1,1,14,14,0.0036516,"\int \frac{1}{a^2-b^2 x^2} \, dx","Integrate[(a^2 - b^2*x^2)^(-1),x]","\frac{\tanh ^{-1}\left(\frac{b x}{a}\right)}{a b}","\frac{\tanh ^{-1}\left(\frac{b x}{a}\right)}{a b}",1,"ArcTanh[(b*x)/a]/(a*b)","A",1
2,1,14,14,0.003234,"\int \frac{1}{a^2+b^2 x^2} \, dx","Integrate[(a^2 + b^2*x^2)^(-1),x]","\frac{\tan ^{-1}\left(\frac{b x}{a}\right)}{a b}","\frac{\tan ^{-1}\left(\frac{b x}{a}\right)}{a b}",1,"ArcTan[(b*x)/a]/(a*b)","A",1
3,1,37,13,0.008663,"\int \sec (2 a x) \, dx","Integrate[Sec[2*a*x],x]","\frac{\log (\sin (a x)+\cos (a x))}{2 a}-\frac{\log (\cos (a x)-\sin (a x))}{2 a}","\frac{\tanh ^{-1}(\sin (2 a x))}{2 a}",1,"-1/2*Log[Cos[a*x] - Sin[a*x]]/a + Log[Cos[a*x] + Sin[a*x]]/(2*a)","B",1
4,1,23,11,0.0067123,"\int \frac{1}{4} \csc \left(\frac{x}{3}\right) \, dx","Integrate[Csc[x/3]/4,x]","\frac{1}{4} \left(3 \log \left(\sin \left(\frac{x}{6}\right)\right)-3 \log \left(\cos \left(\frac{x}{6}\right)\right)\right)","-\frac{3}{4} \tanh ^{-1}\left(\cos \left(\frac{x}{3}\right)\right)",1,"(-3*Log[Cos[x/6]] + 3*Log[Sin[x/6]])/4","B",1
5,1,15,15,0.006418,"\int -\sec \left(\frac{\pi }{4}+2 x\right) \, dx","Integrate[-Sec[Pi/4 + 2*x],x]","-\frac{1}{2} \tanh ^{-1}\left(\sin \left(2 x+\frac{\pi }{4}\right)\right)","-\frac{1}{2} \tanh ^{-1}\left(\sin \left(2 x+\frac{\pi }{4}\right)\right)",1,"-1/2*ArcTanh[Sin[Pi/4 + 2*x]]","A",1
6,1,2,2,0.0015634,"\int \sec (x) \tan (x) \, dx","Integrate[Sec[x]*Tan[x],x]","\sec (x)","\sec (x)",1,"Sec[x]","A",1
7,1,4,4,0.0017641,"\int \cot (x) \csc (x) \, dx","Integrate[Cot[x]*Csc[x],x]","-\csc (x)","-\csc (x)",1,"-Csc[x]","A",1
8,1,6,6,0.0138896,"\int \csc (2 x) \tan (x) \, dx","Integrate[Csc[2*x]*Tan[x],x]","\frac{\tan (x)}{2}","\frac{\tan (x)}{2}",1,"Tan[x]/2","A",1
9,1,6,9,0.0038013,"\int \frac{1}{1+\cos (x)} \, dx","Integrate[(1 + Cos[x])^(-1),x]","\tan \left(\frac{x}{2}\right)","\frac{\sin (x)}{\cos (x)+1}",1,"Tan[x/2]","A",1
10,1,8,12,0.0086813,"\int \frac{1}{1-\cos (x)} \, dx","Integrate[(1 - Cos[x])^(-1),x]","-\cot \left(\frac{x}{2}\right)","-\frac{\sin (x)}{1-\cos (x)}",1,"-Cot[x/2]","A",1
11,1,12,12,0.0186994,"\int \frac{\sin (x)}{a-b \cos (x)} \, dx","Integrate[Sin[x]/(a - b*Cos[x]),x]","\frac{\log (a-b \cos (x))}{b}","\frac{\log (a-b \cos (x))}{b}",1,"Log[a - b*Cos[x]]/b","A",1
12,1,15,15,0.0095678,"\int \frac{\cos (x)}{a^2+b^2 \sin ^2(x)} \, dx","Integrate[Cos[x]/(a^2 + b^2*Sin[x]^2),x]","\frac{\tan ^{-1}\left(\frac{b \sin (x)}{a}\right)}{a b}","\frac{\tan ^{-1}\left(\frac{b \sin (x)}{a}\right)}{a b}",1,"ArcTan[(b*Sin[x])/a]/(a*b)","A",1
13,1,15,15,0.0097257,"\int \frac{\cos (x)}{a^2-b^2 \sin ^2(x)} \, dx","Integrate[Cos[x]/(a^2 - b^2*Sin[x]^2),x]","\frac{\tanh ^{-1}\left(\frac{b \sin (x)}{a}\right)}{a b}","\frac{\tanh ^{-1}\left(\frac{b \sin (x)}{a}\right)}{a b}",1,"ArcTanh[(b*Sin[x])/a]/(a*b)","A",1
14,1,17,17,0.0095862,"\int \frac{\sin (2 x)}{a^2+b^2 \sin ^2(x)} \, dx","Integrate[Sin[2*x]/(a^2 + b^2*Sin[x]^2),x]","\frac{\log \left(a^2+b^2 \sin ^2(x)\right)}{b^2}","\frac{\log \left(a^2+b^2 \sin ^2(x)\right)}{b^2}",1,"Log[a^2 + b^2*Sin[x]^2]/b^2","A",1
15,1,19,19,0.0102279,"\int \frac{\sin (2 x)}{a^2-b^2 \sin ^2(x)} \, dx","Integrate[Sin[2*x]/(a^2 - b^2*Sin[x]^2),x]","-\frac{\log \left(a^2-b^2 \sin ^2(x)\right)}{b^2}","-\frac{\log \left(a^2-b^2 \sin ^2(x)\right)}{b^2}",1,"-(Log[a^2 - b^2*Sin[x]^2]/b^2)","A",1
16,1,22,18,0.0150296,"\int \frac{\sin (2 x)}{a^2+b^2 \cos ^2(x)} \, dx","Integrate[Sin[2*x]/(a^2 + b^2*Cos[x]^2),x]","-\frac{\log \left(a^2-b^2 \sin ^2(x)+b^2\right)}{b^2}","-\frac{\log \left(a^2+b^2 \cos ^2(x)\right)}{b^2}",1,"-(Log[a^2 + b^2 - b^2*Sin[x]^2]/b^2)","A",1
17,1,22,18,0.0135181,"\int \frac{\sin (2 x)}{a^2-b^2 \cos ^2(x)} \, dx","Integrate[Sin[2*x]/(a^2 - b^2*Cos[x]^2),x]","\frac{\log \left(a^2+b^2 \sin ^2(x)-b^2\right)}{b^2}","\frac{\log \left(a^2-b^2 \cos ^2(x)\right)}{b^2}",1,"Log[a^2 - b^2 + b^2*Sin[x]^2]/b^2","A",1
18,1,19,41,0.0262918,"\int \frac{1}{4-\cos ^2(x)} \, dx","Integrate[(4 - Cos[x]^2)^(-1),x]","\frac{\tan ^{-1}\left(\frac{2 \tan (x)}{\sqrt{3}}\right)}{2 \sqrt{3}}","\frac{x}{2 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{\sin (x) \cos (x)}{\sin ^2(x)+2 \sqrt{3}+3}\right)}{2 \sqrt{3}}",1,"ArcTan[(2*Tan[x])/Sqrt[3]]/(2*Sqrt[3])","A",1
19,1,6,6,0.0026932,"\int \frac{e^x}{-1+e^{2 x}} \, dx","Integrate[E^x/(-1 + E^(2*x)),x]","-\tanh ^{-1}\left(e^x\right)","-\tanh ^{-1}\left(e^x\right)",1,"-ArcTanh[E^x]","A",1
20,1,3,3,0.0046646,"\int \frac{1}{x \log (x)} \, dx","Integrate[1/(x*Log[x]),x]","\log (\log (x))","\log (\log (x))",1,"Log[Log[x]]","A",1
21,1,3,3,0.0111207,"\int \frac{1}{x \left(1+\log ^2(x)\right)} \, dx","Integrate[1/(x*(1 + Log[x]^2)),x]","\tan ^{-1}(\log (x))","\tan ^{-1}(\log (x))",1,"ArcTan[Log[x]]","A",1
22,1,7,9,0.0088428,"\int \frac{1}{x (1-\log (x))} \, dx","Integrate[1/(x*(1 - Log[x])),x]","-\log (\log (x)-1)","-\log (1-\log (x))",1,"-Log[-1 + Log[x]]","A",1
23,1,9,9,0.0158818,"\int \frac{1}{x \left(1+\log \left(\frac{x}{a}\right)\right)} \, dx","Integrate[1/(x*(1 + Log[x/a])),x]","\log \left(\log \left(\frac{x}{a}\right)+1\right)","\log \left(\log \left(\frac{x}{a}\right)+1\right)",1,"Log[1 + Log[x/a]]","A",1
24,1,25,25,0.0135573,"\int \frac{\left(1-\sqrt{x}+x\right)^2}{x^2} \, dx","Integrate[(1 - Sqrt[x] + x)^2/x^2,x]","x-4 \sqrt{x}+\frac{4}{\sqrt{x}}-\frac{1}{x}+3 \log (x)","x-4 \sqrt{x}+\frac{4}{\sqrt{x}}-\frac{1}{x}+3 \log (x)",1,"-x^(-1) + 4/Sqrt[x] - 4*Sqrt[x] + x + 3*Log[x]","A",1
25,1,30,30,0.0177988,"\int \frac{\left(2-x^{2/3}\right) \left(\sqrt{x}+x\right)}{x^{3/2}} \, dx","Integrate[((2 - x^(2/3))*(Sqrt[x] + x))/x^(3/2),x]","-\frac{6 x^{7/6}}{7}-\frac{3 x^{2/3}}{2}+4 \sqrt{x}+2 \log (x)","-\frac{6 x^{7/6}}{7}-\frac{3 x^{2/3}}{2}+4 \sqrt{x}+2 \log (x)",1,"4*Sqrt[x] - (3*x^(2/3))/2 - (6*x^(7/6))/7 + 2*Log[x]","A",1
26,1,10,10,0.0020353,"\int \frac{-1+2 x}{3+2 x} \, dx","Integrate[(-1 + 2*x)/(3 + 2*x),x]","x-2 \log (2 x+3)","x-2 \log (2 x+3)",1,"x - 2*Log[3 + 2*x]","A",1
27,1,47,47,0.0306672,"\int \frac{-5+2 x}{-2+3 x^2} \, dx","Integrate[(-5 + 2*x)/(-2 + 3*x^2),x]","\frac{1}{12} \left(4-5 \sqrt{6}\right) \log \left(\sqrt{6}-3 x\right)+\frac{1}{12} \left(4+5 \sqrt{6}\right) \log \left(3 x+\sqrt{6}\right)","\frac{1}{12} \left(4-5 \sqrt{6}\right) \log \left(\sqrt{6}-3 x\right)+\frac{1}{12} \left(4+5 \sqrt{6}\right) \log \left(3 x+\sqrt{6}\right)",1,"((4 - 5*Sqrt[6])*Log[Sqrt[6] - 3*x])/12 + ((4 + 5*Sqrt[6])*Log[Sqrt[6] + 3*x])/12","A",1
28,1,30,30,0.013777,"\int \frac{-5+2 x}{2+3 x^2} \, dx","Integrate[(-5 + 2*x)/(2 + 3*x^2),x]","\frac{1}{3} \log \left(3 x^2+2\right)-\frac{5 \tan ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{\sqrt{6}}","\frac{1}{3} \log \left(3 x^2+2\right)-\frac{5 \tan ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{\sqrt{6}}",1,"(-5*ArcTan[Sqrt[3/2]*x])/Sqrt[6] + Log[2 + 3*x^2]/3","A",1
29,1,21,21,0.0122163,"\int \sin \left(\frac{x}{4}\right) \sin (x) \, dx","Integrate[Sin[x/4]*Sin[x],x]","\frac{2}{3} \sin \left(\frac{3 x}{4}\right)-\frac{2}{5} \sin \left(\frac{5 x}{4}\right)","\frac{2}{3} \sin \left(\frac{3 x}{4}\right)-\frac{2}{5} \sin \left(\frac{5 x}{4}\right)",1,"(2*Sin[(3*x)/4])/3 - (2*Sin[(5*x)/4])/5","A",1
30,1,15,15,0.0064641,"\int \cos (3 x) \cos (4 x) \, dx","Integrate[Cos[3*x]*Cos[4*x],x]","\frac{\sin (x)}{2}+\frac{1}{14} \sin (7 x)","\frac{\sin (x)}{2}+\frac{1}{14} \sin (7 x)",1,"Sin[x]/2 + Sin[7*x]/14","A",1
31,1,21,21,0.0810793,"\int -\tan (a-x) \tan (x) \, dx","Integrate[-(Tan[a - x]*Tan[x]),x]","\cot (a) \log (\cos (a-x))-\cot (a) \log (\cos (x))-x","\cot (a) \log (\cos (a-x))-\cot (a) \log (\cos (x))-x",1,"-x + Cot[a]*Log[Cos[a - x]] - Cot[a]*Log[Cos[x]]","A",1
32,1,14,14,0.0017923,"\int \sin ^2(x) \, dx","Integrate[Sin[x]^2,x]","\frac{x}{2}-\frac{1}{4} \sin (2 x)","\frac{x}{2}-\frac{1}{2} \sin (x) \cos (x)",1,"x/2 - Sin[2*x]/4","A",1
33,1,14,14,0.0017548,"\int \cos ^2(x) \, dx","Integrate[Cos[x]^2,x]","\frac{x}{2}+\frac{1}{4} \sin (2 x)","\frac{x}{2}+\frac{1}{2} \sin (x) \cos (x)",1,"x/2 + Sin[2*x]/4","A",1
34,1,8,8,0.0011883,"\int \cos ^3(x) \sin (x) \, dx","Integrate[Cos[x]^3*Sin[x],x]","-\frac{1}{4} \cos ^4(x)","-\frac{1}{4} \cos ^4(x)",1,"-1/4*Cos[x]^4","A",1
35,1,11,11,0.0073147,"\int \cot ^3(x) \csc (x) \, dx","Integrate[Cot[x]^3*Csc[x],x]","\csc (x)-\frac{\csc ^3(x)}{3}","\csc (x)-\frac{\csc ^3(x)}{3}",1,"Csc[x] - Csc[x]^3/3","A",1
36,1,6,7,0.0074528,"\int \csc ^2(x) \sec ^2(x) \, dx","Integrate[Csc[x]^2*Sec[x]^2,x]","-2 \cot (2 x)","\tan (x)-\cot (x)",1,"-2*Cot[2*x]","A",1
37,1,28,14,0.0136262,"\int \cot ^2\left(\frac{3 x}{4}\right) \, dx","Integrate[Cot[(3*x)/4]^2,x]","-\frac{4}{3} \cot \left(\frac{3 x}{4}\right) \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};-\tan ^2\left(\frac{3 x}{4}\right)\right)","-x-\frac{4}{3} \cot \left(\frac{3 x}{4}\right)",1,"(-4*Cot[(3*x)/4]*Hypergeometric2F1[-1/2, 1, 1/2, -Tan[(3*x)/4]^2])/3","C",1
38,1,26,16,0.0111488,"\int (1+\tan (2 x))^2 \, dx","Integrate[(1 + Tan[2*x])^2,x]","x-\frac{1}{2} \tan ^{-1}(\tan (2 x))+\frac{1}{2} \tan (2 x)-\log (\cos (2 x))","\frac{1}{2} \tan (2 x)-\log (\cos (2 x))",1,"x - ArcTan[Tan[2*x]]/2 - Log[Cos[2*x]] + Tan[2*x]/2","A",1
39,1,10,10,0.015934,"\int (-\cot (x)+\tan (x))^2 \, dx","Integrate[(-Cot[x] + Tan[x])^2,x]","-4 x+\tan (x)-\cot (x)","-4 x+\tan (x)-\cot (x)",1,"-4*x - Cot[x] + Tan[x]","A",1
40,1,12,14,0.0067814,"\int (-\sec (x)+\tan (x))^2 \, dx","Integrate[(-Sec[x] + Tan[x])^2,x]","-x+2 \tan (x)-2 \sec (x)","-x-\frac{2 \cos (x)}{\sin (x)+1}",1,"-x - 2*Sec[x] + 2*Tan[x]","A",1
41,1,25,11,0.0426746,"\int \frac{\sin (x)}{1+\sin (x)} \, dx","Integrate[Sin[x]/(1 + Sin[x]),x]","x-\frac{2 \sin \left(\frac{x}{2}\right)}{\sin \left(\frac{x}{2}\right)+\cos \left(\frac{x}{2}\right)}","x+\frac{\cos (x)}{\sin (x)+1}",1,"x - (2*Sin[x/2])/(Cos[x/2] + Sin[x/2])","B",1
42,1,21,16,0.0231004,"\int \frac{\cos (x)}{1-\cos (x)} \, dx","Integrate[Cos[x]/(1 - Cos[x]),x]","\frac{2 x \sin ^2\left(\frac{x}{2}\right)+\sin (x)}{\cos (x)-1}","-x-\frac{\sin (x)}{1-\cos (x)}",1,"(2*x*Sin[x/2]^2 + Sin[x])/(-1 + Cos[x])","A",1
43,1,25,25,0.0135145,"\int e^{-x/2} \left(-1+e^{x/2}\right)^3 \, dx","Integrate[(-1 + E^(x/2))^3/E^(x/2),x]","3 x+2 e^{-x/2}-6 e^{x/2}+e^x","3 x+2 e^{-x/2}-6 e^{x/2}+e^x",1,"2/E^(x/2) - 6*E^(x/2) + E^x + 3*x","A",1
44,1,21,21,0.0029335,"\int \frac{1}{5-6 x+x^2} \, dx","Integrate[(5 - 6*x + x^2)^(-1),x]","\frac{1}{4} \log (5-x)-\frac{1}{4} \log (1-x)","\frac{1}{4} \log (5-x)-\frac{1}{4} \log (1-x)",1,"-1/4*Log[1 - x] + Log[5 - x]/4","A",1
45,1,14,14,0.0050191,"\int \frac{x^2}{13-6 x^3+x^6} \, dx","Integrate[x^2/(13 - 6*x^3 + x^6),x]","\frac{1}{6} \tan ^{-1}\left(\frac{1}{2} \left(x^3-3\right)\right)","\frac{1}{6} \tan ^{-1}\left(\frac{1}{2} \left(x^3-3\right)\right)",1,"ArcTan[(-3 + x^3)/2]/6","A",1
46,1,47,51,0.0267724,"\int \frac{2+x}{-1-4 x+x^2} \, dx","Integrate[(2 + x)/(-1 - 4*x + x^2),x]","\frac{1}{10} \left(5+4 \sqrt{5}\right) \log \left(-x+\sqrt{5}+2\right)+\frac{1}{10} \left(5-4 \sqrt{5}\right) \log \left(x+\sqrt{5}-2\right)","\frac{1}{10} \left(5-4 \sqrt{5}\right) \log \left(-x-\sqrt{5}+2\right)+\frac{1}{10} \left(5+4 \sqrt{5}\right) \log \left(-x+\sqrt{5}+2\right)",1,"((5 + 4*Sqrt[5])*Log[2 + Sqrt[5] - x])/10 + ((5 - 4*Sqrt[5])*Log[-2 + Sqrt[5] + x])/10","A",1
47,1,33,33,0.0136603,"\int \frac{1}{1+\sqrt[3]{1+x}} \, dx","Integrate[(1 + (1 + x)^(1/3))^(-1),x]","\frac{3}{2} (x+1)^{2/3}-3 \sqrt[3]{x+1}+3 \log \left(\sqrt[3]{x+1}+1\right)","\frac{3}{2} (x+1)^{2/3}-3 \sqrt[3]{x+1}+3 \log \left(\sqrt[3]{x+1}+1\right)",1,"-3*(1 + x)^(1/3) + (3*(1 + x)^(2/3))/2 + 3*Log[1 + (1 + x)^(1/3)]","A",1
48,1,29,29,0.0072337,"\int \frac{1}{\sqrt{x} (b+a x)} \, dx","Integrate[1/(Sqrt[x]*(b + a*x)),x]","\frac{2 \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{\sqrt{a} \sqrt{b}}","\frac{2 \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{\sqrt{a} \sqrt{b}}",1,"(2*ArcTan[(Sqrt[a]*Sqrt[x])/Sqrt[b]])/(Sqrt[a]*Sqrt[b])","A",1
49,1,20,27,0.0070056,"\int x^3 \sqrt{1+x^2} \, dx","Integrate[x^3*Sqrt[1 + x^2],x]","\frac{1}{15} \left(x^2+1\right)^{3/2} \left(3 x^2-2\right)","\frac{1}{5} \left(x^2+1\right)^{5/2}-\frac{1}{3} \left(x^2+1\right)^{3/2}",1,"((1 + x^2)^(3/2)*(-2 + 3*x^2))/15","A",1
50,1,22,22,0.0039057,"\int \frac{x}{\sqrt{a^4-x^4}} \, dx","Integrate[x/Sqrt[a^4 - x^4],x]","\frac{1}{2} \tan ^{-1}\left(\frac{x^2}{\sqrt{a^4-x^4}}\right)","\frac{1}{2} \tan ^{-1}\left(\frac{x^2}{\sqrt{a^4-x^4}}\right)",1,"ArcTan[x^2/Sqrt[a^4 - x^4]]/2","A",1
51,1,22,22,0.0042549,"\int \frac{1}{x \sqrt{-a^2+x^2}} \, dx","Integrate[1/(x*Sqrt[-a^2 + x^2]),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{x^2-a^2}}{a}\right)}{a}","\frac{\tan ^{-1}\left(\frac{\sqrt{x^2-a^2}}{a}\right)}{a}",1,"ArcTan[Sqrt[-a^2 + x^2]/a]/a","A",1
52,1,23,23,0.0040779,"\int \frac{1}{x \sqrt{a^2-x^2}} \, dx","Integrate[1/(x*Sqrt[a^2 - x^2]),x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{a^2-x^2}}{a}\right)}{a}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{a^2-x^2}}{a}\right)}{a}",1,"-(ArcTanh[Sqrt[a^2 - x^2]/a]/a)","A",1
53,1,21,21,0.0033568,"\int \frac{1}{x \sqrt{a^2+x^2}} \, dx","Integrate[1/(x*Sqrt[a^2 + x^2]),x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{a^2+x^2}}{a}\right)}{a}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{a^2+x^2}}{a}\right)}{a}",1,"-(ArcTanh[Sqrt[a^2 + x^2]/a]/a)","A",1
54,1,12,12,0.0068631,"\int \frac{1}{\sqrt{2+x-x^2}} \, dx","Integrate[1/Sqrt[2 + x - x^2],x]","-\sin ^{-1}\left(\frac{1}{3} (1-2 x)\right)","-\sin ^{-1}\left(\frac{1}{3} (1-2 x)\right)",1,"-ArcSin[(1 - 2*x)/3]","A",1
55,1,18,19,0.0087504,"\int \frac{1}{\sqrt{5-4 x+3 x^2}} \, dx","Integrate[1/Sqrt[5 - 4*x + 3*x^2],x]","\frac{\sinh ^{-1}\left(\frac{3 x-2}{\sqrt{11}}\right)}{\sqrt{3}}","-\frac{\sinh ^{-1}\left(\frac{2-3 x}{\sqrt{11}}\right)}{\sqrt{3}}",1,"ArcSinh[(-2 + 3*x)/Sqrt[11]]/Sqrt[3]","A",1
56,1,12,8,0.0087549,"\int \frac{1}{\sqrt{x-x^2}} \, dx","Integrate[1/Sqrt[x - x^2],x]","-2 \sin ^{-1}\left(\sqrt{1-x}\right)","-\sin ^{-1}(1-2 x)",1,"-2*ArcSin[Sqrt[1 - x]]","A",1
57,1,27,27,0.0063709,"\int \frac{1+2 x}{\sqrt{2+x-x^2}} \, dx","Integrate[(1 + 2*x)/Sqrt[2 + x - x^2],x]","-2 \sqrt{-x^2+x+2}-2 \sin ^{-1}\left(\frac{1}{3} (1-2 x)\right)","-2 \sqrt{-x^2+x+2}-2 \sin ^{-1}\left(\frac{1}{3} (1-2 x)\right)",1,"-2*Sqrt[2 + x - x^2] - 2*ArcSin[(1 - 2*x)/3]","A",1
58,1,32,32,0.0061358,"\int \frac{1}{x \sqrt{2+x-x^2}} \, dx","Integrate[1/(x*Sqrt[2 + x - x^2]),x]","-\frac{\tanh ^{-1}\left(\frac{x+4}{2 \sqrt{2} \sqrt{-x^2+x+2}}\right)}{\sqrt{2}}","-\frac{\tanh ^{-1}\left(\frac{x+4}{2 \sqrt{2} \sqrt{-x^2+x+2}}\right)}{\sqrt{2}}",1,"-(ArcTanh[(4 + x)/(2*Sqrt[2]*Sqrt[2 + x - x^2])]/Sqrt[2])","A",1
59,1,21,21,0.0046308,"\int \frac{1}{(-2+x) \sqrt{2+x-x^2}} \, dx","Integrate[1/((-2 + x)*Sqrt[2 + x - x^2]),x]","-\frac{2 \sqrt{-x^2+x+2}}{6-3 x}","\frac{2 \sqrt{-x^2+x+2}}{3 (x-2)}",1,"(-2*Sqrt[2 + x - x^2])/(6 - 3*x)","A",1
60,1,54,28,0.0641829,"\int \frac{\csc (x) (2+3 \sin (x))}{1-\cos (x)} \, dx","Integrate[(Csc[x]*(2 + 3*Sin[x]))/(1 - Cos[x]),x]","\frac{1}{2} \csc ^2\left(\frac{x}{2}\right) \left(-3 \sin (x)+\log \left(\sin \left(\frac{x}{2}\right)\right)-\log \left(\cos \left(\frac{x}{2}\right)\right)+\cos (x) \left(\log \left(\cos \left(\frac{x}{2}\right)\right)-\log \left(\sin \left(\frac{x}{2}\right)\right)\right)-1\right)","-\frac{1}{1-\cos (x)}-\frac{3 \sin (x)}{1-\cos (x)}-\tanh ^{-1}(\cos (x))",1,"(Csc[x/2]^2*(-1 - Log[Cos[x/2]] + Cos[x]*(Log[Cos[x/2]] - Log[Sin[x/2]]) + Log[Sin[x/2]] - 3*Sin[x]))/2","A",1
61,1,17,37,0.0524195,"\int \frac{1}{2+3 \cos ^2(x)} \, dx","Integrate[(2 + 3*Cos[x]^2)^(-1),x]","\frac{\tan ^{-1}\left(\sqrt{\frac{2}{5}} \tan (x)\right)}{\sqrt{10}}","\frac{x}{\sqrt{10}}-\frac{\tan ^{-1}\left(\frac{3 \sin (x) \cos (x)}{3 \cos ^2(x)+\sqrt{10}+2}\right)}{\sqrt{10}}",1,"ArcTan[Sqrt[2/5]*Tan[x]]/Sqrt[10]","A",1
62,1,21,14,0.0179212,"\int \csc (2 x) (1-\tan (x)) \, dx","Integrate[Csc[2*x]*(1 - Tan[x]),x]","-\frac{\tan (x)}{2}+\frac{1}{2} \log (\sin (x))-\frac{1}{2} \log (\cos (x))","\frac{1}{2} \log (\tan (x))-\frac{\tan (x)}{2}",1,"-1/2*Log[Cos[x]] + Log[Sin[x]]/2 - Tan[x]/2","A",1
63,1,23,11,0.0070661,"\int \frac{1+\tan ^2(x)}{1-\tan ^2(x)} \, dx","Integrate[(1 + Tan[x]^2)/(1 - Tan[x]^2),x]","\frac{1}{2} \log (\sin (x)+\cos (x))-\frac{1}{2} \log (\cos (x)-\sin (x))","\frac{1}{2} \tanh ^{-1}(2 \sin (x) \cos (x))",1,"-1/2*Log[Cos[x] - Sin[x]] + Log[Cos[x] + Sin[x]]/2","B",1
64,1,19,18,0.0170884,"\int \left(a^2-4 \cos ^2(x)\right)^{3/4} \sin (2 x) \, dx","Integrate[(a^2 - 4*Cos[x]^2)^(3/4)*Sin[2*x],x]","\frac{1}{7} \left(a^2+4 \sin ^2(x)-4\right)^{7/4}","\frac{1}{7} \left(a^2-4 \cos ^2(x)\right)^{7/4}",1,"(-4 + a^2 + 4*Sin[x]^2)^(7/4)/7","A",1
65,1,18,18,0.0197951,"\int \frac{\sin (2 x)}{\sqrt[3]{a^2-4 \sin ^2(x)}} \, dx","Integrate[Sin[2*x]/(a^2 - 4*Sin[x]^2)^(1/3),x]","-\frac{3}{8} \left(a^2-4 \sin ^2(x)\right)^{2/3}","-\frac{3}{8} \left(a^2-4 \sin ^2(x)\right)^{2/3}",1,"(-3*(a^2 - 4*Sin[x]^2)^(2/3))/8","A",1
66,1,17,17,0.0054626,"\int \frac{1}{\sqrt{-1+a^{2 x}}} \, dx","Integrate[1/Sqrt[-1 + a^(2*x)],x]","\frac{\tan ^{-1}\left(\sqrt{a^{2 x}-1}\right)}{\log (a)}","\frac{\tan ^{-1}\left(\sqrt{a^{2 x}-1}\right)}{\log (a)}",1,"ArcTan[Sqrt[-1 + a^(2*x)]]/Log[a]","A",1
67,1,20,20,0.0041184,"\int \frac{e^{x/2}}{\sqrt{-1+e^x}} \, dx","Integrate[E^(x/2)/Sqrt[-1 + E^x],x]","2 \tanh ^{-1}\left(\frac{e^{x/2}}{\sqrt{e^x-1}}\right)","2 \tanh ^{-1}\left(\frac{e^{x/2}}{\sqrt{e^x-1}}\right)",1,"2*ArcTanh[E^(x/2)/Sqrt[-1 + E^x]]","A",1
68,1,12,12,0.0052617,"\int \frac{\tan ^{-1}(x)^n}{1+x^2} \, dx","Integrate[ArcTan[x]^n/(1 + x^2),x]","\frac{\tan ^{-1}(x)^{n+1}}{n+1}","\frac{\tan ^{-1}(x)^{n+1}}{n+1}",1,"ArcTan[x]^(1 + n)/(1 + n)","A",1
69,1,42,42,0.0443265,"\int \frac{\sin ^{-1}\left(\frac{x}{a}\right)^{3/2}}{\sqrt{a^2-x^2}} \, dx","Integrate[ArcSin[x/a]^(3/2)/Sqrt[a^2 - x^2],x]","\frac{2 a \sqrt{1-\frac{x^2}{a^2}} \sin ^{-1}\left(\frac{x}{a}\right)^{5/2}}{5 \sqrt{a^2-x^2}}","\frac{2 a \sqrt{1-\frac{x^2}{a^2}} \sin ^{-1}\left(\frac{x}{a}\right)^{5/2}}{5 \sqrt{a^2-x^2}}",1,"(2*a*Sqrt[1 - x^2/a^2]*ArcSin[x/a]^(5/2))/(5*Sqrt[a^2 - x^2])","A",1
70,1,8,8,0.0065706,"\int \frac{1}{\sqrt{1-x^2} \cos ^{-1}(x)^3} \, dx","Integrate[1/(Sqrt[1 - x^2]*ArcCos[x]^3),x]","\frac{1}{2 \cos ^{-1}(x)^2}","\frac{1}{2 \cos ^{-1}(x)^2}",1,"1/(2*ArcCos[x]^2)","A",1
71,1,28,28,0.0011526,"\int x \log ^2(x) \, dx","Integrate[x*Log[x]^2,x]","\frac{x^2}{4}+\frac{1}{2} x^2 \log ^2(x)-\frac{1}{2} x^2 \log (x)","\frac{x^2}{4}+\frac{1}{2} x^2 \log ^2(x)-\frac{1}{2} x^2 \log (x)",1,"x^2/4 - (x^2*Log[x])/2 + (x^2*Log[x]^2)/2","A",1
72,1,17,17,0.0009989,"\int \frac{\log (x)}{x^5} \, dx","Integrate[Log[x]/x^5,x]","-\frac{1}{16 x^4}-\frac{\log (x)}{4 x^4}","-\frac{1}{16 x^4}-\frac{\log (x)}{4 x^4}",1,"-1/16*1/x^4 - Log[x]/(4*x^4)","A",1
73,1,38,36,0.0058704,"\int x^2 \log \left(\frac{-1+x}{x}\right) \, dx","Integrate[x^2*Log[(-1 + x)/x],x]","\frac{1}{3} x^3 \log \left(\frac{x-1}{x}\right)-\frac{x^2}{6}-\frac{x}{3}-\frac{1}{3} \log (1-x)","\frac{1}{3} x^3 \log \left(\frac{x-1}{x}\right)-\frac{x^2}{6}-\frac{x}{3}-\frac{1}{3} \log (x-1)",1,"-1/3*x - x^2/6 - Log[1 - x]/3 + (x^3*Log[(-1 + x)/x])/3","A",1
74,1,23,19,0.0020774,"\int \cos ^5(x) \, dx","Integrate[Cos[x]^5,x]","\frac{5 \sin (x)}{8}+\frac{5}{48} \sin (3 x)+\frac{1}{80} \sin (5 x)","\frac{\sin ^5(x)}{5}-\frac{2 \sin ^3(x)}{3}+\sin (x)",1,"(5*Sin[x])/8 + (5*Sin[3*x])/48 + Sin[5*x]/80","A",1
75,1,30,34,0.0115863,"\int \cos ^4(x) \sin ^2(x) \, dx","Integrate[Cos[x]^4*Sin[x]^2,x]","\frac{x}{16}+\frac{1}{64} \sin (2 x)-\frac{1}{64} \sin (4 x)-\frac{1}{192} \sin (6 x)","\frac{x}{16}-\frac{1}{6} \sin (x) \cos ^5(x)+\frac{1}{24} \sin (x) \cos ^3(x)+\frac{1}{16} \sin (x) \cos (x)",1,"x/16 + Sin[2*x]/64 - Sin[4*x]/64 - Sin[6*x]/192","A",1
76,1,71,26,0.0060871,"\int \csc ^5(x) \, dx","Integrate[Csc[x]^5,x]","-\frac{1}{64} \csc ^4\left(\frac{x}{2}\right)-\frac{3}{32} \csc ^2\left(\frac{x}{2}\right)+\frac{1}{64} \sec ^4\left(\frac{x}{2}\right)+\frac{3}{32} \sec ^2\left(\frac{x}{2}\right)+\frac{3}{8} \log \left(\sin \left(\frac{x}{2}\right)\right)-\frac{3}{8} \log \left(\cos \left(\frac{x}{2}\right)\right)","-\frac{3}{8} \tanh ^{-1}(\cos (x))-\frac{1}{4} \cot (x) \csc ^3(x)-\frac{3}{8} \cot (x) \csc (x)",1,"(-3*Csc[x/2]^2)/32 - Csc[x/2]^4/64 - (3*Log[Cos[x/2]])/8 + (3*Log[Sin[x/2]])/8 + (3*Sec[x/2]^2)/32 + Sec[x/2]^4/64","B",1
77,1,14,23,0.0191512,"\int e^{-x} \sin (x) \, dx","Integrate[Sin[x]/E^x,x]","-\frac{1}{2} e^{-x} (\sin (x)+\cos (x))","-\frac{1}{2} e^{-x} \sin (x)-\frac{1}{2} e^{-x} \cos (x)",1,"-1/2*(Cos[x] + Sin[x])/E^x","A",1
78,1,22,27,0.0356008,"\int e^{2 x} \sin (3 x) \, dx","Integrate[E^(2*x)*Sin[3*x],x]","\frac{1}{13} e^{2 x} (2 \sin (3 x)-3 \cos (3 x))","\frac{2}{13} e^{2 x} \sin (3 x)-\frac{3}{13} e^{2 x} \cos (3 x)",1,"(E^(2*x)*(-3*Cos[3*x] + 2*Sin[3*x]))/13","A",1
79,1,20,31,0.0202229,"\int a^x \cos (x) \, dx","Integrate[a^x*Cos[x],x]","\frac{a^x (\log (a) \cos (x)+\sin (x))}{\log ^2(a)+1}","\frac{a^x \sin (x)}{\log ^2(a)+1}+\frac{a^x \log (a) \cos (x)}{\log ^2(a)+1}",1,"(a^x*(Cos[x]*Log[a] + Sin[x]))/(1 + Log[a]^2)","A",1
80,1,17,17,0.0020094,"\int \cos (\log (x)) \, dx","Integrate[Cos[Log[x]],x]","\frac{1}{2} x \sin (\log (x))+\frac{1}{2} x \cos (\log (x))","\frac{1}{2} x \sin (\log (x))+\frac{1}{2} x \cos (\log (x))",1,"(x*Cos[Log[x]])/2 + (x*Sin[Log[x]])/2","A",1
81,1,12,12,0.0159175,"\int \log (\cos (x)) \sec ^2(x) \, dx","Integrate[Log[Cos[x]]*Sec[x]^2,x]","-x+\tan (x)+\tan (x) \log (\cos (x))","-x+\tan (x)+\tan (x) \log (\cos (x))",1,"-x + Tan[x] + Log[Cos[x]]*Tan[x]","A",1
82,1,15,15,0.0186589,"\int x \tan ^2(x) \, dx","Integrate[x*Tan[x]^2,x]","-\frac{x^2}{2}+x \tan (x)+\log (\cos (x))","-\frac{x^2}{2}+x \tan (x)+\log (\cos (x))",1,"-1/2*x^2 + Log[Cos[x]] + x*Tan[x]","A",1
83,1,22,22,0.0026719,"\int \frac{\sin ^{-1}(x)}{x^2} \, dx","Integrate[ArcSin[x]/x^2,x]","-\tanh ^{-1}\left(\sqrt{1-x^2}\right)-\frac{\sin ^{-1}(x)}{x}","-\tanh ^{-1}\left(\sqrt{1-x^2}\right)-\frac{\sin ^{-1}(x)}{x}",1,"-(ArcSin[x]/x) - ArcTanh[Sqrt[1 - x^2]]","A",1
84,1,25,25,0.00672,"\int \sin ^{-1}(x)^2 \, dx","Integrate[ArcSin[x]^2,x]","2 \sqrt{1-x^2} \sin ^{-1}(x)-2 x+x \sin ^{-1}(x)^2","2 \sqrt{1-x^2} \sin ^{-1}(x)-2 x+x \sin ^{-1}(x)^2",1,"-2*x + 2*Sqrt[1 - x^2]*ArcSin[x] + x*ArcSin[x]^2","A",1
85,1,23,23,0.0151129,"\int \frac{x^2 \tan ^{-1}(x)}{1+x^2} \, dx","Integrate[(x^2*ArcTan[x])/(1 + x^2),x]","-\frac{1}{2} \log \left(x^2+1\right)-\frac{1}{2} \tan ^{-1}(x)^2+x \tan ^{-1}(x)","-\frac{1}{2} \log \left(x^2+1\right)-\frac{1}{2} \tan ^{-1}(x)^2+x \tan ^{-1}(x)",1,"x*ArcTan[x] - ArcTan[x]^2/2 - Log[1 + x^2]/2","A",1
86,1,49,38,0.063292,"\int \cos ^{-1}\left(\sqrt{\frac{x}{1+x}}\right) \, dx","Integrate[ArcCos[Sqrt[x/(1 + x)]],x]","x \cos ^{-1}\left(\sqrt{\frac{x}{x+1}}\right)+\frac{\sqrt{\frac{x}{(x+1)^2}} (x+1) \left(\sqrt{x}-\tan ^{-1}\left(\sqrt{x}\right)\right)}{\sqrt{x}}","(x+1) \left(\sqrt{\frac{1}{x+1}} \sqrt{\frac{x}{x+1}}+\cos ^{-1}\left(\sqrt{\frac{x}{x+1}}\right)\right)",1,"x*ArcCos[Sqrt[x/(1 + x)]] + (Sqrt[x/(1 + x)^2]*(1 + x)*(Sqrt[x] - ArcTan[Sqrt[x]]))/Sqrt[x]","A",1
87,1,25,25,0.0024066,"\int \left(2 x+3 x^2\right)^3 \, dx","Integrate[(2*x + 3*x^2)^3,x]","\frac{27 x^7}{7}+9 x^6+\frac{36 x^5}{5}+2 x^4","\frac{27 x^7}{7}+9 x^6+\frac{36 x^5}{5}+2 x^4",1,"2*x^4 + (36*x^5)/5 + 9*x^6 + (27*x^7)/7","A",1
88,1,39,39,0.0012698,"\int (-1+x) \left(-1+2 x+3 x^2\right)^2 \, dx","Integrate[(-1 + x)*(-1 + 2*x + 3*x^2)^2,x]","\frac{3 x^6}{2}+\frac{3 x^5}{5}-\frac{7 x^4}{2}-\frac{2 x^3}{3}+\frac{5 x^2}{2}-x","\frac{3 x^6}{2}+\frac{3 x^5}{5}-\frac{7 x^4}{2}-\frac{2 x^3}{3}+\frac{5 x^2}{2}-x",1,"-x + (5*x^2)/2 - (2*x^3)/3 - (7*x^4)/2 + (3*x^5)/5 + (3*x^6)/2","A",1
89,1,23,23,0.0093997,"\int x^{-1+k} \left(a+b x^k\right)^n \, dx","Integrate[x^(-1 + k)*(a + b*x^k)^n,x]","\frac{\left(a+b x^k\right)^{n+1}}{b k (n+1)}","\frac{\left(a+b x^k\right)^{n+1}}{b k (n+1)}",1,"(a + b*x^k)^(1 + n)/(b*k*(1 + n))","A",1
90,1,27,30,0.0068912,"\int \frac{x^3}{1+2 x} \, dx","Integrate[x^3/(1 + 2*x),x]","\frac{1}{96} \left(16 x^3-12 x^2+12 x-6 \log (2 x+1)+11\right)","\frac{x^3}{6}-\frac{x^2}{8}+\frac{x}{8}-\frac{1}{16} \log (2 x+1)",1,"(11 + 12*x - 12*x^2 + 16*x^3 - 6*Log[1 + 2*x])/96","A",1
91,1,35,41,0.0126189,"\int \frac{x^6}{2+3 x^2} \, dx","Integrate[x^6/(2 + 3*x^2),x]","\frac{1}{405} \left(27 x^5-30 x^3+60 x-20 \sqrt{6} \tan ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right)","\frac{x^5}{15}-\frac{2 x^3}{27}+\frac{4 x}{27}-\frac{4}{27} \sqrt{\frac{2}{3}} \tan ^{-1}\left(\sqrt{\frac{3}{2}} x\right)",1,"(60*x - 30*x^3 + 27*x^5 - 20*Sqrt[6]*ArcTan[Sqrt[3/2]*x])/405","A",1
92,1,21,21,0.0035248,"\int \frac{1}{2-7 x+3 x^2} \, dx","Integrate[(2 - 7*x + 3*x^2)^(-1),x]","\frac{1}{5} \log (2-x)-\frac{1}{5} \log (1-3 x)","\frac{1}{5} \log (2-x)-\frac{1}{5} \log (1-3 x)",1,"-1/5*Log[1 - 3*x] + Log[2 - x]/5","A",1
93,1,32,33,0.0095026,"\int \frac{-1+3 x}{1-x+x^2} \, dx","Integrate[(-1 + 3*x)/(1 - x + x^2),x]","\frac{3}{2} \log \left(x^2-x+1\right)+\frac{\tan ^{-1}\left(\frac{2 x-1}{\sqrt{3}}\right)}{\sqrt{3}}","\frac{3}{2} \log \left(x^2-x+1\right)-\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{\sqrt{3}}",1,"ArcTan[(-1 + 2*x)/Sqrt[3]]/Sqrt[3] + (3*Log[1 - x + x^2])/2","A",1
94,1,25,25,0.0041511,"\int \frac{x^2}{5+2 x+x^2} \, dx","Integrate[x^2/(5 + 2*x + x^2),x]","-\log \left(x^2+2 x+5\right)+x-\frac{3}{2} \tan ^{-1}\left(\frac{x+1}{2}\right)","-\log \left(x^2+2 x+5\right)+x-\frac{3}{2} \tan ^{-1}\left(\frac{x+1}{2}\right)",1,"x - (3*ArcTan[(1 + x)/2])/2 - Log[5 + 2*x + x^2]","A",1
95,1,47,47,0.0170151,"\int \frac{4 x^2-5 x^3+6 x^4}{1-x+2 x^2} \, dx","Integrate[(4*x^2 - 5*x^3 + 6*x^4)/(1 - x + 2*x^2),x]","x^3-\frac{x^2}{2}+\frac{1}{4} \log \left(2 x^2-x+1\right)+\frac{\tan ^{-1}\left(\frac{4 x-1}{\sqrt{7}}\right)}{2 \sqrt{7}}","x^3-\frac{x^2}{2}+\frac{1}{4} \log \left(2 x^2-x+1\right)-\frac{\tan ^{-1}\left(\frac{1-4 x}{\sqrt{7}}\right)}{2 \sqrt{7}}",1,"-1/2*x^2 + x^3 + ArcTan[(-1 + 4*x)/Sqrt[7]]/(2*Sqrt[7]) + Log[1 - x + 2*x^2]/4","A",1
96,1,25,25,0.0056295,"\int \frac{-1+x+x^2}{-6 x+x^2+x^3} \, dx","Integrate[(-1 + x + x^2)/(-6*x + x^2 + x^3),x]","\frac{1}{2} \log (2-x)+\frac{\log (x)}{6}+\frac{1}{3} \log (x+3)","\frac{1}{2} \log (2-x)+\frac{\log (x)}{6}+\frac{1}{3} \log (x+3)",1,"Log[2 - x]/2 + Log[x]/6 + Log[3 + x]/3","A",1
97,1,29,33,0.0144603,"\int \frac{11 a^2-7 a x+5 x^2}{-6 a^3+11 a^2 x-6 a x^2+x^3} \, dx","Integrate[(11*a^2 - 7*a*x + 5*x^2)/(-6*a^3 + 11*a^2*x - 6*a*x^2 + x^3),x]","\frac{35}{2} \log (x-3 a)-17 \log (x-2 a)+\frac{9}{2} \log (x-a)","\frac{9}{2} \log (a-x)-17 \log (2 a-x)+\frac{35}{2} \log (3 a-x)",1,"(35*Log[-3*a + x])/2 - 17*Log[-2*a + x] + (9*Log[-a + x])/2","A",1
98,1,37,37,0.0071247,"\int \frac{2-x+x^2}{4-5 x^2+x^4} \, dx","Integrate[(2 - x + x^2)/(4 - 5*x^2 + x^4),x]","-\frac{1}{3} \log (1-x)+\frac{1}{3} \log (2-x)+\frac{2}{3} \log (x+1)-\frac{2}{3} \log (x+2)","-\frac{1}{3} \log (1-x)+\frac{1}{3} \log (2-x)+\frac{2}{3} \log (x+1)-\frac{2}{3} \log (x+2)",1,"-1/3*Log[1 - x] + Log[2 - x]/3 + (2*Log[1 + x])/3 - (2*Log[2 + x])/3","A",1
99,1,69,31,0.0177779,"\int \frac{-5+2 x^2}{6-5 x^2+x^4} \, dx","Integrate[(-5 + 2*x^2)/(6 - 5*x^2 + x^4),x]","\frac{1}{12} \left(3 \sqrt{2} \log \left(\sqrt{2}-x\right)+2 \sqrt{3} \log \left(\sqrt{3}-x\right)-3 \sqrt{2} \log \left(x+\sqrt{2}\right)-2 \sqrt{3} \log \left(x+\sqrt{3}\right)\right)","-\frac{\tanh ^{-1}\left(\frac{x}{\sqrt{2}}\right)}{\sqrt{2}}-\frac{\tanh ^{-1}\left(\frac{x}{\sqrt{3}}\right)}{\sqrt{3}}",1,"(3*Sqrt[2]*Log[Sqrt[2] - x] + 2*Sqrt[3]*Log[Sqrt[3] - x] - 3*Sqrt[2]*Log[Sqrt[2] + x] - 2*Sqrt[3]*Log[Sqrt[3] + x])/12","B",1
100,1,41,41,0.0077072,"\int \frac{1}{(-4+x) (-3+x) (-2+x) (-1+x)} \, dx","Integrate[1/((-4 + x)*(-3 + x)*(-2 + x)*(-1 + x)),x]","-\frac{1}{6} \log (1-x)+\frac{1}{2} \log (2-x)-\frac{1}{2} \log (3-x)+\frac{1}{6} \log (4-x)","-\frac{1}{6} \log (1-x)+\frac{1}{2} \log (2-x)-\frac{1}{2} \log (3-x)+\frac{1}{6} \log (4-x)",1,"-1/6*Log[1 - x] + Log[2 - x]/2 - Log[3 - x]/2 + Log[4 - x]/6","A",1
101,1,16,25,0.0094345,"\int \frac{1+x^2}{(-1+x)^3} \, dx","Integrate[(1 + x^2)/(-1 + x)^3,x]","\frac{1-2 x}{(x-1)^2}+\log (x-1)","\frac{2}{1-x}-\frac{1}{(1-x)^2}+\log (1-x)",1,"(1 - 2*x)/(-1 + x)^2 + Log[-1 + x]","A",1
102,1,36,36,0.0143069,"\int \frac{x^5}{(3+x)^2} \, dx","Integrate[x^5/(3 + x)^2,x]","\frac{1}{4} \left(x^4-8 x^3+54 x^2-432 x+\frac{972}{x+3}-2079\right)+405 \log (x+3)","\frac{x^4}{4}-2 x^3+\frac{27 x^2}{2}-108 x+\frac{243}{x+3}+405 \log (x+3)",1,"(-2079 - 432*x + 54*x^2 - 8*x^3 + x^4 + 972/(3 + x))/4 + 405*Log[3 + x]","A",1
103,1,37,41,0.0205367,"\int \frac{-2+5 x^3}{-27+18 x^2-8 x^3+x^4} \, dx","Integrate[(-2 + 5*x^3)/(-27 + 18*x^2 - 8*x^3 + x^4),x]","-\frac{407}{16 (x-3)}-\frac{133}{8 (x-3)^2}+\frac{313}{64} \log (3-x)+\frac{7}{64} \log (x+1)","\frac{407}{16 (3-x)}-\frac{133}{8 (3-x)^2}+\frac{313}{64} \log (3-x)+\frac{7}{64} \log (x+1)",1,"-133/(8*(-3 + x)^2) - 407/(16*(-3 + x)) + (313*Log[3 - x])/64 + (7*Log[1 + x])/64","A",1
104,1,27,27,0.0174446,"\int \frac{-9+3 x-6 x^2+x^3}{(3+x)^2 (4+x)^2} \, dx","Integrate[(-9 + 3*x - 6*x^2 + x^3)/((3 + x)^2*(4 + x)^2),x]","\frac{99}{x+3}+\frac{181}{x+4}+264 \log (x+3)-263 \log (x+4)","\frac{99}{x+3}+\frac{181}{x+4}+264 \log (x+3)-263 \log (x+4)",1,"99/(3 + x) + 181/(4 + x) + 264*Log[3 + x] - 263*Log[4 + x]","A",1
105,1,47,39,0.0176359,"\int \frac{2+x^2+x^3}{x \left(-1+x^2\right)^2} \, dx","Integrate[(2 + x^2 + x^3)/(x*(-1 + x^2)^2),x]","\frac{1}{4} \left(-\frac{4}{x^2-1}-4 \log \left(1-x^2\right)-\frac{2}{x-1}+\log (1-x)+8 \log (x)-\log (x+1)\right)","\frac{x+3}{2 \left(1-x^2\right)}-\frac{3}{4} \log (1-x)+2 \log (x)-\frac{5}{4} \log (x+1)",1,"(-2/(-1 + x) - 4/(-1 + x^2) + Log[1 - x] + 8*Log[x] - Log[1 + x] - 4*Log[1 - x^2])/4","A",1
106,1,40,46,0.0161186,"\int \frac{1}{x^3-x^4-x^5+x^6} \, dx","Integrate[(x^3 - x^4 - x^5 + x^6)^(-1),x]","\frac{1}{4} \left(-\frac{2}{x^2}-\frac{2}{x-1}-\frac{4}{x}-7 \log (1-x)+8 \log (x)-\log (x+1)\right)","-\frac{1}{2 x^2}+\frac{1}{2 (1-x)}-\frac{1}{x}-\frac{7}{4} \log (1-x)+2 \log (x)-\frac{1}{4} \log (x+1)",1,"(-2/(-1 + x) - 2/x^2 - 4/x - 7*Log[1 - x] + 8*Log[x] - Log[1 + x])/4","A",1
107,1,29,29,0.0076452,"\int \frac{1+x^4}{-1+x-x^2+x^3} \, dx","Integrate[(1 + x^4)/(-1 + x - x^2 + x^3),x]","\frac{x^2}{2}-\frac{1}{2} \log \left(x^2+1\right)+x+\log (1-x)-\tan ^{-1}(x)","\frac{x^2}{2}-\frac{1}{2} \log \left(x^2+1\right)+x+\log (1-x)-\tan ^{-1}(x)",1,"x + x^2/2 - ArcTan[x] + Log[1 - x] - Log[1 + x^2]/2","A",1
108,1,27,27,0.0071935,"\int \frac{1}{x (1+x) \left(1+x^2\right)} \, dx","Integrate[1/(x*(1 + x)*(1 + x^2)),x]","-\frac{1}{4} \log \left(x^2+1\right)+\log (x)-\frac{1}{2} \log (x+1)-\frac{1}{2} \tan ^{-1}(x)","-\frac{1}{4} \log \left(x^2+1\right)+\log (x)-\frac{1}{2} \log (x+1)-\frac{1}{2} \tan ^{-1}(x)",1,"-1/2*ArcTan[x] + Log[x] - Log[1 + x]/2 - Log[1 + x^2]/4","A",1
109,1,32,24,0.0106504,"\int \frac{x^2}{-2+x^2+x^4} \, dx","Integrate[x^2/(-2 + x^2 + x^4),x]","\frac{1}{6} \left(\log (1-x)-\log (x+1)+2 \sqrt{2} \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right)","\frac{1}{3} \sqrt{2} \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)-\frac{1}{3} \tanh ^{-1}(x)",1,"(2*Sqrt[2]*ArcTan[x/Sqrt[2]] + Log[1 - x] - Log[1 + x])/6","A",1
110,1,41,41,0.0234377,"\int \frac{6 x+4 x^2+x^3}{2+4 x+3 x^2+2 x^3+x^4} \, dx","Integrate[(6*x + 4*x^2 + x^3)/(2 + 4*x + 3*x^2 + 2*x^3 + x^4),x]","\frac{2}{3} \log \left(x^2+2\right)+\frac{1}{x+1}-\frac{1}{3} \log (x+1)+\frac{4}{3} \sqrt{2} \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)","\frac{2}{3} \log \left(x^2+2\right)+\frac{1}{x+1}-\frac{1}{3} \log (x+1)+\frac{4}{3} \sqrt{2} \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)",1,"(1 + x)^(-1) + (4*Sqrt[2]*ArcTan[x/Sqrt[2]])/3 - Log[1 + x]/3 + (2*Log[2 + x^2])/3","A",1
111,1,40,46,0.020051,"\int \frac{x}{(1+x) (1+2 x)^2 \left(1+x^2\right)} \, dx","Integrate[x/((1 + x)*(1 + 2*x)^2*(1 + x^2)),x]","\frac{1}{100} \left(-7 \log \left(x^2+1\right)+\frac{40}{2 x+1}-50 \log (x+1)+64 \log (2 x+1)+2 \tan ^{-1}(x)\right)","-\frac{7}{100} \log \left(x^2+1\right)+\frac{2}{5 (2 x+1)}-\frac{1}{2} \log (x+1)+\frac{16}{25} \log (2 x+1)+\frac{1}{50} \tan ^{-1}(x)",1,"(40/(1 + 2*x) + 2*ArcTan[x] - 50*Log[1 + x] + 64*Log[1 + 2*x] - 7*Log[1 + x^2])/100","A",1
112,1,37,47,0.0255533,"\int \frac{-2+x+3 x^2}{(-1+x)^3 \left(1+x^2\right)} \, dx","Integrate[(-2 + x + 3*x^2)/((-1 + x)^3*(1 + x^2)),x]","\frac{1}{4} \left(3 \log \left(x^2+1\right)-\frac{10}{x-1}-\frac{2}{(x-1)^2}-6 \log (x-1)-4 \tan ^{-1}(x)\right)","\frac{3}{4} \log \left(x^2+1\right)+\frac{5}{2 (1-x)}-\frac{1}{2 (1-x)^2}-\frac{3}{2} \log (1-x)-\tan ^{-1}(x)",1,"(-2/(-1 + x)^2 - 10/(-1 + x) - 4*ArcTan[x] - 6*Log[-1 + x] + 3*Log[1 + x^2])/4","A",1
113,1,73,67,0.056661,"\int \frac{1}{1+x^2+x^4} \, dx","Integrate[(1 + x^2 + x^4)^(-1),x]","\frac{i \left(\sqrt{1-i \sqrt{3}} \tan ^{-1}\left(\frac{1}{2} \left(\sqrt{3}-i\right) x\right)-\sqrt{1+i \sqrt{3}} \tan ^{-1}\left(\frac{1}{2} \left(\sqrt{3}+i\right) x\right)\right)}{\sqrt{6}}","-\frac{1}{4} \log \left(x^2-x+1\right)+\frac{1}{4} \log \left(x^2+x+1\right)-\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{2 \sqrt{3}}",1,"(I*(Sqrt[1 - I*Sqrt[3]]*ArcTan[((-I + Sqrt[3])*x)/2] - Sqrt[1 + I*Sqrt[3]]*ArcTan[((I + Sqrt[3])*x)/2]))/Sqrt[6]","C",0
114,1,67,48,0.0184069,"\int \frac{3+2 x^3}{-9 x+x^5} \, dx","Integrate[(3 + 2*x^3)/(-9*x + x^5),x]","\frac{1}{12} \left(\log \left(9-x^4\right)-4 \log (x)+2 \sqrt{3} \log \left(3-\sqrt{3} x\right)-2 \sqrt{3} \log \left(\sqrt{3} x+3\right)+4 \sqrt{3} \tan ^{-1}\left(\frac{x}{\sqrt{3}}\right)\right)","\frac{1}{12} \log \left(9-x^4\right)-\frac{\log (x)}{3}+\frac{\tan ^{-1}\left(\frac{x}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{\tanh ^{-1}\left(\frac{x}{\sqrt{3}}\right)}{\sqrt{3}}",1,"(4*Sqrt[3]*ArcTan[x/Sqrt[3]] - 4*Log[x] + 2*Sqrt[3]*Log[3 - Sqrt[3]*x] - 2*Sqrt[3]*Log[3 + Sqrt[3]*x] + Log[9 - x^4])/12","A",1
115,1,46,58,0.0263674,"\int \frac{-20+8 x+5 x^3}{(-4+x)^3 \left(8-4 x+x^2\right)} \, dx","Integrate[(-20 + 8*x + 5*x^3)/((-4 + x)^3*(8 - 4*x + x^2)),x]","\frac{1}{32} \left(45 \log \left(x^2-4 x+8\right)-\frac{328}{x-4}-\frac{664}{(x-4)^2}-90 \log (x-4)+6 \tan ^{-1}\left(\frac{x-2}{2}\right)\right)","\frac{45}{32} \log \left(x^2-4 x+8\right)+\frac{41}{4 (4-x)}-\frac{83}{4 (4-x)^2}-\frac{45}{16} \log (4-x)-\frac{3}{16} \tan ^{-1}\left(1-\frac{x}{2}\right)",1,"(-664/(-4 + x)^2 - 328/(-4 + x) + 6*ArcTan[(-2 + x)/2] - 90*Log[-4 + x] + 45*Log[8 - 4*x + x^2])/32","A",1
116,1,47,51,0.0227845,"\int \frac{1}{\left(1+x^2\right) \left(2+x^2\right) \left(3+x^2\right) \left(4+x^2\right)} \, dx","Integrate[1/((1 + x^2)*(2 + x^2)*(3 + x^2)*(4 + x^2)),x]","\frac{1}{12} \left(-\tan ^{-1}\left(\frac{x}{2}\right)+2 \tan ^{-1}(x)-3 \sqrt{2} \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{x}{\sqrt{3}}\right)\right)","-\frac{1}{12} \tan ^{-1}\left(\frac{x}{2}\right)+\frac{1}{6} \tan ^{-1}(x)-\frac{\tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)}{2 \sqrt{2}}+\frac{\tan ^{-1}\left(\frac{x}{\sqrt{3}}\right)}{2 \sqrt{3}}",1,"(-ArcTan[x/2] + 2*ArcTan[x] - 3*Sqrt[2]*ArcTan[x/Sqrt[2]] + 2*Sqrt[3]*ArcTan[x/Sqrt[3]])/12","A",1
117,1,41,41,0.0081871,"\int \frac{x}{\left(1+x^2\right) \left(2+x^2\right) \left(3+x^2\right) \left(4+x^2\right)} \, dx","Integrate[x/((1 + x^2)*(2 + x^2)*(3 + x^2)*(4 + x^2)),x]","\frac{1}{12} \log \left(x^2+1\right)-\frac{1}{4} \log \left(x^2+2\right)+\frac{1}{4} \log \left(x^2+3\right)-\frac{1}{12} \log \left(x^2+4\right)","\frac{1}{12} \log \left(x^2+1\right)-\frac{1}{4} \log \left(x^2+2\right)+\frac{1}{4} \log \left(x^2+3\right)-\frac{1}{12} \log \left(x^2+4\right)",1,"Log[1 + x^2]/12 - Log[2 + x^2]/4 + Log[3 + x^2]/4 - Log[4 + x^2]/12","A",1
118,1,52,56,0.0113931,"\int \frac{1}{a^3+x^3} \, dx","Integrate[(a^3 + x^3)^(-1),x]","\frac{-\log \left(a^2-a x+x^2\right)+2 \log (a+x)+2 \sqrt{3} \tan ^{-1}\left(\frac{2 x-a}{\sqrt{3} a}\right)}{6 a^2}","-\frac{\log \left(a^2-a x+x^2\right)}{6 a^2}+\frac{\log (a+x)}{3 a^2}-\frac{\tan ^{-1}\left(\frac{a-2 x}{\sqrt{3} a}\right)}{\sqrt{3} a^2}",1,"(2*Sqrt[3]*ArcTan[(-a + 2*x)/(Sqrt[3]*a)] + 2*Log[a + x] - Log[a^2 - a*x + x^2])/(6*a^2)","A",1
119,1,50,56,0.0055579,"\int \frac{x}{a^3+x^3} \, dx","Integrate[x/(a^3 + x^3),x]","\frac{\log \left(a^2-a x+x^2\right)-2 \log (a+x)+2 \sqrt{3} \tan ^{-1}\left(\frac{2 x-a}{\sqrt{3} a}\right)}{6 a}","\frac{\log \left(a^2-a x+x^2\right)}{6 a}-\frac{\log (a+x)}{3 a}-\frac{\tan ^{-1}\left(\frac{a-2 x}{\sqrt{3} a}\right)}{\sqrt{3} a}",1,"(2*Sqrt[3]*ArcTan[(-a + 2*x)/(Sqrt[3]*a)] - 2*Log[a + x] + Log[a^2 - a*x + x^2])/(6*a)","A",1
120,1,12,12,0.0023822,"\int \frac{x^2}{a^3+x^3} \, dx","Integrate[x^2/(a^3 + x^3),x]","\frac{1}{3} \log \left(a^3+x^3\right)","\frac{1}{3} \log \left(a^3+x^3\right)",1,"Log[a^3 + x^3]/3","A",1
121,1,22,22,0.0042649,"\int \frac{1}{x \left(a^3+x^3\right)} \, dx","Integrate[1/(x*(a^3 + x^3)),x]","\frac{\log (x)}{a^3}-\frac{\log \left(a^3+x^3\right)}{3 a^3}","\frac{\log (x)}{a^3}-\frac{\log \left(a^3+x^3\right)}{3 a^3}",1,"Log[x]/a^3 - Log[a^3 + x^3]/(3*a^3)","A",1
122,1,60,63,0.0139257,"\int \frac{1}{x^2 \left(a^3+x^3\right)} \, dx","Integrate[1/(x^2*(a^3 + x^3)),x]","-\frac{x \log \left(a^2-a x+x^2\right)-2 x \log (a+x)+2 \sqrt{3} x \tan ^{-1}\left(\frac{2 x-a}{\sqrt{3} a}\right)+6 a}{6 a^4 x}","\frac{\log (a+x)}{3 a^4}+\frac{\tan ^{-1}\left(\frac{a-2 x}{\sqrt{3} a}\right)}{\sqrt{3} a^4}-\frac{1}{a^3 x}-\frac{\log \left(a^2-a x+x^2\right)}{6 a^4}",1,"-1/6*(6*a + 2*Sqrt[3]*x*ArcTan[(-a + 2*x)/(Sqrt[3]*a)] - 2*x*Log[a + x] + x*Log[a^2 - a*x + x^2])/(a^4*x)","A",1
123,1,68,65,0.0153,"\int \frac{1}{x^3 \left(a^3+x^3\right)} \, dx","Integrate[1/(x^3*(a^3 + x^3)),x]","-\frac{\log (a+x)}{3 a^5}-\frac{\tan ^{-1}\left(\frac{2 x-a}{\sqrt{3} a}\right)}{\sqrt{3} a^5}-\frac{1}{2 a^3 x^2}+\frac{\log \left(a^2-a x+x^2\right)}{6 a^5}","-\frac{\log (a+x)}{3 a^5}+\frac{\tan ^{-1}\left(\frac{a-2 x}{\sqrt{3} a}\right)}{\sqrt{3} a^5}-\frac{1}{2 a^3 x^2}+\frac{\log \left(a^2-a x+x^2\right)}{6 a^5}",1,"-1/2*1/(a^3*x^2) - ArcTan[(-a + 2*x)/(Sqrt[3]*a)]/(Sqrt[3]*a^5) - Log[a + x]/(3*a^5) + Log[a^2 - a*x + x^2]/(6*a^5)","A",1
124,1,33,33,0.005419,"\int \frac{1}{x^4 \left(a^3+x^3\right)} \, dx","Integrate[1/(x^4*(a^3 + x^3)),x]","-\frac{\log (x)}{a^6}-\frac{1}{3 a^3 x^3}+\frac{\log \left(a^3+x^3\right)}{3 a^6}","-\frac{\log (x)}{a^6}-\frac{1}{3 a^3 x^3}+\frac{\log \left(a^3+x^3\right)}{3 a^6}",1,"-1/3*1/(a^3*x^3) - Log[x]/a^6 + Log[a^3 + x^3]/(3*a^6)","A",1
125,1,74,73,0.0124036,"\int \frac{1}{x^5 \left(a^3+x^3\right)} \, dx","Integrate[1/(x^5*(a^3 + x^3)),x]","-\frac{\log (a+x)}{3 a^7}+\frac{\tan ^{-1}\left(\frac{2 x-a}{\sqrt{3} a}\right)}{\sqrt{3} a^7}+\frac{1}{a^6 x}-\frac{1}{4 a^3 x^4}+\frac{\log \left(a^2-a x+x^2\right)}{6 a^7}","-\frac{\log (a+x)}{3 a^7}-\frac{\tan ^{-1}\left(\frac{a-2 x}{\sqrt{3} a}\right)}{\sqrt{3} a^7}+\frac{1}{a^6 x}-\frac{1}{4 a^3 x^4}+\frac{\log \left(a^2-a x+x^2\right)}{6 a^7}",1,"-1/4*1/(a^3*x^4) + 1/(a^6*x) + ArcTan[(-a + 2*x)/(Sqrt[3]*a)]/(Sqrt[3]*a^7) - Log[a + x]/(3*a^7) + Log[a^2 - a*x + x^2]/(6*a^7)","A",1
126,1,45,46,0.0095684,"\int \frac{x^{-m}}{a^3+x^3} \, dx","Integrate[1/(x^m*(a^3 + x^3)),x]","-\frac{x^{1-m} \, _2F_1\left(1,\frac{1}{3}-\frac{m}{3};\frac{4}{3}-\frac{m}{3};-\frac{x^3}{a^3}\right)}{a^3 (m-1)}","\frac{x^{1-m} \, _2F_1\left(1,\frac{1-m}{3};\frac{4-m}{3};-\frac{x^3}{a^3}\right)}{a^3 (1-m)}",1,"-((x^(1 - m)*Hypergeometric2F1[1, 1/3 - m/3, 4/3 - m/3, -(x^3/a^3)])/(a^3*(-1 + m)))","A",1
127,1,38,27,0.0045444,"\int \frac{1}{a^4-x^4} \, dx","Integrate[(a^4 - x^4)^(-1),x]","-\frac{\log (a-x)}{4 a^3}+\frac{\log (a+x)}{4 a^3}+\frac{\tan ^{-1}\left(\frac{x}{a}\right)}{2 a^3}","\frac{\tan ^{-1}\left(\frac{x}{a}\right)}{2 a^3}+\frac{\tanh ^{-1}\left(\frac{x}{a}\right)}{2 a^3}",1,"ArcTan[x/a]/(2*a^3) - Log[a - x]/(4*a^3) + Log[a + x]/(4*a^3)","A",1
128,1,15,15,0.0039933,"\int \frac{x}{a^4-x^4} \, dx","Integrate[x/(a^4 - x^4),x]","\frac{\tanh ^{-1}\left(\frac{x^2}{a^2}\right)}{2 a^2}","\frac{\tanh ^{-1}\left(\frac{x^2}{a^2}\right)}{2 a^2}",1,"ArcTanh[x^2/a^2]/(2*a^2)","A",1
129,1,24,24,0.0062315,"\int \frac{1}{x \left(a^4-x^4\right)} \, dx","Integrate[1/(x*(a^4 - x^4)),x]","\frac{\log (x)}{a^4}-\frac{\log \left(x^4-a^4\right)}{4 a^4}","\frac{\log (x)}{a^4}-\frac{\log \left(a^4-x^4\right)}{4 a^4}",1,"Log[x]/a^4 - Log[-a^4 + x^4]/(4*a^4)","A",1
130,1,46,35,0.0071081,"\int \frac{1}{x^2 \left(a^4-x^4\right)} \, dx","Integrate[1/(x^2*(a^4 - x^4)),x]","-\frac{\log (a-x)}{4 a^5}+\frac{\log (a+x)}{4 a^5}-\frac{\tan ^{-1}\left(\frac{x}{a}\right)}{2 a^5}-\frac{1}{a^4 x}","-\frac{\tan ^{-1}\left(\frac{x}{a}\right)}{2 a^5}+\frac{\tanh ^{-1}\left(\frac{x}{a}\right)}{2 a^5}-\frac{1}{a^4 x}",1,"-(1/(a^4*x)) - ArcTan[x/a]/(2*a^5) - Log[a - x]/(4*a^5) + Log[a + x]/(4*a^5)","A",1
131,1,50,26,0.0067413,"\int \frac{1}{x^3 \left(a^4-x^4\right)} \, dx","Integrate[1/(x^3*(a^4 - x^4)),x]","-\frac{\log (a-x)}{4 a^6}-\frac{\log (a+x)}{4 a^6}-\frac{1}{2 a^4 x^2}+\frac{\log \left(a^2+x^2\right)}{4 a^6}","\frac{\tanh ^{-1}\left(\frac{x^2}{a^2}\right)}{2 a^6}-\frac{1}{2 a^4 x^2}",1,"-1/2*1/(a^4*x^2) - Log[a - x]/(4*a^6) - Log[a + x]/(4*a^6) + Log[a^2 + x^2]/(4*a^6)","A",1
132,1,48,37,0.0072205,"\int \frac{1}{x^4 \left(a^4-x^4\right)} \, dx","Integrate[1/(x^4*(a^4 - x^4)),x]","-\frac{\log (a-x)}{4 a^7}+\frac{\log (a+x)}{4 a^7}+\frac{\tan ^{-1}\left(\frac{x}{a}\right)}{2 a^7}-\frac{1}{3 a^4 x^3}","\frac{\tan ^{-1}\left(\frac{x}{a}\right)}{2 a^7}+\frac{\tanh ^{-1}\left(\frac{x}{a}\right)}{2 a^7}-\frac{1}{3 a^4 x^3}",1,"-1/3*1/(a^4*x^3) + ArcTan[x/a]/(2*a^7) - Log[a - x]/(4*a^7) + Log[a + x]/(4*a^7)","A",1
133,1,44,45,0.0098067,"\int \frac{x^{-m}}{a^4-x^4} \, dx","Integrate[1/(x^m*(a^4 - x^4)),x]","-\frac{x^{1-m} \, _2F_1\left(1,\frac{1}{4}-\frac{m}{4};\frac{5}{4}-\frac{m}{4};\frac{x^4}{a^4}\right)}{a^4 (m-1)}","\frac{x^{1-m} \, _2F_1\left(1,\frac{1-m}{4};\frac{5-m}{4};\frac{x^4}{a^4}\right)}{a^4 (1-m)}",1,"-((x^(1 - m)*Hypergeometric2F1[1, 1/4 - m/4, 5/4 - m/4, x^4/a^4])/(a^4*(-1 + m)))","A",1
134,1,15,15,0.0034663,"\int \frac{x}{a^4+x^4} \, dx","Integrate[x/(a^4 + x^4),x]","\frac{\tan ^{-1}\left(\frac{x^2}{a^2}\right)}{2 a^2}","\frac{\tan ^{-1}\left(\frac{x^2}{a^2}\right)}{2 a^2}",1,"ArcTan[x^2/a^2]/(2*a^2)","A",1
135,1,79,109,0.0287578,"\int \frac{x^2}{a^4+x^4} \, dx","Integrate[x^2/(a^4 + x^4),x]","\frac{\log \left(a^2-\sqrt{2} a x+x^2\right)-\log \left(a^2+\sqrt{2} a x+x^2\right)-2 \tan ^{-1}\left(1-\frac{\sqrt{2} x}{a}\right)+2 \tan ^{-1}\left(\frac{\sqrt{2} x}{a}+1\right)}{4 \sqrt{2} a}","\frac{\log \left(a^2-\sqrt{2} a x+x^2\right)}{4 \sqrt{2} a}-\frac{\log \left(a^2+\sqrt{2} a x+x^2\right)}{4 \sqrt{2} a}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} x}{a}\right)}{2 \sqrt{2} a}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} x}{a}+1\right)}{2 \sqrt{2} a}",1,"(-2*ArcTan[1 - (Sqrt[2]*x)/a] + 2*ArcTan[1 + (Sqrt[2]*x)/a] + Log[a^2 - Sqrt[2]*a*x + x^2] - Log[a^2 + Sqrt[2]*a*x + x^2])/(4*Sqrt[2]*a)","A",1
136,1,204,201,0.1668611,"\int \frac{1}{a^5+x^5} \, dx","Integrate[(a^5 + x^5)^(-1),x]","-\frac{-\sqrt{5} \log \left(a^2+\frac{1}{2} \left(\sqrt{5}-1\right) a x+x^2\right)+\log \left(a^2+\frac{1}{2} \left(\sqrt{5}-1\right) a x+x^2\right)+\sqrt{5} \log \left(a^2-\frac{1}{2} \left(1+\sqrt{5}\right) a x+x^2\right)+\log \left(a^2-\frac{1}{2} \left(1+\sqrt{5}\right) a x+x^2\right)-4 \log (a+x)-2 \sqrt{2 \left(5+\sqrt{5}\right)} \tan ^{-1}\left(\frac{\left(\sqrt{5}-1\right) a+4 x}{\sqrt{2 \left(5+\sqrt{5}\right)} a}\right)-2 \sqrt{10-2 \sqrt{5}} \tan ^{-1}\left(\frac{4 x-\left(1+\sqrt{5}\right) a}{\sqrt{10-2 \sqrt{5}} a}\right)}{20 a^4}","\frac{\log (a+x)}{5 a^4}-\frac{\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} \tan ^{-1}\left(\frac{\left(1-\sqrt{5}\right) a-4 x}{\sqrt{2 \left(5+\sqrt{5}\right)} a}\right)}{5 a^4}-\frac{\sqrt{\frac{1}{2} \left(5-\sqrt{5}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{1}{10} \left(5+\sqrt{5}\right)} \left(\left(1+\sqrt{5}\right) a-4 x\right)}{2 a}\right)}{5 a^4}-\frac{\left(1-\sqrt{5}\right) \log \left(a^2-\frac{1}{2} \left(1-\sqrt{5}\right) a x+x^2\right)}{20 a^4}-\frac{\left(1+\sqrt{5}\right) \log \left(a^2-\frac{1}{2} \left(1+\sqrt{5}\right) a x+x^2\right)}{20 a^4}",1,"-1/20*(-2*Sqrt[2*(5 + Sqrt[5])]*ArcTan[((-1 + Sqrt[5])*a + 4*x)/(Sqrt[2*(5 + Sqrt[5])]*a)] - 2*Sqrt[10 - 2*Sqrt[5]]*ArcTan[(-((1 + Sqrt[5])*a) + 4*x)/(Sqrt[10 - 2*Sqrt[5]]*a)] - 4*Log[a + x] + Log[a^2 + ((-1 + Sqrt[5])*a*x)/2 + x^2] - Sqrt[5]*Log[a^2 + ((-1 + Sqrt[5])*a*x)/2 + x^2] + Log[a^2 - ((1 + Sqrt[5])*a*x)/2 + x^2] + Sqrt[5]*Log[a^2 - ((1 + Sqrt[5])*a*x)/2 + x^2])/a^4","A",1
137,1,204,201,0.0739387,"\int \frac{x}{a^5+x^5} \, dx","Integrate[x/(a^5 + x^5),x]","\frac{\sqrt{5} \log \left(a^2+\frac{1}{2} \left(\sqrt{5}-1\right) a x+x^2\right)+\log \left(a^2+\frac{1}{2} \left(\sqrt{5}-1\right) a x+x^2\right)-\sqrt{5} \log \left(a^2-\frac{1}{2} \left(1+\sqrt{5}\right) a x+x^2\right)+\log \left(a^2-\frac{1}{2} \left(1+\sqrt{5}\right) a x+x^2\right)-4 \log (a+x)-2 \sqrt{10-2 \sqrt{5}} \tan ^{-1}\left(\frac{\left(\sqrt{5}-1\right) a+4 x}{\sqrt{2 \left(5+\sqrt{5}\right)} a}\right)+2 \sqrt{2 \left(5+\sqrt{5}\right)} \tan ^{-1}\left(\frac{4 x-\left(1+\sqrt{5}\right) a}{\sqrt{10-2 \sqrt{5}} a}\right)}{20 a^3}","-\frac{\log (a+x)}{5 a^3}+\frac{\sqrt{\frac{1}{2} \left(5-\sqrt{5}\right)} \tan ^{-1}\left(\frac{\left(1-\sqrt{5}\right) a-4 x}{\sqrt{2 \left(5+\sqrt{5}\right)} a}\right)}{5 a^3}-\frac{\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{1}{10} \left(5+\sqrt{5}\right)} \left(\left(1+\sqrt{5}\right) a-4 x\right)}{2 a}\right)}{5 a^3}+\frac{\left(1+\sqrt{5}\right) \log \left(a^2-\frac{1}{2} \left(1-\sqrt{5}\right) a x+x^2\right)}{20 a^3}+\frac{\left(1-\sqrt{5}\right) \log \left(a^2-\frac{1}{2} \left(1+\sqrt{5}\right) a x+x^2\right)}{20 a^3}",1,"(-2*Sqrt[10 - 2*Sqrt[5]]*ArcTan[((-1 + Sqrt[5])*a + 4*x)/(Sqrt[2*(5 + Sqrt[5])]*a)] + 2*Sqrt[2*(5 + Sqrt[5])]*ArcTan[(-((1 + Sqrt[5])*a) + 4*x)/(Sqrt[10 - 2*Sqrt[5]]*a)] - 4*Log[a + x] + Log[a^2 + ((-1 + Sqrt[5])*a*x)/2 + x^2] + Sqrt[5]*Log[a^2 + ((-1 + Sqrt[5])*a*x)/2 + x^2] + Log[a^2 - ((1 + Sqrt[5])*a*x)/2 + x^2] - Sqrt[5]*Log[a^2 - ((1 + Sqrt[5])*a*x)/2 + x^2])/(20*a^3)","A",0
138,1,204,201,0.0902341,"\int \frac{x^2}{a^5+x^5} \, dx","Integrate[x^2/(a^5 + x^5),x]","-\frac{\sqrt{5} \log \left(a^2+\frac{1}{2} \left(\sqrt{5}-1\right) a x+x^2\right)+\log \left(a^2+\frac{1}{2} \left(\sqrt{5}-1\right) a x+x^2\right)-\sqrt{5} \log \left(a^2-\frac{1}{2} \left(1+\sqrt{5}\right) a x+x^2\right)+\log \left(a^2-\frac{1}{2} \left(1+\sqrt{5}\right) a x+x^2\right)-4 \log (a+x)+2 \sqrt{10-2 \sqrt{5}} \tan ^{-1}\left(\frac{\left(\sqrt{5}-1\right) a+4 x}{\sqrt{2 \left(5+\sqrt{5}\right)} a}\right)-2 \sqrt{2 \left(5+\sqrt{5}\right)} \tan ^{-1}\left(\frac{4 x-\left(1+\sqrt{5}\right) a}{\sqrt{10-2 \sqrt{5}} a}\right)}{20 a^2}","-\frac{\left(1+\sqrt{5}\right) \log \left(a^2-\frac{1}{2} \left(1-\sqrt{5}\right) a x+x^2\right)}{20 a^2}-\frac{\left(1-\sqrt{5}\right) \log \left(a^2-\frac{1}{2} \left(1+\sqrt{5}\right) a x+x^2\right)}{20 a^2}+\frac{\log (a+x)}{5 a^2}+\frac{\sqrt{\frac{1}{2} \left(5-\sqrt{5}\right)} \tan ^{-1}\left(\frac{\left(1-\sqrt{5}\right) a-4 x}{\sqrt{2 \left(5+\sqrt{5}\right)} a}\right)}{5 a^2}-\frac{\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{1}{10} \left(5+\sqrt{5}\right)} \left(\left(1+\sqrt{5}\right) a-4 x\right)}{2 a}\right)}{5 a^2}",1,"-1/20*(2*Sqrt[10 - 2*Sqrt[5]]*ArcTan[((-1 + Sqrt[5])*a + 4*x)/(Sqrt[2*(5 + Sqrt[5])]*a)] - 2*Sqrt[2*(5 + Sqrt[5])]*ArcTan[(-((1 + Sqrt[5])*a) + 4*x)/(Sqrt[10 - 2*Sqrt[5]]*a)] - 4*Log[a + x] + Log[a^2 + ((-1 + Sqrt[5])*a*x)/2 + x^2] + Sqrt[5]*Log[a^2 + ((-1 + Sqrt[5])*a*x)/2 + x^2] + Log[a^2 - ((1 + Sqrt[5])*a*x)/2 + x^2] - Sqrt[5]*Log[a^2 - ((1 + Sqrt[5])*a*x)/2 + x^2])/a^2","A",0
139,1,204,201,0.0606032,"\int \frac{x^3}{a^5+x^5} \, dx","Integrate[x^3/(a^5 + x^5),x]","\frac{-\sqrt{5} \log \left(a^2+\frac{1}{2} \left(\sqrt{5}-1\right) a x+x^2\right)+\log \left(a^2+\frac{1}{2} \left(\sqrt{5}-1\right) a x+x^2\right)+\sqrt{5} \log \left(a^2-\frac{1}{2} \left(1+\sqrt{5}\right) a x+x^2\right)+\log \left(a^2-\frac{1}{2} \left(1+\sqrt{5}\right) a x+x^2\right)-4 \log (a+x)+2 \sqrt{2 \left(5+\sqrt{5}\right)} \tan ^{-1}\left(\frac{\left(\sqrt{5}-1\right) a+4 x}{\sqrt{2 \left(5+\sqrt{5}\right)} a}\right)+2 \sqrt{10-2 \sqrt{5}} \tan ^{-1}\left(\frac{4 x-\left(1+\sqrt{5}\right) a}{\sqrt{10-2 \sqrt{5}} a}\right)}{20 a}","\frac{\left(1-\sqrt{5}\right) \log \left(a^2-\frac{1}{2} \left(1-\sqrt{5}\right) a x+x^2\right)}{20 a}+\frac{\left(1+\sqrt{5}\right) \log \left(a^2-\frac{1}{2} \left(1+\sqrt{5}\right) a x+x^2\right)}{20 a}-\frac{\log (a+x)}{5 a}-\frac{\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} \tan ^{-1}\left(\frac{\left(1-\sqrt{5}\right) a-4 x}{\sqrt{2 \left(5+\sqrt{5}\right)} a}\right)}{5 a}-\frac{\sqrt{\frac{1}{2} \left(5-\sqrt{5}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{1}{10} \left(5+\sqrt{5}\right)} \left(\left(1+\sqrt{5}\right) a-4 x\right)}{2 a}\right)}{5 a}",1,"(2*Sqrt[2*(5 + Sqrt[5])]*ArcTan[((-1 + Sqrt[5])*a + 4*x)/(Sqrt[2*(5 + Sqrt[5])]*a)] + 2*Sqrt[10 - 2*Sqrt[5]]*ArcTan[(-((1 + Sqrt[5])*a) + 4*x)/(Sqrt[10 - 2*Sqrt[5]]*a)] - 4*Log[a + x] + Log[a^2 + ((-1 + Sqrt[5])*a*x)/2 + x^2] - Sqrt[5]*Log[a^2 + ((-1 + Sqrt[5])*a*x)/2 + x^2] + Log[a^2 - ((1 + Sqrt[5])*a*x)/2 + x^2] + Sqrt[5]*Log[a^2 - ((1 + Sqrt[5])*a*x)/2 + x^2])/(20*a)","A",1
140,1,12,12,0.0028292,"\int \frac{x^4}{a^5+x^5} \, dx","Integrate[x^4/(a^5 + x^5),x]","\frac{1}{5} \log \left(a^5+x^5\right)","\frac{1}{5} \log \left(a^5+x^5\right)",1,"Log[a^5 + x^5]/5","A",1
141,1,22,22,0.0052523,"\int \frac{1}{x \left(a^5+x^5\right)} \, dx","Integrate[1/(x*(a^5 + x^5)),x]","\frac{\log (x)}{a^5}-\frac{\log \left(a^5+x^5\right)}{5 a^5}","\frac{\log (x)}{a^5}-\frac{\log \left(a^5+x^5\right)}{5 a^5}",1,"Log[x]/a^5 - Log[a^5 + x^5]/(5*a^5)","A",1
142,1,172,209,0.1709187,"\int \frac{1}{x^2 \left(a^5+x^5\right)} \, dx","Integrate[1/(x^2*(a^5 + x^5)),x]","-\frac{-\left(\sqrt{5}-1\right) \log \left(a^2+\frac{1}{2} \left(\sqrt{5}-1\right) a x+x^2\right)+\left(1+\sqrt{5}\right) \log \left(a^2-\frac{1}{2} \left(1+\sqrt{5}\right) a x+x^2\right)+\frac{20 a}{x}-4 \log (a+x)+2 \sqrt{2 \left(5+\sqrt{5}\right)} \tan ^{-1}\left(\frac{\left(\sqrt{5}-1\right) a+4 x}{\sqrt{2 \left(5+\sqrt{5}\right)} a}\right)+2 \sqrt{10-2 \sqrt{5}} \tan ^{-1}\left(\frac{4 x-\left(1+\sqrt{5}\right) a}{\sqrt{10-2 \sqrt{5}} a}\right)}{20 a^6}","\frac{\log (a+x)}{5 a^6}+\frac{\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} \tan ^{-1}\left(\frac{\left(1-\sqrt{5}\right) a-4 x}{\sqrt{2 \left(5+\sqrt{5}\right)} a}\right)}{5 a^6}+\frac{\sqrt{\frac{1}{2} \left(5-\sqrt{5}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{1}{10} \left(5+\sqrt{5}\right)} \left(\left(1+\sqrt{5}\right) a-4 x\right)}{2 a}\right)}{5 a^6}-\frac{1}{a^5 x}-\frac{\left(1-\sqrt{5}\right) \log \left(a^2-\frac{1}{2} \left(1-\sqrt{5}\right) a x+x^2\right)}{20 a^6}-\frac{\left(1+\sqrt{5}\right) \log \left(a^2-\frac{1}{2} \left(1+\sqrt{5}\right) a x+x^2\right)}{20 a^6}",1,"-1/20*((20*a)/x + 2*Sqrt[2*(5 + Sqrt[5])]*ArcTan[((-1 + Sqrt[5])*a + 4*x)/(Sqrt[2*(5 + Sqrt[5])]*a)] + 2*Sqrt[10 - 2*Sqrt[5]]*ArcTan[(-((1 + Sqrt[5])*a) + 4*x)/(Sqrt[10 - 2*Sqrt[5]]*a)] - 4*Log[a + x] - (-1 + Sqrt[5])*Log[a^2 + ((-1 + Sqrt[5])*a*x)/2 + x^2] + (1 + Sqrt[5])*Log[a^2 - ((1 + Sqrt[5])*a*x)/2 + x^2])/a^6","A",1
143,1,174,211,0.1650147,"\int \frac{1}{x^3 \left(a^5+x^5\right)} \, dx","Integrate[1/(x^3*(a^5 + x^5)),x]","-\frac{\frac{10 a^2}{x^2}-\left(1+\sqrt{5}\right) \log \left(a^2+\frac{1}{2} \left(\sqrt{5}-1\right) a x+x^2\right)+\left(\sqrt{5}-1\right) \log \left(a^2-\frac{1}{2} \left(1+\sqrt{5}\right) a x+x^2\right)+4 \log (a+x)-2 \sqrt{10-2 \sqrt{5}} \tan ^{-1}\left(\frac{\left(\sqrt{5}-1\right) a+4 x}{\sqrt{2 \left(5+\sqrt{5}\right)} a}\right)+2 \sqrt{2 \left(5+\sqrt{5}\right)} \tan ^{-1}\left(\frac{4 x-\left(1+\sqrt{5}\right) a}{\sqrt{10-2 \sqrt{5}} a}\right)}{20 a^7}","-\frac{\log (a+x)}{5 a^7}-\frac{\sqrt{\frac{1}{2} \left(5-\sqrt{5}\right)} \tan ^{-1}\left(\frac{\left(1-\sqrt{5}\right) a-4 x}{\sqrt{2 \left(5+\sqrt{5}\right)} a}\right)}{5 a^7}+\frac{\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{1}{10} \left(5+\sqrt{5}\right)} \left(\left(1+\sqrt{5}\right) a-4 x\right)}{2 a}\right)}{5 a^7}-\frac{1}{2 a^5 x^2}+\frac{\left(1+\sqrt{5}\right) \log \left(a^2-\frac{1}{2} \left(1-\sqrt{5}\right) a x+x^2\right)}{20 a^7}+\frac{\left(1-\sqrt{5}\right) \log \left(a^2-\frac{1}{2} \left(1+\sqrt{5}\right) a x+x^2\right)}{20 a^7}",1,"-1/20*((10*a^2)/x^2 - 2*Sqrt[10 - 2*Sqrt[5]]*ArcTan[((-1 + Sqrt[5])*a + 4*x)/(Sqrt[2*(5 + Sqrt[5])]*a)] + 2*Sqrt[2*(5 + Sqrt[5])]*ArcTan[(-((1 + Sqrt[5])*a) + 4*x)/(Sqrt[10 - 2*Sqrt[5]]*a)] + 4*Log[a + x] - (1 + Sqrt[5])*Log[a^2 + ((-1 + Sqrt[5])*a*x)/2 + x^2] + (-1 + Sqrt[5])*Log[a^2 - ((1 + Sqrt[5])*a*x)/2 + x^2])/a^7","A",0
144,1,175,211,0.1372078,"\int \frac{1}{x^4 \left(a^5+x^5\right)} \, dx","Integrate[1/(x^4*(a^5 + x^5)),x]","\frac{-\frac{20 a^3}{x^3}-3 \left(1+\sqrt{5}\right) \log \left(a^2+\frac{1}{2} \left(\sqrt{5}-1\right) a x+x^2\right)+3 \left(\sqrt{5}-1\right) \log \left(a^2-\frac{1}{2} \left(1+\sqrt{5}\right) a x+x^2\right)+12 \log (a+x)+6 \sqrt{10-2 \sqrt{5}} \tan ^{-1}\left(\frac{\left(\sqrt{5}-1\right) a+4 x}{\sqrt{2 \left(5+\sqrt{5}\right)} a}\right)-6 \sqrt{2 \left(5+\sqrt{5}\right)} \tan ^{-1}\left(\frac{4 x-\left(1+\sqrt{5}\right) a}{\sqrt{10-2 \sqrt{5}} a}\right)}{60 a^8}","\frac{\log (a+x)}{5 a^8}-\frac{\sqrt{\frac{1}{2} \left(5-\sqrt{5}\right)} \tan ^{-1}\left(\frac{\left(1-\sqrt{5}\right) a-4 x}{\sqrt{2 \left(5+\sqrt{5}\right)} a}\right)}{5 a^8}+\frac{\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{1}{10} \left(5+\sqrt{5}\right)} \left(\left(1+\sqrt{5}\right) a-4 x\right)}{2 a}\right)}{5 a^8}-\frac{1}{3 a^5 x^3}-\frac{\left(1+\sqrt{5}\right) \log \left(a^2-\frac{1}{2} \left(1-\sqrt{5}\right) a x+x^2\right)}{20 a^8}-\frac{\left(1-\sqrt{5}\right) \log \left(a^2-\frac{1}{2} \left(1+\sqrt{5}\right) a x+x^2\right)}{20 a^8}",1,"((-20*a^3)/x^3 + 6*Sqrt[10 - 2*Sqrt[5]]*ArcTan[((-1 + Sqrt[5])*a + 4*x)/(Sqrt[2*(5 + Sqrt[5])]*a)] - 6*Sqrt[2*(5 + Sqrt[5])]*ArcTan[(-((1 + Sqrt[5])*a) + 4*x)/(Sqrt[10 - 2*Sqrt[5]]*a)] + 12*Log[a + x] - 3*(1 + Sqrt[5])*Log[a^2 + ((-1 + Sqrt[5])*a*x)/2 + x^2] + 3*(-1 + Sqrt[5])*Log[a^2 - ((1 + Sqrt[5])*a*x)/2 + x^2])/(60*a^8)","A",0
145,1,45,46,0.0112453,"\int \frac{x^{-m}}{a^5+x^5} \, dx","Integrate[1/(x^m*(a^5 + x^5)),x]","-\frac{x^{1-m} \, _2F_1\left(1,\frac{1}{5}-\frac{m}{5};\frac{6}{5}-\frac{m}{5};-\frac{x^5}{a^5}\right)}{a^5 (m-1)}","\frac{x^{1-m} \, _2F_1\left(1,\frac{1-m}{5};\frac{6-m}{5};-\frac{x^5}{a^5}\right)}{a^5 (1-m)}",1,"-((x^(1 - m)*Hypergeometric2F1[1, 1/5 - m/5, 6/5 - m/5, -(x^5/a^5)])/(a^5*(-1 + m)))","A",1
146,1,21,35,0.006956,"\int \frac{1+x^4}{1+x^6} \, dx","Integrate[(1 + x^4)/(1 + x^6),x]","\frac{2}{3} \tan ^{-1}(x)-\frac{1}{3} \tan ^{-1}\left(\frac{x}{x^2-1}\right)","-\frac{1}{3} \tan ^{-1}\left(\sqrt{3}-2 x\right)+\frac{2}{3} \tan ^{-1}(x)+\frac{1}{3} \tan ^{-1}\left(2 x+\sqrt{3}\right)",1,"(2*ArcTan[x])/3 - ArcTan[x/(-1 + x^2)]/3","A",1
147,1,51,60,0.0311602,"\int \frac{1}{\left(5+3 x+x^2\right)^3} \, dx","Integrate[(5 + 3*x + x^2)^(-3),x]","\frac{\frac{11 (2 x+3) \left(6 x^2+18 x+41\right)}{\left(x^2+3 x+5\right)^2}+24 \sqrt{11} \tan ^{-1}\left(\frac{2 x+3}{\sqrt{11}}\right)}{2662}","\frac{3 (2 x+3)}{121 \left(x^2+3 x+5\right)}+\frac{2 x+3}{22 \left(x^2+3 x+5\right)^2}+\frac{12 \tan ^{-1}\left(\frac{2 x+3}{\sqrt{11}}\right)}{121 \sqrt{11}}",1,"((11*(3 + 2*x)*(41 + 18*x + 6*x^2))/(5 + 3*x + x^2)^2 + 24*Sqrt[11]*ArcTan[(3 + 2*x)/Sqrt[11]])/2662","A",1
148,1,30,43,0.0127658,"\int \frac{1+x^2+x^4}{\left(1+x^2\right)^4} \, dx","Integrate[(1 + x^2 + x^4)/(1 + x^2)^4,x]","\frac{1}{48} \left(\frac{x \left(21 x^4+40 x^2+27\right)}{\left(x^2+1\right)^3}+21 \tan ^{-1}(x)\right)","\frac{7 x}{16 \left(x^2+1\right)}-\frac{x}{24 \left(x^2+1\right)^2}+\frac{x}{6 \left(x^2+1\right)^3}+\frac{7}{16} \tan ^{-1}(x)",1,"((x*(27 + 40*x^2 + 21*x^4))/(1 + x^2)^3 + 21*ArcTan[x])/48","A",1
149,1,88,90,0.0945253,"\int \frac{B+A x}{\left(c+2 b x+a x^2\right)^2} \, dx","Integrate[(B + A*x)/(c + 2*b*x + a*x^2)^2,x]","\frac{\frac{(A b-a B) \tan ^{-1}\left(\frac{a x+b}{\sqrt{a c-b^2}}\right)}{\sqrt{a c-b^2}}+\frac{-a B x+A b x+A c-b B}{x (a x+2 b)+c}}{2 \left(b^2-a c\right)}","-\frac{-x (A b-a B)-A c+b B}{2 \left(b^2-a c\right) \left(a x^2+2 b x+c\right)}-\frac{(A b-a B) \tanh ^{-1}\left(\frac{a x+b}{\sqrt{b^2-a c}}\right)}{2 \left(b^2-a c\right)^{3/2}}",1,"((-(b*B) + A*c + A*b*x - a*B*x)/(c + x*(2*b + a*x)) + ((A*b - a*B)*ArcTan[(b + a*x)/Sqrt[-b^2 + a*c]])/Sqrt[-b^2 + a*c])/(2*(b^2 - a*c))","A",1
150,1,38,38,0.0163561,"\int \frac{-41+55 x-27 x^2+5 x^3}{\left(5-4 x+x^2\right)^2} \, dx","Integrate[(-41 + 55*x - 27*x^2 + 5*x^3)/(5 - 4*x + x^2)^2,x]","\frac{1-x}{x^2-4 x+5}+\frac{5}{2} \log \left(x^2-4 x+5\right)-2 \tan ^{-1}(2-x)","\frac{1-x}{x^2-4 x+5}+\frac{5}{2} \log \left(x^2-4 x+5\right)-2 \tan ^{-1}(2-x)",1,"(1 - x)/(5 - 4*x + x^2) - 2*ArcTan[2 - x] + (5*Log[5 - 4*x + x^2])/2","A",1
151,1,49,57,0.0248266,"\int \frac{1}{\left(-1+x^3\right)^2} \, dx","Integrate[(-1 + x^3)^(-2),x]","\frac{1}{9} \left(-\frac{3 x}{x^3-1}+\log \left(x^2+x+1\right)-2 \log (1-x)+2 \sqrt{3} \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)\right)","\frac{x}{3 \left(1-x^3\right)}+\frac{1}{9} \log \left(x^2+x+1\right)-\frac{2}{9} \log (1-x)+\frac{2 \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{3 \sqrt{3}}",1,"((-3*x)/(-1 + x^3) + 2*Sqrt[3]*ArcTan[(1 + 2*x)/Sqrt[3]] - 2*Log[1 - x] + Log[1 + x + x^2])/9","A",1
152,1,33,36,0.0163254,"\int \frac{4+3 x^4}{x^2 \left(1+x^2\right)^3} \, dx","Integrate[(4 + 3*x^4)/(x^2*(1 + x^2)^3),x]","-\frac{57 x^4+103 x^2+32}{8 x \left(x^2+1\right)^2}-\frac{57}{8} \tan ^{-1}(x)","-\frac{25 x}{8 \left(x^2+1\right)}-\frac{7 x}{4 \left(x^2+1\right)^2}-\frac{4}{x}-\frac{57}{8} \tan ^{-1}(x)",1,"-1/8*(32 + 103*x^2 + 57*x^4)/(x*(1 + x^2)^2) - (57*ArcTan[x])/8","A",1
153,1,78,49,0.014921,"\int \frac{x}{1+x^6} \, dx","Integrate[x/(1 + x^6),x]","\frac{1}{12} \left(2 \log \left(x^2+1\right)-\log \left(x^2-\sqrt{3} x+1\right)-\log \left(x^2+\sqrt{3} x+1\right)-2 \sqrt{3} \tan ^{-1}\left(\sqrt{3}-2 x\right)-2 \sqrt{3} \tan ^{-1}\left(2 x+\sqrt{3}\right)\right)","\frac{1}{6} \log \left(x^2+1\right)-\frac{\tan ^{-1}\left(\frac{1-2 x^2}{\sqrt{3}}\right)}{2 \sqrt{3}}-\frac{1}{12} \log \left(x^4-x^2+1\right)",1,"(-2*Sqrt[3]*ArcTan[Sqrt[3] - 2*x] - 2*Sqrt[3]*ArcTan[Sqrt[3] + 2*x] + 2*Log[1 + x^2] - Log[1 - Sqrt[3]*x + x^2] - Log[1 + Sqrt[3]*x + x^2])/12","A",1
154,1,20,13,0.0248718,"\int \frac{-1+x^{-1+n}}{-n x+x^n} \, dx","Integrate[(-1 + x^(-1 + n))/(-(n*x) + x^n),x]","\frac{\log \left(1-n x^{1-n}\right)}{n}+\log (x)","\frac{\log \left(x^n-n x\right)}{n}",1,"Log[x] + Log[1 - n*x^(1 - n)]/n","A",1
155,1,38,41,0.0116084,"\int \frac{x^3}{1-2 x^2+3 x^4} \, dx","Integrate[x^3/(1 - 2*x^2 + 3*x^4),x]","\frac{1}{12} \left(\sqrt{2} \tan ^{-1}\left(\frac{3 x^2-1}{\sqrt{2}}\right)+\log \left(3 x^4-2 x^2+1\right)\right)","\frac{1}{12} \log \left(3 x^4-2 x^2+1\right)-\frac{\tan ^{-1}\left(\frac{1-3 x^2}{\sqrt{2}}\right)}{6 \sqrt{2}}",1,"(Sqrt[2]*ArcTan[(-1 + 3*x^2)/Sqrt[2]] + Log[1 - 2*x^2 + 3*x^4])/12","A",1
156,1,32,32,0.0053062,"\int \frac{x^5}{-4+x^2+3 x^4} \, dx","Integrate[x^5/(-4 + x^2 + 3*x^4),x]","\frac{x^2}{6}+\frac{1}{14} \log \left(1-x^2\right)-\frac{8}{63} \log \left(3 x^2+4\right)","\frac{x^2}{6}+\frac{1}{14} \log \left(1-x^2\right)-\frac{8}{63} \log \left(3 x^2+4\right)",1,"x^2/6 + Log[1 - x^2]/14 - (8*Log[4 + 3*x^2])/63","A",1
157,1,25,25,0.0045169,"\int \frac{x^2}{9-10 x^3+x^6} \, dx","Integrate[x^2/(9 - 10*x^3 + x^6),x]","\frac{1}{24} \log \left(9-x^3\right)-\frac{1}{24} \log \left(1-x^3\right)","\frac{1}{24} \log \left(9-x^3\right)-\frac{1}{24} \log \left(1-x^3\right)",1,"-1/24*Log[1 - x^3] + Log[9 - x^3]/24","A",1
158,1,24,36,0.0135652,"\int \frac{1-4 x^2+x^3}{(-2+x)^4} \, dx","Integrate[(1 - 4*x^2 + x^3)/(-2 + x)^4,x]","\frac{-6 x^2+30 x-29}{3 (x-2)^3}+\log (x-2)","\frac{2}{2-x}+\frac{2}{(2-x)^2}-\frac{7}{3 (2-x)^3}+\log (2-x)",1,"(-29 + 30*x - 6*x^2)/(3*(-2 + x)^3) + Log[-2 + x]","A",1
159,1,24,45,0.0062024,"\int \frac{x^3}{(-1+x)^{12}} \, dx","Integrate[x^3/(-1 + x)^12,x]","\frac{-165 x^3+55 x^2-11 x+1}{1320 (x-1)^{11}}","-\frac{1}{8 (1-x)^8}+\frac{1}{3 (1-x)^9}-\frac{3}{10 (1-x)^{10}}+\frac{1}{11 (1-x)^{11}}",1,"(1 - 11*x + 55*x^2 - 165*x^3)/(1320*(-1 + x)^11)","A",1
160,1,41,55,0.0127682,"\int \frac{-3 x+x^4}{(1+2 x)^5} \, dx","Integrate[(-3*x + x^4)/(1 + 2*x)^5,x]","\frac{384 x^3+432 x^2+368 x+12 (2 x+1)^4 \log (2 x+1)+49}{384 (2 x+1)^4}","\frac{1}{8 (2 x+1)}-\frac{3}{32 (2 x+1)^2}+\frac{7}{24 (2 x+1)^3}-\frac{25}{128 (2 x+1)^4}+\frac{1}{32} \log (2 x+1)",1,"(49 + 368*x + 432*x^2 + 384*x^3 + 12*(1 + 2*x)^4*Log[1 + 2*x])/(384*(1 + 2*x)^4)","A",1
161,1,38,36,0.0243868,"\int \frac{1}{(-1+x)^2 (1+x)^3} \, dx","Integrate[1/((-1 + x)^2*(1 + x)^3),x]","\frac{1}{16} \left(\frac{-6 x^2-6 x+4}{(x-1) (x+1)^2}-3 \log (x-1)+3 \log (x+1)\right)","\frac{1}{8 (1-x)}-\frac{1}{4 (x+1)}-\frac{1}{8 (x+1)^2}+\frac{3}{8} \tanh ^{-1}(x)",1,"((4 - 6*x - 6*x^2)/((-1 + x)*(1 + x)^2) - 3*Log[-1 + x] + 3*Log[1 + x])/16","A",1
162,1,31,35,0.0173925,"\int \frac{1}{(5-6 x)^2 x^2} \, dx","Integrate[1/((5 - 6*x)^2*x^2),x]","\frac{1}{125} \left(\frac{30}{5-6 x}-\frac{5}{x}-12 \log (5-6 x)+12 \log (x)\right)","\frac{6}{25 (5-6 x)}-\frac{1}{25 x}-\frac{12}{125} \log (5-6 x)+\frac{12 \log (x)}{125}",1,"(30/(5 - 6*x) - 5/x - 12*Log[5 - 6*x] + 12*Log[x])/125","A",1
163,1,46,61,0.0242392,"\int \frac{1}{\left(-3-2 x+x^2\right)^3} \, dx","Integrate[(-3 - 2*x + x^2)^(-3),x]","\frac{1}{512} \left(\frac{4 \left(3 x^3-9 x^2-11 x+17\right)}{\left(x^2-2 x-3\right)^2}+3 \log (3-x)-3 \log (x+1)\right)","\frac{3 (1-x)}{128 \left(-x^2+2 x+3\right)}+\frac{1-x}{16 \left(-x^2+2 x+3\right)^2}+\frac{3}{512} \log (3-x)-\frac{3}{512} \log (x+1)",1,"((4*(17 - 11*x - 9*x^2 + 3*x^3))/(-3 - 2*x + x^2)^2 + 3*Log[3 - x] - 3*Log[1 + x])/512","A",1
164,1,36,51,0.0168954,"\int \frac{1}{\left(13-4 x+x^2\right)^3} \, dx","Integrate[(13 - 4*x + x^2)^(-3),x]","\frac{1}{648} \left(\frac{3 (x-2) \left(x^2-4 x+19\right)}{\left(x^2-4 x+13\right)^2}+\tan ^{-1}\left(\frac{x-2}{3}\right)\right)","-\frac{2-x}{216 \left(x^2-4 x+13\right)}-\frac{2-x}{36 \left(x^2-4 x+13\right)^2}+\frac{1}{648} \tan ^{-1}\left(\frac{x-2}{3}\right)",1,"((3*(-2 + x)*(19 - 4*x + x^2))/(13 - 4*x + x^2)^2 + ArcTan[(-2 + x)/3])/648","A",1
165,1,54,54,0.0474015,"\int \frac{1}{(2+x)^3 (3+x)^4} \, dx","Integrate[1/((2 + x)^3*(3 + x)^4),x]","\frac{4}{x+2}+\frac{6}{x+3}-\frac{1}{2 (x+2)^2}+\frac{3}{2 (x+3)^2}+\frac{1}{3 (x+3)^3}+10 \log (x+2)-10 \log (x+3)","\frac{4}{x+2}+\frac{6}{x+3}-\frac{1}{2 (x+2)^2}+\frac{3}{2 (x+3)^2}+\frac{1}{3 (x+3)^3}+10 \log (x+2)-10 \log (x+3)",1,"-1/2*1/(2 + x)^2 + 4/(2 + x) + 1/(3*(3 + x)^3) + 3/(2*(3 + x)^2) + 6/(3 + x) + 10*Log[2 + x] - 10*Log[3 + x]","A",1
166,1,53,36,0.0380555,"\int \frac{x^6}{\left(-2+x^2\right)^2} \, dx","Integrate[x^6/(-2 + x^2)^2,x]","\frac{x^3}{3}-\frac{2 x}{x^2-2}+4 x+\frac{5 \log \left(\sqrt{2}-x\right)}{\sqrt{2}}-\frac{5 \log \left(x+\sqrt{2}\right)}{\sqrt{2}}","\frac{x^3}{3}-\frac{2 x}{x^2-2}+4 x-5 \sqrt{2} \tanh ^{-1}\left(\frac{x}{\sqrt{2}}\right)",1,"4*x + x^3/3 - (2*x)/(-2 + x^2) + (5*Log[Sqrt[2] - x])/Sqrt[2] - (5*Log[Sqrt[2] + x])/Sqrt[2]","A",1
167,1,40,58,0.0210734,"\int \frac{x^8}{\left(4+x^2\right)^4} \, dx","Integrate[x^8/(4 + x^2)^4,x]","\frac{x \left(12 x^6+231 x^4+1120 x^2+1680\right)}{12 \left(x^2+4\right)^3}-\frac{35}{8} \tan ^{-1}\left(\frac{x}{2}\right)","-\frac{x^7}{6 \left(x^2+4\right)^3}-\frac{7 x^5}{24 \left(x^2+4\right)^2}-\frac{35 x^3}{48 \left(x^2+4\right)}+\frac{35 x}{16}-\frac{35}{8} \tan ^{-1}\left(\frac{x}{2}\right)",1,"(x*(1680 + 1120*x^2 + 231*x^4 + 12*x^6))/(12*(4 + x^2)^3) - (35*ArcTan[x/2])/8","A",1
168,1,43,43,0.0346507,"\int \frac{-4+7 x}{\left(5+2 x+3 x^2\right)^2} \, dx","Integrate[(-4 + 7*x)/(5 + 2*x + 3*x^2)^2,x]","\frac{-19 x-39}{28 \left(3 x^2+2 x+5\right)}-\frac{19 \tan ^{-1}\left(\frac{3 x+1}{\sqrt{14}}\right)}{28 \sqrt{14}}","-\frac{19 x+39}{28 \left(3 x^2+2 x+5\right)}-\frac{19 \tan ^{-1}\left(\frac{3 x+1}{\sqrt{14}}\right)}{28 \sqrt{14}}",1,"(-39 - 19*x)/(28*(5 + 2*x + 3*x^2)) - (19*ArcTan[(1 + 3*x)/Sqrt[14]])/(28*Sqrt[14])","A",1
169,1,62,43,0.0415835,"\int \frac{5-4 x}{\left(-2-4 x+3 x^2\right)^2} \, dx","Integrate[(5 - 4*x)/(-2 - 4*x + 3*x^2)^2,x]","\frac{18-7 x}{20 \left(3 x^2-4 x-2\right)}-\frac{7 \log \left(-3 x+\sqrt{10}+2\right)}{40 \sqrt{10}}+\frac{7 \log \left(3 x+\sqrt{10}-2\right)}{40 \sqrt{10}}","-\frac{18-7 x}{20 \left(-3 x^2+4 x+2\right)}-\frac{7 \tanh ^{-1}\left(\frac{2-3 x}{\sqrt{10}}\right)}{20 \sqrt{10}}",1,"(18 - 7*x)/(20*(-2 - 4*x + 3*x^2)) - (7*Log[2 + Sqrt[10] - 3*x])/(40*Sqrt[10]) + (7*Log[-2 + Sqrt[10] + 3*x])/(40*Sqrt[10])","A",1
170,1,25,37,0.0116465,"\int \frac{x^5}{\left(1+x^4\right)^3} \, dx","Integrate[x^5/(1 + x^4)^3,x]","\frac{1}{16} \left(\tan ^{-1}\left(x^2\right)+\frac{\left(x^4-1\right) x^2}{\left(x^4+1\right)^2}\right)","\frac{1}{16} \tan ^{-1}\left(x^2\right)+\frac{x^2}{16 \left(x^4+1\right)}-\frac{x^2}{8 \left(x^4+1\right)^2}",1,"((x^2*(-1 + x^4))/(1 + x^4)^2 + ArcTan[x^2])/16","A",1
171,1,26,32,0.0155644,"\int \frac{x \left(1+x^2\right)^3}{\left(2+2 x^2+x^4\right)^2} \, dx","Integrate[(x*(1 + x^2)^3)/(2 + 2*x^2 + x^4)^2,x]","\frac{1}{4} \left(\frac{1}{\left(x^2+1\right)^2+1}+\log \left(\left(x^2+1\right)^2+1\right)\right)","\frac{1}{4 \left(x^4+2 x^2+2\right)}+\frac{1}{4} \log \left(x^4+2 x^2+2\right)",1,"((1 + (1 + x^2)^2)^(-1) + Log[1 + (1 + x^2)^2])/4","A",1
172,1,13,13,0.003906,"\int \frac{x^3}{\left(a^4+x^4\right)^3} \, dx","Integrate[x^3/(a^4 + x^4)^3,x]","-\frac{1}{8 \left(a^4+x^4\right)^2}","-\frac{1}{8 \left(a^4+x^4\right)^2}",1,"-1/8*1/(a^4 + x^4)^2","A",1
173,1,46,54,0.0311968,"\int \frac{1}{x \left(a^4+x^4\right)^3} \, dx","Integrate[1/(x*(a^4 + x^4)^3),x]","\frac{-2 \log \left(a^4+x^4\right)+\frac{3 a^8+2 a^4 x^4}{\left(a^4+x^4\right)^2}+8 \log (x)}{8 a^{12}}","\frac{\log (x)}{a^{12}}+\frac{1}{8 a^4 \left(a^4+x^4\right)^2}-\frac{\log \left(a^4+x^4\right)}{4 a^{12}}+\frac{1}{4 a^8 \left(a^4+x^4\right)}",1,"((3*a^8 + 2*a^4*x^4)/(a^4 + x^4)^2 + 8*Log[x] - 2*Log[a^4 + x^4])/(8*a^12)","A",1
174,1,134,157,0.1177416,"\int \frac{1}{x^2 \left(a^4+x^4\right)^3} \, dx","Integrate[1/(x^2*(a^4 + x^4)^3),x]","-\frac{\frac{104 a x^3}{a^4+x^4}+45 \sqrt{2} \log \left(a^2-\sqrt{2} a x+x^2\right)-45 \sqrt{2} \log \left(a^2+\sqrt{2} a x+x^2\right)+\frac{32 a^5 x^3}{\left(a^4+x^4\right)^2}+\frac{256 a}{x}-90 \sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} x}{a}\right)+90 \sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} x}{a}+1\right)}{256 a^{13}}","\frac{45 \tan ^{-1}\left(1-\frac{\sqrt{2} x}{a}\right)}{64 \sqrt{2} a^{13}}-\frac{45 \tan ^{-1}\left(\frac{\sqrt{2} x}{a}+1\right)}{64 \sqrt{2} a^{13}}-\frac{45}{32 a^{12} x}+\frac{1}{8 a^4 x \left(a^4+x^4\right)^2}-\frac{45 \log \left(a^2-\sqrt{2} a x+x^2\right)}{128 \sqrt{2} a^{13}}+\frac{45 \log \left(a^2+\sqrt{2} a x+x^2\right)}{128 \sqrt{2} a^{13}}+\frac{9}{32 a^8 x \left(a^4+x^4\right)}",1,"-1/256*((256*a)/x + (32*a^5*x^3)/(a^4 + x^4)^2 + (104*a*x^3)/(a^4 + x^4) - 90*Sqrt[2]*ArcTan[1 - (Sqrt[2]*x)/a] + 90*Sqrt[2]*ArcTan[1 + (Sqrt[2]*x)/a] + 45*Sqrt[2]*Log[a^2 - Sqrt[2]*a*x + x^2] - 45*Sqrt[2]*Log[a^2 + Sqrt[2]*a*x + x^2])/a^13","A",1
175,1,75,64,0.049927,"\int \frac{1}{x^3 \left(a^4+x^4\right)^3} \, dx","Integrate[1/(x^3*(a^4 + x^4)^3),x]","\frac{-\frac{a^2 \left(8 a^8+25 a^4 x^4+15 x^8\right)}{x^2 \left(a^4+x^4\right)^2}+15 \tan ^{-1}\left(1-\frac{\sqrt{2} x}{a}\right)+15 \tan ^{-1}\left(\frac{\sqrt{2} x}{a}+1\right)}{16 a^{14}}","-\frac{15}{16 a^{12} x^2}+\frac{1}{8 a^4 x^2 \left(a^4+x^4\right)^2}-\frac{15 \tan ^{-1}\left(\frac{x^2}{a^2}\right)}{16 a^{14}}+\frac{5}{16 a^8 x^2 \left(a^4+x^4\right)}",1,"(-((a^2*(8*a^8 + 25*a^4*x^4 + 15*x^8))/(x^2*(a^4 + x^4)^2)) + 15*ArcTan[1 - (Sqrt[2]*x)/a] + 15*ArcTan[1 + (Sqrt[2]*x)/a])/(16*a^14)","A",1
176,1,33,39,0.0140073,"\int \frac{x^{14}}{\left(3+2 x^5\right)^3} \, dx","Integrate[x^14/(3 + 2*x^5)^3,x]","\frac{1}{80} \left(\frac{3 \left(8 x^5+9\right)}{\left(2 x^5+3\right)^2}+2 \log \left(2 x^5+3\right)\right)","\frac{3}{20 \left(2 x^5+3\right)}-\frac{9}{80 \left(2 x^5+3\right)^2}+\frac{1}{40} \log \left(2 x^5+3\right)",1,"((3*(9 + 8*x^5))/(3 + 2*x^5)^2 + 2*Log[3 + 2*x^5])/80","A",1
177,1,293,319,0.3117675,"\int \frac{x^6}{\left(3+2 x^5\right)^3} \, dx","Integrate[x^6/(3 + 2*x^5)^3,x]","\frac{2^{3/5} 3^{2/5} \left(1+\sqrt{5}\right) \log \left(2^{2/5} 3^{3/5} x^2+\left(\frac{3}{2}\right)^{4/5} \left(\sqrt{5}-1\right) x+3\right)-2^{3/5} 3^{2/5} \left(\sqrt{5}-1\right) \log \left(2^{2/5} 3^{3/5} x^2-\left(\frac{3}{2}\right)^{4/5} \left(1+\sqrt{5}\right) x+3\right)+\frac{40 x^2}{2 x^5+3}-\frac{300 x^2}{\left(2 x^5+3\right)^2}-4\ 2^{3/5} 3^{2/5} \log \left(\sqrt[5]{2} 3^{4/5} x+3\right)-4 \sqrt[10]{2} 3^{2/5} \sqrt{5-\sqrt{5}} \tan ^{-1}\left(\frac{4 \sqrt[5]{2} 3^{4/5} x+3 \sqrt{5}-3}{3 \sqrt{2 \left(5+\sqrt{5}\right)}}\right)+4 \sqrt[10]{2} 3^{2/5} \sqrt{5+\sqrt{5}} \tan ^{-1}\left(\frac{4 \sqrt[5]{2} 3^{4/5} x-3 \left(1+\sqrt{5}\right)}{3 \sqrt{10-2 \sqrt{5}}}\right)}{6000}","\frac{\left(1+\sqrt{5}\right) \log \left(2^{2/5} x^2-\frac{\sqrt[5]{3} \left(1-\sqrt{5}\right) x}{2^{4/5}}+3^{2/5}\right)}{1000\ 2^{2/5} 3^{3/5}}+\frac{\left(1-\sqrt{5}\right) \log \left(2^{2/5} x^2-\frac{\sqrt[5]{3} \left(1+\sqrt{5}\right) x}{2^{4/5}}+3^{2/5}\right)}{1000\ 2^{2/5} 3^{3/5}}+\frac{x^2}{150 \left(2 x^5+3\right)}-\frac{x^2}{20 \left(2 x^5+3\right)^2}-\frac{\log \left(\sqrt[5]{2} x+\sqrt[5]{3}\right)}{250\ 2^{2/5} 3^{3/5}}-\frac{\sqrt{5+\sqrt{5}} \tan ^{-1}\left(\sqrt{\frac{1}{5} \left(5+2 \sqrt{5}\right)}-\frac{2\ 2^{7/10} x}{\sqrt[5]{3} \sqrt{5-\sqrt{5}}}\right)}{250\ 2^{9/10} 3^{3/5}}-\frac{\sqrt{5-\sqrt{5}} \tan ^{-1}\left(\frac{2\ 2^{7/10} x}{\sqrt[5]{3} \sqrt{5+\sqrt{5}}}+\sqrt{\frac{1}{5} \left(5-2 \sqrt{5}\right)}\right)}{250\ 2^{9/10} 3^{3/5}}",1,"((-300*x^2)/(3 + 2*x^5)^2 + (40*x^2)/(3 + 2*x^5) - 4*2^(1/10)*3^(2/5)*Sqrt[5 - Sqrt[5]]*ArcTan[(-3 + 3*Sqrt[5] + 4*2^(1/5)*3^(4/5)*x)/(3*Sqrt[2*(5 + Sqrt[5])])] + 4*2^(1/10)*3^(2/5)*Sqrt[5 + Sqrt[5]]*ArcTan[(-3*(1 + Sqrt[5]) + 4*2^(1/5)*3^(4/5)*x)/(3*Sqrt[10 - 2*Sqrt[5]])] - 4*2^(3/5)*3^(2/5)*Log[3 + 2^(1/5)*3^(4/5)*x] + 2^(3/5)*3^(2/5)*(1 + Sqrt[5])*Log[3 + (3/2)^(4/5)*(-1 + Sqrt[5])*x + 2^(2/5)*3^(3/5)*x^2] - 2^(3/5)*3^(2/5)*(-1 + Sqrt[5])*Log[3 - (3/2)^(4/5)*(1 + Sqrt[5])*x + 2^(2/5)*3^(3/5)*x^2])/6000","A",1
178,1,65,59,0.0741943,"\int \frac{9}{5 x^2 \left(3-2 x^2\right)^3} \, dx","Integrate[9/(5*x^2*(3 - 2*x^2)^3),x]","\frac{1}{240} \left(-\frac{12 \left(10 x^4-25 x^2+12\right)}{x \left(3-2 x^2\right)^2}-5 \sqrt{6} \log \left(\sqrt{6}-2 x\right)+5 \sqrt{6} \log \left(2 x+\sqrt{6}\right)\right)","\frac{1}{8 x \left(3-2 x^2\right)}+\frac{3}{20 x \left(3-2 x^2\right)^2}-\frac{1}{8 x}+\frac{\tanh ^{-1}\left(\sqrt{\frac{2}{3}} x\right)}{4 \sqrt{6}}",1,"((-12*(12 - 25*x^2 + 10*x^4))/(x*(3 - 2*x^2)^2) - 5*Sqrt[6]*Log[Sqrt[6] - 2*x] + 5*Sqrt[6]*Log[Sqrt[6] + 2*x])/240","A",1
179,1,33,36,0.0143943,"\int \frac{4+3 x^4}{x^2 \left(1+x^2\right)^3} \, dx","Integrate[(4 + 3*x^4)/(x^2*(1 + x^2)^3),x]","-\frac{57 x^4+103 x^2+32}{8 x \left(x^2+1\right)^2}-\frac{57}{8} \tan ^{-1}(x)","-\frac{25 x}{8 \left(x^2+1\right)}-\frac{7 x}{4 \left(x^2+1\right)^2}-\frac{4}{x}-\frac{57}{8} \tan ^{-1}(x)",1,"-1/8*(32 + 103*x^2 + 57*x^4)/(x*(1 + x^2)^2) - (57*ArcTan[x])/8","A",1
180,1,32,38,0.0553425,"\int \frac{5-3 x+6 x^2+5 x^3-x^4}{-1+x+2 x^2-2 x^3-x^4+x^5} \, dx","Integrate[(5 - 3*x + 6*x^2 + 5*x^3 - x^4)/(-1 + x + 2*x^2 - 2*x^3 - x^4 + x^5),x]","-\frac{2}{x-1}+\frac{1}{x+1}-\frac{3}{2 (x-1)^2}+\log (x-1)-2 \log (x+1)","\frac{2}{1-x}+\frac{1}{x+1}-\frac{3}{2 (1-x)^2}+\log (1-x)-2 \log (x+1)",1,"-3/(2*(-1 + x)^2) - 2/(-1 + x) + (1 + x)^(-1) + Log[-1 + x] - 2*Log[1 + x]","A",1
181,1,65,64,0.0377986,"\int \frac{1+x^2}{x \left(1+x^3\right)^2} \, dx","Integrate[(1 + x^2)/(x*(1 + x^3)^2),x]","\frac{1}{18} \left(-6 \log \left(x^3+1\right)+\log \left(x^2-x+1\right)+\frac{6 \left(x^2+1\right)}{x^3+1}+18 \log (x)-2 \log (x+1)+2 \sqrt{3} \tan ^{-1}\left(\frac{2 x-1}{\sqrt{3}}\right)\right)","-\frac{5}{18} \log \left(x^2-x+1\right)+\frac{x \left(x-x^2\right)}{3 \left(x^3+1\right)}+\log (x)-\frac{4}{9} \log (x+1)-\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{3 \sqrt{3}}",1,"((6*(1 + x^2))/(1 + x^3) + 2*Sqrt[3]*ArcTan[(-1 + 2*x)/Sqrt[3]] + 18*Log[x] - 2*Log[1 + x] + Log[1 - x + x^2] - 6*Log[1 + x^3])/18","A",1
182,1,63,63,0.0404387,"\int \frac{-2-3 x+x^2}{(1+x)^2 \left(1+x+x^2\right)^2} \, dx","Integrate[(-2 - 3*x + x^2)/((1 + x)^2*(1 + x + x^2)^2),x]","-\frac{5 x+7}{3 \left(x^2+x+1\right)}+\frac{1}{2} \log \left(x^2+x+1\right)-\frac{2}{x+1}-\log (x+1)-\frac{25 \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{3 \sqrt{3}}","-\frac{5 x+7}{3 \left(x^2+x+1\right)}+\frac{1}{2} \log \left(x^2+x+1\right)-\frac{2}{x+1}-\log (x+1)-\frac{25 \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{3 \sqrt{3}}",1,"-2/(1 + x) - (7 + 5*x)/(3*(1 + x + x^2)) - (25*ArcTan[(1 + 2*x)/Sqrt[3]])/(3*Sqrt[3]) - Log[1 + x] + Log[1 + x + x^2]/2","A",1
183,1,46,43,0.0178391,"\int \frac{1}{(1-4 x)^3 (2-3 x)} \, dx","Integrate[1/((1 - 4*x)^3*(2 - 3*x)),x]","\frac{120 x+18 (1-4 x)^2 \log (8-12 x)-18 (1-4 x)^2 \log (4 x-1)-5}{250 (1-4 x)^2}","-\frac{3}{25 (1-4 x)}+\frac{1}{10 (1-4 x)^2}-\frac{9}{125} \log (1-4 x)+\frac{9}{125} \log (2-3 x)",1,"(-5 + 120*x + 18*(1 - 4*x)^2*Log[8 - 12*x] - 18*(1 - 4*x)^2*Log[-1 + 4*x])/(250*(1 - 4*x)^2)","A",1
184,1,20,27,0.0080858,"\int \frac{x^3}{\left(2-5 x^2\right)^7} \, dx","Integrate[x^3/(2 - 5*x^2)^7,x]","\frac{15 x^2-1}{750 \left(2-5 x^2\right)^6}","\frac{1}{150 \left(2-5 x^2\right)^6}-\frac{1}{250 \left(2-5 x^2\right)^5}",1,"(-1 + 15*x^2)/(750*(2 - 5*x^2)^6)","A",1
185,1,44,46,0.0161293,"\int \frac{x^7}{\left(2-5 x^2\right)^3} \, dx","Integrate[x^7/(2 - 5*x^2)^3,x]","-\frac{125 x^6-150 x^4+6 \left(2-5 x^2\right)^2 \log \left(5 x^2-2\right)+12}{1250 \left(2-5 x^2\right)^2}","-\frac{x^2}{250}-\frac{6}{625 \left(2-5 x^2\right)}+\frac{2}{625 \left(2-5 x^2\right)^2}-\frac{3}{625} \log \left(2-5 x^2\right)",1,"-1/1250*(12 - 150*x^4 + 125*x^6 + 6*(2 - 5*x^2)^2*Log[-2 + 5*x^2])/(2 - 5*x^2)^2","A",1
186,1,39,44,0.0227468,"\int \frac{1}{(-2+x)^3 (1+x)^2} \, dx","Integrate[1/((-2 + x)^3*(1 + x)^2),x]","\frac{1}{54} \left(\frac{3 \left(2 x^2-5 x-1\right)}{(x-2)^2 (x+1)}+2 \log (x-2)-2 \log (x+1)\right)","\frac{2}{27 (x-2)}+\frac{1}{27 (x+1)}-\frac{1}{18 (x-2)^2}+\frac{1}{27} \log (x-2)-\frac{1}{27} \log (x+1)",1,"((3*(-1 - 5*x + 2*x^2))/((-2 + x)^2*(1 + x)) + 2*Log[-2 + x] - 2*Log[1 + x])/54","A",1
187,1,54,54,0.0204154,"\int \frac{1}{(2+x)^3 (3+x)^4} \, dx","Integrate[1/((2 + x)^3*(3 + x)^4),x]","\frac{4}{x+2}+\frac{6}{x+3}-\frac{1}{2 (x+2)^2}+\frac{3}{2 (x+3)^2}+\frac{1}{3 (x+3)^3}+10 \log (x+2)-10 \log (x+3)","\frac{4}{x+2}+\frac{6}{x+3}-\frac{1}{2 (x+2)^2}+\frac{3}{2 (x+3)^2}+\frac{1}{3 (x+3)^3}+10 \log (x+2)-10 \log (x+3)",1,"-1/2*1/(2 + x)^2 + 4/(2 + x) + 1/(3*(3 + x)^3) + 3/(2*(3 + x)^2) + 6/(3 + x) + 10*Log[2 + x] - 10*Log[3 + x]","A",1
188,1,36,36,0.0146286,"\int \frac{x^5}{(3+x)^2} \, dx","Integrate[x^5/(3 + x)^2,x]","\frac{1}{4} \left(x^4-8 x^3+54 x^2-432 x+\frac{972}{x+3}-2079\right)+405 \log (x+3)","\frac{x^4}{4}-2 x^3+\frac{27 x^2}{2}-108 x+\frac{243}{x+3}+405 \log (x+3)",1,"(-2079 - 432*x + 54*x^2 - 8*x^3 + x^4 + 972/(3 + x))/4 + 405*Log[3 + x]","A",1
189,1,41,44,0.0129343,"\int (\text{b1}+\text{c1} x) \left(a+2 b x+c x^2\right) \, dx","Integrate[(b1 + c1*x)*(a + 2*b*x + c*x^2),x]","\frac{1}{12} x (6 a (2 \text{b1}+\text{c1} x)+x (4 b (3 \text{b1}+2 \text{c1} x)+c x (4 \text{b1}+3 \text{c1} x)))","\frac{1}{2} x^2 (a \text{c1}+2 b \text{b1})+a \text{b1} x+\frac{1}{3} x^3 (2 b \text{c1}+\text{b1} c)+\frac{1}{4} c \text{c1} x^4",1,"(x*(6*a*(2*b1 + c1*x) + x*(4*b*(3*b1 + 2*c1*x) + c*x*(4*b1 + 3*c1*x))))/12","A",1
190,1,91,96,0.0313079,"\int (\text{b1}+\text{c1} x) \left(a+2 b x+c x^2\right)^2 \, dx","Integrate[(b1 + c1*x)*(a + 2*b*x + c*x^2)^2,x]","\frac{1}{30} x \left(15 a^2 (2 \text{b1}+\text{c1} x)+5 a x (4 b (3 \text{b1}+2 \text{c1} x)+c x (4 \text{b1}+3 \text{c1} x))+x^2 \left(10 b^2 (4 \text{b1}+3 \text{c1} x)+6 b c x (5 \text{b1}+4 \text{c1} x)+c^2 x^2 (6 \text{b1}+5 \text{c1} x)\right)\right)","a^2 \text{b1} x+\frac{1}{2} x^4 \left(a c \text{c1}+2 b^2 \text{c1}+2 b \text{b1} c\right)+\frac{2}{3} x^3 \left(2 a b \text{c1}+a \text{b1} c+2 b^2 \text{b1}\right)+\frac{1}{2} a x^2 (a \text{c1}+4 b \text{b1})+\frac{1}{5} c x^5 (4 b \text{c1}+\text{b1} c)+\frac{1}{6} c^2 \text{c1} x^6",1,"(x*(15*a^2*(2*b1 + c1*x) + 5*a*x*(4*b*(3*b1 + 2*c1*x) + c*x*(4*b1 + 3*c1*x)) + x^2*(10*b^2*(4*b1 + 3*c1*x) + 6*b*c*x*(5*b1 + 4*c1*x) + c^2*x^2*(6*b1 + 5*c1*x))))/30","A",1
191,1,167,167,0.0332965,"\int (\text{b1}+\text{c1} x) \left(a+2 b x+c x^2\right)^3 \, dx","Integrate[(b1 + c1*x)*(a + 2*b*x + c*x^2)^3,x]","a^3 \text{b1} x+\frac{1}{4} x^4 \left(3 a^2 c \text{c1}+12 a b^2 \text{c1}+12 a b \text{b1} c+8 b^3 \text{b1}\right)+\frac{1}{2} a^2 x^2 (a \text{c1}+6 b \text{b1})+\frac{1}{2} c x^6 \left(a c \text{c1}+4 b^2 \text{c1}+2 b \text{b1} c\right)+a x^3 \left(2 a b \text{c1}+a \text{b1} c+4 b^2 \text{b1}\right)+\frac{1}{5} x^5 \left(12 a b c \text{c1}+3 a \text{b1} c^2+8 b^3 \text{c1}+12 b^2 \text{b1} c\right)+\frac{1}{7} c^2 x^7 (6 b \text{c1}+\text{b1} c)+\frac{1}{8} c^3 \text{c1} x^8","a^3 \text{b1} x+\frac{1}{4} x^4 \left(3 a^2 c \text{c1}+12 a b^2 \text{c1}+12 a b \text{b1} c+8 b^3 \text{b1}\right)+\frac{1}{2} a^2 x^2 (a \text{c1}+6 b \text{b1})+\frac{1}{2} c x^6 \left(a c \text{c1}+4 b^2 \text{c1}+2 b \text{b1} c\right)+a x^3 \left(2 a b \text{c1}+a \text{b1} c+4 b^2 \text{b1}\right)+\frac{1}{5} x^5 \left(12 a b c \text{c1}+3 a \text{b1} c^2+8 b^3 \text{c1}+12 b^2 \text{b1} c\right)+\frac{1}{7} c^2 x^7 (6 b \text{c1}+\text{b1} c)+\frac{1}{8} c^3 \text{c1} x^8",1,"a^3*b1*x + (a^2*(6*b*b1 + a*c1)*x^2)/2 + a*(4*b^2*b1 + a*b1*c + 2*a*b*c1)*x^3 + ((8*b^3*b1 + 12*a*b*b1*c + 12*a*b^2*c1 + 3*a^2*c*c1)*x^4)/4 + ((12*b^2*b1*c + 3*a*b1*c^2 + 8*b^3*c1 + 12*a*b*c*c1)*x^5)/5 + (c*(2*b*b1*c + 4*b^2*c1 + a*c*c1)*x^6)/2 + (c^2*(b1*c + 6*b*c1)*x^7)/7 + (c^3*c1*x^8)/8","A",1
192,1,263,263,0.0637488,"\int (\text{b1}+\text{c1} x) \left(a+2 b x+c x^2\right)^4 \, dx","Integrate[(b1 + c1*x)*(a + 2*b*x + c*x^2)^4,x]","a^4 \text{b1} x+\frac{1}{2} a^3 x^2 (a \text{c1}+8 b \text{b1})+\frac{4}{3} a^2 x^3 \left(2 a b \text{c1}+a \text{b1} c+6 b^2 \text{b1}\right)+a x^4 \left(a^2 c \text{c1}+6 a b^2 \text{c1}+6 a b \text{b1} c+8 b^3 \text{b1}\right)+\frac{1}{3} x^6 \left(3 a^2 c^2 \text{c1}+24 a b^2 c \text{c1}+12 a b \text{b1} c^2+8 b^4 \text{c1}+16 b^3 \text{b1} c\right)+\frac{2}{5} x^5 \left(12 a^2 b c \text{c1}+3 a^2 \text{b1} c^2+16 a b^3 \text{c1}+24 a b^2 \text{b1} c+8 b^4 \text{b1}\right)+\frac{1}{2} c^2 x^8 \left(a c \text{c1}+6 b^2 \text{c1}+2 b \text{b1} c\right)+\frac{4}{7} c x^7 \left(6 a b c \text{c1}+a \text{b1} c^2+8 b^3 \text{c1}+6 b^2 \text{b1} c\right)+\frac{1}{9} c^3 x^9 (8 b \text{c1}+\text{b1} c)+\frac{1}{10} c^4 \text{c1} x^{10}","a^4 \text{b1} x+\frac{1}{2} a^3 x^2 (a \text{c1}+8 b \text{b1})+\frac{4}{3} a^2 x^3 \left(2 a b \text{c1}+a \text{b1} c+6 b^2 \text{b1}\right)+a x^4 \left(a^2 c \text{c1}+6 a b^2 \text{c1}+6 a b \text{b1} c+8 b^3 \text{b1}\right)+\frac{1}{3} x^6 \left(3 a^2 c^2 \text{c1}+24 a b^2 c \text{c1}+12 a b \text{b1} c^2+8 b^4 \text{c1}+16 b^3 \text{b1} c\right)+\frac{2}{5} x^5 \left(12 a^2 b c \text{c1}+3 a^2 \text{b1} c^2+16 a b^3 \text{c1}+24 a b^2 \text{b1} c+8 b^4 \text{b1}\right)+\frac{1}{2} c^2 x^8 \left(a c \text{c1}+6 b^2 \text{c1}+2 b \text{b1} c\right)+\frac{4}{7} c x^7 \left(6 a b c \text{c1}+a \text{b1} c^2+8 b^3 \text{c1}+6 b^2 \text{b1} c\right)+\frac{1}{9} c^3 x^9 (8 b \text{c1}+\text{b1} c)+\frac{1}{10} c^4 \text{c1} x^{10}",1,"a^4*b1*x + (a^3*(8*b*b1 + a*c1)*x^2)/2 + (4*a^2*(6*b^2*b1 + a*b1*c + 2*a*b*c1)*x^3)/3 + a*(8*b^3*b1 + 6*a*b*b1*c + 6*a*b^2*c1 + a^2*c*c1)*x^4 + (2*(8*b^4*b1 + 24*a*b^2*b1*c + 3*a^2*b1*c^2 + 16*a*b^3*c1 + 12*a^2*b*c*c1)*x^5)/5 + ((16*b^3*b1*c + 12*a*b*b1*c^2 + 8*b^4*c1 + 24*a*b^2*c*c1 + 3*a^2*c^2*c1)*x^6)/3 + (4*c*(6*b^2*b1*c + a*b1*c^2 + 8*b^3*c1 + 6*a*b*c*c1)*x^7)/7 + (c^2*(2*b*b1*c + 6*b^2*c1 + a*c*c1)*x^8)/2 + (c^3*(b1*c + 8*b*c1)*x^9)/9 + (c^4*c1*x^10)/10","A",1
193,1,267,159,0.4589088,"\int (\text{b1}+\text{c1} x) \left(a+2 b x+c x^2\right)^n \, dx","Integrate[(b1 + c1*x)*(a + 2*b*x + c*x^2)^n,x]","\frac{1}{2} (a+x (2 b+c x))^n \left(\text{c1} x^2 \left(\frac{-\sqrt{b^2-a c}+b+c x}{b-\sqrt{b^2-a c}}\right)^{-n} \left(\frac{\sqrt{b^2-a c}+b+c x}{\sqrt{b^2-a c}+b}\right)^{-n} F_1\left(2;-n,-n;3;-\frac{c x}{b+\sqrt{b^2-a c}},\frac{c x}{\sqrt{b^2-a c}-b}\right)+\frac{\text{b1} 2^{n+1} \left(-\sqrt{b^2-a c}+b+c x\right) \left(\frac{\sqrt{b^2-a c}+b+c x}{\sqrt{b^2-a c}}\right)^{-n} \, _2F_1\left(-n,n+1;n+2;\frac{-b-c x+\sqrt{b^2-a c}}{2 \sqrt{b^2-a c}}\right)}{c (n+1)}\right)","\frac{\text{c1} \left(a+2 b x+c x^2\right)^{n+1}}{2 c (n+1)}-\frac{2^n (\text{b1} c-b \text{c1}) \left(-\frac{-\sqrt{b^2-a c}+b+c x}{\sqrt{b^2-a c}}\right)^{-n-1} \left(a+2 b x+c x^2\right)^{n+1} \, _2F_1\left(-n,n+1;n+2;\frac{b+c x+\sqrt{b^2-a c}}{2 \sqrt{b^2-a c}}\right)}{c (n+1) \sqrt{b^2-a c}}",1,"((a + x*(2*b + c*x))^n*((c1*x^2*AppellF1[2, -n, -n, 3, -((c*x)/(b + Sqrt[b^2 - a*c])), (c*x)/(-b + Sqrt[b^2 - a*c])])/(((b - Sqrt[b^2 - a*c] + c*x)/(b - Sqrt[b^2 - a*c]))^n*((b + Sqrt[b^2 - a*c] + c*x)/(b + Sqrt[b^2 - a*c]))^n) + (2^(1 + n)*b1*(b - Sqrt[b^2 - a*c] + c*x)*Hypergeometric2F1[-n, 1 + n, 2 + n, (-b + Sqrt[b^2 - a*c] - c*x)/(2*Sqrt[b^2 - a*c])])/(c*(1 + n)*((b + Sqrt[b^2 - a*c] + c*x)/Sqrt[b^2 - a*c])^n)))/2","C",0
194,1,66,65,0.0453184,"\int \frac{\text{b1}+\text{c1} x}{a+2 b x+c x^2} \, dx","Integrate[(b1 + c1*x)/(a + 2*b*x + c*x^2),x]","\frac{(\text{b1} c-b \text{c1}) \tan ^{-1}\left(\frac{b+c x}{\sqrt{a c-b^2}}\right)}{c \sqrt{a c-b^2}}+\frac{\text{c1} \log \left(a+2 b x+c x^2\right)}{2 c}","\frac{\text{c1} \log \left(a+2 b x+c x^2\right)}{2 c}-\frac{(\text{b1} c-b \text{c1}) \tanh ^{-1}\left(\frac{b+c x}{\sqrt{b^2-a c}}\right)}{c \sqrt{b^2-a c}}",1,"((b1*c - b*c1)*ArcTan[(b + c*x)/Sqrt[-b^2 + a*c]])/(c*Sqrt[-b^2 + a*c]) + (c1*Log[a + 2*b*x + c*x^2])/(2*c)","A",1
195,1,88,89,0.0793378,"\int \frac{\text{b1}+\text{c1} x}{\left(a+2 b x+c x^2\right)^2} \, dx","Integrate[(b1 + c1*x)/(a + 2*b*x + c*x^2)^2,x]","\frac{\frac{(b \text{c1}-\text{b1} c) \tan ^{-1}\left(\frac{b+c x}{\sqrt{a c-b^2}}\right)}{\sqrt{a c-b^2}}+\frac{a \text{c1}-b \text{b1}+b \text{c1} x-\text{b1} c x}{a+x (2 b+c x)}}{2 \left(b^2-a c\right)}","\frac{(\text{b1} c-b \text{c1}) \tanh ^{-1}\left(\frac{b+c x}{\sqrt{b^2-a c}}\right)}{2 \left(b^2-a c\right)^{3/2}}-\frac{-a \text{c1}+x (\text{b1} c-b \text{c1})+b \text{b1}}{2 \left(b^2-a c\right) \left(a+2 b x+c x^2\right)}",1,"((-(b*b1) + a*c1 - b1*c*x + b*c1*x)/(a + x*(2*b + c*x)) + ((-(b1*c) + b*c1)*ArcTan[(b + c*x)/Sqrt[-b^2 + a*c]])/Sqrt[-b^2 + a*c])/(2*(b^2 - a*c))","A",1
196,1,127,130,0.1412134,"\int \frac{\text{b1}+\text{c1} x}{\left(a+2 b x+c x^2\right)^3} \, dx","Integrate[(b1 + c1*x)/(a + 2*b*x + c*x^2)^3,x]","\frac{\frac{2 \left(b^2-a c\right) (a \text{c1}-b \text{b1}+b \text{c1} x-\text{b1} c x)}{(a+x (2 b+c x))^2}+\frac{3 c (\text{b1} c-b \text{c1}) \tan ^{-1}\left(\frac{b+c x}{\sqrt{a c-b^2}}\right)}{\sqrt{a c-b^2}}+\frac{3 (b+c x) (\text{b1} c-b \text{c1})}{a+x (2 b+c x)}}{8 \left(b^2-a c\right)^2}","\frac{3 (b+c x) (\text{b1} c-b \text{c1})}{8 \left(b^2-a c\right)^2 \left(a+2 b x+c x^2\right)}-\frac{-a \text{c1}+x (\text{b1} c-b \text{c1})+b \text{b1}}{4 \left(b^2-a c\right) \left(a+2 b x+c x^2\right)^2}-\frac{3 c (\text{b1} c-b \text{c1}) \tanh ^{-1}\left(\frac{b+c x}{\sqrt{b^2-a c}}\right)}{8 \left(b^2-a c\right)^{5/2}}",1,"((2*(b^2 - a*c)*(-(b*b1) + a*c1 - b1*c*x + b*c1*x))/(a + x*(2*b + c*x))^2 + (3*(b1*c - b*c1)*(b + c*x))/(a + x*(2*b + c*x)) + (3*c*(b1*c - b*c1)*ArcTan[(b + c*x)/Sqrt[-b^2 + a*c]])/Sqrt[-b^2 + a*c])/(8*(b^2 - a*c)^2)","A",1
197,1,168,173,0.227621,"\int \frac{\text{b1}+\text{c1} x}{\left(a+2 b x+c x^2\right)^4} \, dx","Integrate[(b1 + c1*x)/(a + 2*b*x + c*x^2)^4,x]","\frac{\frac{15 c^2 (b \text{c1}-\text{b1} c) \tan ^{-1}\left(\frac{b+c x}{\sqrt{a c-b^2}}\right)}{\sqrt{a c-b^2}}-\frac{10 \left(b^2-a c\right) (b+c x) (b \text{c1}-\text{b1} c)}{(a+x (2 b+c x))^2}+\frac{8 \left(b^2-a c\right)^2 (a \text{c1}-b \text{b1}+b \text{c1} x-\text{b1} c x)}{(a+x (2 b+c x))^3}+\frac{15 c (b+c x) (b \text{c1}-\text{b1} c)}{a+x (2 b+c x)}}{48 \left(b^2-a c\right)^3}","\frac{5 c^2 (\text{b1} c-b \text{c1}) \tanh ^{-1}\left(\frac{b+c x}{\sqrt{b^2-a c}}\right)}{16 \left(b^2-a c\right)^{7/2}}-\frac{5 c (b+c x) (\text{b1} c-b \text{c1})}{16 \left(b^2-a c\right)^3 \left(a+2 b x+c x^2\right)}+\frac{5 (b+c x) (\text{b1} c-b \text{c1})}{24 \left(b^2-a c\right)^2 \left(a+2 b x+c x^2\right)^2}-\frac{-a \text{c1}+x (\text{b1} c-b \text{c1})+b \text{b1}}{6 \left(b^2-a c\right) \left(a+2 b x+c x^2\right)^3}",1,"((8*(b^2 - a*c)^2*(-(b*b1) + a*c1 - b1*c*x + b*c1*x))/(a + x*(2*b + c*x))^3 - (10*(b^2 - a*c)*(-(b1*c) + b*c1)*(b + c*x))/(a + x*(2*b + c*x))^2 + (15*c*(-(b1*c) + b*c1)*(b + c*x))/(a + x*(2*b + c*x)) + (15*c^2*(-(b1*c) + b*c1)*ArcTan[(b + c*x)/Sqrt[-b^2 + a*c]])/Sqrt[-b^2 + a*c])/(48*(b^2 - a*c)^3)","A",1
198,1,264,169,0.4117696,"\int (\text{b1}+\text{c1} x) \left(a+2 b x+c x^2\right)^{-n} \, dx","Integrate[(b1 + c1*x)/(a + 2*b*x + c*x^2)^n,x]","\frac{1}{2} (a+x (2 b+c x))^{-n} \left(\text{c1} x^2 \left(\frac{-\sqrt{b^2-a c}+b+c x}{b-\sqrt{b^2-a c}}\right)^n \left(\frac{\sqrt{b^2-a c}+b+c x}{\sqrt{b^2-a c}+b}\right)^n F_1\left(2;n,n;3;-\frac{c x}{b+\sqrt{b^2-a c}},\frac{c x}{\sqrt{b^2-a c}-b}\right)-\frac{\text{b1} 2^{1-n} \left(-\sqrt{b^2-a c}+b+c x\right) \left(\frac{\sqrt{b^2-a c}+b+c x}{\sqrt{b^2-a c}}\right)^n \, _2F_1\left(1-n,n;2-n;\frac{-b-c x+\sqrt{b^2-a c}}{2 \sqrt{b^2-a c}}\right)}{c (n-1)}\right)","\frac{\text{c1} \left(a+2 b x+c x^2\right)^{1-n}}{2 c (1-n)}-\frac{2^{-n} (\text{b1} c-b \text{c1}) \left(-\frac{-\sqrt{b^2-a c}+b+c x}{\sqrt{b^2-a c}}\right)^{n-1} \left(a+2 b x+c x^2\right)^{1-n} \, _2F_1\left(1-n,n;2-n;\frac{b+c x+\sqrt{b^2-a c}}{2 \sqrt{b^2-a c}}\right)}{c (1-n) \sqrt{b^2-a c}}",1,"(c1*x^2*((b - Sqrt[b^2 - a*c] + c*x)/(b - Sqrt[b^2 - a*c]))^n*((b + Sqrt[b^2 - a*c] + c*x)/(b + Sqrt[b^2 - a*c]))^n*AppellF1[2, n, n, 3, -((c*x)/(b + Sqrt[b^2 - a*c])), (c*x)/(-b + Sqrt[b^2 - a*c])] - (2^(1 - n)*b1*(b - Sqrt[b^2 - a*c] + c*x)*((b + Sqrt[b^2 - a*c] + c*x)/Sqrt[b^2 - a*c])^n*Hypergeometric2F1[1 - n, n, 2 - n, (-b + Sqrt[b^2 - a*c] - c*x)/(2*Sqrt[b^2 - a*c])])/(c*(-1 + n)))/(2*(a + x*(2*b + c*x))^n)","C",0
199,1,44,49,0.0205526,"\int \frac{x}{3+6 x+2 x^2} \, dx","Integrate[x/(3 + 6*x + 2*x^2),x]","\frac{1}{4} \left(\left(1+\sqrt{3}\right) \log \left(2 x+\sqrt{3}+3\right)-\left(\sqrt{3}-1\right) \log \left(-2 x+\sqrt{3}-3\right)\right)","\frac{1}{4} \left(1-\sqrt{3}\right) \log \left(2 x-\sqrt{3}+3\right)+\frac{1}{4} \left(1+\sqrt{3}\right) \log \left(2 x+\sqrt{3}+3\right)",1,"(-((-1 + Sqrt[3])*Log[-3 + Sqrt[3] - 2*x]) + (1 + Sqrt[3])*Log[3 + Sqrt[3] + 2*x])/4","A",1
200,1,70,61,0.0491933,"\int \frac{-3+2 x}{\left(3+6 x+2 x^2\right)^3} \, dx","Integrate[(-3 + 2*x)/(3 + 6*x + 2*x^2)^3,x]","\frac{1}{12} \left(-\frac{3 \left(8 x^3+36 x^2+44 x+13\right)}{\left(2 x^2+6 x+3\right)^2}-2 \sqrt{3} \log \left(-2 x+\sqrt{3}-3\right)+2 \sqrt{3} \log \left(2 x+\sqrt{3}+3\right)\right)","-\frac{2 x+3}{2 \left(2 x^2+6 x+3\right)}+\frac{4 x+5}{4 \left(2 x^2+6 x+3\right)^2}+\frac{\tanh ^{-1}\left(\frac{2 x+3}{\sqrt{3}}\right)}{\sqrt{3}}",1,"((-3*(13 + 44*x + 36*x^2 + 8*x^3))/(3 + 6*x + 2*x^2)^2 - 2*Sqrt[3]*Log[-3 + Sqrt[3] - 2*x] + 2*Sqrt[3]*Log[3 + Sqrt[3] + 2*x])/12","A",1
201,1,33,36,0.0166361,"\int \frac{-1+x}{\left(4+5 x+x^2\right)^2} \, dx","Integrate[(-1 + x)/(4 + 5*x + x^2)^2,x]","\frac{1}{27} \left(\frac{21 x+39}{x^2+5 x+4}+7 \log (x+1)-7 \log (x+4)\right)","\frac{7 x+13}{9 \left(x^2+5 x+4\right)}+\frac{7}{27} \log (x+1)-\frac{7}{27} \log (x+4)",1,"((39 + 21*x)/(4 + 5*x + x^2) + 7*Log[1 + x] - 7*Log[4 + x])/27","A",1
202,1,87,87,0.0324654,"\int \frac{1}{\left(2+3 x+x^2\right)^5} \, dx","Integrate[(2 + 3*x + x^2)^(-5),x]","\frac{-2 x-3}{4 \left(x^2+3 x+2\right)^4}+\frac{35 (2 x+3)}{x^2+3 x+2}-\frac{35 (2 x+3)}{6 \left(x^2+3 x+2\right)^2}+\frac{7 (2 x+3)}{6 \left(x^2+3 x+2\right)^3}+70 \log (x+1)-70 \log (x+2)","\frac{-2 x-3}{4 \left(x^2+3 x+2\right)^4}+\frac{35 (2 x+3)}{x^2+3 x+2}-\frac{35 (2 x+3)}{6 \left(x^2+3 x+2\right)^2}+\frac{7 (2 x+3)}{6 \left(x^2+3 x+2\right)^3}+70 \log (x+1)-70 \log (x+2)",1,"(-3 - 2*x)/(4*(2 + 3*x + x^2)^4) + (7*(3 + 2*x))/(6*(2 + 3*x + x^2)^3) - (35*(3 + 2*x))/(6*(2 + 3*x + x^2)^2) + (35*(3 + 2*x))/(2 + 3*x + x^2) + 70*Log[1 + x] - 70*Log[2 + x]","A",1
203,1,70,81,0.0367558,"\int \frac{1}{x^3 \left(7-6 x+2 x^2\right)^2} \, dx","Integrate[1/(x^3*(7 - 6*x + 2*x^2)^2),x]","\frac{-\frac{140 (9 x-41)}{2 x^2-6 x+7}-\frac{1225}{x^2}-2000 \log \left(2 x^2-6 x+7\right)-\frac{4200}{x}+4000 \log (x)+468 \sqrt{5} \tan ^{-1}\left(\frac{2 x-3}{\sqrt{5}}\right)}{120050}","-\frac{2-3 x}{35 x^2 \left(2 x^2-6 x+7\right)}-\frac{1}{490 x^2}-\frac{40 \log \left(2 x^2-6 x+7\right)}{2401}-\frac{69}{1715 x}+\frac{80 \log (x)}{2401}-\frac{234 \tan ^{-1}\left(\frac{3-2 x}{\sqrt{5}}\right)}{12005 \sqrt{5}}",1,"(-1225/x^2 - 4200/x - (140*(-41 + 9*x))/(7 - 6*x + 2*x^2) + 468*Sqrt[5]*ArcTan[(-3 + 2*x)/Sqrt[5]] + 4000*Log[x] - 2000*Log[7 - 6*x + 2*x^2])/120050","A",1
204,1,87,104,0.0305939,"\int \frac{x^9}{\left(2+3 x+x^2\right)^5} \, dx","Integrate[x^9/(2 + 3*x + x^2)^5,x]","\frac{3 (456 x+451)}{4 \left(x^2+3 x+2\right)^2}-\frac{2 (729 x+1114)}{x^2+3 x+2}+\frac{1998 x+415}{12 \left(x^2+3 x+2\right)^3}+\frac{513 x+514}{4 \left(x^2+3 x+2\right)^4}-1471 \log (x+1)+1472 \log (x+2)","-\frac{(1593 x+2206) x^2}{2 \left(x^2+3 x+2\right)}+\frac{(3 x+4) x^8}{4 \left(x^2+3 x+2\right)^4}-\frac{(81 x+110) x^6}{12 \left(x^2+3 x+2\right)^3}+\frac{(135 x+184) x^4}{2 \left(x^2+3 x+2\right)^2}+735 x-1471 \log (x+1)+1472 \log (x+2)",1,"(514 + 513*x)/(4*(2 + 3*x + x^2)^4) + (415 + 1998*x)/(12*(2 + 3*x + x^2)^3) + (3*(451 + 456*x))/(4*(2 + 3*x + x^2)^2) - (2*(1114 + 729*x))/(2 + 3*x + x^2) - 1471*Log[1 + x] + 1472*Log[2 + x]","A",1
205,1,99,102,0.055776,"\int \frac{(1+2 x)^2}{\left(3+5 x+2 x^2\right)^5} \, dx","Integrate[(1 + 2*x)^2/(3 + 5*x + 2*x^2)^5,x]","\frac{620 (4 x+5)}{2 x^2+5 x+3}-\frac{155 (4 x+5)}{3 \left(2 x^2+5 x+3\right)^2}+\frac{31 (4 x+5)}{6 \left(2 x^2+5 x+3\right)^3}-\frac{10 x+11}{4 \left(2 x^2+5 x+3\right)^4}+2480 \log (2 (x+1))-2480 \log (2 x+3)","\frac{620 (4 x+5)}{2 x^2+5 x+3}-\frac{155 (4 x+5)}{3 \left(2 x^2+5 x+3\right)^2}+\frac{62 x+73}{3 \left(2 x^2+5 x+3\right)^3}+\frac{(2 x+1) (6 x+7)}{4 \left(2 x^2+5 x+3\right)^4}+2480 \log (x+1)-2480 \log (2 x+3)",1,"-1/4*(11 + 10*x)/(3 + 5*x + 2*x^2)^4 + (31*(5 + 4*x))/(6*(3 + 5*x + 2*x^2)^3) - (155*(5 + 4*x))/(3*(3 + 5*x + 2*x^2)^2) + (620*(5 + 4*x))/(3 + 5*x + 2*x^2) + 2480*Log[2*(1 + x)] - 2480*Log[3 + 2*x]","A",1
206,1,40,40,0.0056072,"\int \frac{\left(a-b x^2\right)^3}{x^7} \, dx","Integrate[(a - b*x^2)^3/x^7,x]","-\frac{a^3}{6 x^6}+\frac{3 a^2 b}{4 x^4}-\frac{3 a b^2}{2 x^2}-b^3 \log (x)","-\frac{a^3}{6 x^6}+\frac{3 a^2 b}{4 x^4}-\frac{3 a b^2}{2 x^2}-b^3 \log (x)",1,"-1/6*a^3/x^6 + (3*a^2*b)/(4*x^4) - (3*a*b^2)/(2*x^2) - b^3*Log[x]","A",1
207,1,62,83,0.0234746,"\int \frac{x^{13}}{\left(a^4+x^4\right)^5} \, dx","Integrate[x^13/(a^4 + x^4)^5,x]","\frac{15 \tan ^{-1}\left(\frac{x^2}{a^2}\right)-\frac{a^2 x^2 \left(15 a^{12}+55 a^8 x^4+73 a^4 x^8-15 x^{12}\right)}{\left(a^4+x^4\right)^4}}{768 a^6}","-\frac{x^{10}}{16 \left(a^4+x^4\right)^4}-\frac{5 x^6}{96 \left(a^4+x^4\right)^3}+\frac{5 x^2}{256 a^4 \left(a^4+x^4\right)}-\frac{5 x^2}{128 \left(a^4+x^4\right)^2}+\frac{5 \tan ^{-1}\left(\frac{x^2}{a^2}\right)}{256 a^6}",1,"(-((a^2*x^2*(15*a^12 + 55*a^8*x^4 + 73*a^4*x^8 - 15*x^12))/(a^4 + x^4)^4) + 15*ArcTan[x^2/a^2])/(768*a^6)","A",1
208,1,49,49,0.0227307,"\int \left(2 \sqrt{x}-x\right)^2 x^{3/2} \left(1+x^2\right) \, dx","Integrate[(2*Sqrt[x] - x)^2*x^(3/2)*(1 + x^2),x]","\frac{2 x^{13/2}}{13}+\frac{8 x^{11/2}}{11}+\frac{2 x^{9/2}}{9}+\frac{8 x^{7/2}}{7}-\frac{2 x^6}{3}-x^4","\frac{2 x^{13/2}}{13}+\frac{8 x^{11/2}}{11}+\frac{2 x^{9/2}}{9}+\frac{8 x^{7/2}}{7}-\frac{2 x^6}{3}-x^4",1,"(8*x^(7/2))/7 - x^4 + (2*x^(9/2))/9 + (8*x^(11/2))/11 - (2*x^6)/3 + (2*x^(13/2))/13","A",1
209,1,55,55,0.0467954,"\int \left(-3 x^{3/5}+x^{3/2}\right)^2 \left(-\frac{x^{2/3}}{3}+4 x^{3/2}\right) \, dx","Integrate[(-3*x^(3/5) + x^(3/2))^2*(-1/3*x^(2/3) + 4*x^(3/2)),x]","\frac{8 x^{11/2}}{11}-\frac{x^{14/3}}{14}-\frac{120 x^{23/5}}{23}+\frac{60 x^{113/30}}{113}+\frac{360 x^{37/10}}{37}-\frac{45 x^{43/15}}{43}","\frac{8 x^{11/2}}{11}-\frac{x^{14/3}}{14}-\frac{120 x^{23/5}}{23}+\frac{60 x^{113/30}}{113}+\frac{360 x^{37/10}}{37}-\frac{45 x^{43/15}}{43}",1,"(-45*x^(43/15))/43 + (360*x^(37/10))/37 + (60*x^(113/30))/113 - (120*x^(23/5))/23 - x^(14/3)/14 + (8*x^(11/2))/11","A",1
210,1,22,22,0.0084087,"\int \frac{1}{1+\sqrt{1+x}} \, dx","Integrate[(1 + Sqrt[1 + x])^(-1),x]","2 \sqrt{x+1}-2 \log \left(\sqrt{x+1}+1\right)","2 \sqrt{x+1}-2 \log \left(\sqrt{x+1}+1\right)",1,"2*Sqrt[1 + x] - 2*Log[1 + Sqrt[1 + x]]","A",1
211,1,19,15,0.0154142,"\int \frac{x}{1+\sqrt{1+x}} \, dx","Integrate[x/(1 + Sqrt[1 + x]),x]","2 \left(\frac{1}{3} (x+1)^{3/2}-\frac{x}{2}\right)","\frac{2}{3} (x+1)^{3/2}-x",1,"2*(-1/2*x + (1 + x)^(3/2)/3)","A",1
212,1,24,25,0.0106433,"\int \frac{1+\sqrt{1+x}}{-1+\sqrt{1+x}} \, dx","Integrate[(1 + Sqrt[1 + x])/(-1 + Sqrt[1 + x]),x]","x+4 \left(\sqrt{x+1}+\log \left(1-\sqrt{x+1}\right)\right)","x+4 \sqrt{x+1}+4 \log \left(1-\sqrt{x+1}\right)",1,"x + 4*(Sqrt[1 + x] + Log[1 - Sqrt[1 + x]])","A",1
213,1,33,33,0.0208778,"\int \frac{1}{-\sqrt{1+x}+(1+x)^{2/3}} \, dx","Integrate[(-Sqrt[1 + x] + (1 + x)^(2/3))^(-1),x]","3 \left(\sqrt[3]{x+1}+2 \sqrt[6]{x+1}+2 \log \left(1-\sqrt[6]{x+1}\right)\right)","3 \sqrt[3]{x+1}+6 \sqrt[6]{x+1}+6 \log \left(1-\sqrt[6]{x+1}\right)",1,"3*(2*(1 + x)^(1/6) + (1 + x)^(1/3) + 2*Log[1 - (1 + x)^(1/6)])","A",1
214,1,24,29,0.0077799,"\int \frac{\sqrt[3]{1+\sqrt[4]{x}}}{\sqrt{x}} \, dx","Integrate[(1 + x^(1/4))^(1/3)/Sqrt[x],x]","\frac{3}{7} \left(\sqrt[4]{x}+1\right)^{4/3} \left(4 \sqrt[4]{x}-3\right)","\frac{12}{7} \left(\sqrt[4]{x}+1\right)^{7/3}-3 \left(\sqrt[4]{x}+1\right)^{4/3}",1,"(3*(1 + x^(1/4))^(4/3)*(-3 + 4*x^(1/4)))/7","A",1
215,1,20,52,0.0046482,"\int \frac{1}{x^3 (1+x)^{3/2}} \, dx","Integrate[1/(x^3*(1 + x)^(3/2)),x]","\frac{2 \, _2F_1\left(-\frac{1}{2},3;\frac{1}{2};x+1\right)}{\sqrt{x+1}}","-\frac{1}{2 x^2 \sqrt{x+1}}+\frac{5}{4 x \sqrt{x+1}}+\frac{15}{4 \sqrt{x+1}}-\frac{15}{4} \tanh ^{-1}\left(\sqrt{x+1}\right)",1,"(2*Hypergeometric2F1[-1/2, 3, 1/2, 1 + x])/Sqrt[1 + x]","C",1
216,1,26,118,0.0063954,"\int \frac{1}{(1-x)^{7/2} x^5} \, dx","Integrate[1/((1 - x)^(7/2)*x^5),x]","\frac{2 \, _2F_1\left(-\frac{5}{2},5;-\frac{3}{2};1-x\right)}{5 (1-x)^{5/2}}","-\frac{1}{4 (1-x)^{5/2} x^4}-\frac{13}{24 (1-x)^{5/2} x^3}-\frac{143}{96 (1-x)^{5/2} x^2}+\frac{3003}{64 \sqrt{1-x}}-\frac{429}{64 (1-x)^{5/2} x}+\frac{1001}{64 (1-x)^{3/2}}+\frac{3003}{320 (1-x)^{5/2}}-\frac{3003}{64} \tanh ^{-1}\left(\sqrt{1-x}\right)",1,"(2*Hypergeometric2F1[-5/2, 5, -3/2, 1 - x])/(5*(1 - x)^(5/2))","C",1
217,1,22,104,0.004316,"\int \frac{1}{(-1+x)^{2/3} x^5} \, dx","Integrate[1/((-1 + x)^(2/3)*x^5),x]","3 \sqrt[3]{x-1} \, _2F_1\left(\frac{1}{3},5;\frac{4}{3};1-x\right)","\frac{\sqrt[3]{x-1}}{4 x^4}+\frac{11 \sqrt[3]{x-1}}{36 x^3}+\frac{11 \sqrt[3]{x-1}}{27 x^2}+\frac{55 \sqrt[3]{x-1}}{81 x}+\frac{55}{81} \log \left(\sqrt[3]{x-1}+1\right)-\frac{55 \log (x)}{243}-\frac{110 \tan ^{-1}\left(\frac{1-2 \sqrt[3]{x-1}}{\sqrt{3}}\right)}{81 \sqrt{3}}",1,"3*(-1 + x)^(1/3)*Hypergeometric2F1[1/3, 5, 4/3, 1 - x]","C",1
218,1,67,38,0.0257593,"\int \sqrt{\frac{1-x}{1+x}} \, dx","Integrate[Sqrt[(1 - x)/(1 + x)],x]","\frac{\sqrt{\frac{1-x}{x+1}} \sqrt{x+1} \left(\sqrt{x+1} (x-1)+2 \sqrt{1-x} \sin ^{-1}\left(\frac{\sqrt{1-x}}{\sqrt{2}}\right)\right)}{x-1}","\sqrt{\frac{1-x}{x+1}} (x+1)-2 \tan ^{-1}\left(\sqrt{\frac{1-x}{x+1}}\right)",1,"(Sqrt[(1 - x)/(1 + x)]*Sqrt[1 + x]*((-1 + x)*Sqrt[1 + x] + 2*Sqrt[1 - x]*ArcSin[Sqrt[1 - x]/Sqrt[2]]))/(-1 + x)","A",1
219,1,115,92,0.2908609,"\int x \sqrt{\frac{-a+x}{b-x}} \, dx","Integrate[x*Sqrt[(-a + x)/(b - x)],x]","\frac{\sqrt{\frac{x-a}{b-x}} \left((b-x) (a-3 b-2 x) \sqrt{\frac{a-x}{a-b}}-\sqrt{a-b} (a+3 b) \sqrt{b-x} \sinh ^{-1}\left(\frac{\sqrt{b-x}}{\sqrt{a-b}}\right)\right)}{4 \sqrt{\frac{a-x}{a-b}}}","\frac{1}{2} (b-x)^2 \sqrt{\frac{x-a}{b-x}}+\frac{1}{4} (a-5 b) (b-x) \sqrt{\frac{x-a}{b-x}}-\frac{1}{4} (a-b) (a+3 b) \tan ^{-1}\left(\sqrt{\frac{x-a}{b-x}}\right)",1,"(Sqrt[(-a + x)/(b - x)]*((a - 3*b - 2*x)*Sqrt[(a - x)/(a - b)]*(b - x) - Sqrt[a - b]*(a + 3*b)*Sqrt[b - x]*ArcSinh[Sqrt[b - x]/Sqrt[a - b]]))/(4*Sqrt[(a - x)/(a - b)])","A",1
220,1,47,54,0.1483221,"\int \frac{\sqrt{-5+x} \sqrt{3+x}}{(-1+x) \left(-25+x^2\right)} \, dx","Integrate[(Sqrt[-5 + x]*Sqrt[3 + x])/((-1 + x)*(-25 + x^2)),x]","\frac{1}{15} \left(5 \tan ^{-1}\left(\sqrt{\frac{x-5}{x+3}}\right)+\sqrt{5} \tanh ^{-1}\left(\frac{\sqrt{\frac{x-5}{x+3}}}{\sqrt{5}}\right)\right)","\frac{1}{6} \tan ^{-1}\left(\frac{1}{4} \sqrt{x-5} \sqrt{x+3}\right)+\frac{\tanh ^{-1}\left(\frac{\sqrt{5} \sqrt{x+3}}{\sqrt{x-5}}\right)}{3 \sqrt{5}}",1,"(5*ArcTan[Sqrt[(-5 + x)/(3 + x)]] + Sqrt[5]*ArcTanh[Sqrt[(-5 + x)/(3 + x)]/Sqrt[5]])/15","A",0
221,1,153,304,0.506293,"\int \frac{x^2 \sqrt{1+x} \sqrt[4]{1-x^2}}{\sqrt{1-x} \left(\sqrt{1-x}-\sqrt{1+x}\right)} \, dx","Integrate[(x^2*Sqrt[1 + x]*(1 - x^2)^(1/4))/(Sqrt[1 - x]*(Sqrt[1 - x] - Sqrt[1 + x])),x]","\frac{\sqrt[4]{1-x^2} \, _2F_1\left(\frac{1}{4},\frac{1}{4};\frac{5}{4};\frac{1-x}{2}\right)}{8 \sqrt[4]{2} \sqrt[4]{x+1}}+\frac{5 \left(1-x^2\right)^{3/4} \, _2F_1\left(\frac{3}{4},\frac{3}{4};\frac{7}{4};\frac{1-x}{2}\right)}{24\ 2^{3/4} (x+1)^{3/4}}-\frac{1}{48} \sqrt{x+1} \sqrt[4]{1-x^2} \left(8 x^2-\frac{\sqrt{1-x^2} \left(8 x^2+22 x+29\right)}{x+1}+2 x-7\right)","\frac{1}{6} \sqrt{x+1} \left(1-x^2\right)^{5/4}+\frac{x \left(1-x^2\right)^{5/4}}{6 \sqrt{1-x}}+\frac{7 \left(1-x^2\right)^{5/4}}{24 \sqrt{1-x}}+\frac{1}{24} (x+1)^{3/4} (1-x)^{5/4}+\frac{5}{16} \sqrt[4]{x+1} (1-x)^{3/4}-\frac{1}{16} (x+1)^{3/4} \sqrt[4]{1-x}+\frac{\log \left(\frac{\sqrt{1-x}}{\sqrt{x+1}}-\frac{\sqrt{2} \sqrt[4]{1-x}}{\sqrt[4]{x+1}}+1\right)}{8 \sqrt{2}}-\frac{\log \left(\frac{\sqrt{1-x}}{\sqrt{x+1}}+\frac{\sqrt{2} \sqrt[4]{1-x}}{\sqrt[4]{x+1}}+1\right)}{8 \sqrt{2}}-\frac{3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-x}}{\sqrt[4]{x+1}}\right)}{8 \sqrt{2}}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-x}}{\sqrt[4]{x+1}}+1\right)}{8 \sqrt{2}}",1,"-1/48*(Sqrt[1 + x]*(1 - x^2)^(1/4)*(-7 + 2*x + 8*x^2 - (Sqrt[1 - x^2]*(29 + 22*x + 8*x^2))/(1 + x))) + ((1 - x^2)^(1/4)*Hypergeometric2F1[1/4, 1/4, 5/4, (1 - x)/2])/(8*2^(1/4)*(1 + x)^(1/4)) + (5*(1 - x^2)^(3/4)*Hypergeometric2F1[3/4, 3/4, 7/4, (1 - x)/2])/(24*2^(3/4)*(1 + x)^(3/4))","C",1
222,1,348,292,0.783298,"\int \frac{\sqrt{1-x} x (1+x)^{2/3}}{-(1-x)^{5/6} \sqrt[3]{1+x}+(1-x)^{2/3} \sqrt{1+x}} \, dx","Integrate[(Sqrt[1 - x]*x*(1 + x)^(2/3))/(-((1 - x)^(5/6)*(1 + x)^(1/3)) + (1 - x)^(2/3)*Sqrt[1 + x]),x]","-\frac{5 \sqrt{1-x^2} \, _2F_1\left(\frac{1}{6},\frac{1}{6};\frac{7}{6};\frac{1-x}{2}\right)}{6 \sqrt[6]{2} \sqrt[3]{1-x} \sqrt{x+1}}-\frac{2^{2/3} \sqrt[3]{1-x^2} \, _2F_1\left(\frac{1}{3},\frac{1}{3};\frac{4}{3};\frac{1-x}{2}\right)}{3 \sqrt[3]{x+1}}-\frac{1}{12} \sqrt[3]{x+1} \left(-4\ 2^{2/3} \, _2F_1\left(\frac{1}{3},\frac{1}{3};\frac{4}{3};\frac{x+1}{2}\right)+\frac{(3 x+10) \left(1-x^2\right)^{5/6}}{x+1}-\frac{(3 x+2) \sqrt{1-x^2}}{\sqrt[3]{1-x}}-(3 x+1) \sqrt[3]{1-x^2}-3 \sqrt[3]{1-x} x \sqrt[6]{1-x^2}-\frac{3 \sqrt[3]{1-x} x (x+2)}{\sqrt[3]{1-x^2}}+(1-x)^{2/3} (1-3 x)\right)-\frac{7 \left(1-x^2\right)^{5/6} \, _2F_1\left(\frac{5}{6},\frac{5}{6};\frac{11}{6};\frac{1-x}{2}\right)}{30\ 2^{5/6} (x+1)^{5/6}}+\frac{(1-x)^{5/6} (x+1)^{5/6} \sin ^{-1}(x)}{4 \left(1-x^2\right)^{5/6}}","-\frac{1}{12} (1-x)^{2/3} \sqrt[3]{x+1} (1-3 x)-\frac{1}{4} (1-x) (x+3)+\frac{1}{12} \sqrt[3]{1-x} (x+1)^{2/3} (3 x+1)+\frac{1}{12} \sqrt[6]{1-x} (x+1)^{5/6} (3 x+2)-\frac{1}{12} (1-x)^{5/6} \sqrt[6]{x+1} (3 x+10)+\frac{1}{4} \sqrt{1-x} x \sqrt{x+1}+\frac{1}{6} \tan ^{-1}\left(\frac{\sqrt[6]{x+1}}{\sqrt[6]{1-x}}\right)-\frac{4 \tan ^{-1}\left(\frac{\sqrt[3]{1-x}-2 \sqrt[3]{x+1}}{\sqrt{3} \sqrt[3]{1-x}}\right)}{3 \sqrt{3}}-\frac{5}{6} \tan ^{-1}\left(\frac{\sqrt[3]{1-x}-\sqrt[3]{x+1}}{\sqrt[6]{1-x} \sqrt[6]{x+1}}\right)+\frac{\tanh ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{1-x} \sqrt[6]{x+1}}{\sqrt[3]{1-x}+\sqrt[3]{x+1}}\right)}{6 \sqrt{3}}",1,"((1 - x)^(5/6)*(1 + x)^(5/6)*ArcSin[x])/(4*(1 - x^2)^(5/6)) - (5*Sqrt[1 - x^2]*Hypergeometric2F1[1/6, 1/6, 7/6, (1 - x)/2])/(6*2^(1/6)*(1 - x)^(1/3)*Sqrt[1 + x]) - (2^(2/3)*(1 - x^2)^(1/3)*Hypergeometric2F1[1/3, 1/3, 4/3, (1 - x)/2])/(3*(1 + x)^(1/3)) - ((1 + x)^(1/3)*((1 - 3*x)*(1 - x)^(2/3) - (3*(1 - x)^(1/3)*x*(2 + x))/(1 - x^2)^(1/3) - 3*(1 - x)^(1/3)*x*(1 - x^2)^(1/6) - (1 + 3*x)*(1 - x^2)^(1/3) - ((2 + 3*x)*Sqrt[1 - x^2])/(1 - x)^(1/3) + ((10 + 3*x)*(1 - x^2)^(5/6))/(1 + x) - 4*2^(2/3)*Hypergeometric2F1[1/3, 1/3, 4/3, (1 + x)/2]))/12 - (7*(1 - x^2)^(5/6)*Hypergeometric2F1[5/6, 5/6, 11/6, (1 - x)/2])/(30*2^(5/6)*(1 + x)^(5/6))","C",0
223,1,25,25,0.010339,"\int \frac{1}{\sqrt[3]{(-1+x)^4 (1+x)^2}} \, dx","Integrate[((-1 + x)^4*(1 + x)^2)^(-1/3),x]","-\frac{3 (x-1) (x+1)}{2 \sqrt[3]{(x-1)^4 (x+1)^2}}","-\frac{3 (x-1) (x+1)}{2 \sqrt[3]{(x-1)^4 (x+1)^2}}",1,"(-3*(-1 + x)*(1 + x))/(2*((-1 + x)^4*(1 + x)^2)^(1/3))","A",1
224,1,25,25,0.0122073,"\int \frac{1}{\sqrt[4]{(-1+x)^3 (2+x)^5}} \, dx","Integrate[((-1 + x)^3*(2 + x)^5)^(-1/4),x]","\frac{4 (x-1) (x+2)}{3 \sqrt[4]{(x-1)^3 (x+2)^5}}","\frac{4 (x-1) (x+2)}{3 \sqrt[4]{(x-1)^3 (x+2)^5}}",1,"(4*(-1 + x)*(2 + x))/(3*((-1 + x)^3*(2 + x)^5)^(1/4))","A",1
225,1,30,53,0.0153206,"\int \frac{1}{\sqrt[3]{(-1+x)^7 (1+x)^2}} \, dx","Integrate[((-1 + x)^7*(1 + x)^2)^(-1/3),x]","\frac{3 (x-1) (x+1) (3 x-5)}{16 \sqrt[3]{(x-1)^7 (x+1)^2}}","\frac{9 (x-1)^2 (x+1)}{16 \sqrt[3]{(x-1)^7 (x+1)^2}}-\frac{3 (x-1) (x+1)}{8 \sqrt[3]{(x-1)^7 (x+1)^2}}",1,"(3*(-1 + x)*(1 + x)*(-5 + 3*x))/(16*((-1 + x)^7*(1 + x)^2)^(1/3))","A",1
226,1,49,67,0.0121948,"\int \frac{1}{\sqrt[3]{(-1+x)^2 (1+x)}} \, dx","Integrate[((-1 + x)^2*(1 + x))^(-1/3),x]","\frac{3 (x-1) \sqrt[3]{x+1} \, _2F_1\left(\frac{1}{3},\frac{1}{3};\frac{4}{3};\frac{1-x}{2}\right)}{\sqrt[3]{2} \sqrt[3]{(x-1)^2 (x+1)}}","-\frac{1}{2} \log (x+1)-\frac{3}{2} \log \left(1-\frac{x-1}{\sqrt[3]{(x-1)^2 (x+1)}}\right)+\sqrt{3} \tan ^{-1}\left(\frac{\frac{2 (x-1)}{\sqrt[3]{(x-1)^2 (x+1)}}+1}{\sqrt{3}}\right)",1,"(3*(-1 + x)*(1 + x)^(1/3)*Hypergeometric2F1[1/3, 1/3, 4/3, (1 - x)/2])/(2^(1/3)*((-1 + x)^2*(1 + x))^(1/3))","C",1
227,1,114,122,0.1482633,"\int \frac{\frac{1}{x}+x}{\sqrt{(-2+x) (1+x)^3}} \, dx","Integrate[(x^(-1) + x)/Sqrt[(-2 + x)*(1 + x)^3],x]","-\frac{(x+1) \left(-4 (2-x)^{3/2}-6 (x-2) \sqrt{x+1} \sin ^{-1}\left(\frac{\sqrt{2-x}}{\sqrt{3}}\right)-3 \sqrt{2} \sqrt{-(x-2)^2} \sqrt{x+1} \tan ^{-1}\left(\frac{\sqrt{\frac{x-2}{x+1}}}{\sqrt{2}}\right)\right)}{3 \sqrt{2-x} \sqrt{(x-2) (x+1)^3}}","-\frac{4 (x-2) (x+1)}{3 \sqrt{(x-2) (x+1)^3}}-\frac{\sqrt{2} \sqrt{x-2} (x+1)^{3/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{x+1}}{\sqrt{x-2}}\right)}{\sqrt{(x-2) (x+1)^3}}+\frac{2 \sqrt{x-2} (x+1)^{3/2} \sinh ^{-1}\left(\frac{\sqrt{x-2}}{\sqrt{3}}\right)}{\sqrt{(x-2) (x+1)^3}}",1,"-1/3*((1 + x)*(-4*(2 - x)^(3/2) - 6*(-2 + x)*Sqrt[1 + x]*ArcSin[Sqrt[2 - x]/Sqrt[3]] - 3*Sqrt[2]*Sqrt[-(-2 + x)^2]*Sqrt[1 + x]*ArcTan[Sqrt[(-2 + x)/(1 + x)]/Sqrt[2]]))/(Sqrt[2 - x]*Sqrt[(-2 + x)*(1 + x)^3])","A",0
228,1,112,150,0.0715504,"\int \frac{\sqrt[3]{(-1+x)^2 (1+x)}}{x^2} \, dx","Integrate[((-1 + x)^2*(1 + x))^(1/3)/x^2,x]","\frac{\sqrt[3]{(x-1)^2 (x+1)} \left(3 (x+1) \left(3\ 2^{2/3} \sqrt[3]{1-x} x \, _2F_1\left(\frac{1}{3},\frac{1}{3};\frac{4}{3};\frac{x+1}{2}\right)-2 x+2\right)-2 \left(\frac{1}{x}+1\right)^{2/3} \sqrt[3]{\frac{x-1}{x}} x F_1\left(1;\frac{1}{3},\frac{2}{3};2;\frac{1}{x},-\frac{1}{x}\right)\right)}{6 x \left(x^2-1\right)}","-\frac{\sqrt[3]{(x-1)^2 (x+1)}}{x}+\frac{\log (x)}{6}-\frac{2}{3} \log (x+1)-\frac{3}{2} \log \left(1-\frac{x-1}{\sqrt[3]{(x-1)^2 (x+1)}}\right)-\frac{1}{2} \log \left(\frac{x-1}{\sqrt[3]{(x-1)^2 (x+1)}}+1\right)-\frac{\tan ^{-1}\left(\frac{1-\frac{2 (x-1)}{\sqrt[3]{(x-1)^2 (x+1)}}}{\sqrt{3}}\right)}{\sqrt{3}}-\sqrt{3} \tan ^{-1}\left(\frac{\frac{2 (x-1)}{\sqrt[3]{(x-1)^2 (x+1)}}+1}{\sqrt{3}}\right)",1,"(((-1 + x)^2*(1 + x))^(1/3)*(-2*(1 + x^(-1))^(2/3)*((-1 + x)/x)^(1/3)*x*AppellF1[1, 1/3, 2/3, 2, x^(-1), -x^(-1)] + 3*(1 + x)*(2 - 2*x + 3*2^(2/3)*(1 - x)^(1/3)*x*Hypergeometric2F1[1/3, 1/3, 4/3, (1 + x)/2])))/(6*x*(-1 + x^2))","C",0
229,1,27,43,0.0101632,"\int \frac{1}{\left(-3-2 x+x^2\right)^{5/2}} \, dx","Integrate[(-3 - 2*x + x^2)^(-5/2),x]","\frac{(x-1) \left(x^2-2 x-5\right)}{24 \left(x^2-2 x-3\right)^{3/2}}","\frac{1-x}{12 \left(x^2-2 x-3\right)^{3/2}}-\frac{1-x}{24 \sqrt{x^2-2 x-3}}",1,"((-1 + x)*(-5 - 2*x + x^2))/(24*(-3 - 2*x + x^2)^(3/2))","A",1
230,1,37,42,0.0087326,"\int \frac{1}{\sqrt{9+3 x-5 x^2+x^3}} \, dx","Integrate[1/Sqrt[9 + 3*x - 5*x^2 + x^3],x]","-\frac{(x-3) \sqrt{x+1} \tanh ^{-1}\left(\frac{\sqrt{x+1}}{2}\right)}{\sqrt{(x-3)^2 (x+1)}}","\frac{(3-x) \sqrt{x+1} \tanh ^{-1}\left(\frac{\sqrt{x+1}}{2}\right)}{\sqrt{x^3-5 x^2+3 x+9}}",1,"-(((-3 + x)*Sqrt[1 + x]*ArcTanh[Sqrt[1 + x]/2])/Sqrt[(-3 + x)^2*(1 + x)])","A",1
231,1,35,139,0.007153,"\int \frac{1}{\left(9+3 x-5 x^2+x^3\right)^{3/2}} \, dx","Integrate[(9 + 3*x - 5*x^2 + x^3)^(-3/2),x]","\frac{(x-3) \, _2F_1\left(-\frac{1}{2},3;\frac{1}{2};\frac{x+1}{4}\right)}{32 \sqrt{(x-3)^2 (x+1)}}","-\frac{15 (x+1) (3-x)^3}{256 \left(x^3-5 x^2+3 x+9\right)^{3/2}}+\frac{5 (x+1) (3-x)^2}{64 \left(x^3-5 x^2+3 x+9\right)^{3/2}}+\frac{(x+1) (3-x)}{8 \left(x^3-5 x^2+3 x+9\right)^{3/2}}+\frac{15 (x+1)^{3/2} (3-x)^3 \tanh ^{-1}\left(\frac{\sqrt{x+1}}{2}\right)}{512 \left(x^3-5 x^2+3 x+9\right)^{3/2}}",1,"((-3 + x)*Hypergeometric2F1[-1/2, 3, 1/2, (1 + x)/4])/(32*Sqrt[(-3 + x)^2*(1 + x)])","C",1
232,1,49,75,0.0133031,"\int \frac{1}{\sqrt[3]{9+3 x-5 x^2+x^3}} \, dx","Integrate[(9 + 3*x - 5*x^2 + x^3)^(-1/3),x]","\frac{3 (x-3) \sqrt[3]{x+1} \, _2F_1\left(\frac{1}{3},\frac{1}{3};\frac{4}{3};\frac{3-x}{4}\right)}{2^{2/3} \sqrt[3]{(x-3)^2 (x+1)}}","-\frac{3}{2} \log \left(1-\frac{x-3}{\sqrt[3]{x^3-5 x^2+3 x+9}}\right)+\sqrt{3} \tan ^{-1}\left(\frac{\frac{2 (x-3)}{\sqrt[3]{x^3-5 x^2+3 x+9}}+1}{\sqrt{3}}\right)-\frac{1}{2} \log (x+1)",1,"(3*(-3 + x)*(1 + x)^(1/3)*Hypergeometric2F1[1/3, 1/3, 4/3, (3 - x)/4])/(2^(2/3)*((-3 + x)^2*(1 + x))^(1/3))","C",1
233,1,23,29,0.0089738,"\int \frac{1}{\left(9+3 x-5 x^2+x^3\right)^{2/3}} \, dx","Integrate[(9 + 3*x - 5*x^2 + x^3)^(-2/3),x]","-\frac{3 (x-3) (x+1)}{4 \left((x-3)^2 (x+1)\right)^{2/3}}","\frac{3 (3-x) (x+1)}{4 \left(x^3-5 x^2+3 x+9\right)^{2/3}}",1,"(-3*(-3 + x)*(1 + x))/(4*((-3 + x)^2*(1 + x))^(2/3))","A",1
234,1,32,92,0.0092639,"\int \frac{1}{\left(9+3 x-5 x^2+x^3\right)^{4/3}} \, dx","Integrate[(9 + 3*x - 5*x^2 + x^3)^(-4/3),x]","\frac{3 \left(9 x^2-42 x+29\right)}{320 (x-3) \sqrt[3]{(x-3)^2 (x+1)}}","-\frac{27 (x+1) (3-x)^3}{320 \left(x^3-5 x^2+3 x+9\right)^{4/3}}+\frac{9 (x+1) (3-x)^2}{80 \left(x^3-5 x^2+3 x+9\right)^{4/3}}+\frac{3 (x+1) (3-x)}{20 \left(x^3-5 x^2+3 x+9\right)^{4/3}}",1,"(3*(29 - 42*x + 9*x^2))/(320*(-3 + x)*((-3 + x)^2*(1 + x))^(1/3))","A",1
235,1,19,19,0.0109632,"\int \frac{1}{\sqrt{4+3 x-2 x^2}} \, dx","Integrate[1/Sqrt[4 + 3*x - 2*x^2],x]","-\frac{\sin ^{-1}\left(\frac{3-4 x}{\sqrt{41}}\right)}{\sqrt{2}}","-\frac{\sin ^{-1}\left(\frac{3-4 x}{\sqrt{41}}\right)}{\sqrt{2}}",1,"-(ArcSin[(3 - 4*x)/Sqrt[41]]/Sqrt[2])","A",1
236,1,8,8,0.006307,"\int \frac{1}{\sqrt{-3+4 x-x^2}} \, dx","Integrate[1/Sqrt[-3 + 4*x - x^2],x]","-\sin ^{-1}(2-x)","-\sin ^{-1}(2-x)",1,"-ArcSin[2 - x]","A",1
237,1,12,12,0.007192,"\int \frac{1}{\sqrt{-2-5 x-3 x^2}} \, dx","Integrate[1/Sqrt[-2 - 5*x - 3*x^2],x]","\frac{\sin ^{-1}(6 x+5)}{\sqrt{3}}","\frac{\sin ^{-1}(6 x+5)}{\sqrt{3}}",1,"ArcSin[5 + 6*x]/Sqrt[3]","A",1
238,1,31,31,0.0087403,"\int \frac{1}{\sqrt{1-x^2} \left(4+x^2\right)} \, dx","Integrate[1/(Sqrt[1 - x^2]*(4 + x^2)),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{5} x}{2 \sqrt{1-x^2}}\right)}{2 \sqrt{5}}","\frac{\tan ^{-1}\left(\frac{\sqrt{5} x}{2 \sqrt{1-x^2}}\right)}{2 \sqrt{5}}",1,"ArcTan[(Sqrt[5]*x)/(2*Sqrt[1 - x^2])]/(2*Sqrt[5])","A",1
239,1,31,31,0.011129,"\int \frac{1}{\left(4+x^2\right) \sqrt{1+4 x^2}} \, dx","Integrate[1/((4 + x^2)*Sqrt[1 + 4*x^2]),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{15} x}{2 \sqrt{4 x^2+1}}\right)}{2 \sqrt{15}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{15} x}{2 \sqrt{4 x^2+1}}\right)}{2 \sqrt{15}}",1,"ArcTanh[(Sqrt[15]*x)/(2*Sqrt[1 + 4*x^2])]/(2*Sqrt[15])","A",1
240,1,24,24,0.0100338,"\int \frac{x}{\left(3-x^2\right) \sqrt{5-x^2}} \, dx","Integrate[x/((3 - x^2)*Sqrt[5 - x^2]),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{5-x^2}}{\sqrt{2}}\right)}{\sqrt{2}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{5-x^2}}{\sqrt{2}}\right)}{\sqrt{2}}",1,"ArcTanh[Sqrt[5 - x^2]/Sqrt[2]]/Sqrt[2]","A",1
241,1,25,25,0.0093713,"\int \frac{x}{\sqrt{3-x^2} \left(5-x^2\right)} \, dx","Integrate[x/(Sqrt[3 - x^2]*(5 - x^2)),x]","-\frac{\tan ^{-1}\left(\frac{\sqrt{3-x^2}}{\sqrt{2}}\right)}{\sqrt{2}}","-\frac{\tan ^{-1}\left(\frac{\sqrt{3-x^2}}{\sqrt{2}}\right)}{\sqrt{2}}",1,"-(ArcTan[Sqrt[3 - x^2]/Sqrt[2]]/Sqrt[2])","A",1
242,1,96,43,0.0514087,"\int \frac{1}{\sqrt{2+x^2} \left(-1+x^4\right)} \, dx","Integrate[1/(Sqrt[2 + x^2]*(-1 + x^4)),x]","\frac{1}{12} \left(-3 \tan ^{-1}\left(\frac{-x+2 i}{\sqrt{x^2+2}}\right)+3 \tan ^{-1}\left(\frac{x+2 i}{\sqrt{x^2+2}}\right)+\sqrt{3} \tanh ^{-1}\left(\frac{2-x}{\sqrt{3} \sqrt{x^2+2}}\right)-\sqrt{3} \tanh ^{-1}\left(\frac{x+2}{\sqrt{3} \sqrt{x^2+2}}\right)\right)","-\frac{1}{2} \tan ^{-1}\left(\frac{x}{\sqrt{x^2+2}}\right)-\frac{\tanh ^{-1}\left(\frac{\sqrt{3} x}{\sqrt{x^2+2}}\right)}{2 \sqrt{3}}",1,"(-3*ArcTan[(2*I - x)/Sqrt[2 + x^2]] + 3*ArcTan[(2*I + x)/Sqrt[2 + x^2]] + Sqrt[3]*ArcTanh[(2 - x)/(Sqrt[3]*Sqrt[2 + x^2])] - Sqrt[3]*ArcTanh[(2 + x)/(Sqrt[3]*Sqrt[2 + x^2])])/12","C",1
243,1,61,62,0.0260403,"\int \frac{x}{\left(-1+x^2\right) \sqrt{4+2 x+x^2}} \, dx","Integrate[x/((-1 + x^2)*Sqrt[4 + 2*x + x^2]),x]","\frac{1}{42} \left(-3 \sqrt{7} \tanh ^{-1}\left(\frac{2 x+5}{\sqrt{7} \sqrt{x^2+2 x+4}}\right)-7 \sqrt{3} \tanh ^{-1}\left(\frac{\sqrt{(x+1)^2+3}}{\sqrt{3}}\right)\right)","-\frac{\tanh ^{-1}\left(\frac{2 x+5}{\sqrt{7} \sqrt{x^2+2 x+4}}\right)}{2 \sqrt{7}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{x^2+2 x+4}}{\sqrt{3}}\right)}{2 \sqrt{3}}",1,"(-3*Sqrt[7]*ArcTanh[(5 + 2*x)/(Sqrt[7]*Sqrt[4 + 2*x + x^2])] - 7*Sqrt[3]*ArcTanh[Sqrt[3 + (1 + x)^2]/Sqrt[3]])/42","A",1
244,1,159,82,0.3642901,"\int \frac{1}{\sqrt{5+2 x+x^2} \left(-8+x^3\right)} \, dx","Integrate[1/(Sqrt[5 + 2*x + x^2]*(-8 + x^3)),x]","\frac{1}{312} \left(-2 \sqrt{13} \tanh ^{-1}\left(\frac{3 x+7}{\sqrt{13} \sqrt{x^2+2 x+5}}\right)-13 \left(\left(\sqrt{3}+i\right) \tan ^{-1}\left(\frac{2 \left(\sqrt[3]{-1}-2\right) x+5 i \sqrt{3}+1}{\sqrt{2-2 i \sqrt{3}} \sqrt{x^2+2 x+5}}\right)+\left(\sqrt{3}-i\right) \tan ^{-1}\left(\frac{-2 \left(2+(-1)^{2/3}\right) x-5 i \sqrt{3}+1}{\sqrt{2+2 i \sqrt{3}} \sqrt{x^2+2 x+5}}\right)\right)\right)","-\frac{\tan ^{-1}\left(\frac{x+1}{\sqrt{3} \sqrt{x^2+2 x+5}}\right)}{4 \sqrt{3}}-\frac{\tanh ^{-1}\left(\frac{3 x+7}{\sqrt{13} \sqrt{x^2+2 x+5}}\right)}{12 \sqrt{13}}+\frac{1}{12} \tanh ^{-1}\left(\sqrt{x^2+2 x+5}\right)",1,"(-13*((I + Sqrt[3])*ArcTan[(1 + (5*I)*Sqrt[3] + 2*(-2 + (-1)^(1/3))*x)/(Sqrt[2 - (2*I)*Sqrt[3]]*Sqrt[5 + 2*x + x^2])] + (-I + Sqrt[3])*ArcTan[(1 - (5*I)*Sqrt[3] - 2*(2 + (-1)^(2/3))*x)/(Sqrt[2 + (2*I)*Sqrt[3]]*Sqrt[5 + 2*x + x^2])]) - 2*Sqrt[13]*ArcTanh[(7 + 3*x)/(Sqrt[13]*Sqrt[5 + 2*x + x^2])])/312","C",1
245,1,114,63,0.1132574,"\int \frac{x}{\left(4+x+x^2\right) \sqrt{5+4 x+4 x^2}} \, dx","Integrate[x/((4 + x + x^2)*Sqrt[5 + 4*x + 4*x^2]),x]","\frac{\left(\sqrt{15}-i\right) \tan ^{-1}\left(\frac{-2 i \sqrt{15} x-i \sqrt{15}+4}{\sqrt{11} \sqrt{4 x^2+4 x+5}}\right)+\left(\sqrt{15}+i\right) \tan ^{-1}\left(\frac{2 i \sqrt{15} x+i \sqrt{15}+4}{\sqrt{11} \sqrt{4 x^2+4 x+5}}\right)}{2 \sqrt{165}}","\frac{\tan ^{-1}\left(\frac{\sqrt{4 x^2+4 x+5}}{\sqrt{11}}\right)}{\sqrt{11}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{\frac{11}{15}} (2 x+1)}{\sqrt{4 x^2+4 x+5}}\right)}{\sqrt{165}}",1,"((-I + Sqrt[15])*ArcTan[(4 - I*Sqrt[15] - (2*I)*Sqrt[15]*x)/(Sqrt[11]*Sqrt[5 + 4*x + 4*x^2])] + (I + Sqrt[15])*ArcTan[(4 + I*Sqrt[15] + (2*I)*Sqrt[15]*x)/(Sqrt[11]*Sqrt[5 + 4*x + 4*x^2])])/(2*Sqrt[165])","C",1
246,1,80,56,0.0275887,"\int \frac{3+x}{\left(1+x^2\right) \sqrt{1+x+x^2}} \, dx","Integrate[(3 + x)/((1 + x^2)*Sqrt[1 + x + x^2]),x]","\left(\frac{1}{2}+\frac{i}{2}\right) (-1)^{3/4} \left((2+i) \tan ^{-1}\left(\frac{\sqrt[4]{-1} ((2+i) x+(1+2 i))}{2 \sqrt{x^2+x+1}}\right)+(1+2 i) \tanh ^{-1}\left(\frac{(-1)^{3/4} ((1+2 i) x+(2+i))}{2 \sqrt{x^2+x+1}}\right)\right)","\sqrt{2} \tanh ^{-1}\left(\frac{x+1}{\sqrt{2} \sqrt{x^2+x+1}}\right)-2 \sqrt{2} \tan ^{-1}\left(\frac{1-x}{\sqrt{2} \sqrt{x^2+x+1}}\right)",1,"(1/2 + I/2)*(-1)^(3/4)*((2 + I)*ArcTan[((-1)^(1/4)*((1 + 2*I) + (2 + I)*x))/(2*Sqrt[1 + x + x^2])] + (1 + 2*I)*ArcTanh[((-1)^(3/4)*((2 + I) + (1 + 2*I)*x))/(2*Sqrt[1 + x + x^2])])","C",1
247,1,174,70,0.4504245,"\int \frac{1+2 x}{\sqrt{-1+6 x+x^2} \left(4+4 x+3 x^2\right)} \, dx","Integrate[(1 + 2*x)/(Sqrt[-1 + 6*x + x^2]*(4 + 4*x + 3*x^2)),x]","-\frac{\sqrt{7-4 i \sqrt{2}} \left(8 \sqrt{2}+13 i\right) \tan ^{-1}\left(\frac{\left(-7-2 i \sqrt{2}\right) x-6 i \sqrt{2}+9}{\sqrt{7 \left(7-4 i \sqrt{2}\right)} \sqrt{x^2+6 x-1}}\right)+\sqrt{7+4 i \sqrt{2}} \left(8 \sqrt{2}-13 i\right) \tan ^{-1}\left(\frac{\left(-7+2 i \sqrt{2}\right) x+6 i \sqrt{2}+9}{\sqrt{7 \left(7+4 i \sqrt{2}\right)} \sqrt{x^2+6 x-1}}\right)}{108 \sqrt{14}}","-\frac{5 \tan ^{-1}\left(\frac{\sqrt{\frac{7}{2}} (2-x)}{2 \sqrt{x^2+6 x-1}}\right)}{6 \sqrt{14}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{7} (x+1)}{\sqrt{x^2+6 x-1}}\right)}{3 \sqrt{7}}",1,"-1/108*(Sqrt[7 - (4*I)*Sqrt[2]]*(13*I + 8*Sqrt[2])*ArcTan[(9 - (6*I)*Sqrt[2] + (-7 - (2*I)*Sqrt[2])*x)/(Sqrt[7*(7 - (4*I)*Sqrt[2])]*Sqrt[-1 + 6*x + x^2])] + Sqrt[7 + (4*I)*Sqrt[2]]*(-13*I + 8*Sqrt[2])*ArcTan[(9 + (6*I)*Sqrt[2] + (-7 + (2*I)*Sqrt[2])*x)/(Sqrt[7*(7 + (4*I)*Sqrt[2])]*Sqrt[-1 + 6*x + x^2])])/Sqrt[14]","C",1
248,1,94,80,0.1202393,"\int \frac{B+A x}{\left(17-18 x+5 x^2\right) \sqrt{13-22 x+10 x^2}} \, dx","Integrate[(B + A*x)/((17 - 18*x + 5*x^2)*Sqrt[13 - 22*x + 10*x^2]),x]","\frac{((4-i) A+(2-i) B) \tan ^{-1}\left(\frac{(2-18 i)-(1-18 i) x}{\sqrt{35} \sqrt{10 x^2-22 x+13}}\right)+((1-4 i) A+(1-2 i) B) \tanh ^{-1}\left(\frac{(18-i) x-(18-2 i)}{\sqrt{35} \sqrt{10 x^2-22 x+13}}\right)}{4 \sqrt{35}}","-\frac{(2 A+B) \tan ^{-1}\left(\frac{\sqrt{35} (2-x)}{\sqrt{10 x^2-22 x+13}}\right)}{\sqrt{35}}-\frac{(A+B) \tanh ^{-1}\left(\frac{\sqrt{35} (1-x)}{2 \sqrt{10 x^2-22 x+13}}\right)}{2 \sqrt{35}}",1,"(((4 - I)*A + (2 - I)*B)*ArcTan[((2 - 18*I) - (1 - 18*I)*x)/(Sqrt[35]*Sqrt[13 - 22*x + 10*x^2])] + ((1 - 4*I)*A + (1 - 2*I)*B)*ArcTanh[((-18 + 2*I) + (18 - I)*x)/(Sqrt[35]*Sqrt[13 - 22*x + 10*x^2])])/(4*Sqrt[35])","C",1
249,1,76,38,0.0403833,"\int \frac{-2+x}{\left(17-18 x+5 x^2\right) \sqrt{13-22 x+10 x^2}} \, dx","Integrate[(-2 + x)/((17 - 18*x + 5*x^2)*Sqrt[13 - 22*x + 10*x^2]),x]","\frac{i \left(\tan ^{-1}\left(\frac{(2-18 i)-(1-18 i) x}{\sqrt{35} \sqrt{10 x^2-22 x+13}}\right)+i \tanh ^{-1}\left(\frac{(18-i) x-(18-2 i)}{\sqrt{35} \sqrt{10 x^2-22 x+13}}\right)\right)}{4 \sqrt{35}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{35} (1-x)}{2 \sqrt{10 x^2-22 x+13}}\right)}{2 \sqrt{35}}",1,"((I/4)*(ArcTan[((2 - 18*I) - (1 - 18*I)*x)/(Sqrt[35]*Sqrt[13 - 22*x + 10*x^2])] + I*ArcTanh[((-18 + 2*I) + (18 - I)*x)/(Sqrt[35]*Sqrt[13 - 22*x + 10*x^2])]))/Sqrt[35]","C",1
250,1,40,65,0.0221297,"\int x^4 \sqrt{5-x^2} \, dx","Integrate[x^4*Sqrt[5 - x^2],x]","\frac{1}{48} \left(x \sqrt{5-x^2} \left(8 x^4-10 x^2-75\right)+375 \sin ^{-1}\left(\frac{x}{\sqrt{5}}\right)\right)","-\frac{25}{16} \sqrt{5-x^2} x+\frac{1}{6} \sqrt{5-x^2} x^5-\frac{5}{24} \sqrt{5-x^2} x^3+\frac{125}{16} \sin ^{-1}\left(\frac{x}{\sqrt{5}}\right)",1,"(x*Sqrt[5 - x^2]*(-75 - 10*x^2 + 8*x^4) + 375*ArcSin[x/Sqrt[5]])/48","A",1
251,1,28,49,0.0058683,"\int \frac{1}{x^6 \sqrt{2+x^2}} \, dx","Integrate[1/(x^6*Sqrt[2 + x^2]),x]","-\frac{\sqrt{x^2+2} \left(2 x^4-2 x^2+3\right)}{30 x^5}","-\frac{\sqrt{x^2+2}}{15 x}-\frac{\sqrt{x^2+2}}{10 x^5}+\frac{\sqrt{x^2+2}}{15 x^3}",1,"-1/30*(Sqrt[2 + x^2]*(3 - 2*x^2 + 2*x^4))/x^5","A",1
252,1,28,49,0.0077353,"\int \frac{1}{\left(3+2 x^2\right)^{7/2}} \, dx","Integrate[(3 + 2*x^2)^(-7/2),x]","\frac{x \left(32 x^4+120 x^2+135\right)}{405 \left(2 x^2+3\right)^{5/2}}","\frac{8 x}{405 \sqrt{2 x^2+3}}+\frac{4 x}{135 \left(2 x^2+3\right)^{3/2}}+\frac{x}{15 \left(2 x^2+3\right)^{5/2}}",1,"(x*(135 + 120*x^2 + 32*x^4))/(405*(3 + 2*x^2)^(5/2))","A",1
253,1,12,12,0.027086,"\int \frac{x}{1+x^2+a \sqrt{1+x^2}} \, dx","Integrate[x/(1 + x^2 + a*Sqrt[1 + x^2]),x]","\log \left(a+\sqrt{x^2+1}\right)","\log \left(a+\sqrt{x^2+1}\right)",1,"Log[a + Sqrt[1 + x^2]]","A",1
254,1,12,12,0.0117605,"\int \frac{1-x+x^2}{\left(1+x^2\right)^{3/2}} \, dx","Integrate[(1 - x + x^2)/(1 + x^2)^(3/2),x]","\frac{1}{\sqrt{x^2+1}}+\sinh ^{-1}(x)","\frac{1}{\sqrt{x^2+1}}+\sinh ^{-1}(x)",1,"1/Sqrt[1 + x^2] + ArcSinh[x]","A",1
255,1,27,27,0.0142679,"\int \frac{\sqrt{1+x^2}}{2+x^2} \, dx","Integrate[Sqrt[1 + x^2]/(2 + x^2),x]","\sinh ^{-1}(x)-\frac{\tanh ^{-1}\left(\frac{x}{\sqrt{2} \sqrt{x^2+1}}\right)}{\sqrt{2}}","\sinh ^{-1}(x)-\frac{\tanh ^{-1}\left(\frac{x}{\sqrt{2} \sqrt{x^2+1}}\right)}{\sqrt{2}}",1,"ArcSinh[x] - ArcTanh[x/(Sqrt[2]*Sqrt[1 + x^2])]/Sqrt[2]","A",1
256,1,74,48,0.205844,"\int \frac{1}{\sqrt{1+x^2} \left(2+x^2\right)^2} \, dx","Integrate[1/(Sqrt[1 + x^2]*(2 + x^2)^2),x]","\frac{\sqrt{x^2+1} \left(3 \sqrt{2} \sqrt{\frac{x^2}{x^2+1}} \left(x^2+2\right) \tanh ^{-1}\left(\sqrt{\frac{x^2}{2 x^2+2}}\right)-2 x^2\right)}{8 x \left(x^2+2\right)}","\frac{3 \tanh ^{-1}\left(\frac{x}{\sqrt{2} \sqrt{x^2+1}}\right)}{4 \sqrt{2}}-\frac{x \sqrt{x^2+1}}{4 \left(x^2+2\right)}",1,"(Sqrt[1 + x^2]*(-2*x^2 + 3*Sqrt[2]*Sqrt[x^2/(1 + x^2)]*(2 + x^2)*ArcTanh[Sqrt[x^2/(2 + 2*x^2)]]))/(8*x*(2 + x^2))","A",1
257,1,41,41,0.0303765,"\int \frac{x^2}{\left(-6+x^2\right) \sqrt{-2+x^2}} \, dx","Integrate[x^2/((-6 + x^2)*Sqrt[-2 + x^2]),x]","\log \left(\sqrt{x^2-2}+x\right)-\sqrt{\frac{3}{2}} \tanh ^{-1}\left(\frac{\sqrt{\frac{2}{3}} x}{\sqrt{x^2-2}}\right)","\tanh ^{-1}\left(\frac{x}{\sqrt{x^2-2}}\right)-\sqrt{\frac{3}{2}} \tanh ^{-1}\left(\frac{\sqrt{\frac{2}{3}} x}{\sqrt{x^2-2}}\right)",1,"-(Sqrt[3/2]*ArcTanh[(Sqrt[2/3]*x)/Sqrt[-2 + x^2]]) + Log[x + Sqrt[-2 + x^2]]","A",1
258,1,85,47,0.1570054,"\int \frac{5+x^2}{\sqrt{1-x^2} \left(1+x^2\right)^2} \, dx","Integrate[(5 + x^2)/(Sqrt[1 - x^2]*(1 + x^2)^2),x]","\frac{\sqrt{1-x^2} x}{x^2+1}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{1-x^2}}\right)}{\sqrt{2}}+\frac{3 x \tanh ^{-1}\left(\sqrt{2} \sqrt{\frac{x^2}{x^2-1}}\right)}{\sqrt{2} \sqrt{-x^2}}","\frac{\sqrt{1-x^2} x}{x^2+1}+2 \sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{1-x^2}}\right)",1,"(x*Sqrt[1 - x^2])/(1 + x^2) + ArcTan[(Sqrt[2]*x)/Sqrt[1 - x^2]]/Sqrt[2] + (3*x*ArcTanh[Sqrt[2]*Sqrt[x^2/(-1 + x^2)]])/(Sqrt[2]*Sqrt[-x^2])","A",1
259,1,137,88,0.2049768,"\int \frac{4 x-\sqrt{1-x^2}}{5+\sqrt{1-x^2}} \, dx","Integrate[(4*x - Sqrt[1 - x^2])/(5 + Sqrt[1 - x^2]),x]","-4 \sqrt{1-x^2}+10 \log \left(x^2+24\right)-10 \log \left(\left(x^2+24\right)^2\right)+10 \log \left(\left(x^2+24\right) \left(-x^2+10 \sqrt{1-x^2}+26\right)\right)+\frac{25 \tan ^{-1}\left(\frac{4 x^2+409 \sqrt{1-x^2} x+96}{10 \sqrt{6} \left(17 x^2-1\right)}\right)}{2 \sqrt{6}}-x+5 \sin ^{-1}(x)+\frac{25 \tan ^{-1}\left(\frac{x}{2 \sqrt{6}}\right)}{2 \sqrt{6}}","-4 \sqrt{1-x^2}+20 \log \left(\sqrt{1-x^2}+5\right)-\frac{25 \tan ^{-1}\left(\frac{5 x}{2 \sqrt{6} \sqrt{1-x^2}}\right)}{2 \sqrt{6}}-x+5 \sin ^{-1}(x)+\frac{25 \tan ^{-1}\left(\frac{x}{2 \sqrt{6}}\right)}{2 \sqrt{6}}",1,"-x - 4*Sqrt[1 - x^2] + 5*ArcSin[x] + (25*ArcTan[x/(2*Sqrt[6])])/(2*Sqrt[6]) + (25*ArcTan[(96 + 4*x^2 + 409*x*Sqrt[1 - x^2])/(10*Sqrt[6]*(-1 + 17*x^2))])/(2*Sqrt[6]) + 10*Log[24 + x^2] - 10*Log[(24 + x^2)^2] + 10*Log[(24 + x^2)*(26 - x^2 + 10*Sqrt[1 - x^2])]","A",1
260,1,261,136,1.0074896,"\int \frac{x^2 \left(2-\sqrt{1+x^2}\right)}{\sqrt{1+x^2} \left(1-x^3+\left(1+x^2\right)^{3/2}\right)} \, dx","Integrate[(x^2*(2 - Sqrt[1 + x^2]))/(Sqrt[1 + x^2]*(1 - x^3 + (1 + x^2)^(3/2))),x]","\frac{1}{162} \left(-27 x^2-27 \sqrt{x^2+1} x+144 \sqrt{x^2+1}-21 \log \left(3 x^2+2 x+3\right)+\sqrt{1-2 i \sqrt{2}} \left(11 \sqrt{2}-i\right) \tanh ^{-1}\left(\frac{-2 i \sqrt{2} x-x+3}{\sqrt{2+4 i \sqrt{2}} \sqrt{x^2+1}}\right)+11 \sqrt{2+4 i \sqrt{2}} \tanh ^{-1}\left(\frac{2 i \sqrt{2} x-x+3}{\sqrt{2-4 i \sqrt{2}} \sqrt{x^2+1}}\right)+i \sqrt{1+2 i \sqrt{2}} \tanh ^{-1}\left(\frac{2 i \sqrt{2} x-x+3}{\sqrt{2-4 i \sqrt{2}} \sqrt{x^2+1}}\right)+144 x+24 \sqrt{2} \tan ^{-1}\left(\frac{3 x+1}{2 \sqrt{2}}\right)-123 \sinh ^{-1}(x)\right)","-\frac{x^2}{6}-\frac{1}{6} \sqrt{x^2+1} x+\frac{8 \sqrt{x^2+1}}{9}-\frac{7}{54} \log \left(3 x^2+2 x+3\right)+\frac{4}{27} \sqrt{2} \tan ^{-1}\left(\frac{x+1}{\sqrt{2} \sqrt{x^2+1}}\right)+\frac{7}{27} \tanh ^{-1}\left(\frac{1-x}{2 \sqrt{x^2+1}}\right)+\frac{8 x}{9}+\frac{4}{27} \sqrt{2} \tan ^{-1}\left(\frac{3 x+1}{2 \sqrt{2}}\right)-\frac{41}{54} \sinh ^{-1}(x)",1,"(144*x - 27*x^2 + 144*Sqrt[1 + x^2] - 27*x*Sqrt[1 + x^2] - 123*ArcSinh[x] + 24*Sqrt[2]*ArcTan[(1 + 3*x)/(2*Sqrt[2])] + Sqrt[1 - (2*I)*Sqrt[2]]*(-I + 11*Sqrt[2])*ArcTanh[(3 - x - (2*I)*Sqrt[2]*x)/(Sqrt[2 + (4*I)*Sqrt[2]]*Sqrt[1 + x^2])] + I*Sqrt[1 + (2*I)*Sqrt[2]]*ArcTanh[(3 - x + (2*I)*Sqrt[2]*x)/(Sqrt[2 - (4*I)*Sqrt[2]]*Sqrt[1 + x^2])] + 11*Sqrt[2 + (4*I)*Sqrt[2]]*ArcTanh[(3 - x + (2*I)*Sqrt[2]*x)/(Sqrt[2 - (4*I)*Sqrt[2]]*Sqrt[1 + x^2])] - 21*Log[3 + 2*x + 3*x^2])/162","C",1
261,1,72,64,0.1200118,"\int x \sqrt{2 r x-x^2} \, dx","Integrate[x*Sqrt[2*r*x - x^2],x]","\frac{1}{6} \sqrt{-x (x-2 r)} \left(\frac{6 r^{5/2} \sin ^{-1}\left(\frac{\sqrt{x}}{\sqrt{2} \sqrt{r}}\right)}{\sqrt{x} \sqrt{2-\frac{x}{r}}}-3 r^2-r x+2 x^2\right)","r^3 \tan ^{-1}\left(\frac{x}{\sqrt{2 r x-x^2}}\right)-\frac{1}{2} r (r-x) \sqrt{2 r x-x^2}-\frac{1}{3} \left(2 r x-x^2\right)^{3/2}",1,"(Sqrt[-(x*(-2*r + x))]*(-3*r^2 - r*x + 2*x^2 + (6*r^(5/2)*ArcSin[Sqrt[x]/(Sqrt[2]*Sqrt[r])])/(Sqrt[x]*Sqrt[2 - x/r])))/6","A",1
262,1,80,89,0.1034053,"\int x^2 \sqrt{2 r x-x^2} \, dx","Integrate[x^2*Sqrt[2*r*x - x^2],x]","\frac{1}{24} \sqrt{-x (x-2 r)} \left(\frac{30 r^{7/2} \sin ^{-1}\left(\frac{\sqrt{x}}{\sqrt{2} \sqrt{r}}\right)}{\sqrt{x} \sqrt{2-\frac{x}{r}}}-15 r^3-5 r^2 x-2 r x^2+6 x^3\right)","\frac{5}{4} r^4 \tan ^{-1}\left(\frac{x}{\sqrt{2 r x-x^2}}\right)-\frac{5}{8} r^2 (r-x) \sqrt{2 r x-x^2}-\frac{5}{12} r \left(2 r x-x^2\right)^{3/2}-\frac{1}{4} x \left(2 r x-x^2\right)^{3/2}",1,"(Sqrt[-(x*(-2*r + x))]*(-15*r^3 - 5*r^2*x - 2*r*x^2 + 6*x^3 + (30*r^(7/2)*ArcSin[Sqrt[x]/(Sqrt[2]*Sqrt[r])])/(Sqrt[x]*Sqrt[2 - x/r])))/24","A",1
263,1,88,113,0.1179144,"\int x^3 \sqrt{2 r x-x^2} \, dx","Integrate[x^3*Sqrt[2*r*x - x^2],x]","\frac{1}{120} \sqrt{-x (x-2 r)} \left(\frac{210 r^{9/2} \sin ^{-1}\left(\frac{\sqrt{x}}{\sqrt{2} \sqrt{r}}\right)}{\sqrt{x} \sqrt{2-\frac{x}{r}}}-105 r^4-35 r^3 x-14 r^2 x^2-6 r x^3+24 x^4\right)","\frac{7}{4} r^5 \tan ^{-1}\left(\frac{x}{\sqrt{2 r x-x^2}}\right)-\frac{7}{8} r^3 (r-x) \sqrt{2 r x-x^2}-\frac{7}{12} r^2 \left(2 r x-x^2\right)^{3/2}-\frac{7}{20} r x \left(2 r x-x^2\right)^{3/2}-\frac{1}{5} x^2 \left(2 r x-x^2\right)^{3/2}",1,"(Sqrt[-(x*(-2*r + x))]*(-105*r^4 - 35*r^3*x - 14*r^2*x^2 - 6*r*x^3 + 24*x^4 + (210*r^(9/2)*ArcSin[Sqrt[x]/(Sqrt[2]*Sqrt[r])])/(Sqrt[x]*Sqrt[2 - x/r])))/120","A",1
264,1,64,49,0.0295776,"\int \frac{1}{\left(-1+x^2\right) \sqrt{2 x+x^2}} \, dx","Integrate[1/((-1 + x^2)*Sqrt[2*x + x^2]),x]","-\frac{\sqrt{x} \sqrt{x+2} \left(3 \tan ^{-1}\left(\sqrt{\frac{x}{x+2}}\right)+\sqrt{3} \tanh ^{-1}\left(\sqrt{3} \sqrt{\frac{x}{x+2}}\right)\right)}{3 \sqrt{x (x+2)}}","-\frac{1}{2} \tan ^{-1}\left(\sqrt{x^2+2 x}\right)-\frac{\tanh ^{-1}\left(\frac{2 x+1}{\sqrt{3} \sqrt{x^2+2 x}}\right)}{2 \sqrt{3}}",1,"-1/3*(Sqrt[x]*Sqrt[2 + x]*(3*ArcTan[Sqrt[x/(2 + x)]] + Sqrt[3]*ArcTanh[Sqrt[3]*Sqrt[x/(2 + x)]]))/Sqrt[x*(2 + x)]","A",1
265,1,72,79,0.0884346,"\int \frac{-2+3 x}{(1+x)^3 \sqrt{2 x-x^2}} \, dx","Integrate[(-2 + 3*x)/((1 + x)^3*Sqrt[2*x - x^2]),x]","\frac{x \left(4 x^2+x-18\right)-2 \sqrt{3} \sqrt{x-2} \sqrt{x} (x+1)^2 \tanh ^{-1}\left(\frac{\sqrt{\frac{x-2}{x}}}{\sqrt{3}}\right)}{6 \sqrt{-((x-2) x)} (x+1)^2}","-\frac{2 \sqrt{2 x-x^2}}{3 (x+1)}-\frac{5 \sqrt{2 x-x^2}}{6 (x+1)^2}+\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3} \sqrt{2 x-x^2}}\right)}{2 \sqrt{3}}",1,"(x*(-18 + x + 4*x^2) - 2*Sqrt[3]*Sqrt[-2 + x]*Sqrt[x]*(1 + x)^2*ArcTanh[Sqrt[(-2 + x)/x]/Sqrt[3]])/(6*Sqrt[-((-2 + x)*x)]*(1 + x)^2)","A",0
266,1,12,12,0.0055266,"\int \frac{1}{\sqrt{1+x+x^2}} \, dx","Integrate[1/Sqrt[1 + x + x^2],x]","\sinh ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)","\sinh ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)",1,"ArcSinh[(1 + 2*x)/Sqrt[3]]","A",1
267,1,41,53,0.0204862,"\int \frac{x^3}{\sqrt{1+x+x^2}} \, dx","Integrate[x^3/Sqrt[1 + x + x^2],x]","\frac{1}{48} \left(2 \sqrt{x^2+x+1} \left(8 x^2-10 x-1\right)+21 \sinh ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)\right)","\frac{1}{3} \sqrt{x^2+x+1} x^2-\frac{1}{24} (10 x+1) \sqrt{x^2+x+1}+\frac{7}{16} \sinh ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)",1,"(2*Sqrt[1 + x + x^2]*(-1 - 10*x + 8*x^2) + 21*ArcSinh[(1 + 2*x)/Sqrt[3]])/48","A",1
268,1,19,19,0.005544,"\int \frac{1}{\left(1+x+x^2\right)^{3/2}} \, dx","Integrate[(1 + x + x^2)^(-3/2),x]","\frac{2 (2 x+1)}{3 \sqrt{x^2+x+1}}","\frac{2 (2 x+1)}{3 \sqrt{x^2+x+1}}",1,"(2*(1 + 2*x))/(3*Sqrt[1 + x + x^2])","A",1
269,1,17,17,0.0394418,"\int \frac{x}{\left(1+x+x^2\right)^{3/2}} \, dx","Integrate[x/(1 + x + x^2)^(3/2),x]","-\frac{2 (x+2)}{3 \sqrt{x^2+x+1}}","-\frac{2 (x+2)}{3 \sqrt{x^2+x+1}}",1,"(-2*(2 + x))/(3*Sqrt[1 + x + x^2])","A",1
270,1,48,56,0.0139676,"\int \frac{x^3}{\left(1+x+x^2\right)^{3/2}} \, dx","Integrate[x^3/(1 + x + x^2)^(3/2),x]","\frac{6 x^2-9 \sqrt{x^2+x+1} \sinh ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)+14 x+10}{6 \sqrt{x^2+x+1}}","-\frac{2 (x+2) x^2}{3 \sqrt{x^2+x+1}}+\frac{1}{3} (2 x+5) \sqrt{x^2+x+1}-\frac{3}{2} \sinh ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)",1,"(10 + 14*x + 6*x^2 - 9*Sqrt[1 + x + x^2]*ArcSinh[(1 + 2*x)/Sqrt[3]])/(6*Sqrt[1 + x + x^2])","A",1
271,1,46,65,0.0220757,"\int x^2 \sqrt{1+x+x^2} \, dx","Integrate[x^2*Sqrt[1 + x + x^2],x]","\frac{1}{384} \left(2 \sqrt{x^2+x+1} \left(48 x^3+8 x^2+14 x-37\right)+9 \sinh ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)\right)","\frac{1}{4} x \left(x^2+x+1\right)^{3/2}-\frac{5}{24} \left(x^2+x+1\right)^{3/2}+\frac{1}{64} (2 x+1) \sqrt{x^2+x+1}+\frac{3}{128} \sinh ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)",1,"(2*Sqrt[1 + x + x^2]*(-37 + 14*x + 8*x^2 + 48*x^3) + 9*ArcSinh[(1 + 2*x)/Sqrt[3]])/384","A",1
272,1,46,55,0.0163444,"\int \left(1+x+x^2\right)^{3/2} \, dx","Integrate[(1 + x + x^2)^(3/2),x]","\frac{1}{128} \left(2 \sqrt{x^2+x+1} \left(16 x^3+24 x^2+42 x+17\right)+27 \sinh ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)\right)","\frac{1}{8} (2 x+1) \left(x^2+x+1\right)^{3/2}+\frac{9}{64} (2 x+1) \sqrt{x^2+x+1}+\frac{27}{128} \sinh ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)",1,"(2*Sqrt[1 + x + x^2]*(17 + 42*x + 24*x^2 + 16*x^3) + 27*ArcSinh[(1 + 2*x)/Sqrt[3]])/128","A",1
273,1,56,74,0.026416,"\int \left(1+x+x^2\right)^{5/2} \, dx","Integrate[(1 + x + x^2)^(5/2),x]","\frac{2 \sqrt{x^2+x+1} \left(256 x^5+640 x^4+1264 x^3+1256 x^2+1142 x+383\right)+405 \sinh ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{3072}","\frac{1}{12} (2 x+1) \left(x^2+x+1\right)^{5/2}+\frac{5}{64} (2 x+1) \left(x^2+x+1\right)^{3/2}+\frac{45}{512} (2 x+1) \sqrt{x^2+x+1}+\frac{135 \sinh ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{1024}",1,"(2*Sqrt[1 + x + x^2]*(383 + 1142*x + 1256*x^2 + 1264*x^3 + 640*x^4 + 256*x^5) + 405*ArcSinh[(1 + 2*x)/Sqrt[3]])/3072","A",1
274,1,38,38,0.0096612,"\int \frac{1}{x^2 \sqrt{1+x+x^2}} \, dx","Integrate[1/(x^2*Sqrt[1 + x + x^2]),x]","\frac{1}{2} \tanh ^{-1}\left(\frac{x+2}{2 \sqrt{x^2+x+1}}\right)-\frac{\sqrt{x^2+x+1}}{x}","\frac{1}{2} \tanh ^{-1}\left(\frac{x+2}{2 \sqrt{x^2+x+1}}\right)-\frac{\sqrt{x^2+x+1}}{x}",1,"-(Sqrt[1 + x + x^2]/x) + ArcTanh[(2 + x)/(2*Sqrt[1 + x + x^2])]/2","A",1
275,1,43,57,0.0163095,"\int \frac{1}{x^3 \sqrt{1+x+x^2}} \, dx","Integrate[1/(x^3*Sqrt[1 + x + x^2]),x]","\frac{1}{8} \left(\frac{2 \sqrt{x^2+x+1} (3 x-2)}{x^2}+\tanh ^{-1}\left(\frac{x+2}{2 \sqrt{x^2+x+1}}\right)\right)","\frac{3 \sqrt{x^2+x+1}}{4 x}-\frac{\sqrt{x^2+x+1}}{2 x^2}+\frac{1}{8} \tanh ^{-1}\left(\frac{x+2}{2 \sqrt{x^2+x+1}}\right)",1,"((2*(-2 + 3*x)*Sqrt[1 + x + x^2])/x^2 + ArcTanh[(2 + x)/(2*Sqrt[1 + x + x^2])])/8","A",1
276,1,50,62,0.0189138,"\int \frac{1}{x^2 \left(1+x+x^2\right)^{3/2}} \, dx","Integrate[1/(x^2*(1 + x + x^2)^(3/2)),x]","\frac{3}{2} \tanh ^{-1}\left(\frac{x+2}{2 \sqrt{x^2+x+1}}\right)-\frac{5 x^2+7 x+3}{3 x \sqrt{x^2+x+1}}","\frac{2 (1-x)}{3 x \sqrt{x^2+x+1}}-\frac{5 \sqrt{x^2+x+1}}{3 x}+\frac{3}{2} \tanh ^{-1}\left(\frac{x+2}{2 \sqrt{x^2+x+1}}\right)",1,"-1/3*(3 + 7*x + 5*x^2)/(x*Sqrt[1 + x + x^2]) + (3*ArcTanh[(2 + x)/(2*Sqrt[1 + x + x^2])])/2","A",1
277,1,65,79,0.013546,"\int \frac{1}{x^3 \left(1+x+x^2\right)^{3/2}} \, dx","Integrate[1/(x^3*(1 + x + x^2)^(3/2)),x]","\frac{74 x^3+46 x^2-9 \sqrt{x^2+x+1} x^2 \tanh ^{-1}\left(\frac{x+2}{2 \sqrt{x^2+x+1}}\right)+30 x-12}{24 x^2 \sqrt{x^2+x+1}}","\frac{2 (1-x)}{3 x^2 \sqrt{x^2+x+1}}+\frac{37 \sqrt{x^2+x+1}}{12 x}-\frac{7 \sqrt{x^2+x+1}}{6 x^2}-\frac{3}{8} \tanh ^{-1}\left(\frac{x+2}{2 \sqrt{x^2+x+1}}\right)",1,"(-12 + 30*x + 46*x^2 + 74*x^3 - 9*x^2*Sqrt[1 + x + x^2]*ArcTanh[(2 + x)/(2*Sqrt[1 + x + x^2])])/(24*x^2*Sqrt[1 + x + x^2])","A",1
278,1,22,22,0.0034484,"\int \frac{1}{(1+x) \sqrt{1+x+x^2}} \, dx","Integrate[1/((1 + x)*Sqrt[1 + x + x^2]),x]","-\tanh ^{-1}\left(\frac{1-x}{2 \sqrt{x^2+x+1}}\right)","-\tanh ^{-1}\left(\frac{1-x}{2 \sqrt{x^2+x+1}}\right)",1,"-ArcTanh[(1 - x)/(2*Sqrt[1 + x + x^2])]","A",1
279,1,83,86,0.0692405,"\int \frac{1}{\sqrt{4+2 x+x^2} \left(-x+x^3\right)} \, dx","Integrate[1/(Sqrt[4 + 2*x + x^2]*(-x + x^3)),x]","\frac{1}{42} \left(21 \tanh ^{-1}\left(\frac{x+4}{2 \sqrt{x^2+2 x+4}}\right)-3 \sqrt{7} \tanh ^{-1}\left(\frac{2 x+5}{\sqrt{7} \sqrt{x^2+2 x+4}}\right)-7 \sqrt{3} \tanh ^{-1}\left(\frac{\sqrt{(x+1)^2+3}}{\sqrt{3}}\right)\right)","\frac{1}{2} \tanh ^{-1}\left(\frac{x+4}{2 \sqrt{x^2+2 x+4}}\right)-\frac{\tanh ^{-1}\left(\frac{2 x+5}{\sqrt{7} \sqrt{x^2+2 x+4}}\right)}{2 \sqrt{7}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{x^2+2 x+4}}{\sqrt{3}}\right)}{2 \sqrt{3}}",1,"(21*ArcTanh[(4 + x)/(2*Sqrt[4 + 2*x + x^2])] - 3*Sqrt[7]*ArcTanh[(5 + 2*x)/(Sqrt[7]*Sqrt[4 + 2*x + x^2])] - 7*Sqrt[3]*ArcTanh[Sqrt[3 + (1 + x)^2]/Sqrt[3]])/42","A",1
280,1,61,62,0.0431863,"\int \frac{\sqrt{4+2 x+x^2}}{(-1+x)^2} \, dx","Integrate[Sqrt[4 + 2*x + x^2]/(-1 + x)^2,x]","-\frac{\sqrt{x^2+2 x+4}}{x-1}-\frac{2 \tanh ^{-1}\left(\frac{2 x+5}{\sqrt{7} \sqrt{x^2+2 x+4}}\right)}{\sqrt{7}}+\sinh ^{-1}\left(\frac{x+1}{\sqrt{3}}\right)","\frac{\sqrt{x^2+2 x+4}}{1-x}-\frac{2 \tanh ^{-1}\left(\frac{2 x+5}{\sqrt{7} \sqrt{x^2+2 x+4}}\right)}{\sqrt{7}}+\sinh ^{-1}\left(\frac{x+1}{\sqrt{3}}\right)",1,"-(Sqrt[4 + 2*x + x^2]/(-1 + x)) + ArcSinh[(1 + x)/Sqrt[3]] - (2*ArcTanh[(5 + 2*x)/(Sqrt[7]*Sqrt[4 + 2*x + x^2])])/Sqrt[7]","A",1
281,1,146,76,0.3997149,"\int \frac{3+2 x}{\left(3+2 x+x^2\right)^2 \sqrt{4+2 x+x^2}} \, dx","Integrate[(3 + 2*x)/((3 + 2*x + x^2)^2*Sqrt[4 + 2*x + x^2]),x]","\frac{1}{32} \left(8 \left(\frac{\sqrt{x^2+2 x+4} (x-3)}{x^2+2 x+3}-2 \log \left(\left(x^2+2 x+3\right)^2\right)+2 \log \left(\left(x^2+2 x+3\right) \left(x^2+2 \sqrt{x^2+2 x+4}+2 x+5\right)\right)\right)-4 \sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \left(5 x^2+10 x+4\right)}{4 x^2+\left(11 \sqrt{x^2+2 x+4}+8\right) x+11 \sqrt{x^2+2 x+4}+12}\right)\right)","-\frac{\sqrt{x^2+2 x+4} (3-x)}{4 \left(x^2+2 x+3\right)}-\frac{\tan ^{-1}\left(\frac{x+1}{\sqrt{2} \sqrt{x^2+2 x+4}}\right)}{4 \sqrt{2}}+\tanh ^{-1}\left(\sqrt{x^2+2 x+4}\right)",1,"(-4*Sqrt[2]*ArcTan[(Sqrt[2]*(4 + 10*x + 5*x^2))/(12 + 4*x^2 + 11*Sqrt[4 + 2*x + x^2] + x*(8 + 11*Sqrt[4 + 2*x + x^2]))] + 8*(((-3 + x)*Sqrt[4 + 2*x + x^2])/(3 + 2*x + x^2) - 2*Log[(3 + 2*x + x^2)^2] + 2*Log[(3 + 2*x + x^2)*(5 + 2*x + x^2 + 2*Sqrt[4 + 2*x + x^2])]))/32","A",1
282,1,26,36,0.0125786,"\int \frac{3 x^2+2 x^3}{\sqrt{-3+2 x+x^2} \left(-3+x+2 x^2\right)} \, dx","Integrate[(3*x^2 + 2*x^3)/(Sqrt[-3 + 2*x + x^2]*(-3 + x + 2*x^2)),x]","\frac{2 x^2+3 x-9}{2 \sqrt{x^2+2 x-3}}","\frac{\sqrt{x^2+2 x-3}}{2 (1-x)}+\sqrt{x^2+2 x-3}",1,"(-9 + 3*x + 2*x^2)/(2*Sqrt[-3 + 2*x + x^2])","A",1
283,1,134,87,0.1593916,"\int \frac{1+x^4}{\left(1+x+x^2\right) \sqrt{2+x+x^2}} \, dx","Integrate[(1 + x^4)/((1 + x + x^2)*Sqrt[2 + x + x^2]),x]","\frac{1}{24} \left(6 \sqrt{x^2+x+2} (2 x-7)-4 i \left(\sqrt{3}-3 i\right) \tanh ^{-1}\left(\frac{-2 i \sqrt{3} x-i \sqrt{3}+7}{4 \sqrt{x^2+x+2}}\right)+4 i \left(\sqrt{3}+3 i\right) \tanh ^{-1}\left(\frac{2 i \sqrt{3} x+i \sqrt{3}+7}{4 \sqrt{x^2+x+2}}\right)-3 \sinh ^{-1}\left(\frac{2 x+1}{\sqrt{7}}\right)\right)","\frac{1}{2} \sqrt{x^2+x+2} x-\frac{7}{4} \sqrt{x^2+x+2}+\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3} \sqrt{x^2+x+2}}\right)}{\sqrt{3}}-\tanh ^{-1}\left(\sqrt{x^2+x+2}\right)-\frac{1}{8} \sinh ^{-1}\left(\frac{2 x+1}{\sqrt{7}}\right)",1,"(6*(-7 + 2*x)*Sqrt[2 + x + x^2] - 3*ArcSinh[(1 + 2*x)/Sqrt[7]] - (4*I)*(-3*I + Sqrt[3])*ArcTanh[(7 - I*Sqrt[3] - (2*I)*Sqrt[3]*x)/(4*Sqrt[2 + x + x^2])] + (4*I)*(3*I + Sqrt[3])*ArcTanh[(7 + I*Sqrt[3] + (2*I)*Sqrt[3]*x)/(4*Sqrt[2 + x + x^2])])/24","C",1
284,1,39,58,0.0124313,"\int \frac{1}{\left(4+2 x+x^2\right)^{7/2}} \, dx","Integrate[(4 + 2*x + x^2)^(-7/2),x]","\frac{(x+1) \left(8 x^4+32 x^3+108 x^2+152 x+203\right)}{405 \left(x^2+2 x+4\right)^{5/2}}","\frac{8 (x+1)}{405 \sqrt{x^2+2 x+4}}+\frac{4 (x+1)}{135 \left(x^2+2 x+4\right)^{3/2}}+\frac{x+1}{15 \left(x^2+2 x+4\right)^{5/2}}",1,"((1 + x)*(203 + 152*x + 108*x^2 + 32*x^3 + 8*x^4))/(405*(4 + 2*x + x^2)^(5/2))","A",1
285,1,33,47,0.0180304,"\int \frac{1}{\left(1+8 x+3 x^2\right)^{5/2}} \, dx","Integrate[(1 + 8*x + 3*x^2)^(-5/2),x]","\frac{(3 x+4) \left(18 x^2+48 x-7\right)}{507 \left(3 x^2+8 x+1\right)^{3/2}}","\frac{2 (3 x+4)}{169 \sqrt{3 x^2+8 x+1}}-\frac{3 x+4}{39 \left(3 x^2+8 x+1\right)^{3/2}}",1,"((4 + 3*x)*(-7 + 48*x + 18*x^2))/(507*(1 + 8*x + 3*x^2)^(3/2))","A",1
286,1,33,47,0.0134993,"\int \frac{1}{\left(5+4 x-3 x^2\right)^{5/2}} \, dx","Integrate[(5 + 4*x - 3*x^2)^(-5/2),x]","-\frac{(3 x-2) \left(18 x^2-24 x-49\right)}{1083 \left(-3 x^2+4 x+5\right)^{3/2}}","-\frac{2 (2-3 x)}{361 \sqrt{-3 x^2+4 x+5}}-\frac{2-3 x}{57 \left(-3 x^2+4 x+5\right)^{3/2}}",1,"-1/1083*((-2 + 3*x)*(-49 - 24*x + 18*x^2))/(5 + 4*x - 3*x^2)^(3/2)","A",1
287,1,30,29,0.0220431,"\int \frac{1}{1+\sqrt{2+2 x+x^2}} \, dx","Integrate[(1 + Sqrt[2 + 2*x + x^2])^(-1),x]","\frac{-\sqrt{x^2+2 x+2}+(x+1) \sinh ^{-1}(x+1)+1}{x+1}","-\frac{\sqrt{x^2+2 x+2}}{x+1}+\frac{1}{x+1}+\sinh ^{-1}(x+1)",1,"(1 - Sqrt[2 + 2*x + x^2] + (1 + x)*ArcSinh[1 + x])/(1 + x)","A",1
288,1,59,45,0.0352367,"\int \frac{1}{x+\sqrt{1+x+x^2}} \, dx","Integrate[(x + Sqrt[1 + x + x^2])^(-1),x]","\frac{3}{2 \left(2 \left(\sqrt{x^2+x+1}+x\right)+1\right)}+2 \log \left(\sqrt{x^2+x+1}+x\right)-\frac{3}{2} \log \left(2 \left(\sqrt{x^2+x+1}+x\right)+1\right)","\sqrt{x^2+x+1}+2 \log \left(\sqrt{x^2+x+1}+x\right)-x-\frac{3}{2} \sinh ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)",1,"3/(2*(1 + 2*(x + Sqrt[1 + x + x^2]))) + 2*Log[x + Sqrt[1 + x + x^2]] - (3*Log[1 + 2*(x + Sqrt[1 + x + x^2])])/2","A",1
289,1,71,79,0.0843537,"\int \frac{x^2}{1+2 x+2 \sqrt{1+x+x^2}} \, dx","Integrate[x^2/(1 + 2*x + 2*Sqrt[1 + x + x^2]),x]","\frac{1}{576} \left(-96 x^4-64 x^3+96 \left(x^2+x+1\right)^{3/2} x-80 \left(x^2+x+1\right)^{3/2}+6 (2 x+1) \sqrt{x^2+x+1}+9 \sinh ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)\right)","-\frac{x^4}{6}-\frac{x^3}{9}+\frac{1}{6} \left(x^2+x+1\right)^{3/2} x-\frac{5}{36} \left(x^2+x+1\right)^{3/2}+\frac{1}{96} (2 x+1) \sqrt{x^2+x+1}+\frac{1}{64} \sinh ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)",1,"(-64*x^3 - 96*x^4 + 6*(1 + 2*x)*Sqrt[1 + x + x^2] - 80*(1 + x + x^2)^(3/2) + 96*x*(1 + x + x^2)^(3/2) + 9*ArcSinh[(1 + 2*x)/Sqrt[3]])/576","A",1
290,1,80,80,0.1194446,"\int \frac{-3 x+\sqrt{1+x+x^2}}{-1+\sqrt{1+x+x^2}} \, dx","Integrate[(-3*x + Sqrt[1 + x + x^2])/(-1 + Sqrt[1 + x + x^2]),x]","-3 \sqrt{x^2+x+1}+4 \tanh ^{-1}\left(\frac{1-x}{2 \sqrt{x^2+x+1}}\right)-\tanh ^{-1}\left(\frac{x+2}{2 \sqrt{x^2+x+1}}\right)+x+\log (x)-4 \log (x+1)+\frac{5}{2} \sinh ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)","-3 \sqrt{x^2+x+1}+4 \tanh ^{-1}\left(\frac{1-x}{2 \sqrt{x^2+x+1}}\right)-\tanh ^{-1}\left(\frac{x+2}{2 \sqrt{x^2+x+1}}\right)+x+\log (x)-4 \log (x+1)+\frac{5}{2} \sinh ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)",1,"x - 3*Sqrt[1 + x + x^2] + (5*ArcSinh[(1 + 2*x)/Sqrt[3]])/2 + 4*ArcTanh[(1 - x)/(2*Sqrt[1 + x + x^2])] - ArcTanh[(2 + x)/(2*Sqrt[1 + x + x^2])] + Log[x] - 4*Log[1 + x]","A",1
291,1,151,158,0.3416787,"\int \frac{1+x}{-\sqrt{1+x+x^2}+\sqrt{4+2 x+x^2}} \, dx","Integrate[(1 + x)/(-Sqrt[1 + x + x^2] + Sqrt[4 + 2*x + x^2]),x]","\frac{1}{8} \left(2 \left(2 \sqrt{x^2+x+1} x+2 \sqrt{x^2+2 x+4} x-7 \sqrt{x^2+x+1}-6 \sqrt{x^2+2 x+4}-8 \sqrt{7} \tanh ^{-1}\left(\frac{5 x+1}{2 \sqrt{7} \sqrt{x^2+x+1}}\right)+8 \sqrt{7} \tanh ^{-1}\left(\frac{1-2 x}{\sqrt{7} \sqrt{x^2+2 x+4}}\right)\right)+44 \sinh ^{-1}\left(\frac{x+1}{\sqrt{3}}\right)+43 \sinh ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)\right)","\frac{1}{2} \sqrt{x^2+2 x+4} (x+1)+\frac{1}{4} (2 x+1) \sqrt{x^2+x+1}-2 \sqrt{x^2+x+1}-2 \sqrt{x^2+2 x+4}-2 \sqrt{7} \tanh ^{-1}\left(\frac{5 x+1}{2 \sqrt{7} \sqrt{x^2+x+1}}\right)+2 \sqrt{7} \tanh ^{-1}\left(\frac{1-2 x}{\sqrt{7} \sqrt{x^2+2 x+4}}\right)+\frac{11}{2} \sinh ^{-1}\left(\frac{x+1}{\sqrt{3}}\right)+\frac{43}{8} \sinh ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)",1,"(44*ArcSinh[(1 + x)/Sqrt[3]] + 43*ArcSinh[(1 + 2*x)/Sqrt[3]] + 2*(-7*Sqrt[1 + x + x^2] + 2*x*Sqrt[1 + x + x^2] - 6*Sqrt[4 + 2*x + x^2] + 2*x*Sqrt[4 + 2*x + x^2] - 8*Sqrt[7]*ArcTanh[(1 + 5*x)/(2*Sqrt[7]*Sqrt[1 + x + x^2])] + 8*Sqrt[7]*ArcTanh[(1 - 2*x)/(Sqrt[7]*Sqrt[4 + 2*x + x^2])]))/8","A",1
292,1,22,41,0.0042069,"\int \frac{1}{\sqrt{-1+x} x^3} \, dx","Integrate[1/(Sqrt[-1 + x]*x^3),x]","2 \sqrt{x-1} \, _2F_1\left(\frac{1}{2},3;\frac{3}{2};1-x\right)","\frac{\sqrt{x-1}}{2 x^2}+\frac{3 \sqrt{x-1}}{4 x}+\frac{3}{4} \tan ^{-1}\left(\sqrt{x-1}\right)",1,"2*Sqrt[-1 + x]*Hypergeometric2F1[1/2, 3, 3/2, 1 - x]","C",1
293,1,13,13,0.0065309,"\int \frac{1}{\left(1-\frac{3}{x}\right)^{4/3} x^2} \, dx","Integrate[1/((1 - 3/x)^(4/3)*x^2),x]","-\frac{1}{\sqrt[3]{\frac{x-3}{x}}}","-\frac{1}{\sqrt[3]{1-\frac{3}{x}}}",1,"-((-3 + x)/x)^(-1/3)","A",1
294,1,26,71,0.005578,"\int \frac{(-1+3 x)^{4/3}}{x^2} \, dx","Integrate[(-1 + 3*x)^(4/3)/x^2,x]","\frac{9}{7} (3 x-1)^{7/3} \, _2F_1\left(2,\frac{7}{3};\frac{10}{3};1-3 x\right)","-\frac{(3 x-1)^{4/3}}{x}+12 \sqrt[3]{3 x-1}+2 \log (x)-6 \log \left(\sqrt[3]{3 x-1}+1\right)+4 \sqrt{3} \tan ^{-1}\left(\frac{1-2 \sqrt[3]{3 x-1}}{\sqrt{3}}\right)",1,"(9*(-1 + 3*x)^(7/3)*Hypergeometric2F1[2, 7/3, 10/3, 1 - 3*x])/7","C",1
295,1,23,40,0.0126664,"\int (4-3 x)^{4/3} x^2 \, dx","Integrate[(4 - 3*x)^(4/3)*x^2,x]","-\frac{1}{455} (4-3 x)^{7/3} \left(35 x^2+28 x+16\right)","-\frac{1}{117} (4-3 x)^{13/3}+\frac{4}{45} (4-3 x)^{10/3}-\frac{16}{63} (4-3 x)^{7/3}",1,"-1/455*((4 - 3*x)^(7/3)*(16 + 28*x + 35*x^2))","A",1
296,1,48,48,0.0143954,"\int \frac{\left(1-2 \sqrt[3]{x}\right)^{3/4}}{x} \, dx","Integrate[(1 - 2*x^(1/3))^(3/4)/x,x]","4 \left(1-2 \sqrt[3]{x}\right)^{3/4}+6 \tan ^{-1}\left(\sqrt[4]{1-2 \sqrt[3]{x}}\right)-6 \tanh ^{-1}\left(\sqrt[4]{1-2 \sqrt[3]{x}}\right)","4 \left(1-2 \sqrt[3]{x}\right)^{3/4}+6 \tan ^{-1}\left(\sqrt[4]{1-2 \sqrt[3]{x}}\right)-6 \tanh ^{-1}\left(\sqrt[4]{1-2 \sqrt[3]{x}}\right)",1,"4*(1 - 2*x^(1/3))^(3/4) + 6*ArcTan[(1 - 2*x^(1/3))^(1/4)] - 6*ArcTanh[(1 - 2*x^(1/3))^(1/4)]","A",1
297,1,36,69,0.0148849,"\int \frac{x}{\left(3-2 \sqrt{x}\right)^{3/4}} \, dx","Integrate[x/(3 - 2*Sqrt[x])^(3/4),x]","-\frac{4}{65} \sqrt[4]{3-2 \sqrt{x}} \left(5 x^{3/2}+10 x+24 \sqrt{x}+144\right)","\frac{1}{26} \left(3-2 \sqrt{x}\right)^{13/4}-\frac{1}{2} \left(3-2 \sqrt{x}\right)^{9/4}+\frac{27}{10} \left(3-2 \sqrt{x}\right)^{5/4}-\frac{27}{2} \sqrt[4]{3-2 \sqrt{x}}",1,"(-4*(3 - 2*Sqrt[x])^(1/4)*(144 + 24*Sqrt[x] + 10*x + 5*x^(3/2)))/65","A",1
298,1,34,193,0.0091403,"\int \frac{\left(-1+2 \sqrt{x}\right)^{5/4}}{x^2} \, dx","Integrate[(-1 + 2*Sqrt[x])^(5/4)/x^2,x]","\frac{32}{9} \left(2 \sqrt{x}-1\right)^{9/4} \, _2F_1\left(\frac{9}{4},3;\frac{13}{4};1-2 \sqrt{x}\right)","-\frac{\left(2 \sqrt{x}-1\right)^{5/4}}{x}-\frac{5 \sqrt[4]{2 \sqrt{x}-1}}{2 \sqrt{x}}-\frac{5 \log \left(\sqrt{2 \sqrt{x}-1}-\sqrt{2} \sqrt[4]{2 \sqrt{x}-1}+1\right)}{4 \sqrt{2}}+\frac{5 \log \left(\sqrt{2 \sqrt{x}-1}+\sqrt{2} \sqrt[4]{2 \sqrt{x}-1}+1\right)}{4 \sqrt{2}}-\frac{5 \tan ^{-1}\left(1-\sqrt{2} \sqrt[4]{2 \sqrt{x}-1}\right)}{2 \sqrt{2}}+\frac{5 \tan ^{-1}\left(\sqrt{2} \sqrt[4]{2 \sqrt{x}-1}+1\right)}{2 \sqrt{2}}",1,"(32*(-1 + 2*Sqrt[x])^(9/4)*Hypergeometric2F1[9/4, 3, 13/4, 1 - 2*Sqrt[x]])/9","C",1
299,1,13,13,0.0035738,"\int x^6 \sqrt[3]{1+x^7} \, dx","Integrate[x^6*(1 + x^7)^(1/3),x]","\frac{3}{28} \left(x^7+1\right)^{4/3}","\frac{3}{28} \left(x^7+1\right)^{4/3}",1,"(3*(1 + x^7)^(4/3))/28","A",1
300,1,13,13,0.0031406,"\int \frac{x^6}{\left(1+x^7\right)^{5/3}} \, dx","Integrate[x^6/(1 + x^7)^(5/3),x]","-\frac{3}{14 \left(x^7+1\right)^{2/3}}","-\frac{3}{14 \left(x^7+1\right)^{2/3}}",1,"-3/(14*(1 + x^7)^(2/3))","A",1
301,1,84,59,0.0251528,"\int \frac{1}{x \left(-27+2 x^7\right)^{2/3}} \, dx","Integrate[1/(x*(-27 + 2*x^7)^(2/3)),x]","\frac{1}{63} \log \left(\sqrt[3]{2 x^7-27}+3\right)-\frac{1}{126} \log \left(\left(2 x^7-27\right)^{2/3}-3 \sqrt[3]{2 x^7-27}+9\right)+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{2 x^7-27}-3}{3 \sqrt{3}}\right)}{21 \sqrt{3}}","\frac{1}{42} \log \left(\sqrt[3]{2 x^7-27}+3\right)-\frac{\tan ^{-1}\left(\frac{3-2 \sqrt[3]{2 x^7-27}}{3 \sqrt{3}}\right)}{21 \sqrt{3}}-\frac{\log (x)}{18}",1,"ArcTan[(-3 + 2*(-27 + 2*x^7)^(1/3))/(3*Sqrt[3])]/(21*Sqrt[3]) + Log[3 + (-27 + 2*x^7)^(1/3)]/63 - Log[9 - 3*(-27 + 2*x^7)^(1/3) + (-27 + 2*x^7)^(2/3)]/126","A",1
302,1,26,70,0.0065063,"\int \frac{\left(1+x^7\right)^{2/3}}{x^8} \, dx","Integrate[(1 + x^7)^(2/3)/x^8,x]","\frac{3}{35} \left(x^7+1\right)^{5/3} \, _2F_1\left(\frac{5}{3},2;\frac{8}{3};x^7+1\right)","-\frac{\left(x^7+1\right)^{2/3}}{7 x^7}+\frac{1}{7} \log \left(1-\sqrt[3]{x^7+1}\right)+\frac{2 \tan ^{-1}\left(\frac{2 \sqrt[3]{x^7+1}+1}{\sqrt{3}}\right)}{7 \sqrt{3}}-\frac{\log (x)}{3}",1,"(3*(1 + x^7)^(5/3)*Hypergeometric2F1[5/3, 2, 8/3, 1 + x^7])/35","C",1
303,1,27,68,0.0061123,"\int \frac{\sqrt[4]{3+4 x^4}}{x^2} \, dx","Integrate[(3 + 4*x^4)^(1/4)/x^2,x]","-\frac{\sqrt[4]{3} \, _2F_1\left(-\frac{1}{4},-\frac{1}{4};\frac{3}{4};-\frac{4 x^4}{3}\right)}{x}","-\frac{\sqrt[4]{4 x^4+3}}{x}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt[4]{4 x^4+3}}\right)}{\sqrt{2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt[4]{4 x^4+3}}\right)}{\sqrt{2}}",1,"-((3^(1/4)*Hypergeometric2F1[-1/4, -1/4, 3/4, (-4*x^4)/3])/x)","C",1
304,1,26,93,0.0060345,"\int x^2 \left(3+4 x^4\right)^{5/4} \, dx","Integrate[x^2*(3 + 4*x^4)^(5/4),x]","\sqrt[4]{3} x^3 \, _2F_1\left(-\frac{5}{4},\frac{3}{4};\frac{7}{4};-\frac{4 x^4}{3}\right)","-\frac{45 \tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt[4]{4 x^4+3}}\right)}{128 \sqrt{2}}+\frac{45 \tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt[4]{4 x^4+3}}\right)}{128 \sqrt{2}}+\frac{1}{8} \left(4 x^4+3\right)^{5/4} x^3+\frac{15}{32} \sqrt[4]{4 x^4+3} x^3",1,"3^(1/4)*x^3*Hypergeometric2F1[-5/4, 3/4, 7/4, (-4*x^4)/3]","C",1
305,1,43,93,0.0137249,"\int x^6 \sqrt[4]{3+4 x^4} \, dx","Integrate[x^6*(3 + 4*x^4)^(1/4),x]","\frac{1}{32} x^3 \left(\left(4 x^4+3\right)^{5/4}-3 \sqrt[4]{3} \, _2F_1\left(-\frac{1}{4},\frac{3}{4};\frac{7}{4};-\frac{4 x^4}{3}\right)\right)","\frac{27 \tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt[4]{4 x^4+3}}\right)}{512 \sqrt{2}}-\frac{27 \tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt[4]{4 x^4+3}}\right)}{512 \sqrt{2}}+\frac{1}{8} \sqrt[4]{4 x^4+3} x^7+\frac{3}{128} \sqrt[4]{4 x^4+3} x^3",1,"(x^3*((3 + 4*x^4)^(5/4) - 3*3^(1/4)*Hypergeometric2F1[-1/4, 3/4, 7/4, (-4*x^4)/3]))/32","C",1
306,1,40,93,0.0109668,"\int \sqrt[3]{x \left(1-x^2\right)} \, dx","Integrate[(x*(1 - x^2))^(1/3),x]","\frac{3 x \sqrt[3]{x-x^3} \, _2F_1\left(-\frac{1}{3},\frac{2}{3};\frac{5}{3};x^2\right)}{4 \sqrt[3]{1-x^2}}","\frac{1}{2} \sqrt[3]{x \left(1-x^2\right)} x-\frac{1}{4} \log \left(\sqrt[3]{x \left(1-x^2\right)}+x\right)+\frac{\tan ^{-1}\left(\frac{2 x-\sqrt[3]{x \left(1-x^2\right)}}{\sqrt{3} \sqrt[3]{x \left(1-x^2\right)}}\right)}{2 \sqrt{3}}+\frac{\log (x)}{12}",1,"(3*x*(x - x^3)^(1/3)*Hypergeometric2F1[-1/3, 2/3, 5/3, x^2])/(4*(1 - x^2)^(1/3))","C",1
307,1,83,126,0.0521033,"\int \sqrt{\left(1+\sqrt[3]{x}\right) x} \, dx","Integrate[Sqrt[(1 + x^(1/3))*x],x]","\frac{\sqrt{x^{4/3}+x} \left(\sqrt{\sqrt[3]{x}+1} \sqrt[6]{x} \left(384 x^{4/3}-56 x^{2/3}+48 x+70 \sqrt[3]{x}-105\right)+105 \sinh ^{-1}\left(\sqrt[6]{x}\right)\right)}{640 \sqrt{\sqrt[3]{x}+1} \sqrt{x}}","\frac{3}{40} \sqrt{\left(\sqrt[3]{x}+1\right) x} x^{2/3}+\frac{21}{128} \tanh ^{-1}\left(\frac{x^{2/3}}{\sqrt{\left(\sqrt[3]{x}+1\right) x}}\right)+\frac{3}{5} \sqrt{\left(\sqrt[3]{x}+1\right) x} x-\frac{7}{80} \sqrt{\left(\sqrt[3]{x}+1\right) x} \sqrt[3]{x}+\frac{7}{64} \sqrt{\left(\sqrt[3]{x}+1\right) x}-\frac{21 \sqrt{\left(\sqrt[3]{x}+1\right) x}}{128 \sqrt[3]{x}}",1,"(Sqrt[x + x^(4/3)]*(Sqrt[1 + x^(1/3)]*x^(1/6)*(-105 + 70*x^(1/3) - 56*x^(2/3) + 48*x + 384*x^(4/3)) + 105*ArcSinh[x^(1/6)]))/(640*Sqrt[1 + x^(1/3)]*Sqrt[x])","A",1
308,1,29,34,0.0149945,"\int \frac{x^3}{\left(-1+x^4\right) \sqrt{1+2 x^8}} \, dx","Integrate[x^3/((-1 + x^4)*Sqrt[1 + 2*x^8]),x]","-\frac{\tanh ^{-1}\left(\frac{2 x^4+1}{\sqrt{6 x^8+3}}\right)}{4 \sqrt{3}}","-\frac{\tanh ^{-1}\left(\frac{2 x^4+1}{\sqrt{3} \sqrt{2 x^8+1}}\right)}{4 \sqrt{3}}",1,"-1/4*ArcTanh[(1 + 2*x^4)/Sqrt[3 + 6*x^8]]/Sqrt[3]","A",1
309,1,47,58,0.0186313,"\int x^9 \sqrt{1+x^5+x^{10}} \, dx","Integrate[x^9*Sqrt[1 + x^5 + x^10],x]","\frac{1}{240} \left(2 \sqrt{x^{10}+x^5+1} \left(8 x^{10}+2 x^5+5\right)-9 \sinh ^{-1}\left(\frac{2 x^5+1}{\sqrt{3}}\right)\right)","-\frac{3}{80} \sinh ^{-1}\left(\frac{2 x^5+1}{\sqrt{3}}\right)+\frac{1}{15} \left(x^{10}+x^5+1\right)^{3/2}-\frac{1}{40} \left(2 x^5+1\right) \sqrt{x^{10}+x^5+1}",1,"(2*Sqrt[1 + x^5 + x^10]*(5 + 2*x^5 + 8*x^10) - 9*ArcSinh[(1 + 2*x^5)/Sqrt[3]])/240","A",1
310,1,55,71,0.028167,"\int \frac{1}{x^5 \sqrt{4+2 x^2+x^4}} \, dx","Integrate[1/(x^5*Sqrt[4 + 2*x^2 + x^4]),x]","\frac{1}{128} \left(\frac{2 \sqrt{x^4+2 x^2+4} \left(3 x^2-4\right)}{x^4}+\tanh ^{-1}\left(\frac{x^2+4}{2 \sqrt{x^4+2 x^2+4}}\right)\right)","\frac{3 \sqrt{x^4+2 x^2+4}}{64 x^2}-\frac{\sqrt{x^4+2 x^2+4}}{16 x^4}+\frac{1}{128} \tanh ^{-1}\left(\frac{x^2+4}{2 \sqrt{x^4+2 x^2+4}}\right)",1,"((2*(-4 + 3*x^2)*Sqrt[4 + 2*x^2 + x^4])/x^4 + ArcTanh[(4 + x^2)/(2*Sqrt[4 + 2*x^2 + x^4])])/128","A",1
311,1,57,21,0.0156167,"\int \frac{-1+x^2}{x \sqrt{1+3 x^2+x^4}} \, dx","Integrate[(-1 + x^2)/(x*Sqrt[1 + 3*x^2 + x^4]),x]","\frac{1}{2} \left(\tanh ^{-1}\left(\frac{2 x^2+3}{2 \sqrt{x^4+3 x^2+1}}\right)+\tanh ^{-1}\left(\frac{3 x^2+2}{2 \sqrt{x^4+3 x^2+1}}\right)\right)","\tanh ^{-1}\left(\frac{x^2+1}{\sqrt{x^4+3 x^2+1}}\right)",1,"(ArcTanh[(3 + 2*x^2)/(2*Sqrt[1 + 3*x^2 + x^4])] + ArcTanh[(2 + 3*x^2)/(2*Sqrt[1 + 3*x^2 + x^4])])/2","B",1
312,1,75,17,0.0571477,"\int \left(-3 x+2 x^3\right) \left(-3 x^2+x^4\right)^{3/5} \, dx","Integrate[(-3*x + 2*x^3)*(-3*x^2 + x^4)^(3/5),x]","\frac{5 \left(x^2 \left(x^2-3\right)\right)^{3/5} \left(16 x^4 \, _2F_1\left(-\frac{3}{5},\frac{13}{5};\frac{18}{5};\frac{x^2}{3}\right)-39 x^2 \, _2F_1\left(-\frac{3}{5},\frac{8}{5};\frac{13}{5};\frac{x^2}{3}\right)\right)}{208 \left(1-\frac{x^2}{3}\right)^{3/5}}","\frac{5}{16} \left(x^4-3 x^2\right)^{8/5}",1,"(5*(x^2*(-3 + x^2))^(3/5)*(-39*x^2*Hypergeometric2F1[-3/5, 8/5, 13/5, x^2/3] + 16*x^4*Hypergeometric2F1[-3/5, 13/5, 18/5, x^2/3]))/(208*(1 - x^2/3)^(3/5))","C",1
313,1,40,46,0.0841168,"\int \frac{-2 x^5+3 x^8-x^2 \left(-1+3 x^3\right)^{2/3}}{\left(-1+3 x^3\right)^{3/4}} \, dx","Integrate[(-2*x^5 + 3*x^8 - x^2*(-1 + 3*x^3)^(2/3))/(-1 + 3*x^3)^(3/4),x]","-\frac{4 \sqrt[4]{3 x^3-1} \left(-99 x^6+66 x^3+81 \left(3 x^3-1\right)^{2/3}+88\right)}{2673}","\frac{4}{243} \left(3 x^3-1\right)^{9/4}-\frac{4}{33} \left(3 x^3-1\right)^{11/12}-\frac{4}{27} \sqrt[4]{3 x^3-1}",1,"(-4*(-1 + 3*x^3)^(1/4)*(88 + 66*x^3 - 99*x^6 + 81*(-1 + 3*x^3)^(2/3)))/2673","A",1
314,1,104,78,0.0792995,"\int \frac{1}{\left(-1+x^3\right) \sqrt[3]{2+x^3}} \, dx","Integrate[1/((-1 + x^3)*(2 + x^3)^(1/3)),x]","\frac{\sqrt{3} \left(2 \log \left(1-\frac{\sqrt[3]{3} x}{\sqrt[3]{x^3+2}}\right)-\log \left(\frac{\sqrt[3]{3} x}{\sqrt[3]{x^3+2}}+\frac{3^{2/3} x^2}{\left(x^3+2\right)^{2/3}}+1\right)\right)-6 \tan ^{-1}\left(\frac{2 x}{\sqrt[6]{3} \sqrt[3]{x^3+2}}+\frac{1}{\sqrt{3}}\right)}{6\ 3^{5/6}}","-\frac{\log \left(x^3-1\right)}{6 \sqrt[3]{3}}+\frac{\log \left(\sqrt[3]{3} x-\sqrt[3]{x^3+2}\right)}{2 \sqrt[3]{3}}-\frac{\tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{3} x}{\sqrt[3]{x^3+2}}+1}{\sqrt{3}}\right)}{3^{5/6}}",1,"(-6*ArcTan[1/Sqrt[3] + (2*x)/(3^(1/6)*(2 + x^3)^(1/3))] + Sqrt[3]*(2*Log[1 - (3^(1/3)*x)/(2 + x^3)^(1/3)] - Log[1 + (3^(2/3)*x^2)/(2 + x^3)^(2/3) + (3^(1/3)*x)/(2 + x^3)^(1/3)]))/(6*3^(5/6))","A",1
315,1,120,141,0.0579734,"\int \frac{1}{\left(1+x^4\right) \sqrt[4]{2+x^4}} \, dx","Integrate[1/((1 + x^4)*(2 + x^4)^(1/4)),x]","\frac{-2 \tan ^{-1}\left(1-\frac{\sqrt{2} x}{\sqrt[4]{x^4+2}}\right)+2 \tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt[4]{x^4+2}}+1\right)-\log \left(-\frac{\sqrt{2} x}{\sqrt[4]{x^4+2}}+\frac{x^2}{\sqrt{x^4+2}}+1\right)+\log \left(\frac{\sqrt{2} x}{\sqrt[4]{x^4+2}}+\frac{x^2}{\sqrt{x^4+2}}+1\right)}{4 \sqrt{2}}","-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} x}{\sqrt[4]{x^4+2}}\right)}{2 \sqrt{2}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt[4]{x^4+2}}+1\right)}{2 \sqrt{2}}-\frac{\log \left(-\frac{\sqrt{2} x}{\sqrt[4]{x^4+2}}+\frac{x^2}{\sqrt{x^4+2}}+1\right)}{4 \sqrt{2}}+\frac{\log \left(\frac{\sqrt{2} x}{\sqrt[4]{x^4+2}}+\frac{x^2}{\sqrt{x^4+2}}+1\right)}{4 \sqrt{2}}",1,"(-2*ArcTan[1 - (Sqrt[2]*x)/(2 + x^4)^(1/4)] + 2*ArcTan[1 + (Sqrt[2]*x)/(2 + x^4)^(1/4)] - Log[1 + x^2/Sqrt[2 + x^4] - (Sqrt[2]*x)/(2 + x^4)^(1/4)] + Log[1 + x^2/Sqrt[2 + x^4] + (Sqrt[2]*x)/(2 + x^4)^(1/4)])/(4*Sqrt[2])","A",1
316,1,91,63,0.0349222,"\int \frac{-1+x^3}{\sqrt[3]{2+x^3}} \, dx","Integrate[(-1 + x^3)/(2 + x^3)^(1/3),x]","\frac{1}{18} \left(6 \left(x^3+2\right)^{2/3} x+10 \log \left(1-\frac{x}{\sqrt[3]{x^3+2}}\right)-10 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3+2}}+1}{\sqrt{3}}\right)-5 \log \left(\frac{x}{\sqrt[3]{x^3+2}}+\frac{x^2}{\left(x^3+2\right)^{2/3}}+1\right)\right)","\frac{1}{3} \left(x^3+2\right)^{2/3} x+\frac{5}{6} \log \left(\sqrt[3]{x^3+2}-x\right)-\frac{5 \tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3+2}}+1}{\sqrt{3}}\right)}{3 \sqrt{3}}",1,"(6*x*(2 + x^3)^(2/3) - 10*Sqrt[3]*ArcTan[(1 + (2*x)/(2 + x^3)^(1/3))/Sqrt[3]] + 10*Log[1 - x/(2 + x^3)^(1/3)] - 5*Log[1 + x^2/(2 + x^3)^(2/3) + x/(2 + x^3)^(1/3)])/18","A",1
317,1,41,74,0.0126436,"\int \frac{\left(1+x^4\right)^{3/4}}{\left(2+x^4\right)^2} \, dx","Integrate[(1 + x^4)^(3/4)/(2 + x^4)^2,x]","\frac{x \, _2F_1\left(-\frac{3}{4},\frac{1}{4};\frac{5}{4};-\frac{x^4}{x^4+2}\right)}{2\ 2^{3/4} \sqrt[4]{x^4+2}}","\frac{\left(x^4+1\right)^{3/4} x}{8 \left(x^4+2\right)}+\frac{3 \tan ^{-1}\left(\frac{x}{\sqrt[4]{2} \sqrt[4]{x^4+1}}\right)}{16\ 2^{3/4}}+\frac{3 \tanh ^{-1}\left(\frac{x}{\sqrt[4]{2} \sqrt[4]{x^4+1}}\right)}{16\ 2^{3/4}}",1,"(x*Hypergeometric2F1[-3/4, 1/4, 5/4, -(x^4/(2 + x^4))])/(2*2^(3/4)*(2 + x^4)^(1/4))","C",0
318,1,26,48,0.0172485,"\int \frac{\left(-2+x^5\right)^2}{\left(3+x^5\right)^{16/5}} \, dx","Integrate[(-2 + x^5)^2/(3 + x^5)^(16/5),x]","\frac{x \left(97 x^{10}+462 x^5+1188\right)}{891 \left(x^5+3\right)^{11/5}}","\frac{97 x}{891 \sqrt[5]{x^5+3}}+\frac{5 x}{297 \left(x^5+3\right)^{6/5}}-\frac{5 \left(x^5-2\right) x}{33 \left(x^5+3\right)^{11/5}}",1,"(x*(1188 + 462*x^5 + 97*x^10))/(891*(3 + x^5)^(11/5))","A",1
319,1,120,90,0.1551539,"\int \frac{1}{\left(3 x+3 x^2+x^3\right) \sqrt[3]{3+3 x+3 x^2+x^3}} \, dx","Integrate[1/((3*x + 3*x^2 + x^3)*(3 + 3*x + 3*x^2 + x^3)^(1/3)),x]","\frac{\sqrt{3} \left(2 \log \left(1-\frac{\sqrt[3]{3} (x+1)}{\sqrt[3]{(x+1)^3+2}}\right)-\log \left(\frac{3^{2/3} (x+1)^2}{\left((x+1)^3+2\right)^{2/3}}+\frac{\sqrt[3]{3} (x+1)}{\sqrt[3]{(x+1)^3+2}}+1\right)\right)-6 \tan ^{-1}\left(\frac{2 (x+1)}{\sqrt[6]{3} \sqrt[3]{(x+1)^3+2}}+\frac{1}{\sqrt{3}}\right)}{6\ 3^{5/6}}","-\frac{\log \left(1-(x+1)^3\right)}{6 \sqrt[3]{3}}+\frac{\log \left(\sqrt[3]{3} (x+1)-\sqrt[3]{(x+1)^3+2}\right)}{2 \sqrt[3]{3}}-\frac{\tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{3} (x+1)}{\sqrt[3]{(x+1)^3+2}}+1}{\sqrt{3}}\right)}{3^{5/6}}",1,"(-6*ArcTan[1/Sqrt[3] + (2*(1 + x))/(3^(1/6)*(2 + (1 + x)^3)^(1/3))] + Sqrt[3]*(2*Log[1 - (3^(1/3)*(1 + x))/(2 + (1 + x)^3)^(1/3)] - Log[1 + (3^(2/3)*(1 + x)^2)/(2 + (1 + x)^3)^(2/3) + (3^(1/3)*(1 + x))/(2 + (1 + x)^3)^(1/3)]))/(6*3^(5/6))","A",1
320,1,40,23,0.1001871,"\int \frac{1-x^2}{\left(1+x^2\right) \sqrt{1+x^4}} \, dx","Integrate[(1 - x^2)/((1 + x^2)*Sqrt[1 + x^4]),x]","\sqrt[4]{-1} \left(\operatorname{EllipticF}\left(i \sinh ^{-1}\left(\sqrt[4]{-1} x\right),-1\right)-2 \Pi \left(-i;\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)\right)","\frac{\tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}}\right)}{\sqrt{2}}",1,"(-1)^(1/4)*(EllipticF[I*ArcSinh[(-1)^(1/4)*x], -1] - 2*EllipticPi[-I, I*ArcSinh[(-1)^(1/4)*x], -1])","C",1
321,1,36,23,0.0941371,"\int \frac{1+x^2}{\left(1-x^2\right) \sqrt{1+x^4}} \, dx","Integrate[(1 + x^2)/((1 - x^2)*Sqrt[1 + x^4]),x]","\sqrt[4]{-1} \left(\operatorname{EllipticF}\left(i \sinh ^{-1}\left(\sqrt[4]{-1} x\right),-1\right)-2 \Pi \left(i;\left.\sin ^{-1}\left((-1)^{3/4} x\right)\right|-1\right)\right)","\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}}\right)}{\sqrt{2}}",1,"(-1)^(1/4)*(EllipticF[I*ArcSinh[(-1)^(1/4)*x], -1] - 2*EllipticPi[I, ArcSin[(-1)^(3/4)*x], -1])","C",1
322,1,21,16,0.0177775,"\int \frac{1+x^2}{x \sqrt{1+x^4}} \, dx","Integrate[(1 + x^2)/(x*Sqrt[1 + x^4]),x]","\frac{1}{2} \left(\sinh ^{-1}\left(x^2\right)-\tanh ^{-1}\left(\sqrt{x^4+1}\right)\right)","\tanh ^{-1}\left(\frac{x^2-1}{\sqrt{x^4+1}}\right)",1,"(ArcSinh[x^2] - ArcTanh[Sqrt[1 + x^4]])/2","A",1
323,1,19,16,0.0150721,"\int \frac{-1+x^2}{x \sqrt{1+x^4}} \, dx","Integrate[(-1 + x^2)/(x*Sqrt[1 + x^4]),x]","\frac{1}{2} \left(\tanh ^{-1}\left(\sqrt{x^4+1}\right)+\sinh ^{-1}\left(x^2\right)\right)","\tanh ^{-1}\left(\frac{x^2+1}{\sqrt{x^4+1}}\right)",1,"(ArcSinh[x^2] + ArcTanh[Sqrt[1 + x^4]])/2","A",1
324,1,522,26,1.3178087,"\int \frac{1+x^2}{\left(1-x^2\right) \sqrt{1+x^2+x^4}} \, dx","Integrate[(1 + x^2)/((1 - x^2)*Sqrt[1 + x^2 + x^4]),x]","\frac{(-1)^{2/3} \left(-\sqrt[3]{-1} \left(\sqrt[3]{-1}-1\right)^2 \left(1+\sqrt[3]{-1}\right) \sqrt{\sqrt[3]{-1} x^2+1} \sqrt{1-(-1)^{2/3} x^2} \operatorname{EllipticF}\left(i \sinh ^{-1}\left((-1)^{5/6} x\right),(-1)^{2/3}\right)-2 i \sqrt{3} \sqrt{\frac{(-1)^{2/3}-x}{\left(1+\sqrt[3]{-1}\right) \left(\sqrt[3]{-1}-x\right)}} \sqrt{\frac{x+(-1)^{2/3}}{-\sqrt[3]{-1} x+x-1}} \sqrt{\frac{-\sqrt[3]{-1} x+x+1}{\left(1+\sqrt[3]{-1}\right) \left(\sqrt[3]{-1}-x\right)}} \left(\sqrt[3]{-1}-x\right)^2 \left(\left(1+\sqrt[3]{-1}\right) \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{-\sqrt[3]{-1} x+x+1}{\left(1+\sqrt[3]{-1}\right) \left(\sqrt[3]{-1}-x\right)}}\right),-3\right)-2 \sqrt[3]{-1} \Pi \left(-1;\left.\sin ^{-1}\left(\sqrt{\frac{-\sqrt[3]{-1} x+x+1}{\left(1+\sqrt[3]{-1}\right) \left(\sqrt[3]{-1}-x\right)}}\right)\right|-3\right)\right)+2 i \sqrt{3} \sqrt{\frac{(-1)^{2/3}-x}{\left(1+\sqrt[3]{-1}\right) \left(\sqrt[3]{-1}-x\right)}} \sqrt{\frac{x+(-1)^{2/3}}{-\sqrt[3]{-1} x+x-1}} \sqrt{\frac{-\sqrt[3]{-1} x+x+1}{\left(1+\sqrt[3]{-1}\right) \left(\sqrt[3]{-1}-x\right)}} \left(\sqrt[3]{-1}-x\right)^2 \left(\left(\sqrt[3]{-1}-1\right) \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{-\sqrt[3]{-1} x+x+1}{\left(1+\sqrt[3]{-1}\right) \left(\sqrt[3]{-1}-x\right)}}\right),-3\right)-2 \sqrt[3]{-1} \Pi \left(3;\left.\sin ^{-1}\left(\sqrt{\frac{-\sqrt[3]{-1} x+x+1}{\left(1+\sqrt[3]{-1}\right) \left(\sqrt[3]{-1}-x\right)}}\right)\right|-3\right)\right)\right)}{\left(1-(-1)^{2/3}\right) \sqrt{x^4+x^2+1}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{3} x}{\sqrt{x^4+x^2+1}}\right)}{\sqrt{3}}",1,"((-1)^(2/3)*(-((-1)^(1/3)*(-1 + (-1)^(1/3))^2*(1 + (-1)^(1/3))*Sqrt[1 + (-1)^(1/3)*x^2]*Sqrt[1 - (-1)^(2/3)*x^2]*EllipticF[I*ArcSinh[(-1)^(5/6)*x], (-1)^(2/3)]) - (2*I)*Sqrt[3]*((-1)^(1/3) - x)^2*Sqrt[((-1)^(2/3) - x)/((1 + (-1)^(1/3))*((-1)^(1/3) - x))]*Sqrt[((-1)^(2/3) + x)/(-1 + x - (-1)^(1/3)*x)]*Sqrt[(1 + x - (-1)^(1/3)*x)/((1 + (-1)^(1/3))*((-1)^(1/3) - x))]*((1 + (-1)^(1/3))*EllipticF[ArcSin[Sqrt[(1 + x - (-1)^(1/3)*x)/((1 + (-1)^(1/3))*((-1)^(1/3) - x))]], -3] - 2*(-1)^(1/3)*EllipticPi[-1, ArcSin[Sqrt[(1 + x - (-1)^(1/3)*x)/((1 + (-1)^(1/3))*((-1)^(1/3) - x))]], -3]) + (2*I)*Sqrt[3]*((-1)^(1/3) - x)^2*Sqrt[((-1)^(2/3) - x)/((1 + (-1)^(1/3))*((-1)^(1/3) - x))]*Sqrt[((-1)^(2/3) + x)/(-1 + x - (-1)^(1/3)*x)]*Sqrt[(1 + x - (-1)^(1/3)*x)/((1 + (-1)^(1/3))*((-1)^(1/3) - x))]*((-1 + (-1)^(1/3))*EllipticF[ArcSin[Sqrt[(1 + x - (-1)^(1/3)*x)/((1 + (-1)^(1/3))*((-1)^(1/3) - x))]], -3] - 2*(-1)^(1/3)*EllipticPi[3, ArcSin[Sqrt[(1 + x - (-1)^(1/3)*x)/((1 + (-1)^(1/3))*((-1)^(1/3) - x))]], -3])))/((1 - (-1)^(2/3))*Sqrt[1 + x^2 + x^4])","C",0
325,1,94,15,0.1308471,"\int \frac{1-x^2}{\left(1+x^2\right) \sqrt{1+x^2+x^4}} \, dx","Integrate[(1 - x^2)/((1 + x^2)*Sqrt[1 + x^2 + x^4]),x]","-\frac{(-1)^{2/3} \sqrt{\sqrt[3]{-1} x^2+1} \sqrt{1-(-1)^{2/3} x^2} \left(\operatorname{EllipticF}\left(i \sinh ^{-1}\left((-1)^{5/6} x\right),(-1)^{2/3}\right)-2 \Pi \left(\sqrt[3]{-1};i \sinh ^{-1}\left((-1)^{5/6} x\right)|(-1)^{2/3}\right)\right)}{\sqrt{x^4+x^2+1}}","\tan ^{-1}\left(\frac{x}{\sqrt{x^4+x^2+1}}\right)",1,"-(((-1)^(2/3)*Sqrt[1 + (-1)^(1/3)*x^2]*Sqrt[1 - (-1)^(2/3)*x^2]*(EllipticF[I*ArcSinh[(-1)^(5/6)*x], (-1)^(2/3)] - 2*EllipticPi[(-1)^(1/3), I*ArcSinh[(-1)^(5/6)*x], (-1)^(2/3)]))/Sqrt[1 + x^2 + x^4])","C",1
326,1,16,16,0.034643,"\int \frac{-1+x^4}{x^2 \sqrt{1+x^2+x^4}} \, dx","Integrate[(-1 + x^4)/(x^2*Sqrt[1 + x^2 + x^4]),x]","\frac{\sqrt{x^4+x^2+1}}{x}","\frac{\sqrt{x^4+x^2+1}}{x}",1,"Sqrt[1 + x^2 + x^4]/x","A",1
327,1,17955,74,6.4658037,"\int \frac{1-x^2}{\left(1+2 a x+x^2\right) \sqrt{1+2 a x+2 b x^2+2 a x^3+x^4}} \, dx","Integrate[(1 - x^2)/((1 + 2*a*x + x^2)*Sqrt[1 + 2*a*x + 2*b*x^2 + 2*a*x^3 + x^4]),x]","\text{Result too large to show}","\frac{\tan ^{-1}\left(\frac{2 x \left(a^2-b+1\right)+a x^2+a}{\sqrt{2} \sqrt{1-b} \sqrt{2 a x^3+2 a x+2 b x^2+x^4+1}}\right)}{\sqrt{2} \sqrt{1-b}}",1,"Result too large to show","C",0
328,1,24,22,1.1159409,"\int \frac{1}{\left(1+x^4\right) \sqrt{-x^2+\sqrt{1+x^4}}} \, dx","Integrate[1/((1 + x^4)*Sqrt[-x^2 + Sqrt[1 + x^4]]),x]","\cot ^{-1}\left(\frac{\sqrt{\sqrt{x^4+1}-x^2}}{x}\right)","\tan ^{-1}\left(\frac{x}{\sqrt{\sqrt{x^4+1}-x^2}}\right)",1,"ArcCot[Sqrt[-x^2 + Sqrt[1 + x^4]]/x]","A",1
329,1,26,24,0.0880795,"\int \frac{1}{\left(1+x^{2 n}\right) \sqrt{-x^2+\left(1+x^{2 n}\right)^{\frac{1}{n}}}} \, dx","Integrate[1/((1 + x^(2*n))*Sqrt[-x^2 + (1 + x^(2*n))^n^(-1)]),x]","\cot ^{-1}\left(\frac{\sqrt{\left(x^{2 n}+1\right)^{\frac{1}{n}}-x^2}}{x}\right)","\tan ^{-1}\left(\frac{x}{\sqrt{\left(x^{2 n}+1\right)^{\frac{1}{n}}-x^2}}\right)",1,"ArcCot[Sqrt[-x^2 + (1 + x^(2*n))^n^(-1)]/x]","A",1
330,1,14,14,0.0022571,"\int \cos ^2(x) \, dx","Integrate[Cos[x]^2,x]","\frac{x}{2}+\frac{1}{4} \sin (2 x)","\frac{x}{2}+\frac{1}{2} \sin (x) \cos (x)",1,"x/2 + Sin[2*x]/4","A",1
331,1,15,11,0.0019874,"\int \cos ^3(x) \, dx","Integrate[Cos[x]^3,x]","\frac{3 \sin (x)}{4}+\frac{1}{12} \sin (3 x)","\sin (x)-\frac{\sin ^3(x)}{3}",1,"(3*Sin[x])/4 + Sin[3*x]/12","A",1
332,1,22,24,0.0021329,"\int \sin ^4(x) \, dx","Integrate[Sin[x]^4,x]","\frac{3 x}{8}-\frac{1}{4} \sin (2 x)+\frac{1}{32} \sin (4 x)","\frac{3 x}{8}-\frac{1}{4} \sin ^3(x) \cos (x)-\frac{3}{8} \sin (x) \cos (x)",1,"(3*x)/8 - Sin[2*x]/4 + Sin[4*x]/32","A",1
333,1,30,34,0.002041,"\int \cos ^6(x) \, dx","Integrate[Cos[x]^6,x]","\frac{5 x}{16}+\frac{15}{64} \sin (2 x)+\frac{3}{64} \sin (4 x)+\frac{1}{192} \sin (6 x)","\frac{5 x}{16}+\frac{1}{6} \sin (x) \cos ^5(x)+\frac{5}{24} \sin (x) \cos ^3(x)+\frac{5}{16} \sin (x) \cos (x)",1,"(5*x)/16 + (15*Sin[2*x])/64 + (3*Sin[4*x])/64 + Sin[6*x]/192","A",1
334,1,38,44,0.0021373,"\int \sin ^8(x) \, dx","Integrate[Sin[x]^8,x]","\frac{35 x}{128}-\frac{7}{32} \sin (2 x)+\frac{7}{128} \sin (4 x)-\frac{1}{96} \sin (6 x)+\frac{\sin (8 x)}{1024}","\frac{35 x}{128}-\frac{1}{8} \sin ^7(x) \cos (x)-\frac{7}{48} \sin ^5(x) \cos (x)-\frac{35}{192} \sin ^3(x) \cos (x)-\frac{35}{128} \sin (x) \cos (x)",1,"(35*x)/128 - (7*Sin[2*x])/32 + (7*Sin[4*x])/128 - Sin[6*x]/96 + Sin[8*x]/1024","A",1
335,1,21,20,0.0199167,"\int \cos ^4\left(\frac{\pi }{4}+\frac{x}{2}\right) \, dx","Integrate[Cos[Pi/4 + x/2]^4,x]","\frac{1}{16} (6 x+8 \cos (x)-2 \sin (x) \cos (x)+3 \pi )","\frac{3 x}{8}+\frac{\cos (x)}{2}-\frac{1}{8} \sin (x) \cos (x)",1,"(3*Pi + 6*x + 8*Cos[x] - 2*Cos[x]*Sin[x])/16","A",1
336,1,31,31,0.017669,"\int -\sin ^3\left(\frac{\pi }{12}-3 x\right) \, dx","Integrate[-Sin[Pi/12 - 3*x]^3,x]","\frac{1}{36} \cos \left(3 \left(\frac{\pi }{12}-3 x\right)\right)-\frac{1}{4} \cos \left(\frac{\pi }{12}-3 x\right)","\frac{1}{9} \cos ^3\left(\frac{\pi }{12}-3 x\right)-\frac{1}{3} \cos \left(\frac{\pi }{12}-3 x\right)",1,"-1/4*Cos[Pi/12 - 3*x] + Cos[3*(Pi/12 - 3*x)]/36","A",1
337,1,27,21,0.0034331,"\int \csc ^6(x) \, dx","Integrate[Csc[x]^6,x]","-\frac{8 \cot (x)}{15}-\frac{1}{5} \cot (x) \csc ^4(x)-\frac{4}{15} \cot (x) \csc ^2(x)","-\frac{1}{5} \cot ^5(x)-\frac{2 \cot ^3(x)}{3}-\cot (x)",1,"(-8*Cot[x])/15 - (4*Cot[x]*Csc[x]^2)/15 - (Cot[x]*Csc[x]^4)/5","A",1
338,1,95,36,0.0081615,"\int \csc ^7(x) \, dx","Integrate[Csc[x]^7,x]","-\frac{1}{384} \csc ^6\left(\frac{x}{2}\right)-\frac{1}{64} \csc ^4\left(\frac{x}{2}\right)-\frac{5}{64} \csc ^2\left(\frac{x}{2}\right)+\frac{1}{384} \sec ^6\left(\frac{x}{2}\right)+\frac{1}{64} \sec ^4\left(\frac{x}{2}\right)+\frac{5}{64} \sec ^2\left(\frac{x}{2}\right)+\frac{5}{16} \log \left(\sin \left(\frac{x}{2}\right)\right)-\frac{5}{16} \log \left(\cos \left(\frac{x}{2}\right)\right)","-\frac{5}{16} \tanh ^{-1}(\cos (x))-\frac{1}{6} \cot (x) \csc ^5(x)-\frac{5}{24} \cot (x) \csc ^3(x)-\frac{5}{16} \cot (x) \csc (x)",1,"(-5*Csc[x/2]^2)/64 - Csc[x/2]^4/64 - Csc[x/2]^6/384 - (5*Log[Cos[x/2]])/16 + (5*Log[Sin[x/2]])/16 + (5*Sec[x/2]^2)/64 + Sec[x/2]^4/64 + Sec[x/2]^6/384","B",1
339,1,57,41,0.0077725,"\int \sec ^{12}(x) \, dx","Integrate[Sec[x]^12,x]","\frac{256 \tan (x)}{693}+\frac{1}{11} \tan (x) \sec ^{10}(x)+\frac{10}{99} \tan (x) \sec ^8(x)+\frac{80}{693} \tan (x) \sec ^6(x)+\frac{32}{231} \tan (x) \sec ^4(x)+\frac{128}{693} \tan (x) \sec ^2(x)","\frac{\tan ^{11}(x)}{11}+\frac{5 \tan ^9(x)}{9}+\frac{10 \tan ^7(x)}{7}+2 \tan ^5(x)+\frac{5 \tan ^3(x)}{3}+\tan (x)",1,"(256*Tan[x])/693 + (128*Sec[x]^2*Tan[x])/693 + (32*Sec[x]^4*Tan[x])/231 + (80*Sec[x]^6*Tan[x])/693 + (10*Sec[x]^8*Tan[x])/99 + (Sec[x]^10*Tan[x])/11","A",1
340,1,40,40,0.0125459,"\int \sec ^3\left(\frac{\pi }{4}+3 x\right) \, dx","Integrate[Sec[Pi/4 + 3*x]^3,x]","\frac{1}{6} \tanh ^{-1}\left(\sin \left(3 x+\frac{\pi }{4}\right)\right)+\frac{1}{6} \tan \left(3 x+\frac{\pi }{4}\right) \sec \left(3 x+\frac{\pi }{4}\right)","\frac{1}{6} \tanh ^{-1}\left(\sin \left(3 x+\frac{\pi }{4}\right)\right)+\frac{1}{6} \tan \left(3 x+\frac{\pi }{4}\right) \sec \left(3 x+\frac{\pi }{4}\right)",1,"ArcTanh[Sin[Pi/4 + 3*x]]/6 + (Sec[Pi/4 + 3*x]*Tan[Pi/4 + 3*x])/6","A",1
341,1,30,22,0.0041535,"\int \tan ^6(x) \, dx","Integrate[Tan[x]^6,x]","-x+\frac{23 \tan (x)}{15}+\frac{1}{5} \tan (x) \sec ^4(x)-\frac{11}{15} \tan (x) \sec ^2(x)","-x+\frac{\tan ^5(x)}{5}-\frac{\tan ^3(x)}{3}+\tan (x)",1,"-x + (23*Tan[x])/15 - (11*Sec[x]^2*Tan[x])/15 + (Sec[x]^4*Tan[x])/5","A",1
342,1,16,20,0.0035577,"\int \cot ^5(x) \, dx","Integrate[Cot[x]^5,x]","-\frac{1}{4} \csc ^4(x)+\csc ^2(x)+\log (\sin (x))","-\frac{1}{4} \cot ^4(x)+\frac{\cot ^2(x)}{2}+\log (\sin (x))",1,"Csc[x]^2 - Csc[x]^4/4 + Log[Sin[x]]","A",1
343,1,40,32,0.0174934,"\int \cot ^4\left(\frac{\pi }{4}+\frac{x}{3}\right) \, dx","Integrate[Cot[Pi/4 + x/3]^4,x]","-\cot ^3\left(\frac{x}{3}+\frac{\pi }{4}\right) \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};-\tan ^2\left(\frac{x}{3}+\frac{\pi }{4}\right)\right)","x-\cot ^3\left(\frac{x}{3}+\frac{\pi }{4}\right)+3 \cot \left(\frac{x}{3}+\frac{\pi }{4}\right)",1,"-(Cot[Pi/4 + x/3]^3*Hypergeometric2F1[-3/2, 1, -1/2, -Tan[Pi/4 + x/3]^2])","C",1
344,1,46,56,0.0157726,"\int \cos ^6(x) \sin ^4(x) \, dx","Integrate[Cos[x]^6*Sin[x]^4,x]","\frac{3 x}{256}+\frac{1}{512} \sin (2 x)-\frac{1}{256} \sin (4 x)-\frac{\sin (6 x)}{1024}+\frac{\sin (8 x)}{2048}+\frac{\sin (10 x)}{5120}","\frac{3 x}{256}-\frac{1}{10} \sin ^3(x) \cos ^7(x)-\frac{3}{80} \sin (x) \cos ^7(x)+\frac{1}{160} \sin (x) \cos ^5(x)+\frac{1}{128} \sin (x) \cos ^3(x)+\frac{3}{256} \sin (x) \cos (x)",1,"(3*x)/256 + Sin[2*x]/512 - Sin[4*x]/256 - Sin[6*x]/1024 + Sin[8*x]/2048 + Sin[10*x]/5120","A",1
345,1,55,33,0.0228139,"\int \cos ^6(x) \sin ^7(x) \, dx","Integrate[Cos[x]^6*Sin[x]^7,x]","-\frac{5 \cos (x)}{1024}-\frac{5 \cos (3 x)}{4096}+\frac{3 \cos (5 x)}{4096}+\frac{3 \cos (7 x)}{14336}-\frac{\cos (9 x)}{6144}-\frac{\cos (11 x)}{45056}+\frac{\cos (13 x)}{53248}","\frac{\cos ^{13}(x)}{13}-\frac{3 \cos ^{11}(x)}{11}+\frac{\cos ^9(x)}{3}-\frac{\cos ^7(x)}{7}",1,"(-5*Cos[x])/1024 - (5*Cos[3*x])/4096 + (3*Cos[5*x])/4096 + (3*Cos[7*x])/14336 - Cos[9*x]/6144 - Cos[11*x]/45056 + Cos[13*x]/53248","A",1
346,1,46,46,0.0107477,"\int \sin ^{10}(x) \tan (x) \, dx","Integrate[Sin[x]^10*Tan[x],x]","\frac{\cos ^{10}(x)}{10}-\frac{5 \cos ^8(x)}{8}+\frac{5 \cos ^6(x)}{3}-\frac{5 \cos ^4(x)}{2}+\frac{5 \cos ^2(x)}{2}-\log (\cos (x))","\frac{\cos ^{10}(x)}{10}-\frac{5 \cos ^8(x)}{8}+\frac{5 \cos ^6(x)}{3}-\frac{5 \cos ^4(x)}{2}+\frac{5 \cos ^2(x)}{2}-\log (\cos (x))",1,"(5*Cos[x]^2)/2 - (5*Cos[x]^4)/2 + (5*Cos[x]^6)/3 - (5*Cos[x]^8)/8 + Cos[x]^10/10 - Log[Cos[x]]","A",1
347,1,53,41,0.0289979,"\int \csc ^6(x) \sec ^6(x) \, dx","Integrate[Csc[x]^6*Sec[x]^6,x]","\frac{128 \tan (x)}{15}-\frac{128 \cot (x)}{15}-\frac{1}{5} \cot (x) \csc ^4(x)-\frac{19}{15} \cot (x) \csc ^2(x)+\frac{1}{5} \tan (x) \sec ^4(x)+\frac{19}{15} \tan (x) \sec ^2(x)","\frac{\tan ^5(x)}{5}+\frac{5 \tan ^3(x)}{3}+10 \tan (x)-\frac{1}{5} \cot ^5(x)-\frac{5 \cot ^3(x)}{3}-10 \cot (x)",1,"(-128*Cot[x])/15 - (19*Cot[x]*Csc[x]^2)/15 - (Cot[x]*Csc[x]^4)/5 + (128*Tan[x])/15 + (19*Sec[x]^2*Tan[x])/15 + (Sec[x]^4*Tan[x])/5","A",1
348,1,14,24,0.0046059,"\int \cos ^2(x) \sin ^2(x) \, dx","Integrate[Cos[x]^2*Sin[x]^2,x]","\frac{x}{8}-\frac{1}{32} \sin (4 x)","\frac{x}{8}-\frac{1}{4} \sin (x) \cos ^3(x)+\frac{1}{8} \sin (x) \cos (x)",1,"x/8 - Sin[4*x]/32","A",1
349,1,22,46,0.0067314,"\int \cos ^4(x) \sin ^4(x) \, dx","Integrate[Cos[x]^4*Sin[x]^4,x]","\frac{3 x}{128}-\frac{1}{128} \sin (4 x)+\frac{\sin (8 x)}{1024}","\frac{3 x}{128}-\frac{1}{8} \sin ^3(x) \cos ^5(x)-\frac{1}{16} \sin (x) \cos ^5(x)+\frac{1}{64} \sin (x) \cos ^3(x)+\frac{3}{128} \sin (x) \cos (x)",1,"(3*x)/128 - Sin[4*x]/128 + Sin[8*x]/1024","A",1
350,1,30,68,0.0109269,"\int \cos ^6(x) \sin ^6(x) \, dx","Integrate[Cos[x]^6*Sin[x]^6,x]","\frac{5 x}{1024}-\frac{15 \sin (4 x)}{8192}+\frac{3 \sin (8 x)}{8192}-\frac{\sin (12 x)}{24576}","\frac{5 x}{1024}-\frac{1}{12} \sin ^5(x) \cos ^7(x)-\frac{1}{24} \sin ^3(x) \cos ^7(x)-\frac{1}{64} \sin (x) \cos ^7(x)+\frac{1}{384} \sin (x) \cos ^5(x)+\frac{5 \sin (x) \cos ^3(x)}{1536}+\frac{5 \sin (x) \cos (x)}{1024}",1,"(5*x)/1024 - (15*Sin[4*x])/8192 + (3*Sin[8*x])/8192 - Sin[12*x]/24576","A",1
351,1,38,90,0.0151611,"\int \cos ^8(x) \sin ^8(x) \, dx","Integrate[Cos[x]^8*Sin[x]^8,x]","\frac{35 x}{32768}-\frac{7 \sin (4 x)}{16384}+\frac{7 \sin (8 x)}{65536}-\frac{\sin (12 x)}{49152}+\frac{\sin (16 x)}{524288}","\frac{35 x}{32768}-\frac{1}{16} \sin ^7(x) \cos ^9(x)-\frac{1}{32} \sin ^5(x) \cos ^9(x)-\frac{5}{384} \sin ^3(x) \cos ^9(x)-\frac{1}{256} \sin (x) \cos ^9(x)+\frac{\sin (x) \cos ^7(x)}{2048}+\frac{7 \sin (x) \cos ^5(x)}{12288}+\frac{35 \sin (x) \cos ^3(x)}{49152}+\frac{35 \sin (x) \cos (x)}{32768}",1,"(35*x)/32768 - (7*Sin[4*x])/16384 + (7*Sin[8*x])/65536 - Sin[12*x]/49152 + Sin[16*x]/524288","A",1
352,1,58,68,0.0566914,"\int \cos ^{2 m}(x) \sin ^{2 m}(x) \, dx","Integrate[Cos[x]^(2*m)*Sin[x]^(2*m),x]","\frac{\sin ^{2 m+1}(x) \cos ^{2 m-1}(x) \cos ^2(x)^{\frac{1}{2}-m} \, _2F_1\left(\frac{1}{2}-m,m+\frac{1}{2};m+\frac{3}{2};\sin ^2(x)\right)}{2 m+1}","\frac{\sin ^{2 m+1}(x) \cos ^{2 m-1}(x) \cos ^2(x)^{\frac{1}{2}-m} \, _2F_1\left(\frac{1}{2} (1-2 m),\frac{1}{2} (2 m+1);\frac{1}{2} (2 m+3);\sin ^2(x)\right)}{2 m+1}",1,"(Cos[x]^(-1 + 2*m)*(Cos[x]^2)^(1/2 - m)*Hypergeometric2F1[1/2 - m, 1/2 + m, 3/2 + m, Sin[x]^2]*Sin[x]^(1 + 2*m))/(1 + 2*m)","A",1
353,1,45,32,0.0687421,"\int \csc ^3\left(\frac{\pi }{4}+2 x\right) \sec \left(\frac{\pi }{4}+2 x\right) \, dx","Integrate[Csc[Pi/4 + 2*x]^3*Sec[Pi/4 + 2*x],x]","\frac{1}{4} \left(-\csc ^2\left(2 x+\frac{\pi }{4}\right)+2 \log \left(\sin \left(2 x+\frac{\pi }{4}\right)\right)-2 \log \left(\cos \left(\frac{1}{4} (8 x+\pi )\right)\right)\right)","\frac{1}{2} \log \left(\tan \left(2 x+\frac{\pi }{4}\right)\right)-\frac{1}{4} \cot ^2\left(2 x+\frac{\pi }{4}\right)",1,"(-Csc[Pi/4 + 2*x]^2 - 2*Log[Cos[(Pi + 8*x)/4]] + 2*Log[Sin[Pi/4 + 2*x]])/4","A",1
354,1,8,8,0.002791,"\int \sec ^2(x) \tan ^2(x) \, dx","Integrate[Sec[x]^2*Tan[x]^2,x]","\frac{\tan ^3(x)}{3}","\frac{\tan ^3(x)}{3}",1,"Tan[x]^3/3","A",1
355,1,11,11,0.0071724,"\int \cot ^3(x) \csc (x) \, dx","Integrate[Cot[x]^3*Csc[x],x]","\csc (x)-\frac{\csc ^3(x)}{3}","\csc (x)-\frac{\csc ^3(x)}{3}",1,"Csc[x] - Csc[x]^3/3","A",1
356,1,8,8,0.0048985,"\int \sec ^3(x) \tan (x) \, dx","Integrate[Sec[x]^3*Tan[x],x]","\frac{\sec ^3(x)}{3}","\frac{\sec ^3(x)}{3}",1,"Sec[x]^3/3","A",1
357,1,71,26,0.0201395,"\int \cot ^2(x) \csc ^3(x) \, dx","Integrate[Cot[x]^2*Csc[x]^3,x]","-\frac{1}{64} \csc ^4\left(\frac{x}{2}\right)+\frac{1}{32} \csc ^2\left(\frac{x}{2}\right)+\frac{1}{64} \sec ^4\left(\frac{x}{2}\right)-\frac{1}{32} \sec ^2\left(\frac{x}{2}\right)-\frac{1}{8} \log \left(\sin \left(\frac{x}{2}\right)\right)+\frac{1}{8} \log \left(\cos \left(\frac{x}{2}\right)\right)","\frac{1}{8} \tanh ^{-1}(\cos (x))-\frac{1}{4} \cot (x) \csc ^3(x)+\frac{1}{8} \cot (x) \csc (x)",1,"Csc[x/2]^2/32 - Csc[x/2]^4/64 + Log[Cos[x/2]]/8 - Log[Sin[x/2]]/8 - Sec[x/2]^2/32 + Sec[x/2]^4/64","B",1
358,1,17,17,0.0083477,"\int \cot ^3(x) \csc ^4(x) \, dx","Integrate[Cot[x]^3*Csc[x]^4,x]","\frac{\csc ^4(x)}{4}-\frac{\csc ^6(x)}{6}","\frac{\csc ^4(x)}{4}-\frac{\csc ^6(x)}{6}",1,"Csc[x]^4/4 - Csc[x]^6/6","A",1
359,1,24,31,0.0539269,"\int \sec ^{\frac{13}{2}}(x) \sin ^5(x) \, dx","Integrate[Sec[x]^(13/2)*Sin[x]^5,x]","\frac{1}{924} (44 \cos (2 x)+77 \cos (4 x)+135) \sec ^{\frac{11}{2}}(x)","\frac{2}{11} \sec ^{\frac{11}{2}}(x)-\frac{4}{7} \sec ^{\frac{7}{2}}(x)+\frac{2}{3} \sec ^{\frac{3}{2}}(x)",1,"((135 + 44*Cos[2*x] + 77*Cos[4*x])*Sec[x]^(11/2))/924","A",1
360,1,22,21,0.0389294,"\int \sec ^4(x) \tan ^{\frac{3}{2}}(x) \, dx","Integrate[Sec[x]^4*Tan[x]^(3/2),x]","\frac{2}{45} (2 \cos (2 x)+7) \tan ^{\frac{5}{2}}(x) \sec ^2(x)","\frac{2}{9} \tan ^{\frac{9}{2}}(x)+\frac{2}{5} \tan ^{\frac{5}{2}}(x)",1,"(2*(7 + 2*Cos[2*x])*Sec[x]^2*Tan[x]^(5/2))/45","A",1
361,1,95,38,0.0200058,"\int \cot ^4(x) \csc ^3(x) \, dx","Integrate[Cot[x]^4*Csc[x]^3,x]","-\frac{1}{384} \csc ^6\left(\frac{x}{2}\right)+\frac{1}{64} \csc ^4\left(\frac{x}{2}\right)-\frac{1}{64} \csc ^2\left(\frac{x}{2}\right)+\frac{1}{384} \sec ^6\left(\frac{x}{2}\right)-\frac{1}{64} \sec ^4\left(\frac{x}{2}\right)+\frac{1}{64} \sec ^2\left(\frac{x}{2}\right)+\frac{1}{16} \log \left(\sin \left(\frac{x}{2}\right)\right)-\frac{1}{16} \log \left(\cos \left(\frac{x}{2}\right)\right)","-\frac{1}{16} \tanh ^{-1}(\cos (x))-\frac{1}{6} \cot ^3(x) \csc ^3(x)+\frac{1}{8} \cot (x) \csc ^3(x)-\frac{1}{16} \cot (x) \csc (x)",1,"-1/64*Csc[x/2]^2 + Csc[x/2]^4/64 - Csc[x/2]^6/384 - Log[Cos[x/2]]/16 + Log[Sin[x/2]]/16 + Sec[x/2]^2/64 - Sec[x/2]^4/64 + Sec[x/2]^6/384","B",1
362,1,74,76,0.0776352,"\int \sec ^3\left(\frac{\pi }{4}+\frac{x}{2}\right) \tan ^2\left(\frac{\pi }{4}+\frac{x}{2}\right) \, dx","Integrate[Sec[Pi/4 + x/2]^3*Tan[Pi/4 + x/2]^2,x]","-\frac{1}{4} \tanh ^{-1}\left(\sin \left(\frac{x}{2}+\frac{\pi }{4}\right)\right)+\frac{1}{2} \sin \left(\frac{x}{2}+\frac{\pi }{4}\right) \sec ^4\left(\frac{1}{4} (2 x+\pi )\right)-\frac{1}{4} \sin \left(\frac{x}{2}+\frac{\pi }{4}\right) \sec ^2\left(\frac{1}{4} (2 x+\pi )\right)","-\frac{1}{4} \tanh ^{-1}\left(\sin \left(\frac{x}{2}+\frac{\pi }{4}\right)\right)+\frac{1}{2} \tan \left(\frac{x}{2}+\frac{\pi }{4}\right) \sec ^3\left(\frac{x}{2}+\frac{\pi }{4}\right)-\frac{1}{4} \tan \left(\frac{x}{2}+\frac{\pi }{4}\right) \sec \left(\frac{x}{2}+\frac{\pi }{4}\right)",1,"-1/4*ArcTanh[Sin[Pi/4 + x/2]] - (Sec[(Pi + 2*x)/4]^2*Sin[Pi/4 + x/2])/4 + (Sec[(Pi + 2*x)/4]^4*Sin[Pi/4 + x/2])/2","A",1
363,1,127,88,2.0186161,"\int \left(1+\cot ^3(x)\right) \left(a \sec ^2(x)-\sin (2 x)\right)^2 \, dx","Integrate[(1 + Cot[x]^3)*(a*Sec[x]^2 - Sin[2*x])^2,x]","-\frac{2 \sin (x) \cos ^3(x) \left(\sin (2 x)-a \sec ^2(x)\right)^2 \left(-8 a^2 (\cos (2 x)+2) \sec ^2(x)-3 \cot (x) \left(-4 a^2 \csc ^2(x)+8 a^2 \log (\sin (x))-8 a^2 \log (\cos (x))+32 a x+32 a \log (\cos (x))+4 x-\sin (4 x)+12 \cos (2 x)+\cos (4 x)+32 \log (\sin (x))\right)-96 a \cot ^2(x)\right)}{3 (-4 a+2 \sin (2 x)+\sin (4 x))^2}","\frac{1}{3} a^2 \tan ^3(x)+a^2 \tan (x)-\frac{1}{2} a^2 \cot ^2(x)+\left(a^2+4\right) \log (\sin (x))+4 a x+4 a \cot (x)+(4-a) a \log (\cos (x))+\frac{x}{2}+\cos ^4(x)+2 \cos ^2(x)-\sin (x) \cos ^3(x)+\frac{1}{2} \sin (x) \cos (x)",1,"(-2*Cos[x]^3*Sin[x]*(-(a*Sec[x]^2) + Sin[2*x])^2*(-96*a*Cot[x]^2 - 8*a^2*(2 + Cos[2*x])*Sec[x]^2 - 3*Cot[x]*(4*x + 32*a*x + 12*Cos[2*x] + Cos[4*x] - 4*a^2*Csc[x]^2 + 32*a*Log[Cos[x]] - 8*a^2*Log[Cos[x]] + 32*Log[Sin[x]] + 8*a^2*Log[Sin[x]] - Sin[4*x])))/(3*(-4*a + 2*Sin[2*x] + Sin[4*x])^2)","A",1
364,1,74,70,0.0878584,"\int (4-3 \cos (x)) \left(1-\frac{\sin (x)}{2}\right)^4 \, dx","Integrate[(4 - 3*Cos[x])*(1 - Sin[x]/2)^4,x]","\frac{227 x}{32}-\frac{531 \sin (x)}{128}-\frac{25}{16} \sin (2 x)+\frac{99}{256} \sin (3 x)+\frac{1}{128} \sin (4 x)-\frac{3 \sin (5 x)}{1280}+\frac{19 \cos (x)}{2}-\frac{27}{16} \cos (2 x)-\frac{1}{6} \cos (3 x)+\frac{3}{64} \cos (4 x)","\frac{227 x}{32}-\frac{3}{80} \sin ^5(x)+\frac{3 \sin ^4(x)}{8}-\frac{3 \sin ^3(x)}{2}-3 \sin (x)-\frac{2 \cos ^3(x)}{3}-3 \cos ^2(x)+10 \cos (x)-\frac{1}{16} \sin ^3(x) \cos (x)-\frac{99}{32} \sin (x) \cos (x)",1,"(227*x)/32 + (19*Cos[x])/2 - (27*Cos[2*x])/16 - Cos[3*x]/6 + (3*Cos[4*x])/64 - (531*Sin[x])/128 - (25*Sin[2*x])/16 + (99*Sin[3*x])/256 + Sin[4*x]/128 - (3*Sin[5*x])/1280","A",1
365,1,29,33,0.0252886,"\int \left(\frac{1}{2}-3 \cot (x)\right) (3-2 \cot (x))^3 \, dx","Integrate[(1/2 - 3*Cot[x])*(3 - 2*Cot[x])^3,x]","-\frac{285 x}{2}-148 \cot (x)+56 \csc ^2(x)+4 \log (\sin (x))-8 \cot (x) \csc ^2(x)","-\frac{285 x}{2}+(3-2 \cot (x))^3+5 (3-2 \cot (x))^2-42 \cot (x)+4 \log (\sin (x))",1,"(-285*x)/2 - 148*Cot[x] + 56*Csc[x]^2 - 8*Cot[x]*Csc[x]^2 + 4*Log[Sin[x]]","A",1
366,1,20,16,0.0174289,"\int \cos (5 x) \sec ^5(x) \, dx","Integrate[Cos[5*x]*Sec[x]^5,x]","16 x-\frac{50 \tan (x)}{3}+\frac{5}{3} \tan (x) \sec ^2(x)","16 x+\frac{5 \tan ^3(x)}{3}-15 \tan (x)",1,"16*x - (50*Tan[x])/3 + (5*Sec[x]^2*Tan[x])/3","A",1
367,1,12,12,0.0104792,"\int \cos (4 x) \sec (x) \, dx","Integrate[Cos[4*x]*Sec[x],x]","\tanh ^{-1}(\sin (x))-\frac{8 \sin ^3(x)}{3}","\tanh ^{-1}(\sin (x))-\frac{8 \sin ^3(x)}{3}",1,"ArcTanh[Sin[x]] - (8*Sin[x]^3)/3","A",1
368,1,17,17,0.0064116,"\int \cos (x) \cos (4 x) \, dx","Integrate[Cos[x]*Cos[4*x],x]","\frac{1}{6} \sin (3 x)+\frac{1}{10} \sin (5 x)","\frac{1}{6} \sin (3 x)+\frac{1}{10} \sin (5 x)",1,"Sin[3*x]/6 + Sin[5*x]/10","A",1
369,1,26,26,0.0503699,"\int \cos (4 x) \sec ^5(x) \, dx","Integrate[Cos[4*x]*Sec[x]^5,x]","\frac{1}{8} \left(35 \tanh ^{-1}(\sin (x))-27 \tan (x) \sec ^3(x)+29 \tan ^3(x) \sec (x)\right)","\frac{35}{8} \tanh ^{-1}(\sin (x))+\frac{1}{4} \tan (x) \sec ^3(x)-\frac{29}{8} \tan (x) \sec (x)",1,"(35*ArcTanh[Sin[x]] - 27*Sec[x]^3*Tan[x] + 29*Sec[x]*Tan[x]^3)/8","A",1
370,1,38,38,0.0123494,"\int \cos ^4(x) \cos (4 x) \, dx","Integrate[Cos[x]^4*Cos[4*x],x]","\frac{x}{16}+\frac{1}{8} \sin (2 x)+\frac{3}{32} \sin (4 x)+\frac{1}{24} \sin (6 x)+\frac{1}{128} \sin (8 x)","\frac{x}{16}+\frac{1}{8} \sin (2 x)+\frac{3}{32} \sin (4 x)+\frac{1}{24} \sin (6 x)+\frac{1}{128} \sin (8 x)",1,"x/16 + Sin[2*x]/8 + (3*Sin[4*x])/32 + Sin[6*x]/24 + Sin[8*x]/128","A",1
371,1,20,20,0.0127795,"\int \cos (5 x) \csc ^5(x) \, dx","Integrate[Cos[5*x]*Csc[x]^5,x]","-\frac{1}{4} \csc ^4(x)+6 \csc ^2(x)+16 \log (\sin (x))","-\frac{1}{4} \csc ^4(x)+6 \csc ^2(x)+16 \log (\sin (x))",1,"6*Csc[x]^2 - Csc[x]^4/4 + 16*Log[Sin[x]]","A",1
372,1,12,12,0.0102595,"\int \csc ^4(x) \sin (4 x) \, dx","Integrate[Csc[x]^4*Sin[4*x],x]","-2 \csc ^2(x)-8 \log (\sin (x))","-2 \csc ^2(x)-8 \log (\sin (x))",1,"-2*Csc[x]^2 - 8*Log[Sin[x]]","A",1
373,1,39,64,0.0388211,"\int \frac{\cot (x)}{2+\sin (2 x)} \, dx","Integrate[Cot[x]/(2 + Sin[2*x]),x]","\frac{1}{12} \left(-2 \sqrt{3} \tan ^{-1}\left(\frac{2 \tan (x)+1}{\sqrt{3}}\right)+6 \log (\sin (x))-3 \log (\sin (2 x)+2)\right)","-\frac{x}{2 \sqrt{3}}+\frac{1}{2} \log (\sin (x))+\frac{\tan ^{-1}\left(\frac{1-2 \cos ^2(x)}{2 \sin (x) \cos (x)+\sqrt{3}+2}\right)}{2 \sqrt{3}}-\frac{1}{4} \log (\sin (x) \cos (x)+1)",1,"(-2*Sqrt[3]*ArcTan[(1 + 2*Tan[x])/Sqrt[3]] + 6*Log[Sin[x]] - 3*Log[2 + Sin[2*x]])/12","A",1
374,1,17,11,0.0125361,"\int \cos (x) \cot (x) \sec (3 x) \, dx","Integrate[Cos[x]*Cot[x]*Sec[3*x],x]","\log (\sin (x))-\frac{1}{2} \log \left(1-4 \sin ^2(x)\right)","-\frac{1}{2} \log \left(\csc ^2(x)-4\right)",1,"Log[Sin[x]] - Log[1 - 4*Sin[x]^2]/2","A",1
375,1,7,7,0.0333163,"\int \frac{\sin (2 x)}{\cos ^4(x)+\sin ^4(x)} \, dx","Integrate[Sin[2*x]/(Cos[x]^4 + Sin[x]^4),x]","-\tan ^{-1}(\cos (2 x))","-\tan ^{-1}(\cos (2 x))",1,"-ArcTan[Cos[2*x]]","A",1
376,1,33,53,0.0626603,"\int \frac{1}{4+\sqrt{3} \cos (x)+\sin (x)} \, dx","Integrate[(4 + Sqrt[3]*Cos[x] + Sin[x])^(-1),x]","-\frac{\tan ^{-1}\left(\frac{\left(\sqrt{3}-4\right) \tan \left(\frac{x}{2}\right)-1}{2 \sqrt{3}}\right)}{\sqrt{3}}","\frac{x}{2 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{\cos (x)-\sqrt{3} \sin (x)}{\sin (x)+\sqrt{3} \cos (x)+2 \left(2+\sqrt{3}\right)}\right)}{\sqrt{3}}",1,"-(ArcTan[(-1 + (-4 + Sqrt[3])*Tan[x/2])/(2*Sqrt[3])]/Sqrt[3])","A",1
377,1,22,33,0.0471894,"\int \frac{1}{3+4 \cos (x)+4 \sin (x)} \, dx","Integrate[(3 + 4*Cos[x] + 4*Sin[x])^(-1),x]","\frac{2 \tanh ^{-1}\left(\frac{\tan \left(\frac{x}{2}\right)-4}{\sqrt{23}}\right)}{\sqrt{23}}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{23} (\cos (x)-\sin (x))}{3 \sin (x)+3 \cos (x)+8}\right)}{\sqrt{23}}",1,"(2*ArcTanh[(-4 + Tan[x/2])/Sqrt[23]])/Sqrt[23]","A",1
378,1,9,27,0.0234822,"\int \frac{1}{4-3 \cos ^2(x)+5 \sin ^2(x)} \, dx","Integrate[(4 - 3*Cos[x]^2 + 5*Sin[x]^2)^(-1),x]","\frac{1}{3} \tan ^{-1}(3 \tan (x))","\frac{x}{3}+\frac{1}{3} \tan ^{-1}\left(\frac{2 \sin (x) \cos (x)}{2 \sin ^2(x)+1}\right)",1,"ArcTan[3*Tan[x]]/3","A",1
379,1,41,28,0.0430919,"\int \frac{1}{4+4 \cot (x)+\tan (x)} \, dx","Integrate[(4 + 4*Cot[x] + Tan[x])^(-1),x]","\frac{4 x-3 \log (\sin (x)+2 \cos (x))+\cot (x) (8 x-6 \log (\sin (x)+2 \cos (x)))-5}{50 \cot (x)+25}","\frac{4 x}{25}+\frac{2}{5 (\tan (x)+2)}-\frac{3}{25} \log (\sin (x)+2 \cos (x))",1,"(-5 + 4*x + Cot[x]*(8*x - 6*Log[2*Cos[x] + Sin[x]]) - 3*Log[2*Cos[x] + Sin[x]])/(25 + 50*Cot[x])","A",1
380,1,58,67,0.1223894,"\int \frac{1}{(2 \sec (x)+\sin (x))^2} \, dx","Integrate[(2*Sec[x] + Sin[x])^(-2),x]","\frac{(\sin (2 x)+4) \sec ^2(x) \left(15 (\cos (2 x)-15)+8 \sqrt{15} (\sin (2 x)+4) \tan ^{-1}\left(\frac{4 \tan (x)+1}{\sqrt{15}}\right)\right)}{900 (\sin (x)+2 \sec (x))^2}","\frac{8 x}{15 \sqrt{15}}+\frac{4 \tan (x)+1}{15 \left(2 \tan ^2(x)+\tan (x)+2\right)}-\frac{8 \tan ^{-1}\left(\frac{1-2 \cos ^2(x)}{2 \sin (x) \cos (x)+\sqrt{15}+4}\right)}{15 \sqrt{15}}",1,"(Sec[x]^2*(4 + Sin[2*x])*(15*(-15 + Cos[2*x]) + 8*Sqrt[15]*ArcTan[(1 + 4*Tan[x])/Sqrt[15]]*(4 + Sin[2*x])))/(900*(2*Sec[x] + Sin[x])^2)","A",1
381,1,54,55,0.089855,"\int \frac{1}{(\cos (x)+2 \sec (x))^2} \, dx","Integrate[(Cos[x] + 2*Sec[x])^(-2),x]","\frac{(\cos (2 x)+5) \sec ^4(x) \left(6 \sin (2 x)+\sqrt{6} (\cos (2 x)+5) \tan ^{-1}\left(\sqrt{\frac{2}{3}} \tan (x)\right)\right)}{144 \left(2 \sec ^2(x)+1\right)^2}","\frac{x}{6 \sqrt{6}}+\frac{\tan (x)}{6 \left(2 \tan ^2(x)+3\right)}-\frac{\tan ^{-1}\left(\frac{\sin (x) \cos (x)}{\cos ^2(x)+\sqrt{6}+2}\right)}{6 \sqrt{6}}",1,"((5 + Cos[2*x])*Sec[x]^4*(Sqrt[6]*ArcTan[Sqrt[2/3]*Tan[x]]*(5 + Cos[2*x]) + 6*Sin[2*x]))/(144*(1 + 2*Sec[x]^2)^2)","A",1
382,1,70,42,0.2247764,"\int \frac{5-\tan (x)-6 \tan ^2(x)}{(1+3 \tan (x))^3} \, dx","Integrate[(5 - Tan[x] - 6*Tan[x]^2)/(1 + 3*Tan[x])^3,x]","-\frac{670 x+560 \log (3 \sin (x)+\cos (x))-4 \cos (2 x) (134 x+112 \log (3 \sin (x)+\cos (x))-405)+6 \sin (2 x) (67 x+56 \log (3 \sin (x)+\cos (x))-90)-1305}{500 (3 \sin (x)+\cos (x))^2}","-\frac{67 x}{250}-\frac{29}{50 (3 \tan (x)+1)}-\frac{7}{10 (3 \tan (x)+1)^2}-\frac{28}{125} \log (3 \sin (x)+\cos (x))",1,"-1/500*(-1305 + 670*x + 560*Log[Cos[x] + 3*Sin[x]] - 4*Cos[2*x]*(-405 + 134*x + 112*Log[Cos[x] + 3*Sin[x]]) + 6*(-90 + 67*x + 56*Log[Cos[x] + 3*Sin[x]])*Sin[2*x])/(Cos[x] + 3*Sin[x])^2","A",1
383,1,9,9,0.0071445,"\int \cos ^2(x) \sec (3 x) \, dx","Integrate[Cos[x]^2*Sec[3*x],x]","\frac{1}{2} \tanh ^{-1}(2 \sin (x))","\frac{1}{2} \tanh ^{-1}(2 \sin (x))",1,"ArcTanh[2*Sin[x]]/2","A",1
384,1,174,15,0.3839636,"\int \sec (2 x) \sin (x) \, dx","Integrate[Sec[2*x]*Sin[x],x]","\frac{4 \tanh ^{-1}\left(\tan \left(\frac{x}{2}\right)+\sqrt{2}\right)-\log \left(-\sqrt{2} \sin (x)-\sqrt{2} \cos (x)+2\right)+\log \left(-\sqrt{2} \sin (x)+\sqrt{2} \cos (x)+2\right)+2 i \tan ^{-1}\left(\frac{\cos \left(\frac{x}{2}\right)-\left(\sqrt{2}-1\right) \sin \left(\frac{x}{2}\right)}{\left(1+\sqrt{2}\right) \cos \left(\frac{x}{2}\right)-\sin \left(\frac{x}{2}\right)}\right)-2 i \tan ^{-1}\left(\frac{\cos \left(\frac{x}{2}\right)-\left(1+\sqrt{2}\right) \sin \left(\frac{x}{2}\right)}{\left(\sqrt{2}-1\right) \cos \left(\frac{x}{2}\right)-\sin \left(\frac{x}{2}\right)}\right)}{4 \sqrt{2}}","\frac{\tanh ^{-1}\left(\sqrt{2} \cos (x)\right)}{\sqrt{2}}",1,"((2*I)*ArcTan[(Cos[x/2] - (-1 + Sqrt[2])*Sin[x/2])/((1 + Sqrt[2])*Cos[x/2] - Sin[x/2])] - (2*I)*ArcTan[(Cos[x/2] - (1 + Sqrt[2])*Sin[x/2])/((-1 + Sqrt[2])*Cos[x/2] - Sin[x/2])] + 4*ArcTanh[Sqrt[2] + Tan[x/2]] - Log[2 - Sqrt[2]*Cos[x] - Sqrt[2]*Sin[x]] + Log[2 + Sqrt[2]*Cos[x] - Sqrt[2]*Sin[x]])/(4*Sqrt[2])","C",1
385,1,28,17,0.015526,"\int \sec (2 x) \sin ^2(x) \, dx","Integrate[Sec[2*x]*Sin[x]^2,x]","-\frac{x}{2}-\frac{1}{4} \log (\cos (x)-\sin (x))+\frac{1}{4} \log (\sin (x)+\cos (x))","\frac{1}{4} \tanh ^{-1}(2 \sin (x) \cos (x))-\frac{x}{2}",1,"-1/2*x - Log[Cos[x] - Sin[x]]/4 + Log[Cos[x] + Sin[x]]/4","A",1
386,1,21,21,0.0167867,"\int \sec (3 x) \sin ^3(x) \, dx","Integrate[Sec[3*x]*Sin[x]^3,x]","\frac{1}{3} \log (\cos (x))-\frac{1}{24} \log \left(1-4 \sin ^2(x)\right)","\frac{1}{3} \log (\cos (x))-\frac{1}{24} \log \left(3-4 \cos ^2(x)\right)",1,"Log[Cos[x]]/3 - Log[1 - 4*Sin[x]^2]/24","A",1
387,1,21,21,0.0081005,"\int \cos (x) \csc (3 x) \, dx","Integrate[Cos[x]*Csc[3*x],x]","\frac{1}{3} \log (\sin (x))-\frac{1}{6} \log \left(3-4 \sin ^2(x)\right)","\frac{1}{3} \log (\sin (x))-\frac{1}{6} \log \left(3-4 \sin ^2(x)\right)",1,"Log[Sin[x]]/3 - Log[3 - 4*Sin[x]^2]/6","A",1
388,1,26,26,0.0227977,"\int \csc (4 x) \sin (x) \, dx","Integrate[Csc[4*x]*Sin[x],x]","\frac{\tanh ^{-1}\left(\sqrt{2} \sin (x)\right)}{2 \sqrt{2}}-\frac{1}{4} \tanh ^{-1}(\sin (x))","\frac{\tanh ^{-1}\left(\sqrt{2} \sin (x)\right)}{2 \sqrt{2}}-\frac{1}{4} \tanh ^{-1}(\sin (x))",1,"-1/4*ArcTanh[Sin[x]] + ArcTanh[Sqrt[2]*Sin[x]]/(2*Sqrt[2])","A",1
389,1,218,26,0.3428576,"\int \csc (4 x) \sin ^3(x) \, dx","Integrate[Csc[4*x]*Sin[x]^3,x]","\frac{2 \log \left(2 \sin (x)+\sqrt{2}\right)+4 \sqrt{2} \log \left(\cos \left(\frac{x}{2}\right)-\sin \left(\frac{x}{2}\right)\right)-4 \sqrt{2} \log \left(\sin \left(\frac{x}{2}\right)+\cos \left(\frac{x}{2}\right)\right)-\log \left(-\sqrt{2} \sin (x)-\sqrt{2} \cos (x)+2\right)-\log \left(-\sqrt{2} \sin (x)+\sqrt{2} \cos (x)+2\right)-2 i \tan ^{-1}\left(\frac{\cos \left(\frac{x}{2}\right)-\left(\sqrt{2}-1\right) \sin \left(\frac{x}{2}\right)}{\left(1+\sqrt{2}\right) \cos \left(\frac{x}{2}\right)-\sin \left(\frac{x}{2}\right)}\right)-2 i \tan ^{-1}\left(\frac{\cos \left(\frac{x}{2}\right)-\left(1+\sqrt{2}\right) \sin \left(\frac{x}{2}\right)}{\left(\sqrt{2}-1\right) \cos \left(\frac{x}{2}\right)-\sin \left(\frac{x}{2}\right)}\right)}{16 \sqrt{2}}","\frac{\tanh ^{-1}\left(\sqrt{2} \sin (x)\right)}{4 \sqrt{2}}-\frac{1}{4} \tanh ^{-1}(\sin (x))",1,"((-2*I)*ArcTan[(Cos[x/2] - (-1 + Sqrt[2])*Sin[x/2])/((1 + Sqrt[2])*Cos[x/2] - Sin[x/2])] - (2*I)*ArcTan[(Cos[x/2] - (1 + Sqrt[2])*Sin[x/2])/((-1 + Sqrt[2])*Cos[x/2] - Sin[x/2])] + 4*Sqrt[2]*Log[Cos[x/2] - Sin[x/2]] - 4*Sqrt[2]*Log[Cos[x/2] + Sin[x/2]] + 2*Log[Sqrt[2] + 2*Sin[x]] - Log[2 - Sqrt[2]*Cos[x] - Sqrt[2]*Sin[x]] - Log[2 + Sqrt[2]*Cos[x] - Sqrt[2]*Sin[x]])/(16*Sqrt[2])","C",1
390,1,25,16,0.0148866,"\int \sqrt{1+\sin (2 x)} \, dx","Integrate[Sqrt[1 + Sin[2*x]],x]","\frac{\sqrt{\sin (2 x)+1} (\sin (x)-\cos (x))}{\sin (x)+\cos (x)}","-\frac{\cos (2 x)}{\sqrt{\sin (2 x)+1}}",1,"((-Cos[x] + Sin[x])*Sqrt[1 + Sin[2*x]])/(Cos[x] + Sin[x])","A",1
391,1,27,17,0.0147867,"\int \sqrt{1-\sin (2 x)} \, dx","Integrate[Sqrt[1 - Sin[2*x]],x]","\frac{\sqrt{1-\sin (2 x)} (\sin (x)+\cos (x))}{\cos (x)-\sin (x)}","\frac{\cos (2 x)}{\sqrt{1-\sin (2 x)}}",1,"((Cos[x] + Sin[x])*Sqrt[1 - Sin[2*x]])/(Cos[x] - Sin[x])","A",1
392,1,47,27,0.0165324,"\int \frac{1}{\sqrt{1+\cos (2 x)}} \, dx","Integrate[1/Sqrt[1 + Cos[2*x]],x]","-\frac{\cos (x) \left(\log \left(\cos \left(\frac{x}{2}\right)-\sin \left(\frac{x}{2}\right)\right)-\log \left(\sin \left(\frac{x}{2}\right)+\cos \left(\frac{x}{2}\right)\right)\right)}{\sqrt{\cos (2 x)+1}}","\frac{\tanh ^{-1}\left(\frac{\sin (2 x)}{\sqrt{2} \sqrt{\cos (2 x)+1}}\right)}{\sqrt{2}}",1,"-((Cos[x]*(Log[Cos[x/2] - Sin[x/2]] - Log[Cos[x/2] + Sin[x/2]]))/Sqrt[1 + Cos[2*x]])","A",1
393,1,33,30,0.0163725,"\int \frac{1}{\sqrt{1-\cos (2 x)}} \, dx","Integrate[1/Sqrt[1 - Cos[2*x]],x]","-\frac{\sin (x) \left(\log \left(\cos \left(\frac{x}{2}\right)\right)-\log \left(\sin \left(\frac{x}{2}\right)\right)\right)}{\sqrt{1-\cos (2 x)}}","-\frac{\tanh ^{-1}\left(\frac{\sin (2 x)}{\sqrt{2} \sqrt{1-\cos (2 x)}}\right)}{\sqrt{2}}",1,"-(((Log[Cos[x/2]] - Log[Sin[x/2]])*Sin[x])/Sqrt[1 - Cos[2*x]])","A",1
394,1,61,53,0.1371796,"\int \frac{1}{(1-\cos (3 x))^{3/2}} \, dx","Integrate[(1 - Cos[3*x])^(-3/2),x]","-\frac{\sin ^3\left(\frac{3 x}{2}\right) \left(\csc ^2\left(\frac{3 x}{4}\right)-\sec ^2\left(\frac{3 x}{4}\right)-4 \log \left(\sin \left(\frac{3 x}{4}\right)\right)+4 \log \left(\cos \left(\frac{3 x}{4}\right)\right)\right)}{12 (1-\cos (3 x))^{3/2}}","-\frac{\sin (3 x)}{6 (1-\cos (3 x))^{3/2}}-\frac{\tanh ^{-1}\left(\frac{\sin (3 x)}{\sqrt{2} \sqrt{1-\cos (3 x)}}\right)}{6 \sqrt{2}}",1,"-1/12*((Csc[(3*x)/4]^2 + 4*Log[Cos[(3*x)/4]] - 4*Log[Sin[(3*x)/4]] - Sec[(3*x)/4]^2)*Sin[(3*x)/2]^3)/(1 - Cos[3*x])^(3/2)","A",1
395,1,76,73,0.1729775,"\int \left(1-\sin \left(\frac{2 x}{3}\right)\right)^{5/2} \, dx","Integrate[(1 - Sin[(2*x)/3])^(5/2),x]","\frac{\left(1-\sin \left(\frac{2 x}{3}\right)\right)^{5/2} \left(150 \sin \left(\frac{x}{3}\right)-25 \sin (x)-3 \sin \left(\frac{5 x}{3}\right)+150 \cos \left(\frac{x}{3}\right)+25 \cos (x)-3 \cos \left(\frac{5 x}{3}\right)\right)}{20 \left(\cos \left(\frac{x}{3}\right)-\sin \left(\frac{x}{3}\right)\right)^5}","\frac{3}{5} \left(1-\sin \left(\frac{2 x}{3}\right)\right)^{3/2} \cos \left(\frac{2 x}{3}\right)+\frac{8}{5} \sqrt{1-\sin \left(\frac{2 x}{3}\right)} \cos \left(\frac{2 x}{3}\right)+\frac{32 \cos \left(\frac{2 x}{3}\right)}{5 \sqrt{1-\sin \left(\frac{2 x}{3}\right)}}",1,"((1 - Sin[(2*x)/3])^(5/2)*(150*Cos[x/3] + 25*Cos[x] - 3*Cos[(5*x)/3] + 150*Sin[x/3] - 25*Sin[x] - 3*Sin[(5*x)/3]))/(20*(Cos[x/3] - Sin[x/3])^5)","A",1
396,1,36,55,0.0793235,"\int \frac{\cos (x) \left(-\cos ^2(x)+2 \sqrt[4]{1+2 \sin (x)}\right)}{(1+2 \sin (x))^{3/2}} \, dx","Integrate[(Cos[x]*(-Cos[x]^2 + 2*(1 + 2*Sin[x])^(1/4)))/(1 + 2*Sin[x])^(3/2),x]","-\frac{4 \sin (x)+24 \sqrt[4]{2 \sin (x)+1}+\cos (2 x)-3}{6 \sqrt{2 \sin (x)+1}}","\frac{1}{12} (2 \sin (x)+1)^{3/2}-\frac{1}{2} \sqrt{2 \sin (x)+1}-\frac{4}{\sqrt[4]{2 \sin (x)+1}}+\frac{3}{4 \sqrt{2 \sin (x)+1}}",1,"-1/6*(-3 + Cos[2*x] + 4*Sin[x] + 24*(1 + 2*Sin[x])^(1/4))/Sqrt[1 + 2*Sin[x]]","A",1
397,1,24,98,0.0131482,"\int \sqrt{\tan (x)} \, dx","Integrate[Sqrt[Tan[x]],x]","\frac{2}{3} \tan ^{\frac{3}{2}}(x) \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};-\tan ^2(x)\right)","-\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (x)}\right)}{\sqrt{2}}+\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{\tan (x)}+1\right)}{\sqrt{2}}+\frac{\log \left(\tan (x)-\sqrt{2} \sqrt{\tan (x)}+1\right)}{2 \sqrt{2}}-\frac{\log \left(\tan (x)+\sqrt{2} \sqrt{\tan (x)}+1\right)}{2 \sqrt{2}}",1,"(2*Hypergeometric2F1[3/4, 1, 7/4, -Tan[x]^2]*Tan[x]^(3/2))/3","C",1
398,1,69,57,0.0517332,"\int \frac{1}{\sqrt[3]{\tan (5 x)}} \, dx","Integrate[Tan[5*x]^(-1/3),x]","\frac{1}{10} \sqrt{3} \tan ^{-1}\left(\frac{2 \tan ^{\frac{2}{3}}(5 x)-1}{\sqrt{3}}\right)+\frac{1}{10} \log \left(\tan ^{\frac{2}{3}}(5 x)+1\right)-\frac{1}{20} \log \left(\tan ^{\frac{4}{3}}(5 x)-\tan ^{\frac{2}{3}}(5 x)+1\right)","-\frac{1}{10} \sqrt{3} \tan ^{-1}\left(\frac{1-2 \tan ^{\frac{2}{3}}(5 x)}{\sqrt{3}}\right)+\frac{3}{20} \log \left(\tan ^{\frac{2}{3}}(5 x)+1\right)-\frac{1}{20} \log \left(\tan ^2(5 x)+1\right)",1,"(Sqrt[3]*ArcTan[(-1 + 2*Tan[5*x]^(2/3))/Sqrt[3]])/10 + Log[1 + Tan[5*x]^(2/3)]/10 - Log[1 - Tan[5*x]^(2/3) + Tan[5*x]^(4/3)]/20","A",1
399,1,73,87,0.0962272,"\int \frac{1}{(4+3 \tan (2 x))^{3/2}} \, dx","Integrate[(4 + 3*Tan[2*x])^(-3/2),x]","-\frac{(3+4 i) \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\left(\frac{4}{25}-\frac{3 i}{25}\right) (3 \tan (2 x)+4)\right)+(3-4 i) \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\left(\frac{4}{25}+\frac{3 i}{25}\right) (3 \tan (2 x)+4)\right)}{50 \sqrt{3 \tan (2 x)+4}}","-\frac{9 \tan ^{-1}\left(\frac{1-3 \tan (2 x)}{\sqrt{2} \sqrt{3 \tan (2 x)+4}}\right)}{250 \sqrt{2}}-\frac{3}{25 \sqrt{3 \tan (2 x)+4}}+\frac{13 \tanh ^{-1}\left(\frac{\tan (2 x)+3}{\sqrt{2} \sqrt{3 \tan (2 x)+4}}\right)}{250 \sqrt{2}}",1,"-1/50*((3 + 4*I)*Hypergeometric2F1[-1/2, 1, 1/2, (4/25 - (3*I)/25)*(4 + 3*Tan[2*x])] + (3 - 4*I)*Hypergeometric2F1[-1/2, 1, 1/2, (4/25 + (3*I)/25)*(4 + 3*Tan[2*x])])/Sqrt[4 + 3*Tan[2*x]]","C",1
400,1,38,40,1.2552877,"\int \frac{\sec ^2(x) \left(-\sqrt{4-3 \tan (x)}+3 \tan (x)\right)}{(4-3 \tan (x))^{3/2}} \, dx","Integrate[(Sec[x]^2*(-Sqrt[4 - 3*Tan[x]] + 3*Tan[x]))/(4 - 3*Tan[x])^(3/2),x]","\frac{-6 \tan (x)+\sqrt{4-3 \tan (x)} \log (4-3 \tan (x))+16}{3 \sqrt{4-3 \tan (x)}}","\frac{2}{3} \sqrt{4-3 \tan (x)}+\frac{8}{3 \sqrt{4-3 \tan (x)}}+\frac{1}{3} \log (4-3 \tan (x))",1,"(16 + Log[4 - 3*Tan[x]]*Sqrt[4 - 3*Tan[x]] - 6*Tan[x])/(3*Sqrt[4 - 3*Tan[x]])","A",1
401,1,62,84,0.2843396,"\int \frac{\tan (x)}{\left(-1+\sqrt{\tan (x)}\right)^2} \, dx","Integrate[Tan[x]/(-1 + Sqrt[Tan[x]])^2,x]","-\frac{2}{3} \tan ^{\frac{3}{2}}(x) \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};-\tan ^2(x)\right)-\frac{1}{2} \tan ^{-1}(\tan (x))+\frac{1}{1-\sqrt{\tan (x)}}+\log \left(1-\sqrt{\tan (x)}\right)+\frac{1}{2} \log (\cos (x))","-\frac{x}{2}+\frac{\tan ^{-1}\left(\frac{1-\tan (x)}{\sqrt{2} \sqrt{\tan (x)}}\right)}{\sqrt{2}}+\frac{1}{1-\sqrt{\tan (x)}}+\log \left(1-\sqrt{\tan (x)}\right)+\frac{1}{2} \log (\cos (x))+\frac{\tanh ^{-1}\left(\frac{\tan (x)+1}{\sqrt{2} \sqrt{\tan (x)}}\right)}{\sqrt{2}}",1,"-1/2*ArcTan[Tan[x]] + Log[Cos[x]]/2 + Log[1 - Sqrt[Tan[x]]] + (1 - Sqrt[Tan[x]])^(-1) - (2*Hypergeometric2F1[3/4, 1, 7/4, -Tan[x]^2]*Tan[x]^(3/2))/3","C",1
402,1,31,31,0.0421194,"\int \frac{\sin (x)}{\sqrt{\sin (2 x)}} \, dx","Integrate[Sin[x]/Sqrt[Sin[2*x]],x]","\frac{1}{2} \left(-\sin ^{-1}(\cos (x)-\sin (x))-\log \left(\sin (x)+\sqrt{\sin (2 x)}+\cos (x)\right)\right)","-\frac{1}{2} \sin ^{-1}(\cos (x)-\sin (x))-\frac{1}{2} \log \left(\sin (x)+\sqrt{\sin (2 x)}+\cos (x)\right)",1,"(-ArcSin[Cos[x] - Sin[x]] - Log[Cos[x] + Sin[x] + Sqrt[Sin[2*x]]])/2","A",1
403,1,29,31,0.0311523,"\int \frac{\cos (x)}{\sqrt{\sin (2 x)}} \, dx","Integrate[Cos[x]/Sqrt[Sin[2*x]],x]","\frac{1}{2} \left(\log \left(\sin (x)+\sqrt{\sin (2 x)}+\cos (x)\right)-\sin ^{-1}(\cos (x)-\sin (x))\right)","\frac{1}{2} \log \left(\sin (x)+\sqrt{\sin (2 x)}+\cos (x)\right)-\frac{1}{2} \sin ^{-1}(\cos (x)-\sin (x))",1,"(-ArcSin[Cos[x] - Sin[x]] + Log[Cos[x] + Sin[x] + Sqrt[Sin[2*x]]])/2","A",1
404,1,41,45,0.0400463,"\int \sin (x) \sqrt{\sin (2 x)} \, dx","Integrate[Sin[x]*Sqrt[Sin[2*x]],x]","\frac{1}{4} \left(-\sin ^{-1}(\cos (x)-\sin (x))-2 \sqrt{\sin (2 x)} \cos (x)+\log \left(\sin (x)+\sqrt{\sin (2 x)}+\cos (x)\right)\right)","-\frac{1}{4} \sin ^{-1}(\cos (x)-\sin (x))-\frac{1}{2} \sqrt{\sin (2 x)} \cos (x)+\frac{1}{4} \log \left(\sin (x)+\sqrt{\sin (2 x)}+\cos (x)\right)",1,"(-ArcSin[Cos[x] - Sin[x]] + Log[Cos[x] + Sin[x] + Sqrt[Sin[2*x]]] - 2*Cos[x]*Sqrt[Sin[2*x]])/4","A",1
405,1,43,47,0.0639995,"\int (\cos (x)-\sin (x)) \sqrt{\sin (2 x)} \, dx","Integrate[(Cos[x] - Sin[x])*Sqrt[Sin[2*x]],x]","\frac{1}{2} \left(\sin (x) \sqrt{\sin (2 x)}+\sqrt{\sin (2 x)} \cos (x)-\log \left(\sin (x)+\sqrt{\sin (2 x)}+\cos (x)\right)\right)","\frac{1}{2} \sin (x) \sqrt{\sin (2 x)}+\frac{1}{2} \sqrt{\sin (2 x)} \cos (x)-\frac{1}{2} \log \left(\sin (x)+\sqrt{\sin (2 x)}+\cos (x)\right)",1,"(-Log[Cos[x] + Sin[x] + Sqrt[Sin[2*x]]] + Cos[x]*Sqrt[Sin[2*x]] + Sin[x]*Sqrt[Sin[2*x]])/2","A",1
406,1,50,61,0.0924134,"\int \frac{\sin ^7(x)}{\sin ^{\frac{7}{2}}(2 x)} \, dx","Integrate[Sin[x]^7/Sin[2*x]^(7/2),x]","\frac{1}{80} \left(2 \sqrt{\sin (2 x)} \sec (x) \left(\sec ^2(x)-6\right)+5 \left(\log \left(\sin (x)+\sqrt{\sin (2 x)}+\cos (x)\right)-\sin ^{-1}(\cos (x)-\sin (x))\right)\right)","\frac{\sin ^5(x)}{5 \sin ^{\frac{5}{2}}(2 x)}-\frac{\sin (x)}{4 \sqrt{\sin (2 x)}}-\frac{1}{16} \sin ^{-1}(\cos (x)-\sin (x))+\frac{1}{16} \log \left(\sin (x)+\sqrt{\sin (2 x)}+\cos (x)\right)",1,"(5*(-ArcSin[Cos[x] - Sin[x]] + Log[Cos[x] + Sin[x] + Sqrt[Sin[2*x]]]) + 2*Sec[x]*(-6 + Sec[x]^2)*Sqrt[Sin[2*x]])/80","A",1
407,1,56,61,0.0779693,"\int \frac{\cos ^7(x)}{\sin ^{\frac{7}{2}}(2 x)} \, dx","Integrate[Cos[x]^7/Sin[2*x]^(7/2),x]","\sqrt{\sin (2 x)} \left(\frac{3 \csc (x)}{20}-\frac{\csc ^3(x)}{40}\right)+\frac{1}{16} \left(-\sin ^{-1}(\cos (x)-\sin (x))-\log \left(\sin (x)+\sqrt{\sin (2 x)}+\cos (x)\right)\right)","-\frac{\cos ^5(x)}{5 \sin ^{\frac{5}{2}}(2 x)}-\frac{1}{16} \sin ^{-1}(\cos (x)-\sin (x))+\frac{\cos (x)}{4 \sqrt{\sin (2 x)}}-\frac{1}{16} \log \left(\sin (x)+\sqrt{\sin (2 x)}+\cos (x)\right)",1,"(-ArcSin[Cos[x] - Sin[x]] - Log[Cos[x] + Sin[x] + Sqrt[Sin[2*x]]])/16 + ((3*Csc[x])/20 - Csc[x]^3/40)*Sqrt[Sin[2*x]]","A",1
408,1,16,16,0.0336672,"\int \csc ^5(x) \sin ^{\frac{3}{2}}(2 x) \, dx","Integrate[Csc[x]^5*Sin[2*x]^(3/2),x]","-\frac{1}{5} \sin ^{\frac{5}{2}}(2 x) \csc ^5(x)","-\frac{1}{5} \sin ^{\frac{5}{2}}(2 x) \csc ^5(x)",1,"-1/5*(Csc[x]^5*Sin[2*x]^(5/2))","A",1
409,1,20,31,0.0313049,"\int \frac{\sec ^3(x)}{\sqrt{\sin (2 x)}} \, dx","Integrate[Sec[x]^3/Sqrt[Sin[2*x]],x]","\frac{1}{5} \sqrt{\sin (2 x)} \sec (x) \left(\sec ^2(x)+4\right)","\frac{1}{5} \sqrt{\sin (2 x)} \sec ^3(x)+\frac{4}{5} \sqrt{\sin (2 x)} \sec (x)",1,"(Sec[x]*(4 + Sec[x]^2)*Sqrt[Sin[2*x]])/5","A",1
410,1,24,29,0.0323087,"\int \frac{\csc (x)}{\sin ^{\frac{3}{2}}(2 x)} \, dx","Integrate[Csc[x]/Sin[2*x]^(3/2),x]","\sqrt{\sin (2 x)} \left(\frac{\sec (x)}{2}-\frac{1}{6} \cot (x) \csc (x)\right)","\frac{4 \sin (x)}{3 \sqrt{\sin (2 x)}}-\frac{2 \cos (x)}{3 \sin ^{\frac{3}{2}}(2 x)}",1,"(-1/6*(Cot[x]*Csc[x]) + Sec[x]/2)*Sqrt[Sin[2*x]]","A",1
411,1,150,68,6.381905,"\int \frac{\cos ^3(x) (\cos (2 x)-3 \tan (x))}{\left(\sin ^2(x)-\sin (2 x)\right) \sin ^{\frac{5}{2}}(2 x)} \, dx","Integrate[(Cos[x]^3*(Cos[2*x] - 3*Tan[x]))/((Sin[x]^2 - Sin[2*x])*Sin[2*x]^(5/2)),x]","\frac{\sqrt{\sin (2 x)} \cos (x) (\cos (2 x)-3 \tan (x)) \left(\frac{1}{15} \csc (x) \left(-50 \cot (x)+12 \csc ^2(x)-147\right)-33 \sqrt{\frac{\cos (x)}{2 \cos (x)-2}} \sqrt{\tan \left(\frac{x}{2}\right)} \sec (x) \left(\operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{1}{\sqrt{\tan \left(\frac{x}{2}\right)}}\right),-1\right)-\Pi \left(-\frac{2}{-1+\sqrt{5}};\left.\sin ^{-1}\left(\frac{1}{\sqrt{\tan \left(\frac{x}{2}\right)}}\right)\right|-1\right)-\Pi \left(\frac{1}{2} \left(-1+\sqrt{5}\right);\left.\sin ^{-1}\left(\frac{1}{\sqrt{\tan \left(\frac{x}{2}\right)}}\right)\right|-1\right)\right)\right)}{16 (-6 \sin (x)+\cos (x)+\cos (3 x))}","-\frac{9 \cos (x)}{16 \sqrt{\sin (2 x)}}+\frac{\cos (x) \cot ^2(x)}{20 \sqrt{\sin (2 x)}}-\frac{5 \cos (x) \cot (x)}{24 \sqrt{\sin (2 x)}}+\frac{33}{32} \tanh ^{-1}\left(\frac{1}{2} \sqrt{\sin (2 x)} \sec (x)\right)",1,"(Cos[x]*Sqrt[Sin[2*x]]*((Csc[x]*(-147 - 50*Cot[x] + 12*Csc[x]^2))/15 - 33*Sqrt[Cos[x]/(-2 + 2*Cos[x])]*(EllipticF[ArcSin[1/Sqrt[Tan[x/2]]], -1] - EllipticPi[-2/(-1 + Sqrt[5]), ArcSin[1/Sqrt[Tan[x/2]]], -1] - EllipticPi[(-1 + Sqrt[5])/2, ArcSin[1/Sqrt[Tan[x/2]]], -1])*Sec[x]*Sqrt[Tan[x/2]])*(Cos[2*x] - 3*Tan[x]))/(16*(Cos[x] + Cos[3*x] - 6*Sin[x]))","C",1
412,1,19,19,0.0080758,"\int \sqrt{\sec ^4(x) \tan (x)} \, dx","Integrate[Sqrt[Sec[x]^4*Tan[x]],x]","\frac{2}{3} \sin (x) \cos (x) \sqrt{\tan (x) \sec ^4(x)}","\frac{2}{3} \sin (x) \cos (x) \sqrt{\tan (x) \sec ^4(x)}",1,"(2*Cos[x]*Sin[x]*Sqrt[Sec[x]^4*Tan[x]])/3","A",1
413,1,66,92,0.0799963,"\int \sqrt{\sin ^4(x) \tan (x)} \, dx","Integrate[Sqrt[Sin[x]^4*Tan[x]],x]","-\frac{1}{8} \sqrt{\sin (2 x)} \csc ^3(x) \sqrt{\sin ^4(x) \tan (x)} \left(2 \sin (x) \sqrt{\sin (2 x)}+3 \sin ^{-1}(\cos (x)-\sin (x))+3 \log \left(\sin (x)+\sqrt{\sin (2 x)}+\cos (x)\right)\right)","-\frac{1}{2} \cot (x) \sqrt{\sin ^4(x) \tan (x)}+\frac{3 \tan ^{-1}\left(\frac{(1-\cot (x)) \csc ^2(x) \sqrt{\sin ^4(x) \tan (x)}}{\sqrt{2}}\right)}{4 \sqrt{2}}+\frac{3 \log \left(\sin (x)+\cos (x)-\sqrt{2} \cot (x) \csc (x) \sqrt{\sin ^4(x) \tan (x)}\right)}{4 \sqrt{2}}",1,"-1/8*(Csc[x]^3*(3*ArcSin[Cos[x] - Sin[x]] + 3*Log[Cos[x] + Sin[x] + Sqrt[Sin[2*x]]] + 2*Sin[x]*Sqrt[Sin[2*x]])*Sqrt[Sin[2*x]]*Sqrt[Sin[x]^4*Tan[x]])","A",1
414,1,63,47,0.1530913,"\int \sqrt[3]{\sec ^{12}(x) \tan ^2(x)} \, dx","Integrate[(Sec[x]^12*Tan[x]^2)^(1/3),x]","\frac{3 \sin (x) \cos (x) \left(8 \left(-\tan ^2(x)\right)^{5/6}+3 \cos (2 x) \left(\left(-\tan ^2(x)\right)^{5/6}-1\right)-3\right) \sqrt[3]{\tan ^2(x) \sec ^{12}(x)}}{55 \left(-\tan ^2(x)\right)^{5/6}}","\frac{3}{5} \sin (x) \cos ^3(x) \sqrt[3]{\tan ^2(x) \sec ^{12}(x)}+\frac{3}{11} \sin ^3(x) \cos (x) \sqrt[3]{\tan ^2(x) \sec ^{12}(x)}",1,"(3*Cos[x]*Sin[x]*(Sec[x]^12*Tan[x]^2)^(1/3)*(-3 + 8*(-Tan[x]^2)^(5/6) + 3*Cos[2*x]*(-1 + (-Tan[x]^2)^(5/6))))/(55*(-Tan[x]^2)^(5/6))","A",1
415,1,35,70,0.0568793,"\int \frac{1}{\sqrt[4]{\cos ^{11}(x) \sin ^{13}(x)}} \, dx","Integrate[(Cos[x]^11*Sin[x]^13)^(-1/4),x]","-\frac{4 \sin (x) \cos (x) (8 \cos (2 x)-16 \cos (4 x)+15)}{63 \sqrt[4]{\sin ^{13}(x) \cos ^{11}(x)}}","\frac{4 \sin ^5(x) \cos (x)}{7 \sqrt[4]{\sin ^{13}(x) \cos ^{11}(x)}}-\frac{4 \sin (x) \cos ^5(x)}{9 \sqrt[4]{\sin ^{13}(x) \cos ^{11}(x)}}-\frac{8 \sin ^3(x) \cos ^3(x)}{\sqrt[4]{\sin ^{13}(x) \cos ^{11}(x)}}",1,"(-4*Cos[x]*(15 + 8*Cos[2*x] - 16*Cos[4*x])*Sin[x])/(63*(Cos[x]^11*Sin[x]^13)^(1/4))","A",1
416,1,105,108,0.2754329,"\int \frac{\cos (2 x)-\sqrt{\sin (2 x)}}{\sqrt{\cos ^3(x) \sin (x)}} \, dx","Integrate[(Cos[2*x] - Sqrt[Sin[2*x]])/Sqrt[Cos[x]^3*Sin[x]],x]","\frac{-4 \sin (x) \cos ^3(x) \, _2F_1\left(\frac{3}{4},\frac{3}{4};\frac{7}{4};\cos ^2(x)\right)-3 \sqrt[4]{\sin ^2(x)} \cos (x) \left(2 \sin (x)+\sqrt{\sin (2 x)} \left(\log \left(\sin \left(\frac{x}{2}\right)+\cos \left(\frac{x}{2}\right)\right)-\log \left(\cos \left(\frac{x}{2}\right)-\sin \left(\frac{x}{2}\right)\right)\right)\right)}{3 \sqrt[4]{\sin ^2(x)} \sqrt{\sin (x) \cos ^3(x)}}","-\frac{\sqrt{\sin (2 x)} \cos (x) \sin ^{-1}(\cos (x)-\sin (x))}{\sqrt{\sin (x) \cos ^3(x)}}-\frac{\sin (2 x)}{\sqrt{\sin (x) \cos ^3(x)}}-\frac{\sqrt{\sin (2 x)} \cos (x) \tanh ^{-1}(\sin (x))}{\sqrt{\sin (x) \cos ^3(x)}}-\sqrt{2} \log \left(\sin (x)+\cos (x)-\sqrt{2} \sec (x) \sqrt{\sin (x) \cos ^3(x)}\right)",1,"(-4*Cos[x]^3*Hypergeometric2F1[3/4, 3/4, 7/4, Cos[x]^2]*Sin[x] - 3*Cos[x]*(Sin[x]^2)^(1/4)*(2*Sin[x] + (-Log[Cos[x/2] - Sin[x/2]] + Log[Cos[x/2] + Sin[x/2]])*Sqrt[Sin[2*x]]))/(3*Sqrt[Cos[x]^3*Sin[x]]*(Sin[x]^2)^(1/4))","C",1
417,1,385,364,11.3710102,"\int \frac{\sqrt{\cos (x) \sin ^3(x)}-2 \sin (2 x)}{-\sqrt{\cos ^3(x) \sin (x)}+\sqrt{\tan (x)}} \, dx","Integrate[(Sqrt[Cos[x]*Sin[x]^3] - 2*Sin[2*x])/(-Sqrt[Cos[x]^3*Sin[x]] + Sqrt[Tan[x]]),x]","\frac{4 \sqrt{2} \cos ^2(x)^{3/4} \tan ^{\frac{3}{2}}(x) \, _2F_1\left(\frac{3}{4},\frac{3}{4};\frac{7}{4};\frac{2 \sin ^2(x)}{\cos (2 x)+3}\right)}{3 (\cos (2 x)+3)^{3/4}}+\frac{4}{\sqrt{\tan (x)}}+4 \csc (x) \sec (x) \sqrt{\sin (x) \cos ^3(x)}-\frac{(1+i) \sec ^4\left(\frac{x}{2}\right) \sqrt{\sin (x) \cos ^3(x)} \left((4+4 i) \Pi \left(-i;\left.\sin ^{-1}\left(\sqrt{\tan \left(\frac{x}{2}\right)}\right)\right|-1\right)-(4+4 i) \Pi \left(i;\left.\sin ^{-1}\left(\sqrt{\tan \left(\frac{x}{2}\right)}\right)\right|-1\right)+\sqrt[4]{-1} \left(-\Pi \left(-\sqrt[4]{-1};\left.\sin ^{-1}\left(\sqrt{\tan \left(\frac{x}{2}\right)}\right)\right|-1\right)+\Pi \left(\sqrt[4]{-1};\left.\sin ^{-1}\left(\sqrt{\tan \left(\frac{x}{2}\right)}\right)\right|-1\right)-\Pi \left(-(-1)^{3/4};\left.\sin ^{-1}\left(\sqrt{\tan \left(\frac{x}{2}\right)}\right)\right|-1\right)+\Pi \left((-1)^{3/4};\left.\sin ^{-1}\left(\sqrt{\tan \left(\frac{x}{2}\right)}\right)\right|-1\right)\right)\right)}{\sqrt{\tan \left(\frac{x}{2}\right)} \left(\tan ^2\left(\frac{x}{2}\right)-1\right) \sqrt{\cos (x) \sec ^2\left(\frac{x}{2}\right)}}+\frac{1}{4} \sqrt{\tan (x)} \csc ^2(x) \left(2 \log (\tan (x))-\log \left(\tan ^2(x)+2\right)\right) \sqrt{\sin ^3(x) \cos (x)}-\frac{\cos (x) \csc \left(\frac{x}{2}\right) \sec \left(\frac{x}{2}\right) \sqrt{\sin ^3(x) \cos (x)} \left(-\log \left(\tan ^4\left(\frac{x}{2}\right)+1\right)-2 \log \left(\tan \left(\frac{x}{2}\right)\right)+4 \log \left(\sec ^2\left(\frac{x}{2}\right)\right)\right)}{8 \sqrt{\sin (x) \cos ^3(x)}}","-\sqrt[4]{2} \tan ^{-1}\left(\frac{\sqrt{2}-\tan (x)}{2^{3/4} \sqrt{\tan (x)}}\right)+\frac{4}{\sqrt{\tan (x)}}-\sqrt[4]{2} \coth ^{-1}\left(\frac{\tan (x)+\sqrt{2}}{2^{3/4} \sqrt{\tan (x)}}\right)-2 \sqrt{2} \tan ^{-1}\left(\frac{\cos (x) (\cos (x)-\sin (x))}{\sqrt{2} \sqrt{\sin (x) \cos ^3(x)}}\right)+\sqrt[4]{2} \tan ^{-1}\left(\frac{\cos (x) \left(\sqrt{2} \cos (x)-\sin (x)\right)}{2^{3/4} \sqrt{\sin (x) \cos ^3(x)}}\right)-2 \sqrt{2} \coth ^{-1}\left(\frac{\cos (x) (\sin (x)+\cos (x))}{\sqrt{2} \sqrt{\sin (x) \cos ^3(x)}}\right)+\sqrt[4]{2} \coth ^{-1}\left(\frac{\cos (x) \left(\sin (x)+\sqrt{2} \cos (x)\right)}{2^{3/4} \sqrt{\sin (x) \cos ^3(x)}}\right)+4 \csc (x) \sec (x) \sqrt{\sin (x) \cos ^3(x)}+\frac{1}{2} \csc ^2(x) \sec ^2(x) \log (\sin (x)) \sqrt{\sin (x) \cos ^3(x)} \sqrt{\sin ^3(x) \cos (x)}-\frac{1}{4} \sqrt{\tan (x)} \csc ^2(x) \log \left(\cos ^2(x)+1\right) \sqrt{\sin ^3(x) \cos (x)}+\frac{1}{4} \csc ^2(x) \sec ^2(x) \log \left(\cos ^2(x)+1\right) \sqrt{\sin (x) \cos ^3(x)} \sqrt{\sin ^3(x) \cos (x)}+\frac{1}{2} \sqrt{\tan (x)} \csc ^2(x) \log (\sin (x)) \sqrt{\sin ^3(x) \cos (x)}",1,"4*Csc[x]*Sec[x]*Sqrt[Cos[x]^3*Sin[x]] - (Cos[x]*Csc[x/2]*(4*Log[Sec[x/2]^2] - 2*Log[Tan[x/2]] - Log[1 + Tan[x/2]^4])*Sec[x/2]*Sqrt[Cos[x]*Sin[x]^3])/(8*Sqrt[Cos[x]^3*Sin[x]]) - ((1 + I)*((4 + 4*I)*EllipticPi[-I, ArcSin[Sqrt[Tan[x/2]]], -1] - (4 + 4*I)*EllipticPi[I, ArcSin[Sqrt[Tan[x/2]]], -1] + (-1)^(1/4)*(-EllipticPi[-(-1)^(1/4), ArcSin[Sqrt[Tan[x/2]]], -1] + EllipticPi[(-1)^(1/4), ArcSin[Sqrt[Tan[x/2]]], -1] - EllipticPi[-(-1)^(3/4), ArcSin[Sqrt[Tan[x/2]]], -1] + EllipticPi[(-1)^(3/4), ArcSin[Sqrt[Tan[x/2]]], -1]))*Sec[x/2]^4*Sqrt[Cos[x]^3*Sin[x]])/(Sqrt[Cos[x]*Sec[x/2]^2]*Sqrt[Tan[x/2]]*(-1 + Tan[x/2]^2)) + 4/Sqrt[Tan[x]] + (Csc[x]^2*(2*Log[Tan[x]] - Log[2 + Tan[x]^2])*Sqrt[Cos[x]*Sin[x]^3]*Sqrt[Tan[x]])/4 + (4*Sqrt[2]*(Cos[x]^2)^(3/4)*Hypergeometric2F1[3/4, 3/4, 7/4, (2*Sin[x]^2)/(3 + Cos[2*x])]*Tan[x]^(3/2))/(3*(3 + Cos[2*x])^(3/4))","C",0
418,1,58,125,0.3451428,"\int \frac{-3 \tan (x)+\sqrt[3]{\sec ^6(x) \tan (x)}}{\left(\cos ^5(x) \sin (x)\right)^{2/3}} \, dx","Integrate[(-3*Tan[x] + (Sec[x]^6*Tan[x])^(1/3))/(Cos[x]^5*Sin[x])^(2/3),x]","-\frac{3 \sin (x) \left(924 \sin (x)+252 \sin (3 x)-5 (158 \cos (x)+57 \cos (3 x)+9 \cos (5 x)) \sqrt[3]{\tan (x) \sec ^6(x)}\right)}{2240 \left(\sin (x) \cos ^5(x)\right)^{2/3}}","-\frac{9 \sin ^4(x)}{10 \left(\sin (x) \cos ^5(x)\right)^{2/3}}-\frac{9}{4} \sec ^8(x) \left(\sin (x) \cos ^5(x)\right)^{4/3}+\frac{3}{14} \tan ^4(x) \sqrt[3]{\sin (x) \cos ^5(x)} \sqrt[3]{\tan (x) \sec ^6(x)}+\frac{3}{4} \tan ^2(x) \sqrt[3]{\sin (x) \cos ^5(x)} \sqrt[3]{\tan (x) \sec ^6(x)}+\frac{3}{2} \sqrt[3]{\sin (x) \cos ^5(x)} \sqrt[3]{\tan (x) \sec ^6(x)}",1,"(-3*Sin[x]*(924*Sin[x] + 252*Sin[3*x] - 5*(158*Cos[x] + 57*Cos[3*x] + 9*Cos[5*x])*(Sec[x]^6*Tan[x])^(1/3)))/(2240*(Cos[x]^5*Sin[x])^(2/3))","A",1
419,1,61,73,0.1172426,"\int \left(1+2 \cos ^2(x)\right)^{5/2} \sin (x) \, dx","Integrate[(1 + 2*Cos[x]^2)^(5/2)*Sin[x],x]","\frac{1}{96} \left(-2 \sqrt{\cos (2 x)+2} (92 \cos (x)+23 \cos (3 x)+2 \cos (5 x))-15 \sqrt{2} \log \left(\sqrt{2} \cos (x)+\sqrt{\cos (2 x)+2}\right)\right)","-\frac{1}{6} \cos (x) \left(2 \cos ^2(x)+1\right)^{5/2}-\frac{5}{24} \cos (x) \left(2 \cos ^2(x)+1\right)^{3/2}-\frac{5}{16} \cos (x) \sqrt{2 \cos ^2(x)+1}-\frac{5 \sinh ^{-1}\left(\sqrt{2} \cos (x)\right)}{16 \sqrt{2}}",1,"(-2*Sqrt[2 + Cos[2*x]]*(92*Cos[x] + 23*Cos[3*x] + 2*Cos[5*x]) - 15*Sqrt[2]*Log[Sqrt[2]*Cos[x] + Sqrt[2 + Cos[2*x]]])/96","A",1
420,1,48,69,0.0695442,"\int \cos (x) \left(5 \cos ^2(x)+\sin ^2(x)\right)^{5/2} \, dx","Integrate[Cos[x]*(5*Cos[x]^2 + Sin[x]^2)^(5/2),x]","\frac{1}{96} \left(1875 \sin ^{-1}\left(\frac{2 \sin (x)}{\sqrt{5}}\right)+2 (515 \sin (x)+90 \sin (3 x)+8 \sin (5 x)) \sqrt{2 \cos (2 x)+3}\right)","\frac{625}{32} \sin ^{-1}\left(\frac{2 \sin (x)}{\sqrt{5}}\right)+\frac{1}{6} \sin (x) \left(5-4 \sin ^2(x)\right)^{5/2}+\frac{25}{24} \sin (x) \left(5-4 \sin ^2(x)\right)^{3/2}+\frac{125}{16} \sin (x) \sqrt{5-4 \sin ^2(x)}",1,"(1875*ArcSin[(2*Sin[x])/Sqrt[5]] + 2*Sqrt[3 + 2*Cos[2*x]]*(515*Sin[x] + 90*Sin[3*x] + 8*Sin[5*x]))/96","A",1
421,1,61,58,0.07223,"\int \cos (x) \left(-\cos ^2(x)-5 \sin ^2(x)\right)^{3/2} \, dx","Integrate[Cos[x]*(-Cos[x]^2 - 5*Sin[x]^2)^(3/2),x]","\frac{\sqrt{2 \cos (2 x)-3} \left(2 (2 \sin (3 x)-11 \sin (x)) \sqrt{3-2 \cos (2 x)}-3 \sinh ^{-1}(2 \sin (x))\right)}{16 \sqrt{4 \sin ^2(x)+1}}","\frac{1}{4} \sin (x) \left(-4 \sin ^2(x)-1\right)^{3/2}-\frac{3}{8} \sin (x) \sqrt{-4 \sin ^2(x)-1}+\frac{3}{16} \tan ^{-1}\left(\frac{2 \sin (x)}{\sqrt{-4 \sin ^2(x)-1}}\right)",1,"(Sqrt[-3 + 2*Cos[2*x]]*(-3*ArcSinh[2*Sin[x]] + 2*Sqrt[3 - 2*Cos[2*x]]*(-11*Sin[x] + 2*Sin[3*x])))/(16*Sqrt[1 + 4*Sin[x]^2])","A",1
422,1,37,55,0.0853669,"\int \frac{\sin (x)}{\left(5 \cos ^2(x)-2 \sin ^2(x)\right)^{7/2}} \, dx","Integrate[Sin[x]/(5*Cos[x]^2 - 2*Sin[x]^2)^(7/2),x]","\frac{\cos (x) (56 \cos (2 x)+49 \cos (4 x)+67)}{15 \sqrt{2} (7 \cos (2 x)+3)^{5/2}}","\frac{\cos (x)}{15 \sqrt{7 \cos ^2(x)-2}}-\frac{\cos (x)}{15 \left(7 \cos ^2(x)-2\right)^{3/2}}+\frac{\cos (x)}{10 \left(7 \cos ^2(x)-2\right)^{5/2}}",1,"(Cos[x]*(67 + 56*Cos[2*x] + 49*Cos[4*x]))/(15*Sqrt[2]*(3 + 7*Cos[2*x])^(5/2))","A",1
423,1,39,39,0.0947724,"\int \frac{\cos (x) \cos (2 x)}{\left(2-5 \sin ^2(x)\right)^{3/2}} \, dx","Integrate[(Cos[x]*Cos[2*x])/(2 - 5*Sin[x]^2)^(3/2),x]","\frac{1}{50} \left(4 \sqrt{5} \sin ^{-1}\left(\sqrt{\frac{5}{2}} \sin (x)\right)+\frac{5 \sin (x)}{\sqrt{2-5 \sin ^2(x)}}\right)","\frac{2 \sin ^{-1}\left(\sqrt{\frac{5}{2}} \sin (x)\right)}{5 \sqrt{5}}+\frac{\sin (x)}{10 \sqrt{2-5 \sin ^2(x)}}",1,"(4*Sqrt[5]*ArcSin[Sqrt[5/2]*Sin[x]] + (5*Sin[x])/Sqrt[2 - 5*Sin[x]^2])/50","A",1
424,1,63,48,0.291926,"\int \frac{\sin (5 x)}{\left(5 \cos ^2(x)+9 \sin ^2(x)\right)^{5/2}} \, dx","Integrate[Sin[5*x]/(5*Cos[x]^2 + 9*Sin[x]^2)^(5/2),x]","\frac{2550 \cos (x)-590 \cos (3 x)+243 i (7-2 \cos (2 x))^{3/2} \log \left(\sqrt{7-2 \cos (2 x)}+2 i \cos (x)\right)}{486 (7-2 \cos (2 x))^{3/2}}","\frac{295 \cos (x)}{243 \sqrt{9-4 \cos ^2(x)}}-\frac{55 \cos (x)}{27 \left(9-4 \cos ^2(x)\right)^{3/2}}-\frac{1}{2} \sin ^{-1}\left(\frac{2 \cos (x)}{3}\right)",1,"(2550*Cos[x] - 590*Cos[3*x] + (243*I)*(7 - 2*Cos[2*x])^(3/2)*Log[(2*I)*Cos[x] + Sqrt[7 - 2*Cos[2*x]]])/(486*(7 - 2*Cos[2*x])^(3/2))","C",1
425,1,28,49,0.0851852,"\int \frac{\cos (x) \cos (2 x) \sin (3 x)}{\left(-5+4 \sin ^2(x)\right)^{5/2}} \, dx","Integrate[(Cos[x]*Cos[2*x]*Sin[3*x])/(-5 + 4*Sin[x]^2)^(5/2),x]","\frac{11 \cos (2 x)+\cos (4 x)+12}{4 \left(4 \sin ^2(x)-5\right)^{3/2}}","\frac{1}{8} \sqrt{4 \sin ^2(x)-5}-\frac{5}{8 \sqrt{4 \sin ^2(x)-5}}-\frac{1}{4 \left(4 \sin ^2(x)-5\right)^{3/2}}",1,"(12 + 11*Cos[2*x] + Cos[4*x])/(4*(-5 + 4*Sin[x]^2)^(3/2))","A",1
426,1,338,111,2.3172149,"\int \frac{\csc ^2(x) \left(-2 \cos ^3(x) (-1+\sin (x))+\cos (2 x) \sin (x)\right)}{\sqrt{-5+\sin ^2(x)}} \, dx","Integrate[(Csc[x]^2*(-2*Cos[x]^3*(-1 + Sin[x]) + Cos[2*x]*Sin[x]))/Sqrt[-5 + Sin[x]^2],x]","\frac{(16-32 i) \sqrt{5} \sqrt{\frac{(1+2 i) (\cos (x)-2 i)}{\cos (x)+1}} \sqrt{\frac{(1-2 i) (\cos (x)+2 i)}{\cos (x)+1}} \cos ^2\left(\frac{x}{2}\right) \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{(1+2 i) \tan \left(\frac{x}{2}\right)}{\sqrt{5}}\right),-\frac{7}{25}+\frac{24 i}{25}\right)-(32-64 i) \sqrt{5} \sqrt{\frac{(1+2 i) (\cos (x)-2 i)}{\cos (x)+1}} \sqrt{\frac{(1-2 i) (\cos (x)+2 i)}{\cos (x)+1}} \cos ^2\left(\frac{x}{2}\right) \Pi \left(\frac{3}{5}+\frac{4 i}{5};\sin ^{-1}\left(\frac{(1+2 i) \tan \left(\frac{x}{2}\right)}{\sqrt{5}}\right)|-\frac{7}{25}+\frac{24 i}{25}\right)-5 \left(18 \csc (x)+10 i \sqrt{2} \sqrt{-\cos (2 x)-9} \log \left(\sqrt{-\cos (2 x)-9}+i \sqrt{2} \cos (x)\right)+\sqrt{10} \sqrt{-\cos (2 x)-9} \tan ^{-1}\left(\frac{\sqrt{10} \cos (x)}{\sqrt{-\cos (2 x)-9}}\right)+2 \sqrt{10} \sqrt{-\cos (2 x)-9} \tan ^{-1}\left(\frac{\sqrt{-\cos (2 x)-9}}{\sqrt{10}}\right)+2 \cos (2 x) \csc (x)+5 \sin (3 x) \csc (x)+85\right)}{25 \sqrt{2} \sqrt{-\cos (2 x)-9}}","2 \sqrt{\sin ^2(x)-5}-\frac{2 \tan ^{-1}\left(\frac{\sqrt{\sin ^2(x)-5}}{\sqrt{5}}\right)}{\sqrt{5}}-2 \tanh ^{-1}\left(\frac{\sin (x)}{\sqrt{\sin ^2(x)-5}}\right)+\frac{2}{5} \sqrt{\sin ^2(x)-5} \csc (x)+2 \tan ^{-1}\left(\frac{\cos (x)}{\sqrt{\sin ^2(x)-5}}\right)-\frac{\tan ^{-1}\left(\frac{\sqrt{5} \cos (x)}{\sqrt{\sin ^2(x)-5}}\right)}{\sqrt{5}}",1,"((16 - 32*I)*Sqrt[5]*Cos[x/2]^2*Sqrt[((1 + 2*I)*(-2*I + Cos[x]))/(1 + Cos[x])]*Sqrt[((1 - 2*I)*(2*I + Cos[x]))/(1 + Cos[x])]*EllipticF[ArcSin[((1 + 2*I)*Tan[x/2])/Sqrt[5]], -7/25 + (24*I)/25] - (32 - 64*I)*Sqrt[5]*Cos[x/2]^2*Sqrt[((1 + 2*I)*(-2*I + Cos[x]))/(1 + Cos[x])]*Sqrt[((1 - 2*I)*(2*I + Cos[x]))/(1 + Cos[x])]*EllipticPi[3/5 + (4*I)/5, ArcSin[((1 + 2*I)*Tan[x/2])/Sqrt[5]], -7/25 + (24*I)/25] - 5*(85 + Sqrt[10]*ArcTan[(Sqrt[10]*Cos[x])/Sqrt[-9 - Cos[2*x]]]*Sqrt[-9 - Cos[2*x]] + 2*Sqrt[10]*ArcTan[Sqrt[-9 - Cos[2*x]]/Sqrt[10]]*Sqrt[-9 - Cos[2*x]] + 18*Csc[x] + 2*Cos[2*x]*Csc[x] + (10*I)*Sqrt[2]*Sqrt[-9 - Cos[2*x]]*Log[I*Sqrt[2]*Cos[x] + Sqrt[-9 - Cos[2*x]]] + 5*Csc[x]*Sin[3*x]))/(25*Sqrt[2]*Sqrt[-9 - Cos[2*x]])","C",1
427,1,156,112,0.335013,"\int \frac{\cos (3 x)}{-\sqrt{-1+8 \cos ^2(x)}+\sqrt{3 \cos ^2(x)-\sin ^2(x)}} \, dx","Integrate[Cos[3*x]/(-Sqrt[-1 + 8*Cos[x]^2] + Sqrt[3*Cos[x]^2 - Sin[x]^2]),x]","\frac{1}{8} \left(5 \sqrt{2} \sin ^{-1}\left(2 \sqrt{\frac{2}{7}} \sin (x)\right)+6 \sin ^{-1}\left(\frac{2 \sin (x)}{\sqrt{3}}\right)-4 \sin (x) \sqrt{2 \cos (2 x)+1}-4 \sin (x) \sqrt{4 \cos (2 x)+3}+3 \tan ^{-1}\left(\frac{7-8 \sin (x)}{\sqrt{4 \cos (2 x)+3}}\right)+3 \tan ^{-1}\left(\frac{3-4 \sin (x)}{\sqrt{2 \cos (2 x)+1}}\right)-3 \tan ^{-1}\left(\frac{4 \sin (x)+3}{\sqrt{2 \cos (2 x)+1}}\right)-3 \tan ^{-1}\left(\frac{8 \sin (x)+7}{\sqrt{4 \cos (2 x)+3}}\right)\right)","\frac{5 \sin ^{-1}\left(2 \sqrt{\frac{2}{7}} \sin (x)\right)}{4 \sqrt{2}}+\frac{3}{4} \sin ^{-1}\left(\frac{2 \sin (x)}{\sqrt{3}}\right)-\frac{1}{2} \sin (x) \sqrt{4 \cos ^2(x)-1}-\frac{1}{2} \sin (x) \sqrt{8 \cos ^2(x)-1}-\frac{3}{4} \tan ^{-1}\left(\frac{\sin (x)}{\sqrt{4 \cos ^2(x)-1}}\right)-\frac{3}{4} \tan ^{-1}\left(\frac{\sin (x)}{\sqrt{8 \cos ^2(x)-1}}\right)",1,"(5*Sqrt[2]*ArcSin[2*Sqrt[2/7]*Sin[x]] + 6*ArcSin[(2*Sin[x])/Sqrt[3]] + 3*ArcTan[(7 - 8*Sin[x])/Sqrt[3 + 4*Cos[2*x]]] + 3*ArcTan[(3 - 4*Sin[x])/Sqrt[1 + 2*Cos[2*x]]] - 3*ArcTan[(3 + 4*Sin[x])/Sqrt[1 + 2*Cos[2*x]]] - 3*ArcTan[(7 + 8*Sin[x])/Sqrt[3 + 4*Cos[2*x]]] - 4*Sqrt[1 + 2*Cos[2*x]]*Sin[x] - 4*Sqrt[3 + 4*Cos[2*x]]*Sin[x])/8","A",1
428,1,29,33,0.0368837,"\int \left(2-3 \sin ^2(x)\right)^{3/5} \sin (4 x) \, dx","Integrate[(2 - 3*Sin[x]^2)^(3/5)*Sin[4*x],x]","-\frac{5 (3 \cos (2 x)+1)^{8/5} (24 \cos (2 x)-5)}{936\ 2^{3/5}}","\frac{5}{36} \left(2-3 \sin ^2(x)\right)^{8/5}-\frac{20}{117} \left(2-3 \sin ^2(x)\right)^{13/5}",1,"(-5*(1 + 3*Cos[2*x])^(8/5)*(-5 + 24*Cos[2*x]))/(936*2^(3/5))","A",1
429,1,32,33,0.0170807,"\int \cos (x) \sqrt{\cos (2 x)} \, dx","Integrate[Cos[x]*Sqrt[Cos[2*x]],x]","\frac{1}{4} \left(\sqrt{2} \sin ^{-1}\left(\sqrt{2} \sin (x)\right)+2 \sin (x) \sqrt{\cos (2 x)}\right)","\frac{\sin ^{-1}\left(\sqrt{2} \sin (x)\right)}{2 \sqrt{2}}+\frac{1}{2} \sin (x) \sqrt{\cos (2 x)}",1,"(Sqrt[2]*ArcSin[Sqrt[2]*Sin[x]] + 2*Sqrt[Cos[2*x]]*Sin[x])/4","A",1
430,1,49,55,0.0934702,"\int \cos ^{\frac{3}{2}}(2 x) \sin (x) \, dx","Integrate[Cos[2*x]^(3/2)*Sin[x],x]","-\frac{1}{8} \sqrt{\cos (2 x)} (\cos (3 x)-2 \cos (x))-\frac{3 \log \left(\sqrt{2} \cos (x)+\sqrt{\cos (2 x)}\right)}{8 \sqrt{2}}","-\frac{1}{4} \cos (x) \cos ^{\frac{3}{2}}(2 x)+\frac{3}{8} \cos (x) \sqrt{\cos (2 x)}-\frac{3 \tanh ^{-1}\left(\frac{\sqrt{2} \cos (x)}{\sqrt{\cos (2 x)}}\right)}{8 \sqrt{2}}",1,"-1/8*(Sqrt[Cos[2*x]]*(-2*Cos[x] + Cos[3*x])) - (3*Log[Sqrt[2]*Cos[x] + Sqrt[Cos[2*x]]])/(8*Sqrt[2])","A",1
431,1,16,16,0.033019,"\int \frac{\sin (x)}{\cos ^{\frac{5}{2}}(2 x)} \, dx","Integrate[Sin[x]/Cos[2*x]^(5/2),x]","-\frac{\cos (3 x)}{3 \cos ^{\frac{3}{2}}(2 x)}","-\frac{\cos (3 x)}{3 \cos ^{\frac{3}{2}}(2 x)}",1,"-1/3*Cos[3*x]/Cos[2*x]^(3/2)","A",1
432,1,49,49,0.088312,"\int \cos ^{\frac{3}{2}}(2 x) \sec ^3(x) \, dx","Integrate[Cos[2*x]^(3/2)*Sec[x]^3,x]","\frac{1}{2} \left(4 \sqrt{2} \sin ^{-1}\left(\sqrt{2} \sin (x)\right)-5 \tan ^{-1}\left(\frac{\sin (x)}{\sqrt{\cos (2 x)}}\right)-\sqrt{\cos (2 x)} \tan (x) \sec (x)\right)","2 \sqrt{2} \sin ^{-1}\left(\sqrt{2} \sin (x)\right)-\frac{5}{2} \tan ^{-1}\left(\frac{\sin (x)}{\sqrt{\cos (2 x)}}\right)-\frac{1}{2} \sqrt{\cos (2 x)} \tan (x) \sec (x)",1,"(4*Sqrt[2]*ArcSin[Sqrt[2]*Sin[x]] - 5*ArcTan[Sin[x]/Sqrt[Cos[2*x]]] - Sqrt[Cos[2*x]]*Sec[x]*Tan[x])/2","A",1
433,1,62,87,0.1985278,"\int \frac{\sin ^2(x) \left(3 \sin ^3(x)-\cos (x) \sin (4 x)\right)}{\cos ^{\frac{7}{2}}(2 x)} \, dx","Integrate[(Sin[x]^2*(3*Sin[x]^3 - Cos[x]*Sin[4*x]))/Cos[2*x]^(7/2),x]","\frac{250 \cos (x)+45 \cos (3 x)+169 \cos (5 x)-120 \sqrt{2} \cos ^{\frac{5}{2}}(2 x) \log \left(\sqrt{2} \cos (x)+\sqrt{\cos (2 x)}\right)}{240 \cos ^{\frac{5}{2}}(2 x)}","-\frac{11 \cos (x)}{20 \cos ^{\frac{3}{2}}(2 x)}-\frac{2 \cos ^3(x)}{3 \cos ^{\frac{3}{2}}(2 x)}+\frac{63 \cos (x)}{20 \sqrt{\cos (2 x)}}+\frac{3 \sin ^2(x) \cos (x)}{10 \cos ^{\frac{5}{2}}(2 x)}-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \cos (x)}{\sqrt{\cos (2 x)}}\right)}{\sqrt{2}}",1,"(250*Cos[x] + 45*Cos[3*x] + 169*Cos[5*x] - 120*Sqrt[2]*Cos[2*x]^(5/2)*Log[Sqrt[2]*Cos[x] + Sqrt[Cos[2*x]]])/(240*Cos[2*x]^(5/2))","A",1
434,1,115,68,0.1998824,"\int \left(4-5 \sec ^2(x)\right)^{3/2} \, dx","Integrate[(4 - 5*Sec[x]^2)^(3/2),x]","-\frac{\left(4 \cos ^2(x)-5\right) \sec (x) \sqrt{4-5 \sec ^2(x)} \left(5 \sin (x) \sqrt{2 \cos (2 x)-3}+16 i \cos ^2(x) \log \left(\sqrt{2 \cos (2 x)-3}+2 i \sin (x)\right)+7 \sqrt{5} \cos ^2(x) \tan ^{-1}\left(\frac{\sqrt{5} \sin (x)}{\sqrt{2 \cos (2 x)-3}}\right)\right)}{2 (2 \cos (2 x)-3)^{3/2}}","-\frac{5}{2} \tan (x) \sqrt{-5 \tan ^2(x)-1}+8 \tan ^{-1}\left(\frac{2 \tan (x)}{\sqrt{-5 \tan ^2(x)-1}}\right)-\frac{7}{2} \sqrt{5} \tan ^{-1}\left(\frac{\sqrt{5} \tan (x)}{\sqrt{-5 \tan ^2(x)-1}}\right)",1,"-1/2*((-5 + 4*Cos[x]^2)*Sec[x]*Sqrt[4 - 5*Sec[x]^2]*(7*Sqrt[5]*ArcTan[(Sqrt[5]*Sin[x])/Sqrt[-3 + 2*Cos[2*x]]]*Cos[x]^2 + (16*I)*Cos[x]^2*Log[Sqrt[-3 + 2*Cos[2*x]] + (2*I)*Sin[x]] + 5*Sqrt[-3 + 2*Cos[2*x]]*Sin[x]))/(-3 + 2*Cos[2*x])^(3/2)","C",1
435,1,79,40,0.1180659,"\int \frac{1}{\left(4-5 \sec ^2(x)\right)^{3/2}} \, dx","Integrate[(4 - 5*Sec[x]^2)^(-3/2),x]","-\frac{(2 \cos (2 x)-3)^{3/2} \sec ^3(x) \left(10 \sin (x) \sqrt{3-2 \cos (2 x)}+(2 \cos (2 x)-3) \sinh ^{-1}(2 \sin (x))\right)}{8 \sqrt{-\left(4 \sin ^2(x)+1\right)^2} \left(4-5 \sec ^2(x)\right)^{3/2}}","\frac{1}{8} \tan ^{-1}\left(\frac{2 \tan (x)}{\sqrt{-5 \tan ^2(x)-1}}\right)-\frac{5 \tan (x)}{4 \sqrt{-5 \tan ^2(x)-1}}",1,"-1/8*((-3 + 2*Cos[2*x])^(3/2)*Sec[x]^3*(ArcSinh[2*Sin[x]]*(-3 + 2*Cos[2*x]) + 10*Sqrt[3 - 2*Cos[2*x]]*Sin[x]))/((4 - 5*Sec[x]^2)^(3/2)*Sqrt[-(1 + 4*Sin[x]^2)^2])","A",0
436,1,131,94,0.5241421,"\int \frac{-2 \cot ^2(x)+\sin (x)}{\left(1+5 \tan ^2(x)\right)^{3/2}} \, dx","Integrate[(-2*Cot[x]^2 + Sin[x])/(1 + 5*Tan[x]^2)^(3/2),x]","-\frac{\sin ^2(x) (2 \cos (2 x)-3)^{3/2} \tan (x) \left(2 \cot ^2(x) \csc (x)-1\right) \left(\sqrt{4 \sin ^2(x)+1} \left(16 \csc ^3(x)-3 \csc ^2(x)+164 \csc (x)-2\right)-2 \left(\csc ^2(x)+4\right) \sinh ^{-1}(2 \sin (x))\right)}{2 \sqrt{-(3-2 \cos (2 x))^2} \sqrt{5 \tan ^2(x)+1} \left(\cot ^2(x)+5\right) (-3 \sin (x)+\sin (3 x)+4 \cos (2 x)+4)}","-\frac{1}{8} \cos (x) \sqrt{5 \tan ^2(x)+1}-\frac{\cos (x)}{4 \sqrt{5 \tan ^2(x)+1}}-\frac{1}{4} \tanh ^{-1}\left(\frac{2 \tan (x)}{\sqrt{5 \tan ^2(x)+1}}\right)+\frac{9}{2} \sqrt{5 \tan ^2(x)+1} \cot (x)-\frac{5 \cot (x)}{2 \sqrt{5 \tan ^2(x)+1}}",1,"-1/2*((-3 + 2*Cos[2*x])^(3/2)*(-1 + 2*Cot[x]^2*Csc[x])*Sin[x]^2*(-2*ArcSinh[2*Sin[x]]*(4 + Csc[x]^2) + (-2 + 164*Csc[x] - 3*Csc[x]^2 + 16*Csc[x]^3)*Sqrt[1 + 4*Sin[x]^2])*Tan[x])/(Sqrt[-(3 - 2*Cos[2*x])^2]*(5 + Cot[x]^2)*(4 + 4*Cos[2*x] - 3*Sin[x] + Sin[3*x])*Sqrt[1 + 5*Tan[x]^2])","A",1
437,1,36,39,0.0760739,"\int \frac{(-3+\cos (2 x)) \sec ^4(x)}{\sqrt{4-\cot ^2(x)}} \, dx","Integrate[((-3 + Cos[2*x])*Sec[x]^4)/Sqrt[4 - Cot[x]^2],x]","\frac{(\cos (2 x)+3) (5 \cos (2 x)-3) \csc (x) \sec ^3(x)}{12 \sqrt{4-\cot ^2(x)}}","-\frac{1}{3} \tan ^3(x) \sqrt{4-\cot ^2(x)}-\frac{2}{3} \tan (x) \sqrt{4-\cot ^2(x)}",1,"((3 + Cos[2*x])*(-3 + 5*Cos[2*x])*Csc[x]*Sec[x]^3)/(12*Sqrt[4 - Cot[x]^2])","A",1
438,1,255,73,2.568161,"\int \frac{\left(3+\sin ^2(x)\right) \tan ^3(x)}{\left(-2+\cos ^2(x)\right) \left(5-4 \sec ^2(x)\right)^{3/2}} \, dx","Integrate[((3 + Sin[x]^2)*Tan[x]^3)/((-2 + Cos[x]^2)*(5 - 4*Sec[x]^2)^(3/2)),x]","\frac{15 \sin ^2(x) \sqrt{15 \cos (2 x)-9} \tanh ^{-1}\left(\frac{\sqrt{5 \cos (2 x)-3}}{\sqrt{6} \sqrt{\cos ^2(x)}}\right)-2 \left(15 \sqrt{2} \sqrt{\sin ^2(x)} \sqrt{\sin ^2(2 x)}+9 \sqrt{5} \sin ^2(x) \sqrt{5 \cos (2 x)-3} \left(\log \left(10 \sin ^2(x)\right)-\log \left(5 \left(\sqrt{10} \sqrt{\sin ^2(x)} \sqrt{\sin ^2(2 x)}+\sqrt{5 \cos (2 x)-3} \cos (2 x)-\sqrt{5 \cos (2 x)-3}\right)\right)\right)+10 \sqrt{\sin ^2(x)} \sqrt{\sin ^2(2 x)} \sqrt{15 \cos (2 x)-9} \sec (x) \tanh ^{-1}\left(\frac{\sqrt{6} \cos (x)}{\sqrt{5 \cos (2 x)-3}}\right)\right)}{225 \sqrt{\sin ^2(x)} \sqrt{\sin ^2(2 x)} \sqrt{10-8 \sec ^2(x)}}","-\frac{2}{15 \sqrt{5-4 \sec ^2(x)}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{5-4 \sec ^2(x)}}{\sqrt{3}}\right)}{6 \sqrt{3}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{5-4 \sec ^2(x)}}{\sqrt{5}}\right)}{5 \sqrt{5}}",1,"(15*ArcTanh[Sqrt[-3 + 5*Cos[2*x]]/(Sqrt[6]*Sqrt[Cos[x]^2])]*Sqrt[-9 + 15*Cos[2*x]]*Sin[x]^2 - 2*(9*Sqrt[5]*Sqrt[-3 + 5*Cos[2*x]]*(Log[10*Sin[x]^2] - Log[5*(-Sqrt[-3 + 5*Cos[2*x]] + Cos[2*x]*Sqrt[-3 + 5*Cos[2*x]] + Sqrt[10]*Sqrt[Sin[x]^2]*Sqrt[Sin[2*x]^2])])*Sin[x]^2 + 15*Sqrt[2]*Sqrt[Sin[x]^2]*Sqrt[Sin[2*x]^2] + 10*ArcTanh[(Sqrt[6]*Cos[x])/Sqrt[-3 + 5*Cos[2*x]]]*Sqrt[-9 + 15*Cos[2*x]]*Sec[x]*Sqrt[Sin[x]^2]*Sqrt[Sin[2*x]^2]))/(225*Sqrt[10 - 8*Sec[x]^2]*Sqrt[Sin[x]^2]*Sqrt[Sin[2*x]^2])","B",0
439,1,116,57,0.9230737,"\int \frac{\csc ^2(x) \left(\sec ^2(x)-3 \tan (x) \sqrt{4 \sec ^2(x)+5 \tan ^2(x)}\right)}{\left(4 \sec ^2(x)+5 \tan ^2(x)\right)^{3/2}} \, dx","Integrate[(Csc[x]^2*(Sec[x]^2 - 3*Tan[x]*Sqrt[4*Sec[x]^2 + 5*Tan[x]^2]))/(4*Sec[x]^2 + 5*Tan[x]^2)^(3/2),x]","\frac{-5 \tan (x)+5 \cot (x)-9 \csc (x) \sec (x)-6 \sqrt{2} \log \left(\tan \left(\frac{x}{2}\right)\right) \sqrt{5 \tan ^2(x)+13 \sec ^2(x)-5}+6 \sqrt{\frac{13-5 \cos (2 x)}{\cos (2 x)+1}} \log \left(\tan ^4\left(\frac{x}{2}\right)+7 \tan ^2\left(\frac{x}{2}\right)+1\right)}{16 \sqrt{\frac{13-5 \cos (2 x)}{\cos (2 x)+1}}}","-\frac{7 \tan (x)}{8 \sqrt{9 \tan ^2(x)+4}}+\frac{3}{8} \log \left(9 \tan ^2(x)+4\right)-\frac{3}{4} \log (\tan (x))-\frac{\cot (x)}{4 \sqrt{9 \tan ^2(x)+4}}",1,"(5*Cot[x] + 6*Sqrt[(13 - 5*Cos[2*x])/(1 + Cos[2*x])]*Log[1 + 7*Tan[x/2]^2 + Tan[x/2]^4] - 9*Csc[x]*Sec[x] - 5*Tan[x] - 6*Sqrt[2]*Log[Tan[x/2]]*Sqrt[-5 + 13*Sec[x]^2 + 5*Tan[x]^2])/(16*Sqrt[(13 - 5*Cos[2*x])/(1 + Cos[2*x])])","B",1
440,1,49,66,0.069364,"\int \tan (x) \left(1+5 \tan ^2(x)\right)^{5/2} \, dx","Integrate[Tan[x]*(1 + 5*Tan[x]^2)^(5/2),x]","\frac{5 \sqrt{5} \left(5 \tan ^2(x)+1\right)^{5/2} \, _2F_1\left(-\frac{5}{2},-\frac{5}{2};-\frac{3}{2};\frac{4 \cos ^2(x)}{5}\right)}{(3-2 \cos (2 x))^{5/2}}","\frac{1}{5} \left(5 \tan ^2(x)+1\right)^{5/2}-\frac{4}{3} \left(5 \tan ^2(x)+1\right)^{3/2}+16 \sqrt{5 \tan ^2(x)+1}-32 \tan ^{-1}\left(\frac{1}{2} \sqrt{5 \tan ^2(x)+1}\right)",1,"(5*Sqrt[5]*Hypergeometric2F1[-5/2, -5/2, -3/2, (4*Cos[x]^2)/5]*(1 + 5*Tan[x]^2)^(5/2))/(3 - 2*Cos[2*x])^(5/2)","C",1
441,1,71,54,0.4112117,"\int \frac{\tan (x)}{\left(1+5 \tan ^2(x)\right)^{5/2}} \, dx","Integrate[Tan[x]/(1 + 5*Tan[x]^2)^(5/2),x]","\frac{(2 \cos (2 x)-3) \sec ^5(x) \left(-6 \cos (x)+8 \cos (3 x)-3 (2 \cos (2 x)-3)^{3/2} \log \left(2 \cos (x)+\sqrt{2 \cos (2 x)-3}\right)\right)}{96 \left(5 \tan ^2(x)+1\right)^{5/2}}","\frac{1}{16 \sqrt{5 \tan ^2(x)+1}}-\frac{1}{12 \left(5 \tan ^2(x)+1\right)^{3/2}}+\frac{1}{32} \tan ^{-1}\left(\frac{1}{2} \sqrt{5 \tan ^2(x)+1}\right)",1,"((-3 + 2*Cos[2*x])*(-6*Cos[x] + 8*Cos[3*x] - 3*(-3 + 2*Cos[2*x])^(3/2)*Log[2*Cos[x] + Sqrt[-3 + 2*Cos[2*x]]])*Sec[x]^5)/(96*(1 + 5*Tan[x]^2)^(5/2))","A",1
442,1,105,133,0.1363423,"\int \frac{\tan (x)}{\sqrt[3]{a^3+b^3 \tan ^2(x)}} \, dx","Integrate[Tan[x]/(a^3 + b^3*Tan[x]^2)^(1/3),x]","\frac{2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{a^3+b^3 \tan ^2(x)}}{\sqrt[3]{a^3-b^3}}+1}{\sqrt{3}}\right)+3 \log \left(\sqrt[3]{a^3-b^3}-\sqrt[3]{a^3+b^3 \tan ^2(x)}\right)+2 \log (\cos (x))}{4 \sqrt[3]{a^3-b^3}}","\frac{\sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{a^3+b^3 \tan ^2(x)}}{\sqrt[3]{a^3-b^3}}+1}{\sqrt{3}}\right)}{2 \sqrt[3]{a^3-b^3}}+\frac{3 \log \left(\sqrt[3]{a^3-b^3}-\sqrt[3]{a^3+b^3 \tan ^2(x)}\right)}{4 \sqrt[3]{a^3-b^3}}+\frac{\log (\cos (x))}{2 \sqrt[3]{a^3-b^3}}",1,"(2*Sqrt[3]*ArcTan[(1 + (2*(a^3 + b^3*Tan[x]^2)^(1/3))/(a^3 - b^3)^(1/3))/Sqrt[3]] + 2*Log[Cos[x]] + 3*Log[(a^3 - b^3)^(1/3) - (a^3 + b^3*Tan[x]^2)^(1/3)])/(4*(a^3 - b^3)^(1/3))","A",1
443,1,42,69,0.0892366,"\int \tan (x) \left(1-7 \tan ^2(x)\right)^{2/3} \, dx","Integrate[Tan[x]*(1 - 7*Tan[x]^2)^(2/3),x]","-\frac{3}{4} \left(1-7 \tan ^2(x)\right)^{2/3} \left(\, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{1}{8} (4 \cos (2 x)-3) \sec ^2(x)\right)-1\right)","\frac{3}{4} \left(1-7 \tan ^2(x)\right)^{2/3}+2 \sqrt{3} \tan ^{-1}\left(\frac{\sqrt[3]{1-7 \tan ^2(x)}+1}{\sqrt{3}}\right)+3 \log \left(2-\sqrt[3]{1-7 \tan ^2(x)}\right)+2 \log (\cos (x))",1,"(-3*(-1 + Hypergeometric2F1[2/3, 1, 5/3, ((-3 + 4*Cos[2*x])*Sec[x]^2)/8])*(1 - 7*Tan[x]^2)^(2/3))/4","C",1
444,1,256,52,0.30127,"\int \frac{\cot (x)}{\sqrt[4]{a^4+b^4 \csc ^2(x)}} \, dx","Integrate[Cot[x]/(a^4 + b^4*Csc[x]^2)^(1/4),x]","\frac{\sqrt[4]{a^4 \cos (2 x)-a^4-2 b^4} \left(-2 \tan ^{-1}\left(1-\frac{\sqrt{2} a \sqrt{\sin (x)}}{\sqrt[4]{a^4 \left(-\sin ^2(x)\right)-b^4}}\right)+2 \tan ^{-1}\left(\frac{\sqrt{2} a \sqrt{\sin (x)}}{\sqrt[4]{a^4 \left(-\sin ^2(x)\right)-b^4}}+1\right)-\log \left(-\frac{\sqrt{2} a \sqrt{\sin (x)}}{\sqrt[4]{a^4 \left(-\sin ^2(x)\right)-b^4}}+\frac{a^2 \sin (x)}{\sqrt{a^4 \left(-\sin ^2(x)\right)-b^4}}+1\right)+\log \left(\frac{\sqrt{2} a \sqrt{\sin (x)}}{\sqrt[4]{a^4 \left(-\sin ^2(x)\right)-b^4}}+\frac{a^2 \sin (x)}{\sqrt{a^4 \left(-\sin ^2(x)\right)-b^4}}+1\right)\right)}{2\ 2^{3/4} a \sqrt{\sin (x)} \sqrt[4]{a^4+b^4 \csc ^2(x)}}","\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a^4+b^4 \csc ^2(x)}}{a}\right)}{a}-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a^4+b^4 \csc ^2(x)}}{a}\right)}{a}",1,"((-a^4 - 2*b^4 + a^4*Cos[2*x])^(1/4)*(-2*ArcTan[1 - (Sqrt[2]*a*Sqrt[Sin[x]])/(-b^4 - a^4*Sin[x]^2)^(1/4)] + 2*ArcTan[1 + (Sqrt[2]*a*Sqrt[Sin[x]])/(-b^4 - a^4*Sin[x]^2)^(1/4)] - Log[1 + (a^2*Sin[x])/Sqrt[-b^4 - a^4*Sin[x]^2] - (Sqrt[2]*a*Sqrt[Sin[x]])/(-b^4 - a^4*Sin[x]^2)^(1/4)] + Log[1 + (a^2*Sin[x])/Sqrt[-b^4 - a^4*Sin[x]^2] + (Sqrt[2]*a*Sqrt[Sin[x]])/(-b^4 - a^4*Sin[x]^2)^(1/4)]))/(2*2^(3/4)*a*(a^4 + b^4*Csc[x]^2)^(1/4)*Sqrt[Sin[x]])","B",1
445,1,245,54,0.2823365,"\int \frac{\cot (x)}{\sqrt[4]{a^4-b^4 \csc ^2(x)}} \, dx","Integrate[Cot[x]/(a^4 - b^4*Csc[x]^2)^(1/4),x]","\frac{\sqrt[4]{a^4 \cos (2 x)-a^4+2 b^4} \left(-2 \tan ^{-1}\left(1-\frac{\sqrt{2} a \sqrt{\sin (x)}}{\sqrt[4]{b^4-a^4 \sin ^2(x)}}\right)+2 \tan ^{-1}\left(\frac{\sqrt{2} a \sqrt{\sin (x)}}{\sqrt[4]{b^4-a^4 \sin ^2(x)}}+1\right)-\log \left(-\frac{\sqrt{2} a \sqrt{\sin (x)}}{\sqrt[4]{b^4-a^4 \sin ^2(x)}}+\frac{a^2 \sin (x)}{\sqrt{b^4-a^4 \sin ^2(x)}}+1\right)+\log \left(\frac{\sqrt{2} a \sqrt{\sin (x)}}{\sqrt[4]{b^4-a^4 \sin ^2(x)}}+\frac{a^2 \sin (x)}{\sqrt{b^4-a^4 \sin ^2(x)}}+1\right)\right)}{2\ 2^{3/4} a \sqrt{\sin (x)} \sqrt[4]{a^4-b^4 \csc ^2(x)}}","\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a^4-b^4 \csc ^2(x)}}{a}\right)}{a}-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a^4-b^4 \csc ^2(x)}}{a}\right)}{a}",1,"((-a^4 + 2*b^4 + a^4*Cos[2*x])^(1/4)*(-2*ArcTan[1 - (Sqrt[2]*a*Sqrt[Sin[x]])/(b^4 - a^4*Sin[x]^2)^(1/4)] + 2*ArcTan[1 + (Sqrt[2]*a*Sqrt[Sin[x]])/(b^4 - a^4*Sin[x]^2)^(1/4)] - Log[1 + (a^2*Sin[x])/Sqrt[b^4 - a^4*Sin[x]^2] - (Sqrt[2]*a*Sqrt[Sin[x]])/(b^4 - a^4*Sin[x]^2)^(1/4)] + Log[1 + (a^2*Sin[x])/Sqrt[b^4 - a^4*Sin[x]^2] + (Sqrt[2]*a*Sqrt[Sin[x]])/(b^4 - a^4*Sin[x]^2)^(1/4)]))/(2*2^(3/4)*a*(a^4 - b^4*Csc[x]^2)^(1/4)*Sqrt[Sin[x]])","B",1
446,1,4397,133,50.4430792,"\int \frac{\sec ^2(x) \tan (x) \left(\sqrt[3]{1-3 \sec ^2(x)} \sin ^2(x)+3 \tan ^2(x)\right)}{\left(1-3 \sec ^2(x)\right)^{5/6} \left(1-\sqrt{1-3 \sec ^2(x)}\right)} \, dx","Integrate[(Sec[x]^2*Tan[x]*((1 - 3*Sec[x]^2)^(1/3)*Sin[x]^2 + 3*Tan[x]^2))/((1 - 3*Sec[x]^2)^(5/6)*(1 - Sqrt[1 - 3*Sec[x]^2])),x]","\text{Result too large to show}","-\frac{1}{4} \left(1-3 \sec ^2(x)\right)^{2/3}-\sqrt[6]{1-3 \sec ^2(x)}+\frac{1}{2 \left(1-\sqrt{1-3 \sec ^2(x)}\right)}+\frac{1}{4} \log \left(\sec ^2(x)\right)-\frac{3}{2} \log \left(1-\sqrt[6]{1-3 \sec ^2(x)}\right)+\frac{1}{3} \log \left(1-\sqrt{1-3 \sec ^2(x)}\right)+\sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[6]{1-3 \sec ^2(x)}+1}{\sqrt{3}}\right)",1,"(-3*(6 + ((-5 + Cos[2*x])/(1 + Cos[2*x]))^(1/3) + Cos[2*x]*((-5 + Cos[2*x])/(1 + Cos[2*x]))^(1/3))*(3*Sec[x]^2 + (1 - 3*Sec[x]^2)^(1/3))*Sin[x]^2*Tan[x]*(-2 - 3*Tan[x]^2)^(5/6)*(1 + Tan[x]^2)*(2 + 3*Tan[x]^2)*(-8*AppellF1[1, 1/2, 1, 2, (-3*Tan[x]^2)/2, -Tan[x]^2] + 4*AppellF1[2, 1/2, 2, 3, (-3*Tan[x]^2)/2, -Tan[x]^2]*Tan[x]^2 + 3*AppellF1[2, 3/2, 1, 3, (-3*Tan[x]^2)/2, -Tan[x]^2]*Tan[x]^2)^2*((4*AppellF1[2, 1/2, 2, 3, (-3*Tan[x]^2)/2, -Tan[x]^2] + 3*AppellF1[2, 3/2, 1, 3, (-3*Tan[x]^2)/2, -Tan[x]^2])*Tan[x]^2*(30*3^(2/3)*Hypergeometric2F1[1/3, 1/3, 4/3, (3 + 3*Tan[x]^2)^(-1)]*Sqrt[-2 - 3*Tan[x]^2]*(1 + Tan[x]^2)*((2 + 3*Tan[x]^2)/(1 + Tan[x]^2))^(1/3) + 12*3^(1/6)*Hypergeometric2F1[5/6, 5/6, 11/6, (3 + 3*Tan[x]^2)^(-1)]*(1 + Tan[x]^2)*((2 + 3*Tan[x]^2)/(1 + Tan[x]^2))^(5/6) + 5*(2*Log[1 + Tan[x]^2]*(-2 - 3*Tan[x]^2)^(5/6)*(1 + Tan[x]^2) + 9*Tan[x]^4*(4 + Sqrt[-2 - 3*Tan[x]^2]) + 3*Tan[x]^2*(20 - 2*(-2 - 3*Tan[x]^2)^(1/3) + 5*Sqrt[-2 - 3*Tan[x]^2]) + 2*(12 - 2*(-2 - 3*Tan[x]^2)^(1/3) + 3*Sqrt[-2 - 3*Tan[x]^2] + (-2 - 3*Tan[x]^2)^(5/6)))) - 8*AppellF1[1, 1/2, 1, 2, (-3*Tan[x]^2)/2, -Tan[x]^2]*(30*3^(2/3)*Hypergeometric2F1[1/3, 1/3, 4/3, (3 + 3*Tan[x]^2)^(-1)]*Sqrt[-2 - 3*Tan[x]^2]*(1 + Tan[x]^2)*((2 + 3*Tan[x]^2)/(1 + Tan[x]^2))^(1/3) + 12*3^(1/6)*Hypergeometric2F1[5/6, 5/6, 11/6, (3 + 3*Tan[x]^2)^(-1)]*(1 + Tan[x]^2)*((2 + 3*Tan[x]^2)/(1 + Tan[x]^2))^(5/6) + 5*(2*Log[1 + Tan[x]^2]*(-2 - 3*Tan[x]^2)^(5/6)*(1 + Tan[x]^2) + 9*Tan[x]^4*(4 + Sqrt[-2 - 3*Tan[x]^2]) + Tan[x]^2*(60 - 7*(-2 - 3*Tan[x]^2)^(1/3) + 15*Sqrt[-2 - 3*Tan[x]^2]) + 2*(12 - 2*(-2 - 3*Tan[x]^2)^(1/3) + 3*Sqrt[-2 - 3*Tan[x]^2] + (-2 - 3*Tan[x]^2)^(5/6))))))/(10*2^(1/6)*(-1 + Sqrt[(-5 + Cos[2*x])/(1 + Cos[2*x])])*(1 - 3*Sec[x]^2)^(5/6)*(6 + (1 - 3*Sec[x]^2)^(1/3) + Cos[2*x]*(1 - 3*Sec[x]^2)^(1/3))*(-4 - 6*Tan[x]^2)^(5/6)*(-8*AppellF1[1, 1/2, 1, 2, (-3*Tan[x]^2)/2, -Tan[x]^2] + (4*AppellF1[2, 1/2, 2, 3, (-3*Tan[x]^2)/2, -Tan[x]^2] + 3*AppellF1[2, 3/2, 1, 3, (-3*Tan[x]^2)/2, -Tan[x]^2])*Tan[x]^2)*(1152*AppellF1[1, 1/2, 1, 2, (-3*Tan[x]^2)/2, -Tan[x]^2]^2*Tan[x]^3 + 2880*AppellF1[1, 1/2, 1, 2, (-3*Tan[x]^2)/2, -Tan[x]^2]^2*Tan[x]^5 - 1152*AppellF1[1, 1/2, 1, 2, (-3*Tan[x]^2)/2, -Tan[x]^2]*AppellF1[2, 1/2, 2, 3, (-3*Tan[x]^2)/2, -Tan[x]^2]*Tan[x]^5 - 864*AppellF1[1, 1/2, 1, 2, (-3*Tan[x]^2)/2, -Tan[x]^2]*AppellF1[2, 3/2, 1, 3, (-3*Tan[x]^2)/2, -Tan[x]^2]*Tan[x]^5 + 1728*AppellF1[1, 1/2, 1, 2, (-3*Tan[x]^2)/2, -Tan[x]^2]^2*Tan[x]^7 - 2880*AppellF1[1, 1/2, 1, 2, (-3*Tan[x]^2)/2, -Tan[x]^2]*AppellF1[2, 1/2, 2, 3, (-3*Tan[x]^2)/2, -Tan[x]^2]*Tan[x]^7 + 288*AppellF1[2, 1/2, 2, 3, (-3*Tan[x]^2)/2, -Tan[x]^2]^2*Tan[x]^7 - 2160*AppellF1[1, 1/2, 1, 2, (-3*Tan[x]^2)/2, -Tan[x]^2]*AppellF1[2, 3/2, 1, 3, (-3*Tan[x]^2)/2, -Tan[x]^2]*Tan[x]^7 + 432*AppellF1[2, 1/2, 2, 3, (-3*Tan[x]^2)/2, -Tan[x]^2]*AppellF1[2, 3/2, 1, 3, (-3*Tan[x]^2)/2, -Tan[x]^2]*Tan[x]^7 + 162*AppellF1[2, 3/2, 1, 3, (-3*Tan[x]^2)/2, -Tan[x]^2]^2*Tan[x]^7 - 1728*AppellF1[1, 1/2, 1, 2, (-3*Tan[x]^2)/2, -Tan[x]^2]*AppellF1[2, 1/2, 2, 3, (-3*Tan[x]^2)/2, -Tan[x]^2]*Tan[x]^9 + 720*AppellF1[2, 1/2, 2, 3, (-3*Tan[x]^2)/2, -Tan[x]^2]^2*Tan[x]^9 - 1296*AppellF1[1, 1/2, 1, 2, (-3*Tan[x]^2)/2, -Tan[x]^2]*AppellF1[2, 3/2, 1, 3, (-3*Tan[x]^2)/2, -Tan[x]^2]*Tan[x]^9 + 1080*AppellF1[2, 1/2, 2, 3, (-3*Tan[x]^2)/2, -Tan[x]^2]*AppellF1[2, 3/2, 1, 3, (-3*Tan[x]^2)/2, -Tan[x]^2]*Tan[x]^9 + 405*AppellF1[2, 3/2, 1, 3, (-3*Tan[x]^2)/2, -Tan[x]^2]^2*Tan[x]^9 + 432*AppellF1[2, 1/2, 2, 3, (-3*Tan[x]^2)/2, -Tan[x]^2]^2*Tan[x]^11 + 648*AppellF1[2, 1/2, 2, 3, (-3*Tan[x]^2)/2, -Tan[x]^2]*AppellF1[2, 3/2, 1, 3, (-3*Tan[x]^2)/2, -Tan[x]^2]*Tan[x]^11 + 243*AppellF1[2, 3/2, 1, 3, (-3*Tan[x]^2)/2, -Tan[x]^2]^2*Tan[x]^11 + 720*AppellF1[1, 1/2, 1, 2, (-3*Tan[x]^2)/2, -Tan[x]^2]^2*Tan[x]^3*(-2 - 3*Tan[x]^2)^(1/3) - 192*AppellF1[1, 1/2, 1, 2, (-3*Tan[x]^2)/2, -Tan[x]^2]*AppellF1[2, 1/2, 2, 3, (-3*Tan[x]^2)/2, -Tan[x]^2]*Tan[x]^3*(-2 - 3*Tan[x]^2)^(1/3) - 144*AppellF1[1, 1/2, 1, 2, (-3*Tan[x]^2)/2, -Tan[x]^2]*AppellF1[2, 3/2, 1, 3, (-3*Tan[x]^2)/2, -Tan[x]^2]*Tan[x]^3*(-2 - 3*Tan[x]^2)^(1/3) + 1008*AppellF1[1, 1/2, 1, 2, (-3*Tan[x]^2)/2, -Tan[x]^2]^2*Tan[x]^5*(-2 - 3*Tan[x]^2)^(1/3) - 1032*AppellF1[1, 1/2, 1, 2, (-3*Tan[x]^2)/2, -Tan[x]^2]*AppellF1[2, 1/2, 2, 3, (-3*Tan[x]^2)/2, -Tan[x]^2]*Tan[x]^5*(-2 - 3*Tan[x]^2)^(1/3) - 774*AppellF1[1, 1/2, 1, 2, (-3*Tan[x]^2)/2, -Tan[x]^2]*AppellF1[2, 3/2, 1, 3, (-3*Tan[x]^2)/2, -Tan[x]^2]*Tan[x]^5*(-2 - 3*Tan[x]^2)^(1/3) + 128*AppellF1[1, 1/2, 1, 2, (-3*Tan[x]^2)/2, -Tan[x]^2]*AppellF1[3, 1/2, 3, 4, (-3*Tan[x]^2)/2, -Tan[x]^2]*Tan[x]^5*(-2 - 3*Tan[x]^2)^(1/3) + 96*AppellF1[1, 1/2, 1, 2, (-3*Tan[x]^2)/2, -Tan[x]^2]*AppellF1[3, 3/2, 2, 4, (-3*Tan[x]^2)/2, -Tan[x]^2]*Tan[x]^5*(-2 - 3*Tan[x]^2)^(1/3) + 108*AppellF1[1, 1/2, 1, 2, (-3*Tan[x]^2)/2, -Tan[x]^2]*AppellF1[3, 5/2, 1, 4, (-3*Tan[x]^2)/2, -Tan[x]^2]*Tan[x]^5*(-2 - 3*Tan[x]^2)^(1/3) - 1080*AppellF1[1, 1/2, 1, 2, (-3*Tan[x]^2)/2, -Tan[x]^2]*AppellF1[2, 1/2, 2, 3, (-3*Tan[x]^2)/2, -Tan[x]^2]*Tan[x]^7*(-2 - 3*Tan[x]^2)^(1/3) + 96*AppellF1[2, 1/2, 2, 3, (-3*Tan[x]^2)/2, -Tan[x]^2]^2*Tan[x]^7*(-2 - 3*Tan[x]^2)^(1/3) - 810*AppellF1[1, 1/2, 1, 2, (-3*Tan[x]^2)/2, -Tan[x]^2]*AppellF1[2, 3/2, 1, 3, (-3*Tan[x]^2)/2, -Tan[x]^2]*Tan[x]^7*(-2 - 3*Tan[x]^2)^(1/3) + 144*AppellF1[2, 1/2, 2, 3, (-3*Tan[x]^2)/2, -Tan[x]^2]*AppellF1[2, 3/2, 1, 3, (-3*Tan[x]^2)/2, -Tan[x]^2]*Tan[x]^7*(-2 - 3*Tan[x]^2)^(1/3) + 54*AppellF1[2, 3/2, 1, 3, (-3*Tan[x]^2)/2, -Tan[x]^2]^2*Tan[x]^7*(-2 - 3*Tan[x]^2)^(1/3) + 320*AppellF1[1, 1/2, 1, 2, (-3*Tan[x]^2)/2, -Tan[x]^2]*AppellF1[3, 1/2, 3, 4, (-3*Tan[x]^2)/2, -Tan[x]^2]*Tan[x]^7*(-2 - 3*Tan[x]^2)^(1/3) + 240*AppellF1[1, 1/2, 1, 2, (-3*Tan[x]^2)/2, -Tan[x]^2]*AppellF1[3, 3/2, 2, 4, (-3*Tan[x]^2)/2, -Tan[x]^2]*Tan[x]^7*(-2 - 3*Tan[x]^2)^(1/3) + 270*AppellF1[1, 1/2, 1, 2, (-3*Tan[x]^2)/2, -Tan[x]^2]*AppellF1[3, 5/2, 1, 4, (-3*Tan[x]^2)/2, -Tan[x]^2]*Tan[x]^7*(-2 - 3*Tan[x]^2)^(1/3) + 144*AppellF1[2, 1/2, 2, 3, (-3*Tan[x]^2)/2, -Tan[x]^2]^2*Tan[x]^9*(-2 - 3*Tan[x]^2)^(1/3) + 216*AppellF1[2, 1/2, 2, 3, (-3*Tan[x]^2)/2, -Tan[x]^2]*AppellF1[2, 3/2, 1, 3, (-3*Tan[x]^2)/2, -Tan[x]^2]*Tan[x]^9*(-2 - 3*Tan[x]^2)^(1/3) + 81*AppellF1[2, 3/2, 1, 3, (-3*Tan[x]^2)/2, -Tan[x]^2]^2*Tan[x]^9*(-2 - 3*Tan[x]^2)^(1/3) + 192*AppellF1[1, 1/2, 1, 2, (-3*Tan[x]^2)/2, -Tan[x]^2]*AppellF1[3, 1/2, 3, 4, (-3*Tan[x]^2)/2, -Tan[x]^2]*Tan[x]^9*(-2 - 3*Tan[x]^2)^(1/3) + 144*AppellF1[1, 1/2, 1, 2, (-3*Tan[x]^2)/2, -Tan[x]^2]*AppellF1[3, 3/2, 2, 4, (-3*Tan[x]^2)/2, -Tan[x]^2]*Tan[x]^9*(-2 - 3*Tan[x]^2)^(1/3) + 162*AppellF1[1, 1/2, 1, 2, (-3*Tan[x]^2)/2, -Tan[x]^2]*AppellF1[3, 5/2, 1, 4, (-3*Tan[x]^2)/2, -Tan[x]^2]*Tan[x]^9*(-2 - 3*Tan[x]^2)^(1/3) + 1152*AppellF1[1, 1/2, 1, 2, (-3*Tan[x]^2)/2, -Tan[x]^2]^2*Tan[x]^3*Sqrt[-2 - 3*Tan[x]^2] + 2880*AppellF1[1, 1/2, 1, 2, (-3*Tan[x]^2)/2, -Tan[x]^2]^2*Tan[x]^5*Sqrt[-2 - 3*Tan[x]^2] - 1152*AppellF1[1, 1/2, 1, 2, (-3*Tan[x]^2)/2, -Tan[x]^2]*AppellF1[2, 1/2, 2, 3, (-3*Tan[x]^2)/2, -Tan[x]^2]*Tan[x]^5*Sqrt[-2 - 3*Tan[x]^2] - 864*AppellF1[1, 1/2, 1, 2, (-3*Tan[x]^2)/2, -Tan[x]^2]*AppellF1[2, 3/2, 1, 3, (-3*Tan[x]^2)/2, -Tan[x]^2]*Tan[x]^5*Sqrt[-2 - 3*Tan[x]^2] + 1728*AppellF1[1, 1/2, 1, 2, (-3*Tan[x]^2)/2, -Tan[x]^2]^2*Tan[x]^7*Sqrt[-2 - 3*Tan[x]^2] - 2880*AppellF1[1, 1/2, 1, 2, (-3*Tan[x]^2)/2, -Tan[x]^2]*AppellF1[2, 1/2, 2, 3, (-3*Tan[x]^2)/2, -Tan[x]^2]*Tan[x]^7*Sqrt[-2 - 3*Tan[x]^2] + 288*AppellF1[2, 1/2, 2, 3, (-3*Tan[x]^2)/2, -Tan[x]^2]^2*Tan[x]^7*Sqrt[-2 - 3*Tan[x]^2] - 2160*AppellF1[1, 1/2, 1, 2, (-3*Tan[x]^2)/2, -Tan[x]^2]*AppellF1[2, 3/2, 1, 3, (-3*Tan[x]^2)/2, -Tan[x]^2]*Tan[x]^7*Sqrt[-2 - 3*Tan[x]^2] + 432*AppellF1[2, 1/2, 2, 3, (-3*Tan[x]^2)/2, -Tan[x]^2]*AppellF1[2, 3/2, 1, 3, (-3*Tan[x]^2)/2, -Tan[x]^2]*Tan[x]^7*Sqrt[-2 - 3*Tan[x]^2] + 162*AppellF1[2, 3/2, 1, 3, (-3*Tan[x]^2)/2, -Tan[x]^2]^2*Tan[x]^7*Sqrt[-2 - 3*Tan[x]^2] - 1728*AppellF1[1, 1/2, 1, 2, (-3*Tan[x]^2)/2, -Tan[x]^2]*AppellF1[2, 1/2, 2, 3, (-3*Tan[x]^2)/2, -Tan[x]^2]*Tan[x]^9*Sqrt[-2 - 3*Tan[x]^2] + 720*AppellF1[2, 1/2, 2, 3, (-3*Tan[x]^2)/2, -Tan[x]^2]^2*Tan[x]^9*Sqrt[-2 - 3*Tan[x]^2] - 1296*AppellF1[1, 1/2, 1, 2, (-3*Tan[x]^2)/2, -Tan[x]^2]*AppellF1[2, 3/2, 1, 3, (-3*Tan[x]^2)/2, -Tan[x]^2]*Tan[x]^9*Sqrt[-2 - 3*Tan[x]^2] + 1080*AppellF1[2, 1/2, 2, 3, (-3*Tan[x]^2)/2, -Tan[x]^2]*AppellF1[2, 3/2, 1, 3, (-3*Tan[x]^2)/2, -Tan[x]^2]*Tan[x]^9*Sqrt[-2 - 3*Tan[x]^2] + 405*AppellF1[2, 3/2, 1, 3, (-3*Tan[x]^2)/2, -Tan[x]^2]^2*Tan[x]^9*Sqrt[-2 - 3*Tan[x]^2] + 432*AppellF1[2, 1/2, 2, 3, (-3*Tan[x]^2)/2, -Tan[x]^2]^2*Tan[x]^11*Sqrt[-2 - 3*Tan[x]^2] + 648*AppellF1[2, 1/2, 2, 3, (-3*Tan[x]^2)/2, -Tan[x]^2]*AppellF1[2, 3/2, 1, 3, (-3*Tan[x]^2)/2, -Tan[x]^2]*Tan[x]^11*Sqrt[-2 - 3*Tan[x]^2] + 243*AppellF1[2, 3/2, 1, 3, (-3*Tan[x]^2)/2, -Tan[x]^2]^2*Tan[x]^11*Sqrt[-2 - 3*Tan[x]^2] + 384*AppellF1[1, 1/2, 1, 2, (-3*Tan[x]^2)/2, -Tan[x]^2]^2*Tan[x]^3*(-2 - 3*Tan[x]^2)^(5/6) + 576*AppellF1[1, 1/2, 1, 2, (-3*Tan[x]^2)/2, -Tan[x]^2]^2*Tan[x]^5*(-2 - 3*Tan[x]^2)^(5/6) - 384*AppellF1[1, 1/2, 1, 2, (-3*Tan[x]^2)/2, -Tan[x]^2]*AppellF1[2, 1/2, 2, 3, (-3*Tan[x]^2)/2, -Tan[x]^2]*Tan[x]^5*(-2 - 3*Tan[x]^2)^(5/6) - 288*AppellF1[1, 1/2, 1, 2, (-3*Tan[x]^2)/2, -Tan[x]^2]*AppellF1[2, 3/2, 1, 3, (-3*Tan[x]^2)/2, -Tan[x]^2]*Tan[x]^5*(-2 - 3*Tan[x]^2)^(5/6) - 576*AppellF1[1, 1/2, 1, 2, (-3*Tan[x]^2)/2, -Tan[x]^2]*AppellF1[2, 1/2, 2, 3, (-3*Tan[x]^2)/2, -Tan[x]^2]*Tan[x]^7*(-2 - 3*Tan[x]^2)^(5/6) + 96*AppellF1[2, 1/2, 2, 3, (-3*Tan[x]^2)/2, -Tan[x]^2]^2*Tan[x]^7*(-2 - 3*Tan[x]^2)^(5/6) - 432*AppellF1[1, 1/2, 1, 2, (-3*Tan[x]^2)/2, -Tan[x]^2]*AppellF1[2, 3/2, 1, 3, (-3*Tan[x]^2)/2, -Tan[x]^2]*Tan[x]^7*(-2 - 3*Tan[x]^2)^(5/6) + 144*AppellF1[2, 1/2, 2, 3, (-3*Tan[x]^2)/2, -Tan[x]^2]*AppellF1[2, 3/2, 1, 3, (-3*Tan[x]^2)/2, -Tan[x]^2]*Tan[x]^7*(-2 - 3*Tan[x]^2)^(5/6) + 54*AppellF1[2, 3/2, 1, 3, (-3*Tan[x]^2)/2, -Tan[x]^2]^2*Tan[x]^7*(-2 - 3*Tan[x]^2)^(5/6) + 144*AppellF1[2, 1/2, 2, 3, (-3*Tan[x]^2)/2, -Tan[x]^2]^2*Tan[x]^9*(-2 - 3*Tan[x]^2)^(5/6) + 216*AppellF1[2, 1/2, 2, 3, (-3*Tan[x]^2)/2, -Tan[x]^2]*AppellF1[2, 3/2, 1, 3, (-3*Tan[x]^2)/2, -Tan[x]^2]*Tan[x]^9*(-2 - 3*Tan[x]^2)^(5/6) + 81*AppellF1[2, 3/2, 1, 3, (-3*Tan[x]^2)/2, -Tan[x]^2]^2*Tan[x]^9*(-2 - 3*Tan[x]^2)^(5/6)))","C",0
447,1,168,100,4.832065,"\int \frac{\sec ^2(x) \left(-\cos (2 x)+2 \tan ^2(x)\right)}{(\tan (x) \tan (2 x))^{3/2}} \, dx","Integrate[(Sec[x]^2*(-Cos[2*x] + 2*Tan[x]^2))/(Tan[x]*Tan[2*x])^(3/2),x]","\frac{\tan ^2(2 x) \left(2 \tan ^2(x)-\cos (2 x)\right) \left(-3 \sin (x) \cos (x) \tan ^{-1}\left(\sqrt{\tan ^2(x)-1}\right) \sqrt{\tan ^2(x)-1}+\frac{4 \sqrt{2} \cos (2 x) \tan (x) \left(\sqrt{2} \tanh ^{-1}\left(\sqrt{1-\tan ^2(x)}\right)-2 \tanh ^{-1}\left(\frac{1}{2} \sqrt{2-2 \tan ^2(x)}\right)\right)}{\sqrt{1-\tan ^2(x)}}+\frac{1}{3} \left(-3 \cot (x)-4 \sin (x) \cos (x)+(9 \cos (2 x)+5) \tan ^3(x)\right)\right)}{2 (6 \cos (2 x)+\cos (4 x)-3) (\tan (x) \tan (2 x))^{3/2}}","\frac{2 \tan ^3(x)}{3 (\tan (x) \tan (2 x))^{3/2}}+\frac{3 \tan (x)}{4 \sqrt{\tan (x) \tan (2 x)}}+\frac{\tan (x)}{2 (\tan (x) \tan (2 x))^{3/2}}+2 \tanh ^{-1}\left(\frac{\tan (x)}{\sqrt{\tan (x) \tan (2 x)}}\right)-\frac{11 \tanh ^{-1}\left(\frac{\sqrt{2} \tan (x)}{\sqrt{\tan (x) \tan (2 x)}}\right)}{4 \sqrt{2}}",1,"((-Cos[2*x] + 2*Tan[x]^2)*((4*Sqrt[2]*(-2*ArcTanh[Sqrt[2 - 2*Tan[x]^2]/2] + Sqrt[2]*ArcTanh[Sqrt[1 - Tan[x]^2]])*Cos[2*x]*Tan[x])/Sqrt[1 - Tan[x]^2] - 3*ArcTan[Sqrt[-1 + Tan[x]^2]]*Cos[x]*Sin[x]*Sqrt[-1 + Tan[x]^2] + (-3*Cot[x] - 4*Cos[x]*Sin[x] + (5 + 9*Cos[2*x])*Tan[x]^3)/3)*Tan[2*x]^2)/(2*(-3 + 6*Cos[2*x] + Cos[4*x])*(Tan[x]*Tan[2*x])^(3/2))","A",1
448,1,47,112,0.0431556,"\int \frac{\tan (x)}{\left(a^3-b^3 \cos ^n(x)\right)^{4/3}} \, dx","Integrate[Tan[x]/(a^3 - b^3*Cos[x]^n)^(4/3),x]","-\frac{3 \, _2F_1\left(-\frac{1}{3},1;\frac{2}{3};1-\frac{b^3 \cos ^n(x)}{a^3}\right)}{a^3 n \sqrt[3]{a^3-b^3 \cos ^n(x)}}","\frac{\log (\cos (x))}{2 a^4}-\frac{3}{a^3 n \sqrt[3]{a^3-b^3 \cos ^n(x)}}-\frac{3 \log \left(a-\sqrt[3]{a^3-b^3 \cos ^n(x)}\right)}{2 a^4 n}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3-b^3 \cos ^n(x)}+a}{\sqrt{3} a}\right)}{a^4 n}",1,"(-3*Hypergeometric2F1[-1/3, 1, 2/3, 1 - (b^3*Cos[x]^n)/a^3])/(a^3*n*(a^3 - b^3*Cos[x]^n)^(1/3))","C",1
449,1,154,95,0.1382487,"\int \left(1+2 \cos ^9(x)\right)^{5/6} \tan (x) \, dx","Integrate[(1 + 2*Cos[x]^9)^(5/6)*Tan[x],x]","\frac{1}{90} \left(-12 \left(2 \cos ^9(x)+1\right)^{5/6}-5 \log \left(\sqrt[3]{2 \cos ^9(x)+1}-\sqrt[6]{2 \cos ^9(x)+1}+1\right)+5 \log \left(\sqrt[3]{2 \cos ^9(x)+1}+\sqrt[6]{2 \cos ^9(x)+1}+1\right)+10 \sqrt{3} \tan ^{-1}\left(\frac{1-2 \sqrt[6]{2 \cos ^9(x)+1}}{\sqrt{3}}\right)-10 \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[6]{2 \cos ^9(x)+1}+1}{\sqrt{3}}\right)+20 \tanh ^{-1}\left(\sqrt[6]{2 \cos ^9(x)+1}\right)\right)","-\frac{2}{15} \left(2 \cos ^9(x)+1\right)^{5/6}+\frac{\tan ^{-1}\left(\frac{1-\sqrt[3]{2 \cos ^9(x)+1}}{\sqrt{3} \sqrt[6]{2 \cos ^9(x)+1}}\right)}{3 \sqrt{3}}+\frac{1}{3} \tanh ^{-1}\left(\sqrt[6]{2 \cos ^9(x)+1}\right)-\frac{1}{9} \tanh ^{-1}\left(\sqrt{2 \cos ^9(x)+1}\right)",1,"(10*Sqrt[3]*ArcTan[(1 - 2*(1 + 2*Cos[x]^9)^(1/6))/Sqrt[3]] - 10*Sqrt[3]*ArcTan[(1 + 2*(1 + 2*Cos[x]^9)^(1/6))/Sqrt[3]] + 20*ArcTanh[(1 + 2*Cos[x]^9)^(1/6)] - 12*(1 + 2*Cos[x]^9)^(5/6) - 5*Log[1 - (1 + 2*Cos[x]^9)^(1/6) + (1 + 2*Cos[x]^9)^(1/3)] + 5*Log[1 + (1 + 2*Cos[x]^9)^(1/6) + (1 + 2*Cos[x]^9)^(1/3)])/90","A",1
450,1,30,49,0.4977587,"\int \frac{\cos (x) \sin ^8(x)}{\left(2-5 \sin ^3(x)\right)^{4/3}} \, dx","Integrate[(Cos[x]*Sin[x]^8)/(2 - 5*Sin[x]^3)^(4/3),x]","\frac{-25 \sin ^6(x)-30 \sin ^3(x)+36}{625 \sqrt[3]{2-5 \sin ^3(x)}}","-\frac{1}{625} \left(2-5 \sin ^3(x)\right)^{5/3}+\frac{2}{125} \left(2-5 \sin ^3(x)\right)^{2/3}+\frac{4}{125 \sqrt[3]{2-5 \sin ^3(x)}}",1,"(36 - 30*Sin[x]^3 - 25*Sin[x]^6)/(625*(2 - 5*Sin[x]^3)^(1/3))","A",1
451,1,42,20,0.2125346,"\int \frac{\sec ^2(x) \tan (x) \left(1+\sqrt[3]{1-8 \tan ^2(x)}\right)}{\left(1-8 \tan ^2(x)\right)^{2/3}} \, dx","Integrate[(Sec[x]^2*Tan[x]*(1 + (1 - 8*Tan[x]^2)^(1/3)))/(1 - 8*Tan[x]^2)^(2/3),x]","-\frac{3 (9 \cos (2 x)-7) \left(\sqrt[3]{1-8 \tan ^2(x)}+2\right) \sec ^2(x)}{64 \left(1-8 \tan ^2(x)\right)^{2/3}}","-\frac{3}{32} \left(\sqrt[3]{1-8 \tan ^2(x)}+1\right)^2",1,"(-3*(-7 + 9*Cos[2*x])*Sec[x]^2*(2 + (1 - 8*Tan[x]^2)^(1/3)))/(64*(1 - 8*Tan[x]^2)^(2/3))","B",1
452,1,58,27,4.3002778,"\int \frac{\csc (x) \sec (x) \left(1+\sqrt[3]{1-8 \tan ^2(x)}\right)}{\left(1-8 \tan ^2(x)\right)^{2/3}} \, dx","Integrate[(Csc[x]*Sec[x]*(1 + (1 - 8*Tan[x]^2)^(1/3)))/(1 - 8*Tan[x]^2)^(2/3),x]","\frac{1}{4} \left(5 \log \left(1-\sqrt[3]{1-8 \tan ^2(x)}\right)-\log \left(\left(1-8 \tan ^2(x)\right)^{2/3}+\sqrt[3]{1-8 \tan ^2(x)}+1\right)-2 \log (\tan (x))\right)","\frac{3}{2} \log \left(1-\sqrt[3]{1-8 \tan ^2(x)}\right)-\log (\tan (x))",1,"(-2*Log[Tan[x]] + 5*Log[1 - (1 - 8*Tan[x]^2)^(1/3)] - Log[1 + (1 - 8*Tan[x]^2)^(1/3) + (1 - 8*Tan[x]^2)^(2/3)])/4","B",1
453,1,89,101,0.4260473,"\int \frac{\left(5 \cos ^2(x)-\sqrt{-1+5 \sin ^2(x)}\right) \tan (x)}{\sqrt[4]{-1+5 \sin ^2(x)} \left(2+\sqrt{-1+5 \sin ^2(x)}\right)} \, dx","Integrate[((5*Cos[x]^2 - Sqrt[-1 + 5*Sin[x]^2])*Tan[x])/((-1 + 5*Sin[x]^2)^(1/4)*(2 + Sqrt[-1 + 5*Sin[x]^2])),x]","\frac{1}{4} \left(-2 \sqrt[4]{4-5 \cos ^2(x)} \left(\frac{1}{\sqrt{4-5 \cos ^2(x)}+2}-4\right)-6 \sqrt{2} \tan ^{-1}\left(\frac{\sqrt[4]{3-5 \cos (2 x)}}{2^{3/4}}\right)-\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt[4]{3-5 \cos (2 x)}}{2^{3/4}}\right)\right)","2 \sqrt[4]{5 \sin ^2(x)-1}-\frac{\sqrt[4]{5 \sin ^2(x)-1}}{2 \left(\sqrt{5 \sin ^2(x)-1}+2\right)}-\frac{3 \tan ^{-1}\left(\frac{\sqrt[4]{5 \sin ^2(x)-1}}{\sqrt{2}}\right)}{\sqrt{2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{5 \sin ^2(x)-1}}{\sqrt{2}}\right)}{2 \sqrt{2}}",1,"(-6*Sqrt[2]*ArcTan[(3 - 5*Cos[2*x])^(1/4)/2^(3/4)] - Sqrt[2]*ArcTanh[(3 - 5*Cos[2*x])^(1/4)/2^(3/4)] - 2*(4 - 5*Cos[x]^2)^(1/4)*(-4 + (2 + Sqrt[4 - 5*Cos[x]^2])^(-1)))/4","A",1
454,1,140,25,0.3155342,"\int \cos ^3(x) \cos ^{\frac{2}{3}}(2 x) \sin (x) \, dx","Integrate[Cos[x]^3*Cos[2*x]^(2/3)*Sin[x],x]","-\frac{3}{40} \cos ^{\frac{5}{3}}(2 x)-\frac{3 e^{-6 i x} \sqrt[3]{1+e^{4 i x}} \left(2 e^{4 i x} \, _2F_1\left(-\frac{1}{3},\frac{1}{3};\frac{2}{3};-e^{4 i x}\right)+e^{8 i x} \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{5}{3};-e^{4 i x}\right)+\left(1+e^{4 i x}\right)^{2/3} \left(1+e^{8 i x}\right)\right)}{256\ 2^{2/3} \sqrt[3]{e^{-2 i x}+e^{2 i x}}}","-\frac{3}{64} \cos ^{\frac{8}{3}}(2 x)-\frac{3}{40} \cos ^{\frac{5}{3}}(2 x)",1,"(-3*Cos[2*x]^(5/3))/40 - (3*(1 + E^((4*I)*x))^(1/3)*((1 + E^((4*I)*x))^(2/3)*(1 + E^((8*I)*x)) + 2*E^((4*I)*x)*Hypergeometric2F1[-1/3, 1/3, 2/3, -E^((4*I)*x)] + E^((8*I)*x)*Hypergeometric2F1[1/3, 2/3, 5/3, -E^((4*I)*x)]))/(256*2^(2/3)*E^((6*I)*x)*(E^((-2*I)*x) + E^((2*I)*x))^(1/3))","C",1
455,1,153,102,0.1257944,"\int \frac{\sin ^6(x) \tan (x)}{\cos ^{\frac{3}{4}}(2 x)} \, dx","Integrate[(Sin[x]^6*Tan[x])/Cos[2*x]^(3/4),x]","\frac{1}{360} \left(-72 \cos ^{\frac{5}{4}}(2 x)+5 \cos (4 x) \sqrt[4]{\cos (2 x)}+635 \sqrt[4]{\cos (2 x)}+90 \sqrt{2} \log \left(\sqrt{\cos (2 x)}-\sqrt{2} \sqrt[4]{\cos (2 x)}+1\right)-90 \sqrt{2} \log \left(\sqrt{\cos (2 x)}+\sqrt{2} \sqrt[4]{\cos (2 x)}+1\right)+180 \sqrt{2} \tan ^{-1}\left(1-\sqrt{2} \sqrt[4]{\cos (2 x)}\right)-180 \sqrt{2} \tan ^{-1}\left(\sqrt{2} \sqrt[4]{\cos (2 x)}+1\right)\right)","\frac{1}{36} \cos ^{\frac{9}{4}}(2 x)-\frac{1}{5} \cos ^{\frac{5}{4}}(2 x)+\frac{7}{4} \sqrt[4]{\cos (2 x)}+\frac{\tan ^{-1}\left(\frac{1-\sqrt{\cos (2 x)}}{\sqrt{2} \sqrt[4]{\cos (2 x)}}\right)}{\sqrt{2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{\cos (2 x)}+1}{\sqrt{2} \sqrt[4]{\cos (2 x)}}\right)}{\sqrt{2}}",1,"(180*Sqrt[2]*ArcTan[1 - Sqrt[2]*Cos[2*x]^(1/4)] - 180*Sqrt[2]*ArcTan[1 + Sqrt[2]*Cos[2*x]^(1/4)] + 635*Cos[2*x]^(1/4) - 72*Cos[2*x]^(5/4) + 5*Cos[2*x]^(1/4)*Cos[4*x] + 90*Sqrt[2]*Log[1 - Sqrt[2]*Cos[2*x]^(1/4) + Sqrt[Cos[2*x]]] - 90*Sqrt[2]*Log[1 + Sqrt[2]*Cos[2*x]^(1/4) + Sqrt[Cos[2*x]]])/360","A",1
456,1,45,17,0.0747138,"\int \sqrt{\tan (x) \tan (2 x)} \, dx","Integrate[Sqrt[Tan[x]*Tan[2*x]],x]","-\frac{\sqrt{\cos (2 x)} \sqrt{\tan (x) \tan (2 x)} \csc (x) \tanh ^{-1}\left(\frac{\sqrt{2} \cos (x)}{\sqrt{\cos (2 x)}}\right)}{\sqrt{2}}","-\tanh ^{-1}\left(\frac{\tan (x)}{\sqrt{\tan (x) \tan (2 x)}}\right)",1,"-((ArcTanh[(Sqrt[2]*Cos[x])/Sqrt[Cos[2*x]]]*Sqrt[Cos[2*x]]*Csc[x]*Sqrt[Tan[x]*Tan[2*x]])/Sqrt[2])","B",1
457,1,52,32,0.0726629,"\int \sqrt{\cot (2 x) \tan (x)} \, dx","Integrate[Sqrt[Cot[2*x]*Tan[x]],x]","\frac{\cos (x) \sqrt{\tan (x) \cot (2 x)} \left(\sqrt{2} \sin ^{-1}\left(\sqrt{2} \sin (x)\right)-\tan ^{-1}\left(\frac{\sin (x)}{\sqrt{\cos (2 x)}}\right)\right)}{\sqrt{\cos (2 x)}}","\tan ^{-1}\left(\frac{\sqrt{2} \tan (x)}{\sqrt{1-\tan ^2(x)}}\right)-\frac{\sin ^{-1}(\tan (x))}{\sqrt{2}}",1,"((Sqrt[2]*ArcSin[Sqrt[2]*Sin[x]] - ArcTan[Sin[x]/Sqrt[Cos[2*x]]])*Cos[x]*Sqrt[Cot[2*x]*Tan[x]])/Sqrt[Cos[2*x]]","A",1
458,1,31,31,0.0044671,"\int \frac{1}{x^5 \left(5+x^2\right)} \, dx","Integrate[1/(x^5*(5 + x^2)),x]","-\frac{1}{20 x^4}+\frac{1}{50 x^2}-\frac{1}{250} \log \left(x^2+5\right)+\frac{\log (x)}{125}","-\frac{1}{20 x^4}+\frac{1}{50 x^2}-\frac{1}{250} \log \left(x^2+5\right)+\frac{\log (x)}{125}",1,"-1/20*1/x^4 + 1/(50*x^2) + Log[x]/125 - Log[5 + x^2]/250","A",1
459,1,39,39,0.0164549,"\int \frac{1}{x^6 \left(5+x^2\right)} \, dx","Integrate[1/(x^6*(5 + x^2)),x]","-\frac{1}{25 x^5}+\frac{1}{75 x^3}-\frac{1}{125 x}-\frac{\tan ^{-1}\left(\frac{x}{\sqrt{5}}\right)}{125 \sqrt{5}}","-\frac{1}{25 x^5}+\frac{1}{75 x^3}-\frac{1}{125 x}-\frac{\tan ^{-1}\left(\frac{x}{\sqrt{5}}\right)}{125 \sqrt{5}}",1,"-1/25*1/x^5 + 1/(75*x^3) - 1/(125*x) - ArcTan[x/Sqrt[5]]/(125*Sqrt[5])","A",1
460,1,40,58,0.021028,"\int \frac{1}{x \left(-4+x^2\right)^4} \, dx","Integrate[1/(x*(-4 + x^2)^4),x]","\frac{-3 \log \left(4-x^2\right)-\frac{4 \left(3 x^4-30 x^2+88\right)}{\left(x^2-4\right)^3}+6 \log (x)}{1536}","\frac{1}{128 \left(4-x^2\right)}+\frac{1}{64 \left(4-x^2\right)^2}+\frac{1}{24 \left(4-x^2\right)^3}-\frac{1}{512} \log \left(4-x^2\right)+\frac{\log (x)}{256}",1,"((-4*(88 - 30*x^2 + 3*x^4))/(-4 + x^2)^3 + 6*Log[x] - 3*Log[4 - x^2])/1536","A",1
461,1,30,52,0.0079707,"\int \frac{1}{x \left(-2+x^2\right)^{5/2}} \, dx","Integrate[1/(x*(-2 + x^2)^(5/2)),x]","-\frac{\, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};1-\frac{x^2}{2}\right)}{6 \left(x^2-2\right)^{3/2}}","\frac{1}{4 \sqrt{x^2-2}}-\frac{1}{6 \left(x^2-2\right)^{3/2}}+\frac{\tan ^{-1}\left(\frac{\sqrt{x^2-2}}{\sqrt{2}}\right)}{4 \sqrt{2}}",1,"-1/6*Hypergeometric2F1[-3/2, 1, -1/2, 1 - x^2/2]/(-2 + x^2)^(3/2)","C",1
462,1,47,61,0.0190043,"\int \frac{\left(-10+x^2\right)^{5/2}}{x} \, dx","Integrate[(-10 + x^2)^(5/2)/x,x]","\frac{1}{15} \sqrt{x^2-10} \left(3 x^4-110 x^2+2300\right)-100 \sqrt{10} \tan ^{-1}\left(\sqrt{\frac{x^2}{10}-1}\right)","\frac{1}{5} \left(x^2-10\right)^{5/2}-\frac{10}{3} \left(x^2-10\right)^{3/2}+100 \sqrt{x^2-10}-100 \sqrt{10} \tan ^{-1}\left(\frac{\sqrt{x^2-10}}{\sqrt{10}}\right)",1,"(Sqrt[-10 + x^2]*(2300 - 110*x^2 + 3*x^4))/15 - 100*Sqrt[10]*ArcTan[Sqrt[-1 + x^2/10]]","A",1
463,1,15,16,0.0023185,"\int x^{1+2 n} \, dx","Integrate[x^(1 + 2*n),x]","\frac{x^{2 n+2}}{2 n+2}","\frac{x^{2 (n+1)}}{2 (n+1)}",1,"x^(2 + 2*n)/(2 + 2*n)","A",1
464,1,36,46,0.0130738,"\int \frac{x^7}{\left(-5+x^2\right)^3} \, dx","Integrate[x^7/(-5 + x^2)^3,x]","\frac{1}{4} \left(2 x^2-\frac{150}{x^2-5}-\frac{125}{\left(x^2-5\right)^2}+30 \log \left(x^2-5\right)\right)","\frac{x^2}{2}+\frac{75}{2 \left(5-x^2\right)}-\frac{125}{4 \left(5-x^2\right)^2}+\frac{15}{2} \log \left(5-x^2\right)",1,"(2*x^2 - 125/(-5 + x^2)^2 - 150/(-5 + x^2) + 30*Log[-5 + x^2])/4","A",1
465,1,23,40,0.0084248,"\int \frac{-4 x^3+3 x^5}{\left(-1+x^2\right)^5} \, dx","Integrate[(-4*x^3 + 3*x^5)/(-1 + x^2)^5,x]","\frac{-18 x^4+28 x^2-7}{24 \left(x^2-1\right)^4}","-\frac{3}{4 \left(1-x^2\right)^2}+\frac{1}{3 \left(1-x^2\right)^3}+\frac{1}{8 \left(1-x^2\right)^4}",1,"(-7 + 28*x^2 - 18*x^4)/(24*(-1 + x^2)^4)","A",1
466,1,20,27,0.0067733,"\int x^3 \left(1+x^2\right)^{9/14} \, dx","Integrate[x^3*(1 + x^2)^(9/14),x]","\frac{7}{851} \left(x^2+1\right)^{23/14} \left(23 x^2-14\right)","\frac{7}{37} \left(x^2+1\right)^{37/14}-\frac{7}{23} \left(x^2+1\right)^{23/14}",1,"(7*(1 + x^2)^(23/14)*(-14 + 23*x^2))/851","A",1
467,1,25,38,0.0095983,"\int \frac{x^5}{\left(-4+x^2\right)^{13/6}} \, dx","Integrate[x^5/(-4 + x^2)^(13/6),x]","\frac{3 \left(7 x^4-336 x^2+1152\right)}{35 \left(x^2-4\right)^{7/6}}","\frac{3}{5} \left(x^2-4\right)^{5/6}-\frac{24}{\sqrt[6]{x^2-4}}-\frac{48}{7 \left(x^2-4\right)^{7/6}}",1,"(3*(1152 - 336*x^2 + 7*x^4))/(35*(-4 + x^2)^(7/6))","A",1
468,1,23,33,0.0058015,"\int \frac{1}{\left(1+2 x^2\right)^{5/2}} \, dx","Integrate[(1 + 2*x^2)^(-5/2),x]","\frac{x \left(4 x^2+3\right)}{3 \left(2 x^2+1\right)^{3/2}}","\frac{2 x}{3 \sqrt{2 x^2+1}}+\frac{x}{3 \left(2 x^2+1\right)^{3/2}}",1,"(x*(3 + 4*x^2))/(3*(1 + 2*x^2)^(3/2))","A",1
469,1,26,43,0.0147492,"\int \frac{1}{\left(-1-2 x+x^2\right)^{5/2}} \, dx","Integrate[(-1 - 2*x + x^2)^(-5/2),x]","\frac{x^3-3 x^2+2}{6 \left(x^2-2 x-1\right)^{3/2}}","\frac{1-x}{6 \left(x^2-2 x-1\right)^{3/2}}-\frac{1-x}{6 \sqrt{x^2-2 x-1}}",1,"(2 - 3*x^2 + x^3)/(6*(-1 - 2*x + x^2)^(3/2))","A",1
470,1,28,47,0.0056977,"\int \frac{1}{x^4 \left(-8+x^2\right)^{3/2}} \, dx","Integrate[1/(x^4*(-8 + x^2)^(3/2)),x]","\frac{-x^4+4 x^2+8}{192 x^3 \sqrt{x^2-8}}","-\frac{x}{192 \sqrt{x^2-8}}+\frac{1}{48 \sqrt{x^2-8} x}+\frac{1}{24 \sqrt{x^2-8} x^3}",1,"(8 + 4*x^2 - x^4)/(192*x^3*Sqrt[-8 + x^2])","A",1
471,1,19,28,0.0065807,"\int \frac{\left(5+x^2\right)^2}{x^{13/3}} \, dx","Integrate[(5 + x^2)^2/x^(13/3),x]","\frac{3 \left(x^4-5 x^2-5\right)}{2 x^{10/3}}","\frac{3 x^{2/3}}{2}-\frac{15}{2 x^{4/3}}-\frac{15}{2 x^{10/3}}",1,"(3*(-5 - 5*x^2 + x^4))/(2*x^(10/3))","A",1
472,1,49,52,0.026192,"\int \frac{1}{x^7 \left(1+x^2\right)^3} \, dx","Integrate[1/(x^7*(1 + x^2)^3),x]","5 \log \left(x^2+1\right)-\frac{60 x^8+90 x^6+20 x^4-5 x^2+2}{12 x^6 \left(x^2+1\right)^2}-10 \log (x)","-\frac{1}{6 x^6}+\frac{3}{4 x^4}-\frac{2}{x^2+1}-\frac{3}{x^2}-\frac{1}{4 \left(x^2+1\right)^2}+5 \log \left(x^2+1\right)-10 \log (x)",1,"-1/12*(2 - 5*x^2 + 20*x^4 + 90*x^6 + 60*x^8)/(x^6*(1 + x^2)^2) - 10*Log[x] + 5*Log[1 + x^2]","A",1
473,1,25,25,0.0092001,"\int \frac{\left(\frac{2+x^2}{x^2}\right)^{7/9}}{\left(2+x^2\right)^{3/2}} \, dx","Integrate[((2 + x^2)/x^2)^(7/9)/(2 + x^2)^(3/2),x]","-\frac{9 \left(\frac{2}{x^2}+1\right)^{7/9} x}{10 \sqrt{x^2+2}}","-\frac{9 \left(\frac{2}{x^2}+1\right)^{7/9} x}{10 \sqrt{x^2+2}}",1,"(-9*(1 + 2/x^2)^(7/9)*x)/(10*Sqrt[2 + x^2])","A",1
474,1,35,50,0.0247078,"\int \frac{x^4}{\left(\sqrt{10}-x^2\right)^{9/2}} \, dx","Integrate[x^4/(Sqrt[10] - x^2)^(9/2),x]","\frac{7 \sqrt{10} x^5-2 x^7}{350 \left(\sqrt{10}-x^2\right)^{7/2}}","\frac{x^5}{175 \left(\sqrt{10}-x^2\right)^{5/2}}+\frac{x^5}{7 \sqrt{10} \left(\sqrt{10}-x^2\right)^{7/2}}",1,"(7*Sqrt[10]*x^5 - 2*x^7)/(350*(Sqrt[10] - x^2)^(7/2))","A",1
475,1,24,24,0.0173286,"\int \frac{x^2}{\left(3-x^2\right)^{3/2}} \, dx","Integrate[x^2/(3 - x^2)^(3/2),x]","\frac{x}{\sqrt{3-x^2}}-\sin ^{-1}\left(\frac{x}{\sqrt{3}}\right)","\frac{x}{\sqrt{3-x^2}}-\sin ^{-1}\left(\frac{x}{\sqrt{3}}\right)",1,"x/Sqrt[3 - x^2] - ArcSin[x/Sqrt[3]]","A",1
476,1,24,40,0.0035258,"\int \frac{\left(25-x^2\right)^{3/2}}{x^4} \, dx","Integrate[(25 - x^2)^(3/2)/x^4,x]","-\frac{125 \, _2F_1\left(-\frac{3}{2},-\frac{3}{2};-\frac{1}{2};\frac{x^2}{25}\right)}{3 x^3}","\frac{\sqrt{25-x^2}}{x}-\frac{\left(25-x^2\right)^{3/2}}{3 x^3}+\sin ^{-1}\left(\frac{x}{5}\right)",1,"(-125*Hypergeometric2F1[-3/2, -3/2, -1/2, x^2/25])/(3*x^3)","C",1
477,1,28,49,0.0106882,"\int \frac{1}{\left(1-2 x^2\right)^{7/2}} \, dx","Integrate[(1 - 2*x^2)^(-7/2),x]","\frac{x \left(32 x^4-40 x^2+15\right)}{15 \left(1-2 x^2\right)^{5/2}}","\frac{8 x}{15 \sqrt{1-2 x^2}}+\frac{4 x}{15 \left(1-2 x^2\right)^{3/2}}+\frac{x}{5 \left(1-2 x^2\right)^{5/2}}",1,"(x*(15 - 40*x^2 + 32*x^4))/(15*(1 - 2*x^2)^(5/2))","A",1
478,1,29,47,0.0110629,"\int \frac{1}{\left(-7+6 x-x^2\right)^{5/2}} \, dx","Integrate[(-7 + 6*x - x^2)^(-5/2),x]","-\frac{(x-3) \left(x^2-6 x+6\right)}{6 \left(-x^2+6 x-7\right)^{3/2}}","-\frac{3-x}{6 \sqrt{-x^2+6 x-7}}-\frac{3-x}{6 \left(-x^2+6 x-7\right)^{3/2}}",1,"-1/6*((-3 + x)*(6 - 6*x + x^2))/(-7 + 6*x - x^2)^(3/2)","A",1
479,1,36,36,0.0016063,"\int \left(1-2 x-2 x^2\right)^3 \, dx","Integrate[(1 - 2*x - 2*x^2)^3,x]","-\frac{8 x^7}{7}-4 x^6-\frac{12 x^5}{5}+4 x^4+2 x^3-3 x^2+x","-\frac{8 x^7}{7}-4 x^6-\frac{12 x^5}{5}+4 x^4+2 x^3-3 x^2+x",1,"x - 3*x^2 + 2*x^3 + 4*x^4 - (12*x^5)/5 - 4*x^6 - (8*x^7)/7","A",1
480,1,39,39,0.0016885,"\int (-1+5 x) \left(-1-x+x^2\right)^2 \, dx","Integrate[(-1 + 5*x)*(-1 - x + x^2)^2,x]","\frac{5 x^6}{6}-\frac{11 x^5}{5}-\frac{3 x^4}{4}+\frac{11 x^3}{3}+\frac{3 x^2}{2}-x","\frac{5 x^6}{6}-\frac{11 x^5}{5}-\frac{3 x^4}{4}+\frac{11 x^3}{3}+\frac{3 x^2}{2}-x",1,"-x + (3*x^2)/2 + (11*x^3)/3 - (3*x^4)/4 - (11*x^5)/5 + (5*x^6)/6","A",1
481,1,33,47,0.048552,"\int \frac{1+3 x}{\left(1-8 x+2 x^2\right)^{5/2}} \, dx","Integrate[(1 + 3*x)/(1 - 8*x + 2*x^2)^(5/2),x]","\frac{8 x^3-48 x^2+54 x-1}{42 \left(2 x^2-8 x+1\right)^{3/2}}","\frac{1-2 x}{6 \left(2 x^2-8 x+1\right)^{3/2}}-\frac{2 (2-x)}{21 \sqrt{2 x^2-8 x+1}}",1,"(-1 + 54*x - 48*x^2 + 8*x^3)/(42*(1 - 8*x + 2*x^2)^(3/2))","A",1
482,1,33,45,0.1148897,"\int \frac{-1-8 x+8 x^3}{\left(1+2 x-4 x^2\right)^{5/2}} \, dx","Integrate[(-1 - 8*x + 8*x^3)/(1 + 2*x - 4*x^2)^(5/2),x]","-\frac{-488 x^3+216 x^2+156 x+27}{75 \left(-4 x^2+2 x+1\right)^{3/2}}","-\frac{4 (x+1)}{15 \left(-4 x^2+2 x+1\right)^{3/2}}-\frac{122 x+7}{75 \sqrt{-4 x^2+2 x+1}}",1,"-1/75*(27 + 156*x + 216*x^2 - 488*x^3)/(1 + 2*x - 4*x^2)^(3/2)","A",1
483,1,67,83,0.0537607,"\int x^2 \cos ^5(x) \, dx","Integrate[x^2*Cos[x]^5,x]","\frac{5}{8} \left(x^2-2\right) \sin (x)+\frac{5}{432} \left(9 x^2-2\right) \sin (3 x)+\frac{\left(25 x^2-2\right) \sin (5 x)}{2000}+\frac{5}{4} x \cos (x)+\frac{5}{72} x \cos (3 x)+\frac{1}{200} x \cos (5 x)","\frac{8}{15} x^2 \sin (x)+\frac{1}{5} x^2 \sin (x) \cos ^4(x)+\frac{4}{15} x^2 \sin (x) \cos ^2(x)-\frac{2 \sin ^5(x)}{125}+\frac{76 \sin ^3(x)}{675}-\frac{298 \sin (x)}{225}+\frac{2}{25} x \cos ^5(x)+\frac{8}{45} x \cos ^3(x)+\frac{16}{15} x \cos (x)",1,"(5*x*Cos[x])/4 + (5*x*Cos[3*x])/72 + (x*Cos[5*x])/200 + (5*(-2 + x^2)*Sin[x])/8 + (5*(-2 + 9*x^2)*Sin[3*x])/432 + ((-2 + 25*x^2)*Sin[5*x])/2000","A",1
484,1,51,73,0.101112,"\int x^3 \sin ^3(x) \, dx","Integrate[x^3*Sin[x]^3,x]","\frac{1}{108} \left(243 \left(x^2-2\right) \sin (x)-\left(9 x^2-2\right) \sin (3 x)-81 x \left(x^2-6\right) \cos (x)+3 x \left(3 x^2-2\right) \cos (3 x)\right)","-\frac{2}{3} x^3 \cos (x)-\frac{1}{3} x^3 \sin ^2(x) \cos (x)+\frac{1}{3} x^2 \sin ^3(x)+2 x^2 \sin (x)-\frac{2 \sin ^3(x)}{27}-\frac{40 \sin (x)}{9}+\frac{40}{9} x \cos (x)+\frac{2}{9} x \sin ^2(x) \cos (x)",1,"(-81*x*(-6 + x^2)*Cos[x] + 3*x*(-2 + 3*x^2)*Cos[3*x] + 243*(-2 + x^2)*Sin[x] - (-2 + 9*x^2)*Sin[3*x])/108","A",1
485,1,70,105,0.0919715,"\int x^2 \sin ^6(x) \, dx","Integrate[x^2*Sin[x]^6,x]","\frac{1440 x^3-1620 \left(2 x^2-1\right) \sin (2 x)+81 \left(8 x^2-1\right) \sin (4 x)-4 \left(18 x^2-1\right) \sin (6 x)-3240 x \cos (2 x)+324 x \cos (4 x)-24 x \cos (6 x)}{13824}","\frac{5 x^3}{48}-\frac{1}{6} x^2 \sin ^5(x) \cos (x)-\frac{5}{24} x^2 \sin ^3(x) \cos (x)-\frac{5}{16} x^2 \sin (x) \cos (x)-\frac{245 x}{1152}+\frac{1}{18} x \sin ^6(x)+\frac{5}{48} x \sin ^4(x)+\frac{5}{16} x \sin ^2(x)+\frac{1}{108} \sin ^5(x) \cos (x)+\frac{65 \sin ^3(x) \cos (x)}{1728}+\frac{245 \sin (x) \cos (x)}{1152}",1,"(1440*x^3 - 3240*x*Cos[2*x] + 324*x*Cos[4*x] - 24*x*Cos[6*x] - 1620*(-1 + 2*x^2)*Sin[2*x] + 81*(-1 + 8*x^2)*Sin[4*x] - 4*(-1 + 18*x^2)*Sin[6*x])/13824","A",1
486,1,39,44,0.1323239,"\int x^2 \cos (x) \sin ^2(x) \, dx","Integrate[x^2*Cos[x]*Sin[x]^2,x]","\frac{1}{54} \left(\sin (x) \left(9 x^2+\left(2-9 x^2\right) \cos (2 x)-26\right)+27 x \cos (x)-3 x \cos (3 x)\right)","\frac{1}{3} x^2 \sin ^3(x)-\frac{2 \sin ^3(x)}{27}-\frac{4 \sin (x)}{9}+\frac{4}{9} x \cos (x)+\frac{2}{9} x \sin ^2(x) \cos (x)",1,"(27*x*Cos[x] - 3*x*Cos[3*x] + (-26 + 9*x^2 + (2 - 9*x^2)*Cos[2*x])*Sin[x])/54","A",1
487,1,33,33,0.0331036,"\int x \cos ^2(x) \cot ^2(x) \, dx","Integrate[x*Cos[x]^2*Cot[x]^2,x]","-\frac{3 x^2}{4}-\frac{1}{4} x \sin (2 x)-\frac{1}{8} \cos (2 x)-x \cot (x)+\log (\sin (x))","-\frac{3 x^2}{4}-\frac{\cos ^2(x)}{4}-x \cot (x)+\log (\sin (x))-\frac{1}{2} x \sin (x) \cos (x)",1,"(-3*x^2)/4 - Cos[2*x]/8 - x*Cot[x] + Log[Sin[x]] - (x*Sin[2*x])/4","A",1
488,1,104,30,0.1256522,"\int x \sec (x) \tan ^3(x) \, dx","Integrate[x*Sec[x]*Tan[x]^3,x]","-\frac{1}{24} \sec ^3(x) \left(4 x+2 \sin (2 x)+12 x \cos (2 x)+5 \cos (3 x) \log \left(\cos \left(\frac{x}{2}\right)-\sin \left(\frac{x}{2}\right)\right)+15 \cos (x) \left(\log \left(\cos \left(\frac{x}{2}\right)-\sin \left(\frac{x}{2}\right)\right)-\log \left(\sin \left(\frac{x}{2}\right)+\cos \left(\frac{x}{2}\right)\right)\right)-5 \cos (3 x) \log \left(\sin \left(\frac{x}{2}\right)+\cos \left(\frac{x}{2}\right)\right)\right)","\frac{1}{3} x \sec ^3(x)-x \sec (x)+\frac{5}{6} \tanh ^{-1}(\sin (x))-\frac{1}{6} \tan (x) \sec (x)",1,"-1/24*(Sec[x]^3*(4*x + 12*x*Cos[2*x] + 5*Cos[3*x]*Log[Cos[x/2] - Sin[x/2]] + 15*Cos[x]*(Log[Cos[x/2] - Sin[x/2]] - Log[Cos[x/2] + Sin[x/2]]) - 5*Cos[3*x]*Log[Cos[x/2] + Sin[x/2]] + 2*Sin[2*x]))","B",1
489,1,16,16,0.0179959,"\int x \sec ^2(x) \tan (x) \, dx","Integrate[x*Sec[x]^2*Tan[x],x]","\frac{1}{2} x \sec ^2(x)-\frac{\tan (x)}{2}","\frac{1}{2} x \sec ^2(x)-\frac{\tan (x)}{2}",1,"(x*Sec[x]^2)/2 - Tan[x]/2","A",1
490,1,57,62,0.0170804,"\int x \sin ^2(x) \tan (x) \, dx","Integrate[x*Sin[x]^2*Tan[x],x]","\frac{1}{2} i \operatorname{PolyLog}\left(2,-e^{2 i x}\right)+\frac{i x^2}{2}-x \log \left(1+e^{2 i x}\right)-\frac{1}{8} \sin (2 x)+\frac{1}{4} x \cos (2 x)","\frac{1}{2} i \operatorname{PolyLog}\left(2,-e^{2 i x}\right)+\frac{i x^2}{2}+\frac{x}{4}-x \log \left(1+e^{2 i x}\right)-\frac{1}{2} x \sin ^2(x)-\frac{1}{4} \sin (x) \cos (x)",1,"(I/2)*x^2 + (x*Cos[2*x])/4 - x*Log[1 + E^((2*I)*x)] + (I/2)*PolyLog[2, -E^((2*I)*x)] - Sin[2*x]/8","A",1
491,1,54,59,0.0143383,"\int x \tan ^3(x) \, dx","Integrate[x*Tan[x]^3,x]","-\frac{1}{2} i \operatorname{PolyLog}\left(2,-e^{2 i x}\right)-\frac{i x^2}{2}+x \log \left(1+e^{2 i x}\right)-\frac{\tan (x)}{2}+\frac{1}{2} x \sec ^2(x)","-\frac{1}{2} i \operatorname{PolyLog}\left(2,-e^{2 i x}\right)-\frac{i x^2}{2}+\frac{x}{2}+x \log \left(1+e^{2 i x}\right)+\frac{1}{2} x \tan ^2(x)-\frac{\tan (x)}{2}",1,"(-1/2*I)*x^2 + x*Log[1 + E^((2*I)*x)] - (I/2)*PolyLog[2, -E^((2*I)*x)] + (x*Sec[x]^2)/2 - Tan[x]/2","A",1
492,1,14,12,0.2331136,"\int \frac{2 x+\sin (2 x)}{(\cos (x)+x \sin (x))^2} \, dx","Integrate[(2*x + Sin[2*x])/(Cos[x] + x*Sin[x])^2,x]","\frac{2 x \sin (x)}{x \sin (x)+\cos (x)}","\frac{2}{\frac{\cot (x)}{x}+1}",1,"(2*x*Sin[x])/(Cos[x] + x*Sin[x])","A",1
493,1,19,20,0.2446783,"\int \frac{x^2}{(x \cos (x)-\sin (x))^2} \, dx","Integrate[x^2/(x*Cos[x] - Sin[x])^2,x]","\frac{x \sin (x)+\cos (x)}{x \cos (x)-\sin (x)}","\frac{x \csc (x)}{x \cos (x)-\sin (x)}-\cot (x)",1,"(Cos[x] + x*Sin[x])/(x*Cos[x] - Sin[x])","A",1
494,1,22,22,0.0139918,"\int a^{m x} b^{n x} \, dx","Integrate[a^(m*x)*b^(n*x),x]","\frac{a^{m x} b^{n x}}{m \log (a)+n \log (b)}","\frac{a^{m x} b^{n x}}{m \log (a)+n \log (b)}",1,"(a^(m*x)*b^(n*x))/(m*Log[a] + n*Log[b])","A",1
495,1,46,34,0.0558392,"\int a^{-x} b^{-x} \left(a^x-b^x\right)^2 \, dx","Integrate[(a^x - b^x)^2/(a^x*b^x),x]","\frac{e^{x (\log (a)-\log (b))}}{\log (a)-\log (b)}+\frac{e^{x (\log (b)-\log (a))}}{\log (b)-\log (a)}-2 x","\frac{a^x b^{-x}-a^{-x} b^x}{\log (a)-\log (b)}-2 x",1,"-2*x + E^(x*(Log[a] - Log[b]))/(Log[a] - Log[b]) + E^(x*(-Log[a] + Log[b]))/(-Log[a] + Log[b])","A",1
496,1,9,9,0.0029112,"\int \left(-e^{-x}+e^x\right) \, dx","Integrate[-E^(-x) + E^x,x]","e^{-x}+e^x","e^{-x}+e^x",1,"E^(-x) + E^x","A",1
497,1,22,22,0.0058692,"\int \left(-e^{-x}+e^x\right)^2 \, dx","Integrate[(-E^(-x) + E^x)^2,x]","-2 x-\frac{e^{-2 x}}{2}+\frac{e^{2 x}}{2}","-2 x-\frac{e^{-2 x}}{2}+\frac{e^{2 x}}{2}",1,"-1/2*1/E^(2*x) + E^(2*x)/2 - 2*x","A",1
498,1,30,31,0.0137064,"\int \left(-e^{-x}+e^x\right)^3 \, dx","Integrate[(-E^(-x) + E^x)^3,x]","\frac{1}{3} e^{-3 x} \left(-9 e^{2 x}-9 e^{4 x}+e^{6 x}+1\right)","\frac{e^{-3 x}}{3}-3 e^{-x}-3 e^x+\frac{e^{3 x}}{3}",1,"(1 - 9*E^(2*x) - 9*E^(4*x) + E^(6*x))/(3*E^(3*x))","A",1
499,1,34,36,0.0218701,"\int \left(-e^{-x}+e^x\right)^4 \, dx","Integrate[(-E^(-x) + E^x)^4,x]","\frac{1}{4} \left(24 x-e^{-4 x}+8 e^{-2 x}-8 e^{2 x}+e^{4 x}\right)","6 x-\frac{e^{-4 x}}{4}+2 e^{-2 x}-2 e^{2 x}+\frac{e^{4 x}}{4}",1,"(-E^(-4*x) + 8/E^(2*x) - 8*E^(2*x) + E^(4*x) + 24*x)/4","A",1
500,1,45,48,0.010967,"\int \left(-e^{-x}+e^x\right)^n \, dx","Integrate[(-E^(-x) + E^x)^n,x]","\frac{\left(e^{2 x}-1\right) \left(e^x-e^{-x}\right)^n \, _2F_1\left(1,\frac{n}{2}+1;1-\frac{n}{2};e^{2 x}\right)}{n}","-\frac{\left(1-e^{2 x}\right) \left(e^x-e^{-x}\right)^n \, _2F_1\left(1,\frac{n+2}{2};1-\frac{n}{2};e^{2 x}\right)}{n}",1,"((-E^(-x) + E^x)^n*(-1 + E^(2*x))*Hypergeometric2F1[1, 1 + n/2, 1 - n/2, E^(2*x)])/n","A",1
501,1,33,43,0.0329666,"\int \left(a^{-4 x}-a^{2 x}\right)^3 \, dx","Integrate[(a^(-4*x) - a^(2*x))^3,x]","-\frac{a^{-12 x}-6 a^{-6 x}+2 a^{6 x}-36 x \log (a)}{12 \log (a)}","-\frac{a^{-12 x}}{12 \log (a)}+\frac{a^{-6 x}}{2 \log (a)}-\frac{a^{6 x}}{6 \log (a)}+3 x",1,"-1/12*(a^(-12*x) - 6/a^(6*x) + 2*a^(6*x) - 36*x*Log[a])/Log[a]","A",1
502,1,27,27,0.0059843,"\int \left(a^{k x}+a^{l x}\right) \, dx","Integrate[a^(k*x) + a^(l*x),x]","\frac{a^{k x}}{k \log (a)}+\frac{a^{l x}}{l \log (a)}","\frac{a^{k x}}{k \log (a)}+\frac{a^{l x}}{l \log (a)}",1,"a^(k*x)/(k*Log[a]) + a^(l*x)/(l*Log[a])","A",1
503,1,53,53,0.0467827,"\int \left(a^{k x}+a^{l x}\right)^2 \, dx","Integrate[(a^(k*x) + a^(l*x))^2,x]","\frac{2 a^{x (k+l)}}{\log (a) (k+l)}+\frac{a^{2 k x}}{2 k \log (a)}+\frac{a^{2 l x}}{2 l \log (a)}","\frac{2 a^{x (k+l)}}{\log (a) (k+l)}+\frac{a^{2 k x}}{2 k \log (a)}+\frac{a^{2 l x}}{2 l \log (a)}",1,"a^(2*k*x)/(2*k*Log[a]) + a^(2*l*x)/(2*l*Log[a]) + (2*a^((k + l)*x))/((k + l)*Log[a])","A",1
504,1,65,79,0.0954078,"\int \left(a^{k x}+a^{l x}\right)^3 \, dx","Integrate[(a^(k*x) + a^(l*x))^3,x]","\frac{\frac{9 a^{x (2 k+l)}}{2 k+l}+\frac{9 a^{x (k+2 l)}}{k+2 l}+\frac{a^{3 k x}}{k}+\frac{a^{3 l x}}{l}}{3 \log (a)}","\frac{3 a^{x (2 k+l)}}{\log (a) (2 k+l)}+\frac{3 a^{x (k+2 l)}}{\log (a) (k+2 l)}+\frac{a^{3 k x}}{3 k \log (a)}+\frac{a^{3 l x}}{3 l \log (a)}",1,"(a^(3*k*x)/k + a^(3*l*x)/l + (9*a^((2*k + l)*x))/(2*k + l) + (9*a^((k + 2*l)*x))/(k + 2*l))/(3*Log[a])","A",1
505,1,80,98,0.1007545,"\int \left(a^{k x}+a^{l x}\right)^4 \, dx","Integrate[(a^(k*x) + a^(l*x))^4,x]","\frac{\frac{12 a^{2 x (k+l)}}{k+l}+\frac{16 a^{x (3 k+l)}}{3 k+l}+\frac{16 a^{x (k+3 l)}}{k+3 l}+\frac{a^{4 k x}}{k}+\frac{a^{4 l x}}{l}}{4 \log (a)}","\frac{3 a^{2 x (k+l)}}{\log (a) (k+l)}+\frac{4 a^{x (3 k+l)}}{\log (a) (3 k+l)}+\frac{4 a^{x (k+3 l)}}{\log (a) (k+3 l)}+\frac{a^{4 k x}}{4 k \log (a)}+\frac{a^{4 l x}}{4 l \log (a)}",1,"(a^(4*k*x)/k + a^(4*l*x)/l + (12*a^(2*(k + l)*x))/(k + l) + (16*a^((3*k + l)*x))/(3*k + l) + (16*a^((k + 3*l)*x))/(k + 3*l))/(4*Log[a])","A",1
506,1,73,72,0.0309329,"\int \left(a^{k x}+a^{l x}\right)^n \, dx","Integrate[(a^(k*x) + a^(l*x))^n,x]","\frac{\left(a^{x (l-k)}+1\right) \left(a^{k x}+a^{l x}\right)^n \, _2F_1\left(1,\frac{k n}{l-k}+n+1;\frac{k n}{l-k}+1;-a^{(l-k) x}\right)}{k n \log (a)}","\frac{\left(a^{x (k-l)}+1\right) \left(a^{k x}+a^{l x}\right)^n \, _2F_1\left(1,\frac{k n}{k-l}+1;\frac{l n}{k-l}+1;-a^{(k-l) x}\right)}{l n \log (a)}",1,"((a^(k*x) + a^(l*x))^n*(1 + a^((-k + l)*x))*Hypergeometric2F1[1, 1 + n + (k*n)/(-k + l), 1 + (k*n)/(-k + l), -a^((-k + l)*x)])/(k*n*Log[a])","A",0
507,1,28,28,0.0065326,"\int \left(a^{k x}-a^{l x}\right) \, dx","Integrate[a^(k*x) - a^(l*x),x]","\frac{a^{k x}}{k \log (a)}-\frac{a^{l x}}{l \log (a)}","\frac{a^{k x}}{k \log (a)}-\frac{a^{l x}}{l \log (a)}",1,"a^(k*x)/(k*Log[a]) - a^(l*x)/(l*Log[a])","A",1
508,1,53,53,0.034477,"\int \left(a^{k x}-a^{l x}\right)^2 \, dx","Integrate[(a^(k*x) - a^(l*x))^2,x]","-\frac{2 a^{x (k+l)}}{\log (a) (k+l)}+\frac{a^{2 k x}}{2 k \log (a)}+\frac{a^{2 l x}}{2 l \log (a)}","-\frac{2 a^{x (k+l)}}{\log (a) (k+l)}+\frac{a^{2 k x}}{2 k \log (a)}+\frac{a^{2 l x}}{2 l \log (a)}",1,"a^(2*k*x)/(2*k*Log[a]) + a^(2*l*x)/(2*l*Log[a]) - (2*a^((k + l)*x))/((k + l)*Log[a])","A",1
509,1,66,79,0.0728791,"\int \left(a^{k x}-a^{l x}\right)^3 \, dx","Integrate[(a^(k*x) - a^(l*x))^3,x]","\frac{-\frac{9 a^{x (2 k+l)}}{2 k+l}+\frac{9 a^{x (k+2 l)}}{k+2 l}+\frac{a^{3 k x}}{k}-\frac{a^{3 l x}}{l}}{3 \log (a)}","-\frac{3 a^{x (2 k+l)}}{\log (a) (2 k+l)}+\frac{3 a^{x (k+2 l)}}{\log (a) (k+2 l)}+\frac{a^{3 k x}}{3 k \log (a)}-\frac{a^{3 l x}}{3 l \log (a)}",1,"(a^(3*k*x)/k - a^(3*l*x)/l - (9*a^((2*k + l)*x))/(2*k + l) + (9*a^((k + 2*l)*x))/(k + 2*l))/(3*Log[a])","A",1
510,1,80,98,0.0738992,"\int \left(a^{k x}-a^{l x}\right)^4 \, dx","Integrate[(a^(k*x) - a^(l*x))^4,x]","\frac{\frac{12 a^{2 x (k+l)}}{k+l}-\frac{16 a^{x (3 k+l)}}{3 k+l}-\frac{16 a^{x (k+3 l)}}{k+3 l}+\frac{a^{4 k x}}{k}+\frac{a^{4 l x}}{l}}{4 \log (a)}","\frac{3 a^{2 x (k+l)}}{\log (a) (k+l)}-\frac{4 a^{x (3 k+l)}}{\log (a) (3 k+l)}-\frac{4 a^{x (k+3 l)}}{\log (a) (k+3 l)}+\frac{a^{4 k x}}{4 k \log (a)}+\frac{a^{4 l x}}{4 l \log (a)}",1,"(a^(4*k*x)/k + a^(4*l*x)/l + (12*a^(2*(k + l)*x))/(k + l) - (16*a^((3*k + l)*x))/(3*k + l) - (16*a^((k + 3*l)*x))/(k + 3*l))/(4*Log[a])","A",1
511,1,75,74,0.0271454,"\int \left(a^{k x}-a^{l x}\right)^n \, dx","Integrate[(a^(k*x) - a^(l*x))^n,x]","\frac{\left(1-a^{x (l-k)}\right) \left(a^{k x}-a^{l x}\right)^n \, _2F_1\left(1,\frac{k n}{l-k}+n+1;\frac{k n}{l-k}+1;a^{(l-k) x}\right)}{k n \log (a)}","\frac{\left(1-a^{x (k-l)}\right) \left(a^{k x}-a^{l x}\right)^n \, _2F_1\left(1,\frac{k n}{k-l}+1;\frac{l n}{k-l}+1;a^{(k-l) x}\right)}{l n \log (a)}",1,"((a^(k*x) - a^(l*x))^n*(1 - a^((-k + l)*x))*Hypergeometric2F1[1, 1 + n + (k*n)/(-k + l), 1 + (k*n)/(-k + l), a^((-k + l)*x)])/(k*n*Log[a])","A",0
512,1,15,15,0.0048005,"\int \left(1+a^{m x}\right) \, dx","Integrate[1 + a^(m*x),x]","\frac{a^{m x}}{m \log (a)}+x","\frac{a^{m x}}{m \log (a)}+x",1,"x + a^(m*x)/(m*Log[a])","A",1
513,1,31,33,0.0119221,"\int \left(1+a^{m x}\right)^2 \, dx","Integrate[(1 + a^(m*x))^2,x]","\frac{2 a^{m x}+\frac{1}{2} a^{2 m x}+m x \log (a)}{m \log (a)}","\frac{2 a^{m x}}{m \log (a)}+\frac{a^{2 m x}}{2 m \log (a)}+x",1,"(2*a^(m*x) + a^(2*m*x)/2 + m*x*Log[a])/(m*Log[a])","A",1
514,1,35,50,0.027548,"\int \left(1+a^{m x}\right)^3 \, dx","Integrate[(1 + a^(m*x))^3,x]","\frac{\left(9 a^{m x}+2 a^{2 m x}+18\right) a^{m x}}{6 m \log (a)}+x","\frac{3 a^{m x}}{m \log (a)}+\frac{3 a^{2 m x}}{2 m \log (a)}+\frac{a^{3 m x}}{3 m \log (a)}+x",1,"x + (a^(m*x)*(18 + 9*a^(m*x) + 2*a^(2*m*x)))/(6*m*Log[a])","A",1
515,1,49,65,0.0222398,"\int \left(1+a^{m x}\right)^4 \, dx","Integrate[(1 + a^(m*x))^4,x]","\frac{4 a^{m x}+3 a^{2 m x}+\frac{4}{3} a^{3 m x}+\frac{1}{4} a^{4 m x}+m x \log (a)}{m \log (a)}","\frac{4 a^{m x}}{m \log (a)}+\frac{3 a^{2 m x}}{m \log (a)}+\frac{4 a^{3 m x}}{3 m \log (a)}+\frac{a^{4 m x}}{4 m \log (a)}+x",1,"(4*a^(m*x) + 3*a^(2*m*x) + (4*a^(3*m*x))/3 + a^(4*m*x)/4 + m*x*Log[a])/(m*Log[a])","A",1
516,1,40,40,0.0127575,"\int \left(1+a^{m x}\right)^n \, dx","Integrate[(1 + a^(m*x))^n,x]","-\frac{\left(a^{m x}+1\right)^{n+1} \, _2F_1\left(1,n+1;n+2;a^{m x}+1\right)}{m (n+1) \log (a)}","-\frac{\left(a^{m x}+1\right)^{n+1} \, _2F_1\left(1,n+1;n+2;a^{m x}+1\right)}{m (n+1) \log (a)}",1,"-(((1 + a^(m*x))^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, 1 + a^(m*x)])/(m*(1 + n)*Log[a]))","A",1
517,1,16,16,0.0047105,"\int \left(1-a^{m x}\right) \, dx","Integrate[1 - a^(m*x),x]","x-\frac{a^{m x}}{m \log (a)}","x-\frac{a^{m x}}{m \log (a)}",1,"x - a^(m*x)/(m*Log[a])","A",1
518,1,25,33,0.0177835,"\int \left(1-a^{m x}\right)^2 \, dx","Integrate[(1 - a^(m*x))^2,x]","\frac{\left(a^{m x}-4\right) a^{m x}}{2 m \log (a)}+x","-\frac{2 a^{m x}}{m \log (a)}+\frac{a^{2 m x}}{2 m \log (a)}+x",1,"x + (a^(m*x)*(-4 + a^(m*x)))/(2*m*Log[a])","A",1
519,1,35,50,0.0282823,"\int \left(1-a^{m x}\right)^3 \, dx","Integrate[(1 - a^(m*x))^3,x]","x-\frac{a^{m x} \left(-9 a^{m x}+2 a^{2 m x}+18\right)}{6 m \log (a)}","-\frac{3 a^{m x}}{m \log (a)}+\frac{3 a^{2 m x}}{2 m \log (a)}-\frac{a^{3 m x}}{3 m \log (a)}+x",1,"x - (a^(m*x)*(18 - 9*a^(m*x) + 2*a^(2*m*x)))/(6*m*Log[a])","A",1
520,1,49,65,0.0178623,"\int \left(1-a^{m x}\right)^4 \, dx","Integrate[(1 - a^(m*x))^4,x]","\frac{-4 a^{m x}+3 a^{2 m x}-\frac{4}{3} a^{3 m x}+\frac{1}{4} a^{4 m x}+m x \log (a)}{m \log (a)}","-\frac{4 a^{m x}}{m \log (a)}+\frac{3 a^{2 m x}}{m \log (a)}-\frac{4 a^{3 m x}}{3 m \log (a)}+\frac{a^{4 m x}}{4 m \log (a)}+x",1,"(-4*a^(m*x) + 3*a^(2*m*x) - (4*a^(3*m*x))/3 + a^(4*m*x)/4 + m*x*Log[a])/(m*Log[a])","A",1
521,1,44,44,0.0148751,"\int \left(1-a^{m x}\right)^n \, dx","Integrate[(1 - a^(m*x))^n,x]","-\frac{\left(1-a^{m x}\right)^{n+1} \, _2F_1\left(1,n+1;n+2;1-a^{m x}\right)}{m (n+1) \log (a)}","-\frac{\left(1-a^{m x}\right)^{n+1} \, _2F_1\left(1,n+1;n+2;1-a^{m x}\right)}{m (n+1) \log (a)}",1,"-(((1 - a^(m*x))^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, 1 - a^(m*x)])/(m*(1 + n)*Log[a]))","A",1
522,1,24,24,0.0056704,"\int \frac{1}{b+a e^{n x}} \, dx","Integrate[(b + a*E^(n*x))^(-1),x]","\frac{x}{b}-\frac{\log \left(a e^{n x}+b\right)}{b n}","\frac{x}{b}-\frac{\log \left(a e^{n x}+b\right)}{b n}",1,"x/b - Log[b + a*E^(n*x)]/(b*n)","A",1
523,1,97,100,0.0550869,"\int \frac{e^x}{b+a e^{3 x}} \, dx","Integrate[E^x/(b + a*E^(3*x)),x]","-\frac{\log \left(a^{2/3} e^{2 x}-\sqrt[3]{a} \sqrt[3]{b} e^x+b^{2/3}\right)-2 \log \left(\sqrt[3]{a} e^x+\sqrt[3]{b}\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{a} e^x}{\sqrt[3]{b}}}{\sqrt{3}}\right)}{6 \sqrt[3]{a} b^{2/3}}","\frac{\log \left(\sqrt[3]{a} e^x+\sqrt[3]{b}\right)}{2 \sqrt[3]{a} b^{2/3}}-\frac{\log \left(a e^{3 x}+b\right)}{6 \sqrt[3]{a} b^{2/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{b}-2 \sqrt[3]{a} e^x}{\sqrt{3} \sqrt[3]{b}}\right)}{\sqrt{3} \sqrt[3]{a} b^{2/3}}",1,"-1/6*(2*Sqrt[3]*ArcTan[(1 - (2*a^(1/3)*E^x)/b^(1/3))/Sqrt[3]] - 2*Log[b^(1/3) + a^(1/3)*E^x] + Log[b^(2/3) - a^(1/3)*b^(1/3)*E^x + a^(2/3)*E^(2*x)])/(a^(1/3)*b^(2/3))","A",1
524,1,12,12,0.0093389,"\int \frac{-1+e^x}{1+e^x} \, dx","Integrate[(-1 + E^x)/(1 + E^x),x]","2 \log \left(e^x+1\right)-x","2 \log \left(e^x+1\right)-x",1,"-x + 2*Log[1 + E^x]","A",1
525,1,44,47,0.0220166,"\int \frac{e^{4 x}}{1-2 e^{2 x}+3 e^{4 x}} \, dx","Integrate[E^(4*x)/(1 - 2*E^(2*x) + 3*E^(4*x)),x]","\frac{1}{12} \left(\log \left(-2 e^{2 x}+3 e^{4 x}+1\right)+\sqrt{2} \tan ^{-1}\left(\frac{3 e^{2 x}-1}{\sqrt{2}}\right)\right)","\frac{1}{12} \log \left(-2 e^{2 x}+3 e^{4 x}+1\right)-\frac{\tan ^{-1}\left(\frac{1-3 e^{2 x}}{\sqrt{2}}\right)}{6 \sqrt{2}}",1,"(Sqrt[2]*ArcTan[(-1 + 3*E^(2*x))/Sqrt[2]] + Log[1 - 2*E^(2*x) + 3*E^(4*x)])/12","A",1
526,1,51,39,0.0448005,"\int \frac{e^x+e^{5 x}}{-1+e^x-e^{2 x}+e^{3 x}} \, dx","Integrate[(E^x + E^(5*x))/(-1 + E^x - E^(2*x) + E^(3*x)),x]","\frac{1}{2} \left(2 e^x+e^{2 x}+(-1+i) \log \left(-e^x+i\right)+2 \log \left(1-e^x\right)-(1+i) \log \left(e^x+i\right)\right)","e^x+\frac{e^{2 x}}{2}+\log \left(1-e^x\right)-\frac{1}{2} \log \left(e^{2 x}+1\right)-\tan ^{-1}\left(e^x\right)",1,"(2*E^x + E^(2*x) - (1 - I)*Log[I - E^x] + 2*Log[1 - E^x] - (1 + I)*Log[I + E^x])/2","C",1
527,1,30,30,0.0411396,"\int e^{n x} \left(a+b e^{n x}\right)^{r/s} \, dx","Integrate[E^(n*x)*(a + b*E^(n*x))^(r/s),x]","\frac{s \left(a+b e^{n x}\right)^{\frac{r}{s}+1}}{b n r+b n s}","\frac{s \left(a+b e^{n x}\right)^{\frac{r+s}{s}}}{b n (r+s)}",1,"((a + b*E^(n*x))^(1 + r/s)*s)/(b*n*r + b*n*s)","A",1
528,1,54,54,0.0387252,"\int \sqrt[4]{1-2 e^{x/3}} \, dx","Integrate[(1 - 2*E^(x/3))^(1/4),x]","12 \sqrt[4]{1-2 e^{x/3}}-6 \tan ^{-1}\left(\sqrt[4]{1-2 e^{x/3}}\right)-6 \tanh ^{-1}\left(\sqrt[4]{1-2 e^{x/3}}\right)","12 \sqrt[4]{1-2 e^{x/3}}-6 \tan ^{-1}\left(\sqrt[4]{1-2 e^{x/3}}\right)-6 \tanh ^{-1}\left(\sqrt[4]{1-2 e^{x/3}}\right)",1,"12*(1 - 2*E^(x/3))^(1/4) - 6*ArcTan[(1 - 2*E^(x/3))^(1/4)] - 6*ArcTanh[(1 - 2*E^(x/3))^(1/4)]","A",1
529,1,59,59,0.0230751,"\int \left(a+b e^{n x}\right)^{r/s} \, dx","Integrate[(a + b*E^(n*x))^(r/s),x]","-\frac{s \left(a+b e^{n x}\right)^{\frac{r+s}{s}} \, _2F_1\left(1,\frac{r+s}{s};\frac{r}{s}+2;\frac{e^{n x} b}{a}+1\right)}{a n (r+s)}","-\frac{s \left(a+b e^{n x}\right)^{\frac{r+s}{s}} \, _2F_1\left(1,\frac{r+s}{s};\frac{r}{s}+2;\frac{e^{n x} b}{a}+1\right)}{a n (r+s)}",1,"-(((a + b*E^(n*x))^((r + s)/s)*s*Hypergeometric2F1[1, (r + s)/s, 2 + r/s, 1 + (b*E^(n*x))/a])/(a*n*(r + s)))","A",1
530,1,18,18,0.0059504,"\int \frac{e^x}{\sqrt{a^2+e^{2 x}}} \, dx","Integrate[E^x/Sqrt[a^2 + E^(2*x)],x]","\tanh ^{-1}\left(\frac{e^x}{\sqrt{a^2+e^{2 x}}}\right)","\tanh ^{-1}\left(\frac{e^x}{\sqrt{a^2+e^{2 x}}}\right)",1,"ArcTanh[E^x/Sqrt[a^2 + E^(2*x)]]","A",1
531,1,20,20,0.0062572,"\int \frac{e^x}{\sqrt{-a^2+e^{2 x}}} \, dx","Integrate[E^x/Sqrt[-a^2 + E^(2*x)],x]","\tanh ^{-1}\left(\frac{e^x}{\sqrt{e^{2 x}-a^2}}\right)","\tanh ^{-1}\left(\frac{e^x}{\sqrt{e^{2 x}-a^2}}\right)",1,"ArcTanh[E^x/Sqrt[-a^2 + E^(2*x)]]","A",1
532,1,40,40,0.0217378,"\int \frac{e^{3 x/4}}{\left(-2+e^{3 x/4}\right) \sqrt{-2+e^{3 x/4}+e^{3 x/2}}} \, dx","Integrate[E^((3*x)/4)/((-2 + E^((3*x)/4))*Sqrt[-2 + E^((3*x)/4) + E^((3*x)/2)]),x]","-\frac{2}{3} \tanh ^{-1}\left(\frac{5 e^{3 x/4}-2}{4 \sqrt{e^{3 x/4}+e^{3 x/2}-2}}\right)","\frac{2}{3} \tanh ^{-1}\left(\frac{2-5 e^{3 x/4}}{4 \sqrt{e^{3 x/4}+e^{3 x/2}-2}}\right)",1,"(-2*ArcTanh[(-2 + 5*E^((3*x)/4))/(4*Sqrt[-2 + E^((3*x)/4) + E^((3*x)/2)])])/3","A",1
533,1,54,37,0.0174085,"\int e^{-2 x} \left(-3+e^{7 x}\right)^{2/3} \, dx","Integrate[(-3 + E^(7*x))^(2/3)/E^(2*x),x]","-\frac{e^{-2 x} \left(e^{7 x}-3\right)^{2/3} \, _2F_1\left(-\frac{2}{3},-\frac{2}{7};\frac{5}{7};\frac{e^{7 x}}{3}\right)}{2 \left(1-\frac{e^{7 x}}{3}\right)^{2/3}}","\frac{1}{6} e^{-2 x} \left(e^{7 x}-3\right)^{5/3} \, _2F_1\left(1,\frac{29}{21};\frac{5}{7};\frac{e^{7 x}}{3}\right)",1,"-1/2*((-3 + E^(7*x))^(2/3)*Hypergeometric2F1[-2/3, -2/7, 5/7, E^(7*x)/3])/(E^(2*x)*(1 - E^(7*x)/3)^(2/3))","A",1
534,1,44,73,0.0214831,"\int \frac{e^{2 x}}{\left(3-e^{x/2}\right)^{3/4}} \, dx","Integrate[E^(2*x)/(3 - E^(x/2))^(3/4),x]","-\frac{8}{65} \sqrt[4]{3-e^{x/2}} \left(96 e^{x/2}+20 e^x+5 e^{3 x/2}+1152\right)","\frac{8}{13} \left(3-e^{x/2}\right)^{13/4}-8 \left(3-e^{x/2}\right)^{9/4}+\frac{216}{5} \left(3-e^{x/2}\right)^{5/4}-216 \sqrt[4]{3-e^{x/2}}",1,"(-8*(3 - E^(x/2))^(1/4)*(1152 + 96*E^(x/2) + 20*E^x + 5*E^((3*x)/2)))/65","A",1
535,1,23,44,0.0077248,"\int e^{-x/2} x^3 \, dx","Integrate[x^3/E^(x/2),x]","e^{-x/2} \left(-2 x^3-12 x^2-48 x-96\right)","-2 e^{-x/2} x^3-12 e^{-x/2} x^2-48 e^{-x/2} x-96 e^{-x/2}",1,"(-96 - 48*x - 12*x^2 - 2*x^3)/E^(x/2)","A",1
536,1,26,39,0.023592,"\int \frac{e^{-x/2}}{x^3} \, dx","Integrate[1/(E^(x/2)*x^3),x]","\frac{1}{8} \left(\text{Ei}\left(-\frac{x}{2}\right)+\frac{2 e^{-x/2} (x-2)}{x^2}\right)","\frac{\text{Ei}\left(-\frac{x}{2}\right)}{8}-\frac{e^{-x/2}}{2 x^2}+\frac{e^{-x/2}}{4 x}",1,"((2*(-2 + x))/(E^(x/2)*x^2) + ExpIntegralEi[-1/2*x])/8","A",1
537,1,29,44,0.0105209,"\int a^{3 x} x^2 \, dx","Integrate[a^(3*x)*x^2,x]","\frac{a^{3 x} \left(9 x^2 \log ^2(a)-6 x \log (a)+2\right)}{27 \log ^3(a)}","\frac{x^2 a^{3 x}}{3 \log (a)}+\frac{2 a^{3 x}}{27 \log ^3(a)}-\frac{2 x a^{3 x}}{9 \log ^2(a)}",1,"(a^(3*x)*(2 - 6*x*Log[a] + 9*x^2*Log[a]^2))/(27*Log[a]^3)","A",1
538,1,12,12,0.005117,"\int e^{x^2} x \left(1+x^2\right) \, dx","Integrate[E^x^2*x*(1 + x^2),x]","\frac{1}{2} e^{x^2} x^2","\frac{1}{2} e^{x^2} x^2",1,"(E^x^2*x^2)/2","A",1
539,1,31,32,0.0364727,"\int \frac{x}{\left(e^{-x}+e^x\right)^2} \, dx","Integrate[x/(E^(-x) + E^x)^2,x]","\frac{e^{2 x} x}{2 e^{2 x}+2}-\frac{1}{4} \log \left(e^{2 x}+1\right)","-\frac{x}{2 \left(e^{2 x}+1\right)}+\frac{x}{2}-\frac{1}{4} \log \left(e^{2 x}+1\right)",1,"(E^(2*x)*x)/(2 + 2*E^(2*x)) - Log[1 + E^(2*x)]/4","A",1
540,1,15,15,0.0261579,"\int \frac{e^x \left(1-x-x^2\right)}{\sqrt{1-x^2}} \, dx","Integrate[(E^x*(1 - x - x^2))/Sqrt[1 - x^2],x]","e^x \sqrt{1-x^2}","e^x \sqrt{1-x^2}",1,"E^x*Sqrt[1 - x^2]","A",1
541,1,22,27,0.0276753,"\int e^{-3 x} \cos (2 x) \, dx","Integrate[Cos[2*x]/E^(3*x),x]","\frac{1}{13} e^{-3 x} (2 \sin (2 x)-3 \cos (2 x))","\frac{2}{13} e^{-3 x} \sin (2 x)-\frac{3}{13} e^{-3 x} \cos (2 x)",1,"(-3*Cos[2*x] + 2*Sin[2*x])/(13*E^(3*x))","A",1
542,1,26,35,0.0622053,"\int \frac{\cos \left(\frac{x}{2}\right)+\sin \left(\frac{x}{2}\right)}{\sqrt[3]{e^x}} \, dx","Integrate[(Cos[x/2] + Sin[x/2])/(E^x)^(1/3),x]","\frac{6 \left(\sin \left(\frac{x}{2}\right)-5 \cos \left(\frac{x}{2}\right)\right)}{13 \sqrt[3]{e^x}}","\frac{6 \sin \left(\frac{x}{2}\right)}{13 \sqrt[3]{e^x}}-\frac{30 \cos \left(\frac{x}{2}\right)}{13 \sqrt[3]{e^x}}",1,"(6*(-5*Cos[x/2] + Sin[x/2]))/(13*(E^x)^(1/3))","A",1
543,1,37,57,0.0676912,"\int \frac{\cos \left(\frac{3 x}{2}\right)}{\sqrt[4]{3^{3 x}}} \, dx","Integrate[Cos[(3*x)/2]/(3^(3*x))^(1/4),x]","-\frac{4 \left(\log (3) \cos \left(\frac{3 x}{2}\right)-2 \sin \left(\frac{3 x}{2}\right)\right)}{3 \sqrt[4]{27^x} \left(4+\log ^2(3)\right)}","\frac{8 \sin \left(\frac{3 x}{2}\right)}{3 \sqrt[4]{3^{3 x}} \left(4+\log ^2(3)\right)}-\frac{4 \log (3) \cos \left(\frac{3 x}{2}\right)}{3 \sqrt[4]{3^{3 x}} \left(4+\log ^2(3)\right)}",1,"(-4*(Cos[(3*x)/2]*Log[3] - 2*Sin[(3*x)/2]))/(3*(27^x)^(1/4)*(4 + Log[3]^2))","A",1
544,1,39,54,0.0345136,"\int e^{m x} \cos ^2(x) \, dx","Integrate[E^(m*x)*Cos[x]^2,x]","\frac{e^{m x} \left(m^2 \cos (2 x)+m^2+2 m \sin (2 x)+4\right)}{2 m \left(m^2+4\right)}","\frac{2 e^{m x}}{m \left(m^2+4\right)}+\frac{m e^{m x} \cos ^2(x)}{m^2+4}+\frac{2 e^{m x} \sin (x) \cos (x)}{m^2+4}",1,"(E^(m*x)*(4 + m^2 + m^2*Cos[2*x] + 2*m*Sin[2*x]))/(2*m*(4 + m^2))","A",1
545,1,64,82,0.1799264,"\int e^{m x} \sin ^3(x) \, dx","Integrate[E^(m*x)*Sin[x]^3,x]","\frac{e^{m x} \left(-3 \left(m^2+9\right) \cos (x)+3 \left(m^2+1\right) \cos (3 x)-2 m \sin (x) \left(\left(m^2+1\right) \cos (2 x)-m^2-13\right)\right)}{4 \left(m^4+10 m^2+9\right)}","\frac{m e^{m x} \sin ^3(x)}{m^2+9}-\frac{3 e^{m x} \sin ^2(x) \cos (x)}{m^2+9}+\frac{6 m e^{m x} \sin (x)}{m^4+10 m^2+9}-\frac{6 e^{m x} \cos (x)}{m^4+10 m^2+9}",1,"(E^(m*x)*(-3*(9 + m^2)*Cos[x] + 3*(1 + m^2)*Cos[3*x] - 2*m*(-13 - m^2 + (1 + m^2)*Cos[2*x])*Sin[x]))/(4*(9 + 10*m^2 + m^4))","A",1
546,1,36,79,0.0436096,"\int \frac{\cos ^3\left(\frac{x}{3}\right)}{\sqrt{e^x}} \, dx","Integrate[Cos[x/3]^3/Sqrt[E^x],x]","\frac{90 \sin \left(\frac{x}{3}\right)+26 \sin (x)-135 \cos \left(\frac{x}{3}\right)-13 \cos (x)}{130 \sqrt{e^x}}","\frac{32 \sin \left(\frac{x}{3}\right)}{65 \sqrt{e^x}}-\frac{2 \cos ^3\left(\frac{x}{3}\right)}{5 \sqrt{e^x}}-\frac{48 \cos \left(\frac{x}{3}\right)}{65 \sqrt{e^x}}+\frac{4 \sin \left(\frac{x}{3}\right) \cos ^2\left(\frac{x}{3}\right)}{5 \sqrt{e^x}}",1,"(-135*Cos[x/3] - 13*Cos[x] + 90*Sin[x/3] + 26*Sin[x])/(130*Sqrt[E^x])","A",1
547,1,21,36,0.035642,"\int e^{2 x} \cos ^2(x) \sin ^2(x) \, dx","Integrate[E^(2*x)*Cos[x]^2*Sin[x]^2,x]","-\frac{1}{80} e^{2 x} (2 \sin (4 x)+\cos (4 x)-5)","\frac{e^{2 x}}{16}-\frac{1}{40} e^{2 x} \sin (4 x)-\frac{1}{80} e^{2 x} \cos (4 x)",1,"-1/80*(E^(2*x)*(-5 + Cos[4*x] + 2*Sin[4*x]))","A",1
548,1,21,36,0.0446109,"\int e^{3 x} \cos ^2\left(\frac{3 x}{2}\right) \sin ^2\left(\frac{3 x}{2}\right) \, dx","Integrate[E^(3*x)*Cos[(3*x)/2]^2*Sin[(3*x)/2]^2,x]","-\frac{1}{120} e^{3 x} (2 \sin (6 x)+\cos (6 x)-5)","\frac{e^{3 x}}{24}-\frac{1}{60} e^{3 x} \sin (6 x)-\frac{1}{120} e^{3 x} \cos (6 x)",1,"-1/120*(E^(3*x)*(-5 + Cos[6*x] + 2*Sin[6*x]))","A",1
549,1,97,58,0.2630689,"\int e^{m x} \tan ^2(x) \, dx","Integrate[E^(m*x)*Tan[x]^2,x]","\frac{e^{m x} \left(\frac{i m^2 e^{2 i x} \, _2F_1\left(1,1-\frac{i m}{2};2-\frac{i m}{2};-e^{2 i x}\right)}{m+2 i}-i m \, _2F_1\left(1,-\frac{i m}{2};1-\frac{i m}{2};-e^{2 i x}\right)+m \tan (x)-1\right)}{m}","-\frac{e^{m x}}{m}+\frac{4 e^{(m+2 i) x} \, _2F_1\left(2,1-\frac{i m}{2};2-\frac{i m}{2};-e^{2 i x}\right)}{m+2 i}",1,"(E^(m*x)*(-1 + (I*E^((2*I)*x)*m^2*Hypergeometric2F1[1, 1 - (I/2)*m, 2 - (I/2)*m, -E^((2*I)*x)])/(2*I + m) - I*m*Hypergeometric2F1[1, (-1/2*I)*m, 1 - (I/2)*m, -E^((2*I)*x)] + m*Tan[x]))/m","A",1
550,1,90,45,0.2006633,"\int e^{m x} \csc ^2(x) \, dx","Integrate[E^(m*x)*Csc[x]^2,x]","\frac{e^{m x} \left(m e^{2 i x} \, _2F_1\left(1,1-\frac{i m}{2};2-\frac{i m}{2};e^{2 i x}\right)+(m+2 i) \left(\, _2F_1\left(1,-\frac{i m}{2};1-\frac{i m}{2};e^{2 i x}\right)-i \cot (x)\right)\right)}{-2+i m}","-\frac{4 e^{(m+2 i) x} \, _2F_1\left(2,1-\frac{i m}{2};2-\frac{i m}{2};e^{2 i x}\right)}{m+2 i}",1,"(E^(m*x)*(E^((2*I)*x)*m*Hypergeometric2F1[1, 1 - (I/2)*m, 2 - (I/2)*m, E^((2*I)*x)] + (2*I + m)*((-I)*Cot[x] + Hypergeometric2F1[1, (-1/2*I)*m, 1 - (I/2)*m, E^((2*I)*x)])))/(-2 + I*m)","A",1
551,1,66,51,0.0503384,"\int e^{m x} \sec ^3(x) \, dx","Integrate[E^(m*x)*Sec[x]^3,x]","\frac{1}{2} e^{m x} \left(\sec (x) (\tan (x)-m)+2 (m-i) e^{i x} \, _2F_1\left(1,\frac{1}{2}-\frac{i m}{2};\frac{3}{2}-\frac{i m}{2};-e^{2 i x}\right)\right)","\frac{8 e^{(m+3 i) x} \, _2F_1\left(3,\frac{1}{2} (3-i m);\frac{1}{2} (5-i m);-e^{2 i x}\right)}{m+3 i}",1,"(E^(m*x)*(2*E^(I*x)*(-I + m)*Hypergeometric2F1[1, 1/2 - (I/2)*m, 3/2 - (I/2)*m, -E^((2*I)*x)] + Sec[x]*(-m + Tan[x])))/2","A",1
552,1,28,28,0.0097563,"\int \frac{e^x}{1+\cos (x)} \, dx","Integrate[E^x/(1 + Cos[x]),x]","(1-i) e^{(1+i) x} \, _2F_1\left(1-i,2;2-i;-e^{i x}\right)","(1-i) e^{(1+i) x} \, _2F_1\left(1-i,2;2-i;-e^{i x}\right)",1,"(1 - I)*E^((1 + I)*x)*Hypergeometric2F1[1 - I, 2, 2 - I, -E^(I*x)]","A",1
553,1,84,26,0.0756883,"\int \frac{e^x}{1-\cos (x)} \, dx","Integrate[E^x/(1 - Cos[x]),x]","\frac{(1+i) e^x \sin \left(\frac{x}{2}\right) \left((1+i) \, _2F_1\left(-i,1;1-i;e^{i x}\right) \sin \left(\frac{x}{2}\right)+e^{i x} \, _2F_1\left(1,1-i;2-i;e^{i x}\right) \sin \left(\frac{x}{2}\right)+(1-i) \cos \left(\frac{x}{2}\right)\right)}{\cos (x)-1}","(-1+i) e^{(1+i) x} \, _2F_1\left(1-i,2;2-i;e^{i x}\right)",1,"((1 + I)*E^x*Sin[x/2]*((1 - I)*Cos[x/2] + (1 + I)*Hypergeometric2F1[-I, 1, 1 - I, E^(I*x)]*Sin[x/2] + E^(I*x)*Hypergeometric2F1[1, 1 - I, 2 - I, E^(I*x)]*Sin[x/2]))/(-1 + Cos[x])","B",1
554,1,61,30,0.6207869,"\int \frac{e^x}{1+\sin (x)} \, dx","Integrate[E^x/(1 + Sin[x]),x]","\frac{2 e^x \sin \left(\frac{x}{2}\right)}{\sin \left(\frac{x}{2}\right)+\cos \left(\frac{x}{2}\right)}-(1-i) (\sinh (x)+\cosh (x)) (1-(1-i) \, _2F_1(-i,1;1-i;i \cos (x)-\sin (x)))","(-1+i) e^{(1-i) x} \, _2F_1\left(1+i,2;2+i;-i e^{-i x}\right)",1,"(2*E^x*Sin[x/2])/(Cos[x/2] + Sin[x/2]) - (1 - I)*(1 - (1 - I)*Hypergeometric2F1[-I, 1, 1 - I, I*Cos[x] - Sin[x]])*(Cosh[x] + Sinh[x])","B",1
555,1,61,30,0.682443,"\int \frac{e^x}{1-\sin (x)} \, dx","Integrate[E^x/(1 - Sin[x]),x]","\frac{2 e^x \sin \left(\frac{x}{2}\right)}{\cos \left(\frac{x}{2}\right)-\sin \left(\frac{x}{2}\right)}+(1+i) (\sinh (x)+\cosh (x)) (1-(1+i) \, _2F_1(-i,1;1-i;\sin (x)-i \cos (x)))","(1+i) e^{(1+i) x} \, _2F_1\left(1-i,2;2-i;-i e^{i x}\right)",1,"(2*E^x*Sin[x/2])/(Cos[x/2] - Sin[x/2]) + (1 + I)*(1 - (1 + I)*Hypergeometric2F1[-I, 1, 1 - I, (-I)*Cos[x] + Sin[x]])*(Cosh[x] + Sinh[x])","B",1
556,1,11,15,0.2321558,"\int \frac{e^x (1-\sin (x))}{1-\cos (x)} \, dx","Integrate[(E^x*(1 - Sin[x]))/(1 - Cos[x]),x]","-e^x \cot \left(\frac{x}{2}\right)","-\frac{e^x \sin (x)}{1-\cos (x)}",1,"-(E^x*Cot[x/2])","A",1
557,1,100,41,0.224956,"\int \frac{e^x (1+\sin (x))}{1-\cos (x)} \, dx","Integrate[(E^x*(1 + Sin[x]))/(1 - Cos[x]),x]","\frac{2 e^x \sin \left(\frac{x}{2}\right) (\sin (x)+1) \left(2 i \, _2F_1\left(-i,1;1-i;e^{i x}\right) \sin \left(\frac{x}{2}\right)+(1+i) e^{i x} \, _2F_1\left(1,1-i;2-i;e^{i x}\right) \sin \left(\frac{x}{2}\right)+\cos \left(\frac{x}{2}\right)\right)}{(\cos (x)-1) \left(\sin \left(\frac{x}{2}\right)+\cos \left(\frac{x}{2}\right)\right)^2}","\frac{e^x \sin (x)}{1-\cos (x)}-(2-2 i) e^{(1+i) x} \, _2F_1\left(1-i,2;2-i;e^{i x}\right)",1,"(2*E^x*Sin[x/2]*(Cos[x/2] + (2*I)*Hypergeometric2F1[-I, 1, 1 - I, E^(I*x)]*Sin[x/2] + (1 + I)*E^(I*x)*Hypergeometric2F1[1, 1 - I, 2 - I, E^(I*x)]*Sin[x/2])*(1 + Sin[x]))/((-1 + Cos[x])*(Cos[x/2] + Sin[x/2])^2)","B",1
558,1,10,12,0.1919376,"\int \frac{e^x (1+\sin (x))}{1+\cos (x)} \, dx","Integrate[(E^x*(1 + Sin[x]))/(1 + Cos[x]),x]","e^x \tan \left(\frac{x}{2}\right)","\frac{e^x \sin (x)}{\cos (x)+1}",1,"E^x*Tan[x/2]","A",1
559,1,87,42,0.2274972,"\int \frac{e^x (1-\sin (x))}{1+\cos (x)} \, dx","Integrate[(E^x*(1 - Sin[x]))/(1 + Cos[x]),x]","-\frac{2 e^x \cos \left(\frac{x}{2}\right) \left(2 i \, _2F_1\left(-i,1;1-i;-e^{i x}\right) \cos \left(\frac{x}{2}\right)-(1+i) e^{i x} \, _2F_1\left(1,1-i;2-i;-e^{i x}\right) \cos \left(\frac{x}{2}\right)-\sin \left(\frac{x}{2}\right)\right)}{\cos (x)+1}","-\frac{e^x \sin (x)}{\cos (x)+1}+(2-2 i) e^{(1+i) x} \, _2F_1\left(1-i,2;2-i;-e^{i x}\right)",1,"(-2*E^x*Cos[x/2]*((2*I)*Cos[x/2]*Hypergeometric2F1[-I, 1, 1 - I, -E^(I*x)] - (1 + I)*E^(I*x)*Cos[x/2]*Hypergeometric2F1[1, 1 - I, 2 - I, -E^(I*x)] - Sin[x/2]))/(1 + Cos[x])","B",1
560,1,72,46,0.7579314,"\int \frac{e^x (1-\cos (x))}{1-\sin (x)} \, dx","Integrate[(E^x*(1 - Cos[x]))/(1 - Sin[x]),x]","\frac{1}{2} (\cos (x)-1) \csc ^2\left(\frac{x}{2}\right) \left(4 i (\sinh (x)+\cosh (x)) \, _2F_1(-i,1;1-i;\sin (x)-i \cos (x))-\frac{e^x \left((1+2 i) \cot \left(\frac{x}{2}\right)+(1-2 i)\right)}{\cot \left(\frac{x}{2}\right)-1}\right)","-\frac{e^x \cos (x)}{1-\sin (x)}+(2+2 i) e^{(1+i) x} \, _2F_1\left(1-i,2;2-i;-i e^{i x}\right)",1,"((-1 + Cos[x])*Csc[x/2]^2*(-((E^x*((1 - 2*I) + (1 + 2*I)*Cot[x/2]))/(-1 + Cot[x/2])) + (4*I)*Hypergeometric2F1[-I, 1, 1 - I, (-I)*Cos[x] + Sin[x]]*(Cosh[x] + Sinh[x])))/2","A",1
561,1,23,14,0.0750398,"\int \frac{e^x (1+\cos (x))}{1-\sin (x)} \, dx","Integrate[(E^x*(1 + Cos[x]))/(1 - Sin[x]),x]","-\frac{e^x \left(\tan \left(\frac{x}{2}\right)+1\right)}{\tan \left(\frac{x}{2}\right)-1}","\frac{e^x \cos (x)}{1-\sin (x)}",1,"-((E^x*(1 + Tan[x/2]))/(-1 + Tan[x/2]))","A",1
562,1,73,43,0.2023821,"\int \frac{e^x (1+\cos (x))}{1+\sin (x)} \, dx","Integrate[(E^x*(1 + Cos[x]))/(1 + Sin[x]),x]","\frac{1}{2} (\cos (x)+1) \sec ^2\left(\frac{x}{2}\right) \left(\frac{e^x \left((1+2 i) \tan \left(\frac{x}{2}\right)-(1-2 i)\right)}{\tan \left(\frac{x}{2}\right)+1}-4 i (\sinh (x)+\cosh (x)) \, _2F_1(-i,1;1-i;i \cos (x)-\sin (x))\right)","\frac{e^x \cos (x)}{\sin (x)+1}-(2+2 i) e^{(1+i) x} \, _2F_1\left(1-i,2;2-i;i e^{i x}\right)",1,"((1 + Cos[x])*Sec[x/2]^2*((-4*I)*Hypergeometric2F1[-I, 1, 1 - I, I*Cos[x] - Sin[x]]*(Cosh[x] + Sinh[x]) + (E^x*((-1 + 2*I) + (1 + 2*I)*Tan[x/2]))/(1 + Tan[x/2])))/2","A",1
563,1,23,13,0.0664627,"\int \frac{e^x (1-\cos (x))}{1+\sin (x)} \, dx","Integrate[(E^x*(1 - Cos[x]))/(1 + Sin[x]),x]","-\frac{e^x \left(\cot \left(\frac{x}{2}\right)-1\right)}{\cot \left(\frac{x}{2}\right)+1}","-\frac{e^x \cos (x)}{\sin (x)+1}",1,"-((E^x*(-1 + Cot[x/2]))/(1 + Cot[x/2]))","A",1
564,1,18,30,0.026639,"\int e^x x \cos (x) \, dx","Integrate[E^x*x*Cos[x],x]","\frac{1}{2} e^x ((x-1) \sin (x)+x \cos (x))","-\frac{1}{2} e^x \sin (x)+\frac{1}{2} e^x x \sin (x)+\frac{1}{2} e^x x \cos (x)",1,"(E^x*(x*Cos[x] + (-1 + x)*Sin[x]))/2","A",1
565,1,25,50,0.0400312,"\int e^x x^2 \sin (x) \, dx","Integrate[E^x*x^2*Sin[x],x]","\frac{1}{2} e^x \left(\left(x^2-1\right) \sin (x)-(x-1)^2 \cos (x)\right)","\frac{1}{2} e^x x^2 \sin (x)-\frac{1}{2} e^x x^2 \cos (x)-\frac{1}{2} e^x \sin (x)+e^x x \cos (x)-\frac{1}{2} e^x \cos (x)",1,"(E^x*(-((-1 + x)^2*Cos[x]) + (-1 + x^2)*Sin[x]))/2","A",1
566,1,38,75,0.0385444,"\int e^{-3 x} x^2 \sin (x) \, dx","Integrate[(x^2*Sin[x])/E^(3*x),x]","\frac{1}{250} e^{-3 x} \left(-\left(75 x^2+40 x+9\right) \sin (x)-\left(\left(25 x^2+30 x+13\right) \cos (x)\right)\right)","-\frac{3}{10} e^{-3 x} x^2 \sin (x)-\frac{1}{10} e^{-3 x} x^2 \cos (x)-\frac{4}{25} e^{-3 x} x \sin (x)-\frac{9}{250} e^{-3 x} \sin (x)-\frac{3}{25} e^{-3 x} x \cos (x)-\frac{13}{250} e^{-3 x} \cos (x)",1,"(-((13 + 30*x + 25*x^2)*Cos[x]) - (9 + 40*x + 75*x^2)*Sin[x])/(250*E^(3*x))","A",1
567,1,72,187,0.1589752,"\int e^{x/2} x^2 \cos ^3(x) \, dx","Integrate[E^(x/2)*x^2*Cos[x]^3,x]","\frac{e^{x/2} \left(303918 \left(25 x^2-40 x-8\right) \sin (x)+750 \left(1369 x^2-296 x-264\right) \sin (3 x)+151959 \left(25 x^2+60 x-88\right) \cos (x)+125 \left(1369 x^2+5180 x-856\right) \cos (3 x)\right)}{12663250}","\frac{96}{185} e^{x/2} x^2 \sin (x)+\frac{2}{37} e^{x/2} x^2 \cos ^3(x)+\frac{48}{185} e^{x/2} x^2 \cos (x)+\frac{12}{37} e^{x/2} x^2 \sin (x) \cos ^2(x)-\frac{24}{125} e^{x/2} \sin (x)-\frac{24}{25} e^{x/2} x \sin (x)-\frac{792 e^{x/2} \sin (3 x)}{50653}-\frac{24 e^{x/2} x \sin (3 x)}{1369}-\frac{132}{125} e^{x/2} \cos (x)+\frac{18}{25} e^{x/2} x \cos (x)-\frac{428 e^{x/2} \cos (3 x)}{50653}+\frac{70 e^{x/2} x \cos (3 x)}{1369}",1,"(E^(x/2)*(151959*(-88 + 60*x + 25*x^2)*Cos[x] + 125*(-856 + 5180*x + 1369*x^2)*Cos[3*x] + 303918*(-8 - 40*x + 25*x^2)*Sin[x] + 750*(-264 - 296*x + 1369*x^2)*Sin[3*x]))/12663250","A",1
568,1,40,87,0.0838056,"\int e^{2 x} x^2 \sin (4 x) \, dx","Integrate[E^(2*x)*x^2*Sin[4*x],x]","\frac{1}{500} e^{2 x} \left(\left(50 x^2+30 x-11\right) \sin (4 x)+\left(-100 x^2+40 x+2\right) \cos (4 x)\right)","\frac{1}{10} e^{2 x} x^2 \sin (4 x)-\frac{1}{5} e^{2 x} x^2 \cos (4 x)+\frac{3}{50} e^{2 x} x \sin (4 x)-\frac{11}{500} e^{2 x} \sin (4 x)+\frac{2}{25} e^{2 x} x \cos (4 x)+\frac{1}{250} e^{2 x} \cos (4 x)",1,"(E^(2*x)*((2 + 40*x - 100*x^2)*Cos[4*x] + (-11 + 30*x + 50*x^2)*Sin[4*x]))/500","A",1
569,1,76,185,0.2162417,"\int e^{x/2} x^2 \cos (x) \sin ^2(x) \, dx","Integrate[E^(x/2)*x^2*Cos[x]*Sin[x]^2,x]","\frac{e^{x/2} \left(50653 \left(2 \left(25 x^2-40 x-8\right) \sin (x)+\left(25 x^2+60 x-88\right) \cos (x)\right)-125 \left(6 \left(1369 x^2-296 x-264\right) \sin (3 x)+\left(1369 x^2+5180 x-856\right) \cos (3 x)\right)\right)}{12663250}","\frac{1}{5} e^{x/2} x^2 \sin (x)-\frac{3}{37} e^{x/2} x^2 \sin (3 x)+\frac{1}{10} e^{x/2} x^2 \cos (x)-\frac{1}{74} e^{x/2} x^2 \cos (3 x)-\frac{8}{25} e^{x/2} x \sin (x)+\frac{24 e^{x/2} x \sin (3 x)}{1369}-\frac{8}{125} e^{x/2} \sin (x)+\frac{792 e^{x/2} \sin (3 x)}{50653}+\frac{6}{25} e^{x/2} x \cos (x)-\frac{70 e^{x/2} x \cos (3 x)}{1369}-\frac{44}{125} e^{x/2} \cos (x)+\frac{428 e^{x/2} \cos (3 x)}{50653}",1,"(E^(x/2)*(50653*((-88 + 60*x + 25*x^2)*Cos[x] + 2*(-8 - 40*x + 25*x^2)*Sin[x]) - 125*((-856 + 5180*x + 1369*x^2)*Cos[3*x] + 6*(-264 - 296*x + 1369*x^2)*Sin[3*x])))/12663250","A",1
570,1,2,2,0.0026245,"\int \cosh (x) \, dx","Integrate[Cosh[x],x]","\sinh (x)","\sinh (x)",1,"Sinh[x]","A",1
571,1,2,2,0.0011025,"\int \sinh (x) \, dx","Integrate[Sinh[x],x]","\cosh (x)","\cosh (x)",1,"Cosh[x]","A",1
572,1,3,3,0.0035938,"\int \tanh (x) \, dx","Integrate[Tanh[x],x]","\log (\cosh (x))","\log (\cosh (x))",1,"Log[Cosh[x]]","A",1
573,1,3,3,0.0021449,"\int \coth (x) \, dx","Integrate[Coth[x],x]","\log (\sinh (x))","\log (\sinh (x))",1,"Log[Sinh[x]]","A",1
574,1,9,3,0.0041526,"\int \text{sech}(x) \, dx","Integrate[Sech[x],x]","2 \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)","\tan ^{-1}(\sinh (x))",1,"2*ArcTan[Tanh[x/2]]","B",1
575,1,7,5,0.0048489,"\int \text{csch}(x) \, dx","Integrate[Csch[x],x]","\log \left(\tanh \left(\frac{x}{2}\right)\right)","-\tanh ^{-1}(\cosh (x))",1,"Log[Tanh[x/2]]","A",1
576,1,14,14,0.0018877,"\int \cosh ^2(x) \, dx","Integrate[Cosh[x]^2,x]","\frac{x}{2}+\frac{1}{4} \sinh (2 x)","\frac{x}{2}+\frac{1}{2} \sinh (x) \cosh (x)",1,"x/2 + Sinh[2*x]/4","A",1
577,1,23,19,0.0022319,"\int \sinh ^5(x) \, dx","Integrate[Sinh[x]^5,x]","\frac{5 \cosh (x)}{8}-\frac{5}{48} \cosh (3 x)+\frac{1}{80} \cosh (5 x)","\frac{\cosh ^5(x)}{5}-\frac{2 \cosh ^3(x)}{3}+\cosh (x)",1,"(5*Cosh[x])/8 - (5*Cosh[3*x])/48 + Cosh[5*x]/80","A",1
578,1,18,14,0.0033268,"\int \tanh ^4(x) \, dx","Integrate[Tanh[x]^4,x]","x-\frac{4 \tanh (x)}{3}+\frac{1}{3} \tanh (x) \text{sech}^2(x)","x-\frac{1}{3} \tanh ^3(x)-\tanh (x)",1,"x - (4*Tanh[x])/3 + (Sech[x]^2*Tanh[x])/3","A",1
579,1,36,16,0.0040636,"\int \text{csch}^3(x) \, dx","Integrate[Csch[x]^3,x]","-\frac{1}{8} \text{csch}^2\left(\frac{x}{2}\right)-\frac{1}{8} \text{sech}^2\left(\frac{x}{2}\right)-\frac{1}{2} \log \left(\tanh \left(\frac{x}{2}\right)\right)","\frac{1}{2} \tanh ^{-1}(\cosh (x))-\frac{1}{2} \coth (x) \text{csch}(x)",1,"-1/8*Csch[x/2]^2 - Log[Tanh[x/2]]/2 - Sech[x/2]^2/8","B",1
580,1,30,26,0.0040475,"\int \text{sech}^5(x) \, dx","Integrate[Sech[x]^5,x]","\frac{3}{4} \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)+\frac{1}{4} \tanh (x) \text{sech}^3(x)+\frac{3}{8} \tanh (x) \text{sech}(x)","\frac{3}{8} \tan ^{-1}(\sinh (x))+\frac{1}{4} \tanh (x) \text{sech}^3(x)+\frac{3}{8} \tanh (x) \text{sech}(x)",1,"(3*ArcTan[Tanh[x/2]])/4 + (3*Sech[x]*Tanh[x])/8 + (Sech[x]^3*Tanh[x])/4","A",1
581,1,18,18,0.0069422,"\int \sinh ^4(x) \tanh (x) \, dx","Integrate[Sinh[x]^4*Tanh[x],x]","\frac{\cosh ^4(x)}{4}-\cosh ^2(x)+\log (\cosh (x))","\frac{\cosh ^4(x)}{4}-\cosh ^2(x)+\log (\cosh (x))",1,"-Cosh[x]^2 + Cosh[x]^4/4 + Log[Cosh[x]]","A",1
582,1,27,31,0.0542579,"\int \text{sech}^{\frac{23}{4}}(x) \sinh ^5(x) \, dx","Integrate[Sech[x]^(23/4)*Sinh[x]^5,x]","\text{sech}^{\frac{3}{4}}(x) \left(-\frac{4}{19} \text{sech}^4(x)+\frac{8 \text{sech}^2(x)}{11}-\frac{4}{3}\right)","-\frac{4}{19} \text{sech}^{\frac{19}{4}}(x)+\frac{8}{11} \text{sech}^{\frac{11}{4}}(x)-\frac{4}{3} \text{sech}^{\frac{3}{4}}(x)",1,"Sech[x]^(3/4)*(-4/3 + (8*Sech[x]^2)/11 - (4*Sech[x]^4)/19)","A",1
583,1,41,41,0.0333077,"\int \frac{1}{a+b \cosh (x)} \, dx","Integrate[(a + b*Cosh[x])^(-1),x]","-\frac{2 \tan ^{-1}\left(\frac{(a-b) \tanh \left(\frac{x}{2}\right)}{\sqrt{b^2-a^2}}\right)}{\sqrt{b^2-a^2}}","\frac{2 \tanh ^{-1}\left(\frac{(a-b) \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2-b^2}}\right)}{\sqrt{a^2-b^2}}",1,"(-2*ArcTan[((a - b)*Tanh[x/2])/Sqrt[-a^2 + b^2]])/Sqrt[-a^2 + b^2]","A",1
584,1,16,25,0.0117938,"\int \frac{1}{(1+\cosh (x))^2} \, dx","Integrate[(1 + Cosh[x])^(-2),x]","\frac{\sinh (x) (\cosh (x)+2)}{3 (\cosh (x)+1)^2}","\frac{\sinh (x)}{3 (\cosh (x)+1)}+\frac{\sinh (x)}{3 (\cosh (x)+1)^2}",1,"((2 + Cosh[x])*Sinh[x])/(3*(1 + Cosh[x])^2)","A",1
585,1,29,39,0.0685653,"\int \frac{1}{a+b \tanh (x)} \, dx","Integrate[(a + b*Tanh[x])^(-1),x]","\frac{a x-b \log (a \cosh (x)+b \sinh (x))}{a^2-b^2}","\frac{a x}{a^2-b^2}-\frac{b \log (a \cosh (x)+b \sinh (x))}{a^2-b^2}",1,"(a*x - b*Log[a*Cosh[x] + b*Sinh[x]])/(a^2 - b^2)","A",1
586,1,31,31,0.0680836,"\int \frac{1}{a^2+b^2 \cosh ^2(x)} \, dx","Integrate[(a^2 + b^2*Cosh[x]^2)^(-1),x]","\frac{\tanh ^{-1}\left(\frac{a \tanh (x)}{\sqrt{a^2+b^2}}\right)}{a \sqrt{a^2+b^2}}","\frac{\tanh ^{-1}\left(\frac{a \tanh (x)}{\sqrt{a^2+b^2}}\right)}{a \sqrt{a^2+b^2}}",1,"ArcTanh[(a*Tanh[x])/Sqrt[a^2 + b^2]]/(a*Sqrt[a^2 + b^2])","A",1
587,1,35,35,0.0483482,"\int \frac{1}{a^2-b^2 \cosh ^2(x)} \, dx","Integrate[(a^2 - b^2*Cosh[x]^2)^(-1),x]","\frac{\tanh ^{-1}\left(\frac{a \tanh (x)}{\sqrt{a^2-b^2}}\right)}{a \sqrt{a^2-b^2}}","\frac{\tanh ^{-1}\left(\frac{a \tanh (x)}{\sqrt{a^2-b^2}}\right)}{a \sqrt{a^2-b^2}}",1,"ArcTanh[(a*Tanh[x])/Sqrt[a^2 - b^2]]/(a*Sqrt[a^2 - b^2])","A",1
588,1,24,25,0.1020166,"\int \frac{1}{1-\sinh ^4(x)} \, dx","Integrate[(1 - Sinh[x]^4)^(-1),x]","\frac{1}{4} \left(\sqrt{2} \tanh ^{-1}\left(\sqrt{2} \tanh (x)\right)+2 \tanh (x)\right)","\frac{\tanh ^{-1}\left(\sqrt{2} \tanh (x)\right)}{2 \sqrt{2}}+\frac{\tanh (x)}{2}",1,"(Sqrt[2]*ArcTanh[Sqrt[2]*Tanh[x]] + 2*Tanh[x])/4","A",1
589,1,37,33,0.1398464,"\int \frac{\cosh ^3(x)-\sinh ^3(x)}{\cosh ^3(x)+\sinh ^3(x)} \, dx","Integrate[(Cosh[x]^3 - Sinh[x]^3)/(Cosh[x]^3 + Sinh[x]^3),x]","\frac{1}{18} \left(3 \sinh (2 x)-3 \cosh (2 x)+8 \sqrt{3} \tan ^{-1}\left(\frac{2 \tanh (x)-1}{\sqrt{3}}\right)\right)","-\frac{1}{3 (\tanh (x)+1)}-\frac{4 \tan ^{-1}\left(\frac{1-2 \tanh (x)}{\sqrt{3}}\right)}{3 \sqrt{3}}",1,"(8*Sqrt[3]*ArcTan[(-1 + 2*Tanh[x])/Sqrt[3]] - 3*Cosh[2*x] + 3*Sinh[2*x])/18","A",1
590,1,30,30,0.0104094,"\int \cosh (x) \cosh (2 x) \cosh (3 x) \, dx","Integrate[Cosh[x]*Cosh[2*x]*Cosh[3*x],x]","\frac{x}{4}+\frac{1}{8} \sinh (2 x)+\frac{1}{16} \sinh (4 x)+\frac{1}{24} \sinh (6 x)","\frac{x}{4}+\frac{1}{8} \sinh (2 x)+\frac{1}{16} \sinh (4 x)+\frac{1}{24} \sinh (6 x)",1,"x/4 + Sinh[2*x]/8 + Sinh[4*x]/16 + Sinh[6*x]/24","A",1
591,1,30,30,0.0110083,"\int \cosh \left(\frac{3 x}{2}\right) \sinh (x) \sinh \left(\frac{5 x}{2}\right) \, dx","Integrate[Cosh[(3*x)/2]*Sinh[x]*Sinh[(5*x)/2],x]","-\frac{x}{4}+\frac{1}{8} \sinh (2 x)-\frac{1}{12} \sinh (3 x)+\frac{1}{20} \sinh (5 x)","-\frac{x}{4}+\frac{1}{8} \sinh (2 x)-\frac{1}{12} \sinh (3 x)+\frac{1}{20} \sinh (5 x)",1,"-1/4*x + Sinh[2*x]/8 - Sinh[3*x]/12 + Sinh[5*x]/20","A",1
592,1,392,69,30.3845527,"\int \frac{\cosh (x) (-\cosh (2 x)+\tanh (x))}{\sqrt{\sinh (2 x)} \left(\sinh ^2(x)+\sinh (2 x)\right)} \, dx","Integrate[(Cosh[x]*(-Cosh[2*x] + Tanh[x]))/(Sqrt[Sinh[2*x]]*(Sinh[x]^2 + Sinh[2*x])),x]","\frac{\sqrt{\sinh (2 x)} (\tanh (x)-\cosh (2 x)) \left(-3 \coth (x)+\frac{\sqrt[4]{-1} \cosh (x) \sqrt{\tanh ^3\left(\frac{x}{2}\right)+\tanh \left(\frac{x}{2}\right)} \left(\frac{8 \sqrt[6]{-1} \left(2 \left(\sqrt[3]{-1}-1\right) \Pi \left(i;\left.\sin ^{-1}\left((-1)^{3/4} \sqrt{\tanh \left(\frac{x}{2}\right)}\right)\right|-1\right)+\left(3-3 i \sqrt{3}\right) \Pi \left(-i;\left.i \sinh ^{-1}\left(\sqrt[4]{-1} \sqrt{\tanh \left(\frac{x}{2}\right)}\right)\right|-1\right)+i \left(\sqrt{3}+i\right) \Pi \left(-\sqrt[6]{-1};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} \sqrt{\tanh \left(\frac{x}{2}\right)}\right)\right|-1\right)+2 \left(\sqrt[3]{-1}-1\right) \Pi \left(-(-1)^{5/6};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} \sqrt{\tanh \left(\frac{x}{2}\right)}\right)\right|-1\right)\right)}{\left(\sqrt{3}-i\right) \sqrt{\tanh ^2\left(\frac{x}{2}\right)+1}}-\frac{9 \coth \left(\frac{x}{2}\right) \left(\operatorname{EllipticF}\left(i \sinh ^{-1}\left(\frac{\sqrt[4]{-1}}{\sqrt{\tanh \left(\frac{x}{2}\right)}}\right),-1\right)-\Pi \left(-\sqrt[6]{-1};\left.i \sinh ^{-1}\left(\frac{\sqrt[4]{-1}}{\sqrt{\tanh \left(\frac{x}{2}\right)}}\right)\right|-1\right)-\Pi \left(-(-1)^{5/6};\left.i \sinh ^{-1}\left(\frac{\sqrt[4]{-1}}{\sqrt{\tanh \left(\frac{x}{2}\right)}}\right)\right|-1\right)\right)}{\sqrt{\coth ^2\left(\frac{x}{2}\right)+1}}\right)}{(\cosh (x)+1) \sqrt{\tanh \left(\frac{x}{2}\right)} \sqrt{\frac{\sinh (2 x)}{(\cosh (x)+1)^2}}}\right)}{3 (-2 \sinh (x)+\cosh (x)+\cosh (3 x))}","\frac{1}{6} \tan ^{-1}\left(\frac{\sinh (x)}{\sqrt{\sinh (2 x)}}\right)+\frac{\cosh (x)}{\sqrt{\sinh (2 x)}}+\sqrt{2} \tan ^{-1}\left(\text{sech}(x) \sqrt{\sinh (x) \cosh (x)}\right)-\frac{1}{3} \sqrt{2} \tanh ^{-1}\left(\text{sech}(x) \sqrt{\sinh (x) \cosh (x)}\right)",1,"(Sqrt[Sinh[2*x]]*(-3*Coth[x] + ((-1)^(1/4)*Cosh[x]*Sqrt[Tanh[x/2] + Tanh[x/2]^3]*((-9*Coth[x/2]*(EllipticF[I*ArcSinh[(-1)^(1/4)/Sqrt[Tanh[x/2]]], -1] - EllipticPi[-(-1)^(1/6), I*ArcSinh[(-1)^(1/4)/Sqrt[Tanh[x/2]]], -1] - EllipticPi[-(-1)^(5/6), I*ArcSinh[(-1)^(1/4)/Sqrt[Tanh[x/2]]], -1]))/Sqrt[1 + Coth[x/2]^2] + (8*(-1)^(1/6)*((3 - (3*I)*Sqrt[3])*EllipticPi[-I, I*ArcSinh[(-1)^(1/4)*Sqrt[Tanh[x/2]]], -1] + 2*(-1 + (-1)^(1/3))*EllipticPi[I, ArcSin[(-1)^(3/4)*Sqrt[Tanh[x/2]]], -1] + I*(I + Sqrt[3])*EllipticPi[-(-1)^(1/6), I*ArcSinh[(-1)^(1/4)*Sqrt[Tanh[x/2]]], -1] + 2*(-1 + (-1)^(1/3))*EllipticPi[-(-1)^(5/6), I*ArcSinh[(-1)^(1/4)*Sqrt[Tanh[x/2]]], -1]))/((-I + Sqrt[3])*Sqrt[1 + Tanh[x/2]^2])))/((1 + Cosh[x])*Sqrt[Sinh[2*x]/(1 + Cosh[x])^2]*Sqrt[Tanh[x/2]]))*(-Cosh[2*x] + Tanh[x]))/(3*(Cosh[x] + Cosh[3*x] - 2*Sinh[x]))","C",0
593,1,26,37,0.0715832,"\int \frac{\sinh (x)}{\left(-9+4 \cosh ^2(x)\right)^{5/2}} \, dx","Integrate[Sinh[x]/(-9 + 4*Cosh[x]^2)^(5/2),x]","\frac{\cosh (x) (4 \cosh (2 x)-23)}{243 (2 \cosh (2 x)-7)^{3/2}}","\frac{2 \cosh (x)}{243 \sqrt{4 \cosh ^2(x)-9}}-\frac{\cosh (x)}{27 \left(4 \cosh ^2(x)-9\right)^{3/2}}",1,"(Cosh[x]*(-23 + 4*Cosh[2*x]))/(243*(-7 + 2*Cosh[2*x])^(3/2))","A",1
594,1,21,29,0.0558286,"\int \frac{\sinh ^2(x) \sinh (2 x)}{\left(1-\sinh ^2(x)\right)^{3/2}} \, dx","Integrate[(Sinh[x]^2*Sinh[2*x])/(1 - Sinh[x]^2)^(3/2),x]","\frac{5-\cosh (2 x)}{\sqrt{1-\sinh ^2(x)}}","2 \sqrt{1-\sinh ^2(x)}+\frac{2}{\sqrt{1-\sinh ^2(x)}}",1,"(5 - Cosh[2*x])/Sqrt[1 - Sinh[x]^2]","A",1
595,1,15,15,0.0111243,"\int \frac{\cosh (x)}{\sqrt{\cosh (2 x)}} \, dx","Integrate[Cosh[x]/Sqrt[Cosh[2*x]],x]","\frac{\sinh ^{-1}\left(\sqrt{2} \sinh (x)\right)}{\sqrt{2}}","\frac{\sinh ^{-1}\left(\sqrt{2} \sinh (x)\right)}{\sqrt{2}}",1,"ArcSinh[Sqrt[2]*Sinh[x]]/Sqrt[2]","A",1
596,1,16,16,0.0229255,"\int x \tanh ^2(x) \, dx","Integrate[x*Tanh[x]^2,x]","\frac{x^2}{2}-x \tanh (x)+\log (\cosh (x))","\frac{x^2}{2}-x \tanh (x)+\log (\cosh (x))",1,"x^2/2 + Log[Cosh[x]] - x*Tanh[x]","A",1
597,1,16,16,0.0232609,"\int x \coth ^2(x) \, dx","Integrate[x*Coth[x]^2,x]","\frac{x^2}{2}-x \coth (x)+\log (\sinh (x))","\frac{x^2}{2}-x \coth (x)+\log (\sinh (x))",1,"x^2/2 - x*Coth[x] + Log[Sinh[x]]","A",1
598,1,23,20,0.1026057,"\int \frac{x+\cosh (x)+\sinh (x)}{\cosh (x)-\sinh (x)} \, dx","Integrate[(x + Cosh[x] + Sinh[x])/(Cosh[x] - Sinh[x]),x]","(x-1) \sinh (x)+\frac{1}{2} \cosh (2 x)+(x+\sinh (x)-1) \cosh (x)","e^x x-e^x+\frac{e^{2 x}}{2}",1,"Cosh[2*x]/2 + (-1 + x)*Sinh[x] + Cosh[x]*(-1 + x + Sinh[x])","A",1
599,1,20,15,0.0860242,"\int \frac{x+\cosh (x)+\sinh (x)}{1+\cosh (x)} \, dx","Integrate[(x + Cosh[x] + Sinh[x])/(1 + Cosh[x]),x]","\frac{\sinh (x) \left(x+x \coth \left(\frac{x}{2}\right)-1\right)}{\cosh (x)+1}","x-(1-x) \tanh \left(\frac{x}{2}\right)",1,"((-1 + x + x*Coth[x/2])*Sinh[x])/(1 + Cosh[x])","A",1
600,1,20,20,0.0111348,"\int e^{2 x} \text{csch}^4(x) \, dx","Integrate[E^(2*x)*Csch[x]^4,x]","\frac{8 e^{6 x}}{3 \left(1-e^{2 x}\right)^3}","\frac{8 e^{6 x}}{3 \left(1-e^{2 x}\right)^3}",1,"(8*E^(6*x))/(3*(1 - E^(2*x))^3)","A",1
601,1,13,13,0.0154216,"\int e^{-2 x} \text{sech}^4(x) \, dx","Integrate[Sech[x]^4/E^(2*x),x]","-\frac{8}{3 \left(e^{2 x}+1\right)^3}","-\frac{8}{3 \left(e^{2 x}+1\right)^3}",1,"-8/(3*(1 + E^(2*x))^3)","A",1
602,1,9,9,0.002147,"\int \frac{e^x}{\cosh (x)-\sinh (x)} \, dx","Integrate[E^x/(Cosh[x] - Sinh[x]),x]","\frac{e^{2 x}}{2}","\frac{e^{2 x}}{2}",1,"E^(2*x)/2","A",1
603,1,18,13,0.0300659,"\int \frac{e^{m x}}{\cosh (x)+\sinh (x)} \, dx","Integrate[E^(m*x)/(Cosh[x] + Sinh[x]),x]","\frac{e^{m x} (\cosh (x)-\sinh (x))}{m-1}","\frac{e^{(m-1) x}}{m-1}",1,"(E^(m*x)*(Cosh[x] - Sinh[x]))/(-1 + m)","A",1
604,1,1,1,0.0011347,"\int \frac{e^x}{\cosh (x)+\sinh (x)} \, dx","Integrate[E^x/(Cosh[x] + Sinh[x]),x]","x","x",1,"x","A",1
605,1,36,22,0.0352392,"\int \frac{e^x}{1-\cosh (x)} \, dx","Integrate[E^x/(1 - Cosh[x]),x]","\frac{4 \left(\frac{1}{1-e^x}+\log \left(1-e^x\right)\right) \sinh ^2\left(\frac{x}{2}\right)}{1-\cosh (x)}","-\frac{2}{1-e^x}-2 \log \left(1-e^x\right)",1,"(4*((1 - E^x)^(-1) + Log[1 - E^x])*Sinh[x/2]^2)/(1 - Cosh[x])","A",1
606,1,18,13,0.0368899,"\int \frac{e^x (1+\sinh (x))}{1+\cosh (x)} \, dx","Integrate[(E^x*(1 + Sinh[x]))/(1 + Cosh[x]),x]","\frac{e^x+e^{2 x}+2}{e^x+1}","e^x+\frac{2}{e^x+1}",1,"(2 + E^x + E^(2*x))/(1 + E^x)","A",1
607,1,20,15,0.0368568,"\int \frac{e^x (1-\sinh (x))}{1-\cosh (x)} \, dx","Integrate[(E^x*(1 - Sinh[x]))/(1 - Cosh[x]),x]","\frac{-e^x+e^{2 x}+2}{e^x-1}","e^x-\frac{2}{1-e^x}",1,"(2 - E^x + E^(2*x))/(-1 + E^x)","A",1
608,1,19,26,0.0084468,"\int x^m \log (x) \, dx","Integrate[x^m*Log[x],x]","\frac{x^{m+1} ((m+1) \log (x)-1)}{(m+1)^2}","\frac{x^{m+1} \log (x)}{m+1}-\frac{x^{m+1}}{(m+1)^2}",1,"(x^(1 + m)*(-1 + (1 + m)*Log[x]))/(1 + m)^2","A",1
609,1,30,42,0.0166989,"\int x^m \log ^2(x) \, dx","Integrate[x^m*Log[x]^2,x]","\frac{x^{m+1} \left((m+1)^2 \log ^2(x)-2 (m+1) \log (x)+2\right)}{(m+1)^3}","\frac{2 x^{m+1}}{(m+1)^3}+\frac{x^{m+1} \log ^2(x)}{m+1}-\frac{2 x^{m+1} \log (x)}{(m+1)^2}",1,"(x^(1 + m)*(2 - 2*(1 + m)*Log[x] + (1 + m)^2*Log[x]^2))/(1 + m)^3","A",1
610,1,21,34,0.0048786,"\int \frac{\log ^2(x)}{x^{5/2}} \, dx","Integrate[Log[x]^2/x^(5/2),x]","-\frac{2 \left(9 \log ^2(x)+12 \log (x)+8\right)}{27 x^{3/2}}","-\frac{16}{27 x^{3/2}}-\frac{2 \log ^2(x)}{3 x^{3/2}}-\frac{8 \log (x)}{9 x^{3/2}}",1,"(-2*(8 + 12*Log[x] + 9*Log[x]^2))/(27*x^(3/2))","A",1
611,1,28,28,0.0017098,"\int (a+b x) \log (x) \, dx","Integrate[(a + b*x)*Log[x],x]","-a x+a x \log (x)-\frac{b x^2}{4}+\frac{1}{2} b x^2 \log (x)","-a x+a x \log (x)-\frac{b x^2}{4}+\frac{1}{2} b x^2 \log (x)",1,"-(a*x) - (b*x^2)/4 + a*x*Log[x] + (b*x^2*Log[x])/2","A",1
612,1,81,67,0.0307104,"\int (a+b x)^3 \log (x) \, dx","Integrate[(a + b*x)^3*Log[x],x]","-a^3 x+a^3 x \log (x)-\frac{3}{4} a^2 b x^2+\frac{3}{2} a^2 b x^2 \log (x)-\frac{1}{3} a b^2 x^3+a b^2 x^3 \log (x)-\frac{1}{16} b^3 x^4+\frac{1}{4} b^3 x^4 \log (x)","-\frac{a^4 \log (x)}{4 b}-a^3 x-\frac{3}{4} a^2 b x^2-\frac{1}{3} a b^2 x^3+\frac{\log (x) (a+b x)^4}{4 b}-\frac{b^3 x^4}{16}",1,"-(a^3*x) - (3*a^2*b*x^2)/4 - (a*b^2*x^3)/3 - (b^3*x^4)/16 + a^3*x*Log[x] + (3*a^2*b*x^2*Log[x])/2 + a*b^2*x^3*Log[x] + (b^3*x^4*Log[x])/4","A",1
613,1,23,23,0.0032107,"\int \left(-1-8 \log ^2(x)+3 \log ^3(x)\right) \, dx","Integrate[-1 - 8*Log[x]^2 + 3*Log[x]^3,x]","-35 x+3 x \log ^3(x)-17 x \log ^2(x)+34 x \log (x)","-35 x+3 x \log ^3(x)-17 x \log ^2(x)+34 x \log (x)",1,"-35*x + 34*x*Log[x] - 17*x*Log[x]^2 + 3*x*Log[x]^3","A",1
614,1,60,60,0.0046051,"\int \left(1+x^4\right) \left(1-2 \log (x)+\log ^3(x)\right) \, dx","Integrate[(1 + x^4)*(1 - 2*Log[x] + Log[x]^3),x]","\frac{169 x^5}{625}+\frac{1}{5} x^5 \log ^3(x)-\frac{3}{25} x^5 \log ^2(x)-\frac{44}{125} x^5 \log (x)-3 x+x \log ^3(x)-3 x \log ^2(x)+4 x \log (x)","\frac{169 x^5}{625}+\frac{1}{5} x^5 \log ^3(x)-\frac{3}{25} x^5 \log ^2(x)-\frac{44}{125} x^5 \log (x)-3 x+x \log ^3(x)-3 x \log ^2(x)+4 x \log (x)",1,"-3*x + (169*x^5)/625 + 4*x*Log[x] - (44*x^5*Log[x])/125 - 3*x*Log[x]^2 - (3*x^5*Log[x]^2)/25 + x*Log[x]^3 + (x^5*Log[x]^3)/5","A",1
615,1,43,43,0.0182435,"\int \frac{1}{x^3 \log ^4(x)} \, dx","Integrate[1/(x^3*Log[x]^4),x]","-\frac{4}{3} \text{Ei}(-2 \log (x))-\frac{1}{3 x^2 \log ^3(x)}+\frac{1}{3 x^2 \log ^2(x)}-\frac{2}{3 x^2 \log (x)}","-\frac{4}{3} \text{Ei}(-2 \log (x))-\frac{1}{3 x^2 \log ^3(x)}+\frac{1}{3 x^2 \log ^2(x)}-\frac{2}{3 x^2 \log (x)}",1,"(-4*ExpIntegralEi[-2*Log[x]])/3 - 1/(3*x^2*Log[x]^3) + 1/(3*x^2*Log[x]^2) - 2/(3*x^2*Log[x])","A",1
616,1,30,29,0.00357,"\int \frac{\log (x)}{a+b x} \, dx","Integrate[Log[x]/(a + b*x),x]","\frac{\operatorname{PolyLog}\left(2,-\frac{b x}{a}\right)}{b}+\frac{\log (x) \log \left(\frac{a+b x}{a}\right)}{b}","\frac{\operatorname{PolyLog}\left(2,-\frac{b x}{a}\right)}{b}+\frac{\log (x) \log \left(\frac{b x}{a}+1\right)}{b}",1,"(Log[x]*Log[(a + b*x)/a])/b + PolyLog[2, -((b*x)/a)]/b","A",1
617,1,27,29,0.0176534,"\int \frac{\log (x)}{(a+b x)^2} \, dx","Integrate[Log[x]/(a + b*x)^2,x]","\frac{\frac{x \log (x)}{a+b x}-\frac{\log (a+b x)}{b}}{a}","\frac{x \log (x)}{a (a+b x)}-\frac{\log (a+b x)}{a b}",1,"((x*Log[x])/(a + b*x) - Log[a + b*x]/b)/a","A",1
618,1,12,12,0.0031193,"\int \frac{\log ^n(x)}{x} \, dx","Integrate[Log[x]^n/x,x]","\frac{\log ^{n+1}(x)}{n+1}","\frac{\log ^{n+1}(x)}{n+1}",1,"Log[x]^(1 + n)/(1 + n)","A",1
619,1,19,19,0.0108216,"\int \frac{(a+b \log (x))^n}{x} \, dx","Integrate[(a + b*Log[x])^n/x,x]","\frac{(a+b \log (x))^{n+1}}{b (n+1)}","\frac{(a+b \log (x))^{n+1}}{b (n+1)}",1,"(a + b*Log[x])^(1 + n)/(b*(1 + n))","A",1
620,1,11,11,0.0161962,"\int \frac{1}{x (a+b \log (x))} \, dx","Integrate[1/(x*(a + b*Log[x])),x]","\frac{\log (a+b \log (x))}{b}","\frac{\log (a+b \log (x))}{b}",1,"Log[a + b*Log[x]]/b","A",1
621,1,23,23,0.0166981,"\int \frac{(a+b \log (x))^{-n}}{x} \, dx","Integrate[1/(x*(a + b*Log[x])^n),x]","\frac{(a+b \log (x))^{1-n}}{b (1-n)}","\frac{(a+b \log (x))^{1-n}}{b (1-n)}",1,"(a + b*Log[x])^(1 - n)/(b*(1 - n))","A",1
622,1,46,16,0.0254098,"\int \frac{1}{x \sqrt{a^2+\log ^2(x)}} \, dx","Integrate[1/(x*Sqrt[a^2 + Log[x]^2]),x]","\frac{1}{2} \log \left(\frac{\log (x)}{\sqrt{a^2+\log ^2(x)}}+1\right)-\frac{1}{2} \log \left(1-\frac{\log (x)}{\sqrt{a^2+\log ^2(x)}}\right)","\tanh ^{-1}\left(\frac{\log (x)}{\sqrt{a^2+\log ^2(x)}}\right)",1,"-1/2*Log[1 - Log[x]/Sqrt[a^2 + Log[x]^2]] + Log[1 + Log[x]/Sqrt[a^2 + Log[x]^2]]/2","B",1
623,1,50,18,0.0368261,"\int \frac{1}{x \sqrt{-a^2+\log ^2(x)}} \, dx","Integrate[1/(x*Sqrt[-a^2 + Log[x]^2]),x]","\frac{1}{2} \log \left(\frac{\log (x)}{\sqrt{\log ^2(x)-a^2}}+1\right)-\frac{1}{2} \log \left(1-\frac{\log (x)}{\sqrt{\log ^2(x)-a^2}}\right)","\tanh ^{-1}\left(\frac{\log (x)}{\sqrt{\log ^2(x)-a^2}}\right)",1,"-1/2*Log[1 - Log[x]/Sqrt[-a^2 + Log[x]^2]] + Log[1 + Log[x]/Sqrt[-a^2 + Log[x]^2]]/2","B",1
624,1,18,18,0.034453,"\int \frac{1}{x \sqrt{a^2-\log ^2(x)}} \, dx","Integrate[1/(x*Sqrt[a^2 - Log[x]^2]),x]","\tan ^{-1}\left(\frac{\log (x)}{\sqrt{a^2-\log ^2(x)}}\right)","\tan ^{-1}\left(\frac{\log (x)}{\sqrt{a^2-\log ^2(x)}}\right)",1,"ArcTan[Log[x]/Sqrt[a^2 - Log[x]^2]]","A",1
625,1,22,22,0.0191496,"\int \frac{1}{x \log (x) \sqrt{a^2+\log ^2(x)}} \, dx","Integrate[1/(x*Log[x]*Sqrt[a^2 + Log[x]^2]),x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{a^2+\log ^2(x)}}{a}\right)}{a}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{a^2+\log ^2(x)}}{a}\right)}{a}",1,"-(ArcTanh[Sqrt[a^2 + Log[x]^2]/a]/a)","A",1
626,1,24,24,0.0218237,"\int \frac{1}{x \log (x) \sqrt{a^2-\log ^2(x)}} \, dx","Integrate[1/(x*Log[x]*Sqrt[a^2 - Log[x]^2]),x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{a^2-\log ^2(x)}}{a}\right)}{a}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{a^2-\log ^2(x)}}{a}\right)}{a}",1,"-(ArcTanh[Sqrt[a^2 - Log[x]^2]/a]/a)","A",1
627,1,23,23,0.0206624,"\int \frac{1}{x \log (x) \sqrt{-a^2+\log ^2(x)}} \, dx","Integrate[1/(x*Log[x]*Sqrt[-a^2 + Log[x]^2]),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{\log ^2(x)-a^2}}{a}\right)}{a}","\frac{\tan ^{-1}\left(\frac{\sqrt{\log ^2(x)-a^2}}{a}\right)}{a}",1,"ArcTan[Sqrt[-a^2 + Log[x]^2]/a]/a","A",1
628,1,11,11,0.0047028,"\int \frac{\log (\log (x))}{x} \, dx","Integrate[Log[Log[x]]/x,x]","\log (x) \log (\log (x))-\log (x)","\log (x) \log (\log (x))-\log (x)",1,"-Log[x] + Log[x]*Log[Log[x]]","A",1
629,1,20,20,0.0068185,"\int \frac{\log ^2(\log (x))}{x} \, dx","Integrate[Log[Log[x]]^2/x,x]","\log (x) \log ^2(\log (x))-2 \log (x) \log (\log (x))+2 \log (x)","\log (x) \log ^2(\log (x))-2 \log (x) \log (\log (x))+2 \log (x)",1,"2*Log[x] - 2*Log[x]*Log[Log[x]] + Log[x]*Log[Log[x]]^2","A",1
630,1,29,29,0.0106578,"\int \frac{\log ^3(\log (x))}{x} \, dx","Integrate[Log[Log[x]]^3/x,x]","\log (x) \log ^3(\log (x))-3 \log (x) \log ^2(\log (x))+6 \log (x) \log (\log (x))-6 \log (x)","\log (x) \log ^3(\log (x))-3 \log (x) \log ^2(\log (x))+6 \log (x) \log (\log (x))-6 \log (x)",1,"-6*Log[x] + 6*Log[x]*Log[Log[x]] - 3*Log[x]*Log[Log[x]]^2 + Log[x]*Log[Log[x]]^3","A",1
631,1,38,38,0.0094567,"\int \frac{\log ^4(\log (x))}{x} \, dx","Integrate[Log[Log[x]]^4/x,x]","\log (x) \log ^4(\log (x))-4 \log (x) \log ^3(\log (x))+12 \log (x) \log ^2(\log (x))-24 \log (x) \log (\log (x))+24 \log (x)","\log (x) \log ^4(\log (x))-4 \log (x) \log ^3(\log (x))+12 \log (x) \log ^2(\log (x))-24 \log (x) \log (\log (x))+24 \log (x)",1,"24*Log[x] - 24*Log[x]*Log[Log[x]] + 12*Log[x]*Log[Log[x]]^2 - 4*Log[x]*Log[Log[x]]^3 + Log[x]*Log[Log[x]]^4","A",1
632,1,24,24,0.0061488,"\int \frac{\log ^n(\log (x))}{x} \, dx","Integrate[Log[Log[x]]^n/x,x]","(-\log (\log (x)))^{-n} \log ^n(\log (x)) \Gamma (n+1,-\log (\log (x)))","(-\log (\log (x)))^{-n} \log ^n(\log (x)) \Gamma (n+1,-\log (\log (x)))",1,"(Gamma[1 + n, -Log[Log[x]]]*Log[Log[x]]^n)/(-Log[Log[x]])^n","A",1
633,1,4,4,0.0099054,"\int \frac{\cot (x)}{\log (\sin (x))} \, dx","Integrate[Cot[x]/Log[Sin[x]],x]","\log (\log (\sin (x)))","\log (\log (\sin (x)))",1,"Log[Log[Sin[x]]]","A",1
634,1,7,7,0.0042029,"\int (\cos (x)+\sec (x)) \tan (x) \, dx","Integrate[(Cos[x] + Sec[x])*Tan[x],x]","\sec (x)-\cos (x)","\sec (x)-\cos (x)",1,"-Cos[x] + Sec[x]","A",1
635,1,11,11,0.007523,"\int \log (\cosh (x)) \sinh (x) \, dx","Integrate[Log[Cosh[x]]*Sinh[x],x]","\cosh (x) \log (\cosh (x))-\cosh (x)","\cosh (x) \log (\cosh (x))-\cosh (x)",1,"-Cosh[x] + Cosh[x]*Log[Cosh[x]]","A",1
636,1,9,9,0.0038181,"\int \log (\cosh (x)) \tanh (x) \, dx","Integrate[Log[Cosh[x]]*Tanh[x],x]","\frac{1}{2} \log ^2(\cosh (x))","\frac{1}{2} \log ^2(\cosh (x))",1,"Log[Cosh[x]]^2/2","A",1
637,1,26,26,0.0195873,"\int \log \left(x-\sqrt{1+x^2}\right) \, dx","Integrate[Log[x - Sqrt[1 + x^2]],x]","\sqrt{x^2+1}+x \log \left(x-\sqrt{x^2+1}\right)","\sqrt{x^2+1}+x \log \left(x-\sqrt{x^2+1}\right)",1,"Sqrt[1 + x^2] + x*Log[x - Sqrt[1 + x^2]]","A",1
638,1,27,35,0.0115776,"\int \frac{\log (-1+x)}{x^3} \, dx","Integrate[Log[-1 + x]/x^3,x]","\frac{1}{2} \left(-\frac{\log (x-1)}{x^2}+\frac{1}{x}+\log (1-x)-\log (x)\right)","-\frac{\log (x-1)}{2 x^2}+\frac{1}{2 x}+\frac{1}{2} \log (1-x)-\frac{\log (x)}{2}",1,"(x^(-1) + Log[1 - x] - Log[-1 + x]/x^2 - Log[x])/2","A",1
639,1,24,32,0.0412993,"\int \left(-e^{-x}+e^x\right) \log \left(1+e^{2 x}\right) \, dx","Integrate[(-E^(-x) + E^x)*Log[1 + E^(2*x)],x]","\left(e^{-x}+e^x\right) \log \left(e^{2 x}+1\right)-2 e^x","-2 e^x+e^{-x} \log \left(e^{2 x}+1\right)+e^x \log \left(e^{2 x}+1\right)",1,"-2*E^x + (E^(-x) + E^x)*Log[1 + E^(2*x)]","A",1
640,1,42,52,0.042303,"\int e^{3 x/2} \log \left(-1+e^x\right) \, dx","Integrate[E^((3*x)/2)*Log[-1 + E^x],x]","\frac{2}{9} \left(e^{x/2} \left(3 e^x \log \left(e^x-1\right)-2 \left(e^x+3\right)\right)+6 \tanh ^{-1}\left(e^{x/2}\right)\right)","-\frac{4 e^{x/2}}{3}-\frac{4}{9} e^{3 x/2}+\frac{2}{3} e^{3 x/2} \log \left(e^x-1\right)+\frac{4}{3} \tanh ^{-1}\left(e^{x/2}\right)",1,"(2*(6*ArcTanh[E^(x/2)] + E^(x/2)*(-2*(3 + E^x) + 3*E^x*Log[-1 + E^x])))/9","A",1
641,1,30,30,0.0115223,"\int \cos ^3(x) \log (\sin (x)) \, dx","Integrate[Cos[x]^3*Log[Sin[x]],x]","\frac{\sin ^3(x)}{9}-\sin (x)-\frac{1}{3} \sin ^3(x) \log (\sin (x))+\sin (x) \log (\sin (x))","\frac{\sin ^3(x)}{9}-\sin (x)-\frac{1}{3} \sin ^3(x) \log (\sin (x))+\sin (x) \log (\sin (x))",1,"-Sin[x] + Log[Sin[x]]*Sin[x] + Sin[x]^3/9 - (Log[Sin[x]]*Sin[x]^3)/3","A",1
642,1,29,30,0.0872657,"\int \log (\tan (x)) \sec ^4(x) \, dx","Integrate[Log[Tan[x]]*Sec[x]^4,x]","\frac{1}{9} \tan (x) \left(\sec ^2(x) (6 \log (\tan (x))+3 \cos (2 x) \log (\tan (x))-1)-8\right)","-\frac{\tan ^3(x)}{9}-\tan (x)+\frac{1}{3} \tan ^3(x) \log (\tan (x))+\tan (x) \log (\tan (x))",1,"((-8 + (-1 + 6*Log[Tan[x]] + 3*Cos[2*x]*Log[Tan[x]])*Sec[x]^2)*Tan[x])/9","A",1
643,1,32,28,0.1012877,"\int \frac{\log \left(\cos \left(\frac{x}{2}\right)\right)}{1+\cos (x)} \, dx","Integrate[Log[Cos[x/2]]/(1 + Cos[x]),x]","-\frac{\sin (x) \left(x \cot \left(\frac{x}{2}\right)-2 \left(\log \left(\cos \left(\frac{x}{2}\right)\right)+1\right)\right)}{2 (\cos (x)+1)}","-\frac{x}{2}+\tan \left(\frac{x}{2}\right)+\frac{\sin (x) \log \left(\cos \left(\frac{x}{2}\right)\right)}{\cos (x)+1}",1,"-1/2*((x*Cot[x/2] - 2*(1 + Log[Cos[x/2]]))*Sin[x])/(1 + Cos[x])","A",1
644,1,56,60,0.1549632,"\int \frac{\cos (x) \log (\sin (x))}{(1+\cos (x))^2} \, dx","Integrate[(Cos[x]*Log[Sin[x]])/(1 + Cos[x])^2,x]","-\frac{1}{18} \sec ^3\left(\frac{x}{2}\right) \left(9 x \cos \left(\frac{x}{2}\right)+3 x \cos \left(\frac{3 x}{2}\right)-\sin \left(\frac{x}{2}\right) (3 \log (\sin (x))+\cos (x) (6 \log (\sin (x))+8)+7)\right)","-\frac{2 x}{3}+\frac{8 \sin (x)}{9 (\cos (x)+1)}-\frac{\sin (x)}{9 (\cos (x)+1)^2}+\frac{2 \sin (x) \log (\sin (x))}{3 (\cos (x)+1)}-\frac{\sin (x) \log (\sin (x))}{3 (\cos (x)+1)^2}",1,"-1/18*(Sec[x/2]^3*(9*x*Cos[x/2] + 3*x*Cos[(3*x)/2] - (7 + 3*Log[Sin[x]] + Cos[x]*(8 + 6*Log[Sin[x]]))*Sin[x/2]))","A",1
645,1,52,65,0.0330795,"\int \frac{\cos ^{-1}(x)^2}{x^5} \, dx","Integrate[ArcCos[x]^2/x^5,x]","-\frac{\cos ^{-1}(x)^2}{4 x^4}-\frac{1}{12 x^2}+\frac{\sqrt{1-x^2} \left(2 x^2+1\right) \cos ^{-1}(x)}{6 x^3}+\frac{\log (x)}{3}","-\frac{\cos ^{-1}(x)^2}{4 x^4}-\frac{1}{12 x^2}+\frac{\sqrt{1-x^2} \cos ^{-1}(x)}{3 x}+\frac{\sqrt{1-x^2} \cos ^{-1}(x)}{6 x^3}+\frac{\log (x)}{3}",1,"-1/12*1/x^2 + (Sqrt[1 - x^2]*(1 + 2*x^2)*ArcCos[x])/(6*x^3) - ArcCos[x]^2/(4*x^4) + Log[x]/3","A",1
646,1,42,61,0.026167,"\int x^2 \sin ^{-1}(x)^2 \, dx","Integrate[x^2*ArcSin[x]^2,x]","\frac{1}{27} \left(9 x^3 \sin ^{-1}(x)^2-2 \left(x^2+6\right) x+6 \sqrt{1-x^2} \left(x^2+2\right) \sin ^{-1}(x)\right)","-\frac{2 x^3}{27}+\frac{1}{3} x^3 \sin ^{-1}(x)^2+\frac{2}{9} \sqrt{1-x^2} x^2 \sin ^{-1}(x)+\frac{4}{9} \sqrt{1-x^2} \sin ^{-1}(x)-\frac{4 x}{9}",1,"(-2*x*(6 + x^2) + 6*Sqrt[1 - x^2]*(2 + x^2)*ArcSin[x] + 9*x^3*ArcSin[x]^2)/27","A",1
647,1,37,53,0.0215272,"\int x^3 \tan ^{-1}(x)^2 \, dx","Integrate[x^3*ArcTan[x]^2,x]","\frac{1}{12} \left(3 \left(x^4-1\right) \tan ^{-1}(x)^2+x^2-4 \log \left(x^2+1\right)-2 \left(x^2-3\right) x \tan ^{-1}(x)\right)","\frac{1}{4} x^4 \tan ^{-1}(x)^2-\frac{1}{6} x^3 \tan ^{-1}(x)+\frac{x^2}{12}-\frac{1}{3} \log \left(x^2+1\right)+\frac{1}{2} x \tan ^{-1}(x)-\frac{1}{4} \tan ^{-1}(x)^2",1,"(x^2 - 2*x*(-3 + x^2)*ArcTan[x] + 3*(-1 + x^4)*ArcTan[x]^2 - 4*Log[1 + x^2])/12","A",1
648,1,56,61,0.0179498,"\int \frac{\tan ^{-1}(x)^2}{x^5} \, dx","Integrate[ArcTan[x]^2/x^5,x]","\frac{\left(x^4-1\right) \tan ^{-1}(x)^2}{4 x^4}-\frac{1}{12 x^2}+\frac{1}{3} \log \left(x^2+1\right)+\frac{\left(3 x^2-1\right) \tan ^{-1}(x)}{6 x^3}-\frac{2 \log (x)}{3}","-\frac{\tan ^{-1}(x)^2}{4 x^4}-\frac{\tan ^{-1}(x)}{6 x^3}-\frac{1}{12 x^2}+\frac{1}{3} \log \left(x^2+1\right)-\frac{2 \log (x)}{3}+\frac{1}{4} \tan ^{-1}(x)^2+\frac{\tan ^{-1}(x)}{2 x}",1,"-1/12*1/x^2 + ((-1 + 3*x^2)*ArcTan[x])/(6*x^3) + ((-1 + x^4)*ArcTan[x]^2)/(4*x^4) - (2*Log[x])/3 + Log[1 + x^2]/3","A",1
649,1,42,63,0.0478164,"\int x^3 \csc ^{-1}(x)^2 \, dx","Integrate[x^3*ArcCsc[x]^2,x]","\frac{1}{12} \left(3 x^4 \csc ^{-1}(x)^2+x^2+2 \sqrt{1-\frac{1}{x^2}} \left(x^2+2\right) x \csc ^{-1}(x)+4 \log (x)\right)","\frac{1}{4} x^4 \csc ^{-1}(x)^2+\frac{x^2}{12}+\frac{1}{3} \sqrt{1-\frac{1}{x^2}} x \csc ^{-1}(x)+\frac{1}{6} \sqrt{1-\frac{1}{x^2}} x^3 \csc ^{-1}(x)+\frac{\log (x)}{3}",1,"(x^2 + 2*Sqrt[1 - x^(-2)]*x*(2 + x^2)*ArcCsc[x] + 3*x^4*ArcCsc[x]^2 + 4*Log[x])/12","A",1
650,1,92,148,0.0816975,"\int \frac{\sec ^{-1}(x)^4}{x^5} \, dx","Integrate[ArcSec[x]^4/x^5,x]","\frac{4 \left(3 x^4-8\right) \sec ^{-1}(x)^4-45 x^2+16 \sqrt{1-\frac{1}{x^2}} x \left(3 x^2+2\right) \sec ^{-1}(x)^3-6 \sqrt{1-\frac{1}{x^2}} x \left(15 x^2+2\right) \sec ^{-1}(x)+\left(-45 x^4+72 x^2+24\right) \sec ^{-1}(x)^2-3}{128 x^4}","-\frac{3}{128 x^4}-\frac{\sec ^{-1}(x)^4}{4 x^4}+\frac{3 \sec ^{-1}(x)^2}{16 x^4}-\frac{45}{128 x^2}+\frac{3 \sqrt{1-\frac{1}{x^2}} \sec ^{-1}(x)^3}{8 x}+\frac{9 \sec ^{-1}(x)^2}{16 x^2}-\frac{45 \sqrt{1-\frac{1}{x^2}} \sec ^{-1}(x)}{64 x}+\frac{\sqrt{1-\frac{1}{x^2}} \sec ^{-1}(x)^3}{4 x^3}-\frac{3 \sqrt{1-\frac{1}{x^2}} \sec ^{-1}(x)}{32 x^3}+\frac{3}{32} \sec ^{-1}(x)^4-\frac{45}{128} \sec ^{-1}(x)^2",1,"(-3 - 45*x^2 - 6*Sqrt[1 - x^(-2)]*x*(2 + 15*x^2)*ArcSec[x] + (24 + 72*x^2 - 45*x^4)*ArcSec[x]^2 + 16*Sqrt[1 - x^(-2)]*x*(2 + 3*x^2)*ArcSec[x]^3 + 4*(-8 + 3*x^4)*ArcSec[x]^4)/(128*x^4)","A",1
651,1,30,34,0.0085642,"\int \sqrt{1-x^2} \sin ^{-1}(x) \, dx","Integrate[Sqrt[1 - x^2]*ArcSin[x],x]","\frac{1}{4} \left(-x^2+2 \sqrt{1-x^2} x \sin ^{-1}(x)+\sin ^{-1}(x)^2\right)","-\frac{x^2}{4}+\frac{1}{2} \sqrt{1-x^2} x \sin ^{-1}(x)+\frac{1}{4} \sin ^{-1}(x)^2",1,"(-x^2 + 2*x*Sqrt[1 - x^2]*ArcSin[x] + ArcSin[x]^2)/4","A",1
652,1,30,34,0.0151961,"\int \sqrt{1-x^2} \cos ^{-1}(x) \, dx","Integrate[Sqrt[1 - x^2]*ArcCos[x],x]","\frac{1}{4} \left(x^2+2 \sqrt{1-x^2} x \cos ^{-1}(x)-\cos ^{-1}(x)^2\right)","\frac{x^2}{4}+\frac{1}{2} \sqrt{1-x^2} x \cos ^{-1}(x)-\frac{1}{4} \cos ^{-1}(x)^2",1,"(x^2 + 2*x*Sqrt[1 - x^2]*ArcCos[x] - ArcCos[x]^2)/4","A",1
653,1,26,30,0.0302643,"\int x \sqrt{1-x^2} \cos ^{-1}(x) \, dx","Integrate[x*Sqrt[1 - x^2]*ArcCos[x],x]","\frac{1}{9} \left(x^3-3 \left(1-x^2\right)^{3/2} \cos ^{-1}(x)-3 x\right)","\frac{x^3}{9}-\frac{1}{3} \left(1-x^2\right)^{3/2} \cos ^{-1}(x)-\frac{x}{3}",1,"(-3*x + x^3 - 3*(1 - x^2)^(3/2)*ArcCos[x])/9","A",1
654,1,42,59,0.0372085,"\int \left(1-x^2\right)^{3/2} \sin ^{-1}(x) \, dx","Integrate[(1 - x^2)^(3/2)*ArcSin[x],x]","\frac{1}{16} \left(x^4-5 x^2-2 \sqrt{1-x^2} \left(2 x^2-5\right) x \sin ^{-1}(x)+3 \sin ^{-1}(x)^2\right)","\frac{x^4}{16}-\frac{5 x^2}{16}+\frac{1}{4} \left(1-x^2\right)^{3/2} x \sin ^{-1}(x)+\frac{3}{8} \sqrt{1-x^2} x \sin ^{-1}(x)+\frac{3}{16} \sin ^{-1}(x)^2",1,"(-5*x^2 + x^4 - 2*x*Sqrt[1 - x^2]*(-5 + 2*x^2)*ArcSin[x] + 3*ArcSin[x]^2)/16","A",1
655,1,35,37,0.0164343,"\int x \left(1-x^2\right)^{3/2} \sin ^{-1}(x) \, dx","Integrate[x*(1 - x^2)^(3/2)*ArcSin[x],x]","\frac{1}{5} \left(\frac{x^5}{5}-\frac{2 x^3}{3}-\left(1-x^2\right)^{5/2} \sin ^{-1}(x)+x\right)","\frac{x^5}{25}-\frac{2 x^3}{15}-\frac{1}{5} \left(1-x^2\right)^{5/2} \sin ^{-1}(x)+\frac{x}{5}",1,"(x - (2*x^3)/3 + x^5/5 - (1 - x^2)^(5/2)*ArcSin[x])/5","A",1
656,1,47,61,0.0551797,"\int x^3 \left(1-x^2\right)^{3/2} \cos ^{-1}(x) \, dx","Integrate[x^3*(1 - x^2)^(3/2)*ArcCos[x],x]","-\frac{1}{35} \left(5 x^2+2\right) \left(1-x^2\right)^{5/2} \cos ^{-1}(x)-\frac{x \left(75 x^6-168 x^4+35 x^2+210\right)}{3675}","-\frac{x^7}{49}+\frac{8 x^5}{175}-\frac{x^3}{105}+\frac{1}{7} \left(1-x^2\right)^{7/2} \cos ^{-1}(x)-\frac{1}{5} \left(1-x^2\right)^{5/2} \cos ^{-1}(x)-\frac{2 x}{35}",1,"-1/3675*(x*(210 + 35*x^2 - 168*x^4 + 75*x^6)) - ((1 - x^2)^(5/2)*(2 + 5*x^2)*ArcCos[x])/35","A",1
657,1,119,95,0.2814318,"\int \frac{\left(1-x^2\right)^{3/2} \cos ^{-1}(x)}{x} \, dx","Integrate[((1 - x^2)^(3/2)*ArcCos[x])/x,x]","-i \operatorname{PolyLog}\left(2,-i e^{i \cos ^{-1}(x)}\right)+i \operatorname{PolyLog}\left(2,i e^{i \cos ^{-1}(x)}\right)+\sqrt{1-x^2} \cos ^{-1}(x)+\frac{1}{36} \left(12 \left(1-x^2\right)^{3/2} \cos ^{-1}(x)+9 x-\cos \left(3 \cos ^{-1}(x)\right)\right)+x-\cos ^{-1}(x) \log \left(1-i e^{i \cos ^{-1}(x)}\right)+\cos ^{-1}(x) \log \left(1+i e^{i \cos ^{-1}(x)}\right)","-i \operatorname{PolyLog}\left(2,-i e^{i \cos ^{-1}(x)}\right)+i \operatorname{PolyLog}\left(2,i e^{i \cos ^{-1}(x)}\right)-\frac{x^3}{9}+\frac{1}{3} \left(1-x^2\right)^{3/2} \cos ^{-1}(x)+\sqrt{1-x^2} \cos ^{-1}(x)+\frac{4 x}{3}+2 i \cos ^{-1}(x) \tan ^{-1}\left(e^{i \cos ^{-1}(x)}\right)",1,"x + Sqrt[1 - x^2]*ArcCos[x] + (9*x + 12*(1 - x^2)^(3/2)*ArcCos[x] - Cos[3*ArcCos[x]])/36 - ArcCos[x]*Log[1 - I*E^(I*ArcCos[x])] + ArcCos[x]*Log[1 + I*E^(I*ArcCos[x])] - I*PolyLog[2, (-I)*E^(I*ArcCos[x])] + I*PolyLog[2, I*E^(I*ArcCos[x])]","A",0
658,1,36,41,0.0399969,"\int \frac{\left(1-x^2\right)^{3/2} \sin ^{-1}(x)}{x^6} \, dx","Integrate[((1 - x^2)^(3/2)*ArcSin[x])/x^6,x]","-\frac{-4 x^5 \log (x)-4 x^3+4 \left(1-x^2\right)^{5/2} \sin ^{-1}(x)+x}{20 x^5}","-\frac{1}{20 x^4}+\frac{1}{5 x^2}-\frac{\left(1-x^2\right)^{5/2} \sin ^{-1}(x)}{5 x^5}+\frac{\log (x)}{5}",1,"-1/20*(x - 4*x^3 + 4*(1 - x^2)^(5/2)*ArcSin[x] - 4*x^5*Log[x])/x^5","A",1
659,1,28,34,0.013103,"\int \frac{x^2 \sin ^{-1}(x)}{\sqrt{1-x^2}} \, dx","Integrate[(x^2*ArcSin[x])/Sqrt[1 - x^2],x]","\frac{1}{4} \left(x^2-2 \sqrt{1-x^2} x \sin ^{-1}(x)+\sin ^{-1}(x)^2\right)","\frac{x^2}{4}-\frac{1}{2} \sqrt{1-x^2} x \sin ^{-1}(x)+\frac{1}{4} \sin ^{-1}(x)^2",1,"(x^2 - 2*x*Sqrt[1 - x^2]*ArcSin[x] + ArcSin[x]^2)/4","A",1
660,1,43,61,0.0228679,"\int \frac{x^4 \sin ^{-1}(x)}{\sqrt{1-x^2}} \, dx","Integrate[(x^4*ArcSin[x])/Sqrt[1 - x^2],x]","\frac{1}{16} \left(\left(x^2+3\right) x^2-2 \sqrt{1-x^2} \left(2 x^2+3\right) x \sin ^{-1}(x)+3 \sin ^{-1}(x)^2\right)","\frac{x^4}{16}+\frac{3 x^2}{16}-\frac{3}{8} \sqrt{1-x^2} x \sin ^{-1}(x)-\frac{1}{4} \sqrt{1-x^2} x^3 \sin ^{-1}(x)+\frac{3}{16} \sin ^{-1}(x)^2",1,"(x^2*(3 + x^2) - 2*x*Sqrt[1 - x^2]*(3 + 2*x^2)*ArcSin[x] + 3*ArcSin[x]^2)/16","A",1
661,1,19,19,0.012593,"\int \frac{x \sin ^{-1}(x)}{\left(1-x^2\right)^{3/2}} \, dx","Integrate[(x*ArcSin[x])/(1 - x^2)^(3/2),x]","\frac{\sin ^{-1}(x)}{\sqrt{1-x^2}}-\tanh ^{-1}(x)","\frac{\sin ^{-1}(x)}{\sqrt{1-x^2}}-\tanh ^{-1}(x)",1,"ArcSin[x]/Sqrt[1 - x^2] - ArcTanh[x]","A",1
662,1,32,17,0.0477092,"\int \frac{x \cos ^{-1}(x)}{\left(1-x^2\right)^{3/2}} \, dx","Integrate[(x*ArcCos[x])/(1 - x^2)^(3/2),x]","\frac{1}{2} \left(\frac{2 \cos ^{-1}(x)}{\sqrt{1-x^2}}-\log (1-x)+\log (x+1)\right)","\frac{\cos ^{-1}(x)}{\sqrt{1-x^2}}+\tanh ^{-1}(x)",1,"((2*ArcCos[x])/Sqrt[1 - x^2] - Log[1 - x] + Log[1 + x])/2","A",1
663,1,45,62,0.0968951,"\int \frac{\sin ^{-1}(x)}{\left(1-x^2\right)^{5/2}} \, dx","Integrate[ArcSin[x]/(1 - x^2)^(5/2),x]","\frac{1}{6} \left(\frac{1}{x^2-1}+2 \log \left(1-x^2\right)-\frac{2 x \left(2 x^2-3\right) \sin ^{-1}(x)}{\left(1-x^2\right)^{3/2}}\right)","-\frac{1}{6 \left(1-x^2\right)}+\frac{1}{3} \log \left(1-x^2\right)+\frac{2 x \sin ^{-1}(x)}{3 \sqrt{1-x^2}}+\frac{x \sin ^{-1}(x)}{3 \left(1-x^2\right)^{3/2}}",1,"((-1 + x^2)^(-1) - (2*x*(-3 + 2*x^2)*ArcSin[x])/(1 - x^2)^(3/2) + 2*Log[1 - x^2])/6","A",1
664,1,40,36,0.069613,"\int \frac{x^3 \sin ^{-1}(x)}{\left(1-x^2\right)^{3/2}} \, dx","Integrate[(x^3*ArcSin[x])/(1 - x^2)^(3/2),x]","\frac{1}{2} \left(-\frac{2 \left(x^2-2\right) \sin ^{-1}(x)}{\sqrt{1-x^2}}-2 x+\log (1-x)-\log (x+1)\right)","\sqrt{1-x^2} \sin ^{-1}(x)+\frac{\sin ^{-1}(x)}{\sqrt{1-x^2}}-x-\tanh ^{-1}(x)",1,"(-2*x - (2*(-2 + x^2)*ArcSin[x])/Sqrt[1 - x^2] + Log[1 - x] - Log[1 + x])/2","A",1
665,1,112,62,0.191063,"\int \frac{\sin ^{-1}(x)}{x \left(1-x^2\right)^{3/2}} \, dx","Integrate[ArcSin[x]/(x*(1 - x^2)^(3/2)),x]","i \operatorname{PolyLog}\left(2,-e^{i \sin ^{-1}(x)}\right)-i \operatorname{PolyLog}\left(2,e^{i \sin ^{-1}(x)}\right)+\frac{\sin ^{-1}(x)}{\sqrt{1-x^2}}+\sin ^{-1}(x) \log \left(1-e^{i \sin ^{-1}(x)}\right)-\sin ^{-1}(x) \log \left(1+e^{i \sin ^{-1}(x)}\right)+\log \left(\cos \left(\frac{1}{2} \sin ^{-1}(x)\right)-\sin \left(\frac{1}{2} \sin ^{-1}(x)\right)\right)-\log \left(\sin \left(\frac{1}{2} \sin ^{-1}(x)\right)+\cos \left(\frac{1}{2} \sin ^{-1}(x)\right)\right)","i \operatorname{PolyLog}\left(2,-e^{i \sin ^{-1}(x)}\right)-i \operatorname{PolyLog}\left(2,e^{i \sin ^{-1}(x)}\right)+\frac{\sin ^{-1}(x)}{\sqrt{1-x^2}}-\tanh ^{-1}(x)-2 \sin ^{-1}(x) \tanh ^{-1}\left(e^{i \sin ^{-1}(x)}\right)",1,"ArcSin[x]/Sqrt[1 - x^2] + ArcSin[x]*Log[1 - E^(I*ArcSin[x])] - ArcSin[x]*Log[1 + E^(I*ArcSin[x])] + Log[Cos[ArcSin[x]/2] - Sin[ArcSin[x]/2]] - Log[Cos[ArcSin[x]/2] + Sin[ArcSin[x]/2]] + I*PolyLog[2, -E^(I*ArcSin[x])] - I*PolyLog[2, E^(I*ArcSin[x])]","A",0
666,1,38,54,0.0493908,"\int \frac{\cos ^{-1}(x)}{x^4 \sqrt{1-x^2}} \, dx","Integrate[ArcCos[x]/(x^4*Sqrt[1 - x^2]),x]","\frac{-4 x^3 \log (x)-2 \sqrt{1-x^2} \left(2 x^2+1\right) \cos ^{-1}(x)+x}{6 x^3}","\frac{1}{6 x^2}-\frac{2 \sqrt{1-x^2} \cos ^{-1}(x)}{3 x}-\frac{\sqrt{1-x^2} \cos ^{-1}(x)}{3 x^3}-\frac{2 \log (x)}{3}",1,"(x - 2*Sqrt[1 - x^2]*(1 + 2*x^2)*ArcCos[x] - 4*x^3*Log[x])/(6*x^3)","A",1
667,1,50,66,0.0594877,"\int x \sqrt{1-x^2} \cos ^{-1}(x)^2 \, dx","Integrate[x*Sqrt[1 - x^2]*ArcCos[x]^2,x]","\frac{1}{27} \left(-2 \sqrt{1-x^2} \left(x^2-7\right)-9 \left(1-x^2\right)^{3/2} \cos ^{-1}(x)^2+6 x \left(x^2-3\right) \cos ^{-1}(x)\right)","\frac{2}{9} x^3 \cos ^{-1}(x)+\frac{2}{27} \left(1-x^2\right)^{3/2}+\frac{4 \sqrt{1-x^2}}{9}-\frac{1}{3} \left(1-x^2\right)^{3/2} \cos ^{-1}(x)^2-\frac{2}{3} x \cos ^{-1}(x)",1,"(-2*Sqrt[1 - x^2]*(-7 + x^2) + 6*x*(-3 + x^2)*ArcCos[x] - 9*(1 - x^2)^(3/2)*ArcCos[x]^2)/27","A",1
668,1,60,73,0.0248172,"\int \frac{x^2 \sin ^{-1}(x)^3}{\sqrt{1-x^2}} \, dx","Integrate[(x^2*ArcSin[x]^3)/Sqrt[1 - x^2],x]","\frac{1}{8} \left(-3 x^2-4 x \sqrt{1-x^2} \sin ^{-1}(x)^3+\left(6 x^2-3\right) \sin ^{-1}(x)^2+6 x \sqrt{1-x^2} \sin ^{-1}(x)+\sin ^{-1}(x)^4\right)","-\frac{3 x^2}{8}-\frac{1}{2} x \sqrt{1-x^2} \sin ^{-1}(x)^3+\frac{3}{4} x^2 \sin ^{-1}(x)^2+\frac{3}{4} x \sqrt{1-x^2} \sin ^{-1}(x)+\frac{1}{8} \sin ^{-1}(x)^4-\frac{3}{8} \sin ^{-1}(x)^2",1,"(-3*x^2 + 6*x*Sqrt[1 - x^2]*ArcSin[x] + (-3 + 6*x^2)*ArcSin[x]^2 - 4*x*Sqrt[1 - x^2]*ArcSin[x]^3 + ArcSin[x]^4)/8","A",1
669,1,21,32,0.0211864,"\int \frac{x \tan ^{-1}(x)}{\left(1+x^2\right)^2} \, dx","Integrate[(x*ArcTan[x])/(1 + x^2)^2,x]","\frac{\left(x^2-1\right) \tan ^{-1}(x)+x}{4 \left(x^2+1\right)}","\frac{x}{4 \left(x^2+1\right)}-\frac{\tan ^{-1}(x)}{2 \left(x^2+1\right)}+\frac{1}{4} \tan ^{-1}(x)",1,"(x + (-1 + x^2)*ArcTan[x])/(4*(1 + x^2))","A",1
670,1,36,44,0.017866,"\int \frac{x \tan ^{-1}(x)}{\left(1+x^2\right)^3} \, dx","Integrate[(x*ArcTan[x])/(1 + x^2)^3,x]","\frac{x \left(3 x^2+5\right)+\left(3 x^4+6 x^2-5\right) \tan ^{-1}(x)}{32 \left(x^2+1\right)^2}","\frac{3 x}{32 \left(x^2+1\right)}+\frac{x}{16 \left(x^2+1\right)^2}-\frac{\tan ^{-1}(x)}{4 \left(x^2+1\right)^2}+\frac{3}{32} \tan ^{-1}(x)",1,"(x*(5 + 3*x^2) + (-5 + 6*x^2 + 3*x^4)*ArcTan[x])/(32*(1 + x^2)^2)","A",1
671,1,23,23,0.0169565,"\int \frac{x^2 \tan ^{-1}(x)}{1+x^2} \, dx","Integrate[(x^2*ArcTan[x])/(1 + x^2),x]","-\frac{1}{2} \log \left(x^2+1\right)-\frac{1}{2} \tan ^{-1}(x)^2+x \tan ^{-1}(x)","-\frac{1}{2} \log \left(x^2+1\right)-\frac{1}{2} \tan ^{-1}(x)^2+x \tan ^{-1}(x)",1,"x*ArcTan[x] - ArcTan[x]^2/2 - Log[1 + x^2]/2","A",1
672,1,57,67,0.0254972,"\int \frac{x^3 \tan ^{-1}(x)}{1+x^2} \, dx","Integrate[(x^3*ArcTan[x])/(1 + x^2),x]","\frac{1}{2} \left(i \operatorname{PolyLog}\left(2,\frac{x+i}{x-i}\right)+\left(x^2+2 \log \left(-\frac{2 i}{x-i}\right)+1\right) \tan ^{-1}(x)-x+i \tan ^{-1}(x)^2\right)","\frac{1}{2} i \operatorname{PolyLog}\left(2,1-\frac{2}{1+i x}\right)+\frac{1}{2} x^2 \tan ^{-1}(x)-\frac{x}{2}+\frac{1}{2} i \tan ^{-1}(x)^2+\frac{1}{2} \tan ^{-1}(x)+\log \left(\frac{2}{1+i x}\right) \tan ^{-1}(x)",1,"(-x + I*ArcTan[x]^2 + ArcTan[x]*(1 + x^2 + 2*Log[(-2*I)/(-I + x)]) + I*PolyLog[2, (I + x)/(-I + x)])/2","A",1
673,1,28,34,0.0280597,"\int \frac{x^2 \tan ^{-1}(x)}{\left(1+x^2\right)^2} \, dx","Integrate[(x^2*ArcTan[x])/(1 + x^2)^2,x]","\frac{\left(x^2+1\right) \tan ^{-1}(x)^2-2 x \tan ^{-1}(x)-1}{4 \left(x^2+1\right)}","-\frac{1}{4 \left(x^2+1\right)}-\frac{x \tan ^{-1}(x)}{2 \left(x^2+1\right)}+\frac{1}{4} \tan ^{-1}(x)^2",1,"(-1 - 2*x*ArcTan[x] + (1 + x^2)*ArcTan[x]^2)/(4*(1 + x^2))","A",1
674,1,64,79,0.0792496,"\int \frac{x^3 \tan ^{-1}(x)}{\left(1+x^2\right)^2} \, dx","Integrate[(x^3*ArcTan[x])/(1 + x^2)^2,x]","\frac{1}{2} i \operatorname{PolyLog}\left(2,-e^{2 i \tan ^{-1}(x)}\right)+\frac{1}{2} i \tan ^{-1}(x)^2-\tan ^{-1}(x) \log \left(1+e^{2 i \tan ^{-1}(x)}\right)-\frac{1}{8} \sin \left(2 \tan ^{-1}(x)\right)+\frac{1}{4} \tan ^{-1}(x) \cos \left(2 \tan ^{-1}(x)\right)","-\frac{1}{2} i \operatorname{PolyLog}\left(2,1-\frac{2}{1+i x}\right)-\frac{x}{4 \left(x^2+1\right)}+\frac{\tan ^{-1}(x)}{2 \left(x^2+1\right)}-\frac{1}{2} i \tan ^{-1}(x)^2-\frac{1}{4} \tan ^{-1}(x)-\log \left(\frac{2}{1+i x}\right) \tan ^{-1}(x)",1,"(I/2)*ArcTan[x]^2 + (ArcTan[x]*Cos[2*ArcTan[x]])/4 - ArcTan[x]*Log[1 + E^((2*I)*ArcTan[x])] + (I/2)*PolyLog[2, -E^((2*I)*ArcTan[x])] - Sin[2*ArcTan[x]]/8","A",0
675,1,70,89,0.2250474,"\int \frac{x^5 \tan ^{-1}(x)}{\left(1+x^2\right)^2} \, dx","Integrate[(x^5*ArcTan[x])/(1 + x^2)^2,x]","\frac{1}{8} \left(-8 i \operatorname{PolyLog}\left(2,-e^{2 i \tan ^{-1}(x)}\right)+4 \left(x^2+1\right) \tan ^{-1}(x)-4 x-8 i \tan ^{-1}(x)^2+16 \tan ^{-1}(x) \log \left(1+e^{2 i \tan ^{-1}(x)}\right)+\sin \left(2 \tan ^{-1}(x)\right)-2 \tan ^{-1}(x) \cos \left(2 \tan ^{-1}(x)\right)\right)","i \operatorname{PolyLog}\left(2,1-\frac{2}{1+i x}\right)+\frac{x}{4 \left(x^2+1\right)}+\frac{1}{2} x^2 \tan ^{-1}(x)-\frac{\tan ^{-1}(x)}{2 \left(x^2+1\right)}-\frac{x}{2}+i \tan ^{-1}(x)^2+\frac{3}{4} \tan ^{-1}(x)+2 \log \left(\frac{2}{1+i x}\right) \tan ^{-1}(x)",1,"(-4*x + 4*(1 + x^2)*ArcTan[x] - (8*I)*ArcTan[x]^2 - 2*ArcTan[x]*Cos[2*ArcTan[x]] + 16*ArcTan[x]*Log[1 + E^((2*I)*ArcTan[x])] - (8*I)*PolyLog[2, -E^((2*I)*ArcTan[x])] + Sin[2*ArcTan[x]])/8","A",0
676,1,22,22,0.0065099,"\int \frac{\left(1+x^2\right) \tan ^{-1}(x)}{x^2} \, dx","Integrate[((1 + x^2)*ArcTan[x])/x^2,x]","-\log \left(x^2+1\right)+\log (x)+x \tan ^{-1}(x)-\frac{\tan ^{-1}(x)}{x}","-\log \left(x^2+1\right)+\log (x)+x \tan ^{-1}(x)-\frac{\tan ^{-1}(x)}{x}",1,"-(ArcTan[x]/x) + x*ArcTan[x] + Log[x] - Log[1 + x^2]","A",1
677,1,59,31,0.0060755,"\int \frac{\left(1+x^2\right) \tan ^{-1}(x)}{x^5} \, dx","Integrate[((1 + x^2)*ArcTan[x])/x^5,x]","-\frac{\, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};-x^2\right)}{2 x}-\frac{\, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};-x^2\right)}{12 x^3}-\frac{\tan ^{-1}(x)}{4 x^4}-\frac{\tan ^{-1}(x)}{2 x^2}","-\frac{1}{12 x^3}-\frac{\left(x^2+1\right)^2 \tan ^{-1}(x)}{4 x^4}-\frac{1}{4 x}",1,"-1/4*ArcTan[x]/x^4 - ArcTan[x]/(2*x^2) - Hypergeometric2F1[-3/2, 1, -1/2, -x^2]/(12*x^3) - Hypergeometric2F1[-1/2, 1, 1/2, -x^2]/(2*x)","C",1
678,1,81,63,0.008331,"\int \frac{\left(1+x^2\right)^2 \tan ^{-1}(x)}{x^5} \, dx","Integrate[((1 + x^2)^2*ArcTan[x])/x^5,x]","\frac{1}{2} i \operatorname{PolyLog}(2,-i x)-\frac{1}{2} i \operatorname{PolyLog}(2,i x)-\frac{\, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};-x^2\right)}{x}-\frac{\, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};-x^2\right)}{12 x^3}-\frac{\tan ^{-1}(x)}{4 x^4}-\frac{\tan ^{-1}(x)}{x^2}","\frac{1}{2} i \operatorname{PolyLog}(2,-i x)-\frac{1}{2} i \operatorname{PolyLog}(2,i x)-\frac{\tan ^{-1}(x)}{4 x^4}-\frac{1}{12 x^3}-\frac{\tan ^{-1}(x)}{x^2}-\frac{3}{4 x}-\frac{3}{4} \tan ^{-1}(x)",1,"-1/4*ArcTan[x]/x^4 - ArcTan[x]/x^2 - Hypergeometric2F1[-3/2, 1, -1/2, -x^2]/(12*x^3) - Hypergeometric2F1[-1/2, 1, 1/2, -x^2]/x + (I/2)*PolyLog[2, (-I)*x] - (I/2)*PolyLog[2, I*x]","C",0
679,1,28,28,0.0070298,"\int \frac{\tan ^{-1}(x)}{x^2 \left(1+x^2\right)} \, dx","Integrate[ArcTan[x]/(x^2*(1 + x^2)),x]","-\frac{1}{2} \log \left(x^2+1\right)+\log (x)-\frac{1}{2} \tan ^{-1}(x)^2-\frac{\tan ^{-1}(x)}{x}","-\frac{1}{2} \log \left(x^2+1\right)+\log (x)-\frac{1}{2} \tan ^{-1}(x)^2-\frac{\tan ^{-1}(x)}{x}",1,"-(ArcTan[x]/x) - ArcTan[x]^2/2 + Log[x] - Log[1 + x^2]/2","A",1
680,1,38,39,0.0249752,"\int \frac{\tan ^{-1}(x)^2}{x^3} \, dx","Integrate[ArcTan[x]^2/x^3,x]","-\frac{1}{2} \log \left(x^2+1\right)+\frac{\left(-x^2-1\right) \tan ^{-1}(x)^2}{2 x^2}+\log (x)-\frac{\tan ^{-1}(x)}{x}","-\frac{1}{2} \log \left(x^2+1\right)-\frac{\tan ^{-1}(x)^2}{2 x^2}+\log (x)-\frac{1}{2} \tan ^{-1}(x)^2-\frac{\tan ^{-1}(x)}{x}",1,"-(ArcTan[x]/x) + ((-1 - x^2)*ArcTan[x]^2)/(2*x^2) + Log[x] - Log[1 + x^2]/2","A",1
681,1,56,60,0.0259548,"\int \frac{\left(1+x^2\right) \tan ^{-1}(x)^2}{x^5} \, dx","Integrate[((1 + x^2)*ArcTan[x]^2)/x^5,x]","\frac{-2 \left(3 x^3+x\right) \tan ^{-1}(x)+x^2 \left(4 x^2 \log (x)-2 x^2 \log \left(x^2+1\right)-1\right)-3 \left(x^2+1\right)^2 \tan ^{-1}(x)^2}{12 x^4}","-\frac{\tan ^{-1}(x)}{6 x^3}-\frac{1}{12 x^2}-\frac{1}{6} \log \left(x^2+1\right)-\frac{\left(x^2+1\right)^2 \tan ^{-1}(x)^2}{4 x^4}+\frac{\log (x)}{3}-\frac{\tan ^{-1}(x)}{2 x}",1,"(-2*(x + 3*x^3)*ArcTan[x] - 3*(1 + x^2)^2*ArcTan[x]^2 + x^2*(-1 + 4*x^2*Log[x] - 2*x^2*Log[1 + x^2]))/(12*x^4)","A",1
682,1,47,79,0.0558377,"\int \frac{x^3 \tan ^{-1}(x)^2}{\left(1+x^2\right)^3} \, dx","Integrate[(x^3*ArcTan[x]^2)/(1 + x^2)^3,x]","\frac{5 x^2+2 \left(5 x^2+3\right) x \tan ^{-1}(x)+\left(5 x^4-6 x^2-3\right) \tan ^{-1}(x)^2+4}{32 \left(x^2+1\right)^2}","\frac{5}{32 \left(x^2+1\right)}-\frac{1}{32 \left(x^2+1\right)^2}+\frac{3 x \tan ^{-1}(x)}{16 \left(x^2+1\right)}+\frac{x^4 \tan ^{-1}(x)^2}{4 \left(x^2+1\right)^2}+\frac{x^3 \tan ^{-1}(x)}{8 \left(x^2+1\right)^2}-\frac{3}{32} \tan ^{-1}(x)^2",1,"(4 + 5*x^2 + 2*x*(3 + 5*x^2)*ArcTan[x] + (-3 - 6*x^2 + 5*x^4)*ArcTan[x]^2)/(32*(1 + x^2)^2)","A",1
683,1,116,107,0.2022217,"\int \frac{\sqrt{-1+x^2} \sec ^{-1}(x)}{x^2} \, dx","Integrate[(Sqrt[-1 + x^2]*ArcSec[x])/x^2,x]","-\frac{\sqrt{1-\frac{1}{x^2}} \left(-i x \operatorname{PolyLog}\left(2,-i e^{i \sec ^{-1}(x)}\right)+i x \operatorname{PolyLog}\left(2,i e^{i \sec ^{-1}(x)}\right)+\sqrt{1-\frac{1}{x^2}} x \sec ^{-1}(x)-x \sec ^{-1}(x) \log \left(1-i e^{i \sec ^{-1}(x)}\right)+x \sec ^{-1}(x) \log \left(1+i e^{i \sec ^{-1}(x)}\right)+1\right)}{\sqrt{x^2-1}}","\frac{i \sqrt{x^2} \operatorname{PolyLog}\left(2,-i e^{i \sec ^{-1}(x)}\right)}{x}-\frac{i \sqrt{x^2} \operatorname{PolyLog}\left(2,i e^{i \sec ^{-1}(x)}\right)}{x}-\frac{1}{\sqrt{x^2}}-\frac{\sqrt{x^2-1} \sec ^{-1}(x)}{x}-\frac{2 i \sqrt{x^2} \sec ^{-1}(x) \tan ^{-1}\left(e^{i \sec ^{-1}(x)}\right)}{x}",1,"-((Sqrt[1 - x^(-2)]*(1 + Sqrt[1 - x^(-2)]*x*ArcSec[x] - x*ArcSec[x]*Log[1 - I*E^(I*ArcSec[x])] + x*ArcSec[x]*Log[1 + I*E^(I*ArcSec[x])] - I*x*PolyLog[2, (-I)*E^(I*ArcSec[x])] + I*x*PolyLog[2, I*E^(I*ArcSec[x])]))/Sqrt[-1 + x^2])","A",0
684,1,86,106,0.3078061,"\int \frac{\left(-1+x^2\right)^{5/2} \csc ^{-1}(x)}{x^3} \, dx","Integrate[((-1 + x^2)^(5/2)*ArcCsc[x])/x^3,x]","\frac{\sqrt{x^2-1} \left(4 x^2+\csc ^{-1}(x) \left(8 \sqrt{1-\frac{1}{x^2}} x \left(x^2-7\right)-6 \sin \left(2 \csc ^{-1}(x)\right)\right)+48 \log \left(\frac{1}{x}\right)-8 \log (x)-30 \csc ^{-1}(x)^2-3 \cos \left(2 \csc ^{-1}(x)\right)\right)}{24 \sqrt{1-\frac{1}{x^2}} x}","-\frac{7 x \log (x)}{3 \sqrt{x^2}}+\frac{\left(x^2-1\right)^{5/2} \csc ^{-1}(x)}{3 x^2}-\frac{5 \left(x^2-1\right)^{3/2} \csc ^{-1}(x)}{3 x^2}-\frac{5 \sqrt{x^2-1} \csc ^{-1}(x)}{2 x^2}-\frac{5 x \csc ^{-1}(x)^2}{4 \sqrt{x^2}}+\frac{2 x^4+3}{12 x \sqrt{x^2}}",1,"(Sqrt[-1 + x^2]*(4*x^2 - 30*ArcCsc[x]^2 - 3*Cos[2*ArcCsc[x]] + 48*Log[x^(-1)] - 8*Log[x] + ArcCsc[x]*(8*Sqrt[1 - x^(-2)]*x*(-7 + x^2) - 6*Sin[2*ArcCsc[x]])))/(24*Sqrt[1 - x^(-2)]*x)","A",1
685,1,48,41,0.0609768,"\int \frac{\sqrt{-1+x^2} \sec ^{-1}(x)}{x^4} \, dx","Integrate[(Sqrt[-1 + x^2]*ArcSec[x])/x^4,x]","\frac{\sqrt{1-\frac{1}{x^2}} x \left(3 x^2-1\right)+3 \left(x^2-1\right)^2 \sec ^{-1}(x)}{9 x^3 \sqrt{x^2-1}}","\frac{1}{3 \sqrt{x^2}}-\frac{1}{9 \left(x^2\right)^{3/2}}+\frac{\left(x^2-1\right)^{3/2} \sec ^{-1}(x)}{3 x^3}",1,"(Sqrt[1 - x^(-2)]*x*(-1 + 3*x^2) + 3*(-1 + x^2)^2*ArcSec[x])/(9*x^3*Sqrt[-1 + x^2])","A",1
686,1,67,65,0.1379985,"\int \frac{\sec ^{-1}(x)}{\left(-1+x^2\right)^{5/2}} \, dx","Integrate[ArcSec[x]/(-1 + x^2)^(5/2),x]","\frac{\sqrt{1-\frac{1}{x^2}} x \left(-5 \left(x^2-1\right) \log (1-x)+5 \left(x^2-1\right) \log (x+1)-2 x\right)+4 x \left(2 x^2-3\right) \sec ^{-1}(x)}{12 \left(x^2-1\right)^{3/2}}","\frac{\sqrt{x^2}}{6 \left(1-x^2\right)}+\frac{2 x \sec ^{-1}(x)}{3 \sqrt{x^2-1}}-\frac{x \sec ^{-1}(x)}{3 \left(x^2-1\right)^{3/2}}+\frac{5}{6} \coth ^{-1}\left(\sqrt{x^2}\right)",1,"(4*x*(-3 + 2*x^2)*ArcSec[x] + Sqrt[1 - x^(-2)]*x*(-2*x - 5*(-1 + x^2)*Log[1 - x] + 5*(-1 + x^2)*Log[1 + x]))/(12*(-1 + x^2)^(3/2))","A",1
687,1,61,51,0.1221076,"\int \frac{x^2 \sec ^{-1}(x)}{\left(-1+x^2\right)^{5/2}} \, dx","Integrate[(x^2*ArcSec[x])/(-1 + x^2)^(5/2),x]","\frac{\sqrt{1-\frac{1}{x^2}} x \left(\left(x^2-1\right) \log (1-x)-\left(x^2-1\right) \log (x+1)-2 x\right)-4 x^3 \sec ^{-1}(x)}{12 \left(x^2-1\right)^{3/2}}","\frac{\sqrt{x^2}}{6 \left(1-x^2\right)}-\frac{1}{6} \coth ^{-1}\left(\sqrt{x^2}\right)-\frac{x^3 \sec ^{-1}(x)}{3 \left(x^2-1\right)^{3/2}}",1,"(-4*x^3*ArcSec[x] + Sqrt[1 - x^(-2)]*x*(-2*x + (-1 + x^2)*Log[1 - x] - (-1 + x^2)*Log[1 + x]))/(12*(-1 + x^2)^(3/2))","A",1
688,1,72,82,0.2152469,"\int \frac{x^3 \sec ^{-1}(x)}{\left(-1+x^2\right)^{5/2}} \, dx","Integrate[(x^3*ArcSec[x])/(-1 + x^2)^(5/2),x]","\frac{-\frac{\left(x^2-1\right) \left(4 \left(x^2-1\right) \log (x)-2 \left(x^2-1\right) \log \left(1-x^2\right)+1\right)}{\sqrt{1-\frac{1}{x^2}} x}-2 \left(3 x^2-2\right) \sec ^{-1}(x)}{6 \left(x^2-1\right)^{3/2}}","\frac{x}{6 \sqrt{x^2} \left(1-x^2\right)}-\frac{2 x \log (x)}{3 \sqrt{x^2}}+\frac{x \log \left(x^2-1\right)}{3 \sqrt{x^2}}-\frac{\sec ^{-1}(x)}{\sqrt{x^2-1}}-\frac{\sec ^{-1}(x)}{3 \left(x^2-1\right)^{3/2}}",1,"(-2*(-2 + 3*x^2)*ArcSec[x] - ((-1 + x^2)*(1 + 4*(-1 + x^2)*Log[x] - 2*(-1 + x^2)*Log[1 - x^2]))/(Sqrt[1 - x^(-2)]*x))/(6*(-1 + x^2)^(3/2))","A",1
689,1,383,175,1.9887663,"\int \frac{x^6 \sec ^{-1}(x)}{\left(-1+x^2\right)^{5/2}} \, dx","Integrate[(x^6*ArcSec[x])/(-1 + x^2)^(5/2),x]","-\frac{x^5 \left(-60 i \sqrt{1-\frac{1}{x^2}} \sin ^2\left(2 \sec ^{-1}(x)\right) \operatorname{PolyLog}\left(2,-i e^{i \sec ^{-1}(x)}\right)+60 i \sqrt{1-\frac{1}{x^2}} \sin ^2\left(2 \sec ^{-1}(x)\right) \operatorname{PolyLog}\left(2,i e^{i \sec ^{-1}(x)}\right)-30 \sqrt{1-\frac{1}{x^2}} \sec ^{-1}(x) \log \left(1-i e^{i \sec ^{-1}(x)}\right)+30 \sqrt{1-\frac{1}{x^2}} \sec ^{-1}(x) \log \left(1+i e^{i \sec ^{-1}(x)}\right)-26 \sqrt{1-\frac{1}{x^2}} \log \left(\sin \left(\frac{1}{2} \sec ^{-1}(x)\right)\right)+26 \sqrt{1-\frac{1}{x^2}} \log \left(\cos \left(\frac{1}{2} \sec ^{-1}(x)\right)\right)+22 \sec ^{-1}(x)+40 \sec ^{-1}(x) \cos \left(2 \sec ^{-1}(x)\right)-30 \sec ^{-1}(x) \cos \left(4 \sec ^{-1}(x)\right)+16 \sin \left(2 \sec ^{-1}(x)\right)-4 \sin \left(4 \sec ^{-1}(x)\right)-15 \sec ^{-1}(x) \log \left(1-i e^{i \sec ^{-1}(x)}\right) \sin \left(3 \sec ^{-1}(x)\right)+15 \sec ^{-1}(x) \log \left(1+i e^{i \sec ^{-1}(x)}\right) \sin \left(3 \sec ^{-1}(x)\right)-13 \sin \left(3 \sec ^{-1}(x)\right) \log \left(\sin \left(\frac{1}{2} \sec ^{-1}(x)\right)\right)+15 \sec ^{-1}(x) \log \left(1-i e^{i \sec ^{-1}(x)}\right) \sin \left(5 \sec ^{-1}(x)\right)-15 \sec ^{-1}(x) \log \left(1+i e^{i \sec ^{-1}(x)}\right) \sin \left(5 \sec ^{-1}(x)\right)+13 \sin \left(5 \sec ^{-1}(x)\right) \log \left(\sin \left(\frac{1}{2} \sec ^{-1}(x)\right)\right)+13 \sin \left(3 \sec ^{-1}(x)\right) \log \left(\cos \left(\frac{1}{2} \sec ^{-1}(x)\right)\right)-13 \sin \left(5 \sec ^{-1}(x)\right) \log \left(\cos \left(\frac{1}{2} \sec ^{-1}(x)\right)\right)\right)}{96 \left(x^2-1\right)^{3/2}}","\frac{5 i \sqrt{x^2} \operatorname{PolyLog}\left(2,-i e^{i \sec ^{-1}(x)}\right)}{2 x}-\frac{5 i \sqrt{x^2} \operatorname{PolyLog}\left(2,i e^{i \sec ^{-1}(x)}\right)}{2 x}+\frac{\sqrt{x^2} \left(2-3 x^2\right)}{6 \left(x^2-1\right)}-\frac{5 x \sec ^{-1}(x)}{2 \sqrt{x^2-1}}-\frac{13}{6} \coth ^{-1}\left(\sqrt{x^2}\right)-\frac{5 i \sqrt{x^2} \sec ^{-1}(x) \tan ^{-1}\left(e^{i \sec ^{-1}(x)}\right)}{x}+\frac{x^5 \sec ^{-1}(x)}{2 \left(x^2-1\right)^{3/2}}-\frac{5 x^3 \sec ^{-1}(x)}{6 \left(x^2-1\right)^{3/2}}",1,"-1/96*(x^5*(22*ArcSec[x] + 40*ArcSec[x]*Cos[2*ArcSec[x]] - 30*ArcSec[x]*Cos[4*ArcSec[x]] - 30*Sqrt[1 - x^(-2)]*ArcSec[x]*Log[1 - I*E^(I*ArcSec[x])] + 30*Sqrt[1 - x^(-2)]*ArcSec[x]*Log[1 + I*E^(I*ArcSec[x])] + 26*Sqrt[1 - x^(-2)]*Log[Cos[ArcSec[x]/2]] - 26*Sqrt[1 - x^(-2)]*Log[Sin[ArcSec[x]/2]] + 16*Sin[2*ArcSec[x]] - (60*I)*Sqrt[1 - x^(-2)]*PolyLog[2, (-I)*E^(I*ArcSec[x])]*Sin[2*ArcSec[x]]^2 + (60*I)*Sqrt[1 - x^(-2)]*PolyLog[2, I*E^(I*ArcSec[x])]*Sin[2*ArcSec[x]]^2 - 15*ArcSec[x]*Log[1 - I*E^(I*ArcSec[x])]*Sin[3*ArcSec[x]] + 15*ArcSec[x]*Log[1 + I*E^(I*ArcSec[x])]*Sin[3*ArcSec[x]] + 13*Log[Cos[ArcSec[x]/2]]*Sin[3*ArcSec[x]] - 13*Log[Sin[ArcSec[x]/2]]*Sin[3*ArcSec[x]] - 4*Sin[4*ArcSec[x]] + 15*ArcSec[x]*Log[1 - I*E^(I*ArcSec[x])]*Sin[5*ArcSec[x]] - 15*ArcSec[x]*Log[1 + I*E^(I*ArcSec[x])]*Sin[5*ArcSec[x]] - 13*Log[Cos[ArcSec[x]/2]]*Sin[5*ArcSec[x]] + 13*Log[Sin[ArcSec[x]/2]]*Sin[5*ArcSec[x]]))/(-1 + x^2)^(3/2)","B",0
690,1,35,23,0.0464737,"\int \frac{\sec ^{-1}(x)}{x^2 \sqrt{-1+x^2}} \, dx","Integrate[ArcSec[x]/(x^2*Sqrt[-1 + x^2]),x]","\frac{\sqrt{1-\frac{1}{x^2}} x+\left(x^2-1\right) \sec ^{-1}(x)}{x \sqrt{x^2-1}}","\frac{1}{\sqrt{x^2}}+\frac{\sqrt{x^2-1} \sec ^{-1}(x)}{x}",1,"(Sqrt[1 - x^(-2)]*x + (-1 + x^2)*ArcSec[x])/(x*Sqrt[-1 + x^2])","A",1
691,1,79,70,0.1657041,"\int \frac{\csc ^{-1}(x)}{x^2 \left(-1+x^2\right)^{5/2}} \, dx","Integrate[ArcCsc[x]/(x^2*(-1 + x^2)^(5/2)),x]","\frac{\sqrt{1-\frac{1}{x^2}} x \left(-10 x^2+11 \left(x^2-1\right) x \log (1-x)-11 \left(x^2-1\right) x \log (x+1)+12\right)+4 \left(8 x^4-12 x^2+3\right) \csc ^{-1}(x)}{12 x \left(x^2-1\right)^{3/2}}","-\frac{1}{\sqrt{x^2}}+\frac{\sqrt{x^2}}{6 \left(x^2-1\right)}-\frac{11}{6} \coth ^{-1}\left(\sqrt{x^2}\right)+\frac{\left(8 x^4-12 x^2+3\right) \csc ^{-1}(x)}{3 x \left(x^2-1\right)^{3/2}}",1,"(4*(3 - 12*x^2 + 8*x^4)*ArcCsc[x] + Sqrt[1 - x^(-2)]*x*(12 - 10*x^2 + 11*x*(-1 + x^2)*Log[1 - x] - 11*x*(-1 + x^2)*Log[1 + x]))/(12*x*(-1 + x^2)^(3/2))","A",1
692,1,76,74,0.0802775,"\int \frac{\csc ^{-1}(x)^4}{x^2 \sqrt{-1+x^2}} \, dx","Integrate[ArcCsc[x]^4/(x^2*Sqrt[-1 + x^2]),x]","\frac{24 \left(x^2-1\right)+\left(x^2-1\right) \csc ^{-1}(x)^4-4 \sqrt{1-\frac{1}{x^2}} x \csc ^{-1}(x)^3-12 \left(x^2-1\right) \csc ^{-1}(x)^2+24 \sqrt{1-\frac{1}{x^2}} x \csc ^{-1}(x)}{x \sqrt{x^2-1}}","\frac{24 \sqrt{x^2-1}}{x}+\frac{\sqrt{x^2-1} \csc ^{-1}(x)^4}{x}-\frac{4 \csc ^{-1}(x)^3}{\sqrt{x^2}}-\frac{12 \sqrt{x^2-1} \csc ^{-1}(x)^2}{x}+\frac{24 \csc ^{-1}(x)}{\sqrt{x^2}}",1,"(24*(-1 + x^2) + 24*Sqrt[1 - x^(-2)]*x*ArcCsc[x] - 12*(-1 + x^2)*ArcCsc[x]^2 - 4*Sqrt[1 - x^(-2)]*x*ArcCsc[x]^3 + (-1 + x^2)*ArcCsc[x]^4)/(x*Sqrt[-1 + x^2])","A",1
693,1,84,133,0.3127704,"\int \frac{\left(-1+x^2\right)^{3/2} \sec ^{-1}(x)^2}{x^5} \, dx","Integrate[((-1 + x^2)^(3/2)*ArcSec[x]^2)/x^5,x]","\frac{\sqrt{x^2-1} \left(32 \sec ^{-1}(x)^3+4 \sec ^{-1}(x) \left(\cos \left(4 \sec ^{-1}(x)\right)-16 \cos \left(2 \sec ^{-1}(x)\right)\right)+8 \sec ^{-1}(x)^2 \left(\sin \left(4 \sec ^{-1}(x)\right)-8 \sin \left(2 \sec ^{-1}(x)\right)\right)+32 \sin \left(2 \sec ^{-1}(x)\right)-\sin \left(4 \sec ^{-1}(x)\right)\right)}{256 \sqrt{1-\frac{1}{x^2}} x}","\frac{x \sec ^{-1}(x)^3}{8 \sqrt{x^2}}-\frac{3 \sqrt{x^2-1} \sec ^{-1}(x)^2}{8 x^2}+\frac{9 x \sec ^{-1}(x)}{64 \sqrt{x^2}}-\frac{3 \sec ^{-1}(x)}{8 x \sqrt{x^2}}+\frac{\sqrt{x^2-1} \left(17 x^2-2\right)}{64 x^4}-\frac{\left(x^2-1\right)^{3/2} \sec ^{-1}(x)^2}{4 x^4}+\frac{\left(x^2-1\right)^2 \sec ^{-1}(x)}{8 x^3 \sqrt{x^2}}",1,"(Sqrt[-1 + x^2]*(32*ArcSec[x]^3 + 4*ArcSec[x]*(-16*Cos[2*ArcSec[x]] + Cos[4*ArcSec[x]]) + 32*Sin[2*ArcSec[x]] - Sin[4*ArcSec[x]] + 8*ArcSec[x]^2*(-8*Sin[2*ArcSec[x]] + Sin[4*ArcSec[x]])))/(256*Sqrt[1 - x^(-2)]*x)","A",1
694,1,92,110,0.1093997,"\int \frac{\sqrt{-1+x^2} \sec ^{-1}(x)^3}{x^4} \, dx","Integrate[(Sqrt[-1 + x^2]*ArcSec[x]^3)/x^4,x]","\frac{2 \sqrt{1-\frac{1}{x^2}} x \left(1-21 x^2\right)+9 \left(x^2-1\right)^2 \sec ^{-1}(x)^3+9 \sqrt{1-\frac{1}{x^2}} x \left(3 x^2-1\right) \sec ^{-1}(x)^2-6 \left(7 x^4-8 x^2+1\right) \sec ^{-1}(x)}{27 x^3 \sqrt{x^2-1}}","\frac{2 \left(1-21 x^2\right)}{27 \left(x^2\right)^{3/2}}+\frac{\left(x^2-1\right) \sec ^{-1}(x)^2}{3 \left(x^2\right)^{3/2}}+\frac{2 \sec ^{-1}(x)^2}{3 \sqrt{x^2}}-\frac{4 \sqrt{x^2-1} \sec ^{-1}(x)}{3 x}+\frac{\left(x^2-1\right)^{3/2} \sec ^{-1}(x)^3}{3 x^3}-\frac{2 \left(x^2-1\right)^{3/2} \sec ^{-1}(x)}{9 x^3}",1,"(2*Sqrt[1 - x^(-2)]*x*(1 - 21*x^2) - 6*(1 - 8*x^2 + 7*x^4)*ArcSec[x] + 9*Sqrt[1 - x^(-2)]*x*(-1 + 3*x^2)*ArcSec[x]^2 + 9*(-1 + x^2)^2*ArcSec[x]^3)/(27*x^3*Sqrt[-1 + x^2])","A",1
695,1,99,55,0.1703432,"\int \sin ^{-1}\left(\sqrt{\frac{-a+x}{a+x}}\right) \, dx","Integrate[ArcSin[Sqrt[(-a + x)/(a + x)]],x]","x \sin ^{-1}\left(\sqrt{\frac{x-a}{a+x}}\right)+\frac{\sqrt{\frac{a}{a+x}} \left(\sqrt{2} \sqrt{a} \sqrt{x-a} \tan ^{-1}\left(\frac{\sqrt{x-a}}{\sqrt{2} \sqrt{a}}\right)+2 a-2 x\right)}{\sqrt{2} \sqrt{\frac{x-a}{a+x}}}","(a+x) \sin ^{-1}\left(\sqrt{\frac{x-a}{a+x}}\right)-\frac{\sqrt{2} a \sqrt{\frac{x-a}{a+x}}}{\sqrt{\frac{a}{a+x}}}",1,"x*ArcSin[Sqrt[(-a + x)/(a + x)]] + (Sqrt[a/(a + x)]*(2*a - 2*x + Sqrt[2]*Sqrt[a]*Sqrt[-a + x]*ArcTan[Sqrt[-a + x]/(Sqrt[2]*Sqrt[a])]))/(Sqrt[2]*Sqrt[(-a + x)/(a + x)])","A",1
696,1,71,40,0.0612257,"\int \tan ^{-1}\left(\sqrt{\frac{-a+x}{a+x}}\right) \, dx","Integrate[ArcTan[Sqrt[(-a + x)/(a + x)]],x]","x \tan ^{-1}\left(\sqrt{\frac{x-a}{a+x}}\right)-\frac{a \sqrt{x-a} \tanh ^{-1}\left(\frac{\sqrt{x-a}}{\sqrt{a+x}}\right)}{\sqrt{\frac{x-a}{a+x}} \sqrt{a+x}}","x \tan ^{-1}\left(\sqrt{-\frac{a-x}{a+x}}\right)-a \tanh ^{-1}\left(\sqrt{-\frac{a-x}{a+x}}\right)",1,"x*ArcTan[Sqrt[(-a + x)/(a + x)]] - (a*Sqrt[-a + x]*ArcTanh[Sqrt[-a + x]/Sqrt[a + x]])/(Sqrt[(-a + x)/(a + x)]*Sqrt[a + x])","A",1
697,1,35,39,0.0466893,"\int \frac{\tan ^{-1}(x)}{(1+x)^3} \, dx","Integrate[ArcTan[x]/(1 + x)^3,x]","\frac{1}{8} \left(-\log \left(x^2+1\right)-\frac{2}{x+1}+2 \log (x+1)-\frac{4 \tan ^{-1}(x)}{(x+1)^2}\right)","-\frac{1}{8} \log \left(x^2+1\right)-\frac{1}{4 (x+1)}+\frac{1}{4} \log (x+1)-\frac{\tan ^{-1}(x)}{2 (x+1)^2}",1,"(-2/(1 + x) - (4*ArcTan[x])/(1 + x)^2 + 2*Log[1 + x] - Log[1 + x^2])/8","A",1
698,1,105,122,0.033665,"\int -\frac{\tan ^{-1}(a-x)}{a+x} \, dx","Integrate[-(ArcTan[a - x]/(a + x)),x]","-\frac{1}{2} i \left(\operatorname{PolyLog}\left(2,\frac{a-x+i}{2 a+i}\right)-\operatorname{PolyLog}\left(2,\frac{-a+x+i}{-2 a+i}\right)-\log (1+i (a-x)) \log \left(\frac{a+x}{2 a-i}\right)+\log (-i a+i x+1) \log \left(\frac{a+x}{2 a+i}\right)\right)","-\frac{1}{2} i \operatorname{PolyLog}\left(2,1-\frac{2}{1-i (a-x)}\right)+\frac{1}{2} i \operatorname{PolyLog}\left(2,1+\frac{2 (a+x)}{(-2 a+i) (1-i (a-x))}\right)+\log \left(\frac{2}{1-i (a-x)}\right) \tan ^{-1}(a-x)-\log \left(-\frac{2 (a+x)}{(-2 a+i) (1-i (a-x))}\right) \tan ^{-1}(a-x)",1,"(-1/2*I)*(-(Log[1 + I*(a - x)]*Log[(a + x)/(-I + 2*a)]) + Log[1 - I*a + I*x]*Log[(a + x)/(I + 2*a)] + PolyLog[2, (I + a - x)/(I + 2*a)] - PolyLog[2, (I - a + x)/(I - 2*a)])","A",0
699,1,28,28,0.0295184,"\int \frac{\sin ^{-1}\left(\sqrt{1-x^2}\right)}{\sqrt{1-x^2}} \, dx","Integrate[ArcSin[Sqrt[1 - x^2]]/Sqrt[1 - x^2],x]","-\frac{\sqrt{x^2} \sin ^{-1}\left(\sqrt{1-x^2}\right)^2}{2 x}","-\frac{\sqrt{x^2} \sin ^{-1}\left(\sqrt{1-x^2}\right)^2}{2 x}",1,"-1/2*(Sqrt[x^2]*ArcSin[Sqrt[1 - x^2]]^2)/x","A",1
700,1,31,31,0.0404197,"\int \frac{x \tan ^{-1}\left(\sqrt{1+x^2}\right)}{\sqrt{1+x^2}} \, dx","Integrate[(x*ArcTan[Sqrt[1 + x^2]])/Sqrt[1 + x^2],x]","\sqrt{x^2+1} \tan ^{-1}\left(\sqrt{x^2+1}\right)-\frac{1}{2} \log \left(x^2+2\right)","\sqrt{x^2+1} \tan ^{-1}\left(\sqrt{x^2+1}\right)-\frac{1}{2} \log \left(x^2+2\right)",1,"Sqrt[1 + x^2]*ArcTan[Sqrt[1 + x^2]] - Log[2 + x^2]/2","A",1
701,1,61,57,0.149504,"\int \frac{\sin ^{-1}(x)}{(1-x)^{5/2}} \, dx","Integrate[ArcSin[x]/(1 - x)^(5/2),x]","\frac{1}{6} \left(-\frac{2 \left(\sqrt{1-x^2}-2 \sin ^{-1}(x)\right)}{(1-x)^{3/2}}-\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{1-x^2}}{\sqrt{2-2 x}}\right)\right)","-\frac{\sqrt{x+1}}{3 (1-x)}+\frac{2 \sin ^{-1}(x)}{3 (1-x)^{3/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{x+1}}{\sqrt{2}}\right)}{3 \sqrt{2}}",1,"((-2*(Sqrt[1 - x^2] - 2*ArcSin[x]))/(1 - x)^(3/2) - Sqrt[2]*ArcTanh[Sqrt[1 - x^2]/Sqrt[2 - 2*x]])/6","A",1
702,1,72,82,0.1126102,"\int (-1+x)^{5/2} \csc ^{-1}(x) \, dx","Integrate[(-1 + x)^(5/2)*ArcCsc[x],x]","\frac{4 \sqrt{1-\frac{1}{x^2}} x \left(3 x^2-19 x+83\right)}{105 \sqrt{x-1}}+\frac{4}{7} \tanh ^{-1}\left(\frac{\sqrt{1-\frac{1}{x^2}} x}{\sqrt{x-1}}\right)+\frac{2}{7} (x-1)^{7/2} \csc ^{-1}(x)","\frac{4 x \sqrt{x^2-1} \left(3 x^2-19 x+83\right)}{105 \sqrt{x^2} \sqrt{x-1}}+\frac{4 x \tanh ^{-1}\left(\frac{\sqrt{x^2-1}}{\sqrt{x-1}}\right)}{7 \sqrt{x^2}}+\frac{2}{7} (x-1)^{7/2} \csc ^{-1}(x)",1,"(4*Sqrt[1 - x^(-2)]*x*(83 - 19*x + 3*x^2))/(105*Sqrt[-1 + x]) + (2*(-1 + x)^(7/2)*ArcCsc[x])/7 + (4*ArcTanh[(Sqrt[1 - x^(-2)]*x)/Sqrt[-1 + x]])/7","A",1
703,1,66,49,0.270687,"\int \sin ^{-1}(\sinh (x)) \text{sech}^4(x) \, dx","Integrate[ArcSin[Sinh[x]]*Sech[x]^4,x]","\frac{1}{12} \left(8 i \log \left(\sqrt{3-\cosh (2 x)}+i \sqrt{2} \cosh (x)\right)+\sqrt{6-2 \cosh (2 x)} \text{sech}(x)+4 (\cosh (2 x)+2) \tanh (x) \text{sech}^2(x) \sin ^{-1}(\sinh (x))\right)","-\frac{2}{3} \sin ^{-1}\left(\frac{\cosh (x)}{\sqrt{2}}\right)+\frac{1}{6} \sqrt{1-\sinh ^2(x)} \text{sech}(x)-\frac{1}{3} \tanh ^3(x) \sin ^{-1}(\sinh (x))+\tanh (x) \sin ^{-1}(\sinh (x))",1,"((8*I)*Log[I*Sqrt[2]*Cosh[x] + Sqrt[3 - Cosh[2*x]]] + Sqrt[6 - 2*Cosh[2*x]]*Sech[x] + 4*ArcSin[Sinh[x]]*(2 + Cosh[2*x])*Sech[x]^2*Tanh[x])/12","C",1
704,1,40,36,0.2260029,"\int \cot ^{-1}(\cosh (x)) \coth (x) \text{csch}^3(x) \, dx","Integrate[ArcCot[Cosh[x]]*Coth[x]*Csch[x]^3,x]","\frac{1}{24} \left(2 \sqrt{2} \tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{2}}\right)+\text{csch}^3(x) \left(-\cosh (x)+\cosh (3 x)-8 \cot ^{-1}(\cosh (x))\right)\right)","\frac{\tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{2}}\right)}{6 \sqrt{2}}+\frac{\coth (x)}{6}-\frac{1}{3} \text{csch}^3(x) \cot ^{-1}(\cosh (x))",1,"(2*Sqrt[2]*ArcTanh[Tanh[x]/Sqrt[2]] + (-8*ArcCot[Cosh[x]] - Cosh[x] + Cosh[3*x])*Csch[x]^3)/24","A",1
705,1,64,28,0.9715989,"\int e^x \sin ^{-1}(\tanh (x)) \, dx","Integrate[E^x*ArcSin[Tanh[x]],x]","e^x \sin ^{-1}\left(\frac{e^{2 x}-1}{e^{2 x}+1}\right)-e^{-x} \sqrt{\frac{e^{2 x}}{\left(e^{2 x}+1\right)^2}} \left(e^{2 x}+1\right) \log \left(e^{2 x}+1\right)","e^x \sin ^{-1}(\tanh (x))-\log \left(e^{2 x}+1\right) \cosh (x) \sqrt{\text{sech}^2(x)}",1,"E^x*ArcSin[(-1 + E^(2*x))/(1 + E^(2*x))] - (Sqrt[E^(2*x)/(1 + E^(2*x))^2]*(1 + E^(2*x))*Log[1 + E^(2*x)])/E^x","B",0