1,1,77,0,0.1338896,"\int \frac{1}{2 \sqrt{3} b^{3/2}-9 b x+9 x^3} \, dx","Int[(2*Sqrt[3]*b^(3/2) - 9*b*x + 9*x^3)^(-1),x]","\frac{1}{3 \sqrt{3} \sqrt{b} \left(\sqrt{3} \sqrt{b}-3 x\right)}-\frac{\log \left(\sqrt{b}-\sqrt{3} x\right)}{27 b}+\frac{\log \left(2 \sqrt{b}+\sqrt{3} x\right)}{27 b}","\frac{1}{3 \sqrt{3} \sqrt{b} \left(\sqrt{3} \sqrt{b}-3 x\right)}-\frac{\log \left(\sqrt{b}-\sqrt{3} x\right)}{27 b}+\frac{\log \left(2 \sqrt{b}+\sqrt{3} x\right)}{27 b}",1,"1/(3*Sqrt[3]*Sqrt[b]*(Sqrt[3]*Sqrt[b] - 3*x)) - Log[Sqrt[b] - Sqrt[3]*x]/(27*b) + Log[2*Sqrt[b] + Sqrt[3]*x]/(27*b)","A",3,2,24,0.08333,1,"{2063, 44}"
2,1,30,0,0.0177064,"\int \left(a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3\right)^p \, dx","Int[(a^3 + 3*a^2*b*x + 3*a*b^2*x^2 + b^3*x^3)^p,x]","\frac{\left(\frac{a}{b}+x\right) \left(b^3 \left(\frac{a}{b}+x\right)^3\right)^p}{3 p+1}","\frac{\left(\frac{a}{b}+x\right) \left(b^3 \left(\frac{a}{b}+x\right)^3\right)^p}{3 p+1}",1,"((a/b + x)*(b^3*(a/b + x)^3)^p)/(1 + 3*p)","A",3,3,29,0.1034,1,"{2067, 15, 30}"
3,1,14,0,0.0074009,"\int \left(a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3\right)^3 \, dx","Int[(a^3 + 3*a^2*b*x + 3*a*b^2*x^2 + b^3*x^3)^3,x]","\frac{(a+b x)^{10}}{10 b}","\frac{(a+b x)^{10}}{10 b}",1,"(a + b*x)^10/(10*b)","A",2,2,29,0.06897,1,"{2059, 32}"
4,1,14,0,0.007188,"\int \left(a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3\right)^2 \, dx","Int[(a^3 + 3*a^2*b*x + 3*a*b^2*x^2 + b^3*x^3)^2,x]","\frac{(a+b x)^7}{7 b}","\frac{(a+b x)^7}{7 b}",1,"(a + b*x)^7/(7*b)","A",2,2,29,0.06897,1,"{2059, 32}"
5,1,35,0,0.0068023,"\int \left(a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3\right) \, dx","Int[a^3 + 3*a^2*b*x + 3*a*b^2*x^2 + b^3*x^3,x]","\frac{3}{2} a^2 b x^2+a^3 x+a b^2 x^3+\frac{b^3 x^4}{4}","\frac{3}{2} a^2 b x^2+a^3 x+a b^2 x^3+\frac{b^3 x^4}{4}",1,"a^3*x + (3*a^2*b*x^2)/2 + a*b^2*x^3 + (b^3*x^4)/4","A",1,0,27,0,1,"{}"
6,1,14,0,0.0085853,"\int \frac{1}{a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3} \, dx","Int[(a^3 + 3*a^2*b*x + 3*a*b^2*x^2 + b^3*x^3)^(-1),x]","-\frac{1}{2 b (a+b x)^2}","-\frac{1}{2 b (a+b x)^2}",1,"-1/(2*b*(a + b*x)^2)","A",2,2,29,0.06897,1,"{2058, 32}"
7,1,14,0,0.0086401,"\int \frac{1}{\left(a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3\right)^2} \, dx","Int[(a^3 + 3*a^2*b*x + 3*a*b^2*x^2 + b^3*x^3)^(-2),x]","-\frac{1}{5 b (a+b x)^5}","-\frac{1}{5 b (a+b x)^5}",1,"-1/(5*b*(a + b*x)^5)","A",2,2,29,0.06897,1,"{2058, 32}"
8,1,14,0,0.0081347,"\int \frac{1}{\left(a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3\right)^3} \, dx","Int[(a^3 + 3*a^2*b*x + 3*a*b^2*x^2 + b^3*x^3)^(-3),x]","-\frac{1}{8 b (a+b x)^8}","-\frac{1}{8 b (a+b x)^8}",1,"-1/(8*b*(a + b*x)^8)","A",2,2,29,0.06897,1,"{2058, 32}"
9,1,84,0,0.1245733,"\int \left(3 a b+3 b^2 x+3 b c x^2+c^2 x^3\right)^3 \, dx","Int[(3*a*b + 3*b^2*x + 3*b*c*x^2 + c^2*x^3)^3,x]","-\frac{3 b \left(b^2-3 a c\right) (b+c x)^7}{7 c^4}+\frac{3 b^2 \left(b^2-3 a c\right)^2 (b+c x)^4}{4 c^4}-\frac{b^3 x \left(b^2-3 a c\right)^3}{c^3}+\frac{(b+c x)^{10}}{10 c^4}","-\frac{3 b \left(b^2-3 a c\right) (b+c x)^7}{7 c^4}+\frac{3 b^2 \left(b^2-3 a c\right)^2 (b+c x)^4}{4 c^4}-\frac{b^3 x \left(b^2-3 a c\right)^3}{c^3}+\frac{(b+c x)^{10}}{10 c^4}",1,"-((b^3*(b^2 - 3*a*c)^3*x)/c^3) + (3*b^2*(b^2 - 3*a*c)^2*(b + c*x)^4)/(4*c^4) - (3*b*(b^2 - 3*a*c)*(b + c*x)^7)/(7*c^4) + (b + c*x)^10/(10*c^4)","A",3,2,27,0.07407,1,"{2060, 194}"
10,1,56,0,0.0678793,"\int \left(3 a b+3 b^2 x+3 b c x^2+c^2 x^3\right)^2 \, dx","Int[(3*a*b + 3*b^2*x + 3*b*c*x^2 + c^2*x^3)^2,x]","-\frac{b \left(b^2-3 a c\right) (b+c x)^4}{2 c^3}+\frac{b^2 x \left(b^2-3 a c\right)^2}{c^2}+\frac{(b+c x)^7}{7 c^3}","-\frac{b \left(b^2-3 a c\right) (b+c x)^4}{2 c^3}+\frac{b^2 x \left(b^2-3 a c\right)^2}{c^2}+\frac{(b+c x)^7}{7 c^3}",1,"(b^2*(b^2 - 3*a*c)^2*x)/c^2 - (b*(b^2 - 3*a*c)*(b + c*x)^4)/(2*c^3) + (b + c*x)^7/(7*c^3)","A",3,2,27,0.07407,1,"{2060, 194}"
11,1,32,0,0.0058015,"\int \left(3 a b+3 b^2 x+3 b c x^2+c^2 x^3\right) \, dx","Int[3*a*b + 3*b^2*x + 3*b*c*x^2 + c^2*x^3,x]","3 a b x+\frac{3 b^2 x^2}{2}+b c x^3+\frac{c^2 x^4}{4}","3 a b x+\frac{3 b^2 x^2}{2}+b c x^3+\frac{c^2 x^4}{4}",1,"3*a*b*x + (3*b^2*x^2)/2 + b*c*x^3 + (c^2*x^4)/4","A",1,0,25,0,1,"{}"
12,1,188,0,0.3119877,"\int \frac{1}{3 a b+3 b^2 x+3 b c x^2+c^2 x^3} \, dx","Int[(3*a*b + 3*b^2*x + 3*b*c*x^2 + c^2*x^3)^(-1),x]","-\frac{\log \left(\sqrt[3]{b} c \sqrt[3]{b^2-3 a c} \left(\frac{b}{c}+x\right)+b^{2/3} \left(b^2-3 a c\right)^{2/3}+c^2 \left(\frac{b}{c}+x\right)^2\right)}{6 b^{2/3} \left(b^2-3 a c\right)^{2/3}}+\frac{\log \left(-\sqrt[3]{b} \sqrt[3]{b^2-3 a c}+b+c x\right)}{3 b^{2/3} \left(b^2-3 a c\right)^{2/3}}-\frac{\tan ^{-1}\left(\frac{\frac{2 (b+c x)}{\sqrt[3]{b^2-3 a c}}+\sqrt[3]{b}}{\sqrt{3} \sqrt[3]{b}}\right)}{\sqrt{3} b^{2/3} \left(b^2-3 a c\right)^{2/3}}","-\frac{\log \left(\sqrt[3]{b} c \sqrt[3]{b^2-3 a c} \left(\frac{b}{c}+x\right)+b^{2/3} \left(b^2-3 a c\right)^{2/3}+c^2 \left(\frac{b}{c}+x\right)^2\right)}{6 b^{2/3} \left(b^2-3 a c\right)^{2/3}}+\frac{\log \left(-\sqrt[3]{b} \sqrt[3]{b^2-3 a c}+b+c x\right)}{3 b^{2/3} \left(b^2-3 a c\right)^{2/3}}-\frac{\tan ^{-1}\left(\frac{\frac{2 (b+c x)}{\sqrt[3]{b^2-3 a c}}+\sqrt[3]{b}}{\sqrt{3} \sqrt[3]{b}}\right)}{\sqrt{3} b^{2/3} \left(b^2-3 a c\right)^{2/3}}",1,"-(ArcTan[(b^(1/3) + (2*(b + c*x))/(b^2 - 3*a*c)^(1/3))/(Sqrt[3]*b^(1/3))]/(Sqrt[3]*b^(2/3)*(b^2 - 3*a*c)^(2/3))) + Log[b - b^(1/3)*(b^2 - 3*a*c)^(1/3) + c*x]/(3*b^(2/3)*(b^2 - 3*a*c)^(2/3)) - Log[b^(2/3)*(b^2 - 3*a*c)^(2/3) + b^(1/3)*c*(b^2 - 3*a*c)^(1/3)*(b/c + x) + c^2*(b/c + x)^2]/(6*b^(2/3)*(b^2 - 3*a*c)^(2/3))","A",7,7,27,0.2593,1,"{2067, 200, 31, 634, 617, 204, 628}"
13,1,245,0,0.2485427,"\int \frac{1}{\left(3 a b+3 b^2 x+3 b c x^2+c^2 x^3\right)^2} \, dx","Int[(3*a*b + 3*b^2*x + 3*b*c*x^2 + c^2*x^3)^(-2),x]","-\frac{c \left(\frac{b}{c}+x\right)}{3 b \left(b^2-3 a c\right) \left(3 a b+3 b^2 x+3 b c x^2+c^2 x^3\right)}+\frac{c \log \left(\sqrt[3]{b} c \sqrt[3]{b^2-3 a c} \left(\frac{b}{c}+x\right)+b^{2/3} \left(b^2-3 a c\right)^{2/3}+c^2 \left(\frac{b}{c}+x\right)^2\right)}{9 b^{5/3} \left(b^2-3 a c\right)^{5/3}}-\frac{2 c \log \left(-\sqrt[3]{b} \sqrt[3]{b^2-3 a c}+b+c x\right)}{9 b^{5/3} \left(b^2-3 a c\right)^{5/3}}+\frac{2 c \tan ^{-1}\left(\frac{\frac{2 (b+c x)}{\sqrt[3]{b^2-3 a c}}+\sqrt[3]{b}}{\sqrt{3} \sqrt[3]{b}}\right)}{3 \sqrt{3} b^{5/3} \left(b^2-3 a c\right)^{5/3}}","-\frac{c \left(\frac{b}{c}+x\right)}{3 b \left(b^2-3 a c\right) \left(3 a b+3 b^2 x+3 b c x^2+c^2 x^3\right)}+\frac{c \log \left(\sqrt[3]{b} c \sqrt[3]{b^2-3 a c} \left(\frac{b}{c}+x\right)+b^{2/3} \left(b^2-3 a c\right)^{2/3}+c^2 \left(\frac{b}{c}+x\right)^2\right)}{9 b^{5/3} \left(b^2-3 a c\right)^{5/3}}-\frac{2 c \log \left(-\sqrt[3]{b} \sqrt[3]{b^2-3 a c}+b+c x\right)}{9 b^{5/3} \left(b^2-3 a c\right)^{5/3}}+\frac{2 c \tan ^{-1}\left(\frac{\frac{2 (b+c x)}{\sqrt[3]{b^2-3 a c}}+\sqrt[3]{b}}{\sqrt{3} \sqrt[3]{b}}\right)}{3 \sqrt{3} b^{5/3} \left(b^2-3 a c\right)^{5/3}}",1,"-(c*(b/c + x))/(3*b*(b^2 - 3*a*c)*(3*a*b + 3*b^2*x + 3*b*c*x^2 + c^2*x^3)) + (2*c*ArcTan[(b^(1/3) + (2*(b + c*x))/(b^2 - 3*a*c)^(1/3))/(Sqrt[3]*b^(1/3))])/(3*Sqrt[3]*b^(5/3)*(b^2 - 3*a*c)^(5/3)) - (2*c*Log[b - b^(1/3)*(b^2 - 3*a*c)^(1/3) + c*x])/(9*b^(5/3)*(b^2 - 3*a*c)^(5/3)) + (c*Log[b^(2/3)*(b^2 - 3*a*c)^(2/3) + b^(1/3)*c*(b^2 - 3*a*c)^(1/3)*(b/c + x) + c^2*(b/c + x)^2])/(9*b^(5/3)*(b^2 - 3*a*c)^(5/3))","A",8,8,27,0.2963,1,"{2067, 199, 200, 31, 634, 617, 204, 628}"
14,1,305,0,0.3019381,"\int \frac{1}{\left(3 a b+3 b^2 x+3 b c x^2+c^2 x^3\right)^3} \, dx","Int[(3*a*b + 3*b^2*x + 3*b*c*x^2 + c^2*x^3)^(-3),x]","\frac{5 c^2 \left(\frac{b}{c}+x\right)}{18 b^2 \left(b^2-3 a c\right)^2 \left(3 a b+3 b^2 x+3 b c x^2+c^2 x^3\right)}-\frac{c \left(\frac{b}{c}+x\right)}{6 b \left(b^2-3 a c\right) \left(3 a b+3 b^2 x+3 b c x^2+c^2 x^3\right)^2}+\frac{5 c^2 \log \left(-\sqrt[3]{b} \sqrt[3]{b^2-3 a c}+b+c x\right)}{27 b^{8/3} \left(b^2-3 a c\right)^{8/3}}-\frac{5 c^2 \log \left(\sqrt[3]{b} c \sqrt[3]{b^2-3 a c} \left(\frac{b}{c}+x\right)+b^{2/3} \left(b^2-3 a c\right)^{2/3}+c^2 \left(\frac{b}{c}+x\right)^2\right)}{54 b^{8/3} \left(b^2-3 a c\right)^{8/3}}-\frac{5 c^2 \tan ^{-1}\left(\frac{\frac{2 (b+c x)}{\sqrt[3]{b^2-3 a c}}+\sqrt[3]{b}}{\sqrt{3} \sqrt[3]{b}}\right)}{9 \sqrt{3} b^{8/3} \left(b^2-3 a c\right)^{8/3}}","\frac{5 c^2 \left(\frac{b}{c}+x\right)}{18 b^2 \left(b^2-3 a c\right)^2 \left(3 a b+3 b^2 x+3 b c x^2+c^2 x^3\right)}-\frac{c \left(\frac{b}{c}+x\right)}{6 b \left(b^2-3 a c\right) \left(3 a b+3 b^2 x+3 b c x^2+c^2 x^3\right)^2}+\frac{5 c^2 \log \left(-\sqrt[3]{b} \sqrt[3]{b^2-3 a c}+b+c x\right)}{27 b^{8/3} \left(b^2-3 a c\right)^{8/3}}-\frac{5 c^2 \log \left(\sqrt[3]{b} c \sqrt[3]{b^2-3 a c} \left(\frac{b}{c}+x\right)+b^{2/3} \left(b^2-3 a c\right)^{2/3}+c^2 \left(\frac{b}{c}+x\right)^2\right)}{54 b^{8/3} \left(b^2-3 a c\right)^{8/3}}-\frac{5 c^2 \tan ^{-1}\left(\frac{\frac{2 (b+c x)}{\sqrt[3]{b^2-3 a c}}+\sqrt[3]{b}}{\sqrt{3} \sqrt[3]{b}}\right)}{9 \sqrt{3} b^{8/3} \left(b^2-3 a c\right)^{8/3}}",1,"-(c*(b/c + x))/(6*b*(b^2 - 3*a*c)*(3*a*b + 3*b^2*x + 3*b*c*x^2 + c^2*x^3)^2) + (5*c^2*(b/c + x))/(18*b^2*(b^2 - 3*a*c)^2*(3*a*b + 3*b^2*x + 3*b*c*x^2 + c^2*x^3)) - (5*c^2*ArcTan[(b^(1/3) + (2*(b + c*x))/(b^2 - 3*a*c)^(1/3))/(Sqrt[3]*b^(1/3))])/(9*Sqrt[3]*b^(8/3)*(b^2 - 3*a*c)^(8/3)) + (5*c^2*Log[b - b^(1/3)*(b^2 - 3*a*c)^(1/3) + c*x])/(27*b^(8/3)*(b^2 - 3*a*c)^(8/3)) - (5*c^2*Log[b^(2/3)*(b^2 - 3*a*c)^(2/3) + b^(1/3)*c*(b^2 - 3*a*c)^(1/3)*(b/c + x) + c^2*(b/c + x)^2])/(54*b^(8/3)*(b^2 - 3*a*c)^(8/3))","A",9,8,27,0.2963,1,"{2067, 199, 200, 31, 634, 617, 204, 628}"
15,1,361,0,0.6584368,"\int \left(a c e+(b c e+a d e+a c f) x+(b d e+b c f+a d f) x^2+b d f x^3\right)^3 \, dx","Int[(a*c*e + (b*c*e + a*d*e + a*c*f)*x + (b*d*e + b*c*f + a*d*f)*x^2 + b*d*f*x^3)^3,x]","\frac{3 d f (a+b x)^8 \left(5 a^2 d^2 f^2-5 a b d f (c f+d e)+b^2 \left(c^2 f^2+3 c d e f+d^2 e^2\right)\right)}{8 b^7}+\frac{(a+b x)^7 (-2 a d f+b c f+b d e) \left(10 a^2 d^2 f^2-10 a b d f (c f+d e)+b^2 \left(c^2 f^2+8 c d e f+d^2 e^2\right)\right)}{7 b^7}+\frac{(a+b x)^6 (b c-a d) (b e-a f) \left(5 a^2 d^2 f^2-5 a b d f (c f+d e)+b^2 \left(c^2 f^2+3 c d e f+d^2 e^2\right)\right)}{2 b^7}+\frac{d^2 f^2 (a+b x)^9 (-2 a d f+b c f+b d e)}{3 b^7}+\frac{3 (a+b x)^5 (b c-a d)^2 (b e-a f)^2 (-2 a d f+b c f+b d e)}{5 b^7}+\frac{(a+b x)^4 (b c-a d)^3 (b e-a f)^3}{4 b^7}+\frac{d^3 f^3 (a+b x)^{10}}{10 b^7}","\frac{3 d f (a+b x)^8 \left(5 a^2 d^2 f^2-5 a b d f (c f+d e)+b^2 \left(c^2 f^2+3 c d e f+d^2 e^2\right)\right)}{8 b^7}+\frac{(a+b x)^7 (-2 a d f+b c f+b d e) \left(10 a^2 d^2 f^2-10 a b d f (c f+d e)+b^2 \left(c^2 f^2+8 c d e f+d^2 e^2\right)\right)}{7 b^7}+\frac{(a+b x)^6 (b c-a d) (b e-a f) \left(5 a^2 d^2 f^2-5 a b d f (c f+d e)+b^2 \left(c^2 f^2+3 c d e f+d^2 e^2\right)\right)}{2 b^7}+\frac{d^2 f^2 (a+b x)^9 (-2 a d f+b c f+b d e)}{3 b^7}+\frac{3 (a+b x)^5 (b c-a d)^2 (b e-a f)^2 (-2 a d f+b c f+b d e)}{5 b^7}+\frac{(a+b x)^4 (b c-a d)^3 (b e-a f)^3}{4 b^7}+\frac{d^3 f^3 (a+b x)^{10}}{10 b^7}",1,"((b*c - a*d)^3*(b*e - a*f)^3*(a + b*x)^4)/(4*b^7) + (3*(b*c - a*d)^2*(b*e - a*f)^2*(b*d*e + b*c*f - 2*a*d*f)*(a + b*x)^5)/(5*b^7) + ((b*c - a*d)*(b*e - a*f)*(5*a^2*d^2*f^2 - 5*a*b*d*f*(d*e + c*f) + b^2*(d^2*e^2 + 3*c*d*e*f + c^2*f^2))*(a + b*x)^6)/(2*b^7) + ((b*d*e + b*c*f - 2*a*d*f)*(10*a^2*d^2*f^2 - 10*a*b*d*f*(d*e + c*f) + b^2*(d^2*e^2 + 8*c*d*e*f + c^2*f^2))*(a + b*x)^7)/(7*b^7) + (3*d*f*(5*a^2*d^2*f^2 - 5*a*b*d*f*(d*e + c*f) + b^2*(d^2*e^2 + 3*c*d*e*f + c^2*f^2))*(a + b*x)^8)/(8*b^7) + (d^2*f^2*(b*d*e + b*c*f - 2*a*d*f)*(a + b*x)^9)/(3*b^7) + (d^3*f^3*(a + b*x)^10)/(10*b^7)","A",3,2,46,0.04348,1,"{2059, 88}"
16,1,193,0,0.2314486,"\int \left(a c e+(b c e+a d e+a c f) x+(b d e+b c f+a d f) x^2+b d f x^3\right)^2 \, dx","Int[(a*c*e + (b*c*e + a*d*e + a*c*f)*x + (b*d*e + b*c*f + a*d*f)*x^2 + b*d*f*x^3)^2,x]","\frac{(a+b x)^5 \left(6 a^2 d^2 f^2-6 a b d f (c f+d e)+b^2 \left(c^2 f^2+4 c d e f+d^2 e^2\right)\right)}{5 b^5}+\frac{d f (a+b x)^6 (-2 a d f+b c f+b d e)}{3 b^5}+\frac{(a+b x)^4 (b c-a d) (b e-a f) (-2 a d f+b c f+b d e)}{2 b^5}+\frac{(a+b x)^3 (b c-a d)^2 (b e-a f)^2}{3 b^5}+\frac{d^2 f^2 (a+b x)^7}{7 b^5}","\frac{(a+b x)^5 \left(6 a^2 d^2 f^2-6 a b d f (c f+d e)+b^2 \left(c^2 f^2+4 c d e f+d^2 e^2\right)\right)}{5 b^5}+\frac{d f (a+b x)^6 (-2 a d f+b c f+b d e)}{3 b^5}+\frac{(a+b x)^4 (b c-a d) (b e-a f) (-2 a d f+b c f+b d e)}{2 b^5}+\frac{(a+b x)^3 (b c-a d)^2 (b e-a f)^2}{3 b^5}+\frac{d^2 f^2 (a+b x)^7}{7 b^5}",1,"((b*c - a*d)^2*(b*e - a*f)^2*(a + b*x)^3)/(3*b^5) + ((b*c - a*d)*(b*e - a*f)*(b*d*e + b*c*f - 2*a*d*f)*(a + b*x)^4)/(2*b^5) + ((6*a^2*d^2*f^2 - 6*a*b*d*f*(d*e + c*f) + b^2*(d^2*e^2 + 4*c*d*e*f + c^2*f^2))*(a + b*x)^5)/(5*b^5) + (d*f*(b*d*e + b*c*f - 2*a*d*f)*(a + b*x)^6)/(3*b^5) + (d^2*f^2*(a + b*x)^7)/(7*b^5)","A",3,2,46,0.04348,1,"{2059, 88}"
17,1,56,0,0.0164289,"\int \left(a c e+(b c e+a d e+a c f) x+(b d e+b c f+a d f) x^2+b d f x^3\right) \, dx","Int[a*c*e + (b*c*e + a*d*e + a*c*f)*x + (b*d*e + b*c*f + a*d*f)*x^2 + b*d*f*x^3,x]","\frac{1}{3} x^3 (a d f+b c f+b d e)+\frac{1}{2} x^2 (a c f+a d e+b c e)+a c e x+\frac{1}{4} b d f x^4","\frac{1}{3} x^3 (a d f+b c f+b d e)+\frac{1}{2} x^2 (a c f+a d e+b c e)+a c e x+\frac{1}{4} b d f x^4",1,"a*c*e*x + ((b*c*e + a*d*e + a*c*f)*x^2)/2 + ((b*d*e + b*c*f + a*d*f)*x^3)/3 + (b*d*f*x^4)/4","A",1,0,44,0,1,"{}"
18,1,86,0,0.0733537,"\int \frac{1}{a c e+(b c e+a d e+a c f) x+(b d e+b c f+a d f) x^2+b d f x^3} \, dx","Int[(a*c*e + (b*c*e + a*d*e + a*c*f)*x + (b*d*e + b*c*f + a*d*f)*x^2 + b*d*f*x^3)^(-1),x]","\frac{b \log (a+b x)}{(b c-a d) (b e-a f)}-\frac{d \log (c+d x)}{(b c-a d) (d e-c f)}+\frac{f \log (e+f x)}{(b e-a f) (d e-c f)}","\frac{b \log (a+b x)}{(b c-a d) (b e-a f)}-\frac{d \log (c+d x)}{(b c-a d) (d e-c f)}+\frac{f \log (e+f x)}{(b e-a f) (d e-c f)}",1,"(b*Log[a + b*x])/((b*c - a*d)*(b*e - a*f)) - (d*Log[c + d*x])/((b*c - a*d)*(d*e - c*f)) + (f*Log[e + f*x])/((b*e - a*f)*(d*e - c*f))","A",2,1,46,0.02174,1,"{2058}"
19,1,234,0,0.4051776,"\int \frac{1}{\left(a c e+(b c e+a d e+a c f) x+(b d e+b c f+a d f) x^2+b d f x^3\right)^2} \, dx","Int[(a*c*e + (b*c*e + a*d*e + a*c*f)*x + (b*d*e + b*c*f + a*d*f)*x^2 + b*d*f*x^3)^(-2),x]","-\frac{b^3}{(a+b x) (b c-a d)^2 (b e-a f)^2}-\frac{2 b^3 \log (a+b x) (-2 a d f+b c f+b d e)}{(b c-a d)^3 (b e-a f)^3}-\frac{d^3}{(c+d x) (b c-a d)^2 (d e-c f)^2}+\frac{2 d^3 \log (c+d x) (a d f-2 b c f+b d e)}{(b c-a d)^3 (d e-c f)^3}-\frac{f^3}{(e+f x) (b e-a f)^2 (d e-c f)^2}+\frac{2 f^3 \log (e+f x) (-a d f-b c f+2 b d e)}{(b e-a f)^3 (d e-c f)^3}","-\frac{b^3}{(a+b x) (b c-a d)^2 (b e-a f)^2}-\frac{2 b^3 \log (a+b x) (-2 a d f+b c f+b d e)}{(b c-a d)^3 (b e-a f)^3}-\frac{d^3}{(c+d x) (b c-a d)^2 (d e-c f)^2}+\frac{2 d^3 \log (c+d x) (a d f-2 b c f+b d e)}{(b c-a d)^3 (d e-c f)^3}-\frac{f^3}{(e+f x) (b e-a f)^2 (d e-c f)^2}+\frac{2 f^3 \log (e+f x) (-a d f-b c f+2 b d e)}{(b e-a f)^3 (d e-c f)^3}",1,"-(b^3/((b*c - a*d)^2*(b*e - a*f)^2*(a + b*x))) - d^3/((b*c - a*d)^2*(d*e - c*f)^2*(c + d*x)) - f^3/((b*e - a*f)^2*(d*e - c*f)^2*(e + f*x)) - (2*b^3*(b*d*e + b*c*f - 2*a*d*f)*Log[a + b*x])/((b*c - a*d)^3*(b*e - a*f)^3) + (2*d^3*(b*d*e - 2*b*c*f + a*d*f)*Log[c + d*x])/((b*c - a*d)^3*(d*e - c*f)^3) + (2*f^3*(2*b*d*e - b*c*f - a*d*f)*Log[e + f*x])/((b*e - a*f)^3*(d*e - c*f)^3)","A",2,1,46,0.02174,1,"{2058}"
20,1,495,0,1.4617896,"\int \frac{1}{\left(a c e+(b c e+a d e+a c f) x+(b d e+b c f+a d f) x^2+b d f x^3\right)^3} \, dx","Int[(a*c*e + (b*c*e + a*d*e + a*c*f)*x + (b*d*e + b*c*f + a*d*f)*x^2 + b*d*f*x^3)^(-3),x]","\frac{3 b^5 \log (a+b x) \left(7 a^2 d^2 f^2-7 a b d f (c f+d e)+b^2 \left(2 c^2 f^2+3 c d e f+2 d^2 e^2\right)\right)}{(b c-a d)^5 (b e-a f)^5}-\frac{3 d^5 \log (c+d x) \left(2 a^2 d^2 f^2+a b d f (3 d e-7 c f)+b^2 \left(7 c^2 f^2-7 c d e f+2 d^2 e^2\right)\right)}{(b c-a d)^5 (d e-c f)^5}+\frac{3 f^5 \log (e+f x) \left(2 a^2 d^2 f^2-a b d f (7 d e-3 c f)+b^2 \left(2 c^2 f^2-7 c d e f+7 d^2 e^2\right)\right)}{(b e-a f)^5 (d e-c f)^5}+\frac{3 b^5 (-2 a d f+b c f+b d e)}{(a+b x) (b c-a d)^4 (b e-a f)^4}-\frac{b^5}{2 (a+b x)^2 (b c-a d)^3 (b e-a f)^3}+\frac{3 d^5 (a d f-2 b c f+b d e)}{(c+d x) (b c-a d)^4 (d e-c f)^4}+\frac{d^5}{2 (c+d x)^2 (b c-a d)^3 (d e-c f)^3}-\frac{3 f^5 (-a d f-b c f+2 b d e)}{(e+f x) (b e-a f)^4 (d e-c f)^4}-\frac{f^5}{2 (e+f x)^2 (b e-a f)^3 (d e-c f)^3}","\frac{3 b^5 \log (a+b x) \left(7 a^2 d^2 f^2-7 a b d f (c f+d e)+b^2 \left(2 c^2 f^2+3 c d e f+2 d^2 e^2\right)\right)}{(b c-a d)^5 (b e-a f)^5}-\frac{3 d^5 \log (c+d x) \left(2 a^2 d^2 f^2+a b d f (3 d e-7 c f)+b^2 \left(7 c^2 f^2-7 c d e f+2 d^2 e^2\right)\right)}{(b c-a d)^5 (d e-c f)^5}+\frac{3 f^5 \log (e+f x) \left(2 a^2 d^2 f^2-a b d f (7 d e-3 c f)+b^2 \left(2 c^2 f^2-7 c d e f+7 d^2 e^2\right)\right)}{(b e-a f)^5 (d e-c f)^5}+\frac{3 b^5 (-2 a d f+b c f+b d e)}{(a+b x) (b c-a d)^4 (b e-a f)^4}-\frac{b^5}{2 (a+b x)^2 (b c-a d)^3 (b e-a f)^3}+\frac{3 d^5 (a d f-2 b c f+b d e)}{(c+d x) (b c-a d)^4 (d e-c f)^4}+\frac{d^5}{2 (c+d x)^2 (b c-a d)^3 (d e-c f)^3}-\frac{3 f^5 (-a d f-b c f+2 b d e)}{(e+f x) (b e-a f)^4 (d e-c f)^4}-\frac{f^5}{2 (e+f x)^2 (b e-a f)^3 (d e-c f)^3}",1,"-b^5/(2*(b*c - a*d)^3*(b*e - a*f)^3*(a + b*x)^2) + (3*b^5*(b*d*e + b*c*f - 2*a*d*f))/((b*c - a*d)^4*(b*e - a*f)^4*(a + b*x)) + d^5/(2*(b*c - a*d)^3*(d*e - c*f)^3*(c + d*x)^2) + (3*d^5*(b*d*e - 2*b*c*f + a*d*f))/((b*c - a*d)^4*(d*e - c*f)^4*(c + d*x)) - f^5/(2*(b*e - a*f)^3*(d*e - c*f)^3*(e + f*x)^2) - (3*f^5*(2*b*d*e - b*c*f - a*d*f))/((b*e - a*f)^4*(d*e - c*f)^4*(e + f*x)) + (3*b^5*(7*a^2*d^2*f^2 - 7*a*b*d*f*(d*e + c*f) + b^2*(2*d^2*e^2 + 3*c*d*e*f + 2*c^2*f^2))*Log[a + b*x])/((b*c - a*d)^5*(b*e - a*f)^5) - (3*d^5*(2*a^2*d^2*f^2 + a*b*d*f*(3*d*e - 7*c*f) + b^2*(2*d^2*e^2 - 7*c*d*e*f + 7*c^2*f^2))*Log[c + d*x])/((b*c - a*d)^5*(d*e - c*f)^5) + (3*f^5*(2*a^2*d^2*f^2 - a*b*d*f*(7*d*e - 3*c*f) + b^2*(7*d^2*e^2 - 7*c*d*e*f + 2*c^2*f^2))*Log[e + f*x])/((b*e - a*f)^5*(d*e - c*f)^5)","A",2,1,46,0.02174,1,"{2058}"
21,1,25,0,0.0146004,"\int \frac{1}{1+x+x^2+x^3} \, dx","Int[(1 + x + x^2 + x^3)^(-1),x]","-\frac{1}{4} \log \left(x^2+1\right)+\frac{1}{2} \log (x+1)+\frac{1}{2} \tan ^{-1}(x)","-\frac{1}{4} \log \left(x^2+1\right)+\frac{1}{2} \log (x+1)+\frac{1}{2} \tan ^{-1}(x)",1,"ArcTan[x]/2 + Log[1 + x]/2 - Log[1 + x^2]/4","A",5,4,11,0.3636,1,"{2058, 635, 203, 260}"
22,1,31,0,0.0198343,"\int \frac{1}{-1+4 x-4 x^2+16 x^3} \, dx","Int[(-1 + 4*x - 4*x^2 + 16*x^3)^(-1),x]","-\frac{1}{10} \log \left(4 x^2+1\right)+\frac{1}{5} \log (1-4 x)-\frac{1}{10} \tan ^{-1}(2 x)","-\frac{1}{10} \log \left(4 x^2+1\right)+\frac{1}{5} \log (1-4 x)-\frac{1}{10} \tan ^{-1}(2 x)",1,"-ArcTan[2*x]/10 + Log[1 - 4*x]/5 - Log[1 + 4*x^2]/10","A",5,4,17,0.2353,1,"{2058, 635, 203, 260}"
23,1,10,0,0.0014073,"\int \frac{1}{d x^3} \, dx","Int[1/(d*x^3),x]","-\frac{1}{2 d x^2}","-\frac{1}{2 d x^2}",1,"-1/(2*d*x^2)","A",2,2,7,0.2857,1,"{12, 30}"
24,1,28,0,0.0151371,"\int \frac{1}{c x^2+d x^3} \, dx","Int[(c*x^2 + d*x^3)^(-1),x]","-\frac{d \log (x)}{c^2}+\frac{d \log (c+d x)}{c^2}-\frac{1}{c x}","-\frac{d \log (x)}{c^2}+\frac{d \log (c+d x)}{c^2}-\frac{1}{c x}",1,"-(1/(c*x)) - (d*Log[x])/c^2 + (d*Log[c + d*x])/c^2","A",3,2,13,0.1538,1,"{1593, 44}"
25,1,22,0,0.0115629,"\int \frac{1}{b x+d x^3} \, dx","Int[(b*x + d*x^3)^(-1),x]","\frac{\log (x)}{b}-\frac{\log \left(b+d x^2\right)}{2 b}","\frac{\log (x)}{b}-\frac{\log \left(b+d x^2\right)}{2 b}",1,"Log[x]/b - Log[b + d*x^2]/(2*b)","A",5,5,11,0.4545,1,"{1593, 266, 36, 29, 31}"
26,1,62,0,0.0545669,"\int \frac{1}{b x+c x^2+d x^3} \, dx","Int[(b*x + c*x^2 + d*x^3)^(-1),x]","\frac{c \tanh ^{-1}\left(\frac{c+2 d x}{\sqrt{c^2-4 b d}}\right)}{b \sqrt{c^2-4 b d}}-\frac{\log \left(b+c x+d x^2\right)}{2 b}+\frac{\log (x)}{b}","\frac{c \tanh ^{-1}\left(\frac{c+2 d x}{\sqrt{c^2-4 b d}}\right)}{b \sqrt{c^2-4 b d}}-\frac{\log \left(b+c x+d x^2\right)}{2 b}+\frac{\log (x)}{b}",1,"(c*ArcTanh[(c + 2*d*x)/Sqrt[c^2 - 4*b*d]])/(b*Sqrt[c^2 - 4*b*d]) + Log[x]/b - Log[b + c*x + d*x^2]/(2*b)","A",7,7,16,0.4375,1,"{1594, 705, 29, 634, 618, 206, 628}"
27,1,115,0,0.0630292,"\int \frac{1}{a+d x^3} \, dx","Int[(a + d*x^3)^(-1),x]","-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{d} x+d^{2/3} x^2\right)}{6 a^{2/3} \sqrt[3]{d}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{d} x\right)}{3 a^{2/3} \sqrt[3]{d}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{d} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} \sqrt[3]{d}}","-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{d} x+d^{2/3} x^2\right)}{6 a^{2/3} \sqrt[3]{d}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{d} x\right)}{3 a^{2/3} \sqrt[3]{d}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{d} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} \sqrt[3]{d}}",1,"-(ArcTan[(a^(1/3) - 2*d^(1/3)*x)/(Sqrt[3]*a^(1/3))]/(Sqrt[3]*a^(2/3)*d^(1/3))) + Log[a^(1/3) + d^(1/3)*x]/(3*a^(2/3)*d^(1/3)) - Log[a^(2/3) - a^(1/3)*d^(1/3)*x + d^(2/3)*x^2]/(6*a^(2/3)*d^(1/3))","A",6,6,9,0.6667,1,"{200, 31, 634, 617, 204, 628}"
28,1,16,0,0.0040014,"\int \left(d x^3\right)^n \, dx","Int[(d*x^3)^n,x]","\frac{x \left(d x^3\right)^n}{3 n+1}","\frac{x \left(d x^3\right)^n}{3 n+1}",1,"(x*(d*x^3)^n)/(1 + 3*n)","A",2,2,7,0.2857,1,"{15, 30}"
29,1,55,0,0.0192491,"\int \left(c x^2+d x^3\right)^n \, dx","Int[(c*x^2 + d*x^3)^n,x]","\frac{x \left(\frac{d x}{c}+1\right)^{-n} \left(c x^2+d x^3\right)^n \text{Hypergeometric2F1}\left(-n,2 n+1,2 (n+1),-\frac{d x}{c}\right)}{2 n+1}","\frac{x \left(\frac{d x}{c}+1\right)^{-n} \left(c x^2+d x^3\right)^n \text{Hypergeometric2F1}\left(-n,2 n+1,2 (n+1),-\frac{d x}{c}\right)}{2 n+1}",1,"(x*(c*x^2 + d*x^3)^n*Hypergeometric2F1[-n, 1 + 2*n, 2*(1 + n), -((d*x)/c)])/((1 + 2*n)*(1 + (d*x)/c)^n)","A",3,3,13,0.2308,1,"{2011, 66, 64}"
30,1,59,0,0.0227277,"\int \left(b x+d x^3\right)^n \, dx","Int[(b*x + d*x^3)^n,x]","\frac{x \left(\frac{d x^2}{b}+1\right)^{-n} \left(b x+d x^3\right)^n \text{Hypergeometric2F1}\left(-n,\frac{n+1}{2},\frac{n+3}{2},-\frac{d x^2}{b}\right)}{n+1}","\frac{x \left(b+d x^2\right) \left(b x+d x^3\right)^n \text{Hypergeometric2F1}\left(1,\frac{3 (n+1)}{2},\frac{n+3}{2},-\frac{d x^2}{b}\right)}{b (n+1)}",1,"(x*(b*x + d*x^3)^n*Hypergeometric2F1[-n, (1 + n)/2, (3 + n)/2, -((d*x^2)/b)])/((1 + n)*(1 + (d*x^2)/b)^n)","A",3,3,11,0.2727,1,"{2011, 365, 364}"
31,1,132,0,0.1583537,"\int \left(b x+c x^2+d x^3\right)^n \, dx","Int[(b*x + c*x^2 + d*x^3)^n,x]","\frac{x \left(\frac{2 d x}{c-\sqrt{c^2-4 b d}}+1\right)^{-n} \left(\frac{2 d x}{\sqrt{c^2-4 b d}+c}+1\right)^{-n} \left(b x+c x^2+d x^3\right)^n F_1\left(n+1;-n,-n;n+2;-\frac{2 d x}{c-\sqrt{c^2-4 b d}},-\frac{2 d x}{c+\sqrt{c^2-4 b d}}\right)}{n+1}","\frac{x \left(\frac{2 d x}{c-\sqrt{c^2-4 b d}}+1\right)^{-n} \left(\frac{2 d x}{\sqrt{c^2-4 b d}+c}+1\right)^{-n} \left(b x+c x^2+d x^3\right)^n F_1\left(n+1;-n,-n;n+2;-\frac{2 d x}{c-\sqrt{c^2-4 b d}},-\frac{2 d x}{c+\sqrt{c^2-4 b d}}\right)}{n+1}",1,"(x*(b*x + c*x^2 + d*x^3)^n*AppellF1[1 + n, -n, -n, 2 + n, (-2*d*x)/(c - Sqrt[c^2 - 4*b*d]), (-2*d*x)/(c + Sqrt[c^2 - 4*b*d])])/((1 + n)*(1 + (2*d*x)/(c - Sqrt[c^2 - 4*b*d]))^n*(1 + (2*d*x)/(c + Sqrt[c^2 - 4*b*d]))^n)","A",3,3,16,0.1875,1,"{1908, 759, 133}"
32,1,44,0,0.0088327,"\int \left(a+d x^3\right)^n \, dx","Int[(a + d*x^3)^n,x]","x \left(a+d x^3\right)^n \left(\frac{d x^3}{a}+1\right)^{-n} \, _2F_1\left(\frac{1}{3},-n;\frac{4}{3};-\frac{d x^3}{a}\right)","\frac{x \left(a+d x^3\right)^{n+1} \, _2F_1\left(1,n+\frac{4}{3};\frac{4}{3};-\frac{d x^3}{a}\right)}{a}",1,"(x*(a + d*x^3)^n*Hypergeometric2F1[1/3, -n, 4/3, -((d*x^3)/a)])/(1 + (d*x^3)/a)^n","A",2,2,9,0.2222,1,"{246, 245}"
33,1,270,0,0.5386155,"\int \left(4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4\right)^4 \, dx","Int[(4*a*c + 4*c^2*x^2 + 4*c*d*x^3 + d^2*x^4)^4,x]","\frac{2}{9} c^2 \left(48 a^2 d^4+120 a c^3 d^2+35 c^6\right) \left(\frac{c}{d}+x\right)^9+\frac{4}{13} c d^4 \left(4 a d^2+7 c^3\right) \left(\frac{c}{d}+x\right)^{13}-\frac{8}{11} c^3 d^2 \left(12 a d^2+7 c^3\right) \left(\frac{c}{d}+x\right)^{11}-\frac{8 c^4 \left(4 a d^2+c^3\right) \left(12 a d^2+7 c^3\right) \left(\frac{c}{d}+x\right)^7}{7 d^2}+\frac{4 c^3 \left(4 a d^2+c^3\right)^2 \left(4 a d^2+7 c^3\right) \left(\frac{c}{d}+x\right)^5}{5 d^4}-\frac{8 c^5 \left(4 a d^2+c^3\right)^3 \left(\frac{c}{d}+x\right)^3}{3 d^6}+\frac{c^4 x \left(4 a d^2+c^3\right)^4}{d^8}-\frac{8}{15} c^2 d^6 \left(\frac{c}{d}+x\right)^{15}+\frac{1}{17} d^8 \left(\frac{c}{d}+x\right)^{17}","\frac{2}{9} c^2 \left(48 a^2 d^4+120 a c^3 d^2+35 c^6\right) \left(\frac{c}{d}+x\right)^9+\frac{4}{13} c d^4 \left(4 a d^2+7 c^3\right) \left(\frac{c}{d}+x\right)^{13}-\frac{8}{11} c^3 d^2 \left(12 a d^2+7 c^3\right) \left(\frac{c}{d}+x\right)^{11}-\frac{8 c^4 \left(4 a d^2+c^3\right) \left(12 a d^2+7 c^3\right) \left(\frac{c}{d}+x\right)^7}{7 d^2}+\frac{4 c^3 \left(4 a d^2+c^3\right)^2 \left(4 a d^2+7 c^3\right) \left(\frac{c}{d}+x\right)^5}{5 d^4}-\frac{8 c^5 \left(4 a d^2+c^3\right)^3 \left(\frac{c}{d}+x\right)^3}{3 d^6}+\frac{c^4 x \left(4 a d^2+c^3\right)^4}{d^8}-\frac{8}{15} c^2 d^6 \left(\frac{c}{d}+x\right)^{15}+\frac{1}{17} d^8 \left(\frac{c}{d}+x\right)^{17}",1,"(c^4*(c^3 + 4*a*d^2)^4*x)/d^8 - (8*c^5*(c^3 + 4*a*d^2)^3*(c/d + x)^3)/(3*d^6) + (4*c^3*(c^3 + 4*a*d^2)^2*(7*c^3 + 4*a*d^2)*(c/d + x)^5)/(5*d^4) - (8*c^4*(c^3 + 4*a*d^2)*(7*c^3 + 12*a*d^2)*(c/d + x)^7)/(7*d^2) + (2*c^2*(35*c^6 + 120*a*c^3*d^2 + 48*a^2*d^4)*(c/d + x)^9)/9 - (8*c^3*d^2*(7*c^3 + 12*a*d^2)*(c/d + x)^11)/11 + (4*c*d^4*(7*c^3 + 4*a*d^2)*(c/d + x)^13)/13 - (8*c^2*d^6*(c/d + x)^15)/15 + (d^8*(c/d + x)^17)/17","A",3,2,29,0.06897,1,"{1106, 1090}"
34,1,171,0,0.0919228,"\int \left(4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4\right)^3 \, dx","Int[(4*a*c + 4*c^2*x^2 + 4*c*d*x^3 + d^2*x^4)^3,x]","48 a^2 c^3 d x^4+64 a^2 c^4 x^3+64 a^3 c^3 x+\frac{4}{3} c d^2 x^9 \left(a d^2+20 c^3\right)+12 c^2 d x^8 \left(a d^2+2 c^3\right)+\frac{32}{7} c^3 x^7 \left(9 a d^2+2 c^3\right)+\frac{48}{5} a c^2 x^5 \left(a d^2+4 c^3\right)+64 a c^4 d x^6+\frac{60}{11} c^2 d^4 x^{11}+16 c^3 d^3 x^{10}+c d^5 x^{12}+\frac{d^6 x^{13}}{13}","48 a^2 c^3 d x^4+64 a^2 c^4 x^3+64 a^3 c^3 x+\frac{4}{3} c d^2 x^9 \left(a d^2+20 c^3\right)+12 c^2 d x^8 \left(a d^2+2 c^3\right)+\frac{32}{7} c^3 x^7 \left(9 a d^2+2 c^3\right)+\frac{48}{5} a c^2 x^5 \left(a d^2+4 c^3\right)+64 a c^4 d x^6+\frac{60}{11} c^2 d^4 x^{11}+16 c^3 d^3 x^{10}+c d^5 x^{12}+\frac{d^6 x^{13}}{13}",1,"64*a^3*c^3*x + 64*a^2*c^4*x^3 + 48*a^2*c^3*d*x^4 + (48*a*c^2*(4*c^3 + a*d^2)*x^5)/5 + 64*a*c^4*d*x^6 + (32*c^3*(2*c^3 + 9*a*d^2)*x^7)/7 + 12*c^2*d*(2*c^3 + a*d^2)*x^8 + (4*c*d^2*(20*c^3 + a*d^2)*x^9)/3 + 16*c^3*d^3*x^10 + (60*c^2*d^4*x^11)/11 + c*d^5*x^12 + (d^6*x^13)/13","A",2,1,29,0.03448,1,"{2061}"
35,1,92,0,0.0430304,"\int \left(4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4\right)^2 \, dx","Int[(4*a*c + 4*c^2*x^2 + 4*c*d*x^3 + d^2*x^4)^2,x]","16 a^2 c^2 x+\frac{8}{5} c x^5 \left(a d^2+2 c^3\right)+8 a c^2 d x^4+\frac{32}{3} a c^3 x^3+\frac{24}{7} c^2 d^2 x^7+\frac{16}{3} c^3 d x^6+c d^3 x^8+\frac{d^4 x^9}{9}","16 a^2 c^2 x+\frac{8}{5} c x^5 \left(a d^2+2 c^3\right)+8 a c^2 d x^4+\frac{32}{3} a c^3 x^3+\frac{24}{7} c^2 d^2 x^7+\frac{16}{3} c^3 d x^6+c d^3 x^8+\frac{d^4 x^9}{9}",1,"16*a^2*c^2*x + (32*a*c^3*x^3)/3 + 8*a*c^2*d*x^4 + (8*c*(2*c^3 + a*d^2)*x^5)/5 + (16*c^3*d*x^6)/3 + (24*c^2*d^2*x^7)/7 + c*d^3*x^8 + (d^4*x^9)/9","A",2,1,29,0.03448,1,"{2061}"
36,1,32,0,0.0058112,"\int \left(4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4\right) \, dx","Int[4*a*c + 4*c^2*x^2 + 4*c*d*x^3 + d^2*x^4,x]","4 a c x+\frac{4 c^2 x^3}{3}+c d x^4+\frac{d^2 x^5}{5}","4 a c x+\frac{4 c^2 x^3}{3}+c d x^4+\frac{d^2 x^5}{5}",1,"4*a*c*x + (4*c^2*x^3)/3 + c*d*x^4 + (d^2*x^5)/5","A",1,0,27,0,1,"{}"
37,1,529,0,0.8957485,"\int \frac{1}{4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4} \, dx","Int[(4*a*c + 4*c^2*x^2 + 4*c*d*x^3 + d^2*x^4)^(-1),x]","-\frac{d \log \left(-\sqrt{2} \sqrt[4]{c} d \sqrt{\sqrt{4 a d^2+c^3}+c^{3/2}} \left(\frac{c}{d}+x\right)+\sqrt{c} \sqrt{4 a d^2+c^3}+d^2 \left(\frac{c}{d}+x\right)^2\right)}{4 \sqrt{2} c^{3/4} \sqrt{4 a d^2+c^3} \sqrt{\sqrt{4 a d^2+c^3}+c^{3/2}}}+\frac{d \log \left(\sqrt{2} \sqrt[4]{c} d \sqrt{\sqrt{4 a d^2+c^3}+c^{3/2}} \left(\frac{c}{d}+x\right)+\sqrt{c} \sqrt{4 a d^2+c^3}+d^2 \left(\frac{c}{d}+x\right)^2\right)}{4 \sqrt{2} c^{3/4} \sqrt{4 a d^2+c^3} \sqrt{\sqrt{4 a d^2+c^3}+c^{3/2}}}-\frac{d \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{\sqrt{4 a d^2+c^3}+c^{3/2}}+\sqrt{2} c+\sqrt{2} d x}{\sqrt[4]{c} \sqrt{c^{3/2}-\sqrt{4 a d^2+c^3}}}\right)}{2 \sqrt{2} c^{3/4} \sqrt{4 a d^2+c^3} \sqrt{c^{3/2}-\sqrt{4 a d^2+c^3}}}+\frac{d \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{\sqrt{4 a d^2+c^3}+c^{3/2}}-\sqrt{2} (c+d x)}{\sqrt[4]{c} \sqrt{c^{3/2}-\sqrt{4 a d^2+c^3}}}\right)}{2 \sqrt{2} c^{3/4} \sqrt{4 a d^2+c^3} \sqrt{c^{3/2}-\sqrt{4 a d^2+c^3}}}","-\frac{d \log \left(-\sqrt{2} \sqrt[4]{c} d \sqrt{\sqrt{4 a d^2+c^3}+c^{3/2}} \left(\frac{c}{d}+x\right)+\sqrt{c} \sqrt{4 a d^2+c^3}+d^2 \left(\frac{c}{d}+x\right)^2\right)}{4 \sqrt{2} c^{3/4} \sqrt{4 a d^2+c^3} \sqrt{\sqrt{4 a d^2+c^3}+c^{3/2}}}+\frac{d \log \left(\sqrt{2} \sqrt[4]{c} d \sqrt{\sqrt{4 a d^2+c^3}+c^{3/2}} \left(\frac{c}{d}+x\right)+\sqrt{c} \sqrt{4 a d^2+c^3}+d^2 \left(\frac{c}{d}+x\right)^2\right)}{4 \sqrt{2} c^{3/4} \sqrt{4 a d^2+c^3} \sqrt{\sqrt{4 a d^2+c^3}+c^{3/2}}}-\frac{d \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{\sqrt{4 a d^2+c^3}+c^{3/2}}+\sqrt{2} c+\sqrt{2} d x}{\sqrt[4]{c} \sqrt{c^{3/2}-\sqrt{4 a d^2+c^3}}}\right)}{2 \sqrt{2} c^{3/4} \sqrt{4 a d^2+c^3} \sqrt{c^{3/2}-\sqrt{4 a d^2+c^3}}}+\frac{d \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{\sqrt{4 a d^2+c^3}+c^{3/2}}-\sqrt{2} (c+d x)}{\sqrt[4]{c} \sqrt{c^{3/2}-\sqrt{4 a d^2+c^3}}}\right)}{2 \sqrt{2} c^{3/4} \sqrt{4 a d^2+c^3} \sqrt{c^{3/2}-\sqrt{4 a d^2+c^3}}}",1,"-(d*ArcTanh[(Sqrt[2]*c + c^(1/4)*Sqrt[c^(3/2) + Sqrt[c^3 + 4*a*d^2]] + Sqrt[2]*d*x)/(c^(1/4)*Sqrt[c^(3/2) - Sqrt[c^3 + 4*a*d^2]])])/(2*Sqrt[2]*c^(3/4)*Sqrt[c^3 + 4*a*d^2]*Sqrt[c^(3/2) - Sqrt[c^3 + 4*a*d^2]]) + (d*ArcTanh[(c^(1/4)*Sqrt[c^(3/2) + Sqrt[c^3 + 4*a*d^2]] - Sqrt[2]*(c + d*x))/(c^(1/4)*Sqrt[c^(3/2) - Sqrt[c^3 + 4*a*d^2]])])/(2*Sqrt[2]*c^(3/4)*Sqrt[c^3 + 4*a*d^2]*Sqrt[c^(3/2) - Sqrt[c^3 + 4*a*d^2]]) - (d*Log[Sqrt[c]*Sqrt[c^3 + 4*a*d^2] - Sqrt[2]*c^(1/4)*d*Sqrt[c^(3/2) + Sqrt[c^3 + 4*a*d^2]]*(c/d + x) + d^2*(c/d + x)^2])/(4*Sqrt[2]*c^(3/4)*Sqrt[c^3 + 4*a*d^2]*Sqrt[c^(3/2) + Sqrt[c^3 + 4*a*d^2]]) + (d*Log[Sqrt[c]*Sqrt[c^3 + 4*a*d^2] + Sqrt[2]*c^(1/4)*d*Sqrt[c^(3/2) + Sqrt[c^3 + 4*a*d^2]]*(c/d + x) + d^2*(c/d + x)^2])/(4*Sqrt[2]*c^(3/4)*Sqrt[c^3 + 4*a*d^2]*Sqrt[c^(3/2) + Sqrt[c^3 + 4*a*d^2]])","A",10,6,29,0.2069,1,"{1106, 1094, 634, 618, 206, 628}"
38,1,746,0,1.3281657,"\int \frac{1}{\left(4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4\right)^2} \, dx","Int[(4*a*c + 4*c^2*x^2 + 4*c*d*x^3 + d^2*x^4)^(-2),x]","-\frac{\left(\frac{c}{d}+x\right) \left(-4 a d^2+c^3-c d^2 \left(\frac{c}{d}+x\right)^2\right)}{16 a c \left(4 a d^2+c^3\right) \left(4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4\right)}-\frac{d \left(-c^{3/2} \sqrt{4 a d^2+c^3}+12 a d^2+c^3\right) \log \left(-\sqrt{2} \sqrt[4]{c} d \sqrt{\sqrt{4 a d^2+c^3}+c^{3/2}} \left(\frac{c}{d}+x\right)+\sqrt{c} \sqrt{4 a d^2+c^3}+d^2 \left(\frac{c}{d}+x\right)^2\right)}{64 \sqrt{2} a c^{7/4} \left(4 a d^2+c^3\right)^{3/2} \sqrt{\sqrt{4 a d^2+c^3}+c^{3/2}}}+\frac{d \left(-c^{3/2} \sqrt{4 a d^2+c^3}+12 a d^2+c^3\right) \log \left(\sqrt{2} \sqrt[4]{c} d \sqrt{\sqrt{4 a d^2+c^3}+c^{3/2}} \left(\frac{c}{d}+x\right)+\sqrt{c} \sqrt{4 a d^2+c^3}+d^2 \left(\frac{c}{d}+x\right)^2\right)}{64 \sqrt{2} a c^{7/4} \left(4 a d^2+c^3\right)^{3/2} \sqrt{\sqrt{4 a d^2+c^3}+c^{3/2}}}-\frac{d \left(c^{3/2} \sqrt{4 a d^2+c^3}+12 a d^2+c^3\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{\sqrt{4 a d^2+c^3}+c^{3/2}}+\sqrt{2} c+\sqrt{2} d x}{\sqrt[4]{c} \sqrt{c^{3/2}-\sqrt{4 a d^2+c^3}}}\right)}{32 \sqrt{2} a c^{7/4} \left(4 a d^2+c^3\right)^{3/2} \sqrt{c^{3/2}-\sqrt{4 a d^2+c^3}}}+\frac{d \left(c^{3/2} \sqrt{4 a d^2+c^3}+12 a d^2+c^3\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{\sqrt{4 a d^2+c^3}+c^{3/2}}-\sqrt{2} (c+d x)}{\sqrt[4]{c} \sqrt{c^{3/2}-\sqrt{4 a d^2+c^3}}}\right)}{32 \sqrt{2} a c^{7/4} \left(4 a d^2+c^3\right)^{3/2} \sqrt{c^{3/2}-\sqrt{4 a d^2+c^3}}}","-\frac{\left(\frac{c}{d}+x\right) \left(-4 a d^2+c^3-c d^2 \left(\frac{c}{d}+x\right)^2\right)}{16 a c \left(4 a d^2+c^3\right) \left(4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4\right)}-\frac{d \left(-c^{3/2} \sqrt{4 a d^2+c^3}+12 a d^2+c^3\right) \log \left(-\sqrt{2} \sqrt[4]{c} d \sqrt{\sqrt{4 a d^2+c^3}+c^{3/2}} \left(\frac{c}{d}+x\right)+\sqrt{c} \sqrt{4 a d^2+c^3}+d^2 \left(\frac{c}{d}+x\right)^2\right)}{64 \sqrt{2} a c^{7/4} \left(4 a d^2+c^3\right)^{3/2} \sqrt{\sqrt{4 a d^2+c^3}+c^{3/2}}}+\frac{d \left(-c^{3/2} \sqrt{4 a d^2+c^3}+12 a d^2+c^3\right) \log \left(\sqrt{2} \sqrt[4]{c} d \sqrt{\sqrt{4 a d^2+c^3}+c^{3/2}} \left(\frac{c}{d}+x\right)+\sqrt{c} \sqrt{4 a d^2+c^3}+d^2 \left(\frac{c}{d}+x\right)^2\right)}{64 \sqrt{2} a c^{7/4} \left(4 a d^2+c^3\right)^{3/2} \sqrt{\sqrt{4 a d^2+c^3}+c^{3/2}}}-\frac{d \left(c^{3/2} \sqrt{4 a d^2+c^3}+12 a d^2+c^3\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{\sqrt{4 a d^2+c^3}+c^{3/2}}+\sqrt{2} c+\sqrt{2} d x}{\sqrt[4]{c} \sqrt{c^{3/2}-\sqrt{4 a d^2+c^3}}}\right)}{32 \sqrt{2} a c^{7/4} \left(4 a d^2+c^3\right)^{3/2} \sqrt{c^{3/2}-\sqrt{4 a d^2+c^3}}}+\frac{d \left(c^{3/2} \sqrt{4 a d^2+c^3}+12 a d^2+c^3\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{\sqrt{4 a d^2+c^3}+c^{3/2}}-\sqrt{2} (c+d x)}{\sqrt[4]{c} \sqrt{c^{3/2}-\sqrt{4 a d^2+c^3}}}\right)}{32 \sqrt{2} a c^{7/4} \left(4 a d^2+c^3\right)^{3/2} \sqrt{c^{3/2}-\sqrt{4 a d^2+c^3}}}",1,"-((c/d + x)*(c^3 - 4*a*d^2 - c*d^2*(c/d + x)^2))/(16*a*c*(c^3 + 4*a*d^2)*(4*a*c + 4*c^2*x^2 + 4*c*d*x^3 + d^2*x^4)) - (d*(c^3 + 12*a*d^2 + c^(3/2)*Sqrt[c^3 + 4*a*d^2])*ArcTanh[(Sqrt[2]*c + c^(1/4)*Sqrt[c^(3/2) + Sqrt[c^3 + 4*a*d^2]] + Sqrt[2]*d*x)/(c^(1/4)*Sqrt[c^(3/2) - Sqrt[c^3 + 4*a*d^2]])])/(32*Sqrt[2]*a*c^(7/4)*(c^3 + 4*a*d^2)^(3/2)*Sqrt[c^(3/2) - Sqrt[c^3 + 4*a*d^2]]) + (d*(c^3 + 12*a*d^2 + c^(3/2)*Sqrt[c^3 + 4*a*d^2])*ArcTanh[(c^(1/4)*Sqrt[c^(3/2) + Sqrt[c^3 + 4*a*d^2]] - Sqrt[2]*(c + d*x))/(c^(1/4)*Sqrt[c^(3/2) - Sqrt[c^3 + 4*a*d^2]])])/(32*Sqrt[2]*a*c^(7/4)*(c^3 + 4*a*d^2)^(3/2)*Sqrt[c^(3/2) - Sqrt[c^3 + 4*a*d^2]]) - (d*(c^3 + 12*a*d^2 - c^(3/2)*Sqrt[c^3 + 4*a*d^2])*Log[Sqrt[c]*Sqrt[c^3 + 4*a*d^2] - Sqrt[2]*c^(1/4)*d*Sqrt[c^(3/2) + Sqrt[c^3 + 4*a*d^2]]*(c/d + x) + d^2*(c/d + x)^2])/(64*Sqrt[2]*a*c^(7/4)*(c^3 + 4*a*d^2)^(3/2)*Sqrt[c^(3/2) + Sqrt[c^3 + 4*a*d^2]]) + (d*(c^3 + 12*a*d^2 - c^(3/2)*Sqrt[c^3 + 4*a*d^2])*Log[Sqrt[c]*Sqrt[c^3 + 4*a*d^2] + Sqrt[2]*c^(1/4)*d*Sqrt[c^(3/2) + Sqrt[c^3 + 4*a*d^2]]*(c/d + x) + d^2*(c/d + x)^2])/(64*Sqrt[2]*a*c^(7/4)*(c^3 + 4*a*d^2)^(3/2)*Sqrt[c^(3/2) + Sqrt[c^3 + 4*a*d^2]])","A",11,7,29,0.2414,1,"{1106, 1092, 1169, 634, 618, 206, 628}"
39,1,295,0,0.5323947,"\int \left(8 a e^2-d^3 x+8 d e^2 x^3+8 e^3 x^4\right)^4 \, dx","Int[(8*a*e^2 - d^3*x + 8*d*e^2*x^3 + 8*e^3*x^4)^4,x]","\frac{1}{24} e^4 \left(65536 a^2 e^6+20992 a d^4 e^3+601 d^8\right) \left(\frac{d}{4 e}+x\right)^9+\frac{64}{13} e^8 \left(256 a e^3+59 d^4\right) \left(\frac{d}{4 e}+x\right)^{13}-\frac{72}{11} d^2 e^6 \left(256 a e^3+17 d^4\right) \left(\frac{d}{4 e}+x\right)^{11}-\frac{9}{224} d^2 e^2 \left(256 a e^3+5 d^4\right) \left(256 a e^3+17 d^4\right) \left(\frac{d}{4 e}+x\right)^7+\frac{\left(256 a e^3+5 d^4\right)^2 \left(256 a e^3+59 d^4\right) \left(\frac{d}{4 e}+x\right)^5}{5120}-\frac{d^2 \left(256 a e^3+5 d^4\right)^3 \left(\frac{d}{4 e}+x\right)^3}{8192 e^2}+\frac{x \left(256 a e^3+5 d^4\right)^4}{1048576 e^4}-\frac{2048}{5} d^2 e^{10} \left(\frac{d}{4 e}+x\right)^{15}+\frac{4096}{17} e^{12} \left(\frac{d}{4 e}+x\right)^{17}","\frac{1}{24} e^4 \left(65536 a^2 e^6+20992 a d^4 e^3+601 d^8\right) \left(\frac{d}{4 e}+x\right)^9+\frac{64}{13} e^8 \left(256 a e^3+59 d^4\right) \left(\frac{d}{4 e}+x\right)^{13}-\frac{72}{11} d^2 e^6 \left(256 a e^3+17 d^4\right) \left(\frac{d}{4 e}+x\right)^{11}-\frac{9}{224} d^2 e^2 \left(256 a e^3+5 d^4\right) \left(256 a e^3+17 d^4\right) \left(\frac{d}{4 e}+x\right)^7+\frac{\left(256 a e^3+5 d^4\right)^2 \left(256 a e^3+59 d^4\right) \left(\frac{d}{4 e}+x\right)^5}{5120}-\frac{d^2 \left(256 a e^3+5 d^4\right)^3 \left(\frac{d}{4 e}+x\right)^3}{8192 e^2}+\frac{x \left(256 a e^3+5 d^4\right)^4}{1048576 e^4}-\frac{2048}{5} d^2 e^{10} \left(\frac{d}{4 e}+x\right)^{15}+\frac{4096}{17} e^{12} \left(\frac{d}{4 e}+x\right)^{17}",1,"((5*d^4 + 256*a*e^3)^4*x)/(1048576*e^4) - (d^2*(5*d^4 + 256*a*e^3)^3*(d/(4*e) + x)^3)/(8192*e^2) + ((5*d^4 + 256*a*e^3)^2*(59*d^4 + 256*a*e^3)*(d/(4*e) + x)^5)/5120 - (9*d^2*e^2*(5*d^4 + 256*a*e^3)*(17*d^4 + 256*a*e^3)*(d/(4*e) + x)^7)/224 + (e^4*(601*d^8 + 20992*a*d^4*e^3 + 65536*a^2*e^6)*(d/(4*e) + x)^9)/24 - (72*d^2*e^6*(17*d^4 + 256*a*e^3)*(d/(4*e) + x)^11)/11 + (64*e^8*(59*d^4 + 256*a*e^3)*(d/(4*e) + x)^13)/13 - (2048*d^2*e^10*(d/(4*e) + x)^15)/5 + (4096*e^12*(d/(4*e) + x)^17)/17","A",3,2,32,0.06250,1,"{1106, 1090}"
40,1,203,0,0.1229578,"\int \left(8 a e^2-d^3 x+8 d e^2 x^3+8 e^3 x^4\right)^3 \, dx","Int[(8*a*e^2 - d^3*x + 8*d*e^2*x^3 + 8*e^3*x^4)^3,x]","-\frac{1}{4} d x^4 \left(d^8-1536 a^2 e^6\right)-96 a^2 d^3 e^4 x^2+512 a^3 e^6 x-\frac{128}{3} e^5 x^9 \left(d^4-4 a e^3\right)-24 d e^4 x^8 \left(d^4-16 a e^3\right)+\frac{24}{7} d^2 e^3 x^7 \left(64 a e^3+d^4\right)+4 d^3 e^2 x^6 \left(d^4-16 a e^3\right)-\frac{384}{5} a e^4 x^5 \left(d^4-4 a e^3\right)+8 a d^6 e^2 x^3+\frac{1536}{11} d^2 e^7 x^{11}+32 d^3 e^6 x^{10}+128 d e^8 x^{12}+\frac{512 e^9 x^{13}}{13}","-\frac{1}{4} d x^4 \left(d^8-1536 a^2 e^6\right)-96 a^2 d^3 e^4 x^2+512 a^3 e^6 x-\frac{128}{3} e^5 x^9 \left(d^4-4 a e^3\right)-24 d e^4 x^8 \left(d^4-16 a e^3\right)+\frac{24}{7} d^2 e^3 x^7 \left(64 a e^3+d^4\right)+4 d^3 e^2 x^6 \left(d^4-16 a e^3\right)-\frac{384}{5} a e^4 x^5 \left(d^4-4 a e^3\right)+8 a d^6 e^2 x^3+\frac{1536}{11} d^2 e^7 x^{11}+32 d^3 e^6 x^{10}+128 d e^8 x^{12}+\frac{512 e^9 x^{13}}{13}",1,"512*a^3*e^6*x - 96*a^2*d^3*e^4*x^2 + 8*a*d^6*e^2*x^3 - (d*(d^8 - 1536*a^2*e^6)*x^4)/4 - (384*a*e^4*(d^4 - 4*a*e^3)*x^5)/5 + 4*d^3*e^2*(d^4 - 16*a*e^3)*x^6 + (24*d^2*e^3*(d^4 + 64*a*e^3)*x^7)/7 - 24*d*e^4*(d^4 - 16*a*e^3)*x^8 - (128*e^5*(d^4 - 4*a*e^3)*x^9)/3 + 32*d^3*e^6*x^10 + (1536*d^2*e^7*x^11)/11 + 128*d*e^8*x^12 + (512*e^9*x^13)/13","A",2,1,32,0.03125,1,"{2061}"
41,1,107,0,0.0509105,"\int \left(8 a e^2-d^3 x+8 d e^2 x^3+8 e^3 x^4\right)^2 \, dx","Int[(8*a*e^2 - d^3*x + 8*d*e^2*x^3 + 8*e^3*x^4)^2,x]","64 a^2 e^4 x-\frac{16}{5} e^2 x^5 \left(d^4-8 a e^3\right)-8 a d^3 e^2 x^2+32 a d e^4 x^4+\frac{64}{7} d^2 e^4 x^7-\frac{8}{3} d^3 e^3 x^6+\frac{d^6 x^3}{3}+16 d e^5 x^8+\frac{64 e^6 x^9}{9}","64 a^2 e^4 x-\frac{16}{5} e^2 x^5 \left(d^4-8 a e^3\right)-8 a d^3 e^2 x^2+32 a d e^4 x^4+\frac{64}{7} d^2 e^4 x^7-\frac{8}{3} d^3 e^3 x^6+\frac{d^6 x^3}{3}+16 d e^5 x^8+\frac{64 e^6 x^9}{9}",1,"64*a^2*e^4*x - 8*a*d^3*e^2*x^2 + (d^6*x^3)/3 + 32*a*d*e^4*x^4 - (16*e^2*(d^4 - 8*a*e^3)*x^5)/5 - (8*d^3*e^3*x^6)/3 + (64*d^2*e^4*x^7)/7 + 16*d*e^5*x^8 + (64*e^6*x^9)/9","A",2,1,32,0.03125,1,"{2061}"
42,1,37,0,0.0073737,"\int \left(8 a e^2-d^3 x+8 d e^2 x^3+8 e^3 x^4\right) \, dx","Int[8*a*e^2 - d^3*x + 8*d*e^2*x^3 + 8*e^3*x^4,x]","8 a e^2 x-\frac{d^3 x^2}{2}+2 d e^2 x^4+\frac{8 e^3 x^5}{5}","8 a e^2 x-\frac{d^3 x^2}{2}+2 d e^2 x^4+\frac{8 e^3 x^5}{5}",1,"8*a*e^2*x - (d^3*x^2)/2 + 2*d*e^2*x^4 + (8*e^3*x^5)/5","A",1,0,30,0,1,"{}"
43,1,153,0,0.2544351,"\int \frac{1}{8 a e^2-d^3 x+8 d e^2 x^3+8 e^3 x^4} \, dx","Int[(8*a*e^2 - d^3*x + 8*d*e^2*x^3 + 8*e^3*x^4)^(-1),x]","\frac{2 \tanh ^{-1}\left(\frac{d+4 e x}{\sqrt{3 d^2-2 \sqrt{d^4-64 a e^3}}}\right)}{\sqrt{d^4-64 a e^3} \sqrt{3 d^2-2 \sqrt{d^4-64 a e^3}}}-\frac{2 \tanh ^{-1}\left(\frac{d+4 e x}{\sqrt{2 \sqrt{d^4-64 a e^3}+3 d^2}}\right)}{\sqrt{d^4-64 a e^3} \sqrt{2 \sqrt{d^4-64 a e^3}+3 d^2}}","\frac{2 \tanh ^{-1}\left(\frac{d+4 e x}{\sqrt{3 d^2-2 \sqrt{d^4-64 a e^3}}}\right)}{\sqrt{d^4-64 a e^3} \sqrt{3 d^2-2 \sqrt{d^4-64 a e^3}}}-\frac{2 \tanh ^{-1}\left(\frac{d+4 e x}{\sqrt{2 \sqrt{d^4-64 a e^3}+3 d^2}}\right)}{\sqrt{d^4-64 a e^3} \sqrt{2 \sqrt{d^4-64 a e^3}+3 d^2}}",1,"(2*ArcTanh[(d + 4*e*x)/Sqrt[3*d^2 - 2*Sqrt[d^4 - 64*a*e^3]]])/(Sqrt[d^4 - 64*a*e^3]*Sqrt[3*d^2 - 2*Sqrt[d^4 - 64*a*e^3]]) - (2*ArcTanh[(d + 4*e*x)/Sqrt[3*d^2 + 2*Sqrt[d^4 - 64*a*e^3]]])/(Sqrt[d^4 - 64*a*e^3]*Sqrt[3*d^2 + 2*Sqrt[d^4 - 64*a*e^3]])","A",4,3,32,0.09375,1,"{1106, 1093, 208}"
44,1,342,0,0.532286,"\int \frac{1}{\left(8 a e^2-d^3 x+8 d e^2 x^3+8 e^3 x^4\right)^2} \, dx","Int[(8*a*e^2 - d^3*x + 8*d*e^2*x^3 + 8*e^3*x^4)^(-2),x]","\frac{2 e \left(\frac{d}{4 e}+x\right) \left(-256 a e^3-48 d^2 e^2 \left(\frac{d}{4 e}+x\right)^2+13 d^4\right)}{\left(-16384 a^2 e^6-64 a d^4 e^3+5 d^8\right) \left(8 a e^2-d^3 x+8 d e^2 x^3+8 e^3 x^4\right)}-\frac{24 e \left(-d^2 \sqrt{d^4-64 a e^3}+128 a e^3+d^4\right) \tanh ^{-1}\left(\frac{d+4 e x}{\sqrt{3 d^2-2 \sqrt{d^4-64 a e^3}}}\right)}{\left(d^4-64 a e^3\right)^{3/2} \left(256 a e^3+5 d^4\right) \sqrt{3 d^2-2 \sqrt{d^4-64 a e^3}}}+\frac{24 e \left(d^2 \sqrt{d^4-64 a e^3}+128 a e^3+d^4\right) \tanh ^{-1}\left(\frac{d+4 e x}{\sqrt{2 \sqrt{d^4-64 a e^3}+3 d^2}}\right)}{\left(d^4-64 a e^3\right)^{3/2} \left(256 a e^3+5 d^4\right) \sqrt{2 \sqrt{d^4-64 a e^3}+3 d^2}}","\frac{2 e \left(\frac{d}{4 e}+x\right) \left(-256 a e^3-48 d^2 e^2 \left(\frac{d}{4 e}+x\right)^2+13 d^4\right)}{\left(-16384 a^2 e^6-64 a d^4 e^3+5 d^8\right) \left(8 a e^2-d^3 x+8 d e^2 x^3+8 e^3 x^4\right)}-\frac{24 e \left(-d^2 \sqrt{d^4-64 a e^3}+128 a e^3+d^4\right) \tanh ^{-1}\left(\frac{d+4 e x}{\sqrt{3 d^2-2 \sqrt{d^4-64 a e^3}}}\right)}{\left(d^4-64 a e^3\right)^{3/2} \left(256 a e^3+5 d^4\right) \sqrt{3 d^2-2 \sqrt{d^4-64 a e^3}}}+\frac{24 e \left(d^2 \sqrt{d^4-64 a e^3}+128 a e^3+d^4\right) \tanh ^{-1}\left(\frac{d+4 e x}{\sqrt{2 \sqrt{d^4-64 a e^3}+3 d^2}}\right)}{\left(d^4-64 a e^3\right)^{3/2} \left(256 a e^3+5 d^4\right) \sqrt{2 \sqrt{d^4-64 a e^3}+3 d^2}}",1,"(2*e*(d/(4*e) + x)*(13*d^4 - 256*a*e^3 - 48*d^2*e^2*(d/(4*e) + x)^2))/((5*d^8 - 64*a*d^4*e^3 - 16384*a^2*e^6)*(8*a*e^2 - d^3*x + 8*d*e^2*x^3 + 8*e^3*x^4)) - (24*e*(d^4 + 128*a*e^3 - d^2*Sqrt[d^4 - 64*a*e^3])*ArcTanh[(d + 4*e*x)/Sqrt[3*d^2 - 2*Sqrt[d^4 - 64*a*e^3]]])/((d^4 - 64*a*e^3)^(3/2)*(5*d^4 + 256*a*e^3)*Sqrt[3*d^2 - 2*Sqrt[d^4 - 64*a*e^3]]) + (24*e*(d^4 + 128*a*e^3 + d^2*Sqrt[d^4 - 64*a*e^3])*ArcTanh[(d + 4*e*x)/Sqrt[3*d^2 + 2*Sqrt[d^4 - 64*a*e^3]]])/((d^4 - 64*a*e^3)^(3/2)*(5*d^4 + 256*a*e^3)*Sqrt[3*d^2 + 2*Sqrt[d^4 - 64*a*e^3]])","A",5,4,32,0.1250,1,"{1106, 1092, 1166, 208}"
45,1,96,0,0.0301725,"\int \left(8+8 x-x^3+8 x^4\right)^4 \, dx","Int[(8 + 8*x - x^3 + 8*x^4)^4,x]","\frac{4096 x^{17}}{17}-128 x^{16}+\frac{128 x^{15}}{5}+1168 x^{14}+\frac{10241 x^{13}}{13}-448 x^{12}+\frac{25312 x^{11}}{11}+\frac{21488 x^{10}}{5}+1408 x^9+1376 x^8+6784 x^7+7168 x^6+\frac{14336 x^5}{5}+3584 x^4+8192 x^3+8192 x^2+4096 x","\frac{4096 x^{17}}{17}-128 x^{16}+\frac{128 x^{15}}{5}+1168 x^{14}+\frac{10241 x^{13}}{13}-448 x^{12}+\frac{25312 x^{11}}{11}+\frac{21488 x^{10}}{5}+1408 x^9+1376 x^8+6784 x^7+7168 x^6+\frac{14336 x^5}{5}+3584 x^4+8192 x^3+8192 x^2+4096 x",1,"4096*x + 8192*x^2 + 8192*x^3 + 3584*x^4 + (14336*x^5)/5 + 7168*x^6 + 6784*x^7 + 1376*x^8 + 1408*x^9 + (21488*x^10)/5 + (25312*x^11)/11 - 448*x^12 + (10241*x^13)/13 + 1168*x^14 + (128*x^15)/5 - 128*x^16 + (4096*x^17)/17","A",2,1,17,0.05882,1,"{2061}"
46,1,74,0,0.0225196,"\int \left(8+8 x-x^3+8 x^4\right)^3 \, dx","Int[(8 + 8*x - x^3 + 8*x^4)^3,x]","\frac{512 x^{13}}{13}-16 x^{12}+\frac{24 x^{11}}{11}+\frac{307 x^{10}}{2}+128 x^9-45 x^8+\frac{1560 x^7}{7}+480 x^6+\frac{1152 x^5}{5}+80 x^4+512 x^3+768 x^2+512 x","\frac{512 x^{13}}{13}-16 x^{12}+\frac{24 x^{11}}{11}+\frac{307 x^{10}}{2}+128 x^9-45 x^8+\frac{1560 x^7}{7}+480 x^6+\frac{1152 x^5}{5}+80 x^4+512 x^3+768 x^2+512 x",1,"512*x + 768*x^2 + 512*x^3 + 80*x^4 + (1152*x^5)/5 + 480*x^6 + (1560*x^7)/7 - 45*x^8 + 128*x^9 + (307*x^10)/2 + (24*x^11)/11 - 16*x^12 + (512*x^13)/13","A",2,1,17,0.05882,1,"{2061}"
47,1,54,0,0.0165229,"\int \left(8+8 x-x^3+8 x^4\right)^2 \, dx","Int[(8 + 8*x - x^3 + 8*x^4)^2,x]","\frac{64 x^9}{9}-2 x^8+\frac{x^7}{7}+\frac{64 x^6}{3}+\frac{112 x^5}{5}-4 x^4+\frac{64 x^3}{3}+64 x^2+64 x","\frac{64 x^9}{9}-2 x^8+\frac{x^7}{7}+\frac{64 x^6}{3}+\frac{112 x^5}{5}-4 x^4+\frac{64 x^3}{3}+64 x^2+64 x",1,"64*x + 64*x^2 + (64*x^3)/3 - 4*x^4 + (112*x^5)/5 + (64*x^6)/3 + x^7/7 - 2*x^8 + (64*x^9)/9","A",2,1,17,0.05882,1,"{2061}"
48,1,23,0,0.0030522,"\int \left(8+8 x-x^3+8 x^4\right) \, dx","Int[8 + 8*x - x^3 + 8*x^4,x]","\frac{8 x^5}{5}-\frac{x^4}{4}+4 x^2+8 x","\frac{8 x^5}{5}-\frac{x^4}{4}+4 x^2+8 x",1,"8*x + 4*x^2 - x^4/4 + (8*x^5)/5","A",1,0,15,0,1,"{}"
49,1,268,0,0.3962499,"\int \frac{1}{8+8 x-x^3+8 x^4} \, dx","Int[(8 + 8*x - x^3 + 8*x^4)^(-1),x]","-\frac{1}{24} \sqrt{\frac{67 \sqrt{29}-109}{1218}} \log \left(\left(\frac{4}{x}+1\right)^2-\sqrt{6 \left(1+\sqrt{29}\right)} \left(\frac{4}{x}+1\right)+3 \sqrt{29}\right)+\frac{1}{24} \sqrt{\frac{67 \sqrt{29}-109}{1218}} \log \left(\left(\frac{4}{x}+1\right)^2+\sqrt{6 \left(1+\sqrt{29}\right)} \left(\frac{4}{x}+1\right)+3 \sqrt{29}\right)-\frac{\tan ^{-1}\left(\frac{3-\left(\frac{4}{x}+1\right)^2}{6 \sqrt{7}}\right)}{12 \sqrt{7}}-\frac{1}{12} \sqrt{\frac{109+67 \sqrt{29}}{1218}} \tan ^{-1}\left(\frac{\frac{8}{x}-\sqrt{6 \left(1+\sqrt{29}\right)}+2}{\sqrt{6 \left(\sqrt{29}-1\right)}}\right)-\frac{1}{12} \sqrt{\frac{109+67 \sqrt{29}}{1218}} \tan ^{-1}\left(\frac{\frac{8}{x}+\sqrt{6 \left(1+\sqrt{29}\right)}+2}{\sqrt{6 \left(\sqrt{29}-1\right)}}\right)","-\frac{1}{24} \sqrt{\frac{67 \sqrt{29}-109}{1218}} \log \left(\left(\frac{4}{x}+1\right)^2-\sqrt{6 \left(1+\sqrt{29}\right)} \left(\frac{4}{x}+1\right)+3 \sqrt{29}\right)+\frac{1}{24} \sqrt{\frac{67 \sqrt{29}-109}{1218}} \log \left(\left(\frac{4}{x}+1\right)^2+\sqrt{6 \left(1+\sqrt{29}\right)} \left(\frac{4}{x}+1\right)+3 \sqrt{29}\right)-\frac{\tan ^{-1}\left(\frac{3-\left(\frac{4}{x}+1\right)^2}{6 \sqrt{7}}\right)}{12 \sqrt{7}}-\frac{1}{12} \sqrt{\frac{109+67 \sqrt{29}}{1218}} \tan ^{-1}\left(\frac{\frac{8}{x}-\sqrt{6 \left(1+\sqrt{29}\right)}+2}{\sqrt{6 \left(\sqrt{29}-1\right)}}\right)-\frac{1}{12} \sqrt{\frac{109+67 \sqrt{29}}{1218}} \tan ^{-1}\left(\frac{\frac{8}{x}+\sqrt{6 \left(1+\sqrt{29}\right)}+2}{\sqrt{6 \left(\sqrt{29}-1\right)}}\right)",1,"-ArcTan[(3 - (1 + 4/x)^2)/(6*Sqrt[7])]/(12*Sqrt[7]) - (Sqrt[(109 + 67*Sqrt[29])/1218]*ArcTan[(2 - Sqrt[6*(1 + Sqrt[29])] + 8/x)/Sqrt[6*(-1 + Sqrt[29])]])/12 - (Sqrt[(109 + 67*Sqrt[29])/1218]*ArcTan[(2 + Sqrt[6*(1 + Sqrt[29])] + 8/x)/Sqrt[6*(-1 + Sqrt[29])]])/12 - (Sqrt[(-109 + 67*Sqrt[29])/1218]*Log[3*Sqrt[29] - Sqrt[6*(1 + Sqrt[29])]*(1 + 4/x) + (1 + 4/x)^2])/24 + (Sqrt[(-109 + 67*Sqrt[29])/1218]*Log[3*Sqrt[29] + Sqrt[6*(1 + Sqrt[29])]*(1 + 4/x) + (1 + 4/x)^2])/24","A",16,9,17,0.5294,1,"{2069, 12, 1673, 1169, 634, 618, 204, 628, 1107}"
50,1,357,0,0.3966718,"\int \frac{1}{\left(8+8 x-x^3+8 x^4\right)^2} \, dx","Int[(8 + 8*x - x^3 + 8*x^4)^(-2),x]","-\frac{29 \left(\frac{4}{x}+1\right)^2+207}{336 \left(\left(\frac{4}{x}+1\right)^4-6 \left(\frac{4}{x}+1\right)^2+261\right)}+\frac{5 \left(199 \left(\frac{4}{x}+1\right)^2+5157\right) \left(\frac{4}{x}+1\right)}{87696 \left(\left(\frac{4}{x}+1\right)^4-6 \left(\frac{4}{x}+1\right)^2+261\right)}-\frac{\sqrt{\frac{45923327 \sqrt{29}-180983329}{1218}} \log \left(\left(\frac{4}{x}+1\right)^2-\sqrt{6 \left(1+\sqrt{29}\right)} \left(\frac{4}{x}+1\right)+3 \sqrt{29}\right)}{175392}+\frac{\sqrt{\frac{45923327 \sqrt{29}-180983329}{1218}} \log \left(\left(\frac{4}{x}+1\right)^2+\sqrt{6 \left(1+\sqrt{29}\right)} \left(\frac{4}{x}+1\right)+3 \sqrt{29}\right)}{175392}-\frac{17 \tan ^{-1}\left(\frac{3-\left(\frac{4}{x}+1\right)^2}{6 \sqrt{7}}\right)}{1008 \sqrt{7}}-\frac{\sqrt{\frac{180983329+45923327 \sqrt{29}}{1218}} \tan ^{-1}\left(\frac{\frac{8}{x}-\sqrt{6 \left(1+\sqrt{29}\right)}+2}{\sqrt{6 \left(\sqrt{29}-1\right)}}\right)}{87696}-\frac{\sqrt{\frac{180983329+45923327 \sqrt{29}}{1218}} \tan ^{-1}\left(\frac{\frac{8}{x}+\sqrt{6 \left(1+\sqrt{29}\right)}+2}{\sqrt{6 \left(\sqrt{29}-1\right)}}\right)}{87696}","-\frac{29 \left(\frac{4}{x}+1\right)^2+207}{336 \left(\left(\frac{4}{x}+1\right)^4-6 \left(\frac{4}{x}+1\right)^2+261\right)}+\frac{5 \left(199 \left(\frac{4}{x}+1\right)^2+5157\right) \left(\frac{4}{x}+1\right)}{87696 \left(\left(\frac{4}{x}+1\right)^4-6 \left(\frac{4}{x}+1\right)^2+261\right)}-\frac{\sqrt{\frac{45923327 \sqrt{29}-180983329}{1218}} \log \left(\left(\frac{4}{x}+1\right)^2-\sqrt{6 \left(1+\sqrt{29}\right)} \left(\frac{4}{x}+1\right)+3 \sqrt{29}\right)}{175392}+\frac{\sqrt{\frac{45923327 \sqrt{29}-180983329}{1218}} \log \left(\left(\frac{4}{x}+1\right)^2+\sqrt{6 \left(1+\sqrt{29}\right)} \left(\frac{4}{x}+1\right)+3 \sqrt{29}\right)}{175392}-\frac{17 \tan ^{-1}\left(\frac{3-\left(\frac{4}{x}+1\right)^2}{6 \sqrt{7}}\right)}{1008 \sqrt{7}}-\frac{\sqrt{\frac{180983329+45923327 \sqrt{29}}{1218}} \tan ^{-1}\left(\frac{\frac{8}{x}-\sqrt{6 \left(1+\sqrt{29}\right)}+2}{\sqrt{6 \left(\sqrt{29}-1\right)}}\right)}{87696}-\frac{\sqrt{\frac{180983329+45923327 \sqrt{29}}{1218}} \tan ^{-1}\left(\frac{\frac{8}{x}+\sqrt{6 \left(1+\sqrt{29}\right)}+2}{\sqrt{6 \left(\sqrt{29}-1\right)}}\right)}{87696}",1,"-(207 + 29*(1 + 4/x)^2)/(336*(261 - 6*(1 + 4/x)^2 + (1 + 4/x)^4)) + (5*(5157 + 199*(1 + 4/x)^2)*(1 + 4/x))/(87696*(261 - 6*(1 + 4/x)^2 + (1 + 4/x)^4)) - (17*ArcTan[(3 - (1 + 4/x)^2)/(6*Sqrt[7])])/(1008*Sqrt[7]) - (Sqrt[(180983329 + 45923327*Sqrt[29])/1218]*ArcTan[(2 - Sqrt[6*(1 + Sqrt[29])] + 8/x)/Sqrt[6*(-1 + Sqrt[29])]])/87696 - (Sqrt[(180983329 + 45923327*Sqrt[29])/1218]*ArcTan[(2 + Sqrt[6*(1 + Sqrt[29])] + 8/x)/Sqrt[6*(-1 + Sqrt[29])]])/87696 - (Sqrt[(-180983329 + 45923327*Sqrt[29])/1218]*Log[3*Sqrt[29] - Sqrt[6*(1 + Sqrt[29])]*(1 + 4/x) + (1 + 4/x)^2])/175392 + (Sqrt[(-180983329 + 45923327*Sqrt[29])/1218]*Log[3*Sqrt[29] + Sqrt[6*(1 + Sqrt[29])]*(1 + 4/x) + (1 + 4/x)^2])/175392","A",18,11,17,0.6471,1,"{2069, 12, 1673, 1678, 1169, 634, 618, 204, 628, 1663, 1660}"
51,1,97,0,0.027978,"\int \left(1+4 x+4 x^2+4 x^4\right)^4 \, dx","Int[(1 + 4*x + 4*x^2 + 4*x^4)^4,x]","\frac{256 x^{17}}{17}+\frac{1024 x^{15}}{15}+\frac{512 x^{14}}{7}+\frac{1792 x^{13}}{13}+256 x^{12}+\frac{3328 x^{11}}{11}+384 x^{10}+\frac{4192 x^9}{9}+448 x^8+\frac{2752 x^7}{7}+\frac{992 x^6}{3}+\frac{1136 x^5}{5}+112 x^4+\frac{112 x^3}{3}+8 x^2+x","\frac{256 x^{17}}{17}+\frac{1024 x^{15}}{15}+\frac{512 x^{14}}{7}+\frac{1792 x^{13}}{13}+256 x^{12}+\frac{3328 x^{11}}{11}+384 x^{10}+\frac{4192 x^9}{9}+448 x^8+\frac{2752 x^7}{7}+\frac{992 x^6}{3}+\frac{1136 x^5}{5}+112 x^4+\frac{112 x^3}{3}+8 x^2+x",1,"x + 8*x^2 + (112*x^3)/3 + 112*x^4 + (1136*x^5)/5 + (992*x^6)/3 + (2752*x^7)/7 + 448*x^8 + (4192*x^9)/9 + 384*x^10 + (3328*x^11)/11 + 256*x^12 + (1792*x^13)/13 + (512*x^14)/7 + (1024*x^15)/15 + (256*x^17)/17","A",2,1,17,0.05882,1,"{2061}"
52,1,69,0,0.0200803,"\int \left(1+4 x+4 x^2+4 x^4\right)^3 \, dx","Int[(1 + 4*x + 4*x^2 + 4*x^4)^3,x]","\frac{64 x^{13}}{13}+\frac{192 x^{11}}{11}+\frac{96 x^{10}}{5}+\frac{80 x^9}{3}+48 x^8+\frac{352 x^7}{7}+48 x^6+\frac{252 x^5}{5}+40 x^4+20 x^3+6 x^2+x","\frac{64 x^{13}}{13}+\frac{192 x^{11}}{11}+\frac{96 x^{10}}{5}+\frac{80 x^9}{3}+48 x^8+\frac{352 x^7}{7}+48 x^6+\frac{252 x^5}{5}+40 x^4+20 x^3+6 x^2+x",1,"x + 6*x^2 + 20*x^3 + 40*x^4 + (252*x^5)/5 + 48*x^6 + (352*x^7)/7 + 48*x^8 + (80*x^9)/3 + (96*x^10)/5 + (192*x^11)/11 + (64*x^13)/13","A",2,1,17,0.05882,1,"{2061}"
53,1,45,0,0.0148994,"\int \left(1+4 x+4 x^2+4 x^4\right)^2 \, dx","Int[(1 + 4*x + 4*x^2 + 4*x^4)^2,x]","\frac{16 x^9}{9}+\frac{32 x^7}{7}+\frac{16 x^6}{3}+\frac{24 x^5}{5}+8 x^4+8 x^3+4 x^2+x","\frac{16 x^9}{9}+\frac{32 x^7}{7}+\frac{16 x^6}{3}+\frac{24 x^5}{5}+8 x^4+8 x^3+4 x^2+x",1,"x + 4*x^2 + 8*x^3 + 8*x^4 + (24*x^5)/5 + (16*x^6)/3 + (32*x^7)/7 + (16*x^9)/9","A",2,1,17,0.05882,1,"{2061}"
54,1,21,0,0.0026362,"\int \left(1+4 x+4 x^2+4 x^4\right) \, dx","Int[1 + 4*x + 4*x^2 + 4*x^4,x]","\frac{4 x^5}{5}+\frac{4 x^3}{3}+2 x^2+x","\frac{4 x^5}{5}+\frac{4 x^3}{3}+2 x^2+x",1,"x + 2*x^2 + (4*x^3)/3 + (4*x^5)/5","A",1,0,15,0,1,"{}"
55,1,234,0,0.3154223,"\int \frac{1}{1+4 x+4 x^2+4 x^4} \, dx","Int[(1 + 4*x + 4*x^2 + 4*x^4)^(-1),x]","-\frac{1}{4} \sqrt{\frac{1}{5} \left(\sqrt{5}-2\right)} \log \left(\left(\frac{1}{x}+1\right)^2-\sqrt{2 \left(1+\sqrt{5}\right)} \left(\frac{1}{x}+1\right)+\sqrt{5}\right)+\frac{1}{4} \sqrt{\frac{1}{5} \left(\sqrt{5}-2\right)} \log \left(\left(\frac{1}{x}+1\right)^2+\sqrt{2 \left(1+\sqrt{5}\right)} \left(\frac{1}{x}+1\right)+\sqrt{5}\right)+\frac{1}{2} \tan ^{-1}\left(\frac{1}{2} \left(\left(\frac{1}{x}+1\right)^2-1\right)\right)-\frac{1}{2} \sqrt{\frac{1}{5} \left(2+\sqrt{5}\right)} \tan ^{-1}\left(\frac{\frac{2}{x}-\sqrt{2 \left(1+\sqrt{5}\right)}+2}{\sqrt{2 \left(\sqrt{5}-1\right)}}\right)-\frac{1}{2} \sqrt{\frac{1}{5} \left(2+\sqrt{5}\right)} \tan ^{-1}\left(\frac{\frac{2}{x}+\sqrt{2 \left(1+\sqrt{5}\right)}+2}{\sqrt{2 \left(\sqrt{5}-1\right)}}\right)","-\frac{1}{4} \sqrt{\frac{1}{5} \left(\sqrt{5}-2\right)} \log \left(\left(\frac{1}{x}+1\right)^2-\sqrt{2 \left(1+\sqrt{5}\right)} \left(\frac{1}{x}+1\right)+\sqrt{5}\right)+\frac{1}{4} \sqrt{\frac{1}{5} \left(\sqrt{5}-2\right)} \log \left(\left(\frac{1}{x}+1\right)^2+\sqrt{2 \left(1+\sqrt{5}\right)} \left(\frac{1}{x}+1\right)+\sqrt{5}\right)+\frac{1}{2} \tan ^{-1}\left(\frac{1}{2} \left(\left(\frac{1}{x}+1\right)^2-1\right)\right)-\frac{1}{2} \sqrt{\frac{1}{5} \left(2+\sqrt{5}\right)} \tan ^{-1}\left(\frac{\frac{2}{x}-\sqrt{2 \left(1+\sqrt{5}\right)}+2}{\sqrt{2 \left(\sqrt{5}-1\right)}}\right)-\frac{1}{2} \sqrt{\frac{1}{5} \left(2+\sqrt{5}\right)} \tan ^{-1}\left(\frac{\frac{2}{x}+\sqrt{2 \left(1+\sqrt{5}\right)}+2}{\sqrt{2 \left(\sqrt{5}-1\right)}}\right)",1,"ArcTan[(-1 + (1 + x^(-1))^2)/2]/2 - (Sqrt[(2 + Sqrt[5])/5]*ArcTan[(2 - Sqrt[2*(1 + Sqrt[5])] + 2/x)/Sqrt[2*(-1 + Sqrt[5])]])/2 - (Sqrt[(2 + Sqrt[5])/5]*ArcTan[(2 + Sqrt[2*(1 + Sqrt[5])] + 2/x)/Sqrt[2*(-1 + Sqrt[5])]])/2 - (Sqrt[(-2 + Sqrt[5])/5]*Log[Sqrt[5] - Sqrt[2*(1 + Sqrt[5])]*(1 + x^(-1)) + (1 + x^(-1))^2])/4 + (Sqrt[(-2 + Sqrt[5])/5]*Log[Sqrt[5] + Sqrt[2*(1 + Sqrt[5])]*(1 + x^(-1)) + (1 + x^(-1))^2])/4","A",15,9,17,0.5294,1,"{2069, 1673, 1169, 634, 618, 204, 628, 12, 1107}"
56,1,317,0,0.3347238,"\int \frac{1}{\left(1+4 x+4 x^2+4 x^4\right)^2} \, dx","Int[(1 + 4*x + 4*x^2 + 4*x^4)^(-2),x]","-\frac{17-\left(\frac{1}{x}+1\right)^2}{2 \left(\left(\frac{1}{x}+1\right)^4-2 \left(\frac{1}{x}+1\right)^2+5\right)}+\frac{\left(59-17 \left(\frac{1}{x}+1\right)^2\right) \left(\frac{1}{x}+1\right)}{10 \left(\left(\frac{1}{x}+1\right)^4-2 \left(\frac{1}{x}+1\right)^2+5\right)}+\frac{1}{40} \sqrt{\frac{1}{10} \left(2665 \sqrt{5}-5959\right)} \log \left(\left(\frac{1}{x}+1\right)^2-\sqrt{2 \left(1+\sqrt{5}\right)} \left(\frac{1}{x}+1\right)+\sqrt{5}\right)-\frac{1}{40} \sqrt{\frac{1}{10} \left(2665 \sqrt{5}-5959\right)} \log \left(\left(\frac{1}{x}+1\right)^2+\sqrt{2 \left(1+\sqrt{5}\right)} \left(\frac{1}{x}+1\right)+\sqrt{5}\right)+\frac{7}{4} \tan ^{-1}\left(\frac{1}{2} \left(\left(\frac{1}{x}+1\right)^2-1\right)\right)-\frac{1}{20} \sqrt{\frac{1}{10} \left(5959+2665 \sqrt{5}\right)} \tan ^{-1}\left(\frac{\frac{2}{x}-\sqrt{2 \left(1+\sqrt{5}\right)}+2}{\sqrt{2 \left(\sqrt{5}-1\right)}}\right)-\frac{1}{20} \sqrt{\frac{1}{10} \left(5959+2665 \sqrt{5}\right)} \tan ^{-1}\left(\frac{\frac{2}{x}+\sqrt{2 \left(1+\sqrt{5}\right)}+2}{\sqrt{2 \left(\sqrt{5}-1\right)}}\right)","-\frac{17-\left(\frac{1}{x}+1\right)^2}{2 \left(\left(\frac{1}{x}+1\right)^4-2 \left(\frac{1}{x}+1\right)^2+5\right)}+\frac{\left(59-17 \left(\frac{1}{x}+1\right)^2\right) \left(\frac{1}{x}+1\right)}{10 \left(\left(\frac{1}{x}+1\right)^4-2 \left(\frac{1}{x}+1\right)^2+5\right)}+\frac{1}{40} \sqrt{\frac{1}{10} \left(2665 \sqrt{5}-5959\right)} \log \left(\left(\frac{1}{x}+1\right)^2-\sqrt{2 \left(1+\sqrt{5}\right)} \left(\frac{1}{x}+1\right)+\sqrt{5}\right)-\frac{1}{40} \sqrt{\frac{1}{10} \left(2665 \sqrt{5}-5959\right)} \log \left(\left(\frac{1}{x}+1\right)^2+\sqrt{2 \left(1+\sqrt{5}\right)} \left(\frac{1}{x}+1\right)+\sqrt{5}\right)+\frac{7}{4} \tan ^{-1}\left(\frac{1}{2} \left(\left(\frac{1}{x}+1\right)^2-1\right)\right)-\frac{1}{20} \sqrt{\frac{1}{10} \left(5959+2665 \sqrt{5}\right)} \tan ^{-1}\left(\frac{\frac{2}{x}-\sqrt{2 \left(1+\sqrt{5}\right)}+2}{\sqrt{2 \left(\sqrt{5}-1\right)}}\right)-\frac{1}{20} \sqrt{\frac{1}{10} \left(5959+2665 \sqrt{5}\right)} \tan ^{-1}\left(\frac{\frac{2}{x}+\sqrt{2 \left(1+\sqrt{5}\right)}+2}{\sqrt{2 \left(\sqrt{5}-1\right)}}\right)",1,"-(17 - (1 + x^(-1))^2)/(2*(5 - 2*(1 + x^(-1))^2 + (1 + x^(-1))^4)) + ((59 - 17*(1 + x^(-1))^2)*(1 + x^(-1)))/(10*(5 - 2*(1 + x^(-1))^2 + (1 + x^(-1))^4)) + (7*ArcTan[(-1 + (1 + x^(-1))^2)/2])/4 - (Sqrt[(5959 + 2665*Sqrt[5])/10]*ArcTan[(2 - Sqrt[2*(1 + Sqrt[5])] + 2/x)/Sqrt[2*(-1 + Sqrt[5])]])/20 - (Sqrt[(5959 + 2665*Sqrt[5])/10]*ArcTan[(2 + Sqrt[2*(1 + Sqrt[5])] + 2/x)/Sqrt[2*(-1 + Sqrt[5])]])/20 + (Sqrt[(-5959 + 2665*Sqrt[5])/10]*Log[Sqrt[5] - Sqrt[2*(1 + Sqrt[5])]*(1 + x^(-1)) + (1 + x^(-1))^2])/40 - (Sqrt[(-5959 + 2665*Sqrt[5])/10]*Log[Sqrt[5] + Sqrt[2*(1 + Sqrt[5])]*(1 + x^(-1)) + (1 + x^(-1))^2])/40","A",17,11,17,0.6471,1,"{2069, 1673, 1678, 1169, 634, 618, 204, 628, 1663, 1660, 12}"
57,1,104,0,0.0337367,"\int \left(8+24 x+8 x^2-15 x^3+8 x^4\right)^4 \, dx","Int[(8 + 24*x + 8*x^2 - 15*x^3 + 8*x^4)^4,x]","\frac{4096 x^{17}}{17}-1920 x^{16}+\frac{102784 x^{15}}{15}-\frac{75504 x^{14}}{7}-\frac{12095 x^{13}}{13}+31128 x^{12}-\frac{331040 x^{11}}{11}-\frac{169584 x^{10}}{5}+\frac{641152 x^9}{9}+36384 x^8-\frac{566912 x^7}{7}-30720 x^6+\frac{538624 x^5}{5}+139776 x^4+\frac{237568 x^3}{3}+24576 x^2+4096 x","\frac{4096 x^{17}}{17}-1920 x^{16}+\frac{102784 x^{15}}{15}-\frac{75504 x^{14}}{7}-\frac{12095 x^{13}}{13}+31128 x^{12}-\frac{331040 x^{11}}{11}-\frac{169584 x^{10}}{5}+\frac{641152 x^9}{9}+36384 x^8-\frac{566912 x^7}{7}-30720 x^6+\frac{538624 x^5}{5}+139776 x^4+\frac{237568 x^3}{3}+24576 x^2+4096 x",1,"4096*x + 24576*x^2 + (237568*x^3)/3 + 139776*x^4 + (538624*x^5)/5 - 30720*x^6 - (566912*x^7)/7 + 36384*x^8 + (641152*x^9)/9 - (169584*x^10)/5 - (331040*x^11)/11 + 31128*x^12 - (12095*x^13)/13 - (75504*x^14)/7 + (102784*x^15)/15 - 1920*x^16 + (4096*x^17)/17","A",2,1,22,0.04545,1,"{2061}"
58,1,76,0,0.023682,"\int \left(8+24 x+8 x^2-15 x^3+8 x^4\right)^3 \, dx","Int[(8 + 24*x + 8*x^2 - 15*x^3 + 8*x^4)^3,x]","\frac{512 x^{13}}{13}-240 x^{12}+\frac{6936 x^{11}}{11}-\frac{4527 x^{10}}{10}-\frac{2936 x^9}{3}+2097 x^8+\frac{5528 x^7}{7}-2976 x^6-\frac{384 x^5}{5}+5040 x^4+5120 x^3+2304 x^2+512 x","\frac{512 x^{13}}{13}-240 x^{12}+\frac{6936 x^{11}}{11}-\frac{4527 x^{10}}{10}-\frac{2936 x^9}{3}+2097 x^8+\frac{5528 x^7}{7}-2976 x^6-\frac{384 x^5}{5}+5040 x^4+5120 x^3+2304 x^2+512 x",1,"512*x + 2304*x^2 + 5120*x^3 + 5040*x^4 - (384*x^5)/5 - 2976*x^6 + (5528*x^7)/7 + 2097*x^8 - (2936*x^9)/3 - (4527*x^10)/10 + (6936*x^11)/11 - 240*x^12 + (512*x^13)/13","A",2,1,22,0.04545,1,"{2061}"
59,1,52,0,0.0160692,"\int \left(8+24 x+8 x^2-15 x^3+8 x^4\right)^2 \, dx","Int[(8 + 24*x + 8*x^2 - 15*x^3 + 8*x^4)^2,x]","\frac{64 x^9}{9}-30 x^8+\frac{353 x^7}{7}+24 x^6-\frac{528 x^5}{5}+36 x^4+\frac{704 x^3}{3}+192 x^2+64 x","\frac{64 x^9}{9}-30 x^8+\frac{353 x^7}{7}+24 x^6-\frac{528 x^5}{5}+36 x^4+\frac{704 x^3}{3}+192 x^2+64 x",1,"64*x + 192*x^2 + (704*x^3)/3 + 36*x^4 - (528*x^5)/5 + 24*x^6 + (353*x^7)/7 - 30*x^8 + (64*x^9)/9","A",2,1,22,0.04545,1,"{2061}"
60,1,30,0,0.0038845,"\int \left(8+24 x+8 x^2-15 x^3+8 x^4\right) \, dx","Int[8 + 24*x + 8*x^2 - 15*x^3 + 8*x^4,x]","\frac{8 x^5}{5}-\frac{15 x^4}{4}+\frac{8 x^3}{3}+12 x^2+8 x","\frac{8 x^5}{5}-\frac{15 x^4}{4}+\frac{8 x^3}{3}+12 x^2+8 x",1,"8*x + 12*x^2 + (8*x^3)/3 - (15*x^4)/4 + (8*x^5)/5","A",1,0,20,0,1,"{}"
61,1,263,0,0.4928242,"\int \frac{1}{8+24 x+8 x^2-15 x^3+8 x^4} \, dx","Int[(8 + 24*x + 8*x^2 - 15*x^3 + 8*x^4)^(-1),x]","\frac{1}{4} \sqrt{\frac{3}{13}} \tan ^{-1}\left(\frac{-5 x^2+12 x+8}{\sqrt{39} x^2}\right)-\frac{1}{8} \sqrt{\frac{235 \sqrt{517}-5167}{40326}} \log \left(\left(\frac{4}{x}+3\right)^2-\sqrt{2 \left(19+\sqrt{517}\right)} \left(\frac{4}{x}+3\right)+\sqrt{517}\right)+\frac{1}{8} \sqrt{\frac{235 \sqrt{517}-5167}{40326}} \log \left(\left(\frac{4}{x}+3\right)^2+\sqrt{2 \left(19+\sqrt{517}\right)} \left(\frac{4}{x}+3\right)+\sqrt{517}\right)-\frac{1}{4} \sqrt{\frac{5167+235 \sqrt{517}}{40326}} \tan ^{-1}\left(\frac{\frac{8}{x}-\sqrt{2 \left(19+\sqrt{517}\right)}+6}{\sqrt{2 \left(\sqrt{517}-19\right)}}\right)-\frac{1}{4} \sqrt{\frac{5167+235 \sqrt{517}}{40326}} \tan ^{-1}\left(\frac{\frac{8}{x}+\sqrt{2 \left(19+\sqrt{517}\right)}+6}{\sqrt{2 \left(\sqrt{517}-19\right)}}\right)","\frac{1}{4} \sqrt{\frac{3}{13}} \tan ^{-1}\left(\frac{-5 x^2+12 x+8}{\sqrt{39} x^2}\right)-\frac{1}{8} \sqrt{\frac{235 \sqrt{517}-5167}{40326}} \log \left(\left(\frac{4}{x}+3\right)^2-\sqrt{2 \left(19+\sqrt{517}\right)} \left(\frac{4}{x}+3\right)+\sqrt{517}\right)+\frac{1}{8} \sqrt{\frac{235 \sqrt{517}-5167}{40326}} \log \left(\left(\frac{4}{x}+3\right)^2+\sqrt{2 \left(19+\sqrt{517}\right)} \left(\frac{4}{x}+3\right)+\sqrt{517}\right)-\frac{1}{4} \sqrt{\frac{5167+235 \sqrt{517}}{40326}} \tan ^{-1}\left(\frac{\frac{8}{x}-\sqrt{2 \left(19+\sqrt{517}\right)}+6}{\sqrt{2 \left(\sqrt{517}-19\right)}}\right)-\frac{1}{4} \sqrt{\frac{5167+235 \sqrt{517}}{40326}} \tan ^{-1}\left(\frac{\frac{8}{x}+\sqrt{2 \left(19+\sqrt{517}\right)}+6}{\sqrt{2 \left(\sqrt{517}-19\right)}}\right)",1,"-(Sqrt[(5167 + 235*Sqrt[517])/40326]*ArcTan[(6 - Sqrt[2*(19 + Sqrt[517])] + 8/x)/Sqrt[2*(-19 + Sqrt[517])]])/4 - (Sqrt[(5167 + 235*Sqrt[517])/40326]*ArcTan[(6 + Sqrt[2*(19 + Sqrt[517])] + 8/x)/Sqrt[2*(-19 + Sqrt[517])]])/4 + (Sqrt[3/13]*ArcTan[(8 + 12*x - 5*x^2)/(Sqrt[39]*x^2)])/4 - (Sqrt[(-5167 + 235*Sqrt[517])/40326]*Log[Sqrt[517] - Sqrt[2*(19 + Sqrt[517])]*(3 + 4/x) + (3 + 4/x)^2])/8 + (Sqrt[(-5167 + 235*Sqrt[517])/40326]*Log[Sqrt[517] + Sqrt[2*(19 + Sqrt[517])]*(3 + 4/x) + (3 + 4/x)^2])/8","A",16,9,22,0.4091,1,"{2069, 12, 1673, 1169, 634, 618, 204, 628, 1107}"
62,1,366,0,0.5076289,"\int \frac{1}{\left(8+24 x+8 x^2-15 x^3+8 x^4\right)^2} \, dx","Int[(8 + 24*x + 8*x^2 - 15*x^3 + 8*x^4)^(-2),x]","\frac{73}{208} \sqrt{\frac{3}{13}} \tan ^{-1}\left(\frac{-5 x^2+12 x+8}{\sqrt{39} x^2}\right)-\frac{3 \left(3359-107 \left(\frac{4}{x}+3\right)^2\right)}{208 \left(\left(\frac{4}{x}+3\right)^4-38 \left(\frac{4}{x}+3\right)^2+517\right)}+\frac{\left(3327931-129631 \left(\frac{4}{x}+3\right)^2\right) \left(\frac{4}{x}+3\right)}{322608 \left(\left(\frac{4}{x}+3\right)^4-38 \left(\frac{4}{x}+3\right)^2+517\right)}-\frac{\sqrt{\frac{2623170438295 \sqrt{517}-59644114671451}{40326}} \log \left(\left(\frac{4}{x}+3\right)^2-\sqrt{2 \left(19+\sqrt{517}\right)} \left(\frac{4}{x}+3\right)+\sqrt{517}\right)}{645216}+\frac{\sqrt{\frac{2623170438295 \sqrt{517}-59644114671451}{40326}} \log \left(\left(\frac{4}{x}+3\right)^2+\sqrt{2 \left(19+\sqrt{517}\right)} \left(\frac{4}{x}+3\right)+\sqrt{517}\right)}{645216}-\frac{\sqrt{\frac{19+\sqrt{517}}{40326}} \left(1678181+74897 \sqrt{517}\right) \tan ^{-1}\left(\frac{\frac{8}{x}-\sqrt{2 \left(19+\sqrt{517}\right)}+6}{\sqrt{2 \left(\sqrt{517}-19\right)}}\right)}{645216}-\frac{\sqrt{\frac{19+\sqrt{517}}{40326}} \left(1678181+74897 \sqrt{517}\right) \tan ^{-1}\left(\frac{\frac{8}{x}+\sqrt{2 \left(19+\sqrt{517}\right)}+6}{\sqrt{2 \left(\sqrt{517}-19\right)}}\right)}{645216}","\frac{73}{208} \sqrt{\frac{3}{13}} \tan ^{-1}\left(\frac{-5 x^2+12 x+8}{\sqrt{39} x^2}\right)-\frac{3 \left(3359-107 \left(\frac{4}{x}+3\right)^2\right)}{208 \left(\left(\frac{4}{x}+3\right)^4-38 \left(\frac{4}{x}+3\right)^2+517\right)}+\frac{\left(3327931-129631 \left(\frac{4}{x}+3\right)^2\right) \left(\frac{4}{x}+3\right)}{322608 \left(\left(\frac{4}{x}+3\right)^4-38 \left(\frac{4}{x}+3\right)^2+517\right)}-\frac{\sqrt{\frac{2623170438295 \sqrt{517}-59644114671451}{40326}} \log \left(\left(\frac{4}{x}+3\right)^2-\sqrt{2 \left(19+\sqrt{517}\right)} \left(\frac{4}{x}+3\right)+\sqrt{517}\right)}{645216}+\frac{\sqrt{\frac{2623170438295 \sqrt{517}-59644114671451}{40326}} \log \left(\left(\frac{4}{x}+3\right)^2+\sqrt{2 \left(19+\sqrt{517}\right)} \left(\frac{4}{x}+3\right)+\sqrt{517}\right)}{645216}-\frac{\sqrt{\frac{19+\sqrt{517}}{40326}} \left(1678181+74897 \sqrt{517}\right) \tan ^{-1}\left(\frac{\frac{8}{x}-\sqrt{2 \left(19+\sqrt{517}\right)}+6}{\sqrt{2 \left(\sqrt{517}-19\right)}}\right)}{645216}-\frac{\sqrt{\frac{19+\sqrt{517}}{40326}} \left(1678181+74897 \sqrt{517}\right) \tan ^{-1}\left(\frac{\frac{8}{x}+\sqrt{2 \left(19+\sqrt{517}\right)}+6}{\sqrt{2 \left(\sqrt{517}-19\right)}}\right)}{645216}",1,"(-3*(3359 - 107*(3 + 4/x)^2))/(208*(517 - 38*(3 + 4/x)^2 + (3 + 4/x)^4)) + ((3327931 - 129631*(3 + 4/x)^2)*(3 + 4/x))/(322608*(517 - 38*(3 + 4/x)^2 + (3 + 4/x)^4)) - (Sqrt[(19 + Sqrt[517])/40326]*(1678181 + 74897*Sqrt[517])*ArcTan[(6 - Sqrt[2*(19 + Sqrt[517])] + 8/x)/Sqrt[2*(-19 + Sqrt[517])]])/645216 - (Sqrt[(19 + Sqrt[517])/40326]*(1678181 + 74897*Sqrt[517])*ArcTan[(6 + Sqrt[2*(19 + Sqrt[517])] + 8/x)/Sqrt[2*(-19 + Sqrt[517])]])/645216 + (73*Sqrt[3/13]*ArcTan[(8 + 12*x - 5*x^2)/(Sqrt[39]*x^2)])/208 - (Sqrt[(-59644114671451 + 2623170438295*Sqrt[517])/40326]*Log[Sqrt[517] - Sqrt[2*(19 + Sqrt[517])]*(3 + 4/x) + (3 + 4/x)^2])/645216 + (Sqrt[(-59644114671451 + 2623170438295*Sqrt[517])/40326]*Log[Sqrt[517] + Sqrt[2*(19 + Sqrt[517])]*(3 + 4/x) + (3 + 4/x)^2])/645216","A",18,11,22,0.5000,1,"{2069, 12, 1673, 1678, 1169, 634, 618, 204, 628, 1663, 1660}"
63,1,14,0,0.0169574,"\int \left(a^5+5 a^4 b x+10 a^3 b^2 x^2+10 a^2 b^3 x^3+5 a b^4 x^4+b^5 x^5\right)^3 \, dx","Int[(a^5 + 5*a^4*b*x + 10*a^3*b^2*x^2 + 10*a^2*b^3*x^3 + 5*a*b^4*x^4 + b^5*x^5)^3,x]","\frac{(a+b x)^{16}}{16 b}","\frac{(a+b x)^{16}}{16 b}",1,"(a + b*x)^16/(16*b)","A",2,2,51,0.03922,1,"{2059, 32}"
64,1,14,0,0.017942,"\int \left(a^5+5 a^4 b x+10 a^3 b^2 x^2+10 a^2 b^3 x^3+5 a b^4 x^4+b^5 x^5\right)^2 \, dx","Int[(a^5 + 5*a^4*b*x + 10*a^3*b^2*x^2 + 10*a^2*b^3*x^3 + 5*a*b^4*x^4 + b^5*x^5)^2,x]","\frac{(a+b x)^{11}}{11 b}","\frac{(a+b x)^{11}}{11 b}",1,"(a + b*x)^11/(11*b)","A",2,2,51,0.03922,1,"{2059, 32}"
65,1,61,0,0.014024,"\int \left(a^5+5 a^4 b x+10 a^3 b^2 x^2+10 a^2 b^3 x^3+5 a b^4 x^4+b^5 x^5\right) \, dx","Int[a^5 + 5*a^4*b*x + 10*a^3*b^2*x^2 + 10*a^2*b^3*x^3 + 5*a*b^4*x^4 + b^5*x^5,x]","\frac{5}{2} a^2 b^3 x^4+\frac{10}{3} a^3 b^2 x^3+\frac{5}{2} a^4 b x^2+a^5 x+a b^4 x^5+\frac{b^5 x^6}{6}","\frac{(a+b x)^6}{6 b}",1,"a^5*x + (5*a^4*b*x^2)/2 + (10*a^3*b^2*x^3)/3 + (5*a^2*b^3*x^4)/2 + a*b^4*x^5 + (b^5*x^6)/6","B",1,0,49,0,1,"{}"
66,1,14,0,0.0176062,"\int \frac{1}{a^5+5 a^4 b x+10 a^3 b^2 x^2+10 a^2 b^3 x^3+5 a b^4 x^4+b^5 x^5} \, dx","Int[(a^5 + 5*a^4*b*x + 10*a^3*b^2*x^2 + 10*a^2*b^3*x^3 + 5*a*b^4*x^4 + b^5*x^5)^(-1),x]","-\frac{1}{4 b (a+b x)^4}","-\frac{1}{4 b (a+b x)^4}",1,"-1/(4*b*(a + b*x)^4)","A",2,2,51,0.03922,1,"{2058, 32}"
67,1,14,0,0.0167872,"\int \frac{1}{\left(a^5+5 a^4 b x+10 a^3 b^2 x^2+10 a^2 b^3 x^3+5 a b^4 x^4+b^5 x^5\right)^2} \, dx","Int[(a^5 + 5*a^4*b*x + 10*a^3*b^2*x^2 + 10*a^2*b^3*x^3 + 5*a*b^4*x^4 + b^5*x^5)^(-2),x]","-\frac{1}{9 b (a+b x)^9}","-\frac{1}{9 b (a+b x)^9}",1,"-1/(9*b*(a + b*x)^9)","A",2,2,51,0.03922,1,"{2058, 32}"
68,1,14,0,0.0181846,"\int \frac{1}{\left(a^5+5 a^4 b x+10 a^3 b^2 x^2+10 a^2 b^3 x^3+5 a b^4 x^4+b^5 x^5\right)^3} \, dx","Int[(a^5 + 5*a^4*b*x + 10*a^3*b^2*x^2 + 10*a^2*b^3*x^3 + 5*a*b^4*x^4 + b^5*x^5)^(-3),x]","-\frac{1}{14 b (a+b x)^{14}}","-\frac{1}{14 b (a+b x)^{14}}",1,"-1/(14*b*(a + b*x)^14)","A",2,2,51,0.03922,1,"{2058, 32}"
69,1,38,0,0.0249394,"\int \frac{1}{1+x^2+x^3+x^5} \, dx","Int[(1 + x^2 + x^3 + x^5)^(-1),x]","\frac{1}{4} \log \left(x^2+1\right)-\frac{1}{3} \log \left(x^2-x+1\right)+\frac{1}{6} \log (x+1)+\frac{1}{2} \tan ^{-1}(x)","\frac{1}{4} \log \left(x^2+1\right)-\frac{1}{3} \log \left(x^2-x+1\right)+\frac{1}{6} \log (x+1)+\frac{1}{2} \tan ^{-1}(x)",1,"ArcTan[x]/2 + Log[1 + x]/6 + Log[1 + x^2]/4 - Log[1 - x + x^2]/3","A",6,5,13,0.3846,1,"{2058, 635, 203, 260, 628}"
70,1,84,0,0.0855259,"\int \left(3-19 x^2+32 x^4-16 x^6\right)^4 \, dx","Int[(3 - 19*x^2 + 32*x^4 - 16*x^6)^4,x]","\frac{65536 x^{25}}{25}-\frac{524288 x^{23}}{23}+\frac{1884160 x^{21}}{21}-\frac{4014080 x^{19}}{19}+\frac{5633536 x^{17}}{17}-\frac{1094656 x^{15}}{3}+\frac{3764416 x^{13}}{13}-\frac{1841600 x^{11}}{11}+\frac{634321 x^9}{9}-\frac{149700 x^7}{7}+4590 x^5-684 x^3+81 x","\frac{65536 x^{25}}{25}-\frac{524288 x^{23}}{23}+\frac{1884160 x^{21}}{21}-\frac{4014080 x^{19}}{19}+\frac{5633536 x^{17}}{17}-\frac{1094656 x^{15}}{3}+\frac{3764416 x^{13}}{13}-\frac{1841600 x^{11}}{11}+\frac{634321 x^9}{9}-\frac{149700 x^7}{7}+4590 x^5-684 x^3+81 x",1,"81*x - 684*x^3 + 4590*x^5 - (149700*x^7)/7 + (634321*x^9)/9 - (1841600*x^11)/11 + (3764416*x^13)/13 - (1094656*x^15)/3 + (5633536*x^17)/17 - (4014080*x^19)/19 + (1884160*x^21)/21 - (524288*x^23)/23 + (65536*x^25)/25","A",5,3,19,0.1579,1,"{2059, 517, 521}"
71,1,63,0,0.0757429,"\int \left(3-19 x^2+32 x^4-16 x^6\right)^3 \, dx","Int[(3 - 19*x^2 + 32*x^4 - 16*x^6)^3,x]","-\frac{4096 x^{19}}{19}+\frac{24576 x^{17}}{17}-\frac{21248 x^{15}}{5}+\frac{93440 x^{13}}{13}-\frac{84912 x^{11}}{11}+\frac{16448 x^9}{3}-2605 x^7+\frac{4113 x^5}{5}-171 x^3+27 x","-\frac{4096 x^{19}}{19}+\frac{24576 x^{17}}{17}-\frac{21248 x^{15}}{5}+\frac{93440 x^{13}}{13}-\frac{84912 x^{11}}{11}+\frac{16448 x^9}{3}-2605 x^7+\frac{4113 x^5}{5}-171 x^3+27 x",1,"27*x - 171*x^3 + (4113*x^5)/5 - 2605*x^7 + (16448*x^9)/3 - (84912*x^11)/11 + (93440*x^13)/13 - (21248*x^15)/5 + (24576*x^17)/17 - (4096*x^19)/19","A",5,3,19,0.1579,1,"{2059, 517, 521}"
72,1,44,0,0.0693192,"\int \left(3-19 x^2+32 x^4-16 x^6\right)^2 \, dx","Int[(3 - 19*x^2 + 32*x^4 - 16*x^6)^2,x]","\frac{256 x^{13}}{13}-\frac{1024 x^{11}}{11}+\frac{544 x^9}{3}-\frac{1312 x^7}{7}+\frac{553 x^5}{5}-38 x^3+9 x","\frac{256 x^{13}}{13}-\frac{1024 x^{11}}{11}+\frac{544 x^9}{3}-\frac{1312 x^7}{7}+\frac{553 x^5}{5}-38 x^3+9 x",1,"9*x - 38*x^3 + (553*x^5)/5 - (1312*x^7)/7 + (544*x^9)/3 - (1024*x^11)/11 + (256*x^13)/13","A",5,3,19,0.1579,1,"{2059, 517, 521}"
73,1,25,0,0.0031791,"\int \left(3-19 x^2+32 x^4-16 x^6\right) \, dx","Int[3 - 19*x^2 + 32*x^4 - 16*x^6,x]","-\frac{16 x^7}{7}+\frac{32 x^5}{5}-\frac{19 x^3}{3}+3 x","-\frac{16 x^7}{7}+\frac{32 x^5}{5}-\frac{19 x^3}{3}+3 x",1,"3*x - (19*x^3)/3 + (32*x^5)/5 - (16*x^7)/7","A",1,0,17,0,1,"{}"
74,1,31,0,0.0228096,"\int \frac{1}{3-19 x^2+32 x^4-16 x^6} \, dx","Int[(3 - 19*x^2 + 32*x^4 - 16*x^6)^(-1),x]","\frac{1}{3} \tanh ^{-1}(x)+\frac{1}{3} \tanh ^{-1}(2 x)-\frac{\tanh ^{-1}\left(\frac{2 x}{\sqrt{3}}\right)}{\sqrt{3}}","\frac{1}{3} \tanh ^{-1}(x)+\frac{1}{3} \tanh ^{-1}(2 x)-\frac{\tanh ^{-1}\left(\frac{2 x}{\sqrt{3}}\right)}{\sqrt{3}}",1,"ArcTanh[x]/3 + ArcTanh[2*x]/3 - ArcTanh[(2*x)/Sqrt[3]]/Sqrt[3]","A",5,2,19,0.1053,1,"{2057, 207}"
75,1,89,0,0.0614828,"\int \frac{1}{\left(3-19 x^2+32 x^4-16 x^6\right)^2} \, dx","Int[(3 - 19*x^2 + 32*x^4 - 16*x^6)^(-2),x]","\frac{2 x}{3 \left(3-4 x^2\right)}+\frac{1}{18 (1-2 x)}+\frac{1}{36 (1-x)}-\frac{1}{36 (x+1)}-\frac{1}{18 (2 x+1)}+\frac{67}{54} \tanh ^{-1}(x)-\frac{7}{27} \tanh ^{-1}(2 x)-\frac{5 \tanh ^{-1}\left(\frac{2 x}{\sqrt{3}}\right)}{3 \sqrt{3}}","\frac{2 x}{3 \left(3-4 x^2\right)}+\frac{1}{18 (1-2 x)}+\frac{1}{36 (1-x)}-\frac{1}{36 (x+1)}-\frac{1}{18 (2 x+1)}+\frac{67}{54} \tanh ^{-1}(x)-\frac{7}{27} \tanh ^{-1}(2 x)-\frac{5 \tanh ^{-1}\left(\frac{2 x}{\sqrt{3}}\right)}{3 \sqrt{3}}",1,"1/(18*(1 - 2*x)) + 1/(36*(1 - x)) - 1/(36*(1 + x)) - 1/(18*(1 + 2*x)) + (2*x)/(3*(3 - 4*x^2)) + (67*ArcTanh[x])/54 - (7*ArcTanh[2*x])/27 - (5*ArcTanh[(2*x)/Sqrt[3]])/(3*Sqrt[3])","A",7,3,19,0.1579,1,"{2057, 207, 199}"
76,1,161,0,0.1193769,"\int \frac{1}{\left(3-19 x^2+32 x^4-16 x^6\right)^3} \, dx","Int[(3 - 19*x^2 + 32*x^4 - 16*x^6)^(-3),x]","\frac{5 x}{3 \left(3-4 x^2\right)}-\frac{2 x}{3 \left(3-4 x^2\right)^2}-\frac{7}{108 (1-2 x)}+\frac{67}{432 (1-x)}-\frac{67}{432 (x+1)}+\frac{7}{108 (2 x+1)}+\frac{1}{108 (1-2 x)^2}+\frac{1}{432 (1-x)^2}-\frac{1}{432 (x+1)^2}-\frac{1}{108 (2 x+1)^2}+\frac{3913}{648} \tanh ^{-1}(x)+\frac{67}{162} \tanh ^{-1}(2 x)-4 \sqrt{3} \tanh ^{-1}\left(\frac{2 x}{\sqrt{3}}\right)+\frac{5 \tanh ^{-1}\left(\frac{2 x}{\sqrt{3}}\right)}{6 \sqrt{3}}","\frac{5 x}{3 \left(3-4 x^2\right)}-\frac{2 x}{3 \left(3-4 x^2\right)^2}-\frac{7}{108 (1-2 x)}+\frac{67}{432 (1-x)}-\frac{67}{432 (x+1)}+\frac{7}{108 (2 x+1)}+\frac{1}{108 (1-2 x)^2}+\frac{1}{432 (1-x)^2}-\frac{1}{432 (x+1)^2}-\frac{1}{108 (2 x+1)^2}+\frac{3913}{648} \tanh ^{-1}(x)+\frac{67}{162} \tanh ^{-1}(2 x)-4 \sqrt{3} \tanh ^{-1}\left(\frac{2 x}{\sqrt{3}}\right)+\frac{5 \tanh ^{-1}\left(\frac{2 x}{\sqrt{3}}\right)}{6 \sqrt{3}}",1,"1/(108*(1 - 2*x)^2) - 7/(108*(1 - 2*x)) + 1/(432*(1 - x)^2) + 67/(432*(1 - x)) - 1/(432*(1 + x)^2) - 67/(432*(1 + x)) - 1/(108*(1 + 2*x)^2) + 7/(108*(1 + 2*x)) - (2*x)/(3*(3 - 4*x^2)^2) + (5*x)/(3*(3 - 4*x^2)) + (3913*ArcTanh[x])/648 + (67*ArcTanh[2*x])/162 + (5*ArcTanh[(2*x)/Sqrt[3]])/(6*Sqrt[3]) - 4*Sqrt[3]*ArcTanh[(2*x)/Sqrt[3]]","A",10,3,19,0.1579,1,"{2057, 207, 199}"
77,1,205,0,0.1300076,"\int \frac{1}{\left(-1+7 x^2-7 x^4+x^6\right)^2} \, dx","Int[(-1 + 7*x^2 - 7*x^4 + x^6)^(-2),x]","-\frac{41-17 x}{256 \left(-x^2+2 x+1\right)}+\frac{17 x+41}{256 \left(-x^2-2 x+1\right)}+\frac{1}{64 (1-x)}-\frac{1}{64 (x+1)}+\frac{1}{512} \left(2-7 \sqrt{2}\right) \log \left(-x-\sqrt{2}+1\right)+\frac{1}{512} \left(2+7 \sqrt{2}\right) \log \left(-x+\sqrt{2}+1\right)-\frac{1}{512} \left(2-7 \sqrt{2}\right) \log \left(x-\sqrt{2}+1\right)-\frac{1}{512} \left(2+7 \sqrt{2}\right) \log \left(x+\sqrt{2}+1\right)-\frac{17 \tanh ^{-1}\left(\frac{1-x}{\sqrt{2}}\right)}{256 \sqrt{2}}+\frac{5}{32} \tanh ^{-1}(x)+\frac{17 \tanh ^{-1}\left(\frac{x+1}{\sqrt{2}}\right)}{256 \sqrt{2}}","\frac{x}{32 \left(1-x^2\right)}+\frac{\left(99-17 x^2\right) x}{128 \left(x^4-6 x^2+1\right)}+\frac{5}{32} \tanh ^{-1}(x)+\frac{1}{512} \left(3 \sqrt{2}-4\right) \tanh ^{-1}\left(\left(\sqrt{2}-1\right) x\right)+\frac{1}{512} \left(4+3 \sqrt{2}\right) \tanh ^{-1}\left(\left(1+\sqrt{2}\right) x\right)",1,"1/(64*(1 - x)) - 1/(64*(1 + x)) + (41 + 17*x)/(256*(1 - 2*x - x^2)) - (41 - 17*x)/(256*(1 + 2*x - x^2)) - (17*ArcTanh[(1 - x)/Sqrt[2]])/(256*Sqrt[2]) + (5*ArcTanh[x])/32 + (17*ArcTanh[(1 + x)/Sqrt[2]])/(256*Sqrt[2]) + ((2 - 7*Sqrt[2])*Log[1 - Sqrt[2] - x])/512 + ((2 + 7*Sqrt[2])*Log[1 + Sqrt[2] - x])/512 - ((2 - 7*Sqrt[2])*Log[1 - Sqrt[2] + x])/512 - ((2 + 7*Sqrt[2])*Log[1 + Sqrt[2] + x])/512","B",15,7,17,0.4118,1,"{2057, 207, 638, 618, 206, 632, 31}"
78,1,78,0,0.0630097,"\int \frac{x^3}{c+(a+b x)^2} \, dx","Int[x^3/(c + (a + b*x)^2),x]","\frac{\left(3 a^2-c\right) \log \left((a+b x)^2+c\right)}{2 b^4}-\frac{a \left(a^2-3 c\right) \tan ^{-1}\left(\frac{a+b x}{\sqrt{c}}\right)}{b^4 \sqrt{c}}+\frac{(a+b x)^2}{2 b^4}-\frac{3 a x}{b^3}","\frac{\left(3 a^2-c\right) \log \left((a+b x)^2+c\right)}{2 b^4}-\frac{a \left(a^2-3 c\right) \tan ^{-1}\left(\frac{a+b x}{\sqrt{c}}\right)}{b^4 \sqrt{c}}+\frac{(a+b x)^2}{2 b^4}-\frac{3 a x}{b^3}",1,"(-3*a*x)/b^3 + (a + b*x)^2/(2*b^4) - (a*(a^2 - 3*c)*ArcTan[(a + b*x)/Sqrt[c]])/(b^4*Sqrt[c]) + ((3*a^2 - c)*Log[c + (a + b*x)^2])/(2*b^4)","A",6,5,15,0.3333,1,"{371, 702, 635, 203, 260}"
79,1,50,0,0.0387091,"\int \frac{x^2}{c+(a+b x)^2} \, dx","Int[x^2/(c + (a + b*x)^2),x]","\frac{\left(a^2-c\right) \tan ^{-1}\left(\frac{a+b x}{\sqrt{c}}\right)}{b^3 \sqrt{c}}-\frac{a \log \left((a+b x)^2+c\right)}{b^3}+\frac{x}{b^2}","\frac{\left(a^2-c\right) \tan ^{-1}\left(\frac{a+b x}{\sqrt{c}}\right)}{b^3 \sqrt{c}}-\frac{a \log \left((a+b x)^2+c\right)}{b^3}+\frac{x}{b^2}",1,"x/b^2 + ((a^2 - c)*ArcTan[(a + b*x)/Sqrt[c]])/(b^3*Sqrt[c]) - (a*Log[c + (a + b*x)^2])/b^3","A",6,5,15,0.3333,1,"{371, 702, 635, 203, 260}"
80,1,41,0,0.0212057,"\int \frac{x}{c+(a+b x)^2} \, dx","Int[x/(c + (a + b*x)^2),x]","\frac{\log \left((a+b x)^2+c\right)}{2 b^2}-\frac{a \tan ^{-1}\left(\frac{a+b x}{\sqrt{c}}\right)}{b^2 \sqrt{c}}","\frac{\log \left((a+b x)^2+c\right)}{2 b^2}-\frac{a \tan ^{-1}\left(\frac{a+b x}{\sqrt{c}}\right)}{b^2 \sqrt{c}}",1,"-((a*ArcTan[(a + b*x)/Sqrt[c]])/(b^2*Sqrt[c])) + Log[c + (a + b*x)^2]/(2*b^2)","A",4,4,13,0.3077,1,"{371, 635, 203, 260}"
81,1,21,0,0.0081073,"\int \frac{1}{c+(a+b x)^2} \, dx","Int[(c + (a + b*x)^2)^(-1),x]","\frac{\tan ^{-1}\left(\frac{a+b x}{\sqrt{c}}\right)}{b \sqrt{c}}","\frac{\tan ^{-1}\left(\frac{a+b x}{\sqrt{c}}\right)}{b \sqrt{c}}",1,"ArcTan[(a + b*x)/Sqrt[c]]/(b*Sqrt[c])","A",2,2,11,0.1818,1,"{247, 203}"
82,1,59,0,0.0351043,"\int \frac{1}{x \left(c+(a+b x)^2\right)} \, dx","Int[1/(x*(c + (a + b*x)^2)),x]","-\frac{\log \left((a+b x)^2+c\right)}{2 \left(a^2+c\right)}-\frac{a \tan ^{-1}\left(\frac{a+b x}{\sqrt{c}}\right)}{\sqrt{c} \left(a^2+c\right)}+\frac{\log (x)}{a^2+c}","-\frac{\log \left((a+b x)^2+c\right)}{2 \left(a^2+c\right)}-\frac{a \tan ^{-1}\left(\frac{a+b x}{\sqrt{c}}\right)}{\sqrt{c} \left(a^2+c\right)}+\frac{\log (x)}{a^2+c}",1,"-((a*ArcTan[(a + b*x)/Sqrt[c]])/(Sqrt[c]*(a^2 + c))) + Log[x]/(a^2 + c) - Log[c + (a + b*x)^2]/(2*(a^2 + c))","A",6,6,15,0.4000,1,"{371, 706, 31, 635, 203, 260}"
83,1,79,0,0.0861113,"\int \frac{1}{x^2 \left(c+(a+b x)^2\right)} \, dx","Int[1/(x^2*(c + (a + b*x)^2)),x]","-\frac{2 a b \log (x)}{\left(a^2+c\right)^2}+\frac{a b \log \left((a+b x)^2+c\right)}{\left(a^2+c\right)^2}+\frac{b \left(a^2-c\right) \tan ^{-1}\left(\frac{a+b x}{\sqrt{c}}\right)}{\sqrt{c} \left(a^2+c\right)^2}-\frac{1}{x \left(a^2+c\right)}","-\frac{2 a b \log (x)}{\left(a^2+c\right)^2}+\frac{a b \log \left((a+b x)^2+c\right)}{\left(a^2+c\right)^2}+\frac{b \left(a^2-c\right) \tan ^{-1}\left(\frac{a+b x}{\sqrt{c}}\right)}{\sqrt{c} \left(a^2+c\right)^2}-\frac{1}{x \left(a^2+c\right)}",1,"-(1/((a^2 + c)*x)) + (b*(a^2 - c)*ArcTan[(a + b*x)/Sqrt[c]])/(Sqrt[c]*(a^2 + c)^2) - (2*a*b*Log[x])/(a^2 + c)^2 + (a*b*Log[c + (a + b*x)^2])/(a^2 + c)^2","A",7,6,15,0.4000,1,"{371, 710, 801, 635, 203, 260}"
84,1,121,0,0.1253463,"\int \frac{1}{x^3 \left(c+(a+b x)^2\right)} \, dx","Int[1/(x^3*(c + (a + b*x)^2)),x]","\frac{b^2 \left(3 a^2-c\right) \log (x)}{\left(a^2+c\right)^3}-\frac{b^2 \left(3 a^2-c\right) \log \left((a+b x)^2+c\right)}{2 \left(a^2+c\right)^3}-\frac{a b^2 \left(a^2-3 c\right) \tan ^{-1}\left(\frac{a+b x}{\sqrt{c}}\right)}{\sqrt{c} \left(a^2+c\right)^3}+\frac{2 a b}{x \left(a^2+c\right)^2}-\frac{1}{2 x^2 \left(a^2+c\right)}","\frac{b^2 \left(3 a^2-c\right) \log (x)}{\left(a^2+c\right)^3}-\frac{b^2 \left(3 a^2-c\right) \log \left((a+b x)^2+c\right)}{2 \left(a^2+c\right)^3}-\frac{a b^2 \left(a^2-3 c\right) \tan ^{-1}\left(\frac{a+b x}{\sqrt{c}}\right)}{\sqrt{c} \left(a^2+c\right)^3}+\frac{2 a b}{x \left(a^2+c\right)^2}-\frac{1}{2 x^2 \left(a^2+c\right)}",1,"-1/(2*(a^2 + c)*x^2) + (2*a*b)/((a^2 + c)^2*x) - (a*b^2*(a^2 - 3*c)*ArcTan[(a + b*x)/Sqrt[c]])/(Sqrt[c]*(a^2 + c)^3) + (b^2*(3*a^2 - c)*Log[x])/(a^2 + c)^3 - (b^2*(3*a^2 - c)*Log[c + (a + b*x)^2])/(2*(a^2 + c)^3)","A",7,6,15,0.4000,1,"{371, 710, 801, 635, 203, 260}"
85,1,31,0,0.0235124,"\int \frac{1}{a+b (c+d x)^2} \, dx","Int[(a + b*(c + d*x)^2)^(-1),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{b} (c+d x)}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b} d}","\frac{\tan ^{-1}\left(\frac{\sqrt{b} (c+d x)}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b} d}",1,"ArcTan[(Sqrt[b]*(c + d*x))/Sqrt[a]]/(Sqrt[a]*Sqrt[b]*d)","A",2,2,13,0.1538,1,"{247, 205}"
86,1,63,0,0.0329842,"\int \frac{1}{\left(a+b (c+d x)^2\right)^2} \, dx","Int[(a + b*(c + d*x)^2)^(-2),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{b} (c+d x)}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b} d}+\frac{c+d x}{2 a d \left(a+b (c+d x)^2\right)}","\frac{\tan ^{-1}\left(\frac{\sqrt{b} (c+d x)}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b} d}+\frac{c+d x}{2 a d \left(a+b (c+d x)^2\right)}",1,"(c + d*x)/(2*a*d*(a + b*(c + d*x)^2)) + ArcTan[(Sqrt[b]*(c + d*x))/Sqrt[a]]/(2*a^(3/2)*Sqrt[b]*d)","A",3,3,13,0.2308,1,"{247, 199, 205}"
87,1,91,0,0.0482007,"\int \frac{1}{\left(a+b (c+d x)^2\right)^3} \, dx","Int[(a + b*(c + d*x)^2)^(-3),x]","\frac{3 (c+d x)}{8 a^2 d \left(a+b (c+d x)^2\right)}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{b} (c+d x)}{\sqrt{a}}\right)}{8 a^{5/2} \sqrt{b} d}+\frac{c+d x}{4 a d \left(a+b (c+d x)^2\right)^2}","\frac{3 (c+d x)}{8 a^2 d \left(a+b (c+d x)^2\right)}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{b} (c+d x)}{\sqrt{a}}\right)}{8 a^{5/2} \sqrt{b} d}+\frac{c+d x}{4 a d \left(a+b (c+d x)^2\right)^2}",1,"(c + d*x)/(4*a*d*(a + b*(c + d*x)^2)^2) + (3*(c + d*x))/(8*a^2*d*(a + b*(c + d*x)^2)) + (3*ArcTan[(Sqrt[b]*(c + d*x))/Sqrt[a]])/(8*a^(5/2)*Sqrt[b]*d)","A",4,3,13,0.2308,1,"{247, 199, 205}"
88,1,35,0,0.0353452,"\int \frac{1}{\sqrt{-a}+b (c+d x)^2} \, dx","Int[(Sqrt[-a] + b*(c + d*x)^2)^(-1),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{b} (c+d x)}{\sqrt[4]{-a}}\right)}{\sqrt[4]{-a} \sqrt{b} d}","\frac{\tan ^{-1}\left(\frac{\sqrt{b} (c+d x)}{\sqrt[4]{-a}}\right)}{\sqrt[4]{-a} \sqrt{b} d}",1,"ArcTan[(Sqrt[b]*(c + d*x))/(-a)^(1/4)]/((-a)^(1/4)*Sqrt[b]*d)","A",2,2,19,0.1053,1,"{247, 205}"
89,1,10,0,0.002813,"\int \frac{1}{1+(c+d x)^2} \, dx","Int[(1 + (c + d*x)^2)^(-1),x]","\frac{\tan ^{-1}(c+d x)}{d}","\frac{\tan ^{-1}(c+d x)}{d}",1,"ArcTan[c + d*x]/d","A",2,2,11,0.1818,1,"{247, 203}"
90,1,37,0,0.0095384,"\int \frac{1}{\left(1+(c+d x)^2\right)^2} \, dx","Int[(1 + (c + d*x)^2)^(-2),x]","\frac{c+d x}{2 d \left((c+d x)^2+1\right)}+\frac{\tan ^{-1}(c+d x)}{2 d}","\frac{c+d x}{2 d \left((c+d x)^2+1\right)}+\frac{\tan ^{-1}(c+d x)}{2 d}",1,"(c + d*x)/(2*d*(1 + (c + d*x)^2)) + ArcTan[c + d*x]/(2*d)","A",3,3,11,0.2727,1,"{247, 199, 203}"
91,1,60,0,0.0163135,"\int \frac{1}{\left(1+(c+d x)^2\right)^3} \, dx","Int[(1 + (c + d*x)^2)^(-3),x]","\frac{3 (c+d x)}{8 d \left((c+d x)^2+1\right)}+\frac{c+d x}{4 d \left((c+d x)^2+1\right)^2}+\frac{3 \tan ^{-1}(c+d x)}{8 d}","\frac{3 (c+d x)}{8 d \left((c+d x)^2+1\right)}+\frac{c+d x}{4 d \left((c+d x)^2+1\right)^2}+\frac{3 \tan ^{-1}(c+d x)}{8 d}",1,"(c + d*x)/(4*d*(1 + (c + d*x)^2)^2) + (3*(c + d*x))/(8*d*(1 + (c + d*x)^2)) + (3*ArcTan[c + d*x])/(8*d)","A",4,3,11,0.2727,1,"{247, 199, 203}"
92,1,10,0,0.0029759,"\int \frac{1}{1-(c+d x)^2} \, dx","Int[(1 - (c + d*x)^2)^(-1),x]","\frac{\tanh ^{-1}(c+d x)}{d}","\frac{\tanh ^{-1}(c+d x)}{d}",1,"ArcTanh[c + d*x]/d","A",2,2,13,0.1538,1,"{247, 206}"
93,1,39,0,0.0126135,"\int \frac{1}{\left(1-(c+d x)^2\right)^2} \, dx","Int[(1 - (c + d*x)^2)^(-2),x]","\frac{c+d x}{2 d \left(1-(c+d x)^2\right)}+\frac{\tanh ^{-1}(c+d x)}{2 d}","\frac{c+d x}{2 d \left(1-(c+d x)^2\right)}+\frac{\tanh ^{-1}(c+d x)}{2 d}",1,"(c + d*x)/(2*d*(1 - (c + d*x)^2)) + ArcTanh[c + d*x]/(2*d)","A",3,3,13,0.2308,1,"{247, 199, 206}"
94,1,64,0,0.0223646,"\int \frac{1}{\left(1-(c+d x)^2\right)^3} \, dx","Int[(1 - (c + d*x)^2)^(-3),x]","\frac{3 (c+d x)}{8 d \left(1-(c+d x)^2\right)}+\frac{c+d x}{4 d \left(1-(c+d x)^2\right)^2}+\frac{3 \tanh ^{-1}(c+d x)}{8 d}","\frac{3 (c+d x)}{8 d \left(1-(c+d x)^2\right)}+\frac{c+d x}{4 d \left(1-(c+d x)^2\right)^2}+\frac{3 \tanh ^{-1}(c+d x)}{8 d}",1,"(c + d*x)/(4*d*(1 - (c + d*x)^2)^2) + (3*(c + d*x))/(8*d*(1 - (c + d*x)^2)) + (3*ArcTanh[c + d*x])/(8*d)","A",4,3,13,0.2308,1,"{247, 199, 206}"
95,1,4,0,0.0018798,"\int \frac{1}{1-(1+x)^2} \, dx","Int[(1 - (1 + x)^2)^(-1),x]","\tanh ^{-1}(x+1)","\tanh ^{-1}(x+1)",1,"ArcTanh[1 + x]","A",2,2,11,0.1818,1,"{247, 206}"
96,1,27,0,0.0072031,"\int \frac{1}{\left(1-(1+x)^2\right)^2} \, dx","Int[(1 - (1 + x)^2)^(-2),x]","\frac{x+1}{2 \left(1-(x+1)^2\right)}+\frac{1}{2} \tanh ^{-1}(x+1)","\frac{x+1}{2 \left(1-(x+1)^2\right)}+\frac{1}{2} \tanh ^{-1}(x+1)",1,"(1 + x)/(2*(1 - (1 + x)^2)) + ArcTanh[1 + x]/2","A",3,3,11,0.2727,1,"{247, 199, 206}"
97,1,45,0,0.0122762,"\int \frac{1}{\left(1-(1+x)^2\right)^3} \, dx","Int[(1 - (1 + x)^2)^(-3),x]","\frac{3 (x+1)}{8 \left(1-(x+1)^2\right)}+\frac{x+1}{4 \left(1-(x+1)^2\right)^2}+\frac{3}{8} \tanh ^{-1}(x+1)","\frac{3 (x+1)}{8 \left(1-(x+1)^2\right)}+\frac{x+1}{4 \left(1-(x+1)^2\right)^2}+\frac{3}{8} \tanh ^{-1}(x+1)",1,"(1 + x)/(4*(1 - (1 + x)^2)^2) + (3*(1 + x))/(8*(1 - (1 + x)^2)) + (3*ArcTanh[1 + x])/8","A",4,3,11,0.2727,1,"{247, 199, 206}"
98,1,59,0,0.0553684,"\int \frac{\left(1+(a+b x)^2\right)^2}{x} \, dx","Int[(1 + (a + b*x)^2)^2/x,x]","\frac{1}{2} \left(a^2+2\right) (a+b x)^2+a \left(a^2+2\right) b x+\left(a^2+1\right)^2 \log (x)+\frac{1}{4} (a+b x)^4+\frac{1}{3} a (a+b x)^3","\frac{1}{2} \left(a^2+2\right) (a+b x)^2+a \left(a^2+2\right) b x+\left(a^2+1\right)^2 \log (x)+\frac{1}{4} (a+b x)^4+\frac{1}{3} a (a+b x)^3",1,"a*(2 + a^2)*b*x + ((2 + a^2)*(a + b*x)^2)/2 + (a*(a + b*x)^3)/3 + (a + b*x)^4/4 + (1 + a^2)^2*Log[x]","A",3,2,15,0.1333,1,"{371, 697}"
99,1,10,0,0.0112678,"\int \frac{x^2}{1+(-1+x)^2} \, dx","Int[x^2/(1 + (-1 + x)^2),x]","x+\log \left((x-1)^2+1\right)","x+\log \left((x-1)^2+1\right)",1,"x + Log[1 + (-1 + x)^2]","A",4,3,13,0.2308,1,"{371, 702, 260}"
100,1,44,0,0.0258208,"\int \frac{x^2}{\sqrt{1-(1+x)^2}} \, dx","Int[x^2/Sqrt[1 - (1 + x)^2],x]","-\frac{1}{2} \sqrt{1-(x+1)^2} x+\frac{3}{2} \sqrt{1-(x+1)^2}+\frac{3}{2} \sin ^{-1}(x+1)","-\frac{1}{2} \sqrt{1-(x+1)^2} x+\frac{3}{2} \sqrt{1-(x+1)^2}+\frac{3}{2} \sin ^{-1}(x+1)",1,"(3*Sqrt[1 - (1 + x)^2])/2 - (x*Sqrt[1 - (1 + x)^2])/2 + (3*ArcSin[1 + x])/2","A",4,4,17,0.2353,1,"{371, 671, 641, 216}"
101,1,67,0,0.0485348,"\int \frac{x^2}{\sqrt{1-(a+b x)^2}} \, dx","Int[x^2/Sqrt[1 - (a + b*x)^2],x]","\frac{\left(2 a^2+1\right) \sin ^{-1}(a+b x)}{2 b^3}+\frac{3 a \sqrt{1-(a+b x)^2}}{2 b^3}-\frac{x \sqrt{1-(a+b x)^2}}{2 b^2}","\frac{\left(2 a^2+1\right) \sin ^{-1}(a+b x)}{2 b^3}+\frac{3 a \sqrt{1-(a+b x)^2}}{2 b^3}-\frac{x \sqrt{1-(a+b x)^2}}{2 b^2}",1,"(3*a*Sqrt[1 - (a + b*x)^2])/(2*b^3) - (x*Sqrt[1 - (a + b*x)^2])/(2*b^2) + ((1 + 2*a^2)*ArcSin[a + b*x])/(2*b^3)","A",4,4,19,0.2105,1,"{371, 743, 641, 216}"
102,1,63,0,0.0404596,"\int \frac{x^2}{\sqrt{1+(a+b x)^2}} \, dx","Int[x^2/Sqrt[1 + (a + b*x)^2],x]","-\frac{\left(1-2 a^2\right) \sinh ^{-1}(a+b x)}{2 b^3}-\frac{3 a \sqrt{(a+b x)^2+1}}{2 b^3}+\frac{x \sqrt{(a+b x)^2+1}}{2 b^2}","-\frac{\left(1-2 a^2\right) \sinh ^{-1}(a+b x)}{2 b^3}-\frac{3 a \sqrt{(a+b x)^2+1}}{2 b^3}+\frac{x \sqrt{(a+b x)^2+1}}{2 b^2}",1,"(-3*a*Sqrt[1 + (a + b*x)^2])/(2*b^3) + (x*Sqrt[1 + (a + b*x)^2])/(2*b^2) - ((1 - 2*a^2)*ArcSinh[a + b*x])/(2*b^3)","A",4,4,17,0.2353,1,"{371, 743, 641, 215}"
103,1,234,0,0.3716342,"\int \frac{x^3}{a+b (c+d x)^3} \, dx","Int[x^3/(a + b*(c + d*x)^3),x]","-\frac{\left(3 \sqrt[3]{a} b^{2/3} c^2+a+b c^3\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{3 a^{2/3} b^{4/3} d^4}+\frac{\left(3 \sqrt[3]{a} b^{2/3} c^2+a+b c^3\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{6 a^{2/3} b^{4/3} d^4}+\frac{\left(-3 \sqrt[3]{a} b^{2/3} c^2+a+b c^3\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} b^{4/3} d^4}-\frac{c \log \left(a+b (c+d x)^3\right)}{b d^4}+\frac{x}{b d^3}","-\frac{\left(3 \sqrt[3]{a} b^{2/3} c^2+a+b c^3\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{3 a^{2/3} b^{4/3} d^4}+\frac{\left(3 \sqrt[3]{a} b^{2/3} c^2+a+b c^3\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{6 a^{2/3} b^{4/3} d^4}+\frac{\left(-3 \sqrt[3]{a} b^{2/3} c^2+a+b c^3\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} b^{4/3} d^4}-\frac{c \log \left(a+b (c+d x)^3\right)}{b d^4}+\frac{x}{b d^3}",1,"x/(b*d^3) + ((a - 3*a^(1/3)*b^(2/3)*c^2 + b*c^3)*ArcTan[(a^(1/3) - 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(2/3)*b^(4/3)*d^4) - ((a + 3*a^(1/3)*b^(2/3)*c^2 + b*c^3)*Log[a^(1/3) + b^(1/3)*(c + d*x)])/(3*a^(2/3)*b^(4/3)*d^4) + ((a + 3*a^(1/3)*b^(2/3)*c^2 + b*c^3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2])/(6*a^(2/3)*b^(4/3)*d^4) - (c*Log[a + b*(c + d*x)^3])/(b*d^4)","A",11,10,17,0.5882,1,"{371, 1887, 1871, 1860, 31, 634, 617, 204, 628, 260}"
104,1,210,0,0.2281649,"\int \frac{x^2}{a+b (c+d x)^3} \, dx","Int[x^2/(a + b*(c + d*x)^3),x]","\frac{c \left(2 \sqrt[3]{a}+\sqrt[3]{b} c\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{3 a^{2/3} b^{2/3} d^3}-\frac{c \left(2 \sqrt[3]{a}+\sqrt[3]{b} c\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{6 a^{2/3} b^{2/3} d^3}+\frac{c \left(2 \sqrt[3]{a}-\sqrt[3]{b} c\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} b^{2/3} d^3}+\frac{\log \left(a+b (c+d x)^3\right)}{3 b d^3}","\frac{c \left(2 \sqrt[3]{a}+\sqrt[3]{b} c\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{3 a^{2/3} b^{2/3} d^3}-\frac{c \left(2 \sqrt[3]{a}+\sqrt[3]{b} c\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{6 a^{2/3} b^{2/3} d^3}+\frac{c \left(2 \sqrt[3]{a}-\sqrt[3]{b} c\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} b^{2/3} d^3}+\frac{\log \left(a+b (c+d x)^3\right)}{3 b d^3}",1,"(c*(2*a^(1/3) - b^(1/3)*c)*ArcTan[(a^(1/3) - 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(2/3)*b^(2/3)*d^3) + (c*(2*a^(1/3) + b^(1/3)*c)*Log[a^(1/3) + b^(1/3)*(c + d*x)])/(3*a^(2/3)*b^(2/3)*d^3) - (c*(2*a^(1/3) + b^(1/3)*c)*Log[a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2])/(6*a^(2/3)*b^(2/3)*d^3) + Log[a + b*(c + d*x)^3]/(3*b*d^3)","A",9,9,17,0.5294,1,"{371, 1871, 1860, 31, 634, 617, 204, 628, 260}"
105,1,180,0,0.1562574,"\int \frac{x}{a+b (c+d x)^3} \, dx","Int[x/(a + b*(c + d*x)^3),x]","-\frac{\left(\sqrt[3]{a}+\sqrt[3]{b} c\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{3 a^{2/3} b^{2/3} d^2}+\frac{\left(\sqrt[3]{a}+\sqrt[3]{b} c\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{6 a^{2/3} b^{2/3} d^2}-\frac{\left(\sqrt[3]{a}-\sqrt[3]{b} c\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} b^{2/3} d^2}","-\frac{\left(\sqrt[3]{a}+\sqrt[3]{b} c\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{3 a^{2/3} b^{2/3} d^2}+\frac{\left(\sqrt[3]{a}+\sqrt[3]{b} c\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{6 a^{2/3} b^{2/3} d^2}-\frac{\left(\sqrt[3]{a}-\sqrt[3]{b} c\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} b^{2/3} d^2}",1,"-(((a^(1/3) - b^(1/3)*c)*ArcTan[(a^(1/3) - 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(2/3)*b^(2/3)*d^2)) - ((a^(1/3) + b^(1/3)*c)*Log[a^(1/3) + b^(1/3)*(c + d*x)])/(3*a^(2/3)*b^(2/3)*d^2) + ((a^(1/3) + b^(1/3)*c)*Log[a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2])/(6*a^(2/3)*b^(2/3)*d^2)","A",7,7,15,0.4667,1,"{371, 1860, 31, 634, 617, 204, 628}"
106,1,140,0,0.1072311,"\int \frac{1}{a+b (c+d x)^3} \, dx","Int[(a + b*(c + d*x)^3)^(-1),x]","-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{6 a^{2/3} \sqrt[3]{b} d}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{3 a^{2/3} \sqrt[3]{b} d}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} \sqrt[3]{b} d}","-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{6 a^{2/3} \sqrt[3]{b} d}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{3 a^{2/3} \sqrt[3]{b} d}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} \sqrt[3]{b} d}",1,"-(ArcTan[(a^(1/3) - 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))]/(Sqrt[3]*a^(2/3)*b^(1/3)*d)) + Log[a^(1/3) + b^(1/3)*(c + d*x)]/(3*a^(2/3)*b^(1/3)*d) - Log[a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2]/(6*a^(2/3)*b^(1/3)*d)","A",7,7,13,0.5385,1,"{247, 200, 31, 634, 617, 204, 628}"
107,1,238,0,0.4817974,"\int \frac{1}{x \left(a+b (c+d x)^3\right)} \, dx","Int[1/(x*(a + b*(c + d*x)^3)),x]","-\frac{\sqrt[3]{b} c \left(\sqrt[3]{a}-\sqrt[3]{b} c\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{6 a^{2/3} \left(a+b c^3\right)}+\frac{\sqrt[3]{b} c \left(\sqrt[3]{a}-\sqrt[3]{b} c\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{3 a^{2/3} \left(a+b c^3\right)}+\frac{\sqrt[3]{b} c \left(\sqrt[3]{a}+\sqrt[3]{b} c\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} \left(a+b c^3\right)}-\frac{\log \left(a+b (c+d x)^3\right)}{3 \left(a+b c^3\right)}+\frac{\log (x)}{a+b c^3}","-\frac{\left(2 \sqrt[3]{a}-\sqrt[3]{b} c\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{6 a^{2/3} \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} c+b^{2/3} c^2\right)}+\frac{\sqrt[3]{b} c \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} c+b^{2/3} c^2\right)}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{3 a^{2/3} \left(\sqrt[3]{a}+\sqrt[3]{b} c\right)}+\frac{\log (x)}{a+b c^3}",1,"(b^(1/3)*c*(a^(1/3) + b^(1/3)*c)*ArcTan[(a^(1/3) - 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(2/3)*(a + b*c^3)) + Log[x]/(a + b*c^3) + (b^(1/3)*c*(a^(1/3) - b^(1/3)*c)*Log[a^(1/3) + b^(1/3)*(c + d*x)])/(3*a^(2/3)*(a + b*c^3)) - (b^(1/3)*c*(a^(1/3) - b^(1/3)*c)*Log[a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2])/(6*a^(2/3)*(a + b*c^3)) - Log[a + b*(c + d*x)^3]/(3*(a + b*c^3))","A",11,10,17,0.5882,1,"{371, 6725, 1871, 1860, 31, 634, 617, 204, 628, 260}"
108,1,312,0,0.5447474,"\int \frac{1}{x^2 \left(a+b (c+d x)^3\right)} \, dx","Int[1/(x^2*(a + b*(c + d*x)^3)),x]","\frac{b^{2/3} d \left(-\frac{\sqrt[3]{a} \left(a-2 b c^3\right)}{\sqrt[3]{b}}+2 a c-b c^4\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{6 a^{2/3} \left(a+b c^3\right)^2}+\frac{\sqrt[3]{b} d \left(\sqrt[3]{a} \left(a-2 b c^3\right)-\sqrt[3]{b} c \left(2 a-b c^3\right)\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{3 a^{2/3} \left(a+b c^3\right)^2}+\frac{\sqrt[3]{b} d \left(\sqrt[3]{a}-\sqrt[3]{b} c\right) \left(\sqrt[3]{a}+\sqrt[3]{b} c\right)^3 \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} \left(a+b c^3\right)^2}-\frac{3 b c^2 d \log (x)}{\left(a+b c^3\right)^2}+\frac{b c^2 d \log \left(a+b (c+d x)^3\right)}{\left(a+b c^3\right)^2}-\frac{1}{x \left(a+b c^3\right)}","-\frac{\sqrt[3]{b} d \left(\sqrt[3]{a} \left(a-2 b c^3\right)-\sqrt[3]{b} c \left(2 a-b c^3\right)\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{6 a^{2/3} \left(a+b c^3\right)^2}+\frac{\sqrt[3]{b} d \left(\sqrt[3]{a} \left(a-2 b c^3\right)-\sqrt[3]{b} c \left(2 a-b c^3\right)\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{3 a^{2/3} \left(a+b c^3\right)^2}+\frac{\sqrt[3]{b} d \left(\sqrt[3]{a}-\sqrt[3]{b} c\right) \left(\sqrt[3]{a}+\sqrt[3]{b} c\right)^3 \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} \left(a+b c^3\right)^2}-\frac{3 b c^2 d \log (x)}{\left(a+b c^3\right)^2}+\frac{b c^2 d \log \left(a+b (c+d x)^3\right)}{\left(a+b c^3\right)^2}-\frac{1}{x \left(a+b c^3\right)}",1,"-(1/((a + b*c^3)*x)) + (b^(1/3)*(a^(1/3) - b^(1/3)*c)*(a^(1/3) + b^(1/3)*c)^3*d*ArcTan[(a^(1/3) - 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(2/3)*(a + b*c^3)^2) - (3*b*c^2*d*Log[x])/(a + b*c^3)^2 + (b^(1/3)*(a^(1/3)*(a - 2*b*c^3) - b^(1/3)*c*(2*a - b*c^3))*d*Log[a^(1/3) + b^(1/3)*(c + d*x)])/(3*a^(2/3)*(a + b*c^3)^2) + (b^(2/3)*(2*a*c - b*c^4 - (a^(1/3)*(a - 2*b*c^3))/b^(1/3))*d*Log[a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2])/(6*a^(2/3)*(a + b*c^3)^2) + (b*c^2*d*Log[a + b*(c + d*x)^3])/(a + b*c^3)^2","A",11,10,17,0.5882,1,"{371, 6725, 1871, 1860, 31, 634, 617, 204, 628, 260}"
109,1,393,0,0.6039578,"\int \frac{1}{x^3 \left(a+b (c+d x)^3\right)} \, dx","Int[1/(x^3*(a + b*(c + d*x)^3)),x]","-\frac{b^{2/3} d^2 \left(6 a^{4/3} b^{2/3} c^2+a^2-3 \sqrt[3]{a} b^{5/3} c^5-7 a b c^3+b^2 c^6\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{3 a^{2/3} \left(a+b c^3\right)^3}+\frac{b^{2/3} d^2 \left(6 a^{4/3} b^{2/3} c^2+a^2-3 \sqrt[3]{a} b^{5/3} c^5-7 a b c^3+b^2 c^6\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{6 a^{2/3} \left(a+b c^3\right)^3}+\frac{b^{2/3} d^2 \left(-3 a^{2/3} \sqrt[3]{b} c+a+b c^3\right) \left(\sqrt[3]{a}+\sqrt[3]{b} c\right)^3 \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} \left(a+b c^3\right)^3}-\frac{3 b c d^2 \log (x) \left(a-2 b c^3\right)}{\left(a+b c^3\right)^3}+\frac{b c d^2 \left(a-2 b c^3\right) \log \left(a+b (c+d x)^3\right)}{\left(a+b c^3\right)^3}+\frac{3 b c^2 d}{x \left(a+b c^3\right)^2}-\frac{1}{2 x^2 \left(a+b c^3\right)}","-\frac{b^{2/3} d^2 \left(6 a^{4/3} b^{2/3} c^2+a^2-3 \sqrt[3]{a} b^{5/3} c^5-7 a b c^3+b^2 c^6\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{3 a^{2/3} \left(a+b c^3\right)^3}+\frac{b^{2/3} d^2 \left(6 a^{4/3} b^{2/3} c^2+a^2-3 \sqrt[3]{a} b^{5/3} c^5-7 a b c^3+b^2 c^6\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{6 a^{2/3} \left(a+b c^3\right)^3}+\frac{b^{2/3} d^2 \left(-3 a^{2/3} \sqrt[3]{b} c+a+b c^3\right) \left(\sqrt[3]{a}+\sqrt[3]{b} c\right)^3 \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} \left(a+b c^3\right)^3}-\frac{3 b c d^2 \log (x) \left(a-2 b c^3\right)}{\left(a+b c^3\right)^3}+\frac{b c d^2 \left(a-2 b c^3\right) \log \left(a+b (c+d x)^3\right)}{\left(a+b c^3\right)^3}+\frac{3 b c^2 d}{x \left(a+b c^3\right)^2}-\frac{1}{2 x^2 \left(a+b c^3\right)}",1,"-1/(2*(a + b*c^3)*x^2) + (3*b*c^2*d)/((a + b*c^3)^2*x) + (b^(2/3)*(a^(1/3) + b^(1/3)*c)^3*(a - 3*a^(2/3)*b^(1/3)*c + b*c^3)*d^2*ArcTan[(a^(1/3) - 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(2/3)*(a + b*c^3)^3) - (3*b*c*(a - 2*b*c^3)*d^2*Log[x])/(a + b*c^3)^3 - (b^(2/3)*(a^2 + 6*a^(4/3)*b^(2/3)*c^2 - 7*a*b*c^3 - 3*a^(1/3)*b^(5/3)*c^5 + b^2*c^6)*d^2*Log[a^(1/3) + b^(1/3)*(c + d*x)])/(3*a^(2/3)*(a + b*c^3)^3) + (b^(2/3)*(a^2 + 6*a^(4/3)*b^(2/3)*c^2 - 7*a*b*c^3 - 3*a^(1/3)*b^(5/3)*c^5 + b^2*c^6)*d^2*Log[a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2])/(6*a^(2/3)*(a + b*c^3)^3) + (b*c*(a - 2*b*c^3)*d^2*Log[a + b*(c + d*x)^3])/(a + b*c^3)^3","A",11,10,17,0.5882,1,"{371, 6725, 1871, 1860, 31, 634, 617, 204, 628, 260}"
110,1,356,0,0.4256317,"\int \frac{x^3}{a+b (c+d x)^4} \, dx","Int[x^3/(a + b*(c + d*x)^4),x]","-\frac{c \left(3 \sqrt{a}-\sqrt{b} c^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} (c+d x)+\sqrt{a}+\sqrt{b} (c+d x)^2\right)}{4 \sqrt{2} a^{3/4} b^{3/4} d^4}+\frac{c \left(3 \sqrt{a}-\sqrt{b} c^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} (c+d x)+\sqrt{a}+\sqrt{b} (c+d x)^2\right)}{4 \sqrt{2} a^{3/4} b^{3/4} d^4}+\frac{c \left(3 \sqrt{a}+\sqrt{b} c^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} (c+d x)}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} b^{3/4} d^4}-\frac{c \left(3 \sqrt{a}+\sqrt{b} c^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} (c+d x)}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} b^{3/4} d^4}+\frac{3 c^2 \tan ^{-1}\left(\frac{\sqrt{b} (c+d x)^2}{\sqrt{a}}\right)}{2 \sqrt{a} \sqrt{b} d^4}+\frac{\log \left(a+b (c+d x)^4\right)}{4 b d^4}","-\frac{c \left(3 \sqrt{a}-\sqrt{b} c^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} (c+d x)+\sqrt{a}+\sqrt{b} (c+d x)^2\right)}{4 \sqrt{2} a^{3/4} b^{3/4} d^4}+\frac{c \left(3 \sqrt{a}-\sqrt{b} c^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} (c+d x)+\sqrt{a}+\sqrt{b} (c+d x)^2\right)}{4 \sqrt{2} a^{3/4} b^{3/4} d^4}+\frac{c \left(3 \sqrt{a}+\sqrt{b} c^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} (c+d x)}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} b^{3/4} d^4}-\frac{c \left(3 \sqrt{a}+\sqrt{b} c^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} (c+d x)}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} b^{3/4} d^4}+\frac{3 c^2 \tan ^{-1}\left(\frac{\sqrt{b} (c+d x)^2}{\sqrt{a}}\right)}{2 \sqrt{a} \sqrt{b} d^4}+\frac{\log \left(a+b (c+d x)^4\right)}{4 b d^4}",1,"(3*c^2*ArcTan[(Sqrt[b]*(c + d*x)^2)/Sqrt[a]])/(2*Sqrt[a]*Sqrt[b]*d^4) + (c*(3*Sqrt[a] + Sqrt[b]*c^2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*(c + d*x))/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*b^(3/4)*d^4) - (c*(3*Sqrt[a] + Sqrt[b]*c^2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*(c + d*x))/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*b^(3/4)*d^4) - (c*(3*Sqrt[a] - Sqrt[b]*c^2)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*(c + d*x) + Sqrt[b]*(c + d*x)^2])/(4*Sqrt[2]*a^(3/4)*b^(3/4)*d^4) + (c*(3*Sqrt[a] - Sqrt[b]*c^2)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*(c + d*x) + Sqrt[b]*(c + d*x)^2])/(4*Sqrt[2]*a^(3/4)*b^(3/4)*d^4) + Log[a + b*(c + d*x)^4]/(4*b*d^4)","A",16,12,17,0.7059,1,"{371, 1876, 1248, 635, 205, 260, 1168, 1162, 617, 204, 1165, 628}"
111,1,318,0,0.3124805,"\int \frac{x^2}{a+b (c+d x)^4} \, dx","Int[x^2/(a + b*(c + d*x)^4),x]","\frac{\left(\sqrt{a}-\sqrt{b} c^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} (c+d x)+\sqrt{a}+\sqrt{b} (c+d x)^2\right)}{4 \sqrt{2} a^{3/4} b^{3/4} d^3}-\frac{\left(\sqrt{a}-\sqrt{b} c^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} (c+d x)+\sqrt{a}+\sqrt{b} (c+d x)^2\right)}{4 \sqrt{2} a^{3/4} b^{3/4} d^3}-\frac{\left(\sqrt{a}+\sqrt{b} c^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} (c+d x)}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} b^{3/4} d^3}+\frac{\left(\sqrt{a}+\sqrt{b} c^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} (c+d x)}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} b^{3/4} d^3}-\frac{c \tan ^{-1}\left(\frac{\sqrt{b} (c+d x)^2}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b} d^3}","\frac{\left(\sqrt{a}-\sqrt{b} c^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} (c+d x)+\sqrt{a}+\sqrt{b} (c+d x)^2\right)}{4 \sqrt{2} a^{3/4} b^{3/4} d^3}-\frac{\left(\sqrt{a}-\sqrt{b} c^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} (c+d x)+\sqrt{a}+\sqrt{b} (c+d x)^2\right)}{4 \sqrt{2} a^{3/4} b^{3/4} d^3}-\frac{\left(\sqrt{a}+\sqrt{b} c^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} (c+d x)}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} b^{3/4} d^3}+\frac{\left(\sqrt{a}+\sqrt{b} c^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} (c+d x)}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} b^{3/4} d^3}-\frac{c \tan ^{-1}\left(\frac{\sqrt{b} (c+d x)^2}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b} d^3}",1,"-((c*ArcTan[(Sqrt[b]*(c + d*x)^2)/Sqrt[a]])/(Sqrt[a]*Sqrt[b]*d^3)) - ((Sqrt[a] + Sqrt[b]*c^2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*(c + d*x))/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*b^(3/4)*d^3) + ((Sqrt[a] + Sqrt[b]*c^2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*(c + d*x))/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*b^(3/4)*d^3) + ((Sqrt[a] - Sqrt[b]*c^2)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*(c + d*x) + Sqrt[b]*(c + d*x)^2])/(4*Sqrt[2]*a^(3/4)*b^(3/4)*d^3) - ((Sqrt[a] - Sqrt[b]*c^2)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*(c + d*x) + Sqrt[b]*(c + d*x)^2])/(4*Sqrt[2]*a^(3/4)*b^(3/4)*d^3)","A",14,10,17,0.5882,1,"{371, 1876, 275, 205, 1168, 1162, 617, 204, 1165, 628}"
112,1,261,0,0.2637202,"\int \frac{x}{a+b (c+d x)^4} \, dx","Int[x/(a + b*(c + d*x)^4),x]","\frac{c \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} (c+d x)+\sqrt{a}+\sqrt{b} (c+d x)^2\right)}{4 \sqrt{2} a^{3/4} \sqrt[4]{b} d^2}-\frac{c \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} (c+d x)+\sqrt{a}+\sqrt{b} (c+d x)^2\right)}{4 \sqrt{2} a^{3/4} \sqrt[4]{b} d^2}+\frac{c \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} (c+d x)}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} \sqrt[4]{b} d^2}-\frac{c \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} (c+d x)}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} \sqrt[4]{b} d^2}+\frac{\tan ^{-1}\left(\frac{\sqrt{b} (c+d x)^2}{\sqrt{a}}\right)}{2 \sqrt{a} \sqrt{b} d^2}","\frac{c \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} (c+d x)+\sqrt{a}+\sqrt{b} (c+d x)^2\right)}{4 \sqrt{2} a^{3/4} \sqrt[4]{b} d^2}-\frac{c \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} (c+d x)+\sqrt{a}+\sqrt{b} (c+d x)^2\right)}{4 \sqrt{2} a^{3/4} \sqrt[4]{b} d^2}+\frac{c \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} (c+d x)}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} \sqrt[4]{b} d^2}-\frac{c \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} (c+d x)}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} \sqrt[4]{b} d^2}+\frac{\tan ^{-1}\left(\frac{\sqrt{b} (c+d x)^2}{\sqrt{a}}\right)}{2 \sqrt{a} \sqrt{b} d^2}",1,"ArcTan[(Sqrt[b]*(c + d*x)^2)/Sqrt[a]]/(2*Sqrt[a]*Sqrt[b]*d^2) + (c*ArcTan[1 - (Sqrt[2]*b^(1/4)*(c + d*x))/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*b^(1/4)*d^2) - (c*ArcTan[1 + (Sqrt[2]*b^(1/4)*(c + d*x))/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*b^(1/4)*d^2) + (c*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*(c + d*x) + Sqrt[b]*(c + d*x)^2])/(4*Sqrt[2]*a^(3/4)*b^(1/4)*d^2) - (c*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*(c + d*x) + Sqrt[b]*(c + d*x)^2])/(4*Sqrt[2]*a^(3/4)*b^(1/4)*d^2)","A",14,10,15,0.6667,1,"{371, 1876, 211, 1165, 628, 1162, 617, 204, 275, 205}"
113,1,221,0,0.185432,"\int \frac{1}{a+b (c+d x)^4} \, dx","Int[(a + b*(c + d*x)^4)^(-1),x]","-\frac{\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} (c+d x)+\sqrt{a}+\sqrt{b} (c+d x)^2\right)}{4 \sqrt{2} a^{3/4} \sqrt[4]{b} d}+\frac{\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} (c+d x)+\sqrt{a}+\sqrt{b} (c+d x)^2\right)}{4 \sqrt{2} a^{3/4} \sqrt[4]{b} d}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} (c+d x)}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} \sqrt[4]{b} d}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} (c+d x)}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} \sqrt[4]{b} d}","-\frac{\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} (c+d x)+\sqrt{a}+\sqrt{b} (c+d x)^2\right)}{4 \sqrt{2} a^{3/4} \sqrt[4]{b} d}+\frac{\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} (c+d x)+\sqrt{a}+\sqrt{b} (c+d x)^2\right)}{4 \sqrt{2} a^{3/4} \sqrt[4]{b} d}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} (c+d x)}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} \sqrt[4]{b} d}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} (c+d x)}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} \sqrt[4]{b} d}",1,"-ArcTan[1 - (Sqrt[2]*b^(1/4)*(c + d*x))/a^(1/4)]/(2*Sqrt[2]*a^(3/4)*b^(1/4)*d) + ArcTan[1 + (Sqrt[2]*b^(1/4)*(c + d*x))/a^(1/4)]/(2*Sqrt[2]*a^(3/4)*b^(1/4)*d) - Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*(c + d*x) + Sqrt[b]*(c + d*x)^2]/(4*Sqrt[2]*a^(3/4)*b^(1/4)*d) + Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*(c + d*x) + Sqrt[b]*(c + d*x)^2]/(4*Sqrt[2]*a^(3/4)*b^(1/4)*d)","A",10,7,13,0.5385,1,"{247, 211, 1165, 628, 1162, 617, 204}"
114,1,393,0,0.4662806,"\int \frac{1}{x \left(a+b (c+d x)^4\right)} \, dx","Int[1/(x*(a + b*(c + d*x)^4)),x]","-\frac{\sqrt[4]{b} c \left(\sqrt{a}-\sqrt{b} c^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} (c+d x)+\sqrt{a}+\sqrt{b} (c+d x)^2\right)}{4 \sqrt{2} a^{3/4} \left(a+b c^4\right)}+\frac{\sqrt[4]{b} c \left(\sqrt{a}-\sqrt{b} c^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} (c+d x)+\sqrt{a}+\sqrt{b} (c+d x)^2\right)}{4 \sqrt{2} a^{3/4} \left(a+b c^4\right)}+\frac{\sqrt[4]{b} c \left(\sqrt{a}+\sqrt{b} c^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} (c+d x)}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} \left(a+b c^4\right)}-\frac{\sqrt[4]{b} c \left(\sqrt{a}+\sqrt{b} c^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} (c+d x)}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} \left(a+b c^4\right)}-\frac{\log \left(a+b (c+d x)^4\right)}{4 \left(a+b c^4\right)}-\frac{\sqrt{b} c^2 \tan ^{-1}\left(\frac{\sqrt{b} (c+d x)^2}{\sqrt{a}}\right)}{2 \sqrt{a} \left(a+b c^4\right)}+\frac{\log (x)}{a+b c^4}","-\frac{\sqrt[4]{b} c \left(\sqrt{a}-\sqrt{b} c^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} (c+d x)+\sqrt{a}+\sqrt{b} (c+d x)^2\right)}{4 \sqrt{2} a^{3/4} \left(a+b c^4\right)}+\frac{\sqrt[4]{b} c \left(\sqrt{a}-\sqrt{b} c^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} (c+d x)+\sqrt{a}+\sqrt{b} (c+d x)^2\right)}{4 \sqrt{2} a^{3/4} \left(a+b c^4\right)}+\frac{\sqrt[4]{b} c \left(\sqrt{a}+\sqrt{b} c^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} (c+d x)}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} \left(a+b c^4\right)}-\frac{\sqrt[4]{b} c \left(\sqrt{a}+\sqrt{b} c^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} (c+d x)}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} \left(a+b c^4\right)}-\frac{\log \left(a+b (c+d x)^4\right)}{4 \left(a+b c^4\right)}-\frac{\sqrt{b} c^2 \tan ^{-1}\left(\frac{\sqrt{b} (c+d x)^2}{\sqrt{a}}\right)}{2 \sqrt{a} \left(a+b c^4\right)}+\frac{\log (x)}{a+b c^4}",1,"-(Sqrt[b]*c^2*ArcTan[(Sqrt[b]*(c + d*x)^2)/Sqrt[a]])/(2*Sqrt[a]*(a + b*c^4)) + (b^(1/4)*c*(Sqrt[a] + Sqrt[b]*c^2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*(c + d*x))/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*(a + b*c^4)) - (b^(1/4)*c*(Sqrt[a] + Sqrt[b]*c^2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*(c + d*x))/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*(a + b*c^4)) + Log[x]/(a + b*c^4) - (b^(1/4)*c*(Sqrt[a] - Sqrt[b]*c^2)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*(c + d*x) + Sqrt[b]*(c + d*x)^2])/(4*Sqrt[2]*a^(3/4)*(a + b*c^4)) + (b^(1/4)*c*(Sqrt[a] - Sqrt[b]*c^2)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*(c + d*x) + Sqrt[b]*(c + d*x)^2])/(4*Sqrt[2]*a^(3/4)*(a + b*c^4)) - Log[a + b*(c + d*x)^4]/(4*(a + b*c^4))","A",18,13,17,0.7647,1,"{371, 6725, 1876, 1248, 635, 205, 260, 1168, 1162, 617, 204, 1165, 628}"
115,1,496,0,0.894138,"\int \frac{1}{x^2 \left(a+b (c+d x)^4\right)} \, dx","Int[1/(x^2*(a + b*(c + d*x)^4)),x]","-\frac{\sqrt[4]{b} d \left(\sqrt{a} \left(a-3 b c^4\right)-\sqrt{b} c^2 \left(3 a-b c^4\right)\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} (c+d x)+\sqrt{a}+\sqrt{b} (c+d x)^2\right)}{4 \sqrt{2} a^{3/4} \left(a+b c^4\right)^2}+\frac{\sqrt[4]{b} d \left(\sqrt{a} \left(a-3 b c^4\right)-\sqrt{b} c^2 \left(3 a-b c^4\right)\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} (c+d x)+\sqrt{a}+\sqrt{b} (c+d x)^2\right)}{4 \sqrt{2} a^{3/4} \left(a+b c^4\right)^2}+\frac{\sqrt[4]{b} d \left(\sqrt{b} c^2 \left(3 a-b c^4\right)+\sqrt{a} \left(a-3 b c^4\right)\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} (c+d x)}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} \left(a+b c^4\right)^2}-\frac{\sqrt[4]{b} d \left(\sqrt{b} c^2 \left(3 a-b c^4\right)+\sqrt{a} \left(a-3 b c^4\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} (c+d x)}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} \left(a+b c^4\right)^2}-\frac{4 b c^3 d \log (x)}{\left(a+b c^4\right)^2}+\frac{b c^3 d \log \left(a+b (c+d x)^4\right)}{\left(a+b c^4\right)^2}-\frac{\sqrt{b} c d \left(a-b c^4\right) \tan ^{-1}\left(\frac{\sqrt{b} (c+d x)^2}{\sqrt{a}}\right)}{\sqrt{a} \left(a+b c^4\right)^2}-\frac{1}{x \left(a+b c^4\right)}","-\frac{\sqrt[4]{b} d \left(\sqrt{a} \left(a-3 b c^4\right)-\sqrt{b} c^2 \left(3 a-b c^4\right)\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} (c+d x)+\sqrt{a}+\sqrt{b} (c+d x)^2\right)}{4 \sqrt{2} a^{3/4} \left(a+b c^4\right)^2}+\frac{\sqrt[4]{b} d \left(\sqrt{a} \left(a-3 b c^4\right)-\sqrt{b} c^2 \left(3 a-b c^4\right)\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} (c+d x)+\sqrt{a}+\sqrt{b} (c+d x)^2\right)}{4 \sqrt{2} a^{3/4} \left(a+b c^4\right)^2}+\frac{\sqrt[4]{b} d \left(\sqrt{b} c^2 \left(3 a-b c^4\right)+\sqrt{a} \left(a-3 b c^4\right)\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} (c+d x)}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} \left(a+b c^4\right)^2}-\frac{\sqrt[4]{b} d \left(\sqrt{b} c^2 \left(3 a-b c^4\right)+\sqrt{a} \left(a-3 b c^4\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} (c+d x)}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} \left(a+b c^4\right)^2}-\frac{4 b c^3 d \log (x)}{\left(a+b c^4\right)^2}+\frac{b c^3 d \log \left(a+b (c+d x)^4\right)}{\left(a+b c^4\right)^2}-\frac{\sqrt{b} c d \left(a-b c^4\right) \tan ^{-1}\left(\frac{\sqrt{b} (c+d x)^2}{\sqrt{a}}\right)}{\sqrt{a} \left(a+b c^4\right)^2}-\frac{1}{x \left(a+b c^4\right)}",1,"-(1/((a + b*c^4)*x)) - (Sqrt[b]*c*(a - b*c^4)*d*ArcTan[(Sqrt[b]*(c + d*x)^2)/Sqrt[a]])/(Sqrt[a]*(a + b*c^4)^2) + (b^(1/4)*(Sqrt[a]*(a - 3*b*c^4) + Sqrt[b]*c^2*(3*a - b*c^4))*d*ArcTan[1 - (Sqrt[2]*b^(1/4)*(c + d*x))/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*(a + b*c^4)^2) - (b^(1/4)*(Sqrt[a]*(a - 3*b*c^4) + Sqrt[b]*c^2*(3*a - b*c^4))*d*ArcTan[1 + (Sqrt[2]*b^(1/4)*(c + d*x))/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*(a + b*c^4)^2) - (4*b*c^3*d*Log[x])/(a + b*c^4)^2 - (b^(1/4)*(Sqrt[a]*(a - 3*b*c^4) - Sqrt[b]*c^2*(3*a - b*c^4))*d*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*(c + d*x) + Sqrt[b]*(c + d*x)^2])/(4*Sqrt[2]*a^(3/4)*(a + b*c^4)^2) + (b^(1/4)*(Sqrt[a]*(a - 3*b*c^4) - Sqrt[b]*c^2*(3*a - b*c^4))*d*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*(c + d*x) + Sqrt[b]*(c + d*x)^2])/(4*Sqrt[2]*a^(3/4)*(a + b*c^4)^2) + (b*c^3*d*Log[a + b*(c + d*x)^4])/(a + b*c^4)^2","A",18,13,17,0.7647,1,"{371, 6725, 1876, 1248, 635, 205, 260, 1168, 1162, 617, 204, 1165, 628}"
116,1,123,0,0.2397452,"\int \left(a+8 x-8 x^2+4 x^3-x^4\right)^4 \, dx","Int[(a + 8*x - 8*x^2 + 4*x^3 - x^4)^4,x]","-\frac{2}{9} \left(-3 a^2+6 a+37\right) (x-1)^9+\frac{4}{13} (3-a) (x-1)^{13}-\frac{8}{11} (3 a+5) (x-1)^{11}+\frac{8}{7} (a+3) (3 a+5) (x-1)^7+\frac{4}{5} (3-a) (a+3)^2 (x-1)^5-\frac{8}{3} (a+3)^3 (x-1)^3+(a+3)^4 x+\frac{1}{17} (x-1)^{17}+\frac{8}{15} (x-1)^{15}","-\frac{2}{9} \left(-3 a^2+6 a+37\right) (x-1)^9+\frac{4}{13} (3-a) (x-1)^{13}-\frac{8}{11} (3 a+5) (x-1)^{11}+\frac{8}{7} (a+3) (3 a+5) (x-1)^7+\frac{4}{5} (3-a) (a+3)^2 (x-1)^5-\frac{8}{3} (a+3)^3 (x-1)^3+(a+3)^4 x+\frac{1}{17} (x-1)^{17}+\frac{8}{15} (x-1)^{15}",1,"(-8*(3 + a)^3*(-1 + x)^3)/3 + (4*(3 - a)*(3 + a)^2*(-1 + x)^5)/5 + (8*(3 + a)*(5 + 3*a)*(-1 + x)^7)/7 - (2*(37 + 6*a - 3*a^2)*(-1 + x)^9)/9 - (8*(5 + 3*a)*(-1 + x)^11)/11 + (4*(3 - a)*(-1 + x)^13)/13 + (8*(-1 + x)^15)/15 + (-1 + x)^17/17 + (3 + a)^4*x","A",3,2,22,0.09091,1,"{1106, 1090}"
117,1,120,0,0.0631218,"\int \left(a+8 x-8 x^2+4 x^3-x^4\right)^3 \, dx","Int[(a + 8*x - 8*x^2 + 4*x^3 - x^4)^3,x]","-\frac{3}{5} \left(a^2-128 a+512\right) x^5+\left(3 a^2-96 a+128\right) x^4+12 a^2 x^2+a^3 x-\frac{1}{3} (256-a) x^9+3 (64-a) x^8-\frac{32}{7} (70-3 a) x^7+8 (48-5 a) x^6+8 (8-a) a x^3-\frac{x^{13}}{13}+x^{12}-\frac{72 x^{11}}{11}+28 x^{10}","-\frac{3}{5} \left(a^2-128 a+512\right) x^5+\left(3 a^2-96 a+128\right) x^4+12 a^2 x^2+a^3 x-\frac{1}{3} (256-a) x^9+3 (64-a) x^8-\frac{32}{7} (70-3 a) x^7+8 (48-5 a) x^6+8 (8-a) a x^3-\frac{x^{13}}{13}+x^{12}-\frac{72 x^{11}}{11}+28 x^{10}",1,"a^3*x + 12*a^2*x^2 + 8*(8 - a)*a*x^3 + (128 - 96*a + 3*a^2)*x^4 - (3*(512 - 128*a + a^2)*x^5)/5 + 8*(48 - 5*a)*x^6 - (32*(70 - 3*a)*x^7)/7 + 3*(64 - a)*x^8 - ((256 - a)*x^9)/3 + 28*x^10 - (72*x^11)/11 + x^12 - x^13/13","A",2,1,22,0.04545,1,"{2061}"
118,1,72,0,0.0297305,"\int \left(a+8 x-8 x^2+4 x^3-x^4\right)^2 \, dx","Int[(a + 8*x - 8*x^2 + 4*x^3 - x^4)^2,x]","a^2 x+\frac{2}{5} (64-a) x^5-2 (16-a) x^4+\frac{16}{3} (4-a) x^3+8 a x^2+\frac{x^9}{9}-x^8+\frac{32 x^7}{7}-\frac{40 x^6}{3}","a^2 x+\frac{2}{5} (64-a) x^5-2 (16-a) x^4+\frac{16}{3} (4-a) x^3+8 a x^2+\frac{x^9}{9}-x^8+\frac{32 x^7}{7}-\frac{40 x^6}{3}",1,"a^2*x + 8*a*x^2 + (16*(4 - a)*x^3)/3 - 2*(16 - a)*x^4 + (2*(64 - a)*x^5)/5 - (40*x^6)/3 + (32*x^7)/7 - x^8 + x^9/9","A",2,1,22,0.04545,1,"{2061}"
119,1,26,0,0.00396,"\int \left(a+8 x-8 x^2+4 x^3-x^4\right) \, dx","Int[a + 8*x - 8*x^2 + 4*x^3 - x^4,x]","a x-\frac{x^5}{5}+x^4-\frac{8 x^3}{3}+4 x^2","a x-\frac{x^5}{5}+x^4-\frac{8 x^3}{3}+4 x^2",1,"a*x + 4*x^2 - (8*x^3)/3 + x^4 - x^5/5","A",1,0,20,0,1,"{}"
120,1,89,0,0.086782,"\int \frac{1}{a+8 x-8 x^2+4 x^3-x^4} \, dx","Int[(a + 8*x - 8*x^2 + 4*x^3 - x^4)^(-1),x]","\frac{\tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)}{2 \sqrt{a+4} \sqrt{\sqrt{a+4}+1}}-\frac{\tan ^{-1}\left(\frac{x-1}{\sqrt{1-\sqrt{a+4}}}\right)}{2 \sqrt{a+4} \sqrt{1-\sqrt{a+4}}}","\frac{\tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)}{2 \sqrt{a+4} \sqrt{\sqrt{a+4}+1}}-\frac{\tan ^{-1}\left(\frac{x-1}{\sqrt{1-\sqrt{a+4}}}\right)}{2 \sqrt{a+4} \sqrt{1-\sqrt{a+4}}}",1,"-ArcTan[(-1 + x)/Sqrt[1 - Sqrt[4 + a]]]/(2*Sqrt[4 + a]*Sqrt[1 - Sqrt[4 + a]]) + ArcTan[(-1 + x)/Sqrt[1 + Sqrt[4 + a]]]/(2*Sqrt[4 + a]*Sqrt[1 + Sqrt[4 + a]])","A",4,3,22,0.1364,1,"{1106, 1093, 204}"
121,1,169,0,0.291298,"\int \frac{1}{\left(a+8 x-8 x^2+4 x^3-x^4\right)^2} \, dx","Int[(a + 8*x - 8*x^2 + 4*x^3 - x^4)^(-2),x]","\frac{(x-1) \left(a+(x-1)^2+5\right)}{4 \left(a^2+7 a+12\right) \left(a-(x-1)^4-2 (x-1)^2+3\right)}-\frac{\left(3 a+\sqrt{a+4}+10\right) \tan ^{-1}\left(\frac{x-1}{\sqrt{1-\sqrt{a+4}}}\right)}{8 (a+3) (a+4)^{3/2} \sqrt{1-\sqrt{a+4}}}+\frac{\left(3 a-\sqrt{a+4}+10\right) \tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)}{8 (a+3) (a+4)^{3/2} \sqrt{\sqrt{a+4}+1}}","\frac{(x-1) \left(a+(x-1)^2+5\right)}{4 \left(a^2+7 a+12\right) \left(a-(x-1)^4-2 (x-1)^2+3\right)}-\frac{\left(3 a+\sqrt{a+4}+10\right) \tan ^{-1}\left(\frac{x-1}{\sqrt{1-\sqrt{a+4}}}\right)}{8 (a+3) (a+4)^{3/2} \sqrt{1-\sqrt{a+4}}}+\frac{\left(3 a-\sqrt{a+4}+10\right) \tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)}{8 (a+3) (a+4)^{3/2} \sqrt{\sqrt{a+4}+1}}",1,"((5 + a + (-1 + x)^2)*(-1 + x))/(4*(12 + 7*a + a^2)*(3 + a - 2*(-1 + x)^2 - (-1 + x)^4)) - ((10 + 3*a + Sqrt[4 + a])*ArcTan[(-1 + x)/Sqrt[1 - Sqrt[4 + a]]])/(8*(3 + a)*(4 + a)^(3/2)*Sqrt[1 - Sqrt[4 + a]]) + ((10 + 3*a - Sqrt[4 + a])*ArcTan[(-1 + x)/Sqrt[1 + Sqrt[4 + a]]])/(8*(3 + a)*(4 + a)^(3/2)*Sqrt[1 + Sqrt[4 + a]])","A",5,4,22,0.1818,1,"{1106, 1092, 1166, 204}"
122,1,252,0,0.5319244,"\int \frac{1}{\left(a+8 x-8 x^2+4 x^3-x^4\right)^3} \, dx","Int[(a + 8*x - 8*x^2 + 4*x^3 - x^4)^(-3),x]","\frac{(x-1) \left(a+(x-1)^2+5\right)}{8 \left(a^2+7 a+12\right) \left(a-(x-1)^4-2 (x-1)^2+3\right)^2}-\frac{3 \left(7 a^2+\left(4 \sqrt{a+4}+47\right) a+14 \sqrt{a+4}+80\right) \tan ^{-1}\left(\frac{x-1}{\sqrt{1-\sqrt{a+4}}}\right)}{64 (a+3)^2 (a+4)^{5/2} \sqrt{1-\sqrt{a+4}}}-\frac{3 \left(-\frac{7 a^2+47 a+80}{\sqrt{a+4}}+4 a+14\right) \tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)}{64 (a+3)^2 (a+4)^2 \sqrt{\sqrt{a+4}+1}}+\frac{(x-1) \left(6 (2 a+7) (x-1)^2+(a+6) (7 a+25)\right)}{32 (a+3)^2 (a+4)^2 \left(a-(x-1)^4-2 (x-1)^2+3\right)}","\frac{(x-1) \left(a+(x-1)^2+5\right)}{8 \left(a^2+7 a+12\right) \left(a-(x-1)^4-2 (x-1)^2+3\right)^2}-\frac{3 \left(7 a^2+\left(4 \sqrt{a+4}+47\right) a+14 \sqrt{a+4}+80\right) \tan ^{-1}\left(\frac{x-1}{\sqrt{1-\sqrt{a+4}}}\right)}{64 (a+3)^2 (a+4)^{5/2} \sqrt{1-\sqrt{a+4}}}-\frac{3 \left(-\frac{7 a^2+47 a+80}{\sqrt{a+4}}+4 a+14\right) \tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)}{64 (a+3)^2 (a+4)^2 \sqrt{\sqrt{a+4}+1}}+\frac{(x-1) \left(6 (2 a+7) (x-1)^2+(a+6) (7 a+25)\right)}{32 (a+3)^2 (a+4)^2 \left(a-(x-1)^4-2 (x-1)^2+3\right)}",1,"((5 + a + (-1 + x)^2)*(-1 + x))/(8*(12 + 7*a + a^2)*(3 + a - 2*(-1 + x)^2 - (-1 + x)^4)^2) + (((6 + a)*(25 + 7*a) + 6*(7 + 2*a)*(-1 + x)^2)*(-1 + x))/(32*(3 + a)^2*(4 + a)^2*(3 + a - 2*(-1 + x)^2 - (-1 + x)^4)) - (3*(80 + 7*a^2 + 14*Sqrt[4 + a] + a*(47 + 4*Sqrt[4 + a]))*ArcTan[(-1 + x)/Sqrt[1 - Sqrt[4 + a]]])/(64*(3 + a)^2*(4 + a)^(5/2)*Sqrt[1 - Sqrt[4 + a]]) - (3*(14 + 4*a - (80 + 47*a + 7*a^2)/Sqrt[4 + a])*ArcTan[(-1 + x)/Sqrt[1 + Sqrt[4 + a]]])/(64*(3 + a)^2*(4 + a)^2*Sqrt[1 + Sqrt[4 + a]])","A",6,5,22,0.2273,1,"{1106, 1092, 1178, 1166, 204}"
123,1,210,0,0.2256371,"\int x \left(a+8 x-8 x^2+4 x^3-x^4\right)^4 \, dx","Int[x*(a + 8*x - 8*x^2 + 4*x^3 - x^4)^4,x]","\frac{1}{5} \left(3 a^2-1536 a+20480\right) x^{10}-\frac{16}{3} \left(a^2-128 a+896\right) x^9-\frac{32}{7} \left(15 a^2-288 a+512\right) x^7+\frac{2}{3} \left(-a^3+192 a^2-1536 a+1024\right) x^6+\frac{16}{5} a \left(a^2-48 a+128\right) x^5+8 (12-a) a^2 x^4+\frac{32 a^3 x^3}{3}+\frac{a^4 x^2}{2}+\frac{2}{7} (640-a) x^{14}-\frac{16}{13} (464-3 a) x^{13}+\frac{8}{3} (524-9 a) x^{12}-\frac{32}{11} (928-35 a) x^{11}+8 (128-3 a) (4-a) x^8+\frac{x^{18}}{18}-\frac{16 x^{17}}{17}+8 x^{16}-\frac{224 x^{15}}{5}","\frac{1}{5} \left(3 a^2-1536 a+20480\right) x^{10}-\frac{16}{3} \left(a^2-128 a+896\right) x^9-\frac{32}{7} \left(15 a^2-288 a+512\right) x^7+\frac{2}{3} \left(-a^3+192 a^2-1536 a+1024\right) x^6+\frac{16}{5} a \left(a^2-48 a+128\right) x^5+8 (12-a) a^2 x^4+\frac{32 a^3 x^3}{3}+\frac{a^4 x^2}{2}+\frac{2}{7} (640-a) x^{14}-\frac{16}{13} (464-3 a) x^{13}+\frac{8}{3} (524-9 a) x^{12}-\frac{32}{11} (928-35 a) x^{11}+8 (128-3 a) (4-a) x^8+\frac{x^{18}}{18}-\frac{16 x^{17}}{17}+8 x^{16}-\frac{224 x^{15}}{5}",1,"(a^4*x^2)/2 + (32*a^3*x^3)/3 + 8*(12 - a)*a^2*x^4 + (16*a*(128 - 48*a + a^2)*x^5)/5 + (2*(1024 - 1536*a + 192*a^2 - a^3)*x^6)/3 - (32*(512 - 288*a + 15*a^2)*x^7)/7 + 8*(128 - 3*a)*(4 - a)*x^8 - (16*(896 - 128*a + a^2)*x^9)/3 + ((20480 - 1536*a + 3*a^2)*x^10)/5 - (32*(928 - 35*a)*x^11)/11 + (8*(524 - 9*a)*x^12)/3 - (16*(464 - 3*a)*x^13)/13 + (2*(640 - a)*x^14)/7 - (224*x^15)/5 + 8*x^16 - (16*x^17)/17 + x^18/18","A",2,1,24,0.04167,1,"{6742}"
124,1,134,0,0.1402923,"\int x \left(a+8 x-8 x^2+4 x^3-x^4\right)^3 \, dx","Int[x*(a + 8*x - 8*x^2 + 4*x^3 - x^4)^3,x]","-\frac{1}{2} \left(a^2-128 a+512\right) x^6+\frac{4}{5} \left(3 a^2-96 a+128\right) x^5+8 a^2 x^3+\frac{a^3 x^2}{2}-\frac{3}{10} (256-a) x^{10}+\frac{8}{3} (64-a) x^9-4 (70-3 a) x^8+\frac{48}{7} (48-5 a) x^7+6 (8-a) a x^4-\frac{x^{14}}{14}+\frac{12 x^{13}}{13}-6 x^{12}+\frac{280 x^{11}}{11}","-\frac{1}{2} \left(a^2-128 a+512\right) x^6+\frac{4}{5} \left(3 a^2-96 a+128\right) x^5+8 a^2 x^3+\frac{a^3 x^2}{2}-\frac{3}{10} (256-a) x^{10}+\frac{8}{3} (64-a) x^9-4 (70-3 a) x^8+\frac{48}{7} (48-5 a) x^7+6 (8-a) a x^4-\frac{x^{14}}{14}+\frac{12 x^{13}}{13}-6 x^{12}+\frac{280 x^{11}}{11}",1,"(a^3*x^2)/2 + 8*a^2*x^3 + 6*(8 - a)*a*x^4 + (4*(128 - 96*a + 3*a^2)*x^5)/5 - ((512 - 128*a + a^2)*x^6)/2 + (48*(48 - 5*a)*x^7)/7 - 4*(70 - 3*a)*x^8 + (8*(64 - a)*x^9)/3 - (3*(256 - a)*x^10)/10 + (280*x^11)/11 - 6*x^12 + (12*x^13)/13 - x^14/14","A",2,1,24,0.04167,1,"{6742}"
125,1,79,0,0.0759102,"\int x \left(a+8 x-8 x^2+4 x^3-x^4\right)^2 \, dx","Int[x*(a + 8*x - 8*x^2 + 4*x^3 - x^4)^2,x]","\frac{a^2 x^2}{2}+\frac{1}{3} (64-a) x^6-\frac{8}{5} (16-a) x^5+4 (4-a) x^4+\frac{16 a x^3}{3}+\frac{x^{10}}{10}-\frac{8 x^9}{9}+4 x^8-\frac{80 x^7}{7}","\frac{a^2 x^2}{2}+\frac{1}{3} (64-a) x^6-\frac{8}{5} (16-a) x^5+4 (4-a) x^4+\frac{16 a x^3}{3}+\frac{x^{10}}{10}-\frac{8 x^9}{9}+4 x^8-\frac{80 x^7}{7}",1,"(a^2*x^2)/2 + (16*a*x^3)/3 + 4*(4 - a)*x^4 - (8*(16 - a)*x^5)/5 + ((64 - a)*x^6)/3 - (80*x^7)/7 + 4*x^8 - (8*x^9)/9 + x^10/10","A",2,1,24,0.04167,1,"{6742}"
126,1,35,0,0.0099643,"\int x \left(a+8 x-8 x^2+4 x^3-x^4\right) \, dx","Int[x*(a + 8*x - 8*x^2 + 4*x^3 - x^4),x]","\frac{a x^2}{2}-\frac{x^6}{6}+\frac{4 x^5}{5}-2 x^4+\frac{8 x^3}{3}","\frac{a x^2}{2}-\frac{x^6}{6}+\frac{4 x^5}{5}-2 x^4+\frac{8 x^3}{3}",1,"(a*x^2)/2 + (8*x^3)/3 - 2*x^4 + (4*x^5)/5 - x^6/6","A",2,1,22,0.04545,1,"{14}"
127,1,116,0,0.0830145,"\int \frac{x}{a+8 x-8 x^2+4 x^3-x^4} \, dx","Int[x/(a + 8*x - 8*x^2 + 4*x^3 - x^4),x]","-\frac{\tan ^{-1}\left(\frac{x-1}{\sqrt{1-\sqrt{a+4}}}\right)}{2 \sqrt{a+4} \sqrt{1-\sqrt{a+4}}}+\frac{\tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)}{2 \sqrt{a+4} \sqrt{\sqrt{a+4}+1}}+\frac{\tanh ^{-1}\left(\frac{(x-1)^2+1}{\sqrt{a+4}}\right)}{2 \sqrt{a+4}}","-\frac{\tan ^{-1}\left(\frac{x-1}{\sqrt{1-\sqrt{a+4}}}\right)}{2 \sqrt{a+4} \sqrt{1-\sqrt{a+4}}}+\frac{\tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)}{2 \sqrt{a+4} \sqrt{\sqrt{a+4}+1}}+\frac{\tanh ^{-1}\left(\frac{(x-1)^2+1}{\sqrt{a+4}}\right)}{2 \sqrt{a+4}}",1,"-ArcTan[(-1 + x)/Sqrt[1 - Sqrt[4 + a]]]/(2*Sqrt[4 + a]*Sqrt[1 - Sqrt[4 + a]]) + ArcTan[(-1 + x)/Sqrt[1 + Sqrt[4 + a]]]/(2*Sqrt[4 + a]*Sqrt[1 + Sqrt[4 + a]]) + ArcTanh[(1 + (-1 + x)^2)/Sqrt[4 + a]]/(2*Sqrt[4 + a])","A",8,7,24,0.2917,1,"{1680, 1673, 1093, 204, 1107, 618, 206}"
128,1,231,0,0.2405004,"\int \frac{x}{\left(a+8 x-8 x^2+4 x^3-x^4\right)^2} \, dx","Int[x/(a + 8*x - 8*x^2 + 4*x^3 - x^4)^2,x]","\frac{(x-1) \left(a+(x-1)^2+5\right)}{4 \left(a^2+7 a+12\right) \left(a-(x-1)^4-2 (x-1)^2+3\right)}+\frac{(x-1)^2+1}{4 (a+4) \left(a-(x-1)^4-2 (x-1)^2+3\right)}-\frac{\left(3 a+\sqrt{a+4}+10\right) \tan ^{-1}\left(\frac{x-1}{\sqrt{1-\sqrt{a+4}}}\right)}{8 (a+3) (a+4)^{3/2} \sqrt{1-\sqrt{a+4}}}+\frac{\left(3 a-\sqrt{a+4}+10\right) \tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)}{8 (a+3) (a+4)^{3/2} \sqrt{\sqrt{a+4}+1}}+\frac{\tanh ^{-1}\left(\frac{(x-1)^2+1}{\sqrt{a+4}}\right)}{4 (a+4)^{3/2}}","\frac{(x-1) \left(a+(x-1)^2+5\right)}{4 \left(a^2+7 a+12\right) \left(a-(x-1)^4-2 (x-1)^2+3\right)}+\frac{(x-1)^2+1}{4 (a+4) \left(a-(x-1)^4-2 (x-1)^2+3\right)}-\frac{\left(3 a+\sqrt{a+4}+10\right) \tan ^{-1}\left(\frac{x-1}{\sqrt{1-\sqrt{a+4}}}\right)}{8 (a+3) (a+4)^{3/2} \sqrt{1-\sqrt{a+4}}}+\frac{\left(3 a-\sqrt{a+4}+10\right) \tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)}{8 (a+3) (a+4)^{3/2} \sqrt{\sqrt{a+4}+1}}+\frac{\tanh ^{-1}\left(\frac{(x-1)^2+1}{\sqrt{a+4}}\right)}{4 (a+4)^{3/2}}",1,"(1 + (-1 + x)^2)/(4*(4 + a)*(3 + a - 2*(-1 + x)^2 - (-1 + x)^4)) + ((5 + a + (-1 + x)^2)*(-1 + x))/(4*(12 + 7*a + a^2)*(3 + a - 2*(-1 + x)^2 - (-1 + x)^4)) - ((10 + 3*a + Sqrt[4 + a])*ArcTan[(-1 + x)/Sqrt[1 - Sqrt[4 + a]]])/(8*(3 + a)*(4 + a)^(3/2)*Sqrt[1 - Sqrt[4 + a]]) + ((10 + 3*a - Sqrt[4 + a])*ArcTan[(-1 + x)/Sqrt[1 + Sqrt[4 + a]]])/(8*(3 + a)*(4 + a)^(3/2)*Sqrt[1 + Sqrt[4 + a]]) + ArcTanh[(1 + (-1 + x)^2)/Sqrt[4 + a]]/(4*(4 + a)^(3/2))","A",10,9,24,0.3750,1,"{1680, 1673, 1092, 1166, 204, 1107, 614, 618, 206}"
129,1,349,0,0.3687677,"\int \frac{x}{\left(a+8 x-8 x^2+4 x^3-x^4\right)^3} \, dx","Int[x/(a + 8*x - 8*x^2 + 4*x^3 - x^4)^3,x]","\frac{(x-1) \left(a+(x-1)^2+5\right)}{8 \left(a^2+7 a+12\right) \left(a-(x-1)^4-2 (x-1)^2+3\right)^2}-\frac{3 \left(7 a^2+\left(4 \sqrt{a+4}+47\right) a+14 \sqrt{a+4}+80\right) \tan ^{-1}\left(\frac{x-1}{\sqrt{1-\sqrt{a+4}}}\right)}{64 (a+3)^2 (a+4)^{5/2} \sqrt{1-\sqrt{a+4}}}-\frac{3 \left(-\frac{7 a^2+47 a+80}{\sqrt{a+4}}+4 a+14\right) \tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)}{64 (a+3)^2 (a+4)^2 \sqrt{\sqrt{a+4}+1}}+\frac{3 \left((x-1)^2+1\right)}{16 (a+4)^2 \left(a-(x-1)^4-2 (x-1)^2+3\right)}+\frac{(x-1)^2+1}{8 (a+4) \left(a-(x-1)^4-2 (x-1)^2+3\right)^2}+\frac{(x-1) \left(6 (2 a+7) (x-1)^2+(a+6) (7 a+25)\right)}{32 (a+3)^2 (a+4)^2 \left(a-(x-1)^4-2 (x-1)^2+3\right)}+\frac{3 \tanh ^{-1}\left(\frac{(x-1)^2+1}{\sqrt{a+4}}\right)}{16 (a+4)^{5/2}}","\frac{(x-1) \left(a+(x-1)^2+5\right)}{8 \left(a^2+7 a+12\right) \left(a-(x-1)^4-2 (x-1)^2+3\right)^2}-\frac{3 \left(7 a^2+\left(4 \sqrt{a+4}+47\right) a+14 \sqrt{a+4}+80\right) \tan ^{-1}\left(\frac{x-1}{\sqrt{1-\sqrt{a+4}}}\right)}{64 (a+3)^2 (a+4)^{5/2} \sqrt{1-\sqrt{a+4}}}-\frac{3 \left(-\frac{7 a^2+47 a+80}{\sqrt{a+4}}+4 a+14\right) \tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)}{64 (a+3)^2 (a+4)^2 \sqrt{\sqrt{a+4}+1}}+\frac{3 \left((x-1)^2+1\right)}{16 (a+4)^2 \left(a-(x-1)^4-2 (x-1)^2+3\right)}+\frac{(x-1)^2+1}{8 (a+4) \left(a-(x-1)^4-2 (x-1)^2+3\right)^2}+\frac{(x-1) \left(6 (2 a+7) (x-1)^2+(a+6) (7 a+25)\right)}{32 (a+3)^2 (a+4)^2 \left(a-(x-1)^4-2 (x-1)^2+3\right)}+\frac{3 \tanh ^{-1}\left(\frac{(x-1)^2+1}{\sqrt{a+4}}\right)}{16 (a+4)^{5/2}}",1,"(1 + (-1 + x)^2)/(8*(4 + a)*(3 + a - 2*(-1 + x)^2 - (-1 + x)^4)^2) + (3*(1 + (-1 + x)^2))/(16*(4 + a)^2*(3 + a - 2*(-1 + x)^2 - (-1 + x)^4)) + ((5 + a + (-1 + x)^2)*(-1 + x))/(8*(12 + 7*a + a^2)*(3 + a - 2*(-1 + x)^2 - (-1 + x)^4)^2) + (((6 + a)*(25 + 7*a) + 6*(7 + 2*a)*(-1 + x)^2)*(-1 + x))/(32*(3 + a)^2*(4 + a)^2*(3 + a - 2*(-1 + x)^2 - (-1 + x)^4)) - (3*(80 + 7*a^2 + 14*Sqrt[4 + a] + a*(47 + 4*Sqrt[4 + a]))*ArcTan[(-1 + x)/Sqrt[1 - Sqrt[4 + a]]])/(64*(3 + a)^2*(4 + a)^(5/2)*Sqrt[1 - Sqrt[4 + a]]) - (3*(14 + 4*a - (80 + 47*a + 7*a^2)/Sqrt[4 + a])*ArcTan[(-1 + x)/Sqrt[1 + Sqrt[4 + a]]])/(64*(3 + a)^2*(4 + a)^2*Sqrt[1 + Sqrt[4 + a]]) + (3*ArcTanh[(1 + (-1 + x)^2)/Sqrt[4 + a]])/(16*(4 + a)^(5/2))","A",12,10,24,0.4167,1,"{1680, 1673, 1092, 1178, 1166, 204, 1107, 614, 618, 206}"
130,1,210,0,0.1636922,"\int x^2 \left(a+8 x-8 x^2+4 x^3-x^4\right)^4 \, dx","Int[x^2*(a + 8*x - 8*x^2 + 4*x^3 - x^4)^4,x]","\frac{2}{11} \left(3 a^2-1536 a+20480\right) x^{11}-\frac{24}{5} \left(a^2-128 a+896\right) x^{10}-4 \left(15 a^2-288 a+512\right) x^8+\frac{4}{7} \left(-a^3+192 a^2-1536 a+1024\right) x^7+\frac{8}{3} a \left(a^2-48 a+128\right) x^6+\frac{32}{5} (12-a) a^2 x^5+8 a^3 x^4+\frac{a^4 x^3}{3}+\frac{4}{15} (640-a) x^{15}-\frac{8}{7} (464-3 a) x^{14}+\frac{32}{13} (524-9 a) x^{13}-\frac{8}{3} (928-35 a) x^{12}+\frac{64}{9} (128-3 a) (4-a) x^9+\frac{x^{19}}{19}-\frac{8 x^{18}}{9}+\frac{128 x^{17}}{17}-42 x^{16}","\frac{2}{11} \left(3 a^2-1536 a+20480\right) x^{11}-\frac{24}{5} \left(a^2-128 a+896\right) x^{10}-4 \left(15 a^2-288 a+512\right) x^8+\frac{4}{7} \left(-a^3+192 a^2-1536 a+1024\right) x^7+\frac{8}{3} a \left(a^2-48 a+128\right) x^6+\frac{32}{5} (12-a) a^2 x^5+8 a^3 x^4+\frac{a^4 x^3}{3}+\frac{4}{15} (640-a) x^{15}-\frac{8}{7} (464-3 a) x^{14}+\frac{32}{13} (524-9 a) x^{13}-\frac{8}{3} (928-35 a) x^{12}+\frac{64}{9} (128-3 a) (4-a) x^9+\frac{x^{19}}{19}-\frac{8 x^{18}}{9}+\frac{128 x^{17}}{17}-42 x^{16}",1,"(a^4*x^3)/3 + 8*a^3*x^4 + (32*(12 - a)*a^2*x^5)/5 + (8*a*(128 - 48*a + a^2)*x^6)/3 + (4*(1024 - 1536*a + 192*a^2 - a^3)*x^7)/7 - 4*(512 - 288*a + 15*a^2)*x^8 + (64*(128 - 3*a)*(4 - a)*x^9)/9 - (24*(896 - 128*a + a^2)*x^10)/5 + (2*(20480 - 1536*a + 3*a^2)*x^11)/11 - (8*(928 - 35*a)*x^12)/3 + (32*(524 - 9*a)*x^13)/13 - (8*(464 - 3*a)*x^14)/7 + (4*(640 - a)*x^15)/15 - 42*x^16 + (128*x^17)/17 - (8*x^18)/9 + x^19/19","A",2,1,26,0.03846,1,"{6742}"
131,1,138,0,0.1208109,"\int x^2 \left(a+8 x-8 x^2+4 x^3-x^4\right)^3 \, dx","Int[x^2*(a + 8*x - 8*x^2 + 4*x^3 - x^4)^3,x]","-\frac{3}{7} \left(a^2-128 a+512\right) x^7+\frac{2}{3} \left(3 a^2-96 a+128\right) x^6+6 a^2 x^4+\frac{a^3 x^3}{3}-\frac{3}{11} (256-a) x^{11}+\frac{12}{5} (64-a) x^{10}-\frac{32}{9} (70-3 a) x^9+6 (48-5 a) x^8+\frac{24}{5} (8-a) a x^5-\frac{x^{15}}{15}+\frac{6 x^{14}}{7}-\frac{72 x^{13}}{13}+\frac{70 x^{12}}{3}","-\frac{3}{7} \left(a^2-128 a+512\right) x^7+\frac{2}{3} \left(3 a^2-96 a+128\right) x^6+6 a^2 x^4+\frac{a^3 x^3}{3}-\frac{3}{11} (256-a) x^{11}+\frac{12}{5} (64-a) x^{10}-\frac{32}{9} (70-3 a) x^9+6 (48-5 a) x^8+\frac{24}{5} (8-a) a x^5-\frac{x^{15}}{15}+\frac{6 x^{14}}{7}-\frac{72 x^{13}}{13}+\frac{70 x^{12}}{3}",1,"(a^3*x^3)/3 + 6*a^2*x^4 + (24*(8 - a)*a*x^5)/5 + (2*(128 - 96*a + 3*a^2)*x^6)/3 - (3*(512 - 128*a + a^2)*x^7)/7 + 6*(48 - 5*a)*x^8 - (32*(70 - 3*a)*x^9)/9 + (12*(64 - a)*x^10)/5 - (3*(256 - a)*x^11)/11 + (70*x^12)/3 - (72*x^13)/13 + (6*x^14)/7 - x^15/15","A",2,1,26,0.03846,1,"{6742}"
132,1,79,0,0.0767837,"\int x^2 \left(a+8 x-8 x^2+4 x^3-x^4\right)^2 \, dx","Int[x^2*(a + 8*x - 8*x^2 + 4*x^3 - x^4)^2,x]","\frac{a^2 x^3}{3}+\frac{2}{7} (64-a) x^7-\frac{4}{3} (16-a) x^6+\frac{16}{5} (4-a) x^5+4 a x^4+\frac{x^{11}}{11}-\frac{4 x^{10}}{5}+\frac{32 x^9}{9}-10 x^8","\frac{a^2 x^3}{3}+\frac{2}{7} (64-a) x^7-\frac{4}{3} (16-a) x^6+\frac{16}{5} (4-a) x^5+4 a x^4+\frac{x^{11}}{11}-\frac{4 x^{10}}{5}+\frac{32 x^9}{9}-10 x^8",1,"(a^2*x^3)/3 + 4*a*x^4 + (16*(4 - a)*x^5)/5 - (4*(16 - a)*x^6)/3 + (2*(64 - a)*x^7)/7 - 10*x^8 + (32*x^9)/9 - (4*x^10)/5 + x^11/11","A",2,1,26,0.03846,1,"{6742}"
133,1,35,0,0.0090193,"\int x^2 \left(a+8 x-8 x^2+4 x^3-x^4\right) \, dx","Int[x^2*(a + 8*x - 8*x^2 + 4*x^3 - x^4),x]","\frac{a x^3}{3}-\frac{x^7}{7}+\frac{2 x^6}{3}-\frac{8 x^5}{5}+2 x^4","\frac{a x^3}{3}-\frac{x^7}{7}+\frac{2 x^6}{3}-\frac{8 x^5}{5}+2 x^4",1,"(a*x^3)/3 + 2*x^4 - (8*x^5)/5 + (2*x^6)/3 - x^7/7","A",2,1,24,0.04167,1,"{14}"
134,1,99,0,0.0870459,"\int \frac{x^2}{a+8 x-8 x^2+4 x^3-x^4} \, dx","Int[x^2/(a + 8*x - 8*x^2 + 4*x^3 - x^4),x]","-\frac{\tan ^{-1}\left(\frac{x-1}{\sqrt{1-\sqrt{a+4}}}\right)}{2 \sqrt{1-\sqrt{a+4}}}-\frac{\tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)}{2 \sqrt{\sqrt{a+4}+1}}+\frac{\tanh ^{-1}\left(\frac{(x-1)^2+1}{\sqrt{a+4}}\right)}{\sqrt{a+4}}","-\frac{\tan ^{-1}\left(\frac{x-1}{\sqrt{1-\sqrt{a+4}}}\right)}{2 \sqrt{1-\sqrt{a+4}}}-\frac{\tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)}{2 \sqrt{\sqrt{a+4}+1}}+\frac{\tanh ^{-1}\left(\frac{(x-1)^2+1}{\sqrt{a+4}}\right)}{\sqrt{a+4}}",1,"-ArcTan[(-1 + x)/Sqrt[1 - Sqrt[4 + a]]]/(2*Sqrt[1 - Sqrt[4 + a]]) - ArcTan[(-1 + x)/Sqrt[1 + Sqrt[4 + a]]]/(2*Sqrt[1 + Sqrt[4 + a]]) + ArcTanh[(1 + (-1 + x)^2)/Sqrt[4 + a]]/Sqrt[4 + a]","A",9,8,26,0.3077,1,"{1680, 1673, 1166, 204, 12, 1107, 618, 206}"
135,1,225,0,0.2126088,"\int \frac{x^2}{\left(a+8 x-8 x^2+4 x^3-x^4\right)^2} \, dx","Int[x^2/(a + 8*x - 8*x^2 + 4*x^3 - x^4)^2,x]","\frac{(a+4) \left((x-1)^2+2\right) (x-1)}{4 \left(a^2+7 a+12\right) \left(a-(x-1)^4-2 (x-1)^2+3\right)}+\frac{(x-1)^2+1}{2 (a+4) \left(a-(x-1)^4-2 (x-1)^2+3\right)}-\frac{\left(a+\sqrt{a+4}+4\right) \tan ^{-1}\left(\frac{x-1}{\sqrt{1-\sqrt{a+4}}}\right)}{8 (a+3) (a+4) \sqrt{1-\sqrt{a+4}}}-\frac{\left(a-\sqrt{a+4}+4\right) \tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)}{8 (a+3) (a+4) \sqrt{\sqrt{a+4}+1}}+\frac{\tanh ^{-1}\left(\frac{(x-1)^2+1}{\sqrt{a+4}}\right)}{2 (a+4)^{3/2}}","\frac{(a+4) \left((x-1)^2+2\right) (x-1)}{4 \left(a^2+7 a+12\right) \left(a-(x-1)^4-2 (x-1)^2+3\right)}+\frac{(x-1)^2+1}{2 (a+4) \left(a-(x-1)^4-2 (x-1)^2+3\right)}-\frac{\left(a+\sqrt{a+4}+4\right) \tan ^{-1}\left(\frac{x-1}{\sqrt{1-\sqrt{a+4}}}\right)}{8 (a+3) (a+4) \sqrt{1-\sqrt{a+4}}}-\frac{\left(a-\sqrt{a+4}+4\right) \tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)}{8 (a+3) (a+4) \sqrt{\sqrt{a+4}+1}}+\frac{\tanh ^{-1}\left(\frac{(x-1)^2+1}{\sqrt{a+4}}\right)}{2 (a+4)^{3/2}}",1,"(1 + (-1 + x)^2)/(2*(4 + a)*(3 + a - 2*(-1 + x)^2 - (-1 + x)^4)) + ((4 + a)*(2 + (-1 + x)^2)*(-1 + x))/(4*(12 + 7*a + a^2)*(3 + a - 2*(-1 + x)^2 - (-1 + x)^4)) - ((4 + a + Sqrt[4 + a])*ArcTan[(-1 + x)/Sqrt[1 - Sqrt[4 + a]]])/(8*(3 + a)*(4 + a)*Sqrt[1 - Sqrt[4 + a]]) - ((4 + a - Sqrt[4 + a])*ArcTan[(-1 + x)/Sqrt[1 + Sqrt[4 + a]]])/(8*(3 + a)*(4 + a)*Sqrt[1 + Sqrt[4 + a]]) + ArcTanh[(1 + (-1 + x)^2)/Sqrt[4 + a]]/(2*(4 + a)^(3/2))","A",11,10,26,0.3846,1,"{1680, 1673, 1178, 1166, 204, 12, 1107, 614, 618, 206}"
136,1,545,0,1.4764534,"\int \frac{x^4}{27 a^3+27 a^2 b x^2+27 a^2 c x^3+9 a b^2 x^4+b^3 x^6} \, dx","Int[x^4/(27*a^3 + 27*a^2*b*x^2 + 27*a^2*c*x^3 + 9*a*b^2*x^4 + b^3*x^6),x]","-\frac{\sqrt[3]{-1} \left(3 \sqrt[3]{a} c^{2/3}+2 \sqrt[3]{-1} b\right) \tan ^{-1}\left(\frac{3 \sqrt[3]{-1} a^{2/3} \sqrt[3]{c}-2 b x}{\sqrt{3} \sqrt{a} \sqrt{4 b-3 (-1)^{2/3} \sqrt[3]{a} c^{2/3}}}\right)}{3 \sqrt{3} \left(1+\sqrt[3]{-1}\right)^2 a^{5/6} b^2 c^{2/3} \sqrt{4 b-3 (-1)^{2/3} \sqrt[3]{a} c^{2/3}}}-\frac{\left(2 b-3 \sqrt[3]{a} c^{2/3}\right) \tan ^{-1}\left(\frac{3 a^{2/3} \sqrt[3]{c}+2 b x}{\sqrt{3} \sqrt{a} \sqrt{4 b-3 \sqrt[3]{a} c^{2/3}}}\right)}{9 \sqrt{3} a^{5/6} b^2 c^{2/3} \sqrt{4 b-3 \sqrt[3]{a} c^{2/3}}}-\frac{(-1)^{2/3} \left(3 \sqrt[3]{-1} \sqrt[3]{a} c^{2/3}+2 b\right) \tan ^{-1}\left(\frac{3 (-1)^{2/3} a^{2/3} \sqrt[3]{c}+2 b x}{\sqrt{3} \sqrt{a} \sqrt{3 \sqrt[3]{-1} \sqrt[3]{a} c^{2/3}+4 b}}\right)}{3 \sqrt{3} \left(1-\sqrt[3]{-1}\right) \left(1+\sqrt[3]{-1}\right)^2 a^{5/6} b^2 c^{2/3} \sqrt{3 \sqrt[3]{-1} \sqrt[3]{a} c^{2/3}+4 b}}-\frac{\log \left(3 a^{2/3} \sqrt[3]{c} x+3 a+b x^2\right)}{18 a^{2/3} b^2 \sqrt[3]{c}}+\frac{\log \left(-3 \sqrt[3]{-1} a^{2/3} \sqrt[3]{c} x+3 a+b x^2\right)}{6 \left(1+\sqrt[3]{-1}\right)^2 a^{2/3} b^2 \sqrt[3]{c}}+\frac{\sqrt[3]{-1} \log \left(3 (-1)^{2/3} a^{2/3} \sqrt[3]{c} x+3 a+b x^2\right)}{18 a^{2/3} b^2 \sqrt[3]{c}}","-\frac{\sqrt[3]{-1} \left(3 \sqrt[3]{a} c^{2/3}+2 \sqrt[3]{-1} b\right) \tan ^{-1}\left(\frac{3 \sqrt[3]{-1} a^{2/3} \sqrt[3]{c}-2 b x}{\sqrt{3} \sqrt{a} \sqrt{4 b-3 (-1)^{2/3} \sqrt[3]{a} c^{2/3}}}\right)}{3 \sqrt{3} \left(1+\sqrt[3]{-1}\right)^2 a^{5/6} b^2 c^{2/3} \sqrt{4 b-3 (-1)^{2/3} \sqrt[3]{a} c^{2/3}}}-\frac{\left(2 b-3 \sqrt[3]{a} c^{2/3}\right) \tan ^{-1}\left(\frac{3 a^{2/3} \sqrt[3]{c}+2 b x}{\sqrt{3} \sqrt{a} \sqrt{4 b-3 \sqrt[3]{a} c^{2/3}}}\right)}{9 \sqrt{3} a^{5/6} b^2 c^{2/3} \sqrt{4 b-3 \sqrt[3]{a} c^{2/3}}}-\frac{(-1)^{2/3} \left(3 \sqrt[3]{-1} \sqrt[3]{a} c^{2/3}+2 b\right) \tan ^{-1}\left(\frac{3 (-1)^{2/3} a^{2/3} \sqrt[3]{c}+2 b x}{\sqrt{3} \sqrt{a} \sqrt{3 \sqrt[3]{-1} \sqrt[3]{a} c^{2/3}+4 b}}\right)}{3 \sqrt{3} \left(1-\sqrt[3]{-1}\right) \left(1+\sqrt[3]{-1}\right)^2 a^{5/6} b^2 c^{2/3} \sqrt{3 \sqrt[3]{-1} \sqrt[3]{a} c^{2/3}+4 b}}-\frac{\log \left(3 a^{2/3} \sqrt[3]{c} x+3 a+b x^2\right)}{18 a^{2/3} b^2 \sqrt[3]{c}}+\frac{\log \left(-3 \sqrt[3]{-1} a^{2/3} \sqrt[3]{c} x+3 a+b x^2\right)}{6 \left(1+\sqrt[3]{-1}\right)^2 a^{2/3} b^2 \sqrt[3]{c}}+\frac{\sqrt[3]{-1} \log \left(3 (-1)^{2/3} a^{2/3} \sqrt[3]{c} x+3 a+b x^2\right)}{18 a^{2/3} b^2 \sqrt[3]{c}}",1,"-((-1)^(1/3)*(2*(-1)^(1/3)*b + 3*a^(1/3)*c^(2/3))*ArcTan[(3*(-1)^(1/3)*a^(2/3)*c^(1/3) - 2*b*x)/(Sqrt[3]*Sqrt[a]*Sqrt[4*b - 3*(-1)^(2/3)*a^(1/3)*c^(2/3)])])/(3*Sqrt[3]*(1 + (-1)^(1/3))^2*a^(5/6)*b^2*Sqrt[4*b - 3*(-1)^(2/3)*a^(1/3)*c^(2/3)]*c^(2/3)) - ((2*b - 3*a^(1/3)*c^(2/3))*ArcTan[(3*a^(2/3)*c^(1/3) + 2*b*x)/(Sqrt[3]*Sqrt[a]*Sqrt[4*b - 3*a^(1/3)*c^(2/3)])])/(9*Sqrt[3]*a^(5/6)*b^2*Sqrt[4*b - 3*a^(1/3)*c^(2/3)]*c^(2/3)) - ((-1)^(2/3)*(2*b + 3*(-1)^(1/3)*a^(1/3)*c^(2/3))*ArcTan[(3*(-1)^(2/3)*a^(2/3)*c^(1/3) + 2*b*x)/(Sqrt[3]*Sqrt[a]*Sqrt[4*b + 3*(-1)^(1/3)*a^(1/3)*c^(2/3)])])/(3*Sqrt[3]*(1 - (-1)^(1/3))*(1 + (-1)^(1/3))^2*a^(5/6)*b^2*Sqrt[4*b + 3*(-1)^(1/3)*a^(1/3)*c^(2/3)]*c^(2/3)) - Log[3*a + 3*a^(2/3)*c^(1/3)*x + b*x^2]/(18*a^(2/3)*b^2*c^(1/3)) + Log[3*a - 3*(-1)^(1/3)*a^(2/3)*c^(1/3)*x + b*x^2]/(6*(1 + (-1)^(1/3))^2*a^(2/3)*b^2*c^(1/3)) + ((-1)^(1/3)*Log[3*a + 3*(-1)^(2/3)*a^(2/3)*c^(1/3)*x + b*x^2])/(18*a^(2/3)*b^2*c^(1/3))","A",14,5,46,0.1087,1,"{2097, 634, 618, 204, 628}"
137,1,487,0,0.7559034,"\int \frac{x^3}{27 a^3+27 a^2 b x^2+27 a^2 c x^3+9 a b^2 x^4+b^3 x^6} \, dx","Int[x^3/(27*a^3 + 27*a^2*b*x^2 + 27*a^2*c*x^3 + 9*a*b^2*x^4 + b^3*x^6),x]","\frac{\log \left(3 a^{2/3} \sqrt[3]{c} x+3 a+b x^2\right)}{54 a^{4/3} b c^{2/3}}-\frac{(-1)^{2/3} \log \left(-3 \sqrt[3]{-1} a^{2/3} \sqrt[3]{c} x+3 a+b x^2\right)}{18 \left(1+\sqrt[3]{-1}\right)^2 a^{4/3} b c^{2/3}}+\frac{(-1)^{2/3} \log \left(3 (-1)^{2/3} a^{2/3} \sqrt[3]{c} x+3 a+b x^2\right)}{54 a^{4/3} b c^{2/3}}-\frac{\tan ^{-1}\left(\frac{3 \sqrt[3]{-1} a^{2/3} \sqrt[3]{c}-2 b x}{\sqrt{3} \sqrt{a} \sqrt{4 b-3 (-1)^{2/3} \sqrt[3]{a} c^{2/3}}}\right)}{3 \sqrt{3} \left(1+\sqrt[3]{-1}\right)^2 a^{7/6} b \sqrt[3]{c} \sqrt{4 b-3 (-1)^{2/3} \sqrt[3]{a} c^{2/3}}}-\frac{\tan ^{-1}\left(\frac{3 a^{2/3} \sqrt[3]{c}+2 b x}{\sqrt{3} \sqrt{a} \sqrt{4 b-3 \sqrt[3]{a} c^{2/3}}}\right)}{9 \sqrt{3} a^{7/6} b \sqrt[3]{c} \sqrt{4 b-3 \sqrt[3]{a} c^{2/3}}}+\frac{\sqrt[3]{-1} \tan ^{-1}\left(\frac{3 (-1)^{2/3} a^{2/3} \sqrt[3]{c}+2 b x}{\sqrt{3} \sqrt{a} \sqrt{3 \sqrt[3]{-1} \sqrt[3]{a} c^{2/3}+4 b}}\right)}{3 \sqrt{3} \left(1-\sqrt[3]{-1}\right) \left(1+\sqrt[3]{-1}\right)^2 a^{7/6} b \sqrt[3]{c} \sqrt{3 \sqrt[3]{-1} \sqrt[3]{a} c^{2/3}+4 b}}","\frac{\log \left(3 a^{2/3} \sqrt[3]{c} x+3 a+b x^2\right)}{54 a^{4/3} b c^{2/3}}-\frac{(-1)^{2/3} \log \left(-3 \sqrt[3]{-1} a^{2/3} \sqrt[3]{c} x+3 a+b x^2\right)}{18 \left(1+\sqrt[3]{-1}\right)^2 a^{4/3} b c^{2/3}}+\frac{(-1)^{2/3} \log \left(3 (-1)^{2/3} a^{2/3} \sqrt[3]{c} x+3 a+b x^2\right)}{54 a^{4/3} b c^{2/3}}-\frac{\tan ^{-1}\left(\frac{3 \sqrt[3]{-1} a^{2/3} \sqrt[3]{c}-2 b x}{\sqrt{3} \sqrt{a} \sqrt{4 b-3 (-1)^{2/3} \sqrt[3]{a} c^{2/3}}}\right)}{3 \sqrt{3} \left(1+\sqrt[3]{-1}\right)^2 a^{7/6} b \sqrt[3]{c} \sqrt{4 b-3 (-1)^{2/3} \sqrt[3]{a} c^{2/3}}}-\frac{\tan ^{-1}\left(\frac{3 a^{2/3} \sqrt[3]{c}+2 b x}{\sqrt{3} \sqrt{a} \sqrt{4 b-3 \sqrt[3]{a} c^{2/3}}}\right)}{9 \sqrt{3} a^{7/6} b \sqrt[3]{c} \sqrt{4 b-3 \sqrt[3]{a} c^{2/3}}}+\frac{\sqrt[3]{-1} \tan ^{-1}\left(\frac{3 (-1)^{2/3} a^{2/3} \sqrt[3]{c}+2 b x}{\sqrt{3} \sqrt{a} \sqrt{3 \sqrt[3]{-1} \sqrt[3]{a} c^{2/3}+4 b}}\right)}{3 \sqrt{3} \left(1-\sqrt[3]{-1}\right) \left(1+\sqrt[3]{-1}\right)^2 a^{7/6} b \sqrt[3]{c} \sqrt{3 \sqrt[3]{-1} \sqrt[3]{a} c^{2/3}+4 b}}",1,"-ArcTan[(3*(-1)^(1/3)*a^(2/3)*c^(1/3) - 2*b*x)/(Sqrt[3]*Sqrt[a]*Sqrt[4*b - 3*(-1)^(2/3)*a^(1/3)*c^(2/3)])]/(3*Sqrt[3]*(1 + (-1)^(1/3))^2*a^(7/6)*b*Sqrt[4*b - 3*(-1)^(2/3)*a^(1/3)*c^(2/3)]*c^(1/3)) - ArcTan[(3*a^(2/3)*c^(1/3) + 2*b*x)/(Sqrt[3]*Sqrt[a]*Sqrt[4*b - 3*a^(1/3)*c^(2/3)])]/(9*Sqrt[3]*a^(7/6)*b*Sqrt[4*b - 3*a^(1/3)*c^(2/3)]*c^(1/3)) + ((-1)^(1/3)*ArcTan[(3*(-1)^(2/3)*a^(2/3)*c^(1/3) + 2*b*x)/(Sqrt[3]*Sqrt[a]*Sqrt[4*b + 3*(-1)^(1/3)*a^(1/3)*c^(2/3)])])/(3*Sqrt[3]*(1 - (-1)^(1/3))*(1 + (-1)^(1/3))^2*a^(7/6)*b*Sqrt[4*b + 3*(-1)^(1/3)*a^(1/3)*c^(2/3)]*c^(1/3)) + Log[3*a + 3*a^(2/3)*c^(1/3)*x + b*x^2]/(54*a^(4/3)*b*c^(2/3)) - ((-1)^(2/3)*Log[3*a - 3*(-1)^(1/3)*a^(2/3)*c^(1/3)*x + b*x^2])/(18*(1 + (-1)^(1/3))^2*a^(4/3)*b*c^(2/3)) + ((-1)^(2/3)*Log[3*a + 3*(-1)^(2/3)*a^(2/3)*c^(1/3)*x + b*x^2])/(54*a^(4/3)*b*c^(2/3))","A",14,5,46,0.1087,1,"{2097, 634, 618, 204, 628}"
138,1,334,0,0.4696588,"\int \frac{x^2}{27 a^3+27 a^2 b x^2+27 a^2 c x^3+9 a b^2 x^4+b^3 x^6} \, dx","Int[x^2/(27*a^3 + 27*a^2*b*x^2 + 27*a^2*c*x^3 + 9*a*b^2*x^4 + b^3*x^6),x]","\frac{2 (-1)^{2/3} \tan ^{-1}\left(\frac{3 \sqrt[3]{-1} a^{2/3} \sqrt[3]{c}-2 b x}{\sqrt{3} \sqrt{a} \sqrt{4 b-3 (-1)^{2/3} \sqrt[3]{a} c^{2/3}}}\right)}{9 \sqrt{3} \left(1+\sqrt[3]{-1}\right)^2 a^{11/6} c^{2/3} \sqrt{4 b-3 (-1)^{2/3} \sqrt[3]{a} c^{2/3}}}+\frac{2 \tan ^{-1}\left(\frac{3 a^{2/3} \sqrt[3]{c}+2 b x}{\sqrt{3} \sqrt{a} \sqrt{4 b-3 \sqrt[3]{a} c^{2/3}}}\right)}{27 \sqrt{3} a^{11/6} c^{2/3} \sqrt{4 b-3 \sqrt[3]{a} c^{2/3}}}+\frac{2 (-1)^{2/3} \tan ^{-1}\left(\frac{3 (-1)^{2/3} a^{2/3} \sqrt[3]{c}+2 b x}{\sqrt{3} \sqrt{a} \sqrt{3 \sqrt[3]{-1} \sqrt[3]{a} c^{2/3}+4 b}}\right)}{9 \sqrt{3} \left(1-\sqrt[3]{-1}\right) \left(1+\sqrt[3]{-1}\right)^2 a^{11/6} c^{2/3} \sqrt{3 \sqrt[3]{-1} \sqrt[3]{a} c^{2/3}+4 b}}","\frac{2 (-1)^{2/3} \tan ^{-1}\left(\frac{3 \sqrt[3]{-1} a^{2/3} \sqrt[3]{c}-2 b x}{\sqrt{3} \sqrt{a} \sqrt{4 b-3 (-1)^{2/3} \sqrt[3]{a} c^{2/3}}}\right)}{9 \sqrt{3} \left(1+\sqrt[3]{-1}\right)^2 a^{11/6} c^{2/3} \sqrt{4 b-3 (-1)^{2/3} \sqrt[3]{a} c^{2/3}}}+\frac{2 \tan ^{-1}\left(\frac{3 a^{2/3} \sqrt[3]{c}+2 b x}{\sqrt{3} \sqrt{a} \sqrt{4 b-3 \sqrt[3]{a} c^{2/3}}}\right)}{27 \sqrt{3} a^{11/6} c^{2/3} \sqrt{4 b-3 \sqrt[3]{a} c^{2/3}}}+\frac{2 (-1)^{2/3} \tan ^{-1}\left(\frac{3 (-1)^{2/3} a^{2/3} \sqrt[3]{c}+2 b x}{\sqrt{3} \sqrt{a} \sqrt{3 \sqrt[3]{-1} \sqrt[3]{a} c^{2/3}+4 b}}\right)}{9 \sqrt{3} \left(1-\sqrt[3]{-1}\right) \left(1+\sqrt[3]{-1}\right)^2 a^{11/6} c^{2/3} \sqrt{3 \sqrt[3]{-1} \sqrt[3]{a} c^{2/3}+4 b}}",1,"(2*(-1)^(2/3)*ArcTan[(3*(-1)^(1/3)*a^(2/3)*c^(1/3) - 2*b*x)/(Sqrt[3]*Sqrt[a]*Sqrt[4*b - 3*(-1)^(2/3)*a^(1/3)*c^(2/3)])])/(9*Sqrt[3]*(1 + (-1)^(1/3))^2*a^(11/6)*Sqrt[4*b - 3*(-1)^(2/3)*a^(1/3)*c^(2/3)]*c^(2/3)) + (2*ArcTan[(3*a^(2/3)*c^(1/3) + 2*b*x)/(Sqrt[3]*Sqrt[a]*Sqrt[4*b - 3*a^(1/3)*c^(2/3)])])/(27*Sqrt[3]*a^(11/6)*Sqrt[4*b - 3*a^(1/3)*c^(2/3)]*c^(2/3)) + (2*(-1)^(2/3)*ArcTan[(3*(-1)^(2/3)*a^(2/3)*c^(1/3) + 2*b*x)/(Sqrt[3]*Sqrt[a]*Sqrt[4*b + 3*(-1)^(1/3)*a^(1/3)*c^(2/3)])])/(9*Sqrt[3]*(1 - (-1)^(1/3))*(1 + (-1)^(1/3))^2*a^(11/6)*Sqrt[4*b + 3*(-1)^(1/3)*a^(1/3)*c^(2/3)]*c^(2/3))","A",8,3,46,0.06522,1,"{2097, 618, 204}"
139,1,469,0,0.6844319,"\int \frac{x}{27 a^3+27 a^2 b x^2+27 a^2 c x^3+9 a b^2 x^4+b^3 x^6} \, dx","Int[x/(27*a^3 + 27*a^2*b*x^2 + 27*a^2*c*x^3 + 9*a*b^2*x^4 + b^3*x^6),x]","-\frac{\log \left(3 a^{2/3} \sqrt[3]{c} x+3 a+b x^2\right)}{162 a^{7/3} c^{2/3}}+\frac{(-1)^{2/3} \log \left(-3 \sqrt[3]{-1} a^{2/3} \sqrt[3]{c} x+3 a+b x^2\right)}{54 \left(1+\sqrt[3]{-1}\right)^2 a^{7/3} c^{2/3}}-\frac{(-1)^{2/3} \log \left(3 (-1)^{2/3} a^{2/3} \sqrt[3]{c} x+3 a+b x^2\right)}{162 a^{7/3} c^{2/3}}-\frac{\tan ^{-1}\left(\frac{3 \sqrt[3]{-1} a^{2/3} \sqrt[3]{c}-2 b x}{\sqrt{3} \sqrt{a} \sqrt{4 b-3 (-1)^{2/3} \sqrt[3]{a} c^{2/3}}}\right)}{9 \sqrt{3} \left(1+\sqrt[3]{-1}\right)^2 a^{13/6} \sqrt[3]{c} \sqrt{4 b-3 (-1)^{2/3} \sqrt[3]{a} c^{2/3}}}-\frac{\tan ^{-1}\left(\frac{3 a^{2/3} \sqrt[3]{c}+2 b x}{\sqrt{3} \sqrt{a} \sqrt{4 b-3 \sqrt[3]{a} c^{2/3}}}\right)}{27 \sqrt{3} a^{13/6} \sqrt[3]{c} \sqrt{4 b-3 \sqrt[3]{a} c^{2/3}}}+\frac{\sqrt[3]{-1} \tan ^{-1}\left(\frac{3 (-1)^{2/3} a^{2/3} \sqrt[3]{c}+2 b x}{\sqrt{3} \sqrt{a} \sqrt{3 \sqrt[3]{-1} \sqrt[3]{a} c^{2/3}+4 b}}\right)}{9 \sqrt{3} \left(1-\sqrt[3]{-1}\right) \left(1+\sqrt[3]{-1}\right)^2 a^{13/6} \sqrt[3]{c} \sqrt{3 \sqrt[3]{-1} \sqrt[3]{a} c^{2/3}+4 b}}","-\frac{\log \left(3 a^{2/3} \sqrt[3]{c} x+3 a+b x^2\right)}{162 a^{7/3} c^{2/3}}+\frac{(-1)^{2/3} \log \left(-3 \sqrt[3]{-1} a^{2/3} \sqrt[3]{c} x+3 a+b x^2\right)}{54 \left(1+\sqrt[3]{-1}\right)^2 a^{7/3} c^{2/3}}-\frac{(-1)^{2/3} \log \left(3 (-1)^{2/3} a^{2/3} \sqrt[3]{c} x+3 a+b x^2\right)}{162 a^{7/3} c^{2/3}}-\frac{\tan ^{-1}\left(\frac{3 \sqrt[3]{-1} a^{2/3} \sqrt[3]{c}-2 b x}{\sqrt{3} \sqrt{a} \sqrt{4 b-3 (-1)^{2/3} \sqrt[3]{a} c^{2/3}}}\right)}{9 \sqrt{3} \left(1+\sqrt[3]{-1}\right)^2 a^{13/6} \sqrt[3]{c} \sqrt{4 b-3 (-1)^{2/3} \sqrt[3]{a} c^{2/3}}}-\frac{\tan ^{-1}\left(\frac{3 a^{2/3} \sqrt[3]{c}+2 b x}{\sqrt{3} \sqrt{a} \sqrt{4 b-3 \sqrt[3]{a} c^{2/3}}}\right)}{27 \sqrt{3} a^{13/6} \sqrt[3]{c} \sqrt{4 b-3 \sqrt[3]{a} c^{2/3}}}+\frac{\sqrt[3]{-1} \tan ^{-1}\left(\frac{3 (-1)^{2/3} a^{2/3} \sqrt[3]{c}+2 b x}{\sqrt{3} \sqrt{a} \sqrt{3 \sqrt[3]{-1} \sqrt[3]{a} c^{2/3}+4 b}}\right)}{9 \sqrt{3} \left(1-\sqrt[3]{-1}\right) \left(1+\sqrt[3]{-1}\right)^2 a^{13/6} \sqrt[3]{c} \sqrt{3 \sqrt[3]{-1} \sqrt[3]{a} c^{2/3}+4 b}}",1,"-ArcTan[(3*(-1)^(1/3)*a^(2/3)*c^(1/3) - 2*b*x)/(Sqrt[3]*Sqrt[a]*Sqrt[4*b - 3*(-1)^(2/3)*a^(1/3)*c^(2/3)])]/(9*Sqrt[3]*(1 + (-1)^(1/3))^2*a^(13/6)*Sqrt[4*b - 3*(-1)^(2/3)*a^(1/3)*c^(2/3)]*c^(1/3)) - ArcTan[(3*a^(2/3)*c^(1/3) + 2*b*x)/(Sqrt[3]*Sqrt[a]*Sqrt[4*b - 3*a^(1/3)*c^(2/3)])]/(27*Sqrt[3]*a^(13/6)*Sqrt[4*b - 3*a^(1/3)*c^(2/3)]*c^(1/3)) + ((-1)^(1/3)*ArcTan[(3*(-1)^(2/3)*a^(2/3)*c^(1/3) + 2*b*x)/(Sqrt[3]*Sqrt[a]*Sqrt[4*b + 3*(-1)^(1/3)*a^(1/3)*c^(2/3)])])/(9*Sqrt[3]*(1 - (-1)^(1/3))*(1 + (-1)^(1/3))^2*a^(13/6)*Sqrt[4*b + 3*(-1)^(1/3)*a^(1/3)*c^(2/3)]*c^(1/3)) - Log[3*a + 3*a^(2/3)*c^(1/3)*x + b*x^2]/(162*a^(7/3)*c^(2/3)) + ((-1)^(2/3)*Log[3*a - 3*(-1)^(1/3)*a^(2/3)*c^(1/3)*x + b*x^2])/(54*(1 + (-1)^(1/3))^2*a^(7/3)*c^(2/3)) - ((-1)^(2/3)*Log[3*a + 3*(-1)^(2/3)*a^(2/3)*c^(1/3)*x + b*x^2])/(162*a^(7/3)*c^(2/3))","A",14,5,44,0.1136,1,"{2097, 634, 618, 204, 628}"
140,1,522,0,0.8608407,"\int \frac{1}{27 a^3+27 a^2 b x^2+27 a^2 c x^3+9 a b^2 x^4+b^3 x^6} \, dx","Int[(27*a^3 + 27*a^2*b*x^2 + 27*a^2*c*x^3 + 9*a*b^2*x^4 + b^3*x^6)^(-1),x]","-\frac{\sqrt[3]{-1} \left(3 \sqrt[3]{a} c^{2/3}+2 \sqrt[3]{-1} b\right) \tan ^{-1}\left(\frac{3 \sqrt[3]{-1} a^{2/3} \sqrt[3]{c}-2 b x}{\sqrt{3} \sqrt{a} \sqrt{4 b-3 (-1)^{2/3} \sqrt[3]{a} c^{2/3}}}\right)}{27 \sqrt{3} \left(1+\sqrt[3]{-1}\right)^2 a^{17/6} c^{2/3} \sqrt{4 b-3 (-1)^{2/3} \sqrt[3]{a} c^{2/3}}}-\frac{\left(2 b-3 \sqrt[3]{a} c^{2/3}\right) \tan ^{-1}\left(\frac{3 a^{2/3} \sqrt[3]{c}+2 b x}{\sqrt{3} \sqrt{a} \sqrt{4 b-3 \sqrt[3]{a} c^{2/3}}}\right)}{81 \sqrt{3} a^{17/6} c^{2/3} \sqrt{4 b-3 \sqrt[3]{a} c^{2/3}}}-\frac{\left(2 (-1)^{2/3} b-3 \sqrt[3]{a} c^{2/3}\right) \tan ^{-1}\left(\frac{3 (-1)^{2/3} a^{2/3} \sqrt[3]{c}+2 b x}{\sqrt{3} \sqrt{a} \sqrt{3 \sqrt[3]{-1} \sqrt[3]{a} c^{2/3}+4 b}}\right)}{27 \sqrt{3} \left(1-\sqrt[3]{-1}\right) \left(1+\sqrt[3]{-1}\right)^2 a^{17/6} c^{2/3} \sqrt{3 \sqrt[3]{-1} \sqrt[3]{a} c^{2/3}+4 b}}+\frac{\log \left(3 a^{2/3} \sqrt[3]{c} x+3 a+b x^2\right)}{162 a^{8/3} \sqrt[3]{c}}-\frac{\log \left(-3 \sqrt[3]{-1} a^{2/3} \sqrt[3]{c} x+3 a+b x^2\right)}{54 \left(1+\sqrt[3]{-1}\right)^2 a^{8/3} \sqrt[3]{c}}-\frac{\sqrt[3]{-1} \log \left(3 (-1)^{2/3} a^{2/3} \sqrt[3]{c} x+3 a+b x^2\right)}{162 a^{8/3} \sqrt[3]{c}}","-\frac{\sqrt[3]{-1} \left(3 \sqrt[3]{a} c^{2/3}+2 \sqrt[3]{-1} b\right) \tan ^{-1}\left(\frac{3 \sqrt[3]{-1} a^{2/3} \sqrt[3]{c}-2 b x}{\sqrt{3} \sqrt{a} \sqrt{4 b-3 (-1)^{2/3} \sqrt[3]{a} c^{2/3}}}\right)}{27 \sqrt{3} \left(1+\sqrt[3]{-1}\right)^2 a^{17/6} c^{2/3} \sqrt{4 b-3 (-1)^{2/3} \sqrt[3]{a} c^{2/3}}}-\frac{\left(2 b-3 \sqrt[3]{a} c^{2/3}\right) \tan ^{-1}\left(\frac{3 a^{2/3} \sqrt[3]{c}+2 b x}{\sqrt{3} \sqrt{a} \sqrt{4 b-3 \sqrt[3]{a} c^{2/3}}}\right)}{81 \sqrt{3} a^{17/6} c^{2/3} \sqrt{4 b-3 \sqrt[3]{a} c^{2/3}}}-\frac{\left(2 (-1)^{2/3} b-3 \sqrt[3]{a} c^{2/3}\right) \tan ^{-1}\left(\frac{3 (-1)^{2/3} a^{2/3} \sqrt[3]{c}+2 b x}{\sqrt{3} \sqrt{a} \sqrt{3 \sqrt[3]{-1} \sqrt[3]{a} c^{2/3}+4 b}}\right)}{27 \sqrt{3} \left(1-\sqrt[3]{-1}\right) \left(1+\sqrt[3]{-1}\right)^2 a^{17/6} c^{2/3} \sqrt{3 \sqrt[3]{-1} \sqrt[3]{a} c^{2/3}+4 b}}+\frac{\log \left(3 a^{2/3} \sqrt[3]{c} x+3 a+b x^2\right)}{162 a^{8/3} \sqrt[3]{c}}-\frac{\log \left(-3 \sqrt[3]{-1} a^{2/3} \sqrt[3]{c} x+3 a+b x^2\right)}{54 \left(1+\sqrt[3]{-1}\right)^2 a^{8/3} \sqrt[3]{c}}-\frac{\sqrt[3]{-1} \log \left(3 (-1)^{2/3} a^{2/3} \sqrt[3]{c} x+3 a+b x^2\right)}{162 a^{8/3} \sqrt[3]{c}}",1,"-((-1)^(1/3)*(2*(-1)^(1/3)*b + 3*a^(1/3)*c^(2/3))*ArcTan[(3*(-1)^(1/3)*a^(2/3)*c^(1/3) - 2*b*x)/(Sqrt[3]*Sqrt[a]*Sqrt[4*b - 3*(-1)^(2/3)*a^(1/3)*c^(2/3)])])/(27*Sqrt[3]*(1 + (-1)^(1/3))^2*a^(17/6)*Sqrt[4*b - 3*(-1)^(2/3)*a^(1/3)*c^(2/3)]*c^(2/3)) - ((2*b - 3*a^(1/3)*c^(2/3))*ArcTan[(3*a^(2/3)*c^(1/3) + 2*b*x)/(Sqrt[3]*Sqrt[a]*Sqrt[4*b - 3*a^(1/3)*c^(2/3)])])/(81*Sqrt[3]*a^(17/6)*Sqrt[4*b - 3*a^(1/3)*c^(2/3)]*c^(2/3)) - ((2*(-1)^(2/3)*b - 3*a^(1/3)*c^(2/3))*ArcTan[(3*(-1)^(2/3)*a^(2/3)*c^(1/3) + 2*b*x)/(Sqrt[3]*Sqrt[a]*Sqrt[4*b + 3*(-1)^(1/3)*a^(1/3)*c^(2/3)])])/(27*Sqrt[3]*(1 - (-1)^(1/3))*(1 + (-1)^(1/3))^2*a^(17/6)*Sqrt[4*b + 3*(-1)^(1/3)*a^(1/3)*c^(2/3)]*c^(2/3)) + Log[3*a + 3*a^(2/3)*c^(1/3)*x + b*x^2]/(162*a^(8/3)*c^(1/3)) - Log[3*a - 3*(-1)^(1/3)*a^(2/3)*c^(1/3)*x + b*x^2]/(54*(1 + (-1)^(1/3))^2*a^(8/3)*c^(1/3)) - ((-1)^(1/3)*Log[3*a + 3*(-1)^(2/3)*a^(2/3)*c^(1/3)*x + b*x^2])/(162*a^(8/3)*c^(1/3))","A",14,5,42,0.1190,1,"{2070, 634, 618, 204, 628}"
141,1,563,0,1.1565298,"\int \frac{1}{x \left(27 a^3+27 a^2 b x^2+27 a^2 c x^3+9 a b^2 x^4+b^3 x^6\right)} \, dx","Int[1/(x*(27*a^3 + 27*a^2*b*x^2 + 27*a^2*c*x^3 + 9*a*b^2*x^4 + b^3*x^6)),x]","-\frac{\left(3 \sqrt[3]{a}-\frac{b}{c^{2/3}}\right) \log \left(3 a^{2/3} \sqrt[3]{c} x+3 a+b x^2\right)}{486 a^{10/3}}-\frac{\left(6 \sqrt[3]{a} c^{2/3}+i \sqrt{3} b+b\right) \log \left(-3 \sqrt[3]{-1} a^{2/3} \sqrt[3]{c} x+3 a+b x^2\right)}{972 a^{10/3} c^{2/3}}-\frac{\left(3 \sqrt[3]{a}-\frac{(-1)^{2/3} b}{c^{2/3}}\right) \log \left(3 (-1)^{2/3} a^{2/3} \sqrt[3]{c} x+3 a+b x^2\right)}{486 a^{10/3}}+\frac{\left(b-(-1)^{2/3} \sqrt[3]{a} c^{2/3}\right) \tan ^{-1}\left(\frac{3 \sqrt[3]{-1} a^{2/3} \sqrt[3]{c}-2 b x}{\sqrt{3} \sqrt{a} \sqrt{4 b-3 (-1)^{2/3} \sqrt[3]{a} c^{2/3}}}\right)}{9 \sqrt{3} \left(1+\sqrt[3]{-1}\right)^2 a^{19/6} \sqrt[3]{c} \sqrt{4 b-3 (-1)^{2/3} \sqrt[3]{a} c^{2/3}}}+\frac{\left(b-\sqrt[3]{a} c^{2/3}\right) \tan ^{-1}\left(\frac{3 a^{2/3} \sqrt[3]{c}+2 b x}{\sqrt{3} \sqrt{a} \sqrt{4 b-3 \sqrt[3]{a} c^{2/3}}}\right)}{27 \sqrt{3} a^{19/6} \sqrt[3]{c} \sqrt{4 b-3 \sqrt[3]{a} c^{2/3}}}+\frac{(-1)^{2/3} \left((-1)^{2/3} b-\sqrt[3]{a} c^{2/3}\right) \tan ^{-1}\left(\frac{3 (-1)^{2/3} a^{2/3} \sqrt[3]{c}+2 b x}{\sqrt{3} \sqrt{a} \sqrt{3 \sqrt[3]{-1} \sqrt[3]{a} c^{2/3}+4 b}}\right)}{9 \sqrt{3} \left(1-\sqrt[3]{-1}\right) \left(1+\sqrt[3]{-1}\right)^2 a^{19/6} \sqrt[3]{c} \sqrt{3 \sqrt[3]{-1} \sqrt[3]{a} c^{2/3}+4 b}}+\frac{\log (x)}{27 a^3}","-\frac{\left(3 \sqrt[3]{a}-\frac{b}{c^{2/3}}\right) \log \left(3 a^{2/3} \sqrt[3]{c} x+3 a+b x^2\right)}{486 a^{10/3}}-\frac{\left(6 \sqrt[3]{a} c^{2/3}+i \sqrt{3} b+b\right) \log \left(-3 \sqrt[3]{-1} a^{2/3} \sqrt[3]{c} x+3 a+b x^2\right)}{972 a^{10/3} c^{2/3}}-\frac{\left(3 \sqrt[3]{a}-\frac{(-1)^{2/3} b}{c^{2/3}}\right) \log \left(3 (-1)^{2/3} a^{2/3} \sqrt[3]{c} x+3 a+b x^2\right)}{486 a^{10/3}}+\frac{\left(b-(-1)^{2/3} \sqrt[3]{a} c^{2/3}\right) \tan ^{-1}\left(\frac{3 \sqrt[3]{-1} a^{2/3} \sqrt[3]{c}-2 b x}{\sqrt{3} \sqrt{a} \sqrt{4 b-3 (-1)^{2/3} \sqrt[3]{a} c^{2/3}}}\right)}{9 \sqrt{3} \left(1+\sqrt[3]{-1}\right)^2 a^{19/6} \sqrt[3]{c} \sqrt{4 b-3 (-1)^{2/3} \sqrt[3]{a} c^{2/3}}}+\frac{\left(b-\sqrt[3]{a} c^{2/3}\right) \tan ^{-1}\left(\frac{3 a^{2/3} \sqrt[3]{c}+2 b x}{\sqrt{3} \sqrt{a} \sqrt{4 b-3 \sqrt[3]{a} c^{2/3}}}\right)}{27 \sqrt{3} a^{19/6} \sqrt[3]{c} \sqrt{4 b-3 \sqrt[3]{a} c^{2/3}}}+\frac{(-1)^{2/3} \left((-1)^{2/3} b-\sqrt[3]{a} c^{2/3}\right) \tan ^{-1}\left(\frac{3 (-1)^{2/3} a^{2/3} \sqrt[3]{c}+2 b x}{\sqrt{3} \sqrt{a} \sqrt{3 \sqrt[3]{-1} \sqrt[3]{a} c^{2/3}+4 b}}\right)}{9 \sqrt{3} \left(1-\sqrt[3]{-1}\right) \left(1+\sqrt[3]{-1}\right)^2 a^{19/6} \sqrt[3]{c} \sqrt{3 \sqrt[3]{-1} \sqrt[3]{a} c^{2/3}+4 b}}+\frac{\log (x)}{27 a^3}",1,"((b - (-1)^(2/3)*a^(1/3)*c^(2/3))*ArcTan[(3*(-1)^(1/3)*a^(2/3)*c^(1/3) - 2*b*x)/(Sqrt[3]*Sqrt[a]*Sqrt[4*b - 3*(-1)^(2/3)*a^(1/3)*c^(2/3)])])/(9*Sqrt[3]*(1 + (-1)^(1/3))^2*a^(19/6)*Sqrt[4*b - 3*(-1)^(2/3)*a^(1/3)*c^(2/3)]*c^(1/3)) + ((b - a^(1/3)*c^(2/3))*ArcTan[(3*a^(2/3)*c^(1/3) + 2*b*x)/(Sqrt[3]*Sqrt[a]*Sqrt[4*b - 3*a^(1/3)*c^(2/3)])])/(27*Sqrt[3]*a^(19/6)*Sqrt[4*b - 3*a^(1/3)*c^(2/3)]*c^(1/3)) + ((-1)^(2/3)*((-1)^(2/3)*b - a^(1/3)*c^(2/3))*ArcTan[(3*(-1)^(2/3)*a^(2/3)*c^(1/3) + 2*b*x)/(Sqrt[3]*Sqrt[a]*Sqrt[4*b + 3*(-1)^(1/3)*a^(1/3)*c^(2/3)])])/(9*Sqrt[3]*(1 - (-1)^(1/3))*(1 + (-1)^(1/3))^2*a^(19/6)*Sqrt[4*b + 3*(-1)^(1/3)*a^(1/3)*c^(2/3)]*c^(1/3)) + Log[x]/(27*a^3) - ((3*a^(1/3) - b/c^(2/3))*Log[3*a + 3*a^(2/3)*c^(1/3)*x + b*x^2])/(486*a^(10/3)) - ((b + I*Sqrt[3]*b + 6*a^(1/3)*c^(2/3))*Log[3*a - 3*(-1)^(1/3)*a^(2/3)*c^(1/3)*x + b*x^2])/(972*a^(10/3)*c^(2/3)) - ((3*a^(1/3) - ((-1)^(2/3)*b)/c^(2/3))*Log[3*a + 3*(-1)^(2/3)*a^(2/3)*c^(1/3)*x + b*x^2])/(486*a^(10/3))","A",14,5,46,0.1087,1,"{2097, 634, 618, 204, 628}"
142,1,640,0,1.3795737,"\int \frac{1}{x^2 \left(27 a^3+27 a^2 b x^2+27 a^2 c x^3+9 a b^2 x^4+b^3 x^6\right)} \, dx","Int[1/(x^2*(27*a^3 + 27*a^2*b*x^2 + 27*a^2*c*x^3 + 9*a*b^2*x^4 + b^3*x^6)),x]","\frac{\left(9 a^{2/3} c^{4/3}+12 \sqrt[3]{-1} \sqrt[3]{a} b c^{2/3}+2 (-1)^{2/3} b^2\right) \tan ^{-1}\left(\frac{3 \sqrt[3]{-1} a^{2/3} \sqrt[3]{c}-2 b x}{\sqrt{3} \sqrt{a} \sqrt{4 b-3 (-1)^{2/3} \sqrt[3]{a} c^{2/3}}}\right)}{81 \sqrt{3} \left(1+\sqrt[3]{-1}\right)^2 a^{23/6} c^{2/3} \sqrt{4 b-3 (-1)^{2/3} \sqrt[3]{a} c^{2/3}}}+\frac{\left(9 a^{2/3} c^{4/3}-12 \sqrt[3]{a} b c^{2/3}+2 b^2\right) \tan ^{-1}\left(\frac{3 a^{2/3} \sqrt[3]{c}+2 b x}{\sqrt{3} \sqrt{a} \sqrt{4 b-3 \sqrt[3]{a} c^{2/3}}}\right)}{243 \sqrt{3} a^{23/6} c^{2/3} \sqrt{4 b-3 \sqrt[3]{a} c^{2/3}}}+\frac{\left(-9 \sqrt[3]{-1} a^{2/3} c^{4/3}-12 \sqrt[3]{a} b c^{2/3}+2 (-1)^{2/3} b^2\right) \tan ^{-1}\left(\frac{3 (-1)^{2/3} a^{2/3} \sqrt[3]{c}+2 b x}{\sqrt{3} \sqrt{a} \sqrt{3 \sqrt[3]{-1} \sqrt[3]{a} c^{2/3}+4 b}}\right)}{81 \sqrt{3} \left(1-\sqrt[3]{-1}\right) \left(1+\sqrt[3]{-1}\right)^2 a^{23/6} c^{2/3} \sqrt{3 \sqrt[3]{-1} \sqrt[3]{a} c^{2/3}+4 b}}-\frac{\left(2 b-3 \sqrt[3]{a} c^{2/3}\right) \log \left(3 a^{2/3} \sqrt[3]{c} x+3 a+b x^2\right)}{486 a^{11/3} \sqrt[3]{c}}+\frac{\left(2 b-3 (-1)^{2/3} \sqrt[3]{a} c^{2/3}\right) \log \left(-3 \sqrt[3]{-1} a^{2/3} \sqrt[3]{c} x+3 a+b x^2\right)}{162 \left(1+\sqrt[3]{-1}\right)^2 a^{11/3} \sqrt[3]{c}}+\frac{\sqrt[3]{-1} \left(3 \sqrt[3]{-1} \sqrt[3]{a} c^{2/3}+2 b\right) \log \left(3 (-1)^{2/3} a^{2/3} \sqrt[3]{c} x+3 a+b x^2\right)}{486 a^{11/3} \sqrt[3]{c}}-\frac{1}{27 a^3 x}","\frac{\left(9 a^{2/3} c^{4/3}+12 \sqrt[3]{-1} \sqrt[3]{a} b c^{2/3}+2 (-1)^{2/3} b^2\right) \tan ^{-1}\left(\frac{3 \sqrt[3]{-1} a^{2/3} \sqrt[3]{c}-2 b x}{\sqrt{3} \sqrt{a} \sqrt{4 b-3 (-1)^{2/3} \sqrt[3]{a} c^{2/3}}}\right)}{81 \sqrt{3} \left(1+\sqrt[3]{-1}\right)^2 a^{23/6} c^{2/3} \sqrt{4 b-3 (-1)^{2/3} \sqrt[3]{a} c^{2/3}}}+\frac{\left(9 a^{2/3} c^{4/3}-12 \sqrt[3]{a} b c^{2/3}+2 b^2\right) \tan ^{-1}\left(\frac{3 a^{2/3} \sqrt[3]{c}+2 b x}{\sqrt{3} \sqrt{a} \sqrt{4 b-3 \sqrt[3]{a} c^{2/3}}}\right)}{243 \sqrt{3} a^{23/6} c^{2/3} \sqrt{4 b-3 \sqrt[3]{a} c^{2/3}}}+\frac{(-1)^{2/3} \left(9 (-1)^{2/3} a^{2/3} c^{4/3}+12 \sqrt[3]{-1} \sqrt[3]{a} b c^{2/3}+2 b^2\right) \tan ^{-1}\left(\frac{3 (-1)^{2/3} a^{2/3} \sqrt[3]{c}+2 b x}{\sqrt{3} \sqrt{a} \sqrt{3 \sqrt[3]{-1} \sqrt[3]{a} c^{2/3}+4 b}}\right)}{81 \sqrt{3} \left(1-\sqrt[3]{-1}\right) \left(1+\sqrt[3]{-1}\right)^2 a^{23/6} c^{2/3} \sqrt{3 \sqrt[3]{-1} \sqrt[3]{a} c^{2/3}+4 b}}-\frac{\left(2 b-3 \sqrt[3]{a} c^{2/3}\right) \log \left(3 a^{2/3} \sqrt[3]{c} x+3 a+b x^2\right)}{486 a^{11/3} \sqrt[3]{c}}+\frac{\left(2 b-3 (-1)^{2/3} \sqrt[3]{a} c^{2/3}\right) \log \left(-3 \sqrt[3]{-1} a^{2/3} \sqrt[3]{c} x+3 a+b x^2\right)}{162 \left(1+\sqrt[3]{-1}\right)^2 a^{11/3} \sqrt[3]{c}}+\frac{\sqrt[3]{-1} \left(3 \sqrt[3]{-1} \sqrt[3]{a} c^{2/3}+2 b\right) \log \left(3 (-1)^{2/3} a^{2/3} \sqrt[3]{c} x+3 a+b x^2\right)}{486 a^{11/3} \sqrt[3]{c}}-\frac{1}{27 a^3 x}",1,"-1/(27*a^3*x) + ((2*(-1)^(2/3)*b^2 + 12*(-1)^(1/3)*a^(1/3)*b*c^(2/3) + 9*a^(2/3)*c^(4/3))*ArcTan[(3*(-1)^(1/3)*a^(2/3)*c^(1/3) - 2*b*x)/(Sqrt[3]*Sqrt[a]*Sqrt[4*b - 3*(-1)^(2/3)*a^(1/3)*c^(2/3)])])/(81*Sqrt[3]*(1 + (-1)^(1/3))^2*a^(23/6)*Sqrt[4*b - 3*(-1)^(2/3)*a^(1/3)*c^(2/3)]*c^(2/3)) + ((2*b^2 - 12*a^(1/3)*b*c^(2/3) + 9*a^(2/3)*c^(4/3))*ArcTan[(3*a^(2/3)*c^(1/3) + 2*b*x)/(Sqrt[3]*Sqrt[a]*Sqrt[4*b - 3*a^(1/3)*c^(2/3)])])/(243*Sqrt[3]*a^(23/6)*Sqrt[4*b - 3*a^(1/3)*c^(2/3)]*c^(2/3)) + ((2*(-1)^(2/3)*b^2 - 12*a^(1/3)*b*c^(2/3) - 9*(-1)^(1/3)*a^(2/3)*c^(4/3))*ArcTan[(3*(-1)^(2/3)*a^(2/3)*c^(1/3) + 2*b*x)/(Sqrt[3]*Sqrt[a]*Sqrt[4*b + 3*(-1)^(1/3)*a^(1/3)*c^(2/3)])])/(81*Sqrt[3]*(1 - (-1)^(1/3))*(1 + (-1)^(1/3))^2*a^(23/6)*Sqrt[4*b + 3*(-1)^(1/3)*a^(1/3)*c^(2/3)]*c^(2/3)) - ((2*b - 3*a^(1/3)*c^(2/3))*Log[3*a + 3*a^(2/3)*c^(1/3)*x + b*x^2])/(486*a^(11/3)*c^(1/3)) + ((2*b - 3*(-1)^(2/3)*a^(1/3)*c^(2/3))*Log[3*a - 3*(-1)^(1/3)*a^(2/3)*c^(1/3)*x + b*x^2])/(162*(1 + (-1)^(1/3))^2*a^(11/3)*c^(1/3)) + ((-1)^(1/3)*(2*b + 3*(-1)^(1/3)*a^(1/3)*c^(2/3))*Log[3*a + 3*(-1)^(2/3)*a^(2/3)*c^(1/3)*x + b*x^2])/(486*a^(11/3)*c^(1/3))","A",14,5,46,0.1087,1,"{2097, 634, 618, 204, 628}"
143,1,395,0,1.4384746,"\int \frac{x^5}{216+108 x^2+324 x^3+18 x^4+x^6} \, dx","Int[x^5/(216 + 108*x^2 + 324*x^3 + 18*x^4 + x^6),x]","\frac{1}{216} \left(36+2^{2/3} \sqrt[3]{3} \left(1+i \sqrt{3}\right)\right) \log \left(x^2-3 \sqrt[3]{-3} 2^{2/3} x+6\right)+\frac{1}{108} \left(18-(-2)^{2/3} \sqrt[3]{3}\right) \log \left(x^2+3 (-2)^{2/3} \sqrt[3]{3} x+6\right)+\frac{1}{108} \left(18-2^{2/3} \sqrt[3]{3}\right) \log \left(x^2+3\ 2^{2/3} \sqrt[3]{3} x+6\right)-\frac{\sqrt[3]{-2} \left(1+\sqrt[3]{-2} 3^{2/3}\right) \tan ^{-1}\left(\frac{2 x+3 (-2)^{2/3} \sqrt[3]{3}}{\sqrt{6 \left(4+3 \sqrt[3]{-2} 3^{2/3}\right)}}\right)}{3^{5/6} \sqrt{8+9 i \sqrt[3]{2} \sqrt[6]{3}+3 \sqrt[3]{2} 3^{2/3}}}+\frac{\sqrt[6]{\frac{3}{2}} \left(1-(-3)^{2/3} \sqrt[3]{2}\right) \tan ^{-1}\left(\frac{\sqrt[6]{2} \left(3 \sqrt[3]{-3}-\sqrt[3]{2} x\right)}{\sqrt{3 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)}}\right)}{\left(1+\sqrt[3]{-1}\right)^2 \sqrt{4-3 (-3)^{2/3} \sqrt[3]{2}}}-\frac{\left(1-\sqrt[3]{2} 3^{2/3}\right) \tanh ^{-1}\left(\frac{\sqrt[6]{2} \left(\sqrt[3]{2} x+3 \sqrt[3]{3}\right)}{\sqrt{3 \left(3 \sqrt[3]{2} 3^{2/3}-4\right)}}\right)}{\sqrt[6]{2} 3^{5/6} \sqrt{3 \sqrt[3]{2} 3^{2/3}-4}}","\frac{1}{216} \left(36+2^{2/3} \sqrt[3]{3} \left(1+i \sqrt{3}\right)\right) \log \left(x^2-3 \sqrt[3]{-3} 2^{2/3} x+6\right)+\frac{1}{108} \left(18-(-2)^{2/3} \sqrt[3]{3}\right) \log \left(x^2+3 (-2)^{2/3} \sqrt[3]{3} x+6\right)+\frac{1}{108} \left(18-2^{2/3} \sqrt[3]{3}\right) \log \left(x^2+3\ 2^{2/3} \sqrt[3]{3} x+6\right)-\frac{\sqrt[3]{-2} \left(1+\sqrt[3]{-2} 3^{2/3}\right) \tan ^{-1}\left(\frac{2 x+3 (-2)^{2/3} \sqrt[3]{3}}{\sqrt{6 \left(4+3 \sqrt[3]{-2} 3^{2/3}\right)}}\right)}{3^{5/6} \sqrt{8+9 i \sqrt[3]{2} \sqrt[6]{3}+3 \sqrt[3]{2} 3^{2/3}}}+\frac{\sqrt[6]{\frac{3}{2}} \left(1-(-3)^{2/3} \sqrt[3]{2}\right) \tan ^{-1}\left(\frac{\sqrt[6]{2} \left(3 \sqrt[3]{-3}-\sqrt[3]{2} x\right)}{\sqrt{3 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)}}\right)}{\left(1+\sqrt[3]{-1}\right)^2 \sqrt{4-3 (-3)^{2/3} \sqrt[3]{2}}}-\frac{\left(1-\sqrt[3]{2} 3^{2/3}\right) \tanh ^{-1}\left(\frac{\sqrt[6]{2} \left(\sqrt[3]{2} x+3 \sqrt[3]{3}\right)}{\sqrt{3 \left(3 \sqrt[3]{2} 3^{2/3}-4\right)}}\right)}{\sqrt[6]{2} 3^{5/6} \sqrt{3 \sqrt[3]{2} 3^{2/3}-4}}",1,"-(((-2)^(1/3)*(1 + (-2)^(1/3)*3^(2/3))*ArcTan[(3*(-2)^(2/3)*3^(1/3) + 2*x)/Sqrt[6*(4 + 3*(-2)^(1/3)*3^(2/3))]])/(3^(5/6)*Sqrt[8 + (9*I)*2^(1/3)*3^(1/6) + 3*2^(1/3)*3^(2/3)])) + ((3/2)^(1/6)*(1 - (-3)^(2/3)*2^(1/3))*ArcTan[(2^(1/6)*(3*(-3)^(1/3) - 2^(1/3)*x))/Sqrt[3*(4 - 3*(-3)^(2/3)*2^(1/3))]])/((1 + (-1)^(1/3))^2*Sqrt[4 - 3*(-3)^(2/3)*2^(1/3)]) - ((1 - 2^(1/3)*3^(2/3))*ArcTanh[(2^(1/6)*(3*3^(1/3) + 2^(1/3)*x))/Sqrt[3*(-4 + 3*2^(1/3)*3^(2/3))]])/(2^(1/6)*3^(5/6)*Sqrt[-4 + 3*2^(1/3)*3^(2/3)]) + ((36 + 2^(2/3)*3^(1/3)*(1 + I*Sqrt[3]))*Log[6 - 3*(-3)^(1/3)*2^(2/3)*x + x^2])/216 + ((18 - (-2)^(2/3)*3^(1/3))*Log[6 + 3*(-2)^(2/3)*3^(1/3)*x + x^2])/108 + ((18 - 2^(2/3)*3^(1/3))*Log[6 + 3*2^(2/3)*3^(1/3)*x + x^2])/108","A",14,6,26,0.2308,1,"{2097, 634, 618, 204, 628, 206}"
144,1,377,0,0.9097803,"\int \frac{x^4}{216+108 x^2+324 x^3+18 x^4+x^6} \, dx","Int[x^4/(216 + 108*x^2 + 324*x^3 + 18*x^4 + x^6),x]","\frac{\log \left(x^2-3 \sqrt[3]{-3} 2^{2/3} x+6\right)}{6\ 2^{2/3} \sqrt[3]{3} \left(1+\sqrt[3]{-1}\right)^2}+\frac{\sqrt[3]{-\frac{1}{3}} \log \left(x^2+3 (-2)^{2/3} \sqrt[3]{3} x+6\right)}{18\ 2^{2/3}}-\frac{\log \left(x^2+3\ 2^{2/3} \sqrt[3]{3} x+6\right)}{18\ 2^{2/3} \sqrt[3]{3}}+\frac{(-1)^{2/3} \left(3 (-3)^{2/3}-2^{2/3}\right) \tan ^{-1}\left(\frac{3 \sqrt[3]{-3} 2^{2/3}-2 x}{\sqrt{6 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)}}\right)}{9 \sqrt[6]{3} \left(1+\sqrt[3]{-1}\right)^2 \sqrt{2 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)}}+\frac{\left(9-(-2)^{2/3} \sqrt[3]{3}\right) \tan ^{-1}\left(\frac{2 x+3 (-2)^{2/3} \sqrt[3]{3}}{\sqrt{6 \left(4+3 \sqrt[3]{-2} 3^{2/3}\right)}}\right)}{27 \sqrt{3 \left(8+9 i \sqrt[3]{2} \sqrt[6]{3}+3 \sqrt[3]{2} 3^{2/3}\right)}}-\frac{\left(9-2^{2/3} \sqrt[3]{3}\right) \tanh ^{-1}\left(\frac{\sqrt[6]{2} \left(\sqrt[3]{2} x+3 \sqrt[3]{3}\right)}{\sqrt{3 \left(3 \sqrt[3]{2} 3^{2/3}-4\right)}}\right)}{27 \sqrt{6 \left(3 \sqrt[3]{2} 3^{2/3}-4\right)}}","\frac{\log \left(x^2-3 \sqrt[3]{-3} 2^{2/3} x+6\right)}{6\ 2^{2/3} \sqrt[3]{3} \left(1+\sqrt[3]{-1}\right)^2}+\frac{\sqrt[3]{-\frac{1}{3}} \log \left(x^2+3 (-2)^{2/3} \sqrt[3]{3} x+6\right)}{18\ 2^{2/3}}-\frac{\log \left(x^2+3\ 2^{2/3} \sqrt[3]{3} x+6\right)}{18\ 2^{2/3} \sqrt[3]{3}}+\frac{(-1)^{2/3} \left(3 (-3)^{2/3}-2^{2/3}\right) \tan ^{-1}\left(\frac{3 \sqrt[3]{-3} 2^{2/3}-2 x}{\sqrt{6 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)}}\right)}{9 \sqrt[6]{3} \left(1+\sqrt[3]{-1}\right)^2 \sqrt{2 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)}}+\frac{\left(9-(-2)^{2/3} \sqrt[3]{3}\right) \tan ^{-1}\left(\frac{2 x+3 (-2)^{2/3} \sqrt[3]{3}}{\sqrt{6 \left(4+3 \sqrt[3]{-2} 3^{2/3}\right)}}\right)}{27 \sqrt{3 \left(8+9 i \sqrt[3]{2} \sqrt[6]{3}+3 \sqrt[3]{2} 3^{2/3}\right)}}-\frac{\left(9-2^{2/3} \sqrt[3]{3}\right) \tanh ^{-1}\left(\frac{\sqrt[6]{2} \left(\sqrt[3]{2} x+3 \sqrt[3]{3}\right)}{\sqrt{3 \left(3 \sqrt[3]{2} 3^{2/3}-4\right)}}\right)}{27 \sqrt{6 \left(3 \sqrt[3]{2} 3^{2/3}-4\right)}}",1,"((-1)^(2/3)*(3*(-3)^(2/3) - 2^(2/3))*ArcTan[(3*(-3)^(1/3)*2^(2/3) - 2*x)/Sqrt[6*(4 - 3*(-3)^(2/3)*2^(1/3))]])/(9*3^(1/6)*(1 + (-1)^(1/3))^2*Sqrt[2*(4 - 3*(-3)^(2/3)*2^(1/3))]) + ((9 - (-2)^(2/3)*3^(1/3))*ArcTan[(3*(-2)^(2/3)*3^(1/3) + 2*x)/Sqrt[6*(4 + 3*(-2)^(1/3)*3^(2/3))]])/(27*Sqrt[3*(8 + (9*I)*2^(1/3)*3^(1/6) + 3*2^(1/3)*3^(2/3))]) - ((9 - 2^(2/3)*3^(1/3))*ArcTanh[(2^(1/6)*(3*3^(1/3) + 2^(1/3)*x))/Sqrt[3*(-4 + 3*2^(1/3)*3^(2/3))]])/(27*Sqrt[6*(-4 + 3*2^(1/3)*3^(2/3))]) + Log[6 - 3*(-3)^(1/3)*2^(2/3)*x + x^2]/(6*2^(2/3)*3^(1/3)*(1 + (-1)^(1/3))^2) + ((-1/3)^(1/3)*Log[6 + 3*(-2)^(2/3)*3^(1/3)*x + x^2])/(18*2^(2/3)) - Log[6 + 3*2^(2/3)*3^(1/3)*x + x^2]/(18*2^(2/3)*3^(1/3))","A",14,6,26,0.2308,1,"{2097, 634, 618, 204, 628, 206}"
145,1,361,0,0.5149182,"\int \frac{x^3}{216+108 x^2+324 x^3+18 x^4+x^6} \, dx","Int[x^3/(216 + 108*x^2 + 324*x^3 + 18*x^4 + x^6),x]","-\frac{(-1)^{2/3} \log \left(x^2-3 \sqrt[3]{-3} 2^{2/3} x+6\right)}{36 \sqrt[3]{2} 3^{2/3} \left(1+\sqrt[3]{-1}\right)^2}+\frac{(-1)^{2/3} \log \left(x^2+3 (-2)^{2/3} \sqrt[3]{3} x+6\right)}{108 \sqrt[3]{2} 3^{2/3}}+\frac{\log \left(x^2+3\ 2^{2/3} \sqrt[3]{3} x+6\right)}{108 \sqrt[3]{2} 3^{2/3}}-\frac{\tan ^{-1}\left(\frac{3 \sqrt[3]{-3} 2^{2/3}-2 x}{\sqrt{6 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)}}\right)}{6 \sqrt[6]{2} 3^{5/6} \left(1+\sqrt[3]{-1}\right)^2 \sqrt{4-3 (-3)^{2/3} \sqrt[3]{2}}}+\frac{\sqrt[3]{-1} \tan ^{-1}\left(\frac{2 x+3 (-2)^{2/3} \sqrt[3]{3}}{\sqrt{6 \left(4+3 \sqrt[3]{-2} 3^{2/3}\right)}}\right)}{9\ 2^{2/3} 3^{5/6} \sqrt{8+9 i \sqrt[3]{2} \sqrt[6]{3}+3 \sqrt[3]{2} 3^{2/3}}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[6]{2} \left(\sqrt[3]{2} x+3 \sqrt[3]{3}\right)}{\sqrt{3 \left(3 \sqrt[3]{2} 3^{2/3}-4\right)}}\right)}{18 \sqrt[6]{2} 3^{5/6} \sqrt{3 \sqrt[3]{2} 3^{2/3}-4}}","-\frac{(-1)^{2/3} \log \left(x^2-3 \sqrt[3]{-3} 2^{2/3} x+6\right)}{36 \sqrt[3]{2} 3^{2/3} \left(1+\sqrt[3]{-1}\right)^2}+\frac{(-1)^{2/3} \log \left(x^2+3 (-2)^{2/3} \sqrt[3]{3} x+6\right)}{108 \sqrt[3]{2} 3^{2/3}}+\frac{\log \left(x^2+3\ 2^{2/3} \sqrt[3]{3} x+6\right)}{108 \sqrt[3]{2} 3^{2/3}}-\frac{\tan ^{-1}\left(\frac{3 \sqrt[3]{-3} 2^{2/3}-2 x}{\sqrt{6 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)}}\right)}{6 \sqrt[6]{2} 3^{5/6} \left(1+\sqrt[3]{-1}\right)^2 \sqrt{4-3 (-3)^{2/3} \sqrt[3]{2}}}+\frac{\sqrt[3]{-1} \tan ^{-1}\left(\frac{2 x+3 (-2)^{2/3} \sqrt[3]{3}}{\sqrt{6 \left(4+3 \sqrt[3]{-2} 3^{2/3}\right)}}\right)}{9\ 2^{2/3} 3^{5/6} \sqrt{8+9 i \sqrt[3]{2} \sqrt[6]{3}+3 \sqrt[3]{2} 3^{2/3}}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[6]{2} \left(\sqrt[3]{2} x+3 \sqrt[3]{3}\right)}{\sqrt{3 \left(3 \sqrt[3]{2} 3^{2/3}-4\right)}}\right)}{18 \sqrt[6]{2} 3^{5/6} \sqrt{3 \sqrt[3]{2} 3^{2/3}-4}}",1,"-ArcTan[(3*(-3)^(1/3)*2^(2/3) - 2*x)/Sqrt[6*(4 - 3*(-3)^(2/3)*2^(1/3))]]/(6*2^(1/6)*3^(5/6)*(1 + (-1)^(1/3))^2*Sqrt[4 - 3*(-3)^(2/3)*2^(1/3)]) + ((-1)^(1/3)*ArcTan[(3*(-2)^(2/3)*3^(1/3) + 2*x)/Sqrt[6*(4 + 3*(-2)^(1/3)*3^(2/3))]])/(9*2^(2/3)*3^(5/6)*Sqrt[8 + (9*I)*2^(1/3)*3^(1/6) + 3*2^(1/3)*3^(2/3)]) + ArcTanh[(2^(1/6)*(3*3^(1/3) + 2^(1/3)*x))/Sqrt[3*(-4 + 3*2^(1/3)*3^(2/3))]]/(18*2^(1/6)*3^(5/6)*Sqrt[-4 + 3*2^(1/3)*3^(2/3)]) - ((-1)^(2/3)*Log[6 - 3*(-3)^(1/3)*2^(2/3)*x + x^2])/(36*2^(1/3)*3^(2/3)*(1 + (-1)^(1/3))^2) + ((-1)^(2/3)*Log[6 + 3*(-2)^(2/3)*3^(1/3)*x + x^2])/(108*2^(1/3)*3^(2/3)) + Log[6 + 3*2^(2/3)*3^(1/3)*x + x^2]/(108*2^(1/3)*3^(2/3))","A",14,6,26,0.2308,1,"{2097, 634, 618, 204, 628, 206}"
146,1,248,0,0.3225486,"\int \frac{x^2}{216+108 x^2+324 x^3+18 x^4+x^6} \, dx","Int[x^2/(216 + 108*x^2 + 324*x^3 + 18*x^4 + x^6),x]","\frac{(-1)^{2/3} \tan ^{-1}\left(\frac{3 \sqrt[3]{-3} 2^{2/3}-2 x}{\sqrt{6 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)}}\right)}{27\ 2^{5/6} \sqrt[6]{3} \left(1+\sqrt[3]{-1}\right)^2 \sqrt{4-3 (-3)^{2/3} \sqrt[3]{2}}}+\frac{(-1)^{2/3} \tan ^{-1}\left(\frac{2 x+3 (-2)^{2/3} \sqrt[3]{3}}{\sqrt{6 \left(4+3 \sqrt[3]{-2} 3^{2/3}\right)}}\right)}{81 \sqrt[3]{2} \sqrt[6]{3} \sqrt{8+9 i \sqrt[3]{2} \sqrt[6]{3}+3 \sqrt[3]{2} 3^{2/3}}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[6]{2} \left(\sqrt[3]{2} x+3 \sqrt[3]{3}\right)}{\sqrt{3 \left(3 \sqrt[3]{2} 3^{2/3}-4\right)}}\right)}{81\ 2^{5/6} \sqrt[6]{3} \sqrt{3 \sqrt[3]{2} 3^{2/3}-4}}","\frac{(-1)^{2/3} \tan ^{-1}\left(\frac{3 \sqrt[3]{-3} 2^{2/3}-2 x}{\sqrt{6 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)}}\right)}{27\ 2^{5/6} \sqrt[6]{3} \left(1+\sqrt[3]{-1}\right)^2 \sqrt{4-3 (-3)^{2/3} \sqrt[3]{2}}}+\frac{(-1)^{2/3} \tan ^{-1}\left(\frac{2 x+3 (-2)^{2/3} \sqrt[3]{3}}{\sqrt{6 \left(4+3 \sqrt[3]{-2} 3^{2/3}\right)}}\right)}{81 \sqrt[3]{2} \sqrt[6]{3} \sqrt{8+9 i \sqrt[3]{2} \sqrt[6]{3}+3 \sqrt[3]{2} 3^{2/3}}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[6]{2} \left(\sqrt[3]{2} x+3 \sqrt[3]{3}\right)}{\sqrt{3 \left(3 \sqrt[3]{2} 3^{2/3}-4\right)}}\right)}{81\ 2^{5/6} \sqrt[6]{3} \sqrt{3 \sqrt[3]{2} 3^{2/3}-4}}",1,"((-1)^(2/3)*ArcTan[(3*(-3)^(1/3)*2^(2/3) - 2*x)/Sqrt[6*(4 - 3*(-3)^(2/3)*2^(1/3))]])/(27*2^(5/6)*3^(1/6)*(1 + (-1)^(1/3))^2*Sqrt[4 - 3*(-3)^(2/3)*2^(1/3)]) + ((-1)^(2/3)*ArcTan[(3*(-2)^(2/3)*3^(1/3) + 2*x)/Sqrt[6*(4 + 3*(-2)^(1/3)*3^(2/3))]])/(81*2^(1/3)*3^(1/6)*Sqrt[8 + (9*I)*2^(1/3)*3^(1/6) + 3*2^(1/3)*3^(2/3)]) - ArcTanh[(2^(1/6)*(3*3^(1/3) + 2^(1/3)*x))/Sqrt[3*(-4 + 3*2^(1/3)*3^(2/3))]]/(81*2^(5/6)*3^(1/6)*Sqrt[-4 + 3*2^(1/3)*3^(2/3)])","A",8,4,26,0.1538,1,"{2097, 618, 204, 206}"
147,1,361,0,0.5475542,"\int \frac{x}{216+108 x^2+324 x^3+18 x^4+x^6} \, dx","Int[x/(216 + 108*x^2 + 324*x^3 + 18*x^4 + x^6),x]","\frac{(-1)^{2/3} \log \left(x^2-3 \sqrt[3]{-3} 2^{2/3} x+6\right)}{216 \sqrt[3]{2} 3^{2/3} \left(1+\sqrt[3]{-1}\right)^2}-\frac{(-1)^{2/3} \log \left(x^2+3 (-2)^{2/3} \sqrt[3]{3} x+6\right)}{648 \sqrt[3]{2} 3^{2/3}}-\frac{\log \left(x^2+3\ 2^{2/3} \sqrt[3]{3} x+6\right)}{648 \sqrt[3]{2} 3^{2/3}}-\frac{\tan ^{-1}\left(\frac{3 \sqrt[3]{-3} 2^{2/3}-2 x}{\sqrt{6 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)}}\right)}{36 \sqrt[6]{2} 3^{5/6} \left(1+\sqrt[3]{-1}\right)^2 \sqrt{4-3 (-3)^{2/3} \sqrt[3]{2}}}+\frac{\sqrt[3]{-1} \tan ^{-1}\left(\frac{2 x+3 (-2)^{2/3} \sqrt[3]{3}}{\sqrt{6 \left(4+3 \sqrt[3]{-2} 3^{2/3}\right)}}\right)}{54\ 2^{2/3} 3^{5/6} \sqrt{8+9 i \sqrt[3]{2} \sqrt[6]{3}+3 \sqrt[3]{2} 3^{2/3}}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[6]{2} \left(\sqrt[3]{2} x+3 \sqrt[3]{3}\right)}{\sqrt{3 \left(3 \sqrt[3]{2} 3^{2/3}-4\right)}}\right)}{108 \sqrt[6]{2} 3^{5/6} \sqrt{3 \sqrt[3]{2} 3^{2/3}-4}}","\frac{(-1)^{2/3} \log \left(x^2-3 \sqrt[3]{-3} 2^{2/3} x+6\right)}{216 \sqrt[3]{2} 3^{2/3} \left(1+\sqrt[3]{-1}\right)^2}-\frac{(-1)^{2/3} \log \left(x^2+3 (-2)^{2/3} \sqrt[3]{3} x+6\right)}{648 \sqrt[3]{2} 3^{2/3}}-\frac{\log \left(x^2+3\ 2^{2/3} \sqrt[3]{3} x+6\right)}{648 \sqrt[3]{2} 3^{2/3}}-\frac{\tan ^{-1}\left(\frac{3 \sqrt[3]{-3} 2^{2/3}-2 x}{\sqrt{6 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)}}\right)}{36 \sqrt[6]{2} 3^{5/6} \left(1+\sqrt[3]{-1}\right)^2 \sqrt{4-3 (-3)^{2/3} \sqrt[3]{2}}}+\frac{\sqrt[3]{-1} \tan ^{-1}\left(\frac{2 x+3 (-2)^{2/3} \sqrt[3]{3}}{\sqrt{6 \left(4+3 \sqrt[3]{-2} 3^{2/3}\right)}}\right)}{54\ 2^{2/3} 3^{5/6} \sqrt{8+9 i \sqrt[3]{2} \sqrt[6]{3}+3 \sqrt[3]{2} 3^{2/3}}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[6]{2} \left(\sqrt[3]{2} x+3 \sqrt[3]{3}\right)}{\sqrt{3 \left(3 \sqrt[3]{2} 3^{2/3}-4\right)}}\right)}{108 \sqrt[6]{2} 3^{5/6} \sqrt{3 \sqrt[3]{2} 3^{2/3}-4}}",1,"-ArcTan[(3*(-3)^(1/3)*2^(2/3) - 2*x)/Sqrt[6*(4 - 3*(-3)^(2/3)*2^(1/3))]]/(36*2^(1/6)*3^(5/6)*(1 + (-1)^(1/3))^2*Sqrt[4 - 3*(-3)^(2/3)*2^(1/3)]) + ((-1)^(1/3)*ArcTan[(3*(-2)^(2/3)*3^(1/3) + 2*x)/Sqrt[6*(4 + 3*(-2)^(1/3)*3^(2/3))]])/(54*2^(2/3)*3^(5/6)*Sqrt[8 + (9*I)*2^(1/3)*3^(1/6) + 3*2^(1/3)*3^(2/3)]) + ArcTanh[(2^(1/6)*(3*3^(1/3) + 2^(1/3)*x))/Sqrt[3*(-4 + 3*2^(1/3)*3^(2/3))]]/(108*2^(1/6)*3^(5/6)*Sqrt[-4 + 3*2^(1/3)*3^(2/3)]) + ((-1)^(2/3)*Log[6 - 3*(-3)^(1/3)*2^(2/3)*x + x^2])/(216*2^(1/3)*3^(2/3)*(1 + (-1)^(1/3))^2) - ((-1)^(2/3)*Log[6 + 3*(-2)^(2/3)*3^(1/3)*x + x^2])/(648*2^(1/3)*3^(2/3)) - Log[6 + 3*2^(2/3)*3^(1/3)*x + x^2]/(648*2^(1/3)*3^(2/3))","A",14,6,24,0.2500,1,"{2097, 634, 618, 204, 628, 206}"
148,1,377,0,0.7209513,"\int \frac{1}{216+108 x^2+324 x^3+18 x^4+x^6} \, dx","Int[(216 + 108*x^2 + 324*x^3 + 18*x^4 + x^6)^(-1),x]","-\frac{\log \left(x^2-3 \sqrt[3]{-3} 2^{2/3} x+6\right)}{216\ 2^{2/3} \sqrt[3]{3} \left(1+\sqrt[3]{-1}\right)^2}-\frac{\sqrt[3]{-\frac{1}{3}} \log \left(x^2+3 (-2)^{2/3} \sqrt[3]{3} x+6\right)}{648\ 2^{2/3}}+\frac{\log \left(x^2+3\ 2^{2/3} \sqrt[3]{3} x+6\right)}{648\ 2^{2/3} \sqrt[3]{3}}+\frac{(-1)^{2/3} \left(3 (-3)^{2/3}-2^{2/3}\right) \tan ^{-1}\left(\frac{3 \sqrt[3]{-3} 2^{2/3}-2 x}{\sqrt{6 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)}}\right)}{324 \sqrt[6]{3} \left(1+\sqrt[3]{-1}\right)^2 \sqrt{2 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)}}+\frac{\left(9-(-2)^{2/3} \sqrt[3]{3}\right) \tan ^{-1}\left(\frac{2 x+3 (-2)^{2/3} \sqrt[3]{3}}{\sqrt{6 \left(4+3 \sqrt[3]{-2} 3^{2/3}\right)}}\right)}{972 \sqrt{3 \left(8+9 i \sqrt[3]{2} \sqrt[6]{3}+3 \sqrt[3]{2} 3^{2/3}\right)}}-\frac{\left(9-2^{2/3} \sqrt[3]{3}\right) \tanh ^{-1}\left(\frac{\sqrt[6]{2} \left(\sqrt[3]{2} x+3 \sqrt[3]{3}\right)}{\sqrt{3 \left(3 \sqrt[3]{2} 3^{2/3}-4\right)}}\right)}{972 \sqrt{6 \left(3 \sqrt[3]{2} 3^{2/3}-4\right)}}","-\frac{\log \left(x^2-3 \sqrt[3]{-3} 2^{2/3} x+6\right)}{216\ 2^{2/3} \sqrt[3]{3} \left(1+\sqrt[3]{-1}\right)^2}-\frac{\sqrt[3]{-\frac{1}{3}} \log \left(x^2+3 (-2)^{2/3} \sqrt[3]{3} x+6\right)}{648\ 2^{2/3}}+\frac{\log \left(x^2+3\ 2^{2/3} \sqrt[3]{3} x+6\right)}{648\ 2^{2/3} \sqrt[3]{3}}+\frac{(-1)^{2/3} \left(3 (-3)^{2/3}-2^{2/3}\right) \tan ^{-1}\left(\frac{3 \sqrt[3]{-3} 2^{2/3}-2 x}{\sqrt{6 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)}}\right)}{324 \sqrt[6]{3} \left(1+\sqrt[3]{-1}\right)^2 \sqrt{2 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)}}+\frac{\left(9-(-2)^{2/3} \sqrt[3]{3}\right) \tan ^{-1}\left(\frac{2 x+3 (-2)^{2/3} \sqrt[3]{3}}{\sqrt{6 \left(4+3 \sqrt[3]{-2} 3^{2/3}\right)}}\right)}{972 \sqrt{3 \left(8+9 i \sqrt[3]{2} \sqrt[6]{3}+3 \sqrt[3]{2} 3^{2/3}\right)}}-\frac{\left(9-2^{2/3} \sqrt[3]{3}\right) \tanh ^{-1}\left(\frac{\sqrt[6]{2} \left(\sqrt[3]{2} x+3 \sqrt[3]{3}\right)}{\sqrt{3 \left(3 \sqrt[3]{2} 3^{2/3}-4\right)}}\right)}{972 \sqrt{6 \left(3 \sqrt[3]{2} 3^{2/3}-4\right)}}",1,"((-1)^(2/3)*(3*(-3)^(2/3) - 2^(2/3))*ArcTan[(3*(-3)^(1/3)*2^(2/3) - 2*x)/Sqrt[6*(4 - 3*(-3)^(2/3)*2^(1/3))]])/(324*3^(1/6)*(1 + (-1)^(1/3))^2*Sqrt[2*(4 - 3*(-3)^(2/3)*2^(1/3))]) + ((9 - (-2)^(2/3)*3^(1/3))*ArcTan[(3*(-2)^(2/3)*3^(1/3) + 2*x)/Sqrt[6*(4 + 3*(-2)^(1/3)*3^(2/3))]])/(972*Sqrt[3*(8 + (9*I)*2^(1/3)*3^(1/6) + 3*2^(1/3)*3^(2/3))]) - ((9 - 2^(2/3)*3^(1/3))*ArcTanh[(2^(1/6)*(3*3^(1/3) + 2^(1/3)*x))/Sqrt[3*(-4 + 3*2^(1/3)*3^(2/3))]])/(972*Sqrt[6*(-4 + 3*2^(1/3)*3^(2/3))]) - Log[6 - 3*(-3)^(1/3)*2^(2/3)*x + x^2]/(216*2^(2/3)*3^(1/3)*(1 + (-1)^(1/3))^2) - ((-1/3)^(1/3)*Log[6 + 3*(-2)^(2/3)*3^(1/3)*x + x^2])/(648*2^(2/3)) + Log[6 + 3*2^(2/3)*3^(1/3)*x + x^2]/(648*2^(2/3)*3^(1/3))","A",14,6,22,0.2727,1,"{2070, 634, 618, 204, 628, 206}"
149,1,415,0,0.9016066,"\int \frac{1}{x \left(216+108 x^2+324 x^3+18 x^4+x^6\right)} \, dx","Int[1/(x*(216 + 108*x^2 + 324*x^3 + 18*x^4 + x^6)),x]","-\frac{\left(36+2^{2/3} \sqrt[3]{3} \left(1+i \sqrt{3}\right)\right) \log \left(x^2-3 \sqrt[3]{-3} 2^{2/3} x+6\right)}{46656}-\frac{\left(18-(-2)^{2/3} \sqrt[3]{3}\right) \log \left(x^2+3 (-2)^{2/3} \sqrt[3]{3} x+6\right)}{23328}-\frac{\left(18-2^{2/3} \sqrt[3]{3}\right) \log \left(x^2+3\ 2^{2/3} \sqrt[3]{3} x+6\right)}{23328}+\frac{\log (x)}{216}+\frac{(-1)^{2/3} \left((-2)^{2/3}-2\ 3^{2/3}\right) \tan ^{-1}\left(\frac{2 x+3 (-2)^{2/3} \sqrt[3]{3}}{\sqrt{6 \left(4+3 \sqrt[3]{-2} 3^{2/3}\right)}}\right)}{216 \sqrt[3]{2} 3^{5/6} \sqrt{8+9 i \sqrt[3]{2} \sqrt[6]{3}+3 \sqrt[3]{2} 3^{2/3}}}-\frac{(-1)^{2/3} \left(\sqrt[3]{-3}+3 \sqrt[3]{2}\right) \tan ^{-1}\left(\frac{\sqrt[6]{2} \left(3 \sqrt[3]{-3}-\sqrt[3]{2} x\right)}{\sqrt{3 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)}}\right)}{216 \sqrt[6]{6} \left(1+\sqrt[3]{-1}\right)^2 \sqrt{4-3 (-3)^{2/3} \sqrt[3]{2}}}-\frac{\left(1-\sqrt[3]{2} 3^{2/3}\right) \tanh ^{-1}\left(\frac{\sqrt[6]{2} \left(\sqrt[3]{2} x+3 \sqrt[3]{3}\right)}{\sqrt{3 \left(3 \sqrt[3]{2} 3^{2/3}-4\right)}}\right)}{216 \sqrt[6]{2} 3^{5/6} \sqrt{3 \sqrt[3]{2} 3^{2/3}-4}}","-\frac{\left(36+2^{2/3} \sqrt[3]{3} \left(1+i \sqrt{3}\right)\right) \log \left(x^2-3 \sqrt[3]{-3} 2^{2/3} x+6\right)}{46656}-\frac{\left(18-(-2)^{2/3} \sqrt[3]{3}\right) \log \left(x^2+3 (-2)^{2/3} \sqrt[3]{3} x+6\right)}{23328}-\frac{\left(18-2^{2/3} \sqrt[3]{3}\right) \log \left(x^2+3\ 2^{2/3} \sqrt[3]{3} x+6\right)}{23328}+\frac{\log (x)}{216}+\frac{(-1)^{2/3} \left((-2)^{2/3}-2\ 3^{2/3}\right) \tan ^{-1}\left(\frac{2 x+3 (-2)^{2/3} \sqrt[3]{3}}{\sqrt{6 \left(4+3 \sqrt[3]{-2} 3^{2/3}\right)}}\right)}{216 \sqrt[3]{2} 3^{5/6} \sqrt{8+9 i \sqrt[3]{2} \sqrt[6]{3}+3 \sqrt[3]{2} 3^{2/3}}}-\frac{(-1)^{2/3} \left(\sqrt[3]{-3}+3 \sqrt[3]{2}\right) \tan ^{-1}\left(\frac{\sqrt[6]{2} \left(3 \sqrt[3]{-3}-\sqrt[3]{2} x\right)}{\sqrt{3 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)}}\right)}{216 \sqrt[6]{6} \left(1+\sqrt[3]{-1}\right)^2 \sqrt{4-3 (-3)^{2/3} \sqrt[3]{2}}}-\frac{\left(1-\sqrt[3]{2} 3^{2/3}\right) \tanh ^{-1}\left(\frac{\sqrt[6]{2} \left(\sqrt[3]{2} x+3 \sqrt[3]{3}\right)}{\sqrt{3 \left(3 \sqrt[3]{2} 3^{2/3}-4\right)}}\right)}{216 \sqrt[6]{2} 3^{5/6} \sqrt{3 \sqrt[3]{2} 3^{2/3}-4}}",1,"((-1)^(2/3)*((-2)^(2/3) - 2*3^(2/3))*ArcTan[(3*(-2)^(2/3)*3^(1/3) + 2*x)/Sqrt[6*(4 + 3*(-2)^(1/3)*3^(2/3))]])/(216*2^(1/3)*3^(5/6)*Sqrt[8 + (9*I)*2^(1/3)*3^(1/6) + 3*2^(1/3)*3^(2/3)]) - ((-1)^(2/3)*((-3)^(1/3) + 3*2^(1/3))*ArcTan[(2^(1/6)*(3*(-3)^(1/3) - 2^(1/3)*x))/Sqrt[3*(4 - 3*(-3)^(2/3)*2^(1/3))]])/(216*6^(1/6)*(1 + (-1)^(1/3))^2*Sqrt[4 - 3*(-3)^(2/3)*2^(1/3)]) - ((1 - 2^(1/3)*3^(2/3))*ArcTanh[(2^(1/6)*(3*3^(1/3) + 2^(1/3)*x))/Sqrt[3*(-4 + 3*2^(1/3)*3^(2/3))]])/(216*2^(1/6)*3^(5/6)*Sqrt[-4 + 3*2^(1/3)*3^(2/3)]) + Log[x]/216 - ((36 + 2^(2/3)*3^(1/3)*(1 + I*Sqrt[3]))*Log[6 - 3*(-3)^(1/3)*2^(2/3)*x + x^2])/46656 - ((18 - (-2)^(2/3)*3^(1/3))*Log[6 + 3*(-2)^(2/3)*3^(1/3)*x + x^2])/23328 - ((18 - 2^(2/3)*3^(1/3))*Log[6 + 3*2^(2/3)*3^(1/3)*x + x^2])/23328","A",14,6,26,0.2308,1,"{2097, 634, 618, 204, 628, 206}"
150,1,448,0,1.1018658,"\int \frac{1}{x^2 \left(216+108 x^2+324 x^3+18 x^4+x^6\right)} \, dx","Int[1/(x^2*(216 + 108*x^2 + 324*x^3 + 18*x^4 + x^6)),x]","-\frac{(-1)^{2/3} \left(9+\sqrt[3]{-3} 2^{2/3}\right) \log \left(x^2-3 \sqrt[3]{-3} 2^{2/3} x+6\right)}{1296 \sqrt[3]{2} 3^{2/3} \left(1+\sqrt[3]{-1}\right)^2}+\frac{\left(3 (-6)^{2/3}+2 \sqrt[3]{-2}\right) \log \left(x^2+3 (-2)^{2/3} \sqrt[3]{3} x+6\right)}{7776 \sqrt[3]{3}}-\frac{\left(2^{2/3}-3\ 3^{2/3}\right) \log \left(x^2+3\ 2^{2/3} \sqrt[3]{3} x+6\right)}{3888 \sqrt[3]{6}}-\frac{1}{216 x}-\frac{\left(27 \sqrt[3]{-6}-(-2)^{2/3}+12\ 3^{2/3}\right) \tan ^{-1}\left(\frac{2 x+3 (-2)^{2/3} \sqrt[3]{3}}{\sqrt{6 \left(4+3 \sqrt[3]{-2} 3^{2/3}\right)}}\right)}{5832 \sqrt[6]{3} \sqrt{8+9 i \sqrt[3]{2} \sqrt[6]{3}+3 \sqrt[3]{2} 3^{2/3}}}-\frac{(-1)^{2/3} \left(6 (-6)^{2/3}+27 \sqrt[3]{-3}-\sqrt[3]{2}\right) \tan ^{-1}\left(\frac{\sqrt[6]{2} \left(3 \sqrt[3]{-3}-\sqrt[3]{2} x\right)}{\sqrt{3 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)}}\right)}{1944 \sqrt[6]{6} \left(1+\sqrt[3]{-1}\right)^2 \sqrt{4-3 (-3)^{2/3} \sqrt[3]{2}}}-\frac{\left(\sqrt[3]{2}+27 \sqrt[3]{3}-6\ 6^{2/3}\right) \tanh ^{-1}\left(\frac{\sqrt[6]{2} \left(\sqrt[3]{2} x+3 \sqrt[3]{3}\right)}{\sqrt{3 \left(3 \sqrt[3]{2} 3^{2/3}-4\right)}}\right)}{5832 \sqrt[6]{6} \sqrt{3 \sqrt[3]{2} 3^{2/3}-4}}","-\frac{(-1)^{2/3} \left(9+\sqrt[3]{-3} 2^{2/3}\right) \log \left(x^2-3 \sqrt[3]{-3} 2^{2/3} x+6\right)}{1296 \sqrt[3]{2} 3^{2/3} \left(1+\sqrt[3]{-1}\right)^2}+\frac{\left(3 (-6)^{2/3}+2 \sqrt[3]{-2}\right) \log \left(x^2+3 (-2)^{2/3} \sqrt[3]{3} x+6\right)}{7776 \sqrt[3]{3}}-\frac{\left(2^{2/3}-3\ 3^{2/3}\right) \log \left(x^2+3\ 2^{2/3} \sqrt[3]{3} x+6\right)}{3888 \sqrt[3]{6}}-\frac{1}{216 x}-\frac{\left(27 \sqrt[3]{-6}-(-2)^{2/3}+12\ 3^{2/3}\right) \tan ^{-1}\left(\frac{2 x+3 (-2)^{2/3} \sqrt[3]{3}}{\sqrt{6 \left(4+3 \sqrt[3]{-2} 3^{2/3}\right)}}\right)}{5832 \sqrt[6]{3} \sqrt{8+9 i \sqrt[3]{2} \sqrt[6]{3}+3 \sqrt[3]{2} 3^{2/3}}}-\frac{(-1)^{2/3} \left(6 (-6)^{2/3}+27 \sqrt[3]{-3}-\sqrt[3]{2}\right) \tan ^{-1}\left(\frac{\sqrt[6]{2} \left(3 \sqrt[3]{-3}-\sqrt[3]{2} x\right)}{\sqrt{3 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)}}\right)}{1944 \sqrt[6]{6} \left(1+\sqrt[3]{-1}\right)^2 \sqrt{4-3 (-3)^{2/3} \sqrt[3]{2}}}-\frac{\left(\sqrt[3]{2}+27 \sqrt[3]{3}-6\ 6^{2/3}\right) \tanh ^{-1}\left(\frac{\sqrt[6]{2} \left(\sqrt[3]{2} x+3 \sqrt[3]{3}\right)}{\sqrt{3 \left(3 \sqrt[3]{2} 3^{2/3}-4\right)}}\right)}{5832 \sqrt[6]{6} \sqrt{3 \sqrt[3]{2} 3^{2/3}-4}}",1,"-1/(216*x) - ((27*(-6)^(1/3) - (-2)^(2/3) + 12*3^(2/3))*ArcTan[(3*(-2)^(2/3)*3^(1/3) + 2*x)/Sqrt[6*(4 + 3*(-2)^(1/3)*3^(2/3))]])/(5832*3^(1/6)*Sqrt[8 + (9*I)*2^(1/3)*3^(1/6) + 3*2^(1/3)*3^(2/3)]) - ((-1)^(2/3)*(6*(-6)^(2/3) + 27*(-3)^(1/3) - 2^(1/3))*ArcTan[(2^(1/6)*(3*(-3)^(1/3) - 2^(1/3)*x))/Sqrt[3*(4 - 3*(-3)^(2/3)*2^(1/3))]])/(1944*6^(1/6)*(1 + (-1)^(1/3))^2*Sqrt[4 - 3*(-3)^(2/3)*2^(1/3)]) - ((2^(1/3) + 27*3^(1/3) - 6*6^(2/3))*ArcTanh[(2^(1/6)*(3*3^(1/3) + 2^(1/3)*x))/Sqrt[3*(-4 + 3*2^(1/3)*3^(2/3))]])/(5832*6^(1/6)*Sqrt[-4 + 3*2^(1/3)*3^(2/3)]) - ((-1)^(2/3)*(9 + (-3)^(1/3)*2^(2/3))*Log[6 - 3*(-3)^(1/3)*2^(2/3)*x + x^2])/(1296*2^(1/3)*3^(2/3)*(1 + (-1)^(1/3))^2) + ((3*(-6)^(2/3) + 2*(-2)^(1/3))*Log[6 + 3*(-2)^(2/3)*3^(1/3)*x + x^2])/(7776*3^(1/3)) - ((2^(2/3) - 3*3^(2/3))*Log[6 + 3*2^(2/3)*3^(1/3)*x + x^2])/(3888*6^(1/3))","A",14,6,26,0.2308,1,"{2097, 634, 618, 204, 628, 206}"
151,1,1064,0,2.5038075,"\int \frac{x^8}{\left(216+108 x^2+324 x^3+18 x^4+x^6\right)^2} \, dx","Int[x^8/(216 + 108*x^2 + 324*x^3 + 18*x^4 + x^6)^2,x]","-\frac{\sqrt[3]{-\frac{1}{3}} \left(\left(2+27 (-2)^{2/3} \sqrt[3]{3}+12 \sqrt[3]{-2} 3^{2/3}\right) x+9 \left(6-(-2)^{2/3} \sqrt[3]{3}\right)\right)}{729\ 2^{2/3} \left(8+9 i \sqrt[3]{2} \sqrt[6]{3}+3 \sqrt[3]{2} 3^{2/3}\right) \left(x^2+3 (-2)^{2/3} \sqrt[3]{3} x+6\right)}-\frac{\sqrt[3]{-1} \left(2+27 (-2)^{2/3} \sqrt[3]{3}+12 \sqrt[3]{-2} 3^{2/3}\right) \tan ^{-1}\left(\frac{2 x+3 (-2)^{2/3} \sqrt[3]{3}}{\sqrt{6 \left(4+3 \sqrt[3]{-2} 3^{2/3}\right)}}\right)}{162 \sqrt[6]{2} 3^{5/6} \left(1-\sqrt[3]{-1}\right)^2 \left(1+\sqrt[3]{-1}\right)^4 \left(4+3 \sqrt[3]{-2} 3^{2/3}\right)^{3/2}}-\frac{i \left((-2)^{2/3}+6\ 3^{2/3}\right) \tan ^{-1}\left(\frac{2 x+3 (-2)^{2/3} \sqrt[3]{3}}{\sqrt{6 \left(4+3 \sqrt[3]{-2} 3^{2/3}\right)}}\right)}{162\ 2^{5/6} \sqrt[3]{3} \left(1+\sqrt[3]{-1}\right)^5 \sqrt{4+3 \sqrt[3]{-2} 3^{2/3}}}+\frac{\left(i 2^{2/3}-9 \sqrt[6]{3}-3 i 3^{2/3}\right) \tan ^{-1}\left(\frac{\sqrt[6]{2} \left(3 \sqrt[3]{-3}-\sqrt[3]{2} x\right)}{\sqrt{3 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)}}\right)}{162\ 2^{5/6} \sqrt[3]{3} \left(1+\sqrt[3]{-1}\right)^5 \sqrt{4-3 (-3)^{2/3} \sqrt[3]{2}}}-\frac{\sqrt[3]{-1} \left(6 (-6)^{2/3}+27 \sqrt[3]{-3}-\sqrt[3]{2}\right) \tan ^{-1}\left(\frac{\sqrt[6]{2} \left(3 \sqrt[3]{-3}-\sqrt[3]{2} x\right)}{\sqrt{3 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)}}\right)}{81 \sqrt{2} 3^{5/6} \left(1+\sqrt[3]{-1}\right)^4 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)^{3/2}}+\frac{\left(\sqrt[3]{2}+27 \sqrt[3]{3}-6\ 6^{2/3}\right) \tanh ^{-1}\left(\frac{\sqrt[6]{2} \left(\sqrt[3]{2} x+3 \sqrt[3]{3}\right)}{\sqrt{3 \left(-4+3 \sqrt[3]{2} 3^{2/3}\right)}}\right)}{81 \sqrt{2} 3^{5/6} \left(1-\sqrt[3]{-1}\right)^2 \left(1+\sqrt[3]{-1}\right)^4 \left(-4+3 \sqrt[3]{2} 3^{2/3}\right)^{3/2}}-\frac{\left(1+3 \sqrt[3]{2} 3^{2/3}\right) \tanh ^{-1}\left(\frac{\sqrt[6]{2} \left(\sqrt[3]{2} x+3 \sqrt[3]{3}\right)}{\sqrt{3 \left(-4+3 \sqrt[3]{2} 3^{2/3}\right)}}\right)}{1458 \sqrt[6]{2} 3^{5/6} \sqrt{-4+3 \sqrt[3]{2} 3^{2/3}}}-\frac{\log \left(x^2-3 \sqrt[3]{-3} 2^{2/3} x+6\right)}{972 \sqrt[3]{2} 3^{2/3} \left(1+\sqrt[3]{-1}\right)^4}+\frac{i \log \left(x^2+3 (-2)^{2/3} \sqrt[3]{3} x+6\right)}{972 \sqrt[3]{2} \sqrt[6]{3} \left(1+\sqrt[3]{-1}\right)^5}-\frac{\log \left(x^2+3\ 2^{2/3} \sqrt[3]{3} x+6\right)}{8748 \sqrt[3]{2} 3^{2/3}}-\frac{\sqrt[3]{-\frac{1}{3}} \left(\left(2-3\ 2^{2/3} \left(2 (-6)^{2/3}+9 \sqrt[3]{-3}\right)\right) x+9 \left(6+\sqrt[3]{-3} 2^{2/3}\right)\right)}{162\ 2^{2/3} \left(1+\sqrt[3]{-1}\right)^4 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right) \left(x^2-3 \sqrt[3]{-3} 2^{2/3} x+6\right)}+\frac{\left(2+2^{2/3} \left(27 \sqrt[3]{3}-6\ 6^{2/3}\right)\right) x+9 \left(6-2^{2/3} \sqrt[3]{3}\right)}{1458\ 2^{2/3} \sqrt[3]{3} \left(4-3 \sqrt[3]{2} 3^{2/3}\right) \left(x^2+3\ 2^{2/3} \sqrt[3]{3} x+6\right)}","-\frac{\sqrt[3]{-\frac{1}{3}} \left(\left(2+27 (-2)^{2/3} \sqrt[3]{3}+12 \sqrt[3]{-2} 3^{2/3}\right) x+9 \left(6-(-2)^{2/3} \sqrt[3]{3}\right)\right)}{729\ 2^{2/3} \left(8+9 i \sqrt[3]{2} \sqrt[6]{3}+3 \sqrt[3]{2} 3^{2/3}\right) \left(x^2+3 (-2)^{2/3} \sqrt[3]{3} x+6\right)}-\frac{\sqrt[3]{-1} \left(2+27 (-2)^{2/3} \sqrt[3]{3}+12 \sqrt[3]{-2} 3^{2/3}\right) \tan ^{-1}\left(\frac{2 x+3 (-2)^{2/3} \sqrt[3]{3}}{\sqrt{6 \left(4+3 \sqrt[3]{-2} 3^{2/3}\right)}}\right)}{162 \sqrt[6]{2} 3^{5/6} \left(1-\sqrt[3]{-1}\right)^2 \left(1+\sqrt[3]{-1}\right)^4 \left(4+3 \sqrt[3]{-2} 3^{2/3}\right)^{3/2}}-\frac{i \left((-2)^{2/3}+6\ 3^{2/3}\right) \tan ^{-1}\left(\frac{2 x+3 (-2)^{2/3} \sqrt[3]{3}}{\sqrt{6 \left(4+3 \sqrt[3]{-2} 3^{2/3}\right)}}\right)}{162\ 2^{5/6} \sqrt[3]{3} \left(1+\sqrt[3]{-1}\right)^5 \sqrt{4+3 \sqrt[3]{-2} 3^{2/3}}}+\frac{\left(i 2^{2/3}-9 \sqrt[6]{3}-3 i 3^{2/3}\right) \tan ^{-1}\left(\frac{\sqrt[6]{2} \left(3 \sqrt[3]{-3}-\sqrt[3]{2} x\right)}{\sqrt{3 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)}}\right)}{162\ 2^{5/6} \sqrt[3]{3} \left(1+\sqrt[3]{-1}\right)^5 \sqrt{4-3 (-3)^{2/3} \sqrt[3]{2}}}-\frac{\sqrt[3]{-1} \left(6 (-6)^{2/3}+27 \sqrt[3]{-3}-\sqrt[3]{2}\right) \tan ^{-1}\left(\frac{\sqrt[6]{2} \left(3 \sqrt[3]{-3}-\sqrt[3]{2} x\right)}{\sqrt{3 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)}}\right)}{81 \sqrt{2} 3^{5/6} \left(1+\sqrt[3]{-1}\right)^4 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)^{3/2}}+\frac{\left(\sqrt[3]{2}+27 \sqrt[3]{3}-6\ 6^{2/3}\right) \tanh ^{-1}\left(\frac{\sqrt[6]{2} \left(\sqrt[3]{2} x+3 \sqrt[3]{3}\right)}{\sqrt{3 \left(-4+3 \sqrt[3]{2} 3^{2/3}\right)}}\right)}{81 \sqrt{2} 3^{5/6} \left(1-\sqrt[3]{-1}\right)^2 \left(1+\sqrt[3]{-1}\right)^4 \left(-4+3 \sqrt[3]{2} 3^{2/3}\right)^{3/2}}-\frac{\left(1+3 \sqrt[3]{2} 3^{2/3}\right) \tanh ^{-1}\left(\frac{\sqrt[6]{2} \left(\sqrt[3]{2} x+3 \sqrt[3]{3}\right)}{\sqrt{3 \left(-4+3 \sqrt[3]{2} 3^{2/3}\right)}}\right)}{1458 \sqrt[6]{2} 3^{5/6} \sqrt{-4+3 \sqrt[3]{2} 3^{2/3}}}-\frac{\log \left(x^2-3 \sqrt[3]{-3} 2^{2/3} x+6\right)}{972 \sqrt[3]{2} 3^{2/3} \left(1+\sqrt[3]{-1}\right)^4}+\frac{i \log \left(x^2+3 (-2)^{2/3} \sqrt[3]{3} x+6\right)}{972 \sqrt[3]{2} \sqrt[6]{3} \left(1+\sqrt[3]{-1}\right)^5}-\frac{\log \left(x^2+3\ 2^{2/3} \sqrt[3]{3} x+6\right)}{8748 \sqrt[3]{2} 3^{2/3}}-\frac{\sqrt[3]{-\frac{1}{3}} \left(\left(2-2^{2/3} \left(6 (-6)^{2/3}+27 \sqrt[3]{-3}\right)\right) x+9 \left(6+\sqrt[3]{-3} 2^{2/3}\right)\right)}{162\ 2^{2/3} \left(1+\sqrt[3]{-1}\right)^4 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right) \left(x^2-3 \sqrt[3]{-3} 2^{2/3} x+6\right)}+\frac{\left(2+2^{2/3} \left(27 \sqrt[3]{3}-6\ 6^{2/3}\right)\right) x+9 \left(6-2^{2/3} \sqrt[3]{3}\right)}{1458\ 2^{2/3} \sqrt[3]{3} \left(4-3 \sqrt[3]{2} 3^{2/3}\right) \left(x^2+3\ 2^{2/3} \sqrt[3]{3} x+6\right)}",1,"-((-1/3)^(1/3)*(9*(6 + (-3)^(1/3)*2^(2/3)) + (2 - 3*2^(2/3)*(2*(-6)^(2/3) + 9*(-3)^(1/3)))*x))/(162*2^(2/3)*(1 + (-1)^(1/3))^4*(4 - 3*(-3)^(2/3)*2^(1/3))*(6 - 3*(-3)^(1/3)*2^(2/3)*x + x^2)) - ((-1/3)^(1/3)*(9*(6 - (-2)^(2/3)*3^(1/3)) + (2 + 27*(-2)^(2/3)*3^(1/3) + 12*(-2)^(1/3)*3^(2/3))*x))/(729*2^(2/3)*(8 + (9*I)*2^(1/3)*3^(1/6) + 3*2^(1/3)*3^(2/3))*(6 + 3*(-2)^(2/3)*3^(1/3)*x + x^2)) + (9*(6 - 2^(2/3)*3^(1/3)) + (2 + 2^(2/3)*(27*3^(1/3) - 6*6^(2/3)))*x)/(1458*2^(2/3)*3^(1/3)*(4 - 3*2^(1/3)*3^(2/3))*(6 + 3*2^(2/3)*3^(1/3)*x + x^2)) - ((I/162)*((-2)^(2/3) + 6*3^(2/3))*ArcTan[(3*(-2)^(2/3)*3^(1/3) + 2*x)/Sqrt[6*(4 + 3*(-2)^(1/3)*3^(2/3))]])/(2^(5/6)*3^(1/3)*(1 + (-1)^(1/3))^5*Sqrt[4 + 3*(-2)^(1/3)*3^(2/3)]) - ((-1)^(1/3)*(2 + 27*(-2)^(2/3)*3^(1/3) + 12*(-2)^(1/3)*3^(2/3))*ArcTan[(3*(-2)^(2/3)*3^(1/3) + 2*x)/Sqrt[6*(4 + 3*(-2)^(1/3)*3^(2/3))]])/(162*2^(1/6)*3^(5/6)*(1 - (-1)^(1/3))^2*(1 + (-1)^(1/3))^4*(4 + 3*(-2)^(1/3)*3^(2/3))^(3/2)) - ((-1)^(1/3)*(6*(-6)^(2/3) + 27*(-3)^(1/3) - 2^(1/3))*ArcTan[(2^(1/6)*(3*(-3)^(1/3) - 2^(1/3)*x))/Sqrt[3*(4 - 3*(-3)^(2/3)*2^(1/3))]])/(81*Sqrt[2]*3^(5/6)*(1 + (-1)^(1/3))^4*(4 - 3*(-3)^(2/3)*2^(1/3))^(3/2)) + ((I*2^(2/3) - 9*3^(1/6) - (3*I)*3^(2/3))*ArcTan[(2^(1/6)*(3*(-3)^(1/3) - 2^(1/3)*x))/Sqrt[3*(4 - 3*(-3)^(2/3)*2^(1/3))]])/(162*2^(5/6)*3^(1/3)*(1 + (-1)^(1/3))^5*Sqrt[4 - 3*(-3)^(2/3)*2^(1/3)]) - ((1 + 3*2^(1/3)*3^(2/3))*ArcTanh[(2^(1/6)*(3*3^(1/3) + 2^(1/3)*x))/Sqrt[3*(-4 + 3*2^(1/3)*3^(2/3))]])/(1458*2^(1/6)*3^(5/6)*Sqrt[-4 + 3*2^(1/3)*3^(2/3)]) + ((2^(1/3) + 27*3^(1/3) - 6*6^(2/3))*ArcTanh[(2^(1/6)*(3*3^(1/3) + 2^(1/3)*x))/Sqrt[3*(-4 + 3*2^(1/3)*3^(2/3))]])/(81*Sqrt[2]*3^(5/6)*(1 - (-1)^(1/3))^2*(1 + (-1)^(1/3))^4*(-4 + 3*2^(1/3)*3^(2/3))^(3/2)) - Log[6 - 3*(-3)^(1/3)*2^(2/3)*x + x^2]/(972*2^(1/3)*3^(2/3)*(1 + (-1)^(1/3))^4) + ((I/972)*Log[6 + 3*(-2)^(2/3)*3^(1/3)*x + x^2])/(2^(1/3)*3^(1/6)*(1 + (-1)^(1/3))^5) - Log[6 + 3*2^(2/3)*3^(1/3)*x + x^2]/(8748*2^(1/3)*3^(2/3))","A",23,7,26,0.2692,1,"{2097, 638, 618, 204, 634, 628, 206}"
152,1,1005,0,2.4025734,"\int \frac{x^7}{\left(216+108 x^2+324 x^3+18 x^4+x^6\right)^2} \, dx","Int[x^7/(216 + 108*x^2 + 324*x^3 + 18*x^4 + x^6)^2,x]","\frac{2 \left(2-3 \sqrt[3]{2} 3^{2/3}\right)-3 \left(6-2^{2/3} \sqrt[3]{3}\right) x}{2916\ 2^{2/3} \sqrt[3]{3} \left(4-3 \sqrt[3]{2} 3^{2/3}\right) \left(x^2+3\ 2^{2/3} \sqrt[3]{3} x+6\right)}+\frac{\left(9 i+\sqrt[3]{3} \left(2 i 2^{2/3}-9 \sqrt[6]{3}+2\ 2^{2/3} \sqrt{3}\right)\right) \tan ^{-1}\left(\frac{3 \sqrt[3]{-3} 2^{2/3}-2 x}{\sqrt{6 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)}}\right)}{5832 \left(1+\sqrt[3]{-1}\right)^5 \sqrt{2 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)}}+\frac{\left(9 \sqrt[6]{3}+i \left(4\ 2^{2/3}-3\ 3^{2/3}\right)\right) \tan ^{-1}\left(\frac{2 x+3 (-2)^{2/3} \sqrt[3]{3}}{\sqrt{6 \left(4+3 \sqrt[3]{-2} 3^{2/3}\right)}}\right)}{1944\ 3^{2/3} \left(1+\sqrt[3]{-1}\right)^5 \sqrt{2 \left(4+3 \sqrt[3]{-2} 3^{2/3}\right)}}+\frac{\left(1+\sqrt[3]{-2} 3^{2/3}\right) \tan ^{-1}\left(\frac{2 x+3 (-2)^{2/3} \sqrt[3]{3}}{\sqrt{6 \left(4+3 \sqrt[3]{-2} 3^{2/3}\right)}}\right)}{54 \sqrt{6} \left(1-\sqrt[3]{-1}\right)^2 \left(1+\sqrt[3]{-1}\right)^4 \left(4+3 \sqrt[3]{-2} 3^{2/3}\right)^{3/2}}-\frac{\sqrt[3]{-1} \left(\sqrt[3]{-3}+3 \sqrt[3]{2}\right) \tan ^{-1}\left(\frac{\sqrt[6]{2} \left(3 \sqrt[3]{-3}-\sqrt[3]{2} x\right)}{\sqrt{3 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)}}\right)}{54 \sqrt{2} 3^{5/6} \left(1+\sqrt[3]{-1}\right)^4 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)^{3/2}}+\frac{\left(2\ 2^{2/3}+3\ 3^{2/3}\right) \tanh ^{-1}\left(\frac{\sqrt[6]{2} \left(\sqrt[3]{2} x+3 \sqrt[3]{3}\right)}{\sqrt{3 \left(-4+3 \sqrt[3]{2} 3^{2/3}\right)}}\right)}{26244 \sqrt[6]{3} \sqrt{2 \left(-4+3 \sqrt[3]{2} 3^{2/3}\right)}}+\frac{\left(1-\sqrt[3]{2} 3^{2/3}\right) \tanh ^{-1}\left(\frac{\sqrt[6]{2} \left(\sqrt[3]{2} x+3 \sqrt[3]{3}\right)}{\sqrt{3 \left(-4+3 \sqrt[3]{2} 3^{2/3}\right)}}\right)}{54 \sqrt{6} \left(1-\sqrt[3]{-1}\right)^2 \left(1+\sqrt[3]{-1}\right)^4 \left(-4+3 \sqrt[3]{2} 3^{2/3}\right)^{3/2}}+\frac{i \log \left(x^2-3 \sqrt[3]{-3} 2^{2/3} x+6\right)}{648\ 2^{2/3} 3^{5/6} \left(1+\sqrt[3]{-1}\right)^5}-\frac{\left(i+\sqrt{3}\right) \log \left(x^2+3 (-2)^{2/3} \sqrt[3]{3} x+6\right)}{1296\ 2^{2/3} 3^{5/6} \left(1+\sqrt[3]{-1}\right)^5}-\frac{\log \left(x^2+3\ 2^{2/3} \sqrt[3]{3} x+6\right)}{17496\ 2^{2/3} \sqrt[3]{3}}-\frac{2 \left(2 \sqrt[3]{-1} 3^{2/3}+9 \sqrt[3]{6}\right)-9 \left((-2)^{2/3}+2 \sqrt[3]{-1} 3^{2/3}\right) x}{972\ 2^{2/3} \left(1+\sqrt[3]{-1}\right)^4 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right) \left(x^2-3 \sqrt[3]{-3} 2^{2/3} x+6\right)}-\frac{\sqrt[3]{-6} \left(9 \sqrt[3]{-2}+2 \sqrt[3]{3}\right)-9 \left(1+\sqrt[3]{-2} 3^{2/3}\right) x}{4374 \left(8+9 i \sqrt[3]{2} \sqrt[6]{3}+3 \sqrt[3]{2} 3^{2/3}\right) \left(x^2+3 (-2)^{2/3} \sqrt[3]{3} x+6\right)}","\frac{2 \left(2-3 \sqrt[3]{2} 3^{2/3}\right)-3 \left(6-2^{2/3} \sqrt[3]{3}\right) x}{2916\ 2^{2/3} \sqrt[3]{3} \left(4-3 \sqrt[3]{2} 3^{2/3}\right) \left(x^2+3\ 2^{2/3} \sqrt[3]{3} x+6\right)}+\frac{\left(9 i+\sqrt[3]{3} \left(2 i 2^{2/3}-9 \sqrt[6]{3}+2\ 2^{2/3} \sqrt{3}\right)\right) \tan ^{-1}\left(\frac{3 \sqrt[3]{-3} 2^{2/3}-2 x}{\sqrt{6 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)}}\right)}{5832 \left(1+\sqrt[3]{-1}\right)^5 \sqrt{2 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)}}+\frac{\left(9 \sqrt[6]{3}+i \left(4\ 2^{2/3}-3\ 3^{2/3}\right)\right) \tan ^{-1}\left(\frac{2 x+3 (-2)^{2/3} \sqrt[3]{3}}{\sqrt{6 \left(4+3 \sqrt[3]{-2} 3^{2/3}\right)}}\right)}{1944\ 3^{2/3} \left(1+\sqrt[3]{-1}\right)^5 \sqrt{2 \left(4+3 \sqrt[3]{-2} 3^{2/3}\right)}}+\frac{\left(1+\sqrt[3]{-2} 3^{2/3}\right) \tan ^{-1}\left(\frac{2 x+3 (-2)^{2/3} \sqrt[3]{3}}{\sqrt{6 \left(4+3 \sqrt[3]{-2} 3^{2/3}\right)}}\right)}{54 \sqrt{6} \left(1-\sqrt[3]{-1}\right)^2 \left(1+\sqrt[3]{-1}\right)^4 \left(4+3 \sqrt[3]{-2} 3^{2/3}\right)^{3/2}}-\frac{\sqrt[3]{-1} \left(\sqrt[3]{-3}+3 \sqrt[3]{2}\right) \tan ^{-1}\left(\frac{\sqrt[6]{2} \left(3 \sqrt[3]{-3}-\sqrt[3]{2} x\right)}{\sqrt{3 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)}}\right)}{54 \sqrt{2} 3^{5/6} \left(1+\sqrt[3]{-1}\right)^4 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)^{3/2}}+\frac{\left(2\ 2^{2/3}+3\ 3^{2/3}\right) \tanh ^{-1}\left(\frac{\sqrt[6]{2} \left(\sqrt[3]{2} x+3 \sqrt[3]{3}\right)}{\sqrt{3 \left(-4+3 \sqrt[3]{2} 3^{2/3}\right)}}\right)}{26244 \sqrt[6]{3} \sqrt{2 \left(-4+3 \sqrt[3]{2} 3^{2/3}\right)}}+\frac{\left(1-\sqrt[3]{2} 3^{2/3}\right) \tanh ^{-1}\left(\frac{\sqrt[6]{2} \left(\sqrt[3]{2} x+3 \sqrt[3]{3}\right)}{\sqrt{3 \left(-4+3 \sqrt[3]{2} 3^{2/3}\right)}}\right)}{54 \sqrt{6} \left(1-\sqrt[3]{-1}\right)^2 \left(1+\sqrt[3]{-1}\right)^4 \left(-4+3 \sqrt[3]{2} 3^{2/3}\right)^{3/2}}+\frac{i \log \left(x^2-3 \sqrt[3]{-3} 2^{2/3} x+6\right)}{648\ 2^{2/3} 3^{5/6} \left(1+\sqrt[3]{-1}\right)^5}-\frac{\left(i+\sqrt{3}\right) \log \left(x^2+3 (-2)^{2/3} \sqrt[3]{3} x+6\right)}{1296\ 2^{2/3} 3^{5/6} \left(1+\sqrt[3]{-1}\right)^5}-\frac{\log \left(x^2+3\ 2^{2/3} \sqrt[3]{3} x+6\right)}{17496\ 2^{2/3} \sqrt[3]{3}}-\frac{2 \left(2 \sqrt[3]{-1} 3^{2/3}+9 \sqrt[3]{6}\right)-9 \left((-2)^{2/3}+2 \sqrt[3]{-1} 3^{2/3}\right) x}{972\ 2^{2/3} \left(1+\sqrt[3]{-1}\right)^4 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right) \left(x^2-3 \sqrt[3]{-3} 2^{2/3} x+6\right)}-\frac{\sqrt[3]{-6} \left(9 \sqrt[3]{-2}+2 \sqrt[3]{3}\right)-9 \left(1+\sqrt[3]{-2} 3^{2/3}\right) x}{4374 \left(8+9 i \sqrt[3]{2} \sqrt[6]{3}+3 \sqrt[3]{2} 3^{2/3}\right) \left(x^2+3 (-2)^{2/3} \sqrt[3]{3} x+6\right)}",1,"-(2*(2*(-1)^(1/3)*3^(2/3) + 9*6^(1/3)) - 9*((-2)^(2/3) + 2*(-1)^(1/3)*3^(2/3))*x)/(972*2^(2/3)*(1 + (-1)^(1/3))^4*(4 - 3*(-3)^(2/3)*2^(1/3))*(6 - 3*(-3)^(1/3)*2^(2/3)*x + x^2)) - ((-6)^(1/3)*(9*(-2)^(1/3) + 2*3^(1/3)) - 9*(1 + (-2)^(1/3)*3^(2/3))*x)/(4374*(8 + (9*I)*2^(1/3)*3^(1/6) + 3*2^(1/3)*3^(2/3))*(6 + 3*(-2)^(2/3)*3^(1/3)*x + x^2)) + (2*(2 - 3*2^(1/3)*3^(2/3)) - 3*(6 - 2^(2/3)*3^(1/3))*x)/(2916*2^(2/3)*3^(1/3)*(4 - 3*2^(1/3)*3^(2/3))*(6 + 3*2^(2/3)*3^(1/3)*x + x^2)) + ((9*I + 3^(1/3)*((2*I)*2^(2/3) - 9*3^(1/6) + 2*2^(2/3)*Sqrt[3]))*ArcTan[(3*(-3)^(1/3)*2^(2/3) - 2*x)/Sqrt[6*(4 - 3*(-3)^(2/3)*2^(1/3))]])/(5832*(1 + (-1)^(1/3))^5*Sqrt[2*(4 - 3*(-3)^(2/3)*2^(1/3))]) + ((1 + (-2)^(1/3)*3^(2/3))*ArcTan[(3*(-2)^(2/3)*3^(1/3) + 2*x)/Sqrt[6*(4 + 3*(-2)^(1/3)*3^(2/3))]])/(54*Sqrt[6]*(1 - (-1)^(1/3))^2*(1 + (-1)^(1/3))^4*(4 + 3*(-2)^(1/3)*3^(2/3))^(3/2)) + ((9*3^(1/6) + I*(4*2^(2/3) - 3*3^(2/3)))*ArcTan[(3*(-2)^(2/3)*3^(1/3) + 2*x)/Sqrt[6*(4 + 3*(-2)^(1/3)*3^(2/3))]])/(1944*3^(2/3)*(1 + (-1)^(1/3))^5*Sqrt[2*(4 + 3*(-2)^(1/3)*3^(2/3))]) - ((-1)^(1/3)*((-3)^(1/3) + 3*2^(1/3))*ArcTan[(2^(1/6)*(3*(-3)^(1/3) - 2^(1/3)*x))/Sqrt[3*(4 - 3*(-3)^(2/3)*2^(1/3))]])/(54*Sqrt[2]*3^(5/6)*(1 + (-1)^(1/3))^4*(4 - 3*(-3)^(2/3)*2^(1/3))^(3/2)) + ((1 - 2^(1/3)*3^(2/3))*ArcTanh[(2^(1/6)*(3*3^(1/3) + 2^(1/3)*x))/Sqrt[3*(-4 + 3*2^(1/3)*3^(2/3))]])/(54*Sqrt[6]*(1 - (-1)^(1/3))^2*(1 + (-1)^(1/3))^4*(-4 + 3*2^(1/3)*3^(2/3))^(3/2)) + ((2*2^(2/3) + 3*3^(2/3))*ArcTanh[(2^(1/6)*(3*3^(1/3) + 2^(1/3)*x))/Sqrt[3*(-4 + 3*2^(1/3)*3^(2/3))]])/(26244*3^(1/6)*Sqrt[2*(-4 + 3*2^(1/3)*3^(2/3))]) + ((I/648)*Log[6 - 3*(-3)^(1/3)*2^(2/3)*x + x^2])/(2^(2/3)*3^(5/6)*(1 + (-1)^(1/3))^5) - ((I + Sqrt[3])*Log[6 + 3*(-2)^(2/3)*3^(1/3)*x + x^2])/(1296*2^(2/3)*3^(5/6)*(1 + (-1)^(1/3))^5) - Log[6 + 3*2^(2/3)*3^(1/3)*x + x^2]/(17496*2^(2/3)*3^(1/3))","A",23,7,26,0.2692,1,"{2097, 634, 618, 204, 628, 638, 206}"
153,1,677,0,1.5532567,"\int \frac{x^6}{\left(216+108 x^2+324 x^3+18 x^4+x^6\right)^2} \, dx","Int[x^6/(216 + 108*x^2 + 324*x^3 + 18*x^4 + x^6)^2,x]","\frac{\sqrt[3]{6} \left(9+\sqrt[3]{-3} 2^{2/3}\right) x+9 (-2)^{2/3}}{2916\ 2^{2/3} \left(1+\sqrt[3]{-1}\right)^4 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right) \left(x^2-3 \sqrt[3]{-3} 2^{2/3} x+6\right)}+\frac{\sqrt[3]{-1} 3^{2/3} \left(2+3 \sqrt[3]{-2} 3^{2/3}\right) x+9\ 2^{2/3}}{13122\ 2^{2/3} \left(8+9 i \sqrt[3]{2} \sqrt[6]{3}+3 \sqrt[3]{2} 3^{2/3}\right) \left(x^2+3 (-2)^{2/3} \sqrt[3]{3} x+6\right)}+\frac{3\ 2^{2/3} \sqrt[3]{3}-\left(2-3 \sqrt[3]{2} 3^{2/3}\right) x}{8748\ 2^{2/3} \sqrt[3]{3} \left(4-3 \sqrt[3]{2} 3^{2/3}\right) \left(x^2+3\ 2^{2/3} \sqrt[3]{3} x+6\right)}+\frac{\sqrt[6]{-\frac{1}{3}} \log \left(x^2-3 \sqrt[3]{-3} 2^{2/3} x+6\right)}{5832 \sqrt[3]{2} \left(1+\sqrt[3]{-1}\right)^5}-\frac{i \log \left(x^2+3 (-2)^{2/3} \sqrt[3]{3} x+6\right)}{5832 \sqrt[3]{2} \sqrt[6]{3} \left(1+\sqrt[3]{-1}\right)^5}+\frac{\log \left(x^2+3\ 2^{2/3} \sqrt[3]{3} x+6\right)}{52488 \sqrt[3]{2} 3^{2/3}}+\frac{\sqrt[3]{-1} \left(3 (-3)^{2/3}-2^{2/3}\right) \tan ^{-1}\left(\frac{3 \sqrt[3]{-3} 2^{2/3}-2 x}{\sqrt{6 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)}}\right)}{486\ 6^{5/6} \left(1+\sqrt[3]{-1}\right)^4 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)^{3/2}}+\frac{\left(3 (-3)^{2/3}+\sqrt[3]{-1} 2^{2/3}\right) \tan ^{-1}\left(\frac{2 x+3 (-2)^{2/3} \sqrt[3]{3}}{\sqrt{6 \left(4+3 \sqrt[3]{-2} 3^{2/3}\right)}}\right)}{486\ 6^{5/6} \left(1-\sqrt[3]{-1}\right)^2 \left(1+\sqrt[3]{-1}\right)^4 \left(4+3 \sqrt[3]{-2} 3^{2/3}\right)^{3/2}}-\frac{\left(2^{2/3}-3\ 3^{2/3}\right) \tanh ^{-1}\left(\frac{\sqrt[6]{2} \left(\sqrt[3]{2} x+3 \sqrt[3]{3}\right)}{\sqrt{3 \left(3 \sqrt[3]{2} 3^{2/3}-4\right)}}\right)}{486\ 6^{5/6} \left(1-\sqrt[3]{-1}\right)^2 \left(1+\sqrt[3]{-1}\right)^4 \left(3 \sqrt[3]{2} 3^{2/3}-4\right)^{3/2}}","\frac{\sqrt[3]{6} \left(9+\sqrt[3]{-3} 2^{2/3}\right) x+9 (-2)^{2/3}}{2916\ 2^{2/3} \left(1+\sqrt[3]{-1}\right)^4 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right) \left(x^2-3 \sqrt[3]{-3} 2^{2/3} x+6\right)}+\frac{\sqrt[3]{-1} 3^{2/3} \left(2+3 \sqrt[3]{-2} 3^{2/3}\right) x+9\ 2^{2/3}}{13122\ 2^{2/3} \left(8+9 i \sqrt[3]{2} \sqrt[6]{3}+3 \sqrt[3]{2} 3^{2/3}\right) \left(x^2+3 (-2)^{2/3} \sqrt[3]{3} x+6\right)}+\frac{3\ 2^{2/3} \sqrt[3]{3}-\left(2-3 \sqrt[3]{2} 3^{2/3}\right) x}{8748\ 2^{2/3} \sqrt[3]{3} \left(4-3 \sqrt[3]{2} 3^{2/3}\right) \left(x^2+3\ 2^{2/3} \sqrt[3]{3} x+6\right)}+\frac{\sqrt[6]{-\frac{1}{3}} \log \left(x^2-3 \sqrt[3]{-3} 2^{2/3} x+6\right)}{5832 \sqrt[3]{2} \left(1+\sqrt[3]{-1}\right)^5}-\frac{i \log \left(x^2+3 (-2)^{2/3} \sqrt[3]{3} x+6\right)}{5832 \sqrt[3]{2} \sqrt[6]{3} \left(1+\sqrt[3]{-1}\right)^5}+\frac{\log \left(x^2+3\ 2^{2/3} \sqrt[3]{3} x+6\right)}{52488 \sqrt[3]{2} 3^{2/3}}+\frac{\sqrt[3]{-1} \left(3 (-3)^{2/3}-2^{2/3}\right) \tan ^{-1}\left(\frac{3 \sqrt[3]{-3} 2^{2/3}-2 x}{\sqrt{6 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)}}\right)}{486\ 6^{5/6} \left(1+\sqrt[3]{-1}\right)^4 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)^{3/2}}+\frac{\left(3 (-3)^{2/3}+\sqrt[3]{-1} 2^{2/3}\right) \tan ^{-1}\left(\frac{2 x+3 (-2)^{2/3} \sqrt[3]{3}}{\sqrt{6 \left(4+3 \sqrt[3]{-2} 3^{2/3}\right)}}\right)}{486\ 6^{5/6} \left(1-\sqrt[3]{-1}\right)^2 \left(1+\sqrt[3]{-1}\right)^4 \left(4+3 \sqrt[3]{-2} 3^{2/3}\right)^{3/2}}-\frac{\left(2^{2/3}-3\ 3^{2/3}\right) \tanh ^{-1}\left(\frac{\sqrt[6]{2} \left(\sqrt[3]{2} x+3 \sqrt[3]{3}\right)}{\sqrt{3 \left(3 \sqrt[3]{2} 3^{2/3}-4\right)}}\right)}{486\ 6^{5/6} \left(1-\sqrt[3]{-1}\right)^2 \left(1+\sqrt[3]{-1}\right)^4 \left(3 \sqrt[3]{2} 3^{2/3}-4\right)^{3/2}}",1,"(9*(-2)^(2/3) + 6^(1/3)*(9 + (-3)^(1/3)*2^(2/3))*x)/(2916*2^(2/3)*(1 + (-1)^(1/3))^4*(4 - 3*(-3)^(2/3)*2^(1/3))*(6 - 3*(-3)^(1/3)*2^(2/3)*x + x^2)) + (9*2^(2/3) + (-1)^(1/3)*3^(2/3)*(2 + 3*(-2)^(1/3)*3^(2/3))*x)/(13122*2^(2/3)*(8 + (9*I)*2^(1/3)*3^(1/6) + 3*2^(1/3)*3^(2/3))*(6 + 3*(-2)^(2/3)*3^(1/3)*x + x^2)) + (3*2^(2/3)*3^(1/3) - (2 - 3*2^(1/3)*3^(2/3))*x)/(8748*2^(2/3)*3^(1/3)*(4 - 3*2^(1/3)*3^(2/3))*(6 + 3*2^(2/3)*3^(1/3)*x + x^2)) + ((-1)^(1/3)*(3*(-3)^(2/3) - 2^(2/3))*ArcTan[(3*(-3)^(1/3)*2^(2/3) - 2*x)/Sqrt[6*(4 - 3*(-3)^(2/3)*2^(1/3))]])/(486*6^(5/6)*(1 + (-1)^(1/3))^4*(4 - 3*(-3)^(2/3)*2^(1/3))^(3/2)) + ((3*(-3)^(2/3) + (-1)^(1/3)*2^(2/3))*ArcTan[(3*(-2)^(2/3)*3^(1/3) + 2*x)/Sqrt[6*(4 + 3*(-2)^(1/3)*3^(2/3))]])/(486*6^(5/6)*(1 - (-1)^(1/3))^2*(1 + (-1)^(1/3))^4*(4 + 3*(-2)^(1/3)*3^(2/3))^(3/2)) - ((2^(2/3) - 3*3^(2/3))*ArcTanh[(2^(1/6)*(3*3^(1/3) + 2^(1/3)*x))/Sqrt[3*(-4 + 3*2^(1/3)*3^(2/3))]])/(486*6^(5/6)*(1 - (-1)^(1/3))^2*(1 + (-1)^(1/3))^4*(-4 + 3*2^(1/3)*3^(2/3))^(3/2)) + ((-1/3)^(1/6)*Log[6 - 3*(-3)^(1/3)*2^(2/3)*x + x^2])/(5832*2^(1/3)*(1 + (-1)^(1/3))^5) - ((I/5832)*Log[6 + 3*(-2)^(2/3)*3^(1/3)*x + x^2])/(2^(1/3)*3^(1/6)*(1 + (-1)^(1/3))^5) + Log[6 + 3*2^(2/3)*3^(1/3)*x + x^2]/(52488*2^(1/3)*3^(2/3))","A",14,6,26,0.2308,1,"{2097, 638, 618, 204, 628, 206}"
154,1,682,0,1.2351831,"\int \frac{x^5}{\left(216+108 x^2+324 x^3+18 x^4+x^6\right)^2} \, dx","Int[x^5/(216 + 108*x^2 + 324*x^3 + 18*x^4 + x^6)^2,x]","\frac{\sqrt[3]{-\frac{1}{3}} \left(4-\sqrt[3]{-3} 2^{2/3} x\right)}{1944\ 2^{2/3} \left(1+\sqrt[3]{-1}\right)^4 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right) \left(x^2-3 \sqrt[3]{-3} 2^{2/3} x+6\right)}+\frac{\sqrt[3]{-\frac{1}{3}} \left((-2)^{2/3} \sqrt[3]{3} x+4\right)}{8748\ 2^{2/3} \left(8+9 i \sqrt[3]{2} \sqrt[6]{3}+3 \sqrt[3]{2} 3^{2/3}\right) \left(x^2+3 (-2)^{2/3} \sqrt[3]{3} x+6\right)}-\frac{2^{2/3} \sqrt[3]{3} x+4}{17496\ 2^{2/3} \sqrt[3]{3} \left(4-3 \sqrt[3]{2} 3^{2/3}\right) \left(x^2+3\ 2^{2/3} \sqrt[3]{3} x+6\right)}+\frac{\tan ^{-1}\left(\frac{3 \sqrt[3]{-3} 2^{2/3}-2 x}{\sqrt{6 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)}}\right)}{4374 \sqrt{3} \left(8-9 i \sqrt[3]{2} \sqrt[6]{3}+3 \sqrt[3]{2} 3^{2/3}\right)^{3/2}}-\frac{\tan ^{-1}\left(\frac{3 \sqrt[3]{-3} 2^{2/3}-2 x}{\sqrt{6 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)}}\right)}{4374\ 2^{5/6} \sqrt[6]{3} \left(1+\sqrt[3]{-1}\right)^4 \sqrt{4-3 (-3)^{2/3} \sqrt[3]{2}}}-\frac{\tan ^{-1}\left(\frac{2 x+3 (-2)^{2/3} \sqrt[3]{3}}{\sqrt{6 \left(4+3 \sqrt[3]{-2} 3^{2/3}\right)}}\right)}{4374 \sqrt{3} \left(8+9 i \sqrt[3]{2} \sqrt[6]{3}+3 \sqrt[3]{2} 3^{2/3}\right)^{3/2}}-\frac{i \tan ^{-1}\left(\frac{2 x+3 (-2)^{2/3} \sqrt[3]{3}}{\sqrt{6 \left(4+3 \sqrt[3]{-2} 3^{2/3}\right)}}\right)}{1458\ 2^{5/6} 3^{2/3} \left(1+\sqrt[3]{-1}\right)^5 \sqrt{4+3 \sqrt[3]{-2} 3^{2/3}}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[6]{2} \left(\sqrt[3]{2} x+3 \sqrt[3]{3}\right)}{\sqrt{3 \left(3 \sqrt[3]{2} 3^{2/3}-4\right)}}\right)}{39366\ 2^{5/6} \sqrt[6]{3} \sqrt{3 \sqrt[3]{2} 3^{2/3}-4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[6]{2} \left(\sqrt[3]{2} x+3 \sqrt[3]{3}\right)}{\sqrt{3 \left(3 \sqrt[3]{2} 3^{2/3}-4\right)}}\right)}{8748 \sqrt{6} \left(3 \sqrt[3]{2} 3^{2/3}-4\right)^{3/2}}","\frac{\sqrt[3]{-\frac{1}{3}} \left(4-\sqrt[3]{-3} 2^{2/3} x\right)}{1944\ 2^{2/3} \left(1+\sqrt[3]{-1}\right)^4 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right) \left(x^2-3 \sqrt[3]{-3} 2^{2/3} x+6\right)}+\frac{\sqrt[3]{-\frac{1}{3}} \left((-2)^{2/3} \sqrt[3]{3} x+4\right)}{8748\ 2^{2/3} \left(8+9 i \sqrt[3]{2} \sqrt[6]{3}+3 \sqrt[3]{2} 3^{2/3}\right) \left(x^2+3 (-2)^{2/3} \sqrt[3]{3} x+6\right)}-\frac{2^{2/3} \sqrt[3]{3} x+4}{17496\ 2^{2/3} \sqrt[3]{3} \left(4-3 \sqrt[3]{2} 3^{2/3}\right) \left(x^2+3\ 2^{2/3} \sqrt[3]{3} x+6\right)}+\frac{\tan ^{-1}\left(\frac{3 \sqrt[3]{-3} 2^{2/3}-2 x}{\sqrt{6 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)}}\right)}{4374 \sqrt{3} \left(8-9 i \sqrt[3]{2} \sqrt[6]{3}+3 \sqrt[3]{2} 3^{2/3}\right)^{3/2}}-\frac{\tan ^{-1}\left(\frac{3 \sqrt[3]{-3} 2^{2/3}-2 x}{\sqrt{6 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)}}\right)}{4374\ 2^{5/6} \sqrt[6]{3} \left(1+\sqrt[3]{-1}\right)^4 \sqrt{4-3 (-3)^{2/3} \sqrt[3]{2}}}-\frac{\tan ^{-1}\left(\frac{2 x+3 (-2)^{2/3} \sqrt[3]{3}}{\sqrt{6 \left(4+3 \sqrt[3]{-2} 3^{2/3}\right)}}\right)}{4374 \sqrt{3} \left(8+9 i \sqrt[3]{2} \sqrt[6]{3}+3 \sqrt[3]{2} 3^{2/3}\right)^{3/2}}-\frac{i \tan ^{-1}\left(\frac{2 x+3 (-2)^{2/3} \sqrt[3]{3}}{\sqrt{6 \left(4+3 \sqrt[3]{-2} 3^{2/3}\right)}}\right)}{1458\ 2^{5/6} 3^{2/3} \left(1+\sqrt[3]{-1}\right)^5 \sqrt{4+3 \sqrt[3]{-2} 3^{2/3}}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[6]{2} \left(\sqrt[3]{2} x+3 \sqrt[3]{3}\right)}{\sqrt{3 \left(3 \sqrt[3]{2} 3^{2/3}-4\right)}}\right)}{39366\ 2^{5/6} \sqrt[6]{3} \sqrt{3 \sqrt[3]{2} 3^{2/3}-4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[6]{2} \left(\sqrt[3]{2} x+3 \sqrt[3]{3}\right)}{\sqrt{3 \left(3 \sqrt[3]{2} 3^{2/3}-4\right)}}\right)}{8748 \sqrt{6} \left(3 \sqrt[3]{2} 3^{2/3}-4\right)^{3/2}}",1,"((-1/3)^(1/3)*(4 - (-3)^(1/3)*2^(2/3)*x))/(1944*2^(2/3)*(1 + (-1)^(1/3))^4*(4 - 3*(-3)^(2/3)*2^(1/3))*(6 - 3*(-3)^(1/3)*2^(2/3)*x + x^2)) + ((-1/3)^(1/3)*(4 + (-2)^(2/3)*3^(1/3)*x))/(8748*2^(2/3)*(8 + (9*I)*2^(1/3)*3^(1/6) + 3*2^(1/3)*3^(2/3))*(6 + 3*(-2)^(2/3)*3^(1/3)*x + x^2)) - (4 + 2^(2/3)*3^(1/3)*x)/(17496*2^(2/3)*3^(1/3)*(4 - 3*2^(1/3)*3^(2/3))*(6 + 3*2^(2/3)*3^(1/3)*x + x^2)) - ArcTan[(3*(-3)^(1/3)*2^(2/3) - 2*x)/Sqrt[6*(4 - 3*(-3)^(2/3)*2^(1/3))]]/(4374*2^(5/6)*3^(1/6)*(1 + (-1)^(1/3))^4*Sqrt[4 - 3*(-3)^(2/3)*2^(1/3)]) + ArcTan[(3*(-3)^(1/3)*2^(2/3) - 2*x)/Sqrt[6*(4 - 3*(-3)^(2/3)*2^(1/3))]]/(4374*Sqrt[3]*(8 - (9*I)*2^(1/3)*3^(1/6) + 3*2^(1/3)*3^(2/3))^(3/2)) - ((I/1458)*ArcTan[(3*(-2)^(2/3)*3^(1/3) + 2*x)/Sqrt[6*(4 + 3*(-2)^(1/3)*3^(2/3))]])/(2^(5/6)*3^(2/3)*(1 + (-1)^(1/3))^5*Sqrt[4 + 3*(-2)^(1/3)*3^(2/3)]) - ArcTan[(3*(-2)^(2/3)*3^(1/3) + 2*x)/Sqrt[6*(4 + 3*(-2)^(1/3)*3^(2/3))]]/(4374*Sqrt[3]*(8 + (9*I)*2^(1/3)*3^(1/6) + 3*2^(1/3)*3^(2/3))^(3/2)) - ArcTanh[(2^(1/6)*(3*3^(1/3) + 2^(1/3)*x))/Sqrt[3*(-4 + 3*2^(1/3)*3^(2/3))]]/(8748*Sqrt[6]*(-4 + 3*2^(1/3)*3^(2/3))^(3/2)) - ArcTanh[(2^(1/6)*(3*3^(1/3) + 2^(1/3)*x))/Sqrt[3*(-4 + 3*2^(1/3)*3^(2/3))]]/(39366*2^(5/6)*3^(1/6)*Sqrt[-4 + 3*2^(1/3)*3^(2/3)])","A",17,5,26,0.1923,1,"{2097, 638, 618, 204, 206}"
155,1,850,0,1.4696491,"\int \frac{x^4}{\left(216+108 x^2+324 x^3+18 x^4+x^6\right)^2} \, dx","Int[x^4/(216 + 108*x^2 + 324*x^3 + 18*x^4 + x^6)^2,x]","\frac{\sqrt[3]{-\frac{1}{3}} \left(3 \sqrt[3]{-3} 2^{2/3}-2 x\right)}{5832\ 2^{2/3} \left(1+\sqrt[3]{-1}\right)^4 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right) \left(x^2-3 \sqrt[3]{-3} 2^{2/3} x+6\right)}+\frac{\sqrt[3]{-1} \tan ^{-1}\left(\frac{3 \sqrt[3]{-3} 2^{2/3}-2 x}{\sqrt{6 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)}}\right)}{729\ 2^{2/3} 3^{5/6} \left(1+\sqrt[3]{-1}\right)^4 \left(8-9 i \sqrt[3]{2} \sqrt[6]{3}+3 \sqrt[3]{2} 3^{2/3}\right)^{3/2}}-\frac{\left(i+\sqrt{3}\right) \tan ^{-1}\left(\frac{2 x+3 (-2)^{2/3} \sqrt[3]{3}}{\sqrt{6 \left(4+3 \sqrt[3]{-2} 3^{2/3}\right)}}\right)}{11664 \sqrt[6]{2} \sqrt[3]{3} \left(1+\sqrt[3]{-1}\right)^5 \sqrt{4+3 \sqrt[3]{-2} 3^{2/3}}}-\frac{\sqrt[3]{-1} \tan ^{-1}\left(\frac{2 x+3 (-2)^{2/3} \sqrt[3]{3}}{\sqrt{6 \left(4+3 \sqrt[3]{-2} 3^{2/3}\right)}}\right)}{2916 \sqrt[6]{2} 3^{5/6} \left(1-\sqrt[3]{-1}\right)^2 \left(1+\sqrt[3]{-1}\right)^4 \left(4+3 \sqrt[3]{-2} 3^{2/3}\right)^{3/2}}-\frac{i \tan ^{-1}\left(\frac{\sqrt[6]{2} \left(3 \sqrt[3]{-3}-\sqrt[3]{2} x\right)}{\sqrt{3 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)}}\right)}{5832 \sqrt[6]{2} \sqrt[3]{3} \left(1+\sqrt[3]{-1}\right)^5 \sqrt{4-3 (-3)^{2/3} \sqrt[3]{2}}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[6]{2} \left(\sqrt[3]{2} x+3 \sqrt[3]{3}\right)}{\sqrt{3 \left(-4+3 \sqrt[3]{2} 3^{2/3}\right)}}\right)}{52488 \sqrt[6]{2} 3^{5/6} \sqrt{-4+3 \sqrt[3]{2} 3^{2/3}}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[6]{2} \left(\sqrt[3]{2} x+3 \sqrt[3]{3}\right)}{\sqrt{3 \left(-4+3 \sqrt[3]{2} 3^{2/3}\right)}}\right)}{26244 \sqrt[6]{2} 3^{5/6} \left(-4+3 \sqrt[3]{2} 3^{2/3}\right)^{3/2}}-\frac{\log \left(x^2-3 \sqrt[3]{-3} 2^{2/3} x+6\right)}{34992 \sqrt[3]{2} 3^{2/3} \left(1+\sqrt[3]{-1}\right)^4}+\frac{i \log \left(x^2+3 (-2)^{2/3} \sqrt[3]{3} x+6\right)}{34992 \sqrt[3]{2} \sqrt[6]{3} \left(1+\sqrt[3]{-1}\right)^5}-\frac{\log \left(x^2+3\ 2^{2/3} \sqrt[3]{3} x+6\right)}{314928 \sqrt[3]{2} 3^{2/3}}-\frac{\sqrt[3]{-\frac{1}{3}} \left(2 x+3 (-2)^{2/3} \sqrt[3]{3}\right)}{26244\ 2^{2/3} \left(8+9 i \sqrt[3]{2} \sqrt[6]{3}+3 \sqrt[3]{2} 3^{2/3}\right) \left(x^2+3 (-2)^{2/3} \sqrt[3]{3} x+6\right)}-\frac{\sqrt[3]{2} x+3 \sqrt[3]{3}}{52488 \left(9 \sqrt[3]{2}-4 \sqrt[3]{3}\right) \left(x^2+3\ 2^{2/3} \sqrt[3]{3} x+6\right)}","\frac{\sqrt[3]{-\frac{1}{3}} \left(3 \sqrt[3]{-3} 2^{2/3}-2 x\right)}{5832\ 2^{2/3} \left(1+\sqrt[3]{-1}\right)^4 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right) \left(x^2-3 \sqrt[3]{-3} 2^{2/3} x+6\right)}+\frac{\sqrt[3]{-1} \tan ^{-1}\left(\frac{3 \sqrt[3]{-3} 2^{2/3}-2 x}{\sqrt{6 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)}}\right)}{729\ 2^{2/3} 3^{5/6} \left(1+\sqrt[3]{-1}\right)^4 \left(8-9 i \sqrt[3]{2} \sqrt[6]{3}+3 \sqrt[3]{2} 3^{2/3}\right)^{3/2}}-\frac{\left(i+\sqrt{3}\right) \tan ^{-1}\left(\frac{2 x+3 (-2)^{2/3} \sqrt[3]{3}}{\sqrt{6 \left(4+3 \sqrt[3]{-2} 3^{2/3}\right)}}\right)}{11664 \sqrt[6]{2} \sqrt[3]{3} \left(1+\sqrt[3]{-1}\right)^5 \sqrt{4+3 \sqrt[3]{-2} 3^{2/3}}}-\frac{\sqrt[3]{-1} \tan ^{-1}\left(\frac{2 x+3 (-2)^{2/3} \sqrt[3]{3}}{\sqrt{6 \left(4+3 \sqrt[3]{-2} 3^{2/3}\right)}}\right)}{2916 \sqrt[6]{2} 3^{5/6} \left(1-\sqrt[3]{-1}\right)^2 \left(1+\sqrt[3]{-1}\right)^4 \left(4+3 \sqrt[3]{-2} 3^{2/3}\right)^{3/2}}-\frac{i \tan ^{-1}\left(\frac{\sqrt[6]{2} \left(3 \sqrt[3]{-3}-\sqrt[3]{2} x\right)}{\sqrt{3 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)}}\right)}{5832 \sqrt[6]{2} \sqrt[3]{3} \left(1+\sqrt[3]{-1}\right)^5 \sqrt{4-3 (-3)^{2/3} \sqrt[3]{2}}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[6]{2} \left(\sqrt[3]{2} x+3 \sqrt[3]{3}\right)}{\sqrt{3 \left(-4+3 \sqrt[3]{2} 3^{2/3}\right)}}\right)}{52488 \sqrt[6]{2} 3^{5/6} \sqrt{-4+3 \sqrt[3]{2} 3^{2/3}}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[6]{2} \left(\sqrt[3]{2} x+3 \sqrt[3]{3}\right)}{\sqrt{3 \left(-4+3 \sqrt[3]{2} 3^{2/3}\right)}}\right)}{26244 \sqrt[6]{2} 3^{5/6} \left(-4+3 \sqrt[3]{2} 3^{2/3}\right)^{3/2}}-\frac{\log \left(x^2-3 \sqrt[3]{-3} 2^{2/3} x+6\right)}{34992 \sqrt[3]{2} 3^{2/3} \left(1+\sqrt[3]{-1}\right)^4}+\frac{i \log \left(x^2+3 (-2)^{2/3} \sqrt[3]{3} x+6\right)}{34992 \sqrt[3]{2} \sqrt[6]{3} \left(1+\sqrt[3]{-1}\right)^5}-\frac{\log \left(x^2+3\ 2^{2/3} \sqrt[3]{3} x+6\right)}{314928 \sqrt[3]{2} 3^{2/3}}-\frac{\sqrt[3]{-\frac{1}{3}} \left(2 x+3 (-2)^{2/3} \sqrt[3]{3}\right)}{26244\ 2^{2/3} \left(8+9 i \sqrt[3]{2} \sqrt[6]{3}+3 \sqrt[3]{2} 3^{2/3}\right) \left(x^2+3 (-2)^{2/3} \sqrt[3]{3} x+6\right)}-\frac{\sqrt[3]{2} x+3 \sqrt[3]{3}}{52488 \left(9 \sqrt[3]{2}-4 \sqrt[3]{3}\right) \left(x^2+3\ 2^{2/3} \sqrt[3]{3} x+6\right)}",1,"((-1/3)^(1/3)*(3*(-3)^(1/3)*2^(2/3) - 2*x))/(5832*2^(2/3)*(1 + (-1)^(1/3))^4*(4 - 3*(-3)^(2/3)*2^(1/3))*(6 - 3*(-3)^(1/3)*2^(2/3)*x + x^2)) - ((-1/3)^(1/3)*(3*(-2)^(2/3)*3^(1/3) + 2*x))/(26244*2^(2/3)*(8 + (9*I)*2^(1/3)*3^(1/6) + 3*2^(1/3)*3^(2/3))*(6 + 3*(-2)^(2/3)*3^(1/3)*x + x^2)) - (3*3^(1/3) + 2^(1/3)*x)/(52488*(9*2^(1/3) - 4*3^(1/3))*(6 + 3*2^(2/3)*3^(1/3)*x + x^2)) + ((-1)^(1/3)*ArcTan[(3*(-3)^(1/3)*2^(2/3) - 2*x)/Sqrt[6*(4 - 3*(-3)^(2/3)*2^(1/3))]])/(729*2^(2/3)*3^(5/6)*(1 + (-1)^(1/3))^4*(8 - (9*I)*2^(1/3)*3^(1/6) + 3*2^(1/3)*3^(2/3))^(3/2)) - ((-1)^(1/3)*ArcTan[(3*(-2)^(2/3)*3^(1/3) + 2*x)/Sqrt[6*(4 + 3*(-2)^(1/3)*3^(2/3))]])/(2916*2^(1/6)*3^(5/6)*(1 - (-1)^(1/3))^2*(1 + (-1)^(1/3))^4*(4 + 3*(-2)^(1/3)*3^(2/3))^(3/2)) - ((I + Sqrt[3])*ArcTan[(3*(-2)^(2/3)*3^(1/3) + 2*x)/Sqrt[6*(4 + 3*(-2)^(1/3)*3^(2/3))]])/(11664*2^(1/6)*3^(1/3)*(1 + (-1)^(1/3))^5*Sqrt[4 + 3*(-2)^(1/3)*3^(2/3)]) - ((I/5832)*ArcTan[(2^(1/6)*(3*(-3)^(1/3) - 2^(1/3)*x))/Sqrt[3*(4 - 3*(-3)^(2/3)*2^(1/3))]])/(2^(1/6)*3^(1/3)*(1 + (-1)^(1/3))^5*Sqrt[4 - 3*(-3)^(2/3)*2^(1/3)]) + ArcTanh[(2^(1/6)*(3*3^(1/3) + 2^(1/3)*x))/Sqrt[3*(-4 + 3*2^(1/3)*3^(2/3))]]/(26244*2^(1/6)*3^(5/6)*(-4 + 3*2^(1/3)*3^(2/3))^(3/2)) + ArcTanh[(2^(1/6)*(3*3^(1/3) + 2^(1/3)*x))/Sqrt[3*(-4 + 3*2^(1/3)*3^(2/3))]]/(52488*2^(1/6)*3^(5/6)*Sqrt[-4 + 3*2^(1/3)*3^(2/3)]) - Log[6 - 3*(-3)^(1/3)*2^(2/3)*x + x^2]/(34992*2^(1/3)*3^(2/3)*(1 + (-1)^(1/3))^4) + ((I/34992)*Log[6 + 3*(-2)^(2/3)*3^(1/3)*x + x^2])/(2^(1/3)*3^(1/6)*(1 + (-1)^(1/3))^5) - Log[6 + 3*2^(2/3)*3^(1/3)*x + x^2]/(314928*2^(1/3)*3^(2/3))","A",23,7,26,0.2692,1,"{2097, 614, 618, 204, 634, 628, 206}"
156,1,873,0,1.9155069,"\int \frac{x^3}{\left(216+108 x^2+324 x^3+18 x^4+x^6\right)^2} \, dx","Int[x^3/(216 + 108*x^2 + 324*x^3 + 18*x^4 + x^6)^2,x]","\frac{\sqrt[3]{-6} \left(2 \sqrt[3]{-3}+9 \sqrt[3]{2}\right)-3 x}{157464 \left(8-9 i \sqrt[3]{2} \sqrt[6]{3}+3 \sqrt[3]{2} 3^{2/3}\right) \left(x^2-3 \sqrt[3]{-3} 2^{2/3} x+6\right)}-\frac{\left(9 i-\sqrt[3]{3} \left(2 i 2^{2/3}+9 \sqrt[6]{3}+2\ 2^{2/3} \sqrt{3}\right)\right) \tan ^{-1}\left(\frac{3 \sqrt[3]{-3} 2^{2/3}-2 x}{\sqrt{6 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)}}\right)}{209952 \left(1+\sqrt[3]{-1}\right)^5 \sqrt{2 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)}}+\frac{\tan ^{-1}\left(\frac{3 \sqrt[3]{-3} 2^{2/3}-2 x}{\sqrt{6 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)}}\right)}{26244 \sqrt{3} \left(8-9 i \sqrt[3]{2} \sqrt[6]{3}+3 \sqrt[3]{2} 3^{2/3}\right)^{3/2}}+\frac{\left(9 i+\sqrt[3]{3} \left(4 i 2^{2/3}-9 \sqrt[6]{3}\right)\right) \tan ^{-1}\left(\frac{2 x+3 (-2)^{2/3} \sqrt[3]{3}}{\sqrt{6 \left(4+3 \sqrt[3]{-2} 3^{2/3}\right)}}\right)}{209952 \left(1+\sqrt[3]{-1}\right)^5 \sqrt{2 \left(4+3 \sqrt[3]{-2} 3^{2/3}\right)}}-\frac{\tan ^{-1}\left(\frac{2 x+3 (-2)^{2/3} \sqrt[3]{3}}{\sqrt{6 \left(4+3 \sqrt[3]{-2} 3^{2/3}\right)}}\right)}{26244 \sqrt{3} \left(8+9 i \sqrt[3]{2} \sqrt[6]{3}+3 \sqrt[3]{2} 3^{2/3}\right)^{3/2}}+\frac{\left(2\ 2^{2/3}-3\ 3^{2/3}\right) \tanh ^{-1}\left(\frac{\sqrt[6]{2} \left(\sqrt[3]{2} x+3 \sqrt[3]{3}\right)}{\sqrt{3 \left(-4+3 \sqrt[3]{2} 3^{2/3}\right)}}\right)}{944784 \sqrt[6]{3} \sqrt{2 \left(-4+3 \sqrt[3]{2} 3^{2/3}\right)}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[6]{2} \left(\sqrt[3]{2} x+3 \sqrt[3]{3}\right)}{\sqrt{3 \left(-4+3 \sqrt[3]{2} 3^{2/3}\right)}}\right)}{52488 \sqrt{6} \left(-4+3 \sqrt[3]{2} 3^{2/3}\right)^{3/2}}-\frac{i \log \left(x^2-3 \sqrt[3]{-3} 2^{2/3} x+6\right)}{23328\ 2^{2/3} 3^{5/6} \left(1+\sqrt[3]{-1}\right)^5}+\frac{\left(i+\sqrt{3}\right) \log \left(x^2+3 (-2)^{2/3} \sqrt[3]{3} x+6\right)}{46656\ 2^{2/3} 3^{5/6} \left(1+\sqrt[3]{-1}\right)^5}+\frac{\log \left(x^2+3\ 2^{2/3} \sqrt[3]{3} x+6\right)}{629856\ 2^{2/3} \sqrt[3]{3}}-\frac{3 x+\sqrt[3]{-6} \left(9 \sqrt[3]{-2}+2 \sqrt[3]{3}\right)}{157464 \left(8+9 i \sqrt[3]{2} \sqrt[6]{3}+3 \sqrt[3]{2} 3^{2/3}\right) \left(x^2+3 (-2)^{2/3} \sqrt[3]{3} x+6\right)}-\frac{-\sqrt[3]{3} x-3\ 6^{2/3}+2 \sqrt[3]{2}}{104976 \left(9 \sqrt[3]{2}-4 \sqrt[3]{3}\right) \left(x^2+3\ 2^{2/3} \sqrt[3]{3} x+6\right)}","\frac{\sqrt[3]{-6} \left(2 \sqrt[3]{-3}+9 \sqrt[3]{2}\right)-3 x}{157464 \left(8-9 i \sqrt[3]{2} \sqrt[6]{3}+3 \sqrt[3]{2} 3^{2/3}\right) \left(x^2-3 \sqrt[3]{-3} 2^{2/3} x+6\right)}-\frac{\left(9 i-\sqrt[3]{3} \left(2 i 2^{2/3}+9 \sqrt[6]{3}+2\ 2^{2/3} \sqrt{3}\right)\right) \tan ^{-1}\left(\frac{3 \sqrt[3]{-3} 2^{2/3}-2 x}{\sqrt{6 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)}}\right)}{209952 \left(1+\sqrt[3]{-1}\right)^5 \sqrt{2 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)}}+\frac{\tan ^{-1}\left(\frac{3 \sqrt[3]{-3} 2^{2/3}-2 x}{\sqrt{6 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)}}\right)}{26244 \sqrt{3} \left(8-9 i \sqrt[3]{2} \sqrt[6]{3}+3 \sqrt[3]{2} 3^{2/3}\right)^{3/2}}+\frac{\left(9 i+\sqrt[3]{3} \left(4 i 2^{2/3}-9 \sqrt[6]{3}\right)\right) \tan ^{-1}\left(\frac{2 x+3 (-2)^{2/3} \sqrt[3]{3}}{\sqrt{6 \left(4+3 \sqrt[3]{-2} 3^{2/3}\right)}}\right)}{209952 \left(1+\sqrt[3]{-1}\right)^5 \sqrt{2 \left(4+3 \sqrt[3]{-2} 3^{2/3}\right)}}-\frac{\tan ^{-1}\left(\frac{2 x+3 (-2)^{2/3} \sqrt[3]{3}}{\sqrt{6 \left(4+3 \sqrt[3]{-2} 3^{2/3}\right)}}\right)}{26244 \sqrt{3} \left(8+9 i \sqrt[3]{2} \sqrt[6]{3}+3 \sqrt[3]{2} 3^{2/3}\right)^{3/2}}+\frac{\left(2\ 2^{2/3}-3\ 3^{2/3}\right) \tanh ^{-1}\left(\frac{\sqrt[6]{2} \left(\sqrt[3]{2} x+3 \sqrt[3]{3}\right)}{\sqrt{3 \left(-4+3 \sqrt[3]{2} 3^{2/3}\right)}}\right)}{944784 \sqrt[6]{3} \sqrt{2 \left(-4+3 \sqrt[3]{2} 3^{2/3}\right)}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[6]{2} \left(\sqrt[3]{2} x+3 \sqrt[3]{3}\right)}{\sqrt{3 \left(-4+3 \sqrt[3]{2} 3^{2/3}\right)}}\right)}{52488 \sqrt{6} \left(-4+3 \sqrt[3]{2} 3^{2/3}\right)^{3/2}}-\frac{i \log \left(x^2-3 \sqrt[3]{-3} 2^{2/3} x+6\right)}{23328\ 2^{2/3} 3^{5/6} \left(1+\sqrt[3]{-1}\right)^5}+\frac{\left(i+\sqrt{3}\right) \log \left(x^2+3 (-2)^{2/3} \sqrt[3]{3} x+6\right)}{46656\ 2^{2/3} 3^{5/6} \left(1+\sqrt[3]{-1}\right)^5}+\frac{\log \left(x^2+3\ 2^{2/3} \sqrt[3]{3} x+6\right)}{629856\ 2^{2/3} \sqrt[3]{3}}-\frac{3 x+\sqrt[3]{-6} \left(9 \sqrt[3]{-2}+2 \sqrt[3]{3}\right)}{157464 \left(8+9 i \sqrt[3]{2} \sqrt[6]{3}+3 \sqrt[3]{2} 3^{2/3}\right) \left(x^2+3 (-2)^{2/3} \sqrt[3]{3} x+6\right)}-\frac{-\sqrt[3]{3} x-3\ 6^{2/3}+2 \sqrt[3]{2}}{104976 \left(9 \sqrt[3]{2}-4 \sqrt[3]{3}\right) \left(x^2+3\ 2^{2/3} \sqrt[3]{3} x+6\right)}",1,"((-6)^(1/3)*(2*(-3)^(1/3) + 9*2^(1/3)) - 3*x)/(157464*(8 - (9*I)*2^(1/3)*3^(1/6) + 3*2^(1/3)*3^(2/3))*(6 - 3*(-3)^(1/3)*2^(2/3)*x + x^2)) - ((-6)^(1/3)*(9*(-2)^(1/3) + 2*3^(1/3)) + 3*x)/(157464*(8 + (9*I)*2^(1/3)*3^(1/6) + 3*2^(1/3)*3^(2/3))*(6 + 3*(-2)^(2/3)*3^(1/3)*x + x^2)) - (2*2^(1/3) - 3*6^(2/3) - 3^(1/3)*x)/(104976*(9*2^(1/3) - 4*3^(1/3))*(6 + 3*2^(2/3)*3^(1/3)*x + x^2)) + ArcTan[(3*(-3)^(1/3)*2^(2/3) - 2*x)/Sqrt[6*(4 - 3*(-3)^(2/3)*2^(1/3))]]/(26244*Sqrt[3]*(8 - (9*I)*2^(1/3)*3^(1/6) + 3*2^(1/3)*3^(2/3))^(3/2)) - ((9*I - 3^(1/3)*((2*I)*2^(2/3) + 9*3^(1/6) + 2*2^(2/3)*Sqrt[3]))*ArcTan[(3*(-3)^(1/3)*2^(2/3) - 2*x)/Sqrt[6*(4 - 3*(-3)^(2/3)*2^(1/3))]])/(209952*(1 + (-1)^(1/3))^5*Sqrt[2*(4 - 3*(-3)^(2/3)*2^(1/3))]) - ArcTan[(3*(-2)^(2/3)*3^(1/3) + 2*x)/Sqrt[6*(4 + 3*(-2)^(1/3)*3^(2/3))]]/(26244*Sqrt[3]*(8 + (9*I)*2^(1/3)*3^(1/6) + 3*2^(1/3)*3^(2/3))^(3/2)) + ((9*I + 3^(1/3)*((4*I)*2^(2/3) - 9*3^(1/6)))*ArcTan[(3*(-2)^(2/3)*3^(1/3) + 2*x)/Sqrt[6*(4 + 3*(-2)^(1/3)*3^(2/3))]])/(209952*(1 + (-1)^(1/3))^5*Sqrt[2*(4 + 3*(-2)^(1/3)*3^(2/3))]) - ArcTanh[(2^(1/6)*(3*3^(1/3) + 2^(1/3)*x))/Sqrt[3*(-4 + 3*2^(1/3)*3^(2/3))]]/(52488*Sqrt[6]*(-4 + 3*2^(1/3)*3^(2/3))^(3/2)) + ((2*2^(2/3) - 3*3^(2/3))*ArcTanh[(2^(1/6)*(3*3^(1/3) + 2^(1/3)*x))/Sqrt[3*(-4 + 3*2^(1/3)*3^(2/3))]])/(944784*3^(1/6)*Sqrt[2*(-4 + 3*2^(1/3)*3^(2/3))]) - ((I/23328)*Log[6 - 3*(-3)^(1/3)*2^(2/3)*x + x^2])/(2^(2/3)*3^(5/6)*(1 + (-1)^(1/3))^5) + ((I + Sqrt[3])*Log[6 + 3*(-2)^(2/3)*3^(1/3)*x + x^2])/(46656*2^(2/3)*3^(5/6)*(1 + (-1)^(1/3))^5) + Log[6 + 3*2^(2/3)*3^(1/3)*x + x^2]/(629856*2^(2/3)*3^(1/3))","A",23,7,26,0.2692,1,"{2097, 638, 618, 204, 634, 628, 206}"
157,1,986,0,1.9269772,"\int \frac{x^2}{\left(216+108 x^2+324 x^3+18 x^4+x^6\right)^2} \, dx","Int[x^2/(216 + 108*x^2 + 324*x^3 + 18*x^4 + x^6)^2,x]","-\frac{27 \left((-2)^{2/3}+2 \sqrt[3]{-1} 3^{2/3}\right)-\sqrt[3]{6} \left(9+\sqrt[3]{-3} 2^{2/3}\right) x}{104976\ 2^{2/3} \left(1+\sqrt[3]{-1}\right)^4 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right) \left(x^2-3 \sqrt[3]{-3} 2^{2/3} x+6\right)}-\frac{\left(1+i \sqrt{3}+3 \sqrt[3]{2} 3^{2/3}\right) \tan ^{-1}\left(\frac{3 \sqrt[3]{-3} 2^{2/3}-2 x}{\sqrt{6 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)}}\right)}{8748\ 2^{2/3} 3^{5/6} \left(1+\sqrt[3]{-1}\right)^4 \left(8-9 i \sqrt[3]{2} \sqrt[6]{3}+3 \sqrt[3]{2} 3^{2/3}\right)^{3/2}}+\frac{\left(i+\sqrt{3}\right) \tan ^{-1}\left(\frac{2 x+3 (-2)^{2/3} \sqrt[3]{3}}{\sqrt{6 \left(4+3 \sqrt[3]{-2} 3^{2/3}\right)}}\right)}{34992 \sqrt[6]{2} \sqrt[3]{3} \left(1+\sqrt[3]{-1}\right)^5 \sqrt{4+3 \sqrt[3]{-2} 3^{2/3}}}+\frac{\left(3 (-3)^{2/3}+\sqrt[3]{-1} 2^{2/3}\right) \tan ^{-1}\left(\frac{2 x+3 (-2)^{2/3} \sqrt[3]{3}}{\sqrt{6 \left(4+3 \sqrt[3]{-2} 3^{2/3}\right)}}\right)}{17496\ 6^{5/6} \left(1-\sqrt[3]{-1}\right)^2 \left(1+\sqrt[3]{-1}\right)^4 \left(4+3 \sqrt[3]{-2} 3^{2/3}\right)^{3/2}}+\frac{i \tan ^{-1}\left(\frac{\sqrt[6]{2} \left(3 \sqrt[3]{-3}-\sqrt[3]{2} x\right)}{\sqrt{3 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)}}\right)}{17496 \sqrt[6]{2} \sqrt[3]{3} \left(1+\sqrt[3]{-1}\right)^5 \sqrt{4-3 (-3)^{2/3} \sqrt[3]{2}}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[6]{2} \left(\sqrt[3]{2} x+3 \sqrt[3]{3}\right)}{\sqrt{3 \left(-4+3 \sqrt[3]{2} 3^{2/3}\right)}}\right)}{157464 \sqrt[6]{2} 3^{5/6} \sqrt{-4+3 \sqrt[3]{2} 3^{2/3}}}-\frac{\left(2^{2/3}-3\ 3^{2/3}\right) \tanh ^{-1}\left(\frac{\sqrt[6]{2} \left(\sqrt[3]{2} x+3 \sqrt[3]{3}\right)}{\sqrt{3 \left(-4+3 \sqrt[3]{2} 3^{2/3}\right)}}\right)}{17496\ 6^{5/6} \left(1-\sqrt[3]{-1}\right)^2 \left(1+\sqrt[3]{-1}\right)^4 \left(-4+3 \sqrt[3]{2} 3^{2/3}\right)^{3/2}}+\frac{\left(i+\sqrt{3}\right) \log \left(x^2-3 \sqrt[3]{-3} 2^{2/3} x+6\right)}{419904 \sqrt[3]{2} \sqrt[6]{3} \left(1+\sqrt[3]{-1}\right)^5}-\frac{i \log \left(x^2+3 (-2)^{2/3} \sqrt[3]{3} x+6\right)}{209952 \sqrt[3]{2} \sqrt[6]{3} \left(1+\sqrt[3]{-1}\right)^5}+\frac{\log \left(x^2+3\ 2^{2/3} \sqrt[3]{3} x+6\right)}{1889568 \sqrt[3]{2} 3^{2/3}}-\frac{27\ 2^{2/3} \left(1+\sqrt[3]{-2} 3^{2/3}\right)-\sqrt[3]{-1} 3^{2/3} \left(2+3 \sqrt[3]{-2} 3^{2/3}\right) x}{472392\ 2^{2/3} \left(8+9 i \sqrt[3]{2} \sqrt[6]{3}+3 \sqrt[3]{2} 3^{2/3}\right) \left(x^2+3 (-2)^{2/3} \sqrt[3]{3} x+6\right)}+\frac{9 \left(6-2^{2/3} \sqrt[3]{3}\right)-\left(2-3 \sqrt[3]{2} 3^{2/3}\right) x}{314928\ 2^{2/3} \sqrt[3]{3} \left(4-3 \sqrt[3]{2} 3^{2/3}\right) \left(x^2+3\ 2^{2/3} \sqrt[3]{3} x+6\right)}","-\frac{27 \left((-2)^{2/3}+2 \sqrt[3]{-1} 3^{2/3}\right)-\sqrt[3]{6} \left(9+\sqrt[3]{-3} 2^{2/3}\right) x}{104976\ 2^{2/3} \left(1+\sqrt[3]{-1}\right)^4 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right) \left(x^2-3 \sqrt[3]{-3} 2^{2/3} x+6\right)}-\frac{\left(1+i \sqrt{3}+3 \sqrt[3]{2} 3^{2/3}\right) \tan ^{-1}\left(\frac{3 \sqrt[3]{-3} 2^{2/3}-2 x}{\sqrt{6 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)}}\right)}{8748\ 2^{2/3} 3^{5/6} \left(1+\sqrt[3]{-1}\right)^4 \left(8-9 i \sqrt[3]{2} \sqrt[6]{3}+3 \sqrt[3]{2} 3^{2/3}\right)^{3/2}}+\frac{\left(i+\sqrt{3}\right) \tan ^{-1}\left(\frac{2 x+3 (-2)^{2/3} \sqrt[3]{3}}{\sqrt{6 \left(4+3 \sqrt[3]{-2} 3^{2/3}\right)}}\right)}{34992 \sqrt[6]{2} \sqrt[3]{3} \left(1+\sqrt[3]{-1}\right)^5 \sqrt{4+3 \sqrt[3]{-2} 3^{2/3}}}+\frac{\left(3 (-3)^{2/3}+\sqrt[3]{-1} 2^{2/3}\right) \tan ^{-1}\left(\frac{2 x+3 (-2)^{2/3} \sqrt[3]{3}}{\sqrt{6 \left(4+3 \sqrt[3]{-2} 3^{2/3}\right)}}\right)}{17496\ 6^{5/6} \left(1-\sqrt[3]{-1}\right)^2 \left(1+\sqrt[3]{-1}\right)^4 \left(4+3 \sqrt[3]{-2} 3^{2/3}\right)^{3/2}}+\frac{i \tan ^{-1}\left(\frac{\sqrt[6]{2} \left(3 \sqrt[3]{-3}-\sqrt[3]{2} x\right)}{\sqrt{3 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)}}\right)}{17496 \sqrt[6]{2} \sqrt[3]{3} \left(1+\sqrt[3]{-1}\right)^5 \sqrt{4-3 (-3)^{2/3} \sqrt[3]{2}}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[6]{2} \left(\sqrt[3]{2} x+3 \sqrt[3]{3}\right)}{\sqrt{3 \left(-4+3 \sqrt[3]{2} 3^{2/3}\right)}}\right)}{157464 \sqrt[6]{2} 3^{5/6} \sqrt{-4+3 \sqrt[3]{2} 3^{2/3}}}-\frac{\left(2^{2/3}-3\ 3^{2/3}\right) \tanh ^{-1}\left(\frac{\sqrt[6]{2} \left(\sqrt[3]{2} x+3 \sqrt[3]{3}\right)}{\sqrt{3 \left(-4+3 \sqrt[3]{2} 3^{2/3}\right)}}\right)}{17496\ 6^{5/6} \left(1-\sqrt[3]{-1}\right)^2 \left(1+\sqrt[3]{-1}\right)^4 \left(-4+3 \sqrt[3]{2} 3^{2/3}\right)^{3/2}}+\frac{\left(i+\sqrt{3}\right) \log \left(x^2-3 \sqrt[3]{-3} 2^{2/3} x+6\right)}{419904 \sqrt[3]{2} \sqrt[6]{3} \left(1+\sqrt[3]{-1}\right)^5}-\frac{i \log \left(x^2+3 (-2)^{2/3} \sqrt[3]{3} x+6\right)}{209952 \sqrt[3]{2} \sqrt[6]{3} \left(1+\sqrt[3]{-1}\right)^5}+\frac{\log \left(x^2+3\ 2^{2/3} \sqrt[3]{3} x+6\right)}{1889568 \sqrt[3]{2} 3^{2/3}}-\frac{27\ 2^{2/3} \left(1+\sqrt[3]{-2} 3^{2/3}\right)-\sqrt[3]{-1} 3^{2/3} \left(2+3 \sqrt[3]{-2} 3^{2/3}\right) x}{472392\ 2^{2/3} \left(8+9 i \sqrt[3]{2} \sqrt[6]{3}+3 \sqrt[3]{2} 3^{2/3}\right) \left(x^2+3 (-2)^{2/3} \sqrt[3]{3} x+6\right)}+\frac{9 \left(6-2^{2/3} \sqrt[3]{3}\right)-\left(2-3 \sqrt[3]{2} 3^{2/3}\right) x}{314928\ 2^{2/3} \sqrt[3]{3} \left(4-3 \sqrt[3]{2} 3^{2/3}\right) \left(x^2+3\ 2^{2/3} \sqrt[3]{3} x+6\right)}",1,"-(27*((-2)^(2/3) + 2*(-1)^(1/3)*3^(2/3)) - 6^(1/3)*(9 + (-3)^(1/3)*2^(2/3))*x)/(104976*2^(2/3)*(1 + (-1)^(1/3))^4*(4 - 3*(-3)^(2/3)*2^(1/3))*(6 - 3*(-3)^(1/3)*2^(2/3)*x + x^2)) - (27*2^(2/3)*(1 + (-2)^(1/3)*3^(2/3)) - (-1)^(1/3)*3^(2/3)*(2 + 3*(-2)^(1/3)*3^(2/3))*x)/(472392*2^(2/3)*(8 + (9*I)*2^(1/3)*3^(1/6) + 3*2^(1/3)*3^(2/3))*(6 + 3*(-2)^(2/3)*3^(1/3)*x + x^2)) + (9*(6 - 2^(2/3)*3^(1/3)) - (2 - 3*2^(1/3)*3^(2/3))*x)/(314928*2^(2/3)*3^(1/3)*(4 - 3*2^(1/3)*3^(2/3))*(6 + 3*2^(2/3)*3^(1/3)*x + x^2)) - ((1 + I*Sqrt[3] + 3*2^(1/3)*3^(2/3))*ArcTan[(3*(-3)^(1/3)*2^(2/3) - 2*x)/Sqrt[6*(4 - 3*(-3)^(2/3)*2^(1/3))]])/(8748*2^(2/3)*3^(5/6)*(1 + (-1)^(1/3))^4*(8 - (9*I)*2^(1/3)*3^(1/6) + 3*2^(1/3)*3^(2/3))^(3/2)) + ((3*(-3)^(2/3) + (-1)^(1/3)*2^(2/3))*ArcTan[(3*(-2)^(2/3)*3^(1/3) + 2*x)/Sqrt[6*(4 + 3*(-2)^(1/3)*3^(2/3))]])/(17496*6^(5/6)*(1 - (-1)^(1/3))^2*(1 + (-1)^(1/3))^4*(4 + 3*(-2)^(1/3)*3^(2/3))^(3/2)) + ((I + Sqrt[3])*ArcTan[(3*(-2)^(2/3)*3^(1/3) + 2*x)/Sqrt[6*(4 + 3*(-2)^(1/3)*3^(2/3))]])/(34992*2^(1/6)*3^(1/3)*(1 + (-1)^(1/3))^5*Sqrt[4 + 3*(-2)^(1/3)*3^(2/3)]) + ((I/17496)*ArcTan[(2^(1/6)*(3*(-3)^(1/3) - 2^(1/3)*x))/Sqrt[3*(4 - 3*(-3)^(2/3)*2^(1/3))]])/(2^(1/6)*3^(1/3)*(1 + (-1)^(1/3))^5*Sqrt[4 - 3*(-3)^(2/3)*2^(1/3)]) - ((2^(2/3) - 3*3^(2/3))*ArcTanh[(2^(1/6)*(3*3^(1/3) + 2^(1/3)*x))/Sqrt[3*(-4 + 3*2^(1/3)*3^(2/3))]])/(17496*6^(5/6)*(1 - (-1)^(1/3))^2*(1 + (-1)^(1/3))^4*(-4 + 3*2^(1/3)*3^(2/3))^(3/2)) - ArcTanh[(2^(1/6)*(3*3^(1/3) + 2^(1/3)*x))/Sqrt[3*(-4 + 3*2^(1/3)*3^(2/3))]]/(157464*2^(1/6)*3^(5/6)*Sqrt[-4 + 3*2^(1/3)*3^(2/3)]) + ((I + Sqrt[3])*Log[6 - 3*(-3)^(1/3)*2^(2/3)*x + x^2])/(419904*2^(1/3)*3^(1/6)*(1 + (-1)^(1/3))^5) - ((I/209952)*Log[6 + 3*(-2)^(2/3)*3^(1/3)*x + x^2])/(2^(1/3)*3^(1/6)*(1 + (-1)^(1/3))^5) + Log[6 + 3*2^(2/3)*3^(1/3)*x + x^2]/(1889568*2^(1/3)*3^(2/3))","A",23,7,26,0.2692,1,"{2097, 638, 618, 204, 634, 628, 206}"
158,1,25,0,0.0553536,"\int \frac{a^2 c+a^2 d x+2 a b c x^2+2 a b d x^3+b^2 c x^4+b^2 d x^5}{c+d x} \, dx","Int[(a^2*c + a^2*d*x + 2*a*b*c*x^2 + 2*a*b*d*x^3 + b^2*c*x^4 + b^2*d*x^5)/(c + d*x),x]","a^2 x+\frac{2}{3} a b x^3+\frac{b^2 x^5}{5}","a^2 x+\frac{2}{3} a b x^3+\frac{b^2 x^5}{5}",1,"a^2*x + (2*a*b*x^3)/3 + (b^2*x^5)/5","A",2,1,52,0.01923,1,"{1586}"
159,1,94,0,0.127105,"\int \frac{a^2 c+a^2 d x+2 a b c x^2+2 a b d x^3+b^2 c x^4+b^2 d x^5}{(c+d x)^2} \, dx","Int[(a^2*c + a^2*d*x + 2*a*b*c*x^2 + 2*a*b*d*x^3 + b^2*c*x^4 + b^2*d*x^5)/(c + d*x)^2,x]","\frac{b x^2 \left(2 a d^2+b c^2\right)}{2 d^3}-\frac{b c x \left(2 a d^2+b c^2\right)}{d^4}+\frac{\left(a d^2+b c^2\right)^2 \log (c+d x)}{d^5}-\frac{b^2 c x^3}{3 d^2}+\frac{b^2 x^4}{4 d}","\frac{b x^2 \left(2 a d^2+b c^2\right)}{2 d^3}-\frac{b c x \left(2 a d^2+b c^2\right)}{d^4}+\frac{\left(a d^2+b c^2\right)^2 \log (c+d x)}{d^5}-\frac{b^2 c x^3}{3 d^2}+\frac{b^2 x^4}{4 d}",1,"-((b*c*(b*c^2 + 2*a*d^2)*x)/d^4) + (b*(b*c^2 + 2*a*d^2)*x^2)/(2*d^3) - (b^2*c*x^3)/(3*d^2) + (b^2*x^4)/(4*d) + ((b*c^2 + a*d^2)^2*Log[c + d*x])/d^5","A",4,3,52,0.05769,1,"{1586, 28, 697}"
160,1,15,0,0.0181078,"\int (b+2 c x) \left(b x+c x^2\right)^{13} \, dx","Int[(b + 2*c*x)*(b*x + c*x^2)^13,x]","\frac{1}{14} \left(b x+c x^2\right)^{14}","\frac{1}{14} \left(b x+c x^2\right)^{14}",1,"(b*x + c*x^2)^14/14","A",1,1,18,0.05556,1,"{629}"
161,1,16,0,0.0548421,"\int x^{14} \left(b+2 c x^2\right) \left(b x+c x^3\right)^{13} \, dx","Int[x^14*(b + 2*c*x^2)*(b*x + c*x^3)^13,x]","\frac{1}{28} x^{28} \left(b+c x^2\right)^{14}","\frac{1}{28} x^{28} \left(b+c x^2\right)^{14}",1,"(x^28*(b + c*x^2)^14)/28","A",3,3,23,0.1304,1,"{1584, 446, 74}"
162,1,16,0,0.0497209,"\int x^{28} \left(b+2 c x^3\right) \left(b x+c x^4\right)^{13} \, dx","Int[x^28*(b + 2*c*x^3)*(b*x + c*x^4)^13,x]","\frac{1}{42} x^{42} \left(b+c x^3\right)^{14}","\frac{1}{42} x^{42} \left(b+c x^3\right)^{14}",1,"(x^42*(b + c*x^3)^14)/42","A",3,3,23,0.1304,1,"{1584, 446, 74}"
163,1,21,0,0.0313831,"\int x^{14 (-1+n)} \left(b+2 c x^n\right) \left(b x+c x^{1+n}\right)^{13} \, dx","Int[x^(14*(-1 + n))*(b + 2*c*x^n)*(b*x + c*x^(1 + n))^13,x]","\frac{x^{14 n} \left(b+c x^n\right)^{14}}{14 n}","\frac{x^{14 n} \left(b+c x^n\right)^{14}}{14 n}",1,"(x^(14*n)*(b + c*x^n)^14)/(14*n)","A",3,3,29,0.1034,1,"{1584, 446, 74}"
164,1,10,0,0.0039648,"\int \frac{b+2 c x}{b x+c x^2} \, dx","Int[(b + 2*c*x)/(b*x + c*x^2),x]","\log \left(b x+c x^2\right)","\log \left(b x+c x^2\right)",1,"Log[b*x + c*x^2]","A",1,1,18,0.05556,1,"{628}"
165,1,15,0,0.0264676,"\int \frac{b+2 c x^2}{b x+c x^3} \, dx","Int[(b + 2*c*x^2)/(b*x + c*x^3),x]","\frac{1}{2} \log \left(b+c x^2\right)+\log (x)","\frac{1}{2} \log \left(b+c x^2\right)+\log (x)",1,"Log[x] + Log[b + c*x^2]/2","A",4,3,20,0.1500,1,"{1593, 446, 72}"
166,1,15,0,0.0265704,"\int \frac{b+2 c x^3}{b x+c x^4} \, dx","Int[(b + 2*c*x^3)/(b*x + c*x^4),x]","\frac{1}{3} \log \left(b+c x^3\right)+\log (x)","\frac{1}{3} \log \left(b+c x^3\right)+\log (x)",1,"Log[x] + Log[b + c*x^3]/3","A",4,3,20,0.1500,1,"{1593, 446, 72}"
167,1,15,0,0.0253765,"\int \frac{b+2 c x^n}{b x+c x^{1+n}} \, dx","Int[(b + 2*c*x^n)/(b*x + c*x^(1 + n)),x]","\frac{\log \left(b+c x^n\right)}{n}+\log (x)","\frac{\log \left(b+c x^n\right)}{n}+\log (x)",1,"Log[x] + Log[b + c*x^n]/n","A",4,3,22,0.1364,1,"{1593, 446, 72}"
168,1,15,0,0.0039839,"\int \frac{b+2 c x}{\left(b x+c x^2\right)^8} \, dx","Int[(b + 2*c*x)/(b*x + c*x^2)^8,x]","-\frac{1}{7 \left(b x+c x^2\right)^7}","-\frac{1}{7 \left(b x+c x^2\right)^7}",1,"-1/(7*(b*x + c*x^2)^7)","A",1,1,18,0.05556,1,"{629}"
169,1,16,0,0.023114,"\int \frac{b+2 c x^2}{x^7 \left(b x+c x^3\right)^8} \, dx","Int[(b + 2*c*x^2)/(x^7*(b*x + c*x^3)^8),x]","-\frac{1}{14 x^{14} \left(b+c x^2\right)^7}","-\frac{1}{14 x^{14} \left(b+c x^2\right)^7}",1,"-1/(14*x^14*(b + c*x^2)^7)","A",3,3,23,0.1304,1,"{1584, 446, 74}"
170,1,16,0,0.0232854,"\int \frac{b+2 c x^3}{x^{14} \left(b x+c x^4\right)^8} \, dx","Int[(b + 2*c*x^3)/(x^14*(b*x + c*x^4)^8),x]","-\frac{1}{21 x^{21} \left(b+c x^3\right)^7}","-\frac{1}{21 x^{21} \left(b+c x^3\right)^7}",1,"-1/(21*x^21*(b + c*x^3)^7)","A",3,3,23,0.1304,1,"{1584, 446, 74}"
171,1,21,0,0.0323436,"\int \frac{x^{-7 (-1+n)} \left(b+2 c x^n\right)}{\left(b x+c x^{1+n}\right)^8} \, dx","Int[(b + 2*c*x^n)/(x^(7*(-1 + n))*(b*x + c*x^(1 + n))^8),x]","-\frac{x^{-7 n}}{7 n \left(b+c x^n\right)^7}","-\frac{x^{-7 n}}{7 n \left(b+c x^n\right)^7}",1,"-1/(7*n*x^(7*n)*(b + c*x^n)^7)","A",3,3,29,0.1034,1,"{1584, 446, 74}"
172,1,19,0,0.0054707,"\int (b+2 c x) \left(b x+c x^2\right)^p \, dx","Int[(b + 2*c*x)*(b*x + c*x^2)^p,x]","\frac{\left(b x+c x^2\right)^{p+1}}{p+1}","\frac{\left(b x+c x^2\right)^{p+1}}{p+1}",1,"(b*x + c*x^2)^(1 + p)/(1 + p)","A",1,1,18,0.05556,1,"{629}"
173,1,27,0,0.0230009,"\int x^{1+p} \left(b+2 c x^2\right) \left(b x+c x^3\right)^p \, dx","Int[x^(1 + p)*(b + 2*c*x^2)*(b*x + c*x^3)^p,x]","\frac{x^{p+1} \left(b x+c x^3\right)^{p+1}}{2 (p+1)}","\frac{x^{p+1} \left(b x+c x^3\right)^{p+1}}{2 (p+1)}",1,"(x^(1 + p)*(b*x + c*x^3)^(1 + p))/(2*(1 + p))","A",1,1,25,0.04000,1,"{1590}"
174,1,116,0,0.1018325,"\int \left(b x^{1+p} \left(b x+c x^3\right)^p+2 c x^{3+p} \left(b x+c x^3\right)^p\right) \, dx","Int[b*x^(1 + p)*(b*x + c*x^3)^p + 2*c*x^(3 + p)*(b*x + c*x^3)^p,x]","\frac{b x^{p+2} \left(b x+c x^3\right)^p \left(\frac{c x^2}{b}+1\right)^{-p} \, _2F_1\left(-p,p+1;p+2;-\frac{c x^2}{b}\right)}{2 (p+1)}+\frac{c x^{p+4} \left(b x+c x^3\right)^p \left(\frac{c x^2}{b}+1\right)^{-p} \, _2F_1\left(-p,p+2;p+3;-\frac{c x^2}{b}\right)}{p+2}","\frac{x^{p+1} \left(b x+c x^3\right)^{p+1}}{2 (p+1)}",1,"(b*x^(2 + p)*(b*x + c*x^3)^p*Hypergeometric2F1[-p, 1 + p, 2 + p, -((c*x^2)/b)])/(2*(1 + p)*(1 + (c*x^2)/b)^p) + (c*x^(4 + p)*(b*x + c*x^3)^p*Hypergeometric2F1[-p, 2 + p, 3 + p, -((c*x^2)/b)])/((2 + p)*(1 + (c*x^2)/b)^p)","C",7,3,38,0.07895,1,"{2032, 365, 364}"
175,1,29,0,0.0238577,"\int x^{2 (1+p)} \left(b+2 c x^3\right) \left(b x+c x^4\right)^p \, dx","Int[x^(2*(1 + p))*(b + 2*c*x^3)*(b*x + c*x^4)^p,x]","\frac{x^{2 (p+1)} \left(b x+c x^4\right)^{p+1}}{3 (p+1)}","\frac{x^{2 (p+1)} \left(b x+c x^4\right)^{p+1}}{3 (p+1)}",1,"(x^(2*(1 + p))*(b*x + c*x^4)^(1 + p))/(3*(1 + p))","A",1,1,27,0.03704,1,"{1590}"
176,1,36,0,0.085884,"\int x^{(-1+n) (1+p)} \left(b+2 c x^n\right) \left(b x+c x^{1+n}\right)^p \, dx","Int[x^((-1 + n)*(1 + p))*(b + 2*c*x^n)*(b*x + c*x^(1 + n))^p,x]","\frac{x^{-(1-n) (p+1)} \left(b x+c x^{n+1}\right)^{p+1}}{n (p+1)}","\frac{x^{-(1-n) (p+1)} \left(b x+c x^{n+1}\right)^{p+1}}{n (p+1)}",1,"(b*x + c*x^(1 + n))^(1 + p)/(n*(1 + p)*x^((1 - n)*(1 + p)))","A",1,1,31,0.03226,1,"{2036}"
177,1,32,0,0.0340129,"\int \frac{a^2 c+a^2 d x+2 a b c x^2+2 a b d x^3+b^2 c x^4+b^2 d x^5}{a+b x^2} \, dx","Int[(a^2*c + a^2*d*x + 2*a*b*c*x^2 + 2*a*b*d*x^3 + b^2*c*x^4 + b^2*d*x^5)/(a + b*x^2),x]","a c x+\frac{1}{2} a d x^2+\frac{1}{3} b c x^3+\frac{1}{4} b d x^4","a c x+\frac{1}{2} a d x^2+\frac{1}{3} b c x^3+\frac{1}{4} b d x^4",1,"a*c*x + (a*d*x^2)/2 + (b*c*x^3)/3 + (b*d*x^4)/4","A",2,1,54,0.01852,1,"{1586}"
178,1,12,0,0.0485936,"\int \frac{a^2 c+a^2 d x+2 a b c x^2+2 a b d x^3+b^2 c x^4+b^2 d x^5}{\left(a+b x^2\right)^2} \, dx","Int[(a^2*c + a^2*d*x + 2*a*b*c*x^2 + 2*a*b*d*x^3 + b^2*c*x^4 + b^2*d*x^5)/(a + b*x^2)^2,x]","c x+\frac{d x^2}{2}","c x+\frac{d x^2}{2}",1,"c*x + (d*x^2)/2","A",3,1,54,0.01852,1,"{1586}"
179,1,42,0,0.0573733,"\int \frac{a^2 c+a^2 d x+2 a b c x^2+2 a b d x^3+b^2 c x^4+b^2 d x^5}{\left(a+b x^2\right)^3} \, dx","Int[(a^2*c + a^2*d*x + 2*a*b*c*x^2 + 2*a*b*d*x^3 + b^2*c*x^4 + b^2*d*x^5)/(a + b*x^2)^3,x]","\frac{c \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b}}+\frac{d \log \left(a+b x^2\right)}{2 b}","\frac{c \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b}}+\frac{d \log \left(a+b x^2\right)}{2 b}",1,"(c*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(Sqrt[a]*Sqrt[b]) + (d*Log[a + b*x^2])/(2*b)","A",5,4,54,0.07407,1,"{1586, 635, 205, 260}"
180,1,25,0,0.0239676,"\int \left(b+2 c x+3 d x^2\right) \left(a+b x+c x^2+d x^3\right)^n \, dx","Int[(b + 2*c*x + 3*d*x^2)*(a + b*x + c*x^2 + d*x^3)^n,x]","\frac{\left(a+b x+c x^2+d x^3\right)^{n+1}}{n+1}","\frac{\left(a+b x+c x^2+d x^3\right)^{n+1}}{n+1}",1,"(a + b*x + c*x^2 + d*x^3)^(1 + n)/(1 + n)","A",1,1,30,0.03333,1,"{1588}"
181,1,24,0,0.0175243,"\int \left(b+2 c x+3 d x^2\right) \left(b x+c x^2+d x^3\right)^n \, dx","Int[(b + 2*c*x + 3*d*x^2)*(b*x + c*x^2 + d*x^3)^n,x]","\frac{\left(b x+c x^2+d x^3\right)^{n+1}}{n+1}","\frac{\left(b x+c x^2+d x^3\right)^{n+1}}{n+1}",1,"(b*x + c*x^2 + d*x^3)^(1 + n)/(1 + n)","A",1,1,29,0.03448,1,"{1588}"
182,1,25,0,0.0212676,"\int x^n \left(b+c x+d x^2\right)^n \left(b+2 c x+3 d x^2\right) \, dx","Int[x^n*(b + c*x + d*x^2)^n*(b + 2*c*x + 3*d*x^2),x]","\frac{x^{n+1} \left(b+c x+d x^2\right)^{n+1}}{n+1}","\frac{x^{n+1} \left(b+c x+d x^2\right)^{n+1}}{n+1}",1,"(x^(1 + n)*(b + c*x + d*x^2)^(1 + n))/(1 + n)","A",1,1,28,0.03571,1,"{1590}"
183,1,20,0,0.0099577,"\int \left(b+3 d x^2\right) \left(a+b x+d x^3\right)^n \, dx","Int[(b + 3*d*x^2)*(a + b*x + d*x^3)^n,x]","\frac{\left(a+b x+d x^3\right)^{n+1}}{n+1}","\frac{\left(a+b x+d x^3\right)^{n+1}}{n+1}",1,"(a + b*x + d*x^3)^(1 + n)/(1 + n)","A",1,1,21,0.04762,1,"{1588}"
184,1,19,0,0.0089349,"\int \left(b+3 d x^2\right) \left(b x+d x^3\right)^n \, dx","Int[(b + 3*d*x^2)*(b*x + d*x^3)^n,x]","\frac{\left(b x+d x^3\right)^{n+1}}{n+1}","\frac{\left(b x+d x^3\right)^{n+1}}{n+1}",1,"(b*x + d*x^3)^(1 + n)/(1 + n)","A",1,1,20,0.05000,1,"{1588}"
185,1,22,0,0.0080456,"\int x^n \left(b+d x^2\right)^n \left(b+3 d x^2\right) \, dx","Int[x^n*(b + d*x^2)^n*(b + 3*d*x^2),x]","\frac{x^{n+1} \left(b+d x^2\right)^{n+1}}{n+1}","\frac{x^{n+1} \left(b+d x^2\right)^{n+1}}{n+1}",1,"(x^(1 + n)*(b + d*x^2)^(1 + n))/(1 + n)","A",1,1,21,0.04762,1,"{449}"
186,1,22,0,0.0177172,"\int \left(2 c x+3 d x^2\right) \left(a+c x^2+d x^3\right)^n \, dx","Int[(2*c*x + 3*d*x^2)*(a + c*x^2 + d*x^3)^n,x]","\frac{\left(a+c x^2+d x^3\right)^{n+1}}{n+1}","\frac{\left(a+c x^2+d x^3\right)^{n+1}}{n+1}",1,"(a + c*x^2 + d*x^3)^(1 + n)/(1 + n)","A",1,1,26,0.03846,1,"{1588}"
187,1,21,0,0.0116747,"\int \left(2 c x+3 d x^2\right) \left(c x^2+d x^3\right)^n \, dx","Int[(2*c*x + 3*d*x^2)*(c*x^2 + d*x^3)^n,x]","\frac{\left(c x^2+d x^3\right)^{n+1}}{n+1}","\frac{\left(c x^2+d x^3\right)^{n+1}}{n+1}",1,"(c*x^2 + d*x^3)^(1 + n)/(1 + n)","A",1,1,25,0.04000,1,"{1588}"
188,1,24,0,0.0234698,"\int x^n \left(c x+d x^2\right)^n \left(2 c x+3 d x^2\right) \, dx","Int[x^n*(c*x + d*x^2)^n*(2*c*x + 3*d*x^2),x]","\frac{x^{n+1} \left(c x+d x^2\right)^{n+1}}{n+1}","\frac{x^{n+1} \left(c x+d x^2\right)^{n+1}}{n+1}",1,"(x^(1 + n)*(c*x + d*x^2)^(1 + n))/(1 + n)","A",2,2,26,0.07692,1,"{1584, 763}"
189,1,22,0,0.009202,"\int x^{2 n} (c+d x)^n \left(2 c x+3 d x^2\right) \, dx","Int[x^(2*n)*(c + d*x)^n*(2*c*x + 3*d*x^2),x]","\frac{x^{2 (n+1)} (c+d x)^{n+1}}{n+1}","\frac{x^{2 (n+1)} (c+d x)^{n+1}}{n+1}",1,"(x^(2*(1 + n))*(c + d*x)^(1 + n))/(1 + n)","A",1,1,24,0.04167,1,"{845}"
190,1,22,0,0.0133484,"\int x (2 c+3 d x) \left(a+c x^2+d x^3\right)^n \, dx","Int[x*(2*c + 3*d*x)*(a + c*x^2 + d*x^3)^n,x]","\frac{\left(a+c x^2+d x^3\right)^{n+1}}{n+1}","\frac{\left(a+c x^2+d x^3\right)^{n+1}}{n+1}",1,"(a + c*x^2 + d*x^3)^(1 + n)/(1 + n)","A",1,1,24,0.04167,1,"{1588}"
191,1,21,0,0.012103,"\int x (2 c+3 d x) \left(c x^2+d x^3\right)^n \, dx","Int[x*(2*c + 3*d*x)*(c*x^2 + d*x^3)^n,x]","\frac{\left(c x^2+d x^3\right)^{n+1}}{n+1}","\frac{\left(c x^2+d x^3\right)^{n+1}}{n+1}",1,"(c*x^2 + d*x^3)^(1 + n)/(1 + n)","A",1,1,23,0.04348,1,"{1588}"
192,1,21,0,0.1251667,"\int \left(b+2 c x+3 d x^2\right) \left(a+b x+c x^2+d x^3\right)^7 \, dx","Int[(b + 2*c*x + 3*d*x^2)*(a + b*x + c*x^2 + d*x^3)^7,x]","\frac{1}{8} \left(a+b x+c x^2+d x^3\right)^8","\frac{1}{8} \left(a+b x+c x^2+d x^3\right)^8",1,"(a + b*x + c*x^2 + d*x^3)^8/8","A",1,1,30,0.03333,1,"{1588}"
193,1,20,0,0.0521532,"\int \left(b+2 c x+3 d x^2\right) \left(b x+c x^2+d x^3\right)^7 \, dx","Int[(b + 2*c*x + 3*d*x^2)*(b*x + c*x^2 + d*x^3)^7,x]","\frac{1}{8} \left(b x+c x^2+d x^3\right)^8","\frac{1}{8} \left(b x+c x^2+d x^3\right)^8",1,"(b*x + c*x^2 + d*x^3)^8/8","A",1,1,29,0.03448,1,"{1588}"
194,1,19,0,0.0693817,"\int x^7 \left(b+c x+d x^2\right)^7 \left(b+2 c x+3 d x^2\right) \, dx","Int[x^7*(b + c*x + d*x^2)^7*(b + 2*c*x + 3*d*x^2),x]","\frac{1}{8} x^8 \left(b+c x+d x^2\right)^8","\frac{1}{8} x^8 \left(b+c x+d x^2\right)^8",1,"(x^8*(b + c*x + d*x^2)^8)/8","A",1,1,28,0.03571,1,"{1588}"
195,1,16,0,0.0243779,"\int \left(b+3 d x^2\right) \left(a+b x+d x^3\right)^7 \, dx","Int[(b + 3*d*x^2)*(a + b*x + d*x^3)^7,x]","\frac{1}{8} \left(a+b x+d x^3\right)^8","\frac{1}{8} \left(a+b x+d x^3\right)^8",1,"(a + b*x + d*x^3)^8/8","A",1,1,21,0.04762,1,"{1588}"
196,1,15,0,0.0127609,"\int \left(b+3 d x^2\right) \left(b x+d x^3\right)^7 \, dx","Int[(b + 3*d*x^2)*(b*x + d*x^3)^7,x]","\frac{1}{8} \left(b x+d x^3\right)^8","\frac{1}{8} \left(b x+d x^3\right)^8",1,"(b*x + d*x^3)^8/8","A",1,1,20,0.05000,1,"{1588}"
197,1,16,0,0.0280873,"\int x^7 \left(b+d x^2\right)^7 \left(b+3 d x^2\right) \, dx","Int[x^7*(b + d*x^2)^7*(b + 3*d*x^2),x]","\frac{1}{8} x^8 \left(b+d x^2\right)^8","\frac{1}{8} x^8 \left(b+d x^2\right)^8",1,"(x^8*(b + d*x^2)^8)/8","A",2,2,21,0.09524,1,"{446, 74}"
198,1,18,0,0.0441323,"\int \left(2 c x+3 d x^2\right) \left(a+c x^2+d x^3\right)^7 \, dx","Int[(2*c*x + 3*d*x^2)*(a + c*x^2 + d*x^3)^7,x]","\frac{1}{8} \left(a+c x^2+d x^3\right)^8","\frac{1}{8} \left(a+c x^2+d x^3\right)^8",1,"(a + c*x^2 + d*x^3)^8/8","A",1,1,26,0.03846,1,"{1588}"
199,1,17,0,0.0251481,"\int \left(2 c x+3 d x^2\right) \left(c x^2+d x^3\right)^7 \, dx","Int[(2*c*x + 3*d*x^2)*(c*x^2 + d*x^3)^7,x]","\frac{1}{8} \left(c x^2+d x^3\right)^8","\frac{1}{8} \left(c x^2+d x^3\right)^8",1,"(c*x^2 + d*x^3)^8/8","A",1,1,25,0.04000,1,"{1588}"
200,1,14,0,0.2271216,"\int x^7 \left(c x+d x^2\right)^7 \left(2 c x+3 d x^2\right) \, dx","Int[x^7*(c*x + d*x^2)^7*(2*c*x + 3*d*x^2),x]","\frac{1}{8} x^{16} (c+d x)^8","\frac{1}{8} x^{16} (c+d x)^8",1,"(x^16*(c + d*x)^8)/8","A",2,2,26,0.07692,1,"{1584, 845}"
201,1,14,0,0.0105136,"\int x^{14} (c+d x)^7 \left(2 c x+3 d x^2\right) \, dx","Int[x^14*(c + d*x)^7*(2*c*x + 3*d*x^2),x]","\frac{1}{8} x^{16} (c+d x)^8","\frac{1}{8} x^{16} (c+d x)^8",1,"(x^16*(c + d*x)^8)/8","A",1,1,22,0.04545,1,"{845}"
202,1,18,0,0.0596462,"\int x (2 c+3 d x) \left(a+c x^2+d x^3\right)^7 \, dx","Int[x*(2*c + 3*d*x)*(a + c*x^2 + d*x^3)^7,x]","\frac{1}{8} \left(a+c x^2+d x^3\right)^8","\frac{1}{8} \left(a+c x^2+d x^3\right)^8",1,"(a + c*x^2 + d*x^3)^8/8","A",1,1,24,0.04167,1,"{1588}"
203,1,14,0,0.0219512,"\int x (2 c+3 d x) \left(c x^2+d x^3\right)^7 \, dx","Int[x*(2*c + 3*d*x)*(c*x^2 + d*x^3)^7,x]","\frac{1}{8} x^{16} (c+d x)^8","\frac{1}{8} x^{16} (c+d x)^8",1,"(x^16*(c + d*x)^8)/8","A",2,2,23,0.08696,1,"{1584, 74}"
204,1,18,0,0.0190387,"\int x^8 (2 c+3 d x) \left(c x+d x^2\right)^7 \, dx","Int[x^8*(2*c + 3*d*x)*(c*x + d*x^2)^7,x]","\frac{1}{8} x^8 \left(c x+d x^2\right)^8","\frac{1}{8} x^8 \left(c x+d x^2\right)^8",1,"(x^8*(c*x + d*x^2)^8)/8","A",1,1,23,0.04348,1,"{763}"
205,1,14,0,0.0019092,"\int x^{15} (c+d x)^7 (2 c+3 d x) \, dx","Int[x^15*(c + d*x)^7*(2*c + 3*d*x),x]","\frac{1}{8} x^{16} (c+d x)^8","\frac{1}{8} x^{16} (c+d x)^8",1,"(x^16*(c + d*x)^8)/8","A",1,1,19,0.05263,1,"{74}"
206,1,28,0,0.0270042,"\int (a+b x) \left(1+\left(a x+\frac{b x^2}{2}\right)^4\right) \, dx","Int[(a + b*x)*(1 + (a*x + (b*x^2)/2)^4),x]","\frac{1}{160} x^5 (2 a+b x)^5+a x+\frac{b x^2}{2}","\frac{1}{160} x^5 (2 a+b x)^5+a x+\frac{b x^2}{2}",1,"a*x + (b*x^2)/2 + (x^5*(2*a + b*x)^5)/160","A",2,1,22,0.04545,1,"{1591}"
207,1,31,0,0.0311218,"\int (a+b x) \left(1+\left(c+a x+\frac{b x^2}{2}\right)^4\right) \, dx","Int[(a + b*x)*(1 + (c + a*x + (b*x^2)/2)^4),x]","\frac{1}{5} \left(a x+\frac{b x^2}{2}+c\right)^5+a x+\frac{b x^2}{2}","\frac{1}{5} \left(a x+\frac{b x^2}{2}+c\right)^5+a x+\frac{b x^2}{2}",1,"a*x + (b*x^2)/2 + (c + a*x + (b*x^2)/2)^5/5","A",2,1,23,0.04348,1,"{1591}"
208,1,34,0,0.0084399,"\int (a+b x) \left(1+\left(a x+\frac{b x^2}{2}\right)^n\right) \, dx","Int[(a + b*x)*(1 + (a*x + (b*x^2)/2)^n),x]","\frac{\left(a x+\frac{b x^2}{2}\right)^{n+1}}{n+1}+a x+\frac{b x^2}{2}","\frac{\left(a x+\frac{b x^2}{2}\right)^{n+1}}{n+1}+a x+\frac{b x^2}{2}",1,"a*x + (b*x^2)/2 + (a*x + (b*x^2)/2)^(1 + n)/(1 + n)","A",2,1,22,0.04545,1,"{1591}"
209,1,35,0,0.0090755,"\int (a+b x) \left(1+\left(c+a x+\frac{b x^2}{2}\right)^n\right) \, dx","Int[(a + b*x)*(1 + (c + a*x + (b*x^2)/2)^n),x]","\frac{\left(a x+\frac{b x^2}{2}+c\right)^{n+1}}{n+1}+a x+\frac{b x^2}{2}","\frac{\left(a x+\frac{b x^2}{2}+c\right)^{n+1}}{n+1}+a x+\frac{b x^2}{2}",1,"a*x + (b*x^2)/2 + (c + a*x + (b*x^2)/2)^(1 + n)/(1 + n)","A",2,1,23,0.04348,1,"{1591}"
210,1,30,0,0.0198891,"\int \left(a+c x^2\right) \left(1+\left(a x+\frac{c x^3}{3}\right)^5\right) \, dx","Int[(a + c*x^2)*(1 + (a*x + (c*x^3)/3)^5),x]","\frac{1}{6} \left(a x+\frac{c x^3}{3}\right)^6+a x+\frac{c x^3}{3}","\frac{1}{6} \left(a x+\frac{c x^3}{3}\right)^6+a x+\frac{c x^3}{3}",1,"a*x + (c*x^3)/3 + (a*x + (c*x^3)/3)^6/6","A",2,1,24,0.04167,1,"{1591}"
211,1,31,0,0.0384825,"\int \left(a+c x^2\right) \left(1+\left(d+a x+\frac{c x^3}{3}\right)^5\right) \, dx","Int[(a + c*x^2)*(1 + (d + a*x + (c*x^3)/3)^5),x]","\frac{1}{6} \left(a x+\frac{c x^3}{3}+d\right)^6+a x+\frac{c x^3}{3}","\frac{1}{6} \left(a x+\frac{c x^3}{3}+d\right)^6+a x+\frac{c x^3}{3}",1,"a*x + (c*x^3)/3 + (d + a*x + (c*x^3)/3)^6/6","A",2,1,25,0.04000,1,"{1591}"
212,1,34,0,0.0329058,"\int \left(b x+c x^2\right) \left(1+\left(\frac{b x^2}{2}+\frac{c x^3}{3}\right)^5\right) \, dx","Int[(b*x + c*x^2)*(1 + ((b*x^2)/2 + (c*x^3)/3)^5),x]","\frac{x^{12} (3 b+2 c x)^6}{279936}+\frac{b x^2}{2}+\frac{c x^3}{3}","\frac{x^{12} (3 b+2 c x)^6}{279936}+\frac{b x^2}{2}+\frac{c x^3}{3}",1,"(b*x^2)/2 + (c*x^3)/3 + (x^12*(3*b + 2*c*x)^6)/279936","A",2,1,31,0.03226,1,"{1591}"
213,1,41,0,0.0452143,"\int \left(b x+c x^2\right) \left(1+\left(d+\frac{b x^2}{2}+\frac{c x^3}{3}\right)^5\right) \, dx","Int[(b*x + c*x^2)*(1 + (d + (b*x^2)/2 + (c*x^3)/3)^5),x]","\frac{1}{6} \left(\frac{b x^2}{2}+\frac{c x^3}{3}+d\right)^6+\frac{b x^2}{2}+\frac{c x^3}{3}","\frac{1}{6} \left(\frac{b x^2}{2}+\frac{c x^3}{3}+d\right)^6+\frac{b x^2}{2}+\frac{c x^3}{3}",1,"(b*x^2)/2 + (c*x^3)/3 + (d + (b*x^2)/2 + (c*x^3)/3)^6/6","A",2,1,32,0.03125,1,"{1591}"
214,1,46,0,0.046813,"\int \left(a+b x+c x^2\right) \left(1+\left(a x+\frac{b x^2}{2}+\frac{c x^3}{3}\right)^5\right) \, dx","Int[(a + b*x + c*x^2)*(1 + (a*x + (b*x^2)/2 + (c*x^3)/3)^5),x]","\frac{1}{6} \left(a x+\frac{b x^2}{2}+\frac{c x^3}{3}\right)^6+a x+\frac{b x^2}{2}+\frac{c x^3}{3}","\frac{1}{6} \left(a x+\frac{b x^2}{2}+\frac{c x^3}{3}\right)^6+a x+\frac{b x^2}{2}+\frac{c x^3}{3}",1,"a*x + (b*x^2)/2 + (c*x^3)/3 + (a*x + (b*x^2)/2 + (c*x^3)/3)^6/6","A",2,1,35,0.02857,1,"{1591}"
215,1,47,0,0.0908815,"\int \left(a+b x+c x^2\right) \left(1+\left(d+a x+\frac{b x^2}{2}+\frac{c x^3}{3}\right)^5\right) \, dx","Int[(a + b*x + c*x^2)*(1 + (d + a*x + (b*x^2)/2 + (c*x^3)/3)^5),x]","\frac{1}{6} \left(a x+\frac{b x^2}{2}+\frac{c x^3}{3}+d\right)^6+a x+\frac{b x^2}{2}+\frac{c x^3}{3}","\frac{1}{6} \left(a x+\frac{b x^2}{2}+\frac{c x^3}{3}+d\right)^6+a x+\frac{b x^2}{2}+\frac{c x^3}{3}",1,"a*x + (b*x^2)/2 + (c*x^3)/3 + (d + a*x + (b*x^2)/2 + (c*x^3)/3)^6/6","A",2,1,36,0.02778,1,"{1591}"
216,1,34,0,0.0090691,"\int \left(a+c x^2\right) \left(1+\left(a x+\frac{c x^3}{3}\right)^n\right) \, dx","Int[(a + c*x^2)*(1 + (a*x + (c*x^3)/3)^n),x]","\frac{\left(a x+\frac{c x^3}{3}\right)^{n+1}}{n+1}+a x+\frac{c x^3}{3}","\frac{\left(a x+\frac{c x^3}{3}\right)^{n+1}}{n+1}+a x+\frac{c x^3}{3}",1,"a*x + (c*x^3)/3 + (a*x + (c*x^3)/3)^(1 + n)/(1 + n)","A",2,1,24,0.04167,1,"{1591}"
217,1,44,0,0.0095982,"\int \left(b x+c x^2\right) \left(1+\left(\frac{b x^2}{2}+\frac{c x^3}{3}\right)^n\right) \, dx","Int[(b*x + c*x^2)*(1 + ((b*x^2)/2 + (c*x^3)/3)^n),x]","\frac{\left(\frac{b x^2}{2}+\frac{c x^3}{3}\right)^{n+1}}{n+1}+\frac{b x^2}{2}+\frac{c x^3}{3}","\frac{\left(\frac{b x^2}{2}+\frac{c x^3}{3}\right)^{n+1}}{n+1}+\frac{b x^2}{2}+\frac{c x^3}{3}",1,"(b*x^2)/2 + (c*x^3)/3 + ((b*x^2)/2 + (c*x^3)/3)^(1 + n)/(1 + n)","A",2,1,31,0.03226,1,"{1591}"
218,1,50,0,0.0091307,"\int \left(a+b x+c x^2\right) \left(1+\left(a x+\frac{b x^2}{2}+\frac{c x^3}{3}\right)^n\right) \, dx","Int[(a + b*x + c*x^2)*(1 + (a*x + (b*x^2)/2 + (c*x^3)/3)^n),x]","\frac{\left(a x+\frac{b x^2}{2}+\frac{c x^3}{3}\right)^{n+1}}{n+1}+a x+\frac{b x^2}{2}+\frac{c x^3}{3}","\frac{\left(a x+\frac{b x^2}{2}+\frac{c x^3}{3}\right)^{n+1}}{n+1}+a x+\frac{b x^2}{2}+\frac{c x^3}{3}",1,"a*x + (b*x^2)/2 + (c*x^3)/3 + (a*x + (b*x^2)/2 + (c*x^3)/3)^(1 + n)/(1 + n)","A",2,1,35,0.02857,1,"{1591}"
219,1,19,0,0.0088695,"\int \left(-4+4 x+x^2\right) \left(5-12 x+6 x^2+x^3\right) \, dx","Int[(-4 + 4*x + x^2)*(5 - 12*x + 6*x^2 + x^3),x]","\frac{1}{6} \left(x^3+6 x^2-12 x+5\right)^2","\frac{1}{6} \left(x^3+6 x^2-12 x+5\right)^2",1,"(5 - 12*x + 6*x^2 + x^3)^2/6","A",1,1,22,0.04545,1,"{1588}"
220,1,16,0,0.0066653,"\int \left(2 x+x^3\right) \left(1+4 x^2+x^4\right) \, dx","Int[(2*x + x^3)*(1 + 4*x^2 + x^4),x]","\frac{1}{8} \left(x^4+4 x^2+1\right)^2","\frac{1}{8} \left(x^4+4 x^2+1\right)^2",1,"(1 + 4*x^2 + x^4)^2/8","A",1,1,18,0.05556,1,"{1588}"
221,1,96,0,0.1977816,"\int (1+2 x) \left(x+x^2\right)^3 \left(-18+7 \left(x+x^2\right)^3\right)^2 \, dx","Int[(1 + 2*x)*(x + x^2)^3*(-18 + 7*(x + x^2)^3)^2,x]","\frac{49 x^{20}}{10}+49 x^{19}+\frac{441 x^{18}}{2}+588 x^{17}+1029 x^{16}+\frac{6174 x^{15}}{5}+993 x^{14}+336 x^{13}-\frac{1071 x^{12}}{2}-1211 x^{11}-\frac{12551 x^{10}}{10}-756 x^9-171 x^8+288 x^7+486 x^6+324 x^5+81 x^4","\frac{49}{10} x^{10} (x+1)^{10}-36 x^7 (x+1)^7+81 x^4 (x+1)^4",1,"81*x^4 + 324*x^5 + 486*x^6 + 288*x^7 - 171*x^8 - 756*x^9 - (12551*x^10)/10 - 1211*x^11 - (1071*x^12)/2 + 336*x^13 + 993*x^14 + (6174*x^15)/5 + 1029*x^16 + 588*x^17 + (441*x^18)/2 + 49*x^19 + (49*x^20)/10","B",3,2,26,0.07692,1,"{1593, 1612}"
222,1,96,0,0.1541923,"\int x^3 (1+x)^3 (1+2 x) \left(-18+7 x^3 (1+x)^3\right)^2 \, dx","Int[x^3*(1 + x)^3*(1 + 2*x)*(-18 + 7*x^3*(1 + x)^3)^2,x]","\frac{49 x^{20}}{10}+49 x^{19}+\frac{441 x^{18}}{2}+588 x^{17}+1029 x^{16}+\frac{6174 x^{15}}{5}+993 x^{14}+336 x^{13}-\frac{1071 x^{12}}{2}-1211 x^{11}-\frac{12551 x^{10}}{10}-756 x^9-171 x^8+288 x^7+486 x^6+324 x^5+81 x^4","\frac{49}{10} x^{10} (x+1)^{10}-36 x^7 (x+1)^7+81 x^4 (x+1)^4",1,"81*x^4 + 324*x^5 + 486*x^6 + 288*x^7 - 171*x^8 - 756*x^9 - (12551*x^10)/10 - 1211*x^11 - (1071*x^12)/2 + 336*x^13 + 993*x^14 + (6174*x^15)/5 + 1029*x^16 + 588*x^17 + (441*x^18)/2 + 49*x^19 + (49*x^20)/10","B",2,1,28,0.03571,1,"{1612}"
223,1,14,0,0.0075984,"\int \frac{2-x^2}{\left(1-6 x+x^3\right)^5} \, dx","Int[(2 - x^2)/(1 - 6*x + x^3)^5,x]","\frac{1}{12 \left(x^3-6 x+1\right)^4}","\frac{1}{12 \left(x^3-6 x+1\right)^4}",1,"1/(12*(1 - 6*x + x^3)^4)","A",1,1,18,0.05556,1,"{1588}"
224,1,15,0,0.0092377,"\int \frac{2 x+x^2}{4+3 x^2+x^3} \, dx","Int[(2*x + x^2)/(4 + 3*x^2 + x^3),x]","\frac{1}{3} \log \left(x^3+3 x^2+4\right)","\frac{1}{3} \log \left(x^3+3 x^2+4\right)",1,"Log[4 + 3*x^2 + x^3]/3","A",1,1,20,0.05000,1,"{1587}"
225,1,17,0,0.0095623,"\int \frac{1+x+x^3}{4 x+2 x^2+x^4} \, dx","Int[(1 + x + x^3)/(4*x + 2*x^2 + x^4),x]","\frac{1}{4} \log \left(x^4+2 x^2+4 x\right)","\frac{1}{4} \log \left(x^4+2 x^2+4 x\right)",1,"Log[4*x + 2*x^2 + x^4]/4","A",1,1,21,0.04762,1,"{1587}"
226,1,40,0,0.0968871,"\int \frac{b c-a d-2 a e x-b e x^2-3 a f x^2-2 b f x^3}{\left(c+d x+e x^2+f x^3\right)^2} \, dx","Int[(b*c - a*d - 2*a*e*x - b*e*x^2 - 3*a*f*x^2 - 2*b*f*x^3)/(c + d*x + e*x^2 + f*x^3)^2,x]","\frac{a}{c+d x+e x^2+f x^3}+\frac{b x}{c+d x+e x^2+f x^3}","\frac{a}{c+d x+e x^2+f x^3}+\frac{b x}{c+d x+e x^2+f x^3}",1,"a/(c + d*x + e*x^2 + f*x^3) + (b*x)/(c + d*x + e*x^2 + f*x^3)","A",3,3,52,0.05769,1,"{6, 2102, 1588}"
227,1,605,0,4.5353084,"\int \frac{A+B x+C x^2+D x^3}{a+b x+c x^2+b x^3+a x^4} \, dx","Int[(A + B*x + C*x^2 + D*x^3)/(a + b*x + c*x^2 + b*x^3 + a*x^4),x]","\frac{\tan ^{-1}\left(\frac{-\sqrt{8 a^2-4 a c+b^2}+4 a x+b}{\sqrt{2} \sqrt{-b \left(b-\sqrt{8 a^2-4 a c+b^2}\right)+4 a^2+2 a c}}\right) \left(-a \left(A \left(b-\sqrt{8 a^2-4 a c+b^2}\right)-C \sqrt{8 a^2-4 a c+b^2}+b C+2 c D\right)+b D \left(b-\sqrt{8 a^2-4 a c+b^2}\right)+4 a^2 B\right)}{\sqrt{2} a \sqrt{8 a^2-4 a c+b^2} \sqrt{-b \left(b-\sqrt{8 a^2-4 a c+b^2}\right)+4 a^2+2 a c}}-\frac{\tan ^{-1}\left(\frac{\sqrt{8 a^2-4 a c+b^2}+4 a x+b}{\sqrt{2} \sqrt{-b \left(\sqrt{8 a^2-4 a c+b^2}+b\right)+4 a^2+2 a c}}\right) \left(-a \left(A \left(\sqrt{8 a^2-4 a c+b^2}+b\right)+C \sqrt{8 a^2-4 a c+b^2}+b C+2 c D\right)+b D \left(\sqrt{8 a^2-4 a c+b^2}+b\right)+4 a^2 B\right)}{\sqrt{2} a \sqrt{8 a^2-4 a c+b^2} \sqrt{-b \left(\sqrt{8 a^2-4 a c+b^2}+b\right)+4 a^2+2 a c}}-\frac{\log \left(x \left(b-\sqrt{8 a^2-4 a c+b^2}\right)+2 a x^2+2 a\right) \left(D \left(b-\sqrt{8 a^2-4 a c+b^2}\right)+2 a (A-C)\right)}{4 a \sqrt{8 a^2-4 a c+b^2}}+\frac{\log \left(x \left(\sqrt{8 a^2-4 a c+b^2}+b\right)+2 a x^2+2 a\right) \left(D \left(\sqrt{8 a^2-4 a c+b^2}+b\right)+2 a (A-C)\right)}{4 a \sqrt{8 a^2-4 a c+b^2}}","\frac{\tan ^{-1}\left(\frac{-\sqrt{8 a^2-4 a c+b^2}+4 a x+b}{\sqrt{2} \sqrt{-b \left(b-\sqrt{8 a^2-4 a c+b^2}\right)+4 a^2+2 a c}}\right) \left(-a \left(A \left(b-\sqrt{8 a^2-4 a c+b^2}\right)-C \sqrt{8 a^2-4 a c+b^2}+b C+2 c D\right)+b D \left(b-\sqrt{8 a^2-4 a c+b^2}\right)+4 a^2 B\right)}{\sqrt{2} a \sqrt{8 a^2-4 a c+b^2} \sqrt{-b \left(b-\sqrt{8 a^2-4 a c+b^2}\right)+4 a^2+2 a c}}-\frac{\tan ^{-1}\left(\frac{\sqrt{8 a^2-4 a c+b^2}+4 a x+b}{\sqrt{2} \sqrt{-b \left(\sqrt{8 a^2-4 a c+b^2}+b\right)+4 a^2+2 a c}}\right) \left(-a \left(A \left(\sqrt{8 a^2-4 a c+b^2}+b\right)+C \sqrt{8 a^2-4 a c+b^2}+b C+2 c D\right)+b D \left(\sqrt{8 a^2-4 a c+b^2}+b\right)+4 a^2 B\right)}{\sqrt{2} a \sqrt{8 a^2-4 a c+b^2} \sqrt{-b \left(\sqrt{8 a^2-4 a c+b^2}+b\right)+4 a^2+2 a c}}-\frac{\log \left(x \left(b-\sqrt{8 a^2-4 a c+b^2}\right)+2 a x^2+2 a\right) \left(D \left(b-\sqrt{8 a^2-4 a c+b^2}\right)+2 a (A-C)\right)}{4 a \sqrt{8 a^2-4 a c+b^2}}+\frac{\log \left(x \left(\sqrt{8 a^2-4 a c+b^2}+b\right)+2 a x^2+2 a\right) \left(D \left(\sqrt{8 a^2-4 a c+b^2}+b\right)+2 a (A-C)\right)}{4 a \sqrt{8 a^2-4 a c+b^2}}",1,"((4*a^2*B + b*(b - Sqrt[8*a^2 + b^2 - 4*a*c])*D - a*(A*(b - Sqrt[8*a^2 + b^2 - 4*a*c]) + b*C - Sqrt[8*a^2 + b^2 - 4*a*c]*C + 2*c*D))*ArcTan[(b - Sqrt[8*a^2 + b^2 - 4*a*c] + 4*a*x)/(Sqrt[2]*Sqrt[4*a^2 + 2*a*c - b*(b - Sqrt[8*a^2 + b^2 - 4*a*c])])])/(Sqrt[2]*a*Sqrt[8*a^2 + b^2 - 4*a*c]*Sqrt[4*a^2 + 2*a*c - b*(b - Sqrt[8*a^2 + b^2 - 4*a*c])]) - ((4*a^2*B + b*(b + Sqrt[8*a^2 + b^2 - 4*a*c])*D - a*(A*(b + Sqrt[8*a^2 + b^2 - 4*a*c]) + b*C + Sqrt[8*a^2 + b^2 - 4*a*c]*C + 2*c*D))*ArcTan[(b + Sqrt[8*a^2 + b^2 - 4*a*c] + 4*a*x)/(Sqrt[2]*Sqrt[4*a^2 + 2*a*c - b*(b + Sqrt[8*a^2 + b^2 - 4*a*c])])])/(Sqrt[2]*a*Sqrt[8*a^2 + b^2 - 4*a*c]*Sqrt[4*a^2 + 2*a*c - b*(b + Sqrt[8*a^2 + b^2 - 4*a*c])]) - ((2*a*(A - C) + (b - Sqrt[8*a^2 + b^2 - 4*a*c])*D)*Log[2*a + (b - Sqrt[8*a^2 + b^2 - 4*a*c])*x + 2*a*x^2])/(4*a*Sqrt[8*a^2 + b^2 - 4*a*c]) + ((2*a*(A - C) + (b + Sqrt[8*a^2 + b^2 - 4*a*c])*D)*Log[2*a + (b + Sqrt[8*a^2 + b^2 - 4*a*c])*x + 2*a*x^2])/(4*a*Sqrt[8*a^2 + b^2 - 4*a*c])","A",9,5,38,0.1316,1,"{2086, 634, 618, 204, 628}"
228,1,63,0,0.0655793,"\int \frac{2+x-4 x^2+2 x^3}{1-x+x^2-x^3+x^4} \, dx","Int[(2 + x - 4*x^2 + 2*x^3)/(1 - x + x^2 - x^3 + x^4),x]","-\frac{2 \log \left(2 x^2-\left(1-\sqrt{5}\right) x+2\right)}{1-\sqrt{5}}-\frac{2 \log \left(2 x^2-\left(1+\sqrt{5}\right) x+2\right)}{1+\sqrt{5}}","-\frac{2 \log \left(2 x^2-\left(1-\sqrt{5}\right) x+2\right)}{1-\sqrt{5}}-\frac{2 \log \left(2 x^2-\left(1+\sqrt{5}\right) x+2\right)}{1+\sqrt{5}}",1,"(-2*Log[2 - (1 - Sqrt[5])*x + 2*x^2])/(1 - Sqrt[5]) - (2*Log[2 - (1 + Sqrt[5])*x + 2*x^2])/(1 + Sqrt[5])","A",3,2,32,0.06250,1,"{2086, 628}"
229,1,14,0,0.0502709,"\int \frac{3 x+3 x^2+x^3}{1+4 x+6 x^2+4 x^3+x^4} \, dx","Int[(3*x + 3*x^2 + x^3)/(1 + 4*x + 6*x^2 + 4*x^3 + x^4),x]","\frac{1}{3 (x+1)^3}+\log (x+1)","\frac{1}{3 (x+1)^3}+\log (x+1)",1,"1/(3*(1 + x)^3) + Log[1 + x]","A",4,3,33,0.09091,1,"{1594, 1680, 14}"
230,1,28,0,0.0283567,"\int \frac{-1+3 x-3 x^2+x^3}{1+4 x+6 x^2+4 x^3+x^4} \, dx","Int[(-1 + 3*x - 3*x^2 + x^3)/(1 + 4*x + 6*x^2 + 4*x^3 + x^4),x]","\frac{6}{x+1}-\frac{6}{(x+1)^2}+\frac{8}{3 (x+1)^3}+\log (x+1)","\frac{6}{x+1}-\frac{6}{(x+1)^2}+\frac{8}{3 (x+1)^3}+\log (x+1)",1,"8/(3*(1 + x)^3) - 6/(1 + x)^2 + 6/(1 + x) + Log[1 + x]","A",3,2,34,0.05882,1,"{1680, 43}"
231,1,59,0,0.0906975,"\int \frac{9-40 x-18 x^2+174 x^4+24 x^5+26 x^6-39 x^8}{\left(3+2 x^2+x^4\right)^3} \, dx","Int[(9 - 40*x - 18*x^2 + 174*x^4 + 24*x^5 + 26*x^6 - 39*x^8)/(3 + 2*x^2 + x^4)^3,x]","\frac{13 x}{x^4+2 x^2+3}-\frac{2 \left(13 x^2+18\right) x}{\left(x^4+2 x^2+3\right)^2}+\frac{2 \left(1-2 x^2\right)}{\left(x^4+2 x^2+3\right)^2}","\frac{13 x}{x^4+2 x^2+3}-\frac{2 \left(13 x^2+18\right) x}{\left(x^4+2 x^2+3\right)^2}+\frac{2 \left(1-2 x^2\right)}{\left(x^4+2 x^2+3\right)^2}",1,"(2*(1 - 2*x^2))/(3 + 2*x^2 + x^4)^2 - (2*x*(18 + 13*x^2))/(3 + 2*x^2 + x^4)^2 + (13*x)/(3 + 2*x^2 + x^4)","A",6,6,43,0.1395,1,"{1673, 1678, 1588, 1663, 1660, 8}"
232,1,11,0,0.0068737,"\int \frac{-1+4 x^5}{\left(1+x+x^5\right)^2} \, dx","Int[(-1 + 4*x^5)/(1 + x + x^5)^2,x]","-\frac{x}{x^5+x+1}","-\frac{x}{x^5+x+1}",1,"-(x/(1 + x + x^5))","A",1,1,16,0.06250,1,"{1588}"
233,1,205,0,0.1486454,"\int \frac{1+x^2}{\left(1-7 x^2+7 x^4-x^6\right)^2} \, dx","Int[(1 + x^2)/(1 - 7*x^2 + 7*x^4 - x^6)^2,x]","-\frac{12-5 x}{64 \left(-x^2+2 x+1\right)}+\frac{5 x+12}{64 \left(-x^2-2 x+1\right)}+\frac{1}{32 (1-x)}-\frac{1}{32 (x+1)}-\frac{3}{256} \left(2+3 \sqrt{2}\right) \log \left(-x-\sqrt{2}+1\right)-\frac{3}{256} \left(2-3 \sqrt{2}\right) \log \left(-x+\sqrt{2}+1\right)+\frac{3}{256} \left(2+3 \sqrt{2}\right) \log \left(x-\sqrt{2}+1\right)+\frac{3}{256} \left(2-3 \sqrt{2}\right) \log \left(x+\sqrt{2}+1\right)-\frac{5 \tanh ^{-1}\left(\frac{1-x}{\sqrt{2}}\right)}{64 \sqrt{2}}+\frac{1}{4} \tanh ^{-1}(x)+\frac{5 \tanh ^{-1}\left(\frac{x+1}{\sqrt{2}}\right)}{64 \sqrt{2}}","\frac{x}{16 \left(1-x^2\right)}+\frac{\left(29-5 x^2\right) x}{32 \left(x^4-6 x^2+1\right)}+\frac{1}{4} \tanh ^{-1}(x)+\frac{1}{64} \left(\left(3-2 \sqrt{2}\right) \tanh ^{-1}\left(\left(\sqrt{2}-1\right) x\right)-\left(3+2 \sqrt{2}\right) \tanh ^{-1}\left(\left(1+\sqrt{2}\right) x\right)\right)",1,"1/(32*(1 - x)) - 1/(32*(1 + x)) + (12 + 5*x)/(64*(1 - 2*x - x^2)) - (12 - 5*x)/(64*(1 + 2*x - x^2)) - (5*ArcTanh[(1 - x)/Sqrt[2]])/(64*Sqrt[2]) + ArcTanh[x]/4 + (5*ArcTanh[(1 + x)/Sqrt[2]])/(64*Sqrt[2]) - (3*(2 + 3*Sqrt[2])*Log[1 - Sqrt[2] - x])/256 - (3*(2 - 3*Sqrt[2])*Log[1 + Sqrt[2] - x])/256 + (3*(2 + 3*Sqrt[2])*Log[1 - Sqrt[2] + x])/256 + (3*(2 - 3*Sqrt[2])*Log[1 + Sqrt[2] + x])/256","B",15,7,25,0.2800,1,"{2073, 207, 638, 618, 206, 632, 31}"
234,1,25,0,0.0247382,"\int x^m \left(a+b x+c x^2+d x^3\right)^p (a (1+m)+x (b (2+m+p)+x (c (3+m+2 p)+d (4+m+3 p) x))) \, dx","Int[x^m*(a + b*x + c*x^2 + d*x^3)^p*(a*(1 + m) + x*(b*(2 + m + p) + x*(c*(3 + m + 2*p) + d*(4 + m + 3*p)*x))),x]","x^{m+1} \left(a+b x+c x^2+d x^3\right)^{p+1}","x^{m+1} \left(a+b x+c x^2+d x^3\right)^{p+1}",1,"x^(1 + m)*(a + b*x + c*x^2 + d*x^3)^(1 + p)","A",1,1,56,0.01786,1,"{1590}"
235,1,23,0,0.0819645,"\int x^2 \left(a+b x+c x^2+d x^3\right)^p \left(3 a+b (4+p) x+c (5+2 p) x^2+d (6+3 p) x^3\right) \, dx","Int[x^2*(a + b*x + c*x^2 + d*x^3)^p*(3*a + b*(4 + p)*x + c*(5 + 2*p)*x^2 + d*(6 + 3*p)*x^3),x]","x^3 \left(a+b x+c x^2+d x^3\right)^{p+1}","x^3 \left(a+b x+c x^2+d x^3\right)^{p+1}",1,"x^3*(a + b*x + c*x^2 + d*x^3)^(1 + p)","A",1,1,51,0.01961,1,"{1588}"
236,1,23,0,0.0590147,"\int x \left(a+b x+c x^2+d x^3\right)^p \left(2 a+b (3+p) x+c (4+2 p) x^2+d (5+3 p) x^3\right) \, dx","Int[x*(a + b*x + c*x^2 + d*x^3)^p*(2*a + b*(3 + p)*x + c*(4 + 2*p)*x^2 + d*(5 + 3*p)*x^3),x]","x^2 \left(a+b x+c x^2+d x^3\right)^{p+1}","x^2 \left(a+b x+c x^2+d x^3\right)^{p+1}",1,"x^2*(a + b*x + c*x^2 + d*x^3)^(1 + p)","A",1,1,49,0.02041,1,"{1588}"
237,1,21,0,0.0436484,"\int \left(a+b x+c x^2+d x^3\right)^p \left(a+b (2+p) x+c (3+2 p) x^2+d (4+3 p) x^3\right) \, dx","Int[(a + b*x + c*x^2 + d*x^3)^p*(a + b*(2 + p)*x + c*(3 + 2*p)*x^2 + d*(4 + 3*p)*x^3),x]","x \left(a+b x+c x^2+d x^3\right)^{p+1}","x \left(a+b x+c x^2+d x^3\right)^{p+1}",1,"x*(a + b*x + c*x^2 + d*x^3)^(1 + p)","A",1,1,46,0.02174,1,"{1588}"
238,1,19,0,0.0427075,"\int \frac{\left(a+b x+c x^2+d x^3\right)^p \left(b (1+p) x+c (2+2 p) x^2+d (3+3 p) x^3\right)}{x} \, dx","Int[((a + b*x + c*x^2 + d*x^3)^p*(b*(1 + p)*x + c*(2 + 2*p)*x^2 + d*(3 + 3*p)*x^3))/x,x]","\left(a+b x+c x^2+d x^3\right)^{p+1}","\left(a+b x+c x^2+d x^3\right)^{p+1}",1,"(a + b*x + c*x^2 + d*x^3)^(1 + p)","A",2,2,48,0.04167,1,"{1585, 1588}"
239,1,23,0,0.033962,"\int \frac{\left(a+b x+c x^2+d x^3\right)^p \left(-a+b p x+c (1+2 p) x^2+d (2+3 p) x^3\right)}{x^2} \, dx","Int[((a + b*x + c*x^2 + d*x^3)^p*(-a + b*p*x + c*(1 + 2*p)*x^2 + d*(2 + 3*p)*x^3))/x^2,x]","\frac{\left(a+b x+c x^2+d x^3\right)^{p+1}}{x}","\frac{\left(a+b x+c x^2+d x^3\right)^{p+1}}{x}",1,"(a + b*x + c*x^2 + d*x^3)^(1 + p)/x","A",1,1,49,0.02041,1,"{1590}"
240,1,23,0,0.0353046,"\int \frac{\left(a+b x+c x^2+d x^3\right)^p \left(-2 a+b (-1+p) x+2 c p x^2+d (1+3 p) x^3\right)}{x^3} \, dx","Int[((a + b*x + c*x^2 + d*x^3)^p*(-2*a + b*(-1 + p)*x + 2*c*p*x^2 + d*(1 + 3*p)*x^3))/x^3,x]","\frac{\left(a+b x+c x^2+d x^3\right)^{p+1}}{x^2}","\frac{\left(a+b x+c x^2+d x^3\right)^{p+1}}{x^2}",1,"(a + b*x + c*x^2 + d*x^3)^(1 + p)/x^2","A",1,1,48,0.02083,1,"{1590}"
241,1,23,0,0.0358817,"\int \frac{\left(a+b x+c x^2+d x^3\right)^p \left(-3 a+b (-2+p) x+c (-1+2 p) x^2+3 d p x^3\right)}{x^4} \, dx","Int[((a + b*x + c*x^2 + d*x^3)^p*(-3*a + b*(-2 + p)*x + c*(-1 + 2*p)*x^2 + 3*d*p*x^3))/x^4,x]","\frac{\left(a+b x+c x^2+d x^3\right)^{p+1}}{x^3}","\frac{\left(a+b x+c x^2+d x^3\right)^{p+1}}{x^3}",1,"(a + b*x + c*x^2 + d*x^3)^(1 + p)/x^3","A",1,1,48,0.02083,1,"{1590}"
242,1,97,0,0.1375176,"\int \frac{x^4 \left(5+x+3 x^2+2 x^3\right)}{2+x+3 x^2+x^3+2 x^4} \, dx","Int[(x^4*(5 + x + 3*x^2 + 2*x^3))/(2 + x + 3*x^2 + x^3 + 2*x^4),x]","\frac{x^4}{4}+\frac{x^3}{3}-\frac{3 x^2}{4}+\frac{1}{3} \log \left(x^2+x+1\right)-\frac{13}{48} \log \left(2 x^2-x+2\right)+\frac{5 x}{4}+\frac{1}{24} \sqrt{\frac{5}{3}} \tan ^{-1}\left(\frac{1-4 x}{\sqrt{15}}\right)-\frac{10 \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{3 \sqrt{3}}","\frac{x^4}{4}+\frac{x^3}{3}-\frac{3 x^2}{4}+\frac{1}{3} \log \left(x^2+x+1\right)-\frac{13}{48} \log \left(2 x^2-x+2\right)+\frac{5 x}{4}+\frac{1}{24} \sqrt{\frac{5}{3}} \tan ^{-1}\left(\frac{1-4 x}{\sqrt{15}}\right)-\frac{10 \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{3 \sqrt{3}}",1,"(5*x)/4 - (3*x^2)/4 + x^3/3 + x^4/4 + (Sqrt[5/3]*ArcTan[(1 - 4*x)/Sqrt[15]])/24 - (10*ArcTan[(1 + 2*x)/Sqrt[3]])/(3*Sqrt[3]) + Log[1 + x + x^2]/3 - (13*Log[2 - x + 2*x^2])/48","A",10,5,35,0.1429,1,"{2075, 634, 618, 204, 628}"
243,1,90,0,0.1226146,"\int \frac{x^3 \left(5+x+3 x^2+2 x^3\right)}{2+x+3 x^2+x^3+2 x^4} \, dx","Int[(x^3*(5 + x + 3*x^2 + 2*x^3))/(2 + x + 3*x^2 + x^3 + 2*x^4),x]","\frac{x^3}{3}+\frac{x^2}{2}+\frac{2}{3} \log \left(x^2+x+1\right)-\frac{1}{24} \log \left(2 x^2-x+2\right)-\frac{3 x}{2}+\frac{5}{12} \sqrt{\frac{5}{3}} \tan ^{-1}\left(\frac{1-4 x}{\sqrt{15}}\right)+\frac{8 \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{3 \sqrt{3}}","\frac{x^3}{3}+\frac{x^2}{2}+\frac{2}{3} \log \left(x^2+x+1\right)-\frac{1}{24} \log \left(2 x^2-x+2\right)-\frac{3 x}{2}+\frac{5}{12} \sqrt{\frac{5}{3}} \tan ^{-1}\left(\frac{1-4 x}{\sqrt{15}}\right)+\frac{8 \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{3 \sqrt{3}}",1,"(-3*x)/2 + x^2/2 + x^3/3 + (5*Sqrt[5/3]*ArcTan[(1 - 4*x)/Sqrt[15]])/12 + (8*ArcTan[(1 + 2*x)/Sqrt[3]])/(3*Sqrt[3]) + (2*Log[1 + x + x^2])/3 - Log[2 - x + 2*x^2]/24","A",10,5,35,0.1429,1,"{2075, 634, 618, 204, 628}"
244,1,77,0,0.1207019,"\int \frac{x^2 \left(5+x+3 x^2+2 x^3\right)}{2+x+3 x^2+x^3+2 x^4} \, dx","Int[(x^2*(5 + x + 3*x^2 + 2*x^3))/(2 + x + 3*x^2 + x^3 + 2*x^4),x]","\frac{x^2}{2}-\log \left(x^2+x+1\right)+\frac{1}{4} \log \left(2 x^2-x+2\right)+x+\frac{1}{6} \sqrt{\frac{5}{3}} \tan ^{-1}\left(\frac{1-4 x}{\sqrt{15}}\right)+\frac{2 \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{3 \sqrt{3}}","\frac{x^2}{2}-\log \left(x^2+x+1\right)+\frac{1}{4} \log \left(2 x^2-x+2\right)+x+\frac{1}{6} \sqrt{\frac{5}{3}} \tan ^{-1}\left(\frac{1-4 x}{\sqrt{15}}\right)+\frac{2 \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{3 \sqrt{3}}",1,"x + x^2/2 + (Sqrt[5/3]*ArcTan[(1 - 4*x)/Sqrt[15]])/6 + (2*ArcTan[(1 + 2*x)/Sqrt[3]])/(3*Sqrt[3]) - Log[1 + x + x^2] + Log[2 - x + 2*x^2]/4","A",10,5,35,0.1429,1,"{2075, 634, 618, 204, 628}"
245,1,72,0,0.0926255,"\int \frac{x \left(5+x+3 x^2+2 x^3\right)}{2+x+3 x^2+x^3+2 x^4} \, dx","Int[(x*(5 + x + 3*x^2 + 2*x^3))/(2 + x + 3*x^2 + x^3 + 2*x^4),x]","\frac{1}{3} \log \left(x^2+x+1\right)+\frac{1}{6} \log \left(2 x^2-x+2\right)+x-\frac{1}{3} \sqrt{\frac{5}{3}} \tan ^{-1}\left(\frac{1-4 x}{\sqrt{15}}\right)-\frac{10 \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{3 \sqrt{3}}","\frac{1}{3} \log \left(x^2+x+1\right)+\frac{1}{6} \log \left(2 x^2-x+2\right)+x-\frac{1}{3} \sqrt{\frac{5}{3}} \tan ^{-1}\left(\frac{1-4 x}{\sqrt{15}}\right)-\frac{10 \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{3 \sqrt{3}}",1,"x - (Sqrt[5/3]*ArcTan[(1 - 4*x)/Sqrt[15]])/3 - (10*ArcTan[(1 + 2*x)/Sqrt[3]])/(3*Sqrt[3]) + Log[1 + x + x^2]/3 + Log[2 - x + 2*x^2]/6","A",10,5,33,0.1515,1,"{2075, 634, 618, 204, 628}"
246,1,71,0,0.0782529,"\int \frac{5+x+3 x^2+2 x^3}{2+x+3 x^2+x^3+2 x^4} \, dx","Int[(5 + x + 3*x^2 + 2*x^3)/(2 + x + 3*x^2 + x^3 + 2*x^4),x]","\frac{2}{3} \log \left(x^2+x+1\right)-\frac{1}{6} \log \left(2 x^2-x+2\right)-\frac{1}{3} \sqrt{\frac{5}{3}} \tan ^{-1}\left(\frac{1-4 x}{\sqrt{15}}\right)+\frac{8 \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{3 \sqrt{3}}","\frac{2}{3} \log \left(x^2+x+1\right)-\frac{1}{6} \log \left(2 x^2-x+2\right)-\frac{1}{3} \sqrt{\frac{5}{3}} \tan ^{-1}\left(\frac{1-4 x}{\sqrt{15}}\right)+\frac{8 \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{3 \sqrt{3}}",1,"-(Sqrt[5/3]*ArcTan[(1 - 4*x)/Sqrt[15]])/3 + (8*ArcTan[(1 + 2*x)/Sqrt[3]])/(3*Sqrt[3]) + (2*Log[1 + x + x^2])/3 - Log[2 - x + 2*x^2]/6","A",10,5,32,0.1562,1,"{2074, 634, 618, 204, 628}"
247,1,75,0,0.1350822,"\int \frac{5+x+3 x^2+2 x^3}{x \left(2+x+3 x^2+x^3+2 x^4\right)} \, dx","Int[(5 + x + 3*x^2 + 2*x^3)/(x*(2 + x + 3*x^2 + x^3 + 2*x^4)),x]","-\log \left(x^2+x+1\right)-\frac{1}{4} \log \left(2 x^2-x+2\right)+\frac{5 \log (x)}{2}+\frac{1}{6} \sqrt{\frac{5}{3}} \tan ^{-1}\left(\frac{1-4 x}{\sqrt{15}}\right)+\frac{2 \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{3 \sqrt{3}}","-\log \left(x^2+x+1\right)-\frac{1}{4} \log \left(2 x^2-x+2\right)+\frac{5 \log (x)}{2}+\frac{1}{6} \sqrt{\frac{5}{3}} \tan ^{-1}\left(\frac{1-4 x}{\sqrt{15}}\right)+\frac{2 \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{3 \sqrt{3}}",1,"(Sqrt[5/3]*ArcTan[(1 - 4*x)/Sqrt[15]])/6 + (2*ArcTan[(1 + 2*x)/Sqrt[3]])/(3*Sqrt[3]) + (5*Log[x])/2 - Log[1 + x + x^2] - Log[2 - x + 2*x^2]/4","A",13,6,35,0.1714,1,"{2087, 800, 634, 618, 204, 628}"
248,1,84,0,0.1519566,"\int \frac{5+x+3 x^2+2 x^3}{x^2 \left(2+x+3 x^2+x^3+2 x^4\right)} \, dx","Int[(5 + x + 3*x^2 + 2*x^3)/(x^2*(2 + x + 3*x^2 + x^3 + 2*x^4)),x]","\frac{1}{3} \log \left(x^2+x+1\right)+\frac{1}{24} \log \left(2 x^2-x+2\right)-\frac{5}{2 x}-\frac{3 \log (x)}{4}+\frac{5}{12} \sqrt{\frac{5}{3}} \tan ^{-1}\left(\frac{1-4 x}{\sqrt{15}}\right)-\frac{10 \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{3 \sqrt{3}}","\frac{1}{3} \log \left(x^2+x+1\right)+\frac{1}{24} \log \left(2 x^2-x+2\right)-\frac{5}{2 x}-\frac{3 \log (x)}{4}+\frac{5}{12} \sqrt{\frac{5}{3}} \tan ^{-1}\left(\frac{1-4 x}{\sqrt{15}}\right)-\frac{10 \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{3 \sqrt{3}}",1,"-5/(2*x) + (5*Sqrt[5/3]*ArcTan[(1 - 4*x)/Sqrt[15]])/12 - (10*ArcTan[(1 + 2*x)/Sqrt[3]])/(3*Sqrt[3]) - (3*Log[x])/4 + Log[1 + x + x^2]/3 + Log[2 - x + 2*x^2]/24","A",13,6,35,0.1714,1,"{2087, 800, 634, 618, 204, 628}"
249,1,91,0,0.1568172,"\int \frac{5+x+3 x^2+2 x^3}{x^3 \left(2+x+3 x^2+x^3+2 x^4\right)} \, dx","Int[(5 + x + 3*x^2 + 2*x^3)/(x^3*(2 + x + 3*x^2 + x^3 + 2*x^4)),x]","-\frac{5}{4 x^2}+\frac{2}{3} \log \left(x^2+x+1\right)+\frac{13}{48} \log \left(2 x^2-x+2\right)+\frac{3}{4 x}-\frac{15 \log (x)}{8}+\frac{1}{24} \sqrt{\frac{5}{3}} \tan ^{-1}\left(\frac{1-4 x}{\sqrt{15}}\right)+\frac{8 \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{3 \sqrt{3}}","-\frac{5}{4 x^2}+\frac{2}{3} \log \left(x^2+x+1\right)+\frac{13}{48} \log \left(2 x^2-x+2\right)+\frac{3}{4 x}-\frac{15 \log (x)}{8}+\frac{1}{24} \sqrt{\frac{5}{3}} \tan ^{-1}\left(\frac{1-4 x}{\sqrt{15}}\right)+\frac{8 \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{3 \sqrt{3}}",1,"-5/(4*x^2) + 3/(4*x) + (Sqrt[5/3]*ArcTan[(1 - 4*x)/Sqrt[15]])/24 + (8*ArcTan[(1 + 2*x)/Sqrt[3]])/(3*Sqrt[3]) - (15*Log[x])/8 + (2*Log[1 + x + x^2])/3 + (13*Log[2 - x + 2*x^2])/48","A",13,6,35,0.1714,1,"{2087, 800, 634, 618, 204, 628}"
250,1,307,0,0.5783272,"\int \frac{x^3 \left(5+x+3 x^2+2 x^3\right)}{2+x+5 x^2+x^3+2 x^4} \, dx","Int[(x^3*(5 + x + 3*x^2 + 2*x^3))/(2 + x + 5*x^2 + x^3 + 2*x^4),x]","\frac{1}{42} \left(7+5 i \sqrt{7}\right) x^3+\frac{1}{42} \left(7-5 i \sqrt{7}\right) x^3+\frac{1}{28} \left(7+5 i \sqrt{7}\right) x^2+\frac{1}{28} \left(7-5 i \sqrt{7}\right) x^2+\frac{3}{112} \left(7-11 i \sqrt{7}\right) \log \left(4 x^2+\left(1-i \sqrt{7}\right) x+4\right)+\frac{3}{112} \left(7+11 i \sqrt{7}\right) \log \left(4 x^2+\left(1+i \sqrt{7}\right) x+4\right)-\frac{1}{28} \left(35+9 i \sqrt{7}\right) x-\frac{1}{28} \left(35-9 i \sqrt{7}\right) x+\frac{11 \left(5 \sqrt{7}+9 i\right) \tan ^{-1}\left(\frac{8 x-i \sqrt{7}+1}{\sqrt{2 \left(35+i \sqrt{7}\right)}}\right)}{4 \sqrt{14 \left(35+i \sqrt{7}\right)}}-\frac{11 \left(-5 \sqrt{7}+9 i\right) \tan ^{-1}\left(\frac{8 x+i \sqrt{7}+1}{\sqrt{2 \left(35-i \sqrt{7}\right)}}\right)}{4 \sqrt{14 \left(35-i \sqrt{7}\right)}}","\frac{1}{42} \left(7+5 i \sqrt{7}\right) x^3+\frac{1}{42} \left(7-5 i \sqrt{7}\right) x^3+\frac{1}{28} \left(7+5 i \sqrt{7}\right) x^2+\frac{1}{28} \left(7-5 i \sqrt{7}\right) x^2+\frac{3}{112} \left(7-11 i \sqrt{7}\right) \log \left(4 x^2+\left(1-i \sqrt{7}\right) x+4\right)+\frac{3}{112} \left(7+11 i \sqrt{7}\right) \log \left(4 x^2+\left(1+i \sqrt{7}\right) x+4\right)-\frac{1}{28} \left(35+9 i \sqrt{7}\right) x-\frac{1}{28} \left(35-9 i \sqrt{7}\right) x+\frac{11 \left(5 \sqrt{7}+9 i\right) \tan ^{-1}\left(\frac{8 x-i \sqrt{7}+1}{\sqrt{2 \left(35+i \sqrt{7}\right)}}\right)}{4 \sqrt{14 \left(35+i \sqrt{7}\right)}}-\frac{11 \left(-5 \sqrt{7}+9 i\right) \tan ^{-1}\left(\frac{8 x+i \sqrt{7}+1}{\sqrt{2 \left(35-i \sqrt{7}\right)}}\right)}{4 \sqrt{14 \left(35-i \sqrt{7}\right)}}",1,"-((35 - (9*I)*Sqrt[7])*x)/28 - ((35 + (9*I)*Sqrt[7])*x)/28 + ((7 - (5*I)*Sqrt[7])*x^2)/28 + ((7 + (5*I)*Sqrt[7])*x^2)/28 + ((7 - (5*I)*Sqrt[7])*x^3)/42 + ((7 + (5*I)*Sqrt[7])*x^3)/42 + (11*(9*I + 5*Sqrt[7])*ArcTan[(1 - I*Sqrt[7] + 8*x)/Sqrt[2*(35 + I*Sqrt[7])]])/(4*Sqrt[14*(35 + I*Sqrt[7])]) - (11*(9*I - 5*Sqrt[7])*ArcTan[(1 + I*Sqrt[7] + 8*x)/Sqrt[2*(35 - I*Sqrt[7])]])/(4*Sqrt[14*(35 - I*Sqrt[7])]) + (3*(7 - (11*I)*Sqrt[7])*Log[4 + (1 - I*Sqrt[7])*x + 4*x^2])/112 + (3*(7 + (11*I)*Sqrt[7])*Log[4 + (1 + I*Sqrt[7])*x + 4*x^2])/112","A",13,6,35,0.1714,1,"{2087, 800, 634, 618, 204, 628}"
251,1,269,0,0.3920765,"\int \frac{x^2 \left(5+x+3 x^2+2 x^3\right)}{2+x+5 x^2+x^3+2 x^4} \, dx","Int[(x^2*(5 + x + 3*x^2 + 2*x^3))/(2 + x + 5*x^2 + x^3 + 2*x^4),x]","\frac{1}{28} \left(7+5 i \sqrt{7}\right) x^2+\frac{1}{28} \left(7-5 i \sqrt{7}\right) x^2-\frac{1}{56} \left(35+9 i \sqrt{7}\right) \log \left(4 x^2+\left(1-i \sqrt{7}\right) x+4\right)-\frac{1}{56} \left(35-9 i \sqrt{7}\right) \log \left(4 x^2+\left(1+i \sqrt{7}\right) x+4\right)+\frac{1}{14} \left(7+5 i \sqrt{7}\right) x+\frac{1}{14} \left(7-5 i \sqrt{7}\right) x-\frac{\left(\sqrt{7}+53 i\right) \tan ^{-1}\left(\frac{8 x-i \sqrt{7}+1}{\sqrt{2 \left(35+i \sqrt{7}\right)}}\right)}{2 \sqrt{14 \left(35+i \sqrt{7}\right)}}+\frac{\left(-\sqrt{7}+53 i\right) \tan ^{-1}\left(\frac{8 x+i \sqrt{7}+1}{\sqrt{2 \left(35-i \sqrt{7}\right)}}\right)}{2 \sqrt{14 \left(35-i \sqrt{7}\right)}}","\frac{1}{28} \left(7+5 i \sqrt{7}\right) x^2+\frac{1}{28} \left(7-5 i \sqrt{7}\right) x^2-\frac{1}{56} \left(35+9 i \sqrt{7}\right) \log \left(4 x^2+\left(1-i \sqrt{7}\right) x+4\right)-\frac{1}{56} \left(35-9 i \sqrt{7}\right) \log \left(4 x^2+\left(1+i \sqrt{7}\right) x+4\right)+\frac{1}{14} \left(7+5 i \sqrt{7}\right) x+\frac{1}{14} \left(7-5 i \sqrt{7}\right) x-\frac{\left(\sqrt{7}+53 i\right) \tan ^{-1}\left(\frac{8 x-i \sqrt{7}+1}{\sqrt{2 \left(35+i \sqrt{7}\right)}}\right)}{2 \sqrt{14 \left(35+i \sqrt{7}\right)}}+\frac{\left(-\sqrt{7}+53 i\right) \tan ^{-1}\left(\frac{8 x+i \sqrt{7}+1}{\sqrt{2 \left(35-i \sqrt{7}\right)}}\right)}{2 \sqrt{14 \left(35-i \sqrt{7}\right)}}",1,"((7 - (5*I)*Sqrt[7])*x)/14 + ((7 + (5*I)*Sqrt[7])*x)/14 + ((7 - (5*I)*Sqrt[7])*x^2)/28 + ((7 + (5*I)*Sqrt[7])*x^2)/28 - ((53*I + Sqrt[7])*ArcTan[(1 - I*Sqrt[7] + 8*x)/Sqrt[2*(35 + I*Sqrt[7])]])/(2*Sqrt[14*(35 + I*Sqrt[7])]) + ((53*I - Sqrt[7])*ArcTan[(1 + I*Sqrt[7] + 8*x)/Sqrt[2*(35 - I*Sqrt[7])]])/(2*Sqrt[14*(35 - I*Sqrt[7])]) - ((35 + (9*I)*Sqrt[7])*Log[4 + (1 - I*Sqrt[7])*x + 4*x^2])/56 - ((35 - (9*I)*Sqrt[7])*Log[4 + (1 + I*Sqrt[7])*x + 4*x^2])/56","A",13,6,35,0.1714,1,"{2087, 800, 634, 618, 204, 628}"
252,1,230,0,0.3572676,"\int \frac{x \left(5+x+3 x^2+2 x^3\right)}{2+x+5 x^2+x^3+2 x^4} \, dx","Int[(x*(5 + x + 3*x^2 + 2*x^3))/(2 + x + 5*x^2 + x^3 + 2*x^4),x]","\frac{1}{28} \left(7+5 i \sqrt{7}\right) \log \left(4 x^2+\left(1-i \sqrt{7}\right) x+4\right)+\frac{1}{28} \left(7-5 i \sqrt{7}\right) \log \left(4 x^2+\left(1+i \sqrt{7}\right) x+4\right)+\frac{1}{14} \left(7+5 i \sqrt{7}\right) x+\frac{1}{14} \left(7-5 i \sqrt{7}\right) x-\frac{\left(7 \sqrt{7}+19 i\right) \tan ^{-1}\left(\frac{8 x-i \sqrt{7}+1}{\sqrt{2 \left(35+i \sqrt{7}\right)}}\right)}{\sqrt{14 \left(35+i \sqrt{7}\right)}}+\frac{\left(-7 \sqrt{7}+19 i\right) \tan ^{-1}\left(\frac{8 x+i \sqrt{7}+1}{\sqrt{2 \left(35-i \sqrt{7}\right)}}\right)}{\sqrt{14 \left(35-i \sqrt{7}\right)}}","\frac{1}{28} \left(7+5 i \sqrt{7}\right) \log \left(4 x^2+\left(1-i \sqrt{7}\right) x+4\right)+\frac{1}{28} \left(7-5 i \sqrt{7}\right) \log \left(4 x^2+\left(1+i \sqrt{7}\right) x+4\right)+\frac{1}{14} \left(7+5 i \sqrt{7}\right) x+\frac{1}{14} \left(7-5 i \sqrt{7}\right) x-\frac{\left(7 \sqrt{7}+19 i\right) \tan ^{-1}\left(\frac{8 x-i \sqrt{7}+1}{\sqrt{2 \left(35+i \sqrt{7}\right)}}\right)}{\sqrt{14 \left(35+i \sqrt{7}\right)}}+\frac{\left(-7 \sqrt{7}+19 i\right) \tan ^{-1}\left(\frac{8 x+i \sqrt{7}+1}{\sqrt{2 \left(35-i \sqrt{7}\right)}}\right)}{\sqrt{14 \left(35-i \sqrt{7}\right)}}",1,"((7 - (5*I)*Sqrt[7])*x)/14 + ((7 + (5*I)*Sqrt[7])*x)/14 - ((19*I + 7*Sqrt[7])*ArcTan[(1 - I*Sqrt[7] + 8*x)/Sqrt[2*(35 + I*Sqrt[7])]])/Sqrt[14*(35 + I*Sqrt[7])] + ((19*I - 7*Sqrt[7])*ArcTan[(1 + I*Sqrt[7] + 8*x)/Sqrt[2*(35 - I*Sqrt[7])]])/Sqrt[14*(35 - I*Sqrt[7])] + ((7 + (5*I)*Sqrt[7])*Log[4 + (1 - I*Sqrt[7])*x + 4*x^2])/28 + ((7 - (5*I)*Sqrt[7])*Log[4 + (1 + I*Sqrt[7])*x + 4*x^2])/28","A",11,6,33,0.1818,1,"{2087, 773, 634, 618, 204, 628}"
253,1,198,0,0.1944117,"\int \frac{5+x+3 x^2+2 x^3}{2+x+5 x^2+x^3+2 x^4} \, dx","Int[(5 + x + 3*x^2 + 2*x^3)/(2 + x + 5*x^2 + x^3 + 2*x^4),x]","\frac{1}{28} \left(7+5 i \sqrt{7}\right) \log \left(4 x^2+\left(1-i \sqrt{7}\right) x+4\right)+\frac{1}{28} \left(7-5 i \sqrt{7}\right) \log \left(4 x^2+\left(1+i \sqrt{7}\right) x+4\right)+\frac{\left(7 \sqrt{7}+19 i\right) \tan ^{-1}\left(\frac{8 x-i \sqrt{7}+1}{\sqrt{2 \left(35+i \sqrt{7}\right)}}\right)}{\sqrt{14 \left(35+i \sqrt{7}\right)}}-\frac{\left(-7 \sqrt{7}+19 i\right) \tan ^{-1}\left(\frac{8 x+i \sqrt{7}+1}{\sqrt{2 \left(35-i \sqrt{7}\right)}}\right)}{\sqrt{14 \left(35-i \sqrt{7}\right)}}","\frac{1}{28} \left(7+5 i \sqrt{7}\right) \log \left(4 x^2+\left(1-i \sqrt{7}\right) x+4\right)+\frac{1}{28} \left(7-5 i \sqrt{7}\right) \log \left(4 x^2+\left(1+i \sqrt{7}\right) x+4\right)+\frac{\left(7 \sqrt{7}+19 i\right) \tan ^{-1}\left(\frac{8 x-i \sqrt{7}+1}{\sqrt{2 \left(35+i \sqrt{7}\right)}}\right)}{\sqrt{14 \left(35+i \sqrt{7}\right)}}-\frac{\left(-7 \sqrt{7}+19 i\right) \tan ^{-1}\left(\frac{8 x+i \sqrt{7}+1}{\sqrt{2 \left(35-i \sqrt{7}\right)}}\right)}{\sqrt{14 \left(35-i \sqrt{7}\right)}}",1,"((19*I + 7*Sqrt[7])*ArcTan[(1 - I*Sqrt[7] + 8*x)/Sqrt[2*(35 + I*Sqrt[7])]])/Sqrt[14*(35 + I*Sqrt[7])] - ((19*I - 7*Sqrt[7])*ArcTan[(1 + I*Sqrt[7] + 8*x)/Sqrt[2*(35 - I*Sqrt[7])]])/Sqrt[14*(35 - I*Sqrt[7])] + ((7 + (5*I)*Sqrt[7])*Log[4 + (1 - I*Sqrt[7])*x + 4*x^2])/28 + ((7 - (5*I)*Sqrt[7])*Log[4 + (1 + I*Sqrt[7])*x + 4*x^2])/28","A",9,5,32,0.1562,1,"{2086, 634, 618, 204, 628}"
254,1,245,0,0.473188,"\int \frac{5+x+3 x^2+2 x^3}{x \left(2+x+5 x^2+x^3+2 x^4\right)} \, dx","Int[(5 + x + 3*x^2 + 2*x^3)/(x*(2 + x + 5*x^2 + x^3 + 2*x^4)),x]","-\frac{1}{56} \left(35-9 i \sqrt{7}\right) \log \left(4 i x^2+\left(-\sqrt{7}+i\right) x+4 i\right)-\frac{1}{56} \left(35+9 i \sqrt{7}\right) \log \left(4 i x^2+\left(\sqrt{7}+i\right) x+4 i\right)+\frac{1}{28} \left(35+9 i \sqrt{7}\right) \log (x)+\frac{1}{28} \left(35-9 i \sqrt{7}\right) \log (x)-\frac{\left(53+i \sqrt{7}\right) \tanh ^{-1}\left(\frac{8 i x-\sqrt{7}+i}{\sqrt{2 \left(35-i \sqrt{7}\right)}}\right)}{2 \sqrt{14 \left(35-i \sqrt{7}\right)}}+\frac{\left(53-i \sqrt{7}\right) \tanh ^{-1}\left(\frac{8 i x+\sqrt{7}+i}{\sqrt{2 \left(35+i \sqrt{7}\right)}}\right)}{2 \sqrt{14 \left(35+i \sqrt{7}\right)}}","-\frac{1}{56} \left(35-9 i \sqrt{7}\right) \log \left(4 i x^2+\left(-\sqrt{7}+i\right) x+4 i\right)-\frac{1}{56} \left(35+9 i \sqrt{7}\right) \log \left(4 i x^2+\left(\sqrt{7}+i\right) x+4 i\right)+\frac{1}{28} \left(35+9 i \sqrt{7}\right) \log (x)+\frac{1}{28} \left(35-9 i \sqrt{7}\right) \log (x)-\frac{\left(53+i \sqrt{7}\right) \tanh ^{-1}\left(\frac{8 i x-\sqrt{7}+i}{\sqrt{2 \left(35-i \sqrt{7}\right)}}\right)}{2 \sqrt{14 \left(35-i \sqrt{7}\right)}}+\frac{\left(53-i \sqrt{7}\right) \tanh ^{-1}\left(\frac{8 i x+\sqrt{7}+i}{\sqrt{2 \left(35+i \sqrt{7}\right)}}\right)}{2 \sqrt{14 \left(35+i \sqrt{7}\right)}}",1,"-((53 + I*Sqrt[7])*ArcTanh[(I - Sqrt[7] + (8*I)*x)/Sqrt[2*(35 - I*Sqrt[7])]])/(2*Sqrt[14*(35 - I*Sqrt[7])]) + ((53 - I*Sqrt[7])*ArcTanh[(I + Sqrt[7] + (8*I)*x)/Sqrt[2*(35 + I*Sqrt[7])]])/(2*Sqrt[14*(35 + I*Sqrt[7])]) + ((35 - (9*I)*Sqrt[7])*Log[x])/28 + ((35 + (9*I)*Sqrt[7])*Log[x])/28 - ((35 - (9*I)*Sqrt[7])*Log[4*I + (I - Sqrt[7])*x + (4*I)*x^2])/56 - ((35 + (9*I)*Sqrt[7])*Log[4*I + (I + Sqrt[7])*x + (4*I)*x^2])/56","A",13,6,35,0.1714,1,"{2087, 800, 634, 618, 206, 628}"
255,1,281,0,0.4673154,"\int \frac{5+x+3 x^2+2 x^3}{x^2 \left(2+x+5 x^2+x^3+2 x^4\right)} \, dx","Int[(5 + x + 3*x^2 + 2*x^3)/(x^2*(2 + x + 5*x^2 + x^3 + 2*x^4)),x]","\frac{3}{112} \left(7+11 i \sqrt{7}\right) \log \left(4 i x^2+\left(-\sqrt{7}+i\right) x+4 i\right)+\frac{3}{112} \left(7-11 i \sqrt{7}\right) \log \left(4 i x^2+\left(\sqrt{7}+i\right) x+4 i\right)-\frac{35+9 i \sqrt{7}}{28 x}-\frac{35-9 i \sqrt{7}}{28 x}-\frac{3}{56} \left(7+11 i \sqrt{7}\right) \log (x)-\frac{3}{56} \left(7-11 i \sqrt{7}\right) \log (x)+\frac{11 \left(9+5 i \sqrt{7}\right) \tanh ^{-1}\left(\frac{8 i x-\sqrt{7}+i}{\sqrt{2 \left(35-i \sqrt{7}\right)}}\right)}{4 \sqrt{14 \left(35-i \sqrt{7}\right)}}-\frac{11 \left(9-5 i \sqrt{7}\right) \tanh ^{-1}\left(\frac{8 i x+\sqrt{7}+i}{\sqrt{2 \left(35+i \sqrt{7}\right)}}\right)}{4 \sqrt{14 \left(35+i \sqrt{7}\right)}}","\frac{3}{112} \left(7+11 i \sqrt{7}\right) \log \left(4 i x^2+\left(-\sqrt{7}+i\right) x+4 i\right)+\frac{3}{112} \left(7-11 i \sqrt{7}\right) \log \left(4 i x^2+\left(\sqrt{7}+i\right) x+4 i\right)-\frac{35+9 i \sqrt{7}}{28 x}-\frac{35-9 i \sqrt{7}}{28 x}-\frac{3}{56} \left(7+11 i \sqrt{7}\right) \log (x)-\frac{3}{56} \left(7-11 i \sqrt{7}\right) \log (x)+\frac{11 \left(9+5 i \sqrt{7}\right) \tanh ^{-1}\left(\frac{8 i x-\sqrt{7}+i}{\sqrt{2 \left(35-i \sqrt{7}\right)}}\right)}{4 \sqrt{14 \left(35-i \sqrt{7}\right)}}-\frac{11 \left(9-5 i \sqrt{7}\right) \tanh ^{-1}\left(\frac{8 i x+\sqrt{7}+i}{\sqrt{2 \left(35+i \sqrt{7}\right)}}\right)}{4 \sqrt{14 \left(35+i \sqrt{7}\right)}}",1,"-(35 - (9*I)*Sqrt[7])/(28*x) - (35 + (9*I)*Sqrt[7])/(28*x) + (11*(9 + (5*I)*Sqrt[7])*ArcTanh[(I - Sqrt[7] + (8*I)*x)/Sqrt[2*(35 - I*Sqrt[7])]])/(4*Sqrt[14*(35 - I*Sqrt[7])]) - (11*(9 - (5*I)*Sqrt[7])*ArcTanh[(I + Sqrt[7] + (8*I)*x)/Sqrt[2*(35 + I*Sqrt[7])]])/(4*Sqrt[14*(35 + I*Sqrt[7])]) - (3*(7 - (11*I)*Sqrt[7])*Log[x])/56 - (3*(7 + (11*I)*Sqrt[7])*Log[x])/56 + (3*(7 + (11*I)*Sqrt[7])*Log[4*I + (I - Sqrt[7])*x + (4*I)*x^2])/112 + (3*(7 - (11*I)*Sqrt[7])*Log[4*I + (I + Sqrt[7])*x + (4*I)*x^2])/112","A",13,6,35,0.1714,1,"{2087, 800, 634, 618, 206, 628}"
256,1,317,0,0.5394177,"\int \frac{5+x+3 x^2+2 x^3}{x^3 \left(2+x+5 x^2+x^3+2 x^4\right)} \, dx","Int[(5 + x + 3*x^2 + 2*x^3)/(x^3*(2 + x + 5*x^2 + x^3 + 2*x^4)),x]","-\frac{35+9 i \sqrt{7}}{56 x^2}-\frac{35-9 i \sqrt{7}}{56 x^2}+\frac{1}{32} \left(35-9 i \sqrt{7}\right) \log \left(4 i x^2+\left(-\sqrt{7}+i\right) x+4 i\right)+\frac{1}{32} \left(35+9 i \sqrt{7}\right) \log \left(4 i x^2+\left(\sqrt{7}+i\right) x+4 i\right)+\frac{3 \left(7+11 i \sqrt{7}\right)}{56 x}+\frac{3 \left(7-11 i \sqrt{7}\right)}{56 x}-\frac{1}{16} \left(35+9 i \sqrt{7}\right) \log (x)-\frac{1}{16} \left(35-9 i \sqrt{7}\right) \log (x)+\frac{\left(355-73 i \sqrt{7}\right) \tanh ^{-1}\left(\frac{8 i x-\sqrt{7}+i}{\sqrt{2 \left(35-i \sqrt{7}\right)}}\right)}{8 \sqrt{14 \left(35-i \sqrt{7}\right)}}-\frac{\left(355+73 i \sqrt{7}\right) \tanh ^{-1}\left(\frac{8 i x+\sqrt{7}+i}{\sqrt{2 \left(35+i \sqrt{7}\right)}}\right)}{8 \sqrt{14 \left(35+i \sqrt{7}\right)}}","-\frac{35+9 i \sqrt{7}}{56 x^2}-\frac{35-9 i \sqrt{7}}{56 x^2}+\frac{1}{32} \left(35-9 i \sqrt{7}\right) \log \left(4 i x^2+\left(-\sqrt{7}+i\right) x+4 i\right)+\frac{1}{32} \left(35+9 i \sqrt{7}\right) \log \left(4 i x^2+\left(\sqrt{7}+i\right) x+4 i\right)+\frac{3 \left(7+11 i \sqrt{7}\right)}{56 x}+\frac{3 \left(7-11 i \sqrt{7}\right)}{56 x}-\frac{1}{16} \left(35+9 i \sqrt{7}\right) \log (x)-\frac{1}{16} \left(35-9 i \sqrt{7}\right) \log (x)+\frac{\left(355-73 i \sqrt{7}\right) \tanh ^{-1}\left(\frac{8 i x-\sqrt{7}+i}{\sqrt{2 \left(35-i \sqrt{7}\right)}}\right)}{8 \sqrt{14 \left(35-i \sqrt{7}\right)}}-\frac{\left(355+73 i \sqrt{7}\right) \tanh ^{-1}\left(\frac{8 i x+\sqrt{7}+i}{\sqrt{2 \left(35+i \sqrt{7}\right)}}\right)}{8 \sqrt{14 \left(35+i \sqrt{7}\right)}}",1,"-(35 - (9*I)*Sqrt[7])/(56*x^2) - (35 + (9*I)*Sqrt[7])/(56*x^2) + (3*(7 - (11*I)*Sqrt[7]))/(56*x) + (3*(7 + (11*I)*Sqrt[7]))/(56*x) + ((355 - (73*I)*Sqrt[7])*ArcTanh[(I - Sqrt[7] + (8*I)*x)/Sqrt[2*(35 - I*Sqrt[7])]])/(8*Sqrt[14*(35 - I*Sqrt[7])]) - ((355 + (73*I)*Sqrt[7])*ArcTanh[(I + Sqrt[7] + (8*I)*x)/Sqrt[2*(35 + I*Sqrt[7])]])/(8*Sqrt[14*(35 + I*Sqrt[7])]) - ((35 - (9*I)*Sqrt[7])*Log[x])/16 - ((35 + (9*I)*Sqrt[7])*Log[x])/16 + ((35 - (9*I)*Sqrt[7])*Log[4*I + (I - Sqrt[7])*x + (4*I)*x^2])/32 + ((35 + (9*I)*Sqrt[7])*Log[4*I + (I + Sqrt[7])*x + (4*I)*x^2])/32","A",13,6,35,0.1714,1,"{2087, 800, 634, 618, 206, 628}"
257,1,19,0,0.1047994,"\int \frac{x^2 \left(3 a+b x^2\right)}{a^2+2 a b x^2+b^2 x^4+c^2 x^6} \, dx","Int[(x^2*(3*a + b*x^2))/(a^2 + 2*a*b*x^2 + b^2*x^4 + c^2*x^6),x]","\frac{\tan ^{-1}\left(\frac{c x^3}{a+b x^2}\right)}{c}","\frac{\tan ^{-1}\left(\frac{c x^3}{a+b x^2}\right)}{c}",1,"ArcTan[(c*x^3)/(a + b*x^2)]/c","A",2,2,40,0.05000,1,"{2094, 205}"
258,1,43,0,0.0669825,"\int \frac{1-3 x^4}{(-2+x) \left(1+x^2\right)^2} \, dx","Int[(1 - 3*x^4)/((-2 + x)*(1 + x^2)^2),x]","-\frac{1-2 x}{5 \left(x^2+1\right)}-\frac{14}{25} \log \left(x^2+1\right)-\frac{47}{25} \log (2-x)-\frac{46}{25} \tan ^{-1}(x)","-\frac{1-2 x}{5 \left(x^2+1\right)}-\frac{14}{25} \log \left(x^2+1\right)-\frac{47}{25} \log (2-x)-\frac{46}{25} \tan ^{-1}(x)",1,"-(1 - 2*x)/(5*(1 + x^2)) - (46*ArcTan[x])/25 - (47*Log[2 - x])/25 - (14*Log[1 + x^2])/25","A",6,5,20,0.2500,1,"{1647, 1629, 635, 203, 260}"
259,1,17,0,0.0370496,"\int \frac{-9-9 x+2 x^2}{-9 x+x^3} \, dx","Int[(-9 - 9*x + 2*x^2)/(-9*x + x^3),x]","-\log (3-x)+\log (x)+2 \log (x+3)","-\log (3-x)+\log (x)+2 \log (x+3)",1,"-Log[3 - x] + Log[x] + 2*Log[3 + x]","A",3,2,20,0.1000,1,"{1593, 1802}"
260,1,25,0,0.0372468,"\int \frac{1+2 x^2+x^5}{-x+x^3} \, dx","Int[(1 + 2*x^2 + x^5)/(-x + x^3),x]","\frac{x^3}{3}+x+2 \log (1-x)-\log (x)+\log (x+1)","\frac{x^3}{3}+x+2 \log (1-x)-\log (x)+\log (x+1)",1,"x + x^3/3 + 2*Log[1 - x] - Log[x] + Log[1 + x]","A",3,2,20,0.1000,1,"{1593, 1802}"
261,1,22,0,0.0133821,"\int \frac{3+2 x^2}{(-1+x)^2 x} \, dx","Int[(3 + 2*x^2)/((-1 + x)^2*x),x]","\frac{5}{1-x}-\log (1-x)+3 \log (x)","\frac{5}{1-x}-\log (1-x)+3 \log (x)",1,"5/(1 - x) - Log[1 - x] + 3*Log[x]","A",2,1,16,0.06250,1,"{894}"
262,1,27,0,0.0389818,"\int \frac{-1+2 x^2}{(-1+4 x) \left(1+x^2\right)} \, dx","Int[(-1 + 2*x^2)/((-1 + 4*x)*(1 + x^2)),x]","\frac{6}{17} \log \left(x^2+1\right)-\frac{7}{34} \log (1-4 x)+\frac{3}{17} \tan ^{-1}(x)","\frac{6}{17} \log \left(x^2+1\right)-\frac{7}{34} \log (1-4 x)+\frac{3}{17} \tan ^{-1}(x)",1,"(3*ArcTan[x])/17 - (7*Log[1 - 4*x])/34 + (6*Log[1 + x^2])/17","A",5,4,22,0.1818,1,"{1629, 635, 203, 260}"
263,1,21,0,0.0145165,"\int \frac{-3+2 x-3 x^2+x^3}{1+x^2} \, dx","Int[(-3 + 2*x - 3*x^2 + x^3)/(1 + x^2),x]","\frac{x^2}{2}+\frac{1}{2} \log \left(x^2+1\right)-3 x","\frac{x^2}{2}+\frac{1}{2} \log \left(x^2+1\right)-3 x",1,"-3*x + x^2/2 + Log[1 + x^2]/2","A",3,2,21,0.09524,1,"{1810, 260}"
264,1,27,0,0.0257398,"\int \frac{x+10 x^2+6 x^3+x^4}{10+6 x+x^2} \, dx","Int[(x + 10*x^2 + 6*x^3 + x^4)/(10 + 6*x + x^2),x]","\frac{x^3}{3}+\frac{1}{2} \log \left(x^2+6 x+10\right)-3 \tan ^{-1}(x+3)","\frac{x^3}{3}+\frac{1}{2} \log \left(x^2+6 x+10\right)-3 \tan ^{-1}(x+3)",1,"x^3/3 - 3*ArcTan[3 + x] + Log[10 + 6*x + x^2]/2","A",6,5,26,0.1923,1,"{1657, 634, 618, 204, 628}"
265,1,39,0,0.0199904,"\int \frac{1}{-18+27 x-7 x^2-3 x^3+x^4} \, dx","Int[(-18 + 27*x - 7*x^2 - 3*x^3 + x^4)^(-1),x]","\frac{1}{8} \log (1-x)-\frac{1}{5} \log (2-x)+\frac{1}{12} \log (3-x)-\frac{1}{120} \log (x+3)","\frac{1}{8} \log (1-x)-\frac{1}{5} \log (2-x)+\frac{1}{12} \log (3-x)-\frac{1}{120} \log (x+3)",1,"Log[1 - x]/8 - Log[2 - x]/5 + Log[3 - x]/12 - Log[3 + x]/120","A",2,1,20,0.05000,1,"{2058}"
266,1,22,0,0.0145268,"\int \frac{1+x^3}{-2+x} \, dx","Int[(1 + x^3)/(-2 + x),x]","\frac{x^3}{3}+x^2+4 x+9 \log (2-x)","\frac{x^3}{3}+x^2+4 x+9 \log (2-x)",1,"4*x + x^2 + x^3/3 + 9*Log[2 - x]","A",2,1,11,0.09091,1,"{1850}"
267,1,15,0,0.0291245,"\int \frac{3 x-4 x^2+3 x^3}{1+x^2} \, dx","Int[(3*x - 4*x^2 + 3*x^3)/(1 + x^2),x]","\frac{3 x^2}{2}-4 x+4 \tan ^{-1}(x)","\frac{3 x^2}{2}-4 x+4 \tan ^{-1}(x)",1,"-4*x + (3*x^2)/2 + 4*ArcTan[x]","A",4,3,22,0.1364,1,"{1594, 1802, 203}"
268,1,12,0,0.0207068,"\int \frac{5+3 x}{1-x-x^2+x^3} \, dx","Int[(5 + 3*x)/(1 - x - x^2 + x^3),x]","\frac{4}{1-x}+\tanh ^{-1}(x)","\frac{4}{1-x}+\tanh ^{-1}(x)",1,"4/(1 - x) + ArcTanh[x]","A",3,2,21,0.09524,1,"{2074, 206}"
269,1,25,0,0.0356623,"\int \frac{-1-x-x^3+x^4}{-x^2+x^3} \, dx","Int[(-1 - x - x^3 + x^4)/(-x^2 + x^3),x]","\frac{x^2}{2}-\frac{1}{x}-2 \log (1-x)+2 \log (x)","\frac{x^2}{2}-\frac{1}{x}-2 \log (1-x)+2 \log (x)",1,"-x^(-1) + x^2/2 - 2*Log[1 - x] + 2*Log[x]","A",3,2,25,0.08000,1,"{1593, 1620}"
270,1,13,0,0.0283439,"\int \frac{2+x+x^2+x^3}{2+3 x^2+x^4} \, dx","Int[(2 + x + x^2 + x^3)/(2 + 3*x^2 + x^4),x]","\frac{1}{2} \log \left(x^2+2\right)+\tan ^{-1}(x)","\frac{1}{2} \log \left(x^2+2\right)+\tan ^{-1}(x)",1,"ArcTan[x] + Log[2 + x^2]/2","A",6,6,22,0.2727,1,"{1673, 1149, 203, 1247, 626, 31}"
271,1,35,0,0.0336383,"\int \frac{-4+8 x-4 x^2+4 x^3-x^4+x^5}{\left(2+x^2\right)^3} \, dx","Int[(-4 + 8*x - 4*x^2 + 4*x^3 - x^4 + x^5)/(2 + x^2)^3,x]","-\frac{1}{\left(x^2+2\right)^2}+\frac{1}{2} \log \left(x^2+2\right)-\frac{\tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)}{\sqrt{2}}","-\frac{1}{\left(x^2+2\right)^2}+\frac{1}{2} \log \left(x^2+2\right)-\frac{\tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)}{\sqrt{2}}",1,"-(2 + x^2)^(-2) - ArcTan[x/Sqrt[2]]/Sqrt[2] + Log[2 + x^2]/2","A",5,5,31,0.1613,1,"{1814, 1586, 635, 203, 260}"
272,1,23,0,0.0367433,"\int \frac{-1-3 x+x^2}{-2 x+x^2+x^3} \, dx","Int[(-1 - 3*x + x^2)/(-2*x + x^2 + x^3),x]","-\log (1-x)+\frac{\log (x)}{2}+\frac{3}{2} \log (x+2)","-\log (1-x)+\frac{\log (x)}{2}+\frac{3}{2} \log (x+2)",1,"-Log[1 - x] + Log[x]/2 + (3*Log[2 + x])/2","A",3,2,21,0.09524,1,"{1594, 1628}"
273,1,23,0,0.0540768,"\int \frac{3-x+3 x^2-2 x^3+x^4}{3 x-2 x^2+x^3} \, dx","Int[(3 - x + 3*x^2 - 2*x^3 + x^4)/(3*x - 2*x^2 + x^3),x]","\frac{x^2}{2}-\frac{1}{2} \log \left(x^2-2 x+3\right)+\log (x)","\frac{x^2}{2}-\frac{1}{2} \log \left(x^2-2 x+3\right)+\log (x)",1,"x^2/2 + Log[x] - Log[3 - 2*x + x^2]/2","A",4,3,33,0.09091,1,"{1594, 1628, 628}"
274,1,29,0,0.0137334,"\int \frac{-1+x+x^3}{\left(1+x^2\right)^2} \, dx","Int[(-1 + x + x^3)/(1 + x^2)^2,x]","-\frac{x}{2 \left(x^2+1\right)}+\frac{1}{2} \log \left(x^2+1\right)-\frac{1}{2} \tan ^{-1}(x)","-\frac{x}{2 \left(x^2+1\right)}+\frac{1}{2} \log \left(x^2+1\right)-\frac{1}{2} \tan ^{-1}(x)",1,"-x/(2*(1 + x^2)) - ArcTan[x]/2 + Log[1 + x^2]/2","A",4,4,14,0.2857,1,"{1814, 635, 203, 260}"
275,1,44,0,0.2425294,"\int \frac{1+2 x-x^2+8 x^3+x^4}{\left(x+x^2\right) \left(1+x^3\right)} \, dx","Int[(1 + 2*x - x^2 + 8*x^3 + x^4)/((x + x^2)*(1 + x^3)),x]","\log \left(x^2-x+1\right)-\frac{3}{x+1}+\log (x)-2 \log (x+1)-\frac{2 \tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{\sqrt{3}}","\log \left(x^2-x+1\right)-\frac{3}{x+1}+\log (x)-2 \log (x+1)-\frac{2 \tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{\sqrt{3}}",1,"-3/(1 + x) - (2*ArcTan[(1 - 2*x)/Sqrt[3]])/Sqrt[3] + Log[x] - 2*Log[1 + x] + Log[1 - x + x^2]","A",7,6,33,0.1818,1,"{1593, 6725, 634, 618, 204, 628}"
276,1,46,0,0.1332399,"\int \frac{15-5 x+x^2+x^3}{\left(5+x^2\right) \left(3+2 x+x^2\right)} \, dx","Int[(15 - 5*x + x^2 + x^3)/((5 + x^2)*(3 + 2*x + x^2)),x]","\frac{1}{2} \log \left(x^2+2 x+3\right)-\sqrt{5} \tan ^{-1}\left(\frac{x}{\sqrt{5}}\right)+\frac{5 \tan ^{-1}\left(\frac{x+1}{\sqrt{2}}\right)}{\sqrt{2}}","\frac{1}{2} \log \left(x^2+2 x+3\right)-\sqrt{5} \tan ^{-1}\left(\frac{x}{\sqrt{5}}\right)+\frac{5 \tan ^{-1}\left(\frac{x+1}{\sqrt{2}}\right)}{\sqrt{2}}",1,"-(Sqrt[5]*ArcTan[x/Sqrt[5]]) + (5*ArcTan[(1 + x)/Sqrt[2]])/Sqrt[2] + Log[3 + 2*x + x^2]/2","A",7,6,29,0.2069,1,"{6725, 203, 634, 618, 204, 628}"
277,1,33,0,0.1656212,"\int \frac{-3+25 x+23 x^2+32 x^3+15 x^4+7 x^5+x^6}{\left(1+x^2\right)^2 \left(2+x+x^2\right)^2} \, dx","Int[(-3 + 25*x + 23*x^2 + 32*x^3 + 15*x^4 + 7*x^5 + x^6)/((1 + x^2)^2*(2 + x + x^2)^2),x]","-\frac{3}{x^2+1}+\frac{1}{x^2+x+2}+\log \left(x^2+1\right)-\log \left(x^2+x+2\right)","-\frac{3}{x^2+1}+\frac{1}{x^2+x+2}+\log \left(x^2+1\right)-\log \left(x^2+x+2\right)",1,"-3/(1 + x^2) + (2 + x + x^2)^(-1) + Log[1 + x^2] - Log[2 + x + x^2]","A",6,5,44,0.1136,1,"{6742, 261, 260, 629, 628}"
278,1,17,0,0.0065376,"\int \frac{1}{\left(1+x^2\right) \left(4+x^2\right)} \, dx","Int[1/((1 + x^2)*(4 + x^2)),x]","\frac{1}{3} \tan ^{-1}(x)-\frac{1}{6} \tan ^{-1}\left(\frac{x}{2}\right)","\frac{1}{3} \tan ^{-1}(x)-\frac{1}{6} \tan ^{-1}\left(\frac{x}{2}\right)",1,"-ArcTan[x/2]/6 + ArcTan[x]/3","A",3,2,15,0.1333,1,"{391, 203}"
279,1,24,0,0.0183818,"\int \frac{a+b x^3}{1+x^2} \, dx","Int[(a + b*x^3)/(1 + x^2),x]","a \tan ^{-1}(x)+\frac{b x^2}{2}-\frac{1}{2} b \log \left(x^2+1\right)","a \tan ^{-1}(x)+\frac{b x^2}{2}-\frac{1}{2} b \log \left(x^2+1\right)",1,"(b*x^2)/2 + a*ArcTan[x] - (b*Log[1 + x^2])/2","A",5,4,15,0.2667,1,"{1810, 635, 203, 260}"
280,1,15,0,0.0604497,"\int \frac{x+x^2}{(4+x) \left(-4+x^2\right)} \, dx","Int[(x + x^2)/((4 + x)*(-4 + x^2)),x]","\log (x+4)-\frac{1}{2} \tanh ^{-1}\left(\frac{x}{2}\right)","\log (x+4)-\frac{1}{2} \tanh ^{-1}\left(\frac{x}{2}\right)",1,"-ArcTanh[x/2]/2 + Log[4 + x]","A",4,3,18,0.1667,1,"{1593, 1629, 207}"
281,1,20,0,0.0121168,"\int \frac{4+x^2}{\left(1+x^2\right) \left(2+x^2\right)} \, dx","Int[(4 + x^2)/((1 + x^2)*(2 + x^2)),x]","3 \tan ^{-1}(x)-\sqrt{2} \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)","3 \tan ^{-1}(x)-\sqrt{2} \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)",1,"3*ArcTan[x] - Sqrt[2]*ArcTan[x/Sqrt[2]]","A",3,2,20,0.1000,1,"{522, 203}"
282,1,37,0,0.0397911,"\int \frac{5-4 x+3 x^2+x^4}{(-1+x)^2 \left(1+x^2\right)} \, dx","Int[(5 - 4*x + 3*x^2 + x^4)/((-1 + x)^2*(1 + x^2)),x]","\frac{3}{4} \log \left(x^2+1\right)+x+\frac{5}{2 (1-x)}+\frac{1}{2} \log (1-x)+2 \tan ^{-1}(x)","\frac{3}{4} \log \left(x^2+1\right)+x+\frac{5}{2 (1-x)}+\frac{1}{2} \log (1-x)+2 \tan ^{-1}(x)",1,"5/(2*(1 - x)) + x + 2*ArcTan[x] + Log[1 - x]/2 + (3*Log[1 + x^2])/4","A",5,4,26,0.1538,1,"{1629, 635, 203, 260}"
283,1,26,0,0.0107413,"\int \frac{1+x^4}{2+x^2} \, dx","Int[(1 + x^4)/(2 + x^2),x]","\frac{x^3}{3}-2 x+\frac{5 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)}{\sqrt{2}}","\frac{x^3}{3}-2 x+\frac{5 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)}{\sqrt{2}}",1,"-2*x + x^3/3 + (5*ArcTan[x/Sqrt[2]])/Sqrt[2]","A",3,2,13,0.1538,1,"{1154, 203}"
284,1,12,0,0.0320389,"\int \frac{2+2 x+x^4}{x^4+x^5} \, dx","Int[(2 + 2*x + x^4)/(x^4 + x^5),x]","\log (x+1)-\frac{2}{3 x^3}","\log (x+1)-\frac{2}{3 x^3}",1,"-2/(3*x^3) + Log[1 + x]","A",3,2,18,0.1111,1,"{1593, 1620}"
285,1,21,0,0.0298171,"\int \frac{-1-5 x+2 x^2}{2-x-2 x^2+x^3} \, dx","Int[(-1 - 5*x + 2*x^2)/(2 - x - 2*x^2 + x^3),x]","2 \log (1-x)-\log (2-x)+\log (x+1)","2 \log (1-x)-\log (2-x)+\log (x+1)",1,"2*Log[1 - x] - Log[2 - x] + Log[1 + x]","A",2,1,26,0.03846,1,"{2074}"
286,1,22,0,0.0145003,"\int \frac{2+x+x^3}{1+2 x^2+x^4} \, dx","Int[(2 + x + x^3)/(1 + 2*x^2 + x^4),x]","\frac{x}{x^2+1}+\frac{1}{2} \log \left(x^2+1\right)+\tan ^{-1}(x)","\frac{x}{x^2+1}+\frac{1}{2} \log \left(x^2+1\right)+\tan ^{-1}(x)",1,"x/(1 + x^2) + ArcTan[x] + Log[1 + x^2]/2","A",5,5,19,0.2632,1,"{28, 1814, 635, 203, 260}"
287,1,24,0,0.0159376,"\int \frac{1+2 x+x^2+x^3}{1+2 x^2+x^4} \, dx","Int[(1 + 2*x + x^2 + x^3)/(1 + 2*x^2 + x^4),x]","-\frac{1}{2 \left(x^2+1\right)}+\frac{1}{2} \log \left(x^2+1\right)+\tan ^{-1}(x)","-\frac{1}{2 \left(x^2+1\right)}+\frac{1}{2} \log \left(x^2+1\right)+\tan ^{-1}(x)",1,"-1/(2*(1 + x^2)) + ArcTan[x] + Log[1 + x^2]/2","A",5,5,24,0.2083,1,"{28, 1814, 635, 203, 260}"
288,1,36,0,0.0261453,"\int \frac{3+4 x}{\left(1+x^2\right) \left(2+x^2\right)} \, dx","Int[(3 + 4*x)/((1 + x^2)*(2 + x^2)),x]","2 \log \left(x^2+1\right)-2 \log \left(x^2+2\right)+3 \tan ^{-1}(x)-\frac{3 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)}{\sqrt{2}}","2 \log \left(x^2+1\right)-2 \log \left(x^2+2\right)+3 \tan ^{-1}(x)-\frac{3 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)}{\sqrt{2}}",1,"3*ArcTan[x] - (3*ArcTan[x/Sqrt[2]])/Sqrt[2] + 2*Log[1 + x^2] - 2*Log[2 + x^2]","A",8,6,20,0.3000,1,"{1010, 391, 203, 444, 36, 31}"
289,1,37,0,0.023859,"\int \frac{2+x}{\left(1+x^2\right) \left(4+x^2\right)} \, dx","Int[(2 + x)/((1 + x^2)*(4 + x^2)),x]","\frac{1}{6} \log \left(x^2+1\right)-\frac{1}{6} \log \left(x^2+4\right)-\frac{1}{3} \tan ^{-1}\left(\frac{x}{2}\right)+\frac{2}{3} \tan ^{-1}(x)","\frac{1}{6} \log \left(x^2+1\right)-\frac{1}{6} \log \left(x^2+4\right)-\frac{1}{3} \tan ^{-1}\left(\frac{x}{2}\right)+\frac{2}{3} \tan ^{-1}(x)",1,"-ArcTan[x/2]/3 + (2*ArcTan[x])/3 + Log[1 + x^2]/6 - Log[4 + x^2]/6","A",8,6,18,0.3333,1,"{1010, 391, 203, 444, 36, 31}"
290,1,29,0,0.0165118,"\int \frac{2-x+x^3}{-7-6 x+x^2} \, dx","Int[(2 - x + x^3)/(-7 - 6*x + x^2),x]","\frac{x^2}{2}+6 x+\frac{169}{4} \log (7-x)-\frac{1}{4} \log (x+1)","\frac{x^2}{2}+6 x+\frac{169}{4} \log (7-x)-\frac{1}{4} \log (x+1)",1,"6*x + x^2/2 + (169*Log[7 - x])/4 - Log[1 + x]/4","A",5,3,19,0.1579,1,"{1657, 632, 31}"
291,1,19,0,0.0132435,"\int \frac{-1+x^5}{-1+x^2} \, dx","Int[(-1 + x^5)/(-1 + x^2),x]","\frac{x^4}{4}+\frac{x^2}{2}+\log (x+1)","\frac{x^4}{4}+\frac{x^2}{2}+\log (x+1)",1,"x^2/2 + x^4/4 + Log[1 + x]","A",4,3,13,0.2308,1,"{1810, 627, 31}"
292,1,41,0,0.0278992,"\int \frac{5+2 x-x^2+x^3}{1+x+x^2} \, dx","Int[(5 + 2*x - x^2 + x^3)/(1 + x + x^2),x]","\frac{x^2}{2}+\frac{3}{2} \log \left(x^2+x+1\right)-2 x+\frac{11 \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{\sqrt{3}}","\frac{x^2}{2}+\frac{3}{2} \log \left(x^2+x+1\right)-2 x+\frac{11 \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{\sqrt{3}}",1,"-2*x + x^2/2 + (11*ArcTan[(1 + 2*x)/Sqrt[3]])/Sqrt[3] + (3*Log[1 + x + x^2])/2","A",6,5,22,0.2273,1,"{1657, 634, 618, 204, 628}"
293,1,41,0,0.0276182,"\int \frac{-3+x-2 x^3+x^4}{10-8 x+2 x^2} \, dx","Int[(-3 + x - 2*x^3 + x^4)/(10 - 8*x + 2*x^2),x]","\frac{x^3}{6}+\frac{x^2}{2}+\frac{3}{4} \log \left(x^2-4 x+5\right)+\frac{3 x}{2}+6 \tan ^{-1}(2-x)","\frac{x^3}{6}+\frac{x^2}{2}+\frac{3}{4} \log \left(x^2-4 x+5\right)+\frac{3 x}{2}+6 \tan ^{-1}(2-x)",1,"(3*x)/2 + x^2/2 + x^3/6 + 6*ArcTan[2 - x] + (3*Log[5 - 4*x + x^2])/4","A",6,5,24,0.2083,1,"{1657, 634, 618, 204, 628}"
294,1,30,0,0.0576631,"\int \frac{1+2 x+3 x^2+x^3}{(-3+x) (-2+x) (-1+x)} \, dx","Int[(1 + 2*x + 3*x^2 + x^3)/((-3 + x)*(-2 + x)*(-1 + x)),x]","x+\frac{7}{2} \log (1-x)-25 \log (2-x)+\frac{61}{2} \log (3-x)","x+\frac{7}{2} \log (1-x)-25 \log (2-x)+\frac{61}{2} \log (3-x)",1,"x + (7*Log[1 - x])/2 - 25*Log[2 - x] + (61*Log[3 - x])/2","A",2,1,29,0.03448,1,"{1612}"
295,1,35,0,0.0397596,"\int \frac{2-7 x+x^2-x^3+x^4}{-24-14 x+x^2+x^3} \, dx","Int[(2 - 7*x + x^2 - x^3 + x^4)/(-24 - 14*x + x^2 + x^3),x]","\frac{x^2}{2}-2 x+\frac{13}{3} \log (4-x)-\frac{22}{3} \log (x+2)+20 \log (x+3)","\frac{x^2}{2}-2 x+\frac{13}{3} \log (4-x)-\frac{22}{3} \log (x+2)+20 \log (x+3)",1,"-2*x + x^2/2 + (13*Log[4 - x])/3 - (22*Log[2 + x])/3 + 20*Log[3 + x]","A",2,1,30,0.03333,1,"{2074}"
296,1,34,0,0.0574547,"\int \frac{2+x^2}{(-1+x)^2 x (1+x)} \, dx","Int[(2 + x^2)/((-1 + x)^2*x*(1 + x)),x]","\frac{3}{2 (1-x)}-\frac{5}{4} \log (1-x)+2 \log (x)-\frac{3}{4} \log (x+1)","\frac{3}{2 (1-x)}-\frac{5}{4} \log (1-x)+2 \log (x)-\frac{3}{4} \log (x+1)",1,"3/(2*(1 - x)) - (5*Log[1 - x])/4 + 2*Log[x] - (3*Log[1 + x])/4","A",2,1,19,0.05263,1,"{1612}"
297,1,42,0,0.0209896,"\int \frac{3+x^2+x^3}{\left(2+x^2\right)^2} \, dx","Int[(3 + x^2 + x^3)/(2 + x^2)^2,x]","\frac{x+4}{4 \left(x^2+2\right)}+\frac{1}{2} \log \left(x^2+2\right)+\frac{5 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)}{4 \sqrt{2}}","\frac{x+4}{4 \left(x^2+2\right)}+\frac{1}{2} \log \left(x^2+2\right)+\frac{5 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)}{4 \sqrt{2}}",1,"(4 + x)/(4*(2 + x^2)) + (5*ArcTan[x/Sqrt[2]])/(4*Sqrt[2]) + Log[2 + x^2]/2","A",4,4,16,0.2500,1,"{1814, 635, 203, 260}"
298,1,49,0,0.1567065,"\int \frac{-35+70 x-4 x^2+2 x^3}{\left(26-10 x+x^2\right) \left(17-2 x+x^2\right)} \, dx","Int[(-35 + 70*x - 4*x^2 + 2*x^3)/((26 - 10*x + x^2)*(17 - 2*x + x^2)),x]","\frac{1003 \log \left(x^2-10 x+26\right)}{1025}+\frac{22 \log \left(x^2-2 x+17\right)}{1025}-\frac{15033 \tan ^{-1}(5-x)}{1025}-\frac{4607 \tan ^{-1}\left(\frac{x-1}{4}\right)}{4100}","\frac{1003 \log \left(x^2-10 x+26\right)}{1025}+\frac{22 \log \left(x^2-2 x+17\right)}{1025}-\frac{15033 \tan ^{-1}(5-x)}{1025}-\frac{4607 \tan ^{-1}\left(\frac{x-1}{4}\right)}{4100}",1,"(-15033*ArcTan[5 - x])/1025 - (4607*ArcTan[(-1 + x)/4])/4100 + (1003*Log[26 - 10*x + x^2])/1025 + (22*Log[17 - 2*x + x^2])/1025","A",10,5,36,0.1389,1,"{6728, 634, 618, 204, 628}"
299,1,29,0,0.0528289,"\int \frac{2+x^2}{(-5+x) (-3+x) (4+x)} \, dx","Int[(2 + x^2)/((-5 + x)*(-3 + x)*(4 + x)),x]","-\frac{11}{14} \log (3-x)+\frac{3}{2} \log (5-x)+\frac{2}{7} \log (x+4)","-\frac{11}{14} \log (3-x)+\frac{3}{2} \log (5-x)+\frac{2}{7} \log (x+4)",1,"(-11*Log[3 - x])/14 + (3*Log[5 - x])/2 + (2*Log[4 + x])/7","A",2,1,21,0.04762,1,"{1612}"
300,1,46,0,0.0444875,"\int \frac{x^4}{(-1+x) \left(2+x^2\right)} \, dx","Int[x^4/((-1 + x)*(2 + x^2)),x]","\frac{x^2}{2}-\frac{2}{3} \log \left(x^2+2\right)+x+\frac{1}{3} \log (1-x)-\frac{2}{3} \sqrt{2} \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)","\frac{x^2}{2}-\frac{2}{3} \log \left(x^2+2\right)+x+\frac{1}{3} \log (1-x)-\frac{2}{3} \sqrt{2} \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)",1,"x + x^2/2 - (2*Sqrt[2]*ArcTan[x/Sqrt[2]])/3 + Log[1 - x]/3 - (2*Log[2 + x^2])/3","A",5,4,16,0.2500,1,"{1629, 635, 203, 260}"
301,1,16,0,0.0249667,"\int \frac{-1+7 x+2 x^2}{-1-x+x^2+x^3} \, dx","Int[(-1 + 7*x + 2*x^2)/(-1 - x + x^2 + x^3),x]","2 \log (1-x)-\frac{3}{x+1}","2 \log (1-x)-\frac{3}{x+1}",1,"-3/(1 + x) + 2*Log[1 - x]","A",2,1,24,0.04167,1,"{2074}"
302,1,21,0,0.0192289,"\int \frac{1+2 x}{-1+3 x-3 x^2+x^3} \, dx","Int[(1 + 2*x)/(-1 + 3*x - 3*x^2 + x^3),x]","\frac{2}{1-x}-\frac{3}{2 (1-x)^2}","\frac{2}{1-x}-\frac{3}{2 (1-x)^2}",1,"-3/(2*(1 - x)^2) + 2/(1 - x)","A",2,1,21,0.04762,1,"{2074}"
303,1,15,0,0.0270943,"\int \frac{5-5 x+7 x^2+x^3}{(-1+x)^2 (1+x)^3} \, dx","Int[(5 - 5*x + 7*x^2 + x^3)/((-1 + x)^2*(1 + x)^3),x]","\frac{1}{1-x}-\frac{2}{(x+1)^2}","\frac{1}{1-x}-\frac{2}{(x+1)^2}",1,"(1 - x)^(-1) - 2/(1 + x)^2","A",2,1,24,0.04167,1,"{1620}"
304,1,31,0,0.0421315,"\int \frac{1+3 x+3 x^2}{1+2 x+2 x^2+x^3} \, dx","Int[(1 + 3*x + 3*x^2)/(1 + 2*x + 2*x^2 + x^3),x]","\log \left(x^2+x+1\right)+\log (x+1)-\frac{2 \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{\sqrt{3}}","\log \left(x^2+x+1\right)+\log (x+1)-\frac{2 \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{\sqrt{3}}",1,"(-2*ArcTan[(1 + 2*x)/Sqrt[3]])/Sqrt[3] + Log[1 + x] + Log[1 + x + x^2]","A",6,5,26,0.1923,1,"{2074, 634, 618, 204, 628}"
305,1,25,0,0.0417384,"\int \frac{-1+2 x+x^2}{-2 x+3 x^2+2 x^3} \, dx","Int[(-1 + 2*x + x^2)/(-2*x + 3*x^2 + 2*x^3),x]","\frac{1}{10} \log (1-2 x)+\frac{\log (x)}{2}-\frac{1}{10} \log (x+2)","\frac{1}{10} \log (1-2 x)+\frac{\log (x)}{2}-\frac{1}{10} \log (x+2)",1,"Log[1 - 2*x]/10 + Log[x]/2 - Log[2 + x]/10","A",3,2,25,0.08000,1,"{1594, 1628}"
306,1,30,0,0.0298323,"\int \frac{1+4 x-2 x^2+x^4}{1-x-x^2+x^3} \, dx","Int[(1 + 4*x - 2*x^2 + x^4)/(1 - x - x^2 + x^3),x]","\frac{x^2}{2}+x+\frac{2}{1-x}+\log (1-x)-\log (x+1)","\frac{x^2}{2}+x+\frac{2}{1-x}+\log (1-x)-\log (x+1)",1,"2/(1 - x) + x + x^2/2 + Log[1 - x] - Log[1 + x]","A",2,1,29,0.03448,1,"{2074}"
307,1,23,0,0.0378514,"\int \frac{4-x+2 x^2}{4 x+x^3} \, dx","Int[(4 - x + 2*x^2)/(4*x + x^3),x]","\frac{1}{2} \log \left(x^2+4\right)+\log (x)-\frac{1}{2} \tan ^{-1}\left(\frac{x}{2}\right)","\frac{1}{2} \log \left(x^2+4\right)+\log (x)-\frac{1}{2} \tan ^{-1}\left(\frac{x}{2}\right)",1,"-ArcTan[x/2]/2 + Log[x] + Log[4 + x^2]/2","A",6,5,20,0.2500,1,"{1593, 1802, 635, 203, 260}"
308,1,103,0,0.4758189,"\int \frac{1+x^2+x^3}{(-1+x) x \left(1+x^2\right)^3 \left(1+x+x^2\right)} \, dx","Int[(1 + x^2 + x^3)/((-1 + x)*x*(1 + x^2)^3*(1 + x + x^2)),x]","-\frac{3 (1-x)}{8 \left(x^2+1\right)}+\frac{3 x}{16 \left(x^2+1\right)}+\frac{x+1}{8 \left(x^2+1\right)^2}+\frac{15}{16} \log \left(x^2+1\right)-\frac{1}{2} \log \left(x^2+x+1\right)+\frac{1}{8} \log (1-x)-\log (x)+\frac{7}{16} \tan ^{-1}(x)-\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{\sqrt{3}}","-\frac{3 (1-x)}{8 \left(x^2+1\right)}+\frac{3 x}{16 \left(x^2+1\right)}+\frac{x+1}{8 \left(x^2+1\right)^2}+\frac{15}{16} \log \left(x^2+1\right)-\frac{1}{2} \log \left(x^2+x+1\right)+\frac{1}{8} \log (1-x)-\log (x)+\frac{7}{16} \tan ^{-1}(x)-\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{\sqrt{3}}",1,"(1 + x)/(8*(1 + x^2)^2) - (3*(1 - x))/(8*(1 + x^2)) + (3*x)/(16*(1 + x^2)) + (7*ArcTan[x])/16 - ArcTan[(1 + 2*x)/Sqrt[3]]/Sqrt[3] + Log[1 - x]/8 - Log[x] + (15*Log[1 + x^2])/16 - Log[1 + x + x^2]/2","A",14,10,32,0.3125,1,"{6728, 639, 199, 203, 635, 260, 634, 618, 204, 628}"
309,1,33,0,0.0167461,"\int \frac{1-3 x+2 x^2-x^3}{\left(1+x^2\right)^2} \, dx","Int[(1 - 3*x + 2*x^2 - x^3)/(1 + x^2)^2,x]","\frac{2-x}{2 \left(x^2+1\right)}-\frac{1}{2} \log \left(x^2+1\right)+\frac{3}{2} \tan ^{-1}(x)","\frac{2-x}{2 \left(x^2+1\right)}-\frac{1}{2} \log \left(x^2+1\right)+\frac{3}{2} \tan ^{-1}(x)",1,"(2 - x)/(2*(1 + x^2)) + (3*ArcTan[x])/2 - Log[1 + x^2]/2","A",4,4,23,0.1739,1,"{1814, 635, 203, 260}"
310,1,33,0,0.0409266,"\int \frac{1-3 x+2 x^2-x^3}{x \left(1+x^2\right)^2} \, dx","Int[(1 - 3*x + 2*x^2 - x^3)/(x*(1 + x^2)^2),x]","-\frac{2 x+1}{2 \left(x^2+1\right)}-\frac{1}{2} \log \left(x^2+1\right)+\log (x)-2 \tan ^{-1}(x)","-\frac{2 x+1}{2 \left(x^2+1\right)}-\frac{1}{2} \log \left(x^2+1\right)+\log (x)-2 \tan ^{-1}(x)",1,"-(1 + 2*x)/(2*(1 + x^2)) - 2*ArcTan[x] + Log[x] - Log[1 + x^2]/2","A",6,5,26,0.1923,1,"{1805, 801, 635, 203, 260}"
311,1,25,0,0.040968,"\int \frac{1-x-x^2+x^3+x^4}{-x+x^3} \, dx","Int[(1 - x - x^2 + x^3 + x^4)/(-x + x^3),x]","\frac{x^2}{2}+\frac{1}{2} \log \left(1-x^2\right)+x-\log (x)","\frac{x^2}{2}+\frac{1}{2} \log \left(1-x^2\right)+x-\log (x)",1,"x + x^2/2 - Log[x] + Log[1 - x^2]/2","A",4,3,26,0.1154,1,"{1593, 1802, 260}"
312,1,36,0,0.1153051,"\int \frac{2-4 x^2+x^3}{\left(1+x^2\right) \left(2+x^2\right)} \, dx","Int[(2 - 4*x^2 + x^3)/((1 + x^2)*(2 + x^2)),x]","-\frac{1}{2} \log \left(x^2+1\right)+\log \left(x^2+2\right)+6 \tan ^{-1}(x)-5 \sqrt{2} \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)","-\frac{1}{2} \log \left(x^2+1\right)+\log \left(x^2+2\right)+6 \tan ^{-1}(x)-5 \sqrt{2} \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)",1,"6*ArcTan[x] - 5*Sqrt[2]*ArcTan[x/Sqrt[2]] - Log[1 + x^2]/2 + Log[2 + x^2]","A",8,4,25,0.1600,1,"{6725, 635, 203, 260}"
313,1,29,0,0.1068504,"\int \frac{1+x^2+x^4}{\left(1+x^2\right) \left(4+x^2\right)^2} \, dx","Int[(1 + x^2 + x^4)/((1 + x^2)*(4 + x^2)^2),x]","-\frac{13 x}{24 \left(x^2+4\right)}+\frac{25}{144} \tan ^{-1}\left(\frac{x}{2}\right)+\frac{1}{9} \tan ^{-1}(x)","-\frac{13 x}{24 \left(x^2+4\right)}+\frac{25}{144} \tan ^{-1}\left(\frac{x}{2}\right)+\frac{1}{9} \tan ^{-1}(x)",1,"(-13*x)/(24*(4 + x^2)) + (25*ArcTan[x/2])/144 + ArcTan[x]/9","A",6,3,23,0.1304,1,"{6725, 203, 199}"
314,1,46,0,0.0578528,"\int \frac{1+x^2+x^3}{2 x^2+x^3+x^4} \, dx","Int[(1 + x^2 + x^3)/(2*x^2 + x^3 + x^4),x]","\frac{5}{8} \log \left(x^2+x+2\right)-\frac{1}{2 x}-\frac{\log (x)}{4}+\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{7}}\right)}{4 \sqrt{7}}","\frac{5}{8} \log \left(x^2+x+2\right)-\frac{1}{2 x}-\frac{\log (x)}{4}+\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{7}}\right)}{4 \sqrt{7}}",1,"-1/(2*x) + ArcTan[(1 + 2*x)/Sqrt[7]]/(4*Sqrt[7]) - Log[x]/4 + (5*Log[2 + x + x^2])/8","A",7,6,23,0.2609,1,"{1594, 1628, 634, 618, 204, 628}"
315,1,26,0,0.0150512,"\int \frac{1-12 x+x^2+x^3}{-12+x+x^2} \, dx","Int[(1 - 12*x + x^2 + x^3)/(-12 + x + x^2),x]","\frac{x^2}{2}+\frac{1}{7} \log (3-x)-\frac{1}{7} \log (x+4)","\frac{x^2}{2}-\frac{2}{7} \tanh ^{-1}\left(\frac{1}{7} (2 x+1)\right)",1,"x^2/2 + Log[3 - x]/7 - Log[4 + x]/7","A",5,3,20,0.1500,1,"{1657, 616, 31}"
316,1,17,0,0.0391746,"\int \frac{-3+5 x+6 x^2}{-3 x+2 x^2+x^3} \, dx","Int[(-3 + 5*x + 6*x^2)/(-3*x + 2*x^2 + x^3),x]","2 \log (1-x)+\log (x)+3 \log (x+3)","2 \log (1-x)+\log (x)+3 \log (x+3)",1,"2*Log[1 - x] + Log[x] + 3*Log[3 + x]","A",3,2,25,0.08000,1,"{1594, 1628}"
317,1,14,0,0.0245166,"\int \frac{-2+3 x+5 x^2}{2 x^2+x^3} \, dx","Int[(-2 + 3*x + 5*x^2)/(2*x^2 + x^3),x]","\frac{1}{x}+2 \log (x)+3 \log (x+2)","\frac{1}{x}+2 \log (x)+3 \log (x+2)",1,"x^(-1) + 2*Log[x] + 3*Log[2 + x]","A",3,2,22,0.09091,1,"{1593, 893}"
318,1,19,0,0.0273159,"\int \frac{18-2 x-4 x^2}{-6+x+4 x^2+x^3} \, dx","Int[(18 - 2*x - 4*x^2)/(-6 + x + 4*x^2 + x^3),x]","\log (1-x)-2 \log (x+2)-3 \log (x+3)","\log (1-x)-2 \log (x+2)-3 \log (x+3)",1,"Log[1 - x] - 2*Log[2 + x] - 3*Log[3 + x]","A",2,1,24,0.04167,1,"{2074}"
319,1,23,0,0.0289438,"\int \frac{1+x-2 x^2+x^3}{4+5 x^2+x^4} \, dx","Int[(1 + x - 2*x^2 + x^3)/(4 + 5*x^2 + x^4),x]","\frac{1}{2} \log \left(x^2+4\right)-\frac{3}{2} \tan ^{-1}\left(\frac{x}{2}\right)+\tan ^{-1}(x)","\frac{1}{2} \log \left(x^2+4\right)-\frac{3}{2} \tan ^{-1}\left(\frac{x}{2}\right)+\tan ^{-1}(x)",1,"(-3*ArcTan[x/2])/2 + ArcTan[x] + Log[4 + x^2]/2","A",7,6,24,0.2500,1,"{1673, 1166, 203, 1247, 626, 31}"
320,1,63,0,0.0877549,"\int \frac{-32+5 x-27 x^2+4 x^3}{-70-299 x-286 x^2+50 x^3-13 x^4+30 x^5} \, dx","Int[(-32 + 5*x - 27*x^2 + 4*x^3)/(-70 - 299*x - 286*x^2 + 50*x^3 - 13*x^4 + 30*x^5),x]","\frac{11049 \log \left(x^2+x+5\right)}{260015}-\frac{3146 \log (7-3 x)}{80155}-\frac{334}{323} \log (2 x+1)+\frac{4822 \log (5 x+2)}{4879}+\frac{3988 \tan ^{-1}\left(\frac{2 x+1}{\sqrt{19}}\right)}{13685 \sqrt{19}}","\frac{11049 \log \left(x^2+x+5\right)}{260015}-\frac{3146 \log (7-3 x)}{80155}-\frac{334}{323} \log (2 x+1)+\frac{4822 \log (5 x+2)}{4879}+\frac{3988 \tan ^{-1}\left(\frac{2 x+1}{\sqrt{19}}\right)}{13685 \sqrt{19}}",1,"(3988*ArcTan[(1 + 2*x)/Sqrt[19]])/(13685*Sqrt[19]) - (3146*Log[7 - 3*x])/80155 - (334*Log[1 + 2*x])/323 + (4822*Log[2 + 5*x])/4879 + (11049*Log[5 + x + x^2])/260015","A",6,5,43,0.1163,1,"{2074, 634, 618, 204, 628}"
321,1,86,0,0.0989439,"\int \frac{8-13 x^2-7 x^3+12 x^5}{4-20 x+41 x^2-80 x^3+116 x^4-80 x^5+100 x^6} \, dx","Int[(8 - 13*x^2 - 7*x^3 + 12*x^5)/(4 - 20*x + 41*x^2 - 80*x^3 + 116*x^4 - 80*x^5 + 100*x^6),x]","-\frac{502 x+313}{1452 \left(2 x^2+1\right)}+\frac{2843 \log \left(2 x^2+1\right)}{7986}+\frac{5828}{9075 (2-5 x)}-\frac{59096 \log (2-5 x)}{99825}+\frac{272 \sqrt{2} \tan ^{-1}\left(\sqrt{2} x\right)}{1331}-\frac{251 \tan ^{-1}\left(\sqrt{2} x\right)}{726 \sqrt{2}}","-\frac{502 x+313}{1452 \left(2 x^2+1\right)}+\frac{2843 \log \left(2 x^2+1\right)}{7986}+\frac{5828}{9075 (2-5 x)}-\frac{59096 \log (2-5 x)}{99825}+\frac{503 \tan ^{-1}\left(\sqrt{2} x\right)}{7986 \sqrt{2}}",1,"5828/(9075*(2 - 5*x)) - (313 + 502*x)/(1452*(1 + 2*x^2)) - (251*ArcTan[Sqrt[2]*x])/(726*Sqrt[2]) + (272*Sqrt[2]*ArcTan[Sqrt[2]*x])/1331 - (59096*Log[2 - 5*x])/99825 + (2843*Log[1 + 2*x^2])/7986","A",7,5,50,0.1000,1,"{2074, 639, 203, 635, 260}"
322,1,17,0,0.0128914,"\int \frac{9+x^4}{x^2 \left(9+x^2\right)} \, dx","Int[(9 + x^4)/(x^2*(9 + x^2)),x]","x-\frac{1}{x}-\frac{10}{3} \tan ^{-1}\left(\frac{x}{3}\right)","x-\frac{1}{x}-\frac{10}{3} \tan ^{-1}\left(\frac{x}{3}\right)",1,"-x^(-1) + x - (10*ArcTan[x/3])/3","A",3,2,16,0.1250,1,"{1262, 203}"
323,1,19,0,0.0267939,"\int \frac{2 x+x^4}{1+x^2} \, dx","Int[(2*x + x^4)/(1 + x^2),x]","\frac{x^3}{3}+\log \left(x^2+1\right)-x+\tan ^{-1}(x)","\frac{x^3}{3}+\log \left(x^2+1\right)-x+\tan ^{-1}(x)",1,"-x + x^3/3 + ArcTan[x] + Log[1 + x^2]","A",6,5,15,0.3333,1,"{1593, 1802, 635, 203, 260}"
324,1,9,0,0.0752009,"\int \frac{-x+x^3}{(-1+x)^2 \left(1+x^2\right)} \, dx","Int[(-x + x^3)/((-1 + x)^2*(1 + x^2)),x]","\log (1-x)+\tan ^{-1}(x)","\log (1-x)+\tan ^{-1}(x)",1,"ArcTan[x] + Log[1 - x]","A",5,4,20,0.2000,1,"{1586, 1593, 1629, 203}"
325,1,12,0,0.0162013,"\int \frac{2+5 x+3 x^2+2 x^3}{1+x+x^2} \, dx","Int[(2 + 5*x + 3*x^2 + 2*x^3)/(1 + x + x^2),x]","x^2+\log \left(x^2+x+1\right)+x","x^2+\log \left(x^2+x+1\right)+x",1,"x + x^2 + Log[1 + x + x^2]","A",3,2,24,0.08333,1,"{1657, 628}"
326,1,65,0,0.0615783,"\int \frac{3-4 x-5 x^2+3 x^3}{x^3 \left(-1+x+x^2\right)} \, dx","Int[(3 - 4*x - 5*x^2 + 3*x^3)/(x^3*(-1 + x + x^2)),x]","\frac{3}{2 x^2}-\frac{1}{x}+3 \log (x)-\frac{1}{10} \left(15-\sqrt{5}\right) \log \left(2 x-\sqrt{5}+1\right)-\frac{1}{10} \left(15+\sqrt{5}\right) \log \left(2 x+\sqrt{5}+1\right)","\frac{3}{2 x^2}-\frac{1}{x}+3 \log (x)-\frac{1}{10} \left(15-\sqrt{5}\right) \log \left(2 x-\sqrt{5}+1\right)-\frac{1}{10} \left(15+\sqrt{5}\right) \log \left(2 x+\sqrt{5}+1\right)",1,"3/(2*x^2) - x^(-1) + 3*Log[x] - ((15 - Sqrt[5])*Log[1 - Sqrt[5] + 2*x])/10 - ((15 + Sqrt[5])*Log[1 + Sqrt[5] + 2*x])/10","A",5,3,27,0.1111,1,"{1628, 632, 31}"
327,1,28,0,0.0219627,"\int \frac{4+8 x+5 x^2+2 x^3}{\left(2+2 x+x^2\right)^2} \, dx","Int[(4 + 8*x + 5*x^2 + 2*x^3)/(2 + 2*x + x^2)^2,x]","-\frac{1}{x^2+2 x+2}+\log \left(x^2+2 x+2\right)-\tan ^{-1}(x+1)","-\frac{1}{x^2+2 x+2}+\log \left(x^2+2 x+2\right)-\tan ^{-1}(x+1)",1,"-(2 + 2*x + x^2)^(-1) - ArcTan[1 + x] + Log[2 + 2*x + x^2]","A",5,5,26,0.1923,1,"{1660, 634, 617, 204, 628}"
328,1,32,0,0.0400596,"\int \frac{(-1+x)^4 x^4}{1+x^2} \, dx","Int[((-1 + x)^4*x^4)/(1 + x^2),x]","\frac{x^7}{7}-\frac{2 x^6}{3}+x^5-\frac{4 x^3}{3}+4 x-4 \tan ^{-1}(x)","\frac{x^7}{7}-\frac{2 x^6}{3}+x^5-\frac{4 x^3}{3}+4 x-4 \tan ^{-1}(x)",1,"4*x - (4*x^3)/3 + x^5 - (2*x^6)/3 + x^7/7 - 4*ArcTan[x]","A",3,2,16,0.1250,1,"{1629, 203}"
329,1,41,0,0.0487104,"\int \frac{-20 x+4 x^2}{9-10 x^2+x^4} \, dx","Int[(-20*x + 4*x^2)/(9 - 10*x^2 + x^4),x]","\frac{5}{4} \log \left(1-x^2\right)-\frac{5}{4} \log \left(9-x^2\right)-\frac{3}{2} \tanh ^{-1}\left(\frac{x}{3}\right)+\frac{1}{2} \tanh ^{-1}(x)","\log (1-x)-\frac{1}{2} \log (3-x)+\frac{3}{2} \log (x+1)-2 \log (x+3)",1,"(-3*ArcTanh[x/3])/2 + ArcTanh[x]/2 + (5*Log[1 - x^2])/4 - (5*Log[9 - x^2])/4","A",11,8,22,0.3636,1,"{1593, 1662, 12, 1107, 616, 31, 1130, 207}"
330,1,24,0,0.1668004,"\int \frac{-1+x+4 x^3}{(-1+x) x^2 \left(1+x^2\right)} \, dx","Int[(-1 + x + 4*x^3)/((-1 + x)*x^2*(1 + x^2)),x]","-\log \left(x^2+1\right)-\frac{1}{x}+2 \log (1-x)+\tan ^{-1}(x)","-\log \left(x^2+1\right)-\frac{1}{x}+2 \log (1-x)+\tan ^{-1}(x)",1,"-x^(-1) + ArcTan[x] + 2*Log[1 - x] - Log[1 + x^2]","A",5,4,24,0.1667,1,"{6725, 635, 203, 260}"
331,1,23,0,0.0246163,"\int \frac{1-3 x+2 x^2-4 x^3+x^4}{\left(1+x^2\right)^3} \, dx","Int[(1 - 3*x + 2*x^2 - 4*x^3 + x^4)/(1 + x^2)^3,x]","\frac{2}{x^2+1}-\frac{1}{4 \left(x^2+1\right)^2}+\tan ^{-1}(x)","\frac{2}{x^2+1}-\frac{1}{4 \left(x^2+1\right)^2}+\tan ^{-1}(x)",1,"-1/(4*(1 + x^2)^2) + 2/(1 + x^2) + ArcTan[x]","A",4,3,26,0.1154,1,"{1814, 12, 203}"
332,1,23,0,0.0387941,"\int \frac{1-3 x+2 x^2-4 x^3+x^4}{1+3 x^2+3 x^4+x^6} \, dx","Int[(1 - 3*x + 2*x^2 - 4*x^3 + x^4)/(1 + 3*x^2 + 3*x^4 + x^6),x]","\frac{2}{x^2+1}-\frac{1}{4 \left(x^2+1\right)^2}+\tan ^{-1}(x)","\frac{2}{x^2+1}-\frac{1}{4 \left(x^2+1\right)^2}+\tan ^{-1}(x)",1,"-1/(4*(1 + x^2)^2) + 2/(1 + x^2) + ArcTan[x]","A",5,3,36,0.08333,1,"{2073, 261, 203}"
333,1,13,0,0.0490023,"\int \frac{1+x+2 x^2+2 x^3}{x^2+x^3+x^4} \, dx","Int[(1 + x + 2*x^2 + 2*x^3)/(x^2 + x^3 + x^4),x]","\log \left(x^2+x+1\right)-\frac{1}{x}","\log \left(x^2+x+1\right)-\frac{1}{x}",1,"-x^(-1) + Log[1 + x + x^2]","A",4,3,26,0.1154,1,"{1594, 1628, 628}"
334,1,206,0,0.2735971,"\int \frac{x^2 (c+d x)^2}{a+b x^3} \, dx","Int[(x^2*(c + d*x)^2)/(a + b*x^3),x]","\frac{\sqrt[3]{a} d \left(2 \sqrt[3]{b} c-\sqrt[3]{a} d\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 b^{5/3}}-\frac{\sqrt[3]{a} d \left(2 \sqrt[3]{b} c-\sqrt[3]{a} d\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 b^{5/3}}+\frac{\sqrt[3]{a} d \left(\sqrt[3]{a} d+2 \sqrt[3]{b} c\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} b^{5/3}}+\frac{c^2 \log \left(a+b x^3\right)}{3 b}+\frac{2 c d x}{b}+\frac{d^2 x^2}{2 b}","\frac{\sqrt[3]{a} d \left(2 \sqrt[3]{b} c-\sqrt[3]{a} d\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 b^{5/3}}-\frac{\sqrt[3]{a} d \left(2 \sqrt[3]{b} c-\sqrt[3]{a} d\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 b^{5/3}}+\frac{\sqrt[3]{a} d \left(\sqrt[3]{a} d+2 \sqrt[3]{b} c\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} b^{5/3}}+\frac{c^2 \log \left(a+b x^3\right)}{3 b}+\frac{2 c d x}{b}+\frac{d^2 x^2}{2 b}",1,"(2*c*d*x)/b + (d^2*x^2)/(2*b) + (a^(1/3)*d*(2*b^(1/3)*c + a^(1/3)*d)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*b^(5/3)) - (a^(1/3)*d*(2*b^(1/3)*c - a^(1/3)*d)*Log[a^(1/3) + b^(1/3)*x])/(3*b^(5/3)) + (a^(1/3)*d*(2*b^(1/3)*c - a^(1/3)*d)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*b^(5/3)) + (c^2*Log[a + b*x^3])/(3*b)","A",10,9,20,0.4500,1,"{1887, 1871, 1860, 31, 634, 617, 204, 628, 260}"
335,1,45,0,0.0669286,"\int \frac{-x+2 x^3+4 x^5}{\left(3+2 x^2+x^4\right)^2} \, dx","Int[(-x + 2*x^3 + 4*x^5)/(3 + 2*x^2 + x^4)^2,x]","\frac{5-7 x^2}{8 \left(x^4+2 x^2+3\right)}+\frac{9 \tan ^{-1}\left(\frac{x^2+1}{\sqrt{2}}\right)}{8 \sqrt{2}}","\frac{5-7 x^2}{8 \left(x^4+2 x^2+3\right)}+\frac{9 \tan ^{-1}\left(\frac{x^2+1}{\sqrt{2}}\right)}{8 \sqrt{2}}",1,"(5 - 7*x^2)/(8*(3 + 2*x^2 + x^4)) + (9*ArcTan[(1 + x^2)/Sqrt[2]])/(8*Sqrt[2])","A",6,6,27,0.2222,1,"{1594, 1663, 1660, 12, 618, 204}"
336,1,59,0,0.0642882,"\int \frac{x+x^5}{\left(1+2 x^2+2 x^4\right)^3} \, dx","Int[(x + x^5)/(1 + 2*x^2 + 2*x^4)^3,x]","\frac{2 x^2+1}{2 \left(2 x^4+2 x^2+1\right)}+\frac{4 x^2+3}{16 \left(2 x^4+2 x^2+1\right)^2}+\tan ^{-1}\left(2 x^2+1\right)","\frac{2 x^2+1}{2 \left(2 x^4+2 x^2+1\right)}+\frac{4 x^2+3}{16 \left(2 x^4+2 x^2+1\right)^2}+\tan ^{-1}\left(2 x^2+1\right)",1,"(3 + 4*x^2)/(16*(1 + 2*x^2 + 2*x^4)^2) + (1 + 2*x^2)/(2*(1 + 2*x^2 + 2*x^4)) + ArcTan[1 + 2*x^2]","A",7,7,20,0.3500,1,"{1593, 1663, 1660, 12, 614, 617, 204}"
337,1,209,0,0.3708055,"\int \frac{a+b x+c x^2}{d+e x^2+f x^4} \, dx","Int[(a + b*x + c*x^2)/(d + e*x^2 + f*x^4),x]","\frac{\left(c-\frac{c e-2 a f}{\sqrt{e^2-4 d f}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{f} x}{\sqrt{e-\sqrt{e^2-4 d f}}}\right)}{\sqrt{2} \sqrt{f} \sqrt{e-\sqrt{e^2-4 d f}}}+\frac{\left(\frac{c e-2 a f}{\sqrt{e^2-4 d f}}+c\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{f} x}{\sqrt{\sqrt{e^2-4 d f}+e}}\right)}{\sqrt{2} \sqrt{f} \sqrt{\sqrt{e^2-4 d f}+e}}-\frac{b \tanh ^{-1}\left(\frac{e+2 f x^2}{\sqrt{e^2-4 d f}}\right)}{\sqrt{e^2-4 d f}}","\frac{\left(c-\frac{c e-2 a f}{\sqrt{e^2-4 d f}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{f} x}{\sqrt{e-\sqrt{e^2-4 d f}}}\right)}{\sqrt{2} \sqrt{f} \sqrt{e-\sqrt{e^2-4 d f}}}+\frac{\left(\frac{c e-2 a f}{\sqrt{e^2-4 d f}}+c\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{f} x}{\sqrt{\sqrt{e^2-4 d f}+e}}\right)}{\sqrt{2} \sqrt{f} \sqrt{\sqrt{e^2-4 d f}+e}}-\frac{b \tanh ^{-1}\left(\frac{e+2 f x^2}{\sqrt{e^2-4 d f}}\right)}{\sqrt{e^2-4 d f}}",1,"((c - (c*e - 2*a*f)/Sqrt[e^2 - 4*d*f])*ArcTan[(Sqrt[2]*Sqrt[f]*x)/Sqrt[e - Sqrt[e^2 - 4*d*f]]])/(Sqrt[2]*Sqrt[f]*Sqrt[e - Sqrt[e^2 - 4*d*f]]) + ((c + (c*e - 2*a*f)/Sqrt[e^2 - 4*d*f])*ArcTan[(Sqrt[2]*Sqrt[f]*x)/Sqrt[e + Sqrt[e^2 - 4*d*f]]])/(Sqrt[2]*Sqrt[f]*Sqrt[e + Sqrt[e^2 - 4*d*f]]) - (b*ArcTanh[(e + 2*f*x^2)/Sqrt[e^2 - 4*d*f]])/Sqrt[e^2 - 4*d*f]","A",8,7,25,0.2800,1,"{1673, 1166, 205, 12, 1107, 618, 206}"
338,1,224,0,0.3894238,"\int \frac{(d+e x)^2}{a+b x^2+c x^4} \, dx","Int[(d + e*x)^2/(a + b*x^2 + c*x^4),x]","\frac{\left(\frac{2 c d^2-b e^2}{\sqrt{b^2-4 a c}}+e^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} \sqrt{c} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(e^2-\frac{2 c d^2-b e^2}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} \sqrt{c} \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{2 d e \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\sqrt{b^2-4 a c}}","\frac{\left(\frac{2 c d^2-b e^2}{\sqrt{b^2-4 a c}}+e^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} \sqrt{c} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(e^2-\frac{2 c d^2-b e^2}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} \sqrt{c} \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{2 d e \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\sqrt{b^2-4 a c}}",1,"((e^2 + (2*c*d^2 - b*e^2)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*Sqrt[c]*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + ((e^2 - (2*c*d^2 - b*e^2)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*Sqrt[c]*Sqrt[b + Sqrt[b^2 - 4*a*c]]) - (2*d*e*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/Sqrt[b^2 - 4*a*c]","A",8,7,22,0.3182,1,"{1673, 1166, 205, 12, 1107, 618, 206}"
339,1,56,0,0.0466322,"\int \frac{x^2}{(a+b x) (c+d x)} \, dx","Int[x^2/((a + b*x)*(c + d*x)),x]","\frac{a^2 \log (a+b x)}{b^2 (b c-a d)}-\frac{c^2 \log (c+d x)}{d^2 (b c-a d)}+\frac{x}{b d}","\frac{a^2 \log (a+b x)}{b^2 (b c-a d)}-\frac{c^2 \log (c+d x)}{d^2 (b c-a d)}+\frac{x}{b d}",1,"x/(b*d) + (a^2*Log[a + b*x])/(b^2*(b*c - a*d)) - (c^2*Log[c + d*x])/(d^2*(b*c - a*d))","A",2,1,18,0.05556,1,"{72}"
340,1,96,0,0.1080432,"\int \frac{x^2}{(c+d x) \left(a+b x^2\right)} \, dx","Int[x^2/((c + d*x)*(a + b*x^2)),x]","\frac{a d \log \left(a+b x^2\right)}{2 b \left(a d^2+b c^2\right)}+\frac{c^2 \log (c+d x)}{d \left(a d^2+b c^2\right)}-\frac{\sqrt{a} c \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{b} \left(a d^2+b c^2\right)}","\frac{a d \log \left(a+b x^2\right)}{2 b \left(a d^2+b c^2\right)}+\frac{c^2 \log (c+d x)}{d \left(a d^2+b c^2\right)}-\frac{\sqrt{a} c \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{b} \left(a d^2+b c^2\right)}",1,"-((Sqrt[a]*c*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(Sqrt[b]*(b*c^2 + a*d^2))) + (c^2*Log[c + d*x])/(d*(b*c^2 + a*d^2)) + (a*d*Log[a + b*x^2])/(2*b*(b*c^2 + a*d^2))","A",5,4,20,0.2000,1,"{1629, 635, 205, 260}"
341,1,264,0,0.4722209,"\int \frac{x^2}{(c+d x) \left(a+b x^3\right)} \, dx","Int[x^2/((c + d*x)*(a + b*x^3)),x]","-\frac{\sqrt[3]{a} d \left(\sqrt[3]{a} d+\sqrt[3]{b} c\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 b^{2/3} \left(b c^3-a d^3\right)}-\frac{\sqrt[3]{a} d \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} b^{2/3} \left(a^{2/3} d^2+\sqrt[3]{a} \sqrt[3]{b} c d+b^{2/3} c^2\right)}+\frac{\sqrt[3]{a} d \left(\sqrt[3]{a} d+\sqrt[3]{b} c\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 b^{2/3} \left(b c^3-a d^3\right)}+\frac{c^2 \log \left(a+b x^3\right)}{3 \left(b c^3-a d^3\right)}-\frac{c^2 \log (c+d x)}{b c^3-a d^3}","-\frac{\sqrt[3]{a} d \left(\sqrt[3]{a} d+\sqrt[3]{b} c\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 b^{2/3} \left(b c^3-a d^3\right)}-\frac{\sqrt[3]{a} d \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} b^{2/3} \left(a^{2/3} d^2+\sqrt[3]{a} \sqrt[3]{b} c d+b^{2/3} c^2\right)}+\frac{\sqrt[3]{a} d \left(\sqrt[3]{a} d+\sqrt[3]{b} c\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 b^{2/3} \left(b c^3-a d^3\right)}+\frac{c^2 \log \left(a+b x^3\right)}{3 \left(b c^3-a d^3\right)}-\frac{c^2 \log (c+d x)}{b c^3-a d^3}",1,"-((a^(1/3)*d*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*b^(2/3)*(b^(2/3)*c^2 + a^(1/3)*b^(1/3)*c*d + a^(2/3)*d^2))) + (a^(1/3)*d*(b^(1/3)*c + a^(1/3)*d)*Log[a^(1/3) + b^(1/3)*x])/(3*b^(2/3)*(b*c^3 - a*d^3)) - (c^2*Log[c + d*x])/(b*c^3 - a*d^3) - (a^(1/3)*d*(b^(1/3)*c + a^(1/3)*d)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*b^(2/3)*(b*c^3 - a*d^3)) + (c^2*Log[a + b*x^3])/(3*(b*c^3 - a*d^3))","A",10,9,20,0.4500,1,"{6725, 1871, 1860, 31, 634, 617, 204, 628, 260}"
342,1,417,0,0.546728,"\int \frac{x^2}{(c+d x) \left(a+b x^4\right)} \, dx","Int[x^2/((c + d*x)*(a + b*x^4)),x]","-\frac{c^2 d \log \left(a+b x^4\right)}{4 \left(a d^4+b c^4\right)}+\frac{c \left(\sqrt{a} d^2+\sqrt{b} c^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \left(a d^4+b c^4\right)}-\frac{c \left(\sqrt{a} d^2+\sqrt{b} c^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \left(a d^4+b c^4\right)}+\frac{\sqrt{a} d^3 \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{2 \sqrt{b} \left(a d^4+b c^4\right)}+\frac{c^2 d \log (c+d x)}{a d^4+b c^4}-\frac{c \left(\sqrt{b} c^2-\sqrt{a} d^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \left(a d^4+b c^4\right)}+\frac{c \left(\sqrt{b} c^2-\sqrt{a} d^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \left(a d^4+b c^4\right)}","-\frac{c^2 d \log \left(a+b x^4\right)}{4 \left(a d^4+b c^4\right)}+\frac{c \left(\sqrt{a} d^2+\sqrt{b} c^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \left(a d^4+b c^4\right)}-\frac{c \left(\sqrt{a} d^2+\sqrt{b} c^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \left(a d^4+b c^4\right)}+\frac{\sqrt{a} d^3 \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{2 \sqrt{b} \left(a d^4+b c^4\right)}+\frac{c^2 d \log (c+d x)}{a d^4+b c^4}-\frac{c \left(\sqrt{b} c^2-\sqrt{a} d^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \left(a d^4+b c^4\right)}+\frac{c \left(\sqrt{b} c^2-\sqrt{a} d^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \left(a d^4+b c^4\right)}",1,"(Sqrt[a]*d^3*ArcTan[(Sqrt[b]*x^2)/Sqrt[a]])/(2*Sqrt[b]*(b*c^4 + a*d^4)) - (c*(Sqrt[b]*c^2 - Sqrt[a]*d^2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(1/4)*b^(1/4)*(b*c^4 + a*d^4)) + (c*(Sqrt[b]*c^2 - Sqrt[a]*d^2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(1/4)*b^(1/4)*(b*c^4 + a*d^4)) + (c^2*d*Log[c + d*x])/(b*c^4 + a*d^4) + (c*(Sqrt[b]*c^2 + Sqrt[a]*d^2)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(4*Sqrt[2]*a^(1/4)*b^(1/4)*(b*c^4 + a*d^4)) - (c*(Sqrt[b]*c^2 + Sqrt[a]*d^2)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(4*Sqrt[2]*a^(1/4)*b^(1/4)*(b*c^4 + a*d^4)) - (c^2*d*Log[a + b*x^4])/(4*(b*c^4 + a*d^4))","A",16,12,20,0.6000,1,"{6725, 1461, 1168, 1162, 617, 204, 1165, 628, 1248, 635, 205, 260}"
343,1,16,0,0.0082498,"\int \frac{x}{(1-x) (1+x)^2} \, dx","Int[x/((1 - x)*(1 + x)^2),x]","\frac{1}{2 (x+1)}+\frac{1}{2} \tanh ^{-1}(x)","\frac{1}{2 (x+1)}+\frac{1}{2} \tanh ^{-1}(x)",1,"1/(2*(1 + x)) + ArcTanh[x]/2","A",3,2,14,0.1429,1,"{77, 207}"
344,1,19,0,0.0125273,"\int \frac{x^2}{\left(1-x^2\right) \left(1+x^2\right)^2} \, dx","Int[x^2/((1 - x^2)*(1 + x^2)^2),x]","\frac{1}{4} \tanh ^{-1}(x)-\frac{x}{4 \left(x^2+1\right)}","\frac{1}{4} \tanh ^{-1}(x)-\frac{x}{4 \left(x^2+1\right)}",1,"-x/(4*(1 + x^2)) + ArcTanh[x]/4","A",2,2,20,0.1000,1,"{471, 206}"
345,1,97,0,0.0707737,"\int \frac{x^3}{\left(1-x^3\right) \left(1+x^3\right)^2} \, dx","Int[x^3/((1 - x^3)*(1 + x^3)^2),x]","-\frac{x}{6 \left(x^3+1\right)}+\frac{1}{72} \log \left(x^2-x+1\right)+\frac{1}{24} \log \left(x^2+x+1\right)-\frac{1}{12} \log (1-x)-\frac{1}{36} \log (x+1)+\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{12 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{4 \sqrt{3}}","-\frac{x}{6 \left(x^3+1\right)}+\frac{1}{72} \log \left(x^2-x+1\right)+\frac{1}{24} \log \left(x^2+x+1\right)-\frac{1}{12} \log (1-x)-\frac{1}{36} \log (x+1)+\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{12 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{4 \sqrt{3}}",1,"-x/(6*(1 + x^3)) + ArcTan[(1 - 2*x)/Sqrt[3]]/(12*Sqrt[3]) + ArcTan[(1 + 2*x)/Sqrt[3]]/(4*Sqrt[3]) - Log[1 - x]/12 - Log[1 + x]/36 + Log[1 - x + x^2]/72 + Log[1 + x + x^2]/24","A",14,8,20,0.4000,1,"{471, 522, 200, 31, 634, 618, 204, 628}"
346,1,15,0,0.1064783,"\int \frac{9+x+3 x^2+x^3}{\left(1+x^2\right) \left(3+x^2\right)} \, dx","Int[(9 + x + 3*x^2 + x^3)/((1 + x^2)*(3 + x^2)),x]","\frac{1}{2} \log \left(x^2+3\right)+3 \tan ^{-1}(x)","\frac{1}{2} \log \left(x^2+3\right)+3 \tan ^{-1}(x)",1,"3*ArcTan[x] + Log[3 + x^2]/2","A",4,3,26,0.1154,1,"{6725, 203, 260}"
347,1,13,0,0.0940804,"\int \frac{3+x+x^2+x^3}{\left(1+x^2\right) \left(3+x^2\right)} \, dx","Int[(3 + x + x^2 + x^3)/((1 + x^2)*(3 + x^2)),x]","\frac{1}{2} \log \left(x^2+3\right)+\tan ^{-1}(x)","\frac{1}{2} \log \left(x^2+3\right)+\tan ^{-1}(x)",1,"ArcTan[x] + Log[3 + x^2]/2","A",4,3,24,0.1250,1,"{6725, 203, 260}"
348,1,29,0,0.1175703,"\int \frac{-4+6 x-x^2+3 x^3}{\left(1+x^2\right) \left(2+x^2\right)} \, dx","Int[(-4 + 6*x - x^2 + 3*x^3)/((1 + x^2)*(2 + x^2)),x]","\frac{3}{2} \log \left(x^2+1\right)-3 \tan ^{-1}(x)+\sqrt{2} \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)","\frac{3}{2} \log \left(x^2+1\right)-3 \tan ^{-1}(x)+\sqrt{2} \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)",1,"-3*ArcTan[x] + Sqrt[2]*ArcTan[x/Sqrt[2]] + (3*Log[1 + x^2])/2","A",6,4,30,0.1333,1,"{6725, 635, 203, 260}"
349,1,14,0,0.0106012,"\int \frac{1}{\left(4-4 x+x^2\right) \left(5-4 x+x^2\right)} \, dx","Int[1/((4 - 4*x + x^2)*(5 - 4*x + x^2)),x]","\frac{1}{2-x}+\tan ^{-1}(2-x)","\frac{1}{2-x}+\tan ^{-1}(2-x)",1,"(2 - x)^(-1) + ArcTan[2 - x]","A",4,4,21,0.1905,1,"{27, 693, 618, 204}"
350,1,12,0,0.0106617,"\int \frac{-3+x+x^2}{(-3+x) x^2} \, dx","Int[(-3 + x + x^2)/((-3 + x)*x^2),x]","\log (3-x)-\frac{1}{x}","\log (3-x)-\frac{1}{x}",1,"-x^(-1) + Log[3 - x]","A",2,1,15,0.06667,1,"{893}"
351,1,11,0,0.0343319,"\int \frac{1+x+4 x^2}{x+4 x^3} \, dx","Int[(1 + x + 4*x^2)/(x + 4*x^3),x]","\log (x)+\frac{1}{2} \tan ^{-1}(2 x)","\log (x)+\frac{1}{2} \tan ^{-1}(2 x)",1,"ArcTan[2*x]/2 + Log[x]","A",4,3,18,0.1667,1,"{1593, 1802, 203}"
352,1,12,0,0.0213736,"\int \frac{1-x+3 x^2}{-x^2+x^3} \, dx","Int[(1 - x + 3*x^2)/(-x^2 + x^3),x]","\frac{1}{x}+3 \log (1-x)","\frac{1}{x}+3 \log (1-x)",1,"x^(-1) + 3*Log[1 - x]","A",3,2,22,0.09091,1,"{1593, 893}"
353,1,12,0,0.0176414,"\int \frac{4+3 x+x^2}{x+x^2} \, dx","Int[(4 + 3*x + x^2)/(x + x^2),x]","x+4 \log (x)-2 \log (x+1)","x+4 \log (x)-2 \log (x+1)",1,"x + 4*Log[x] - 2*Log[1 + x]","A",3,2,16,0.1250,1,"{1593, 893}"
354,1,17,0,0.0370974,"\int \frac{4+x+3 x^2}{x+x^3} \, dx","Int[(4 + x + 3*x^2)/(x + x^3),x]","-\frac{1}{2} \log \left(x^2+1\right)+4 \log (x)+\tan ^{-1}(x)","-\frac{1}{2} \log \left(x^2+1\right)+4 \log (x)+\tan ^{-1}(x)",1,"ArcTan[x] + 4*Log[x] - Log[1 + x^2]/2","A",6,5,16,0.3125,1,"{1593, 1802, 635, 203, 260}"
355,1,13,0,0.0347155,"\int \frac{7-4 x+8 x^2}{(1+4 x) \left(1+x^2\right)} \, dx","Int[(7 - 4*x + 8*x^2)/((1 + 4*x)*(1 + x^2)),x]","2 \log (4 x+1)-\tan ^{-1}(x)","2 \log (4 x+1)-\tan ^{-1}(x)",1,"-ArcTan[x] + 2*Log[1 + 4*x]","A",3,2,25,0.08000,1,"{1629, 204}"
356,1,28,0,0.0111347,"\int \frac{x^2}{(-1+x) \left(1+2 x+x^2\right)} \, dx","Int[x^2/((-1 + x)*(1 + 2*x + x^2)),x]","\frac{1}{2 (x+1)}+\frac{1}{4} \log (1-x)+\frac{3}{4} \log (x+1)","\frac{1}{2 (x+1)}+\frac{1}{4} \log (1-x)+\frac{3}{4} \log (x+1)",1,"1/(2*(1 + x)) + Log[1 - x]/4 + (3*Log[1 + x])/4","A",3,2,19,0.1053,1,"{27, 88}"
357,1,32,0,0.0261727,"\int \frac{-4+3 x+x^2}{(-1+2 x)^2 (3+2 x)} \, dx","Int[(-4 + 3*x + x^2)/((-1 + 2*x)^2*(3 + 2*x)),x]","-\frac{9}{32 (1-2 x)}+\frac{41}{128} \log (1-2 x)-\frac{25}{128} \log (2 x+3)","-\frac{9}{32 (1-2 x)}+\frac{41}{128} \log (1-2 x)-\frac{25}{128} \log (2 x+3)",1,"-9/(32*(1 - 2*x)) + (41*Log[1 - 2*x])/128 - (25*Log[3 + 2*x])/128","A",2,1,23,0.04348,1,"{893}"
358,1,23,0,0.033852,"\int \frac{5-4 x+3 x^2}{(-1+x) \left(1+x^2\right)} \, dx","Int[(5 - 4*x + 3*x^2)/((-1 + x)*(1 + x^2)),x]","\frac{1}{2} \log \left(x^2+1\right)+2 \log (1-x)-3 \tan ^{-1}(x)","\frac{1}{2} \log \left(x^2+1\right)+2 \log (1-x)-3 \tan ^{-1}(x)",1,"-3*ArcTan[x] + 2*Log[1 - x] + Log[1 + x^2]/2","A",5,4,23,0.1739,1,"{1629, 635, 203, 260}"
359,1,24,0,0.0345563,"\int \frac{-1-2 x+x^2}{(-1+x)^2 \left(1+x^2\right)} \, dx","Int[(-1 - 2*x + x^2)/((-1 + x)^2*(1 + x^2)),x]","-\frac{1}{2} \log \left(x^2+1\right)+\frac{1}{x-1}+\log (1-x)+\tan ^{-1}(x)","-\frac{1}{2} \log \left(x^2+1\right)+\frac{1}{x-1}+\log (1-x)+\tan ^{-1}(x)",1,"(-1 + x)^(-1) + ArcTan[x] + Log[1 - x] - Log[1 + x^2]/2","A",5,4,21,0.1905,1,"{1629, 635, 203, 260}"
360,1,49,0,0.1420562,"\int \frac{5+x^3}{\left(10-6 x+x^2\right) \left(\frac{1}{2}-x+x^2\right)} \, dx","Int[(5 + x^3)/((10 - 6*x + x^2)*(1/2 - x + x^2)),x]","\frac{56}{221} \log \left(x^2-6 x+10\right)+\frac{109}{442} \log \left(2 x^2-2 x+1\right)-\frac{261}{221} \tan ^{-1}(1-2 x)-\frac{1026}{221} \tan ^{-1}(3-x)","\frac{56}{221} \log \left(x^2-6 x+10\right)+\frac{109}{442} \log \left(2 x^2-2 x+1\right)-\frac{261}{221} \tan ^{-1}(1-2 x)-\frac{1026}{221} \tan ^{-1}(3-x)",1,"(-261*ArcTan[1 - 2*x])/221 - (1026*ArcTan[3 - x])/221 + (56*Log[10 - 6*x + x^2])/221 + (109*Log[1 - 2*x + 2*x^2])/442","A",10,6,28,0.2143,1,"{6728, 634, 618, 204, 628, 617}"
361,1,25,0,0.0545906,"\int \frac{4+3 x+x^2}{(-3+x) (-2+x) (-1+x)} \, dx","Int[(4 + 3*x + x^2)/((-3 + x)*(-2 + x)*(-1 + x)),x]","4 \log (1-x)-14 \log (2-x)+11 \log (3-x)","4 \log (1-x)-14 \log (2-x)+11 \log (3-x)",1,"4*Log[1 - x] - 14*Log[2 - x] + 11*Log[3 - x]","A",2,1,24,0.04167,1,"{1612}"
362,1,60,0,0.2464477,"\int \frac{1+16 x}{(5+x)^2 (-3+2 x) \left(1+x+x^2\right)} \, dx","Int[(1 + 16*x)/((5 + x)^2*(-3 + 2*x)*(1 + x + x^2)),x]","-\frac{481 \log \left(x^2+x+1\right)}{5586}-\frac{79}{273 (x+5)}+\frac{200 \log (3-2 x)}{3211}+\frac{2731 \log (x+5)}{24843}+\frac{451 \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{2793 \sqrt{3}}","-\frac{481 \log \left(x^2+x+1\right)}{5586}-\frac{79}{273 (x+5)}+\frac{200 \log (3-2 x)}{3211}+\frac{2731 \log (x+5)}{24843}+\frac{451 \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{2793 \sqrt{3}}",1,"-79/(273*(5 + x)) + (451*ArcTan[(1 + 2*x)/Sqrt[3]])/(2793*Sqrt[3]) + (200*Log[3 - 2*x])/3211 + (2731*Log[5 + x])/24843 - (481*Log[1 + x + x^2])/5586","A",6,5,26,0.1923,1,"{6728, 634, 618, 204, 628}"
363,1,11,0,0.0074939,"\int \frac{-1+x^3}{1+x+x^2} \, dx","Int[(-1 + x^3)/(1 + x + x^2),x]","\frac{x^2}{2}-x","\frac{x^2}{2}-x",1,"-x + x^2/2","A",2,1,14,0.07143,1,"{1586}"
364,1,29,0,0.0161322,"\int \frac{-3+x^3}{-7-6 x+x^2} \, dx","Int[(-3 + x^3)/(-7 - 6*x + x^2),x]","\frac{x^2}{2}+6 x+\frac{85}{2} \log (7-x)+\frac{1}{2} \log (x+1)","\frac{x^2}{2}+6 x+\frac{85}{2} \log (7-x)+\frac{1}{2} \log (x+1)",1,"6*x + x^2/2 + (85*Log[7 - x])/2 + Log[1 + x]/2","A",5,3,16,0.1875,1,"{1657, 632, 31}"
365,1,45,0,0.0248464,"\int \frac{1+x^3}{\left(13+4 x+x^2\right)^2} \, dx","Int[(1 + x^3)/(13 + 4*x + x^2)^2,x]","\frac{47 x+67}{18 \left(x^2+4 x+13\right)}+\frac{1}{2} \log \left(x^2+4 x+13\right)-\frac{61}{54} \tan ^{-1}\left(\frac{x+2}{3}\right)","\frac{47 x+67}{18 \left(x^2+4 x+13\right)}+\frac{1}{2} \log \left(x^2+4 x+13\right)-\frac{61}{54} \tan ^{-1}\left(\frac{x+2}{3}\right)",1,"(67 + 47*x)/(18*(13 + 4*x + x^2)) - (61*ArcTan[(2 + x)/3])/54 + Log[13 + 4*x + x^2]/2","A",5,5,16,0.3125,1,"{1660, 634, 618, 204, 628}"
366,1,32,0,0.254368,"\int \frac{-32+36 x-42 x^2+21 x^3-10 x^4+3 x^5}{x \left(1+x^2\right) \left(4+x^2\right)^2} \, dx","Int[(-32 + 36*x - 42*x^2 + 21*x^3 - 10*x^4 + 3*x^5)/(x*(1 + x^2)*(4 + x^2)^2),x]","\frac{1}{x^2+4}+\log \left(x^2+4\right)-2 \log (x)+\frac{1}{2} \tan ^{-1}\left(\frac{x}{2}\right)+2 \tan ^{-1}(x)","\frac{1}{x^2+4}+\log \left(x^2+4\right)-2 \log (x)+\frac{1}{2} \tan ^{-1}\left(\frac{x}{2}\right)+2 \tan ^{-1}(x)",1,"(4 + x^2)^(-1) + ArcTan[x/2]/2 + 2*ArcTan[x] - 2*Log[x] + Log[4 + x^2]","A",7,5,43,0.1163,1,"{6725, 203, 261, 635, 260}"
367,1,148,0,0.1359809,"\int \frac{-1+x^4+7 x^5+x^9}{-7+6 x^4+x^8} \, dx","Int[(-1 + x^4 + 7*x^5 + x^9)/(-7 + 6*x^4 + x^8),x]","\frac{x^2}{2}-\frac{\log \left(x^2-\sqrt{2} \sqrt[4]{7} x+\sqrt{7}\right)}{4 \sqrt{2} 7^{3/4}}+\frac{\log \left(x^2+\sqrt{2} \sqrt[4]{7} x+\sqrt{7}\right)}{4 \sqrt{2} 7^{3/4}}-\frac{1}{2} \tanh ^{-1}\left(x^2\right)-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} x}{\sqrt[4]{7}}\right)}{2 \sqrt{2} 7^{3/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt[4]{7}}+1\right)}{2 \sqrt{2} 7^{3/4}}","\frac{x^2}{2}-\frac{\log \left(x^2-\sqrt{2} \sqrt[4]{7} x+\sqrt{7}\right)}{4 \sqrt{2} 7^{3/4}}+\frac{\log \left(x^2+\sqrt{2} \sqrt[4]{7} x+\sqrt{7}\right)}{4 \sqrt{2} 7^{3/4}}-\frac{1}{2} \tanh ^{-1}\left(x^2\right)-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} x}{\sqrt[4]{7}}\right)}{2 \sqrt{2} 7^{3/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt[4]{7}}+1\right)}{2 \sqrt{2} 7^{3/4}}",1,"x^2/2 - ArcTan[1 - (Sqrt[2]*x)/7^(1/4)]/(2*Sqrt[2]*7^(3/4)) + ArcTan[1 + (Sqrt[2]*x)/7^(1/4)]/(2*Sqrt[2]*7^(3/4)) - ArcTanh[x^2]/2 - Log[Sqrt[7] - Sqrt[2]*7^(1/4)*x + x^2]/(4*Sqrt[2]*7^(3/4)) + Log[Sqrt[7] + Sqrt[2]*7^(1/4)*x + x^2]/(4*Sqrt[2]*7^(3/4))","A",17,13,26,0.5000,1,"{1790, 1403, 211, 1165, 628, 1162, 617, 204, 1584, 1478, 275, 321, 207}"
368,1,112,0,0.1140546,"\int \frac{1+x^3+x^6}{x+x^5} \, dx","Int[(1 + x^3 + x^6)/(x + x^5),x]","\frac{x^2}{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{1}{4} \log \left(x^4+1\right)-\frac{1}{2} \tan ^{-1}\left(x^2\right)+\log (x)-\frac{\tan ^{-1}\left(1-\sqrt{2} x\right)}{2 \sqrt{2}}+\frac{\tan ^{-1}\left(\sqrt{2} x+1\right)}{2 \sqrt{2}}","\frac{x^2}{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{1}{4} \log \left(x^4+1\right)-\frac{1}{2} \tan ^{-1}\left(x^2\right)+\log (x)-\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,"x^2/2 - ArcTan[x^2]/2 - ArcTan[1 - Sqrt[2]*x]/(2*Sqrt[2]) + ArcTan[1 + Sqrt[2]*x]/(2*Sqrt[2]) + Log[x] + Log[1 - Sqrt[2]*x + x^2]/(4*Sqrt[2]) - Log[1 + Sqrt[2]*x + x^2]/(4*Sqrt[2]) - Log[1 + x^4]/4","A",18,13,16,0.8125,1,"{1593, 1833, 297, 1162, 617, 204, 1165, 628, 1834, 1248, 635, 203, 260}"
369,1,14,0,0.0163195,"\int \frac{1+x^2}{-x+x^2} \, dx","Int[(1 + x^2)/(-x + x^2),x]","x+2 \log (1-x)-\log (x)","x+2 \log (1-x)-\log (x)",1,"x + 2*Log[1 - x] - Log[x]","A",3,2,15,0.1333,1,"{1593, 894}"
370,1,12,0,0.0293969,"\int \frac{1+x^3}{-x+x^3} \, dx","Int[(1 + x^3)/(-x + x^3),x]","x+\log (1-x)-\log (x)","x+\log (1-x)-\log (x)",1,"x + Log[1 - x] - Log[x]","A",3,2,15,0.1333,1,"{1593, 1802}"
371,1,17,0,0.0295838,"\int \frac{1+x^3}{-x^2+x^3} \, dx","Int[(1 + x^3)/(-x^2 + x^3),x]","x+\frac{1}{x}+2 \log (1-x)-\log (x)","x+\frac{1}{x}+2 \log (1-x)-\log (x)",1,"x^(-1) + x + 2*Log[1 - x] - Log[x]","A",3,2,17,0.1176,1,"{1593, 1620}"
372,1,17,0,0.0293711,"\int \frac{-1+x^5}{-x+x^3} \, dx","Int[(-1 + x^5)/(-x + x^3),x]","\frac{x^3}{3}+x+\log (x)-\log (x+1)","\frac{x^3}{3}+x+\log (x)-\log (x+1)",1,"x + x^3/3 + Log[x] - Log[1 + x]","A",3,2,15,0.1333,1,"{1593, 1802}"
373,1,18,0,0.0298592,"\int \frac{1+x^4}{x^3+x^5} \, dx","Int[(1 + x^4)/(x^3 + x^5),x]","-\frac{1}{2 x^2}+\log \left(x^2+1\right)-\log (x)","-\frac{1}{2 x^2}+\log \left(x^2+1\right)-\log (x)",1,"-1/(2*x^2) - Log[x] + Log[1 + x^2]","A",4,3,15,0.2000,1,"{1593, 1252, 894}"
374,1,10,0,0.0186148,"\int \frac{1+x^2}{x+2 x^2+x^3} \, dx","Int[(1 + x^2)/(x + 2*x^2 + x^3),x]","\frac{2}{x+1}+\log (x)","\frac{2}{x+1}+\log (x)",1,"2/(1 + x) + Log[x]","A",4,3,18,0.1667,1,"{1594, 27, 894}"
375,1,42,0,0.0400056,"\int \frac{1+x^5}{-10 x-3 x^2+x^3} \, dx","Int[(1 + x^5)/(-10*x - 3*x^2 + x^3),x]","\frac{x^3}{3}+\frac{3 x^2}{2}+19 x+\frac{3126}{35} \log (5-x)-\frac{\log (x)}{10}-\frac{31}{14} \log (x+2)","\frac{x^3}{3}+\frac{3 x^2}{2}+19 x+\frac{3126}{35} \log (5-x)-\frac{\log (x)}{10}-\frac{31}{14} \log (x+2)",1,"19*x + (3*x^2)/2 + x^3/3 + (3126*Log[5 - x])/35 - Log[x]/10 - (31*Log[2 + x])/14","A",3,2,20,0.1000,1,"{1594, 1628}"
376,1,46,0,0.1254262,"\int \frac{15-5 x+x^2+x^3}{\left(5+x^2\right) \left(3+2 x+x^2\right)} \, dx","Int[(15 - 5*x + x^2 + x^3)/((5 + x^2)*(3 + 2*x + x^2)),x]","\frac{1}{2} \log \left(x^2+2 x+3\right)-\sqrt{5} \tan ^{-1}\left(\frac{x}{\sqrt{5}}\right)+\frac{5 \tan ^{-1}\left(\frac{x+1}{\sqrt{2}}\right)}{\sqrt{2}}","\frac{1}{2} \log \left(x^2+2 x+3\right)-\sqrt{5} \tan ^{-1}\left(\frac{x}{\sqrt{5}}\right)+\frac{5 \tan ^{-1}\left(\frac{x+1}{\sqrt{2}}\right)}{\sqrt{2}}",1,"-(Sqrt[5]*ArcTan[x/Sqrt[5]]) + (5*ArcTan[(1 + x)/Sqrt[2]])/Sqrt[2] + Log[3 + 2*x + x^2]/2","A",7,6,29,0.2069,1,"{6725, 203, 634, 618, 204, 628}"
377,1,19,0,0.0618751,"\int \frac{1}{\left(1+x^2\right) \left(3+\frac{10 x}{1+x^2}\right)} \, dx","Int[1/((1 + x^2)*(3 + (10*x)/(1 + x^2))),x]","\frac{1}{8} \log (3 x+1)-\frac{1}{8} \log (x+3)","\frac{1}{8} \log (3 x+1)-\frac{1}{8} \log (x+3)",1,"-Log[3 + x]/8 + Log[1 + 3*x]/8","A",4,3,22,0.1364,1,"{6688, 616, 31}"
378,1,40,0,0.020967,"\int \frac{x^3}{13+\frac{2}{x}+15 x} \, dx","Int[x^3/(13 + 2/x + 15*x),x]","\frac{x^3}{45}-\frac{13 x^2}{450}+\frac{139 x}{3375}-\frac{16}{567} \log (3 x+2)+\frac{\log (5 x+1)}{4375}","\frac{x^3}{45}-\frac{13 x^2}{450}+\frac{139 x}{3375}-\frac{16}{567} \log (3 x+2)+\frac{\log (5 x+1)}{4375}",1,"(139*x)/3375 - (13*x^2)/450 + x^3/45 - (16*Log[2 + 3*x])/567 + Log[1 + 5*x]/4375","A",6,4,16,0.2500,1,"{1386, 701, 632, 31}"
379,1,33,0,0.0203888,"\int \frac{x^2}{13+\frac{2}{x}+15 x} \, dx","Int[x^2/(13 + 2/x + 15*x),x]","\frac{x^2}{30}-\frac{13 x}{225}+\frac{8}{189} \log (3 x+2)-\frac{1}{875} \log (5 x+1)","\frac{x^2}{30}-\frac{13 x}{225}+\frac{8}{189} \log (3 x+2)-\frac{1}{875} \log (5 x+1)",1,"(-13*x)/225 + x^2/30 + (8*Log[2 + 3*x])/189 - Log[1 + 5*x]/875","A",6,4,16,0.2500,1,"{1386, 701, 632, 31}"
380,1,26,0,0.0147503,"\int \frac{x}{13+\frac{2}{x}+15 x} \, dx","Int[x/(13 + 2/x + 15*x),x]","\frac{x}{15}-\frac{4}{63} \log (3 x+2)+\frac{1}{175} \log (5 x+1)","\frac{x}{15}-\frac{4}{63} \log (3 x+2)+\frac{1}{175} \log (5 x+1)",1,"x/15 - (4*Log[2 + 3*x])/63 + Log[1 + 5*x]/175","A",5,4,14,0.2857,1,"{1386, 703, 632, 31}"
381,1,21,0,0.0073871,"\int \frac{1}{13+\frac{2}{x}+15 x} \, dx","Int[(13 + 2/x + 15*x)^(-1),x]","\frac{2}{21} \log (3 x+2)-\frac{1}{35} \log (5 x+1)","\frac{2}{21} \log (3 x+2)-\frac{1}{35} \log (5 x+1)",1,"(2*Log[2 + 3*x])/21 - Log[1 + 5*x]/35","A",4,3,12,0.2500,1,"{1350, 632, 31}"
382,1,21,0,0.0104293,"\int \frac{1}{x \left(13+\frac{2}{x}+15 x\right)} \, dx","Int[1/(x*(13 + 2/x + 15*x)),x]","\frac{1}{7} \log (5 x+1)-\frac{1}{7} \log (3 x+2)","\frac{1}{7} \log (5 x+1)-\frac{1}{7} \log (3 x+2)",1,"-Log[2 + 3*x]/7 + Log[1 + 5*x]/7","A",4,3,16,0.1875,1,"{1386, 616, 31}"
383,1,27,0,0.0157206,"\int \frac{1}{x^2 \left(13+\frac{2}{x}+15 x\right)} \, dx","Int[1/(x^2*(13 + 2/x + 15*x)),x]","\frac{\log (x)}{2}+\frac{3}{14} \log (3 x+2)-\frac{5}{7} \log (5 x+1)","\frac{\log (x)}{2}+\frac{3}{14} \log (3 x+2)-\frac{5}{7} \log (5 x+1)",1,"Log[x]/2 + (3*Log[2 + 3*x])/14 - (5*Log[1 + 5*x])/7","A",6,5,16,0.3125,1,"{1386, 705, 29, 632, 31}"
384,1,34,0,0.0297196,"\int \frac{1}{x^3 \left(13+\frac{2}{x}+15 x\right)} \, dx","Int[1/(x^3*(13 + 2/x + 15*x)),x]","-\frac{1}{2 x}-\frac{13 \log (x)}{4}-\frac{9}{28} \log (3 x+2)+\frac{25}{7} \log (5 x+1)","-\frac{1}{2 x}-\frac{13 \log (x)}{4}-\frac{9}{28} \log (3 x+2)+\frac{25}{7} \log (5 x+1)",1,"-1/(2*x) - (13*Log[x])/4 - (9*Log[2 + 3*x])/28 + (25*Log[1 + 5*x])/7","A",4,3,16,0.1875,1,"{1386, 709, 800}"
385,1,41,0,0.0338796,"\int \frac{1}{x^4 \left(13+\frac{2}{x}+15 x\right)} \, dx","Int[1/(x^4*(13 + 2/x + 15*x)),x]","-\frac{1}{4 x^2}+\frac{13}{4 x}+\frac{139 \log (x)}{8}+\frac{27}{56} \log (3 x+2)-\frac{125}{7} \log (5 x+1)","-\frac{1}{4 x^2}+\frac{13}{4 x}+\frac{139 \log (x)}{8}+\frac{27}{56} \log (3 x+2)-\frac{125}{7} \log (5 x+1)",1,"-1/(4*x^2) + 13/(4*x) + (139*Log[x])/8 + (27*Log[2 + 3*x])/56 - (125*Log[1 + 5*x])/7","A",4,3,16,0.1875,1,"{1386, 709, 800}"
386,1,48,0,0.040875,"\int \frac{1}{x^5 \left(13+\frac{2}{x}+15 x\right)} \, dx","Int[1/(x^5*(13 + 2/x + 15*x)),x]","\frac{13}{8 x^2}-\frac{1}{6 x^3}-\frac{139}{8 x}-\frac{1417 \log (x)}{16}-\frac{81}{112} \log (3 x+2)+\frac{625}{7} \log (5 x+1)","\frac{13}{8 x^2}-\frac{1}{6 x^3}-\frac{139}{8 x}-\frac{1417 \log (x)}{16}-\frac{81}{112} \log (3 x+2)+\frac{625}{7} \log (5 x+1)",1,"-1/(6*x^3) + 13/(8*x^2) - 139/(8*x) - (1417*Log[x])/16 - (81*Log[2 + 3*x])/112 + (625*Log[1 + 5*x])/7","A",4,3,16,0.1875,1,"{1386, 709, 800}"
387,1,157,0,0.1682973,"\int \frac{x^2}{2-\left(1+x^2\right)^4} \, dx","Int[x^2/(2 - (1 + x^2)^4),x]","\frac{i \sqrt{1-i \sqrt[4]{2}} \tan ^{-1}\left(\frac{x}{\sqrt{1-i \sqrt[4]{2}}}\right)}{4\ 2^{3/4}}-\frac{i \sqrt{1+i \sqrt[4]{2}} \tan ^{-1}\left(\frac{x}{\sqrt{1+i \sqrt[4]{2}}}\right)}{4\ 2^{3/4}}-\frac{\sqrt{1+\sqrt[4]{2}} \tan ^{-1}\left(\frac{x}{\sqrt{1+\sqrt[4]{2}}}\right)}{4\ 2^{3/4}}+\frac{\sqrt{\sqrt[4]{2}-1} \tanh ^{-1}\left(\frac{x}{\sqrt{\sqrt[4]{2}-1}}\right)}{4\ 2^{3/4}}","\frac{i \sqrt{1-i \sqrt[4]{2}} \tan ^{-1}\left(\frac{x}{\sqrt{1-i \sqrt[4]{2}}}\right)}{4\ 2^{3/4}}-\frac{i \sqrt{1+i \sqrt[4]{2}} \tan ^{-1}\left(\frac{x}{\sqrt{1+i \sqrt[4]{2}}}\right)}{4\ 2^{3/4}}-\frac{\sqrt{1+\sqrt[4]{2}} \tan ^{-1}\left(\frac{x}{\sqrt{1+\sqrt[4]{2}}}\right)}{4\ 2^{3/4}}+\frac{\sqrt{\sqrt[4]{2}-1} \tanh ^{-1}\left(\frac{x}{\sqrt{\sqrt[4]{2}-1}}\right)}{4\ 2^{3/4}}",1,"((I/4)*Sqrt[1 - I*2^(1/4)]*ArcTan[x/Sqrt[1 - I*2^(1/4)]])/2^(3/4) - ((I/4)*Sqrt[1 + I*2^(1/4)]*ArcTan[x/Sqrt[1 + I*2^(1/4)]])/2^(3/4) - (Sqrt[1 + 2^(1/4)]*ArcTan[x/Sqrt[1 + 2^(1/4)]])/(4*2^(3/4)) + (Sqrt[-1 + 2^(1/4)]*ArcTanh[x/Sqrt[-1 + 2^(1/4)]])/(4*2^(3/4))","A",8,5,17,0.2941,1,"{6740, 206, 203, 1972, 205}"
388,1,157,0,0.1115251,"\int \frac{x^2}{2-\left(1-x^2\right)^4} \, dx","Int[x^2/(2 - (1 - x^2)^4),x]","-\frac{\sqrt{\sqrt[4]{2}-1} \tan ^{-1}\left(\frac{x}{\sqrt{\sqrt[4]{2}-1}}\right)}{4\ 2^{3/4}}-\frac{i \sqrt{1-i \sqrt[4]{2}} \tanh ^{-1}\left(\frac{x}{\sqrt{1-i \sqrt[4]{2}}}\right)}{4\ 2^{3/4}}+\frac{i \sqrt{1+i \sqrt[4]{2}} \tanh ^{-1}\left(\frac{x}{\sqrt{1+i \sqrt[4]{2}}}\right)}{4\ 2^{3/4}}+\frac{\sqrt{1+\sqrt[4]{2}} \tanh ^{-1}\left(\frac{x}{\sqrt{1+\sqrt[4]{2}}}\right)}{4\ 2^{3/4}}","-\frac{\sqrt{\sqrt[4]{2}-1} \tan ^{-1}\left(\frac{x}{\sqrt{\sqrt[4]{2}-1}}\right)}{4\ 2^{3/4}}-\frac{i \sqrt{1-i \sqrt[4]{2}} \tanh ^{-1}\left(\frac{x}{\sqrt{1-i \sqrt[4]{2}}}\right)}{4\ 2^{3/4}}+\frac{i \sqrt{1+i \sqrt[4]{2}} \tanh ^{-1}\left(\frac{x}{\sqrt{1+i \sqrt[4]{2}}}\right)}{4\ 2^{3/4}}+\frac{\sqrt{1+\sqrt[4]{2}} \tanh ^{-1}\left(\frac{x}{\sqrt{1+\sqrt[4]{2}}}\right)}{4\ 2^{3/4}}",1,"-(Sqrt[-1 + 2^(1/4)]*ArcTan[x/Sqrt[-1 + 2^(1/4)]])/(4*2^(3/4)) - ((I/4)*Sqrt[1 - I*2^(1/4)]*ArcTanh[x/Sqrt[1 - I*2^(1/4)]])/2^(3/4) + ((I/4)*Sqrt[1 + I*2^(1/4)]*ArcTanh[x/Sqrt[1 + I*2^(1/4)]])/2^(3/4) + (Sqrt[1 + 2^(1/4)]*ArcTanh[x/Sqrt[1 + 2^(1/4)]])/(4*2^(3/4))","A",8,5,19,0.2632,1,"{6740, 206, 203, 1972, 208}"
389,1,188,0,0.2760791,"\int \frac{x^2}{2+\left(1+x^2\right)^4} \, dx","Int[x^2/(2 + (1 + x^2)^4),x]","\frac{\sqrt[4]{-1} \sqrt{1-\sqrt[4]{-2}} \tan ^{-1}\left(\frac{x}{\sqrt{1-\sqrt[4]{-2}}}\right)}{4\ 2^{3/4}}-\frac{(-1)^{3/4} \sqrt{1+i \sqrt[4]{-2}} \tan ^{-1}\left(\frac{x}{\sqrt{1+i \sqrt[4]{-2}}}\right)}{4\ 2^{3/4}}-\frac{\sqrt[4]{-1} \sqrt{1+\sqrt[4]{-2}} \tan ^{-1}\left(\frac{x}{\sqrt{1+\sqrt[4]{-2}}}\right)}{4\ 2^{3/4}}+\frac{1}{8} i \left(\sqrt[4]{-2}+\sqrt{2}\right) \sqrt{\frac{1+i}{2^{3/4}+(1+i)}} \tan ^{-1}\left(\sqrt{\frac{1+i}{2^{3/4}+(1+i)}} x\right)","\frac{\sqrt[4]{-1} \sqrt{1-\sqrt[4]{-2}} \tan ^{-1}\left(\frac{x}{\sqrt{1-\sqrt[4]{-2}}}\right)}{4\ 2^{3/4}}-\frac{(-1)^{3/4} \sqrt{1+i \sqrt[4]{-2}} \tan ^{-1}\left(\frac{x}{\sqrt{1+i \sqrt[4]{-2}}}\right)}{4\ 2^{3/4}}-\frac{\sqrt[4]{-1} \sqrt{1+\sqrt[4]{-2}} \tan ^{-1}\left(\frac{x}{\sqrt{1+\sqrt[4]{-2}}}\right)}{4\ 2^{3/4}}+\frac{1}{8} i \left(\sqrt[4]{-2}+\sqrt{2}\right) \sqrt{\frac{1+i}{2^{3/4}+(1+i)}} \tan ^{-1}\left(\sqrt{\frac{1+i}{2^{3/4}+(1+i)}} x\right)",1,"((-1)^(1/4)*Sqrt[1 - (-2)^(1/4)]*ArcTan[x/Sqrt[1 - (-2)^(1/4)]])/(4*2^(3/4)) - ((-1)^(3/4)*Sqrt[1 + I*(-2)^(1/4)]*ArcTan[x/Sqrt[1 + I*(-2)^(1/4)]])/(4*2^(3/4)) - ((-1)^(1/4)*Sqrt[1 + (-2)^(1/4)]*ArcTan[x/Sqrt[1 + (-2)^(1/4)]])/(4*2^(3/4)) + (I/8)*((-2)^(1/4) + Sqrt[2])*Sqrt[(1 + I)/((1 + I) + 2^(3/4))]*ArcTan[Sqrt[(1 + I)/((1 + I) + 2^(3/4))]*x]","A",8,5,15,0.3333,1,"{6740, 204, 203, 1972, 205}"
390,1,188,0,0.1557244,"\int \frac{x^2}{2+\left(1-x^2\right)^4} \, dx","Int[x^2/(2 + (1 - x^2)^4),x]","-\frac{\sqrt[4]{-1} \sqrt{1-\sqrt[4]{-2}} \tanh ^{-1}\left(\frac{x}{\sqrt{1-\sqrt[4]{-2}}}\right)}{4\ 2^{3/4}}+\frac{(-1)^{3/4} \sqrt{1+i \sqrt[4]{-2}} \tanh ^{-1}\left(\frac{x}{\sqrt{1+i \sqrt[4]{-2}}}\right)}{4\ 2^{3/4}}+\frac{\sqrt[4]{-1} \sqrt{1+\sqrt[4]{-2}} \tanh ^{-1}\left(\frac{x}{\sqrt{1+\sqrt[4]{-2}}}\right)}{4\ 2^{3/4}}-\frac{1}{8} i \left(\sqrt[4]{-2}+\sqrt{2}\right) \sqrt{\frac{1+i}{2^{3/4}+(1+i)}} \tanh ^{-1}\left(\sqrt{\frac{1+i}{2^{3/4}+(1+i)}} x\right)","-\frac{\sqrt[4]{-1} \sqrt{1-\sqrt[4]{-2}} \tanh ^{-1}\left(\frac{x}{\sqrt{1-\sqrt[4]{-2}}}\right)}{4\ 2^{3/4}}+\frac{(-1)^{3/4} \sqrt{1+i \sqrt[4]{-2}} \tanh ^{-1}\left(\frac{x}{\sqrt{1+i \sqrt[4]{-2}}}\right)}{4\ 2^{3/4}}+\frac{\sqrt[4]{-1} \sqrt{1+\sqrt[4]{-2}} \tanh ^{-1}\left(\frac{x}{\sqrt{1+\sqrt[4]{-2}}}\right)}{4\ 2^{3/4}}-\frac{1}{8} i \left(\sqrt[4]{-2}+\sqrt{2}\right) \sqrt{\frac{1+i}{2^{3/4}+(1+i)}} \tanh ^{-1}\left(\sqrt{\frac{1+i}{2^{3/4}+(1+i)}} x\right)",1,"-((-1)^(1/4)*Sqrt[1 - (-2)^(1/4)]*ArcTanh[x/Sqrt[1 - (-2)^(1/4)]])/(4*2^(3/4)) + ((-1)^(3/4)*Sqrt[1 + I*(-2)^(1/4)]*ArcTanh[x/Sqrt[1 + I*(-2)^(1/4)]])/(4*2^(3/4)) + ((-1)^(1/4)*Sqrt[1 + (-2)^(1/4)]*ArcTanh[x/Sqrt[1 + (-2)^(1/4)]])/(4*2^(3/4)) - (I/8)*((-2)^(1/4) + Sqrt[2])*Sqrt[(1 + I)/((1 + I) + 2^(3/4))]*ArcTanh[Sqrt[(1 + I)/((1 + I) + 2^(3/4))]*x]","A",8,5,17,0.2941,1,"{6740, 206, 207, 1972, 208}"
391,1,663,0,1.1077484,"\int \frac{1-x^2}{a+b \left(1-x^2\right)^4} \, dx","Int[(1 - x^2)/(a + b*(1 - x^2)^4),x]","\frac{\sqrt{\sqrt{\sqrt{-a}+\sqrt{b}}+\sqrt[4]{b}} \log \left(-\sqrt{2} \sqrt[8]{b} x \sqrt{\sqrt{\sqrt{-a}+\sqrt{b}}+\sqrt[4]{b}}+\sqrt{\sqrt{-a}+\sqrt{b}}+\sqrt[4]{b} x^2\right)}{8 \sqrt{2} \sqrt{-a} b^{3/8} \sqrt{\sqrt{-a}+\sqrt{b}}}-\frac{\sqrt{\sqrt{\sqrt{-a}+\sqrt{b}}+\sqrt[4]{b}} \log \left(\sqrt{2} \sqrt[8]{b} x \sqrt{\sqrt{\sqrt{-a}+\sqrt{b}}+\sqrt[4]{b}}+\sqrt{\sqrt{-a}+\sqrt{b}}+\sqrt[4]{b} x^2\right)}{8 \sqrt{2} \sqrt{-a} b^{3/8} \sqrt{\sqrt{-a}+\sqrt{b}}}-\frac{\tan ^{-1}\left(\frac{\sqrt[8]{b} x}{\sqrt{\sqrt[4]{-a}-\sqrt[4]{b}}}\right)}{4 \sqrt{-a} b^{3/8} \sqrt{\sqrt[4]{-a}-\sqrt[4]{b}}}-\frac{\sqrt{\sqrt{\sqrt{-a}+\sqrt{b}}-\sqrt[4]{b}} \tan ^{-1}\left(\frac{\sqrt{\sqrt{\sqrt{-a}+\sqrt{b}}+\sqrt[4]{b}}-\sqrt{2} \sqrt[8]{b} x}{\sqrt{\sqrt{\sqrt{-a}+\sqrt{b}}-\sqrt[4]{b}}}\right)}{4 \sqrt{2} \sqrt{-a} b^{3/8} \sqrt{\sqrt{-a}+\sqrt{b}}}+\frac{\sqrt{\sqrt{\sqrt{-a}+\sqrt{b}}-\sqrt[4]{b}} \tan ^{-1}\left(\frac{\sqrt{\sqrt{\sqrt{-a}+\sqrt{b}}+\sqrt[4]{b}}+\sqrt{2} \sqrt[8]{b} x}{\sqrt{\sqrt{\sqrt{-a}+\sqrt{b}}-\sqrt[4]{b}}}\right)}{4 \sqrt{2} \sqrt{-a} b^{3/8} \sqrt{\sqrt{-a}+\sqrt{b}}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{b} x}{\sqrt{\sqrt[4]{-a}+\sqrt[4]{b}}}\right)}{4 \sqrt{-a} b^{3/8} \sqrt{\sqrt[4]{-a}+\sqrt[4]{b}}}","\frac{\sqrt{\sqrt{\sqrt{-a}+\sqrt{b}}+\sqrt[4]{b}} \log \left(-\sqrt{2} \sqrt[8]{b} x \sqrt{\sqrt{\sqrt{-a}+\sqrt{b}}+\sqrt[4]{b}}+\sqrt{\sqrt{-a}+\sqrt{b}}+\sqrt[4]{b} x^2\right)}{8 \sqrt{2} \sqrt{-a} b^{3/8} \sqrt{\sqrt{-a}+\sqrt{b}}}-\frac{\sqrt{\sqrt{\sqrt{-a}+\sqrt{b}}+\sqrt[4]{b}} \log \left(\sqrt{2} \sqrt[8]{b} x \sqrt{\sqrt{\sqrt{-a}+\sqrt{b}}+\sqrt[4]{b}}+\sqrt{\sqrt{-a}+\sqrt{b}}+\sqrt[4]{b} x^2\right)}{8 \sqrt{2} \sqrt{-a} b^{3/8} \sqrt{\sqrt{-a}+\sqrt{b}}}-\frac{\tan ^{-1}\left(\frac{\sqrt[8]{b} x}{\sqrt{\sqrt[4]{-a}-\sqrt[4]{b}}}\right)}{4 \sqrt{-a} b^{3/8} \sqrt{\sqrt[4]{-a}-\sqrt[4]{b}}}-\frac{\sqrt{\sqrt{\sqrt{-a}+\sqrt{b}}-\sqrt[4]{b}} \tan ^{-1}\left(\frac{\sqrt{\sqrt{\sqrt{-a}+\sqrt{b}}+\sqrt[4]{b}}-\sqrt{2} \sqrt[8]{b} x}{\sqrt{\sqrt{\sqrt{-a}+\sqrt{b}}-\sqrt[4]{b}}}\right)}{4 \sqrt{2} \sqrt{-a} b^{3/8} \sqrt{\sqrt{-a}+\sqrt{b}}}+\frac{\sqrt{\sqrt{\sqrt{-a}+\sqrt{b}}-\sqrt[4]{b}} \tan ^{-1}\left(\frac{\sqrt{\sqrt{\sqrt{-a}+\sqrt{b}}+\sqrt[4]{b}}+\sqrt{2} \sqrt[8]{b} x}{\sqrt{\sqrt{\sqrt{-a}+\sqrt{b}}-\sqrt[4]{b}}}\right)}{4 \sqrt{2} \sqrt{-a} b^{3/8} \sqrt{\sqrt{-a}+\sqrt{b}}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{b} x}{\sqrt{\sqrt[4]{-a}+\sqrt[4]{b}}}\right)}{4 \sqrt{-a} b^{3/8} \sqrt{\sqrt[4]{-a}+\sqrt[4]{b}}}",1,"-ArcTan[(b^(1/8)*x)/Sqrt[(-a)^(1/4) - b^(1/4)]]/(4*Sqrt[-a]*Sqrt[(-a)^(1/4) - b^(1/4)]*b^(3/8)) - (Sqrt[Sqrt[Sqrt[-a] + Sqrt[b]] - b^(1/4)]*ArcTan[(Sqrt[Sqrt[Sqrt[-a] + Sqrt[b]] + b^(1/4)] - Sqrt[2]*b^(1/8)*x)/Sqrt[Sqrt[Sqrt[-a] + Sqrt[b]] - b^(1/4)]])/(4*Sqrt[2]*Sqrt[-a]*Sqrt[Sqrt[-a] + Sqrt[b]]*b^(3/8)) + (Sqrt[Sqrt[Sqrt[-a] + Sqrt[b]] - b^(1/4)]*ArcTan[(Sqrt[Sqrt[Sqrt[-a] + Sqrt[b]] + b^(1/4)] + Sqrt[2]*b^(1/8)*x)/Sqrt[Sqrt[Sqrt[-a] + Sqrt[b]] - b^(1/4)]])/(4*Sqrt[2]*Sqrt[-a]*Sqrt[Sqrt[-a] + Sqrt[b]]*b^(3/8)) + ArcTanh[(b^(1/8)*x)/Sqrt[(-a)^(1/4) + b^(1/4)]]/(4*Sqrt[-a]*Sqrt[(-a)^(1/4) + b^(1/4)]*b^(3/8)) + (Sqrt[Sqrt[Sqrt[-a] + Sqrt[b]] + b^(1/4)]*Log[Sqrt[Sqrt[-a] + Sqrt[b]] - Sqrt[2]*Sqrt[Sqrt[Sqrt[-a] + Sqrt[b]] + b^(1/4)]*b^(1/8)*x + b^(1/4)*x^2])/(8*Sqrt[2]*Sqrt[-a]*Sqrt[Sqrt[-a] + Sqrt[b]]*b^(3/8)) - (Sqrt[Sqrt[Sqrt[-a] + Sqrt[b]] + b^(1/4)]*Log[Sqrt[Sqrt[-a] + Sqrt[b]] + Sqrt[2]*Sqrt[Sqrt[Sqrt[-a] + Sqrt[b]] + b^(1/4)]*b^(1/8)*x + b^(1/4)*x^2])/(8*Sqrt[2]*Sqrt[-a]*Sqrt[Sqrt[-a] + Sqrt[b]]*b^(3/8))","A",16,10,23,0.4348,1,"{6740, 1990, 1166, 205, 208, 1169, 634, 618, 204, 628}"
392,1,663,0,0.6482217,"\int \frac{1-x^2}{a+b \left(-1+x^2\right)^4} \, dx","Int[(1 - x^2)/(a + b*(-1 + x^2)^4),x]","\frac{\sqrt{\sqrt{\sqrt{-a}+\sqrt{b}}+\sqrt[4]{b}} \log \left(-\sqrt{2} \sqrt[8]{b} x \sqrt{\sqrt{\sqrt{-a}+\sqrt{b}}+\sqrt[4]{b}}+\sqrt{\sqrt{-a}+\sqrt{b}}+\sqrt[4]{b} x^2\right)}{8 \sqrt{2} \sqrt{-a} b^{3/8} \sqrt{\sqrt{-a}+\sqrt{b}}}-\frac{\sqrt{\sqrt{\sqrt{-a}+\sqrt{b}}+\sqrt[4]{b}} \log \left(\sqrt{2} \sqrt[8]{b} x \sqrt{\sqrt{\sqrt{-a}+\sqrt{b}}+\sqrt[4]{b}}+\sqrt{\sqrt{-a}+\sqrt{b}}+\sqrt[4]{b} x^2\right)}{8 \sqrt{2} \sqrt{-a} b^{3/8} \sqrt{\sqrt{-a}+\sqrt{b}}}-\frac{\tan ^{-1}\left(\frac{\sqrt[8]{b} x}{\sqrt{\sqrt[4]{-a}-\sqrt[4]{b}}}\right)}{4 \sqrt{-a} b^{3/8} \sqrt{\sqrt[4]{-a}-\sqrt[4]{b}}}-\frac{\sqrt{\sqrt{\sqrt{-a}+\sqrt{b}}-\sqrt[4]{b}} \tan ^{-1}\left(\frac{\sqrt{\sqrt{\sqrt{-a}+\sqrt{b}}+\sqrt[4]{b}}-\sqrt{2} \sqrt[8]{b} x}{\sqrt{\sqrt{\sqrt{-a}+\sqrt{b}}-\sqrt[4]{b}}}\right)}{4 \sqrt{2} \sqrt{-a} b^{3/8} \sqrt{\sqrt{-a}+\sqrt{b}}}+\frac{\sqrt{\sqrt{\sqrt{-a}+\sqrt{b}}-\sqrt[4]{b}} \tan ^{-1}\left(\frac{\sqrt{\sqrt{\sqrt{-a}+\sqrt{b}}+\sqrt[4]{b}}+\sqrt{2} \sqrt[8]{b} x}{\sqrt{\sqrt{\sqrt{-a}+\sqrt{b}}-\sqrt[4]{b}}}\right)}{4 \sqrt{2} \sqrt{-a} b^{3/8} \sqrt{\sqrt{-a}+\sqrt{b}}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{b} x}{\sqrt{\sqrt[4]{-a}+\sqrt[4]{b}}}\right)}{4 \sqrt{-a} b^{3/8} \sqrt{\sqrt[4]{-a}+\sqrt[4]{b}}}","\frac{\sqrt{\sqrt{\sqrt{-a}+\sqrt{b}}+\sqrt[4]{b}} \log \left(-\sqrt{2} \sqrt[8]{b} x \sqrt{\sqrt{\sqrt{-a}+\sqrt{b}}+\sqrt[4]{b}}+\sqrt{\sqrt{-a}+\sqrt{b}}+\sqrt[4]{b} x^2\right)}{8 \sqrt{2} \sqrt{-a} b^{3/8} \sqrt{\sqrt{-a}+\sqrt{b}}}-\frac{\sqrt{\sqrt{\sqrt{-a}+\sqrt{b}}+\sqrt[4]{b}} \log \left(\sqrt{2} \sqrt[8]{b} x \sqrt{\sqrt{\sqrt{-a}+\sqrt{b}}+\sqrt[4]{b}}+\sqrt{\sqrt{-a}+\sqrt{b}}+\sqrt[4]{b} x^2\right)}{8 \sqrt{2} \sqrt{-a} b^{3/8} \sqrt{\sqrt{-a}+\sqrt{b}}}-\frac{\tan ^{-1}\left(\frac{\sqrt[8]{b} x}{\sqrt{\sqrt[4]{-a}-\sqrt[4]{b}}}\right)}{4 \sqrt{-a} b^{3/8} \sqrt{\sqrt[4]{-a}-\sqrt[4]{b}}}-\frac{\sqrt{\sqrt{\sqrt{-a}+\sqrt{b}}-\sqrt[4]{b}} \tan ^{-1}\left(\frac{\sqrt{\sqrt{\sqrt{-a}+\sqrt{b}}+\sqrt[4]{b}}-\sqrt{2} \sqrt[8]{b} x}{\sqrt{\sqrt{\sqrt{-a}+\sqrt{b}}-\sqrt[4]{b}}}\right)}{4 \sqrt{2} \sqrt{-a} b^{3/8} \sqrt{\sqrt{-a}+\sqrt{b}}}+\frac{\sqrt{\sqrt{\sqrt{-a}+\sqrt{b}}-\sqrt[4]{b}} \tan ^{-1}\left(\frac{\sqrt{\sqrt{\sqrt{-a}+\sqrt{b}}+\sqrt[4]{b}}+\sqrt{2} \sqrt[8]{b} x}{\sqrt{\sqrt{\sqrt{-a}+\sqrt{b}}-\sqrt[4]{b}}}\right)}{4 \sqrt{2} \sqrt{-a} b^{3/8} \sqrt{\sqrt{-a}+\sqrt{b}}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{b} x}{\sqrt{\sqrt[4]{-a}+\sqrt[4]{b}}}\right)}{4 \sqrt{-a} b^{3/8} \sqrt{\sqrt[4]{-a}+\sqrt[4]{b}}}",1,"-ArcTan[(b^(1/8)*x)/Sqrt[(-a)^(1/4) - b^(1/4)]]/(4*Sqrt[-a]*Sqrt[(-a)^(1/4) - b^(1/4)]*b^(3/8)) - (Sqrt[Sqrt[Sqrt[-a] + Sqrt[b]] - b^(1/4)]*ArcTan[(Sqrt[Sqrt[Sqrt[-a] + Sqrt[b]] + b^(1/4)] - Sqrt[2]*b^(1/8)*x)/Sqrt[Sqrt[Sqrt[-a] + Sqrt[b]] - b^(1/4)]])/(4*Sqrt[2]*Sqrt[-a]*Sqrt[Sqrt[-a] + Sqrt[b]]*b^(3/8)) + (Sqrt[Sqrt[Sqrt[-a] + Sqrt[b]] - b^(1/4)]*ArcTan[(Sqrt[Sqrt[Sqrt[-a] + Sqrt[b]] + b^(1/4)] + Sqrt[2]*b^(1/8)*x)/Sqrt[Sqrt[Sqrt[-a] + Sqrt[b]] - b^(1/4)]])/(4*Sqrt[2]*Sqrt[-a]*Sqrt[Sqrt[-a] + Sqrt[b]]*b^(3/8)) + ArcTanh[(b^(1/8)*x)/Sqrt[(-a)^(1/4) + b^(1/4)]]/(4*Sqrt[-a]*Sqrt[(-a)^(1/4) + b^(1/4)]*b^(3/8)) + (Sqrt[Sqrt[Sqrt[-a] + Sqrt[b]] + b^(1/4)]*Log[Sqrt[Sqrt[-a] + Sqrt[b]] - Sqrt[2]*Sqrt[Sqrt[Sqrt[-a] + Sqrt[b]] + b^(1/4)]*b^(1/8)*x + b^(1/4)*x^2])/(8*Sqrt[2]*Sqrt[-a]*Sqrt[Sqrt[-a] + Sqrt[b]]*b^(3/8)) - (Sqrt[Sqrt[Sqrt[-a] + Sqrt[b]] + b^(1/4)]*Log[Sqrt[Sqrt[-a] + Sqrt[b]] + Sqrt[2]*Sqrt[Sqrt[Sqrt[-a] + Sqrt[b]] + b^(1/4)]*b^(1/8)*x + b^(1/4)*x^2])/(8*Sqrt[2]*Sqrt[-a]*Sqrt[Sqrt[-a] + Sqrt[b]]*b^(3/8))","A",17,10,21,0.4762,1,"{6740, 1990, 1166, 205, 208, 1169, 634, 618, 204, 628}"
393,0,0,0,0.380003,"\int \frac{\left(1+x^2\right)^2}{a x^6+b \left(1+x^2\right)^3} \, dx","Int[(1 + x^2)^2/(a*x^6 + b*(1 + x^2)^3),x]","\int \frac{\left(1+x^2\right)^2}{a x^6+b \left(1+x^2\right)^3} \, dx","\frac{\tan ^{-1}\left(\frac{x \sqrt{\sqrt[3]{a}+\sqrt[3]{b}}}{\sqrt[6]{b}}\right)}{3 b^{5/6} \sqrt{\sqrt[3]{a}+\sqrt[3]{b}}}+\frac{\tan ^{-1}\left(\frac{x \sqrt{\sqrt[3]{b}-\sqrt[3]{-1} \sqrt[3]{a}}}{\sqrt[6]{b}}\right)}{3 b^{5/6} \sqrt{\sqrt[3]{b}-\sqrt[3]{-1} \sqrt[3]{a}}}+\frac{\tan ^{-1}\left(\frac{x \sqrt{(-1)^{2/3} \sqrt[3]{a}+\sqrt[3]{b}}}{\sqrt[6]{b}}\right)}{3 b^{5/6} \sqrt{(-1)^{2/3} \sqrt[3]{a}+\sqrt[3]{b}}}",1,"Defer[Int][(a*x^6 + b*(1 + x^2)^3)^(-1), x] + 2*Defer[Int][x^2/(a*x^6 + b*(1 + x^2)^3), x] + Defer[Int][x^4/(a*x^6 + b*(1 + x^2)^3), x]","F",0,0,0,0,-1,"{}"
394,1,320,0,0.2561013,"\int \frac{(d+e x)^3}{a+c x^4} \, dx","Int[(d + e*x)^3/(a + c*x^4),x]","-\frac{d \left(\sqrt{c} d^2-3 \sqrt{a} e^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{3/4} c^{3/4}}+\frac{d \left(\sqrt{c} d^2-3 \sqrt{a} e^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{3/4} c^{3/4}}-\frac{d \left(3 \sqrt{a} e^2+\sqrt{c} d^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} c^{3/4}}+\frac{d \left(3 \sqrt{a} e^2+\sqrt{c} d^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} c^{3/4}}+\frac{3 d^2 e \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{2 \sqrt{a} \sqrt{c}}+\frac{e^3 \log \left(a+c x^4\right)}{4 c}","-\frac{d \left(\sqrt{c} d^2-3 \sqrt{a} e^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{3/4} c^{3/4}}+\frac{d \left(\sqrt{c} d^2-3 \sqrt{a} e^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{3/4} c^{3/4}}-\frac{d \left(3 \sqrt{a} e^2+\sqrt{c} d^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} c^{3/4}}+\frac{d \left(3 \sqrt{a} e^2+\sqrt{c} d^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} c^{3/4}}+\frac{3 d^2 e \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{2 \sqrt{a} \sqrt{c}}+\frac{e^3 \log \left(a+c x^4\right)}{4 c}",1,"(3*d^2*e*ArcTan[(Sqrt[c]*x^2)/Sqrt[a]])/(2*Sqrt[a]*Sqrt[c]) - (d*(Sqrt[c]*d^2 + 3*Sqrt[a]*e^2)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*c^(3/4)) + (d*(Sqrt[c]*d^2 + 3*Sqrt[a]*e^2)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*c^(3/4)) - (d*(Sqrt[c]*d^2 - 3*Sqrt[a]*e^2)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(4*Sqrt[2]*a^(3/4)*c^(3/4)) + (d*(Sqrt[c]*d^2 - 3*Sqrt[a]*e^2)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(4*Sqrt[2]*a^(3/4)*c^(3/4)) + (e^3*Log[a + c*x^4])/(4*c)","A",15,11,17,0.6471,1,"{1876, 1168, 1162, 617, 204, 1165, 628, 1248, 635, 205, 260}"
395,1,291,0,0.1980063,"\int \frac{(d+e x)^2}{a+c x^4} \, dx","Int[(d + e*x)^2/(a + c*x^4),x]","-\frac{\left(\sqrt{c} d^2-\sqrt{a} e^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{3/4} c^{3/4}}+\frac{\left(\sqrt{c} d^2-\sqrt{a} e^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{3/4} c^{3/4}}-\frac{\left(\sqrt{a} e^2+\sqrt{c} d^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} c^{3/4}}+\frac{\left(\sqrt{a} e^2+\sqrt{c} d^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} c^{3/4}}+\frac{d e \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{c}}","-\frac{\left(\sqrt{c} d^2-\sqrt{a} e^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{3/4} c^{3/4}}+\frac{\left(\sqrt{c} d^2-\sqrt{a} e^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{3/4} c^{3/4}}-\frac{\left(\sqrt{a} e^2+\sqrt{c} d^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} c^{3/4}}+\frac{\left(\sqrt{a} e^2+\sqrt{c} d^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} c^{3/4}}+\frac{d e \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{c}}",1,"(d*e*ArcTan[(Sqrt[c]*x^2)/Sqrt[a]])/(Sqrt[a]*Sqrt[c]) - ((Sqrt[c]*d^2 + Sqrt[a]*e^2)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*c^(3/4)) + ((Sqrt[c]*d^2 + Sqrt[a]*e^2)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*c^(3/4)) - ((Sqrt[c]*d^2 - Sqrt[a]*e^2)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(4*Sqrt[2]*a^(3/4)*c^(3/4)) + ((Sqrt[c]*d^2 - Sqrt[a]*e^2)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(4*Sqrt[2]*a^(3/4)*c^(3/4))","A",13,9,17,0.5294,1,"{1876, 275, 205, 1168, 1162, 617, 204, 1165, 628}"
396,1,219,0,0.1739486,"\int \frac{d+e x}{a+c x^4} \, dx","Int[(d + e*x)/(a + c*x^4),x]","-\frac{d \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{3/4} \sqrt[4]{c}}+\frac{d \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{3/4} \sqrt[4]{c}}-\frac{d \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} \sqrt[4]{c}}+\frac{d \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} \sqrt[4]{c}}+\frac{e \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{2 \sqrt{a} \sqrt{c}}","-\frac{d \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{3/4} \sqrt[4]{c}}+\frac{d \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{3/4} \sqrt[4]{c}}-\frac{d \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} \sqrt[4]{c}}+\frac{d \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} \sqrt[4]{c}}+\frac{e \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{2 \sqrt{a} \sqrt{c}}",1,"(e*ArcTan[(Sqrt[c]*x^2)/Sqrt[a]])/(2*Sqrt[a]*Sqrt[c]) - (d*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*c^(1/4)) + (d*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*c^(1/4)) - (d*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(4*Sqrt[2]*a^(3/4)*c^(1/4)) + (d*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(4*Sqrt[2]*a^(3/4)*c^(1/4))","A",13,9,15,0.6000,1,"{1876, 211, 1165, 628, 1162, 617, 204, 275, 205}"
397,1,185,0,0.0983566,"\int \frac{1}{a+c x^4} \, dx","Int[(a + c*x^4)^(-1),x]","-\frac{\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{3/4} \sqrt[4]{c}}+\frac{\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{3/4} \sqrt[4]{c}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} \sqrt[4]{c}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} \sqrt[4]{c}}","-\frac{\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{3/4} \sqrt[4]{c}}+\frac{\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{3/4} \sqrt[4]{c}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} \sqrt[4]{c}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} \sqrt[4]{c}}",1,"-ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)]/(2*Sqrt[2]*a^(3/4)*c^(1/4)) + ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)]/(2*Sqrt[2]*a^(3/4)*c^(1/4)) - Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2]/(4*Sqrt[2]*a^(3/4)*c^(1/4)) + Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2]/(4*Sqrt[2]*a^(3/4)*c^(1/4))","A",9,6,9,0.6667,1,"{211, 1165, 628, 1162, 617, 204}"
398,1,416,0,0.4284819,"\int \frac{1}{(d+e x) \left(a+c x^4\right)} \, dx","Int[1/((d + e*x)*(a + c*x^4)),x]","-\frac{\sqrt[4]{c} d \left(\sqrt{c} d^2-\sqrt{a} e^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{3/4} \left(a e^4+c d^4\right)}+\frac{\sqrt[4]{c} d \left(\sqrt{c} d^2-\sqrt{a} e^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{3/4} \left(a e^4+c d^4\right)}-\frac{\sqrt[4]{c} d \left(\sqrt{a} e^2+\sqrt{c} d^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} \left(a e^4+c d^4\right)}+\frac{\sqrt[4]{c} d \left(\sqrt{a} e^2+\sqrt{c} d^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} \left(a e^4+c d^4\right)}-\frac{e^3 \log \left(a+c x^4\right)}{4 \left(a e^4+c d^4\right)}-\frac{\sqrt{c} d^2 e \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{2 \sqrt{a} \left(a e^4+c d^4\right)}+\frac{e^3 \log (d+e x)}{a e^4+c d^4}","-\frac{\sqrt[4]{c} d \left(\sqrt{c} d^2-\sqrt{a} e^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{3/4} \left(a e^4+c d^4\right)}+\frac{\sqrt[4]{c} d \left(\sqrt{c} d^2-\sqrt{a} e^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{3/4} \left(a e^4+c d^4\right)}-\frac{\sqrt[4]{c} d \left(\sqrt{a} e^2+\sqrt{c} d^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} \left(a e^4+c d^4\right)}+\frac{\sqrt[4]{c} d \left(\sqrt{a} e^2+\sqrt{c} d^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} \left(a e^4+c d^4\right)}-\frac{e^3 \log \left(a+c x^4\right)}{4 \left(a e^4+c d^4\right)}-\frac{\sqrt{c} d^2 e \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{2 \sqrt{a} \left(a e^4+c d^4\right)}+\frac{e^3 \log (d+e x)}{a e^4+c d^4}",1,"-(Sqrt[c]*d^2*e*ArcTan[(Sqrt[c]*x^2)/Sqrt[a]])/(2*Sqrt[a]*(c*d^4 + a*e^4)) - (c^(1/4)*d*(Sqrt[c]*d^2 + Sqrt[a]*e^2)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*(c*d^4 + a*e^4)) + (c^(1/4)*d*(Sqrt[c]*d^2 + Sqrt[a]*e^2)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*(c*d^4 + a*e^4)) + (e^3*Log[d + e*x])/(c*d^4 + a*e^4) - (c^(1/4)*d*(Sqrt[c]*d^2 - Sqrt[a]*e^2)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(4*Sqrt[2]*a^(3/4)*(c*d^4 + a*e^4)) + (c^(1/4)*d*(Sqrt[c]*d^2 - Sqrt[a]*e^2)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(4*Sqrt[2]*a^(3/4)*(c*d^4 + a*e^4)) - (e^3*Log[a + c*x^4])/(4*(c*d^4 + a*e^4))","A",17,12,17,0.7059,1,"{6725, 1876, 1168, 1162, 617, 204, 1165, 628, 1248, 635, 205, 260}"
399,1,552,0,0.8083231,"\int \frac{1}{(d+e x)^2 \left(a+c x^4\right)} \, dx","Int[1/((d + e*x)^2*(a + c*x^4)),x]","-\frac{\sqrt[4]{c} \left(\sqrt{c} d^2 \left(c d^4-3 a e^4\right)-\sqrt{a} e^2 \left(3 c d^4-a e^4\right)\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{3/4} \left(a e^4+c d^4\right)^2}+\frac{\sqrt[4]{c} \left(\sqrt{c} d^2 \left(c d^4-3 a e^4\right)-\sqrt{a} e^2 \left(3 c d^4-a e^4\right)\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{3/4} \left(a e^4+c d^4\right)^2}-\frac{\sqrt[4]{c} \left(\sqrt{c} d^2 \left(c d^4-3 a e^4\right)+\sqrt{a} e^2 \left(3 c d^4-a e^4\right)\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} \left(a e^4+c d^4\right)^2}+\frac{\sqrt[4]{c} \left(\sqrt{c} d^2 \left(c d^4-3 a e^4\right)+\sqrt{a} e^2 \left(3 c d^4-a e^4\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} \left(a e^4+c d^4\right)^2}-\frac{c d^3 e^3 \log \left(a+c x^4\right)}{\left(a e^4+c d^4\right)^2}-\frac{\sqrt{c} d e \left(c d^4-a e^4\right) \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{\sqrt{a} \left(a e^4+c d^4\right)^2}-\frac{e^3}{(d+e x) \left(a e^4+c d^4\right)}+\frac{4 c d^3 e^3 \log (d+e x)}{\left(a e^4+c d^4\right)^2}","-\frac{\sqrt[4]{c} \left(\sqrt{c} d^2 \left(c d^4-3 a e^4\right)-\sqrt{a} e^2 \left(3 c d^4-a e^4\right)\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{3/4} \left(a e^4+c d^4\right)^2}+\frac{\sqrt[4]{c} \left(\sqrt{c} d^2 \left(c d^4-3 a e^4\right)-\sqrt{a} e^2 \left(3 c d^4-a e^4\right)\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{3/4} \left(a e^4+c d^4\right)^2}-\frac{\sqrt[4]{c} \left(\sqrt{c} d^2 \left(c d^4-3 a e^4\right)+\sqrt{a} e^2 \left(3 c d^4-a e^4\right)\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} \left(a e^4+c d^4\right)^2}+\frac{\sqrt[4]{c} \left(\sqrt{c} d^2 \left(c d^4-3 a e^4\right)+\sqrt{a} e^2 \left(3 c d^4-a e^4\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} \left(a e^4+c d^4\right)^2}-\frac{c d^3 e^3 \log \left(a+c x^4\right)}{\left(a e^4+c d^4\right)^2}-\frac{\sqrt{c} d e \left(c d^4-a e^4\right) \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{\sqrt{a} \left(a e^4+c d^4\right)^2}-\frac{e^3}{(d+e x) \left(a e^4+c d^4\right)}+\frac{4 c d^3 e^3 \log (d+e x)}{\left(a e^4+c d^4\right)^2}",1,"-(e^3/((c*d^4 + a*e^4)*(d + e*x))) - (Sqrt[c]*d*e*(c*d^4 - a*e^4)*ArcTan[(Sqrt[c]*x^2)/Sqrt[a]])/(Sqrt[a]*(c*d^4 + a*e^4)^2) - (c^(1/4)*(Sqrt[c]*d^2*(c*d^4 - 3*a*e^4) + Sqrt[a]*e^2*(3*c*d^4 - a*e^4))*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*(c*d^4 + a*e^4)^2) + (c^(1/4)*(Sqrt[c]*d^2*(c*d^4 - 3*a*e^4) + Sqrt[a]*e^2*(3*c*d^4 - a*e^4))*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*(c*d^4 + a*e^4)^2) + (4*c*d^3*e^3*Log[d + e*x])/(c*d^4 + a*e^4)^2 - (c^(1/4)*(Sqrt[c]*d^2*(c*d^4 - 3*a*e^4) - Sqrt[a]*e^2*(3*c*d^4 - a*e^4))*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(4*Sqrt[2]*a^(3/4)*(c*d^4 + a*e^4)^2) + (c^(1/4)*(Sqrt[c]*d^2*(c*d^4 - 3*a*e^4) - Sqrt[a]*e^2*(3*c*d^4 - a*e^4))*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(4*Sqrt[2]*a^(3/4)*(c*d^4 + a*e^4)^2) - (c*d^3*e^3*Log[a + c*x^4])/(c*d^4 + a*e^4)^2","A",17,12,17,0.7059,1,"{6725, 1876, 1248, 635, 205, 260, 1168, 1162, 617, 204, 1165, 628}"
400,1,680,0,0.9498673,"\int \frac{1}{(d+e x)^3 \left(a+c x^4\right)} \, dx","Int[1/((d + e*x)^3*(a + c*x^4)),x]","-\frac{c^{3/4} d \left(3 a^2 e^8-12 a c d^4 e^4-2 \sqrt{a} \sqrt{c} d^2 e^2 \left(3 c d^4-5 a e^4\right)+c^2 d^8\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{3/4} \left(a e^4+c d^4\right)^3}+\frac{c^{3/4} d \left(3 a^2 e^8-12 a c d^4 e^4-2 \sqrt{a} \sqrt{c} d^2 e^2 \left(3 c d^4-5 a e^4\right)+c^2 d^8\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{3/4} \left(a e^4+c d^4\right)^3}-\frac{\sqrt{c} e \left(a^2 e^8-12 a c d^4 e^4+3 c^2 d^8\right) \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{2 \sqrt{a} \left(a e^4+c d^4\right)^3}-\frac{c^{3/4} d \left(3 a^2 e^8-12 a c d^4 e^4+2 \sqrt{a} \sqrt{c} d^2 e^2 \left(3 c d^4-5 a e^4\right)+c^2 d^8\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} \left(a e^4+c d^4\right)^3}+\frac{c^{3/4} d \left(3 a^2 e^8-12 a c d^4 e^4+2 \sqrt{a} \sqrt{c} d^2 e^2 \left(3 c d^4-5 a e^4\right)+c^2 d^8\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} \left(a e^4+c d^4\right)^3}-\frac{c d^2 e^3 \left(5 c d^4-3 a e^4\right) \log \left(a+c x^4\right)}{2 \left(a e^4+c d^4\right)^3}-\frac{4 c d^3 e^3}{(d+e x) \left(a e^4+c d^4\right)^2}-\frac{e^3}{2 (d+e x)^2 \left(a e^4+c d^4\right)}+\frac{2 c d^2 e^3 \left(5 c d^4-3 a e^4\right) \log (d+e x)}{\left(a e^4+c d^4\right)^3}","-\frac{c^{3/4} d \left(3 a^2 e^8-12 a c d^4 e^4-2 \sqrt{a} \sqrt{c} d^2 e^2 \left(3 c d^4-5 a e^4\right)+c^2 d^8\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{3/4} \left(a e^4+c d^4\right)^3}+\frac{c^{3/4} d \left(3 a^2 e^8-12 a c d^4 e^4-2 \sqrt{a} \sqrt{c} d^2 e^2 \left(3 c d^4-5 a e^4\right)+c^2 d^8\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{3/4} \left(a e^4+c d^4\right)^3}-\frac{\sqrt{c} e \left(a^2 e^8-12 a c d^4 e^4+3 c^2 d^8\right) \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{2 \sqrt{a} \left(a e^4+c d^4\right)^3}-\frac{c^{3/4} d \left(3 a^2 e^8-12 a c d^4 e^4+2 \sqrt{a} \sqrt{c} d^2 e^2 \left(3 c d^4-5 a e^4\right)+c^2 d^8\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} \left(a e^4+c d^4\right)^3}+\frac{c^{3/4} d \left(3 a^2 e^8-12 a c d^4 e^4+2 \sqrt{a} \sqrt{c} d^2 e^2 \left(3 c d^4-5 a e^4\right)+c^2 d^8\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} \left(a e^4+c d^4\right)^3}-\frac{c d^2 e^3 \left(5 c d^4-3 a e^4\right) \log \left(a+c x^4\right)}{2 \left(a e^4+c d^4\right)^3}-\frac{4 c d^3 e^3}{(d+e x) \left(a e^4+c d^4\right)^2}-\frac{e^3}{2 (d+e x)^2 \left(a e^4+c d^4\right)}+\frac{2 c d^2 e^3 \left(5 c d^4-3 a e^4\right) \log (d+e x)}{\left(a e^4+c d^4\right)^3}",1,"-e^3/(2*(c*d^4 + a*e^4)*(d + e*x)^2) - (4*c*d^3*e^3)/((c*d^4 + a*e^4)^2*(d + e*x)) - (Sqrt[c]*e*(3*c^2*d^8 - 12*a*c*d^4*e^4 + a^2*e^8)*ArcTan[(Sqrt[c]*x^2)/Sqrt[a]])/(2*Sqrt[a]*(c*d^4 + a*e^4)^3) - (c^(3/4)*d*(c^2*d^8 - 12*a*c*d^4*e^4 + 3*a^2*e^8 + 2*Sqrt[a]*Sqrt[c]*d^2*e^2*(3*c*d^4 - 5*a*e^4))*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*(c*d^4 + a*e^4)^3) + (c^(3/4)*d*(c^2*d^8 - 12*a*c*d^4*e^4 + 3*a^2*e^8 + 2*Sqrt[a]*Sqrt[c]*d^2*e^2*(3*c*d^4 - 5*a*e^4))*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*(c*d^4 + a*e^4)^3) + (2*c*d^2*e^3*(5*c*d^4 - 3*a*e^4)*Log[d + e*x])/(c*d^4 + a*e^4)^3 - (c^(3/4)*d*(c^2*d^8 - 12*a*c*d^4*e^4 + 3*a^2*e^8 - 2*Sqrt[a]*Sqrt[c]*d^2*e^2*(3*c*d^4 - 5*a*e^4))*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(4*Sqrt[2]*a^(3/4)*(c*d^4 + a*e^4)^3) + (c^(3/4)*d*(c^2*d^8 - 12*a*c*d^4*e^4 + 3*a^2*e^8 - 2*Sqrt[a]*Sqrt[c]*d^2*e^2*(3*c*d^4 - 5*a*e^4))*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(4*Sqrt[2]*a^(3/4)*(c*d^4 + a*e^4)^3) - (c*d^2*e^3*(5*c*d^4 - 3*a*e^4)*Log[a + c*x^4])/(2*(c*d^4 + a*e^4)^3)","A",17,12,17,0.7059,1,"{6725, 1876, 1168, 1162, 617, 204, 1165, 628, 1248, 635, 205, 260}"
401,1,349,0,0.2983677,"\int \frac{(d+e x)^3}{\left(a+c x^4\right)^2} \, dx","Int[(d + e*x)^3/(a + c*x^4)^2,x]","-\frac{3 d \left(\sqrt{c} d^2-\sqrt{a} e^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{16 \sqrt{2} a^{7/4} c^{3/4}}+\frac{3 d \left(\sqrt{c} d^2-\sqrt{a} e^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{16 \sqrt{2} a^{7/4} c^{3/4}}-\frac{3 d \left(\sqrt{a} e^2+\sqrt{c} d^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} a^{7/4} c^{3/4}}+\frac{3 d \left(\sqrt{a} e^2+\sqrt{c} d^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} a^{7/4} c^{3/4}}+\frac{3 d^2 e \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{4 a^{3/2} \sqrt{c}}-\frac{a e^3-c x \left(3 d^2 e x+d^3+3 d e^2 x^2\right)}{4 a c \left(a+c x^4\right)}","-\frac{3 d \left(\sqrt{c} d^2-\sqrt{a} e^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{16 \sqrt{2} a^{7/4} c^{3/4}}+\frac{3 d \left(\sqrt{c} d^2-\sqrt{a} e^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{16 \sqrt{2} a^{7/4} c^{3/4}}-\frac{3 d \left(\sqrt{a} e^2+\sqrt{c} d^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} a^{7/4} c^{3/4}}+\frac{3 d \left(\sqrt{a} e^2+\sqrt{c} d^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} a^{7/4} c^{3/4}}+\frac{3 d^2 e \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{4 a^{3/2} \sqrt{c}}-\frac{a e^3-c x \left(3 d^2 e x+d^3+3 d e^2 x^2\right)}{4 a c \left(a+c x^4\right)}",1,"-(a*e^3 - c*x*(d^3 + 3*d^2*e*x + 3*d*e^2*x^2))/(4*a*c*(a + c*x^4)) + (3*d^2*e*ArcTan[(Sqrt[c]*x^2)/Sqrt[a]])/(4*a^(3/2)*Sqrt[c]) - (3*d*(Sqrt[c]*d^2 + Sqrt[a]*e^2)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(7/4)*c^(3/4)) + (3*d*(Sqrt[c]*d^2 + Sqrt[a]*e^2)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(7/4)*c^(3/4)) - (3*d*(Sqrt[c]*d^2 - Sqrt[a]*e^2)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(16*Sqrt[2]*a^(7/4)*c^(3/4)) + (3*d*(Sqrt[c]*d^2 - Sqrt[a]*e^2)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(16*Sqrt[2]*a^(7/4)*c^(3/4))","A",16,12,17,0.7059,1,"{1854, 27, 12, 1876, 275, 205, 1168, 1162, 617, 204, 1165, 628}"
402,1,322,0,0.2691605,"\int \frac{(d+e x)^2}{\left(a+c x^4\right)^2} \, dx","Int[(d + e*x)^2/(a + c*x^4)^2,x]","-\frac{\left(3 \sqrt{c} d^2-\sqrt{a} e^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{16 \sqrt{2} a^{7/4} c^{3/4}}+\frac{\left(3 \sqrt{c} d^2-\sqrt{a} e^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{16 \sqrt{2} a^{7/4} c^{3/4}}-\frac{\left(\sqrt{a} e^2+3 \sqrt{c} d^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} a^{7/4} c^{3/4}}+\frac{\left(\sqrt{a} e^2+3 \sqrt{c} d^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} a^{7/4} c^{3/4}}+\frac{d e \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{c}}+\frac{x (d+e x)^2}{4 a \left(a+c x^4\right)}","-\frac{\left(3 \sqrt{c} d^2-\sqrt{a} e^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{16 \sqrt{2} a^{7/4} c^{3/4}}+\frac{\left(3 \sqrt{c} d^2-\sqrt{a} e^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{16 \sqrt{2} a^{7/4} c^{3/4}}-\frac{\left(\sqrt{a} e^2+3 \sqrt{c} d^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} a^{7/4} c^{3/4}}+\frac{\left(\sqrt{a} e^2+3 \sqrt{c} d^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} a^{7/4} c^{3/4}}+\frac{d e \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{c}}+\frac{x (d+e x)^2}{4 a \left(a+c x^4\right)}",1,"(x*(d + e*x)^2)/(4*a*(a + c*x^4)) + (d*e*ArcTan[(Sqrt[c]*x^2)/Sqrt[a]])/(2*a^(3/2)*Sqrt[c]) - ((3*Sqrt[c]*d^2 + Sqrt[a]*e^2)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(7/4)*c^(3/4)) + ((3*Sqrt[c]*d^2 + Sqrt[a]*e^2)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(7/4)*c^(3/4)) - ((3*Sqrt[c]*d^2 - Sqrt[a]*e^2)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(16*Sqrt[2]*a^(7/4)*c^(3/4)) + ((3*Sqrt[c]*d^2 - Sqrt[a]*e^2)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(16*Sqrt[2]*a^(7/4)*c^(3/4))","A",14,10,17,0.5882,1,"{1855, 1876, 275, 205, 1168, 1162, 617, 204, 1165, 628}"
403,1,241,0,0.1890062,"\int \frac{d+e x}{\left(a+c x^4\right)^2} \, dx","Int[(d + e*x)/(a + c*x^4)^2,x]","-\frac{3 d \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{16 \sqrt{2} a^{7/4} \sqrt[4]{c}}+\frac{3 d \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{16 \sqrt{2} a^{7/4} \sqrt[4]{c}}-\frac{3 d \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} a^{7/4} \sqrt[4]{c}}+\frac{3 d \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} a^{7/4} \sqrt[4]{c}}+\frac{e \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{4 a^{3/2} \sqrt{c}}+\frac{x (d+e x)}{4 a \left(a+c x^4\right)}","-\frac{3 d \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{16 \sqrt{2} a^{7/4} \sqrt[4]{c}}+\frac{3 d \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{16 \sqrt{2} a^{7/4} \sqrt[4]{c}}-\frac{3 d \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} a^{7/4} \sqrt[4]{c}}+\frac{3 d \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} a^{7/4} \sqrt[4]{c}}+\frac{e \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{4 a^{3/2} \sqrt{c}}+\frac{x (d+e x)}{4 a \left(a+c x^4\right)}",1,"(x*(d + e*x))/(4*a*(a + c*x^4)) + (e*ArcTan[(Sqrt[c]*x^2)/Sqrt[a]])/(4*a^(3/2)*Sqrt[c]) - (3*d*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(7/4)*c^(1/4)) + (3*d*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(7/4)*c^(1/4)) - (3*d*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(16*Sqrt[2]*a^(7/4)*c^(1/4)) + (3*d*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(16*Sqrt[2]*a^(7/4)*c^(1/4))","A",14,10,15,0.6667,1,"{1855, 1876, 211, 1165, 628, 1162, 617, 204, 275, 205}"
404,1,202,0,0.1156758,"\int \frac{1}{\left(a+c x^4\right)^2} \, dx","Int[(a + c*x^4)^(-2),x]","-\frac{3 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{16 \sqrt{2} a^{7/4} \sqrt[4]{c}}+\frac{3 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{16 \sqrt{2} a^{7/4} \sqrt[4]{c}}-\frac{3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} a^{7/4} \sqrt[4]{c}}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} a^{7/4} \sqrt[4]{c}}+\frac{x}{4 a \left(a+c x^4\right)}","-\frac{3 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{16 \sqrt{2} a^{7/4} \sqrt[4]{c}}+\frac{3 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{16 \sqrt{2} a^{7/4} \sqrt[4]{c}}-\frac{3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} a^{7/4} \sqrt[4]{c}}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} a^{7/4} \sqrt[4]{c}}+\frac{x}{4 a \left(a+c x^4\right)}",1,"x/(4*a*(a + c*x^4)) - (3*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(7/4)*c^(1/4)) + (3*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(7/4)*c^(1/4)) - (3*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(16*Sqrt[2]*a^(7/4)*c^(1/4)) + (3*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(16*Sqrt[2]*a^(7/4)*c^(1/4))","A",10,7,9,0.7778,1,"{199, 211, 1165, 628, 1162, 617, 204}"
405,1,855,0,0.849351,"\int \frac{1}{(d+e x) \left(a+c x^4\right)^2} \, dx","Int[1/((d + e*x)*(a + c*x^4)^2),x]","\frac{\log (d+e x) e^7}{\left(c d^4+a e^4\right)^2}-\frac{\log \left(c x^4+a\right) e^7}{4 \left(c d^4+a e^4\right)^2}-\frac{\sqrt{c} d^2 \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right) e^5}{2 \sqrt{a} \left(c d^4+a e^4\right)^2}-\frac{\sqrt[4]{c} d \left(\sqrt{c} d^2+\sqrt{a} e^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right) e^4}{2 \sqrt{2} a^{3/4} \left(c d^4+a e^4\right)^2}+\frac{\sqrt[4]{c} d \left(\sqrt{c} d^2+\sqrt{a} e^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right) e^4}{2 \sqrt{2} a^{3/4} \left(c d^4+a e^4\right)^2}-\frac{\sqrt[4]{c} d \left(\sqrt{c} d^2-\sqrt{a} e^2\right) \log \left(\sqrt{c} x^2-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right) e^4}{4 \sqrt{2} a^{3/4} \left(c d^4+a e^4\right)^2}+\frac{\sqrt[4]{c} d \left(\sqrt{c} d^2-\sqrt{a} e^2\right) \log \left(\sqrt{c} x^2+\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right) e^4}{4 \sqrt{2} a^{3/4} \left(c d^4+a e^4\right)^2}-\frac{\sqrt{c} d^2 \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right) e}{4 a^{3/2} \left(c d^4+a e^4\right)}+\frac{a e^3+c x \left(d^3-e x d^2+e^2 x^2 d\right)}{4 a \left(c d^4+a e^4\right) \left(c x^4+a\right)}-\frac{\sqrt[4]{c} d \left(3 \sqrt{c} d^2+\sqrt{a} e^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} a^{7/4} \left(c d^4+a e^4\right)}+\frac{\sqrt[4]{c} d \left(3 \sqrt{c} d^2+\sqrt{a} e^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} a^{7/4} \left(c d^4+a e^4\right)}-\frac{\sqrt[4]{c} d \left(3 \sqrt{c} d^2-\sqrt{a} e^2\right) \log \left(\sqrt{c} x^2-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right)}{16 \sqrt{2} a^{7/4} \left(c d^4+a e^4\right)}+\frac{\sqrt[4]{c} d \left(3 \sqrt{c} d^2-\sqrt{a} e^2\right) \log \left(\sqrt{c} x^2+\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right)}{16 \sqrt{2} a^{7/4} \left(c d^4+a e^4\right)}","\frac{\log (d+e x) e^7}{\left(c d^4+a e^4\right)^2}-\frac{\log \left(c x^4+a\right) e^7}{4 \left(c d^4+a e^4\right)^2}-\frac{\sqrt{c} d^2 \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right) e^5}{2 \sqrt{a} \left(c d^4+a e^4\right)^2}-\frac{\sqrt[4]{c} d \left(\sqrt{c} d^2+\sqrt{a} e^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right) e^4}{2 \sqrt{2} a^{3/4} \left(c d^4+a e^4\right)^2}+\frac{\sqrt[4]{c} d \left(\sqrt{c} d^2+\sqrt{a} e^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right) e^4}{2 \sqrt{2} a^{3/4} \left(c d^4+a e^4\right)^2}-\frac{\sqrt[4]{c} d \left(\sqrt{c} d^2-\sqrt{a} e^2\right) \log \left(\sqrt{c} x^2-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right) e^4}{4 \sqrt{2} a^{3/4} \left(c d^4+a e^4\right)^2}+\frac{\sqrt[4]{c} d \left(\sqrt{c} d^2-\sqrt{a} e^2\right) \log \left(\sqrt{c} x^2+\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right) e^4}{4 \sqrt{2} a^{3/4} \left(c d^4+a e^4\right)^2}-\frac{\sqrt{c} d^2 \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right) e}{4 a^{3/2} \left(c d^4+a e^4\right)}+\frac{a e^3+c x \left(d^3-e x d^2+e^2 x^2 d\right)}{4 a \left(c d^4+a e^4\right) \left(c x^4+a\right)}-\frac{\sqrt[4]{c} d \left(3 \sqrt{c} d^2+\sqrt{a} e^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} a^{7/4} \left(c d^4+a e^4\right)}+\frac{\sqrt[4]{c} d \left(3 \sqrt{c} d^2+\sqrt{a} e^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} a^{7/4} \left(c d^4+a e^4\right)}-\frac{\sqrt[4]{c} d \left(3 \sqrt{c} d^2-\sqrt{a} e^2\right) \log \left(\sqrt{c} x^2-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right)}{16 \sqrt{2} a^{7/4} \left(c d^4+a e^4\right)}+\frac{\sqrt[4]{c} d \left(3 \sqrt{c} d^2-\sqrt{a} e^2\right) \log \left(\sqrt{c} x^2+\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right)}{16 \sqrt{2} a^{7/4} \left(c d^4+a e^4\right)}",1,"(a*e^3 + c*x*(d^3 - d^2*e*x + d*e^2*x^2))/(4*a*(c*d^4 + a*e^4)*(a + c*x^4)) - (Sqrt[c]*d^2*e^5*ArcTan[(Sqrt[c]*x^2)/Sqrt[a]])/(2*Sqrt[a]*(c*d^4 + a*e^4)^2) - (Sqrt[c]*d^2*e*ArcTan[(Sqrt[c]*x^2)/Sqrt[a]])/(4*a^(3/2)*(c*d^4 + a*e^4)) - (c^(1/4)*d*e^4*(Sqrt[c]*d^2 + Sqrt[a]*e^2)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*(c*d^4 + a*e^4)^2) - (c^(1/4)*d*(3*Sqrt[c]*d^2 + Sqrt[a]*e^2)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(7/4)*(c*d^4 + a*e^4)) + (c^(1/4)*d*e^4*(Sqrt[c]*d^2 + Sqrt[a]*e^2)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*(c*d^4 + a*e^4)^2) + (c^(1/4)*d*(3*Sqrt[c]*d^2 + Sqrt[a]*e^2)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(7/4)*(c*d^4 + a*e^4)) + (e^7*Log[d + e*x])/(c*d^4 + a*e^4)^2 - (c^(1/4)*d*e^4*(Sqrt[c]*d^2 - Sqrt[a]*e^2)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(4*Sqrt[2]*a^(3/4)*(c*d^4 + a*e^4)^2) - (c^(1/4)*d*(3*Sqrt[c]*d^2 - Sqrt[a]*e^2)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(16*Sqrt[2]*a^(7/4)*(c*d^4 + a*e^4)) + (c^(1/4)*d*e^4*(Sqrt[c]*d^2 - Sqrt[a]*e^2)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(4*Sqrt[2]*a^(3/4)*(c*d^4 + a*e^4)^2) + (c^(1/4)*d*(3*Sqrt[c]*d^2 - Sqrt[a]*e^2)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(16*Sqrt[2]*a^(7/4)*(c*d^4 + a*e^4)) - (e^7*Log[a + c*x^4])/(4*(c*d^4 + a*e^4)^2)","A",31,14,17,0.8235,1,"{6742, 1854, 1876, 275, 205, 1168, 1162, 617, 204, 1165, 628, 1248, 635, 260}"
406,1,1141,0,1.65882,"\int \frac{1}{(d+e x)^2 \left(a+c x^4\right)^2} \, dx","Int[1/((d + e*x)^2*(a + c*x^4)^2),x]","\frac{8 c d^3 \log (d+e x) e^7}{\left(c d^4+a e^4\right)^3}-\frac{2 c d^3 \log \left(c x^4+a\right) e^7}{\left(c d^4+a e^4\right)^3}-\frac{e^7}{\left(c d^4+a e^4\right)^2 (d+e x)}-\frac{\sqrt{c} d \left(3 c d^4-a e^4\right) \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right) e^5}{\sqrt{a} \left(c d^4+a e^4\right)^3}-\frac{\sqrt[4]{c} \left(\sqrt{c} \left(5 c d^4-3 a e^4\right) d^2+\sqrt{a} e^2 \left(7 c d^4-a e^4\right)\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right) e^4}{2 \sqrt{2} a^{3/4} \left(c d^4+a e^4\right)^3}+\frac{\sqrt[4]{c} \left(\sqrt{c} \left(5 c d^4-3 a e^4\right) d^2+\sqrt{a} e^2 \left(7 c d^4-a e^4\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right) e^4}{2 \sqrt{2} a^{3/4} \left(c d^4+a e^4\right)^3}-\frac{\sqrt[4]{c} \left(\sqrt{c} d^2 \left(5 c d^4-3 a e^4\right)-\sqrt{a} e^2 \left(7 c d^4-a e^4\right)\right) \log \left(\sqrt{c} x^2-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right) e^4}{4 \sqrt{2} a^{3/4} \left(c d^4+a e^4\right)^3}+\frac{\sqrt[4]{c} \left(\sqrt{c} d^2 \left(5 c d^4-3 a e^4\right)-\sqrt{a} e^2 \left(7 c d^4-a e^4\right)\right) \log \left(\sqrt{c} x^2+\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right) e^4}{4 \sqrt{2} a^{3/4} \left(c d^4+a e^4\right)^3}-\frac{\sqrt{c} d \left(c d^4-a e^4\right) \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right) e}{2 a^{3/2} \left(c d^4+a e^4\right)^2}+\frac{c \left(4 a d^3 e^3+x \left(\left(c d^4-3 a e^4\right) d^2-2 e \left(c d^4-a e^4\right) x d+e^2 \left(3 c d^4-a e^4\right) x^2\right)\right)}{4 a \left(c d^4+a e^4\right)^2 \left(c x^4+a\right)}-\frac{\sqrt[4]{c} \left(3 \sqrt{c} \left(c d^4-3 a e^4\right) d^2+\sqrt{a} e^2 \left(3 c d^4-a e^4\right)\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} a^{7/4} \left(c d^4+a e^4\right)^2}+\frac{\sqrt[4]{c} \left(3 \sqrt{c} \left(c d^4-3 a e^4\right) d^2+\sqrt{a} e^2 \left(3 c d^4-a e^4\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} a^{7/4} \left(c d^4+a e^4\right)^2}-\frac{\sqrt[4]{c} \left(3 \sqrt{c} d^2 \left(c d^4-3 a e^4\right)-\sqrt{a} e^2 \left(3 c d^4-a e^4\right)\right) \log \left(\sqrt{c} x^2-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right)}{16 \sqrt{2} a^{7/4} \left(c d^4+a e^4\right)^2}+\frac{\sqrt[4]{c} \left(3 \sqrt{c} d^2 \left(c d^4-3 a e^4\right)-\sqrt{a} e^2 \left(3 c d^4-a e^4\right)\right) \log \left(\sqrt{c} x^2+\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right)}{16 \sqrt{2} a^{7/4} \left(c d^4+a e^4\right)^2}","\frac{8 c d^3 \log (d+e x) e^7}{\left(c d^4+a e^4\right)^3}-\frac{2 c d^3 \log \left(c x^4+a\right) e^7}{\left(c d^4+a e^4\right)^3}-\frac{e^7}{\left(c d^4+a e^4\right)^2 (d+e x)}-\frac{\sqrt{c} d \left(3 c d^4-a e^4\right) \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right) e^5}{\sqrt{a} \left(c d^4+a e^4\right)^3}-\frac{\sqrt[4]{c} \left(\sqrt{c} \left(5 c d^4-3 a e^4\right) d^2+\sqrt{a} e^2 \left(7 c d^4-a e^4\right)\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right) e^4}{2 \sqrt{2} a^{3/4} \left(c d^4+a e^4\right)^3}+\frac{\sqrt[4]{c} \left(\sqrt{c} \left(5 c d^4-3 a e^4\right) d^2+\sqrt{a} e^2 \left(7 c d^4-a e^4\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right) e^4}{2 \sqrt{2} a^{3/4} \left(c d^4+a e^4\right)^3}-\frac{\sqrt[4]{c} \left(\sqrt{c} d^2 \left(5 c d^4-3 a e^4\right)-\sqrt{a} e^2 \left(7 c d^4-a e^4\right)\right) \log \left(\sqrt{c} x^2-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right) e^4}{4 \sqrt{2} a^{3/4} \left(c d^4+a e^4\right)^3}+\frac{\sqrt[4]{c} \left(\sqrt{c} d^2 \left(5 c d^4-3 a e^4\right)-\sqrt{a} e^2 \left(7 c d^4-a e^4\right)\right) \log \left(\sqrt{c} x^2+\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right) e^4}{4 \sqrt{2} a^{3/4} \left(c d^4+a e^4\right)^3}-\frac{\sqrt{c} d \left(c d^4-a e^4\right) \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right) e}{2 a^{3/2} \left(c d^4+a e^4\right)^2}+\frac{c \left(4 a d^3 e^3+x \left(\left(c d^4-3 a e^4\right) d^2-2 e \left(c d^4-a e^4\right) x d+e^2 \left(3 c d^4-a e^4\right) x^2\right)\right)}{4 a \left(c d^4+a e^4\right)^2 \left(c x^4+a\right)}-\frac{\sqrt[4]{c} \left(3 \sqrt{c} \left(c d^4-3 a e^4\right) d^2+\sqrt{a} e^2 \left(3 c d^4-a e^4\right)\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} a^{7/4} \left(c d^4+a e^4\right)^2}+\frac{\sqrt[4]{c} \left(3 \sqrt{c} \left(c d^4-3 a e^4\right) d^2+\sqrt{a} e^2 \left(3 c d^4-a e^4\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} a^{7/4} \left(c d^4+a e^4\right)^2}-\frac{\sqrt[4]{c} \left(3 \sqrt{c} d^2 \left(c d^4-3 a e^4\right)-\sqrt{a} e^2 \left(3 c d^4-a e^4\right)\right) \log \left(\sqrt{c} x^2-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right)}{16 \sqrt{2} a^{7/4} \left(c d^4+a e^4\right)^2}+\frac{\sqrt[4]{c} \left(3 \sqrt{c} d^2 \left(c d^4-3 a e^4\right)-\sqrt{a} e^2 \left(3 c d^4-a e^4\right)\right) \log \left(\sqrt{c} x^2+\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right)}{16 \sqrt{2} a^{7/4} \left(c d^4+a e^4\right)^2}",1,"-(e^7/((c*d^4 + a*e^4)^2*(d + e*x))) + (c*(4*a*d^3*e^3 + x*(d^2*(c*d^4 - 3*a*e^4) - 2*d*e*(c*d^4 - a*e^4)*x + e^2*(3*c*d^4 - a*e^4)*x^2)))/(4*a*(c*d^4 + a*e^4)^2*(a + c*x^4)) - (Sqrt[c]*d*e^5*(3*c*d^4 - a*e^4)*ArcTan[(Sqrt[c]*x^2)/Sqrt[a]])/(Sqrt[a]*(c*d^4 + a*e^4)^3) - (Sqrt[c]*d*e*(c*d^4 - a*e^4)*ArcTan[(Sqrt[c]*x^2)/Sqrt[a]])/(2*a^(3/2)*(c*d^4 + a*e^4)^2) - (c^(1/4)*(3*Sqrt[c]*d^2*(c*d^4 - 3*a*e^4) + Sqrt[a]*e^2*(3*c*d^4 - a*e^4))*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(7/4)*(c*d^4 + a*e^4)^2) - (c^(1/4)*e^4*(Sqrt[c]*d^2*(5*c*d^4 - 3*a*e^4) + Sqrt[a]*e^2*(7*c*d^4 - a*e^4))*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*(c*d^4 + a*e^4)^3) + (c^(1/4)*(3*Sqrt[c]*d^2*(c*d^4 - 3*a*e^4) + Sqrt[a]*e^2*(3*c*d^4 - a*e^4))*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(7/4)*(c*d^4 + a*e^4)^2) + (c^(1/4)*e^4*(Sqrt[c]*d^2*(5*c*d^4 - 3*a*e^4) + Sqrt[a]*e^2*(7*c*d^4 - a*e^4))*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*(c*d^4 + a*e^4)^3) + (8*c*d^3*e^7*Log[d + e*x])/(c*d^4 + a*e^4)^3 - (c^(1/4)*(3*Sqrt[c]*d^2*(c*d^4 - 3*a*e^4) - Sqrt[a]*e^2*(3*c*d^4 - a*e^4))*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(16*Sqrt[2]*a^(7/4)*(c*d^4 + a*e^4)^2) - (c^(1/4)*e^4*(Sqrt[c]*d^2*(5*c*d^4 - 3*a*e^4) - Sqrt[a]*e^2*(7*c*d^4 - a*e^4))*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(4*Sqrt[2]*a^(3/4)*(c*d^4 + a*e^4)^3) + (c^(1/4)*(3*Sqrt[c]*d^2*(c*d^4 - 3*a*e^4) - Sqrt[a]*e^2*(3*c*d^4 - a*e^4))*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(16*Sqrt[2]*a^(7/4)*(c*d^4 + a*e^4)^2) + (c^(1/4)*e^4*(Sqrt[c]*d^2*(5*c*d^4 - 3*a*e^4) - Sqrt[a]*e^2*(7*c*d^4 - a*e^4))*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(4*Sqrt[2]*a^(3/4)*(c*d^4 + a*e^4)^3) - (2*c*d^3*e^7*Log[a + c*x^4])/(c*d^4 + a*e^4)^3","A",31,14,17,0.8235,1,"{6742, 1854, 1876, 275, 205, 1168, 1162, 617, 204, 1165, 628, 1248, 635, 260}"
407,1,1384,0,1.9627472,"\int \frac{1}{(d+e x)^3 \left(a+c x^4\right)^2} \, dx","Int[1/((d + e*x)^3*(a + c*x^4)^2),x]","\frac{12 c d^2 \left(3 c d^4-a e^4\right) \log (d+e x) e^7}{\left(c d^4+a e^4\right)^4}-\frac{3 c d^2 \left(3 c d^4-a e^4\right) \log \left(c x^4+a\right) e^7}{\left(c d^4+a e^4\right)^4}-\frac{8 c d^3 e^7}{\left(c d^4+a e^4\right)^3 (d+e x)}-\frac{e^7}{2 \left(c d^4+a e^4\right)^2 (d+e x)^2}-\frac{\sqrt{c} \left(21 c^2 d^8-26 a c e^4 d^4+a^2 e^8\right) \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right) e^5}{2 \sqrt{a} \left(c d^4+a e^4\right)^4}-\frac{c^{3/4} d \left(4 \sqrt{a} \sqrt{c} d^2 \left(7 c d^4-5 a e^4\right) e^2+3 \left(5 c^2 d^8-10 a c e^4 d^4+a^2 e^8\right)\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right) e^4}{2 \sqrt{2} a^{3/4} \left(c d^4+a e^4\right)^4}+\frac{c^{3/4} d \left(4 \sqrt{a} \sqrt{c} d^2 \left(7 c d^4-5 a e^4\right) e^2+3 \left(5 c^2 d^8-10 a c e^4 d^4+a^2 e^8\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right) e^4}{2 \sqrt{2} a^{3/4} \left(c d^4+a e^4\right)^4}+\frac{c^{3/4} d \left(4 \sqrt{a} \sqrt{c} d^2 e^2 \left(7 c d^4-5 a e^4\right)-3 \left(5 c^2 d^8-10 a c e^4 d^4+a^2 e^8\right)\right) \log \left(\sqrt{c} x^2-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right) e^4}{4 \sqrt{2} a^{3/4} \left(c d^4+a e^4\right)^4}-\frac{c^{3/4} d \left(4 \sqrt{a} \sqrt{c} d^2 e^2 \left(7 c d^4-5 a e^4\right)-3 \left(5 c^2 d^8-10 a c e^4 d^4+a^2 e^8\right)\right) \log \left(\sqrt{c} x^2+\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right) e^4}{4 \sqrt{2} a^{3/4} \left(c d^4+a e^4\right)^4}-\frac{\sqrt{c} \left(3 c^2 d^8-12 a c e^4 d^4+a^2 e^8\right) \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right) e}{4 a^{3/2} \left(c d^4+a e^4\right)^3}+\frac{c \left(2 a d^2 \left(5 c d^4-3 a e^4\right) e^3+x \left(2 c e^2 \left(3 c d^4-5 a e^4\right) x^2 d^3+\left(c^2 d^8-12 a c e^4 d^4+3 a^2 e^8\right) d-e \left(3 c^2 d^8-12 a c e^4 d^4+a^2 e^8\right) x\right)\right)}{4 a \left(c d^4+a e^4\right)^3 \left(c x^4+a\right)}-\frac{c^{3/4} d \left(3 c^2 d^8-36 a c e^4 d^4+2 \sqrt{a} \sqrt{c} e^2 \left(3 c d^4-5 a e^4\right) d^2+9 a^2 e^8\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} a^{7/4} \left(c d^4+a e^4\right)^3}+\frac{c^{3/4} d \left(3 c^2 d^8-36 a c e^4 d^4+2 \sqrt{a} \sqrt{c} e^2 \left(3 c d^4-5 a e^4\right) d^2+9 a^2 e^8\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} a^{7/4} \left(c d^4+a e^4\right)^3}-\frac{c^{3/4} d \left(3 c^2 d^8-36 a c e^4 d^4-2 \sqrt{a} \sqrt{c} e^2 \left(3 c d^4-5 a e^4\right) d^2+9 a^2 e^8\right) \log \left(\sqrt{c} x^2-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right)}{16 \sqrt{2} a^{7/4} \left(c d^4+a e^4\right)^3}+\frac{c^{3/4} d \left(3 c^2 d^8-36 a c e^4 d^4-2 \sqrt{a} \sqrt{c} e^2 \left(3 c d^4-5 a e^4\right) d^2+9 a^2 e^8\right) \log \left(\sqrt{c} x^2+\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right)}{16 \sqrt{2} a^{7/4} \left(c d^4+a e^4\right)^3}","\frac{12 c d^2 \left(3 c d^4-a e^4\right) \log (d+e x) e^7}{\left(c d^4+a e^4\right)^4}-\frac{3 c d^2 \left(3 c d^4-a e^4\right) \log \left(c x^4+a\right) e^7}{\left(c d^4+a e^4\right)^4}-\frac{8 c d^3 e^7}{\left(c d^4+a e^4\right)^3 (d+e x)}-\frac{e^7}{2 \left(c d^4+a e^4\right)^2 (d+e x)^2}-\frac{\sqrt{c} \left(21 c^2 d^8-26 a c e^4 d^4+a^2 e^8\right) \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right) e^5}{2 \sqrt{a} \left(c d^4+a e^4\right)^4}-\frac{c^{3/4} d \left(4 \sqrt{a} \sqrt{c} d^2 \left(7 c d^4-5 a e^4\right) e^2+3 \left(5 c^2 d^8-10 a c e^4 d^4+a^2 e^8\right)\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right) e^4}{2 \sqrt{2} a^{3/4} \left(c d^4+a e^4\right)^4}+\frac{c^{3/4} d \left(4 \sqrt{a} \sqrt{c} d^2 \left(7 c d^4-5 a e^4\right) e^2+3 \left(5 c^2 d^8-10 a c e^4 d^4+a^2 e^8\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right) e^4}{2 \sqrt{2} a^{3/4} \left(c d^4+a e^4\right)^4}+\frac{c^{3/4} d \left(4 \sqrt{a} \sqrt{c} d^2 e^2 \left(7 c d^4-5 a e^4\right)-3 \left(5 c^2 d^8-10 a c e^4 d^4+a^2 e^8\right)\right) \log \left(\sqrt{c} x^2-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right) e^4}{4 \sqrt{2} a^{3/4} \left(c d^4+a e^4\right)^4}-\frac{c^{3/4} d \left(4 \sqrt{a} \sqrt{c} d^2 e^2 \left(7 c d^4-5 a e^4\right)-3 \left(5 c^2 d^8-10 a c e^4 d^4+a^2 e^8\right)\right) \log \left(\sqrt{c} x^2+\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right) e^4}{4 \sqrt{2} a^{3/4} \left(c d^4+a e^4\right)^4}-\frac{\sqrt{c} \left(3 c^2 d^8-12 a c e^4 d^4+a^2 e^8\right) \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right) e}{4 a^{3/2} \left(c d^4+a e^4\right)^3}+\frac{c \left(2 a d^2 \left(5 c d^4-3 a e^4\right) e^3+x \left(2 c e^2 \left(3 c d^4-5 a e^4\right) x^2 d^3+\left(c^2 d^8-12 a c e^4 d^4+3 a^2 e^8\right) d-e \left(3 c^2 d^8-12 a c e^4 d^4+a^2 e^8\right) x\right)\right)}{4 a \left(c d^4+a e^4\right)^3 \left(c x^4+a\right)}-\frac{c^{3/4} d \left(3 c^2 d^8-36 a c e^4 d^4+2 \sqrt{a} \sqrt{c} e^2 \left(3 c d^4-5 a e^4\right) d^2+9 a^2 e^8\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} a^{7/4} \left(c d^4+a e^4\right)^3}+\frac{c^{3/4} d \left(3 c^2 d^8-36 a c e^4 d^4+2 \sqrt{a} \sqrt{c} e^2 \left(3 c d^4-5 a e^4\right) d^2+9 a^2 e^8\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} a^{7/4} \left(c d^4+a e^4\right)^3}-\frac{c^{3/4} d \left(3 c^2 d^8-36 a c e^4 d^4-2 \sqrt{a} \sqrt{c} e^2 \left(3 c d^4-5 a e^4\right) d^2+9 a^2 e^8\right) \log \left(\sqrt{c} x^2-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right)}{16 \sqrt{2} a^{7/4} \left(c d^4+a e^4\right)^3}+\frac{c^{3/4} d \left(3 c^2 d^8-36 a c e^4 d^4-2 \sqrt{a} \sqrt{c} e^2 \left(3 c d^4-5 a e^4\right) d^2+9 a^2 e^8\right) \log \left(\sqrt{c} x^2+\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right)}{16 \sqrt{2} a^{7/4} \left(c d^4+a e^4\right)^3}",1,"-e^7/(2*(c*d^4 + a*e^4)^2*(d + e*x)^2) - (8*c*d^3*e^7)/((c*d^4 + a*e^4)^3*(d + e*x)) + (c*(2*a*d^2*e^3*(5*c*d^4 - 3*a*e^4) + x*(d*(c^2*d^8 - 12*a*c*d^4*e^4 + 3*a^2*e^8) - e*(3*c^2*d^8 - 12*a*c*d^4*e^4 + a^2*e^8)*x + 2*c*d^3*e^2*(3*c*d^4 - 5*a*e^4)*x^2)))/(4*a*(c*d^4 + a*e^4)^3*(a + c*x^4)) - (Sqrt[c]*e^5*(21*c^2*d^8 - 26*a*c*d^4*e^4 + a^2*e^8)*ArcTan[(Sqrt[c]*x^2)/Sqrt[a]])/(2*Sqrt[a]*(c*d^4 + a*e^4)^4) - (Sqrt[c]*e*(3*c^2*d^8 - 12*a*c*d^4*e^4 + a^2*e^8)*ArcTan[(Sqrt[c]*x^2)/Sqrt[a]])/(4*a^(3/2)*(c*d^4 + a*e^4)^3) - (c^(3/4)*d*(3*c^2*d^8 - 36*a*c*d^4*e^4 + 9*a^2*e^8 + 2*Sqrt[a]*Sqrt[c]*d^2*e^2*(3*c*d^4 - 5*a*e^4))*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(7/4)*(c*d^4 + a*e^4)^3) - (c^(3/4)*d*e^4*(4*Sqrt[a]*Sqrt[c]*d^2*e^2*(7*c*d^4 - 5*a*e^4) + 3*(5*c^2*d^8 - 10*a*c*d^4*e^4 + a^2*e^8))*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*(c*d^4 + a*e^4)^4) + (c^(3/4)*d*(3*c^2*d^8 - 36*a*c*d^4*e^4 + 9*a^2*e^8 + 2*Sqrt[a]*Sqrt[c]*d^2*e^2*(3*c*d^4 - 5*a*e^4))*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(7/4)*(c*d^4 + a*e^4)^3) + (c^(3/4)*d*e^4*(4*Sqrt[a]*Sqrt[c]*d^2*e^2*(7*c*d^4 - 5*a*e^4) + 3*(5*c^2*d^8 - 10*a*c*d^4*e^4 + a^2*e^8))*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*(c*d^4 + a*e^4)^4) + (12*c*d^2*e^7*(3*c*d^4 - a*e^4)*Log[d + e*x])/(c*d^4 + a*e^4)^4 - (c^(3/4)*d*(3*c^2*d^8 - 36*a*c*d^4*e^4 + 9*a^2*e^8 - 2*Sqrt[a]*Sqrt[c]*d^2*e^2*(3*c*d^4 - 5*a*e^4))*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(16*Sqrt[2]*a^(7/4)*(c*d^4 + a*e^4)^3) + (c^(3/4)*d*e^4*(4*Sqrt[a]*Sqrt[c]*d^2*e^2*(7*c*d^4 - 5*a*e^4) - 3*(5*c^2*d^8 - 10*a*c*d^4*e^4 + a^2*e^8))*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(4*Sqrt[2]*a^(3/4)*(c*d^4 + a*e^4)^4) + (c^(3/4)*d*(3*c^2*d^8 - 36*a*c*d^4*e^4 + 9*a^2*e^8 - 2*Sqrt[a]*Sqrt[c]*d^2*e^2*(3*c*d^4 - 5*a*e^4))*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(16*Sqrt[2]*a^(7/4)*(c*d^4 + a*e^4)^3) - (c^(3/4)*d*e^4*(4*Sqrt[a]*Sqrt[c]*d^2*e^2*(7*c*d^4 - 5*a*e^4) - 3*(5*c^2*d^8 - 10*a*c*d^4*e^4 + a^2*e^8))*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(4*Sqrt[2]*a^(3/4)*(c*d^4 + a*e^4)^4) - (3*c*d^2*e^7*(3*c*d^4 - a*e^4)*Log[a + c*x^4])/(c*d^4 + a*e^4)^4","A",31,14,17,0.8235,1,"{6742, 1854, 1876, 275, 205, 1168, 1162, 617, 204, 1165, 628, 1248, 635, 260}"
408,1,394,0,0.3462376,"\int \frac{(d+e x)^3}{\left(a+c x^4\right)^3} \, dx","Int[(d + e*x)^3/(a + c*x^4)^3,x]","-\frac{3 d \left(7 \sqrt{c} d^2-5 \sqrt{a} e^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{128 \sqrt{2} a^{11/4} c^{3/4}}+\frac{3 d \left(7 \sqrt{c} d^2-5 \sqrt{a} e^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{128 \sqrt{2} a^{11/4} c^{3/4}}-\frac{3 d \left(5 \sqrt{a} e^2+7 \sqrt{c} d^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{64 \sqrt{2} a^{11/4} c^{3/4}}+\frac{3 d \left(5 \sqrt{a} e^2+7 \sqrt{c} d^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{64 \sqrt{2} a^{11/4} c^{3/4}}+\frac{x \left(18 d^2 e x+7 d^3+15 d e^2 x^2\right)}{32 a^2 \left(a+c x^4\right)}+\frac{9 d^2 e \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{16 a^{5/2} \sqrt{c}}-\frac{a e^3-c x \left(3 d^2 e x+d^3+3 d e^2 x^2\right)}{8 a c \left(a+c x^4\right)^2}","-\frac{3 d \left(7 \sqrt{c} d^2-5 \sqrt{a} e^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{128 \sqrt{2} a^{11/4} c^{3/4}}+\frac{3 d \left(7 \sqrt{c} d^2-5 \sqrt{a} e^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{128 \sqrt{2} a^{11/4} c^{3/4}}-\frac{3 d \left(5 \sqrt{a} e^2+7 \sqrt{c} d^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{64 \sqrt{2} a^{11/4} c^{3/4}}+\frac{3 d \left(5 \sqrt{a} e^2+7 \sqrt{c} d^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{64 \sqrt{2} a^{11/4} c^{3/4}}+\frac{x \left(18 d^2 e x+7 d^3+15 d e^2 x^2\right)}{32 a^2 \left(a+c x^4\right)}+\frac{9 d^2 e \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{16 a^{5/2} \sqrt{c}}-\frac{a e^3-c x \left(3 d^2 e x+d^3+3 d e^2 x^2\right)}{8 a c \left(a+c x^4\right)^2}",1,"(x*(7*d^3 + 18*d^2*e*x + 15*d*e^2*x^2))/(32*a^2*(a + c*x^4)) - (a*e^3 - c*x*(d^3 + 3*d^2*e*x + 3*d*e^2*x^2))/(8*a*c*(a + c*x^4)^2) + (9*d^2*e*ArcTan[(Sqrt[c]*x^2)/Sqrt[a]])/(16*a^(5/2)*Sqrt[c]) - (3*d*(7*Sqrt[c]*d^2 + 5*Sqrt[a]*e^2)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(64*Sqrt[2]*a^(11/4)*c^(3/4)) + (3*d*(7*Sqrt[c]*d^2 + 5*Sqrt[a]*e^2)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(64*Sqrt[2]*a^(11/4)*c^(3/4)) - (3*d*(7*Sqrt[c]*d^2 - 5*Sqrt[a]*e^2)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(128*Sqrt[2]*a^(11/4)*c^(3/4)) + (3*d*(7*Sqrt[c]*d^2 - 5*Sqrt[a]*e^2)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(128*Sqrt[2]*a^(11/4)*c^(3/4))","A",15,11,17,0.6471,1,"{1854, 1855, 1876, 275, 205, 1168, 1162, 617, 204, 1165, 628}"
409,1,360,0,0.3264188,"\int \frac{(d+e x)^2}{\left(a+c x^4\right)^3} \, dx","Int[(d + e*x)^2/(a + c*x^4)^3,x]","-\frac{\left(21 \sqrt{c} d^2-5 \sqrt{a} e^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{128 \sqrt{2} a^{11/4} c^{3/4}}+\frac{\left(21 \sqrt{c} d^2-5 \sqrt{a} e^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{128 \sqrt{2} a^{11/4} c^{3/4}}-\frac{\left(5 \sqrt{a} e^2+21 \sqrt{c} d^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{64 \sqrt{2} a^{11/4} c^{3/4}}+\frac{\left(5 \sqrt{a} e^2+21 \sqrt{c} d^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{64 \sqrt{2} a^{11/4} c^{3/4}}+\frac{x \left(7 d^2+12 d e x+5 e^2 x^2\right)}{32 a^2 \left(a+c x^4\right)}+\frac{3 d e \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{8 a^{5/2} \sqrt{c}}+\frac{x (d+e x)^2}{8 a \left(a+c x^4\right)^2}","-\frac{\left(21 \sqrt{c} d^2-5 \sqrt{a} e^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{128 \sqrt{2} a^{11/4} c^{3/4}}+\frac{\left(21 \sqrt{c} d^2-5 \sqrt{a} e^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{128 \sqrt{2} a^{11/4} c^{3/4}}-\frac{\left(5 \sqrt{a} e^2+21 \sqrt{c} d^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{64 \sqrt{2} a^{11/4} c^{3/4}}+\frac{\left(5 \sqrt{a} e^2+21 \sqrt{c} d^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{64 \sqrt{2} a^{11/4} c^{3/4}}+\frac{x \left(7 d^2+12 d e x+5 e^2 x^2\right)}{32 a^2 \left(a+c x^4\right)}+\frac{3 d e \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{8 a^{5/2} \sqrt{c}}+\frac{x (d+e x)^2}{8 a \left(a+c x^4\right)^2}",1,"(x*(d + e*x)^2)/(8*a*(a + c*x^4)^2) + (x*(7*d^2 + 12*d*e*x + 5*e^2*x^2))/(32*a^2*(a + c*x^4)) + (3*d*e*ArcTan[(Sqrt[c]*x^2)/Sqrt[a]])/(8*a^(5/2)*Sqrt[c]) - ((21*Sqrt[c]*d^2 + 5*Sqrt[a]*e^2)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(64*Sqrt[2]*a^(11/4)*c^(3/4)) + ((21*Sqrt[c]*d^2 + 5*Sqrt[a]*e^2)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(64*Sqrt[2]*a^(11/4)*c^(3/4)) - ((21*Sqrt[c]*d^2 - 5*Sqrt[a]*e^2)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(128*Sqrt[2]*a^(11/4)*c^(3/4)) + ((21*Sqrt[c]*d^2 - 5*Sqrt[a]*e^2)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(128*Sqrt[2]*a^(11/4)*c^(3/4))","A",15,10,17,0.5882,1,"{1855, 1876, 275, 205, 1168, 1162, 617, 204, 1165, 628}"
410,1,266,0,0.2493028,"\int \frac{d+e x}{\left(a+c x^4\right)^3} \, dx","Int[(d + e*x)/(a + c*x^4)^3,x]","\frac{x (7 d+6 e x)}{32 a^2 \left(a+c x^4\right)}-\frac{21 d \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{128 \sqrt{2} a^{11/4} \sqrt[4]{c}}+\frac{21 d \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{128 \sqrt{2} a^{11/4} \sqrt[4]{c}}-\frac{21 d \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{64 \sqrt{2} a^{11/4} \sqrt[4]{c}}+\frac{21 d \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{64 \sqrt{2} a^{11/4} \sqrt[4]{c}}+\frac{3 e \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{16 a^{5/2} \sqrt{c}}+\frac{x (d+e x)}{8 a \left(a+c x^4\right)^2}","\frac{x (7 d+6 e x)}{32 a^2 \left(a+c x^4\right)}-\frac{21 d \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{128 \sqrt{2} a^{11/4} \sqrt[4]{c}}+\frac{21 d \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{128 \sqrt{2} a^{11/4} \sqrt[4]{c}}-\frac{21 d \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{64 \sqrt{2} a^{11/4} \sqrt[4]{c}}+\frac{21 d \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{64 \sqrt{2} a^{11/4} \sqrt[4]{c}}+\frac{3 e \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{16 a^{5/2} \sqrt{c}}+\frac{x (d+e x)}{8 a \left(a+c x^4\right)^2}",1,"(x*(d + e*x))/(8*a*(a + c*x^4)^2) + (x*(7*d + 6*e*x))/(32*a^2*(a + c*x^4)) + (3*e*ArcTan[(Sqrt[c]*x^2)/Sqrt[a]])/(16*a^(5/2)*Sqrt[c]) - (21*d*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(64*Sqrt[2]*a^(11/4)*c^(1/4)) + (21*d*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(64*Sqrt[2]*a^(11/4)*c^(1/4)) - (21*d*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(128*Sqrt[2]*a^(11/4)*c^(1/4)) + (21*d*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(128*Sqrt[2]*a^(11/4)*c^(1/4))","A",15,10,15,0.6667,1,"{1855, 1876, 211, 1165, 628, 1162, 617, 204, 275, 205}"
411,1,219,0,0.1415741,"\int \frac{1}{\left(a+c x^4\right)^3} \, dx","Int[(a + c*x^4)^(-3),x]","\frac{7 x}{32 a^2 \left(a+c x^4\right)}-\frac{21 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{128 \sqrt{2} a^{11/4} \sqrt[4]{c}}+\frac{21 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{128 \sqrt{2} a^{11/4} \sqrt[4]{c}}-\frac{21 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{64 \sqrt{2} a^{11/4} \sqrt[4]{c}}+\frac{21 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{64 \sqrt{2} a^{11/4} \sqrt[4]{c}}+\frac{x}{8 a \left(a+c x^4\right)^2}","\frac{7 x}{32 a^2 \left(a+c x^4\right)}-\frac{21 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{128 \sqrt{2} a^{11/4} \sqrt[4]{c}}+\frac{21 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{128 \sqrt{2} a^{11/4} \sqrt[4]{c}}-\frac{21 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{64 \sqrt{2} a^{11/4} \sqrt[4]{c}}+\frac{21 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{64 \sqrt{2} a^{11/4} \sqrt[4]{c}}+\frac{x}{8 a \left(a+c x^4\right)^2}",1,"x/(8*a*(a + c*x^4)^2) + (7*x)/(32*a^2*(a + c*x^4)) - (21*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(64*Sqrt[2]*a^(11/4)*c^(1/4)) + (21*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(64*Sqrt[2]*a^(11/4)*c^(1/4)) - (21*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(128*Sqrt[2]*a^(11/4)*c^(1/4)) + (21*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(128*Sqrt[2]*a^(11/4)*c^(1/4))","A",11,7,9,0.7778,1,"{199, 211, 1165, 628, 1162, 617, 204}"
412,1,1352,0,1.411647,"\int \frac{1}{(d+e x) \left(a+c x^4\right)^3} \, dx","Int[1/((d + e*x)*(a + c*x^4)^3),x]","\frac{\log (d+e x) e^{11}}{\left(c d^4+a e^4\right)^3}-\frac{\log \left(c x^4+a\right) e^{11}}{4 \left(c d^4+a e^4\right)^3}-\frac{\sqrt{c} d^2 \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right) e^9}{2 \sqrt{a} \left(c d^4+a e^4\right)^3}-\frac{\sqrt[4]{c} d \left(\sqrt{c} d^2+\sqrt{a} e^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right) e^8}{2 \sqrt{2} a^{3/4} \left(c d^4+a e^4\right)^3}+\frac{\sqrt[4]{c} d \left(\sqrt{c} d^2+\sqrt{a} e^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right) e^8}{2 \sqrt{2} a^{3/4} \left(c d^4+a e^4\right)^3}-\frac{\sqrt[4]{c} d \left(\sqrt{c} d^2-\sqrt{a} e^2\right) \log \left(\sqrt{c} x^2-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right) e^8}{4 \sqrt{2} a^{3/4} \left(c d^4+a e^4\right)^3}+\frac{\sqrt[4]{c} d \left(\sqrt{c} d^2-\sqrt{a} e^2\right) \log \left(\sqrt{c} x^2+\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right) e^8}{4 \sqrt{2} a^{3/4} \left(c d^4+a e^4\right)^3}-\frac{\sqrt{c} d^2 \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right) e^5}{4 a^{3/2} \left(c d^4+a e^4\right)^2}+\frac{\left(a e^3+c x \left(d^3-e x d^2+e^2 x^2 d\right)\right) e^4}{4 a \left(c d^4+a e^4\right)^2 \left(c x^4+a\right)}-\frac{\sqrt[4]{c} d \left(3 \sqrt{c} d^2+\sqrt{a} e^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right) e^4}{8 \sqrt{2} a^{7/4} \left(c d^4+a e^4\right)^2}+\frac{\sqrt[4]{c} d \left(3 \sqrt{c} d^2+\sqrt{a} e^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right) e^4}{8 \sqrt{2} a^{7/4} \left(c d^4+a e^4\right)^2}-\frac{\sqrt[4]{c} d \left(3 \sqrt{c} d^2-\sqrt{a} e^2\right) \log \left(\sqrt{c} x^2-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right) e^4}{16 \sqrt{2} a^{7/4} \left(c d^4+a e^4\right)^2}+\frac{\sqrt[4]{c} d \left(3 \sqrt{c} d^2-\sqrt{a} e^2\right) \log \left(\sqrt{c} x^2+\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right) e^4}{16 \sqrt{2} a^{7/4} \left(c d^4+a e^4\right)^2}-\frac{3 \sqrt{c} d^2 \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right) e}{16 a^{5/2} \left(c d^4+a e^4\right)}+\frac{a e^3+c x \left(d^3-e x d^2+e^2 x^2 d\right)}{8 a \left(c d^4+a e^4\right) \left(c x^4+a\right)^2}-\frac{\sqrt[4]{c} d \left(21 \sqrt{c} d^2+5 \sqrt{a} e^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{64 \sqrt{2} a^{11/4} \left(c d^4+a e^4\right)}+\frac{\sqrt[4]{c} d \left(21 \sqrt{c} d^2+5 \sqrt{a} e^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{64 \sqrt{2} a^{11/4} \left(c d^4+a e^4\right)}-\frac{\sqrt[4]{c} d \left(21 \sqrt{c} d^2-5 \sqrt{a} e^2\right) \log \left(\sqrt{c} x^2-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right)}{128 \sqrt{2} a^{11/4} \left(c d^4+a e^4\right)}+\frac{\sqrt[4]{c} d \left(21 \sqrt{c} d^2-5 \sqrt{a} e^2\right) \log \left(\sqrt{c} x^2+\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right)}{128 \sqrt{2} a^{11/4} \left(c d^4+a e^4\right)}+\frac{c x \left(7 d^3-6 e x d^2+5 e^2 x^2 d\right)}{32 a^2 \left(c d^4+a e^4\right) \left(c x^4+a\right)}","\frac{\log (d+e x) e^{11}}{\left(c d^4+a e^4\right)^3}-\frac{\log \left(c x^4+a\right) e^{11}}{4 \left(c d^4+a e^4\right)^3}-\frac{\sqrt{c} d^2 \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right) e^9}{2 \sqrt{a} \left(c d^4+a e^4\right)^3}-\frac{\sqrt[4]{c} d \left(\sqrt{c} d^2+\sqrt{a} e^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right) e^8}{2 \sqrt{2} a^{3/4} \left(c d^4+a e^4\right)^3}+\frac{\sqrt[4]{c} d \left(\sqrt{c} d^2+\sqrt{a} e^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right) e^8}{2 \sqrt{2} a^{3/4} \left(c d^4+a e^4\right)^3}-\frac{\sqrt[4]{c} d \left(\sqrt{c} d^2-\sqrt{a} e^2\right) \log \left(\sqrt{c} x^2-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right) e^8}{4 \sqrt{2} a^{3/4} \left(c d^4+a e^4\right)^3}+\frac{\sqrt[4]{c} d \left(\sqrt{c} d^2-\sqrt{a} e^2\right) \log \left(\sqrt{c} x^2+\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right) e^8}{4 \sqrt{2} a^{3/4} \left(c d^4+a e^4\right)^3}-\frac{\sqrt{c} d^2 \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right) e^5}{4 a^{3/2} \left(c d^4+a e^4\right)^2}+\frac{\left(a e^3+c x \left(d^3-e x d^2+e^2 x^2 d\right)\right) e^4}{4 a \left(c d^4+a e^4\right)^2 \left(c x^4+a\right)}-\frac{\sqrt[4]{c} d \left(3 \sqrt{c} d^2+\sqrt{a} e^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right) e^4}{8 \sqrt{2} a^{7/4} \left(c d^4+a e^4\right)^2}+\frac{\sqrt[4]{c} d \left(3 \sqrt{c} d^2+\sqrt{a} e^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right) e^4}{8 \sqrt{2} a^{7/4} \left(c d^4+a e^4\right)^2}-\frac{\sqrt[4]{c} d \left(3 \sqrt{c} d^2-\sqrt{a} e^2\right) \log \left(\sqrt{c} x^2-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right) e^4}{16 \sqrt{2} a^{7/4} \left(c d^4+a e^4\right)^2}+\frac{\sqrt[4]{c} d \left(3 \sqrt{c} d^2-\sqrt{a} e^2\right) \log \left(\sqrt{c} x^2+\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right) e^4}{16 \sqrt{2} a^{7/4} \left(c d^4+a e^4\right)^2}-\frac{3 \sqrt{c} d^2 \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right) e}{16 a^{5/2} \left(c d^4+a e^4\right)}+\frac{a e^3+c x \left(d^3-e x d^2+e^2 x^2 d\right)}{8 a \left(c d^4+a e^4\right) \left(c x^4+a\right)^2}-\frac{\sqrt[4]{c} d \left(21 \sqrt{c} d^2+5 \sqrt{a} e^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{64 \sqrt{2} a^{11/4} \left(c d^4+a e^4\right)}+\frac{\sqrt[4]{c} d \left(21 \sqrt{c} d^2+5 \sqrt{a} e^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{64 \sqrt{2} a^{11/4} \left(c d^4+a e^4\right)}-\frac{\sqrt[4]{c} d \left(21 \sqrt{c} d^2-5 \sqrt{a} e^2\right) \log \left(\sqrt{c} x^2-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right)}{128 \sqrt{2} a^{11/4} \left(c d^4+a e^4\right)}+\frac{\sqrt[4]{c} d \left(21 \sqrt{c} d^2-5 \sqrt{a} e^2\right) \log \left(\sqrt{c} x^2+\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right)}{128 \sqrt{2} a^{11/4} \left(c d^4+a e^4\right)}+\frac{c x \left(7 d^3-6 e x d^2+5 e^2 x^2 d\right)}{32 a^2 \left(c d^4+a e^4\right) \left(c x^4+a\right)}",1,"(c*x*(7*d^3 - 6*d^2*e*x + 5*d*e^2*x^2))/(32*a^2*(c*d^4 + a*e^4)*(a + c*x^4)) + (a*e^3 + c*x*(d^3 - d^2*e*x + d*e^2*x^2))/(8*a*(c*d^4 + a*e^4)*(a + c*x^4)^2) + (e^4*(a*e^3 + c*x*(d^3 - d^2*e*x + d*e^2*x^2)))/(4*a*(c*d^4 + a*e^4)^2*(a + c*x^4)) - (Sqrt[c]*d^2*e^9*ArcTan[(Sqrt[c]*x^2)/Sqrt[a]])/(2*Sqrt[a]*(c*d^4 + a*e^4)^3) - (Sqrt[c]*d^2*e^5*ArcTan[(Sqrt[c]*x^2)/Sqrt[a]])/(4*a^(3/2)*(c*d^4 + a*e^4)^2) - (3*Sqrt[c]*d^2*e*ArcTan[(Sqrt[c]*x^2)/Sqrt[a]])/(16*a^(5/2)*(c*d^4 + a*e^4)) - (c^(1/4)*d*e^8*(Sqrt[c]*d^2 + Sqrt[a]*e^2)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*(c*d^4 + a*e^4)^3) - (c^(1/4)*d*e^4*(3*Sqrt[c]*d^2 + Sqrt[a]*e^2)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(7/4)*(c*d^4 + a*e^4)^2) - (c^(1/4)*d*(21*Sqrt[c]*d^2 + 5*Sqrt[a]*e^2)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(64*Sqrt[2]*a^(11/4)*(c*d^4 + a*e^4)) + (c^(1/4)*d*e^8*(Sqrt[c]*d^2 + Sqrt[a]*e^2)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*(c*d^4 + a*e^4)^3) + (c^(1/4)*d*e^4*(3*Sqrt[c]*d^2 + Sqrt[a]*e^2)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(7/4)*(c*d^4 + a*e^4)^2) + (c^(1/4)*d*(21*Sqrt[c]*d^2 + 5*Sqrt[a]*e^2)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(64*Sqrt[2]*a^(11/4)*(c*d^4 + a*e^4)) + (e^11*Log[d + e*x])/(c*d^4 + a*e^4)^3 - (c^(1/4)*d*e^8*(Sqrt[c]*d^2 - Sqrt[a]*e^2)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(4*Sqrt[2]*a^(3/4)*(c*d^4 + a*e^4)^3) - (c^(1/4)*d*e^4*(3*Sqrt[c]*d^2 - Sqrt[a]*e^2)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(16*Sqrt[2]*a^(7/4)*(c*d^4 + a*e^4)^2) - (c^(1/4)*d*(21*Sqrt[c]*d^2 - 5*Sqrt[a]*e^2)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(128*Sqrt[2]*a^(11/4)*(c*d^4 + a*e^4)) + (c^(1/4)*d*e^8*(Sqrt[c]*d^2 - Sqrt[a]*e^2)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(4*Sqrt[2]*a^(3/4)*(c*d^4 + a*e^4)^3) + (c^(1/4)*d*e^4*(3*Sqrt[c]*d^2 - Sqrt[a]*e^2)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(16*Sqrt[2]*a^(7/4)*(c*d^4 + a*e^4)^2) + (c^(1/4)*d*(21*Sqrt[c]*d^2 - 5*Sqrt[a]*e^2)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(128*Sqrt[2]*a^(11/4)*(c*d^4 + a*e^4)) - (e^11*Log[a + c*x^4])/(4*(c*d^4 + a*e^4)^3)","A",46,15,17,0.8824,1,"{6742, 1854, 1855, 1876, 275, 205, 1168, 1162, 617, 204, 1165, 628, 1248, 635, 260}"
413,1,1830,0,2.781417,"\int \frac{1}{(d+e x)^2 \left(a+c x^4\right)^3} \, dx","Int[1/((d + e*x)^2*(a + c*x^4)^3),x]","\frac{12 c d^3 \log (d+e x) e^{11}}{\left(c d^4+a e^4\right)^4}-\frac{3 c d^3 \log \left(c x^4+a\right) e^{11}}{\left(c d^4+a e^4\right)^4}-\frac{e^{11}}{\left(c d^4+a e^4\right)^3 (d+e x)}-\frac{\sqrt{c} d \left(5 c d^4-a e^4\right) \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right) e^9}{\sqrt{a} \left(c d^4+a e^4\right)^4}-\frac{\sqrt[4]{c} \left(3 \sqrt{c} \left(3 c d^4-a e^4\right) d^2+\sqrt{a} e^2 \left(11 c d^4-a e^4\right)\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right) e^8}{2 \sqrt{2} a^{3/4} \left(c d^4+a e^4\right)^4}+\frac{\sqrt[4]{c} \left(3 \sqrt{c} \left(3 c d^4-a e^4\right) d^2+\sqrt{a} e^2 \left(11 c d^4-a e^4\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right) e^8}{2 \sqrt{2} a^{3/4} \left(c d^4+a e^4\right)^4}-\frac{\sqrt[4]{c} \left(9 c^{3/2} d^6-11 \sqrt{a} c e^2 d^4-3 a \sqrt{c} e^4 d^2+a^{3/2} e^6\right) \log \left(\sqrt{c} x^2-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right) e^8}{4 \sqrt{2} a^{3/4} \left(c d^4+a e^4\right)^4}+\frac{\sqrt[4]{c} \left(9 c^{3/2} d^6-11 \sqrt{a} c e^2 d^4-3 a \sqrt{c} e^4 d^2+a^{3/2} e^6\right) \log \left(\sqrt{c} x^2+\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right) e^8}{4 \sqrt{2} a^{3/4} \left(c d^4+a e^4\right)^4}-\frac{\sqrt{c} d \left(3 c d^4-a e^4\right) \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right) e^5}{2 a^{3/2} \left(c d^4+a e^4\right)^3}+\frac{c \left(8 a d^3 e^3+x \left(\left(5 c d^4-3 a e^4\right) d^2-2 e \left(3 c d^4-a e^4\right) x d+e^2 \left(7 c d^4-a e^4\right) x^2\right)\right) e^4}{4 a \left(c d^4+a e^4\right)^3 \left(c x^4+a\right)}-\frac{\sqrt[4]{c} \left(3 \sqrt{c} \left(5 c d^4-3 a e^4\right) d^2+\sqrt{a} e^2 \left(7 c d^4-a e^4\right)\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right) e^4}{8 \sqrt{2} a^{7/4} \left(c d^4+a e^4\right)^3}+\frac{\sqrt[4]{c} \left(3 \sqrt{c} \left(5 c d^4-3 a e^4\right) d^2+\sqrt{a} e^2 \left(7 c d^4-a e^4\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right) e^4}{8 \sqrt{2} a^{7/4} \left(c d^4+a e^4\right)^3}-\frac{\sqrt[4]{c} \left(3 \sqrt{c} d^2 \left(5 c d^4-3 a e^4\right)-\sqrt{a} e^2 \left(7 c d^4-a e^4\right)\right) \log \left(\sqrt{c} x^2-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right) e^4}{16 \sqrt{2} a^{7/4} \left(c d^4+a e^4\right)^3}+\frac{\sqrt[4]{c} \left(3 \sqrt{c} d^2 \left(5 c d^4-3 a e^4\right)-\sqrt{a} e^2 \left(7 c d^4-a e^4\right)\right) \log \left(\sqrt{c} x^2+\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right) e^4}{16 \sqrt{2} a^{7/4} \left(c d^4+a e^4\right)^3}-\frac{3 \sqrt{c} d \left(c d^4-a e^4\right) \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right) e}{8 a^{5/2} \left(c d^4+a e^4\right)^2}+\frac{c \left(4 a d^3 e^3+x \left(\left(c d^4-3 a e^4\right) d^2-2 e \left(c d^4-a e^4\right) x d+e^2 \left(3 c d^4-a e^4\right) x^2\right)\right)}{8 a \left(c d^4+a e^4\right)^2 \left(c x^4+a\right)^2}-\frac{\sqrt[4]{c} \left(21 \sqrt{c} \left(c d^4-3 a e^4\right) d^2+5 \sqrt{a} e^2 \left(3 c d^4-a e^4\right)\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{64 \sqrt{2} a^{11/4} \left(c d^4+a e^4\right)^2}+\frac{\sqrt[4]{c} \left(21 \sqrt{c} \left(c d^4-3 a e^4\right) d^2+5 \sqrt{a} e^2 \left(3 c d^4-a e^4\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{64 \sqrt{2} a^{11/4} \left(c d^4+a e^4\right)^2}-\frac{\sqrt[4]{c} \left(21 \sqrt{c} d^2 \left(c d^4-3 a e^4\right)-5 \sqrt{a} e^2 \left(3 c d^4-a e^4\right)\right) \log \left(\sqrt{c} x^2-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right)}{128 \sqrt{2} a^{11/4} \left(c d^4+a e^4\right)^2}+\frac{\sqrt[4]{c} \left(21 \sqrt{c} d^2 \left(c d^4-3 a e^4\right)-5 \sqrt{a} e^2 \left(3 c d^4-a e^4\right)\right) \log \left(\sqrt{c} x^2+\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right)}{128 \sqrt{2} a^{11/4} \left(c d^4+a e^4\right)^2}+\frac{c x \left(7 \left(c d^4-3 a e^4\right) d^2-12 e \left(c d^4-a e^4\right) x d+5 e^2 \left(3 c d^4-a e^4\right) x^2\right)}{32 a^2 \left(c d^4+a e^4\right)^2 \left(c x^4+a\right)}","\frac{12 c d^3 \log (d+e x) e^{11}}{\left(c d^4+a e^4\right)^4}-\frac{3 c d^3 \log \left(c x^4+a\right) e^{11}}{\left(c d^4+a e^4\right)^4}-\frac{e^{11}}{\left(c d^4+a e^4\right)^3 (d+e x)}-\frac{\sqrt{c} d \left(5 c d^4-a e^4\right) \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right) e^9}{\sqrt{a} \left(c d^4+a e^4\right)^4}-\frac{\sqrt[4]{c} \left(3 \sqrt{c} \left(3 c d^4-a e^4\right) d^2+\sqrt{a} e^2 \left(11 c d^4-a e^4\right)\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right) e^8}{2 \sqrt{2} a^{3/4} \left(c d^4+a e^4\right)^4}+\frac{\sqrt[4]{c} \left(3 \sqrt{c} \left(3 c d^4-a e^4\right) d^2+\sqrt{a} e^2 \left(11 c d^4-a e^4\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right) e^8}{2 \sqrt{2} a^{3/4} \left(c d^4+a e^4\right)^4}-\frac{\sqrt[4]{c} \left(9 c^{3/2} d^6-11 \sqrt{a} c e^2 d^4-3 a \sqrt{c} e^4 d^2+a^{3/2} e^6\right) \log \left(\sqrt{c} x^2-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right) e^8}{4 \sqrt{2} a^{3/4} \left(c d^4+a e^4\right)^4}+\frac{\sqrt[4]{c} \left(9 c^{3/2} d^6-11 \sqrt{a} c e^2 d^4-3 a \sqrt{c} e^4 d^2+a^{3/2} e^6\right) \log \left(\sqrt{c} x^2+\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right) e^8}{4 \sqrt{2} a^{3/4} \left(c d^4+a e^4\right)^4}-\frac{\sqrt{c} d \left(3 c d^4-a e^4\right) \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right) e^5}{2 a^{3/2} \left(c d^4+a e^4\right)^3}+\frac{c \left(8 a d^3 e^3+x \left(\left(5 c d^4-3 a e^4\right) d^2-2 e \left(3 c d^4-a e^4\right) x d+e^2 \left(7 c d^4-a e^4\right) x^2\right)\right) e^4}{4 a \left(c d^4+a e^4\right)^3 \left(c x^4+a\right)}-\frac{\sqrt[4]{c} \left(3 \sqrt{c} \left(5 c d^4-3 a e^4\right) d^2+\sqrt{a} e^2 \left(7 c d^4-a e^4\right)\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right) e^4}{8 \sqrt{2} a^{7/4} \left(c d^4+a e^4\right)^3}+\frac{\sqrt[4]{c} \left(3 \sqrt{c} \left(5 c d^4-3 a e^4\right) d^2+\sqrt{a} e^2 \left(7 c d^4-a e^4\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right) e^4}{8 \sqrt{2} a^{7/4} \left(c d^4+a e^4\right)^3}-\frac{\sqrt[4]{c} \left(3 \sqrt{c} d^2 \left(5 c d^4-3 a e^4\right)-\sqrt{a} e^2 \left(7 c d^4-a e^4\right)\right) \log \left(\sqrt{c} x^2-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right) e^4}{16 \sqrt{2} a^{7/4} \left(c d^4+a e^4\right)^3}+\frac{\sqrt[4]{c} \left(3 \sqrt{c} d^2 \left(5 c d^4-3 a e^4\right)-\sqrt{a} e^2 \left(7 c d^4-a e^4\right)\right) \log \left(\sqrt{c} x^2+\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right) e^4}{16 \sqrt{2} a^{7/4} \left(c d^4+a e^4\right)^3}-\frac{3 \sqrt{c} d \left(c d^4-a e^4\right) \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right) e}{8 a^{5/2} \left(c d^4+a e^4\right)^2}+\frac{c \left(4 a d^3 e^3+x \left(\left(c d^4-3 a e^4\right) d^2-2 e \left(c d^4-a e^4\right) x d+e^2 \left(3 c d^4-a e^4\right) x^2\right)\right)}{8 a \left(c d^4+a e^4\right)^2 \left(c x^4+a\right)^2}-\frac{\sqrt[4]{c} \left(21 \sqrt{c} \left(c d^4-3 a e^4\right) d^2+5 \sqrt{a} e^2 \left(3 c d^4-a e^4\right)\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{64 \sqrt{2} a^{11/4} \left(c d^4+a e^4\right)^2}+\frac{\sqrt[4]{c} \left(21 \sqrt{c} \left(c d^4-3 a e^4\right) d^2+5 \sqrt{a} e^2 \left(3 c d^4-a e^4\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{64 \sqrt{2} a^{11/4} \left(c d^4+a e^4\right)^2}-\frac{\sqrt[4]{c} \left(21 \sqrt{c} d^2 \left(c d^4-3 a e^4\right)-5 \sqrt{a} e^2 \left(3 c d^4-a e^4\right)\right) \log \left(\sqrt{c} x^2-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right)}{128 \sqrt{2} a^{11/4} \left(c d^4+a e^4\right)^2}+\frac{\sqrt[4]{c} \left(21 \sqrt{c} d^2 \left(c d^4-3 a e^4\right)-5 \sqrt{a} e^2 \left(3 c d^4-a e^4\right)\right) \log \left(\sqrt{c} x^2+\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right)}{128 \sqrt{2} a^{11/4} \left(c d^4+a e^4\right)^2}+\frac{c x \left(7 \left(c d^4-3 a e^4\right) d^2-12 e \left(c d^4-a e^4\right) x d+5 e^2 \left(3 c d^4-a e^4\right) x^2\right)}{32 a^2 \left(c d^4+a e^4\right)^2 \left(c x^4+a\right)}",1,"-(e^11/((c*d^4 + a*e^4)^3*(d + e*x))) + (c*x*(7*d^2*(c*d^4 - 3*a*e^4) - 12*d*e*(c*d^4 - a*e^4)*x + 5*e^2*(3*c*d^4 - a*e^4)*x^2))/(32*a^2*(c*d^4 + a*e^4)^2*(a + c*x^4)) + (c*(4*a*d^3*e^3 + x*(d^2*(c*d^4 - 3*a*e^4) - 2*d*e*(c*d^4 - a*e^4)*x + e^2*(3*c*d^4 - a*e^4)*x^2)))/(8*a*(c*d^4 + a*e^4)^2*(a + c*x^4)^2) + (c*e^4*(8*a*d^3*e^3 + x*(d^2*(5*c*d^4 - 3*a*e^4) - 2*d*e*(3*c*d^4 - a*e^4)*x + e^2*(7*c*d^4 - a*e^4)*x^2)))/(4*a*(c*d^4 + a*e^4)^3*(a + c*x^4)) - (Sqrt[c]*d*e^9*(5*c*d^4 - a*e^4)*ArcTan[(Sqrt[c]*x^2)/Sqrt[a]])/(Sqrt[a]*(c*d^4 + a*e^4)^4) - (Sqrt[c]*d*e^5*(3*c*d^4 - a*e^4)*ArcTan[(Sqrt[c]*x^2)/Sqrt[a]])/(2*a^(3/2)*(c*d^4 + a*e^4)^3) - (3*Sqrt[c]*d*e*(c*d^4 - a*e^4)*ArcTan[(Sqrt[c]*x^2)/Sqrt[a]])/(8*a^(5/2)*(c*d^4 + a*e^4)^2) - (c^(1/4)*(21*Sqrt[c]*d^2*(c*d^4 - 3*a*e^4) + 5*Sqrt[a]*e^2*(3*c*d^4 - a*e^4))*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(64*Sqrt[2]*a^(11/4)*(c*d^4 + a*e^4)^2) - (c^(1/4)*e^4*(3*Sqrt[c]*d^2*(5*c*d^4 - 3*a*e^4) + Sqrt[a]*e^2*(7*c*d^4 - a*e^4))*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(7/4)*(c*d^4 + a*e^4)^3) - (c^(1/4)*e^8*(3*Sqrt[c]*d^2*(3*c*d^4 - a*e^4) + Sqrt[a]*e^2*(11*c*d^4 - a*e^4))*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*(c*d^4 + a*e^4)^4) + (c^(1/4)*(21*Sqrt[c]*d^2*(c*d^4 - 3*a*e^4) + 5*Sqrt[a]*e^2*(3*c*d^4 - a*e^4))*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(64*Sqrt[2]*a^(11/4)*(c*d^4 + a*e^4)^2) + (c^(1/4)*e^4*(3*Sqrt[c]*d^2*(5*c*d^4 - 3*a*e^4) + Sqrt[a]*e^2*(7*c*d^4 - a*e^4))*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(7/4)*(c*d^4 + a*e^4)^3) + (c^(1/4)*e^8*(3*Sqrt[c]*d^2*(3*c*d^4 - a*e^4) + Sqrt[a]*e^2*(11*c*d^4 - a*e^4))*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*(c*d^4 + a*e^4)^4) + (12*c*d^3*e^11*Log[d + e*x])/(c*d^4 + a*e^4)^4 - (c^(1/4)*e^8*(9*c^(3/2)*d^6 - 11*Sqrt[a]*c*d^4*e^2 - 3*a*Sqrt[c]*d^2*e^4 + a^(3/2)*e^6)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(4*Sqrt[2]*a^(3/4)*(c*d^4 + a*e^4)^4) - (c^(1/4)*(21*Sqrt[c]*d^2*(c*d^4 - 3*a*e^4) - 5*Sqrt[a]*e^2*(3*c*d^4 - a*e^4))*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(128*Sqrt[2]*a^(11/4)*(c*d^4 + a*e^4)^2) - (c^(1/4)*e^4*(3*Sqrt[c]*d^2*(5*c*d^4 - 3*a*e^4) - Sqrt[a]*e^2*(7*c*d^4 - a*e^4))*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(16*Sqrt[2]*a^(7/4)*(c*d^4 + a*e^4)^3) + (c^(1/4)*e^8*(9*c^(3/2)*d^6 - 11*Sqrt[a]*c*d^4*e^2 - 3*a*Sqrt[c]*d^2*e^4 + a^(3/2)*e^6)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(4*Sqrt[2]*a^(3/4)*(c*d^4 + a*e^4)^4) + (c^(1/4)*(21*Sqrt[c]*d^2*(c*d^4 - 3*a*e^4) - 5*Sqrt[a]*e^2*(3*c*d^4 - a*e^4))*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(128*Sqrt[2]*a^(11/4)*(c*d^4 + a*e^4)^2) + (c^(1/4)*e^4*(3*Sqrt[c]*d^2*(5*c*d^4 - 3*a*e^4) - Sqrt[a]*e^2*(7*c*d^4 - a*e^4))*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(16*Sqrt[2]*a^(7/4)*(c*d^4 + a*e^4)^3) - (3*c*d^3*e^11*Log[a + c*x^4])/(c*d^4 + a*e^4)^4","A",46,15,17,0.8824,1,"{6742, 1854, 1855, 1876, 275, 205, 1168, 1162, 617, 204, 1165, 628, 1248, 635, 260}"
414,1,2204,0,3.1647964,"\int \frac{1}{(d+e x)^3 \left(a+c x^4\right)^3} \, dx","Int[1/((d + e*x)^3*(a + c*x^4)^3),x]","\frac{6 c d^2 \left(13 c d^4-3 a e^4\right) \log (d+e x) e^{11}}{\left(c d^4+a e^4\right)^5}-\frac{3 c d^2 \left(13 c d^4-3 a e^4\right) \log \left(c x^4+a\right) e^{11}}{2 \left(c d^4+a e^4\right)^5}-\frac{12 c d^3 e^{11}}{\left(c d^4+a e^4\right)^4 (d+e x)}-\frac{e^{11}}{2 \left(c d^4+a e^4\right)^3 (d+e x)^2}-\frac{\sqrt{c} \left(55 c^2 d^8-40 a c e^4 d^4+a^2 e^8\right) \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right) e^9}{2 \sqrt{a} \left(c d^4+a e^4\right)^5}-\frac{3 c^{3/4} d \left(15 c^2 d^8-16 a c e^4 d^4+2 \sqrt{a} \sqrt{c} e^2 \left(11 c d^4-5 a e^4\right) d^2+a^2 e^8\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right) e^8}{2 \sqrt{2} a^{3/4} \left(c d^4+a e^4\right)^5}+\frac{3 c^{3/4} d \left(15 c^2 d^8-16 a c e^4 d^4+2 \sqrt{a} \sqrt{c} e^2 \left(11 c d^4-5 a e^4\right) d^2+a^2 e^8\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right) e^8}{2 \sqrt{2} a^{3/4} \left(c d^4+a e^4\right)^5}-\frac{3 c^{3/4} d \left(15 c^2 d^8-16 a c e^4 d^4-2 \sqrt{a} \sqrt{c} e^2 \left(11 c d^4-5 a e^4\right) d^2+a^2 e^8\right) \log \left(\sqrt{c} x^2-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right) e^8}{4 \sqrt{2} a^{3/4} \left(c d^4+a e^4\right)^5}+\frac{3 c^{3/4} d \left(15 c^2 d^8-16 a c e^4 d^4-2 \sqrt{a} \sqrt{c} e^2 \left(11 c d^4-5 a e^4\right) d^2+a^2 e^8\right) \log \left(\sqrt{c} x^2+\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right) e^8}{4 \sqrt{2} a^{3/4} \left(c d^4+a e^4\right)^5}-\frac{\sqrt{c} \left(21 c^2 d^8-26 a c e^4 d^4+a^2 e^8\right) \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right) e^5}{4 a^{3/2} \left(c d^4+a e^4\right)^4}+\frac{c \left(12 a d^2 \left(3 c d^4-a e^4\right) e^3+x \left(4 c e^2 \left(7 c d^4-5 a e^4\right) x^2 d^3+3 \left(5 c^2 d^8-10 a c e^4 d^4+a^2 e^8\right) d-e \left(21 c^2 d^8-26 a c e^4 d^4+a^2 e^8\right) x\right)\right) e^4}{4 a \left(c d^4+a e^4\right)^4 \left(c x^4+a\right)}-\frac{c^{3/4} d \left(4 \sqrt{a} \sqrt{c} d^2 \left(7 c d^4-5 a e^4\right) e^2+9 \left(5 c^2 d^8-10 a c e^4 d^4+a^2 e^8\right)\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right) e^4}{8 \sqrt{2} a^{7/4} \left(c d^4+a e^4\right)^4}+\frac{c^{3/4} d \left(4 \sqrt{a} \sqrt{c} d^2 \left(7 c d^4-5 a e^4\right) e^2+9 \left(5 c^2 d^8-10 a c e^4 d^4+a^2 e^8\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right) e^4}{8 \sqrt{2} a^{7/4} \left(c d^4+a e^4\right)^4}+\frac{c^{3/4} d \left(4 \sqrt{a} \sqrt{c} d^2 e^2 \left(7 c d^4-5 a e^4\right)-9 \left(5 c^2 d^8-10 a c e^4 d^4+a^2 e^8\right)\right) \log \left(\sqrt{c} x^2-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right) e^4}{16 \sqrt{2} a^{7/4} \left(c d^4+a e^4\right)^4}-\frac{c^{3/4} d \left(4 \sqrt{a} \sqrt{c} d^2 e^2 \left(7 c d^4-5 a e^4\right)-9 \left(5 c^2 d^8-10 a c e^4 d^4+a^2 e^8\right)\right) \log \left(\sqrt{c} x^2+\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right) e^4}{16 \sqrt{2} a^{7/4} \left(c d^4+a e^4\right)^4}-\frac{3 \sqrt{c} \left(3 c^2 d^8-12 a c e^4 d^4+a^2 e^8\right) \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right) e}{16 a^{5/2} \left(c d^4+a e^4\right)^3}+\frac{c \left(2 a d^2 \left(5 c d^4-3 a e^4\right) e^3+x \left(2 c e^2 \left(3 c d^4-5 a e^4\right) x^2 d^3+\left(c^2 d^8-12 a c e^4 d^4+3 a^2 e^8\right) d-e \left(3 c^2 d^8-12 a c e^4 d^4+a^2 e^8\right) x\right)\right)}{8 a \left(c d^4+a e^4\right)^3 \left(c x^4+a\right)^2}-\frac{c^{3/4} d \left(10 \sqrt{a} \sqrt{c} d^2 \left(3 c d^4-5 a e^4\right) e^2+21 \left(c^2 d^8-12 a c e^4 d^4+3 a^2 e^8\right)\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{64 \sqrt{2} a^{11/4} \left(c d^4+a e^4\right)^3}+\frac{c^{3/4} d \left(10 \sqrt{a} \sqrt{c} d^2 \left(3 c d^4-5 a e^4\right) e^2+21 \left(c^2 d^8-12 a c e^4 d^4+3 a^2 e^8\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{64 \sqrt{2} a^{11/4} \left(c d^4+a e^4\right)^3}+\frac{c^{3/4} d \left(10 \sqrt{a} \sqrt{c} d^2 e^2 \left(3 c d^4-5 a e^4\right)-21 \left(c^2 d^8-12 a c e^4 d^4+3 a^2 e^8\right)\right) \log \left(\sqrt{c} x^2-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right)}{128 \sqrt{2} a^{11/4} \left(c d^4+a e^4\right)^3}-\frac{c^{3/4} d \left(10 \sqrt{a} \sqrt{c} d^2 e^2 \left(3 c d^4-5 a e^4\right)-21 \left(c^2 d^8-12 a c e^4 d^4+3 a^2 e^8\right)\right) \log \left(\sqrt{c} x^2+\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right)}{128 \sqrt{2} a^{11/4} \left(c d^4+a e^4\right)^3}+\frac{c x \left(10 c e^2 \left(3 c d^4-5 a e^4\right) x^2 d^3+7 \left(c^2 d^8-12 a c e^4 d^4+3 a^2 e^8\right) d-6 e \left(3 c^2 d^8-12 a c e^4 d^4+a^2 e^8\right) x\right)}{32 a^2 \left(c d^4+a e^4\right)^3 \left(c x^4+a\right)}","\frac{6 c d^2 \left(13 c d^4-3 a e^4\right) \log (d+e x) e^{11}}{\left(c d^4+a e^4\right)^5}-\frac{3 c d^2 \left(13 c d^4-3 a e^4\right) \log \left(c x^4+a\right) e^{11}}{2 \left(c d^4+a e^4\right)^5}-\frac{12 c d^3 e^{11}}{\left(c d^4+a e^4\right)^4 (d+e x)}-\frac{e^{11}}{2 \left(c d^4+a e^4\right)^3 (d+e x)^2}-\frac{\sqrt{c} \left(55 c^2 d^8-40 a c e^4 d^4+a^2 e^8\right) \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right) e^9}{2 \sqrt{a} \left(c d^4+a e^4\right)^5}-\frac{3 c^{3/4} d \left(15 c^2 d^8-16 a c e^4 d^4+2 \sqrt{a} \sqrt{c} e^2 \left(11 c d^4-5 a e^4\right) d^2+a^2 e^8\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right) e^8}{2 \sqrt{2} a^{3/4} \left(c d^4+a e^4\right)^5}+\frac{3 c^{3/4} d \left(15 c^2 d^8-16 a c e^4 d^4+2 \sqrt{a} \sqrt{c} e^2 \left(11 c d^4-5 a e^4\right) d^2+a^2 e^8\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right) e^8}{2 \sqrt{2} a^{3/4} \left(c d^4+a e^4\right)^5}-\frac{3 c^{3/4} d \left(15 c^2 d^8-16 a c e^4 d^4-2 \sqrt{a} \sqrt{c} e^2 \left(11 c d^4-5 a e^4\right) d^2+a^2 e^8\right) \log \left(\sqrt{c} x^2-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right) e^8}{4 \sqrt{2} a^{3/4} \left(c d^4+a e^4\right)^5}+\frac{3 c^{3/4} d \left(15 c^2 d^8-16 a c e^4 d^4-2 \sqrt{a} \sqrt{c} e^2 \left(11 c d^4-5 a e^4\right) d^2+a^2 e^8\right) \log \left(\sqrt{c} x^2+\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right) e^8}{4 \sqrt{2} a^{3/4} \left(c d^4+a e^4\right)^5}-\frac{\sqrt{c} \left(21 c^2 d^8-26 a c e^4 d^4+a^2 e^8\right) \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right) e^5}{4 a^{3/2} \left(c d^4+a e^4\right)^4}+\frac{c \left(12 a d^2 \left(3 c d^4-a e^4\right) e^3+x \left(4 c e^2 \left(7 c d^4-5 a e^4\right) x^2 d^3+3 \left(5 c^2 d^8-10 a c e^4 d^4+a^2 e^8\right) d-e \left(21 c^2 d^8-26 a c e^4 d^4+a^2 e^8\right) x\right)\right) e^4}{4 a \left(c d^4+a e^4\right)^4 \left(c x^4+a\right)}-\frac{c^{3/4} d \left(4 \sqrt{a} \sqrt{c} d^2 \left(7 c d^4-5 a e^4\right) e^2+9 \left(5 c^2 d^8-10 a c e^4 d^4+a^2 e^8\right)\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right) e^4}{8 \sqrt{2} a^{7/4} \left(c d^4+a e^4\right)^4}+\frac{c^{3/4} d \left(4 \sqrt{a} \sqrt{c} d^2 \left(7 c d^4-5 a e^4\right) e^2+9 \left(5 c^2 d^8-10 a c e^4 d^4+a^2 e^8\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right) e^4}{8 \sqrt{2} a^{7/4} \left(c d^4+a e^4\right)^4}+\frac{c^{3/4} d \left(4 \sqrt{a} \sqrt{c} d^2 e^2 \left(7 c d^4-5 a e^4\right)-9 \left(5 c^2 d^8-10 a c e^4 d^4+a^2 e^8\right)\right) \log \left(\sqrt{c} x^2-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right) e^4}{16 \sqrt{2} a^{7/4} \left(c d^4+a e^4\right)^4}-\frac{c^{3/4} d \left(4 \sqrt{a} \sqrt{c} d^2 e^2 \left(7 c d^4-5 a e^4\right)-9 \left(5 c^2 d^8-10 a c e^4 d^4+a^2 e^8\right)\right) \log \left(\sqrt{c} x^2+\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right) e^4}{16 \sqrt{2} a^{7/4} \left(c d^4+a e^4\right)^4}-\frac{3 \sqrt{c} \left(3 c^2 d^8-12 a c e^4 d^4+a^2 e^8\right) \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right) e}{16 a^{5/2} \left(c d^4+a e^4\right)^3}+\frac{c \left(2 a d^2 \left(5 c d^4-3 a e^4\right) e^3+x \left(2 c e^2 \left(3 c d^4-5 a e^4\right) x^2 d^3+\left(c^2 d^8-12 a c e^4 d^4+3 a^2 e^8\right) d-e \left(3 c^2 d^8-12 a c e^4 d^4+a^2 e^8\right) x\right)\right)}{8 a \left(c d^4+a e^4\right)^3 \left(c x^4+a\right)^2}-\frac{c^{3/4} d \left(10 \sqrt{a} \sqrt{c} d^2 \left(3 c d^4-5 a e^4\right) e^2+21 \left(c^2 d^8-12 a c e^4 d^4+3 a^2 e^8\right)\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{64 \sqrt{2} a^{11/4} \left(c d^4+a e^4\right)^3}+\frac{c^{3/4} d \left(10 \sqrt{a} \sqrt{c} d^2 \left(3 c d^4-5 a e^4\right) e^2+21 \left(c^2 d^8-12 a c e^4 d^4+3 a^2 e^8\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{64 \sqrt{2} a^{11/4} \left(c d^4+a e^4\right)^3}+\frac{c^{3/4} d \left(10 \sqrt{a} \sqrt{c} d^2 e^2 \left(3 c d^4-5 a e^4\right)-21 \left(c^2 d^8-12 a c e^4 d^4+3 a^2 e^8\right)\right) \log \left(\sqrt{c} x^2-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right)}{128 \sqrt{2} a^{11/4} \left(c d^4+a e^4\right)^3}-\frac{c^{3/4} d \left(10 \sqrt{a} \sqrt{c} d^2 e^2 \left(3 c d^4-5 a e^4\right)-21 \left(c^2 d^8-12 a c e^4 d^4+3 a^2 e^8\right)\right) \log \left(\sqrt{c} x^2+\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right)}{128 \sqrt{2} a^{11/4} \left(c d^4+a e^4\right)^3}+\frac{c x \left(10 c e^2 \left(3 c d^4-5 a e^4\right) x^2 d^3+7 \left(c^2 d^8-12 a c e^4 d^4+3 a^2 e^8\right) d-6 e \left(3 c^2 d^8-12 a c e^4 d^4+a^2 e^8\right) x\right)}{32 a^2 \left(c d^4+a e^4\right)^3 \left(c x^4+a\right)}",1,"-e^11/(2*(c*d^4 + a*e^4)^3*(d + e*x)^2) - (12*c*d^3*e^11)/((c*d^4 + a*e^4)^4*(d + e*x)) + (c*x*(7*d*(c^2*d^8 - 12*a*c*d^4*e^4 + 3*a^2*e^8) - 6*e*(3*c^2*d^8 - 12*a*c*d^4*e^4 + a^2*e^8)*x + 10*c*d^3*e^2*(3*c*d^4 - 5*a*e^4)*x^2))/(32*a^2*(c*d^4 + a*e^4)^3*(a + c*x^4)) + (c*(2*a*d^2*e^3*(5*c*d^4 - 3*a*e^4) + x*(d*(c^2*d^8 - 12*a*c*d^4*e^4 + 3*a^2*e^8) - e*(3*c^2*d^8 - 12*a*c*d^4*e^4 + a^2*e^8)*x + 2*c*d^3*e^2*(3*c*d^4 - 5*a*e^4)*x^2)))/(8*a*(c*d^4 + a*e^4)^3*(a + c*x^4)^2) + (c*e^4*(12*a*d^2*e^3*(3*c*d^4 - a*e^4) + x*(3*d*(5*c^2*d^8 - 10*a*c*d^4*e^4 + a^2*e^8) - e*(21*c^2*d^8 - 26*a*c*d^4*e^4 + a^2*e^8)*x + 4*c*d^3*e^2*(7*c*d^4 - 5*a*e^4)*x^2)))/(4*a*(c*d^4 + a*e^4)^4*(a + c*x^4)) - (Sqrt[c]*e^9*(55*c^2*d^8 - 40*a*c*d^4*e^4 + a^2*e^8)*ArcTan[(Sqrt[c]*x^2)/Sqrt[a]])/(2*Sqrt[a]*(c*d^4 + a*e^4)^5) - (Sqrt[c]*e^5*(21*c^2*d^8 - 26*a*c*d^4*e^4 + a^2*e^8)*ArcTan[(Sqrt[c]*x^2)/Sqrt[a]])/(4*a^(3/2)*(c*d^4 + a*e^4)^4) - (3*Sqrt[c]*e*(3*c^2*d^8 - 12*a*c*d^4*e^4 + a^2*e^8)*ArcTan[(Sqrt[c]*x^2)/Sqrt[a]])/(16*a^(5/2)*(c*d^4 + a*e^4)^3) - (3*c^(3/4)*d*e^8*(15*c^2*d^8 - 16*a*c*d^4*e^4 + a^2*e^8 + 2*Sqrt[a]*Sqrt[c]*d^2*e^2*(11*c*d^4 - 5*a*e^4))*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*(c*d^4 + a*e^4)^5) - (c^(3/4)*d*e^4*(4*Sqrt[a]*Sqrt[c]*d^2*e^2*(7*c*d^4 - 5*a*e^4) + 9*(5*c^2*d^8 - 10*a*c*d^4*e^4 + a^2*e^8))*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(7/4)*(c*d^4 + a*e^4)^4) - (c^(3/4)*d*(10*Sqrt[a]*Sqrt[c]*d^2*e^2*(3*c*d^4 - 5*a*e^4) + 21*(c^2*d^8 - 12*a*c*d^4*e^4 + 3*a^2*e^8))*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(64*Sqrt[2]*a^(11/4)*(c*d^4 + a*e^4)^3) + (3*c^(3/4)*d*e^8*(15*c^2*d^8 - 16*a*c*d^4*e^4 + a^2*e^8 + 2*Sqrt[a]*Sqrt[c]*d^2*e^2*(11*c*d^4 - 5*a*e^4))*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*(c*d^4 + a*e^4)^5) + (c^(3/4)*d*e^4*(4*Sqrt[a]*Sqrt[c]*d^2*e^2*(7*c*d^4 - 5*a*e^4) + 9*(5*c^2*d^8 - 10*a*c*d^4*e^4 + a^2*e^8))*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(7/4)*(c*d^4 + a*e^4)^4) + (c^(3/4)*d*(10*Sqrt[a]*Sqrt[c]*d^2*e^2*(3*c*d^4 - 5*a*e^4) + 21*(c^2*d^8 - 12*a*c*d^4*e^4 + 3*a^2*e^8))*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(64*Sqrt[2]*a^(11/4)*(c*d^4 + a*e^4)^3) + (6*c*d^2*e^11*(13*c*d^4 - 3*a*e^4)*Log[d + e*x])/(c*d^4 + a*e^4)^5 - (3*c^(3/4)*d*e^8*(15*c^2*d^8 - 16*a*c*d^4*e^4 + a^2*e^8 - 2*Sqrt[a]*Sqrt[c]*d^2*e^2*(11*c*d^4 - 5*a*e^4))*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(4*Sqrt[2]*a^(3/4)*(c*d^4 + a*e^4)^5) + (c^(3/4)*d*e^4*(4*Sqrt[a]*Sqrt[c]*d^2*e^2*(7*c*d^4 - 5*a*e^4) - 9*(5*c^2*d^8 - 10*a*c*d^4*e^4 + a^2*e^8))*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(16*Sqrt[2]*a^(7/4)*(c*d^4 + a*e^4)^4) + (c^(3/4)*d*(10*Sqrt[a]*Sqrt[c]*d^2*e^2*(3*c*d^4 - 5*a*e^4) - 21*(c^2*d^8 - 12*a*c*d^4*e^4 + 3*a^2*e^8))*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(128*Sqrt[2]*a^(11/4)*(c*d^4 + a*e^4)^3) + (3*c^(3/4)*d*e^8*(15*c^2*d^8 - 16*a*c*d^4*e^4 + a^2*e^8 - 2*Sqrt[a]*Sqrt[c]*d^2*e^2*(11*c*d^4 - 5*a*e^4))*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(4*Sqrt[2]*a^(3/4)*(c*d^4 + a*e^4)^5) - (c^(3/4)*d*e^4*(4*Sqrt[a]*Sqrt[c]*d^2*e^2*(7*c*d^4 - 5*a*e^4) - 9*(5*c^2*d^8 - 10*a*c*d^4*e^4 + a^2*e^8))*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(16*Sqrt[2]*a^(7/4)*(c*d^4 + a*e^4)^4) - (c^(3/4)*d*(10*Sqrt[a]*Sqrt[c]*d^2*e^2*(3*c*d^4 - 5*a*e^4) - 21*(c^2*d^8 - 12*a*c*d^4*e^4 + 3*a^2*e^8))*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(128*Sqrt[2]*a^(11/4)*(c*d^4 + a*e^4)^3) - (3*c*d^2*e^11*(13*c*d^4 - 3*a*e^4)*Log[a + c*x^4])/(2*(c*d^4 + a*e^4)^5)","A",46,15,17,0.8824,1,"{6742, 1854, 1855, 1876, 275, 205, 1168, 1162, 617, 204, 1165, 628, 1248, 635, 260}"
415,1,32,0,0.0191008,"\int \frac{-1+x}{1-x+x^2} \, dx","Int[(-1 + x)/(1 - x + x^2),x]","\frac{1}{2} \log \left(x^2-x+1\right)+\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{\sqrt{3}}","\frac{1}{2} \log \left(x^2-x+1\right)+\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{\sqrt{3}}",1,"ArcTan[(1 - 2*x)/Sqrt[3]]/Sqrt[3] + Log[1 - x + x^2]/2","A",4,4,14,0.2857,1,"{634, 618, 204, 628}"
416,1,32,0,0.029412,"\int \frac{-1+x^2}{1+x^3} \, dx","Int[(-1 + x^2)/(1 + x^3),x]","\frac{1}{2} \log \left(x^2-x+1\right)+\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{\sqrt{3}}","\frac{1}{2} \log \left(x^2-x+1\right)+\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{\sqrt{3}}",1,"ArcTan[(1 - 2*x)/Sqrt[3]]/Sqrt[3] + Log[1 - x + x^2]/2","A",5,5,13,0.3846,1,"{1872, 634, 618, 204, 628}"
417,1,32,0,0.0168806,"\int \frac{-4+3 x}{4-2 x+x^2} \, dx","Int[(-4 + 3*x)/(4 - 2*x + x^2),x]","\frac{3}{2} \log \left(x^2-2 x+4\right)+\frac{\tan ^{-1}\left(\frac{1-x}{\sqrt{3}}\right)}{\sqrt{3}}","\frac{3}{2} \log \left(x^2-2 x+4\right)+\frac{\tan ^{-1}\left(\frac{1-x}{\sqrt{3}}\right)}{\sqrt{3}}",1,"ArcTan[(1 - x)/Sqrt[3]]/Sqrt[3] + (3*Log[4 - 2*x + x^2])/2","A",4,4,16,0.2500,1,"{634, 618, 204, 628}"
418,1,32,0,0.035154,"\int \frac{-8+2 x+3 x^2}{8+x^3} \, dx","Int[(-8 + 2*x + 3*x^2)/(8 + x^3),x]","\frac{3}{2} \log \left(x^2-2 x+4\right)+\frac{\tan ^{-1}\left(\frac{1-x}{\sqrt{3}}\right)}{\sqrt{3}}","\frac{3}{2} \log \left(x^2-2 x+4\right)+\frac{\tan ^{-1}\left(\frac{1-x}{\sqrt{3}}\right)}{\sqrt{3}}",1,"ArcTan[(1 - x)/Sqrt[3]]/Sqrt[3] + (3*Log[4 - 2*x + x^2])/2","A",5,5,18,0.2778,1,"{1872, 634, 618, 204, 628}"
419,1,45,0,0.0119036,"\int \frac{2+x}{-1+2 x+x^2} \, dx","Int[(2 + x)/(-1 + 2*x + x^2),x]","\frac{1}{4} \left(2+\sqrt{2}\right) \log \left(x-\sqrt{2}+1\right)+\frac{1}{4} \left(2-\sqrt{2}\right) \log \left(x+\sqrt{2}+1\right)","\frac{1}{4} \left(2+\sqrt{2}\right) \log \left(x-\sqrt{2}+1\right)+\frac{1}{4} \left(2-\sqrt{2}\right) \log \left(x+\sqrt{2}+1\right)",1,"((2 + Sqrt[2])*Log[1 - Sqrt[2] + x])/4 + ((2 - Sqrt[2])*Log[1 + Sqrt[2] + x])/4","A",3,2,14,0.1429,1,"{632, 31}"
420,1,45,0,0.0209227,"\int \frac{-4+x^2}{2-5 x+x^3} \, dx","Int[(-4 + x^2)/(2 - 5*x + x^3),x]","\frac{1}{4} \left(2+\sqrt{2}\right) \log \left(x-\sqrt{2}+1\right)+\frac{1}{4} \left(2-\sqrt{2}\right) \log \left(x+\sqrt{2}+1\right)","\frac{1}{4} \left(2+\sqrt{2}\right) \log \left(x-\sqrt{2}+1\right)+\frac{1}{4} \left(2-\sqrt{2}\right) \log \left(x+\sqrt{2}+1\right)",1,"((2 + Sqrt[2])*Log[1 - Sqrt[2] + x])/4 + ((2 - Sqrt[2])*Log[1 + Sqrt[2] + x])/4","A",4,3,16,0.1875,1,"{2055, 632, 31}"
421,1,6,0,0.0024724,"\int \frac{2}{-1+4 x^2} \, dx","Int[2/(-1 + 4*x^2),x]","-\tanh ^{-1}(2 x)","-\tanh ^{-1}(2 x)",1,"-ArcTanh[2*x]","A",2,2,11,0.1818,1,"{12, 207}"
422,1,21,0,0.0035305,"\int \left(\frac{1}{-1+2 x}-\frac{1}{1+2 x}\right) \, dx","Int[(-1 + 2*x)^(-1) - (1 + 2*x)^(-1),x]","\frac{1}{2} \log (1-2 x)-\frac{1}{2} \log (2 x+1)","\frac{1}{2} \log (1-2 x)-\frac{1}{2} \log (2 x+1)",1,"Log[1 - 2*x]/2 - Log[1 + 2*x]/2","A",1,0,17,0,1,"{}"
423,1,13,0,0.0021836,"\int \frac{x}{\left(1-x^2\right)^5} \, dx","Int[x/(1 - x^2)^5,x]","\frac{1}{8 \left(1-x^2\right)^4}","\frac{1}{8 \left(1-x^2\right)^4}",1,"1/(8*(1 - x^2)^4)","A",1,1,11,0.09091,1,"{261}"
424,1,81,0,0.0118387,"\int \left(-\frac{1}{32 (-1+x)^5}+\frac{3}{64 (-1+x)^4}-\frac{5}{128 (-1+x)^3}+\frac{5}{256 (-1+x)^2}-\frac{1}{32 (1+x)^5}-\frac{3}{64 (1+x)^4}-\frac{5}{128 (1+x)^3}-\frac{5}{256 (1+x)^2}\right) \, dx","Int[-1/(32*(-1 + x)^5) + 3/(64*(-1 + x)^4) - 5/(128*(-1 + x)^3) + 5/(256*(-1 + x)^2) - 1/(32*(1 + x)^5) - 3/(64*(1 + x)^4) - 5/(128*(1 + x)^3) - 5/(256*(1 + x)^2),x]","\frac{5}{256 (x+1)}+\frac{5}{256 (x+1)^2}+\frac{1}{64 (x+1)^3}+\frac{1}{128 (x+1)^4}+\frac{5}{256 (1-x)}+\frac{5}{256 (1-x)^2}+\frac{1}{64 (1-x)^3}+\frac{1}{128 (1-x)^4}","\frac{1}{8 \left(1-x^2\right)^4}",1,"1/(128*(1 - x)^4) + 1/(64*(1 - x)^3) + 5/(256*(1 - x)^2) + 5/(256*(1 - x)) + 1/(128*(1 + x)^4) + 1/(64*(1 + x)^3) + 5/(256*(1 + x)^2) + 5/(256*(1 + x))","B",1,0,73,0,1,"{}"
425,1,69,0,0.1106302,"\int \frac{1+x^6}{-1+x^6} \, dx","Int[(1 + x^6)/(-1 + x^6),x]","\frac{1}{6} \log \left(x^2-x+1\right)-\frac{1}{6} \log \left(x^2+x+1\right)+x+\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{2}{3} \tanh ^{-1}(x)","\frac{1}{6} \log \left(x^2-x+1\right)-\frac{1}{6} \log \left(x^2+x+1\right)+x+\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{2}{3} \tanh ^{-1}(x)",1,"x + ArcTan[(1 - 2*x)/Sqrt[3]]/Sqrt[3] - ArcTan[(1 + 2*x)/Sqrt[3]]/Sqrt[3] - (2*ArcTanh[x])/3 + Log[1 - x + x^2]/6 - Log[1 + x + x^2]/6","A",11,7,13,0.5385,1,"{388, 210, 634, 618, 204, 628, 206}"
426,1,69,0,0.1235167,"\int \frac{\frac{1}{x^3}+x^3}{-\frac{1}{x^3}+x^3} \, dx","Int[(x^(-3) + x^3)/(-x^(-3) + x^3),x]","\frac{1}{6} \log \left(x^2-x+1\right)-\frac{1}{6} \log \left(x^2+x+1\right)+x+\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{2}{3} \tanh ^{-1}(x)","\frac{1}{6} \log \left(x^2-x+1\right)-\frac{1}{6} \log \left(x^2+x+1\right)+x+\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{2}{3} \tanh ^{-1}(x)",1,"x + ArcTan[(1 - 2*x)/Sqrt[3]]/Sqrt[3] - ArcTan[(1 + 2*x)/Sqrt[3]]/Sqrt[3] - (2*ArcTanh[x])/3 + Log[1 - x + x^2]/6 - Log[1 + x + x^2]/6","A",13,9,19,0.4737,1,"{1593, 1584, 388, 210, 634, 618, 204, 628, 206}"
427,1,24,0,0.0188889,"\int \frac{-x+x^3}{6+2 x} \, dx","Int[(-x + x^3)/(6 + 2*x),x]","\frac{x^3}{6}-\frac{3 x^2}{4}+4 x-12 \log (x+3)","\frac{x^3}{6}-\frac{3 x^2}{4}+4 x-12 \log (x+3)",1,"4*x - (3*x^2)/4 + x^3/6 - 12*Log[3 + x]","A",3,2,15,0.1333,1,"{1593, 772}"
428,1,26,0,0.0163843,"\int \frac{x+x^3}{-1+x} \, dx","Int[(x + x^3)/(-1 + x),x]","\frac{x^3}{3}+\frac{x^2}{2}+2 x+2 \log (1-x)","\frac{x^3}{3}+\frac{x^2}{2}+2 x+2 \log (1-x)",1,"2*x + x^2/2 + x^3/3 + 2*Log[1 - x]","A",3,2,11,0.1818,1,"{1593, 772}"
429,1,17,0,0.0058426,"\int (a c+(b c+d) x) \, dx","Int[a*c + (b*c + d)*x,x]","a c x+\frac{1}{2} x^2 (b c+d)","a c x+\frac{1}{2} x^2 (b c+d)",1,"a*c*x + ((b*c + d)*x^2)/2","A",1,0,11,0,1,"{}"
430,1,24,0,0.004717,"\int (d x+c (a+b x)) \, dx","Int[d*x + c*(a + b*x),x]","\frac{c (a+b x)^2}{2 b}+\frac{d x^2}{2}","\frac{c (a+b x)^2}{2 b}+\frac{d x^2}{2}",1,"(d*x^2)/2 + (c*(a + b*x)^2)/(2*b)","A",1,0,11,0,1,"{}"
431,1,22,0,0.0189116,"\int \frac{4+4 x}{x^2 \left(1+x^2\right)} \, dx","Int[(4 + 4*x)/(x^2*(1 + x^2)),x]","-2 \log \left(x^2+1\right)-\frac{4}{x}+4 \log (x)-4 \tan ^{-1}(x)","-2 \log \left(x^2+1\right)-\frac{4}{x}+4 \log (x)-4 \tan ^{-1}(x)",1,"-4/x - 4*ArcTan[x] + 4*Log[x] - 2*Log[1 + x^2]","A",5,4,16,0.2500,1,"{801, 635, 203, 260}"
432,1,17,0,0.0128238,"\int \frac{24+8 x}{x \left(-4+x^2\right)} \, dx","Int[(24 + 8*x)/(x*(-4 + x^2)),x]","5 \log (2-x)-6 \log (x)+\log (x+2)","5 \log (2-x)-6 \log (x)+\log (x+2)",1,"5*Log[2 - x] - 6*Log[x] + Log[2 + x]","A",2,1,16,0.06250,1,"{801}"
433,1,19,0,0.0210393,"\int \frac{-1+x^2}{-2 x+x^3} \, dx","Int[(-1 + x^2)/(-2*x + x^3),x]","\frac{1}{4} \log \left(2-x^2\right)+\frac{\log (x)}{2}","\frac{1}{4} \log \left(2-x^2\right)+\frac{\log (x)}{2}",1,"Log[x]/2 + Log[2 - x^2]/4","A",4,3,15,0.2000,1,"{1593, 446, 72}"
434,1,12,0,0.006125,"\int \frac{1+x^2}{3 x+x^3} \, dx","Int[(1 + x^2)/(3*x + x^3),x]","\frac{1}{3} \log \left(x^3+3 x\right)","\frac{1}{3} \log \left(x^3+3 x\right)",1,"Log[3*x + x^3]/3","A",1,1,15,0.06667,1,"{1587}"
435,1,10,0,0.0090229,"\int \frac{a+3 b x^2}{a x+b x^3} \, dx","Int[(a + 3*b*x^2)/(a*x + b*x^3),x]","\log \left(a x+b x^3\right)","\log \left(a x+b x^3\right)",1,"Log[a*x + b*x^3]","A",1,1,20,0.05000,1,"{1587}"
436,1,17,0,0.0181711,"\int \frac{-2+4 x}{-x+x^3} \, dx","Int[(-2 + 4*x)/(-x + x^3),x]","\log (1-x)+2 \log (x)-3 \log (x+1)","\log (1-x)+2 \log (x)-3 \log (x+1)",1,"Log[1 - x] + 2*Log[x] - 3*Log[1 + x]","A",3,2,15,0.1333,1,"{1593, 801}"
437,1,23,0,0.020751,"\int \frac{4+x}{4 x+x^3} \, dx","Int[(4 + x)/(4*x + x^3),x]","-\frac{1}{2} \log \left(x^2+4\right)+\log (x)+\frac{1}{2} \tan ^{-1}\left(\frac{x}{2}\right)","-\frac{1}{2} \log \left(x^2+4\right)+\log (x)+\frac{1}{2} \tan ^{-1}\left(\frac{x}{2}\right)",1,"ArcTan[x/2]/2 + Log[x] - Log[4 + x^2]/2","A",6,5,13,0.3846,1,"{1593, 801, 635, 203, 260}"
438,1,15,0,0.0089732,"\int \frac{-x+2 x^3}{1-x^2+x^4} \, dx","Int[(-x + 2*x^3)/(1 - x^2 + x^4),x]","\frac{1}{2} \log \left(x^4-x^2+1\right)","\frac{1}{2} \log \left(x^4-x^2+1\right)",1,"Log[1 - x^2 + x^4]/2","A",1,1,22,0.04545,1,"{1587}"
439,1,21,0,0.0213803,"\int \frac{-3+x}{2 x+3 x^2+x^3} \, dx","Int[(-3 + x)/(2*x + 3*x^2 + x^3),x]","-\frac{3 \log (x)}{2}+4 \log (x+1)-\frac{5}{2} \log (x+2)","-\frac{3 \log (x)}{2}+4 \log (x+1)-\frac{5}{2} \log (x+2)",1,"(-3*Log[x])/2 + 4*Log[1 + x] - (5*Log[2 + x])/2","A",3,2,18,0.1111,1,"{1594, 800}"
440,1,10,0,0.0103235,"\int \frac{2+4 x}{x^2+2 x^3+x^4} \, dx","Int[(2 + 4*x)/(x^2 + 2*x^3 + x^4),x]","-\frac{2}{x (x+1)}","-\frac{2}{x (x+1)}",1,"-2/(x*(1 + x))","A",3,3,20,0.1500,1,"{1594, 27, 74}"
441,1,25,0,0.0208231,"\int \frac{1+x}{-6 x+x^2+x^3} \, dx","Int[(1 + x)/(-6*x + x^2 + x^3),x]","\frac{3}{10} \log (2-x)-\frac{\log (x)}{6}-\frac{2}{15} \log (x+3)","\frac{3}{10} \log (2-x)-\frac{\log (x)}{6}-\frac{2}{15} \log (x+3)",1,"(3*Log[2 - x])/10 - Log[x]/6 - (2*Log[3 + x])/15","A",3,2,16,0.1250,1,"{1594, 800}"
442,1,14,0,0.0248439,"\int \frac{4 x^2+x^3}{x+x^3} \, dx","Int[(4*x^2 + x^3)/(x + x^3),x]","2 \log \left(x^2+1\right)+x-\tan ^{-1}(x)","2 \log \left(x^2+1\right)+x-\tan ^{-1}(x)",1,"x - ArcTan[x] + 2*Log[1 + x^2]","A",6,6,17,0.3529,1,"{1593, 1584, 774, 635, 203, 260}"
443,1,13,0,0.0070267,"\int \frac{x+2 x^3}{\left(x^2+x^4\right)^3} \, dx","Int[(x + 2*x^3)/(x^2 + x^4)^3,x]","-\frac{1}{4 \left(x^4+x^2\right)^2}","-\frac{1}{4 \left(x^4+x^2\right)^2}",1,"-1/(4*(x^2 + x^4)^2)","A",1,1,17,0.05882,1,"{1588}"
444,1,26,0,0.0452603,"\int \frac{a x^2+b x^3}{c x^2+d x^3} \, dx","Int[(a*x^2 + b*x^3)/(c*x^2 + d*x^3),x]","\frac{b x}{d}-\frac{(b c-a d) \log (c+d x)}{d^2}","\frac{b x}{d}-\frac{(b c-a d) \log (c+d x)}{d^2}",1,"(b*x)/d - ((b*c - a*d)*Log[c + d*x])/d^2","A",4,3,25,0.1200,1,"{1593, 1584, 43}"
445,1,6,0,0.0079106,"\int \frac{x+x^2}{-2 x-x^2+x^3} \, dx","Int[(x + x^2)/(-2*x - x^2 + x^3),x]","\log (2-x)","\log (2-x)",1,"Log[2 - x]","A",2,2,20,0.1000,1,"{1586, 31}"
446,1,20,0,0.0146122,"\int \frac{1-5 x^2}{x^3 \left(1+x^2\right)} \, dx","Int[(1 - 5*x^2)/(x^3*(1 + x^2)),x]","-\frac{1}{2 x^2}+3 \log \left(x^2+1\right)-6 \log (x)","-\frac{1}{2 x^2}+3 \log \left(x^2+1\right)-6 \log (x)",1,"-1/(2*x^2) - 6*Log[x] + 3*Log[1 + x^2]","A",3,2,18,0.1111,1,"{446, 77}"
447,1,38,0,0.0254795,"\int \frac{2 x}{(-1+x) \left(5+x^2\right)} \, dx","Int[(2*x)/((-1 + x)*(5 + x^2)),x]","-\frac{1}{6} \log \left(x^2+5\right)+\frac{1}{3} \log (1-x)+\frac{1}{3} \sqrt{5} \tan ^{-1}\left(\frac{x}{\sqrt{5}}\right)","-\frac{1}{6} \log \left(x^2+5\right)+\frac{1}{3} \log (1-x)+\frac{1}{3} \sqrt{5} \tan ^{-1}\left(\frac{x}{\sqrt{5}}\right)",1,"(Sqrt[5]*ArcTan[x/Sqrt[5]])/3 + Log[1 - x]/3 - Log[5 + x^2]/6","A",6,5,15,0.3333,1,"{12, 801, 635, 203, 260}"
448,1,17,0,0.0082738,"\int \frac{2+x^2}{2+x} \, dx","Int[(2 + x^2)/(2 + x),x]","\frac{x^2}{2}-2 x+6 \log (x+2)","\frac{x^2}{2}-2 x+6 \log (x+2)",1,"-2*x + x^2/2 + 6*Log[2 + x]","A",2,1,11,0.09091,1,"{697}"
449,1,31,0,0.0120286,"\int \frac{1}{(-3+x) \left(4+x^2\right)} \, dx","Int[1/((-3 + x)*(4 + x^2)),x]","-\frac{1}{26} \log \left(x^2+4\right)+\frac{1}{13} \log (3-x)-\frac{3}{26} \tan ^{-1}\left(\frac{x}{2}\right)","-\frac{1}{26} \log \left(x^2+4\right)+\frac{1}{13} \log (3-x)-\frac{3}{26} \tan ^{-1}\left(\frac{x}{2}\right)",1,"(-3*ArcTan[x/2])/26 + Log[3 - x]/13 - Log[4 + x^2]/26","A",5,5,13,0.3846,1,"{706, 31, 635, 203, 260}"
450,1,19,0,0.0167028,"\int \frac{-2+3 x^6}{x \left(5+2 x^6\right)} \, dx","Int[(-2 + 3*x^6)/(x*(5 + 2*x^6)),x]","\frac{19}{60} \log \left(2 x^6+5\right)-\frac{2 \log (x)}{5}","\frac{19}{60} \log \left(2 x^6+5\right)-\frac{2 \log (x)}{5}",1,"(-2*Log[x])/5 + (19*Log[5 + 2*x^6])/60","A",3,2,20,0.1000,1,"{446, 72}"
451,1,11,0,0.0049503,"\int \frac{3+2 x}{(-2+x) (5+x)} \, dx","Int[(3 + 2*x)/((-2 + x)*(5 + x)),x]","\log (2-x)+\log (x+5)","\log (2-x)+\log (x+5)",1,"Log[2 - x] + Log[5 + x]","A",2,1,16,0.06250,1,"{72}"
452,1,18,0,0.0140661,"\int \frac{x^4}{4+5 x^2+x^4} \, dx","Int[x^4/(4 + 5*x^2 + x^4),x]","x-\frac{8}{3} \tan ^{-1}\left(\frac{x}{2}\right)+\frac{1}{3} \tan ^{-1}(x)","x-\frac{8}{3} \tan ^{-1}\left(\frac{x}{2}\right)+\frac{1}{3} \tan ^{-1}(x)",1,"x - (8*ArcTan[x/2])/3 + ArcTan[x]/3","A",4,3,16,0.1875,1,"{1122, 1166, 203}"
453,1,46,0,0.0234159,"\int \frac{1}{(1+x) (2+x)^2 (3+x)^3} \, dx","Int[1/((1 + x)*(2 + x)^2*(3 + x)^3),x]","\frac{1}{x+2}+\frac{5}{4 (x+3)}+\frac{1}{4 (x+3)^2}+\frac{1}{8} \log (x+1)+2 \log (x+2)-\frac{17}{8} \log (x+3)","\frac{1}{x+2}+\frac{5}{4 (x+3)}+\frac{1}{4 (x+3)^2}+\frac{1}{8} \log (x+1)+2 \log (x+2)-\frac{17}{8} \log (x+3)",1,"(2 + x)^(-1) + 1/(4*(3 + x)^2) + 5/(4*(3 + x)) + Log[1 + x]/8 + 2*Log[2 + x] - (17*Log[3 + x])/8","A",2,1,16,0.06250,1,"{88}"
454,1,12,0,0.0021809,"\int \frac{x}{-1+x^2} \, dx","Int[x/(-1 + x^2),x]","\frac{1}{2} \log \left(1-x^2\right)","\frac{1}{2} \log \left(1-x^2\right)",1,"Log[1 - x^2]/2","A",1,1,9,0.1111,1,"{260}"
455,1,21,0,0.0028625,"\int \frac{1}{\left(-1+x^2\right)^2} \, dx","Int[(-1 + x^2)^(-2),x]","\frac{x}{2 \left(1-x^2\right)}+\frac{1}{2} \tanh ^{-1}(x)","\frac{x}{2 \left(1-x^2\right)}+\frac{1}{2} \tanh ^{-1}(x)",1,"x/(2*(1 - x^2)) + ArcTanh[x]/2","A",2,2,7,0.2857,1,"{199, 207}"
456,1,19,0,0.0037943,"\int \frac{x^2}{\left(1+x^2\right)^2} \, dx","Int[x^2/(1 + x^2)^2,x]","\frac{1}{2} \tan ^{-1}(x)-\frac{x}{2 \left(x^2+1\right)}","\frac{1}{2} \tan ^{-1}(x)-\frac{x}{2 \left(x^2+1\right)}",1,"-x/(2*(1 + x^2)) + ArcTan[x]/2","A",2,2,11,0.1818,1,"{288, 203}"
457,1,10,0,0.0009813,"\int \frac{1}{2+3 x} \, dx","Int[(2 + 3*x)^(-1),x]","\frac{1}{3} \log (3 x+2)","\frac{1}{3} \log (3 x+2)",1,"Log[2 + 3*x]/3","A",1,1,7,0.1429,1,"{31}"
458,1,10,0,0.0025235,"\int \frac{1}{a^2+x^2} \, dx","Int[(a^2 + x^2)^(-1),x]","\frac{\tan ^{-1}\left(\frac{x}{a}\right)}{a}","\frac{\tan ^{-1}\left(\frac{x}{a}\right)}{a}",1,"ArcTan[x/a]/a","A",1,1,9,0.1111,1,"{203}"
459,1,24,0,0.0068038,"\int \frac{1}{a+b x^2} \, dx","Int[(a + b*x^2)^(-1),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b}}","\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b}}",1,"ArcTan[(Sqrt[b]*x)/Sqrt[a]]/(Sqrt[a]*Sqrt[b])","A",1,1,9,0.1111,1,"{205}"
460,1,19,0,0.0111904,"\int \frac{1}{2-x+x^2} \, dx","Int[(2 - x + x^2)^(-1),x]","-\frac{2 \tan ^{-1}\left(\frac{1-2 x}{\sqrt{7}}\right)}{\sqrt{7}}","-\frac{2 \tan ^{-1}\left(\frac{1-2 x}{\sqrt{7}}\right)}{\sqrt{7}}",1,"(-2*ArcTan[(1 - 2*x)/Sqrt[7]])/Sqrt[7]","A",2,2,10,0.2000,1,"{618, 204}"
461,1,22,0,0.0068336,"\int x^2 \left(4-x^2\right)^2 \, dx","Int[x^2*(4 - x^2)^2,x]","\frac{x^7}{7}-\frac{8 x^5}{5}+\frac{16 x^3}{3}","\frac{x^7}{7}-\frac{8 x^5}{5}+\frac{16 x^3}{3}",1,"(16*x^3)/3 - (8*x^5)/5 + x^7/7","A",2,1,13,0.07692,1,"{270}"
462,1,22,0,0.0053139,"\int x \left(1-x^3\right)^2 \, dx","Int[x*(1 - x^3)^2,x]","\frac{x^8}{8}-\frac{2 x^5}{5}+\frac{x^2}{2}","\frac{x^8}{8}-\frac{2 x^5}{5}+\frac{x^2}{2}",1,"x^2/2 - (2*x^5)/5 + x^8/8","A",2,1,11,0.09091,1,"{270}"
463,1,16,0,0.0050837,"\int \frac{-4+5 x^2+x^3}{x^2} \, dx","Int[(-4 + 5*x^2 + x^3)/x^2,x]","\frac{x^2}{2}+5 x+\frac{4}{x}","\frac{x^2}{2}+5 x+\frac{4}{x}",1,"4/x + 5*x + x^2/2","A",2,1,14,0.07143,1,"{14}"
464,1,37,0,0.0208234,"\int \frac{-1+x}{3-4 x+3 x^2} \, dx","Int[(-1 + x)/(3 - 4*x + 3*x^2),x]","\frac{1}{6} \log \left(3 x^2-4 x+3\right)+\frac{\tan ^{-1}\left(\frac{2-3 x}{\sqrt{5}}\right)}{3 \sqrt{5}}","\frac{1}{6} \log \left(3 x^2-4 x+3\right)+\frac{\tan ^{-1}\left(\frac{2-3 x}{\sqrt{5}}\right)}{3 \sqrt{5}}",1,"ArcTan[(2 - 3*x)/Sqrt[5]]/(3*Sqrt[5]) + Log[3 - 4*x + 3*x^2]/6","A",4,4,16,0.2500,1,"{634, 618, 204, 628}"
465,1,14,0,0.0036466,"\int \left(2+x^3\right)^2 \, dx","Int[(2 + x^3)^2,x]","\frac{x^7}{7}+x^4+4 x","\frac{x^7}{7}+x^4+4 x",1,"4*x + x^4 + x^7/7","A",2,1,7,0.1429,1,"{194}"
466,1,11,0,0.0037104,"\int \frac{-4+x^2}{2+x} \, dx","Int[(-4 + x^2)/(2 + x),x]","\frac{x^2}{2}-2 x","\frac{x^2}{2}-2 x",1,"-2*x + x^2/2","A",2,1,11,0.09091,1,"{627}"
467,1,25,0,0.0096625,"\int \frac{1}{(2+x) \left(1+x^2\right)} \, dx","Int[1/((2 + x)*(1 + x^2)),x]","-\frac{1}{10} \log \left(x^2+1\right)+\frac{1}{5} \log (x+2)+\frac{2}{5} \tan ^{-1}(x)","-\frac{1}{10} \log \left(x^2+1\right)+\frac{1}{5} \log (x+2)+\frac{2}{5} \tan ^{-1}(x)",1,"(2*ArcTan[x])/5 + Log[2 + x]/5 - Log[1 + x^2]/10","A",5,5,13,0.3846,1,"{706, 31, 635, 203, 260}"
468,1,25,0,0.0101712,"\int \frac{1}{(1+x) \left(1+x^2\right)} \, dx","Int[1/((1 + x)*(1 + x^2)),x]","-\frac{1}{4} \log \left(x^2+1\right)+\frac{1}{2} \log (x+1)+\frac{1}{2} \tan ^{-1}(x)","-\frac{1}{4} \log \left(x^2+1\right)+\frac{1}{2} \log (x+1)+\frac{1}{2} \tan ^{-1}(x)",1,"ArcTan[x]/2 + Log[1 + x]/2 - Log[1 + x^2]/4","A",5,5,13,0.3846,1,"{706, 31, 635, 203, 260}"
469,1,25,0,0.0170756,"\int \frac{x}{(1+x) \left(1+x^2\right)} \, dx","Int[x/((1 + x)*(1 + x^2)),x]","\frac{1}{4} \log \left(x^2+1\right)-\frac{1}{2} \log (x+1)+\frac{1}{2} \tan ^{-1}(x)","\frac{1}{4} \log \left(x^2+1\right)-\frac{1}{2} \log (x+1)+\frac{1}{2} \tan ^{-1}(x)",1,"ArcTan[x]/2 - Log[1 + x]/2 + Log[1 + x^2]/4","A",5,4,14,0.2857,1,"{801, 635, 203, 260}"
470,1,7,0,0.0059376,"\int \frac{2 x+x^2}{(1+x)^2} \, dx","Int[(2*x + x^2)/(1 + x)^2,x]","x+\frac{1}{x+1}","\frac{x^2}{x+1}",1,"x + (1 + x)^(-1)","A",2,1,13,0.07692,1,"{683}"
471,1,22,0,0.0106643,"\int \frac{-10+x^2}{4+9 x^2+2 x^4} \, dx","Int[(-10 + x^2)/(4 + 9*x^2 + 2*x^4),x]","\tan ^{-1}\left(\frac{x}{2}\right)-\frac{3 \tan ^{-1}\left(\sqrt{2} x\right)}{\sqrt{2}}","\tan ^{-1}\left(\frac{x}{2}\right)-\frac{3 \tan ^{-1}\left(\sqrt{2} x\right)}{\sqrt{2}}",1,"ArcTan[x/2] - (3*ArcTan[Sqrt[2]*x])/Sqrt[2]","A",3,2,20,0.1000,1,"{1166, 203}"
472,1,37,0,0.0223993,"\int \frac{31+5 x}{11-4 x+3 x^2} \, dx","Int[(31 + 5*x)/(11 - 4*x + 3*x^2),x]","\frac{5}{6} \log \left(3 x^2-4 x+11\right)-\frac{103 \tan ^{-1}\left(\frac{2-3 x}{\sqrt{29}}\right)}{3 \sqrt{29}}","\frac{5}{6} \log \left(3 x^2-4 x+11\right)-\frac{103 \tan ^{-1}\left(\frac{2-3 x}{\sqrt{29}}\right)}{3 \sqrt{29}}",1,"(-103*ArcTan[(2 - 3*x)/Sqrt[29]])/(3*Sqrt[29]) + (5*Log[11 - 4*x + 3*x^2])/6","A",4,4,18,0.2222,1,"{634, 618, 204, 628}"
473,1,15,0,0.0039203,"\int \frac{-2+x^2+x^3}{x^4} \, dx","Int[(-2 + x^2 + x^3)/x^4,x]","\frac{2}{3 x^3}-\frac{1}{x}+\log (x)","\frac{2}{3 x^3}-\frac{1}{x}+\log (x)",1,"2/(3*x^3) - x^(-1) + Log[x]","A",2,1,12,0.08333,1,"{14}"
474,1,15,0,0.0035479,"\int \frac{1+x+x^3}{x^2} \, dx","Int[(1 + x + x^3)/x^2,x]","\frac{x^2}{2}-\frac{1}{x}+\log (x)","\frac{x^2}{2}-\frac{1}{x}+\log (x)",1,"-x^(-1) + x^2/2 + Log[x]","A",2,1,10,0.1000,1,"{14}"
475,1,11,0,0.0112308,"\int \frac{-2+x^2}{x \left(2+x^2\right)} \, dx","Int[(-2 + x^2)/(x*(2 + x^2)),x]","\log \left(x^2+2\right)-\log (x)","\log \left(x^2+2\right)-\log (x)",1,"-Log[x] + Log[2 + x^2]","A",3,2,16,0.1250,1,"{446, 72}"
476,1,22,0,0.0042643,"\int (-3+x) \left(-7+4 x^2\right) \, dx","Int[(-3 + x)*(-7 + 4*x^2),x]","-4 x^3+\frac{1}{16} \left(7-4 x^2\right)^2+21 x","-4 x^3+\frac{1}{16} \left(7-4 x^2\right)^2+21 x",1,"21*x - 4*x^3 + (7 - 4*x^2)^2/16","A",2,1,11,0.09091,1,"{641}"
477,1,11,0,0.0010748,"\int (-2+7 x)^3 \, dx","Int[(-2 + 7*x)^3,x]","\frac{1}{28} (2-7 x)^4","\frac{1}{28} (2-7 x)^4",1,"(2 - 7*x)^4/28","A",1,1,7,0.1429,1,"{32}"
478,1,13,0,0.010276,"\int \frac{-7+4 x^2}{3+2 x} \, dx","Int[(-7 + 4*x^2)/(3 + 2*x),x]","x^2-3 x+\log (2 x+3)","x^2-3 x+\log (2 x+3)",1,"-3*x + x^2 + Log[3 + 2*x]","A",2,1,15,0.06667,1,"{697}"
479,1,16,0,0.0062877,"\int \frac{1+x}{(-1+x) x^2} \, dx","Int[(1 + x)/((-1 + x)*x^2),x]","\frac{1}{x}+2 \log (1-x)-2 \log (x)","\frac{1}{x}+2 \log (1-x)-2 \log (x)",1,"x^(-1) + 2*Log[1 - x] - 2*Log[x]","A",2,1,12,0.08333,1,"{77}"
480,1,27,0,0.0107282,"\int \frac{1}{4 x^2+4 x^3+x^4} \, dx","Int[(4*x^2 + 4*x^3 + x^4)^(-1),x]","\frac{x+1}{2 \left(1-(x+1)^2\right)}+\frac{1}{2} \tanh ^{-1}(x+1)","\frac{x+1}{2 \left(1-(x+1)^2\right)}+\frac{1}{2} \tanh ^{-1}(x+1)",1,"(1 + x)/(2*(1 - (1 + x)^2)) + ArcTanh[1 + x]/2","A",3,3,16,0.1875,1,"{1106, 199, 206}"
481,1,17,0,0.0083317,"\int \frac{1+x^2}{1+x} \, dx","Int[(1 + x^2)/(1 + x),x]","\frac{x^2}{2}-x+2 \log (x+1)","\frac{x^2}{2}-x+2 \log (x+1)",1,"-x + x^2/2 + 2*Log[1 + x]","A",2,1,11,0.09091,1,"{697}"
482,1,18,0,0.0060952,"\int \frac{-1+3 x-3 x^2+x^3}{x^2} \, dx","Int[(-1 + 3*x - 3*x^2 + x^3)/x^2,x]","\frac{x^2}{2}-3 x+\frac{1}{x}+3 \log (x)","\frac{x^2}{2}-3 x+\frac{1}{x}+3 \log (x)",1,"x^(-1) - 3*x + x^2/2 + 3*Log[x]","A",2,1,17,0.05882,1,"{14}"
483,1,18,0,0.0103565,"\int \left(\frac{1}{2} \left(3-\sqrt{37}\right)+x\right) \left(\frac{1}{2} \left(3+\sqrt{37}\right)+x\right) \, dx","Int[((3 - Sqrt[37])/2 + x)*((3 + Sqrt[37])/2 + x),x]","\frac{x^3}{3}+\frac{3 x^2}{2}-7 x","\frac{x^3}{3}+\frac{3 x^2}{2}-7 x",1,"-7*x + (3*x^2)/2 + x^3/3","A",2,1,29,0.03448,1,"{43}"
484,1,23,0,0.0177378,"\int \frac{4+3 x^2+2 x^3}{(1+x)^4} \, dx","Int[(4 + 3*x^2 + 2*x^3)/(1 + x)^4,x]","\frac{3}{x+1}-\frac{5}{3 (x+1)^3}+2 \log (x+1)","\frac{3}{x+1}-\frac{5}{3 (x+1)^3}+2 \log (x+1)",1,"-5/(3*(1 + x)^3) + 3/(1 + x) + 2*Log[1 + x]","A",2,1,18,0.05556,1,"{1850}"
485,1,16,0,0.0117033,"\int \frac{x}{(1+x)^2 \left(1+x^2\right)} \, dx","Int[x/((1 + x)^2*(1 + x^2)),x]","\frac{1}{2 (x+1)}+\frac{1}{2} \tan ^{-1}(x)","\frac{1}{2 (x+1)}+\frac{1}{2} \tan ^{-1}(x)",1,"1/(2*(1 + x)) + ArcTan[x]/2","A",3,2,14,0.1429,1,"{801, 203}"
486,1,29,0,0.020162,"\int \frac{7-2 x+3 x^2-x^3+x^4}{2+x} \, dx","Int[(7 - 2*x + 3*x^2 - x^3 + x^4)/(2 + x),x]","\frac{x^4}{4}-x^3+\frac{9 x^2}{2}-20 x+47 \log (x+2)","\frac{x^4}{4}-x^3+\frac{9 x^2}{2}-20 x+47 \log (x+2)",1,"-20*x + (9*x^2)/2 - x^3 + x^4/4 + 47*Log[2 + x]","A",2,1,24,0.04167,1,"{1850}"
487,1,16,0,0.0060318,"\int \frac{-1+x^3}{-1+x} \, dx","Int[(-1 + x^3)/(-1 + x),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",2,1,11,0.09091,1,"{1586}"
488,1,17,0,0.0145243,"\int \frac{2+2 x}{(-1+x)^3 \left(1+x^2\right)} \, dx","Int[(2 + 2*x)/((-1 + x)^3*(1 + x^2)),x]","\frac{1}{x-1}-\frac{1}{(1-x)^2}+\tan ^{-1}(x)","\frac{1}{x-1}-\frac{1}{(1-x)^2}+\tan ^{-1}(x)",1,"-(1 - x)^(-2) + (-1 + x)^(-1) + ArcTan[x]","A",3,2,18,0.1111,1,"{801, 203}"
489,1,47,0,0.0658729,"\int \frac{1}{b x+c (d+e x)^2} \, dx","Int[(b*x + c*(d + e*x)^2)^(-1),x]","-\frac{2 \tanh ^{-1}\left(\frac{b+2 c e (d+e x)}{\sqrt{b} \sqrt{b+4 c d e}}\right)}{\sqrt{b} \sqrt{b+4 c d e}}","-\frac{2 \tanh ^{-1}\left(\frac{b+2 c e (d+e x)}{\sqrt{b} \sqrt{b+4 c d e}}\right)}{\sqrt{b} \sqrt{b+4 c d e}}",1,"(-2*ArcTanh[(b + 2*c*e*(d + e*x))/(Sqrt[b]*Sqrt[b + 4*c*d*e])])/(Sqrt[b]*Sqrt[b + 4*c*d*e])","A",3,3,15,0.2000,1,"{1981, 618, 206}"
490,1,57,0,0.0815414,"\int \frac{1}{a+b x+c (d+e x)^2} \, dx","Int[(a + b*x + c*(d + e*x)^2)^(-1),x]","-\frac{2 \tanh ^{-1}\left(\frac{b+2 c e (d+e x)}{\sqrt{-4 a c e^2+b^2+4 b c d e}}\right)}{\sqrt{-4 a c e^2+b^2+4 b c d e}}","-\frac{2 \tanh ^{-1}\left(\frac{b+2 c e (d+e x)}{\sqrt{-4 a c e^2+b^2+4 b c d e}}\right)}{\sqrt{-4 a c e^2+b^2+4 b c d e}}",1,"(-2*ArcTanh[(b + 2*c*e*(d + e*x))/Sqrt[b^2 + 4*b*c*d*e - 4*a*c*e^2]])/Sqrt[b^2 + 4*b*c*d*e - 4*a*c*e^2]","A",3,3,16,0.1875,1,"{1981, 618, 206}"
491,1,188,0,0.1889428,"\int \frac{x^2}{1+\left(-1+x^2\right)^2} \, dx","Int[x^2/(1 + (-1 + x^2)^2),x]","\frac{\log \left(x^2-\sqrt{2 \left(1+\sqrt{2}\right)} x+\sqrt{2}\right)}{4 \sqrt{2 \left(1+\sqrt{2}\right)}}-\frac{\log \left(x^2+\sqrt{2 \left(1+\sqrt{2}\right)} x+\sqrt{2}\right)}{4 \sqrt{2 \left(1+\sqrt{2}\right)}}-\frac{1}{2} \sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)}-2 x}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)+\frac{1}{2} \sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tan ^{-1}\left(\frac{2 x+\sqrt{2 \left(1+\sqrt{2}\right)}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)","\frac{\log \left(x^2-\sqrt{2 \left(1+\sqrt{2}\right)} x+\sqrt{2}\right)}{4 \sqrt{2 \left(1+\sqrt{2}\right)}}-\frac{\log \left(x^2+\sqrt{2 \left(1+\sqrt{2}\right)} x+\sqrt{2}\right)}{4 \sqrt{2 \left(1+\sqrt{2}\right)}}-\frac{1}{2} \sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)}-2 x}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)+\frac{1}{2} \sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tan ^{-1}\left(\frac{2 x+\sqrt{2 \left(1+\sqrt{2}\right)}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)",1,"-(Sqrt[(1 + Sqrt[2])/2]*ArcTan[(Sqrt[2*(1 + Sqrt[2])] - 2*x)/Sqrt[2*(-1 + Sqrt[2])]])/2 + (Sqrt[(1 + Sqrt[2])/2]*ArcTan[(Sqrt[2*(1 + Sqrt[2])] + 2*x)/Sqrt[2*(-1 + Sqrt[2])]])/2 + Log[Sqrt[2] - Sqrt[2*(1 + Sqrt[2])]*x + x^2]/(4*Sqrt[2*(1 + Sqrt[2])]) - Log[Sqrt[2] + Sqrt[2*(1 + Sqrt[2])]*x + x^2]/(4*Sqrt[2*(1 + Sqrt[2])])","A",10,7,15,0.4667,1,"{1989, 1127, 1161, 618, 204, 1164, 628}"
492,1,60,0,0.1359843,"\int -\frac{15-36 x+5 x^2+12 x^3-34 x^4+140 x^5+15 x^6+8 x^7-30 x^9}{\left(3+x+x^4\right)^4} \, dx","Int[-((15 - 36*x + 5*x^2 + 12*x^3 - 34*x^4 + 140*x^5 + 15*x^6 + 8*x^7 - 30*x^9)/(3 + x + x^4)^4),x]","-\frac{5 x^6}{\left(x^4+x+3\right)^3}+\frac{x^4}{\left(x^4+x+3\right)^3}+\frac{5 x^2}{\left(x^4+x+3\right)^3}-\frac{3 x}{\left(x^4+x+3\right)^3}+\frac{2}{\left(x^4+x+3\right)^3}","-\frac{5 x^6}{\left(x^4+x+3\right)^3}+\frac{x^4}{\left(x^4+x+3\right)^3}+\frac{5 x^2}{\left(x^4+x+3\right)^3}-\frac{3 x}{\left(x^4+x+3\right)^3}+\frac{2}{\left(x^4+x+3\right)^3}",1,"2/(3 + x + x^4)^3 - (3*x)/(3 + x + x^4)^3 + (5*x^2)/(3 + x + x^4)^3 + x^4/(3 + x + x^4)^3 - (5*x^6)/(3 + x + x^4)^3","A",5,2,50,0.04000,1,"{2102, 1588}"
493,0,0,0,0.3112774,"\int \left(\frac{3 \left(-47+228 x+120 x^2+19 x^3\right)}{\left(3+x+x^4\right)^4}+\frac{42-320 x-75 x^2-8 x^3}{\left(3+x+x^4\right)^3}+\frac{30 x}{\left(3+x+x^4\right)^2}\right) \, dx","Int[(3*(-47 + 228*x + 120*x^2 + 19*x^3))/(3 + x + x^4)^4 + (42 - 320*x - 75*x^2 - 8*x^3)/(3 + x + x^4)^3 + (30*x)/(3 + x + x^4)^2,x]","\int \left(\frac{3 \left(-47+228 x+120 x^2+19 x^3\right)}{\left(3+x+x^4\right)^4}+\frac{42-320 x-75 x^2-8 x^3}{\left(3+x+x^4\right)^3}+\frac{30 x}{\left(3+x+x^4\right)^2}\right) \, dx","\frac{-5 x^6+x^4+5 x^2-3 x+2}{\left(x^4+x+3\right)^3}",1,"-19/(4*(3 + x + x^4)^3) + (3 + x + x^4)^(-2) - (621*Defer[Int][(3 + x + x^4)^(-4), x])/4 + 684*Defer[Int][x/(3 + x + x^4)^4, x] + 360*Defer[Int][x^2/(3 + x + x^4)^4, x] + 44*Defer[Int][(3 + x + x^4)^(-3), x] - 320*Defer[Int][x/(3 + x + x^4)^3, x] - 75*Defer[Int][x^2/(3 + x + x^4)^3, x] + 30*Defer[Int][x/(3 + x + x^4)^2, x]","F",0,0,0,0,-1,"{}"
494,0,0,0,0.4331484,"\int \left(\frac{-3+10 x+4 x^3-30 x^5}{\left(3+x+x^4\right)^3}-\frac{3 \left(1+4 x^3\right) \left(2-3 x+5 x^2+x^4-5 x^6\right)}{\left(3+x+x^4\right)^4}\right) \, dx","Int[(-3 + 10*x + 4*x^3 - 30*x^5)/(3 + x + x^4)^3 - (3*(1 + 4*x^3)*(2 - 3*x + 5*x^2 + x^4 - 5*x^6))/(3 + x + x^4)^4,x]","\int \left(\frac{-3+10 x+4 x^3-30 x^5}{\left(3+x+x^4\right)^3}-\frac{3 \left(1+4 x^3\right) \left(2-3 x+5 x^2+x^4-5 x^6\right)}{\left(3+x+x^4\right)^4}\right) \, dx","\frac{-5 x^6+x^4+5 x^2-3 x+2}{\left(x^4+x+3\right)^3}",1,"7/(2*(3 + x + x^4)^3) - (63*x)/(22*(3 + x + x^4)^3) - (12*x^2)/(3 + x + x^4)^3 - (5*x^3)/(3 + x + x^4)^3 + (3*x^4)/(2*(3 + x + x^4)^3) - (10*x^6)/(3 + x + x^4)^3 - 1/(2*(3 + x + x^4)^2) + (5*x^2)/(3 + x + x^4)^2 + (144*Defer[Int][(3 + x + x^4)^(-4), x])/11 + (828*Defer[Int][x/(3 + x + x^4)^4, x])/11 + 18*Defer[Int][x^2/(3 + x + x^4)^4, x] - 4*Defer[Int][(3 + x + x^4)^(-3), x] - 20*Defer[Int][x/(3 + x + x^4)^3, x]","F",0,0,0,0,-1,"{}"