1,1,165,0,3.111417," ","integrate((e*x**3+d)/(c*x**6+a),x)","\operatorname{RootSum} {\left(46656 t^{6} a^{5} c^{4} + t^{3} \left(432 a^{4} c^{2} e^{3} - 1296 a^{3} c^{3} d^{2} e\right) + a^{3} e^{6} + 3 a^{2} c d^{2} e^{4} + 3 a c^{2} d^{4} e^{2} + c^{3} d^{6}, \left( t \mapsto t \log{\left(x + \frac{- 1296 t^{4} a^{4} c^{2} e - 6 t a^{3} e^{4} + 36 t a^{2} c d^{2} e^{2} - 6 t a c^{2} d^{4}}{3 a^{2} d e^{4} + 2 a c d^{3} e^{2} - c^{2} d^{5}} \right)} \right)\right)}"," ",0,"RootSum(46656*_t**6*a**5*c**4 + _t**3*(432*a**4*c**2*e**3 - 1296*a**3*c**3*d**2*e) + a**3*e**6 + 3*a**2*c*d**2*e**4 + 3*a*c**2*d**4*e**2 + c**3*d**6, Lambda(_t, _t*log(x + (-1296*_t**4*a**4*c**2*e - 6*_t*a**3*e**4 + 36*_t*a**2*c*d**2*e**2 - 6*_t*a*c**2*d**4)/(3*a**2*d*e**4 + 2*a*c*d**3*e**2 - c**2*d**5))))","A",0
2,1,168,0,3.123207," ","integrate((e*x**3+d)/(-c*x**6+a),x)","- \operatorname{RootSum} {\left(46656 t^{6} a^{5} c^{4} + t^{3} \left(- 432 a^{4} c^{2} e^{3} - 1296 a^{3} c^{3} d^{2} e\right) + a^{3} e^{6} - 3 a^{2} c d^{2} e^{4} + 3 a c^{2} d^{4} e^{2} - c^{3} d^{6}, \left( t \mapsto t \log{\left(x + \frac{- 1296 t^{4} a^{4} c^{2} e + 6 t a^{3} e^{4} + 36 t a^{2} c d^{2} e^{2} + 6 t a c^{2} d^{4}}{3 a^{2} d e^{4} - 2 a c d^{3} e^{2} - c^{2} d^{5}} \right)} \right)\right)}"," ",0,"-RootSum(46656*_t**6*a**5*c**4 + _t**3*(-432*a**4*c**2*e**3 - 1296*a**3*c**3*d**2*e) + a**3*e**6 - 3*a**2*c*d**2*e**4 + 3*a*c**2*d**4*e**2 - c**3*d**6, Lambda(_t, _t*log(x + (-1296*_t**4*a**4*c**2*e + 6*_t*a**3*e**4 + 36*_t*a**2*c*d**2*e**2 + 6*_t*a*c**2*d**4)/(3*a**2*d*e**4 - 2*a*c*d**3*e**2 - c**2*d**5))))","A",0
3,-1,0,0,0.000000," ","integrate((e*x**4+d)/(c*x**8+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
4,-1,0,0,0.000000," ","integrate((e*x**4+d)/(-c*x**8+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
5,1,136,0,8.502551," ","integrate((e*x**4+d)/(e**2*x**8+b*x**4+d**2),x)","\operatorname{RootSum} {\left(t^{8} \left(65536 b^{4} d^{2} + 524288 b^{3} d^{3} e + 1572864 b^{2} d^{4} e^{2} + 2097152 b d^{5} e^{3} + 1048576 d^{6} e^{4}\right) + t^{4} \left(256 b^{3} + 1024 b^{2} d e + 1024 b d^{2} e^{2}\right) + e^{2}, \left( t \mapsto t \log{\left(x + \frac{1024 t^{5} b^{2} d^{2} + 4096 t^{5} b d^{3} e + 4096 t^{5} d^{4} e^{2} + 4 t b + 4 t d e}{e} \right)} \right)\right)}"," ",0,"RootSum(_t**8*(65536*b**4*d**2 + 524288*b**3*d**3*e + 1572864*b**2*d**4*e**2 + 2097152*b*d**5*e**3 + 1048576*d**6*e**4) + _t**4*(256*b**3 + 1024*b**2*d*e + 1024*b*d**2*e**2) + e**2, Lambda(_t, _t*log(x + (1024*_t**5*b**2*d**2 + 4096*_t**5*b*d**3*e + 4096*_t**5*d**4*e**2 + 4*_t*b + 4*_t*d*e)/e)))","A",0
6,1,136,0,7.139490," ","integrate((e*x**4+d)/(e**2*x**8+f*x**4+d**2),x)","\operatorname{RootSum} {\left(t^{8} \left(1048576 d^{6} e^{4} + 2097152 d^{5} e^{3} f + 1572864 d^{4} e^{2} f^{2} + 524288 d^{3} e f^{3} + 65536 d^{2} f^{4}\right) + t^{4} \left(1024 d^{2} e^{2} f + 1024 d e f^{2} + 256 f^{3}\right) + e^{2}, \left( t \mapsto t \log{\left(x + \frac{4096 t^{5} d^{4} e^{2} + 4096 t^{5} d^{3} e f + 1024 t^{5} d^{2} f^{2} + 4 t d e + 4 t f}{e} \right)} \right)\right)}"," ",0,"RootSum(_t**8*(1048576*d**6*e**4 + 2097152*d**5*e**3*f + 1572864*d**4*e**2*f**2 + 524288*d**3*e*f**3 + 65536*d**2*f**4) + _t**4*(1024*d**2*e**2*f + 1024*d*e*f**2 + 256*f**3) + e**2, Lambda(_t, _t*log(x + (4096*_t**5*d**4*e**2 + 4096*_t**5*d**3*e*f + 1024*_t**5*d**2*f**2 + 4*_t*d*e + 4*_t*f)/e)))","A",0
7,1,136,0,8.250790," ","integrate((e*x**4+d)/(e**2*x**8-b*x**4+d**2),x)","\operatorname{RootSum} {\left(t^{8} \left(65536 b^{4} d^{2} - 524288 b^{3} d^{3} e + 1572864 b^{2} d^{4} e^{2} - 2097152 b d^{5} e^{3} + 1048576 d^{6} e^{4}\right) + t^{4} \left(- 256 b^{3} + 1024 b^{2} d e - 1024 b d^{2} e^{2}\right) + e^{2}, \left( t \mapsto t \log{\left(x + \frac{1024 t^{5} b^{2} d^{2} - 4096 t^{5} b d^{3} e + 4096 t^{5} d^{4} e^{2} - 4 t b + 4 t d e}{e} \right)} \right)\right)}"," ",0,"RootSum(_t**8*(65536*b**4*d**2 - 524288*b**3*d**3*e + 1572864*b**2*d**4*e**2 - 2097152*b*d**5*e**3 + 1048576*d**6*e**4) + _t**4*(-256*b**3 + 1024*b**2*d*e - 1024*b*d**2*e**2) + e**2, Lambda(_t, _t*log(x + (1024*_t**5*b**2*d**2 - 4096*_t**5*b*d**3*e + 4096*_t**5*d**4*e**2 - 4*_t*b + 4*_t*d*e)/e)))","A",0
8,1,136,0,7.254777," ","integrate((e*x**4+d)/(e**2*x**8-f*x**4+d**2),x)","\operatorname{RootSum} {\left(t^{8} \left(1048576 d^{6} e^{4} - 2097152 d^{5} e^{3} f + 1572864 d^{4} e^{2} f^{2} - 524288 d^{3} e f^{3} + 65536 d^{2} f^{4}\right) + t^{4} \left(- 1024 d^{2} e^{2} f + 1024 d e f^{2} - 256 f^{3}\right) + e^{2}, \left( t \mapsto t \log{\left(x + \frac{4096 t^{5} d^{4} e^{2} - 4096 t^{5} d^{3} e f + 1024 t^{5} d^{2} f^{2} + 4 t d e - 4 t f}{e} \right)} \right)\right)}"," ",0,"RootSum(_t**8*(1048576*d**6*e**4 - 2097152*d**5*e**3*f + 1572864*d**4*e**2*f**2 - 524288*d**3*e*f**3 + 65536*d**2*f**4) + _t**4*(-1024*d**2*e**2*f + 1024*d*e*f**2 - 256*f**3) + e**2, Lambda(_t, _t*log(x + (4096*_t**5*d**4*e**2 - 4096*_t**5*d**3*e*f + 1024*_t**5*d**2*f**2 + 4*_t*d*e - 4*_t*f)/e)))","A",0
9,1,75,0,3.669054," ","integrate((x**4+1)/(x**8+b*x**4+1),x)","\operatorname{RootSum} {\left(t^{8} \left(65536 b^{4} + 524288 b^{3} + 1572864 b^{2} + 2097152 b + 1048576\right) + t^{4} \left(256 b^{3} + 1024 b^{2} + 1024 b\right) + 1, \left( t \mapsto t \log{\left(1024 t^{5} b^{2} + 4096 t^{5} b + 4096 t^{5} + 4 t b + 4 t + x \right)} \right)\right)}"," ",0,"RootSum(_t**8*(65536*b**4 + 524288*b**3 + 1572864*b**2 + 2097152*b + 1048576) + _t**4*(256*b**3 + 1024*b**2 + 1024*b) + 1, Lambda(_t, _t*log(1024*_t**5*b**2 + 4096*_t**5*b + 4096*_t**5 + 4*_t*b + 4*_t + x)))","A",0
10,1,24,0,1.475388," ","integrate((x**4+1)/(x**8+3*x**4+1),x)","\operatorname{RootSum} {\left(40960000 t^{8} + 19200 t^{4} + 1, \left( t \mapsto t \log{\left(25600 t^{5} + 16 t + x \right)} \right)\right)}"," ",0,"RootSum(40960000*_t**8 + 19200*_t**4 + 1, Lambda(_t, _t*log(25600*_t**5 + 16*_t + x)))","A",0
11,1,73,0,0.154170," ","integrate((x**4+1)/(x**8+2*x**4+1),x)","- \frac{\sqrt{2} \log{\left(x^{2} - \sqrt{2} x + 1 \right)}}{8} + \frac{\sqrt{2} \log{\left(x^{2} + \sqrt{2} x + 1 \right)}}{8} + \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} x - 1 \right)}}{4} + \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} x + 1 \right)}}{4}"," ",0,"-sqrt(2)*log(x**2 - sqrt(2)*x + 1)/8 + sqrt(2)*log(x**2 + sqrt(2)*x + 1)/8 + sqrt(2)*atan(sqrt(2)*x - 1)/4 + sqrt(2)*atan(sqrt(2)*x + 1)/4","A",0
12,1,190,0,0.701571," ","integrate((x**4+1)/(x**8+x**4+1),x)","\left(- \frac{1}{8} - \frac{\sqrt{3} i}{24}\right) \log{\left(x - 1 - \frac{\sqrt{3} i}{3} + 9216 \left(- \frac{1}{8} - \frac{\sqrt{3} i}{24}\right)^{5} \right)} + \left(- \frac{1}{8} + \frac{\sqrt{3} i}{24}\right) \log{\left(x - 1 + 9216 \left(- \frac{1}{8} + \frac{\sqrt{3} i}{24}\right)^{5} + \frac{\sqrt{3} i}{3} \right)} + \left(\frac{1}{8} - \frac{\sqrt{3} i}{24}\right) \log{\left(x + 1 - \frac{\sqrt{3} i}{3} + 9216 \left(\frac{1}{8} - \frac{\sqrt{3} i}{24}\right)^{5} \right)} + \left(\frac{1}{8} + \frac{\sqrt{3} i}{24}\right) \log{\left(x + 1 + 9216 \left(\frac{1}{8} + \frac{\sqrt{3} i}{24}\right)^{5} + \frac{\sqrt{3} i}{3} \right)} + \operatorname{RootSum} {\left(2304 t^{4} + 48 t^{2} + 1, \left( t \mapsto t \log{\left(9216 t^{5} + 8 t + x \right)} \right)\right)}"," ",0,"(-1/8 - sqrt(3)*I/24)*log(x - 1 - sqrt(3)*I/3 + 9216*(-1/8 - sqrt(3)*I/24)**5) + (-1/8 + sqrt(3)*I/24)*log(x - 1 + 9216*(-1/8 + sqrt(3)*I/24)**5 + sqrt(3)*I/3) + (1/8 - sqrt(3)*I/24)*log(x + 1 - sqrt(3)*I/3 + 9216*(1/8 - sqrt(3)*I/24)**5) + (1/8 + sqrt(3)*I/24)*log(x + 1 + 9216*(1/8 + sqrt(3)*I/24)**5 + sqrt(3)*I/3) + RootSum(2304*_t**4 + 48*_t**2 + 1, Lambda(_t, _t*log(9216*_t**5 + 8*_t + x)))","C",0
13,1,19,0,2.784380," ","integrate((x**4+1)/(x**8+1),x)","\operatorname{RootSum} {\left(1048576 t^{8} + 1, \left( t \mapsto t \log{\left(4096 t^{5} + 4 t + x \right)} \right)\right)}"," ",0,"RootSum(1048576*_t**8 + 1, Lambda(_t, _t*log(4096*_t**5 + 4*_t + x)))","A",0
14,1,20,0,3.100406," ","integrate((x**4+1)/(x**8-x**4+1),x)","\operatorname{RootSum} {\left(65536 t^{8} - 256 t^{4} + 1, \left( t \mapsto t \log{\left(1024 t^{5} + x \right)} \right)\right)}"," ",0,"RootSum(65536*_t**8 - 256*_t**4 + 1, Lambda(_t, _t*log(1024*_t**5 + x)))","A",0
15,1,26,0,0.146918," ","integrate((x**4+1)/(x**8-2*x**4+1),x)","- \frac{x}{2 x^{4} - 2} - \frac{\log{\left(x - 1 \right)}}{8} + \frac{\log{\left(x + 1 \right)}}{8} + \frac{\operatorname{atan}{\left(x \right)}}{4}"," ",0,"-x/(2*x**4 - 2) - log(x - 1)/8 + log(x + 1)/8 + atan(x)/4","A",0
16,1,49,0,1.188548," ","integrate((x**4+1)/(x**8-3*x**4+1),x)","\operatorname{RootSum} {\left(256 t^{4} - 16 t^{2} - 1, \left( t \mapsto t \log{\left(1024 t^{5} - 8 t + x \right)} \right)\right)} + \operatorname{RootSum} {\left(256 t^{4} + 16 t^{2} - 1, \left( t \mapsto t \log{\left(1024 t^{5} - 8 t + x \right)} \right)\right)}"," ",0,"RootSum(256*_t**4 - 16*_t**2 - 1, Lambda(_t, _t*log(1024*_t**5 - 8*_t + x))) + RootSum(256*_t**4 + 16*_t**2 - 1, Lambda(_t, _t*log(1024*_t**5 - 8*_t + x)))","A",0
17,1,24,0,0.192358," ","integrate((x**4+1)/(x**8-4*x**4+1),x)","\operatorname{RootSum} {\left(1048576 t^{8} - 4096 t^{4} + 1, \left( t \mapsto t \log{\left(4096 t^{5} - 12 t + x \right)} \right)\right)}"," ",0,"RootSum(1048576*_t**8 - 4096*_t**4 + 1, Lambda(_t, _t*log(4096*_t**5 - 12*_t + x)))","A",0
18,1,24,0,0.194506," ","integrate((x**4+1)/(x**8-5*x**4+1),x)","\operatorname{RootSum} {\left(5308416 t^{8} - 11520 t^{4} + 1, \left( t \mapsto t \log{\left(9216 t^{5} - 16 t + x \right)} \right)\right)}"," ",0,"RootSum(5308416*_t**8 - 11520*_t**4 + 1, Lambda(_t, _t*log(9216*_t**5 - 16*_t + x)))","A",0
19,1,49,0,1.156937," ","integrate((x**4+1)/(x**8-6*x**4+1),x)","\operatorname{RootSum} {\left(4096 t^{4} - 128 t^{2} - 1, \left( t \mapsto t \log{\left(16384 t^{5} - 20 t + x \right)} \right)\right)} + \operatorname{RootSum} {\left(4096 t^{4} + 128 t^{2} - 1, \left( t \mapsto t \log{\left(16384 t^{5} - 20 t + x \right)} \right)\right)}"," ",0,"RootSum(4096*_t**4 - 128*_t**2 - 1, Lambda(_t, _t*log(16384*_t**5 - 20*_t + x))) + RootSum(4096*_t**4 + 128*_t**2 - 1, Lambda(_t, _t*log(16384*_t**5 - 20*_t + x)))","A",0
20,1,76,0,3.631641," ","integrate((-x**4+1)/(x**8+b*x**4+1),x)","- \operatorname{RootSum} {\left(t^{8} \left(65536 b^{4} - 524288 b^{3} + 1572864 b^{2} - 2097152 b + 1048576\right) + t^{4} \left(256 b^{3} - 1024 b^{2} + 1024 b\right) + 1, \left( t \mapsto t \log{\left(1024 t^{5} b^{2} - 4096 t^{5} b + 4096 t^{5} + 4 t b - 4 t + x \right)} \right)\right)}"," ",0,"-RootSum(_t**8*(65536*b**4 - 524288*b**3 + 1572864*b**2 - 2097152*b + 1048576) + _t**4*(256*b**3 - 1024*b**2 + 1024*b) + 1, Lambda(_t, _t*log(1024*_t**5*b**2 - 4096*_t**5*b + 4096*_t**5 + 4*_t*b - 4*_t + x)))","A",0
21,1,26,0,1.454643," ","integrate((-x**4+1)/(x**8+3*x**4+1),x)","- \operatorname{RootSum} {\left(65536 t^{8} + 768 t^{4} + 1, \left( t \mapsto t \log{\left(1024 t^{5} + 8 t + x \right)} \right)\right)}"," ",0,"-RootSum(65536*_t**8 + 768*_t**4 + 1, Lambda(_t, _t*log(1024*_t**5 + 8*_t + x)))","A",0
22,1,82,0,0.176349," ","integrate((-x**4+1)/(x**8+2*x**4+1),x)","\frac{x}{2 x^{4} + 2} - \frac{\sqrt{2} \log{\left(x^{2} - \sqrt{2} x + 1 \right)}}{16} + \frac{\sqrt{2} \log{\left(x^{2} + \sqrt{2} x + 1 \right)}}{16} + \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} x - 1 \right)}}{8} + \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} x + 1 \right)}}{8}"," ",0,"x/(2*x**4 + 2) - sqrt(2)*log(x**2 - sqrt(2)*x + 1)/16 + sqrt(2)*log(x**2 + sqrt(2)*x + 1)/16 + sqrt(2)*atan(sqrt(2)*x - 1)/8 + sqrt(2)*atan(sqrt(2)*x + 1)/8","A",0
23,1,148,0,0.621437," ","integrate((-x**4+1)/(x**8+x**4+1),x)","- \left(- \frac{1}{8} - \frac{\sqrt{3} i}{8}\right) \log{\left(x + 1024 \left(- \frac{1}{8} - \frac{\sqrt{3} i}{8}\right)^{5} \right)} - \left(- \frac{1}{8} + \frac{\sqrt{3} i}{8}\right) \log{\left(x + 1024 \left(- \frac{1}{8} + \frac{\sqrt{3} i}{8}\right)^{5} \right)} - \left(\frac{1}{8} - \frac{\sqrt{3} i}{8}\right) \log{\left(x + 1024 \left(\frac{1}{8} - \frac{\sqrt{3} i}{8}\right)^{5} \right)} - \left(\frac{1}{8} + \frac{\sqrt{3} i}{8}\right) \log{\left(x + 1024 \left(\frac{1}{8} + \frac{\sqrt{3} i}{8}\right)^{5} \right)} - \operatorname{RootSum} {\left(256 t^{4} - 16 t^{2} + 1, \left( t \mapsto t \log{\left(1024 t^{5} + x \right)} \right)\right)}"," ",0,"-(-1/8 - sqrt(3)*I/8)*log(x + 1024*(-1/8 - sqrt(3)*I/8)**5) - (-1/8 + sqrt(3)*I/8)*log(x + 1024*(-1/8 + sqrt(3)*I/8)**5) - (1/8 - sqrt(3)*I/8)*log(x + 1024*(1/8 - sqrt(3)*I/8)**5) - (1/8 + sqrt(3)*I/8)*log(x + 1024*(1/8 + sqrt(3)*I/8)**5) - RootSum(256*_t**4 - 16*_t**2 + 1, Lambda(_t, _t*log(1024*_t**5 + x)))","C",0
24,1,20,0,2.746497," ","integrate((-x**4+1)/(x**8+1),x)","- \operatorname{RootSum} {\left(1048576 t^{8} + 1, \left( t \mapsto t \log{\left(4096 t^{5} - 4 t + x \right)} \right)\right)}"," ",0,"-RootSum(1048576*_t**8 + 1, Lambda(_t, _t*log(4096*_t**5 - 4*_t + x)))","A",0
25,1,26,0,3.102899," ","integrate((-x**4+1)/(x**8-x**4+1),x)","- \operatorname{RootSum} {\left(5308416 t^{8} - 2304 t^{4} + 1, \left( t \mapsto t \log{\left(9216 t^{5} - 8 t + x \right)} \right)\right)}"," ",0,"-RootSum(5308416*_t**8 - 2304*_t**4 + 1, Lambda(_t, _t*log(9216*_t**5 - 8*_t + x)))","A",0
26,1,17,0,0.130464," ","integrate((-x**4+1)/(x**8-2*x**4+1),x)","- \frac{\log{\left(x - 1 \right)}}{4} + \frac{\log{\left(x + 1 \right)}}{4} + \frac{\operatorname{atan}{\left(x \right)}}{2}"," ",0,"-log(x - 1)/4 + log(x + 1)/4 + atan(x)/2","B",0
27,1,51,0,1.172411," ","integrate((-x**4+1)/(x**8-3*x**4+1),x)","- \operatorname{RootSum} {\left(6400 t^{4} - 80 t^{2} - 1, \left( t \mapsto t \log{\left(25600 t^{5} - 16 t + x \right)} \right)\right)} - \operatorname{RootSum} {\left(6400 t^{4} + 80 t^{2} - 1, \left( t \mapsto t \log{\left(25600 t^{5} - 16 t + x \right)} \right)\right)}"," ",0,"-RootSum(6400*_t**4 - 80*_t**2 - 1, Lambda(_t, _t*log(25600*_t**5 - 16*_t + x))) - RootSum(6400*_t**4 + 80*_t**2 - 1, Lambda(_t, _t*log(25600*_t**5 - 16*_t + x)))","A",0
28,1,26,0,0.197648," ","integrate((-x**4+1)/(x**8-4*x**4+1),x)","- \operatorname{RootSum} {\left(84934656 t^{8} - 36864 t^{4} + 1, \left( t \mapsto t \log{\left(36864 t^{5} - 20 t + x \right)} \right)\right)}"," ",0,"-RootSum(84934656*_t**8 - 36864*_t**4 + 1, Lambda(_t, _t*log(36864*_t**5 - 20*_t + x)))","A",0
29,1,26,0,0.194059," ","integrate((-x**4+1)/(x**8-5*x**4+1),x)","- \operatorname{RootSum} {\left(157351936 t^{8} - 62720 t^{4} + 1, \left( t \mapsto t \log{\left(50176 t^{5} - 24 t + x \right)} \right)\right)}"," ",0,"-RootSum(157351936*_t**8 - 62720*_t**4 + 1, Lambda(_t, _t*log(50176*_t**5 - 24*_t + x)))","A",0
30,1,51,0,1.164605," ","integrate((-x**4+1)/(x**8-6*x**4+1),x)","- \operatorname{RootSum} {\left(16384 t^{4} - 256 t^{2} - 1, \left( t \mapsto t \log{\left(65536 t^{5} - 28 t + x \right)} \right)\right)} - \operatorname{RootSum} {\left(16384 t^{4} + 256 t^{2} - 1, \left( t \mapsto t \log{\left(65536 t^{5} - 28 t + x \right)} \right)\right)}"," ",0,"-RootSum(16384*_t**4 - 256*_t**2 - 1, Lambda(_t, _t*log(65536*_t**5 - 28*_t + x))) - RootSum(16384*_t**4 + 256*_t**2 - 1, Lambda(_t, _t*log(65536*_t**5 - 28*_t + x)))","A",0
31,1,163,0,0.904218," ","integrate((-1+2*x**4+3**(1/2))/(x**8-x**4+1),x)","\frac{\sqrt{2} \left(2 \operatorname{atan}{\left(x \left(\frac{\sqrt{6}}{1 + \sqrt{3}} + \frac{2 \sqrt{2}}{1 + \sqrt{3}}\right) \right)} + 2 \operatorname{atan}{\left(x^{3} \left(\frac{\sqrt{6}}{1 + \sqrt{3}} + \frac{2 \sqrt{2}}{1 + \sqrt{3}}\right) - \sqrt{2} x \right)}\right)}{4} - \frac{\sqrt{2} \log{\left(x^{2} - \frac{\sqrt{2} x \left(\frac{2}{\sqrt{3} + 2} + \frac{2 \sqrt{3}}{\sqrt{3} + 2}\right)}{4} + 1 \right)}}{4} + \frac{\sqrt{2} \log{\left(x^{2} + \frac{\sqrt{2} x \left(\frac{2}{\sqrt{3} + 2} + \frac{2 \sqrt{3}}{\sqrt{3} + 2}\right)}{4} + 1 \right)}}{4}"," ",0,"sqrt(2)*(2*atan(x*(sqrt(6)/(1 + sqrt(3)) + 2*sqrt(2)/(1 + sqrt(3)))) + 2*atan(x**3*(sqrt(6)/(1 + sqrt(3)) + 2*sqrt(2)/(1 + sqrt(3))) - sqrt(2)*x))/4 - sqrt(2)*log(x**2 - sqrt(2)*x*(2/(sqrt(3) + 2) + 2*sqrt(3)/(sqrt(3) + 2))/4 + 1)/4 + sqrt(2)*log(x**2 + sqrt(2)*x*(2/(sqrt(3) + 2) + 2*sqrt(3)/(sqrt(3) + 2))/4 + 1)/4","A",0
32,-2,0,0,0.000000," ","integrate((1+x**4*(1+3**(1/2)))/(x**8-x**4+1),x)","\text{Exception raised: PolynomialError}"," ",0,"Exception raised: PolynomialError","F(-2)",0
33,-2,0,0,0.000000," ","integrate((3+x**4*(-3+3**(1/2))-2*3**(1/2))/(x**8-x**4+1),x)","\text{Exception raised: PolynomialError}"," ",0,"Exception raised: PolynomialError","F(-2)",0
34,1,112,0,0.282619," ","integrate((d+e/x)/(c+a/x**2),x)","\left(\frac{e}{2 c} - \frac{d \sqrt{- a c^{3}}}{2 c^{3}}\right) \log{\left(x + \frac{- 2 c \left(\frac{e}{2 c} - \frac{d \sqrt{- a c^{3}}}{2 c^{3}}\right) + e}{d} \right)} + \left(\frac{e}{2 c} + \frac{d \sqrt{- a c^{3}}}{2 c^{3}}\right) \log{\left(x + \frac{- 2 c \left(\frac{e}{2 c} + \frac{d \sqrt{- a c^{3}}}{2 c^{3}}\right) + e}{d} \right)} + \frac{d x}{c}"," ",0,"(e/(2*c) - d*sqrt(-a*c**3)/(2*c**3))*log(x + (-2*c*(e/(2*c) - d*sqrt(-a*c**3)/(2*c**3)) + e)/d) + (e/(2*c) + d*sqrt(-a*c**3)/(2*c**3))*log(x + (-2*c*(e/(2*c) + d*sqrt(-a*c**3)/(2*c**3)) + e)/d) + d*x/c","B",0
35,1,423,0,1.371523," ","integrate((d+e/x)/(c+a/x**2+b/x),x)","\left(- \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c d - b^{2} d + b c e\right)}{2 c^{2} \left(4 a c - b^{2}\right)} - \frac{b d - c e}{2 c^{2}}\right) \log{\left(x + \frac{- a b d - 4 a c^{2} \left(- \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c d - b^{2} d + b c e\right)}{2 c^{2} \left(4 a c - b^{2}\right)} - \frac{b d - c e}{2 c^{2}}\right) + 2 a c e + b^{2} c \left(- \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c d - b^{2} d + b c e\right)}{2 c^{2} \left(4 a c - b^{2}\right)} - \frac{b d - c e}{2 c^{2}}\right)}{2 a c d - b^{2} d + b c e} \right)} + \left(\frac{\sqrt{- 4 a c + b^{2}} \left(2 a c d - b^{2} d + b c e\right)}{2 c^{2} \left(4 a c - b^{2}\right)} - \frac{b d - c e}{2 c^{2}}\right) \log{\left(x + \frac{- a b d - 4 a c^{2} \left(\frac{\sqrt{- 4 a c + b^{2}} \left(2 a c d - b^{2} d + b c e\right)}{2 c^{2} \left(4 a c - b^{2}\right)} - \frac{b d - c e}{2 c^{2}}\right) + 2 a c e + b^{2} c \left(\frac{\sqrt{- 4 a c + b^{2}} \left(2 a c d - b^{2} d + b c e\right)}{2 c^{2} \left(4 a c - b^{2}\right)} - \frac{b d - c e}{2 c^{2}}\right)}{2 a c d - b^{2} d + b c e} \right)} + \frac{d x}{c}"," ",0,"(-sqrt(-4*a*c + b**2)*(2*a*c*d - b**2*d + b*c*e)/(2*c**2*(4*a*c - b**2)) - (b*d - c*e)/(2*c**2))*log(x + (-a*b*d - 4*a*c**2*(-sqrt(-4*a*c + b**2)*(2*a*c*d - b**2*d + b*c*e)/(2*c**2*(4*a*c - b**2)) - (b*d - c*e)/(2*c**2)) + 2*a*c*e + b**2*c*(-sqrt(-4*a*c + b**2)*(2*a*c*d - b**2*d + b*c*e)/(2*c**2*(4*a*c - b**2)) - (b*d - c*e)/(2*c**2)))/(2*a*c*d - b**2*d + b*c*e)) + (sqrt(-4*a*c + b**2)*(2*a*c*d - b**2*d + b*c*e)/(2*c**2*(4*a*c - b**2)) - (b*d - c*e)/(2*c**2))*log(x + (-a*b*d - 4*a*c**2*(sqrt(-4*a*c + b**2)*(2*a*c*d - b**2*d + b*c*e)/(2*c**2*(4*a*c - b**2)) - (b*d - c*e)/(2*c**2)) + 2*a*c*e + b**2*c*(sqrt(-4*a*c + b**2)*(2*a*c*d - b**2*d + b*c*e)/(2*c**2*(4*a*c - b**2)) - (b*d - c*e)/(2*c**2)))/(2*a*c*d - b**2*d + b*c*e)) + d*x/c","B",0
36,1,109,0,0.703716," ","integrate((d+e/x**2)/(c+a/x**4),x)","\operatorname{RootSum} {\left(256 t^{4} a c^{5} - 64 t^{2} a c^{3} d e + a^{2} d^{4} + 2 a c d^{2} e^{2} + c^{2} e^{4}, \left( t \mapsto t \log{\left(x + \frac{- 64 t^{3} a c^{4} e - 4 t a^{2} c d^{3} + 12 t a c^{2} d e^{2}}{a^{2} d^{4} - c^{2} e^{4}} \right)} \right)\right)} + \frac{d x}{c}"," ",0,"RootSum(256*_t**4*a*c**5 - 64*_t**2*a*c**3*d*e + a**2*d**4 + 2*a*c*d**2*e**2 + c**2*e**4, Lambda(_t, _t*log(x + (-64*_t**3*a*c**4*e - 4*_t*a**2*c*d**3 + 12*_t*a*c**2*d*e**2)/(a**2*d**4 - c**2*e**4)))) + d*x/c","A",0
37,-1,0,0,0.000000," ","integrate((d+e/x**2)/(c+a/x**4+b/x**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
38,1,167,0,2.981463," ","integrate((d+e/x**3)/(c+a/x**6),x)","\operatorname{RootSum} {\left(46656 t^{6} a^{2} c^{7} + t^{3} \left(- 1296 a^{2} c^{4} d^{2} e + 432 a c^{5} e^{3}\right) + a^{3} d^{6} + 3 a^{2} c d^{4} e^{2} + 3 a c^{2} d^{2} e^{4} + c^{3} e^{6}, \left( t \mapsto t \log{\left(x + \frac{- 1296 t^{4} a c^{5} e - 6 t a^{2} c d^{4} + 36 t a c^{2} d^{2} e^{2} - 6 t c^{3} e^{4}}{a^{2} d^{5} - 2 a c d^{3} e^{2} - 3 c^{2} d e^{4}} \right)} \right)\right)} + \frac{d x}{c}"," ",0,"RootSum(46656*_t**6*a**2*c**7 + _t**3*(-1296*a**2*c**4*d**2*e + 432*a*c**5*e**3) + a**3*d**6 + 3*a**2*c*d**4*e**2 + 3*a*c**2*d**2*e**4 + c**3*e**6, Lambda(_t, _t*log(x + (-1296*_t**4*a*c**5*e - 6*_t*a**2*c*d**4 + 36*_t*a*c**2*d**2*e**2 - 6*_t*c**3*e**4)/(a**2*d**5 - 2*a*c*d**3*e**2 - 3*c**2*d*e**4)))) + d*x/c","A",0
39,-1,0,0,0.000000," ","integrate((d+e/x**3)/(c+a/x**6+b/x**3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
40,-1,0,0,0.000000," ","integrate((d+e/x**4)/(c+a/x**8),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
41,-1,0,0,0.000000," ","integrate((d+e/x**4)/(c+a/x**8+b/x**4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
42,1,337,0,10.965414," ","integrate((d+e*x**n)**3/(a+c*x**(2*n)),x)","- \frac{3 d e^{2} x \Phi\left(\frac{a x^{- 2 n} e^{i \pi}}{c}, 1, \frac{e^{i \pi}}{2 n}\right) \Gamma\left(\frac{1}{2 n}\right)}{4 c n^{2} \Gamma\left(1 + \frac{1}{2 n}\right)} + \frac{d^{3} x \Phi\left(\frac{c x^{2 n} e^{i \pi}}{a}, 1, \frac{1}{2 n}\right) \Gamma\left(\frac{1}{2 n}\right)}{4 a n^{2} \Gamma\left(1 + \frac{1}{2 n}\right)} + \frac{3 d^{2} e x x^{n} \Phi\left(\frac{c x^{2 n} e^{i \pi}}{a}, 1, \frac{1}{2} + \frac{1}{2 n}\right) \Gamma\left(\frac{1}{2} + \frac{1}{2 n}\right)}{4 a n \Gamma\left(\frac{3}{2} + \frac{1}{2 n}\right)} + \frac{3 d^{2} e x x^{n} \Phi\left(\frac{c x^{2 n} e^{i \pi}}{a}, 1, \frac{1}{2} + \frac{1}{2 n}\right) \Gamma\left(\frac{1}{2} + \frac{1}{2 n}\right)}{4 a n^{2} \Gamma\left(\frac{3}{2} + \frac{1}{2 n}\right)} + \frac{3 e^{3} x x^{3 n} \Phi\left(\frac{c x^{2 n} e^{i \pi}}{a}, 1, \frac{3}{2} + \frac{1}{2 n}\right) \Gamma\left(\frac{3}{2} + \frac{1}{2 n}\right)}{4 a n \Gamma\left(\frac{5}{2} + \frac{1}{2 n}\right)} + \frac{e^{3} x x^{3 n} \Phi\left(\frac{c x^{2 n} e^{i \pi}}{a}, 1, \frac{3}{2} + \frac{1}{2 n}\right) \Gamma\left(\frac{3}{2} + \frac{1}{2 n}\right)}{4 a n^{2} \Gamma\left(\frac{5}{2} + \frac{1}{2 n}\right)}"," ",0,"-3*d*e**2*x*lerchphi(a*x**(-2*n)*exp_polar(I*pi)/c, 1, exp_polar(I*pi)/(2*n))*gamma(1/(2*n))/(4*c*n**2*gamma(1 + 1/(2*n))) + d**3*x*lerchphi(c*x**(2*n)*exp_polar(I*pi)/a, 1, 1/(2*n))*gamma(1/(2*n))/(4*a*n**2*gamma(1 + 1/(2*n))) + 3*d**2*e*x*x**n*lerchphi(c*x**(2*n)*exp_polar(I*pi)/a, 1, 1/2 + 1/(2*n))*gamma(1/2 + 1/(2*n))/(4*a*n*gamma(3/2 + 1/(2*n))) + 3*d**2*e*x*x**n*lerchphi(c*x**(2*n)*exp_polar(I*pi)/a, 1, 1/2 + 1/(2*n))*gamma(1/2 + 1/(2*n))/(4*a*n**2*gamma(3/2 + 1/(2*n))) + 3*e**3*x*x**(3*n)*lerchphi(c*x**(2*n)*exp_polar(I*pi)/a, 1, 3/2 + 1/(2*n))*gamma(3/2 + 1/(2*n))/(4*a*n*gamma(5/2 + 1/(2*n))) + e**3*x*x**(3*n)*lerchphi(c*x**(2*n)*exp_polar(I*pi)/a, 1, 3/2 + 1/(2*n))*gamma(3/2 + 1/(2*n))/(4*a*n**2*gamma(5/2 + 1/(2*n)))","C",0
43,1,207,0,7.651227," ","integrate((d+e*x**n)**2/(a+c*x**(2*n)),x)","- \frac{e^{2} x \Phi\left(\frac{a x^{- 2 n} e^{i \pi}}{c}, 1, \frac{e^{i \pi}}{2 n}\right) \Gamma\left(\frac{1}{2 n}\right)}{4 c n^{2} \Gamma\left(1 + \frac{1}{2 n}\right)} + \frac{d^{2} x \Phi\left(\frac{c x^{2 n} e^{i \pi}}{a}, 1, \frac{1}{2 n}\right) \Gamma\left(\frac{1}{2 n}\right)}{4 a n^{2} \Gamma\left(1 + \frac{1}{2 n}\right)} + \frac{d e x x^{n} \Phi\left(\frac{c x^{2 n} e^{i \pi}}{a}, 1, \frac{1}{2} + \frac{1}{2 n}\right) \Gamma\left(\frac{1}{2} + \frac{1}{2 n}\right)}{2 a n \Gamma\left(\frac{3}{2} + \frac{1}{2 n}\right)} + \frac{d e x x^{n} \Phi\left(\frac{c x^{2 n} e^{i \pi}}{a}, 1, \frac{1}{2} + \frac{1}{2 n}\right) \Gamma\left(\frac{1}{2} + \frac{1}{2 n}\right)}{2 a n^{2} \Gamma\left(\frac{3}{2} + \frac{1}{2 n}\right)}"," ",0,"-e**2*x*lerchphi(a*x**(-2*n)*exp_polar(I*pi)/c, 1, exp_polar(I*pi)/(2*n))*gamma(1/(2*n))/(4*c*n**2*gamma(1 + 1/(2*n))) + d**2*x*lerchphi(c*x**(2*n)*exp_polar(I*pi)/a, 1, 1/(2*n))*gamma(1/(2*n))/(4*a*n**2*gamma(1 + 1/(2*n))) + d*e*x*x**n*lerchphi(c*x**(2*n)*exp_polar(I*pi)/a, 1, 1/2 + 1/(2*n))*gamma(1/2 + 1/(2*n))/(2*a*n*gamma(3/2 + 1/(2*n))) + d*e*x*x**n*lerchphi(c*x**(2*n)*exp_polar(I*pi)/a, 1, 1/2 + 1/(2*n))*gamma(1/2 + 1/(2*n))/(2*a*n**2*gamma(3/2 + 1/(2*n)))","C",0
44,1,153,0,5.543203," ","integrate((d+e*x**n)/(a+c*x**(2*n)),x)","\frac{d x \Phi\left(\frac{c x^{2 n} e^{i \pi}}{a}, 1, \frac{1}{2 n}\right) \Gamma\left(\frac{1}{2 n}\right)}{4 a n^{2} \Gamma\left(1 + \frac{1}{2 n}\right)} + \frac{e x x^{n} \Phi\left(\frac{c x^{2 n} e^{i \pi}}{a}, 1, \frac{1}{2} + \frac{1}{2 n}\right) \Gamma\left(\frac{1}{2} + \frac{1}{2 n}\right)}{4 a n \Gamma\left(\frac{3}{2} + \frac{1}{2 n}\right)} + \frac{e x x^{n} \Phi\left(\frac{c x^{2 n} e^{i \pi}}{a}, 1, \frac{1}{2} + \frac{1}{2 n}\right) \Gamma\left(\frac{1}{2} + \frac{1}{2 n}\right)}{4 a n^{2} \Gamma\left(\frac{3}{2} + \frac{1}{2 n}\right)}"," ",0,"d*x*lerchphi(c*x**(2*n)*exp_polar(I*pi)/a, 1, 1/(2*n))*gamma(1/(2*n))/(4*a*n**2*gamma(1 + 1/(2*n))) + e*x*x**n*lerchphi(c*x**(2*n)*exp_polar(I*pi)/a, 1, 1/2 + 1/(2*n))*gamma(1/2 + 1/(2*n))/(4*a*n*gamma(3/2 + 1/(2*n))) + e*x*x**n*lerchphi(c*x**(2*n)*exp_polar(I*pi)/a, 1, 1/2 + 1/(2*n))*gamma(1/2 + 1/(2*n))/(4*a*n**2*gamma(3/2 + 1/(2*n)))","C",0
45,-2,0,0,0.000000," ","integrate(1/(d+e*x**n)/(a+c*x**(2*n)),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
46,-2,0,0,0.000000," ","integrate(1/(d+e*x**n)**2/(a+c*x**(2*n)),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
47,1,158,0,5.702807," ","integrate((d+e*x**n)/(a-c*x**(2*n)),x)","\frac{d x \Phi\left(\frac{c x^{2 n} e^{2 i \pi}}{a}, 1, \frac{1}{2 n}\right) \Gamma\left(\frac{1}{2 n}\right)}{4 a n^{2} \Gamma\left(1 + \frac{1}{2 n}\right)} + \frac{e x x^{n} \Phi\left(\frac{c x^{2 n} e^{2 i \pi}}{a}, 1, \frac{1}{2} + \frac{1}{2 n}\right) \Gamma\left(\frac{1}{2} + \frac{1}{2 n}\right)}{4 a n \Gamma\left(\frac{3}{2} + \frac{1}{2 n}\right)} + \frac{e x x^{n} \Phi\left(\frac{c x^{2 n} e^{2 i \pi}}{a}, 1, \frac{1}{2} + \frac{1}{2 n}\right) \Gamma\left(\frac{1}{2} + \frac{1}{2 n}\right)}{4 a n^{2} \Gamma\left(\frac{3}{2} + \frac{1}{2 n}\right)}"," ",0,"d*x*lerchphi(c*x**(2*n)*exp_polar(2*I*pi)/a, 1, 1/(2*n))*gamma(1/(2*n))/(4*a*n**2*gamma(1 + 1/(2*n))) + e*x*x**n*lerchphi(c*x**(2*n)*exp_polar(2*I*pi)/a, 1, 1/2 + 1/(2*n))*gamma(1/2 + 1/(2*n))/(4*a*n*gamma(3/2 + 1/(2*n))) + e*x*x**n*lerchphi(c*x**(2*n)*exp_polar(2*I*pi)/a, 1, 1/2 + 1/(2*n))*gamma(1/2 + 1/(2*n))/(4*a*n**2*gamma(3/2 + 1/(2*n)))","C",0
48,-1,0,0,0.000000," ","integrate((d+e*x**n)**3/(a+c*x**(2*n))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
49,-1,0,0,0.000000," ","integrate((d+e*x**n)**2/(a+c*x**(2*n))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
50,-1,0,0,0.000000," ","integrate((d+e*x**n)/(a+c*x**(2*n))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
51,-1,0,0,0.000000," ","integrate(1/(d+e*x**n)/(a+c*x**(2*n))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
52,-1,0,0,0.000000," ","integrate(1/(d+e*x**n)**2/(a+c*x**(2*n))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
53,-1,0,0,0.000000," ","integrate((d+e*x**n)**3/(a+c*x**(2*n))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
54,-1,0,0,0.000000," ","integrate((d+e*x**n)**2/(a+c*x**(2*n))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
55,-1,0,0,0.000000," ","integrate((d+e*x**n)/(a+c*x**(2*n))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
56,-1,0,0,0.000000," ","integrate(1/(d+e*x**n)/(a+c*x**(2*n))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
57,-1,0,0,0.000000," ","integrate(1/(d+e*x**n)**2/(a+c*x**(2*n))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
58,0,0,0,0.000000," ","integrate(1/(d+e*x**n)/(a+c*x**(2*n))**(1/2),x)","\int \frac{1}{\sqrt{a + c x^{2 n}} \left(d + e x^{n}\right)}\, dx"," ",0,"Integral(1/(sqrt(a + c*x**(2*n))*(d + e*x**n)), x)","F",0
59,-1,0,0,0.000000," ","integrate((d+e*x**n)**q*(a+c*x**(2*n))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
60,-1,0,0,0.000000," ","integrate((d+e*x**n)**3*(a+c*x**(2*n))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
61,-1,0,0,0.000000," ","integrate((d+e*x**n)**2*(a+c*x**(2*n))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
62,-1,0,0,0.000000," ","integrate((d+e*x**n)*(a+c*x**(2*n))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
63,-1,0,0,0.000000," ","integrate((a+c*x**(2*n))**p/(d+e*x**n),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
64,-1,0,0,0.000000," ","integrate((a+c*x**(2*n))**p/(d+e*x**n)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
65,-1,0,0,0.000000," ","integrate((a+c*x**(2*n))**p/(d+e*x**n)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
66,1,656,0,1.320330," ","integrate((d+e*x**n)*(a+b*x**n+c*x**(2*n)),x)","\begin{cases} a d x + a e \log{\left(x \right)} + b d \log{\left(x \right)} - \frac{b e}{x} - \frac{c d}{x} - \frac{c e}{2 x^{2}} & \text{for}\: n = -1 \\a d x + 2 a e \sqrt{x} + 2 b d \sqrt{x} + b e \log{\left(x \right)} + c d \log{\left(x \right)} - \frac{2 c e}{\sqrt{x}} & \text{for}\: n = - \frac{1}{2} \\a d x + \frac{3 a e x^{\frac{2}{3}}}{2} + \frac{3 b d x^{\frac{2}{3}}}{2} + 3 b e \sqrt[3]{x} + 3 c d \sqrt[3]{x} + c e \log{\left(x \right)} & \text{for}\: n = - \frac{1}{3} \\\frac{6 a d n^{3} x}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{11 a d n^{2} x}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{6 a d n x}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{a d x}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{6 a e n^{2} x x^{n}}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{5 a e n x x^{n}}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{a e x x^{n}}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{6 b d n^{2} x x^{n}}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{5 b d n x x^{n}}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{b d x x^{n}}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{3 b e n^{2} x x^{2 n}}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{4 b e n x x^{2 n}}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{b e x x^{2 n}}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{3 c d n^{2} x x^{2 n}}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{4 c d n x x^{2 n}}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{c d x x^{2 n}}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{2 c e n^{2} x x^{3 n}}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{3 c e n x x^{3 n}}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{c e x x^{3 n}}{6 n^{3} + 11 n^{2} + 6 n + 1} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*d*x + a*e*log(x) + b*d*log(x) - b*e/x - c*d/x - c*e/(2*x**2), Eq(n, -1)), (a*d*x + 2*a*e*sqrt(x) + 2*b*d*sqrt(x) + b*e*log(x) + c*d*log(x) - 2*c*e/sqrt(x), Eq(n, -1/2)), (a*d*x + 3*a*e*x**(2/3)/2 + 3*b*d*x**(2/3)/2 + 3*b*e*x**(1/3) + 3*c*d*x**(1/3) + c*e*log(x), Eq(n, -1/3)), (6*a*d*n**3*x/(6*n**3 + 11*n**2 + 6*n + 1) + 11*a*d*n**2*x/(6*n**3 + 11*n**2 + 6*n + 1) + 6*a*d*n*x/(6*n**3 + 11*n**2 + 6*n + 1) + a*d*x/(6*n**3 + 11*n**2 + 6*n + 1) + 6*a*e*n**2*x*x**n/(6*n**3 + 11*n**2 + 6*n + 1) + 5*a*e*n*x*x**n/(6*n**3 + 11*n**2 + 6*n + 1) + a*e*x*x**n/(6*n**3 + 11*n**2 + 6*n + 1) + 6*b*d*n**2*x*x**n/(6*n**3 + 11*n**2 + 6*n + 1) + 5*b*d*n*x*x**n/(6*n**3 + 11*n**2 + 6*n + 1) + b*d*x*x**n/(6*n**3 + 11*n**2 + 6*n + 1) + 3*b*e*n**2*x*x**(2*n)/(6*n**3 + 11*n**2 + 6*n + 1) + 4*b*e*n*x*x**(2*n)/(6*n**3 + 11*n**2 + 6*n + 1) + b*e*x*x**(2*n)/(6*n**3 + 11*n**2 + 6*n + 1) + 3*c*d*n**2*x*x**(2*n)/(6*n**3 + 11*n**2 + 6*n + 1) + 4*c*d*n*x*x**(2*n)/(6*n**3 + 11*n**2 + 6*n + 1) + c*d*x*x**(2*n)/(6*n**3 + 11*n**2 + 6*n + 1) + 2*c*e*n**2*x*x**(3*n)/(6*n**3 + 11*n**2 + 6*n + 1) + 3*c*e*n*x*x**(3*n)/(6*n**3 + 11*n**2 + 6*n + 1) + c*e*x*x**(3*n)/(6*n**3 + 11*n**2 + 6*n + 1), True))","A",0
67,1,3128,0,10.968333," ","integrate((d+e*x**n)*(a+b*x**n+c*x**(2*n))**2,x)","\begin{cases} a^{2} d x + a^{2} e \log{\left(x \right)} + 2 a b d \log{\left(x \right)} - \frac{2 a b e}{x} - \frac{2 a c d}{x} - \frac{a c e}{x^{2}} - \frac{b^{2} d}{x} - \frac{b^{2} e}{2 x^{2}} - \frac{b c d}{x^{2}} - \frac{2 b c e}{3 x^{3}} - \frac{c^{2} d}{3 x^{3}} - \frac{c^{2} e}{4 x^{4}} & \text{for}\: n = -1 \\a^{2} d x + 2 a^{2} e \sqrt{x} + 4 a b d \sqrt{x} + 2 a b e \log{\left(x \right)} + 2 a c d \log{\left(x \right)} - \frac{4 a c e}{\sqrt{x}} + b^{2} d \log{\left(x \right)} - \frac{2 b^{2} e}{\sqrt{x}} - \frac{4 b c d}{\sqrt{x}} - \frac{2 b c e}{x} - \frac{c^{2} d}{x} - \frac{2 c^{2} e}{3 x^{\frac{3}{2}}} & \text{for}\: n = - \frac{1}{2} \\a^{2} d x + \frac{3 a^{2} e x^{\frac{2}{3}}}{2} + 3 a b d x^{\frac{2}{3}} + 6 a b e \sqrt[3]{x} + 6 a c d \sqrt[3]{x} + 2 a c e \log{\left(x \right)} + 3 b^{2} d \sqrt[3]{x} + b^{2} e \log{\left(x \right)} + 2 b c d \log{\left(x \right)} - \frac{6 b c e}{\sqrt[3]{x}} - \frac{3 c^{2} d}{\sqrt[3]{x}} - \frac{3 c^{2} e}{2 x^{\frac{2}{3}}} & \text{for}\: n = - \frac{1}{3} \\a^{2} d x + \frac{4 a^{2} e x^{\frac{3}{4}}}{3} + \frac{8 a b d x^{\frac{3}{4}}}{3} + 4 a b e \sqrt{x} + 4 a c d \sqrt{x} + 8 a c e \sqrt[4]{x} + 2 b^{2} d \sqrt{x} + 4 b^{2} e \sqrt[4]{x} + 8 b c d \sqrt[4]{x} + 2 b c e \log{\left(x \right)} + c^{2} d \log{\left(x \right)} - \frac{4 c^{2} e}{\sqrt[4]{x}} & \text{for}\: n = - \frac{1}{4} \\a^{2} d x + \frac{5 a^{2} e x^{\frac{4}{5}}}{4} + \frac{5 a b d x^{\frac{4}{5}}}{2} + \frac{10 a b e x^{\frac{3}{5}}}{3} + \frac{10 a c d x^{\frac{3}{5}}}{3} + 5 a c e x^{\frac{2}{5}} + \frac{5 b^{2} d x^{\frac{3}{5}}}{3} + \frac{5 b^{2} e x^{\frac{2}{5}}}{2} + 5 b c d x^{\frac{2}{5}} + 10 b c e \sqrt[5]{x} + 5 c^{2} d \sqrt[5]{x} + c^{2} e \log{\left(x \right)} & \text{for}\: n = - \frac{1}{5} \\\frac{120 a^{2} d n^{5} x}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{274 a^{2} d n^{4} x}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{225 a^{2} d n^{3} x}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{85 a^{2} d n^{2} x}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{15 a^{2} d n x}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{a^{2} d x}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{120 a^{2} e n^{4} x x^{n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{154 a^{2} e n^{3} x x^{n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{71 a^{2} e n^{2} x x^{n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{14 a^{2} e n x x^{n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{a^{2} e x x^{n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{240 a b d n^{4} x x^{n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{308 a b d n^{3} x x^{n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{142 a b d n^{2} x x^{n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{28 a b d n x x^{n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{2 a b d x x^{n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{120 a b e n^{4} x x^{2 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{214 a b e n^{3} x x^{2 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{118 a b e n^{2} x x^{2 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{26 a b e n x x^{2 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{2 a b e x x^{2 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{120 a c d n^{4} x x^{2 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{214 a c d n^{3} x x^{2 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{118 a c d n^{2} x x^{2 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{26 a c d n x x^{2 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{2 a c d x x^{2 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{80 a c e n^{4} x x^{3 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{156 a c e n^{3} x x^{3 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{98 a c e n^{2} x x^{3 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{24 a c e n x x^{3 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{2 a c e x x^{3 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{60 b^{2} d n^{4} x x^{2 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{107 b^{2} d n^{3} x x^{2 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{59 b^{2} d n^{2} x x^{2 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{13 b^{2} d n x x^{2 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{b^{2} d x x^{2 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{40 b^{2} e n^{4} x x^{3 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{78 b^{2} e n^{3} x x^{3 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{49 b^{2} e n^{2} x x^{3 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{12 b^{2} e n x x^{3 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{b^{2} e x x^{3 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{80 b c d n^{4} x x^{3 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{156 b c d n^{3} x x^{3 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{98 b c d n^{2} x x^{3 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{24 b c d n x x^{3 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{2 b c d x x^{3 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{60 b c e n^{4} x x^{4 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{122 b c e n^{3} x x^{4 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{82 b c e n^{2} x x^{4 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{22 b c e n x x^{4 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{2 b c e x x^{4 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{30 c^{2} d n^{4} x x^{4 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{61 c^{2} d n^{3} x x^{4 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{41 c^{2} d n^{2} x x^{4 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{11 c^{2} d n x x^{4 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{c^{2} d x x^{4 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{24 c^{2} e n^{4} x x^{5 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{50 c^{2} e n^{3} x x^{5 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{35 c^{2} e n^{2} x x^{5 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{10 c^{2} e n x x^{5 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{c^{2} e x x^{5 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*d*x + a**2*e*log(x) + 2*a*b*d*log(x) - 2*a*b*e/x - 2*a*c*d/x - a*c*e/x**2 - b**2*d/x - b**2*e/(2*x**2) - b*c*d/x**2 - 2*b*c*e/(3*x**3) - c**2*d/(3*x**3) - c**2*e/(4*x**4), Eq(n, -1)), (a**2*d*x + 2*a**2*e*sqrt(x) + 4*a*b*d*sqrt(x) + 2*a*b*e*log(x) + 2*a*c*d*log(x) - 4*a*c*e/sqrt(x) + b**2*d*log(x) - 2*b**2*e/sqrt(x) - 4*b*c*d/sqrt(x) - 2*b*c*e/x - c**2*d/x - 2*c**2*e/(3*x**(3/2)), Eq(n, -1/2)), (a**2*d*x + 3*a**2*e*x**(2/3)/2 + 3*a*b*d*x**(2/3) + 6*a*b*e*x**(1/3) + 6*a*c*d*x**(1/3) + 2*a*c*e*log(x) + 3*b**2*d*x**(1/3) + b**2*e*log(x) + 2*b*c*d*log(x) - 6*b*c*e/x**(1/3) - 3*c**2*d/x**(1/3) - 3*c**2*e/(2*x**(2/3)), Eq(n, -1/3)), (a**2*d*x + 4*a**2*e*x**(3/4)/3 + 8*a*b*d*x**(3/4)/3 + 4*a*b*e*sqrt(x) + 4*a*c*d*sqrt(x) + 8*a*c*e*x**(1/4) + 2*b**2*d*sqrt(x) + 4*b**2*e*x**(1/4) + 8*b*c*d*x**(1/4) + 2*b*c*e*log(x) + c**2*d*log(x) - 4*c**2*e/x**(1/4), Eq(n, -1/4)), (a**2*d*x + 5*a**2*e*x**(4/5)/4 + 5*a*b*d*x**(4/5)/2 + 10*a*b*e*x**(3/5)/3 + 10*a*c*d*x**(3/5)/3 + 5*a*c*e*x**(2/5) + 5*b**2*d*x**(3/5)/3 + 5*b**2*e*x**(2/5)/2 + 5*b*c*d*x**(2/5) + 10*b*c*e*x**(1/5) + 5*c**2*d*x**(1/5) + c**2*e*log(x), Eq(n, -1/5)), (120*a**2*d*n**5*x/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 274*a**2*d*n**4*x/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 225*a**2*d*n**3*x/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 85*a**2*d*n**2*x/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 15*a**2*d*n*x/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + a**2*d*x/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 120*a**2*e*n**4*x*x**n/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 154*a**2*e*n**3*x*x**n/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 71*a**2*e*n**2*x*x**n/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 14*a**2*e*n*x*x**n/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + a**2*e*x*x**n/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 240*a*b*d*n**4*x*x**n/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 308*a*b*d*n**3*x*x**n/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 142*a*b*d*n**2*x*x**n/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 28*a*b*d*n*x*x**n/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 2*a*b*d*x*x**n/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 120*a*b*e*n**4*x*x**(2*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 214*a*b*e*n**3*x*x**(2*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 118*a*b*e*n**2*x*x**(2*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 26*a*b*e*n*x*x**(2*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 2*a*b*e*x*x**(2*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 120*a*c*d*n**4*x*x**(2*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 214*a*c*d*n**3*x*x**(2*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 118*a*c*d*n**2*x*x**(2*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 26*a*c*d*n*x*x**(2*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 2*a*c*d*x*x**(2*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 80*a*c*e*n**4*x*x**(3*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 156*a*c*e*n**3*x*x**(3*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 98*a*c*e*n**2*x*x**(3*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 24*a*c*e*n*x*x**(3*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 2*a*c*e*x*x**(3*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 60*b**2*d*n**4*x*x**(2*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 107*b**2*d*n**3*x*x**(2*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 59*b**2*d*n**2*x*x**(2*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 13*b**2*d*n*x*x**(2*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + b**2*d*x*x**(2*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 40*b**2*e*n**4*x*x**(3*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 78*b**2*e*n**3*x*x**(3*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 49*b**2*e*n**2*x*x**(3*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 12*b**2*e*n*x*x**(3*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + b**2*e*x*x**(3*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 80*b*c*d*n**4*x*x**(3*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 156*b*c*d*n**3*x*x**(3*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 98*b*c*d*n**2*x*x**(3*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 24*b*c*d*n*x*x**(3*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 2*b*c*d*x*x**(3*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 60*b*c*e*n**4*x*x**(4*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 122*b*c*e*n**3*x*x**(4*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 82*b*c*e*n**2*x*x**(4*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 22*b*c*e*n*x*x**(4*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 2*b*c*e*x*x**(4*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 30*c**2*d*n**4*x*x**(4*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 61*c**2*d*n**3*x*x**(4*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 41*c**2*d*n**2*x*x**(4*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 11*c**2*d*n*x*x**(4*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + c**2*d*x*x**(4*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 24*c**2*e*n**4*x*x**(5*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 50*c**2*e*n**3*x*x**(5*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 35*c**2*e*n**2*x*x**(5*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 10*c**2*e*n*x*x**(5*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + c**2*e*x*x**(5*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1), True))","A",0
68,1,9190,0,89.545322," ","integrate((d+e*x**n)*(a+b*x**n+c*x**(2*n))**3,x)","\begin{cases} a^{3} d x + a^{3} e \log{\left(x \right)} + 3 a^{2} b d \log{\left(x \right)} - \frac{3 a^{2} b e}{x} - \frac{3 a^{2} c d}{x} - \frac{3 a^{2} c e}{2 x^{2}} - \frac{3 a b^{2} d}{x} - \frac{3 a b^{2} e}{2 x^{2}} - \frac{3 a b c d}{x^{2}} - \frac{2 a b c e}{x^{3}} - \frac{a c^{2} d}{x^{3}} - \frac{3 a c^{2} e}{4 x^{4}} - \frac{b^{3} d}{2 x^{2}} - \frac{b^{3} e}{3 x^{3}} - \frac{b^{2} c d}{x^{3}} - \frac{3 b^{2} c e}{4 x^{4}} - \frac{3 b c^{2} d}{4 x^{4}} - \frac{3 b c^{2} e}{5 x^{5}} - \frac{c^{3} d}{5 x^{5}} - \frac{c^{3} e}{6 x^{6}} & \text{for}\: n = -1 \\a^{3} d x + 2 a^{3} e \sqrt{x} + 6 a^{2} b d \sqrt{x} + 3 a^{2} b e \log{\left(x \right)} + 3 a^{2} c d \log{\left(x \right)} - \frac{6 a^{2} c e}{\sqrt{x}} + 3 a b^{2} d \log{\left(x \right)} - \frac{6 a b^{2} e}{\sqrt{x}} - \frac{12 a b c d}{\sqrt{x}} - \frac{6 a b c e}{x} - \frac{3 a c^{2} d}{x} - \frac{2 a c^{2} e}{x^{\frac{3}{2}}} - \frac{2 b^{3} d}{\sqrt{x}} - \frac{b^{3} e}{x} - \frac{3 b^{2} c d}{x} - \frac{2 b^{2} c e}{x^{\frac{3}{2}}} - \frac{2 b c^{2} d}{x^{\frac{3}{2}}} - \frac{3 b c^{2} e}{2 x^{2}} - \frac{c^{3} d}{2 x^{2}} - \frac{2 c^{3} e}{5 x^{\frac{5}{2}}} & \text{for}\: n = - \frac{1}{2} \\a^{3} d x + \frac{3 a^{3} e x^{\frac{2}{3}}}{2} + \frac{9 a^{2} b d x^{\frac{2}{3}}}{2} + 9 a^{2} b e \sqrt[3]{x} + 9 a^{2} c d \sqrt[3]{x} + 3 a^{2} c e \log{\left(x \right)} + 9 a b^{2} d \sqrt[3]{x} + 3 a b^{2} e \log{\left(x \right)} + 6 a b c d \log{\left(x \right)} - \frac{18 a b c e}{\sqrt[3]{x}} - \frac{9 a c^{2} d}{\sqrt[3]{x}} - \frac{9 a c^{2} e}{2 x^{\frac{2}{3}}} + b^{3} d \log{\left(x \right)} - \frac{3 b^{3} e}{\sqrt[3]{x}} - \frac{9 b^{2} c d}{\sqrt[3]{x}} - \frac{9 b^{2} c e}{2 x^{\frac{2}{3}}} - \frac{9 b c^{2} d}{2 x^{\frac{2}{3}}} - \frac{3 b c^{2} e}{x} - \frac{c^{3} d}{x} - \frac{3 c^{3} e}{4 x^{\frac{4}{3}}} & \text{for}\: n = - \frac{1}{3} \\a^{3} d x + \frac{4 a^{3} e x^{\frac{3}{4}}}{3} + 4 a^{2} b d x^{\frac{3}{4}} + 6 a^{2} b e \sqrt{x} + 6 a^{2} c d \sqrt{x} + 12 a^{2} c e \sqrt[4]{x} + 6 a b^{2} d \sqrt{x} + 12 a b^{2} e \sqrt[4]{x} + 24 a b c d \sqrt[4]{x} + 6 a b c e \log{\left(x \right)} + 3 a c^{2} d \log{\left(x \right)} - \frac{12 a c^{2} e}{\sqrt[4]{x}} + 4 b^{3} d \sqrt[4]{x} + b^{3} e \log{\left(x \right)} + 3 b^{2} c d \log{\left(x \right)} - \frac{12 b^{2} c e}{\sqrt[4]{x}} - \frac{12 b c^{2} d}{\sqrt[4]{x}} - \frac{6 b c^{2} e}{\sqrt{x}} - \frac{2 c^{3} d}{\sqrt{x}} - \frac{4 c^{3} e}{3 x^{\frac{3}{4}}} & \text{for}\: n = - \frac{1}{4} \\a^{3} d x + \frac{5 a^{3} e x^{\frac{4}{5}}}{4} + \frac{15 a^{2} b d x^{\frac{4}{5}}}{4} + 5 a^{2} b e x^{\frac{3}{5}} + 5 a^{2} c d x^{\frac{3}{5}} + \frac{15 a^{2} c e x^{\frac{2}{5}}}{2} + 5 a b^{2} d x^{\frac{3}{5}} + \frac{15 a b^{2} e x^{\frac{2}{5}}}{2} + 15 a b c d x^{\frac{2}{5}} + 30 a b c e \sqrt[5]{x} + 15 a c^{2} d \sqrt[5]{x} + 3 a c^{2} e \log{\left(x \right)} + \frac{5 b^{3} d x^{\frac{2}{5}}}{2} + 5 b^{3} e \sqrt[5]{x} + 15 b^{2} c d \sqrt[5]{x} + 3 b^{2} c e \log{\left(x \right)} + 3 b c^{2} d \log{\left(x \right)} - \frac{15 b c^{2} e}{\sqrt[5]{x}} - \frac{5 c^{3} d}{\sqrt[5]{x}} - \frac{5 c^{3} e}{2 x^{\frac{2}{5}}} & \text{for}\: n = - \frac{1}{5} \\a^{3} d x + \frac{6 a^{3} e x^{\frac{5}{6}}}{5} + \frac{18 a^{2} b d x^{\frac{5}{6}}}{5} + \frac{9 a^{2} b e x^{\frac{2}{3}}}{2} + \frac{9 a^{2} c d x^{\frac{2}{3}}}{2} + 6 a^{2} c e \sqrt{x} + \frac{9 a b^{2} d x^{\frac{2}{3}}}{2} + 6 a b^{2} e \sqrt{x} + 12 a b c d \sqrt{x} + 18 a b c e \sqrt[3]{x} + 9 a c^{2} d \sqrt[3]{x} + 18 a c^{2} e \sqrt[6]{x} + 2 b^{3} d \sqrt{x} + 3 b^{3} e \sqrt[3]{x} + 9 b^{2} c d \sqrt[3]{x} + 18 b^{2} c e \sqrt[6]{x} + 18 b c^{2} d \sqrt[6]{x} + 3 b c^{2} e \log{\left(x \right)} + c^{3} d \log{\left(x \right)} - \frac{6 c^{3} e}{\sqrt[6]{x}} & \text{for}\: n = - \frac{1}{6} \\a^{3} d x + \frac{7 a^{3} e x^{\frac{6}{7}}}{6} + \frac{7 a^{2} b d x^{\frac{6}{7}}}{2} + \frac{21 a^{2} b e x^{\frac{5}{7}}}{5} + \frac{21 a^{2} c d x^{\frac{5}{7}}}{5} + \frac{21 a^{2} c e x^{\frac{4}{7}}}{4} + \frac{21 a b^{2} d x^{\frac{5}{7}}}{5} + \frac{21 a b^{2} e x^{\frac{4}{7}}}{4} + \frac{21 a b c d x^{\frac{4}{7}}}{2} + 14 a b c e x^{\frac{3}{7}} + 7 a c^{2} d x^{\frac{3}{7}} + \frac{21 a c^{2} e x^{\frac{2}{7}}}{2} + \frac{7 b^{3} d x^{\frac{4}{7}}}{4} + \frac{7 b^{3} e x^{\frac{3}{7}}}{3} + 7 b^{2} c d x^{\frac{3}{7}} + \frac{21 b^{2} c e x^{\frac{2}{7}}}{2} + \frac{21 b c^{2} d x^{\frac{2}{7}}}{2} + 21 b c^{2} e \sqrt[7]{x} + 7 c^{3} d \sqrt[7]{x} + c^{3} e \log{\left(x \right)} & \text{for}\: n = - \frac{1}{7} \\\frac{5040 a^{3} d n^{7} x}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{13068 a^{3} d n^{6} x}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{13132 a^{3} d n^{5} x}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{6769 a^{3} d n^{4} x}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{1960 a^{3} d n^{3} x}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{322 a^{3} d n^{2} x}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{28 a^{3} d n x}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{a^{3} d x}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{5040 a^{3} e n^{6} x x^{n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{8028 a^{3} e n^{5} x x^{n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{5104 a^{3} e n^{4} x x^{n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{1665 a^{3} e n^{3} x x^{n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{295 a^{3} e n^{2} x x^{n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{27 a^{3} e n x x^{n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{a^{3} e x x^{n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{15120 a^{2} b d n^{6} x x^{n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{24084 a^{2} b d n^{5} x x^{n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{15312 a^{2} b d n^{4} x x^{n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{4995 a^{2} b d n^{3} x x^{n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{885 a^{2} b d n^{2} x x^{n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{81 a^{2} b d n x x^{n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{3 a^{2} b d x x^{n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{7560 a^{2} b e n^{6} x x^{2 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{15822 a^{2} b e n^{5} x x^{2 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{11787 a^{2} b e n^{4} x x^{2 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{4260 a^{2} b e n^{3} x x^{2 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{810 a^{2} b e n^{2} x x^{2 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{78 a^{2} b e n x x^{2 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{3 a^{2} b e x x^{2 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{7560 a^{2} c d n^{6} x x^{2 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{15822 a^{2} c d n^{5} x x^{2 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{11787 a^{2} c d n^{4} x x^{2 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{4260 a^{2} c d n^{3} x x^{2 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{810 a^{2} c d n^{2} x x^{2 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{78 a^{2} c d n x x^{2 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{3 a^{2} c d x x^{2 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{5040 a^{2} c e n^{6} x x^{3 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{11388 a^{2} c e n^{5} x x^{3 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{9336 a^{2} c e n^{4} x x^{3 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{3657 a^{2} c e n^{3} x x^{3 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{741 a^{2} c e n^{2} x x^{3 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{75 a^{2} c e n x x^{3 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{3 a^{2} c e x x^{3 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{7560 a b^{2} d n^{6} x x^{2 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{15822 a b^{2} d n^{5} x x^{2 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{11787 a b^{2} d n^{4} x x^{2 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{4260 a b^{2} d n^{3} x x^{2 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{810 a b^{2} d n^{2} x x^{2 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{78 a b^{2} d n x x^{2 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{3 a b^{2} d x x^{2 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{5040 a b^{2} e n^{6} x x^{3 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{11388 a b^{2} e n^{5} x x^{3 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{9336 a b^{2} e n^{4} x x^{3 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{3657 a b^{2} e n^{3} x x^{3 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{741 a b^{2} e n^{2} x x^{3 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{75 a b^{2} e n x x^{3 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{3 a b^{2} e x x^{3 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{10080 a b c d n^{6} x x^{3 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{22776 a b c d n^{5} x x^{3 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{18672 a b c d n^{4} x x^{3 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{7314 a b c d n^{3} x x^{3 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{1482 a b c d n^{2} x x^{3 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{150 a b c d n x x^{3 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{6 a b c d x x^{3 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{7560 a b c e n^{6} x x^{4 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{17712 a b c e n^{5} x x^{4 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{15270 a b c e n^{4} x x^{4 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{6336 a b c e n^{3} x x^{4 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{1356 a b c e n^{2} x x^{4 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{144 a b c e n x x^{4 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{6 a b c e x x^{4 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{3780 a c^{2} d n^{6} x x^{4 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{8856 a c^{2} d n^{5} x x^{4 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{7635 a c^{2} d n^{4} x x^{4 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{3168 a c^{2} d n^{3} x x^{4 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{678 a c^{2} d n^{2} x x^{4 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{72 a c^{2} d n x x^{4 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{3 a c^{2} d x x^{4 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{3024 a c^{2} e n^{6} x x^{5 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{7236 a c^{2} e n^{5} x x^{5 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{6432 a c^{2} e n^{4} x x^{5 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{2775 a c^{2} e n^{3} x x^{5 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{621 a c^{2} e n^{2} x x^{5 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{69 a c^{2} e n x x^{5 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{3 a c^{2} e x x^{5 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{1680 b^{3} d n^{6} x x^{3 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{3796 b^{3} d n^{5} x x^{3 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{3112 b^{3} d n^{4} x x^{3 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{1219 b^{3} d n^{3} x x^{3 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{247 b^{3} d n^{2} x x^{3 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{25 b^{3} d n x x^{3 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{b^{3} d x x^{3 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{1260 b^{3} e n^{6} x x^{4 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{2952 b^{3} e n^{5} x x^{4 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{2545 b^{3} e n^{4} x x^{4 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{1056 b^{3} e n^{3} x x^{4 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{226 b^{3} e n^{2} x x^{4 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{24 b^{3} e n x x^{4 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{b^{3} e x x^{4 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{3780 b^{2} c d n^{6} x x^{4 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{8856 b^{2} c d n^{5} x x^{4 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{7635 b^{2} c d n^{4} x x^{4 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{3168 b^{2} c d n^{3} x x^{4 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{678 b^{2} c d n^{2} x x^{4 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{72 b^{2} c d n x x^{4 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{3 b^{2} c d x x^{4 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{3024 b^{2} c e n^{6} x x^{5 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{7236 b^{2} c e n^{5} x x^{5 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{6432 b^{2} c e n^{4} x x^{5 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{2775 b^{2} c e n^{3} x x^{5 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{621 b^{2} c e n^{2} x x^{5 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{69 b^{2} c e n x x^{5 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{3 b^{2} c e x x^{5 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{3024 b c^{2} d n^{6} x x^{5 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{7236 b c^{2} d n^{5} x x^{5 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{6432 b c^{2} d n^{4} x x^{5 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{2775 b c^{2} d n^{3} x x^{5 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{621 b c^{2} d n^{2} x x^{5 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{69 b c^{2} d n x x^{5 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{3 b c^{2} d x x^{5 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{2520 b c^{2} e n^{6} x x^{6 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{6114 b c^{2} e n^{5} x x^{6 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{5547 b c^{2} e n^{4} x x^{6 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{2460 b c^{2} e n^{3} x x^{6 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{570 b c^{2} e n^{2} x x^{6 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{66 b c^{2} e n x x^{6 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{3 b c^{2} e x x^{6 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{840 c^{3} d n^{6} x x^{6 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{2038 c^{3} d n^{5} x x^{6 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{1849 c^{3} d n^{4} x x^{6 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{820 c^{3} d n^{3} x x^{6 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{190 c^{3} d n^{2} x x^{6 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{22 c^{3} d n x x^{6 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{c^{3} d x x^{6 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{720 c^{3} e n^{6} x x^{7 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{1764 c^{3} e n^{5} x x^{7 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{1624 c^{3} e n^{4} x x^{7 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{735 c^{3} e n^{3} x x^{7 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{175 c^{3} e n^{2} x x^{7 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{21 c^{3} e n x x^{7 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} + \frac{c^{3} e x x^{7 n}}{5040 n^{7} + 13068 n^{6} + 13132 n^{5} + 6769 n^{4} + 1960 n^{3} + 322 n^{2} + 28 n + 1} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*d*x + a**3*e*log(x) + 3*a**2*b*d*log(x) - 3*a**2*b*e/x - 3*a**2*c*d/x - 3*a**2*c*e/(2*x**2) - 3*a*b**2*d/x - 3*a*b**2*e/(2*x**2) - 3*a*b*c*d/x**2 - 2*a*b*c*e/x**3 - a*c**2*d/x**3 - 3*a*c**2*e/(4*x**4) - b**3*d/(2*x**2) - b**3*e/(3*x**3) - b**2*c*d/x**3 - 3*b**2*c*e/(4*x**4) - 3*b*c**2*d/(4*x**4) - 3*b*c**2*e/(5*x**5) - c**3*d/(5*x**5) - c**3*e/(6*x**6), Eq(n, -1)), (a**3*d*x + 2*a**3*e*sqrt(x) + 6*a**2*b*d*sqrt(x) + 3*a**2*b*e*log(x) + 3*a**2*c*d*log(x) - 6*a**2*c*e/sqrt(x) + 3*a*b**2*d*log(x) - 6*a*b**2*e/sqrt(x) - 12*a*b*c*d/sqrt(x) - 6*a*b*c*e/x - 3*a*c**2*d/x - 2*a*c**2*e/x**(3/2) - 2*b**3*d/sqrt(x) - b**3*e/x - 3*b**2*c*d/x - 2*b**2*c*e/x**(3/2) - 2*b*c**2*d/x**(3/2) - 3*b*c**2*e/(2*x**2) - c**3*d/(2*x**2) - 2*c**3*e/(5*x**(5/2)), Eq(n, -1/2)), (a**3*d*x + 3*a**3*e*x**(2/3)/2 + 9*a**2*b*d*x**(2/3)/2 + 9*a**2*b*e*x**(1/3) + 9*a**2*c*d*x**(1/3) + 3*a**2*c*e*log(x) + 9*a*b**2*d*x**(1/3) + 3*a*b**2*e*log(x) + 6*a*b*c*d*log(x) - 18*a*b*c*e/x**(1/3) - 9*a*c**2*d/x**(1/3) - 9*a*c**2*e/(2*x**(2/3)) + b**3*d*log(x) - 3*b**3*e/x**(1/3) - 9*b**2*c*d/x**(1/3) - 9*b**2*c*e/(2*x**(2/3)) - 9*b*c**2*d/(2*x**(2/3)) - 3*b*c**2*e/x - c**3*d/x - 3*c**3*e/(4*x**(4/3)), Eq(n, -1/3)), (a**3*d*x + 4*a**3*e*x**(3/4)/3 + 4*a**2*b*d*x**(3/4) + 6*a**2*b*e*sqrt(x) + 6*a**2*c*d*sqrt(x) + 12*a**2*c*e*x**(1/4) + 6*a*b**2*d*sqrt(x) + 12*a*b**2*e*x**(1/4) + 24*a*b*c*d*x**(1/4) + 6*a*b*c*e*log(x) + 3*a*c**2*d*log(x) - 12*a*c**2*e/x**(1/4) + 4*b**3*d*x**(1/4) + b**3*e*log(x) + 3*b**2*c*d*log(x) - 12*b**2*c*e/x**(1/4) - 12*b*c**2*d/x**(1/4) - 6*b*c**2*e/sqrt(x) - 2*c**3*d/sqrt(x) - 4*c**3*e/(3*x**(3/4)), Eq(n, -1/4)), (a**3*d*x + 5*a**3*e*x**(4/5)/4 + 15*a**2*b*d*x**(4/5)/4 + 5*a**2*b*e*x**(3/5) + 5*a**2*c*d*x**(3/5) + 15*a**2*c*e*x**(2/5)/2 + 5*a*b**2*d*x**(3/5) + 15*a*b**2*e*x**(2/5)/2 + 15*a*b*c*d*x**(2/5) + 30*a*b*c*e*x**(1/5) + 15*a*c**2*d*x**(1/5) + 3*a*c**2*e*log(x) + 5*b**3*d*x**(2/5)/2 + 5*b**3*e*x**(1/5) + 15*b**2*c*d*x**(1/5) + 3*b**2*c*e*log(x) + 3*b*c**2*d*log(x) - 15*b*c**2*e/x**(1/5) - 5*c**3*d/x**(1/5) - 5*c**3*e/(2*x**(2/5)), Eq(n, -1/5)), (a**3*d*x + 6*a**3*e*x**(5/6)/5 + 18*a**2*b*d*x**(5/6)/5 + 9*a**2*b*e*x**(2/3)/2 + 9*a**2*c*d*x**(2/3)/2 + 6*a**2*c*e*sqrt(x) + 9*a*b**2*d*x**(2/3)/2 + 6*a*b**2*e*sqrt(x) + 12*a*b*c*d*sqrt(x) + 18*a*b*c*e*x**(1/3) + 9*a*c**2*d*x**(1/3) + 18*a*c**2*e*x**(1/6) + 2*b**3*d*sqrt(x) + 3*b**3*e*x**(1/3) + 9*b**2*c*d*x**(1/3) + 18*b**2*c*e*x**(1/6) + 18*b*c**2*d*x**(1/6) + 3*b*c**2*e*log(x) + c**3*d*log(x) - 6*c**3*e/x**(1/6), Eq(n, -1/6)), (a**3*d*x + 7*a**3*e*x**(6/7)/6 + 7*a**2*b*d*x**(6/7)/2 + 21*a**2*b*e*x**(5/7)/5 + 21*a**2*c*d*x**(5/7)/5 + 21*a**2*c*e*x**(4/7)/4 + 21*a*b**2*d*x**(5/7)/5 + 21*a*b**2*e*x**(4/7)/4 + 21*a*b*c*d*x**(4/7)/2 + 14*a*b*c*e*x**(3/7) + 7*a*c**2*d*x**(3/7) + 21*a*c**2*e*x**(2/7)/2 + 7*b**3*d*x**(4/7)/4 + 7*b**3*e*x**(3/7)/3 + 7*b**2*c*d*x**(3/7) + 21*b**2*c*e*x**(2/7)/2 + 21*b*c**2*d*x**(2/7)/2 + 21*b*c**2*e*x**(1/7) + 7*c**3*d*x**(1/7) + c**3*e*log(x), Eq(n, -1/7)), (5040*a**3*d*n**7*x/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 13068*a**3*d*n**6*x/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 13132*a**3*d*n**5*x/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 6769*a**3*d*n**4*x/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 1960*a**3*d*n**3*x/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 322*a**3*d*n**2*x/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 28*a**3*d*n*x/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + a**3*d*x/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 5040*a**3*e*n**6*x*x**n/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 8028*a**3*e*n**5*x*x**n/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 5104*a**3*e*n**4*x*x**n/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 1665*a**3*e*n**3*x*x**n/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 295*a**3*e*n**2*x*x**n/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 27*a**3*e*n*x*x**n/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + a**3*e*x*x**n/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 15120*a**2*b*d*n**6*x*x**n/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 24084*a**2*b*d*n**5*x*x**n/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 15312*a**2*b*d*n**4*x*x**n/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 4995*a**2*b*d*n**3*x*x**n/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 885*a**2*b*d*n**2*x*x**n/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 81*a**2*b*d*n*x*x**n/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 3*a**2*b*d*x*x**n/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 7560*a**2*b*e*n**6*x*x**(2*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 15822*a**2*b*e*n**5*x*x**(2*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 11787*a**2*b*e*n**4*x*x**(2*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 4260*a**2*b*e*n**3*x*x**(2*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 810*a**2*b*e*n**2*x*x**(2*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 78*a**2*b*e*n*x*x**(2*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 3*a**2*b*e*x*x**(2*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 7560*a**2*c*d*n**6*x*x**(2*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 15822*a**2*c*d*n**5*x*x**(2*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 11787*a**2*c*d*n**4*x*x**(2*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 4260*a**2*c*d*n**3*x*x**(2*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 810*a**2*c*d*n**2*x*x**(2*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 78*a**2*c*d*n*x*x**(2*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 3*a**2*c*d*x*x**(2*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 5040*a**2*c*e*n**6*x*x**(3*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 11388*a**2*c*e*n**5*x*x**(3*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 9336*a**2*c*e*n**4*x*x**(3*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 3657*a**2*c*e*n**3*x*x**(3*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 741*a**2*c*e*n**2*x*x**(3*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 75*a**2*c*e*n*x*x**(3*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 3*a**2*c*e*x*x**(3*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 7560*a*b**2*d*n**6*x*x**(2*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 15822*a*b**2*d*n**5*x*x**(2*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 11787*a*b**2*d*n**4*x*x**(2*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 4260*a*b**2*d*n**3*x*x**(2*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 810*a*b**2*d*n**2*x*x**(2*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 78*a*b**2*d*n*x*x**(2*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 3*a*b**2*d*x*x**(2*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 5040*a*b**2*e*n**6*x*x**(3*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 11388*a*b**2*e*n**5*x*x**(3*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 9336*a*b**2*e*n**4*x*x**(3*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 3657*a*b**2*e*n**3*x*x**(3*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 741*a*b**2*e*n**2*x*x**(3*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 75*a*b**2*e*n*x*x**(3*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 3*a*b**2*e*x*x**(3*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 10080*a*b*c*d*n**6*x*x**(3*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 22776*a*b*c*d*n**5*x*x**(3*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 18672*a*b*c*d*n**4*x*x**(3*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 7314*a*b*c*d*n**3*x*x**(3*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 1482*a*b*c*d*n**2*x*x**(3*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 150*a*b*c*d*n*x*x**(3*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 6*a*b*c*d*x*x**(3*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 7560*a*b*c*e*n**6*x*x**(4*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 17712*a*b*c*e*n**5*x*x**(4*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 15270*a*b*c*e*n**4*x*x**(4*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 6336*a*b*c*e*n**3*x*x**(4*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 1356*a*b*c*e*n**2*x*x**(4*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 144*a*b*c*e*n*x*x**(4*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 6*a*b*c*e*x*x**(4*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 3780*a*c**2*d*n**6*x*x**(4*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 8856*a*c**2*d*n**5*x*x**(4*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 7635*a*c**2*d*n**4*x*x**(4*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 3168*a*c**2*d*n**3*x*x**(4*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 678*a*c**2*d*n**2*x*x**(4*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 72*a*c**2*d*n*x*x**(4*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 3*a*c**2*d*x*x**(4*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 3024*a*c**2*e*n**6*x*x**(5*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 7236*a*c**2*e*n**5*x*x**(5*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 6432*a*c**2*e*n**4*x*x**(5*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 2775*a*c**2*e*n**3*x*x**(5*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 621*a*c**2*e*n**2*x*x**(5*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 69*a*c**2*e*n*x*x**(5*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 3*a*c**2*e*x*x**(5*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 1680*b**3*d*n**6*x*x**(3*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 3796*b**3*d*n**5*x*x**(3*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 3112*b**3*d*n**4*x*x**(3*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 1219*b**3*d*n**3*x*x**(3*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 247*b**3*d*n**2*x*x**(3*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 25*b**3*d*n*x*x**(3*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + b**3*d*x*x**(3*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 1260*b**3*e*n**6*x*x**(4*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 2952*b**3*e*n**5*x*x**(4*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 2545*b**3*e*n**4*x*x**(4*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 1056*b**3*e*n**3*x*x**(4*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 226*b**3*e*n**2*x*x**(4*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 24*b**3*e*n*x*x**(4*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + b**3*e*x*x**(4*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 3780*b**2*c*d*n**6*x*x**(4*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 8856*b**2*c*d*n**5*x*x**(4*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 7635*b**2*c*d*n**4*x*x**(4*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 3168*b**2*c*d*n**3*x*x**(4*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 678*b**2*c*d*n**2*x*x**(4*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 72*b**2*c*d*n*x*x**(4*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 3*b**2*c*d*x*x**(4*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 3024*b**2*c*e*n**6*x*x**(5*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 7236*b**2*c*e*n**5*x*x**(5*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 6432*b**2*c*e*n**4*x*x**(5*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 2775*b**2*c*e*n**3*x*x**(5*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 621*b**2*c*e*n**2*x*x**(5*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 69*b**2*c*e*n*x*x**(5*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 3*b**2*c*e*x*x**(5*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 3024*b*c**2*d*n**6*x*x**(5*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 7236*b*c**2*d*n**5*x*x**(5*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 6432*b*c**2*d*n**4*x*x**(5*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 2775*b*c**2*d*n**3*x*x**(5*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 621*b*c**2*d*n**2*x*x**(5*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 69*b*c**2*d*n*x*x**(5*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 3*b*c**2*d*x*x**(5*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 2520*b*c**2*e*n**6*x*x**(6*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 6114*b*c**2*e*n**5*x*x**(6*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 5547*b*c**2*e*n**4*x*x**(6*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 2460*b*c**2*e*n**3*x*x**(6*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 570*b*c**2*e*n**2*x*x**(6*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 66*b*c**2*e*n*x*x**(6*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 3*b*c**2*e*x*x**(6*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 840*c**3*d*n**6*x*x**(6*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 2038*c**3*d*n**5*x*x**(6*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 1849*c**3*d*n**4*x*x**(6*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 820*c**3*d*n**3*x*x**(6*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 190*c**3*d*n**2*x*x**(6*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 22*c**3*d*n*x*x**(6*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + c**3*d*x*x**(6*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 720*c**3*e*n**6*x*x**(7*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 1764*c**3*e*n**5*x*x**(7*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 1624*c**3*e*n**4*x*x**(7*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 735*c**3*e*n**3*x*x**(7*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 175*c**3*e*n**2*x*x**(7*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + 21*c**3*e*n*x*x**(7*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1) + c**3*e*x*x**(7*n)/(5040*n**7 + 13068*n**6 + 13132*n**5 + 6769*n**4 + 1960*n**3 + 322*n**2 + 28*n + 1), True))","A",0
69,-1,0,0,0.000000," ","integrate((d+e*x**n)**3/(a+b*x**n+c*x**(2*n)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
70,0,0,0,0.000000," ","integrate((d+e*x**n)**2/(a+b*x**n+c*x**(2*n)),x)","\int \frac{\left(d + e x^{n}\right)^{2}}{a + b x^{n} + c x^{2 n}}\, dx"," ",0,"Integral((d + e*x**n)**2/(a + b*x**n + c*x**(2*n)), x)","F",0
71,0,0,0,0.000000," ","integrate((d+e*x**n)/(a+b*x**n+c*x**(2*n)),x)","\int \frac{d + e x^{n}}{a + b x^{n} + c x^{2 n}}\, dx"," ",0,"Integral((d + e*x**n)/(a + b*x**n + c*x**(2*n)), x)","F",0
72,-2,0,0,0.000000," ","integrate(1/(d+e*x**n)/(a+b*x**n+c*x**(2*n)),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
73,-2,0,0,0.000000," ","integrate(1/(d+e*x**n)**2/(a+b*x**n+c*x**(2*n)),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
74,-2,0,0,0.000000," ","integrate(1/(d+e*x**n)**3/(a+b*x**n+c*x**(2*n)),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
75,-1,0,0,0.000000," ","integrate((d+e*x**n)**3/(a+b*x**n+c*x**(2*n))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
76,-1,0,0,0.000000," ","integrate((d+e*x**n)**2/(a+b*x**n+c*x**(2*n))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
77,-1,0,0,0.000000," ","integrate((d+e*x**n)/(a+b*x**n+c*x**(2*n))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
78,-1,0,0,0.000000," ","integrate(1/(d+e*x**n)/(a+b*x**n+c*x**(2*n))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
79,-1,0,0,0.000000," ","integrate(1/(d+e*x**n)**2/(a+b*x**n+c*x**(2*n))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
80,-1,0,0,0.000000," ","integrate((d+e*x**n)**3/(a+b*x**n+c*x**(2*n))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
81,-1,0,0,0.000000," ","integrate((d+e*x**n)**2/(a+b*x**n+c*x**(2*n))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
82,-1,0,0,0.000000," ","integrate((d+e*x**n)/(a+b*x**n+c*x**(2*n))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
83,-1,0,0,0.000000," ","integrate(1/(d+e*x**n)/(a+b*x**n+c*x**(2*n))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
84,-1,0,0,0.000000," ","integrate(1/(d+e*x**n)**2/(a+b*x**n+c*x**(2*n))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
85,0,0,0,0.000000," ","integrate((d+e*x**n)*(a+b*x**n+c*x**(2*n))**(1/2),x)","\int \left(d + e x^{n}\right) \sqrt{a + b x^{n} + c x^{2 n}}\, dx"," ",0,"Integral((d + e*x**n)*sqrt(a + b*x**n + c*x**(2*n)), x)","F",0
86,0,0,0,0.000000," ","integrate((d+e*x**n)*(a+b*x**n+c*x**(2*n))**(3/2),x)","\int \left(d + e x^{n}\right) \left(a + b x^{n} + c x^{2 n}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((d + e*x**n)*(a + b*x**n + c*x**(2*n))**(3/2), x)","F",0
87,0,0,0,0.000000," ","integrate((d+e*x**n)/(a+b*x**n+c*x**(2*n))**(1/2),x)","\int \frac{d + e x^{n}}{\sqrt{a + b x^{n} + c x^{2 n}}}\, dx"," ",0,"Integral((d + e*x**n)/sqrt(a + b*x**n + c*x**(2*n)), x)","F",0
88,-1,0,0,0.000000," ","integrate((d+e*x**n)/(a+b*x**n+c*x**(2*n))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
89,-1,0,0,0.000000," ","integrate((d+e*x**n)/(a+b*x**n+c*x**(2*n))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
90,-1,0,0,0.000000," ","integrate((d+e*x**n)**q*(a+b*x**n+c*x**(2*n))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
91,-1,0,0,0.000000," ","integrate((d+e*x**n)**3*(a+b*x**n+c*x**(2*n))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
92,-1,0,0,0.000000," ","integrate((d+e*x**n)**2*(a+b*x**n+c*x**(2*n))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
93,-1,0,0,0.000000," ","integrate((d+e*x**n)*(a+b*x**n+c*x**(2*n))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
94,-1,0,0,0.000000," ","integrate((a+b*x**n+c*x**(2*n))**p/(d+e*x**n),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
95,-1,0,0,0.000000," ","integrate((a+b*x**n+c*x**(2*n))**p/(d+e*x**n)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
96,-1,0,0,0.000000," ","integrate((a+b*x**n+c*x**(2*n))**p/(d+e*x**n)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
