1,1,143,77,0.0738729,"\int \frac{1}{2 \sqrt{3} b^{3/2}-9 b x+9 x^3} \, dx","Integrate[(2*Sqrt[3]*b^(3/2) - 9*b*x + 9*x^3)^(-1),x]","-\frac{\left(3 x-\sqrt{3} \sqrt{b}\right) \left(2 \sqrt{3} \sqrt{b}+3 x\right) \left(\left(3 x-\sqrt{3} \sqrt{b}\right) \log \left(3 x-\sqrt{3} \sqrt{b}\right)+\left(\sqrt{3} \sqrt{b}-3 x\right) \log \left(2 \sqrt{3} \sqrt{b}+3 x\right)+3 \sqrt{3} \sqrt{b}\right)}{81 b \left(2 \sqrt{3} b^{3/2}-9 b x+9 x^3\right)}","\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,"-1/81*((-(Sqrt[3]*Sqrt[b]) + 3*x)*(2*Sqrt[3]*Sqrt[b] + 3*x)*(3*Sqrt[3]*Sqrt[b] + (-(Sqrt[3]*Sqrt[b]) + 3*x)*Log[-(Sqrt[3]*Sqrt[b]) + 3*x] + (Sqrt[3]*Sqrt[b] - 3*x)*Log[2*Sqrt[3]*Sqrt[b] + 3*x]))/(b*(2*Sqrt[3]*b^(3/2) - 9*b*x + 9*x^3))","A",1
2,1,23,30,0.1054551,"\int \left(a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3\right)^p \, dx","Integrate[(a^3 + 3*a^2*b*x + 3*a*b^2*x^2 + b^3*x^3)^p,x]","\frac{(a+b x) \left((a+b x)^3\right)^p}{3 b p+b}","\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)*((a + b*x)^3)^p)/(b + 3*b*p)","A",1
3,1,14,14,0.0010971,"\int \left(a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3\right)^3 \, dx","Integrate[(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",1
4,1,14,14,0.0013479,"\int \left(a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3\right)^2 \, dx","Integrate[(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",1
5,1,35,35,0.0000869,"\int \left(a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3\right) \, dx","Integrate[a^3 + 3*a^2*b*x + 3*a*b^2*x^2 + b^3*x^3,x]","a^3 x+\frac{3}{2} a^2 b x^2+a b^2 x^3+\frac{b^3 x^4}{4}","a^3 x+\frac{3}{2} a^2 b x^2+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
6,1,14,14,0.004734,"\int \frac{1}{a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3} \, dx","Integrate[(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*1/(b*(a + b*x)^2)","A",1
7,1,14,14,0.004459,"\int \frac{1}{\left(a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3\right)^2} \, dx","Integrate[(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*1/(b*(a + b*x)^5)","A",1
8,1,14,14,0.0033303,"\int \frac{1}{\left(a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3\right)^3} \, dx","Integrate[(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*1/(b*(a + b*x)^8)","A",1
9,1,159,84,0.0245772,"\int \left(3 a b+3 b^2 x+3 b c x^2+c^2 x^3\right)^3 \, dx","Integrate[(3*a*b + 3*b^2*x + 3*b*c*x^2 + c^2*x^3)^3,x]","27 a^3 b^3 x+\frac{81}{2} a^2 b^4 x^2+\frac{27}{4} b^2 x^4 \left(a^2 c^2+6 a b^2 c+b^4\right)+\frac{9}{7} b c^3 x^7 \left(a c+9 b^2\right)+9 b^2 c^2 x^6 \left(a c+2 b^2\right)+\frac{27}{5} b^3 c x^5 \left(5 a c+3 b^2\right)+27 a b^3 x^3 \left(a c+b^2\right)+\frac{9}{2} b^2 c^4 x^8+b c^5 x^9+\frac{c^6 x^{10}}{10}","-\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,"27*a^3*b^3*x + (81*a^2*b^4*x^2)/2 + 27*a*b^3*(b^2 + a*c)*x^3 + (27*b^2*(b^4 + 6*a*b^2*c + a^2*c^2)*x^4)/4 + (27*b^3*c*(3*b^2 + 5*a*c)*x^5)/5 + 9*b^2*c^2*(2*b^2 + a*c)*x^6 + (9*b*c^3*(9*b^2 + a*c)*x^7)/7 + (9*b^2*c^4*x^8)/2 + b*c^5*x^9 + (c^6*x^10)/10","A",1
10,1,82,56,0.0097837,"\int \left(3 a b+3 b^2 x+3 b c x^2+c^2 x^3\right)^2 \, dx","Integrate[(3*a*b + 3*b^2*x + 3*b*c*x^2 + c^2*x^3)^2,x]","9 a^2 b^2 x+9 a b^3 x^2+\frac{3}{2} b c x^4 \left(a c+3 b^2\right)+3 b^2 x^3 \left(2 a c+b^2\right)+3 b^2 c^2 x^5+b c^3 x^6+\frac{c^4 x^7}{7}","-\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,"9*a^2*b^2*x + 9*a*b^3*x^2 + 3*b^2*(b^2 + 2*a*c)*x^3 + (3*b*c*(3*b^2 + a*c)*x^4)/2 + 3*b^2*c^2*x^5 + b*c^3*x^6 + (c^4*x^7)/7","A",1
11,1,32,32,0.0001767,"\int \left(3 a b+3 b^2 x+3 b c x^2+c^2 x^3\right) \, dx","Integrate[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
12,1,63,188,0.0211573,"\int \frac{1}{3 a b+3 b^2 x+3 b c x^2+c^2 x^3} \, dx","Integrate[(3*a*b + 3*b^2*x + 3*b*c*x^2 + c^2*x^3)^(-1),x]","\frac{1}{3} \text{RootSum}\left[\text{$\#$1}^3 c^2+3 \text{$\#$1}^2 b c+3 \text{$\#$1} b^2+3 a b\&,\frac{\log (x-\text{$\#$1})}{\text{$\#$1}^2 c^2+2 \text{$\#$1} b c+b^2}\&\right]","-\frac{\log \left(\sqrt[3]{b} c \sqrt[3]{b^2-3 a c} \left(\frac{b}{c}+x\right)+b^{2/3} \left(b^2-3 a c\right)^{2/3}+c^2 \left(\frac{b}{c}+x\right)^2\right)}{6 b^{2/3} \left(b^2-3 a c\right)^{2/3}}+\frac{\log \left(-\sqrt[3]{b} \sqrt[3]{b^2-3 a c}+b+c x\right)}{3 b^{2/3} \left(b^2-3 a c\right)^{2/3}}-\frac{\tan ^{-1}\left(\frac{\frac{2 (b+c x)}{\sqrt[3]{b^2-3 a c}}+\sqrt[3]{b}}{\sqrt{3} \sqrt[3]{b}}\right)}{\sqrt{3} b^{2/3} \left(b^2-3 a c\right)^{2/3}}",1,"RootSum[3*a*b + 3*b^2*#1 + 3*b*c*#1^2 + c^2*#1^3 & , Log[x - #1]/(b^2 + 2*b*c*#1 + c^2*#1^2) & ]/3","C",1
13,1,112,245,0.0656853,"\int \frac{1}{\left(3 a b+3 b^2 x+3 b c x^2+c^2 x^3\right)^2} \, dx","Integrate[(3*a*b + 3*b^2*x + 3*b*c*x^2 + c^2*x^3)^(-2),x]","-\frac{2 c \text{RootSum}\left[\text{$\#$1}^3 c^2+3 \text{$\#$1}^2 b c+3 \text{$\#$1} b^2+3 a b\&,\frac{\log (x-\text{$\#$1})}{\text{$\#$1}^2 c^2+2 \text{$\#$1} b c+b^2}\&\right]+\frac{3 (b+c x)}{3 a b+x \left(3 b^2+3 b c x+c^2 x^2\right)}}{9 \left(b^3-3 a b c\right)}","-\frac{c \left(\frac{b}{c}+x\right)}{3 b \left(b^2-3 a c\right) \left(3 a b+3 b^2 x+3 b c x^2+c^2 x^3\right)}+\frac{c \log \left(\sqrt[3]{b} c \sqrt[3]{b^2-3 a c} \left(\frac{b}{c}+x\right)+b^{2/3} \left(b^2-3 a c\right)^{2/3}+c^2 \left(\frac{b}{c}+x\right)^2\right)}{9 b^{5/3} \left(b^2-3 a c\right)^{5/3}}-\frac{2 c \log \left(-\sqrt[3]{b} \sqrt[3]{b^2-3 a c}+b+c x\right)}{9 b^{5/3} \left(b^2-3 a c\right)^{5/3}}+\frac{2 c \tan ^{-1}\left(\frac{\frac{2 (b+c x)}{\sqrt[3]{b^2-3 a c}}+\sqrt[3]{b}}{\sqrt{3} \sqrt[3]{b}}\right)}{3 \sqrt{3} b^{5/3} \left(b^2-3 a c\right)^{5/3}}",1,"-1/9*((3*(b + c*x))/(3*a*b + x*(3*b^2 + 3*b*c*x + c^2*x^2)) + 2*c*RootSum[3*a*b + 3*b^2*#1 + 3*b*c*#1^2 + c^2*#1^3 & , Log[x - #1]/(b^2 + 2*b*c*#1 + c^2*#1^2) & ])/(b^3 - 3*a*b*c)","C",1
14,1,149,305,0.0895455,"\int \frac{1}{\left(3 a b+3 b^2 x+3 b c x^2+c^2 x^3\right)^3} \, dx","Integrate[(3*a*b + 3*b^2*x + 3*b*c*x^2 + c^2*x^3)^(-3),x]","\frac{10 c^2 \text{RootSum}\left[\text{$\#$1}^3 c^2+3 \text{$\#$1}^2 b c+3 \text{$\#$1} b^2+3 a b\&,\frac{\log (x-\text{$\#$1})}{\text{$\#$1}^2 c^2+2 \text{$\#$1} b c+b^2}\&\right]-\frac{3 (b+c x) \left(-3 b c \left(8 a+5 c x^2\right)+3 b^3-15 b^2 c x-5 c^3 x^3\right)}{\left(3 a b+x \left(3 b^2+3 b c x+c^2 x^2\right)\right)^2}}{54 \left(b^3-3 a b c\right)^2}","\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,"((-3*(b + c*x)*(3*b^3 - 15*b^2*c*x - 5*c^3*x^3 - 3*b*c*(8*a + 5*c*x^2)))/(3*a*b + x*(3*b^2 + 3*b*c*x + c^2*x^2))^2 + 10*c^2*RootSum[3*a*b + 3*b^2*#1 + 3*b*c*#1^2 + c^2*#1^3 & , Log[x - #1]/(b^2 + 2*b*c*#1 + c^2*#1^2) & ])/(54*(b^3 - 3*a*b*c)^2)","C",1
15,1,653,361,0.2243411,"\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","Integrate[(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]","a^3 c^3 e^3 x+\frac{3}{8} b d f x^8 \left(a^2 d^2 f^2+3 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)+a c e x^3 \left(a^2 \left(c^2 f^2+3 c d e f+d^2 e^2\right)+3 a b c e (c f+d e)+b^2 c^2 e^2\right)+\frac{3}{2} a^2 c^2 e^2 x^2 (a c f+a d e+b c e)+\frac{1}{7} x^7 \left(a^3 d^3 f^3+9 a^2 b d^2 f^2 (c f+d e)+9 a b^2 d f \left(c^2 f^2+3 c d e f+d^2 e^2\right)+b^3 \left(c^3 f^3+9 c^2 d e f^2+9 c d^2 e^2 f+d^3 e^3\right)\right)+\frac{1}{2} x^6 \left(a^3 d^2 f^2 (c f+d e)+3 a^2 b d f \left(c^2 f^2+3 c d e f+d^2 e^2\right)+a b^2 \left(c^3 f^3+9 c^2 d e f^2+9 c d^2 e^2 f+d^3 e^3\right)+b^3 c e \left(c^2 f^2+3 c d e f+d^2 e^2\right)\right)+\frac{3}{5} x^5 \left(a^3 d f \left(c^2 f^2+3 c d e f+d^2 e^2\right)+a^2 b \left(c^3 f^3+9 c^2 d e f^2+9 c d^2 e^2 f+d^3 e^3\right)+3 a b^2 c e \left(c^2 f^2+3 c d e f+d^2 e^2\right)+b^3 c^2 e^2 (c f+d e)\right)+\frac{1}{4} x^4 \left(a^3 \left(c^3 f^3+9 c^2 d e f^2+9 c d^2 e^2 f+d^3 e^3\right)+9 a^2 b c e \left(c^2 f^2+3 c d e f+d^2 e^2\right)+9 a b^2 c^2 e^2 (c f+d e)+b^3 c^3 e^3\right)+\frac{1}{3} b^2 d^2 f^2 x^9 (a d f+b c f+b d e)+\frac{1}{10} b^3 d^3 f^3 x^{10}","\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,"a^3*c^3*e^3*x + (3*a^2*c^2*e^2*(b*c*e + a*d*e + a*c*f)*x^2)/2 + a*c*e*(b^2*c^2*e^2 + 3*a*b*c*e*(d*e + c*f) + a^2*(d^2*e^2 + 3*c*d*e*f + c^2*f^2))*x^3 + ((b^3*c^3*e^3 + 9*a*b^2*c^2*e^2*(d*e + c*f) + 9*a^2*b*c*e*(d^2*e^2 + 3*c*d*e*f + c^2*f^2) + a^3*(d^3*e^3 + 9*c*d^2*e^2*f + 9*c^2*d*e*f^2 + c^3*f^3))*x^4)/4 + (3*(b^3*c^2*e^2*(d*e + c*f) + 3*a*b^2*c*e*(d^2*e^2 + 3*c*d*e*f + c^2*f^2) + a^3*d*f*(d^2*e^2 + 3*c*d*e*f + c^2*f^2) + a^2*b*(d^3*e^3 + 9*c*d^2*e^2*f + 9*c^2*d*e*f^2 + c^3*f^3))*x^5)/5 + ((a^3*d^2*f^2*(d*e + c*f) + b^3*c*e*(d^2*e^2 + 3*c*d*e*f + c^2*f^2) + 3*a^2*b*d*f*(d^2*e^2 + 3*c*d*e*f + c^2*f^2) + a*b^2*(d^3*e^3 + 9*c*d^2*e^2*f + 9*c^2*d*e*f^2 + c^3*f^3))*x^6)/2 + ((a^3*d^3*f^3 + 9*a^2*b*d^2*f^2*(d*e + c*f) + 9*a*b^2*d*f*(d^2*e^2 + 3*c*d*e*f + c^2*f^2) + b^3*(d^3*e^3 + 9*c*d^2*e^2*f + 9*c^2*d*e*f^2 + c^3*f^3))*x^7)/7 + (3*b*d*f*(a^2*d^2*f^2 + 3*a*b*d*f*(d*e + c*f) + b^2*(d^2*e^2 + 3*c*d*e*f + c^2*f^2))*x^8)/8 + (b^2*d^2*f^2*(b*d*e + b*c*f + a*d*f)*x^9)/3 + (b^3*d^3*f^3*x^10)/10","A",1
16,1,241,193,0.0859617,"\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","Integrate[(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{1}{5} x^5 \left(a^2 d^2 f^2+4 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)+\frac{1}{2} x^4 \left(a^2 d f (c f+d e)+a b \left(c^2 f^2+4 c d e f+d^2 e^2\right)+b^2 c e (c f+d e)\right)+\frac{1}{3} x^3 \left(a^2 \left(c^2 f^2+4 c d e f+d^2 e^2\right)+4 a b c e (c f+d e)+b^2 c^2 e^2\right)+a^2 c^2 e^2 x+\frac{1}{3} b d f x^6 (a d f+b c f+b d e)+a c e x^2 (a c f+a d e+b c e)+\frac{1}{7} b^2 d^2 f^2 x^7","\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,"a^2*c^2*e^2*x + a*c*e*(b*c*e + a*d*e + a*c*f)*x^2 + ((b^2*c^2*e^2 + 4*a*b*c*e*(d*e + c*f) + a^2*(d^2*e^2 + 4*c*d*e*f + c^2*f^2))*x^3)/3 + ((b^2*c*e*(d*e + c*f) + a^2*d*f*(d*e + c*f) + a*b*(d^2*e^2 + 4*c*d*e*f + c^2*f^2))*x^4)/2 + ((a^2*d^2*f^2 + 4*a*b*d*f*(d*e + c*f) + b^2*(d^2*e^2 + 4*c*d*e*f + c^2*f^2))*x^5)/5 + (b*d*f*(b*d*e + b*c*f + a*d*f)*x^6)/3 + (b^2*d^2*f^2*x^7)/7","A",1
17,1,76,56,0.0001077,"\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","Integrate[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]","a c e x+\frac{1}{2} a c f x^2+\frac{1}{2} a d e x^2+\frac{1}{3} a d f x^3+\frac{1}{2} b c e x^2+\frac{1}{3} b c f x^3+\frac{1}{3} b d e x^3+\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*x^2)/2 + (a*d*e*x^2)/2 + (a*c*f*x^2)/2 + (b*d*e*x^3)/3 + (b*c*f*x^3)/3 + (a*d*f*x^3)/3 + (b*d*f*x^4)/4","A",1
18,1,80,86,0.0567879,"\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","Integrate[(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) (c f-d e)+d (b e-a f) \log (c+d x)+f (a d-b c) \log (e+f x)}{(b c-a d) (b e-a f) (c f-d e)}","\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*(-(d*e) + c*f)*Log[a + b*x] + d*(b*e - a*f)*Log[c + d*x] + (-(b*c) + a*d)*f*Log[e + f*x])/((b*c - a*d)*(b*e - a*f)*(-(d*e) + c*f))","A",1
19,1,232,234,0.5519269,"\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","Integrate[(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 (c f-d e)^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",1
20,1,490,495,1.1920537,"\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","Integrate[(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{1}{2} \left(\frac{6 f^5 \log (e+f x) \left(2 a^2 d^2 f^2+a b d f (3 c f-7 d e)+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{6 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 (c f-d e)^5}+\frac{6 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{6 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}{(a+b x)^2 (b c-a d)^3 (b e-a f)^3}+\frac{6 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}{(c+d x)^2 (b c-a d)^3 (c f-d e)^3}+\frac{6 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}{(e+f x)^2 (b e-a f)^3 (d e-c f)^3}\right)","\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 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 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 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/((b*c - a*d)^3*(b*e - a*f)^3*(a + b*x)^2)) + (6*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/((b*c - a*d)^3*(-(d*e) + c*f)^3*(c + d*x)^2) + (6*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/((b*e - a*f)^3*(d*e - c*f)^3*(e + f*x)^2) + (6*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)) + (6*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) + (6*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) + (6*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))/2","A",1
21,1,25,25,0.0094699,"\int \frac{1}{1+x+x^2+x^3} \, dx","Integrate[(1 + x + x^2 + x^3)^(-1),x]","-\frac{1}{4} \log \left(x^2+1\right)+\frac{1}{2} \log (x+1)+\frac{1}{2} \tan ^{-1}(x)","-\frac{1}{4} \log \left(x^2+1\right)+\frac{1}{2} \log (x+1)+\frac{1}{2} \tan ^{-1}(x)",1,"ArcTan[x]/2 + Log[1 + x]/2 - Log[1 + x^2]/4","A",1
22,1,31,31,0.0067048,"\int \frac{1}{-1+4 x-4 x^2+16 x^3} \, dx","Integrate[(-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,"-1/10*ArcTan[2*x] + Log[1 - 4*x]/5 - Log[1 + 4*x^2]/10","A",1
23,1,10,10,0.0003344,"\int \frac{1}{d x^3} \, dx","Integrate[1/(d*x^3),x]","-\frac{1}{2 d x^2}","-\frac{1}{2 d x^2}",1,"-1/2*1/(d*x^2)","A",1
24,1,28,28,0.0058836,"\int \frac{1}{c x^2+d x^3} \, dx","Integrate[(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",1
25,1,22,22,0.006561,"\int \frac{1}{b x+d x^3} \, dx","Integrate[(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",1
26,1,61,62,0.0818521,"\int \frac{1}{b x+c x^2+d x^3} \, dx","Integrate[(b*x + c*x^2 + d*x^3)^(-1),x]","-\frac{\frac{2 c \tan ^{-1}\left(\frac{c+2 d x}{\sqrt{4 b d-c^2}}\right)}{\sqrt{4 b d-c^2}}+\log (b+x (c+d x))-2 \log (x)}{2 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,"-1/2*((2*c*ArcTan[(c + 2*d*x)/Sqrt[-c^2 + 4*b*d]])/Sqrt[-c^2 + 4*b*d] - 2*Log[x] + Log[b + x*(c + d*x)])/b","A",1
27,1,89,115,0.0360948,"\int \frac{1}{a+d x^3} \, dx","Integrate[(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)-2 \log \left(\sqrt[3]{a}+\sqrt[3]{d} x\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} x}{\sqrt[3]{a}}}{\sqrt{3}}\right)}{6 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,"-1/6*(2*Sqrt[3]*ArcTan[(1 - (2*d^(1/3)*x)/a^(1/3))/Sqrt[3]] - 2*Log[a^(1/3) + d^(1/3)*x] + Log[a^(2/3) - a^(1/3)*d^(1/3)*x + d^(2/3)*x^2])/(a^(2/3)*d^(1/3))","A",1
28,1,16,16,0.0021145,"\int \left(d x^3\right)^n \, dx","Integrate[(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",1
29,1,53,55,0.0124874,"\int \left(c x^2+d x^3\right)^n \, dx","Integrate[(c*x^2 + d*x^3)^n,x]","\frac{x \left(x^2 (c+d x)\right)^n \left(\frac{d x}{c}+1\right)^{-n} \, _2F_1\left(-n,2 n+1;2 n+2;-\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 \, _2F_1\left(-n,2 n+1;2 (n+1);-\frac{d x}{c}\right)}{2 n+1}",1,"(x*(x^2*(c + d*x))^n*Hypergeometric2F1[-n, 1 + 2*n, 2 + 2*n, -((d*x)/c)])/((1 + 2*n)*(1 + (d*x)/c)^n)","A",1
30,1,61,53,0.0157639,"\int \left(b x+d x^3\right)^n \, dx","Integrate[(b*x + d*x^3)^n,x]","\frac{x \left(x \left(b+d x^2\right)\right)^n \left(\frac{d x^2}{b}+1\right)^{-n} \, _2F_1\left(-n,\frac{n+1}{2};\frac{n+1}{2}+1;-\frac{d x^2}{b}\right)}{n+1}","\frac{x \left(b+d x^2\right) \left(b x+d x^3\right)^n \, _2F_1\left(1,\frac{3 (n+1)}{2};\frac{n+3}{2};-\frac{d x^2}{b}\right)}{b (n+1)}",1,"(x*(x*(b + d*x^2))^n*Hypergeometric2F1[-n, (1 + n)/2, 1 + (1 + n)/2, -((d*x^2)/b)])/((1 + n)*(1 + (d*x^2)/b)^n)","A",1
31,1,157,132,0.3598029,"\int \left(b x+c x^2+d x^3\right)^n \, dx","Integrate[(b*x + c*x^2 + d*x^3)^n,x]","\frac{x \left(\frac{-\sqrt{c^2-4 b d}+c+2 d x}{c-\sqrt{c^2-4 b d}}\right)^{-n} \left(\frac{\sqrt{c^2-4 b d}+c+2 d x}{\sqrt{c^2-4 b d}+c}\right)^{-n} (x (b+x (c+d x)))^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}{\sqrt{c^2-4 b d}-c}\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*(x*(b + x*(c + d*x)))^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)*((c - Sqrt[c^2 - 4*b*d] + 2*d*x)/(c - Sqrt[c^2 - 4*b*d]))^n*((c + Sqrt[c^2 - 4*b*d] + 2*d*x)/(c + Sqrt[c^2 - 4*b*d]))^n)","A",0
32,1,196,35,0.1951476,"\int \left(a+d x^3\right)^n \, dx","Integrate[(a + d*x^3)^n,x]","\frac{2^{-n} \left((-1)^{2/3} \sqrt[3]{a}+\sqrt[3]{d} x\right) \left(\frac{\sqrt[3]{a}+(-1)^{2/3} \sqrt[3]{d} x}{\left(1+\sqrt[3]{-1}\right) \sqrt[3]{a}}\right)^{-n} \left(\frac{i \left(\frac{\sqrt[3]{d} x}{\sqrt[3]{a}}+1\right)}{\sqrt{3}+3 i}\right)^{-n} \left(a+d x^3\right)^n F_1\left(n+1;-n,-n;n+2;-\frac{i \left(\sqrt[3]{d} x+(-1)^{2/3} \sqrt[3]{a}\right)}{\sqrt{3} \sqrt[3]{a}},\frac{-\frac{2 i \sqrt[3]{d} x}{\sqrt[3]{a}}+\sqrt{3}+i}{3 i+\sqrt{3}}\right)}{\sqrt[3]{d} (n+1)}","\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,"(((-1)^(2/3)*a^(1/3) + d^(1/3)*x)*(a + d*x^3)^n*AppellF1[1 + n, -n, -n, 2 + n, ((-I)*((-1)^(2/3)*a^(1/3) + d^(1/3)*x))/(Sqrt[3]*a^(1/3)), (I + Sqrt[3] - ((2*I)*d^(1/3)*x)/a^(1/3))/(3*I + Sqrt[3])])/(2^n*d^(1/3)*(1 + n)*((a^(1/3) + (-1)^(2/3)*d^(1/3)*x)/((1 + (-1)^(1/3))*a^(1/3)))^n*((I*(1 + (d^(1/3)*x)/a^(1/3)))/(3*I + Sqrt[3]))^n)","C",0
33,1,285,270,0.0401152,"\int \left(4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4\right)^4 \, dx","Integrate[(4*a*c + 4*c^2*x^2 + 4*c*d*x^3 + d^2*x^4)^4,x]","256 a^4 c^4 x+\frac{1024}{3} a^3 c^5 x^3+256 a^3 c^4 d x^4+512 a^2 c^5 d x^6+\frac{256}{5} a^2 c^3 x^5 \left(a d^2+6 c^3\right)+\frac{32}{9} c^2 x^9 \left(3 a^2 d^4+120 a c^3 d^2+8 c^6\right)+\frac{64}{11} c^3 d^2 x^{11} \left(15 a d^2+28 c^3\right)+96 a c^3 d x^8 \left(a d^2+4 c^3\right)+\frac{16}{13} c d^4 x^{13} \left(a d^2+70 c^3\right)+\frac{256}{5} c^4 d x^{10} \left(5 a d^2+2 c^3\right)+\frac{256}{7} a c^4 x^7 \left(9 a d^2+4 c^3\right)+\frac{16}{3} c^2 d^3 x^{12} \left(3 a d^2+28 c^3\right)+32 c^3 d^5 x^{14}+\frac{112}{15} c^2 d^6 x^{15}+c d^7 x^{16}+\frac{d^8 x^{17}}{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{8}{11} c^3 d^2 \left(12 a d^2+7 c^3\right) \left(\frac{c}{d}+x\right)^{11}+\frac{4}{13} c d^4 \left(4 a d^2+7 c^3\right) \left(\frac{c}{d}+x\right)^{13}+\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{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{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,"256*a^4*c^4*x + (1024*a^3*c^5*x^3)/3 + 256*a^3*c^4*d*x^4 + (256*a^2*c^3*(6*c^3 + a*d^2)*x^5)/5 + 512*a^2*c^5*d*x^6 + (256*a*c^4*(4*c^3 + 9*a*d^2)*x^7)/7 + 96*a*c^3*d*(4*c^3 + a*d^2)*x^8 + (32*c^2*(8*c^6 + 120*a*c^3*d^2 + 3*a^2*d^4)*x^9)/9 + (256*c^4*d*(2*c^3 + 5*a*d^2)*x^10)/5 + (64*c^3*d^2*(28*c^3 + 15*a*d^2)*x^11)/11 + (16*c^2*d^3*(28*c^3 + 3*a*d^2)*x^12)/3 + (16*c*d^4*(70*c^3 + a*d^2)*x^13)/13 + 32*c^3*d^5*x^14 + (112*c^2*d^6*x^15)/15 + c*d^7*x^16 + (d^8*x^17)/17","A",1
34,1,171,171,0.0282719,"\int \left(4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4\right)^3 \, dx","Integrate[(4*a*c + 4*c^2*x^2 + 4*c*d*x^3 + d^2*x^4)^3,x]","64 a^3 c^3 x+64 a^2 c^4 x^3+48 a^2 c^3 d x^4+64 a c^4 d x^6+\frac{4}{3} c d^2 x^9 \left(a d^2+20 c^3\right)+\frac{32}{7} c^3 x^7 \left(9 a d^2+2 c^3\right)+12 c^2 d x^8 \left(a d^2+2 c^3\right)+\frac{48}{5} a c^2 x^5 \left(a d^2+4 c^3\right)+16 c^3 d^3 x^{10}+\frac{60}{11} c^2 d^4 x^{11}+c d^5 x^{12}+\frac{d^6 x^{13}}{13}","64 a^3 c^3 x+64 a^2 c^4 x^3+48 a^2 c^3 d x^4+64 a c^4 d x^6+\frac{4}{3} c d^2 x^9 \left(a d^2+20 c^3\right)+\frac{32}{7} c^3 x^7 \left(9 a d^2+2 c^3\right)+12 c^2 d x^8 \left(a d^2+2 c^3\right)+\frac{48}{5} a c^2 x^5 \left(a d^2+4 c^3\right)+16 c^3 d^3 x^{10}+\frac{60}{11} c^2 d^4 x^{11}+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",1
35,1,92,92,0.0205785,"\int \left(4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4\right)^2 \, dx","Integrate[(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)+\frac{32}{3} a c^3 x^3+8 a c^2 d x^4+\frac{16}{3} c^3 d x^6+\frac{24}{7} c^2 d^2 x^7+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)+\frac{32}{3} a c^3 x^3+8 a c^2 d x^4+\frac{16}{3} c^3 d x^6+\frac{24}{7} c^2 d^2 x^7+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",1
36,1,32,32,0.0001079,"\int \left(4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4\right) \, dx","Integrate[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
37,1,71,529,0.0270504,"\int \frac{1}{4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4} \, dx","Integrate[(4*a*c + 4*c^2*x^2 + 4*c*d*x^3 + d^2*x^4)^(-1),x]","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^4 d^2+4 \text{$\#$1}^3 c d+4 \text{$\#$1}^2 c^2+4 a c\&,\frac{\log (x-\text{$\#$1})}{\text{$\#$1}^3 d^2+3 \text{$\#$1}^2 c d+2 \text{$\#$1} c^2}\&\right]","-\frac{d \log \left(\sqrt{c} \sqrt{4 a d^2+c^3}-\sqrt{2} \sqrt[4]{c} d \sqrt{\sqrt{4 a d^2+c^3}+c^{3/2}} \left(\frac{c}{d}+x\right)+d^2 \left(\frac{c}{d}+x\right)^2\right)}{4 \sqrt{2} c^{3/4} \sqrt{4 a d^2+c^3} \sqrt{\sqrt{4 a d^2+c^3}+c^{3/2}}}+\frac{d \log \left(\sqrt{c} \sqrt{4 a d^2+c^3}+\sqrt{2} \sqrt[4]{c} d \sqrt{\sqrt{4 a d^2+c^3}+c^{3/2}} \left(\frac{c}{d}+x\right)+d^2 \left(\frac{c}{d}+x\right)^2\right)}{4 \sqrt{2} c^{3/4} \sqrt{4 a d^2+c^3} \sqrt{\sqrt{4 a d^2+c^3}+c^{3/2}}}-\frac{d \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{\sqrt{4 a d^2+c^3}+c^{3/2}}+\sqrt{2} c+\sqrt{2} d x}{\sqrt[4]{c} \sqrt{c^{3/2}-\sqrt{4 a d^2+c^3}}}\right)}{2 \sqrt{2} c^{3/4} \sqrt{4 a d^2+c^3} \sqrt{c^{3/2}-\sqrt{4 a d^2+c^3}}}+\frac{d \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{\sqrt{4 a d^2+c^3}+c^{3/2}}-\sqrt{2} (c+d x)}{\sqrt[4]{c} \sqrt{c^{3/2}-\sqrt{4 a d^2+c^3}}}\right)}{2 \sqrt{2} c^{3/4} \sqrt{4 a d^2+c^3} \sqrt{c^{3/2}-\sqrt{4 a d^2+c^3}}}",1,"RootSum[4*a*c + 4*c^2*#1^2 + 4*c*d*#1^3 + d^2*#1^4 & , Log[x - #1]/(2*c^2*#1 + 3*c*d*#1^2 + d^2*#1^3) & ]/4","C",1
38,1,182,746,0.1156277,"\int \frac{1}{\left(4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4\right)^2} \, dx","Integrate[(4*a*c + 4*c^2*x^2 + 4*c*d*x^3 + d^2*x^4)^(-2),x]","\frac{\text{RootSum}\left[\text{$\#$1}^4 d^2+4 \text{$\#$1}^3 c d+4 \text{$\#$1}^2 c^2+4 a c\&,\frac{\text{$\#$1}^2 c d^2 \log (x-\text{$\#$1})+12 a d^2 \log (x-\text{$\#$1})+2 c^3 \log (x-\text{$\#$1})+2 \text{$\#$1} c^2 d \log (x-\text{$\#$1})}{\text{$\#$1}^3 d^2+3 \text{$\#$1}^2 c d+2 \text{$\#$1} c^2}\&\right]+\frac{4 (c+d x) (4 a d+c x (2 c+d x))}{4 a c+x^2 (2 c+d x)^2}}{64 a c \left(4 a d^2+c^3\right)}","-\frac{d \left(-c^{3/2} \sqrt{4 a d^2+c^3}+12 a d^2+c^3\right) \log \left(\sqrt{c} \sqrt{4 a d^2+c^3}-\sqrt{2} \sqrt[4]{c} d \sqrt{\sqrt{4 a d^2+c^3}+c^{3/2}} \left(\frac{c}{d}+x\right)+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{c} \sqrt{4 a d^2+c^3}+\sqrt{2} \sqrt[4]{c} d \sqrt{\sqrt{4 a d^2+c^3}+c^{3/2}} \left(\frac{c}{d}+x\right)+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)}",1,"((4*(c + d*x)*(4*a*d + c*x*(2*c + d*x)))/(4*a*c + x^2*(2*c + d*x)^2) + RootSum[4*a*c + 4*c^2*#1^2 + 4*c*d*#1^3 + d^2*#1^4 & , (2*c^3*Log[x - #1] + 12*a*d^2*Log[x - #1] + 2*c^2*d*Log[x - #1]*#1 + c*d^2*Log[x - #1]*#1^2)/(2*c^2*#1 + 3*c*d*#1^2 + d^2*#1^3) & ])/(64*a*c*(c^3 + 4*a*d^2))","C",1
39,1,345,295,0.0545092,"\int \left(8 a e^2-d^3 x+8 d e^2 x^3+8 e^3 x^4\right)^4 \, dx","Integrate[(8*a*e^2 - d^3*x + 8*d*e^2*x^3 + 8*e^3*x^4)^4,x]","4096 a^4 e^8 x-1024 a^3 d^3 e^6 x^2+8 a d e^2 x^4 \left(512 a^2 e^6-d^8\right)+128 a^2 d^6 e^4 x^3-4 d e^3 x^8 \left(-1536 a^2 e^6+192 a d^4 e^3+d^8\right)+\frac{128}{3} e^4 x^9 \left(64 a^2 e^6-32 a d^4 e^3+d^8\right)-\frac{32}{7} d^2 e^2 x^7 \left(-768 a^2 e^6-24 a d^4 e^3+d^8\right)+\frac{1}{5} x^5 \left(16384 a^3 e^9-6144 a^2 d^4 e^6+d^{12}\right)+\frac{2048}{13} e^8 x^{13} \left(8 a e^3-d^4\right)-512 d e^7 x^{12} \left(d^4-8 a e^3\right)+\frac{128}{5} d^3 e^5 x^{10} \left(40 a e^3+3 d^4\right)-128 a d^3 e^4 x^6 \left(8 a e^3-d^4\right)+\frac{128}{11} d^2 e^6 x^{11} \left(384 a e^3-13 d^4\right)+1024 d^3 e^9 x^{14}+\frac{8192}{5} d^2 e^{10} x^{15}+1024 d e^{11} x^{16}+\frac{4096 e^{12} x^{17}}{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{\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{64}{13} e^8 \left(256 a e^3+59 d^4\right) \left(\frac{d}{4 e}+x\right)^{13}+\frac{x \left(256 a e^3+5 d^4\right)^4}{1048576 e^4}-\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{d^2 \left(256 a e^3+5 d^4\right)^3 \left(\frac{d}{4 e}+x\right)^3}{8192 e^2}-\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,"4096*a^4*e^8*x - 1024*a^3*d^3*e^6*x^2 + 128*a^2*d^6*e^4*x^3 + 8*a*d*e^2*(-d^8 + 512*a^2*e^6)*x^4 + ((d^12 - 6144*a^2*d^4*e^6 + 16384*a^3*e^9)*x^5)/5 - 128*a*d^3*e^4*(-d^4 + 8*a*e^3)*x^6 - (32*d^2*e^2*(d^8 - 24*a*d^4*e^3 - 768*a^2*e^6)*x^7)/7 - 4*d*e^3*(d^8 + 192*a*d^4*e^3 - 1536*a^2*e^6)*x^8 + (128*e^4*(d^8 - 32*a*d^4*e^3 + 64*a^2*e^6)*x^9)/3 + (128*d^3*e^5*(3*d^4 + 40*a*e^3)*x^10)/5 + (128*d^2*e^6*(-13*d^4 + 384*a*e^3)*x^11)/11 - 512*d*e^7*(d^4 - 8*a*e^3)*x^12 + (2048*e^8*(-d^4 + 8*a*e^3)*x^13)/13 + 1024*d^3*e^9*x^14 + (8192*d^2*e^10*x^15)/5 + 1024*d*e^11*x^16 + (4096*e^12*x^17)/17","A",1
40,1,207,203,0.0287495,"\int \left(8 a e^2-d^3 x+8 d e^2 x^3+8 e^3 x^4\right)^3 \, dx","Integrate[(8*a*e^2 - d^3*x + 8*d*e^2*x^3 + 8*e^3*x^4)^3,x]","512 a^3 e^6 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+8 a d^6 e^2 x^3+\frac{128}{3} e^5 x^9 \left(4 a e^3-d^4\right)-24 d e^4 x^8 \left(d^4-16 a e^3\right)+\frac{384}{5} a e^4 x^5 \left(4 a e^3-d^4\right)+4 d^3 e^2 x^6 \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)+32 d^3 e^6 x^{10}+\frac{1536}{11} d^2 e^7 x^{11}+128 d e^8 x^{12}+\frac{512 e^9 x^{13}}{13}","512 a^3 e^6 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+8 a d^6 e^2 x^3-\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{384}{5} a e^4 x^5 \left(d^4-4 a e^3\right)+4 d^3 e^2 x^6 \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)+32 d^3 e^6 x^{10}+\frac{1536}{11} d^2 e^7 x^{11}+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",1
41,1,109,107,0.0145216,"\int \left(8 a e^2-d^3 x+8 d e^2 x^3+8 e^3 x^4\right)^2 \, dx","Integrate[(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(8 a e^3-d^4\right)-8 a d^3 e^2 x^2+32 a d e^4 x^4+\frac{d^6 x^3}{3}-\frac{8}{3} d^3 e^3 x^6+\frac{64}{7} d^2 e^4 x^7+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{d^6 x^3}{3}-\frac{8}{3} d^3 e^3 x^6+\frac{64}{7} d^2 e^4 x^7+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",1
42,1,37,37,0.000101,"\int \left(8 a e^2-d^3 x+8 d e^2 x^3+8 e^3 x^4\right) \, dx","Integrate[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
43,1,71,153,0.0334638,"\int \frac{1}{8 a e^2-d^3 x+8 d e^2 x^3+8 e^3 x^4} \, dx","Integrate[(8*a*e^2 - d^3*x + 8*d*e^2*x^3 + 8*e^3*x^4)^(-1),x]","-\text{RootSum}\left[8 \text{$\#$1}^4 e^3+8 \text{$\#$1}^3 d e^2-\text{$\#$1} d^3+8 a e^2\&,\frac{\log (x-\text{$\#$1})}{-32 \text{$\#$1}^3 e^3-24 \text{$\#$1}^2 d e^2+d^3}\&\right]","\frac{2 \tanh ^{-1}\left(\frac{d+4 e x}{\sqrt{3 d^2-2 \sqrt{d^4-64 a e^3}}}\right)}{\sqrt{d^4-64 a e^3} \sqrt{3 d^2-2 \sqrt{d^4-64 a e^3}}}-\frac{2 \tanh ^{-1}\left(\frac{d+4 e x}{\sqrt{2 \sqrt{d^4-64 a e^3}+3 d^2}}\right)}{\sqrt{d^4-64 a e^3} \sqrt{2 \sqrt{d^4-64 a e^3}+3 d^2}}",1,"-RootSum[8*a*e^2 - d^3*#1 + 8*d*e^2*#1^3 + 8*e^3*#1^4 & , Log[x - #1]/(d^3 - 24*d*e^2*#1^2 - 32*e^3*#1^3) & ]","C",1
44,1,234,342,0.1926477,"\int \frac{1}{\left(8 a e^2-d^3 x+8 d e^2 x^3+8 e^3 x^4\right)^2} \, dx","Integrate[(8*a*e^2 - d^3*x + 8*d*e^2*x^3 + 8*e^3*x^4)^(-2),x]","\frac{48 e^2 \text{RootSum}\left[8 \text{$\#$1}^4 e^3+8 \text{$\#$1}^3 d e^2-\text{$\#$1} d^3+8 a e^2\&,\frac{2 \text{$\#$1}^2 d^2 e \log (x-\text{$\#$1})+32 a e^2 \log (x-\text{$\#$1})+\text{$\#$1} d^3 \log (x-\text{$\#$1})}{32 \text{$\#$1}^3 e^3+24 \text{$\#$1}^2 d e^2-d^3}\&\right]}{16384 a^2 e^6+64 a d^4 e^3-5 d^8}+\frac{(d+4 e x) \left(-128 a e^3+5 d^4-12 d^3 e x-24 d^2 e^2 x^2\right)}{\left(d^4-64 a e^3\right) \left(256 a e^3+5 d^4\right) \left(8 a e^2-d^3 x+8 d e^2 x^3+8 e^3 x^4\right)}","\frac{2 e \left(\frac{d}{4 e}+x\right) \left(-256 a e^3+13 d^4-48 d^2 e^2 \left(\frac{d}{4 e}+x\right)^2\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,"((d + 4*e*x)*(5*d^4 - 128*a*e^3 - 12*d^3*e*x - 24*d^2*e^2*x^2))/((d^4 - 64*a*e^3)*(5*d^4 + 256*a*e^3)*(8*a*e^2 - d^3*x + 8*d*e^2*x^3 + 8*e^3*x^4)) + (48*e^2*RootSum[8*a*e^2 - d^3*#1 + 8*d*e^2*#1^3 + 8*e^3*#1^4 & , (32*a*e^2*Log[x - #1] + d^3*Log[x - #1]*#1 + 2*d^2*e*Log[x - #1]*#1^2)/(-d^3 + 24*d*e^2*#1^2 + 32*e^3*#1^3) & ])/(-5*d^8 + 64*a*d^4*e^3 + 16384*a^2*e^6)","C",1
45,1,96,96,0.0026038,"\int \left(8+8 x-x^3+8 x^4\right)^4 \, dx","Integrate[(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",1
46,1,74,74,0.0013325,"\int \left(8+8 x-x^3+8 x^4\right)^3 \, dx","Integrate[(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",1
47,1,54,54,0.0012675,"\int \left(8+8 x-x^3+8 x^4\right)^2 \, dx","Integrate[(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",1
48,1,23,23,0.0000838,"\int \left(8+8 x-x^3+8 x^4\right) \, dx","Integrate[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
49,1,45,268,0.0100735,"\int \frac{1}{8+8 x-x^3+8 x^4} \, dx","Integrate[(8 + 8*x - x^3 + 8*x^4)^(-1),x]","\text{RootSum}\left[8 \text{$\#$1}^4-\text{$\#$1}^3+8 \text{$\#$1}+8\&,\frac{\log (x-\text{$\#$1})}{32 \text{$\#$1}^3-3 \text{$\#$1}^2+8}\&\right]","-\frac{1}{24} \sqrt{\frac{67 \sqrt{29}-109}{1218}} \log \left(\left(\frac{4}{x}+1\right)^2-\sqrt{6 \left(1+\sqrt{29}\right)} \left(\frac{4}{x}+1\right)+3 \sqrt{29}\right)+\frac{1}{24} \sqrt{\frac{67 \sqrt{29}-109}{1218}} \log \left(\left(\frac{4}{x}+1\right)^2+\sqrt{6 \left(1+\sqrt{29}\right)} \left(\frac{4}{x}+1\right)+3 \sqrt{29}\right)-\frac{\tan ^{-1}\left(\frac{3-\left(\frac{4}{x}+1\right)^2}{6 \sqrt{7}}\right)}{12 \sqrt{7}}-\frac{1}{12} \sqrt{\frac{109+67 \sqrt{29}}{1218}} \tan ^{-1}\left(\frac{\frac{8}{x}-\sqrt{6 \left(1+\sqrt{29}\right)}+2}{\sqrt{6 \left(\sqrt{29}-1\right)}}\right)-\frac{1}{12} \sqrt{\frac{109+67 \sqrt{29}}{1218}} \tan ^{-1}\left(\frac{\frac{8}{x}+\sqrt{6 \left(1+\sqrt{29}\right)}+2}{\sqrt{6 \left(\sqrt{29}-1\right)}}\right)",1,"RootSum[8 + 8*#1 - #1^3 + 8*#1^4 & , Log[x - #1]/(8 - 3*#1^2 + 32*#1^3) & ]","C",1
50,1,113,357,0.0181442,"\int \frac{1}{\left(8+8 x-x^3+8 x^4\right)^2} \, dx","Integrate[(8 + 8*x - x^3 + 8*x^4)^(-2),x]","\frac{\text{RootSum}\left[8 \text{$\#$1}^4-\text{$\#$1}^3+8 \text{$\#$1}+8\&,\frac{392 \text{$\#$1}^2 \log (x-\text{$\#$1})-1097 \text{$\#$1} \log (x-\text{$\#$1})+2243 \log (x-\text{$\#$1})}{32 \text{$\#$1}^3-3 \text{$\#$1}^2+8}\&\right]}{21924}+\frac{784 x^3-1146 x^2+1539 x+544}{43848 \left(8 x^4-x^3+8 x+8\right)}","-\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,"(544 + 1539*x - 1146*x^2 + 784*x^3)/(43848*(8 + 8*x - x^3 + 8*x^4)) + RootSum[8 + 8*#1 - #1^3 + 8*#1^4 & , (2243*Log[x - #1] - 1097*Log[x - #1]*#1 + 392*Log[x - #1]*#1^2)/(8 - 3*#1^2 + 32*#1^3) & ]/21924","C",1
51,1,97,97,0.0018751,"\int \left(1+4 x+4 x^2+4 x^4\right)^4 \, dx","Integrate[(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",1
52,1,69,69,0.0010864,"\int \left(1+4 x+4 x^2+4 x^4\right)^3 \, dx","Integrate[(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",1
53,1,45,45,0.0012665,"\int \left(1+4 x+4 x^2+4 x^4\right)^2 \, dx","Integrate[(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",1
54,1,21,21,0.0000855,"\int \left(1+4 x+4 x^2+4 x^4\right) \, dx","Integrate[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
55,1,47,234,0.0156843,"\int \frac{1}{1+4 x+4 x^2+4 x^4} \, dx","Integrate[(1 + 4*x + 4*x^2 + 4*x^4)^(-1),x]","\frac{1}{4} \text{RootSum}\left[4 \text{$\#$1}^4+4 \text{$\#$1}^2+4 \text{$\#$1}+1\&,\frac{\log (x-\text{$\#$1})}{4 \text{$\#$1}^3+2 \text{$\#$1}+1}\&\right]","-\frac{1}{4} \sqrt{\frac{1}{5} \left(\sqrt{5}-2\right)} \log \left(\left(\frac{1}{x}+1\right)^2-\sqrt{2 \left(1+\sqrt{5}\right)} \left(\frac{1}{x}+1\right)+\sqrt{5}\right)+\frac{1}{4} \sqrt{\frac{1}{5} \left(\sqrt{5}-2\right)} \log \left(\left(\frac{1}{x}+1\right)^2+\sqrt{2 \left(1+\sqrt{5}\right)} \left(\frac{1}{x}+1\right)+\sqrt{5}\right)+\frac{1}{2} \tan ^{-1}\left(\frac{1}{2} \left(\left(\frac{1}{x}+1\right)^2-1\right)\right)-\frac{1}{2} \sqrt{\frac{1}{5} \left(2+\sqrt{5}\right)} \tan ^{-1}\left(\frac{\frac{2}{x}-\sqrt{2 \left(1+\sqrt{5}\right)}+2}{\sqrt{2 \left(\sqrt{5}-1\right)}}\right)-\frac{1}{2} \sqrt{\frac{1}{5} \left(2+\sqrt{5}\right)} \tan ^{-1}\left(\frac{\frac{2}{x}+\sqrt{2 \left(1+\sqrt{5}\right)}+2}{\sqrt{2 \left(\sqrt{5}-1\right)}}\right)",1,"RootSum[1 + 4*#1 + 4*#1^2 + 4*#1^4 & , Log[x - #1]/(1 + 2*#1 + 4*#1^3) & ]/4","C",1
56,1,108,317,0.0242803,"\int \frac{1}{\left(1+4 x+4 x^2+4 x^4\right)^2} \, dx","Integrate[(1 + 4*x + 4*x^2 + 4*x^4)^(-2),x]","\frac{1}{40} \left(\text{RootSum}\left[4 \text{$\#$1}^4+4 \text{$\#$1}^2+4 \text{$\#$1}+1\&,\frac{18 \text{$\#$1}^2 \log (x-\text{$\#$1})-16 \text{$\#$1} \log (x-\text{$\#$1})+27 \log (x-\text{$\#$1})}{4 \text{$\#$1}^3+2 \text{$\#$1}+1}\&\right]+\frac{72 x^3-32 x^2+84 x+38}{4 x^4+4 x^2+4 x+1}\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,"((38 + 84*x - 32*x^2 + 72*x^3)/(1 + 4*x + 4*x^2 + 4*x^4) + RootSum[1 + 4*#1 + 4*#1^2 + 4*#1^4 & , (27*Log[x - #1] - 16*Log[x - #1]*#1 + 18*Log[x - #1]*#1^2)/(1 + 2*#1 + 4*#1^3) & ])/40","C",1
57,1,104,104,0.00209,"\int \left(8+24 x+8 x^2-15 x^3+8 x^4\right)^4 \, dx","Integrate[(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",1
58,1,76,76,0.0012646,"\int \left(8+24 x+8 x^2-15 x^3+8 x^4\right)^3 \, dx","Integrate[(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",1
59,1,52,52,0.0014724,"\int \left(8+24 x+8 x^2-15 x^3+8 x^4\right)^2 \, dx","Integrate[(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",1
60,1,30,30,0.0000917,"\int \left(8+24 x+8 x^2-15 x^3+8 x^4\right) \, dx","Integrate[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
61,1,55,263,0.0147628,"\int \frac{1}{8+24 x+8 x^2-15 x^3+8 x^4} \, dx","Integrate[(8 + 24*x + 8*x^2 - 15*x^3 + 8*x^4)^(-1),x]","\text{RootSum}\left[8 \text{$\#$1}^4-15 \text{$\#$1}^3+8 \text{$\#$1}^2+24 \text{$\#$1}+8\&,\frac{\log (x-\text{$\#$1})}{32 \text{$\#$1}^3-45 \text{$\#$1}^2+16 \text{$\#$1}+24}\&\right]","\frac{1}{4} \sqrt{\frac{3}{13}} \tan ^{-1}\left(\frac{-5 x^2+12 x+8}{\sqrt{39} x^2}\right)-\frac{1}{8} \sqrt{\frac{235 \sqrt{517}-5167}{40326}} \log \left(\left(\frac{4}{x}+3\right)^2-\sqrt{2 \left(19+\sqrt{517}\right)} \left(\frac{4}{x}+3\right)+\sqrt{517}\right)+\frac{1}{8} \sqrt{\frac{235 \sqrt{517}-5167}{40326}} \log \left(\left(\frac{4}{x}+3\right)^2+\sqrt{2 \left(19+\sqrt{517}\right)} \left(\frac{4}{x}+3\right)+\sqrt{517}\right)-\frac{1}{4} \sqrt{\frac{5167+235 \sqrt{517}}{40326}} \tan ^{-1}\left(\frac{\frac{8}{x}-\sqrt{2 \left(19+\sqrt{517}\right)}+6}{\sqrt{2 \left(\sqrt{517}-19\right)}}\right)-\frac{1}{4} \sqrt{\frac{5167+235 \sqrt{517}}{40326}} \tan ^{-1}\left(\frac{\frac{8}{x}+\sqrt{2 \left(19+\sqrt{517}\right)}+6}{\sqrt{2 \left(\sqrt{517}-19\right)}}\right)",1,"RootSum[8 + 24*#1 + 8*#1^2 - 15*#1^3 + 8*#1^4 & , Log[x - #1]/(24 + 16*#1 - 45*#1^2 + 32*#1^3) & ]","C",1
62,1,128,366,0.0285721,"\int \frac{1}{\left(8+24 x+8 x^2-15 x^3+8 x^4\right)^2} \, dx","Integrate[(8 + 24*x + 8*x^2 - 15*x^3 + 8*x^4)^(-2),x]","\frac{\text{RootSum}\left[8 \text{$\#$1}^4-15 \text{$\#$1}^3+8 \text{$\#$1}^2+24 \text{$\#$1}+8\&,\frac{19640 \text{$\#$1}^2 \log (x-\text{$\#$1})-57489 \text{$\#$1} \log (x-\text{$\#$1})+74897 \log (x-\text{$\#$1})}{32 \text{$\#$1}^3-45 \text{$\#$1}^2+16 \text{$\#$1}+24}\&\right]}{80652}+\frac{39280 x^3-94314 x^2+89033 x+72888}{161304 \left(8 x^4-15 x^3+8 x^2+24 x+8\right)}","\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,"(72888 + 89033*x - 94314*x^2 + 39280*x^3)/(161304*(8 + 24*x + 8*x^2 - 15*x^3 + 8*x^4)) + RootSum[8 + 24*#1 + 8*#1^2 - 15*#1^3 + 8*#1^4 & , (74897*Log[x - #1] - 57489*Log[x - #1]*#1 + 19640*Log[x - #1]*#1^2)/(24 + 16*#1 - 45*#1^2 + 32*#1^3) & ]/80652","C",1
63,1,14,14,0.0017241,"\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","Integrate[(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",1
64,1,14,14,0.0012199,"\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","Integrate[(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",1
65,1,61,14,0.0001105,"\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","Integrate[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]","a^5 x+\frac{5}{2} a^4 b x^2+\frac{10}{3} a^3 b^2 x^3+\frac{5}{2} a^2 b^3 x^4+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
66,1,14,14,0.0042731,"\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","Integrate[(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*1/(b*(a + b*x)^4)","A",1
67,1,14,14,0.0035819,"\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","Integrate[(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*1/(b*(a + b*x)^9)","A",1
68,1,14,14,0.0049632,"\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","Integrate[(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*1/(b*(a + b*x)^14)","A",1
69,1,38,38,0.0084878,"\int \frac{1}{1+x^2+x^3+x^5} \, dx","Integrate[(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",1
70,1,84,84,0.0024637,"\int \left(3-19 x^2+32 x^4-16 x^6\right)^4 \, dx","Integrate[(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",1
71,1,63,63,0.0021739,"\int \left(3-19 x^2+32 x^4-16 x^6\right)^3 \, dx","Integrate[(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",1
72,1,44,44,0.0008488,"\int \left(3-19 x^2+32 x^4-16 x^6\right)^2 \, dx","Integrate[(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",1
73,1,25,25,0.0000921,"\int \left(3-19 x^2+32 x^4-16 x^6\right) \, dx","Integrate[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
74,1,62,31,0.0181372,"\int \frac{1}{3-19 x^2+32 x^4-16 x^6} \, dx","Integrate[(3 - 19*x^2 + 32*x^4 - 16*x^6)^(-1),x]","\frac{1}{6} \left(-\log \left(2 x^2-3 x+1\right)+\log \left(2 x^2+3 x+1\right)+\sqrt{3} \log \left(\sqrt{3}-2 x\right)-\sqrt{3} \log \left(2 x+\sqrt{3}\right)\right)","\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,"(Sqrt[3]*Log[Sqrt[3] - 2*x] - Sqrt[3]*Log[Sqrt[3] + 2*x] - Log[1 - 3*x + 2*x^2] + Log[1 + 3*x + 2*x^2])/6","A",1
75,1,103,89,0.0626449,"\int \frac{1}{\left(3-19 x^2+32 x^4-16 x^6\right)^2} \, dx","Integrate[(3 - 19*x^2 + 32*x^4 - 16*x^6)^(-2),x]","\frac{1}{108} \left(-\frac{6 x \left(80 x^4-104 x^2+27\right)}{16 x^6-32 x^4+19 x^2-3}+14 \log (1-2 x)+30 \sqrt{3} \log \left(\sqrt{3}-2 x\right)-67 \log (1-x)+67 \log (x+1)-14 \log (2 x+1)-30 \sqrt{3} \log \left(2 x+\sqrt{3}\right)\right)","\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,"((-6*x*(27 - 104*x^2 + 80*x^4))/(-3 + 19*x^2 - 32*x^4 + 16*x^6) + 14*Log[1 - 2*x] + 30*Sqrt[3]*Log[Sqrt[3] - 2*x] - 67*Log[1 - x] + 67*Log[1 + x] - 14*Log[1 + 2*x] - 30*Sqrt[3]*Log[Sqrt[3] + 2*x])/108","A",1
76,1,137,161,0.0915207,"\int \frac{1}{\left(3-19 x^2+32 x^4-16 x^6\right)^3} \, dx","Integrate[(3 - 19*x^2 + 32*x^4 - 16*x^6)^(-3),x]","\frac{\frac{36 x \left(80 x^4-104 x^2+27\right)}{\left(-16 x^6+32 x^4-19 x^2+3\right)^2}-\frac{6 x \left(2288 x^4-2384 x^2+345\right)}{16 x^6-32 x^4+19 x^2-3}-268 \log (1-2 x)+2412 \sqrt{3} \log \left(\sqrt{3}-2 x\right)-3913 \log (1-x)+3913 \log (x+1)+268 \log (2 x+1)-2412 \sqrt{3} \log \left(2 x+\sqrt{3}\right)}{1296}","\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,"((36*x*(27 - 104*x^2 + 80*x^4))/(3 - 19*x^2 + 32*x^4 - 16*x^6)^2 - (6*x*(345 - 2384*x^2 + 2288*x^4))/(-3 + 19*x^2 - 32*x^4 + 16*x^6) - 268*Log[1 - 2*x] + 2412*Sqrt[3]*Log[Sqrt[3] - 2*x] - 3913*Log[1 - x] + 3913*Log[1 + x] + 268*Log[1 + 2*x] - 2412*Sqrt[3]*Log[Sqrt[3] + 2*x])/1296","A",1
77,1,132,91,0.1025801,"\int \frac{1}{\left(-1+7 x^2-7 x^4+x^6\right)^2} \, dx","Integrate[(-1 + 7*x^2 - 7*x^4 + x^6)^(-2),x]","\frac{-\frac{8 x \left(21 x^4-140 x^2+103\right)}{x^6-7 x^4+7 x^2-1}-80 \log (1-x)-\left(4+3 \sqrt{2}\right) \log \left(-x+\sqrt{2}-1\right)+\left(4-3 \sqrt{2}\right) \log \left(-x+\sqrt{2}+1\right)+80 \log (x+1)+\left(4+3 \sqrt{2}\right) \log \left(x+\sqrt{2}-1\right)+\left(3 \sqrt{2}-4\right) \log \left(x+\sqrt{2}+1\right)}{1024}","\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,"((-8*x*(103 - 140*x^2 + 21*x^4))/(-1 + 7*x^2 - 7*x^4 + x^6) - 80*Log[1 - x] - (4 + 3*Sqrt[2])*Log[-1 + Sqrt[2] - x] + (4 - 3*Sqrt[2])*Log[1 + Sqrt[2] - x] + 80*Log[1 + x] + (4 + 3*Sqrt[2])*Log[-1 + Sqrt[2] + x] + (-4 + 3*Sqrt[2])*Log[1 + Sqrt[2] + x])/1024","A",1
78,1,73,78,0.0670828,"\int \frac{x^3}{c+(a+b x)^2} \, dx","Integrate[x^3/(c + (a + b*x)^2),x]","\frac{-\frac{2 \left(a^3-3 a c\right) \tan ^{-1}\left(\frac{a+b x}{\sqrt{c}}\right)}{\sqrt{c}}+\left(3 a^2-c\right) \log \left(a^2+2 a b x+b^2 x^2+c\right)+b x (b x-4 a)}{2 b^4}","\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,"(b*x*(-4*a + b*x) - (2*(a^3 - 3*a*c)*ArcTan[(a + b*x)/Sqrt[c]])/Sqrt[c] + (3*a^2 - c)*Log[a^2 + c + 2*a*b*x + b^2*x^2])/(2*b^4)","A",1
79,1,54,50,0.0327212,"\int \frac{x^2}{c+(a+b x)^2} \, dx","Integrate[x^2/(c + (a + b*x)^2),x]","\frac{-a \log \left(a^2+2 a b x+b^2 x^2+c\right)+\frac{\left(a^2-c\right) \tan ^{-1}\left(\frac{a+b x}{\sqrt{c}}\right)}{\sqrt{c}}+b x}{b^3}","\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,"(b*x + ((a^2 - c)*ArcTan[(a + b*x)/Sqrt[c]])/Sqrt[c] - a*Log[a^2 + c + 2*a*b*x + b^2*x^2])/b^3","A",1
80,1,38,41,0.0156568,"\int \frac{x}{c+(a+b x)^2} \, dx","Integrate[x/(c + (a + b*x)^2),x]","\frac{\log \left((a+b x)^2+c\right)-\frac{2 a \tan ^{-1}\left(\frac{a+b x}{\sqrt{c}}\right)}{\sqrt{c}}}{2 b^2}","\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,"((-2*a*ArcTan[(a + b*x)/Sqrt[c]])/Sqrt[c] + Log[c + (a + b*x)^2])/(2*b^2)","A",1
81,1,21,21,0.0038259,"\int \frac{1}{c+(a+b x)^2} \, dx","Integrate[(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",1
82,1,48,59,0.0407394,"\int \frac{1}{x \left(c+(a+b x)^2\right)} \, dx","Integrate[1/(x*(c + (a + b*x)^2)),x]","-\frac{\log \left((a+b x)^2+c\right)+\frac{2 a \tan ^{-1}\left(\frac{a+b x}{\sqrt{c}}\right)}{\sqrt{c}}-2 \log (b x)}{2 \left(a^2+c\right)}","-\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,"-1/2*((2*a*ArcTan[(a + b*x)/Sqrt[c]])/Sqrt[c] - 2*Log[b*x] + Log[c + (a + b*x)^2])/(a^2 + c)","A",1
83,1,81,79,0.0530391,"\int \frac{1}{x^2 \left(c+(a+b x)^2\right)} \, dx","Integrate[1/(x^2*(c + (a + b*x)^2)),x]","\frac{b x \left(a^2-c\right) \tan ^{-1}\left(\frac{a+b x}{\sqrt{c}}\right)-\sqrt{c} \left(-a b x \log \left(a^2+2 a b x+b^2 x^2+c\right)+a^2+2 a b x \log (x)+c\right)}{\sqrt{c} x \left(a^2+c\right)^2}","-\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,"(b*(a^2 - c)*x*ArcTan[(a + b*x)/Sqrt[c]] - Sqrt[c]*(a^2 + c + 2*a*b*x*Log[x] - a*b*x*Log[a^2 + c + 2*a*b*x + b^2*x^2]))/(Sqrt[c]*(a^2 + c)^2*x)","A",1
84,1,106,121,0.1655287,"\int \frac{1}{x^3 \left(c+(a+b x)^2\right)} \, dx","Integrate[1/(x^3*(c + (a + b*x)^2)),x]","-\frac{b^2 \left(3 a^2-c\right) \log \left(a^2+2 a b x+b^2 x^2+c\right)+2 b^2 \left(c-3 a^2\right) \log (x)+\frac{2 a b^2 \left(a^2-3 c\right) \tan ^{-1}\left(\frac{a+b x}{\sqrt{c}}\right)}{\sqrt{c}}+\frac{\left(a^2+c\right) \left(a^2-4 a b x+c\right)}{x^2}}{2 \left(a^2+c\right)^3}","\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)*(a^2 + c - 4*a*b*x))/x^2 + (2*a*b^2*(a^2 - 3*c)*ArcTan[(a + b*x)/Sqrt[c]])/Sqrt[c] + 2*b^2*(-3*a^2 + c)*Log[x] + b^2*(3*a^2 - c)*Log[a^2 + c + 2*a*b*x + b^2*x^2])/(a^2 + c)^3","A",1
85,1,31,31,0.0116174,"\int \frac{1}{a+b (c+d x)^2} \, dx","Integrate[(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",1
86,1,60,63,0.035161,"\int \frac{1}{\left(a+b (c+d x)^2\right)^2} \, dx","Integrate[(a + b*(c + d*x)^2)^(-2),x]","\frac{\frac{\sqrt{a} (c+d x)}{a+b (c+d x)^2}+\frac{\tan ^{-1}\left(\frac{\sqrt{b} (c+d x)}{\sqrt{a}}\right)}{\sqrt{b}}}{2 a^{3/2} d}","\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,"((Sqrt[a]*(c + d*x))/(a + b*(c + d*x)^2) + ArcTan[(Sqrt[b]*(c + d*x))/Sqrt[a]]/Sqrt[b])/(2*a^(3/2)*d)","A",1
87,1,75,91,0.0706508,"\int \frac{1}{\left(a+b (c+d x)^2\right)^3} \, dx","Integrate[(a + b*(c + d*x)^2)^(-3),x]","\frac{\frac{\sqrt{a} (c+d x) \left(5 a+3 b (c+d x)^2\right)}{\left(a+b (c+d x)^2\right)^2}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{b} (c+d x)}{\sqrt{a}}\right)}{\sqrt{b}}}{8 a^{5/2} d}","\frac{3 \tan ^{-1}\left(\frac{\sqrt{b} (c+d x)}{\sqrt{a}}\right)}{8 a^{5/2} \sqrt{b} d}+\frac{3 (c+d x)}{8 a^2 d \left(a+b (c+d x)^2\right)}+\frac{c+d x}{4 a d \left(a+b (c+d x)^2\right)^2}",1,"((Sqrt[a]*(c + d*x)*(5*a + 3*b*(c + d*x)^2))/(a + b*(c + d*x)^2)^2 + (3*ArcTan[(Sqrt[b]*(c + d*x))/Sqrt[a]])/Sqrt[b])/(8*a^(5/2)*d)","A",1
88,1,35,35,0.0191442,"\int \frac{1}{\sqrt{-a}+b (c+d x)^2} \, dx","Integrate[(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",1
89,1,10,10,0.0051844,"\int \frac{1}{1+(c+d x)^2} \, dx","Integrate[(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",1
90,1,31,37,0.0135392,"\int \frac{1}{\left(1+(c+d x)^2\right)^2} \, dx","Integrate[(1 + (c + d*x)^2)^(-2),x]","\frac{\frac{c+d x}{(c+d x)^2+1}+\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)/(1 + (c + d*x)^2) + ArcTan[c + d*x])/(2*d)","A",1
91,1,52,60,0.0195366,"\int \frac{1}{\left(1+(c+d x)^2\right)^3} \, dx","Integrate[(1 + (c + d*x)^2)^(-3),x]","\frac{\frac{3 (c+d x)}{(c+d x)^2+1}+\frac{2 (c+d x)}{\left((c+d x)^2+1\right)^2}+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,"((2*(c + d*x))/(1 + (c + d*x)^2)^2 + (3*(c + d*x))/(1 + (c + d*x)^2) + 3*ArcTan[c + d*x])/(8*d)","A",1
92,1,32,10,0.0058162,"\int \frac{1}{1-(c+d x)^2} \, dx","Integrate[(1 - (c + d*x)^2)^(-1),x]","\frac{\log (c+d x+1)}{2 d}-\frac{\log (-c-d x+1)}{2 d}","\frac{\tanh ^{-1}(c+d x)}{d}",1,"-1/2*Log[1 - c - d*x]/d + Log[1 + c + d*x]/(2*d)","B",1
93,1,45,39,0.0256313,"\int \frac{1}{\left(1-(c+d x)^2\right)^2} \, dx","Integrate[(1 - (c + d*x)^2)^(-2),x]","\frac{-\frac{2 (c+d x)}{(c+d x)^2-1}-\log (-c-d x+1)+\log (c+d x+1)}{4 d}","\frac{c+d x}{2 d \left(1-(c+d x)^2\right)}+\frac{\tanh ^{-1}(c+d x)}{2 d}",1,"((-2*(c + d*x))/(-1 + (c + d*x)^2) - Log[1 - c - d*x] + Log[1 + c + d*x])/(4*d)","A",1
94,1,65,64,0.0321879,"\int \frac{1}{\left(1-(c+d x)^2\right)^3} \, dx","Integrate[(1 - (c + d*x)^2)^(-3),x]","\frac{-\frac{6 (c+d x)}{(c+d x)^2-1}+\frac{4 (c+d x)}{\left((c+d x)^2-1\right)^2}-3 \log (-c-d x+1)+3 \log (c+d x+1)}{16 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,"((4*(c + d*x))/(-1 + (c + d*x)^2)^2 - (6*(c + d*x))/(-1 + (c + d*x)^2) - 3*Log[1 - c - d*x] + 3*Log[1 + c + d*x])/(16*d)","A",1
95,1,15,4,0.002461,"\int \frac{1}{1-(1+x)^2} \, dx","Integrate[(1 - (1 + x)^2)^(-1),x]","\frac{1}{2} \log (x+2)-\frac{\log (x)}{2}","\tanh ^{-1}(x+1)",1,"-1/2*Log[x] + Log[2 + x]/2","B",1
96,1,26,27,0.0178767,"\int \frac{1}{\left(1-(1+x)^2\right)^2} \, dx","Integrate[(1 - (1 + x)^2)^(-2),x]","\frac{1}{4} \left(-\frac{2 (x+1)}{x (x+2)}-\log (x)+\log (x+2)\right)","\frac{x+1}{2 \left(1-(x+1)^2\right)}+\frac{1}{2} \tanh ^{-1}(x+1)",1,"((-2*(1 + x))/(x*(2 + x)) - Log[x] + Log[2 + x])/4","A",1
97,1,37,45,0.0176157,"\int \frac{1}{\left(1-(1+x)^2\right)^3} \, dx","Integrate[(1 - (1 + x)^2)^(-3),x]","\frac{1}{16} \left(\frac{1}{x^2}-\frac{3}{x}-\frac{3}{x+2}-\frac{1}{(x+2)^2}-3 \log (x)+3 \log (x+2)\right)","\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,"(x^(-2) - 3/x - (2 + x)^(-2) - 3/(2 + x) - 3*Log[x] + 3*Log[2 + x])/16","A",1
98,1,64,59,0.0281575,"\int \frac{\left(1+(a+b x)^2\right)^2}{x} \, dx","Integrate[(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) (a+b x)+\left(a^2+1\right)^2 \log (b 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)*(a + 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[b*x]","A",1
99,1,11,10,0.0068118,"\int \frac{x^2}{1+(-1+x)^2} \, dx","Integrate[x^2/(1 + (-1 + x)^2),x]","\log \left(x^2-2 x+2\right)+x","x+\log \left((x-1)^2+1\right)",1,"x + Log[2 - 2*x + x^2]","A",1
100,1,51,44,0.0315908,"\int \frac{x^2}{\sqrt{1-(1+x)^2}} \, dx","Integrate[x^2/Sqrt[1 - (1 + x)^2],x]","\frac{x \left(x^2-x-6\right)+6 \sqrt{x} \sqrt{x+2} \sinh ^{-1}\left(\frac{\sqrt{x}}{\sqrt{2}}\right)}{2 \sqrt{-x (x+2)}}","-\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,"(x*(-6 - x + x^2) + 6*Sqrt[x]*Sqrt[2 + x]*ArcSinh[Sqrt[x]/Sqrt[2]])/(2*Sqrt[-(x*(2 + x))])","A",1
101,1,55,67,0.0856189,"\int \frac{x^2}{\sqrt{1-(a+b x)^2}} \, dx","Integrate[x^2/Sqrt[1 - (a + b*x)^2],x]","\frac{\sqrt{-a^2-2 a b x-b^2 x^2+1} (3 a-b x)+\left(2 a^2+1\right) \sin ^{-1}(a+b x)}{2 b^3}","\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 - b*x)*Sqrt[1 - a^2 - 2*a*b*x - b^2*x^2] + (1 + 2*a^2)*ArcSin[a + b*x])/(2*b^3)","A",1
102,1,51,63,0.0882275,"\int \frac{x^2}{\sqrt{1+(a+b x)^2}} \, dx","Integrate[x^2/Sqrt[1 + (a + b*x)^2],x]","\frac{\sqrt{a^2+2 a b x+b^2 x^2+1} (b x-3 a)+\left(2 a^2-1\right) \sinh ^{-1}(a+b x)}{2 b^3}","-\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 + b*x)*Sqrt[1 + a^2 + 2*a*b*x + b^2*x^2] + (-1 + 2*a^2)*ArcSinh[a + b*x])/(2*b^3)","A",1
103,1,132,234,0.0553569,"\int \frac{x^3}{a+b (c+d x)^3} \, dx","Integrate[x^3/(a + b*(c + d*x)^3),x]","-\frac{\text{RootSum}\left[\text{$\#$1}^3 b d^3+3 \text{$\#$1}^2 b c d^2+3 \text{$\#$1} b c^2 d+a+b c^3\&,\frac{3 \text{$\#$1}^2 b c d^2 \log (x-\text{$\#$1})+a \log (x-\text{$\#$1})+b c^3 \log (x-\text{$\#$1})+3 \text{$\#$1} b c^2 d \log (x-\text{$\#$1})}{\text{$\#$1}^2 d^2+2 \text{$\#$1} c d+c^2}\&\right]-3 b d x}{3 b^2 d^4}","-\frac{\left(3 \sqrt[3]{a} b^{2/3} c^2+a+b c^3\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{3 a^{2/3} b^{4/3} d^4}+\frac{\left(3 \sqrt[3]{a} b^{2/3} c^2+a+b c^3\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{6 a^{2/3} b^{4/3} d^4}+\frac{\left(-3 \sqrt[3]{a} b^{2/3} c^2+a+b c^3\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} b^{4/3} d^4}-\frac{c \log \left(a+b (c+d x)^3\right)}{b d^4}+\frac{x}{b d^3}",1,"-1/3*(-3*b*d*x + RootSum[a + b*c^3 + 3*b*c^2*d*#1 + 3*b*c*d^2*#1^2 + b*d^3*#1^3 & , (a*Log[x - #1] + b*c^3*Log[x - #1] + 3*b*c^2*d*Log[x - #1]*#1 + 3*b*c*d^2*Log[x - #1]*#1^2)/(c^2 + 2*c*d*#1 + d^2*#1^2) & ])/(b^2*d^4)","C",1
104,1,81,210,0.0346745,"\int \frac{x^2}{a+b (c+d x)^3} \, dx","Integrate[x^2/(a + b*(c + d*x)^3),x]","\frac{\text{RootSum}\left[\text{$\#$1}^3 b d^3+3 \text{$\#$1}^2 b c d^2+3 \text{$\#$1} b c^2 d+a+b c^3\&,\frac{\text{$\#$1}^2 \log (x-\text{$\#$1})}{\text{$\#$1}^2 d^2+2 \text{$\#$1} c d+c^2}\&\right]}{3 b d}","\frac{c \left(2 \sqrt[3]{a}+\sqrt[3]{b} c\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{3 a^{2/3} b^{2/3} d^3}-\frac{c \left(2 \sqrt[3]{a}+\sqrt[3]{b} c\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{6 a^{2/3} b^{2/3} d^3}+\frac{c \left(2 \sqrt[3]{a}-\sqrt[3]{b} c\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} b^{2/3} d^3}+\frac{\log \left(a+b (c+d x)^3\right)}{3 b d^3}",1,"RootSum[a + b*c^3 + 3*b*c^2*d*#1 + 3*b*c*d^2*#1^2 + b*d^3*#1^3 & , (Log[x - #1]*#1^2)/(c^2 + 2*c*d*#1 + d^2*#1^2) & ]/(3*b*d)","C",1
105,1,79,180,0.0222974,"\int \frac{x}{a+b (c+d x)^3} \, dx","Integrate[x/(a + b*(c + d*x)^3),x]","\frac{\text{RootSum}\left[\text{$\#$1}^3 b d^3+3 \text{$\#$1}^2 b c d^2+3 \text{$\#$1} b c^2 d+a+b c^3\&,\frac{\text{$\#$1} \log (x-\text{$\#$1})}{\text{$\#$1}^2 d^2+2 \text{$\#$1} c d+c^2}\&\right]}{3 b d}","-\frac{\left(\sqrt[3]{a}+\sqrt[3]{b} c\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{3 a^{2/3} b^{2/3} d^2}+\frac{\left(\sqrt[3]{a}+\sqrt[3]{b} c\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{6 a^{2/3} b^{2/3} d^2}-\frac{\left(\sqrt[3]{a}-\sqrt[3]{b} c\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} b^{2/3} d^2}",1,"RootSum[a + b*c^3 + 3*b*c^2*d*#1 + 3*b*c*d^2*#1^2 + b*d^3*#1^3 & , (Log[x - #1]*#1)/(c^2 + 2*c*d*#1 + d^2*#1^2) & ]/(3*b*d)","C",1
106,1,116,140,0.0330777,"\int \frac{1}{a+b (c+d x)^3} \, dx","Integrate[(a + b*(c + d*x)^3)^(-1),x]","\frac{-\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)+2 \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{b} (c+d x)-\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{6 a^{2/3} \sqrt[3]{b} d}","-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{6 a^{2/3} \sqrt[3]{b} d}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{3 a^{2/3} \sqrt[3]{b} d}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} \sqrt[3]{b} d}",1,"(2*Sqrt[3]*ArcTan[(-a^(1/3) + 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))] + 2*Log[a^(1/3) + b^(1/3)*(c + d*x)] - Log[a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2])/(6*a^(2/3)*b^(1/3)*d)","A",1
107,1,119,224,0.0554416,"\int \frac{1}{x \left(a+b (c+d x)^3\right)} \, dx","Integrate[1/(x*(a + b*(c + d*x)^3)),x]","-\frac{\text{RootSum}\left[\text{$\#$1}^3 b d^3+3 \text{$\#$1}^2 b c d^2+3 \text{$\#$1} b c^2 d+a+b c^3\&,\frac{\text{$\#$1}^2 d^2 \log (x-\text{$\#$1})+3 c^2 \log (x-\text{$\#$1})+3 \text{$\#$1} c d \log (x-\text{$\#$1})}{\text{$\#$1}^2 d^2+2 \text{$\#$1} c d+c^2}\&\right]-3 \log (x)}{3 \left(a+b c^3\right)}","-\frac{\left(2 \sqrt[3]{a}-\sqrt[3]{b} c\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{6 a^{2/3} \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} c+b^{2/3} c^2\right)}+\frac{\sqrt[3]{b} c \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} c+b^{2/3} c^2\right)}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{3 a^{2/3} \left(\sqrt[3]{a}+\sqrt[3]{b} c\right)}+\frac{\log (x)}{a+b c^3}",1,"-1/3*(-3*Log[x] + RootSum[a + b*c^3 + 3*b*c^2*d*#1 + 3*b*c*d^2*#1^2 + b*d^3*#1^3 & , (3*c^2*Log[x - #1] + 3*c*d*Log[x - #1]*#1 + d^2*Log[x - #1]*#1^2)/(c^2 + 2*c*d*#1 + d^2*#1^2) & ])/(a + b*c^3)","C",1
108,1,173,314,0.1048117,"\int \frac{1}{x^2 \left(a+b (c+d x)^3\right)} \, dx","Integrate[1/(x^2*(a + b*(c + d*x)^3)),x]","\frac{d x \text{RootSum}\left[\text{$\#$1}^3 b d^3+3 \text{$\#$1}^2 b c d^2+3 \text{$\#$1} b c^2 d+a+b c^3\&,\frac{3 \text{$\#$1}^2 b c^2 d^2 \log (x-\text{$\#$1})-3 a c \log (x-\text{$\#$1})-\text{$\#$1} a d \log (x-\text{$\#$1})+6 b c^4 \log (x-\text{$\#$1})+8 \text{$\#$1} b c^3 d \log (x-\text{$\#$1})}{\text{$\#$1}^2 d^2+2 \text{$\#$1} c d+c^2}\&\right]-3 \left(a+b c^3+3 b c^2 d x \log (x)\right)}{3 x \left(a+b c^3\right)^2}","-\frac{\sqrt[3]{b} d \left(\sqrt[3]{a} \left(a-2 b c^3\right)-\sqrt[3]{b} c \left(2 a-b c^3\right)\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{6 a^{2/3} \left(a+b c^3\right)^2}+\frac{\sqrt[3]{b} d \left(\sqrt[3]{a} \left(a-2 b c^3\right)-\sqrt[3]{b} c \left(2 a-b c^3\right)\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{3 a^{2/3} \left(a+b c^3\right)^2}+\frac{\sqrt[3]{b} d \left(\sqrt[3]{a}-\sqrt[3]{b} c\right) \left(\sqrt[3]{a}+\sqrt[3]{b} c\right)^3 \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} \left(a+b c^3\right)^2}-\frac{1}{x \left(a+b c^3\right)}-\frac{3 b c^2 d \log (x)}{\left(a+b c^3\right)^2}+\frac{b c^2 d \log \left(a+b (c+d x)^3\right)}{\left(a+b c^3\right)^2}",1,"(-3*(a + b*c^3 + 3*b*c^2*d*x*Log[x]) + d*x*RootSum[a + b*c^3 + 3*b*c^2*d*#1 + 3*b*c*d^2*#1^2 + b*d^3*#1^3 & , (-3*a*c*Log[x - #1] + 6*b*c^4*Log[x - #1] - a*d*Log[x - #1]*#1 + 8*b*c^3*d*Log[x - #1]*#1 + 3*b*c^2*d^2*Log[x - #1]*#1^2)/(c^2 + 2*c*d*#1 + d^2*#1^2) & ])/(3*(a + b*c^3)^2*x)","C",1
109,1,244,393,0.1702479,"\int \frac{1}{x^3 \left(a+b (c+d x)^3\right)} \, dx","Integrate[1/(x^3*(a + b*(c + d*x)^3)),x]","-\frac{2 d^2 x^2 \text{RootSum}\left[\text{$\#$1}^3 b d^3+3 \text{$\#$1}^2 b c d^2+3 \text{$\#$1} b c^2 d+a+b c^3\&,\frac{-3 \text{$\#$1}^2 a b c d^2 \log (x-\text{$\#$1})+6 \text{$\#$1}^2 b^2 c^4 d^2 \log (x-\text{$\#$1})+a^2 \log (x-\text{$\#$1})-16 a b c^3 \log (x-\text{$\#$1})-12 \text{$\#$1} a b c^2 d \log (x-\text{$\#$1})+10 b^2 c^6 \log (x-\text{$\#$1})+15 \text{$\#$1} b^2 c^5 d \log (x-\text{$\#$1})}{\text{$\#$1}^2 d^2+2 \text{$\#$1} c d+c^2}\&\right]+18 b c d^2 x^2 \log (x) \left(a-2 b c^3\right)+3 \left(a+b c^3\right) \left(a+b c^2 (c-6 d x)\right)}{6 x^2 \left(a+b c^3\right)^3}","\frac{b^{2/3} d^2 \left(-3 a^{2/3} \sqrt[3]{b} c+a+b c^3\right) \left(\sqrt[3]{a}+\sqrt[3]{b} c\right)^3 \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} \left(a+b c^3\right)^3}-\frac{b^{2/3} d^2 \left(6 a^{4/3} b^{2/3} c^2+a^2-3 \sqrt[3]{a} b^{5/3} c^5-7 a b c^3+b^2 c^6\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{3 a^{2/3} \left(a+b c^3\right)^3}+\frac{b^{2/3} d^2 \left(6 a^{4/3} b^{2/3} c^2+a^2-3 \sqrt[3]{a} b^{5/3} c^5-7 a b c^3+b^2 c^6\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{6 a^{2/3} \left(a+b c^3\right)^3}-\frac{3 b c d^2 \log (x) \left(a-2 b c^3\right)}{\left(a+b c^3\right)^3}+\frac{b c d^2 \left(a-2 b c^3\right) \log \left(a+b (c+d x)^3\right)}{\left(a+b c^3\right)^3}-\frac{1}{2 x^2 \left(a+b c^3\right)}+\frac{3 b c^2 d}{x \left(a+b c^3\right)^2}",1,"-1/6*(3*(a + b*c^3)*(a + b*c^2*(c - 6*d*x)) + 18*b*c*(a - 2*b*c^3)*d^2*x^2*Log[x] + 2*d^2*x^2*RootSum[a + b*c^3 + 3*b*c^2*d*#1 + 3*b*c*d^2*#1^2 + b*d^3*#1^3 & , (a^2*Log[x - #1] - 16*a*b*c^3*Log[x - #1] + 10*b^2*c^6*Log[x - #1] - 12*a*b*c^2*d*Log[x - #1]*#1 + 15*b^2*c^5*d*Log[x - #1]*#1 - 3*a*b*c*d^2*Log[x - #1]*#1^2 + 6*b^2*c^4*d^2*Log[x - #1]*#1^2)/(c^2 + 2*c*d*#1 + d^2*#1^2) & ])/((a + b*c^3)^3*x^2)","C",1
110,1,106,356,0.0550414,"\int \frac{x^3}{a+b (c+d x)^4} \, dx","Integrate[x^3/(a + b*(c + d*x)^4),x]","\frac{\text{RootSum}\left[\text{$\#$1}^4 b d^4+4 \text{$\#$1}^3 b c d^3+6 \text{$\#$1}^2 b c^2 d^2+4 \text{$\#$1} b c^3 d+a+b c^4\&,\frac{\text{$\#$1}^3 \log (x-\text{$\#$1})}{\text{$\#$1}^3 d^3+3 \text{$\#$1}^2 c d^2+3 \text{$\#$1} c^2 d+c^3}\&\right]}{4 b d}","-\frac{c \left(3 \sqrt{a}-\sqrt{b} c^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} (c+d x)+\sqrt{a}+\sqrt{b} (c+d x)^2\right)}{4 \sqrt{2} a^{3/4} b^{3/4} d^4}+\frac{c \left(3 \sqrt{a}-\sqrt{b} c^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} (c+d x)+\sqrt{a}+\sqrt{b} (c+d x)^2\right)}{4 \sqrt{2} a^{3/4} b^{3/4} d^4}+\frac{c \left(3 \sqrt{a}+\sqrt{b} c^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} (c+d x)}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} b^{3/4} d^4}-\frac{c \left(3 \sqrt{a}+\sqrt{b} c^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} (c+d x)}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} b^{3/4} d^4}+\frac{3 c^2 \tan ^{-1}\left(\frac{\sqrt{b} (c+d x)^2}{\sqrt{a}}\right)}{2 \sqrt{a} \sqrt{b} d^4}+\frac{\log \left(a+b (c+d x)^4\right)}{4 b d^4}",1,"RootSum[a + b*c^4 + 4*b*c^3*d*#1 + 6*b*c^2*d^2*#1^2 + 4*b*c*d^3*#1^3 + b*d^4*#1^4 & , (Log[x - #1]*#1^3)/(c^3 + 3*c^2*d*#1 + 3*c*d^2*#1^2 + d^3*#1^3) & ]/(4*b*d)","C",1
111,1,106,318,0.0358383,"\int \frac{x^2}{a+b (c+d x)^4} \, dx","Integrate[x^2/(a + b*(c + d*x)^4),x]","\frac{\text{RootSum}\left[\text{$\#$1}^4 b d^4+4 \text{$\#$1}^3 b c d^3+6 \text{$\#$1}^2 b c^2 d^2+4 \text{$\#$1} b c^3 d+a+b c^4\&,\frac{\text{$\#$1}^2 \log (x-\text{$\#$1})}{\text{$\#$1}^3 d^3+3 \text{$\#$1}^2 c d^2+3 \text{$\#$1} c^2 d+c^3}\&\right]}{4 b d}","\frac{\left(\sqrt{a}-\sqrt{b} c^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} (c+d x)+\sqrt{a}+\sqrt{b} (c+d x)^2\right)}{4 \sqrt{2} a^{3/4} b^{3/4} d^3}-\frac{\left(\sqrt{a}-\sqrt{b} c^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} (c+d x)+\sqrt{a}+\sqrt{b} (c+d x)^2\right)}{4 \sqrt{2} a^{3/4} b^{3/4} d^3}-\frac{\left(\sqrt{a}+\sqrt{b} c^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} (c+d x)}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} b^{3/4} d^3}+\frac{\left(\sqrt{a}+\sqrt{b} c^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} (c+d x)}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} b^{3/4} d^3}-\frac{c \tan ^{-1}\left(\frac{\sqrt{b} (c+d x)^2}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b} d^3}",1,"RootSum[a + b*c^4 + 4*b*c^3*d*#1 + 6*b*c^2*d^2*#1^2 + 4*b*c*d^3*#1^3 + b*d^4*#1^4 & , (Log[x - #1]*#1^2)/(c^3 + 3*c^2*d*#1 + 3*c*d^2*#1^2 + d^3*#1^3) & ]/(4*b*d)","C",1
112,1,104,261,0.0337034,"\int \frac{x}{a+b (c+d x)^4} \, dx","Integrate[x/(a + b*(c + d*x)^4),x]","\frac{\text{RootSum}\left[\text{$\#$1}^4 b d^4+4 \text{$\#$1}^3 b c d^3+6 \text{$\#$1}^2 b c^2 d^2+4 \text{$\#$1} b c^3 d+a+b c^4\&,\frac{\text{$\#$1} \log (x-\text{$\#$1})}{\text{$\#$1}^3 d^3+3 \text{$\#$1}^2 c d^2+3 \text{$\#$1} c^2 d+c^3}\&\right]}{4 b d}","\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,"RootSum[a + b*c^4 + 4*b*c^3*d*#1 + 6*b*c^2*d^2*#1^2 + 4*b*c*d^3*#1^3 + b*d^4*#1^4 & , (Log[x - #1]*#1)/(c^3 + 3*c^2*d*#1 + 3*c*d^2*#1^2 + d^3*#1^3) & ]/(4*b*d)","C",1
113,1,161,221,0.0994627,"\int \frac{1}{a+b (c+d x)^4} \, dx","Integrate[(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)+\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} (c+d x)+\sqrt{a}+\sqrt{b} (c+d x)^2\right)-2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} (c+d x)}{\sqrt[4]{a}}\right)+2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} (c+d x)}{\sqrt[4]{a}}+1\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{\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,"(-2*ArcTan[1 - (Sqrt[2]*b^(1/4)*(c + d*x))/a^(1/4)] + 2*ArcTan[1 + (Sqrt[2]*b^(1/4)*(c + d*x))/a^(1/4)] - Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*(c + d*x) + Sqrt[b]*(c + d*x)^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^(1/4)*d)","A",1
114,1,163,393,0.0728299,"\int \frac{1}{x \left(a+b (c+d x)^4\right)} \, dx","Integrate[1/(x*(a + b*(c + d*x)^4)),x]","-\frac{\text{RootSum}\left[\text{$\#$1}^4 b d^4+4 \text{$\#$1}^3 b c d^3+6 \text{$\#$1}^2 b c^2 d^2+4 \text{$\#$1} b c^3 d+a+b c^4\&,\frac{\text{$\#$1}^3 d^3 \log (x-\text{$\#$1})+4 \text{$\#$1}^2 c d^2 \log (x-\text{$\#$1})+4 c^3 \log (x-\text{$\#$1})+6 \text{$\#$1} c^2 d \log (x-\text{$\#$1})}{\text{$\#$1}^3 d^3+3 \text{$\#$1}^2 c d^2+3 \text{$\#$1} c^2 d+c^3}\&\right]-4 \log (x)}{4 \left(a+b c^4\right)}","-\frac{\sqrt[4]{b} c \left(\sqrt{a}-\sqrt{b} c^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} (c+d x)+\sqrt{a}+\sqrt{b} (c+d x)^2\right)}{4 \sqrt{2} a^{3/4} \left(a+b c^4\right)}+\frac{\sqrt[4]{b} c \left(\sqrt{a}-\sqrt{b} c^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} (c+d x)+\sqrt{a}+\sqrt{b} (c+d x)^2\right)}{4 \sqrt{2} a^{3/4} \left(a+b c^4\right)}+\frac{\sqrt[4]{b} c \left(\sqrt{a}+\sqrt{b} c^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} (c+d x)}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} \left(a+b c^4\right)}-\frac{\sqrt[4]{b} c \left(\sqrt{a}+\sqrt{b} c^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} (c+d x)}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} \left(a+b c^4\right)}-\frac{\log \left(a+b (c+d x)^4\right)}{4 \left(a+b c^4\right)}+\frac{\log (x)}{a+b c^4}-\frac{\sqrt{b} c^2 \tan ^{-1}\left(\frac{\sqrt{b} (c+d x)^2}{\sqrt{a}}\right)}{2 \sqrt{a} \left(a+b c^4\right)}",1,"-1/4*(-4*Log[x] + RootSum[a + b*c^4 + 4*b*c^3*d*#1 + 6*b*c^2*d^2*#1^2 + 4*b*c*d^3*#1^3 + b*d^4*#1^4 & , (4*c^3*Log[x - #1] + 6*c^2*d*Log[x - #1]*#1 + 4*c*d^2*Log[x - #1]*#1^2 + d^3*Log[x - #1]*#1^3)/(c^3 + 3*c^2*d*#1 + 3*c*d^2*#1^2 + d^3*#1^3) & ])/(a + b*c^4)","C",1
115,1,238,496,0.1315736,"\int \frac{1}{x^2 \left(a+b (c+d x)^4\right)} \, dx","Integrate[1/(x^2*(a + b*(c + d*x)^4)),x]","\frac{d x \text{RootSum}\left[\text{$\#$1}^4 b d^4+4 \text{$\#$1}^3 b c d^3+6 \text{$\#$1}^2 b c^2 d^2+4 \text{$\#$1} b c^3 d+a+b c^4\&,\frac{4 \text{$\#$1}^3 b c^3 d^3 \log (x-\text{$\#$1})-\text{$\#$1}^2 a d^2 \log (x-\text{$\#$1})+15 \text{$\#$1}^2 b c^4 d^2 \log (x-\text{$\#$1})-6 a c^2 \log (x-\text{$\#$1})-4 \text{$\#$1} a c d \log (x-\text{$\#$1})+10 b c^6 \log (x-\text{$\#$1})+20 \text{$\#$1} b c^5 d \log (x-\text{$\#$1})}{\text{$\#$1}^3 d^3+3 \text{$\#$1}^2 c d^2+3 \text{$\#$1} c^2 d+c^3}\&\right]-4 \left(a+b c^4+4 b c^3 d x \log (x)\right)}{4 x \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{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) \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{a} \left(a-3 b c^4\right)+\sqrt{b} c^2 \left(3 a-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{\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{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}",1,"(-4*(a + b*c^4 + 4*b*c^3*d*x*Log[x]) + d*x*RootSum[a + b*c^4 + 4*b*c^3*d*#1 + 6*b*c^2*d^2*#1^2 + 4*b*c*d^3*#1^3 + b*d^4*#1^4 & , (-6*a*c^2*Log[x - #1] + 10*b*c^6*Log[x - #1] - 4*a*c*d*Log[x - #1]*#1 + 20*b*c^5*d*Log[x - #1]*#1 - a*d^2*Log[x - #1]*#1^2 + 15*b*c^4*d^2*Log[x - #1]*#1^2 + 4*b*c^3*d^3*Log[x - #1]*#1^3)/(c^3 + 3*c^2*d*#1 + 3*c*d^2*#1^2 + d^3*#1^3) & ])/(4*(a + b*c^4)^2*x)","C",1
116,1,195,123,0.0366398,"\int \left(a+8 x-8 x^2+4 x^3-x^4\right)^4 \, dx","Integrate[(a + 8*x - 8*x^2 + 4*x^3 - x^4)^4,x]","a^4 x+16 a^3 x^2+\frac{2}{9} \left(3 a^2-1536 a+20480\right) x^9-6 \left(a^2-128 a+896\right) x^8+\frac{64}{7} \left(3 a^2-140 a+512\right) x^7-\frac{16}{3} \left(15 a^2-288 a+512\right) x^6+4 a \left(a^2-48 a+128\right) x^4-\frac{32}{3} (a-12) a^2 x^3-\frac{4}{5} \left(a^3-192 a^2+1536 a-1024\right) x^5-\frac{4}{13} (a-640) x^{13}+\frac{4}{3} (3 a-464) x^{12}-\frac{32}{11} (9 a-524) x^{11}+\frac{16}{5} (35 a-928) x^{10}+\frac{x^{17}}{17}-x^{16}+\frac{128 x^{15}}{15}-48 x^{14}","-\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,"a^4*x + 16*a^3*x^2 - (32*(-12 + a)*a^2*x^3)/3 + 4*a*(128 - 48*a + a^2)*x^4 - (4*(-1024 + 1536*a - 192*a^2 + a^3)*x^5)/5 - (16*(512 - 288*a + 15*a^2)*x^6)/3 + (64*(512 - 140*a + 3*a^2)*x^7)/7 - 6*(896 - 128*a + a^2)*x^8 + (2*(20480 - 1536*a + 3*a^2)*x^9)/9 + (16*(-928 + 35*a)*x^10)/5 - (32*(-524 + 9*a)*x^11)/11 + (4*(-464 + 3*a)*x^12)/3 - (4*(-640 + a)*x^13)/13 - 48*x^14 + (128*x^15)/15 - x^16 + x^17/17","A",1
117,1,114,120,0.0195495,"\int \left(a+8 x-8 x^2+4 x^3-x^4\right)^3 \, dx","Integrate[(a + 8*x - 8*x^2 + 4*x^3 - x^4)^3,x]","a^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+\frac{1}{3} (a-256) x^9-3 (a-64) x^8+\frac{32}{7} (3 a-70) x^7-8 (5 a-48) x^6-8 (a-8) a x^3-\frac{x^{13}}{13}+x^{12}-\frac{72 x^{11}}{11}+28 x^{10}","a^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-\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",1
118,1,66,72,0.0078662,"\int \left(a+8 x-8 x^2+4 x^3-x^4\right)^2 \, dx","Integrate[(a + 8*x - 8*x^2 + 4*x^3 - x^4)^2,x]","a^2 x-\frac{2}{5} (a-64) x^5+2 (a-16) x^4-\frac{16}{3} (a-4) 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",1
119,1,26,26,0.0000872,"\int \left(a+8 x-8 x^2+4 x^3-x^4\right) \, dx","Integrate[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
120,1,57,89,0.0225888,"\int \frac{1}{a+8 x-8 x^2+4 x^3-x^4} \, dx","Integrate[(a + 8*x - 8*x^2 + 4*x^3 - x^4)^(-1),x]","-\frac{1}{4} \text{RootSum}\left[-\text{$\#$1}^4+4 \text{$\#$1}^3-8 \text{$\#$1}^2+8 \text{$\#$1}+a\&,\frac{\log (x-\text{$\#$1})}{\text{$\#$1}^3-3 \text{$\#$1}^2+4 \text{$\#$1}-2}\&\right]","\frac{\tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)}{2 \sqrt{a+4} \sqrt{\sqrt{a+4}+1}}-\frac{\tan ^{-1}\left(\frac{x-1}{\sqrt{1-\sqrt{a+4}}}\right)}{2 \sqrt{a+4} \sqrt{1-\sqrt{a+4}}}",1,"-1/4*RootSum[a + 8*#1 - 8*#1^2 + 4*#1^3 - #1^4 & , Log[x - #1]/(-2 + 4*#1 - 3*#1^2 + #1^3) & ]","C",1
121,1,150,169,0.0748326,"\int \frac{1}{\left(a+8 x-8 x^2+4 x^3-x^4\right)^2} \, dx","Integrate[(a + 8*x - 8*x^2 + 4*x^3 - x^4)^(-2),x]","\frac{(x-1) \left(a+x^2-2 x+6\right)}{4 (a+3) (a+4) \left(a-x \left(x^3-4 x^2+8 x-8\right)\right)}-\frac{\text{RootSum}\left[-\text{$\#$1}^4+4 \text{$\#$1}^3-8 \text{$\#$1}^2+8 \text{$\#$1}+a\&,\frac{\text{$\#$1}^2 \log (x-\text{$\#$1})+3 a \log (x-\text{$\#$1})-2 \text{$\#$1} \log (x-\text{$\#$1})+12 \log (x-\text{$\#$1})}{\text{$\#$1}^3-3 \text{$\#$1}^2+4 \text{$\#$1}-2}\&\right]}{16 \left(a^2+7 a+12\right)}","\frac{(x-1) \left(a+(x-1)^2+5\right)}{4 \left(a^2+7 a+12\right) \left(a-(x-1)^4-2 (x-1)^2+3\right)}-\frac{\left(3 a+\sqrt{a+4}+10\right) \tan ^{-1}\left(\frac{x-1}{\sqrt{1-\sqrt{a+4}}}\right)}{8 (a+3) (a+4)^{3/2} \sqrt{1-\sqrt{a+4}}}+\frac{\left(3 a-\sqrt{a+4}+10\right) \tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)}{8 (a+3) (a+4)^{3/2} \sqrt{\sqrt{a+4}+1}}",1,"((-1 + x)*(6 + a - 2*x + x^2))/(4*(3 + a)*(4 + a)*(a - x*(-8 + 8*x - 4*x^2 + x^3))) - RootSum[a + 8*#1 - 8*#1^2 + 4*#1^3 - #1^4 & , (12*Log[x - #1] + 3*a*Log[x - #1] - 2*Log[x - #1]*#1 + Log[x - #1]*#1^2)/(-2 + 4*#1 - 3*#1^2 + #1^3) & ]/(16*(12 + 7*a + a^2))","C",1
122,1,254,252,0.1496278,"\int \frac{1}{\left(a+8 x-8 x^2+4 x^3-x^4\right)^3} \, dx","Integrate[(a + 8*x - 8*x^2 + 4*x^3 - x^4)^(-3),x]","\frac{1}{128} \left(-\frac{3 \text{RootSum}\left[-\text{$\#$1}^4+4 \text{$\#$1}^3-8 \text{$\#$1}^2+8 \text{$\#$1}+a\&,\frac{4 \text{$\#$1}^2 a \log (x-\text{$\#$1})+14 \text{$\#$1}^2 \log (x-\text{$\#$1})+7 a^2 \log (x-\text{$\#$1})+55 a \log (x-\text{$\#$1})-8 \text{$\#$1} a \log (x-\text{$\#$1})+108 \log (x-\text{$\#$1})-28 \text{$\#$1} \log (x-\text{$\#$1})}{\text{$\#$1}^3-3 \text{$\#$1}^2+4 \text{$\#$1}-2}\&\right]}{\left(a^2+7 a+12\right)^2}+\frac{4 (x-1) \left(7 a^2+a \left(12 x^2-24 x+79\right)+6 \left(7 x^2-14 x+32\right)\right)}{(a+3)^2 (a+4)^2 \left(a-x \left(x^3-4 x^2+8 x-8\right)\right)}+\frac{16 (x-1) \left(a+x^2-2 x+6\right)}{(a+3) (a+4) \left(a-x \left(x^3-4 x^2+8 x-8\right)\right)^2}\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,"((16*(-1 + x)*(6 + a - 2*x + x^2))/((3 + a)*(4 + a)*(a - x*(-8 + 8*x - 4*x^2 + x^3))^2) + (4*(-1 + x)*(7*a^2 + 6*(32 - 14*x + 7*x^2) + a*(79 - 24*x + 12*x^2)))/((3 + a)^2*(4 + a)^2*(a - x*(-8 + 8*x - 4*x^2 + x^3))) - (3*RootSum[a + 8*#1 - 8*#1^2 + 4*#1^3 - #1^4 & , (108*Log[x - #1] + 55*a*Log[x - #1] + 7*a^2*Log[x - #1] - 28*Log[x - #1]*#1 - 8*a*Log[x - #1]*#1 + 14*Log[x - #1]*#1^2 + 4*a*Log[x - #1]*#1^2)/(-2 + 4*#1 - 3*#1^2 + #1^3) & ])/(12 + 7*a + a^2)^2)/128","C",1
123,1,204,210,0.0353859,"\int x \left(a+8 x-8 x^2+4 x^3-x^4\right)^4 \, dx","Integrate[x*(a + 8*x - 8*x^2 + 4*x^3 - x^4)^4,x]","\frac{a^4 x^2}{2}+\frac{32 a^3 x^3}{3}+\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+8 \left(3 a^2-140 a+512\right) x^8-\frac{32}{7} \left(15 a^2-288 a+512\right) x^7+\frac{16}{5} a \left(a^2-48 a+128\right) x^5-8 (a-12) a^2 x^4-\frac{2}{3} \left(a^3-192 a^2+1536 a-1024\right) x^6-\frac{2}{7} (a-640) x^{14}+\frac{16}{13} (3 a-464) x^{13}-\frac{8}{3} (9 a-524) x^{12}+\frac{32}{11} (35 a-928) x^{11}+\frac{x^{18}}{18}-\frac{16 x^{17}}{17}+8 x^{16}-\frac{224 x^{15}}{5}","\frac{a^4 x^2}{2}+\frac{32 a^3 x^3}{3}+\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{16}{5} a \left(a^2-48 a+128\right) x^5+8 (12-a) a^2 x^4+\frac{2}{3} \left(-a^3+192 a^2-1536 a+1024\right) x^6+\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*(512 - 140*a + 3*a^2)*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",1
124,1,130,134,0.0198456,"\int x \left(a+8 x-8 x^2+4 x^3-x^4\right)^3 \, dx","Integrate[x*(a + 8*x - 8*x^2 + 4*x^3 - x^4)^3,x]","\frac{a^3 x^2}{2}+\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{3}{10} (a-256) x^{10}-\frac{8}{3} (a-64) x^9+4 (3 a-70) x^8-\frac{48}{7} (5 a-48) x^7-6 (a-8) a x^4-\frac{x^{14}}{14}+\frac{12 x^{13}}{13}-6 x^{12}+\frac{280 x^{11}}{11}","\frac{a^3 x^2}{2}-\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{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",1
125,1,75,79,0.0078832,"\int x \left(a+8 x-8 x^2+4 x^3-x^4\right)^2 \, dx","Integrate[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} (a-16) x^5-4 (a-4) 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",1
126,1,35,35,0.0021283,"\int x \left(a+8 x-8 x^2+4 x^3-x^4\right) \, dx","Integrate[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",1
127,1,59,116,0.0169099,"\int \frac{x}{a+8 x-8 x^2+4 x^3-x^4} \, dx","Integrate[x/(a + 8*x - 8*x^2 + 4*x^3 - x^4),x]","-\frac{1}{4} \text{RootSum}\left[-\text{$\#$1}^4+4 \text{$\#$1}^3-8 \text{$\#$1}^2+8 \text{$\#$1}+a\&,\frac{\text{$\#$1} \log (x-\text{$\#$1})}{\text{$\#$1}^3-3 \text{$\#$1}^2+4 \text{$\#$1}-2}\&\right]","-\frac{\tan ^{-1}\left(\frac{x-1}{\sqrt{1-\sqrt{a+4}}}\right)}{2 \sqrt{a+4} \sqrt{1-\sqrt{a+4}}}+\frac{\tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)}{2 \sqrt{a+4} \sqrt{\sqrt{a+4}+1}}+\frac{\tanh ^{-1}\left(\frac{(x-1)^2+1}{\sqrt{a+4}}\right)}{2 \sqrt{a+4}}",1,"-1/4*RootSum[a + 8*#1 - 8*#1^2 + 4*#1^3 - #1^4 & , (Log[x - #1]*#1)/(-2 + 4*#1 - 3*#1^2 + #1^3) & ]","C",1
128,1,166,231,0.072493,"\int \frac{x}{\left(a+8 x-8 x^2+4 x^3-x^4\right)^2} \, dx","Integrate[x/(a + 8*x - 8*x^2 + 4*x^3 - x^4)^2,x]","\frac{a x^2-a x+a+x^3+2 x}{4 (a+3) (a+4) \left(a-x \left(x^3-4 x^2+8 x-8\right)\right)}-\frac{\text{RootSum}\left[-\text{$\#$1}^4+4 \text{$\#$1}^3-8 \text{$\#$1}^2+8 \text{$\#$1}+a\&,\frac{\text{$\#$1}^2 \log (x-\text{$\#$1})+2 \text{$\#$1} a \log (x-\text{$\#$1})+a \log (x-\text{$\#$1})+4 \text{$\#$1} \log (x-\text{$\#$1})+6 \log (x-\text{$\#$1})}{\text{$\#$1}^3-3 \text{$\#$1}^2+4 \text{$\#$1}-2}\&\right]}{16 \left(a^2+7 a+12\right)}","\frac{(x-1) \left(a+(x-1)^2+5\right)}{4 \left(a^2+7 a+12\right) \left(a-(x-1)^4-2 (x-1)^2+3\right)}+\frac{(x-1)^2+1}{4 (a+4) \left(a-(x-1)^4-2 (x-1)^2+3\right)}-\frac{\left(3 a+\sqrt{a+4}+10\right) \tan ^{-1}\left(\frac{x-1}{\sqrt{1-\sqrt{a+4}}}\right)}{8 (a+3) (a+4)^{3/2} \sqrt{1-\sqrt{a+4}}}+\frac{\left(3 a-\sqrt{a+4}+10\right) \tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)}{8 (a+3) (a+4)^{3/2} \sqrt{\sqrt{a+4}+1}}+\frac{\tanh ^{-1}\left(\frac{(x-1)^2+1}{\sqrt{a+4}}\right)}{4 (a+4)^{3/2}}",1,"(a + 2*x - a*x + a*x^2 + x^3)/(4*(3 + a)*(4 + a)*(a - x*(-8 + 8*x - 4*x^2 + x^3))) - RootSum[a + 8*#1 - 8*#1^2 + 4*#1^3 - #1^4 & , (6*Log[x - #1] + a*Log[x - #1] + 4*Log[x - #1]*#1 + 2*a*Log[x - #1]*#1 + Log[x - #1]*#1^2)/(-2 + 4*#1 - 3*#1^2 + #1^3) & ]/(16*(12 + 7*a + a^2))","C",1
129,1,284,349,0.1635351,"\int \frac{x}{\left(a+8 x-8 x^2+4 x^3-x^4\right)^3} \, dx","Integrate[x/(a + 8*x - 8*x^2 + 4*x^3 - x^4)^3,x]","\frac{1}{128} \left(-\frac{3 \text{RootSum}\left[-\text{$\#$1}^4+4 \text{$\#$1}^3-8 \text{$\#$1}^2+8 \text{$\#$1}+a\&,\frac{4 \text{$\#$1}^2 a \log (x-\text{$\#$1})+14 \text{$\#$1}^2 \log (x-\text{$\#$1})+3 a^2 \log (x-\text{$\#$1})+4 \text{$\#$1} a^2 \log (x-\text{$\#$1})+31 a \log (x-\text{$\#$1})+16 \text{$\#$1} a \log (x-\text{$\#$1})+72 \log (x-\text{$\#$1})+8 \text{$\#$1} \log (x-\text{$\#$1})}{\text{$\#$1}^3-3 \text{$\#$1}^2+4 \text{$\#$1}-2}\&\right]}{\left(a^2+7 a+12\right)^2}+\frac{4 \left(a^2 \left(6 x^2-5 x+5\right)+a \left(12 x^3+31 x-7\right)+6 \left(7 x^3-12 x^2+28 x-14\right)\right)}{(a+3)^2 (a+4)^2 \left(a-x \left(x^3-4 x^2+8 x-8\right)\right)}+\frac{16 \left(a x^2-a x+a+x^3+2 x\right)}{(a+3) (a+4) \left(a-x \left(x^3-4 x^2+8 x-8\right)\right)^2}\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{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,"((16*(a + 2*x - a*x + a*x^2 + x^3))/((3 + a)*(4 + a)*(a - x*(-8 + 8*x - 4*x^2 + x^3))^2) + (4*(a^2*(5 - 5*x + 6*x^2) + 6*(-14 + 28*x - 12*x^2 + 7*x^3) + a*(-7 + 31*x + 12*x^3)))/((3 + a)^2*(4 + a)^2*(a - x*(-8 + 8*x - 4*x^2 + x^3))) - (3*RootSum[a + 8*#1 - 8*#1^2 + 4*#1^3 - #1^4 & , (72*Log[x - #1] + 31*a*Log[x - #1] + 3*a^2*Log[x - #1] + 8*Log[x - #1]*#1 + 16*a*Log[x - #1]*#1 + 4*a^2*Log[x - #1]*#1 + 14*Log[x - #1]*#1^2 + 4*a*Log[x - #1]*#1^2)/(-2 + 4*#1 - 3*#1^2 + #1^3) & ])/(12 + 7*a + a^2)^2)/128","C",1
130,1,204,210,0.0359767,"\int x^2 \left(a+8 x-8 x^2+4 x^3-x^4\right)^4 \, dx","Integrate[x^2*(a + 8*x - 8*x^2 + 4*x^3 - x^4)^4,x]","\frac{a^4 x^3}{3}+8 a^3 x^4+\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}+\frac{64}{9} \left(3 a^2-140 a+512\right) x^9-4 \left(15 a^2-288 a+512\right) x^8+\frac{8}{3} a \left(a^2-48 a+128\right) x^6-\frac{32}{5} (a-12) a^2 x^5-\frac{4}{7} \left(a^3-192 a^2+1536 a-1024\right) x^7-\frac{4}{15} (a-640) x^{15}+\frac{8}{7} (3 a-464) x^{14}-\frac{32}{13} (9 a-524) x^{13}+\frac{8}{3} (35 a-928) x^{12}+\frac{x^{19}}{19}-\frac{8 x^{18}}{9}+\frac{128 x^{17}}{17}-42 x^{16}","\frac{a^4 x^3}{3}+8 a^3 x^4+\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{8}{3} a \left(a^2-48 a+128\right) x^6+\frac{32}{5} (12-a) a^2 x^5+\frac{4}{7} \left(-a^3+192 a^2-1536 a+1024\right) x^7+\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*(512 - 140*a + 3*a^2)*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",1
131,1,132,138,0.0194462,"\int x^2 \left(a+8 x-8 x^2+4 x^3-x^4\right)^3 \, dx","Integrate[x^2*(a + 8*x - 8*x^2 + 4*x^3 - x^4)^3,x]","\frac{a^3 x^3}{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{3}{11} (a-256) x^{11}-\frac{12}{5} (a-64) x^{10}+\frac{32}{9} (3 a-70) x^9-6 (5 a-48) x^8-\frac{24}{5} (a-8) a x^5-\frac{x^{15}}{15}+\frac{6 x^{14}}{7}-\frac{72 x^{13}}{13}+\frac{70 x^{12}}{3}","\frac{a^3 x^3}{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{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",1
132,1,73,79,0.0097586,"\int x^2 \left(a+8 x-8 x^2+4 x^3-x^4\right)^2 \, dx","Integrate[x^2*(a + 8*x - 8*x^2 + 4*x^3 - x^4)^2,x]","\frac{a^2 x^3}{3}-\frac{2}{7} (a-64) x^7+\frac{4}{3} (a-16) x^6-\frac{16}{5} (a-4) 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",1
133,1,35,35,0.0037377,"\int x^2 \left(a+8 x-8 x^2+4 x^3-x^4\right) \, dx","Integrate[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",1
134,1,61,99,0.0164218,"\int \frac{x^2}{a+8 x-8 x^2+4 x^3-x^4} \, dx","Integrate[x^2/(a + 8*x - 8*x^2 + 4*x^3 - x^4),x]","-\frac{1}{4} \text{RootSum}\left[-\text{$\#$1}^4+4 \text{$\#$1}^3-8 \text{$\#$1}^2+8 \text{$\#$1}+a\&,\frac{\text{$\#$1}^2 \log (x-\text{$\#$1})}{\text{$\#$1}^3-3 \text{$\#$1}^2+4 \text{$\#$1}-2}\&\right]","-\frac{\tan ^{-1}\left(\frac{x-1}{\sqrt{1-\sqrt{a+4}}}\right)}{2 \sqrt{1-\sqrt{a+4}}}-\frac{\tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)}{2 \sqrt{\sqrt{a+4}+1}}+\frac{\tanh ^{-1}\left(\frac{(x-1)^2+1}{\sqrt{a+4}}\right)}{\sqrt{a+4}}",1,"-1/4*RootSum[a + 8*#1 - 8*#1^2 + 4*#1^3 - #1^4 & , (Log[x - #1]*#1^2)/(-2 + 4*#1 - 3*#1^2 + #1^3) & ]","C",1
135,1,182,225,0.0762193,"\int \frac{x^2}{\left(a+8 x-8 x^2+4 x^3-x^4\right)^2} \, dx","Integrate[x^2/(a + 8*x - 8*x^2 + 4*x^3 - x^4)^2,x]","\frac{a \left(x^3-x^2+x+1\right)+2 x \left(2 x^2-3 x+4\right)}{4 (a+3) (a+4) \left(a-x \left(x^3-4 x^2+8 x-8\right)\right)}-\frac{\text{RootSum}\left[-\text{$\#$1}^4+4 \text{$\#$1}^3-8 \text{$\#$1}^2+8 \text{$\#$1}+a\&,\frac{\text{$\#$1}^2 a \log (x-\text{$\#$1})+4 \text{$\#$1}^2 \log (x-\text{$\#$1})+2 \text{$\#$1} a \log (x-\text{$\#$1})-a \log (x-\text{$\#$1})+4 \text{$\#$1} \log (x-\text{$\#$1})}{\text{$\#$1}^3-3 \text{$\#$1}^2+4 \text{$\#$1}-2}\&\right]}{16 \left(a^2+7 a+12\right)}","\frac{(a+4) \left((x-1)^2+2\right) (x-1)}{4 \left(a^2+7 a+12\right) \left(a-(x-1)^4-2 (x-1)^2+3\right)}+\frac{(x-1)^2+1}{2 (a+4) \left(a-(x-1)^4-2 (x-1)^2+3\right)}-\frac{\left(a+\sqrt{a+4}+4\right) \tan ^{-1}\left(\frac{x-1}{\sqrt{1-\sqrt{a+4}}}\right)}{8 (a+3) (a+4) \sqrt{1-\sqrt{a+4}}}-\frac{\left(a-\sqrt{a+4}+4\right) \tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)}{8 (a+3) (a+4) \sqrt{\sqrt{a+4}+1}}+\frac{\tanh ^{-1}\left(\frac{(x-1)^2+1}{\sqrt{a+4}}\right)}{2 (a+4)^{3/2}}",1,"(2*x*(4 - 3*x + 2*x^2) + a*(1 + x - x^2 + x^3))/(4*(3 + a)*(4 + a)*(a - x*(-8 + 8*x - 4*x^2 + x^3))) - RootSum[a + 8*#1 - 8*#1^2 + 4*#1^3 - #1^4 & , (-(a*Log[x - #1]) + 4*Log[x - #1]*#1 + 2*a*Log[x - #1]*#1 + 4*Log[x - #1]*#1^2 + a*Log[x - #1]*#1^2)/(-2 + 4*#1 - 3*#1^2 + #1^3) & ]/(16*(12 + 7*a + a^2))","C",1
136,1,99,545,0.0685057,"\int \frac{x^4}{27 a^3+27 a^2 b x^2+27 a^2 c x^3+9 a b^2 x^4+b^3 x^6} \, dx","Integrate[x^4/(27*a^3 + 27*a^2*b*x^2 + 27*a^2*c*x^3 + 9*a*b^2*x^4 + b^3*x^6),x]","\frac{1}{3} \text{RootSum}\left[\text{$\#$1}^6 b^3+9 \text{$\#$1}^4 a b^2+27 \text{$\#$1}^3 a^2 c+27 \text{$\#$1}^2 a^2 b+27 a^3\&,\frac{\text{$\#$1}^3 \log (x-\text{$\#$1})}{2 \text{$\#$1}^4 b^3+12 \text{$\#$1}^2 a b^2+27 \text{$\#$1} a^2 c+18 a^2 b}\&\right]","-\frac{\sqrt[3]{-1} \left(3 \sqrt[3]{a} c^{2/3}+2 \sqrt[3]{-1} b\right) \tan ^{-1}\left(\frac{3 \sqrt[3]{-1} a^{2/3} \sqrt[3]{c}-2 b x}{\sqrt{3} \sqrt{a} \sqrt{4 b-3 (-1)^{2/3} \sqrt[3]{a} c^{2/3}}}\right)}{3 \sqrt{3} \left(1+\sqrt[3]{-1}\right)^2 a^{5/6} b^2 c^{2/3} \sqrt{4 b-3 (-1)^{2/3} \sqrt[3]{a} c^{2/3}}}-\frac{\left(2 b-3 \sqrt[3]{a} c^{2/3}\right) \tan ^{-1}\left(\frac{3 a^{2/3} \sqrt[3]{c}+2 b x}{\sqrt{3} \sqrt{a} \sqrt{4 b-3 \sqrt[3]{a} c^{2/3}}}\right)}{9 \sqrt{3} a^{5/6} b^2 c^{2/3} \sqrt{4 b-3 \sqrt[3]{a} c^{2/3}}}-\frac{(-1)^{2/3} \left(3 \sqrt[3]{-1} \sqrt[3]{a} c^{2/3}+2 b\right) \tan ^{-1}\left(\frac{3 (-1)^{2/3} a^{2/3} \sqrt[3]{c}+2 b x}{\sqrt{3} \sqrt{a} \sqrt{3 \sqrt[3]{-1} \sqrt[3]{a} c^{2/3}+4 b}}\right)}{3 \sqrt{3} \left(1-\sqrt[3]{-1}\right) \left(1+\sqrt[3]{-1}\right)^2 a^{5/6} b^2 c^{2/3} \sqrt{3 \sqrt[3]{-1} \sqrt[3]{a} c^{2/3}+4 b}}-\frac{\log \left(3 a^{2/3} \sqrt[3]{c} x+3 a+b x^2\right)}{18 a^{2/3} b^2 \sqrt[3]{c}}+\frac{\log \left(-3 \sqrt[3]{-1} a^{2/3} \sqrt[3]{c} x+3 a+b x^2\right)}{6 \left(1+\sqrt[3]{-1}\right)^2 a^{2/3} b^2 \sqrt[3]{c}}+\frac{\sqrt[3]{-1} \log \left(3 (-1)^{2/3} a^{2/3} \sqrt[3]{c} x+3 a+b x^2\right)}{18 a^{2/3} b^2 \sqrt[3]{c}}",1,"RootSum[27*a^3 + 27*a^2*b*#1^2 + 27*a^2*c*#1^3 + 9*a*b^2*#1^4 + b^3*#1^6 & , (Log[x - #1]*#1^3)/(18*a^2*b + 27*a^2*c*#1 + 12*a*b^2*#1^2 + 2*b^3*#1^4) & ]/3","C",1
137,1,99,487,0.0491452,"\int \frac{x^3}{27 a^3+27 a^2 b x^2+27 a^2 c x^3+9 a b^2 x^4+b^3 x^6} \, dx","Integrate[x^3/(27*a^3 + 27*a^2*b*x^2 + 27*a^2*c*x^3 + 9*a*b^2*x^4 + b^3*x^6),x]","\frac{1}{3} \text{RootSum}\left[\text{$\#$1}^6 b^3+9 \text{$\#$1}^4 a b^2+27 \text{$\#$1}^3 a^2 c+27 \text{$\#$1}^2 a^2 b+27 a^3\&,\frac{\text{$\#$1}^2 \log (x-\text{$\#$1})}{2 \text{$\#$1}^4 b^3+12 \text{$\#$1}^2 a b^2+27 \text{$\#$1} a^2 c+18 a^2 b}\&\right]","\frac{\log \left(3 a^{2/3} \sqrt[3]{c} x+3 a+b x^2\right)}{54 a^{4/3} b c^{2/3}}-\frac{(-1)^{2/3} \log \left(-3 \sqrt[3]{-1} a^{2/3} \sqrt[3]{c} x+3 a+b x^2\right)}{18 \left(1+\sqrt[3]{-1}\right)^2 a^{4/3} b c^{2/3}}+\frac{(-1)^{2/3} \log \left(3 (-1)^{2/3} a^{2/3} \sqrt[3]{c} x+3 a+b x^2\right)}{54 a^{4/3} b c^{2/3}}-\frac{\tan ^{-1}\left(\frac{3 \sqrt[3]{-1} a^{2/3} \sqrt[3]{c}-2 b x}{\sqrt{3} \sqrt{a} \sqrt{4 b-3 (-1)^{2/3} \sqrt[3]{a} c^{2/3}}}\right)}{3 \sqrt{3} \left(1+\sqrt[3]{-1}\right)^2 a^{7/6} b \sqrt[3]{c} \sqrt{4 b-3 (-1)^{2/3} \sqrt[3]{a} c^{2/3}}}-\frac{\tan ^{-1}\left(\frac{3 a^{2/3} \sqrt[3]{c}+2 b x}{\sqrt{3} \sqrt{a} \sqrt{4 b-3 \sqrt[3]{a} c^{2/3}}}\right)}{9 \sqrt{3} a^{7/6} b \sqrt[3]{c} \sqrt{4 b-3 \sqrt[3]{a} c^{2/3}}}+\frac{\sqrt[3]{-1} \tan ^{-1}\left(\frac{3 (-1)^{2/3} a^{2/3} \sqrt[3]{c}+2 b x}{\sqrt{3} \sqrt{a} \sqrt{3 \sqrt[3]{-1} \sqrt[3]{a} c^{2/3}+4 b}}\right)}{3 \sqrt{3} \left(1-\sqrt[3]{-1}\right) \left(1+\sqrt[3]{-1}\right)^2 a^{7/6} b \sqrt[3]{c} \sqrt{3 \sqrt[3]{-1} \sqrt[3]{a} c^{2/3}+4 b}}",1,"RootSum[27*a^3 + 27*a^2*b*#1^2 + 27*a^2*c*#1^3 + 9*a*b^2*#1^4 + b^3*#1^6 & , (Log[x - #1]*#1^2)/(18*a^2*b + 27*a^2*c*#1 + 12*a*b^2*#1^2 + 2*b^3*#1^4) & ]/3","C",1
138,1,97,334,0.0585888,"\int \frac{x^2}{27 a^3+27 a^2 b x^2+27 a^2 c x^3+9 a b^2 x^4+b^3 x^6} \, dx","Integrate[x^2/(27*a^3 + 27*a^2*b*x^2 + 27*a^2*c*x^3 + 9*a*b^2*x^4 + b^3*x^6),x]","\frac{1}{3} \text{RootSum}\left[\text{$\#$1}^6 b^3+9 \text{$\#$1}^4 a b^2+27 \text{$\#$1}^3 a^2 c+27 \text{$\#$1}^2 a^2 b+27 a^3\&,\frac{\text{$\#$1} \log (x-\text{$\#$1})}{2 \text{$\#$1}^4 b^3+12 \text{$\#$1}^2 a b^2+27 \text{$\#$1} a^2 c+18 a^2 b}\&\right]","\frac{2 (-1)^{2/3} \tan ^{-1}\left(\frac{3 \sqrt[3]{-1} a^{2/3} \sqrt[3]{c}-2 b x}{\sqrt{3} \sqrt{a} \sqrt{4 b-3 (-1)^{2/3} \sqrt[3]{a} c^{2/3}}}\right)}{9 \sqrt{3} \left(1+\sqrt[3]{-1}\right)^2 a^{11/6} c^{2/3} \sqrt{4 b-3 (-1)^{2/3} \sqrt[3]{a} c^{2/3}}}+\frac{2 \tan ^{-1}\left(\frac{3 a^{2/3} \sqrt[3]{c}+2 b x}{\sqrt{3} \sqrt{a} \sqrt{4 b-3 \sqrt[3]{a} c^{2/3}}}\right)}{27 \sqrt{3} a^{11/6} c^{2/3} \sqrt{4 b-3 \sqrt[3]{a} c^{2/3}}}+\frac{2 (-1)^{2/3} \tan ^{-1}\left(\frac{3 (-1)^{2/3} a^{2/3} \sqrt[3]{c}+2 b x}{\sqrt{3} \sqrt{a} \sqrt{3 \sqrt[3]{-1} \sqrt[3]{a} c^{2/3}+4 b}}\right)}{9 \sqrt{3} \left(1-\sqrt[3]{-1}\right) \left(1+\sqrt[3]{-1}\right)^2 a^{11/6} c^{2/3} \sqrt{3 \sqrt[3]{-1} \sqrt[3]{a} c^{2/3}+4 b}}",1,"RootSum[27*a^3 + 27*a^2*b*#1^2 + 27*a^2*c*#1^3 + 9*a*b^2*#1^4 + b^3*#1^6 & , (Log[x - #1]*#1)/(18*a^2*b + 27*a^2*c*#1 + 12*a*b^2*#1^2 + 2*b^3*#1^4) & ]/3","C",1
139,1,95,469,0.046691,"\int \frac{x}{27 a^3+27 a^2 b x^2+27 a^2 c x^3+9 a b^2 x^4+b^3 x^6} \, dx","Integrate[x/(27*a^3 + 27*a^2*b*x^2 + 27*a^2*c*x^3 + 9*a*b^2*x^4 + b^3*x^6),x]","\frac{1}{3} \text{RootSum}\left[\text{$\#$1}^6 b^3+9 \text{$\#$1}^4 a b^2+27 \text{$\#$1}^3 a^2 c+27 \text{$\#$1}^2 a^2 b+27 a^3\&,\frac{\log (x-\text{$\#$1})}{2 \text{$\#$1}^4 b^3+12 \text{$\#$1}^2 a b^2+27 \text{$\#$1} a^2 c+18 a^2 b}\&\right]","-\frac{\log \left(3 a^{2/3} \sqrt[3]{c} x+3 a+b x^2\right)}{162 a^{7/3} c^{2/3}}+\frac{(-1)^{2/3} \log \left(-3 \sqrt[3]{-1} a^{2/3} \sqrt[3]{c} x+3 a+b x^2\right)}{54 \left(1+\sqrt[3]{-1}\right)^2 a^{7/3} c^{2/3}}-\frac{(-1)^{2/3} \log \left(3 (-1)^{2/3} a^{2/3} \sqrt[3]{c} x+3 a+b x^2\right)}{162 a^{7/3} c^{2/3}}-\frac{\tan ^{-1}\left(\frac{3 \sqrt[3]{-1} a^{2/3} \sqrt[3]{c}-2 b x}{\sqrt{3} \sqrt{a} \sqrt{4 b-3 (-1)^{2/3} \sqrt[3]{a} c^{2/3}}}\right)}{9 \sqrt{3} \left(1+\sqrt[3]{-1}\right)^2 a^{13/6} \sqrt[3]{c} \sqrt{4 b-3 (-1)^{2/3} \sqrt[3]{a} c^{2/3}}}-\frac{\tan ^{-1}\left(\frac{3 a^{2/3} \sqrt[3]{c}+2 b x}{\sqrt{3} \sqrt{a} \sqrt{4 b-3 \sqrt[3]{a} c^{2/3}}}\right)}{27 \sqrt{3} a^{13/6} \sqrt[3]{c} \sqrt{4 b-3 \sqrt[3]{a} c^{2/3}}}+\frac{\sqrt[3]{-1} \tan ^{-1}\left(\frac{3 (-1)^{2/3} a^{2/3} \sqrt[3]{c}+2 b x}{\sqrt{3} \sqrt{a} \sqrt{3 \sqrt[3]{-1} \sqrt[3]{a} c^{2/3}+4 b}}\right)}{9 \sqrt{3} \left(1-\sqrt[3]{-1}\right) \left(1+\sqrt[3]{-1}\right)^2 a^{13/6} \sqrt[3]{c} \sqrt{3 \sqrt[3]{-1} \sqrt[3]{a} c^{2/3}+4 b}}",1,"RootSum[27*a^3 + 27*a^2*b*#1^2 + 27*a^2*c*#1^3 + 9*a*b^2*#1^4 + b^3*#1^6 & , Log[x - #1]/(18*a^2*b + 27*a^2*c*#1 + 12*a*b^2*#1^2 + 2*b^3*#1^4) & ]/3","C",1
140,1,99,522,0.0663519,"\int \frac{1}{27 a^3+27 a^2 b x^2+27 a^2 c x^3+9 a b^2 x^4+b^3 x^6} \, dx","Integrate[(27*a^3 + 27*a^2*b*x^2 + 27*a^2*c*x^3 + 9*a*b^2*x^4 + b^3*x^6)^(-1),x]","\frac{1}{3} \text{RootSum}\left[\text{$\#$1}^6 b^3+9 \text{$\#$1}^4 a b^2+27 \text{$\#$1}^3 a^2 c+27 \text{$\#$1}^2 a^2 b+27 a^3\&,\frac{\log (x-\text{$\#$1})}{2 \text{$\#$1}^5 b^3+12 \text{$\#$1}^3 a b^2+27 \text{$\#$1}^2 a^2 c+18 \text{$\#$1} a^2 b}\&\right]","-\frac{\sqrt[3]{-1} \left(3 \sqrt[3]{a} c^{2/3}+2 \sqrt[3]{-1} b\right) \tan ^{-1}\left(\frac{3 \sqrt[3]{-1} a^{2/3} \sqrt[3]{c}-2 b x}{\sqrt{3} \sqrt{a} \sqrt{4 b-3 (-1)^{2/3} \sqrt[3]{a} c^{2/3}}}\right)}{27 \sqrt{3} \left(1+\sqrt[3]{-1}\right)^2 a^{17/6} c^{2/3} \sqrt{4 b-3 (-1)^{2/3} \sqrt[3]{a} c^{2/3}}}-\frac{\left(2 b-3 \sqrt[3]{a} c^{2/3}\right) \tan ^{-1}\left(\frac{3 a^{2/3} \sqrt[3]{c}+2 b x}{\sqrt{3} \sqrt{a} \sqrt{4 b-3 \sqrt[3]{a} c^{2/3}}}\right)}{81 \sqrt{3} a^{17/6} c^{2/3} \sqrt{4 b-3 \sqrt[3]{a} c^{2/3}}}-\frac{\left(2 (-1)^{2/3} b-3 \sqrt[3]{a} c^{2/3}\right) \tan ^{-1}\left(\frac{3 (-1)^{2/3} a^{2/3} \sqrt[3]{c}+2 b x}{\sqrt{3} \sqrt{a} \sqrt{3 \sqrt[3]{-1} \sqrt[3]{a} c^{2/3}+4 b}}\right)}{27 \sqrt{3} \left(1-\sqrt[3]{-1}\right) \left(1+\sqrt[3]{-1}\right)^2 a^{17/6} c^{2/3} \sqrt{3 \sqrt[3]{-1} \sqrt[3]{a} c^{2/3}+4 b}}+\frac{\log \left(3 a^{2/3} \sqrt[3]{c} x+3 a+b x^2\right)}{162 a^{8/3} \sqrt[3]{c}}-\frac{\log \left(-3 \sqrt[3]{-1} a^{2/3} \sqrt[3]{c} x+3 a+b x^2\right)}{54 \left(1+\sqrt[3]{-1}\right)^2 a^{8/3} \sqrt[3]{c}}-\frac{\sqrt[3]{-1} \log \left(3 (-1)^{2/3} a^{2/3} \sqrt[3]{c} x+3 a+b x^2\right)}{162 a^{8/3} \sqrt[3]{c}}",1,"RootSum[27*a^3 + 27*a^2*b*#1^2 + 27*a^2*c*#1^3 + 9*a*b^2*#1^4 + b^3*#1^6 & , Log[x - #1]/(18*a^2*b*#1 + 27*a^2*c*#1^2 + 12*a*b^2*#1^3 + 2*b^3*#1^5) & ]/3","C",1
141,1,157,563,0.1154993,"\int \frac{1}{x \left(27 a^3+27 a^2 b x^2+27 a^2 c x^3+9 a b^2 x^4+b^3 x^6\right)} \, dx","Integrate[1/(x*(27*a^3 + 27*a^2*b*x^2 + 27*a^2*c*x^3 + 9*a*b^2*x^4 + b^3*x^6)),x]","-\frac{\text{RootSum}\left[\text{$\#$1}^6 b^3+9 \text{$\#$1}^4 a b^2+27 \text{$\#$1}^3 a^2 c+27 \text{$\#$1}^2 a^2 b+27 a^3\&,\frac{\text{$\#$1}^4 b^3 \log (x-\text{$\#$1})+9 \text{$\#$1}^2 a b^2 \log (x-\text{$\#$1})+27 a^2 b \log (x-\text{$\#$1})+27 \text{$\#$1} a^2 c \log (x-\text{$\#$1})}{2 \text{$\#$1}^4 b^3+12 \text{$\#$1}^2 a b^2+27 \text{$\#$1} a^2 c+18 a^2 b}\&\right]-3 \log (x)}{81 a^3}","-\frac{\left(3 \sqrt[3]{a}-\frac{b}{c^{2/3}}\right) \log \left(3 a^{2/3} \sqrt[3]{c} x+3 a+b x^2\right)}{486 a^{10/3}}-\frac{\left(6 \sqrt[3]{a} c^{2/3}+i \sqrt{3} b+b\right) \log \left(-3 \sqrt[3]{-1} a^{2/3} \sqrt[3]{c} x+3 a+b x^2\right)}{972 a^{10/3} c^{2/3}}-\frac{\left(3 \sqrt[3]{a}-\frac{(-1)^{2/3} b}{c^{2/3}}\right) \log \left(3 (-1)^{2/3} a^{2/3} \sqrt[3]{c} x+3 a+b x^2\right)}{486 a^{10/3}}+\frac{\left(b-(-1)^{2/3} \sqrt[3]{a} c^{2/3}\right) \tan ^{-1}\left(\frac{3 \sqrt[3]{-1} a^{2/3} \sqrt[3]{c}-2 b x}{\sqrt{3} \sqrt{a} \sqrt{4 b-3 (-1)^{2/3} \sqrt[3]{a} c^{2/3}}}\right)}{9 \sqrt{3} \left(1+\sqrt[3]{-1}\right)^2 a^{19/6} \sqrt[3]{c} \sqrt{4 b-3 (-1)^{2/3} \sqrt[3]{a} c^{2/3}}}+\frac{\left(b-\sqrt[3]{a} c^{2/3}\right) \tan ^{-1}\left(\frac{3 a^{2/3} \sqrt[3]{c}+2 b x}{\sqrt{3} \sqrt{a} \sqrt{4 b-3 \sqrt[3]{a} c^{2/3}}}\right)}{27 \sqrt{3} a^{19/6} \sqrt[3]{c} \sqrt{4 b-3 \sqrt[3]{a} c^{2/3}}}+\frac{(-1)^{2/3} \left((-1)^{2/3} b-\sqrt[3]{a} c^{2/3}\right) \tan ^{-1}\left(\frac{3 (-1)^{2/3} a^{2/3} \sqrt[3]{c}+2 b x}{\sqrt{3} \sqrt{a} \sqrt{3 \sqrt[3]{-1} \sqrt[3]{a} c^{2/3}+4 b}}\right)}{9 \sqrt{3} \left(1-\sqrt[3]{-1}\right) \left(1+\sqrt[3]{-1}\right)^2 a^{19/6} \sqrt[3]{c} \sqrt{3 \sqrt[3]{-1} \sqrt[3]{a} c^{2/3}+4 b}}+\frac{\log (x)}{27 a^3}",1,"-1/81*(-3*Log[x] + RootSum[27*a^3 + 27*a^2*b*#1^2 + 27*a^2*c*#1^3 + 9*a*b^2*#1^4 + b^3*#1^6 & , (27*a^2*b*Log[x - #1] + 27*a^2*c*Log[x - #1]*#1 + 9*a*b^2*Log[x - #1]*#1^2 + b^3*Log[x - #1]*#1^4)/(18*a^2*b + 27*a^2*c*#1 + 12*a*b^2*#1^2 + 2*b^3*#1^4) & ])/a^3","C",1
142,1,163,645,0.1393126,"\int \frac{1}{x^2 \left(27 a^3+27 a^2 b x^2+27 a^2 c x^3+9 a b^2 x^4+b^3 x^6\right)} \, dx","Integrate[1/(x^2*(27*a^3 + 27*a^2*b*x^2 + 27*a^2*c*x^3 + 9*a*b^2*x^4 + b^3*x^6)),x]","-\frac{x \text{RootSum}\left[\text{$\#$1}^6 b^3+9 \text{$\#$1}^4 a b^2+27 \text{$\#$1}^3 a^2 c+27 \text{$\#$1}^2 a^2 b+27 a^3\&,\frac{\text{$\#$1}^4 b^3 \log (x-\text{$\#$1})+9 \text{$\#$1}^2 a b^2 \log (x-\text{$\#$1})+27 a^2 b \log (x-\text{$\#$1})+27 \text{$\#$1} a^2 c \log (x-\text{$\#$1})}{2 \text{$\#$1}^5 b^3+12 \text{$\#$1}^3 a b^2+27 \text{$\#$1}^2 a^2 c+18 \text{$\#$1} a^2 b}\&\right]+3}{81 a^3 x}","\frac{\left(9 a^{2/3} c^{4/3}+12 \sqrt[3]{-1} \sqrt[3]{a} b c^{2/3}+2 (-1)^{2/3} b^2\right) \tan ^{-1}\left(\frac{3 \sqrt[3]{-1} a^{2/3} \sqrt[3]{c}-2 b x}{\sqrt{3} \sqrt{a} \sqrt{4 b-3 (-1)^{2/3} \sqrt[3]{a} c^{2/3}}}\right)}{81 \sqrt{3} \left(1+\sqrt[3]{-1}\right)^2 a^{23/6} c^{2/3} \sqrt{4 b-3 (-1)^{2/3} \sqrt[3]{a} c^{2/3}}}+\frac{\left(9 a^{2/3} c^{4/3}-12 \sqrt[3]{a} b c^{2/3}+2 b^2\right) \tan ^{-1}\left(\frac{3 a^{2/3} \sqrt[3]{c}+2 b x}{\sqrt{3} \sqrt{a} \sqrt{4 b-3 \sqrt[3]{a} c^{2/3}}}\right)}{243 \sqrt{3} a^{23/6} c^{2/3} \sqrt{4 b-3 \sqrt[3]{a} c^{2/3}}}+\frac{(-1)^{2/3} \left(9 (-1)^{2/3} a^{2/3} c^{4/3}+12 \sqrt[3]{-1} \sqrt[3]{a} b c^{2/3}+2 b^2\right) \tan ^{-1}\left(\frac{3 (-1)^{2/3} a^{2/3} \sqrt[3]{c}+2 b x}{\sqrt{3} \sqrt{a} \sqrt{3 \sqrt[3]{-1} \sqrt[3]{a} c^{2/3}+4 b}}\right)}{81 \sqrt{3} \left(1-\sqrt[3]{-1}\right) \left(1+\sqrt[3]{-1}\right)^2 a^{23/6} c^{2/3} \sqrt{3 \sqrt[3]{-1} \sqrt[3]{a} c^{2/3}+4 b}}-\frac{\left(2 b-3 \sqrt[3]{a} c^{2/3}\right) \log \left(3 a^{2/3} \sqrt[3]{c} x+3 a+b x^2\right)}{486 a^{11/3} \sqrt[3]{c}}+\frac{\left(2 b-3 (-1)^{2/3} \sqrt[3]{a} c^{2/3}\right) \log \left(-3 \sqrt[3]{-1} a^{2/3} \sqrt[3]{c} x+3 a+b x^2\right)}{162 \left(1+\sqrt[3]{-1}\right)^2 a^{11/3} \sqrt[3]{c}}+\frac{\sqrt[3]{-1} \left(3 \sqrt[3]{-1} \sqrt[3]{a} c^{2/3}+2 b\right) \log \left(3 (-1)^{2/3} a^{2/3} \sqrt[3]{c} x+3 a+b x^2\right)}{486 a^{11/3} \sqrt[3]{c}}-\frac{1}{27 a^3 x}",1,"-1/81*(3 + x*RootSum[27*a^3 + 27*a^2*b*#1^2 + 27*a^2*c*#1^3 + 9*a*b^2*#1^4 + b^3*#1^6 & , (27*a^2*b*Log[x - #1] + 27*a^2*c*Log[x - #1]*#1 + 9*a*b^2*Log[x - #1]*#1^2 + b^3*Log[x - #1]*#1^4)/(18*a^2*b*#1 + 27*a^2*c*#1^2 + 12*a*b^2*#1^3 + 2*b^3*#1^5) & ])/(a^3*x)","C",1
143,1,61,395,0.0226392,"\int \frac{x^5}{216+108 x^2+324 x^3+18 x^4+x^6} \, dx","Integrate[x^5/(216 + 108*x^2 + 324*x^3 + 18*x^4 + x^6),x]","\frac{1}{6} \text{RootSum}\left[\text{$\#$1}^6+18 \text{$\#$1}^4+324 \text{$\#$1}^3+108 \text{$\#$1}^2+216\&,\frac{\text{$\#$1}^4 \log (x-\text{$\#$1})}{\text{$\#$1}^4+12 \text{$\#$1}^2+162 \text{$\#$1}+36}\&\right]","\frac{1}{216} \left(36+2^{2/3} \sqrt[3]{3} \left(1+i \sqrt{3}\right)\right) \log \left(x^2-3 \sqrt[3]{-3} 2^{2/3} x+6\right)+\frac{1}{108} \left(18-(-2)^{2/3} \sqrt[3]{3}\right) \log \left(x^2+3 (-2)^{2/3} \sqrt[3]{3} x+6\right)+\frac{1}{108} \left(18-2^{2/3} \sqrt[3]{3}\right) \log \left(x^2+3\ 2^{2/3} \sqrt[3]{3} x+6\right)-\frac{\sqrt[3]{-2} \left(1+\sqrt[3]{-2} 3^{2/3}\right) \tan ^{-1}\left(\frac{2 x+3 (-2)^{2/3} \sqrt[3]{3}}{\sqrt{6 \left(4+3 \sqrt[3]{-2} 3^{2/3}\right)}}\right)}{3^{5/6} \sqrt{8+9 i \sqrt[3]{2} \sqrt[6]{3}+3 \sqrt[3]{2} 3^{2/3}}}+\frac{\sqrt[6]{\frac{3}{2}} \left(1-(-3)^{2/3} \sqrt[3]{2}\right) \tan ^{-1}\left(\frac{\sqrt[6]{2} \left(3 \sqrt[3]{-3}-\sqrt[3]{2} x\right)}{\sqrt{3 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)}}\right)}{\left(1+\sqrt[3]{-1}\right)^2 \sqrt{4-3 (-3)^{2/3} \sqrt[3]{2}}}-\frac{\left(1-\sqrt[3]{2} 3^{2/3}\right) \tanh ^{-1}\left(\frac{\sqrt[6]{2} \left(\sqrt[3]{2} x+3 \sqrt[3]{3}\right)}{\sqrt{3 \left(3 \sqrt[3]{2} 3^{2/3}-4\right)}}\right)}{\sqrt[6]{2} 3^{5/6} \sqrt{3 \sqrt[3]{2} 3^{2/3}-4}}",1,"RootSum[216 + 108*#1^2 + 324*#1^3 + 18*#1^4 + #1^6 & , (Log[x - #1]*#1^4)/(36 + 162*#1 + 12*#1^2 + #1^4) & ]/6","C",1
144,1,61,377,0.0137812,"\int \frac{x^4}{216+108 x^2+324 x^3+18 x^4+x^6} \, dx","Integrate[x^4/(216 + 108*x^2 + 324*x^3 + 18*x^4 + x^6),x]","\frac{1}{6} \text{RootSum}\left[\text{$\#$1}^6+18 \text{$\#$1}^4+324 \text{$\#$1}^3+108 \text{$\#$1}^2+216\&,\frac{\text{$\#$1}^3 \log (x-\text{$\#$1})}{\text{$\#$1}^4+12 \text{$\#$1}^2+162 \text{$\#$1}+36}\&\right]","\frac{\log \left(x^2-3 \sqrt[3]{-3} 2^{2/3} x+6\right)}{6\ 2^{2/3} \sqrt[3]{3} \left(1+\sqrt[3]{-1}\right)^2}+\frac{\sqrt[3]{-\frac{1}{3}} \log \left(x^2+3 (-2)^{2/3} \sqrt[3]{3} x+6\right)}{18\ 2^{2/3}}-\frac{\log \left(x^2+3\ 2^{2/3} \sqrt[3]{3} x+6\right)}{18\ 2^{2/3} \sqrt[3]{3}}+\frac{(-1)^{2/3} \left(3 (-3)^{2/3}-2^{2/3}\right) \tan ^{-1}\left(\frac{3 \sqrt[3]{-3} 2^{2/3}-2 x}{\sqrt{6 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)}}\right)}{9 \sqrt[6]{3} \left(1+\sqrt[3]{-1}\right)^2 \sqrt{2 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)}}+\frac{\left(9-(-2)^{2/3} \sqrt[3]{3}\right) \tan ^{-1}\left(\frac{2 x+3 (-2)^{2/3} \sqrt[3]{3}}{\sqrt{6 \left(4+3 \sqrt[3]{-2} 3^{2/3}\right)}}\right)}{27 \sqrt{3 \left(8+9 i \sqrt[3]{2} \sqrt[6]{3}+3 \sqrt[3]{2} 3^{2/3}\right)}}-\frac{\left(9-2^{2/3} \sqrt[3]{3}\right) \tanh ^{-1}\left(\frac{\sqrt[6]{2} \left(\sqrt[3]{2} x+3 \sqrt[3]{3}\right)}{\sqrt{3 \left(3 \sqrt[3]{2} 3^{2/3}-4\right)}}\right)}{27 \sqrt{6 \left(3 \sqrt[3]{2} 3^{2/3}-4\right)}}",1,"RootSum[216 + 108*#1^2 + 324*#1^3 + 18*#1^4 + #1^6 & , (Log[x - #1]*#1^3)/(36 + 162*#1 + 12*#1^2 + #1^4) & ]/6","C",1
145,1,61,361,0.0148101,"\int \frac{x^3}{216+108 x^2+324 x^3+18 x^4+x^6} \, dx","Integrate[x^3/(216 + 108*x^2 + 324*x^3 + 18*x^4 + x^6),x]","\frac{1}{6} \text{RootSum}\left[\text{$\#$1}^6+18 \text{$\#$1}^4+324 \text{$\#$1}^3+108 \text{$\#$1}^2+216\&,\frac{\text{$\#$1}^2 \log (x-\text{$\#$1})}{\text{$\#$1}^4+12 \text{$\#$1}^2+162 \text{$\#$1}+36}\&\right]","-\frac{(-1)^{2/3} \log \left(x^2-3 \sqrt[3]{-3} 2^{2/3} x+6\right)}{36 \sqrt[3]{2} 3^{2/3} \left(1+\sqrt[3]{-1}\right)^2}+\frac{(-1)^{2/3} \log \left(x^2+3 (-2)^{2/3} \sqrt[3]{3} x+6\right)}{108 \sqrt[3]{2} 3^{2/3}}+\frac{\log \left(x^2+3\ 2^{2/3} \sqrt[3]{3} x+6\right)}{108 \sqrt[3]{2} 3^{2/3}}-\frac{\tan ^{-1}\left(\frac{3 \sqrt[3]{-3} 2^{2/3}-2 x}{\sqrt{6 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)}}\right)}{6 \sqrt[6]{2} 3^{5/6} \left(1+\sqrt[3]{-1}\right)^2 \sqrt{4-3 (-3)^{2/3} \sqrt[3]{2}}}+\frac{\sqrt[3]{-1} \tan ^{-1}\left(\frac{2 x+3 (-2)^{2/3} \sqrt[3]{3}}{\sqrt{6 \left(4+3 \sqrt[3]{-2} 3^{2/3}\right)}}\right)}{9\ 2^{2/3} 3^{5/6} \sqrt{8+9 i \sqrt[3]{2} \sqrt[6]{3}+3 \sqrt[3]{2} 3^{2/3}}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[6]{2} \left(\sqrt[3]{2} x+3 \sqrt[3]{3}\right)}{\sqrt{3 \left(3 \sqrt[3]{2} 3^{2/3}-4\right)}}\right)}{18 \sqrt[6]{2} 3^{5/6} \sqrt{3 \sqrt[3]{2} 3^{2/3}-4}}",1,"RootSum[216 + 108*#1^2 + 324*#1^3 + 18*#1^4 + #1^6 & , (Log[x - #1]*#1^2)/(36 + 162*#1 + 12*#1^2 + #1^4) & ]/6","C",1
146,1,59,248,0.0125427,"\int \frac{x^2}{216+108 x^2+324 x^3+18 x^4+x^6} \, dx","Integrate[x^2/(216 + 108*x^2 + 324*x^3 + 18*x^4 + x^6),x]","\frac{1}{6} \text{RootSum}\left[\text{$\#$1}^6+18 \text{$\#$1}^4+324 \text{$\#$1}^3+108 \text{$\#$1}^2+216\&,\frac{\text{$\#$1} \log (x-\text{$\#$1})}{\text{$\#$1}^4+12 \text{$\#$1}^2+162 \text{$\#$1}+36}\&\right]","\frac{(-1)^{2/3} \tan ^{-1}\left(\frac{3 \sqrt[3]{-3} 2^{2/3}-2 x}{\sqrt{6 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)}}\right)}{27\ 2^{5/6} \sqrt[6]{3} \left(1+\sqrt[3]{-1}\right)^2 \sqrt{4-3 (-3)^{2/3} \sqrt[3]{2}}}+\frac{(-1)^{2/3} \tan ^{-1}\left(\frac{2 x+3 (-2)^{2/3} \sqrt[3]{3}}{\sqrt{6 \left(4+3 \sqrt[3]{-2} 3^{2/3}\right)}}\right)}{81 \sqrt[3]{2} \sqrt[6]{3} \sqrt{8+9 i \sqrt[3]{2} \sqrt[6]{3}+3 \sqrt[3]{2} 3^{2/3}}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[6]{2} \left(\sqrt[3]{2} x+3 \sqrt[3]{3}\right)}{\sqrt{3 \left(3 \sqrt[3]{2} 3^{2/3}-4\right)}}\right)}{81\ 2^{5/6} \sqrt[6]{3} \sqrt{3 \sqrt[3]{2} 3^{2/3}-4}}",1,"RootSum[216 + 108*#1^2 + 324*#1^3 + 18*#1^4 + #1^6 & , (Log[x - #1]*#1)/(36 + 162*#1 + 12*#1^2 + #1^4) & ]/6","C",1
147,1,57,361,0.0155205,"\int \frac{x}{216+108 x^2+324 x^3+18 x^4+x^6} \, dx","Integrate[x/(216 + 108*x^2 + 324*x^3 + 18*x^4 + x^6),x]","\frac{1}{6} \text{RootSum}\left[\text{$\#$1}^6+18 \text{$\#$1}^4+324 \text{$\#$1}^3+108 \text{$\#$1}^2+216\&,\frac{\log (x-\text{$\#$1})}{\text{$\#$1}^4+12 \text{$\#$1}^2+162 \text{$\#$1}+36}\&\right]","\frac{(-1)^{2/3} \log \left(x^2-3 \sqrt[3]{-3} 2^{2/3} x+6\right)}{216 \sqrt[3]{2} 3^{2/3} \left(1+\sqrt[3]{-1}\right)^2}-\frac{(-1)^{2/3} \log \left(x^2+3 (-2)^{2/3} \sqrt[3]{3} x+6\right)}{648 \sqrt[3]{2} 3^{2/3}}-\frac{\log \left(x^2+3\ 2^{2/3} \sqrt[3]{3} x+6\right)}{648 \sqrt[3]{2} 3^{2/3}}-\frac{\tan ^{-1}\left(\frac{3 \sqrt[3]{-3} 2^{2/3}-2 x}{\sqrt{6 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)}}\right)}{36 \sqrt[6]{2} 3^{5/6} \left(1+\sqrt[3]{-1}\right)^2 \sqrt{4-3 (-3)^{2/3} \sqrt[3]{2}}}+\frac{\sqrt[3]{-1} \tan ^{-1}\left(\frac{2 x+3 (-2)^{2/3} \sqrt[3]{3}}{\sqrt{6 \left(4+3 \sqrt[3]{-2} 3^{2/3}\right)}}\right)}{54\ 2^{2/3} 3^{5/6} \sqrt{8+9 i \sqrt[3]{2} \sqrt[6]{3}+3 \sqrt[3]{2} 3^{2/3}}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[6]{2} \left(\sqrt[3]{2} x+3 \sqrt[3]{3}\right)}{\sqrt{3 \left(3 \sqrt[3]{2} 3^{2/3}-4\right)}}\right)}{108 \sqrt[6]{2} 3^{5/6} \sqrt{3 \sqrt[3]{2} 3^{2/3}-4}}",1,"RootSum[216 + 108*#1^2 + 324*#1^3 + 18*#1^4 + #1^6 & , Log[x - #1]/(36 + 162*#1 + 12*#1^2 + #1^4) & ]/6","C",1
148,1,62,377,0.0126348,"\int \frac{1}{216+108 x^2+324 x^3+18 x^4+x^6} \, dx","Integrate[(216 + 108*x^2 + 324*x^3 + 18*x^4 + x^6)^(-1),x]","\frac{1}{6} \text{RootSum}\left[\text{$\#$1}^6+18 \text{$\#$1}^4+324 \text{$\#$1}^3+108 \text{$\#$1}^2+216\&,\frac{\log (x-\text{$\#$1})}{\text{$\#$1}^5+12 \text{$\#$1}^3+162 \text{$\#$1}^2+36 \text{$\#$1}}\&\right]","-\frac{\log \left(x^2-3 \sqrt[3]{-3} 2^{2/3} x+6\right)}{216\ 2^{2/3} \sqrt[3]{3} \left(1+\sqrt[3]{-1}\right)^2}-\frac{\sqrt[3]{-\frac{1}{3}} \log \left(x^2+3 (-2)^{2/3} \sqrt[3]{3} x+6\right)}{648\ 2^{2/3}}+\frac{\log \left(x^2+3\ 2^{2/3} \sqrt[3]{3} x+6\right)}{648\ 2^{2/3} \sqrt[3]{3}}+\frac{(-1)^{2/3} \left(3 (-3)^{2/3}-2^{2/3}\right) \tan ^{-1}\left(\frac{3 \sqrt[3]{-3} 2^{2/3}-2 x}{\sqrt{6 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)}}\right)}{324 \sqrt[6]{3} \left(1+\sqrt[3]{-1}\right)^2 \sqrt{2 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)}}+\frac{\left(9-(-2)^{2/3} \sqrt[3]{3}\right) \tan ^{-1}\left(\frac{2 x+3 (-2)^{2/3} \sqrt[3]{3}}{\sqrt{6 \left(4+3 \sqrt[3]{-2} 3^{2/3}\right)}}\right)}{972 \sqrt{3 \left(8+9 i \sqrt[3]{2} \sqrt[6]{3}+3 \sqrt[3]{2} 3^{2/3}\right)}}-\frac{\left(9-2^{2/3} \sqrt[3]{3}\right) \tanh ^{-1}\left(\frac{\sqrt[6]{2} \left(\sqrt[3]{2} x+3 \sqrt[3]{3}\right)}{\sqrt{3 \left(3 \sqrt[3]{2} 3^{2/3}-4\right)}}\right)}{972 \sqrt{6 \left(3 \sqrt[3]{2} 3^{2/3}-4\right)}}",1,"RootSum[216 + 108*#1^2 + 324*#1^3 + 18*#1^4 + #1^6 & , Log[x - #1]/(36*#1 + 162*#1^2 + 12*#1^3 + #1^5) & ]/6","C",1
149,1,103,415,0.0190663,"\int \frac{1}{x \left(216+108 x^2+324 x^3+18 x^4+x^6\right)} \, dx","Integrate[1/(x*(216 + 108*x^2 + 324*x^3 + 18*x^4 + x^6)),x]","\frac{\log (x)}{216}-\frac{\text{RootSum}\left[\text{$\#$1}^6+18 \text{$\#$1}^4+324 \text{$\#$1}^3+108 \text{$\#$1}^2+216\&,\frac{\text{$\#$1}^4 \log (x-\text{$\#$1})+18 \text{$\#$1}^2 \log (x-\text{$\#$1})+324 \text{$\#$1} \log (x-\text{$\#$1})+108 \log (x-\text{$\#$1})}{\text{$\#$1}^4+12 \text{$\#$1}^2+162 \text{$\#$1}+36}\&\right]}{1296}","-\frac{\left(36+2^{2/3} \sqrt[3]{3} \left(1+i \sqrt{3}\right)\right) \log \left(x^2-3 \sqrt[3]{-3} 2^{2/3} x+6\right)}{46656}-\frac{\left(18-(-2)^{2/3} \sqrt[3]{3}\right) \log \left(x^2+3 (-2)^{2/3} \sqrt[3]{3} x+6\right)}{23328}-\frac{\left(18-2^{2/3} \sqrt[3]{3}\right) \log \left(x^2+3\ 2^{2/3} \sqrt[3]{3} x+6\right)}{23328}+\frac{\log (x)}{216}+\frac{(-1)^{2/3} \left((-2)^{2/3}-2\ 3^{2/3}\right) \tan ^{-1}\left(\frac{2 x+3 (-2)^{2/3} \sqrt[3]{3}}{\sqrt{6 \left(4+3 \sqrt[3]{-2} 3^{2/3}\right)}}\right)}{216 \sqrt[3]{2} 3^{5/6} \sqrt{8+9 i \sqrt[3]{2} \sqrt[6]{3}+3 \sqrt[3]{2} 3^{2/3}}}-\frac{(-1)^{2/3} \left(\sqrt[3]{-3}+3 \sqrt[3]{2}\right) \tan ^{-1}\left(\frac{\sqrt[6]{2} \left(3 \sqrt[3]{-3}-\sqrt[3]{2} x\right)}{\sqrt{3 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)}}\right)}{216 \sqrt[6]{6} \left(1+\sqrt[3]{-1}\right)^2 \sqrt{4-3 (-3)^{2/3} \sqrt[3]{2}}}-\frac{\left(1-\sqrt[3]{2} 3^{2/3}\right) \tanh ^{-1}\left(\frac{\sqrt[6]{2} \left(\sqrt[3]{2} x+3 \sqrt[3]{3}\right)}{\sqrt{3 \left(3 \sqrt[3]{2} 3^{2/3}-4\right)}}\right)}{216 \sqrt[6]{2} 3^{5/6} \sqrt{3 \sqrt[3]{2} 3^{2/3}-4}}",1,"Log[x]/216 - RootSum[216 + 108*#1^2 + 324*#1^3 + 18*#1^4 + #1^6 & , (108*Log[x - #1] + 324*Log[x - #1]*#1 + 18*Log[x - #1]*#1^2 + Log[x - #1]*#1^4)/(36 + 162*#1 + 12*#1^2 + #1^4) & ]/1296","C",1
150,1,109,448,0.0208972,"\int \frac{1}{x^2 \left(216+108 x^2+324 x^3+18 x^4+x^6\right)} \, dx","Integrate[1/(x^2*(216 + 108*x^2 + 324*x^3 + 18*x^4 + x^6)),x]","-\frac{\text{RootSum}\left[\text{$\#$1}^6+18 \text{$\#$1}^4+324 \text{$\#$1}^3+108 \text{$\#$1}^2+216\&,\frac{\text{$\#$1}^4 \log (x-\text{$\#$1})+18 \text{$\#$1}^2 \log (x-\text{$\#$1})+324 \text{$\#$1} \log (x-\text{$\#$1})+108 \log (x-\text{$\#$1})}{\text{$\#$1}^5+12 \text{$\#$1}^3+162 \text{$\#$1}^2+36 \text{$\#$1}}\&\right]}{1296}-\frac{1}{216 x}","-\frac{(-1)^{2/3} \left(9+\sqrt[3]{-3} 2^{2/3}\right) \log \left(x^2-3 \sqrt[3]{-3} 2^{2/3} x+6\right)}{1296 \sqrt[3]{2} 3^{2/3} \left(1+\sqrt[3]{-1}\right)^2}+\frac{\left(3 (-6)^{2/3}+2 \sqrt[3]{-2}\right) \log \left(x^2+3 (-2)^{2/3} \sqrt[3]{3} x+6\right)}{7776 \sqrt[3]{3}}-\frac{\left(2^{2/3}-3\ 3^{2/3}\right) \log \left(x^2+3\ 2^{2/3} \sqrt[3]{3} x+6\right)}{3888 \sqrt[3]{6}}-\frac{1}{216 x}-\frac{\left(27 \sqrt[3]{-6}-(-2)^{2/3}+12\ 3^{2/3}\right) \tan ^{-1}\left(\frac{2 x+3 (-2)^{2/3} \sqrt[3]{3}}{\sqrt{6 \left(4+3 \sqrt[3]{-2} 3^{2/3}\right)}}\right)}{5832 \sqrt[6]{3} \sqrt{8+9 i \sqrt[3]{2} \sqrt[6]{3}+3 \sqrt[3]{2} 3^{2/3}}}-\frac{(-1)^{2/3} \left(6 (-6)^{2/3}+27 \sqrt[3]{-3}-\sqrt[3]{2}\right) \tan ^{-1}\left(\frac{\sqrt[6]{2} \left(3 \sqrt[3]{-3}-\sqrt[3]{2} x\right)}{\sqrt{3 \left(4-3 (-3)^{2/3} \sqrt[3]{2}\right)}}\right)}{1944 \sqrt[6]{6} \left(1+\sqrt[3]{-1}\right)^2 \sqrt{4-3 (-3)^{2/3} \sqrt[3]{2}}}-\frac{\left(\sqrt[3]{2}+27 \sqrt[3]{3}-6\ 6^{2/3}\right) \tanh ^{-1}\left(\frac{\sqrt[6]{2} \left(\sqrt[3]{2} x+3 \sqrt[3]{3}\right)}{\sqrt{3 \left(3 \sqrt[3]{2} 3^{2/3}-4\right)}}\right)}{5832 \sqrt[6]{6} \sqrt{3 \sqrt[3]{2} 3^{2/3}-4}}",1,"-1/216*1/x - RootSum[216 + 108*#1^2 + 324*#1^3 + 18*#1^4 + #1^6 & , (108*Log[x - #1] + 324*Log[x - #1]*#1 + 18*Log[x - #1]*#1^2 + Log[x - #1]*#1^4)/(36*#1 + 162*#1^2 + 12*#1^3 + #1^5) & ]/1296","C",1
151,1,167,1064,0.0397991,"\int \frac{x^8}{\left(216+108 x^2+324 x^3+18 x^4+x^6\right)^2} \, dx","Integrate[x^8/(216 + 108*x^2 + 324*x^3 + 18*x^4 + x^6)^2,x]","\frac{-9 x^5-203 x^4-11610 x^3-3990 x^2+324 x-7884}{34182 \left(x^6+18 x^4+324 x^3+108 x^2+216\right)}-\frac{\text{RootSum}\left[\text{$\#$1}^6+18 \text{$\#$1}^4+324 \text{$\#$1}^3+108 \text{$\#$1}^2+216\&,\frac{9 \text{$\#$1}^4 \log (x-\text{$\#$1})+406 \text{$\#$1}^3 \log (x-\text{$\#$1})+324 \text{$\#$1}^2 \log (x-\text{$\#$1})-96 \text{$\#$1} \log (x-\text{$\#$1})+324 \log (x-\text{$\#$1})}{\text{$\#$1}^5+12 \text{$\#$1}^3+162 \text{$\#$1}^2+36 \text{$\#$1}}\&\right]}{205092}","-\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,"(-7884 + 324*x - 3990*x^2 - 11610*x^3 - 203*x^4 - 9*x^5)/(34182*(216 + 108*x^2 + 324*x^3 + 18*x^4 + x^6)) - RootSum[216 + 108*#1^2 + 324*#1^3 + 18*#1^4 + #1^6 & , (324*Log[x - #1] - 96*Log[x - #1]*#1 + 324*Log[x - #1]*#1^2 + 406*Log[x - #1]*#1^3 + 9*Log[x - #1]*#1^4)/(36*#1 + 162*#1^2 + 12*#1^3 + #1^5) & ]/205092","C",0
152,1,167,1005,0.0299959,"\int \frac{x^7}{\left(216+108 x^2+324 x^3+18 x^4+x^6\right)^2} \, dx","Integrate[x^7/(216 + 108*x^2 + 324*x^3 + 18*x^4 + x^6)^2,x]","\frac{\text{RootSum}\left[\text{$\#$1}^6+18 \text{$\#$1}^4+324 \text{$\#$1}^3+108 \text{$\#$1}^2+216\&,\frac{73 \text{$\#$1}^4 \log (x-\text{$\#$1})-36 \text{$\#$1}^3 \log (x-\text{$\#$1})+96 \text{$\#$1}^2 \log (x-\text{$\#$1})-216 \text{$\#$1} \log (x-\text{$\#$1})+96 \log (x-\text{$\#$1})}{\text{$\#$1}^5+12 \text{$\#$1}^3+162 \text{$\#$1}^2+36 \text{$\#$1}}\&\right]}{410184}+\frac{73 x^5-18 x^4+908 x^3+432 x^2-96 x+648}{68364 \left(x^6+18 x^4+324 x^3+108 x^2+216\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,"(648 - 96*x + 432*x^2 + 908*x^3 - 18*x^4 + 73*x^5)/(68364*(216 + 108*x^2 + 324*x^3 + 18*x^4 + x^6)) + RootSum[216 + 108*#1^2 + 324*#1^3 + 18*#1^4 + #1^6 & , (96*Log[x - #1] - 216*Log[x - #1]*#1 + 96*Log[x - #1]*#1^2 - 36*Log[x - #1]*#1^3 + 73*Log[x - #1]*#1^4)/(36*#1 + 162*#1^2 + 12*#1^3 + #1^5) & ]/410184","C",0
153,1,167,677,0.0452594,"\int \frac{x^6}{\left(216+108 x^2+324 x^3+18 x^4+x^6\right)^2} \, dx","Integrate[x^6/(216 + 108*x^2 + 324*x^3 + 18*x^4 + x^6)^2,x]","\frac{-3 x^5+73 x^4-72 x^3-64 x^2+108 x-96}{68364 \left(x^6+18 x^4+324 x^3+108 x^2+216\right)}-\frac{\text{RootSum}\left[\text{$\#$1}^6+18 \text{$\#$1}^4+324 \text{$\#$1}^3+108 \text{$\#$1}^2+216\&,\frac{3 \text{$\#$1}^4 \log (x-\text{$\#$1})-146 \text{$\#$1}^3 \log (x-\text{$\#$1})+108 \text{$\#$1}^2 \log (x-\text{$\#$1})-32 \text{$\#$1} \log (x-\text{$\#$1})+108 \log (x-\text{$\#$1})}{\text{$\#$1}^5+12 \text{$\#$1}^3+162 \text{$\#$1}^2+36 \text{$\#$1}}\&\right]}{410184}","\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,"(-96 + 108*x - 64*x^2 - 72*x^3 + 73*x^4 - 3*x^5)/(68364*(216 + 108*x^2 + 324*x^3 + 18*x^4 + x^6)) - RootSum[216 + 108*#1^2 + 324*#1^3 + 18*#1^4 + #1^6 & , (108*Log[x - #1] - 32*Log[x - #1]*#1 + 108*Log[x - #1]*#1^2 - 146*Log[x - #1]*#1^3 + 3*Log[x - #1]*#1^4)/(36*#1 + 162*#1^2 + 12*#1^3 + #1^5) & ]/410184","C",0
154,1,167,682,0.0264099,"\int \frac{x^5}{\left(216+108 x^2+324 x^3+18 x^4+x^6\right)^2} \, dx","Integrate[x^5/(216 + 108*x^2 + 324*x^3 + 18*x^4 + x^6)^2,x]","\frac{\text{RootSum}\left[\text{$\#$1}^6+18 \text{$\#$1}^4+324 \text{$\#$1}^3+108 \text{$\#$1}^2+216\&,\frac{4 \text{$\#$1}^4 \log (x-\text{$\#$1})-54 \text{$\#$1}^3 \log (x-\text{$\#$1})+2043 \text{$\#$1}^2 \log (x-\text{$\#$1})-324 \text{$\#$1} \log (x-\text{$\#$1})+144 \log (x-\text{$\#$1})}{\text{$\#$1}^5+12 \text{$\#$1}^3+162 \text{$\#$1}^2+36 \text{$\#$1}}\&\right]}{3691656}+\frac{4 x^5-27 x^4+729 x^3+648 x^2-144 x+972}{615276 \left(x^6+18 x^4+324 x^3+108 x^2+216\right)}","\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,"(972 - 144*x + 648*x^2 + 729*x^3 - 27*x^4 + 4*x^5)/(615276*(216 + 108*x^2 + 324*x^3 + 18*x^4 + x^6)) + RootSum[216 + 108*#1^2 + 324*#1^3 + 18*#1^4 + #1^6 & , (144*Log[x - #1] - 324*Log[x - #1]*#1 + 2043*Log[x - #1]*#1^2 - 54*Log[x - #1]*#1^3 + 4*Log[x - #1]*#1^4)/(36*#1 + 162*#1^2 + 12*#1^3 + #1^5) & ]/3691656","C",0
155,1,167,850,0.0364137,"\int \frac{x^4}{\left(216+108 x^2+324 x^3+18 x^4+x^6\right)^2} \, dx","Integrate[x^4/(216 + 108*x^2 + 324*x^3 + 18*x^4 + x^6)^2,x]","\frac{-9 x^5+8 x^4-216 x^3-1458 x^2+324 x-288}{1230552 \left(x^6+18 x^4+324 x^3+108 x^2+216\right)}-\frac{\text{RootSum}\left[\text{$\#$1}^6+18 \text{$\#$1}^4+324 \text{$\#$1}^3+108 \text{$\#$1}^2+216\&,\frac{9 \text{$\#$1}^4 \log (x-\text{$\#$1})-16 \text{$\#$1}^3 \log (x-\text{$\#$1})+324 \text{$\#$1}^2 \log (x-\text{$\#$1})-2628 \text{$\#$1} \log (x-\text{$\#$1})+324 \log (x-\text{$\#$1})}{\text{$\#$1}^5+12 \text{$\#$1}^3+162 \text{$\#$1}^2+36 \text{$\#$1}}\&\right]}{7383312}","\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,"(-288 + 324*x - 1458*x^2 - 216*x^3 + 8*x^4 - 9*x^5)/(1230552*(216 + 108*x^2 + 324*x^3 + 18*x^4 + x^6)) - RootSum[216 + 108*#1^2 + 324*#1^3 + 18*#1^4 + #1^6 & , (324*Log[x - #1] - 2628*Log[x - #1]*#1 + 324*Log[x - #1]*#1^2 - 16*Log[x - #1]*#1^3 + 9*Log[x - #1]*#1^4)/(36*#1 + 162*#1^2 + 12*#1^3 + #1^5) & ]/7383312","C",0
156,1,167,873,0.0278079,"\int \frac{x^3}{\left(216+108 x^2+324 x^3+18 x^4+x^6\right)^2} \, dx","Integrate[x^3/(216 + 108*x^2 + 324*x^3 + 18*x^4 + x^6)^2,x]","\frac{\text{RootSum}\left[\text{$\#$1}^6+18 \text{$\#$1}^4+324 \text{$\#$1}^3+108 \text{$\#$1}^2+216\&,\frac{2 \text{$\#$1}^4 \log (x-\text{$\#$1})-27 \text{$\#$1}^3 \log (x-\text{$\#$1})+72 \text{$\#$1}^2 \log (x-\text{$\#$1})-162 \text{$\#$1} \log (x-\text{$\#$1})+1971 \log (x-\text{$\#$1})}{\text{$\#$1}^5+12 \text{$\#$1}^3+162 \text{$\#$1}^2+36 \text{$\#$1}}\&\right]}{11074968}+\frac{4 x^5-27 x^4+96 x^3+648 x^2-3942 x+972}{3691656 \left(x^6+18 x^4+324 x^3+108 x^2+216\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,"(972 - 3942*x + 648*x^2 + 96*x^3 - 27*x^4 + 4*x^5)/(3691656*(216 + 108*x^2 + 324*x^3 + 18*x^4 + x^6)) + RootSum[216 + 108*#1^2 + 324*#1^3 + 18*#1^4 + #1^6 & , (1971*Log[x - #1] - 162*Log[x - #1]*#1 + 72*Log[x - #1]*#1^2 - 27*Log[x - #1]*#1^3 + 2*Log[x - #1]*#1^4)/(36*#1 + 162*#1^2 + 12*#1^3 + #1^5) & ]/11074968","C",0
157,1,167,986,0.0346645,"\int \frac{x^2}{\left(216+108 x^2+324 x^3+18 x^4+x^6\right)^2} \, dx","Integrate[x^2/(216 + 108*x^2 + 324*x^3 + 18*x^4 + x^6)^2,x]","\frac{-9 x^5+8 x^4-216 x^3-2724 x^2+324 x-7884}{7383312 \left(x^6+18 x^4+324 x^3+108 x^2+216\right)}-\frac{\text{RootSum}\left[\text{$\#$1}^6+18 \text{$\#$1}^4+324 \text{$\#$1}^3+108 \text{$\#$1}^2+216\&,\frac{9 \text{$\#$1}^4 \log (x-\text{$\#$1})-16 \text{$\#$1}^3 \log (x-\text{$\#$1})+324 \text{$\#$1}^2 \log (x-\text{$\#$1})+2436 \text{$\#$1} \log (x-\text{$\#$1})+324 \log (x-\text{$\#$1})}{\text{$\#$1}^5+12 \text{$\#$1}^3+162 \text{$\#$1}^2+36 \text{$\#$1}}\&\right]}{44299872}","-\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,"(-7884 + 324*x - 2724*x^2 - 216*x^3 + 8*x^4 - 9*x^5)/(7383312*(216 + 108*x^2 + 324*x^3 + 18*x^4 + x^6)) - RootSum[216 + 108*#1^2 + 324*#1^3 + 18*#1^4 + #1^6 & , (324*Log[x - #1] + 2436*Log[x - #1]*#1 + 324*Log[x - #1]*#1^2 - 16*Log[x - #1]*#1^3 + 9*Log[x - #1]*#1^4)/(36*#1 + 162*#1^2 + 12*#1^3 + #1^5) & ]/44299872","C",0
158,1,25,25,0.001777,"\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","Integrate[(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",1
159,1,79,94,0.0372948,"\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","Integrate[(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{12 \left(a d^2+b c^2\right)^2 \log (c+d x)+b d x \left(12 a d^2 (d x-2 c)+b \left(-12 c^3+6 c^2 d x-4 c d^2 x^2+3 d^3 x^3\right)\right)}{12 d^5}","\frac{\left(a d^2+b c^2\right)^2 \log (c+d x)}{d^5}-\frac{b c x \left(2 a d^2+b c^2\right)}{d^4}+\frac{b x^2 \left(2 a d^2+b c^2\right)}{2 d^3}-\frac{b^2 c x^3}{3 d^2}+\frac{b^2 x^4}{4 d}",1,"(b*d*x*(12*a*d^2*(-2*c + d*x) + b*(-12*c^3 + 6*c^2*d*x - 4*c*d^2*x^2 + 3*d^3*x^3)) + 12*(b*c^2 + a*d^2)^2*Log[c + d*x])/(12*d^5)","A",1
160,1,172,15,0.0055765,"\int (b+2 c x) \left(b x+c x^2\right)^{13} \, dx","Integrate[(b + 2*c*x)*(b*x + c*x^2)^13,x]","\frac{b^{14} x^{14}}{14}+b^{13} c x^{15}+\frac{13}{2} b^{12} c^2 x^{16}+26 b^{11} c^3 x^{17}+\frac{143}{2} b^{10} c^4 x^{18}+143 b^9 c^5 x^{19}+\frac{429}{2} b^8 c^6 x^{20}+\frac{1716}{7} b^7 c^7 x^{21}+\frac{429}{2} b^6 c^8 x^{22}+143 b^5 c^9 x^{23}+\frac{143}{2} b^4 c^{10} x^{24}+26 b^3 c^{11} x^{25}+\frac{13}{2} b^2 c^{12} x^{26}+b c^{13} x^{27}+\frac{c^{14} x^{28}}{14}","\frac{1}{14} \left(b x+c x^2\right)^{14}",1,"(b^14*x^14)/14 + b^13*c*x^15 + (13*b^12*c^2*x^16)/2 + 26*b^11*c^3*x^17 + (143*b^10*c^4*x^18)/2 + 143*b^9*c^5*x^19 + (429*b^8*c^6*x^20)/2 + (1716*b^7*c^7*x^21)/7 + (429*b^6*c^8*x^22)/2 + 143*b^5*c^9*x^23 + (143*b^4*c^10*x^24)/2 + 26*b^3*c^11*x^25 + (13*b^2*c^12*x^26)/2 + b*c^13*x^27 + (c^14*x^28)/14","B",1
161,1,182,16,0.0059096,"\int x^{14} \left(b+2 c x^2\right) \left(b x+c x^3\right)^{13} \, dx","Integrate[x^14*(b + 2*c*x^2)*(b*x + c*x^3)^13,x]","\frac{b^{14} x^{28}}{28}+\frac{1}{2} b^{13} c x^{30}+\frac{13}{4} b^{12} c^2 x^{32}+13 b^{11} c^3 x^{34}+\frac{143}{4} b^{10} c^4 x^{36}+\frac{143}{2} b^9 c^5 x^{38}+\frac{429}{4} b^8 c^6 x^{40}+\frac{858}{7} b^7 c^7 x^{42}+\frac{429}{4} b^6 c^8 x^{44}+\frac{143}{2} b^5 c^9 x^{46}+\frac{143}{4} b^4 c^{10} x^{48}+13 b^3 c^{11} x^{50}+\frac{13}{4} b^2 c^{12} x^{52}+\frac{1}{2} b c^{13} x^{54}+\frac{c^{14} x^{56}}{28}","\frac{1}{28} x^{28} \left(b+c x^2\right)^{14}",1,"(b^14*x^28)/28 + (b^13*c*x^30)/2 + (13*b^12*c^2*x^32)/4 + 13*b^11*c^3*x^34 + (143*b^10*c^4*x^36)/4 + (143*b^9*c^5*x^38)/2 + (429*b^8*c^6*x^40)/4 + (858*b^7*c^7*x^42)/7 + (429*b^6*c^8*x^44)/4 + (143*b^5*c^9*x^46)/2 + (143*b^4*c^10*x^48)/4 + 13*b^3*c^11*x^50 + (13*b^2*c^12*x^52)/4 + (b*c^13*x^54)/2 + (c^14*x^56)/28","B",1
162,1,186,16,0.0061819,"\int x^{28} \left(b+2 c x^3\right) \left(b x+c x^4\right)^{13} \, dx","Integrate[x^28*(b + 2*c*x^3)*(b*x + c*x^4)^13,x]","\frac{b^{14} x^{42}}{42}+\frac{1}{3} b^{13} c x^{45}+\frac{13}{6} b^{12} c^2 x^{48}+\frac{26}{3} b^{11} c^3 x^{51}+\frac{143}{6} b^{10} c^4 x^{54}+\frac{143}{3} b^9 c^5 x^{57}+\frac{143}{2} b^8 c^6 x^{60}+\frac{572}{7} b^7 c^7 x^{63}+\frac{143}{2} b^6 c^8 x^{66}+\frac{143}{3} b^5 c^9 x^{69}+\frac{143}{6} b^4 c^{10} x^{72}+\frac{26}{3} b^3 c^{11} x^{75}+\frac{13}{6} b^2 c^{12} x^{78}+\frac{1}{3} b c^{13} x^{81}+\frac{c^{14} x^{84}}{42}","\frac{1}{42} x^{42} \left(b+c x^3\right)^{14}",1,"(b^14*x^42)/42 + (b^13*c*x^45)/3 + (13*b^12*c^2*x^48)/6 + (26*b^11*c^3*x^51)/3 + (143*b^10*c^4*x^54)/6 + (143*b^9*c^5*x^57)/3 + (143*b^8*c^6*x^60)/2 + (572*b^7*c^7*x^63)/7 + (143*b^6*c^8*x^66)/2 + (143*b^5*c^9*x^69)/3 + (143*b^4*c^10*x^72)/6 + (26*b^3*c^11*x^75)/3 + (13*b^2*c^12*x^78)/6 + (b*c^13*x^81)/3 + (c^14*x^84)/42","B",1
163,1,21,21,0.1176409,"\int x^{14 (-1+n)} \left(b+2 c x^n\right) \left(b x+c x^{1+n}\right)^{13} \, dx","Integrate[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",1
164,1,9,10,0.0039697,"\int \frac{b+2 c x}{b x+c x^2} \, dx","Integrate[(b + 2*c*x)/(b*x + c*x^2),x]","\log (b+c x)+\log (x)","\log \left(b x+c x^2\right)",1,"Log[x] + Log[b + c*x]","A",1
165,1,15,15,0.0055215,"\int \frac{b+2 c x^2}{b x+c x^3} \, dx","Integrate[(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",1
166,1,15,15,0.0053172,"\int \frac{b+2 c x^3}{b x+c x^4} \, dx","Integrate[(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",1
167,1,15,15,0.0112181,"\int \frac{b+2 c x^n}{b x+c x^{1+n}} \, dx","Integrate[(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",1
168,1,14,15,0.0205055,"\int \frac{b+2 c x}{\left(b x+c x^2\right)^8} \, dx","Integrate[(b + 2*c*x)/(b*x + c*x^2)^8,x]","-\frac{1}{7 x^7 (b+c x)^7}","-\frac{1}{7 \left(b x+c x^2\right)^7}",1,"-1/7*1/(x^7*(b + c*x)^7)","A",1
169,1,16,16,0.028786,"\int \frac{b+2 c x^2}{x^7 \left(b x+c x^3\right)^8} \, dx","Integrate[(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*1/(x^14*(b + c*x^2)^7)","A",1
170,1,16,16,0.0358417,"\int \frac{b+2 c x^3}{x^{14} \left(b x+c x^4\right)^8} \, dx","Integrate[(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*1/(x^21*(b + c*x^3)^7)","A",1
171,1,21,21,0.1776517,"\int \frac{x^{-7 (-1+n)} \left(b+2 c x^n\right)}{\left(b x+c x^{1+n}\right)^8} \, dx","Integrate[(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*1/(n*x^(7*n)*(b + c*x^n)^7)","A",1
172,1,17,19,0.0094033,"\int (b+2 c x) \left(b x+c x^2\right)^p \, dx","Integrate[(b + 2*c*x)*(b*x + c*x^2)^p,x]","\frac{(x (b+c x))^{p+1}}{p+1}","\frac{\left(b x+c x^2\right)^{p+1}}{p+1}",1,"(x*(b + c*x))^(1 + p)/(1 + p)","A",1
173,1,97,27,0.0745925,"\int x^{1+p} \left(b+2 c x^2\right) \left(b x+c x^3\right)^p \, dx","Integrate[x^(1 + p)*(b + 2*c*x^2)*(b*x + c*x^3)^p,x]","\frac{x^{p+2} \left(x \left(b+c x^2\right)\right)^p \left(\frac{c x^2}{b}+1\right)^{-p} \left(2 c (p+1) x^2 \, _2F_1\left(-p,p+2;p+3;-\frac{c x^2}{b}\right)+b (p+2) \, _2F_1\left(-p,p+1;p+2;-\frac{c x^2}{b}\right)\right)}{2 (p+1) (p+2)}","\frac{x^{p+1} \left(b x+c x^3\right)^{p+1}}{2 (p+1)}",1,"(x^(2 + p)*(x*(b + c*x^2))^p*(b*(2 + p)*Hypergeometric2F1[-p, 1 + p, 2 + p, -((c*x^2)/b)] + 2*c*(1 + p)*x^2*Hypergeometric2F1[-p, 2 + p, 3 + p, -((c*x^2)/b)]))/(2*(1 + p)*(2 + p)*(1 + (c*x^2)/b)^p)","C",1
174,1,97,27,0.0267487,"\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","Integrate[b*x^(1 + p)*(b*x + c*x^3)^p + 2*c*x^(3 + p)*(b*x + c*x^3)^p,x]","\frac{x^{p+2} \left(x \left(b+c x^2\right)\right)^p \left(\frac{c x^2}{b}+1\right)^{-p} \left(2 c (p+1) x^2 \, _2F_1\left(-p,p+2;p+3;-\frac{c x^2}{b}\right)+b (p+2) \, _2F_1\left(-p,p+1;p+2;-\frac{c x^2}{b}\right)\right)}{2 (p+1) (p+2)}","\frac{x^{p+1} \left(b x+c x^3\right)^{p+1}}{2 (p+1)}",1,"(x^(2 + p)*(x*(b + c*x^2))^p*(b*(2 + p)*Hypergeometric2F1[-p, 1 + p, 2 + p, -((c*x^2)/b)] + 2*c*(1 + p)*x^2*Hypergeometric2F1[-p, 2 + p, 3 + p, -((c*x^2)/b)]))/(2*(1 + p)*(2 + p)*(1 + (c*x^2)/b)^p)","C",1
175,1,99,29,0.077162,"\int x^{2 (1+p)} \left(b+2 c x^3\right) \left(b x+c x^4\right)^p \, dx","Integrate[x^(2*(1 + p))*(b + 2*c*x^3)*(b*x + c*x^4)^p,x]","\frac{x^{2 p+3} \left(x \left(b+c x^3\right)\right)^p \left(\frac{c x^3}{b}+1\right)^{-p} \left(2 c (p+1) x^3 \, _2F_1\left(-p,p+2;p+3;-\frac{c x^3}{b}\right)+b (p+2) \, _2F_1\left(-p,p+1;p+2;-\frac{c x^3}{b}\right)\right)}{3 (p+1) (p+2)}","\frac{x^{2 (p+1)} \left(b x+c x^4\right)^{p+1}}{3 (p+1)}",1,"(x^(3 + 2*p)*(x*(b + c*x^3))^p*(b*(2 + p)*Hypergeometric2F1[-p, 1 + p, 2 + p, -((c*x^3)/b)] + 2*c*(1 + p)*x^3*Hypergeometric2F1[-p, 2 + p, 3 + p, -((c*x^3)/b)]))/(3*(1 + p)*(2 + p)*(1 + (c*x^3)/b)^p)","C",1
176,1,108,36,0.1656295,"\int x^{(-1+n) (1+p)} \left(b+2 c x^n\right) \left(b x+c x^{1+n}\right)^p \, dx","Integrate[x^((-1 + n)*(1 + p))*(b + 2*c*x^n)*(b*x + c*x^(1 + n))^p,x]","\frac{x^{-p} \left(x \left(b+c x^n\right)\right)^p \left(\frac{c x^n}{b}+1\right)^{-p} \left(b (p+2) x^{n (p+1)} \, _2F_1\left(-p,p+1;p+2;-\frac{c x^n}{b}\right)+2 c (p+1) x^{n (p+2)} \, _2F_1\left(-p,p+2;p+3;-\frac{c x^n}{b}\right)\right)}{n (p+1) (p+2)}","\frac{x^{-((1-n) (p+1))} \left(b x+c x^{n+1}\right)^{p+1}}{n (p+1)}",1,"((x*(b + c*x^n))^p*(b*(2 + p)*x^(n*(1 + p))*Hypergeometric2F1[-p, 1 + p, 2 + p, -((c*x^n)/b)] + 2*c*(1 + p)*x^(n*(2 + p))*Hypergeometric2F1[-p, 2 + p, 3 + p, -((c*x^n)/b)]))/(n*(1 + p)*(2 + p)*x^p*(1 + (c*x^n)/b)^p)","C",1
177,1,32,32,0.0018889,"\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","Integrate[(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",1
178,1,12,12,0.000723,"\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","Integrate[(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",1
179,1,42,42,0.0149031,"\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","Integrate[(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",1
180,1,23,25,0.0149371,"\int \left(b+2 c x+3 d x^2\right) \left(a+b x+c x^2+d x^3\right)^n \, dx","Integrate[(b + 2*c*x + 3*d*x^2)*(a + b*x + c*x^2 + d*x^3)^n,x]","\frac{(a+x (b+x (c+d x)))^{n+1}}{n+1}","\frac{\left(a+b x+c x^2+d x^3\right)^{n+1}}{n+1}",1,"(a + x*(b + x*(c + d*x)))^(1 + n)/(1 + n)","A",1
181,1,21,24,0.0473835,"\int \left(b+2 c x+3 d x^2\right) \left(b x+c x^2+d x^3\right)^n \, dx","Integrate[(b + 2*c*x + 3*d*x^2)*(b*x + c*x^2 + d*x^3)^n,x]","\frac{(x (b+x (c+d x)))^{n+1}}{n+1}","\frac{\left(b x+c x^2+d x^3\right)^{n+1}}{n+1}",1,"(x*(b + x*(c + d*x)))^(1 + n)/(1 + n)","A",1
182,1,24,25,0.0220901,"\int x^n \left(b+c x+d x^2\right)^n \left(b+2 c x+3 d x^2\right) \, dx","Integrate[x^n*(b + c*x + d*x^2)^n*(b + 2*c*x + 3*d*x^2),x]","\frac{x^{n+1} (b+x (c+d x))^{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 + x*(c + d*x))^(1 + n))/(1 + n)","A",1
183,1,20,20,0.0083721,"\int \left(b+3 d x^2\right) \left(a+b x+d x^3\right)^n \, dx","Integrate[(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
184,1,106,19,0.0658047,"\int \left(b+3 d x^2\right) \left(b x+d x^3\right)^n \, dx","Integrate[(b + 3*d*x^2)*(b*x + d*x^3)^n,x]","\frac{x \left(x \left(b+d x^2\right)\right)^n \left(\frac{d x^2}{b}+1\right)^{-n} \left(3 d (n+1) x^2 \, _2F_1\left(-n,\frac{n+3}{2};\frac{n+5}{2};-\frac{d x^2}{b}\right)+b (n+3) \, _2F_1\left(-n,\frac{n+1}{2};\frac{n+3}{2};-\frac{d x^2}{b}\right)\right)}{(n+1) (n+3)}","\frac{\left(b x+d x^3\right)^{n+1}}{n+1}",1,"(x*(x*(b + d*x^2))^n*(b*(3 + n)*Hypergeometric2F1[-n, (1 + n)/2, (3 + n)/2, -((d*x^2)/b)] + 3*d*(1 + n)*x^2*Hypergeometric2F1[-n, (3 + n)/2, (5 + n)/2, -((d*x^2)/b)]))/((1 + n)*(3 + n)*(1 + (d*x^2)/b)^n)","C",1
185,1,108,22,0.0355207,"\int x^n \left(b+d x^2\right)^n \left(b+3 d x^2\right) \, dx","Integrate[x^n*(b + d*x^2)^n*(b + 3*d*x^2),x]","\frac{x^{n+1} \left(b+d x^2\right)^n \left(\frac{d x^2}{b}+1\right)^{-n} \left(3 d (n+1) x^2 \, _2F_1\left(-n,\frac{n+3}{2};\frac{n+5}{2};-\frac{d x^2}{b}\right)+b (n+3) \, _2F_1\left(-n,\frac{n+1}{2};\frac{n+3}{2};-\frac{d x^2}{b}\right)\right)}{(n+1) (n+3)}","\frac{x^{n+1} \left(b+d x^2\right)^{n+1}}{n+1}",1,"(x^(1 + n)*(b + d*x^2)^n*(b*(3 + n)*Hypergeometric2F1[-n, (1 + n)/2, (3 + n)/2, -((d*x^2)/b)] + 3*d*(1 + n)*x^2*Hypergeometric2F1[-n, (3 + n)/2, (5 + n)/2, -((d*x^2)/b)]))/((1 + n)*(3 + n)*(1 + (d*x^2)/b)^n)","C",1
186,1,21,22,0.0118679,"\int \left(2 c x+3 d x^2\right) \left(a+c x^2+d x^3\right)^n \, dx","Integrate[(2*c*x + 3*d*x^2)*(a + c*x^2 + d*x^3)^n,x]","\frac{\left(a+x^2 (c+d x)\right)^{n+1}}{n+1}","\frac{\left(a+c x^2+d x^3\right)^{n+1}}{n+1}",1,"(a + x^2*(c + d*x))^(1 + n)/(1 + n)","A",1
187,1,19,21,0.0111748,"\int \left(2 c x+3 d x^2\right) \left(c x^2+d x^3\right)^n \, dx","Integrate[(2*c*x + 3*d*x^2)*(c*x^2 + d*x^3)^n,x]","\frac{\left(x^2 (c+d x)\right)^{n+1}}{n+1}","\frac{\left(c x^2+d x^3\right)^{n+1}}{n+1}",1,"(x^2*(c + d*x))^(1 + n)/(1 + n)","A",1
188,1,22,24,0.0135573,"\int x^n \left(c x+d x^2\right)^n \left(2 c x+3 d x^2\right) \, dx","Integrate[x^n*(c*x + d*x^2)^n*(2*c*x + 3*d*x^2),x]","\frac{x^{n+1} (x (c+d x))^{n+1}}{n+1}","\frac{x^{n+1} \left(c x+d x^2\right)^{n+1}}{n+1}",1,"(x^(1 + n)*(x*(c + d*x))^(1 + n))/(1 + n)","A",1
189,1,22,22,0.0104349,"\int x^{2 n} (c+d x)^n \left(2 c x+3 d x^2\right) \, dx","Integrate[x^(2*n)*(c + d*x)^n*(2*c*x + 3*d*x^2),x]","\frac{x^{2 n+2} (c+d x)^{n+1}}{n+1}","\frac{x^{2 (n+1)} (c+d x)^{n+1}}{n+1}",1,"(x^(2 + 2*n)*(c + d*x)^(1 + n))/(1 + n)","A",1
190,1,21,22,0.0061229,"\int x (2 c+3 d x) \left(a+c x^2+d x^3\right)^n \, dx","Integrate[x*(2*c + 3*d*x)*(a + c*x^2 + d*x^3)^n,x]","\frac{\left(a+x^2 (c+d x)\right)^{n+1}}{n+1}","\frac{\left(a+c x^2+d x^3\right)^{n+1}}{n+1}",1,"(a + x^2*(c + d*x))^(1 + n)/(1 + n)","A",1
191,1,19,21,0.0048022,"\int x (2 c+3 d x) \left(c x^2+d x^3\right)^n \, dx","Integrate[x*(2*c + 3*d*x)*(c*x^2 + d*x^3)^n,x]","\frac{\left(x^2 (c+d x)\right)^{n+1}}{n+1}","\frac{\left(c x^2+d x^3\right)^{n+1}}{n+1}",1,"(x^2*(c + d*x))^(1 + n)/(1 + n)","A",1
192,1,143,21,0.1507741,"\int \left(b+2 c x+3 d x^2\right) \left(a+b x+c x^2+d x^3\right)^7 \, dx","Integrate[(b + 2*c*x + 3*d*x^2)*(a + b*x + c*x^2 + d*x^3)^7,x]","\frac{1}{8} x (b+x (c+d x)) \left(8 a^7+28 a^6 x (b+x (c+d x))+56 a^5 x^2 (b+x (c+d x))^2+70 a^4 x^3 (b+x (c+d x))^3+56 a^3 x^4 (b+x (c+d x))^4+28 a^2 x^5 (b+x (c+d x))^5+8 a x^6 (b+x (c+d x))^6+x^7 (b+x (c+d x))^7\right)","\frac{1}{8} \left(a+b x+c x^2+d x^3\right)^8",1,"(x*(b + x*(c + d*x))*(8*a^7 + 28*a^6*x*(b + x*(c + d*x)) + 56*a^5*x^2*(b + x*(c + d*x))^2 + 70*a^4*x^3*(b + x*(c + d*x))^3 + 56*a^3*x^4*(b + x*(c + d*x))^4 + 28*a^2*x^5*(b + x*(c + d*x))^5 + 8*a*x^6*(b + x*(c + d*x))^6 + x^7*(b + x*(c + d*x))^7))/8","B",1
193,1,18,20,0.0363249,"\int \left(b+2 c x+3 d x^2\right) \left(b x+c x^2+d x^3\right)^7 \, dx","Integrate[(b + 2*c*x + 3*d*x^2)*(b*x + c*x^2 + d*x^3)^7,x]","\frac{1}{8} x^8 (b+x (c+d x))^8","\frac{1}{8} \left(b x+c x^2+d x^3\right)^8",1,"(x^8*(b + x*(c + d*x))^8)/8","A",1
194,1,18,19,0.016909,"\int x^7 \left(b+c x+d x^2\right)^7 \left(b+2 c x+3 d x^2\right) \, dx","Integrate[x^7*(b + c*x + d*x^2)^7*(b + 2*c*x + 3*d*x^2),x]","\frac{1}{8} x^8 (b+x (c+d x))^8","\frac{1}{8} x^8 \left(b+c x+d x^2\right)^8",1,"(x^8*(b + x*(c + d*x))^8)/8","A",1
195,1,127,16,0.055793,"\int \left(b+3 d x^2\right) \left(a+b x+d x^3\right)^7 \, dx","Integrate[(b + 3*d*x^2)*(a + b*x + d*x^3)^7,x]","\frac{1}{8} x \left(b+d x^2\right) \left(8 a^7+28 a^6 x \left(b+d x^2\right)+56 a^5 x^2 \left(b+d x^2\right)^2+70 a^4 x^3 \left(b+d x^2\right)^3+56 a^3 x^4 \left(b+d x^2\right)^4+28 a^2 x^5 \left(b+d x^2\right)^5+8 a x^6 \left(b+d x^2\right)^6+x^7 \left(b+d x^2\right)^7\right)","\frac{1}{8} \left(a+b x+d x^3\right)^8",1,"(x*(b + d*x^2)*(8*a^7 + 28*a^6*x*(b + d*x^2) + 56*a^5*x^2*(b + d*x^2)^2 + 70*a^4*x^3*(b + d*x^2)^3 + 56*a^3*x^4*(b + d*x^2)^4 + 28*a^2*x^5*(b + d*x^2)^5 + 8*a*x^6*(b + d*x^2)^6 + x^7*(b + d*x^2)^7))/8","B",1
196,1,98,15,0.0033045,"\int \left(b+3 d x^2\right) \left(b x+d x^3\right)^7 \, dx","Integrate[(b + 3*d*x^2)*(b*x + d*x^3)^7,x]","\frac{b^8 x^8}{8}+b^7 d x^{10}+\frac{7}{2} b^6 d^2 x^{12}+7 b^5 d^3 x^{14}+\frac{35}{4} b^4 d^4 x^{16}+7 b^3 d^5 x^{18}+\frac{7}{2} b^2 d^6 x^{20}+b d^7 x^{22}+\frac{d^8 x^{24}}{8}","\frac{1}{8} \left(b x+d x^3\right)^8",1,"(b^8*x^8)/8 + b^7*d*x^10 + (7*b^6*d^2*x^12)/2 + 7*b^5*d^3*x^14 + (35*b^4*d^4*x^16)/4 + 7*b^3*d^5*x^18 + (7*b^2*d^6*x^20)/2 + b*d^7*x^22 + (d^8*x^24)/8","B",1
197,1,98,16,0.0025133,"\int x^7 \left(b+d x^2\right)^7 \left(b+3 d x^2\right) \, dx","Integrate[x^7*(b + d*x^2)^7*(b + 3*d*x^2),x]","\frac{b^8 x^8}{8}+b^7 d x^{10}+\frac{7}{2} b^6 d^2 x^{12}+7 b^5 d^3 x^{14}+\frac{35}{4} b^4 d^4 x^{16}+7 b^3 d^5 x^{18}+\frac{7}{2} b^2 d^6 x^{20}+b d^7 x^{22}+\frac{d^8 x^{24}}{8}","\frac{1}{8} x^8 \left(b+d x^2\right)^8",1,"(b^8*x^8)/8 + b^7*d*x^10 + (7*b^6*d^2*x^12)/2 + 7*b^5*d^3*x^14 + (35*b^4*d^4*x^16)/4 + 7*b^3*d^5*x^18 + (7*b^2*d^6*x^20)/2 + b*d^7*x^22 + (d^8*x^24)/8","B",1
198,1,115,18,0.0528345,"\int \left(2 c x+3 d x^2\right) \left(a+c x^2+d x^3\right)^7 \, dx","Integrate[(2*c*x + 3*d*x^2)*(a + c*x^2 + d*x^3)^7,x]","\frac{1}{8} x^2 (c+d x) \left(8 a^7+28 a^6 x^2 (c+d x)+56 a^5 x^4 (c+d x)^2+70 a^4 x^6 (c+d x)^3+56 a^3 x^8 (c+d x)^4+28 a^2 x^{10} (c+d x)^5+8 a x^{12} (c+d x)^6+x^{14} (c+d x)^7\right)","\frac{1}{8} \left(a+c x^2+d x^3\right)^8",1,"(x^2*(c + d*x)*(8*a^7 + 28*a^6*x^2*(c + d*x) + 56*a^5*x^4*(c + d*x)^2 + 70*a^4*x^6*(c + d*x)^3 + 56*a^3*x^8*(c + d*x)^4 + 28*a^2*x^10*(c + d*x)^5 + 8*a*x^12*(c + d*x)^6 + x^14*(c + d*x)^7))/8","B",1
199,1,98,17,0.0032699,"\int \left(2 c x+3 d x^2\right) \left(c x^2+d x^3\right)^7 \, dx","Integrate[(2*c*x + 3*d*x^2)*(c*x^2 + d*x^3)^7,x]","\frac{c^8 x^{16}}{8}+c^7 d x^{17}+\frac{7}{2} c^6 d^2 x^{18}+7 c^5 d^3 x^{19}+\frac{35}{4} c^4 d^4 x^{20}+7 c^3 d^5 x^{21}+\frac{7}{2} c^2 d^6 x^{22}+c d^7 x^{23}+\frac{d^8 x^{24}}{8}","\frac{1}{8} \left(c x^2+d x^3\right)^8",1,"(c^8*x^16)/8 + c^7*d*x^17 + (7*c^6*d^2*x^18)/2 + 7*c^5*d^3*x^19 + (35*c^4*d^4*x^20)/4 + 7*c^3*d^5*x^21 + (7*c^2*d^6*x^22)/2 + c*d^7*x^23 + (d^8*x^24)/8","B",1
200,1,98,14,0.0028831,"\int x^7 \left(c x+d x^2\right)^7 \left(2 c x+3 d x^2\right) \, dx","Integrate[x^7*(c*x + d*x^2)^7*(2*c*x + 3*d*x^2),x]","\frac{c^8 x^{16}}{8}+c^7 d x^{17}+\frac{7}{2} c^6 d^2 x^{18}+7 c^5 d^3 x^{19}+\frac{35}{4} c^4 d^4 x^{20}+7 c^3 d^5 x^{21}+\frac{7}{2} c^2 d^6 x^{22}+c d^7 x^{23}+\frac{d^8 x^{24}}{8}","\frac{1}{8} x^{16} (c+d x)^8",1,"(c^8*x^16)/8 + c^7*d*x^17 + (7*c^6*d^2*x^18)/2 + 7*c^5*d^3*x^19 + (35*c^4*d^4*x^20)/4 + 7*c^3*d^5*x^21 + (7*c^2*d^6*x^22)/2 + c*d^7*x^23 + (d^8*x^24)/8","B",1
201,1,98,14,0.0027373,"\int x^{14} (c+d x)^7 \left(2 c x+3 d x^2\right) \, dx","Integrate[x^14*(c + d*x)^7*(2*c*x + 3*d*x^2),x]","\frac{c^8 x^{16}}{8}+c^7 d x^{17}+\frac{7}{2} c^6 d^2 x^{18}+7 c^5 d^3 x^{19}+\frac{35}{4} c^4 d^4 x^{20}+7 c^3 d^5 x^{21}+\frac{7}{2} c^2 d^6 x^{22}+c d^7 x^{23}+\frac{d^8 x^{24}}{8}","\frac{1}{8} x^{16} (c+d x)^8",1,"(c^8*x^16)/8 + c^7*d*x^17 + (7*c^6*d^2*x^18)/2 + 7*c^5*d^3*x^19 + (35*c^4*d^4*x^20)/4 + 7*c^3*d^5*x^21 + (7*c^2*d^6*x^22)/2 + c*d^7*x^23 + (d^8*x^24)/8","B",1
202,1,115,18,0.0112737,"\int x (2 c+3 d x) \left(a+c x^2+d x^3\right)^7 \, dx","Integrate[x*(2*c + 3*d*x)*(a + c*x^2 + d*x^3)^7,x]","\frac{1}{8} x^2 (c+d x) \left(8 a^7+28 a^6 x^2 (c+d x)+56 a^5 x^4 (c+d x)^2+70 a^4 x^6 (c+d x)^3+56 a^3 x^8 (c+d x)^4+28 a^2 x^{10} (c+d x)^5+8 a x^{12} (c+d x)^6+x^{14} (c+d x)^7\right)","\frac{1}{8} \left(a+c x^2+d x^3\right)^8",1,"(x^2*(c + d*x)*(8*a^7 + 28*a^6*x^2*(c + d*x) + 56*a^5*x^4*(c + d*x)^2 + 70*a^4*x^6*(c + d*x)^3 + 56*a^3*x^8*(c + d*x)^4 + 28*a^2*x^10*(c + d*x)^5 + 8*a*x^12*(c + d*x)^6 + x^14*(c + d*x)^7))/8","B",1
203,1,98,14,0.0027637,"\int x (2 c+3 d x) \left(c x^2+d x^3\right)^7 \, dx","Integrate[x*(2*c + 3*d*x)*(c*x^2 + d*x^3)^7,x]","\frac{c^8 x^{16}}{8}+c^7 d x^{17}+\frac{7}{2} c^6 d^2 x^{18}+7 c^5 d^3 x^{19}+\frac{35}{4} c^4 d^4 x^{20}+7 c^3 d^5 x^{21}+\frac{7}{2} c^2 d^6 x^{22}+c d^7 x^{23}+\frac{d^8 x^{24}}{8}","\frac{1}{8} x^{16} (c+d x)^8",1,"(c^8*x^16)/8 + c^7*d*x^17 + (7*c^6*d^2*x^18)/2 + 7*c^5*d^3*x^19 + (35*c^4*d^4*x^20)/4 + 7*c^3*d^5*x^21 + (7*c^2*d^6*x^22)/2 + c*d^7*x^23 + (d^8*x^24)/8","B",1
204,1,98,18,0.0026708,"\int x^8 (2 c+3 d x) \left(c x+d x^2\right)^7 \, dx","Integrate[x^8*(2*c + 3*d*x)*(c*x + d*x^2)^7,x]","\frac{c^8 x^{16}}{8}+c^7 d x^{17}+\frac{7}{2} c^6 d^2 x^{18}+7 c^5 d^3 x^{19}+\frac{35}{4} c^4 d^4 x^{20}+7 c^3 d^5 x^{21}+\frac{7}{2} c^2 d^6 x^{22}+c d^7 x^{23}+\frac{d^8 x^{24}}{8}","\frac{1}{8} x^8 \left(c x+d x^2\right)^8",1,"(c^8*x^16)/8 + c^7*d*x^17 + (7*c^6*d^2*x^18)/2 + 7*c^5*d^3*x^19 + (35*c^4*d^4*x^20)/4 + 7*c^3*d^5*x^21 + (7*c^2*d^6*x^22)/2 + c*d^7*x^23 + (d^8*x^24)/8","B",1
205,1,98,14,0.0024594,"\int x^{15} (c+d x)^7 (2 c+3 d x) \, dx","Integrate[x^15*(c + d*x)^7*(2*c + 3*d*x),x]","\frac{c^8 x^{16}}{8}+c^7 d x^{17}+\frac{7}{2} c^6 d^2 x^{18}+7 c^5 d^3 x^{19}+\frac{35}{4} c^4 d^4 x^{20}+7 c^3 d^5 x^{21}+\frac{7}{2} c^2 d^6 x^{22}+c d^7 x^{23}+\frac{d^8 x^{24}}{8}","\frac{1}{8} x^{16} (c+d x)^8",1,"(c^8*x^16)/8 + c^7*d*x^17 + (7*c^6*d^2*x^18)/2 + 7*c^5*d^3*x^19 + (35*c^4*d^4*x^20)/4 + 7*c^3*d^5*x^21 + (7*c^2*d^6*x^22)/2 + c*d^7*x^23 + (d^8*x^24)/8","B",1
206,1,80,28,0.0054508,"\int (a+b x) \left(1+\left(a x+\frac{b x^2}{2}\right)^4\right) \, dx","Integrate[(a + b*x)*(1 + (a*x + (b*x^2)/2)^4),x]","\frac{a^5 x^5}{5}+\frac{1}{2} a^4 b x^6+\frac{1}{2} a^3 b^2 x^7+\frac{1}{4} a^2 b^3 x^8+\frac{1}{16} a b^4 x^9+a x+\frac{b^5 x^{10}}{160}+\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 + (a^5*x^5)/5 + (a^4*b*x^6)/2 + (a^3*b^2*x^7)/2 + (a^2*b^3*x^8)/4 + (a*b^4*x^9)/16 + (b^5*x^10)/160","B",1
207,1,108,31,0.0353218,"\int (a+b x) \left(1+\left(c+a x+\frac{b x^2}{2}\right)^4\right) \, dx","Integrate[(a + b*x)*(1 + (c + a*x + (b*x^2)/2)^4),x]","\frac{1}{160} x (2 a+b x) \left(16 a^4 x^4+32 a^3 b x^5+24 a^2 b^2 x^6+8 a b^3 x^7+80 c^3 x (2 a+b x)+40 c^2 x^2 (2 a+b x)^2+10 c x^3 (2 a+b x)^3+b^4 x^8+80 c^4+80\right)","\frac{1}{5} \left(a x+\frac{b x^2}{2}+c\right)^5+a x+\frac{b x^2}{2}",1,"(x*(2*a + b*x)*(80 + 80*c^4 + 16*a^4*x^4 + 32*a^3*b*x^5 + 24*a^2*b^2*x^6 + 8*a*b^3*x^7 + b^4*x^8 + 80*c^3*x*(2*a + b*x) + 40*c^2*x^2*(2*a + b*x)^2 + 10*c*x^3*(2*a + b*x)^3))/160","B",1
208,1,34,34,0.0592345,"\int (a+b x) \left(1+\left(a x+\frac{b x^2}{2}\right)^n\right) \, dx","Integrate[(a + b*x)*(1 + (a*x + (b*x^2)/2)^n),x]","\frac{x (2 a+b x) \left(\left(a x+\frac{b x^2}{2}\right)^n+n+1\right)}{2 (n+1)}","\frac{\left(a x+\frac{b x^2}{2}\right)^{n+1}}{n+1}+a x+\frac{b x^2}{2}",1,"(x*(2*a + b*x)*(1 + n + (a*x + (b*x^2)/2)^n))/(2*(1 + n))","A",1
209,1,35,35,0.0555947,"\int (a+b x) \left(1+\left(c+a x+\frac{b x^2}{2}\right)^n\right) \, dx","Integrate[(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",1
210,1,93,30,0.006364,"\int \left(a+c x^2\right) \left(1+\left(a x+\frac{c x^3}{3}\right)^5\right) \, dx","Integrate[(a + c*x^2)*(1 + (a*x + (c*x^3)/3)^5),x]","\frac{a^6 x^6}{6}+\frac{1}{3} a^5 c x^8+\frac{5}{18} a^4 c^2 x^{10}+\frac{10}{81} a^3 c^3 x^{12}+\frac{5}{162} a^2 c^4 x^{14}+\frac{1}{243} a c^5 x^{16}+a x+\frac{c^6 x^{18}}{4374}+\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^6*x^6)/6 + (a^5*c*x^8)/3 + (5*a^4*c^2*x^10)/18 + (10*a^3*c^3*x^12)/81 + (5*a^2*c^4*x^14)/162 + (a*c^5*x^16)/243 + (c^6*x^18)/4374","B",1
211,1,140,31,0.0457064,"\int \left(a+c x^2\right) \left(1+\left(d+a x+\frac{c x^3}{3}\right)^5\right) \, dx","Integrate[(a + c*x^2)*(1 + (d + a*x + (c*x^3)/3)^5),x]","\frac{x \left(3 a+c x^2\right) \left(243 a^5 x^5+405 a^4 c x^7+270 a^3 c^2 x^9+90 a^2 c^3 x^{11}+15 a c^4 x^{13}+1215 d^4 \left(3 a x+c x^3\right)+540 d^3 \left(3 a x+c x^3\right)^2+135 d^2 \left(3 a x+c x^3\right)^3+18 d \left(3 a x+c x^3\right)^4+c^5 x^{15}+1458 d^5+1458\right)}{4374}","\frac{1}{6} \left(a x+\frac{c x^3}{3}+d\right)^6+a x+\frac{c x^3}{3}",1,"(x*(3*a + c*x^2)*(1458 + 1458*d^5 + 243*a^5*x^5 + 405*a^4*c*x^7 + 270*a^3*c^2*x^9 + 90*a^2*c^3*x^11 + 15*a*c^4*x^13 + c^5*x^15 + 1215*d^4*(3*a*x + c*x^3) + 540*d^3*(3*a*x + c*x^3)^2 + 135*d^2*(3*a*x + c*x^3)^3 + 18*d*(3*a*x + c*x^3)^4))/4374","B",1
212,1,98,34,0.0077506,"\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","Integrate[(b*x + c*x^2)*(1 + ((b*x^2)/2 + (c*x^3)/3)^5),x]","\frac{b^6 x^{12}}{384}+\frac{1}{96} b^5 c x^{13}+\frac{5}{288} b^4 c^2 x^{14}+\frac{5}{324} b^3 c^3 x^{15}+\frac{5}{648} b^2 c^4 x^{16}+\frac{1}{486} b c^5 x^{17}+\frac{b x^2}{2}+\frac{c^6 x^{18}}{4374}+\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 + (b^6*x^12)/384 + (b^5*c*x^13)/96 + (5*b^4*c^2*x^14)/288 + (5*b^3*c^3*x^15)/324 + (5*b^2*c^4*x^16)/648 + (b*c^5*x^17)/486 + (c^6*x^18)/4374","B",1
213,1,146,41,0.0505921,"\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","Integrate[(b*x + c*x^2)*(1 + (d + (b*x^2)/2 + (c*x^3)/3)^5),x]","\frac{x^2 (3 b+2 c x) \left(243 b^5 x^{10}+810 b^4 c x^{11}+1080 b^3 c^2 x^{12}+720 b^2 c^3 x^{13}+240 b c^4 x^{14}+19440 d^4 x^2 (3 b+2 c x)+4320 d^3 x^4 (3 b+2 c x)^2+540 d^2 x^6 (3 b+2 c x)^3+36 d x^8 (3 b+2 c x)^4+32 c^5 x^{15}+46656 d^5+46656\right)}{279936}","\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,"(x^2*(3*b + 2*c*x)*(46656 + 46656*d^5 + 243*b^5*x^10 + 810*b^4*c*x^11 + 1080*b^3*c^2*x^12 + 720*b^2*c^3*x^13 + 240*b*c^4*x^14 + 32*c^5*x^15 + 19440*d^4*x^2*(3*b + 2*c*x) + 4320*d^3*x^4*(3*b + 2*c*x)^2 + 540*d^2*x^6*(3*b + 2*c*x)^3 + 36*d*x^8*(3*b + 2*c*x)^4))/279936","B",1
214,1,244,46,0.0629398,"\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","Integrate[(a + b*x + c*x^2)*(1 + (a*x + (b*x^2)/2 + (c*x^3)/3)^5),x]","\frac{a^6 x^6}{6}+\frac{1}{6} a^5 x^7 (3 b+2 c x)+\frac{5}{72} a^4 x^8 (3 b+2 c x)^2+\frac{5}{324} a^3 x^9 (3 b+2 c x)^3+\frac{5 a^2 x^{10} (3 b+2 c x)^4}{2592}+a \left(\frac{b^5 x^{11}}{32}+\frac{5}{48} b^4 c x^{12}+\frac{5}{36} b^3 c^2 x^{13}+\frac{5}{54} b^2 c^3 x^{14}+\frac{5}{162} b c^4 x^{15}+\frac{c^5 x^{16}}{243}+x\right)+\frac{x^2 \left(729 b^6 x^{10}+2916 b^5 c x^{11}+4860 b^4 c^2 x^{12}+4320 b^3 c^3 x^{13}+2160 b^2 c^4 x^{14}+576 b \left(c^5 x^{15}+243\right)+64 c x \left(c^5 x^{15}+1458\right)\right)}{279936}","\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^6*x^6)/6 + (a^5*x^7*(3*b + 2*c*x))/6 + (5*a^4*x^8*(3*b + 2*c*x)^2)/72 + (5*a^3*x^9*(3*b + 2*c*x)^3)/324 + (5*a^2*x^10*(3*b + 2*c*x)^4)/2592 + a*(x + (b^5*x^11)/32 + (5*b^4*c*x^12)/48 + (5*b^3*c^2*x^13)/36 + (5*b^2*c^3*x^14)/54 + (5*b*c^4*x^15)/162 + (c^5*x^16)/243) + (x^2*(729*b^6*x^10 + 2916*b^5*c*x^11 + 4860*b^4*c^2*x^12 + 4320*b^3*c^3*x^13 + 2160*b^2*c^4*x^14 + 576*b*(243 + c^5*x^15) + 64*c*x*(1458 + c^5*x^15)))/279936","B",1
215,1,248,47,0.123029,"\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","Integrate[(a + b*x + c*x^2)*(1 + (d + a*x + (b*x^2)/2 + (c*x^3)/3)^5),x]","\frac{x (6 a+x (3 b+2 c x)) \left(7776 a^5 x^5+6480 a^4 x^6 (3 b+2 c x)+2160 a^3 x^7 (3 b+2 c x)^2+360 a^2 x^8 (3 b+2 c x)^3+19440 d^4 x (6 a+x (3 b+2 c x))+4320 d^3 x^2 (6 a+x (3 b+2 c x))^2+540 d^2 x^3 (6 a+x (3 b+2 c x))^3+36 d x^4 (6 a+x (3 b+2 c x))^4+30 a x^9 (3 b+2 c x)^4+243 b^5 x^{10}+810 b^4 c x^{11}+1080 b^3 c^2 x^{12}+720 b^2 c^3 x^{13}+240 b c^4 x^{14}+32 c^5 x^{15}+46656 d^5+46656\right)}{279936}","\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,"(x*(6*a + x*(3*b + 2*c*x))*(46656 + 46656*d^5 + 7776*a^5*x^5 + 243*b^5*x^10 + 810*b^4*c*x^11 + 1080*b^3*c^2*x^12 + 720*b^2*c^3*x^13 + 240*b*c^4*x^14 + 32*c^5*x^15 + 6480*a^4*x^6*(3*b + 2*c*x) + 2160*a^3*x^7*(3*b + 2*c*x)^2 + 360*a^2*x^8*(3*b + 2*c*x)^3 + 30*a*x^9*(3*b + 2*c*x)^4 + 19440*d^4*x*(6*a + x*(3*b + 2*c*x)) + 4320*d^3*x^2*(6*a + x*(3*b + 2*c*x))^2 + 540*d^2*x^3*(6*a + x*(3*b + 2*c*x))^3 + 36*d*x^4*(6*a + x*(3*b + 2*c*x))^4))/279936","B",1
216,1,36,34,0.0681868,"\int \left(a+c x^2\right) \left(1+\left(a x+\frac{c x^3}{3}\right)^n\right) \, dx","Integrate[(a + c*x^2)*(1 + (a*x + (c*x^3)/3)^n),x]","\frac{x \left(3 a+c x^2\right) \left(\left(a x+\frac{c x^3}{3}\right)^n+n+1\right)}{3 (n+1)}","\frac{\left(a x+\frac{c x^3}{3}\right)^{n+1}}{n+1}+a x+\frac{c x^3}{3}",1,"(x*(3*a + c*x^2)*(1 + n + (a*x + (c*x^3)/3)^n))/(3*(1 + n))","A",1
217,1,42,44,0.086482,"\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","Integrate[(b*x + c*x^2)*(1 + ((b*x^2)/2 + (c*x^3)/3)^n),x]","\frac{x^2 (3 b+2 c x) \left(\left(\frac{b x^2}{2}+\frac{c x^3}{3}\right)^n+n+1\right)}{6 (n+1)}","\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,"(x^2*(3*b + 2*c*x)*(1 + n + ((b*x^2)/2 + (c*x^3)/3)^n))/(6*(1 + n))","A",1
218,1,49,50,0.1927716,"\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","Integrate[(a + b*x + c*x^2)*(1 + (a*x + (b*x^2)/2 + (c*x^3)/3)^n),x]","\frac{x (6 a+x (3 b+2 c x)) \left(\left(a x+\frac{b x^2}{2}+\frac{c x^3}{3}\right)^n+n+1\right)}{6 (n+1)}","\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,"(x*(6*a + x*(3*b + 2*c*x))*(1 + n + (a*x + (b*x^2)/2 + (c*x^3)/3)^n))/(6*(1 + n))","A",1
219,1,33,19,0.0017629,"\int \left(-4+4 x+x^2\right) \left(5-12 x+6 x^2+x^3\right) \, dx","Integrate[(-4 + 4*x + x^2)*(5 - 12*x + 6*x^2 + x^3),x]","\frac{x^6}{6}+2 x^5+2 x^4-\frac{67 x^3}{3}+34 x^2-20 x","\frac{1}{6} \left(x^3+6 x^2-12 x+5\right)^2",1,"-20*x + 34*x^2 - (67*x^3)/3 + 2*x^4 + 2*x^5 + x^6/6","A",1
220,1,21,16,0.0015953,"\int \left(2 x+x^3\right) \left(1+4 x^2+x^4\right) \, dx","Integrate[(2*x + x^3)*(1 + 4*x^2 + x^4),x]","\frac{x^8}{8}+x^6+\frac{9 x^4}{4}+x^2","\frac{1}{8} \left(x^4+4 x^2+1\right)^2",1,"x^2 + (9*x^4)/4 + x^6 + x^8/8","A",1
221,1,96,33,0.0061938,"\int (1+2 x) \left(x+x^2\right)^3 \left(-18+7 \left(x+x^2\right)^3\right)^2 \, dx","Integrate[(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",1
222,1,96,33,0.004945,"\int x^3 (1+x)^3 (1+2 x) \left(-18+7 x^3 (1+x)^3\right)^2 \, dx","Integrate[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",1
223,1,14,14,0.0055517,"\int \frac{2-x^2}{\left(1-6 x+x^3\right)^5} \, dx","Integrate[(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
224,1,15,15,0.0044811,"\int \frac{2 x+x^2}{4+3 x^2+x^3} \, dx","Integrate[(2*x + x^2)/(4 + 3*x^2 + x^3),x]","\frac{1}{3} \log \left(x^3+3 x^2+4\right)","\frac{1}{3} \log \left(x^3+3 x^2+4\right)",1,"Log[4 + 3*x^2 + x^3]/3","A",1
225,1,20,17,0.0055412,"\int \frac{1+x+x^3}{4 x+2 x^2+x^4} \, dx","Integrate[(1 + x + x^3)/(4*x + 2*x^2 + x^4),x]","\frac{1}{4} \log \left(x^3+2 x+4\right)+\frac{\log (x)}{4}","\frac{1}{4} \log \left(x^4+2 x^2+4 x\right)",1,"Log[x]/4 + Log[4 + 2*x + x^3]/4","A",1
226,1,23,40,0.0594587,"\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","Integrate[(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+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 + b*x)/(c + d*x + e*x^2 + f*x^3)","A",1
227,1,98,605,0.0693137,"\int \frac{A+B x+C x^2+D x^3}{a+b x+c x^2+b x^3+a x^4} \, dx","Integrate[(A + B*x + C*x^2 + D*x^3)/(a + b*x + c*x^2 + b*x^3 + a*x^4),x]","\text{RootSum}\left[\text{$\#$1}^4 a+\text{$\#$1}^3 b+\text{$\#$1}^2 c+\text{$\#$1} b+a\&,\frac{\text{$\#$1}^3 D \log (x-\text{$\#$1})+\text{$\#$1}^2 C \log (x-\text{$\#$1})+A \log (x-\text{$\#$1})+\text{$\#$1} B \log (x-\text{$\#$1})}{4 \text{$\#$1}^3 a+3 \text{$\#$1}^2 b+2 \text{$\#$1} c+b}\&\right]","\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,"RootSum[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , (A*Log[x - #1] + B*Log[x - #1]*#1 + C*Log[x - #1]*#1^2 + D*Log[x - #1]*#1^3)/(b + 2*c*#1 + 3*b*#1^2 + 4*a*#1^3) & ]","C",1
228,1,55,63,0.0286527,"\int \frac{2+x-4 x^2+2 x^3}{1-x+x^2-x^3+x^4} \, dx","Integrate[(2 + x - 4*x^2 + 2*x^3)/(1 - x + x^2 - x^3 + x^4),x]","\frac{1}{2} \left(\left(1+\sqrt{5}\right) \log \left(2 x^2+\left(\sqrt{5}-1\right) x+2\right)-\left(\sqrt{5}-1\right) \log \left(-2 x^2+\sqrt{5} x+x-2\right)\right)","-\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,"(-((-1 + Sqrt[5])*Log[-2 + x + Sqrt[5]*x - 2*x^2]) + (1 + Sqrt[5])*Log[2 + (-1 + Sqrt[5])*x + 2*x^2])/2","A",1
229,1,14,14,0.0076894,"\int \frac{3 x+3 x^2+x^3}{1+4 x+6 x^2+4 x^3+x^4} \, dx","Integrate[(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",1
230,1,24,28,0.0128552,"\int \frac{-1+3 x-3 x^2+x^3}{1+4 x+6 x^2+4 x^3+x^4} \, dx","Integrate[(-1 + 3*x - 3*x^2 + x^3)/(1 + 4*x + 6*x^2 + 4*x^3 + x^4),x]","\frac{2 \left(9 x^2+9 x+4\right)}{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,"(2*(4 + 9*x + 9*x^2))/(3*(1 + x)^3) + Log[1 + x]","A",1
231,1,28,59,0.0121913,"\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","Integrate[(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^5-4 x^2+3 x+2}{\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 + 3*x - 4*x^2 + 13*x^5)/(3 + 2*x^2 + x^4)^2","A",1
232,1,11,11,0.0067844,"\int \frac{-1+4 x^5}{\left(1+x+x^5\right)^2} \, dx","Integrate[(-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
233,1,132,91,0.0900443,"\int \frac{1+x^2}{\left(1-7 x^2+7 x^4-x^6\right)^2} \, dx","Integrate[(1 + x^2)/(1 - 7*x^2 + 7*x^4 - x^6)^2,x]","\frac{1}{128} \left(-\frac{4 x \left(7 x^4-46 x^2+31\right)}{x^6-7 x^4+7 x^2-1}-16 \log (1-x)+\left(3+2 \sqrt{2}\right) \log \left(-x+\sqrt{2}-1\right)+\left(2 \sqrt{2}-3\right) \log \left(-x+\sqrt{2}+1\right)+16 \log (x+1)-\left(3+2 \sqrt{2}\right) \log \left(x+\sqrt{2}-1\right)+\left(3-2 \sqrt{2}\right) \log \left(x+\sqrt{2}+1\right)\right)","\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,"((-4*x*(31 - 46*x^2 + 7*x^4))/(-1 + 7*x^2 - 7*x^4 + x^6) - 16*Log[1 - x] + (3 + 2*Sqrt[2])*Log[-1 + Sqrt[2] - x] + (-3 + 2*Sqrt[2])*Log[1 + Sqrt[2] - x] + 16*Log[1 + x] - (3 + 2*Sqrt[2])*Log[-1 + Sqrt[2] + x] + (3 - 2*Sqrt[2])*Log[1 + Sqrt[2] + x])/128","A",1
234,1,23,25,0.37485,"\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","Integrate[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} (a+x (b+x (c+d x)))^{p+1}","x^{m+1} \left(a+b x+c x^2+d x^3\right)^{p+1}",1,"x^(1 + m)*(a + x*(b + x*(c + d*x)))^(1 + p)","A",1
235,1,21,23,0.2330602,"\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","Integrate[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 (a+x (b+x (c+d x)))^{p+1}","x^3 \left(a+b x+c x^2+d x^3\right)^{p+1}",1,"x^3*(a + x*(b + x*(c + d*x)))^(1 + p)","A",1
236,1,21,23,0.1774252,"\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","Integrate[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 (a+x (b+x (c+d x)))^{p+1}","x^2 \left(a+b x+c x^2+d x^3\right)^{p+1}",1,"x^2*(a + x*(b + x*(c + d*x)))^(1 + p)","A",1
237,1,19,21,0.1222857,"\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","Integrate[(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 (a+x (b+x (c+d x)))^{p+1}","x \left(a+b x+c x^2+d x^3\right)^{p+1}",1,"x*(a + x*(b + x*(c + d*x)))^(1 + p)","A",1
238,1,17,19,0.0097266,"\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","Integrate[((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]","(a+x (b+x (c+d x)))^{p+1}","\left(a+b x+c x^2+d x^3\right)^{p+1}",1,"(a + x*(b + x*(c + d*x)))^(1 + p)","A",1
239,1,21,23,0.176047,"\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","Integrate[((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{(a+x (b+x (c+d x)))^{p+1}}{x}","\frac{\left(a+b x+c x^2+d x^3\right)^{p+1}}{x}",1,"(a + x*(b + x*(c + d*x)))^(1 + p)/x","A",1
240,1,21,23,0.1993393,"\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","Integrate[((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{(a+x (b+x (c+d x)))^{p+1}}{x^2}","\frac{\left(a+b x+c x^2+d x^3\right)^{p+1}}{x^2}",1,"(a + x*(b + x*(c + d*x)))^(1 + p)/x^2","A",1
241,1,21,23,0.1881324,"\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","Integrate[((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{(a+x (b+x (c+d x)))^{p+1}}{x^3}","\frac{\left(a+b x+c x^2+d x^3\right)^{p+1}}{x^3}",1,"(a + x*(b + x*(c + d*x)))^(1 + p)/x^3","A",1
242,1,83,97,0.0363144,"\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","Integrate[(x^4*(5 + x + 3*x^2 + 2*x^3))/(2 + x + 3*x^2 + x^3 + 2*x^4),x]","\frac{1}{144} \left(36 x^4+48 x^3-108 x^2+48 \log \left(x^2+x+1\right)-39 \log \left(2 x^2-x+2\right)+180 x-160 \sqrt{3} \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)-2 \sqrt{15} \tan ^{-1}\left(\frac{4 x-1}{\sqrt{15}}\right)\right)","\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,"(180*x - 108*x^2 + 48*x^3 + 36*x^4 - 160*Sqrt[3]*ArcTan[(1 + 2*x)/Sqrt[3]] - 2*Sqrt[15]*ArcTan[(-1 + 4*x)/Sqrt[15]] + 48*Log[1 + x + x^2] - 39*Log[2 - x + 2*x^2])/144","A",1
243,1,78,90,0.0229941,"\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","Integrate[(x^3*(5 + x + 3*x^2 + 2*x^3))/(2 + x + 3*x^2 + x^3 + 2*x^4),x]","\frac{1}{72} \left(24 x^3+36 x^2+48 \log \left(x^2+x+1\right)-3 \log \left(2 x^2-x+2\right)-108 x+64 \sqrt{3} \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)-10 \sqrt{15} \tan ^{-1}\left(\frac{4 x-1}{\sqrt{15}}\right)\right)","\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,"(-108*x + 36*x^2 + 24*x^3 + 64*Sqrt[3]*ArcTan[(1 + 2*x)/Sqrt[3]] - 10*Sqrt[15]*ArcTan[(-1 + 4*x)/Sqrt[15]] + 48*Log[1 + x + x^2] - 3*Log[2 - x + 2*x^2])/72","A",1
244,1,72,77,0.0309717,"\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","Integrate[(x^2*(5 + x + 3*x^2 + 2*x^3))/(2 + x + 3*x^2 + x^3 + 2*x^4),x]","\frac{1}{36} \left(9 \left(-4 \log \left(x^2+x+1\right)+\log \left(2 x^2-x+2\right)+2 x (x+2)\right)+8 \sqrt{3} \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)-2 \sqrt{15} \tan ^{-1}\left(\frac{4 x-1}{\sqrt{15}}\right)\right)","\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,"(8*Sqrt[3]*ArcTan[(1 + 2*x)/Sqrt[3]] - 2*Sqrt[15]*ArcTan[(-1 + 4*x)/Sqrt[15]] + 9*(2*x*(2 + x) - 4*Log[1 + x + x^2] + Log[2 - x + 2*x^2]))/36","A",1
245,1,69,72,0.0225613,"\int \frac{x \left(5+x+3 x^2+2 x^3\right)}{2+x+3 x^2+x^3+2 x^4} \, dx","Integrate[(x*(5 + x + 3*x^2 + 2*x^3))/(2 + x + 3*x^2 + x^3 + 2*x^4),x]","\frac{1}{18} \left(3 \left(2 \log \left(x^2+x+1\right)+\log \left(2 x^2-x+2\right)+6 x\right)-20 \sqrt{3} \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)+2 \sqrt{15} \tan ^{-1}\left(\frac{4 x-1}{\sqrt{15}}\right)\right)","\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,"(-20*Sqrt[3]*ArcTan[(1 + 2*x)/Sqrt[3]] + 2*Sqrt[15]*ArcTan[(-1 + 4*x)/Sqrt[15]] + 3*(6*x + 2*Log[1 + x + x^2] + Log[2 - x + 2*x^2]))/18","A",1
246,1,65,71,0.0173682,"\int \frac{5+x+3 x^2+2 x^3}{2+x+3 x^2+x^3+2 x^4} \, dx","Integrate[(5 + x + 3*x^2 + 2*x^3)/(2 + x + 3*x^2 + x^3 + 2*x^4),x]","\frac{1}{18} \left(12 \log \left(x^2+x+1\right)-3 \log \left(2 x^2-x+2\right)+16 \sqrt{3} \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)+2 \sqrt{15} \tan ^{-1}\left(\frac{4 x-1}{\sqrt{15}}\right)\right)","\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,"(16*Sqrt[3]*ArcTan[(1 + 2*x)/Sqrt[3]] + 2*Sqrt[15]*ArcTan[(-1 + 4*x)/Sqrt[15]] + 12*Log[1 + x + x^2] - 3*Log[2 - x + 2*x^2])/18","A",1
247,1,69,75,0.0193066,"\int \frac{5+x+3 x^2+2 x^3}{x \left(2+x+3 x^2+x^3+2 x^4\right)} \, dx","Integrate[(5 + x + 3*x^2 + 2*x^3)/(x*(2 + x + 3*x^2 + x^3 + 2*x^4)),x]","\frac{1}{36} \left(-36 \log \left(x^2+x+1\right)-9 \log \left(2 x^2-x+2\right)+90 \log (x)+8 \sqrt{3} \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)-2 \sqrt{15} \tan ^{-1}\left(\frac{4 x-1}{\sqrt{15}}\right)\right)","-\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,"(8*Sqrt[3]*ArcTan[(1 + 2*x)/Sqrt[3]] - 2*Sqrt[15]*ArcTan[(-1 + 4*x)/Sqrt[15]] + 90*Log[x] - 36*Log[1 + x + x^2] - 9*Log[2 - x + 2*x^2])/36","A",1
248,1,78,84,0.0330277,"\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","Integrate[(5 + x + 3*x^2 + 2*x^3)/(x^2*(2 + x + 3*x^2 + x^3 + 2*x^4)),x]","-\frac{-24 x \log \left(x^2+x+1\right)-3 x \log \left(2 x^2-x+2\right)+54 x \log (x)+80 \sqrt{3} x \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)+10 \sqrt{15} x \tan ^{-1}\left(\frac{4 x-1}{\sqrt{15}}\right)+180}{72 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}}",1,"-1/72*(180 + 80*Sqrt[3]*x*ArcTan[(1 + 2*x)/Sqrt[3]] + 10*Sqrt[15]*x*ArcTan[(-1 + 4*x)/Sqrt[15]] + 54*x*Log[x] - 24*x*Log[1 + x + x^2] - 3*x*Log[2 - x + 2*x^2])/x","A",1
249,1,82,91,0.0552553,"\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","Integrate[(5 + x + 3*x^2 + 2*x^3)/(x^3*(2 + x + 3*x^2 + x^3 + 2*x^4)),x]","\frac{1}{144} \left(3 \left(-\frac{60}{x^2}+32 \log \left(x^2+x+1\right)+13 \log \left(2 x^2-x+2\right)+\frac{36}{x}-90 \log (x)\right)+128 \sqrt{3} \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)-2 \sqrt{15} \tan ^{-1}\left(\frac{4 x-1}{\sqrt{15}}\right)\right)","-\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,"(128*Sqrt[3]*ArcTan[(1 + 2*x)/Sqrt[3]] - 2*Sqrt[15]*ArcTan[(-1 + 4*x)/Sqrt[15]] + 3*(-60/x^2 + 36/x - 90*Log[x] + 32*Log[1 + x + x^2] + 13*Log[2 - x + 2*x^2]))/144","A",1
250,1,109,307,0.020766,"\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","Integrate[(x^3*(5 + x + 3*x^2 + 2*x^3))/(2 + x + 5*x^2 + x^3 + 2*x^4),x]","\frac{1}{6} \left(3 \text{RootSum}\left[2 \text{$\#$1}^4+\text{$\#$1}^3+5 \text{$\#$1}^2+\text{$\#$1}+2\&,\frac{3 \text{$\#$1}^3 \log (x-\text{$\#$1})+19 \text{$\#$1}^2 \log (x-\text{$\#$1})+\text{$\#$1} \log (x-\text{$\#$1})+10 \log (x-\text{$\#$1})}{8 \text{$\#$1}^3+3 \text{$\#$1}^2+10 \text{$\#$1}+1}\&\right]+x \left(2 x^2+3 x-15\right)\right)","\frac{1}{42} \left(7+5 i \sqrt{7}\right) x^3+\frac{1}{42} \left(7-5 i \sqrt{7}\right) x^3+\frac{1}{28} \left(7+5 i \sqrt{7}\right) x^2+\frac{1}{28} \left(7-5 i \sqrt{7}\right) x^2+\frac{3}{112} \left(7-11 i \sqrt{7}\right) \log \left(4 x^2+\left(1-i \sqrt{7}\right) x+4\right)+\frac{3}{112} \left(7+11 i \sqrt{7}\right) \log \left(4 x^2+\left(1+i \sqrt{7}\right) x+4\right)-\frac{1}{28} \left(35+9 i \sqrt{7}\right) x-\frac{1}{28} \left(35-9 i \sqrt{7}\right) x+\frac{11 \left(5 \sqrt{7}+9 i\right) \tan ^{-1}\left(\frac{8 x-i \sqrt{7}+1}{\sqrt{2 \left(35+i \sqrt{7}\right)}}\right)}{4 \sqrt{14 \left(35+i \sqrt{7}\right)}}-\frac{11 \left(-5 \sqrt{7}+9 i\right) \tan ^{-1}\left(\frac{8 x+i \sqrt{7}+1}{\sqrt{2 \left(35-i \sqrt{7}\right)}}\right)}{4 \sqrt{14 \left(35-i \sqrt{7}\right)}}",1,"(x*(-15 + 3*x + 2*x^2) + 3*RootSum[2 + #1 + 5*#1^2 + #1^3 + 2*#1^4 & , (10*Log[x - #1] + Log[x - #1]*#1 + 19*Log[x - #1]*#1^2 + 3*Log[x - #1]*#1^3)/(1 + 10*#1 + 3*#1^2 + 8*#1^3) & ])/6","C",1
251,1,101,269,0.0163759,"\int \frac{x^2 \left(5+x+3 x^2+2 x^3\right)}{2+x+5 x^2+x^3+2 x^4} \, dx","Integrate[(x^2*(5 + x + 3*x^2 + 2*x^3))/(2 + x + 5*x^2 + x^3 + 2*x^4),x]","-\text{RootSum}\left[2 \text{$\#$1}^4+\text{$\#$1}^3+5 \text{$\#$1}^2+\text{$\#$1}+2\&,\frac{5 \text{$\#$1}^3 \log (x-\text{$\#$1})+\text{$\#$1}^2 \log (x-\text{$\#$1})+3 \text{$\#$1} \log (x-\text{$\#$1})+2 \log (x-\text{$\#$1})}{8 \text{$\#$1}^3+3 \text{$\#$1}^2+10 \text{$\#$1}+1}\&\right]+\frac{x^2}{2}+x","\frac{1}{28} \left(7+5 i \sqrt{7}\right) x^2+\frac{1}{28} \left(7-5 i \sqrt{7}\right) x^2-\frac{1}{56} \left(35+9 i \sqrt{7}\right) \log \left(4 x^2+\left(1-i \sqrt{7}\right) x+4\right)-\frac{1}{56} \left(35-9 i \sqrt{7}\right) \log \left(4 x^2+\left(1+i \sqrt{7}\right) x+4\right)+\frac{1}{14} \left(7+5 i \sqrt{7}\right) x+\frac{1}{14} \left(7-5 i \sqrt{7}\right) x-\frac{\left(\sqrt{7}+53 i\right) \tan ^{-1}\left(\frac{8 x-i \sqrt{7}+1}{\sqrt{2 \left(35+i \sqrt{7}\right)}}\right)}{2 \sqrt{14 \left(35+i \sqrt{7}\right)}}+\frac{\left(-\sqrt{7}+53 i\right) \tan ^{-1}\left(\frac{8 x+i \sqrt{7}+1}{\sqrt{2 \left(35-i \sqrt{7}\right)}}\right)}{2 \sqrt{14 \left(35-i \sqrt{7}\right)}}",1,"x + x^2/2 - RootSum[2 + #1 + 5*#1^2 + #1^3 + 2*#1^4 & , (2*Log[x - #1] + 3*Log[x - #1]*#1 + Log[x - #1]*#1^2 + 5*Log[x - #1]*#1^3)/(1 + 10*#1 + 3*#1^2 + 8*#1^3) & ]","C",1
252,1,94,230,0.0149583,"\int \frac{x \left(5+x+3 x^2+2 x^3\right)}{2+x+5 x^2+x^3+2 x^4} \, dx","Integrate[(x*(5 + x + 3*x^2 + 2*x^3))/(2 + x + 5*x^2 + x^3 + 2*x^4),x]","2 \text{RootSum}\left[2 \text{$\#$1}^4+\text{$\#$1}^3+5 \text{$\#$1}^2+\text{$\#$1}+2\&,\frac{\text{$\#$1}^3 \log (x-\text{$\#$1})-2 \text{$\#$1}^2 \log (x-\text{$\#$1})+2 \text{$\#$1} \log (x-\text{$\#$1})-\log (x-\text{$\#$1})}{8 \text{$\#$1}^3+3 \text{$\#$1}^2+10 \text{$\#$1}+1}\&\right]+x","\frac{1}{28} \left(7+5 i \sqrt{7}\right) \log \left(4 x^2+\left(1-i \sqrt{7}\right) x+4\right)+\frac{1}{28} \left(7-5 i \sqrt{7}\right) \log \left(4 x^2+\left(1+i \sqrt{7}\right) x+4\right)+\frac{1}{14} \left(7+5 i \sqrt{7}\right) x+\frac{1}{14} \left(7-5 i \sqrt{7}\right) x-\frac{\left(7 \sqrt{7}+19 i\right) \tan ^{-1}\left(\frac{8 x-i \sqrt{7}+1}{\sqrt{2 \left(35+i \sqrt{7}\right)}}\right)}{\sqrt{14 \left(35+i \sqrt{7}\right)}}+\frac{\left(-7 \sqrt{7}+19 i\right) \tan ^{-1}\left(\frac{8 x+i \sqrt{7}+1}{\sqrt{2 \left(35-i \sqrt{7}\right)}}\right)}{\sqrt{14 \left(35-i \sqrt{7}\right)}}",1,"x + 2*RootSum[2 + #1 + 5*#1^2 + #1^3 + 2*#1^4 & , (-Log[x - #1] + 2*Log[x - #1]*#1 - 2*Log[x - #1]*#1^2 + Log[x - #1]*#1^3)/(1 + 10*#1 + 3*#1^2 + 8*#1^3) & ]","C",1
253,1,90,198,0.0132443,"\int \frac{5+x+3 x^2+2 x^3}{2+x+5 x^2+x^3+2 x^4} \, dx","Integrate[(5 + x + 3*x^2 + 2*x^3)/(2 + x + 5*x^2 + x^3 + 2*x^4),x]","\text{RootSum}\left[2 \text{$\#$1}^4+\text{$\#$1}^3+5 \text{$\#$1}^2+\text{$\#$1}+2\&,\frac{2 \text{$\#$1}^3 \log (x-\text{$\#$1})+3 \text{$\#$1}^2 \log (x-\text{$\#$1})+\text{$\#$1} \log (x-\text{$\#$1})+5 \log (x-\text{$\#$1})}{8 \text{$\#$1}^3+3 \text{$\#$1}^2+10 \text{$\#$1}+1}\&\right]","\frac{1}{28} \left(7+5 i \sqrt{7}\right) \log \left(4 x^2+\left(1-i \sqrt{7}\right) x+4\right)+\frac{1}{28} \left(7-5 i \sqrt{7}\right) \log \left(4 x^2+\left(1+i \sqrt{7}\right) x+4\right)+\frac{\left(7 \sqrt{7}+19 i\right) \tan ^{-1}\left(\frac{8 x-i \sqrt{7}+1}{\sqrt{2 \left(35+i \sqrt{7}\right)}}\right)}{\sqrt{14 \left(35+i \sqrt{7}\right)}}-\frac{\left(-7 \sqrt{7}+19 i\right) \tan ^{-1}\left(\frac{8 x+i \sqrt{7}+1}{\sqrt{2 \left(35-i \sqrt{7}\right)}}\right)}{\sqrt{14 \left(35-i \sqrt{7}\right)}}",1,"RootSum[2 + #1 + 5*#1^2 + #1^3 + 2*#1^4 & , (5*Log[x - #1] + Log[x - #1]*#1 + 3*Log[x - #1]*#1^2 + 2*Log[x - #1]*#1^3)/(1 + 10*#1 + 3*#1^2 + 8*#1^3) & ]","C",1
254,1,101,245,0.0197684,"\int \frac{5+x+3 x^2+2 x^3}{x \left(2+x+5 x^2+x^3+2 x^4\right)} \, dx","Integrate[(5 + x + 3*x^2 + 2*x^3)/(x*(2 + x + 5*x^2 + x^3 + 2*x^4)),x]","\frac{5 \log (x)}{2}-\frac{1}{2} \text{RootSum}\left[2 \text{$\#$1}^4+\text{$\#$1}^3+5 \text{$\#$1}^2+\text{$\#$1}+2\&,\frac{10 \text{$\#$1}^3 \log (x-\text{$\#$1})+\text{$\#$1}^2 \log (x-\text{$\#$1})+19 \text{$\#$1} \log (x-\text{$\#$1})+3 \log (x-\text{$\#$1})}{8 \text{$\#$1}^3+3 \text{$\#$1}^2+10 \text{$\#$1}+1}\&\right]","-\frac{1}{56} \left(35-9 i \sqrt{7}\right) \log \left(4 i x^2+\left(-\sqrt{7}+i\right) x+4 i\right)-\frac{1}{56} \left(35+9 i \sqrt{7}\right) \log \left(4 i x^2+\left(\sqrt{7}+i\right) x+4 i\right)+\frac{1}{28} \left(35+9 i \sqrt{7}\right) \log (x)+\frac{1}{28} \left(35-9 i \sqrt{7}\right) \log (x)-\frac{\left(53+i \sqrt{7}\right) \tanh ^{-1}\left(\frac{8 i x-\sqrt{7}+i}{\sqrt{2 \left(35-i \sqrt{7}\right)}}\right)}{2 \sqrt{14 \left(35-i \sqrt{7}\right)}}+\frac{\left(53-i \sqrt{7}\right) \tanh ^{-1}\left(\frac{8 i x+\sqrt{7}+i}{\sqrt{2 \left(35+i \sqrt{7}\right)}}\right)}{2 \sqrt{14 \left(35+i \sqrt{7}\right)}}",1,"(5*Log[x])/2 - RootSum[2 + #1 + 5*#1^2 + #1^3 + 2*#1^4 & , (3*Log[x - #1] + 19*Log[x - #1]*#1 + Log[x - #1]*#1^2 + 10*Log[x - #1]*#1^3)/(1 + 10*#1 + 3*#1^2 + 8*#1^3) & ]/2","C",1
255,1,109,281,0.0180843,"\int \frac{5+x+3 x^2+2 x^3}{x^2 \left(2+x+5 x^2+x^3+2 x^4\right)} \, dx","Integrate[(5 + x + 3*x^2 + 2*x^3)/(x^2*(2 + x + 5*x^2 + x^3 + 2*x^4)),x]","\frac{1}{4} \text{RootSum}\left[2 \text{$\#$1}^4+\text{$\#$1}^3+5 \text{$\#$1}^2+\text{$\#$1}+2\&,\frac{6 \text{$\#$1}^3 \log (x-\text{$\#$1})-17 \text{$\#$1}^2 \log (x-\text{$\#$1})+13 \text{$\#$1} \log (x-\text{$\#$1})-35 \log (x-\text{$\#$1})}{8 \text{$\#$1}^3+3 \text{$\#$1}^2+10 \text{$\#$1}+1}\&\right]-\frac{5}{2 x}-\frac{3 \log (x)}{4}","\frac{3}{112} \left(7+11 i \sqrt{7}\right) \log \left(4 i x^2+\left(-\sqrt{7}+i\right) x+4 i\right)+\frac{3}{112} \left(7-11 i \sqrt{7}\right) \log \left(4 i x^2+\left(\sqrt{7}+i\right) x+4 i\right)-\frac{35+9 i \sqrt{7}}{28 x}-\frac{35-9 i \sqrt{7}}{28 x}-\frac{3}{56} \left(7+11 i \sqrt{7}\right) \log (x)-\frac{3}{56} \left(7-11 i \sqrt{7}\right) \log (x)+\frac{11 \left(9+5 i \sqrt{7}\right) \tanh ^{-1}\left(\frac{8 i x-\sqrt{7}+i}{\sqrt{2 \left(35-i \sqrt{7}\right)}}\right)}{4 \sqrt{14 \left(35-i \sqrt{7}\right)}}-\frac{11 \left(9-5 i \sqrt{7}\right) \tanh ^{-1}\left(\frac{8 i x+\sqrt{7}+i}{\sqrt{2 \left(35+i \sqrt{7}\right)}}\right)}{4 \sqrt{14 \left(35+i \sqrt{7}\right)}}",1,"-5/(2*x) - (3*Log[x])/4 + RootSum[2 + #1 + 5*#1^2 + #1^3 + 2*#1^4 & , (-35*Log[x - #1] + 13*Log[x - #1]*#1 - 17*Log[x - #1]*#1^2 + 6*Log[x - #1]*#1^3)/(1 + 10*#1 + 3*#1^2 + 8*#1^3) & ]/4","C",1
256,1,116,317,0.018869,"\int \frac{5+x+3 x^2+2 x^3}{x^3 \left(2+x+5 x^2+x^3+2 x^4\right)} \, dx","Integrate[(5 + x + 3*x^2 + 2*x^3)/(x^3*(2 + x + 5*x^2 + x^3 + 2*x^4)),x]","\frac{1}{8} \text{RootSum}\left[2 \text{$\#$1}^4+\text{$\#$1}^3+5 \text{$\#$1}^2+\text{$\#$1}+2\&,\frac{70 \text{$\#$1}^3 \log (x-\text{$\#$1})+47 \text{$\#$1}^2 \log (x-\text{$\#$1})+141 \text{$\#$1} \log (x-\text{$\#$1})+61 \log (x-\text{$\#$1})}{8 \text{$\#$1}^3+3 \text{$\#$1}^2+10 \text{$\#$1}+1}\&\right]-\frac{5}{4 x^2}+\frac{3}{4 x}-\frac{35 \log (x)}{8}","-\frac{35+9 i \sqrt{7}}{56 x^2}-\frac{35-9 i \sqrt{7}}{56 x^2}+\frac{1}{32} \left(35-9 i \sqrt{7}\right) \log \left(4 i x^2+\left(-\sqrt{7}+i\right) x+4 i\right)+\frac{1}{32} \left(35+9 i \sqrt{7}\right) \log \left(4 i x^2+\left(\sqrt{7}+i\right) x+4 i\right)+\frac{3 \left(7+11 i \sqrt{7}\right)}{56 x}+\frac{3 \left(7-11 i \sqrt{7}\right)}{56 x}-\frac{1}{16} \left(35+9 i \sqrt{7}\right) \log (x)-\frac{1}{16} \left(35-9 i \sqrt{7}\right) \log (x)+\frac{\left(355-73 i \sqrt{7}\right) \tanh ^{-1}\left(\frac{8 i x-\sqrt{7}+i}{\sqrt{2 \left(35-i \sqrt{7}\right)}}\right)}{8 \sqrt{14 \left(35-i \sqrt{7}\right)}}-\frac{\left(355+73 i \sqrt{7}\right) \tanh ^{-1}\left(\frac{8 i x+\sqrt{7}+i}{\sqrt{2 \left(35+i \sqrt{7}\right)}}\right)}{8 \sqrt{14 \left(35+i \sqrt{7}\right)}}",1,"-5/(4*x^2) + 3/(4*x) - (35*Log[x])/8 + RootSum[2 + #1 + 5*#1^2 + #1^3 + 2*#1^4 & , (61*Log[x - #1] + 141*Log[x - #1]*#1 + 47*Log[x - #1]*#1^2 + 70*Log[x - #1]*#1^3)/(1 + 10*#1 + 3*#1^2 + 8*#1^3) & ]/8","C",1
257,1,87,19,0.0474154,"\int \frac{x^2 \left(3 a+b x^2\right)}{a^2+2 a b x^2+b^2 x^4+c^2 x^6} \, dx","Integrate[(x^2*(3*a + b*x^2))/(a^2 + 2*a*b*x^2 + b^2*x^4 + c^2*x^6),x]","\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^6 c^2+\text{$\#$1}^4 b^2+2 \text{$\#$1}^2 a b+a^2\&,\frac{\text{$\#$1}^3 b \log (x-\text{$\#$1})+3 \text{$\#$1} a \log (x-\text{$\#$1})}{3 \text{$\#$1}^4 c^2+2 \text{$\#$1}^2 b^2+2 a b}\&\right]","\frac{\tan ^{-1}\left(\frac{c x^3}{a+b x^2}\right)}{c}",1,"RootSum[a^2 + 2*a*b*#1^2 + b^2*#1^4 + c^2*#1^6 & , (3*a*Log[x - #1]*#1 + b*Log[x - #1]*#1^3)/(2*a*b + 2*b^2*#1^2 + 3*c^2*#1^4) & ]/2","C",1
258,1,57,43,0.0226722,"\int \frac{1-3 x^4}{(-2+x) \left(1+x^2\right)^2} \, dx","Integrate[(1 - 3*x^4)/((-2 + x)*(1 + x^2)^2),x]","\frac{2 (x-2)+3}{5 \left((x-2)^2+4 (x-2)+5\right)}-\frac{14}{25} \log \left((x-2)^2+4 (x-2)+5\right)-\frac{47}{25} \log (x-2)-\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,"(3 + 2*(-2 + x))/(5*(5 + 4*(-2 + x) + (-2 + x)^2)) - (46*ArcTan[x])/25 - (14*Log[5 + 4*(-2 + x) + (-2 + x)^2])/25 - (47*Log[-2 + x])/25","A",1
259,1,17,17,0.0048847,"\int \frac{-9-9 x+2 x^2}{-9 x+x^3} \, dx","Integrate[(-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",1
260,1,25,25,0.0057025,"\int \frac{1+2 x^2+x^5}{-x+x^3} \, dx","Integrate[(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",1
261,1,20,22,0.0098333,"\int \frac{3+2 x^2}{(-1+x)^2 x} \, dx","Integrate[(3 + 2*x^2)/((-1 + x)^2*x),x]","-\frac{5}{x-1}-\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",1
262,1,38,27,0.0108012,"\int \frac{-1+2 x^2}{(-1+4 x) \left(1+x^2\right)} \, dx","Integrate[(-1 + 2*x^2)/((-1 + 4*x)*(1 + x^2)),x]","-\frac{7}{34} \log (4 x-1)+\frac{6}{17} \log \left((4 x-1)^2+2 (4 x-1)+17\right)+\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[17 + 2*(-1 + 4*x) + (-1 + 4*x)^2])/17","A",1
263,1,21,21,0.0043111,"\int \frac{-3+2 x-3 x^2+x^3}{1+x^2} \, dx","Integrate[(-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",1
264,1,27,27,0.0071845,"\int \frac{x+10 x^2+6 x^3+x^4}{10+6 x+x^2} \, dx","Integrate[(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",1
265,1,39,39,0.0181698,"\int \frac{1}{-18+27 x-7 x^2-3 x^3+x^4} \, dx","Integrate[(-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",1
266,1,23,22,0.0036512,"\int \frac{1+x^3}{-2+x} \, dx","Integrate[(1 + x^3)/(-2 + x),x]","\frac{x^3}{3}+x^2+4 x+9 \log (x-2)-\frac{44}{3}","\frac{x^3}{3}+x^2+4 x+9 \log (2-x)",1,"-44/3 + 4*x + x^2 + x^3/3 + 9*Log[-2 + x]","A",1
267,1,15,15,0.0048747,"\int \frac{3 x-4 x^2+3 x^3}{1+x^2} \, dx","Integrate[(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",1
268,1,24,12,0.0108631,"\int \frac{5+3 x}{1-x-x^2+x^3} \, dx","Integrate[(5 + 3*x)/(1 - x - x^2 + x^3),x]","-\frac{4}{x-1}-\frac{1}{2} \log (x-1)+\frac{1}{2} \log (x+1)","\frac{4}{1-x}+\tanh ^{-1}(x)",1,"-4/(-1 + x) - Log[-1 + x]/2 + Log[1 + x]/2","A",1
269,1,25,25,0.0058705,"\int \frac{-1-x-x^3+x^4}{-x^2+x^3} \, dx","Integrate[(-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",1
270,1,13,13,0.006477,"\int \frac{2+x+x^2+x^3}{2+3 x^2+x^4} \, dx","Integrate[(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",1
271,1,35,35,0.0169864,"\int \frac{-4+8 x-4 x^2+4 x^3-x^4+x^5}{\left(2+x^2\right)^3} \, dx","Integrate[(-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",1
272,1,23,23,0.0054652,"\int \frac{-1-3 x+x^2}{-2 x+x^2+x^3} \, dx","Integrate[(-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",1
273,1,23,23,0.0072613,"\int \frac{3-x+3 x^2-2 x^3+x^4}{3 x-2 x^2+x^3} \, dx","Integrate[(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",1
274,1,25,29,0.0096512,"\int \frac{-1+x+x^3}{\left(1+x^2\right)^2} \, dx","Integrate[(-1 + x + x^3)/(1 + x^2)^2,x]","\frac{1}{2} \left(-\frac{x}{x^2+1}+\log \left(x^2+1\right)-\tan ^{-1}(x)\right)","-\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/(1 + x^2)) - ArcTan[x] + Log[1 + x^2])/2","A",1
275,1,44,44,0.0243203,"\int \frac{1+2 x-x^2+8 x^3+x^4}{\left(x+x^2\right) \left(1+x^3\right)} \, dx","Integrate[(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{2 x-1}{\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",1
276,1,46,46,0.0201012,"\int \frac{15-5 x+x^2+x^3}{\left(5+x^2\right) \left(3+2 x+x^2\right)} \, dx","Integrate[(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",1
277,1,33,33,0.0220142,"\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","Integrate[(-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",1
278,1,17,17,0.0062371,"\int \frac{1}{\left(1+x^2\right) \left(4+x^2\right)} \, dx","Integrate[1/((1 + x^2)*(4 + x^2)),x]","\frac{1}{6} \tan ^{-1}\left(\frac{2}{x}\right)+\frac{1}{3} \tan ^{-1}(x)","\frac{1}{3} \tan ^{-1}(x)-\frac{1}{6} \tan ^{-1}\left(\frac{x}{2}\right)",1,"ArcTan[2/x]/6 + ArcTan[x]/3","A",1
279,1,22,24,0.0091442,"\int \frac{a+b x^3}{1+x^2} \, dx","Integrate[(a + b*x^3)/(1 + x^2),x]","a \tan ^{-1}(x)+\frac{1}{2} b \left(x^2-\log \left(x^2+1\right)\right)","a \tan ^{-1}(x)+\frac{b x^2}{2}-\frac{1}{2} b \log \left(x^2+1\right)",1,"a*ArcTan[x] + (b*(x^2 - Log[1 + x^2]))/2","A",1
280,1,23,15,0.0057765,"\int \frac{x+x^2}{(4+x) \left(-4+x^2\right)} \, dx","Integrate[(x + x^2)/((4 + x)*(-4 + x^2)),x]","\frac{1}{4} \log (2-x)-\frac{1}{4} \log (x+2)+\log (x+4)","\log (x+4)-\frac{1}{2} \tanh ^{-1}\left(\frac{x}{2}\right)",1,"Log[2 - x]/4 - Log[2 + x]/4 + Log[4 + x]","A",1
281,1,20,20,0.0093558,"\int \frac{4+x^2}{\left(1+x^2\right) \left(2+x^2\right)} \, dx","Integrate[(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",1
282,1,33,37,0.0227994,"\int \frac{5-4 x+3 x^2+x^4}{(-1+x)^2 \left(1+x^2\right)} \, dx","Integrate[(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}{2-2 x}+\frac{1}{2} \log (x-1)+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 - 2*x) + x + 2*ArcTan[x] + Log[-1 + x]/2 + (3*Log[1 + x^2])/4","A",1
283,1,26,26,0.007974,"\int \frac{1+x^4}{2+x^2} \, dx","Integrate[(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",1
284,1,12,12,0.0041177,"\int \frac{2+2 x+x^4}{x^4+x^5} \, dx","Integrate[(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",1
285,1,21,21,0.0065903,"\int \frac{-1-5 x+2 x^2}{2-x-2 x^2+x^3} \, dx","Integrate[(-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",1
286,1,22,22,0.0082429,"\int \frac{2+x+x^3}{1+2 x^2+x^4} \, dx","Integrate[(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",1
287,1,24,24,0.0106734,"\int \frac{1+2 x+x^2+x^3}{1+2 x^2+x^4} \, dx","Integrate[(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/(1 + x^2) + ArcTan[x] + Log[1 + x^2]/2","A",1
288,1,36,36,0.0151321,"\int \frac{3+4 x}{\left(1+x^2\right) \left(2+x^2\right)} \, dx","Integrate[(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",1
289,1,37,37,0.0078776,"\int \frac{2+x}{\left(1+x^2\right) \left(4+x^2\right)} \, dx","Integrate[(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,"-1/3*ArcTan[x/2] + (2*ArcTan[x])/3 + Log[1 + x^2]/6 - Log[4 + x^2]/6","A",1
290,1,29,29,0.0055146,"\int \frac{2-x+x^3}{-7-6 x+x^2} \, dx","Integrate[(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",1
291,1,19,19,0.00376,"\int \frac{-1+x^5}{-1+x^2} \, dx","Integrate[(-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",1
292,1,41,41,0.0141809,"\int \frac{5+2 x-x^2+x^3}{1+x+x^2} \, dx","Integrate[(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",1
293,1,39,41,0.0069368,"\int \frac{-3+x-2 x^3+x^4}{10-8 x+2 x^2} \, dx","Integrate[(-3 + x - 2*x^3 + x^4)/(10 - 8*x + 2*x^2),x]","\frac{1}{2} \left(\frac{x^3}{3}+x^2+\frac{3}{2} \log \left(x^2-4 x+5\right)+3 x+12 \tan ^{-1}(2-x)\right)","\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 + x^2 + x^3/3 + 12*ArcTan[2 - x] + (3*Log[5 - 4*x + x^2])/2)/2","A",1
294,1,24,30,0.0106242,"\int \frac{1+2 x+3 x^2+x^3}{(-3+x) (-2+x) (-1+x)} \, dx","Integrate[(1 + 2*x + 3*x^2 + x^3)/((-3 + x)*(-2 + x)*(-1 + x)),x]","x+\frac{61}{2} \log (x-3)-25 \log (x-2)+\frac{7}{2} \log (x-1)","x+\frac{7}{2} \log (1-x)-25 \log (2-x)+\frac{61}{2} \log (3-x)",1,"x + (61*Log[-3 + x])/2 - 25*Log[-2 + x] + (7*Log[-1 + x])/2","A",1
295,1,35,35,0.0075131,"\int \frac{2-7 x+x^2-x^3+x^4}{-24-14 x+x^2+x^3} \, dx","Integrate[(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",1
296,1,32,34,0.0141257,"\int \frac{2+x^2}{(-1+x)^2 x (1+x)} \, dx","Integrate[(2 + x^2)/((-1 + x)^2*x*(1 + x)),x]","-\frac{3}{2 (x-1)}-\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",1
297,1,42,42,0.0212006,"\int \frac{3+x^2+x^3}{\left(2+x^2\right)^2} \, dx","Integrate[(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",1
298,1,49,49,0.0128462,"\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","Integrate[(-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",1
299,1,29,29,0.0072785,"\int \frac{2+x^2}{(-5+x) (-3+x) (4+x)} \, dx","Integrate[(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",1
300,1,43,46,0.0164653,"\int \frac{x^4}{(-1+x) \left(2+x^2\right)} \, dx","Integrate[x^4/((-1 + x)*(2 + x^2)),x]","\frac{1}{6} \left(3 x^2-4 \log \left(x^2+2\right)+6 x+2 \log (x-1)-4 \sqrt{2} \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)-9\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,"(-9 + 6*x + 3*x^2 - 4*Sqrt[2]*ArcTan[x/Sqrt[2]] + 2*Log[-1 + x] - 4*Log[2 + x^2])/6","A",1
301,1,14,16,0.007336,"\int \frac{-1+7 x+2 x^2}{-1-x+x^2+x^3} \, dx","Integrate[(-1 + 7*x + 2*x^2)/(-1 - x + x^2 + x^3),x]","2 \log (x-1)-\frac{3}{x+1}","2 \log (1-x)-\frac{3}{x+1}",1,"-3/(1 + x) + 2*Log[-1 + x]","A",1
302,1,14,21,0.0031363,"\int \frac{1+2 x}{-1+3 x-3 x^2+x^3} \, dx","Integrate[(1 + 2*x)/(-1 + 3*x - 3*x^2 + x^3),x]","\frac{1-4 x}{2 (x-1)^2}","\frac{2}{1-x}-\frac{3}{2 (1-x)^2}",1,"(1 - 4*x)/(2*(-1 + x)^2)","A",1
303,1,15,15,0.0113422,"\int \frac{5-5 x+7 x^2+x^3}{(-1+x)^2 (1+x)^3} \, dx","Integrate[(5 - 5*x + 7*x^2 + x^3)/((-1 + x)^2*(1 + x)^3),x]","-\frac{2}{(x+1)^2}-\frac{1}{x-1}","\frac{1}{1-x}-\frac{2}{(x+1)^2}",1,"-(-1 + x)^(-1) - 2/(1 + x)^2","A",1
304,1,31,31,0.0118369,"\int \frac{1+3 x+3 x^2}{1+2 x+2 x^2+x^3} \, dx","Integrate[(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",1
305,1,25,25,0.0062065,"\int \frac{-1+2 x+x^2}{-2 x+3 x^2+2 x^3} \, dx","Integrate[(-1 + 2*x + x^2)/(-2*x + 3*x^2 + 2*x^3),x]","\frac{1}{10} \log (1-2 x)+\frac{\log (x)}{2}-\frac{1}{10} \log (x+2)","\frac{1}{10} \log (1-2 x)+\frac{\log (x)}{2}-\frac{1}{10} \log (x+2)",1,"Log[1 - 2*x]/10 + Log[x]/2 - Log[2 + x]/10","A",1
306,1,29,30,0.0152358,"\int \frac{1+4 x-2 x^2+x^4}{1-x-x^2+x^3} \, dx","Integrate[(1 + 4*x - 2*x^2 + x^4)/(1 - x - x^2 + x^3),x]","\frac{1}{2} (x+1)^2-\frac{2}{x-1}+\log (1-x)-\log (x+1)","\frac{x^2}{2}+x+\frac{2}{1-x}+\log (1-x)-\log (x+1)",1,"-2/(-1 + x) + (1 + x)^2/2 + Log[1 - x] - Log[1 + x]","A",1
307,1,23,23,0.0047908,"\int \frac{4-x+2 x^2}{4 x+x^3} \, dx","Integrate[(4 - x + 2*x^2)/(4*x + x^3),x]","\frac{1}{2} \log \left(x^2+4\right)+\log (x)-\frac{1}{2} \tan ^{-1}\left(\frac{x}{2}\right)","\frac{1}{2} \log \left(x^2+4\right)+\log (x)-\frac{1}{2} \tan ^{-1}\left(\frac{x}{2}\right)",1,"-1/2*ArcTan[x/2] + Log[x] + Log[4 + x^2]/2","A",1
308,1,93,103,0.0433693,"\int \frac{1+x^2+x^3}{(-1+x) x \left(1+x^2\right)^3 \left(1+x+x^2\right)} \, dx","Integrate[(1 + x^2 + x^3)/((-1 + x)*x*(1 + x^2)^3*(1 + x + x^2)),x]","\frac{1}{48} \left(-14 \log \left(1-x^3\right)+\frac{6 (x+1)}{\left(x^2+1\right)^2}+\frac{9 (3 x-2)}{x^2+1}+45 \log \left(x^2+1\right)-10 \log \left(x^2+x+1\right)+20 \log (1-x)-48 \log (x)+21 \tan ^{-1}(x)-16 \sqrt{3} \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)\right)","-\frac{3 (1-x)}{8 \left(x^2+1\right)}+\frac{3 x}{16 \left(x^2+1\right)}+\frac{x+1}{8 \left(x^2+1\right)^2}+\frac{15}{16} \log \left(x^2+1\right)-\frac{1}{2} \log \left(x^2+x+1\right)+\frac{1}{8} \log (1-x)-\log (x)+\frac{7}{16} \tan ^{-1}(x)-\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{\sqrt{3}}",1,"((6*(1 + x))/(1 + x^2)^2 + (9*(-2 + 3*x))/(1 + x^2) + 21*ArcTan[x] - 16*Sqrt[3]*ArcTan[(1 + 2*x)/Sqrt[3]] + 20*Log[1 - x] - 48*Log[x] + 45*Log[1 + x^2] - 10*Log[1 + x + x^2] - 14*Log[1 - x^3])/48","A",1
309,1,30,33,0.0106389,"\int \frac{1-3 x+2 x^2-x^3}{\left(1+x^2\right)^2} \, dx","Integrate[(1 - 3*x + 2*x^2 - x^3)/(1 + x^2)^2,x]","\frac{1}{2} \left(\frac{2-x}{x^2+1}-\log \left(x^2+1\right)+3 \tan ^{-1}(x)\right)","\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)/(1 + x^2) + 3*ArcTan[x] - Log[1 + x^2])/2","A",1
310,1,33,33,0.0186177,"\int \frac{1-3 x+2 x^2-x^3}{x \left(1+x^2\right)^2} \, dx","Integrate[(1 - 3*x + 2*x^2 - x^3)/(x*(1 + x^2)^2),x]","\frac{-2 x-1}{2 \left(x^2+1\right)}-\frac{1}{2} \log \left(x^2+1\right)+\log (x)-2 \tan ^{-1}(x)","-\frac{2 x+1}{2 \left(x^2+1\right)}-\frac{1}{2} \log \left(x^2+1\right)+\log (x)-2 \tan ^{-1}(x)",1,"(-1 - 2*x)/(2*(1 + x^2)) - 2*ArcTan[x] + Log[x] - Log[1 + x^2]/2","A",1
311,1,25,25,0.0050434,"\int \frac{1-x-x^2+x^3+x^4}{-x+x^3} \, dx","Integrate[(1 - x - x^2 + x^3 + x^4)/(-x + x^3),x]","\frac{x^2}{2}+\frac{1}{2} \log \left(1-x^2\right)+x-\log (x)","\frac{x^2}{2}+\frac{1}{2} \log \left(1-x^2\right)+x-\log (x)",1,"x + x^2/2 - Log[x] + Log[1 - x^2]/2","A",1
312,1,36,36,0.0145591,"\int \frac{2-4 x^2+x^3}{\left(1+x^2\right) \left(2+x^2\right)} \, dx","Integrate[(2 - 4*x^2 + x^3)/((1 + x^2)*(2 + x^2)),x]","-\frac{1}{2} \log \left(x^2+1\right)+\log \left(x^2+2\right)+6 \tan ^{-1}(x)-5 \sqrt{2} \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)","-\frac{1}{2} \log \left(x^2+1\right)+\log \left(x^2+2\right)+6 \tan ^{-1}(x)-5 \sqrt{2} \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)",1,"6*ArcTan[x] - 5*Sqrt[2]*ArcTan[x/Sqrt[2]] - Log[1 + x^2]/2 + Log[2 + x^2]","A",1
313,1,29,29,0.0166009,"\int \frac{1+x^2+x^4}{\left(1+x^2\right) \left(4+x^2\right)^2} \, dx","Integrate[(1 + x^2 + x^4)/((1 + x^2)*(4 + x^2)^2),x]","-\frac{13 x}{24 \left(x^2+4\right)}+\frac{25}{144} \tan ^{-1}\left(\frac{x}{2}\right)+\frac{1}{9} \tan ^{-1}(x)","-\frac{13 x}{24 \left(x^2+4\right)}+\frac{25}{144} \tan ^{-1}\left(\frac{x}{2}\right)+\frac{1}{9} \tan ^{-1}(x)",1,"(-13*x)/(24*(4 + x^2)) + (25*ArcTan[x/2])/144 + ArcTan[x]/9","A",1
314,1,46,46,0.0255263,"\int \frac{1+x^2+x^3}{2 x^2+x^3+x^4} \, dx","Integrate[(1 + x^2 + x^3)/(2*x^2 + x^3 + x^4),x]","\frac{5}{8} \log \left(x^2+x+2\right)-\frac{1}{2 x}-\frac{\log (x)}{4}+\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{7}}\right)}{4 \sqrt{7}}","\frac{5}{8} \log \left(x^2+x+2\right)-\frac{1}{2 x}-\frac{\log (x)}{4}+\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{7}}\right)}{4 \sqrt{7}}",1,"-1/2*1/x + ArcTan[(1 + 2*x)/Sqrt[7]]/(4*Sqrt[7]) - Log[x]/4 + (5*Log[2 + x + x^2])/8","A",1
315,1,26,22,0.005503,"\int \frac{1-12 x+x^2+x^3}{-12+x+x^2} \, dx","Integrate[(1 - 12*x + x^2 + x^3)/(-12 + x + x^2),x]","\frac{x^2}{2}+\frac{1}{7} \log (3-x)-\frac{1}{7} \log (x+4)","\frac{x^2}{2}-\frac{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",1
316,1,17,17,0.0062606,"\int \frac{-3+5 x+6 x^2}{-3 x+2 x^2+x^3} \, dx","Integrate[(-3 + 5*x + 6*x^2)/(-3*x + 2*x^2 + x^3),x]","2 \log (1-x)+\log (x)+3 \log (x+3)","2 \log (1-x)+\log (x)+3 \log (x+3)",1,"2*Log[1 - x] + Log[x] + 3*Log[3 + x]","A",1
317,1,14,14,0.0038084,"\int \frac{-2+3 x+5 x^2}{2 x^2+x^3} \, dx","Integrate[(-2 + 3*x + 5*x^2)/(2*x^2 + x^3),x]","\frac{1}{x}+2 \log (x)+3 \log (x+2)","\frac{1}{x}+2 \log (x)+3 \log (x+2)",1,"x^(-1) + 2*Log[x] + 3*Log[2 + x]","A",1
318,1,25,19,0.0073365,"\int \frac{18-2 x-4 x^2}{-6+x+4 x^2+x^3} \, dx","Integrate[(18 - 2*x - 4*x^2)/(-6 + x + 4*x^2 + x^3),x]","-2 \left(-\frac{1}{2} \log (1-x)+\log (x+2)+\frac{3}{2} \log (x+3)\right)","\log (1-x)-2 \log (x+2)-3 \log (x+3)",1,"-2*(-1/2*Log[1 - x] + Log[2 + x] + (3*Log[3 + x])/2)","A",1
319,1,23,23,0.0091169,"\int \frac{1+x-2 x^2+x^3}{4+5 x^2+x^4} \, dx","Integrate[(1 + x - 2*x^2 + x^3)/(4 + 5*x^2 + x^4),x]","\frac{1}{2} \log \left(x^2+4\right)-\frac{3}{2} \tan ^{-1}\left(\frac{x}{2}\right)+\tan ^{-1}(x)","\frac{1}{2} \log \left(x^2+4\right)-\frac{3}{2} \tan ^{-1}\left(\frac{x}{2}\right)+\tan ^{-1}(x)",1,"(-3*ArcTan[x/2])/2 + ArcTan[x] + Log[4 + x^2]/2","A",1
320,1,57,63,0.0265842,"\int \frac{-32+5 x-27 x^2+4 x^3}{-70-299 x-286 x^2+50 x^3-13 x^4+30 x^5} \, dx","Integrate[(-32 + 5*x - 27*x^2 + 4*x^3)/(-70 - 299*x - 286*x^2 + 50*x^3 - 13*x^4 + 30*x^5),x]","\frac{453009 \log \left(x^2+x+5\right)-418418 \log (7-3 x)-11023670 \log (2 x+1)+10536070 \log (5 x+2)+163508 \sqrt{19} \tan ^{-1}\left(\frac{2 x+1}{\sqrt{19}}\right)}{10660615}","\frac{11049 \log \left(x^2+x+5\right)}{260015}-\frac{3146 \log (7-3 x)}{80155}-\frac{334}{323} \log (2 x+1)+\frac{4822 \log (5 x+2)}{4879}+\frac{3988 \tan ^{-1}\left(\frac{2 x+1}{\sqrt{19}}\right)}{13685 \sqrt{19}}",1,"(163508*Sqrt[19]*ArcTan[(1 + 2*x)/Sqrt[19]] - 418418*Log[7 - 3*x] - 11023670*Log[1 + 2*x] + 10536070*Log[2 + 5*x] + 453009*Log[5 + x + x^2])/10660615","A",1
321,1,67,69,0.0474085,"\int \frac{8-13 x^2-7 x^3+12 x^5}{4-20 x+41 x^2-80 x^3+116 x^4-80 x^5+100 x^6} \, dx","Integrate[(8 - 13*x^2 - 7*x^3 + 12*x^5)/(4 - 20*x + 41*x^2 - 80*x^3 + 116*x^4 - 80*x^5 + 100*x^6),x]","\frac{142150 \log \left(2 x^2+1\right)-\frac{33 \left(36458 x^2+4675 x+2554\right)}{10 x^3-4 x^2+5 x-2}-236384 \log (2-5 x)+12575 \sqrt{2} \tan ^{-1}\left(\sqrt{2} x\right)}{399300}","-\frac{502 x+313}{1452 \left(2 x^2+1\right)}+\frac{2843 \log \left(2 x^2+1\right)}{7986}+\frac{5828}{9075 (2-5 x)}-\frac{59096 \log (2-5 x)}{99825}+\frac{503 \tan ^{-1}\left(\sqrt{2} x\right)}{7986 \sqrt{2}}",1,"((-33*(2554 + 4675*x + 36458*x^2))/(-2 + 5*x - 4*x^2 + 10*x^3) + 12575*Sqrt[2]*ArcTan[Sqrt[2]*x] - 236384*Log[2 - 5*x] + 142150*Log[1 + 2*x^2])/399300","A",1
322,1,17,17,0.0056112,"\int \frac{9+x^4}{x^2 \left(9+x^2\right)} \, dx","Integrate[(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",1
323,1,19,19,0.0047441,"\int \frac{2 x+x^4}{1+x^2} \, dx","Integrate[(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",1
324,1,9,9,0.0057797,"\int \frac{-x+x^3}{(-1+x)^2 \left(1+x^2\right)} \, dx","Integrate[(-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",1
325,1,12,12,0.0049557,"\int \frac{2+5 x+3 x^2+2 x^3}{1+x+x^2} \, dx","Integrate[(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",1
326,1,58,65,0.0360077,"\int \frac{3-4 x-5 x^2+3 x^3}{x^3 \left(-1+x+x^2\right)} \, dx","Integrate[(3 - 4*x - 5*x^2 + 3*x^3)/(x^3*(-1 + x + x^2)),x]","\frac{1}{10} \left(\frac{15}{x^2}-\frac{10}{x}+\left(\sqrt{5}-15\right) \log \left(-2 x+\sqrt{5}-1\right)+30 \log (x)-\left(15+\sqrt{5}\right) \log \left(2 x+\sqrt{5}+1\right)\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,"(15/x^2 - 10/x + (-15 + Sqrt[5])*Log[-1 + Sqrt[5] - 2*x] + 30*Log[x] - (15 + Sqrt[5])*Log[1 + Sqrt[5] + 2*x])/10","A",1
327,1,28,28,0.0109419,"\int \frac{4+8 x+5 x^2+2 x^3}{\left(2+2 x+x^2\right)^2} \, dx","Integrate[(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",1
328,1,32,32,0.0234011,"\int \frac{(-1+x)^4 x^4}{1+x^2} \, dx","Integrate[((-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",1
329,1,39,31,0.0070636,"\int \frac{-20 x+4 x^2}{9-10 x^2+x^4} \, dx","Integrate[(-20*x + 4*x^2)/(9 - 10*x^2 + x^4),x]","4 \left(\frac{1}{4} \log (1-x)-\frac{1}{8} \log (3-x)+\frac{3}{8} \log (x+1)-\frac{1}{2} \log (x+3)\right)","\log (1-x)-\frac{1}{2} \log (3-x)+\frac{3}{2} \log (x+1)-2 \log (x+3)",1,"4*(Log[1 - x]/4 - Log[3 - x]/8 + (3*Log[1 + x])/8 - Log[3 + x]/2)","A",1
330,1,24,24,0.0089712,"\int \frac{-1+x+4 x^3}{(-1+x) x^2 \left(1+x^2\right)} \, dx","Integrate[(-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",1
331,1,23,23,0.0108758,"\int \frac{1-3 x+2 x^2-4 x^3+x^4}{\left(1+x^2\right)^3} \, dx","Integrate[(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/(1 + x^2)^2 + 2/(1 + x^2) + ArcTan[x]","A",1
332,1,23,23,0.0055388,"\int \frac{1-3 x+2 x^2-4 x^3+x^4}{1+3 x^2+3 x^4+x^6} \, dx","Integrate[(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/(1 + x^2)^2 + 2/(1 + x^2) + ArcTan[x]","A",1
333,1,13,13,0.0053982,"\int \frac{1+x+2 x^2+2 x^3}{x^2+x^3+x^4} \, dx","Integrate[(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",1
334,1,193,206,0.1068448,"\int \frac{x^2 (c+d x)^2}{a+b x^3} \, dx","Integrate[(x^2*(c + d*x)^2)/(a + b*x^3),x]","\frac{-\sqrt[3]{a} d \left(\sqrt[3]{a} d-2 \sqrt[3]{b} c\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)+2 b^{2/3} c^2 \log \left(a+b x^3\right)+2 \sqrt[3]{a} d \left(\sqrt[3]{a} d-2 \sqrt[3]{b} c\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)+2 \sqrt{3} \sqrt[3]{a} d \left(\sqrt[3]{a} d+2 \sqrt[3]{b} c\right) \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a}}}{\sqrt{3}}\right)+12 b^{2/3} c d x+3 b^{2/3} d^2 x^2}{6 b^{5/3}}","\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,"(12*b^(2/3)*c*d*x + 3*b^(2/3)*d^2*x^2 + 2*Sqrt[3]*a^(1/3)*d*(2*b^(1/3)*c + a^(1/3)*d)*ArcTan[(1 - (2*b^(1/3)*x)/a^(1/3))/Sqrt[3]] + 2*a^(1/3)*d*(-2*b^(1/3)*c + a^(1/3)*d)*Log[a^(1/3) + b^(1/3)*x] - 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] + 2*b^(2/3)*c^2*Log[a + b*x^3])/(6*b^(5/3))","A",1
335,1,45,45,0.0245908,"\int \frac{-x+2 x^3+4 x^5}{\left(3+2 x^2+x^4\right)^2} \, dx","Integrate[(-x + 2*x^3 + 4*x^5)/(3 + 2*x^2 + x^4)^2,x]","\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}}+\frac{5-7 x^2}{8 \left(x^4+2 x^2+3\right)}",1,"(5 - 7*x^2)/(8*(3 + 2*x^2 + x^4)) + (9*ArcTan[(1 + x^2)/Sqrt[2]])/(8*Sqrt[2])","A",1
336,1,44,59,0.0213435,"\int \frac{x+x^5}{\left(1+2 x^2+2 x^4\right)^3} \, dx","Integrate[(x + x^5)/(1 + 2*x^2 + 2*x^4)^3,x]","\tan ^{-1}\left(2 x^2+1\right)+\frac{32 x^6+48 x^4+36 x^2+11}{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}",1,"(11 + 36*x^2 + 48*x^4 + 32*x^6)/(16*(1 + 2*x^2 + 2*x^4)^2) + ArcTan[1 + 2*x^2]","A",1
337,1,234,209,0.2546423,"\int \frac{a+b x+c x^2}{d+e x^2+f x^4} \, dx","Integrate[(a + b*x + c*x^2)/(d + e*x^2 + f*x^4),x]","\frac{\frac{\sqrt{2} \left(2 a f+c \left(\sqrt{e^2-4 d f}-e\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{f} x}{\sqrt{e-\sqrt{e^2-4 d f}}}\right)}{\sqrt{f} \sqrt{e-\sqrt{e^2-4 d f}}}+\frac{\sqrt{2} \left(c \left(\sqrt{e^2-4 d f}+e\right)-2 a f\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{f} x}{\sqrt{\sqrt{e^2-4 d f}+e}}\right)}{\sqrt{f} \sqrt{\sqrt{e^2-4 d f}+e}}+b \log \left(\sqrt{e^2-4 d f}-e-2 f x^2\right)-b \log \left(\sqrt{e^2-4 d f}+e+2 f x^2\right)}{2 \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,"((Sqrt[2]*(2*a*f + c*(-e + Sqrt[e^2 - 4*d*f]))*ArcTan[(Sqrt[2]*Sqrt[f]*x)/Sqrt[e - Sqrt[e^2 - 4*d*f]]])/(Sqrt[f]*Sqrt[e - Sqrt[e^2 - 4*d*f]]) + (Sqrt[2]*(-2*a*f + c*(e + Sqrt[e^2 - 4*d*f]))*ArcTan[(Sqrt[2]*Sqrt[f]*x)/Sqrt[e + Sqrt[e^2 - 4*d*f]]])/(Sqrt[f]*Sqrt[e + Sqrt[e^2 - 4*d*f]]) + b*Log[-e + Sqrt[e^2 - 4*d*f] - 2*f*x^2] - b*Log[e + Sqrt[e^2 - 4*d*f] + 2*f*x^2])/(2*Sqrt[e^2 - 4*d*f])","A",1
338,1,245,224,0.2477711,"\int \frac{(d+e x)^2}{a+b x^2+c x^4} \, dx","Integrate[(d + e*x)^2/(a + b*x^2 + c*x^4),x]","\frac{\frac{\sqrt{2} \left(e^2 \left(\sqrt{b^2-4 a c}-b\right)+2 c d^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{c} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt{2} \left(e^2 \left(\sqrt{b^2-4 a c}+b\right)-2 c d^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{c} \sqrt{\sqrt{b^2-4 a c}+b}}+2 d e \log \left(\sqrt{b^2-4 a c}-b-2 c x^2\right)-2 d e \log \left(\sqrt{b^2-4 a c}+b+2 c x^2\right)}{2 \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,"((Sqrt[2]*(2*c*d^2 + (-b + Sqrt[b^2 - 4*a*c])*e^2)*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[c]*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + (Sqrt[2]*(-2*c*d^2 + (b + Sqrt[b^2 - 4*a*c])*e^2)*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[c]*Sqrt[b + Sqrt[b^2 - 4*a*c]]) + 2*d*e*Log[-b + Sqrt[b^2 - 4*a*c] - 2*c*x^2] - 2*d*e*Log[b + Sqrt[b^2 - 4*a*c] + 2*c*x^2])/(2*Sqrt[b^2 - 4*a*c])","A",1
339,1,56,56,0.0271924,"\int \frac{x^2}{(a+b x) (c+d x)} \, dx","Integrate[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",1
340,1,73,96,0.0349111,"\int \frac{x^2}{(c+d x) \left(a+b x^2\right)} \, dx","Integrate[x^2/((c + d*x)*(a + b*x^2)),x]","\frac{-2 \sqrt{a} \sqrt{b} c d \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)+a d^2 \log \left(a+b x^2\right)+2 b c^2 \log (c+d x)}{2 a b d^3+2 b^2 c^2 d}","\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,"(-2*Sqrt[a]*Sqrt[b]*c*d*ArcTan[(Sqrt[b]*x)/Sqrt[a]] + 2*b*c^2*Log[c + d*x] + a*d^2*Log[a + b*x^2])/(2*b^2*c^2*d + 2*a*b*d^3)","A",1
341,1,228,264,0.0904825,"\int \frac{x^2}{(c+d x) \left(a+b x^3\right)} \, dx","Integrate[x^2/((c + d*x)*(a + b*x^3)),x]","\frac{-\sqrt[3]{a} \sqrt[3]{b} c d \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)-a^{2/3} d^2 \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)+2 b^{2/3} c^2 \log \left(a+b x^3\right)+2 \sqrt[3]{a} d \left(\sqrt[3]{a} d+\sqrt[3]{b} c\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)+2 \sqrt{3} \sqrt[3]{a} d \left(\sqrt[3]{a} d-\sqrt[3]{b} c\right) \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a}}}{\sqrt{3}}\right)-6 b^{2/3} c^2 \log (c+d x)}{6 b^{2/3} \left(b c^3-a d^3\right)}","-\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,"(2*Sqrt[3]*a^(1/3)*d*(-(b^(1/3)*c) + a^(1/3)*d)*ArcTan[(1 - (2*b^(1/3)*x)/a^(1/3))/Sqrt[3]] + 2*a^(1/3)*d*(b^(1/3)*c + a^(1/3)*d)*Log[a^(1/3) + b^(1/3)*x] - 6*b^(2/3)*c^2*Log[c + d*x] - a^(1/3)*b^(1/3)*c*d*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2] - a^(2/3)*d^2*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2] + 2*b^(2/3)*c^2*Log[a + b*x^3])/(6*b^(2/3)*(b*c^3 - a*d^3))","A",1
342,1,370,417,0.2299615,"\int \frac{x^2}{(c+d x) \left(a+b x^4\right)} \, dx","Integrate[x^2/((c + d*x)*(a + b*x^4)),x]","\frac{-2 \left(2 a^{3/4} d^3-\sqrt{2} \sqrt{a} \sqrt[4]{b} c d^2+\sqrt{2} b^{3/4} c^3\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)+2 \left(-2 a^{3/4} d^3-\sqrt{2} \sqrt{a} \sqrt[4]{b} c d^2+\sqrt{2} b^{3/4} c^3\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)+\sqrt[4]{b} c \left(\sqrt{2} \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)-\sqrt{2} \sqrt{b} c^2 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)-2 \sqrt[4]{a} \sqrt[4]{b} c d \log \left(a+b x^4\right)+8 \sqrt[4]{a} \sqrt[4]{b} c d \log (c+d x)-\sqrt{2} \sqrt{a} d^2 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)\right)}{8 \sqrt[4]{a} \sqrt{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 \left(a+b x^4\right)}{4 \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{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{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,"(-2*(Sqrt[2]*b^(3/4)*c^3 - Sqrt[2]*Sqrt[a]*b^(1/4)*c*d^2 + 2*a^(3/4)*d^3)*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/a^(1/4)] + 2*(Sqrt[2]*b^(3/4)*c^3 - Sqrt[2]*Sqrt[a]*b^(1/4)*c*d^2 - 2*a^(3/4)*d^3)*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/a^(1/4)] + b^(1/4)*c*(8*a^(1/4)*b^(1/4)*c*d*Log[c + d*x] + Sqrt[2]*(Sqrt[b]*c^2 + Sqrt[a]*d^2)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2] - Sqrt[2]*Sqrt[b]*c^2*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2] - Sqrt[2]*Sqrt[a]*d^2*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2] - 2*a^(1/4)*b^(1/4)*c*d*Log[a + b*x^4]))/(8*a^(1/4)*Sqrt[b]*(b*c^4 + a*d^4))","A",1
343,1,24,16,0.0093059,"\int \frac{x}{(1-x) (1+x)^2} \, dx","Integrate[x/((1 - x)*(1 + x)^2),x]","\frac{1}{4} \left(\frac{2}{x+1}-\log (1-x)+\log (x+1)\right)","\frac{1}{2 (x+1)}+\frac{1}{2} \tanh ^{-1}(x)",1,"(2/(1 + x) - Log[1 - x] + Log[1 + x])/4","A",1
344,1,27,19,0.0114283,"\int \frac{x^2}{\left(1-x^2\right) \left(1+x^2\right)^2} \, dx","Integrate[x^2/((1 - x^2)*(1 + x^2)^2),x]","\frac{1}{8} \left(-\frac{2 x}{x^2+1}-\log (1-x)+\log (x+1)\right)","\frac{1}{4} \tanh ^{-1}(x)-\frac{x}{4 \left(x^2+1\right)}",1,"((-2*x)/(1 + x^2) - Log[1 - x] + Log[1 + x])/8","A",1
345,1,85,97,0.049759,"\int \frac{x^3}{\left(1-x^3\right) \left(1+x^3\right)^2} \, dx","Integrate[x^3/((1 - x^3)*(1 + x^3)^2),x]","\frac{1}{72} \left(-\frac{12 x}{x^3+1}+\log \left(x^2-x+1\right)+3 \log \left(x^2+x+1\right)-6 \log (1-x)-2 \log (x+1)-2 \sqrt{3} \tan ^{-1}\left(\frac{2 x-1}{\sqrt{3}}\right)+6 \sqrt{3} \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)\right)","-\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,"((-12*x)/(1 + x^3) - 2*Sqrt[3]*ArcTan[(-1 + 2*x)/Sqrt[3]] + 6*Sqrt[3]*ArcTan[(1 + 2*x)/Sqrt[3]] - 6*Log[1 - x] - 2*Log[1 + x] + Log[1 - x + x^2] + 3*Log[1 + x + x^2])/72","A",1
346,1,15,15,0.0078713,"\int \frac{9+x+3 x^2+x^3}{\left(1+x^2\right) \left(3+x^2\right)} \, dx","Integrate[(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",1
347,1,13,13,0.0066578,"\int \frac{3+x+x^2+x^3}{\left(1+x^2\right) \left(3+x^2\right)} \, dx","Integrate[(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",1
348,1,29,29,0.0137891,"\int \frac{-4+6 x-x^2+3 x^3}{\left(1+x^2\right) \left(2+x^2\right)} \, dx","Integrate[(-4 + 6*x - x^2 + 3*x^3)/((1 + x^2)*(2 + x^2)),x]","\frac{3}{2} \log \left(x^2+1\right)-3 \tan ^{-1}(x)+\sqrt{2} \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)","\frac{3}{2} \log \left(x^2+1\right)-3 \tan ^{-1}(x)+\sqrt{2} \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)",1,"-3*ArcTan[x] + Sqrt[2]*ArcTan[x/Sqrt[2]] + (3*Log[1 + x^2])/2","A",1
349,1,14,14,0.0083106,"\int \frac{1}{\left(4-4 x+x^2\right) \left(5-4 x+x^2\right)} \, dx","Integrate[1/((4 - 4*x + x^2)*(5 - 4*x + x^2)),x]","\tan ^{-1}(2-x)-\frac{1}{x-2}","\frac{1}{2-x}+\tan ^{-1}(2-x)",1,"-(-2 + x)^(-1) + ArcTan[2 - x]","A",1
350,1,12,12,0.0030714,"\int \frac{-3+x+x^2}{(-3+x) x^2} \, dx","Integrate[(-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",1
351,1,11,11,0.0048868,"\int \frac{1+x+4 x^2}{x+4 x^3} \, dx","Integrate[(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",1
352,1,12,12,0.0034316,"\int \frac{1-x+3 x^2}{-x^2+x^3} \, dx","Integrate[(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",1
353,1,12,12,0.0032696,"\int \frac{4+3 x+x^2}{x+x^2} \, dx","Integrate[(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",1
354,1,17,17,0.0048093,"\int \frac{4+x+3 x^2}{x+x^3} \, dx","Integrate[(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",1
355,1,13,13,0.0080824,"\int \frac{7-4 x+8 x^2}{(1+4 x) \left(1+x^2\right)} \, dx","Integrate[(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",1
356,1,22,28,0.0145854,"\int \frac{x^2}{(-1+x) \left(1+2 x+x^2\right)} \, dx","Integrate[x^2/((-1 + x)*(1 + 2*x + x^2)),x]","\frac{1}{4} \left(\frac{2}{x+1}+\log (x-1)+3 \log (x+1)\right)","\frac{1}{2 (x+1)}+\frac{1}{4} \log (1-x)+\frac{3}{4} \log (x+1)",1,"(2/(1 + x) + Log[-1 + x] + 3*Log[1 + x])/4","A",1
357,1,32,32,0.0165143,"\int \frac{-4+3 x+x^2}{(-1+2 x)^2 (3+2 x)} \, dx","Integrate[(-4 + 3*x + x^2)/((-1 + 2*x)^2*(3 + 2*x)),x]","\frac{9}{32 (2 x-1)}+\frac{41}{128} \log (1-2 x)-\frac{25}{128} \log (2 x+3)","-\frac{9}{32 (1-2 x)}+\frac{41}{128} \log (1-2 x)-\frac{25}{128} \log (2 x+3)",1,"9/(32*(-1 + 2*x)) + (41*Log[1 - 2*x])/128 - (25*Log[3 + 2*x])/128","A",1
358,1,28,23,0.007523,"\int \frac{5-4 x+3 x^2}{(-1+x) \left(1+x^2\right)} \, dx","Integrate[(5 - 4*x + 3*x^2)/((-1 + x)*(1 + x^2)),x]","\frac{1}{2} \log \left((x-1)^2+2 (x-1)+2\right)+2 \log (x-1)-3 \tan ^{-1}(x)","\frac{1}{2} \log \left(x^2+1\right)+2 \log (1-x)-3 \tan ^{-1}(x)",1,"-3*ArcTan[x] + Log[2 + 2*(-1 + x) + (-1 + x)^2]/2 + 2*Log[-1 + x]","A",1
359,1,22,24,0.0142937,"\int \frac{-1-2 x+x^2}{(-1+x)^2 \left(1+x^2\right)} \, dx","Integrate[(-1 - 2*x + x^2)/((-1 + x)^2*(1 + x^2)),x]","-\frac{1}{2} \log \left(x^2+1\right)+\frac{1}{x-1}+\log (x-1)+\tan ^{-1}(x)","-\frac{1}{2} \log \left(x^2+1\right)+\frac{1}{x-1}+\log (1-x)+\tan ^{-1}(x)",1,"(-1 + x)^(-1) + ArcTan[x] + Log[-1 + x] - Log[1 + x^2]/2","A",1
360,1,49,49,0.01411,"\int \frac{5+x^3}{\left(10-6 x+x^2\right) \left(\frac{1}{2}-x+x^2\right)} \, dx","Integrate[(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",1
361,1,19,25,0.0080431,"\int \frac{4+3 x+x^2}{(-3+x) (-2+x) (-1+x)} \, dx","Integrate[(4 + 3*x + x^2)/((-3 + x)*(-2 + x)*(-1 + x)),x]","11 \log (x-3)-14 \log (x-2)+4 \log (x-1)","4 \log (1-x)-14 \log (2-x)+11 \log (3-x)",1,"11*Log[-3 + x] - 14*Log[-2 + x] + 4*Log[-1 + x]","A",1
362,1,54,60,0.0526072,"\int \frac{1+16 x}{(5+x)^2 (-3+2 x) \left(1+x+x^2\right)} \, dx","Integrate[(1 + 16*x)/((5 + x)^2*(-3 + 2*x)*(1 + x + x^2)),x]","\frac{-243867 \log \left(x^2+x+1\right)-\frac{819546}{x+5}+176400 \log (3-2 x)+311334 \log (x+5)+152438 \sqrt{3} \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{2832102}","-\frac{481 \log \left(x^2+x+1\right)}{5586}-\frac{79}{273 (x+5)}+\frac{200 \log (3-2 x)}{3211}+\frac{2731 \log (x+5)}{24843}+\frac{451 \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{2793 \sqrt{3}}",1,"(-819546/(5 + x) + 152438*Sqrt[3]*ArcTan[(1 + 2*x)/Sqrt[3]] + 176400*Log[3 - 2*x] + 311334*Log[5 + x] - 243867*Log[1 + x + x^2])/2832102","A",1
363,1,11,11,0.0004597,"\int \frac{-1+x^3}{1+x+x^2} \, dx","Integrate[(-1 + x^3)/(1 + x + x^2),x]","\frac{x^2}{2}-x","\frac{x^2}{2}-x",1,"-x + x^2/2","A",1
364,1,29,29,0.0051231,"\int \frac{-3+x^3}{-7-6 x+x^2} \, dx","Integrate[(-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",1
365,1,45,45,0.0131684,"\int \frac{1+x^3}{\left(13+4 x+x^2\right)^2} \, dx","Integrate[(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",1
366,1,32,32,0.0187078,"\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","Integrate[(-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",1
367,1,159,148,0.0683567,"\int \frac{-1+x^4+7 x^5+x^9}{-7+6 x^4+x^8} \, dx","Integrate[(-1 + x^4 + 7*x^5 + x^9)/(-7 + 6*x^4 + x^8),x]","\frac{1}{56} \left(28 x^2-14 \log \left(x^2+1\right)-\sqrt{2} \sqrt[4]{7} \log \left(\sqrt{7} x^2-\sqrt{2} 7^{3/4} x+7\right)+\sqrt{2} \sqrt[4]{7} \log \left(\sqrt{7} x^2+\sqrt{2} 7^{3/4} x+7\right)+14 \log (1-x)+14 \log (x+1)-2 \sqrt{2} \sqrt[4]{7} \tan ^{-1}\left(1-\frac{\sqrt{2} x}{\sqrt[4]{7}}\right)+2 \sqrt{2} \sqrt[4]{7} \tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt[4]{7}}+1\right)\right)","\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,"(28*x^2 - 2*Sqrt[2]*7^(1/4)*ArcTan[1 - (Sqrt[2]*x)/7^(1/4)] + 2*Sqrt[2]*7^(1/4)*ArcTan[1 + (Sqrt[2]*x)/7^(1/4)] + 14*Log[1 - x] + 14*Log[1 + x] - 14*Log[1 + x^2] - Sqrt[2]*7^(1/4)*Log[7 - Sqrt[2]*7^(3/4)*x + Sqrt[7]*x^2] + Sqrt[2]*7^(1/4)*Log[7 + Sqrt[2]*7^(3/4)*x + Sqrt[7]*x^2])/56","A",1
368,1,101,112,0.0494668,"\int \frac{1+x^3+x^6}{x+x^5} \, dx","Integrate[(1 + x^3 + x^6)/(x + x^5),x]","\frac{1}{8} \left(-2 \log \left(x^4+1\right)+4 x^2+\sqrt{2} \log \left(x^2-\sqrt{2} x+1\right)-\sqrt{2} \log \left(x^2+\sqrt{2} x+1\right)+8 \log (x)-2 \left(\sqrt{2}-2\right) \tan ^{-1}\left(1-\sqrt{2} x\right)+2 \left(2+\sqrt{2}\right) \tan ^{-1}\left(\sqrt{2} x+1\right)\right)","-\frac{1}{4} \log \left(x^4+1\right)+\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}{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,"(4*x^2 - 2*(-2 + Sqrt[2])*ArcTan[1 - Sqrt[2]*x] + 2*(2 + Sqrt[2])*ArcTan[1 + Sqrt[2]*x] + 8*Log[x] + Sqrt[2]*Log[1 - Sqrt[2]*x + x^2] - Sqrt[2]*Log[1 + Sqrt[2]*x + x^2] - 2*Log[1 + x^4])/8","A",1
369,1,14,14,0.0034047,"\int \frac{1+x^2}{-x+x^2} \, dx","Integrate[(1 + x^2)/(-x + x^2),x]","x+2 \log (1-x)-\log (x)","x+2 \log (1-x)-\log (x)",1,"x + 2*Log[1 - x] - Log[x]","A",1
370,1,12,12,0.004598,"\int \frac{1+x^3}{-x+x^3} \, dx","Integrate[(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",1
371,1,17,17,0.0036284,"\int \frac{1+x^3}{-x^2+x^3} \, dx","Integrate[(1 + x^3)/(-x^2 + x^3),x]","x+\frac{1}{x}+2 \log (1-x)-\log (x)","x+\frac{1}{x}+2 \log (1-x)-\log (x)",1,"x^(-1) + x + 2*Log[1 - x] - Log[x]","A",1
372,1,17,17,0.004474,"\int \frac{-1+x^5}{-x+x^3} \, dx","Integrate[(-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",1
373,1,18,18,0.0044377,"\int \frac{1+x^4}{x^3+x^5} \, dx","Integrate[(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*1/x^2 - Log[x] + Log[1 + x^2]","A",1
374,1,10,10,0.0047599,"\int \frac{1+x^2}{x+2 x^2+x^3} \, dx","Integrate[(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",1
375,1,42,42,0.0068167,"\int \frac{1+x^5}{-10 x-3 x^2+x^3} \, dx","Integrate[(1 + x^5)/(-10*x - 3*x^2 + x^3),x]","\frac{x^3}{3}+\frac{3 x^2}{2}+19 x+\frac{3126}{35} \log (5-x)-\frac{\log (x)}{10}-\frac{31}{14} \log (x+2)","\frac{x^3}{3}+\frac{3 x^2}{2}+19 x+\frac{3126}{35} \log (5-x)-\frac{\log (x)}{10}-\frac{31}{14} \log (x+2)",1,"19*x + (3*x^2)/2 + x^3/3 + (3126*Log[5 - x])/35 - Log[x]/10 - (31*Log[2 + x])/14","A",1
376,1,46,46,0.0169403,"\int \frac{15-5 x+x^2+x^3}{\left(5+x^2\right) \left(3+2 x+x^2\right)} \, dx","Integrate[(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",1
377,1,19,19,0.0030853,"\int \frac{1}{\left(1+x^2\right) \left(3+\frac{10 x}{1+x^2}\right)} \, dx","Integrate[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,"-1/8*Log[3 + x] + Log[1 + 3*x]/8","A",1
378,1,40,40,0.005312,"\int \frac{x^3}{13+\frac{2}{x}+15 x} \, dx","Integrate[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",1
379,1,33,33,0.00434,"\int \frac{x^2}{13+\frac{2}{x}+15 x} \, dx","Integrate[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",1
380,1,26,26,0.0046028,"\int \frac{x}{13+\frac{2}{x}+15 x} \, dx","Integrate[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",1
381,1,21,21,0.0030264,"\int \frac{1}{13+\frac{2}{x}+15 x} \, dx","Integrate[(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",1
382,1,21,21,0.0026797,"\int \frac{1}{x \left(13+\frac{2}{x}+15 x\right)} \, dx","Integrate[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,"-1/7*Log[2 + 3*x] + Log[1 + 5*x]/7","A",1
383,1,27,27,0.004485,"\int \frac{1}{x^2 \left(13+\frac{2}{x}+15 x\right)} \, dx","Integrate[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",1
384,1,34,34,0.004215,"\int \frac{1}{x^3 \left(13+\frac{2}{x}+15 x\right)} \, dx","Integrate[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*1/x - (13*Log[x])/4 - (9*Log[2 + 3*x])/28 + (25*Log[1 + 5*x])/7","A",1
385,1,41,41,0.0048665,"\int \frac{1}{x^4 \left(13+\frac{2}{x}+15 x\right)} \, dx","Integrate[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*1/x^2 + 13/(4*x) + (139*Log[x])/8 + (27*Log[2 + 3*x])/56 - (125*Log[1 + 5*x])/7","A",1
386,1,48,48,0.0050797,"\int \frac{1}{x^5 \left(13+\frac{2}{x}+15 x\right)} \, dx","Integrate[1/(x^5*(13 + 2/x + 15*x)),x]","-\frac{1}{6 x^3}+\frac{13}{8 x^2}-\frac{139}{8 x}-\frac{1417 \log (x)}{16}-\frac{81}{112} \log (3 x+2)+\frac{625}{7} \log (5 x+1)","-\frac{1}{6 x^3}+\frac{13}{8 x^2}-\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*1/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",1
387,1,61,157,0.0161084,"\int \frac{x^2}{2-\left(1+x^2\right)^4} \, dx","Integrate[x^2/(2 - (1 + x^2)^4),x]","-\frac{1}{8} \text{RootSum}\left[\text{$\#$1}^8+4 \text{$\#$1}^6+6 \text{$\#$1}^4+4 \text{$\#$1}^2-1\&,\frac{\text{$\#$1} \log (x-\text{$\#$1})}{\text{$\#$1}^6+3 \text{$\#$1}^4+3 \text{$\#$1}^2+1}\&\right]","\frac{i \sqrt{1-i \sqrt[4]{2}} \tan ^{-1}\left(\frac{x}{\sqrt{1-i \sqrt[4]{2}}}\right)}{4\ 2^{3/4}}-\frac{i \sqrt{1+i \sqrt[4]{2}} \tan ^{-1}\left(\frac{x}{\sqrt{1+i \sqrt[4]{2}}}\right)}{4\ 2^{3/4}}-\frac{\sqrt{1+\sqrt[4]{2}} \tan ^{-1}\left(\frac{x}{\sqrt{1+\sqrt[4]{2}}}\right)}{4\ 2^{3/4}}+\frac{\sqrt{\sqrt[4]{2}-1} \tanh ^{-1}\left(\frac{x}{\sqrt{\sqrt[4]{2}-1}}\right)}{4\ 2^{3/4}}",1,"-1/8*RootSum[-1 + 4*#1^2 + 6*#1^4 + 4*#1^6 + #1^8 & , (Log[x - #1]*#1)/(1 + 3*#1^2 + 3*#1^4 + #1^6) & ]","C",1
388,1,61,157,0.0171003,"\int \frac{x^2}{2-\left(1-x^2\right)^4} \, dx","Integrate[x^2/(2 - (1 - x^2)^4),x]","-\frac{1}{8} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+6 \text{$\#$1}^4-4 \text{$\#$1}^2-1\&,\frac{\text{$\#$1} \log (x-\text{$\#$1})}{\text{$\#$1}^6-3 \text{$\#$1}^4+3 \text{$\#$1}^2-1}\&\right]","-\frac{\sqrt{\sqrt[4]{2}-1} \tan ^{-1}\left(\frac{x}{\sqrt{\sqrt[4]{2}-1}}\right)}{4\ 2^{3/4}}-\frac{i \sqrt{1-i \sqrt[4]{2}} \tanh ^{-1}\left(\frac{x}{\sqrt{1-i \sqrt[4]{2}}}\right)}{4\ 2^{3/4}}+\frac{i \sqrt{1+i \sqrt[4]{2}} \tanh ^{-1}\left(\frac{x}{\sqrt{1+i \sqrt[4]{2}}}\right)}{4\ 2^{3/4}}+\frac{\sqrt{1+\sqrt[4]{2}} \tanh ^{-1}\left(\frac{x}{\sqrt{1+\sqrt[4]{2}}}\right)}{4\ 2^{3/4}}",1,"-1/8*RootSum[-1 - 4*#1^2 + 6*#1^4 - 4*#1^6 + #1^8 & , (Log[x - #1]*#1)/(-1 + 3*#1^2 - 3*#1^4 + #1^6) & ]","C",1
389,1,61,188,0.0128559,"\int \frac{x^2}{2+\left(1+x^2\right)^4} \, dx","Integrate[x^2/(2 + (1 + x^2)^4),x]","\frac{1}{8} \text{RootSum}\left[\text{$\#$1}^8+4 \text{$\#$1}^6+6 \text{$\#$1}^4+4 \text{$\#$1}^2+3\&,\frac{\text{$\#$1} \log (x-\text{$\#$1})}{\text{$\#$1}^6+3 \text{$\#$1}^4+3 \text{$\#$1}^2+1}\&\right]","\frac{\sqrt[4]{-1} \sqrt{1-\sqrt[4]{-2}} \tan ^{-1}\left(\frac{x}{\sqrt{1-\sqrt[4]{-2}}}\right)}{4\ 2^{3/4}}-\frac{(-1)^{3/4} \sqrt{1+i \sqrt[4]{-2}} \tan ^{-1}\left(\frac{x}{\sqrt{1+i \sqrt[4]{-2}}}\right)}{4\ 2^{3/4}}-\frac{\sqrt[4]{-1} \sqrt{1+\sqrt[4]{-2}} \tan ^{-1}\left(\frac{x}{\sqrt{1+\sqrt[4]{-2}}}\right)}{4\ 2^{3/4}}+\frac{1}{8} i \left(\sqrt[4]{-2}+\sqrt{2}\right) \sqrt{\frac{1+i}{2^{3/4}+(1+i)}} \tan ^{-1}\left(\sqrt{\frac{1+i}{2^{3/4}+(1+i)}} x\right)",1,"RootSum[3 + 4*#1^2 + 6*#1^4 + 4*#1^6 + #1^8 & , (Log[x - #1]*#1)/(1 + 3*#1^2 + 3*#1^4 + #1^6) & ]/8","C",1
390,1,61,188,0.0132025,"\int \frac{x^2}{2+\left(1-x^2\right)^4} \, dx","Integrate[x^2/(2 + (1 - x^2)^4),x]","\frac{1}{8} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+6 \text{$\#$1}^4-4 \text{$\#$1}^2+3\&,\frac{\text{$\#$1} \log (x-\text{$\#$1})}{\text{$\#$1}^6-3 \text{$\#$1}^4+3 \text{$\#$1}^2-1}\&\right]","-\frac{\sqrt[4]{-1} \sqrt{1-\sqrt[4]{-2}} \tanh ^{-1}\left(\frac{x}{\sqrt{1-\sqrt[4]{-2}}}\right)}{4\ 2^{3/4}}+\frac{(-1)^{3/4} \sqrt{1+i \sqrt[4]{-2}} \tanh ^{-1}\left(\frac{x}{\sqrt{1+i \sqrt[4]{-2}}}\right)}{4\ 2^{3/4}}+\frac{\sqrt[4]{-1} \sqrt{1+\sqrt[4]{-2}} \tanh ^{-1}\left(\frac{x}{\sqrt{1+\sqrt[4]{-2}}}\right)}{4\ 2^{3/4}}-\frac{1}{8} i \left(\sqrt[4]{-2}+\sqrt{2}\right) \sqrt{\frac{1+i}{2^{3/4}+(1+i)}} \tanh ^{-1}\left(\sqrt{\frac{1+i}{2^{3/4}+(1+i)}} x\right)",1,"RootSum[3 - 4*#1^2 + 6*#1^4 - 4*#1^6 + #1^8 & , (Log[x - #1]*#1)/(-1 + 3*#1^2 - 3*#1^4 + #1^6) & ]/8","C",1
391,1,63,663,0.0373941,"\int \frac{1-x^2}{a+b \left(1-x^2\right)^4} \, dx","Integrate[(1 - x^2)/(a + b*(1 - x^2)^4),x]","-\frac{\text{RootSum}\left[\text{$\#$1}^8 b-4 \text{$\#$1}^6 b+6 \text{$\#$1}^4 b-4 \text{$\#$1}^2 b+a+b\&,\frac{\log (x-\text{$\#$1})}{\text{$\#$1}^5-2 \text{$\#$1}^3+\text{$\#$1}}\&\right]}{8 b}","\frac{\sqrt{\sqrt{\sqrt{-a}+\sqrt{b}}+\sqrt[4]{b}} \log \left(-\sqrt{2} \sqrt[8]{b} x \sqrt{\sqrt{\sqrt{-a}+\sqrt{b}}+\sqrt[4]{b}}+\sqrt{\sqrt{-a}+\sqrt{b}}+\sqrt[4]{b} x^2\right)}{8 \sqrt{2} \sqrt{-a} b^{3/8} \sqrt{\sqrt{-a}+\sqrt{b}}}-\frac{\sqrt{\sqrt{\sqrt{-a}+\sqrt{b}}+\sqrt[4]{b}} \log \left(\sqrt{2} \sqrt[8]{b} x \sqrt{\sqrt{\sqrt{-a}+\sqrt{b}}+\sqrt[4]{b}}+\sqrt{\sqrt{-a}+\sqrt{b}}+\sqrt[4]{b} x^2\right)}{8 \sqrt{2} \sqrt{-a} b^{3/8} \sqrt{\sqrt{-a}+\sqrt{b}}}-\frac{\tan ^{-1}\left(\frac{\sqrt[8]{b} x}{\sqrt{\sqrt[4]{-a}-\sqrt[4]{b}}}\right)}{4 \sqrt{-a} b^{3/8} \sqrt{\sqrt[4]{-a}-\sqrt[4]{b}}}-\frac{\sqrt{\sqrt{\sqrt{-a}+\sqrt{b}}-\sqrt[4]{b}} \tan ^{-1}\left(\frac{\sqrt{\sqrt{\sqrt{-a}+\sqrt{b}}+\sqrt[4]{b}}-\sqrt{2} \sqrt[8]{b} x}{\sqrt{\sqrt{\sqrt{-a}+\sqrt{b}}-\sqrt[4]{b}}}\right)}{4 \sqrt{2} \sqrt{-a} b^{3/8} \sqrt{\sqrt{-a}+\sqrt{b}}}+\frac{\sqrt{\sqrt{\sqrt{-a}+\sqrt{b}}-\sqrt[4]{b}} \tan ^{-1}\left(\frac{\sqrt{\sqrt{\sqrt{-a}+\sqrt{b}}+\sqrt[4]{b}}+\sqrt{2} \sqrt[8]{b} x}{\sqrt{\sqrt{\sqrt{-a}+\sqrt{b}}-\sqrt[4]{b}}}\right)}{4 \sqrt{2} \sqrt{-a} b^{3/8} \sqrt{\sqrt{-a}+\sqrt{b}}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{b} x}{\sqrt{\sqrt[4]{-a}+\sqrt[4]{b}}}\right)}{4 \sqrt{-a} b^{3/8} \sqrt{\sqrt[4]{-a}+\sqrt[4]{b}}}",1,"-1/8*RootSum[a + b - 4*b*#1^2 + 6*b*#1^4 - 4*b*#1^6 + b*#1^8 & , Log[x - #1]/(#1 - 2*#1^3 + #1^5) & ]/b","C",1
392,1,63,663,0.0311387,"\int \frac{1-x^2}{a+b \left(-1+x^2\right)^4} \, dx","Integrate[(1 - x^2)/(a + b*(-1 + x^2)^4),x]","-\frac{\text{RootSum}\left[\text{$\#$1}^8 b-4 \text{$\#$1}^6 b+6 \text{$\#$1}^4 b-4 \text{$\#$1}^2 b+a+b\&,\frac{\log (x-\text{$\#$1})}{\text{$\#$1}^5-2 \text{$\#$1}^3+\text{$\#$1}}\&\right]}{8 b}","\frac{\sqrt{\sqrt{\sqrt{-a}+\sqrt{b}}+\sqrt[4]{b}} \log \left(-\sqrt{2} \sqrt[8]{b} x \sqrt{\sqrt{\sqrt{-a}+\sqrt{b}}+\sqrt[4]{b}}+\sqrt{\sqrt{-a}+\sqrt{b}}+\sqrt[4]{b} x^2\right)}{8 \sqrt{2} \sqrt{-a} b^{3/8} \sqrt{\sqrt{-a}+\sqrt{b}}}-\frac{\sqrt{\sqrt{\sqrt{-a}+\sqrt{b}}+\sqrt[4]{b}} \log \left(\sqrt{2} \sqrt[8]{b} x \sqrt{\sqrt{\sqrt{-a}+\sqrt{b}}+\sqrt[4]{b}}+\sqrt{\sqrt{-a}+\sqrt{b}}+\sqrt[4]{b} x^2\right)}{8 \sqrt{2} \sqrt{-a} b^{3/8} \sqrt{\sqrt{-a}+\sqrt{b}}}-\frac{\tan ^{-1}\left(\frac{\sqrt[8]{b} x}{\sqrt{\sqrt[4]{-a}-\sqrt[4]{b}}}\right)}{4 \sqrt{-a} b^{3/8} \sqrt{\sqrt[4]{-a}-\sqrt[4]{b}}}-\frac{\sqrt{\sqrt{\sqrt{-a}+\sqrt{b}}-\sqrt[4]{b}} \tan ^{-1}\left(\frac{\sqrt{\sqrt{\sqrt{-a}+\sqrt{b}}+\sqrt[4]{b}}-\sqrt{2} \sqrt[8]{b} x}{\sqrt{\sqrt{\sqrt{-a}+\sqrt{b}}-\sqrt[4]{b}}}\right)}{4 \sqrt{2} \sqrt{-a} b^{3/8} \sqrt{\sqrt{-a}+\sqrt{b}}}+\frac{\sqrt{\sqrt{\sqrt{-a}+\sqrt{b}}-\sqrt[4]{b}} \tan ^{-1}\left(\frac{\sqrt{\sqrt{\sqrt{-a}+\sqrt{b}}+\sqrt[4]{b}}+\sqrt{2} \sqrt[8]{b} x}{\sqrt{\sqrt{\sqrt{-a}+\sqrt{b}}-\sqrt[4]{b}}}\right)}{4 \sqrt{2} \sqrt{-a} b^{3/8} \sqrt{\sqrt{-a}+\sqrt{b}}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{b} x}{\sqrt{\sqrt[4]{-a}+\sqrt[4]{b}}}\right)}{4 \sqrt{-a} b^{3/8} \sqrt{\sqrt[4]{-a}+\sqrt[4]{b}}}",1,"-1/8*RootSum[a + b - 4*b*#1^2 + 6*b*#1^4 - 4*b*#1^6 + b*#1^8 & , Log[x - #1]/(#1 - 2*#1^3 + #1^5) & ]/b","C",1
393,1,95,168,0.061094,"\int \frac{\left(1+x^2\right)^2}{a x^6+b \left(1+x^2\right)^3} \, dx","Integrate[(1 + x^2)^2/(a*x^6 + b*(1 + x^2)^3),x]","\frac{1}{6} \text{RootSum}\left[\text{$\#$1}^6 a+\text{$\#$1}^6 b+3 \text{$\#$1}^4 b+3 \text{$\#$1}^2 b+b\&,\frac{\text{$\#$1}^4 \log (x-\text{$\#$1})+2 \text{$\#$1}^2 \log (x-\text{$\#$1})+\log (x-\text{$\#$1})}{\text{$\#$1}^5 a+\text{$\#$1}^5 b+2 \text{$\#$1}^3 b+\text{$\#$1} b}\&\right]","\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,"RootSum[b + 3*b*#1^2 + 3*b*#1^4 + a*#1^6 + b*#1^6 & , (Log[x - #1] + 2*Log[x - #1]*#1^2 + Log[x - #1]*#1^4)/(b*#1 + 2*b*#1^3 + a*#1^5 + b*#1^5) & ]/6","C",1
394,1,322,320,0.2491964,"\int \frac{(d+e x)^3}{a+c x^4} \, dx","Integrate[(d + e*x)^3/(a + c*x^4),x]","\frac{-\sqrt{2} \sqrt[4]{c} \left(\sqrt[4]{a} \sqrt{c} d^3-3 a^{3/4} d e^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)+\sqrt{2} \sqrt[4]{c} \left(\sqrt[4]{a} \sqrt{c} d^3-3 a^{3/4} d e^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)-2 \sqrt[4]{a} \sqrt[4]{c} d \left(6 \sqrt[4]{a} \sqrt[4]{c} d e+3 \sqrt{2} \sqrt{a} e^2+\sqrt{2} \sqrt{c} d^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)+2 \sqrt[4]{a} \sqrt[4]{c} d \left(-6 \sqrt[4]{a} \sqrt[4]{c} d e+3 \sqrt{2} \sqrt{a} e^2+\sqrt{2} \sqrt{c} d^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)+2 a e^3 \log \left(a+c x^4\right)}{8 a 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,"(-2*a^(1/4)*c^(1/4)*d*(Sqrt[2]*Sqrt[c]*d^2 + 6*a^(1/4)*c^(1/4)*d*e + 3*Sqrt[2]*Sqrt[a]*e^2)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)] + 2*a^(1/4)*c^(1/4)*d*(Sqrt[2]*Sqrt[c]*d^2 - 6*a^(1/4)*c^(1/4)*d*e + 3*Sqrt[2]*Sqrt[a]*e^2)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)] - Sqrt[2]*c^(1/4)*(a^(1/4)*Sqrt[c]*d^3 - 3*a^(3/4)*d*e^2)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2] + Sqrt[2]*c^(1/4)*(a^(1/4)*Sqrt[c]*d^3 - 3*a^(3/4)*d*e^2)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2] + 2*a*e^3*Log[a + c*x^4])/(8*a*c)","A",1
395,1,243,291,0.0995484,"\int \frac{(d+e x)^2}{a+c x^4} \, dx","Integrate[(d + e*x)^2/(a + c*x^4),x]","\frac{-\sqrt{2} \left(\sqrt{c} d^2-\sqrt{a} e^2\right) \left(\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)-\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)\right)-2 \left(4 \sqrt[4]{a} \sqrt[4]{c} d e+\sqrt{2} \sqrt{a} e^2+\sqrt{2} \sqrt{c} d^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)+2 \left(-4 \sqrt[4]{a} \sqrt[4]{c} d e+\sqrt{2} \sqrt{a} e^2+\sqrt{2} \sqrt{c} d^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{8 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{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,"(-2*(Sqrt[2]*Sqrt[c]*d^2 + 4*a^(1/4)*c^(1/4)*d*e + Sqrt[2]*Sqrt[a]*e^2)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)] + 2*(Sqrt[2]*Sqrt[c]*d^2 - 4*a^(1/4)*c^(1/4)*d*e + Sqrt[2]*Sqrt[a]*e^2)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)] - Sqrt[2]*(Sqrt[c]*d^2 - Sqrt[a]*e^2)*(Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2] - Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2]))/(8*a^(3/4)*c^(3/4))","A",1
396,1,184,219,0.0587665,"\int \frac{d+e x}{a+c x^4} \, dx","Integrate[(d + e*x)/(a + c*x^4),x]","\frac{-2 \left(2 \sqrt[4]{a} e+\sqrt{2} \sqrt[4]{c} d\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)+2 \left(\sqrt{2} \sqrt[4]{c} d-2 \sqrt[4]{a} e\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)+\sqrt{2} \sqrt[4]{c} d \left(\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)-\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)\right)}{8 a^{3/4} \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,"(-2*(Sqrt[2]*c^(1/4)*d + 2*a^(1/4)*e)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)] + 2*(Sqrt[2]*c^(1/4)*d - 2*a^(1/4)*e)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)] + Sqrt[2]*c^(1/4)*d*(-Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2] + Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2]))/(8*a^(3/4)*Sqrt[c])","A",1
397,1,134,185,0.0176751,"\int \frac{1}{a+c x^4} \, dx","Integrate[(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)+\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)-2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)+2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\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{\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,"(-2*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)] + 2*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)] - Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2] + 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",1
398,1,404,416,0.1492774,"\int \frac{1}{(d+e x) \left(a+c x^4\right)} \, dx","Integrate[1/((d + e*x)*(a + c*x^4)),x]","\frac{-2 a^{3/4} e^3 \log \left(a+c x^4\right)+8 a^{3/4} e^3 \log (d+e x)-\sqrt{2} c^{3/4} d^3 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)+\sqrt{2} c^{3/4} d^3 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)-2 \sqrt[4]{c} d \left(-2 \sqrt[4]{a} \sqrt[4]{c} d e+\sqrt{2} \sqrt{a} e^2+\sqrt{2} \sqrt{c} d^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)+2 \sqrt[4]{c} d \left(2 \sqrt[4]{a} \sqrt[4]{c} d e+\sqrt{2} \sqrt{a} e^2+\sqrt{2} \sqrt{c} d^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)+\sqrt{2} \sqrt{a} \sqrt[4]{c} d e^2 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)-\sqrt{2} \sqrt{a} \sqrt[4]{c} d e^2 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{8 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{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{e^3 \log (d+e x)}{a e^4+c d^4}-\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)}",1,"(-2*c^(1/4)*d*(Sqrt[2]*Sqrt[c]*d^2 - 2*a^(1/4)*c^(1/4)*d*e + Sqrt[2]*Sqrt[a]*e^2)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)] + 2*c^(1/4)*d*(Sqrt[2]*Sqrt[c]*d^2 + 2*a^(1/4)*c^(1/4)*d*e + Sqrt[2]*Sqrt[a]*e^2)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)] + 8*a^(3/4)*e^3*Log[d + e*x] - Sqrt[2]*c^(3/4)*d^3*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2] + Sqrt[2]*Sqrt[a]*c^(1/4)*d*e^2*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2] + Sqrt[2]*c^(3/4)*d^3*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2] - Sqrt[2]*Sqrt[a]*c^(1/4)*d*e^2*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2] - 2*a^(3/4)*e^3*Log[a + c*x^4])/(8*a^(3/4)*(c*d^4 + a*e^4))","A",1
399,1,524,552,0.6064906,"\int \frac{1}{(d+e x)^2 \left(a+c x^4\right)} \, dx","Integrate[1/((d + e*x)^2*(a + c*x^4)),x]","\frac{-\frac{\sqrt{2} \sqrt[4]{c} \left(a^{3/2} e^6-3 \sqrt{a} c d^4 e^2-3 a \sqrt{c} d^2 e^4+c^{3/2} d^6\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{a^{3/4}}+\frac{\sqrt{2} \sqrt[4]{c} \left(a^{3/2} e^6-3 \sqrt{a} c d^4 e^2-3 a \sqrt{c} d^2 e^4+c^{3/2} d^6\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{a^{3/4}}+\frac{2 \sqrt[4]{c} \left(\sqrt{a} e^2-\sqrt{c} d^2\right) \left(-4 a^{3/4} \sqrt[4]{c} d e^3-4 \sqrt[4]{a} c^{3/4} d^3 e+4 \sqrt{2} \sqrt{a} \sqrt{c} d^2 e^2+\sqrt{2} a e^4+\sqrt{2} c d^4\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{a^{3/4}}+\frac{2 \sqrt[4]{c} \left(\sqrt{c} d^2-\sqrt{a} e^2\right) \left(4 a^{3/4} \sqrt[4]{c} d e^3+4 \sqrt[4]{a} c^{3/4} d^3 e+4 \sqrt{2} \sqrt{a} \sqrt{c} d^2 e^2+\sqrt{2} a e^4+\sqrt{2} c d^4\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{a^{3/4}}-\frac{8 e^3 \left(a e^4+c d^4\right)}{d+e x}-8 c d^3 e^3 \log \left(a+c x^4\right)+32 c d^3 e^3 \log (d+e x)}{8 \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{a} e^2 \left(3 c d^4-a e^4\right)+\sqrt{c} d^2 \left(c d^4-3 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{a} e^2 \left(3 c d^4-a e^4\right)+\sqrt{c} d^2 \left(c d^4-3 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{\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{c d^3 e^3 \log \left(a+c x^4\right)}{\left(a e^4+c d^4\right)^2}+\frac{4 c d^3 e^3 \log (d+e x)}{\left(a e^4+c d^4\right)^2}",1,"((-8*e^3*(c*d^4 + a*e^4))/(d + e*x) + (2*c^(1/4)*(-(Sqrt[c]*d^2) + Sqrt[a]*e^2)*(Sqrt[2]*c*d^4 - 4*a^(1/4)*c^(3/4)*d^3*e + 4*Sqrt[2]*Sqrt[a]*Sqrt[c]*d^2*e^2 - 4*a^(3/4)*c^(1/4)*d*e^3 + Sqrt[2]*a*e^4)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/a^(3/4) + (2*c^(1/4)*(Sqrt[c]*d^2 - Sqrt[a]*e^2)*(Sqrt[2]*c*d^4 + 4*a^(1/4)*c^(3/4)*d^3*e + 4*Sqrt[2]*Sqrt[a]*Sqrt[c]*d^2*e^2 + 4*a^(3/4)*c^(1/4)*d*e^3 + Sqrt[2]*a*e^4)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/a^(3/4) + 32*c*d^3*e^3*Log[d + e*x] - (Sqrt[2]*c^(1/4)*(c^(3/2)*d^6 - 3*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])/a^(3/4) + (Sqrt[2]*c^(1/4)*(c^(3/2)*d^6 - 3*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])/a^(3/4) - 8*c*d^3*e^3*Log[a + c*x^4])/(8*(c*d^4 + a*e^4)^2)","A",1
400,1,738,680,0.9288796,"\int \frac{1}{(d+e x)^3 \left(a+c x^4\right)} \, dx","Integrate[1/((d + e*x)^3*(a + c*x^4)),x]","\frac{-4 a^{3/4} e^3 \left(a e^4+c d^4\right)^2-32 a^{3/4} c d^3 e^3 (d+e x) \left(a e^4+c d^4\right)+4 a^{3/4} c d^2 e^3 (d+e x)^2 \left(3 a e^4-5 c d^4\right) \log \left(a+c x^4\right)+16 a^{3/4} c d^2 e^3 (d+e x)^2 \left(5 c d^4-3 a e^4\right) \log (d+e x)-\sqrt{2} c^{3/4} d (d+e x)^2 \left(10 a^{3/2} \sqrt{c} d^2 e^6+3 a^2 e^8-6 \sqrt{a} c^{3/2} d^6 e^2-12 a c d^4 e^4+c^2 d^8\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)+\sqrt{2} c^{3/4} d (d+e x)^2 \left(10 a^{3/2} \sqrt{c} d^2 e^6+3 a^2 e^8-6 \sqrt{a} c^{3/2} d^6 e^2-12 a c d^4 e^4+c^2 d^8\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)-2 \sqrt{c} (d+e x)^2 \left(-10 \sqrt{2} a^{3/2} c^{3/4} d^3 e^6+24 a^{5/4} c d^4 e^5-2 a^{9/4} e^9+3 \sqrt{2} a^2 \sqrt[4]{c} d e^8+6 \sqrt{2} \sqrt{a} c^{7/4} d^7 e^2-12 \sqrt{2} a c^{5/4} d^5 e^4-6 \sqrt[4]{a} c^2 d^8 e+\sqrt{2} c^{9/4} d^9\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)+2 \sqrt{c} (d+e x)^2 \left(-10 \sqrt{2} a^{3/2} c^{3/4} d^3 e^6-24 a^{5/4} c d^4 e^5+2 a^{9/4} e^9+3 \sqrt{2} a^2 \sqrt[4]{c} d e^8+6 \sqrt{2} \sqrt{a} c^{7/4} d^7 e^2-12 \sqrt{2} a c^{5/4} d^5 e^4+6 \sqrt[4]{a} c^2 d^8 e+\sqrt{2} c^{9/4} d^9\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{8 a^{3/4} (d+e x)^2 \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) \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{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{e^3}{2 (d+e x)^2 \left(a e^4+c d^4\right)}-\frac{4 c d^3 e^3}{(d+e x) \left(a e^4+c d^4\right)^2}-\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{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,"(-4*a^(3/4)*e^3*(c*d^4 + a*e^4)^2 - 32*a^(3/4)*c*d^3*e^3*(c*d^4 + a*e^4)*(d + e*x) - 2*Sqrt[c]*(Sqrt[2]*c^(9/4)*d^9 - 6*a^(1/4)*c^2*d^8*e + 6*Sqrt[2]*Sqrt[a]*c^(7/4)*d^7*e^2 - 12*Sqrt[2]*a*c^(5/4)*d^5*e^4 + 24*a^(5/4)*c*d^4*e^5 - 10*Sqrt[2]*a^(3/2)*c^(3/4)*d^3*e^6 + 3*Sqrt[2]*a^2*c^(1/4)*d*e^8 - 2*a^(9/4)*e^9)*(d + e*x)^2*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)] + 2*Sqrt[c]*(Sqrt[2]*c^(9/4)*d^9 + 6*a^(1/4)*c^2*d^8*e + 6*Sqrt[2]*Sqrt[a]*c^(7/4)*d^7*e^2 - 12*Sqrt[2]*a*c^(5/4)*d^5*e^4 - 24*a^(5/4)*c*d^4*e^5 - 10*Sqrt[2]*a^(3/2)*c^(3/4)*d^3*e^6 + 3*Sqrt[2]*a^2*c^(1/4)*d*e^8 + 2*a^(9/4)*e^9)*(d + e*x)^2*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)] + 16*a^(3/4)*c*d^2*e^3*(5*c*d^4 - 3*a*e^4)*(d + e*x)^2*Log[d + e*x] - Sqrt[2]*c^(3/4)*d*(c^2*d^8 - 6*Sqrt[a]*c^(3/2)*d^6*e^2 - 12*a*c*d^4*e^4 + 10*a^(3/2)*Sqrt[c]*d^2*e^6 + 3*a^2*e^8)*(d + e*x)^2*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2] + Sqrt[2]*c^(3/4)*d*(c^2*d^8 - 6*Sqrt[a]*c^(3/2)*d^6*e^2 - 12*a*c*d^4*e^4 + 10*a^(3/2)*Sqrt[c]*d^2*e^6 + 3*a^2*e^8)*(d + e*x)^2*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2] + 4*a^(3/4)*c*d^2*e^3*(-5*c*d^4 + 3*a*e^4)*(d + e*x)^2*Log[a + c*x^4])/(8*a^(3/4)*(c*d^4 + a*e^4)^3*(d + e*x)^2)","A",1
401,1,347,349,0.3737617,"\int \frac{(d+e x)^3}{\left(a+c x^4\right)^2} \, dx","Integrate[(d + e*x)^3/(a + c*x^4)^2,x]","\frac{3 \sqrt{2} \sqrt[4]{c} \left(a^{3/4} d e^2-\sqrt[4]{a} \sqrt{c} d^3\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)+3 \sqrt{2} \sqrt[4]{c} \left(\sqrt[4]{a} \sqrt{c} d^3-a^{3/4} d e^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)-6 \sqrt[4]{a} \sqrt[4]{c} d \left(4 \sqrt[4]{a} \sqrt[4]{c} d e+\sqrt{2} \sqrt{a} e^2+\sqrt{2} \sqrt{c} d^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)+6 \sqrt[4]{a} \sqrt[4]{c} d \left(-4 \sqrt[4]{a} \sqrt[4]{c} d e+\sqrt{2} \sqrt{a} e^2+\sqrt{2} \sqrt{c} d^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)-\frac{8 a \left(a e^3-c d x \left(d^2+3 d e x+3 e^2 x^2\right)\right)}{a+c x^4}}{32 a^2 c}","-\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(d^3+3 d^2 e x+3 d e^2 x^2\right)}{4 a c \left(a+c x^4\right)}",1,"((-8*a*(a*e^3 - c*d*x*(d^2 + 3*d*e*x + 3*e^2*x^2)))/(a + c*x^4) - 6*a^(1/4)*c^(1/4)*d*(Sqrt[2]*Sqrt[c]*d^2 + 4*a^(1/4)*c^(1/4)*d*e + Sqrt[2]*Sqrt[a]*e^2)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)] + 6*a^(1/4)*c^(1/4)*d*(Sqrt[2]*Sqrt[c]*d^2 - 4*a^(1/4)*c^(1/4)*d*e + Sqrt[2]*Sqrt[a]*e^2)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)] + 3*Sqrt[2]*c^(1/4)*(-(a^(1/4)*Sqrt[c]*d^3) + a^(3/4)*d*e^2)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2] + 3*Sqrt[2]*c^(1/4)*(a^(1/4)*Sqrt[c]*d^3 - a^(3/4)*d*e^2)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(32*a^2*c)","A",1
402,1,321,322,0.3162202,"\int \frac{(d+e x)^2}{\left(a+c x^4\right)^2} \, dx","Integrate[(d + e*x)^2/(a + c*x^4)^2,x]","\frac{\frac{\sqrt{2} \left(a^{3/4} e^2-3 \sqrt[4]{a} \sqrt{c} d^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{c^{3/4}}+\frac{\sqrt{2} \left(3 \sqrt[4]{a} \sqrt{c} d^2-a^{3/4} e^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{c^{3/4}}-\frac{2 \sqrt[4]{a} \left(8 \sqrt[4]{a} \sqrt[4]{c} d e+\sqrt{2} \sqrt{a} e^2+3 \sqrt{2} \sqrt{c} d^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{c^{3/4}}+\frac{2 \sqrt[4]{a} \left(-8 \sqrt[4]{a} \sqrt[4]{c} d e+\sqrt{2} \sqrt{a} e^2+3 \sqrt{2} \sqrt{c} d^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{c^{3/4}}+\frac{8 a x (d+e x)^2}{a+c x^4}}{32 a^2}","-\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,"((8*a*x*(d + e*x)^2)/(a + c*x^4) - (2*a^(1/4)*(3*Sqrt[2]*Sqrt[c]*d^2 + 8*a^(1/4)*c^(1/4)*d*e + Sqrt[2]*Sqrt[a]*e^2)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/c^(3/4) + (2*a^(1/4)*(3*Sqrt[2]*Sqrt[c]*d^2 - 8*a^(1/4)*c^(1/4)*d*e + Sqrt[2]*Sqrt[a]*e^2)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/c^(3/4) + (Sqrt[2]*(-3*a^(1/4)*Sqrt[c]*d^2 + a^(3/4)*e^2)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/c^(3/4) + (Sqrt[2]*(3*a^(1/4)*Sqrt[c]*d^2 - a^(3/4)*e^2)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/c^(3/4))/(32*a^2)","A",1
403,1,224,241,0.189491,"\int \frac{d+e x}{\left(a+c x^4\right)^2} \, dx","Integrate[(d + e*x)/(a + c*x^4)^2,x]","\frac{\frac{8 a^{3/4} x (d+e x)}{a+c x^4}-\frac{2 \left(4 \sqrt[4]{a} e+3 \sqrt{2} \sqrt[4]{c} d\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{\sqrt{c}}+\frac{2 \left(3 \sqrt{2} \sqrt[4]{c} d-4 \sqrt[4]{a} e\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{\sqrt{c}}-\frac{3 \sqrt{2} d \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{\sqrt[4]{c}}+\frac{3 \sqrt{2} d \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{\sqrt[4]{c}}}{32 a^{7/4}}","-\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,"((8*a^(3/4)*x*(d + e*x))/(a + c*x^4) - (2*(3*Sqrt[2]*c^(1/4)*d + 4*a^(1/4)*e)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/Sqrt[c] + (2*(3*Sqrt[2]*c^(1/4)*d - 4*a^(1/4)*e)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/Sqrt[c] - (3*Sqrt[2]*d*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/c^(1/4) + (3*Sqrt[2]*d*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/c^(1/4))/(32*a^(7/4))","A",1
404,1,183,202,0.1072193,"\int \frac{1}{\left(a+c x^4\right)^2} \, dx","Integrate[(a + c*x^4)^(-2),x]","\frac{\frac{8 a^{3/4} x}{a+c x^4}-\frac{3 \sqrt{2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{\sqrt[4]{c}}+\frac{3 \sqrt{2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{\sqrt[4]{c}}-\frac{6 \sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{\sqrt[4]{c}}+\frac{6 \sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{\sqrt[4]{c}}}{32 a^{7/4}}","-\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,"((8*a^(3/4)*x)/(a + c*x^4) - (6*Sqrt[2]*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/c^(1/4) + (6*Sqrt[2]*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/c^(1/4) - (3*Sqrt[2]*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/c^(1/4) + (3*Sqrt[2]*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/c^(1/4))/(32*a^(7/4))","A",1
405,1,558,855,0.3914942,"\int \frac{1}{(d+e x) \left(a+c x^4\right)^2} \, dx","Integrate[1/((d + e*x)*(a + c*x^4)^2),x]","\frac{\frac{\sqrt{2} \sqrt[4]{c} \left(5 a^{3/2} d e^6+\sqrt{a} c d^5 e^2-7 a \sqrt{c} d^3 e^4-3 c^{3/2} d^7\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{a^{7/4}}+\frac{\sqrt{2} \sqrt[4]{c} \left(-5 a^{3/2} d e^6-\sqrt{a} c d^5 e^2+7 a \sqrt{c} d^3 e^4+3 c^{3/2} d^7\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{a^{7/4}}-\frac{2 \sqrt[4]{c} d \left(-12 a^{5/4} \sqrt[4]{c} d e^5+5 \sqrt{2} a^{3/2} e^6-4 \sqrt[4]{a} c^{5/4} d^5 e+\sqrt{2} \sqrt{a} c d^4 e^2+7 \sqrt{2} a \sqrt{c} d^2 e^4+3 \sqrt{2} c^{3/2} d^6\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{a^{7/4}}+\frac{2 \sqrt[4]{c} d \left(12 a^{5/4} \sqrt[4]{c} d e^5+5 \sqrt{2} a^{3/2} e^6+4 \sqrt[4]{a} c^{5/4} d^5 e+\sqrt{2} \sqrt{a} c d^4 e^2+7 \sqrt{2} a \sqrt{c} d^2 e^4+3 \sqrt{2} c^{3/2} d^6\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{a^{7/4}}+\frac{8 \left(a e^4+c d^4\right) \left(a e^3+c d x \left(d^2-d e x+e^2 x^2\right)\right)}{a \left(a+c x^4\right)}-8 e^7 \log \left(a+c x^4\right)+32 e^7 \log (d+e x)}{32 \left(a e^4+c d^4\right)^2}","\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,"((8*(c*d^4 + a*e^4)*(a*e^3 + c*d*x*(d^2 - d*e*x + e^2*x^2)))/(a*(a + c*x^4)) - (2*c^(1/4)*d*(3*Sqrt[2]*c^(3/2)*d^6 - 4*a^(1/4)*c^(5/4)*d^5*e + Sqrt[2]*Sqrt[a]*c*d^4*e^2 + 7*Sqrt[2]*a*Sqrt[c]*d^2*e^4 - 12*a^(5/4)*c^(1/4)*d*e^5 + 5*Sqrt[2]*a^(3/2)*e^6)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/a^(7/4) + (2*c^(1/4)*d*(3*Sqrt[2]*c^(3/2)*d^6 + 4*a^(1/4)*c^(5/4)*d^5*e + Sqrt[2]*Sqrt[a]*c*d^4*e^2 + 7*Sqrt[2]*a*Sqrt[c]*d^2*e^4 + 12*a^(5/4)*c^(1/4)*d*e^5 + 5*Sqrt[2]*a^(3/2)*e^6)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/a^(7/4) + 32*e^7*Log[d + e*x] + (Sqrt[2]*c^(1/4)*(-3*c^(3/2)*d^7 + Sqrt[a]*c*d^5*e^2 - 7*a*Sqrt[c]*d^3*e^4 + 5*a^(3/2)*d*e^6)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/a^(7/4) + (Sqrt[2]*c^(1/4)*(3*c^(3/2)*d^7 - Sqrt[a]*c*d^5*e^2 + 7*a*Sqrt[c]*d^3*e^4 - 5*a^(3/2)*d*e^6)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/a^(7/4) - 8*e^7*Log[a + c*x^4])/(32*(c*d^4 + a*e^4)^2)","A",1
406,1,807,1141,0.8646505,"\int \frac{1}{(d+e x)^2 \left(a+c x^4\right)^2} \, dx","Integrate[1/((d + e*x)^2*(a + c*x^4)^2),x]","\frac{256 c d^3 \log (d+e x) e^7-64 c d^3 \log \left(c x^4+a\right) e^7-\frac{32 \left(c d^4+a e^4\right) e^7}{d+e x}+\frac{8 c \left(c d^4+a e^4\right) \left(c x \left(d^2-2 e x d+3 e^2 x^2\right) d^4+a e^3 \left(4 d^3-3 e x d^2+2 e^2 x^2 d-e^3 x^3\right)\right)}{a \left(c x^4+a\right)}+\frac{2 \sqrt[4]{c} \left(-3 \sqrt{2} c^{5/2} d^{10}+8 \sqrt[4]{a} c^{9/4} e d^9-3 \sqrt{2} \sqrt{a} c^2 e^2 d^8-14 \sqrt{2} a c^{3/2} e^4 d^6+48 a^{5/4} c^{5/4} e^5 d^5-30 \sqrt{2} a^{3/2} c e^6 d^4+21 \sqrt{2} a^2 \sqrt{c} e^8 d^2-24 a^{9/4} \sqrt[4]{c} e^9 d+5 \sqrt{2} a^{5/2} e^{10}\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{a^{7/4}}+\frac{2 \sqrt[4]{c} \left(3 \sqrt{2} c^{5/2} d^{10}+8 \sqrt[4]{a} c^{9/4} e d^9+3 \sqrt{2} \sqrt{a} c^2 e^2 d^8+14 \sqrt{2} a c^{3/2} e^4 d^6+48 a^{5/4} c^{5/4} e^5 d^5+30 \sqrt{2} a^{3/2} c e^6 d^4-21 \sqrt{2} a^2 \sqrt{c} e^8 d^2-24 a^{9/4} \sqrt[4]{c} e^9 d-5 \sqrt{2} a^{5/2} e^{10}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{a^{7/4}}-\frac{\sqrt{2} \sqrt[4]{c} \left(3 c^{5/2} d^{10}-3 \sqrt{a} c^2 e^2 d^8+14 a c^{3/2} e^4 d^6-30 a^{3/2} c e^6 d^4-21 a^2 \sqrt{c} e^8 d^2+5 a^{5/2} e^{10}\right) \log \left(\sqrt{c} x^2-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right)}{a^{7/4}}+\frac{\sqrt{2} \sqrt[4]{c} \left(3 c^{5/2} d^{10}-3 \sqrt{a} c^2 e^2 d^8+14 a c^{3/2} e^4 d^6-30 a^{3/2} c e^6 d^4-21 a^2 \sqrt{c} e^8 d^2+5 a^{5/2} e^{10}\right) \log \left(\sqrt{c} x^2+\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right)}{a^{7/4}}}{32 \left(c d^4+a e^4\right)^3}","\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,"((-32*e^7*(c*d^4 + a*e^4))/(d + e*x) + (8*c*(c*d^4 + a*e^4)*(c*d^4*x*(d^2 - 2*d*e*x + 3*e^2*x^2) + a*e^3*(4*d^3 - 3*d^2*e*x + 2*d*e^2*x^2 - e^3*x^3)))/(a*(a + c*x^4)) + (2*c^(1/4)*(-3*Sqrt[2]*c^(5/2)*d^10 + 8*a^(1/4)*c^(9/4)*d^9*e - 3*Sqrt[2]*Sqrt[a]*c^2*d^8*e^2 - 14*Sqrt[2]*a*c^(3/2)*d^6*e^4 + 48*a^(5/4)*c^(5/4)*d^5*e^5 - 30*Sqrt[2]*a^(3/2)*c*d^4*e^6 + 21*Sqrt[2]*a^2*Sqrt[c]*d^2*e^8 - 24*a^(9/4)*c^(1/4)*d*e^9 + 5*Sqrt[2]*a^(5/2)*e^10)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/a^(7/4) + (2*c^(1/4)*(3*Sqrt[2]*c^(5/2)*d^10 + 8*a^(1/4)*c^(9/4)*d^9*e + 3*Sqrt[2]*Sqrt[a]*c^2*d^8*e^2 + 14*Sqrt[2]*a*c^(3/2)*d^6*e^4 + 48*a^(5/4)*c^(5/4)*d^5*e^5 + 30*Sqrt[2]*a^(3/2)*c*d^4*e^6 - 21*Sqrt[2]*a^2*Sqrt[c]*d^2*e^8 - 24*a^(9/4)*c^(1/4)*d*e^9 - 5*Sqrt[2]*a^(5/2)*e^10)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/a^(7/4) + 256*c*d^3*e^7*Log[d + e*x] - (Sqrt[2]*c^(1/4)*(3*c^(5/2)*d^10 - 3*Sqrt[a]*c^2*d^8*e^2 + 14*a*c^(3/2)*d^6*e^4 - 30*a^(3/2)*c*d^4*e^6 - 21*a^2*Sqrt[c]*d^2*e^8 + 5*a^(5/2)*e^10)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/a^(7/4) + (Sqrt[2]*c^(1/4)*(3*c^(5/2)*d^10 - 3*Sqrt[a]*c^2*d^8*e^2 + 14*a*c^(3/2)*d^6*e^4 - 30*a^(3/2)*c*d^4*e^6 - 21*a^2*Sqrt[c]*d^2*e^8 + 5*a^(5/2)*e^10)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/a^(7/4) - 64*c*d^3*e^7*Log[a + c*x^4])/(32*(c*d^4 + a*e^4)^3)","A",1
407,1,996,1384,1.3570442,"\int \frac{1}{(d+e x)^3 \left(a+c x^4\right)^2} \, dx","Integrate[1/((d + e*x)^3*(a + c*x^4)^2),x]","\frac{384 c d^2 \left(3 c d^4-a e^4\right) \log (d+e x) e^7-96 c d^2 \left(3 c d^4-a e^4\right) \log \left(c x^4+a\right) e^7-\frac{256 c d^3 \left(c d^4+a e^4\right) e^7}{d+e x}-\frac{16 \left(c d^4+a e^4\right)^2 e^7}{(d+e x)^2}+\frac{8 c \left(c d^4+a e^4\right) \left(c^2 x \left(d^2-3 e x d+6 e^2 x^2\right) d^7+2 a c e^3 \left(5 d^3-6 e x d^2+6 e^2 x^2 d-5 e^3 x^3\right) d^3-a^2 e^7 \left(6 d^2-3 e x d+e^2 x^2\right)\right)}{a \left(c x^4+a\right)}-\frac{6 \sqrt{c} \left(\sqrt{2} c^{13/4} d^{13}-4 \sqrt[4]{a} c^3 e d^{12}+2 \sqrt{2} \sqrt{a} c^{11/4} e^2 d^{11}+9 \sqrt{2} a c^{9/4} e^4 d^9-44 a^{5/4} c^2 e^5 d^8+36 \sqrt{2} a^{3/2} c^{7/4} e^6 d^7-49 \sqrt{2} a^2 c^{5/4} e^8 d^5+84 a^{9/4} c e^9 d^4-30 \sqrt{2} a^{5/2} c^{3/4} e^{10} d^3+7 \sqrt{2} a^3 \sqrt[4]{c} e^{12} d-4 a^{13/4} e^{13}\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{a^{7/4}}+\frac{6 \sqrt{c} \left(\sqrt{2} c^{13/4} d^{13}+4 \sqrt[4]{a} c^3 e d^{12}+2 \sqrt{2} \sqrt{a} c^{11/4} e^2 d^{11}+9 \sqrt{2} a c^{9/4} e^4 d^9+44 a^{5/4} c^2 e^5 d^8+36 \sqrt{2} a^{3/2} c^{7/4} e^6 d^7-49 \sqrt{2} a^2 c^{5/4} e^8 d^5-84 a^{9/4} c e^9 d^4-30 \sqrt{2} a^{5/2} c^{3/4} e^{10} d^3+7 \sqrt{2} a^3 \sqrt[4]{c} e^{12} d+4 a^{13/4} e^{13}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{a^{7/4}}-\frac{3 \sqrt{2} c^{3/4} \left(c^3 d^{13}-2 \sqrt{a} c^{5/2} e^2 d^{11}+9 a c^2 e^4 d^9-36 a^{3/2} c^{3/2} e^6 d^7-49 a^2 c e^8 d^5+30 a^{5/2} \sqrt{c} e^{10} d^3+7 a^3 e^{12} d\right) \log \left(\sqrt{c} x^2-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right)}{a^{7/4}}+\frac{3 \sqrt{2} c^{3/4} \left(c^3 d^{13}-2 \sqrt{a} c^{5/2} e^2 d^{11}+9 a c^2 e^4 d^9-36 a^{3/2} c^{3/2} e^6 d^7-49 a^2 c e^8 d^5+30 a^{5/2} \sqrt{c} e^{10} d^3+7 a^3 e^{12} d\right) \log \left(\sqrt{c} x^2+\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right)}{a^{7/4}}}{32 \left(c d^4+a e^4\right)^4}","\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,"((-16*e^7*(c*d^4 + a*e^4)^2)/(d + e*x)^2 - (256*c*d^3*e^7*(c*d^4 + a*e^4))/(d + e*x) + (8*c*(c*d^4 + a*e^4)*(-(a^2*e^7*(6*d^2 - 3*d*e*x + e^2*x^2)) + c^2*d^7*x*(d^2 - 3*d*e*x + 6*e^2*x^2) + 2*a*c*d^3*e^3*(5*d^3 - 6*d^2*e*x + 6*d*e^2*x^2 - 5*e^3*x^3)))/(a*(a + c*x^4)) - (6*Sqrt[c]*(Sqrt[2]*c^(13/4)*d^13 - 4*a^(1/4)*c^3*d^12*e + 2*Sqrt[2]*Sqrt[a]*c^(11/4)*d^11*e^2 + 9*Sqrt[2]*a*c^(9/4)*d^9*e^4 - 44*a^(5/4)*c^2*d^8*e^5 + 36*Sqrt[2]*a^(3/2)*c^(7/4)*d^7*e^6 - 49*Sqrt[2]*a^2*c^(5/4)*d^5*e^8 + 84*a^(9/4)*c*d^4*e^9 - 30*Sqrt[2]*a^(5/2)*c^(3/4)*d^3*e^10 + 7*Sqrt[2]*a^3*c^(1/4)*d*e^12 - 4*a^(13/4)*e^13)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/a^(7/4) + (6*Sqrt[c]*(Sqrt[2]*c^(13/4)*d^13 + 4*a^(1/4)*c^3*d^12*e + 2*Sqrt[2]*Sqrt[a]*c^(11/4)*d^11*e^2 + 9*Sqrt[2]*a*c^(9/4)*d^9*e^4 + 44*a^(5/4)*c^2*d^8*e^5 + 36*Sqrt[2]*a^(3/2)*c^(7/4)*d^7*e^6 - 49*Sqrt[2]*a^2*c^(5/4)*d^5*e^8 - 84*a^(9/4)*c*d^4*e^9 - 30*Sqrt[2]*a^(5/2)*c^(3/4)*d^3*e^10 + 7*Sqrt[2]*a^3*c^(1/4)*d*e^12 + 4*a^(13/4)*e^13)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/a^(7/4) + 384*c*d^2*e^7*(3*c*d^4 - a*e^4)*Log[d + e*x] - (3*Sqrt[2]*c^(3/4)*(c^3*d^13 - 2*Sqrt[a]*c^(5/2)*d^11*e^2 + 9*a*c^2*d^9*e^4 - 36*a^(3/2)*c^(3/2)*d^7*e^6 - 49*a^2*c*d^5*e^8 + 30*a^(5/2)*Sqrt[c]*d^3*e^10 + 7*a^3*d*e^12)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/a^(7/4) + (3*Sqrt[2]*c^(3/4)*(c^3*d^13 - 2*Sqrt[a]*c^(5/2)*d^11*e^2 + 9*a*c^2*d^9*e^4 - 36*a^(3/2)*c^(3/2)*d^7*e^6 - 49*a^2*c*d^5*e^8 + 30*a^(5/2)*Sqrt[c]*d^3*e^10 + 7*a^3*d*e^12)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/a^(7/4) - 96*c*d^2*e^7*(3*c*d^4 - a*e^4)*Log[a + c*x^4])/(32*(c*d^4 + a*e^4)^4)","A",1
408,1,388,394,0.3512979,"\int \frac{(d+e x)^3}{\left(a+c x^4\right)^3} \, dx","Integrate[(d + e*x)^3/(a + c*x^4)^3,x]","\frac{\frac{3 \sqrt{2} \left(5 a^{3/4} d e^2-7 \sqrt[4]{a} \sqrt{c} d^3\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{c^{3/4}}+\frac{3 \sqrt{2} \left(7 \sqrt[4]{a} \sqrt{c} d^3-5 a^{3/4} d e^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{c^{3/4}}-\frac{32 a^2 \left(a e^3-c d x \left(d^2+3 d e x+3 e^2 x^2\right)\right)}{c \left(a+c x^4\right)^2}-\frac{6 \sqrt[4]{a} d \left(24 \sqrt[4]{a} \sqrt[4]{c} d e+5 \sqrt{2} \sqrt{a} e^2+7 \sqrt{2} \sqrt{c} d^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{c^{3/4}}+\frac{6 \sqrt[4]{a} d \left(-24 \sqrt[4]{a} \sqrt[4]{c} d e+5 \sqrt{2} \sqrt{a} e^2+7 \sqrt{2} \sqrt{c} d^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{c^{3/4}}+\frac{8 a d x \left(7 d^2+18 d e x+15 e^2 x^2\right)}{a+c x^4}}{256 a^3}","-\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{9 d^2 e \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{16 a^{5/2} \sqrt{c}}+\frac{x \left(7 d^3+18 d^2 e x+15 d e^2 x^2\right)}{32 a^2 \left(a+c x^4\right)}-\frac{a e^3-c x \left(d^3+3 d^2 e x+3 d e^2 x^2\right)}{8 a c \left(a+c x^4\right)^2}",1,"((8*a*d*x*(7*d^2 + 18*d*e*x + 15*e^2*x^2))/(a + c*x^4) - (32*a^2*(a*e^3 - c*d*x*(d^2 + 3*d*e*x + 3*e^2*x^2)))/(c*(a + c*x^4)^2) - (6*a^(1/4)*d*(7*Sqrt[2]*Sqrt[c]*d^2 + 24*a^(1/4)*c^(1/4)*d*e + 5*Sqrt[2]*Sqrt[a]*e^2)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/c^(3/4) + (6*a^(1/4)*d*(7*Sqrt[2]*Sqrt[c]*d^2 - 24*a^(1/4)*c^(1/4)*d*e + 5*Sqrt[2]*Sqrt[a]*e^2)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/c^(3/4) + (3*Sqrt[2]*(-7*a^(1/4)*Sqrt[c]*d^3 + 5*a^(3/4)*d*e^2)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/c^(3/4) + (3*Sqrt[2]*(7*a^(1/4)*Sqrt[c]*d^3 - 5*a^(3/4)*d*e^2)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/c^(3/4))/(256*a^3)","A",1
409,1,358,360,0.2939244,"\int \frac{(d+e x)^2}{\left(a+c x^4\right)^3} \, dx","Integrate[(d + e*x)^2/(a + c*x^4)^3,x]","\frac{\frac{\sqrt{2} \left(5 a^{3/4} e^2-21 \sqrt[4]{a} \sqrt{c} d^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{c^{3/4}}+\frac{\sqrt{2} \left(21 \sqrt[4]{a} \sqrt{c} d^2-5 a^{3/4} e^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{c^{3/4}}+\frac{32 a^2 x (d+e x)^2}{\left(a+c x^4\right)^2}-\frac{2 \sqrt[4]{a} \left(48 \sqrt[4]{a} \sqrt[4]{c} d e+5 \sqrt{2} \sqrt{a} e^2+21 \sqrt{2} \sqrt{c} d^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{c^{3/4}}+\frac{2 \sqrt[4]{a} \left(-48 \sqrt[4]{a} \sqrt[4]{c} d e+5 \sqrt{2} \sqrt{a} e^2+21 \sqrt{2} \sqrt{c} d^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{c^{3/4}}+\frac{8 a x \left(7 d^2+12 d e x+5 e^2 x^2\right)}{a+c x^4}}{256 a^3}","-\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{3 d e \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{8 a^{5/2} \sqrt{c}}+\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{x (d+e x)^2}{8 a \left(a+c x^4\right)^2}",1,"((32*a^2*x*(d + e*x)^2)/(a + c*x^4)^2 + (8*a*x*(7*d^2 + 12*d*e*x + 5*e^2*x^2))/(a + c*x^4) - (2*a^(1/4)*(21*Sqrt[2]*Sqrt[c]*d^2 + 48*a^(1/4)*c^(1/4)*d*e + 5*Sqrt[2]*Sqrt[a]*e^2)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/c^(3/4) + (2*a^(1/4)*(21*Sqrt[2]*Sqrt[c]*d^2 - 48*a^(1/4)*c^(1/4)*d*e + 5*Sqrt[2]*Sqrt[a]*e^2)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/c^(3/4) + (Sqrt[2]*(-21*a^(1/4)*Sqrt[c]*d^2 + 5*a^(3/4)*e^2)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/c^(3/4) + (Sqrt[2]*(21*a^(1/4)*Sqrt[c]*d^2 - 5*a^(3/4)*e^2)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/c^(3/4))/(256*a^3)","A",1
410,1,249,266,0.2055878,"\int \frac{d+e x}{\left(a+c x^4\right)^3} \, dx","Integrate[(d + e*x)/(a + c*x^4)^3,x]","\frac{\frac{32 a^{7/4} x (d+e x)}{\left(a+c x^4\right)^2}+\frac{8 a^{3/4} x (7 d+6 e x)}{a+c x^4}-\frac{6 \left(8 \sqrt[4]{a} e+7 \sqrt{2} \sqrt[4]{c} d\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{\sqrt{c}}+\frac{6 \left(7 \sqrt{2} \sqrt[4]{c} d-8 \sqrt[4]{a} e\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{\sqrt{c}}-\frac{21 \sqrt{2} d \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{\sqrt[4]{c}}+\frac{21 \sqrt{2} d \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{\sqrt[4]{c}}}{256 a^{11/4}}","-\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 (7 d+6 e x)}{32 a^2 \left(a+c x^4\right)}+\frac{x (d+e x)}{8 a \left(a+c x^4\right)^2}",1,"((32*a^(7/4)*x*(d + e*x))/(a + c*x^4)^2 + (8*a^(3/4)*x*(7*d + 6*e*x))/(a + c*x^4) - (6*(7*Sqrt[2]*c^(1/4)*d + 8*a^(1/4)*e)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/Sqrt[c] + (6*(7*Sqrt[2]*c^(1/4)*d - 8*a^(1/4)*e)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/Sqrt[c] - (21*Sqrt[2]*d*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/c^(1/4) + (21*Sqrt[2]*d*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/c^(1/4))/(256*a^(11/4))","A",1
411,1,200,219,0.0833797,"\int \frac{1}{\left(a+c x^4\right)^3} \, dx","Integrate[(a + c*x^4)^(-3),x]","\frac{\frac{32 a^{7/4} x}{\left(a+c x^4\right)^2}+\frac{56 a^{3/4} x}{a+c x^4}-\frac{21 \sqrt{2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{\sqrt[4]{c}}+\frac{21 \sqrt{2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{\sqrt[4]{c}}-\frac{42 \sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{\sqrt[4]{c}}+\frac{42 \sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{\sqrt[4]{c}}}{256 a^{11/4}}","-\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{7 x}{32 a^2 \left(a+c x^4\right)}+\frac{x}{8 a \left(a+c x^4\right)^2}",1,"((32*a^(7/4)*x)/(a + c*x^4)^2 + (56*a^(3/4)*x)/(a + c*x^4) - (42*Sqrt[2]*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/c^(1/4) + (42*Sqrt[2]*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/c^(1/4) - (21*Sqrt[2]*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/c^(1/4) + (21*Sqrt[2]*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/c^(1/4))/(256*a^(11/4))","A",1
412,1,835,1352,0.7376097,"\int \frac{1}{(d+e x) \left(a+c x^4\right)^3} \, dx","Integrate[1/((d + e*x)*(a + c*x^4)^3),x]","\frac{256 \log (d+e x) e^{11}-64 \log \left(c x^4+a\right) e^{11}+\frac{32 \left(c d^4+a e^4\right)^2 \left(a e^3+c d x \left(d^2-e x d+e^2 x^2\right)\right)}{a \left(c x^4+a\right)^2}+\frac{8 \left(c d^4+a e^4\right) \left(8 a^2 e^7+a c d x \left(15 d^2-14 e x d+13 e^2 x^2\right) e^4+c^2 d^5 x \left(7 d^2-6 e x d+5 e^2 x^2\right)\right)}{a^2 \left(c x^4+a\right)}-\frac{2 \sqrt[4]{c} d \left(21 \sqrt{2} c^{5/2} d^{10}-24 \sqrt[4]{a} c^{9/4} e d^9+5 \sqrt{2} \sqrt{a} c^2 e^2 d^8+66 \sqrt{2} a c^{3/2} e^4 d^6-80 a^{5/4} c^{5/4} e^5 d^5+18 \sqrt{2} a^{3/2} c e^6 d^4+77 \sqrt{2} a^2 \sqrt{c} e^8 d^2-120 a^{9/4} \sqrt[4]{c} e^9 d+45 \sqrt{2} a^{5/2} e^{10}\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{a^{11/4}}+\frac{2 \sqrt[4]{c} d \left(21 \sqrt{2} c^{5/2} d^{10}+24 \sqrt[4]{a} c^{9/4} e d^9+5 \sqrt{2} \sqrt{a} c^2 e^2 d^8+66 \sqrt{2} a c^{3/2} e^4 d^6+80 a^{5/4} c^{5/4} e^5 d^5+18 \sqrt{2} a^{3/2} c e^6 d^4+77 \sqrt{2} a^2 \sqrt{c} e^8 d^2+120 a^{9/4} \sqrt[4]{c} e^9 d+45 \sqrt{2} a^{5/2} e^{10}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{a^{11/4}}+\frac{\sqrt{2} \sqrt[4]{c} \left(-21 c^{5/2} d^{11}+5 \sqrt{a} c^2 e^2 d^9-66 a c^{3/2} e^4 d^7+18 a^{3/2} c e^6 d^5-77 a^2 \sqrt{c} e^8 d^3+45 a^{5/2} e^{10} d\right) \log \left(\sqrt{c} x^2-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right)}{a^{11/4}}+\frac{\sqrt{2} \sqrt[4]{c} \left(21 c^{5/2} d^{11}-5 \sqrt{a} c^2 e^2 d^9+66 a c^{3/2} e^4 d^7-18 a^{3/2} c e^6 d^5+77 a^2 \sqrt{c} e^8 d^3-45 a^{5/2} e^{10} d\right) \log \left(\sqrt{c} x^2+\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right)}{a^{11/4}}}{256 \left(c d^4+a e^4\right)^3}","\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,"((32*(c*d^4 + a*e^4)^2*(a*e^3 + c*d*x*(d^2 - d*e*x + e^2*x^2)))/(a*(a + c*x^4)^2) + (8*(c*d^4 + a*e^4)*(8*a^2*e^7 + c^2*d^5*x*(7*d^2 - 6*d*e*x + 5*e^2*x^2) + a*c*d*e^4*x*(15*d^2 - 14*d*e*x + 13*e^2*x^2)))/(a^2*(a + c*x^4)) - (2*c^(1/4)*d*(21*Sqrt[2]*c^(5/2)*d^10 - 24*a^(1/4)*c^(9/4)*d^9*e + 5*Sqrt[2]*Sqrt[a]*c^2*d^8*e^2 + 66*Sqrt[2]*a*c^(3/2)*d^6*e^4 - 80*a^(5/4)*c^(5/4)*d^5*e^5 + 18*Sqrt[2]*a^(3/2)*c*d^4*e^6 + 77*Sqrt[2]*a^2*Sqrt[c]*d^2*e^8 - 120*a^(9/4)*c^(1/4)*d*e^9 + 45*Sqrt[2]*a^(5/2)*e^10)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/a^(11/4) + (2*c^(1/4)*d*(21*Sqrt[2]*c^(5/2)*d^10 + 24*a^(1/4)*c^(9/4)*d^9*e + 5*Sqrt[2]*Sqrt[a]*c^2*d^8*e^2 + 66*Sqrt[2]*a*c^(3/2)*d^6*e^4 + 80*a^(5/4)*c^(5/4)*d^5*e^5 + 18*Sqrt[2]*a^(3/2)*c*d^4*e^6 + 77*Sqrt[2]*a^2*Sqrt[c]*d^2*e^8 + 120*a^(9/4)*c^(1/4)*d*e^9 + 45*Sqrt[2]*a^(5/2)*e^10)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/a^(11/4) + 256*e^11*Log[d + e*x] + (Sqrt[2]*c^(1/4)*(-21*c^(5/2)*d^11 + 5*Sqrt[a]*c^2*d^9*e^2 - 66*a*c^(3/2)*d^7*e^4 + 18*a^(3/2)*c*d^5*e^6 - 77*a^2*Sqrt[c]*d^3*e^8 + 45*a^(5/2)*d*e^10)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/a^(11/4) + (Sqrt[2]*c^(1/4)*(21*c^(5/2)*d^11 - 5*Sqrt[a]*c^2*d^9*e^2 + 66*a*c^(3/2)*d^7*e^4 - 18*a^(3/2)*c*d^5*e^6 + 77*a^2*Sqrt[c]*d^3*e^8 - 45*a^(5/2)*d*e^10)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/a^(11/4) - 64*e^11*Log[a + c*x^4])/(256*(c*d^4 + a*e^4)^3)","A",1
413,1,1115,1830,1.5506198,"\int \frac{1}{(d+e x)^2 \left(a+c x^4\right)^3} \, dx","Integrate[1/((d + e*x)^2*(a + c*x^4)^3),x]","\frac{3072 c d^3 \log (d+e x) e^{11}-768 c d^3 \log \left(c x^4+a\right) e^{11}-\frac{256 \left(c d^4+a e^4\right) e^{11}}{d+e x}+\frac{8 c \left(c d^4+a e^4\right) \left(c^2 x \left(7 d^2-12 e x d+15 e^2 x^2\right) d^8+2 a c e^4 x \left(13 d^2-24 e x d+33 e^2 x^2\right) d^4+a^2 e^7 \left(64 d^3-45 e x d^2+28 e^2 x^2 d-13 e^3 x^3\right)\right)}{a^2 \left(c x^4+a\right)}+\frac{32 c \left(c d^4+a e^4\right)^2 \left(c x \left(d^2-2 e x d+3 e^2 x^2\right) d^4+a e^3 \left(4 d^3-3 e x d^2+2 e^2 x^2 d-e^3 x^3\right)\right)}{a \left(c x^4+a\right)^2}-\frac{6 \sqrt[4]{c} \left(7 \sqrt{2} c^{7/2} d^{14}-16 \sqrt[4]{a} c^{13/4} e d^{13}+5 \sqrt{2} \sqrt{a} c^3 e^2 d^{12}+33 \sqrt{2} a c^{5/2} e^4 d^{10}-80 a^{5/4} c^{9/4} e^5 d^9+27 \sqrt{2} a^{3/2} c^2 e^6 d^8+77 \sqrt{2} a^2 c^{3/2} e^8 d^6-240 a^{9/4} c^{5/4} e^9 d^5+135 \sqrt{2} a^{5/2} c e^{10} d^4-77 \sqrt{2} a^3 \sqrt{c} e^{12} d^2+80 a^{13/4} \sqrt[4]{c} e^{13} d-15 \sqrt{2} a^{7/2} e^{14}\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{a^{11/4}}+\frac{6 \sqrt[4]{c} \left(7 \sqrt{2} c^{7/2} d^{14}+16 \sqrt[4]{a} c^{13/4} e d^{13}+5 \sqrt{2} \sqrt{a} c^3 e^2 d^{12}+33 \sqrt{2} a c^{5/2} e^4 d^{10}+80 a^{5/4} c^{9/4} e^5 d^9+27 \sqrt{2} a^{3/2} c^2 e^6 d^8+77 \sqrt{2} a^2 c^{3/2} e^8 d^6+240 a^{9/4} c^{5/4} e^9 d^5+135 \sqrt{2} a^{5/2} c e^{10} d^4-77 \sqrt{2} a^3 \sqrt{c} e^{12} d^2-80 a^{13/4} \sqrt[4]{c} e^{13} d-15 \sqrt{2} a^{7/2} e^{14}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{a^{11/4}}-\frac{3 \sqrt{2} \sqrt[4]{c} \left(7 c^{7/2} d^{14}-5 \sqrt{a} c^3 e^2 d^{12}+33 a c^{5/2} e^4 d^{10}-27 a^{3/2} c^2 e^6 d^8+77 a^2 c^{3/2} e^8 d^6-135 a^{5/2} c e^{10} d^4-77 a^3 \sqrt{c} e^{12} d^2+15 a^{7/2} e^{14}\right) \log \left(\sqrt{c} x^2-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right)}{a^{11/4}}+\frac{3 \sqrt{2} \sqrt[4]{c} \left(7 c^{7/2} d^{14}-5 \sqrt{a} c^3 e^2 d^{12}+33 a c^{5/2} e^4 d^{10}-27 a^{3/2} c^2 e^6 d^8+77 a^2 c^{3/2} e^8 d^6-135 a^{5/2} c e^{10} d^4-77 a^3 \sqrt{c} e^{12} d^2+15 a^{7/2} e^{14}\right) \log \left(\sqrt{c} x^2+\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right)}{a^{11/4}}}{256 \left(c d^4+a e^4\right)^4}","\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,"((-256*e^11*(c*d^4 + a*e^4))/(d + e*x) + (8*c*(c*d^4 + a*e^4)*(c^2*d^8*x*(7*d^2 - 12*d*e*x + 15*e^2*x^2) + 2*a*c*d^4*e^4*x*(13*d^2 - 24*d*e*x + 33*e^2*x^2) + a^2*e^7*(64*d^3 - 45*d^2*e*x + 28*d*e^2*x^2 - 13*e^3*x^3)))/(a^2*(a + c*x^4)) + (32*c*(c*d^4 + a*e^4)^2*(c*d^4*x*(d^2 - 2*d*e*x + 3*e^2*x^2) + a*e^3*(4*d^3 - 3*d^2*e*x + 2*d*e^2*x^2 - e^3*x^3)))/(a*(a + c*x^4)^2) - (6*c^(1/4)*(7*Sqrt[2]*c^(7/2)*d^14 - 16*a^(1/4)*c^(13/4)*d^13*e + 5*Sqrt[2]*Sqrt[a]*c^3*d^12*e^2 + 33*Sqrt[2]*a*c^(5/2)*d^10*e^4 - 80*a^(5/4)*c^(9/4)*d^9*e^5 + 27*Sqrt[2]*a^(3/2)*c^2*d^8*e^6 + 77*Sqrt[2]*a^2*c^(3/2)*d^6*e^8 - 240*a^(9/4)*c^(5/4)*d^5*e^9 + 135*Sqrt[2]*a^(5/2)*c*d^4*e^10 - 77*Sqrt[2]*a^3*Sqrt[c]*d^2*e^12 + 80*a^(13/4)*c^(1/4)*d*e^13 - 15*Sqrt[2]*a^(7/2)*e^14)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/a^(11/4) + (6*c^(1/4)*(7*Sqrt[2]*c^(7/2)*d^14 + 16*a^(1/4)*c^(13/4)*d^13*e + 5*Sqrt[2]*Sqrt[a]*c^3*d^12*e^2 + 33*Sqrt[2]*a*c^(5/2)*d^10*e^4 + 80*a^(5/4)*c^(9/4)*d^9*e^5 + 27*Sqrt[2]*a^(3/2)*c^2*d^8*e^6 + 77*Sqrt[2]*a^2*c^(3/2)*d^6*e^8 + 240*a^(9/4)*c^(5/4)*d^5*e^9 + 135*Sqrt[2]*a^(5/2)*c*d^4*e^10 - 77*Sqrt[2]*a^3*Sqrt[c]*d^2*e^12 - 80*a^(13/4)*c^(1/4)*d*e^13 - 15*Sqrt[2]*a^(7/2)*e^14)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/a^(11/4) + 3072*c*d^3*e^11*Log[d + e*x] - (3*Sqrt[2]*c^(1/4)*(7*c^(7/2)*d^14 - 5*Sqrt[a]*c^3*d^12*e^2 + 33*a*c^(5/2)*d^10*e^4 - 27*a^(3/2)*c^2*d^8*e^6 + 77*a^2*c^(3/2)*d^6*e^8 - 135*a^(5/2)*c*d^4*e^10 - 77*a^3*Sqrt[c]*d^2*e^12 + 15*a^(7/2)*e^14)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/a^(11/4) + (3*Sqrt[2]*c^(1/4)*(7*c^(7/2)*d^14 - 5*Sqrt[a]*c^3*d^12*e^2 + 33*a*c^(5/2)*d^10*e^4 - 27*a^(3/2)*c^2*d^8*e^6 + 77*a^2*c^(3/2)*d^6*e^8 - 135*a^(5/2)*c*d^4*e^10 - 77*a^3*Sqrt[c]*d^2*e^12 + 15*a^(7/2)*e^14)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/a^(11/4) - 768*c*d^3*e^11*Log[a + c*x^4])/(256*(c*d^4 + a*e^4)^4)","A",1
414,1,1338,2204,2.8733582,"\int \frac{1}{(d+e x)^3 \left(a+c x^4\right)^3} \, dx","Integrate[1/((d + e*x)^3*(a + c*x^4)^3),x]","\frac{1536 c d^2 \left(13 c d^4-3 a e^4\right) \log (d+e x) e^{11}-384 c d^2 \left(13 c d^4-3 a e^4\right) \log \left(c x^4+a\right) e^{11}-\frac{3072 c d^3 \left(c d^4+a e^4\right) e^{11}}{d+e x}-\frac{128 \left(c d^4+a e^4\right)^2 e^{11}}{(d+e x)^2}+\frac{8 c \left(c d^4+a e^4\right) \left(c^3 x \left(7 d^2-18 e x d+30 e^2 x^2\right) d^{11}+a c^2 e^4 x \left(43 d^2-114 e x d+204 e^2 x^2\right) d^7+a^2 c e^7 \left(288 d^3-303 e x d^2+274 e^2 x^2 d-210 e^3 x^3\right) d^3+a^3 e^{11} \left(-96 d^2+45 e x d-14 e^2 x^2\right)\right)}{a^2 \left(c x^4+a\right)}+\frac{32 c \left(c d^4+a e^4\right)^2 \left(c^2 x \left(d^2-3 e x d+6 e^2 x^2\right) d^7+2 a c e^3 \left(5 d^3-6 e x d^2+6 e^2 x^2 d-5 e^3 x^3\right) d^3-a^2 e^7 \left(6 d^2-3 e x d+e^2 x^2\right)\right)}{a \left(c x^4+a\right)^2}-\frac{6 \sqrt{c} \left(7 \sqrt{2} c^{17/4} d^{17}-24 \sqrt[4]{a} c^4 e d^{16}+10 \sqrt{2} \sqrt{a} c^{15/4} e^2 d^{15}+50 \sqrt{2} a c^{13/4} e^4 d^{13}-176 a^{5/4} c^3 e^5 d^{12}+78 \sqrt{2} a^{3/2} c^{11/4} e^6 d^{11}+220 \sqrt{2} a^2 c^{9/4} e^8 d^9-960 a^{9/4} c^2 e^9 d^8+702 \sqrt{2} a^{5/2} c^{7/4} e^{10} d^7-770 \sqrt{2} a^3 c^{5/4} e^{12} d^5+1200 a^{13/4} c e^{13} d^4-390 \sqrt{2} a^{7/2} c^{3/4} e^{14} d^3+77 \sqrt{2} a^4 \sqrt[4]{c} e^{16} d-40 a^{17/4} e^{17}\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{a^{11/4}}+\frac{6 \sqrt{c} \left(7 \sqrt{2} c^{17/4} d^{17}+24 \sqrt[4]{a} c^4 e d^{16}+10 \sqrt{2} \sqrt{a} c^{15/4} e^2 d^{15}+50 \sqrt{2} a c^{13/4} e^4 d^{13}+176 a^{5/4} c^3 e^5 d^{12}+78 \sqrt{2} a^{3/2} c^{11/4} e^6 d^{11}+220 \sqrt{2} a^2 c^{9/4} e^8 d^9+960 a^{9/4} c^2 e^9 d^8+702 \sqrt{2} a^{5/2} c^{7/4} e^{10} d^7-770 \sqrt{2} a^3 c^{5/4} e^{12} d^5-1200 a^{13/4} c e^{13} d^4-390 \sqrt{2} a^{7/2} c^{3/4} e^{14} d^3+77 \sqrt{2} a^4 \sqrt[4]{c} e^{16} d+40 a^{17/4} e^{17}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{a^{11/4}}-\frac{3 \sqrt{2} c^{3/4} \left(7 c^4 d^{17}-10 \sqrt{a} c^{7/2} e^2 d^{15}+50 a c^3 e^4 d^{13}-78 a^{3/2} c^{5/2} e^6 d^{11}+220 a^2 c^2 e^8 d^9-702 a^{5/2} c^{3/2} e^{10} d^7-770 a^3 c e^{12} d^5+390 a^{7/2} \sqrt{c} e^{14} d^3+77 a^4 e^{16} d\right) \log \left(\sqrt{c} x^2-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right)}{a^{11/4}}+\frac{3 \sqrt{2} c^{3/4} \left(7 c^4 d^{17}-10 \sqrt{a} c^{7/2} e^2 d^{15}+50 a c^3 e^4 d^{13}-78 a^{3/2} c^{5/2} e^6 d^{11}+220 a^2 c^2 e^8 d^9-702 a^{5/2} c^{3/2} e^{10} d^7-770 a^3 c e^{12} d^5+390 a^{7/2} \sqrt{c} e^{14} d^3+77 a^4 e^{16} d\right) \log \left(\sqrt{c} x^2+\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right)}{a^{11/4}}}{256 \left(c d^4+a e^4\right)^5}","\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,"((-128*e^11*(c*d^4 + a*e^4)^2)/(d + e*x)^2 - (3072*c*d^3*e^11*(c*d^4 + a*e^4))/(d + e*x) + (8*c*(c*d^4 + a*e^4)*(a^3*e^11*(-96*d^2 + 45*d*e*x - 14*e^2*x^2) + c^3*d^11*x*(7*d^2 - 18*d*e*x + 30*e^2*x^2) + a*c^2*d^7*e^4*x*(43*d^2 - 114*d*e*x + 204*e^2*x^2) + a^2*c*d^3*e^7*(288*d^3 - 303*d^2*e*x + 274*d*e^2*x^2 - 210*e^3*x^3)))/(a^2*(a + c*x^4)) + (32*c*(c*d^4 + a*e^4)^2*(-(a^2*e^7*(6*d^2 - 3*d*e*x + e^2*x^2)) + c^2*d^7*x*(d^2 - 3*d*e*x + 6*e^2*x^2) + 2*a*c*d^3*e^3*(5*d^3 - 6*d^2*e*x + 6*d*e^2*x^2 - 5*e^3*x^3)))/(a*(a + c*x^4)^2) - (6*Sqrt[c]*(7*Sqrt[2]*c^(17/4)*d^17 - 24*a^(1/4)*c^4*d^16*e + 10*Sqrt[2]*Sqrt[a]*c^(15/4)*d^15*e^2 + 50*Sqrt[2]*a*c^(13/4)*d^13*e^4 - 176*a^(5/4)*c^3*d^12*e^5 + 78*Sqrt[2]*a^(3/2)*c^(11/4)*d^11*e^6 + 220*Sqrt[2]*a^2*c^(9/4)*d^9*e^8 - 960*a^(9/4)*c^2*d^8*e^9 + 702*Sqrt[2]*a^(5/2)*c^(7/4)*d^7*e^10 - 770*Sqrt[2]*a^3*c^(5/4)*d^5*e^12 + 1200*a^(13/4)*c*d^4*e^13 - 390*Sqrt[2]*a^(7/2)*c^(3/4)*d^3*e^14 + 77*Sqrt[2]*a^4*c^(1/4)*d*e^16 - 40*a^(17/4)*e^17)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/a^(11/4) + (6*Sqrt[c]*(7*Sqrt[2]*c^(17/4)*d^17 + 24*a^(1/4)*c^4*d^16*e + 10*Sqrt[2]*Sqrt[a]*c^(15/4)*d^15*e^2 + 50*Sqrt[2]*a*c^(13/4)*d^13*e^4 + 176*a^(5/4)*c^3*d^12*e^5 + 78*Sqrt[2]*a^(3/2)*c^(11/4)*d^11*e^6 + 220*Sqrt[2]*a^2*c^(9/4)*d^9*e^8 + 960*a^(9/4)*c^2*d^8*e^9 + 702*Sqrt[2]*a^(5/2)*c^(7/4)*d^7*e^10 - 770*Sqrt[2]*a^3*c^(5/4)*d^5*e^12 - 1200*a^(13/4)*c*d^4*e^13 - 390*Sqrt[2]*a^(7/2)*c^(3/4)*d^3*e^14 + 77*Sqrt[2]*a^4*c^(1/4)*d*e^16 + 40*a^(17/4)*e^17)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/a^(11/4) + 1536*c*d^2*e^11*(13*c*d^4 - 3*a*e^4)*Log[d + e*x] - (3*Sqrt[2]*c^(3/4)*(7*c^4*d^17 - 10*Sqrt[a]*c^(7/2)*d^15*e^2 + 50*a*c^3*d^13*e^4 - 78*a^(3/2)*c^(5/2)*d^11*e^6 + 220*a^2*c^2*d^9*e^8 - 702*a^(5/2)*c^(3/2)*d^7*e^10 - 770*a^3*c*d^5*e^12 + 390*a^(7/2)*Sqrt[c]*d^3*e^14 + 77*a^4*d*e^16)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/a^(11/4) + (3*Sqrt[2]*c^(3/4)*(7*c^4*d^17 - 10*Sqrt[a]*c^(7/2)*d^15*e^2 + 50*a*c^3*d^13*e^4 - 78*a^(3/2)*c^(5/2)*d^11*e^6 + 220*a^2*c^2*d^9*e^8 - 702*a^(5/2)*c^(3/2)*d^7*e^10 - 770*a^3*c*d^5*e^12 + 390*a^(7/2)*Sqrt[c]*d^3*e^14 + 77*a^4*d*e^16)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/a^(11/4) - 384*c*d^2*e^11*(13*c*d^4 - 3*a*e^4)*Log[a + c*x^4])/(256*(c*d^4 + a*e^4)^5)","A",1
415,1,33,32,0.0096327,"\int \frac{-1+x}{1-x+x^2} \, dx","Integrate[(-1 + x)/(1 - x + x^2),x]","\frac{1}{2} \log \left(x^2-x+1\right)-\frac{\tan ^{-1}\left(\frac{2 x-1}{\sqrt{3}}\right)}{\sqrt{3}}","\frac{1}{2} \log \left(x^2-x+1\right)+\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{\sqrt{3}}",1,"-(ArcTan[(-1 + 2*x)/Sqrt[3]]/Sqrt[3]) + Log[1 - x + x^2]/2","A",1
416,1,33,32,0.0056956,"\int \frac{-1+x^2}{1+x^3} \, dx","Integrate[(-1 + x^2)/(1 + x^3),x]","\frac{1}{2} \log \left(x^2-x+1\right)-\frac{\tan ^{-1}\left(\frac{2 x-1}{\sqrt{3}}\right)}{\sqrt{3}}","\frac{1}{2} \log \left(x^2-x+1\right)+\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{\sqrt{3}}",1,"-(ArcTan[(-1 + 2*x)/Sqrt[3]]/Sqrt[3]) + Log[1 - x + x^2]/2","A",1
417,1,31,32,0.0086126,"\int \frac{-4+3 x}{4-2 x+x^2} \, dx","Integrate[(-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{x-1}{\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",1
418,1,31,32,0.0051862,"\int \frac{-8+2 x+3 x^2}{8+x^3} \, dx","Integrate[(-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{x-1}{\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",1
419,1,42,45,0.0220776,"\int \frac{2+x}{-1+2 x+x^2} \, dx","Integrate[(2 + x)/(-1 + 2*x + x^2),x]","\frac{1}{4} \left(\left(2+\sqrt{2}\right) \log \left(-x+\sqrt{2}-1\right)-\left(\sqrt{2}-2\right) \log \left(x+\sqrt{2}+1\right)\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] - (-2 + Sqrt[2])*Log[1 + Sqrt[2] + x])/4","A",1
420,1,42,45,0.0051176,"\int \frac{-4+x^2}{2-5 x+x^3} \, dx","Integrate[(-4 + x^2)/(2 - 5*x + x^3),x]","\frac{1}{4} \left(\left(2+\sqrt{2}\right) \log \left(-x+\sqrt{2}-1\right)-\left(\sqrt{2}-2\right) \log \left(x+\sqrt{2}+1\right)\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] - (-2 + Sqrt[2])*Log[1 + Sqrt[2] + x])/4","A",1
421,1,23,6,0.003276,"\int \frac{2}{-1+4 x^2} \, dx","Integrate[2/(-1 + 4*x^2),x]","2 \left(\frac{1}{4} \log (1-2 x)-\frac{1}{4} \log (2 x+1)\right)","-\tanh ^{-1}(2 x)",1,"2*(Log[1 - 2*x]/4 - Log[1 + 2*x]/4)","B",1
422,1,23,21,0.0025914,"\int \left(\frac{1}{-1+2 x}-\frac{1}{1+2 x}\right) \, dx","Integrate[(-1 + 2*x)^(-1) - (1 + 2*x)^(-1),x]","2 \left(\frac{1}{4} \log (1-2 x)-\frac{1}{4} \log (2 x+1)\right)","\frac{1}{2} \log (1-2 x)-\frac{1}{2} \log (2 x+1)",1,"2*(Log[1 - 2*x]/4 - Log[1 + 2*x]/4)","A",1
423,1,11,13,0.002646,"\int \frac{x}{\left(1-x^2\right)^5} \, dx","Integrate[x/(1 - x^2)^5,x]","\frac{1}{8 \left(x^2-1\right)^4}","\frac{1}{8 \left(1-x^2\right)^4}",1,"1/(8*(-1 + x^2)^4)","A",1
424,1,11,13,0.0016251,"\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","Integrate[-1/32*1/(-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{1}{8 \left(x^2-1\right)^4}","\frac{1}{8 \left(1-x^2\right)^4}",1,"1/(8*(-1 + x^2)^4)","A",1
425,1,78,69,0.0140783,"\int \frac{1+x^6}{-1+x^6} \, dx","Integrate[(1 + x^6)/(-1 + x^6),x]","\frac{1}{6} \left(\log \left(x^2-x+1\right)-\log \left(x^2+x+1\right)+6 x+2 \log (1-x)-2 \log (x+1)-2 \sqrt{3} \tan ^{-1}\left(\frac{2 x-1}{\sqrt{3}}\right)-2 \sqrt{3} \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)\right)","\frac{1}{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,"(6*x - 2*Sqrt[3]*ArcTan[(-1 + 2*x)/Sqrt[3]] - 2*Sqrt[3]*ArcTan[(1 + 2*x)/Sqrt[3]] + 2*Log[1 - x] - 2*Log[1 + x] + Log[1 - x + x^2] - Log[1 + x + x^2])/6","A",1
426,1,78,69,0.0057072,"\int \frac{\frac{1}{x^3}+x^3}{-\frac{1}{x^3}+x^3} \, dx","Integrate[(x^(-3) + x^3)/(-x^(-3) + x^3),x]","\frac{1}{6} \left(\log \left(x^2-x+1\right)-\log \left(x^2+x+1\right)+6 x+2 \log (1-x)-2 \log (x+1)-2 \sqrt{3} \tan ^{-1}\left(\frac{2 x-1}{\sqrt{3}}\right)-2 \sqrt{3} \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)\right)","\frac{1}{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,"(6*x - 2*Sqrt[3]*ArcTan[(-1 + 2*x)/Sqrt[3]] - 2*Sqrt[3]*ArcTan[(1 + 2*x)/Sqrt[3]] + 2*Log[1 - x] - 2*Log[1 + x] + Log[1 - x + x^2] - Log[1 + x + x^2])/6","A",1
427,1,31,24,0.0058512,"\int \frac{-x+x^3}{6+2 x} \, dx","Integrate[(-x + x^3)/(6 + 2*x),x]","\frac{1}{2} \left(\frac{x^3}{3}-\frac{3 x^2}{2}+8 x-24 \log (x+3)+\frac{93}{2}\right)","\frac{x^3}{6}-\frac{3 x^2}{4}+4 x-12 \log (x+3)",1,"(93/2 + 8*x - (3*x^2)/2 + x^3/3 - 24*Log[3 + x])/2","A",1
428,1,25,26,0.0041985,"\int \frac{x+x^3}{-1+x} \, dx","Integrate[(x + x^3)/(-1 + x),x]","\frac{1}{6} \left(2 x^3+3 x^2+12 x+12 \log (x-1)-17\right)","\frac{x^3}{3}+\frac{x^2}{2}+2 x+2 \log (1-x)",1,"(-17 + 12*x + 3*x^2 + 2*x^3 + 12*Log[-1 + x])/6","A",1
429,1,22,17,0.000073,"\int (a c+(b c+d) x) \, dx","Integrate[a*c + (b*c + d)*x,x]","a c x+\frac{1}{2} b c x^2+\frac{d x^2}{2}","a c x+\frac{1}{2} x^2 (b c+d)",1,"a*c*x + (b*c*x^2)/2 + (d*x^2)/2","A",1
430,1,22,24,0.0012142,"\int (d x+c (a+b x)) \, dx","Integrate[d*x + c*(a + b*x),x]","a c x+\frac{1}{2} b c x^2+\frac{d x^2}{2}","\frac{c (a+b x)^2}{2 b}+\frac{d x^2}{2}",1,"a*c*x + (b*c*x^2)/2 + (d*x^2)/2","A",1
431,1,24,22,0.005525,"\int \frac{4+4 x}{x^2 \left(1+x^2\right)} \, dx","Integrate[(4 + 4*x)/(x^2*(1 + x^2)),x]","4 \left(-\frac{1}{2} \log \left(x^2+1\right)-\frac{1}{x}+\log (x)-\tan ^{-1}(x)\right)","-2 \log \left(x^2+1\right)-\frac{4}{x}+4 \log (x)-4 \tan ^{-1}(x)",1,"4*(-x^(-1) - ArcTan[x] + Log[x] - Log[1 + x^2]/2)","A",1
432,1,27,17,0.0044664,"\int \frac{24+8 x}{x \left(-4+x^2\right)} \, dx","Integrate[(24 + 8*x)/(x*(-4 + x^2)),x]","8 \left(\frac{5}{8} \log (2-x)-\frac{3 \log (x)}{4}+\frac{1}{8} \log (x+2)\right)","5 \log (2-x)-6 \log (x)+\log (x+2)",1,"8*((5*Log[2 - x])/8 - (3*Log[x])/4 + Log[2 + x]/8)","A",1
433,1,19,19,0.0036639,"\int \frac{-1+x^2}{-2 x+x^3} \, dx","Integrate[(-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",1
434,1,17,12,0.0035649,"\int \frac{1+x^2}{3 x+x^3} \, dx","Integrate[(1 + x^2)/(3*x + x^3),x]","\frac{1}{3} \log \left(x^2+3\right)+\frac{\log (x)}{3}","\frac{1}{3} \log \left(x^3+3 x\right)",1,"Log[x]/3 + Log[3 + x^2]/3","A",1
435,1,11,10,0.0059471,"\int \frac{a+3 b x^2}{a x+b x^3} \, dx","Integrate[(a + 3*b*x^2)/(a*x + b*x^3),x]","\log \left(a+b x^2\right)+\log (x)","\log \left(a x+b x^3\right)",1,"Log[x] + Log[a + b*x^2]","A",1
436,1,17,17,0.0058267,"\int \frac{-2+4 x}{-x+x^3} \, dx","Integrate[(-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",1
437,1,23,23,0.0042494,"\int \frac{4+x}{4 x+x^3} \, dx","Integrate[(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",1
438,1,15,15,0.0042915,"\int \frac{-x+2 x^3}{1-x^2+x^4} \, dx","Integrate[(-x + 2*x^3)/(1 - x^2 + x^4),x]","\frac{1}{2} \log \left(x^4-x^2+1\right)","\frac{1}{2} \log \left(x^4-x^2+1\right)",1,"Log[1 - x^2 + x^4]/2","A",1
439,1,21,21,0.0053219,"\int \frac{-3+x}{2 x+3 x^2+x^3} \, dx","Integrate[(-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",1
440,1,9,10,0.0051114,"\int \frac{2+4 x}{x^2+2 x^3+x^4} \, dx","Integrate[(2 + 4*x)/(x^2 + 2*x^3 + x^4),x]","-\frac{2}{x^2+x}","-\frac{2}{x (x+1)}",1,"-2/(x + x^2)","A",1
441,1,25,25,0.0052087,"\int \frac{1+x}{-6 x+x^2+x^3} \, dx","Integrate[(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",1
442,1,14,14,0.0039205,"\int \frac{4 x^2+x^3}{x+x^3} \, dx","Integrate[(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",1
443,1,14,13,0.006539,"\int \frac{x+2 x^3}{\left(x^2+x^4\right)^3} \, dx","Integrate[(x + 2*x^3)/(x^2 + x^4)^3,x]","-\frac{1}{4 x^4 \left(x^2+1\right)^2}","-\frac{1}{4 \left(x^4+x^2\right)^2}",1,"-1/4*1/(x^4*(1 + x^2)^2)","A",1
444,1,25,26,0.0077822,"\int \frac{a x^2+b x^3}{c x^2+d x^3} \, dx","Integrate[(a*x^2 + b*x^3)/(c*x^2 + d*x^3),x]","\frac{(a d-b c) \log (c+d x)}{d^2}+\frac{b x}{d}","\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",1
445,1,4,6,0.0008986,"\int \frac{x+x^2}{-2 x-x^2+x^3} \, dx","Integrate[(x + x^2)/(-2*x - x^2 + x^3),x]","\log (x-2)","\log (2-x)",1,"Log[-2 + x]","A",1
446,1,20,20,0.0048644,"\int \frac{1-5 x^2}{x^3 \left(1+x^2\right)} \, dx","Integrate[(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*1/x^2 - 6*Log[x] + 3*Log[1 + x^2]","A",1
447,1,40,38,0.009916,"\int \frac{2 x}{(-1+x) \left(5+x^2\right)} \, dx","Integrate[(2*x)/((-1 + x)*(5 + x^2)),x]","2 \left(-\frac{1}{12} \log \left(x^2+5\right)+\frac{1}{6} \log (1-x)+\frac{1}{6} \sqrt{5} \tan ^{-1}\left(\frac{x}{\sqrt{5}}\right)\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,"2*((Sqrt[5]*ArcTan[x/Sqrt[5]])/6 + Log[1 - x]/6 - Log[5 + x^2]/12)","A",1
448,1,18,17,0.0035246,"\int \frac{2+x^2}{2+x} \, dx","Integrate[(2 + x^2)/(2 + x),x]","\frac{x^2}{2}-2 x+6 \log (x+2)-6","\frac{x^2}{2}-2 x+6 \log (x+2)",1,"-6 - 2*x + x^2/2 + 6*Log[2 + x]","A",1
449,1,36,31,0.0054412,"\int \frac{1}{(-3+x) \left(4+x^2\right)} \, dx","Integrate[1/((-3 + x)*(4 + x^2)),x]","-\frac{1}{26} \log \left((x-3)^2+6 (x-3)+13\right)+\frac{1}{13} \log (x-3)-\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[13 + 6*(-3 + x) + (-3 + x)^2]/26 + Log[-3 + x]/13","A",1
450,1,19,19,0.0055497,"\int \frac{-2+3 x^6}{x \left(5+2 x^6\right)} \, dx","Integrate[(-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",1
451,1,9,11,0.0038505,"\int \frac{3+2 x}{(-2+x) (5+x)} \, dx","Integrate[(3 + 2*x)/((-2 + x)*(5 + x)),x]","\log (x-2)+\log (x+5)","\log (2-x)+\log (x+5)",1,"Log[-2 + x] + Log[5 + x]","A",1
452,1,18,18,0.0087576,"\int \frac{x^4}{4+5 x^2+x^4} \, dx","Integrate[x^4/(4 + 5*x^2 + x^4),x]","x+\frac{8}{3} \tan ^{-1}\left(\frac{2}{x}\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[2/x])/3 + ArcTan[x]/3","A",1
453,1,44,46,0.0187543,"\int \frac{1}{(1+x) (2+x)^2 (3+x)^3} \, dx","Integrate[1/((1 + x)*(2 + x)^2*(3 + x)^3),x]","\frac{1}{8} \left(\frac{8}{x+2}+\frac{10}{x+3}+\frac{2}{(x+3)^2}+\log (-x-1)+16 \log (x+2)-17 \log (x+3)\right)","\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,"(8/(2 + x) + 2/(3 + x)^2 + 10/(3 + x) + Log[-1 - x] + 16*Log[2 + x] - 17*Log[3 + x])/8","A",1
454,1,10,12,0.0013752,"\int \frac{x}{-1+x^2} \, dx","Integrate[x/(-1 + x^2),x]","\frac{1}{2} \log \left(x^2-1\right)","\frac{1}{2} \log \left(1-x^2\right)",1,"Log[-1 + x^2]/2","A",1
455,1,27,21,0.0075467,"\int \frac{1}{\left(-1+x^2\right)^2} \, dx","Integrate[(-1 + x^2)^(-2),x]","\frac{1}{4} \left(-\frac{2 x}{x^2-1}-\log (1-x)+\log (x+1)\right)","\frac{x}{2 \left(1-x^2\right)}+\frac{1}{2} \tanh ^{-1}(x)",1,"((-2*x)/(-1 + x^2) - Log[1 - x] + Log[1 + x])/4","A",1
456,1,19,19,0.0081101,"\int \frac{x^2}{\left(1+x^2\right)^2} \, dx","Integrate[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,"-1/2*x/(1 + x^2) + ArcTan[x]/2","A",1
457,1,10,10,0.0009491,"\int \frac{1}{2+3 x} \, dx","Integrate[(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
458,1,10,10,0.0022705,"\int \frac{1}{a^2+x^2} \, dx","Integrate[(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
459,1,24,24,0.0043133,"\int \frac{1}{a+b x^2} \, dx","Integrate[(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
460,1,19,19,0.0064251,"\int \frac{1}{2-x+x^2} \, dx","Integrate[(2 - x + x^2)^(-1),x]","\frac{2 \tan ^{-1}\left(\frac{2 x-1}{\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",1
461,1,22,22,0.0007373,"\int x^2 \left(4-x^2\right)^2 \, dx","Integrate[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",1
462,1,22,22,0.0007666,"\int x \left(1-x^3\right)^2 \, dx","Integrate[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",1
463,1,16,16,0.000947,"\int \frac{-4+5 x^2+x^3}{x^2} \, dx","Integrate[(-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",1
464,1,37,37,0.0102724,"\int \frac{-1+x}{3-4 x+3 x^2} \, dx","Integrate[(-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{3 x-2}{\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,"-1/3*ArcTan[(-2 + 3*x)/Sqrt[5]]/Sqrt[5] + Log[3 - 4*x + 3*x^2]/6","A",1
465,1,14,14,0.0004291,"\int \left(2+x^3\right)^2 \, dx","Integrate[(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",1
466,1,11,11,0.0004251,"\int \frac{-4+x^2}{2+x} \, dx","Integrate[(-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",1
467,1,25,25,0.0058009,"\int \frac{1}{(2+x) \left(1+x^2\right)} \, dx","Integrate[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",1
468,1,25,25,0.0053107,"\int \frac{1}{(1+x) \left(1+x^2\right)} \, dx","Integrate[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",1
469,1,25,25,0.0058623,"\int \frac{x}{(1+x) \left(1+x^2\right)} \, dx","Integrate[x/((1 + x)*(1 + x^2)),x]","\frac{1}{4} \log \left(x^2+1\right)-\frac{1}{2} \log (x+1)+\frac{1}{2} \tan ^{-1}(x)","\frac{1}{4} \log \left(x^2+1\right)-\frac{1}{2} \log (x+1)+\frac{1}{2} \tan ^{-1}(x)",1,"ArcTan[x]/2 - Log[1 + x]/2 + Log[1 + x^2]/4","A",1
470,1,7,9,0.0029173,"\int \frac{2 x+x^2}{(1+x)^2} \, dx","Integrate[(2*x + x^2)/(1 + x)^2,x]","x+\frac{1}{x+1}","\frac{x^2}{x+1}",1,"x + (1 + x)^(-1)","A",1
471,1,22,22,0.0125107,"\int \frac{-10+x^2}{4+9 x^2+2 x^4} \, dx","Integrate[(-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",1
472,1,37,37,0.0133152,"\int \frac{31+5 x}{11-4 x+3 x^2} \, dx","Integrate[(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{3 x-2}{\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",1
473,1,15,15,0.0018469,"\int \frac{-2+x^2+x^3}{x^4} \, dx","Integrate[(-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",1
474,1,15,15,0.0007836,"\int \frac{1+x+x^3}{x^2} \, dx","Integrate[(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",1
475,1,11,11,0.003265,"\int \frac{-2+x^2}{x \left(2+x^2\right)} \, dx","Integrate[(-2 + x^2)/(x*(2 + x^2)),x]","\log \left(x^2+2\right)-\log (x)","\log \left(x^2+2\right)-\log (x)",1,"-Log[x] + Log[2 + x^2]","A",1
476,1,19,22,0.0009965,"\int (-3+x) \left(-7+4 x^2\right) \, dx","Integrate[(-3 + x)*(-7 + 4*x^2),x]","x^4-4 x^3-\frac{7 x^2}{2}+21 x","-4 x^3+\frac{1}{16} \left(7-4 x^2\right)^2+21 x",1,"21*x - (7*x^2)/2 - 4*x^3 + x^4","A",1
477,1,11,11,0.0014966,"\int (-2+7 x)^3 \, dx","Integrate[(-2 + 7*x)^3,x]","\frac{1}{28} (7 x-2)^4","\frac{1}{28} (2-7 x)^4",1,"(-2 + 7*x)^4/28","A",1
478,1,16,13,0.0036996,"\int \frac{-7+4 x^2}{3+2 x} \, dx","Integrate[(-7 + 4*x^2)/(3 + 2*x),x]","x^2-3 x+\log (2 x+3)-\frac{27}{4}","x^2-3 x+\log (2 x+3)",1,"-27/4 - 3*x + x^2 + Log[3 + 2*x]","A",1
479,1,16,16,0.0025747,"\int \frac{1+x}{(-1+x) x^2} \, dx","Integrate[(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",1
480,1,26,27,0.0163392,"\int \frac{1}{4 x^2+4 x^3+x^4} \, dx","Integrate[(4*x^2 + 4*x^3 + x^4)^(-1),x]","\frac{1}{4} \left(-\frac{2 (x+1)}{x (x+2)}-\log (x)+\log (x+2)\right)","\frac{x+1}{2 \left(1-(x+1)^2\right)}+\frac{1}{2} \tanh ^{-1}(x+1)",1,"((-2*(1 + x))/(x*(2 + x)) - Log[x] + Log[2 + x])/4","A",1
481,1,18,17,0.0028924,"\int \frac{1+x^2}{1+x} \, dx","Integrate[(1 + x^2)/(1 + x),x]","\frac{1}{2} \left(x^2-2 x+4 \log (x+1)-3\right)","\frac{x^2}{2}-x+2 \log (x+1)",1,"(-3 - 2*x + x^2 + 4*Log[1 + x])/2","A",1
482,1,18,18,0.0010472,"\int \frac{-1+3 x-3 x^2+x^3}{x^2} \, dx","Integrate[(-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",1
483,1,18,18,0.0007038,"\int \left(\frac{1}{2} \left(3-\sqrt{37}\right)+x\right) \left(\frac{1}{2} \left(3+\sqrt{37}\right)+x\right) \, dx","Integrate[((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",1
484,1,23,23,0.0101164,"\int \frac{4+3 x^2+2 x^3}{(1+x)^4} \, dx","Integrate[(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",1
485,1,12,16,0.0063657,"\int \frac{x}{(1+x)^2 \left(1+x^2\right)} \, dx","Integrate[x/((1 + x)^2*(1 + x^2)),x]","\frac{1}{2} \left(\frac{1}{x+1}+\tan ^{-1}(x)\right)","\frac{1}{2 (x+1)}+\frac{1}{2} \tan ^{-1}(x)",1,"((1 + x)^(-1) + ArcTan[x])/2","A",1
486,1,30,29,0.0076729,"\int \frac{7-2 x+3 x^2-x^3+x^4}{2+x} \, dx","Integrate[(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)-70","\frac{x^4}{4}-x^3+\frac{9 x^2}{2}-20 x+47 \log (x+2)",1,"-70 - 20*x + (9*x^2)/2 - x^3 + x^4/4 + 47*Log[2 + x]","A",1
487,1,16,16,0.0004429,"\int \frac{-1+x^3}{-1+x} \, dx","Integrate[(-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",1
488,1,17,17,0.0122613,"\int \frac{2+2 x}{(-1+x)^3 \left(1+x^2\right)} \, dx","Integrate[(2 + 2*x)/((-1 + x)^3*(1 + x^2)),x]","\frac{x+(x-1)^2 \tan ^{-1}(x)-2}{(x-1)^2}","\frac{1}{x-1}-\frac{1}{(1-x)^2}+\tan ^{-1}(x)",1,"(-2 + x + (-1 + x)^2*ArcTan[x])/(-1 + x)^2","A",1
489,1,47,47,0.024515,"\int \frac{1}{b x+c (d+e x)^2} \, dx","Integrate[(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",1
490,1,61,57,0.0272396,"\int \frac{1}{a+b x+c (d+e x)^2} \, dx","Integrate[(a + b*x + c*(d + e*x)^2)^(-1),x]","\frac{2 \tan ^{-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*ArcTan[(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",1
491,1,39,188,0.0313972,"\int \frac{x^2}{1+\left(-1+x^2\right)^2} \, dx","Integrate[x^2/(1 + (-1 + x^2)^2),x]","-\frac{\tan ^{-1}\left(\frac{x}{\sqrt{-1-i}}\right)}{(-1-i)^{3/2}}-\frac{\tan ^{-1}\left(\frac{x}{\sqrt{-1+i}}\right)}{(-1+i)^{3/2}}","\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,"-(ArcTan[x/Sqrt[-1 - I]]/(-1 - I)^(3/2)) - ArcTan[x/Sqrt[-1 + I]]/(-1 + I)^(3/2)","C",1
492,1,27,60,0.0152792,"\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","Integrate[-((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+x^4+5 x^2-3 x+2}{\left(x^4+x+3\right)^3}","\frac{x^4}{\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{5 x^2}{\left(x^4+x+3\right)^3}",1,"(2 - 3*x + 5*x^2 + x^4 - 5*x^6)/(3 + x + x^4)^3","A",1
493,1,27,27,0.0096392,"\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","Integrate[(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]","\frac{-5 x^6+x^4+5 x^2-3 x+2}{\left(x^4+x+3\right)^3}","\frac{-5 x^6+x^4+5 x^2-3 x+2}{\left(x^4+x+3\right)^3}",1,"(2 - 3*x + 5*x^2 + x^4 - 5*x^6)/(3 + x + x^4)^3","A",1
494,1,27,27,0.009842,"\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","Integrate[(-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]","\frac{-5 x^6+x^4+5 x^2-3 x+2}{\left(x^4+x+3\right)^3}","\frac{-5 x^6+x^4+5 x^2-3 x+2}{\left(x^4+x+3\right)^3}",1,"(2 - 3*x + 5*x^2 + x^4 - 5*x^6)/(3 + x + x^4)^3","A",1