1,1,16,16,0.0000754,"\int \left(1+x+x^2\right) \, dx","Integrate[1 + x + x^2,x]","\frac{x^3}{3}+\frac{x^2}{2}+x","\frac{x^3}{3}+\frac{x^2}{2}+x",1,"x + x^2/2 + x^3/3","A",1
2,1,22,22,0.0013164,"\int x^2 \left(x+2 x^2\right)^2 \, dx","Integrate[x^2*(x + 2*x^2)^2,x]","\frac{4 x^7}{7}+\frac{2 x^6}{3}+\frac{x^5}{5}","\frac{4 x^7}{7}+\frac{2 x^6}{3}+\frac{x^5}{5}",1,"x^5/5 + (2*x^6)/3 + (4*x^7)/7","A",1
3,1,22,22,0.0007418,"\int x \left(1+2 x+x^2\right) \, dx","Integrate[x*(1 + 2*x + x^2),x]","\frac{x^4}{4}+\frac{2 x^3}{3}+\frac{x^2}{2}","\frac{x^4}{4}+\frac{2 x^3}{3}+\frac{x^2}{2}",1,"x^2/2 + (2*x^3)/3 + x^4/4","A",1
4,1,2,2,0.000145,"\int \frac{1}{x} \, dx","Integrate[x^(-1),x]","\log (x)","\log (x)",1,"Log[x]","A",1
5,1,24,36,0.0116843,"\int \frac{(1+x)^3}{(-1+x)^4} \, dx","Integrate[(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
6,1,28,32,0.0117568,"\int \frac{1}{(-1+x) x (1+x)^2} \, dx","Integrate[1/((-1 + x)*x*(1 + x)^2),x]","\frac{1}{4} \left(-\frac{2}{x+1}+\log (1-x)-4 \log (x)+3 \log (x+1)\right)","-\frac{1}{2 (x+1)}+\frac{1}{4} \log (1-x)-\log (x)+\frac{3}{4} \log (x+1)",1,"(-2/(1 + x) + Log[1 - x] - 4*Log[x] + 3*Log[1 + x])/4","A",1
7,1,34,40,0.0168642,"\int \frac{b+a x}{(-p+x) (-q+x)} \, dx","Integrate[(b + a*x)/((-p + x)*(-q + x)),x]","\frac{(a p+b) \log (x-p)-(a q+b) \log (x-q)}{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] - (b + a*q)*Log[-q + x])/(p - q)","A",1
8,1,38,34,0.010949,"\int \frac{1}{c+b x+a x^2} \, dx","Integrate[(c + b*x + a*x^2)^(-1),x]","\frac{2 \tan ^{-1}\left(\frac{2 a x+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 + 2*a*x)/Sqrt[-b^2 + 4*a*c]])/Sqrt[-b^2 + 4*a*c]","A",1
9,1,16,16,0.0062675,"\int \frac{b+a x}{1+x^2} \, dx","Integrate[(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
10,1,16,19,0.0047615,"\int \frac{1}{3-2 x+x^2} \, dx","Integrate[(3 - 2*x + x^2)^(-1),x]","\frac{\tan ^{-1}\left(\frac{x-1}{\sqrt{2}}\right)}{\sqrt{2}}","-\frac{\tan ^{-1}\left(\frac{1-x}{\sqrt{2}}\right)}{\sqrt{2}}",1,"ArcTan[(-1 + x)/Sqrt[2]]/Sqrt[2]","A",1
11,1,35,49,0.0232082,"\int \frac{1}{(-1+x)^2 \left(1+x^2\right)^2} \, dx","Integrate[1/((-1 + x)^2*(1 + x^2)^2),x]","\frac{1}{4} \left(-\frac{1}{x^2+1}+\log \left(x^2+1\right)+\frac{1}{1-x}-2 \log (x-1)+\tan ^{-1}(x)\right)","-\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 - x)^(-1) - (1 + x^2)^(-1) + ArcTan[x] - 2*Log[-1 + x] + Log[1 + x^2])/4","A",1
12,1,62,68,0.0315984,"\int \frac{x}{(-a+x) (-b+x) (-c+x)} \, dx","Integrate[x/((-a + x)*(-b + x)*(-c + x)),x]","\frac{a (b-c) \log (x-a)+b (c-a) \log (x-b)+c (a-b) \log (x-c)}{(a-b) (a-c) (b-c)}","\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*(b - c)*Log[-a + x] + b*(-a + c)*Log[-b + x] + (a - b)*c*Log[-c + x])/((a - b)*(a - c)*(b - c))","A",1
13,1,34,47,0.0103404,"\int \frac{x}{\left(a^2+x^2\right) \left(b^2+x^2\right)} \, dx","Integrate[x/((a^2 + x^2)*(b^2 + x^2)),x]","\frac{\log \left(b^2+x^2\right)-\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,"(-Log[a^2 + x^2] + Log[b^2 + x^2])/(2*(a^2 - b^2))","A",1
14,1,30,40,0.0145033,"\int \frac{x^2}{\left(a^2+x^2\right) \left(b^2+x^2\right)} \, dx","Integrate[x^2/((a^2 + x^2)*(b^2 + x^2)),x]","\frac{a \tan ^{-1}\left(\frac{x}{a}\right)-b \tan ^{-1}\left(\frac{x}{b}\right)}{a^2-b^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] - b*ArcTan[x/b])/(a^2 - b^2)","A",1
15,1,27,27,0.0047346,"\int \frac{x}{(-1+x) \left(1+x^2\right)} \, dx","Integrate[x/((-1 + x)*(1 + x^2)),x]","-\frac{1}{4} \log \left(x^2+1\right)+\frac{1}{2} \log (1-x)+\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
16,1,40,41,0.0085761,"\int \frac{x}{1+x^3} \, dx","Integrate[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-1}{\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 + 2*x)/Sqrt[3]]/Sqrt[3] - Log[1 + x]/3 + Log[1 - x + x^2]/6","A",1
17,1,34,43,0.0210173,"\int \frac{x^3}{(-1+x)^2 \left(1+x^3\right)} \, dx","Integrate[x^3/((-1 + x)^2*(1 + x^3)),x]","\frac{1}{12} \left(-\frac{6}{x-1}+9 \log (x-1)-\log (x+1)-4 \log \left((x-1)^2+x\right)\right)","-\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,"(-6/(-1 + x) + 9*Log[-1 + x] - Log[1 + x] - 4*Log[(-1 + x)^2 + x])/12","A",1
18,1,64,85,0.0189689,"\int \frac{1}{1+x^4} \, dx","Integrate[(1 + x^4)^(-1),x]","\frac{-\log \left(x^2-\sqrt{2} x+1\right)+\log \left(x^2+\sqrt{2} x+1\right)-2 \tan ^{-1}\left(1-\sqrt{2} x\right)+2 \tan ^{-1}\left(\sqrt{2} x+1\right)}{4 \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,"(-2*ArcTan[1 - Sqrt[2]*x] + 2*ArcTan[1 + Sqrt[2]*x] - Log[1 - Sqrt[2]*x + x^2] + Log[1 + Sqrt[2]*x + x^2])/(4*Sqrt[2])","A",1
19,1,64,85,0.0101368,"\int \frac{x^2}{1+x^4} \, dx","Integrate[x^2/(1 + x^4),x]","\frac{\log \left(x^2-\sqrt{2} x+1\right)-\log \left(x^2+\sqrt{2} x+1\right)-2 \tan ^{-1}\left(1-\sqrt{2} x\right)+2 \tan ^{-1}\left(\sqrt{2} x+1\right)}{4 \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,"(-2*ArcTan[1 - Sqrt[2]*x] + 2*ArcTan[1 + Sqrt[2]*x] + Log[1 - Sqrt[2]*x + x^2] - Log[1 + Sqrt[2]*x + x^2])/(4*Sqrt[2])","A",1
20,1,73,67,0.0560381,"\int \frac{1}{1+x^2+x^4} \, dx","Integrate[(1 + x^2 + x^4)^(-1),x]","\frac{i \left(\sqrt{1-i \sqrt{3}} \tan ^{-1}\left(\frac{1}{2} \left(\sqrt{3}-i\right) x\right)-\sqrt{1+i \sqrt{3}} \tan ^{-1}\left(\frac{1}{2} \left(\sqrt{3}+i\right) x\right)\right)}{\sqrt{6}}","-\frac{1}{4} \log \left(x^2-x+1\right)+\frac{1}{4} \log \left(x^2+x+1\right)-\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{2 \sqrt{3}}",1,"(I*(Sqrt[1 - I*Sqrt[3]]*ArcTan[((-I + Sqrt[3])*x)/2] - Sqrt[1 + I*Sqrt[3]]*ArcTan[((I + Sqrt[3])*x)/2]))/Sqrt[6]","C",0
21,1,17,18,0.0102234,"\int (a+b x)^p \, dx","Integrate[(a + b*x)^p,x]","\frac{(a+b x)^{p+1}}{b p+b}","\frac{(a+b x)^{p+1}}{b (p+1)}",1,"(a + b*x)^(1 + p)/(b + b*p)","A",1
22,1,33,39,0.0189019,"\int x (a+b x)^p \, dx","Integrate[x*(a + b*x)^p,x]","\frac{(a+b x)^{p+1} (b (p+1) x-a)}{b^2 (p+1) (p+2)}","\frac{(a+b x)^{p+2}}{b^2 (p+2)}-\frac{a (a+b x)^{p+1}}{b^2 (p+1)}",1,"((a + b*x)^(1 + p)*(-a + b*(1 + p)*x))/(b^2*(1 + p)*(2 + p))","A",1
23,1,57,60,0.0296757,"\int x^2 (a+b x)^p \, dx","Integrate[x^2*(a + b*x)^p,x]","\frac{(a+b x)^{p+1} \left(2 a^2-2 a b (p+1) x+b^2 \left(p^2+3 p+2\right) x^2\right)}{b^3 (p+1) (p+2) (p+3)}","\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,"((a + b*x)^(1 + p)*(2*a^2 - 2*a*b*(1 + p)*x + b^2*(2 + 3*p + p^2)*x^2))/(b^3*(1 + p)*(2 + p)*(3 + p))","A",1
24,1,10,10,0.0011167,"\int \frac{1}{a+b x} \, dx","Integrate[(a + b*x)^(-1),x]","\frac{\log (a+b x)}{b}","\frac{\log (a+b x)}{b}",1,"Log[a + b*x]/b","A",1
25,1,12,12,0.0029589,"\int \frac{1}{(a+b x)^2} \, dx","Integrate[(a + b*x)^(-2),x]","-\frac{1}{b (a+b x)}","-\frac{1}{b (a+b x)}",1,"-(1/(b*(a + b*x)))","A",1
26,1,18,18,0.002787,"\int \frac{x}{a+b x} \, dx","Integrate[x/(a + b*x),x]","\frac{x}{b}-\frac{a \log (a+b x)}{b^2}","\frac{x}{b}-\frac{a \log (a+b x)}{b^2}",1,"x/b - (a*Log[a + b*x])/b^2","A",1
27,1,31,31,0.003487,"\int \frac{x^2}{a+b x} \, dx","Integrate[x^2/(a + b*x),x]","\frac{a^2 \log (a+b x)}{b^3}-\frac{a x}{b^2}+\frac{x^2}{2 b}","\frac{a^2 \log (a+b x)}{b^3}-\frac{a x}{b^2}+\frac{x^2}{2 b}",1,"-((a*x)/b^2) + x^2/(2*b) + (a^2*Log[a + b*x])/b^3","A",1
28,1,18,18,0.0038575,"\int \frac{1}{x (a+b x)} \, dx","Integrate[1/(x*(a + b*x)),x]","\frac{\log (x)}{a}-\frac{\log (a+b x)}{a}","\frac{\log (x)}{a}-\frac{\log (a+b x)}{a}",1,"Log[x]/a - Log[a + b*x]/a","A",1
29,1,28,28,0.0045292,"\int \frac{1}{x^2 (a+b x)} \, dx","Integrate[1/(x^2*(a + b*x)),x]","-\frac{b \log (x)}{a^2}+\frac{b \log (a+b x)}{a^2}-\frac{1}{a x}","-\frac{b \log (x)}{a^2}+\frac{b \log (a+b x)}{a^2}-\frac{1}{a x}",1,"-(1/(a*x)) - (b*Log[x])/a^2 + (b*Log[a + b*x])/a^2","A",1
30,1,35,42,0.0387979,"\int \frac{1}{x^2 (a+b x)^2} \, dx","Integrate[1/(x^2*(a + b*x)^2),x]","-\frac{a \left(\frac{b}{a+b x}+\frac{1}{x}\right)-2 b \log (a+b x)+2 b \log (x)}{a^3}","-\frac{2 b \log (x)}{a^3}+\frac{2 b \log (a+b x)}{a^3}-\frac{b}{a^2 (a+b x)}-\frac{1}{a^2 x}",1,"-((a*(x^(-1) + b/(a + b*x)) + 2*b*Log[x] - 2*b*Log[a + b*x])/a^3)","A",1
31,1,10,10,0.0024129,"\int \frac{1}{c^2+x^2} \, dx","Integrate[(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
32,1,10,10,0.0026761,"\int \frac{1}{c^2-x^2} \, dx","Integrate[(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
33,1,66,78,0.0219362,"\int \frac{1}{-1+2 x^3} \, dx","Integrate[(-1 + 2*x^3)^(-1),x]","-\frac{\log \left(2^{2/3} x^2+\sqrt[3]{2} x+1\right)-2 \log \left(1-\sqrt[3]{2} x\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{2} x+1}{\sqrt{3}}\right)}{6 \sqrt[3]{2}}","-\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,"-1/6*(2*Sqrt[3]*ArcTan[(1 + 2*2^(1/3)*x)/Sqrt[3]] - 2*Log[1 - 2^(1/3)*x] + Log[1 + 2^(1/3)*x + 2^(2/3)*x^2])/2^(1/3)","A",1
34,1,65,74,0.0184932,"\int \frac{1}{-2+x^3} \, dx","Integrate[(-2 + x^3)^(-1),x]","-\frac{\log \left(\sqrt[3]{2} x^2+2^{2/3} x+2\right)-2 \log \left(2-2^{2/3} x\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{2^{2/3} x+1}{\sqrt{3}}\right)}{6\ 2^{2/3}}","-\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,"-1/6*(2*Sqrt[3]*ArcTan[(1 + 2^(2/3)*x)/Sqrt[3]] - 2*Log[2 - 2^(2/3)*x] + Log[2 + 2^(2/3)*x + 2^(1/3)*x^2])/2^(2/3)","A",1
35,1,89,115,0.025985,"\int \frac{1}{-b+a x^3} \, dx","Integrate[(-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)-2 \log \left(\sqrt[3]{b}-\sqrt[3]{a} x\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{a} x}{\sqrt[3]{b}}+1}{\sqrt{3}}\right)}{6 \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,"-1/6*(2*Sqrt[3]*ArcTan[(1 + (2*a^(1/3)*x)/b^(1/3))/Sqrt[3]] - 2*Log[b^(1/3) - a^(1/3)*x] + Log[b^(2/3) + a^(1/3)*b^(1/3)*x + a^(2/3)*x^2])/(a^(1/3)*b^(2/3))","A",1
36,1,43,35,0.0187877,"\int \frac{1}{-2+x^4} \, dx","Integrate[(-2 + x^4)^(-1),x]","-\frac{-\log \left(2-2^{3/4} x\right)+\log \left(2^{3/4} x+2\right)+2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{2}}\right)}{4\ 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,"-1/4*(2*ArcTan[x/2^(1/4)] - Log[2 - 2^(3/4)*x] + Log[2 + 2^(3/4)*x])/2^(3/4)","A",1
37,1,43,35,0.0151258,"\int \frac{1}{-1+5 x^4} \, dx","Integrate[(-1 + 5*x^4)^(-1),x]","-\frac{-\log \left(1-\sqrt[4]{5} x\right)+\log \left(\sqrt[4]{5} x+1\right)+2 \tan ^{-1}\left(\sqrt[4]{5} x\right)}{4 \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,"-1/4*(2*ArcTan[5^(1/4)*x] - Log[1 - 5^(1/4)*x] + Log[1 + 5^(1/4)*x])/5^(1/4)","A",1
38,1,120,171,0.0493993,"\int \frac{1}{7+3 x^4} \, dx","Integrate[(7 + 3*x^4)^(-1),x]","\frac{-\log \left(\sqrt{21} x^2-\sqrt{2} \sqrt[4]{3} 7^{3/4} x+7\right)+\log \left(\sqrt{21} x^2+\sqrt{2} \sqrt[4]{3} 7^{3/4} x+7\right)-2 \tan ^{-1}\left(1-\sqrt[4]{\frac{3}{7}} \sqrt{2} x\right)+2 \tan ^{-1}\left(\sqrt[4]{\frac{3}{7}} \sqrt{2} x+1\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{\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,"(-2*ArcTan[1 - (3/7)^(1/4)*Sqrt[2]*x] + 2*ArcTan[1 + (3/7)^(1/4)*Sqrt[2]*x] - Log[7 - Sqrt[2]*3^(1/4)*7^(3/4)*x + Sqrt[21]*x^2] + Log[7 + Sqrt[2]*3^(1/4)*7^(3/4)*x + Sqrt[21]*x^2])/(4*Sqrt[2]*3^(1/4)*7^(3/4))","A",1
39,1,68,73,0.0531933,"\int \frac{1}{-1+3 x^2+x^4} \, dx","Integrate[(-1 + 3*x^2 + x^4)^(-1),x]","-\frac{\sqrt{\sqrt{13}-3} \tan ^{-1}\left(\sqrt{\frac{2}{3+\sqrt{13}}} x\right)+\sqrt{3+\sqrt{13}} \tanh ^{-1}\left(\sqrt{\frac{2}{\sqrt{13}-3}} x\right)}{\sqrt{26}}","-\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]]*ArcTan[Sqrt[2/(3 + Sqrt[13])]*x] + Sqrt[3 + Sqrt[13]]*ArcTanh[Sqrt[2/(-3 + Sqrt[13])]*x])/Sqrt[26])","A",1
40,1,68,73,0.0266629,"\int \frac{1}{-1-3 x^2+x^4} \, dx","Integrate[(-1 - 3*x^2 + x^4)^(-1),x]","-\frac{\sqrt{3+\sqrt{13}} \tan ^{-1}\left(\sqrt{\frac{2}{\sqrt{13}-3}} x\right)+\sqrt{\sqrt{13}-3} \tanh ^{-1}\left(\sqrt{\frac{2}{3+\sqrt{13}}} x\right)}{\sqrt{26}}","-\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]]*ArcTan[Sqrt[2/(-3 + Sqrt[13])]*x] + Sqrt[-3 + Sqrt[13]]*ArcTanh[Sqrt[2/(3 + Sqrt[13])]*x])/Sqrt[26])","A",1
41,1,83,72,0.037131,"\int \frac{1}{1-3 x^2+x^4} \, dx","Integrate[(1 - 3*x^2 + x^4)^(-1),x]","\frac{1}{20} \left(-\left(\left(5+\sqrt{5}\right) \log \left(-2 x+\sqrt{5}-1\right)\right)-\left(\sqrt{5}-5\right) \log \left(-2 x+\sqrt{5}+1\right)+\left(5+\sqrt{5}\right) \log \left(2 x+\sqrt{5}-1\right)+\left(\sqrt{5}-5\right) \log \left(2 x+\sqrt{5}+1\right)\right)","\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])*Log[-1 + Sqrt[5] - 2*x]) - (-5 + Sqrt[5])*Log[1 + Sqrt[5] - 2*x] + (5 + Sqrt[5])*Log[-1 + Sqrt[5] + 2*x] + (-5 + Sqrt[5])*Log[1 + Sqrt[5] + 2*x])/20","A",1
42,1,67,67,0.0309613,"\int \frac{1}{1-4 x^2+x^4} \, dx","Integrate[(1 - 4*x^2 + x^4)^(-1),x]","\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)}}","\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,"ArcTanh[x/Sqrt[2 - Sqrt[3]]]/(2*Sqrt[3*(2 - Sqrt[3])]) - ArcTanh[x/Sqrt[2 + Sqrt[3]]]/(2*Sqrt[3*(2 + Sqrt[3])])","A",1
43,1,67,67,0.0195316,"\int \frac{1}{1+4 x^2+x^4} \, dx","Integrate[(1 + 4*x^2 + x^4)^(-1),x]","\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)}}","\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,"ArcTan[x/Sqrt[2 - Sqrt[3]]]/(2*Sqrt[3*(2 - Sqrt[3])]) - ArcTan[x/Sqrt[2 + Sqrt[3]]]/(2*Sqrt[3*(2 + Sqrt[3])])","A",1
44,1,91,196,0.0532395,"\int \frac{1}{2+x^2+x^4} \, dx","Integrate[(2 + x^2 + x^4)^(-1),x]","\frac{i \tan ^{-1}\left(\frac{x}{\sqrt{\frac{1}{2} \left(1+i \sqrt{7}\right)}}\right)}{\sqrt{\frac{7}{2} \left(1+i \sqrt{7}\right)}}-\frac{i \tan ^{-1}\left(\frac{x}{\sqrt{\frac{1}{2} \left(1-i \sqrt{7}\right)}}\right)}{\sqrt{\frac{7}{2} \left(1-i \sqrt{7}\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,"((-I)*ArcTan[x/Sqrt[(1 - I*Sqrt[7])/2]])/Sqrt[(7*(1 - I*Sqrt[7]))/2] + (I*ArcTan[x/Sqrt[(1 + I*Sqrt[7])/2]])/Sqrt[(7*(1 + I*Sqrt[7]))/2]","C",1
45,1,91,196,0.0827981,"\int \frac{1}{2-x^2+x^4} \, dx","Integrate[(2 - x^2 + x^4)^(-1),x]","\frac{i \tan ^{-1}\left(\frac{x}{\sqrt{\frac{1}{2} \left(-1+i \sqrt{7}\right)}}\right)}{\sqrt{\frac{7}{2} \left(-1+i \sqrt{7}\right)}}-\frac{i \tan ^{-1}\left(\frac{x}{\sqrt{\frac{1}{2} \left(-1-i \sqrt{7}\right)}}\right)}{\sqrt{\frac{7}{2} \left(-1-i \sqrt{7}\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,"((-I)*ArcTan[x/Sqrt[(-1 - I*Sqrt[7])/2]])/Sqrt[(7*(-1 - I*Sqrt[7]))/2] + (I*ArcTan[x/Sqrt[(-1 + I*Sqrt[7])/2]])/Sqrt[(7*(-1 + I*Sqrt[7]))/2]","C",1
46,1,75,73,0.0166321,"\int \frac{1}{-1+x^6} \, dx","Integrate[(-1 + x^6)^(-1),x]","\frac{1}{12} \left(\log \left(x^2-x+1\right)-\log \left(x^2+x+1\right)+2 \log (1-x)-2 \log (x+1)-2 \sqrt{3} \tan ^{-1}\left(\frac{2 x-1}{\sqrt{3}}\right)-2 \sqrt{3} \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)\right)","\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,"(-2*Sqrt[3]*ArcTan[(-1 + 2*x)/Sqrt[3]] - 2*Sqrt[3]*ArcTan[(1 + 2*x)/Sqrt[3]] + 2*Log[1 - x] - 2*Log[1 + x] + Log[1 - x + x^2] - Log[1 + x + x^2])/12","A",1
47,1,122,138,0.0394243,"\int \frac{1}{-2+x^6} \, dx","Integrate[(-2 + x^6)^(-1),x]","-\frac{-\log \left(2^{2/3} x^2-2^{5/6} x+2\right)+\log \left(2^{2/3} x^2+2^{5/6} x+2\right)-2 \log \left(2-2^{5/6} x\right)+2 \log \left(2^{5/6} x+2\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{2^{5/6} x-1}{\sqrt{3}}\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{2^{5/6} x+1}{\sqrt{3}}\right)}{12\ 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,"-1/12*(2*Sqrt[3]*ArcTan[(-1 + 2^(5/6)*x)/Sqrt[3]] + 2*Sqrt[3]*ArcTan[(1 + 2^(5/6)*x)/Sqrt[3]] - 2*Log[2 - 2^(5/6)*x] + 2*Log[2 + 2^(5/6)*x] - Log[2 - 2^(5/6)*x + 2^(2/3)*x^2] + Log[2 + 2^(5/6)*x + 2^(2/3)*x^2])/2^(5/6)","A",1
48,1,115,138,0.0259352,"\int \frac{1}{2+x^6} \, dx","Integrate[(2 + x^6)^(-1),x]","\frac{-\sqrt{3} \log \left(2^{2/3} x^2-2^{5/6} \sqrt{3} x+2\right)+\sqrt{3} \log \left(2^{2/3} x^2+2^{5/6} \sqrt{3} x+2\right)+4 \tan ^{-1}\left(\frac{x}{\sqrt[6]{2}}\right)-2 \tan ^{-1}\left(\sqrt{3}-2^{5/6} x\right)+2 \tan ^{-1}\left(2^{5/6} x+\sqrt{3}\right)}{12\ 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,"(4*ArcTan[x/2^(1/6)] - 2*ArcTan[Sqrt[3] - 2^(5/6)*x] + 2*ArcTan[Sqrt[3] + 2^(5/6)*x] - Sqrt[3]*Log[2 - 2^(5/6)*Sqrt[3]*x + 2^(2/3)*x^2] + Sqrt[3]*Log[2 + 2^(5/6)*Sqrt[3]*x + 2^(2/3)*x^2])/(12*2^(5/6))","A",1
49,1,209,339,0.0065698,"\int \frac{1}{1+x^8} \, dx","Integrate[(1 + x^8)^(-1),x]","-\frac{1}{8} \sin \left(\frac{\pi }{8}\right) \log \left(x^2-2 x \sin \left(\frac{\pi }{8}\right)+1\right)+\frac{1}{8} \sin \left(\frac{\pi }{8}\right) \log \left(x^2+2 x \sin \left(\frac{\pi }{8}\right)+1\right)-\frac{1}{8} \cos \left(\frac{\pi }{8}\right) \log \left(x^2-2 x \cos \left(\frac{\pi }{8}\right)+1\right)+\frac{1}{8} \cos \left(\frac{\pi }{8}\right) \log \left(x^2+2 x \cos \left(\frac{\pi }{8}\right)+1\right)+\frac{1}{4} \sin \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\csc \left(\frac{\pi }{8}\right) \left(x-\cos \left(\frac{\pi }{8}\right)\right)\right)+\frac{1}{4} \sin \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\csc \left(\frac{\pi }{8}\right) \left(x+\cos \left(\frac{\pi }{8}\right)\right)\right)+\frac{1}{4} \cos \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\sec \left(\frac{\pi }{8}\right) \left(x-\sin \left(\frac{\pi }{8}\right)\right)\right)+\frac{1}{4} \cos \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\sec \left(\frac{\pi }{8}\right) \left(x+\sin \left(\frac{\pi }{8}\right)\right)\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,"(ArcTan[Sec[Pi/8]*(x - Sin[Pi/8])]*Cos[Pi/8])/4 + (ArcTan[Sec[Pi/8]*(x + Sin[Pi/8])]*Cos[Pi/8])/4 - (Cos[Pi/8]*Log[1 + x^2 - 2*x*Cos[Pi/8]])/8 + (Cos[Pi/8]*Log[1 + x^2 + 2*x*Cos[Pi/8]])/8 + (ArcTan[(x - Cos[Pi/8])*Csc[Pi/8]]*Sin[Pi/8])/4 + (ArcTan[(x + Cos[Pi/8])*Csc[Pi/8]]*Sin[Pi/8])/4 - (Log[1 + x^2 - 2*x*Sin[Pi/8]]*Sin[Pi/8])/8 + (Log[1 + x^2 + 2*x*Sin[Pi/8]]*Sin[Pi/8])/8","A",1
50,1,98,97,0.024372,"\int \frac{1}{-1+x^8} \, dx","Integrate[(-1 + x^8)^(-1),x]","\frac{1}{16} \left(\sqrt{2} \log \left(x^2-\sqrt{2} x+1\right)-\sqrt{2} \log \left(x^2+\sqrt{2} x+1\right)+2 \log (1-x)-2 \log (x+1)-4 \tan ^{-1}(x)+2 \sqrt{2} \tan ^{-1}\left(1-\sqrt{2} x\right)-2 \sqrt{2} \tan ^{-1}\left(\sqrt{2} x+1\right)\right)","\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,"(-4*ArcTan[x] + 2*Sqrt[2]*ArcTan[1 - Sqrt[2]*x] - 2*Sqrt[2]*ArcTan[1 + Sqrt[2]*x] + 2*Log[1 - x] - 2*Log[1 + x] + Sqrt[2]*Log[1 - Sqrt[2]*x + x^2] - Sqrt[2]*Log[1 + Sqrt[2]*x + x^2])/16","A",1
51,1,42,275,0.0123579,"\int \frac{1}{1-x^4+x^8} \, dx","Integrate[(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
52,1,260,49,0.1147688,"\int \frac{x^7}{1+x^{12}} \, dx","Integrate[x^7/(1 + x^12),x]","\frac{1}{24} \left(-2 \log \left(x^2-\sqrt{2} x+1\right)-2 \log \left(x^2+\sqrt{2} x+1\right)+\log \left(2 x^2-\sqrt{6} x+\sqrt{2} x+2\right)+\log \left(2 x^2+\sqrt{2} \left(\sqrt{3}-1\right) x+2\right)+\log \left(2 x^2-\left(\sqrt{2}+\sqrt{6}\right) x+2\right)+\log \left(2 x^2+\left(\sqrt{2}+\sqrt{6}\right) x+2\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{-2 \sqrt{2} x+\sqrt{3}+1}{1-\sqrt{3}}\right)-2 \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt{2} x-\sqrt{3}+1}{1+\sqrt{3}}\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt{2} x+\sqrt{3}-1}{1+\sqrt{3}}\right)-2 \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt{2} x+\sqrt{3}+1}{\sqrt{3}-1}\right)\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,"(2*Sqrt[3]*ArcTan[(1 + Sqrt[3] - 2*Sqrt[2]*x)/(1 - Sqrt[3])] - 2*Sqrt[3]*ArcTan[(1 - Sqrt[3] + 2*Sqrt[2]*x)/(1 + Sqrt[3])] + 2*Sqrt[3]*ArcTan[(-1 + Sqrt[3] + 2*Sqrt[2]*x)/(1 + Sqrt[3])] - 2*Sqrt[3]*ArcTan[(1 + Sqrt[3] + 2*Sqrt[2]*x)/(-1 + Sqrt[3])] - 2*Log[1 - Sqrt[2]*x + x^2] - 2*Log[1 + Sqrt[2]*x + x^2] + Log[2 + Sqrt[2]*x - Sqrt[6]*x + 2*x^2] + Log[2 + Sqrt[2]*(-1 + Sqrt[3])*x + 2*x^2] + Log[2 - (Sqrt[2] + Sqrt[6])*x + 2*x^2] + Log[2 + (Sqrt[2] + Sqrt[6])*x + 2*x^2])/24","B",1
53,1,8,8,0.0006648,"\int \log (x) \, dx","Integrate[Log[x],x]","x \log (x)-x","x \log (x)-x",1,"-x + x*Log[x]","A",1
54,1,17,17,0.0008382,"\int x \log (x) \, dx","Integrate[x*Log[x],x]","\frac{1}{2} x^2 \log (x)-\frac{x^2}{4}","\frac{1}{2} x^2 \log (x)-\frac{x^2}{4}",1,"-1/4*x^2 + (x^2*Log[x])/2","A",1
55,1,17,17,0.0010288,"\int x^2 \log (x) \, dx","Integrate[x^2*Log[x],x]","\frac{1}{3} x^3 \log (x)-\frac{x^3}{9}","\frac{1}{3} x^3 \log (x)-\frac{x^3}{9}",1,"-1/9*x^3 + (x^3*Log[x])/3","A",1
56,1,19,26,0.0076019,"\int x^p \log (x) \, dx","Integrate[x^p*Log[x],x]","\frac{x^{p+1} ((p+1) \log (x)-1)}{(p+1)^2}","\frac{x^{p+1} \log (x)}{p+1}-\frac{x^{p+1}}{(p+1)^2}",1,"(x^(1 + p)*(-1 + (1 + p)*Log[x]))/(1 + p)^2","A",1
57,1,15,15,0.0009537,"\int \log ^2(x) \, dx","Integrate[Log[x]^2,x]","2 x+x \log ^2(x)-2 x \log (x)","2 x+x \log ^2(x)-2 x \log (x)",1,"2*x - 2*x*Log[x] + x*Log[x]^2","A",1
58,1,127,127,0.003505,"\int x^9 \log ^{11}(x) \, dx","Integrate[x^9*Log[x]^11,x]","-\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}","-\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,"(-6237*x^10)/156250000 + (6237*x^10*Log[x])/15625000 - (6237*x^10*Log[x]^2)/3125000 + (2079*x^10*Log[x]^3)/312500 - (2079*x^10*Log[x]^4)/125000 + (2079*x^10*Log[x]^5)/62500 - (693*x^10*Log[x]^6)/12500 + (99*x^10*Log[x]^7)/1250 - (99*x^10*Log[x]^8)/1000 + (11*x^10*Log[x]^9)/100 - (11*x^10*Log[x]^10)/100 + (x^10*Log[x]^11)/10","A",1
59,1,8,8,0.0011812,"\int \frac{\log ^2(x)}{x} \, dx","Integrate[Log[x]^2/x,x]","\frac{\log ^3(x)}{3}","\frac{\log ^3(x)}{3}",1,"Log[x]^3/3","A",1
60,0,0,2,0.0022353,"\int \frac{1}{\log (x)} \, dx","Integrate[Log[x]^(-1),x]","\int \frac{1}{\log (x)} \, dx","\operatorname{LogIntegral}(x)",1,"Integrate[Log[x]^(-1), x]","F",-1
61,1,5,4,0.0112758,"\int \frac{1}{\log (1+x)} \, dx","Integrate[Log[1 + x]^(-1),x]","\operatorname{ExpIntegralEi}(\log (x+1))","\operatorname{LogIntegral}(x+1)",1,"ExpIntegralEi[Log[1 + x]]","A",1
62,1,3,3,0.0044923,"\int \frac{1}{x \log (x)} \, dx","Integrate[1/(x*Log[x]),x]","\log (\log (x))","\log (\log (x))",1,"Log[Log[x]]","A",1
63,1,17,17,0.0280162,"\int \frac{1}{x^2 \log ^2(x)} \, dx","Integrate[1/(x^2*Log[x]^2),x]","-\text{Ei}(-\log (x))-\frac{1}{x \log (x)}","-\text{Ei}(-\log (x))-\frac{1}{x \log (x)}",1,"-ExpIntegralEi[-Log[x]] - 1/(x*Log[x])","A",1
64,1,12,12,0.0029299,"\int \frac{\log ^p(x)}{x} \, dx","Integrate[Log[x]^p/x,x]","\frac{\log ^{p+1}(x)}{p+1}","\frac{\log ^{p+1}(x)}{p+1}",1,"Log[x]^(1 + p)/(1 + p)","A",1
65,1,28,28,0.0014294,"\int (b+a x) \log (x) \, dx","Integrate[(b + a*x)*Log[x],x]","-\frac{a x^2}{4}+\frac{1}{2} a x^2 \log (x)-b x+b x \log (x)","-\frac{a x^2}{4}+\frac{1}{2} a x^2 \log (x)-b x+b x \log (x)",1,"-(b*x) - (a*x^2)/4 + b*x*Log[x] + (a*x^2*Log[x])/2","A",1
66,1,53,54,0.0103506,"\int (b+a x)^2 \log (x) \, dx","Integrate[(b + a*x)^2*Log[x],x]","-\frac{1}{9} a^2 x^3+\frac{1}{3} a^2 x^3 \log (x)-\frac{1}{2} a b x^2+a b x^2 \log (x)-b^2 x+b^2 x \log (x)","-\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,"-(b^2*x) - (a*b*x^2)/2 - (a^2*x^3)/9 + b^2*x*Log[x] + a*b*x^2*Log[x] + (a^2*x^3*Log[x])/3","A",1
67,1,27,29,0.0121433,"\int \frac{\log (x)}{(b+a x)^2} \, dx","Integrate[Log[x]/(b + a*x)^2,x]","\frac{\frac{x \log (x)}{a x+b}-\frac{\log (a x+b)}{a}}{b}","\frac{x \log (x)}{b (a x+b)}-\frac{\log (a x+b)}{a b}",1,"((x*Log[x])/(b + a*x) - Log[b + a*x]/a)/b","A",1
68,1,46,46,0.0148562,"\int x \log (b+a x) \, dx","Integrate[x*Log[b + a*x],x]","-\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}","-\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,"(b*x)/(2*a) - x^2/4 - (b^2*Log[b + a*x])/(2*a^2) + (x^2*Log[b + a*x])/2","A",1
69,1,59,59,0.0185823,"\int x^2 \log (b+a x) \, dx","Integrate[x^2*Log[b + a*x],x]","\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}","\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,"-1/3*(b^2*x)/a^2 + (b*x^2)/(6*a) - x^3/9 + (b^3*Log[b + a*x])/(3*a^3) + (x^3*Log[b + a*x])/3","A",1
70,1,23,23,0.0016687,"\int \log \left(a^2+x^2\right) \, dx","Integrate[Log[a^2 + x^2],x]","x \log \left(a^2+x^2\right)+2 a \tan ^{-1}\left(\frac{x}{a}\right)-2 x","x \log \left(a^2+x^2\right)+2 a \tan ^{-1}\left(\frac{x}{a}\right)-2 x",1,"-2*x + 2*a*ArcTan[x/a] + x*Log[a^2 + x^2]","A",1
71,1,26,27,0.0033691,"\int x \log \left(a^2+x^2\right) \, dx","Integrate[x*Log[a^2 + x^2],x]","\frac{1}{2} \left(\left(a^2+x^2\right) \log \left(a^2+x^2\right)-x^2\right)","\frac{1}{2} \left(a^2+x^2\right) \log \left(a^2+x^2\right)-\frac{x^2}{2}",1,"(-x^2 + (a^2 + x^2)*Log[a^2 + x^2])/2","A",1
72,1,44,44,0.0023313,"\int x^2 \log \left(a^2+x^2\right) \, dx","Integrate[x^2*Log[a^2 + x^2],x]","-\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}","-\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,"(2*a^2*x)/3 - (2*x^3)/9 - (2*a^3*ArcTan[x/a])/3 + (x^3*Log[a^2 + x^2])/3","A",1
73,1,54,54,0.0026989,"\int x^4 \log \left(a^2+x^2\right) \, dx","Integrate[x^4*Log[a^2 + x^2],x]","\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}","\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,"(-2*a^4*x)/5 + (2*a^2*x^3)/15 - (2*x^5)/25 + (2*a^5*ArcTan[x/a])/5 + (x^5*Log[a^2 + x^2])/5","A",1
74,1,25,25,0.0024813,"\int \log \left(-a^2+x^2\right) \, dx","Integrate[Log[-a^2 + x^2],x]","x \log \left(x^2-a^2\right)+2 a \tanh ^{-1}\left(\frac{x}{a}\right)-2 x","x \log \left(x^2-a^2\right)+2 a \tanh ^{-1}\left(\frac{x}{a}\right)-2 x",1,"-2*x + 2*a*ArcTanh[x/a] + x*Log[-a^2 + x^2]","A",1
75,0,0,8,0.0294213,"\int \log (\log (\log (\log (x)))) \, dx","Integrate[Log[Log[Log[Log[x]]]],x]","\int \log (\log (\log (\log (x)))) \, dx","\text{Int}(\log (\log (\log (\log (x)))),x)",0,"Integrate[Log[Log[Log[Log[x]]]], x]","A",-1
76,1,4,4,0.0010747,"\int \sin (x) \, dx","Integrate[Sin[x],x]","-\cos (x)","-\cos (x)",1,"-Cos[x]","A",1
77,1,2,2,0.0010418,"\int \cos (x) \, dx","Integrate[Cos[x],x]","\sin (x)","\sin (x)",1,"Sin[x]","A",1
78,1,5,5,0.0020743,"\int \tan (x) \, dx","Integrate[Tan[x],x]","-\log (\cos (x))","-\log (\cos (x))",1,"-Log[Cos[x]]","A",1
79,1,3,3,0.0020869,"\int \cot (x) \, dx","Integrate[Cot[x],x]","\log (\sin (x))","\log (\sin (x))",1,"Log[Sin[x]]","A",1
80,1,27,21,0.0421978,"\int \frac{1}{(1+\tan (x))^2} \, dx","Integrate[(1 + Tan[x])^(-2),x]","\frac{\tan (x)+\log (\sin (x)+\cos (x))+\tan (x) \log (\sin (x)+\cos (x))}{2 \tan (x)+2}","\frac{1}{2} \log (\sin (x)+\cos (x))-\frac{1}{2 (\tan (x)+1)}",1,"(Log[Cos[x] + Sin[x]] + Tan[x] + Log[Cos[x] + Sin[x]]*Tan[x])/(2 + 2*Tan[x])","A",1
81,1,33,3,0.004997,"\int \sec (x) \, dx","Integrate[Sec[x],x]","\log \left(\sin \left(\frac{x}{2}\right)+\cos \left(\frac{x}{2}\right)\right)-\log \left(\cos \left(\frac{x}{2}\right)-\sin \left(\frac{x}{2}\right)\right)","\tanh ^{-1}(\sin (x))",1,"-Log[Cos[x/2] - Sin[x/2]] + Log[Cos[x/2] + Sin[x/2]]","B",1
82,1,17,5,0.0027235,"\int \csc (x) \, dx","Integrate[Csc[x],x]","\log \left(\sin \left(\frac{x}{2}\right)\right)-\log \left(\cos \left(\frac{x}{2}\right)\right)","-\tanh ^{-1}(\cos (x))",1,"-Log[Cos[x/2]] + Log[Sin[x/2]]","B",1
83,1,14,14,0.0017597,"\int \sin ^2(x) \, dx","Integrate[Sin[x]^2,x]","\frac{x}{2}-\frac{1}{4} \sin (2 x)","\frac{x}{2}-\frac{1}{2} \sin (x) \cos (x)",1,"x/2 - Sin[2*x]/4","A",1
84,1,20,20,0.002044,"\int x^3 \sin \left(x^2\right) \, dx","Integrate[x^3*Sin[x^2],x]","\frac{\sin \left(x^2\right)}{2}-\frac{1}{2} x^2 \cos \left(x^2\right)","\frac{\sin \left(x^2\right)}{2}-\frac{1}{2} x^2 \cos \left(x^2\right)",1,"-1/2*(x^2*Cos[x^2]) + Sin[x^2]/2","A",1
85,1,15,13,0.0019562,"\int \sin ^3(x) \, dx","Integrate[Sin[x]^3,x]","\frac{1}{12} \cos (3 x)-\frac{3 \cos (x)}{4}","\frac{\cos ^3(x)}{3}-\cos (x)",1,"(-3*Cos[x])/4 + Cos[3*x]/12","A",1
86,1,44,44,0.0387946,"\int \sin ^p(x) \, dx","Integrate[Sin[x]^p,x]","-\cos (x) \sin ^{p+1}(x) \sin ^2(x)^{\frac{1}{2} (-p-1)} \, _2F_1\left(\frac{1}{2},\frac{1-p}{2};\frac{3}{2};\cos ^2(x)\right)","\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,"-(Cos[x]*Hypergeometric2F1[1/2, (1 - p)/2, 3/2, Cos[x]^2]*Sin[x]^(1 + p)*(Sin[x]^2)^((-1 - p)/2))","A",1
87,1,19,19,0.0040191,"\int \cos (x) \left(1+\sin ^2(x)\right)^2 \, dx","Integrate[Cos[x]*(1 + Sin[x]^2)^2,x]","\frac{\sin ^5(x)}{5}+\frac{2 \sin ^3(x)}{3}+\sin (x)","\frac{\sin ^5(x)}{5}+\frac{2 \sin ^3(x)}{3}+\sin (x)",1,"Sin[x] + (2*Sin[x]^3)/3 + Sin[x]^5/5","A",1
88,1,14,14,0.0018731,"\int \cos ^2(x) \, dx","Integrate[Cos[x]^2,x]","\frac{x}{2}+\frac{1}{4} \sin (2 x)","\frac{x}{2}+\frac{1}{2} \sin (x) \cos (x)",1,"x/2 + Sin[2*x]/4","A",1
89,1,15,11,0.0020392,"\int \cos ^3(x) \, dx","Integrate[Cos[x]^3,x]","\frac{3 \sin (x)}{4}+\frac{1}{12} \sin (3 x)","\sin (x)-\frac{\sin ^3(x)}{3}",1,"(3*Sin[x])/4 + Sin[3*x]/12","A",1
90,1,2,2,0.0017995,"\int \sec ^2(x) \, dx","Integrate[Sec[x]^2,x]","\tan (x)","\tan (x)",1,"Tan[x]","A",1
91,1,15,15,0.0054092,"\int \sin (x) \sin (2 x) \, dx","Integrate[Sin[x]*Sin[2*x],x]","\frac{\sin (x)}{2}-\frac{1}{6} \sin (3 x)","\frac{\sin (x)}{2}-\frac{1}{6} \sin (3 x)",1,"Sin[x]/2 - Sin[3*x]/6","A",1
92,1,8,8,0.0026481,"\int x \sin (x) \, dx","Integrate[x*Sin[x],x]","\sin (x)-x \cos (x)","\sin (x)-x \cos (x)",1,"-(x*Cos[x]) + Sin[x]","A",1
93,1,15,17,0.0159291,"\int x^2 \sin (x) \, dx","Integrate[x^2*Sin[x],x]","2 x \sin (x)-\left(x^2-2\right) \cos (x)","x^2 (-\cos (x))+2 x \sin (x)+2 \cos (x)",1,"-((-2 + x^2)*Cos[x]) + 2*x*Sin[x]","A",1
94,1,25,25,0.0110454,"\int x \sin ^2(x) \, dx","Integrate[x*Sin[x]^2,x]","\frac{x^2}{4}-\frac{1}{4} x \sin (2 x)-\frac{1}{8} \cos (2 x)","\frac{x^2}{4}+\frac{\sin ^2(x)}{4}-\frac{1}{2} x \sin (x) \cos (x)",1,"x^2/4 - Cos[2*x]/8 - (x*Sin[2*x])/4","A",1
95,1,29,41,0.0370305,"\int x^2 \sin ^2(x) \, dx","Integrate[x^2*Sin[x]^2,x]","\frac{1}{24} \left(4 x^3+\left(3-6 x^2\right) \sin (2 x)-6 x \cos (2 x)\right)","\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,"(4*x^3 - 6*x*Cos[2*x] + (3 - 6*x^2)*Sin[2*x])/24","A",1
96,1,31,33,0.008579,"\int x \sin ^3(x) \, dx","Integrate[x*Sin[x]^3,x]","\frac{3 \sin (x)}{4}-\frac{1}{36} \sin (3 x)-\frac{3}{4} x \cos (x)+\frac{1}{12} x \cos (3 x)","\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,"(-3*x*Cos[x])/4 + (x*Cos[3*x])/12 + (3*Sin[x])/4 - Sin[3*x]/36","A",1
97,1,7,7,0.0023592,"\int x \cos (x) \, dx","Integrate[x*Cos[x],x]","x \sin (x)+\cos (x)","x \sin (x)+\cos (x)",1,"Cos[x] + x*Sin[x]","A",1
98,1,14,16,0.0129419,"\int x^2 \cos (x) \, dx","Integrate[x^2*Cos[x],x]","\left(x^2-2\right) \sin (x)+2 x \cos (x)","x^2 \sin (x)-2 \sin (x)+2 x \cos (x)",1,"2*x*Cos[x] + (-2 + x^2)*Sin[x]","A",1
99,1,25,25,0.0117172,"\int x \cos ^2(x) \, dx","Integrate[x*Cos[x]^2,x]","\frac{x^2}{4}+\frac{1}{4} x \sin (2 x)+\frac{1}{8} \cos (2 x)","\frac{x^2}{4}+\frac{\cos ^2(x)}{4}+\frac{1}{2} x \sin (x) \cos (x)",1,"x^2/4 + Cos[2*x]/8 + (x*Sin[2*x])/4","A",1
100,1,29,41,0.0345818,"\int x^2 \cos ^2(x) \, dx","Integrate[x^2*Cos[x]^2,x]","\frac{1}{24} \left(4 x^3+\left(6 x^2-3\right) \sin (2 x)+6 x \cos (2 x)\right)","\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,"(4*x^3 + 6*x*Cos[2*x] + (-3 + 6*x^2)*Sin[2*x])/24","A",1
101,1,31,33,0.0085393,"\int x \cos ^3(x) \, dx","Integrate[x*Cos[x]^3,x]","\frac{3}{4} x \sin (x)+\frac{1}{12} x \sin (3 x)+\frac{3 \cos (x)}{4}+\frac{1}{36} \cos (3 x)","\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,"(3*Cos[x])/4 + Cos[3*x]/36 + (3*x*Sin[x])/4 + (x*Sin[3*x])/12","A",1
102,1,2,2,0.0116613,"\int \frac{\sin (x)}{x} \, dx","Integrate[Sin[x]/x,x]","\text{Si}(x)","\text{Si}(x)",1,"SinIntegral[x]","A",1
103,1,2,2,0.0019916,"\int \frac{\cos (x)}{x} \, dx","Integrate[Cos[x]/x,x]","\operatorname{CosIntegral}(x)","\operatorname{CosIntegral}(x)",1,"CosIntegral[x]","A",1
104,1,10,10,0.0017668,"\int \frac{\sin (x)}{x^2} \, dx","Integrate[Sin[x]/x^2,x]","\operatorname{CosIntegral}(x)-\frac{\sin (x)}{x}","\operatorname{CosIntegral}(x)-\frac{\sin (x)}{x}",1,"CosIntegral[x] - Sin[x]/x","A",1
105,1,15,15,0.0132926,"\int \frac{\sin ^2(x)}{x} \, dx","Integrate[Sin[x]^2/x,x]","\frac{\log (x)}{2}-\frac{1}{2} \operatorname{CosIntegral}(2 x)","\frac{\log (x)}{2}-\frac{1}{2} \operatorname{CosIntegral}(2 x)",1,"-1/2*CosIntegral[2*x] + Log[x]/2","A",1
106,1,12,12,0.0034479,"\int \tan ^3(x) \, dx","Integrate[Tan[x]^3,x]","\frac{\sec ^2(x)}{2}+\log (\cos (x))","\frac{\tan ^2(x)}{2}+\log (\cos (x))",1,"Log[Cos[x]] + Sec[x]^2/2","A",1
107,1,22,11,0.0068928,"\int \sin (a+b x) \, dx","Integrate[Sin[a + b*x],x]","\frac{\sin (a) \sin (b x)}{b}-\frac{\cos (a) \cos (b x)}{b}","-\frac{\cos (a+b x)}{b}",1,"-((Cos[a]*Cos[b*x])/b) + (Sin[a]*Sin[b*x])/b","A",1
108,1,21,10,0.0091451,"\int \cos (a+b x) \, dx","Integrate[Cos[a + b*x],x]","\frac{\sin (a) \cos (b x)}{b}+\frac{\cos (a) \sin (b x)}{b}","\frac{\sin (a+b x)}{b}",1,"(Cos[b*x]*Sin[a])/b + (Cos[a]*Sin[b*x])/b","B",1
109,1,12,12,0.0087429,"\int \tan (a+b x) \, dx","Integrate[Tan[a + b*x],x]","-\frac{\log (\cos (a+b x))}{b}","-\frac{\log (\cos (a+b x))}{b}",1,"-(Log[Cos[a + b*x]]/b)","A",1
110,1,19,11,0.0098517,"\int \cot (a+b x) \, dx","Integrate[Cot[a + b*x],x]","\frac{\log (\tan (a+b x))+\log (\cos (a+b x))}{b}","\frac{\log (\sin (a+b x))}{b}",1,"(Log[Cos[a + b*x]] + Log[Tan[a + b*x]])/b","A",1
111,1,38,12,0.0140847,"\int \csc (a+b x) \, dx","Integrate[Csc[a + b*x],x]","\frac{\log \left(\sin \left(\frac{a}{2}+\frac{b x}{2}\right)\right)}{b}-\frac{\log \left(\cos \left(\frac{a}{2}+\frac{b x}{2}\right)\right)}{b}","-\frac{\tanh ^{-1}(\cos (a+b x))}{b}",1,"-(Log[Cos[a/2 + (b*x)/2]]/b) + Log[Sin[a/2 + (b*x)/2]]/b","B",1
112,1,11,11,0.0016878,"\int \sec (a+b x) \, dx","Integrate[Sec[a + b*x],x]","\frac{\tanh ^{-1}(\sin (a+b x))}{b}","\frac{\tanh ^{-1}(\sin (a+b x))}{b}",1,"ArcTanh[Sin[a + b*x]]/b","A",1
113,1,23,25,0.026891,"\int \sin ^2(a+b x) \, dx","Integrate[Sin[a + b*x]^2,x]","-\frac{\sin (2 (a+b x))-2 (a+b x)}{4 b}","\frac{x}{2}-\frac{\sin (a+b x) \cos (a+b x)}{2 b}",1,"-1/4*(-2*(a + b*x) + Sin[2*(a + b*x)])/b","A",1
114,1,29,27,0.0107735,"\int \sin ^3(a+b x) \, dx","Integrate[Sin[a + b*x]^3,x]","\frac{\cos (3 (a+b x))}{12 b}-\frac{3 \cos (a+b x)}{4 b}","\frac{\cos ^3(a+b x)}{3 b}-\frac{\cos (a+b x)}{b}",1,"(-3*Cos[a + b*x])/(4*b) + Cos[3*(a + b*x)]/(12*b)","A",1
115,1,23,25,0.0174753,"\int \cos ^2(a+b x) \, dx","Integrate[Cos[a + b*x]^2,x]","\frac{2 (a+b x)+\sin (2 (a+b x))}{4 b}","\frac{\sin (a+b x) \cos (a+b x)}{2 b}+\frac{x}{2}",1,"(2*(a + b*x) + Sin[2*(a + b*x)])/(4*b)","A",1
116,1,26,26,0.0073834,"\int \cos ^3(a+b x) \, dx","Integrate[Cos[a + b*x]^3,x]","\frac{\sin (a+b x)}{b}-\frac{\sin ^3(a+b x)}{3 b}","\frac{\sin (a+b x)}{b}-\frac{\sin ^3(a+b x)}{3 b}",1,"Sin[a + b*x]/b - Sin[a + b*x]^3/(3*b)","A",1
117,1,10,10,0.0029357,"\int \sec ^2(a+b x) \, dx","Integrate[Sec[a + b*x]^2,x]","\frac{\tan (a+b x)}{b}","\frac{\tan (a+b x)}{b}",1,"Tan[a + b*x]/b","A",1
118,1,6,9,0.003763,"\int \frac{1}{1+\cos (x)} \, dx","Integrate[(1 + Cos[x])^(-1),x]","\tan \left(\frac{x}{2}\right)","\frac{\sin (x)}{\cos (x)+1}",1,"Tan[x/2]","A",1
119,1,8,12,0.0089182,"\int \frac{1}{1-\cos (x)} \, dx","Integrate[(1 - Cos[x])^(-1),x]","-\cot \left(\frac{x}{2}\right)","-\frac{\sin (x)}{1-\cos (x)}",1,"-Cot[x/2]","A",1
120,1,23,10,0.0090963,"\int \frac{1}{1+\sin (x)} \, dx","Integrate[(1 + Sin[x])^(-1),x]","\frac{2 \sin \left(\frac{x}{2}\right)}{\sin \left(\frac{x}{2}\right)+\cos \left(\frac{x}{2}\right)}","-\frac{\cos (x)}{\sin (x)+1}",1,"(2*Sin[x/2])/(Cos[x/2] + Sin[x/2])","B",1
121,1,25,11,0.0117326,"\int \frac{1}{1-\sin (x)} \, dx","Integrate[(1 - Sin[x])^(-1),x]","\frac{2 \sin \left(\frac{x}{2}\right)}{\cos \left(\frac{x}{2}\right)-\sin \left(\frac{x}{2}\right)}","\frac{\cos (x)}{1-\sin (x)}",1,"(2*Sin[x/2])/(Cos[x/2] - Sin[x/2])","B",1
122,1,40,40,0.038367,"\int \frac{1}{a+b \sin (x)} \, dx","Integrate[(a + b*Sin[x])^(-1),x]","\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}}","\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,"(2*ArcTan[(b + a*Tan[x/2])/Sqrt[a^2 - b^2]])/Sqrt[a^2 - b^2]","A",1
123,1,44,47,0.0620563,"\int \frac{1}{a+\cos (x)+b \sin (x)} \, dx","Integrate[(a + Cos[x] + b*Sin[x])^(-1),x]","\frac{2 \tan ^{-1}\left(\frac{(a-1) \tan \left(\frac{x}{2}\right)+b}{\sqrt{a^2-b^2-1}}\right)}{\sqrt{a^2-b^2-1}}","-\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,"(2*ArcTan[(b + (-1 + a)*Tan[x/2])/Sqrt[-1 + a^2 - b^2]])/Sqrt[-1 + a^2 - b^2]","A",1
124,1,47,73,0.120503,"\int x^2 \sin ^2(a+b x) \, dx","Integrate[x^2*Sin[a + b*x]^2,x]","\frac{\left(3-6 b^2 x^2\right) \sin (2 (a+b x))-6 b x \cos (2 (a+b x))+4 b^3 x^3}{24 b^3}","\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,"(4*b^3*x^3 - 6*b*x*Cos[2*(a + b*x)] + (3 - 6*b^2*x^2)*Sin[2*(a + b*x)])/(24*b^3)","A",1
125,1,15,15,0.0052656,"\int \cos (x) \cos (2 x) \, dx","Integrate[Cos[x]*Cos[2*x],x]","\frac{\sin (x)}{2}+\frac{1}{6} \sin (3 x)","\frac{\sin (x)}{2}+\frac{1}{6} \sin (3 x)",1,"Sin[x]/2 + Sin[3*x]/6","A",1
126,1,47,73,0.1221615,"\int x^2 \cos ^2(a+b x) \, dx","Integrate[x^2*Cos[a + b*x]^2,x]","\frac{\left(6 b^2 x^2-3\right) \sin (2 (a+b x))+6 b x \cos (2 (a+b x))+4 b^3 x^3}{24 b^3}","-\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,"(4*b^3*x^3 + 6*b*x*Cos[2*(a + b*x)] + (-3 + 6*b^2*x^2)*Sin[2*(a + b*x)])/(24*b^3)","A",1
127,1,14,14,0.0032043,"\int \cot ^3(x) \, dx","Integrate[Cot[x]^3,x]","-\frac{1}{2} \csc ^2(x)-\log (\sin (x))","-\frac{1}{2} \cot ^2(x)-\log (\sin (x))",1,"-1/2*Csc[x]^2 - Log[Sin[x]]","A",1
128,1,101,104,0.1543095,"\int x^3 \tan ^4(x) \, dx","Integrate[x^3*Tan[x]^4,x]","4 i x \operatorname{PolyLog}\left(2,-e^{2 i x}\right)-2 \operatorname{PolyLog}\left(3,-e^{2 i x}\right)+\frac{x^4}{4}+\frac{4 i x^3}{3}-\frac{4}{3} x^3 \tan (x)+\frac{1}{3} x^3 \tan (x) \sec ^2(x)-4 x^2 \log \left(1+e^{2 i x}\right)-\frac{1}{2} x^2 \sec ^2(x)+x \tan (x)+\log (\cos (x))","4 i x \operatorname{PolyLog}\left(2,-e^{2 i x}\right)-2 \operatorname{PolyLog}\left(3,-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,"((4*I)/3)*x^3 + x^4/4 - 4*x^2*Log[1 + E^((2*I)*x)] + Log[Cos[x]] + (4*I)*x*PolyLog[2, -E^((2*I)*x)] - 2*PolyLog[3, -E^((2*I)*x)] - (x^2*Sec[x]^2)/2 + x*Tan[x] - (4*x^3*Tan[x])/3 + (x^3*Sec[x]^2*Tan[x])/3","A",1
129,1,133,153,0.3317681,"\int x^3 \tan ^6(x) \, dx","Integrate[x^3*Tan[x]^6,x]","\frac{1}{60} \left(-276 i x \operatorname{PolyLog}\left(2,-e^{2 i x}\right)+138 \operatorname{PolyLog}\left(3,-e^{2 i x}\right)-15 x^4-92 i x^3+92 x^3 \tan (x)+12 x^3 \tan (x) \sec ^4(x)-44 x^3 \tan (x) \sec ^2(x)+276 x^2 \log \left(1+e^{2 i x}\right)-9 x^2 \sec ^4(x)+66 x^2 \sec ^2(x)-120 x \tan (x)-3 \sec ^2(x)-120 \log (\cos (x))+6 x \tan (x) \sec ^2(x)\right)","-\frac{23}{5} i x \operatorname{PolyLog}\left(2,-e^{2 i x}\right)+\frac{23}{10} \operatorname{PolyLog}\left(3,-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,"((-92*I)*x^3 - 15*x^4 + 276*x^2*Log[1 + E^((2*I)*x)] - 120*Log[Cos[x]] - (276*I)*x*PolyLog[2, -E^((2*I)*x)] + 138*PolyLog[3, -E^((2*I)*x)] - 3*Sec[x]^2 + 66*x^2*Sec[x]^2 - 9*x^2*Sec[x]^4 - 120*x*Tan[x] + 92*x^3*Tan[x] + 6*x*Sec[x]^2*Tan[x] - 44*x^3*Sec[x]^2*Tan[x] + 12*x^3*Sec[x]^4*Tan[x])/60","A",1
130,1,15,15,0.0142177,"\int x \tan ^2(x) \, dx","Integrate[x*Tan[x]^2,x]","-\frac{x^2}{2}+x \tan (x)+\log (\cos (x))","-\frac{x^2}{2}+x \tan (x)+\log (\cos (x))",1,"-1/2*x^2 + Log[Cos[x]] + x*Tan[x]","A",1
131,1,15,15,0.0059828,"\int \cos (3 x) \sin (2 x) \, dx","Integrate[Cos[3*x]*Sin[2*x],x]","\frac{\cos (x)}{2}-\frac{1}{10} \cos (5 x)","\frac{\cos (x)}{2}-\frac{1}{10} \cos (5 x)",1,"Cos[x]/2 - Cos[5*x]/10","A",1
132,1,14,24,0.004627,"\int \cos ^2(x) \sin ^2(x) \, dx","Integrate[Cos[x]^2*Sin[x]^2,x]","\frac{x}{8}-\frac{1}{32} \sin (4 x)","\frac{x}{8}-\frac{1}{4} \sin (x) \cos ^3(x)+\frac{1}{8} \sin (x) \cos (x)",1,"x/8 - Sin[4*x]/32","A",1
133,1,6,7,0.0072184,"\int \csc ^2(x) \sec ^2(x) \, dx","Integrate[Csc[x]^2*Sec[x]^2,x]","-2 \cot (2 x)","\tan (x)-\cot (x)",1,"-2*Cot[2*x]","A",1
134,1,22,32,0.0198306,"\int d^x \sin (x) \, dx","Integrate[d^x*Sin[x],x]","\frac{d^x (\log (d) \sin (x)-\cos (x))}{\log ^2(d)+1}","\frac{d^x \log (d) \sin (x)}{\log ^2(d)+1}-\frac{d^x \cos (x)}{\log ^2(d)+1}",1,"(d^x*(-Cos[x] + Log[d]*Sin[x]))/(1 + Log[d]^2)","A",1
135,1,20,31,0.0175622,"\int d^x \cos (x) \, dx","Integrate[d^x*Cos[x],x]","\frac{d^x (\log (d) \cos (x)+\sin (x))}{\log ^2(d)+1}","\frac{d^x \sin (x)}{\log ^2(d)+1}+\frac{d^x \log (d) \cos (x)}{\log ^2(d)+1}",1,"(d^x*(Cos[x]*Log[d] + Sin[x]))/(1 + Log[d]^2)","A",1
136,1,50,84,0.0516248,"\int d^x x \sin (x) \, dx","Integrate[d^x*x*Sin[x],x]","\frac{d^x \left(\sin (x) \left(x \log ^3(d)+x \log (d)-\log ^2(d)+1\right)-\cos (x) \left(x \log ^2(d)-2 \log (d)+x\right)\right)}{\left(\log ^2(d)+1\right)^2}","\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,"(d^x*(-(Cos[x]*(x - 2*Log[d] + x*Log[d]^2)) + (1 + x*Log[d] - Log[d]^2 + x*Log[d]^3)*Sin[x]))/(1 + Log[d]^2)^2","A",1
137,1,49,83,0.0481275,"\int d^x x \cos (x) \, dx","Integrate[d^x*x*Cos[x],x]","\frac{d^x \left(\sin (x) \left(x \log ^2(d)-2 \log (d)+x\right)+\cos (x) \left(x \log ^3(d)+x \log (d)-\log ^2(d)+1\right)\right)}{\left(\log ^2(d)+1\right)^2}","\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,"(d^x*(Cos[x]*(1 + x*Log[d] - Log[d]^2 + x*Log[d]^3) + (x - 2*Log[d] + x*Log[d]^2)*Sin[x]))/(1 + Log[d]^2)^2","A",1
138,1,94,162,0.0889618,"\int d^x x^2 \sin (x) \, dx","Integrate[d^x*x^2*Sin[x],x]","\frac{d^x \left(\sin (x) \left(x^2 \log ^5(d)+2 \left(x^2+1\right) \log ^3(d)+\left(x^2-6\right) \log (d)-2 x \log ^4(d)+2 x\right)-\cos (x) \left(x^2 \log ^4(d)+2 \left(x^2+3\right) \log ^2(d)-4 x \log ^3(d)-4 x \log (d)+x^2-2\right)\right)}{\left(\log ^2(d)+1\right)^3}","\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,"(d^x*(-(Cos[x]*(-2 + x^2 - 4*x*Log[d] + 2*(3 + x^2)*Log[d]^2 - 4*x*Log[d]^3 + x^2*Log[d]^4)) + (2*x + (-6 + x^2)*Log[d] + 2*(1 + x^2)*Log[d]^3 - 2*x*Log[d]^4 + x^2*Log[d]^5)*Sin[x]))/(1 + Log[d]^2)^3","A",1
139,1,93,161,0.0760752,"\int d^x x^2 \cos (x) \, dx","Integrate[d^x*x^2*Cos[x],x]","\frac{d^x \left(\sin (x) \left(x^2 \log ^4(d)+2 \left(x^2+3\right) \log ^2(d)-4 x \log ^3(d)-4 x \log (d)+x^2-2\right)+\cos (x) \left(x^2 \log ^5(d)+2 \left(x^2+1\right) \log ^3(d)+\left(x^2-6\right) \log (d)-2 x \log ^4(d)+2 x\right)\right)}{\left(\log ^2(d)+1\right)^3}","\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,"(d^x*(Cos[x]*(2*x + (-6 + x^2)*Log[d] + 2*(1 + x^2)*Log[d]^3 - 2*x*Log[d]^4 + x^2*Log[d]^5) + (-2 + x^2 - 4*x*Log[d] + 2*(3 + x^2)*Log[d]^2 - 4*x*Log[d]^3 + x^2*Log[d]^4)*Sin[x]))/(1 + Log[d]^2)^3","A",1
140,1,169,261,0.152183,"\int d^x x^3 \sin (x) \, dx","Integrate[d^x*x^3*Sin[x],x]","\frac{d^x \left(\sin (x) \left(x^3 \log ^7(d)-3 x^2 \log ^6(d)+3 x \left(x^2+2\right) \log ^5(d)-3 \left(x^2+2\right) \log ^4(d)+3 x \left(x^2-4\right) \log ^3(d)+3 \left(x^2+12\right) \log ^2(d)+x \left(x^2-18\right) \log (d)+3 \left(x^2-2\right)\right)-\cos (x) \left(x^3 \log ^6(d)-6 x^2 \log ^5(d)+3 x \left(x^2+6\right) \log ^4(d)-12 \left(x^2+2\right) \log ^3(d)+3 x \left(x^2+4\right) \log ^2(d)-6 \left(x^2-4\right) \log (d)+x \left(x^2-6\right)\right)\right)}{\left(\log ^2(d)+1\right)^4}","\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,"(d^x*(-(Cos[x]*(x*(-6 + x^2) - 6*(-4 + x^2)*Log[d] + 3*x*(4 + x^2)*Log[d]^2 - 12*(2 + x^2)*Log[d]^3 + 3*x*(6 + x^2)*Log[d]^4 - 6*x^2*Log[d]^5 + x^3*Log[d]^6)) + (3*(-2 + x^2) + x*(-18 + x^2)*Log[d] + 3*(12 + x^2)*Log[d]^2 + 3*x*(-4 + x^2)*Log[d]^3 - 3*(2 + x^2)*Log[d]^4 + 3*x*(2 + x^2)*Log[d]^5 - 3*x^2*Log[d]^6 + x^3*Log[d]^7)*Sin[x]))/(1 + Log[d]^2)^4","A",1
141,1,168,260,0.1276991,"\int d^x x^3 \cos (x) \, dx","Integrate[d^x*x^3*Cos[x],x]","\frac{d^x \left(\sin (x) \left(x^3 \log ^6(d)-6 x^2 \log ^5(d)+3 x \left(x^2+6\right) \log ^4(d)-12 \left(x^2+2\right) \log ^3(d)+3 x \left(x^2+4\right) \log ^2(d)-6 \left(x^2-4\right) \log (d)+x \left(x^2-6\right)\right)+\cos (x) \left(x^3 \log ^7(d)-3 x^2 \log ^6(d)+3 x \left(x^2+2\right) \log ^5(d)-3 \left(x^2+2\right) \log ^4(d)+3 x \left(x^2-4\right) \log ^3(d)+3 \left(x^2+12\right) \log ^2(d)+x \left(x^2-18\right) \log (d)+3 \left(x^2-2\right)\right)\right)}{\left(\log ^2(d)+1\right)^4}","\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,"(d^x*(Cos[x]*(3*(-2 + x^2) + x*(-18 + x^2)*Log[d] + 3*(12 + x^2)*Log[d]^2 + 3*x*(-4 + x^2)*Log[d]^3 - 3*(2 + x^2)*Log[d]^4 + 3*x*(2 + x^2)*Log[d]^5 - 3*x^2*Log[d]^6 + x^3*Log[d]^7) + (x*(-6 + x^2) - 6*(-4 + x^2)*Log[d] + 3*x*(4 + x^2)*Log[d]^2 - 12*(2 + x^2)*Log[d]^3 + 3*x*(6 + x^2)*Log[d]^4 - 6*x^2*Log[d]^5 + x^3*Log[d]^6)*Sin[x]))/(1 + Log[d]^2)^4","A",1
142,1,25,25,0.0105367,"\int \sin (x) \sin (2 x) \sin (3 x) \, dx","Integrate[Sin[x]*Sin[2*x]*Sin[3*x],x]","-\frac{1}{8} \cos (2 x)-\frac{1}{16} \cos (4 x)+\frac{1}{24} \cos (6 x)","-\frac{1}{8} \cos (2 x)-\frac{1}{16} \cos (4 x)+\frac{1}{24} \cos (6 x)",1,"-1/8*Cos[2*x] - Cos[4*x]/16 + Cos[6*x]/24","A",1
143,1,30,30,0.0099666,"\int \cos (x) \cos (2 x) \cos (3 x) \, dx","Integrate[Cos[x]*Cos[2*x]*Cos[3*x],x]","\frac{x}{4}+\frac{1}{8} \sin (2 x)+\frac{1}{16} \sin (4 x)+\frac{1}{24} \sin (6 x)","\frac{x}{4}+\frac{1}{8} \sin (2 x)+\frac{1}{16} \sin (4 x)+\frac{1}{24} \sin (6 x)",1,"x/4 + Sin[2*x]/8 + Sin[4*x]/16 + Sin[6*x]/24","A",1
144,1,55,85,0.0768392,"\int x^2 \sin ^3(k x) \, dx","Integrate[x^2*Sin[k*x]^3,x]","\frac{-81 \left(k^2 x^2-2\right) \cos (k x)+\left(9 k^2 x^2-2\right) \cos (3 k x)-6 k x (\sin (3 k x)-27 \sin (k x))}{108 k^3}","-\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,"(-81*(-2 + k^2*x^2)*Cos[k*x] + (-2 + 9*k^2*x^2)*Cos[3*k*x] - 6*k*x*(-27*Sin[k*x] + Sin[3*k*x]))/(108*k^3)","A",1
145,0,0,14,0.132346,"\int x \cos (k \csc (x)) \cot (x) \csc (x) \, dx","Integrate[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)",0,"Integrate[x*Cos[k*Csc[x]]*Cot[x]*Csc[x], x]","A",-1
146,1,12,12,0.0133634,"\int \cot \left(\frac{x}{2}\right) \cot (x) \, dx","Integrate[Cot[x/2]*Cot[x],x]","-x-\cot \left(\frac{x}{2}\right)","-x-\cot \left(\frac{x}{2}\right)",1,"-x - Cot[x/2]","A",1
147,1,76,77,0.2560231,"\int \frac{\sin (a x)}{(b+c \sin (a x))^2} \, dx","Integrate[Sin[a*x]/(b + c*Sin[a*x])^2,x]","-\frac{\frac{2 c \tan ^{-1}\left(\frac{b \tan \left(\frac{a x}{2}\right)+c}{\sqrt{b^2-c^2}}\right)}{\left(b^2-c^2\right)^{3/2}}+\frac{b \cos (a x)}{(b-c) (b+c) (c \sin (a x)+b)}}{a}","-\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,"-(((2*c*ArcTan[(c + b*Tan[(a*x)/2])/Sqrt[b^2 - c^2]])/(b^2 - c^2)^(3/2) + (b*Cos[a*x])/((b - c)*(b + c)*(b + c*Sin[a*x])))/a)","A",1
148,1,17,17,0.0029444,"\int \sin (\log (x)) \, dx","Integrate[Sin[Log[x]],x]","\frac{1}{2} x \sin (\log (x))-\frac{1}{2} x \cos (\log (x))","\frac{1}{2} x \sin (\log (x))-\frac{1}{2} x \cos (\log (x))",1,"-1/2*(x*Cos[Log[x]]) + (x*Sin[Log[x]])/2","A",1
149,1,17,17,0.0029439,"\int \cos (\log (x)) \, dx","Integrate[Cos[Log[x]],x]","\frac{1}{2} x \sin (\log (x))+\frac{1}{2} x \cos (\log (x))","\frac{1}{2} x \sin (\log (x))+\frac{1}{2} x \cos (\log (x))",1,"(x*Cos[Log[x]])/2 + (x*Sin[Log[x]])/2","A",1
150,1,3,3,0.0002608,"\int e^x \, dx","Integrate[E^x,x]","e^x","e^x",1,"E^x","A",1
151,1,8,8,0.0007234,"\int a^x \, dx","Integrate[a^x,x]","\frac{a^x}{\log (a)}","\frac{a^x}{\log (a)}",1,"a^x/Log[a]","A",1
152,1,9,9,0.0010573,"\int e^{a x} \, dx","Integrate[E^(a*x),x]","\frac{e^{a x}}{a}","\frac{e^{a x}}{a}",1,"E^(a*x)/a","A",1
153,1,4,4,0.0063897,"\int \frac{e^{a x}}{x} \, dx","Integrate[E^(a*x)/x,x]","\operatorname{ExpIntegralEi}(a x)","\operatorname{ExpIntegralEi}(a x)",1,"ExpIntegralEi[a*x]","A",1
154,1,24,24,0.0054208,"\int \frac{1}{a+b e^{m x}} \, dx","Integrate[(a + b*E^(m*x))^(-1),x]","\frac{x}{a}-\frac{\log \left(a+b e^{m x}\right)}{a m}","\frac{x}{a}-\frac{\log \left(a+b e^{m x}\right)}{a m}",1,"x/a - Log[a + b*E^(m*x)]/(a*m)","A",1
155,1,12,12,0.0090164,"\int \frac{e^{2 x}}{1+e^x} \, dx","Integrate[E^(2*x)/(1 + E^x),x]","e^x-\log \left(e^x+1\right)","e^x-\log \left(e^x+1\right)",1,"E^x - Log[1 + E^x]","A",1
156,1,13,13,0.0039308,"\int e^{2 x+a x} \, dx","Integrate[E^(2*x + a*x),x]","\frac{e^{(a+2) x}}{a+2}","\frac{e^{(a+2) x}}{a+2}",1,"E^((2 + a)*x)/(2 + a)","A",1
157,1,31,31,0.0095709,"\int \frac{1}{b e^{-m x}+a e^{m x}} \, dx","Integrate[(b/E^(m*x) + a*E^(m*x))^(-1),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{a} e^{m x}}{\sqrt{b}}\right)}{\sqrt{a} \sqrt{b} m}","\frac{\tan ^{-1}\left(\frac{\sqrt{a} e^{m x}}{\sqrt{b}}\right)}{\sqrt{a} \sqrt{b} m}",1,"ArcTan[(Sqrt[a]*E^(m*x))/Sqrt[b]]/(Sqrt[a]*Sqrt[b]*m)","A",1
158,1,14,21,0.0059157,"\int e^{a x} x \, dx","Integrate[E^(a*x)*x,x]","\frac{e^{a x} (a x-1)}{a^2}","\frac{x e^{a x}}{a}-\frac{e^{a x}}{a^2}",1,"(E^(a*x)*(-1 + a*x))/a^2","A",1
159,1,102,163,0.0111208,"\int e^x x^{20} \, dx","Integrate[E^x*x^20,x]","e^x \left(x^{20}-20 x^{19}+380 x^{18}-6840 x^{17}+116280 x^{16}-1860480 x^{15}+27907200 x^{14}-390700800 x^{13}+5079110400 x^{12}-60949324800 x^{11}+670442572800 x^{10}-6704425728000 x^9+60339831552000 x^8-482718652416000 x^7+3379030566912000 x^6-20274183401472000 x^5+101370917007360000 x^4-405483668029440000 x^3+1216451004088320000 x^2-2432902008176640000 x+2432902008176640000\right)","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,"E^x*(2432902008176640000 - 2432902008176640000*x + 1216451004088320000*x^2 - 405483668029440000*x^3 + 101370917007360000*x^4 - 20274183401472000*x^5 + 3379030566912000*x^6 - 482718652416000*x^7 + 60339831552000*x^8 - 6704425728000*x^9 + 670442572800*x^10 - 60949324800*x^11 + 5079110400*x^12 - 390700800*x^13 + 27907200*x^14 - 1860480*x^15 + 116280*x^16 - 6840*x^17 + 380*x^18 - 20*x^19 + x^20)","A",1
160,1,18,18,0.0114147,"\int a^x b^{-x} \, dx","Integrate[a^x/b^x,x]","\frac{a^x b^{-x}}{\log (a)-\log (b)}","\frac{a^x b^{-x}}{\log (a)-\log (b)}",1,"a^x/(b^x*(Log[a] - Log[b]))","A",1
161,1,14,14,0.0073401,"\int a^x b^x \, dx","Integrate[a^x*b^x,x]","\frac{a^x b^x}{\log (a)+\log (b)}","\frac{a^x b^x}{\log (a)+\log (b)}",1,"(a^x*b^x)/(Log[a] + Log[b])","A",1
162,1,17,17,0.0119701,"\int \frac{a^x}{x^2} \, dx","Integrate[a^x/x^2,x]","\log (a) \text{Ei}(x \log (a))-\frac{a^x}{x}","\log (a) \text{Ei}(x \log (a))-\frac{a^x}{x}",1,"-(a^x/x) + ExpIntegralEi[x*Log[a]]*Log[a]","A",1
163,1,43,64,0.1349867,"\int \frac{a^x x}{(1+b x)^2} \, dx","Integrate[(a^x*x)/(1 + b*x)^2,x]","\frac{a^{-1/b} (b-\log (a)) \text{Ei}\left(\frac{(b x+1) \log (a)}{b}\right)+\frac{b a^x}{b x+1}}{b^3}","-\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,"((a^x*b)/(1 + b*x) + (ExpIntegralEi[((1 + b*x)*Log[a])/b]*(b - Log[a]))/a^b^(-1))/b^3","A",1
164,1,16,16,0.0470061,"\int \frac{e^{a x} x}{(1+a x)^2} \, dx","Integrate[(E^(a*x)*x)/(1 + a*x)^2,x]","\frac{e^{a x}}{a^2 (a x+1)}","\frac{e^{a x}}{a^2 (a x+1)}",1,"E^(a*x)/(a^2*(1 + a*x))","A",1
165,1,13,13,0.0019221,"\int k^{x^2} x \, dx","Integrate[k^x^2*x,x]","\frac{k^{x^2}}{2 \log (k)}","\frac{k^{x^2}}{2 \log (k)}",1,"k^x^2/(2*Log[k])","A",1
166,1,11,11,0.0016005,"\int e^{x^2} \, dx","Integrate[E^x^2,x]","\frac{1}{2} \sqrt{\pi } \operatorname{Erfi}(x)","\frac{1}{2} \sqrt{\pi } \operatorname{Erfi}(x)",1,"(Sqrt[Pi]*Erfi[x])/2","A",1
167,1,9,9,0.0013007,"\int e^{x^2} x \, dx","Integrate[E^x^2*x,x]","\frac{e^{x^2}}{2}","\frac{e^{x^2}}{2}",1,"E^x^2/2","A",1
168,1,17,27,0.0118174,"\int \frac{e^{\frac{1}{x}} (1+x)}{x^4} \, dx","Integrate[(E^x^(-1)*(1 + x))/x^4,x]","\frac{e^{\frac{1}{x}} \left(-x^2+x-1\right)}{x^2}","-\frac{e^{\frac{1}{x}}}{x^2}-e^{\frac{1}{x}}+\frac{e^{\frac{1}{x}}}{x}",1,"(E^x^(-1)*(-1 + x - x^2))/x^2","A",1
169,1,25,25,0.1667635,"\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","Integrate[(E^(1 - E^x^2*x + 2*x^2)*(x + 2*x^3))/(1 - E^x^2*x)^2,x]","-\frac{e^{1-e^{x^2} x}}{e^{x^2} x-1}","-\frac{e^{1-e^{x^2} x}}{e^{x^2} x-1}",1,"-(E^(1 - E^x^2*x)/(-1 + E^x^2*x))","A",1
170,0,0,12,0.0180546,"\int e^{e^{e^{e^x}}} \, dx","Integrate[E^E^E^E^x,x]","\int e^{e^{e^{e^x}}} \, dx","\text{Int}\left(e^{e^{e^{e^x}}},x\right)",0,"Integrate[E^E^E^E^x, x]","A",-1
171,1,11,11,0.0060053,"\int e^x \log (x) \, dx","Integrate[E^x*Log[x],x]","e^x \log (x)-\text{Ei}(x)","e^x \log (x)-\text{Ei}(x)",1,"-ExpIntegralEi[x] + E^x*Log[x]","A",1
172,1,17,22,0.012216,"\int e^x x \log (x) \, dx","Integrate[E^x*x*Log[x],x]","\text{Ei}(x)-e^x+e^x (x-1) \log (x)","\text{Ei}(x)-e^x-e^x \log (x)+e^x x \log (x)",1,"-E^x + ExpIntegralEi[x] + E^x*(-1 + x)*Log[x]","A",1
173,1,17,23,0.0050149,"\int e^{2 x} \log \left(e^x\right) \, dx","Integrate[E^(2*x)*Log[E^x],x]","\frac{1}{4} e^{2 x} \left(2 \log \left(e^x\right)-1\right)","\frac{1}{2} e^{2 x} \log \left(e^x\right)-\frac{e^{2 x}}{4}",1,"(E^(2*x)*(-1 + 2*Log[E^x]))/4","A",1
174,1,16,16,0.0000925,"\int \left(2 x+\sqrt{2} x^2\right) \, dx","Integrate[2*x + Sqrt[2]*x^2,x]","\frac{\sqrt{2} x^3}{3}+x^2","\frac{\sqrt{2} x^3}{3}+x^2",1,"x^2 + (Sqrt[2]*x^3)/3","A",1
175,1,43,57,0.0239429,"\int \frac{\log (x)}{\sqrt{b+a x}} \, dx","Integrate[Log[x]/Sqrt[b + a*x],x]","\frac{2 (\log (x)-2) \sqrt{a x+b}+4 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{a x+b}}{\sqrt{b}}\right)}{a}","-\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,"(4*Sqrt[b]*ArcTanh[Sqrt[b + a*x]/Sqrt[b]] + 2*Sqrt[b + a*x]*(-2 + Log[x]))/a","A",1
176,1,118,116,0.29006,"\int \sqrt{a+b x} \sqrt{c+d x} \, dx","Integrate[Sqrt[a + b*x]*Sqrt[c + d*x],x]","\frac{b \sqrt{d} \sqrt{a+b x} (c+d x) (a d+b (c+2 d x))-(b c-a d)^{5/2} \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{4 b^2 d^{3/2} \sqrt{c+d x}}","-\frac{(b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{4 b^{3/2} d^{3/2}}+\frac{\sqrt{a+b x} \sqrt{c+d x} (b c-a d)}{4 b d}+\frac{(a+b x)^{3/2} \sqrt{c+d x}}{2 b}",1,"(b*Sqrt[d]*Sqrt[a + b*x]*(c + d*x)*(a*d + b*(c + 2*d*x)) - (b*c - a*d)^(5/2)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(4*b^2*d^(3/2)*Sqrt[c + d*x])","A",1
177,1,16,16,0.0047779,"\int \sqrt{a+b x} \, dx","Integrate[Sqrt[a + b*x],x]","\frac{2 (a+b x)^{3/2}}{3 b}","\frac{2 (a+b x)^{3/2}}{3 b}",1,"(2*(a + b*x)^(3/2))/(3*b)","A",1
178,1,24,34,0.0121155,"\int x \sqrt{a+b x} \, dx","Integrate[x*Sqrt[a + b*x],x]","\frac{2 (a+b x)^{3/2} (3 b x-2 a)}{15 b^2}","\frac{2 (a+b x)^{5/2}}{5 b^2}-\frac{2 a (a+b x)^{3/2}}{3 b^2}",1,"(2*(a + b*x)^(3/2)*(-2*a + 3*b*x))/(15*b^2)","A",1
179,1,35,53,0.0168535,"\int x^2 \sqrt{a+b x} \, dx","Integrate[x^2*Sqrt[a + b*x],x]","\frac{2 (a+b x)^{3/2} \left(8 a^2-12 a b x+15 b^2 x^2\right)}{105 b^3}","\frac{2 a^2 (a+b x)^{3/2}}{3 b^3}+\frac{2 (a+b x)^{7/2}}{7 b^3}-\frac{4 a (a+b x)^{5/2}}{5 b^3}",1,"(2*(a + b*x)^(3/2)*(8*a^2 - 12*a*b*x + 15*b^2*x^2))/(105*b^3)","A",1
180,1,35,35,0.0087542,"\int \frac{\sqrt{a+b x}}{x} \, dx","Integrate[Sqrt[a + b*x]/x,x]","2 \sqrt{a+b x}-2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)","2 \sqrt{a+b x}-2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)",1,"2*Sqrt[a + b*x] - 2*Sqrt[a]*ArcTanh[Sqrt[a + b*x]/Sqrt[a]]","A",1
181,1,47,39,0.0271405,"\int \frac{\sqrt{a+b x}}{x^2} \, dx","Integrate[Sqrt[a + b*x]/x^2,x]","-\frac{b x \sqrt{\frac{b x}{a}+1} \tanh ^{-1}\left(\sqrt{\frac{b x}{a}+1}\right)+a+b x}{x \sqrt{a+b x}}","-\frac{\sqrt{a+b x}}{x}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{\sqrt{a}}",1,"-((a + b*x + b*x*Sqrt[1 + (b*x)/a]*ArcTanh[Sqrt[1 + (b*x)/a]])/(x*Sqrt[a + b*x]))","A",1
182,1,14,14,0.003409,"\int \frac{1}{\sqrt{a+b x}} \, dx","Integrate[1/Sqrt[a + b*x],x]","\frac{2 \sqrt{a+b x}}{b}","\frac{2 \sqrt{a+b x}}{b}",1,"(2*Sqrt[a + b*x])/b","A",1
183,1,23,32,0.0103458,"\int \frac{x}{\sqrt{a+b x}} \, dx","Integrate[x/Sqrt[a + b*x],x]","\frac{2 (b x-2 a) \sqrt{a+b x}}{3 b^2}","\frac{2 (a+b x)^{3/2}}{3 b^2}-\frac{2 a \sqrt{a+b x}}{b^2}",1,"(2*(-2*a + b*x)*Sqrt[a + b*x])/(3*b^2)","A",1
184,1,35,51,0.0152247,"\int \frac{x^2}{\sqrt{a+b x}} \, dx","Integrate[x^2/Sqrt[a + b*x],x]","\frac{2 \sqrt{a+b x} \left(8 a^2-4 a b x+3 b^2 x^2\right)}{15 b^3}","\frac{2 a^2 \sqrt{a+b x}}{b^3}+\frac{2 (a+b x)^{5/2}}{5 b^3}-\frac{4 a (a+b x)^{3/2}}{3 b^3}",1,"(2*Sqrt[a + b*x]*(8*a^2 - 4*a*b*x + 3*b^2*x^2))/(15*b^3)","A",1
185,1,23,23,0.0038712,"\int \frac{1}{x \sqrt{a+b x}} \, dx","Integrate[1/(x*Sqrt[a + b*x]),x]","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{\sqrt{a}}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{\sqrt{a}}",1,"(-2*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/Sqrt[a]","A",1
186,1,47,41,0.0641872,"\int \frac{1}{x^2 \sqrt{a+b x}} \, dx","Integrate[1/(x^2*Sqrt[a + b*x]),x]","\frac{\sqrt{a+b x} \left(\frac{b \tanh ^{-1}\left(\sqrt{\frac{b x}{a}+1}\right)}{\sqrt{\frac{b x}{a}+1}}-\frac{a}{x}\right)}{a^2}","\frac{b \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{a^{3/2}}-\frac{\sqrt{a+b x}}{a x}",1,"(Sqrt[a + b*x]*(-(a/x) + (b*ArcTanh[Sqrt[1 + (b*x)/a]])/Sqrt[1 + (b*x)/a]))/a^2","A",1
187,1,24,23,0.0134434,"\int (a+b x)^{p/2} \, dx","Integrate[(a + b*x)^(p/2),x]","\frac{2 (a+b x)^{\frac{p}{2}+1}}{b p+2 b}","\frac{2 (a+b x)^{\frac{p+2}{2}}}{b (p+2)}",1,"(2*(a + b*x)^(1 + p/2))/(2*b + b*p)","A",1
188,1,38,48,0.0210039,"\int x (a+b x)^{p/2} \, dx","Integrate[x*(a + b*x)^(p/2),x]","\frac{2 (a+b x)^{\frac{p}{2}+1} (b (p+2) x-2 a)}{b^2 (p+2) (p+4)}","\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,"(2*(a + b*x)^(1 + p/2)*(-2*a + b*(2 + p)*x))/(b^2*(2 + p)*(4 + p))","A",1
189,1,48,55,0.0351443,"\int \tan ^{-1}\left(\frac{-\sqrt{2}+2 x}{\sqrt{2}}\right) \, dx","Integrate[ArcTan[(-Sqrt[2] + 2*x)/Sqrt[2]],x]","\frac{1}{4} \left(2 \left(\sqrt{2}-2 x\right) \tan ^{-1}\left(1-\sqrt{2} x\right)-\sqrt{2} \log \left(x^2-\sqrt{2} x+1\right)\right)","-\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,"(2*(Sqrt[2] - 2*x)*ArcTan[1 - Sqrt[2]*x] - Sqrt[2]*Log[1 - Sqrt[2]*x + x^2])/4","A",1
190,1,38,12,0.0026307,"\int \frac{1}{\sqrt{-1+x^2}} \, dx","Integrate[1/Sqrt[-1 + x^2],x]","\frac{1}{2} \log \left(\frac{x}{\sqrt{x^2-1}}+1\right)-\frac{1}{2} \log \left(1-\frac{x}{\sqrt{x^2-1}}\right)","\tanh ^{-1}\left(\frac{x}{\sqrt{x^2-1}}\right)",1,"-1/2*Log[1 - x/Sqrt[-1 + x^2]] + Log[1 + x/Sqrt[-1 + x^2]]/2","B",1
191,1,31,43,0.0123757,"\int \sqrt{x} \sqrt{1+x} \, dx","Integrate[Sqrt[x]*Sqrt[1 + x],x]","\frac{1}{4} \left(\sqrt{x} \sqrt{x+1} (2 x+1)-\sinh ^{-1}\left(\sqrt{x}\right)\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,"(Sqrt[x]*Sqrt[1 + x]*(1 + 2*x) - ArcSinh[Sqrt[x]])/4","A",1
192,1,22,22,0.014207,"\int \sin \left(\sqrt{x}\right) \, dx","Integrate[Sin[Sqrt[x]],x]","2 \sin \left(\sqrt{x}\right)-2 \sqrt{x} \cos \left(\sqrt{x}\right)","2 \sin \left(\sqrt{x}\right)-2 \sqrt{x} \cos \left(\sqrt{x}\right)",1,"-2*Sqrt[x]*Cos[Sqrt[x]] + 2*Sin[Sqrt[x]]","A",1
193,1,13,13,0.0023622,"\int \frac{x}{\left(1-x^2\right)^{9/8}} \, dx","Integrate[x/(1 - x^2)^(9/8),x]","\frac{4}{\sqrt[8]{1-x^2}}","\frac{4}{\sqrt[8]{1-x^2}}",1,"4/(1 - x^2)^(1/8)","A",1
194,1,8,8,0.0025949,"\int \frac{x}{\sqrt{1-x^4}} \, dx","Integrate[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
195,1,14,14,0.0024692,"\int \frac{1}{x \sqrt{1+x^4}} \, dx","Integrate[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
196,1,18,18,0.003045,"\int \frac{x}{\sqrt{1+x^2+x^4}} \, dx","Integrate[x/Sqrt[1 + x^2 + x^4],x]","\frac{1}{2} \sinh ^{-1}\left(\frac{2 x^2+1}{\sqrt{3}}\right)","\frac{1}{2} \sinh ^{-1}\left(\frac{2 x^2+1}{\sqrt{3}}\right)",1,"ArcSinh[(1 + 2*x^2)/Sqrt[3]]/2","A",1
197,1,28,30,0.0038687,"\int \frac{1}{x \sqrt{-1+x^2-x^4}} \, dx","Integrate[1/(x*Sqrt[-1 + x^2 - x^4]),x]","\frac{1}{2} \tan ^{-1}\left(\frac{x^2-2}{2 \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,"ArcTan[(-2 + x^2)/(2*Sqrt[-1 + x^2 - x^4])]/2","A",1
198,1,16,17,0.0066955,"\int \frac{1+x}{(1-x)^2 \sqrt{1+x^2}} \, dx","Integrate[(1 + x)/((1 - x)^2*Sqrt[1 + x^2]),x]","-\frac{\sqrt{x^2+1}}{x-1}","\frac{\sqrt{x^2+1}}{1-x}",1,"-(Sqrt[1 + x^2]/(-1 + x))","A",1
199,1,2,2,0.0031286,"\int \frac{1}{\sqrt{1+x^2}} \, dx","Integrate[1/Sqrt[1 + x^2],x]","\sinh ^{-1}(x)","\sinh ^{-1}(x)",1,"ArcSinh[x]","A",1
200,1,30,20,0.0183547,"\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","Integrate[(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]","\frac{1}{2} \left(2 \sqrt{x}+2 \sqrt{x+1}+2 \sqrt{x+2}\right)","\sqrt{x}+\sqrt{x+1}+\sqrt{x+2}",1,"(2*Sqrt[x] + 2*Sqrt[1 + x] + 2*Sqrt[2 + x])/2","A",1
201,1,24,24,0.1673152,"\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","Integrate[(-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
202,1,71,27,0.008127,"\int \left(\frac{10}{\sqrt{-4+x^2}}+\frac{1}{\sqrt{-1+x^2}}\right) \, dx","Integrate[10/Sqrt[-4 + x^2] + 1/Sqrt[-1 + x^2],x]","-5 \log \left(1-\frac{x}{\sqrt{x^2-4}}\right)+5 \log \left(\frac{x}{\sqrt{x^2-4}}+1\right)-\frac{1}{2} \log \left(1-\frac{x}{\sqrt{x^2-1}}\right)+\frac{1}{2} \log \left(\frac{x}{\sqrt{x^2-1}}+1\right)","10 \tanh ^{-1}\left(\frac{x}{\sqrt{x^2-4}}\right)+\tanh ^{-1}\left(\frac{x}{\sqrt{x^2-1}}\right)",1,"-5*Log[1 - x/Sqrt[-4 + x^2]] + 5*Log[1 + x/Sqrt[-4 + x^2]] - Log[1 - x/Sqrt[-1 + x^2]]/2 + Log[1 + x/Sqrt[-1 + x^2]]/2","B",1
203,1,127,82,0.0704769,"\int \frac{\sqrt{x+\sqrt{a^2+x^2}}}{x} \, dx","Integrate[Sqrt[x + Sqrt[a^2 + x^2]]/x,x]","-\frac{2 \sqrt{a^2+x^2} \left(\sqrt{a^2+x^2}+x\right) \left(-\sqrt{\sqrt{a^2+x^2}+x}+\sqrt{a} \tan ^{-1}\left(\frac{\sqrt{\sqrt{a^2+x^2}+x}}{\sqrt{a}}\right)+\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a^2+x^2}+x}}{\sqrt{a}}\right)\right)}{x \left(\sqrt{a^2+x^2}+x\right)+a^2}","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[a^2 + x^2]*(x + Sqrt[a^2 + x^2])*(-Sqrt[x + Sqrt[a^2 + x^2]] + Sqrt[a]*ArcTan[Sqrt[x + Sqrt[a^2 + x^2]]/Sqrt[a]] + Sqrt[a]*ArcTanh[Sqrt[x + Sqrt[a^2 + x^2]]/Sqrt[a]]))/(a^2 + x*(x + Sqrt[a^2 + x^2]))","A",1
204,1,12,12,0.0222701,"\int \frac{3 x^2}{2 \left(1+x^3+\sqrt{1+x^3}\right)} \, dx","Integrate[(3*x^2)/(2*(1 + x^3 + Sqrt[1 + x^3])),x]","\log \left(\sqrt{x^3+1}+1\right)","\log \left(\sqrt{x^3+1}+1\right)",1,"Log[1 + Sqrt[1 + x^3]]","A",1
205,1,40,40,0.0100965,"\int \frac{1}{\sqrt{-\alpha ^2+2 h r^2}} \, dr","Integrate[1/Sqrt[-alpha^2 + 2*h*r^2],r]","\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{h} r}{\sqrt{2 h r^2-\alpha ^2}}\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,"ArcTanh[(Sqrt[2]*Sqrt[h]*r)/Sqrt[-alpha^2 + 2*h*r^2]]/(Sqrt[2]*Sqrt[h])","A",1
206,1,46,46,0.0112576,"\int \frac{1}{r \sqrt{-\alpha ^2-\epsilon ^2+2 h r^2}} \, dr","Integrate[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
207,1,39,37,0.0188364,"\int \frac{1}{r \sqrt{-\alpha ^2-2 k r+2 h r^2}} \, dr","Integrate[1/(r*Sqrt[-alpha^2 - 2*k*r + 2*h*r^2]),r]","\frac{\tan ^{-1}\left(\frac{-\alpha ^2-k r}{\alpha  \sqrt{2 r (h r-k)-\alpha ^2}}\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,"ArcTan[(-alpha^2 - k*r)/(alpha*Sqrt[-alpha^2 + 2*r*(-k + h*r)])]/alpha","A",1
208,1,65,61,0.0299979,"\int \frac{1}{r \sqrt{-\alpha ^2-\epsilon ^2-2 k r+2 h r^2}} \, dr","Integrate[1/(r*Sqrt[-alpha^2 - epsilon^2 - 2*k*r + 2*h*r^2]),r]","\frac{\tan ^{-1}\left(\frac{-\alpha ^2-\epsilon ^2-k r}{\sqrt{\alpha ^2+\epsilon ^2} \sqrt{-\alpha ^2-\epsilon ^2+2 r (h r-k)}}\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,"ArcTan[(-alpha^2 - epsilon^2 - k*r)/(Sqrt[alpha^2 + epsilon^2]*Sqrt[-alpha^2 - epsilon^2 + 2*r*(-k + h*r)])]/Sqrt[alpha^2 + epsilon^2]","A",1
209,1,23,23,0.0042521,"\int \frac{r}{\sqrt{-\alpha ^2+2 e r^2}} \, dr","Integrate[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
210,1,28,28,0.0051319,"\int \frac{r}{\sqrt{-\alpha ^2-\epsilon ^2+2 e r^2}} \, dr","Integrate[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
211,1,56,56,0.023483,"\int \frac{r}{\sqrt{-\alpha ^2+2 e r^2-2 k r^4}} \, dr","Integrate[r/Sqrt[-alpha^2 + 2*e*r^2 - 2*k*r^4],r]","-\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}}","-\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,"-1/2*ArcTan[(e - 2*k*r^2)/(Sqrt[2]*Sqrt[k]*Sqrt[-alpha^2 + 2*e*r^2 - 2*k*r^4])]/(Sqrt[2]*Sqrt[k])","A",1
212,1,82,81,0.102358,"\int \frac{r}{\sqrt{-\alpha ^2-2 k r+2 e r^2}} \, dr","Integrate[r/Sqrt[-alpha^2 - 2*k*r + 2*e*r^2],r]","\frac{1}{4} \left(\frac{\sqrt{2} k \tanh ^{-1}\left(\frac{2 e r-k}{\sqrt{2} \sqrt{e} \sqrt{2 r (e r-k)-\alpha ^2}}\right)}{e^{3/2}}+\frac{2 \sqrt{2 r (e r-k)-\alpha ^2}}{e}\right)","\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,"((2*Sqrt[-alpha^2 + 2*r*(-k + e*r)])/e + (Sqrt[2]*k*ArcTanh[(-k + 2*e*r)/(Sqrt[2]*Sqrt[e]*Sqrt[-alpha^2 + 2*r*(-k + e*r)])])/e^(3/2))/4","A",1
213,1,49,44,0.0080184,"\int \frac{1}{r \sqrt{-\alpha ^2+2 h r^2-2 k r^4}} \, dr","Integrate[1/(r*Sqrt[-alpha^2 + 2*h*r^2 - 2*k*r^4]),r]","\frac{\tan ^{-1}\left(\frac{2 h r^2-2 \alpha ^2}{2 \alpha  \sqrt{-\alpha ^2+2 h r^2-2 k r^4}}\right)}{2 \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[(-2*alpha^2 + 2*h*r^2)/(2*alpha*Sqrt[-alpha^2 + 2*h*r^2 - 2*k*r^4])]/(2*alpha)","A",1
214,1,71,68,0.0250003,"\int \frac{1}{r \sqrt{-\alpha ^2-\epsilon ^2+2 h r^2-2 k r^4}} \, dr","Integrate[1/(r*Sqrt[-alpha^2 - epsilon^2 + 2*h*r^2 - 2*k*r^4]),r]","\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}}","-\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[(-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])]/(2*Sqrt[alpha^2 + epsilon^2])","A",1
215,1,13,13,0.0063827,"\int a \cos (5+3 x) \sin ^2(5+3 x) \, dx","Integrate[a*Cos[5 + 3*x]*Sin[5 + 3*x]^2,x]","\frac{1}{9} a \sin ^3(3 x+5)","\frac{1}{9} a \sin ^3(3 x+5)",1,"(a*Sin[5 + 3*x]^3)/9","A",1
216,1,19,19,0.0011211,"\int \frac{\log \left(x^2\right)}{x^3} \, dx","Integrate[Log[x^2]/x^3,x]","-\frac{1}{2 x^2}-\frac{\log \left(x^2\right)}{2 x^2}","-\frac{1}{2 x^2}-\frac{\log \left(x^2\right)}{2 x^2}",1,"-1/2*1/x^2 - Log[x^2]/(2*x^2)","A",1
217,1,12,12,0.0261866,"\int x \sin (a+x) \, dx","Integrate[x*Sin[a + x],x]","\sin (a+x)-x \cos (a+x)","\sin (a+x)-x \cos (a+x)",1,"-(x*Cos[a + x]) + Sin[a + x]","A",1
218,1,11,11,0.0076775,"\int \frac{e^{-x} (-1+(1-x) \log (x))}{\log ^2(x)} \, dx","Integrate[(-1 + (1 - x)*Log[x])/(E^x*Log[x]^2),x]","\frac{e^{-x} x}{\log (x)}","\frac{e^{-x} x}{\log (x)}",1,"x/(E^x*Log[x])","A",1
219,1,27,27,0.0046955,"\int \frac{x^3}{b+a x^2} \, dx","Integrate[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
220,1,21,33,0.0064789,"\int \frac{\sqrt{x}}{(1+x)^{7/2}} \, dx","Integrate[Sqrt[x]/(1 + x)^(7/2),x]","\frac{2 x^{3/2} (2 x+5)}{15 (x+1)^{5/2}}","\frac{4 x^{3/2}}{15 (x+1)^{3/2}}+\frac{2 x^{3/2}}{5 (x+1)^{5/2}}",1,"(2*x^(3/2)*(5 + 2*x))/(15*(1 + x)^(5/2))","A",1
221,1,9,9,0.0020512,"\int \frac{1}{x (1+x)} \, dx","Integrate[1/(x*(1 + x)),x]","\log (x)-\log (x+1)","\log (x)-\log (x+1)",1,"Log[x] - Log[1 + x]","A",1
222,1,19,19,0.0031417,"\int \frac{1}{\sqrt{x} (-1+2 x)} \, dx","Integrate[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
223,1,16,19,0.0032838,"\int \sqrt{x} \left(1+x^2\right) \, dx","Integrate[Sqrt[x]*(1 + x^2),x]","\frac{2}{21} x^{3/2} \left(3 x^2+7\right)","\frac{2 x^{7/2}}{7}+\frac{2 x^{3/2}}{3}",1,"(2*x^(3/2)*(7 + 3*x^2))/21","A",1
224,1,112,88,0.0420205,"\int \frac{\sqrt[3]{-a+x}}{x} \, dx","Integrate[(-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-\frac{2 \sqrt[3]{x-a}}{\sqrt[3]{a}}}{\sqrt{3}}\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 - (2*(-a + x)^(1/3))/a^(1/3))/Sqrt[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
225,1,9,9,0.0022448,"\int x \sinh (x) \, dx","Integrate[x*Sinh[x],x]","x \cosh (x)-\sinh (x)","x \cosh (x)-\sinh (x)",1,"x*Cosh[x] - Sinh[x]","A",1
226,1,9,9,0.0022645,"\int x \cosh (x) \, dx","Integrate[x*Cosh[x],x]","x \sinh (x)-\cosh (x)","x \sinh (x)-\cosh (x)",1,"-Cosh[x] + x*Sinh[x]","A",1
227,1,9,9,0.0046192,"\int \tanh (2 x) \, dx","Integrate[Tanh[2*x],x]","\frac{1}{2} \log (\cosh (2 x))","\frac{1}{2} \log (\cosh (2 x))",1,"Log[Cosh[2*x]]/2","A",1
228,1,12,12,0.0867114,"\int \frac{-1+i \text{eps} \sinh (x)}{i a-x+i \text{eps} \cosh (x)} \, dx","Integrate[(-1 + I*eps*Sinh[x])/(I*a - x + I*eps*Cosh[x]),x]","\log (a+\text{eps} \cosh (x)+i x)","\log (a+\text{eps} \cosh (x)+i x)",1,"Log[a + I*x + eps*Cosh[x]]","A",1
229,1,28,28,0.0155655,"\int \cos ^2(x) \sin (3+2 x) \, dx","Integrate[Cos[x]^2*Sin[3 + 2*x],x]","\frac{1}{4} x \sin (3)-\frac{1}{4} \cos (2 x+3)-\frac{1}{16} \cos (4 x+3)","\frac{1}{4} x \sin (3)-\frac{1}{4} \cos (2 x+3)-\frac{1}{16} \cos (4 x+3)",1,"-1/4*Cos[3 + 2*x] - Cos[3 + 4*x]/16 + (x*Sin[3])/4","A",1
230,1,21,21,0.0026548,"\int x \tan ^{-1}(x) \, dx","Integrate[x*ArcTan[x],x]","\frac{1}{2} x^2 \tan ^{-1}(x)-\frac{x}{2}+\frac{1}{2} \tan ^{-1}(x)","\frac{1}{2} x^2 \tan ^{-1}(x)-\frac{x}{2}+\frac{1}{2} \tan ^{-1}(x)",1,"-1/2*x + ArcTan[x]/2 + (x^2*ArcTan[x])/2","A",1
231,1,21,21,0.0025978,"\int x \cot ^{-1}(x) \, dx","Integrate[x*ArcCot[x],x]","\frac{1}{2} x^2 \cot ^{-1}(x)+\frac{x}{2}-\frac{1}{2} \tan ^{-1}(x)","\frac{1}{2} x^2 \cot ^{-1}(x)+\frac{x}{2}-\frac{1}{2} \tan ^{-1}(x)",1,"x/2 + (x^2*ArcCot[x])/2 - ArcTan[x]/2","A",1
232,1,22,23,0.0032659,"\int x \log \left(a+x^2\right) \, dx","Integrate[x*Log[a + x^2],x]","\frac{1}{2} \left(\left(a+x^2\right) \log \left(a+x^2\right)-x^2\right)","\frac{1}{2} \left(a+x^2\right) \log \left(a+x^2\right)-\frac{x^2}{2}",1,"(-x^2 + (a + x^2)*Log[a + x^2])/2","A",1
233,1,18,18,0.0189279,"\int \cos (x) \sin (a+x) \, dx","Integrate[Cos[x]*Sin[a + x],x]","\frac{1}{4} (2 x \sin (a)-\cos (a+2 x))","\frac{1}{2} x \sin (a)-\frac{1}{4} \cos (a+2 x)",1,"(-Cos[a + 2*x] + 2*x*Sin[a])/4","A",1
234,1,18,18,0.0132736,"\int \cos (a+x) \sin (x) \, dx","Integrate[Cos[a + x]*Sin[x],x]","\frac{1}{4} (-2 x \sin (a)-\cos (a+2 x))","-\frac{1}{2} x \sin (a)-\frac{1}{4} \cos (a+2 x)",1,"(-Cos[a + 2*x] - 2*x*Sin[a])/4","A",1
235,1,40,12,0.0124497,"\int \sqrt{1+\sin (x)} \, dx","Integrate[Sqrt[1 + Sin[x]],x]","\frac{2 \sqrt{\sin (x)+1} \left(\sin \left(\frac{x}{2}\right)-\cos \left(\frac{x}{2}\right)\right)}{\sin \left(\frac{x}{2}\right)+\cos \left(\frac{x}{2}\right)}","-\frac{2 \cos (x)}{\sqrt{\sin (x)+1}}",1,"(2*(-Cos[x/2] + Sin[x/2])*Sqrt[1 + Sin[x]])/(Cos[x/2] + Sin[x/2])","B",1
236,1,42,14,0.012577,"\int \sqrt{1-\sin (x)} \, dx","Integrate[Sqrt[1 - Sin[x]],x]","\frac{2 \sqrt{1-\sin (x)} \left(\sin \left(\frac{x}{2}\right)+\cos \left(\frac{x}{2}\right)\right)}{\cos \left(\frac{x}{2}\right)-\sin \left(\frac{x}{2}\right)}","\frac{2 \cos (x)}{\sqrt{1-\sin (x)}}",1,"(2*(Cos[x/2] + Sin[x/2])*Sqrt[1 - Sin[x]])/(Cos[x/2] - Sin[x/2])","B",1
237,1,16,12,0.0067071,"\int \sqrt{1+\cos (x)} \, dx","Integrate[Sqrt[1 + Cos[x]],x]","2 \sqrt{\cos (x)+1} \tan \left(\frac{x}{2}\right)","\frac{2 \sin (x)}{\sqrt{\cos (x)+1}}",1,"2*Sqrt[1 + Cos[x]]*Tan[x/2]","A",1
238,1,18,14,0.0080983,"\int \sqrt{1-\cos (x)} \, dx","Integrate[Sqrt[1 - Cos[x]],x]","-2 \sqrt{1-\cos (x)} \cot \left(\frac{x}{2}\right)","-\frac{2 \sin (x)}{\sqrt{1-\cos (x)}}",1,"-2*Sqrt[1 - Cos[x]]*Cot[x/2]","A",1
239,1,17,21,0.0185204,"\int \frac{1}{-\sqrt{-1+x}+\sqrt{x}} \, dx","Integrate[(-Sqrt[-1 + x] + Sqrt[x])^(-1),x]","\frac{2}{3} \left(x^{3/2}+(x-1)^{3/2}\right)","\frac{2 x^{3/2}}{3}+\frac{2}{3} (x-1)^{3/2}",1,"(2*((-1 + x)^(3/2) + x^(3/2)))/3","A",1
240,1,24,24,0.0098625,"\int \frac{1}{1-\sqrt{1+x}} \, dx","Integrate[(1 - Sqrt[1 + x])^(-1),x]","-2 \sqrt{x+1}-2 \log \left(1-\sqrt{x+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
241,1,12,12,0.0022974,"\int \frac{x}{\sqrt{36+x^4}} \, dx","Integrate[x/Sqrt[36 + x^4],x]","\frac{1}{2} \sinh ^{-1}\left(\frac{x^2}{6}\right)","\frac{1}{2} \sinh ^{-1}\left(\frac{x^2}{6}\right)",1,"ArcSinh[x^2/6]/2","A",1
242,1,32,32,0.0118413,"\int \frac{1}{\sqrt[3]{x}+\sqrt{x}} \, dx","Integrate[(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
243,1,33,33,0.0128498,"\int \log \left(2+3 x^2\right) \, dx","Integrate[Log[2 + 3*x^2],x]","x \log \left(3 x^2+2\right)-2 x+2 \sqrt{\frac{2}{3}} \tan ^{-1}\left(\sqrt{\frac{3}{2}} x\right)","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,"-2*x + 2*Sqrt[2/3]*ArcTan[Sqrt[3/2]*x] + x*Log[2 + 3*x^2]","A",1
244,1,3,3,0.0021235,"\int \cot (x) \, dx","Integrate[Cot[x],x]","\log (\sin (x))","\log (\sin (x))",1,"Log[Sin[x]]","A",1
245,1,18,12,0.0032448,"\int \cot ^4(x) \, dx","Integrate[Cot[x]^4,x]","x+\frac{4 \cot (x)}{3}-\frac{1}{3} \cot (x) \csc ^2(x)","x-\frac{1}{3} \cot ^3(x)+\cot (x)",1,"x + (4*Cot[x])/3 - (Cot[x]*Csc[x]^2)/3","A",1
246,1,3,3,0.0020815,"\int \tanh (x) \, dx","Integrate[Tanh[x],x]","\log (\cosh (x))","\log (\cosh (x))",1,"Log[Cosh[x]]","A",1
247,1,3,3,0.0022052,"\int \coth (x) \, dx","Integrate[Coth[x],x]","\log (\sinh (x))","\log (\sinh (x))",1,"Log[Sinh[x]]","A",1
248,1,8,8,0.0007082,"\int b^x \, dx","Integrate[b^x,x]","\frac{b^x}{\log (b)}","\frac{b^x}{\log (b)}",1,"b^x/Log[b]","A",1
249,1,29,49,0.0088244,"\int \sqrt{2+\frac{1}{x^4}+x^4} \, dx","Integrate[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
250,1,17,16,0.0031036,"\int \frac{1+2 x}{2+3 x} \, dx","Integrate[(1 + 2*x)/(2 + 3*x),x]","\frac{1}{9} (6 x-\log (3 x+2)+4)","\frac{2 x}{3}-\frac{1}{9} \log (3 x+2)",1,"(4 + 6*x - Log[2 + 3*x])/9","A",1
251,1,36,40,0.0104407,"\int x \log \left(x+\sqrt{1+x^2}\right) \, dx","Integrate[x*Log[x + Sqrt[1 + x^2]],x]","\frac{1}{4} \left(-\sqrt{x^2+1} x+2 x^2 \log \left(\sqrt{x^2+1}+x\right)+\sinh ^{-1}(x)\right)","-\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,"(-(x*Sqrt[1 + x^2]) + ArcSinh[x] + 2*x^2*Log[x + Sqrt[1 + x^2]])/4","A",1
252,1,67,128,0.1731845,"\int x \left(1+e^x \sin (x)\right)^2 \, dx","Integrate[x*(1 + E^x*Sin[x])^2,x]","\frac{1}{8} \left(4 x^2+e^{2 x} (2 x-1)+8 e^x x \sin (x)-e^{2 x} x \cos (2 x)-8 e^x (x-1) \cos (x)-e^{2 x} (2 x-1) \sin (x) \cos (x)\right)","\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,"(4*x^2 + E^(2*x)*(-1 + 2*x) - 8*E^x*(-1 + x)*Cos[x] - E^(2*x)*x*Cos[2*x] + 8*E^x*x*Sin[x] - E^(2*x)*(-1 + 2*x)*Cos[x]*Sin[x])/8","A",1
253,1,18,30,0.0269352,"\int e^x x \cos (x) \, dx","Integrate[E^x*x*Cos[x],x]","\frac{1}{2} e^x ((x-1) \sin (x)+x \cos (x))","-\frac{1}{2} e^x \sin (x)+\frac{1}{2} e^x x \sin (x)+\frac{1}{2} e^x x \cos (x)",1,"(E^x*(x*Cos[x] + (-1 + x)*Sin[x]))/2","A",1
254,1,9,11,0.00142,"\int \frac{1}{(-3+x)^4} \, dx","Integrate[(-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
255,1,40,40,0.0086097,"\int \frac{x}{-1+x^3} \, dx","Integrate[x/(-1 + x^3),x]","-\frac{1}{6} \log \left(x^2+x+1\right)+\frac{1}{3} \log (1-x)+\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{\sqrt{3}}","-\frac{1}{6} \log \left(x^2+x+1\right)+\frac{1}{3} \log (1-x)+\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{\sqrt{3}}",1,"ArcTan[(1 + 2*x)/Sqrt[3]]/Sqrt[3] + Log[1 - x]/3 - Log[1 + x + x^2]/6","A",1
256,1,23,8,0.0030653,"\int \frac{x}{-1+x^4} \, dx","Integrate[x/(-1 + x^4),x]","\frac{1}{4} \log \left(1-x^2\right)-\frac{1}{4} \log \left(x^2+1\right)","-\frac{1}{2} \tanh ^{-1}\left(x^2\right)",1,"Log[1 - x^2]/4 - Log[1 + x^2]/4","B",1
257,1,194,227,0.275027,"\int \frac{\left(1+x^3\right) \log (x)}{2+x^4} \, dx","Integrate[((1 + x^3)*Log[x])/(2 + x^4),x]","\frac{1}{8} \left(\left(2+\frac{1-i}{\sqrt[4]{2}}\right) \operatorname{PolyLog}\left(2,-\frac{(1+i) x}{2^{3/4}}\right)+\left(2+\sqrt[4]{-2}\right) \operatorname{PolyLog}\left(2,-\frac{(1-i) x}{2^{3/4}}\right)-\left(\sqrt[4]{-2}-2\right) \operatorname{PolyLog}\left(2,\frac{(1-i) x}{2^{3/4}}\right)+\left(2+i \sqrt[4]{-2}\right) \operatorname{PolyLog}\left(2,\frac{(1+i) x}{2^{3/4}}\right)+\left(2+i \sqrt[4]{-2}\right) \log (x) \log \left(1-\sqrt[4]{-\frac{1}{2}} x\right)+\left(2+\frac{1-i}{\sqrt[4]{2}}\right) \log (x) \log \left(\sqrt[4]{-\frac{1}{2}} x+1\right)-\left(\sqrt[4]{-2}-2\right) \log (x) \log \left(1-\frac{(1-i) x}{2^{3/4}}\right)+\left(2+\sqrt[4]{-2}\right) \log (x) \log \left(1+\frac{(1-i) x}{2^{3/4}}\right)\right)","\frac{1}{16} \left(4+(1-i) 2^{3/4}\right) \operatorname{PolyLog}\left(2,-\frac{(1+i) x}{2^{3/4}}\right)+\frac{1}{8} \left(2+i \sqrt[4]{-2}\right) \operatorname{PolyLog}\left(2,\frac{(1+i) x}{2^{3/4}}\right)+\frac{1}{8} \left(2-\sqrt[4]{-2}\right) \operatorname{PolyLog}\left(2,-\frac{(-1)^{3/4} x}{\sqrt[4]{2}}\right)+\frac{1}{8} \left(2+\sqrt[4]{-2}\right) \operatorname{PolyLog}\left(2,\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,"((2 + I*(-2)^(1/4))*Log[x]*Log[1 - (-1/2)^(1/4)*x] + (2 + (1 - I)/2^(1/4))*Log[x]*Log[1 + (-1/2)^(1/4)*x] - (-2 + (-2)^(1/4))*Log[x]*Log[1 - ((1 - I)*x)/2^(3/4)] + (2 + (-2)^(1/4))*Log[x]*Log[1 + ((1 - I)*x)/2^(3/4)] + (2 + (1 - I)/2^(1/4))*PolyLog[2, ((-1 - I)*x)/2^(3/4)] + (2 + (-2)^(1/4))*PolyLog[2, ((-1 + I)*x)/2^(3/4)] - (-2 + (-2)^(1/4))*PolyLog[2, ((1 - I)*x)/2^(3/4)] + (2 + I*(-2)^(1/4))*PolyLog[2, ((1 + I)*x)/2^(3/4)])/8","A",1
258,1,30,24,0.003214,"\int (\log (x)+\log (1+x)+\log (2+x)) \, dx","Integrate[Log[x] + Log[1 + x] + Log[2 + x],x]","-3 x+x \log (x)+x \log (x+1)+x \log (x+2)+\log (x+1)+2 \log (x+2)","-3 x+x \log (x)+(x+1) \log (x+1)+(x+2) \log (x+2)",1,"-3*x + x*Log[x] + Log[1 + x] + x*Log[1 + x] + 2*Log[2 + x] + x*Log[2 + x]","A",1
259,1,71,78,0.0234192,"\int \frac{1}{5+x^3} \, dx","Integrate[(5 + x^3)^(-1),x]","\frac{-\log \left(\sqrt[3]{5} x^2-5^{2/3} x+5\right)+2 \log \left(5^{2/3} x+5\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{2\ 5^{2/3} x-5}{5 \sqrt{3}}\right)}{6\ 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,"(2*Sqrt[3]*ArcTan[(-5 + 2*5^(2/3)*x)/(5*Sqrt[3])] + 2*Log[5 + 5^(2/3)*x] - Log[5 - 5^(2/3)*x + 5^(1/3)*x^2])/(6*5^(2/3))","A",1
260,1,2,2,0.003407,"\int \frac{1}{\sqrt{1+x^2}} \, dx","Integrate[1/Sqrt[1 + x^2],x]","\sinh ^{-1}(x)","\sinh ^{-1}(x)",1,"ArcSinh[x]","A",1
261,1,27,27,0.0067628,"\int \sqrt{3+x^2} \, dx","Integrate[Sqrt[3 + x^2],x]","\frac{1}{2} \sqrt{x^2+3} x+\frac{3}{2} \sinh ^{-1}\left(\frac{x}{\sqrt{3}}\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*ArcSinh[x/Sqrt[3]])/2","A",1
262,1,10,10,0.0029735,"\int \frac{x}{(1+x)^2} \, dx","Integrate[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
263,1,16,16,0.0031232,"\int \sin ^{-1}(x) \, dx","Integrate[ArcSin[x],x]","\sqrt{1-x^2}+x \sin ^{-1}(x)","\sqrt{1-x^2}+x \sin ^{-1}(x)",1,"Sqrt[1 - x^2] + x*ArcSin[x]","A",1
264,1,29,40,0.0123155,"\int x^2 \sin ^{-1}(x) \, dx","Integrate[x^2*ArcSin[x],x]","\frac{1}{9} \left(3 x^3 \sin ^{-1}(x)+\sqrt{1-x^2} \left(x^2+2\right)\right)","\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,"(Sqrt[1 - x^2]*(2 + x^2) + 3*x^3*ArcSin[x])/9","A",1
265,1,29,21,0.0297028,"\int \frac{\sec ^2(x)}{1+\sec ^2(x)-3 \tan (x)} \, dx","Integrate[Sec[x]^2/(1 + Sec[x]^2 - 3*Tan[x]),x]","2 \left(\frac{1}{2} \log (2 \cos (x)-\sin (x))-\frac{1}{2} \log (\cos (x)-\sin (x))\right)","\log (2 \cos (x)-\sin (x))-\log (\cos (x)-\sin (x))",1,"2*(-1/2*Log[Cos[x] - Sin[x]] + Log[2*Cos[x] - Sin[x]]/2)","A",1
266,1,14,14,0.0018284,"\int \cos ^2(x) \, dx","Integrate[Cos[x]^2,x]","\frac{x}{2}+\frac{1}{4} \sin (2 x)","\frac{x}{2}+\frac{1}{2} \sin (x) \cos (x)",1,"x/2 + Sin[2*x]/4","A",1
267,1,18,18,0.0039193,"\int \frac{-2-3 x+5 x^2}{(-2+x) x^2} \, dx","Integrate[(-2 - 3*x + 5*x^2)/((-2 + x)*x^2),x]","-\frac{1}{x}+3 \log (2-x)+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
268,1,10,10,0.0046055,"\int \frac{1}{\sqrt{9+4 x^2}} \, dx","Integrate[1/Sqrt[9 + 4*x^2],x]","\frac{1}{2} \sinh ^{-1}\left(\frac{2 x}{3}\right)","\frac{1}{2} \sinh ^{-1}\left(\frac{2 x}{3}\right)",1,"ArcSinh[(2*x)/3]/2","A",1
269,1,6,6,0.0038324,"\int \frac{1}{\sqrt{4+x^2}} \, dx","Integrate[1/Sqrt[4 + x^2],x]","\sinh ^{-1}\left(\frac{x}{2}\right)","\sinh ^{-1}\left(\frac{x}{2}\right)",1,"ArcSinh[x/2]","A",1
270,1,21,21,0.0094785,"\int \frac{1}{10-12 x+9 x^2} \, dx","Integrate[(10 - 12*x + 9*x^2)^(-1),x]","\frac{\tan ^{-1}\left(\frac{3 x-2}{\sqrt{6}}\right)}{3 \sqrt{6}}","-\frac{\tan ^{-1}\left(\frac{2-3 x}{\sqrt{6}}\right)}{3 \sqrt{6}}",1,"ArcTan[(-2 + 3*x)/Sqrt[6]]/(3*Sqrt[6])","A",1
271,1,51,53,0.0206836,"\int \frac{1}{x^4-2 x^5+2 x^6-2 x^7+x^8} \, dx","Integrate[(x^4 - 2*x^5 + 2*x^6 - 2*x^7 + x^8)^(-1),x]","-\frac{1}{3 x^3}-\frac{1}{x^2}+\frac{1}{4} \log \left(x^2+1\right)-\frac{1}{2 (x-1)}-\frac{2}{x}-\frac{5}{2} \log (1-x)+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,"-1/2*1/(-1 + x) - 1/(3*x^3) - x^(-2) - 2/x - (5*Log[1 - x])/2 + 2*Log[x] + Log[1 + x^2]/4","A",1
272,1,49,49,0.0268716,"\int \frac{d+c x+b x^2+a x^3}{(-3+x) x (1+x)} \, dx","Integrate[(d + c*x + b*x^2 + a*x^3)/((-3 + x)*x*(1 + x)),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)","\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
273,0,0,15,0.2383528,"\int \frac{1}{\left(2-\log \left(1+x^2\right)\right)^5} \, dx","Integrate[(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)",0,"Integrate[(2 - Log[1 + x^2])^(-5), x]","A",-1
274,1,28,28,0.1737092,"\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","Integrate[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]","e^{x^2} \log (x)-\frac{\log (x)}{x+\log ^2(x)}+\log \left(x+\log ^2(x)\right)","e^{x^2} \log (x)-\frac{\log (x)}{x+\log ^2(x)}+\log \left(x+\log ^2(x)\right)",1,"E^x^2*Log[x] - Log[x]/(x + Log[x]^2) + Log[x + Log[x]^2]","A",1
275,1,136,199,0.2361905,"\int e^{\frac{x}{2}+x z} x^4 \sin ^4(\pi  z) \, dz","Integrate[E^(x/2 + x*z)*x^4*Sin[Pi*z]^4,z]","\frac{x^4 e^{x \left(z+\frac{1}{2}\right)} \left(3 x^4-8 \pi  x^3 \sin (2 \pi  z)+4 \pi  x^3 \sin (4 \pi  z)-4 \left(x^2+16 \pi ^2\right) x^2 \cos (2 \pi  z)+\left(x^2+4 \pi ^2\right) x^2 \cos (4 \pi  z)+60 \pi ^2 x^2-128 \pi ^3 x \sin (2 \pi  z)+16 \pi ^3 x \sin (4 \pi  z)+192 \pi ^4\right)}{8 \left(x^5+20 \pi ^2 x^3+64 \pi ^4 x\right)}","\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,"(E^(x*(1/2 + z))*x^4*(192*Pi^4 + 60*Pi^2*x^2 + 3*x^4 - 4*x^2*(16*Pi^2 + x^2)*Cos[2*Pi*z] + x^2*(4*Pi^2 + x^2)*Cos[4*Pi*z] - 128*Pi^3*x*Sin[2*Pi*z] - 8*Pi*x^3*Sin[2*Pi*z] + 16*Pi^3*x*Sin[4*Pi*z] + 4*Pi*x^3*Sin[4*Pi*z]))/(8*(64*Pi^4*x + 20*Pi^2*x^3 + x^5))","A",1
276,1,18,18,0.0068422,"\int \text{erf}(x) \, dx","Integrate[Erf[x],x]","x \text{erf}(x)+\frac{e^{-x^2}}{\sqrt{\pi }}","x \text{erf}(x)+\frac{e^{-x^2}}{\sqrt{\pi }}",1,"1/(E^x^2*Sqrt[Pi]) + x*Erf[x]","A",1
277,1,24,24,0.0297745,"\int \text{erf}(a+x) \, dx","Integrate[Erf[a + x],x]","(a+x) \text{erf}(a+x)+\frac{e^{-(a+x)^2}}{\sqrt{\pi }}","(a+x) \text{erf}(a+x)+\frac{e^{-(a+x)^2}}{\sqrt{\pi }}",1,"1/(E^(a + x)^2*Sqrt[Pi]) + (a + x)*Erf[a + x]","A",1
278,1,5137,94,6.4432171,"\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","Integrate[(-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]","\text{Result too large to show}","\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,"Result too large to show","C",1
279,1,630,142,1.569419,"\int \frac{(1+2 y) \sqrt{1-5 y-5 y^2}}{y (1+y) (2+y) \sqrt{1-y-y^2}} \, dy","Integrate[((1 + 2*y)*Sqrt[1 - 5*y - 5*y^2])/(y*(1 + y)*(2 + y)*Sqrt[1 - y - y^2]),y]","\frac{\left(-1-\frac{2}{\sqrt{5}}\right) \left(2 y+\sqrt{5}+1\right)^2 \sqrt{\frac{10 y+3 \sqrt{5}+5}{10 y+5 \sqrt{5}+5}} \left(20 \left(\sqrt{5} \sqrt{\frac{-10 y+3 \sqrt{5}-5}{2 y+\sqrt{5}+1}} \sqrt{\frac{-2 y+\sqrt{5}-1}{2 y+\sqrt{5}+1}}-4 \sqrt{\frac{-10 y+3 \sqrt{5}-5}{2 y+\sqrt{5}+1}} \sqrt{\frac{-2 y+\sqrt{5}-1}{2 y+\sqrt{5}+1}}-2 \sqrt{5} \sqrt{-\frac{2 \sqrt{5} y+\sqrt{5}-5}{2 y+\sqrt{5}+1}} \sqrt{-\frac{2 \sqrt{5} y+\sqrt{5}-3}{2 y+\sqrt{5}+1}}+5 \sqrt{-\frac{2 \sqrt{5} y+\sqrt{5}-5}{2 y+\sqrt{5}+1}} \sqrt{-\frac{2 \sqrt{5} y+\sqrt{5}-3}{2 y+\sqrt{5}+1}}\right) \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{2 \sqrt{\frac{10 y+3 \sqrt{5}+5}{2 y+\sqrt{5}+1}}}{\sqrt{15}}\right),\frac{15}{16}\right)+\sqrt{\frac{-10 y+3 \sqrt{5}-5}{2 y+\sqrt{5}+1}} \sqrt{\frac{-2 y+\sqrt{5}-1}{2 y+\sqrt{5}+1}} \left(9 \sqrt{5} \Pi \left(\frac{5}{8}-\frac{\sqrt{5}}{8};\sin ^{-1}\left(\frac{2 \sqrt{\frac{10 y+3 \sqrt{5}+5}{2 y+\sqrt{5}+1}}}{\sqrt{15}}\right)|\frac{15}{16}\right)+\left(9 \sqrt{5}-20\right) \Pi \left(-\frac{3}{8} \left(-5+\sqrt{5}\right);\sin ^{-1}\left(\frac{2 \sqrt{\frac{10 y+3 \sqrt{5}+5}{2 y+\sqrt{5}+1}}}{\sqrt{15}}\right)|\frac{15}{16}\right)+2 \sqrt{5} \Pi \left(\frac{3}{8} \left(5+\sqrt{5}\right);\sin ^{-1}\left(\frac{2 \sqrt{\frac{10 y+3 \sqrt{5}+5}{2 y+\sqrt{5}+1}}}{\sqrt{15}}\right)|\frac{15}{16}\right)\right)\right)}{16 \sqrt{-5 y^2-5 y+1} \sqrt{-y^2-y+1}}","-\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,"((-1 - 2/Sqrt[5])*(1 + Sqrt[5] + 2*y)^2*Sqrt[(5 + 3*Sqrt[5] + 10*y)/(5 + 5*Sqrt[5] + 10*y)]*(20*(-4*Sqrt[(-5 + 3*Sqrt[5] - 10*y)/(1 + Sqrt[5] + 2*y)]*Sqrt[(-1 + Sqrt[5] - 2*y)/(1 + Sqrt[5] + 2*y)] + Sqrt[5]*Sqrt[(-5 + 3*Sqrt[5] - 10*y)/(1 + Sqrt[5] + 2*y)]*Sqrt[(-1 + Sqrt[5] - 2*y)/(1 + Sqrt[5] + 2*y)] + 5*Sqrt[-((-5 + Sqrt[5] + 2*Sqrt[5]*y)/(1 + Sqrt[5] + 2*y))]*Sqrt[-((-3 + Sqrt[5] + 2*Sqrt[5]*y)/(1 + Sqrt[5] + 2*y))] - 2*Sqrt[5]*Sqrt[-((-5 + Sqrt[5] + 2*Sqrt[5]*y)/(1 + Sqrt[5] + 2*y))]*Sqrt[-((-3 + Sqrt[5] + 2*Sqrt[5]*y)/(1 + Sqrt[5] + 2*y))])*EllipticF[ArcSin[(2*Sqrt[(5 + 3*Sqrt[5] + 10*y)/(1 + Sqrt[5] + 2*y)])/Sqrt[15]], 15/16] + Sqrt[(-5 + 3*Sqrt[5] - 10*y)/(1 + Sqrt[5] + 2*y)]*Sqrt[(-1 + Sqrt[5] - 2*y)/(1 + Sqrt[5] + 2*y)]*(9*Sqrt[5]*EllipticPi[5/8 - Sqrt[5]/8, ArcSin[(2*Sqrt[(5 + 3*Sqrt[5] + 10*y)/(1 + Sqrt[5] + 2*y)])/Sqrt[15]], 15/16] + (-20 + 9*Sqrt[5])*EllipticPi[(-3*(-5 + Sqrt[5]))/8, ArcSin[(2*Sqrt[(5 + 3*Sqrt[5] + 10*y)/(1 + Sqrt[5] + 2*y)])/Sqrt[15]], 15/16] + 2*Sqrt[5]*EllipticPi[(3*(5 + Sqrt[5]))/8, ArcSin[(2*Sqrt[(5 + 3*Sqrt[5] + 10*y)/(1 + Sqrt[5] + 2*y)])/Sqrt[15]], 15/16])))/(16*Sqrt[1 - 5*y - 5*y^2]*Sqrt[1 - y - y^2])","C",0
280,1,97,21,1.3511097,"\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","Integrate[(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]","\frac{1}{4} \log \left(-5 x^2-4 \sqrt{x^2-4} \sqrt{x^2-1}+17\right)+\frac{1}{4} \log \left(-2 x^2-2 \sqrt{x^2-4} \sqrt{x^2-1}+5\right)-\frac{1}{2} \tanh ^{-1}\left(\sqrt{x^2-4}\right)+\frac{1}{2} \tanh ^{-1}\left(\frac{\sqrt{x^2-1}}{2}\right)","\log \left(\sqrt{x^2-4}+\sqrt{x^2-1}+1\right)",1,"-1/2*ArcTanh[Sqrt[-4 + x^2]] + ArcTanh[Sqrt[-1 + x^2]/2]/2 + Log[17 - 5*x^2 - 4*Sqrt[-4 + x^2]*Sqrt[-1 + x^2]]/4 + Log[5 - 2*x^2 - 2*Sqrt[-4 + x^2]*Sqrt[-1 + x^2]]/4","B",1
281,1,3168,4030,6.0425935,"\int \left(\sqrt{9-4 \sqrt{2}} x-\sqrt{2} \sqrt{1+4 x+2 x^2+x^4}\right) \, dx","Integrate[Sqrt[9 - 4*Sqrt[2]]*x - Sqrt[2]*Sqrt[1 + 4*x + 2*x^2 + x^4],x]","\text{Result too large to show}","\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} \operatorname{EllipticF}\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,"(Sqrt[9 - 4*Sqrt[2]]*x^2)/2 - (Sqrt[2]*x*Sqrt[1 + 4*x + 2*x^2 + x^4])/3 - (2*Sqrt[2]*((6*(x - Root[1 + 3*#1 - #1^2 + #1^3 & , 1, 0])^2*(-(EllipticF[ArcSin[Sqrt[-(((1 + x)*(Root[1 + 3*#1 - #1^2 + #1^3 & , 1, 0] - Root[1 + 3*#1 - #1^2 + #1^3 & , 3, 0]))/((x - Root[1 + 3*#1 - #1^2 + #1^3 & , 1, 0])*(1 + Root[1 + 3*#1 - #1^2 + #1^3 & , 3, 0])))]], ((Root[1 + 3*#1 - #1^2 + #1^3 & , 1, 0] - Root[1 + 3*#1 - #1^2 + #1^3 & , 2, 0])*(1 + Root[1 + 3*#1 - #1^2 + #1^3 & , 3, 0]))/((1 + Root[1 + 3*#1 - #1^2 + #1^3 & , 2, 0])*(Root[1 + 3*#1 - #1^2 + #1^3 & , 1, 0] - Root[1 + 3*#1 - #1^2 + #1^3 & , 3, 0]))]*Root[1 + 3*#1 - #1^2 + #1^3 & , 1, 0]) + EllipticPi[(1 + Root[1 + 3*#1 - #1^2 + #1^3 & , 3, 0])/(-Root[1 + 3*#1 - #1^2 + #1^3 & , 1, 0] + Root[1 + 3*#1 - #1^2 + #1^3 & , 3, 0]), ArcSin[Sqrt[-(((1 + x)*(Root[1 + 3*#1 - #1^2 + #1^3 & , 1, 0] - Root[1 + 3*#1 - #1^2 + #1^3 & , 3, 0]))/((x - Root[1 + 3*#1 - #1^2 + #1^3 & , 1, 0])*(1 + Root[1 + 3*#1 - #1^2 + #1^3 & , 3, 0])))]], ((Root[1 + 3*#1 - #1^2 + #1^3 & , 1, 0] - Root[1 + 3*#1 - #1^2 + #1^3 & , 2, 0])*(1 + Root[1 + 3*#1 - #1^2 + #1^3 & , 3, 0]))/((1 + Root[1 + 3*#1 - #1^2 + #1^3 & , 2, 0])*(Root[1 + 3*#1 - #1^2 + #1^3 & , 1, 0] - Root[1 + 3*#1 - #1^2 + #1^3 & , 3, 0]))]*(1 + Root[1 + 3*#1 - #1^2 + #1^3 & , 1, 0]))*Sqrt[(x - Root[1 + 3*#1 - #1^2 + #1^3 & , 2, 0])/((x - Root[1 + 3*#1 - #1^2 + #1^3 & , 1, 0])*(1 + Root[1 + 3*#1 - #1^2 + #1^3 & , 2, 0]))]*(-1 - Root[1 + 3*#1 - #1^2 + #1^3 & , 3, 0])*Sqrt[(x - Root[1 + 3*#1 - #1^2 + #1^3 & , 3, 0])/((x - Root[1 + 3*#1 - #1^2 + #1^3 & , 1, 0])*(1 + Root[1 + 3*#1 - #1^2 + #1^3 & , 3, 0]))]*Sqrt[-(((1 + x)*(Root[1 + 3*#1 - #1^2 + #1^3 & , 1, 0] - Root[1 + 3*#1 - #1^2 + #1^3 & , 3, 0]))/((x - Root[1 + 3*#1 - #1^2 + #1^3 & , 1, 0])*(1 + Root[1 + 3*#1 - #1^2 + #1^3 & , 3, 0])))])/(Sqrt[1 + 4*x + 2*x^2 + x^4]*(Root[1 + 3*#1 - #1^2 + #1^3 & , 1, 0] - Root[1 + 3*#1 - #1^2 + #1^3 & , 3, 0])) + (2*EllipticF[ArcSin[Sqrt[((1 + x)*(-Root[1 + 3*#1 - #1^2 + #1^3 & , 1, 0] + Root[1 + 3*#1 - #1^2 + #1^3 & , 3, 0]))/((x - Root[1 + 3*#1 - #1^2 + #1^3 & , 1, 0])*(1 + Root[1 + 3*#1 - #1^2 + #1^3 & , 3, 0]))]], ((Root[1 + 3*#1 - #1^2 + #1^3 & , 1, 0] - Root[1 + 3*#1 - #1^2 + #1^3 & , 2, 0])*(-1 - Root[1 + 3*#1 - #1^2 + #1^3 & , 3, 0]))/((-1 - Root[1 + 3*#1 - #1^2 + #1^3 & , 2, 0])*(Root[1 + 3*#1 - #1^2 + #1^3 & , 1, 0] - Root[1 + 3*#1 - #1^2 + #1^3 & , 3, 0]))]*(x - Root[1 + 3*#1 - #1^2 + #1^3 & , 1, 0])^2*Sqrt[(x - Root[1 + 3*#1 - #1^2 + #1^3 & , 2, 0])/((x - Root[1 + 3*#1 - #1^2 + #1^3 & , 1, 0])*(1 + Root[1 + 3*#1 - #1^2 + #1^3 & , 2, 0]))]*(-1 - Root[1 + 3*#1 - #1^2 + #1^3 & , 3, 0])*Sqrt[(x - Root[1 + 3*#1 - #1^2 + #1^3 & , 3, 0])/((x - Root[1 + 3*#1 - #1^2 + #1^3 & , 1, 0])*(1 + Root[1 + 3*#1 - #1^2 + #1^3 & , 3, 0]))]*Sqrt[((1 + x)*(-Root[1 + 3*#1 - #1^2 + #1^3 & , 1, 0] + Root[1 + 3*#1 - #1^2 + #1^3 & , 3, 0]))/((x - Root[1 + 3*#1 - #1^2 + #1^3 & , 1, 0])*(1 + Root[1 + 3*#1 - #1^2 + #1^3 & , 3, 0]))])/(Sqrt[1 + 4*x + 2*x^2 + x^4]*(-Root[1 + 3*#1 - #1^2 + #1^3 & , 1, 0] + Root[1 + 3*#1 - #1^2 + #1^3 & , 3, 0])) + ((1 + x)*(x - Root[1 + 3*#1 - #1^2 + #1^3 & , 2, 0])*(x - Root[1 + 3*#1 - #1^2 + #1^3 & , 3, 0]) + (x - Root[1 + 3*#1 - #1^2 + #1^3 & , 1, 0])^2*(1 + Root[1 + 3*#1 - #1^2 + #1^3 & , 1, 0])*Sqrt[(x - Root[1 + 3*#1 - #1^2 + #1^3 & , 2, 0])/((x - Root[1 + 3*#1 - #1^2 + #1^3 & , 1, 0])*(1 + Root[1 + 3*#1 - #1^2 + #1^3 & , 2, 0]))]*Sqrt[(x - Root[1 + 3*#1 - #1^2 + #1^3 & , 3, 0])/((x - Root[1 + 3*#1 - #1^2 + #1^3 & , 1, 0])*(1 + Root[1 + 3*#1 - #1^2 + #1^3 & , 3, 0]))]*Sqrt[-(((1 + x)*(Root[1 + 3*#1 - #1^2 + #1^3 & , 1, 0] - Root[1 + 3*#1 - #1^2 + #1^3 & , 3, 0]))/((x - Root[1 + 3*#1 - #1^2 + #1^3 & , 1, 0])*(1 + Root[1 + 3*#1 - #1^2 + #1^3 & , 3, 0])))]*(1 + Root[1 + 3*#1 - #1^2 + #1^3 & , 3, 0])*((EllipticE[ArcSin[Sqrt[-(((1 + x)*(Root[1 + 3*#1 - #1^2 + #1^3 & , 1, 0] - Root[1 + 3*#1 - #1^2 + #1^3 & , 3, 0]))/((x - Root[1 + 3*#1 - #1^2 + #1^3 & , 1, 0])*(1 + Root[1 + 3*#1 - #1^2 + #1^3 & , 3, 0])))]], ((Root[1 + 3*#1 - #1^2 + #1^3 & , 1, 0] - Root[1 + 3*#1 - #1^2 + #1^3 & , 2, 0])*(1 + Root[1 + 3*#1 - #1^2 + #1^3 & , 3, 0]))/((1 + Root[1 + 3*#1 - #1^2 + #1^3 & , 2, 0])*(Root[1 + 3*#1 - #1^2 + #1^3 & , 1, 0] - Root[1 + 3*#1 - #1^2 + #1^3 & , 3, 0]))]*(1 + Root[1 + 3*#1 - #1^2 + #1^3 & , 2, 0]))/(1 + Root[1 + 3*#1 - #1^2 + #1^3 & , 1, 0]) - (EllipticPi[(1 + Root[1 + 3*#1 - #1^2 + #1^3 & , 3, 0])/(-Root[1 + 3*#1 - #1^2 + #1^3 & , 1, 0] + Root[1 + 3*#1 - #1^2 + #1^3 & , 3, 0]), ArcSin[Sqrt[-(((1 + x)*(Root[1 + 3*#1 - #1^2 + #1^3 & , 1, 0] - Root[1 + 3*#1 - #1^2 + #1^3 & , 3, 0]))/((x - Root[1 + 3*#1 - #1^2 + #1^3 & , 1, 0])*(1 + Root[1 + 3*#1 - #1^2 + #1^3 & , 3, 0])))]], ((Root[1 + 3*#1 - #1^2 + #1^3 & , 1, 0] - Root[1 + 3*#1 - #1^2 + #1^3 & , 2, 0])*(1 + Root[1 + 3*#1 - #1^2 + #1^3 & , 3, 0]))/((1 + Root[1 + 3*#1 - #1^2 + #1^3 & , 2, 0])*(Root[1 + 3*#1 - #1^2 + #1^3 & , 1, 0] - Root[1 + 3*#1 - #1^2 + #1^3 & , 3, 0]))]*(1 - Root[1 + 3*#1 - #1^2 + #1^3 & , 1, 0] - Root[1 + 3*#1 - #1^2 + #1^3 & , 2, 0] - Root[1 + 3*#1 - #1^2 + #1^3 & , 3, 0]))/(-Root[1 + 3*#1 - #1^2 + #1^3 & , 1, 0] + Root[1 + 3*#1 - #1^2 + #1^3 & , 3, 0]) + (EllipticF[ArcSin[Sqrt[-(((1 + x)*(Root[1 + 3*#1 - #1^2 + #1^3 & , 1, 0] - Root[1 + 3*#1 - #1^2 + #1^3 & , 3, 0]))/((x - Root[1 + 3*#1 - #1^2 + #1^3 & , 1, 0])*(1 + Root[1 + 3*#1 - #1^2 + #1^3 & , 3, 0])))]], ((Root[1 + 3*#1 - #1^2 + #1^3 & , 1, 0] - Root[1 + 3*#1 - #1^2 + #1^3 & , 2, 0])*(1 + Root[1 + 3*#1 - #1^2 + #1^3 & , 3, 0]))/((1 + Root[1 + 3*#1 - #1^2 + #1^3 & , 2, 0])*(Root[1 + 3*#1 - #1^2 + #1^3 & , 1, 0] - Root[1 + 3*#1 - #1^2 + #1^3 & , 3, 0]))]*(Root[1 + 3*#1 - #1^2 + #1^3 & , 1, 0] + Root[1 + 3*#1 - #1^2 + #1^3 & , 1, 0]*(-Root[1 + 3*#1 - #1^2 + #1^3 & , 1, 0] - Root[1 + 3*#1 - #1^2 + #1^3 & , 3, 0]) - Root[1 + 3*#1 - #1^2 + #1^3 & , 3, 0]))/((1 + Root[1 + 3*#1 - #1^2 + #1^3 & , 1, 0])*(-Root[1 + 3*#1 - #1^2 + #1^3 & , 1, 0] + Root[1 + 3*#1 - #1^2 + #1^3 & , 3, 0]))))/Sqrt[1 + 4*x + 2*x^2 + x^4]))/3","C",0
282,1,181,330,0.1452877,"\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","Integrate[(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]","\frac{1}{384} \pi ^2 \left(\frac{e^{-\frac{x}{y}} \left(-4 \text{mc}^9+3 \text{mc}^8+144 \text{mc}^5 x y-16 \text{mc}^3 x y (11 x+5 y)+24 \text{mc}^2 x y (x+y)+12 \text{mc}^3 x y \left(12 \text{mc}^2-3 \text{mc}+8 (x+y)\right) \log \left(\frac{x}{\text{mc}^2}\right)-12 \text{mc} x y \left(x^2+2 x y+2 y^2\right)-3 x y \left(x^2+2 x y+2 y^2\right)\right)}{x}-\frac{\text{mc}^3 \left(4 \text{mc}^6-3 \text{mc}^5+48 \text{mc}^4 y-24 \text{mc}^3 y+144 \text{mc}^2 y^2-36 \text{mc} y^2+96 y^3\right) \text{Ei}\left(-\frac{x}{y}\right)}{y}\right)","\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,"(Pi^2*(-((mc^3*(-3*mc^5 + 4*mc^6 - 24*mc^3*y + 48*mc^4*y - 36*mc*y^2 + 144*mc^2*y^2 + 96*y^3)*ExpIntegralEi[-(x/y)])/y) + (3*mc^8 - 4*mc^9 + 144*mc^5*x*y + 24*mc^2*x*y*(x + y) - 16*mc^3*x*y*(11*x + 5*y) - 3*x*y*(x^2 + 2*x*y + 2*y^2) - 12*mc*x*y*(x^2 + 2*x*y + 2*y^2) + 12*mc^3*x*y*(-3*mc + 12*mc^2 + 8*(x + y))*Log[x/mc^2])/(E^(x/y)*x)))/384","A",1
283,1,4,4,0.001479,"\int \sec (x) \sin (2 x) \, dx","Integrate[Sec[x]*Sin[2*x],x]","-2 \cos (x)","-2 \cos (x)",1,"-2*Cos[x]","A",1
284,1,71,71,0.0385486,"\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","Integrate[(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(\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)","\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 + Sqrt[2]*x + Sqrt[2]*x^2 - x^7] - (-1 + Sqrt[2])*Log[-1 + (-1 + Sqrt[2])*x + Sqrt[2]*x^2 + x^7])/2","A",1