1,1,14,0,0.0076569,"\int \frac{1}{a^2-b^2 x^2} \, dx","Int[(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",1,1,14,0.07143,1,"{208}"
2,1,14,0,0.0048183,"\int \frac{1}{a^2+b^2 x^2} \, dx","Int[(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",1,1,13,0.07692,1,"{205}"
3,1,13,0,0.0037081,"\int \sec (2 a x) \, dx","Int[Sec[2*a*x],x]","\frac{\tanh ^{-1}(\sin (2 a x))}{2 a}","\frac{\tanh ^{-1}(\sin (2 a x))}{2 a}",1,"ArcTanh[Sin[2*a*x]]/(2*a)","A",1,1,5,0.2000,1,"{3770}"
4,1,11,0,0.0032333,"\int \frac{1}{4} \csc \left(\frac{x}{3}\right) \, dx","Int[Csc[x/3]/4,x]","-\frac{3}{4} \tanh ^{-1}\left(\cos \left(\frac{x}{3}\right)\right)","-\frac{3}{4} \tanh ^{-1}\left(\cos \left(\frac{x}{3}\right)\right)",1,"(-3*ArcTanh[Cos[x/3]])/4","A",2,2,10,0.2000,1,"{12, 3770}"
5,1,15,0,0.0034344,"\int -\sec \left(\frac{\pi }{4}+2 x\right) \, dx","Int[-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,"-ArcTanh[Sin[Pi/4 + 2*x]]/2","A",1,1,12,0.08333,1,"{3770}"
6,1,2,0,0.0058834,"\int \sec (x) \tan (x) \, dx","Int[Sec[x]*Tan[x],x]","\sec (x)","\sec (x)",1,"Sec[x]","A",2,2,5,0.4000,1,"{2606, 8}"
7,1,4,0,0.006253,"\int \cot (x) \csc (x) \, dx","Int[Cot[x]*Csc[x],x]","-\csc (x)","-\csc (x)",1,"-Csc[x]","A",2,2,5,0.4000,1,"{2606, 8}"
8,1,6,0,0.0235679,"\int \csc (2 x) \tan (x) \, dx","Int[Csc[2*x]*Tan[x],x]","\frac{\tan (x)}{2}","\frac{\tan (x)}{2}",1,"Tan[x]/2","A",2,1,7,0.1429,1,"{8}"
9,1,9,0,0.0067796,"\int \frac{1}{1+\cos (x)} \, dx","Int[(1 + Cos[x])^(-1),x]","\frac{\sin (x)}{\cos (x)+1}","\frac{\sin (x)}{\cos (x)+1}",1,"Sin[x]/(1 + Cos[x])","A",1,1,6,0.1667,1,"{2648}"
10,1,12,0,0.0079056,"\int \frac{1}{1-\cos (x)} \, dx","Int[(1 - Cos[x])^(-1),x]","-\frac{\sin (x)}{1-\cos (x)}","-\frac{\sin (x)}{1-\cos (x)}",1,"-(Sin[x]/(1 - Cos[x]))","A",1,1,8,0.1250,1,"{2648}"
11,1,12,0,0.0226925,"\int \frac{\sin (x)}{a-b \cos (x)} \, dx","Int[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",2,2,12,0.1667,1,"{2668, 31}"
12,1,15,0,0.0260214,"\int \frac{\cos (x)}{a^2+b^2 \sin ^2(x)} \, dx","Int[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",2,2,17,0.1176,1,"{3190, 205}"
13,1,15,0,0.027777,"\int \frac{\cos (x)}{a^2-b^2 \sin ^2(x)} \, dx","Int[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",2,2,18,0.1111,1,"{3190, 208}"
14,1,17,0,0.0353553,"\int \frac{\sin (2 x)}{a^2+b^2 \sin ^2(x)} \, dx","Int[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",3,2,19,0.1053,1,"{12, 260}"
15,1,19,0,0.0376124,"\int \frac{\sin (2 x)}{a^2-b^2 \sin ^2(x)} \, dx","Int[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",3,2,20,0.1000,1,"{12, 260}"
16,1,22,0,0.0404996,"\int \frac{\sin (2 x)}{a^2+b^2 \cos ^2(x)} \, dx","Int[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",3,2,19,0.1053,1,"{12, 260}"
17,1,22,0,0.0423405,"\int \frac{\sin (2 x)}{a^2-b^2 \cos ^2(x)} \, dx","Int[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",3,2,20,0.1000,1,"{12, 260}"
18,1,41,0,0.0168743,"\int \frac{1}{4-\cos ^2(x)} \, dx","Int[(4 - Cos[x]^2)^(-1),x]","\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}}","\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,"x/(2*Sqrt[3]) + ArcTan[(Cos[x]*Sin[x])/(3 + 2*Sqrt[3] + Sin[x]^2)]/(2*Sqrt[3])","A",2,2,10,0.2000,1,"{3181, 203}"
19,1,6,0,0.0181226,"\int \frac{e^x}{-1+e^{2 x}} \, dx","Int[E^x/(-1 + E^(2*x)),x]","-\tanh ^{-1}\left(e^x\right)","-\tanh ^{-1}\left(e^x\right)",1,"-ArcTanh[E^x]","A",2,2,13,0.1538,1,"{2249, 207}"
20,1,3,0,0.0123612,"\int \frac{1}{x \log (x)} \, dx","Int[1/(x*Log[x]),x]","\log (\log (x))","\log (\log (x))",1,"Log[Log[x]]","A",2,2,8,0.2500,1,"{2302, 29}"
21,1,3,0,0.0192723,"\int \frac{1}{x \left(1+\log ^2(x)\right)} \, dx","Int[1/(x*(1 + Log[x]^2)),x]","\tan ^{-1}(\log (x))","\tan ^{-1}(\log (x))",1,"ArcTan[Log[x]]","A",2,1,12,0.08333,1,"{203}"
22,1,9,0,0.0202668,"\int \frac{1}{x (1-\log (x))} \, dx","Int[1/(x*(1 - Log[x])),x]","-\log (1-\log (x))","-\log (1-\log (x))",1,"-Log[1 - Log[x]]","A",2,2,12,0.1667,1,"{2302, 29}"
23,1,9,0,0.0180361,"\int \frac{1}{x \left(1+\log \left(\frac{x}{a}\right)\right)} \, dx","Int[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",2,2,14,0.1429,1,"{2302, 29}"
24,1,25,0,0.0184495,"\int \frac{\left(1-\sqrt{x}+x\right)^2}{x^2} \, dx","Int[(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",3,2,16,0.1250,1,"{1357, 698}"
25,1,30,0,0.0941351,"\int \frac{\left(2-x^{2/3}\right) \left(\sqrt{x}+x\right)}{x^{3/2}} \, dx","Int[((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",4,2,22,0.09091,1,"{1584, 1820}"
26,1,10,0,0.0050317,"\int \frac{-1+2 x}{3+2 x} \, dx","Int[(-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",2,1,13,0.07692,1,"{43}"
27,1,47,0,0.0227613,"\int \frac{-5+2 x}{-2+3 x^2} \, dx","Int[(-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",3,2,15,0.1333,1,"{633, 31}"
28,1,30,0,0.0081567,"\int \frac{-5+2 x}{2+3 x^2} \, dx","Int[(-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",3,3,15,0.2000,1,"{635, 203, 260}"
29,1,21,0,0.0080012,"\int \sin \left(\frac{x}{4}\right) \sin (x) \, dx","Int[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",1,1,9,0.1111,1,"{4282}"
30,1,15,0,0.0082189,"\int \cos (3 x) \cos (4 x) \, dx","Int[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",1,1,9,0.1111,1,"{4283}"
31,1,21,0,0.033836,"\int -\tan (a-x) \tan (x) \, dx","Int[-(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",4,3,10,0.3000,1,"{4612, 4610, 3475}"
32,1,14,0,0.0050332,"\int \sin ^2(x) \, dx","Int[Sin[x]^2,x]","\frac{x}{2}-\frac{1}{2} \sin (x) \cos (x)","\frac{x}{2}-\frac{1}{2} \sin (x) \cos (x)",1,"x/2 - (Cos[x]*Sin[x])/2","A",2,2,4,0.5000,1,"{2635, 8}"
33,1,14,0,0.0058507,"\int \cos ^2(x) \, dx","Int[Cos[x]^2,x]","\frac{x}{2}+\frac{1}{2} \sin (x) \cos (x)","\frac{x}{2}+\frac{1}{2} \sin (x) \cos (x)",1,"x/2 + (Cos[x]*Sin[x])/2","A",2,2,4,0.5000,1,"{2635, 8}"
34,1,8,0,0.0122785,"\int \cos ^3(x) \sin (x) \, dx","Int[Cos[x]^3*Sin[x],x]","-\frac{1}{4} \cos ^4(x)","-\frac{1}{4} \cos ^4(x)",1,"-Cos[x]^4/4","A",2,2,7,0.2857,1,"{2565, 30}"
35,1,11,0,0.0150474,"\int \cot ^3(x) \csc (x) \, dx","Int[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",2,1,7,0.1429,1,"{2606}"
36,1,7,0,0.0237016,"\int \csc ^2(x) \sec ^2(x) \, dx","Int[Csc[x]^2*Sec[x]^2,x]","\tan (x)-\cot (x)","\tan (x)-\cot (x)",1,"-Cot[x] + Tan[x]","A",3,2,9,0.2222,1,"{2620, 14}"
37,1,14,0,0.0062183,"\int \cot ^2\left(\frac{3 x}{4}\right) \, dx","Int[Cot[(3*x)/4]^2,x]","-x-\frac{4}{3} \cot \left(\frac{3 x}{4}\right)","-x-\frac{4}{3} \cot \left(\frac{3 x}{4}\right)",1,"-x - (4*Cot[(3*x)/4])/3","A",2,2,8,0.2500,1,"{3473, 8}"
38,1,16,0,0.0109919,"\int (1+\tan (2 x))^2 \, dx","Int[(1 + Tan[2*x])^2,x]","\frac{1}{2} \tan (2 x)-\log (\cos (2 x))","\frac{1}{2} \tan (2 x)-\log (\cos (2 x))",1,"-Log[Cos[2*x]] + Tan[2*x]/2","A",2,2,8,0.2500,1,"{3477, 3475}"
39,1,10,0,0.0275772,"\int (-\cot (x)+\tan (x))^2 \, dx","Int[(-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",4,2,9,0.2222,1,"{461, 203}"
40,1,14,0,0.0631115,"\int (-\sec (x)+\tan (x))^2 \, dx","Int[(-Sec[x] + Tan[x])^2,x]","-x-\frac{2 \cos (x)}{\sin (x)+1}","-x-\frac{2 \cos (x)}{\sin (x)+1}",1,"-x - (2*Cos[x])/(1 + Sin[x])","A",4,4,9,0.4444,1,"{4391, 2670, 2680, 8}"
41,1,11,0,0.0218378,"\int \frac{\sin (x)}{1+\sin (x)} \, dx","Int[Sin[x]/(1 + Sin[x]),x]","x+\frac{\cos (x)}{\sin (x)+1}","x+\frac{\cos (x)}{\sin (x)+1}",1,"x + Cos[x]/(1 + Sin[x])","A",2,2,9,0.2222,1,"{2735, 2648}"
42,1,16,0,0.0263574,"\int \frac{\cos (x)}{1-\cos (x)} \, dx","Int[Cos[x]/(1 - Cos[x]),x]","-x-\frac{\sin (x)}{1-\cos (x)}","-x-\frac{\sin (x)}{1-\cos (x)}",1,"-x - Sin[x]/(1 - Cos[x])","A",2,2,11,0.1818,1,"{2735, 2648}"
43,1,25,0,0.0246283,"\int e^{-x/2} \left(-1+e^{x/2}\right)^3 \, dx","Int[(-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",3,2,19,0.1053,1,"{2248, 43}"
44,1,21,0,0.0041527,"\int \frac{1}{5-6 x+x^2} \, dx","Int[(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,"-Log[1 - x]/4 + Log[5 - x]/4","A",3,2,10,0.2000,1,"{616, 31}"
45,1,14,0,0.0159955,"\int \frac{x^2}{13-6 x^3+x^6} \, dx","Int[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",3,3,16,0.1875,1,"{1352, 618, 204}"
46,1,51,0,0.0158961,"\int \frac{2+x}{-1-4 x+x^2} \, dx","Int[(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",3,2,14,0.1429,1,"{632, 31}"
47,1,33,0,0.0101715,"\int \frac{1}{1+\sqrt[3]{1+x}} \, dx","Int[(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",4,3,11,0.2727,1,"{247, 190, 43}"
48,1,29,0,0.013797,"\int \frac{1}{\sqrt{x} (b+a x)} \, dx","Int[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",2,2,13,0.1538,1,"{63, 205}"
49,1,27,0,0.0101029,"\int x^3 \sqrt{1+x^2} \, dx","Int[x^3*Sqrt[1 + x^2],x]","\frac{1}{5} \left(x^2+1\right)^{5/2}-\frac{1}{3} \left(x^2+1\right)^{3/2}","\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)/3 + (1 + x^2)^(5/2)/5","A",3,2,13,0.1538,1,"{266, 43}"
50,1,22,0,0.0092697,"\int \frac{x}{\sqrt{a^4-x^4}} \, dx","Int[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",3,3,15,0.2000,1,"{275, 217, 203}"
51,1,22,0,0.0125473,"\int \frac{1}{x \sqrt{-a^2+x^2}} \, dx","Int[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",3,3,17,0.1765,1,"{266, 63, 203}"
52,1,23,0,0.0141744,"\int \frac{1}{x \sqrt{a^2-x^2}} \, dx","Int[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",3,3,17,0.1765,1,"{266, 63, 206}"
53,1,21,0,0.0127425,"\int \frac{1}{x \sqrt{a^2+x^2}} \, dx","Int[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",3,3,15,0.2000,1,"{266, 63, 207}"
54,1,12,0,0.0061394,"\int \frac{1}{\sqrt{2+x-x^2}} \, dx","Int[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",2,2,12,0.1667,1,"{619, 216}"
55,1,19,0,0.0119958,"\int \frac{1}{\sqrt{5-4 x+3 x^2}} \, dx","Int[1/Sqrt[5 - 4*x + 3*x^2],x]","-\frac{\sinh ^{-1}\left(\frac{2-3 x}{\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",2,2,14,0.1429,1,"{619, 215}"
56,1,8,0,0.0031741,"\int \frac{1}{\sqrt{x-x^2}} \, dx","Int[1/Sqrt[x - x^2],x]","-\sin ^{-1}(1-2 x)","-\sin ^{-1}(1-2 x)",1,"-ArcSin[1 - 2*x]","A",2,2,11,0.1818,1,"{619, 216}"
57,1,27,0,0.0099554,"\int \frac{1+2 x}{\sqrt{2+x-x^2}} \, dx","Int[(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",3,3,18,0.1667,1,"{640, 619, 216}"
58,1,32,0,0.0105747,"\int \frac{1}{x \sqrt{2+x-x^2}} \, dx","Int[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",2,2,16,0.1250,1,"{724, 206}"
59,1,23,0,0.0054853,"\int \frac{1}{(-2+x) \sqrt{2+x-x^2}} \, dx","Int[1/((-2 + x)*Sqrt[2 + x - x^2]),x]","-\frac{2 \sqrt{-x^2+x+2}}{3 (2-x)}","\frac{2 \sqrt{-x^2+x+2}}{3 (x-2)}",1,"(-2*Sqrt[2 + x - x^2])/(3*(2 - x))","A",1,1,18,0.05556,1,"{650}"
60,1,28,0,0.1294701,"\int \frac{\csc (x) (2+3 \sin (x))}{1-\cos (x)} \, dx","Int[(Csc[x]*(2 + 3*Sin[x]))/(1 - Cos[x]),x]","-\frac{1}{1-\cos (x)}-\frac{3 \sin (x)}{1-\cos (x)}-\tanh ^{-1}(\cos (x))","-\frac{1}{1-\cos (x)}-\frac{3 \sin (x)}{1-\cos (x)}-\tanh ^{-1}(\cos (x))",1,"-ArcTanh[Cos[x]] - (1 - Cos[x])^(-1) - (3*Sin[x])/(1 - Cos[x])","A",7,5,17,0.2941,1,"{4401, 2648, 2667, 44, 207}"
61,1,48,0,0.0213491,"\int \frac{1}{2+3 \cos ^2(x)} \, dx","Int[(2 + 3*Cos[x]^2)^(-1),x]","\frac{x}{\sqrt{10}}-\frac{\tan ^{-1}\left(\frac{\left(\sqrt{\frac{5}{2}}-1\right) \sin (x) \cos (x)}{\left(\sqrt{\frac{5}{2}}-1\right) \cos ^2(x)+1}\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,"x/Sqrt[10] - ArcTan[((-1 + Sqrt[5/2])*Cos[x]*Sin[x])/(1 + (-1 + Sqrt[5/2])*Cos[x]^2)]/Sqrt[10]","A",2,2,10,0.2000,1,"{3181, 203}"
62,1,14,0,0.0339943,"\int \csc (2 x) (1-\tan (x)) \, dx","Int[Csc[2*x]*(1 - Tan[x]),x]","\frac{1}{2} \log (\tan (x))-\frac{\tan (x)}{2}","\frac{1}{2} \log (\tan (x))-\frac{\tan (x)}{2}",1,"Log[Tan[x]]/2 - Tan[x]/2","A",3,1,11,0.09091,1,"{12}"
63,1,11,0,0.0305843,"\int \frac{1+\tan ^2(x)}{1-\tan ^2(x)} \, dx","Int[(1 + Tan[x]^2)/(1 - Tan[x]^2),x]","\frac{1}{2} \tanh ^{-1}(2 \sin (x) \cos (x))","\frac{1}{2} \tanh ^{-1}(2 \sin (x) \cos (x))",1,"ArcTanh[2*Cos[x]*Sin[x]]/2","A",2,1,17,0.05882,1,"{206}"
64,1,19,0,0.0474616,"\int \left(a^2-4 \cos ^2(x)\right)^{3/4} \sin (2 x) \, dx","Int[(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",3,2,19,0.1053,1,"{12, 261}"
65,1,18,0,0.044924,"\int \frac{\sin (2 x)}{\sqrt[3]{a^2-4 \sin ^2(x)}} \, dx","Int[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",3,2,19,0.1053,1,"{12, 261}"
66,1,17,0,0.0129283,"\int \frac{1}{\sqrt{-1+a^{2 x}}} \, dx","Int[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",3,3,11,0.2727,1,"{2282, 63, 203}"
67,1,20,0,0.0258523,"\int \frac{e^{x/2}}{\sqrt{-1+e^x}} \, dx","Int[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",3,3,17,0.1765,1,"{2249, 217, 206}"
68,1,12,0,0.0232248,"\int \frac{\tan ^{-1}(x)^n}{1+x^2} \, dx","Int[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",1,1,12,0.08333,1,"{4884}"
69,1,42,0,0.0654377,"\int \frac{\sin ^{-1}\left(\frac{x}{a}\right)^{3/2}}{\sqrt{a^2-x^2}} \, dx","Int[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",2,2,24,0.08333,1,"{4643, 4641}"
70,1,8,0,0.024774,"\int \frac{1}{\sqrt{1-x^2} \cos ^{-1}(x)^3} \, dx","Int[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",1,1,16,0.06250,1,"{4642}"
71,1,28,0,0.0096363,"\int x \log ^2(x) \, dx","Int[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",2,2,6,0.3333,1,"{2305, 2304}"
72,1,17,0,0.006899,"\int \frac{\log (x)}{x^5} \, dx","Int[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*x^4) - Log[x]/(4*x^4)","A",1,1,6,0.1667,1,"{2304}"
73,1,38,0,0.0255435,"\int x^2 \log \left(\frac{-1+x}{x}\right) \, dx","Int[x^2*Log[(-1 + x)/x],x]","-\frac{x^2}{6}+\frac{1}{3} x^3 \log \left(1-\frac{1}{x}\right)-\frac{x}{3}-\frac{1}{3} \log (1-x)","-\frac{x^2}{6}+\frac{1}{3} x^3 \log \left(\frac{x-1}{x}\right)-\frac{x}{3}-\frac{1}{3} \log (x-1)",1,"-x/3 - x^2/6 + (x^3*Log[1 - x^(-1)])/3 - Log[1 - x]/3","A",5,4,12,0.3333,1,"{2461, 2455, 263, 43}"
74,1,19,0,0.0083754,"\int \cos ^5(x) \, dx","Int[Cos[x]^5,x]","\frac{\sin ^5(x)}{5}-\frac{2 \sin ^3(x)}{3}+\sin (x)","\frac{\sin ^5(x)}{5}-\frac{2 \sin ^3(x)}{3}+\sin (x)",1,"Sin[x] - (2*Sin[x]^3)/3 + Sin[x]^5/5","A",2,1,4,0.2500,1,"{2633}"
75,1,34,0,0.0339044,"\int \cos ^4(x) \sin ^2(x) \, dx","Int[Cos[x]^4*Sin[x]^2,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)","\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 + (Cos[x]*Sin[x])/16 + (Cos[x]^3*Sin[x])/24 - (Cos[x]^5*Sin[x])/6","A",4,3,9,0.3333,1,"{2568, 2635, 8}"
76,1,26,0,0.0124967,"\int \csc ^5(x) \, dx","Int[Csc[x]^5,x]","-\frac{3}{8} \tanh ^{-1}(\cos (x))-\frac{1}{4} \cot (x) \csc ^3(x)-\frac{3}{8} \cot (x) \csc (x)","-\frac{3}{8} \tanh ^{-1}(\cos (x))-\frac{1}{4} \cot (x) \csc ^3(x)-\frac{3}{8} \cot (x) \csc (x)",1,"(-3*ArcTanh[Cos[x]])/8 - (3*Cot[x]*Csc[x])/8 - (Cot[x]*Csc[x]^3)/4","A",3,2,4,0.5000,1,"{3768, 3770}"
77,1,23,0,0.0084535,"\int e^{-x} \sin (x) \, dx","Int[Sin[x]/E^x,x]","-\frac{1}{2} e^{-x} \sin (x)-\frac{1}{2} e^{-x} \cos (x)","-\frac{1}{2} e^{-x} \sin (x)-\frac{1}{2} e^{-x} \cos (x)",1,"-Cos[x]/(2*E^x) - Sin[x]/(2*E^x)","A",1,1,8,0.1250,1,"{4432}"
78,1,27,0,0.0093931,"\int e^{2 x} \sin (3 x) \, dx","Int[E^(2*x)*Sin[3*x],x]","\frac{2}{13} e^{2 x} \sin (3 x)-\frac{3}{13} e^{2 x} \cos (3 x)","\frac{2}{13} e^{2 x} \sin (3 x)-\frac{3}{13} e^{2 x} \cos (3 x)",1,"(-3*E^(2*x)*Cos[3*x])/13 + (2*E^(2*x)*Sin[3*x])/13","A",1,1,10,0.1000,1,"{4432}"
79,1,31,0,0.0099713,"\int a^x \cos (x) \, dx","Int[a^x*Cos[x],x]","\frac{a^x \sin (x)}{\log ^2(a)+1}+\frac{a^x \log (a) \cos (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])/(1 + Log[a]^2) + (a^x*Sin[x])/(1 + Log[a]^2)","A",1,1,6,0.1667,1,"{4433}"
80,1,17,0,0.0029857,"\int \cos (\log (x)) \, dx","Int[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",1,1,3,0.3333,1,"{4476}"
81,1,12,0,0.019235,"\int \log (\cos (x)) \sec ^2(x) \, dx","Int[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",3,4,8,0.5000,1,"{3767, 8, 2554, 3473}"
82,1,15,0,0.0143883,"\int x \tan ^2(x) \, dx","Int[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,"-x^2/2 + Log[Cos[x]] + x*Tan[x]","A",3,3,6,0.5000,1,"{3720, 3475, 30}"
83,1,22,0,0.0152534,"\int \frac{\sin ^{-1}(x)}{x^2} \, dx","Int[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",4,4,6,0.6667,1,"{4627, 266, 63, 206}"
84,1,25,0,0.0323284,"\int \sin ^{-1}(x)^2 \, dx","Int[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",3,3,4,0.7500,1,"{4619, 4677, 8}"
85,1,23,0,0.0474393,"\int \frac{x^2 \tan ^{-1}(x)}{1+x^2} \, dx","Int[(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",4,4,13,0.3077,1,"{4916, 4846, 260, 4884}"
86,1,57,0,0.0305641,"\int \cos ^{-1}\left(\sqrt{\frac{x}{1+x}}\right) \, dx","Int[ArcCos[Sqrt[x/(1 + x)]],x]","\sqrt{\frac{x}{(x+1)^2}} (x+1)+x \cos ^{-1}\left(\sqrt{\frac{x}{x+1}}\right)-\frac{\sqrt{\frac{x}{(x+1)^2}} (x+1) \tan ^{-1}\left(\sqrt{x}\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,"Sqrt[x/(1 + x)^2]*(1 + x) + x*ArcCos[Sqrt[x/(1 + x)]] - (Sqrt[x/(1 + x)^2]*(1 + x)*ArcTan[Sqrt[x]])/Sqrt[x]","A",6,6,12,0.5000,1,"{4841, 12, 6719, 50, 63, 203}"
87,1,25,0,0.0071173,"\int \left(2 x+3 x^2\right)^3 \, dx","Int[(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",2,1,11,0.09091,1,"{611}"
88,1,39,0,0.0157301,"\int (-1+x) \left(-1+2 x+3 x^2\right)^2 \, dx","Int[(-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",2,1,16,0.06250,1,"{631}"
89,1,23,0,0.0077646,"\int x^{-1+k} \left(a+b x^k\right)^n \, dx","Int[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",1,1,15,0.06667,1,"{261}"
90,1,30,0,0.0113922,"\int \frac{x^3}{1+2 x} \, dx","Int[x^3/(1 + 2*x),x]","\frac{x^3}{6}-\frac{x^2}{8}+\frac{x}{8}-\frac{1}{16} \log (2 x+1)","\frac{x^3}{6}-\frac{x^2}{8}+\frac{x}{8}-\frac{1}{16} \log (2 x+1)",1,"x/8 - x^2/8 + x^3/6 - Log[1 + 2*x]/16","A",2,1,11,0.09091,1,"{43}"
91,1,41,0,0.0122719,"\int \frac{x^6}{2+3 x^2} \, dx","Int[x^6/(2 + 3*x^2),x]","\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)","\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,"(4*x)/27 - (2*x^3)/27 + x^5/15 - (4*Sqrt[2/3]*ArcTan[Sqrt[3/2]*x])/27","A",3,2,13,0.1538,1,"{302, 203}"
92,1,21,0,0.0055049,"\int \frac{1}{2-7 x+3 x^2} \, dx","Int[(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,"-Log[1 - 3*x]/5 + Log[2 - x]/5","A",3,2,12,0.1667,1,"{616, 31}"
93,1,33,0,0.0167352,"\int \frac{-1+3 x}{1-x+x^2} \, dx","Int[(-1 + 3*x)/(1 - x + x^2),x]","\frac{3}{2} \log \left(x^2-x+1\right)-\frac{\tan ^{-1}\left(\frac{1-2 x}{\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",4,4,16,0.2500,1,"{634, 618, 204, 628}"
94,1,25,0,0.0159191,"\int \frac{x^2}{5+2 x+x^2} \, dx","Int[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",5,5,14,0.3571,1,"{703, 634, 618, 204, 628}"
95,1,47,0,0.0623759,"\int \frac{4 x^2-5 x^3+6 x^4}{1-x+2 x^2} \, dx","Int[(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{1-4 x}{\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,"-x^2/2 + x^3 - ArcTan[(1 - 4*x)/Sqrt[7]]/(2*Sqrt[7]) + Log[1 - x + 2*x^2]/4","A",7,6,29,0.2069,1,"{1594, 1628, 634, 618, 204, 628}"
96,1,25,0,0.0365624,"\int \frac{-1+x+x^2}{-6 x+x^2+x^3} \, dx","Int[(-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",3,2,19,0.1053,1,"{1594, 1628}"
97,1,33,0,0.0538914,"\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","Int[(11*a^2 - 7*a*x + 5*x^2)/(-6*a^3 + 11*a^2*x - 6*a*x^2 + x^3),x]","\frac{9}{2} \log (a-x)-17 \log (2 a-x)+\frac{35}{2} \log (3 a-x)","\frac{9}{2} \log (a-x)-17 \log (2 a-x)+\frac{35}{2} \log (3 a-x)",1,"(9*Log[a - x])/2 - 17*Log[2*a - x] + (35*Log[3*a - x])/2","A",2,1,39,0.02564,1,"{2074}"
98,1,61,0,0.0370515,"\int \frac{2-x+x^2}{4-5 x^2+x^4} \, dx","Int[(2 - x + x^2)/(4 - 5*x^2 + x^4),x]","\frac{1}{6} \log \left(1-x^2\right)-\frac{1}{6} \log \left(4-x^2\right)-\frac{1}{2} \log (1-x)+\frac{1}{2} \log (2-x)+\frac{1}{2} \log (x+1)-\frac{1}{2} \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,"-Log[1 - x]/2 + Log[2 - x]/2 + Log[1 + x]/2 - Log[2 + x]/2 + Log[1 - x^2]/6 - Log[4 - x^2]/6","A",12,5,21,0.2381,1,"{1673, 1161, 616, 31, 1107}"
99,1,31,0,0.0090298,"\int \frac{-5+2 x^2}{6-5 x^2+x^4} \, dx","Int[(-5 + 2*x^2)/(6 - 5*x^2 + x^4),x]","-\frac{\tanh ^{-1}\left(\frac{x}{\sqrt{2}}\right)}{\sqrt{2}}-\frac{\tanh ^{-1}\left(\frac{x}{\sqrt{3}}\right)}{\sqrt{3}}","-\frac{\tanh ^{-1}\left(\frac{x}{\sqrt{2}}\right)}{\sqrt{2}}-\frac{\tanh ^{-1}\left(\frac{x}{\sqrt{3}}\right)}{\sqrt{3}}",1,"-(ArcTanh[x/Sqrt[2]]/Sqrt[2]) - ArcTanh[x/Sqrt[3]]/Sqrt[3]","A",3,2,20,0.1000,1,"{1166, 207}"
100,1,41,0,0.0204782,"\int \frac{1}{(-4+x) (-3+x) (-2+x) (-1+x)} \, dx","Int[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,"-Log[1 - x]/6 + Log[2 - x]/2 - Log[3 - x]/2 + Log[4 - x]/6","A",2,1,21,0.04762,1,"{180}"
101,1,25,0,0.0105989,"\int \frac{1+x^2}{(-1+x)^3} \, dx","Int[(1 + x^2)/(-1 + x)^3,x]","\frac{2}{1-x}-\frac{1}{(1-x)^2}+\log (1-x)","\frac{2}{1-x}-\frac{1}{(1-x)^2}+\log (1-x)",1,"-(1 - x)^(-2) + 2/(1 - x) + Log[1 - x]","A",2,1,11,0.09091,1,"{697}"
102,1,36,0,0.0166641,"\int \frac{x^5}{(3+x)^2} \, dx","Int[x^5/(3 + x)^2,x]","\frac{x^4}{4}-2 x^3+\frac{27 x^2}{2}-108 x+\frac{243}{x+3}+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,"-108*x + (27*x^2)/2 - 2*x^3 + x^4/4 + 243/(3 + x) + 405*Log[3 + x]","A",2,1,9,0.1111,1,"{43}"
103,1,41,0,0.0370383,"\int \frac{-2+5 x^3}{-27+18 x^2-8 x^3+x^4} \, dx","Int[(-2 + 5*x^3)/(-27 + 18*x^2 - 8*x^3 + x^4),x]","\frac{407}{16 (3-x)}-\frac{133}{8 (3-x)^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",2,1,25,0.04000,1,"{2074}"
104,1,27,0,0.0359,"\int \frac{-9+3 x-6 x^2+x^3}{(3+x)^2 (4+x)^2} \, dx","Int[(-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",2,1,24,0.04167,1,"{1620}"
105,1,39,0,0.0362482,"\int \frac{2+x^2+x^3}{x \left(-1+x^2\right)^2} \, dx","Int[(2 + x^2 + x^3)/(x*(-1 + x^2)^2),x]","\frac{x+3}{2 \left(1-x^2\right)}-\frac{3}{4} \log (1-x)+2 \log (x)-\frac{5}{4} \log (x+1)","\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,"(3 + x)/(2*(1 - x^2)) - (3*Log[1 - x])/4 + 2*Log[x] - (5*Log[1 + x])/4","A",3,2,19,0.1053,1,"{1805, 801}"
106,1,46,0,0.0224983,"\int \frac{1}{x^3-x^4-x^5+x^6} \, dx","Int[(x^3 - x^4 - x^5 + x^6)^(-1),x]","-\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)","-\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,"1/(2*(1 - x)) - 1/(2*x^2) - x^(-1) - (7*Log[1 - x])/4 + 2*Log[x] - Log[1 + x]/4","A",2,1,19,0.05263,1,"{2058}"
107,1,29,0,0.0282889,"\int \frac{1+x^4}{-1+x-x^2+x^3} \, dx","Int[(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",5,4,19,0.2105,1,"{2074, 635, 203, 260}"
108,1,27,0,0.0248596,"\int \frac{1}{x (1+x) \left(1+x^2\right)} \, dx","Int[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,"-ArcTan[x]/2 + Log[x] - Log[1 + x]/2 - Log[1 + x^2]/4","A",5,4,16,0.2500,1,"{894, 635, 203, 260}"
109,1,24,0,0.0099284,"\int \frac{x^2}{-2+x^2+x^4} \, dx","Int[x^2/(-2 + x^2 + x^4),x]","\frac{1}{3} \sqrt{2} \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)-\frac{1}{3} \tanh ^{-1}(x)","\frac{1}{3} \sqrt{2} \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)-\frac{1}{3} \tanh ^{-1}(x)",1,"(Sqrt[2]*ArcTan[x/Sqrt[2]])/3 - ArcTanh[x]/3","A",3,3,14,0.2143,1,"{1130, 203, 207}"
110,1,41,0,0.0870716,"\int \frac{6 x+4 x^2+x^3}{2+4 x+3 x^2+2 x^3+x^4} \, dx","Int[(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",6,5,33,0.1515,1,"{1594, 2075, 635, 203, 260}"
111,1,46,0,0.2043994,"\int \frac{x}{(1+x) (1+2 x)^2 \left(1+x^2\right)} \, dx","Int[x/((1 + x)*(1 + 2*x)^2*(1 + x^2)),x]","-\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)","-\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,"2/(5*(1 + 2*x)) + ArcTan[x]/50 - Log[1 + x]/2 + (16*Log[1 + 2*x])/25 - (7*Log[1 + x^2])/100","A",5,4,21,0.1905,1,"{6725, 635, 203, 260}"
112,1,47,0,0.0428182,"\int \frac{-2+x+3 x^2}{(-1+x)^3 \left(1+x^2\right)} \, dx","Int[(-2 + x + 3*x^2)/((-1 + x)^3*(1 + x^2)),x]","\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)","\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,"-1/(2*(1 - x)^2) + 5/(2*(1 - x)) - ArcTan[x] - (3*Log[1 - x])/2 + (3*Log[1 + x^2])/4","A",5,4,21,0.1905,1,"{1629, 635, 203, 260}"
113,1,67,0,0.0380003,"\int \frac{1}{1+x^2+x^4} \, dx","Int[(1 + x^2 + x^4)^(-1),x]","-\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}}","-\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,"-ArcTan[(1 - 2*x)/Sqrt[3]]/(2*Sqrt[3]) + ArcTan[(1 + 2*x)/Sqrt[3]]/(2*Sqrt[3]) - Log[1 - x + x^2]/4 + Log[1 + x + x^2]/4","A",9,5,10,0.5000,1,"{1094, 634, 618, 204, 628}"
114,1,48,0,0.0526631,"\int \frac{3+2 x^3}{-9 x+x^5} \, dx","Int[(3 + 2*x^3)/(-9*x + x^5),x]","\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}}","\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,"ArcTan[x/Sqrt[3]]/Sqrt[3] - ArcTanh[x/Sqrt[3]]/Sqrt[3] - Log[x]/3 + Log[9 - x^4]/12","A",10,9,17,0.5294,1,"{1593, 1831, 266, 36, 31, 29, 298, 203, 206}"
115,1,58,0,0.0550267,"\int \frac{-20+8 x+5 x^3}{(-4+x)^3 \left(8-4 x+x^2\right)} \, dx","Int[(-20 + 8*x + 5*x^3)/((-4 + x)^3*(8 - 4*x + x^2)),x]","\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)","\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,"-83/(4*(4 - x)^2) + 41/(4*(4 - x)) - (3*ArcTan[1 - x/2])/16 - (45*Log[4 - x])/16 + (45*Log[8 - 4*x + x^2])/32","A",6,5,26,0.1923,1,"{1628, 634, 617, 204, 628}"
116,1,51,0,0.284273,"\int \frac{1}{\left(1+x^2\right) \left(2+x^2\right) \left(3+x^2\right) \left(4+x^2\right)} \, dx","Int[1/((1 + x^2)*(2 + x^2)*(3 + x^2)*(4 + x^2)),x]","-\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}}","-\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]/12 + ArcTan[x]/6 - ArcTan[x/Sqrt[2]]/(2*Sqrt[2]) + ArcTan[x/Sqrt[3]]/(2*Sqrt[3])","A",6,2,29,0.06897,1,"{6725, 203}"
117,1,41,0,0.3114239,"\int \frac{x}{\left(1+x^2\right) \left(2+x^2\right) \left(3+x^2\right) \left(4+x^2\right)} \, dx","Int[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",3,2,30,0.06667,1,"{6694, 180}"
118,1,56,0,0.0303337,"\int \frac{1}{a^3+x^3} \, dx","Int[(a^3 + x^3)^(-1),x]","-\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}","-\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,"-(ArcTan[(a - 2*x)/(Sqrt[3]*a)]/(Sqrt[3]*a^2)) + Log[a + x]/(3*a^2) - Log[a^2 - a*x + x^2]/(6*a^2)","A",6,6,9,0.6667,1,"{200, 31, 634, 617, 204, 628}"
119,1,56,0,0.0277833,"\int \frac{x}{a^3+x^3} \, dx","Int[x/(a^3 + x^3),x]","\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}","\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,"-(ArcTan[(a - 2*x)/(Sqrt[3]*a)]/(Sqrt[3]*a)) - Log[a + x]/(3*a) + Log[a^2 - a*x + x^2]/(6*a)","A",6,6,11,0.5455,1,"{292, 31, 634, 617, 204, 628}"
120,1,12,0,0.0026214,"\int \frac{x^2}{a^3+x^3} \, dx","Int[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",1,1,13,0.07692,1,"{260}"
121,1,22,0,0.0083182,"\int \frac{1}{x \left(a^3+x^3\right)} \, dx","Int[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",4,4,13,0.3077,1,"{266, 36, 29, 31}"
122,1,63,0,0.0370236,"\int \frac{1}{x^2 \left(a^3+x^3\right)} \, dx","Int[1/(x^2*(a^3 + x^3)),x]","-\frac{\log \left(a^2-a x+x^2\right)}{6 a^4}-\frac{1}{a^3 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{\log \left(a^2-a x+x^2\right)}{6 a^4}-\frac{1}{a^3 x}+\frac{\log (a+x)}{3 a^4}+\frac{\tan ^{-1}\left(\frac{a-2 x}{\sqrt{3} a}\right)}{\sqrt{3} a^4}",1,"-(1/(a^3*x)) + ArcTan[(a - 2*x)/(Sqrt[3]*a)]/(Sqrt[3]*a^4) + Log[a + x]/(3*a^4) - Log[a^2 - a*x + x^2]/(6*a^4)","A",7,7,13,0.5385,1,"{325, 292, 31, 634, 617, 204, 628}"
123,1,65,0,0.0386181,"\int \frac{1}{x^3 \left(a^3+x^3\right)} \, dx","Int[1/(x^3*(a^3 + x^3)),x]","-\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}-\frac{\log (a+x)}{3 a^5}+\frac{\tan ^{-1}\left(\frac{a-2 x}{\sqrt{3} a}\right)}{\sqrt{3} a^5}",1,"-1/(2*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",7,7,13,0.5385,1,"{325, 200, 31, 634, 617, 204, 628}"
124,1,33,0,0.0195942,"\int \frac{1}{x^4 \left(a^3+x^3\right)} \, dx","Int[1/(x^4*(a^3 + x^3)),x]","-\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}-\frac{\log (x)}{a^6}",1,"-1/(3*a^3*x^3) - Log[x]/a^6 + Log[a^3 + x^3]/(3*a^6)","A",3,2,13,0.1538,1,"{266, 44}"
125,1,73,0,0.0440198,"\int \frac{1}{x^5 \left(a^3+x^3\right)} \, dx","Int[1/(x^5*(a^3 + x^3)),x]","-\frac{1}{4 a^3 x^4}+\frac{\log \left(a^2-a x+x^2\right)}{6 a^7}+\frac{1}{a^6 x}-\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}{4 a^3 x^4}+\frac{\log \left(a^2-a x+x^2\right)}{6 a^7}+\frac{1}{a^6 x}-\frac{\log (a+x)}{3 a^7}-\frac{\tan ^{-1}\left(\frac{a-2 x}{\sqrt{3} a}\right)}{\sqrt{3} a^7}",1,"-1/(4*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",8,7,13,0.5385,1,"{325, 292, 31, 634, 617, 204, 628}"
126,1,46,0,0.010311,"\int \frac{x^{-m}}{a^3+x^3} \, dx","Int[1/(x^m*(a^3 + x^3)),x]","\frac{x^{1-m} \text{Hypergeometric2F1}\left(1,\frac{1-m}{3},\frac{4-m}{3},-\frac{x^3}{a^3}\right)}{a^3 (1-m)}","\frac{x^{1-m} \text{Hypergeometric2F1}\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 - m)/3, (4 - m)/3, -(x^3/a^3)])/(a^3*(1 - m))","A",1,1,15,0.06667,1,"{364}"
127,1,27,0,0.0080693,"\int \frac{1}{a^4-x^4} \, dx","Int[(a^4 - x^4)^(-1),x]","\frac{\tan ^{-1}\left(\frac{x}{a}\right)}{2 a^3}+\frac{\tanh ^{-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) + ArcTanh[x/a]/(2*a^3)","A",3,3,11,0.2727,1,"{212, 206, 203}"
128,1,15,0,0.0065664,"\int \frac{x}{a^4-x^4} \, dx","Int[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",2,2,13,0.1538,1,"{275, 206}"
129,1,24,0,0.0099267,"\int \frac{1}{x \left(a^4-x^4\right)} \, dx","Int[1/(x*(a^4 - x^4)),x]","\frac{\log (x)}{a^4}-\frac{\log \left(a^4-x^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",4,4,15,0.2667,1,"{266, 36, 31, 29}"
130,1,35,0,0.013661,"\int \frac{1}{x^2 \left(a^4-x^4\right)} \, dx","Int[1/(x^2*(a^4 - x^4)),x]","-\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}-\frac{\tan ^{-1}\left(\frac{x}{a}\right)}{2 a^5}+\frac{\tanh ^{-1}\left(\frac{x}{a}\right)}{2 a^5}",1,"-(1/(a^4*x)) - ArcTan[x/a]/(2*a^5) + ArcTanh[x/a]/(2*a^5)","A",4,4,15,0.2667,1,"{325, 298, 203, 206}"
131,1,26,0,0.0121596,"\int \frac{1}{x^3 \left(a^4-x^4\right)} \, dx","Int[1/(x^3*(a^4 - x^4)),x]","\frac{\tanh ^{-1}\left(\frac{x^2}{a^2}\right)}{2 a^6}-\frac{1}{2 a^4 x^2}","\frac{\tanh ^{-1}\left(\frac{x^2}{a^2}\right)}{2 a^6}-\frac{1}{2 a^4 x^2}",1,"-1/(2*a^4*x^2) + ArcTanh[x^2/a^2]/(2*a^6)","A",3,3,15,0.2000,1,"{275, 325, 206}"
132,1,37,0,0.0122327,"\int \frac{1}{x^4 \left(a^4-x^4\right)} \, dx","Int[1/(x^4*(a^4 - x^4)),x]","-\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}+\frac{\tan ^{-1}\left(\frac{x}{a}\right)}{2 a^7}+\frac{\tanh ^{-1}\left(\frac{x}{a}\right)}{2 a^7}",1,"-1/(3*a^4*x^3) + ArcTan[x/a]/(2*a^7) + ArcTanh[x/a]/(2*a^7)","A",4,4,15,0.2667,1,"{325, 212, 206, 203}"
133,1,45,0,0.0084131,"\int \frac{x^{-m}}{a^4-x^4} \, dx","Int[1/(x^m*(a^4 - x^4)),x]","\frac{x^{1-m} \text{Hypergeometric2F1}\left(1,\frac{1-m}{4},\frac{5-m}{4},\frac{x^4}{a^4}\right)}{a^4 (1-m)}","\frac{x^{1-m} \text{Hypergeometric2F1}\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 - m)/4, (5 - m)/4, x^4/a^4])/(a^4*(1 - m))","A",1,1,17,0.05882,1,"{364}"
134,1,15,0,0.0055853,"\int \frac{x}{a^4+x^4} \, dx","Int[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",2,2,11,0.1818,1,"{275, 203}"
135,1,109,0,0.0616562,"\int \frac{x^2}{a^4+x^4} \, dx","Int[x^2/(a^4 + x^4),x]","\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}","\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,"-ArcTan[1 - (Sqrt[2]*x)/a]/(2*Sqrt[2]*a) + ArcTan[1 + (Sqrt[2]*x)/a]/(2*Sqrt[2]*a) + Log[a^2 - Sqrt[2]*a*x + x^2]/(4*Sqrt[2]*a) - Log[a^2 + Sqrt[2]*a*x + x^2]/(4*Sqrt[2]*a)","A",9,6,13,0.4615,1,"{297, 1162, 617, 204, 1165, 628}"
136,1,201,0,0.3142954,"\int \frac{1}{a^5+x^5} \, dx","Int[(a^5 + x^5)^(-1),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^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{\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}+\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}",1,"-(Sqrt[(5 + Sqrt[5])/2]*ArcTan[((1 - Sqrt[5])*a - 4*x)/(Sqrt[2*(5 + Sqrt[5])]*a)])/(5*a^4) - (Sqrt[(5 - Sqrt[5])/2]*ArcTan[(Sqrt[(5 + Sqrt[5])/10]*((1 + Sqrt[5])*a - 4*x))/(2*a)])/(5*a^4) + Log[a + x]/(5*a^4) - ((1 - Sqrt[5])*Log[a^2 - ((1 - Sqrt[5])*a*x)/2 + x^2])/(20*a^4) - ((1 + Sqrt[5])*Log[a^2 - ((1 + Sqrt[5])*a*x)/2 + x^2])/(20*a^4)","A",6,6,9,0.6667,1,"{201, 634, 618, 204, 628, 31}"
137,1,201,0,0.2712106,"\int \frac{x}{a^5+x^5} \, dx","Int[x/(a^5 + x^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^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{\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}-\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}",1,"(Sqrt[(5 - Sqrt[5])/2]*ArcTan[((1 - Sqrt[5])*a - 4*x)/(Sqrt[2*(5 + Sqrt[5])]*a)])/(5*a^3) - (Sqrt[(5 + Sqrt[5])/2]*ArcTan[(Sqrt[(5 + Sqrt[5])/10]*((1 + Sqrt[5])*a - 4*x))/(2*a)])/(5*a^3) - Log[a + x]/(5*a^3) + ((1 + Sqrt[5])*Log[a^2 - ((1 - Sqrt[5])*a*x)/2 + x^2])/(20*a^3) + ((1 - Sqrt[5])*Log[a^2 - ((1 + Sqrt[5])*a*x)/2 + x^2])/(20*a^3)","A",6,6,11,0.5455,1,"{293, 634, 618, 204, 628, 31}"
138,1,201,0,0.3166462,"\int \frac{x^2}{a^5+x^5} \, dx","Int[x^2/(a^5 + x^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^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}","-\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,"(Sqrt[(5 - Sqrt[5])/2]*ArcTan[((1 - Sqrt[5])*a - 4*x)/(Sqrt[2*(5 + Sqrt[5])]*a)])/(5*a^2) - (Sqrt[(5 + Sqrt[5])/2]*ArcTan[(Sqrt[(5 + Sqrt[5])/10]*((1 + Sqrt[5])*a - 4*x))/(2*a)])/(5*a^2) + Log[a + x]/(5*a^2) - ((1 + Sqrt[5])*Log[a^2 - ((1 - Sqrt[5])*a*x)/2 + x^2])/(20*a^2) - ((1 - Sqrt[5])*Log[a^2 - ((1 + Sqrt[5])*a*x)/2 + x^2])/(20*a^2)","A",6,6,13,0.4615,1,"{293, 634, 618, 204, 628, 31}"
139,1,201,0,0.3128357,"\int \frac{x^3}{a^5+x^5} \, dx","Int[x^3/(a^5 + x^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}+\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}","\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,"-(Sqrt[(5 + Sqrt[5])/2]*ArcTan[((1 - Sqrt[5])*a - 4*x)/(Sqrt[2*(5 + Sqrt[5])]*a)])/(5*a) - (Sqrt[(5 - Sqrt[5])/2]*ArcTan[(Sqrt[(5 + Sqrt[5])/10]*((1 + Sqrt[5])*a - 4*x))/(2*a)])/(5*a) - Log[a + x]/(5*a) + ((1 - Sqrt[5])*Log[a^2 - ((1 - Sqrt[5])*a*x)/2 + x^2])/(20*a) + ((1 + Sqrt[5])*Log[a^2 - ((1 + Sqrt[5])*a*x)/2 + x^2])/(20*a)","A",6,6,13,0.4615,1,"{293, 634, 618, 204, 628, 31}"
140,1,12,0,0.002512,"\int \frac{x^4}{a^5+x^5} \, dx","Int[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",1,1,13,0.07692,1,"{260}"
141,1,22,0,0.0083307,"\int \frac{1}{x \left(a^5+x^5\right)} \, dx","Int[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",4,4,13,0.3077,1,"{266, 36, 29, 31}"
142,1,209,0,0.3294939,"\int \frac{1}{x^2 \left(a^5+x^5\right)} \, dx","Int[1/(x^2*(a^5 + x^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}-\frac{1}{a^5 x}+\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{\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}-\frac{1}{a^5 x}+\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}",1,"-(1/(a^5*x)) + (Sqrt[(5 + Sqrt[5])/2]*ArcTan[((1 - Sqrt[5])*a - 4*x)/(Sqrt[2*(5 + Sqrt[5])]*a)])/(5*a^6) + (Sqrt[(5 - Sqrt[5])/2]*ArcTan[(Sqrt[(5 + Sqrt[5])/10]*((1 + Sqrt[5])*a - 4*x))/(2*a)])/(5*a^6) + Log[a + x]/(5*a^6) - ((1 - Sqrt[5])*Log[a^2 - ((1 - Sqrt[5])*a*x)/2 + x^2])/(20*a^6) - ((1 + Sqrt[5])*Log[a^2 - ((1 + Sqrt[5])*a*x)/2 + x^2])/(20*a^6)","A",7,7,13,0.5385,1,"{325, 293, 634, 618, 204, 628, 31}"
143,1,211,0,0.3274944,"\int \frac{1}{x^3 \left(a^5+x^5\right)} \, dx","Int[1/(x^3*(a^5 + x^5)),x]","-\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}-\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}-\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}",1,"-1/(2*a^5*x^2) - (Sqrt[(5 - Sqrt[5])/2]*ArcTan[((1 - Sqrt[5])*a - 4*x)/(Sqrt[2*(5 + Sqrt[5])]*a)])/(5*a^7) + (Sqrt[(5 + Sqrt[5])/2]*ArcTan[(Sqrt[(5 + Sqrt[5])/10]*((1 + Sqrt[5])*a - 4*x))/(2*a)])/(5*a^7) - Log[a + x]/(5*a^7) + ((1 + Sqrt[5])*Log[a^2 - ((1 - Sqrt[5])*a*x)/2 + x^2])/(20*a^7) + ((1 - Sqrt[5])*Log[a^2 - ((1 + Sqrt[5])*a*x)/2 + x^2])/(20*a^7)","A",7,7,13,0.5385,1,"{325, 293, 634, 618, 204, 628, 31}"
144,1,211,0,0.288057,"\int \frac{1}{x^4 \left(a^5+x^5\right)} \, dx","Int[1/(x^4*(a^5 + x^5)),x]","-\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}+\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}+\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}",1,"-1/(3*a^5*x^3) - (Sqrt[(5 - Sqrt[5])/2]*ArcTan[((1 - Sqrt[5])*a - 4*x)/(Sqrt[2*(5 + Sqrt[5])]*a)])/(5*a^8) + (Sqrt[(5 + Sqrt[5])/2]*ArcTan[(Sqrt[(5 + Sqrt[5])/10]*((1 + Sqrt[5])*a - 4*x))/(2*a)])/(5*a^8) + Log[a + x]/(5*a^8) - ((1 + Sqrt[5])*Log[a^2 - ((1 - Sqrt[5])*a*x)/2 + x^2])/(20*a^8) - ((1 - Sqrt[5])*Log[a^2 - ((1 + Sqrt[5])*a*x)/2 + x^2])/(20*a^8)","A",7,7,13,0.5385,1,"{325, 293, 634, 618, 204, 628, 31}"
145,1,46,0,0.0095126,"\int \frac{x^{-m}}{a^5+x^5} \, dx","Int[1/(x^m*(a^5 + x^5)),x]","\frac{x^{1-m} \text{Hypergeometric2F1}\left(1,\frac{1-m}{5},\frac{6-m}{5},-\frac{x^5}{a^5}\right)}{a^5 (1-m)}","\frac{x^{1-m} \text{Hypergeometric2F1}\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 - m)/5, (6 - m)/5, -(x^5/a^5)])/(a^5*(1 - m))","A",1,1,15,0.06667,1,"{364}"
146,1,35,0,0.4253975,"\int \frac{1+x^4}{1+x^6} \, dx","Int[(1 + x^4)/(1 + x^6),x]","-\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)","-\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,"-ArcTan[Sqrt[3] - 2*x]/3 + (2*ArcTan[x])/3 + ArcTan[Sqrt[3] + 2*x]/3","A",22,8,13,0.6154,1,"{1876, 209, 634, 618, 204, 628, 203, 295}"
147,1,60,0,0.02187,"\int \frac{1}{\left(5+3 x+x^2\right)^3} \, dx","Int[(5 + 3*x + x^2)^(-3),x]","\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}}","\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,"(3 + 2*x)/(22*(5 + 3*x + x^2)^2) + (3*(3 + 2*x))/(121*(5 + 3*x + x^2)) + (12*ArcTan[(3 + 2*x)/Sqrt[11]])/(121*Sqrt[11])","A",4,3,10,0.3000,1,"{614, 618, 204}"
148,1,43,0,0.0135686,"\int \frac{1+x^2+x^4}{\left(1+x^2\right)^4} \, dx","Int[(1 + x^2 + x^4)/(1 + x^2)^4,x]","\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)","\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/(6*(1 + x^2)^3) - x/(24*(1 + x^2)^2) + (7*x)/(16*(1 + x^2)) + (7*ArcTan[x])/16","A",4,4,16,0.2500,1,"{1157, 385, 199, 203}"
149,1,90,0,0.0709111,"\int \frac{B+A x}{\left(c+2 b x+a x^2\right)^2} \, dx","Int[(B + A*x)/(c + 2*b*x + a*x^2)^2,x]","-\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}}","-\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 - a*B)*x)/(2*(b^2 - a*c)*(c + 2*b*x + a*x^2)) - ((A*b - a*B)*ArcTanh[(b + a*x)/Sqrt[b^2 - a*c]])/(2*(b^2 - a*c)^(3/2))","A",3,3,19,0.1579,1,"{638, 618, 206}"
150,1,38,0,0.0258385,"\int \frac{-41+55 x-27 x^2+5 x^3}{\left(5-4 x+x^2\right)^2} \, dx","Int[(-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",5,5,26,0.1923,1,"{1660, 634, 618, 204, 628}"
151,1,57,0,0.0244686,"\int \frac{1}{\left(-1+x^3\right)^2} \, dx","Int[(-1 + x^3)^(-2),x]","\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}}","\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,"x/(3*(1 - x^3)) + (2*ArcTan[(1 + 2*x)/Sqrt[3]])/(3*Sqrt[3]) - (2*Log[1 - x])/9 + Log[1 + x + x^2]/9","A",7,7,7,1.000,1,"{199, 200, 31, 634, 618, 204, 628}"
152,1,36,0,0.0232351,"\int \frac{4+3 x^4}{x^2 \left(1+x^2\right)^3} \, dx","Int[(4 + 3*x^4)/(x^2*(1 + x^2)^3),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)","-\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,"-4/x - (7*x)/(4*(1 + x^2)^2) - (25*x)/(8*(1 + x^2)) - (57*ArcTan[x])/8","A",4,4,18,0.2222,1,"{1260, 456, 453, 203}"
153,1,49,0,0.0369044,"\int \frac{x}{1+x^6} \, dx","Int[x/(1 + x^6),x]","\frac{1}{6} \log \left(x^2+1\right)-\frac{1}{12} \log \left(x^4-x^2+1\right)-\frac{\tan ^{-1}\left(\frac{1-2 x^2}{\sqrt{3}}\right)}{2 \sqrt{3}}","\frac{1}{6} \log \left(x^2+1\right)-\frac{1}{12} \log \left(x^4-x^2+1\right)-\frac{\tan ^{-1}\left(\frac{1-2 x^2}{\sqrt{3}}\right)}{2 \sqrt{3}}",1,"-ArcTan[(1 - 2*x^2)/Sqrt[3]]/(2*Sqrt[3]) + Log[1 + x^2]/6 - Log[1 - x^2 + x^4]/12","A",7,7,9,0.7778,1,"{275, 200, 31, 634, 618, 204, 628}"
154,1,20,0,0.0455255,"\int \frac{-1+x^{-1+n}}{-n x+x^n} \, dx","Int[(-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",5,4,18,0.2222,1,"{1593, 514, 446, 72}"
155,1,41,0,0.0403192,"\int \frac{x^3}{1-2 x^2+3 x^4} \, dx","Int[x^3/(1 - 2*x^2 + 3*x^4),x]","\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}}","\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,"-ArcTan[(1 - 3*x^2)/Sqrt[2]]/(6*Sqrt[2]) + Log[1 - 2*x^2 + 3*x^4]/12","A",5,5,18,0.2778,1,"{1114, 634, 618, 204, 628}"
156,1,32,0,0.0245061,"\int \frac{x^5}{-4+x^2+3 x^4} \, dx","Int[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",5,4,16,0.2500,1,"{1114, 703, 632, 31}"
157,1,25,0,0.0171892,"\int \frac{x^2}{9-10 x^3+x^6} \, dx","Int[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,"-Log[1 - x^3]/24 + Log[9 - x^3]/24","A",4,3,16,0.1875,1,"{1352, 616, 31}"
158,1,36,0,0.0219846,"\int \frac{1-4 x^2+x^3}{(-2+x)^4} \, dx","Int[(1 - 4*x^2 + x^3)/(-2 + x)^4,x]","\frac{2}{2-x}+\frac{2}{(2-x)^2}-\frac{7}{3 (2-x)^3}+\log (2-x)","\frac{2}{2-x}+\frac{2}{(2-x)^2}-\frac{7}{3 (2-x)^3}+\log (2-x)",1,"-7/(3*(2 - x)^3) + 2/(2 - x)^2 + 2/(2 - x) + Log[2 - x]","A",2,1,16,0.06250,1,"{1850}"
159,1,45,0,0.0124213,"\int \frac{x^3}{(-1+x)^{12}} \, dx","Int[x^3/(-1 + x)^12,x]","-\frac{1}{8 (1-x)^8}+\frac{1}{3 (1-x)^9}-\frac{3}{10 (1-x)^{10}}+\frac{1}{11 (1-x)^{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*(1 - x)^11) - 3/(10*(1 - x)^10) + 1/(3*(1 - x)^9) - 1/(8*(1 - x)^8)","A",2,1,9,0.1111,1,"{43}"
160,1,55,0,0.0392657,"\int \frac{-3 x+x^4}{(1+2 x)^5} \, dx","Int[(-3*x + x^4)/(1 + 2*x)^5,x]","\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)","\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,"-25/(128*(1 + 2*x)^4) + 7/(24*(1 + 2*x)^3) - 3/(32*(1 + 2*x)^2) + 1/(8*(1 + 2*x)) + Log[1 + 2*x]/32","A",3,2,15,0.1333,1,"{1593, 1620}"
161,1,36,0,0.0151888,"\int \frac{1}{(-1+x)^2 (1+x)^3} \, dx","Int[1/((-1 + x)^2*(1 + x)^3),x]","\frac{1}{8 (1-x)}-\frac{1}{4 (x+1)}-\frac{1}{8 (x+1)^2}+\frac{3}{8} \tanh ^{-1}(x)","\frac{1}{8 (1-x)}-\frac{1}{4 (x+1)}-\frac{1}{8 (x+1)^2}+\frac{3}{8} \tanh ^{-1}(x)",1,"1/(8*(1 - x)) - 1/(8*(1 + x)^2) - 1/(4*(1 + x)) + (3*ArcTanh[x])/8","A",3,2,11,0.1818,1,"{44, 207}"
162,1,35,0,0.0142911,"\int \frac{1}{(5-6 x)^2 x^2} \, dx","Int[1/((5 - 6*x)^2*x^2),x]","\frac{6}{25 (5-6 x)}-\frac{1}{25 x}-\frac{12}{125} \log (5-6 x)+\frac{12 \log (x)}{125}","\frac{6}{25 (5-6 x)}-\frac{1}{25 x}-\frac{12}{125} \log (5-6 x)+\frac{12 \log (x)}{125}",1,"6/(25*(5 - 6*x)) - 1/(25*x) - (12*Log[5 - 6*x])/125 + (12*Log[x])/125","A",2,1,11,0.09091,1,"{44}"
163,1,61,0,0.012479,"\int \frac{1}{\left(-3-2 x+x^2\right)^3} \, dx","Int[(-3 - 2*x + x^2)^(-3),x]","\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)","\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,"(1 - x)/(16*(3 + 2*x - x^2)^2) + (3*(1 - x))/(128*(3 + 2*x - x^2)) + (3*Log[3 - x])/512 - (3*Log[1 + x])/512","A",5,3,10,0.3000,1,"{614, 616, 31}"
164,1,51,0,0.0140963,"\int \frac{1}{\left(13-4 x+x^2\right)^3} \, dx","Int[(13 - 4*x + x^2)^(-3),x]","-\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)","-\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,"-(2 - x)/(36*(13 - 4*x + x^2)^2) - (2 - x)/(216*(13 - 4*x + x^2)) + ArcTan[(-2 + x)/3]/648","A",4,3,10,0.3000,1,"{614, 618, 204}"
165,1,54,0,0.0257839,"\int \frac{1}{(2+x)^3 (3+x)^4} \, dx","Int[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*(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",2,1,11,0.09091,1,"{44}"
166,1,42,0,0.0147501,"\int \frac{x^6}{\left(-2+x^2\right)^2} \, dx","Int[x^6/(-2 + x^2)^2,x]","\frac{x^5}{2 \left(2-x^2\right)}+\frac{5 x^3}{6}+5 x-5 \sqrt{2} \tanh ^{-1}\left(\frac{x}{\sqrt{2}}\right)","\frac{x^3}{3}-\frac{2 x}{x^2-2}+4 x-5 \sqrt{2} \tanh ^{-1}\left(\frac{x}{\sqrt{2}}\right)",1,"5*x + (5*x^3)/6 + x^5/(2*(2 - x^2)) - 5*Sqrt[2]*ArcTanh[x/Sqrt[2]]","A",4,3,11,0.2727,1,"{288, 302, 207}"
167,1,58,0,0.0166097,"\int \frac{x^8}{\left(4+x^2\right)^4} \, dx","Int[x^8/(4 + x^2)^4,x]","-\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)","-\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,"(35*x)/16 - x^7/(6*(4 + x^2)^3) - (7*x^5)/(24*(4 + x^2)^2) - (35*x^3)/(48*(4 + x^2)) - (35*ArcTan[x/2])/8","A",5,3,11,0.2727,1,"{288, 321, 203}"
168,1,43,0,0.0206964,"\int \frac{-4+7 x}{\left(5+2 x+3 x^2\right)^2} \, dx","Int[(-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",3,3,18,0.1667,1,"{638, 618, 204}"
169,1,43,0,0.0230899,"\int \frac{5-4 x}{\left(-2-4 x+3 x^2\right)^2} \, dx","Int[(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 \tanh ^{-1}\left(\frac{2-3 x}{\sqrt{10}}\right)}{20 \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*ArcTanh[(2 - 3*x)/Sqrt[10]])/(20*Sqrt[10])","A",3,3,18,0.1667,1,"{638, 618, 206}"
170,1,37,0,0.0129613,"\int \frac{x^5}{\left(1+x^4\right)^3} \, dx","Int[x^5/(1 + x^4)^3,x]","\frac{x^2}{16 \left(x^4+1\right)}-\frac{x^2}{8 \left(x^4+1\right)^2}+\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}+\frac{1}{16} \tan ^{-1}\left(x^2\right)",1,"-x^2/(8*(1 + x^4)^2) + x^2/(16*(1 + x^4)) + ArcTan[x^2]/16","A",4,4,11,0.3636,1,"{275, 288, 199, 203}"
171,1,39,0,0.0263224,"\int \frac{x \left(1+x^2\right)^3}{\left(2+2 x^2+x^4\right)^2} \, dx","Int[(x*(1 + x^2)^3)/(2 + 2*x^2 + x^4)^2,x]","\frac{1}{4} \log \left(x^4+2 x^2+2\right)-\frac{\left(x^2+1\right)^2}{4 \left(x^4+2 x^2+2\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 + x^2)^2/(4*(2 + 2*x^2 + x^4)) + Log[2 + 2*x^2 + x^4]/4","A",3,3,21,0.1429,1,"{1247, 686, 628}"
172,1,13,0,0.0023815,"\int \frac{x^3}{\left(a^4+x^4\right)^3} \, dx","Int[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*(a^4 + x^4)^2)","A",1,1,13,0.07692,1,"{261}"
173,1,54,0,0.0302035,"\int \frac{1}{x \left(a^4+x^4\right)^3} \, dx","Int[1/(x*(a^4 + x^4)^3),x]","\frac{1}{4 a^8 \left(a^4+x^4\right)}+\frac{1}{8 a^4 \left(a^4+x^4\right)^2}-\frac{\log \left(a^4+x^4\right)}{4 a^{12}}+\frac{\log (x)}{a^{12}}","\frac{1}{4 a^8 \left(a^4+x^4\right)}+\frac{1}{8 a^4 \left(a^4+x^4\right)^2}-\frac{\log \left(a^4+x^4\right)}{4 a^{12}}+\frac{\log (x)}{a^{12}}",1,"1/(8*a^4*(a^4 + x^4)^2) + 1/(4*a^8*(a^4 + x^4)) + Log[x]/a^12 - Log[a^4 + x^4]/(4*a^12)","A",3,2,13,0.1538,1,"{266, 44}"
174,1,157,0,0.1009665,"\int \frac{1}{x^2 \left(a^4+x^4\right)^3} \, dx","Int[1/(x^2*(a^4 + x^4)^3),x]","\frac{9}{32 a^8 x \left(a^4+x^4\right)}+\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{45}{32 a^{12} x}+\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{9}{32 a^8 x \left(a^4+x^4\right)}+\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{45}{32 a^{12} x}+\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}}",1,"-45/(32*a^12*x) + 1/(8*a^4*x*(a^4 + x^4)^2) + 9/(32*a^8*x*(a^4 + x^4)) + (45*ArcTan[1 - (Sqrt[2]*x)/a])/(64*Sqrt[2]*a^13) - (45*ArcTan[1 + (Sqrt[2]*x)/a])/(64*Sqrt[2]*a^13) - (45*Log[a^2 - Sqrt[2]*a*x + x^2])/(128*Sqrt[2]*a^13) + (45*Log[a^2 + Sqrt[2]*a*x + x^2])/(128*Sqrt[2]*a^13)","A",12,8,13,0.6154,1,"{290, 325, 297, 1162, 617, 204, 1165, 628}"
175,1,64,0,0.0302262,"\int \frac{1}{x^3 \left(a^4+x^4\right)^3} \, dx","Int[1/(x^3*(a^4 + x^4)^3),x]","\frac{5}{16 a^8 x^2 \left(a^4+x^4\right)}-\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)}-\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}}",1,"-15/(16*a^12*x^2) + 1/(8*a^4*x^2*(a^4 + x^4)^2) + 5/(16*a^8*x^2*(a^4 + x^4)) - (15*ArcTan[x^2/a^2])/(16*a^14)","A",5,4,13,0.3077,1,"{275, 290, 325, 203}"
176,1,39,0,0.0249247,"\int \frac{x^{14}}{\left(3+2 x^5\right)^3} \, dx","Int[x^14/(3 + 2*x^5)^3,x]","\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)","\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,"-9/(80*(3 + 2*x^5)^2) + 3/(20*(3 + 2*x^5)) + Log[3 + 2*x^5]/40","A",3,2,13,0.1538,1,"{266, 43}"
177,1,319,0,0.5836659,"\int \frac{x^6}{\left(3+2 x^5\right)^3} \, dx","Int[x^6/(3 + 2*x^5)^3,x]","\frac{x^2}{150 \left(2 x^5+3\right)}-\frac{x^2}{20 \left(2 x^5+3\right)^2}+\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{\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}}","\frac{x^2}{150 \left(2 x^5+3\right)}-\frac{x^2}{20 \left(2 x^5+3\right)^2}+\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{\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,"-x^2/(20*(3 + 2*x^5)^2) + x^2/(150*(3 + 2*x^5)) - (Sqrt[5 + Sqrt[5]]*ArcTan[Sqrt[(5 + 2*Sqrt[5])/5] - (2*2^(7/10)*x)/(3^(1/5)*Sqrt[5 - Sqrt[5]])])/(250*2^(9/10)*3^(3/5)) - (Sqrt[5 - Sqrt[5]]*ArcTan[Sqrt[(5 - 2*Sqrt[5])/5] + (2*2^(7/10)*x)/(3^(1/5)*Sqrt[5 + Sqrt[5]])])/(250*2^(9/10)*3^(3/5)) - Log[3^(1/5) + 2^(1/5)*x]/(250*2^(2/5)*3^(3/5)) + ((1 + Sqrt[5])*Log[3^(2/5) - (3^(1/5)*(1 - Sqrt[5])*x)/2^(4/5) + 2^(2/5)*x^2])/(1000*2^(2/5)*3^(3/5)) + ((1 - Sqrt[5])*Log[3^(2/5) - (3^(1/5)*(1 + Sqrt[5])*x)/2^(4/5) + 2^(2/5)*x^2])/(1000*2^(2/5)*3^(3/5))","A",8,8,13,0.6154,1,"{288, 290, 293, 634, 618, 204, 628, 31}"
178,1,59,0,0.0208878,"\int \frac{9}{5 x^2 \left(3-2 x^2\right)^3} \, dx","Int[9/(5*x^2*(3 - 2*x^2)^3),x]","\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}}","\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,"-1/(8*x) + 3/(20*x*(3 - 2*x^2)^2) + 1/(8*x*(3 - 2*x^2)) + ArcTanh[Sqrt[2/3]*x]/(4*Sqrt[6])","A",5,4,16,0.2500,1,"{12, 290, 325, 206}"
179,1,36,0,0.024039,"\int \frac{4+3 x^4}{x^2 \left(1+x^2\right)^3} \, dx","Int[(4 + 3*x^4)/(x^2*(1 + x^2)^3),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)","-\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,"-4/x - (7*x)/(4*(1 + x^2)^2) - (25*x)/(8*(1 + x^2)) - (57*ArcTan[x])/8","A",4,4,18,0.2222,1,"{1260, 456, 453, 203}"
180,1,38,0,0.0619045,"\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","Int[(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}{1-x}+\frac{1}{x+1}-\frac{3}{2 (1-x)^2}+\log (1-x)-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",2,1,44,0.02273,1,"{2074}"
181,1,64,0,0.0730219,"\int \frac{1+x^2}{x \left(1+x^3\right)^2} \, dx","Int[(1 + x^2)/(x*(1 + x^3)^2),x]","\frac{x \left(x-x^2\right)}{3 \left(x^3+1\right)}-\frac{5}{18} \log \left(x^2-x+1\right)+\log (x)-\frac{4}{9} \log (x+1)-\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{3 \sqrt{3}}","\frac{x \left(x-x^2\right)}{3 \left(x^3+1\right)}-\frac{5}{18} \log \left(x^2-x+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,"(x*(x - x^2))/(3*(1 + x^3)) - ArcTan[(1 - 2*x)/Sqrt[3]]/(3*Sqrt[3]) + Log[x] - (4*Log[1 + x])/9 - (5*Log[1 - x + x^2])/18","A",7,6,16,0.3750,1,"{1829, 1834, 634, 618, 204, 628}"
182,1,63,0,0.1211581,"\int \frac{-2-3 x+x^2}{(1+x)^2 \left(1+x+x^2\right)^2} \, dx","Int[(-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",7,6,22,0.2727,1,"{1646, 1628, 634, 618, 204, 628}"
183,1,43,0,0.0194159,"\int \frac{1}{(1-4 x)^3 (2-3 x)} \, dx","Int[1/((1 - 4*x)^3*(2 - 3*x)),x]","-\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)","-\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,"1/(10*(1 - 4*x)^2) - 3/(25*(1 - 4*x)) - (9*Log[1 - 4*x])/125 + (9*Log[2 - 3*x])/125","A",2,1,15,0.06667,1,"{44}"
184,1,27,0,0.0191322,"\int \frac{x^3}{\left(2-5 x^2\right)^7} \, dx","Int[x^3/(2 - 5*x^2)^7,x]","\frac{1}{150 \left(2-5 x^2\right)^6}-\frac{1}{250 \left(2-5 x^2\right)^5}","\frac{1}{150 \left(2-5 x^2\right)^6}-\frac{1}{250 \left(2-5 x^2\right)^5}",1,"1/(150*(2 - 5*x^2)^6) - 1/(250*(2 - 5*x^2)^5)","A",3,2,13,0.1538,1,"{266, 43}"
185,1,46,0,0.0299033,"\int \frac{x^7}{\left(2-5 x^2\right)^3} \, dx","Int[x^7/(2 - 5*x^2)^3,x]","-\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)","-\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,"-x^2/250 + 2/(625*(2 - 5*x^2)^2) - 6/(625*(2 - 5*x^2)) - (3*Log[2 - 5*x^2])/625","A",3,2,13,0.1538,1,"{266, 43}"
186,1,50,0,0.0170013,"\int \frac{1}{(-2+x)^3 (1+x)^2} \, dx","Int[1/((-2 + x)^3*(1 + x)^2),x]","-\frac{2}{27 (2-x)}+\frac{1}{27 (x+1)}-\frac{1}{18 (2-x)^2}+\frac{1}{27} \log (2-x)-\frac{1}{27} \log (x+1)","\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,"-1/(18*(2 - x)^2) - 2/(27*(2 - x)) + 1/(27*(1 + x)) + Log[2 - x]/27 - Log[1 + x]/27","A",2,1,11,0.09091,1,"{44}"
187,1,54,0,0.0182847,"\int \frac{1}{(2+x)^3 (3+x)^4} \, dx","Int[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*(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",2,1,11,0.09091,1,"{44}"
188,1,36,0,0.0151688,"\int \frac{x^5}{(3+x)^2} \, dx","Int[x^5/(3 + x)^2,x]","\frac{x^4}{4}-2 x^3+\frac{27 x^2}{2}-108 x+\frac{243}{x+3}+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,"-108*x + (27*x^2)/2 - 2*x^3 + x^4/4 + 243/(3 + x) + 405*Log[3 + x]","A",2,1,9,0.1111,1,"{43}"
189,1,44,0,0.0365853,"\int (\text{b1}+\text{c1} x) \left(a+2 b x+c x^2\right) \, dx","Int[(b1 + c1*x)*(a + 2*b*x + c*x^2),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","\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,"a*b1*x + ((2*b*b1 + a*c1)*x^2)/2 + ((b1*c + 2*b*c1)*x^3)/3 + (c*c1*x^4)/4","A",2,1,17,0.05882,1,"{631}"
190,1,96,0,0.1044196,"\int (\text{b1}+\text{c1} x) \left(a+2 b x+c x^2\right)^2 \, dx","Int[(b1 + c1*x)*(a + 2*b*x + c*x^2)^2,x]","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","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,"a^2*b1*x + (a*(4*b*b1 + a*c1)*x^2)/2 + (2*(2*b^2*b1 + a*b1*c + 2*a*b*c1)*x^3)/3 + ((2*b*b1*c + 2*b^2*c1 + a*c*c1)*x^4)/2 + (c*(b1*c + 4*b*c1)*x^5)/5 + (c^2*c1*x^6)/6","A",2,1,19,0.05263,1,"{631}"
191,1,167,0,0.1876777,"\int (\text{b1}+\text{c1} x) \left(a+2 b x+c x^2\right)^3 \, dx","Int[(b1 + c1*x)*(a + 2*b*x + c*x^2)^3,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})+a^3 \text{b1} x+\frac{1}{5} x^5 \left(12 a b c \text{c1}+3 a \text{b1} c^2+12 b^2 \text{b1} c+8 b^3 \text{c1}\right)+\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}{7} c^2 x^7 (6 b \text{c1}+\text{b1} c)+\frac{1}{8} c^3 \text{c1} x^8","\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})+a^3 \text{b1} x+\frac{1}{5} x^5 \left(12 a b c \text{c1}+3 a \text{b1} c^2+12 b^2 \text{b1} c+8 b^3 \text{c1}\right)+\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}{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",2,1,19,0.05263,1,"{631}"
192,1,263,0,0.3370786,"\int (\text{b1}+\text{c1} x) \left(a+2 b x+c x^2\right)^4 \, dx","Int[(b1 + c1*x)*(a + 2*b*x + c*x^2)^4,x]","\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+16 b^3 \text{b1} c+8 b^4 \text{c1}\right)+\frac{2}{5} x^5 \left(12 a^2 b c \text{c1}+3 a^2 \text{b1} c^2+24 a b^2 \text{b1} c+16 a b^3 \text{c1}+8 b^4 \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{4}{3} a^2 x^3 \left(2 a b \text{c1}+a \text{b1} c+6 b^2 \text{b1}\right)+\frac{1}{2} a^3 x^2 (a \text{c1}+8 b \text{b1})+a^4 \text{b1} x+\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+6 b^2 \text{b1} c+8 b^3 \text{c1}\right)+\frac{1}{9} c^3 x^9 (8 b \text{c1}+\text{b1} c)+\frac{1}{10} c^4 \text{c1} x^{10}","\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+16 b^3 \text{b1} c+8 b^4 \text{c1}\right)+\frac{2}{5} x^5 \left(12 a^2 b c \text{c1}+3 a^2 \text{b1} c^2+24 a b^2 \text{b1} c+16 a b^3 \text{c1}+8 b^4 \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{4}{3} a^2 x^3 \left(2 a b \text{c1}+a \text{b1} c+6 b^2 \text{b1}\right)+\frac{1}{2} a^3 x^2 (a \text{c1}+8 b \text{b1})+a^4 \text{b1} x+\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+6 b^2 \text{b1} c+8 b^3 \text{c1}\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",2,1,19,0.05263,1,"{631}"
193,1,159,0,0.0817077,"\int (\text{b1}+\text{c1} x) \left(a+2 b x+c x^2\right)^n \, dx","Int[(b1 + c1*x)*(a + 2*b*x + c*x^2)^n,x]","\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} \text{Hypergeometric2F1}\left(-n,n+1,n+2,\frac{\sqrt{b^2-a c}+b+c x}{2 \sqrt{b^2-a c}}\right)}{c (n+1) \sqrt{b^2-a c}}","\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} \text{Hypergeometric2F1}\left(-n,n+1,n+2,\frac{\sqrt{b^2-a c}+b+c x}{2 \sqrt{b^2-a c}}\right)}{c (n+1) \sqrt{b^2-a c}}",1,"(c1*(a + 2*b*x + c*x^2)^(1 + n))/(2*c*(1 + n)) - (2^n*(b1*c - b*c1)*(-((b - Sqrt[b^2 - a*c] + c*x)/Sqrt[b^2 - a*c]))^(-1 - n)*(a + 2*b*x + c*x^2)^(1 + n)*Hypergeometric2F1[-n, 1 + n, 2 + n, (b + Sqrt[b^2 - a*c] + c*x)/(2*Sqrt[b^2 - a*c])])/(c*Sqrt[b^2 - a*c]*(1 + n))","A",2,2,19,0.1053,1,"{640, 624}"
194,1,65,0,0.0415227,"\int \frac{\text{b1}+\text{c1} x}{a+2 b x+c x^2} \, dx","Int[(b1 + c1*x)/(a + 2*b*x + c*x^2),x]","\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}}","\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)*ArcTanh[(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",4,4,19,0.2105,1,"{634, 618, 206, 628}"
195,1,89,0,0.0447332,"\int \frac{\text{b1}+\text{c1} x}{\left(a+2 b x+c x^2\right)^2} \, dx","Int[(b1 + c1*x)/(a + 2*b*x + c*x^2)^2,x]","\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)}","\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 - b*c1)*x)/(2*(b^2 - a*c)*(a + 2*b*x + c*x^2)) + ((b1*c - b*c1)*ArcTanh[(b + c*x)/Sqrt[b^2 - a*c]])/(2*(b^2 - a*c)^(3/2))","A",3,3,19,0.1579,1,"{638, 618, 206}"
196,1,130,0,0.072158,"\int \frac{\text{b1}+\text{c1} x}{\left(a+2 b x+c x^2\right)^3} \, dx","Int[(b1 + c1*x)/(a + 2*b*x + c*x^2)^3,x]","\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}}","\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,"-(b*b1 - a*c1 + (b1*c - b*c1)*x)/(4*(b^2 - a*c)*(a + 2*b*x + c*x^2)^2) + (3*(b1*c - b*c1)*(b + c*x))/(8*(b^2 - a*c)^2*(a + 2*b*x + c*x^2)) - (3*c*(b1*c - b*c1)*ArcTanh[(b + c*x)/Sqrt[b^2 - a*c]])/(8*(b^2 - a*c)^(5/2))","A",4,4,19,0.2105,1,"{638, 614, 618, 206}"
197,1,173,0,0.1098448,"\int \frac{\text{b1}+\text{c1} x}{\left(a+2 b x+c x^2\right)^4} \, dx","Int[(b1 + c1*x)/(a + 2*b*x + c*x^2)^4,x]","\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}","\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,"-(b*b1 - a*c1 + (b1*c - b*c1)*x)/(6*(b^2 - a*c)*(a + 2*b*x + c*x^2)^3) + (5*(b1*c - b*c1)*(b + c*x))/(24*(b^2 - a*c)^2*(a + 2*b*x + c*x^2)^2) - (5*c*(b1*c - b*c1)*(b + c*x))/(16*(b^2 - a*c)^3*(a + 2*b*x + c*x^2)) + (5*c^2*(b1*c - b*c1)*ArcTanh[(b + c*x)/Sqrt[b^2 - a*c]])/(16*(b^2 - a*c)^(7/2))","A",5,4,19,0.2105,1,"{638, 614, 618, 206}"
198,1,169,0,0.0793389,"\int (\text{b1}+\text{c1} x) \left(a+2 b x+c x^2\right)^{-n} \, dx","Int[(b1 + c1*x)/(a + 2*b*x + c*x^2)^n,x]","\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} \text{Hypergeometric2F1}\left(1-n,n,2-n,\frac{\sqrt{b^2-a c}+b+c x}{2 \sqrt{b^2-a c}}\right)}{c (1-n) \sqrt{b^2-a c}}","\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} \text{Hypergeometric2F1}\left(1-n,n,2-n,\frac{\sqrt{b^2-a c}+b+c x}{2 \sqrt{b^2-a c}}\right)}{c (1-n) \sqrt{b^2-a c}}",1,"(c1*(a + 2*b*x + c*x^2)^(1 - n))/(2*c*(1 - n)) - ((b1*c - b*c1)*(-((b - Sqrt[b^2 - a*c] + c*x)/Sqrt[b^2 - a*c]))^(-1 + n)*(a + 2*b*x + c*x^2)^(1 - n)*Hypergeometric2F1[1 - n, n, 2 - n, (b + Sqrt[b^2 - a*c] + c*x)/(2*Sqrt[b^2 - a*c])])/(2^n*c*Sqrt[b^2 - a*c]*(1 - n))","A",2,2,21,0.09524,1,"{640, 624}"
199,1,49,0,0.0155641,"\int \frac{x}{3+6 x+2 x^2} \, dx","Int[x/(3 + 6*x + 2*x^2),x]","\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)","\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])/4 + ((1 + Sqrt[3])*Log[3 + Sqrt[3] + 2*x])/4","A",3,2,14,0.1429,1,"{632, 31}"
200,1,61,0,0.0221754,"\int \frac{-3+2 x}{\left(3+6 x+2 x^2\right)^3} \, dx","Int[(-3 + 2*x)/(3 + 6*x + 2*x^2)^3,x]","-\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}}","-\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,"(5 + 4*x)/(4*(3 + 6*x + 2*x^2)^2) - (3 + 2*x)/(2*(3 + 6*x + 2*x^2)) + ArcTanh[(3 + 2*x)/Sqrt[3]]/Sqrt[3]","A",4,4,18,0.2222,1,"{638, 614, 618, 206}"
201,1,36,0,0.0079996,"\int \frac{-1+x}{\left(4+5 x+x^2\right)^2} \, dx","Int[(-1 + x)/(4 + 5*x + x^2)^2,x]","\frac{7 x+13}{9 \left(x^2+5 x+4\right)}+\frac{7}{27} \log (x+1)-\frac{7}{27} \log (x+4)","\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,"(13 + 7*x)/(9*(4 + 5*x + x^2)) + (7*Log[1 + x])/27 - (7*Log[4 + x])/27","A",4,3,14,0.2143,1,"{638, 616, 31}"
202,1,87,0,0.0232128,"\int \frac{1}{\left(2+3 x+x^2\right)^5} \, dx","Int[(2 + 3*x + x^2)^(-5),x]","\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}-\frac{2 x+3}{4 \left(x^2+3 x+2\right)^4}+70 \log (x+1)-70 \log (x+2)","\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}-\frac{2 x+3}{4 \left(x^2+3 x+2\right)^4}+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",7,3,10,0.3000,1,"{614, 616, 31}"
203,1,81,0,0.0561464,"\int \frac{1}{x^3 \left(7-6 x+2 x^2\right)^2} \, dx","Int[1/(x^3*(7 - 6*x + 2*x^2)^2),x]","-\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}}","-\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,"-1/(490*x^2) - 69/(1715*x) - (2 - 3*x)/(35*x^2*(7 - 6*x + 2*x^2)) - (234*ArcTan[(3 - 2*x)/Sqrt[5]])/(12005*Sqrt[5]) + (80*Log[x])/2401 - (40*Log[7 - 6*x + 2*x^2])/2401","A",7,6,16,0.3750,1,"{740, 800, 634, 618, 204, 628}"
204,1,104,0,0.0737919,"\int \frac{x^9}{\left(2+3 x+x^2\right)^5} \, dx","Int[x^9/(2 + 3*x + x^2)^5,x]","\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}-\frac{(1593 x+2206) x^2}{2 \left(x^2+3 x+2\right)}+735 x-1471 \log (x+1)+1472 \log (x+2)","\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}-\frac{(1593 x+2206) x^2}{2 \left(x^2+3 x+2\right)}+735 x-1471 \log (x+1)+1472 \log (x+2)",1,"735*x + (x^8*(4 + 3*x))/(4*(2 + 3*x + x^2)^4) - (x^6*(110 + 81*x))/(12*(2 + 3*x + x^2)^3) + (x^4*(184 + 135*x))/(2*(2 + 3*x + x^2)^2) - (x^2*(2206 + 1593*x))/(2*(2 + 3*x + x^2)) - 1471*Log[1 + x] + 1472*Log[2 + x]","A",8,5,14,0.3571,1,"{738, 818, 773, 632, 31}"
205,1,102,0,0.0371751,"\int \frac{(1+2 x)^2}{\left(3+5 x+2 x^2\right)^5} \, dx","Int[(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{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)","\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 + 2*x)*(7 + 6*x))/(4*(3 + 5*x + 2*x^2)^4) + (73 + 62*x)/(3*(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[1 + x] - 2480*Log[3 + 2*x]","A",7,5,20,0.2500,1,"{738, 638, 614, 616, 31}"
206,1,40,0,0.0231058,"\int \frac{\left(a-b x^2\right)^3}{x^7} \, dx","Int[(a - b*x^2)^3/x^7,x]","\frac{3 a^2 b}{4 x^4}-\frac{a^3}{6 x^6}-\frac{3 a b^2}{2 x^2}-b^3 \log (x)","\frac{3 a^2 b}{4 x^4}-\frac{a^3}{6 x^6}-\frac{3 a b^2}{2 x^2}-b^3 \log (x)",1,"-a^3/(6*x^6) + (3*a^2*b)/(4*x^4) - (3*a*b^2)/(2*x^2) - b^3*Log[x]","A",3,2,14,0.1429,1,"{266, 43}"
207,1,83,0,0.0391206,"\int \frac{x^{13}}{\left(a^4+x^4\right)^5} \, dx","Int[x^13/(a^4 + x^4)^5,x]","-\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}","-\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,"-x^10/(16*(a^4 + x^4)^4) - (5*x^6)/(96*(a^4 + x^4)^3) - (5*x^2)/(128*(a^4 + x^4)^2) + (5*x^2)/(256*a^4*(a^4 + x^4)) + (5*ArcTan[x^2/a^2])/(256*a^6)","A",6,4,13,0.3077,1,"{275, 288, 199, 203}"
208,1,49,0,0.0566495,"\int \left(2 \sqrt{x}-x\right)^2 x^{3/2} \left(1+x^2\right) \, dx","Int[(2*Sqrt[x] - x)^2*x^(3/2)*(1 + x^2),x]","\frac{2 x^{13/2}}{13}-\frac{2 x^6}{3}+\frac{8 x^{11/2}}{11}+\frac{2 x^{9/2}}{9}-x^4+\frac{8 x^{7/2}}{7}","\frac{2 x^{13/2}}{13}-\frac{2 x^6}{3}+\frac{8 x^{11/2}}{11}+\frac{2 x^{9/2}}{9}-x^4+\frac{8 x^{7/2}}{7}",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",9,4,24,0.1667,1,"{1584, 1820, 266, 43}"
209,1,55,0,0.2378756,"\int \left(-3 x^{3/5}+x^{3/2}\right)^2 \left(-\frac{x^{2/3}}{3}+4 x^{3/2}\right) \, dx","Int[(-3*x^(3/5) + x^(3/2))^2*(-x^(2/3)/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",5,3,33,0.09091,1,"{1593, 1584, 1820}"
210,1,22,0,0.0091146,"\int \frac{1}{1+\sqrt{1+x}} \, dx","Int[(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",4,3,11,0.2727,1,"{247, 190, 43}"
211,1,15,0,0.0063466,"\int \frac{x}{1+\sqrt{1+x}} \, dx","Int[x/(1 + Sqrt[1 + x]),x]","\frac{2}{3} (x+1)^{3/2}-x","\frac{2}{3} (x+1)^{3/2}-x",1,"-x + (2*(1 + x)^(3/2))/3","A",2,1,13,0.07692,1,"{371}"
212,1,25,0,0.0173864,"\int \frac{1+\sqrt{1+x}}{-1+\sqrt{1+x}} \, dx","Int[(1 + Sqrt[1 + x])/(-1 + Sqrt[1 + x]),x]","x+4 \sqrt{x+1}+4 \log \left(1-\sqrt{x+1}\right)","x+4 \sqrt{x+1}+4 \log \left(1-\sqrt{x+1}\right)",1,"x + 4*Sqrt[1 + x] + 4*Log[1 - Sqrt[1 + x]]","A",4,3,21,0.1429,1,"{431, 376, 77}"
213,1,33,0,0.0190299,"\int \frac{1}{-\sqrt{1+x}+(1+x)^{2/3}} \, dx","Int[(-Sqrt[1 + x] + (1 + x)^(2/3))^(-1),x]","3 \sqrt[3]{x+1}+6 \sqrt[6]{x+1}+6 \log \left(1-\sqrt[6]{x+1}\right)","3 \sqrt[3]{x+1}+6 \sqrt[6]{x+1}+6 \log \left(1-\sqrt[6]{x+1}\right)",1,"6*(1 + x)^(1/6) + 3*(1 + x)^(1/3) + 6*Log[1 - (1 + x)^(1/6)]","A",5,4,19,0.2105,1,"{2012, 1593, 266, 43}"
214,1,29,0,0.0089935,"\int \frac{\sqrt[3]{1+\sqrt[4]{x}}}{\sqrt{x}} \, dx","Int[(1 + x^(1/4))^(1/3)/Sqrt[x],x]","\frac{12}{7} \left(\sqrt[4]{x}+1\right)^{7/3}-3 \left(\sqrt[4]{x}+1\right)^{4/3}","\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) + (12*(1 + x^(1/4))^(7/3))/7","A",3,2,17,0.1176,1,"{266, 43}"
215,1,53,0,0.010101,"\int \frac{1}{x^3 (1+x)^{3/2}} \, dx","Int[1/(x^3*(1 + x)^(3/2)),x]","-\frac{5 \sqrt{x+1}}{2 x^2}+\frac{2}{x^2 \sqrt{x+1}}+\frac{15 \sqrt{x+1}}{4 x}-\frac{15}{4} \tanh ^{-1}\left(\sqrt{x+1}\right)","-\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/(x^2*Sqrt[1 + x]) - (5*Sqrt[1 + x])/(2*x^2) + (15*Sqrt[1 + x])/(4*x) - (15*ArcTanh[Sqrt[1 + x]])/4","A",5,3,11,0.2727,1,"{51, 63, 207}"
216,1,127,0,0.0375306,"\int \frac{1}{(1-x)^{7/2} x^5} \, dx","Int[1/((1 - x)^(7/2)*x^5),x]","-\frac{1001 \sqrt{1-x}}{32 x^2}-\frac{1001 \sqrt{1-x}}{40 x^3}-\frac{429 \sqrt{1-x}}{20 x^4}+\frac{286}{15 \sqrt{1-x} x^4}+\frac{26}{15 (1-x)^{3/2} x^4}+\frac{2}{5 (1-x)^{5/2} x^4}-\frac{3003 \sqrt{1-x}}{64 x}-\frac{3003}{64} \tanh ^{-1}\left(\sqrt{1-x}\right)","-\frac{143}{96 (1-x)^{5/2} x^2}-\frac{13}{24 (1-x)^{5/2} x^3}-\frac{1}{4 (1-x)^{5/2} x^4}+\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/(5*(1 - x)^(5/2)*x^4) + 26/(15*(1 - x)^(3/2)*x^4) + 286/(15*Sqrt[1 - x]*x^4) - (429*Sqrt[1 - x])/(20*x^4) - (1001*Sqrt[1 - x])/(40*x^3) - (1001*Sqrt[1 - x])/(32*x^2) - (3003*Sqrt[1 - x])/(64*x) - (3003*ArcTanh[Sqrt[1 - x]])/64","A",9,3,13,0.2308,1,"{51, 63, 206}"
217,1,104,0,0.0400664,"\int \frac{1}{(-1+x)^{2/3} x^5} \, dx","Int[1/((-1 + x)^(2/3)*x^5),x]","\frac{11 \sqrt[3]{x-1}}{27 x^2}+\frac{11 \sqrt[3]{x-1}}{36 x^3}+\frac{\sqrt[3]{x-1}}{4 x^4}+\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}}","\frac{11 \sqrt[3]{x-1}}{27 x^2}+\frac{11 \sqrt[3]{x-1}}{36 x^3}+\frac{\sqrt[3]{x-1}}{4 x^4}+\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,"(-1 + x)^(1/3)/(4*x^4) + (11*(-1 + x)^(1/3))/(36*x^3) + (11*(-1 + x)^(1/3))/(27*x^2) + (55*(-1 + x)^(1/3))/(81*x) - (110*ArcTan[(1 - 2*(-1 + x)^(1/3))/Sqrt[3]])/(81*Sqrt[3]) + (55*Log[1 + (-1 + x)^(1/3)])/81 - (55*Log[x])/243","A",8,5,11,0.4545,1,"{51, 58, 618, 204, 31}"
218,1,38,0,0.0131231,"\int \sqrt{\frac{1-x}{1+x}} \, dx","Int[Sqrt[(1 - x)/(1 + x)],x]","\sqrt{\frac{1-x}{x+1}} (x+1)-2 \tan ^{-1}\left(\sqrt{\frac{1-x}{x+1}}\right)","\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)]*(1 + x) - 2*ArcTan[Sqrt[(1 - x)/(1 + x)]]","A",3,3,15,0.2000,1,"{1959, 288, 204}"
219,1,95,0,0.0589155,"\int x \sqrt{\frac{-a+x}{b-x}} \, dx","Int[x*Sqrt[(-a + x)/(b - x)],x]","\frac{1}{2} (b-x)^2 \sqrt{-\frac{a-x}{b-x}}+\frac{1}{4} (a-5 b) (b-x) \sqrt{-\frac{a-x}{b-x}}-\frac{1}{4} (a-b) (a+3 b) \tan ^{-1}\left(\sqrt{-\frac{a-x}{b-x}}\right)","\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,"((a - 5*b)*Sqrt[-((a - x)/(b - x))]*(b - x))/4 + (Sqrt[-((a - x)/(b - x))]*(b - x)^2)/2 - ((a - b)*(a + 3*b)*ArcTan[Sqrt[-((a - x)/(b - x))]])/4","A",4,4,19,0.2105,1,"{1960, 455, 385, 203}"
220,1,54,0,0.0959866,"\int \frac{\sqrt{-5+x} \sqrt{3+x}}{(-1+x) \left(-25+x^2\right)} \, dx","Int[(Sqrt[-5 + x]*Sqrt[3 + x])/((-1 + x)*(-25 + x^2)),x]","\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}}","\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,"ArcTan[(Sqrt[-5 + x]*Sqrt[3 + x])/4]/6 + ArcTanh[(Sqrt[5]*Sqrt[3 + x])/Sqrt[-5 + x]]/(3*Sqrt[5])","A",6,6,27,0.2222,1,"{1586, 178, 92, 203, 93, 206}"
221,1,319,0,0.8228124,"\int \frac{x^2 \sqrt{1+x} \sqrt[4]{1-x^2}}{\sqrt{1-x} \left(\sqrt{1-x}-\sqrt{1+x}\right)} \, dx","Int[(x^2*Sqrt[1 + x]*(1 - x^2)^(1/4))/(Sqrt[1 - x]*(Sqrt[1 - x] - Sqrt[1 + x])),x]","\frac{\left(1-x^2\right)^{9/4}}{3 (1-x)^{3/2}}+\frac{1}{6} \sqrt{x+1} \left(1-x^2\right)^{5/4}+\frac{1}{6} (1-x)^{7/4} (x+1)^{5/4}+\frac{1}{24} (1-x)^{5/4} (x+1)^{3/4}-\frac{1}{16} \sqrt[4]{1-x} (x+1)^{3/4}+\frac{5}{24} (1-x)^{7/4} \sqrt[4]{x+1}-\frac{5}{48} (1-x)^{3/4} \sqrt[4]{x+1}+\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}}","\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,"(-5*(1 - x)^(3/4)*(1 + x)^(1/4))/48 + (5*(1 - x)^(7/4)*(1 + x)^(1/4))/24 - ((1 - x)^(1/4)*(1 + x)^(3/4))/16 + ((1 - x)^(5/4)*(1 + x)^(3/4))/24 + ((1 - x)^(7/4)*(1 + x)^(5/4))/6 + (Sqrt[1 + x]*(1 - x^2)^(5/4))/6 + (1 - x^2)^(9/4)/(3*(1 - x)^(3/2)) - (3*ArcTan[1 - (Sqrt[2]*(1 - x)^(1/4))/(1 + x)^(1/4)])/(8*Sqrt[2]) + (3*ArcTan[1 + (Sqrt[2]*(1 - x)^(1/4))/(1 + x)^(1/4)])/(8*Sqrt[2]) + Log[1 + Sqrt[1 - x]/Sqrt[1 + x] - (Sqrt[2]*(1 - x)^(1/4))/(1 + x)^(1/4)]/(8*Sqrt[2]) - Log[1 + Sqrt[1 - x]/Sqrt[1 + x] + (Sqrt[2]*(1 - x)^(1/4))/(1 + x)^(1/4)]/(8*Sqrt[2])","A",33,16,52,0.3077,1,"{2103, 795, 675, 50, 63, 240, 211, 1165, 628, 1162, 617, 204, 1633, 793, 331, 297}"
222,1,522,0,1.8463126,"\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","Int[(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{x^2}{4}+\frac{1}{4} \sqrt{1-x^2} x+\frac{x}{2}-\frac{1}{4} (1-x)^{5/6} (x+1)^{7/6}-\frac{1}{4} (1-x)^{7/6} (x+1)^{5/6}+\frac{5}{12} \sqrt[6]{1-x} (x+1)^{5/6}-\frac{1}{4} (1-x)^{4/3} (x+1)^{2/3}+\frac{1}{3} \sqrt[3]{1-x} (x+1)^{2/3}-\frac{1}{4} (1-x)^{5/3} \sqrt[3]{x+1}+\frac{1}{6} (1-x)^{2/3} \sqrt[3]{x+1}-\frac{7}{12} (1-x)^{5/6} \sqrt[6]{x+1}-\frac{1}{9} \log (1-x)+\frac{1}{9} \log (x+1)+\frac{1}{3} \log \left(\frac{\sqrt[3]{1-x}}{\sqrt[3]{x+1}}+1\right)-\frac{\log \left(\frac{\sqrt[3]{1-x}}{\sqrt[3]{x+1}}-\frac{\sqrt{3} \sqrt[6]{1-x}}{\sqrt[6]{x+1}}+1\right)}{12 \sqrt{3}}+\frac{\log \left(\frac{\sqrt[3]{1-x}}{\sqrt[3]{x+1}}+\frac{\sqrt{3} \sqrt[6]{1-x}}{\sqrt[6]{x+1}}+1\right)}{12 \sqrt{3}}-\frac{1}{3} \log \left(\frac{\sqrt[3]{x+1}}{\sqrt[3]{1-x}}+1\right)+\frac{1}{4} \sin ^{-1}(x)-\frac{2}{3} \tan ^{-1}\left(\frac{\sqrt[6]{1-x}}{\sqrt[6]{x+1}}\right)+\frac{2 \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{1-x}}{\sqrt{3} \sqrt[3]{x+1}}\right)}{3 \sqrt{3}}+\frac{1}{3} \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{1-x}}{\sqrt[6]{x+1}}\right)-\frac{1}{3} \tan ^{-1}\left(\frac{2 \sqrt[6]{1-x}}{\sqrt[6]{x+1}}+\sqrt{3}\right)-\frac{2 \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{x+1}}{\sqrt{3} \sqrt[3]{1-x}}\right)}{3 \sqrt{3}}","-\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,"x/2 + x^2/4 - (7*(1 - x)^(5/6)*(1 + x)^(1/6))/12 + ((1 - x)^(2/3)*(1 + x)^(1/3))/6 - ((1 - x)^(5/3)*(1 + x)^(1/3))/4 + ((1 - x)^(1/3)*(1 + x)^(2/3))/3 - ((1 - x)^(4/3)*(1 + x)^(2/3))/4 + (5*(1 - x)^(1/6)*(1 + x)^(5/6))/12 - ((1 - x)^(7/6)*(1 + x)^(5/6))/4 - ((1 - x)^(5/6)*(1 + x)^(7/6))/4 + (x*Sqrt[1 - x^2])/4 + ArcSin[x]/4 - (2*ArcTan[(1 - x)^(1/6)/(1 + x)^(1/6)])/3 + (2*ArcTan[1/Sqrt[3] - (2*(1 - x)^(1/3))/(Sqrt[3]*(1 + x)^(1/3))])/(3*Sqrt[3]) + ArcTan[Sqrt[3] - (2*(1 - x)^(1/6))/(1 + x)^(1/6)]/3 - ArcTan[Sqrt[3] + (2*(1 - x)^(1/6))/(1 + x)^(1/6)]/3 - (2*ArcTan[1/Sqrt[3] - (2*(1 + x)^(1/3))/(Sqrt[3]*(1 - x)^(1/3))])/(3*Sqrt[3]) - Log[1 - x]/9 + Log[1 + x]/9 + Log[1 + (1 - x)^(1/3)/(1 + x)^(1/3)]/3 - Log[1 + (1 - x)^(1/3)/(1 + x)^(1/3) - (Sqrt[3]*(1 - x)^(1/6))/(1 + x)^(1/6)]/(12*Sqrt[3]) + Log[1 + (1 - x)^(1/3)/(1 + x)^(1/3) + (Sqrt[3]*(1 - x)^(1/6))/(1 + x)^(1/6)]/(12*Sqrt[3]) - Log[1 + (1 + x)^(1/3)/(1 - x)^(1/3)]/3","A",46,21,56,0.3750,0,"{6688, 6742, 50, 60, 517, 195, 216, 675, 890, 63, 240, 209, 634, 618, 204, 628, 203, 26, 21, 331, 295}"
223,1,29,0,0.0128641,"\int \frac{1}{\sqrt[3]{(-1+x)^4 (1+x)^2}} \, dx","Int[((-1 + x)^4*(1 + x)^2)^(-1/3),x]","\frac{3 (1-x) (x+1)}{2 \sqrt[3]{(1-x)^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",2,2,15,0.1333,1,"{6719, 37}"
224,1,30,0,0.016036,"\int \frac{1}{\sqrt[4]{(-1+x)^3 (2+x)^5}} \, dx","Int[((-1 + x)^3*(2 + x)^5)^(-1/4),x]","-\frac{4 (1-x) (x+2)}{3 \sqrt[4]{-(1-x)^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",2,2,15,0.1333,1,"{6719, 37}"
225,1,63,0,0.0198843,"\int \frac{1}{\sqrt[3]{(-1+x)^7 (1+x)^2}} \, dx","Int[((-1 + x)^7*(1 + x)^2)^(-1/3),x]","\frac{9 (x+1) (1-x)^2}{16 \sqrt[3]{-(1-x)^7 (x+1)^2}}+\frac{3 (x+1) (1-x)}{8 \sqrt[3]{-(1-x)^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))/(8*(-((1 - x)^7*(1 + x)^2))^(1/3)) + (9*(1 - x)^2*(1 + x))/(16*(-((1 - x)^7*(1 + x)^2))^(1/3))","A",3,3,15,0.2000,1,"{6719, 45, 37}"
226,1,188,0,0.120864,"\int \frac{1}{\sqrt[3]{(-1+x)^2 (1+x)}} \, dx","Int[((-1 + x)^2*(1 + x))^(-1/3),x]","-\frac{(3-3 x)^{2/3} \sqrt[3]{x+1} \log \left(-\frac{8}{3} (x-1)\right)}{2\ 3^{2/3} \sqrt[3]{x^3-x^2-x+1}}-\frac{\sqrt[3]{3} (3-3 x)^{2/3} \sqrt[3]{x+1} \log \left(\frac{\sqrt[3]{3} \sqrt[3]{x+1}}{\sqrt[3]{3-3 x}}+1\right)}{2 \sqrt[3]{x^3-x^2-x+1}}-\frac{(3-3 x)^{2/3} \sqrt[3]{x+1} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{x+1}}{\sqrt[6]{3} \sqrt[3]{3-3 x}}\right)}{\sqrt[6]{3} \sqrt[3]{x^3-x^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 - 3*x)^(2/3)*(1 + x)^(1/3)*ArcTan[1/Sqrt[3] - (2*(1 + x)^(1/3))/(3^(1/6)*(3 - 3*x)^(1/3))])/(3^(1/6)*(1 - x - x^2 + x^3)^(1/3))) - ((3 - 3*x)^(2/3)*(1 + x)^(1/3)*Log[(-8*(-1 + x))/3])/(2*3^(2/3)*(1 - x - x^2 + x^3)^(1/3)) - (3^(1/3)*(3 - 3*x)^(2/3)*(1 + x)^(1/3)*Log[1 + (3^(1/3)*(1 + x)^(1/3))/(3 - 3*x)^(1/3)])/(2*(1 - x - x^2 + x^3)^(1/3))","B",3,3,13,0.2308,1,"{2067, 2064, 60}"
227,1,133,0,0.3459621,"\int \frac{\frac{1}{x}+x}{\sqrt{(-2+x) (1+x)^3}} \, dx","Int[(x^(-1) + x)/Sqrt[(-2 + x)*(1 + x)^3],x]","\frac{4 (2-x) (x+1)}{3 \sqrt{-(2-x) (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{-(2-x) (x+1)^3}}+\frac{2 \sqrt{x-2} (x+1)^{3/2} \sinh ^{-1}\left(\frac{\sqrt{x-2}}{\sqrt{3}}\right)}{\sqrt{-(2-x) (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,"(4*(2 - x)*(1 + x))/(3*Sqrt[-((2 - x)*(1 + x)^3)]) + (2*Sqrt[-2 + x]*(1 + x)^(3/2)*ArcSinh[Sqrt[-2 + x]/Sqrt[3]])/Sqrt[-((2 - x)*(1 + x)^3)] - (Sqrt[2]*Sqrt[-2 + x]*(1 + x)^(3/2)*ArcTan[(Sqrt[2]*Sqrt[1 + x])/Sqrt[-2 + x]])/Sqrt[-((2 - x)*(1 + x)^3)]","A",9,9,19,0.4737,1,"{1593, 6719, 1614, 21, 105, 54, 215, 93, 204}"
228,1,404,0,0.3271809,"\int \frac{\sqrt[3]{(-1+x)^2 (1+x)}}{x^2} \, dx","Int[((-1 + x)^2*(1 + x))^(1/3)/x^2,x]","-\frac{\sqrt[3]{x^3-x^2-x+1}}{x}+\frac{\sqrt[3]{x^3-x^2-x+1} \log (x)}{2 \sqrt[3]{3} (3-3 x)^{2/3} \sqrt[3]{x+1}}-\frac{3^{2/3} \sqrt[3]{x^3-x^2-x+1} \log \left(\frac{4 (x+1)}{3}\right)}{2 (3-3 x)^{2/3} \sqrt[3]{x+1}}-\frac{3\ 3^{2/3} \sqrt[3]{x^3-x^2-x+1} \log \left(\frac{\sqrt[3]{3-3 x}}{\sqrt[3]{3} \sqrt[3]{x+1}}+1\right)}{2 (3-3 x)^{2/3} \sqrt[3]{x+1}}-\frac{3^{2/3} \sqrt[3]{x^3-x^2-x+1} \log \left(\left(\frac{2}{3}\right)^{2/3} \sqrt[3]{3-3 x}-\frac{2^{2/3} \sqrt[3]{x+1}}{\sqrt[3]{3}}\right)}{2 (3-3 x)^{2/3} \sqrt[3]{x+1}}-\frac{3 \sqrt[6]{3} \sqrt[3]{x^3-x^2-x+1} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{3-3 x}}{3^{5/6} \sqrt[3]{x+1}}\right)}{(3-3 x)^{2/3} \sqrt[3]{x+1}}-\frac{\sqrt[6]{3} \sqrt[3]{x^3-x^2-x+1} \tan ^{-1}\left(\frac{2 \sqrt[3]{3-3 x}}{3^{5/6} \sqrt[3]{x+1}}+\frac{1}{\sqrt{3}}\right)}{(3-3 x)^{2/3} \sqrt[3]{x+1}}","-\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 - x^2 + x^3)^(1/3)/x) - (3*3^(1/6)*(1 - x - x^2 + x^3)^(1/3)*ArcTan[1/Sqrt[3] - (2*(3 - 3*x)^(1/3))/(3^(5/6)*(1 + x)^(1/3))])/((3 - 3*x)^(2/3)*(1 + x)^(1/3)) - (3^(1/6)*(1 - x - x^2 + x^3)^(1/3)*ArcTan[1/Sqrt[3] + (2*(3 - 3*x)^(1/3))/(3^(5/6)*(1 + x)^(1/3))])/((3 - 3*x)^(2/3)*(1 + x)^(1/3)) + ((1 - x - x^2 + x^3)^(1/3)*Log[x])/(2*3^(1/3)*(3 - 3*x)^(2/3)*(1 + x)^(1/3)) - (3^(2/3)*(1 - x - x^2 + x^3)^(1/3)*Log[(4*(1 + x))/3])/(2*(3 - 3*x)^(2/3)*(1 + x)^(1/3)) - (3*3^(2/3)*(1 - x - x^2 + x^3)^(1/3)*Log[1 + (3 - 3*x)^(1/3)/(3^(1/3)*(1 + x)^(1/3))])/(2*(3 - 3*x)^(2/3)*(1 + x)^(1/3)) - (3^(2/3)*(1 - x - x^2 + x^3)^(1/3)*Log[(2/3)^(2/3)*(3 - 3*x)^(1/3) - (2^(2/3)*(1 + x)^(1/3))/3^(1/3)])/(2*(3 - 3*x)^(2/3)*(1 + x)^(1/3))","B",6,6,17,0.3529,1,"{2081, 2077, 97, 157, 60, 91}"
229,1,43,0,0.006261,"\int \frac{1}{\left(-3-2 x+x^2\right)^{5/2}} \, dx","Int[(-3 - 2*x + x^2)^(-5/2),x]","\frac{1-x}{12 \left(x^2-2 x-3\right)^{3/2}}-\frac{1-x}{24 \sqrt{x^2-2 x-3}}","\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)/(12*(-3 - 2*x + x^2)^(3/2)) - (1 - x)/(24*Sqrt[-3 - 2*x + x^2])","A",2,2,12,0.1667,1,"{614, 613}"
230,1,42,0,0.0426458,"\int \frac{1}{\sqrt{9+3 x-5 x^2+x^3}} \, dx","Int[1/Sqrt[9 + 3*x - 5*x^2 + x^3],x]","\frac{(3-x) \sqrt{x+1} \tanh ^{-1}\left(\frac{\sqrt{x+1}}{2}\right)}{\sqrt{x^3-5 x^2+3 x+9}}","\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[9 + 3*x - 5*x^2 + x^3]","A",4,4,17,0.2353,1,"{2067, 2064, 63, 206}"
231,1,139,0,0.1269543,"\int \frac{1}{\left(9+3 x-5 x^2+x^3\right)^{3/2}} \, dx","Int[(9 + 3*x - 5*x^2 + x^3)^(-3/2),x]","-\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}}","-\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)*(1 + x))/(8*(9 + 3*x - 5*x^2 + x^3)^(3/2)) + (5*(3 - x)^2*(1 + x))/(64*(9 + 3*x - 5*x^2 + x^3)^(3/2)) - (15*(3 - x)^3*(1 + x))/(256*(9 + 3*x - 5*x^2 + x^3)^(3/2)) + (15*(3 - x)^3*(1 + x)^(3/2)*ArcTanh[Sqrt[1 + x]/2])/(512*(9 + 3*x - 5*x^2 + x^3)^(3/2))","A",7,5,17,0.2941,1,"{2067, 2064, 51, 63, 206}"
232,1,188,0,0.118254,"\int \frac{1}{\sqrt[3]{9+3 x-5 x^2+x^3}} \, dx","Int[(9 + 3*x - 5*x^2 + x^3)^(-1/3),x]","-\frac{(9-3 x)^{2/3} \sqrt[3]{x+1} \log \left(-\frac{32}{3} (x-3)\right)}{2\ 3^{2/3} \sqrt[3]{x^3-5 x^2+3 x+9}}-\frac{\sqrt[3]{3} (9-3 x)^{2/3} \sqrt[3]{x+1} \log \left(\frac{\sqrt[3]{3} \sqrt[3]{x+1}}{\sqrt[3]{9-3 x}}+1\right)}{2 \sqrt[3]{x^3-5 x^2+3 x+9}}-\frac{(9-3 x)^{2/3} \sqrt[3]{x+1} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{x+1}}{\sqrt[6]{3} \sqrt[3]{9-3 x}}\right)}{\sqrt[6]{3} \sqrt[3]{x^3-5 x^2+3 x+9}}","-\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,"-(((9 - 3*x)^(2/3)*(1 + x)^(1/3)*ArcTan[1/Sqrt[3] - (2*(1 + x)^(1/3))/(3^(1/6)*(9 - 3*x)^(1/3))])/(3^(1/6)*(9 + 3*x - 5*x^2 + x^3)^(1/3))) - ((9 - 3*x)^(2/3)*(1 + x)^(1/3)*Log[(-32*(-3 + x))/3])/(2*3^(2/3)*(9 + 3*x - 5*x^2 + x^3)^(1/3)) - (3^(1/3)*(9 - 3*x)^(2/3)*(1 + x)^(1/3)*Log[1 + (3^(1/3)*(1 + x)^(1/3))/(9 - 3*x)^(1/3)])/(2*(9 + 3*x - 5*x^2 + x^3)^(1/3))","B",3,3,17,0.1765,1,"{2067, 2064, 60}"
233,1,29,0,0.0329589,"\int \frac{1}{\left(9+3 x-5 x^2+x^3\right)^{2/3}} \, dx","Int[(9 + 3*x - 5*x^2 + x^3)^(-2/3),x]","\frac{3 (3-x) (x+1)}{4 \left(x^3-5 x^2+3 x+9\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*(9 + 3*x - 5*x^2 + x^3)^(2/3))","A",3,3,17,0.1765,1,"{2067, 2064, 37}"
234,1,92,0,0.0850329,"\int \frac{1}{\left(9+3 x-5 x^2+x^3\right)^{4/3}} \, dx","Int[(9 + 3*x - 5*x^2 + x^3)^(-4/3),x]","-\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}}","-\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*(3 - x)*(1 + x))/(20*(9 + 3*x - 5*x^2 + x^3)^(4/3)) + (9*(3 - x)^2*(1 + x))/(80*(9 + 3*x - 5*x^2 + x^3)^(4/3)) - (27*(3 - x)^3*(1 + x))/(320*(9 + 3*x - 5*x^2 + x^3)^(4/3))","A",5,4,17,0.2353,1,"{2067, 2064, 45, 37}"
235,1,19,0,0.0137482,"\int \frac{1}{\sqrt{4+3 x-2 x^2}} \, dx","Int[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",2,2,14,0.1429,1,"{619, 216}"
236,1,8,0,0.0052765,"\int \frac{1}{\sqrt{-3+4 x-x^2}} \, dx","Int[1/Sqrt[-3 + 4*x - x^2],x]","-\sin ^{-1}(2-x)","-\sin ^{-1}(2-x)",1,"-ArcSin[2 - x]","A",2,2,14,0.1429,1,"{619, 216}"
237,1,12,0,0.0044271,"\int \frac{1}{\sqrt{-2-5 x-3 x^2}} \, dx","Int[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",2,2,14,0.1429,1,"{619, 216}"
238,1,31,0,0.0075575,"\int \frac{1}{\sqrt{1-x^2} \left(4+x^2\right)} \, dx","Int[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",2,2,19,0.1053,1,"{377, 203}"
239,1,31,0,0.0099887,"\int \frac{1}{\left(4+x^2\right) \sqrt{1+4 x^2}} \, dx","Int[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",2,2,19,0.1053,1,"{377, 206}"
240,1,24,0,0.0192104,"\int \frac{x}{\left(3-x^2\right) \sqrt{5-x^2}} \, dx","Int[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",3,3,22,0.1364,1,"{444, 63, 207}"
241,1,25,0,0.0187771,"\int \frac{x}{\sqrt{3-x^2} \left(5-x^2\right)} \, dx","Int[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",3,3,22,0.1364,1,"{444, 63, 203}"
242,1,43,0,0.0197251,"\int \frac{1}{\sqrt{2+x^2} \left(-1+x^4\right)} \, dx","Int[1/(Sqrt[2 + x^2]*(-1 + x^4)),x]","-\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}}","-\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,"-ArcTan[x/Sqrt[2 + x^2]]/2 - ArcTanh[(Sqrt[3]*x)/Sqrt[2 + x^2]]/(2*Sqrt[3])","A",5,4,17,0.2353,1,"{1175, 377, 206, 203}"
243,1,62,0,0.0363772,"\int \frac{x}{\left(-1+x^2\right) \sqrt{4+2 x+x^2}} \, dx","Int[x/((-1 + x^2)*Sqrt[4 + 2*x + x^2]),x]","-\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}}","-\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,"-ArcTanh[(5 + 2*x)/(Sqrt[7]*Sqrt[4 + 2*x + x^2])]/(2*Sqrt[7]) - ArcTanh[Sqrt[4 + 2*x + x^2]/Sqrt[3]]/(2*Sqrt[3])","A",5,5,21,0.2381,1,"{1033, 724, 206, 688, 207}"
244,1,82,0,0.1211049,"\int \frac{1}{\sqrt{5+2 x+x^2} \left(-8+x^3\right)} \, dx","Int[1/(Sqrt[5 + 2*x + x^2]*(-8 + x^3)),x]","-\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)","-\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,"-ArcTan[(1 + x)/(Sqrt[3]*Sqrt[5 + 2*x + x^2])]/(4*Sqrt[3]) - ArcTanh[(7 + 3*x)/(Sqrt[13]*Sqrt[5 + 2*x + x^2])]/(12*Sqrt[13]) + ArcTanh[Sqrt[5 + 2*x + x^2]]/12","A",9,7,20,0.3500,1,"{2074, 724, 206, 1025, 982, 204, 1024}"
245,1,63,0,0.0541548,"\int \frac{x}{\left(4+x+x^2\right) \sqrt{5+4 x+4 x^2}} \, dx","Int[x/((4 + x + x^2)*Sqrt[5 + 4*x + 4*x^2]),x]","\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}}","\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,"ArcTan[Sqrt[5 + 4*x + 4*x^2]/Sqrt[11]]/Sqrt[11] - ArcTanh[(Sqrt[11/15]*(1 + 2*x))/Sqrt[5 + 4*x + 4*x^2]]/Sqrt[165]","A",5,5,24,0.2083,1,"{1025, 982, 207, 1024, 204}"
246,1,56,0,0.0466675,"\int \frac{3+x}{\left(1+x^2\right) \sqrt{1+x+x^2}} \, dx","Int[(3 + x)/((1 + x^2)*Sqrt[1 + x + x^2]),x]","\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)","\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,"-2*Sqrt[2]*ArcTan[(1 - x)/(Sqrt[2]*Sqrt[1 + x + x^2])] + Sqrt[2]*ArcTanh[(1 + x)/(Sqrt[2]*Sqrt[1 + x + x^2])]","A",5,4,21,0.1905,1,"{1036, 1030, 207, 203}"
247,1,70,0,0.0638688,"\int \frac{1+2 x}{\sqrt{-1+6 x+x^2} \left(4+4 x+3 x^2\right)} \, dx","Int[(1 + 2*x)/(Sqrt[-1 + 6*x + x^2]*(4 + 4*x + 3*x^2)),x]","-\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}}","-\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,"(-5*ArcTan[(Sqrt[7/2]*(2 - x))/(2*Sqrt[-1 + 6*x + x^2])])/(6*Sqrt[14]) - ArcTanh[(Sqrt[7]*(1 + x))/Sqrt[-1 + 6*x + x^2]]/(3*Sqrt[7])","A",5,4,30,0.1333,1,"{1035, 1029, 207, 203}"
248,1,89,0,0.1233043,"\int \frac{B+A x}{\left(17-18 x+5 x^2\right) \sqrt{13-22 x+10 x^2}} \, dx","Int[(B + A*x)/((17 - 18*x + 5*x^2)*Sqrt[13 - 22*x + 10*x^2]),x]","-\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} (-x (A+B)+A+B)}{2 \sqrt{10 x^2-22 x+13} (A+B)}\right)}{2 \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,"-(((2*A + B)*ArcTan[(Sqrt[35]*(2 - x))/Sqrt[13 - 22*x + 10*x^2]])/Sqrt[35]) - ((A + B)*ArcTanh[(Sqrt[35]*(A + B - (A + B)*x))/(2*(A + B)*Sqrt[13 - 22*x + 10*x^2])])/(2*Sqrt[35])","A",5,4,32,0.1250,1,"{1035, 1029, 206, 204}"
249,1,38,0,0.0238798,"\int \frac{-2+x}{\left(17-18 x+5 x^2\right) \sqrt{13-22 x+10 x^2}} \, dx","Int[(-2 + x)/((17 - 18*x + 5*x^2)*Sqrt[13 - 22*x + 10*x^2]),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{35} (1-x)}{2 \sqrt{10 x^2-22 x+13}}\right)}{2 \sqrt{35}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{35} (1-x)}{2 \sqrt{10 x^2-22 x+13}}\right)}{2 \sqrt{35}}",1,"ArcTanh[(Sqrt[35]*(1 - x))/(2*Sqrt[13 - 22*x + 10*x^2])]/(2*Sqrt[35])","A",2,2,30,0.06667,1,"{1029, 206}"
250,1,65,0,0.0173211,"\int x^4 \sqrt{5-x^2} \, dx","Int[x^4*Sqrt[5 - x^2],x]","\frac{1}{6} \sqrt{5-x^2} x^5-\frac{5}{24} \sqrt{5-x^2} x^3-\frac{25}{16} \sqrt{5-x^2} x+\frac{125}{16} \sin ^{-1}\left(\frac{x}{\sqrt{5}}\right)","\frac{1}{6} \sqrt{5-x^2} x^5-\frac{5}{24} \sqrt{5-x^2} x^3-\frac{25}{16} \sqrt{5-x^2} x+\frac{125}{16} \sin ^{-1}\left(\frac{x}{\sqrt{5}}\right)",1,"(-25*x*Sqrt[5 - x^2])/16 - (5*x^3*Sqrt[5 - x^2])/24 + (x^5*Sqrt[5 - x^2])/6 + (125*ArcSin[x/Sqrt[5]])/16","A",4,3,15,0.2000,1,"{279, 321, 216}"
251,1,49,0,0.0110739,"\int \frac{1}{x^6 \sqrt{2+x^2}} \, dx","Int[1/(x^6*Sqrt[2 + x^2]),x]","-\frac{\sqrt{x^2+2}}{15 x}+\frac{\sqrt{x^2+2}}{15 x^3}-\frac{\sqrt{x^2+2}}{10 x^5}","-\frac{\sqrt{x^2+2}}{15 x}+\frac{\sqrt{x^2+2}}{15 x^3}-\frac{\sqrt{x^2+2}}{10 x^5}",1,"-Sqrt[2 + x^2]/(10*x^5) + Sqrt[2 + x^2]/(15*x^3) - Sqrt[2 + x^2]/(15*x)","A",3,2,13,0.1538,1,"{271, 264}"
252,1,49,0,0.0077619,"\int \frac{1}{\left(3+2 x^2\right)^{7/2}} \, dx","Int[(3 + 2*x^2)^(-7/2),x]","\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}}","\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/(15*(3 + 2*x^2)^(5/2)) + (4*x)/(135*(3 + 2*x^2)^(3/2)) + (8*x)/(405*Sqrt[3 + 2*x^2])","A",3,2,11,0.1818,1,"{192, 191}"
253,1,12,0,0.0468336,"\int \frac{x}{1+x^2+a \sqrt{1+x^2}} \, dx","Int[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",3,2,20,0.1000,1,"{2155, 31}"
254,1,12,0,0.0127955,"\int \frac{1-x+x^2}{\left(1+x^2\right)^{3/2}} \, dx","Int[(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",2,2,18,0.1111,1,"{1814, 215}"
255,1,27,0,0.0110565,"\int \frac{\sqrt{1+x^2}}{2+x^2} \, dx","Int[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",4,4,17,0.2353,1,"{402, 215, 377, 206}"
256,1,48,0,0.0135447,"\int \frac{1}{\sqrt{1+x^2} \left(2+x^2\right)^2} \, dx","Int[1/(Sqrt[1 + x^2]*(2 + x^2)^2),x]","\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)}","\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,"-(x*Sqrt[1 + x^2])/(4*(2 + x^2)) + (3*ArcTanh[x/(Sqrt[2]*Sqrt[1 + x^2])])/(4*Sqrt[2])","A",3,3,17,0.1765,1,"{382, 377, 206}"
257,1,41,0,0.0218235,"\int \frac{x^2}{\left(-6+x^2\right) \sqrt{-2+x^2}} \, dx","Int[x^2/((-6 + x^2)*Sqrt[-2 + x^2]),x]","\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)","\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,"ArcTanh[x/Sqrt[-2 + x^2]] - Sqrt[3/2]*ArcTanh[(Sqrt[2/3]*x)/Sqrt[-2 + x^2]]","A",5,5,20,0.2500,1,"{483, 217, 206, 377, 207}"
258,1,47,0,0.020665,"\int \frac{5+x^2}{\sqrt{1-x^2} \left(1+x^2\right)^2} \, dx","Int[(5 + x^2)/(Sqrt[1 - x^2]*(1 + x^2)^2),x]","\frac{\sqrt{1-x^2} x}{x^2+1}+2 \sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{1-x^2}}\right)","\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) + 2*Sqrt[2]*ArcTan[(Sqrt[2]*x)/Sqrt[1 - x^2]]","A",4,4,24,0.1667,1,"{527, 12, 377, 203}"
259,1,88,0,0.2387555,"\int \frac{4 x-\sqrt{1-x^2}}{5+\sqrt{1-x^2}} \, dx","Int[(4*x - Sqrt[1 - x^2])/(5 + Sqrt[1 - x^2]),x]","-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}}","-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[(5*x)/(2*Sqrt[6]*Sqrt[1 - x^2])])/(2*Sqrt[6]) + 20*Log[5 + Sqrt[1 - x^2]]","A",15,9,33,0.2727,1,"{6742, 1591, 190, 43, 6740, 203, 402, 216, 377}"
260,1,136,0,1.4960856,"\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","Int[(x^2*(2 - Sqrt[1 + x^2]))/(Sqrt[1 + x^2]*(1 - x^3 + (1 + x^2)^(3/2))),x]","-\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)","-\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,"(8*x)/9 - x^2/6 + (8*Sqrt[1 + x^2])/9 - (x*Sqrt[1 + x^2])/6 - (41*ArcSinh[x])/54 + (4*Sqrt[2]*ArcTan[(1 + 3*x)/(2*Sqrt[2])])/27 + (4*Sqrt[2]*ArcTan[(1 + x)/(Sqrt[2]*Sqrt[1 + x^2])])/27 + (7*ArcTanh[(1 - x)/(2*Sqrt[1 + x^2])])/27 - (7*Log[3 + 2*x + 3*x^2])/54","A",32,14,44,0.3182,1,"{6742, 195, 215, 634, 618, 204, 628, 1020, 12, 1081, 1037, 1031, 206, 261}"
261,1,64,0,0.0172441,"\int x \sqrt{2 r x-x^2} \, dx","Int[x*Sqrt[2*r*x - x^2],x]","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}","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,"-(r*(r - x)*Sqrt[2*r*x - x^2])/2 - (2*r*x - x^2)^(3/2)/3 + r^3*ArcTan[x/Sqrt[2*r*x - x^2]]","A",4,4,16,0.2500,1,"{640, 612, 620, 203}"
262,1,89,0,0.0296294,"\int x^2 \sqrt{2 r x-x^2} \, dx","Int[x^2*Sqrt[2*r*x - x^2],x]","-\frac{5}{8} r^2 (r-x) \sqrt{2 r x-x^2}+\frac{5}{4} r^4 \tan ^{-1}\left(\frac{x}{\sqrt{2 r x-x^2}}\right)-\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}","-\frac{5}{8} r^2 (r-x) \sqrt{2 r x-x^2}+\frac{5}{4} r^4 \tan ^{-1}\left(\frac{x}{\sqrt{2 r x-x^2}}\right)-\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,"(-5*r^2*(r - x)*Sqrt[2*r*x - x^2])/8 - (5*r*(2*r*x - x^2)^(3/2))/12 - (x*(2*r*x - x^2)^(3/2))/4 + (5*r^4*ArcTan[x/Sqrt[2*r*x - x^2]])/4","A",5,5,18,0.2778,1,"{670, 640, 612, 620, 203}"
263,1,113,0,0.0427148,"\int x^3 \sqrt{2 r x-x^2} \, dx","Int[x^3*Sqrt[2*r*x - x^2],x]","-\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}{4} r^5 \tan ^{-1}\left(\frac{x}{\sqrt{2 r x-x^2}}\right)-\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}","-\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}{4} r^5 \tan ^{-1}\left(\frac{x}{\sqrt{2 r x-x^2}}\right)-\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,"(-7*r^3*(r - x)*Sqrt[2*r*x - x^2])/8 - (7*r^2*(2*r*x - x^2)^(3/2))/12 - (7*r*x*(2*r*x - x^2)^(3/2))/20 - (x^2*(2*r*x - x^2)^(3/2))/5 + (7*r^5*ArcTan[x/Sqrt[2*r*x - x^2]])/4","A",6,5,18,0.2778,1,"{670, 640, 612, 620, 203}"
264,1,49,0,0.0305797,"\int \frac{1}{\left(-1+x^2\right) \sqrt{2 x+x^2}} \, dx","Int[1/((-1 + x^2)*Sqrt[2*x + x^2]),x]","-\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}}","-\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,"-ArcTan[Sqrt[2*x + x^2]]/2 - ArcTanh[(1 + 2*x)/(Sqrt[3]*Sqrt[2*x + x^2])]/(2*Sqrt[3])","A",5,5,19,0.2632,1,"{984, 688, 204, 724, 206}"
265,1,79,0,0.044347,"\int \frac{-2+3 x}{(1+x)^3 \sqrt{2 x-x^2}} \, dx","Int[(-2 + 3*x)/((1 + x)^3*Sqrt[2*x - x^2]),x]","-\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}}","-\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,"(-5*Sqrt[2*x - x^2])/(6*(1 + x)^2) - (2*Sqrt[2*x - x^2])/(3*(1 + x)) + ArcTan[(1 - 2*x)/(Sqrt[3]*Sqrt[2*x - x^2])]/(2*Sqrt[3])","A",4,4,24,0.1667,1,"{834, 806, 724, 204}"
266,1,12,0,0.0075392,"\int \frac{1}{\sqrt{1+x+x^2}} \, dx","Int[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",2,2,10,0.2000,1,"{619, 215}"
267,1,53,0,0.023292,"\int \frac{x^3}{\sqrt{1+x+x^2}} \, dx","Int[x^3/Sqrt[1 + x + x^2],x]","\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)","\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,"(x^2*Sqrt[1 + x + x^2])/3 - ((1 + 10*x)*Sqrt[1 + x + x^2])/24 + (7*ArcSinh[(1 + 2*x)/Sqrt[3]])/16","A",4,4,14,0.2857,1,"{742, 779, 619, 215}"
268,1,19,0,0.0019644,"\int \frac{1}{\left(1+x+x^2\right)^{3/2}} \, dx","Int[(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",1,1,10,0.1000,1,"{613}"
269,1,17,0,0.003884,"\int \frac{x}{\left(1+x+x^2\right)^{3/2}} \, dx","Int[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",1,1,12,0.08333,1,"{636}"
270,1,56,0,0.0240697,"\int \frac{x^3}{\left(1+x+x^2\right)^{3/2}} \, dx","Int[x^3/(1 + x + x^2)^(3/2),x]","-\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)","-\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,"(-2*x^2*(2 + x))/(3*Sqrt[1 + x + x^2]) + ((5 + 2*x)*Sqrt[1 + x + x^2])/3 - (3*ArcSinh[(1 + 2*x)/Sqrt[3]])/2","A",4,4,14,0.2857,1,"{738, 779, 619, 215}"
271,1,65,0,0.0242333,"\int x^2 \sqrt{1+x+x^2} \, dx","Int[x^2*Sqrt[1 + x + x^2],x]","\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)","\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,"((1 + 2*x)*Sqrt[1 + x + x^2])/64 - (5*(1 + x + x^2)^(3/2))/24 + (x*(1 + x + x^2)^(3/2))/4 + (3*ArcSinh[(1 + 2*x)/Sqrt[3]])/128","A",5,5,14,0.3571,1,"{742, 640, 612, 619, 215}"
272,1,55,0,0.0138136,"\int \left(1+x+x^2\right)^{3/2} \, dx","Int[(1 + x + x^2)^(3/2),x]","\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)","\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,"(9*(1 + 2*x)*Sqrt[1 + x + x^2])/64 + ((1 + 2*x)*(1 + x + x^2)^(3/2))/8 + (27*ArcSinh[(1 + 2*x)/Sqrt[3]])/128","A",4,3,10,0.3000,1,"{612, 619, 215}"
273,1,74,0,0.0190233,"\int \left(1+x+x^2\right)^{5/2} \, dx","Int[(1 + x + x^2)^(5/2),x]","\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}","\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,"(45*(1 + 2*x)*Sqrt[1 + x + x^2])/512 + (5*(1 + 2*x)*(1 + x + x^2)^(3/2))/64 + ((1 + 2*x)*(1 + x + x^2)^(5/2))/12 + (135*ArcSinh[(1 + 2*x)/Sqrt[3]])/1024","A",5,3,10,0.3000,1,"{612, 619, 215}"
274,1,38,0,0.0131642,"\int \frac{1}{x^2 \sqrt{1+x+x^2}} \, dx","Int[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",3,3,14,0.2143,1,"{730, 724, 206}"
275,1,57,0,0.0239868,"\int \frac{1}{x^3 \sqrt{1+x+x^2}} \, dx","Int[1/(x^3*Sqrt[1 + x + x^2]),x]","\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)","\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,"-Sqrt[1 + x + x^2]/(2*x^2) + (3*Sqrt[1 + x + x^2])/(4*x) + ArcTanh[(2 + x)/(2*Sqrt[1 + x + x^2])]/8","A",4,4,14,0.2857,1,"{744, 806, 724, 206}"
276,1,62,0,0.0266347,"\int \frac{1}{x^2 \left(1+x+x^2\right)^{3/2}} \, dx","Int[1/(x^2*(1 + x + x^2)^(3/2)),x]","\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)","\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,"(2*(1 - x))/(3*x*Sqrt[1 + x + x^2]) - (5*Sqrt[1 + x + x^2])/(3*x) + (3*ArcTanh[(2 + x)/(2*Sqrt[1 + x + x^2])])/2","A",4,4,14,0.2857,1,"{740, 806, 724, 206}"
277,1,79,0,0.0371738,"\int \frac{1}{x^3 \left(1+x+x^2\right)^{3/2}} \, dx","Int[1/(x^3*(1 + x + x^2)^(3/2)),x]","\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)","\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,"(2*(1 - x))/(3*x^2*Sqrt[1 + x + x^2]) - (7*Sqrt[1 + x + x^2])/(6*x^2) + (37*Sqrt[1 + x + x^2])/(12*x) - (3*ArcTanh[(2 + x)/(2*Sqrt[1 + x + x^2])])/8","A",5,5,14,0.3571,1,"{740, 834, 806, 724, 206}"
278,1,22,0,0.0092097,"\int \frac{1}{(1+x) \sqrt{1+x+x^2}} \, dx","Int[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",2,2,16,0.1250,1,"{724, 206}"
279,1,86,0,0.2781943,"\int \frac{1}{\sqrt{4+2 x+x^2} \left(-x+x^3\right)} \, dx","Int[1/(Sqrt[4 + 2*x + x^2]*(-x + x^3)),x]","\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}}","\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,"ArcTanh[(4 + x)/(2*Sqrt[4 + 2*x + x^2])]/2 - ArcTanh[(5 + 2*x)/(Sqrt[7]*Sqrt[4 + 2*x + x^2])]/(2*Sqrt[7]) - ArcTanh[Sqrt[4 + 2*x + x^2]/Sqrt[3]]/(2*Sqrt[3])","A",10,7,22,0.3182,1,"{1593, 6725, 724, 206, 1033, 688, 207}"
280,1,62,0,0.0465202,"\int \frac{\sqrt{4+2 x+x^2}}{(-1+x)^2} \, dx","Int[Sqrt[4 + 2*x + x^2]/(-1 + x)^2,x]","\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)","\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",6,6,18,0.3333,1,"{732, 843, 619, 215, 724, 206}"
281,1,76,0,0.0677463,"\int \frac{3+2 x}{\left(3+2 x+x^2\right)^2 \sqrt{4+2 x+x^2}} \, dx","Int[(3 + 2*x)/((3 + 2*x + x^2)^2*Sqrt[4 + 2*x + x^2]),x]","-\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)","-\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,"-((3 - x)*Sqrt[4 + 2*x + x^2])/(4*(3 + 2*x + x^2)) - ArcTan[(1 + x)/(Sqrt[2]*Sqrt[4 + 2*x + x^2])]/(4*Sqrt[2]) + ArcTanh[Sqrt[4 + 2*x + x^2]]","A",6,6,28,0.2143,1,"{1016, 1025, 982, 204, 1024, 206}"
282,1,36,0,0.127551,"\int \frac{3 x^2+2 x^3}{\sqrt{-3+2 x+x^2} \left(-3+x+2 x^2\right)} \, dx","Int[(3*x^2 + 2*x^3)/(Sqrt[-3 + 2*x + x^2]*(-3 + x + 2*x^2)),x]","\frac{\sqrt{x^2+2 x-3}}{2 (1-x)}+\sqrt{x^2+2 x-3}","\frac{\sqrt{x^2+2 x-3}}{2 (1-x)}+\sqrt{x^2+2 x-3}",1,"Sqrt[-3 + 2*x + x^2] + Sqrt[-3 + 2*x + x^2]/(2*(1 - x))","A",4,4,34,0.1176,1,"{1593, 1586, 1638, 650}"
283,1,87,0,0.2093466,"\int \frac{1+x^4}{\left(1+x+x^2\right) \sqrt{2+x+x^2}} \, dx","Int[(1 + x^4)/((1 + x + x^2)*Sqrt[2 + x + x^2]),x]","\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)","\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,"(-7*Sqrt[2 + x + x^2])/4 + (x*Sqrt[2 + x + x^2])/2 - ArcSinh[(1 + 2*x)/Sqrt[7]]/8 + ArcTan[(1 + 2*x)/(Sqrt[3]*Sqrt[2 + x + x^2])]/Sqrt[3] - ArcTanh[Sqrt[2 + x + x^2]]","A",14,10,24,0.4167,1,"{6728, 640, 619, 215, 742, 1025, 982, 204, 1024, 206}"
284,1,58,0,0.0107579,"\int \frac{1}{\left(4+2 x+x^2\right)^{7/2}} \, dx","Int[(4 + 2*x + x^2)^(-7/2),x]","\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}}","\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)/(15*(4 + 2*x + x^2)^(5/2)) + (4*(1 + x))/(135*(4 + 2*x + x^2)^(3/2)) + (8*(1 + x))/(405*Sqrt[4 + 2*x + x^2])","A",3,2,12,0.1667,1,"{614, 613}"
285,1,47,0,0.0072238,"\int \frac{1}{\left(1+8 x+3 x^2\right)^{5/2}} \, dx","Int[(1 + 8*x + 3*x^2)^(-5/2),x]","\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}}","\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)/(39*(1 + 8*x + 3*x^2)^(3/2)) + (2*(4 + 3*x))/(169*Sqrt[1 + 8*x + 3*x^2])","A",2,2,14,0.1429,1,"{614, 613}"
286,1,47,0,0.0076841,"\int \frac{1}{\left(5+4 x-3 x^2\right)^{5/2}} \, dx","Int[(5 + 4*x - 3*x^2)^(-5/2),x]","-\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}}","-\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,"-(2 - 3*x)/(57*(5 + 4*x - 3*x^2)^(3/2)) - (2*(2 - 3*x))/(361*Sqrt[5 + 4*x - 3*x^2])","A",2,2,14,0.1429,1,"{614, 613}"
287,1,29,0,0.0385381,"\int \frac{1}{1+\sqrt{2+2 x+x^2}} \, dx","Int[(1 + Sqrt[2 + 2*x + x^2])^(-1),x]","-\frac{\sqrt{x^2+2 x+2}}{x+1}+\frac{1}{x+1}+\sinh ^{-1}(x+1)","-\frac{\sqrt{x^2+2 x+2}}{x+1}+\frac{1}{x+1}+\sinh ^{-1}(x+1)",1,"(1 + x)^(-1) - Sqrt[2 + 2*x + x^2]/(1 + x) + ArcSinh[1 + x]","A",5,4,16,0.2500,1,"{6742, 684, 619, 215}"
288,1,59,0,0.0324864,"\int \frac{1}{x+\sqrt{1+x+x^2}} \, dx","Int[(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",3,2,14,0.1429,1,"{2116, 893}"
289,1,79,0,0.135887,"\int \frac{x^2}{1+2 x+2 \sqrt{1+x+x^2}} \, dx","Int[x^2/(1 + 2*x + 2*Sqrt[1 + x + x^2]),x]","-\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)","-\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,"-x^3/9 - x^4/6 + ((1 + 2*x)*Sqrt[1 + x + x^2])/96 - (5*(1 + x + x^2)^(3/2))/36 + (x*(1 + x + x^2)^(3/2))/6 + ArcSinh[(1 + 2*x)/Sqrt[3]]/64","A",7,6,23,0.2609,1,"{6742, 742, 640, 612, 619, 215}"
290,1,80,0,0.3434714,"\int \frac{-3 x+\sqrt{1+x+x^2}}{-1+\sqrt{1+x+x^2}} \, dx","Int[(-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",26,8,29,0.2759,1,"{6742, 734, 843, 619, 215, 724, 206, 6740}"
291,1,158,0,0.5257333,"\int \frac{1+x}{-\sqrt{1+x+x^2}+\sqrt{4+2 x+x^2}} \, dx","Int[(1 + x)/(-Sqrt[1 + x + x^2] + Sqrt[4 + 2*x + x^2]),x]","\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)","\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,"-2*Sqrt[1 + x + x^2] + ((1 + 2*x)*Sqrt[1 + x + x^2])/4 - 2*Sqrt[4 + 2*x + x^2] + ((1 + x)*Sqrt[4 + 2*x + x^2])/2 + (11*ArcSinh[(1 + x)/Sqrt[3]])/2 + (43*ArcSinh[(1 + 2*x)/Sqrt[3]])/8 - 2*Sqrt[7]*ArcTanh[(1 + 5*x)/(2*Sqrt[7]*Sqrt[1 + x + x^2])] + 2*Sqrt[7]*ArcTanh[(1 - 2*x)/(Sqrt[7]*Sqrt[4 + 2*x + x^2])]","A",36,8,31,0.2581,1,"{6742, 734, 843, 619, 215, 724, 206, 612}"
292,1,41,0,0.0085171,"\int \frac{1}{\sqrt{-1+x} x^3} \, dx","Int[1/(Sqrt[-1 + x]*x^3),x]","\frac{\sqrt{x-1}}{2 x^2}+\frac{3 \sqrt{x-1}}{4 x}+\frac{3}{4} \tan ^{-1}\left(\sqrt{x-1}\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,"Sqrt[-1 + x]/(2*x^2) + (3*Sqrt[-1 + x])/(4*x) + (3*ArcTan[Sqrt[-1 + x]])/4","A",4,3,11,0.2727,1,"{51, 63, 203}"
293,1,13,0,0.0037591,"\int \frac{1}{\left(1-\frac{3}{x}\right)^{4/3} x^2} \, dx","Int[1/((1 - 3/x)^(4/3)*x^2),x]","-\frac{1}{\sqrt[3]{1-\frac{3}{x}}}","-\frac{1}{\sqrt[3]{1-\frac{3}{x}}}",1,"-(1 - 3/x)^(-1/3)","A",1,1,15,0.06667,1,"{261}"
294,1,71,0,0.0275319,"\int \frac{(-1+3 x)^{4/3}}{x^2} \, dx","Int[(-1 + 3*x)^(4/3)/x^2,x]","-\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)","-\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,"12*(-1 + 3*x)^(1/3) - (-1 + 3*x)^(4/3)/x + 4*Sqrt[3]*ArcTan[(1 - 2*(-1 + 3*x)^(1/3))/Sqrt[3]] + 2*Log[x] - 6*Log[1 + (-1 + 3*x)^(1/3)]","A",6,6,13,0.4615,1,"{47, 50, 58, 618, 204, 31}"
295,1,40,0,0.0072651,"\int (4-3 x)^{4/3} x^2 \, dx","Int[(4 - 3*x)^(4/3)*x^2,x]","-\frac{1}{117} (4-3 x)^{13/3}+\frac{4}{45} (4-3 x)^{10/3}-\frac{16}{63} (4-3 x)^{7/3}","-\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,"(-16*(4 - 3*x)^(7/3))/63 + (4*(4 - 3*x)^(10/3))/45 - (4 - 3*x)^(13/3)/117","A",2,1,13,0.07692,1,"{43}"
296,1,48,0,0.0176575,"\int \frac{\left(1-2 \sqrt[3]{x}\right)^{3/4}}{x} \, dx","Int[(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",6,6,17,0.3529,1,"{266, 50, 63, 298, 203, 206}"
297,1,69,0,0.0195488,"\int \frac{x}{\left(3-2 \sqrt{x}\right)^{3/4}} \, dx","Int[x/(3 - 2*Sqrt[x])^(3/4),x]","\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}}","\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,"(-27*(3 - 2*Sqrt[x])^(1/4))/2 + (27*(3 - 2*Sqrt[x])^(5/4))/10 - (3 - 2*Sqrt[x])^(9/4)/2 + (3 - 2*Sqrt[x])^(13/4)/26","A",3,2,15,0.1333,1,"{266, 43}"
298,1,193,0,0.1132486,"\int \frac{\left(-1+2 \sqrt{x}\right)^{5/4}}{x^2} \, dx","Int[(-1 + 2*Sqrt[x])^(5/4)/x^2,x]","-\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}}","-\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,"-((-1 + 2*Sqrt[x])^(5/4)/x) - (5*(-1 + 2*Sqrt[x])^(1/4))/(2*Sqrt[x]) - (5*ArcTan[1 - Sqrt[2]*(-1 + 2*Sqrt[x])^(1/4)])/(2*Sqrt[2]) + (5*ArcTan[1 + Sqrt[2]*(-1 + 2*Sqrt[x])^(1/4)])/(2*Sqrt[2]) - (5*Log[1 - Sqrt[2]*(-1 + 2*Sqrt[x])^(1/4) + Sqrt[-1 + 2*Sqrt[x]]])/(4*Sqrt[2]) + (5*Log[1 + Sqrt[2]*(-1 + 2*Sqrt[x])^(1/4) + Sqrt[-1 + 2*Sqrt[x]]])/(4*Sqrt[2])","A",13,9,17,0.5294,1,"{266, 47, 63, 211, 1165, 628, 1162, 617, 204}"
299,1,13,0,0.0027798,"\int x^6 \sqrt[3]{1+x^7} \, dx","Int[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",1,1,13,0.07692,1,"{261}"
300,1,13,0,0.0029647,"\int \frac{x^6}{\left(1+x^7\right)^{5/3}} \, dx","Int[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",1,1,13,0.07692,1,"{261}"
301,1,59,0,0.0371693,"\int \frac{1}{x \left(-27+2 x^7\right)^{2/3}} \, dx","Int[1/(x*(-27 + 2*x^7)^(2/3)),x]","\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}","\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[x]/18 + Log[3 + (-27 + 2*x^7)^(1/3)]/42","A",5,5,15,0.3333,1,"{266, 58, 618, 204, 31}"
302,1,70,0,0.0378973,"\int \frac{\left(1+x^7\right)^{2/3}}{x^8} \, dx","Int[(1 + x^7)^(2/3)/x^8,x]","-\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}","-\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,"-(1 + x^7)^(2/3)/(7*x^7) + (2*ArcTan[(1 + 2*(1 + x^7)^(1/3))/Sqrt[3]])/(7*Sqrt[3]) - Log[x]/3 + Log[1 - (1 + x^7)^(1/3)]/7","A",6,6,13,0.4615,1,"{266, 47, 55, 618, 204, 31}"
303,1,68,0,0.0208885,"\int \frac{\sqrt[4]{3+4 x^4}}{x^2} \, dx","Int[(3 + 4*x^4)^(1/4)/x^2,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}}","-\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 + 4*x^4)^(1/4)/x) - ArcTan[(Sqrt[2]*x)/(3 + 4*x^4)^(1/4)]/Sqrt[2] + ArcTanh[(Sqrt[2]*x)/(3 + 4*x^4)^(1/4)]/Sqrt[2]","A",5,5,15,0.3333,1,"{277, 331, 298, 203, 206}"
304,1,93,0,0.0293518,"\int x^2 \left(3+4 x^4\right)^{5/4} \, dx","Int[x^2*(3 + 4*x^4)^(5/4),x]","\frac{1}{8} \left(4 x^4+3\right)^{5/4} x^3+\frac{15}{32} \sqrt[4]{4 x^4+3} x^3-\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-\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}}",1,"(15*x^3*(3 + 4*x^4)^(1/4))/32 + (x^3*(3 + 4*x^4)^(5/4))/8 - (45*ArcTan[(Sqrt[2]*x)/(3 + 4*x^4)^(1/4)])/(128*Sqrt[2]) + (45*ArcTanh[(Sqrt[2]*x)/(3 + 4*x^4)^(1/4)])/(128*Sqrt[2])","A",6,5,15,0.3333,1,"{279, 331, 298, 203, 206}"
305,1,93,0,0.0285984,"\int x^6 \sqrt[4]{3+4 x^4} \, dx","Int[x^6*(3 + 4*x^4)^(1/4),x]","\frac{1}{8} \sqrt[4]{4 x^4+3} x^7+\frac{3}{128} \sqrt[4]{4 x^4+3} x^3+\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+\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}}",1,"(3*x^3*(3 + 4*x^4)^(1/4))/128 + (x^7*(3 + 4*x^4)^(1/4))/8 + (27*ArcTan[(Sqrt[2]*x)/(3 + 4*x^4)^(1/4)])/(512*Sqrt[2]) - (27*ArcTanh[(Sqrt[2]*x)/(3 + 4*x^4)^(1/4)])/(512*Sqrt[2])","A",6,6,15,0.4000,1,"{279, 321, 331, 298, 203, 206}"
306,1,200,0,0.1439988,"\int \sqrt[3]{x \left(1-x^2\right)} \, dx","Int[(x*(1 - x^2))^(1/3),x]","\frac{1}{2} \sqrt[3]{x-x^3} x+\frac{\left(1-x^2\right)^{2/3} x^{2/3} \log \left(\frac{x^{4/3}}{\left(1-x^2\right)^{2/3}}-\frac{x^{2/3}}{\sqrt[3]{1-x^2}}+1\right)}{12 \left(x-x^3\right)^{2/3}}-\frac{\left(1-x^2\right)^{2/3} x^{2/3} \log \left(\frac{x^{2/3}}{\sqrt[3]{1-x^2}}+1\right)}{6 \left(x-x^3\right)^{2/3}}-\frac{\left(1-x^2\right)^{2/3} x^{2/3} \tan ^{-1}\left(\frac{1-\frac{2 x^{2/3}}{\sqrt[3]{1-x^2}}}{\sqrt{3}}\right)}{2 \sqrt{3} \left(x-x^3\right)^{2/3}}","\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,"(x*(x - x^3)^(1/3))/2 - (x^(2/3)*(1 - x^2)^(2/3)*ArcTan[(1 - (2*x^(2/3))/(1 - x^2)^(1/3))/Sqrt[3]])/(2*Sqrt[3]*(x - x^3)^(2/3)) + (x^(2/3)*(1 - x^2)^(2/3)*Log[1 + x^(4/3)/(1 - x^2)^(2/3) - x^(2/3)/(1 - x^2)^(1/3)])/(12*(x - x^3)^(2/3)) - (x^(2/3)*(1 - x^2)^(2/3)*Log[1 + x^(2/3)/(1 - x^2)^(1/3)])/(6*(x - x^3)^(2/3))","B",12,12,13,0.9231,1,"{1979, 2004, 2032, 329, 275, 331, 292, 31, 634, 618, 204, 628}"
307,1,114,0,0.1153343,"\int \sqrt{\left(1+\sqrt[3]{x}\right) x} \, dx","Int[Sqrt[(1 + x^(1/3))*x],x]","\frac{3}{5} \sqrt{x^{4/3}+x} x+\frac{3}{40} \sqrt{x^{4/3}+x} x^{2/3}-\frac{7}{80} \sqrt{x^{4/3}+x} \sqrt[3]{x}+\frac{7}{64} \sqrt{x^{4/3}+x}-\frac{21 \sqrt{x^{4/3}+x}}{128 \sqrt[3]{x}}+\frac{21}{128} \tanh ^{-1}\left(\frac{x^{2/3}}{\sqrt{x^{4/3}+x}}\right)","\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,"(7*Sqrt[x + x^(4/3)])/64 - (21*Sqrt[x + x^(4/3)])/(128*x^(1/3)) - (7*x^(1/3)*Sqrt[x + x^(4/3)])/80 + (3*x^(2/3)*Sqrt[x + x^(4/3)])/40 + (3*x*Sqrt[x + x^(4/3)])/5 + (21*ArcTanh[x^(2/3)/Sqrt[x + x^(4/3)]])/128","A",8,6,13,0.4615,1,"{1979, 2004, 2024, 2010, 2029, 206}"
308,1,34,0,0.0317954,"\int \frac{x^3}{\left(-1+x^4\right) \sqrt{1+2 x^8}} \, dx","Int[x^3/((-1 + x^4)*Sqrt[1 + 2*x^8]),x]","-\frac{\tanh ^{-1}\left(\frac{2 x^4+1}{\sqrt{3} \sqrt{2 x^8+1}}\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,"-ArcTanh[(1 + 2*x^4)/(Sqrt[3]*Sqrt[1 + 2*x^8])]/(4*Sqrt[3])","A",3,3,22,0.1364,1,"{1469, 725, 206}"
309,1,58,0,0.0370013,"\int x^9 \sqrt{1+x^5+x^{10}} \, dx","Int[x^9*Sqrt[1 + x^5 + x^10],x]","\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}-\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}-\frac{3}{80} \sinh ^{-1}\left(\frac{2 x^5+1}{\sqrt{3}}\right)",1,"-((1 + 2*x^5)*Sqrt[1 + x^5 + x^10])/40 + (1 + x^5 + x^10)^(3/2)/15 - (3*ArcSinh[(1 + 2*x^5)/Sqrt[3]])/80","A",5,5,16,0.3125,1,"{1357, 640, 612, 619, 215}"
310,1,71,0,0.0518186,"\int \frac{1}{x^5 \sqrt{4+2 x^2+x^4}} \, dx","Int[1/(x^5*Sqrt[4 + 2*x^2 + x^4]),x]","\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)","\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,"-Sqrt[4 + 2*x^2 + x^4]/(16*x^4) + (3*Sqrt[4 + 2*x^2 + x^4])/(64*x^2) + ArcTanh[(4 + x^2)/(2*Sqrt[4 + 2*x^2 + x^4])]/128","A",5,5,18,0.2778,1,"{1114, 744, 806, 724, 206}"
311,1,21,0,0.0291543,"\int \frac{-1+x^2}{x \sqrt{1+3 x^2+x^4}} \, dx","Int[(-1 + x^2)/(x*Sqrt[1 + 3*x^2 + x^4]),x]","\tanh ^{-1}\left(\frac{x^2+1}{\sqrt{x^4+3 x^2+1}}\right)","\tanh ^{-1}\left(\frac{x^2+1}{\sqrt{x^4+3 x^2+1}}\right)",1,"ArcTanh[(1 + x^2)/Sqrt[1 + 3*x^2 + x^4]]","A",3,3,23,0.1304,1,"{1251, 838, 206}"
312,1,17,0,0.0102869,"\int \left(-3 x+2 x^3\right) \left(-3 x^2+x^4\right)^{3/5} \, dx","Int[(-3*x + 2*x^3)*(-3*x^2 + x^4)^(3/5),x]","\frac{5}{16} \left(x^4-3 x^2\right)^{8/5}","\frac{5}{16} \left(x^4-3 x^2\right)^{8/5}",1,"(5*(-3*x^2 + x^4)^(8/5))/16","A",1,1,23,0.04348,1,"{1588}"
313,1,46,0,0.1932693,"\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","Int[(-2*x^5 + 3*x^8 - x^2*(-1 + 3*x^3)^(2/3))/(-1 + 3*x^3)^(3/4),x]","\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}","\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))/27 - (4*(-1 + 3*x^3)^(11/12))/33 + (4*(-1 + 3*x^3)^(9/4))/243","A",9,4,39,0.1026,1,"{6742, 266, 43, 261}"
314,1,107,0,0.0708598,"\int \frac{1}{\left(-1+x^3\right) \sqrt[3]{2+x^3}} \, dx","Int[1/((-1 + x^3)*(2 + x^3)^(1/3)),x]","\frac{\log \left(1-\frac{\sqrt[3]{3} x}{\sqrt[3]{x^3+2}}\right)}{3 \sqrt[3]{3}}-\frac{\log \left(\frac{3^{2/3} x^2}{\left(x^3+2\right)^{2/3}}+\frac{\sqrt[3]{3} x}{\sqrt[3]{x^3+2}}+1\right)}{6 \sqrt[3]{3}}-\frac{\tan ^{-1}\left(\frac{2 x}{\sqrt[6]{3} \sqrt[3]{x^3+2}}+\frac{1}{\sqrt{3}}\right)}{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,"-(ArcTan[1/Sqrt[3] + (2*x)/(3^(1/6)*(2 + x^3)^(1/3))]/3^(5/6)) + Log[1 - (3^(1/3)*x)/(2 + x^3)^(1/3)]/(3*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^(1/3))","A",7,7,17,0.4118,1,"{377, 200, 31, 634, 617, 204, 628}"
315,1,141,0,0.0602254,"\int \frac{1}{\left(1+x^4\right) \sqrt[4]{2+x^4}} \, dx","Int[1/((1 + x^4)*(2 + x^4)^(1/4)),x]","-\frac{\log \left(\frac{x^2}{\sqrt{x^4+2}}-\frac{\sqrt{2} x}{\sqrt[4]{x^4+2}}+1\right)}{4 \sqrt{2}}+\frac{\log \left(\frac{x^2}{\sqrt{x^4+2}}+\frac{\sqrt{2} x}{\sqrt[4]{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{x^2}{\sqrt{x^4+2}}-\frac{\sqrt{2} x}{\sqrt[4]{x^4+2}}+1\right)}{4 \sqrt{2}}+\frac{\log \left(\frac{x^2}{\sqrt{x^4+2}}+\frac{\sqrt{2} x}{\sqrt[4]{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}}",1,"-ArcTan[1 - (Sqrt[2]*x)/(2 + x^4)^(1/4)]/(2*Sqrt[2]) + ArcTan[1 + (Sqrt[2]*x)/(2 + x^4)^(1/4)]/(2*Sqrt[2]) - Log[1 + x^2/Sqrt[2 + x^4] - (Sqrt[2]*x)/(2 + x^4)^(1/4)]/(4*Sqrt[2]) + Log[1 + x^2/Sqrt[2 + x^4] + (Sqrt[2]*x)/(2 + x^4)^(1/4)]/(4*Sqrt[2])","A",10,7,17,0.4118,1,"{377, 211, 1165, 628, 1162, 617, 204}"
316,1,63,0,0.0112845,"\int \frac{-1+x^3}{\sqrt[3]{2+x^3}} \, dx","Int[(-1 + x^3)/(2 + x^3)^(1/3),x]","\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}}","\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,"(x*(2 + x^3)^(2/3))/3 - (5*ArcTan[(1 + (2*x)/(2 + x^3)^(1/3))/Sqrt[3]])/(3*Sqrt[3]) + (5*Log[-x + (2 + x^3)^(1/3)])/6","A",2,2,15,0.1333,1,"{388, 239}"
317,1,74,0,0.0243437,"\int \frac{\left(1+x^4\right)^{3/4}}{\left(2+x^4\right)^2} \, dx","Int[(1 + x^4)^(3/4)/(2 + x^4)^2,x]","\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}}","\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*(1 + x^4)^(3/4))/(8*(2 + x^4)) + (3*ArcTan[x/(2^(1/4)*(1 + x^4)^(1/4))])/(16*2^(3/4)) + (3*ArcTanh[x/(2^(1/4)*(1 + x^4)^(1/4))])/(16*2^(3/4))","A",5,5,17,0.2941,1,"{378, 377, 212, 206, 203}"
318,1,59,0,0.0117009,"\int \frac{\left(-2+x^5\right)^2}{\left(3+x^5\right)^{16/5}} \, dx","Int[(-2 + x^5)^2/(3 + x^5)^(16/5),x]","\frac{x \left(2-x^5\right)^2}{33 \left(x^5+3\right)^{11/5}}+\frac{10 x \left(2-x^5\right)}{297 \left(x^5+3\right)^{6/5}}+\frac{100 x}{891 \sqrt[5]{x^5+3}}","\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*(2 - x^5)^2)/(33*(3 + x^5)^(11/5)) + (10*x*(2 - x^5))/(297*(3 + x^5)^(6/5)) + (100*x)/(891*(3 + x^5)^(1/5))","A",3,2,17,0.1176,1,"{378, 191}"
319,1,123,0,0.0824654,"\int \frac{1}{\left(3 x+3 x^2+x^3\right) \sqrt[3]{3+3 x+3 x^2+x^3}} \, dx","Int[1/((3*x + 3*x^2 + x^3)*(3 + 3*x + 3*x^2 + x^3)^(1/3)),x]","\frac{\log \left(1-\frac{\sqrt[3]{3} (x+1)}{\sqrt[3]{(x+1)^3+2}}\right)}{3 \sqrt[3]{3}}-\frac{\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)}{6 \sqrt[3]{3}}-\frac{\tan ^{-1}\left(\frac{2 (x+1)}{\sqrt[6]{3} \sqrt[3]{(x+1)^3+2}}+\frac{1}{\sqrt{3}}\right)}{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,"-(ArcTan[1/Sqrt[3] + (2*(1 + x))/(3^(1/6)*(2 + (1 + x)^3)^(1/3))]/3^(5/6)) + Log[1 - (3^(1/3)*(1 + x))/(2 + (1 + x)^3)^(1/3)]/(3*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^(1/3))","A",9,9,32,0.2812,1,"{432, 431, 377, 200, 31, 634, 617, 204, 628}"
320,1,23,0,0.033677,"\int \frac{1-x^2}{\left(1+x^2\right) \sqrt{1+x^4}} \, dx","Int[(1 - x^2)/((1 + x^2)*Sqrt[1 + x^4]),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}}\right)}{\sqrt{2}}","\frac{\tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}}\right)}{\sqrt{2}}",1,"ArcTan[(Sqrt[2]*x)/Sqrt[1 + x^4]]/Sqrt[2]","A",2,2,24,0.08333,1,"{1699, 203}"
321,1,23,0,0.0359511,"\int \frac{1+x^2}{\left(1-x^2\right) \sqrt{1+x^4}} \, dx","Int[(1 + x^2)/((1 - x^2)*Sqrt[1 + x^4]),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}}\right)}{\sqrt{2}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}}\right)}{\sqrt{2}}",1,"ArcTanh[(Sqrt[2]*x)/Sqrt[1 + x^4]]/Sqrt[2]","A",2,2,24,0.08333,1,"{1699, 206}"
322,1,23,0,0.0241054,"\int \frac{1+x^2}{x \sqrt{1+x^4}} \, dx","Int[(1 + x^2)/(x*Sqrt[1 + x^4]),x]","\frac{1}{2} \sinh ^{-1}\left(x^2\right)-\frac{1}{2} \tanh ^{-1}\left(\sqrt{x^4+1}\right)","\tanh ^{-1}\left(\frac{x^2-1}{\sqrt{x^4+1}}\right)",1,"ArcSinh[x^2]/2 - ArcTanh[Sqrt[1 + x^4]]/2","A",6,6,18,0.3333,1,"{1252, 844, 215, 266, 63, 207}"
323,1,23,0,0.024671,"\int \frac{-1+x^2}{x \sqrt{1+x^4}} \, dx","Int[(-1 + x^2)/(x*Sqrt[1 + x^4]),x]","\frac{1}{2} \sinh ^{-1}\left(x^2\right)+\frac{1}{2} \tanh ^{-1}\left(\sqrt{x^4+1}\right)","\tanh ^{-1}\left(\frac{x^2+1}{\sqrt{x^4+1}}\right)",1,"ArcSinh[x^2]/2 + ArcTanh[Sqrt[1 + x^4]]/2","A",6,6,18,0.3333,1,"{1252, 844, 215, 266, 63, 207}"
324,1,26,0,0.0432189,"\int \frac{1+x^2}{\left(1-x^2\right) \sqrt{1+x^2+x^4}} \, dx","Int[(1 + x^2)/((1 - x^2)*Sqrt[1 + x^2 + x^4]),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{3} x}{\sqrt{x^4+x^2+1}}\right)}{\sqrt{3}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{3} x}{\sqrt{x^4+x^2+1}}\right)}{\sqrt{3}}",1,"ArcTanh[(Sqrt[3]*x)/Sqrt[1 + x^2 + x^4]]/Sqrt[3]","A",2,2,27,0.07407,1,"{1698, 206}"
325,1,15,0,0.0390042,"\int \frac{1-x^2}{\left(1+x^2\right) \sqrt{1+x^2+x^4}} \, dx","Int[(1 - x^2)/((1 + x^2)*Sqrt[1 + x^2 + x^4]),x]","\tan ^{-1}\left(\frac{x}{\sqrt{x^4+x^2+1}}\right)","\tan ^{-1}\left(\frac{x}{\sqrt{x^4+x^2+1}}\right)",1,"ArcTan[x/Sqrt[1 + x^2 + x^4]]","A",2,2,27,0.07407,1,"{1698, 203}"
326,1,16,0,0.0180566,"\int \frac{-1+x^4}{x^2 \sqrt{1+x^2+x^4}} \, dx","Int[(-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",1,1,21,0.04762,1,"{1590}"
327,1,74,0,0.2043046,"\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","Int[(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]","\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}}","\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,"ArcTan[(a + 2*(1 + a^2 - b)*x + a*x^2)/(Sqrt[2]*Sqrt[1 - b]*Sqrt[1 + 2*a*x + 2*b*x^2 + 2*a*x^3 + x^4])]/(Sqrt[2]*Sqrt[1 - b])","A",1,1,44,0.02273,1,"{2084}"
328,1,22,0,0.064396,"\int \frac{1}{\left(1+x^4\right) \sqrt{-x^2+\sqrt{1+x^4}}} \, dx","Int[1/((1 + x^4)*Sqrt[-x^2 + Sqrt[1 + x^4]]),x]","\tan ^{-1}\left(\frac{x}{\sqrt{\sqrt{x^4+1}-x^2}}\right)","\tan ^{-1}\left(\frac{x}{\sqrt{\sqrt{x^4+1}-x^2}}\right)",1,"ArcTan[x/Sqrt[-x^2 + Sqrt[1 + x^4]]]","A",2,2,27,0.07407,1,"{2128, 203}"
329,1,24,0,0.0678271,"\int \frac{1}{\left(1+x^{2 n}\right) \sqrt{-x^2+\left(1+x^{2 n}\right)^{\frac{1}{n}}}} \, dx","Int[1/((1 + x^(2*n))*Sqrt[-x^2 + (1 + x^(2*n))^n^(-1)]),x]","\tan ^{-1}\left(\frac{x}{\sqrt{\left(x^{2 n}+1\right)^{\frac{1}{n}}-x^2}}\right)","\tan ^{-1}\left(\frac{x}{\sqrt{\left(x^{2 n}+1\right)^{\frac{1}{n}}-x^2}}\right)",1,"ArcTan[x/Sqrt[-x^2 + (1 + x^(2*n))^n^(-1)]]","A",2,2,31,0.06452,1,"{2128, 203}"
330,1,14,0,0.0066023,"\int \cos ^2(x) \, dx","Int[Cos[x]^2,x]","\frac{x}{2}+\frac{1}{2} \sin (x) \cos (x)","\frac{x}{2}+\frac{1}{2} \sin (x) \cos (x)",1,"x/2 + (Cos[x]*Sin[x])/2","A",2,2,4,0.5000,1,"{2635, 8}"
331,1,11,0,0.0065874,"\int \cos ^3(x) \, dx","Int[Cos[x]^3,x]","\sin (x)-\frac{\sin ^3(x)}{3}","\sin (x)-\frac{\sin ^3(x)}{3}",1,"Sin[x] - Sin[x]^3/3","A",2,1,4,0.2500,1,"{2633}"
332,1,24,0,0.0099481,"\int \sin ^4(x) \, dx","Int[Sin[x]^4,x]","\frac{3 x}{8}-\frac{1}{4} \sin ^3(x) \cos (x)-\frac{3}{8} \sin (x) \cos (x)","\frac{3 x}{8}-\frac{1}{4} \sin ^3(x) \cos (x)-\frac{3}{8} \sin (x) \cos (x)",1,"(3*x)/8 - (3*Cos[x]*Sin[x])/8 - (Cos[x]*Sin[x]^3)/4","A",3,2,4,0.5000,1,"{2635, 8}"
333,1,34,0,0.0192104,"\int \cos ^6(x) \, dx","Int[Cos[x]^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)","\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 + (5*Cos[x]*Sin[x])/16 + (5*Cos[x]^3*Sin[x])/24 + (Cos[x]^5*Sin[x])/6","A",4,2,4,0.5000,1,"{2635, 8}"
334,1,44,0,0.0214529,"\int \sin ^8(x) \, dx","Int[Sin[x]^8,x]","\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)","\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 - (35*Cos[x]*Sin[x])/128 - (35*Cos[x]*Sin[x]^3)/192 - (7*Cos[x]*Sin[x]^5)/48 - (Cos[x]*Sin[x]^7)/8","A",5,2,4,0.5000,1,"{2635, 8}"
335,1,64,0,0.0160949,"\int \cos ^4\left(\frac{\pi }{4}+\frac{x}{2}\right) \, dx","Int[Cos[Pi/4 + x/2]^4,x]","\frac{3 x}{8}+\frac{1}{2} \sin \left(\frac{x}{2}+\frac{\pi }{4}\right) \cos ^3\left(\frac{x}{2}+\frac{\pi }{4}\right)+\frac{3}{4} \sin \left(\frac{x}{2}+\frac{\pi }{4}\right) \cos \left(\frac{x}{2}+\frac{\pi }{4}\right)","\frac{3 x}{8}+\frac{\cos (x)}{2}-\frac{1}{8} \sin (x) \cos (x)",1,"(3*x)/8 + (3*Cos[Pi/4 + x/2]*Sin[Pi/4 + x/2])/4 + (Cos[Pi/4 + x/2]^3*Sin[Pi/4 + x/2])/2","B",3,2,14,0.1429,1,"{2635, 8}"
336,1,31,0,0.0107794,"\int -\sin ^3\left(\frac{\pi }{12}-3 x\right) \, dx","Int[-Sin[Pi/12 - 3*x]^3,x]","\frac{1}{9} \cos ^3\left(\frac{\pi }{12}-3 x\right)-\frac{1}{3} \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,"-Cos[Pi/12 - 3*x]/3 + Cos[Pi/12 - 3*x]^3/9","A",2,1,14,0.07143,1,"{2633}"
337,1,21,0,0.0089103,"\int \csc ^6(x) \, dx","Int[Csc[x]^6,x]","-\frac{1}{5} \cot ^5(x)-\frac{2 \cot ^3(x)}{3}-\cot (x)","-\frac{1}{5} \cot ^5(x)-\frac{2 \cot ^3(x)}{3}-\cot (x)",1,"-Cot[x] - (2*Cot[x]^3)/3 - Cot[x]^5/5","A",2,1,4,0.2500,1,"{3767}"
338,1,36,0,0.0195031,"\int \csc ^7(x) \, dx","Int[Csc[x]^7,x]","-\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)","-\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*ArcTanh[Cos[x]])/16 - (5*Cot[x]*Csc[x])/16 - (5*Cot[x]*Csc[x]^3)/24 - (Cot[x]*Csc[x]^5)/6","A",4,2,4,0.5000,1,"{3768, 3770}"
339,1,41,0,0.0165278,"\int \sec ^{12}(x) \, dx","Int[Sec[x]^12,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)","\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,"Tan[x] + (5*Tan[x]^3)/3 + 2*Tan[x]^5 + (10*Tan[x]^7)/7 + (5*Tan[x]^9)/9 + Tan[x]^11/11","A",2,1,4,0.2500,1,"{3767}"
340,1,40,0,0.0123502,"\int \sec ^3\left(\frac{\pi }{4}+3 x\right) \, dx","Int[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",2,2,12,0.1667,1,"{3768, 3770}"
341,1,22,0,0.0137087,"\int \tan ^6(x) \, dx","Int[Tan[x]^6,x]","-x+\frac{\tan ^5(x)}{5}-\frac{\tan ^3(x)}{3}+\tan (x)","-x+\frac{\tan ^5(x)}{5}-\frac{\tan ^3(x)}{3}+\tan (x)",1,"-x + Tan[x] - Tan[x]^3/3 + Tan[x]^5/5","A",4,2,4,0.5000,1,"{3473, 8}"
342,1,20,0,0.0150477,"\int \cot ^5(x) \, dx","Int[Cot[x]^5,x]","-\frac{1}{4} \cot ^4(x)+\frac{\cot ^2(x)}{2}+\log (\sin (x))","-\frac{1}{4} \cot ^4(x)+\frac{\cot ^2(x)}{2}+\log (\sin (x))",1,"Cot[x]^2/2 - Cot[x]^4/4 + Log[Sin[x]]","A",3,2,4,0.5000,1,"{3473, 3475}"
343,1,32,0,0.0139363,"\int \cot ^4\left(\frac{\pi }{4}+\frac{x}{3}\right) \, dx","Int[Cot[Pi/4 + x/3]^4,x]","x-\cot ^3\left(\frac{x}{3}+\frac{\pi }{4}\right)+3 \cot \left(\frac{x}{3}+\frac{\pi }{4}\right)","x-\cot ^3\left(\frac{x}{3}+\frac{\pi }{4}\right)+3 \cot \left(\frac{x}{3}+\frac{\pi }{4}\right)",1,"x + 3*Cot[Pi/4 + x/3] - Cot[Pi/4 + x/3]^3","A",3,2,14,0.1429,1,"{3473, 8}"
344,1,56,0,0.0623641,"\int \cos ^6(x) \sin ^4(x) \, dx","Int[Cos[x]^6*Sin[x]^4,x]","\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)","\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 + (3*Cos[x]*Sin[x])/256 + (Cos[x]^3*Sin[x])/128 + (Cos[x]^5*Sin[x])/160 - (3*Cos[x]^7*Sin[x])/80 - (Cos[x]^7*Sin[x]^3)/10","A",6,3,9,0.3333,1,"{2568, 2635, 8}"
345,1,33,0,0.0300866,"\int \cos ^6(x) \sin ^7(x) \, dx","Int[Cos[x]^6*Sin[x]^7,x]","\frac{\cos ^{13}(x)}{13}-\frac{3 \cos ^{11}(x)}{11}+\frac{\cos ^9(x)}{3}-\frac{\cos ^7(x)}{7}","\frac{\cos ^{13}(x)}{13}-\frac{3 \cos ^{11}(x)}{11}+\frac{\cos ^9(x)}{3}-\frac{\cos ^7(x)}{7}",1,"-Cos[x]^7/7 + Cos[x]^9/3 - (3*Cos[x]^11)/11 + Cos[x]^13/13","A",3,2,9,0.2222,1,"{2565, 270}"
346,1,46,0,0.0280991,"\int \sin ^{10}(x) \tan (x) \, dx","Int[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",4,3,7,0.4286,1,"{2590, 266, 43}"
347,1,41,0,0.0338857,"\int \csc ^6(x) \sec ^6(x) \, dx","Int[Csc[x]^6*Sec[x]^6,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)","\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,"-10*Cot[x] - (5*Cot[x]^3)/3 - Cot[x]^5/5 + 10*Tan[x] + (5*Tan[x]^3)/3 + Tan[x]^5/5","A",3,2,9,0.2222,1,"{2620, 270}"
348,1,24,0,0.0272315,"\int \cos ^2(x) \sin ^2(x) \, dx","Int[Cos[x]^2*Sin[x]^2,x]","\frac{x}{8}-\frac{1}{4} \sin (x) \cos ^3(x)+\frac{1}{8} \sin (x) \cos (x)","\frac{x}{8}-\frac{1}{4} \sin (x) \cos ^3(x)+\frac{1}{8} \sin (x) \cos (x)",1,"x/8 + (Cos[x]*Sin[x])/8 - (Cos[x]^3*Sin[x])/4","A",3,3,9,0.3333,1,"{2568, 2635, 8}"
349,1,46,0,0.0569754,"\int \cos ^4(x) \sin ^4(x) \, dx","Int[Cos[x]^4*Sin[x]^4,x]","\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)","\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 + (3*Cos[x]*Sin[x])/128 + (Cos[x]^3*Sin[x])/64 - (Cos[x]^5*Sin[x])/16 - (Cos[x]^5*Sin[x]^3)/8","A",5,3,9,0.3333,1,"{2568, 2635, 8}"
350,1,68,0,0.084813,"\int \cos ^6(x) \sin ^6(x) \, dx","Int[Cos[x]^6*Sin[x]^6,x]","\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}","\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 + (5*Cos[x]*Sin[x])/1024 + (5*Cos[x]^3*Sin[x])/1536 + (Cos[x]^5*Sin[x])/384 - (Cos[x]^7*Sin[x])/64 - (Cos[x]^7*Sin[x]^3)/24 - (Cos[x]^7*Sin[x]^5)/12","A",7,3,9,0.3333,1,"{2568, 2635, 8}"
351,1,90,0,0.1366643,"\int \cos ^8(x) \sin ^8(x) \, dx","Int[Cos[x]^8*Sin[x]^8,x]","\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}","\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 + (35*Cos[x]*Sin[x])/32768 + (35*Cos[x]^3*Sin[x])/49152 + (7*Cos[x]^5*Sin[x])/12288 + (Cos[x]^7*Sin[x])/2048 - (Cos[x]^9*Sin[x])/256 - (5*Cos[x]^9*Sin[x]^3)/384 - (Cos[x]^9*Sin[x]^5)/32 - (Cos[x]^9*Sin[x]^7)/16","A",9,3,9,0.3333,1,"{2568, 2635, 8}"
352,1,68,0,0.0374064,"\int \cos ^{2 m}(x) \sin ^{2 m}(x) \, dx","Int[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} \text{Hypergeometric2F1}\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}","\frac{\sin ^{2 m+1}(x) \cos ^{2 m-1}(x) \cos ^2(x)^{\frac{1}{2}-m} \text{Hypergeometric2F1}\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)/2, (1 + 2*m)/2, (3 + 2*m)/2, Sin[x]^2]*Sin[x]^(1 + 2*m))/(1 + 2*m)","A",1,1,13,0.07692,1,"{2577}"
353,1,32,0,0.0212909,"\int \csc ^3\left(\frac{\pi }{4}+2 x\right) \sec \left(\frac{\pi }{4}+2 x\right) \, dx","Int[Csc[Pi/4 + 2*x]^3*Sec[Pi/4 + 2*x],x]","\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)","\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,"-Cot[Pi/4 + 2*x]^2/4 + Log[Tan[Pi/4 + 2*x]]/2","A",3,2,23,0.08696,1,"{2620, 14}"
354,1,8,0,0.021766,"\int \sec ^2(x) \tan ^2(x) \, dx","Int[Sec[x]^2*Tan[x]^2,x]","\frac{\tan ^3(x)}{3}","\frac{\tan ^3(x)}{3}",1,"Tan[x]^3/3","A",2,2,9,0.2222,1,"{2607, 30}"
355,1,11,0,0.0156247,"\int \cot ^3(x) \csc (x) \, dx","Int[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",2,1,7,0.1429,1,"{2606}"
356,1,8,0,0.0125706,"\int \sec ^3(x) \tan (x) \, dx","Int[Sec[x]^3*Tan[x],x]","\frac{\sec ^3(x)}{3}","\frac{\sec ^3(x)}{3}",1,"Sec[x]^3/3","A",2,2,7,0.2857,1,"{2606, 30}"
357,1,26,0,0.0313486,"\int \cot ^2(x) \csc ^3(x) \, dx","Int[Cot[x]^2*Csc[x]^3,x]","\frac{1}{8} \tanh ^{-1}(\cos (x))-\frac{1}{4} \cot (x) \csc ^3(x)+\frac{1}{8} \cot (x) \csc (x)","\frac{1}{8} \tanh ^{-1}(\cos (x))-\frac{1}{4} \cot (x) \csc ^3(x)+\frac{1}{8} \cot (x) \csc (x)",1,"ArcTanh[Cos[x]]/8 + (Cot[x]*Csc[x])/8 - (Cot[x]*Csc[x]^3)/4","A",3,3,9,0.3333,1,"{2611, 3768, 3770}"
358,1,17,0,0.0260194,"\int \cot ^3(x) \csc ^4(x) \, dx","Int[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",3,2,9,0.2222,1,"{2606, 14}"
359,1,31,0,0.0258051,"\int \sec ^{\frac{13}{2}}(x) \sin ^5(x) \, dx","Int[Sec[x]^(13/2)*Sin[x]^5,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)","\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,"(2*Sec[x]^(3/2))/3 - (4*Sec[x]^(7/2))/7 + (2*Sec[x]^(11/2))/11","A",3,2,11,0.1818,1,"{2622, 270}"
360,1,21,0,0.0241418,"\int \sec ^4(x) \tan ^{\frac{3}{2}}(x) \, dx","Int[Sec[x]^4*Tan[x]^(3/2),x]","\frac{2}{9} \tan ^{\frac{9}{2}}(x)+\frac{2}{5} \tan ^{\frac{5}{2}}(x)","\frac{2}{9} \tan ^{\frac{9}{2}}(x)+\frac{2}{5} \tan ^{\frac{5}{2}}(x)",1,"(2*Tan[x]^(5/2))/5 + (2*Tan[x]^(9/2))/9","A",3,2,11,0.1818,1,"{2607, 14}"
361,1,38,0,0.0530602,"\int \cot ^4(x) \csc ^3(x) \, dx","Int[Cot[x]^4*Csc[x]^3,x]","-\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)","-\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,"-ArcTanh[Cos[x]]/16 - (Cot[x]*Csc[x])/16 + (Cot[x]*Csc[x]^3)/8 - (Cot[x]^3*Csc[x]^3)/6","A",4,3,9,0.3333,1,"{2611, 3768, 3770}"
362,1,76,0,0.039172,"\int \sec ^3\left(\frac{\pi }{4}+\frac{x}{2}\right) \tan ^2\left(\frac{\pi }{4}+\frac{x}{2}\right) \, dx","Int[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} \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)","-\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,"-ArcTanh[Sin[Pi/4 + x/2]]/4 - (Sec[Pi/4 + x/2]*Tan[Pi/4 + x/2])/4 + (Sec[Pi/4 + x/2]^3*Tan[Pi/4 + x/2])/2","A",3,3,29,0.1034,1,"{2611, 3768, 3770}"
363,1,84,0,0.5506529,"\int \left(1+\cot ^3(x)\right) \left(a \sec ^2(x)-\sin (2 x)\right)^2 \, dx","Int[(1 + Cot[x]^3)*(a*Sec[x]^2 - Sin[2*x])^2,x]","\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 (\tan (x))+\frac{1}{2} (8 a+1) x+4 a \cot (x)+4 (a+1) \log (\cos (x))+\cos ^4(x) (1-\tan (x))+\frac{1}{2} \cos ^2(x) (\tan (x)+4)","\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,"((1 + 8*a)*x)/2 + 4*a*Cot[x] - (a^2*Cot[x]^2)/2 + 4*(1 + a)*Log[Cos[x]] + (4 + a^2)*Log[Tan[x]] + Cos[x]^4*(1 - Tan[x]) + a^2*Tan[x] + (a^2*Tan[x]^3)/3 + (Cos[x]^2*(4 + Tan[x]))/2","A",8,5,22,0.2273,1,"{1805, 1802, 635, 203, 260}"
364,1,70,0,0.1530644,"\int (4-3 \cos (x)) \left(1-\frac{\sin (x)}{2}\right)^4 \, dx","Int[(4 - 3*Cos[x])*(1 - Sin[x]/2)^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)","\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 + 10*Cos[x] - 3*Cos[x]^2 - (2*Cos[x]^3)/3 - 3*Sin[x] - (99*Cos[x]*Sin[x])/32 - (3*Sin[x]^3)/2 - (Cos[x]*Sin[x]^3)/16 + (3*Sin[x]^4)/8 - (3*Sin[x]^5)/80","A",15,7,17,0.4118,1,"{4401, 2637, 2668, 2669, 2635, 8, 641}"
365,1,33,0,0.0624847,"\int \left(\frac{1}{2}-3 \cot (x)\right) (3-2 \cot (x))^3 \, dx","Int[(1/2 - 3*Cot[x])*(3 - 2*Cot[x])^3,x]","-\frac{285 x}{2}+(3-2 \cot (x))^3+5 (3-2 \cot (x))^2-42 \cot (x)+4 \log (\sin (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 + 5*(3 - 2*Cot[x])^2 + (3 - 2*Cot[x])^3 - 42*Cot[x] + 4*Log[Sin[x]]","A",4,3,17,0.1765,1,"{3528, 3525, 3475}"
366,1,16,0,0.0428634,"\int \cos (5 x) \sec ^5(x) \, dx","Int[Cos[5*x]*Sec[x]^5,x]","16 x+\frac{5 \tan ^3(x)}{3}-15 \tan (x)","16 x+\frac{5 \tan ^3(x)}{3}-15 \tan (x)",1,"16*x - 15*Tan[x] + (5*Tan[x]^3)/3","A",4,2,9,0.2222,1,"{1153, 203}"
367,1,12,0,0.0231566,"\int \cos (4 x) \sec (x) \, dx","Int[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",4,3,7,0.4286,1,"{4364, 1153, 206}"
368,1,17,0,0.0082524,"\int \cos (x) \cos (4 x) \, dx","Int[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",1,1,7,0.1429,1,"{4283}"
369,1,26,0,0.0300102,"\int \cos (4 x) \sec ^5(x) \, dx","Int[Cos[4*x]*Sec[x]^5,x]","\frac{35}{8} \tanh ^{-1}(\sin (x))+\frac{1}{4} \tan (x) \sec ^3(x)-\frac{29}{8} \tan (x) \sec (x)","\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]])/8 - (29*Sec[x]*Tan[x])/8 + (Sec[x]^3*Tan[x])/4","A",4,4,9,0.4444,1,"{4364, 1157, 385, 206}"
370,1,38,0,0.0302545,"\int \cos ^4(x) \cos (4 x) \, dx","Int[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",6,2,9,0.2222,1,"{4354, 2637}"
371,1,20,0,0.0461352,"\int \cos (5 x) \csc ^5(x) \, dx","Int[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",4,3,9,0.3333,1,"{4366, 1247, 698}"
372,1,12,0,0.0214947,"\int \csc ^4(x) \sin (4 x) \, dx","Int[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",3,1,9,0.1111,1,"{14}"
373,1,65,0,0.0784877,"\int \frac{\cot (x)}{2+\sin (2 x)} \, dx","Int[Cot[x]/(2 + Sin[2*x]),x]","-\frac{x}{2 \sqrt{3}}-\frac{1}{4} \log \left(\tan ^2(x)+\tan (x)+1\right)+\frac{1}{2} \log (\tan (x))+\frac{\tan ^{-1}\left(\frac{1-2 \cos ^2(x)}{2 \sin (x) \cos (x)+\sqrt{3}+2}\right)}{2 \sqrt{3}}","-\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,"-x/(2*Sqrt[3]) + ArcTan[(1 - 2*Cos[x]^2)/(2 + Sqrt[3] + 2*Cos[x]*Sin[x])]/(2*Sqrt[3]) + Log[Tan[x]]/2 - Log[1 + Tan[x] + Tan[x]^2]/4","A",7,6,11,0.5455,1,"{705, 29, 634, 618, 204, 628}"
374,1,17,0,0.0332537,"\int \cos (x) \cot (x) \sec (3 x) \, dx","Int[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",5,5,9,0.5556,1,"{4356, 266, 36, 31, 29}"
375,1,7,0,0.0391762,"\int \frac{\sin (2 x)}{\cos ^4(x)+\sin ^4(x)} \, dx","Int[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",5,4,16,0.2500,1,"{12, 1107, 617, 204}"
376,1,83,0,0.0981272,"\int \frac{1}{4+\sqrt{3} \cos (x)+\sin (x)} \, dx","Int[(4 + Sqrt[3]*Cos[x] + Sin[x])^(-1),x]","\frac{x}{2 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{\left(3-4 \sqrt{3}\right) \sin (x)+\left(4-\sqrt{3}\right) \cos (x)}{\left(4-\sqrt{3}\right) \sin (x)-\left(3-4 \sqrt{3}\right) \cos (x)+2 \left(5+2 \sqrt{3}\right)}\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,"x/(2*Sqrt[3]) + ArcTan[((4 - Sqrt[3])*Cos[x] + (3 - 4*Sqrt[3])*Sin[x])/(2*(5 + 2*Sqrt[3]) - (3 - 4*Sqrt[3])*Cos[x] + (4 - Sqrt[3])*Sin[x])]/Sqrt[3]","A",3,3,14,0.2143,1,"{3124, 617, 204}"
377,1,94,0,0.0735646,"\int \frac{1}{3+4 \cos (x)+4 \sin (x)} \, dx","Int[(3 + 4*Cos[x] + 4*Sin[x])^(-1),x]","\frac{\log \left(\sqrt{23} \sin (x)-4 \sin (x)-4 \sqrt{23} \cos (x)+19 \cos (x)+4 \left(5-\sqrt{23}\right)\right)}{2 \sqrt{23}}-\frac{\log \left(-\sqrt{23} \sin (x)-4 \sin (x)+4 \sqrt{23} \cos (x)+19 \cos (x)+4 \left(5+\sqrt{23}\right)\right)}{2 \sqrt{23}}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{23} (\cos (x)-\sin (x))}{3 \sin (x)+3 \cos (x)+8}\right)}{\sqrt{23}}",1,"-Log[4*(5 + Sqrt[23]) + 19*Cos[x] + 4*Sqrt[23]*Cos[x] - 4*Sin[x] - Sqrt[23]*Sin[x]]/(2*Sqrt[23]) + Log[4*(5 - Sqrt[23]) + 19*Cos[x] - 4*Sqrt[23]*Cos[x] - 4*Sin[x] + Sqrt[23]*Sin[x]]/(2*Sqrt[23])","B",3,3,12,0.2500,1,"{3124, 618, 206}"
378,1,27,0,0.021039,"\int \frac{1}{4-3 \cos ^2(x)+5 \sin ^2(x)} \, dx","Int[(4 - 3*Cos[x]^2 + 5*Sin[x]^2)^(-1),x]","\frac{x}{3}+\frac{1}{3} \tan ^{-1}\left(\frac{2 \sin (x) \cos (x)}{2 \sin ^2(x)+1}\right)","\frac{x}{3}+\frac{1}{3} \tan ^{-1}\left(\frac{2 \sin (x) \cos (x)}{2 \sin ^2(x)+1}\right)",1,"x/3 + ArcTan[(2*Cos[x]*Sin[x])/(1 + 2*Sin[x]^2)]/3","A",2,1,16,0.06250,1,"{203}"
379,1,28,0,0.0407054,"\int \frac{1}{4+4 \cot (x)+\tan (x)} \, dx","Int[(4 + 4*Cot[x] + Tan[x])^(-1),x]","\frac{4 x}{25}+\frac{2}{5 (\tan (x)+2)}-\frac{3}{25} \log (\sin (x)+2 \cos (x))","\frac{4 x}{25}+\frac{2}{5 (\tan (x)+2)}-\frac{3}{25} \log (\sin (x)+2 \cos (x))",1,"(4*x)/25 - (3*Log[2*Cos[x] + Sin[x]])/25 + 2/(5*(2 + Tan[x]))","A",6,4,10,0.4000,1,"{801, 635, 203, 260}"
380,1,67,0,0.0456749,"\int \frac{1}{(2 \sec (x)+\sin (x))^2} \, dx","Int[(2*Sec[x] + Sin[x])^(-2),x]","\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}}","\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,"(8*x)/(15*Sqrt[15]) - (8*ArcTan[(1 - 2*Cos[x]^2)/(4 + Sqrt[15] + 2*Cos[x]*Sin[x])])/(15*Sqrt[15]) + (1 + 4*Tan[x])/(15*(2 + Tan[x] + 2*Tan[x]^2))","A",4,3,9,0.3333,1,"{614, 618, 204}"
381,1,55,0,0.0315169,"\int \frac{1}{(\cos (x)+2 \sec (x))^2} \, dx","Int[(Cos[x] + 2*Sec[x])^(-2),x]","\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}}","\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,"x/(6*Sqrt[6]) - ArcTan[(Cos[x]*Sin[x])/(2 + Sqrt[6] + Cos[x]^2)]/(6*Sqrt[6]) + Tan[x]/(6*(3 + 2*Tan[x]^2))","A",3,2,9,0.2222,1,"{199, 203}"
382,1,42,0,0.0958575,"\int \frac{5-\tan (x)-6 \tan ^2(x)}{(1+3 \tan (x))^3} \, dx","Int[(5 - Tan[x] - 6*Tan[x]^2)/(1 + 3*Tan[x])^3,x]","-\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))","-\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,"(-67*x)/250 - (28*Log[Cos[x] + 3*Sin[x]])/125 - 7/(10*(1 + 3*Tan[x])^2) - 29/(50*(1 + 3*Tan[x]))","A",4,4,21,0.1905,1,"{3628, 3529, 3531, 3530}"
383,1,9,0,0.0224052,"\int \cos ^2(x) \sec (3 x) \, dx","Int[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",2,1,9,0.1111,1,"{206}"
384,1,15,0,0.0144944,"\int \sec (2 x) \sin (x) \, dx","Int[Sec[2*x]*Sin[x],x]","\frac{\tanh ^{-1}\left(\sqrt{2} \cos (x)\right)}{\sqrt{2}}","\frac{\tanh ^{-1}\left(\sqrt{2} \cos (x)\right)}{\sqrt{2}}",1,"ArcTanh[Sqrt[2]*Cos[x]]/Sqrt[2]","A",2,2,7,0.2857,1,"{4357, 207}"
385,1,17,0,0.0417367,"\int \sec (2 x) \sin ^2(x) \, dx","Int[Sec[2*x]*Sin[x]^2,x]","\frac{1}{4} \tanh ^{-1}(2 \sin (x) \cos (x))-\frac{x}{2}","\frac{1}{4} \tanh ^{-1}(2 \sin (x) \cos (x))-\frac{x}{2}",1,"-x/2 + ArcTanh[2*Cos[x]*Sin[x]]/4","A",4,3,9,0.3333,1,"{298, 203, 206}"
386,1,21,0,0.041225,"\int \sec (3 x) \sin ^3(x) \, dx","Int[Sec[3*x]*Sin[x]^3,x]","\frac{1}{3} \log (\cos (x))-\frac{1}{24} \log \left(3-4 \cos ^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[3 - 4*Cos[x]^2]/24","A",4,3,9,0.3333,1,"{4366, 446, 72}"
387,1,21,0,0.0233493,"\int \cos (x) \csc (3 x) \, dx","Int[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",5,5,7,0.7143,1,"{4356, 266, 36, 31, 29}"
388,1,26,0,0.0244572,"\int \csc (4 x) \sin (x) \, dx","Int[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,"-ArcTanh[Sin[x]]/4 + ArcTanh[Sqrt[2]*Sin[x]]/(2*Sqrt[2])","A",4,2,7,0.2857,1,"{1093, 207}"
389,1,26,0,0.0346002,"\int \csc (4 x) \sin ^3(x) \, dx","Int[Csc[4*x]*Sin[x]^3,x]","\frac{\tanh ^{-1}\left(\sqrt{2} \sin (x)\right)}{4 \sqrt{2}}-\frac{1}{4} \tanh ^{-1}(\sin (x))","\frac{\tanh ^{-1}\left(\sqrt{2} \sin (x)\right)}{4 \sqrt{2}}-\frac{1}{4} \tanh ^{-1}(\sin (x))",1,"-ArcTanh[Sin[x]]/4 + ArcTanh[Sqrt[2]*Sin[x]]/(4*Sqrt[2])","A",4,2,9,0.2222,1,"{1130, 207}"
390,1,16,0,0.0086676,"\int \sqrt{1+\sin (2 x)} \, dx","Int[Sqrt[1 + Sin[2*x]],x]","-\frac{\cos (2 x)}{\sqrt{\sin (2 x)+1}}","-\frac{\cos (2 x)}{\sqrt{\sin (2 x)+1}}",1,"-(Cos[2*x]/Sqrt[1 + Sin[2*x]])","A",1,1,10,0.1000,1,"{2646}"
391,1,17,0,0.0119692,"\int \sqrt{1-\sin (2 x)} \, dx","Int[Sqrt[1 - Sin[2*x]],x]","\frac{\cos (2 x)}{\sqrt{1-\sin (2 x)}}","\frac{\cos (2 x)}{\sqrt{1-\sin (2 x)}}",1,"Cos[2*x]/Sqrt[1 - Sin[2*x]]","A",1,1,12,0.08333,1,"{2646}"
392,1,27,0,0.0125423,"\int \frac{1}{\sqrt{1+\cos (2 x)}} \, dx","Int[1/Sqrt[1 + Cos[2*x]],x]","\frac{\tanh ^{-1}\left(\frac{\sin (2 x)}{\sqrt{2} \sqrt{\cos (2 x)+1}}\right)}{\sqrt{2}}","\frac{\tanh ^{-1}\left(\frac{\sin (2 x)}{\sqrt{2} \sqrt{\cos (2 x)+1}}\right)}{\sqrt{2}}",1,"ArcTanh[Sin[2*x]/(Sqrt[2]*Sqrt[1 + Cos[2*x]])]/Sqrt[2]","A",2,2,10,0.2000,1,"{2649, 206}"
393,1,30,0,0.0131854,"\int \frac{1}{\sqrt{1-\cos (2 x)}} \, dx","Int[1/Sqrt[1 - Cos[2*x]],x]","-\frac{\tanh ^{-1}\left(\frac{\sin (2 x)}{\sqrt{2} \sqrt{1-\cos (2 x)}}\right)}{\sqrt{2}}","-\frac{\tanh ^{-1}\left(\frac{\sin (2 x)}{\sqrt{2} \sqrt{1-\cos (2 x)}}\right)}{\sqrt{2}}",1,"-(ArcTanh[Sin[2*x]/(Sqrt[2]*Sqrt[1 - Cos[2*x]])]/Sqrt[2])","A",2,2,12,0.1667,1,"{2649, 206}"
394,1,53,0,0.0282741,"\int \frac{1}{(1-\cos (3 x))^{3/2}} \, dx","Int[(1 - Cos[3*x])^(-3/2),x]","-\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}}","-\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,"-ArcTanh[Sin[3*x]/(Sqrt[2]*Sqrt[1 - Cos[3*x]])]/(6*Sqrt[2]) - Sin[3*x]/(6*(1 - Cos[3*x])^(3/2))","A",3,3,12,0.2500,1,"{2650, 2649, 206}"
395,1,73,0,0.0325273,"\int \left(1-\sin \left(\frac{2 x}{3}\right)\right)^{5/2} \, dx","Int[(1 - Sin[(2*x)/3])^(5/2),x]","\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)}}","\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,"(32*Cos[(2*x)/3])/(5*Sqrt[1 - Sin[(2*x)/3]]) + (8*Cos[(2*x)/3]*Sqrt[1 - Sin[(2*x)/3]])/5 + (3*Cos[(2*x)/3]*(1 - Sin[(2*x)/3])^(3/2))/5","A",3,2,14,0.1429,1,"{2647, 2646}"
396,1,55,0,0.1505974,"\int \frac{\cos (x) \left(-\cos ^2(x)+2 \sqrt[4]{1+2 \sin (x)}\right)}{(1+2 \sin (x))^{3/2}} \, dx","Int[(Cos[x]*(-Cos[x]^2 + 2*(1 + 2*Sin[x])^(1/4)))/(1 + 2*Sin[x])^(3/2),x]","\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}}","\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,"3/(4*Sqrt[1 + 2*Sin[x]]) - 4/(1 + 2*Sin[x])^(1/4) - Sqrt[1 + 2*Sin[x]]/2 + (1 + 2*Sin[x])^(3/2)/12","A",4,2,32,0.06250,1,"{4356, 14}"
397,1,98,0,0.0687999,"\int \sqrt{\tan (x)} \, dx","Int[Sqrt[Tan[x]],x]","-\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}}","-\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,"-(ArcTan[1 - Sqrt[2]*Sqrt[Tan[x]]]/Sqrt[2]) + ArcTan[1 + Sqrt[2]*Sqrt[Tan[x]]]/Sqrt[2] + Log[1 - Sqrt[2]*Sqrt[Tan[x]] + Tan[x]]/(2*Sqrt[2]) - Log[1 + Sqrt[2]*Sqrt[Tan[x]] + Tan[x]]/(2*Sqrt[2])","A",11,8,6,1.333,1,"{3476, 329, 297, 1162, 617, 204, 1165, 628}"
398,1,69,0,0.0584444,"\int \frac{1}{\sqrt[3]{\tan (5 x)}} \, dx","Int[Tan[5*x]^(-1/3),x]","-\frac{1}{10} \sqrt{3} \tan ^{-1}\left(\frac{1-2 \tan ^{\frac{2}{3}}(5 x)}{\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",9,9,8,1.125,1,"{3476, 329, 275, 200, 31, 634, 618, 204, 628}"
399,1,87,0,0.1130877,"\int \frac{1}{(4+3 \tan (2 x))^{3/2}} \, dx","Int[(4 + 3*Tan[2*x])^(-3/2),x]","-\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}}","-\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,"(-9*ArcTan[(1 - 3*Tan[2*x])/(Sqrt[2]*Sqrt[4 + 3*Tan[2*x]])])/(250*Sqrt[2]) + (13*ArcTanh[(3 + Tan[2*x])/(Sqrt[2]*Sqrt[4 + 3*Tan[2*x]])])/(250*Sqrt[2]) - 3/(25*Sqrt[4 + 3*Tan[2*x]])","A",6,5,12,0.4167,1,"{3483, 3536, 3535, 203, 207}"
400,1,40,0,0.1465818,"\int \frac{\sec ^2(x) \left(-\sqrt{4-3 \tan (x)}+3 \tan (x)\right)}{(4-3 \tan (x))^{3/2}} \, dx","Int[(Sec[x]^2*(-Sqrt[4 - 3*Tan[x]] + 3*Tan[x]))/(4 - 3*Tan[x])^(3/2),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))","\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,"Log[4 - 3*Tan[x]]/3 + 8/(3*Sqrt[4 - 3*Tan[x]]) + (2*Sqrt[4 - 3*Tan[x]])/3","A",4,2,32,0.06250,1,"{4342, 43}"
401,1,133,0,0.3710992,"\int \frac{\tan (x)}{\left(-1+\sqrt{\tan (x)}\right)^2} \, dx","Int[Tan[x]/(-1 + Sqrt[Tan[x]])^2,x]","-\frac{x}{2}+\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{1}{1-\sqrt{\tan (x)}}+\log \left(1-\sqrt{\tan (x)}\right)-\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}}+\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,"-x/2 + ArcTan[1 - Sqrt[2]*Sqrt[Tan[x]]]/Sqrt[2] - ArcTan[1 + Sqrt[2]*Sqrt[Tan[x]]]/Sqrt[2] + Log[Cos[x]]/2 + Log[1 - Sqrt[Tan[x]]] - Log[1 - Sqrt[2]*Sqrt[Tan[x]] + Tan[x]]/(2*Sqrt[2]) + Log[1 + Sqrt[2]*Sqrt[Tan[x]] + Tan[x]]/(2*Sqrt[2]) + (1 - Sqrt[Tan[x]])^(-1)","A",19,13,13,1.000,1,"{3670, 6725, 1831, 297, 1162, 617, 204, 1165, 628, 1248, 635, 203, 260}"
402,1,31,0,0.015072,"\int \frac{\sin (x)}{\sqrt{\sin (2 x)}} \, dx","Int[Sin[x]/Sqrt[Sin[2*x]],x]","-\frac{1}{2} \sin ^{-1}(\cos (x)-\sin (x))-\frac{1}{2} \log \left(\sin (x)+\sqrt{\sin (2 x)}+\cos (x)\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]]/2 - Log[Cos[x] + Sin[x] + Sqrt[Sin[2*x]]]/2","A",1,1,11,0.09091,1,"{4306}"
403,1,31,0,0.0146254,"\int \frac{\cos (x)}{\sqrt{\sin (2 x)}} \, dx","Int[Cos[x]/Sqrt[Sin[2*x]],x]","\frac{1}{2} \log \left(\sin (x)+\sqrt{\sin (2 x)}+\cos (x)\right)-\frac{1}{2} \sin ^{-1}(\cos (x)-\sin (x))","\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]]/2 + Log[Cos[x] + Sin[x] + Sqrt[Sin[2*x]]]/2","A",1,1,11,0.09091,1,"{4305}"
404,1,45,0,0.0297949,"\int \sin (x) \sqrt{\sin (2 x)} \, dx","Int[Sin[x]*Sqrt[Sin[2*x]],x]","-\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)","-\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]]/4 + Log[Cos[x] + Sin[x] + Sqrt[Sin[2*x]]]/4 - (Cos[x]*Sqrt[Sin[2*x]])/2","A",2,2,11,0.1818,1,"{4302, 4305}"
405,1,47,0,0.09618,"\int (\cos (x)-\sin (x)) \sqrt{\sin (2 x)} \, dx","Int[(Cos[x] - Sin[x])*Sqrt[Sin[2*x]],x]","\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)","\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]]]/2 + (Cos[x]*Sqrt[Sin[2*x]])/2 + (Sin[x]*Sqrt[Sin[2*x]])/2","A",6,5,16,0.3125,1,"{4401, 4301, 4306, 4302, 4305}"
406,1,61,0,0.0801925,"\int \frac{\sin ^7(x)}{\sin ^{\frac{7}{2}}(2 x)} \, dx","Int[Sin[x]^7/Sin[2*x]^(7/2),x]","\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)","\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,"-ArcSin[Cos[x] - Sin[x]]/16 + Log[Cos[x] + Sin[x] + Sqrt[Sin[2*x]]]/16 + Sin[x]^5/(5*Sin[2*x]^(5/2)) - Sin[x]/(4*Sqrt[Sin[2*x]])","A",4,3,13,0.2308,1,"{4294, 4308, 4305}"
407,1,61,0,0.082215,"\int \frac{\cos ^7(x)}{\sin ^{\frac{7}{2}}(2 x)} \, dx","Int[Cos[x]^7/Sin[2*x]^(7/2),x]","-\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)","-\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]]/16 - Log[Cos[x] + Sin[x] + Sqrt[Sin[2*x]]]/16 - Cos[x]^5/(5*Sin[2*x]^(5/2)) + Cos[x]/(4*Sqrt[Sin[2*x]])","A",4,3,13,0.2308,1,"{4293, 4307, 4306}"
408,1,16,0,0.0224134,"\int \csc ^5(x) \sin ^{\frac{3}{2}}(2 x) \, dx","Int[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,"-(Csc[x]^5*Sin[2*x]^(5/2))/5","A",1,1,13,0.07692,1,"{4292}"
409,1,31,0,0.0413526,"\int \frac{\sec ^3(x)}{\sqrt{\sin (2 x)}} \, dx","Int[Sec[x]^3/Sqrt[Sin[2*x]],x]","\frac{1}{5} \sqrt{\sin (2 x)} \sec ^3(x)+\frac{4}{5} \sqrt{\sin (2 x)} \sec (x)","\frac{1}{5} \sqrt{\sin (2 x)} \sec ^3(x)+\frac{4}{5} \sqrt{\sin (2 x)} \sec (x)",1,"(4*Sec[x]*Sqrt[Sin[2*x]])/5 + (Sec[x]^3*Sqrt[Sin[2*x]])/5","A",2,2,13,0.1538,1,"{4299, 4291}"
410,1,29,0,0.0476002,"\int \frac{\csc (x)}{\sin ^{\frac{3}{2}}(2 x)} \, dx","Int[Csc[x]/Sin[2*x]^(3/2),x]","\frac{4 \sin (x)}{3 \sqrt{\sin (2 x)}}-\frac{2 \cos (x)}{3 \sin ^{\frac{3}{2}}(2 x)}","\frac{4 \sin (x)}{3 \sqrt{\sin (2 x)}}-\frac{2 \cos (x)}{3 \sin ^{\frac{3}{2}}(2 x)}",1,"(-2*Cos[x])/(3*Sin[2*x]^(3/2)) + (4*Sin[x])/(3*Sqrt[Sin[2*x]])","A",3,3,11,0.2727,1,"{4308, 4303, 4292}"
411,1,95,0,0.8559357,"\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","Int[(Cos[x]^3*(Cos[2*x] - 3*Tan[x]))/((Sin[x]^2 - Sin[2*x])*Sin[2*x]^(5/2)),x]","\frac{\cos ^5(x)}{5 \sin ^{\frac{5}{2}}(2 x)}-\frac{5 \sin (x) \cos ^4(x)}{6 \sin ^{\frac{5}{2}}(2 x)}-\frac{9 \sin ^2(x) \cos ^3(x)}{4 \sin ^{\frac{5}{2}}(2 x)}+\frac{33 \sin ^5(x) \tanh ^{-1}\left(\frac{\sqrt{\tan (x)}}{\sqrt{2}}\right)}{4 \sqrt{2} \sin ^{\frac{5}{2}}(2 x) \tan ^{\frac{5}{2}}(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]^5/(5*Sin[2*x]^(5/2)) - (5*Cos[x]^4*Sin[x])/(6*Sin[2*x]^(5/2)) - (9*Cos[x]^3*Sin[x]^2)/(4*Sin[2*x]^(5/2)) + (33*ArcTanh[Sqrt[Tan[x]]/Sqrt[2]]*Sin[x]^5)/(4*Sqrt[2]*Sin[2*x]^(5/2)*Tan[x]^(5/2))","A",6,4,35,0.1143,1,"{4390, 1619, 63, 207}"
412,1,29,0,0.1239448,"\int \sqrt{\sec ^4(x) \tan (x)} \, dx","Int[Sqrt[Sec[x]^4*Tan[x]],x]","\frac{2 \tan ^2(x) \sec ^2(x)}{3 \sqrt{\tan ^5(x)+2 \tan ^3(x)+\tan (x)}}","\frac{2}{3} \sin (x) \cos (x) \sqrt{\tan (x) \sec ^4(x)}",1,"(2*Sec[x]^2*Tan[x]^2)/(3*Sqrt[Tan[x] + 2*Tan[x]^3 + Tan[x]^5])","A",5,4,11,0.3636,1,"{1999, 1954, 1250, 30}"
413,1,204,0,0.2390334,"\int \sqrt{\sin ^4(x) \tan (x)} \, dx","Int[Sqrt[Sin[x]^4*Tan[x]],x]","-\frac{1}{2} \cot (x) \sqrt{\sin ^4(x) \tan (x)}-\frac{3 \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (x)}\right) \sec ^2(x) \sqrt{\sin ^4(x) \tan (x)}}{4 \sqrt{2} \tan ^{\frac{5}{2}}(x)}+\frac{3 \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (x)}+1\right) \sec ^2(x) \sqrt{\sin ^4(x) \tan (x)}}{4 \sqrt{2} \tan ^{\frac{5}{2}}(x)}+\frac{3 \sec ^2(x) \log \left(\tan (x)-\sqrt{2} \sqrt{\tan (x)}+1\right) \sqrt{\sin ^4(x) \tan (x)}}{8 \sqrt{2} \tan ^{\frac{5}{2}}(x)}-\frac{3 \sec ^2(x) \log \left(\tan (x)+\sqrt{2} \sqrt{\tan (x)}+1\right) \sqrt{\sin ^4(x) \tan (x)}}{8 \sqrt{2} \tan ^{\frac{5}{2}}(x)}","-\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,"-(Cot[x]*Sqrt[Sin[x]^4*Tan[x]])/2 - (3*ArcTan[1 - Sqrt[2]*Sqrt[Tan[x]]]*Sec[x]^2*Sqrt[Sin[x]^4*Tan[x]])/(4*Sqrt[2]*Tan[x]^(5/2)) + (3*ArcTan[1 + Sqrt[2]*Sqrt[Tan[x]]]*Sec[x]^2*Sqrt[Sin[x]^4*Tan[x]])/(4*Sqrt[2]*Tan[x]^(5/2)) + (3*Log[1 - Sqrt[2]*Sqrt[Tan[x]] + Tan[x]]*Sec[x]^2*Sqrt[Sin[x]^4*Tan[x]])/(8*Sqrt[2]*Tan[x]^(5/2)) - (3*Log[1 + Sqrt[2]*Sqrt[Tan[x]] + Tan[x]]*Sec[x]^2*Sqrt[Sin[x]^4*Tan[x]])/(8*Sqrt[2]*Tan[x]^(5/2))","B",13,9,11,0.8182,1,"{6719, 288, 329, 297, 1162, 617, 204, 1165, 628}"
414,1,47,0,0.1443407,"\int \sqrt[3]{\sec ^{12}(x) \tan ^2(x)} \, dx","Int[(Sec[x]^12*Tan[x]^2)^(1/3),x]","\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)}","\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]^3*Sin[x]*(Sec[x]^12*Tan[x]^2)^(1/3))/5 + (3*Cos[x]*Sin[x]^3*(Sec[x]^12*Tan[x]^2)^(1/3))/11","A",4,2,13,0.1538,1,"{6719, 14}"
415,1,70,0,0.1955445,"\int \frac{1}{\sqrt[4]{\cos ^{11}(x) \sin ^{13}(x)}} \, dx","Int[(Cos[x]^11*Sin[x]^13)^(-1/4),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)}}+\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)}}+\frac{4 \sin ^5(x) \cos (x)}{7 \sqrt[4]{\sin ^{13}(x) \cos ^{11}(x)}}",1,"(-4*Cos[x]^5*Sin[x])/(9*(Cos[x]^11*Sin[x]^13)^(1/4)) - (8*Cos[x]^3*Sin[x]^3)/(Cos[x]^11*Sin[x]^13)^(1/4) + (4*Cos[x]*Sin[x]^5)/(7*(Cos[x]^11*Sin[x]^13)^(1/4))","A",4,2,13,0.1538,1,"{6719, 270}"
416,1,234,0,1.5398626,"\int \frac{\cos (2 x)-\sqrt{\sin (2 x)}}{\sqrt{\cos ^3(x) \sin (x)}} \, dx","Int[(Cos[2*x] - Sqrt[Sin[2*x]])/Sqrt[Cos[x]^3*Sin[x]],x]","-2 \sec ^2(x) \sqrt{\sin (x) \cos ^3(x)}-\frac{\sqrt{2} \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (x)}\right) \sec ^2(x) \sqrt{\sin (x) \cos ^3(x)}}{\sqrt{\tan (x)}}+\frac{\sqrt{2} \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (x)}+1\right) \sec ^2(x) \sqrt{\sin (x) \cos ^3(x)}}{\sqrt{\tan (x)}}-\frac{\sec ^2(x) \log \left(\tan (x)-\sqrt{2} \sqrt{\tan (x)}+1\right) \sqrt{\sin (x) \cos ^3(x)}}{\sqrt{2} \sqrt{\tan (x)}}+\frac{\sec ^2(x) \log \left(\tan (x)+\sqrt{2} \sqrt{\tan (x)}+1\right) \sqrt{\sin (x) \cos ^3(x)}}{\sqrt{2} \sqrt{\tan (x)}}-\sqrt{2} \cot (x) \sec ^2(x)^{3/2} \sqrt{\sin (x) \cos (x)} \sqrt{\sin (x) \cos ^3(x)} \sinh ^{-1}(\tan (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,"-2*Sec[x]^2*Sqrt[Cos[x]^3*Sin[x]] - Sqrt[2]*ArcSinh[Tan[x]]*Cot[x]*(Sec[x]^2)^(3/2)*Sqrt[Cos[x]*Sin[x]]*Sqrt[Cos[x]^3*Sin[x]] - (Sqrt[2]*ArcTan[1 - Sqrt[2]*Sqrt[Tan[x]]]*Sec[x]^2*Sqrt[Cos[x]^3*Sin[x]])/Sqrt[Tan[x]] + (Sqrt[2]*ArcTan[1 + Sqrt[2]*Sqrt[Tan[x]]]*Sec[x]^2*Sqrt[Cos[x]^3*Sin[x]])/Sqrt[Tan[x]] - (Log[1 - Sqrt[2]*Sqrt[Tan[x]] + Tan[x]]*Sec[x]^2*Sqrt[Cos[x]^3*Sin[x]])/(Sqrt[2]*Sqrt[Tan[x]]) + (Log[1 + Sqrt[2]*Sqrt[Tan[x]] + Tan[x]]*Sec[x]^2*Sqrt[Cos[x]^3*Sin[x]])/(Sqrt[2]*Sqrt[Tan[x]])","B",27,11,27,0.4074,1,"{6719, 6725, 215, 329, 211, 1165, 628, 1162, 617, 204, 321}"
417,1,665,0,4.7302574,"\int \frac{\sqrt{\cos (x) \sin ^3(x)}-2 \sin (2 x)}{-\sqrt{\cos ^3(x) \sin (x)}+\sqrt{\tan (x)}} \, dx","Int[(Sqrt[Cos[x]*Sin[x]^3] - 2*Sin[2*x])/(-Sqrt[Cos[x]^3*Sin[x]] + Sqrt[Tan[x]]),x]","-\sqrt[4]{2} \tan ^{-1}\left(1-\sqrt[4]{2} \sqrt{\tan (x)}\right)+\sqrt[4]{2} \tan ^{-1}\left(\sqrt[4]{2} \sqrt{\tan (x)}+1\right)+\frac{4}{\sqrt{\tan (x)}}+\frac{\log \left(\tan (x)-2^{3/4} \sqrt{\tan (x)}+\sqrt{2}\right)}{2^{3/4}}-\frac{\log \left(\tan (x)+2^{3/4} \sqrt{\tan (x)}+\sqrt{2}\right)}{2^{3/4}}+4 \csc (x) \sec (x) \sqrt{\sin (x) \cos ^3(x)}+\frac{\sqrt[4]{2} \tan ^{-1}\left(1-\sqrt[4]{2} \sqrt{\tan (x)}\right) \sec ^2(x) \sqrt{\sin (x) \cos ^3(x)}}{\sqrt{\tan (x)}}-\frac{\sqrt[4]{2} \tan ^{-1}\left(\sqrt[4]{2} \sqrt{\tan (x)}+1\right) \sec ^2(x) \sqrt{\sin (x) \cos ^3(x)}}{\sqrt{\tan (x)}}-\frac{2 \sqrt{2} \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (x)}\right) \sec ^2(x) \sqrt{\sin (x) \cos ^3(x)}}{\sqrt{\tan (x)}}+\frac{2 \sqrt{2} \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (x)}+1\right) \sec ^2(x) \sqrt{\sin (x) \cos ^3(x)}}{\sqrt{\tan (x)}}+\frac{\sqrt{2} \sec ^2(x) \log \left(\tan (x)-\sqrt{2} \sqrt{\tan (x)}+1\right) \sqrt{\sin (x) \cos ^3(x)}}{\sqrt{\tan (x)}}-\frac{\sqrt{2} \sec ^2(x) \log \left(\tan (x)+\sqrt{2} \sqrt{\tan (x)}+1\right) \sqrt{\sin (x) \cos ^3(x)}}{\sqrt{\tan (x)}}-\frac{\sec ^2(x) \log \left(\tan (x)-2^{3/4} \sqrt{\tan (x)}+\sqrt{2}\right) \sqrt{\sin (x) \cos ^3(x)}}{2^{3/4} \sqrt{\tan (x)}}+\frac{\sec ^2(x) \log \left(\tan (x)+2^{3/4} \sqrt{\tan (x)}+\sqrt{2}\right) \sqrt{\sin (x) \cos ^3(x)}}{2^{3/4} \sqrt{\tan (x)}}-\frac{1}{2} \csc ^2(x) \sec ^2(x) \log \left(\sec ^2(x)\right) \sqrt{\sin (x) \cos ^3(x)} \sqrt{\sin ^3(x) \cos (x)}+\frac{\sec ^2(x) \log (\tan (x)) \sqrt{\sin ^3(x) \cos (x)}}{2 \tan ^{\frac{3}{2}}(x)}-\frac{\sec ^2(x) \log \left(\tan ^2(x)+2\right) \sqrt{\sin ^3(x) \cos (x)}}{4 \tan ^{\frac{3}{2}}(x)}+\frac{1}{4} \csc ^2(x) \sec ^2(x) \log \left(\tan ^2(x)+2\right) \sqrt{\sin (x) \cos ^3(x)} \sqrt{\sin ^3(x) \cos (x)}+\csc ^2(x) \sec ^2(x) \log \left(\sqrt{\tan (x)}\right) \sqrt{\sin (x) \cos ^3(x)} \sqrt{\sin ^3(x) \cos (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}{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} \csc ^2(x) \sec ^2(x) \log (\sin (x)) \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,"-(2^(1/4)*ArcTan[1 - 2^(1/4)*Sqrt[Tan[x]]]) + 2^(1/4)*ArcTan[1 + 2^(1/4)*Sqrt[Tan[x]]] + Log[Sqrt[2] - 2^(3/4)*Sqrt[Tan[x]] + Tan[x]]/2^(3/4) - Log[Sqrt[2] + 2^(3/4)*Sqrt[Tan[x]] + Tan[x]]/2^(3/4) + 4*Csc[x]*Sec[x]*Sqrt[Cos[x]^3*Sin[x]] - (Csc[x]^2*Log[Sec[x]^2]*Sec[x]^2*Sqrt[Cos[x]^3*Sin[x]]*Sqrt[Cos[x]*Sin[x]^3])/2 + Csc[x]^2*Log[Sqrt[Tan[x]]]*Sec[x]^2*Sqrt[Cos[x]^3*Sin[x]]*Sqrt[Cos[x]*Sin[x]^3] + (Csc[x]^2*Log[2 + Tan[x]^2]*Sec[x]^2*Sqrt[Cos[x]^3*Sin[x]]*Sqrt[Cos[x]*Sin[x]^3])/4 + (Log[Tan[x]]*Sec[x]^2*Sqrt[Cos[x]*Sin[x]^3])/(2*Tan[x]^(3/2)) - (Log[2 + Tan[x]^2]*Sec[x]^2*Sqrt[Cos[x]*Sin[x]^3])/(4*Tan[x]^(3/2)) + 4/Sqrt[Tan[x]] + (2^(1/4)*ArcTan[1 - 2^(1/4)*Sqrt[Tan[x]]]*Sec[x]^2*Sqrt[Cos[x]^3*Sin[x]])/Sqrt[Tan[x]] - (2^(1/4)*ArcTan[1 + 2^(1/4)*Sqrt[Tan[x]]]*Sec[x]^2*Sqrt[Cos[x]^3*Sin[x]])/Sqrt[Tan[x]] - (2*Sqrt[2]*ArcTan[1 - Sqrt[2]*Sqrt[Tan[x]]]*Sec[x]^2*Sqrt[Cos[x]^3*Sin[x]])/Sqrt[Tan[x]] + (2*Sqrt[2]*ArcTan[1 + Sqrt[2]*Sqrt[Tan[x]]]*Sec[x]^2*Sqrt[Cos[x]^3*Sin[x]])/Sqrt[Tan[x]] + (Sqrt[2]*Log[1 - Sqrt[2]*Sqrt[Tan[x]] + Tan[x]]*Sec[x]^2*Sqrt[Cos[x]^3*Sin[x]])/Sqrt[Tan[x]] - (Sqrt[2]*Log[1 + Sqrt[2]*Sqrt[Tan[x]] + Tan[x]]*Sec[x]^2*Sqrt[Cos[x]^3*Sin[x]])/Sqrt[Tan[x]] - (Log[Sqrt[2] - 2^(3/4)*Sqrt[Tan[x]] + Tan[x]]*Sec[x]^2*Sqrt[Cos[x]^3*Sin[x]])/(2^(3/4)*Sqrt[Tan[x]]) + (Log[Sqrt[2] + 2^(3/4)*Sqrt[Tan[x]] + Tan[x]]*Sec[x]^2*Sqrt[Cos[x]^3*Sin[x]])/(2^(3/4)*Sqrt[Tan[x]])","A",66,21,41,0.5122,0,"{6725, 6742, 6719, 325, 329, 297, 1162, 617, 204, 1165, 628, 466, 482, 6733, 15, 29, 266, 36, 31, 260, 444}"
418,1,141,0,1.0189087,"\int \frac{-3 \tan (x)+\sqrt[3]{\sec ^6(x) \tan (x)}}{\left(\cos ^5(x) \sin (x)\right)^{2/3}} \, dx","Int[(-3*Tan[x] + (Sec[x]^6*Tan[x])^(1/3))/(Cos[x]^5*Sin[x])^(2/3),x]","-\frac{9 \sin ^2(x) \cos ^2(x)}{4 \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{3 \sin ^3(x) \cos ^3(x) \sqrt[3]{\tan (x) \sec ^6(x)}}{4 \left(\sin (x) \cos ^5(x)\right)^{2/3}}+\frac{3 \sin ^5(x) \cos (x) \sqrt[3]{\tan (x) \sec ^6(x)}}{14 \left(\sin (x) \cos ^5(x)\right)^{2/3}}+\frac{3 \sin (x) \cos ^5(x) \sqrt[3]{\tan (x) \sec ^6(x)}}{2 \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,"(-9*Cos[x]^2*Sin[x]^2)/(4*(Cos[x]^5*Sin[x])^(2/3)) - (9*Sin[x]^4)/(10*(Cos[x]^5*Sin[x])^(2/3)) + (3*Cos[x]^5*Sin[x]*(Sec[x]^6*Tan[x])^(1/3))/(2*(Cos[x]^5*Sin[x])^(2/3)) + (3*Cos[x]^3*Sin[x]^3*(Sec[x]^6*Tan[x])^(1/3))/(4*(Cos[x]^5*Sin[x])^(2/3)) + (3*Cos[x]*Sin[x]^5*(Sec[x]^6*Tan[x])^(1/3))/(14*(Cos[x]^5*Sin[x])^(2/3))","A",13,4,28,0.1429,1,"{6719, 6733, 6742, 14}"
419,1,67,0,0.0465499,"\int \left(1+2 \cos ^2(x)\right)^{5/2} \sin (x) \, dx","Int[(1 + 2*Cos[x]^2)^(5/2)*Sin[x],x]","-\frac{1}{6} \cos (x) (\cos (2 x)+2)^{5/2}-\frac{5}{24} \cos (x) (\cos (2 x)+2)^{3/2}-\frac{5}{16} \cos (x) \sqrt{\cos (2 x)+2}-\frac{5 \sinh ^{-1}\left(\sqrt{2} \cos (x)\right)}{16 \sqrt{2}}","-\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,"(-5*ArcSinh[Sqrt[2]*Cos[x]])/(16*Sqrt[2]) - (5*Cos[x]*Sqrt[2 + Cos[2*x]])/16 - (5*Cos[x]*(2 + Cos[2*x])^(3/2))/24 - (Cos[x]*(2 + Cos[2*x])^(5/2))/6","A",5,3,15,0.2000,1,"{3190, 195, 215}"
420,1,69,0,0.0533013,"\int \cos (x) \left(5 \cos ^2(x)+\sin ^2(x)\right)^{5/2} \, dx","Int[Cos[x]*(5*Cos[x]^2 + Sin[x]^2)^(5/2),x]","\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)}+\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)}+\frac{625}{32} \sin ^{-1}\left(\frac{2 \sin (x)}{\sqrt{5}}\right)",1,"(625*ArcSin[(2*Sin[x])/Sqrt[5]])/32 + (125*Sin[x]*Sqrt[5 - 4*Sin[x]^2])/16 + (25*Sin[x]*(5 - 4*Sin[x]^2)^(3/2))/24 + (Sin[x]*(5 - 4*Sin[x]^2)^(5/2))/6","A",5,3,18,0.1667,1,"{4356, 195, 216}"
421,1,58,0,0.051131,"\int \cos (x) \left(-\cos ^2(x)-5 \sin ^2(x)\right)^{3/2} \, dx","Int[Cos[x]*(-Cos[x]^2 - 5*Sin[x]^2)^(3/2),x]","\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)","\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,"(3*ArcTan[(2*Sin[x])/Sqrt[-1 - 4*Sin[x]^2]])/16 - (3*Sin[x]*Sqrt[-1 - 4*Sin[x]^2])/8 + (Sin[x]*(-1 - 4*Sin[x]^2)^(3/2))/4","A",5,4,20,0.2000,1,"{4356, 195, 217, 203}"
422,1,55,0,0.0535616,"\int \frac{\sin (x)}{\left(5 \cos ^2(x)-2 \sin ^2(x)\right)^{7/2}} \, dx","Int[Sin[x]/(5*Cos[x]^2 - 2*Sin[x]^2)^(7/2),x]","\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}}","\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]/(10*(-2 + 7*Cos[x]^2)^(5/2)) - Cos[x]/(15*(-2 + 7*Cos[x]^2)^(3/2)) + Cos[x]/(15*Sqrt[-2 + 7*Cos[x]^2])","A",4,3,20,0.1500,1,"{4357, 192, 191}"
423,1,39,0,0.0668324,"\int \frac{\cos (x) \cos (2 x)}{\left(2-5 \sin ^2(x)\right)^{3/2}} \, dx","Int[(Cos[x]*Cos[2*x])/(2 - 5*Sin[x]^2)^(3/2),x]","\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)}}","\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,"(2*ArcSin[Sqrt[5/2]*Sin[x]])/(5*Sqrt[5]) + Sin[x]/(10*Sqrt[2 - 5*Sin[x]^2])","A",3,3,19,0.1579,1,"{4356, 385, 216}"
424,1,48,0,0.0722855,"\int \frac{\sin (5 x)}{\left(5 \cos ^2(x)+9 \sin ^2(x)\right)^{5/2}} \, dx","Int[Sin[5*x]/(5*Cos[x]^2 + 9*Sin[x]^2)^(5/2),x]","\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)","\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,"-ArcSin[(2*Cos[x])/3]/2 - (55*Cos[x])/(27*(9 - 4*Cos[x]^2)^(3/2)) + (295*Cos[x])/(243*Sqrt[9 - 4*Cos[x]^2])","A",4,3,22,0.1364,1,"{1157, 385, 216}"
425,1,49,0,0.1158322,"\int \frac{\cos (x) \cos (2 x) \sin (3 x)}{\left(-5+4 \sin ^2(x)\right)^{5/2}} \, dx","Int[(Cos[x]*Cos[2*x]*Sin[3*x])/(-5 + 4*Sin[x]^2)^(5/2),x]","\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}}","\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,"-1/(4*(-5 + 4*Sin[x]^2)^(3/2)) - 5/(8*Sqrt[-5 + 4*Sin[x]^2]) + Sqrt[-5 + 4*Sin[x]^2]/8","A",4,3,23,0.1304,1,"{4356, 1247, 698}"
426,1,119,0,0.5749792,"\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","Int[(Csc[x]^2*(-2*Cos[x]^3*(-1 + Sin[x]) + Cos[2*x]*Sin[x]))/Sqrt[-5 + Sin[x]^2],x]","2 \sqrt{-\cos ^2(x)-4}-2 \tanh ^{-1}\left(\frac{\sin (x)}{\sqrt{\sin ^2(x)-5}}\right)+2 \tan ^{-1}\left(\frac{\cos (x)}{\sqrt{-\cos ^2(x)-4}}\right)-\frac{\tan ^{-1}\left(\frac{\sqrt{5} \cos (x)}{\sqrt{-\cos ^2(x)-4}}\right)}{\sqrt{5}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt{-\cos ^2(x)-4}}{\sqrt{5}}\right)}{\sqrt{5}}+\frac{2}{5} \sqrt{\sin ^2(x)-5} \csc (x)","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,"2*ArcTan[Cos[x]/Sqrt[-4 - Cos[x]^2]] - ArcTan[(Sqrt[5]*Cos[x])/Sqrt[-4 - Cos[x]^2]]/Sqrt[5] - (2*ArcTan[Sqrt[-4 - Cos[x]^2]/Sqrt[5]])/Sqrt[5] - 2*ArcTanh[Sin[x]/Sqrt[-5 + Sin[x]^2]] + 2*Sqrt[-4 - Cos[x]^2] + (2*Csc[x]*Sqrt[-5 + Sin[x]^2])/5","A",18,13,33,0.3939,1,"{4401, 4356, 451, 217, 206, 4366, 6725, 203, 261, 1010, 377, 444, 63}"
427,1,112,0,0.4442859,"\int \frac{\cos (3 x)}{-\sqrt{-1+8 \cos ^2(x)}+\sqrt{3 \cos ^2(x)-\sin ^2(x)}} \, dx","Int[Cos[3*x]/(-Sqrt[-1 + 8*Cos[x]^2] + Sqrt[3*Cos[x]^2 - Sin[x]^2]),x]","\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{7-8 \sin ^2(x)}-\frac{1}{2} \sin (x) \sqrt{3-4 \sin ^2(x)}-\frac{3}{4} \tan ^{-1}\left(\frac{\sin (x)}{\sqrt{7-8 \sin ^2(x)}}\right)-\frac{3}{4} \tan ^{-1}\left(\frac{\sin (x)}{\sqrt{3-4 \sin ^2(x)}}\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*ArcSin[2*Sqrt[2/7]*Sin[x]])/(4*Sqrt[2]) + (3*ArcSin[(2*Sin[x])/Sqrt[3]])/4 - (3*ArcTan[Sin[x]/Sqrt[7 - 8*Sin[x]^2]])/4 - (3*ArcTan[Sin[x]/Sqrt[3 - 4*Sin[x]^2]])/4 - (Sin[x]*Sqrt[7 - 8*Sin[x]^2])/2 - (Sin[x]*Sqrt[3 - 4*Sin[x]^2])/2","A",27,6,39,0.1538,1,"{6742, 402, 216, 377, 204, 195}"
428,1,33,0,0.0608089,"\int \left(2-3 \sin ^2(x)\right)^{3/5} \sin (4 x) \, dx","Int[(2 - 3*Sin[x]^2)^(3/5)*Sin[4*x],x]","\frac{5}{36} \left(2-3 \sin ^2(x)\right)^{8/5}-\frac{20}{117} \left(2-3 \sin ^2(x)\right)^{13/5}","\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*(2 - 3*Sin[x]^2)^(8/5))/36 - (20*(2 - 3*Sin[x]^2)^(13/5))/117","A",5,3,17,0.1765,1,"{12, 444, 43}"
429,1,33,0,0.0220386,"\int \cos (x) \sqrt{\cos (2 x)} \, dx","Int[Cos[x]*Sqrt[Cos[2*x]],x]","\frac{\sin ^{-1}\left(\sqrt{2} \sin (x)\right)}{2 \sqrt{2}}+\frac{1}{2} \sin (x) \sqrt{\cos (2 x)}","\frac{\sin ^{-1}\left(\sqrt{2} \sin (x)\right)}{2 \sqrt{2}}+\frac{1}{2} \sin (x) \sqrt{\cos (2 x)}",1,"ArcSin[Sqrt[2]*Sin[x]]/(2*Sqrt[2]) + (Sqrt[Cos[2*x]]*Sin[x])/2","A",3,3,11,0.2727,1,"{4356, 195, 216}"
430,1,55,0,0.0326769,"\int \cos ^{\frac{3}{2}}(2 x) \sin (x) \, dx","Int[Cos[2*x]^(3/2)*Sin[x],x]","-\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}}","-\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,"(-3*ArcTanh[(Sqrt[2]*Cos[x])/Sqrt[Cos[2*x]]])/(8*Sqrt[2]) + (3*Cos[x]*Sqrt[Cos[2*x]])/8 - (Cos[x]*Cos[2*x]^(3/2))/4","A",5,4,11,0.3636,1,"{4357, 195, 217, 206}"
431,1,16,0,0.0134062,"\int \frac{\sin (x)}{\cos ^{\frac{5}{2}}(2 x)} \, dx","Int[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,"-Cos[3*x]/(3*Cos[2*x]^(3/2))","A",1,1,11,0.09091,1,"{4331}"
432,1,49,0,0.0574821,"\int \cos ^{\frac{3}{2}}(2 x) \sec ^3(x) \, dx","Int[Cos[2*x]^(3/2)*Sec[x]^3,x]","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)","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,"2*Sqrt[2]*ArcSin[Sqrt[2]*Sin[x]] - (5*ArcTan[Sin[x]/Sqrt[Cos[2*x]]])/2 - (Sqrt[Cos[2*x]]*Sec[x]*Tan[x])/2","A",6,6,13,0.4615,1,"{4364, 413, 523, 216, 377, 203}"
433,1,91,0,0.2078269,"\int \frac{\sin ^2(x) \left(3 \sin ^3(x)-\cos (x) \sin (4 x)\right)}{\cos ^{\frac{7}{2}}(2 x)} \, dx","Int[(Sin[x]^2*(3*Sin[x]^3 - Cos[x]*Sin[4*x]))/Cos[2*x]^(7/2),x]","-\frac{2 \cos ^3(x)}{3 \cos ^{\frac{3}{2}}(2 x)}+\frac{13 \cos (x)}{5 \sqrt{\cos (2 x)}}+\frac{3 \sin ^4(x) \cos (x)}{5 \cos ^{\frac{5}{2}}(2 x)}-\frac{4 \sin ^2(x) \cos (x)}{5 \cos ^{\frac{3}{2}}(2 x)}-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \cos (x)}{\sqrt{\cos (2 x)}}\right)}{\sqrt{2}}","-\frac{2 \cos ^3(x)}{3 \cos ^{\frac{3}{2}}(2 x)}-\frac{11 \cos (x)}{20 \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,"-(ArcTanh[(Sqrt[2]*Cos[x])/Sqrt[Cos[2*x]]]/Sqrt[2]) - (2*Cos[x]^3)/(3*Cos[2*x]^(3/2)) + (13*Cos[x])/(5*Sqrt[Cos[2*x]]) - (4*Cos[x]*Sin[x]^2)/(5*Cos[2*x]^(3/2)) + (3*Cos[x]*Sin[x]^4)/(5*Cos[2*x]^(5/2))","A",11,9,28,0.3214,1,"{4377, 12, 452, 288, 217, 206, 4366, 378, 191}"
434,1,68,0,0.0554331,"\int \left(4-5 \sec ^2(x)\right)^{3/2} \, dx","Int[(4 - 5*Sec[x]^2)^(3/2),x]","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)-\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)-\frac{5}{2} \tan (x) \sqrt{-5 \tan ^2(x)-1}",1,"8*ArcTan[(2*Tan[x])/Sqrt[-1 - 5*Tan[x]^2]] - (7*Sqrt[5]*ArcTan[(Sqrt[5]*Tan[x])/Sqrt[-1 - 5*Tan[x]^2]])/2 - (5*Tan[x]*Sqrt[-1 - 5*Tan[x]^2])/2","A",7,6,12,0.5000,1,"{4128, 416, 523, 217, 203, 377}"
435,1,40,0,0.0301136,"\int \frac{1}{\left(4-5 \sec ^2(x)\right)^{3/2}} \, dx","Int[(4 - 5*Sec[x]^2)^(-3/2),x]","\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}}","\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,"ArcTan[(2*Tan[x])/Sqrt[-1 - 5*Tan[x]^2]]/8 - (5*Tan[x])/(4*Sqrt[-1 - 5*Tan[x]^2])","A",4,4,12,0.3333,1,"{4128, 382, 377, 203}"
436,1,94,0,0.1885802,"\int \frac{-2 \cot ^2(x)+\sin (x)}{\left(1+5 \tan ^2(x)\right)^{3/2}} \, dx","Int[(-2*Cot[x]^2 + Sin[x])/(1 + 5*Tan[x]^2)^(3/2),x]","-\frac{5 \sec (x)}{8 \sqrt{5 \sec ^2(x)-4}}+\frac{\cos (x)}{4 \sqrt{5 \sec ^2(x)-4}}-\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}}","-\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,"-ArcTanh[(2*Tan[x])/Sqrt[1 + 5*Tan[x]^2]]/4 + Cos[x]/(4*Sqrt[-4 + 5*Sec[x]^2]) - (5*Sec[x])/(8*Sqrt[-4 + 5*Sec[x]^2]) - (5*Cot[x])/(2*Sqrt[1 + 5*Tan[x]^2]) + (9*Cot[x]*Sqrt[1 + 5*Tan[x]^2])/2","A",10,10,22,0.4545,1,"{4377, 12, 3670, 472, 583, 377, 206, 3664, 271, 191}"
437,1,39,0,0.1494065,"\int \frac{(-3+\cos (2 x)) \sec ^4(x)}{\sqrt{4-\cot ^2(x)}} \, dx","Int[((-3 + Cos[2*x])*Sec[x]^4)/Sqrt[4 - Cot[x]^2],x]","-\frac{1}{3} \tan ^3(x) \sqrt{4-\cot ^2(x)}-\frac{2}{3} \tan (x) \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,"(-2*Sqrt[4 - Cot[x]^2]*Tan[x])/3 - (Sqrt[4 - Cot[x]^2]*Tan[x]^3)/3","A",5,4,23,0.1739,1,"{12, 434, 453, 191}"
438,1,73,0,1.229887,"\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","Int[((3 + Sin[x]^2)*Tan[x]^3)/((-2 + Cos[x]^2)*(5 - 4*Sec[x]^2)^(3/2)),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}}","-\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,"-ArcTanh[Sqrt[5 - 4*Sec[x]^2]/Sqrt[3]]/(6*Sqrt[3]) - ArcTanh[Sqrt[5 - 4*Sec[x]^2]/Sqrt[5]]/(5*Sqrt[5]) - 2/(15*Sqrt[5 - 4*Sec[x]^2])","A",16,12,31,0.3871,1,"{4373, 6725, 261, 266, 51, 63, 206, 514, 446, 85, 156, 207}"
439,1,57,0,0.8490046,"\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","Int[(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{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}}","-\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,"(-3*Log[Tan[x]])/4 + (3*Log[4 + 9*Tan[x]^2])/8 - Cot[x]/(4*Sqrt[4 + 9*Tan[x]^2]) - (7*Tan[x])/(8*Sqrt[4 + 9*Tan[x]^2])","A",10,7,48,0.1458,1,"{6742, 191, 271, 266, 36, 29, 31}"
440,1,66,0,0.0706004,"\int \tan (x) \left(1+5 \tan ^2(x)\right)^{5/2} \, dx","Int[Tan[x]*(1 + 5*Tan[x]^2)^(5/2),x]","\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)","\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,"-32*ArcTan[Sqrt[1 + 5*Tan[x]^2]/2] + 16*Sqrt[1 + 5*Tan[x]^2] - (4*(1 + 5*Tan[x]^2)^(3/2))/3 + (1 + 5*Tan[x]^2)^(5/2)/5","A",7,5,15,0.3333,1,"{3670, 444, 50, 63, 203}"
441,1,54,0,0.0601066,"\int \frac{\tan (x)}{\left(1+5 \tan ^2(x)\right)^{5/2}} \, dx","Int[Tan[x]/(1 + 5*Tan[x]^2)^(5/2),x]","\frac{1}{32} \tan ^{-1}\left(\frac{1}{2} \sqrt{5 \tan ^2(x)+1}\right)+\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)+\frac{1}{16 \sqrt{5 \tan ^2(x)+1}}-\frac{1}{12 \left(5 \tan ^2(x)+1\right)^{3/2}}",1,"ArcTan[Sqrt[1 + 5*Tan[x]^2]/2]/32 - 1/(12*(1 + 5*Tan[x]^2)^(3/2)) + 1/(16*Sqrt[1 + 5*Tan[x]^2])","A",6,5,15,0.3333,1,"{3670, 444, 51, 63, 203}"
442,1,133,0,0.155863,"\int \frac{\tan (x)}{\sqrt[3]{a^3+b^3 \tan ^2(x)}} \, dx","Int[Tan[x]/(a^3 + b^3*Tan[x]^2)^(1/3),x]","\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}}","\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,"(Sqrt[3]*ArcTan[(1 + (2*(a^3 + b^3*Tan[x]^2)^(1/3))/(a^3 - b^3)^(1/3))/Sqrt[3]])/(2*(a^3 - b^3)^(1/3)) + Log[Cos[x]]/(2*(a^3 - b^3)^(1/3)) + (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",6,6,19,0.3158,1,"{3670, 444, 55, 617, 204, 31}"
443,1,69,0,0.0871591,"\int \tan (x) \left(1-7 \tan ^2(x)\right)^{2/3} \, dx","Int[Tan[x]*(1 - 7*Tan[x]^2)^(2/3),x]","2 \sqrt{3} \tan ^{-1}\left(\frac{\sqrt[3]{1-7 \tan ^2(x)}+1}{\sqrt{3}}\right)+\frac{3}{4} \left(1-7 \tan ^2(x)\right)^{2/3}+3 \log \left(2-\sqrt[3]{1-7 \tan ^2(x)}\right)+2 \log (\cos (x))","2 \sqrt{3} \tan ^{-1}\left(\frac{\sqrt[3]{1-7 \tan ^2(x)}+1}{\sqrt{3}}\right)+\frac{3}{4} \left(1-7 \tan ^2(x)\right)^{2/3}+3 \log \left(2-\sqrt[3]{1-7 \tan ^2(x)}\right)+2 \log (\cos (x))",1,"2*Sqrt[3]*ArcTan[(1 + (1 - 7*Tan[x]^2)^(1/3))/Sqrt[3]] + 2*Log[Cos[x]] + 3*Log[2 - (1 - 7*Tan[x]^2)^(1/3)] + (3*(1 - 7*Tan[x]^2)^(2/3))/4","A",7,7,15,0.4667,1,"{3670, 444, 50, 55, 618, 204, 31}"
444,1,52,0,0.0893266,"\int \frac{\cot (x)}{\sqrt[4]{a^4+b^4 \csc ^2(x)}} \, dx","Int[Cot[x]/(a^4 + b^4*Csc[x]^2)^(1/4),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}","\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,"-(ArcTan[(a^4 + b^4*Csc[x]^2)^(1/4)/a]/a) + ArcTanh[(a^4 + b^4*Csc[x]^2)^(1/4)/a]/a","A",6,6,19,0.3158,1,"{4139, 266, 63, 298, 203, 206}"
445,1,54,0,0.0874378,"\int \frac{\cot (x)}{\sqrt[4]{a^4-b^4 \csc ^2(x)}} \, dx","Int[Cot[x]/(a^4 - b^4*Csc[x]^2)^(1/4),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}","\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,"-(ArcTan[(a^4 - b^4*Csc[x]^2)^(1/4)/a]/a) + ArcTanh[(a^4 - b^4*Csc[x]^2)^(1/4)/a]/a","A",6,6,20,0.3000,1,"{4139, 266, 63, 298, 203, 206}"
446,1,174,0,5.1099075,"\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","Int[(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]","\frac{\cos ^2(x)}{6}-\frac{1}{4} \left(1-3 \sec ^2(x)\right)^{2/3}-\sqrt[6]{1-3 \sec ^2(x)}-\frac{3}{2} \log \left(1-\sqrt[6]{1-3 \sec ^2(x)}\right)+\frac{1}{2} \log \left(1-\sqrt{1-3 \sec ^2(x)}\right)+\frac{1}{6} \cos ^2(x) \sqrt{1-3 \sec ^2(x)}+\sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[6]{1-3 \sec ^2(x)}+1}{\sqrt{3}}\right)+\frac{1}{2} \tanh ^{-1}\left(\sqrt{1-3 \sec ^2(x)}\right)+\frac{1}{3} \log \left(1-\sqrt{-\left(3-\cos ^2(x)\right) \sec ^2(x)}\right)","-\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,"Sqrt[3]*ArcTan[(1 + 2*(1 - 3*Sec[x]^2)^(1/6))/Sqrt[3]] + ArcTanh[Sqrt[1 - 3*Sec[x]^2]]/2 + Cos[x]^2/6 + Log[1 - Sqrt[-((3 - Cos[x]^2)*Sec[x]^2)]]/3 - (3*Log[1 - (1 - 3*Sec[x]^2)^(1/6)])/2 + Log[1 - Sqrt[1 - 3*Sec[x]^2]]/2 - (1 - 3*Sec[x]^2)^(1/6) + (Cos[x]^2*Sqrt[1 - 3*Sec[x]^2])/6 - (1 - 3*Sec[x]^2)^(2/3)/4","A",29,16,61,0.2623,1,"{4361, 6742, 6684, 261, 6697, 341, 57, 618, 204, 31, 6688, 266, 47, 63, 206, 25}"
447,1,208,0,1.2259832,"\int \frac{\sec ^2(x) \left(-\cos (2 x)+2 \tan ^2(x)\right)}{(\tan (x) \tan (2 x))^{3/2}} \, dx","Int[(Sec[x]^2*(-Cos[2*x] + 2*Tan[x]^2))/(Tan[x]*Tan[2*x])^(3/2),x]","\frac{\left(1-\tan ^2(x)\right) \tan (x)}{3 \sqrt{2} \sqrt{\frac{\tan ^2(x)}{1-\tan ^2(x)}}}+\frac{3 \tan (x)}{4 \sqrt{2} \sqrt{\frac{\tan ^2(x)}{1-\tan ^2(x)}}}-\frac{11 \tan ^{-1}\left(\sqrt{\tan ^2(x)-1}\right) \tan (x)}{4 \sqrt{2} \sqrt{\frac{\tan ^2(x)}{1-\tan ^2(x)}} \sqrt{\tan ^2(x)-1}}+\frac{2 \tan ^{-1}\left(\frac{\sqrt{\tan ^2(x)-1}}{\sqrt{2}}\right) \tan (x)}{\sqrt{\frac{\tan ^2(x)}{1-\tan ^2(x)}} \sqrt{\tan ^2(x)-1}}+\frac{\left(1-\tan ^2(x)\right) \cot (x)}{4 \sqrt{2} \sqrt{\frac{\tan ^2(x)}{1-\tan ^2(x)}}}","\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,"(3*Tan[x])/(4*Sqrt[2]*Sqrt[Tan[x]^2/(1 - Tan[x]^2)]) + (Cot[x]*(1 - Tan[x]^2))/(4*Sqrt[2]*Sqrt[Tan[x]^2/(1 - Tan[x]^2)]) + (Tan[x]*(1 - Tan[x]^2))/(3*Sqrt[2]*Sqrt[Tan[x]^2/(1 - Tan[x]^2)]) - (11*ArcTan[Sqrt[-1 + Tan[x]^2]]*Tan[x])/(4*Sqrt[2]*Sqrt[Tan[x]^2/(1 - Tan[x]^2)]*Sqrt[-1 + Tan[x]^2]) + (2*ArcTan[Sqrt[-1 + Tan[x]^2]/Sqrt[2]]*Tan[x])/(Sqrt[Tan[x]^2/(1 - Tan[x]^2)]*Sqrt[-1 + Tan[x]^2])","B",21,10,29,0.3448,1,"{4397, 12, 6719, 6725, 266, 47, 50, 63, 203, 444}"
448,1,112,0,0.1685556,"\int \frac{\tan (x)}{\left(a^3-b^3 \cos ^n(x)\right)^{4/3}} \, dx","Int[Tan[x]/(a^3 - b^3*Cos[x]^n)^(4/3),x]","-\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}+\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}+\frac{\log (\cos (x))}{2 a^4}",1,"-((Sqrt[3]*ArcTan[(a + 2*(a^3 - b^3*Cos[x]^n)^(1/3))/(Sqrt[3]*a)])/(a^4*n)) - 3/(a^3*n*(a^3 - b^3*Cos[x]^n)^(1/3)) + Log[Cos[x]]/(2*a^4) - (3*Log[a - (a^3 - b^3*Cos[x]^n)^(1/3)])/(2*a^4*n)","A",7,7,20,0.3500,1,"{3230, 266, 51, 55, 617, 204, 31}"
449,1,162,0,0.2595556,"\int \left(1+2 \cos ^9(x)\right)^{5/6} \tan (x) \, dx","Int[(1 + 2*Cos[x]^9)^(5/6)*Tan[x],x]","-\frac{2}{15} \left(2 \cos ^9(x)+1\right)^{5/6}-\frac{1}{18} \log \left(\sqrt[3]{2 \cos ^9(x)+1}-\sqrt[6]{2 \cos ^9(x)+1}+1\right)+\frac{1}{18} \log \left(\sqrt[3]{2 \cos ^9(x)+1}+\sqrt[6]{2 \cos ^9(x)+1}+1\right)+\frac{\tan ^{-1}\left(\frac{1-2 \sqrt[6]{2 \cos ^9(x)+1}}{\sqrt{3}}\right)}{3 \sqrt{3}}-\frac{\tan ^{-1}\left(\frac{2 \sqrt[6]{2 \cos ^9(x)+1}+1}{\sqrt{3}}\right)}{3 \sqrt{3}}+\frac{2}{9} \tanh ^{-1}\left(\sqrt[6]{2 \cos ^9(x)+1}\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,"ArcTan[(1 - 2*(1 + 2*Cos[x]^9)^(1/6))/Sqrt[3]]/(3*Sqrt[3]) - ArcTan[(1 + 2*(1 + 2*Cos[x]^9)^(1/6))/Sqrt[3]]/(3*Sqrt[3]) + (2*ArcTanh[(1 + 2*Cos[x]^9)^(1/6)])/9 - (2*(1 + 2*Cos[x]^9)^(5/6))/15 - Log[1 - (1 + 2*Cos[x]^9)^(1/6) + (1 + 2*Cos[x]^9)^(1/3)]/18 + Log[1 + (1 + 2*Cos[x]^9)^(1/6) + (1 + 2*Cos[x]^9)^(1/3)]/18","A",14,10,15,0.6667,1,"{3230, 266, 50, 63, 296, 634, 618, 204, 628, 206}"
450,1,49,0,0.1081977,"\int \frac{\cos (x) \sin ^8(x)}{\left(2-5 \sin ^3(x)\right)^{4/3}} \, dx","Int[(Cos[x]*Sin[x]^8)/(2 - 5*Sin[x]^3)^(4/3),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)}}","-\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,"4/(125*(2 - 5*Sin[x]^3)^(1/3)) + (2*(2 - 5*Sin[x]^3)^(2/3))/125 - (2 - 5*Sin[x]^3)^(5/3)/625","A",4,3,19,0.1579,1,"{4334, 266, 43}"
451,1,20,0,0.2251512,"\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","Int[(Sec[x]^2*Tan[x]*(1 + (1 - 8*Tan[x]^2)^(1/3)))/(1 - 8*Tan[x]^2)^(2/3),x]","-\frac{3}{32} \left(\sqrt[3]{1-8 \tan ^2(x)}+1\right)^2","-\frac{3}{32} \left(\sqrt[3]{1-8 \tan ^2(x)}+1\right)^2",1,"(-3*(1 + (1 - 8*Tan[x]^2)^(1/3))^2)/32","A",2,2,33,0.06061,1,"{4342, 6686}"
452,1,35,0,0.9673542,"\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","Int[(Csc[x]*Sec[x]*(1 + (1 - 8*Tan[x]^2)^(1/3)))/(1 - 8*Tan[x]^2)^(2/3),x]","\frac{3}{2} \log \left(1-\sqrt[3]{9-8 \sec ^2(x)}\right)-\frac{1}{2} \log \left(1-\sec ^2(x)\right)","\frac{3}{2} \log \left(1-\sqrt[3]{1-8 \tan ^2(x)}\right)-\log (\tan (x))",1,"-Log[1 - Sec[x]^2]/2 + (3*Log[1 - (9 - 8*Sec[x]^2)^(1/3)])/2","A",15,9,31,0.2903,1,"{4366, 6725, 514, 444, 57, 618, 204, 31, 55}"
453,1,126,0,1.4050798,"\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","Int[((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]","2 \sqrt[4]{4-5 \cos ^2(x)}-\frac{\sqrt[4]{4-5 \cos ^2(x)}}{2 \left(\sqrt{4-5 \cos ^2(x)}+2\right)}-2 \sqrt{2} \tan ^{-1}\left(\frac{\sqrt[4]{4-5 \cos ^2(x)}}{\sqrt{2}}\right)+\frac{\tan ^{-1}\left(\frac{\sqrt[4]{4-5 \cos ^2(x)}}{\sqrt{2}}\right)}{\sqrt{2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{4-5 \cos ^2(x)}}{\sqrt{2}}\right)}{2 \sqrt{2}}","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,"ArcTan[(4 - 5*Cos[x]^2)^(1/4)/Sqrt[2]]/Sqrt[2] - 2*Sqrt[2]*ArcTan[(4 - 5*Cos[x]^2)^(1/4)/Sqrt[2]] - ArcTanh[(4 - 5*Cos[x]^2)^(1/4)/Sqrt[2]]/(2*Sqrt[2]) + 2*(4 - 5*Cos[x]^2)^(1/4) - (4 - 5*Cos[x]^2)^(1/4)/(2*(2 + Sqrt[4 - 5*Cos[x]^2]))","A",14,10,52,0.1923,1,"{4361, 6742, 6697, 341, 50, 63, 203, 470, 522, 207}"
454,1,25,0,0.0606313,"\int \cos ^3(x) \cos ^{\frac{2}{3}}(2 x) \sin (x) \, dx","Int[Cos[x]^3*Cos[2*x]^(2/3)*Sin[x],x]","-\frac{3}{64} \cos ^{\frac{8}{3}}(2 x)-\frac{3}{40} \cos ^{\frac{5}{3}}(2 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*Cos[2*x]^(8/3))/64","A",4,3,15,0.2000,1,"{4357, 266, 43}"
455,1,154,0,0.1924323,"\int \frac{\sin ^6(x) \tan (x)}{\cos ^{\frac{3}{4}}(2 x)} \, dx","Int[(Sin[x]^6*Tan[x])/Cos[2*x]^(3/4),x]","\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{\log \left(\sqrt{\cos (2 x)}-\sqrt{2} \sqrt[4]{\cos (2 x)}+1\right)}{2 \sqrt{2}}-\frac{\log \left(\sqrt{\cos (2 x)}+\sqrt{2} \sqrt[4]{\cos (2 x)}+1\right)}{2 \sqrt{2}}+\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt[4]{\cos (2 x)}\right)}{\sqrt{2}}-\frac{\tan ^{-1}\left(\sqrt{2} \sqrt[4]{\cos (2 x)}+1\right)}{\sqrt{2}}","\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,"ArcTan[1 - Sqrt[2]*Cos[2*x]^(1/4)]/Sqrt[2] - ArcTan[1 + Sqrt[2]*Cos[2*x]^(1/4)]/Sqrt[2] + (7*Cos[2*x]^(1/4))/4 - Cos[2*x]^(5/4)/5 + Cos[2*x]^(9/4)/36 + Log[1 - Sqrt[2]*Cos[2*x]^(1/4) + Sqrt[Cos[2*x]]]/(2*Sqrt[2]) - Log[1 + Sqrt[2]*Cos[2*x]^(1/4) + Sqrt[Cos[2*x]]]/(2*Sqrt[2])","A",14,10,15,0.6667,1,"{4361, 446, 88, 63, 211, 1165, 628, 1162, 617, 204}"
456,1,18,0,0.0190383,"\int \sqrt{\tan (x) \tan (2 x)} \, dx","Int[Sqrt[Tan[x]*Tan[2*x]],x]","-\tanh ^{-1}\left(\frac{\tan (2 x)}{\sqrt{\sec (2 x)-1}}\right)","-\tanh ^{-1}\left(\frac{\tan (x)}{\sqrt{\tan (x) \tan (2 x)}}\right)",1,"-ArcTanh[Tan[2*x]/Sqrt[-1 + Sec[2*x]]]","A",3,3,11,0.2727,1,"{4397, 3774, 207}"
457,1,32,0,0.0385622,"\int \sqrt{\cot (2 x) \tan (x)} \, dx","Int[Sqrt[Cot[2*x]*Tan[x]],x]","\tan ^{-1}\left(\frac{\sqrt{2} \tan (x)}{\sqrt{1-\tan ^2(x)}}\right)-\frac{\sin ^{-1}(\tan (x))}{\sqrt{2}}","\tan ^{-1}\left(\frac{\sqrt{2} \tan (x)}{\sqrt{1-\tan ^2(x)}}\right)-\frac{\sin ^{-1}(\tan (x))}{\sqrt{2}}",1,"-(ArcSin[Tan[x]]/Sqrt[2]) + ArcTan[(Sqrt[2]*Tan[x])/Sqrt[1 - Tan[x]^2]]","A",6,5,11,0.4545,1,"{12, 402, 216, 377, 203}"
458,1,31,0,0.0148877,"\int \frac{1}{x^5 \left(5+x^2\right)} \, dx","Int[1/(x^5*(5 + x^2)),x]","\frac{1}{50 x^2}-\frac{1}{20 x^4}-\frac{1}{250} \log \left(x^2+5\right)+\frac{\log (x)}{125}","\frac{1}{50 x^2}-\frac{1}{20 x^4}-\frac{1}{250} \log \left(x^2+5\right)+\frac{\log (x)}{125}",1,"-1/(20*x^4) + 1/(50*x^2) + Log[x]/125 - Log[5 + x^2]/250","A",3,2,11,0.1818,1,"{266, 44}"
459,1,39,0,0.0139152,"\int \frac{1}{x^6 \left(5+x^2\right)} \, dx","Int[1/(x^6*(5 + x^2)),x]","\frac{1}{75 x^3}-\frac{1}{25 x^5}-\frac{1}{125 x}-\frac{\tan ^{-1}\left(\frac{x}{\sqrt{5}}\right)}{125 \sqrt{5}}","\frac{1}{75 x^3}-\frac{1}{25 x^5}-\frac{1}{125 x}-\frac{\tan ^{-1}\left(\frac{x}{\sqrt{5}}\right)}{125 \sqrt{5}}",1,"-1/(25*x^5) + 1/(75*x^3) - 1/(125*x) - ArcTan[x/Sqrt[5]]/(125*Sqrt[5])","A",4,2,11,0.1818,1,"{325, 203}"
460,1,58,0,0.0319356,"\int \frac{1}{x \left(-4+x^2\right)^4} \, dx","Int[1/(x*(-4 + x^2)^4),x]","\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}","\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,"1/(24*(4 - x^2)^3) + 1/(64*(4 - x^2)^2) + 1/(128*(4 - x^2)) + Log[x]/256 - Log[4 - x^2]/512","A",3,2,11,0.1818,1,"{266, 44}"
461,1,52,0,0.023171,"\int \frac{1}{x \left(-2+x^2\right)^{5/2}} \, dx","Int[1/(x*(-2 + x^2)^(5/2)),x]","\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}}","\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*(-2 + x^2)^(3/2)) + 1/(4*Sqrt[-2 + x^2]) + ArcTan[Sqrt[-2 + x^2]/Sqrt[2]]/(4*Sqrt[2])","A",5,4,13,0.3077,1,"{266, 51, 63, 203}"
462,1,61,0,0.0318791,"\int \frac{\left(-10+x^2\right)^{5/2}}{x} \, dx","Int[(-10 + x^2)^(5/2)/x,x]","\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)","\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,"100*Sqrt[-10 + x^2] - (10*(-10 + x^2)^(3/2))/3 + (-10 + x^2)^(5/2)/5 - 100*Sqrt[10]*ArcTan[Sqrt[-10 + x^2]/Sqrt[10]]","A",6,4,13,0.3077,1,"{266, 50, 63, 203}"
463,1,16,0,0.0025427,"\int x^{1+2 n} \, dx","Int[x^(1 + 2*n),x]","\frac{x^{2 (n+1)}}{2 (n+1)}","\frac{x^{2 (n+1)}}{2 (n+1)}",1,"x^(2*(1 + n))/(2*(1 + n))","A",1,1,7,0.1429,1,"{30}"
464,1,46,0,0.0237345,"\int \frac{x^7}{\left(-5+x^2\right)^3} \, dx","Int[x^7/(-5 + x^2)^3,x]","\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)","\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,"x^2/2 - 125/(4*(5 - x^2)^2) + 75/(2*(5 - x^2)) + (15*Log[5 - x^2])/2","A",3,2,11,0.1818,1,"{266, 43}"
465,1,40,0,0.0353437,"\int \frac{-4 x^3+3 x^5}{\left(-1+x^2\right)^5} \, dx","Int[(-4*x^3 + 3*x^5)/(-1 + x^2)^5,x]","-\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}","-\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,"1/(8*(1 - x^2)^4) + 1/(3*(1 - x^2)^3) - 3/(4*(1 - x^2)^2)","A",4,3,19,0.1579,1,"{1593, 446, 77}"
466,1,27,0,0.0114618,"\int x^3 \left(1+x^2\right)^{9/14} \, dx","Int[x^3*(1 + x^2)^(9/14),x]","\frac{7}{37} \left(x^2+1\right)^{37/14}-\frac{7}{23} \left(x^2+1\right)^{23/14}","\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))/23 + (7*(1 + x^2)^(37/14))/37","A",3,2,13,0.1538,1,"{266, 43}"
467,1,38,0,0.0154403,"\int \frac{x^5}{\left(-4+x^2\right)^{13/6}} \, dx","Int[x^5/(-4 + x^2)^(13/6),x]","\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}}","\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,"-48/(7*(-4 + x^2)^(7/6)) - 24/(-4 + x^2)^(1/6) + (3*(-4 + x^2)^(5/6))/5","A",3,2,13,0.1538,1,"{266, 43}"
468,1,33,0,0.0042804,"\int \frac{1}{\left(1+2 x^2\right)^{5/2}} \, dx","Int[(1 + 2*x^2)^(-5/2),x]","\frac{2 x}{3 \sqrt{2 x^2+1}}+\frac{x}{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*(1 + 2*x^2)^(3/2)) + (2*x)/(3*Sqrt[1 + 2*x^2])","A",2,2,11,0.1818,1,"{192, 191}"
469,1,43,0,0.0061111,"\int \frac{1}{\left(-1-2 x+x^2\right)^{5/2}} \, dx","Int[(-1 - 2*x + x^2)^(-5/2),x]","\frac{1-x}{6 \left(x^2-2 x-1\right)^{3/2}}-\frac{1-x}{6 \sqrt{x^2-2 x-1}}","\frac{1-x}{6 \left(x^2-2 x-1\right)^{3/2}}-\frac{1-x}{6 \sqrt{x^2-2 x-1}}",1,"(1 - x)/(6*(-1 - 2*x + x^2)^(3/2)) - (1 - x)/(6*Sqrt[-1 - 2*x + x^2])","A",2,2,12,0.1667,1,"{614, 613}"
470,1,47,0,0.0094631,"\int \frac{1}{x^4 \left(-8+x^2\right)^{3/2}} \, dx","Int[1/(x^4*(-8 + x^2)^(3/2)),x]","-\frac{x}{192 \sqrt{x^2-8}}+\frac{1}{48 \sqrt{x^2-8} x}+\frac{1}{24 \sqrt{x^2-8} x^3}","-\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,"1/(24*x^3*Sqrt[-8 + x^2]) + 1/(48*x*Sqrt[-8 + x^2]) - x/(192*Sqrt[-8 + x^2])","A",3,2,13,0.1538,1,"{271, 191}"
471,1,28,0,0.0055334,"\int \frac{\left(5+x^2\right)^2}{x^{13/3}} \, dx","Int[(5 + x^2)^2/x^(13/3),x]","\frac{3 x^{2/3}}{2}-\frac{15}{2 x^{4/3}}-\frac{15}{2 x^{10/3}}","\frac{3 x^{2/3}}{2}-\frac{15}{2 x^{4/3}}-\frac{15}{2 x^{10/3}}",1,"-15/(2*x^(10/3)) - 15/(2*x^(4/3)) + (3*x^(2/3))/2","A",2,1,13,0.07692,1,"{270}"
472,1,52,0,0.0280003,"\int \frac{1}{x^7 \left(1+x^2\right)^3} \, dx","Int[1/(x^7*(1 + x^2)^3),x]","-\frac{2}{x^2+1}-\frac{3}{x^2}-\frac{1}{4 \left(x^2+1\right)^2}+\frac{3}{4 x^4}-\frac{1}{6 x^6}+5 \log \left(x^2+1\right)-10 \log (x)","-\frac{2}{x^2+1}-\frac{3}{x^2}-\frac{1}{4 \left(x^2+1\right)^2}+\frac{3}{4 x^4}-\frac{1}{6 x^6}+5 \log \left(x^2+1\right)-10 \log (x)",1,"-1/(6*x^6) + 3/(4*x^4) - 3/x^2 - 1/(4*(1 + x^2)^2) - 2/(1 + x^2) - 10*Log[x] + 5*Log[1 + x^2]","A",3,2,11,0.1818,1,"{266, 44}"
473,1,25,0,0.0569161,"\int \frac{\left(\frac{2+x^2}{x^2}\right)^{7/9}}{\left(2+x^2\right)^{3/2}} \, dx","Int[((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",3,3,23,0.1304,1,"{1991, 435, 264}"
474,1,50,0,0.0151225,"\int \frac{x^4}{\left(\sqrt{10}-x^2\right)^{9/2}} \, dx","Int[x^4/(Sqrt[10] - x^2)^(9/2),x]","\frac{x^5}{5 \sqrt{10} \left(\sqrt{10}-x^2\right)^{7/2}}-\frac{x^7}{175 \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,"x^5/(5*Sqrt[10]*(Sqrt[10] - x^2)^(7/2)) - x^7/(175*(Sqrt[10] - x^2)^(7/2))","A",2,2,19,0.1053,1,"{271, 264}"
475,1,24,0,0.0053872,"\int \frac{x^2}{\left(3-x^2\right)^{3/2}} \, dx","Int[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",2,2,15,0.1333,1,"{288, 216}"
476,1,40,0,0.0085835,"\int \frac{\left(25-x^2\right)^{3/2}}{x^4} \, dx","Int[(25 - x^2)^(3/2)/x^4,x]","-\frac{\left(25-x^2\right)^{3/2}}{3 x^3}+\frac{\sqrt{25-x^2}}{x}+\sin ^{-1}\left(\frac{x}{5}\right)","-\frac{\left(25-x^2\right)^{3/2}}{3 x^3}+\frac{\sqrt{25-x^2}}{x}+\sin ^{-1}\left(\frac{x}{5}\right)",1,"Sqrt[25 - x^2]/x - (25 - x^2)^(3/2)/(3*x^3) + ArcSin[x/5]","A",3,2,15,0.1333,1,"{277, 216}"
477,1,49,0,0.0074578,"\int \frac{1}{\left(1-2 x^2\right)^{7/2}} \, dx","Int[(1 - 2*x^2)^(-7/2),x]","\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}}","\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/(5*(1 - 2*x^2)^(5/2)) + (4*x)/(15*(1 - 2*x^2)^(3/2)) + (8*x)/(15*Sqrt[1 - 2*x^2])","A",3,2,11,0.1818,1,"{192, 191}"
478,1,47,0,0.0074342,"\int \frac{1}{\left(-7+6 x-x^2\right)^{5/2}} \, dx","Int[(-7 + 6*x - x^2)^(-5/2),x]","-\frac{3-x}{6 \sqrt{-x^2+6 x-7}}-\frac{3-x}{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,"-(3 - x)/(6*(-7 + 6*x - x^2)^(3/2)) - (3 - x)/(6*Sqrt[-7 + 6*x - x^2])","A",2,2,14,0.1429,1,"{614, 613}"
479,1,36,0,0.0116741,"\int \left(1-2 x-2 x^2\right)^3 \, dx","Int[(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",2,1,12,0.08333,1,"{611}"
480,1,39,0,0.0141987,"\int (-1+5 x) \left(-1-x+x^2\right)^2 \, dx","Int[(-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",2,1,16,0.06250,1,"{631}"
481,1,47,0,0.0089818,"\int \frac{1+3 x}{\left(1-8 x+2 x^2\right)^{5/2}} \, dx","Int[(1 + 3*x)/(1 - 8*x + 2*x^2)^(5/2),x]","\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}}","\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 - 2*x)/(6*(1 - 8*x + 2*x^2)^(3/2)) - (2*(2 - x))/(21*Sqrt[1 - 8*x + 2*x^2])","A",2,2,20,0.1000,1,"{638, 613}"
482,1,45,0,0.0216626,"\int \frac{-1-8 x+8 x^3}{\left(1+2 x-4 x^2\right)^{5/2}} \, dx","Int[(-1 - 8*x + 8*x^3)/(1 + 2*x - 4*x^2)^(5/2),x]","-\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}}","-\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,"(-4*(1 + x))/(15*(1 + 2*x - 4*x^2)^(3/2)) - (7 + 122*x)/(75*Sqrt[1 + 2*x - 4*x^2])","A",2,2,25,0.08000,1,"{1660, 636}"
483,1,83,0,0.0937162,"\int x^2 \cos ^5(x) \, dx","Int[x^2*Cos[x]^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)","\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,"(16*x*Cos[x])/15 + (8*x*Cos[x]^3)/45 + (2*x*Cos[x]^5)/25 - (298*Sin[x])/225 + (8*x^2*Sin[x])/15 + (4*x^2*Cos[x]^2*Sin[x])/15 + (x^2*Cos[x]^4*Sin[x])/5 + (76*Sin[x]^3)/675 - (2*Sin[x]^5)/125","A",9,4,8,0.5000,1,"{3311, 3296, 2637, 2633}"
484,1,73,0,0.0842397,"\int x^3 \sin ^3(x) \, dx","Int[x^3*Sin[x]^3,x]","\frac{1}{3} x^2 \sin ^3(x)+2 x^2 \sin (x)-\frac{2}{3} x^3 \cos (x)-\frac{1}{3} x^3 \sin ^2(x) \cos (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)","\frac{1}{3} x^2 \sin ^3(x)+2 x^2 \sin (x)-\frac{2}{3} x^3 \cos (x)-\frac{1}{3} x^3 \sin ^2(x) \cos (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,"(40*x*Cos[x])/9 - (2*x^3*Cos[x])/3 - (40*Sin[x])/9 + 2*x^2*Sin[x] + (2*x*Cos[x]*Sin[x]^2)/9 - (x^3*Cos[x]*Sin[x]^2)/3 - (2*Sin[x]^3)/27 + (x^2*Sin[x]^3)/3","A",8,4,8,0.5000,1,"{3311, 3296, 2637, 3310}"
485,1,105,0,0.1097443,"\int x^2 \sin ^6(x) \, dx","Int[x^2*Sin[x]^6,x]","\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}","\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,"(-245*x)/1152 + (5*x^3)/48 + (245*Cos[x]*Sin[x])/1152 - (5*x^2*Cos[x]*Sin[x])/16 + (5*x*Sin[x]^2)/16 + (65*Cos[x]*Sin[x]^3)/1728 - (5*x^2*Cos[x]*Sin[x]^3)/24 + (5*x*Sin[x]^4)/48 + (Cos[x]*Sin[x]^5)/108 - (x^2*Cos[x]*Sin[x]^5)/6 + (x*Sin[x]^6)/18","A",13,4,8,0.5000,1,"{3311, 30, 2635, 8}"
486,1,44,0,0.0420206,"\int x^2 \cos (x) \sin ^2(x) \, dx","Int[x^2*Cos[x]*Sin[x]^2,x]","\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)","\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,"(4*x*Cos[x])/9 - (4*Sin[x])/9 + (2*x*Cos[x]*Sin[x]^2)/9 - (2*Sin[x]^3)/27 + (x^2*Sin[x]^3)/3","A",4,4,10,0.4000,1,"{3443, 3310, 3296, 2637}"
487,1,33,0,0.0544898,"\int x \cos ^2(x) \cot ^2(x) \, dx","Int[x*Cos[x]^2*Cot[x]^2,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)","-\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[x]^2/4 - x*Cot[x] + Log[Sin[x]] - (x*Cos[x]*Sin[x])/2","A",6,5,10,0.5000,1,"{4408, 3310, 30, 3720, 3475}"
488,1,30,0,0.0407061,"\int x \sec (x) \tan ^3(x) \, dx","Int[x*Sec[x]*Tan[x]^3,x]","\frac{1}{3} x \sec ^3(x)-x \sec (x)+\frac{5}{6} \tanh ^{-1}(\sin (x))-\frac{1}{6} \tan (x) \sec (x)","\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,"(5*ArcTanh[Sin[x]])/6 - x*Sec[x] + (x*Sec[x]^3)/3 - (Sec[x]*Tan[x])/6","A",5,4,8,0.5000,1,"{2606, 4417, 3770, 3768}"
489,1,16,0,0.0177302,"\int x \sec ^2(x) \tan (x) \, dx","Int[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",3,3,8,0.3750,1,"{3757, 3767, 8}"
490,1,62,0,0.071817,"\int x \sin ^2(x) \tan (x) \, dx","Int[x*Sin[x]^2*Tan[x],x]","\frac{1}{2} i \text{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)","\frac{1}{2} i \text{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,"x/4 + (I/2)*x^2 - x*Log[1 + E^((2*I)*x)] + (I/2)*PolyLog[2, -E^((2*I)*x)] - (Cos[x]*Sin[x])/4 - (x*Sin[x]^2)/2","A",8,8,8,1.000,1,"{4407, 3443, 2635, 8, 3719, 2190, 2279, 2391}"
491,1,59,0,0.0610901,"\int x \tan ^3(x) \, dx","Int[x*Tan[x]^3,x]","-\frac{1}{2} i \text{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}","-\frac{1}{2} i \text{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,"x/2 - (I/2)*x^2 + x*Log[1 + E^((2*I)*x)] - (I/2)*PolyLog[2, -E^((2*I)*x)] - Tan[x]/2 + (x*Tan[x]^2)/2","A",7,7,6,1.167,1,"{3720, 3473, 8, 3719, 2190, 2279, 2391}"
492,1,12,0,0.0988092,"\int \frac{2 x+\sin (2 x)}{(\cos (x)+x \sin (x))^2} \, dx","Int[(2*x + Sin[2*x])/(Cos[x] + x*Sin[x])^2,x]","\frac{2}{\frac{\cot (x)}{x}+1}","\frac{2}{\frac{\cot (x)}{x}+1}",1,"2/(1 + Cot[x]/x)","A",2,2,18,0.1111,1,"{6711, 32}"
493,1,20,0,0.0341266,"\int \frac{x^2}{(x \cos (x)-\sin (x))^2} \, dx","Int[x^2/(x*Cos[x] - Sin[x])^2,x]","\frac{x \csc (x)}{x \cos (x)-\sin (x)}-\cot (x)","\frac{x \csc (x)}{x \cos (x)-\sin (x)}-\cot (x)",1,"-Cot[x] + (x*Csc[x])/(x*Cos[x] - Sin[x])","A",3,3,15,0.2000,1,"{4594, 3767, 8}"
494,1,22,0,0.0263098,"\int a^{m x} b^{n x} \, dx","Int[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",2,2,11,0.1818,1,"{2287, 2194}"
495,1,41,0,0.2076762,"\int a^{-x} b^{-x} \left(a^x-b^x\right)^2 \, dx","Int[(a^x - b^x)^2/(a^x*b^x),x]","-\frac{a^{-x} b^x}{\log (a)-\log (b)}+\frac{a^x b^{-x}}{\log (a)-\log (b)}-2 x","\frac{a^x b^{-x}-a^{-x} b^x}{\log (a)-\log (b)}-2 x",1,"-2*x + a^x/(b^x*(Log[a] - Log[b])) - b^x/(a^x*(Log[a] - Log[b]))","A",9,4,22,0.1818,1,"{2287, 6742, 2194, 8}"
496,1,9,0,0.0034646,"\int \left(-e^{-x}+e^x\right) \, dx","Int[-E^(-x) + E^x,x]","e^{-x}+e^x","e^{-x}+e^x",1,"E^(-x) + E^x","A",3,1,11,0.09091,1,"{2194}"
497,1,22,0,0.0177986,"\int \left(-e^{-x}+e^x\right)^2 \, dx","Int[(-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*E^(2*x)) + E^(2*x)/2 - 2*x","A",4,3,13,0.2308,1,"{2282, 266, 43}"
498,1,31,0,0.019334,"\int \left(-e^{-x}+e^x\right)^3 \, dx","Int[(-E^(-x) + E^x)^3,x]","\frac{e^{-3 x}}{3}-3 e^{-x}-3 e^x+\frac{e^{3 x}}{3}","\frac{e^{-3 x}}{3}-3 e^{-x}-3 e^x+\frac{e^{3 x}}{3}",1,"1/(3*E^(3*x)) - 3/E^x - 3*E^x + E^(3*x)/3","A",3,2,13,0.1538,1,"{2282, 270}"
499,1,36,0,0.0255405,"\int \left(-e^{-x}+e^x\right)^4 \, dx","Int[(-E^(-x) + E^x)^4,x]","6 x-\frac{e^{-4 x}}{4}+2 e^{-2 x}-2 e^{2 x}+\frac{e^{4 x}}{4}","6 x-\frac{e^{-4 x}}{4}+2 e^{-2 x}-2 e^{2 x}+\frac{e^{4 x}}{4}",1,"-1/(4*E^(4*x)) + 2/E^(2*x) - 2*E^(2*x) + E^(4*x)/4 + 6*x","A",4,3,13,0.2308,1,"{2282, 266, 43}"
500,1,52,0,0.0470604,"\int \left(-e^{-x}+e^x\right)^n \, dx","Int[(-E^(-x) + E^x)^n,x]","-\frac{\left(e^x-e^{-x}\right)^n \left(1-e^{2 x}\right)^{-n} \text{Hypergeometric2F1}\left(-n,-\frac{n}{2},1-\frac{n}{2},e^{2 x}\right)}{n}","-\frac{\left(1-e^{2 x}\right) \left(e^x-e^{-x}\right)^n \text{Hypergeometric2F1}\left(1,\frac{n+2}{2},1-\frac{n}{2},e^{2 x}\right)}{n}",1,"-(((-E^(-x) + E^x)^n*Hypergeometric2F1[-n, -n/2, 1 - n/2, E^(2*x)])/((1 - E^(2*x))^n*n))","A",4,4,13,0.3077,1,"{2282, 2032, 365, 364}"
501,1,43,0,0.0272945,"\int \left(a^{-4 x}-a^{2 x}\right)^3 \, dx","Int[(a^(-4*x) - a^(2*x))^3,x]","-\frac{a^{-12 x}}{12 \log (a)}+\frac{a^{-6 x}}{2 \log (a)}-\frac{a^{6 x}}{6 \log (a)}+3 x","-\frac{a^{-12 x}}{12 \log (a)}+\frac{a^{-6 x}}{2 \log (a)}-\frac{a^{6 x}}{6 \log (a)}+3 x",1,"3*x - 1/(12*a^(12*x)*Log[a]) + 1/(2*a^(6*x)*Log[a]) - a^(6*x)/(6*Log[a])","A",4,3,15,0.2000,1,"{2282, 266, 43}"
502,1,27,0,0.010812,"\int \left(a^{k x}+a^{l x}\right) \, dx","Int[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",3,1,11,0.09091,1,"{2194}"
503,1,53,0,0.0784878,"\int \left(a^{k x}+a^{l x}\right)^2 \, dx","Int[(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",6,2,13,0.1538,1,"{6742, 2194}"
504,1,79,0,0.1001817,"\int \left(a^{k x}+a^{l x}\right)^3 \, dx","Int[(a^(k*x) + a^(l*x))^3,x]","\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)}","\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)/(3*k*Log[a]) + a^(3*l*x)/(3*l*Log[a]) + (3*a^((2*k + l)*x))/((2*k + l)*Log[a]) + (3*a^((k + 2*l)*x))/((k + 2*l)*Log[a])","A",7,2,13,0.1538,1,"{6742, 2194}"
505,1,98,0,0.1247418,"\int \left(a^{k x}+a^{l x}\right)^4 \, dx","Int[(a^(k*x) + a^(l*x))^4,x]","\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)}","\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)/(4*k*Log[a]) + a^(4*l*x)/(4*l*Log[a]) + (3*a^(2*(k + l)*x))/((k + l)*Log[a]) + (4*a^((3*k + l)*x))/((3*k + l)*Log[a]) + (4*a^((k + 3*l)*x))/((k + 3*l)*Log[a])","A",8,2,13,0.1538,1,"{6742, 2194}"
506,1,80,0,0.0771031,"\int \left(a^{k x}+a^{l x}\right)^n \, dx","Int[(a^(k*x) + a^(l*x))^n,x]","\frac{\left(a^{x (-(k-l))}+1\right)^{-n} \left(a^{k x}+a^{l x}\right)^n \text{Hypergeometric2F1}\left(-n,-\frac{k n}{k-l},1-\frac{k n}{k-l},-a^{x (-(k-l))}\right)}{k n \log (a)}","\frac{\left(a^{x (k-l)}+1\right) \left(a^{k x}+a^{l x}\right)^n \text{Hypergeometric2F1}\left(1,\frac{k n}{k-l}+1,\frac{l n}{k-l}+1,-a^{x (k-l)}\right)}{l n \log (a)}",1,"((a^(k*x) + a^(l*x))^n*Hypergeometric2F1[-n, -((k*n)/(k - l)), 1 - (k*n)/(k - l), -a^(-((k - l)*x))])/((1 + a^(-((k - l)*x)))^n*k*n*Log[a])","A",2,2,13,0.1538,1,"{2285, 2251}"
507,1,28,0,0.0083801,"\int \left(a^{k x}-a^{l x}\right) \, dx","Int[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",3,1,13,0.07692,1,"{2194}"
508,1,53,0,0.071417,"\int \left(a^{k x}-a^{l x}\right)^2 \, dx","Int[(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",6,2,15,0.1333,1,"{6742, 2194}"
509,1,79,0,0.0831905,"\int \left(a^{k x}-a^{l x}\right)^3 \, dx","Int[(a^(k*x) - a^(l*x))^3,x]","-\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)}","-\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)/(3*k*Log[a]) - a^(3*l*x)/(3*l*Log[a]) - (3*a^((2*k + l)*x))/((2*k + l)*Log[a]) + (3*a^((k + 2*l)*x))/((k + 2*l)*Log[a])","A",7,2,15,0.1333,1,"{6742, 2194}"
510,1,98,0,0.0984358,"\int \left(a^{k x}-a^{l x}\right)^4 \, dx","Int[(a^(k*x) - a^(l*x))^4,x]","\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)}","\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)/(4*k*Log[a]) + a^(4*l*x)/(4*l*Log[a]) + (3*a^(2*(k + l)*x))/((k + l)*Log[a]) - (4*a^((3*k + l)*x))/((3*k + l)*Log[a]) - (4*a^((k + 3*l)*x))/((k + 3*l)*Log[a])","A",8,2,15,0.1333,1,"{6742, 2194}"
511,1,82,0,0.0623792,"\int \left(a^{k x}-a^{l x}\right)^n \, dx","Int[(a^(k*x) - a^(l*x))^n,x]","\frac{\left(1-a^{x (-(k-l))}\right)^{-n} \left(a^{k x}-a^{l x}\right)^n \text{Hypergeometric2F1}\left(-n,-\frac{k n}{k-l},1-\frac{k n}{k-l},a^{x (-(k-l))}\right)}{k n \log (a)}","\frac{\left(1-a^{x (k-l)}\right) \left(a^{k x}-a^{l x}\right)^n \text{Hypergeometric2F1}\left(1,\frac{k n}{k-l}+1,\frac{l n}{k-l}+1,a^{x (k-l)}\right)}{l n \log (a)}",1,"((a^(k*x) - a^(l*x))^n*Hypergeometric2F1[-n, -((k*n)/(k - l)), 1 - (k*n)/(k - l), a^(-((k - l)*x))])/((1 - a^(-((k - l)*x)))^n*k*n*Log[a])","A",2,2,15,0.1333,1,"{2285, 2251}"
512,1,15,0,0.0055083,"\int \left(1+a^{m x}\right) \, dx","Int[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",2,1,7,0.1429,1,"{2194}"
513,1,33,0,0.0134742,"\int \left(1+a^{m x}\right)^2 \, dx","Int[(1 + a^(m*x))^2,x]","\frac{2 a^{m x}}{m \log (a)}+\frac{a^{2 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 + (2*a^(m*x))/(m*Log[a]) + a^(2*m*x)/(2*m*Log[a])","A",3,2,9,0.2222,1,"{2282, 43}"
514,1,50,0,0.0157746,"\int \left(1+a^{m x}\right)^3 \, dx","Int[(1 + a^(m*x))^3,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","\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 + (3*a^(m*x))/(m*Log[a]) + (3*a^(2*m*x))/(2*m*Log[a]) + a^(3*m*x)/(3*m*Log[a])","A",3,2,9,0.2222,1,"{2282, 43}"
515,1,65,0,0.0191191,"\int \left(1+a^{m x}\right)^4 \, dx","Int[(1 + a^(m*x))^4,x]","\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","\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,"x + (4*a^(m*x))/(m*Log[a]) + (3*a^(2*m*x))/(m*Log[a]) + (4*a^(3*m*x))/(3*m*Log[a]) + a^(4*m*x)/(4*m*Log[a])","A",3,2,9,0.2222,1,"{2282, 43}"
516,1,40,0,0.0210817,"\int \left(1+a^{m x}\right)^n \, dx","Int[(1 + a^(m*x))^n,x]","-\frac{\left(a^{m x}+1\right)^{n+1} \text{Hypergeometric2F1}\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} \text{Hypergeometric2F1}\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",2,2,9,0.2222,1,"{2282, 65}"
517,1,16,0,0.0050012,"\int \left(1-a^{m x}\right) \, dx","Int[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",2,1,9,0.1111,1,"{2194}"
518,1,33,0,0.0134689,"\int \left(1-a^{m x}\right)^2 \, dx","Int[(1 - a^(m*x))^2,x]","-\frac{2 a^{m x}}{m \log (a)}+\frac{a^{2 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 - (2*a^(m*x))/(m*Log[a]) + a^(2*m*x)/(2*m*Log[a])","A",3,2,11,0.1818,1,"{2282, 43}"
519,1,50,0,0.0167983,"\int \left(1-a^{m x}\right)^3 \, dx","Int[(1 - a^(m*x))^3,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","-\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 - (3*a^(m*x))/(m*Log[a]) + (3*a^(2*m*x))/(2*m*Log[a]) - a^(3*m*x)/(3*m*Log[a])","A",3,2,11,0.1818,1,"{2282, 43}"
520,1,65,0,0.0191933,"\int \left(1-a^{m x}\right)^4 \, dx","Int[(1 - a^(m*x))^4,x]","-\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","-\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,"x - (4*a^(m*x))/(m*Log[a]) + (3*a^(2*m*x))/(m*Log[a]) - (4*a^(3*m*x))/(3*m*Log[a]) + a^(4*m*x)/(4*m*Log[a])","A",3,2,11,0.1818,1,"{2282, 43}"
521,1,44,0,0.0187026,"\int \left(1-a^{m x}\right)^n \, dx","Int[(1 - a^(m*x))^n,x]","-\frac{\left(1-a^{m x}\right)^{n+1} \text{Hypergeometric2F1}\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} \text{Hypergeometric2F1}\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",2,2,11,0.1818,1,"{2282, 65}"
522,1,24,0,0.0161057,"\int \frac{1}{b+a e^{n x}} \, dx","Int[(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",4,4,11,0.3636,1,"{2282, 36, 29, 31}"
523,1,123,0,0.0943053,"\int \frac{e^x}{b+a e^{3 x}} \, dx","Int[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)}{6 \sqrt[3]{a} b^{2/3}}+\frac{\log \left(\sqrt[3]{a} e^x+\sqrt[3]{b}\right)}{3 \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}}","\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,"-(ArcTan[(b^(1/3) - 2*a^(1/3)*E^x)/(Sqrt[3]*b^(1/3))]/(Sqrt[3]*a^(1/3)*b^(2/3))) + Log[b^(1/3) + a^(1/3)*E^x]/(3*a^(1/3)*b^(2/3)) - Log[b^(2/3) - a^(1/3)*b^(1/3)*E^x + a^(2/3)*E^(2*x)]/(6*a^(1/3)*b^(2/3))","A",7,7,15,0.4667,1,"{2249, 200, 31, 634, 617, 204, 628}"
524,1,12,0,0.0218481,"\int \frac{-1+e^x}{1+e^x} \, dx","Int[(-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",3,2,13,0.1538,1,"{2282, 72}"
525,1,47,0,0.0591705,"\int \frac{e^{4 x}}{1-2 e^{2 x}+3 e^{4 x}} \, dx","Int[E^(4*x)/(1 - 2*E^(2*x) + 3*E^(4*x)),x]","\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}}","\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,"-ArcTan[(1 - 3*E^(2*x))/Sqrt[2]]/(6*Sqrt[2]) + Log[1 - 2*E^(2*x) + 3*E^(4*x)]/12","A",5,5,24,0.2083,1,"{2282, 634, 618, 204, 628}"
526,1,39,0,0.0615397,"\int \frac{e^x+e^{5 x}}{-1+e^x-e^{2 x}+e^{3 x}} \, dx","Int[(E^x + E^(5*x))/(-1 + E^x - E^(2*x) + E^(3*x)),x]","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)","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,"E^x + E^(2*x)/2 - ArcTan[E^x] + Log[1 - E^x] - Log[1 + E^(2*x)]/2","A",6,5,29,0.1724,1,"{2282, 2074, 635, 203, 260}"
527,1,30,0,0.0384192,"\int e^{n x} \left(a+b e^{n x}\right)^{r/s} \, dx","Int[E^(n*x)*(a + b*E^(n*x))^(r/s),x]","\frac{s \left(a+b e^{n x}\right)^{\frac{r+s}{s}}}{b n (r+s)}","\frac{s \left(a+b e^{n x}\right)^{\frac{r+s}{s}}}{b n (r+s)}",1,"((a + b*E^(n*x))^((r + s)/s)*s)/(b*n*(r + s))","A",2,2,21,0.09524,1,"{2246, 32}"
528,1,54,0,0.021602,"\int \sqrt[4]{1-2 e^{x/3}} \, dx","Int[(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",6,6,15,0.4000,1,"{2282, 50, 63, 212, 206, 203}"
529,1,59,0,0.0305085,"\int \left(a+b e^{n x}\right)^{r/s} \, dx","Int[(a + b*E^(n*x))^(r/s),x]","-\frac{s \left(a+b e^{n x}\right)^{\frac{r+s}{s}} \text{Hypergeometric2F1}\left(1,\frac{r+s}{s},\frac{r}{s}+2,\frac{b e^{n x}}{a}+1\right)}{a n (r+s)}","-\frac{s \left(a+b e^{n x}\right)^{\frac{r+s}{s}} \text{Hypergeometric2F1}\left(1,\frac{r+s}{s},\frac{r}{s}+2,\frac{b e^{n x}}{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",2,2,15,0.1333,1,"{2282, 65}"
530,1,18,0,0.0282844,"\int \frac{e^x}{\sqrt{a^2+e^{2 x}}} \, dx","Int[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",3,3,17,0.1765,1,"{2249, 217, 206}"
531,1,20,0,0.02868,"\int \frac{e^x}{\sqrt{-a^2+e^{2 x}}} \, dx","Int[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",3,3,19,0.1579,1,"{2249, 217, 206}"
532,1,40,0,0.1025061,"\int \frac{e^{3 x/4}}{\left(-2+e^{3 x/4}\right) \sqrt{-2+e^{3 x/4}+e^{3 x/2}}} \, dx","Int[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{2-5 e^{3 x/4}}{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",3,3,39,0.07692,1,"{2282, 724, 206}"
533,1,57,0,0.0517065,"\int e^{-2 x} \left(-3+e^{7 x}\right)^{2/3} \, dx","Int[(-3 + E^(7*x))^(2/3)/E^(2*x),x]","-\frac{3^{2/3} e^{-2 x} \left(e^{7 x}-3\right)^{2/3} \text{Hypergeometric2F1}\left(-\frac{2}{3},-\frac{2}{7},\frac{5}{7},\frac{e^{7 x}}{3}\right)}{2 \left(3-e^{7 x}\right)^{2/3}}","\frac{1}{6} e^{-2 x} \left(e^{7 x}-3\right)^{5/3} \text{Hypergeometric2F1}\left(1,\frac{29}{21},\frac{5}{7},\frac{e^{7 x}}{3}\right)",1,"-(3^(2/3)*(-3 + E^(7*x))^(2/3)*Hypergeometric2F1[-2/3, -2/7, 5/7, E^(7*x)/3])/(2*E^(2*x)*(3 - E^(7*x))^(2/3))","A",4,4,17,0.2353,1,"{2249, 335, 365, 364}"
534,1,73,0,0.0474549,"\int \frac{e^{2 x}}{\left(3-e^{x/2}\right)^{3/4}} \, dx","Int[E^(2*x)/(3 - E^(x/2))^(3/4),x]","\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}}","\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,"-216*(3 - E^(x/2))^(1/4) + (216*(3 - E^(x/2))^(5/4))/5 - 8*(3 - E^(x/2))^(9/4) + (8*(3 - E^(x/2))^(13/4))/13","A",3,2,21,0.09524,1,"{2248, 43}"
535,1,44,0,0.0317714,"\int e^{-x/2} x^3 \, dx","Int[x^3/E^(x/2),x]","-2 e^{-x/2} x^3-12 e^{-x/2} x^2-48 e^{-x/2} x-96 e^{-x/2}","-2 e^{-x/2} x^3-12 e^{-x/2} x^2-48 e^{-x/2} x-96 e^{-x/2}",1,"-96/E^(x/2) - (48*x)/E^(x/2) - (12*x^2)/E^(x/2) - (2*x^3)/E^(x/2)","A",4,2,11,0.1818,1,"{2176, 2194}"
536,1,39,0,0.0330314,"\int \frac{e^{-x/2}}{x^3} \, dx","Int[1/(E^(x/2)*x^3),x]","\frac{1}{8} \text{ExpIntegralEi}\left(-\frac{x}{2}\right)-\frac{e^{-x/2}}{2 x^2}+\frac{e^{-x/2}}{4 x}","\frac{1}{8} \text{ExpIntegralEi}\left(-\frac{x}{2}\right)-\frac{e^{-x/2}}{2 x^2}+\frac{e^{-x/2}}{4 x}",1,"-1/(2*E^(x/2)*x^2) + 1/(4*E^(x/2)*x) + ExpIntegralEi[-x/2]/8","A",3,2,11,0.1818,1,"{2177, 2178}"
537,1,44,0,0.0215737,"\int a^{3 x} x^2 \, dx","Int[a^(3*x)*x^2,x]","\frac{x^2 a^{3 x}}{3 \log (a)}-\frac{2 x a^{3 x}}{9 \log ^2(a)}+\frac{2 a^{3 x}}{27 \log ^3(a)}","\frac{x^2 a^{3 x}}{3 \log (a)}-\frac{2 x a^{3 x}}{9 \log ^2(a)}+\frac{2 a^{3 x}}{27 \log ^3(a)}",1,"(2*a^(3*x))/(27*Log[a]^3) - (2*a^(3*x)*x)/(9*Log[a]^2) + (a^(3*x)*x^2)/(3*Log[a])","A",3,2,9,0.2222,1,"{2176, 2194}"
538,1,12,0,0.0487273,"\int e^{x^2} x \left(1+x^2\right) \, dx","Int[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",5,3,12,0.2500,1,"{2226, 2209, 2212}"
539,1,32,0,0.0550637,"\int \frac{x}{\left(e^{-x}+e^x\right)^2} \, dx","Int[x/(E^(-x) + E^x)^2,x]","-\frac{x}{2 \left(e^{2 x}+1\right)}+\frac{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,"x/2 - x/(2*(1 + E^(2*x))) - Log[1 + E^(2*x)]/4","A",6,6,13,0.4615,1,"{2283, 2191, 2282, 36, 29, 31}"
540,1,15,0,0.0569821,"\int \frac{e^x \left(1-x-x^2\right)}{\sqrt{1-x^2}} \, dx","Int[(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",1,1,25,0.04000,1,"{2288}"
541,1,27,0,0.0105735,"\int e^{-3 x} \cos (2 x) \, dx","Int[Cos[2*x]/E^(3*x),x]","\frac{2}{13} e^{-3 x} \sin (2 x)-\frac{3}{13} e^{-3 x} \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])/(13*E^(3*x)) + (2*Sin[2*x])/(13*E^(3*x))","A",1,1,10,0.1000,1,"{4433}"
542,1,35,0,0.111145,"\int \frac{\cos \left(\frac{x}{2}\right)+\sin \left(\frac{x}{2}\right)}{\sqrt[3]{e^x}} \, dx","Int[(Cos[x/2] + Sin[x/2])/(E^x)^(1/3),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}}","\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,"(-30*Cos[x/2])/(13*(E^x)^(1/3)) + (6*Sin[x/2])/(13*(E^x)^(1/3))","A",6,4,21,0.1905,1,"{2281, 6742, 4433, 4432}"
543,1,57,0,0.0284353,"\int \frac{\cos \left(\frac{3 x}{2}\right)}{\sqrt[4]{3^{3 x}}} \, dx","Int[Cos[(3*x)/2]/(3^(3*x))^(1/4),x]","\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)}","\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])/(3*(3^(3*x))^(1/4)*(4 + Log[3]^2)) + (8*Sin[(3*x)/2])/(3*(3^(3*x))^(1/4)*(4 + Log[3]^2))","A",2,2,16,0.1250,1,"{2281, 4433}"
544,1,54,0,0.0230822,"\int e^{m x} \cos ^2(x) \, dx","Int[E^(m*x)*Cos[x]^2,x]","\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}","\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,"(2*E^(m*x))/(m*(4 + m^2)) + (E^(m*x)*m*Cos[x]^2)/(4 + m^2) + (2*E^(m*x)*Cos[x]*Sin[x])/(4 + m^2)","A",2,2,10,0.2000,1,"{4435, 2194}"
545,1,82,0,0.0353972,"\int e^{m x} \sin ^3(x) \, dx","Int[E^(m*x)*Sin[x]^3,x]","\frac{m e^{m x} \sin ^3(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}-\frac{3 e^{m x} \sin ^2(x) \cos (x)}{m^2+9}","\frac{m e^{m x} \sin ^3(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}-\frac{3 e^{m x} \sin ^2(x) \cos (x)}{m^2+9}",1,"(-6*E^(m*x)*Cos[x])/(9 + 10*m^2 + m^4) + (6*E^(m*x)*m*Sin[x])/(9 + 10*m^2 + m^4) - (3*E^(m*x)*Cos[x]*Sin[x]^2)/(9 + m^2) + (E^(m*x)*m*Sin[x]^3)/(9 + m^2)","A",2,2,10,0.2000,1,"{4434, 4432}"
546,1,79,0,0.0449323,"\int \frac{\cos ^3\left(\frac{x}{3}\right)}{\sqrt{e^x}} \, dx","Int[Cos[x/3]^3/Sqrt[E^x],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}}","\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,"(-48*Cos[x/3])/(65*Sqrt[E^x]) - (2*Cos[x/3]^3)/(5*Sqrt[E^x]) + (32*Sin[x/3])/(65*Sqrt[E^x]) + (4*Cos[x/3]^2*Sin[x/3])/(5*Sqrt[E^x])","A",3,3,16,0.1875,1,"{2281, 4435, 4433}"
547,1,36,0,0.0437049,"\int e^{2 x} \cos ^2(x) \sin ^2(x) \, dx","Int[E^(2*x)*Cos[x]^2*Sin[x]^2,x]","\frac{e^{2 x}}{16}-\frac{1}{40} e^{2 x} \sin (4 x)-\frac{1}{80} e^{2 x} \cos (4 x)","\frac{e^{2 x}}{16}-\frac{1}{40} e^{2 x} \sin (4 x)-\frac{1}{80} e^{2 x} \cos (4 x)",1,"E^(2*x)/16 - (E^(2*x)*Cos[4*x])/80 - (E^(2*x)*Sin[4*x])/40","A",4,3,14,0.2143,1,"{4469, 2194, 4433}"
548,1,36,0,0.0433467,"\int e^{3 x} \cos ^2\left(\frac{3 x}{2}\right) \sin ^2\left(\frac{3 x}{2}\right) \, dx","Int[E^(3*x)*Cos[(3*x)/2]^2*Sin[(3*x)/2]^2,x]","\frac{e^{3 x}}{24}-\frac{1}{60} e^{3 x} \sin (6 x)-\frac{1}{120} e^{3 x} \cos (6 x)","\frac{e^{3 x}}{24}-\frac{1}{60} e^{3 x} \sin (6 x)-\frac{1}{120} e^{3 x} \cos (6 x)",1,"E^(3*x)/24 - (E^(3*x)*Cos[6*x])/120 - (E^(3*x)*Sin[6*x])/60","A",4,3,22,0.1364,1,"{4469, 2194, 4433}"
549,1,85,0,0.0774187,"\int e^{m x} \tan ^2(x) \, dx","Int[E^(m*x)*Tan[x]^2,x]","\frac{4 e^{m x} \text{Hypergeometric2F1}\left(1,-\frac{i m}{2},1-\frac{i m}{2},-e^{2 i x}\right)}{m}-\frac{4 e^{m x} \text{Hypergeometric2F1}\left(2,-\frac{i m}{2},1-\frac{i m}{2},-e^{2 i x}\right)}{m}-\frac{e^{m x}}{m}","-\frac{e^{m x}}{m}+\frac{4 e^{(m+2 i) x} \text{Hypergeometric2F1}\left(2,1-\frac{i m}{2},2-\frac{i m}{2},-e^{2 i x}\right)}{m+2 i}",1,"-(E^(m*x)/m) + (4*E^(m*x)*Hypergeometric2F1[1, (-I/2)*m, 1 - (I/2)*m, -E^((2*I)*x)])/m - (4*E^(m*x)*Hypergeometric2F1[2, (-I/2)*m, 1 - (I/2)*m, -E^((2*I)*x)])/m","A",5,3,10,0.3000,1,"{4442, 2194, 2251}"
550,1,45,0,0.0180852,"\int e^{m x} \csc ^2(x) \, dx","Int[E^(m*x)*Csc[x]^2,x]","-\frac{4 e^{(m+2 i) x} \text{Hypergeometric2F1}\left(2,1-\frac{i m}{2},2-\frac{i m}{2},e^{2 i x}\right)}{m+2 i}","-\frac{4 e^{(m+2 i) x} \text{Hypergeometric2F1}\left(2,1-\frac{i m}{2},2-\frac{i m}{2},e^{2 i x}\right)}{m+2 i}",1,"(-4*E^((2*I + m)*x)*Hypergeometric2F1[2, 1 - (I/2)*m, 2 - (I/2)*m, E^((2*I)*x)])/(2*I + m)","A",1,1,10,0.1000,1,"{4453}"
551,1,77,0,0.0363634,"\int e^{m x} \sec ^3(x) \, dx","Int[E^(m*x)*Sec[x]^3,x]","(-m+i) \left(-e^{(m+i) x}\right) \text{Hypergeometric2F1}\left(1,\frac{1}{2} (1-i m),\frac{1}{2} (3-i m),-e^{2 i x}\right)-\frac{1}{2} m e^{m x} \sec (x)+\frac{1}{2} e^{m x} \tan (x) \sec (x)","\frac{8 e^{(m+3 i) x} \text{Hypergeometric2F1}\left(3,\frac{1}{2} (3-i m),\frac{1}{2} (5-i m),-e^{2 i x}\right)}{m+3 i}",1,"-(E^((I + m)*x)*(I - m)*Hypergeometric2F1[1, (1 - I*m)/2, (3 - I*m)/2, -E^((2*I)*x)]) - (E^(m*x)*m*Sec[x])/2 + (E^(m*x)*Sec[x]*Tan[x])/2","A",2,2,10,0.2000,1,"{4448, 4451}"
552,1,28,0,0.0312807,"\int \frac{e^x}{1+\cos (x)} \, dx","Int[E^x/(1 + Cos[x]),x]","(1-i) e^{(1+i) x} \text{Hypergeometric2F1}\left(1-i,2,2-i,-e^{i x}\right)","(1-i) e^{(1+i) x} \text{Hypergeometric2F1}\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",2,2,10,0.2000,1,"{4457, 4451}"
553,1,26,0,0.0321949,"\int \frac{e^x}{1-\cos (x)} \, dx","Int[E^x/(1 - Cos[x]),x]","(-1+i) e^{(1+i) x} \text{Hypergeometric2F1}\left(1-i,2,2-i,e^{i x}\right)","(-1+i) e^{(1+i) x} \text{Hypergeometric2F1}\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",2,2,12,0.1667,1,"{4458, 4453}"
554,1,30,0,0.0342418,"\int \frac{e^x}{1+\sin (x)} \, dx","Int[E^x/(1 + Sin[x]),x]","(-1+i) e^{(1-i) x} \text{Hypergeometric2F1}\left(1+i,2,2+i,-i e^{-i x}\right)","(-1+i) e^{(1-i) x} \text{Hypergeometric2F1}\left(1+i,2,2+i,-i e^{-i x}\right)",1,"(-1 + I)*E^((1 - I)*x)*Hypergeometric2F1[1 + I, 2, 2 + I, (-I)/E^(I*x)]","A",2,2,10,0.2000,1,"{4456, 4450}"
555,1,30,0,0.0340965,"\int \frac{e^x}{1-\sin (x)} \, dx","Int[E^x/(1 - Sin[x]),x]","(1+i) e^{(1+i) x} \text{Hypergeometric2F1}\left(1-i,2,2-i,-i e^{i x}\right)","(1+i) e^{(1+i) x} \text{Hypergeometric2F1}\left(1-i,2,2-i,-i e^{i x}\right)",1,"(1 + I)*E^((1 + I)*x)*Hypergeometric2F1[1 - I, 2, 2 - I, (-I)*E^(I*x)]","A",2,2,12,0.1667,1,"{4456, 4450}"
556,1,15,0,0.0299952,"\int \frac{e^x (1-\sin (x))}{1-\cos (x)} \, dx","Int[(E^x*(1 - Sin[x]))/(1 - Cos[x]),x]","-\frac{e^x \sin (x)}{1-\cos (x)}","-\frac{e^x \sin (x)}{1-\cos (x)}",1,"-((E^x*Sin[x])/(1 - Cos[x]))","A",1,1,18,0.05556,1,"{2288}"
557,1,45,0,0.1131979,"\int \frac{e^x (1+\sin (x))}{1-\cos (x)} \, dx","Int[(E^x*(1 + Sin[x]))/(1 - Cos[x]),x]","-4 i e^x \text{Hypergeometric2F1}\left(-i,1,1-i,e^{i x}\right)+2 i e^x-\frac{e^x \sin (x)}{1-\cos (x)}","\frac{e^x \sin (x)}{1-\cos (x)}-(2-2 i) e^{(1+i) x} \text{Hypergeometric2F1}\left(1-i,2,2-i,e^{i x}\right)",1,"(2*I)*E^x - (4*I)*E^x*Hypergeometric2F1[-I, 1, 1 - I, E^(I*x)] - (E^x*Sin[x])/(1 - Cos[x])","A",7,6,16,0.3750,1,"{4463, 4461, 4443, 2194, 2251, 2288}"
558,1,12,0,0.0277275,"\int \frac{e^x (1+\sin (x))}{1+\cos (x)} \, dx","Int[(E^x*(1 + Sin[x]))/(1 + Cos[x]),x]","\frac{e^x \sin (x)}{\cos (x)+1}","\frac{e^x \sin (x)}{\cos (x)+1}",1,"(E^x*Sin[x])/(1 + Cos[x])","A",1,1,14,0.07143,1,"{2288}"
559,1,44,0,0.1112785,"\int \frac{e^x (1-\sin (x))}{1+\cos (x)} \, dx","Int[(E^x*(1 - Sin[x]))/(1 + Cos[x]),x]","-4 i e^x \text{Hypergeometric2F1}\left(-i,1,1-i,-e^{i x}\right)+2 i e^x+\frac{e^x \sin (x)}{\cos (x)+1}","-\frac{e^x \sin (x)}{\cos (x)+1}+(2-2 i) e^{(1+i) x} \text{Hypergeometric2F1}\left(1-i,2,2-i,-e^{i x}\right)",1,"(2*I)*E^x - (4*I)*E^x*Hypergeometric2F1[-I, 1, 1 - I, -E^(I*x)] + (E^x*Sin[x])/(1 + Cos[x])","A",7,6,16,0.3750,1,"{4463, 4460, 4442, 2194, 2251, 2288}"
560,1,48,0,0.1285515,"\int \frac{e^x (1-\cos (x))}{1-\sin (x)} \, dx","Int[(E^x*(1 - Cos[x]))/(1 - Sin[x]),x]","-4 i e^x \text{Hypergeometric2F1}\left(-i,1,1-i,-i e^{i x}\right)+2 i e^x+\frac{e^x \cos (x)}{1-\sin (x)}","-\frac{e^x \cos (x)}{1-\sin (x)}+(2+2 i) e^{(1+i) x} \text{Hypergeometric2F1}\left(1-i,2,2-i,-i e^{i x}\right)",1,"(2*I)*E^x - (4*I)*E^x*Hypergeometric2F1[-I, 1, 1 - I, (-I)*E^(I*x)] + (E^x*Cos[x])/(1 - Sin[x])","A",7,6,18,0.3333,1,"{4462, 4459, 4442, 2194, 2251, 2288}"
561,1,14,0,0.0240413,"\int \frac{e^x (1+\cos (x))}{1-\sin (x)} \, dx","Int[(E^x*(1 + Cos[x]))/(1 - Sin[x]),x]","\frac{e^x \cos (x)}{1-\sin (x)}","\frac{e^x \cos (x)}{1-\sin (x)}",1,"(E^x*Cos[x])/(1 - Sin[x])","A",1,1,16,0.06250,1,"{2288}"
562,1,47,0,0.1273772,"\int \frac{e^x (1+\cos (x))}{1+\sin (x)} \, dx","Int[(E^x*(1 + Cos[x]))/(1 + Sin[x]),x]","4 i e^x \text{Hypergeometric2F1}\left(i,1,1+i,-i e^{-i x}\right)-2 i e^x-\frac{e^x \cos (x)}{\sin (x)+1}","\frac{e^x \cos (x)}{\sin (x)+1}-(2+2 i) e^{(1+i) x} \text{Hypergeometric2F1}\left(1-i,2,2-i,i e^{i x}\right)",1,"(-2*I)*E^x + (4*I)*E^x*Hypergeometric2F1[I, 1, 1 + I, (-I)/E^(I*x)] - (E^x*Cos[x])/(1 + Sin[x])","A",7,6,14,0.4286,1,"{4462, 4459, 4442, 2194, 2251, 2288}"
563,1,13,0,0.0230758,"\int \frac{e^x (1-\cos (x))}{1+\sin (x)} \, dx","Int[(E^x*(1 - Cos[x]))/(1 + Sin[x]),x]","-\frac{e^x \cos (x)}{\sin (x)+1}","-\frac{e^x \cos (x)}{\sin (x)+1}",1,"-((E^x*Cos[x])/(1 + Sin[x]))","A",1,1,16,0.06250,1,"{2288}"
564,1,30,0,0.0387418,"\int e^x x \cos (x) \, dx","Int[E^x*x*Cos[x],x]","-\frac{1}{2} e^x \sin (x)+\frac{1}{2} e^x x \sin (x)+\frac{1}{2} e^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])/2 - (E^x*Sin[x])/2 + (E^x*x*Sin[x])/2","A",4,3,7,0.4286,1,"{4433, 4466, 4432}"
565,1,50,0,0.1076961,"\int e^x x^2 \sin (x) \, dx","Int[E^x*x^2*Sin[x],x]","\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)","\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*Cos[x])/2 + E^x*x*Cos[x] - (E^x*x^2*Cos[x])/2 - (E^x*Sin[x])/2 + (E^x*x^2*Sin[x])/2","A",11,5,9,0.5556,1,"{4432, 4465, 14, 4433, 4466}"
566,1,75,0,0.1402771,"\int e^{-3 x} x^2 \sin (x) \, dx","Int[(x^2*Sin[x])/E^(3*x),x]","-\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)","-\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*Cos[x])/(250*E^(3*x)) - (3*x*Cos[x])/(25*E^(3*x)) - (x^2*Cos[x])/(10*E^(3*x)) - (9*Sin[x])/(250*E^(3*x)) - (4*x*Sin[x])/(25*E^(3*x)) - (3*x^2*Sin[x])/(10*E^(3*x))","A",11,5,11,0.4545,1,"{4432, 4465, 14, 4433, 4466}"
567,1,253,0,0.4784781,"\int e^{x/2} x^2 \cos ^3(x) \, dx","Int[E^(x/2)*x^2*Cos[x]^3,x]","\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{1218672 e^{x/2} \sin (x)}{6331625}-\frac{32556 e^{x/2} x \sin (x)}{34225}-\frac{816 e^{x/2} \sin (3 x)}{50653}-\frac{12 e^{x/2} x \sin (3 x)}{1369}+\frac{16 e^{x/2} \cos ^3(x)}{50653}-\frac{8 e^{x/2} x \cos ^3(x)}{1369}-\frac{6687696 e^{x/2} \cos (x)}{6331625}+\frac{24792 e^{x/2} x \cos (x)}{34225}-\frac{432 e^{x/2} \cos (3 x)}{50653}+\frac{72 e^{x/2} x \cos (3 x)}{1369}+\frac{96 e^{x/2} \sin (x) \cos ^2(x)}{50653}-\frac{48 e^{x/2} x \sin (x) \cos ^2(x)}{1369}","\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,"(-6687696*E^(x/2)*Cos[x])/6331625 + (24792*E^(x/2)*x*Cos[x])/34225 + (48*E^(x/2)*x^2*Cos[x])/185 + (16*E^(x/2)*Cos[x]^3)/50653 - (8*E^(x/2)*x*Cos[x]^3)/1369 + (2*E^(x/2)*x^2*Cos[x]^3)/37 - (432*E^(x/2)*Cos[3*x])/50653 + (72*E^(x/2)*x*Cos[3*x])/1369 - (1218672*E^(x/2)*Sin[x])/6331625 - (32556*E^(x/2)*x*Sin[x])/34225 + (96*E^(x/2)*x^2*Sin[x])/185 + (96*E^(x/2)*Cos[x]^2*Sin[x])/50653 - (48*E^(x/2)*x*Cos[x]^2*Sin[x])/1369 + (12*E^(x/2)*x^2*Cos[x]^2*Sin[x])/37 - (816*E^(x/2)*Sin[3*x])/50653 - (12*E^(x/2)*x*Sin[3*x])/1369","A",31,8,15,0.5333,1,"{4435, 4433, 4466, 14, 4432, 4469, 4465, 4470}"
568,1,87,0,0.156602,"\int e^{2 x} x^2 \sin (4 x) \, dx","Int[E^(2*x)*x^2*Sin[4*x],x]","\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)","\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)*Cos[4*x])/250 + (2*E^(2*x)*x*Cos[4*x])/25 - (E^(2*x)*x^2*Cos[4*x])/5 - (11*E^(2*x)*Sin[4*x])/500 + (3*E^(2*x)*x*Sin[4*x])/50 + (E^(2*x)*x^2*Sin[4*x])/10","A",11,5,13,0.3846,1,"{4432, 4465, 14, 4433, 4466}"
569,1,185,0,0.3562143,"\int e^{x/2} x^2 \cos (x) \sin ^2(x) \, dx","Int[E^(x/2)*x^2*Cos[x]*Sin[x]^2,x]","\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}","\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,"(-44*E^(x/2)*Cos[x])/125 + (6*E^(x/2)*x*Cos[x])/25 + (E^(x/2)*x^2*Cos[x])/10 + (428*E^(x/2)*Cos[3*x])/50653 - (70*E^(x/2)*x*Cos[3*x])/1369 - (E^(x/2)*x^2*Cos[3*x])/74 - (8*E^(x/2)*Sin[x])/125 - (8*E^(x/2)*x*Sin[x])/25 + (E^(x/2)*x^2*Sin[x])/5 + (792*E^(x/2)*Sin[3*x])/50653 + (24*E^(x/2)*x*Sin[3*x])/1369 - (3*E^(x/2)*x^2*Sin[3*x])/37","A",24,6,17,0.3529,1,"{4470, 4433, 4466, 14, 4432, 4465}"
570,1,2,0,0.0026886,"\int \cosh (x) \, dx","Int[Cosh[x],x]","\sinh (x)","\sinh (x)",1,"Sinh[x]","A",1,1,2,0.5000,1,"{2637}"
571,1,2,0,0.0029761,"\int \sinh (x) \, dx","Int[Sinh[x],x]","\cosh (x)","\cosh (x)",1,"Cosh[x]","A",1,1,2,0.5000,1,"{2638}"
572,1,3,0,0.0034148,"\int \tanh (x) \, dx","Int[Tanh[x],x]","\log (\cosh (x))","\log (\cosh (x))",1,"Log[Cosh[x]]","A",1,1,2,0.5000,1,"{3475}"
573,1,3,0,0.0035209,"\int \coth (x) \, dx","Int[Coth[x],x]","\log (\sinh (x))","\log (\sinh (x))",1,"Log[Sinh[x]]","A",1,1,2,0.5000,1,"{3475}"
574,1,3,0,0.0032907,"\int \text{sech}(x) \, dx","Int[Sech[x],x]","\tan ^{-1}(\sinh (x))","\tan ^{-1}(\sinh (x))",1,"ArcTan[Sinh[x]]","A",1,1,2,0.5000,1,"{3770}"
575,1,5,0,0.0036311,"\int \text{csch}(x) \, dx","Int[Csch[x],x]","-\tanh ^{-1}(\cosh (x))","-\tanh ^{-1}(\cosh (x))",1,"-ArcTanh[Cosh[x]]","A",1,1,2,0.5000,1,"{3770}"
576,1,14,0,0.0071077,"\int \cosh ^2(x) \, dx","Int[Cosh[x]^2,x]","\frac{x}{2}+\frac{1}{2} \sinh (x) \cosh (x)","\frac{x}{2}+\frac{1}{2} \sinh (x) \cosh (x)",1,"x/2 + (Cosh[x]*Sinh[x])/2","A",2,2,4,0.5000,1,"{2635, 8}"
577,1,19,0,0.01108,"\int \sinh ^5(x) \, dx","Int[Sinh[x]^5,x]","\frac{\cosh ^5(x)}{5}-\frac{2 \cosh ^3(x)}{3}+\cosh (x)","\frac{\cosh ^5(x)}{5}-\frac{2 \cosh ^3(x)}{3}+\cosh (x)",1,"Cosh[x] - (2*Cosh[x]^3)/3 + Cosh[x]^5/5","A",2,1,4,0.2500,1,"{2633}"
578,1,14,0,0.0111177,"\int \tanh ^4(x) \, dx","Int[Tanh[x]^4,x]","x-\frac{1}{3} \tanh ^3(x)-\tanh (x)","x-\frac{1}{3} \tanh ^3(x)-\tanh (x)",1,"x - Tanh[x] - Tanh[x]^3/3","A",3,2,4,0.5000,1,"{3473, 8}"
579,1,16,0,0.0117557,"\int \text{csch}^3(x) \, dx","Int[Csch[x]^3,x]","\frac{1}{2} \tanh ^{-1}(\cosh (x))-\frac{1}{2} \coth (x) \text{csch}(x)","\frac{1}{2} \tanh ^{-1}(\cosh (x))-\frac{1}{2} \coth (x) \text{csch}(x)",1,"ArcTanh[Cosh[x]]/2 - (Coth[x]*Csch[x])/2","A",2,2,4,0.5000,1,"{3768, 3770}"
580,1,26,0,0.0167193,"\int \text{sech}^5(x) \, dx","Int[Sech[x]^5,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)","\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[Sinh[x]])/8 + (3*Sech[x]*Tanh[x])/8 + (Sech[x]^3*Tanh[x])/4","A",3,2,4,0.5000,1,"{3768, 3770}"
581,1,18,0,0.0225872,"\int \sinh ^4(x) \tanh (x) \, dx","Int[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",4,3,7,0.4286,1,"{2590, 266, 43}"
582,1,31,0,0.0311796,"\int \text{sech}^{\frac{23}{4}}(x) \sinh ^5(x) \, dx","Int[Sech[x]^(23/4)*Sinh[x]^5,x]","-\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)","-\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,"(-4*Sech[x]^(3/4))/3 + (8*Sech[x]^(11/4))/11 - (4*Sech[x]^(19/4))/19","A",3,2,11,0.1818,1,"{2622, 270}"
583,1,42,0,0.0491715,"\int \frac{1}{a+b \cosh (x)} \, dx","Int[(a + b*Cosh[x])^(-1),x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a+b}}\right)}{\sqrt{a-b} \sqrt{a+b}}","\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*ArcTanh[(Sqrt[a - b]*Tanh[x/2])/Sqrt[a + b]])/(Sqrt[a - b]*Sqrt[a + b])","A",2,2,8,0.2500,1,"{2659, 208}"
584,1,25,0,0.0166621,"\int \frac{1}{(1+\cosh (x))^2} \, dx","Int[(1 + Cosh[x])^(-2),x]","\frac{\sinh (x)}{3 (\cosh (x)+1)}+\frac{\sinh (x)}{3 (\cosh (x)+1)^2}","\frac{\sinh (x)}{3 (\cosh (x)+1)}+\frac{\sinh (x)}{3 (\cosh (x)+1)^2}",1,"Sinh[x]/(3*(1 + Cosh[x])^2) + Sinh[x]/(3*(1 + Cosh[x]))","A",2,2,6,0.3333,1,"{2650, 2648}"
585,1,39,0,0.0499977,"\int \frac{1}{a+b \tanh (x)} \, dx","Int[(a + b*Tanh[x])^(-1),x]","\frac{a x}{a^2-b^2}-\frac{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)/(a^2 - b^2) - (b*Log[a*Cosh[x] + b*Sinh[x]])/(a^2 - b^2)","A",2,2,8,0.2500,1,"{3484, 3530}"
586,1,31,0,0.0353816,"\int \frac{1}{a^2+b^2 \cosh ^2(x)} \, dx","Int[(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",2,2,14,0.1429,1,"{3181, 208}"
587,1,35,0,0.0369354,"\int \frac{1}{a^2-b^2 \cosh ^2(x)} \, dx","Int[(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",2,2,15,0.1333,1,"{3181, 208}"
588,1,25,0,0.0174735,"\int \frac{1}{1-\sinh ^4(x)} \, dx","Int[(1 - Sinh[x]^4)^(-1),x]","\frac{\tanh ^{-1}\left(\sqrt{2} \tanh (x)\right)}{2 \sqrt{2}}+\frac{\tanh (x)}{2}","\frac{\tanh ^{-1}\left(\sqrt{2} \tanh (x)\right)}{2 \sqrt{2}}+\frac{\tanh (x)}{2}",1,"ArcTanh[Sqrt[2]*Tanh[x]]/(2*Sqrt[2]) + Tanh[x]/2","A",3,3,10,0.3000,1,"{3209, 388, 206}"
589,1,33,0,0.136227,"\int \frac{\cosh ^3(x)-\sinh ^3(x)}{\cosh ^3(x)+\sinh ^3(x)} \, dx","Int[(Cosh[x]^3 - Sinh[x]^3)/(Cosh[x]^3 + Sinh[x]^3),x]","-\frac{1}{3 (\tanh (x)+1)}-\frac{4 \tan ^{-1}\left(\frac{1-2 \tanh (x)}{\sqrt{3}}\right)}{3 \sqrt{3}}","-\frac{1}{3 (\tanh (x)+1)}-\frac{4 \tan ^{-1}\left(\frac{1-2 \tanh (x)}{\sqrt{3}}\right)}{3 \sqrt{3}}",1,"(-4*ArcTan[(1 - 2*Tanh[x])/Sqrt[3]])/(3*Sqrt[3]) - 1/(3*(1 + Tanh[x]))","A",5,3,23,0.1304,1,"{2074, 618, 204}"
590,1,30,0,0.0345891,"\int \cosh (x) \cosh (2 x) \cosh (3 x) \, dx","Int[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",5,2,11,0.1818,1,"{4355, 2637}"
591,1,30,0,0.0343048,"\int \cosh \left(\frac{3 x}{2}\right) \sinh (x) \sinh \left(\frac{5 x}{2}\right) \, dx","Int[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,"-x/4 + Sinh[2*x]/8 - Sinh[3*x]/12 + Sinh[5*x]/20","A",5,2,15,0.1333,1,"{4355, 2637}"
592,1,102,0,0.973021,"\int \frac{\cosh (x) (-\cosh (2 x)+\tanh (x))}{\sqrt{\sinh (2 x)} \left(\sinh ^2(x)+\sinh (2 x)\right)} \, dx","Int[(Cosh[x]*(-Cosh[2*x] + Tanh[x]))/(Sqrt[Sinh[2*x]]*(Sinh[x]^2 + Sinh[2*x])),x]","-\frac{2 \sinh (x) \tanh ^{-1}\left(\sqrt{\tanh (x)}\right)}{3 \sqrt{\sinh (2 x)} \sqrt{\tanh (x)}}+\frac{\cosh (x)}{\sqrt{\sinh (2 x)}}+\frac{2 \sinh (x) \tan ^{-1}\left(\sqrt{\tanh (x)}\right)}{\sqrt{\sinh (2 x)} \sqrt{\tanh (x)}}+\frac{\sinh (x) \tan ^{-1}\left(\frac{\sqrt{\tanh (x)}}{\sqrt{2}}\right)}{3 \sqrt{2} \sqrt{\sinh (2 x)} \sqrt{\tanh (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,"Cosh[x]/Sqrt[Sinh[2*x]] + (2*ArcTan[Sqrt[Tanh[x]]]*Sinh[x])/(Sqrt[Sinh[2*x]]*Sqrt[Tanh[x]]) + (ArcTan[Sqrt[Tanh[x]]/Sqrt[2]]*Sinh[x])/(3*Sqrt[2]*Sqrt[Sinh[2*x]]*Sqrt[Tanh[x]]) - (2*ArcTanh[Sqrt[Tanh[x]]]*Sinh[x])/(3*Sqrt[Sinh[2*x]]*Sqrt[Tanh[x]])","A",8,4,31,0.1290,1,"{4390, 6725, 207, 203}"
593,1,37,0,0.0452293,"\int \frac{\sinh (x)}{\left(-9+4 \cosh ^2(x)\right)^{5/2}} \, dx","Int[Sinh[x]/(-9 + 4*Cosh[x]^2)^(5/2),x]","\frac{2 \cosh (x)}{243 \sqrt{4 \cosh ^2(x)-9}}-\frac{\cosh (x)}{27 \left(4 \cosh ^2(x)-9\right)^{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]/(27*(-9 + 4*Cosh[x]^2)^(3/2)) + (2*Cosh[x])/(243*Sqrt[-9 + 4*Cosh[x]^2])","A",3,3,15,0.2000,1,"{3190, 192, 191}"
594,1,29,0,0.1079057,"\int \frac{\sinh ^2(x) \sinh (2 x)}{\left(1-\sinh ^2(x)\right)^{3/2}} \, dx","Int[(Sinh[x]^2*Sinh[2*x])/(1 - Sinh[x]^2)^(3/2),x]","2 \sqrt{1-\sinh ^2(x)}+\frac{2}{\sqrt{1-\sinh ^2(x)}}","2 \sqrt{1-\sinh ^2(x)}+\frac{2}{\sqrt{1-\sinh ^2(x)}}",1,"2/Sqrt[1 - Sinh[x]^2] + 2*Sqrt[1 - Sinh[x]^2]","A",5,3,21,0.1429,1,"{12, 266, 43}"
595,1,15,0,0.0185004,"\int \frac{\cosh (x)}{\sqrt{\cosh (2 x)}} \, dx","Int[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",2,2,11,0.1818,1,"{4356, 215}"
596,1,16,0,0.0194905,"\int x \tanh ^2(x) \, dx","Int[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",3,3,6,0.5000,1,"{3720, 3475, 30}"
597,1,16,0,0.0207453,"\int x \coth ^2(x) \, dx","Int[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",3,3,6,0.5000,1,"{3720, 3475, 30}"
598,1,20,0,0.0670704,"\int \frac{x+\cosh (x)+\sinh (x)}{\cosh (x)-\sinh (x)} \, dx","Int[(x + Cosh[x] + Sinh[x])/(Cosh[x] - Sinh[x]),x]","e^x x-e^x+\frac{e^{2 x}}{2}","e^x x-e^x+\frac{e^{2 x}}{2}",1,"-E^x + E^(2*x)/2 + E^x*x","A",13,7,16,0.4375,1,"{5648, 6742, 2176, 2194, 2282, 12, 14}"
599,1,15,0,0.1301119,"\int \frac{x+\cosh (x)+\sinh (x)}{1+\cosh (x)} \, dx","Int[(x + Cosh[x] + Sinh[x])/(1 + Cosh[x]),x]","x-(1-x) \tanh \left(\frac{x}{2}\right)","x-(1-x) \tanh \left(\frac{x}{2}\right)",1,"x - (1 - x)*Tanh[x/2]","A",8,4,13,0.3077,1,"{6742, 3318, 4184, 3475}"
600,1,20,0,0.0183473,"\int e^{2 x} \text{csch}^4(x) \, dx","Int[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",3,3,10,0.3000,1,"{2282, 12, 264}"
601,1,13,0,0.01701,"\int e^{-2 x} \text{sech}^4(x) \, dx","Int[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",3,3,10,0.3000,1,"{2282, 12, 261}"
602,1,9,0,0.016691,"\int \frac{e^x}{\cosh (x)-\sinh (x)} \, dx","Int[E^x/(Cosh[x] - Sinh[x]),x]","\frac{e^{2 x}}{2}","\frac{e^{2 x}}{2}",1,"E^(2*x)/2","A",2,2,13,0.1538,1,"{2282, 30}"
603,1,19,0,0.0291286,"\int \frac{e^{m x}}{\cosh (x)+\sinh (x)} \, dx","Int[E^(m*x)/(Cosh[x] + Sinh[x]),x]","-\frac{e^{-(1-m) x}}{1-m}","\frac{e^{(m-1) x}}{m-1}",1,"-(1/(E^((1 - m)*x)*(1 - m)))","A",3,3,13,0.2308,1,"{5648, 2227, 2194}"
604,1,1,0,0.0149549,"\int \frac{e^x}{\cosh (x)+\sinh (x)} \, dx","Int[E^x/(Cosh[x] + Sinh[x]),x]","x","x",1,"x","A",2,2,11,0.1818,1,"{2282, 29}"
605,1,22,0,0.0242695,"\int \frac{e^x}{1-\cosh (x)} \, dx","Int[E^x/(1 - Cosh[x]),x]","-\frac{2}{1-e^x}-2 \log \left(1-e^x\right)","-\frac{2}{1-e^x}-2 \log \left(1-e^x\right)",1,"-2/(1 - E^x) - 2*Log[1 - E^x]","A",4,3,12,0.2500,1,"{2282, 12, 43}"
606,1,13,0,0.030643,"\int \frac{e^x (1+\sinh (x))}{1+\cosh (x)} \, dx","Int[(E^x*(1 + Sinh[x]))/(1 + Cosh[x]),x]","e^x+\frac{2}{e^x+1}","e^x+\frac{2}{e^x+1}",1,"E^x + 2/(1 + E^x)","A",3,2,14,0.1429,1,"{2282, 683}"
607,1,15,0,0.0332623,"\int \frac{e^x (1-\sinh (x))}{1-\cosh (x)} \, dx","Int[(E^x*(1 - Sinh[x]))/(1 - Cosh[x]),x]","e^x-\frac{2}{1-e^x}","e^x-\frac{2}{1-e^x}",1,"E^x - 2/(1 - E^x)","A",3,2,18,0.1111,1,"{2282, 683}"
608,1,26,0,0.0101041,"\int x^m \log (x) \, dx","Int[x^m*Log[x],x]","\frac{x^{m+1} \log (x)}{m+1}-\frac{x^{m+1}}{(m+1)^2}","\frac{x^{m+1} \log (x)}{m+1}-\frac{x^{m+1}}{(m+1)^2}",1,"-(x^(1 + m)/(1 + m)^2) + (x^(1 + m)*Log[x])/(1 + m)","A",1,1,6,0.1667,1,"{2304}"
609,1,42,0,0.0238764,"\int x^m \log ^2(x) \, dx","Int[x^m*Log[x]^2,x]","\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}","\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,"(2*x^(1 + m))/(1 + m)^3 - (2*x^(1 + m)*Log[x])/(1 + m)^2 + (x^(1 + m)*Log[x]^2)/(1 + m)","A",2,2,8,0.2500,1,"{2305, 2304}"
610,1,34,0,0.0202339,"\int \frac{\log ^2(x)}{x^{5/2}} \, dx","Int[Log[x]^2/x^(5/2),x]","-\frac{16}{27 x^{3/2}}-\frac{2 \log ^2(x)}{3 x^{3/2}}-\frac{8 \log (x)}{9 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,"-16/(27*x^(3/2)) - (8*Log[x])/(9*x^(3/2)) - (2*Log[x]^2)/(3*x^(3/2))","A",2,2,10,0.2000,1,"{2305, 2304}"
611,1,29,0,0.0112043,"\int (a+b x) \log (x) \, dx","Int[(a + b*x)*Log[x],x]","\frac{1}{2} \log (x) \left(2 a x+b x^2\right)-a x-\frac{b x^2}{4}","-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 + ((2*a*x + b*x^2)*Log[x])/2","A",2,1,8,0.1250,1,"{2313}"
612,1,67,0,0.0333638,"\int (a+b x)^3 \log (x) \, dx","Int[(a + b*x)^3*Log[x],x]","-\frac{3}{4} a^2 b x^2-\frac{a^4 \log (x)}{4 b}-a^3 x-\frac{1}{3} a b^2 x^3+\frac{\log (x) (a+b x)^4}{4 b}-\frac{b^3 x^4}{16}","-\frac{3}{4} a^2 b x^2-\frac{a^4 \log (x)}{4 b}-a^3 x-\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^4*Log[x])/(4*b) + ((a + b*x)^4*Log[x])/(4*b)","A",4,4,10,0.4000,1,"{32, 2313, 12, 43}"
613,1,23,0,0.0138408,"\int \left(-1-8 \log ^2(x)+3 \log ^3(x)\right) \, dx","Int[-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",6,2,14,0.1429,1,"{2296, 2295}"
614,1,73,0,0.0906383,"\int \left(1+x^4\right) \left(1-2 \log (x)+\log ^3(x)\right) \, dx","Int[(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{6}{125} x^5 \log (x)-\frac{2}{5} \left(x^5+5 x\right) \log (x)-3 x+x \log ^3(x)-3 x \log ^2(x)+6 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 + 6*x*Log[x] + (6*x^5*Log[x])/125 - (2*(5*x + x^5)*Log[x])/5 - 3*x*Log[x]^2 - (3*x^5*Log[x]^2)/25 + x*Log[x]^3 + (x^5*Log[x]^3)/5","A",13,8,16,0.5000,1,"{6742, 2313, 12, 2330, 2296, 2295, 2305, 2304}"
615,1,43,0,0.0592722,"\int \frac{1}{x^3 \log ^4(x)} \, dx","Int[1/(x^3*Log[x]^4),x]","-\frac{4}{3} \text{ExpIntegralEi}(-2 \log (x))+\frac{1}{3 x^2 \log ^2(x)}-\frac{1}{3 x^2 \log ^3(x)}-\frac{2}{3 x^2 \log (x)}","-\frac{4}{3} \text{ExpIntegralEi}(-2 \log (x))+\frac{1}{3 x^2 \log ^2(x)}-\frac{1}{3 x^2 \log ^3(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",5,3,8,0.3750,1,"{2306, 2309, 2178}"
616,1,29,0,0.0202085,"\int \frac{\log (x)}{a+b x} \, dx","Int[Log[x]/(a + b*x),x]","\frac{\text{PolyLog}\left(2,-\frac{b x}{a}\right)}{b}+\frac{\log (x) \log \left(\frac{b x}{a}+1\right)}{b}","\frac{\text{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[1 + (b*x)/a])/b + PolyLog[2, -((b*x)/a)]/b","A",2,2,10,0.2000,1,"{2317, 2391}"
617,1,29,0,0.013455,"\int \frac{\log (x)}{(a+b x)^2} \, dx","Int[Log[x]/(a + b*x)^2,x]","\frac{x \log (x)}{a (a+b x)}-\frac{\log (a+b x)}{a b}","\frac{x \log (x)}{a (a+b x)}-\frac{\log (a+b x)}{a b}",1,"(x*Log[x])/(a*(a + b*x)) - Log[a + b*x]/(a*b)","A",2,2,10,0.2000,1,"{2314, 31}"
618,1,12,0,0.0174533,"\int \frac{\log ^n(x)}{x} \, dx","Int[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",2,2,8,0.2500,1,"{2302, 30}"
619,1,19,0,0.0282467,"\int \frac{(a+b \log (x))^n}{x} \, dx","Int[(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",2,2,12,0.1667,1,"{2302, 30}"
620,1,11,0,0.0237006,"\int \frac{1}{x (a+b \log (x))} \, dx","Int[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",2,2,12,0.1667,1,"{2302, 29}"
621,1,23,0,0.0324734,"\int \frac{(a+b \log (x))^{-n}}{x} \, dx","Int[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",2,2,14,0.1429,1,"{2302, 30}"
622,1,16,0,0.0376583,"\int \frac{1}{x \sqrt{a^2+\log ^2(x)}} \, dx","Int[1/(x*Sqrt[a^2 + Log[x]^2]),x]","\tanh ^{-1}\left(\frac{\log (x)}{\sqrt{a^2+\log ^2(x)}}\right)","\tanh ^{-1}\left(\frac{\log (x)}{\sqrt{a^2+\log ^2(x)}}\right)",1,"ArcTanh[Log[x]/Sqrt[a^2 + Log[x]^2]]","A",3,2,16,0.1250,1,"{217, 206}"
623,1,18,0,0.042227,"\int \frac{1}{x \sqrt{-a^2+\log ^2(x)}} \, dx","Int[1/(x*Sqrt[-a^2 + Log[x]^2]),x]","\tanh ^{-1}\left(\frac{\log (x)}{\sqrt{\log ^2(x)-a^2}}\right)","\tanh ^{-1}\left(\frac{\log (x)}{\sqrt{\log ^2(x)-a^2}}\right)",1,"ArcTanh[Log[x]/Sqrt[-a^2 + Log[x]^2]]","A",3,2,18,0.1111,1,"{217, 206}"
624,1,18,0,0.041188,"\int \frac{1}{x \sqrt{a^2-\log ^2(x)}} \, dx","Int[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",3,2,18,0.1111,1,"{217, 203}"
625,1,22,0,0.0879265,"\int \frac{1}{x \log (x) \sqrt{a^2+\log ^2(x)}} \, dx","Int[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",4,3,20,0.1500,1,"{266, 63, 207}"
626,1,24,0,0.0981423,"\int \frac{1}{x \log (x) \sqrt{a^2-\log ^2(x)}} \, dx","Int[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",4,3,22,0.1364,1,"{266, 63, 206}"
627,1,23,0,0.098703,"\int \frac{1}{x \log (x) \sqrt{-a^2+\log ^2(x)}} \, dx","Int[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",4,3,22,0.1364,1,"{266, 63, 203}"
628,1,11,0,0.0072318,"\int \frac{\log (\log (x))}{x} \, dx","Int[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",1,1,7,0.1429,1,"{2521}"
629,1,20,0,0.0177781,"\int \frac{\log ^2(\log (x))}{x} \, dx","Int[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",3,2,9,0.2222,1,"{2296, 2295}"
630,1,29,0,0.0215285,"\int \frac{\log ^3(\log (x))}{x} \, dx","Int[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",4,2,9,0.2222,1,"{2296, 2295}"
631,1,38,0,0.0256756,"\int \frac{\log ^4(\log (x))}{x} \, dx","Int[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",5,2,9,0.2222,1,"{2296, 2295}"
632,1,24,0,0.032174,"\int \frac{\log ^n(\log (x))}{x} \, dx","Int[Log[Log[x]]^n/x,x]","(-\log (\log (x)))^{-n} \log ^n(\log (x)) \text{Gamma}(n+1,-\log (\log (x)))","(-\log (\log (x)))^{-n} \log ^n(\log (x)) \text{Gamma}(n+1,-\log (\log (x)))",1,"(Gamma[1 + n, -Log[Log[x]]]*Log[Log[x]]^n)/(-Log[Log[x]])^n","A",3,2,9,0.2222,1,"{2299, 2181}"
633,1,4,0,0.0200642,"\int \frac{\cot (x)}{\log (\sin (x))} \, dx","Int[Cot[x]/Log[Sin[x]],x]","\log (\log (\sin (x)))","\log (\log (\sin (x)))",1,"Log[Log[Sin[x]]]","A",3,3,8,0.3750,1,"{4338, 2302, 29}"
634,1,7,0,0.0465842,"\int (\cos (x)+\sec (x)) \tan (x) \, dx","Int[(Cos[x] + Sec[x])*Tan[x],x]","\sec (x)-\cos (x)","\sec (x)-\cos (x)",1,"-Cos[x] + Sec[x]","A",3,1,8,0.1250,1,"{4236}"
635,1,11,0,0.0112569,"\int \log (\cosh (x)) \sinh (x) \, dx","Int[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",2,2,6,0.3333,1,"{2638, 2554}"
636,1,9,0,0.0154075,"\int \log (\cosh (x)) \tanh (x) \, dx","Int[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",2,3,6,0.5000,1,"{3475, 4341, 2301}"
637,1,26,0,0.0053162,"\int \log \left(x-\sqrt{1+x^2}\right) \, dx","Int[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",2,2,14,0.1429,1,"{2534, 261}"
638,1,35,0,0.0145775,"\int \frac{\log (-1+x)}{x^3} \, dx","Int[Log[-1 + x]/x^3,x]","-\frac{\log (x-1)}{2 x^2}+\frac{1}{2 x}+\frac{1}{2} \log (1-x)-\frac{\log (x)}{2}","-\frac{\log (x-1)}{2 x^2}+\frac{1}{2 x}+\frac{1}{2} \log (1-x)-\frac{\log (x)}{2}",1,"1/(2*x) + Log[1 - x]/2 - Log[-1 + x]/(2*x^2) - Log[x]/2","A",3,2,8,0.2500,1,"{2395, 44}"
639,1,32,0,0.0538533,"\int \left(-e^{-x}+e^x\right) \log \left(1+e^{2 x}\right) \, dx","Int[(-E^(-x) + E^x)*Log[1 + E^(2*x)],x]","-2 e^x+e^{-x} \log \left(e^{2 x}+1\right)+e^x \log \left(e^{2 x}+1\right)","-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 + Log[1 + E^(2*x)]/E^x + E^x*Log[1 + E^(2*x)]","A",8,6,20,0.3000,1,"{2282, 2476, 2448, 321, 203, 2455}"
640,1,52,0,0.0436347,"\int e^{3 x/2} \log \left(-1+e^x\right) \, dx","Int[E^((3*x)/2)*Log[-1 + E^x],x]","-\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)","-\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,"(-4*E^(x/2))/3 - (4*E^((3*x)/2))/9 + (4*ArcTanh[E^(x/2)])/3 + (2*E^((3*x)/2)*Log[-1 + E^x])/3","A",6,6,14,0.4286,1,"{2194, 2554, 12, 2248, 302, 207}"
641,1,30,0,0.0348104,"\int \cos ^3(x) \log (\sin (x)) \, dx","Int[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",4,4,8,0.5000,1,"{2633, 2554, 12, 4356}"
642,1,30,0,0.0582128,"\int \log (\tan (x)) \sec ^4(x) \, dx","Int[Log[Tan[x]]*Sec[x]^4,x]","-\frac{\tan ^3(x)}{9}-\tan (x)+\frac{1}{3} \tan ^3(x) \log (\tan (x))+\tan (x) \log (\tan (x))","-\frac{\tan ^3(x)}{9}-\tan (x)+\frac{1}{3} \tan ^3(x) \log (\tan (x))+\tan (x) \log (\tan (x))",1,"-Tan[x] + Log[Tan[x]]*Tan[x] - Tan[x]^3/9 + (Log[Tan[x]]*Tan[x]^3)/3","A",4,3,8,0.3750,1,"{3767, 2554, 12}"
643,1,28,0,0.0347725,"\int \frac{\log \left(\cos \left(\frac{x}{2}\right)\right)}{1+\cos (x)} \, dx","Int[Log[Cos[x/2]]/(1 + Cos[x]),x]","-\frac{x}{2}+\tan \left(\frac{x}{2}\right)+\frac{\sin (x) \log \left(\cos \left(\frac{x}{2}\right)\right)}{\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,"-x/2 + (Log[Cos[x/2]]*Sin[x])/(1 + Cos[x]) + Tan[x/2]","A",4,5,14,0.3571,1,"{2648, 2554, 12, 3473, 8}"
644,1,60,0,0.1321637,"\int \frac{\cos (x) \log (\sin (x))}{(1+\cos (x))^2} \, dx","Int[(Cos[x]*Log[Sin[x]])/(1 + Cos[x])^2,x]","-\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}","-\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,"(-2*x)/3 - Sin[x]/(9*(1 + Cos[x])^2) + (8*Sin[x])/(9*(1 + Cos[x])) - (Log[Sin[x]]*Sin[x])/(3*(1 + Cos[x])^2) + (2*Log[Sin[x]]*Sin[x])/(3*(1 + Cos[x]))","A",6,7,12,0.5833,1,"{2750, 2648, 2554, 12, 2968, 3019, 2735}"
645,1,65,0,0.1091405,"\int \frac{\cos ^{-1}(x)^2}{x^5} \, dx","Int[ArcCos[x]^2/x^5,x]","-\frac{1}{12 x^2}-\frac{\cos ^{-1}(x)^2}{4 x^4}+\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}","-\frac{1}{12 x^2}-\frac{\cos ^{-1}(x)^2}{4 x^4}+\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*x^2) + (Sqrt[1 - x^2]*ArcCos[x])/(6*x^3) + (Sqrt[1 - x^2]*ArcCos[x])/(3*x) - ArcCos[x]^2/(4*x^4) + Log[x]/3","A",5,5,8,0.6250,1,"{4628, 4702, 4682, 29, 30}"
646,1,61,0,0.0938961,"\int x^2 \sin ^{-1}(x)^2 \, dx","Int[x^2*ArcSin[x]^2,x]","-\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}","-\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,"(-4*x)/9 - (2*x^3)/27 + (4*Sqrt[1 - x^2]*ArcSin[x])/9 + (2*x^2*Sqrt[1 - x^2]*ArcSin[x])/9 + (x^3*ArcSin[x]^2)/3","A",5,5,8,0.6250,1,"{4627, 4707, 4677, 8, 30}"
647,1,53,0,0.116431,"\int x^3 \tan ^{-1}(x)^2 \, dx","Int[x^3*ArcTan[x]^2,x]","\frac{x^2}{12}-\frac{1}{3} \log \left(x^2+1\right)+\frac{1}{4} x^4 \tan ^{-1}(x)^2-\frac{1}{6} x^3 \tan ^{-1}(x)+\frac{1}{2} x \tan ^{-1}(x)-\frac{1}{4} \tan ^{-1}(x)^2","\frac{x^2}{12}-\frac{1}{3} \log \left(x^2+1\right)+\frac{1}{4} x^4 \tan ^{-1}(x)^2-\frac{1}{6} x^3 \tan ^{-1}(x)+\frac{1}{2} x \tan ^{-1}(x)-\frac{1}{4} \tan ^{-1}(x)^2",1,"x^2/12 + (x*ArcTan[x])/2 - (x^3*ArcTan[x])/6 - ArcTan[x]^2/4 + (x^4*ArcTan[x]^2)/4 - Log[1 + x^2]/3","A",10,7,8,0.8750,1,"{4852, 4916, 266, 43, 4846, 260, 4884}"
648,1,61,0,0.1261283,"\int \frac{\tan ^{-1}(x)^2}{x^5} \, dx","Int[ArcTan[x]^2/x^5,x]","-\frac{1}{12 x^2}+\frac{1}{3} \log \left(x^2+1\right)-\frac{\tan ^{-1}(x)^2}{4 x^4}-\frac{\tan ^{-1}(x)}{6 x^3}-\frac{2 \log (x)}{3}+\frac{1}{4} \tan ^{-1}(x)^2+\frac{\tan ^{-1}(x)}{2 x}","-\frac{1}{12 x^2}+\frac{1}{3} \log \left(x^2+1\right)-\frac{\tan ^{-1}(x)^2}{4 x^4}-\frac{\tan ^{-1}(x)}{6 x^3}-\frac{2 \log (x)}{3}+\frac{1}{4} \tan ^{-1}(x)^2+\frac{\tan ^{-1}(x)}{2 x}",1,"-1/(12*x^2) - ArcTan[x]/(6*x^3) + ArcTan[x]/(2*x) + ArcTan[x]^2/4 - ArcTan[x]^2/(4*x^4) - (2*Log[x])/3 + Log[1 + x^2]/3","A",13,8,8,1.000,1,"{4852, 4918, 266, 44, 36, 29, 31, 4884}"
649,1,63,0,0.0671453,"\int x^3 \csc ^{-1}(x)^2 \, dx","Int[x^3*ArcCsc[x]^2,x]","\frac{x^2}{12}+\frac{1}{4} x^4 \csc ^{-1}(x)^2+\frac{1}{6} \sqrt{1-\frac{1}{x^2}} x^3 \csc ^{-1}(x)+\frac{1}{3} \sqrt{1-\frac{1}{x^2}} x \csc ^{-1}(x)+\frac{\log (x)}{3}","\frac{x^2}{12}+\frac{1}{4} x^4 \csc ^{-1}(x)^2+\frac{1}{6} \sqrt{1-\frac{1}{x^2}} x^3 \csc ^{-1}(x)+\frac{1}{3} \sqrt{1-\frac{1}{x^2}} x \csc ^{-1}(x)+\frac{\log (x)}{3}",1,"x^2/12 + (Sqrt[1 - x^(-2)]*x*ArcCsc[x])/3 + (Sqrt[1 - x^(-2)]*x^3*ArcCsc[x])/6 + (x^4*ArcCsc[x]^2)/4 + Log[x]/3","A",5,5,8,0.6250,1,"{5223, 3758, 4185, 4184, 3475}"
650,1,148,0,0.1473367,"\int \frac{\sec ^{-1}(x)^4}{x^5} \, dx","Int[ArcSec[x]^4/x^5,x]","-\frac{45}{128 x^2}-\frac{3}{128 x^4}-\frac{\sec ^{-1}(x)^4}{4 x^4}+\frac{3 \sqrt{1-\frac{1}{x^2}} \sec ^{-1}(x)^3}{8 x}+\frac{\sqrt{1-\frac{1}{x^2}} \sec ^{-1}(x)^3}{4 x^3}+\frac{9 \sec ^{-1}(x)^2}{16 x^2}+\frac{3 \sec ^{-1}(x)^2}{16 x^4}-\frac{45 \sqrt{1-\frac{1}{x^2}} \sec ^{-1}(x)}{64 x}-\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","-\frac{45}{128 x^2}-\frac{3}{128 x^4}-\frac{\sec ^{-1}(x)^4}{4 x^4}+\frac{3 \sqrt{1-\frac{1}{x^2}} \sec ^{-1}(x)^3}{8 x}+\frac{\sqrt{1-\frac{1}{x^2}} \sec ^{-1}(x)^3}{4 x^3}+\frac{9 \sec ^{-1}(x)^2}{16 x^2}+\frac{3 \sec ^{-1}(x)^2}{16 x^4}-\frac{45 \sqrt{1-\frac{1}{x^2}} \sec ^{-1}(x)}{64 x}-\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/(128*x^4) - 45/(128*x^2) - (3*Sqrt[1 - x^(-2)]*ArcSec[x])/(32*x^3) - (45*Sqrt[1 - x^(-2)]*ArcSec[x])/(64*x) - (45*ArcSec[x]^2)/128 + (3*ArcSec[x]^2)/(16*x^4) + (9*ArcSec[x]^2)/(16*x^2) + (Sqrt[1 - x^(-2)]*ArcSec[x]^3)/(4*x^3) + (3*Sqrt[1 - x^(-2)]*ArcSec[x]^3)/(8*x) + (3*ArcSec[x]^4)/32 - ArcSec[x]^4/(4*x^4)","A",10,5,8,0.6250,1,"{5222, 3444, 3311, 30, 3310}"
651,1,34,0,0.0292565,"\int \sqrt{1-x^2} \sin ^{-1}(x) \, dx","Int[Sqrt[1 - x^2]*ArcSin[x],x]","-\frac{x^2}{4}+\frac{1}{2} \sqrt{1-x^2} x \sin ^{-1}(x)+\frac{1}{4} \sin ^{-1}(x)^2","-\frac{x^2}{4}+\frac{1}{2} \sqrt{1-x^2} x \sin ^{-1}(x)+\frac{1}{4} \sin ^{-1}(x)^2",1,"-x^2/4 + (x*Sqrt[1 - x^2]*ArcSin[x])/2 + ArcSin[x]^2/4","A",3,3,14,0.2143,1,"{4647, 4641, 30}"
652,1,34,0,0.0299284,"\int \sqrt{1-x^2} \cos ^{-1}(x) \, dx","Int[Sqrt[1 - x^2]*ArcCos[x],x]","\frac{x^2}{4}+\frac{1}{2} \sqrt{1-x^2} x \cos ^{-1}(x)-\frac{1}{4} \cos ^{-1}(x)^2","\frac{x^2}{4}+\frac{1}{2} \sqrt{1-x^2} x \cos ^{-1}(x)-\frac{1}{4} \cos ^{-1}(x)^2",1,"x^2/4 + (x*Sqrt[1 - x^2]*ArcCos[x])/2 - ArcCos[x]^2/4","A",3,3,14,0.2143,1,"{4648, 4642, 30}"
653,1,30,0,0.0313971,"\int x \sqrt{1-x^2} \cos ^{-1}(x) \, dx","Int[x*Sqrt[1 - x^2]*ArcCos[x],x]","\frac{x^3}{9}-\frac{1}{3} \left(1-x^2\right)^{3/2} \cos ^{-1}(x)-\frac{x}{3}","\frac{x^3}{9}-\frac{1}{3} \left(1-x^2\right)^{3/2} \cos ^{-1}(x)-\frac{x}{3}",1,"-x/3 + x^3/9 - ((1 - x^2)^(3/2)*ArcCos[x])/3","A",2,1,15,0.06667,1,"{4678}"
654,1,59,0,0.0497776,"\int \left(1-x^2\right)^{3/2} \sin ^{-1}(x) \, dx","Int[(1 - x^2)^(3/2)*ArcSin[x],x]","\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","\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)/16 + x^4/16 + (3*x*Sqrt[1 - x^2]*ArcSin[x])/8 + (x*(1 - x^2)^(3/2)*ArcSin[x])/4 + (3*ArcSin[x]^2)/16","A",6,5,14,0.3571,1,"{4649, 4647, 4641, 30, 14}"
655,1,37,0,0.0373196,"\int x \left(1-x^2\right)^{3/2} \sin ^{-1}(x) \, dx","Int[x*(1 - x^2)^(3/2)*ArcSin[x],x]","\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}","\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/5 - (2*x^3)/15 + x^5/25 - ((1 - x^2)^(5/2)*ArcSin[x])/5","A",3,2,15,0.1333,1,"{4677, 194}"
656,1,61,0,0.0750953,"\int x^3 \left(1-x^2\right)^{3/2} \cos ^{-1}(x) \, dx","Int[x^3*(1 - x^2)^(3/2)*ArcCos[x],x]","-\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}","-\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,"(-2*x)/35 - x^3/105 + (8*x^5)/175 - x^7/49 - ((1 - x^2)^(5/2)*ArcCos[x])/5 + ((1 - x^2)^(7/2)*ArcCos[x])/7","A",4,5,17,0.2941,1,"{266, 43, 4690, 12, 373}"
657,1,95,0,0.1581509,"\int \frac{\left(1-x^2\right)^{3/2} \cos ^{-1}(x)}{x} \, dx","Int[((1 - x^2)^(3/2)*ArcCos[x])/x,x]","-i \text{PolyLog}\left(2,-i e^{i \cos ^{-1}(x)}\right)+i \text{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)","-i \text{PolyLog}\left(2,-i e^{i \cos ^{-1}(x)}\right)+i \text{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,"(4*x)/3 - x^3/9 + Sqrt[1 - x^2]*ArcCos[x] + ((1 - x^2)^(3/2)*ArcCos[x])/3 + (2*I)*ArcCos[x]*ArcTan[E^(I*ArcCos[x])] - I*PolyLog[2, (-I)*E^(I*ArcCos[x])] + I*PolyLog[2, I*E^(I*ArcCos[x])]","A",10,7,17,0.4118,1,"{4700, 4698, 4710, 4181, 2279, 2391, 8}"
658,1,41,0,0.0591848,"\int \frac{\left(1-x^2\right)^{3/2} \sin ^{-1}(x)}{x^6} \, dx","Int[((1 - x^2)^(3/2)*ArcSin[x])/x^6,x]","\frac{1}{5 x^2}-\frac{1}{20 x^4}-\frac{\left(1-x^2\right)^{5/2} \sin ^{-1}(x)}{5 x^5}+\frac{\log (x)}{5}","\frac{1}{5 x^2}-\frac{1}{20 x^4}-\frac{\left(1-x^2\right)^{5/2} \sin ^{-1}(x)}{5 x^5}+\frac{\log (x)}{5}",1,"-1/(20*x^4) + 1/(5*x^2) - ((1 - x^2)^(5/2)*ArcSin[x])/(5*x^5) + Log[x]/5","A",4,3,17,0.1765,1,"{4681, 266, 43}"
659,1,34,0,0.0597781,"\int \frac{x^2 \sin ^{-1}(x)}{\sqrt{1-x^2}} \, dx","Int[(x^2*ArcSin[x])/Sqrt[1 - x^2],x]","\frac{x^2}{4}-\frac{1}{2} \sqrt{1-x^2} x \sin ^{-1}(x)+\frac{1}{4} \sin ^{-1}(x)^2","\frac{x^2}{4}-\frac{1}{2} \sqrt{1-x^2} x \sin ^{-1}(x)+\frac{1}{4} \sin ^{-1}(x)^2",1,"x^2/4 - (x*Sqrt[1 - x^2]*ArcSin[x])/2 + ArcSin[x]^2/4","A",3,3,17,0.1765,1,"{4707, 4641, 30}"
660,1,61,0,0.106788,"\int \frac{x^4 \sin ^{-1}(x)}{\sqrt{1-x^2}} \, dx","Int[(x^4*ArcSin[x])/Sqrt[1 - x^2],x]","\frac{x^4}{16}+\frac{3 x^2}{16}-\frac{1}{4} \sqrt{1-x^2} x^3 \sin ^{-1}(x)-\frac{3}{8} \sqrt{1-x^2} x \sin ^{-1}(x)+\frac{3}{16} \sin ^{-1}(x)^2","\frac{x^4}{16}+\frac{3 x^2}{16}-\frac{1}{4} \sqrt{1-x^2} x^3 \sin ^{-1}(x)-\frac{3}{8} \sqrt{1-x^2} x \sin ^{-1}(x)+\frac{3}{16} \sin ^{-1}(x)^2",1,"(3*x^2)/16 + x^4/16 - (3*x*Sqrt[1 - x^2]*ArcSin[x])/8 - (x^3*Sqrt[1 - x^2]*ArcSin[x])/4 + (3*ArcSin[x]^2)/16","A",5,3,17,0.1765,1,"{4707, 4641, 30}"
661,1,19,0,0.0375043,"\int \frac{x \sin ^{-1}(x)}{\left(1-x^2\right)^{3/2}} \, dx","Int[(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",2,2,15,0.1333,1,"{4677, 206}"
662,1,17,0,0.0348905,"\int \frac{x \cos ^{-1}(x)}{\left(1-x^2\right)^{3/2}} \, dx","Int[(x*ArcCos[x])/(1 - x^2)^(3/2),x]","\frac{\cos ^{-1}(x)}{\sqrt{1-x^2}}+\tanh ^{-1}(x)","\frac{\cos ^{-1}(x)}{\sqrt{1-x^2}}+\tanh ^{-1}(x)",1,"ArcCos[x]/Sqrt[1 - x^2] + ArcTanh[x]","A",2,2,15,0.1333,1,"{4678, 206}"
663,1,62,0,0.0391695,"\int \frac{\sin ^{-1}(x)}{\left(1-x^2\right)^{5/2}} \, dx","Int[ArcSin[x]/(1 - x^2)^(5/2),x]","-\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}}","-\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/(6*(1 - x^2)) + (x*ArcSin[x])/(3*(1 - x^2)^(3/2)) + (2*x*ArcSin[x])/(3*Sqrt[1 - x^2]) + Log[1 - x^2]/3","A",4,4,14,0.2857,1,"{4655, 4651, 260, 261}"
664,1,36,0,0.0692451,"\int \frac{x^3 \sin ^{-1}(x)}{\left(1-x^2\right)^{3/2}} \, dx","Int[(x^3*ArcSin[x])/(1 - x^2)^(3/2),x]","\sqrt{1-x^2} \sin ^{-1}(x)+\frac{\sin ^{-1}(x)}{\sqrt{1-x^2}}-x-\tanh ^{-1}(x)","\sqrt{1-x^2} \sin ^{-1}(x)+\frac{\sin ^{-1}(x)}{\sqrt{1-x^2}}-x-\tanh ^{-1}(x)",1,"-x + ArcSin[x]/Sqrt[1 - x^2] + Sqrt[1 - x^2]*ArcSin[x] - ArcTanh[x]","A",3,5,17,0.2941,1,"{266, 43, 4689, 388, 206}"
665,1,62,0,0.1159604,"\int \frac{\sin ^{-1}(x)}{x \left(1-x^2\right)^{3/2}} \, dx","Int[ArcSin[x]/(x*(1 - x^2)^(3/2)),x]","i \text{PolyLog}\left(2,-e^{i \sin ^{-1}(x)}\right)-i \text{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)","i \text{PolyLog}\left(2,-e^{i \sin ^{-1}(x)}\right)-i \text{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] - 2*ArcSin[x]*ArcTanh[E^(I*ArcSin[x])] - ArcTanh[x] + I*PolyLog[2, -E^(I*ArcSin[x])] - I*PolyLog[2, E^(I*ArcSin[x])]","A",8,6,17,0.3529,1,"{4705, 4709, 4183, 2279, 2391, 206}"
666,1,54,0,0.0909131,"\int \frac{\cos ^{-1}(x)}{x^4 \sqrt{1-x^2}} \, dx","Int[ArcCos[x]/(x^4*Sqrt[1 - x^2]),x]","\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}","\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,"1/(6*x^2) - (Sqrt[1 - x^2]*ArcCos[x])/(3*x^3) - (2*Sqrt[1 - x^2]*ArcCos[x])/(3*x) - (2*Log[x])/3","A",4,4,17,0.2353,1,"{4702, 4682, 29, 30}"
667,1,66,0,0.0717082,"\int x \sqrt{1-x^2} \cos ^{-1}(x)^2 \, dx","Int[x*Sqrt[1 - x^2]*ArcCos[x]^2,x]","\frac{2}{27} \left(1-x^2\right)^{3/2}+\frac{4 \sqrt{1-x^2}}{9}+\frac{2}{9} x^3 \cos ^{-1}(x)-\frac{1}{3} \left(1-x^2\right)^{3/2} \cos ^{-1}(x)^2-\frac{2}{3} x \cos ^{-1}(x)","\frac{2}{27} \left(1-x^2\right)^{3/2}+\frac{4 \sqrt{1-x^2}}{9}+\frac{2}{9} x^3 \cos ^{-1}(x)-\frac{1}{3} \left(1-x^2\right)^{3/2} \cos ^{-1}(x)^2-\frac{2}{3} x \cos ^{-1}(x)",1,"(4*Sqrt[1 - x^2])/9 + (2*(1 - x^2)^(3/2))/27 - (2*x*ArcCos[x])/3 + (2*x^3*ArcCos[x])/9 - ((1 - x^2)^(3/2)*ArcCos[x]^2)/3","A",5,4,17,0.2353,1,"{4678, 4646, 444, 43}"
668,1,73,0,0.1545274,"\int \frac{x^2 \sin ^{-1}(x)^3}{\sqrt{1-x^2}} \, dx","Int[(x^2*ArcSin[x]^3)/Sqrt[1 - x^2],x]","-\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","-\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)/8 + (3*x*Sqrt[1 - x^2]*ArcSin[x])/4 - (3*ArcSin[x]^2)/8 + (3*x^2*ArcSin[x]^2)/4 - (x*Sqrt[1 - x^2]*ArcSin[x]^3)/2 + ArcSin[x]^4/8","A",6,4,19,0.2105,1,"{4707, 4641, 4627, 30}"
669,1,32,0,0.0259001,"\int \frac{x \tan ^{-1}(x)}{\left(1+x^2\right)^2} \, dx","Int[(x*ArcTan[x])/(1 + x^2)^2,x]","\frac{x}{4 \left(x^2+1\right)}-\frac{\tan ^{-1}(x)}{2 \left(x^2+1\right)}+\frac{1}{4} \tan ^{-1}(x)","\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/(4*(1 + x^2)) + ArcTan[x]/4 - ArcTan[x]/(2*(1 + x^2))","A",3,3,11,0.2727,1,"{4930, 199, 203}"
670,1,44,0,0.0289532,"\int \frac{x \tan ^{-1}(x)}{\left(1+x^2\right)^3} \, dx","Int[(x*ArcTan[x])/(1 + x^2)^3,x]","\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)","\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/(16*(1 + x^2)^2) + (3*x)/(32*(1 + x^2)) + (3*ArcTan[x])/32 - ArcTan[x]/(4*(1 + x^2)^2)","A",4,3,11,0.2727,1,"{4930, 199, 203}"
671,1,23,0,0.0484445,"\int \frac{x^2 \tan ^{-1}(x)}{1+x^2} \, dx","Int[(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",4,4,13,0.3077,1,"{4916, 4846, 260, 4884}"
672,1,67,0,0.0937433,"\int \frac{x^3 \tan ^{-1}(x)}{1+x^2} \, dx","Int[(x^3*ArcTan[x])/(1 + x^2),x]","\frac{1}{2} i \text{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)","\frac{1}{2} i \text{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/2 + ArcTan[x]/2 + (x^2*ArcTan[x])/2 + (I/2)*ArcTan[x]^2 + ArcTan[x]*Log[2/(1 + I*x)] + (I/2)*PolyLog[2, 1 - 2/(1 + I*x)]","A",8,8,13,0.6154,1,"{4916, 4852, 321, 203, 4920, 4854, 2402, 2315}"
673,1,34,0,0.0470394,"\int \frac{x^2 \tan ^{-1}(x)}{\left(1+x^2\right)^2} \, dx","Int[(x^2*ArcTan[x])/(1 + x^2)^2,x]","-\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","-\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/(4*(1 + x^2)) - (x*ArcTan[x])/(2*(1 + x^2)) + ArcTan[x]^2/4","A",2,2,13,0.1538,1,"{4934, 4884}"
674,1,79,0,0.1126801,"\int \frac{x^3 \tan ^{-1}(x)}{\left(1+x^2\right)^2} \, dx","Int[(x^3*ArcTan[x])/(1 + x^2)^2,x]","-\frac{1}{2} i \text{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)","-\frac{1}{2} i \text{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,"-x/(4*(1 + x^2)) - ArcTan[x]/4 + ArcTan[x]/(2*(1 + x^2)) - (I/2)*ArcTan[x]^2 - ArcTan[x]*Log[2/(1 + I*x)] - (I/2)*PolyLog[2, 1 - 2/(1 + I*x)]","A",8,8,13,0.6154,1,"{4964, 4920, 4854, 2402, 2315, 4930, 199, 203}"
675,1,89,0,0.2341942,"\int \frac{x^5 \tan ^{-1}(x)}{\left(1+x^2\right)^2} \, dx","Int[(x^5*ArcTan[x])/(1 + x^2)^2,x]","i \text{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)","i \text{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,"-x/2 + x/(4*(1 + x^2)) + (3*ArcTan[x])/4 + (x^2*ArcTan[x])/2 - ArcTan[x]/(2*(1 + x^2)) + I*ArcTan[x]^2 + 2*ArcTan[x]*Log[2/(1 + I*x)] + I*PolyLog[2, 1 - 2/(1 + I*x)]","A",17,11,13,0.8462,1,"{4964, 4916, 4852, 321, 203, 4920, 4854, 2402, 2315, 4930, 199}"
676,1,22,0,0.0341581,"\int \frac{\left(1+x^2\right) \tan ^{-1}(x)}{x^2} \, dx","Int[((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",8,8,11,0.7273,1,"{4950, 4852, 266, 36, 29, 31, 4846, 260}"
677,1,31,0,0.0231771,"\int \frac{\left(1+x^2\right) \tan ^{-1}(x)}{x^5} \, dx","Int[((1 + x^2)*ArcTan[x])/x^5,x]","-\frac{1}{12 x^3}-\frac{\left(x^2+1\right)^2 \tan ^{-1}(x)}{4 x^4}-\frac{1}{4 x}","-\frac{1}{12 x^3}-\frac{\left(x^2+1\right)^2 \tan ^{-1}(x)}{4 x^4}-\frac{1}{4 x}",1,"-1/(12*x^3) - 1/(4*x) - ((1 + x^2)^2*ArcTan[x])/(4*x^4)","A",3,2,11,0.1818,1,"{4944, 14}"
678,1,63,0,0.0836894,"\int \frac{\left(1+x^2\right)^2 \tan ^{-1}(x)}{x^5} \, dx","Int[((1 + x^2)^2*ArcTan[x])/x^5,x]","\frac{1}{2} i \text{PolyLog}(2,-i x)-\frac{1}{2} i \text{PolyLog}(2,i x)-\frac{1}{12 x^3}-\frac{\tan ^{-1}(x)}{x^2}-\frac{\tan ^{-1}(x)}{4 x^4}-\frac{3}{4 x}-\frac{3}{4} \tan ^{-1}(x)","\frac{1}{2} i \text{PolyLog}(2,-i x)-\frac{1}{2} i \text{PolyLog}(2,i x)-\frac{1}{12 x^3}-\frac{\tan ^{-1}(x)}{x^2}-\frac{\tan ^{-1}(x)}{4 x^4}-\frac{3}{4 x}-\frac{3}{4} \tan ^{-1}(x)",1,"-1/(12*x^3) - 3/(4*x) - (3*ArcTan[x])/4 - ArcTan[x]/(4*x^4) - ArcTan[x]/x^2 + (I/2)*PolyLog[2, (-I)*x] - (I/2)*PolyLog[2, I*x]","A",12,6,13,0.4615,1,"{4948, 4852, 325, 203, 4848, 2391}"
679,1,28,0,0.0574401,"\int \frac{\tan ^{-1}(x)}{x^2 \left(1+x^2\right)} \, dx","Int[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",7,7,13,0.5385,1,"{4918, 4852, 266, 36, 29, 31, 4884}"
680,1,39,0,0.069604,"\int \frac{\tan ^{-1}(x)^2}{x^3} \, dx","Int[ArcTan[x]^2/x^3,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}","-\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) - ArcTan[x]^2/2 - ArcTan[x]^2/(2*x^2) + Log[x] - Log[1 + x^2]/2","A",8,7,8,0.8750,1,"{4852, 4918, 266, 36, 29, 31, 4884}"
681,1,60,0,0.0779685,"\int \frac{\left(1+x^2\right) \tan ^{-1}(x)^2}{x^5} \, dx","Int[((1 + x^2)*ArcTan[x]^2)/x^5,x]","-\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{\tan ^{-1}(x)}{6 x^3}+\frac{\log (x)}{3}-\frac{\tan ^{-1}(x)}{2 x}","-\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{\tan ^{-1}(x)}{6 x^3}+\frac{\log (x)}{3}-\frac{\tan ^{-1}(x)}{2 x}",1,"-1/(12*x^2) - ArcTan[x]/(6*x^3) - ArcTan[x]/(2*x) - ((1 + x^2)^2*ArcTan[x]^2)/(4*x^4) + Log[x]/3 - Log[1 + x^2]/6","A",11,8,13,0.6154,1,"{4944, 4950, 4852, 266, 44, 36, 29, 31}"
682,1,82,0,0.1330307,"\int \frac{x^3 \tan ^{-1}(x)^2}{\left(1+x^2\right)^3} \, dx","Int[(x^3*ArcTan[x]^2)/(1 + x^2)^3,x]","-\frac{x^4}{32 \left(x^2+1\right)^2}+\frac{3}{32 \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 x \tan ^{-1}(x)}{16 \left(x^2+1\right)}-\frac{3}{32} \tan ^{-1}(x)^2","\frac{5}{32 \left(x^2+1\right)}-\frac{1}{32 \left(x^2+1\right)^2}+\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 x \tan ^{-1}(x)}{16 \left(x^2+1\right)}-\frac{3}{32} \tan ^{-1}(x)^2",1,"-x^4/(32*(1 + x^2)^2) + 3/(32*(1 + x^2)) + (x^3*ArcTan[x])/(8*(1 + x^2)^2) + (3*x*ArcTan[x])/(16*(1 + x^2)) - (3*ArcTan[x]^2)/32 + (x^4*ArcTan[x]^2)/(4*(1 + x^2)^2)","A",4,4,15,0.2667,1,"{4944, 4938, 4934, 4884}"
683,1,116,0,0.1537787,"\int \frac{\sqrt{-1+x^2} \sec ^{-1}(x)}{x^2} \, dx","Int[(Sqrt[-1 + x^2]*ArcSec[x])/x^2,x]","\frac{i \sqrt{x^2} \text{PolyLog}\left(2,-i e^{i \sec ^{-1}(x)}\right)}{x}-\frac{i \sqrt{x^2} \text{PolyLog}\left(2,i e^{i \sec ^{-1}(x)}\right)}{x}-\frac{1}{\sqrt{x^2}}-\frac{\sqrt{1-\frac{1}{x^2}} \sqrt{x^2} \sec ^{-1}(x)}{x}-\frac{2 i \sqrt{x^2} \sec ^{-1}(x) \tan ^{-1}\left(e^{i \sec ^{-1}(x)}\right)}{x}","\frac{i \sqrt{x^2} \text{PolyLog}\left(2,-i e^{i \sec ^{-1}(x)}\right)}{x}-\frac{i \sqrt{x^2} \text{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,"-(1/Sqrt[x^2]) - (Sqrt[1 - x^(-2)]*Sqrt[x^2]*ArcSec[x])/x - ((2*I)*Sqrt[x^2]*ArcSec[x]*ArcTan[E^(I*ArcSec[x])])/x + (I*Sqrt[x^2]*PolyLog[2, (-I)*E^(I*ArcSec[x])])/x - (I*Sqrt[x^2]*PolyLog[2, I*E^(I*ArcSec[x])])/x","A",9,7,15,0.4667,1,"{5242, 4698, 4710, 4181, 2279, 2391, 8}"
684,1,133,0,0.1957399,"\int \frac{\left(-1+x^2\right)^{5/2} \csc ^{-1}(x)}{x^3} \, dx","Int[((-1 + x^2)^(5/2)*ArcCsc[x])/x^3,x]","\frac{x \sqrt{x^2}}{6}+\frac{\sqrt{x^2}}{4 x^3}-\frac{7 \sqrt{x^2} \log (x)}{3 x}+\frac{1}{3} \left(x^2\right)^{3/2} \left(1-\frac{1}{x^2}\right)^{5/2} \csc ^{-1}(x)-\frac{5}{3} \sqrt{x^2} \left(1-\frac{1}{x^2}\right)^{3/2} \csc ^{-1}(x)-\frac{5 \sqrt{1-\frac{1}{x^2}} \csc ^{-1}(x)}{2 \sqrt{x^2}}-\frac{5 \sqrt{x^2} \csc ^{-1}(x)^2}{4 x}","\frac{2 x^4+3}{12 x \sqrt{x^2}}-\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}}",1,"Sqrt[x^2]/(4*x^3) + (x*Sqrt[x^2])/6 - (5*Sqrt[1 - x^(-2)]*ArcCsc[x])/(2*Sqrt[x^2]) - (5*(1 - x^(-2))^(3/2)*Sqrt[x^2]*ArcCsc[x])/3 + ((1 - x^(-2))^(5/2)*(x^2)^(3/2)*ArcCsc[x])/3 - (5*Sqrt[x^2]*ArcCsc[x]^2)/(4*x) - (7*Sqrt[x^2]*Log[x])/(3*x)","A",11,8,15,0.5333,1,"{5243, 4695, 4647, 4641, 30, 14, 266, 43}"
685,1,41,0,0.0519343,"\int \frac{\sqrt{-1+x^2} \sec ^{-1}(x)}{x^4} \, dx","Int[(Sqrt[-1 + x^2]*ArcSec[x])/x^4,x]","\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}","\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,"-1/(9*(x^2)^(3/2)) + 1/(3*Sqrt[x^2]) + ((-1 + x^2)^(3/2)*ArcSec[x])/(3*x^3)","A",4,4,15,0.2667,1,"{264, 5238, 12, 14}"
686,1,67,0,0.0306868,"\int \frac{\sec ^{-1}(x)}{\left(-1+x^2\right)^{5/2}} \, dx","Int[ArcSec[x]/(-1 + x^2)^(5/2),x]","\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 x \tanh ^{-1}(x)}{6 \sqrt{x^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,"Sqrt[x^2]/(6*(1 - x^2)) - (x*ArcSec[x])/(3*(-1 + x^2)^(3/2)) + (2*x*ArcSec[x])/(3*Sqrt[-1 + x^2]) + (5*x*ArcTanh[x])/(6*Sqrt[x^2])","A",4,6,12,0.5000,0,"{192, 191, 5228, 12, 385, 206}"
687,1,53,0,0.063826,"\int \frac{x^2 \sec ^{-1}(x)}{\left(-1+x^2\right)^{5/2}} \, dx","Int[(x^2*ArcSec[x])/(-1 + x^2)^(5/2),x]","\frac{\sqrt{x^2}}{6 \left(1-x^2\right)}-\frac{x^3 \sec ^{-1}(x)}{3 \left(x^2-1\right)^{3/2}}-\frac{x \tanh ^{-1}(x)}{6 \sqrt{x^2}}","\frac{\sqrt{x^2}}{6 \left(1-x^2\right)}-\frac{x^3 \sec ^{-1}(x)}{3 \left(x^2-1\right)^{3/2}}-\frac{1}{6} \coth ^{-1}\left(\sqrt{x^2}\right)",1,"Sqrt[x^2]/(6*(1 - x^2)) - (x^3*ArcSec[x])/(3*(-1 + x^2)^(3/2)) - (x*ArcTanh[x])/(6*Sqrt[x^2])","A",4,5,15,0.3333,0,"{264, 5238, 12, 288, 207}"
688,1,84,0,0.0897121,"\int \frac{x^3 \sec ^{-1}(x)}{\left(-1+x^2\right)^{5/2}} \, dx","Int[(x^3*ArcSec[x])/(-1 + x^2)^(5/2),x]","\frac{x}{6 \sqrt{x^2} \left(1-x^2\right)}-\frac{2 x \log (x)}{3 \sqrt{x^2}}+\frac{x \log \left(1-x^2\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}}","\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,"x/(6*Sqrt[x^2]*(1 - x^2)) - ArcSec[x]/(3*(-1 + x^2)^(3/2)) - ArcSec[x]/Sqrt[-1 + x^2] - (2*x*Log[x])/(3*Sqrt[x^2]) + (x*Log[1 - x^2])/(3*Sqrt[x^2])","A",5,6,15,0.4000,0,"{266, 43, 5238, 12, 446, 77}"
689,1,232,0,0.3171061,"\int \frac{x^6 \sec ^{-1}(x)}{\left(-1+x^2\right)^{5/2}} \, dx","Int[(x^6*ArcSec[x])/(-1 + x^2)^(5/2),x]","\frac{5 i \sqrt{x^2} \text{PolyLog}\left(2,-i e^{i \sec ^{-1}(x)}\right)}{2 x}-\frac{5 i \sqrt{x^2} \text{PolyLog}\left(2,i e^{i \sec ^{-1}(x)}\right)}{2 x}+\frac{\sqrt{x^2}}{4 \left(1-\frac{1}{x^2}\right)}-\frac{3 \sqrt{x^2}}{4}-\frac{5}{12 \left(1-\frac{1}{x^2}\right) \sqrt{x^2}}+\frac{x \sqrt{x^2} \sec ^{-1}(x)}{2 \left(1-\frac{1}{x^2}\right)^{3/2}}-\frac{5 \sqrt{x^2} \sec ^{-1}(x)}{2 \sqrt{1-\frac{1}{x^2}} x}-\frac{5 \sqrt{x^2} \sec ^{-1}(x)}{6 \left(1-\frac{1}{x^2}\right)^{3/2} x}-\frac{13 \sqrt{x^2} \coth ^{-1}(x)}{6 x}-\frac{5 i \sqrt{x^2} \sec ^{-1}(x) \tan ^{-1}\left(e^{i \sec ^{-1}(x)}\right)}{x}","\frac{5 i \sqrt{x^2} \text{PolyLog}\left(2,-i e^{i \sec ^{-1}(x)}\right)}{2 x}-\frac{5 i \sqrt{x^2} \text{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{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}}-\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}",1,"-5/(12*(1 - x^(-2))*Sqrt[x^2]) - (3*Sqrt[x^2])/4 + Sqrt[x^2]/(4*(1 - x^(-2))) - (13*Sqrt[x^2]*ArcCoth[x])/(6*x) - (5*Sqrt[x^2]*ArcSec[x])/(6*(1 - x^(-2))^(3/2)*x) - (5*Sqrt[x^2]*ArcSec[x])/(2*Sqrt[1 - x^(-2)]*x) + (x*Sqrt[x^2]*ArcSec[x])/(2*(1 - x^(-2))^(3/2)) - ((5*I)*Sqrt[x^2]*ArcSec[x]*ArcTan[E^(I*ArcSec[x])])/x + (((5*I)/2)*Sqrt[x^2]*PolyLog[2, (-I)*E^(I*ArcSec[x])])/x - (((5*I)/2)*Sqrt[x^2]*PolyLog[2, I*E^(I*ArcSec[x])])/x","A",16,11,15,0.7333,0,"{5242, 4702, 4706, 4710, 4181, 2279, 2391, 206, 199, 290, 325}"
690,1,23,0,0.0478767,"\int \frac{\sec ^{-1}(x)}{x^2 \sqrt{-1+x^2}} \, dx","Int[ArcSec[x]/(x^2*Sqrt[-1 + x^2]),x]","\frac{1}{\sqrt{x^2}}+\frac{\sqrt{x^2-1} \sec ^{-1}(x)}{x}","\frac{1}{\sqrt{x^2}}+\frac{\sqrt{x^2-1} \sec ^{-1}(x)}{x}",1,"1/Sqrt[x^2] + (Sqrt[-1 + x^2]*ArcSec[x])/x","A",2,3,15,0.2000,1,"{264, 5238, 30}"
691,1,91,0,0.085914,"\int \frac{\csc ^{-1}(x)}{x^2 \left(-1+x^2\right)^{5/2}} \, dx","Int[ArcCsc[x]/(x^2*(-1 + x^2)^(5/2)),x]","-\frac{1}{\sqrt{x^2}}-\frac{\sqrt{x^2}}{6 \left(1-x^2\right)}+\frac{8 x \csc ^{-1}(x)}{3 \sqrt{x^2-1}}-\frac{4 x \csc ^{-1}(x)}{3 \left(x^2-1\right)^{3/2}}+\frac{\csc ^{-1}(x)}{x \left(x^2-1\right)^{3/2}}-\frac{11 x \tanh ^{-1}(x)}{6 \sqrt{x^2}}","-\frac{1}{\sqrt{x^2}}+\frac{\sqrt{x^2}}{6 \left(x^2-1\right)}+\frac{\left(8 x^4-12 x^2+3\right) \csc ^{-1}(x)}{3 x \left(x^2-1\right)^{3/2}}-\frac{11}{6} \coth ^{-1}\left(\sqrt{x^2}\right)",1,"-(1/Sqrt[x^2]) - Sqrt[x^2]/(6*(1 - x^2)) + ArcCsc[x]/(x*(-1 + x^2)^(3/2)) - (4*x*ArcCsc[x])/(3*(-1 + x^2)^(3/2)) + (8*x*ArcCsc[x])/(3*Sqrt[-1 + x^2]) - (11*x*ArcTanh[x])/(6*Sqrt[x^2])","A",5,8,15,0.5333,0,"{271, 192, 191, 5239, 12, 1259, 453, 206}"
692,1,101,0,0.1786975,"\int \frac{\csc ^{-1}(x)^4}{x^2 \sqrt{-1+x^2}} \, dx","Int[ArcCsc[x]^4/(x^2*Sqrt[-1 + x^2]),x]","\frac{24 \sqrt{1-\frac{1}{x^2}} \sqrt{x^2}}{x}+\frac{\sqrt{1-\frac{1}{x^2}} \sqrt{x^2} \csc ^{-1}(x)^4}{x}-\frac{4 \csc ^{-1}(x)^3}{\sqrt{x^2}}-\frac{12 \sqrt{1-\frac{1}{x^2}} \sqrt{x^2} \csc ^{-1}(x)^2}{x}+\frac{24 \csc ^{-1}(x)}{\sqrt{x^2}}","\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*Sqrt[1 - x^(-2)]*Sqrt[x^2])/x + (24*ArcCsc[x])/Sqrt[x^2] - (12*Sqrt[1 - x^(-2)]*Sqrt[x^2]*ArcCsc[x]^2)/x - (4*ArcCsc[x]^3)/Sqrt[x^2] + (Sqrt[1 - x^(-2)]*Sqrt[x^2]*ArcCsc[x]^4)/x","A",6,4,17,0.2353,1,"{5243, 4677, 4619, 261}"
693,1,172,0,0.2013474,"\int \frac{\left(-1+x^2\right)^{3/2} \sec ^{-1}(x)^2}{x^5} \, dx","Int[((-1 + x^2)^(3/2)*ArcSec[x]^2)/x^5,x]","\frac{\left(1-\frac{1}{x^2}\right)^{3/2}}{32 \sqrt{x^2}}+\frac{15 \sqrt{1-\frac{1}{x^2}}}{64 \sqrt{x^2}}-\frac{9 \sqrt{x^2} \csc ^{-1}(x)}{64 x}+\frac{\sqrt{x^2} \sec ^{-1}(x)^3}{8 x}-\frac{\left(1-\frac{1}{x^2}\right)^{3/2} \sec ^{-1}(x)^2}{4 \sqrt{x^2}}-\frac{3 \sqrt{1-\frac{1}{x^2}} \sec ^{-1}(x)^2}{8 \sqrt{x^2}}+\frac{\left(1-\frac{1}{x^2}\right)^2 \sqrt{x^2} \sec ^{-1}(x)}{8 x}-\frac{3 \sqrt{x^2} \sec ^{-1}(x)}{8 x^3}","\frac{\sqrt{x^2-1} \left(17 x^2-2\right)}{64 x^4}+\frac{x \sec ^{-1}(x)^3}{8 \sqrt{x^2}}-\frac{\left(x^2-1\right)^{3/2} \sec ^{-1}(x)^2}{4 x^4}-\frac{3 \sqrt{x^2-1} \sec ^{-1}(x)^2}{8 x^2}+\frac{\left(x^2-1\right)^2 \sec ^{-1}(x)}{8 x^3 \sqrt{x^2}}+\frac{9 x \sec ^{-1}(x)}{64 \sqrt{x^2}}-\frac{3 \sec ^{-1}(x)}{8 x \sqrt{x^2}}",1,"(15*Sqrt[1 - x^(-2)])/(64*Sqrt[x^2]) + (1 - x^(-2))^(3/2)/(32*Sqrt[x^2]) - (9*Sqrt[x^2]*ArcCsc[x])/(64*x) - (3*Sqrt[x^2]*ArcSec[x])/(8*x^3) + ((1 - x^(-2))^2*Sqrt[x^2]*ArcSec[x])/(8*x) - (3*Sqrt[1 - x^(-2)]*ArcSec[x]^2)/(8*Sqrt[x^2]) - ((1 - x^(-2))^(3/2)*ArcSec[x]^2)/(4*Sqrt[x^2]) + (Sqrt[x^2]*ArcSec[x]^3)/(8*x)","A",11,9,17,0.5294,1,"{5242, 4650, 4648, 4642, 4628, 321, 216, 4678, 195}"
694,1,146,0,0.1999974,"\int \frac{\sqrt{-1+x^2} \sec ^{-1}(x)^3}{x^4} \, dx","Int[(Sqrt[-1 + x^2]*ArcSec[x]^3)/x^4,x]","\frac{2 \sqrt{x^2}}{27 x^4}-\frac{14}{9 \sqrt{x^2}}+\frac{\left(1-\frac{1}{x^2}\right)^{3/2} \sqrt{x^2} \sec ^{-1}(x)^3}{3 x}+\frac{\left(1-\frac{1}{x^2}\right) \sec ^{-1}(x)^2}{3 \sqrt{x^2}}+\frac{2 \sec ^{-1}(x)^2}{3 \sqrt{x^2}}-\frac{2 \left(1-\frac{1}{x^2}\right)^{3/2} \sqrt{x^2} \sec ^{-1}(x)}{9 x}-\frac{4 \sqrt{1-\frac{1}{x^2}} \sqrt{x^2} \sec ^{-1}(x)}{3 x}","\frac{2 \left(1-21 x^2\right)}{27 \left(x^2\right)^{3/2}}+\frac{\left(x^2-1\right)^{3/2} \sec ^{-1}(x)^3}{3 x^3}+\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{2 \left(x^2-1\right)^{3/2} \sec ^{-1}(x)}{9 x^3}-\frac{4 \sqrt{x^2-1} \sec ^{-1}(x)}{3 x}",1,"-14/(9*Sqrt[x^2]) + (2*Sqrt[x^2])/(27*x^4) - (4*Sqrt[1 - x^(-2)]*Sqrt[x^2]*ArcSec[x])/(3*x) - (2*(1 - x^(-2))^(3/2)*Sqrt[x^2]*ArcSec[x])/(9*x) + (2*ArcSec[x]^2)/(3*Sqrt[x^2]) + ((1 - x^(-2))*ArcSec[x]^2)/(3*Sqrt[x^2]) + ((1 - x^(-2))^(3/2)*Sqrt[x^2]*ArcSec[x]^3)/(3*x)","A",8,5,17,0.2941,1,"{5242, 4678, 4650, 4620, 8}"
695,1,118,0,0.8428753,"\int \sin ^{-1}\left(\sqrt{\frac{-a+x}{a+x}}\right) \, dx","Int[ArcSin[Sqrt[(-a + x)/(a + x)]],x]","-\sqrt{2} \sqrt{\frac{a}{a+x}} \sqrt{-\frac{a-x}{a+x}} (a+x)+x \sin ^{-1}\left(\sqrt{-\frac{a-x}{a+x}}\right)-\frac{a \sqrt{\frac{a}{a+x}} \tanh ^{-1}\left(\frac{\sqrt{-\frac{a-x}{a+x}}}{\sqrt{2} \sqrt{-\frac{a}{a+x}}}\right)}{\sqrt{-\frac{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,"-(Sqrt[2]*Sqrt[a/(a + x)]*Sqrt[-((a - x)/(a + x))]*(a + x)) + x*ArcSin[Sqrt[-((a - x)/(a + x))]] - (a*Sqrt[a/(a + x)]*ArcTanh[Sqrt[-((a - x)/(a + x))]/(Sqrt[2]*Sqrt[-(a/(a + x))])])/Sqrt[-(a/(a + x))]","B",8,7,16,0.4375,1,"{4840, 12, 6677, 6720, 385, 217, 206}"
696,1,40,0,0.0425593,"\int \tan ^{-1}\left(\sqrt{\frac{-a+x}{a+x}}\right) \, dx","Int[ArcTan[Sqrt[(-a + x)/(a + x)]],x]","x \tan ^{-1}\left(\sqrt{-\frac{a-x}{a+x}}\right)-a \tanh ^{-1}\left(\sqrt{-\frac{a-x}{a+x}}\right)","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*ArcTanh[Sqrt[-((a - x)/(a + x))]]","A",4,4,16,0.2500,1,"{5203, 12, 1961, 208}"
697,1,39,0,0.0293697,"\int \frac{\tan ^{-1}(x)}{(1+x)^3} \, dx","Int[ArcTan[x]/(1 + x)^3,x]","-\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}","-\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,"-1/(4*(1 + x)) - ArcTan[x]/(2*(1 + x)^2) + Log[1 + x]/4 - Log[1 + x^2]/8","A",5,4,8,0.5000,1,"{4862, 710, 801, 260}"
698,1,122,0,0.0914153,"\int -\frac{\tan ^{-1}(a-x)}{a+x} \, dx","Int[-(ArcTan[a - x]/(a + x)),x]","-\frac{1}{2} i \text{PolyLog}\left(2,1-\frac{2}{1-i (a-x)}\right)+\frac{1}{2} i \text{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)","-\frac{1}{2} i \text{PolyLog}\left(2,1-\frac{2}{1-i (a-x)}\right)+\frac{1}{2} i \text{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,"ArcTan[a - x]*Log[2/(1 - I*(a - x))] - ArcTan[a - x]*Log[(-2*(a + x))/((I - 2*a)*(1 - I*(a - x)))] - (I/2)*PolyLog[2, 1 - 2/(1 - I*(a - x))] + (I/2)*PolyLog[2, 1 + (2*(a + x))/((I - 2*a)*(1 - I*(a - x)))]","A",5,5,13,0.3846,1,"{5047, 4856, 2402, 2315, 2447}"
699,1,28,0,0.0332714,"\int \frac{\sin ^{-1}\left(\sqrt{1-x^2}\right)}{\sqrt{1-x^2}} \, dx","Int[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,"-(Sqrt[x^2]*ArcSin[Sqrt[1 - x^2]]^2)/(2*x)","A",2,2,24,0.08333,1,"{4834, 4641}"
700,1,31,0,0.0380929,"\int \frac{x \tan ^{-1}\left(\sqrt{1+x^2}\right)}{\sqrt{1+x^2}} \, dx","Int[(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",2,3,21,0.1429,1,"{261, 5207, 260}"
701,1,57,0,0.0316633,"\int \frac{\sin ^{-1}(x)}{(1-x)^{5/2}} \, dx","Int[ArcSin[x]/(1 - x)^(5/2),x]","-\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}}","-\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,"-Sqrt[1 + x]/(3*(1 - x)) + (2*ArcSin[x])/(3*(1 - x)^(3/2)) - ArcTanh[Sqrt[1 + x]/Sqrt[2]]/(3*Sqrt[2])","A",5,5,12,0.4167,1,"{4743, 627, 51, 63, 206}"
702,1,140,0,0.0784756,"\int (-1+x)^{5/2} \csc ^{-1}(x) \, dx","Int[(-1 + x)^(5/2)*ArcCsc[x],x]","\frac{4 (x+1)^3 \sqrt{x-1}}{35 \sqrt{1-\frac{1}{x^2}} x}-\frac{20 (x+1)^2 \sqrt{x-1}}{21 \sqrt{1-\frac{1}{x^2}} x}+\frac{4 (x+1) \sqrt{x-1}}{\sqrt{1-\frac{1}{x^2}} x}+\frac{4 \sqrt{x+1} \sqrt{x-1} \tanh ^{-1}\left(\sqrt{x+1}\right)}{7 \sqrt{1-\frac{1}{x^2}} x}+\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]*(1 + x))/(Sqrt[1 - x^(-2)]*x) - (20*Sqrt[-1 + x]*(1 + x)^2)/(21*Sqrt[1 - x^(-2)]*x) + (4*Sqrt[-1 + x]*(1 + x)^3)/(35*Sqrt[1 - x^(-2)]*x) + (2*(-1 + x)^(7/2)*ArcCsc[x])/7 + (4*Sqrt[-1 + x]*Sqrt[1 + x]*ArcTanh[Sqrt[1 + x]])/(7*Sqrt[1 - x^(-2)]*x)","A",7,6,10,0.6000,1,"{5227, 1574, 892, 88, 63, 207}"
703,1,49,0,0.1404963,"\int \sin ^{-1}(\sinh (x)) \text{sech}^4(x) \, dx","Int[ArcSin[Sinh[x]]*Sech[x]^4,x]","\frac{1}{6} \sqrt{2-\cosh ^2(x)} \text{sech}(x)-\frac{2}{3} \sin ^{-1}\left(\frac{\cosh (x)}{\sqrt{2}}\right)-\frac{1}{3} \tanh ^3(x) \sin ^{-1}(\sinh (x))+\tanh (x) \sin ^{-1}(\sinh (x))","-\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,"(-2*ArcSin[Cosh[x]/Sqrt[2]])/3 + (Sqrt[2 - Cosh[x]^2]*Sech[x])/6 + ArcSin[Sinh[x]]*Tanh[x] - (ArcSin[Sinh[x]]*Tanh[x]^3)/3","A",5,6,8,0.7500,1,"{3767, 4844, 12, 4357, 451, 216}"
704,1,36,0,0.1198807,"\int \cot ^{-1}(\cosh (x)) \coth (x) \text{csch}^3(x) \, dx","Int[ArcCot[Cosh[x]]*Coth[x]*Csch[x]^3,x]","\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))","\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,"ArcTanh[Tanh[x]/Sqrt[2]]/(6*Sqrt[2]) + Coth[x]/6 - (ArcCot[Cosh[x]]*Csch[x]^3)/3","A",6,6,10,0.6000,1,"{2606, 30, 5208, 12, 453, 206}"
705,1,28,0,0.0769321,"\int e^x \sin ^{-1}(\tanh (x)) \, dx","Int[E^x*ArcSin[Tanh[x]],x]","e^x \sin ^{-1}(\tanh (x))-\log \left(e^{2 x}+1\right) \cosh (x) \sqrt{\text{sech}^2(x)}","e^x \sin ^{-1}(\tanh (x))-\log \left(e^{2 x}+1\right) \cosh (x) \sqrt{\text{sech}^2(x)}",1,"E^x*ArcSin[Tanh[x]] - Cosh[x]*Log[1 + E^(2*x)]*Sqrt[Sech[x]^2]","A",5,6,7,0.8571,1,"{2194, 4844, 6720, 2282, 12, 260}"