c + d*x)^(11/6)),x]","\frac{6 \sqrt[6]{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{11/6} \, _2F_1\left(\frac{1}{6},\frac{11}{6};\frac{7}{6};\frac{d (a+b x)}{a d-b c}\right)}{b (c+d x)^{11/6}}","\frac{6 \sqrt[6]{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6} \, _2F_1\left(\frac{1}{6},\frac{11}{6};\frac{7}{6};-\frac{d (a+b x)}{b c-a d}\right)}{(c+d x)^{5/6} (b c-a d)}",1,"(6*(a + b*x)^(1/6)*((b*(c + d*x))/(b*c - a*d))^(11/6)*Hypergeometric2F1[1/6, 11/6, 7/6, (d*(a + b*x))/(-(b*c) + a*d)])/(b*(c + d*x)^(11/6))","A",1
1823,1,79,80,0.040057,"\int \frac{1}{(a+b x)^{5/6} (c+d x)^{17/6}} \, dx","Integrate[1/((a + b*x)^(5/6)*(c + d*x)^(17/6)),x]","\frac{6 b \sqrt[6]{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6} \, _2F_1\left(\frac{1}{6},\frac{17}{6};\frac{7}{6};\frac{d (a+b x)}{a d-b c}\right)}{(c+d x)^{5/6} (b c-a d)^2}","\frac{6 b \sqrt[6]{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6} \, _2F_1\left(\frac{1}{6},\frac{17}{6};\frac{7}{6};-\frac{d (a+b x)}{b c-a d}\right)}{(c+d x)^{5/6} (b c-a d)^2}",1,"(6*b*(a + b*x)^(1/6)*((b*(c + d*x))/(b*c - a*d))^(5/6)*Hypergeometric2F1[1/6, 17/6, 7/6, (d*(a + b*x))/(-(b*c) + a*d)])/((b*c - a*d)^2*(c + d*x)^(5/6))","A",1
1824,1,71,424,0.0558923,"\int \frac{(c+d x)^{11/6}}{(a+b x)^{5/6}} \, dx","Integrate[(c + d*x)^(11/6)/(a + b*x)^(5/6),x]","\frac{6 \sqrt[6]{a+b x} (c+d x)^{11/6} \, _2F_1\left(-\frac{11}{6},\frac{1}{6};\frac{7}{6};\frac{d (a+b x)}{a d-b c}\right)}{b \left(\frac{b (c+d x)}{b c-a d}\right)^{11/6}}","-\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,"(6*(a + b*x)^(1/6)*(c + d*x)^(11/6)*Hypergeometric2F1[-11/6, 1/6, 7/6, (d*(a + b*x))/(-(b*c) + a*d)])/(b*((b*(c + d*x))/(b*c - a*d))^(11/6))","C",1
1825,1,71,378,0.0342611,"\int \frac{(c+d x)^{5/6}}{(a+b x)^{5/6}} \, dx","Integrate[(c + d*x)^(5/6)/(a + b*x)^(5/6),x]","\frac{6 \sqrt[6]{a+b x} (c+d x)^{5/6} \, _2F_1\left(-\frac{5}{6},\frac{1}{6};\frac{7}{6};\frac{d (a+b x)}{a d-b c}\right)}{b \left(\frac{b (c+d x)}{b c-a d}\right)^{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 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,"(6*(a + b*x)^(1/6)*(c + d*x)^(5/6)*Hypergeometric2F1[-5/6, 1/6, 7/6, (d*(a + b*x))/(-(b*c) + a*d)])/(b*((b*(c + d*x))/(b*c - a*d))^(5/6))","C",1
1826,1,71,309,0.0420828,"\int \frac{1}{(a+b x)^{5/6} \sqrt[6]{c+d x}} \, dx","Integrate[1/((a + b*x)^(5/6)*(c + d*x)^(1/6)),x]","\frac{6 \sqrt[6]{a+b x} \sqrt[6]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{1}{6},\frac{1}{6};\frac{7}{6};\frac{d (a+b x)}{a d-b c}\right)}{b \sqrt[6]{c+d x}}","-\frac{\log \left(-\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{2 b^{5/6} \sqrt[6]{d}}+\frac{\log \left(\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{2 b^{5/6} \sqrt[6]{d}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{b^{5/6} \sqrt[6]{d}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}+\frac{1}{\sqrt{3}}\right)}{b^{5/6} \sqrt[6]{d}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{b^{5/6} \sqrt[6]{d}}",1,"(6*(a + b*x)^(1/6)*((b*(c + d*x))/(b*c - a*d))^(1/6)*Hypergeometric2F1[1/6, 1/6, 7/6, (d*(a + b*x))/(-(b*c) + a*d)])/(b*(c + d*x)^(1/6))","C",1
1827,1,30,30,0.0098742,"\int \frac{1}{(a+b x)^{5/6} (c+d x)^{7/6}} \, dx","Integrate[1/((a + b*x)^(5/6)*(c + d*x)^(7/6)),x]","\frac{6 \sqrt[6]{a+b x}}{\sqrt[6]{c+d x} (b c-a d)}","\frac{6 \sqrt[6]{a+b x}}{\sqrt[6]{c+d x} (b c-a d)}",1,"(6*(a + b*x)^(1/6))/((b*c - a*d)*(c + d*x)^(1/6))","A",1
1828,1,46,66,0.0163025,"\int \frac{1}{(a+b x)^{5/6} (c+d x)^{13/6}} \, dx","Integrate[1/((a + b*x)^(5/6)*(c + d*x)^(13/6)),x]","\frac{6 \sqrt[6]{a+b x} (-a d+7 b c+6 b d x)}{7 (c+d x)^{7/6} (b c-a d)^2}","\frac{36 b \sqrt[6]{a+b x}}{7 \sqrt[6]{c+d x} (b c-a d)^2}+\frac{6 \sqrt[6]{a+b x}}{7 (c+d x)^{7/6} (b c-a d)}",1,"(6*(a + b*x)^(1/6)*(7*b*c - a*d + 6*b*d*x))/(7*(b*c - a*d)^2*(c + d*x)^(7/6))","A",1
1829,1,77,101,0.0360983,"\int \frac{1}{(a+b x)^{5/6} (c+d x)^{19/6}} \, dx","Integrate[1/((a + b*x)^(5/6)*(c + d*x)^(19/6)),x]","\frac{6 \sqrt[6]{a+b x} \left(7 a^2 d^2-2 a b d (13 c+6 d x)+b^2 \left(91 c^2+156 c d x+72 d^2 x^2\right)\right)}{91 (c+d x)^{13/6} (b c-a d)^3}","\frac{432 b^2 \sqrt[6]{a+b x}}{91 \sqrt[6]{c+d x} (b c-a d)^3}+\frac{72 b \sqrt[6]{a+b x}}{91 (c+d x)^{7/6} (b c-a d)^2}+\frac{6 \sqrt[6]{a+b x}}{13 (c+d x)^{13/6} (b c-a d)}",1,"(6*(a + b*x)^(1/6)*(7*a^2*d^2 - 2*a*b*d*(13*c + 6*d*x) + b^2*(91*c^2 + 156*c*d*x + 72*d^2*x^2)))/(91*(b*c - a*d)^3*(c + d*x)^(13/6))","A",1
1830,1,118,136,0.0602228,"\int \frac{1}{(a+b x)^{5/6} (c+d x)^{25/6}} \, dx","Integrate[1/((a + b*x)^(5/6)*(c + d*x)^(25/6)),x]","\frac{6 \sqrt[6]{a+b x} \left(-91 a^3 d^3+21 a^2 b d^2 (19 c+6 d x)-3 a b^2 d \left(247 c^2+228 c d x+72 d^2 x^2\right)+b^3 \left(1729 c^3+4446 c^2 d x+4104 c d^2 x^2+1296 d^3 x^3\right)\right)}{1729 (c+d x)^{19/6} (b c-a d)^4}","\frac{7776 b^3 \sqrt[6]{a+b x}}{1729 \sqrt[6]{c+d x} (b c-a d)^4}+\frac{1296 b^2 \sqrt[6]{a+b x}}{1729 (c+d x)^{7/6} (b c-a d)^3}+\frac{108 b \sqrt[6]{a+b x}}{247 (c+d x)^{13/6} (b c-a d)^2}+\frac{6 \sqrt[6]{a+b x}}{19 (c+d x)^{19/6} (b c-a d)}",1,"(6*(a + b*x)^(1/6)*(-91*a^3*d^3 + 21*a^2*b*d^2*(19*c + 6*d*x) - 3*a*b^2*d*(247*c^2 + 228*c*d*x + 72*d^2*x^2) + b^3*(1729*c^3 + 4446*c^2*d*x + 4104*c*d^2*x^2 + 1296*d^3*x^3)))/(1729*(b*c - a*d)^4*(c + d*x)^(19/6))","A",1
1831,1,71,449,0.078912,"\int \frac{(c+d x)^{13/6}}{(a+b x)^{7/6}} \, dx","Integrate[(c + d*x)^(13/6)/(a + b*x)^(7/6),x]","-\frac{6 (c+d x)^{13/6} \, _2F_1\left(-\frac{13}{6},-\frac{1}{6};\frac{5}{6};\frac{d (a+b x)}{a d-b c}\right)}{b \sqrt[6]{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{13/6}}","-\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 \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,"(-6*(c + d*x)^(13/6)*Hypergeometric2F1[-13/6, -1/6, 5/6, (d*(a + b*x))/(-(b*c) + a*d)])/(b*(a + b*x)^(1/6)*((b*(c + d*x))/(b*c - a*d))^(13/6))","C",1
1832,1,71,403,0.0550127,"\int \frac{(c+d x)^{7/6}}{(a+b x)^{7/6}} \, dx","Integrate[(c + d*x)^(7/6)/(a + b*x)^(7/6),x]","-\frac{6 (c+d x)^{7/6} \, _2F_1\left(-\frac{7}{6},-\frac{1}{6};\frac{5}{6};\frac{d (a+b x)}{a d-b c}\right)}{b \sqrt[6]{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{7/6}}","-\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) \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,"(-6*(c + d*x)^(7/6)*Hypergeometric2F1[-7/6, -1/6, 5/6, (d*(a + b*x))/(-(b*c) + a*d)])/(b*(a + b*x)^(1/6)*((b*(c + d*x))/(b*c - a*d))^(7/6))","C",1
1833,1,71,332,0.0308885,"\int \frac{\sqrt[6]{c+d x}}{(a+b x)^{7/6}} \, dx","Integrate[(c + d*x)^(1/6)/(a + b*x)^(7/6),x]","-\frac{6 \sqrt[6]{c+d x} \, _2F_1\left(-\frac{1}{6},-\frac{1}{6};\frac{5}{6};\frac{d (a+b x)}{a d-b c}\right)}{b \sqrt[6]{a+b x} \sqrt[6]{\frac{b (c+d x)}{b c-a d}}}","-\frac{\sqrt[6]{d} \log \left(-\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{2 b^{7/6}}+\frac{\sqrt[6]{d} \log \left(\frac{\sqrt[6]{b} \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{c+d x}}+\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{c+d x}}+\sqrt[3]{b}\right)}{2 b^{7/6}}+\frac{\sqrt{3} \sqrt[6]{d} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{b^{7/6}}-\frac{\sqrt{3} \sqrt[6]{d} \tan ^{-1}\left(\frac{2 \sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt{3} \sqrt[6]{b} \sqrt[6]{c+d x}}+\frac{1}{\sqrt{3}}\right)}{b^{7/6}}+\frac{2 \sqrt[6]{d} \tanh ^{-1}\left(\frac{\sqrt[6]{d} \sqrt[6]{a+b x}}{\sqrt[6]{b} \sqrt[6]{c+d x}}\right)}{b^{7/6}}-\frac{6 \sqrt[6]{c+d x}}{b \sqrt[6]{a+b x}}",1,"(-6*(c + d*x)^(1/6)*Hypergeometric2F1[-1/6, -1/6, 5/6, (d*(a + b*x))/(-(b*c) + a*d)])/(b*(a + b*x)^(1/6)*((b*(c + d*x))/(b*c - a*d))^(1/6))","C",1
1834,1,30,30,0.0103127,"\int \frac{1}{(a+b x)^{7/6} (c+d x)^{5/6}} \, dx","Integrate[1/((a + b*x)^(7/6)*(c + d*x)^(5/6)),x]","\frac{6 \sqrt[6]{c+d x}}{\sqrt[6]{a+b x} (a d-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))/((-(b*c) + a*d)*(a + b*x)^(1/6))","A",1
1835,1,45,64,0.0270372,"\int \frac{1}{(a+b x)^{7/6} (c+d x)^{11/6}} \, dx","Integrate[1/((a + b*x)^(7/6)*(c + d*x)^(11/6)),x]","-\frac{6 (a d+5 b c+6 b d x)}{5 \sqrt[6]{a+b x} (c+d x)^{5/6} (b c-a d)^2}","-\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*(5*b*c + a*d + 6*b*d*x))/(5*(b*c - a*d)^2*(a + b*x)^(1/6)*(c + d*x)^(5/6))","A",1
1836,1,77,98,0.0401376,"\int \frac{1}{(a+b x)^{7/6} (c+d x)^{17/6}} \, dx","Integrate[1/((a + b*x)^(7/6)*(c + d*x)^(17/6)),x]","-\frac{6 \left(-5 a^2 d^2+2 a b d (11 c+6 d x)+b^2 \left(55 c^2+132 c d x+72 d^2 x^2\right)\right)}{55 \sqrt[6]{a+b x} (c+d x)^{11/6} (b c-a d)^3}","-\frac{432 b d (a+b x)^{5/6}}{55 (c+d x)^{5/6} (b c-a d)^3}-\frac{72 d (a+b x)^{5/6}}{11 (c+d x)^{11/6} (b c-a d)^2}-\frac{6}{\sqrt[6]{a+b x} (c+d x)^{11/6} (b c-a d)}",1,"(-6*(-5*a^2*d^2 + 2*a*b*d*(11*c + 6*d*x) + b^2*(55*c^2 + 132*c*d*x + 72*d^2*x^2)))/(55*(b*c - a*d)^3*(a + b*x)^(1/6)*(c + d*x)^(11/6))","A",1
1837,1,118,134,0.0633071,"\int \frac{1}{(a+b x)^{7/6} (c+d x)^{23/6}} \, dx","Integrate[1/((a + b*x)^(7/6)*(c + d*x)^(23/6)),x]","-\frac{6 \left(55 a^3 d^3-15 a^2 b d^2 (17 c+6 d x)+3 a b^2 d \left(187 c^2+204 c d x+72 d^2 x^2\right)+b^3 \left(935 c^3+3366 c^2 d x+3672 c d^2 x^2+1296 d^3 x^3\right)\right)}{935 \sqrt[6]{a+b x} (c+d x)^{17/6} (b c-a d)^4}","-\frac{7776 b^2 d (a+b x)^{5/6}}{935 (c+d x)^{5/6} (b c-a d)^4}-\frac{1296 b d (a+b x)^{5/6}}{187 (c+d x)^{11/6} (b c-a d)^3}-\frac{108 d (a+b x)^{5/6}}{17 (c+d x)^{17/6} (b c-a d)^2}-\frac{6}{\sqrt[6]{a+b x} (c+d x)^{17/6} (b c-a d)}",1,"(-6*(55*a^3*d^3 - 15*a^2*b*d^2*(17*c + 6*d*x) + 3*a*b^2*d*(187*c^2 + 204*c*d*x + 72*d^2*x^2) + b^3*(935*c^3 + 3366*c^2*d*x + 3672*c*d^2*x^2 + 1296*d^3*x^3)))/(935*(b*c - a*d)^4*(a + b*x)^(1/6)*(c + d*x)^(17/6))","A",1
1838,1,71,80,0.0645713,"\int \frac{(c+d x)^{11/6}}{(a+b x)^{7/6}} \, dx","Integrate[(c + d*x)^(11/6)/(a + b*x)^(7/6),x]","-\frac{6 (c+d x)^{11/6} \, _2F_1\left(-\frac{11}{6},-\frac{1}{6};\frac{5}{6};\frac{d (a+b x)}{a d-b c}\right)}{b \sqrt[6]{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{11/6}}","-\frac{6 (c+d x)^{5/6} (b c-a d) \, _2F_1\left(-\frac{11}{6},-\frac{1}{6};\frac{5}{6};-\frac{d (a+b x)}{b c-a d}\right)}{b^2 \sqrt[6]{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6}}",1,"(-6*(c + d*x)^(11/6)*Hypergeometric2F1[-11/6, -1/6, 5/6, (d*(a + b*x))/(-(b*c) + a*d)])/(b*(a + b*x)^(1/6)*((b*(c + d*x))/(b*c - a*d))^(11/6))","A",1
1839,1,71,72,0.0292238,"\int \frac{(c+d x)^{5/6}}{(a+b x)^{7/6}} \, dx","Integrate[(c + d*x)^(5/6)/(a + b*x)^(7/6),x]","-\frac{6 (c+d x)^{5/6} \, _2F_1\left(-\frac{5}{6},-\frac{1}{6};\frac{5}{6};\frac{d (a+b x)}{a d-b c}\right)}{b \sqrt[6]{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6}}","-\frac{6 (c+d x)^{5/6} \, _2F_1\left(-\frac{5}{6},-\frac{1}{6};\frac{5}{6};-\frac{d (a+b x)}{b c-a d}\right)}{b \sqrt[6]{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/6}}",1,"(-6*(c + d*x)^(5/6)*Hypergeometric2F1[-5/6, -1/6, 5/6, (d*(a + b*x))/(-(b*c) + a*d)])/(b*(a + b*x)^(1/6)*((b*(c + d*x))/(b*c - a*d))^(5/6))","A",1
1840,1,71,72,0.0275856,"\int \frac{1}{(a+b x)^{7/6} \sqrt[6]{c+d x}} \, dx","Integrate[1/((a + b*x)^(7/6)*(c + d*x)^(1/6)),x]","-\frac{6 \sqrt[6]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(-\frac{1}{6},\frac{1}{6};\frac{5}{6};\frac{d (a+b x)}{a d-b c}\right)}{b \sqrt[6]{a+b x} \sqrt[6]{c+d x}}","-\frac{6 \sqrt[6]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(-\frac{1}{6},\frac{1}{6};\frac{5}{6};-\frac{d (a+b x)}{b c-a d}\right)}{b \sqrt[6]{a+b x} \sqrt[6]{c+d x}}",1,"(-6*((b*(c + d*x))/(b*c - a*d))^(1/6)*Hypergeometric2F1[-1/6, 1/6, 5/6, (d*(a + b*x))/(-(b*c) + a*d)])/(b*(a + b*x)^(1/6)*(c + d*x)^(1/6))","A",1
1841,1,71,79,0.0460781,"\int \frac{1}{(a+b x)^{7/6} (c+d x)^{7/6}} \, dx","Integrate[1/((a + b*x)^(7/6)*(c + d*x)^(7/6)),x]","-\frac{6 \left(\frac{b (c+d x)}{b c-a d}\right)^{7/6} \, _2F_1\left(-\frac{1}{6},\frac{7}{6};\frac{5}{6};\frac{d (a+b x)}{a d-b c}\right)}{b \sqrt[6]{a+b x} (c+d x)^{7/6}}","-\frac{6 \sqrt[6]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(-\frac{1}{6},\frac{7}{6};\frac{5}{6};-\frac{d (a+b x)}{b c-a d}\right)}{\sqrt[6]{a+b x} \sqrt[6]{c+d x} (b c-a d)}",1,"(-6*((b*(c + d*x))/(b*c - a*d))^(7/6)*Hypergeometric2F1[-1/6, 7/6, 5/6, (d*(a + b*x))/(-(b*c) + a*d)])/(b*(a + b*x)^(1/6)*(c + d*x)^(7/6))","A",1
1842,1,71,80,0.0593956,"\int \frac{1}{(a+b x)^{7/6} (c+d x)^{13/6}} \, dx","Integrate[1/((a + b*x)^(7/6)*(c + d*x)^(13/6)),x]","-\frac{6 \left(\frac{b (c+d x)}{b c-a d}\right)^{13/6} \, _2F_1\left(-\frac{1}{6},\frac{13}{6};\frac{5}{6};\frac{d (a+b x)}{a d-b c}\right)}{b \sqrt[6]{a+b x} (c+d x)^{13/6}}","-\frac{6 b \sqrt[6]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(-\frac{1}{6},\frac{13}{6};\frac{5}{6};-\frac{d (a+b x)}{b c-a d}\right)}{\sqrt[6]{a+b x} \sqrt[6]{c+d x} (b c-a d)^2}",1,"(-6*((b*(c + d*x))/(b*c - a*d))^(13/6)*Hypergeometric2F1[-1/6, 13/6, 5/6, (d*(a + b*x))/(-(b*c) + a*d)])/(b*(a + b*x)^(1/6)*(c + d*x)^(13/6))","A",1
1843,1,79,82,0.0515934,"\int \frac{1}{(a+b x)^{7/6} (c+d x)^{19/6}} \, dx","Integrate[1/((a + b*x)^(7/6)*(c + d*x)^(19/6)),x]","-\frac{6 b \left(\frac{b (c+d x)}{b c-a d}\right)^{7/6} \, _2F_1\left(-\frac{1}{6},\frac{19}{6};\frac{5}{6};\frac{d (a+b x)}{a d-b c}\right)}{\sqrt[6]{a+b x} (c+d x)^{7/6} (b c-a d)^2}","-\frac{6 b^2 \sqrt[6]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(-\frac{1}{6},\frac{19}{6};\frac{5}{6};-\frac{d (a+b x)}{b c-a d}\right)}{\sqrt[6]{a+b x} \sqrt[6]{c+d x} (b c-a d)^3}",1,"(-6*b*((b*(c + d*x))/(b*c - a*d))^(7/6)*Hypergeometric2F1[-1/6, 19/6, 5/6, (d*(a + b*x))/(-(b*c) + a*d)])/((b*c - a*d)^2*(a + b*x)^(1/6)*(c + d*x)^(7/6))","A",1
1844,1,11,11,0.0125041,"\int (a+b x)^m (a+b (2+m) x) \, dx","Integrate[(a + b*x)^m*(a + b*(2 + m)*x),x]","x (a+b x)^{m+1}","x (a+b x)^{m+1}",1,"x*(a + b*x)^(1 + m)","A",1
1845,1,73,61,0.0366288,"\int (a+b x)^m (c+d x)^n \, dx","Integrate[(a + b*x)^m*(c + d*x)^n,x]","\frac{(a+b x)^{m+1} (c+d x)^n \left(\frac{b (c+d x)}{b c-a d}\right)^{-n} \, _2F_1\left(m+1,-n;m+2;\frac{d (a+b x)}{a d-b c}\right)}{b (m+1)}","-\frac{(a+b x)^{m+1} (c+d x)^{n+1} \, _2F_1\left(1,m+n+2;n+2;\frac{b (c+d x)}{b c-a d}\right)}{(n+1) (b c-a d)}",1,"((a + b*x)^(1 + m)*(c + d*x)^n*Hypergeometric2F1[1 + m, -n, 2 + m, (d*(a + b*x))/(-(b*c) + a*d)])/(b*(1 + m)*((b*(c + d*x))/(b*c - a*d))^n)","A",1
1846,1,94,110,0.1073941,"\int (a+b x)^m (c+d x)^3 \, dx","Integrate[(a + b*x)^m*(c + d*x)^3,x]","\frac{(a+b x)^{m+1} \left(\frac{3 d^2 (a+b x)^2 (b c-a d)}{m+3}+\frac{3 d (a+b x) (b c-a d)^2}{m+2}+\frac{(b c-a d)^3}{m+1}+\frac{d^3 (a+b x)^3}{m+4}\right)}{b^4}","\frac{3 d^2 (b c-a d) (a+b x)^{m+3}}{b^4 (m+3)}+\frac{(b c-a d)^3 (a+b x)^{m+1}}{b^4 (m+1)}+\frac{3 d (b c-a d)^2 (a+b x)^{m+2}}{b^4 (m+2)}+\frac{d^3 (a+b x)^{m+4}}{b^4 (m+4)}",1,"((a + b*x)^(1 + m)*((b*c - a*d)^3/(1 + m) + (3*d*(b*c - a*d)^2*(a + b*x))/(2 + m) + (3*d^2*(b*c - a*d)*(a + b*x)^2)/(3 + m) + (d^3*(a + b*x)^3)/(4 + m)))/b^4","A",1
1847,1,67,78,0.0958725,"\int (a+b x)^m (c+d x)^2 \, dx","Integrate[(a + b*x)^m*(c + d*x)^2,x]","\frac{(a+b x)^{m+1} \left(\frac{2 d (a+b x) (b c-a d)}{m+2}+\frac{(b c-a d)^2}{m+1}+\frac{d^2 (a+b x)^2}{m+3}\right)}{b^3}","\frac{(b c-a d)^2 (a+b x)^{m+1}}{b^3 (m+1)}+\frac{2 d (b c-a d) (a+b x)^{m+2}}{b^3 (m+2)}+\frac{d^2 (a+b x)^{m+3}}{b^3 (m+3)}",1,"((a + b*x)^(1 + m)*((b*c - a*d)^2/(1 + m) + (2*d*(b*c - a*d)*(a + b*x))/(2 + m) + (d^2*(a + b*x)^2)/(3 + m)))/b^3","A",1
1848,1,41,46,0.0330764,"\int (a+b x)^m (c+d x) \, dx","Integrate[(a + b*x)^m*(c + d*x),x]","\frac{(a+b x)^{m+1} (-a d+b c (m+2)+b d (m+1) x)}{b^2 (m+1) (m+2)}","\frac{(b c-a d) (a+b x)^{m+1}}{b^2 (m+1)}+\frac{d (a+b x)^{m+2}}{b^2 (m+2)}",1,"((a + b*x)^(1 + m)*(-(a*d) + b*c*(2 + m) + b*d*(1 + m)*x))/(b^2*(1 + m)*(2 + m))","A",1
1849,1,51,51,0.0117975,"\int \frac{(a+b x)^m}{c+d x} \, dx","Integrate[(a + b*x)^m/(c + d*x),x]","-\frac{(a+b x)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{d (a+b x)}{a d-b c}\right)}{(m+1) (a d-b c)}","\frac{(a+b x)^{m+1} \, _2F_1\left(1,m+1;m+2;-\frac{d (a+b x)}{b c-a d}\right)}{(m+1) (b c-a d)}",1,"-(((a + b*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (d*(a + b*x))/(-(b*c) + a*d)])/((-(b*c) + a*d)*(1 + m)))","A",1
1850,1,52,52,0.0224421,"\int \frac{(a+b x)^m}{(c+d x)^2} \, dx","Integrate[(a + b*x)^m/(c + d*x)^2,x]","\frac{b (a+b x)^{m+1} \, _2F_1\left(2,m+1;m+2;-\frac{d (a+b x)}{b c-a d}\right)}{(m+1) (b c-a d)^2}","\frac{b (a+b x)^{m+1} \, _2F_1\left(2,m+1;m+2;-\frac{d (a+b x)}{b c-a d}\right)}{(m+1) (b c-a d)^2}",1,"(b*(a + b*x)^(1 + m)*Hypergeometric2F1[2, 1 + m, 2 + m, -((d*(a + b*x))/(b*c - a*d))])/((b*c - a*d)^2*(1 + m))","A",1
1851,1,54,54,0.0196806,"\int \frac{(a+b x)^m}{(c+d x)^3} \, dx","Integrate[(a + b*x)^m/(c + d*x)^3,x]","\frac{b^2 (a+b x)^{m+1} \, _2F_1\left(3,m+1;m+2;-\frac{d (a+b x)}{b c-a d}\right)}{(m+1) (b c-a d)^3}","\frac{b^2 (a+b x)^{m+1} \, _2F_1\left(3,m+1;m+2;-\frac{d (a+b x)}{b c-a d}\right)}{(m+1) (b c-a d)^3}",1,"(b^2*(a + b*x)^(1 + m)*Hypergeometric2F1[3, 1 + m, 2 + m, -((d*(a + b*x))/(b*c - a*d))])/((b*c - a*d)^3*(1 + m))","A",1
1852,1,95,111,0.1097338,"\int (a+b x)^3 (c+d x)^n \, dx","Integrate[(a + b*x)^3*(c + d*x)^n,x]","\frac{(c+d x)^{n+1} \left(-\frac{3 b^2 (c+d x)^2 (b c-a d)}{n+3}+\frac{3 b (c+d x) (b c-a d)^2}{n+2}-\frac{(b c-a d)^3}{n+1}+\frac{b^3 (c+d x)^3}{n+4}\right)}{d^4}","-\frac{3 b^2 (b c-a d) (c+d x)^{n+3}}{d^4 (n+3)}-\frac{(b c-a d)^3 (c+d x)^{n+1}}{d^4 (n+1)}+\frac{3 b (b c-a d)^2 (c+d x)^{n+2}}{d^4 (n+2)}+\frac{b^3 (c+d x)^{n+4}}{d^4 (n+4)}",1,"((c + d*x)^(1 + n)*(-((b*c - a*d)^3/(1 + n)) + (3*b*(b*c - a*d)^2*(c + d*x))/(2 + n) - (3*b^2*(b*c - a*d)*(c + d*x)^2)/(3 + n) + (b^3*(c + d*x)^3)/(4 + n)))/d^4","A",1
1853,1,67,78,0.0957979,"\int (a+b x)^2 (c+d x)^n \, dx","Integrate[(a + b*x)^2*(c + d*x)^n,x]","\frac{(c+d x)^{n+1} \left(-\frac{2 b (c+d x) (b c-a d)}{n+2}+\frac{(b c-a d)^2}{n+1}+\frac{b^2 (c+d x)^2}{n+3}\right)}{d^3}","\frac{(b c-a d)^2 (c+d x)^{n+1}}{d^3 (n+1)}-\frac{2 b (b c-a d) (c+d x)^{n+2}}{d^3 (n+2)}+\frac{b^2 (c+d x)^{n+3}}{d^3 (n+3)}",1,"((c + d*x)^(1 + n)*((b*c - a*d)^2/(1 + n) - (2*b*(b*c - a*d)*(c + d*x))/(2 + n) + (b^2*(c + d*x)^2)/(3 + n)))/d^3","A",1
1854,1,41,47,0.0365499,"\int (a+b x) (c+d x)^n \, dx","Integrate[(a + b*x)*(c + d*x)^n,x]","\frac{(c+d x)^{n+1} (a d (n+2)-b c+b d (n+1) x)}{d^2 (n+1) (n+2)}","\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,"((c + d*x)^(1 + n)*(-(b*c) + a*d*(2 + n) + b*d*(1 + n)*x))/(d^2*(1 + n)*(2 + n))","A",1
1855,1,17,18,0.0112119,"\int (c+d x)^n \, dx","Integrate[(c + d*x)^n,x]","\frac{(c+d x)^{n+1}}{d n+d}","\frac{(c+d x)^{n+1}}{d (n+1)}",1,"(c + d*x)^(1 + n)/(d + d*n)","A",1
1856,1,51,51,0.0097237,"\int \frac{(c+d x)^n}{a+b x} \, dx","Integrate[(c + d*x)^n/(a + b*x),x]","-\frac{(c+d x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b (c+d x)}{b c-a d}\right)}{(n+1) (b c-a d)}","-\frac{(c+d x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b (c+d x)}{b c-a d}\right)}{(n+1) (b c-a d)}",1,"-(((c + d*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (b*(c + d*x))/(b*c - a*d)])/((b*c - a*d)*(1 + n)))","A",1
1857,1,52,51,0.0217017,"\int \frac{(c+d x)^n}{(a+b x)^2} \, dx","Integrate[(c + d*x)^n/(a + b*x)^2,x]","\frac{d (c+d x)^{n+1} \, _2F_1\left(2,n+1;n+2;-\frac{b (c+d x)}{a d-b c}\right)}{(n+1) (a d-b c)^2}","\frac{d (c+d x)^{n+1} \, _2F_1\left(2,n+1;n+2;\frac{b (c+d x)}{b c-a d}\right)}{(n+1) (b c-a d)^2}",1,"(d*(c + d*x)^(1 + n)*Hypergeometric2F1[2, 1 + n, 2 + n, -((b*(c + d*x))/(-(b*c) + a*d))])/((-(b*c) + a*d)^2*(1 + n))","A",1
1858,1,54,54,0.0195388,"\int \frac{(c+d x)^n}{(a+b x)^3} \, dx","Integrate[(c + d*x)^n/(a + b*x)^3,x]","\frac{d^2 (c+d x)^{n+1} \, _2F_1\left(3,n+1;n+2;-\frac{b (c+d x)}{a d-b c}\right)}{(n+1) (a d-b c)^3}","-\frac{d^2 (c+d x)^{n+1} \, _2F_1\left(3,n+1;n+2;\frac{b (c+d x)}{b c-a d}\right)}{(n+1) (b c-a d)^3}",1,"(d^2*(c + d*x)^(1 + n)*Hypergeometric2F1[3, 1 + n, 2 + n, -((b*(c + d*x))/(-(b*c) + a*d))])/((-(b*c) + a*d)^3*(1 + n))","A",1
1859,1,112,143,0.0966196,"\int (a+b x)^{-4+n} (c+d x)^{-n} \, dx","Integrate[(a + b*x)^(-4 + n)/(c + d*x)^n,x]","\frac{(a+b x)^{n-3} (c+d x)^{1-n} \left(a^2 d^2 \left(n^2-5 n+6\right)-2 a b d (n-3) (c (n-1)+d x)+b^2 \left(c^2 \left(n^2-3 n+2\right)+2 c d (n-1) x+2 d^2 x^2\right)\right)}{(n-3) (n-2) (n-1) (b c-a d)^3}","-\frac{2 d^2 (a+b x)^{n-1} (c+d x)^{1-n}}{(1-n) (2-n) (3-n) (b c-a d)^3}-\frac{(a+b x)^{n-3} (c+d x)^{1-n}}{(3-n) (b c-a d)}+\frac{2 d (a+b x)^{n-2} (c+d x)^{1-n}}{(2-n) (3-n) (b c-a d)^2}",1,"((a + b*x)^(-3 + n)*(c + d*x)^(1 - n)*(a^2*d^2*(6 - 5*n + n^2) - 2*a*b*d*(-3 + n)*(c*(-1 + n) + d*x) + b^2*(c^2*(2 - 3*n + n^2) + 2*c*d*(-1 + n)*x + 2*d^2*x^2)))/((b*c - a*d)^3*(-3 + n)*(-2 + n)*(-1 + n))","A",1
1860,1,59,86,0.0394753,"\int (a+b x)^{-3+n} (c+d x)^{-n} \, dx","Integrate[(a + b*x)^(-3 + n)/(c + d*x)^n,x]","\frac{(a+b x)^{n-2} (c+d x)^{1-n} (-a d (n-2)+b c (n-1)+b d x)}{(n-2) (n-1) (b c-a d)^2}","\frac{d (a+b x)^{n-1} (c+d x)^{1-n}}{(1-n) (2-n) (b c-a d)^2}-\frac{(a+b x)^{n-2} (c+d x)^{1-n}}{(2-n) (b c-a d)}",1,"((a + b*x)^(-2 + n)*(c + d*x)^(1 - n)*(-(a*d*(-2 + n)) + b*c*(-1 + n) + b*d*x))/((b*c - a*d)^2*(-2 + n)*(-1 + n))","A",1
1861,1,36,39,0.0168692,"\int (a+b x)^{-2+n} (c+d x)^{-n} \, dx","Integrate[(a + b*x)^(-2 + n)/(c + d*x)^n,x]","\frac{(a+b x)^{n-1} (c+d x)^{1-n}}{(n-1) (b c-a d)}","-\frac{(a+b x)^{n-1} (c+d x)^{1-n}}{(1-n) (b c-a d)}",1,"((a + b*x)^(-1 + n)*(c + d*x)^(1 - n))/((b*c - a*d)*(-1 + n))","A",1
1862,1,65,66,0.0311237,"\int (a+b x)^{-1+n} (c+d x)^{-n} \, dx","Integrate[(a + b*x)^(-1 + n)/(c + d*x)^n,x]","\frac{(a+b x)^n (c+d x)^{-n} \left(\frac{b (c+d x)}{b c-a d}\right)^n \, _2F_1\left(n,n;n+1;\frac{d (a+b x)}{a d-b c}\right)}{b n}","\frac{(a+b x)^n (c+d x)^{-n} \left(\frac{b (c+d x)}{b c-a d}\right)^n \, _2F_1\left(n,n;n+1;-\frac{d (a+b x)}{b c-a d}\right)}{b n}",1,"((a + b*x)^n*((b*(c + d*x))/(b*c - a*d))^n*Hypergeometric2F1[n, n, 1 + n, (d*(a + b*x))/(-(b*c) + a*d)])/(b*n*(c + d*x)^n)","A",1
1863,1,71,72,0.0275799,"\int (a+b x)^n (c+d x)^{-n} \, dx","Integrate[(a + b*x)^n/(c + d*x)^n,x]","\frac{(a+b x)^{n+1} (c+d x)^{-n} \left(\frac{b (c+d x)}{b c-a d}\right)^n \, _2F_1\left(n,n+1;n+2;\frac{d (a+b x)}{a d-b c}\right)}{b (n+1)}","\frac{(a+b x)^{n+1} (c+d x)^{-n} \left(\frac{b (c+d x)}{b c-a d}\right)^n \, _2F_1\left(n,n+1;n+2;-\frac{d (a+b x)}{b c-a d}\right)}{b (n+1)}",1,"((a + b*x)^(1 + n)*((b*(c + d*x))/(b*c - a*d))^n*Hypergeometric2F1[n, 1 + n, 2 + n, (d*(a + b*x))/(-(b*c) + a*d)])/(b*(1 + n)*(c + d*x)^n)","A",1
1864,1,89,72,0.0583587,"\int (a+b x)^{1+n} (c+d x)^{-n} \, dx","Integrate[(a + b*x)^(1 + n)/(c + d*x)^n,x]","\frac{(b c-a d) (a+b x)^n (c+d x)^{1-n} \left(\frac{d (a+b x)}{a d-b c}\right)^{-n} \, _2F_1\left(-n-1,1-n;2-n;\frac{b (c+d x)}{b c-a d}\right)}{d^2 (n-1)}","\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,"((b*c - a*d)*(a + b*x)^n*(c + d*x)^(1 - n)*Hypergeometric2F1[-1 - n, 1 - n, 2 - n, (b*(c + d*x))/(b*c - a*d)])/(d^2*(-1 + n)*((d*(a + b*x))/(-(b*c) + a*d))^n)","A",1
1865,1,92,72,0.0490884,"\int (a+b x)^{2+n} (c+d x)^{-n} \, dx","Integrate[(a + b*x)^(2 + n)/(c + d*x)^n,x]","-\frac{(b c-a d)^2 (a+b x)^n (c+d x)^{1-n} \left(\frac{d (a+b x)}{a d-b c}\right)^{-n} \, _2F_1\left(-n-2,1-n;2-n;\frac{b (c+d x)}{b c-a d}\right)}{d^3 (n-1)}","\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,"-(((b*c - a*d)^2*(a + b*x)^n*(c + d*x)^(1 - n)*Hypergeometric2F1[-2 - n, 1 - n, 2 - n, (b*(c + d*x))/(b*c - a*d)])/(d^3*(-1 + n)*((d*(a + b*x))/(-(b*c) + a*d))^n))","A",1
1866,1,71,72,0.0296566,"\int (a+b x)^{-n} (c+d x)^n \, dx","Integrate[(c + d*x)^n/(a + b*x)^n,x]","\frac{(a+b x)^{-n} (c+d x)^{n+1} \left(\frac{d (a+b x)}{a d-b c}\right)^n \, _2F_1\left(n,n+1;n+2;\frac{b (c+d x)}{b c-a d}\right)}{d (n+1)}","\frac{(a+b x)^{-n} (c+d x)^{n+1} \left(-\frac{d (a+b x)}{b c-a d}\right)^n \, _2F_1\left(n,n+1;n+2;\frac{b (c+d x)}{b c-a d}\right)}{d (n+1)}",1,"(((d*(a + b*x))/(-(b*c) + a*d))^n*(c + d*x)^(1 + n)*Hypergeometric2F1[n, 1 + n, 2 + n, (b*(c + d*x))/(b*c - a*d)])/(d*(1 + n)*(a + b*x)^n)","A",1
1867,1,74,75,0.0298962,"\int (a+b x)^{-1-n} (c+d x)^n \, dx","Integrate[(a + b*x)^(-1 - n)*(c + d*x)^n,x]","-\frac{(a+b x)^{-n} (c+d x)^n \left(\frac{b (c+d x)}{b c-a d}\right)^{-n} \, _2F_1\left(-n,-n;1-n;\frac{d (a+b x)}{a d-b c}\right)}{b n}","-\frac{(a+b x)^{-n} (c+d x)^n \left(\frac{b (c+d x)}{b c-a d}\right)^{-n} \, _2F_1\left(-n,-n;1-n;-\frac{d (a+b x)}{b c-a d}\right)}{b n}",1,"-(((c + d*x)^n*Hypergeometric2F1[-n, -n, 1 - n, (d*(a + b*x))/(-(b*c) + a*d)])/(b*n*(a + b*x)^n*((b*(c + d*x))/(b*c - a*d))^n))","A",1
1868,1,38,37,0.0205026,"\int (a+b x)^{-2-n} (c+d x)^n \, dx","Integrate[(a + b*x)^(-2 - n)*(c + d*x)^n,x]","\frac{(a+b x)^{-n-1} (c+d x)^{n+1}}{(-n-1) (b c-a d)}","-\frac{(a+b x)^{-n-1} (c+d x)^{n+1}}{(n+1) (b c-a d)}",1,"((a + b*x)^(-1 - n)*(c + d*x)^(1 + n))/((b*c - a*d)*(-1 - n))","A",1
1869,1,60,80,0.0330476,"\int (a+b x)^{-3-n} (c+d x)^n \, dx","Integrate[(a + b*x)^(-3 - n)*(c + d*x)^n,x]","\frac{(a+b x)^{-n-2} (c+d x)^{n+1} (a d (n+2)-b (c n+c-d x))}{(n+1) (n+2) (b c-a d)^2}","\frac{d (a+b x)^{-n-1} (c+d x)^{n+1}}{(n+1) (n+2) (b c-a d)^2}-\frac{(a+b x)^{-n-2} (c+d x)^{n+1}}{(n+2) (b c-a d)}",1,"((a + b*x)^(-2 - n)*(c + d*x)^(1 + n)*(a*d*(2 + n) - b*(c + c*n - d*x)))/((b*c - a*d)^2*(1 + n)*(2 + n))","A",1
1870,1,113,131,0.0842871,"\int (a+b x)^{-4-n} (c+d x)^n \, dx","Integrate[(a + b*x)^(-4 - n)*(c + d*x)^n,x]","-\frac{(a+b x)^{-n-3} (c+d x)^{n+1} \left(a^2 d^2 \left(n^2+5 n+6\right)-2 a b d (n+3) (c n+c-d x)+b^2 \left(c^2 \left(n^2+3 n+2\right)-2 c d (n+1) x+2 d^2 x^2\right)\right)}{(n+1) (n+2) (n+3) (b c-a d)^3}","-\frac{2 d^2 (a+b x)^{-n-1} (c+d x)^{n+1}}{(n+1) (n+2) (n+3) (b c-a d)^3}-\frac{(a+b x)^{-n-3} (c+d x)^{n+1}}{(n+3) (b c-a d)}+\frac{2 d (a+b x)^{-n-2} (c+d x)^{n+1}}{(n+2) (n+3) (b c-a d)^2}",1,"-(((a + b*x)^(-3 - n)*(c + d*x)^(1 + n)*(a^2*d^2*(6 + 5*n + n^2) - 2*a*b*d*(3 + n)*(c + c*n - d*x) + b^2*(c^2*(2 + 3*n + n^2) - 2*c*d*(1 + n)*x + 2*d^2*x^2)))/((b*c - a*d)^3*(1 + n)*(2 + n)*(3 + n)))","A",1
1871,1,195,186,0.1239276,"\int (a+b x)^{-5-n} (c+d x)^n \, dx","Integrate[(a + b*x)^(-5 - n)*(c + d*x)^n,x]","\frac{(a+b x)^{-n-4} (c+d x)^{n+1} \left(a^3 d^3 \left(n^3+9 n^2+26 n+24\right)-3 a^2 b d^2 \left(n^2+7 n+12\right) (c n+c-d x)+3 a b^2 d (n+4) \left(c^2 \left(n^2+3 n+2\right)-2 c d (n+1) x+2 d^2 x^2\right)-\left(b^3 \left(c^3 \left(n^3+6 n^2+11 n+6\right)-3 c^2 d \left(n^2+3 n+2\right) x+6 c d^2 (n+1) x^2-6 d^3 x^3\right)\right)\right)}{(n+1) (n+2) (n+3) (n+4) (b c-a d)^4}","\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,"((a + b*x)^(-4 - n)*(c + d*x)^(1 + n)*(a^3*d^3*(24 + 26*n + 9*n^2 + n^3) - 3*a^2*b*d^2*(12 + 7*n + n^2)*(c + c*n - d*x) + 3*a*b^2*d*(4 + n)*(c^2*(2 + 3*n + n^2) - 2*c*d*(1 + n)*x + 2*d^2*x^2) - b^3*(c^3*(6 + 11*n + 6*n^2 + n^3) - 3*c^2*d*(2 + 3*n + n^2)*x + 6*c*d^2*(1 + n)*x^2 - 6*d^3*x^3)))/((b*c - a*d)^4*(1 + n)*(2 + n)*(3 + n)*(4 + n))","A",1
1872,1,71,72,0.0238314,"\int (a+b x)^n (c+d x)^{-n} \, dx","Integrate[(a + b*x)^n/(c + d*x)^n,x]","\frac{(a+b x)^{n+1} (c+d x)^{-n} \left(\frac{b (c+d x)}{b c-a d}\right)^n \, _2F_1\left(n,n+1;n+2;\frac{d (a+b x)}{a d-b c}\right)}{b (n+1)}","\frac{(a+b x)^{n+1} (c+d x)^{-n} \left(\frac{b (c+d x)}{b c-a d}\right)^n \, _2F_1\left(n,n+1;n+2;-\frac{d (a+b x)}{b c-a d}\right)}{b (n+1)}",1,"((a + b*x)^(1 + n)*((b*(c + d*x))/(b*c - a*d))^n*Hypergeometric2F1[n, 1 + n, 2 + n, (d*(a + b*x))/(-(b*c) + a*d)])/(b*(1 + n)*(c + d*x)^n)","A",1
1873,1,74,75,0.0304204,"\int (a+b x)^n (c+d x)^{-1-n} \, dx","Integrate[(a + b*x)^n*(c + d*x)^(-1 - n),x]","-\frac{(a+b x)^n (c+d x)^{-n} \left(\frac{d (a+b x)}{a d-b c}\right)^{-n} \, _2F_1\left(-n,-n;1-n;\frac{b (c+d x)}{b c-a d}\right)}{d n}","-\frac{(a+b x)^n (c+d x)^{-n} \left(-\frac{d (a+b x)}{b c-a d}\right)^{-n} \, _2F_1\left(-n,-n;1-n;\frac{b (c+d x)}{b c-a d}\right)}{d n}",1,"-(((a + b*x)^n*Hypergeometric2F1[-n, -n, 1 - n, (b*(c + d*x))/(b*c - a*d)])/(d*n*((d*(a + b*x))/(-(b*c) + a*d))^n*(c + d*x)^n))","A",1
1874,1,36,36,0.0128381,"\int (a+b x)^n (c+d x)^{-2-n} \, dx","Integrate[(a + b*x)^n*(c + d*x)^(-2 - n),x]","\frac{(a+b x)^{n+1} (c+d x)^{-n-1}}{(n+1) (b c-a d)}","\frac{(a+b x)^{n+1} (c+d x)^{-n-1}}{(n+1) (b c-a d)}",1,"((a + b*x)^(1 + n)*(c + d*x)^(-1 - n))/((b*c - a*d)*(1 + n))","A",1
1875,1,59,79,0.0367813,"\int (a+b x)^n (c+d x)^{-3-n} \, dx","Integrate[(a + b*x)^n*(c + d*x)^(-3 - n),x]","\frac{(a+b x)^{n+1} (c+d x)^{-n-2} (-a d (n+1)+b c (n+2)+b d x)}{(n+1) (n+2) (b c-a d)^2}","\frac{(a+b x)^{n+1} (c+d x)^{-n-2}}{(n+2) (b c-a d)}+\frac{b (a+b x)^{n+1} (c+d x)^{-n-1}}{(n+1) (n+2) (b c-a d)^2}",1,"((a + b*x)^(1 + n)*(c + d*x)^(-2 - n)*(-(a*d*(1 + n)) + b*c*(2 + n) + b*d*x))/((b*c - a*d)^2*(1 + n)*(2 + n))","A",1
1876,1,112,130,0.0922571,"\int (a+b x)^n (c+d x)^{-4-n} \, dx","Integrate[(a + b*x)^n*(c + d*x)^(-4 - n),x]","\frac{(a+b x)^{n+1} (c+d x)^{-n-3} \left(a^2 d^2 \left(n^2+3 n+2\right)-2 a b d (n+1) (c (n+3)+d x)+b^2 \left(c^2 \left(n^2+5 n+6\right)+2 c d (n+3) x+2 d^2 x^2\right)\right)}{(n+1) (n+2) (n+3) (b c-a d)^3}","\frac{2 b^2 (a+b x)^{n+1} (c+d x)^{-n-1}}{(n+1) (n+2) (n+3) (b c-a d)^3}+\frac{(a+b x)^{n+1} (c+d x)^{-n-3}}{(n+3) (b c-a d)}+\frac{2 b (a+b x)^{n+1} (c+d x)^{-n-2}}{(n+2) (n+3) (b c-a d)^2}",1,"((a + b*x)^(1 + n)*(c + d*x)^(-3 - n)*(a^2*d^2*(2 + 3*n + n^2) - 2*a*b*d*(1 + n)*(c*(3 + n) + d*x) + b^2*(c^2*(6 + 5*n + n^2) + 2*c*d*(3 + n)*x + 2*d^2*x^2)))/((b*c - a*d)^3*(1 + n)*(2 + n)*(3 + n))","A",1
1877,1,195,185,0.1291108,"\int (a+b x)^n (c+d x)^{-5-n} \, dx","Integrate[(a + b*x)^n*(c + d*x)^(-5 - n),x]","\frac{(a+b x)^{n+1} (c+d x)^{-n-4} \left(-a^3 d^3 \left(n^3+6 n^2+11 n+6\right)+3 a^2 b d^2 \left(n^2+3 n+2\right) (c (n+4)+d x)-3 a b^2 d (n+1) \left(c^2 \left(n^2+7 n+12\right)+2 c d (n+4) x+2 d^2 x^2\right)+b^3 \left(c^3 \left(n^3+9 n^2+26 n+24\right)+3 c^2 d \left(n^2+7 n+12\right) x+6 c d^2 (n+4) x^2+6 d^3 x^3\right)\right)}{(n+1) (n+2) (n+3) (n+4) (b c-a d)^4}","\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,"((a + b*x)^(1 + n)*(c + d*x)^(-4 - n)*(-(a^3*d^3*(6 + 11*n + 6*n^2 + n^3)) + 3*a^2*b*d^2*(2 + 3*n + n^2)*(c*(4 + n) + d*x) - 3*a*b^2*d*(1 + n)*(c^2*(12 + 7*n + n^2) + 2*c*d*(4 + n)*x + 2*d^2*x^2) + b^3*(c^3*(24 + 26*n + 9*n^2 + n^3) + 3*c^2*d*(12 + 7*n + n^2)*x + 6*c*d^2*(4 + n)*x^2 + 6*d^3*x^3)))/((b*c - a*d)^4*(1 + n)*(2 + n)*(3 + n)*(4 + n))","A",1
1878,1,75,83,0.0590891,"\int (a+b x)^{-2+n} (c+d x)^{1-n} \, dx","Integrate[(a + b*x)^(-2 + n)*(c + d*x)^(1 - n),x]","\frac{(a+b x)^{n-1} (c+d x)^{1-n} \left(\frac{b (c+d x)}{b c-a d}\right)^{n-1} \, _2F_1\left(n-1,n-1;n;\frac{d (a+b x)}{a d-b c}\right)}{b (n-1)}","-\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,"((a + b*x)^(-1 + n)*(c + d*x)^(1 - n)*((b*(c + d*x))/(b*c - a*d))^(-1 + n)*Hypergeometric2F1[-1 + n, -1 + n, n, (d*(a + b*x))/(-(b*c) + a*d)])/(b*(-1 + n))","A",1
1879,1,83,84,0.0504981,"\int (a+b x)^{1+n} (c+d x)^{-1-n} \, dx","Integrate[(a + b*x)^(1 + n)*(c + d*x)^(-1 - n),x]","\frac{(b c-a d) (a+b x)^n (c+d x)^{-n} \left(\frac{d (a+b x)}{a d-b c}\right)^{-n} \, _2F_1\left(-n-1,-n;1-n;\frac{b (c+d x)}{b c-a d}\right)}{d^2 n}","\frac{(b c-a d) (a+b x)^n (c+d x)^{-n} \left(-\frac{d (a+b x)}{b c-a d}\right)^{-n} \, _2F_1\left(-n-1,-n;1-n;\frac{b (c+d x)}{b c-a d}\right)}{d^2 n}",1,"((b*c - a*d)*(a + b*x)^n*Hypergeometric2F1[-1 - n, -n, 1 - n, (b*(c + d*x))/(b*c - a*d)])/(d^2*n*((d*(a + b*x))/(-(b*c) + a*d))^n*(c + d*x)^n)","A",1
1880,1,51,51,0.0191241,"\int (a+b x)^m (c+d x)^{1+2 n-2 (1+n)} \, dx","Integrate[(a + b*x)^m*(c + d*x)^(1 + 2*n - 2*(1 + n)),x]","-\frac{(a+b x)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{d (a+b x)}{a d-b c}\right)}{(m+1) (a d-b c)}","\frac{(a+b x)^{m+1} \, _2F_1\left(1,m+1;m+2;-\frac{d (a+b x)}{b c-a d}\right)}{(m+1) (b c-a d)}",1,"-(((a + b*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (d*(a + b*x))/(-(b*c) + a*d)])/((-(b*c) + a*d)*(1 + m)))","A",1
1881,1,53,57,0.0295211,"\int \frac{(c+d x)^{1+2 n-2 (1+n)}}{(a+b x)^2} \, dx","Integrate[(c + d*x)^(1 + 2*n - 2*(1 + n))/(a + b*x)^2,x]","\frac{d (a+b x) \log (c+d x)-d (a+b x) \log (a+b x)+a d-b c}{(a+b 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,"(-(b*c) + a*d - d*(a + b*x)*Log[a + b*x] + d*(a + b*x)*Log[c + d*x])/((b*c - a*d)^2*(a + b*x))","A",1
1882,1,54,95,0.0740411,"\int (a+b x)^m (a c (1+m)+b c (2+m) x)^{-3-m} \, dx","Integrate[(a + b*x)^m*(a*c*(1 + m) + b*c*(2 + m)*x)^(-3 - m),x]","\frac{x (a+b x)^{m+1} (a c (m+1)+b c (m+2) x)^{-m}}{a^2 c^3 (m+1) (a (m+1)+b (m+2) x)^2}","\frac{(a+b x)^{m+1} (a c (m+1)+b c (m+2) x)^{-m-1}}{a^2 b c^2 (m+1) (m+2)}-\frac{(a+b x)^{m+1} (a c (m+1)+b c (m+2) x)^{-m-2}}{a b c (m+2)}",1,"(x*(a + b*x)^(1 + m))/(a^2*c^3*(1 + m)*(a*(1 + m) + b*(2 + m)*x)^2*(a*c*(1 + m) + b*c*(2 + m)*x)^m)","A",1
1883,1,46,97,0.0399493,"\int (a+b x)^{-1-\frac{b c}{b c-a d}} (c+d x)^{-1+\frac{a d}{b c-a d}} \, dx","Integrate[(a + b*x)^(-1 - (b*c)/(b*c - a*d))*(c + d*x)^(-1 + (a*d)/(b*c - a*d)),x]","\frac{x (a+b x)^{\frac{b c}{a d-b c}} (c+d x)^{\frac{a d}{b c-a d}}}{a c}","\frac{(a+b x)^{-\frac{a d}{b c-a d}} (c+d x)^{\frac{a d}{b c-a d}}}{a b c}-\frac{(a+b x)^{-\frac{b c}{b c-a d}} (c+d x)^{\frac{a d}{b c-a d}}}{b c}",1,"(x*(a + b*x)^((b*c)/(-(b*c) + a*d))*(c + d*x)^((a*d)/(b*c - a*d)))/(a*c)","A",1
1884,1,46,97,0.0663536,"\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","Integrate[(a + b*x)^((-2*b*c + a*d)/(b*c - a*d))*(c + d*x)^((b*c - 2*a*d)/(-(b*c) + a*d)),x]","\frac{x (a+b x)^{\frac{b c}{a d-b c}} (c+d x)^{\frac{a d}{b c-a d}}}{a c}","\frac{(a+b x)^{-\frac{a d}{b c-a d}} (c+d x)^{\frac{a d}{b c-a d}}}{a b c}-\frac{(a+b x)^{-\frac{b c}{b c-a d}} (c+d x)^{\frac{a d}{b c-a d}}}{b c}",1,"(x*(a + b*x)^((b*c)/(-(b*c) + a*d))*(c + d*x)^((a*d)/(b*c - a*d)))/(a*c)","A",1
1885,1,30,30,0.0071873,"\int \frac{(1-x)^n}{\sqrt{1+x}} \, dx","Integrate[(1 - x)^n/Sqrt[1 + x],x]","2^{n+1} \sqrt{x+1} \, _2F_1\left(\frac{1}{2},-n;\frac{3}{2};\frac{x+1}{2}\right)","2^{n+1} \sqrt{x+1} \, _2F_1\left(\frac{1}{2},-n;\frac{3}{2};\frac{x+1}{2}\right)",1,"2^(1 + n)*Sqrt[1 + x]*Hypergeometric2F1[1/2, -n, 3/2, (1 + x)/2]","A",1
1886,1,35,35,0.0130945,"\int \frac{(1+x)^n}{\sqrt{1-x}} \, dx","Integrate[(1 + x)^n/Sqrt[1 - x],x]","-2^{n+1} \sqrt{1-x} \, _2F_1\left(\frac{1}{2},-n;\frac{3}{2};\frac{1-x}{2}\right)","-2^{n+1} \sqrt{1-x} \, _2F_1\left(\frac{1}{2},-n;\frac{3}{2};\frac{1-x}{2}\right)",1,"-(2^(1 + n)*Sqrt[1 - x]*Hypergeometric2F1[1/2, -n, 3/2, (1 - x)/2])","A",1
1887,1,33,33,0.0173699,"\int (1-x)^n (1+x)^{7/3} \, dx","Integrate[(1 - x)^n*(1 + x)^(7/3),x]","\frac{3}{5} 2^{n-1} (x+1)^{10/3} \, _2F_1\left(\frac{10}{3},-n;\frac{13}{3};\frac{x+1}{2}\right)","\frac{3}{5} 2^{n-1} (x+1)^{10/3} \, _2F_1\left(\frac{10}{3},-n;\frac{13}{3};\frac{x+1}{2}\right)",1,"(3*2^(-1 + n)*(1 + x)^(10/3)*Hypergeometric2F1[10/3, -n, 13/3, (1 + x)/2])/5","A",1
1888,1,37,37,0.0241986,"\int (1-x)^{7/3} (1+x)^n \, dx","Integrate[(1 - x)^(7/3)*(1 + x)^n,x]","-\frac{3}{5} 2^{n-1} (1-x)^{10/3} \, _2F_1\left(\frac{10}{3},-n;\frac{13}{3};\frac{1-x}{2}\right)","-\frac{3}{5} 2^{n-1} (1-x)^{10/3} \, _2F_1\left(\frac{10}{3},-n;\frac{13}{3};\frac{1-x}{2}\right)",1,"(-3*2^(-1 + n)*(1 - x)^(10/3)*Hypergeometric2F1[10/3, -n, 13/3, (1 - x)/2])/5","A",1
1889,1,47,47,0.0196399,"\int (1+2 x)^{-m} (2+3 x)^m \, dx","Integrate[(2 + 3*x)^m/(1 + 2*x)^m,x]","\frac{2^{-m-1} (2 x+1)^{1-m} \, _2F_1(1-m,-m;2-m;-3 (2 x+1))}{1-m}","\frac{2^{-m-1} (2 x+1)^{1-m} \, _2F_1(1-m,-m;2-m;-3 (2 x+1))}{1-m}",1,"(2^(-1 - m)*(1 + 2*x)^(1 - m)*Hypergeometric2F1[1 - m, -m, 2 - m, -3*(1 + 2*x)])/(1 - m)","A",1
1890,1,88,45,0.0420135,"\int \left(\frac{d (a+b x)}{-b c+a d}\right)^m (c+d x)^n \, dx","Integrate[((d*(a + b*x))/(-(b*c) + a*d))^m*(c + d*x)^n,x]","\frac{(a+b x) (c+d x)^n \left(\frac{d (a+b x)}{a d-b c}\right)^m \left(\frac{b (c+d x)}{b c-a d}\right)^{-n} \, _2F_1\left(m+1,-n;m+2;\frac{d (a+b x)}{a d-b c}\right)}{b (m+1)}","\frac{(c+d x)^{n+1} \, _2F_1\left(-m,n+1;n+2;\frac{b (c+d x)}{b c-a d}\right)}{d (n+1)}",1,"((a + b*x)*((d*(a + b*x))/(-(b*c) + a*d))^m*(c + d*x)^n*Hypergeometric2F1[1 + m, -n, 2 + m, (d*(a + b*x))/(-(b*c) + a*d)])/(b*(1 + m)*((b*(c + d*x))/(b*c - a*d))^n)","A",1
1891,1,28,28,0.0000958,"\int \left(a+b x+c x^2+d x^3\right) \, dx","Integrate[a + b*x + c*x^2 + d*x^3,x]","a x+\frac{b x^2}{2}+\frac{c x^3}{3}+\frac{d x^4}{4}","a x+\frac{b x^2}{2}+\frac{c x^3}{3}+\frac{d x^4}{4}",1,"a*x + (b*x^2)/2 + (c*x^3)/3 + (d*x^4)/4","A",1
1892,1,15,15,0.0000974,"\int \left(-x^3+x^4\right) \, dx","Integrate[-x^3 + x^4,x]","\frac{x^5}{5}-\frac{x^4}{4}","\frac{x^5}{5}-\frac{x^4}{4}",1,"-1/4*x^4 + x^5/5","A",1
1893,1,11,11,0.0000711,"\int \left(-1+x^5\right) \, dx","Integrate[-1 + x^5,x]","\frac{x^6}{6}-x","\frac{x^6}{6}-x",1,"-x + x^6/6","A",1
1894,1,9,9,0.0000707,"\int (7+4 x) \, dx","Integrate[7 + 4*x,x]","2 x^2+7 x","2 x^2+7 x",1,"7*x + 2*x^2","A",1
1895,1,14,14,0.0001891,"\int \left(4 x+\pi  x^3\right) \, dx","Integrate[4*x + Pi*x^3,x]","\frac{\pi  x^4}{4}+2 x^2","\frac{\pi  x^4}{4}+2 x^2",1,"2*x^2 + (Pi*x^4)/4","A",1
1896,1,11,11,0.0000956,"\int \left(2 x+5 x^2\right) \, dx","Integrate[2*x + 5*x^2,x]","\frac{5 x^3}{3}+x^2","\frac{5 x^3}{3}+x^2",1,"x^2 + (5*x^3)/3","A",1
1897,1,15,15,0.0000802,"\int \left(\frac{x^2}{2}+\frac{x^3}{3}\right) \, dx","Integrate[x^2/2 + x^3/3,x]","\frac{x^4}{12}+\frac{x^3}{6}","\frac{x^4}{12}+\frac{x^3}{6}",1,"x^3/6 + x^4/12","A",1
1898,1,18,18,0.0001005,"\int \left(3-5 x+2 x^2\right) \, dx","Integrate[3 - 5*x + 2*x^2,x]","\frac{2 x^3}{3}-\frac{5 x^2}{2}+3 x","\frac{2 x^3}{3}-\frac{5 x^2}{2}+3 x",1,"3*x - (5*x^2)/2 + (2*x^3)/3","A",1
1899,1,20,20,0.0001429,"\int \left(-2 x+x^2+x^3\right) \, dx","Integrate[-2*x + x^2 + x^3,x]","\frac{x^4}{4}+\frac{x^3}{3}-x^2","\frac{x^4}{4}+\frac{x^3}{3}-x^2",1,"-x^2 + x^3/3 + x^4/4","A",1
1900,1,16,16,0.0001166,"\int \left(1-x^2-3 x^5\right) \, dx","Integrate[1 - x^2 - 3*x^5,x]","-\frac{x^6}{2}-\frac{x^3}{3}+x","-\frac{x^6}{2}-\frac{x^3}{3}+x",1,"x - x^3/3 - x^6/2","A",1
1901,1,13,13,0.0000804,"\int \left(5+2 x+3 x^2+4 x^3\right) \, dx","Integrate[5 + 2*x + 3*x^2 + 4*x^3,x]","x^4+x^3+x^2+5 x","x^4+x^3+x^2+5 x",1,"5*x + x^2 + x^3 + x^4","A",1
1902,1,22,22,0.0070401,"\int \left(a+\frac{d}{x^3}+\frac{c}{x^2}+\frac{b}{x}\right) \, dx","Integrate[a + d/x^3 + c/x^2 + b/x,x]","a x+b \log (x)-\frac{c}{x}-\frac{d}{2 x^2}","a x+b \log (x)-\frac{c}{x}-\frac{d}{2 x^2}",1,"-1/2*d/x^2 - c/x + a*x + b*Log[x]","A",1
1903,1,22,22,0.0013742,"\int \left(\frac{1}{x^5}+x+x^5\right) \, dx","Integrate[x^(-5) + x + x^5,x]","\frac{x^6}{6}-\frac{1}{4 x^4}+\frac{x^2}{2}","\frac{x^6}{6}-\frac{1}{4 x^4}+\frac{x^2}{2}",1,"-1/4*1/x^4 + x^2/2 + x^6/6","A",1
1904,1,15,15,0.0023186,"\int \left(\frac{1}{x^3}+\frac{1}{x^2}+\frac{1}{x}\right) \, dx","Integrate[x^(-3) + x^(-2) + x^(-1),x]","-\frac{1}{2 x^2}-\frac{1}{x}+\log (x)","-\frac{1}{2 x^2}-\frac{1}{x}+\log (x)",1,"-1/2*1/x^2 - x^(-1) + Log[x]","A",1
1905,1,10,10,0.0018474,"\int \left(-\frac{2}{x^2}+\frac{3}{x}\right) \, dx","Integrate[-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
1906,1,15,15,0.0013126,"\int \left(-\frac{1}{7 x^6}+x^6\right) \, dx","Integrate[-1/7*1/x^6 + x^6,x]","\frac{x^7}{7}+\frac{1}{35 x^5}","\frac{x^7}{7}+\frac{1}{35 x^5}",1,"1/(35*x^5) + x^7/7","A",1
1907,1,11,11,0.0006953,"\int \left(1+\frac{1}{x}+x\right) \, dx","Integrate[1 + x^(-1) + x,x]","\frac{x^2}{2}+x+\log (x)","\frac{x^2}{2}+x+\log (x)",1,"x + x^2/2 + Log[x]","A",1
1908,1,13,13,0.0015315,"\int \left(-\frac{3}{x^3}+\frac{4}{x^2}\right) \, dx","Integrate[-3/x^3 + 4/x^2,x]","\frac{3}{2 x^2}-\frac{4}{x}","\frac{3}{2 x^2}-\frac{4}{x}",1,"3/(2*x^2) - 4/x","A",1
1909,1,13,13,0.0012962,"\int \left(\frac{1}{x}+2 x+x^2\right) \, dx","Integrate[x^(-1) + 2*x + x^2,x]","\frac{x^3}{3}+x^2+\log (x)","\frac{x^3}{3}+x^2+\log (x)",1,"x^2 + x^3/3 + Log[x]","A",1
1910,1,17,17,0.0021802,"\int \left(x^{5/6}-x^3\right) \, dx","Integrate[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
1911,1,13,13,0.0016809,"\int \left(33+\sqrt[33]{x}\right) \, dx","Integrate[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
1912,1,14,15,0.0068267,"\int \left(\frac{1}{2 \sqrt{x}}+2 \sqrt{x}\right) \, dx","Integrate[1/(2*Sqrt[x]) + 2*Sqrt[x],x]","\frac{1}{3} \sqrt{x} (4 x+3)","\frac{4 x^{3/2}}{3}+\sqrt{x}",1,"(Sqrt[x]*(3 + 4*x))/3","A",1
1913,1,15,15,0.0142341,"\int \left(-\frac{1}{x^2}+\frac{10}{x}+6 \sqrt{x}\right) \, dx","Integrate[-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
1914,1,14,17,0.0052846,"\int \left(\frac{1}{x^{3/2}}+x^{3/2}\right) \, dx","Integrate[x^(-3/2) + x^(3/2),x]","\frac{2 \left(x^3-5\right)}{5 \sqrt{x}}","\frac{2 x^{5/2}}{5}-\frac{2}{\sqrt{x}}",1,"(2*(-5 + x^3))/(5*Sqrt[x])","A",1
1915,1,10,15,0.0042683,"\int \left(-5 x^{3/2}+7 x^{5/2}\right) \, dx","Integrate[-5*x^(3/2) + 7*x^(5/2),x]","2 (x-1) x^{5/2}","2 x^{7/2}-2 x^{5/2}",1,"2*(-1 + x)*x^(5/2)","A",1
1916,1,24,24,0.0047003,"\int \left(\frac{2}{\sqrt{x}}+\sqrt{x}-\frac{x}{2}\right) \, dx","Integrate[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
1917,1,23,23,0.0148131,"\int \left(-\frac{2}{x}+\frac{\sqrt{x}}{5}+x^{3/2}\right) \, dx","Integrate[-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