1,1,11,11,0.0011757,"\int x^n \, dx","Integrate[x^n,x]","\frac{x^{n+1}}{n+1}","\frac{x^{n+1}}{n+1}",1,"x^(1 + n)/(1 + n)","A",1
2,1,3,3,0.0001502,"\int e^x \, dx","Integrate[E^x,x]","e^x","e^x",1,"E^x","A",1
3,1,2,2,0.0001376,"\int \frac{1}{x} \, dx","Integrate[x^(-1),x]","\log (x)","\log (x)",1,"Log[x]","A",1
4,1,8,8,0.0006224,"\int a^x \, dx","Integrate[a^x,x]","\frac{a^x}{\log (a)}","\frac{a^x}{\log (a)}",1,"a^x/Log[a]","A",1
5,1,4,4,0.0009927,"\int \sin (x) \, dx","Integrate[Sin[x],x]","-\cos (x)","-\cos (x)",1,"-Cos[x]","A",1
6,1,2,2,0.0010023,"\int \cos (x) \, dx","Integrate[Cos[x],x]","\sin (x)","\sin (x)",1,"Sin[x]","A",1
7,1,2,2,0.0035831,"\int \sec ^2(x) \, dx","Integrate[Sec[x]^2,x]","\tan (x)","\tan (x)",1,"Tan[x]","A",1
8,1,4,4,0.0017051,"\int \csc ^2(x) \, dx","Integrate[Csc[x]^2,x]","-\cot (x)","-\cot (x)",1,"-Cot[x]","A",1
9,1,2,2,0.0014154,"\int \sec (x) \tan (x) \, dx","Integrate[Sec[x]*Tan[x],x]","\sec (x)","\sec (x)",1,"Sec[x]","A",1
10,1,4,4,0.0016613,"\int \cot (x) \csc (x) \, dx","Integrate[Cot[x]*Csc[x],x]","-\csc (x)","-\csc (x)",1,"-Csc[x]","A",1
11,1,2,2,0.0010712,"\int \sinh (x) \, dx","Integrate[Sinh[x],x]","\cosh (x)","\cosh (x)",1,"Cosh[x]","A",1
12,1,2,2,0.0011658,"\int \cosh (x) \, dx","Integrate[Cosh[x],x]","\sinh (x)","\sinh (x)",1,"Sinh[x]","A",1
13,1,5,5,0.0020298,"\int \tan (x) \, dx","Integrate[Tan[x],x]","-\log (\cos (x))","-\log (\cos (x))",1,"-Log[Cos[x]]","A",1
14,1,3,3,0.0019986,"\int \cot (x) \, dx","Integrate[Cot[x],x]","\log (\sin (x))","\log (\sin (x))",1,"Log[Sin[x]]","A",1
15,1,8,8,0.0023791,"\int x \sin (x) \, dx","Integrate[x*Sin[x],x]","\sin (x)-x \cos (x)","\sin (x)-x \cos (x)",1,"-(x*Cos[x]) + Sin[x]","A",1
16,1,8,8,0.0005725,"\int \log (x) \, dx","Integrate[Log[x],x]","x \log (x)-x","x \log (x)-x",1,"-x + x*Log[x]","A",1
17,1,12,19,0.0048383,"\int e^x x^2 \, dx","Integrate[E^x*x^2,x]","e^x \left(x^2-2 x+2\right)","e^x x^2-2 e^x x+2 e^x",1,"E^x*(2 - 2*x + x^2)","A",1
18,1,14,19,0.0047329,"\int e^x \sin (x) \, dx","Integrate[E^x*Sin[x],x]","\frac{1}{2} e^x (\sin (x)-\cos (x))","\frac{1}{2} e^x \sin (x)-\frac{1}{2} e^x \cos (x)",1,"(E^x*(-Cos[x] + Sin[x]))/2","A",1
19,1,15,15,0.0018104,"\int \tan ^{-1}(x) \, dx","Integrate[ArcTan[x],x]","x \tan ^{-1}(x)-\frac{1}{2} \log \left(x^2+1\right)","x \tan ^{-1}(x)-\frac{1}{2} \log \left(x^2+1\right)",1,"x*ArcTan[x] - Log[1 + x^2]/2","A",1
20,1,15,20,0.0042738,"\int e^{2 x} x \, dx","Integrate[E^(2*x)*x,x]","e^{2 x} \left(\frac{x}{2}-\frac{1}{4}\right)","\frac{1}{2} e^{2 x} x-\frac{e^{2 x}}{4}",1,"E^(2*x)*(-1/4 + x/2)","A",1
21,1,7,7,0.0018952,"\int x \cos (x) \, dx","Integrate[x*Cos[x],x]","x \sin (x)+\cos (x)","x \sin (x)+\cos (x)",1,"Cos[x] + x*Sin[x]","A",1
22,1,18,18,0.0110059,"\int x \sin (4 x) \, dx","Integrate[x*Sin[4*x],x]","\frac{1}{16} \sin (4 x)-\frac{1}{4} x \cos (4 x)","\frac{1}{16} \sin (4 x)-\frac{1}{4} x \cos (4 x)",1,"-1/4*(x*Cos[4*x]) + Sin[4*x]/16","A",1
23,1,17,17,0.0007109,"\int x \log (x) \, dx","Integrate[x*Log[x],x]","\frac{1}{2} x^2 \log (x)-\frac{x^2}{4}","\frac{1}{2} x^2 \log (x)-\frac{x^2}{4}",1,"-1/4*x^2 + (x^2*Log[x])/2","A",1
24,1,25,29,0.0281222,"\int x^2 \cos (3 x) \, dx","Integrate[x^2*Cos[3*x],x]","\frac{1}{27} \left(9 x^2-2\right) \sin (3 x)+\frac{2}{9} x \cos (3 x)","\frac{1}{3} x^2 \sin (3 x)-\frac{2}{27} \sin (3 x)+\frac{2}{9} x \cos (3 x)",1,"(2*x*Cos[3*x])/9 + ((-2 + 9*x^2)*Sin[3*x])/27","A",1
25,1,25,29,0.0258844,"\int x^2 \sin (2 x) \, dx","Integrate[x^2*Sin[2*x],x]","\frac{1}{2} x \sin (2 x)-\frac{1}{4} \left(2 x^2-1\right) \cos (2 x)","-\frac{1}{2} x^2 \cos (2 x)+\frac{1}{2} x \sin (2 x)+\frac{1}{4} \cos (2 x)",1,"-1/4*((-1 + 2*x^2)*Cos[2*x]) + (x*Sin[2*x])/2","A",1
26,1,15,15,0.0009694,"\int \log ^2(x) \, dx","Integrate[Log[x]^2,x]","2 x+x \log ^2(x)-2 x \log (x)","2 x+x \log ^2(x)-2 x \log (x)",1,"2*x - 2*x*Log[x] + x*Log[x]^2","A",1
27,1,16,16,0.0033086,"\int \sin ^{-1}(x) \, dx","Integrate[ArcSin[x],x]","\sqrt{1-x^2}+x \sin ^{-1}(x)","\sqrt{1-x^2}+x \sin ^{-1}(x)",1,"Sqrt[1 - x^2] + x*ArcSin[x]","A",1
28,1,18,23,0.0030703,"\int t \cos (t) \sin (t) \, dt","Integrate[t*Cos[t]*Sin[t],t]","\frac{1}{8} \sin (2 t)-\frac{1}{4} t \cos (2 t)","-\frac{t}{4}+\frac{1}{2} t \sin ^2(t)+\frac{1}{4} \sin (t) \cos (t)",1,"-1/4*(t*Cos[2*t]) + Sin[2*t]/8","A",1
29,1,8,8,0.0056197,"\int t \sec ^2(t) \, dt","Integrate[t*Sec[t]^2,t]","t \tan (t)+\log (\cos (t))","t \tan (t)+\log (\cos (t))",1,"Log[Cos[t]] + t*Tan[t]","A",1
30,1,17,17,0.0016101,"\int t^2 \log (t) \, dt","Integrate[t^2*Log[t],t]","\frac{1}{3} t^3 \log (t)-\frac{t^3}{9}","\frac{1}{3} t^3 \log (t)-\frac{t^3}{9}",1,"-1/9*t^3 + (t^3*Log[t])/3","A",1
31,1,17,27,0.0065642,"\int e^t t^3 \, dt","Integrate[E^t*t^3,t]","e^t \left(t^3-3 t^2+6 t-6\right)","e^t t^3-3 e^t t^2+6 e^t t-6 e^t",1,"E^t*(-6 + 6*t - 3*t^2 + t^3)","A",1
32,1,22,27,0.0356821,"\int e^{2 t} \sin (3 t) \, dt","Integrate[E^(2*t)*Sin[3*t],t]","\frac{1}{13} e^{2 t} (2 \sin (3 t)-3 \cos (3 t))","\frac{2}{13} e^{2 t} \sin (3 t)-\frac{3}{13} e^{2 t} \cos (3 t)",1,"(E^(2*t)*(-3*Cos[3*t] + 2*Sin[3*t]))/13","A",1
33,1,20,27,0.0292905,"\int e^{-t} \cos (3 t) \, dt","Integrate[Cos[3*t]/E^t,t]","-\frac{1}{10} e^{-t} (\cos (3 t)-3 \sin (3 t))","\frac{3}{10} e^{-t} \sin (3 t)-\frac{1}{10} e^{-t} \cos (3 t)",1,"-1/10*(Cos[3*t] - 3*Sin[3*t])/E^t","A",1
34,1,9,9,0.0033298,"\int y \sinh (y) \, dy","Integrate[y*Sinh[y],y]","y \cosh (y)-\sinh (y)","y \cosh (y)-\sinh (y)",1,"y*Cosh[y] - Sinh[y]","A",1
35,1,19,19,0.0141381,"\int y \cosh (a y) \, dy","Integrate[y*Cosh[a*y],y]","\frac{y \sinh (a y)}{a}-\frac{\cosh (a y)}{a^2}","\frac{y \sinh (a y)}{a}-\frac{\cosh (a y)}{a^2}",1,"-(Cosh[a*y]/a^2) + (y*Sinh[a*y])/a","A",1
36,1,11,16,0.0051824,"\int e^{-t} t \, dt","Integrate[t/E^t,t]","e^{-t} (-t-1)","-e^{-t} t-e^{-t}",1,"(-1 - t)/E^t","A",1
37,1,15,21,0.0027681,"\int \sqrt{t} \log (t) \, dt","Integrate[Sqrt[t]*Log[t],t]","\frac{2}{9} t^{3/2} (3 \log (t)-2)","\frac{2}{3} t^{3/2} \log (t)-\frac{4 t^{3/2}}{9}",1,"(2*t^(3/2)*(-2 + 3*Log[t]))/9","A",1
38,1,18,18,0.0090858,"\int x \cos (2 x) \, dx","Integrate[x*Cos[2*x],x]","\frac{1}{2} x \sin (2 x)+\frac{1}{4} \cos (2 x)","\frac{1}{2} x \sin (2 x)+\frac{1}{4} \cos (2 x)",1,"Cos[2*x]/4 + (x*Sin[2*x])/2","A",1
39,1,16,26,0.0063336,"\int e^{-x} x^2 \, dx","Integrate[x^2/E^x,x]","e^{-x} \left(-x^2-2 x-2\right)","-e^{-x} x^2-2 e^{-x} x-2 e^{-x}",1,"(-2 - 2*x - x^2)/E^x","A",1
40,1,18,18,0.0025207,"\int \cos ^{-1}(x) \, dx","Integrate[ArcCos[x],x]","x \cos ^{-1}(x)-\sqrt{1-x^2}","x \cos ^{-1}(x)-\sqrt{1-x^2}",1,"-Sqrt[1 - x^2] + x*ArcCos[x]","A",1
41,1,9,9,0.0173538,"\int x \csc ^2(x) \, dx","Integrate[x*Csc[x]^2,x]","\log (\sin (x))-x \cot (x)","\log (\sin (x))-x \cot (x)",1,"-(x*Cot[x]) + Log[Sin[x]]","A",1
42,1,17,17,0.0081283,"\int \cos (5 x) \sin (3 x) \, dx","Integrate[Cos[5*x]*Sin[3*x],x]","\frac{\cos ^2(x)}{2}-\frac{1}{16} \cos (8 x)","\frac{1}{4} \cos (2 x)-\frac{1}{16} \cos (8 x)",1,"Cos[x]^2/2 - Cos[8*x]/16","A",1
43,1,17,17,0.0071406,"\int \sin (2 x) \sin (4 x) \, dx","Integrate[Sin[2*x]*Sin[4*x],x]","\frac{1}{4} \sin (2 x)-\frac{1}{12} \sin (6 x)","\frac{1}{4} \sin (2 x)-\frac{1}{12} \sin (6 x)",1,"Sin[2*x]/4 - Sin[6*x]/12","A",1
44,1,11,11,0.0027653,"\int \cos (x) \log (\sin (x)) \, dx","Integrate[Cos[x]*Log[Sin[x]],x]","\sin (x) \log (\sin (x))-\sin (x)","\sin (x) \log (\sin (x))-\sin (x)",1,"-Sin[x] + Log[Sin[x]]*Sin[x]","A",1
45,1,14,22,0.0018287,"\int e^{x^2} x^3 \, dx","Integrate[E^x^2*x^3,x]","\frac{1}{2} e^{x^2} \left(x^2-1\right)","\frac{1}{2} e^{x^2} x^2-\frac{e^{x^2}}{2}",1,"(E^x^2*(-1 + x^2))/2","A",1
46,1,9,15,0.0115813,"\int e^x (3+2 x) \, dx","Integrate[E^x*(3 + 2*x),x]","e^x (2 x+1)","e^x (2 x+3)-2 e^x",1,"E^x*(1 + 2*x)","A",1
47,1,14,19,0.0033512,"\int 5^x x \, dx","Integrate[5^x*x,x]","\frac{5^x (x \log (5)-1)}{\log ^2(5)}","\frac{5^x x}{\log (5)}-\frac{5^x}{\log ^2(5)}",1,"(5^x*(-1 + x*Log[5]))/Log[5]^2","A",1
48,1,17,17,0.0030313,"\int \cos (\log (x)) \, dx","Integrate[Cos[Log[x]],x]","\frac{1}{2} x \sin (\log (x))+\frac{1}{2} x \cos (\log (x))","\frac{1}{2} x \sin (\log (x))+\frac{1}{2} x \cos (\log (x))",1,"(x*Cos[Log[x]])/2 + (x*Sin[Log[x]])/2","A",1
49,1,16,24,0.0061284,"\int e^{\sqrt{x}} \, dx","Integrate[E^Sqrt[x],x]","2 e^{\sqrt{x}} \left(\sqrt{x}-1\right)","2 e^{\sqrt{x}} \sqrt{x}-2 e^{\sqrt{x}}",1,"2*E^Sqrt[x]*(-1 + Sqrt[x])","A",1
50,1,12,14,0.0007146,"\int \log \left(\sqrt{x}\right) \, dx","Integrate[Log[Sqrt[x]],x]","\frac{1}{2} (x \log (x)-x)","x \log \left(\sqrt{x}\right)-\frac{x}{2}",1,"(-x + x*Log[x])/2","A",1
51,1,17,17,0.0027874,"\int \sin (\log (x)) \, dx","Integrate[Sin[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,"-1/2*(x*Cos[Log[x]]) + (x*Sin[Log[x]])/2","A",1
52,1,22,22,0.0126837,"\int \sin \left(\sqrt{x}\right) \, dx","Integrate[Sin[Sqrt[x]],x]","2 \sin \left(\sqrt{x}\right)-2 \sqrt{x} \cos \left(\sqrt{x}\right)","2 \sin \left(\sqrt{x}\right)-2 \sqrt{x} \cos \left(\sqrt{x}\right)",1,"-2*Sqrt[x]*Cos[Sqrt[x]] + 2*Sin[Sqrt[x]]","A",1
53,1,20,20,0.0097559,"\int x^5 \cos \left(x^3\right) \, dx","Integrate[x^5*Cos[x^3],x]","\frac{1}{3} x^3 \sin \left(x^3\right)+\frac{\cos \left(x^3\right)}{3}","\frac{1}{3} x^3 \sin \left(x^3\right)+\frac{\cos \left(x^3\right)}{3}",1,"Cos[x^3]/3 + (x^3*Sin[x^3])/3","A",1
54,1,19,28,0.0022849,"\int e^{x^2} x^5 \, dx","Integrate[E^x^2*x^5,x]","\frac{1}{2} e^{x^2} \left(x^4-2 x^2+2\right)","-e^{x^2} x^2+e^{x^2}+\frac{1}{2} e^{x^2} x^4",1,"(E^x^2*(2 - 2*x^2 + x^4))/2","A",1
55,1,21,21,0.0026518,"\int x \tan ^{-1}(x) \, dx","Integrate[x*ArcTan[x],x]","\frac{1}{2} x^2 \tan ^{-1}(x)-\frac{x}{2}+\frac{1}{2} \tan ^{-1}(x)","\frac{1}{2} x^2 \tan ^{-1}(x)-\frac{x}{2}+\frac{1}{2} \tan ^{-1}(x)",1,"-1/2*x + ArcTan[x]/2 + (x^2*ArcTan[x])/2","A",1
56,1,18,18,0.0164189,"\int x \cos (\pi  x) \, dx","Integrate[x*Cos[Pi*x],x]","\frac{x \sin (\pi  x)}{\pi }+\frac{\cos (\pi  x)}{\pi ^2}","\frac{x \sin (\pi  x)}{\pi }+\frac{\cos (\pi  x)}{\pi ^2}",1,"Cos[Pi*x]/Pi^2 + (x*Sin[Pi*x])/Pi","A",1
57,1,15,21,0.0023875,"\int \sqrt{x} \log (x) \, dx","Integrate[Sqrt[x]*Log[x],x]","\frac{2}{9} x^{3/2} (3 \log (x)-2)","\frac{2}{3} x^{3/2} \log (x)-\frac{4 x^{3/2}}{9}",1,"(2*x^(3/2)*(-2 + 3*Log[x]))/9","A",1
58,1,14,18,0.0072947,"\int \sin ^2(3 x) \, dx","Integrate[Sin[3*x]^2,x]","\frac{x}{2}-\frac{1}{12} \sin (6 x)","\frac{x}{2}-\frac{1}{6} \sin (3 x) \cos (3 x)",1,"x/2 - Sin[6*x]/12","A",1
59,1,14,14,0.0017769,"\int \cos ^2(x) \, dx","Integrate[Cos[x]^2,x]","\frac{x}{2}+\frac{1}{4} \sin (2 x)","\frac{x}{2}+\frac{1}{2} \sin (x) \cos (x)",1,"x/2 + Sin[2*x]/4","A",1
60,1,22,24,0.0021394,"\int \cos ^4(x) \, dx","Integrate[Cos[x]^4,x]","\frac{3 x}{8}+\frac{1}{4} \sin (2 x)+\frac{1}{32} \sin (4 x)","\frac{3 x}{8}+\frac{1}{4} \sin (x) \cos ^3(x)+\frac{3}{8} \sin (x) \cos (x)",1,"(3*x)/8 + Sin[2*x]/4 + Sin[4*x]/32","A",1
61,1,15,13,0.0018801,"\int \sin ^3(x) \, dx","Integrate[Sin[x]^3,x]","\frac{1}{12} \cos (3 x)-\frac{3 \cos (x)}{4}","\frac{\cos ^3(x)}{3}-\cos (x)",1,"(-3*Cos[x])/4 + Cos[3*x]/12","A",1
62,1,31,17,0.0105613,"\int \cos ^4(x) \sin ^3(x) \, dx","Integrate[Cos[x]^4*Sin[x]^3,x]","-\frac{3 \cos (x)}{64}-\frac{1}{64} \cos (3 x)+\frac{1}{320} \cos (5 x)+\frac{1}{448} \cos (7 x)","\frac{\cos ^7(x)}{7}-\frac{\cos ^5(x)}{5}",1,"(-3*Cos[x])/64 - Cos[3*x]/64 + Cos[5*x]/320 + Cos[7*x]/448","A",1
63,1,31,17,0.0102423,"\int \cos ^3(x) \sin ^4(x) \, dx","Integrate[Cos[x]^3*Sin[x]^4,x]","\frac{3 \sin (x)}{64}-\frac{1}{64} \sin (3 x)-\frac{1}{320} \sin (5 x)+\frac{1}{448} \sin (7 x)","\frac{\sin ^5(x)}{5}-\frac{\sin ^7(x)}{7}",1,"(3*Sin[x])/64 - Sin[3*x]/64 - Sin[5*x]/320 + Sin[7*x]/448","A",1
64,1,30,36,0.008401,"\int \cos ^2(x) \sin ^4(x) \, dx","Integrate[Cos[x]^2*Sin[x]^4,x]","\frac{x}{16}-\frac{1}{64} \sin (2 x)-\frac{1}{64} \sin (4 x)+\frac{1}{192} \sin (6 x)","\frac{x}{16}-\frac{1}{6} \sin ^3(x) \cos ^3(x)-\frac{1}{8} \sin (x) \cos ^3(x)+\frac{1}{16} \sin (x) \cos (x)",1,"x/16 - Sin[2*x]/64 - Sin[4*x]/64 + Sin[6*x]/192","A",1
65,1,14,24,0.0038192,"\int \cos ^2(x) \sin ^2(x) \, dx","Integrate[Cos[x]^2*Sin[x]^2,x]","\frac{x}{8}-\frac{1}{32} \sin (4 x)","\frac{x}{8}-\frac{1}{4} \sin (x) \cos ^3(x)+\frac{1}{8} \sin (x) \cos (x)",1,"x/8 - Sin[4*x]/32","A",1
66,1,18,22,0.0084759,"\int (1-\sin (2 x))^2 \, dx","Integrate[(1 - Sin[2*x])^2,x]","\frac{3 x}{2}-\frac{1}{8} \sin (4 x)+\cos (2 x)","\frac{3 x}{2}+\cos (2 x)-\frac{1}{4} \sin (2 x) \cos (2 x)",1,"(3*x)/2 + Cos[2*x] - Sin[4*x]/8","A",1
67,1,20,20,0.0107706,"\int \cos (x) \sin \left(\frac{\pi }{6}+x\right) \, dx","Integrate[Cos[x]*Sin[Pi/6 + x],x]","\frac{x}{4}-\frac{1}{4} \cos \left(2 x+\frac{\pi }{6}\right)","\frac{x}{4}-\frac{1}{4} \cos \left(2 x+\frac{\pi }{6}\right)",1,"x/4 - Cos[Pi/6 + 2*x]/4","A",1
68,1,25,25,0.0102586,"\int \cos ^5(x) \sin ^5(x) \, dx","Integrate[Cos[x]^5*Sin[x]^5,x]","-\frac{5}{512} \cos (2 x)+\frac{5 \cos (6 x)}{3072}-\frac{\cos (10 x)}{5120}","\frac{\sin ^{10}(x)}{10}-\frac{\sin ^8(x)}{4}+\frac{\sin ^6(x)}{6}",1,"(-5*Cos[2*x])/512 + (5*Cos[6*x])/3072 - Cos[10*x]/5120","A",1
69,1,30,34,0.0020659,"\int \sin ^6(x) \, dx","Integrate[Sin[x]^6,x]","\frac{5 x}{16}-\frac{15}{64} \sin (2 x)+\frac{3}{64} \sin (4 x)-\frac{1}{192} \sin (6 x)","\frac{5 x}{16}-\frac{1}{6} \sin ^5(x) \cos (x)-\frac{5}{24} \sin ^3(x) \cos (x)-\frac{5}{16} \sin (x) \cos (x)",1,"(5*x)/16 - (15*Sin[2*x])/64 + (3*Sin[4*x])/64 - Sin[6*x]/192","A",1
70,1,30,34,0.0020697,"\int \cos ^6(x) \, dx","Integrate[Cos[x]^6,x]","\frac{5 x}{16}+\frac{15}{64} \sin (2 x)+\frac{3}{64} \sin (4 x)+\frac{1}{192} \sin (6 x)","\frac{5 x}{16}+\frac{1}{6} \sin (x) \cos ^5(x)+\frac{5}{24} \sin (x) \cos ^3(x)+\frac{5}{16} \sin (x) \cos (x)",1,"(5*x)/16 + (15*Sin[2*x])/64 + (3*Sin[4*x])/64 + Sin[6*x]/192","A",1
71,1,30,46,0.0134236,"\int \cos ^4(2 x) \sin ^2(2 x) \, dx","Integrate[Cos[2*x]^4*Sin[2*x]^2,x]","\frac{x}{16}+\frac{1}{128} \sin (4 x)-\frac{1}{128} \sin (8 x)-\frac{1}{384} \sin (12 x)","\frac{x}{16}-\frac{1}{12} \sin (2 x) \cos ^5(2 x)+\frac{1}{48} \sin (2 x) \cos ^3(2 x)+\frac{1}{32} \sin (2 x) \cos (2 x)",1,"x/16 + Sin[4*x]/128 - Sin[8*x]/128 - Sin[12*x]/384","A",1
72,1,23,21,0.0019325,"\int \sin ^5(x) \, dx","Integrate[Sin[x]^5,x]","-\frac{5 \cos (x)}{8}+\frac{5}{48} \cos (3 x)-\frac{1}{80} \cos (5 x)","-\frac{1}{5} \cos ^5(x)+\frac{2 \cos ^3(x)}{3}-\cos (x)",1,"(-5*Cos[x])/8 + (5*Cos[3*x])/48 - Cos[5*x]/80","A",1
73,1,22,46,0.0062883,"\int \cos ^4(x) \sin ^4(x) \, dx","Integrate[Cos[x]^4*Sin[x]^4,x]","\frac{3 x}{128}-\frac{1}{128} \sin (4 x)+\frac{\sin (8 x)}{1024}","\frac{3 x}{128}-\frac{1}{8} \sin ^3(x) \cos ^5(x)-\frac{1}{16} \sin (x) \cos ^5(x)+\frac{1}{64} \sin (x) \cos ^3(x)+\frac{3}{128} \sin (x) \cos (x)",1,"(3*x)/128 - Sin[4*x]/128 + Sin[8*x]/1024","A",1
74,1,34,21,0.0617593,"\int \sqrt{\cos (x)} \sin ^3(x) \, dx","Integrate[Sqrt[Cos[x]]*Sin[x]^3,x]","\frac{(3 \cos (2 x)-11) \cos ^2(x)+8 \sqrt[4]{\cos ^2(x)}}{21 \sqrt{\cos (x)}}","\frac{2}{7} \cos ^{\frac{7}{2}}(x)-\frac{2}{3} \cos ^{\frac{3}{2}}(x)",1,"(8*(Cos[x]^2)^(1/4) + Cos[x]^2*(-11 + 3*Cos[2*x]))/(21*Sqrt[Cos[x]])","A",1
75,1,18,21,0.0121656,"\int \cos ^3(x) \sqrt{\sin (x)} \, dx","Integrate[Cos[x]^3*Sqrt[Sin[x]],x]","\frac{1}{21} \sin ^{\frac{3}{2}}(x) (3 \cos (2 x)+11)","\frac{2}{3} \sin ^{\frac{3}{2}}(x)-\frac{2}{7} \sin ^{\frac{7}{2}}(x)",1,"((11 + 3*Cos[2*x])*Sin[x]^(3/2))/21","A",1
76,1,18,19,0.0276233,"\int \frac{\cos ^2\left(\sqrt{x}\right)}{\sqrt{x}} \, dx","Integrate[Cos[Sqrt[x]]^2/Sqrt[x],x]","\sqrt{x}+\frac{1}{2} \sin \left(2 \sqrt{x}\right)","\sqrt{x}+\sin \left(\sqrt{x}\right) \cos \left(\sqrt{x}\right)",1,"Sqrt[x] + Sin[2*Sqrt[x]]/2","A",1
77,1,19,19,0.016282,"\int x \sin ^3\left(x^2\right) \, dx","Integrate[x*Sin[x^2]^3,x]","\frac{1}{24} \cos \left(3 x^2\right)-\frac{3 \cos \left(x^2\right)}{8}","\frac{1}{6} \cos ^3\left(x^2\right)-\frac{\cos \left(x^2\right)}{2}",1,"(-3*Cos[x^2])/8 + Cos[3*x^2]/24","A",1
78,1,14,14,0.0056553,"\int \sin ^2(x) \tan (x) \, dx","Integrate[Sin[x]^2*Tan[x],x]","\frac{\cos ^2(x)}{2}-\log (\cos (x))","\frac{\cos ^2(x)}{2}-\log (\cos (x))",1,"Cos[x]^2/2 - Log[Cos[x]]","A",1
79,1,20,22,0.0231625,"\int \cos ^2(x) \cot ^3(x) \, dx","Integrate[Cos[x]^2*Cot[x]^3,x]","\frac{1}{2} \left(\sin ^2(x)-\csc ^2(x)-4 \log (\sin (x))\right)","\frac{\sin ^2(x)}{2}-\frac{1}{2} \csc ^2(x)-2 \log (\sin (x))",1,"(-Csc[x]^2 - 4*Log[Sin[x]] + Sin[x]^2)/2","A",1
80,1,36,5,0.007211,"\int \sec (x) (1-\sin (x)) \, dx","Integrate[Sec[x]*(1 - Sin[x]),x]","\log (\cos (x))-\log \left(\cos \left(\frac{x}{2}\right)-\sin \left(\frac{x}{2}\right)\right)+\log \left(\sin \left(\frac{x}{2}\right)+\cos \left(\frac{x}{2}\right)\right)","\log (\sin (x)+1)",1,"Log[Cos[x]] - Log[Cos[x/2] - Sin[x/2]] + Log[Cos[x/2] + Sin[x/2]]","B",1
81,1,25,11,0.0123255,"\int \frac{1}{1-\sin (x)} \, dx","Integrate[(1 - Sin[x])^(-1),x]","\frac{2 \sin \left(\frac{x}{2}\right)}{\cos \left(\frac{x}{2}\right)-\sin \left(\frac{x}{2}\right)}","\frac{\cos (x)}{1-\sin (x)}",1,"(2*Sin[x/2])/(Cos[x/2] - Sin[x/2])","B",1
82,1,6,6,0.002513,"\int \tan ^2(x) \, dx","Integrate[Tan[x]^2,x]","\tan (x)-x","\tan (x)-x",1,"-x + Tan[x]","A",1
83,1,18,14,0.003549,"\int \tan ^4(x) \, dx","Integrate[Tan[x]^4,x]","x-\frac{4 \tan (x)}{3}+\frac{1}{3} \tan (x) \sec ^2(x)","x+\frac{\tan ^3(x)}{3}-\tan (x)",1,"x - (4*Tan[x])/3 + (Sec[x]^2*Tan[x])/3","A",1
84,1,17,11,0.0025462,"\int \sec ^4(x) \, dx","Integrate[Sec[x]^4,x]","\frac{2 \tan (x)}{3}+\frac{1}{3} \tan (x) \sec ^2(x)","\frac{\tan ^3(x)}{3}+\tan (x)",1,"(2*Tan[x])/3 + (Sec[x]^2*Tan[x])/3","A",1
85,1,27,19,0.0030484,"\int \sec ^6(x) \, dx","Integrate[Sec[x]^6,x]","\frac{8 \tan (x)}{15}+\frac{1}{5} \tan (x) \sec ^4(x)+\frac{4}{15} \tan (x) \sec ^2(x)","\frac{\tan ^5(x)}{5}+\frac{2 \tan ^3(x)}{3}+\tan (x)",1,"(8*Tan[x])/15 + (4*Sec[x]^2*Tan[x])/15 + (Sec[x]^4*Tan[x])/5","A",1
86,1,8,8,0.0020029,"\int \sec ^2(x) \tan ^4(x) \, dx","Integrate[Sec[x]^2*Tan[x]^4,x]","\frac{\tan ^5(x)}{5}","\frac{\tan ^5(x)}{5}",1,"Tan[x]^5/5","A",1
87,1,27,17,0.0200466,"\int \sec ^4(x) \tan ^2(x) \, dx","Integrate[Sec[x]^4*Tan[x]^2,x]","-\frac{2 \tan (x)}{15}+\frac{1}{5} \tan (x) \sec ^4(x)-\frac{1}{15} \tan (x) \sec ^2(x)","\frac{\tan ^5(x)}{5}+\frac{\tan ^3(x)}{3}",1,"(-2*Tan[x])/15 - (Sec[x]^2*Tan[x])/15 + (Sec[x]^4*Tan[x])/5","A",1
88,1,8,8,0.0045861,"\int \sec ^3(x) \tan (x) \, dx","Integrate[Sec[x]^3*Tan[x],x]","\frac{\sec ^3(x)}{3}","\frac{\sec ^3(x)}{3}",1,"Sec[x]^3/3","A",1
89,1,17,17,0.0239565,"\int \sec ^3(x) \tan ^3(x) \, dx","Integrate[Sec[x]^3*Tan[x]^3,x]","\frac{\sec ^5(x)}{5}-\frac{\sec ^3(x)}{3}","\frac{\sec ^5(x)}{5}-\frac{\sec ^3(x)}{3}",1,"-1/3*Sec[x]^3 + Sec[x]^5/5","A",1
90,1,20,22,0.0033701,"\int \tan ^5(x) \, dx","Integrate[Tan[x]^5,x]","\frac{\sec ^4(x)}{4}-\sec ^2(x)-\log (\cos (x))","\frac{\tan ^4(x)}{4}-\frac{\tan ^2(x)}{2}-\log (\cos (x))",1,"-Log[Cos[x]] - Sec[x]^2 + Sec[x]^4/4","A",1
91,1,30,22,0.0039674,"\int \tan ^6(x) \, dx","Integrate[Tan[x]^6,x]","-x+\frac{23 \tan (x)}{15}+\frac{1}{5} \tan (x) \sec ^4(x)-\frac{11}{15} \tan (x) \sec ^2(x)","-x+\frac{\tan ^5(x)}{5}-\frac{\tan ^3(x)}{3}+\tan (x)",1,"-x + (23*Tan[x])/15 - (11*Sec[x]^2*Tan[x])/15 + (Sec[x]^4*Tan[x])/5","A",1
92,1,19,19,0.0108062,"\int \sec (x) \tan ^5(x) \, dx","Integrate[Sec[x]*Tan[x]^5,x]","\frac{\sec ^5(x)}{5}-\frac{2 \sec ^3(x)}{3}+\sec (x)","\frac{\sec ^5(x)}{5}-\frac{2 \sec ^3(x)}{3}+\sec (x)",1,"Sec[x] - (2*Sec[x]^3)/3 + Sec[x]^5/5","A",1
93,1,25,25,0.0127839,"\int \sec ^3(x) \tan ^5(x) \, dx","Integrate[Sec[x]^3*Tan[x]^5,x]","\frac{\sec ^7(x)}{7}-\frac{2 \sec ^5(x)}{5}+\frac{\sec ^3(x)}{3}","\frac{\sec ^7(x)}{7}-\frac{2 \sec ^5(x)}{5}+\frac{\sec ^3(x)}{3}",1,"Sec[x]^3/3 - (2*Sec[x]^5)/5 + Sec[x]^7/7","A",1
94,1,8,8,0.0048914,"\int \sec ^6(x) \tan (x) \, dx","Integrate[Sec[x]^6*Tan[x],x]","\frac{\sec ^6(x)}{6}","\frac{\sec ^6(x)}{6}",1,"Sec[x]^6/6","A",1
95,1,17,17,0.0133136,"\int \sec ^6(x) \tan ^3(x) \, dx","Integrate[Sec[x]^6*Tan[x]^3,x]","\frac{\sec ^8(x)}{8}-\frac{\sec ^6(x)}{6}","\frac{\sec ^8(x)}{8}-\frac{\sec ^6(x)}{6}",1,"-1/6*Sec[x]^6 + Sec[x]^8/8","A",1
96,1,8,8,0.0044799,"\int \sec ^2(x) \tan (x) \, dx","Integrate[Sec[x]^2*Tan[x],x]","\frac{\sec ^2(x)}{2}","\frac{\sec ^2(x)}{2}",1,"Sec[x]^2/2","A",1
97,1,16,16,0.0068302,"\int \sec (x) \tan ^2(x) \, dx","Integrate[Sec[x]*Tan[x]^2,x]","\frac{1}{2} \tan (x) \sec (x)-\frac{1}{2} \tanh ^{-1}(\sin (x))","\frac{1}{2} \tan (x) \sec (x)-\frac{1}{2} \tanh ^{-1}(\sin (x))",1,"-1/2*ArcTanh[Sin[x]] + (Sec[x]*Tan[x])/2","A",1
98,1,8,8,0.0023395,"\int \cot ^2(x) \, dx","Integrate[Cot[x]^2,x]","-x-\cot (x)","-x-\cot (x)",1,"-x - Cot[x]","A",1
99,1,14,14,0.0030527,"\int \cot ^3(x) \, dx","Integrate[Cot[x]^3,x]","-\frac{1}{2} \csc ^2(x)-\log (\sin (x))","-\frac{1}{2} \cot ^2(x)-\log (\sin (x))",1,"-1/2*Csc[x]^2 - Log[Sin[x]]","A",1
100,1,37,17,0.0281252,"\int \cot ^4(x) \csc ^4(x) \, dx","Integrate[Cot[x]^4*Csc[x]^4,x]","-\frac{2 \cot (x)}{35}-\frac{1}{7} \cot (x) \csc ^6(x)+\frac{8}{35} \cot (x) \csc ^4(x)-\frac{1}{35} \cot (x) \csc ^2(x)","-\frac{1}{7} \cot ^7(x)-\frac{\cot ^5(x)}{5}",1,"(-2*Cot[x])/35 - (Cot[x]*Csc[x]^2)/35 + (8*Cot[x]*Csc[x]^4)/35 - (Cot[x]*Csc[x]^6)/7","B",1
101,1,17,17,0.0080995,"\int \cot ^3(x) \csc ^4(x) \, dx","Integrate[Cot[x]^3*Csc[x]^4,x]","\frac{\csc ^4(x)}{4}-\frac{\csc ^6(x)}{6}","\frac{\csc ^4(x)}{4}-\frac{\csc ^6(x)}{6}",1,"Csc[x]^4/4 - Csc[x]^6/6","A",1
102,1,17,5,0.002758,"\int \csc (x) \, dx","Integrate[Csc[x],x]","\log \left(\sin \left(\frac{x}{2}\right)\right)-\log \left(\cos \left(\frac{x}{2}\right)\right)","-\tanh ^{-1}(\cos (x))",1,"-Log[Cos[x/2]] + Log[Sin[x/2]]","B",1
103,1,47,16,0.0046157,"\int \csc ^3(x) \, dx","Integrate[Csc[x]^3,x]","-\frac{1}{8} \csc ^2\left(\frac{x}{2}\right)+\frac{1}{8} \sec ^2\left(\frac{x}{2}\right)+\frac{1}{2} \log \left(\sin \left(\frac{x}{2}\right)\right)-\frac{1}{2} \log \left(\cos \left(\frac{x}{2}\right)\right)","-\frac{1}{2} \tanh ^{-1}(\cos (x))-\frac{1}{2} \cot (x) \csc (x)",1,"-1/8*Csc[x/2]^2 - Log[Cos[x/2]]/2 + Log[Sin[x/2]]/2 + Sec[x/2]^2/8","B",1
104,1,19,8,0.0043681,"\int \cos (x) \cot (x) \, dx","Integrate[Cos[x]*Cot[x],x]","\cos (x)+\log \left(\sin \left(\frac{x}{2}\right)\right)-\log \left(\cos \left(\frac{x}{2}\right)\right)","\cos (x)-\tanh ^{-1}(\cos (x))",1,"Cos[x] - Log[Cos[x/2]] + Log[Sin[x/2]]","B",1
105,1,17,13,0.0023915,"\int \csc ^4(x) \, dx","Integrate[Csc[x]^4,x]","-\frac{2 \cot (x)}{3}-\frac{1}{3} \cot (x) \csc ^2(x)","-\frac{1}{3} \cot ^3(x)-\cot (x)",1,"(-2*Cot[x])/3 - (Cot[x]*Csc[x]^2)/3","A",1
106,1,17,17,0.006842,"\int \sin (2 x) \sin (5 x) \, dx","Integrate[Sin[2*x]*Sin[5*x],x]","\frac{1}{6} \sin (3 x)-\frac{1}{14} \sin (7 x)","\frac{1}{6} \sin (3 x)-\frac{1}{14} \sin (7 x)",1,"Sin[3*x]/6 - Sin[7*x]/14","A",1
107,1,17,17,0.0055911,"\int \cos (x) \sin (3 x) \, dx","Integrate[Cos[x]*Sin[3*x],x]","-\frac{1}{2} \cos ^2(x)-\frac{1}{8} \cos (4 x)","-\frac{1}{4} \cos (2 x)-\frac{1}{8} \cos (4 x)",1,"-1/2*Cos[x]^2 - Cos[4*x]/8","A",1
108,1,15,15,0.0060688,"\int \cos (3 x) \cos (4 x) \, dx","Integrate[Cos[3*x]*Cos[4*x],x]","\frac{\sin (x)}{2}+\frac{1}{14} \sin (7 x)","\frac{\sin (x)}{2}+\frac{1}{14} \sin (7 x)",1,"Sin[x]/2 + Sin[7*x]/14","A",1
109,1,17,17,0.0069797,"\int \sin (3 x) \sin (6 x) \, dx","Integrate[Sin[3*x]*Sin[6*x],x]","\frac{1}{6} \sin (3 x)-\frac{1}{18} \sin (9 x)","\frac{1}{6} \sin (3 x)-\frac{1}{18} \sin (9 x)",1,"Sin[3*x]/6 - Sin[9*x]/18","A",1
110,1,8,8,0.0012145,"\int \cos ^5(x) \sin (x) \, dx","Integrate[Cos[x]^5*Sin[x],x]","-\frac{1}{6} \cos ^6(x)","-\frac{1}{6} \cos ^6(x)",1,"-1/6*Cos[x]^6","A",1
111,1,30,30,0.0084771,"\int \cos (x) \cos (2 x) \cos (3 x) \, dx","Integrate[Cos[x]*Cos[2*x]*Cos[3*x],x]","\frac{x}{4}+\frac{1}{8} \sin (2 x)+\frac{1}{16} \sin (4 x)+\frac{1}{24} \sin (6 x)","\frac{x}{4}+\frac{1}{8} \sin (2 x)+\frac{1}{16} \sin (4 x)+\frac{1}{24} \sin (6 x)",1,"x/4 + Sin[2*x]/8 + Sin[4*x]/16 + Sin[6*x]/24","A",1
112,1,8,5,0.0018395,"\int \cos ^2(x) \left(1-\tan ^2(x)\right) \, dx","Integrate[Cos[x]^2*(1 - Tan[x]^2),x]","\frac{1}{2} \sin (2 x)","\sin (x) \cos (x)",1,"Sin[2*x]/2","A",1
113,1,61,15,0.0092281,"\int \csc (2 x) (\cos (x)+\sin (x)) \, dx","Integrate[Csc[2*x]*(Cos[x] + Sin[x]),x]","\frac{1}{2} \log \left(\sin \left(\frac{x}{2}\right)\right)-\frac{1}{2} \log \left(\cos \left(\frac{x}{2}\right)\right)-\frac{1}{2} \log \left(\cos \left(\frac{x}{2}\right)-\sin \left(\frac{x}{2}\right)\right)+\frac{1}{2} \log \left(\sin \left(\frac{x}{2}\right)+\cos \left(\frac{x}{2}\right)\right)","\frac{1}{2} \tanh ^{-1}(\sin (x))-\frac{1}{2} \tanh ^{-1}(\cos (x))",1,"-1/2*Log[Cos[x/2]] - Log[Cos[x/2] - Sin[x/2]]/2 + Log[Sin[x/2]]/2 + Log[Cos[x/2] + Sin[x/2]]/2","B",1
114,1,14,14,0.0052598,"\int \sin ^2(x) \tan (x) \, dx","Integrate[Sin[x]^2*Tan[x],x]","\frac{\cos ^2(x)}{2}-\log (\cos (x))","\frac{\cos ^2(x)}{2}-\log (\cos (x))",1,"Cos[x]^2/2 - Log[Cos[x]]","A",1
115,1,20,22,0.0095737,"\int \cos ^2(x) \cot ^3(x) \, dx","Integrate[Cos[x]^2*Cot[x]^3,x]","\frac{1}{2} \left(\sin ^2(x)-\csc ^2(x)-4 \log (\sin (x))\right)","\frac{\sin ^2(x)}{2}-\frac{1}{2} \csc ^2(x)-2 \log (\sin (x))",1,"(-Csc[x]^2 - 4*Log[Sin[x]] + Sin[x]^2)/2","A",1
116,1,8,8,0.0038198,"\int \sec ^3(x) \tan (x) \, dx","Integrate[Sec[x]^3*Tan[x],x]","\frac{\sec ^3(x)}{3}","\frac{\sec ^3(x)}{3}",1,"Sec[x]^3/3","A",1
117,1,17,17,0.0135625,"\int \sec ^3(x) \tan ^3(x) \, dx","Integrate[Sec[x]^3*Tan[x]^3,x]","\frac{\sec ^5(x)}{5}-\frac{\sec ^3(x)}{3}","\frac{\sec ^5(x)}{5}-\frac{\sec ^3(x)}{3}",1,"-1/3*Sec[x]^3 + Sec[x]^5/5","A",1
118,1,25,25,0.0074446,"\int \frac{\sqrt{9-x^2}}{x^2} \, dx","Integrate[Sqrt[9 - x^2]/x^2,x]","-\frac{\sqrt{9-x^2}}{x}-\sin ^{-1}\left(\frac{x}{3}\right)","-\frac{\sqrt{9-x^2}}{x}-\sin ^{-1}\left(\frac{x}{3}\right)",1,"-(Sqrt[9 - x^2]/x) - ArcSin[x/3]","A",1
119,1,16,16,0.0031229,"\int \frac{1}{x^2 \sqrt{4+x^2}} \, dx","Integrate[1/(x^2*Sqrt[4 + x^2]),x]","-\frac{\sqrt{x^2+4}}{4 x}","-\frac{\sqrt{x^2+4}}{4 x}",1,"-1/4*Sqrt[4 + x^2]/x","A",1
120,1,9,9,0.0010831,"\int \frac{x}{\sqrt{4+x^2}} \, dx","Integrate[x/Sqrt[4 + x^2],x]","\sqrt{x^2+4}","\sqrt{x^2+4}",1,"Sqrt[4 + x^2]","A",1
121,1,46,16,0.0034314,"\int \frac{1}{\sqrt{-a^2+x^2}} \, dx","Integrate[1/Sqrt[-a^2 + x^2],x]","\frac{1}{2} \log \left(\frac{x}{\sqrt{x^2-a^2}}+1\right)-\frac{1}{2} \log \left(1-\frac{x}{\sqrt{x^2-a^2}}\right)","\tanh ^{-1}\left(\frac{x}{\sqrt{x^2-a^2}}\right)",1,"-1/2*Log[1 - x/Sqrt[-a^2 + x^2]] + Log[1 + x/Sqrt[-a^2 + x^2]]/2","B",1
122,1,22,31,0.0078731,"\int \frac{x^3}{\left(9+4 x^2\right)^{3/2}} \, dx","Integrate[x^3/(9 + 4*x^2)^(3/2),x]","\frac{2 x^2+9}{8 \sqrt{4 x^2+9}}","\frac{1}{16} \sqrt{4 x^2+9}+\frac{9}{16 \sqrt{4 x^2+9}}",1,"(9 + 2*x^2)/(8*Sqrt[9 + 4*x^2])","A",1
123,1,27,27,0.0073539,"\int \frac{x}{\sqrt{3-2 x-x^2}} \, dx","Integrate[x/Sqrt[3 - 2*x - x^2],x]","\sin ^{-1}\left(\frac{1}{4} (-2 x-2)\right)-\sqrt{-x^2-2 x+3}","\sin ^{-1}\left(\frac{1}{2} (-x-1)\right)-\sqrt{-x^2-2 x+3}",1,"-Sqrt[3 - 2*x - x^2] + ArcSin[(-2 - 2*x)/4]","A",1
124,1,16,16,0.0032116,"\int \frac{1}{x^2 \sqrt{1-x^2}} \, dx","Integrate[1/(x^2*Sqrt[1 - x^2]),x]","-\frac{\sqrt{1-x^2}}{x}","-\frac{\sqrt{1-x^2}}{x}",1,"-(Sqrt[1 - x^2]/x)","A",1
125,1,22,31,0.0102577,"\int x^3 \sqrt{4-x^2} \, dx","Integrate[x^3*Sqrt[4 - x^2],x]","-\frac{1}{15} \left(4-x^2\right)^{3/2} \left(3 x^2+8\right)","\frac{1}{5} \left(4-x^2\right)^{5/2}-\frac{4}{3} \left(4-x^2\right)^{3/2}",1,"-1/15*((4 - x^2)^(3/2)*(8 + 3*x^2))","A",1
126,1,13,13,0.0006222,"\int \frac{x}{\sqrt{1-x^2}} \, dx","Integrate[x/Sqrt[1 - x^2],x]","-\sqrt{1-x^2}","-\sqrt{1-x^2}",1,"-Sqrt[1 - x^2]","A",1
127,1,15,15,0.0018531,"\int x \sqrt{4-x^2} \, dx","Integrate[x*Sqrt[4 - x^2],x]","-\frac{1}{3} \left(4-x^2\right)^{3/2}","-\frac{1}{3} \left(4-x^2\right)^{3/2}",1,"-1/3*(4 - x^2)^(3/2)","A",1
128,1,25,25,0.0077521,"\int \sqrt{1-4 x^2} \, dx","Integrate[Sqrt[1 - 4*x^2],x]","\frac{1}{2} \sqrt{1-4 x^2} x+\frac{1}{4} \sin ^{-1}(2 x)","\frac{1}{2} \sqrt{1-4 x^2} x+\frac{1}{4} \sin ^{-1}(2 x)",1,"(x*Sqrt[1 - 4*x^2])/2 + ArcSin[2*x]/4","A",1
129,1,18,25,0.0049025,"\int \frac{x^3}{\sqrt{4+x^2}} \, dx","Integrate[x^3/Sqrt[4 + x^2],x]","\frac{1}{3} \left(x^2-8\right) \sqrt{x^2+4}","\frac{1}{3} \left(x^2+4\right)^{3/2}-4 \sqrt{x^2+4}",1,"((-8 + x^2)*Sqrt[4 + x^2])/3","A",1
130,1,6,6,0.0038504,"\int \frac{1}{\sqrt{9+x^2}} \, dx","Integrate[1/Sqrt[9 + x^2],x]","\sinh ^{-1}\left(\frac{x}{3}\right)","\sinh ^{-1}\left(\frac{x}{3}\right)",1,"ArcSinh[x/3]","A",1
131,1,18,21,0.0046778,"\int \sqrt{1+x^2} \, dx","Integrate[Sqrt[1 + x^2],x]","\frac{1}{2} \left(\sqrt{x^2+1} x+\sinh ^{-1}(x)\right)","\frac{1}{2} \sqrt{x^2+1} x+\frac{1}{2} \sinh ^{-1}(x)",1,"(x*Sqrt[1 + x^2] + ArcSinh[x])/2","A",1
132,1,46,35,0.0220926,"\int \frac{1}{x^3 \sqrt{-16+x^2}} \, dx","Integrate[1/(x^3*Sqrt[-16 + x^2]),x]","\frac{1}{256} \sqrt{x^2-16} \left(\frac{8}{x^2}+\frac{2 \tanh ^{-1}\left(\sqrt{1-\frac{x^2}{16}}\right)}{\sqrt{16-x^2}}\right)","\frac{\sqrt{x^2-16}}{32 x^2}+\frac{1}{128} \tan ^{-1}\left(\frac{\sqrt{x^2-16}}{4}\right)",1,"(Sqrt[-16 + x^2]*(8/x^2 + (2*ArcTanh[Sqrt[1 - x^2/16]])/Sqrt[16 - x^2]))/256","A",1
133,1,23,23,0.0051663,"\int \frac{\sqrt{-a^2+x^2}}{x^4} \, dx","Integrate[Sqrt[-a^2 + x^2]/x^4,x]","\frac{\left(x^2-a^2\right)^{3/2}}{3 a^2 x^3}","\frac{\left(x^2-a^2\right)^{3/2}}{3 a^2 x^3}",1,"(-a^2 + x^2)^(3/2)/(3*a^2*x^3)","A",1
134,1,30,30,0.0054954,"\int \frac{\sqrt{-4+9 x^2}}{x} \, dx","Integrate[Sqrt[-4 + 9*x^2]/x,x]","\sqrt{9 x^2-4}-2 \tan ^{-1}\left(\frac{1}{2} \sqrt{9 x^2-4}\right)","\sqrt{9 x^2-4}-2 \tan ^{-1}\left(\frac{1}{2} \sqrt{9 x^2-4}\right)",1,"Sqrt[-4 + 9*x^2] - 2*ArcTan[Sqrt[-4 + 9*x^2]/2]","A",1
135,1,18,18,0.0037928,"\int \frac{1}{x^2 \sqrt{-9+16 x^2}} \, dx","Integrate[1/(x^2*Sqrt[-9 + 16*x^2]),x]","\frac{\sqrt{16 x^2-9}}{9 x}","\frac{\sqrt{16 x^2-9}}{9 x}",1,"Sqrt[-9 + 16*x^2]/(9*x)","A",1
136,1,39,34,0.0312665,"\int \frac{x^2}{\left(a^2-x^2\right)^{3/2}} \, dx","Integrate[x^2/(a^2 - x^2)^(3/2),x]","\frac{x-a \sqrt{1-\frac{x^2}{a^2}} \sin ^{-1}\left(\frac{x}{a}\right)}{\sqrt{a^2-x^2}}","\frac{x}{\sqrt{a^2-x^2}}-\tan ^{-1}\left(\frac{x}{\sqrt{a^2-x^2}}\right)",1,"(x - a*Sqrt[1 - x^2/a^2]*ArcSin[x/a])/Sqrt[a^2 - x^2]","A",1
137,1,29,29,0.0097788,"\int \frac{x^2}{\sqrt{5-x^2}} \, dx","Integrate[x^2/Sqrt[5 - x^2],x]","\frac{5}{2} \sin ^{-1}\left(\frac{x}{\sqrt{5}}\right)-\frac{1}{2} x \sqrt{5-x^2}","\frac{5}{2} \sin ^{-1}\left(\frac{x}{\sqrt{5}}\right)-\frac{1}{2} x \sqrt{5-x^2}",1,"-1/2*(x*Sqrt[5 - x^2]) + (5*ArcSin[x/Sqrt[5]])/2","A",1
138,1,23,23,0.0045885,"\int \frac{1}{x \sqrt{3+x^2}} \, dx","Integrate[1/(x*Sqrt[3 + x^2]),x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{x^2+3}}{\sqrt{3}}\right)}{\sqrt{3}}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{x^2+3}}{\sqrt{3}}\right)}{\sqrt{3}}",1,"-(ArcTanh[Sqrt[3 + x^2]/Sqrt[3]]/Sqrt[3])","A",1
139,1,13,13,0.0020342,"\int \frac{x}{\left(4+x^2\right)^{5/2}} \, dx","Integrate[x/(4 + x^2)^(5/2),x]","-\frac{1}{3 \left(x^2+4\right)^{3/2}}","-\frac{1}{3 \left(x^2+4\right)^{3/2}}",1,"-1/3*1/(4 + x^2)^(3/2)","A",1
140,1,22,31,0.0107106,"\int x^3 \sqrt{4-9 x^2} \, dx","Integrate[x^3*Sqrt[4 - 9*x^2],x]","-\frac{\left(4-9 x^2\right)^{3/2} \left(27 x^2+8\right)}{1215}","\frac{1}{405} \left(4-9 x^2\right)^{5/2}-\frac{4}{243} \left(4-9 x^2\right)^{3/2}",1,"-1/1215*((4 - 9*x^2)^(3/2)*(8 + 27*x^2))","A",1
141,1,33,45,0.0165061,"\int x^2 \sqrt{9-x^2} \, dx","Integrate[x^2*Sqrt[9 - x^2],x]","\frac{1}{8} \left(x \sqrt{9-x^2} \left(2 x^2-9\right)+81 \sin ^{-1}\left(\frac{x}{3}\right)\right)","-\frac{9}{8} \sqrt{9-x^2} x+\frac{1}{4} \sqrt{9-x^2} x^3+\frac{81}{8} \sin ^{-1}\left(\frac{x}{3}\right)",1,"(x*Sqrt[9 - x^2]*(-9 + 2*x^2) + 81*ArcSin[x/3])/8","A",1
142,1,13,13,0.0019537,"\int 5 x \sqrt{1+x^2} \, dx","Integrate[5*x*Sqrt[1 + x^2],x]","\frac{5}{3} \left(x^2+1\right)^{3/2}","\frac{5}{3} \left(x^2+1\right)^{3/2}",1,"(5*(1 + x^2)^(3/2))/3","A",1
143,1,16,16,0.0038946,"\int \frac{1}{\left(-25+4 x^2\right)^{3/2}} \, dx","Integrate[(-25 + 4*x^2)^(-3/2),x]","-\frac{x}{25 \sqrt{4 x^2-25}}","-\frac{x}{25 \sqrt{4 x^2-25}}",1,"-1/25*x/Sqrt[-25 + 4*x^2]","A",1
144,1,32,33,0.0418999,"\int \sqrt{2 x-x^2} \, dx","Integrate[Sqrt[2*x - x^2],x]","\frac{1}{2} (x-1) \sqrt{-((x-2) x)}-\sin ^{-1}\left(\sqrt{1-\frac{x}{2}}\right)","-\frac{1}{2} \sqrt{2 x-x^2} (1-x)-\frac{1}{2} \sin ^{-1}(1-x)",1,"((-1 + x)*Sqrt[-((-2 + x)*x)])/2 - ArcSin[Sqrt[1 - x/2]]","A",1
145,1,8,8,0.0055577,"\int \frac{1}{\sqrt{8+4 x+x^2}} \, dx","Integrate[1/Sqrt[8 + 4*x + x^2],x]","\sinh ^{-1}\left(\frac{x+2}{2}\right)","\sinh ^{-1}\left(\frac{x+2}{2}\right)",1,"ArcSinh[(2 + x)/2]","A",1
146,1,24,25,0.0065469,"\int \frac{1}{\sqrt{-8+6 x+9 x^2}} \, dx","Integrate[1/Sqrt[-8 + 6*x + 9*x^2],x]","\frac{1}{3} \log \left(\sqrt{9 x^2+6 x-8}+3 x+1\right)","\frac{1}{3} \tanh ^{-1}\left(\frac{3 x+1}{\sqrt{9 x^2+6 x-8}}\right)",1,"Log[1 + 3*x + Sqrt[-8 + 6*x + 9*x^2]]/3","A",1
147,1,47,44,0.0532259,"\int \frac{x^2}{\sqrt{4 x-x^2}} \, dx","Integrate[x^2/Sqrt[4*x - x^2],x]","\frac{1}{2} \left(-\sqrt{4-x} x^{3/2}-6 \sqrt{-((x-4) x)}-24 \sin ^{-1}\left(\sqrt{1-\frac{x}{4}}\right)\right)","-\frac{1}{2} \sqrt{4 x-x^2} x-3 \sqrt{4 x-x^2}-6 \sin ^{-1}\left(1-\frac{x}{2}\right)",1,"(-(Sqrt[4 - x]*x^(3/2)) - 6*Sqrt[-((-4 + x)*x)] - 24*ArcSin[Sqrt[1 - x/4]])/2","A",1
148,1,23,26,0.0081942,"\int \frac{1}{\left(2+2 x+x^2\right)^2} \, dx","Integrate[(2 + 2*x + x^2)^(-2),x]","\frac{1}{2} \left(\frac{x+1}{x^2+2 x+2}+\tan ^{-1}(x+1)\right)","\frac{x+1}{2 \left(x^2+2 x+2\right)}+\frac{1}{2} \tan ^{-1}(x+1)",1,"((1 + x)/(2 + 2*x + x^2) + ArcTan[1 + x])/2","A",1
149,1,31,43,0.0104113,"\int \frac{1}{\left(5-4 x-x^2\right)^{5/2}} \, dx","Integrate[(5 - 4*x - x^2)^(-5/2),x]","-\frac{(x+2) \left(2 x^2+8 x-19\right)}{243 \left(-x^2-4 x+5\right)^{3/2}}","\frac{2 (x+2)}{243 \sqrt{-x^2-4 x+5}}+\frac{x+2}{27 \left(-x^2-4 x+5\right)^{3/2}}",1,"-1/243*((2 + x)*(-19 + 8*x + 2*x^2))/(5 - 4*x - x^2)^(3/2)","A",1
150,1,32,33,0.0132176,"\int e^t \sqrt{9-e^{2 t}} \, dt","Integrate[E^t*Sqrt[9 - E^(2*t)],t]","\frac{1}{2} \left(e^t \sqrt{9-e^{2 t}}+9 \sin ^{-1}\left(\frac{e^t}{3}\right)\right)","\frac{1}{2} e^t \sqrt{9-e^{2 t}}+\frac{9}{2} \sin ^{-1}\left(\frac{e^t}{3}\right)",1,"(E^t*Sqrt[9 - E^(2*t)] + 9*ArcSin[E^t/3])/2","A",1
151,1,30,30,0.0073144,"\int \sqrt{-9+e^{2 t}} \, dt","Integrate[Sqrt[-9 + E^(2*t)],t]","\sqrt{e^{2 t}-9}-3 \tan ^{-1}\left(\frac{1}{3} \sqrt{e^{2 t}-9}\right)","\sqrt{e^{2 t}-9}-3 \tan ^{-1}\left(\frac{1}{3} \sqrt{e^{2 t}-9}\right)",1,"Sqrt[-9 + E^(2*t)] - 3*ArcTan[Sqrt[-9 + E^(2*t)]/3]","A",1
152,1,42,14,0.0027565,"\int \frac{1}{\sqrt{a^2+x^2}} \, dx","Integrate[1/Sqrt[a^2 + x^2],x]","\frac{1}{2} \log \left(\frac{x}{\sqrt{a^2+x^2}}+1\right)-\frac{1}{2} \log \left(1-\frac{x}{\sqrt{a^2+x^2}}\right)","\tanh ^{-1}\left(\frac{x}{\sqrt{a^2+x^2}}\right)",1,"-1/2*Log[1 - x/Sqrt[a^2 + x^2]] + Log[1 + x/Sqrt[a^2 + x^2]]/2","B",1
153,1,15,15,0.0037156,"\int \frac{5+x}{-2+x+x^2} \, dx","Integrate[(5 + x)/(-2 + x + x^2),x]","2 \log (1-x)-\log (x+2)","2 \log (1-x)-\log (x+2)",1,"2*Log[1 - x] - Log[2 + x]","A",1
154,1,25,26,0.0048574,"\int \frac{x+x^3}{-1+x} \, dx","Integrate[(x + x^3)/(-1 + x),x]","\frac{1}{6} \left(2 x^3+3 x^2+12 x+12 \log (x-1)-17\right)","\frac{x^3}{3}+\frac{x^2}{2}+2 x+2 \log (1-x)",1,"(-17 + 12*x + 3*x^2 + 2*x^3 + 12*Log[-1 + x])/6","A",1
155,1,25,25,0.0068664,"\int \frac{-1+2 x+x^2}{-2 x+3 x^2+2 x^3} \, dx","Integrate[(-1 + 2*x + x^2)/(-2*x + 3*x^2 + 2*x^3),x]","\frac{1}{10} \log (1-2 x)+\frac{\log (x)}{2}-\frac{1}{10} \log (x+2)","\frac{1}{10} \log (1-2 x)+\frac{\log (x)}{2}-\frac{1}{10} \log (x+2)",1,"Log[1 - 2*x]/10 + Log[x]/2 - Log[2 + x]/10","A",1
156,1,29,30,0.0170252,"\int \frac{1+4 x-2 x^2+x^4}{1-x-x^2+x^3} \, dx","Integrate[(1 + 4*x - 2*x^2 + x^4)/(1 - x - x^2 + x^3),x]","\frac{1}{2} (x+1)^2-\frac{2}{x-1}+\log (1-x)-\log (x+1)","\frac{x^2}{2}+x+\frac{2}{1-x}+\log (1-x)-\log (x+1)",1,"-2/(-1 + x) + (1 + x)^2/2 + Log[1 - x] - Log[1 + x]","A",1
157,1,23,23,0.0051146,"\int \frac{4-x+2 x^2}{4 x+x^3} \, dx","Integrate[(4 - x + 2*x^2)/(4*x + x^3),x]","\frac{1}{2} \log \left(x^2+4\right)+\log (x)-\frac{1}{2} \tan ^{-1}\left(\frac{x}{2}\right)","\frac{1}{2} \log \left(x^2+4\right)+\log (x)-\frac{1}{2} \tan ^{-1}\left(\frac{x}{2}\right)",1,"-1/2*ArcTan[x/2] + Log[x] + Log[4 + x^2]/2","A",1
158,1,38,38,0.0109398,"\int \frac{2-3 x+4 x^2}{3-4 x+4 x^2} \, dx","Integrate[(2 - 3*x + 4*x^2)/(3 - 4*x + 4*x^2),x]","\frac{1}{8} \log \left(4 x^2-4 x+3\right)+x-\frac{\tan ^{-1}\left(\frac{2 x-1}{\sqrt{2}}\right)}{4 \sqrt{2}}","\frac{1}{8} \log \left(4 x^2-4 x+3\right)+x+\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{2}}\right)}{4 \sqrt{2}}",1,"x - ArcTan[(-1 + 2*x)/Sqrt[2]]/(4*Sqrt[2]) + Log[3 - 4*x + 4*x^2]/8","A",1
159,1,93,103,0.0485368,"\int \frac{1+x^2+x^3}{(-1+x) x \left(1+x^2\right)^3 \left(1+x+x^2\right)} \, dx","Integrate[(1 + x^2 + x^3)/((-1 + x)*x*(1 + x^2)^3*(1 + x + x^2)),x]","\frac{1}{48} \left(-14 \log \left(1-x^3\right)+\frac{6 (x+1)}{\left(x^2+1\right)^2}+\frac{9 (3 x-2)}{x^2+1}+45 \log \left(x^2+1\right)-10 \log \left(x^2+x+1\right)+20 \log (1-x)-48 \log (x)+21 \tan ^{-1}(x)-16 \sqrt{3} \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)\right)","-\frac{3 (1-x)}{8 \left(x^2+1\right)}+\frac{3 x}{16 \left(x^2+1\right)}+\frac{x+1}{8 \left(x^2+1\right)^2}+\frac{15}{16} \log \left(x^2+1\right)-\frac{1}{2} \log \left(x^2+x+1\right)+\frac{1}{8} \log (1-x)-\log (x)+\frac{7}{16} \tan ^{-1}(x)-\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{\sqrt{3}}",1,"((6*(1 + x))/(1 + x^2)^2 + (9*(-2 + 3*x))/(1 + x^2) + 21*ArcTan[x] - 16*Sqrt[3]*ArcTan[(1 + 2*x)/Sqrt[3]] + 20*Log[1 - x] - 48*Log[x] + 45*Log[1 + x^2] - 10*Log[1 + x + x^2] - 14*Log[1 - x^3])/48","A",1
160,1,33,33,0.0220363,"\int \frac{1-3 x+2 x^2-x^3}{x \left(1+x^2\right)^2} \, dx","Integrate[(1 - 3*x + 2*x^2 - x^3)/(x*(1 + x^2)^2),x]","\frac{-2 x-1}{2 \left(x^2+1\right)}-\frac{1}{2} \log \left(x^2+1\right)+\log (x)-2 \tan ^{-1}(x)","-\frac{2 x+1}{2 \left(x^2+1\right)}-\frac{1}{2} \log \left(x^2+1\right)+\log (x)-2 \tan ^{-1}(x)",1,"(-1 - 2*x)/(2*(1 + x^2)) - 2*ArcTan[x] + Log[x] - Log[1 + x^2]/2","A",1
161,1,16,19,0.0047605,"\int \frac{1}{\left(1+x^2\right)^2} \, dx","Integrate[(1 + x^2)^(-2),x]","\frac{1}{2} \left(\frac{x}{x^2+1}+\tan ^{-1}(x)\right)","\frac{x}{2 \left(x^2+1\right)}+\frac{1}{2} \tan ^{-1}(x)",1,"(x/(1 + x^2) + ArcTan[x])/2","A",1
162,1,19,19,0.0029284,"\int \frac{1}{(-1+x) (2+x)} \, dx","Integrate[1/((-1 + x)*(2 + x)),x]","\frac{1}{3} \log (1-x)-\frac{1}{3} \log (x+2)","\frac{1}{3} \log (1-x)-\frac{1}{3} \log (x+2)",1,"Log[1 - x]/3 - Log[2 + x]/3","A",1
163,1,21,19,0.0030588,"\int \frac{7}{-12+5 x+2 x^2} \, dx","Integrate[7/(-12 + 5*x + 2*x^2),x]","7 \left(\frac{1}{11} \log (3-2 x)-\frac{1}{11} \log (x+4)\right)","\frac{7}{11} \log (3-2 x)-\frac{7}{11} \log (x+4)",1,"7*(Log[3 - 2*x]/11 - Log[4 + x]/11)","A",1
164,1,32,32,0.0166264,"\int \frac{-4+3 x+x^2}{(-1+2 x)^2 (3+2 x)} \, dx","Integrate[(-4 + 3*x + x^2)/((-1 + 2*x)^2*(3 + 2*x)),x]","\frac{9}{32 (2 x-1)}+\frac{41}{128} \log (1-2 x)-\frac{25}{128} \log (2 x+3)","-\frac{9}{32 (1-2 x)}+\frac{41}{128} \log (1-2 x)-\frac{25}{128} \log (2 x+3)",1,"9/(32*(-1 + 2*x)) + (41*Log[1 - 2*x])/128 - (25*Log[3 + 2*x])/128","A",1
165,1,33,43,0.0242817,"\int \frac{-x^2+x^3}{(-6+x) (3+5 x)^3} \, dx","Integrate[(-x^2 + x^3)/((-6 + x)*(3 + 5*x)^3),x]","\frac{\frac{99 (335 x+157)}{(5 x+3)^2}+2500 \log (x-6)+1493 \log (5 x+3)}{499125}","\frac{201}{15125 (5 x+3)}-\frac{12}{1375 (5 x+3)^2}+\frac{20 \log (6-x)}{3993}+\frac{1493 \log (5 x+3)}{499125}",1,"((99*(157 + 335*x))/(3 + 5*x)^2 + 2500*Log[-6 + x] + 1493*Log[3 + 5*x])/499125","A",1
166,1,21,21,0.0023573,"\int \frac{1}{-x^3+x^4} \, dx","Integrate[(-x^3 + x^4)^(-1),x]","\frac{1}{2 x^2}+\frac{1}{x}+\log (1-x)-\log (x)","\frac{1}{2 x^2}+\frac{1}{x}+\log (1-x)-\log (x)",1,"1/(2*x^2) + x^(-1) + Log[1 - x] - Log[x]","A",1
167,1,25,25,0.0058233,"\int \frac{1-x-x^2+x^3+x^4}{-x+x^3} \, dx","Integrate[(1 - x - x^2 + x^3 + x^4)/(-x + x^3),x]","\frac{x^2}{2}+\frac{1}{2} \log \left(1-x^2\right)+x-\log (x)","\frac{x^2}{2}+\frac{1}{2} \log \left(1-x^2\right)+x-\log (x)",1,"x + x^2/2 - Log[x] + Log[1 - x^2]/2","A",1
168,1,11,11,0.0035326,"\int \frac{-2+x^2}{x \left(2+x^2\right)} \, dx","Integrate[(-2 + x^2)/(x*(2 + x^2)),x]","\log \left(x^2+2\right)-\log (x)","\log \left(x^2+2\right)-\log (x)",1,"-Log[x] + Log[2 + x^2]","A",1
169,1,36,36,0.016986,"\int \frac{2-4 x^2+x^3}{\left(1+x^2\right) \left(2+x^2\right)} \, dx","Integrate[(2 - 4*x^2 + x^3)/((1 + x^2)*(2 + x^2)),x]","-\frac{1}{2} \log \left(x^2+1\right)+\log \left(x^2+2\right)+6 \tan ^{-1}(x)-5 \sqrt{2} \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)","-\frac{1}{2} \log \left(x^2+1\right)+\log \left(x^2+2\right)+6 \tan ^{-1}(x)-5 \sqrt{2} \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)",1,"6*ArcTan[x] - 5*Sqrt[2]*ArcTan[x/Sqrt[2]] - Log[1 + x^2]/2 + Log[2 + x^2]","A",1
170,1,29,29,0.0166108,"\int \frac{1+x^2+x^4}{\left(1+x^2\right) \left(4+x^2\right)^2} \, dx","Integrate[(1 + x^2 + x^4)/((1 + x^2)*(4 + x^2)^2),x]","-\frac{13 x}{24 \left(x^2+4\right)}+\frac{25}{144} \tan ^{-1}\left(\frac{x}{2}\right)+\frac{1}{9} \tan ^{-1}(x)","-\frac{13 x}{24 \left(x^2+4\right)}+\frac{25}{144} \tan ^{-1}\left(\frac{x}{2}\right)+\frac{1}{9} \tan ^{-1}(x)",1,"(-13*x)/(24*(4 + x^2)) + (25*ArcTan[x/2])/144 + ArcTan[x]/9","A",1
171,1,54,60,0.0540371,"\int \frac{1+16 x}{(5+x)^2 (-3+2 x) \left(1+x+x^2\right)} \, dx","Integrate[(1 + 16*x)/((5 + x)^2*(-3 + 2*x)*(1 + x + x^2)),x]","\frac{-243867 \log \left(x^2+x+1\right)-\frac{819546}{x+5}+176400 \log (3-2 x)+311334 \log (x+5)+152438 \sqrt{3} \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{2832102}","-\frac{481 \log \left(x^2+x+1\right)}{5586}-\frac{79}{273 (x+5)}+\frac{200 \log (3-2 x)}{3211}+\frac{2731 \log (x+5)}{24843}+\frac{451 \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{2793 \sqrt{3}}",1,"(-819546/(5 + x) + 152438*Sqrt[3]*ArcTan[(1 + 2*x)/Sqrt[3]] + 176400*Log[3 - 2*x] + 311334*Log[5 + x] - 243867*Log[1 + x + x^2])/2832102","A",1
172,1,28,37,0.0131228,"\int \frac{x^4}{\left(9+x^2\right)^3} \, dx","Integrate[x^4/(9 + x^2)^3,x]","\frac{1}{8} \left(\tan ^{-1}\left(\frac{x}{3}\right)-\frac{x \left(5 x^2+27\right)}{\left(x^2+9\right)^2}\right)","-\frac{3 x}{8 \left(x^2+9\right)}-\frac{x^3}{4 \left(x^2+9\right)^2}+\frac{1}{8} \tan ^{-1}\left(\frac{x}{3}\right)",1,"(-((x*(27 + 5*x^2))/(9 + x^2)^2) + ArcTan[x/3])/8","A",1
173,1,78,97,0.0440865,"\int \frac{19 x}{(-1+x)^3 \left(3+5 x+4 x^2\right)^2} \, dx","Integrate[(19*x)/((-1 + x)^3*(3 + 5*x + 4*x^2)^2),x]","\frac{19 \left(\frac{184 (2204 x+975)}{4 x^2+5 x+3}-17457 \log \left(4 x^2+5 x+3\right)+\frac{59248}{x-1}-\frac{25392}{(x-1)^2}+34914 \log (1-x)+36138 \sqrt{23} \tan ^{-1}\left(\frac{8 x+5}{\sqrt{23}}\right)\right)}{7312896}","\frac{19 (44 x+39)}{276 (1-x)^2 \left(4 x^2+5 x+3\right)}-\frac{209 \log \left(4 x^2+5 x+3\right)}{4608}-\frac{1843}{4416 (1-x)}-\frac{399}{736 (1-x)^2}+\frac{209 \log (1-x)}{2304}+\frac{114437 \tan ^{-1}\left(\frac{8 x+5}{\sqrt{23}}\right)}{52992 \sqrt{23}}",1,"(19*(-25392/(-1 + x)^2 + 59248/(-1 + x) + (184*(975 + 2204*x))/(3 + 5*x + 4*x^2) + 36138*Sqrt[23]*ArcTan[(5 + 8*x)/Sqrt[23]] + 34914*Log[1 - x] - 17457*Log[3 + 5*x + 4*x^2]))/7312896","A",1
174,1,46,46,0.0259704,"\int \frac{1+x^2+x^3}{2 x^2+x^3+x^4} \, dx","Integrate[(1 + x^2 + x^3)/(2*x^2 + x^3 + x^4),x]","\frac{5}{8} \log \left(x^2+x+2\right)-\frac{1}{2 x}-\frac{\log (x)}{4}+\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{7}}\right)}{4 \sqrt{7}}","\frac{5}{8} \log \left(x^2+x+2\right)-\frac{1}{2 x}-\frac{\log (x)}{4}+\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{7}}\right)}{4 \sqrt{7}}",1,"-1/2*1/x + ArcTan[(1 + 2*x)/Sqrt[7]]/(4*Sqrt[7]) - Log[x]/4 + (5*Log[2 + x + x^2])/8","A",1
175,1,48,48,0.0121596,"\int \frac{1}{-x^3+x^6} \, dx","Integrate[(-x^3 + x^6)^(-1),x]","\frac{1}{2 x^2}-\frac{1}{6} \log \left(x^2+x+1\right)+\frac{1}{3} \log (1-x)-\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{\sqrt{3}}","\frac{1}{2 x^2}-\frac{1}{6} \log \left(x^2+x+1\right)+\frac{1}{3} \log (1-x)-\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{\sqrt{3}}",1,"1/(2*x^2) - ArcTan[(1 + 2*x)/Sqrt[3]]/Sqrt[3] + Log[1 - x]/3 - Log[1 + x + x^2]/6","A",1
176,1,19,15,0.0031722,"\int \frac{x^2}{1+x} \, dx","Integrate[x^2/(1 + x),x]","\frac{1}{2} (x+1)^2-2 (x+1)+\log (x+1)","\frac{x^2}{2}-x+\log (x+1)",1,"-2*(1 + x) + (1 + x)^2/2 + Log[1 + x]","A",1
177,1,8,10,0.0016701,"\int \frac{x}{-5+x} \, dx","Integrate[x/(-5 + x),x]","x+5 \log (x-5)","x+5 \log (5-x)",1,"x + 5*Log[-5 + x]","A",1
178,1,13,13,0.004094,"\int \frac{-1+4 x}{(-1+x) (2+x)} \, dx","Integrate[(-1 + 4*x)/((-1 + x)*(2 + x)),x]","\log (1-x)+3 \log (x+2)","\log (1-x)+3 \log (x+2)",1,"Log[1 - x] + 3*Log[2 + x]","A",1
179,1,11,11,0.0031883,"\int \frac{1}{(1+x) (2+x)} \, dx","Integrate[1/((1 + x)*(2 + x)),x]","\log (x+1)-\log (x+2)","\log (x+1)-\log (x+2)",1,"Log[1 + x] - Log[2 + x]","A",1
180,1,15,12,0.0028537,"\int \frac{-5+6 x}{3+2 x} \, dx","Integrate[(-5 + 6*x)/(3 + 2*x),x]","3 x-7 \log (2 x+3)+\frac{9}{2}","3 x-7 \log (2 x+3)",1,"9/2 + 3*x - 7*Log[3 + 2*x]","A",1
181,1,19,26,0.0071145,"\int \frac{1}{(a+x) (b+x)} \, dx","Integrate[1/((a + x)*(b + x)),x]","\frac{\log (b+x)-\log (a+x)}{a-b}","\frac{\log (b+x)}{a-b}-\frac{\log (a+x)}{a-b}",1,"(-Log[a + x] + Log[b + x])/(a - b)","A",1
182,1,14,14,0.0044488,"\int \frac{1+x^2}{-x+x^2} \, dx","Integrate[(1 + x^2)/(-x + x^2),x]","x+2 \log (1-x)-\log (x)","x+2 \log (1-x)-\log (x)",1,"x + 2*Log[1 - x] - Log[x]","A",1
183,1,26,26,0.0055716,"\int \frac{1-12 x+x^2+x^3}{-12+x+x^2} \, dx","Integrate[(1 - 12*x + x^2 + x^3)/(-12 + x + x^2),x]","\frac{x^2}{2}+\frac{1}{7} \log (3-x)-\frac{1}{7} \log (x+4)","\frac{x^2}{2}+\frac{1}{7} \log (3-x)-\frac{1}{7} \log (x+4)",1,"x^2/2 + Log[3 - x]/7 - Log[4 + x]/7","A",1
184,1,14,14,0.0048816,"\int \frac{3+2 x}{(1+x)^2} \, dx","Integrate[(3 + 2*x)/(1 + x)^2,x]","2 \log (x+1)-\frac{1}{x+1}","2 \log (x+1)-\frac{1}{x+1}",1,"-(1 + x)^(-1) + 2*Log[1 + x]","A",1
185,1,23,23,0.005071,"\int \frac{1}{x (1+x) (3+2 x)} \, dx","Integrate[1/(x*(1 + x)*(3 + 2*x)),x]","\frac{\log (x)}{3}-\log (x+1)+\frac{2}{3} \log (2 x+3)","\frac{\log (x)}{3}-\log (x+1)+\frac{2}{3} \log (2 x+3)",1,"Log[x]/3 - Log[1 + x] + (2*Log[3 + 2*x])/3","A",1
186,1,17,17,0.0064689,"\int \frac{-3+5 x+6 x^2}{-3 x+2 x^2+x^3} \, dx","Integrate[(-3 + 5*x + 6*x^2)/(-3*x + 2*x^2 + x^3),x]","2 \log (1-x)+\log (x)+3 \log (x+3)","2 \log (1-x)+\log (x)+3 \log (x+3)",1,"2*Log[1 - x] + Log[x] + 3*Log[3 + x]","A",1
187,1,12,12,0.0045315,"\int \frac{x}{4+4 x+x^2} \, dx","Integrate[x/(4 + 4*x + x^2),x]","\frac{2}{x+2}+\log (x+2)","\frac{2}{x+2}+\log (x+2)",1,"2/(2 + x) + Log[2 + x]","A",1
188,1,22,30,0.0094385,"\int \frac{1}{(-1+x)^2 (4+x)} \, dx","Integrate[1/((-1 + x)^2*(4 + x)),x]","\frac{1}{25} \left(-\frac{5}{x-1}-\log (x-1)+\log (x+4)\right)","\frac{1}{5 (1-x)}-\frac{1}{25} \log (1-x)+\frac{1}{25} \log (x+4)",1,"(-5/(-1 + x) - Log[-1 + x] + Log[4 + x])/25","A",1
189,1,26,28,0.0169086,"\int \frac{x^2}{(-3+x) (2+x)^2} \, dx","Integrate[x^2/((-3 + x)*(2 + x)^2),x]","\frac{4}{5 (x+2)}+\frac{9}{25} \log (x-3)+\frac{16}{25} \log (x+2)","\frac{4}{5 (x+2)}+\frac{9}{25} \log (3-x)+\frac{16}{25} \log (x+2)",1,"4/(5*(2 + x)) + (9*Log[-3 + x])/25 + (16*Log[2 + x])/25","A",1
190,1,14,14,0.0037516,"\int \frac{-2+3 x+5 x^2}{2 x^2+x^3} \, dx","Integrate[(-2 + 3*x + 5*x^2)/(2*x^2 + x^3),x]","\frac{1}{x}+2 \log (x)+3 \log (x+2)","\frac{1}{x}+2 \log (x)+3 \log (x+2)",1,"x^(-1) + 2*Log[x] + 3*Log[2 + x]","A",1
191,1,25,19,0.0074176,"\int \frac{18-2 x-4 x^2}{-6+x+4 x^2+x^3} \, dx","Integrate[(18 - 2*x - 4*x^2)/(-6 + x + 4*x^2 + x^3),x]","-2 \left(-\frac{1}{2} \log (1-x)+\log (x+2)+\frac{3}{2} \log (x+3)\right)","\log (1-x)-2 \log (x+2)-3 \log (x+3)",1,"-2*(-1/2*Log[1 - x] + Log[2 + x] + (3*Log[3 + x])/2)","A",1
192,1,15,15,0.0048192,"\int \frac{2 x+x^2}{4+3 x^2+x^3} \, dx","Integrate[(2*x + x^2)/(4 + 3*x^2 + x^3),x]","\frac{1}{3} \log \left(x^3+3 x^2+4\right)","\frac{1}{3} \log \left(x^3+3 x^2+4\right)",1,"Log[4 + 3*x^2 + x^3]/3","A",1
193,1,25,25,0.01165,"\int \frac{1}{(-1+x)^2 x^2} \, dx","Integrate[1/((-1 + x)^2*x^2),x]","-\frac{1}{x-1}-\frac{1}{x}-2 \log (1-x)+2 \log (x)","\frac{1}{1-x}-\frac{1}{x}-2 \log (1-x)+2 \log (x)",1,"-(-1 + x)^(-1) - x^(-1) - 2*Log[1 - x] + 2*Log[x]","A",1
194,1,21,21,0.0095758,"\int \frac{x^2}{(1+x)^3} \, dx","Integrate[x^2/(1 + x)^3,x]","\frac{2}{x+1}-\frac{1}{2 (x+1)^2}+\log (x+1)","\frac{2}{x+1}-\frac{1}{2 (x+1)^2}+\log (x+1)",1,"-1/2*1/(1 + x)^2 + 2/(1 + x) + Log[1 + x]","A",1
195,1,22,8,0.0027764,"\int \frac{1}{-x^2+x^4} \, dx","Integrate[(-x^2 + x^4)^(-1),x]","\frac{1}{x}+\frac{1}{2} \log (1-x)-\frac{1}{2} \log (x+1)","\frac{1}{x}-\tanh ^{-1}(x)",1,"x^(-1) + Log[1 - x]/2 - Log[1 + x]/2","B",1
196,1,15,15,0.0044111,"\int \frac{-x+2 x^3}{1-x^2+x^4} \, dx","Integrate[(-x + 2*x^3)/(1 - x^2 + x^4),x]","\frac{1}{2} \log \left(x^4-x^2+1\right)","\frac{1}{2} \log \left(x^4-x^2+1\right)",1,"Log[1 - x^2 + x^4]/2","A",1
197,1,18,18,0.0027236,"\int \frac{x^3}{1+x^2} \, dx","Integrate[x^3/(1 + x^2),x]","\frac{x^2}{2}-\frac{1}{2} \log \left(x^2+1\right)","\frac{x^2}{2}-\frac{1}{2} \log \left(x^2+1\right)",1,"x^2/2 - Log[1 + x^2]/2","A",1
198,1,20,20,0.004062,"\int \frac{-1+x}{2+2 x+x^2} \, dx","Integrate[(-1 + x)/(2 + 2*x + x^2),x]","\frac{1}{2} \log \left(x^2+2 x+2\right)-2 \tan ^{-1}(x+1)","\frac{1}{2} \log \left(x^2+2 x+2\right)-2 \tan ^{-1}(x+1)",1,"-2*ArcTan[1 + x] + Log[2 + 2*x + x^2]/2","A",1
199,1,31,31,0.0071367,"\int \frac{x}{1+x+x^2} \, dx","Integrate[x/(1 + x + x^2),x]","\frac{1}{2} \log \left(x^2+x+1\right)-\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{\sqrt{3}}","\frac{1}{2} \log \left(x^2+x+1\right)-\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{\sqrt{3}}",1,"-(ArcTan[(1 + 2*x)/Sqrt[3]]/Sqrt[3]) + Log[1 + x + x^2]/2","A",1
200,1,31,27,0.0051197,"\int \frac{7+5 x+4 x^2}{5+4 x+4 x^2} \, dx","Integrate[(7 + 5*x + 4*x^2)/(5 + 4*x + 4*x^2),x]","\frac{1}{8} \log \left(4 x^2+4 x+5\right)+x+\frac{3}{8} \tan ^{-1}\left(\frac{1}{2} (2 x+1)\right)","\frac{1}{8} \log \left(4 x^2+4 x+5\right)+x+\frac{3}{8} \tan ^{-1}\left(x+\frac{1}{2}\right)",1,"x + (3*ArcTan[(1 + 2*x)/2])/8 + Log[5 + 4*x + 4*x^2]/8","A",1
201,1,28,23,0.0075169,"\int \frac{5-4 x+3 x^2}{(-1+x) \left(1+x^2\right)} \, dx","Integrate[(5 - 4*x + 3*x^2)/((-1 + x)*(1 + x^2)),x]","\frac{1}{2} \log \left((x-1)^2+2 (x-1)+2\right)+2 \log (x-1)-3 \tan ^{-1}(x)","\frac{1}{2} \log \left(x^2+1\right)+2 \log (1-x)-3 \tan ^{-1}(x)",1,"-3*ArcTan[x] + Log[2 + 2*(-1 + x) + (-1 + x)^2]/2 + 2*Log[-1 + x]","A",1
202,1,28,28,0.0103871,"\int \frac{3+2 x}{3 x+x^3} \, dx","Integrate[(3 + 2*x)/(3*x + x^3),x]","-\frac{1}{2} \log \left(x^2+3\right)+\log (x)+\frac{2 \tan ^{-1}\left(\frac{x}{\sqrt{3}}\right)}{\sqrt{3}}","-\frac{1}{2} \log \left(x^2+3\right)+\log (x)+\frac{2 \tan ^{-1}\left(\frac{x}{\sqrt{3}}\right)}{\sqrt{3}}",1,"(2*ArcTan[x/Sqrt[3]])/Sqrt[3] + Log[x] - Log[3 + x^2]/2","A",1
203,1,41,41,0.0061293,"\int \frac{1}{-1+x^3} \, dx","Integrate[(-1 + x^3)^(-1),x]","-\frac{1}{6} \log \left(x^2+x+1\right)+\frac{1}{3} \log (1-x)-\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{\sqrt{3}}","-\frac{1}{6} \log \left(x^2+x+1\right)+\frac{1}{3} \log (1-x)-\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{\sqrt{3}}",1,"-(ArcTan[(1 + 2*x)/Sqrt[3]]/Sqrt[3]) + Log[1 - x]/3 - Log[1 + x + x^2]/6","A",1
204,1,42,41,0.0080622,"\int \frac{x^3}{1+x^3} \, dx","Integrate[x^3/(1 + x^3),x]","\frac{1}{6} \log \left(x^2-x+1\right)+x-\frac{1}{3} \log (x+1)-\frac{\tan ^{-1}\left(\frac{2 x-1}{\sqrt{3}}\right)}{\sqrt{3}}","\frac{1}{6} \log \left(x^2-x+1\right)+x-\frac{1}{3} \log (x+1)+\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{\sqrt{3}}",1,"x - ArcTan[(-1 + 2*x)/Sqrt[3]]/Sqrt[3] - Log[1 + x]/3 + Log[1 - x + x^2]/6","A",1
205,1,22,24,0.0159167,"\int \frac{-1-2 x+x^2}{(-1+x)^2 \left(1+x^2\right)} \, dx","Integrate[(-1 - 2*x + x^2)/((-1 + x)^2*(1 + x^2)),x]","-\frac{1}{2} \log \left(x^2+1\right)+\frac{1}{x-1}+\log (x-1)+\tan ^{-1}(x)","-\frac{1}{2} \log \left(x^2+1\right)+\frac{1}{x-1}+\log (1-x)+\tan ^{-1}(x)",1,"(-1 + x)^(-1) + ArcTan[x] + Log[-1 + x] - Log[1 + x^2]/2","A",1
206,1,26,14,0.0046338,"\int \frac{x^4}{-1+x^4} \, dx","Integrate[x^4/(-1 + x^4),x]","x+\frac{1}{4} \log (1-x)-\frac{1}{4} \log (x+1)-\frac{1}{2} \tan ^{-1}(x)","x-\frac{1}{2} \tan ^{-1}(x)-\frac{1}{2} \tanh ^{-1}(x)",1,"x - ArcTan[x]/2 + Log[1 - x]/4 - Log[1 + x]/4","A",1
207,1,29,29,0.0147114,"\int \frac{-4+6 x-x^2+3 x^3}{\left(1+x^2\right) \left(2+x^2\right)} \, dx","Integrate[(-4 + 6*x - x^2 + 3*x^3)/((1 + x^2)*(2 + x^2)),x]","\frac{3}{2} \log \left(x^2+1\right)-3 \tan ^{-1}(x)+\sqrt{2} \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)","\frac{3}{2} \log \left(x^2+1\right)-3 \tan ^{-1}(x)+\sqrt{2} \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)",1,"-3*ArcTan[x] + Sqrt[2]*ArcTan[x/Sqrt[2]] + (3*Log[1 + x^2])/2","A",1
208,1,23,23,0.0100696,"\int \frac{1+x-2 x^2+x^3}{4+5 x^2+x^4} \, dx","Integrate[(1 + x - 2*x^2 + x^3)/(4 + 5*x^2 + x^4),x]","\frac{1}{2} \log \left(x^2+4\right)-\frac{3}{2} \tan ^{-1}\left(\frac{x}{2}\right)+\tan ^{-1}(x)","\frac{1}{2} \log \left(x^2+4\right)-\frac{3}{2} \tan ^{-1}\left(\frac{x}{2}\right)+\tan ^{-1}(x)",1,"(-3*ArcTan[x/2])/2 + ArcTan[x] + Log[4 + x^2]/2","A",1
209,1,39,39,0.0261448,"\int \frac{-3+x}{\left(4+2 x+x^2\right)^2} \, dx","Integrate[(-3 + x)/(4 + 2*x + x^2)^2,x]","\frac{-4 x-7}{6 \left(x^2+2 x+4\right)}-\frac{2 \tan ^{-1}\left(\frac{x+1}{\sqrt{3}}\right)}{3 \sqrt{3}}","\frac{-4 x-7}{6 \left(x^2+2 x+4\right)}-\frac{2 \tan ^{-1}\left(\frac{x+1}{\sqrt{3}}\right)}{3 \sqrt{3}}",1,"(-7 - 4*x)/(6*(4 + 2*x + x^2)) - (2*ArcTan[(1 + x)/Sqrt[3]])/(3*Sqrt[3])","A",1
210,1,10,10,0.0065914,"\int \frac{1+x^4}{x \left(1+x^2\right)^2} \, dx","Integrate[(1 + x^4)/(x*(1 + x^2)^2),x]","\frac{1}{x^2+1}+\log (x)","\frac{1}{x^2+1}+\log (x)",1,"(1 + x^2)^(-1) + Log[x]","A",1
211,1,26,11,0.0952874,"\int \frac{\cos (x) (-3+2 \sin (x))}{2-3 \sin (x)+\sin ^2(x)} \, dx","Integrate[(Cos[x]*(-3 + 2*Sin[x]))/(2 - 3*Sin[x] + Sin[x]^2),x]","\log (2-\sin (x))+2 \log \left(\cos \left(\frac{x}{2}\right)-\sin \left(\frac{x}{2}\right)\right)","\log \left(\sin ^2(x)-3 \sin (x)+2\right)",1,"2*Log[Cos[x/2] - Sin[x/2]] + Log[2 - Sin[x]]","B",1
212,1,82,20,0.2257372,"\int \frac{\cos ^2(x) \sin (x)}{5+\cos ^2(x)} \, dx","Integrate[(Cos[x]^2*Sin[x])/(5 + Cos[x]^2),x]","\frac{1}{20} \left(-20 \cos (x)+21 \sqrt{5} \tan ^{-1}\left(\frac{1}{\sqrt{5}}-\sqrt{\frac{6}{5}} \tan \left(\frac{x}{2}\right)\right)+21 \sqrt{5} \tan ^{-1}\left(\sqrt{\frac{6}{5}} \tan \left(\frac{x}{2}\right)+\frac{1}{\sqrt{5}}\right)-\sqrt{5} \tan ^{-1}\left(\frac{\cos (x)}{\sqrt{5}}\right)\right)","\sqrt{5} \tan ^{-1}\left(\frac{\cos (x)}{\sqrt{5}}\right)-\cos (x)",1,"(-(Sqrt[5]*ArcTan[Cos[x]/Sqrt[5]]) + 21*Sqrt[5]*ArcTan[1/Sqrt[5] - Sqrt[6/5]*Tan[x/2]] + 21*Sqrt[5]*ArcTan[1/Sqrt[5] + Sqrt[6/5]*Tan[x/2]] - 20*Cos[x])/20","B",1
213,1,19,19,0.0026487,"\int \frac{1}{-3+2 x+x^2} \, dx","Integrate[(-3 + 2*x + x^2)^(-1),x]","\frac{1}{4} \log (1-x)-\frac{1}{4} \log (x+3)","\frac{1}{4} \log (1-x)-\frac{1}{4} \log (x+3)",1,"Log[1 - x]/4 - Log[3 + x]/4","A",1
214,1,17,17,0.0021084,"\int \frac{1}{-2 x+x^2} \, dx","Integrate[(-2*x + x^2)^(-1),x]","\frac{1}{2} \log (2-x)-\frac{\log (x)}{2}","\frac{1}{2} \log (2-x)-\frac{\log (x)}{2}",1,"Log[2 - x]/2 - Log[x]/2","A",1
215,1,21,21,0.0045138,"\int \frac{1+2 x}{-7+12 x+4 x^2} \, dx","Integrate[(1 + 2*x)/(-7 + 12*x + 4*x^2),x]","\frac{1}{8} \log (1-2 x)+\frac{3}{8} \log (2 x+7)","\frac{1}{8} \log (1-2 x)+\frac{3}{8} \log (2 x+7)",1,"Log[1 - 2*x]/8 + (3*Log[7 + 2*x])/8","A",1
216,1,44,49,0.0227675,"\int \frac{x}{-1+x+x^2} \, dx","Integrate[x/(-1 + x + x^2),x]","\frac{1}{10} \left(\left(5+\sqrt{5}\right) \log \left(2 x+\sqrt{5}+1\right)-\left(\sqrt{5}-5\right) \log \left(-2 x+\sqrt{5}-1\right)\right)","\frac{1}{10} \left(5-\sqrt{5}\right) \log \left(2 x-\sqrt{5}+1\right)+\frac{1}{10} \left(5+\sqrt{5}\right) \log \left(2 x+\sqrt{5}+1\right)",1,"(-((-5 + Sqrt[5])*Log[-1 + Sqrt[5] - 2*x]) + (5 + Sqrt[5])*Log[1 + Sqrt[5] + 2*x])/10","A",1
217,1,57,63,0.0306465,"\int \frac{-32+5 x-27 x^2+4 x^3}{-70-299 x-286 x^2+50 x^3-13 x^4+30 x^5} \, dx","Integrate[(-32 + 5*x - 27*x^2 + 4*x^3)/(-70 - 299*x - 286*x^2 + 50*x^3 - 13*x^4 + 30*x^5),x]","\frac{453009 \log \left(x^2+x+5\right)-418418 \log (7-3 x)-11023670 \log (2 x+1)+10536070 \log (5 x+2)+163508 \sqrt{19} \tan ^{-1}\left(\frac{2 x+1}{\sqrt{19}}\right)}{10660615}","\frac{11049 \log \left(x^2+x+5\right)}{260015}-\frac{3146 \log (7-3 x)}{80155}-\frac{334}{323} \log (2 x+1)+\frac{4822 \log (5 x+2)}{4879}+\frac{3988 \tan ^{-1}\left(\frac{2 x+1}{\sqrt{19}}\right)}{13685 \sqrt{19}}",1,"(163508*Sqrt[19]*ArcTan[(1 + 2*x)/Sqrt[19]] - 418418*Log[7 - 3*x] - 11023670*Log[1 + 2*x] + 10536070*Log[2 + 5*x] + 453009*Log[5 + x + x^2])/10660615","A",1
218,1,67,86,0.0644845,"\int \frac{8-13 x^2-7 x^3+12 x^5}{4-20 x+41 x^2-80 x^3+116 x^4-80 x^5+100 x^6} \, dx","Integrate[(8 - 13*x^2 - 7*x^3 + 12*x^5)/(4 - 20*x + 41*x^2 - 80*x^3 + 116*x^4 - 80*x^5 + 100*x^6),x]","\frac{142150 \log \left(2 x^2+1\right)-\frac{33 \left(36458 x^2+4675 x+2554\right)}{10 x^3-4 x^2+5 x-2}-236384 \log (2-5 x)+12575 \sqrt{2} \tan ^{-1}\left(\sqrt{2} x\right)}{399300}","-\frac{502 x+313}{1452 \left(2 x^2+1\right)}+\frac{2843 \log \left(2 x^2+1\right)}{7986}+\frac{5828}{9075 (2-5 x)}-\frac{59096 \log (2-5 x)}{99825}+\frac{272 \sqrt{2} \tan ^{-1}\left(\sqrt{2} x\right)}{1331}-\frac{251 \tan ^{-1}\left(\sqrt{2} x\right)}{726 \sqrt{2}}",1,"((-33*(2554 + 4675*x + 36458*x^2))/(-2 + 5*x - 4*x^2 + 10*x^3) + 12575*Sqrt[2]*ArcTan[Sqrt[2]*x] - 236384*Log[2 - 5*x] + 142150*Log[1 + 2*x^2])/399300","A",1
219,1,24,24,0.0056351,"\int \frac{\sqrt{4+x}}{x} \, dx","Integrate[Sqrt[4 + x]/x,x]","2 \sqrt{x+4}-4 \tanh ^{-1}\left(\frac{\sqrt{x+4}}{2}\right)","2 \sqrt{x+4}-4 \tanh ^{-1}\left(\frac{\sqrt{x+4}}{2}\right)",1,"2*Sqrt[4 + x] - 4*ArcTanh[Sqrt[4 + x]/2]","A",1
220,1,22,200,0.0142579,"\int \frac{1}{-\frac{1}{\sqrt[3]{x}}+\sqrt{x}} \, dx","Integrate[(-x^(-1/3) + Sqrt[x])^(-1),x]","-2 \sqrt{x} \left(\, _2F_1\left(\frac{3}{5},1;\frac{8}{5};x^{5/6}\right)-1\right)","2 \sqrt{x}+\frac{6}{5} \log \left(1-\sqrt[6]{x}\right)-\frac{3}{10} \left(1+\sqrt{5}\right) \log \left(2 \sqrt[3]{x}-\sqrt{5} \sqrt[6]{x}+\sqrt[6]{x}+2\right)-\frac{3}{10} \left(1-\sqrt{5}\right) \log \left(2 \sqrt[3]{x}+\sqrt{5} \sqrt[6]{x}+\sqrt[6]{x}+2\right)+\frac{3}{5} \sqrt{2 \left(5-\sqrt{5}\right)} \tan ^{-1}\left(\frac{4 \sqrt[6]{x}-\sqrt{5}+1}{\sqrt{2 \left(5+\sqrt{5}\right)}}\right)-\frac{3}{5} \sqrt{2 \left(5+\sqrt{5}\right)} \tan ^{-1}\left(\frac{1}{2} \sqrt{\frac{1}{10} \left(5+\sqrt{5}\right)} \left(4 \sqrt[6]{x}+\sqrt{5}+1\right)\right)",1,"-2*Sqrt[x]*(-1 + Hypergeometric2F1[3/5, 1, 8/5, x^(5/6)])","C",1
221,1,41,18,0.0182339,"\int \frac{1}{-4 \cos (x)+3 \sin (x)} \, dx","Integrate[(-4*Cos[x] + 3*Sin[x])^(-1),x]","\frac{1}{5} \log \left(\cos \left(\frac{x}{2}\right)-2 \sin \left(\frac{x}{2}\right)\right)-\frac{1}{5} \log \left(\sin \left(\frac{x}{2}\right)+2 \cos \left(\frac{x}{2}\right)\right)","-\frac{1}{5} \tanh ^{-1}\left(\frac{1}{5} (4 \sin (x)+3 \cos (x))\right)",1,"Log[Cos[x/2] - 2*Sin[x/2]]/5 - Log[2*Cos[x/2] + Sin[x/2]]/5","B",1
222,1,18,18,0.0075383,"\int \frac{1}{1+\sqrt{x}} \, dx","Integrate[(1 + Sqrt[x])^(-1),x]","2 \sqrt{x}-2 \log \left(\sqrt{x}+1\right)","2 \sqrt{x}-2 \log \left(\sqrt{x}+1\right)",1,"2*Sqrt[x] - 2*Log[1 + Sqrt[x]]","A",1
223,1,28,32,0.0122855,"\int \frac{1}{1+\frac{1}{\sqrt[3]{x}}} \, dx","Integrate[(1 + x^(-1/3))^(-1),x]","-\frac{3 x^{2/3}}{2}+x+3 \sqrt[3]{x}-3 \log \left(\sqrt[3]{x}+1\right)","-\frac{3 x^{2/3}}{2}+x+3 \sqrt[3]{x}-3 \log \left(\frac{1}{\sqrt[3]{x}}+1\right)-\log (x)",1,"3*x^(1/3) - (3*x^(2/3))/2 + x - 3*Log[1 + x^(1/3)]","A",1
224,1,16,16,0.0036561,"\int \frac{\sqrt{x}}{1+x} \, dx","Integrate[Sqrt[x]/(1 + x),x]","2 \sqrt{x}-2 \tan ^{-1}\left(\sqrt{x}\right)","2 \sqrt{x}-2 \tan ^{-1}\left(\sqrt{x}\right)",1,"2*Sqrt[x] - 2*ArcTan[Sqrt[x]]","A",1
225,1,10,10,0.0020751,"\int \frac{1}{x \sqrt{1+x}} \, dx","Integrate[1/(x*Sqrt[1 + x]),x]","-2 \tanh ^{-1}\left(\sqrt{x+1}\right)","-2 \tanh ^{-1}\left(\sqrt{x+1}\right)",1,"-2*ArcTanh[Sqrt[1 + x]]","A",1
226,1,14,14,0.0024063,"\int \frac{1}{-\sqrt[3]{x}+x} \, dx","Integrate[(-x^(1/3) + x)^(-1),x]","\frac{3}{2} \log \left(1-x^{2/3}\right)","\frac{3}{2} \log \left(1-x^{2/3}\right)",1,"(3*Log[1 - x^(2/3)])/2","A",1
227,1,31,31,0.0110542,"\int \frac{1}{x-\sqrt{2+x}} \, dx","Integrate[(x - Sqrt[2 + x])^(-1),x]","\frac{4}{3} \log \left(2-\sqrt{x+2}\right)+\frac{2}{3} \log \left(\sqrt{x+2}+1\right)","\frac{4}{3} \log \left(2-\sqrt{x+2}\right)+\frac{2}{3} \log \left(\sqrt{x+2}+1\right)",1,"(4*Log[2 - Sqrt[2 + x]])/3 + (2*Log[1 + Sqrt[2 + x]])/3","A",1
228,1,21,32,0.0059943,"\int \frac{x^2}{\sqrt{-1+x}} \, dx","Integrate[x^2/Sqrt[-1 + x],x]","\frac{2}{15} \sqrt{x-1} \left(3 x^2+4 x+8\right)","\frac{2}{5} (x-1)^{5/2}+\frac{4}{3} (x-1)^{3/2}+2 \sqrt{x-1}",1,"(2*Sqrt[-1 + x]*(8 + 4*x + 3*x^2))/15","A",1
229,1,31,31,0.007515,"\int \frac{\sqrt{-1+x}}{1+x} \, dx","Integrate[Sqrt[-1 + x]/(1 + x),x]","2 \sqrt{x-1}-2 \sqrt{2} \tan ^{-1}\left(\frac{\sqrt{x-1}}{\sqrt{2}}\right)","2 \sqrt{x-1}-2 \sqrt{2} \tan ^{-1}\left(\frac{\sqrt{x-1}}{\sqrt{2}}\right)",1,"2*Sqrt[-1 + x] - 2*Sqrt[2]*ArcTan[Sqrt[-1 + x]/Sqrt[2]]","A",1
230,1,22,29,0.0072027,"\int \frac{1}{\sqrt{1+\sqrt{x}}} \, dx","Integrate[1/Sqrt[1 + Sqrt[x]],x]","\frac{4}{3} \left(\sqrt{x}-2\right) \sqrt{\sqrt{x}+1}","\frac{4}{3} \left(\sqrt{x}+1\right)^{3/2}-4 \sqrt{\sqrt{x}+1}",1,"(4*(-2 + Sqrt[x])*Sqrt[1 + Sqrt[x]])/3","A",1
231,1,8,8,0.0019705,"\int \frac{\sqrt{x}}{x+x^2} \, dx","Integrate[Sqrt[x]/(x + x^2),x]","2 \tan ^{-1}\left(\sqrt{x}\right)","2 \tan ^{-1}\left(\sqrt{x}\right)",1,"2*ArcTan[Sqrt[x]]","A",1
232,1,20,21,0.0077223,"\int \frac{1+\sqrt{x}}{-1+\sqrt{x}} \, dx","Integrate[(1 + Sqrt[x])/(-1 + Sqrt[x]),x]","x+4 \left(\sqrt{x}+\log \left(1-\sqrt{x}\right)\right)","x+4 \sqrt{x}+4 \log \left(1-\sqrt{x}\right)",1,"x + 4*(Sqrt[x] + Log[1 - Sqrt[x]])","A",1
233,1,30,30,0.0133247,"\int \frac{1+\frac{1}{\sqrt[3]{x}}}{-1+\frac{1}{\sqrt[3]{x}}} \, dx","Integrate[(1 + x^(-1/3))/(-1 + x^(-1/3)),x]","-3 x^{2/3}-x-6 \sqrt[3]{x}-6 \log \left(1-\sqrt[3]{x}\right)","-3 x^{2/3}-x-6 \sqrt[3]{x}-6 \log \left(1-\sqrt[3]{x}\right)",1,"-6*x^(1/3) - 3*x^(2/3) - x - 6*Log[1 - x^(1/3)]","A",1
234,1,20,27,0.0072281,"\int \frac{x^3}{\sqrt[3]{1+x^2}} \, dx","Integrate[x^3/(1 + x^2)^(1/3),x]","\frac{3}{20} \left(x^2+1\right)^{2/3} \left(2 x^2-3\right)","\frac{3}{10} \left(x^2+1\right)^{5/3}-\frac{3}{4} \left(x^2+1\right)^{2/3}",1,"(3*(1 + x^2)^(2/3)*(-3 + 2*x^2))/20","A",1
235,1,29,201,0.0080382,"\int \frac{\sqrt{x}}{-\frac{1}{\sqrt[3]{x}}+\sqrt{x}} \, dx","Integrate[Sqrt[x]/(-x^(-1/3) + Sqrt[x]),x]","-6 \sqrt[6]{x} \, _2F_1\left(\frac{1}{5},1;\frac{6}{5};x^{5/6}\right)+x+6 \sqrt[6]{x}","x+6 \sqrt[6]{x}+\frac{6}{5} \log \left(1-\sqrt[6]{x}\right)-\frac{3}{10} \left(1-\sqrt{5}\right) \log \left(2 \sqrt[3]{x}-\sqrt{5} \sqrt[6]{x}+\sqrt[6]{x}+2\right)-\frac{3}{10} \left(1+\sqrt{5}\right) \log \left(2 \sqrt[3]{x}+\sqrt{5} \sqrt[6]{x}+\sqrt[6]{x}+2\right)-\frac{3}{5} \sqrt{2 \left(5+\sqrt{5}\right)} \tan ^{-1}\left(\frac{4 \sqrt[6]{x}-\sqrt{5}+1}{\sqrt{2 \left(5+\sqrt{5}\right)}}\right)-\frac{3}{5} \sqrt{2 \left(5-\sqrt{5}\right)} \tan ^{-1}\left(\frac{1}{2} \sqrt{\frac{1}{10} \left(5+\sqrt{5}\right)} \left(4 \sqrt[6]{x}+\sqrt{5}+1\right)\right)",1,"6*x^(1/6) + x - 6*x^(1/6)*Hypergeometric2F1[1/5, 1, 6/5, x^(5/6)]","C",1
236,1,24,62,0.0077952,"\int \frac{1}{\frac{1}{\sqrt[4]{x}}+\sqrt{x}} \, dx","Integrate[(x^(-1/4) + Sqrt[x])^(-1),x]","-2 \sqrt{x} \left(\, _2F_1\left(\frac{2}{3},1;\frac{5}{3};-x^{3/4}\right)-1\right)","2 \sqrt{x}+\frac{4}{3} \log \left(\sqrt[4]{x}+1\right)-\frac{2}{3} \log \left(\sqrt{x}-\sqrt[4]{x}+1\right)+\frac{4 \tan ^{-1}\left(\frac{1-2 \sqrt[4]{x}}{\sqrt{3}}\right)}{\sqrt{3}}",1,"-2*Sqrt[x]*(-1 + Hypergeometric2F1[2/3, 1, 5/3, -x^(3/4)])","C",1
237,1,130,130,0.0401189,"\int \frac{1}{\frac{1}{\sqrt[3]{x}}+\frac{1}{\sqrt[4]{x}}} \, dx","Integrate[(x^(-1/3) + x^(-1/4))^(-1),x]","\frac{4 x^{5/4}}{5}-\frac{6 x^{7/6}}{7}+\frac{12 x^{13/12}}{13}+\frac{12 x^{11/12}}{11}-\frac{6 x^{5/6}}{5}+\frac{4 x^{3/4}}{3}-\frac{3 x^{2/3}}{2}+\frac{12 x^{7/12}}{7}+\frac{12 x^{5/12}}{5}-x-2 \sqrt{x}-3 \sqrt[3]{x}+4 \sqrt[4]{x}-6 \sqrt[6]{x}+12 \sqrt[12]{x}-12 \log \left(\sqrt[12]{x}+1\right)","\frac{4 x^{5/4}}{5}-\frac{6 x^{7/6}}{7}+\frac{12 x^{13/12}}{13}+\frac{12 x^{11/12}}{11}-\frac{6 x^{5/6}}{5}+\frac{4 x^{3/4}}{3}-\frac{3 x^{2/3}}{2}+\frac{12 x^{7/12}}{7}+\frac{12 x^{5/12}}{5}-x-2 \sqrt{x}-3 \sqrt[3]{x}+4 \sqrt[4]{x}-6 \sqrt[6]{x}+12 \sqrt[12]{x}-12 \log \left(\sqrt[12]{x}+1\right)",1,"12*x^(1/12) - 6*x^(1/6) + 4*x^(1/4) - 3*x^(1/3) + (12*x^(5/12))/5 - 2*Sqrt[x] + (12*x^(7/12))/7 - (3*x^(2/3))/2 + (4*x^(3/4))/3 - (6*x^(5/6))/5 + (12*x^(11/12))/11 - x + (12*x^(13/12))/13 - (6*x^(7/6))/7 + (4*x^(5/4))/5 - 12*Log[1 + x^(1/12)]","A",1
238,1,24,24,0.0082845,"\int \sqrt{\frac{1-x}{x}} \, dx","Integrate[Sqrt[(1 - x)/x],x]","\sqrt{\frac{1}{x}-1} x-\tan ^{-1}\left(\sqrt{\frac{1}{x}-1}\right)","\sqrt{\frac{1}{x}-1} x-\tan ^{-1}\left(\sqrt{\frac{1}{x}-1}\right)",1,"Sqrt[-1 + x^(-1)]*x - ArcTan[Sqrt[-1 + x^(-1)]]","A",1
239,1,11,11,0.0090281,"\int \frac{\cos (x)}{\sin (x)+\sin ^2(x)} \, dx","Integrate[Cos[x]/(Sin[x] + Sin[x]^2),x]","\log (\sin (x))-\log (\sin (x)+1)","\log (\sin (x))-\log (\sin (x)+1)",1,"Log[Sin[x]] - Log[1 + Sin[x]]","A",1
240,1,17,17,0.0144618,"\int \frac{e^{2 x}}{2+3 e^x+e^{2 x}} \, dx","Integrate[E^(2*x)/(2 + 3*E^x + E^(2*x)),x]","2 \log \left(e^x+2\right)-\log \left(e^x+1\right)","2 \log \left(e^x+2\right)-\log \left(e^x+1\right)",1,"-Log[1 + E^x] + 2*Log[2 + E^x]","A",1
241,1,12,12,0.0040398,"\int \frac{1}{\sqrt{1+e^x}} \, dx","Integrate[1/Sqrt[1 + E^x],x]","-2 \tanh ^{-1}\left(\sqrt{e^x+1}\right)","-2 \tanh ^{-1}\left(\sqrt{e^x+1}\right)",1,"-2*ArcTanh[Sqrt[1 + E^x]]","A",1
242,1,28,28,0.0091726,"\int \sqrt{1-e^x} \, dx","Integrate[Sqrt[1 - E^x],x]","2 \sqrt{1-e^x}-2 \tanh ^{-1}\left(\sqrt{1-e^x}\right)","2 \sqrt{1-e^x}-2 \tanh ^{-1}\left(\sqrt{1-e^x}\right)",1,"2*Sqrt[1 - E^x] - 2*ArcTanh[Sqrt[1 - E^x]]","A",1
243,1,43,43,0.013598,"\int \frac{1}{3-5 \sin (x)} \, dx","Integrate[(3 - 5*Sin[x])^(-1),x]","\frac{1}{4} \log \left(3 \cos \left(\frac{x}{2}\right)-\sin \left(\frac{x}{2}\right)\right)-\frac{1}{4} \log \left(\cos \left(\frac{x}{2}\right)-3 \sin \left(\frac{x}{2}\right)\right)","\frac{1}{4} \log \left(3 \cos \left(\frac{x}{2}\right)-\sin \left(\frac{x}{2}\right)\right)-\frac{1}{4} \log \left(\cos \left(\frac{x}{2}\right)-3 \sin \left(\frac{x}{2}\right)\right)",1,"-1/4*Log[Cos[x/2] - 3*Sin[x/2]] + Log[3*Cos[x/2] - Sin[x/2]]/4","A",1
244,1,24,21,0.0218902,"\int \frac{1}{\cos (x)+\sin (x)} \, dx","Integrate[(Cos[x] + Sin[x])^(-1),x]","(-1-i) (-1)^{3/4} \tanh ^{-1}\left(\frac{\tan \left(\frac{x}{2}\right)-1}{\sqrt{2}}\right)","-\frac{\tanh ^{-1}\left(\frac{\cos (x)-\sin (x)}{\sqrt{2}}\right)}{\sqrt{2}}",1,"(-1 - I)*(-1)^(3/4)*ArcTanh[(-1 + Tan[x/2])/Sqrt[2]]","C",1
245,1,24,11,0.0169113,"\int \frac{1}{1-\cos (x)+\sin (x)} \, dx","Integrate[(1 - Cos[x] + Sin[x])^(-1),x]","\log \left(\sin \left(\frac{x}{2}\right)\right)-\log \left(\sin \left(\frac{x}{2}\right)+\cos \left(\frac{x}{2}\right)\right)","-\log \left(\cot \left(\frac{x}{2}\right)+1\right)",1,"Log[Sin[x/2]] - Log[Cos[x/2] + Sin[x/2]]","B",1
246,1,43,18,0.0169997,"\int \frac{1}{4 \cos (x)+3 \sin (x)} \, dx","Integrate[(4*Cos[x] + 3*Sin[x])^(-1),x]","\frac{1}{5} \log \left(2 \sin \left(\frac{x}{2}\right)+\cos \left(\frac{x}{2}\right)\right)-\frac{1}{5} \log \left(2 \cos \left(\frac{x}{2}\right)-\sin \left(\frac{x}{2}\right)\right)","-\frac{1}{5} \tanh ^{-1}\left(\frac{1}{5} (3 \cos (x)-4 \sin (x))\right)",1,"-1/5*Log[2*Cos[x/2] - Sin[x/2]] + Log[Cos[x/2] + 2*Sin[x/2]]/5","B",1
247,1,35,24,0.021104,"\int \frac{1}{\sin (x)+\tan (x)} \, dx","Integrate[(Sin[x] + Tan[x])^(-1),x]","-\frac{1}{4} \sec ^2\left(\frac{x}{2}\right)+\frac{1}{2} \log \left(\sin \left(\frac{x}{2}\right)\right)-\frac{1}{2} \log \left(\cos \left(\frac{x}{2}\right)\right)","-\frac{1}{2} \csc ^2(x)-\frac{1}{2} \tanh ^{-1}(\cos (x))+\frac{1}{2} \cot (x) \csc (x)",1,"-1/2*Log[Cos[x/2]] + Log[Sin[x/2]]/2 - Sec[x/2]^2/4","A",1
248,1,39,24,0.0372151,"\int \frac{1}{2 \sin (x)+\sin (2 x)} \, dx","Integrate[(2*Sin[x] + Sin[2*x])^(-1),x]","\frac{1-2 \cos ^2\left(\frac{x}{2}\right) \left(\log \left(\cos \left(\frac{x}{2}\right)\right)-\log \left(\sin \left(\frac{x}{2}\right)\right)\right)}{4 (\cos (x)+1)}","\frac{1}{8} \tan ^2\left(\frac{x}{2}\right)+\frac{1}{4} \log \left(\tan \left(\frac{x}{2}\right)\right)",1,"(1 - 2*Cos[x/2]^2*(Log[Cos[x/2]] - Log[Sin[x/2]]))/(4*(1 + Cos[x]))","A",1
249,1,18,18,0.0187055,"\int \frac{\sec (x)}{1+\sin (x)} \, dx","Integrate[Sec[x]/(1 + Sin[x]),x]","\frac{1}{2} \tanh ^{-1}(\sin (x))-\frac{1}{2 (\sin (x)+1)}","\frac{1}{2} \tanh ^{-1}(\sin (x))-\frac{1}{2 (\sin (x)+1)}",1,"ArcTanh[Sin[x]]/2 - 1/(2*(1 + Sin[x]))","A",1
250,1,38,36,0.0459232,"\int \frac{1}{b \cos (x)+a \sin (x)} \, dx","Integrate[(b*Cos[x] + a*Sin[x])^(-1),x]","\frac{2 \tanh ^{-1}\left(\frac{b \tan \left(\frac{x}{2}\right)-a}{\sqrt{a^2+b^2}}\right)}{\sqrt{a^2+b^2}}","-\frac{\tanh ^{-1}\left(\frac{a \cos (x)-b \sin (x)}{\sqrt{a^2+b^2}}\right)}{\sqrt{a^2+b^2}}",1,"(2*ArcTanh[(-a + b*Tan[x/2])/Sqrt[a^2 + b^2]])/Sqrt[a^2 + b^2]","A",1
251,1,15,15,0.0474166,"\int \frac{1}{b^2 \cos ^2(x)+a^2 \sin ^2(x)} \, dx","Integrate[(b^2*Cos[x]^2 + a^2*Sin[x]^2)^(-1),x]","\frac{\tan ^{-1}\left(\frac{a \tan (x)}{b}\right)}{a b}","\frac{\tan ^{-1}\left(\frac{a \tan (x)}{b}\right)}{a b}",1,"ArcTan[(a*Tan[x])/b]/(a*b)","A",1
252,1,10,12,0.0019567,"\int \frac{x}{-1+x^2} \, dx","Integrate[x/(-1 + x^2),x]","\frac{1}{2} \log \left(x^2-1\right)","\frac{1}{2} \log \left(1-x^2\right)",1,"Log[-1 + x^2]/2","A",1
253,1,17,17,0.0027883,"\int \left(1+\sqrt{x}\right) \sqrt{x} \, dx","Integrate[(1 + Sqrt[x])*Sqrt[x],x]","\frac{2 x^{3/2}}{3}+\frac{x^2}{2}","\frac{2 x^{3/2}}{3}+\frac{x^2}{2}",1,"(2*x^(3/2))/3 + x^2/2","A",1
254,1,8,12,0.0103154,"\int \frac{1}{1-\cos (x)} \, dx","Integrate[(1 - Cos[x])^(-1),x]","-\cot \left(\frac{x}{2}\right)","-\frac{\sin (x)}{1-\cos (x)}",1,"-Cot[x/2]","A",1
255,1,16,16,0.0079234,"\int \sec (x) \tan ^2(x) \, dx","Integrate[Sec[x]*Tan[x]^2,x]","\frac{1}{2} \tan (x) \sec (x)-\frac{1}{2} \tanh ^{-1}(\sin (x))","\frac{1}{2} \tan (x) \sec (x)-\frac{1}{2} \tanh ^{-1}(\sin (x))",1,"-1/2*ArcTanh[Sin[x]] + (Sec[x]*Tan[x])/2","A",1
256,1,17,17,0.0175095,"\int \sec ^3(x) \tan ^3(x) \, dx","Integrate[Sec[x]^3*Tan[x]^3,x]","\frac{\sec ^5(x)}{5}-\frac{\sec ^3(x)}{3}","\frac{\sec ^5(x)}{5}-\frac{\sec ^3(x)}{3}",1,"-1/3*Sec[x]^3 + Sec[x]^5/5","A",1
257,1,16,24,0.0064738,"\int e^{\sqrt{x}} \, dx","Integrate[E^Sqrt[x],x]","2 e^{\sqrt{x}} \left(\sqrt{x}-1\right)","2 e^{\sqrt{x}} \sqrt{x}-2 e^{\sqrt{x}}",1,"2*E^Sqrt[x]*(-1 + Sqrt[x])","A",1
258,1,42,42,0.0086743,"\int \frac{1+x^5}{-10 x-3 x^2+x^3} \, dx","Integrate[(1 + x^5)/(-10*x - 3*x^2 + x^3),x]","\frac{x^3}{3}+\frac{3 x^2}{2}+19 x+\frac{3126}{35} \log (5-x)-\frac{\log (x)}{10}-\frac{31}{14} \log (x+2)","\frac{x^3}{3}+\frac{3 x^2}{2}+19 x+\frac{3126}{35} \log (5-x)-\frac{\log (x)}{10}-\frac{31}{14} \log (x+2)",1,"19*x + (3*x^2)/2 + x^3/3 + (3126*Log[5 - x])/35 - Log[x]/10 - (31*Log[2 + x])/14","A",1
259,1,8,8,0.0018365,"\int \frac{1}{x \sqrt{\log (x)}} \, dx","Integrate[1/(x*Sqrt[Log[x]]),x]","2 \sqrt{\log (x)}","2 \sqrt{\log (x)}",1,"2*Sqrt[Log[x]]","A",1
260,1,12,12,0.0027728,"\int \frac{5+2 x}{-3+x} \, dx","Integrate[(5 + 2*x)/(-3 + x),x]","2 (x-3)+11 \log (x-3)","2 x+11 \log (3-x)",1,"2*(-3 + x) + 11*Log[-3 + x]","A",1
261,1,5,5,0.0054281,"\int e^{e^x+x} \, dx","Integrate[E^(E^x + x),x]","e^{e^x}","e^{e^x}",1,"E^E^x","A",1
262,1,14,24,0.0048345,"\int \cos ^2(x) \sin ^2(x) \, dx","Integrate[Cos[x]^2*Sin[x]^2,x]","\frac{x}{8}-\frac{1}{32} \sin (4 x)","\frac{x}{8}-\frac{1}{4} \sin (x) \cos ^3(x)+\frac{1}{8} \sin (x) \cos (x)",1,"x/8 - Sin[4*x]/32","A",1
263,1,8,8,0.0249394,"\int \frac{-\cos (x)+\sin (x)}{\cos (x)+\sin (x)} \, dx","Integrate[(-Cos[x] + Sin[x])/(Cos[x] + Sin[x]),x]","-\log (\sin (x)+\cos (x))","-\log (\sin (x)+\cos (x))",1,"-Log[Cos[x] + Sin[x]]","A",1
264,1,13,13,0.0019574,"\int \frac{x}{\sqrt{1-x^2}} \, dx","Integrate[x/Sqrt[1 - x^2],x]","-\sqrt{1-x^2}","-\sqrt{1-x^2}",1,"-Sqrt[1 - x^2]","A",1
265,1,17,17,0.0011655,"\int x^3 \log (x) \, dx","Integrate[x^3*Log[x],x]","\frac{1}{4} x^4 \log (x)-\frac{x^4}{16}","\frac{1}{4} x^4 \log (x)-\frac{x^4}{16}",1,"-1/16*x^4 + (x^4*Log[x])/4","A",1
266,1,24,24,0.0054177,"\int \frac{\sqrt{-2+x}}{2+x} \, dx","Integrate[Sqrt[-2 + x]/(2 + x),x]","2 \sqrt{x-2}-4 \tan ^{-1}\left(\frac{\sqrt{x-2}}{2}\right)","2 \sqrt{x-2}-4 \tan ^{-1}\left(\frac{\sqrt{x-2}}{2}\right)",1,"2*Sqrt[-2 + x] - 4*ArcTan[Sqrt[-2 + x]/2]","A",1
267,1,12,12,0.0034492,"\int \frac{x}{(2+x)^2} \, dx","Integrate[x/(2 + x)^2,x]","\frac{2}{x+2}+\log (x+2)","\frac{2}{x+2}+\log (x+2)",1,"2/(2 + x) + Log[2 + x]","A",1
268,1,16,16,0.0017491,"\int \log \left(1+x^2\right) \, dx","Integrate[Log[1 + x^2],x]","x \log \left(x^2+1\right)-2 x+2 \tan ^{-1}(x)","x \log \left(x^2+1\right)-2 x+2 \tan ^{-1}(x)",1,"-2*x + 2*ArcTan[x] + x*Log[1 + x^2]","A",1
269,1,22,22,0.0227199,"\int \frac{\sqrt{1+\log (x)}}{x \log (x)} \, dx","Integrate[Sqrt[1 + Log[x]]/(x*Log[x]),x]","2 \sqrt{\log (x)+1}-2 \tanh ^{-1}\left(\sqrt{\log (x)+1}\right)","2 \sqrt{\log (x)+1}-2 \tanh ^{-1}\left(\sqrt{\log (x)+1}\right)",1,"-2*ArcTanh[Sqrt[1 + Log[x]]] + 2*Sqrt[1 + Log[x]]","A",1
270,1,22,27,0.0185402,"\int \left(1+\sqrt{x}\right)^8 \, dx","Integrate[(1 + Sqrt[x])^8,x]","\frac{1}{45} \left(\sqrt{x}+1\right)^9 \left(9 \sqrt{x}-1\right)","\frac{1}{5} \left(\sqrt{x}+1\right)^{10}-\frac{2}{9} \left(\sqrt{x}+1\right)^9",1,"((1 + Sqrt[x])^9*(-1 + 9*Sqrt[x]))/45","A",1
271,1,17,17,0.0108621,"\int \sec ^4(x) \tan ^3(x) \, dx","Integrate[Sec[x]^4*Tan[x]^3,x]","\frac{\sec ^6(x)}{6}-\frac{\sec ^4(x)}{4}","\frac{\sec ^6(x)}{6}-\frac{\sec ^4(x)}{4}",1,"-1/4*Sec[x]^4 + Sec[x]^6/6","A",1
272,1,22,22,0.003711,"\int \frac{x}{2-2 x+x^2} \, dx","Integrate[x/(2 - 2*x + x^2),x]","\frac{1}{2} \log \left(x^2-2 x+2\right)-\tan ^{-1}(1-x)","\frac{1}{2} \log \left(x^2-2 x+2\right)-\tan ^{-1}(1-x)",1,"-ArcTan[1 - x] + Log[2 - 2*x + x^2]/2","A",1
273,1,28,32,0.0097183,"\int x \sin ^{-1}(x) \, dx","Integrate[x*ArcSin[x],x]","\frac{1}{4} \left(\sqrt{1-x^2} x+\left(2 x^2-1\right) \sin ^{-1}(x)\right)","\frac{1}{4} \sqrt{1-x^2} x+\frac{1}{2} x^2 \sin ^{-1}(x)-\frac{1}{4} \sin ^{-1}(x)",1,"(x*Sqrt[1 - x^2] + (-1 + 2*x^2)*ArcSin[x])/4","A",1
274,1,30,30,0.0055132,"\int \frac{\sqrt{9-x^2}}{x} \, dx","Integrate[Sqrt[9 - x^2]/x,x]","\sqrt{9-x^2}-3 \tanh ^{-1}\left(\frac{\sqrt{9-x^2}}{3}\right)","\sqrt{9-x^2}-3 \tanh ^{-1}\left(\frac{\sqrt{9-x^2}}{3}\right)",1,"Sqrt[9 - x^2] - 3*ArcTanh[Sqrt[9 - x^2]/3]","A",1
275,1,13,13,0.0030368,"\int \frac{x}{2+3 x+x^2} \, dx","Integrate[x/(2 + 3*x + x^2),x]","2 \log (x+2)-\log (x+1)","2 \log (x+2)-\log (x+1)",1,"-Log[1 + x] + 2*Log[2 + x]","A",1
276,1,14,16,0.0133987,"\int x^2 \cosh (x) \, dx","Integrate[x^2*Cosh[x],x]","\left(x^2+2\right) \sinh (x)-2 x \cosh (x)","x^2 \sinh (x)+2 \sinh (x)-2 x \cosh (x)",1,"-2*x*Cosh[x] + (2 + x^2)*Sinh[x]","A",1
277,1,20,17,0.0055263,"\int \frac{1+x+x^3}{4 x+2 x^2+x^4} \, dx","Integrate[(1 + x + x^3)/(4*x + 2*x^2 + x^4),x]","\frac{1}{4} \log \left(x^3+2 x+4\right)+\frac{\log (x)}{4}","\frac{1}{4} \log \left(x^4+2 x^2+4 x\right)",1,"Log[x]/4 + Log[4 + 2*x + x^3]/4","A",1
278,1,3,3,0.0045623,"\int \frac{\cos (x)}{1+\sin ^2(x)} \, dx","Integrate[Cos[x]/(1 + Sin[x]^2),x]","\tan ^{-1}(\sin (x))","\tan ^{-1}(\sin (x))",1,"ArcTan[Sin[x]]","A",1
279,1,22,22,0.0141523,"\int \cos \left(\sqrt{x}\right) \, dx","Integrate[Cos[Sqrt[x]],x]","2 \sqrt{x} \sin \left(\sqrt{x}\right)+2 \cos \left(\sqrt{x}\right)","2 \sqrt{x} \sin \left(\sqrt{x}\right)+2 \cos \left(\sqrt{x}\right)",1,"2*Cos[Sqrt[x]] + 2*Sqrt[x]*Sin[Sqrt[x]]","A",1
280,1,9,9,0.0040225,"\int \sin (\pi  x) \, dx","Integrate[Sin[Pi*x],x]","-\frac{\cos (\pi  x)}{\pi }","-\frac{\cos (\pi  x)}{\pi }",1,"-(Cos[Pi*x]/Pi)","A",1
281,1,12,12,0.0082296,"\int \frac{e^{2 x}}{1+e^x} \, dx","Integrate[E^(2*x)/(1 + E^x),x]","e^x-\log \left(e^x+1\right)","e^x-\log \left(e^x+1\right)",1,"E^x - Log[1 + E^x]","A",1
282,1,22,27,0.0306781,"\int e^{3 x} \cos (5 x) \, dx","Integrate[E^(3*x)*Cos[5*x],x]","\frac{1}{34} e^{3 x} (5 \sin (5 x)+3 \cos (5 x))","\frac{5}{34} e^{3 x} \sin (5 x)+\frac{3}{34} e^{3 x} \cos (5 x)",1,"(E^(3*x)*(3*Cos[5*x] + 5*Sin[5*x]))/34","A",1
283,1,17,17,0.0072821,"\int \cos (3 x) \cos (5 x) \, dx","Integrate[Cos[3*x]*Cos[5*x],x]","\frac{1}{4} \sin (2 x)+\frac{1}{16} \sin (8 x)","\frac{1}{4} \sin (2 x)+\frac{1}{16} \sin (8 x)",1,"Sin[2*x]/4 + Sin[8*x]/16","A",1
284,1,25,25,0.0060232,"\int \frac{1}{1+x+x^2+x^3} \, dx","Integrate[(1 + x + x^2 + x^3)^(-1),x]","-\frac{1}{4} \log \left(x^2+1\right)+\frac{1}{2} \log (x+1)+\frac{1}{2} \tan ^{-1}(x)","-\frac{1}{4} \log \left(x^2+1\right)+\frac{1}{2} \log (x+1)+\frac{1}{2} \tan ^{-1}(x)",1,"ArcTan[x]/2 + Log[1 + x]/2 - Log[1 + x^2]/4","A",1
285,1,28,39,0.0094955,"\int x^2 \log (1+x) \, dx","Integrate[x^2*Log[1 + x],x]","\frac{1}{18} \left(6 \left(x^3+1\right) \log (x+1)+x \left(-2 x^2+3 x-6\right)\right)","-\frac{x^3}{9}+\frac{1}{3} x^3 \log (x+1)+\frac{x^2}{6}-\frac{x}{3}+\frac{1}{3} \log (x+1)",1,"(x*(-6 + 3*x - 2*x^2) + 6*(1 + x^3)*Log[1 + x])/18","A",1
286,1,16,26,0.0032081,"\int e^{-x^3} x^5 \, dx","Integrate[x^5/E^x^3,x]","-\frac{1}{3} e^{-x^3} \left(x^3+1\right)","-\frac{1}{3} e^{-x^3} x^3-\frac{e^{-x^3}}{3}",1,"-1/3*(1 + x^3)/E^x^3","A",1
287,1,18,12,0.0093316,"\int \tan ^2(4 x) \, dx","Integrate[Tan[4*x]^2,x]","\frac{1}{4} \tan (4 x)-\frac{1}{4} \tan ^{-1}(\tan (4 x))","\frac{1}{4} \tan (4 x)-x",1,"-1/4*ArcTan[Tan[4*x]] + Tan[4*x]/4","A",1
288,1,24,25,0.0063132,"\int \frac{1}{\sqrt{-5+12 x+9 x^2}} \, dx","Integrate[1/Sqrt[-5 + 12*x + 9*x^2],x]","\frac{1}{3} \log \left(\sqrt{9 x^2+12 x-5}+3 x+2\right)","\frac{1}{3} \tanh ^{-1}\left(\frac{3 x+2}{\sqrt{9 x^2+12 x-5}}\right)",1,"Log[2 + 3*x + Sqrt[-5 + 12*x + 9*x^2]]/3","A",1
289,1,23,27,0.0059203,"\int x^2 \tan ^{-1}(x) \, dx","Integrate[x^2*ArcTan[x],x]","\frac{1}{6} \left(2 x^3 \tan ^{-1}(x)-x^2+\log \left(x^2+1\right)\right)","\frac{1}{3} x^3 \tan ^{-1}(x)-\frac{x^2}{6}+\frac{1}{6} \log \left(x^2+1\right)",1,"(-x^2 + 2*x^3*ArcTan[x] + Log[1 + x^2])/6","A",1
290,1,19,19,0.0036441,"\int \frac{1-\sqrt{x}}{\sqrt[3]{x}} \, dx","Integrate[(1 - Sqrt[x])/x^(1/3),x]","\frac{3 x^{2/3}}{2}-\frac{6 x^{7/6}}{7}","\frac{3 x^{2/3}}{2}-\frac{6 x^{7/6}}{7}",1,"(3*x^(2/3))/2 - (6*x^(7/6))/7","A",1
291,1,6,6,0.0037284,"\int \frac{1}{-e^{-x}+e^x} \, dx","Integrate[(-E^(-x) + E^x)^(-1),x]","-\tanh ^{-1}\left(e^x\right)","-\tanh ^{-1}\left(e^x\right)",1,"-ArcTanh[E^x]","A",1
292,1,14,14,0.0058404,"\int \frac{x}{10+2 x^2+x^4} \, dx","Integrate[x/(10 + 2*x^2 + x^4),x]","\frac{1}{6} \tan ^{-1}\left(\frac{1}{3} \left(x^2+1\right)\right)","\frac{1}{6} \tan ^{-1}\left(\frac{1}{3} \left(x^2+1\right)\right)",1,"ArcTan[(1 + x^2)/3]/6","A",1
293,1,12,12,0.0020664,"\int \frac{1}{\frac{1}{\sqrt[3]{x}}+x} \, dx","Integrate[(x^(-1/3) + x)^(-1),x]","\frac{3}{4} \log \left(x^{4/3}+1\right)","\frac{3}{4} \log \left(x^{4/3}+1\right)",1,"(3*Log[1 + x^(4/3)])/4","A",1
294,1,30,34,0.0093695,"\int \cos ^4(x) \sin ^2(x) \, dx","Integrate[Cos[x]^4*Sin[x]^2,x]","\frac{x}{16}+\frac{1}{64} \sin (2 x)-\frac{1}{64} \sin (4 x)-\frac{1}{192} \sin (6 x)","\frac{x}{16}-\frac{1}{6} \sin (x) \cos ^5(x)+\frac{1}{24} \sin (x) \cos ^3(x)+\frac{1}{16} \sin (x) \cos (x)",1,"x/16 + Sin[2*x]/64 - Sin[4*x]/64 - Sin[6*x]/192","A",1
295,1,12,12,0.0062061,"\int \frac{1}{\sqrt{5-4 x-x^2}} \, dx","Integrate[1/Sqrt[5 - 4*x - x^2],x]","-\sin ^{-1}\left(\frac{1}{3} (-x-2)\right)","-\sin ^{-1}\left(\frac{1}{3} (-x-2)\right)",1,"-ArcSin[(-2 - x)/3]","A",1
296,1,16,16,0.0276767,"\int \frac{x}{1-x^2+\sqrt{1-x^2}} \, dx","Integrate[x/(1 - x^2 + Sqrt[1 - x^2]),x]","-\log \left(\sqrt{1-x^2}+1\right)","-\log \left(\sqrt{1-x^2}+1\right)",1,"-Log[1 + Sqrt[1 - x^2]]","A",1
297,1,20,7,0.0064169,"\int (1+\cos (x)) \csc (x) \, dx","Integrate[(1 + Cos[x])*Csc[x],x]","\log \left(\sin \left(\frac{x}{2}\right)\right)+\log (\sin (x))-\log \left(\cos \left(\frac{x}{2}\right)\right)","\log (1-\cos (x))",1,"-Log[Cos[x/2]] + Log[Sin[x/2]] + Log[Sin[x]]","B",1
298,1,6,6,0.0022701,"\int \frac{e^x}{-1+e^{2 x}} \, dx","Integrate[E^x/(-1 + E^(2*x)),x]","-\tanh ^{-1}\left(e^x\right)","-\tanh ^{-1}\left(e^x\right)",1,"-ArcTanh[E^x]","A",1
299,1,43,43,0.0092606,"\int \frac{1}{-8+x^3} \, dx","Integrate[(-8 + x^3)^(-1),x]","-\frac{1}{24} \log \left(x^2+2 x+4\right)+\frac{1}{12} \log (2-x)-\frac{\tan ^{-1}\left(\frac{x+1}{\sqrt{3}}\right)}{4 \sqrt{3}}","-\frac{1}{24} \log \left(x^2+2 x+4\right)+\frac{1}{12} \log (2-x)-\frac{\tan ^{-1}\left(\frac{x+1}{\sqrt{3}}\right)}{4 \sqrt{3}}",1,"-1/4*ArcTan[(1 + x)/Sqrt[3]]/Sqrt[3] + Log[2 - x]/12 - Log[4 + 2*x + x^2]/24","A",1
300,1,29,37,0.0170086,"\int x^5 \cosh (x) \, dx","Integrate[x^5*Cosh[x],x]","x \left(x^4+20 x^2+120\right) \sinh (x)-5 \left(x^4+12 x^2+24\right) \cosh (x)","x^5 \sinh (x)-5 x^4 \cosh (x)+20 x^3 \sinh (x)-60 x^2 \cosh (x)+120 x \sinh (x)-120 \cosh (x)",1,"-5*(24 + 12*x^2 + x^4)*Cosh[x] + x*(120 + 20*x^2 + x^4)*Sinh[x]","A",1
301,1,9,9,0.0080452,"\int \csc (x) \log (\tan (x)) \sec (x) \, dx","Integrate[Csc[x]*Log[Tan[x]]*Sec[x],x]","\frac{1}{2} \log ^2(\tan (x))","\frac{1}{2} \log ^2(\tan (x))",1,"Log[Tan[x]]^2/2","A",1
302,1,20,20,0.0000812,"\int \left(-2 x+x^2+x^3\right) \, dx","Integrate[-2*x + x^2 + x^3,x]","\frac{x^4}{4}+\frac{x^3}{3}-x^2","\frac{x^4}{4}+\frac{x^3}{3}-x^2",1,"-x^2 + x^3/3 + x^4/4","A",1
303,1,12,12,0.0106677,"\int \frac{1+e^x}{1-e^x} \, dx","Integrate[(1 + E^x)/(1 - E^x),x]","x-2 \log \left(1-e^x\right)","x-2 \log \left(1-e^x\right)",1,"x - 2*Log[1 - E^x]","A",1
304,1,21,21,0.0047329,"\int \frac{x}{\left(1+x^2\right) \left(4+x^2\right)} \, dx","Integrate[x/((1 + x^2)*(4 + x^2)),x]","\frac{1}{6} \log \left(x^2+1\right)-\frac{1}{6} \log \left(x^2+4\right)","\frac{1}{6} \log \left(x^2+1\right)-\frac{1}{6} \log \left(x^2+4\right)",1,"Log[1 + x^2]/6 - Log[4 + x^2]/6","A",1
305,1,43,43,0.0134817,"\int \frac{1}{4-5 \sin (x)} \, dx","Integrate[(4 - 5*Sin[x])^(-1),x]","\frac{1}{3} \log \left(2 \cos \left(\frac{x}{2}\right)-\sin \left(\frac{x}{2}\right)\right)-\frac{1}{3} \log \left(\cos \left(\frac{x}{2}\right)-2 \sin \left(\frac{x}{2}\right)\right)","\frac{1}{3} \log \left(2 \cos \left(\frac{x}{2}\right)-\sin \left(\frac{x}{2}\right)\right)-\frac{1}{3} \log \left(\cos \left(\frac{x}{2}\right)-2 \sin \left(\frac{x}{2}\right)\right)",1,"-1/3*Log[Cos[x/2] - 2*Sin[x/2]] + Log[2*Cos[x/2] - Sin[x/2]]/3","A",1
306,1,18,24,0.0068349,"\int x \sqrt[3]{c+x} \, dx","Integrate[x*(c + x)^(1/3),x]","\frac{3}{28} (c+x)^{4/3} (4 x-3 c)","\frac{3}{7} (c+x)^{7/3}-\frac{3}{4} c (c+x)^{4/3}",1,"(3*(c + x)^(4/3)*(-3*c + 4*x))/28","A",1
307,1,24,38,0.0080465,"\int e^{\sqrt[3]{x}} \, dx","Integrate[E^x^(1/3),x]","e^{\sqrt[3]{x}} \left(3 x^{2/3}-6 \sqrt[3]{x}+6\right)","3 e^{\sqrt[3]{x}} x^{2/3}-6 e^{\sqrt[3]{x}} \sqrt[3]{x}+6 e^{\sqrt[3]{x}}",1,"E^x^(1/3)*(6 - 6*x^(1/3) + 3*x^(2/3))","A",1
308,1,37,37,0.0169794,"\int \frac{1}{4+x+\sqrt{1+x}} \, dx","Integrate[(4 + x + Sqrt[1 + x])^(-1),x]","\log \left(x+\sqrt{x+1}+4\right)-\frac{2 \tan ^{-1}\left(\frac{2 \sqrt{x+1}+1}{\sqrt{11}}\right)}{\sqrt{11}}","\log \left(x+\sqrt{x+1}+4\right)-\frac{2 \tan ^{-1}\left(\frac{2 \sqrt{x+1}+1}{\sqrt{11}}\right)}{\sqrt{11}}",1,"(-2*ArcTan[(1 + 2*Sqrt[1 + x])/Sqrt[11]])/Sqrt[11] + Log[4 + x + Sqrt[1 + x]]","A",1
309,1,17,17,0.0041676,"\int \frac{1+x^3}{-x^2+x^3} \, dx","Integrate[(1 + x^3)/(-x^2 + x^3),x]","x+\frac{1}{x}+2 \log (1-x)-\log (x)","x+\frac{1}{x}+2 \log (1-x)-\log (x)",1,"x^(-1) + x + 2*Log[1 - x] - Log[x]","A",1
310,1,29,40,0.0605943,"\int \left(-3+4 x+x^2\right) \sin (2 x) \, dx","Integrate[(-3 + 4*x + x^2)*Sin[2*x],x]","\frac{1}{4} \left(\left(-2 x^2-8 x+7\right) \cos (2 x)+2 (x+2) \sin (2 x)\right)","-\frac{1}{2} x^2 \cos (2 x)+\frac{1}{2} x \sin (2 x)+\sin (2 x)-2 x \cos (2 x)+\frac{7}{4} \cos (2 x)",1,"((7 - 8*x - 2*x^2)*Cos[2*x] + 2*(2 + x)*Sin[2*x])/4","A",1
311,1,5,5,2.75299,"\int \cos (\cos (x)) \sin (x) \, dx","Integrate[Cos[Cos[x]]*Sin[x],x]","-\sin (\cos (x))","-\sin (\cos (x))",1,"-Sin[Cos[x]]","A",1
312,1,6,6,0.0047846,"\int \frac{1}{\sqrt{16-x^2}} \, dx","Integrate[1/Sqrt[16 - x^2],x]","\sin ^{-1}\left(\frac{x}{4}\right)","\sin ^{-1}\left(\frac{x}{4}\right)",1,"ArcSin[x/4]","A",1
313,1,24,37,0.0067907,"\int \frac{x^3}{(1+x)^{10}} \, dx","Integrate[x^3/(1 + x)^10,x]","-\frac{84 x^3+36 x^2+9 x+1}{504 (x+1)^9}","-\frac{1}{6 (x+1)^6}+\frac{3}{7 (x+1)^7}-\frac{3}{8 (x+1)^8}+\frac{1}{9 (x+1)^9}",1,"-1/504*(1 + 9*x + 36*x^2 + 84*x^3)/(1 + x)^9","A",1
314,1,21,21,0.0236649,"\int \cot ^3(2 x) \csc ^3(2 x) \, dx","Integrate[Cot[2*x]^3*Csc[2*x]^3,x]","\frac{1}{6} \csc ^3(2 x)-\frac{1}{10} \csc ^5(2 x)","\frac{1}{6} \csc ^3(2 x)-\frac{1}{10} \csc ^5(2 x)",1,"Csc[2*x]^3/6 - Csc[2*x]^5/10","A",1
315,1,30,30,0.057931,"\int (x+\sin (x))^2 \, dx","Integrate[(x + Sin[x])^2,x]","\frac{1}{6} x \left(2 x^2+3\right)+2 \sin (x)-\frac{1}{4} \sin (2 x)-2 x \cos (x)","\frac{x^3}{3}+\frac{x}{2}+2 \sin (x)-2 x \cos (x)-\frac{1}{2} \sin (x) \cos (x)",1,"(x*(3 + 2*x^2))/6 - 2*x*Cos[x] + 2*Sin[x] - Sin[2*x]/4","A",1
316,1,27,4,0.0048478,"\int \frac{e^{\tan ^{-1}(x)}}{1+x^2} \, dx","Integrate[E^ArcTan[x]/(1 + x^2),x]","(1-i x)^{\frac{i}{2}} (1+i x)^{-\frac{i}{2}}","e^{\tan ^{-1}(x)}",1,"(1 - I*x)^(I/2)/(1 + I*x)^(I/2)","C",0
317,1,13,13,0.0030908,"\int \frac{1}{x \left(1+x^4\right)} \, dx","Integrate[1/(x*(1 + x^4)),x]","\log (x)-\frac{1}{4} \log \left(x^4+1\right)","\log (x)-\frac{1}{4} \log \left(x^4+1\right)",1,"Log[x] - Log[1 + x^4]/4","A",1
318,1,24,44,0.0087356,"\int e^{-2 t} t^3 \, dt","Integrate[t^3/E^(2*t),t]","-\frac{1}{8} e^{-2 t} \left(4 t^3+6 t^2+6 t+3\right)","-\frac{1}{2} e^{-2 t} t^3-\frac{3}{4} e^{-2 t} t^2-\frac{3}{4} e^{-2 t} t-\frac{3 e^{-2 t}}{8}",1,"-1/8*(3 + 6*t + 6*t^2 + 4*t^3)/E^(2*t)","A",1
319,1,41,41,0.0090246,"\int \frac{\sqrt{t}}{1+\sqrt[3]{t}} \, dt","Integrate[Sqrt[t]/(1 + t^(1/3)),t]","\frac{6 t^{7/6}}{7}-\frac{6 t^{5/6}}{5}+2 \sqrt{t}-6 \sqrt[6]{t}+6 \tan ^{-1}\left(\sqrt[6]{t}\right)","\frac{6 t^{7/6}}{7}-\frac{6 t^{5/6}}{5}+2 \sqrt{t}-6 \sqrt[6]{t}+6 \tan ^{-1}\left(\sqrt[6]{t}\right)",1,"-6*t^(1/6) + 2*Sqrt[t] - (6*t^(5/6))/5 + (6*t^(7/6))/7 + 6*ArcTan[t^(1/6)]","A",1
320,1,25,25,0.0100765,"\int \sin (x) \sin (2 x) \sin (3 x) \, dx","Integrate[Sin[x]*Sin[2*x]*Sin[3*x],x]","-\frac{1}{8} \cos (2 x)-\frac{1}{16} \cos (4 x)+\frac{1}{24} \cos (6 x)","-\frac{1}{8} \cos (2 x)-\frac{1}{16} \cos (4 x)+\frac{1}{24} \cos (6 x)",1,"-1/8*Cos[2*x] - Cos[4*x]/16 + Cos[6*x]/24","A",1
321,1,12,12,0.0008114,"\int \log \left(\frac{x}{2}\right) \, dx","Integrate[Log[x/2],x]","x \log \left(\frac{x}{2}\right)-x","x \log \left(\frac{x}{2}\right)-x",1,"-x + x*Log[x/2]","A",1
322,1,62,41,0.0243518,"\int \sqrt{\frac{1+x}{1-x}} \, dx","Integrate[Sqrt[(1 + x)/(1 - x)],x]","\frac{\sqrt{\frac{x+1}{1-x}} \left((x-1) \sqrt{x+1}-2 \sqrt{1-x} \sin ^{-1}\left(\frac{\sqrt{1-x}}{\sqrt{2}}\right)\right)}{\sqrt{x+1}}","2 \tan ^{-1}\left(\sqrt{\frac{x+1}{1-x}}\right)-(1-x) \sqrt{\frac{x+1}{1-x}}",1,"(Sqrt[(1 + x)/(1 - x)]*((-1 + x)*Sqrt[1 + x] - 2*Sqrt[1 - x]*ArcSin[Sqrt[1 - x]/Sqrt[2]]))/Sqrt[1 + x]","A",1
323,1,27,34,0.0213557,"\int \frac{x \log (x)}{\sqrt{-1+x^2}} \, dx","Integrate[(x*Log[x])/Sqrt[-1 + x^2],x]","\sqrt{x^2-1} (\log (x)-1)-\tan ^{-1}\left(\frac{1}{\sqrt{x^2-1}}\right)","-\sqrt{x^2-1}+\sqrt{x^2-1} \log (x)+\tan ^{-1}\left(\sqrt{x^2-1}\right)",1,"-ArcTan[1/Sqrt[-1 + x^2]] + Sqrt[-1 + x^2]*(-1 + Log[x])","A",1
324,1,19,19,0.0042884,"\int \frac{a+x}{a^2+x^2} \, dx","Integrate[(a + x)/(a^2 + x^2),x]","\frac{1}{2} \log \left(a^2+x^2\right)+\tan ^{-1}\left(\frac{x}{a}\right)","\frac{1}{2} \log \left(a^2+x^2\right)+\tan ^{-1}\left(\frac{x}{a}\right)",1,"ArcTan[x/a] + Log[a^2 + x^2]/2","A",1
325,1,39,38,0.015105,"\int \sqrt{1+x-x^2} \, dx","Integrate[Sqrt[1 + x - x^2],x]","\left(\frac{x}{2}-\frac{1}{4}\right) \sqrt{-x^2+x+1}-\frac{5}{8} \sin ^{-1}\left(\frac{1-2 x}{\sqrt{5}}\right)","-\frac{1}{4} \sqrt{-x^2+x+1} (1-2 x)-\frac{5}{8} \sin ^{-1}\left(\frac{1-2 x}{\sqrt{5}}\right)",1,"(-1/4 + x/2)*Sqrt[1 + x - x^2] - (5*ArcSin[(1 - 2*x)/Sqrt[5]])/8","A",1
326,1,12,12,0.0040639,"\int \frac{x^4}{16+x^{10}} \, dx","Integrate[x^4/(16 + x^10),x]","\frac{1}{20} \tan ^{-1}\left(\frac{x^5}{4}\right)","\frac{1}{20} \tan ^{-1}\left(\frac{x^5}{4}\right)",1,"ArcTan[x^5/4]/20","A",1
327,1,31,31,0.0102608,"\int \frac{2+x}{2+x+x^2} \, dx","Integrate[(2 + x)/(2 + x + x^2),x]","\frac{1}{2} \log \left(x^2+x+2\right)+\frac{3 \tan ^{-1}\left(\frac{2 x+1}{\sqrt{7}}\right)}{\sqrt{7}}","\frac{1}{2} \log \left(x^2+x+2\right)+\frac{3 \tan ^{-1}\left(\frac{2 x+1}{\sqrt{7}}\right)}{\sqrt{7}}",1,"(3*ArcTan[(1 + 2*x)/Sqrt[7]])/Sqrt[7] + Log[2 + x + x^2]/2","A",1
328,1,37,10,0.0103743,"\int x \sec (x) \tan (x) \, dx","Integrate[x*Sec[x]*Tan[x],x]","x \sec (x)+\log \left(\cos \left(\frac{x}{2}\right)-\sin \left(\frac{x}{2}\right)\right)-\log \left(\sin \left(\frac{x}{2}\right)+\cos \left(\frac{x}{2}\right)\right)","x \sec (x)-\tanh ^{-1}(\sin (x))",1,"Log[Cos[x/2] - Sin[x/2]] - Log[Cos[x/2] + Sin[x/2]] + x*Sec[x]","B",1
329,1,15,15,0.0041978,"\int \frac{x}{-a^4+x^4} \, dx","Integrate[x/(-a^4 + x^4),x]","-\frac{\tanh ^{-1}\left(\frac{x^2}{a^2}\right)}{2 a^2}","-\frac{\tanh ^{-1}\left(\frac{x^2}{a^2}\right)}{2 a^2}",1,"-1/2*ArcTanh[x^2/a^2]/a^2","A",1
330,1,21,21,0.0164731,"\int \frac{1}{\sqrt{x}+\sqrt{1+x}} \, dx","Integrate[(Sqrt[x] + Sqrt[1 + x])^(-1),x]","\frac{2}{3} (x+1)^{3/2}-\frac{2 x^{3/2}}{3}","\frac{2}{3} (x+1)^{3/2}-\frac{2 x^{3/2}}{3}",1,"(-2*x^(3/2))/3 + (2*(1 + x)^(3/2))/3","A",1
331,1,16,23,0.0107067,"\int \frac{1}{1-e^{-x}+2 e^x} \, dx","Integrate[(1 - E^(-x) + 2*E^x)^(-1),x]","-\frac{2}{3} \tanh ^{-1}\left(\frac{1}{3} \left(4 e^x+1\right)\right)","\frac{1}{3} \log \left(1-2 e^x\right)-\frac{1}{3} \log \left(e^x+1\right)",1,"(-2*ArcTanh[(1 + 4*E^x)/3])/3","A",1
332,1,20,20,0.0077232,"\int \frac{\tan ^{-1}\left(\sqrt{x}\right)}{\sqrt{x}} \, dx","Integrate[ArcTan[Sqrt[x]]/Sqrt[x],x]","2 \sqrt{x} \tan ^{-1}\left(\sqrt{x}\right)-\log (x+1)","2 \sqrt{x} \tan ^{-1}\left(\sqrt{x}\right)-\log (x+1)",1,"2*Sqrt[x]*ArcTan[Sqrt[x]] - Log[1 + x]","A",1
333,1,18,18,0.0033016,"\int \frac{\log (1+x)}{x^2} \, dx","Integrate[Log[1 + x]/x^2,x]","\log (x)-\frac{\log (x+1)}{x}-\log (x+1)","\log (x)-\frac{\log (x+1)}{x}-\log (x+1)",1,"Log[x] - Log[1 + x] - Log[1 + x]/x","A",1
334,1,19,12,0.0052323,"\int \frac{1}{-e^x+e^{3 x}} \, dx","Integrate[(-E^x + E^(3*x))^(-1),x]","e^{-x} \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};e^{2 x}\right)","e^{-x}-\tanh ^{-1}\left(e^x\right)",1,"Hypergeometric2F1[-1/2, 1, 1/2, E^(2*x)]/E^x","C",1
335,1,8,8,0.0080501,"\int \frac{1+\cos ^2(x)}{1-\cos ^2(x)} \, dx","Integrate[(1 + Cos[x]^2)/(1 - Cos[x]^2),x]","-x-2 \cot (x)","-x-2 \cot (x)",1,"-x - 2*Cot[x]","A",1
336,1,18,18,0.002348,"\int \frac{1}{x \sqrt{-25+2 x}} \, dx","Integrate[1/(x*Sqrt[-25 + 2*x]),x]","\frac{2}{5} \tan ^{-1}\left(\frac{1}{5} \sqrt{2 x-25}\right)","\frac{2}{5} \tan ^{-1}\left(\frac{1}{5} \sqrt{2 x-25}\right)",1,"(2*ArcTan[Sqrt[-25 + 2*x]/5])/5","A",1
337,1,11,11,0.0165341,"\int \frac{\sin (2 x)}{\sqrt{9-\cos ^4(x)}} \, dx","Integrate[Sin[2*x]/Sqrt[9 - Cos[x]^4],x]","-\sin ^{-1}\left(\frac{\cos ^2(x)}{3}\right)","-\sin ^{-1}\left(\frac{\cos ^2(x)}{3}\right)",1,"-ArcSin[Cos[x]^2/3]","A",1
338,1,30,30,0.0077386,"\int \frac{x^2}{\sqrt{5-4 x^2}} \, dx","Integrate[x^2/Sqrt[5 - 4*x^2],x]","\frac{5}{16} \sin ^{-1}\left(\frac{2 x}{\sqrt{5}}\right)-\frac{1}{8} x \sqrt{5-4 x^2}","\frac{5}{16} \sin ^{-1}\left(\frac{2 x}{\sqrt{5}}\right)-\frac{1}{8} x \sqrt{5-4 x^2}",1,"-1/8*(x*Sqrt[5 - 4*x^2]) + (5*ArcSin[(2*x)/Sqrt[5]])/16","A",1
339,1,20,24,0.0161034,"\int x^3 \sin (x) \, dx","Integrate[x^3*Sin[x],x]","3 \left(x^2-2\right) \sin (x)-x \left(x^2-6\right) \cos (x)","x^3 (-\cos (x))+3 x^2 \sin (x)-6 \sin (x)+6 x \cos (x)",1,"-(x*(-6 + x^2)*Cos[x]) + 3*(-2 + x^2)*Sin[x]","A",1
340,1,38,50,0.0202476,"\int x \sqrt{4+2 x+x^2} \, dx","Integrate[x*Sqrt[4 + 2*x + x^2],x]","\frac{1}{6} \left(\sqrt{x^2+2 x+4} \left(2 x^2+x+5\right)-9 \sinh ^{-1}\left(\frac{x+1}{\sqrt{3}}\right)\right)","\frac{1}{3} \left(x^2+2 x+4\right)^{3/2}-\frac{1}{2} (x+1) \sqrt{x^2+2 x+4}-\frac{3}{2} \sinh ^{-1}\left(\frac{x+1}{\sqrt{3}}\right)",1,"(Sqrt[4 + 2*x + x^2]*(5 + x + 2*x^2) - 9*ArcSinh[(1 + x)/Sqrt[3]])/6","A",1
341,1,11,11,0.001776,"\int x \left(5+x^2\right)^8 \, dx","Integrate[x*(5 + x^2)^8,x]","\frac{1}{18} \left(x^2+5\right)^9","\frac{1}{18} \left(x^2+5\right)^9",1,"(5 + x^2)^9/18","A",1
342,1,31,25,0.0104461,"\int \cos ^2(x) \sin ^5(x) \, dx","Integrate[Cos[x]^2*Sin[x]^5,x]","-\frac{5 \cos (x)}{64}-\frac{1}{192} \cos (3 x)+\frac{3}{320} \cos (5 x)-\frac{1}{448} \cos (7 x)","-\frac{1}{7} \cos ^7(x)+\frac{2 \cos ^5(x)}{5}-\frac{\cos ^3(x)}{3}",1,"(-5*Cos[x])/64 - Cos[3*x]/192 + (3*Cos[5*x])/320 - Cos[7*x]/448","A",1
343,1,22,27,0.0288733,"\int e^{-3 x} \cos (4 x) \, dx","Integrate[Cos[4*x]/E^(3*x),x]","\frac{1}{25} e^{-3 x} (4 \sin (4 x)-3 \cos (4 x))","\frac{4}{25} e^{-3 x} \sin (4 x)-\frac{3}{25} e^{-3 x} \cos (4 x)",1,"(-3*Cos[4*x] + 4*Sin[4*x])/(25*E^(3*x))","A",1
344,1,41,24,0.0091918,"\int \csc ^3\left(\frac{x}{2}\right) \, dx","Integrate[Csc[x/2]^3,x]","-\frac{1}{4} \csc ^2\left(\frac{x}{4}\right)+\frac{1}{4} \sec ^2\left(\frac{x}{4}\right)+\log \left(\sin \left(\frac{x}{4}\right)\right)-\log \left(\cos \left(\frac{x}{4}\right)\right)","-\tanh ^{-1}\left(\cos \left(\frac{x}{2}\right)\right)-\cot \left(\frac{x}{2}\right) \csc \left(\frac{x}{2}\right)",1,"-1/4*Csc[x/4]^2 - Log[Cos[x/4]] + Log[Sin[x/4]] + Sec[x/4]^2/4","A",1
345,1,35,34,0.0158262,"\int \frac{\sqrt{-1+9 x^2}}{x^2} \, dx","Integrate[Sqrt[-1 + 9*x^2]/x^2,x]","\sqrt{9 x^2-1} \left(-\frac{3 \sin ^{-1}(3 x)}{\sqrt{1-9 x^2}}-\frac{1}{x}\right)","3 \tanh ^{-1}\left(\frac{3 x}{\sqrt{9 x^2-1}}\right)-\frac{\sqrt{9 x^2-1}}{x}",1,"Sqrt[-1 + 9*x^2]*(-x^(-1) - (3*ArcSin[3*x])/Sqrt[1 - 9*x^2])","A",1
346,1,30,30,0.0062731,"\int \frac{\sqrt{4-3 x^2}}{x} \, dx","Integrate[Sqrt[4 - 3*x^2]/x,x]","\sqrt{4-3 x^2}-2 \tanh ^{-1}\left(\frac{1}{2} \sqrt{4-3 x^2}\right)","\sqrt{4-3 x^2}-2 \tanh ^{-1}\left(\frac{1}{2} \sqrt{4-3 x^2}\right)",1,"Sqrt[4 - 3*x^2] - 2*ArcTanh[Sqrt[4 - 3*x^2]/2]","A",1
347,1,19,32,0.0064174,"\int e^{3 x} x^2 \, dx","Integrate[E^(3*x)*x^2,x]","\frac{1}{27} e^{3 x} \left(9 x^2-6 x+2\right)","\frac{1}{3} e^{3 x} x^2-\frac{2}{9} e^{3 x} x+\frac{2 e^{3 x}}{27}",1,"(E^(3*x)*(2 - 6*x + 9*x^2))/27","A",1
348,1,31,23,0.0226843,"\int \frac{\cos (x) \sin (x)}{\sqrt{1+\sin (x)}} \, dx","Integrate[(Cos[x]*Sin[x])/Sqrt[1 + Sin[x]],x]","\frac{2 (\sin (x)-2) \left(\sin \left(\frac{x}{2}\right)+\cos \left(\frac{x}{2}\right)\right)^2}{3 \sqrt{\sin (x)+1}}","\frac{2}{3} (\sin (x)+1)^{3/2}-2 \sqrt{\sin (x)+1}",1,"(2*(Cos[x/2] + Sin[x/2])^2*(-2 + Sin[x]))/(3*Sqrt[1 + Sin[x]])","A",1
349,1,24,27,0.0054428,"\int x \sin ^{-1}\left(x^2\right) \, dx","Integrate[x*ArcSin[x^2],x]","\frac{1}{2} \left(\sqrt{1-x^4}+x^2 \sin ^{-1}\left(x^2\right)\right)","\frac{\sqrt{1-x^4}}{2}+\frac{1}{2} x^2 \sin ^{-1}\left(x^2\right)",1,"(Sqrt[1 - x^4] + x^2*ArcSin[x^2])/2","A",1
350,1,32,38,0.0111608,"\int x^3 \sin ^{-1}\left(x^2\right) \, dx","Integrate[x^3*ArcSin[x^2],x]","\frac{1}{8} \left(\sqrt{1-x^4} x^2+\left(2 x^4-1\right) \sin ^{-1}\left(x^2\right)\right)","-\frac{1}{8} \sin ^{-1}\left(x^2\right)+\frac{1}{8} \sqrt{1-x^4} x^2+\frac{1}{4} x^4 \sin ^{-1}\left(x^2\right)",1,"(x^2*Sqrt[1 - x^4] + (-1 + 2*x^4)*ArcSin[x^2])/8","A",1
351,1,5,5,0.005353,"\int e^x \text{sech}\left(e^x\right) \, dx","Integrate[E^x*Sech[E^x],x]","\tan ^{-1}\left(\sinh \left(e^x\right)\right)","\tan ^{-1}\left(\sinh \left(e^x\right)\right)",1,"ArcTan[Sinh[E^x]]","A",1
352,1,25,29,0.0241754,"\int x^2 \cos (3 x) \, dx","Integrate[x^2*Cos[3*x],x]","\frac{1}{27} \left(9 x^2-2\right) \sin (3 x)+\frac{2}{9} x \cos (3 x)","\frac{1}{3} x^2 \sin (3 x)-\frac{2}{27} \sin (3 x)+\frac{2}{9} x \cos (3 x)",1,"(2*x*Cos[3*x])/9 + ((-2 + 9*x^2)*Sin[3*x])/27","A",1
353,1,33,36,0.0165876,"\int \sqrt{5-4 x-x^2} \, dx","Integrate[Sqrt[5 - 4*x - x^2],x]","\frac{1}{2} \left(\sqrt{-x^2-4 x+5} (x+2)+9 \sin ^{-1}\left(\frac{x+2}{3}\right)\right)","\frac{1}{2} (x+2) \sqrt{-x^2-4 x+5}-\frac{9}{2} \sin ^{-1}\left(\frac{1}{3} (-x-2)\right)",1,"((2 + x)*Sqrt[5 - 4*x - x^2] + 9*ArcSin[(2 + x)/3])/2","A",1
354,1,31,28,0.0100141,"\int \frac{x^5}{\sqrt{2}+x^2} \, dx","Integrate[x^5/(Sqrt[2] + x^2),x]","\frac{1}{4} \left(x^4-2 \sqrt{2} x^2+4 \log \left(x^2+\sqrt{2}\right)-6\right)","\frac{x^4}{4}-\frac{x^2}{\sqrt{2}}+\log \left(x^2+\sqrt{2}\right)",1,"(-6 - 2*Sqrt[2]*x^2 + x^4 + 4*Log[Sqrt[2] + x^2])/4","A",1
355,1,58,26,0.1222814,"\int \sec ^5(x) \, dx","Integrate[Sec[x]^5,x]","\frac{1}{16} \left(\frac{1}{2} (11 \sin (x)+3 \sin (3 x)) \sec ^4(x)-6 \log \left(\cos \left(\frac{x}{2}\right)-\sin \left(\frac{x}{2}\right)\right)+6 \log \left(\sin \left(\frac{x}{2}\right)+\cos \left(\frac{x}{2}\right)\right)\right)","\frac{3}{8} \tanh ^{-1}(\sin (x))+\frac{1}{4} \tan (x) \sec ^3(x)+\frac{3}{8} \tan (x) \sec (x)",1,"(-6*Log[Cos[x/2] - Sin[x/2]] + 6*Log[Cos[x/2] + Sin[x/2]] + (Sec[x]^4*(11*Sin[x] + 3*Sin[3*x]))/2)/16","B",1
356,1,30,46,0.0069458,"\int \sin ^6(2 x) \, dx","Integrate[Sin[2*x]^6,x]","\frac{5 x}{16}-\frac{15}{128} \sin (4 x)+\frac{3}{128} \sin (8 x)-\frac{1}{384} \sin (12 x)","\frac{5 x}{16}-\frac{1}{12} \sin ^5(2 x) \cos (2 x)-\frac{5}{48} \sin ^3(2 x) \cos (2 x)-\frac{5}{32} \sin (2 x) \cos (2 x)",1,"(5*x)/16 - (15*Sin[4*x])/128 + (3*Sin[8*x])/128 - Sin[12*x]/384","A",1
357,1,15,20,0.0154741,"\int \cos (x) \log (\sin (x)) \sin ^2(x) \, dx","Integrate[Cos[x]*Log[Sin[x]]*Sin[x]^2,x]","\frac{1}{9} \sin ^3(x) (3 \log (\sin (x))-1)","\frac{1}{3} \sin ^3(x) \log (\sin (x))-\frac{\sin ^3(x)}{9}",1,"((-1 + 3*Log[Sin[x]])*Sin[x]^3)/9","A",1
358,1,21,21,0.0165905,"\int \frac{e^{-x}}{1+2 e^x} \, dx","Integrate[1/(E^x*(1 + 2*E^x)),x]","-2 x-e^{-x}+2 \log \left(2 e^x+1\right)","-2 x-e^{-x}+2 \log \left(2 e^x+1\right)",1,"-E^(-x) - 2*x + 2*Log[1 + 2*E^x]","A",1
359,1,33,37,0.0198284,"\int \sqrt{2+3 \cos (x)} \tan (x) \, dx","Integrate[Sqrt[2 + 3*Cos[x]]*Tan[x],x]","2 \sqrt{2} \tanh ^{-1}\left(\sqrt{\frac{3 \cos (x)}{2}+1}\right)-2 \sqrt{3 \cos (x)+2}","2 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{3 \cos (x)+2}}{\sqrt{2}}\right)-2 \sqrt{3 \cos (x)+2}",1,"2*Sqrt[2]*ArcTanh[Sqrt[1 + (3*Cos[x])/2]] - 2*Sqrt[2 + 3*Cos[x]]","A",1
360,1,40,28,0.0281545,"\int \frac{x}{\sqrt{-4 x+x^2}} \, dx","Integrate[x/Sqrt[-4*x + x^2],x]","\frac{(x-4) x-4 \sqrt{-((x-4) x)} \sin ^{-1}\left(\sqrt{1-\frac{x}{4}}\right)}{\sqrt{(x-4) x}}","\sqrt{x^2-4 x}+4 \tanh ^{-1}\left(\frac{x}{\sqrt{x^2-4 x}}\right)",1,"((-4 + x)*x - 4*Sqrt[-((-4 + x)*x)]*ArcSin[Sqrt[1 - x/4]])/Sqrt[(-4 + x)*x]","A",0
361,1,23,19,0.0020619,"\int \cos ^5(x) \, dx","Integrate[Cos[x]^5,x]","\frac{5 \sin (x)}{8}+\frac{5}{48} \sin (3 x)+\frac{1}{80} \sin (5 x)","\frac{\sin ^5(x)}{5}-\frac{2 \sin ^3(x)}{3}+\sin (x)",1,"(5*Sin[x])/8 + (5*Sin[3*x])/48 + Sin[5*x]/80","A",1
362,1,26,46,0.0069372,"\int e^{-x} x^4 \, dx","Integrate[x^4/E^x,x]","e^{-x} \left(-x^4-4 x^3-12 x^2-24 x-24\right)","-e^{-x} x^4-4 e^{-x} x^3-12 e^{-x} x^2-24 e^{-x} x-24 e^{-x}",1,"(-24 - 24*x - 12*x^2 - 4*x^3 - x^4)/E^x","A",1
363,1,18,18,0.0030099,"\int \frac{x^4}{\sqrt{-2+x^{10}}} \, dx","Integrate[x^4/Sqrt[-2 + x^10],x]","\frac{1}{5} \tanh ^{-1}\left(\frac{x^5}{\sqrt{x^{10}-2}}\right)","\frac{1}{5} \tanh ^{-1}\left(\frac{x^5}{\sqrt{x^{10}-2}}\right)",1,"ArcTanh[x^5/Sqrt[-2 + x^10]]/5","A",1
364,1,22,27,0.0437795,"\int e^x \cos (4+3 x) \, dx","Integrate[E^x*Cos[4 + 3*x],x]","\frac{1}{10} e^x (3 \sin (3 x+4)+\cos (3 x+4))","\frac{3}{10} e^x \sin (3 x+4)+\frac{1}{10} e^x \cos (3 x+4)",1,"(E^x*(Cos[4 + 3*x] + 3*Sin[4 + 3*x]))/10","A",1
365,1,18,18,0.0059808,"\int e^x \log \left(1+e^x\right) \, dx","Integrate[E^x*Log[1 + E^x],x]","\left(e^x+1\right) \log \left(e^x+1\right)-e^x","\left(e^x+1\right) \log \left(e^x+1\right)-e^x",1,"-E^x + (1 + E^x)*Log[1 + E^x]","A",1
366,1,23,27,0.0046965,"\int x^2 \tan ^{-1}(x) \, dx","Integrate[x^2*ArcTan[x],x]","\frac{1}{6} \left(2 x^3 \tan ^{-1}(x)-x^2+\log \left(x^2+1\right)\right)","\frac{1}{3} x^3 \tan ^{-1}(x)-\frac{x^2}{6}+\frac{1}{6} \log \left(x^2+1\right)",1,"(-x^2 + 2*x^3*ArcTan[x] + Log[1 + x^2])/6","A",1
367,1,26,26,0.0062695,"\int \sqrt{-1+e^{2 x}} \, dx","Integrate[Sqrt[-1 + E^(2*x)],x]","\sqrt{e^{2 x}-1}-\tan ^{-1}\left(\sqrt{e^{2 x}-1}\right)","\sqrt{e^{2 x}-1}-\tan ^{-1}\left(\sqrt{e^{2 x}-1}\right)",1,"Sqrt[-1 + E^(2*x)] - ArcTan[Sqrt[-1 + E^(2*x)]]","A",1
368,1,11,15,0.0162727,"\int e^{\sin (x)} \sin (2 x) \, dx","Integrate[E^Sin[x]*Sin[2*x],x]","e^{\sin (x)} (2 \sin (x)-2)","2 e^{\sin (x)} \sin (x)-2 e^{\sin (x)}",1,"E^Sin[x]*(-2 + 2*Sin[x])","A",1
369,1,35,47,0.0185892,"\int x^2 \sqrt{5-x^2} \, dx","Integrate[x^2*Sqrt[5 - x^2],x]","\frac{1}{8} \left(x \sqrt{5-x^2} \left(2 x^2-5\right)+25 \sin ^{-1}\left(\frac{x}{\sqrt{5}}\right)\right)","-\frac{5}{8} \sqrt{5-x^2} x+\frac{1}{4} \sqrt{5-x^2} x^3+\frac{25}{8} \sin ^{-1}\left(\frac{x}{\sqrt{5}}\right)",1,"(x*Sqrt[5 - x^2]*(-5 + 2*x^2) + 25*ArcSin[x/Sqrt[5]])/8","A",1
370,1,36,11,0.0016252,"\int x^2 \left(1+x^3\right)^4 \, dx","Integrate[x^2*(1 + x^3)^4,x]","\frac{x^{15}}{15}+\frac{x^{12}}{3}+\frac{2 x^9}{3}+\frac{2 x^6}{3}+\frac{x^3}{3}","\frac{1}{15} \left(x^3+1\right)^5",1,"x^3/3 + (2*x^6)/3 + (2*x^9)/3 + x^12/3 + x^15/15","B",1
371,1,17,17,0.0061256,"\int \cos ^3(x) \sin ^3(x) \, dx","Integrate[Cos[x]^3*Sin[x]^3,x]","\frac{1}{192} \cos (6 x)-\frac{3}{64} \cos (2 x)","\frac{\sin ^4(x)}{4}-\frac{\sin ^6(x)}{6}",1,"(-3*Cos[2*x])/64 + Cos[6*x]/192","A",1
372,1,27,17,0.0162452,"\int \sec ^4(x) \tan ^2(x) \, dx","Integrate[Sec[x]^4*Tan[x]^2,x]","-\frac{2 \tan (x)}{15}+\frac{1}{5} \tan (x) \sec ^4(x)-\frac{1}{15} \tan (x) \sec ^2(x)","\frac{\tan ^5(x)}{5}+\frac{\tan ^3(x)}{3}",1,"(-2*Tan[x])/15 - (Sec[x]^2*Tan[x])/15 + (Sec[x]^4*Tan[x])/5","A",1
373,1,18,27,0.0059319,"\int x \sqrt{1+2 x} \, dx","Integrate[x*Sqrt[1 + 2*x],x]","\frac{1}{15} (2 x+1)^{3/2} (3 x-1)","\frac{1}{10} (2 x+1)^{5/2}-\frac{1}{6} (2 x+1)^{3/2}",1,"((1 + 2*x)^(3/2)*(-1 + 3*x))/15","A",1
374,1,22,24,0.0018038,"\int \sin ^4(x) \, dx","Integrate[Sin[x]^4,x]","\frac{3 x}{8}-\frac{1}{4} \sin (2 x)+\frac{1}{32} \sin (4 x)","\frac{3 x}{8}-\frac{1}{4} \sin ^3(x) \cos (x)-\frac{3}{8} \sin (x) \cos (x)",1,"(3*x)/8 - Sin[2*x]/4 + Sin[4*x]/32","A",1
375,1,12,12,0.0031261,"\int \tan ^3(x) \, dx","Integrate[Tan[x]^3,x]","\frac{\sec ^2(x)}{2}+\log (\cos (x))","\frac{\tan ^2(x)}{2}+\log (\cos (x))",1,"Log[Cos[x]] + Sec[x]^2/2","A",1
376,1,25,40,0.0080402,"\int x^5 \sqrt{1+x^2} \, dx","Integrate[x^5*Sqrt[1 + x^2],x]","\frac{1}{105} \left(x^2+1\right)^{3/2} \left(15 x^4-12 x^2+8\right)","\frac{1}{7} \left(x^2+1\right)^{7/2}-\frac{2}{5} \left(x^2+1\right)^{5/2}+\frac{1}{3} \left(x^2+1\right)^{3/2}",1,"((1 + x^2)^(3/2)*(8 - 12*x^2 + 15*x^4))/105","A",1