1,1,15,16,0.0024309,"\int \left(1+x+x^2\right) \, dx","IntegrateAlgebraic[1 + x + x^2,x]","\frac{1}{6} x \left(2 x^2+3 x+6\right)","\frac{x^3}{3}+\frac{x^2}{2}+x",1,"(x*(6 + 3*x + 2*x^2))/6","A",1
2,1,17,22,0.0041717,"\int x^2 \left(x+2 x^2\right)^2 \, dx","IntegrateAlgebraic[x^2*(x + 2*x^2)^2,x]","\frac{1}{105} x^5 \left(60 x^2+70 x+21\right)","\frac{4 x^7}{7}+\frac{2 x^6}{3}+\frac{x^5}{5}",1,"(x^5*(21 + 70*x + 60*x^2))/105","A",1
3,1,17,22,0.0037109,"\int x \left(1+2 x+x^2\right) \, dx","IntegrateAlgebraic[x*(1 + 2*x + x^2),x]","\frac{1}{12} x^2 \left(3 x^2+8 x+6\right)","\frac{x^4}{4}+\frac{2 x^3}{3}+\frac{x^2}{2}",1,"(x^2*(6 + 8*x + 3*x^2))/12","A",1
4,1,2,2,0.0012371,"\int \frac{1}{x} \, dx","IntegrateAlgebraic[x^(-1),x]","\log (x)","\log (x)",1,"Log[x]","A",1
5,1,24,36,0.0154534,"\int \frac{(1+x)^3}{(-1+x)^4} \, dx","IntegrateAlgebraic[(1 + x)^3/(-1 + x)^4,x]","\log (x-1)-\frac{2 \left(9 x^2-9 x+4\right)}{3 (x-1)^3}","\frac{6}{1-x}-\frac{6}{(1-x)^2}+\frac{8}{3 (1-x)^3}+\log (1-x)",1,"(-2*(4 - 9*x + 9*x^2))/(3*(-1 + x)^3) + Log[-1 + x]","A",1
6,1,30,32,0.0148635,"\int \frac{1}{(-1+x) x (1+x)^2} \, dx","IntegrateAlgebraic[1/((-1 + x)*x*(1 + x)^2),x]","-\frac{1}{2 (x+1)}+\frac{1}{4} \log (x-1)-\log (x)+\frac{3}{4} \log (x+1)","-\frac{1}{2 (x+1)}+\frac{1}{4} \log (1-x)-\log (x)+\frac{3}{4} \log (x+1)",1,"-1/2*1/(1 + x) + Log[-1 + x]/4 - Log[x] + (3*Log[1 + x])/4","A",1
7,1,42,40,0.0228252,"\int \frac{b+a x}{(-p+x) (-q+x)} \, dx","IntegrateAlgebraic[(b + a*x)/((-p + x)*(-q + x)),x]","\frac{(a p+b) \log (p-x)}{p-q}+\frac{(-a q-b) \log (q-x)}{p-q}","\frac{(a p+b) \log (p-x)}{p-q}-\frac{(a q+b) \log (q-x)}{p-q}",1,"((b + a*p)*Log[p - x])/(p - q) + ((-b - a*q)*Log[q - x])/(p - q)","A",1
8,1,52,34,0.0230189,"\int \frac{1}{c+b x+a x^2} \, dx","IntegrateAlgebraic[(c + b*x + a*x^2)^(-1),x]","\frac{2 \tan ^{-1}\left(\frac{2 a x}{\sqrt{4 a c-b^2}}+\frac{b}{\sqrt{4 a c-b^2}}\right)}{\sqrt{4 a c-b^2}}","-\frac{2 \tanh ^{-1}\left(\frac{2 a x+b}{\sqrt{b^2-4 a c}}\right)}{\sqrt{b^2-4 a c}}",1,"(2*ArcTan[b/Sqrt[-b^2 + 4*a*c] + (2*a*x)/Sqrt[-b^2 + 4*a*c]])/Sqrt[-b^2 + 4*a*c]","A",1
9,1,16,16,0.0084063,"\int \frac{b+a x}{1+x^2} \, dx","IntegrateAlgebraic[(b + a*x)/(1 + x^2),x]","\frac{1}{2} a \log \left(x^2+1\right)+b \tan ^{-1}(x)","\frac{1}{2} a \log \left(x^2+1\right)+b \tan ^{-1}(x)",1,"b*ArcTan[x] + (a*Log[1 + x^2])/2","A",1
10,1,22,19,0.0111261,"\int \frac{1}{3-2 x+x^2} \, dx","IntegrateAlgebraic[(3 - 2*x + x^2)^(-1),x]","-\frac{\tan ^{-1}\left(\frac{1}{\sqrt{2}}-\frac{x}{\sqrt{2}}\right)}{\sqrt{2}}","-\frac{\tan ^{-1}\left(\frac{1-x}{\sqrt{2}}\right)}{\sqrt{2}}",1,"-(ArcTan[1/Sqrt[2] - x/Sqrt[2]]/Sqrt[2])","A",1
11,1,45,49,0.029152,"\int \frac{1}{(-1+x)^2 \left(1+x^2\right)^2} \, dx","IntegrateAlgebraic[1/((-1 + x)^2*(1 + x^2)^2),x]","-\frac{x (x+1)}{4 (x-1) \left(x^2+1\right)}+\frac{1}{4} \log \left(x^2+1\right)-\frac{1}{2} \log (x-1)+\frac{1}{4} \tan ^{-1}(x)","-\frac{1}{4 \left(x^2+1\right)}+\frac{1}{4} \log \left(x^2+1\right)+\frac{1}{4 (1-x)}-\frac{1}{2} \log (1-x)+\frac{1}{4} \tan ^{-1}(x)",1,"-1/4*(x*(1 + x))/((-1 + x)*(1 + x^2)) + ArcTan[x]/4 - Log[-1 + x]/2 + Log[1 + x^2]/4","A",1
12,1,69,68,0.0442527,"\int \frac{x}{(-a+x) (-b+x) (-c+x)} \, dx","IntegrateAlgebraic[x/((-a + x)*(-b + x)*(-c + x)),x]","\frac{a \log (a-x)}{(a-b) (a-c)}-\frac{b \log (b-x)}{(a-b) (b-c)}-\frac{c \log (c-x)}{(a-c) (c-b)}","\frac{a \log (a-x)}{(a-b) (a-c)}-\frac{b \log (b-x)}{(a-b) (b-c)}+\frac{c \log (c-x)}{(a-c) (b-c)}",1,"(a*Log[a - x])/((a - b)*(a - c)) - (b*Log[b - x])/((a - b)*(b - c)) - (c*Log[c - x])/((a - c)*(-b + c))","A",1
13,1,47,47,0.0177567,"\int \frac{x}{\left(a^2+x^2\right) \left(b^2+x^2\right)} \, dx","IntegrateAlgebraic[x/((a^2 + x^2)*(b^2 + x^2)),x]","\frac{\log \left(b^2+x^2\right)}{2 \left(a^2-b^2\right)}-\frac{\log \left(a^2+x^2\right)}{2 \left(a^2-b^2\right)}","\frac{\log \left(b^2+x^2\right)}{2 \left(a^2-b^2\right)}-\frac{\log \left(a^2+x^2\right)}{2 \left(a^2-b^2\right)}",1,"-1/2*Log[a^2 + x^2]/(a^2 - b^2) + Log[b^2 + x^2]/(2*(a^2 - b^2))","A",1
14,1,39,40,0.0211269,"\int \frac{x^2}{\left(a^2+x^2\right) \left(b^2+x^2\right)} \, dx","IntegrateAlgebraic[x^2/((a^2 + x^2)*(b^2 + x^2)),x]","\frac{a \tan ^{-1}\left(\frac{x}{a}\right)}{a^2-b^2}+\frac{b \tan ^{-1}\left(\frac{x}{b}\right)}{b^2-a^2}","\frac{a \tan ^{-1}\left(\frac{x}{a}\right)}{a^2-b^2}-\frac{b \tan ^{-1}\left(\frac{x}{b}\right)}{a^2-b^2}",1,"(a*ArcTan[x/a])/(a^2 - b^2) + (b*ArcTan[x/b])/(-a^2 + b^2)","A",1
15,1,25,27,0.0072732,"\int \frac{x}{(-1+x) \left(1+x^2\right)} \, dx","IntegrateAlgebraic[x/((-1 + x)*(1 + x^2)),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 (1-x)+\frac{1}{2} \tan ^{-1}(x)",1,"ArcTan[x]/2 + Log[-1 + x]/2 - Log[1 + x^2]/4","A",1
16,1,44,41,0.01609,"\int \frac{x}{1+x^3} \, dx","IntegrateAlgebraic[x/(1 + x^3),x]","\frac{1}{6} \log \left(x^2-x+1\right)-\frac{1}{3} \log (x+1)-\frac{\tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 x}{\sqrt{3}}\right)}{\sqrt{3}}","\frac{1}{6} \log \left(x^2-x+1\right)-\frac{1}{3} \log (x+1)-\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{\sqrt{3}}",1,"-(ArcTan[1/Sqrt[3] - (2*x)/Sqrt[3]]/Sqrt[3]) - Log[1 + x]/3 + Log[1 - x + x^2]/6","A",1
17,1,39,43,0.0251317,"\int \frac{x^3}{(-1+x)^2 \left(1+x^3\right)} \, dx","IntegrateAlgebraic[x^3/((-1 + x)^2*(1 + x^3)),x]","-\frac{1}{3} \log \left(x^2-x+1\right)-\frac{1}{2 (x-1)}+\frac{3}{4} \log (x-1)-\frac{1}{12} \log (x+1)","-\frac{1}{3} \log \left(x^2-x+1\right)+\frac{1}{2 (1-x)}+\frac{3}{4} \log (1-x)-\frac{1}{12} \log (x+1)",1,"-1/2*1/(-1 + x) + (3*Log[-1 + x])/4 - Log[1 + x]/12 - Log[1 - x + x^2]/3","A",1
18,1,56,85,0.0000945,"\int \frac{1}{1+x^4} \, dx","IntegrateAlgebraic[(1 + x^4)^(-1),x]","\frac{\tan ^{-1}\left(\frac{\frac{x^2}{\sqrt{2}}-\frac{1}{\sqrt{2}}}{x}\right)}{2 \sqrt{2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x}{x^2+1}\right)}{2 \sqrt{2}}","-\frac{\log \left(x^2-\sqrt{2} x+1\right)}{4 \sqrt{2}}+\frac{\log \left(x^2+\sqrt{2} x+1\right)}{4 \sqrt{2}}-\frac{\tan ^{-1}\left(1-\sqrt{2} x\right)}{2 \sqrt{2}}+\frac{\tan ^{-1}\left(\sqrt{2} x+1\right)}{2 \sqrt{2}}",1,"ArcTan[(-(1/Sqrt[2]) + x^2/Sqrt[2])/x]/(2*Sqrt[2]) + ArcTanh[(Sqrt[2]*x)/(1 + x^2)]/(2*Sqrt[2])","A",1
19,1,56,85,0.0301646,"\int \frac{x^2}{1+x^4} \, dx","IntegrateAlgebraic[x^2/(1 + x^4),x]","\frac{\tan ^{-1}\left(\frac{\frac{x^2}{\sqrt{2}}-\frac{1}{\sqrt{2}}}{x}\right)}{2 \sqrt{2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x}{x^2+1}\right)}{2 \sqrt{2}}","\frac{\log \left(x^2-\sqrt{2} x+1\right)}{4 \sqrt{2}}-\frac{\log \left(x^2+\sqrt{2} x+1\right)}{4 \sqrt{2}}-\frac{\tan ^{-1}\left(1-\sqrt{2} x\right)}{2 \sqrt{2}}+\frac{\tan ^{-1}\left(\sqrt{2} x+1\right)}{2 \sqrt{2}}",1,"ArcTan[(-(1/Sqrt[2]) + x^2/Sqrt[2])/x]/(2*Sqrt[2]) - ArcTanh[(Sqrt[2]*x)/(1 + x^2)]/(2*Sqrt[2])","A",1
20,1,58,67,0.1385233,"\int \frac{1}{1+x^2+x^4} \, dx","IntegrateAlgebraic[(1 + x^2 + x^4)^(-1),x]","\sqrt{\frac{1}{6} \left(-1-i \sqrt{3}\right)} \tan ^{-1}\left(\sqrt[6]{-1} x\right)-\sqrt{\frac{1}{6} \left(-1+i \sqrt{3}\right)} \tan ^{-1}\left((-1)^{5/6} x\right)","-\frac{1}{4} \log \left(x^2-x+1\right)+\frac{1}{4} \log \left(x^2+x+1\right)-\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{2 \sqrt{3}}",1,"Sqrt[(-1 - I*Sqrt[3])/6]*ArcTan[(-1)^(1/6)*x] - Sqrt[(-1 + I*Sqrt[3])/6]*ArcTan[(-1)^(5/6)*x]","C",0
21,0,0,18,0.0000499,"\int (a+b x)^p \, dx","IntegrateAlgebraic[(a + b*x)^p,x]","\int (a+b x)^p \, dx","\frac{(a+b x)^{p+1}}{b (p+1)}",1,"Could not integrate","F",-1
22,0,0,39,0.0000465,"\int x (a+b x)^p \, dx","IntegrateAlgebraic[x*(a + b*x)^p,x]","\int x (a+b x)^p \, dx","\frac{(a+b x)^{p+2}}{b^2 (p+2)}-\frac{a (a+b x)^{p+1}}{b^2 (p+1)}",1,"Could not integrate","F",-1
23,0,0,60,0.0000508,"\int x^2 (a+b x)^p \, dx","IntegrateAlgebraic[x^2*(a + b*x)^p,x]","\int x^2 (a+b x)^p \, dx","\frac{a^2 (a+b x)^{p+1}}{b^3 (p+1)}-\frac{2 a (a+b x)^{p+2}}{b^3 (p+2)}+\frac{(a+b x)^{p+3}}{b^3 (p+3)}",1,"Could not integrate","F",-1
24,1,10,10,0.0031896,"\int \frac{1}{a+b x} \, dx","IntegrateAlgebraic[(a + b*x)^(-1),x]","\frac{\log (a+b x)}{b}","\frac{\log (a+b x)}{b}",1,"Log[a + b*x]/b","A",1
25,1,12,12,0.0054725,"\int \frac{1}{(a+b x)^2} \, dx","IntegrateAlgebraic[(a + b*x)^(-2),x]","-\frac{1}{b (a+b x)}","-\frac{1}{b (a+b x)}",1,"-(1/(b*(a + b*x)))","A",1
26,1,18,18,0.0054925,"\int \frac{x}{a+b x} \, dx","IntegrateAlgebraic[x/(a + b*x),x]","\frac{x}{b}-\frac{a \log (a+b x)}{b^2}","\frac{x}{b}-\frac{a \log (a+b x)}{b^2}",1,"x/b - (a*Log[a + b*x])/b^2","A",1
27,1,29,31,0.0087433,"\int \frac{x^2}{a+b x} \, dx","IntegrateAlgebraic[x^2/(a + b*x),x]","\frac{a^2 \log (a+b x)}{b^3}+\frac{x (b x-2 a)}{2 b^2}","\frac{a^2 \log (a+b x)}{b^3}-\frac{a x}{b^2}+\frac{x^2}{2 b}",1,"(x*(-2*a + b*x))/(2*b^2) + (a^2*Log[a + b*x])/b^3","A",1
28,1,18,18,0.008317,"\int \frac{1}{x (a+b x)} \, dx","IntegrateAlgebraic[1/(x*(a + b*x)),x]","\frac{\log (x)}{a}-\frac{\log (a+b x)}{a}","\frac{\log (x)}{a}-\frac{\log (a+b x)}{a}",1,"Log[x]/a - Log[a + b*x]/a","A",1
29,1,28,28,0.0094214,"\int \frac{1}{x^2 (a+b x)} \, dx","IntegrateAlgebraic[1/(x^2*(a + b*x)),x]","-\frac{b \log (x)}{a^2}+\frac{b \log (a+b x)}{a^2}-\frac{1}{a x}","-\frac{b \log (x)}{a^2}+\frac{b \log (a+b x)}{a^2}-\frac{1}{a x}",1,"-(1/(a*x)) - (b*Log[x])/a^2 + (b*Log[a + b*x])/a^2","A",1
30,1,43,42,0.0469664,"\int \frac{1}{x^2 (a+b x)^2} \, dx","IntegrateAlgebraic[1/(x^2*(a + b*x)^2),x]","-\frac{2 b \log (x)}{a^3}+\frac{2 b \log (a+b x)}{a^3}+\frac{-a-2 b x}{a^2 x (a+b x)}","-\frac{2 b \log (x)}{a^3}+\frac{2 b \log (a+b x)}{a^3}-\frac{b}{a^2 (a+b x)}-\frac{1}{a^2 x}",1,"(-a - 2*b*x)/(a^2*x*(a + b*x)) - (2*b*Log[x])/a^3 + (2*b*Log[a + b*x])/a^3","A",1
31,1,10,10,0.004239,"\int \frac{1}{c^2+x^2} \, dx","IntegrateAlgebraic[(c^2 + x^2)^(-1),x]","\frac{\tan ^{-1}\left(\frac{x}{c}\right)}{c}","\frac{\tan ^{-1}\left(\frac{x}{c}\right)}{c}",1,"ArcTan[x/c]/c","A",1
32,1,10,10,0.0047204,"\int \frac{1}{c^2-x^2} \, dx","IntegrateAlgebraic[(c^2 - x^2)^(-1),x]","\frac{\tanh ^{-1}\left(\frac{x}{c}\right)}{c}","\frac{\tanh ^{-1}\left(\frac{x}{c}\right)}{c}",1,"ArcTanh[x/c]/c","A",1
33,1,80,78,0.0768256,"\int \frac{1}{-1+2 x^3} \, dx","IntegrateAlgebraic[(-1 + 2*x^3)^(-1),x]","-\frac{\log \left(2^{2/3} x^2+\sqrt[3]{2} x+1\right)}{6 \sqrt[3]{2}}+\frac{\log \left(\sqrt[3]{2} x-1\right)}{3 \sqrt[3]{2}}-\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{2} x}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3}}","-\frac{\log \left(2^{2/3} x^2+\sqrt[3]{2} x+1\right)}{6 \sqrt[3]{2}}+\frac{\log \left(1-\sqrt[3]{2} x\right)}{3 \sqrt[3]{2}}-\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{2} x+1}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3}}",1,"-(ArcTan[1/Sqrt[3] + (2*2^(1/3)*x)/Sqrt[3]]/(2^(1/3)*Sqrt[3])) + Log[-1 + 2^(1/3)*x]/(3*2^(1/3)) - Log[1 + 2^(1/3)*x + 2^(2/3)*x^2]/(6*2^(1/3))","A",1
34,1,79,74,0.0767853,"\int \frac{1}{-2+x^3} \, dx","IntegrateAlgebraic[(-2 + x^3)^(-1),x]","-\frac{\log \left(\sqrt[3]{2} x^2+2^{2/3} x+2\right)}{6\ 2^{2/3}}+\frac{\log \left(2^{2/3} x-2\right)}{3\ 2^{2/3}}-\frac{\tan ^{-1}\left(\frac{2^{2/3} x}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3}}","-\frac{\log \left(x^2+\sqrt[3]{2} x+2^{2/3}\right)}{6\ 2^{2/3}}+\frac{\log \left(\sqrt[3]{2}-x\right)}{3\ 2^{2/3}}-\frac{\tan ^{-1}\left(\frac{2^{2/3} x+1}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3}}",1,"-(ArcTan[1/Sqrt[3] + (2^(2/3)*x)/Sqrt[3]]/(2^(2/3)*Sqrt[3])) + Log[-2 + 2^(2/3)*x]/(3*2^(2/3)) - Log[2 + 2^(2/3)*x + 2^(1/3)*x^2]/(6*2^(2/3))","A",1
35,1,114,115,0.0431097,"\int \frac{1}{-b+a x^3} \, dx","IntegrateAlgebraic[(-b + a*x^3)^(-1),x]","-\frac{\log \left(a^{2/3} x^2+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3}\right)}{6 \sqrt[3]{a} b^{2/3}}+\frac{\log \left(\sqrt[3]{b}-\sqrt[3]{a} x\right)}{3 \sqrt[3]{a} b^{2/3}}-\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{a} x}{\sqrt{3} \sqrt[3]{b}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{a} b^{2/3}}","-\frac{\log \left(a^{2/3} x^2+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3}\right)}{6 \sqrt[3]{a} b^{2/3}}+\frac{\log \left(\sqrt[3]{b}-\sqrt[3]{a} x\right)}{3 \sqrt[3]{a} b^{2/3}}-\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{a} x+\sqrt[3]{b}}{\sqrt{3} \sqrt[3]{b}}\right)}{\sqrt{3} \sqrt[3]{a} b^{2/3}}",1,"-(ArcTan[1/Sqrt[3] + (2*a^(1/3)*x)/(Sqrt[3]*b^(1/3))]/(Sqrt[3]*a^(1/3)*b^(2/3))) + Log[b^(1/3) - a^(1/3)*x]/(3*a^(1/3)*b^(2/3)) - Log[b^(2/3) + a^(1/3)*b^(1/3)*x + a^(2/3)*x^2]/(6*a^(1/3)*b^(2/3))","A",1
36,1,35,35,0.0468269,"\int \frac{1}{-2+x^4} \, dx","IntegrateAlgebraic[(-2 + x^4)^(-1),x]","-\frac{\tan ^{-1}\left(\frac{x}{\sqrt[4]{2}}\right)}{2\ 2^{3/4}}-\frac{\tanh ^{-1}\left(\frac{x}{\sqrt[4]{2}}\right)}{2\ 2^{3/4}}","-\frac{\tan ^{-1}\left(\frac{x}{\sqrt[4]{2}}\right)}{2\ 2^{3/4}}-\frac{\tanh ^{-1}\left(\frac{x}{\sqrt[4]{2}}\right)}{2\ 2^{3/4}}",1,"-1/2*ArcTan[x/2^(1/4)]/2^(3/4) - ArcTanh[x/2^(1/4)]/(2*2^(3/4))","A",1
37,1,35,35,0.0386469,"\int \frac{1}{-1+5 x^4} \, dx","IntegrateAlgebraic[(-1 + 5*x^4)^(-1),x]","-\frac{\tan ^{-1}\left(\sqrt[4]{5} x\right)}{2 \sqrt[4]{5}}-\frac{\tanh ^{-1}\left(\sqrt[4]{5} x\right)}{2 \sqrt[4]{5}}","-\frac{\tan ^{-1}\left(\sqrt[4]{5} x\right)}{2 \sqrt[4]{5}}-\frac{\tanh ^{-1}\left(\sqrt[4]{5} x\right)}{2 \sqrt[4]{5}}",1,"-1/2*ArcTan[5^(1/4)*x]/5^(1/4) - ArcTanh[5^(1/4)*x]/(2*5^(1/4))","A",1
38,1,106,171,0.2289171,"\int \frac{1}{7+3 x^4} \, dx","IntegrateAlgebraic[(7 + 3*x^4)^(-1),x]","\frac{\tan ^{-1}\left(\frac{\frac{\sqrt[4]{\frac{3}{7}} x^2}{\sqrt{2}}-\frac{\sqrt[4]{\frac{7}{3}}}{\sqrt{2}}}{x}\right)}{2 \sqrt{2} \sqrt[4]{3} 7^{3/4}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{3} 7^{3/4} x}{\sqrt{21} x^2+7}\right)}{2 \sqrt{2} \sqrt[4]{3} 7^{3/4}}","-\frac{\log \left(3 x^2-\sqrt{2} 3^{3/4} \sqrt[4]{7} x+\sqrt{21}\right)}{4 \sqrt{2} \sqrt[4]{3} 7^{3/4}}+\frac{\log \left(3 x^2+\sqrt{2} 3^{3/4} \sqrt[4]{7} x+\sqrt{21}\right)}{4 \sqrt{2} \sqrt[4]{3} 7^{3/4}}-\frac{\tan ^{-1}\left(1-\sqrt[4]{\frac{3}{7}} \sqrt{2} x\right)}{2 \sqrt{2} \sqrt[4]{3} 7^{3/4}}+\frac{\tan ^{-1}\left(\sqrt[4]{\frac{3}{7}} \sqrt{2} x+1\right)}{2 \sqrt{2} \sqrt[4]{3} 7^{3/4}}",1,"ArcTan[(-((7/3)^(1/4)/Sqrt[2]) + ((3/7)^(1/4)*x^2)/Sqrt[2])/x]/(2*Sqrt[2]*3^(1/4)*7^(3/4)) + ArcTanh[(Sqrt[2]*3^(1/4)*7^(3/4)*x)/(7 + Sqrt[21]*x^2)]/(2*Sqrt[2]*3^(1/4)*7^(3/4))","A",1
39,1,75,73,0.1305695,"\int \frac{1}{-1+3 x^2+x^4} \, dx","IntegrateAlgebraic[(-1 + 3*x^2 + x^4)^(-1),x]","-\sqrt{\frac{1}{26} \left(\sqrt{13}-3\right)} \tan ^{-1}\left(\sqrt{\frac{\sqrt{13}}{2}-\frac{3}{2}} x\right)-\sqrt{\frac{1}{26} \left(3+\sqrt{13}\right)} \tanh ^{-1}\left(\sqrt{\frac{3}{2}+\frac{\sqrt{13}}{2}} x\right)","-\sqrt{\frac{2}{13 \left(3+\sqrt{13}\right)}} \tan ^{-1}\left(\sqrt{\frac{2}{3+\sqrt{13}}} x\right)-\sqrt{\frac{1}{26} \left(3+\sqrt{13}\right)} \tanh ^{-1}\left(\sqrt{\frac{2}{\sqrt{13}-3}} x\right)",1,"-(Sqrt[(-3 + Sqrt[13])/26]*ArcTan[Sqrt[-3/2 + Sqrt[13]/2]*x]) - Sqrt[(3 + Sqrt[13])/26]*ArcTanh[Sqrt[3/2 + Sqrt[13]/2]*x]","A",1
40,1,75,73,0.0804524,"\int \frac{1}{-1-3 x^2+x^4} \, dx","IntegrateAlgebraic[(-1 - 3*x^2 + x^4)^(-1),x]","-\sqrt{\frac{1}{26} \left(3+\sqrt{13}\right)} \tan ^{-1}\left(\sqrt{\frac{3}{2}+\frac{\sqrt{13}}{2}} x\right)-\sqrt{\frac{1}{26} \left(\sqrt{13}-3\right)} \tanh ^{-1}\left(\sqrt{\frac{\sqrt{13}}{2}-\frac{3}{2}} x\right)","-\sqrt{\frac{1}{26} \left(3+\sqrt{13}\right)} \tan ^{-1}\left(\sqrt{\frac{2}{\sqrt{13}-3}} x\right)-\sqrt{\frac{2}{13 \left(3+\sqrt{13}\right)}} \tanh ^{-1}\left(\sqrt{\frac{2}{3+\sqrt{13}}} x\right)",1,"-(Sqrt[(3 + Sqrt[13])/26]*ArcTan[Sqrt[3/2 + Sqrt[13]/2]*x]) - Sqrt[(-3 + Sqrt[13])/26]*ArcTanh[Sqrt[-3/2 + Sqrt[13]/2]*x]","A",1
41,1,49,72,0.0582908,"\int \frac{1}{1-3 x^2+x^4} \, dx","IntegrateAlgebraic[(1 - 3*x^2 + x^4)^(-1),x]","\frac{1}{10} \left(\sqrt{5}-5\right) \tanh ^{-1}\left(\frac{1}{2} \left(\sqrt{5}-1\right) x\right)+\frac{1}{10} \left(5+\sqrt{5}\right) \tanh ^{-1}\left(\frac{1}{2} \left(1+\sqrt{5}\right) x\right)","\sqrt{\frac{1}{10} \left(3+\sqrt{5}\right)} \tanh ^{-1}\left(\sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)-\sqrt{\frac{2}{5 \left(3+\sqrt{5}\right)}} \tanh ^{-1}\left(\sqrt{\frac{2}{3+\sqrt{5}}} x\right)",1,"((-5 + Sqrt[5])*ArcTanh[((-1 + Sqrt[5])*x)/2])/10 + ((5 + Sqrt[5])*ArcTanh[((1 + Sqrt[5])*x)/2])/10","A",1
42,1,71,67,0.1050444,"\int \frac{1}{1-4 x^2+x^4} \, dx","IntegrateAlgebraic[(1 - 4*x^2 + x^4)^(-1),x]","\frac{1}{2} \sqrt{\frac{1}{3} \left(2+\sqrt{3}\right)} \tanh ^{-1}\left(\sqrt{2+\sqrt{3}} x\right)-\frac{1}{2} \sqrt{\frac{1}{3} \left(2-\sqrt{3}\right)} \tanh ^{-1}\left(\sqrt{2-\sqrt{3}} x\right)","\frac{\tanh ^{-1}\left(\frac{x}{\sqrt{2-\sqrt{3}}}\right)}{2 \sqrt{3 \left(2-\sqrt{3}\right)}}-\frac{\tanh ^{-1}\left(\frac{x}{\sqrt{2+\sqrt{3}}}\right)}{2 \sqrt{3 \left(2+\sqrt{3}\right)}}",1,"-1/2*(Sqrt[(2 - Sqrt[3])/3]*ArcTanh[Sqrt[2 - Sqrt[3]]*x]) + (Sqrt[(2 + Sqrt[3])/3]*ArcTanh[Sqrt[2 + Sqrt[3]]*x])/2","A",1
43,1,71,67,0.077819,"\int \frac{1}{1+4 x^2+x^4} \, dx","IntegrateAlgebraic[(1 + 4*x^2 + x^4)^(-1),x]","\frac{1}{2} \sqrt{\frac{1}{3} \left(2+\sqrt{3}\right)} \tan ^{-1}\left(\sqrt{2+\sqrt{3}} x\right)-\frac{1}{2} \sqrt{\frac{1}{3} \left(2-\sqrt{3}\right)} \tan ^{-1}\left(\sqrt{2-\sqrt{3}} x\right)","\frac{\tan ^{-1}\left(\frac{x}{\sqrt{2-\sqrt{3}}}\right)}{2 \sqrt{3 \left(2-\sqrt{3}\right)}}-\frac{\tan ^{-1}\left(\frac{x}{\sqrt{2+\sqrt{3}}}\right)}{2 \sqrt{3 \left(2+\sqrt{3}\right)}}",1,"-1/2*(Sqrt[(2 - Sqrt[3])/3]*ArcTan[Sqrt[2 - Sqrt[3]]*x]) + (Sqrt[(2 + Sqrt[3])/3]*ArcTan[Sqrt[2 + Sqrt[3]]*x])/2","A",1
44,1,91,196,0.1691704,"\int \frac{1}{2+x^2+x^4} \, dx","IntegrateAlgebraic[(2 + x^2 + x^4)^(-1),x]","\frac{1}{2} \sqrt{\frac{1}{7} \left(-1+i \sqrt{7}\right)} \tan ^{-1}\left(\sqrt{\frac{1}{4}-\frac{i \sqrt{7}}{4}} x\right)+\frac{1}{2} \sqrt{\frac{1}{7} \left(-1-i \sqrt{7}\right)} \tan ^{-1}\left(\sqrt{\frac{1}{4}+\frac{i \sqrt{7}}{4}} x\right)","-\frac{\log \left(x^2-\sqrt{2 \sqrt{2}-1} x+\sqrt{2}\right)}{4 \sqrt{2 \left(2 \sqrt{2}-1\right)}}+\frac{\log \left(x^2+\sqrt{2 \sqrt{2}-1} x+\sqrt{2}\right)}{4 \sqrt{2 \left(2 \sqrt{2}-1\right)}}-\frac{1}{2} \sqrt{\frac{1}{14} \left(2 \sqrt{2}-1\right)} \tan ^{-1}\left(\frac{\sqrt{2 \sqrt{2}-1}-2 x}{\sqrt{1+2 \sqrt{2}}}\right)+\frac{1}{2} \sqrt{\frac{1}{14} \left(2 \sqrt{2}-1\right)} \tan ^{-1}\left(\frac{2 x+\sqrt{2 \sqrt{2}-1}}{\sqrt{1+2 \sqrt{2}}}\right)",1,"(Sqrt[(-1 + I*Sqrt[7])/7]*ArcTan[Sqrt[1/4 - (I/4)*Sqrt[7]]*x])/2 + (Sqrt[(-1 - I*Sqrt[7])/7]*ArcTan[Sqrt[1/4 + (I/4)*Sqrt[7]]*x])/2","C",0
45,1,91,196,0.1849343,"\int \frac{1}{2-x^2+x^4} \, dx","IntegrateAlgebraic[(2 - x^2 + x^4)^(-1),x]","\frac{1}{2} \sqrt{\frac{1}{7} \left(1+i \sqrt{7}\right)} \tan ^{-1}\left(\sqrt{-\frac{1}{4}-\frac{i \sqrt{7}}{4}} x\right)+\frac{1}{2} \sqrt{\frac{1}{7} \left(1-i \sqrt{7}\right)} \tan ^{-1}\left(\sqrt{-\frac{1}{4}+\frac{i \sqrt{7}}{4}} x\right)","-\frac{\log \left(x^2-\sqrt{1+2 \sqrt{2}} x+\sqrt{2}\right)}{4 \sqrt{2 \left(1+2 \sqrt{2}\right)}}+\frac{\log \left(x^2+\sqrt{1+2 \sqrt{2}} x+\sqrt{2}\right)}{4 \sqrt{2 \left(1+2 \sqrt{2}\right)}}-\frac{1}{2} \sqrt{\frac{1}{14} \left(1+2 \sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{1+2 \sqrt{2}}-2 x}{\sqrt{2 \sqrt{2}-1}}\right)+\frac{1}{2} \sqrt{\frac{1}{14} \left(1+2 \sqrt{2}\right)} \tan ^{-1}\left(\frac{2 x+\sqrt{1+2 \sqrt{2}}}{\sqrt{2 \sqrt{2}-1}}\right)",1,"(Sqrt[(1 + I*Sqrt[7])/7]*ArcTan[Sqrt[-1/4 - (I/4)*Sqrt[7]]*x])/2 + (Sqrt[(1 - I*Sqrt[7])/7]*ArcTan[Sqrt[-1/4 + (I/4)*Sqrt[7]]*x])/2","C",0
46,1,69,73,0.0338794,"\int \frac{1}{-1+x^6} \, dx","IntegrateAlgebraic[(-1 + x^6)^(-1),x]","-\frac{1}{6} \tanh ^{-1}\left(\frac{x}{x^2+1}\right)+\frac{\tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 x}{\sqrt{3}}\right)}{2 \sqrt{3}}-\frac{\tan ^{-1}\left(\frac{2 x}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3}}-\frac{1}{3} \tanh ^{-1}(x)","\frac{1}{12} \log \left(x^2-x+1\right)-\frac{1}{12} \log \left(x^2+x+1\right)+\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{2 \sqrt{3}}-\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{2 \sqrt{3}}-\frac{1}{3} \tanh ^{-1}(x)",1,"ArcTan[1/Sqrt[3] - (2*x)/Sqrt[3]]/(2*Sqrt[3]) - ArcTan[1/Sqrt[3] + (2*x)/Sqrt[3]]/(2*Sqrt[3]) - ArcTanh[x]/3 - ArcTanh[x/(1 + x^2)]/6","A",1
47,1,115,138,0.1679763,"\int \frac{1}{-2+x^6} \, dx","IntegrateAlgebraic[(-2 + x^6)^(-1),x]","-\frac{\tanh ^{-1}\left(\frac{2^{5/6} x}{2^{2/3} x^2+2}\right)}{6\ 2^{5/6}}+\frac{\tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2^{5/6} x}{\sqrt{3}}\right)}{2\ 2^{5/6} \sqrt{3}}-\frac{\tan ^{-1}\left(\frac{2^{5/6} x}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)}{2\ 2^{5/6} \sqrt{3}}-\frac{\tanh ^{-1}\left(\frac{x}{\sqrt[6]{2}}\right)}{3\ 2^{5/6}}","\frac{\log \left(x^2-\sqrt[6]{2} x+\sqrt[3]{2}\right)}{12\ 2^{5/6}}-\frac{\log \left(x^2+\sqrt[6]{2} x+\sqrt[3]{2}\right)}{12\ 2^{5/6}}+\frac{\tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2^{5/6} x}{\sqrt{3}}\right)}{2\ 2^{5/6} \sqrt{3}}-\frac{\tan ^{-1}\left(\frac{2^{5/6} x}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)}{2\ 2^{5/6} \sqrt{3}}-\frac{\tanh ^{-1}\left(\frac{x}{\sqrt[6]{2}}\right)}{3\ 2^{5/6}}",1,"ArcTan[1/Sqrt[3] - (2^(5/6)*x)/Sqrt[3]]/(2*2^(5/6)*Sqrt[3]) - ArcTan[1/Sqrt[3] + (2^(5/6)*x)/Sqrt[3]]/(2*2^(5/6)*Sqrt[3]) - ArcTanh[x/2^(1/6)]/(3*2^(5/6)) - ArcTanh[(2^(5/6)*x)/(2 + 2^(2/3)*x^2)]/(6*2^(5/6))","A",1
48,1,89,138,0.1298339,"\int \frac{1}{2+x^6} \, dx","IntegrateAlgebraic[(2 + x^6)^(-1),x]","\frac{\tan ^{-1}\left(\frac{\frac{x^2}{\sqrt[6]{2}}-\sqrt[6]{2}}{x}\right)}{6\ 2^{5/6}}+\frac{\tanh ^{-1}\left(\frac{2^{5/6} \sqrt{3} x}{2^{2/3} x^2+2}\right)}{2\ 2^{5/6} \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{x}{\sqrt[6]{2}}\right)}{3\ 2^{5/6}}","-\frac{\log \left(x^2-\sqrt[6]{2} \sqrt{3} x+\sqrt[3]{2}\right)}{4\ 2^{5/6} \sqrt{3}}+\frac{\log \left(x^2+\sqrt[6]{2} \sqrt{3} x+\sqrt[3]{2}\right)}{4\ 2^{5/6} \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{x}{\sqrt[6]{2}}\right)}{3\ 2^{5/6}}-\frac{\tan ^{-1}\left(\sqrt{3}-2^{5/6} x\right)}{6\ 2^{5/6}}+\frac{\tan ^{-1}\left(2^{5/6} x+\sqrt{3}\right)}{6\ 2^{5/6}}",1,"ArcTan[x/2^(1/6)]/(3*2^(5/6)) + ArcTan[(-2^(1/6) + x^2/2^(1/6))/x]/(6*2^(5/6)) + ArcTanh[(2^(5/6)*Sqrt[3]*x)/(2 + 2^(2/3)*x^2)]/(2*2^(5/6)*Sqrt[3])","A",1
49,1,181,339,0.2062898,"\int \frac{1}{1+x^8} \, dx","IntegrateAlgebraic[(1 + x^8)^(-1),x]","\frac{1}{8} \sqrt{2+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{1-\frac{1}{\sqrt{2}}} x^2-\sqrt{1-\frac{1}{\sqrt{2}}}}{x}\right)+\frac{1}{8} \sqrt{2-\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{1+\frac{1}{\sqrt{2}}} x^2-\sqrt{1+\frac{1}{\sqrt{2}}}}{x}\right)+\frac{1}{8} \sqrt{2-\sqrt{2}} \tanh ^{-1}\left(\frac{\sqrt{2-\sqrt{2}} x}{x^2+1}\right)+\frac{1}{8} \sqrt{2+\sqrt{2}} \tanh ^{-1}\left(\frac{\sqrt{2+\sqrt{2}} x}{x^2+1}\right)","-\frac{1}{16} \sqrt{2-\sqrt{2}} \log \left(x^2-\sqrt{2-\sqrt{2}} x+1\right)+\frac{1}{16} \sqrt{2-\sqrt{2}} \log \left(x^2+\sqrt{2-\sqrt{2}} x+1\right)-\frac{1}{16} \sqrt{2+\sqrt{2}} \log \left(x^2-\sqrt{2+\sqrt{2}} x+1\right)+\frac{1}{16} \sqrt{2+\sqrt{2}} \log \left(x^2+\sqrt{2+\sqrt{2}} x+1\right)-\frac{\tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}}-2 x}{\sqrt{2+\sqrt{2}}}\right)}{4 \sqrt{2 \left(2-\sqrt{2}\right)}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}}-2 x}{\sqrt{2-\sqrt{2}}}\right)}{4 \sqrt{2 \left(2+\sqrt{2}\right)}}+\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2-\sqrt{2}}}{\sqrt{2+\sqrt{2}}}\right)}{4 \sqrt{2 \left(2-\sqrt{2}\right)}}+\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2+\sqrt{2}}}{\sqrt{2-\sqrt{2}}}\right)}{4 \sqrt{2 \left(2+\sqrt{2}\right)}}",1,"(Sqrt[2 + Sqrt[2]]*ArcTan[(-Sqrt[1 - 1/Sqrt[2]] + Sqrt[1 - 1/Sqrt[2]]*x^2)/x])/8 + (Sqrt[2 - Sqrt[2]]*ArcTan[(-Sqrt[1 + 1/Sqrt[2]] + Sqrt[1 + 1/Sqrt[2]]*x^2)/x])/8 + (Sqrt[2 - Sqrt[2]]*ArcTanh[(Sqrt[2 - Sqrt[2]]*x)/(1 + x^2)])/8 + (Sqrt[2 + Sqrt[2]]*ArcTanh[(Sqrt[2 + Sqrt[2]]*x)/(1 + x^2)])/8","A",1
50,1,68,97,0.0459508,"\int \frac{1}{-1+x^8} \, dx","IntegrateAlgebraic[(-1 + x^8)^(-1),x]","-\frac{\tan ^{-1}\left(\frac{\frac{x^2}{\sqrt{2}}-\frac{1}{\sqrt{2}}}{x}\right)}{4 \sqrt{2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x}{x^2+1}\right)}{4 \sqrt{2}}-\frac{1}{4} \tan ^{-1}(x)-\frac{1}{4} \tanh ^{-1}(x)","\frac{\log \left(x^2-\sqrt{2} x+1\right)}{8 \sqrt{2}}-\frac{\log \left(x^2+\sqrt{2} x+1\right)}{8 \sqrt{2}}-\frac{1}{4} \tan ^{-1}(x)+\frac{\tan ^{-1}\left(1-\sqrt{2} x\right)}{4 \sqrt{2}}-\frac{\tan ^{-1}\left(\sqrt{2} x+1\right)}{4 \sqrt{2}}-\frac{1}{4} \tanh ^{-1}(x)",1,"-1/4*ArcTan[x] - ArcTan[(-(1/Sqrt[2]) + x^2/Sqrt[2])/x]/(4*Sqrt[2]) - ArcTanh[x]/4 - ArcTanh[(Sqrt[2]*x)/(1 + x^2)]/(4*Sqrt[2])","A",1
51,1,42,275,0.0167674,"\int \frac{1}{1-x^4+x^8} \, dx","IntegrateAlgebraic[(1 - x^4 + x^8)^(-1),x]","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-\text{$\#$1}^4+1\&,\frac{\log (x-\text{$\#$1})}{2 \text{$\#$1}^7-\text{$\#$1}^3}\&\right]","-\frac{\log \left(x^2-\sqrt{2-\sqrt{3}} x+1\right)}{4 \sqrt{6}}+\frac{\log \left(x^2+\sqrt{2-\sqrt{3}} x+1\right)}{4 \sqrt{6}}-\frac{\log \left(x^2-\sqrt{2+\sqrt{3}} x+1\right)}{4 \sqrt{6}}+\frac{\log \left(x^2+\sqrt{2+\sqrt{3}} x+1\right)}{4 \sqrt{6}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2-\sqrt{3}}-2 x}{\sqrt{2+\sqrt{3}}}\right)}{2 \sqrt{6}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2+\sqrt{3}}-2 x}{\sqrt{2-\sqrt{3}}}\right)}{2 \sqrt{6}}+\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2-\sqrt{3}}}{\sqrt{2+\sqrt{3}}}\right)}{2 \sqrt{6}}+\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2+\sqrt{3}}}{\sqrt{2-\sqrt{3}}}\right)}{2 \sqrt{6}}",1,"RootSum[1 - #1^4 + #1^8 & , Log[x - #1]/(-#1^3 + 2*#1^7) & ]/4","C",1
52,1,169,49,0.2219834,"\int \frac{x^7}{1+x^{12}} \, dx","IntegrateAlgebraic[x^7/(1 + x^12),x]","-\frac{\tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 x^4}{\sqrt{3}}\right)}{4 \sqrt{3}}+\frac{1}{24} \log \left(-2 x^2+\sqrt{6} x-\sqrt{2} x-2\right)+\frac{1}{24} \log \left(-2 x^2+\sqrt{6} x+\sqrt{2} x-2\right)-\frac{1}{12} \log \left(-x^2+\sqrt{2} x-1\right)-\frac{1}{12} \log \left(x^2+\sqrt{2} x+1\right)+\frac{1}{24} \log \left(2 x^2+\sqrt{6} x-\sqrt{2} x+2\right)+\frac{1}{24} \log \left(2 x^2+\sqrt{6} x+\sqrt{2} x+2\right)","-\frac{1}{12} \log \left(x^4+1\right)-\frac{\tan ^{-1}\left(\frac{1-2 x^4}{\sqrt{3}}\right)}{4 \sqrt{3}}+\frac{1}{24} \log \left(x^8-x^4+1\right)",1,"-1/4*ArcTan[1/Sqrt[3] - (2*x^4)/Sqrt[3]]/Sqrt[3] + Log[-2 - Sqrt[2]*x + Sqrt[6]*x - 2*x^2]/24 + Log[-2 + Sqrt[2]*x + Sqrt[6]*x - 2*x^2]/24 - Log[-1 + Sqrt[2]*x - x^2]/12 - Log[1 + Sqrt[2]*x + x^2]/12 + Log[2 - Sqrt[2]*x + Sqrt[6]*x + 2*x^2]/24 + Log[2 + Sqrt[2]*x + Sqrt[6]*x + 2*x^2]/24","B",1
53,0,0,8,0.0000282,"\int \log (x) \, dx","IntegrateAlgebraic[Log[x],x]","\int \log (x) \, dx","x \log (x)-x",1,"Could not integrate","F",-1
54,0,0,17,0.00003,"\int x \log (x) \, dx","IntegrateAlgebraic[x*Log[x],x]","\int x \log (x) \, dx","\frac{1}{2} x^2 \log (x)-\frac{x^2}{4}",1,"Could not integrate","F",-1
55,0,0,17,0.0000285,"\int x^2 \log (x) \, dx","IntegrateAlgebraic[x^2*Log[x],x]","\int x^2 \log (x) \, dx","\frac{1}{3} x^3 \log (x)-\frac{x^3}{9}",1,"Could not integrate","F",-1
56,0,0,26,0.0000293,"\int x^p \log (x) \, dx","IntegrateAlgebraic[x^p*Log[x],x]","\int x^p \log (x) \, dx","\frac{x^{p+1} \log (x)}{p+1}-\frac{x^{p+1}}{(p+1)^2}",1,"Could not integrate","F",-1
57,0,0,15,0.0000265,"\int \log ^2(x) \, dx","IntegrateAlgebraic[Log[x]^2,x]","\int \log ^2(x) \, dx","2 x+x \log ^2(x)-2 x \log (x)",1,"Could not integrate","F",-1
58,0,0,127,0.0000304,"\int x^9 \log ^{11}(x) \, dx","IntegrateAlgebraic[x^9*Log[x]^11,x]","\int x^9 \log ^{11}(x) \, dx","-\frac{6237 x^{10}}{156250000}+\frac{1}{10} x^{10} \log ^{11}(x)-\frac{11}{100} x^{10} \log ^{10}(x)+\frac{11}{100} x^{10} \log ^9(x)-\frac{99 x^{10} \log ^8(x)}{1000}+\frac{99 x^{10} \log ^7(x)}{1250}-\frac{693 x^{10} \log ^6(x)}{12500}+\frac{2079 x^{10} \log ^5(x)}{62500}-\frac{2079 x^{10} \log ^4(x)}{125000}+\frac{2079 x^{10} \log ^3(x)}{312500}-\frac{6237 x^{10} \log ^2(x)}{3125000}+\frac{6237 x^{10} \log (x)}{15625000}",1,"Could not integrate","F",-1
59,0,0,8,0.0000343,"\int \frac{\log ^2(x)}{x} \, dx","IntegrateAlgebraic[Log[x]^2/x,x]","\int \frac{\log ^2(x)}{x} \, dx","\frac{\log ^3(x)}{3}",1,"Could not integrate","F",-1
60,0,0,2,0.0000269,"\int \frac{1}{\log (x)} \, dx","IntegrateAlgebraic[Log[x]^(-1),x]","\int \frac{1}{\log (x)} \, dx","\text{li}(x)",1,"Could not integrate","F",-1
61,0,0,4,0.0000373,"\int \frac{1}{\log (1+x)} \, dx","IntegrateAlgebraic[Log[1 + x]^(-1),x]","\int \frac{1}{\log (1+x)} \, dx","\text{li}(x+1)",1,"Could not integrate","F",-1
62,0,0,3,0.0000382,"\int \frac{1}{x \log (x)} \, dx","IntegrateAlgebraic[1/(x*Log[x]),x]","\int \frac{1}{x \log (x)} \, dx","\log (\log (x))",1,"Could not integrate","F",-1
63,0,0,17,0.0000292,"\int \frac{1}{x^2 \log ^2(x)} \, dx","IntegrateAlgebraic[1/(x^2*Log[x]^2),x]","\int \frac{1}{x^2 \log ^2(x)} \, dx","-\text{Ei}(-\log (x))-\frac{1}{x \log (x)}",1,"Could not integrate","F",-1
64,0,0,12,0.0000362,"\int \frac{\log ^p(x)}{x} \, dx","IntegrateAlgebraic[Log[x]^p/x,x]","\int \frac{\log ^p(x)}{x} \, dx","\frac{\log ^{p+1}(x)}{p+1}",1,"Could not integrate","F",-1
65,0,0,28,0.0000317,"\int (b+a x) \log (x) \, dx","IntegrateAlgebraic[(b + a*x)*Log[x],x]","\int (b+a x) \log (x) \, dx","-\frac{a x^2}{4}+\frac{1}{2} a x^2 \log (x)-b x+b x \log (x)",1,"Could not integrate","F",-1
66,0,0,54,0.0000355,"\int (b+a x)^2 \log (x) \, dx","IntegrateAlgebraic[(b + a*x)^2*Log[x],x]","\int (b+a x)^2 \log (x) \, dx","-\frac{a^2 x^3}{9}-\frac{b^3 \log (x)}{3 a}-\frac{1}{2} a b x^2+\frac{\log (x) (a x+b)^3}{3 a}-b^2 x",1,"Could not integrate","F",-1
67,0,0,29,0.0000326,"\int \frac{\log (x)}{(b+a x)^2} \, dx","IntegrateAlgebraic[Log[x]/(b + a*x)^2,x]","\int \frac{\log (x)}{(b+a x)^2} \, dx","\frac{x \log (x)}{b (a x+b)}-\frac{\log (a x+b)}{a b}",1,"Could not integrate","F",-1
68,0,0,46,0.0000315,"\int x \log (b+a x) \, dx","IntegrateAlgebraic[x*Log[b + a*x],x]","\int x \log (b+a x) \, dx","-\frac{b^2 \log (a x+b)}{2 a^2}+\frac{1}{2} x^2 \log (a x+b)+\frac{b x}{2 a}-\frac{x^2}{4}",1,"Could not integrate","F",-1
69,0,0,59,0.0000343,"\int x^2 \log (b+a x) \, dx","IntegrateAlgebraic[x^2*Log[b + a*x],x]","\int x^2 \log (b+a x) \, dx","\frac{b^3 \log (a x+b)}{3 a^3}-\frac{b^2 x}{3 a^2}+\frac{1}{3} x^3 \log (a x+b)+\frac{b x^2}{6 a}-\frac{x^3}{9}",1,"Could not integrate","F",-1
70,0,0,23,0.0000307,"\int \log \left(a^2+x^2\right) \, dx","IntegrateAlgebraic[Log[a^2 + x^2],x]","\int \log \left(a^2+x^2\right) \, dx","x \log \left(a^2+x^2\right)+2 a \tan ^{-1}\left(\frac{x}{a}\right)-2 x",1,"Could not integrate","F",-1
71,0,0,27,0.0000317,"\int x \log \left(a^2+x^2\right) \, dx","IntegrateAlgebraic[x*Log[a^2 + x^2],x]","\int x \log \left(a^2+x^2\right) \, dx","\frac{1}{2} \left(a^2+x^2\right) \log \left(a^2+x^2\right)-\frac{x^2}{2}",1,"Could not integrate","F",-1
72,0,0,44,0.0000341,"\int x^2 \log \left(a^2+x^2\right) \, dx","IntegrateAlgebraic[x^2*Log[a^2 + x^2],x]","\int x^2 \log \left(a^2+x^2\right) \, dx","-\frac{2}{3} a^3 \tan ^{-1}\left(\frac{x}{a}\right)+\frac{1}{3} x^3 \log \left(a^2+x^2\right)+\frac{2 a^2 x}{3}-\frac{2 x^3}{9}",1,"Could not integrate","F",-1
73,0,0,54,0.0000341,"\int x^4 \log \left(a^2+x^2\right) \, dx","IntegrateAlgebraic[x^4*Log[a^2 + x^2],x]","\int x^4 \log \left(a^2+x^2\right) \, dx","\frac{2}{5} a^5 \tan ^{-1}\left(\frac{x}{a}\right)-\frac{2 a^4 x}{5}+\frac{2 a^2 x^3}{15}+\frac{1}{5} x^5 \log \left(a^2+x^2\right)-\frac{2 x^5}{25}",1,"Could not integrate","F",-1
74,0,0,25,0.0000324,"\int \log \left(-a^2+x^2\right) \, dx","IntegrateAlgebraic[Log[-a^2 + x^2],x]","\int \log \left(-a^2+x^2\right) \, dx","x \log \left(x^2-a^2\right)+2 a \tanh ^{-1}\left(\frac{x}{a}\right)-2 x",1,"Could not integrate","F",-1
75,0,0,8,0.0000312,"\int \log (\log (\log (\log (x)))) \, dx","IntegrateAlgebraic[Log[Log[Log[Log[x]]]],x]","\int \log (\log (\log (\log (x)))) \, dx","\text{Int}(\log (\log (\log (\log (x)))),x)",1,"Could not integrate","F",-1
76,0,0,4,0.0000291,"\int \sin (x) \, dx","IntegrateAlgebraic[Sin[x],x]","\int \sin (x) \, dx","-\cos (x)",1,"Could not integrate","F",-1
77,0,0,2,0.0000249,"\int \cos (x) \, dx","IntegrateAlgebraic[Cos[x],x]","\int \cos (x) \, dx","\sin (x)",1,"Could not integrate","F",-1
78,0,0,5,0.0000239,"\int \tan (x) \, dx","IntegrateAlgebraic[Tan[x],x]","\int \tan (x) \, dx","-\log (\cos (x))",1,"Could not integrate","F",-1
79,0,0,3,0.0000229,"\int \cot (x) \, dx","IntegrateAlgebraic[Cot[x],x]","\int \cot (x) \, dx","\log (\sin (x))",1,"Could not integrate","F",-1
80,0,0,21,0.0000259,"\int \frac{1}{(1+\tan (x))^2} \, dx","IntegrateAlgebraic[(1 + Tan[x])^(-2),x]","\int \frac{1}{(1+\tan (x))^2} \, dx","\frac{1}{2} \log (\sin (x)+\cos (x))-\frac{1}{2 (\tan (x)+1)}",1,"Could not integrate","F",-1
81,0,0,3,0.0000246,"\int \sec (x) \, dx","IntegrateAlgebraic[Sec[x],x]","\int \sec (x) \, dx","\tanh ^{-1}(\sin (x))",1,"Could not integrate","F",-1
82,0,0,5,0.0000244,"\int \csc (x) \, dx","IntegrateAlgebraic[Csc[x],x]","\int \csc (x) \, dx","-\tanh ^{-1}(\cos (x))",1,"Could not integrate","F",-1
83,0,0,14,0.0000239,"\int \sin ^2(x) \, dx","IntegrateAlgebraic[Sin[x]^2,x]","\int \sin ^2(x) \, dx","\frac{x}{2}-\frac{1}{2} \sin (x) \cos (x)",1,"Could not integrate","F",-1
84,0,0,20,0.0000544,"\int x^3 \sin \left(x^2\right) \, dx","IntegrateAlgebraic[x^3*Sin[x^2],x]","\int x^3 \sin \left(x^2\right) \, dx","\frac{\sin \left(x^2\right)}{2}-\frac{1}{2} x^2 \cos \left(x^2\right)",1,"Could not integrate","F",-1
85,0,0,13,0.0000284,"\int \sin ^3(x) \, dx","IntegrateAlgebraic[Sin[x]^3,x]","\int \sin ^3(x) \, dx","\frac{\cos ^3(x)}{3}-\cos (x)",1,"Could not integrate","F",-1
86,0,0,44,0.0000258,"\int \sin ^p(x) \, dx","IntegrateAlgebraic[Sin[x]^p,x]","\int \sin ^p(x) \, dx","\frac{\cos (x) \sin ^{p+1}(x) \, _2F_1\left(\frac{1}{2},\frac{p+1}{2};\frac{p+3}{2};\sin ^2(x)\right)}{(p+1) \sqrt{\cos ^2(x)}}",1,"Could not integrate","F",-1
87,0,0,19,0.0000386,"\int \cos (x) \left(1+\sin ^2(x)\right)^2 \, dx","IntegrateAlgebraic[Cos[x]*(1 + Sin[x]^2)^2,x]","\int \cos (x) \left(1+\sin ^2(x)\right)^2 \, dx","\frac{\sin ^5(x)}{5}+\frac{2 \sin ^3(x)}{3}+\sin (x)",1,"Could not integrate","F",-1
88,0,0,14,0.0000291,"\int \cos ^2(x) \, dx","IntegrateAlgebraic[Cos[x]^2,x]","\int \cos ^2(x) \, dx","\frac{x}{2}+\frac{1}{2} \sin (x) \cos (x)",1,"Could not integrate","F",-1
89,0,0,11,0.0000252,"\int \cos ^3(x) \, dx","IntegrateAlgebraic[Cos[x]^3,x]","\int \cos ^3(x) \, dx","\sin (x)-\frac{\sin ^3(x)}{3}",1,"Could not integrate","F",-1
90,0,0,2,0.0000251,"\int \sec ^2(x) \, dx","IntegrateAlgebraic[Sec[x]^2,x]","\int \sec ^2(x) \, dx","\tan (x)",1,"Could not integrate","F",-1
91,0,0,15,0.0000281,"\int \sin (x) \sin (2 x) \, dx","IntegrateAlgebraic[Sin[x]*Sin[2*x],x]","\int \sin (x) \sin (2 x) \, dx","\frac{\sin (x)}{2}-\frac{1}{6} \sin (3 x)",1,"Could not integrate","F",-1
92,0,0,8,0.0000277,"\int x \sin (x) \, dx","IntegrateAlgebraic[x*Sin[x],x]","\int x \sin (x) \, dx","\sin (x)-x \cos (x)",1,"Could not integrate","F",-1
93,0,0,17,0.0000302,"\int x^2 \sin (x) \, dx","IntegrateAlgebraic[x^2*Sin[x],x]","\int x^2 \sin (x) \, dx","x^2 (-\cos (x))+2 x \sin (x)+2 \cos (x)",1,"Could not integrate","F",-1
94,0,0,25,0.0000292,"\int x \sin ^2(x) \, dx","IntegrateAlgebraic[x*Sin[x]^2,x]","\int x \sin ^2(x) \, dx","\frac{x^2}{4}+\frac{\sin ^2(x)}{4}-\frac{1}{2} x \sin (x) \cos (x)",1,"Could not integrate","F",-1
95,0,0,41,0.0000293,"\int x^2 \sin ^2(x) \, dx","IntegrateAlgebraic[x^2*Sin[x]^2,x]","\int x^2 \sin ^2(x) \, dx","\frac{x^3}{6}-\frac{1}{2} x^2 \sin (x) \cos (x)-\frac{x}{4}+\frac{1}{2} x \sin ^2(x)+\frac{1}{4} \sin (x) \cos (x)",1,"Could not integrate","F",-1
96,0,0,33,0.0001142,"\int x \sin ^3(x) \, dx","IntegrateAlgebraic[x*Sin[x]^3,x]","\int x \sin ^3(x) \, dx","\frac{\sin ^3(x)}{9}+\frac{2 \sin (x)}{3}-\frac{2}{3} x \cos (x)-\frac{1}{3} x \sin ^2(x) \cos (x)",1,"Could not integrate","F",-1
97,0,0,7,0.0000288,"\int x \cos (x) \, dx","IntegrateAlgebraic[x*Cos[x],x]","\int x \cos (x) \, dx","x \sin (x)+\cos (x)",1,"Could not integrate","F",-1
98,0,0,16,0.0000337,"\int x^2 \cos (x) \, dx","IntegrateAlgebraic[x^2*Cos[x],x]","\int x^2 \cos (x) \, dx","x^2 \sin (x)-2 \sin (x)+2 x \cos (x)",1,"Could not integrate","F",-1
99,0,0,25,0.0000317,"\int x \cos ^2(x) \, dx","IntegrateAlgebraic[x*Cos[x]^2,x]","\int x \cos ^2(x) \, dx","\frac{x^2}{4}+\frac{\cos ^2(x)}{4}+\frac{1}{2} x \sin (x) \cos (x)",1,"Could not integrate","F",-1
100,0,0,41,0.0000298,"\int x^2 \cos ^2(x) \, dx","IntegrateAlgebraic[x^2*Cos[x]^2,x]","\int x^2 \cos ^2(x) \, dx","\frac{x^3}{6}+\frac{1}{2} x^2 \sin (x) \cos (x)-\frac{x}{4}+\frac{1}{2} x \cos ^2(x)-\frac{1}{4} \sin (x) \cos (x)",1,"Could not integrate","F",-1
101,0,0,33,0.0000456,"\int x \cos ^3(x) \, dx","IntegrateAlgebraic[x*Cos[x]^3,x]","\int x \cos ^3(x) \, dx","\frac{2}{3} x \sin (x)+\frac{\cos ^3(x)}{9}+\frac{2 \cos (x)}{3}+\frac{1}{3} x \sin (x) \cos ^2(x)",1,"Could not integrate","F",-1
102,0,0,2,0.00003,"\int \frac{\sin (x)}{x} \, dx","IntegrateAlgebraic[Sin[x]/x,x]","\int \frac{\sin (x)}{x} \, dx","\text{Si}(x)",1,"Could not integrate","F",-1
103,0,0,2,0.0000359,"\int \frac{\cos (x)}{x} \, dx","IntegrateAlgebraic[Cos[x]/x,x]","\int \frac{\cos (x)}{x} \, dx","\text{Ci}(x)",1,"Could not integrate","F",-1
104,0,0,10,0.0000357,"\int \frac{\sin (x)}{x^2} \, dx","IntegrateAlgebraic[Sin[x]/x^2,x]","\int \frac{\sin (x)}{x^2} \, dx","\text{Ci}(x)-\frac{\sin (x)}{x}",1,"Could not integrate","F",-1
105,0,0,15,0.0000357,"\int \frac{\sin ^2(x)}{x} \, dx","IntegrateAlgebraic[Sin[x]^2/x,x]","\int \frac{\sin ^2(x)}{x} \, dx","\frac{\log (x)}{2}-\frac{\text{Ci}(2 x)}{2}",1,"Could not integrate","F",-1
106,0,0,12,0.0000332,"\int \tan ^3(x) \, dx","IntegrateAlgebraic[Tan[x]^3,x]","\int \tan ^3(x) \, dx","\frac{\tan ^2(x)}{2}+\log (\cos (x))",1,"Could not integrate","F",-1
107,0,0,11,0.0000278,"\int \sin (a+b x) \, dx","IntegrateAlgebraic[Sin[a + b*x],x]","\int \sin (a+b x) \, dx","-\frac{\cos (a+b x)}{b}",1,"Could not integrate","F",-1
108,0,0,10,0.0000271,"\int \cos (a+b x) \, dx","IntegrateAlgebraic[Cos[a + b*x],x]","\int \cos (a+b x) \, dx","\frac{\sin (a+b x)}{b}",1,"Could not integrate","F",-1
109,0,0,12,0.0000269,"\int \tan (a+b x) \, dx","IntegrateAlgebraic[Tan[a + b*x],x]","\int \tan (a+b x) \, dx","-\frac{\log (\cos (a+b x))}{b}",1,"Could not integrate","F",-1
110,0,0,11,0.0000271,"\int \cot (a+b x) \, dx","IntegrateAlgebraic[Cot[a + b*x],x]","\int \cot (a+b x) \, dx","\frac{\log (\sin (a+b x))}{b}",1,"Could not integrate","F",-1
111,0,0,12,0.0000271,"\int \csc (a+b x) \, dx","IntegrateAlgebraic[Csc[a + b*x],x]","\int \csc (a+b x) \, dx","-\frac{\tanh ^{-1}(\cos (a+b x))}{b}",1,"Could not integrate","F",-1
112,0,0,11,0.0000307,"\int \sec (a+b x) \, dx","IntegrateAlgebraic[Sec[a + b*x],x]","\int \sec (a+b x) \, dx","\frac{\tanh ^{-1}(\sin (a+b x))}{b}",1,"Could not integrate","F",-1
113,0,0,25,0.0000299,"\int \sin ^2(a+b x) \, dx","IntegrateAlgebraic[Sin[a + b*x]^2,x]","\int \sin ^2(a+b x) \, dx","\frac{x}{2}-\frac{\sin (a+b x) \cos (a+b x)}{2 b}",1,"Could not integrate","F",-1
114,0,0,27,0.0000307,"\int \sin ^3(a+b x) \, dx","IntegrateAlgebraic[Sin[a + b*x]^3,x]","\int \sin ^3(a+b x) \, dx","\frac{\cos ^3(a+b x)}{3 b}-\frac{\cos (a+b x)}{b}",1,"Could not integrate","F",-1
115,0,0,25,0.0000305,"\int \cos ^2(a+b x) \, dx","IntegrateAlgebraic[Cos[a + b*x]^2,x]","\int \cos ^2(a+b x) \, dx","\frac{\sin (a+b x) \cos (a+b x)}{2 b}+\frac{x}{2}",1,"Could not integrate","F",-1
116,0,0,26,0.0000324,"\int \cos ^3(a+b x) \, dx","IntegrateAlgebraic[Cos[a + b*x]^3,x]","\int \cos ^3(a+b x) \, dx","\frac{\sin (a+b x)}{b}-\frac{\sin ^3(a+b x)}{3 b}",1,"Could not integrate","F",-1
117,0,0,10,0.0000298,"\int \sec ^2(a+b x) \, dx","IntegrateAlgebraic[Sec[a + b*x]^2,x]","\int \sec ^2(a+b x) \, dx","\frac{\tan (a+b x)}{b}",1,"Could not integrate","F",-1
118,0,0,9,0.0000261,"\int \frac{1}{1+\cos (x)} \, dx","IntegrateAlgebraic[(1 + Cos[x])^(-1),x]","\int \frac{1}{1+\cos (x)} \, dx","\frac{\sin (x)}{\cos (x)+1}",1,"Could not integrate","F",-1
119,0,0,12,0.0000268,"\int \frac{1}{1-\cos (x)} \, dx","IntegrateAlgebraic[(1 - Cos[x])^(-1),x]","\int \frac{1}{1-\cos (x)} \, dx","-\frac{\sin (x)}{1-\cos (x)}",1,"Could not integrate","F",-1
120,0,0,10,0.0000276,"\int \frac{1}{1+\sin (x)} \, dx","IntegrateAlgebraic[(1 + Sin[x])^(-1),x]","\int \frac{1}{1+\sin (x)} \, dx","-\frac{\cos (x)}{\sin (x)+1}",1,"Could not integrate","F",-1
121,0,0,11,0.0000267,"\int \frac{1}{1-\sin (x)} \, dx","IntegrateAlgebraic[(1 - Sin[x])^(-1),x]","\int \frac{1}{1-\sin (x)} \, dx","\frac{\cos (x)}{1-\sin (x)}",1,"Could not integrate","F",-1
122,0,0,40,0.0000509,"\int \frac{1}{a+b \sin (x)} \, dx","IntegrateAlgebraic[(a + b*Sin[x])^(-1),x]","\int \frac{1}{a+b \sin (x)} \, dx","\frac{2 \tan ^{-1}\left(\frac{a \tan \left(\frac{x}{2}\right)+b}{\sqrt{a^2-b^2}}\right)}{\sqrt{a^2-b^2}}",1,"Could not integrate","F",-1
123,0,0,47,0.0000308,"\int \frac{1}{a+\cos (x)+b \sin (x)} \, dx","IntegrateAlgebraic[(a + Cos[x] + b*Sin[x])^(-1),x]","\int \frac{1}{a+\cos (x)+b \sin (x)} \, dx","-\frac{2 \tanh ^{-1}\left(\frac{b-(1-a) \tan \left(\frac{x}{2}\right)}{\sqrt{-a^2+b^2+1}}\right)}{\sqrt{-a^2+b^2+1}}",1,"Could not integrate","F",-1
124,0,0,73,0.0000328,"\int x^2 \sin ^2(a+b x) \, dx","IntegrateAlgebraic[x^2*Sin[a + b*x]^2,x]","\int x^2 \sin ^2(a+b x) \, dx","\frac{\sin (a+b x) \cos (a+b x)}{4 b^3}+\frac{x \sin ^2(a+b x)}{2 b^2}-\frac{x^2 \sin (a+b x) \cos (a+b x)}{2 b}-\frac{x}{4 b^2}+\frac{x^3}{6}",1,"Could not integrate","F",-1
125,0,0,15,0.0000347,"\int \cos (x) \cos (2 x) \, dx","IntegrateAlgebraic[Cos[x]*Cos[2*x],x]","\int \cos (x) \cos (2 x) \, dx","\frac{\sin (x)}{2}+\frac{1}{6} \sin (3 x)",1,"Could not integrate","F",-1
126,0,0,73,0.0000581,"\int x^2 \cos ^2(a+b x) \, dx","IntegrateAlgebraic[x^2*Cos[a + b*x]^2,x]","\int x^2 \cos ^2(a+b x) \, dx","-\frac{\sin (a+b x) \cos (a+b x)}{4 b^3}+\frac{x \cos ^2(a+b x)}{2 b^2}+\frac{x^2 \sin (a+b x) \cos (a+b x)}{2 b}-\frac{x}{4 b^2}+\frac{x^3}{6}",1,"Could not integrate","F",-1
127,0,0,14,0.0000297,"\int \cot ^3(x) \, dx","IntegrateAlgebraic[Cot[x]^3,x]","\int \cot ^3(x) \, dx","-\frac{1}{2} \cot ^2(x)-\log (\sin (x))",1,"Could not integrate","F",-1
128,0,0,104,0.0000553,"\int x^3 \tan ^4(x) \, dx","IntegrateAlgebraic[x^3*Tan[x]^4,x]","\int x^3 \tan ^4(x) \, dx","4 i x \text{Li}_2\left(-e^{2 i x}\right)-2 \text{Li}_3\left(-e^{2 i x}\right)+\frac{x^4}{4}+\frac{4 i x^3}{3}+\frac{1}{3} x^3 \tan ^3(x)-x^3 \tan (x)-\frac{x^2}{2}-4 x^2 \log \left(1+e^{2 i x}\right)-\frac{1}{2} x^2 \tan ^2(x)+x \tan (x)+\log (\cos (x))",1,"Could not integrate","F",-1
129,0,0,153,0.0000362,"\int x^3 \tan ^6(x) \, dx","IntegrateAlgebraic[x^3*Tan[x]^6,x]","\int x^3 \tan ^6(x) \, dx","-\frac{23}{5} i x \text{Li}_2\left(-e^{2 i x}\right)+\frac{23}{10} \text{Li}_3\left(-e^{2 i x}\right)-\frac{x^4}{4}-\frac{23 i x^3}{15}+\frac{1}{5} x^3 \tan ^5(x)-\frac{1}{3} x^3 \tan ^3(x)+x^3 \tan (x)+\frac{19 x^2}{20}+\frac{23}{5} x^2 \log \left(1+e^{2 i x}\right)-\frac{3}{20} x^2 \tan ^4(x)+\frac{4}{5} x^2 \tan ^2(x)+\frac{1}{10} x \tan ^3(x)-\frac{\tan ^2(x)}{20}-\frac{19}{10} x \tan (x)-2 \log (\cos (x))",1,"Could not integrate","F",-1
130,0,0,15,0.0000348,"\int x \tan ^2(x) \, dx","IntegrateAlgebraic[x*Tan[x]^2,x]","\int x \tan ^2(x) \, dx","-\frac{x^2}{2}+x \tan (x)+\log (\cos (x))",1,"Could not integrate","F",-1
131,0,0,15,0.0000313,"\int \cos (3 x) \sin (2 x) \, dx","IntegrateAlgebraic[Cos[3*x]*Sin[2*x],x]","\int \cos (3 x) \sin (2 x) \, dx","\frac{\cos (x)}{2}-\frac{1}{10} \cos (5 x)",1,"Could not integrate","F",-1
132,0,0,24,0.0000343,"\int \cos ^2(x) \sin ^2(x) \, dx","IntegrateAlgebraic[Cos[x]^2*Sin[x]^2,x]","\int \cos ^2(x) \sin ^2(x) \, dx","\frac{x}{8}-\frac{1}{4} \sin (x) \cos ^3(x)+\frac{1}{8} \sin (x) \cos (x)",1,"Could not integrate","F",-1
133,0,0,7,0.0000632,"\int \csc ^2(x) \sec ^2(x) \, dx","IntegrateAlgebraic[Csc[x]^2*Sec[x]^2,x]","\int \csc ^2(x) \sec ^2(x) \, dx","\tan (x)-\cot (x)",1,"Could not integrate","F",-1
134,0,0,32,0.0000466,"\int d^x \sin (x) \, dx","IntegrateAlgebraic[d^x*Sin[x],x]","\int d^x \sin (x) \, dx","\frac{d^x \log (d) \sin (x)}{\log ^2(d)+1}-\frac{d^x \cos (x)}{\log ^2(d)+1}",1,"Could not integrate","F",-1
135,0,0,31,0.0000289,"\int d^x \cos (x) \, dx","IntegrateAlgebraic[d^x*Cos[x],x]","\int d^x \cos (x) \, dx","\frac{d^x \sin (x)}{\log ^2(d)+1}+\frac{d^x \log (d) \cos (x)}{\log ^2(d)+1}",1,"Could not integrate","F",-1
136,0,0,84,0.000031,"\int d^x x \sin (x) \, dx","IntegrateAlgebraic[d^x*x*Sin[x],x]","\int d^x x \sin (x) \, dx","\frac{x d^x \log (d) \sin (x)}{\log ^2(d)+1}-\frac{d^x \log ^2(d) \sin (x)}{\left(\log ^2(d)+1\right)^2}+\frac{d^x \sin (x)}{\left(\log ^2(d)+1\right)^2}-\frac{x d^x \cos (x)}{\log ^2(d)+1}+\frac{2 d^x \log (d) \cos (x)}{\left(\log ^2(d)+1\right)^2}",1,"Could not integrate","F",-1
137,0,0,83,0.0000321,"\int d^x x \cos (x) \, dx","IntegrateAlgebraic[d^x*x*Cos[x],x]","\int d^x x \cos (x) \, dx","\frac{x d^x \sin (x)}{\log ^2(d)+1}-\frac{2 d^x \log (d) \sin (x)}{\left(\log ^2(d)+1\right)^2}+\frac{x d^x \log (d) \cos (x)}{\log ^2(d)+1}-\frac{d^x \log ^2(d) \cos (x)}{\left(\log ^2(d)+1\right)^2}+\frac{d^x \cos (x)}{\left(\log ^2(d)+1\right)^2}",1,"Could not integrate","F",-1
138,0,0,162,0.0000602,"\int d^x x^2 \sin (x) \, dx","IntegrateAlgebraic[d^x*x^2*Sin[x],x]","\int d^x x^2 \sin (x) \, dx","\frac{x^2 d^x \log (d) \sin (x)}{\log ^2(d)+1}-\frac{x^2 d^x \cos (x)}{\log ^2(d)+1}-\frac{2 x d^x \log ^2(d) \sin (x)}{\left(\log ^2(d)+1\right)^2}+\frac{2 x d^x \sin (x)}{\left(\log ^2(d)+1\right)^2}-\frac{6 d^x \log (d) \sin (x)}{\left(\log ^2(d)+1\right)^3}+\frac{2 d^x \log ^3(d) \sin (x)}{\left(\log ^2(d)+1\right)^3}+\frac{4 x d^x \log (d) \cos (x)}{\left(\log ^2(d)+1\right)^2}-\frac{6 d^x \log ^2(d) \cos (x)}{\left(\log ^2(d)+1\right)^3}+\frac{2 d^x \cos (x)}{\left(\log ^2(d)+1\right)^3}",1,"Could not integrate","F",-1
139,0,0,161,0.0000375,"\int d^x x^2 \cos (x) \, dx","IntegrateAlgebraic[d^x*x^2*Cos[x],x]","\int d^x x^2 \cos (x) \, dx","\frac{x^2 d^x \sin (x)}{\log ^2(d)+1}+\frac{x^2 d^x \log (d) \cos (x)}{\log ^2(d)+1}-\frac{4 x d^x \log (d) \sin (x)}{\left(\log ^2(d)+1\right)^2}+\frac{6 d^x \log ^2(d) \sin (x)}{\left(\log ^2(d)+1\right)^3}-\frac{2 d^x \sin (x)}{\left(\log ^2(d)+1\right)^3}-\frac{2 x d^x \log ^2(d) \cos (x)}{\left(\log ^2(d)+1\right)^2}+\frac{2 x d^x \cos (x)}{\left(\log ^2(d)+1\right)^2}-\frac{6 d^x \log (d) \cos (x)}{\left(\log ^2(d)+1\right)^3}+\frac{2 d^x \log ^3(d) \cos (x)}{\left(\log ^2(d)+1\right)^3}",1,"Could not integrate","F",-1
140,0,0,261,0.0000367,"\int d^x x^3 \sin (x) \, dx","IntegrateAlgebraic[d^x*x^3*Sin[x],x]","\int d^x x^3 \sin (x) \, dx","\frac{x^3 d^x \log (d) \sin (x)}{\log ^2(d)+1}-\frac{x^3 d^x \cos (x)}{\log ^2(d)+1}+\frac{3 x^2 d^x \sin (x)}{\left(\log ^2(d)+1\right)^2}-\frac{3 x^2 d^x \log ^2(d) \sin (x)}{\left(\log ^2(d)+1\right)^2}+\frac{6 x^2 d^x \log (d) \cos (x)}{\left(\log ^2(d)+1\right)^2}-\frac{18 x d^x \log (d) \sin (x)}{\left(\log ^2(d)+1\right)^3}+\frac{36 d^x \log ^2(d) \sin (x)}{\left(\log ^2(d)+1\right)^4}-\frac{6 d^x \sin (x)}{\left(\log ^2(d)+1\right)^4}-\frac{6 d^x \log ^4(d) \sin (x)}{\left(\log ^2(d)+1\right)^4}+\frac{6 x d^x \log ^3(d) \sin (x)}{\left(\log ^2(d)+1\right)^3}-\frac{18 x d^x \log ^2(d) \cos (x)}{\left(\log ^2(d)+1\right)^3}+\frac{6 x d^x \cos (x)}{\left(\log ^2(d)+1\right)^3}-\frac{24 d^x \log (d) \cos (x)}{\left(\log ^2(d)+1\right)^4}+\frac{24 d^x \log ^3(d) \cos (x)}{\left(\log ^2(d)+1\right)^4}",1,"Could not integrate","F",-1
141,0,0,260,0.0000385,"\int d^x x^3 \cos (x) \, dx","IntegrateAlgebraic[d^x*x^3*Cos[x],x]","\int d^x x^3 \cos (x) \, dx","\frac{x^3 d^x \sin (x)}{\log ^2(d)+1}+\frac{x^3 d^x \log (d) \cos (x)}{\log ^2(d)+1}-\frac{6 x^2 d^x \log (d) \sin (x)}{\left(\log ^2(d)+1\right)^2}-\frac{3 x^2 d^x \log ^2(d) \cos (x)}{\left(\log ^2(d)+1\right)^2}+\frac{3 x^2 d^x \cos (x)}{\left(\log ^2(d)+1\right)^2}+\frac{18 x d^x \log ^2(d) \sin (x)}{\left(\log ^2(d)+1\right)^3}-\frac{6 x d^x \sin (x)}{\left(\log ^2(d)+1\right)^3}+\frac{24 d^x \log (d) \sin (x)}{\left(\log ^2(d)+1\right)^4}-\frac{24 d^x \log ^3(d) \sin (x)}{\left(\log ^2(d)+1\right)^4}-\frac{18 x d^x \log (d) \cos (x)}{\left(\log ^2(d)+1\right)^3}+\frac{36 d^x \log ^2(d) \cos (x)}{\left(\log ^2(d)+1\right)^4}-\frac{6 d^x \cos (x)}{\left(\log ^2(d)+1\right)^4}-\frac{6 d^x \log ^4(d) \cos (x)}{\left(\log ^2(d)+1\right)^4}+\frac{6 x d^x \log ^3(d) \cos (x)}{\left(\log ^2(d)+1\right)^3}",1,"Could not integrate","F",-1
142,0,0,25,0.0000389,"\int \sin (x) \sin (2 x) \sin (3 x) \, dx","IntegrateAlgebraic[Sin[x]*Sin[2*x]*Sin[3*x],x]","\int \sin (x) \sin (2 x) \sin (3 x) \, dx","-\frac{1}{8} \cos (2 x)-\frac{1}{16} \cos (4 x)+\frac{1}{24} \cos (6 x)",1,"Could not integrate","F",-1
143,0,0,30,0.0000341,"\int \cos (x) \cos (2 x) \cos (3 x) \, dx","IntegrateAlgebraic[Cos[x]*Cos[2*x]*Cos[3*x],x]","\int \cos (x) \cos (2 x) \cos (3 x) \, dx","\frac{x}{4}+\frac{1}{8} \sin (2 x)+\frac{1}{16} \sin (4 x)+\frac{1}{24} \sin (6 x)",1,"Could not integrate","F",-1
144,0,0,85,0.0000297,"\int x^2 \sin ^3(k x) \, dx","IntegrateAlgebraic[x^2*Sin[k*x]^3,x]","\int x^2 \sin ^3(k x) \, dx","-\frac{2 \cos ^3(k x)}{27 k^3}+\frac{14 \cos (k x)}{9 k^3}+\frac{2 x \sin ^3(k x)}{9 k^2}+\frac{4 x \sin (k x)}{3 k^2}-\frac{2 x^2 \cos (k x)}{3 k}-\frac{x^2 \sin ^2(k x) \cos (k x)}{3 k}",1,"Could not integrate","F",-1
145,0,0,14,0.0000364,"\int x \cos (k \csc (x)) \cot (x) \csc (x) \, dx","IntegrateAlgebraic[x*Cos[k*Csc[x]]*Cot[x]*Csc[x],x]","\int x \cos (k \csc (x)) \cot (x) \csc (x) \, dx","\text{Int}(x \cot (x) \csc (x) \cos (k \csc (x)),x)",1,"Could not integrate","F",-1
146,0,0,12,0.0000298,"\int \cot \left(\frac{x}{2}\right) \cot (x) \, dx","IntegrateAlgebraic[Cot[x/2]*Cot[x],x]","\int \cot \left(\frac{x}{2}\right) \cot (x) \, dx","-x-\cot \left(\frac{x}{2}\right)",1,"Could not integrate","F",-1
147,0,0,77,0.0000343,"\int \frac{\sin (a x)}{(b+c \sin (a x))^2} \, dx","IntegrateAlgebraic[Sin[a*x]/(b + c*Sin[a*x])^2,x]","\int \frac{\sin (a x)}{(b+c \sin (a x))^2} \, dx","-\frac{2 c \tan ^{-1}\left(\frac{b \tan \left(\frac{a x}{2}\right)+c}{\sqrt{b^2-c^2}}\right)}{a \left(b^2-c^2\right)^{3/2}}-\frac{b \cos (a x)}{a \left(b^2-c^2\right) (c \sin (a x)+b)}",1,"Could not integrate","F",-1
148,0,0,17,0.0000611,"\int \sin (\log (x)) \, dx","IntegrateAlgebraic[Sin[Log[x]],x]","\int \sin (\log (x)) \, dx","\frac{1}{2} x \sin (\log (x))-\frac{1}{2} x \cos (\log (x))",1,"Could not integrate","F",-1
149,0,0,17,0.0000251,"\int \cos (\log (x)) \, dx","IntegrateAlgebraic[Cos[Log[x]],x]","\int \cos (\log (x)) \, dx","\frac{1}{2} x \sin (\log (x))+\frac{1}{2} x \cos (\log (x))",1,"Could not integrate","F",-1
150,0,0,3,0.0000436,"\int e^x \, dx","IntegrateAlgebraic[E^x,x]","\int e^x \, dx","e^x",1,"Could not integrate","F",-1
151,0,0,8,0.0000447,"\int a^x \, dx","IntegrateAlgebraic[a^x,x]","\int a^x \, dx","\frac{a^x}{\log (a)}",1,"Could not integrate","F",-1
152,0,0,9,0.0000458,"\int e^{a x} \, dx","IntegrateAlgebraic[E^(a*x),x]","\int e^{a x} \, dx","\frac{e^{a x}}{a}",1,"Could not integrate","F",-1
153,0,0,4,0.0000524,"\int \frac{e^{a x}}{x} \, dx","IntegrateAlgebraic[E^(a*x)/x,x]","\int \frac{e^{a x}}{x} \, dx","\text{Ei}(a x)",1,"Could not integrate","F",-1
154,0,0,24,0.0000678,"\int \frac{1}{a+b e^{m x}} \, dx","IntegrateAlgebraic[(a + b*E^(m*x))^(-1),x]","\int \frac{1}{a+b e^{m x}} \, dx","\frac{x}{a}-\frac{\log \left(a+b e^{m x}\right)}{a m}",1,"Could not integrate","F",-1
155,0,0,12,0.0000592,"\int \frac{e^{2 x}}{1+e^x} \, dx","IntegrateAlgebraic[E^(2*x)/(1 + E^x),x]","\int \frac{e^{2 x}}{1+e^x} \, dx","e^x-\log \left(e^x+1\right)",1,"Could not integrate","F",-1
156,0,0,13,0.0000496,"\int e^{2 x+a x} \, dx","IntegrateAlgebraic[E^(2*x + a*x),x]","\int e^{2 x+a x} \, dx","\frac{e^{(a+2) x}}{a+2}",1,"Could not integrate","F",-1
157,0,0,31,0.0000647,"\int \frac{1}{b e^{-m x}+a e^{m x}} \, dx","IntegrateAlgebraic[(b/E^(m*x) + a*E^(m*x))^(-1),x]","\int \frac{1}{b e^{-m x}+a e^{m x}} \, dx","\frac{\tan ^{-1}\left(\frac{\sqrt{a} e^{m x}}{\sqrt{b}}\right)}{\sqrt{a} \sqrt{b} m}",1,"Could not integrate","F",-1
158,0,0,21,0.0000805,"\int e^{a x} x \, dx","IntegrateAlgebraic[E^(a*x)*x,x]","\int e^{a x} x \, dx","\frac{x e^{a x}}{a}-\frac{e^{a x}}{a^2}",1,"Could not integrate","F",-1
159,0,0,163,0.0000525,"\int e^x x^{20} \, dx","IntegrateAlgebraic[E^x*x^20,x]","\int e^x x^{20} \, dx","e^x x^{20}-20 e^x x^{19}+380 e^x x^{18}-6840 e^x x^{17}+116280 e^x x^{16}-1860480 e^x x^{15}+27907200 e^x x^{14}-390700800 e^x x^{13}+5079110400 e^x x^{12}-60949324800 e^x x^{11}+670442572800 e^x x^{10}-6704425728000 e^x x^9+60339831552000 e^x x^8-482718652416000 e^x x^7+3379030566912000 e^x x^6-20274183401472000 e^x x^5+101370917007360000 e^x x^4-405483668029440000 e^x x^3+1216451004088320000 e^x x^2-2432902008176640000 e^x x+2432902008176640000 e^x",1,"Could not integrate","F",-1
160,0,0,18,0.0000619,"\int a^x b^{-x} \, dx","IntegrateAlgebraic[a^x/b^x,x]","\int a^x b^{-x} \, dx","\frac{a^x b^{-x}}{\log (a)-\log (b)}",1,"Could not integrate","F",-1
161,0,0,14,0.0000507,"\int a^x b^x \, dx","IntegrateAlgebraic[a^x*b^x,x]","\int a^x b^x \, dx","\frac{a^x b^x}{\log (a)+\log (b)}",1,"Could not integrate","F",-1
162,0,0,17,0.0000508,"\int \frac{a^x}{x^2} \, dx","IntegrateAlgebraic[a^x/x^2,x]","\int \frac{a^x}{x^2} \, dx","\log (a) \text{Ei}(x \log (a))-\frac{a^x}{x}",1,"Could not integrate","F",-1
163,0,0,64,0.0000643,"\int \frac{a^x x}{(1+b x)^2} \, dx","IntegrateAlgebraic[(a^x*x)/(1 + b*x)^2,x]","\int \frac{a^x x}{(1+b x)^2} \, dx","-\frac{a^{-1/b} \log (a) \text{Ei}\left(\frac{(b x+1) \log (a)}{b}\right)}{b^3}+\frac{a^{-1/b} \text{Ei}\left(\frac{(b x+1) \log (a)}{b}\right)}{b^2}+\frac{a^x}{b^2 (b x+1)}",1,"Could not integrate","F",-1
164,0,0,16,0.000067,"\int \frac{e^{a x} x}{(1+a x)^2} \, dx","IntegrateAlgebraic[(E^(a*x)*x)/(1 + a*x)^2,x]","\int \frac{e^{a x} x}{(1+a x)^2} \, dx","\frac{e^{a x}}{a^2 (a x+1)}",1,"Could not integrate","F",-1
165,0,0,13,0.0000594,"\int k^{x^2} x \, dx","IntegrateAlgebraic[k^x^2*x,x]","\int k^{x^2} x \, dx","\frac{k^{x^2}}{2 \log (k)}",1,"Could not integrate","F",-1
166,0,0,11,0.0000493,"\int e^{x^2} \, dx","IntegrateAlgebraic[E^x^2,x]","\int e^{x^2} \, dx","\frac{1}{2} \sqrt{\pi } \text{erfi}(x)",1,"Could not integrate","F",-1
167,0,0,9,0.0000496,"\int e^{x^2} x \, dx","IntegrateAlgebraic[E^x^2*x,x]","\int e^{x^2} x \, dx","\frac{e^{x^2}}{2}",1,"Could not integrate","F",-1
168,0,0,27,0.0000546,"\int \frac{e^{\frac{1}{x}} (1+x)}{x^4} \, dx","IntegrateAlgebraic[(E^x^(-1)*(1 + x))/x^4,x]","\int \frac{e^{\frac{1}{x}} (1+x)}{x^4} \, dx","-\frac{e^{\frac{1}{x}}}{x^2}-e^{\frac{1}{x}}+\frac{e^{\frac{1}{x}}}{x}",1,"Could not integrate","F",-1
169,0,0,25,0.0000897,"\int \frac{e^{1-e^{x^2} x+2 x^2} \left(x+2 x^3\right)}{\left(1-e^{x^2} x\right)^2} \, dx","IntegrateAlgebraic[(E^(1 - E^x^2*x + 2*x^2)*(x + 2*x^3))/(1 - E^x^2*x)^2,x]","\int \frac{e^{1-e^{x^2} x+2 x^2} \left(x+2 x^3\right)}{\left(1-e^{x^2} x\right)^2} \, dx","-\frac{e^{1-e^{x^2} x}}{e^{x^2} x-1}",1,"Could not integrate","F",-1
170,0,0,12,0.0000566,"\int e^{e^{e^{e^x}}} \, dx","IntegrateAlgebraic[E^E^E^E^x,x]","\int e^{e^{e^{e^x}}} \, dx","\text{Int}\left(e^{e^{e^{e^x}}},x\right)",1,"Could not integrate","F",-1
171,0,0,11,0.0000468,"\int e^x \log (x) \, dx","IntegrateAlgebraic[E^x*Log[x],x]","\int e^x \log (x) \, dx","e^x \log (x)-\text{Ei}(x)",1,"Could not integrate","F",-1
172,0,0,22,0.0000371,"\int e^x x \log (x) \, dx","IntegrateAlgebraic[E^x*x*Log[x],x]","\int e^x x \log (x) \, dx","\text{Ei}(x)-e^x-e^x \log (x)+e^x x \log (x)",1,"Could not integrate","F",-1
173,0,0,23,0.0000385,"\int e^{2 x} \log \left(e^x\right) \, dx","IntegrateAlgebraic[E^(2*x)*Log[E^x],x]","\int e^{2 x} \log \left(e^x\right) \, dx","\frac{1}{2} e^{2 x} \log \left(e^x\right)-\frac{e^{2 x}}{4}",1,"Could not integrate","F",-1
174,1,19,16,0.0050025,"\int \left(2 x+\sqrt{2} x^2\right) \, dx","IntegrateAlgebraic[2*x + Sqrt[2]*x^2,x]","\frac{1}{3} \left(\sqrt{2} x^3+3 x^2\right)","\frac{\sqrt{2} x^3}{3}+x^2",1,"(3*x^2 + Sqrt[2]*x^3)/3","A",1
175,0,0,57,0.0000341,"\int \frac{\log (x)}{\sqrt{b+a x}} \, dx","IntegrateAlgebraic[Log[x]/Sqrt[b + a*x],x]","\int \frac{\log (x)}{\sqrt{b+a x}} \, dx","-\frac{4 \sqrt{a x+b}}{a}+\frac{2 \log (x) \sqrt{a x+b}}{a}+\frac{4 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{a x+b}}{\sqrt{b}}\right)}{a}",1,"Could not integrate","F",-1
176,1,1506,116,5.0110428,"\int \sqrt{a+b x} \sqrt{c+d x} \, dx","IntegrateAlgebraic[Sqrt[a + b*x]*Sqrt[c + d*x],x]","\frac{\left(\frac{\sqrt{a+b}}{4 b d}-\frac{\sqrt{a+b x}}{4 b d}\right) \left(\sqrt{c+d}-\sqrt{c+d x}\right) \left(c b+d b+d x b-\sqrt{c+d} \sqrt{c+d x} b+a d-\sqrt{a+b} d \sqrt{a+b x}\right) \left(2 c^4 b^4+2 c^2 d^2 b^4+16 d^4 x^2 b^4+16 c d^3 x^2 b^4+2 c^2 d^2 x^2 b^4+5 c^3 d b^4+16 c d^3 x b^4+22 c^2 d^2 x b^4+5 c^3 d x b^4-16 c d^2 \sqrt{c+d} x \sqrt{c+d x} b^4-4 c^2 d \sqrt{c+d} x \sqrt{c+d x} b^4-2 c^3 \sqrt{c+d} \sqrt{c+d x} b^4-4 c^2 d \sqrt{c+d} \sqrt{c+d x} b^4+12 a c d^3 b^3+11 a c^2 d^2 b^3+16 a d^4 x^2 b^3+12 a c d^3 x^2 b^3+2 a c^3 d b^3+16 a d^4 x b^3+20 a c d^3 x b^3+11 a c^2 d^2 x b^3+12 \sqrt{a+b} c^2 d^2 \sqrt{a+b x} b^3+10 \sqrt{a+b} c^3 d \sqrt{a+b x} b^3+16 \sqrt{a+b} c d^3 x \sqrt{a+b x} b^3+12 \sqrt{a+b} c^2 d^2 x \sqrt{a+b x} b^3+16 a d^3 \sqrt{c+d} x \sqrt{c+d x} b^3-8 a c d^2 \sqrt{c+d} x \sqrt{c+d x} b^3-8 a c d^2 \sqrt{c+d} \sqrt{c+d x} b^3-2 a c^2 d \sqrt{c+d} \sqrt{c+d x} b^3-16 \sqrt{a+b} d^3 \sqrt{c+d} x \sqrt{a+b x} \sqrt{c+d x} b^3-8 \sqrt{a+b} c d^2 \sqrt{c+d} x \sqrt{a+b x} \sqrt{c+d x} b^3-8 \sqrt{a+b} c d^2 \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x} b^3-10 \sqrt{a+b} c^2 d \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x} b^3+2 a^2 d^4 b^2+11 a^2 c d^3 b^2+8 a^2 c^2 d^2 b^2+2 a^2 d^4 x^2 b^2+22 a^2 d^4 x b^2+11 a^2 c d^3 x b^2-8 a \sqrt{a+b} c d^3 \sqrt{a+b x} b^2-6 a \sqrt{a+b} c^2 d^2 \sqrt{a+b x} b^2-16 a \sqrt{a+b} d^4 x \sqrt{a+b x} b^2-8 a \sqrt{a+b} c d^3 x \sqrt{a+b x} b^2+12 a^2 d^3 \sqrt{c+d} x \sqrt{c+d x} b^2+12 a^2 d^3 \sqrt{c+d} \sqrt{c+d x} b^2-6 a^2 c d^2 \sqrt{c+d} \sqrt{c+d x} b^2-8 a \sqrt{a+b} d^3 \sqrt{c+d} x \sqrt{a+b x} \sqrt{c+d x} b^2-8 a \sqrt{a+b} d^3 \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x} b^2+4 a \sqrt{a+b} c d^2 \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x} b^2+5 a^3 d^4 b+2 a^3 c d^3 b+5 a^3 d^4 x b-4 a^2 \sqrt{a+b} d^4 \sqrt{a+b x} b-2 a^2 \sqrt{a+b} c d^3 \sqrt{a+b x} b-4 a^2 \sqrt{a+b} d^4 x \sqrt{a+b x} b+10 a^3 d^3 \sqrt{c+d} \sqrt{c+d x} b-10 a^2 \sqrt{a+b} d^3 \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x} b+2 a^4 d^4-2 a^3 \sqrt{a+b} d^4 \sqrt{a+b x}\right)}{\left(-c b+\sqrt{c+d} \sqrt{c+d x} b+a d-\sqrt{a+b} d \sqrt{a+b x}\right)^4}-\frac{(b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d}-\sqrt{b} \sqrt{c+d x}}{\sqrt{a+b} \sqrt{d}-\sqrt{d} \sqrt{a+b x}}\right)}{2 b^{3/2} d^{3/2}}","-\frac{(b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{4 b^{3/2} d^{3/2}}+\frac{\sqrt{a+b x} \sqrt{c+d x} (b c-a d)}{4 b d}+\frac{(a+b x)^{3/2} \sqrt{c+d x}}{2 b}",1,"((Sqrt[a + b]/(4*b*d) - Sqrt[a + b*x]/(4*b*d))*(Sqrt[c + d] - Sqrt[c + d*x])*(b*c + a*d + b*d + b*d*x - Sqrt[a + b]*d*Sqrt[a + b*x] - b*Sqrt[c + d]*Sqrt[c + d*x])*(2*b^4*c^4 + 2*a*b^3*c^3*d + 5*b^4*c^3*d + 8*a^2*b^2*c^2*d^2 + 11*a*b^3*c^2*d^2 + 2*b^4*c^2*d^2 + 2*a^3*b*c*d^3 + 11*a^2*b^2*c*d^3 + 12*a*b^3*c*d^3 + 2*a^4*d^4 + 5*a^3*b*d^4 + 2*a^2*b^2*d^4 + 5*b^4*c^3*d*x + 11*a*b^3*c^2*d^2*x + 22*b^4*c^2*d^2*x + 11*a^2*b^2*c*d^3*x + 20*a*b^3*c*d^3*x + 16*b^4*c*d^3*x + 5*a^3*b*d^4*x + 22*a^2*b^2*d^4*x + 16*a*b^3*d^4*x + 2*b^4*c^2*d^2*x^2 + 12*a*b^3*c*d^3*x^2 + 16*b^4*c*d^3*x^2 + 2*a^2*b^2*d^4*x^2 + 16*a*b^3*d^4*x^2 + 16*b^4*d^4*x^2 + 10*b^3*Sqrt[a + b]*c^3*d*Sqrt[a + b*x] - 6*a*b^2*Sqrt[a + b]*c^2*d^2*Sqrt[a + b*x] + 12*b^3*Sqrt[a + b]*c^2*d^2*Sqrt[a + b*x] - 2*a^2*b*Sqrt[a + b]*c*d^3*Sqrt[a + b*x] - 8*a*b^2*Sqrt[a + b]*c*d^3*Sqrt[a + b*x] - 2*a^3*Sqrt[a + b]*d^4*Sqrt[a + b*x] - 4*a^2*b*Sqrt[a + b]*d^4*Sqrt[a + b*x] + 12*b^3*Sqrt[a + b]*c^2*d^2*x*Sqrt[a + b*x] - 8*a*b^2*Sqrt[a + b]*c*d^3*x*Sqrt[a + b*x] + 16*b^3*Sqrt[a + b]*c*d^3*x*Sqrt[a + b*x] - 4*a^2*b*Sqrt[a + b]*d^4*x*Sqrt[a + b*x] - 16*a*b^2*Sqrt[a + b]*d^4*x*Sqrt[a + b*x] - 2*b^4*c^3*Sqrt[c + d]*Sqrt[c + d*x] - 2*a*b^3*c^2*d*Sqrt[c + d]*Sqrt[c + d*x] - 4*b^4*c^2*d*Sqrt[c + d]*Sqrt[c + d*x] - 6*a^2*b^2*c*d^2*Sqrt[c + d]*Sqrt[c + d*x] - 8*a*b^3*c*d^2*Sqrt[c + d]*Sqrt[c + d*x] + 10*a^3*b*d^3*Sqrt[c + d]*Sqrt[c + d*x] + 12*a^2*b^2*d^3*Sqrt[c + d]*Sqrt[c + d*x] - 4*b^4*c^2*d*Sqrt[c + d]*x*Sqrt[c + d*x] - 8*a*b^3*c*d^2*Sqrt[c + d]*x*Sqrt[c + d*x] - 16*b^4*c*d^2*Sqrt[c + d]*x*Sqrt[c + d*x] + 12*a^2*b^2*d^3*Sqrt[c + d]*x*Sqrt[c + d*x] + 16*a*b^3*d^3*Sqrt[c + d]*x*Sqrt[c + d*x] - 10*b^3*Sqrt[a + b]*c^2*d*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 4*a*b^2*Sqrt[a + b]*c*d^2*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] - 8*b^3*Sqrt[a + b]*c*d^2*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] - 10*a^2*b*Sqrt[a + b]*d^3*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] - 8*a*b^2*Sqrt[a + b]*d^3*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] - 8*b^3*Sqrt[a + b]*c*d^2*Sqrt[c + d]*x*Sqrt[a + b*x]*Sqrt[c + d*x] - 8*a*b^2*Sqrt[a + b]*d^3*Sqrt[c + d]*x*Sqrt[a + b*x]*Sqrt[c + d*x] - 16*b^3*Sqrt[a + b]*d^3*Sqrt[c + d]*x*Sqrt[a + b*x]*Sqrt[c + d*x]))/(-(b*c) + a*d - Sqrt[a + b]*d*Sqrt[a + b*x] + b*Sqrt[c + d]*Sqrt[c + d*x])^4 - ((b*c - a*d)^2*ArcTanh[(Sqrt[b]*Sqrt[c + d] - Sqrt[b]*Sqrt[c + d*x])/(Sqrt[a + b]*Sqrt[d] - Sqrt[d]*Sqrt[a + b*x])])/(2*b^(3/2)*d^(3/2))","B",1
177,1,16,16,0.0046254,"\int \sqrt{a+b x} \, dx","IntegrateAlgebraic[Sqrt[a + b*x],x]","\frac{2 (a+b x)^{3/2}}{3 b}","\frac{2 (a+b x)^{3/2}}{3 b}",1,"(2*(a + b*x)^(3/2))/(3*b)","A",1
178,1,35,34,0.0106869,"\int x \sqrt{a+b x} \, dx","IntegrateAlgebraic[x*Sqrt[a + b*x],x]","-\frac{2 \sqrt{a+b x} \left(2 a^2-a b x-3 b^2 x^2\right)}{15 b^2}","\frac{2 (a+b x)^{5/2}}{5 b^2}-\frac{2 a (a+b x)^{3/2}}{3 b^2}",1,"(-2*Sqrt[a + b*x]*(2*a^2 - a*b*x - 3*b^2*x^2))/(15*b^2)","A",1
179,1,46,53,0.0152962,"\int x^2 \sqrt{a+b x} \, dx","IntegrateAlgebraic[x^2*Sqrt[a + b*x],x]","\frac{2 \sqrt{a+b x} \left(8 a^3-4 a^2 b x+3 a b^2 x^2+15 b^3 x^3\right)}{105 b^3}","\frac{2 a^2 (a+b x)^{3/2}}{3 b^3}+\frac{2 (a+b x)^{7/2}}{7 b^3}-\frac{4 a (a+b x)^{5/2}}{5 b^3}",1,"(2*Sqrt[a + b*x]*(8*a^3 - 4*a^2*b*x + 3*a*b^2*x^2 + 15*b^3*x^3))/(105*b^3)","A",1
180,1,35,35,0.0178992,"\int \frac{\sqrt{a+b x}}{x} \, dx","IntegrateAlgebraic[Sqrt[a + b*x]/x,x]","2 \sqrt{a+b x}-2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)","2 \sqrt{a+b x}-2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)",1,"2*Sqrt[a + b*x] - 2*Sqrt[a]*ArcTanh[Sqrt[a + b*x]/Sqrt[a]]","A",1
181,1,39,39,0.0328325,"\int \frac{\sqrt{a+b x}}{x^2} \, dx","IntegrateAlgebraic[Sqrt[a + b*x]/x^2,x]","-\frac{\sqrt{a+b x}}{x}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{\sqrt{a}}","-\frac{\sqrt{a+b x}}{x}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{\sqrt{a}}",1,"-(Sqrt[a + b*x]/x) - (b*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/Sqrt[a]","A",1
182,1,14,14,0.0049427,"\int \frac{1}{\sqrt{a+b x}} \, dx","IntegrateAlgebraic[1/Sqrt[a + b*x],x]","\frac{2 \sqrt{a+b x}}{b}","\frac{2 \sqrt{a+b x}}{b}",1,"(2*Sqrt[a + b*x])/b","A",1
183,1,24,32,0.0099885,"\int \frac{x}{\sqrt{a+b x}} \, dx","IntegrateAlgebraic[x/Sqrt[a + b*x],x]","-\frac{2 (2 a-b x) \sqrt{a+b x}}{3 b^2}","\frac{2 (a+b x)^{3/2}}{3 b^2}-\frac{2 a \sqrt{a+b x}}{b^2}",1,"(-2*(2*a - b*x)*Sqrt[a + b*x])/(3*b^2)","A",1
184,1,35,51,0.012444,"\int \frac{x^2}{\sqrt{a+b x}} \, dx","IntegrateAlgebraic[x^2/Sqrt[a + b*x],x]","\frac{2 \sqrt{a+b x} \left(8 a^2-4 a b x+3 b^2 x^2\right)}{15 b^3}","\frac{2 a^2 \sqrt{a+b x}}{b^3}+\frac{2 (a+b x)^{5/2}}{5 b^3}-\frac{4 a (a+b x)^{3/2}}{3 b^3}",1,"(2*Sqrt[a + b*x]*(8*a^2 - 4*a*b*x + 3*b^2*x^2))/(15*b^3)","A",1
185,1,23,23,0.0124648,"\int \frac{1}{x \sqrt{a+b x}} \, dx","IntegrateAlgebraic[1/(x*Sqrt[a + b*x]),x]","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{\sqrt{a}}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{\sqrt{a}}",1,"(-2*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/Sqrt[a]","A",1
186,1,41,41,0.0327126,"\int \frac{1}{x^2 \sqrt{a+b x}} \, dx","IntegrateAlgebraic[1/(x^2*Sqrt[a + b*x]),x]","\frac{b \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{a^{3/2}}-\frac{\sqrt{a+b x}}{a x}","\frac{b \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{a^{3/2}}-\frac{\sqrt{a+b x}}{a x}",1,"-(Sqrt[a + b*x]/(a*x)) + (b*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/a^(3/2)","A",1
187,0,0,23,0.0000589,"\int (a+b x)^{p/2} \, dx","IntegrateAlgebraic[(a + b*x)^(p/2),x]","\int (a+b x)^{p/2} \, dx","\frac{2 (a+b x)^{\frac{p+2}{2}}}{b (p+2)}",1,"Could not integrate","F",-1
188,0,0,48,0.0000533,"\int x (a+b x)^{p/2} \, dx","IntegrateAlgebraic[x*(a + b*x)^(p/2),x]","\int x (a+b x)^{p/2} \, dx","\frac{2 (a+b x)^{\frac{p+4}{2}}}{b^2 (p+4)}-\frac{2 a (a+b x)^{\frac{p+2}{2}}}{b^2 (p+2)}",1,"Could not integrate","F",-1
189,0,0,55,0.0000397,"\int \tan ^{-1}\left(\frac{-\sqrt{2}+2 x}{\sqrt{2}}\right) \, dx","IntegrateAlgebraic[ArcTan[(-Sqrt[2] + 2*x)/Sqrt[2]],x]","\int \tan ^{-1}\left(\frac{-\sqrt{2}+2 x}{\sqrt{2}}\right) \, dx","-\frac{\log \left(x^2-\sqrt{2} x+1\right)}{2 \sqrt{2}}-x \tan ^{-1}\left(1-\sqrt{2} x\right)+\frac{\tan ^{-1}\left(1-\sqrt{2} x\right)}{\sqrt{2}}",1,"Could not integrate","F",-1
190,1,16,12,0.0214481,"\int \frac{1}{\sqrt{-1+x^2}} \, dx","IntegrateAlgebraic[1/Sqrt[-1 + x^2],x]","-\log \left(\sqrt{x^2-1}-x\right)","\tanh ^{-1}\left(\frac{x}{\sqrt{x^2-1}}\right)",1,"-Log[-x + Sqrt[-1 + x^2]]","A",1
191,1,105,43,0.0710459,"\int \sqrt{x} \sqrt{1+x} \, dx","IntegrateAlgebraic[Sqrt[x]*Sqrt[1 + x],x]","\frac{2 x^{7/2}+\left(11-6 \sqrt{x+1}\right) x^{5/2}+\left(13-11 \sqrt{x+1}\right) x^{3/2}+\left(4-4 \sqrt{x+1}\right) \sqrt{x}}{4 (-3 x-4)+4 \sqrt{x+1} (x+4)}-\frac{1}{2} \tanh ^{-1}\left(\frac{\sqrt{x}}{\sqrt{x+1}-1}\right)","\frac{1}{2} \sqrt{x+1} x^{3/2}+\frac{1}{4} \sqrt{x+1} \sqrt{x}-\frac{1}{4} \sinh ^{-1}\left(\sqrt{x}\right)",1,"(2*x^(7/2) + x^(3/2)*(13 - 11*Sqrt[1 + x]) + x^(5/2)*(11 - 6*Sqrt[1 + x]) + Sqrt[x]*(4 - 4*Sqrt[1 + x]))/(4*(-4 - 3*x) + 4*Sqrt[1 + x]*(4 + x)) - ArcTanh[Sqrt[x]/(-1 + Sqrt[1 + x])]/2","B",1
192,0,0,22,0.0000346,"\int \sin \left(\sqrt{x}\right) \, dx","IntegrateAlgebraic[Sin[Sqrt[x]],x]","\int \sin \left(\sqrt{x}\right) \, dx","2 \sin \left(\sqrt{x}\right)-2 \sqrt{x} \cos \left(\sqrt{x}\right)",1,"Could not integrate","F",-1
193,1,20,13,0.0211112,"\int \frac{x}{\left(1-x^2\right)^{9/8}} \, dx","IntegrateAlgebraic[x/(1 - x^2)^(9/8),x]","-\frac{4 \left(1-x^2\right)^{7/8}}{x^2-1}","\frac{4}{\sqrt[8]{1-x^2}}",1,"(-4*(1 - x^2)^(7/8))/(-1 + x^2)","A",1
194,1,8,8,0.075271,"\int \frac{x}{\sqrt{1-x^4}} \, dx","IntegrateAlgebraic[x/Sqrt[1 - x^4],x]","\frac{1}{2} \sin ^{-1}\left(x^2\right)","\frac{1}{2} \sin ^{-1}\left(x^2\right)",1,"ArcSin[x^2]/2","A",1
195,1,14,14,0.0282841,"\int \frac{1}{x \sqrt{1+x^4}} \, dx","IntegrateAlgebraic[1/(x*Sqrt[1 + x^4]),x]","-\frac{1}{2} \tanh ^{-1}\left(\sqrt{x^4+1}\right)","-\frac{1}{2} \tanh ^{-1}\left(\sqrt{x^4+1}\right)",1,"-1/2*ArcTanh[Sqrt[1 + x^4]]","A",1
196,1,26,18,0.0995391,"\int \frac{x}{\sqrt{1+x^2+x^4}} \, dx","IntegrateAlgebraic[x/Sqrt[1 + x^2 + x^4],x]","-\frac{1}{2} \log \left(-2 x^2+2 \sqrt{x^4+x^2+1}-1\right)","\frac{1}{2} \sinh ^{-1}\left(\frac{2 x^2+1}{\sqrt{3}}\right)",1,"-1/2*Log[-1 - 2*x^2 + 2*Sqrt[1 + x^2 + x^4]]","A",1
197,1,27,30,0.138545,"\int \frac{1}{x \sqrt{-1+x^2-x^4}} \, dx","IntegrateAlgebraic[1/(x*Sqrt[-1 + x^2 - x^4]),x]","-i \tanh ^{-1}\left(x^2+i \sqrt{-x^4+x^2-1}\right)","-\frac{1}{2} \tan ^{-1}\left(\frac{2-x^2}{2 \sqrt{-x^4+x^2-1}}\right)",1,"(-I)*ArcTanh[x^2 + I*Sqrt[-1 + x^2 - x^4]]","C",1
198,1,17,17,0.1792681,"\int \frac{1+x}{(1-x)^2 \sqrt{1+x^2}} \, dx","IntegrateAlgebraic[(1 + x)/((1 - x)^2*Sqrt[1 + x^2]),x]","\frac{\sqrt{x^2+1}}{1-x}","\frac{\sqrt{x^2+1}}{1-x}",1,"Sqrt[1 + x^2]/(1 - x)","A",1
199,1,16,2,0.0133515,"\int \frac{1}{\sqrt{1+x^2}} \, dx","IntegrateAlgebraic[1/Sqrt[1 + x^2],x]","-\log \left(\sqrt{x^2+1}-x\right)","\sinh ^{-1}(x)",1,"-Log[-x + Sqrt[1 + x^2]]","B",1
200,1,20,20,2.5636064,"\int \frac{\sqrt{x} \sqrt{1+x}+\sqrt{x} \sqrt{2+x}+\sqrt{1+x} \sqrt{2+x}}{2 \sqrt{x} \sqrt{1+x} \sqrt{2+x}} \, dx","IntegrateAlgebraic[(Sqrt[x]*Sqrt[1 + x] + Sqrt[x]*Sqrt[2 + x] + Sqrt[1 + x]*Sqrt[2 + x])/(2*Sqrt[x]*Sqrt[1 + x]*Sqrt[2 + x]),x]","\sqrt{x}+\sqrt{x+1}+\sqrt{x+2}","\sqrt{x}+\sqrt{x+1}+\sqrt{x+2}",1,"Sqrt[x] + Sqrt[1 + x] + Sqrt[2 + x]","A",1
201,1,24,24,2.901634,"\int \frac{-2 \sqrt{1+x^3}+5 x^4 \sqrt{1+x^3}-3 x^2 \sqrt{1-2 x+x^5}}{2 \sqrt{1+x^3} \sqrt{1-2 x+x^5}} \, dx","IntegrateAlgebraic[(-2*Sqrt[1 + x^3] + 5*x^4*Sqrt[1 + x^3] - 3*x^2*Sqrt[1 - 2*x + x^5])/(2*Sqrt[1 + x^3]*Sqrt[1 - 2*x + x^5]),x]","\sqrt{x^5-2 x+1}-\sqrt{x^3+1}","\sqrt{x^5-2 x+1}-\sqrt{x^3+1}",1,"-Sqrt[1 + x^3] + Sqrt[1 - 2*x + x^5]","A",1
202,1,33,27,1.7442204,"\int \left(\frac{10}{\sqrt{-4+x^2}}+\frac{1}{\sqrt{-1+x^2}}\right) \, dx","IntegrateAlgebraic[10/Sqrt[-4 + x^2] + 1/Sqrt[-1 + x^2],x]","-10 \log \left(\sqrt{x^2-4}-x\right)-\log \left(\sqrt{x^2-1}-x\right)","10 \tanh ^{-1}\left(\frac{x}{\sqrt{x^2-4}}\right)+\tanh ^{-1}\left(\frac{x}{\sqrt{x^2-1}}\right)",1,"-10*Log[-x + Sqrt[-4 + x^2]] - Log[-x + Sqrt[-1 + x^2]]","A",1
203,1,82,82,0.074327,"\int \frac{\sqrt{x+\sqrt{a^2+x^2}}}{x} \, dx","IntegrateAlgebraic[Sqrt[x + Sqrt[a^2 + x^2]]/x,x]","2 \sqrt{\sqrt{a^2+x^2}+x}-2 \sqrt{a} \tan ^{-1}\left(\frac{\sqrt{\sqrt{a^2+x^2}+x}}{\sqrt{a}}\right)-2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a^2+x^2}+x}}{\sqrt{a}}\right)","2 \sqrt{\sqrt{a^2+x^2}+x}-2 \sqrt{a} \tan ^{-1}\left(\frac{\sqrt{\sqrt{a^2+x^2}+x}}{\sqrt{a}}\right)-2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a^2+x^2}+x}}{\sqrt{a}}\right)",1,"2*Sqrt[x + Sqrt[a^2 + x^2]] - 2*Sqrt[a]*ArcTan[Sqrt[x + Sqrt[a^2 + x^2]]/Sqrt[a]] - 2*Sqrt[a]*ArcTanh[Sqrt[x + Sqrt[a^2 + x^2]]/Sqrt[a]]","A",1
204,1,17,12,0.025668,"\int \frac{3 x^2}{2 \left(1+x^3+\sqrt{1+x^3}\right)} \, dx","IntegrateAlgebraic[(3*x^2)/(2*(1 + x^3 + Sqrt[1 + x^3])),x]","\tanh ^{-1}\left(\sqrt{x^3+1}\right)+\frac{3 \log (x)}{2}","\log \left(\sqrt{x^3+1}+1\right)",1,"ArcTanh[Sqrt[1 + x^3]] + (3*Log[x])/2","A",1
205,1,43,40,0.0407795,"\int \frac{1}{\sqrt{-\alpha ^2+2 h r^2}} \, dr","IntegrateAlgebraic[1/Sqrt[-alpha^2 + 2*h*r^2],r]","-\frac{\log \left(\sqrt{2 h r^2-\alpha ^2}-\sqrt{2} \sqrt{h} r\right)}{\sqrt{2} \sqrt{h}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{h} r}{\sqrt{2 h r^2-\alpha ^2}}\right)}{\sqrt{2} \sqrt{h}}",1,"-(Log[-(Sqrt[2]*Sqrt[h]*r) + Sqrt[-alpha^2 + 2*h*r^2]]/(Sqrt[2]*Sqrt[h]))","A",1
206,1,46,46,0.0359482,"\int \frac{1}{r \sqrt{-\alpha ^2-\epsilon ^2+2 h r^2}} \, dr","IntegrateAlgebraic[1/(r*Sqrt[-alpha^2 - epsilon^2 + 2*h*r^2]),r]","\frac{\tan ^{-1}\left(\frac{\sqrt{-\alpha ^2-\epsilon ^2+2 h r^2}}{\sqrt{\alpha ^2+\epsilon ^2}}\right)}{\sqrt{\alpha ^2+\epsilon ^2}}","\frac{\tan ^{-1}\left(\frac{\sqrt{-\alpha ^2-\epsilon ^2+2 h r^2}}{\sqrt{\alpha ^2+\epsilon ^2}}\right)}{\sqrt{\alpha ^2+\epsilon ^2}}",1,"ArcTan[Sqrt[-alpha^2 - epsilon^2 + 2*h*r^2]/Sqrt[alpha^2 + epsilon^2]]/Sqrt[alpha^2 + epsilon^2]","A",1
207,1,47,37,0.1143501,"\int \frac{1}{r \sqrt{-\alpha ^2-2 k r+2 h r^2}} \, dr","IntegrateAlgebraic[1/(r*Sqrt[-alpha^2 - 2*k*r + 2*h*r^2]),r]","-\frac{2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{h} r}{\alpha }-\frac{\sqrt{-\alpha ^2+2 h r^2-2 k r}}{\alpha }\right)}{\alpha }","-\frac{\tan ^{-1}\left(\frac{\alpha ^2+k r}{\alpha  \sqrt{-\alpha ^2+2 h r^2-2 k r}}\right)}{\alpha }",1,"(-2*ArcTan[(Sqrt[2]*Sqrt[h]*r)/alpha - Sqrt[-alpha^2 - 2*k*r + 2*h*r^2]/alpha])/alpha","A",1
208,1,76,61,0.15262,"\int \frac{1}{r \sqrt{-\alpha ^2-\epsilon ^2-2 k r+2 h r^2}} \, dr","IntegrateAlgebraic[1/(r*Sqrt[-alpha^2 - epsilon^2 - 2*k*r + 2*h*r^2]),r]","-\frac{2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{h} r}{\sqrt{\alpha ^2+\epsilon ^2}}-\frac{\sqrt{-\alpha ^2-\epsilon ^2+2 h r^2-2 k r}}{\sqrt{\alpha ^2+\epsilon ^2}}\right)}{\sqrt{\alpha ^2+\epsilon ^2}}","-\frac{\tan ^{-1}\left(\frac{\alpha ^2+\epsilon ^2+k r}{\sqrt{\alpha ^2+\epsilon ^2} \sqrt{-\alpha ^2-\epsilon ^2+2 h r^2-2 k r}}\right)}{\sqrt{\alpha ^2+\epsilon ^2}}",1,"(-2*ArcTan[(Sqrt[2]*Sqrt[h]*r)/Sqrt[alpha^2 + epsilon^2] - Sqrt[-alpha^2 - epsilon^2 - 2*k*r + 2*h*r^2]/Sqrt[alpha^2 + epsilon^2]])/Sqrt[alpha^2 + epsilon^2]","A",1
209,1,23,23,0.0103471,"\int \frac{r}{\sqrt{-\alpha ^2+2 e r^2}} \, dr","IntegrateAlgebraic[r/Sqrt[-alpha^2 + 2*e*r^2],r]","\frac{\sqrt{2 e r^2-\alpha ^2}}{2 e}","\frac{\sqrt{2 e r^2-\alpha ^2}}{2 e}",1,"Sqrt[-alpha^2 + 2*e*r^2]/(2*e)","A",1
210,1,28,28,0.0118564,"\int \frac{r}{\sqrt{-\alpha ^2-\epsilon ^2+2 e r^2}} \, dr","IntegrateAlgebraic[r/Sqrt[-alpha^2 - epsilon^2 + 2*e*r^2],r]","\frac{\sqrt{-\alpha ^2+2 e r^2-\epsilon ^2}}{2 e}","\frac{\sqrt{-\alpha ^2+2 e r^2-\epsilon ^2}}{2 e}",1,"Sqrt[-alpha^2 - epsilon^2 + 2*e*r^2]/(2*e)","A",1
211,1,65,56,0.3191585,"\int \frac{r}{\sqrt{-\alpha ^2+2 e r^2-2 k r^4}} \, dr","IntegrateAlgebraic[r/Sqrt[-alpha^2 + 2*e*r^2 - 2*k*r^4],r]","\frac{\sqrt{-k} \log \left(\sqrt{2} \sqrt{-k} \sqrt{-\alpha ^2+2 e r^2-2 k r^4}-e+2 k r^2\right)}{2 \sqrt{2} k}","-\frac{\tan ^{-1}\left(\frac{e-2 k r^2}{\sqrt{2} \sqrt{k} \sqrt{-\alpha ^2+2 e r^2-2 k r^4}}\right)}{2 \sqrt{2} \sqrt{k}}",1,"(Sqrt[-k]*Log[-e + 2*k*r^2 + Sqrt[2]*Sqrt[-k]*Sqrt[-alpha^2 + 2*e*r^2 - 2*k*r^4]])/(2*Sqrt[2]*k)","A",1
212,1,81,81,0.1838457,"\int \frac{r}{\sqrt{-\alpha ^2-2 k r+2 e r^2}} \, dr","IntegrateAlgebraic[r/Sqrt[-alpha^2 - 2*k*r + 2*e*r^2],r]","\frac{\sqrt{-\alpha ^2+2 e r^2-2 k r}}{2 e}-\frac{k \log \left(\sqrt{2} \sqrt{e} \sqrt{-\alpha ^2+2 e r^2-2 k r}-2 e r+k\right)}{2 \sqrt{2} e^{3/2}}","\frac{\sqrt{-\alpha ^2+2 e r^2-2 k r}}{2 e}-\frac{k \tanh ^{-1}\left(\frac{k-2 e r}{\sqrt{2} \sqrt{e} \sqrt{-\alpha ^2+2 e r^2-2 k r}}\right)}{2 \sqrt{2} e^{3/2}}",1,"Sqrt[-alpha^2 - 2*k*r + 2*e*r^2]/(2*e) - (k*Log[k - 2*e*r + Sqrt[2]*Sqrt[e]*Sqrt[-alpha^2 - 2*k*r + 2*e*r^2]])/(2*Sqrt[2]*e^(3/2))","A",1
213,1,53,44,0.2794584,"\int \frac{1}{r \sqrt{-\alpha ^2+2 h r^2-2 k r^4}} \, dr","IntegrateAlgebraic[1/(r*Sqrt[-alpha^2 + 2*h*r^2 - 2*k*r^4]),r]","-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{-k} r^2}{\alpha }-\frac{\sqrt{-\alpha ^2+2 h r^2-2 k r^4}}{\alpha }\right)}{\alpha }","-\frac{\tan ^{-1}\left(\frac{\alpha ^2-h r^2}{\alpha  \sqrt{-\alpha ^2+2 h r^2-2 k r^4}}\right)}{2 \alpha }",1,"-(ArcTan[(Sqrt[2]*Sqrt[-k]*r^2)/alpha - Sqrt[-alpha^2 + 2*h*r^2 - 2*k*r^4]/alpha]/alpha)","A",1
214,1,82,68,0.3784317,"\int \frac{1}{r \sqrt{-\alpha ^2-\epsilon ^2+2 h r^2-2 k r^4}} \, dr","IntegrateAlgebraic[1/(r*Sqrt[-alpha^2 - epsilon^2 + 2*h*r^2 - 2*k*r^4]),r]","-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{-k} r^2}{\sqrt{\alpha ^2+\epsilon ^2}}-\frac{\sqrt{-\alpha ^2-\epsilon ^2+2 h r^2-2 k r^4}}{\sqrt{\alpha ^2+\epsilon ^2}}\right)}{\sqrt{\alpha ^2+\epsilon ^2}}","-\frac{\tan ^{-1}\left(\frac{\alpha ^2+\epsilon ^2-h r^2}{\sqrt{\alpha ^2+\epsilon ^2} \sqrt{-\alpha ^2-\epsilon ^2+2 h r^2-2 k r^4}}\right)}{2 \sqrt{\alpha ^2+\epsilon ^2}}",1,"-(ArcTan[(Sqrt[2]*Sqrt[-k]*r^2)/Sqrt[alpha^2 + epsilon^2] - Sqrt[-alpha^2 - epsilon^2 + 2*h*r^2 - 2*k*r^4]/Sqrt[alpha^2 + epsilon^2]]/Sqrt[alpha^2 + epsilon^2])","A",1
215,0,0,13,0.0000371,"\int a \cos (5+3 x) \sin ^2(5+3 x) \, dx","IntegrateAlgebraic[a*Cos[5 + 3*x]*Sin[5 + 3*x]^2,x]","\int a \cos (5+3 x) \sin ^2(5+3 x) \, dx","\frac{1}{9} a \sin ^3(3 x+5)",1,"Could not integrate","F",-1
216,0,0,19,0.0000463,"\int \frac{\log \left(x^2\right)}{x^3} \, dx","IntegrateAlgebraic[Log[x^2]/x^3,x]","\int \frac{\log \left(x^2\right)}{x^3} \, dx","-\frac{1}{2 x^2}-\frac{\log \left(x^2\right)}{2 x^2}",1,"Could not integrate","F",-1
217,0,0,12,0.0000315,"\int x \sin (a+x) \, dx","IntegrateAlgebraic[x*Sin[a + x],x]","\int x \sin (a+x) \, dx","\sin (a+x)-x \cos (a+x)",1,"Could not integrate","F",-1
218,0,0,11,0.00004,"\int \frac{e^{-x} (-1+(1-x) \log (x))}{\log ^2(x)} \, dx","IntegrateAlgebraic[(-1 + (1 - x)*Log[x])/(E^x*Log[x]^2),x]","\int \frac{e^{-x} (-1+(1-x) \log (x))}{\log ^2(x)} \, dx","\frac{e^{-x} x}{\log (x)}",1,"Could not integrate","F",-1
219,1,27,27,0.0084462,"\int \frac{x^3}{b+a x^2} \, dx","IntegrateAlgebraic[x^3/(b + a*x^2),x]","\frac{x^2}{2 a}-\frac{b \log \left(a x^2+b\right)}{2 a^2}","\frac{x^2}{2 a}-\frac{b \log \left(a x^2+b\right)}{2 a^2}",1,"x^2/(2*a) - (b*Log[b + a*x^2])/(2*a^2)","A",1
220,1,69,33,0.0364209,"\int \frac{\sqrt{x}}{(1+x)^{7/2}} \, dx","IntegrateAlgebraic[Sqrt[x]/(1 + x)^(7/2),x]","\frac{x^{3/2} \left(\sqrt{x+1}-1\right)^7 \left(-\frac{x^2}{6 \left(\sqrt{x+1}-1\right)^4}+\frac{x}{15 \left(\sqrt{x+1}-1\right)^2}-\frac{1}{6}\right)}{\left(-x+\sqrt{x+1}-1\right)^5}","\frac{4 x^{3/2}}{15 (x+1)^{3/2}}+\frac{2 x^{3/2}}{5 (x+1)^{5/2}}",1,"(x^(3/2)*(-1 + Sqrt[1 + x])^7*(-1/6 - x^2/(6*(-1 + Sqrt[1 + x])^4) + x/(15*(-1 + Sqrt[1 + x])^2)))/(-1 - x + Sqrt[1 + x])^5","B",1
221,1,8,9,0.0039539,"\int \frac{1}{x (1+x)} \, dx","IntegrateAlgebraic[1/(x*(1 + x)),x]","-2 \tanh ^{-1}(2 x+1)","\log (x)-\log (x+1)",1,"-2*ArcTanh[1 + 2*x]","A",1
222,1,19,19,0.0205615,"\int \frac{1}{\sqrt{x} (-1+2 x)} \, dx","IntegrateAlgebraic[1/(Sqrt[x]*(-1 + 2*x)),x]","-\sqrt{2} \tanh ^{-1}\left(\sqrt{2} \sqrt{x}\right)","-\sqrt{2} \tanh ^{-1}\left(\sqrt{2} \sqrt{x}\right)",1,"-(Sqrt[2]*ArcTanh[Sqrt[2]*Sqrt[x]])","A",1
223,1,19,19,0.0054959,"\int \sqrt{x} \left(1+x^2\right) \, dx","IntegrateAlgebraic[Sqrt[x]*(1 + x^2),x]","\frac{2 x^{7/2}}{7}+\frac{2 x^{3/2}}{3}","\frac{2 x^{7/2}}{7}+\frac{2 x^{3/2}}{3}",1,"(2*x^(3/2))/3 + (2*x^(7/2))/7","A",1
224,1,115,88,0.0657821,"\int \frac{\sqrt[3]{-a+x}}{x} \, dx","IntegrateAlgebraic[(-a + x)^(1/3)/x,x]","\frac{1}{2} \sqrt[3]{a} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{x-a}+(x-a)^{2/3}\right)+3 \sqrt[3]{x-a}-\sqrt[3]{a} \log \left(\sqrt[3]{x-a}+\sqrt[3]{a}\right)+\sqrt{3} \sqrt[3]{a} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{x-a}}{\sqrt{3} \sqrt[3]{a}}\right)","3 \sqrt[3]{x-a}+\frac{1}{2} \sqrt[3]{a} \log (x)-\frac{3}{2} \sqrt[3]{a} \log \left(\sqrt[3]{x-a}+\sqrt[3]{a}\right)+\sqrt{3} \sqrt[3]{a} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{x-a}}{\sqrt{3} \sqrt[3]{a}}\right)",1,"3*(-a + x)^(1/3) + Sqrt[3]*a^(1/3)*ArcTan[1/Sqrt[3] - (2*(-a + x)^(1/3))/(Sqrt[3]*a^(1/3))] - a^(1/3)*Log[a^(1/3) + (-a + x)^(1/3)] + (a^(1/3)*Log[a^(2/3) - a^(1/3)*(-a + x)^(1/3) + (-a + x)^(2/3)])/2","A",1
225,0,0,9,0.000033,"\int x \sinh (x) \, dx","IntegrateAlgebraic[x*Sinh[x],x]","\int x \sinh (x) \, dx","x \cosh (x)-\sinh (x)",1,"Could not integrate","F",-1
226,0,0,9,0.00003,"\int x \cosh (x) \, dx","IntegrateAlgebraic[x*Cosh[x],x]","\int x \cosh (x) \, dx","x \sinh (x)-\cosh (x)",1,"Could not integrate","F",-1
227,0,0,9,0.0000272,"\int \tanh (2 x) \, dx","IntegrateAlgebraic[Tanh[2*x],x]","\int \tanh (2 x) \, dx","\frac{1}{2} \log (\cosh (2 x))",1,"Could not integrate","F",-1
228,0,0,12,0.0000373,"\int \frac{-1+i \text{eps} \sinh (x)}{i a-x+i \text{eps} \cosh (x)} \, dx","IntegrateAlgebraic[(-1 + I*eps*Sinh[x])/(I*a - x + I*eps*Cosh[x]),x]","\int \frac{-1+i \text{eps} \sinh (x)}{i a-x+i \text{eps} \cosh (x)} \, dx","\log (a+\text{eps} \cosh (x)+i x)",1,"Could not integrate","F",-1
229,0,0,28,0.0000319,"\int \cos ^2(x) \sin (3+2 x) \, dx","IntegrateAlgebraic[Cos[x]^2*Sin[3 + 2*x],x]","\int \cos ^2(x) \sin (3+2 x) \, dx","\frac{1}{4} x \sin (3)-\frac{1}{4} \cos (2 x+3)-\frac{1}{16} \cos (4 x+3)",1,"Could not integrate","F",-1
230,0,0,21,0.0000296,"\int x \tan ^{-1}(x) \, dx","IntegrateAlgebraic[x*ArcTan[x],x]","\int x \tan ^{-1}(x) \, dx","\frac{1}{2} x^2 \tan ^{-1}(x)-\frac{x}{2}+\frac{1}{2} \tan ^{-1}(x)",1,"Could not integrate","F",-1
231,0,0,21,0.0000292,"\int x \cot ^{-1}(x) \, dx","IntegrateAlgebraic[x*ArcCot[x],x]","\int x \cot ^{-1}(x) \, dx","\frac{1}{2} x^2 \cot ^{-1}(x)+\frac{x}{2}-\frac{1}{2} \tan ^{-1}(x)",1,"Could not integrate","F",-1
232,0,0,23,0.000032,"\int x \log \left(a+x^2\right) \, dx","IntegrateAlgebraic[x*Log[a + x^2],x]","\int x \log \left(a+x^2\right) \, dx","\frac{1}{2} \left(a+x^2\right) \log \left(a+x^2\right)-\frac{x^2}{2}",1,"Could not integrate","F",-1
233,0,0,18,0.0000307,"\int \cos (x) \sin (a+x) \, dx","IntegrateAlgebraic[Cos[x]*Sin[a + x],x]","\int \cos (x) \sin (a+x) \, dx","\frac{1}{2} x \sin (a)-\frac{1}{4} \cos (a+2 x)",1,"Could not integrate","F",-1
234,0,0,18,0.0000308,"\int \cos (a+x) \sin (x) \, dx","IntegrateAlgebraic[Cos[a + x]*Sin[x],x]","\int \cos (a+x) \sin (x) \, dx","-\frac{1}{2} x \sin (a)-\frac{1}{4} \cos (a+2 x)",1,"Could not integrate","F",-1
235,0,0,12,0.0000319,"\int \sqrt{1+\sin (x)} \, dx","IntegrateAlgebraic[Sqrt[1 + Sin[x]],x]","\int \sqrt{1+\sin (x)} \, dx","-\frac{2 \cos (x)}{\sqrt{\sin (x)+1}}",1,"Could not integrate","F",-1
236,0,0,14,0.0000287,"\int \sqrt{1-\sin (x)} \, dx","IntegrateAlgebraic[Sqrt[1 - Sin[x]],x]","\int \sqrt{1-\sin (x)} \, dx","\frac{2 \cos (x)}{\sqrt{1-\sin (x)}}",1,"Could not integrate","F",-1
237,0,0,12,0.0000282,"\int \sqrt{1+\cos (x)} \, dx","IntegrateAlgebraic[Sqrt[1 + Cos[x]],x]","\int \sqrt{1+\cos (x)} \, dx","\frac{2 \sin (x)}{\sqrt{\cos (x)+1}}",1,"Could not integrate","F",-1
238,0,0,14,0.0000276,"\int \sqrt{1-\cos (x)} \, dx","IntegrateAlgebraic[Sqrt[1 - Cos[x]],x]","\int \sqrt{1-\cos (x)} \, dx","-\frac{2 \sin (x)}{\sqrt{1-\cos (x)}}",1,"Could not integrate","F",-1
239,1,87,21,0.0289996,"\int \frac{1}{-\sqrt{-1+x}+\sqrt{x}} \, dx","IntegrateAlgebraic[(-Sqrt[-1 + x] + Sqrt[x])^(-1),x]","\frac{\left(\frac{4 \sqrt{x}+4}{\sqrt{x}-1}-\frac{8 \sqrt{x-1}}{3 \left(\sqrt{x}-1\right)}+\frac{4}{3}\right) \left(\sqrt{x}-1\right)^4}{\left(\sqrt{x-1}-\sqrt{x}+1\right)^3 \left(\sqrt{x-1}+\sqrt{x}-1\right)}","\frac{2 x^{3/2}}{3}+\frac{2}{3} (x-1)^{3/2}",1,"((4/3 + (4 + 4*Sqrt[x])/(-1 + Sqrt[x]) - (8*Sqrt[-1 + x])/(3*(-1 + Sqrt[x])))*(-1 + Sqrt[x])^4)/((1 + Sqrt[-1 + x] - Sqrt[x])^3*(-1 + Sqrt[-1 + x] + Sqrt[x]))","B",1
240,1,22,24,0.0086521,"\int \frac{1}{1-\sqrt{1+x}} \, dx","IntegrateAlgebraic[(1 - Sqrt[1 + x])^(-1),x]","-2 \sqrt{x+1}-2 \log \left(\sqrt{x+1}-1\right)","-2 \sqrt{x+1}-2 \log \left(1-\sqrt{x+1}\right)",1,"-2*Sqrt[1 + x] - 2*Log[-1 + Sqrt[1 + x]]","A",1
241,1,18,12,0.0788827,"\int \frac{x}{\sqrt{36+x^4}} \, dx","IntegrateAlgebraic[x/Sqrt[36 + x^4],x]","\frac{1}{2} \log \left(\sqrt{x^4+36}+x^2\right)","\frac{1}{2} \sinh ^{-1}\left(\frac{x^2}{6}\right)",1,"Log[x^2 + Sqrt[36 + x^4]]/2","A",1
242,1,32,32,0.0121896,"\int \frac{1}{\sqrt[3]{x}+\sqrt{x}} \, dx","IntegrateAlgebraic[(x^(1/3) + Sqrt[x])^(-1),x]","2 \sqrt{x}-3 \sqrt[3]{x}+6 \sqrt[6]{x}-6 \log \left(\sqrt[6]{x}+1\right)","2 \sqrt{x}-3 \sqrt[3]{x}+6 \sqrt[6]{x}-6 \log \left(\sqrt[6]{x}+1\right)",1,"6*x^(1/6) - 3*x^(1/3) + 2*Sqrt[x] - 6*Log[1 + x^(1/6)]","A",1
243,0,0,33,0.0000876,"\int \log \left(2+3 x^2\right) \, dx","IntegrateAlgebraic[Log[2 + 3*x^2],x]","\int \log \left(2+3 x^2\right) \, dx","x \log \left(3 x^2+2\right)-2 x+2 \sqrt{\frac{2}{3}} \tan ^{-1}\left(\sqrt{\frac{3}{2}} x\right)",1,"Could not integrate","F",-1
244,0,0,3,0.0000263,"\int \cot (x) \, dx","IntegrateAlgebraic[Cot[x],x]","\int \cot (x) \, dx","\log (\sin (x))",1,"Could not integrate","F",-1
245,0,0,12,0.0000275,"\int \cot ^4(x) \, dx","IntegrateAlgebraic[Cot[x]^4,x]","\int \cot ^4(x) \, dx","x-\frac{1}{3} \cot ^3(x)+\cot (x)",1,"Could not integrate","F",-1
246,0,0,3,0.0000245,"\int \tanh (x) \, dx","IntegrateAlgebraic[Tanh[x],x]","\int \tanh (x) \, dx","\log (\cosh (x))",1,"Could not integrate","F",-1
247,0,0,3,0.0000249,"\int \coth (x) \, dx","IntegrateAlgebraic[Coth[x],x]","\int \coth (x) \, dx","\log (\sinh (x))",1,"Could not integrate","F",-1
248,0,0,8,0.0000454,"\int b^x \, dx","IntegrateAlgebraic[b^x,x]","\int b^x \, dx","\frac{b^x}{\log (b)}",1,"Could not integrate","F",-1
249,1,29,49,2.5995482,"\int \sqrt{2+\frac{1}{x^4}+x^4} \, dx","IntegrateAlgebraic[Sqrt[2 + x^(-4) + x^4],x]","\frac{x \left(x^4-3\right) \sqrt{x^4+\frac{1}{x^4}+2}}{3 \left(x^4+1\right)}","\frac{x^5 \sqrt{x^4+\frac{1}{x^4}+2}}{3 \left(x^4+1\right)}-\frac{x \sqrt{x^4+\frac{1}{x^4}+2}}{x^4+1}",1,"(x*(-3 + x^4)*Sqrt[2 + x^(-4) + x^4])/(3*(1 + x^4))","A",1
250,1,16,16,0.0052559,"\int \frac{1+2 x}{2+3 x} \, dx","IntegrateAlgebraic[(1 + 2*x)/(2 + 3*x),x]","\frac{2 x}{3}-\frac{1}{9} \log (3 x+2)","\frac{2 x}{3}-\frac{1}{9} \log (3 x+2)",1,"(2*x)/3 - Log[2 + 3*x]/9","A",1
251,0,0,40,0.0000371,"\int x \log \left(x+\sqrt{1+x^2}\right) \, dx","IntegrateAlgebraic[x*Log[x + Sqrt[1 + x^2]],x]","\int x \log \left(x+\sqrt{1+x^2}\right) \, dx","-\frac{1}{4} \sqrt{x^2+1} x+\frac{1}{2} x^2 \log \left(\sqrt{x^2+1}+x\right)+\frac{1}{4} \sinh ^{-1}(x)",1,"Could not integrate","F",-1
252,0,0,128,0.0000358,"\int x \left(1+e^x \sin (x)\right)^2 \, dx","IntegrateAlgebraic[x*(1 + E^x*Sin[x])^2,x]","\int x \left(1+e^x \sin (x)\right)^2 \, dx","\frac{x^2}{2}+\frac{1}{8} e^{2 x} x-\frac{3 e^{2 x}}{32}+\frac{1}{4} e^{2 x} x \sin ^2(x)-\frac{1}{16} e^{2 x} \sin ^2(x)+e^x x \sin (x)+\frac{1}{32} e^{2 x} \sin (2 x)-e^x x \cos (x)+e^x \cos (x)-\frac{1}{32} e^{2 x} \cos (2 x)-\frac{1}{4} e^{2 x} x \sin (x) \cos (x)+\frac{1}{16} e^{2 x} \sin (x) \cos (x)",1,"Could not integrate","F",-1
253,0,0,30,0.0000365,"\int e^x x \cos (x) \, dx","IntegrateAlgebraic[E^x*x*Cos[x],x]","\int e^x x \cos (x) \, dx","-\frac{1}{2} e^x \sin (x)+\frac{1}{2} e^x x \sin (x)+\frac{1}{2} e^x x \cos (x)",1,"Could not integrate","F",-1
254,1,9,11,0.0031273,"\int \frac{1}{(-3+x)^4} \, dx","IntegrateAlgebraic[(-3 + x)^(-4),x]","-\frac{1}{3 (x-3)^3}","\frac{1}{3 (3-x)^3}",1,"-1/3*1/(-3 + x)^3","A",1
255,1,41,40,0.0165878,"\int \frac{x}{-1+x^3} \, dx","IntegrateAlgebraic[x/(-1 + x^3),x]","-\frac{1}{6} \log \left(x^2+x+1\right)+\frac{1}{3} \log (x-1)+\frac{\tan ^{-1}\left(\frac{2 x}{\sqrt{3}}+\frac{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/Sqrt[3] + (2*x)/Sqrt[3]]/Sqrt[3] + Log[-1 + x]/3 - Log[1 + x + x^2]/6","A",1
256,1,8,8,0.0059595,"\int \frac{x}{-1+x^4} \, dx","IntegrateAlgebraic[x/(-1 + x^4),x]","-\frac{1}{2} \tanh ^{-1}\left(x^2\right)","-\frac{1}{2} \tanh ^{-1}\left(x^2\right)",1,"-1/2*ArcTanh[x^2]","A",1
257,0,0,227,0.0000358,"\int \frac{\left(1+x^3\right) \log (x)}{2+x^4} \, dx","IntegrateAlgebraic[((1 + x^3)*Log[x])/(2 + x^4),x]","\int \frac{\left(1+x^3\right) \log (x)}{2+x^4} \, dx","\frac{1}{16} \left(4+(1-i) 2^{3/4}\right) \text{Li}_2\left(-\frac{(1+i) x}{2^{3/4}}\right)+\frac{1}{8} \left(2+i \sqrt[4]{-2}\right) \text{Li}_2\left(\frac{(1+i) x}{2^{3/4}}\right)+\frac{1}{8} \left(2-\sqrt[4]{-2}\right) \text{Li}_2\left(-\frac{(-1)^{3/4} x}{\sqrt[4]{2}}\right)+\frac{1}{8} \left(2+\sqrt[4]{-2}\right) \text{Li}_2\left(\frac{(-1)^{3/4} x}{\sqrt[4]{2}}\right)+\frac{1}{8} \left(2+i \sqrt[4]{-2}\right) \log (x) \log \left(1-\frac{(1+i) x}{2^{3/4}}\right)+\frac{1}{16} \left(4+(1-i) 2^{3/4}\right) \log (x) \log \left(1+\frac{(1+i) x}{2^{3/4}}\right)+\frac{1}{8} \left(2+\sqrt[4]{-2}\right) \log (x) \log \left(1-\frac{(-1)^{3/4} x}{\sqrt[4]{2}}\right)+\frac{1}{8} \left(2-\sqrt[4]{-2}\right) \log (x) \log \left(\frac{(-1)^{3/4} x}{\sqrt[4]{2}}+1\right)",1,"Could not integrate","F",-1
258,0,0,24,0.0000417,"\int (\log (x)+\log (1+x)+\log (2+x)) \, dx","IntegrateAlgebraic[Log[x] + Log[1 + x] + Log[2 + x],x]","\int (\log (x)+\log (1+x)+\log (2+x)) \, dx","-3 x+x \log (x)+(x+1) \log (x+1)+(x+2) \log (x+2)",1,"Could not integrate","F",-1
259,1,81,78,0.0762508,"\int \frac{1}{5+x^3} \, dx","IntegrateAlgebraic[(5 + x^3)^(-1),x]","-\frac{\log \left(-\sqrt[3]{5} x^2+5^{2/3} x-5\right)}{6\ 5^{2/3}}+\frac{\log \left(5^{2/3} x+5\right)}{3\ 5^{2/3}}-\frac{\tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 x}{\sqrt{3} \sqrt[3]{5}}\right)}{\sqrt{3} 5^{2/3}}","-\frac{\log \left(x^2-\sqrt[3]{5} x+5^{2/3}\right)}{6\ 5^{2/3}}+\frac{\log \left(x+\sqrt[3]{5}\right)}{3\ 5^{2/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{5}-2 x}{\sqrt{3} \sqrt[3]{5}}\right)}{\sqrt{3} 5^{2/3}}",1,"-(ArcTan[1/Sqrt[3] - (2*x)/(Sqrt[3]*5^(1/3))]/(Sqrt[3]*5^(2/3))) + Log[5 + 5^(2/3)*x]/(3*5^(2/3)) - Log[-5 + 5^(2/3)*x - 5^(1/3)*x^2]/(6*5^(2/3))","A",1
260,1,16,2,0.0001207,"\int \frac{1}{\sqrt{1+x^2}} \, dx","IntegrateAlgebraic[1/Sqrt[1 + x^2],x]","-\log \left(\sqrt{x^2+1}-x\right)","\sinh ^{-1}(x)",1,"-Log[-x + Sqrt[1 + x^2]]","B",1
261,1,33,27,0.0210239,"\int \sqrt{3+x^2} \, dx","IntegrateAlgebraic[Sqrt[3 + x^2],x]","\frac{1}{2} x \sqrt{x^2+3}-\frac{3}{2} \log \left(\sqrt{x^2+3}-x\right)","\frac{1}{2} \sqrt{x^2+3} x+\frac{3}{2} \sinh ^{-1}\left(\frac{x}{\sqrt{3}}\right)",1,"(x*Sqrt[3 + x^2])/2 - (3*Log[-x + Sqrt[3 + x^2]])/2","A",1
262,1,10,10,0.000085,"\int \frac{x}{(1+x)^2} \, dx","IntegrateAlgebraic[x/(1 + x)^2,x]","\frac{1}{x+1}+\log (x+1)","\frac{1}{x+1}+\log (x+1)",1,"(1 + x)^(-1) + Log[1 + x]","A",1
263,0,0,16,0.0000256,"\int \sin ^{-1}(x) \, dx","IntegrateAlgebraic[ArcSin[x],x]","\int \sin ^{-1}(x) \, dx","\sqrt{1-x^2}+x \sin ^{-1}(x)",1,"Could not integrate","F",-1
264,0,0,40,0.0000281,"\int x^2 \sin ^{-1}(x) \, dx","IntegrateAlgebraic[x^2*ArcSin[x],x]","\int x^2 \sin ^{-1}(x) \, dx","\frac{1}{3} x^3 \sin ^{-1}(x)-\frac{1}{9} \left(1-x^2\right)^{3/2}+\frac{\sqrt{1-x^2}}{3}",1,"Could not integrate","F",-1
265,0,0,21,0.0000447,"\int \frac{\sec ^2(x)}{1+\sec ^2(x)-3 \tan (x)} \, dx","IntegrateAlgebraic[Sec[x]^2/(1 + Sec[x]^2 - 3*Tan[x]),x]","\int \frac{\sec ^2(x)}{1+\sec ^2(x)-3 \tan (x)} \, dx","\log (2 \cos (x)-\sin (x))-\log (\cos (x)-\sin (x))",1,"Could not integrate","F",-1
266,0,0,14,0.0000335,"\int \cos ^2(x) \, dx","IntegrateAlgebraic[Cos[x]^2,x]","\int \cos ^2(x) \, dx","\frac{x}{2}+\frac{1}{2} \sin (x) \cos (x)",1,"Could not integrate","F",-1
267,1,16,18,0.007231,"\int \frac{-2-3 x+5 x^2}{(-2+x) x^2} \, dx","IntegrateAlgebraic[(-2 - 3*x + 5*x^2)/((-2 + x)*x^2),x]","-\frac{1}{x}+3 \log (x-2)+2 \log (x)","-\frac{1}{x}+3 \log (2-x)+2 \log (x)",1,"-x^(-1) + 3*Log[-2 + x] + 2*Log[x]","A",1
268,1,20,10,0.012569,"\int \frac{1}{\sqrt{9+4 x^2}} \, dx","IntegrateAlgebraic[1/Sqrt[9 + 4*x^2],x]","-\frac{1}{2} \log \left(\sqrt{4 x^2+9}-2 x\right)","\frac{1}{2} \sinh ^{-1}\left(\frac{2 x}{3}\right)",1,"-1/2*Log[-2*x + Sqrt[9 + 4*x^2]]","A",1
269,1,16,6,0.0116322,"\int \frac{1}{\sqrt{4+x^2}} \, dx","IntegrateAlgebraic[1/Sqrt[4 + x^2],x]","-\log \left(\sqrt{x^2+4}-x\right)","\sinh ^{-1}\left(\frac{x}{2}\right)",1,"-Log[-x + Sqrt[4 + x^2]]","B",1
270,1,28,21,0.0197478,"\int \frac{1}{10-12 x+9 x^2} \, dx","IntegrateAlgebraic[(10 - 12*x + 9*x^2)^(-1),x]","-\frac{\tan ^{-1}\left(\sqrt{\frac{2}{3}}-\sqrt{\frac{3}{2}} x\right)}{3 \sqrt{6}}","-\frac{\tan ^{-1}\left(\frac{2-3 x}{\sqrt{6}}\right)}{3 \sqrt{6}}",1,"-1/3*ArcTan[Sqrt[2/3] - Sqrt[3/2]*x]/Sqrt[6]","A",1
271,1,50,53,0.0281268,"\int \frac{1}{x^4-2 x^5+2 x^6-2 x^7+x^8} \, dx","IntegrateAlgebraic[(x^4 - 2*x^5 + 2*x^6 - 2*x^7 + x^8)^(-1),x]","\frac{1}{4} \log \left(x^2+1\right)+\frac{-15 x^3+6 x^2+4 x+2}{6 (x-1) x^3}-\frac{5}{2} \log (x-1)+2 \log (x)","-\frac{1}{3 x^3}-\frac{1}{x^2}+\frac{1}{4} \log \left(x^2+1\right)+\frac{1}{2 (1-x)}-\frac{2}{x}-\frac{5}{2} \log (1-x)+2 \log (x)",1,"(2 + 4*x + 6*x^2 - 15*x^3)/(6*(-1 + x)*x^3) - (5*Log[-1 + x])/2 + 2*Log[x] + Log[1 + x^2]/4","A",1
272,1,47,49,0.0339431,"\int \frac{d+c x+b x^2+a x^3}{(-3+x) x (1+x)} \, dx","IntegrateAlgebraic[(d + c*x + b*x^2 + a*x^3)/((-3 + x)*x*(1 + x)),x]","\frac{1}{12} \log (x-3) (27 a+9 b+3 c+d)+\frac{1}{4} \log (x+1) (-a+b-c+d)+a x-\frac{1}{3} d \log (x)","\frac{1}{12} \log (3-x) (27 a+9 b+3 c+d)-\frac{1}{4} \log (x+1) (a-b+c-d)+a x-\frac{1}{3} d \log (x)",1,"a*x + ((27*a + 9*b + 3*c + d)*Log[-3 + x])/12 - (d*Log[x])/3 + ((-a + b - c + d)*Log[1 + x])/4","A",1
273,0,0,15,0.0000361,"\int \frac{1}{\left(2-\log \left(1+x^2\right)\right)^5} \, dx","IntegrateAlgebraic[(2 - Log[1 + x^2])^(-5),x]","\int \frac{1}{\left(2-\log \left(1+x^2\right)\right)^5} \, dx","\text{Int}\left(\frac{1}{\left(2-\log \left(x^2+1\right)\right)^5},x\right)",1,"Could not integrate","F",-1
274,0,0,28,0.0000635,"\int \left(\frac{e^{x^2}}{x}+2 e^{x^2} x \log (x)+\frac{-2+\log (x)}{\left(x+\log ^2(x)\right)^2}+\frac{1+\frac{1}{x}+\frac{2 \log (x)}{x}}{x+\log ^2(x)}\right) \, dx","IntegrateAlgebraic[E^x^2/x + 2*E^x^2*x*Log[x] + (-2 + Log[x])/(x + Log[x]^2)^2 + (1 + x^(-1) + (2*Log[x])/x)/(x + Log[x]^2),x]","\int \left(\frac{e^{x^2}}{x}+2 e^{x^2} x \log (x)+\frac{-2+\log (x)}{\left(x+\log ^2(x)\right)^2}+\frac{1+\frac{1}{x}+\frac{2 \log (x)}{x}}{x+\log ^2(x)}\right) \, dx","e^{x^2} \log (x)-\frac{\log (x)}{x+\log ^2(x)}+\log \left(x+\log ^2(x)\right)",1,"Could not integrate","F",-1
275,0,0,199,0.0000602,"\int e^{\frac{x}{2}+x z} x^4 \sin ^4(\pi  z) \, dz","IntegrateAlgebraic[E^(x/2 + x*z)*x^4*Sin[Pi*z]^4,z]","\int e^{\frac{x}{2}+x z} x^4 \sin ^4(\pi  z) \, dz","\frac{x^5 e^{x z+\frac{x}{2}} \sin ^4(\pi  z)}{x^2+16 \pi ^2}-\frac{4 \pi  x^4 e^{x z+\frac{x}{2}} \sin ^3(\pi  z) \cos (\pi  z)}{x^2+16 \pi ^2}-\frac{24 \pi ^3 x^4 e^{x z+\frac{x}{2}} \sin (\pi  z) \cos (\pi  z)}{x^4+20 \pi ^2 x^2+64 \pi ^4}+\frac{12 \pi ^2 x^5 e^{x z+\frac{x}{2}} \sin ^2(\pi  z)}{x^4+20 \pi ^2 x^2+64 \pi ^4}+\frac{24 \pi ^4 x^3 e^{x z+\frac{x}{2}}}{x^4+20 \pi ^2 x^2+64 \pi ^4}",1,"Could not integrate","F",-1
276,0,0,18,0.0000483,"\int \text{erf}(x) \, dx","IntegrateAlgebraic[Erf[x],x]","\int \text{erf}(x) \, dx","x \text{erf}(x)+\frac{e^{-x^2}}{\sqrt{\pi }}",1,"Could not integrate","F",-1
277,0,0,24,0.0000433,"\int \text{erf}(a+x) \, dx","IntegrateAlgebraic[Erf[a + x],x]","\int \text{erf}(a+x) \, dx","(a+x) \text{erf}(a+x)+\frac{e^{-(a+x)^2}}{\sqrt{\pi }}",1,"Could not integrate","F",-1
278,0,0,94,19.315527,"\int \frac{-8-8 x-x^2-3 x^3+7 x^4+4 x^5+2 x^6}{\left(-1+2 x^2\right)^2 \sqrt{1+2 x^2+4 x^3+x^4}} \, dx","IntegrateAlgebraic[(-8 - 8*x - x^2 - 3*x^3 + 7*x^4 + 4*x^5 + 2*x^6)/((-1 + 2*x^2)^2*Sqrt[1 + 2*x^2 + 4*x^3 + x^4]),x]","\int \frac{-8-8 x-x^2-3 x^3+7 x^4+4 x^5+2 x^6}{\left(-1+2 x^2\right)^2 \sqrt{1+2 x^2+4 x^3+x^4}} \, dx","\frac{(2 x+1) \sqrt{x^4+4 x^3+2 x^2+1}}{2 \left(2 x^2-1\right)}-\tanh ^{-1}\left(\frac{x (x+2) \left(33 x^3+27 x^2-x+7\right)}{\left(31 x^3+37 x^2+2\right) \sqrt{x^4+4 x^3+2 x^2+1}}\right)",1,"Could not integrate","F",-1
279,0,0,142,2.3279825,"\int \frac{(1+2 y) \sqrt{1-5 y-5 y^2}}{y (1+y) (2+y) \sqrt{1-y-y^2}} \, dy","IntegrateAlgebraic[((1 + 2*y)*Sqrt[1 - 5*y - 5*y^2])/(y*(1 + y)*(2 + y)*Sqrt[1 - y - y^2]),y]","\int \frac{(1+2 y) \sqrt{1-5 y-5 y^2}}{y (1+y) (2+y) \sqrt{1-y-y^2}} \, dy","-\frac{1}{4} \tanh ^{-1}\left(\frac{(1-3 y) \sqrt{-5 y^2-5 y+1}}{(1-5 y) \sqrt{-y^2-y+1}}\right)-\frac{1}{2} \tanh ^{-1}\left(\frac{(3 y+4) \sqrt{-5 y^2-5 y+1}}{(5 y+6) \sqrt{-y^2-y+1}}\right)+\frac{9}{4} \tanh ^{-1}\left(\frac{(7 y+11) \sqrt{-5 y^2-5 y+1}}{3 (5 y+7) \sqrt{-y^2-y+1}}\right)",1,"Could not integrate","F",-1
280,1,31,21,0.7439583,"\int \frac{x \left(-\sqrt{-4+x^2}+x^2 \sqrt{-4+x^2}-4 \sqrt{-1+x^2}+x^2 \sqrt{-1+x^2}\right)}{\left(4-5 x^2+x^4\right) \left(1+\sqrt{-4+x^2}+\sqrt{-1+x^2}\right)} \, dx","IntegrateAlgebraic[(x*(-Sqrt[-4 + x^2] + x^2*Sqrt[-4 + x^2] - 4*Sqrt[-1 + x^2] + x^2*Sqrt[-1 + x^2]))/((4 - 5*x^2 + x^4)*(1 + Sqrt[-4 + x^2] + Sqrt[-1 + x^2])),x]","2 \tanh ^{-1}\left(-\frac{2}{3} \sqrt{x^2-4}+\frac{2 \sqrt{x^2-1}}{3}+1\right)","\log \left(\sqrt{x^2-4}+\sqrt{x^2-1}+1\right)",1,"2*ArcTanh[1 - (2*Sqrt[-4 + x^2])/3 + (2*Sqrt[-1 + x^2])/3]","A",1
281,0,0,4030,6.4145023,"\int \left(\sqrt{9-4 \sqrt{2}} x-\sqrt{2} \sqrt{1+4 x+2 x^2+x^4}\right) \, dx","IntegrateAlgebraic[Sqrt[9 - 4*Sqrt[2]]*x - Sqrt[2]*Sqrt[1 + 4*x + 2*x^2 + x^4],x]","\int \left(\sqrt{9-4 \sqrt{2}} x-\sqrt{2} \sqrt{1+4 x+2 x^2+x^4}\right) \, dx","\frac{1}{2} \sqrt{9-4 \sqrt{2}} x^2-\sqrt{2} \left(\frac{1}{3} \sqrt{x^4+2 x^2+4 x+1} (x+1)+\frac{\left(4\ 2^{2/3}+2 \sqrt[3]{-13+3 \sqrt{33}}-\sqrt[3]{2} \left(-13+3 \sqrt{33}\right)^{2/3}\right) \left(4\ 2^{2/3} \left(i+\sqrt{3}\right)-4 i \sqrt[3]{-13+3 \sqrt{33}}+\sqrt[3]{2} \left(-i+\sqrt{3}\right) \left(-13+3 \sqrt{33}\right)^{2/3}\right) \left(4\ 2^{2/3} \left(-i+\sqrt{3}\right)+4 i \sqrt[3]{-13+3 \sqrt{33}}+\sqrt[3]{2} \left(i+\sqrt{3}\right) \left(-13+3 \sqrt{33}\right)^{2/3}\right) \sqrt{\frac{-39+13 i \sqrt{3}-9 i \sqrt{11}+9 \sqrt{33}-4 i \left(-3 i+\sqrt{3}\right) \sqrt[3]{-26+6 \sqrt{33}}}{104-24 \sqrt{33}+\left(-13+13 i \sqrt{3}-9 i \sqrt{11}+3 \sqrt{33}\right) \sqrt[3]{-26+6 \sqrt{33}}+\left(-4-4 i \sqrt{3}\right) \left(-26+6 \sqrt{33}\right)^{2/3}}} \sqrt{\frac{2 \left(-52+12 \sqrt{33}+\sqrt[3]{2} \left(-13+3 \sqrt{33}\right)^{4/3}-4 \left(-26+6 \sqrt{33}\right)^{2/3}\right) x+\left(-7-i \sqrt{3}-3 i \sqrt{11}+\sqrt{33}\right) \left(-26+6 \sqrt{33}\right)^{2/3}+2 \left(1+14 i \sqrt{3}-6 i \sqrt{11}+\sqrt{33}\right) \sqrt[3]{-26+6 \sqrt{33}}-24 \sqrt{33}+104}{\left(-39+13 i \sqrt{3}-9 i \sqrt{11}+9 \sqrt{33}-4 i \left(-3 i+\sqrt{3}\right) \sqrt[3]{-26+6 \sqrt{33}}\right) (x+1)}} \sqrt{\frac{2 \left(-52+12 \sqrt{33}+\sqrt[3]{2} \left(-13+3 \sqrt{33}\right)^{4/3}-4 \left(-26+6 \sqrt{33}\right)^{2/3}\right) x+\left(-7+i \sqrt{3}+3 i \sqrt{11}+\sqrt{33}\right) \left(-26+6 \sqrt{33}\right)^{2/3}+2 \left(1-14 i \sqrt{3}+6 i \sqrt{11}+\sqrt{33}\right) \sqrt[3]{-26+6 \sqrt{33}}-24 \sqrt{33}+104}{\left(-39-13 i \sqrt{3}+9 i \sqrt{11}+9 \sqrt{33}+4 i \left(3 i+\sqrt{3}\right) \sqrt[3]{-26+6 \sqrt{33}}\right) (x+1)}} \sqrt{x^4+2 x^2+4 x+1} \Pi \left(\frac{\sqrt[3]{2} \left(4 \sqrt[3]{2} \left(-3 i+\sqrt{3}\right)+\left(3 i+\sqrt{3}\right) \left(-13+3 \sqrt{33}\right)^{2/3}\right)}{4\ 2^{2/3} \left(-i+\sqrt{3}\right)-8 i \sqrt[3]{-13+3 \sqrt{33}}+\sqrt[3]{2} \left(i+\sqrt{3}\right) \left(-13+3 \sqrt{33}\right)^{2/3}};\sin ^{-1}\left(\frac{\sqrt{\left(-39+9 \sqrt{33}\right) x+4 \left(-26+6 \sqrt{33}\right)^{2/3}-\sqrt[3]{2} \left(-13+3 \sqrt{33}\right)^{4/3}-3 \sqrt{33}+13}}{\sqrt[6]{2} \sqrt{3} \left(-13+3 \sqrt{33}\right)^{2/3} \sqrt{\frac{-39+13 i \sqrt{3}-9 i \sqrt{11}+9 \sqrt{33}-4 i \left(-3 i+\sqrt{3}\right) \sqrt[3]{-26+6 \sqrt{33}}}{104-24 \sqrt{33}+\left(-13+13 i \sqrt{3}-9 i \sqrt{11}+3 \sqrt{33}\right) \sqrt[3]{-26+6 \sqrt{33}}+\left(-4-4 i \sqrt{3}\right) \left(-26+6 \sqrt{33}\right)^{2/3}}} \sqrt{x+1}}\right)|\frac{4 \left(21-7 i \sqrt{3}+3 i \sqrt{11}-3 \sqrt{33}\right)+\left(3+i \sqrt{3}+3 i \sqrt{11}+3 \sqrt{33}\right) \sqrt[3]{-26+6 \sqrt{33}}}{4 \left(21+7 i \sqrt{3}-3 i \sqrt{11}-3 \sqrt{33}\right)+\left(3-i \sqrt{3}-3 i \sqrt{11}+3 \sqrt{33}\right) \sqrt[3]{-26+6 \sqrt{33}}}\right) \sqrt{x+1}}{\sqrt[6]{2} \sqrt{3} \left(-6 i \sqrt[3]{-13+3 \sqrt{33}} x+\sqrt[3]{2} \left(-i+\sqrt{3}\right) \left(-13+3 \sqrt{33}\right)^{2/3}+2 i \sqrt[3]{-13+3 \sqrt{33}}+4\ 2^{2/3} \left(i+\sqrt{3}\right)\right) \left(6 i \sqrt[3]{-13+3 \sqrt{33}} x+\sqrt[3]{2} \left(i+\sqrt{3}\right) \left(-13+3 \sqrt{33}\right)^{2/3}-2 i \sqrt[3]{-13+3 \sqrt{33}}+4\ 2^{2/3} \left(-i+\sqrt{3}\right)\right) \sqrt{\left(-39+9 \sqrt{33}\right) x+4 \left(-26+6 \sqrt{33}\right)^{2/3}-\sqrt[3]{2} \left(-13+3 \sqrt{33}\right)^{4/3}-3 \sqrt{33}+13}}-\frac{8\ 2^{2/3} \sqrt{\frac{3}{-13+3 \sqrt{33}+4 \sqrt[3]{-26+6 \sqrt{33}}}} \sqrt{\frac{i \left(\left(59697-10335 \sqrt{33}\right) x+\sqrt[3]{-26+6 \sqrt{33}} \left(-19899+3445 \sqrt{33}\right)+\left(-26+6 \sqrt{33}\right)^{2/3} \left(-2574+466 \sqrt{33}\right)+3445 \sqrt{33}-19899\right)}{\left(-39-13 i \sqrt{3}+9 i \sqrt{11}+9 \sqrt{33}+4 i \left(3 i+\sqrt{3}\right) \sqrt[3]{-26+6 \sqrt{33}}\right) \left(6 \left(-13+3 \sqrt{33}\right) x+\left(-4-4 i \sqrt{3}\right) \left(-26+6 \sqrt{33}\right)^{2/3}+\left(-13+13 i \sqrt{3}-9 i \sqrt{11}+3 \sqrt{33}\right) \sqrt[3]{-26+6 \sqrt{33}}-6 \sqrt{33}+26\right)}} \sqrt{x^4+2 x^2+4 x+1} E\left(\sin ^{-1}\left(\frac{\sqrt{6 \left(-13+3 \sqrt{33}\right) x+4 i \left(i+\sqrt{3}\right) \left(-26+6 \sqrt{33}\right)^{2/3}+\left(-13-13 i \sqrt{3}+9 i \sqrt{11}+3 \sqrt{33}\right) \sqrt[3]{-26+6 \sqrt{33}}-6 \sqrt{33}+26}}{\sqrt{\frac{39+13 i \sqrt{3}-9 i \sqrt{11}-9 \sqrt{33}+4 \left(3-i \sqrt{3}\right) \sqrt[3]{-26+6 \sqrt{33}}}{39-13 i \sqrt{3}+9 i \sqrt{11}-9 \sqrt{33}+4 \left(3+i \sqrt{3}\right) \sqrt[3]{-26+6 \sqrt{33}}}} \sqrt{6 \left(-13+3 \sqrt{33}\right) x+\left(-4-4 i \sqrt{3}\right) \left(-26+6 \sqrt{33}\right)^{2/3}+\left(-13+13 i \sqrt{3}-9 i \sqrt{11}+3 \sqrt{33}\right) \sqrt[3]{-26+6 \sqrt{33}}-6 \sqrt{33}+26}}\right)|\frac{4 \left(21+7 i \sqrt{3}-3 i \sqrt{11}-3 \sqrt{33}\right)+\left(3-i \sqrt{3}-3 i \sqrt{11}+3 \sqrt{33}\right) \sqrt[3]{-26+6 \sqrt{33}}}{4 \left(21-7 i \sqrt{3}+3 i \sqrt{11}-3 \sqrt{33}\right)+\left(3+i \sqrt{3}+3 i \sqrt{11}+3 \sqrt{33}\right) \sqrt[3]{-26+6 \sqrt{33}}}\right)}{\left(3 \sqrt[3]{-13+3 \sqrt{33}} x-\sqrt[3]{2} \left(-13+3 \sqrt{33}\right)^{2/3}-\sqrt[3]{-13+3 \sqrt{33}}+4\ 2^{2/3}\right) \sqrt{\frac{i (x+1)}{\left(104-24 \sqrt{33}+\left(-13-13 i \sqrt{3}+9 i \sqrt{11}+3 \sqrt{33}\right) \sqrt[3]{-26+6 \sqrt{33}}+4 i \left(i+\sqrt{3}\right) \left(-26+6 \sqrt{33}\right)^{2/3}\right) \left(6 \left(-13+3 \sqrt{33}\right) x+\left(-4-4 i \sqrt{3}\right) \left(-26+6 \sqrt{33}\right)^{2/3}+\left(-13+13 i \sqrt{3}-9 i \sqrt{11}+3 \sqrt{33}\right) \sqrt[3]{-26+6 \sqrt{33}}-6 \sqrt{33}+26\right)}} \sqrt{6 \left(-13+3 \sqrt{33}\right) x+\left(-4-4 i \sqrt{3}\right) \left(-26+6 \sqrt{33}\right)^{2/3}+\left(-13+13 i \sqrt{3}-9 i \sqrt{11}+3 \sqrt{33}\right) \sqrt[3]{-26+6 \sqrt{33}}-6 \sqrt{33}+26} \sqrt{6 \left(-13+3 \sqrt{33}\right) x+4 i \left(i+\sqrt{3}\right) \left(-26+6 \sqrt{33}\right)^{2/3}+\left(-13-13 i \sqrt{3}+9 i \sqrt{11}+3 \sqrt{33}\right) \sqrt[3]{-26+6 \sqrt{33}}-6 \sqrt{33}+26}}+\frac{4 i \sqrt[3]{-13+3 \sqrt{33}} \sqrt{x^4+2 x^2+4 x+1}}{6 i \sqrt[3]{-13+3 \sqrt{33}} x+\sqrt[3]{2} \left(i+\sqrt{3}\right) \left(-13+3 \sqrt{33}\right)^{2/3}-2 i \sqrt[3]{-13+3 \sqrt{33}}+4\ 2^{2/3} \left(-i+\sqrt{3}\right)}-\frac{1}{3} \sqrt{x^4+2 x^2+4 x+1}+\frac{\left(\sqrt[3]{2} \left(13-13 i \sqrt{3}+9 i \sqrt{11}-3 \sqrt{33}\right)+4\ 2^{2/3} \left(1+i \sqrt{3}\right) \sqrt[3]{-13+3 \sqrt{33}}+20 \left(-13+3 \sqrt{33}\right)^{2/3}\right) \left(4\ 2^{2/3} \left(i+\sqrt{3}\right)+8 i \sqrt[3]{-13+3 \sqrt{33}}+\sqrt[3]{2} \left(-i+\sqrt{3}\right) \left(-13+3 \sqrt{33}\right)^{2/3}\right) \sqrt{\frac{52-12 \sqrt{33}-\sqrt[3]{2} \left(-13+3 \sqrt{33}\right)^{4/3}+4 \left(-26+6 \sqrt{33}\right)^{2/3}}{-13+3 \sqrt{33}+4 \sqrt[3]{-26+6 \sqrt{33}}}} \sqrt{\frac{\left(8 i \left(-13+3 \sqrt{33}\right)+\left(13 i-13 \sqrt{3}+9 \sqrt{11}-3 i \sqrt{33}\right) \sqrt[3]{-26+6 \sqrt{33}}+4 \left(i+\sqrt{3}\right) \left(-26+6 \sqrt{33}\right)^{2/3}\right) x+\left(2 i+4 \sqrt{3}-2 i \sqrt{33}\right) \left(-26+6 \sqrt{33}\right)^{2/3}+\left(-43 i-13 \sqrt{3}+9 \sqrt{11}+5 i \sqrt{33}\right) \sqrt[3]{-26+6 \sqrt{33}}-8 i \left(-13+3 \sqrt{33}\right)}{x+1}} \sqrt{x^4+2 x^2+4 x+1} F\left(\sin ^{-1}\left(\frac{\sqrt{52-12 \sqrt{33}-\sqrt[3]{2} \left(-13+3 \sqrt{33}\right)^{4/3}+4 \left(-26+6 \sqrt{33}\right)^{2/3}} \sqrt{6 \left(-13+3 \sqrt{33}\right) x+4 i \left(i+\sqrt{3}\right) \left(-26+6 \sqrt{33}\right)^{2/3}+\left(-13-13 i \sqrt{3}+9 i \sqrt{11}+3 \sqrt{33}\right) \sqrt[3]{-26+6 \sqrt{33}}-6 \sqrt{33}+26}}{\sqrt[6]{2} \sqrt{3} \left(-13+3 \sqrt{33}\right)^{2/3} \sqrt{39+13 i \sqrt{3}-9 i \sqrt{11}-9 \sqrt{33}+4 \left(3-i \sqrt{3}\right) \sqrt[3]{-26+6 \sqrt{33}}} \sqrt{x+1}}\right)|\frac{4 \left(21 i-7 \sqrt{3}+3 \sqrt{11}-3 i \sqrt{33}\right)+\left(3 i+\sqrt{3}+3 \sqrt{11}+3 i \sqrt{33}\right) \sqrt[3]{-26+6 \sqrt{33}}}{-56 \sqrt{3}+24 \sqrt{11}+2 \left(\sqrt{3}+3 \sqrt{11}\right) \sqrt[3]{-26+6 \sqrt{33}}}\right)}{3\ 2^{2/3} 3^{3/4} \sqrt[3]{-13+3 \sqrt{33}} \sqrt{39+13 i \sqrt{3}-9 i \sqrt{11}-9 \sqrt{33}+4 \left(3-i \sqrt{3}\right) \sqrt[3]{-26+6 \sqrt{33}}} \left(6 i \sqrt[3]{-13+3 \sqrt{33}} x+\sqrt[3]{2} \left(i+\sqrt{3}\right) \left(-13+3 \sqrt{33}\right)^{2/3}-2 i \sqrt[3]{-13+3 \sqrt{33}}+4\ 2^{2/3} \left(-i+\sqrt{3}\right)\right) \sqrt{6 \left(-13+3 \sqrt{33}\right) x+4 i \left(i+\sqrt{3}\right) \left(-26+6 \sqrt{33}\right)^{2/3}+\left(-13-13 i \sqrt{3}+9 i \sqrt{11}+3 \sqrt{33}\right) \sqrt[3]{-26+6 \sqrt{33}}-6 \sqrt{33}+26} \sqrt{\frac{\left(104-24 \sqrt{33}+\left(-13-13 i \sqrt{3}+9 i \sqrt{11}+3 \sqrt{33}\right) \sqrt[3]{-26+6 \sqrt{33}}+4 i \left(i+\sqrt{3}\right) \left(-26+6 \sqrt{33}\right)^{2/3}\right) x+\sqrt[3]{-26+6 \sqrt{33}} \left(-41+15 i \sqrt{3}-3 i \sqrt{11}+7 \sqrt{33}\right)-\left(5-3 i \sqrt{3}+3 i \sqrt{11}+\sqrt{33}\right) \left(-26+6 \sqrt{33}\right)^{2/3}+8 \left(-13+3 \sqrt{33}\right)}{\left(-39-13 i \sqrt{3}+9 i \sqrt{11}+9 \sqrt{33}+4 i \left(3 i+\sqrt{3}\right) \sqrt[3]{-26+6 \sqrt{33}}\right) (x+1)}} \sqrt{x+1}}\right)",1,"Could not integrate","F",-1
282,0,0,330,0.000094,"\int \frac{e^{-\frac{x}{y}} \left(\pi ^2 \left(-3 \text{mc}^8+4 \text{mc}^9+24 \text{mc}^6 x-48 \text{mc}^7 x-144 \text{mc}^5 x^2-24 \text{mc}^2 x^3+176 \text{mc}^3 x^3+3 x^4+12 \text{mc} x^4\right)+12 \text{mc}^3 \pi ^2 \left(3 \text{mc}-12 \text{mc}^2-8 x\right) x^2 \log \left(\frac{x}{\text{mc}^2}\right)\right)}{384 x^2} \, dx","IntegrateAlgebraic[(Pi^2*(-3*mc^8 + 4*mc^9 + 24*mc^6*x - 48*mc^7*x - 144*mc^5*x^2 - 24*mc^2*x^3 + 176*mc^3*x^3 + 3*x^4 + 12*mc*x^4) + 12*mc^3*Pi^2*(3*mc - 12*mc^2 - 8*x)*x^2*Log[x/mc^2])/(384*E^(x/y)*x^2),x]","\int \frac{e^{-\frac{x}{y}} \left(\pi ^2 \left(-3 \text{mc}^8+4 \text{mc}^9+24 \text{mc}^6 x-48 \text{mc}^7 x-144 \text{mc}^5 x^2-24 \text{mc}^2 x^3+176 \text{mc}^3 x^3+3 x^4+12 \text{mc} x^4\right)+12 \text{mc}^3 \pi ^2 \left(3 \text{mc}-12 \text{mc}^2-8 x\right) x^2 \log \left(\frac{x}{\text{mc}^2}\right)\right)}{384 x^2} \, dx","\frac{\pi ^2 (3-4 \text{mc}) \text{mc}^8 \text{Ei}\left(-\frac{x}{y}\right)}{384 y}+\frac{1}{16} \pi ^2 (1-2 \text{mc}) \text{mc}^6 \text{Ei}\left(-\frac{x}{y}\right)+\frac{1}{32} \pi ^2 \text{mc}^3 y \left(-12 \text{mc}^2+3 \text{mc}-8 y\right) \text{Ei}\left(-\frac{x}{y}\right)+\frac{\pi ^2 (3-4 \text{mc}) \text{mc}^8 e^{-\frac{x}{y}}}{384 x}+\frac{3}{8} \pi ^2 \text{mc}^5 y e^{-\frac{x}{y}}+\frac{1}{4} \pi ^2 \text{mc}^3 y^2 e^{-\frac{x}{y}}+\frac{1}{48} \pi ^2 (3-22 \text{mc}) \text{mc}^2 y^2 e^{-\frac{x}{y}}+\frac{1}{48} \pi ^2 (3-22 \text{mc}) \text{mc}^2 x y e^{-\frac{x}{y}}+\frac{1}{4} \pi ^2 \text{mc}^3 y^2 e^{-\frac{x}{y}} \log \left(\frac{x}{\text{mc}^2}\right)-\frac{1}{32} \pi ^2 \text{mc}^3 y (3 (1-4 \text{mc}) \text{mc}-8 x) e^{-\frac{x}{y}} \log \left(\frac{x}{\text{mc}^2}\right)-\frac{1}{128} \pi ^2 (4 \text{mc}+1) x^2 y e^{-\frac{x}{y}}-\frac{1}{64} \pi ^2 (4 \text{mc}+1) y^3 e^{-\frac{x}{y}}-\frac{1}{64} \pi ^2 (4 \text{mc}+1) x y^2 e^{-\frac{x}{y}}",1,"Could not integrate","F",-1
283,0,0,4,0.0000361,"\int \sec (x) \sin (2 x) \, dx","IntegrateAlgebraic[Sec[x]*Sin[2*x],x]","\int \sec (x) \sin (2 x) \, dx","-2 \cos (x)",1,"Could not integrate","F",-1
284,1,69,71,0.0588522,"\int \frac{3+3 x-4 x^2-4 x^3-7 x^6+4 x^7+10 x^8+7 x^{13}}{1+2 x-x^2-4 x^3-2 x^4-2 x^7-2 x^8+x^{14}} \, dx","IntegrateAlgebraic[(3 + 3*x - 4*x^2 - 4*x^3 - 7*x^6 + 4*x^7 + 10*x^8 + 7*x^13)/(1 + 2*x - x^2 - 4*x^3 - 2*x^4 - 2*x^7 - 2*x^8 + x^14),x]","\frac{1}{2} \left(1+\sqrt{2}\right) \log \left(x^7+\sqrt{2} \left(-x^2-x\right)-x-1\right)+\frac{1}{2} \left(1-\sqrt{2}\right) \log \left(x^7+\sqrt{2} \left(x^2+x\right)-x-1\right)","\frac{1}{2} \left(\left(1+\sqrt{2}\right) \log \left(-x^7+\sqrt{2} x^2+\sqrt{2} x+x+1\right)-\left(\sqrt{2}-1\right) \log \left(x^7+\sqrt{2} x^2+\left(\sqrt{2}-1\right) x-1\right)\right)",1,"((1 + Sqrt[2])*Log[-1 - x + x^7 + Sqrt[2]*(-x - x^2)])/2 + ((1 - Sqrt[2])*Log[-1 - x + x^7 + Sqrt[2]*(x + x^2)])/2","A",1