1,1,104,0,0.125450," ","integrate((b*x**3+a)*(d*x**3+c)**4,x)","a c^{4} x + \frac{b d^{4} x^{16}}{16} + x^{13} \left(\frac{a d^{4}}{13} + \frac{4 b c d^{3}}{13}\right) + x^{10} \left(\frac{2 a c d^{3}}{5} + \frac{3 b c^{2} d^{2}}{5}\right) + x^{7} \left(\frac{6 a c^{2} d^{2}}{7} + \frac{4 b c^{3} d}{7}\right) + x^{4} \left(a c^{3} d + \frac{b c^{4}}{4}\right)"," ",0,"a*c**4*x + b*d**4*x**16/16 + x**13*(a*d**4/13 + 4*b*c*d**3/13) + x**10*(2*a*c*d**3/5 + 3*b*c**2*d**2/5) + x**7*(6*a*c**2*d**2/7 + 4*b*c**3*d/7) + x**4*(a*c**3*d + b*c**4/4)","A",0
2,1,80,0,0.078754," ","integrate((b*x**3+a)*(d*x**3+c)**3,x)","a c^{3} x + \frac{b d^{3} x^{13}}{13} + x^{10} \left(\frac{a d^{3}}{10} + \frac{3 b c d^{2}}{10}\right) + x^{7} \left(\frac{3 a c d^{2}}{7} + \frac{3 b c^{2} d}{7}\right) + x^{4} \left(\frac{3 a c^{2} d}{4} + \frac{b c^{3}}{4}\right)"," ",0,"a*c**3*x + b*d**3*x**13/13 + x**10*(a*d**3/10 + 3*b*c*d**2/10) + x**7*(3*a*c*d**2/7 + 3*b*c**2*d/7) + x**4*(3*a*c**2*d/4 + b*c**3/4)","A",0
3,1,51,0,0.074393," ","integrate((b*x**3+a)*(d*x**3+c)**2,x)","a c^{2} x + \frac{b d^{2} x^{10}}{10} + x^{7} \left(\frac{a d^{2}}{7} + \frac{2 b c d}{7}\right) + x^{4} \left(\frac{a c d}{2} + \frac{b c^{2}}{4}\right)"," ",0,"a*c**2*x + b*d**2*x**10/10 + x**7*(a*d**2/7 + 2*b*c*d/7) + x**4*(a*c*d/2 + b*c**2/4)","A",0
4,1,26,0,0.065542," ","integrate((b*x**3+a)*(d*x**3+c),x)","a c x + \frac{b d x^{7}}{7} + x^{4} \left(\frac{a d}{4} + \frac{b c}{4}\right)"," ",0,"a*c*x + b*d*x**7/7 + x**4*(a*d/4 + b*c/4)","A",0
5,1,71,0,0.417146," ","integrate((b*x**3+a)/(d*x**3+c),x)","\frac{b x}{d} + \operatorname{RootSum} {\left(27 t^{3} c^{2} d^{4} - a^{3} d^{3} + 3 a^{2} b c d^{2} - 3 a b^{2} c^{2} d + b^{3} c^{3}, \left( t \mapsto t \log{\left(\frac{3 t c d}{a d - b c} + x \right)} \right)\right)}"," ",0,"b*x/d + RootSum(27*_t**3*c**2*d**4 - a**3*d**3 + 3*a**2*b*c*d**2 - 3*a*b**2*c**2*d + b**3*c**3, Lambda(_t, _t*log(3*_t*c*d/(a*d - b*c) + x)))","A",0
6,1,97,0,0.578369," ","integrate((b*x**3+a)/(d*x**3+c)**2,x)","\frac{x \left(a d - b c\right)}{3 c^{2} d + 3 c d^{2} x^{3}} + \operatorname{RootSum} {\left(729 t^{3} c^{5} d^{4} - 8 a^{3} d^{3} - 12 a^{2} b c d^{2} - 6 a b^{2} c^{2} d - b^{3} c^{3}, \left( t \mapsto t \log{\left(\frac{9 t c^{2} d}{2 a d + b c} + x \right)} \right)\right)}"," ",0,"x*(a*d - b*c)/(3*c**2*d + 3*c*d**2*x**3) + RootSum(729*_t**3*c**5*d**4 - 8*a**3*d**3 - 12*a**2*b*c*d**2 - 6*a*b**2*c**2*d - b**3*c**3, Lambda(_t, _t*log(9*_t*c**2*d/(2*a*d + b*c) + x)))","A",0
7,1,133,0,0.777454," ","integrate((b*x**3+a)/(d*x**3+c)**3,x)","\frac{x^{4} \left(5 a d^{2} + b c d\right) + x \left(8 a c d - 2 b c^{2}\right)}{18 c^{4} d + 36 c^{3} d^{2} x^{3} + 18 c^{2} d^{3} x^{6}} + \operatorname{RootSum} {\left(19683 t^{3} c^{8} d^{4} - 125 a^{3} d^{3} - 75 a^{2} b c d^{2} - 15 a b^{2} c^{2} d - b^{3} c^{3}, \left( t \mapsto t \log{\left(\frac{27 t c^{3} d}{5 a d + b c} + x \right)} \right)\right)}"," ",0,"(x**4*(5*a*d**2 + b*c*d) + x*(8*a*c*d - 2*b*c**2))/(18*c**4*d + 36*c**3*d**2*x**3 + 18*c**2*d**3*x**6) + RootSum(19683*_t**3*c**8*d**4 - 125*a**3*d**3 - 75*a**2*b*c*d**2 - 15*a*b**2*c**2*d - b**3*c**3, Lambda(_t, _t*log(27*_t*c**3*d/(5*a*d + b*c) + x)))","A",0
8,1,139,0,0.091356," ","integrate((b*x**3+a)**2*(d*x**3+c)**3,x)","a^{2} c^{3} x + \frac{b^{2} d^{3} x^{16}}{16} + x^{13} \left(\frac{2 a b d^{3}}{13} + \frac{3 b^{2} c d^{2}}{13}\right) + x^{10} \left(\frac{a^{2} d^{3}}{10} + \frac{3 a b c d^{2}}{5} + \frac{3 b^{2} c^{2} d}{10}\right) + x^{7} \left(\frac{3 a^{2} c d^{2}}{7} + \frac{6 a b c^{2} d}{7} + \frac{b^{2} c^{3}}{7}\right) + x^{4} \left(\frac{3 a^{2} c^{2} d}{4} + \frac{a b c^{3}}{2}\right)"," ",0,"a**2*c**3*x + b**2*d**3*x**16/16 + x**13*(2*a*b*d**3/13 + 3*b**2*c*d**2/13) + x**10*(a**2*d**3/10 + 3*a*b*c*d**2/5 + 3*b**2*c**2*d/10) + x**7*(3*a**2*c*d**2/7 + 6*a*b*c**2*d/7 + b**2*c**3/7) + x**4*(3*a**2*c**2*d/4 + a*b*c**3/2)","A",0
9,1,90,0,0.083838," ","integrate((b*x**3+a)**2*(d*x**3+c)**2,x)","a^{2} c^{2} x + \frac{b^{2} d^{2} x^{13}}{13} + x^{10} \left(\frac{a b d^{2}}{5} + \frac{b^{2} c d}{5}\right) + x^{7} \left(\frac{a^{2} d^{2}}{7} + \frac{4 a b c d}{7} + \frac{b^{2} c^{2}}{7}\right) + x^{4} \left(\frac{a^{2} c d}{2} + \frac{a b c^{2}}{2}\right)"," ",0,"a**2*c**2*x + b**2*d**2*x**13/13 + x**10*(a*b*d**2/5 + b**2*c*d/5) + x**7*(a**2*d**2/7 + 4*a*b*c*d/7 + b**2*c**2/7) + x**4*(a**2*c*d/2 + a*b*c**2/2)","A",0
10,1,51,0,0.072453," ","integrate((b*x**3+a)**2*(d*x**3+c),x)","a^{2} c x + \frac{b^{2} d x^{10}}{10} + x^{7} \left(\frac{2 a b d}{7} + \frac{b^{2} c}{7}\right) + x^{4} \left(\frac{a^{2} d}{4} + \frac{a b c}{2}\right)"," ",0,"a**2*c*x + b**2*d*x**10/10 + x**7*(2*a*b*d/7 + b**2*c/7) + x**4*(a**2*d/4 + a*b*c/2)","A",0
11,1,156,0,0.678685," ","integrate((b*x**3+a)**2/(d*x**3+c),x)","\frac{b^{2} x^{4}}{4 d} + x \left(\frac{2 a b}{d} - \frac{b^{2} c}{d^{2}}\right) + \operatorname{RootSum} {\left(27 t^{3} c^{2} d^{7} - a^{6} d^{6} + 6 a^{5} b c d^{5} - 15 a^{4} b^{2} c^{2} d^{4} + 20 a^{3} b^{3} c^{3} d^{3} - 15 a^{2} b^{4} c^{4} d^{2} + 6 a b^{5} c^{5} d - b^{6} c^{6}, \left( t \mapsto t \log{\left(\frac{3 t c d^{2}}{a^{2} d^{2} - 2 a b c d + b^{2} c^{2}} + x \right)} \right)\right)}"," ",0,"b**2*x**4/(4*d) + x*(2*a*b/d - b**2*c/d**2) + RootSum(27*_t**3*c**2*d**7 - a**6*d**6 + 6*a**5*b*c*d**5 - 15*a**4*b**2*c**2*d**4 + 20*a**3*b**3*c**3*d**3 - 15*a**2*b**4*c**4*d**2 + 6*a*b**5*c**5*d - b**6*c**6, Lambda(_t, _t*log(3*_t*c*d**2/(a**2*d**2 - 2*a*b*c*d + b**2*c**2) + x)))","A",0
12,1,189,0,1.135404," ","integrate((b*x**3+a)**2/(d*x**3+c)**2,x)","\frac{b^{2} x}{d^{2}} + \frac{x \left(a^{2} d^{2} - 2 a b c d + b^{2} c^{2}\right)}{3 c^{2} d^{2} + 3 c d^{3} x^{3}} + \operatorname{RootSum} {\left(729 t^{3} c^{5} d^{7} - 8 a^{6} d^{6} - 24 a^{5} b c d^{5} + 24 a^{4} b^{2} c^{2} d^{4} + 88 a^{3} b^{3} c^{3} d^{3} - 48 a^{2} b^{4} c^{4} d^{2} - 96 a b^{5} c^{5} d + 64 b^{6} c^{6}, \left( t \mapsto t \log{\left(\frac{9 t c^{2} d^{2}}{2 a^{2} d^{2} + 2 a b c d - 4 b^{2} c^{2}} + x \right)} \right)\right)}"," ",0,"b**2*x/d**2 + x*(a**2*d**2 - 2*a*b*c*d + b**2*c**2)/(3*c**2*d**2 + 3*c*d**3*x**3) + RootSum(729*_t**3*c**5*d**7 - 8*a**6*d**6 - 24*a**5*b*c*d**5 + 24*a**4*b**2*c**2*d**4 + 88*a**3*b**3*c**3*d**3 - 48*a**2*b**4*c**4*d**2 - 96*a*b**5*c**5*d + 64*b**6*c**6, Lambda(_t, _t*log(9*_t*c**2*d**2/(2*a**2*d**2 + 2*a*b*c*d - 4*b**2*c**2) + x)))","A",0
13,1,233,0,1.622855," ","integrate((b*x**3+a)**2/(d*x**3+c)**3,x)","\frac{x^{4} \left(5 a^{2} d^{3} + 2 a b c d^{2} - 7 b^{2} c^{2} d\right) + x \left(8 a^{2} c d^{2} - 4 a b c^{2} d - 4 b^{2} c^{3}\right)}{18 c^{4} d^{2} + 36 c^{3} d^{3} x^{3} + 18 c^{2} d^{4} x^{6}} + \operatorname{RootSum} {\left(19683 t^{3} c^{8} d^{7} - 125 a^{6} d^{6} - 150 a^{5} b c d^{5} - 210 a^{4} b^{2} c^{2} d^{4} - 128 a^{3} b^{3} c^{3} d^{3} - 84 a^{2} b^{4} c^{4} d^{2} - 24 a b^{5} c^{5} d - 8 b^{6} c^{6}, \left( t \mapsto t \log{\left(\frac{27 t c^{3} d^{2}}{5 a^{2} d^{2} + 2 a b c d + 2 b^{2} c^{2}} + x \right)} \right)\right)}"," ",0,"(x**4*(5*a**2*d**3 + 2*a*b*c*d**2 - 7*b**2*c**2*d) + x*(8*a**2*c*d**2 - 4*a*b*c**2*d - 4*b**2*c**3))/(18*c**4*d**2 + 36*c**3*d**3*x**3 + 18*c**2*d**4*x**6) + RootSum(19683*_t**3*c**8*d**7 - 125*a**6*d**6 - 150*a**5*b*c*d**5 - 210*a**4*b**2*c**2*d**4 - 128*a**3*b**3*c**3*d**3 - 84*a**2*b**4*c**4*d**2 - 24*a*b**5*c**5*d - 8*b**6*c**6, Lambda(_t, _t*log(27*_t*c**3*d**2/(5*a**2*d**2 + 2*a*b*c*d + 2*b**2*c**2) + x)))","A",0
14,1,371,0,1.310480," ","integrate((d*x**3+c)**4/(b*x**3+a),x)","x^{7} \left(- \frac{a d^{4}}{7 b^{2}} + \frac{4 c d^{3}}{7 b}\right) + x^{4} \left(\frac{a^{2} d^{4}}{4 b^{3}} - \frac{a c d^{3}}{b^{2}} + \frac{3 c^{2} d^{2}}{2 b}\right) + x \left(- \frac{a^{3} d^{4}}{b^{4}} + \frac{4 a^{2} c d^{3}}{b^{3}} - \frac{6 a c^{2} d^{2}}{b^{2}} + \frac{4 c^{3} d}{b}\right) + \operatorname{RootSum} {\left(27 t^{3} a^{2} b^{13} - a^{12} d^{12} + 12 a^{11} b c d^{11} - 66 a^{10} b^{2} c^{2} d^{10} + 220 a^{9} b^{3} c^{3} d^{9} - 495 a^{8} b^{4} c^{4} d^{8} + 792 a^{7} b^{5} c^{5} d^{7} - 924 a^{6} b^{6} c^{6} d^{6} + 792 a^{5} b^{7} c^{7} d^{5} - 495 a^{4} b^{8} c^{8} d^{4} + 220 a^{3} b^{9} c^{9} d^{3} - 66 a^{2} b^{10} c^{10} d^{2} + 12 a b^{11} c^{11} d - b^{12} c^{12}, \left( t \mapsto t \log{\left(\frac{3 t a b^{4}}{a^{4} d^{4} - 4 a^{3} b c d^{3} + 6 a^{2} b^{2} c^{2} d^{2} - 4 a b^{3} c^{3} d + b^{4} c^{4}} + x \right)} \right)\right)} + \frac{d^{4} x^{10}}{10 b}"," ",0,"x**7*(-a*d**4/(7*b**2) + 4*c*d**3/(7*b)) + x**4*(a**2*d**4/(4*b**3) - a*c*d**3/b**2 + 3*c**2*d**2/(2*b)) + x*(-a**3*d**4/b**4 + 4*a**2*c*d**3/b**3 - 6*a*c**2*d**2/b**2 + 4*c**3*d/b) + RootSum(27*_t**3*a**2*b**13 - a**12*d**12 + 12*a**11*b*c*d**11 - 66*a**10*b**2*c**2*d**10 + 220*a**9*b**3*c**3*d**9 - 495*a**8*b**4*c**4*d**8 + 792*a**7*b**5*c**5*d**7 - 924*a**6*b**6*c**6*d**6 + 792*a**5*b**7*c**7*d**5 - 495*a**4*b**8*c**8*d**4 + 220*a**3*b**9*c**9*d**3 - 66*a**2*b**10*c**10*d**2 + 12*a*b**11*c**11*d - b**12*c**12, Lambda(_t, _t*log(3*_t*a*b**4/(a**4*d**4 - 4*a**3*b*c*d**3 + 6*a**2*b**2*c**2*d**2 - 4*a*b**3*c**3*d + b**4*c**4) + x))) + d**4*x**10/(10*b)","A",0
15,1,257,0,1.002701," ","integrate((d*x**3+c)**3/(b*x**3+a),x)","x^{4} \left(- \frac{a d^{3}}{4 b^{2}} + \frac{3 c d^{2}}{4 b}\right) + x \left(\frac{a^{2} d^{3}}{b^{3}} - \frac{3 a c d^{2}}{b^{2}} + \frac{3 c^{2} d}{b}\right) + \operatorname{RootSum} {\left(27 t^{3} a^{2} b^{10} + a^{9} d^{9} - 9 a^{8} b c d^{8} + 36 a^{7} b^{2} c^{2} d^{7} - 84 a^{6} b^{3} c^{3} d^{6} + 126 a^{5} b^{4} c^{4} d^{5} - 126 a^{4} b^{5} c^{5} d^{4} + 84 a^{3} b^{6} c^{6} d^{3} - 36 a^{2} b^{7} c^{7} d^{2} + 9 a b^{8} c^{8} d - b^{9} c^{9}, \left( t \mapsto t \log{\left(- \frac{3 t a b^{3}}{a^{3} d^{3} - 3 a^{2} b c d^{2} + 3 a b^{2} c^{2} d - b^{3} c^{3}} + x \right)} \right)\right)} + \frac{d^{3} x^{7}}{7 b}"," ",0,"x**4*(-a*d**3/(4*b**2) + 3*c*d**2/(4*b)) + x*(a**2*d**3/b**3 - 3*a*c*d**2/b**2 + 3*c**2*d/b) + RootSum(27*_t**3*a**2*b**10 + a**9*d**9 - 9*a**8*b*c*d**8 + 36*a**7*b**2*c**2*d**7 - 84*a**6*b**3*c**3*d**6 + 126*a**5*b**4*c**4*d**5 - 126*a**4*b**5*c**5*d**4 + 84*a**3*b**6*c**6*d**3 - 36*a**2*b**7*c**7*d**2 + 9*a*b**8*c**8*d - b**9*c**9, Lambda(_t, _t*log(-3*_t*a*b**3/(a**3*d**3 - 3*a**2*b*c*d**2 + 3*a*b**2*c**2*d - b**3*c**3) + x))) + d**3*x**7/(7*b)","A",0
16,1,156,0,0.690077," ","integrate((d*x**3+c)**2/(b*x**3+a),x)","x \left(- \frac{a d^{2}}{b^{2}} + \frac{2 c d}{b}\right) + \operatorname{RootSum} {\left(27 t^{3} a^{2} b^{7} - a^{6} d^{6} + 6 a^{5} b c d^{5} - 15 a^{4} b^{2} c^{2} d^{4} + 20 a^{3} b^{3} c^{3} d^{3} - 15 a^{2} b^{4} c^{4} d^{2} + 6 a b^{5} c^{5} d - b^{6} c^{6}, \left( t \mapsto t \log{\left(\frac{3 t a b^{2}}{a^{2} d^{2} - 2 a b c d + b^{2} c^{2}} + x \right)} \right)\right)} + \frac{d^{2} x^{4}}{4 b}"," ",0,"x*(-a*d**2/b**2 + 2*c*d/b) + RootSum(27*_t**3*a**2*b**7 - a**6*d**6 + 6*a**5*b*c*d**5 - 15*a**4*b**2*c**2*d**4 + 20*a**3*b**3*c**3*d**3 - 15*a**2*b**4*c**4*d**2 + 6*a*b**5*c**5*d - b**6*c**6, Lambda(_t, _t*log(3*_t*a*b**2/(a**2*d**2 - 2*a*b*c*d + b**2*c**2) + x))) + d**2*x**4/(4*b)","A",0
17,1,71,0,0.436078," ","integrate((d*x**3+c)/(b*x**3+a),x)","\operatorname{RootSum} {\left(27 t^{3} a^{2} b^{4} + a^{3} d^{3} - 3 a^{2} b c d^{2} + 3 a b^{2} c^{2} d - b^{3} c^{3}, \left( t \mapsto t \log{\left(- \frac{3 t a b}{a d - b c} + x \right)} \right)\right)} + \frac{d x}{b}"," ",0,"RootSum(27*_t**3*a**2*b**4 + a**3*d**3 - 3*a**2*b*c*d**2 + 3*a*b**2*c**2*d - b**3*c**3, Lambda(_t, _t*log(-3*_t*a*b/(a*d - b*c) + x))) + d*x/b","A",0
18,1,447,0,79.722367," ","integrate(1/(b*x**3+a)/(d*x**3+c),x)","\operatorname{RootSum} {\left(t^{3} \left(27 a^{5} d^{3} - 81 a^{4} b c d^{2} + 81 a^{3} b^{2} c^{2} d - 27 a^{2} b^{3} c^{3}\right) + b^{2}, \left( t \mapsto t \log{\left(x + \frac{81 t^{4} a^{7} c^{2} d^{5} - 243 t^{4} a^{6} b c^{3} d^{4} + 162 t^{4} a^{5} b^{2} c^{4} d^{3} + 162 t^{4} a^{4} b^{3} c^{5} d^{2} - 243 t^{4} a^{3} b^{4} c^{6} d + 81 t^{4} a^{2} b^{5} c^{7} - 3 t a^{4} d^{4} + 3 t a^{3} b c d^{3} + 3 t a b^{3} c^{3} d - 3 t b^{4} c^{4}}{a^{2} b d^{3} + b^{3} c^{2} d} \right)} \right)\right)} + \operatorname{RootSum} {\left(t^{3} \left(27 a^{3} c^{2} d^{3} - 81 a^{2} b c^{3} d^{2} + 81 a b^{2} c^{4} d - 27 b^{3} c^{5}\right) - d^{2}, \left( t \mapsto t \log{\left(x + \frac{81 t^{4} a^{7} c^{2} d^{5} - 243 t^{4} a^{6} b c^{3} d^{4} + 162 t^{4} a^{5} b^{2} c^{4} d^{3} + 162 t^{4} a^{4} b^{3} c^{5} d^{2} - 243 t^{4} a^{3} b^{4} c^{6} d + 81 t^{4} a^{2} b^{5} c^{7} - 3 t a^{4} d^{4} + 3 t a^{3} b c d^{3} + 3 t a b^{3} c^{3} d - 3 t b^{4} c^{4}}{a^{2} b d^{3} + b^{3} c^{2} d} \right)} \right)\right)}"," ",0,"RootSum(_t**3*(27*a**5*d**3 - 81*a**4*b*c*d**2 + 81*a**3*b**2*c**2*d - 27*a**2*b**3*c**3) + b**2, Lambda(_t, _t*log(x + (81*_t**4*a**7*c**2*d**5 - 243*_t**4*a**6*b*c**3*d**4 + 162*_t**4*a**5*b**2*c**4*d**3 + 162*_t**4*a**4*b**3*c**5*d**2 - 243*_t**4*a**3*b**4*c**6*d + 81*_t**4*a**2*b**5*c**7 - 3*_t*a**4*d**4 + 3*_t*a**3*b*c*d**3 + 3*_t*a*b**3*c**3*d - 3*_t*b**4*c**4)/(a**2*b*d**3 + b**3*c**2*d)))) + RootSum(_t**3*(27*a**3*c**2*d**3 - 81*a**2*b*c**3*d**2 + 81*a*b**2*c**4*d - 27*b**3*c**5) - d**2, Lambda(_t, _t*log(x + (81*_t**4*a**7*c**2*d**5 - 243*_t**4*a**6*b*c**3*d**4 + 162*_t**4*a**5*b**2*c**4*d**3 + 162*_t**4*a**4*b**3*c**5*d**2 - 243*_t**4*a**3*b**4*c**6*d + 81*_t**4*a**2*b**5*c**7 - 3*_t*a**4*d**4 + 3*_t*a**3*b*c*d**3 + 3*_t*a*b**3*c**3*d - 3*_t*b**4*c**4)/(a**2*b*d**3 + b**3*c**2*d))))","A",0
19,-1,0,0,0.000000," ","integrate(1/(b*x**3+a)/(d*x**3+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
20,1,546,0,12.429142," ","integrate((d*x**3+c)**5/(b*x**3+a)**2,x)","x^{7} \left(- \frac{2 a d^{5}}{7 b^{3}} + \frac{5 c d^{4}}{7 b^{2}}\right) + x^{4} \left(\frac{3 a^{2} d^{5}}{4 b^{4}} - \frac{5 a c d^{4}}{2 b^{3}} + \frac{5 c^{2} d^{3}}{2 b^{2}}\right) + x \left(- \frac{4 a^{3} d^{5}}{b^{5}} + \frac{15 a^{2} c d^{4}}{b^{4}} - \frac{20 a c^{2} d^{3}}{b^{3}} + \frac{10 c^{3} d^{2}}{b^{2}}\right) + \frac{x \left(- a^{5} d^{5} + 5 a^{4} b c d^{4} - 10 a^{3} b^{2} c^{2} d^{3} + 10 a^{2} b^{3} c^{3} d^{2} - 5 a b^{4} c^{4} d + b^{5} c^{5}\right)}{3 a^{2} b^{5} + 3 a b^{6} x^{3}} + \operatorname{RootSum} {\left(729 t^{3} a^{5} b^{16} - 2197 a^{15} d^{15} + 25350 a^{14} b c d^{14} - 132990 a^{13} b^{2} c^{2} d^{13} + 418280 a^{12} b^{3} c^{3} d^{12} - 874635 a^{11} b^{4} c^{4} d^{11} + 1271886 a^{10} b^{5} c^{5} d^{10} - 1302400 a^{9} b^{6} c^{6} d^{9} + 922680 a^{8} b^{7} c^{7} d^{8} - 422235 a^{7} b^{8} c^{8} d^{7} + 97570 a^{6} b^{9} c^{9} d^{6} + 7194 a^{5} b^{10} c^{10} d^{5} - 10200 a^{4} b^{11} c^{11} d^{4} + 1435 a^{3} b^{12} c^{12} d^{3} + 330 a^{2} b^{13} c^{13} d^{2} - 60 a b^{14} c^{14} d - 8 b^{15} c^{15}, \left( t \mapsto t \log{\left(\frac{9 t a^{2} b^{5}}{13 a^{5} d^{5} - 50 a^{4} b c d^{4} + 70 a^{3} b^{2} c^{2} d^{3} - 40 a^{2} b^{3} c^{3} d^{2} + 5 a b^{4} c^{4} d + 2 b^{5} c^{5}} + x \right)} \right)\right)} + \frac{d^{5} x^{10}}{10 b^{2}}"," ",0,"x**7*(-2*a*d**5/(7*b**3) + 5*c*d**4/(7*b**2)) + x**4*(3*a**2*d**5/(4*b**4) - 5*a*c*d**4/(2*b**3) + 5*c**2*d**3/(2*b**2)) + x*(-4*a**3*d**5/b**5 + 15*a**2*c*d**4/b**4 - 20*a*c**2*d**3/b**3 + 10*c**3*d**2/b**2) + x*(-a**5*d**5 + 5*a**4*b*c*d**4 - 10*a**3*b**2*c**2*d**3 + 10*a**2*b**3*c**3*d**2 - 5*a*b**4*c**4*d + b**5*c**5)/(3*a**2*b**5 + 3*a*b**6*x**3) + RootSum(729*_t**3*a**5*b**16 - 2197*a**15*d**15 + 25350*a**14*b*c*d**14 - 132990*a**13*b**2*c**2*d**13 + 418280*a**12*b**3*c**3*d**12 - 874635*a**11*b**4*c**4*d**11 + 1271886*a**10*b**5*c**5*d**10 - 1302400*a**9*b**6*c**6*d**9 + 922680*a**8*b**7*c**7*d**8 - 422235*a**7*b**8*c**8*d**7 + 97570*a**6*b**9*c**9*d**6 + 7194*a**5*b**10*c**10*d**5 - 10200*a**4*b**11*c**11*d**4 + 1435*a**3*b**12*c**12*d**3 + 330*a**2*b**13*c**13*d**2 - 60*a*b**14*c**14*d - 8*b**15*c**15, Lambda(_t, _t*log(9*_t*a**2*b**5/(13*a**5*d**5 - 50*a**4*b*c*d**4 + 70*a**3*b**2*c**2*d**3 - 40*a**2*b**3*c**3*d**2 + 5*a*b**4*c**4*d + 2*b**5*c**5) + x))) + d**5*x**10/(10*b**2)","A",0
21,1,405,0,8.536600," ","integrate((d*x**3+c)**4/(b*x**3+a)**2,x)","x^{4} \left(- \frac{a d^{4}}{2 b^{3}} + \frac{c d^{3}}{b^{2}}\right) + x \left(\frac{3 a^{2} d^{4}}{b^{4}} - \frac{8 a c d^{3}}{b^{3}} + \frac{6 c^{2} d^{2}}{b^{2}}\right) + \frac{x \left(a^{4} d^{4} - 4 a^{3} b c d^{3} + 6 a^{2} b^{2} c^{2} d^{2} - 4 a b^{3} c^{3} d + b^{4} c^{4}\right)}{3 a^{2} b^{4} + 3 a b^{5} x^{3}} + \operatorname{RootSum} {\left(729 t^{3} a^{5} b^{13} + 1000 a^{12} d^{12} - 8400 a^{11} b c d^{11} + 30720 a^{10} b^{2} c^{2} d^{10} - 63472 a^{9} b^{3} c^{3} d^{9} + 79848 a^{8} b^{4} c^{4} d^{8} - 60192 a^{7} b^{5} c^{5} d^{7} + 22848 a^{6} b^{6} c^{6} d^{6} + 288 a^{5} b^{7} c^{7} d^{5} - 3528 a^{4} b^{8} c^{8} d^{4} + 752 a^{3} b^{9} c^{9} d^{3} + 192 a^{2} b^{10} c^{10} d^{2} - 48 a b^{11} c^{11} d - 8 b^{12} c^{12}, \left( t \mapsto t \log{\left(- \frac{9 t a^{2} b^{4}}{10 a^{4} d^{4} - 28 a^{3} b c d^{3} + 24 a^{2} b^{2} c^{2} d^{2} - 4 a b^{3} c^{3} d - 2 b^{4} c^{4}} + x \right)} \right)\right)} + \frac{d^{4} x^{7}}{7 b^{2}}"," ",0,"x**4*(-a*d**4/(2*b**3) + c*d**3/b**2) + x*(3*a**2*d**4/b**4 - 8*a*c*d**3/b**3 + 6*c**2*d**2/b**2) + x*(a**4*d**4 - 4*a**3*b*c*d**3 + 6*a**2*b**2*c**2*d**2 - 4*a*b**3*c**3*d + b**4*c**4)/(3*a**2*b**4 + 3*a*b**5*x**3) + RootSum(729*_t**3*a**5*b**13 + 1000*a**12*d**12 - 8400*a**11*b*c*d**11 + 30720*a**10*b**2*c**2*d**10 - 63472*a**9*b**3*c**3*d**9 + 79848*a**8*b**4*c**4*d**8 - 60192*a**7*b**5*c**5*d**7 + 22848*a**6*b**6*c**6*d**6 + 288*a**5*b**7*c**7*d**5 - 3528*a**4*b**8*c**8*d**4 + 752*a**3*b**9*c**9*d**3 + 192*a**2*b**10*c**10*d**2 - 48*a*b**11*c**11*d - 8*b**12*c**12, Lambda(_t, _t*log(-9*_t*a**2*b**4/(10*a**4*d**4 - 28*a**3*b*c*d**3 + 24*a**2*b**2*c**2*d**2 - 4*a*b**3*c**3*d - 2*b**4*c**4) + x))) + d**4*x**7/(7*b**2)","A",0
22,1,291,0,4.330196," ","integrate((d*x**3+c)**3/(b*x**3+a)**2,x)","x \left(- \frac{2 a d^{3}}{b^{3}} + \frac{3 c d^{2}}{b^{2}}\right) + \frac{x \left(- a^{3} d^{3} + 3 a^{2} b c d^{2} - 3 a b^{2} c^{2} d + b^{3} c^{3}\right)}{3 a^{2} b^{3} + 3 a b^{4} x^{3}} + \operatorname{RootSum} {\left(729 t^{3} a^{5} b^{10} - 343 a^{9} d^{9} + 1764 a^{8} b c d^{8} - 3465 a^{7} b^{2} c^{2} d^{7} + 2946 a^{6} b^{3} c^{3} d^{6} - 477 a^{5} b^{4} c^{4} d^{5} - 792 a^{4} b^{5} c^{5} d^{4} + 321 a^{3} b^{6} c^{6} d^{3} + 90 a^{2} b^{7} c^{7} d^{2} - 36 a b^{8} c^{8} d - 8 b^{9} c^{9}, \left( t \mapsto t \log{\left(\frac{9 t a^{2} b^{3}}{7 a^{3} d^{3} - 12 a^{2} b c d^{2} + 3 a b^{2} c^{2} d + 2 b^{3} c^{3}} + x \right)} \right)\right)} + \frac{d^{3} x^{4}}{4 b^{2}}"," ",0,"x*(-2*a*d**3/b**3 + 3*c*d**2/b**2) + x*(-a**3*d**3 + 3*a**2*b*c*d**2 - 3*a*b**2*c**2*d + b**3*c**3)/(3*a**2*b**3 + 3*a*b**4*x**3) + RootSum(729*_t**3*a**5*b**10 - 343*a**9*d**9 + 1764*a**8*b*c*d**8 - 3465*a**7*b**2*c**2*d**7 + 2946*a**6*b**3*c**3*d**6 - 477*a**5*b**4*c**4*d**5 - 792*a**4*b**5*c**5*d**4 + 321*a**3*b**6*c**6*d**3 + 90*a**2*b**7*c**7*d**2 - 36*a*b**8*c**8*d - 8*b**9*c**9, Lambda(_t, _t*log(9*_t*a**2*b**3/(7*a**3*d**3 - 12*a**2*b*c*d**2 + 3*a*b**2*c**2*d + 2*b**3*c**3) + x))) + d**3*x**4/(4*b**2)","A",0
23,1,189,0,2.556166," ","integrate((d*x**3+c)**2/(b*x**3+a)**2,x)","\frac{x \left(a^{2} d^{2} - 2 a b c d + b^{2} c^{2}\right)}{3 a^{2} b^{2} + 3 a b^{3} x^{3}} + \operatorname{RootSum} {\left(729 t^{3} a^{5} b^{7} + 64 a^{6} d^{6} - 96 a^{5} b c d^{5} - 48 a^{4} b^{2} c^{2} d^{4} + 88 a^{3} b^{3} c^{3} d^{3} + 24 a^{2} b^{4} c^{4} d^{2} - 24 a b^{5} c^{5} d - 8 b^{6} c^{6}, \left( t \mapsto t \log{\left(- \frac{9 t a^{2} b^{2}}{4 a^{2} d^{2} - 2 a b c d - 2 b^{2} c^{2}} + x \right)} \right)\right)} + \frac{d^{2} x}{b^{2}}"," ",0,"x*(a**2*d**2 - 2*a*b*c*d + b**2*c**2)/(3*a**2*b**2 + 3*a*b**3*x**3) + RootSum(729*_t**3*a**5*b**7 + 64*a**6*d**6 - 96*a**5*b*c*d**5 - 48*a**4*b**2*c**2*d**4 + 88*a**3*b**3*c**3*d**3 + 24*a**2*b**4*c**4*d**2 - 24*a*b**5*c**5*d - 8*b**6*c**6, Lambda(_t, _t*log(-9*_t*a**2*b**2/(4*a**2*d**2 - 2*a*b*c*d - 2*b**2*c**2) + x))) + d**2*x/b**2","A",0
24,1,97,0,1.418219," ","integrate((d*x**3+c)/(b*x**3+a)**2,x)","\frac{x \left(- a d + b c\right)}{3 a^{2} b + 3 a b^{2} x^{3}} + \operatorname{RootSum} {\left(729 t^{3} a^{5} b^{4} - a^{3} d^{3} - 6 a^{2} b c d^{2} - 12 a b^{2} c^{2} d - 8 b^{3} c^{3}, \left( t \mapsto t \log{\left(\frac{9 t a^{2} b}{a d + 2 b c} + x \right)} \right)\right)}"," ",0,"x*(-a*d + b*c)/(3*a**2*b + 3*a*b**2*x**3) + RootSum(729*_t**3*a**5*b**4 - a**3*d**3 - 6*a**2*b*c*d**2 - 12*a*b**2*c**2*d - 8*b**3*c**3, Lambda(_t, _t*log(9*_t*a**2*b/(a*d + 2*b*c) + x)))","A",0
25,-1,0,0,0.000000," ","integrate(1/(b*x**3+a)**2/(d*x**3+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
26,-1,0,0,0.000000," ","integrate(1/(b*x**3+a)**2/(d*x**3+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
27,1,80,0,4.983818," ","integrate((-b*x**3+a)*(b*x**3+a)**(2/3),x)","\frac{a^{\frac{5}{3}} x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} - \frac{a^{\frac{2}{3}} b x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{7}{3}\right)}"," ",0,"a**(5/3)*x*gamma(1/3)*hyper((-2/3, 1/3), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(4/3)) - a**(2/3)*b*x**4*gamma(4/3)*hyper((-2/3, 4/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(7/3))","C",0
28,1,76,0,5.525387," ","integrate((-b*x**3+a)/(b*x**3+a)**(1/3),x)","\frac{a^{\frac{2}{3}} x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} - \frac{b x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt[3]{a} \Gamma\left(\frac{7}{3}\right)}"," ",0,"a**(2/3)*x*gamma(1/3)*hyper((1/3, 1/3), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(4/3)) - b*x**4*gamma(4/3)*hyper((1/3, 4/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(1/3)*gamma(7/3))","C",0
29,1,70,0,16.136871," ","integrate((-b*x**3+a)/(b*x**3+a)**(4/3),x)","\frac{x \Gamma\left(\frac{1}{3}\right)}{3 \sqrt[3]{a} \sqrt[3]{1 + \frac{b x^{3}}{a}} \Gamma\left(\frac{4}{3}\right)} - \frac{b x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{4}{3}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{4}{3}} \Gamma\left(\frac{7}{3}\right)}"," ",0,"x*gamma(1/3)/(3*a**(1/3)*(1 + b*x**3/a)**(1/3)*gamma(4/3)) - b*x**4*gamma(4/3)*hyper((4/3, 4/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(4/3)*gamma(7/3))","C",0
30,1,190,0,91.680790," ","integrate((-b*x**3+a)/(b*x**3+a)**(7/3),x)","a \left(\frac{4 a x \Gamma\left(\frac{1}{3}\right)}{9 a^{\frac{10}{3}} \sqrt[3]{1 + \frac{b x^{3}}{a}} \Gamma\left(\frac{7}{3}\right) + 9 a^{\frac{7}{3}} b x^{3} \sqrt[3]{1 + \frac{b x^{3}}{a}} \Gamma\left(\frac{7}{3}\right)} + \frac{3 b x^{4} \Gamma\left(\frac{1}{3}\right)}{9 a^{\frac{10}{3}} \sqrt[3]{1 + \frac{b x^{3}}{a}} \Gamma\left(\frac{7}{3}\right) + 9 a^{\frac{7}{3}} b x^{3} \sqrt[3]{1 + \frac{b x^{3}}{a}} \Gamma\left(\frac{7}{3}\right)}\right) - \frac{b x^{4} \Gamma\left(\frac{4}{3}\right)}{3 a^{\frac{7}{3}} \sqrt[3]{1 + \frac{b x^{3}}{a}} \Gamma\left(\frac{7}{3}\right) + 3 a^{\frac{4}{3}} b x^{3} \sqrt[3]{1 + \frac{b x^{3}}{a}} \Gamma\left(\frac{7}{3}\right)}"," ",0,"a*(4*a*x*gamma(1/3)/(9*a**(10/3)*(1 + b*x**3/a)**(1/3)*gamma(7/3) + 9*a**(7/3)*b*x**3*(1 + b*x**3/a)**(1/3)*gamma(7/3)) + 3*b*x**4*gamma(1/3)/(9*a**(10/3)*(1 + b*x**3/a)**(1/3)*gamma(7/3) + 9*a**(7/3)*b*x**3*(1 + b*x**3/a)**(1/3)*gamma(7/3))) - b*x**4*gamma(4/3)/(3*a**(7/3)*(1 + b*x**3/a)**(1/3)*gamma(7/3) + 3*a**(4/3)*b*x**3*(1 + b*x**3/a)**(1/3)*gamma(7/3))","B",0
31,-1,0,0,0.000000," ","integrate((-b*x**3+a)/(b*x**3+a)**(10/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
32,-1,0,0,0.000000," ","integrate((-b*x**3+a)/(b*x**3+a)**(13/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
33,-1,0,0,0.000000," ","integrate((-b*x**3+a)/(b*x**3+a)**(16/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
34,0,0,0,0.000000," ","integrate((b*x**3+a)**(7/3)/(-b*x**3+a),x)","- \int \frac{a^{2} \sqrt[3]{a + b x^{3}}}{- a + b x^{3}}\, dx - \int \frac{b^{2} x^{6} \sqrt[3]{a + b x^{3}}}{- a + b x^{3}}\, dx - \int \frac{2 a b x^{3} \sqrt[3]{a + b x^{3}}}{- a + b x^{3}}\, dx"," ",0,"-Integral(a**2*(a + b*x**3)**(1/3)/(-a + b*x**3), x) - Integral(b**2*x**6*(a + b*x**3)**(1/3)/(-a + b*x**3), x) - Integral(2*a*b*x**3*(a + b*x**3)**(1/3)/(-a + b*x**3), x)","F",0
35,0,0,0,0.000000," ","integrate((b*x**3+a)**(4/3)/(-b*x**3+a),x)","- \int \frac{a \sqrt[3]{a + b x^{3}}}{- a + b x^{3}}\, dx - \int \frac{b x^{3} \sqrt[3]{a + b x^{3}}}{- a + b x^{3}}\, dx"," ",0,"-Integral(a*(a + b*x**3)**(1/3)/(-a + b*x**3), x) - Integral(b*x**3*(a + b*x**3)**(1/3)/(-a + b*x**3), x)","F",0
36,0,0,0,0.000000," ","integrate((b*x**3+a)**(1/3)/(-b*x**3+a),x)","- \int \frac{\sqrt[3]{a + b x^{3}}}{- a + b x^{3}}\, dx"," ",0,"-Integral((a + b*x**3)**(1/3)/(-a + b*x**3), x)","F",0
37,0,0,0,0.000000," ","integrate(1/(-b*x**3+a)/(b*x**3+a)**(2/3),x)","- \int \frac{1}{- a \left(a + b x^{3}\right)^{\frac{2}{3}} + b x^{3} \left(a + b x^{3}\right)^{\frac{2}{3}}}\, dx"," ",0,"-Integral(1/(-a*(a + b*x**3)**(2/3) + b*x**3*(a + b*x**3)**(2/3)), x)","F",0
38,0,0,0,0.000000," ","integrate(1/(-b*x**3+a)/(b*x**3+a)**(5/3),x)","- \int \frac{1}{- a^{2} \left(a + b x^{3}\right)^{\frac{2}{3}} + b^{2} x^{6} \left(a + b x^{3}\right)^{\frac{2}{3}}}\, dx"," ",0,"-Integral(1/(-a**2*(a + b*x**3)**(2/3) + b**2*x**6*(a + b*x**3)**(2/3)), x)","F",0
39,-1,0,0,0.000000," ","integrate(1/(-b*x**3+a)/(b*x**3+a)**(8/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
40,1,126,0,9.173897," ","integrate((-b*x**3+a)**2*(b*x**3+a)**(2/3),x)","\frac{a^{\frac{8}{3}} x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} - \frac{2 a^{\frac{5}{3}} b x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{7}{3}\right)} + \frac{a^{\frac{2}{3}} b^{2} x^{7} \Gamma\left(\frac{7}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{7}{3} \\ \frac{10}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{10}{3}\right)}"," ",0,"a**(8/3)*x*gamma(1/3)*hyper((-2/3, 1/3), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(4/3)) - 2*a**(5/3)*b*x**4*gamma(4/3)*hyper((-2/3, 4/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(7/3)) + a**(2/3)*b**2*x**7*gamma(7/3)*hyper((-2/3, 7/3), (10/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(10/3))","C",0
41,1,121,0,7.598921," ","integrate((-b*x**3+a)**2/(b*x**3+a)**(1/3),x)","\frac{a^{\frac{5}{3}} x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} - \frac{2 a^{\frac{2}{3}} b x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{7}{3}\right)} + \frac{b^{2} x^{7} \Gamma\left(\frac{7}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{7}{3} \\ \frac{10}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt[3]{a} \Gamma\left(\frac{10}{3}\right)}"," ",0,"a**(5/3)*x*gamma(1/3)*hyper((1/3, 1/3), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(4/3)) - 2*a**(2/3)*b*x**4*gamma(4/3)*hyper((1/3, 4/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(7/3)) + b**2*x**7*gamma(7/3)*hyper((1/3, 7/3), (10/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(1/3)*gamma(10/3))","C",0
42,0,0,0,0.000000," ","integrate((-b*x**3+a)**2/(b*x**3+a)**(4/3),x)","\int \frac{\left(- a + b x^{3}\right)^{2}}{\left(a + b x^{3}\right)^{\frac{4}{3}}}\, dx"," ",0,"Integral((-a + b*x**3)**2/(a + b*x**3)**(4/3), x)","F",0
43,0,0,0,0.000000," ","integrate((-b*x**3+a)**2/(b*x**3+a)**(7/3),x)","\int \frac{\left(- a + b x^{3}\right)^{2}}{\left(a + b x^{3}\right)^{\frac{7}{3}}}\, dx"," ",0,"Integral((-a + b*x**3)**2/(a + b*x**3)**(7/3), x)","F",0
44,-1,0,0,0.000000," ","integrate((-b*x**3+a)**2/(b*x**3+a)**(10/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
45,-1,0,0,0.000000," ","integrate((-b*x**3+a)**2/(b*x**3+a)**(13/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
46,-1,0,0,0.000000," ","integrate((-b*x**3+a)**2/(b*x**3+a)**(16/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
47,-1,0,0,0.000000," ","integrate((-b*x**3+a)**2/(b*x**3+a)**(19/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
48,1,168,0,8.409424," ","integrate((-b*x**3+a)**2*(b*x**3+a)**(4/3),x)","\frac{a^{\frac{10}{3}} x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} - \frac{a^{\frac{7}{3}} b x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{7}{3}\right)} - \frac{a^{\frac{4}{3}} b^{2} x^{7} \Gamma\left(\frac{7}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{7}{3} \\ \frac{10}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{10}{3}\right)} + \frac{\sqrt[3]{a} b^{3} x^{10} \Gamma\left(\frac{10}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{10}{3} \\ \frac{13}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{13}{3}\right)}"," ",0,"a**(10/3)*x*gamma(1/3)*hyper((-1/3, 1/3), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(4/3)) - a**(7/3)*b*x**4*gamma(4/3)*hyper((-1/3, 4/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(7/3)) - a**(4/3)*b**2*x**7*gamma(7/3)*hyper((-1/3, 7/3), (10/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(10/3)) + a**(1/3)*b**3*x**10*gamma(10/3)*hyper((-1/3, 10/3), (13/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(13/3))","C",0
49,1,126,0,5.592174," ","integrate((-b*x**3+a)**2*(b*x**3+a)**(1/3),x)","\frac{a^{\frac{7}{3}} x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} - \frac{2 a^{\frac{4}{3}} b x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{7}{3}\right)} + \frac{\sqrt[3]{a} b^{2} x^{7} \Gamma\left(\frac{7}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{7}{3} \\ \frac{10}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{10}{3}\right)}"," ",0,"a**(7/3)*x*gamma(1/3)*hyper((-1/3, 1/3), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(4/3)) - 2*a**(4/3)*b*x**4*gamma(4/3)*hyper((-1/3, 4/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(7/3)) + a**(1/3)*b**2*x**7*gamma(7/3)*hyper((-1/3, 7/3), (10/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(10/3))","C",0
50,1,121,0,5.757883," ","integrate((-b*x**3+a)**2/(b*x**3+a)**(2/3),x)","\frac{a^{\frac{4}{3}} x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{2}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} - \frac{2 \sqrt[3]{a} b x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{2}{3}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{7}{3}\right)} + \frac{b^{2} x^{7} \Gamma\left(\frac{7}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{2}{3}, \frac{7}{3} \\ \frac{10}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{2}{3}} \Gamma\left(\frac{10}{3}\right)}"," ",0,"a**(4/3)*x*gamma(1/3)*hyper((1/3, 2/3), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(4/3)) - 2*a**(1/3)*b*x**4*gamma(4/3)*hyper((2/3, 4/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(7/3)) + b**2*x**7*gamma(7/3)*hyper((2/3, 7/3), (10/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(2/3)*gamma(10/3))","C",0
51,0,0,0,0.000000," ","integrate((-b*x**3+a)**2/(b*x**3+a)**(5/3),x)","\int \frac{\left(- a + b x^{3}\right)^{2}}{\left(a + b x^{3}\right)^{\frac{5}{3}}}\, dx"," ",0,"Integral((-a + b*x**3)**2/(a + b*x**3)**(5/3), x)","F",0
52,-1,0,0,0.000000," ","integrate((-b*x**3+a)**2/(b*x**3+a)**(8/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
53,-1,0,0,0.000000," ","integrate((-b*x**3+a)**2/(b*x**3+a)**(11/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
54,-1,0,0,0.000000," ","integrate((-b*x**3+a)**2/(b*x**3+a)**(14/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
55,-1,0,0,0.000000," ","integrate((-b*x**3+a)**2/(b*x**3+a)**(17/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
56,1,170,0,10.423688," ","integrate((b*x**3+a)**(5/3)*(d*x**3+c),x)","\frac{a^{\frac{5}{3}} c x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} + \frac{a^{\frac{5}{3}} d x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{7}{3}\right)} + \frac{a^{\frac{2}{3}} b c x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{7}{3}\right)} + \frac{a^{\frac{2}{3}} b d x^{7} \Gamma\left(\frac{7}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{7}{3} \\ \frac{10}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{10}{3}\right)}"," ",0,"a**(5/3)*c*x*gamma(1/3)*hyper((-2/3, 1/3), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(4/3)) + a**(5/3)*d*x**4*gamma(4/3)*hyper((-2/3, 4/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(7/3)) + a**(2/3)*b*c*x**4*gamma(4/3)*hyper((-2/3, 4/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(7/3)) + a**(2/3)*b*d*x**7*gamma(7/3)*hyper((-2/3, 7/3), (10/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(10/3))","C",0
57,1,82,0,5.346941," ","integrate((b*x**3+a)**(2/3)*(d*x**3+c),x)","\frac{a^{\frac{2}{3}} c x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} + \frac{a^{\frac{2}{3}} d x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{7}{3}\right)}"," ",0,"a**(2/3)*c*x*gamma(1/3)*hyper((-2/3, 1/3), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(4/3)) + a**(2/3)*d*x**4*gamma(4/3)*hyper((-2/3, 4/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(7/3))","C",0
58,1,78,0,4.439039," ","integrate((d*x**3+c)/(b*x**3+a)**(1/3),x)","\frac{c x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt[3]{a} \Gamma\left(\frac{4}{3}\right)} + \frac{d x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt[3]{a} \Gamma\left(\frac{7}{3}\right)}"," ",0,"c*x*gamma(1/3)*hyper((1/3, 1/3), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(1/3)*gamma(4/3)) + d*x**4*gamma(4/3)*hyper((1/3, 4/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(1/3)*gamma(7/3))","C",0
59,1,71,0,12.828133," ","integrate((d*x**3+c)/(b*x**3+a)**(4/3),x)","\frac{c x \Gamma\left(\frac{1}{3}\right)}{3 a^{\frac{4}{3}} \sqrt[3]{1 + \frac{b x^{3}}{a}} \Gamma\left(\frac{4}{3}\right)} + \frac{d x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{4}{3}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{4}{3}} \Gamma\left(\frac{7}{3}\right)}"," ",0,"c*x*gamma(1/3)/(3*a**(4/3)*(1 + b*x**3/a)**(1/3)*gamma(4/3)) + d*x**4*gamma(4/3)*hyper((4/3, 4/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(4/3)*gamma(7/3))","C",0
60,1,190,0,82.052305," ","integrate((d*x**3+c)/(b*x**3+a)**(7/3),x)","c \left(\frac{4 a x \Gamma\left(\frac{1}{3}\right)}{9 a^{\frac{10}{3}} \sqrt[3]{1 + \frac{b x^{3}}{a}} \Gamma\left(\frac{7}{3}\right) + 9 a^{\frac{7}{3}} b x^{3} \sqrt[3]{1 + \frac{b x^{3}}{a}} \Gamma\left(\frac{7}{3}\right)} + \frac{3 b x^{4} \Gamma\left(\frac{1}{3}\right)}{9 a^{\frac{10}{3}} \sqrt[3]{1 + \frac{b x^{3}}{a}} \Gamma\left(\frac{7}{3}\right) + 9 a^{\frac{7}{3}} b x^{3} \sqrt[3]{1 + \frac{b x^{3}}{a}} \Gamma\left(\frac{7}{3}\right)}\right) + \frac{d x^{4} \Gamma\left(\frac{4}{3}\right)}{3 a^{\frac{7}{3}} \sqrt[3]{1 + \frac{b x^{3}}{a}} \Gamma\left(\frac{7}{3}\right) + 3 a^{\frac{4}{3}} b x^{3} \sqrt[3]{1 + \frac{b x^{3}}{a}} \Gamma\left(\frac{7}{3}\right)}"," ",0,"c*(4*a*x*gamma(1/3)/(9*a**(10/3)*(1 + b*x**3/a)**(1/3)*gamma(7/3) + 9*a**(7/3)*b*x**3*(1 + b*x**3/a)**(1/3)*gamma(7/3)) + 3*b*x**4*gamma(1/3)/(9*a**(10/3)*(1 + b*x**3/a)**(1/3)*gamma(7/3) + 9*a**(7/3)*b*x**3*(1 + b*x**3/a)**(1/3)*gamma(7/3))) + d*x**4*gamma(4/3)/(3*a**(7/3)*(1 + b*x**3/a)**(1/3)*gamma(7/3) + 3*a**(4/3)*b*x**3*(1 + b*x**3/a)**(1/3)*gamma(7/3))","B",0
61,-1,0,0,0.000000," ","integrate((d*x**3+c)/(b*x**3+a)**(10/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
62,-1,0,0,0.000000," ","integrate((d*x**3+c)/(b*x**3+a)**(13/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
63,-1,0,0,0.000000," ","integrate((d*x**3+c)/(b*x**3+a)**(16/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
64,1,265,0,10.987691," ","integrate((b*x**3+a)**(7/3)*(d*x**3+c),x)","\frac{a^{\frac{7}{3}} c x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} + \frac{a^{\frac{7}{3}} d x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{7}{3}\right)} + \frac{2 a^{\frac{4}{3}} b c x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{7}{3}\right)} + \frac{2 a^{\frac{4}{3}} b d x^{7} \Gamma\left(\frac{7}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{7}{3} \\ \frac{10}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{10}{3}\right)} + \frac{\sqrt[3]{a} b^{2} c x^{7} \Gamma\left(\frac{7}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{7}{3} \\ \frac{10}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{10}{3}\right)} + \frac{\sqrt[3]{a} b^{2} d x^{10} \Gamma\left(\frac{10}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{10}{3} \\ \frac{13}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{13}{3}\right)}"," ",0,"a**(7/3)*c*x*gamma(1/3)*hyper((-1/3, 1/3), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(4/3)) + a**(7/3)*d*x**4*gamma(4/3)*hyper((-1/3, 4/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(7/3)) + 2*a**(4/3)*b*c*x**4*gamma(4/3)*hyper((-1/3, 4/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(7/3)) + 2*a**(4/3)*b*d*x**7*gamma(7/3)*hyper((-1/3, 7/3), (10/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(10/3)) + a**(1/3)*b**2*c*x**7*gamma(7/3)*hyper((-1/3, 7/3), (10/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(10/3)) + a**(1/3)*b**2*d*x**10*gamma(10/3)*hyper((-1/3, 10/3), (13/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(13/3))","C",0
65,1,170,0,7.401552," ","integrate((b*x**3+a)**(4/3)*(d*x**3+c),x)","\frac{a^{\frac{4}{3}} c x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} + \frac{a^{\frac{4}{3}} d x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{7}{3}\right)} + \frac{\sqrt[3]{a} b c x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{7}{3}\right)} + \frac{\sqrt[3]{a} b d x^{7} \Gamma\left(\frac{7}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{7}{3} \\ \frac{10}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{10}{3}\right)}"," ",0,"a**(4/3)*c*x*gamma(1/3)*hyper((-1/3, 1/3), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(4/3)) + a**(4/3)*d*x**4*gamma(4/3)*hyper((-1/3, 4/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(7/3)) + a**(1/3)*b*c*x**4*gamma(4/3)*hyper((-1/3, 4/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(7/3)) + a**(1/3)*b*d*x**7*gamma(7/3)*hyper((-1/3, 7/3), (10/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(10/3))","C",0
66,1,82,0,4.965872," ","integrate((b*x**3+a)**(1/3)*(d*x**3+c),x)","\frac{\sqrt[3]{a} c x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} + \frac{\sqrt[3]{a} d x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{7}{3}\right)}"," ",0,"a**(1/3)*c*x*gamma(1/3)*hyper((-1/3, 1/3), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(4/3)) + a**(1/3)*d*x**4*gamma(4/3)*hyper((-1/3, 4/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(7/3))","C",0
67,1,78,0,5.072396," ","integrate((d*x**3+c)/(b*x**3+a)**(2/3),x)","\frac{c x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{2}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{2}{3}} \Gamma\left(\frac{4}{3}\right)} + \frac{d x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{2}{3}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{2}{3}} \Gamma\left(\frac{7}{3}\right)}"," ",0,"c*x*gamma(1/3)*hyper((1/3, 2/3), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(2/3)*gamma(4/3)) + d*x**4*gamma(4/3)*hyper((2/3, 4/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(2/3)*gamma(7/3))","C",0
68,1,78,0,16.363486," ","integrate((d*x**3+c)/(b*x**3+a)**(5/3),x)","\frac{c x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{5}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{5}{3}} \Gamma\left(\frac{4}{3}\right)} + \frac{d x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{4}{3}, \frac{5}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{5}{3}} \Gamma\left(\frac{7}{3}\right)}"," ",0,"c*x*gamma(1/3)*hyper((1/3, 5/3), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(5/3)*gamma(4/3)) + d*x**4*gamma(4/3)*hyper((4/3, 5/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(5/3)*gamma(7/3))","C",0
69,1,78,0,117.701477," ","integrate((d*x**3+c)/(b*x**3+a)**(8/3),x)","\frac{c x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{8}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{8}{3}} \Gamma\left(\frac{4}{3}\right)} + \frac{d x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{4}{3}, \frac{8}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{8}{3}} \Gamma\left(\frac{7}{3}\right)}"," ",0,"c*x*gamma(1/3)*hyper((1/3, 8/3), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(8/3)*gamma(4/3)) + d*x**4*gamma(4/3)*hyper((4/3, 8/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(8/3)*gamma(7/3))","C",0
70,1,270,0,13.130570," ","integrate((b*x**3+a)**(5/3)*(d*x**3+c)**2,x)","\frac{a^{\frac{5}{3}} c^{2} x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} + \frac{2 a^{\frac{5}{3}} c d x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{7}{3}\right)} + \frac{a^{\frac{5}{3}} d^{2} x^{7} \Gamma\left(\frac{7}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{7}{3} \\ \frac{10}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{10}{3}\right)} + \frac{a^{\frac{2}{3}} b c^{2} x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{7}{3}\right)} + \frac{2 a^{\frac{2}{3}} b c d x^{7} \Gamma\left(\frac{7}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{7}{3} \\ \frac{10}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{10}{3}\right)} + \frac{a^{\frac{2}{3}} b d^{2} x^{10} \Gamma\left(\frac{10}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{10}{3} \\ \frac{13}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{13}{3}\right)}"," ",0,"a**(5/3)*c**2*x*gamma(1/3)*hyper((-2/3, 1/3), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(4/3)) + 2*a**(5/3)*c*d*x**4*gamma(4/3)*hyper((-2/3, 4/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(7/3)) + a**(5/3)*d**2*x**7*gamma(7/3)*hyper((-2/3, 7/3), (10/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(10/3)) + a**(2/3)*b*c**2*x**4*gamma(4/3)*hyper((-2/3, 4/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(7/3)) + 2*a**(2/3)*b*c*d*x**7*gamma(7/3)*hyper((-2/3, 7/3), (10/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(10/3)) + a**(2/3)*b*d**2*x**10*gamma(10/3)*hyper((-2/3, 10/3), (13/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(13/3))","C",0
71,1,131,0,7.274725," ","integrate((b*x**3+a)**(2/3)*(d*x**3+c)**2,x)","\frac{a^{\frac{2}{3}} c^{2} x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} + \frac{2 a^{\frac{2}{3}} c d x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{7}{3}\right)} + \frac{a^{\frac{2}{3}} d^{2} x^{7} \Gamma\left(\frac{7}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{7}{3} \\ \frac{10}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{10}{3}\right)}"," ",0,"a**(2/3)*c**2*x*gamma(1/3)*hyper((-2/3, 1/3), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(4/3)) + 2*a**(2/3)*c*d*x**4*gamma(4/3)*hyper((-2/3, 4/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(7/3)) + a**(2/3)*d**2*x**7*gamma(7/3)*hyper((-2/3, 7/3), (10/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(10/3))","C",0
72,1,126,0,6.436612," ","integrate((d*x**3+c)**2/(b*x**3+a)**(1/3),x)","\frac{c^{2} x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt[3]{a} \Gamma\left(\frac{4}{3}\right)} + \frac{2 c d x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt[3]{a} \Gamma\left(\frac{7}{3}\right)} + \frac{d^{2} x^{7} \Gamma\left(\frac{7}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{7}{3} \\ \frac{10}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt[3]{a} \Gamma\left(\frac{10}{3}\right)}"," ",0,"c**2*x*gamma(1/3)*hyper((1/3, 1/3), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(1/3)*gamma(4/3)) + 2*c*d*x**4*gamma(4/3)*hyper((1/3, 4/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(1/3)*gamma(7/3)) + d**2*x**7*gamma(7/3)*hyper((1/3, 7/3), (10/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(1/3)*gamma(10/3))","C",0
73,0,0,0,0.000000," ","integrate((d*x**3+c)**2/(b*x**3+a)**(4/3),x)","\int \frac{\left(c + d x^{3}\right)^{2}}{\left(a + b x^{3}\right)^{\frac{4}{3}}}\, dx"," ",0,"Integral((c + d*x**3)**2/(a + b*x**3)**(4/3), x)","F",0
74,0,0,0,0.000000," ","integrate((d*x**3+c)**2/(b*x**3+a)**(7/3),x)","\int \frac{\left(c + d x^{3}\right)^{2}}{\left(a + b x^{3}\right)^{\frac{7}{3}}}\, dx"," ",0,"Integral((c + d*x**3)**2/(a + b*x**3)**(7/3), x)","F",0
75,-1,0,0,0.000000," ","integrate((d*x**3+c)**2/(b*x**3+a)**(10/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
76,-1,0,0,0.000000," ","integrate((d*x**3+c)**2/(b*x**3+a)**(13/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
77,-1,0,0,0.000000," ","integrate((d*x**3+c)**2/(b*x**3+a)**(16/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
78,-1,0,0,0.000000," ","integrate((d*x**3+c)**2/(b*x**3+a)**(19/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
79,1,418,0,12.603597," ","integrate((b*x**3+a)**(7/3)*(d*x**3+c)**2,x)","\frac{a^{\frac{7}{3}} c^{2} x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} + \frac{2 a^{\frac{7}{3}} c d x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{7}{3}\right)} + \frac{a^{\frac{7}{3}} d^{2} x^{7} \Gamma\left(\frac{7}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{7}{3} \\ \frac{10}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{10}{3}\right)} + \frac{2 a^{\frac{4}{3}} b c^{2} x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{7}{3}\right)} + \frac{4 a^{\frac{4}{3}} b c d x^{7} \Gamma\left(\frac{7}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{7}{3} \\ \frac{10}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{10}{3}\right)} + \frac{2 a^{\frac{4}{3}} b d^{2} x^{10} \Gamma\left(\frac{10}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{10}{3} \\ \frac{13}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{13}{3}\right)} + \frac{\sqrt[3]{a} b^{2} c^{2} x^{7} \Gamma\left(\frac{7}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{7}{3} \\ \frac{10}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{10}{3}\right)} + \frac{2 \sqrt[3]{a} b^{2} c d x^{10} \Gamma\left(\frac{10}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{10}{3} \\ \frac{13}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{13}{3}\right)} + \frac{\sqrt[3]{a} b^{2} d^{2} x^{13} \Gamma\left(\frac{13}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{13}{3} \\ \frac{16}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{16}{3}\right)}"," ",0,"a**(7/3)*c**2*x*gamma(1/3)*hyper((-1/3, 1/3), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(4/3)) + 2*a**(7/3)*c*d*x**4*gamma(4/3)*hyper((-1/3, 4/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(7/3)) + a**(7/3)*d**2*x**7*gamma(7/3)*hyper((-1/3, 7/3), (10/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(10/3)) + 2*a**(4/3)*b*c**2*x**4*gamma(4/3)*hyper((-1/3, 4/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(7/3)) + 4*a**(4/3)*b*c*d*x**7*gamma(7/3)*hyper((-1/3, 7/3), (10/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(10/3)) + 2*a**(4/3)*b*d**2*x**10*gamma(10/3)*hyper((-1/3, 10/3), (13/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(13/3)) + a**(1/3)*b**2*c**2*x**7*gamma(7/3)*hyper((-1/3, 7/3), (10/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(10/3)) + 2*a**(1/3)*b**2*c*d*x**10*gamma(10/3)*hyper((-1/3, 10/3), (13/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(13/3)) + a**(1/3)*b**2*d**2*x**13*gamma(13/3)*hyper((-1/3, 13/3), (16/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(16/3))","C",0
80,1,270,0,7.059174," ","integrate((b*x**3+a)**(4/3)*(d*x**3+c)**2,x)","\frac{a^{\frac{4}{3}} c^{2} x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} + \frac{2 a^{\frac{4}{3}} c d x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{7}{3}\right)} + \frac{a^{\frac{4}{3}} d^{2} x^{7} \Gamma\left(\frac{7}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{7}{3} \\ \frac{10}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{10}{3}\right)} + \frac{\sqrt[3]{a} b c^{2} x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{7}{3}\right)} + \frac{2 \sqrt[3]{a} b c d x^{7} \Gamma\left(\frac{7}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{7}{3} \\ \frac{10}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{10}{3}\right)} + \frac{\sqrt[3]{a} b d^{2} x^{10} \Gamma\left(\frac{10}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{10}{3} \\ \frac{13}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{13}{3}\right)}"," ",0,"a**(4/3)*c**2*x*gamma(1/3)*hyper((-1/3, 1/3), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(4/3)) + 2*a**(4/3)*c*d*x**4*gamma(4/3)*hyper((-1/3, 4/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(7/3)) + a**(4/3)*d**2*x**7*gamma(7/3)*hyper((-1/3, 7/3), (10/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(10/3)) + a**(1/3)*b*c**2*x**4*gamma(4/3)*hyper((-1/3, 4/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(7/3)) + 2*a**(1/3)*b*c*d*x**7*gamma(7/3)*hyper((-1/3, 7/3), (10/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(10/3)) + a**(1/3)*b*d**2*x**10*gamma(10/3)*hyper((-1/3, 10/3), (13/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(13/3))","C",0
81,1,131,0,3.938378," ","integrate((b*x**3+a)**(1/3)*(d*x**3+c)**2,x)","\frac{\sqrt[3]{a} c^{2} x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} + \frac{2 \sqrt[3]{a} c d x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{7}{3}\right)} + \frac{\sqrt[3]{a} d^{2} x^{7} \Gamma\left(\frac{7}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{7}{3} \\ \frac{10}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{10}{3}\right)}"," ",0,"a**(1/3)*c**2*x*gamma(1/3)*hyper((-1/3, 1/3), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(4/3)) + 2*a**(1/3)*c*d*x**4*gamma(4/3)*hyper((-1/3, 4/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(7/3)) + a**(1/3)*d**2*x**7*gamma(7/3)*hyper((-1/3, 7/3), (10/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(10/3))","C",0
82,1,126,0,4.270638," ","integrate((d*x**3+c)**2/(b*x**3+a)**(2/3),x)","\frac{c^{2} x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{2}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{2}{3}} \Gamma\left(\frac{4}{3}\right)} + \frac{2 c d x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{2}{3}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{2}{3}} \Gamma\left(\frac{7}{3}\right)} + \frac{d^{2} x^{7} \Gamma\left(\frac{7}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{2}{3}, \frac{7}{3} \\ \frac{10}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{2}{3}} \Gamma\left(\frac{10}{3}\right)}"," ",0,"c**2*x*gamma(1/3)*hyper((1/3, 2/3), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(2/3)*gamma(4/3)) + 2*c*d*x**4*gamma(4/3)*hyper((2/3, 4/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(2/3)*gamma(7/3)) + d**2*x**7*gamma(7/3)*hyper((2/3, 7/3), (10/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(2/3)*gamma(10/3))","C",0
83,0,0,0,0.000000," ","integrate((d*x**3+c)**2/(b*x**3+a)**(5/3),x)","\int \frac{\left(c + d x^{3}\right)^{2}}{\left(a + b x^{3}\right)^{\frac{5}{3}}}\, dx"," ",0,"Integral((c + d*x**3)**2/(a + b*x**3)**(5/3), x)","F",0
84,0,0,0,0.000000," ","integrate((d*x**3+c)**2/(b*x**3+a)**(8/3),x)","\int \frac{\left(c + d x^{3}\right)^{2}}{\left(a + b x^{3}\right)^{\frac{8}{3}}}\, dx"," ",0,"Integral((c + d*x**3)**2/(a + b*x**3)**(8/3), x)","F",0
85,-1,0,0,0.000000," ","integrate((b*x**3+a)**3/(d*x**3+c)**(13/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
86,-1,0,0,0.000000," ","integrate((b*x**3+a)**(8/3)/(d*x**3+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
87,0,0,0,0.000000," ","integrate((b*x**3+a)**(5/3)/(d*x**3+c),x)","\int \frac{\left(a + b x^{3}\right)^{\frac{5}{3}}}{c + d x^{3}}\, dx"," ",0,"Integral((a + b*x**3)**(5/3)/(c + d*x**3), x)","F",0
88,0,0,0,0.000000," ","integrate((b*x**3+a)**(2/3)/(d*x**3+c),x)","\int \frac{\left(a + b x^{3}\right)^{\frac{2}{3}}}{c + d x^{3}}\, dx"," ",0,"Integral((a + b*x**3)**(2/3)/(c + d*x**3), x)","F",0
89,0,0,0,0.000000," ","integrate(1/(b*x**3+a)**(1/3)/(d*x**3+c),x)","\int \frac{1}{\sqrt[3]{a + b x^{3}} \left(c + d x^{3}\right)}\, dx"," ",0,"Integral(1/((a + b*x**3)**(1/3)*(c + d*x**3)), x)","F",0
90,0,0,0,0.000000," ","integrate(1/(b*x**3+a)**(4/3)/(d*x**3+c),x)","\int \frac{1}{\left(a + b x^{3}\right)^{\frac{4}{3}} \left(c + d x^{3}\right)}\, dx"," ",0,"Integral(1/((a + b*x**3)**(4/3)*(c + d*x**3)), x)","F",0
91,0,0,0,0.000000," ","integrate(1/(b*x**3+a)**(7/3)/(d*x**3+c),x)","\int \frac{1}{\left(a + b x^{3}\right)^{\frac{7}{3}} \left(c + d x^{3}\right)}\, dx"," ",0,"Integral(1/((a + b*x**3)**(7/3)*(c + d*x**3)), x)","F",0
92,0,0,0,0.000000," ","integrate(1/(b*x**3+a)**(10/3)/(d*x**3+c),x)","\int \frac{1}{\left(a + b x^{3}\right)^{\frac{10}{3}} \left(c + d x^{3}\right)}\, dx"," ",0,"Integral(1/((a + b*x**3)**(10/3)*(c + d*x**3)), x)","F",0
93,0,0,0,0.000000," ","integrate((b*x**3+a)**(4/3)/(d*x**3+c),x)","\int \frac{\left(a + b x^{3}\right)^{\frac{4}{3}}}{c + d x^{3}}\, dx"," ",0,"Integral((a + b*x**3)**(4/3)/(c + d*x**3), x)","F",0
94,0,0,0,0.000000," ","integrate((b*x**3+a)**(1/3)/(d*x**3+c),x)","\int \frac{\sqrt[3]{a + b x^{3}}}{c + d x^{3}}\, dx"," ",0,"Integral((a + b*x**3)**(1/3)/(c + d*x**3), x)","F",0
95,0,0,0,0.000000," ","integrate(1/(b*x**3+a)**(2/3)/(d*x**3+c),x)","\int \frac{1}{\left(a + b x^{3}\right)^{\frac{2}{3}} \left(c + d x^{3}\right)}\, dx"," ",0,"Integral(1/((a + b*x**3)**(2/3)*(c + d*x**3)), x)","F",0
96,0,0,0,0.000000," ","integrate(1/(b*x**3+a)**(5/3)/(d*x**3+c),x)","\int \frac{1}{\left(a + b x^{3}\right)^{\frac{5}{3}} \left(c + d x^{3}\right)}\, dx"," ",0,"Integral(1/((a + b*x**3)**(5/3)*(c + d*x**3)), x)","F",0
97,0,0,0,0.000000," ","integrate(1/(b*x**3+a)**(8/3)/(d*x**3+c),x)","\int \frac{1}{\left(a + b x^{3}\right)^{\frac{8}{3}} \left(c + d x^{3}\right)}\, dx"," ",0,"Integral(1/((a + b*x**3)**(8/3)*(c + d*x**3)), x)","F",0
98,-1,0,0,0.000000," ","integrate((b*x**3+a)**(8/3)/(d*x**3+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
99,-1,0,0,0.000000," ","integrate((b*x**3+a)**(5/3)/(d*x**3+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
100,0,0,0,0.000000," ","integrate((b*x**3+a)**(2/3)/(d*x**3+c)**2,x)","\int \frac{\left(a + b x^{3}\right)^{\frac{2}{3}}}{\left(c + d x^{3}\right)^{2}}\, dx"," ",0,"Integral((a + b*x**3)**(2/3)/(c + d*x**3)**2, x)","F",0
101,0,0,0,0.000000," ","integrate(1/(b*x**3+a)**(1/3)/(d*x**3+c)**2,x)","\int \frac{1}{\sqrt[3]{a + b x^{3}} \left(c + d x^{3}\right)^{2}}\, dx"," ",0,"Integral(1/((a + b*x**3)**(1/3)*(c + d*x**3)**2), x)","F",0
102,0,0,0,0.000000," ","integrate(1/(b*x**3+a)**(4/3)/(d*x**3+c)**2,x)","\int \frac{1}{\left(a + b x^{3}\right)^{\frac{4}{3}} \left(c + d x^{3}\right)^{2}}\, dx"," ",0,"Integral(1/((a + b*x**3)**(4/3)*(c + d*x**3)**2), x)","F",0
103,0,0,0,0.000000," ","integrate(1/(b*x**3+a)**(7/3)/(d*x**3+c)**2,x)","\int \frac{1}{\left(a + b x^{3}\right)^{\frac{7}{3}} \left(c + d x^{3}\right)^{2}}\, dx"," ",0,"Integral(1/((a + b*x**3)**(7/3)*(c + d*x**3)**2), x)","F",0
104,0,0,0,0.000000," ","integrate((b*x**3+a)**(4/3)/(d*x**3+c)**2,x)","\int \frac{\left(a + b x^{3}\right)^{\frac{4}{3}}}{\left(c + d x^{3}\right)^{2}}\, dx"," ",0,"Integral((a + b*x**3)**(4/3)/(c + d*x**3)**2, x)","F",0
105,0,0,0,0.000000," ","integrate((b*x**3+a)**(1/3)/(d*x**3+c)**2,x)","\int \frac{\sqrt[3]{a + b x^{3}}}{\left(c + d x^{3}\right)^{2}}\, dx"," ",0,"Integral((a + b*x**3)**(1/3)/(c + d*x**3)**2, x)","F",0
106,0,0,0,0.000000," ","integrate(1/(b*x**3+a)**(2/3)/(d*x**3+c)**2,x)","\int \frac{1}{\left(a + b x^{3}\right)^{\frac{2}{3}} \left(c + d x^{3}\right)^{2}}\, dx"," ",0,"Integral(1/((a + b*x**3)**(2/3)*(c + d*x**3)**2), x)","F",0
107,0,0,0,0.000000," ","integrate(1/(b*x**3+a)**(5/3)/(d*x**3+c)**2,x)","\int \frac{1}{\left(a + b x^{3}\right)^{\frac{5}{3}} \left(c + d x^{3}\right)^{2}}\, dx"," ",0,"Integral(1/((a + b*x**3)**(5/3)*(c + d*x**3)**2), x)","F",0
108,0,0,0,0.000000," ","integrate(1/(b*x**3+a)**(8/3)/(d*x**3+c)**2,x)","\int \frac{1}{\left(a + b x^{3}\right)^{\frac{8}{3}} \left(c + d x^{3}\right)^{2}}\, dx"," ",0,"Integral(1/((a + b*x**3)**(8/3)*(c + d*x**3)**2), x)","F",0
109,-1,0,0,0.000000," ","integrate((b*x**3+a)**(14/3)/(d*x**3+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
110,-1,0,0,0.000000," ","integrate((b*x**3+a)**(11/3)/(d*x**3+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
111,-1,0,0,0.000000," ","integrate((b*x**3+a)**(8/3)/(d*x**3+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
112,-1,0,0,0.000000," ","integrate((b*x**3+a)**(5/3)/(d*x**3+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
113,-1,0,0,0.000000," ","integrate((b*x**3+a)**(2/3)/(d*x**3+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
114,0,0,0,0.000000," ","integrate(1/(b*x**3+a)**(1/3)/(d*x**3+c)**3,x)","\int \frac{1}{\sqrt[3]{a + b x^{3}} \left(c + d x^{3}\right)^{3}}\, dx"," ",0,"Integral(1/((a + b*x**3)**(1/3)*(c + d*x**3)**3), x)","F",0
115,-1,0,0,0.000000," ","integrate(1/(b*x**3+a)**(4/3)/(d*x**3+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
116,-1,0,0,0.000000," ","integrate(1/(b*x**3+a)**(7/3)/(d*x**3+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
117,-1,0,0,0.000000," ","integrate((b*x**3+a)**(4/3)/(d*x**3+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
118,-1,0,0,0.000000," ","integrate((b*x**3+a)**(1/3)/(d*x**3+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
119,0,0,0,0.000000," ","integrate(1/(b*x**3+a)**(2/3)/(d*x**3+c)**3,x)","\int \frac{1}{\left(a + b x^{3}\right)^{\frac{2}{3}} \left(c + d x^{3}\right)^{3}}\, dx"," ",0,"Integral(1/((a + b*x**3)**(2/3)*(c + d*x**3)**3), x)","F",0
120,-1,0,0,0.000000," ","integrate(1/(b*x**3+a)**(5/3)/(d*x**3+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
121,-1,0,0,0.000000," ","integrate(1/(b*x**3+a)**(8/3)/(d*x**3+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
122,-1,0,0,0.000000," ","integrate((b*x**3+a)**(7/4)/(d*x**3+c)**(37/12),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
123,-1,0,0,0.000000," ","integrate((b*x**3+a)**(5/4)/(d*x**3+c)**(31/12),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
124,-1,0,0,0.000000," ","integrate((b*x**3+a)**(3/4)/(d*x**3+c)**(25/12),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
125,-1,0,0,0.000000," ","integrate((b*x**3+a)**(1/4)/(d*x**3+c)**(19/12),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
126,0,0,0,0.000000," ","integrate(1/(b*x**3+a)**(1/4)/(d*x**3+c)**(13/12),x)","\int \frac{1}{\sqrt[4]{a + b x^{3}} \left(c + d x^{3}\right)^{\frac{13}{12}}}\, dx"," ",0,"Integral(1/((a + b*x**3)**(1/4)*(c + d*x**3)**(13/12)), x)","F",0
127,0,0,0,0.000000," ","integrate(1/(b*x**3+a)**(3/4)/(d*x**3+c)**(7/12),x)","\int \frac{1}{\left(a + b x^{3}\right)^{\frac{3}{4}} \left(c + d x^{3}\right)^{\frac{7}{12}}}\, dx"," ",0,"Integral(1/((a + b*x**3)**(3/4)*(c + d*x**3)**(7/12)), x)","F",0
128,0,0,0,0.000000," ","integrate(1/(b*x**3+a)**(5/4)/(d*x**3+c)**(1/12),x)","\int \frac{1}{\left(a + b x^{3}\right)^{\frac{5}{4}} \sqrt[12]{c + d x^{3}}}\, dx"," ",0,"Integral(1/((a + b*x**3)**(5/4)*(c + d*x**3)**(1/12)), x)","F",0
129,0,0,0,0.000000," ","integrate((d*x**3+c)**(5/12)/(b*x**3+a)**(7/4),x)","\int \frac{\left(c + d x^{3}\right)^{\frac{5}{12}}}{\left(a + b x^{3}\right)^{\frac{7}{4}}}\, dx"," ",0,"Integral((c + d*x**3)**(5/12)/(a + b*x**3)**(7/4), x)","F",0
130,-1,0,0,0.000000," ","integrate((d*x**3+c)**(11/12)/(b*x**3+a)**(9/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
131,-1,0,0,0.000000," ","integrate((d*x**3+c)**(17/12)/(b*x**3+a)**(11/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
132,-1,0,0,0.000000," ","integrate((d*x**3+c)**(23/12)/(b*x**3+a)**(13/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
133,-1,0,0,0.000000," ","integrate((b*x**3+a)**m*(d*x**3+c)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
134,-1,0,0,0.000000," ","integrate((b*x**3+a)**2*(d*x**3+c)**q,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
135,1,75,0,82.863657," ","integrate((b*x**3+a)*(d*x**3+c)**q,x)","\frac{a c^{q} x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, - q \\ \frac{4}{3} \end{matrix}\middle| {\frac{d x^{3} e^{i \pi}}{c}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} + \frac{b c^{q} x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{4}{3}, - q \\ \frac{7}{3} \end{matrix}\middle| {\frac{d x^{3} e^{i \pi}}{c}} \right)}}{3 \Gamma\left(\frac{7}{3}\right)}"," ",0,"a*c**q*x*gamma(1/3)*hyper((1/3, -q), (4/3,), d*x**3*exp_polar(I*pi)/c)/(3*gamma(4/3)) + b*c**q*x**4*gamma(4/3)*hyper((4/3, -q), (7/3,), d*x**3*exp_polar(I*pi)/c)/(3*gamma(7/3))","C",0
136,-1,0,0,0.000000," ","integrate((d*x**3+c)**q/(b*x**3+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
137,-1,0,0,0.000000," ","integrate((d*x**3+c)**q/(b*x**3+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
138,-1,0,0,0.000000," ","integrate((b*x**3+a)**m*(d*x**3+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
139,-1,0,0,0.000000," ","integrate((b*x**3+a)**m*(d*x**3+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
140,1,75,0,100.309736," ","integrate((b*x**3+a)**m*(d*x**3+c),x)","\frac{a^{m} c x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, - m \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} + \frac{a^{m} d x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{4}{3}, - m \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{7}{3}\right)}"," ",0,"a**m*c*x*gamma(1/3)*hyper((1/3, -m), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(4/3)) + a**m*d*x**4*gamma(4/3)*hyper((4/3, -m), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(7/3))","C",0
141,1,34,0,15.563455," ","integrate((b*x**3+a)**m,x)","\frac{a^{m} x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, - m \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)}"," ",0,"a**m*x*gamma(1/3)*hyper((1/3, -m), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(4/3))","C",0
142,-1,0,0,0.000000," ","integrate((b*x**3+a)**m/(d*x**3+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
143,-1,0,0,0.000000," ","integrate((b*x**3+a)**m/(d*x**3+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
144,-1,0,0,0.000000," ","integrate((b*x**3+a)**m/(d*x**3+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
145,-1,0,0,0.000000," ","integrate((b*x**3+a)**(-1-b*c/(-3*a*d+3*b*c))*(d*x**3+c)**(-1+a*d/(-3*a*d+3*b*c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
146,1,107,0,0.090016," ","integrate((b*x**4+a)*(d*x**4+c)**4,x)","a c^{4} x + \frac{b d^{4} x^{21}}{21} + x^{17} \left(\frac{a d^{4}}{17} + \frac{4 b c d^{3}}{17}\right) + x^{13} \left(\frac{4 a c d^{3}}{13} + \frac{6 b c^{2} d^{2}}{13}\right) + x^{9} \left(\frac{2 a c^{2} d^{2}}{3} + \frac{4 b c^{3} d}{9}\right) + x^{5} \left(\frac{4 a c^{3} d}{5} + \frac{b c^{4}}{5}\right)"," ",0,"a*c**4*x + b*d**4*x**21/21 + x**17*(a*d**4/17 + 4*b*c*d**3/17) + x**13*(4*a*c*d**3/13 + 6*b*c**2*d**2/13) + x**9*(2*a*c**2*d**2/3 + 4*b*c**3*d/9) + x**5*(4*a*c**3*d/5 + b*c**4/5)","A",0
147,1,76,0,0.084495," ","integrate((b*x**4+a)*(d*x**4+c)**3,x)","a c^{3} x + \frac{b d^{3} x^{17}}{17} + x^{13} \left(\frac{a d^{3}}{13} + \frac{3 b c d^{2}}{13}\right) + x^{9} \left(\frac{a c d^{2}}{3} + \frac{b c^{2} d}{3}\right) + x^{5} \left(\frac{3 a c^{2} d}{5} + \frac{b c^{3}}{5}\right)"," ",0,"a*c**3*x + b*d**3*x**17/17 + x**13*(a*d**3/13 + 3*b*c*d**2/13) + x**9*(a*c*d**2/3 + b*c**2*d/3) + x**5*(3*a*c**2*d/5 + b*c**3/5)","A",0
148,1,53,0,0.077677," ","integrate((b*x**4+a)*(d*x**4+c)**2,x)","a c^{2} x + \frac{b d^{2} x^{13}}{13} + x^{9} \left(\frac{a d^{2}}{9} + \frac{2 b c d}{9}\right) + x^{5} \left(\frac{2 a c d}{5} + \frac{b c^{2}}{5}\right)"," ",0,"a*c**2*x + b*d**2*x**13/13 + x**9*(a*d**2/9 + 2*b*c*d/9) + x**5*(2*a*c*d/5 + b*c**2/5)","A",0
149,1,26,0,0.064557," ","integrate((b*x**4+a)*(d*x**4+c),x)","a c x + \frac{b d x^{9}}{9} + x^{5} \left(\frac{a d}{5} + \frac{b c}{5}\right)"," ",0,"a*c*x + b*d*x**9/9 + x**5*(a*d/5 + b*c/5)","A",0
150,1,87,0,0.659348," ","integrate((b*x**4+a)/(d*x**4+c),x)","\frac{b x}{d} + \operatorname{RootSum} {\left(256 t^{4} c^{3} d^{5} + a^{4} d^{4} - 4 a^{3} b c d^{3} + 6 a^{2} b^{2} c^{2} d^{2} - 4 a b^{3} c^{3} d + b^{4} c^{4}, \left( t \mapsto t \log{\left(\frac{4 t c d}{a d - b c} + x \right)} \right)\right)}"," ",0,"b*x/d + RootSum(256*_t**4*c**3*d**5 + a**4*d**4 - 4*a**3*b*c*d**3 + 6*a**2*b**2*c**2*d**2 - 4*a*b**3*c**3*d + b**4*c**4, Lambda(_t, _t*log(4*_t*c*d/(a*d - b*c) + x)))","A",0
151,1,112,0,0.848779," ","integrate((b*x**4+a)/(d*x**4+c)**2,x)","\frac{x \left(a d - b c\right)}{4 c^{2} d + 4 c d^{2} x^{4}} + \operatorname{RootSum} {\left(65536 t^{4} c^{7} d^{5} + 81 a^{4} d^{4} + 108 a^{3} b c d^{3} + 54 a^{2} b^{2} c^{2} d^{2} + 12 a b^{3} c^{3} d + b^{4} c^{4}, \left( t \mapsto t \log{\left(\frac{16 t c^{2} d}{3 a d + b c} + x \right)} \right)\right)}"," ",0,"x*(a*d - b*c)/(4*c**2*d + 4*c*d**2*x**4) + RootSum(65536*_t**4*c**7*d**5 + 81*a**4*d**4 + 108*a**3*b*c*d**3 + 54*a**2*b**2*c**2*d**2 + 12*a*b**3*c**3*d + b**4*c**4, Lambda(_t, _t*log(16*_t*c**2*d/(3*a*d + b*c) + x)))","A",0
152,1,151,0,1.030859," ","integrate((b*x**4+a)/(d*x**4+c)**3,x)","\frac{x^{5} \left(7 a d^{2} + b c d\right) + x \left(11 a c d - 3 b c^{2}\right)}{32 c^{4} d + 64 c^{3} d^{2} x^{4} + 32 c^{2} d^{3} x^{8}} + \operatorname{RootSum} {\left(268435456 t^{4} c^{11} d^{5} + 194481 a^{4} d^{4} + 111132 a^{3} b c d^{3} + 23814 a^{2} b^{2} c^{2} d^{2} + 2268 a b^{3} c^{3} d + 81 b^{4} c^{4}, \left( t \mapsto t \log{\left(\frac{128 t c^{3} d}{21 a d + 3 b c} + x \right)} \right)\right)}"," ",0,"(x**5*(7*a*d**2 + b*c*d) + x*(11*a*c*d - 3*b*c**2))/(32*c**4*d + 64*c**3*d**2*x**4 + 32*c**2*d**3*x**8) + RootSum(268435456*_t**4*c**11*d**5 + 194481*a**4*d**4 + 111132*a**3*b*c*d**3 + 23814*a**2*b**2*c**2*d**2 + 2268*a*b**3*c**3*d + 81*b**4*c**4, Lambda(_t, _t*log(128*_t*c**3*d/(21*a*d + 3*b*c) + x)))","A",0
153,1,185,0,0.117462," ","integrate((b*x**4+a)**2*(d*x**4+c)**4,x)","a^{2} c^{4} x + \frac{b^{2} d^{4} x^{25}}{25} + x^{21} \left(\frac{2 a b d^{4}}{21} + \frac{4 b^{2} c d^{3}}{21}\right) + x^{17} \left(\frac{a^{2} d^{4}}{17} + \frac{8 a b c d^{3}}{17} + \frac{6 b^{2} c^{2} d^{2}}{17}\right) + x^{13} \left(\frac{4 a^{2} c d^{3}}{13} + \frac{12 a b c^{2} d^{2}}{13} + \frac{4 b^{2} c^{3} d}{13}\right) + x^{9} \left(\frac{2 a^{2} c^{2} d^{2}}{3} + \frac{8 a b c^{3} d}{9} + \frac{b^{2} c^{4}}{9}\right) + x^{5} \left(\frac{4 a^{2} c^{3} d}{5} + \frac{2 a b c^{4}}{5}\right)"," ",0,"a**2*c**4*x + b**2*d**4*x**25/25 + x**21*(2*a*b*d**4/21 + 4*b**2*c*d**3/21) + x**17*(a**2*d**4/17 + 8*a*b*c*d**3/17 + 6*b**2*c**2*d**2/17) + x**13*(4*a**2*c*d**3/13 + 12*a*b*c**2*d**2/13 + 4*b**2*c**3*d/13) + x**9*(2*a**2*c**2*d**2/3 + 8*a*b*c**3*d/9 + b**2*c**4/9) + x**5*(4*a**2*c**3*d/5 + 2*a*b*c**4/5)","A",0
154,1,139,0,0.098268," ","integrate((b*x**4+a)**2*(d*x**4+c)**3,x)","a^{2} c^{3} x + \frac{b^{2} d^{3} x^{21}}{21} + x^{17} \left(\frac{2 a b d^{3}}{17} + \frac{3 b^{2} c d^{2}}{17}\right) + x^{13} \left(\frac{a^{2} d^{3}}{13} + \frac{6 a b c d^{2}}{13} + \frac{3 b^{2} c^{2} d}{13}\right) + x^{9} \left(\frac{a^{2} c d^{2}}{3} + \frac{2 a b c^{2} d}{3} + \frac{b^{2} c^{3}}{9}\right) + x^{5} \left(\frac{3 a^{2} c^{2} d}{5} + \frac{2 a b c^{3}}{5}\right)"," ",0,"a**2*c**3*x + b**2*d**3*x**21/21 + x**17*(2*a*b*d**3/17 + 3*b**2*c*d**2/17) + x**13*(a**2*d**3/13 + 6*a*b*c*d**2/13 + 3*b**2*c**2*d/13) + x**9*(a**2*c*d**2/3 + 2*a*b*c**2*d/3 + b**2*c**3/9) + x**5*(3*a**2*c**2*d/5 + 2*a*b*c**3/5)","A",0
155,1,97,0,0.089831," ","integrate((b*x**4+a)**2*(d*x**4+c)**2,x)","a^{2} c^{2} x + \frac{b^{2} d^{2} x^{17}}{17} + x^{13} \left(\frac{2 a b d^{2}}{13} + \frac{2 b^{2} c d}{13}\right) + x^{9} \left(\frac{a^{2} d^{2}}{9} + \frac{4 a b c d}{9} + \frac{b^{2} c^{2}}{9}\right) + x^{5} \left(\frac{2 a^{2} c d}{5} + \frac{2 a b c^{2}}{5}\right)"," ",0,"a**2*c**2*x + b**2*d**2*x**17/17 + x**13*(2*a*b*d**2/13 + 2*b**2*c*d/13) + x**9*(a**2*d**2/9 + 4*a*b*c*d/9 + b**2*c**2/9) + x**5*(2*a**2*c*d/5 + 2*a*b*c**2/5)","A",0
156,1,53,0,0.080016," ","integrate((b*x**4+a)**2*(d*x**4+c),x)","a^{2} c x + \frac{b^{2} d x^{13}}{13} + x^{9} \left(\frac{2 a b d}{9} + \frac{b^{2} c}{9}\right) + x^{5} \left(\frac{a^{2} d}{5} + \frac{2 a b c}{5}\right)"," ",0,"a**2*c*x + b**2*d*x**13/13 + x**9*(2*a*b*d/9 + b**2*c/9) + x**5*(a**2*d/5 + 2*a*b*c/5)","A",0
157,1,187,0,1.118601," ","integrate((b*x**4+a)**2/(d*x**4+c),x)","\frac{b^{2} x^{5}}{5 d} + x \left(\frac{2 a b}{d} - \frac{b^{2} c}{d^{2}}\right) + \operatorname{RootSum} {\left(256 t^{4} c^{3} d^{9} + a^{8} d^{8} - 8 a^{7} b c d^{7} + 28 a^{6} b^{2} c^{2} d^{6} - 56 a^{5} b^{3} c^{3} d^{5} + 70 a^{4} b^{4} c^{4} d^{4} - 56 a^{3} b^{5} c^{5} d^{3} + 28 a^{2} b^{6} c^{6} d^{2} - 8 a b^{7} c^{7} d + b^{8} c^{8}, \left( t \mapsto t \log{\left(\frac{4 t c d^{2}}{a^{2} d^{2} - 2 a b c d + b^{2} c^{2}} + x \right)} \right)\right)}"," ",0,"b**2*x**5/(5*d) + x*(2*a*b/d - b**2*c/d**2) + RootSum(256*_t**4*c**3*d**9 + a**8*d**8 - 8*a**7*b*c*d**7 + 28*a**6*b**2*c**2*d**6 - 56*a**5*b**3*c**3*d**5 + 70*a**4*b**4*c**4*d**4 - 56*a**3*b**5*c**5*d**3 + 28*a**2*b**6*c**6*d**2 - 8*a*b**7*c**7*d + b**8*c**8, Lambda(_t, _t*log(4*_t*c*d**2/(a**2*d**2 - 2*a*b*c*d + b**2*c**2) + x)))","A",0
158,1,219,0,1.979131," ","integrate((b*x**4+a)**2/(d*x**4+c)**2,x)","\frac{b^{2} x}{d^{2}} + \frac{x \left(a^{2} d^{2} - 2 a b c d + b^{2} c^{2}\right)}{4 c^{2} d^{2} + 4 c d^{3} x^{4}} + \operatorname{RootSum} {\left(65536 t^{4} c^{7} d^{9} + 81 a^{8} d^{8} + 216 a^{7} b c d^{7} - 324 a^{6} b^{2} c^{2} d^{6} - 984 a^{5} b^{3} c^{3} d^{5} + 646 a^{4} b^{4} c^{4} d^{4} + 1640 a^{3} b^{5} c^{5} d^{3} - 900 a^{2} b^{6} c^{6} d^{2} - 1000 a b^{7} c^{7} d + 625 b^{8} c^{8}, \left( t \mapsto t \log{\left(\frac{16 t c^{2} d^{2}}{3 a^{2} d^{2} + 2 a b c d - 5 b^{2} c^{2}} + x \right)} \right)\right)}"," ",0,"b**2*x/d**2 + x*(a**2*d**2 - 2*a*b*c*d + b**2*c**2)/(4*c**2*d**2 + 4*c*d**3*x**4) + RootSum(65536*_t**4*c**7*d**9 + 81*a**8*d**8 + 216*a**7*b*c*d**7 - 324*a**6*b**2*c**2*d**6 - 984*a**5*b**3*c**3*d**5 + 646*a**4*b**4*c**4*d**4 + 1640*a**3*b**5*c**5*d**3 - 900*a**2*b**6*c**6*d**2 - 1000*a*b**7*c**7*d + 625*b**8*c**8, Lambda(_t, _t*log(16*_t*c**2*d**2/(3*a**2*d**2 + 2*a*b*c*d - 5*b**2*c**2) + x)))","A",0
159,1,264,0,5.849724," ","integrate((b*x**4+a)**2/(d*x**4+c)**3,x)","\frac{x^{5} \left(7 a^{2} d^{3} + 2 a b c d^{2} - 9 b^{2} c^{2} d\right) + x \left(11 a^{2} c d^{2} - 6 a b c^{2} d - 5 b^{2} c^{3}\right)}{32 c^{4} d^{2} + 64 c^{3} d^{3} x^{4} + 32 c^{2} d^{4} x^{8}} + \operatorname{RootSum} {\left(268435456 t^{4} c^{11} d^{9} + 194481 a^{8} d^{8} + 222264 a^{7} b c d^{7} + 280476 a^{6} b^{2} c^{2} d^{6} + 176904 a^{5} b^{3} c^{3} d^{5} + 112806 a^{4} b^{4} c^{4} d^{4} + 42120 a^{3} b^{5} c^{5} d^{3} + 15900 a^{2} b^{6} c^{6} d^{2} + 3000 a b^{7} c^{7} d + 625 b^{8} c^{8}, \left( t \mapsto t \log{\left(\frac{128 t c^{3} d^{2}}{21 a^{2} d^{2} + 6 a b c d + 5 b^{2} c^{2}} + x \right)} \right)\right)}"," ",0,"(x**5*(7*a**2*d**3 + 2*a*b*c*d**2 - 9*b**2*c**2*d) + x*(11*a**2*c*d**2 - 6*a*b*c**2*d - 5*b**2*c**3))/(32*c**4*d**2 + 64*c**3*d**3*x**4 + 32*c**2*d**4*x**8) + RootSum(268435456*_t**4*c**11*d**9 + 194481*a**8*d**8 + 222264*a**7*b*c*d**7 + 280476*a**6*b**2*c**2*d**6 + 176904*a**5*b**3*c**3*d**5 + 112806*a**4*b**4*c**4*d**4 + 42120*a**3*b**5*c**5*d**3 + 15900*a**2*b**6*c**6*d**2 + 3000*a*b**7*c**7*d + 625*b**8*c**8, Lambda(_t, _t*log(128*_t*c**3*d**2/(21*a**2*d**2 + 6*a*b*c*d + 5*b**2*c**2) + x)))","A",0
160,1,435,0,3.585040," ","integrate((d*x**4+c)**4/(b*x**4+a),x)","x^{9} \left(- \frac{a d^{4}}{9 b^{2}} + \frac{4 c d^{3}}{9 b}\right) + x^{5} \left(\frac{a^{2} d^{4}}{5 b^{3}} - \frac{4 a c d^{3}}{5 b^{2}} + \frac{6 c^{2} d^{2}}{5 b}\right) + x \left(- \frac{a^{3} d^{4}}{b^{4}} + \frac{4 a^{2} c d^{3}}{b^{3}} - \frac{6 a c^{2} d^{2}}{b^{2}} + \frac{4 c^{3} d}{b}\right) + \operatorname{RootSum} {\left(256 t^{4} a^{3} b^{17} + a^{16} d^{16} - 16 a^{15} b c d^{15} + 120 a^{14} b^{2} c^{2} d^{14} - 560 a^{13} b^{3} c^{3} d^{13} + 1820 a^{12} b^{4} c^{4} d^{12} - 4368 a^{11} b^{5} c^{5} d^{11} + 8008 a^{10} b^{6} c^{6} d^{10} - 11440 a^{9} b^{7} c^{7} d^{9} + 12870 a^{8} b^{8} c^{8} d^{8} - 11440 a^{7} b^{9} c^{9} d^{7} + 8008 a^{6} b^{10} c^{10} d^{6} - 4368 a^{5} b^{11} c^{11} d^{5} + 1820 a^{4} b^{12} c^{12} d^{4} - 560 a^{3} b^{13} c^{13} d^{3} + 120 a^{2} b^{14} c^{14} d^{2} - 16 a b^{15} c^{15} d + b^{16} c^{16}, \left( t \mapsto t \log{\left(\frac{4 t a b^{4}}{a^{4} d^{4} - 4 a^{3} b c d^{3} + 6 a^{2} b^{2} c^{2} d^{2} - 4 a b^{3} c^{3} d + b^{4} c^{4}} + x \right)} \right)\right)} + \frac{d^{4} x^{13}}{13 b}"," ",0,"x**9*(-a*d**4/(9*b**2) + 4*c*d**3/(9*b)) + x**5*(a**2*d**4/(5*b**3) - 4*a*c*d**3/(5*b**2) + 6*c**2*d**2/(5*b)) + x*(-a**3*d**4/b**4 + 4*a**2*c*d**3/b**3 - 6*a*c**2*d**2/b**2 + 4*c**3*d/b) + RootSum(256*_t**4*a**3*b**17 + a**16*d**16 - 16*a**15*b*c*d**15 + 120*a**14*b**2*c**2*d**14 - 560*a**13*b**3*c**3*d**13 + 1820*a**12*b**4*c**4*d**12 - 4368*a**11*b**5*c**5*d**11 + 8008*a**10*b**6*c**6*d**10 - 11440*a**9*b**7*c**7*d**9 + 12870*a**8*b**8*c**8*d**8 - 11440*a**7*b**9*c**9*d**7 + 8008*a**6*b**10*c**10*d**6 - 4368*a**5*b**11*c**11*d**5 + 1820*a**4*b**12*c**12*d**4 - 560*a**3*b**13*c**13*d**3 + 120*a**2*b**14*c**14*d**2 - 16*a*b**15*c**15*d + b**16*c**16, Lambda(_t, _t*log(4*_t*a*b**4/(a**4*d**4 - 4*a**3*b*c*d**3 + 6*a**2*b**2*c**2*d**2 - 4*a*b**3*c**3*d + b**4*c**4) + x))) + d**4*x**13/(13*b)","A",0
161,1,303,0,1.695568," ","integrate((d*x**4+c)**3/(b*x**4+a),x)","x^{5} \left(- \frac{a d^{3}}{5 b^{2}} + \frac{3 c d^{2}}{5 b}\right) + x \left(\frac{a^{2} d^{3}}{b^{3}} - \frac{3 a c d^{2}}{b^{2}} + \frac{3 c^{2} d}{b}\right) + \operatorname{RootSum} {\left(256 t^{4} a^{3} b^{13} + a^{12} d^{12} - 12 a^{11} b c d^{11} + 66 a^{10} b^{2} c^{2} d^{10} - 220 a^{9} b^{3} c^{3} d^{9} + 495 a^{8} b^{4} c^{4} d^{8} - 792 a^{7} b^{5} c^{5} d^{7} + 924 a^{6} b^{6} c^{6} d^{6} - 792 a^{5} b^{7} c^{7} d^{5} + 495 a^{4} b^{8} c^{8} d^{4} - 220 a^{3} b^{9} c^{9} d^{3} + 66 a^{2} b^{10} c^{10} d^{2} - 12 a b^{11} c^{11} d + b^{12} c^{12}, \left( t \mapsto t \log{\left(- \frac{4 t a b^{3}}{a^{3} d^{3} - 3 a^{2} b c d^{2} + 3 a b^{2} c^{2} d - b^{3} c^{3}} + x \right)} \right)\right)} + \frac{d^{3} x^{9}}{9 b}"," ",0,"x**5*(-a*d**3/(5*b**2) + 3*c*d**2/(5*b)) + x*(a**2*d**3/b**3 - 3*a*c*d**2/b**2 + 3*c**2*d/b) + RootSum(256*_t**4*a**3*b**13 + a**12*d**12 - 12*a**11*b*c*d**11 + 66*a**10*b**2*c**2*d**10 - 220*a**9*b**3*c**3*d**9 + 495*a**8*b**4*c**4*d**8 - 792*a**7*b**5*c**5*d**7 + 924*a**6*b**6*c**6*d**6 - 792*a**5*b**7*c**7*d**5 + 495*a**4*b**8*c**8*d**4 - 220*a**3*b**9*c**9*d**3 + 66*a**2*b**10*c**10*d**2 - 12*a*b**11*c**11*d + b**12*c**12, Lambda(_t, _t*log(-4*_t*a*b**3/(a**3*d**3 - 3*a**2*b*c*d**2 + 3*a*b**2*c**2*d - b**3*c**3) + x))) + d**3*x**9/(9*b)","A",0
162,1,187,0,1.083807," ","integrate((d*x**4+c)**2/(b*x**4+a),x)","x \left(- \frac{a d^{2}}{b^{2}} + \frac{2 c d}{b}\right) + \operatorname{RootSum} {\left(256 t^{4} a^{3} b^{9} + a^{8} d^{8} - 8 a^{7} b c d^{7} + 28 a^{6} b^{2} c^{2} d^{6} - 56 a^{5} b^{3} c^{3} d^{5} + 70 a^{4} b^{4} c^{4} d^{4} - 56 a^{3} b^{5} c^{5} d^{3} + 28 a^{2} b^{6} c^{6} d^{2} - 8 a b^{7} c^{7} d + b^{8} c^{8}, \left( t \mapsto t \log{\left(\frac{4 t a b^{2}}{a^{2} d^{2} - 2 a b c d + b^{2} c^{2}} + x \right)} \right)\right)} + \frac{d^{2} x^{5}}{5 b}"," ",0,"x*(-a*d**2/b**2 + 2*c*d/b) + RootSum(256*_t**4*a**3*b**9 + a**8*d**8 - 8*a**7*b*c*d**7 + 28*a**6*b**2*c**2*d**6 - 56*a**5*b**3*c**3*d**5 + 70*a**4*b**4*c**4*d**4 - 56*a**3*b**5*c**5*d**3 + 28*a**2*b**6*c**6*d**2 - 8*a*b**7*c**7*d + b**8*c**8, Lambda(_t, _t*log(4*_t*a*b**2/(a**2*d**2 - 2*a*b*c*d + b**2*c**2) + x))) + d**2*x**5/(5*b)","A",0
163,1,87,0,0.610243," ","integrate((d*x**4+c)/(b*x**4+a),x)","\operatorname{RootSum} {\left(256 t^{4} a^{3} b^{5} + a^{4} d^{4} - 4 a^{3} b c d^{3} + 6 a^{2} b^{2} c^{2} d^{2} - 4 a b^{3} c^{3} d + b^{4} c^{4}, \left( t \mapsto t \log{\left(- \frac{4 t a b}{a d - b c} + x \right)} \right)\right)} + \frac{d x}{b}"," ",0,"RootSum(256*_t**4*a**3*b**5 + a**4*d**4 - 4*a**3*b*c*d**3 + 6*a**2*b**2*c**2*d**2 - 4*a*b**3*c**3*d + b**4*c**4, Lambda(_t, _t*log(-4*_t*a*b/(a*d - b*c) + x))) + d*x/b","A",0
164,-1,0,0,0.000000," ","integrate(1/(b*x**4+a)/(d*x**4+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
165,-1,0,0,0.000000," ","integrate(1/(b*x**4+a)/(d*x**4+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
166,-1,0,0,0.000000," ","integrate((d*x**4+c)**5/(b*x**4+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
167,1,471,0,47.537542," ","integrate((d*x**4+c)**4/(b*x**4+a)**2,x)","x^{5} \left(- \frac{2 a d^{4}}{5 b^{3}} + \frac{4 c d^{3}}{5 b^{2}}\right) + x \left(\frac{3 a^{2} d^{4}}{b^{4}} - \frac{8 a c d^{3}}{b^{3}} + \frac{6 c^{2} d^{2}}{b^{2}}\right) + \frac{x \left(a^{4} d^{4} - 4 a^{3} b c d^{3} + 6 a^{2} b^{2} c^{2} d^{2} - 4 a b^{3} c^{3} d + b^{4} c^{4}\right)}{4 a^{2} b^{4} + 4 a b^{5} x^{4}} + \operatorname{RootSum} {\left(65536 t^{4} a^{7} b^{17} + 28561 a^{16} d^{16} - 316368 a^{15} b c d^{15} + 1577784 a^{14} b^{2} c^{2} d^{14} - 4651504 a^{13} b^{3} c^{3} d^{13} + 8923164 a^{12} b^{4} c^{4} d^{12} - 11486160 a^{11} b^{5} c^{5} d^{11} + 9723912 a^{10} b^{6} c^{6} d^{10} - 4810608 a^{9} b^{7} c^{7} d^{9} + 617958 a^{8} b^{8} c^{8} d^{8} + 772112 a^{7} b^{9} c^{9} d^{7} - 434808 a^{6} b^{10} c^{10} d^{6} + 20400 a^{5} b^{11} c^{11} d^{5} + 45724 a^{4} b^{12} c^{12} d^{4} - 8304 a^{3} b^{13} c^{13} d^{3} - 2376 a^{2} b^{14} c^{14} d^{2} + 432 a b^{15} c^{15} d + 81 b^{16} c^{16}, \left( t \mapsto t \log{\left(- \frac{16 t a^{2} b^{4}}{13 a^{4} d^{4} - 36 a^{3} b c d^{3} + 30 a^{2} b^{2} c^{2} d^{2} - 4 a b^{3} c^{3} d - 3 b^{4} c^{4}} + x \right)} \right)\right)} + \frac{d^{4} x^{9}}{9 b^{2}}"," ",0,"x**5*(-2*a*d**4/(5*b**3) + 4*c*d**3/(5*b**2)) + x*(3*a**2*d**4/b**4 - 8*a*c*d**3/b**3 + 6*c**2*d**2/b**2) + x*(a**4*d**4 - 4*a**3*b*c*d**3 + 6*a**2*b**2*c**2*d**2 - 4*a*b**3*c**3*d + b**4*c**4)/(4*a**2*b**4 + 4*a*b**5*x**4) + RootSum(65536*_t**4*a**7*b**17 + 28561*a**16*d**16 - 316368*a**15*b*c*d**15 + 1577784*a**14*b**2*c**2*d**14 - 4651504*a**13*b**3*c**3*d**13 + 8923164*a**12*b**4*c**4*d**12 - 11486160*a**11*b**5*c**5*d**11 + 9723912*a**10*b**6*c**6*d**10 - 4810608*a**9*b**7*c**7*d**9 + 617958*a**8*b**8*c**8*d**8 + 772112*a**7*b**9*c**9*d**7 - 434808*a**6*b**10*c**10*d**6 + 20400*a**5*b**11*c**11*d**5 + 45724*a**4*b**12*c**12*d**4 - 8304*a**3*b**13*c**13*d**3 - 2376*a**2*b**14*c**14*d**2 + 432*a*b**15*c**15*d + 81*b**16*c**16, Lambda(_t, _t*log(-16*_t*a**2*b**4/(13*a**4*d**4 - 36*a**3*b*c*d**3 + 30*a**2*b**2*c**2*d**2 - 4*a*b**3*c**3*d - 3*b**4*c**4) + x))) + d**4*x**9/(9*b**2)","A",0
168,1,337,0,6.988646," ","integrate((d*x**4+c)**3/(b*x**4+a)**2,x)","x \left(- \frac{2 a d^{3}}{b^{3}} + \frac{3 c d^{2}}{b^{2}}\right) + \frac{x \left(- a^{3} d^{3} + 3 a^{2} b c d^{2} - 3 a b^{2} c^{2} d + b^{3} c^{3}\right)}{4 a^{2} b^{3} + 4 a b^{4} x^{4}} + \operatorname{RootSum} {\left(65536 t^{4} a^{7} b^{13} + 6561 a^{12} d^{12} - 43740 a^{11} b c d^{11} + 118098 a^{10} b^{2} c^{2} d^{10} - 156492 a^{9} b^{3} c^{3} d^{9} + 84159 a^{8} b^{4} c^{4} d^{8} + 26568 a^{7} b^{5} c^{5} d^{7} - 52164 a^{6} b^{6} c^{6} d^{6} + 11016 a^{5} b^{7} c^{7} d^{5} + 10287 a^{4} b^{8} c^{8} d^{4} - 3564 a^{3} b^{9} c^{9} d^{3} - 1134 a^{2} b^{10} c^{10} d^{2} + 324 a b^{11} c^{11} d + 81 b^{12} c^{12}, \left( t \mapsto t \log{\left(\frac{16 t a^{2} b^{3}}{9 a^{3} d^{3} - 15 a^{2} b c d^{2} + 3 a b^{2} c^{2} d + 3 b^{3} c^{3}} + x \right)} \right)\right)} + \frac{d^{3} x^{5}}{5 b^{2}}"," ",0,"x*(-2*a*d**3/b**3 + 3*c*d**2/b**2) + x*(-a**3*d**3 + 3*a**2*b*c*d**2 - 3*a*b**2*c**2*d + b**3*c**3)/(4*a**2*b**3 + 4*a*b**4*x**4) + RootSum(65536*_t**4*a**7*b**13 + 6561*a**12*d**12 - 43740*a**11*b*c*d**11 + 118098*a**10*b**2*c**2*d**10 - 156492*a**9*b**3*c**3*d**9 + 84159*a**8*b**4*c**4*d**8 + 26568*a**7*b**5*c**5*d**7 - 52164*a**6*b**6*c**6*d**6 + 11016*a**5*b**7*c**7*d**5 + 10287*a**4*b**8*c**8*d**4 - 3564*a**3*b**9*c**9*d**3 - 1134*a**2*b**10*c**10*d**2 + 324*a*b**11*c**11*d + 81*b**12*c**12, Lambda(_t, _t*log(16*_t*a**2*b**3/(9*a**3*d**3 - 15*a**2*b*c*d**2 + 3*a*b**2*c**2*d + 3*b**3*c**3) + x))) + d**3*x**5/(5*b**2)","A",0
169,1,219,0,2.173920," ","integrate((d*x**4+c)**2/(b*x**4+a)**2,x)","\frac{x \left(a^{2} d^{2} - 2 a b c d + b^{2} c^{2}\right)}{4 a^{2} b^{2} + 4 a b^{3} x^{4}} + \operatorname{RootSum} {\left(65536 t^{4} a^{7} b^{9} + 625 a^{8} d^{8} - 1000 a^{7} b c d^{7} - 900 a^{6} b^{2} c^{2} d^{6} + 1640 a^{5} b^{3} c^{3} d^{5} + 646 a^{4} b^{4} c^{4} d^{4} - 984 a^{3} b^{5} c^{5} d^{3} - 324 a^{2} b^{6} c^{6} d^{2} + 216 a b^{7} c^{7} d + 81 b^{8} c^{8}, \left( t \mapsto t \log{\left(- \frac{16 t a^{2} b^{2}}{5 a^{2} d^{2} - 2 a b c d - 3 b^{2} c^{2}} + x \right)} \right)\right)} + \frac{d^{2} x}{b^{2}}"," ",0,"x*(a**2*d**2 - 2*a*b*c*d + b**2*c**2)/(4*a**2*b**2 + 4*a*b**3*x**4) + RootSum(65536*_t**4*a**7*b**9 + 625*a**8*d**8 - 1000*a**7*b*c*d**7 - 900*a**6*b**2*c**2*d**6 + 1640*a**5*b**3*c**3*d**5 + 646*a**4*b**4*c**4*d**4 - 984*a**3*b**5*c**5*d**3 - 324*a**2*b**6*c**6*d**2 + 216*a*b**7*c**7*d + 81*b**8*c**8, Lambda(_t, _t*log(-16*_t*a**2*b**2/(5*a**2*d**2 - 2*a*b*c*d - 3*b**2*c**2) + x))) + d**2*x/b**2","A",0
170,1,112,0,0.965163," ","integrate((d*x**4+c)/(b*x**4+a)**2,x)","\frac{x \left(- a d + b c\right)}{4 a^{2} b + 4 a b^{2} x^{4}} + \operatorname{RootSum} {\left(65536 t^{4} a^{7} b^{5} + a^{4} d^{4} + 12 a^{3} b c d^{3} + 54 a^{2} b^{2} c^{2} d^{2} + 108 a b^{3} c^{3} d + 81 b^{4} c^{4}, \left( t \mapsto t \log{\left(\frac{16 t a^{2} b}{a d + 3 b c} + x \right)} \right)\right)}"," ",0,"x*(-a*d + b*c)/(4*a**2*b + 4*a*b**2*x**4) + RootSum(65536*_t**4*a**7*b**5 + a**4*d**4 + 12*a**3*b*c*d**3 + 54*a**2*b**2*c**2*d**2 + 108*a*b**3*c**3*d + 81*b**4*c**4, Lambda(_t, _t*log(16*_t*a**2*b/(a*d + 3*b*c) + x)))","A",0
171,-1,0,0,0.000000," ","integrate(1/(b*x**4+a)**2/(d*x**4+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
172,-1,0,0,0.000000," ","integrate(1/(b*x**4+a)**2/(d*x**4+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
173,0,0,0,0.000000," ","integrate((-b*x**4+a)**(5/2)/(-d*x**4+c),x)","- \int \frac{a^{2} \sqrt{a - b x^{4}}}{- c + d x^{4}}\, dx - \int \frac{b^{2} x^{8} \sqrt{a - b x^{4}}}{- c + d x^{4}}\, dx - \int \left(- \frac{2 a b x^{4} \sqrt{a - b x^{4}}}{- c + d x^{4}}\right)\, dx"," ",0,"-Integral(a**2*sqrt(a - b*x**4)/(-c + d*x**4), x) - Integral(b**2*x**8*sqrt(a - b*x**4)/(-c + d*x**4), x) - Integral(-2*a*b*x**4*sqrt(a - b*x**4)/(-c + d*x**4), x)","F",0
174,0,0,0,0.000000," ","integrate((-b*x**4+a)**(3/2)/(-d*x**4+c),x)","- \int \frac{a \sqrt{a - b x^{4}}}{- c + d x^{4}}\, dx - \int \left(- \frac{b x^{4} \sqrt{a - b x^{4}}}{- c + d x^{4}}\right)\, dx"," ",0,"-Integral(a*sqrt(a - b*x**4)/(-c + d*x**4), x) - Integral(-b*x**4*sqrt(a - b*x**4)/(-c + d*x**4), x)","F",0
175,0,0,0,0.000000," ","integrate((-b*x**4+a)**(1/2)/(-d*x**4+c),x)","- \int \frac{\sqrt{a - b x^{4}}}{- c + d x^{4}}\, dx"," ",0,"-Integral(sqrt(a - b*x**4)/(-c + d*x**4), x)","F",0
176,0,0,0,0.000000," ","integrate(1/(-b*x**4+a)**(1/2)/(-d*x**4+c),x)","- \int \frac{1}{- c \sqrt{a - b x^{4}} + d x^{4} \sqrt{a - b x^{4}}}\, dx"," ",0,"-Integral(1/(-c*sqrt(a - b*x**4) + d*x**4*sqrt(a - b*x**4)), x)","F",0
177,0,0,0,0.000000," ","integrate(1/(-b*x**4+a)**(3/2)/(-d*x**4+c),x)","- \int \frac{1}{- a c \sqrt{a - b x^{4}} + a d x^{4} \sqrt{a - b x^{4}} + b c x^{4} \sqrt{a - b x^{4}} - b d x^{8} \sqrt{a - b x^{4}}}\, dx"," ",0,"-Integral(1/(-a*c*sqrt(a - b*x**4) + a*d*x**4*sqrt(a - b*x**4) + b*c*x**4*sqrt(a - b*x**4) - b*d*x**8*sqrt(a - b*x**4)), x)","F",0
178,-1,0,0,0.000000," ","integrate(1/(-b*x**4+a)**(5/2)/(-d*x**4+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
179,0,0,0,0.000000," ","integrate((b*x**4+a)**(3/2)/(d*x**4+c),x)","\int \frac{\left(a + b x^{4}\right)^{\frac{3}{2}}}{c + d x^{4}}\, dx"," ",0,"Integral((a + b*x**4)**(3/2)/(c + d*x**4), x)","F",0
180,0,0,0,0.000000," ","integrate((b*x**4+a)**(1/2)/(d*x**4+c),x)","\int \frac{\sqrt{a + b x^{4}}}{c + d x^{4}}\, dx"," ",0,"Integral(sqrt(a + b*x**4)/(c + d*x**4), x)","F",0
181,0,0,0,0.000000," ","integrate(1/(b*x**4+a)**(1/2)/(d*x**4+c),x)","\int \frac{1}{\sqrt{a + b x^{4}} \left(c + d x^{4}\right)}\, dx"," ",0,"Integral(1/(sqrt(a + b*x**4)*(c + d*x**4)), x)","F",0
182,0,0,0,0.000000," ","integrate(1/(b*x**4+a)**(3/2)/(d*x**4+c),x)","\int \frac{1}{\left(a + b x^{4}\right)^{\frac{3}{2}} \left(c + d x^{4}\right)}\, dx"," ",0,"Integral(1/((a + b*x**4)**(3/2)*(c + d*x**4)), x)","F",0
183,0,0,0,0.000000," ","integrate(1/(b*x**4+a)**(5/2)/(d*x**4+c),x)","\int \frac{1}{\left(a + b x^{4}\right)^{\frac{5}{2}} \left(c + d x^{4}\right)}\, dx"," ",0,"Integral(1/((a + b*x**4)**(5/2)*(c + d*x**4)), x)","F",0
184,-1,0,0,0.000000," ","integrate((-b*x**4+a)**(7/2)/(-d*x**4+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
185,0,0,0,0.000000," ","integrate((-b*x**4+a)**(5/2)/(-d*x**4+c)**2,x)","\int \frac{\left(a - b x^{4}\right)^{\frac{5}{2}}}{\left(- c + d x^{4}\right)^{2}}\, dx"," ",0,"Integral((a - b*x**4)**(5/2)/(-c + d*x**4)**2, x)","F",0
186,0,0,0,0.000000," ","integrate((-b*x**4+a)**(3/2)/(-d*x**4+c)**2,x)","\int \frac{\left(a - b x^{4}\right)^{\frac{3}{2}}}{\left(- c + d x^{4}\right)^{2}}\, dx"," ",0,"Integral((a - b*x**4)**(3/2)/(-c + d*x**4)**2, x)","F",0
187,0,0,0,0.000000," ","integrate((-b*x**4+a)**(1/2)/(-d*x**4+c)**2,x)","\int \frac{\sqrt{a - b x^{4}}}{\left(- c + d x^{4}\right)^{2}}\, dx"," ",0,"Integral(sqrt(a - b*x**4)/(-c + d*x**4)**2, x)","F",0
188,0,0,0,0.000000," ","integrate(1/(-b*x**4+a)**(1/2)/(-d*x**4+c)**2,x)","\int \frac{1}{\sqrt{a - b x^{4}} \left(- c + d x^{4}\right)^{2}}\, dx"," ",0,"Integral(1/(sqrt(a - b*x**4)*(-c + d*x**4)**2), x)","F",0
189,-1,0,0,0.000000," ","integrate(1/(-b*x**4+a)**(3/2)/(-d*x**4+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
190,0,0,0,0.000000," ","integrate(1/(-b*x**4+a)**(5/2)/(-d*x**4+c)**2,x)","\int \frac{1}{\left(a - b x^{4}\right)^{\frac{5}{2}} \left(- c + d x^{4}\right)^{2}}\, dx"," ",0,"Integral(1/((a - b*x**4)**(5/2)*(-c + d*x**4)**2), x)","F",0
191,0,0,0,0.000000," ","integrate((b*x**4+a)**(1/2)/(-b*c*x**4+a*c),x)","- \frac{\int \frac{\sqrt{a + b x^{4}}}{- a + b x^{4}}\, dx}{c}"," ",0,"-Integral(sqrt(a + b*x**4)/(-a + b*x**4), x)/c","F",0
192,0,0,0,0.000000," ","integrate((-b*x**4+a)**(1/2)/(b*c*x**4+a*c),x)","\frac{\int \frac{\sqrt{a - b x^{4}}}{a + b x^{4}}\, dx}{c}"," ",0,"Integral(sqrt(a - b*x**4)/(a + b*x**4), x)/c","F",0
193,0,0,0,0.000000," ","integrate((b*x**4+a)**(7/4)/(d*x**4+c),x)","\int \frac{\left(a + b x^{4}\right)^{\frac{7}{4}}}{c + d x^{4}}\, dx"," ",0,"Integral((a + b*x**4)**(7/4)/(c + d*x**4), x)","F",0
194,0,0,0,0.000000," ","integrate((b*x**4+a)**(3/4)/(d*x**4+c),x)","\int \frac{\left(a + b x^{4}\right)^{\frac{3}{4}}}{c + d x^{4}}\, dx"," ",0,"Integral((a + b*x**4)**(3/4)/(c + d*x**4), x)","F",0
195,0,0,0,0.000000," ","integrate(1/(b*x**4+a)**(1/4)/(d*x**4+c),x)","\int \frac{1}{\sqrt[4]{a + b x^{4}} \left(c + d x^{4}\right)}\, dx"," ",0,"Integral(1/((a + b*x**4)**(1/4)*(c + d*x**4)), x)","F",0
196,0,0,0,0.000000," ","integrate(1/(b*x**4+a)**(5/4)/(d*x**4+c),x)","\int \frac{1}{\left(a + b x^{4}\right)^{\frac{5}{4}} \left(c + d x^{4}\right)}\, dx"," ",0,"Integral(1/((a + b*x**4)**(5/4)*(c + d*x**4)), x)","F",0
197,0,0,0,0.000000," ","integrate(1/(b*x**4+a)**(9/4)/(d*x**4+c),x)","\int \frac{1}{\left(a + b x^{4}\right)^{\frac{9}{4}} \left(c + d x^{4}\right)}\, dx"," ",0,"Integral(1/((a + b*x**4)**(9/4)*(c + d*x**4)), x)","F",0
198,0,0,0,0.000000," ","integrate(1/(b*x**4+a)**(13/4)/(d*x**4+c),x)","\int \frac{1}{\left(a + b x^{4}\right)^{\frac{13}{4}} \left(c + d x^{4}\right)}\, dx"," ",0,"Integral(1/((a + b*x**4)**(13/4)*(c + d*x**4)), x)","F",0
199,0,0,0,0.000000," ","integrate((b*x**4+a)**(9/4)/(d*x**4+c),x)","\int \frac{\left(a + b x^{4}\right)^{\frac{9}{4}}}{c + d x^{4}}\, dx"," ",0,"Integral((a + b*x**4)**(9/4)/(c + d*x**4), x)","F",0
200,0,0,0,0.000000," ","integrate((b*x**4+a)**(5/4)/(d*x**4+c),x)","\int \frac{\left(a + b x^{4}\right)^{\frac{5}{4}}}{c + d x^{4}}\, dx"," ",0,"Integral((a + b*x**4)**(5/4)/(c + d*x**4), x)","F",0
201,0,0,0,0.000000," ","integrate((b*x**4+a)**(1/4)/(d*x**4+c),x)","\int \frac{\sqrt[4]{a + b x^{4}}}{c + d x^{4}}\, dx"," ",0,"Integral((a + b*x**4)**(1/4)/(c + d*x**4), x)","F",0
202,0,0,0,0.000000," ","integrate(1/(b*x**4+a)**(3/4)/(d*x**4+c),x)","\int \frac{1}{\left(a + b x^{4}\right)^{\frac{3}{4}} \left(c + d x^{4}\right)}\, dx"," ",0,"Integral(1/((a + b*x**4)**(3/4)*(c + d*x**4)), x)","F",0
203,0,0,0,0.000000," ","integrate(1/(b*x**4+a)**(7/4)/(d*x**4+c),x)","\int \frac{1}{\left(a + b x^{4}\right)^{\frac{7}{4}} \left(c + d x^{4}\right)}\, dx"," ",0,"Integral(1/((a + b*x**4)**(7/4)*(c + d*x**4)), x)","F",0
204,0,0,0,0.000000," ","integrate(1/(b*x**4+a)**(11/4)/(d*x**4+c),x)","\int \frac{1}{\left(a + b x^{4}\right)^{\frac{11}{4}} \left(c + d x^{4}\right)}\, dx"," ",0,"Integral(1/((a + b*x**4)**(11/4)*(c + d*x**4)), x)","F",0
205,-1,0,0,0.000000," ","integrate((b*x**4+a)**(11/4)/(d*x**4+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
206,-1,0,0,0.000000," ","integrate((b*x**4+a)**(7/4)/(d*x**4+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
207,0,0,0,0.000000," ","integrate((b*x**4+a)**(3/4)/(d*x**4+c)**2,x)","\int \frac{\left(a + b x^{4}\right)^{\frac{3}{4}}}{\left(c + d x^{4}\right)^{2}}\, dx"," ",0,"Integral((a + b*x**4)**(3/4)/(c + d*x**4)**2, x)","F",0
208,0,0,0,0.000000," ","integrate(1/(b*x**4+a)**(1/4)/(d*x**4+c)**2,x)","\int \frac{1}{\sqrt[4]{a + b x^{4}} \left(c + d x^{4}\right)^{2}}\, dx"," ",0,"Integral(1/((a + b*x**4)**(1/4)*(c + d*x**4)**2), x)","F",0
209,0,0,0,0.000000," ","integrate(1/(b*x**4+a)**(5/4)/(d*x**4+c)**2,x)","\int \frac{1}{\left(a + b x^{4}\right)^{\frac{5}{4}} \left(c + d x^{4}\right)^{2}}\, dx"," ",0,"Integral(1/((a + b*x**4)**(5/4)*(c + d*x**4)**2), x)","F",0
210,0,0,0,0.000000," ","integrate(1/(b*x**4+a)**(9/4)/(d*x**4+c)**2,x)","\int \frac{1}{\left(a + b x^{4}\right)^{\frac{9}{4}} \left(c + d x^{4}\right)^{2}}\, dx"," ",0,"Integral(1/((a + b*x**4)**(9/4)*(c + d*x**4)**2), x)","F",0
211,-1,0,0,0.000000," ","integrate((b*x**4+a)**(9/4)/(d*x**4+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
212,0,0,0,0.000000," ","integrate((b*x**4+a)**(5/4)/(d*x**4+c)**2,x)","\int \frac{\left(a + b x^{4}\right)^{\frac{5}{4}}}{\left(c + d x^{4}\right)^{2}}\, dx"," ",0,"Integral((a + b*x**4)**(5/4)/(c + d*x**4)**2, x)","F",0
213,0,0,0,0.000000," ","integrate((b*x**4+a)**(1/4)/(d*x**4+c)**2,x)","\int \frac{\sqrt[4]{a + b x^{4}}}{\left(c + d x^{4}\right)^{2}}\, dx"," ",0,"Integral((a + b*x**4)**(1/4)/(c + d*x**4)**2, x)","F",0
214,0,0,0,0.000000," ","integrate(1/(b*x**4+a)**(3/4)/(d*x**4+c)**2,x)","\int \frac{1}{\left(a + b x^{4}\right)^{\frac{3}{4}} \left(c + d x^{4}\right)^{2}}\, dx"," ",0,"Integral(1/((a + b*x**4)**(3/4)*(c + d*x**4)**2), x)","F",0
215,-1,0,0,0.000000," ","integrate(1/(b*x**4+a)**(7/4)/(d*x**4+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
216,0,0,0,0.000000," ","integrate(1/(x**4+1)**(1/4)/(x**4+2),x)","\int \frac{1}{\sqrt[4]{x^{4} + 1} \left(x^{4} + 2\right)}\, dx"," ",0,"Integral(1/((x**4 + 1)**(1/4)*(x**4 + 2)), x)","F",0
217,0,0,0,0.000000," ","integrate(1/(a-(a-b)*x**4)/(b*x**4+a)**(1/4),x)","- \int \frac{1}{a x^{4} \sqrt[4]{a + b x^{4}} - a \sqrt[4]{a + b x^{4}} - b x^{4} \sqrt[4]{a + b x^{4}}}\, dx"," ",0,"-Integral(1/(a*x**4*(a + b*x**4)**(1/4) - a*(a + b*x**4)**(1/4) - b*x**4*(a + b*x**4)**(1/4)), x)","F",0
218,-1,0,0,0.000000," ","integrate((b*x**4+a)**p*(d*x**4+c)**q,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
219,1,119,0,166.025936," ","integrate((b*x**4+a)**2*(d*x**4+c)**q,x)","\frac{a^{2} c^{q} x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, - q \\ \frac{5}{4} \end{matrix}\middle| {\frac{d x^{4} e^{i \pi}}{c}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)} + \frac{a b c^{q} x^{5} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{4}, - q \\ \frac{9}{4} \end{matrix}\middle| {\frac{d x^{4} e^{i \pi}}{c}} \right)}}{2 \Gamma\left(\frac{9}{4}\right)} + \frac{b^{2} c^{q} x^{9} \Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{9}{4}, - q \\ \frac{13}{4} \end{matrix}\middle| {\frac{d x^{4} e^{i \pi}}{c}} \right)}}{4 \Gamma\left(\frac{13}{4}\right)}"," ",0,"a**2*c**q*x*gamma(1/4)*hyper((1/4, -q), (5/4,), d*x**4*exp_polar(I*pi)/c)/(4*gamma(5/4)) + a*b*c**q*x**5*gamma(5/4)*hyper((5/4, -q), (9/4,), d*x**4*exp_polar(I*pi)/c)/(2*gamma(9/4)) + b**2*c**q*x**9*gamma(9/4)*hyper((9/4, -q), (13/4,), d*x**4*exp_polar(I*pi)/c)/(4*gamma(13/4))","C",0
220,1,75,0,61.010451," ","integrate((b*x**4+a)*(d*x**4+c)**q,x)","\frac{a c^{q} x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, - q \\ \frac{5}{4} \end{matrix}\middle| {\frac{d x^{4} e^{i \pi}}{c}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)} + \frac{b c^{q} x^{5} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{4}, - q \\ \frac{9}{4} \end{matrix}\middle| {\frac{d x^{4} e^{i \pi}}{c}} \right)}}{4 \Gamma\left(\frac{9}{4}\right)}"," ",0,"a*c**q*x*gamma(1/4)*hyper((1/4, -q), (5/4,), d*x**4*exp_polar(I*pi)/c)/(4*gamma(5/4)) + b*c**q*x**5*gamma(5/4)*hyper((5/4, -q), (9/4,), d*x**4*exp_polar(I*pi)/c)/(4*gamma(9/4))","C",0
221,-1,0,0,0.000000," ","integrate((d*x**4+c)**q/(b*x**4+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
222,-1,0,0,0.000000," ","integrate((d*x**4+c)**q/(b*x**4+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
223,0,0,0,0.000000," ","integrate(1/(b*x**5+a)**(1/5)/(d*x**5+c),x)","\int \frac{1}{\sqrt[5]{a + b x^{5}} \left(c + d x^{5}\right)}\, dx"," ",0,"Integral(1/((a + b*x**5)**(1/5)*(c + d*x**5)), x)","F",0
224,1,454,0,57.222427," ","integrate((c+d/x)**3*(a+b/x)**(1/2),x)","\frac{4 a^{\frac{11}{2}} b^{\frac{3}{2}} d^{3} x^{3} \sqrt{\frac{a x}{b} + 1}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}} + \frac{2 a^{\frac{9}{2}} b^{\frac{5}{2}} d^{3} x^{2} \sqrt{\frac{a x}{b} + 1}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}} - \frac{8 a^{\frac{7}{2}} b^{\frac{7}{2}} d^{3} x \sqrt{\frac{a x}{b} + 1}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}} - \frac{6 a^{\frac{5}{2}} b^{\frac{9}{2}} d^{3} \sqrt{\frac{a x}{b} + 1}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}} - \frac{4 a^{6} b d^{3} x^{\frac{7}{2}}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}} - \frac{4 a^{5} b^{2} d^{3} x^{\frac{5}{2}}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}} - \frac{6 a c^{2} d \operatorname{atan}{\left(\frac{\sqrt{a + \frac{b}{x}}}{\sqrt{- a}} \right)}}{\sqrt{- a}} + \sqrt{b} c^{3} \sqrt{x} \sqrt{\frac{a x}{b} + 1} - 6 c^{2} d \sqrt{a + \frac{b}{x}} + 3 c d^{2} \left(\begin{cases} - \frac{\sqrt{a}}{x} & \text{for}\: b = 0 \\- \frac{2 \left(a + \frac{b}{x}\right)^{\frac{3}{2}}}{3 b} & \text{otherwise} \end{cases}\right) + \frac{b c^{3} \operatorname{asinh}{\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}} \right)}}{\sqrt{a}}"," ",0,"4*a**(11/2)*b**(3/2)*d**3*x**3*sqrt(a*x/b + 1)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2)) + 2*a**(9/2)*b**(5/2)*d**3*x**2*sqrt(a*x/b + 1)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2)) - 8*a**(7/2)*b**(7/2)*d**3*x*sqrt(a*x/b + 1)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2)) - 6*a**(5/2)*b**(9/2)*d**3*sqrt(a*x/b + 1)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2)) - 4*a**6*b*d**3*x**(7/2)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2)) - 4*a**5*b**2*d**3*x**(5/2)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2)) - 6*a*c**2*d*atan(sqrt(a + b/x)/sqrt(-a))/sqrt(-a) + sqrt(b)*c**3*sqrt(x)*sqrt(a*x/b + 1) - 6*c**2*d*sqrt(a + b/x) + 3*c*d**2*Piecewise((-sqrt(a)/x, Eq(b, 0)), (-2*(a + b/x)**(3/2)/(3*b), True)) + b*c**3*asinh(sqrt(a)*sqrt(x)/sqrt(b))/sqrt(a)","A",0
225,1,121,0,36.577589," ","integrate((c+d/x)**2*(a+b/x)**(1/2),x)","- \frac{4 a c d \operatorname{atan}{\left(\frac{\sqrt{a + \frac{b}{x}}}{\sqrt{- a}} \right)}}{\sqrt{- a}} + \sqrt{b} c^{2} \sqrt{x} \sqrt{\frac{a x}{b} + 1} - 4 c d \sqrt{a + \frac{b}{x}} + d^{2} \left(\begin{cases} - \frac{\sqrt{a}}{x} & \text{for}\: b = 0 \\- \frac{2 \left(a + \frac{b}{x}\right)^{\frac{3}{2}}}{3 b} & \text{otherwise} \end{cases}\right) + \frac{b c^{2} \operatorname{asinh}{\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}} \right)}}{\sqrt{a}}"," ",0,"-4*a*c*d*atan(sqrt(a + b/x)/sqrt(-a))/sqrt(-a) + sqrt(b)*c**2*sqrt(x)*sqrt(a*x/b + 1) - 4*c*d*sqrt(a + b/x) + d**2*Piecewise((-sqrt(a)/x, Eq(b, 0)), (-2*(a + b/x)**(3/2)/(3*b), True)) + b*c**2*asinh(sqrt(a)*sqrt(x)/sqrt(b))/sqrt(a)","A",0
226,1,87,0,41.308491," ","integrate((c+d/x)*(a+b/x)**(1/2),x)","- \frac{2 a d \operatorname{atan}{\left(\frac{\sqrt{a + \frac{b}{x}}}{\sqrt{- a}} \right)}}{\sqrt{- a}} + \sqrt{b} c \sqrt{x} \sqrt{\frac{a x}{b} + 1} - 2 d \sqrt{a + \frac{b}{x}} + \frac{b c \operatorname{asinh}{\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}} \right)}}{\sqrt{a}}"," ",0,"-2*a*d*atan(sqrt(a + b/x)/sqrt(-a))/sqrt(-a) + sqrt(b)*c*sqrt(x)*sqrt(a*x/b + 1) - 2*d*sqrt(a + b/x) + b*c*asinh(sqrt(a)*sqrt(x)/sqrt(b))/sqrt(a)","A",0
227,1,42,0,2.189429," ","integrate((a+b/x)**(1/2),x)","\sqrt{b} \sqrt{x} \sqrt{\frac{a x}{b} + 1} + \frac{b \operatorname{asinh}{\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}} \right)}}{\sqrt{a}}"," ",0,"sqrt(b)*sqrt(x)*sqrt(a*x/b + 1) + b*asinh(sqrt(a)*sqrt(x)/sqrt(b))/sqrt(a)","A",0
228,0,0,0,0.000000," ","integrate((a+b/x)**(1/2)/(c+d/x),x)","\int \frac{x \sqrt{a + \frac{b}{x}}}{c x + d}\, dx"," ",0,"Integral(x*sqrt(a + b/x)/(c*x + d), x)","F",0
229,0,0,0,0.000000," ","integrate((a+b/x)**(1/2)/(c+d/x)**2,x)","\int \frac{x^{2} \sqrt{a + \frac{b}{x}}}{\left(c x + d\right)^{2}}\, dx"," ",0,"Integral(x**2*sqrt(a + b/x)/(c*x + d)**2, x)","F",0
230,-1,0,0,0.000000," ","integrate((a+b/x)**(1/2)/(c+d/x)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
231,1,1817,0,123.483047," ","integrate((a+b/x)**(3/2)*(c+d/x)**3,x)","- \frac{16 a^{\frac{19}{2}} b^{\frac{11}{2}} d^{3} x^{6} \sqrt{\frac{a x}{b} + 1}}{105 a^{\frac{13}{2}} b^{7} x^{\frac{13}{2}} + 315 a^{\frac{11}{2}} b^{8} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{9} x^{\frac{9}{2}} + 105 a^{\frac{7}{2}} b^{10} x^{\frac{7}{2}}} - \frac{40 a^{\frac{17}{2}} b^{\frac{13}{2}} d^{3} x^{5} \sqrt{\frac{a x}{b} + 1}}{105 a^{\frac{13}{2}} b^{7} x^{\frac{13}{2}} + 315 a^{\frac{11}{2}} b^{8} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{9} x^{\frac{9}{2}} + 105 a^{\frac{7}{2}} b^{10} x^{\frac{7}{2}}} - \frac{30 a^{\frac{15}{2}} b^{\frac{15}{2}} d^{3} x^{4} \sqrt{\frac{a x}{b} + 1}}{105 a^{\frac{13}{2}} b^{7} x^{\frac{13}{2}} + 315 a^{\frac{11}{2}} b^{8} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{9} x^{\frac{9}{2}} + 105 a^{\frac{7}{2}} b^{10} x^{\frac{7}{2}}} - \frac{40 a^{\frac{13}{2}} b^{\frac{17}{2}} d^{3} x^{3} \sqrt{\frac{a x}{b} + 1}}{105 a^{\frac{13}{2}} b^{7} x^{\frac{13}{2}} + 315 a^{\frac{11}{2}} b^{8} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{9} x^{\frac{9}{2}} + 105 a^{\frac{7}{2}} b^{10} x^{\frac{7}{2}}} + \frac{4 a^{\frac{13}{2}} b^{\frac{3}{2}} d^{3} x^{3} \sqrt{\frac{a x}{b} + 1}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}} - \frac{100 a^{\frac{11}{2}} b^{\frac{19}{2}} d^{3} x^{2} \sqrt{\frac{a x}{b} + 1}}{105 a^{\frac{13}{2}} b^{7} x^{\frac{13}{2}} + 315 a^{\frac{11}{2}} b^{8} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{9} x^{\frac{9}{2}} + 105 a^{\frac{7}{2}} b^{10} x^{\frac{7}{2}}} + \frac{12 a^{\frac{11}{2}} b^{\frac{5}{2}} c d^{2} x^{3} \sqrt{\frac{a x}{b} + 1}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}} + \frac{2 a^{\frac{11}{2}} b^{\frac{5}{2}} d^{3} x^{2} \sqrt{\frac{a x}{b} + 1}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}} - \frac{96 a^{\frac{9}{2}} b^{\frac{21}{2}} d^{3} x \sqrt{\frac{a x}{b} + 1}}{105 a^{\frac{13}{2}} b^{7} x^{\frac{13}{2}} + 315 a^{\frac{11}{2}} b^{8} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{9} x^{\frac{9}{2}} + 105 a^{\frac{7}{2}} b^{10} x^{\frac{7}{2}}} + \frac{6 a^{\frac{9}{2}} b^{\frac{7}{2}} c d^{2} x^{2} \sqrt{\frac{a x}{b} + 1}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}} - \frac{8 a^{\frac{9}{2}} b^{\frac{7}{2}} d^{3} x \sqrt{\frac{a x}{b} + 1}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}} - \frac{30 a^{\frac{7}{2}} b^{\frac{23}{2}} d^{3} \sqrt{\frac{a x}{b} + 1}}{105 a^{\frac{13}{2}} b^{7} x^{\frac{13}{2}} + 315 a^{\frac{11}{2}} b^{8} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{9} x^{\frac{9}{2}} + 105 a^{\frac{7}{2}} b^{10} x^{\frac{7}{2}}} - \frac{24 a^{\frac{7}{2}} b^{\frac{9}{2}} c d^{2} x \sqrt{\frac{a x}{b} + 1}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}} - \frac{6 a^{\frac{7}{2}} b^{\frac{9}{2}} d^{3} \sqrt{\frac{a x}{b} + 1}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}} - \frac{18 a^{\frac{5}{2}} b^{\frac{11}{2}} c d^{2} \sqrt{\frac{a x}{b} + 1}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}} + \sqrt{a} b c^{3} \operatorname{asinh}{\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}} \right)} + \frac{16 a^{10} b^{5} d^{3} x^{\frac{13}{2}}}{105 a^{\frac{13}{2}} b^{7} x^{\frac{13}{2}} + 315 a^{\frac{11}{2}} b^{8} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{9} x^{\frac{9}{2}} + 105 a^{\frac{7}{2}} b^{10} x^{\frac{7}{2}}} + \frac{48 a^{9} b^{6} d^{3} x^{\frac{11}{2}}}{105 a^{\frac{13}{2}} b^{7} x^{\frac{13}{2}} + 315 a^{\frac{11}{2}} b^{8} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{9} x^{\frac{9}{2}} + 105 a^{\frac{7}{2}} b^{10} x^{\frac{7}{2}}} + \frac{48 a^{8} b^{7} d^{3} x^{\frac{9}{2}}}{105 a^{\frac{13}{2}} b^{7} x^{\frac{13}{2}} + 315 a^{\frac{11}{2}} b^{8} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{9} x^{\frac{9}{2}} + 105 a^{\frac{7}{2}} b^{10} x^{\frac{7}{2}}} + \frac{16 a^{7} b^{8} d^{3} x^{\frac{7}{2}}}{105 a^{\frac{13}{2}} b^{7} x^{\frac{13}{2}} + 315 a^{\frac{11}{2}} b^{8} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{9} x^{\frac{9}{2}} + 105 a^{\frac{7}{2}} b^{10} x^{\frac{7}{2}}} - \frac{4 a^{7} b d^{3} x^{\frac{7}{2}}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}} - \frac{12 a^{6} b^{2} c d^{2} x^{\frac{7}{2}}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}} - \frac{4 a^{6} b^{2} d^{3} x^{\frac{5}{2}}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}} - \frac{12 a^{5} b^{3} c d^{2} x^{\frac{5}{2}}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}} - \frac{6 a^{2} c^{2} d \operatorname{atan}{\left(\frac{\sqrt{a + \frac{b}{x}}}{\sqrt{- a}} \right)}}{\sqrt{- a}} + a \sqrt{b} c^{3} \sqrt{x} \sqrt{\frac{a x}{b} + 1} - \frac{2 a b c^{3} \operatorname{atan}{\left(\frac{\sqrt{a + \frac{b}{x}}}{\sqrt{- a}} \right)}}{\sqrt{- a}} - 6 a c^{2} d \sqrt{a + \frac{b}{x}} + 3 a c d^{2} \left(\begin{cases} - \frac{\sqrt{a}}{x} & \text{for}\: b = 0 \\- \frac{2 \left(a + \frac{b}{x}\right)^{\frac{3}{2}}}{3 b} & \text{otherwise} \end{cases}\right) - 2 b c^{3} \sqrt{a + \frac{b}{x}} + 3 b c^{2} d \left(\begin{cases} - \frac{\sqrt{a}}{x} & \text{for}\: b = 0 \\- \frac{2 \left(a + \frac{b}{x}\right)^{\frac{3}{2}}}{3 b} & \text{otherwise} \end{cases}\right)"," ",0,"-16*a**(19/2)*b**(11/2)*d**3*x**6*sqrt(a*x/b + 1)/(105*a**(13/2)*b**7*x**(13/2) + 315*a**(11/2)*b**8*x**(11/2) + 315*a**(9/2)*b**9*x**(9/2) + 105*a**(7/2)*b**10*x**(7/2)) - 40*a**(17/2)*b**(13/2)*d**3*x**5*sqrt(a*x/b + 1)/(105*a**(13/2)*b**7*x**(13/2) + 315*a**(11/2)*b**8*x**(11/2) + 315*a**(9/2)*b**9*x**(9/2) + 105*a**(7/2)*b**10*x**(7/2)) - 30*a**(15/2)*b**(15/2)*d**3*x**4*sqrt(a*x/b + 1)/(105*a**(13/2)*b**7*x**(13/2) + 315*a**(11/2)*b**8*x**(11/2) + 315*a**(9/2)*b**9*x**(9/2) + 105*a**(7/2)*b**10*x**(7/2)) - 40*a**(13/2)*b**(17/2)*d**3*x**3*sqrt(a*x/b + 1)/(105*a**(13/2)*b**7*x**(13/2) + 315*a**(11/2)*b**8*x**(11/2) + 315*a**(9/2)*b**9*x**(9/2) + 105*a**(7/2)*b**10*x**(7/2)) + 4*a**(13/2)*b**(3/2)*d**3*x**3*sqrt(a*x/b + 1)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2)) - 100*a**(11/2)*b**(19/2)*d**3*x**2*sqrt(a*x/b + 1)/(105*a**(13/2)*b**7*x**(13/2) + 315*a**(11/2)*b**8*x**(11/2) + 315*a**(9/2)*b**9*x**(9/2) + 105*a**(7/2)*b**10*x**(7/2)) + 12*a**(11/2)*b**(5/2)*c*d**2*x**3*sqrt(a*x/b + 1)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2)) + 2*a**(11/2)*b**(5/2)*d**3*x**2*sqrt(a*x/b + 1)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2)) - 96*a**(9/2)*b**(21/2)*d**3*x*sqrt(a*x/b + 1)/(105*a**(13/2)*b**7*x**(13/2) + 315*a**(11/2)*b**8*x**(11/2) + 315*a**(9/2)*b**9*x**(9/2) + 105*a**(7/2)*b**10*x**(7/2)) + 6*a**(9/2)*b**(7/2)*c*d**2*x**2*sqrt(a*x/b + 1)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2)) - 8*a**(9/2)*b**(7/2)*d**3*x*sqrt(a*x/b + 1)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2)) - 30*a**(7/2)*b**(23/2)*d**3*sqrt(a*x/b + 1)/(105*a**(13/2)*b**7*x**(13/2) + 315*a**(11/2)*b**8*x**(11/2) + 315*a**(9/2)*b**9*x**(9/2) + 105*a**(7/2)*b**10*x**(7/2)) - 24*a**(7/2)*b**(9/2)*c*d**2*x*sqrt(a*x/b + 1)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2)) - 6*a**(7/2)*b**(9/2)*d**3*sqrt(a*x/b + 1)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2)) - 18*a**(5/2)*b**(11/2)*c*d**2*sqrt(a*x/b + 1)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2)) + sqrt(a)*b*c**3*asinh(sqrt(a)*sqrt(x)/sqrt(b)) + 16*a**10*b**5*d**3*x**(13/2)/(105*a**(13/2)*b**7*x**(13/2) + 315*a**(11/2)*b**8*x**(11/2) + 315*a**(9/2)*b**9*x**(9/2) + 105*a**(7/2)*b**10*x**(7/2)) + 48*a**9*b**6*d**3*x**(11/2)/(105*a**(13/2)*b**7*x**(13/2) + 315*a**(11/2)*b**8*x**(11/2) + 315*a**(9/2)*b**9*x**(9/2) + 105*a**(7/2)*b**10*x**(7/2)) + 48*a**8*b**7*d**3*x**(9/2)/(105*a**(13/2)*b**7*x**(13/2) + 315*a**(11/2)*b**8*x**(11/2) + 315*a**(9/2)*b**9*x**(9/2) + 105*a**(7/2)*b**10*x**(7/2)) + 16*a**7*b**8*d**3*x**(7/2)/(105*a**(13/2)*b**7*x**(13/2) + 315*a**(11/2)*b**8*x**(11/2) + 315*a**(9/2)*b**9*x**(9/2) + 105*a**(7/2)*b**10*x**(7/2)) - 4*a**7*b*d**3*x**(7/2)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2)) - 12*a**6*b**2*c*d**2*x**(7/2)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2)) - 4*a**6*b**2*d**3*x**(5/2)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2)) - 12*a**5*b**3*c*d**2*x**(5/2)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2)) - 6*a**2*c**2*d*atan(sqrt(a + b/x)/sqrt(-a))/sqrt(-a) + a*sqrt(b)*c**3*sqrt(x)*sqrt(a*x/b + 1) - 2*a*b*c**3*atan(sqrt(a + b/x)/sqrt(-a))/sqrt(-a) - 6*a*c**2*d*sqrt(a + b/x) + 3*a*c*d**2*Piecewise((-sqrt(a)/x, Eq(b, 0)), (-2*(a + b/x)**(3/2)/(3*b), True)) - 2*b*c**3*sqrt(a + b/x) + 3*b*c**2*d*Piecewise((-sqrt(a)/x, Eq(b, 0)), (-2*(a + b/x)**(3/2)/(3*b), True))","A",0
232,1,534,0,94.065362," ","integrate((a+b/x)**(3/2)*(c+d/x)**2,x)","\frac{4 a^{\frac{11}{2}} b^{\frac{5}{2}} d^{2} x^{3} \sqrt{\frac{a x}{b} + 1}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}} + \frac{2 a^{\frac{9}{2}} b^{\frac{7}{2}} d^{2} x^{2} \sqrt{\frac{a x}{b} + 1}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}} - \frac{8 a^{\frac{7}{2}} b^{\frac{9}{2}} d^{2} x \sqrt{\frac{a x}{b} + 1}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}} - \frac{6 a^{\frac{5}{2}} b^{\frac{11}{2}} d^{2} \sqrt{\frac{a x}{b} + 1}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}} + \sqrt{a} b c^{2} \operatorname{asinh}{\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}} \right)} - \frac{4 a^{6} b^{2} d^{2} x^{\frac{7}{2}}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}} - \frac{4 a^{5} b^{3} d^{2} x^{\frac{5}{2}}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}} - \frac{4 a^{2} c d \operatorname{atan}{\left(\frac{\sqrt{a + \frac{b}{x}}}{\sqrt{- a}} \right)}}{\sqrt{- a}} + a \sqrt{b} c^{2} \sqrt{x} \sqrt{\frac{a x}{b} + 1} - \frac{2 a b c^{2} \operatorname{atan}{\left(\frac{\sqrt{a + \frac{b}{x}}}{\sqrt{- a}} \right)}}{\sqrt{- a}} - 4 a c d \sqrt{a + \frac{b}{x}} + a d^{2} \left(\begin{cases} - \frac{\sqrt{a}}{x} & \text{for}\: b = 0 \\- \frac{2 \left(a + \frac{b}{x}\right)^{\frac{3}{2}}}{3 b} & \text{otherwise} \end{cases}\right) - 2 b c^{2} \sqrt{a + \frac{b}{x}} + 2 b c d \left(\begin{cases} - \frac{\sqrt{a}}{x} & \text{for}\: b = 0 \\- \frac{2 \left(a + \frac{b}{x}\right)^{\frac{3}{2}}}{3 b} & \text{otherwise} \end{cases}\right)"," ",0,"4*a**(11/2)*b**(5/2)*d**2*x**3*sqrt(a*x/b + 1)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2)) + 2*a**(9/2)*b**(7/2)*d**2*x**2*sqrt(a*x/b + 1)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2)) - 8*a**(7/2)*b**(9/2)*d**2*x*sqrt(a*x/b + 1)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2)) - 6*a**(5/2)*b**(11/2)*d**2*sqrt(a*x/b + 1)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2)) + sqrt(a)*b*c**2*asinh(sqrt(a)*sqrt(x)/sqrt(b)) - 4*a**6*b**2*d**2*x**(7/2)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2)) - 4*a**5*b**3*d**2*x**(5/2)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2)) - 4*a**2*c*d*atan(sqrt(a + b/x)/sqrt(-a))/sqrt(-a) + a*sqrt(b)*c**2*sqrt(x)*sqrt(a*x/b + 1) - 2*a*b*c**2*atan(sqrt(a + b/x)/sqrt(-a))/sqrt(-a) - 4*a*c*d*sqrt(a + b/x) + a*d**2*Piecewise((-sqrt(a)/x, Eq(b, 0)), (-2*(a + b/x)**(3/2)/(3*b), True)) - 2*b*c**2*sqrt(a + b/x) + 2*b*c*d*Piecewise((-sqrt(a)/x, Eq(b, 0)), (-2*(a + b/x)**(3/2)/(3*b), True))","A",0
233,1,163,0,56.146345," ","integrate((a+b/x)**(3/2)*(c+d/x),x)","\sqrt{a} b c \operatorname{asinh}{\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}} \right)} - \frac{2 a^{2} d \operatorname{atan}{\left(\frac{\sqrt{a + \frac{b}{x}}}{\sqrt{- a}} \right)}}{\sqrt{- a}} + a \sqrt{b} c \sqrt{x} \sqrt{\frac{a x}{b} + 1} - \frac{2 a b c \operatorname{atan}{\left(\frac{\sqrt{a + \frac{b}{x}}}{\sqrt{- a}} \right)}}{\sqrt{- a}} - 2 a d \sqrt{a + \frac{b}{x}} - 2 b c \sqrt{a + \frac{b}{x}} + b d \left(\begin{cases} - \frac{\sqrt{a}}{x} & \text{for}\: b = 0 \\- \frac{2 \left(a + \frac{b}{x}\right)^{\frac{3}{2}}}{3 b} & \text{otherwise} \end{cases}\right)"," ",0,"sqrt(a)*b*c*asinh(sqrt(a)*sqrt(x)/sqrt(b)) - 2*a**2*d*atan(sqrt(a + b/x)/sqrt(-a))/sqrt(-a) + a*sqrt(b)*c*sqrt(x)*sqrt(a*x/b + 1) - 2*a*b*c*atan(sqrt(a + b/x)/sqrt(-a))/sqrt(-a) - 2*a*d*sqrt(a + b/x) - 2*b*c*sqrt(a + b/x) + b*d*Piecewise((-sqrt(a)/x, Eq(b, 0)), (-2*(a + b/x)**(3/2)/(3*b), True))","A",0
234,1,92,0,2.691707," ","integrate((a+b/x)**(3/2),x)","3 \sqrt{a} b \operatorname{asinh}{\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}} \right)} + \frac{a^{2} x^{\frac{3}{2}}}{\sqrt{b} \sqrt{\frac{a x}{b} + 1}} - \frac{a \sqrt{b} \sqrt{x}}{\sqrt{\frac{a x}{b} + 1}} - \frac{2 b^{\frac{3}{2}}}{\sqrt{x} \sqrt{\frac{a x}{b} + 1}}"," ",0,"3*sqrt(a)*b*asinh(sqrt(a)*sqrt(x)/sqrt(b)) + a**2*x**(3/2)/(sqrt(b)*sqrt(a*x/b + 1)) - a*sqrt(b)*sqrt(x)/sqrt(a*x/b + 1) - 2*b**(3/2)/(sqrt(x)*sqrt(a*x/b + 1))","B",0
235,0,0,0,0.000000," ","integrate((a+b/x)**(3/2)/(c+d/x),x)","\int \frac{x \left(a + \frac{b}{x}\right)^{\frac{3}{2}}}{c x + d}\, dx"," ",0,"Integral(x*(a + b/x)**(3/2)/(c*x + d), x)","F",0
236,-1,0,0,0.000000," ","integrate((a+b/x)**(3/2)/(c+d/x)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
237,-1,0,0,0.000000," ","integrate((a+b/x)**(3/2)/(c+d/x)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
238,1,5513,0,158.704354," ","integrate((a+b/x)**(5/2)*(c+d/x)**3,x)","\frac{32 a^{\frac{29}{2}} b^{\frac{27}{2}} d^{3} x^{10} \sqrt{\frac{a x}{b} + 1}}{315 a^{\frac{21}{2}} b^{15} x^{\frac{21}{2}} + 1890 a^{\frac{19}{2}} b^{16} x^{\frac{19}{2}} + 4725 a^{\frac{17}{2}} b^{17} x^{\frac{17}{2}} + 6300 a^{\frac{15}{2}} b^{18} x^{\frac{15}{2}} + 4725 a^{\frac{13}{2}} b^{19} x^{\frac{13}{2}} + 1890 a^{\frac{11}{2}} b^{20} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{21} x^{\frac{9}{2}}} + \frac{176 a^{\frac{27}{2}} b^{\frac{29}{2}} d^{3} x^{9} \sqrt{\frac{a x}{b} + 1}}{315 a^{\frac{21}{2}} b^{15} x^{\frac{21}{2}} + 1890 a^{\frac{19}{2}} b^{16} x^{\frac{19}{2}} + 4725 a^{\frac{17}{2}} b^{17} x^{\frac{17}{2}} + 6300 a^{\frac{15}{2}} b^{18} x^{\frac{15}{2}} + 4725 a^{\frac{13}{2}} b^{19} x^{\frac{13}{2}} + 1890 a^{\frac{11}{2}} b^{20} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{21} x^{\frac{9}{2}}} + \frac{396 a^{\frac{25}{2}} b^{\frac{31}{2}} d^{3} x^{8} \sqrt{\frac{a x}{b} + 1}}{315 a^{\frac{21}{2}} b^{15} x^{\frac{21}{2}} + 1890 a^{\frac{19}{2}} b^{16} x^{\frac{19}{2}} + 4725 a^{\frac{17}{2}} b^{17} x^{\frac{17}{2}} + 6300 a^{\frac{15}{2}} b^{18} x^{\frac{15}{2}} + 4725 a^{\frac{13}{2}} b^{19} x^{\frac{13}{2}} + 1890 a^{\frac{11}{2}} b^{20} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{21} x^{\frac{9}{2}}} + \frac{462 a^{\frac{23}{2}} b^{\frac{33}{2}} d^{3} x^{7} \sqrt{\frac{a x}{b} + 1}}{315 a^{\frac{21}{2}} b^{15} x^{\frac{21}{2}} + 1890 a^{\frac{19}{2}} b^{16} x^{\frac{19}{2}} + 4725 a^{\frac{17}{2}} b^{17} x^{\frac{17}{2}} + 6300 a^{\frac{15}{2}} b^{18} x^{\frac{15}{2}} + 4725 a^{\frac{13}{2}} b^{19} x^{\frac{13}{2}} + 1890 a^{\frac{11}{2}} b^{20} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{21} x^{\frac{9}{2}}} + \frac{210 a^{\frac{21}{2}} b^{\frac{35}{2}} d^{3} x^{6} \sqrt{\frac{a x}{b} + 1}}{315 a^{\frac{21}{2}} b^{15} x^{\frac{21}{2}} + 1890 a^{\frac{19}{2}} b^{16} x^{\frac{19}{2}} + 4725 a^{\frac{17}{2}} b^{17} x^{\frac{17}{2}} + 6300 a^{\frac{15}{2}} b^{18} x^{\frac{15}{2}} + 4725 a^{\frac{13}{2}} b^{19} x^{\frac{13}{2}} + 1890 a^{\frac{11}{2}} b^{20} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{21} x^{\frac{9}{2}}} - \frac{32 a^{\frac{21}{2}} b^{\frac{11}{2}} d^{3} x^{6} \sqrt{\frac{a x}{b} + 1}}{105 a^{\frac{13}{2}} b^{7} x^{\frac{13}{2}} + 315 a^{\frac{11}{2}} b^{8} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{9} x^{\frac{9}{2}} + 105 a^{\frac{7}{2}} b^{10} x^{\frac{7}{2}}} - \frac{378 a^{\frac{19}{2}} b^{\frac{37}{2}} d^{3} x^{5} \sqrt{\frac{a x}{b} + 1}}{315 a^{\frac{21}{2}} b^{15} x^{\frac{21}{2}} + 1890 a^{\frac{19}{2}} b^{16} x^{\frac{19}{2}} + 4725 a^{\frac{17}{2}} b^{17} x^{\frac{17}{2}} + 6300 a^{\frac{15}{2}} b^{18} x^{\frac{15}{2}} + 4725 a^{\frac{13}{2}} b^{19} x^{\frac{13}{2}} + 1890 a^{\frac{11}{2}} b^{20} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{21} x^{\frac{9}{2}}} - \frac{48 a^{\frac{19}{2}} b^{\frac{13}{2}} c d^{2} x^{6} \sqrt{\frac{a x}{b} + 1}}{105 a^{\frac{13}{2}} b^{7} x^{\frac{13}{2}} + 315 a^{\frac{11}{2}} b^{8} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{9} x^{\frac{9}{2}} + 105 a^{\frac{7}{2}} b^{10} x^{\frac{7}{2}}} - \frac{80 a^{\frac{19}{2}} b^{\frac{13}{2}} d^{3} x^{5} \sqrt{\frac{a x}{b} + 1}}{105 a^{\frac{13}{2}} b^{7} x^{\frac{13}{2}} + 315 a^{\frac{11}{2}} b^{8} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{9} x^{\frac{9}{2}} + 105 a^{\frac{7}{2}} b^{10} x^{\frac{7}{2}}} - \frac{1134 a^{\frac{17}{2}} b^{\frac{39}{2}} d^{3} x^{4} \sqrt{\frac{a x}{b} + 1}}{315 a^{\frac{21}{2}} b^{15} x^{\frac{21}{2}} + 1890 a^{\frac{19}{2}} b^{16} x^{\frac{19}{2}} + 4725 a^{\frac{17}{2}} b^{17} x^{\frac{17}{2}} + 6300 a^{\frac{15}{2}} b^{18} x^{\frac{15}{2}} + 4725 a^{\frac{13}{2}} b^{19} x^{\frac{13}{2}} + 1890 a^{\frac{11}{2}} b^{20} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{21} x^{\frac{9}{2}}} - \frac{120 a^{\frac{17}{2}} b^{\frac{15}{2}} c d^{2} x^{5} \sqrt{\frac{a x}{b} + 1}}{105 a^{\frac{13}{2}} b^{7} x^{\frac{13}{2}} + 315 a^{\frac{11}{2}} b^{8} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{9} x^{\frac{9}{2}} + 105 a^{\frac{7}{2}} b^{10} x^{\frac{7}{2}}} - \frac{60 a^{\frac{17}{2}} b^{\frac{15}{2}} d^{3} x^{4} \sqrt{\frac{a x}{b} + 1}}{105 a^{\frac{13}{2}} b^{7} x^{\frac{13}{2}} + 315 a^{\frac{11}{2}} b^{8} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{9} x^{\frac{9}{2}} + 105 a^{\frac{7}{2}} b^{10} x^{\frac{7}{2}}} - \frac{1494 a^{\frac{15}{2}} b^{\frac{41}{2}} d^{3} x^{3} \sqrt{\frac{a x}{b} + 1}}{315 a^{\frac{21}{2}} b^{15} x^{\frac{21}{2}} + 1890 a^{\frac{19}{2}} b^{16} x^{\frac{19}{2}} + 4725 a^{\frac{17}{2}} b^{17} x^{\frac{17}{2}} + 6300 a^{\frac{15}{2}} b^{18} x^{\frac{15}{2}} + 4725 a^{\frac{13}{2}} b^{19} x^{\frac{13}{2}} + 1890 a^{\frac{11}{2}} b^{20} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{21} x^{\frac{9}{2}}} - \frac{90 a^{\frac{15}{2}} b^{\frac{17}{2}} c d^{2} x^{4} \sqrt{\frac{a x}{b} + 1}}{105 a^{\frac{13}{2}} b^{7} x^{\frac{13}{2}} + 315 a^{\frac{11}{2}} b^{8} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{9} x^{\frac{9}{2}} + 105 a^{\frac{7}{2}} b^{10} x^{\frac{7}{2}}} - \frac{80 a^{\frac{15}{2}} b^{\frac{17}{2}} d^{3} x^{3} \sqrt{\frac{a x}{b} + 1}}{105 a^{\frac{13}{2}} b^{7} x^{\frac{13}{2}} + 315 a^{\frac{11}{2}} b^{8} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{9} x^{\frac{9}{2}} + 105 a^{\frac{7}{2}} b^{10} x^{\frac{7}{2}}} + \frac{4 a^{\frac{15}{2}} b^{\frac{3}{2}} d^{3} x^{3} \sqrt{\frac{a x}{b} + 1}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}} - \frac{1098 a^{\frac{13}{2}} b^{\frac{43}{2}} d^{3} x^{2} \sqrt{\frac{a x}{b} + 1}}{315 a^{\frac{21}{2}} b^{15} x^{\frac{21}{2}} + 1890 a^{\frac{19}{2}} b^{16} x^{\frac{19}{2}} + 4725 a^{\frac{17}{2}} b^{17} x^{\frac{17}{2}} + 6300 a^{\frac{15}{2}} b^{18} x^{\frac{15}{2}} + 4725 a^{\frac{13}{2}} b^{19} x^{\frac{13}{2}} + 1890 a^{\frac{11}{2}} b^{20} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{21} x^{\frac{9}{2}}} - \frac{120 a^{\frac{13}{2}} b^{\frac{19}{2}} c d^{2} x^{3} \sqrt{\frac{a x}{b} + 1}}{105 a^{\frac{13}{2}} b^{7} x^{\frac{13}{2}} + 315 a^{\frac{11}{2}} b^{8} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{9} x^{\frac{9}{2}} + 105 a^{\frac{7}{2}} b^{10} x^{\frac{7}{2}}} - \frac{200 a^{\frac{13}{2}} b^{\frac{19}{2}} d^{3} x^{2} \sqrt{\frac{a x}{b} + 1}}{105 a^{\frac{13}{2}} b^{7} x^{\frac{13}{2}} + 315 a^{\frac{11}{2}} b^{8} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{9} x^{\frac{9}{2}} + 105 a^{\frac{7}{2}} b^{10} x^{\frac{7}{2}}} + \frac{24 a^{\frac{13}{2}} b^{\frac{5}{2}} c d^{2} x^{3} \sqrt{\frac{a x}{b} + 1}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}} + \frac{2 a^{\frac{13}{2}} b^{\frac{5}{2}} d^{3} x^{2} \sqrt{\frac{a x}{b} + 1}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}} - \frac{430 a^{\frac{11}{2}} b^{\frac{45}{2}} d^{3} x \sqrt{\frac{a x}{b} + 1}}{315 a^{\frac{21}{2}} b^{15} x^{\frac{21}{2}} + 1890 a^{\frac{19}{2}} b^{16} x^{\frac{19}{2}} + 4725 a^{\frac{17}{2}} b^{17} x^{\frac{17}{2}} + 6300 a^{\frac{15}{2}} b^{18} x^{\frac{15}{2}} + 4725 a^{\frac{13}{2}} b^{19} x^{\frac{13}{2}} + 1890 a^{\frac{11}{2}} b^{20} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{21} x^{\frac{9}{2}}} - \frac{300 a^{\frac{11}{2}} b^{\frac{21}{2}} c d^{2} x^{2} \sqrt{\frac{a x}{b} + 1}}{105 a^{\frac{13}{2}} b^{7} x^{\frac{13}{2}} + 315 a^{\frac{11}{2}} b^{8} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{9} x^{\frac{9}{2}} + 105 a^{\frac{7}{2}} b^{10} x^{\frac{7}{2}}} - \frac{192 a^{\frac{11}{2}} b^{\frac{21}{2}} d^{3} x \sqrt{\frac{a x}{b} + 1}}{105 a^{\frac{13}{2}} b^{7} x^{\frac{13}{2}} + 315 a^{\frac{11}{2}} b^{8} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{9} x^{\frac{9}{2}} + 105 a^{\frac{7}{2}} b^{10} x^{\frac{7}{2}}} + \frac{12 a^{\frac{11}{2}} b^{\frac{7}{2}} c^{2} d x^{3} \sqrt{\frac{a x}{b} + 1}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}} + \frac{12 a^{\frac{11}{2}} b^{\frac{7}{2}} c d^{2} x^{2} \sqrt{\frac{a x}{b} + 1}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}} - \frac{8 a^{\frac{11}{2}} b^{\frac{7}{2}} d^{3} x \sqrt{\frac{a x}{b} + 1}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}} - \frac{70 a^{\frac{9}{2}} b^{\frac{47}{2}} d^{3} \sqrt{\frac{a x}{b} + 1}}{315 a^{\frac{21}{2}} b^{15} x^{\frac{21}{2}} + 1890 a^{\frac{19}{2}} b^{16} x^{\frac{19}{2}} + 4725 a^{\frac{17}{2}} b^{17} x^{\frac{17}{2}} + 6300 a^{\frac{15}{2}} b^{18} x^{\frac{15}{2}} + 4725 a^{\frac{13}{2}} b^{19} x^{\frac{13}{2}} + 1890 a^{\frac{11}{2}} b^{20} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{21} x^{\frac{9}{2}}} - \frac{288 a^{\frac{9}{2}} b^{\frac{23}{2}} c d^{2} x \sqrt{\frac{a x}{b} + 1}}{105 a^{\frac{13}{2}} b^{7} x^{\frac{13}{2}} + 315 a^{\frac{11}{2}} b^{8} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{9} x^{\frac{9}{2}} + 105 a^{\frac{7}{2}} b^{10} x^{\frac{7}{2}}} - \frac{60 a^{\frac{9}{2}} b^{\frac{23}{2}} d^{3} \sqrt{\frac{a x}{b} + 1}}{105 a^{\frac{13}{2}} b^{7} x^{\frac{13}{2}} + 315 a^{\frac{11}{2}} b^{8} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{9} x^{\frac{9}{2}} + 105 a^{\frac{7}{2}} b^{10} x^{\frac{7}{2}}} + \frac{6 a^{\frac{9}{2}} b^{\frac{9}{2}} c^{2} d x^{2} \sqrt{\frac{a x}{b} + 1}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}} - \frac{48 a^{\frac{9}{2}} b^{\frac{9}{2}} c d^{2} x \sqrt{\frac{a x}{b} + 1}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}} - \frac{6 a^{\frac{9}{2}} b^{\frac{9}{2}} d^{3} \sqrt{\frac{a x}{b} + 1}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}} - \frac{90 a^{\frac{7}{2}} b^{\frac{25}{2}} c d^{2} \sqrt{\frac{a x}{b} + 1}}{105 a^{\frac{13}{2}} b^{7} x^{\frac{13}{2}} + 315 a^{\frac{11}{2}} b^{8} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{9} x^{\frac{9}{2}} + 105 a^{\frac{7}{2}} b^{10} x^{\frac{7}{2}}} - \frac{24 a^{\frac{7}{2}} b^{\frac{11}{2}} c^{2} d x \sqrt{\frac{a x}{b} + 1}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}} - \frac{36 a^{\frac{7}{2}} b^{\frac{11}{2}} c d^{2} \sqrt{\frac{a x}{b} + 1}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}} - \frac{18 a^{\frac{5}{2}} b^{\frac{13}{2}} c^{2} d \sqrt{\frac{a x}{b} + 1}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}} + a^{\frac{3}{2}} b c^{3} \operatorname{asinh}{\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}} \right)} - \frac{32 a^{15} b^{13} d^{3} x^{\frac{21}{2}}}{315 a^{\frac{21}{2}} b^{15} x^{\frac{21}{2}} + 1890 a^{\frac{19}{2}} b^{16} x^{\frac{19}{2}} + 4725 a^{\frac{17}{2}} b^{17} x^{\frac{17}{2}} + 6300 a^{\frac{15}{2}} b^{18} x^{\frac{15}{2}} + 4725 a^{\frac{13}{2}} b^{19} x^{\frac{13}{2}} + 1890 a^{\frac{11}{2}} b^{20} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{21} x^{\frac{9}{2}}} - \frac{192 a^{14} b^{14} d^{3} x^{\frac{19}{2}}}{315 a^{\frac{21}{2}} b^{15} x^{\frac{21}{2}} + 1890 a^{\frac{19}{2}} b^{16} x^{\frac{19}{2}} + 4725 a^{\frac{17}{2}} b^{17} x^{\frac{17}{2}} + 6300 a^{\frac{15}{2}} b^{18} x^{\frac{15}{2}} + 4725 a^{\frac{13}{2}} b^{19} x^{\frac{13}{2}} + 1890 a^{\frac{11}{2}} b^{20} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{21} x^{\frac{9}{2}}} - \frac{480 a^{13} b^{15} d^{3} x^{\frac{17}{2}}}{315 a^{\frac{21}{2}} b^{15} x^{\frac{21}{2}} + 1890 a^{\frac{19}{2}} b^{16} x^{\frac{19}{2}} + 4725 a^{\frac{17}{2}} b^{17} x^{\frac{17}{2}} + 6300 a^{\frac{15}{2}} b^{18} x^{\frac{15}{2}} + 4725 a^{\frac{13}{2}} b^{19} x^{\frac{13}{2}} + 1890 a^{\frac{11}{2}} b^{20} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{21} x^{\frac{9}{2}}} - \frac{640 a^{12} b^{16} d^{3} x^{\frac{15}{2}}}{315 a^{\frac{21}{2}} b^{15} x^{\frac{21}{2}} + 1890 a^{\frac{19}{2}} b^{16} x^{\frac{19}{2}} + 4725 a^{\frac{17}{2}} b^{17} x^{\frac{17}{2}} + 6300 a^{\frac{15}{2}} b^{18} x^{\frac{15}{2}} + 4725 a^{\frac{13}{2}} b^{19} x^{\frac{13}{2}} + 1890 a^{\frac{11}{2}} b^{20} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{21} x^{\frac{9}{2}}} - \frac{480 a^{11} b^{17} d^{3} x^{\frac{13}{2}}}{315 a^{\frac{21}{2}} b^{15} x^{\frac{21}{2}} + 1890 a^{\frac{19}{2}} b^{16} x^{\frac{19}{2}} + 4725 a^{\frac{17}{2}} b^{17} x^{\frac{17}{2}} + 6300 a^{\frac{15}{2}} b^{18} x^{\frac{15}{2}} + 4725 a^{\frac{13}{2}} b^{19} x^{\frac{13}{2}} + 1890 a^{\frac{11}{2}} b^{20} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{21} x^{\frac{9}{2}}} + \frac{32 a^{11} b^{5} d^{3} x^{\frac{13}{2}}}{105 a^{\frac{13}{2}} b^{7} x^{\frac{13}{2}} + 315 a^{\frac{11}{2}} b^{8} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{9} x^{\frac{9}{2}} + 105 a^{\frac{7}{2}} b^{10} x^{\frac{7}{2}}} - \frac{192 a^{10} b^{18} d^{3} x^{\frac{11}{2}}}{315 a^{\frac{21}{2}} b^{15} x^{\frac{21}{2}} + 1890 a^{\frac{19}{2}} b^{16} x^{\frac{19}{2}} + 4725 a^{\frac{17}{2}} b^{17} x^{\frac{17}{2}} + 6300 a^{\frac{15}{2}} b^{18} x^{\frac{15}{2}} + 4725 a^{\frac{13}{2}} b^{19} x^{\frac{13}{2}} + 1890 a^{\frac{11}{2}} b^{20} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{21} x^{\frac{9}{2}}} + \frac{48 a^{10} b^{6} c d^{2} x^{\frac{13}{2}}}{105 a^{\frac{13}{2}} b^{7} x^{\frac{13}{2}} + 315 a^{\frac{11}{2}} b^{8} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{9} x^{\frac{9}{2}} + 105 a^{\frac{7}{2}} b^{10} x^{\frac{7}{2}}} + \frac{96 a^{10} b^{6} d^{3} x^{\frac{11}{2}}}{105 a^{\frac{13}{2}} b^{7} x^{\frac{13}{2}} + 315 a^{\frac{11}{2}} b^{8} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{9} x^{\frac{9}{2}} + 105 a^{\frac{7}{2}} b^{10} x^{\frac{7}{2}}} - \frac{32 a^{9} b^{19} d^{3} x^{\frac{9}{2}}}{315 a^{\frac{21}{2}} b^{15} x^{\frac{21}{2}} + 1890 a^{\frac{19}{2}} b^{16} x^{\frac{19}{2}} + 4725 a^{\frac{17}{2}} b^{17} x^{\frac{17}{2}} + 6300 a^{\frac{15}{2}} b^{18} x^{\frac{15}{2}} + 4725 a^{\frac{13}{2}} b^{19} x^{\frac{13}{2}} + 1890 a^{\frac{11}{2}} b^{20} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{21} x^{\frac{9}{2}}} + \frac{144 a^{9} b^{7} c d^{2} x^{\frac{11}{2}}}{105 a^{\frac{13}{2}} b^{7} x^{\frac{13}{2}} + 315 a^{\frac{11}{2}} b^{8} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{9} x^{\frac{9}{2}} + 105 a^{\frac{7}{2}} b^{10} x^{\frac{7}{2}}} + \frac{96 a^{9} b^{7} d^{3} x^{\frac{9}{2}}}{105 a^{\frac{13}{2}} b^{7} x^{\frac{13}{2}} + 315 a^{\frac{11}{2}} b^{8} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{9} x^{\frac{9}{2}} + 105 a^{\frac{7}{2}} b^{10} x^{\frac{7}{2}}} + \frac{144 a^{8} b^{8} c d^{2} x^{\frac{9}{2}}}{105 a^{\frac{13}{2}} b^{7} x^{\frac{13}{2}} + 315 a^{\frac{11}{2}} b^{8} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{9} x^{\frac{9}{2}} + 105 a^{\frac{7}{2}} b^{10} x^{\frac{7}{2}}} + \frac{32 a^{8} b^{8} d^{3} x^{\frac{7}{2}}}{105 a^{\frac{13}{2}} b^{7} x^{\frac{13}{2}} + 315 a^{\frac{11}{2}} b^{8} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{9} x^{\frac{9}{2}} + 105 a^{\frac{7}{2}} b^{10} x^{\frac{7}{2}}} - \frac{4 a^{8} b d^{3} x^{\frac{7}{2}}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}} + \frac{48 a^{7} b^{9} c d^{2} x^{\frac{7}{2}}}{105 a^{\frac{13}{2}} b^{7} x^{\frac{13}{2}} + 315 a^{\frac{11}{2}} b^{8} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{9} x^{\frac{9}{2}} + 105 a^{\frac{7}{2}} b^{10} x^{\frac{7}{2}}} - \frac{24 a^{7} b^{2} c d^{2} x^{\frac{7}{2}}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}} - \frac{4 a^{7} b^{2} d^{3} x^{\frac{5}{2}}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}} - \frac{12 a^{6} b^{3} c^{2} d x^{\frac{7}{2}}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}} - \frac{24 a^{6} b^{3} c d^{2} x^{\frac{5}{2}}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}} - \frac{12 a^{5} b^{4} c^{2} d x^{\frac{5}{2}}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}} - \frac{6 a^{3} c^{2} d \operatorname{atan}{\left(\frac{\sqrt{a + \frac{b}{x}}}{\sqrt{- a}} \right)}}{\sqrt{- a}} + a^{2} \sqrt{b} c^{3} \sqrt{x} \sqrt{\frac{a x}{b} + 1} - \frac{4 a^{2} b c^{3} \operatorname{atan}{\left(\frac{\sqrt{a + \frac{b}{x}}}{\sqrt{- a}} \right)}}{\sqrt{- a}} - 6 a^{2} c^{2} d \sqrt{a + \frac{b}{x}} + 3 a^{2} c d^{2} \left(\begin{cases} - \frac{\sqrt{a}}{x} & \text{for}\: b = 0 \\- \frac{2 \left(a + \frac{b}{x}\right)^{\frac{3}{2}}}{3 b} & \text{otherwise} \end{cases}\right) - 4 a b c^{3} \sqrt{a + \frac{b}{x}} + 6 a b c^{2} d \left(\begin{cases} - \frac{\sqrt{a}}{x} & \text{for}\: b = 0 \\- \frac{2 \left(a + \frac{b}{x}\right)^{\frac{3}{2}}}{3 b} & \text{otherwise} \end{cases}\right) + b^{2} c^{3} \left(\begin{cases} - \frac{\sqrt{a}}{x} & \text{for}\: b = 0 \\- \frac{2 \left(a + \frac{b}{x}\right)^{\frac{3}{2}}}{3 b} & \text{otherwise} \end{cases}\right)"," ",0,"32*a**(29/2)*b**(27/2)*d**3*x**10*sqrt(a*x/b + 1)/(315*a**(21/2)*b**15*x**(21/2) + 1890*a**(19/2)*b**16*x**(19/2) + 4725*a**(17/2)*b**17*x**(17/2) + 6300*a**(15/2)*b**18*x**(15/2) + 4725*a**(13/2)*b**19*x**(13/2) + 1890*a**(11/2)*b**20*x**(11/2) + 315*a**(9/2)*b**21*x**(9/2)) + 176*a**(27/2)*b**(29/2)*d**3*x**9*sqrt(a*x/b + 1)/(315*a**(21/2)*b**15*x**(21/2) + 1890*a**(19/2)*b**16*x**(19/2) + 4725*a**(17/2)*b**17*x**(17/2) + 6300*a**(15/2)*b**18*x**(15/2) + 4725*a**(13/2)*b**19*x**(13/2) + 1890*a**(11/2)*b**20*x**(11/2) + 315*a**(9/2)*b**21*x**(9/2)) + 396*a**(25/2)*b**(31/2)*d**3*x**8*sqrt(a*x/b + 1)/(315*a**(21/2)*b**15*x**(21/2) + 1890*a**(19/2)*b**16*x**(19/2) + 4725*a**(17/2)*b**17*x**(17/2) + 6300*a**(15/2)*b**18*x**(15/2) + 4725*a**(13/2)*b**19*x**(13/2) + 1890*a**(11/2)*b**20*x**(11/2) + 315*a**(9/2)*b**21*x**(9/2)) + 462*a**(23/2)*b**(33/2)*d**3*x**7*sqrt(a*x/b + 1)/(315*a**(21/2)*b**15*x**(21/2) + 1890*a**(19/2)*b**16*x**(19/2) + 4725*a**(17/2)*b**17*x**(17/2) + 6300*a**(15/2)*b**18*x**(15/2) + 4725*a**(13/2)*b**19*x**(13/2) + 1890*a**(11/2)*b**20*x**(11/2) + 315*a**(9/2)*b**21*x**(9/2)) + 210*a**(21/2)*b**(35/2)*d**3*x**6*sqrt(a*x/b + 1)/(315*a**(21/2)*b**15*x**(21/2) + 1890*a**(19/2)*b**16*x**(19/2) + 4725*a**(17/2)*b**17*x**(17/2) + 6300*a**(15/2)*b**18*x**(15/2) + 4725*a**(13/2)*b**19*x**(13/2) + 1890*a**(11/2)*b**20*x**(11/2) + 315*a**(9/2)*b**21*x**(9/2)) - 32*a**(21/2)*b**(11/2)*d**3*x**6*sqrt(a*x/b + 1)/(105*a**(13/2)*b**7*x**(13/2) + 315*a**(11/2)*b**8*x**(11/2) + 315*a**(9/2)*b**9*x**(9/2) + 105*a**(7/2)*b**10*x**(7/2)) - 378*a**(19/2)*b**(37/2)*d**3*x**5*sqrt(a*x/b + 1)/(315*a**(21/2)*b**15*x**(21/2) + 1890*a**(19/2)*b**16*x**(19/2) + 4725*a**(17/2)*b**17*x**(17/2) + 6300*a**(15/2)*b**18*x**(15/2) + 4725*a**(13/2)*b**19*x**(13/2) + 1890*a**(11/2)*b**20*x**(11/2) + 315*a**(9/2)*b**21*x**(9/2)) - 48*a**(19/2)*b**(13/2)*c*d**2*x**6*sqrt(a*x/b + 1)/(105*a**(13/2)*b**7*x**(13/2) + 315*a**(11/2)*b**8*x**(11/2) + 315*a**(9/2)*b**9*x**(9/2) + 105*a**(7/2)*b**10*x**(7/2)) - 80*a**(19/2)*b**(13/2)*d**3*x**5*sqrt(a*x/b + 1)/(105*a**(13/2)*b**7*x**(13/2) + 315*a**(11/2)*b**8*x**(11/2) + 315*a**(9/2)*b**9*x**(9/2) + 105*a**(7/2)*b**10*x**(7/2)) - 1134*a**(17/2)*b**(39/2)*d**3*x**4*sqrt(a*x/b + 1)/(315*a**(21/2)*b**15*x**(21/2) + 1890*a**(19/2)*b**16*x**(19/2) + 4725*a**(17/2)*b**17*x**(17/2) + 6300*a**(15/2)*b**18*x**(15/2) + 4725*a**(13/2)*b**19*x**(13/2) + 1890*a**(11/2)*b**20*x**(11/2) + 315*a**(9/2)*b**21*x**(9/2)) - 120*a**(17/2)*b**(15/2)*c*d**2*x**5*sqrt(a*x/b + 1)/(105*a**(13/2)*b**7*x**(13/2) + 315*a**(11/2)*b**8*x**(11/2) + 315*a**(9/2)*b**9*x**(9/2) + 105*a**(7/2)*b**10*x**(7/2)) - 60*a**(17/2)*b**(15/2)*d**3*x**4*sqrt(a*x/b + 1)/(105*a**(13/2)*b**7*x**(13/2) + 315*a**(11/2)*b**8*x**(11/2) + 315*a**(9/2)*b**9*x**(9/2) + 105*a**(7/2)*b**10*x**(7/2)) - 1494*a**(15/2)*b**(41/2)*d**3*x**3*sqrt(a*x/b + 1)/(315*a**(21/2)*b**15*x**(21/2) + 1890*a**(19/2)*b**16*x**(19/2) + 4725*a**(17/2)*b**17*x**(17/2) + 6300*a**(15/2)*b**18*x**(15/2) + 4725*a**(13/2)*b**19*x**(13/2) + 1890*a**(11/2)*b**20*x**(11/2) + 315*a**(9/2)*b**21*x**(9/2)) - 90*a**(15/2)*b**(17/2)*c*d**2*x**4*sqrt(a*x/b + 1)/(105*a**(13/2)*b**7*x**(13/2) + 315*a**(11/2)*b**8*x**(11/2) + 315*a**(9/2)*b**9*x**(9/2) + 105*a**(7/2)*b**10*x**(7/2)) - 80*a**(15/2)*b**(17/2)*d**3*x**3*sqrt(a*x/b + 1)/(105*a**(13/2)*b**7*x**(13/2) + 315*a**(11/2)*b**8*x**(11/2) + 315*a**(9/2)*b**9*x**(9/2) + 105*a**(7/2)*b**10*x**(7/2)) + 4*a**(15/2)*b**(3/2)*d**3*x**3*sqrt(a*x/b + 1)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2)) - 1098*a**(13/2)*b**(43/2)*d**3*x**2*sqrt(a*x/b + 1)/(315*a**(21/2)*b**15*x**(21/2) + 1890*a**(19/2)*b**16*x**(19/2) + 4725*a**(17/2)*b**17*x**(17/2) + 6300*a**(15/2)*b**18*x**(15/2) + 4725*a**(13/2)*b**19*x**(13/2) + 1890*a**(11/2)*b**20*x**(11/2) + 315*a**(9/2)*b**21*x**(9/2)) - 120*a**(13/2)*b**(19/2)*c*d**2*x**3*sqrt(a*x/b + 1)/(105*a**(13/2)*b**7*x**(13/2) + 315*a**(11/2)*b**8*x**(11/2) + 315*a**(9/2)*b**9*x**(9/2) + 105*a**(7/2)*b**10*x**(7/2)) - 200*a**(13/2)*b**(19/2)*d**3*x**2*sqrt(a*x/b + 1)/(105*a**(13/2)*b**7*x**(13/2) + 315*a**(11/2)*b**8*x**(11/2) + 315*a**(9/2)*b**9*x**(9/2) + 105*a**(7/2)*b**10*x**(7/2)) + 24*a**(13/2)*b**(5/2)*c*d**2*x**3*sqrt(a*x/b + 1)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2)) + 2*a**(13/2)*b**(5/2)*d**3*x**2*sqrt(a*x/b + 1)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2)) - 430*a**(11/2)*b**(45/2)*d**3*x*sqrt(a*x/b + 1)/(315*a**(21/2)*b**15*x**(21/2) + 1890*a**(19/2)*b**16*x**(19/2) + 4725*a**(17/2)*b**17*x**(17/2) + 6300*a**(15/2)*b**18*x**(15/2) + 4725*a**(13/2)*b**19*x**(13/2) + 1890*a**(11/2)*b**20*x**(11/2) + 315*a**(9/2)*b**21*x**(9/2)) - 300*a**(11/2)*b**(21/2)*c*d**2*x**2*sqrt(a*x/b + 1)/(105*a**(13/2)*b**7*x**(13/2) + 315*a**(11/2)*b**8*x**(11/2) + 315*a**(9/2)*b**9*x**(9/2) + 105*a**(7/2)*b**10*x**(7/2)) - 192*a**(11/2)*b**(21/2)*d**3*x*sqrt(a*x/b + 1)/(105*a**(13/2)*b**7*x**(13/2) + 315*a**(11/2)*b**8*x**(11/2) + 315*a**(9/2)*b**9*x**(9/2) + 105*a**(7/2)*b**10*x**(7/2)) + 12*a**(11/2)*b**(7/2)*c**2*d*x**3*sqrt(a*x/b + 1)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2)) + 12*a**(11/2)*b**(7/2)*c*d**2*x**2*sqrt(a*x/b + 1)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2)) - 8*a**(11/2)*b**(7/2)*d**3*x*sqrt(a*x/b + 1)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2)) - 70*a**(9/2)*b**(47/2)*d**3*sqrt(a*x/b + 1)/(315*a**(21/2)*b**15*x**(21/2) + 1890*a**(19/2)*b**16*x**(19/2) + 4725*a**(17/2)*b**17*x**(17/2) + 6300*a**(15/2)*b**18*x**(15/2) + 4725*a**(13/2)*b**19*x**(13/2) + 1890*a**(11/2)*b**20*x**(11/2) + 315*a**(9/2)*b**21*x**(9/2)) - 288*a**(9/2)*b**(23/2)*c*d**2*x*sqrt(a*x/b + 1)/(105*a**(13/2)*b**7*x**(13/2) + 315*a**(11/2)*b**8*x**(11/2) + 315*a**(9/2)*b**9*x**(9/2) + 105*a**(7/2)*b**10*x**(7/2)) - 60*a**(9/2)*b**(23/2)*d**3*sqrt(a*x/b + 1)/(105*a**(13/2)*b**7*x**(13/2) + 315*a**(11/2)*b**8*x**(11/2) + 315*a**(9/2)*b**9*x**(9/2) + 105*a**(7/2)*b**10*x**(7/2)) + 6*a**(9/2)*b**(9/2)*c**2*d*x**2*sqrt(a*x/b + 1)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2)) - 48*a**(9/2)*b**(9/2)*c*d**2*x*sqrt(a*x/b + 1)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2)) - 6*a**(9/2)*b**(9/2)*d**3*sqrt(a*x/b + 1)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2)) - 90*a**(7/2)*b**(25/2)*c*d**2*sqrt(a*x/b + 1)/(105*a**(13/2)*b**7*x**(13/2) + 315*a**(11/2)*b**8*x**(11/2) + 315*a**(9/2)*b**9*x**(9/2) + 105*a**(7/2)*b**10*x**(7/2)) - 24*a**(7/2)*b**(11/2)*c**2*d*x*sqrt(a*x/b + 1)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2)) - 36*a**(7/2)*b**(11/2)*c*d**2*sqrt(a*x/b + 1)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2)) - 18*a**(5/2)*b**(13/2)*c**2*d*sqrt(a*x/b + 1)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2)) + a**(3/2)*b*c**3*asinh(sqrt(a)*sqrt(x)/sqrt(b)) - 32*a**15*b**13*d**3*x**(21/2)/(315*a**(21/2)*b**15*x**(21/2) + 1890*a**(19/2)*b**16*x**(19/2) + 4725*a**(17/2)*b**17*x**(17/2) + 6300*a**(15/2)*b**18*x**(15/2) + 4725*a**(13/2)*b**19*x**(13/2) + 1890*a**(11/2)*b**20*x**(11/2) + 315*a**(9/2)*b**21*x**(9/2)) - 192*a**14*b**14*d**3*x**(19/2)/(315*a**(21/2)*b**15*x**(21/2) + 1890*a**(19/2)*b**16*x**(19/2) + 4725*a**(17/2)*b**17*x**(17/2) + 6300*a**(15/2)*b**18*x**(15/2) + 4725*a**(13/2)*b**19*x**(13/2) + 1890*a**(11/2)*b**20*x**(11/2) + 315*a**(9/2)*b**21*x**(9/2)) - 480*a**13*b**15*d**3*x**(17/2)/(315*a**(21/2)*b**15*x**(21/2) + 1890*a**(19/2)*b**16*x**(19/2) + 4725*a**(17/2)*b**17*x**(17/2) + 6300*a**(15/2)*b**18*x**(15/2) + 4725*a**(13/2)*b**19*x**(13/2) + 1890*a**(11/2)*b**20*x**(11/2) + 315*a**(9/2)*b**21*x**(9/2)) - 640*a**12*b**16*d**3*x**(15/2)/(315*a**(21/2)*b**15*x**(21/2) + 1890*a**(19/2)*b**16*x**(19/2) + 4725*a**(17/2)*b**17*x**(17/2) + 6300*a**(15/2)*b**18*x**(15/2) + 4725*a**(13/2)*b**19*x**(13/2) + 1890*a**(11/2)*b**20*x**(11/2) + 315*a**(9/2)*b**21*x**(9/2)) - 480*a**11*b**17*d**3*x**(13/2)/(315*a**(21/2)*b**15*x**(21/2) + 1890*a**(19/2)*b**16*x**(19/2) + 4725*a**(17/2)*b**17*x**(17/2) + 6300*a**(15/2)*b**18*x**(15/2) + 4725*a**(13/2)*b**19*x**(13/2) + 1890*a**(11/2)*b**20*x**(11/2) + 315*a**(9/2)*b**21*x**(9/2)) + 32*a**11*b**5*d**3*x**(13/2)/(105*a**(13/2)*b**7*x**(13/2) + 315*a**(11/2)*b**8*x**(11/2) + 315*a**(9/2)*b**9*x**(9/2) + 105*a**(7/2)*b**10*x**(7/2)) - 192*a**10*b**18*d**3*x**(11/2)/(315*a**(21/2)*b**15*x**(21/2) + 1890*a**(19/2)*b**16*x**(19/2) + 4725*a**(17/2)*b**17*x**(17/2) + 6300*a**(15/2)*b**18*x**(15/2) + 4725*a**(13/2)*b**19*x**(13/2) + 1890*a**(11/2)*b**20*x**(11/2) + 315*a**(9/2)*b**21*x**(9/2)) + 48*a**10*b**6*c*d**2*x**(13/2)/(105*a**(13/2)*b**7*x**(13/2) + 315*a**(11/2)*b**8*x**(11/2) + 315*a**(9/2)*b**9*x**(9/2) + 105*a**(7/2)*b**10*x**(7/2)) + 96*a**10*b**6*d**3*x**(11/2)/(105*a**(13/2)*b**7*x**(13/2) + 315*a**(11/2)*b**8*x**(11/2) + 315*a**(9/2)*b**9*x**(9/2) + 105*a**(7/2)*b**10*x**(7/2)) - 32*a**9*b**19*d**3*x**(9/2)/(315*a**(21/2)*b**15*x**(21/2) + 1890*a**(19/2)*b**16*x**(19/2) + 4725*a**(17/2)*b**17*x**(17/2) + 6300*a**(15/2)*b**18*x**(15/2) + 4725*a**(13/2)*b**19*x**(13/2) + 1890*a**(11/2)*b**20*x**(11/2) + 315*a**(9/2)*b**21*x**(9/2)) + 144*a**9*b**7*c*d**2*x**(11/2)/(105*a**(13/2)*b**7*x**(13/2) + 315*a**(11/2)*b**8*x**(11/2) + 315*a**(9/2)*b**9*x**(9/2) + 105*a**(7/2)*b**10*x**(7/2)) + 96*a**9*b**7*d**3*x**(9/2)/(105*a**(13/2)*b**7*x**(13/2) + 315*a**(11/2)*b**8*x**(11/2) + 315*a**(9/2)*b**9*x**(9/2) + 105*a**(7/2)*b**10*x**(7/2)) + 144*a**8*b**8*c*d**2*x**(9/2)/(105*a**(13/2)*b**7*x**(13/2) + 315*a**(11/2)*b**8*x**(11/2) + 315*a**(9/2)*b**9*x**(9/2) + 105*a**(7/2)*b**10*x**(7/2)) + 32*a**8*b**8*d**3*x**(7/2)/(105*a**(13/2)*b**7*x**(13/2) + 315*a**(11/2)*b**8*x**(11/2) + 315*a**(9/2)*b**9*x**(9/2) + 105*a**(7/2)*b**10*x**(7/2)) - 4*a**8*b*d**3*x**(7/2)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2)) + 48*a**7*b**9*c*d**2*x**(7/2)/(105*a**(13/2)*b**7*x**(13/2) + 315*a**(11/2)*b**8*x**(11/2) + 315*a**(9/2)*b**9*x**(9/2) + 105*a**(7/2)*b**10*x**(7/2)) - 24*a**7*b**2*c*d**2*x**(7/2)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2)) - 4*a**7*b**2*d**3*x**(5/2)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2)) - 12*a**6*b**3*c**2*d*x**(7/2)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2)) - 24*a**6*b**3*c*d**2*x**(5/2)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2)) - 12*a**5*b**4*c**2*d*x**(5/2)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2)) - 6*a**3*c**2*d*atan(sqrt(a + b/x)/sqrt(-a))/sqrt(-a) + a**2*sqrt(b)*c**3*sqrt(x)*sqrt(a*x/b + 1) - 4*a**2*b*c**3*atan(sqrt(a + b/x)/sqrt(-a))/sqrt(-a) - 6*a**2*c**2*d*sqrt(a + b/x) + 3*a**2*c*d**2*Piecewise((-sqrt(a)/x, Eq(b, 0)), (-2*(a + b/x)**(3/2)/(3*b), True)) - 4*a*b*c**3*sqrt(a + b/x) + 6*a*b*c**2*d*Piecewise((-sqrt(a)/x, Eq(b, 0)), (-2*(a + b/x)**(3/2)/(3*b), True)) + b**2*c**3*Piecewise((-sqrt(a)/x, Eq(b, 0)), (-2*(a + b/x)**(3/2)/(3*b), True))","A",0
239,1,1841,0,112.030878," ","integrate((a+b/x)**(5/2)*(c+d/x)**2,x)","- \frac{16 a^{\frac{19}{2}} b^{\frac{13}{2}} d^{2} x^{6} \sqrt{\frac{a x}{b} + 1}}{105 a^{\frac{13}{2}} b^{7} x^{\frac{13}{2}} + 315 a^{\frac{11}{2}} b^{8} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{9} x^{\frac{9}{2}} + 105 a^{\frac{7}{2}} b^{10} x^{\frac{7}{2}}} - \frac{40 a^{\frac{17}{2}} b^{\frac{15}{2}} d^{2} x^{5} \sqrt{\frac{a x}{b} + 1}}{105 a^{\frac{13}{2}} b^{7} x^{\frac{13}{2}} + 315 a^{\frac{11}{2}} b^{8} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{9} x^{\frac{9}{2}} + 105 a^{\frac{7}{2}} b^{10} x^{\frac{7}{2}}} - \frac{30 a^{\frac{15}{2}} b^{\frac{17}{2}} d^{2} x^{4} \sqrt{\frac{a x}{b} + 1}}{105 a^{\frac{13}{2}} b^{7} x^{\frac{13}{2}} + 315 a^{\frac{11}{2}} b^{8} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{9} x^{\frac{9}{2}} + 105 a^{\frac{7}{2}} b^{10} x^{\frac{7}{2}}} - \frac{40 a^{\frac{13}{2}} b^{\frac{19}{2}} d^{2} x^{3} \sqrt{\frac{a x}{b} + 1}}{105 a^{\frac{13}{2}} b^{7} x^{\frac{13}{2}} + 315 a^{\frac{11}{2}} b^{8} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{9} x^{\frac{9}{2}} + 105 a^{\frac{7}{2}} b^{10} x^{\frac{7}{2}}} + \frac{8 a^{\frac{13}{2}} b^{\frac{5}{2}} d^{2} x^{3} \sqrt{\frac{a x}{b} + 1}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}} - \frac{100 a^{\frac{11}{2}} b^{\frac{21}{2}} d^{2} x^{2} \sqrt{\frac{a x}{b} + 1}}{105 a^{\frac{13}{2}} b^{7} x^{\frac{13}{2}} + 315 a^{\frac{11}{2}} b^{8} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{9} x^{\frac{9}{2}} + 105 a^{\frac{7}{2}} b^{10} x^{\frac{7}{2}}} + \frac{8 a^{\frac{11}{2}} b^{\frac{7}{2}} c d x^{3} \sqrt{\frac{a x}{b} + 1}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}} + \frac{4 a^{\frac{11}{2}} b^{\frac{7}{2}} d^{2} x^{2} \sqrt{\frac{a x}{b} + 1}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}} - \frac{96 a^{\frac{9}{2}} b^{\frac{23}{2}} d^{2} x \sqrt{\frac{a x}{b} + 1}}{105 a^{\frac{13}{2}} b^{7} x^{\frac{13}{2}} + 315 a^{\frac{11}{2}} b^{8} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{9} x^{\frac{9}{2}} + 105 a^{\frac{7}{2}} b^{10} x^{\frac{7}{2}}} + \frac{4 a^{\frac{9}{2}} b^{\frac{9}{2}} c d x^{2} \sqrt{\frac{a x}{b} + 1}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}} - \frac{16 a^{\frac{9}{2}} b^{\frac{9}{2}} d^{2} x \sqrt{\frac{a x}{b} + 1}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}} - \frac{30 a^{\frac{7}{2}} b^{\frac{25}{2}} d^{2} \sqrt{\frac{a x}{b} + 1}}{105 a^{\frac{13}{2}} b^{7} x^{\frac{13}{2}} + 315 a^{\frac{11}{2}} b^{8} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{9} x^{\frac{9}{2}} + 105 a^{\frac{7}{2}} b^{10} x^{\frac{7}{2}}} - \frac{16 a^{\frac{7}{2}} b^{\frac{11}{2}} c d x \sqrt{\frac{a x}{b} + 1}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}} - \frac{12 a^{\frac{7}{2}} b^{\frac{11}{2}} d^{2} \sqrt{\frac{a x}{b} + 1}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}} - \frac{12 a^{\frac{5}{2}} b^{\frac{13}{2}} c d \sqrt{\frac{a x}{b} + 1}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}} + a^{\frac{3}{2}} b c^{2} \operatorname{asinh}{\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}} \right)} + \frac{16 a^{10} b^{6} d^{2} x^{\frac{13}{2}}}{105 a^{\frac{13}{2}} b^{7} x^{\frac{13}{2}} + 315 a^{\frac{11}{2}} b^{8} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{9} x^{\frac{9}{2}} + 105 a^{\frac{7}{2}} b^{10} x^{\frac{7}{2}}} + \frac{48 a^{9} b^{7} d^{2} x^{\frac{11}{2}}}{105 a^{\frac{13}{2}} b^{7} x^{\frac{13}{2}} + 315 a^{\frac{11}{2}} b^{8} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{9} x^{\frac{9}{2}} + 105 a^{\frac{7}{2}} b^{10} x^{\frac{7}{2}}} + \frac{48 a^{8} b^{8} d^{2} x^{\frac{9}{2}}}{105 a^{\frac{13}{2}} b^{7} x^{\frac{13}{2}} + 315 a^{\frac{11}{2}} b^{8} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{9} x^{\frac{9}{2}} + 105 a^{\frac{7}{2}} b^{10} x^{\frac{7}{2}}} + \frac{16 a^{7} b^{9} d^{2} x^{\frac{7}{2}}}{105 a^{\frac{13}{2}} b^{7} x^{\frac{13}{2}} + 315 a^{\frac{11}{2}} b^{8} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{9} x^{\frac{9}{2}} + 105 a^{\frac{7}{2}} b^{10} x^{\frac{7}{2}}} - \frac{8 a^{7} b^{2} d^{2} x^{\frac{7}{2}}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}} - \frac{8 a^{6} b^{3} c d x^{\frac{7}{2}}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}} - \frac{8 a^{6} b^{3} d^{2} x^{\frac{5}{2}}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}} - \frac{8 a^{5} b^{4} c d x^{\frac{5}{2}}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}} - \frac{4 a^{3} c d \operatorname{atan}{\left(\frac{\sqrt{a + \frac{b}{x}}}{\sqrt{- a}} \right)}}{\sqrt{- a}} + a^{2} \sqrt{b} c^{2} \sqrt{x} \sqrt{\frac{a x}{b} + 1} - \frac{4 a^{2} b c^{2} \operatorname{atan}{\left(\frac{\sqrt{a + \frac{b}{x}}}{\sqrt{- a}} \right)}}{\sqrt{- a}} - 4 a^{2} c d \sqrt{a + \frac{b}{x}} + a^{2} d^{2} \left(\begin{cases} - \frac{\sqrt{a}}{x} & \text{for}\: b = 0 \\- \frac{2 \left(a + \frac{b}{x}\right)^{\frac{3}{2}}}{3 b} & \text{otherwise} \end{cases}\right) - 4 a b c^{2} \sqrt{a + \frac{b}{x}} + 4 a b c d \left(\begin{cases} - \frac{\sqrt{a}}{x} & \text{for}\: b = 0 \\- \frac{2 \left(a + \frac{b}{x}\right)^{\frac{3}{2}}}{3 b} & \text{otherwise} \end{cases}\right) + b^{2} c^{2} \left(\begin{cases} - \frac{\sqrt{a}}{x} & \text{for}\: b = 0 \\- \frac{2 \left(a + \frac{b}{x}\right)^{\frac{3}{2}}}{3 b} & \text{otherwise} \end{cases}\right)"," ",0,"-16*a**(19/2)*b**(13/2)*d**2*x**6*sqrt(a*x/b + 1)/(105*a**(13/2)*b**7*x**(13/2) + 315*a**(11/2)*b**8*x**(11/2) + 315*a**(9/2)*b**9*x**(9/2) + 105*a**(7/2)*b**10*x**(7/2)) - 40*a**(17/2)*b**(15/2)*d**2*x**5*sqrt(a*x/b + 1)/(105*a**(13/2)*b**7*x**(13/2) + 315*a**(11/2)*b**8*x**(11/2) + 315*a**(9/2)*b**9*x**(9/2) + 105*a**(7/2)*b**10*x**(7/2)) - 30*a**(15/2)*b**(17/2)*d**2*x**4*sqrt(a*x/b + 1)/(105*a**(13/2)*b**7*x**(13/2) + 315*a**(11/2)*b**8*x**(11/2) + 315*a**(9/2)*b**9*x**(9/2) + 105*a**(7/2)*b**10*x**(7/2)) - 40*a**(13/2)*b**(19/2)*d**2*x**3*sqrt(a*x/b + 1)/(105*a**(13/2)*b**7*x**(13/2) + 315*a**(11/2)*b**8*x**(11/2) + 315*a**(9/2)*b**9*x**(9/2) + 105*a**(7/2)*b**10*x**(7/2)) + 8*a**(13/2)*b**(5/2)*d**2*x**3*sqrt(a*x/b + 1)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2)) - 100*a**(11/2)*b**(21/2)*d**2*x**2*sqrt(a*x/b + 1)/(105*a**(13/2)*b**7*x**(13/2) + 315*a**(11/2)*b**8*x**(11/2) + 315*a**(9/2)*b**9*x**(9/2) + 105*a**(7/2)*b**10*x**(7/2)) + 8*a**(11/2)*b**(7/2)*c*d*x**3*sqrt(a*x/b + 1)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2)) + 4*a**(11/2)*b**(7/2)*d**2*x**2*sqrt(a*x/b + 1)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2)) - 96*a**(9/2)*b**(23/2)*d**2*x*sqrt(a*x/b + 1)/(105*a**(13/2)*b**7*x**(13/2) + 315*a**(11/2)*b**8*x**(11/2) + 315*a**(9/2)*b**9*x**(9/2) + 105*a**(7/2)*b**10*x**(7/2)) + 4*a**(9/2)*b**(9/2)*c*d*x**2*sqrt(a*x/b + 1)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2)) - 16*a**(9/2)*b**(9/2)*d**2*x*sqrt(a*x/b + 1)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2)) - 30*a**(7/2)*b**(25/2)*d**2*sqrt(a*x/b + 1)/(105*a**(13/2)*b**7*x**(13/2) + 315*a**(11/2)*b**8*x**(11/2) + 315*a**(9/2)*b**9*x**(9/2) + 105*a**(7/2)*b**10*x**(7/2)) - 16*a**(7/2)*b**(11/2)*c*d*x*sqrt(a*x/b + 1)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2)) - 12*a**(7/2)*b**(11/2)*d**2*sqrt(a*x/b + 1)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2)) - 12*a**(5/2)*b**(13/2)*c*d*sqrt(a*x/b + 1)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2)) + a**(3/2)*b*c**2*asinh(sqrt(a)*sqrt(x)/sqrt(b)) + 16*a**10*b**6*d**2*x**(13/2)/(105*a**(13/2)*b**7*x**(13/2) + 315*a**(11/2)*b**8*x**(11/2) + 315*a**(9/2)*b**9*x**(9/2) + 105*a**(7/2)*b**10*x**(7/2)) + 48*a**9*b**7*d**2*x**(11/2)/(105*a**(13/2)*b**7*x**(13/2) + 315*a**(11/2)*b**8*x**(11/2) + 315*a**(9/2)*b**9*x**(9/2) + 105*a**(7/2)*b**10*x**(7/2)) + 48*a**8*b**8*d**2*x**(9/2)/(105*a**(13/2)*b**7*x**(13/2) + 315*a**(11/2)*b**8*x**(11/2) + 315*a**(9/2)*b**9*x**(9/2) + 105*a**(7/2)*b**10*x**(7/2)) + 16*a**7*b**9*d**2*x**(7/2)/(105*a**(13/2)*b**7*x**(13/2) + 315*a**(11/2)*b**8*x**(11/2) + 315*a**(9/2)*b**9*x**(9/2) + 105*a**(7/2)*b**10*x**(7/2)) - 8*a**7*b**2*d**2*x**(7/2)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2)) - 8*a**6*b**3*c*d*x**(7/2)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2)) - 8*a**6*b**3*d**2*x**(5/2)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2)) - 8*a**5*b**4*c*d*x**(5/2)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2)) - 4*a**3*c*d*atan(sqrt(a + b/x)/sqrt(-a))/sqrt(-a) + a**2*sqrt(b)*c**2*sqrt(x)*sqrt(a*x/b + 1) - 4*a**2*b*c**2*atan(sqrt(a + b/x)/sqrt(-a))/sqrt(-a) - 4*a**2*c*d*sqrt(a + b/x) + a**2*d**2*Piecewise((-sqrt(a)/x, Eq(b, 0)), (-2*(a + b/x)**(3/2)/(3*b), True)) - 4*a*b*c**2*sqrt(a + b/x) + 4*a*b*c*d*Piecewise((-sqrt(a)/x, Eq(b, 0)), (-2*(a + b/x)**(3/2)/(3*b), True)) + b**2*c**2*Piecewise((-sqrt(a)/x, Eq(b, 0)), (-2*(a + b/x)**(3/2)/(3*b), True))","A",0
240,1,520,0,82.772639," ","integrate((a+b/x)**(5/2)*(c+d/x),x)","\frac{4 a^{\frac{11}{2}} b^{\frac{7}{2}} d x^{3} \sqrt{\frac{a x}{b} + 1}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}} + \frac{2 a^{\frac{9}{2}} b^{\frac{9}{2}} d x^{2} \sqrt{\frac{a x}{b} + 1}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}} - \frac{8 a^{\frac{7}{2}} b^{\frac{11}{2}} d x \sqrt{\frac{a x}{b} + 1}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}} - \frac{6 a^{\frac{5}{2}} b^{\frac{13}{2}} d \sqrt{\frac{a x}{b} + 1}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}} + a^{\frac{3}{2}} b c \operatorname{asinh}{\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}} \right)} - \frac{4 a^{6} b^{3} d x^{\frac{7}{2}}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}} - \frac{4 a^{5} b^{4} d x^{\frac{5}{2}}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}} - \frac{2 a^{3} d \operatorname{atan}{\left(\frac{\sqrt{a + \frac{b}{x}}}{\sqrt{- a}} \right)}}{\sqrt{- a}} + a^{2} \sqrt{b} c \sqrt{x} \sqrt{\frac{a x}{b} + 1} - \frac{4 a^{2} b c \operatorname{atan}{\left(\frac{\sqrt{a + \frac{b}{x}}}{\sqrt{- a}} \right)}}{\sqrt{- a}} - 2 a^{2} d \sqrt{a + \frac{b}{x}} - 4 a b c \sqrt{a + \frac{b}{x}} + 2 a b d \left(\begin{cases} - \frac{\sqrt{a}}{x} & \text{for}\: b = 0 \\- \frac{2 \left(a + \frac{b}{x}\right)^{\frac{3}{2}}}{3 b} & \text{otherwise} \end{cases}\right) + b^{2} c \left(\begin{cases} - \frac{\sqrt{a}}{x} & \text{for}\: b = 0 \\- \frac{2 \left(a + \frac{b}{x}\right)^{\frac{3}{2}}}{3 b} & \text{otherwise} \end{cases}\right)"," ",0,"4*a**(11/2)*b**(7/2)*d*x**3*sqrt(a*x/b + 1)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2)) + 2*a**(9/2)*b**(9/2)*d*x**2*sqrt(a*x/b + 1)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2)) - 8*a**(7/2)*b**(11/2)*d*x*sqrt(a*x/b + 1)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2)) - 6*a**(5/2)*b**(13/2)*d*sqrt(a*x/b + 1)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2)) + a**(3/2)*b*c*asinh(sqrt(a)*sqrt(x)/sqrt(b)) - 4*a**6*b**3*d*x**(7/2)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2)) - 4*a**5*b**4*d*x**(5/2)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2)) - 2*a**3*d*atan(sqrt(a + b/x)/sqrt(-a))/sqrt(-a) + a**2*sqrt(b)*c*sqrt(x)*sqrt(a*x/b + 1) - 4*a**2*b*c*atan(sqrt(a + b/x)/sqrt(-a))/sqrt(-a) - 2*a**2*d*sqrt(a + b/x) - 4*a*b*c*sqrt(a + b/x) + 2*a*b*d*Piecewise((-sqrt(a)/x, Eq(b, 0)), (-2*(a + b/x)**(3/2)/(3*b), True)) + b**2*c*Piecewise((-sqrt(a)/x, Eq(b, 0)), (-2*(a + b/x)**(3/2)/(3*b), True))","A",0
241,1,99,0,4.363831," ","integrate((a+b/x)**(5/2),x)","a^{\frac{5}{2}} x \sqrt{1 + \frac{b}{a x}} - \frac{14 a^{\frac{3}{2}} b \sqrt{1 + \frac{b}{a x}}}{3} - \frac{5 a^{\frac{3}{2}} b \log{\left(\frac{b}{a x} \right)}}{2} + 5 a^{\frac{3}{2}} b \log{\left(\sqrt{1 + \frac{b}{a x}} + 1 \right)} - \frac{2 \sqrt{a} b^{2} \sqrt{1 + \frac{b}{a x}}}{3 x}"," ",0,"a**(5/2)*x*sqrt(1 + b/(a*x)) - 14*a**(3/2)*b*sqrt(1 + b/(a*x))/3 - 5*a**(3/2)*b*log(b/(a*x))/2 + 5*a**(3/2)*b*log(sqrt(1 + b/(a*x)) + 1) - 2*sqrt(a)*b**2*sqrt(1 + b/(a*x))/(3*x)","A",0
242,-1,0,0,0.000000," ","integrate((a+b/x)**(5/2)/(c+d/x),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
243,-1,0,0,0.000000," ","integrate((a+b/x)**(5/2)/(c+d/x)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
244,-1,0,0,0.000000," ","integrate((a+b/x)**(5/2)/(c+d/x)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
245,1,386,0,89.998959," ","integrate((c+d/x)**3/(a+b/x)**(1/2),x)","\frac{4 a^{\frac{7}{2}} b^{\frac{3}{2}} d^{3} x^{2} \sqrt{\frac{a x}{b} + 1}}{3 a^{\frac{5}{2}} b^{3} x^{\frac{5}{2}} + 3 a^{\frac{3}{2}} b^{4} x^{\frac{3}{2}}} + \frac{2 a^{\frac{5}{2}} b^{\frac{5}{2}} d^{3} x \sqrt{\frac{a x}{b} + 1}}{3 a^{\frac{5}{2}} b^{3} x^{\frac{5}{2}} + 3 a^{\frac{3}{2}} b^{4} x^{\frac{3}{2}}} - \frac{2 a^{\frac{3}{2}} b^{\frac{7}{2}} d^{3} \sqrt{\frac{a x}{b} + 1}}{3 a^{\frac{5}{2}} b^{3} x^{\frac{5}{2}} + 3 a^{\frac{3}{2}} b^{4} x^{\frac{3}{2}}} - \frac{4 a^{4} b d^{3} x^{\frac{5}{2}}}{3 a^{\frac{5}{2}} b^{3} x^{\frac{5}{2}} + 3 a^{\frac{3}{2}} b^{4} x^{\frac{3}{2}}} - \frac{4 a^{3} b^{2} d^{3} x^{\frac{3}{2}}}{3 a^{\frac{5}{2}} b^{3} x^{\frac{5}{2}} + 3 a^{\frac{3}{2}} b^{4} x^{\frac{3}{2}}} + 3 c d^{2} \left(\begin{cases} - \frac{1}{\sqrt{a} x} & \text{for}\: b = 0 \\- \frac{2 \sqrt{a + \frac{b}{x}}}{b} & \text{otherwise} \end{cases}\right) + \frac{\sqrt{b} c^{3} \sqrt{x} \sqrt{\frac{a x}{b} + 1}}{a} - \frac{6 c^{2} d \operatorname{atan}{\left(\frac{1}{\sqrt{- \frac{1}{a}} \sqrt{a + \frac{b}{x}}} \right)}}{a \sqrt{- \frac{1}{a}}} - \frac{b c^{3} \operatorname{asinh}{\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}} \right)}}{a^{\frac{3}{2}}}"," ",0,"4*a**(7/2)*b**(3/2)*d**3*x**2*sqrt(a*x/b + 1)/(3*a**(5/2)*b**3*x**(5/2) + 3*a**(3/2)*b**4*x**(3/2)) + 2*a**(5/2)*b**(5/2)*d**3*x*sqrt(a*x/b + 1)/(3*a**(5/2)*b**3*x**(5/2) + 3*a**(3/2)*b**4*x**(3/2)) - 2*a**(3/2)*b**(7/2)*d**3*sqrt(a*x/b + 1)/(3*a**(5/2)*b**3*x**(5/2) + 3*a**(3/2)*b**4*x**(3/2)) - 4*a**4*b*d**3*x**(5/2)/(3*a**(5/2)*b**3*x**(5/2) + 3*a**(3/2)*b**4*x**(3/2)) - 4*a**3*b**2*d**3*x**(3/2)/(3*a**(5/2)*b**3*x**(5/2) + 3*a**(3/2)*b**4*x**(3/2)) + 3*c*d**2*Piecewise((-1/(sqrt(a)*x), Eq(b, 0)), (-2*sqrt(a + b/x)/b, True)) + sqrt(b)*c**3*sqrt(x)*sqrt(a*x/b + 1)/a - 6*c**2*d*atan(1/(sqrt(-1/a)*sqrt(a + b/x)))/(a*sqrt(-1/a)) - b*c**3*asinh(sqrt(a)*sqrt(x)/sqrt(b))/a**(3/2)","A",0
246,1,114,0,83.771818," ","integrate((c+d/x)**2/(a+b/x)**(1/2),x)","d^{2} \left(\begin{cases} - \frac{1}{\sqrt{a} x} & \text{for}\: b = 0 \\- \frac{2 \sqrt{a + \frac{b}{x}}}{b} & \text{otherwise} \end{cases}\right) + \frac{\sqrt{b} c^{2} \sqrt{x} \sqrt{\frac{a x}{b} + 1}}{a} - \frac{4 c d \operatorname{atan}{\left(\frac{1}{\sqrt{- \frac{1}{a}} \sqrt{a + \frac{b}{x}}} \right)}}{a \sqrt{- \frac{1}{a}}} - \frac{b c^{2} \operatorname{asinh}{\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}} \right)}}{a^{\frac{3}{2}}}"," ",0,"d**2*Piecewise((-1/(sqrt(a)*x), Eq(b, 0)), (-2*sqrt(a + b/x)/b, True)) + sqrt(b)*c**2*sqrt(x)*sqrt(a*x/b + 1)/a - 4*c*d*atan(1/(sqrt(-1/a)*sqrt(a + b/x)))/(a*sqrt(-1/a)) - b*c**2*asinh(sqrt(a)*sqrt(x)/sqrt(b))/a**(3/2)","A",0
247,1,82,0,60.251878," ","integrate((c+d/x)/(a+b/x)**(1/2),x)","\frac{\sqrt{b} c \sqrt{x} \sqrt{\frac{a x}{b} + 1}}{a} - \frac{2 d \operatorname{atan}{\left(\frac{1}{\sqrt{- \frac{1}{a}} \sqrt{a + \frac{b}{x}}} \right)}}{a \sqrt{- \frac{1}{a}}} - \frac{b c \operatorname{asinh}{\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}} \right)}}{a^{\frac{3}{2}}}"," ",0,"sqrt(b)*c*sqrt(x)*sqrt(a*x/b + 1)/a - 2*d*atan(1/(sqrt(-1/a)*sqrt(a + b/x)))/(a*sqrt(-1/a)) - b*c*asinh(sqrt(a)*sqrt(x)/sqrt(b))/a**(3/2)","A",0
248,1,44,0,3.087851," ","integrate(1/(a+b/x)**(1/2),x)","\frac{\sqrt{b} \sqrt{x} \sqrt{\frac{a x}{b} + 1}}{a} - \frac{b \operatorname{asinh}{\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}} \right)}}{a^{\frac{3}{2}}}"," ",0,"sqrt(b)*sqrt(x)*sqrt(a*x/b + 1)/a - b*asinh(sqrt(a)*sqrt(x)/sqrt(b))/a**(3/2)","A",0
249,0,0,0,0.000000," ","integrate(1/(c+d/x)/(a+b/x)**(1/2),x)","\int \frac{x}{\sqrt{a + \frac{b}{x}} \left(c x + d\right)}\, dx"," ",0,"Integral(x/(sqrt(a + b/x)*(c*x + d)), x)","F",0
250,-1,0,0,0.000000," ","integrate(1/(c+d/x)**2/(a+b/x)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
251,-1,0,0,0.000000," ","integrate(1/(c+d/x)**3/(a+b/x)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
252,0,0,0,0.000000," ","integrate((c+d/x)**3/(a+b/x)**(3/2),x)","\int \frac{\left(c x + d\right)^{3}}{x^{3} \left(a + \frac{b}{x}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((c*x + d)**3/(x**3*(a + b/x)**(3/2)), x)","F",0
253,0,0,0,0.000000," ","integrate((c+d/x)**2/(a+b/x)**(3/2),x)","\int \frac{\left(c x + d\right)^{2}}{x^{2} \left(a + \frac{b}{x}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((c*x + d)**2/(x**2*(a + b/x)**(3/2)), x)","F",0
254,1,224,0,81.343740," ","integrate((c+d/x)/(a+b/x)**(3/2),x)","c \left(\frac{x^{\frac{3}{2}}}{a \sqrt{b} \sqrt{\frac{a x}{b} + 1}} + \frac{3 \sqrt{b} \sqrt{x}}{a^{2} \sqrt{\frac{a x}{b} + 1}} - \frac{3 b \operatorname{asinh}{\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}} \right)}}{a^{\frac{5}{2}}}\right) + d \left(- \frac{2 a^{3} x \sqrt{1 + \frac{b}{a x}}}{a^{\frac{9}{2}} x + a^{\frac{7}{2}} b} - \frac{a^{3} x \log{\left(\frac{b}{a x} \right)}}{a^{\frac{9}{2}} x + a^{\frac{7}{2}} b} + \frac{2 a^{3} x \log{\left(\sqrt{1 + \frac{b}{a x}} + 1 \right)}}{a^{\frac{9}{2}} x + a^{\frac{7}{2}} b} - \frac{a^{2} b \log{\left(\frac{b}{a x} \right)}}{a^{\frac{9}{2}} x + a^{\frac{7}{2}} b} + \frac{2 a^{2} b \log{\left(\sqrt{1 + \frac{b}{a x}} + 1 \right)}}{a^{\frac{9}{2}} x + a^{\frac{7}{2}} b}\right)"," ",0,"c*(x**(3/2)/(a*sqrt(b)*sqrt(a*x/b + 1)) + 3*sqrt(b)*sqrt(x)/(a**2*sqrt(a*x/b + 1)) - 3*b*asinh(sqrt(a)*sqrt(x)/sqrt(b))/a**(5/2)) + d*(-2*a**3*x*sqrt(1 + b/(a*x))/(a**(9/2)*x + a**(7/2)*b) - a**3*x*log(b/(a*x))/(a**(9/2)*x + a**(7/2)*b) + 2*a**3*x*log(sqrt(1 + b/(a*x)) + 1)/(a**(9/2)*x + a**(7/2)*b) - a**2*b*log(b/(a*x))/(a**(9/2)*x + a**(7/2)*b) + 2*a**2*b*log(sqrt(1 + b/(a*x)) + 1)/(a**(9/2)*x + a**(7/2)*b))","B",0
255,1,71,0,4.793870," ","integrate(1/(a+b/x)**(3/2),x)","\frac{x^{\frac{3}{2}}}{a \sqrt{b} \sqrt{\frac{a x}{b} + 1}} + \frac{3 \sqrt{b} \sqrt{x}}{a^{2} \sqrt{\frac{a x}{b} + 1}} - \frac{3 b \operatorname{asinh}{\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}} \right)}}{a^{\frac{5}{2}}}"," ",0,"x**(3/2)/(a*sqrt(b)*sqrt(a*x/b + 1)) + 3*sqrt(b)*sqrt(x)/(a**2*sqrt(a*x/b + 1)) - 3*b*asinh(sqrt(a)*sqrt(x)/sqrt(b))/a**(5/2)","A",0
256,0,0,0,0.000000," ","integrate(1/(a+b/x)**(3/2)/(c+d/x),x)","\int \frac{x}{\left(a + \frac{b}{x}\right)^{\frac{3}{2}} \left(c x + d\right)}\, dx"," ",0,"Integral(x/((a + b/x)**(3/2)*(c*x + d)), x)","F",0
257,-1,0,0,0.000000," ","integrate(1/(a+b/x)**(3/2)/(c+d/x)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
258,-1,0,0,0.000000," ","integrate(1/(a+b/x)**(3/2)/(c+d/x)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
259,0,0,0,0.000000," ","integrate((c+d/x)**3/(a+b/x)**(5/2),x)","\int \frac{\left(c x + d\right)^{3}}{x^{3} \left(a + \frac{b}{x}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((c*x + d)**3/(x**3*(a + b/x)**(5/2)), x)","F",0
260,0,0,0,0.000000," ","integrate((c+d/x)**2/(a+b/x)**(5/2),x)","\int \frac{\left(c x + d\right)^{2}}{x^{2} \left(a + \frac{b}{x}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((c*x + d)**2/(x**2*(a + b/x)**(5/2)), x)","F",0
261,1,1479,0,155.819252," ","integrate((c+d/x)/(a+b/x)**(5/2),x)","c \left(\frac{6 a^{17} x^{4} \sqrt{1 + \frac{b}{a x}}}{6 a^{\frac{39}{2}} x^{3} + 18 a^{\frac{37}{2}} b x^{2} + 18 a^{\frac{35}{2}} b^{2} x + 6 a^{\frac{33}{2}} b^{3}} + \frac{46 a^{16} b x^{3} \sqrt{1 + \frac{b}{a x}}}{6 a^{\frac{39}{2}} x^{3} + 18 a^{\frac{37}{2}} b x^{2} + 18 a^{\frac{35}{2}} b^{2} x + 6 a^{\frac{33}{2}} b^{3}} + \frac{15 a^{16} b x^{3} \log{\left(\frac{b}{a x} \right)}}{6 a^{\frac{39}{2}} x^{3} + 18 a^{\frac{37}{2}} b x^{2} + 18 a^{\frac{35}{2}} b^{2} x + 6 a^{\frac{33}{2}} b^{3}} - \frac{30 a^{16} b x^{3} \log{\left(\sqrt{1 + \frac{b}{a x}} + 1 \right)}}{6 a^{\frac{39}{2}} x^{3} + 18 a^{\frac{37}{2}} b x^{2} + 18 a^{\frac{35}{2}} b^{2} x + 6 a^{\frac{33}{2}} b^{3}} + \frac{70 a^{15} b^{2} x^{2} \sqrt{1 + \frac{b}{a x}}}{6 a^{\frac{39}{2}} x^{3} + 18 a^{\frac{37}{2}} b x^{2} + 18 a^{\frac{35}{2}} b^{2} x + 6 a^{\frac{33}{2}} b^{3}} + \frac{45 a^{15} b^{2} x^{2} \log{\left(\frac{b}{a x} \right)}}{6 a^{\frac{39}{2}} x^{3} + 18 a^{\frac{37}{2}} b x^{2} + 18 a^{\frac{35}{2}} b^{2} x + 6 a^{\frac{33}{2}} b^{3}} - \frac{90 a^{15} b^{2} x^{2} \log{\left(\sqrt{1 + \frac{b}{a x}} + 1 \right)}}{6 a^{\frac{39}{2}} x^{3} + 18 a^{\frac{37}{2}} b x^{2} + 18 a^{\frac{35}{2}} b^{2} x + 6 a^{\frac{33}{2}} b^{3}} + \frac{30 a^{14} b^{3} x \sqrt{1 + \frac{b}{a x}}}{6 a^{\frac{39}{2}} x^{3} + 18 a^{\frac{37}{2}} b x^{2} + 18 a^{\frac{35}{2}} b^{2} x + 6 a^{\frac{33}{2}} b^{3}} + \frac{45 a^{14} b^{3} x \log{\left(\frac{b}{a x} \right)}}{6 a^{\frac{39}{2}} x^{3} + 18 a^{\frac{37}{2}} b x^{2} + 18 a^{\frac{35}{2}} b^{2} x + 6 a^{\frac{33}{2}} b^{3}} - \frac{90 a^{14} b^{3} x \log{\left(\sqrt{1 + \frac{b}{a x}} + 1 \right)}}{6 a^{\frac{39}{2}} x^{3} + 18 a^{\frac{37}{2}} b x^{2} + 18 a^{\frac{35}{2}} b^{2} x + 6 a^{\frac{33}{2}} b^{3}} + \frac{15 a^{13} b^{4} \log{\left(\frac{b}{a x} \right)}}{6 a^{\frac{39}{2}} x^{3} + 18 a^{\frac{37}{2}} b x^{2} + 18 a^{\frac{35}{2}} b^{2} x + 6 a^{\frac{33}{2}} b^{3}} - \frac{30 a^{13} b^{4} \log{\left(\sqrt{1 + \frac{b}{a x}} + 1 \right)}}{6 a^{\frac{39}{2}} x^{3} + 18 a^{\frac{37}{2}} b x^{2} + 18 a^{\frac{35}{2}} b^{2} x + 6 a^{\frac{33}{2}} b^{3}}\right) + d \left(- \frac{8 a^{7} x^{3} \sqrt{1 + \frac{b}{a x}}}{3 a^{\frac{19}{2}} x^{3} + 9 a^{\frac{17}{2}} b x^{2} + 9 a^{\frac{15}{2}} b^{2} x + 3 a^{\frac{13}{2}} b^{3}} - \frac{3 a^{7} x^{3} \log{\left(\frac{b}{a x} \right)}}{3 a^{\frac{19}{2}} x^{3} + 9 a^{\frac{17}{2}} b x^{2} + 9 a^{\frac{15}{2}} b^{2} x + 3 a^{\frac{13}{2}} b^{3}} + \frac{6 a^{7} x^{3} \log{\left(\sqrt{1 + \frac{b}{a x}} + 1 \right)}}{3 a^{\frac{19}{2}} x^{3} + 9 a^{\frac{17}{2}} b x^{2} + 9 a^{\frac{15}{2}} b^{2} x + 3 a^{\frac{13}{2}} b^{3}} - \frac{14 a^{6} b x^{2} \sqrt{1 + \frac{b}{a x}}}{3 a^{\frac{19}{2}} x^{3} + 9 a^{\frac{17}{2}} b x^{2} + 9 a^{\frac{15}{2}} b^{2} x + 3 a^{\frac{13}{2}} b^{3}} - \frac{9 a^{6} b x^{2} \log{\left(\frac{b}{a x} \right)}}{3 a^{\frac{19}{2}} x^{3} + 9 a^{\frac{17}{2}} b x^{2} + 9 a^{\frac{15}{2}} b^{2} x + 3 a^{\frac{13}{2}} b^{3}} + \frac{18 a^{6} b x^{2} \log{\left(\sqrt{1 + \frac{b}{a x}} + 1 \right)}}{3 a^{\frac{19}{2}} x^{3} + 9 a^{\frac{17}{2}} b x^{2} + 9 a^{\frac{15}{2}} b^{2} x + 3 a^{\frac{13}{2}} b^{3}} - \frac{6 a^{5} b^{2} x \sqrt{1 + \frac{b}{a x}}}{3 a^{\frac{19}{2}} x^{3} + 9 a^{\frac{17}{2}} b x^{2} + 9 a^{\frac{15}{2}} b^{2} x + 3 a^{\frac{13}{2}} b^{3}} - \frac{9 a^{5} b^{2} x \log{\left(\frac{b}{a x} \right)}}{3 a^{\frac{19}{2}} x^{3} + 9 a^{\frac{17}{2}} b x^{2} + 9 a^{\frac{15}{2}} b^{2} x + 3 a^{\frac{13}{2}} b^{3}} + \frac{18 a^{5} b^{2} x \log{\left(\sqrt{1 + \frac{b}{a x}} + 1 \right)}}{3 a^{\frac{19}{2}} x^{3} + 9 a^{\frac{17}{2}} b x^{2} + 9 a^{\frac{15}{2}} b^{2} x + 3 a^{\frac{13}{2}} b^{3}} - \frac{3 a^{4} b^{3} \log{\left(\frac{b}{a x} \right)}}{3 a^{\frac{19}{2}} x^{3} + 9 a^{\frac{17}{2}} b x^{2} + 9 a^{\frac{15}{2}} b^{2} x + 3 a^{\frac{13}{2}} b^{3}} + \frac{6 a^{4} b^{3} \log{\left(\sqrt{1 + \frac{b}{a x}} + 1 \right)}}{3 a^{\frac{19}{2}} x^{3} + 9 a^{\frac{17}{2}} b x^{2} + 9 a^{\frac{15}{2}} b^{2} x + 3 a^{\frac{13}{2}} b^{3}}\right)"," ",0,"c*(6*a**17*x**4*sqrt(1 + b/(a*x))/(6*a**(39/2)*x**3 + 18*a**(37/2)*b*x**2 + 18*a**(35/2)*b**2*x + 6*a**(33/2)*b**3) + 46*a**16*b*x**3*sqrt(1 + b/(a*x))/(6*a**(39/2)*x**3 + 18*a**(37/2)*b*x**2 + 18*a**(35/2)*b**2*x + 6*a**(33/2)*b**3) + 15*a**16*b*x**3*log(b/(a*x))/(6*a**(39/2)*x**3 + 18*a**(37/2)*b*x**2 + 18*a**(35/2)*b**2*x + 6*a**(33/2)*b**3) - 30*a**16*b*x**3*log(sqrt(1 + b/(a*x)) + 1)/(6*a**(39/2)*x**3 + 18*a**(37/2)*b*x**2 + 18*a**(35/2)*b**2*x + 6*a**(33/2)*b**3) + 70*a**15*b**2*x**2*sqrt(1 + b/(a*x))/(6*a**(39/2)*x**3 + 18*a**(37/2)*b*x**2 + 18*a**(35/2)*b**2*x + 6*a**(33/2)*b**3) + 45*a**15*b**2*x**2*log(b/(a*x))/(6*a**(39/2)*x**3 + 18*a**(37/2)*b*x**2 + 18*a**(35/2)*b**2*x + 6*a**(33/2)*b**3) - 90*a**15*b**2*x**2*log(sqrt(1 + b/(a*x)) + 1)/(6*a**(39/2)*x**3 + 18*a**(37/2)*b*x**2 + 18*a**(35/2)*b**2*x + 6*a**(33/2)*b**3) + 30*a**14*b**3*x*sqrt(1 + b/(a*x))/(6*a**(39/2)*x**3 + 18*a**(37/2)*b*x**2 + 18*a**(35/2)*b**2*x + 6*a**(33/2)*b**3) + 45*a**14*b**3*x*log(b/(a*x))/(6*a**(39/2)*x**3 + 18*a**(37/2)*b*x**2 + 18*a**(35/2)*b**2*x + 6*a**(33/2)*b**3) - 90*a**14*b**3*x*log(sqrt(1 + b/(a*x)) + 1)/(6*a**(39/2)*x**3 + 18*a**(37/2)*b*x**2 + 18*a**(35/2)*b**2*x + 6*a**(33/2)*b**3) + 15*a**13*b**4*log(b/(a*x))/(6*a**(39/2)*x**3 + 18*a**(37/2)*b*x**2 + 18*a**(35/2)*b**2*x + 6*a**(33/2)*b**3) - 30*a**13*b**4*log(sqrt(1 + b/(a*x)) + 1)/(6*a**(39/2)*x**3 + 18*a**(37/2)*b*x**2 + 18*a**(35/2)*b**2*x + 6*a**(33/2)*b**3)) + d*(-8*a**7*x**3*sqrt(1 + b/(a*x))/(3*a**(19/2)*x**3 + 9*a**(17/2)*b*x**2 + 9*a**(15/2)*b**2*x + 3*a**(13/2)*b**3) - 3*a**7*x**3*log(b/(a*x))/(3*a**(19/2)*x**3 + 9*a**(17/2)*b*x**2 + 9*a**(15/2)*b**2*x + 3*a**(13/2)*b**3) + 6*a**7*x**3*log(sqrt(1 + b/(a*x)) + 1)/(3*a**(19/2)*x**3 + 9*a**(17/2)*b*x**2 + 9*a**(15/2)*b**2*x + 3*a**(13/2)*b**3) - 14*a**6*b*x**2*sqrt(1 + b/(a*x))/(3*a**(19/2)*x**3 + 9*a**(17/2)*b*x**2 + 9*a**(15/2)*b**2*x + 3*a**(13/2)*b**3) - 9*a**6*b*x**2*log(b/(a*x))/(3*a**(19/2)*x**3 + 9*a**(17/2)*b*x**2 + 9*a**(15/2)*b**2*x + 3*a**(13/2)*b**3) + 18*a**6*b*x**2*log(sqrt(1 + b/(a*x)) + 1)/(3*a**(19/2)*x**3 + 9*a**(17/2)*b*x**2 + 9*a**(15/2)*b**2*x + 3*a**(13/2)*b**3) - 6*a**5*b**2*x*sqrt(1 + b/(a*x))/(3*a**(19/2)*x**3 + 9*a**(17/2)*b*x**2 + 9*a**(15/2)*b**2*x + 3*a**(13/2)*b**3) - 9*a**5*b**2*x*log(b/(a*x))/(3*a**(19/2)*x**3 + 9*a**(17/2)*b*x**2 + 9*a**(15/2)*b**2*x + 3*a**(13/2)*b**3) + 18*a**5*b**2*x*log(sqrt(1 + b/(a*x)) + 1)/(3*a**(19/2)*x**3 + 9*a**(17/2)*b*x**2 + 9*a**(15/2)*b**2*x + 3*a**(13/2)*b**3) - 3*a**4*b**3*log(b/(a*x))/(3*a**(19/2)*x**3 + 9*a**(17/2)*b*x**2 + 9*a**(15/2)*b**2*x + 3*a**(13/2)*b**3) + 6*a**4*b**3*log(sqrt(1 + b/(a*x)) + 1)/(3*a**(19/2)*x**3 + 9*a**(17/2)*b*x**2 + 9*a**(15/2)*b**2*x + 3*a**(13/2)*b**3))","B",0
262,1,774,0,7.924560," ","integrate(1/(a+b/x)**(5/2),x)","\frac{6 a^{17} x^{4} \sqrt{1 + \frac{b}{a x}}}{6 a^{\frac{39}{2}} x^{3} + 18 a^{\frac{37}{2}} b x^{2} + 18 a^{\frac{35}{2}} b^{2} x + 6 a^{\frac{33}{2}} b^{3}} + \frac{46 a^{16} b x^{3} \sqrt{1 + \frac{b}{a x}}}{6 a^{\frac{39}{2}} x^{3} + 18 a^{\frac{37}{2}} b x^{2} + 18 a^{\frac{35}{2}} b^{2} x + 6 a^{\frac{33}{2}} b^{3}} + \frac{15 a^{16} b x^{3} \log{\left(\frac{b}{a x} \right)}}{6 a^{\frac{39}{2}} x^{3} + 18 a^{\frac{37}{2}} b x^{2} + 18 a^{\frac{35}{2}} b^{2} x + 6 a^{\frac{33}{2}} b^{3}} - \frac{30 a^{16} b x^{3} \log{\left(\sqrt{1 + \frac{b}{a x}} + 1 \right)}}{6 a^{\frac{39}{2}} x^{3} + 18 a^{\frac{37}{2}} b x^{2} + 18 a^{\frac{35}{2}} b^{2} x + 6 a^{\frac{33}{2}} b^{3}} + \frac{70 a^{15} b^{2} x^{2} \sqrt{1 + \frac{b}{a x}}}{6 a^{\frac{39}{2}} x^{3} + 18 a^{\frac{37}{2}} b x^{2} + 18 a^{\frac{35}{2}} b^{2} x + 6 a^{\frac{33}{2}} b^{3}} + \frac{45 a^{15} b^{2} x^{2} \log{\left(\frac{b}{a x} \right)}}{6 a^{\frac{39}{2}} x^{3} + 18 a^{\frac{37}{2}} b x^{2} + 18 a^{\frac{35}{2}} b^{2} x + 6 a^{\frac{33}{2}} b^{3}} - \frac{90 a^{15} b^{2} x^{2} \log{\left(\sqrt{1 + \frac{b}{a x}} + 1 \right)}}{6 a^{\frac{39}{2}} x^{3} + 18 a^{\frac{37}{2}} b x^{2} + 18 a^{\frac{35}{2}} b^{2} x + 6 a^{\frac{33}{2}} b^{3}} + \frac{30 a^{14} b^{3} x \sqrt{1 + \frac{b}{a x}}}{6 a^{\frac{39}{2}} x^{3} + 18 a^{\frac{37}{2}} b x^{2} + 18 a^{\frac{35}{2}} b^{2} x + 6 a^{\frac{33}{2}} b^{3}} + \frac{45 a^{14} b^{3} x \log{\left(\frac{b}{a x} \right)}}{6 a^{\frac{39}{2}} x^{3} + 18 a^{\frac{37}{2}} b x^{2} + 18 a^{\frac{35}{2}} b^{2} x + 6 a^{\frac{33}{2}} b^{3}} - \frac{90 a^{14} b^{3} x \log{\left(\sqrt{1 + \frac{b}{a x}} + 1 \right)}}{6 a^{\frac{39}{2}} x^{3} + 18 a^{\frac{37}{2}} b x^{2} + 18 a^{\frac{35}{2}} b^{2} x + 6 a^{\frac{33}{2}} b^{3}} + \frac{15 a^{13} b^{4} \log{\left(\frac{b}{a x} \right)}}{6 a^{\frac{39}{2}} x^{3} + 18 a^{\frac{37}{2}} b x^{2} + 18 a^{\frac{35}{2}} b^{2} x + 6 a^{\frac{33}{2}} b^{3}} - \frac{30 a^{13} b^{4} \log{\left(\sqrt{1 + \frac{b}{a x}} + 1 \right)}}{6 a^{\frac{39}{2}} x^{3} + 18 a^{\frac{37}{2}} b x^{2} + 18 a^{\frac{35}{2}} b^{2} x + 6 a^{\frac{33}{2}} b^{3}}"," ",0,"6*a**17*x**4*sqrt(1 + b/(a*x))/(6*a**(39/2)*x**3 + 18*a**(37/2)*b*x**2 + 18*a**(35/2)*b**2*x + 6*a**(33/2)*b**3) + 46*a**16*b*x**3*sqrt(1 + b/(a*x))/(6*a**(39/2)*x**3 + 18*a**(37/2)*b*x**2 + 18*a**(35/2)*b**2*x + 6*a**(33/2)*b**3) + 15*a**16*b*x**3*log(b/(a*x))/(6*a**(39/2)*x**3 + 18*a**(37/2)*b*x**2 + 18*a**(35/2)*b**2*x + 6*a**(33/2)*b**3) - 30*a**16*b*x**3*log(sqrt(1 + b/(a*x)) + 1)/(6*a**(39/2)*x**3 + 18*a**(37/2)*b*x**2 + 18*a**(35/2)*b**2*x + 6*a**(33/2)*b**3) + 70*a**15*b**2*x**2*sqrt(1 + b/(a*x))/(6*a**(39/2)*x**3 + 18*a**(37/2)*b*x**2 + 18*a**(35/2)*b**2*x + 6*a**(33/2)*b**3) + 45*a**15*b**2*x**2*log(b/(a*x))/(6*a**(39/2)*x**3 + 18*a**(37/2)*b*x**2 + 18*a**(35/2)*b**2*x + 6*a**(33/2)*b**3) - 90*a**15*b**2*x**2*log(sqrt(1 + b/(a*x)) + 1)/(6*a**(39/2)*x**3 + 18*a**(37/2)*b*x**2 + 18*a**(35/2)*b**2*x + 6*a**(33/2)*b**3) + 30*a**14*b**3*x*sqrt(1 + b/(a*x))/(6*a**(39/2)*x**3 + 18*a**(37/2)*b*x**2 + 18*a**(35/2)*b**2*x + 6*a**(33/2)*b**3) + 45*a**14*b**3*x*log(b/(a*x))/(6*a**(39/2)*x**3 + 18*a**(37/2)*b*x**2 + 18*a**(35/2)*b**2*x + 6*a**(33/2)*b**3) - 90*a**14*b**3*x*log(sqrt(1 + b/(a*x)) + 1)/(6*a**(39/2)*x**3 + 18*a**(37/2)*b*x**2 + 18*a**(35/2)*b**2*x + 6*a**(33/2)*b**3) + 15*a**13*b**4*log(b/(a*x))/(6*a**(39/2)*x**3 + 18*a**(37/2)*b*x**2 + 18*a**(35/2)*b**2*x + 6*a**(33/2)*b**3) - 30*a**13*b**4*log(sqrt(1 + b/(a*x)) + 1)/(6*a**(39/2)*x**3 + 18*a**(37/2)*b*x**2 + 18*a**(35/2)*b**2*x + 6*a**(33/2)*b**3)","B",0
263,0,0,0,0.000000," ","integrate(1/(a+b/x)**(5/2)/(c+d/x),x)","\int \frac{x}{\left(a + \frac{b}{x}\right)^{\frac{5}{2}} \left(c x + d\right)}\, dx"," ",0,"Integral(x/((a + b/x)**(5/2)*(c*x + d)), x)","F",0
264,-1,0,0,0.000000," ","integrate(1/(a+b/x)**(5/2)/(c+d/x)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
265,-1,0,0,0.000000," ","integrate(1/(a+b/x)**(5/2)/(c+d/x)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
266,0,0,0,0.000000," ","integrate((c+d/x)**(1/2)*(a+b/x)**(1/2),x)","\int \sqrt{a + \frac{b}{x}} \sqrt{c + \frac{d}{x}}\, dx"," ",0,"Integral(sqrt(a + b/x)*sqrt(c + d/x), x)","F",0
267,0,0,0,0.000000," ","integrate((a+b/x)**(1/2)/(c+d/x)**(1/2),x)","\int \frac{\sqrt{a + \frac{b}{x}}}{\sqrt{c + \frac{d}{x}}}\, dx"," ",0,"Integral(sqrt(a + b/x)/sqrt(c + d/x), x)","F",0
268,0,0,0,0.000000," ","integrate((a+b/x)**(1/2)/(c+d/x)**(3/2),x)","\int \frac{\sqrt{a + \frac{b}{x}}}{\left(c + \frac{d}{x}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(a + b/x)/(c + d/x)**(3/2), x)","F",0
269,0,0,0,0.000000," ","integrate((a+b/x)**p*(c+d/x)**q,x)","\int \left(a + \frac{b}{x}\right)^{p} \left(c + \frac{d}{x}\right)^{q}\, dx"," ",0,"Integral((a + b/x)**p*(c + d/x)**q, x)","F",0
270,1,82,0,0.329846," ","integrate((a+b/x**2)/(c+d/x**2),x)","\frac{a x}{c} + \frac{\sqrt{- \frac{1}{c^{3} d}} \left(a d - b c\right) \log{\left(- c d \sqrt{- \frac{1}{c^{3} d}} + x \right)}}{2} - \frac{\sqrt{- \frac{1}{c^{3} d}} \left(a d - b c\right) \log{\left(c d \sqrt{- \frac{1}{c^{3} d}} + x \right)}}{2}"," ",0,"a*x/c + sqrt(-1/(c**3*d))*(a*d - b*c)*log(-c*d*sqrt(-1/(c**3*d)) + x)/2 - sqrt(-1/(c**3*d))*(a*d - b*c)*log(c*d*sqrt(-1/(c**3*d)) + x)/2","B",0
271,0,0,0,0.000000," ","integrate((c+d/x**2)**(1/2)*(a+b/x**2)**(1/2),x)","\int \sqrt{a + \frac{b}{x^{2}}} \sqrt{c + \frac{d}{x^{2}}}\, dx"," ",0,"Integral(sqrt(a + b/x**2)*sqrt(c + d/x**2), x)","F",0
272,0,0,0,0.000000," ","integrate((a+b/x**2)**(1/2)/(c+d/x**2)**(1/2),x)","\int \frac{\sqrt{a + \frac{b}{x^{2}}}}{\sqrt{c + \frac{d}{x^{2}}}}\, dx"," ",0,"Integral(sqrt(a + b/x**2)/sqrt(c + d/x**2), x)","F",0
273,0,0,0,0.000000," ","integrate((a+b/x**2)**(1/2)/(c+d/x**2)**(3/2),x)","\int \frac{\sqrt{a + \frac{b}{x^{2}}}}{\left(c + \frac{d}{x^{2}}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(a + b/x**2)/(c + d/x**2)**(3/2), x)","F",0
274,-1,0,0,0.000000," ","integrate((a+b/x**2)**p*(c+d/x**2)**q,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
275,1,71,0,0.454016," ","integrate((a+b/x**3)/(c+d/x**3),x)","\frac{a x}{c} + \operatorname{RootSum} {\left(27 t^{3} c^{4} d^{2} + a^{3} d^{3} - 3 a^{2} b c d^{2} + 3 a b^{2} c^{2} d - b^{3} c^{3}, \left( t \mapsto t \log{\left(- \frac{3 t c d}{a d - b c} + x \right)} \right)\right)}"," ",0,"a*x/c + RootSum(27*_t**3*c**4*d**2 + a**3*d**3 - 3*a**2*b*c*d**2 + 3*a*b**2*c**2*d - b**3*c**3, Lambda(_t, _t*log(-3*_t*c*d/(a*d - b*c) + x)))","A",0
276,1,82,0,0.298953," ","integrate((a+b*x**(1/2))/(c+d*x**(1/2)),x)","\begin{cases} - \frac{2 a c \log{\left(\frac{c}{d} + \sqrt{x} \right)}}{d^{2}} + \frac{2 a \sqrt{x}}{d} + \frac{2 b c^{2} \log{\left(\frac{c}{d} + \sqrt{x} \right)}}{d^{3}} - \frac{2 b c \sqrt{x}}{d^{2}} + \frac{b x}{d} & \text{for}\: d \neq 0 \\\frac{a x + \frac{2 b x^{\frac{3}{2}}}{3}}{c} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*a*c*log(c/d + sqrt(x))/d**2 + 2*a*sqrt(x)/d + 2*b*c**2*log(c/d + sqrt(x))/d**3 - 2*b*c*sqrt(x)/d**2 + b*x/d, Ne(d, 0)), ((a*x + 2*b*x**(3/2)/3)/c, True))","A",0
277,1,24,0,0.196300," ","integrate((-1+x**(1/3))/(1+x**(1/3)),x)","- 3 x^{\frac{2}{3}} + 6 \sqrt[3]{x} + x - 6 \log{\left(\sqrt[3]{x} + 1 \right)}"," ",0,"-3*x**(2/3) + 6*x**(1/3) + x - 6*log(x**(1/3) + 1)","A",0
278,1,27,0,0.266149," ","integrate((1+x**(2/3))/(-1+x**(2/3)),x)","6 \sqrt[3]{x} + x + 3 \log{\left(\sqrt[3]{x} - 1 \right)} - 3 \log{\left(\sqrt[3]{x} + 1 \right)}"," ",0,"6*x**(1/3) + x + 3*log(x**(1/3) - 1) - 3*log(x**(1/3) + 1)","A",0
279,1,102,0,5.721127," ","integrate((-16+x**(3/4))/(16+x**(3/4)),x)","- 128 \sqrt[4]{x} + x + \frac{256 \sqrt[3]{2} \log{\left(\sqrt[4]{x} + 2 \sqrt[3]{2} \right)}}{3} - \frac{128 \sqrt[3]{2} \log{\left(- 2 \sqrt[3]{2} \sqrt[4]{x} + \sqrt{x} + 4 \cdot 2^{\frac{2}{3}} \right)}}{3} + \frac{256 \sqrt[3]{2} \sqrt{3} \operatorname{atan}{\left(\frac{2^{\frac{2}{3}} \sqrt{3} \sqrt[4]{x}}{6} - \frac{\sqrt{3}}{3} \right)}}{3}"," ",0,"-128*x**(1/4) + x + 256*2**(1/3)*log(x**(1/4) + 2*2**(1/3))/3 - 128*2**(1/3)*log(-2*2**(1/3)*x**(1/4) + sqrt(x) + 4*2**(2/3))/3 + 256*2**(1/3)*sqrt(3)*atan(2**(2/3)*sqrt(3)*x**(1/4)/6 - sqrt(3)/3)/3","A",0
280,1,26,0,0.184492," ","integrate((1+1/x**(1/3))/(-1+1/x**(1/3)),x)","- 3 x^{\frac{2}{3}} - 6 \sqrt[3]{x} - x - 6 \log{\left(\sqrt[3]{x} - 1 \right)}"," ",0,"-3*x**(2/3) - 6*x**(1/3) - x - 6*log(x**(1/3) - 1)","A",0
281,0,0,0,0.000000," ","integrate((a-b*x**n)**(3/2)*(a+b*x**n)**(3/2),x)","\int \left(a - b x^{n}\right)^{\frac{3}{2}} \left(a + b x^{n}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a - b*x**n)**(3/2)*(a + b*x**n)**(3/2), x)","F",0
282,0,0,0,0.000000," ","integrate((a-b*x**n)**(1/2)*(a+b*x**n)**(1/2),x)","\int \sqrt{a - b x^{n}} \sqrt{a + b x^{n}}\, dx"," ",0,"Integral(sqrt(a - b*x**n)*sqrt(a + b*x**n), x)","F",0
283,0,0,0,0.000000," ","integrate((a-b*x**n)**p*(a+b*x**n)**p,x)","\int \left(a - b x^{n}\right)^{p} \left(a + b x^{n}\right)^{p}\, dx"," ",0,"Integral((a - b*x**n)**p*(a + b*x**n)**p, x)","F",0
284,1,2744,0,3.672950," ","integrate((a+b*x**n)*(c+d*x**n)**4,x)","\begin{cases} a c^{4} x + 4 a c^{3} d \log{\left(x \right)} - \frac{6 a c^{2} d^{2}}{x} - \frac{2 a c d^{3}}{x^{2}} - \frac{a d^{4}}{3 x^{3}} + b c^{4} \log{\left(x \right)} - \frac{4 b c^{3} d}{x} - \frac{3 b c^{2} d^{2}}{x^{2}} - \frac{4 b c d^{3}}{3 x^{3}} - \frac{b d^{4}}{4 x^{4}} & \text{for}\: n = -1 \\a c^{4} x + 8 a c^{3} d \sqrt{x} + 6 a c^{2} d^{2} \log{\left(x \right)} - \frac{8 a c d^{3}}{\sqrt{x}} - \frac{a d^{4}}{x} + 2 b c^{4} \sqrt{x} + 4 b c^{3} d \log{\left(x \right)} - \frac{12 b c^{2} d^{2}}{\sqrt{x}} - \frac{4 b c d^{3}}{x} - \frac{2 b d^{4}}{3 x^{\frac{3}{2}}} & \text{for}\: n = - \frac{1}{2} \\a c^{4} x + 6 a c^{3} d x^{\frac{2}{3}} + 18 a c^{2} d^{2} \sqrt[3]{x} + 4 a c d^{3} \log{\left(x \right)} - \frac{3 a d^{4}}{\sqrt[3]{x}} + \frac{3 b c^{4} x^{\frac{2}{3}}}{2} + 12 b c^{3} d \sqrt[3]{x} + 6 b c^{2} d^{2} \log{\left(x \right)} - \frac{12 b c d^{3}}{\sqrt[3]{x}} - \frac{3 b d^{4}}{2 x^{\frac{2}{3}}} & \text{for}\: n = - \frac{1}{3} \\a c^{4} x + \frac{16 a c^{3} d x^{\frac{3}{4}}}{3} + 12 a c^{2} d^{2} \sqrt{x} + 16 a c d^{3} \sqrt[4]{x} + a d^{4} \log{\left(x \right)} + \frac{4 b c^{4} x^{\frac{3}{4}}}{3} + 8 b c^{3} d \sqrt{x} + 24 b c^{2} d^{2} \sqrt[4]{x} + 4 b c d^{3} \log{\left(x \right)} - \frac{4 b d^{4}}{\sqrt[4]{x}} & \text{for}\: n = - \frac{1}{4} \\a c^{4} x + 5 a c^{3} d x^{\frac{4}{5}} + 10 a c^{2} d^{2} x^{\frac{3}{5}} + 10 a c d^{3} x^{\frac{2}{5}} + 5 a d^{4} \sqrt[5]{x} + \frac{5 b c^{4} x^{\frac{4}{5}}}{4} + \frac{20 b c^{3} d x^{\frac{3}{5}}}{3} + 15 b c^{2} d^{2} x^{\frac{2}{5}} + 20 b c d^{3} \sqrt[5]{x} + b d^{4} \log{\left(x \right)} & \text{for}\: n = - \frac{1}{5} \\\frac{120 a c^{4} n^{5} x}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{274 a c^{4} n^{4} x}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{225 a c^{4} n^{3} x}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{85 a c^{4} n^{2} x}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{15 a c^{4} n x}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{a c^{4} x}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{480 a c^{3} d n^{4} x x^{n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{616 a c^{3} d n^{3} x x^{n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{284 a c^{3} d n^{2} x x^{n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{56 a c^{3} d n x x^{n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{4 a c^{3} d x x^{n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{360 a c^{2} d^{2} n^{4} x x^{2 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{642 a c^{2} d^{2} n^{3} x x^{2 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{354 a c^{2} d^{2} n^{2} x x^{2 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{78 a c^{2} d^{2} n x x^{2 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{6 a c^{2} d^{2} x x^{2 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{160 a c d^{3} n^{4} x x^{3 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{312 a c d^{3} n^{3} x x^{3 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{196 a c d^{3} n^{2} x x^{3 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{48 a c d^{3} n x x^{3 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{4 a c d^{3} x x^{3 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{30 a d^{4} n^{4} x x^{4 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{61 a d^{4} n^{3} x x^{4 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{41 a d^{4} n^{2} x x^{4 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{11 a d^{4} n x x^{4 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{a d^{4} x x^{4 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{120 b c^{4} n^{4} x x^{n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{154 b c^{4} n^{3} x x^{n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{71 b c^{4} n^{2} x x^{n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{14 b c^{4} n x x^{n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{b c^{4} x x^{n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{240 b c^{3} d n^{4} x x^{2 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{428 b c^{3} d n^{3} x x^{2 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{236 b c^{3} d n^{2} x x^{2 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{52 b c^{3} d n x x^{2 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{4 b c^{3} d x x^{2 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{240 b c^{2} d^{2} n^{4} x x^{3 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{468 b c^{2} d^{2} n^{3} x x^{3 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{294 b c^{2} d^{2} n^{2} x x^{3 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{72 b c^{2} d^{2} n x x^{3 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{6 b c^{2} d^{2} x x^{3 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{120 b c d^{3} n^{4} x x^{4 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{244 b c d^{3} n^{3} x x^{4 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{164 b c d^{3} n^{2} x x^{4 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{44 b c d^{3} n x x^{4 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{4 b c d^{3} x x^{4 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{24 b d^{4} n^{4} x x^{5 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{50 b d^{4} n^{3} x x^{5 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{35 b d^{4} n^{2} x x^{5 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{10 b d^{4} n x x^{5 n}}{120 n^{5} + 274 n^{4} + 225 n^{3} + 85 n^{2} + 15 n + 1} + \frac{b d^{4} 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*c**4*x + 4*a*c**3*d*log(x) - 6*a*c**2*d**2/x - 2*a*c*d**3/x**2 - a*d**4/(3*x**3) + b*c**4*log(x) - 4*b*c**3*d/x - 3*b*c**2*d**2/x**2 - 4*b*c*d**3/(3*x**3) - b*d**4/(4*x**4), Eq(n, -1)), (a*c**4*x + 8*a*c**3*d*sqrt(x) + 6*a*c**2*d**2*log(x) - 8*a*c*d**3/sqrt(x) - a*d**4/x + 2*b*c**4*sqrt(x) + 4*b*c**3*d*log(x) - 12*b*c**2*d**2/sqrt(x) - 4*b*c*d**3/x - 2*b*d**4/(3*x**(3/2)), Eq(n, -1/2)), (a*c**4*x + 6*a*c**3*d*x**(2/3) + 18*a*c**2*d**2*x**(1/3) + 4*a*c*d**3*log(x) - 3*a*d**4/x**(1/3) + 3*b*c**4*x**(2/3)/2 + 12*b*c**3*d*x**(1/3) + 6*b*c**2*d**2*log(x) - 12*b*c*d**3/x**(1/3) - 3*b*d**4/(2*x**(2/3)), Eq(n, -1/3)), (a*c**4*x + 16*a*c**3*d*x**(3/4)/3 + 12*a*c**2*d**2*sqrt(x) + 16*a*c*d**3*x**(1/4) + a*d**4*log(x) + 4*b*c**4*x**(3/4)/3 + 8*b*c**3*d*sqrt(x) + 24*b*c**2*d**2*x**(1/4) + 4*b*c*d**3*log(x) - 4*b*d**4/x**(1/4), Eq(n, -1/4)), (a*c**4*x + 5*a*c**3*d*x**(4/5) + 10*a*c**2*d**2*x**(3/5) + 10*a*c*d**3*x**(2/5) + 5*a*d**4*x**(1/5) + 5*b*c**4*x**(4/5)/4 + 20*b*c**3*d*x**(3/5)/3 + 15*b*c**2*d**2*x**(2/5) + 20*b*c*d**3*x**(1/5) + b*d**4*log(x), Eq(n, -1/5)), (120*a*c**4*n**5*x/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 274*a*c**4*n**4*x/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 225*a*c**4*n**3*x/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 85*a*c**4*n**2*x/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 15*a*c**4*n*x/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + a*c**4*x/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 480*a*c**3*d*n**4*x*x**n/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 616*a*c**3*d*n**3*x*x**n/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 284*a*c**3*d*n**2*x*x**n/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 56*a*c**3*d*n*x*x**n/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 4*a*c**3*d*x*x**n/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 360*a*c**2*d**2*n**4*x*x**(2*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 642*a*c**2*d**2*n**3*x*x**(2*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 354*a*c**2*d**2*n**2*x*x**(2*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 78*a*c**2*d**2*n*x*x**(2*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 6*a*c**2*d**2*x*x**(2*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 160*a*c*d**3*n**4*x*x**(3*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 312*a*c*d**3*n**3*x*x**(3*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 196*a*c*d**3*n**2*x*x**(3*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 48*a*c*d**3*n*x*x**(3*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 4*a*c*d**3*x*x**(3*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 30*a*d**4*n**4*x*x**(4*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 61*a*d**4*n**3*x*x**(4*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 41*a*d**4*n**2*x*x**(4*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 11*a*d**4*n*x*x**(4*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + a*d**4*x*x**(4*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 120*b*c**4*n**4*x*x**n/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 154*b*c**4*n**3*x*x**n/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 71*b*c**4*n**2*x*x**n/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 14*b*c**4*n*x*x**n/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + b*c**4*x*x**n/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 240*b*c**3*d*n**4*x*x**(2*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 428*b*c**3*d*n**3*x*x**(2*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 236*b*c**3*d*n**2*x*x**(2*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 52*b*c**3*d*n*x*x**(2*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 4*b*c**3*d*x*x**(2*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 240*b*c**2*d**2*n**4*x*x**(3*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 468*b*c**2*d**2*n**3*x*x**(3*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 294*b*c**2*d**2*n**2*x*x**(3*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 72*b*c**2*d**2*n*x*x**(3*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 6*b*c**2*d**2*x*x**(3*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 120*b*c*d**3*n**4*x*x**(4*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 244*b*c*d**3*n**3*x*x**(4*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 164*b*c*d**3*n**2*x*x**(4*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 44*b*c*d**3*n*x*x**(4*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 4*b*c*d**3*x*x**(4*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 24*b*d**4*n**4*x*x**(5*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 50*b*d**4*n**3*x*x**(5*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 35*b*d**4*n**2*x*x**(5*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + 10*b*d**4*n*x*x**(5*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1) + b*d**4*x*x**(5*n)/(120*n**5 + 274*n**4 + 225*n**3 + 85*n**2 + 15*n + 1), True))","A",0
285,1,1540,0,3.345914," ","integrate((a+b*x**n)*(c+d*x**n)**3,x)","\begin{cases} a c^{3} x + 3 a c^{2} d \log{\left(x \right)} - \frac{3 a c d^{2}}{x} - \frac{a d^{3}}{2 x^{2}} + b c^{3} \log{\left(x \right)} - \frac{3 b c^{2} d}{x} - \frac{3 b c d^{2}}{2 x^{2}} - \frac{b d^{3}}{3 x^{3}} & \text{for}\: n = -1 \\a c^{3} x + 6 a c^{2} d \sqrt{x} + 3 a c d^{2} \log{\left(x \right)} - \frac{2 a d^{3}}{\sqrt{x}} + 2 b c^{3} \sqrt{x} + 3 b c^{2} d \log{\left(x \right)} - \frac{6 b c d^{2}}{\sqrt{x}} - \frac{b d^{3}}{x} & \text{for}\: n = - \frac{1}{2} \\a c^{3} x + \frac{9 a c^{2} d x^{\frac{2}{3}}}{2} + 9 a c d^{2} \sqrt[3]{x} + a d^{3} \log{\left(x \right)} + \frac{3 b c^{3} x^{\frac{2}{3}}}{2} + 9 b c^{2} d \sqrt[3]{x} + 3 b c d^{2} \log{\left(x \right)} - \frac{3 b d^{3}}{\sqrt[3]{x}} & \text{for}\: n = - \frac{1}{3} \\a c^{3} x + 4 a c^{2} d x^{\frac{3}{4}} + 6 a c d^{2} \sqrt{x} + 4 a d^{3} \sqrt[4]{x} + \frac{4 b c^{3} x^{\frac{3}{4}}}{3} + 6 b c^{2} d \sqrt{x} + 12 b c d^{2} \sqrt[4]{x} + b d^{3} \log{\left(x \right)} & \text{for}\: n = - \frac{1}{4} \\\frac{24 a c^{3} n^{4} x}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{50 a c^{3} n^{3} x}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{35 a c^{3} n^{2} x}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{10 a c^{3} n x}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{a c^{3} x}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{72 a c^{2} d n^{3} x x^{n}}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{78 a c^{2} d n^{2} x x^{n}}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{27 a c^{2} d n x x^{n}}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{3 a c^{2} d x x^{n}}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{36 a c d^{2} n^{3} x x^{2 n}}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{57 a c d^{2} n^{2} x x^{2 n}}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{24 a c d^{2} n x x^{2 n}}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{3 a c d^{2} x x^{2 n}}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{8 a d^{3} n^{3} x x^{3 n}}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{14 a d^{3} n^{2} x x^{3 n}}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{7 a d^{3} n x x^{3 n}}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{a d^{3} x x^{3 n}}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{24 b c^{3} n^{3} x x^{n}}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{26 b c^{3} n^{2} x x^{n}}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{9 b c^{3} n x x^{n}}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{b c^{3} x x^{n}}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{36 b c^{2} d n^{3} x x^{2 n}}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{57 b c^{2} d n^{2} x x^{2 n}}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{24 b c^{2} d n x x^{2 n}}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{3 b c^{2} d x x^{2 n}}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{24 b c d^{2} n^{3} x x^{3 n}}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{42 b c d^{2} n^{2} x x^{3 n}}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{21 b c d^{2} n x x^{3 n}}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{3 b c d^{2} x x^{3 n}}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{6 b d^{3} n^{3} x x^{4 n}}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{11 b d^{3} n^{2} x x^{4 n}}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{6 b d^{3} n x x^{4 n}}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{b d^{3} x x^{4 n}}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*c**3*x + 3*a*c**2*d*log(x) - 3*a*c*d**2/x - a*d**3/(2*x**2) + b*c**3*log(x) - 3*b*c**2*d/x - 3*b*c*d**2/(2*x**2) - b*d**3/(3*x**3), Eq(n, -1)), (a*c**3*x + 6*a*c**2*d*sqrt(x) + 3*a*c*d**2*log(x) - 2*a*d**3/sqrt(x) + 2*b*c**3*sqrt(x) + 3*b*c**2*d*log(x) - 6*b*c*d**2/sqrt(x) - b*d**3/x, Eq(n, -1/2)), (a*c**3*x + 9*a*c**2*d*x**(2/3)/2 + 9*a*c*d**2*x**(1/3) + a*d**3*log(x) + 3*b*c**3*x**(2/3)/2 + 9*b*c**2*d*x**(1/3) + 3*b*c*d**2*log(x) - 3*b*d**3/x**(1/3), Eq(n, -1/3)), (a*c**3*x + 4*a*c**2*d*x**(3/4) + 6*a*c*d**2*sqrt(x) + 4*a*d**3*x**(1/4) + 4*b*c**3*x**(3/4)/3 + 6*b*c**2*d*sqrt(x) + 12*b*c*d**2*x**(1/4) + b*d**3*log(x), Eq(n, -1/4)), (24*a*c**3*n**4*x/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + 50*a*c**3*n**3*x/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + 35*a*c**3*n**2*x/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + 10*a*c**3*n*x/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + a*c**3*x/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + 72*a*c**2*d*n**3*x*x**n/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + 78*a*c**2*d*n**2*x*x**n/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + 27*a*c**2*d*n*x*x**n/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + 3*a*c**2*d*x*x**n/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + 36*a*c*d**2*n**3*x*x**(2*n)/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + 57*a*c*d**2*n**2*x*x**(2*n)/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + 24*a*c*d**2*n*x*x**(2*n)/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + 3*a*c*d**2*x*x**(2*n)/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + 8*a*d**3*n**3*x*x**(3*n)/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + 14*a*d**3*n**2*x*x**(3*n)/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + 7*a*d**3*n*x*x**(3*n)/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + a*d**3*x*x**(3*n)/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + 24*b*c**3*n**3*x*x**n/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + 26*b*c**3*n**2*x*x**n/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + 9*b*c**3*n*x*x**n/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + b*c**3*x*x**n/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + 36*b*c**2*d*n**3*x*x**(2*n)/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + 57*b*c**2*d*n**2*x*x**(2*n)/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + 24*b*c**2*d*n*x*x**(2*n)/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + 3*b*c**2*d*x*x**(2*n)/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + 24*b*c*d**2*n**3*x*x**(3*n)/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + 42*b*c*d**2*n**2*x*x**(3*n)/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + 21*b*c*d**2*n*x*x**(3*n)/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + 3*b*c*d**2*x*x**(3*n)/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + 6*b*d**3*n**3*x*x**(4*n)/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + 11*b*d**3*n**2*x*x**(4*n)/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + 6*b*d**3*n*x*x**(4*n)/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + b*d**3*x*x**(4*n)/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1), True))","A",0
286,1,726,0,1.956146," ","integrate((a+b*x**n)*(c+d*x**n)**2,x)","\begin{cases} a c^{2} x + 2 a c d \log{\left(x \right)} - \frac{a d^{2}}{x} + b c^{2} \log{\left(x \right)} - \frac{2 b c d}{x} - \frac{b d^{2}}{2 x^{2}} & \text{for}\: n = -1 \\a c^{2} x + 4 a c d \sqrt{x} + a d^{2} \log{\left(x \right)} + 2 b c^{2} \sqrt{x} + 2 b c d \log{\left(x \right)} - \frac{2 b d^{2}}{\sqrt{x}} & \text{for}\: n = - \frac{1}{2} \\a c^{2} x + 3 a c d x^{\frac{2}{3}} + 3 a d^{2} \sqrt[3]{x} + \frac{3 b c^{2} x^{\frac{2}{3}}}{2} + 6 b c d \sqrt[3]{x} + b d^{2} \log{\left(x \right)} & \text{for}\: n = - \frac{1}{3} \\\frac{6 a c^{2} n^{3} x}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{11 a c^{2} n^{2} x}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{6 a c^{2} n x}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{a c^{2} x}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{12 a c d n^{2} x x^{n}}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{10 a c d n x x^{n}}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{2 a c d x x^{n}}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{3 a d^{2} n^{2} x x^{2 n}}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{4 a d^{2} n x x^{2 n}}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{a d^{2} x x^{2 n}}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{6 b c^{2} n^{2} x x^{n}}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{5 b c^{2} n x x^{n}}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{b c^{2} x x^{n}}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{6 b c d n^{2} x x^{2 n}}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{8 b c d n x x^{2 n}}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{2 b c d x x^{2 n}}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{2 b d^{2} n^{2} x x^{3 n}}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{3 b d^{2} n x x^{3 n}}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{b d^{2} x x^{3 n}}{6 n^{3} + 11 n^{2} + 6 n + 1} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*c**2*x + 2*a*c*d*log(x) - a*d**2/x + b*c**2*log(x) - 2*b*c*d/x - b*d**2/(2*x**2), Eq(n, -1)), (a*c**2*x + 4*a*c*d*sqrt(x) + a*d**2*log(x) + 2*b*c**2*sqrt(x) + 2*b*c*d*log(x) - 2*b*d**2/sqrt(x), Eq(n, -1/2)), (a*c**2*x + 3*a*c*d*x**(2/3) + 3*a*d**2*x**(1/3) + 3*b*c**2*x**(2/3)/2 + 6*b*c*d*x**(1/3) + b*d**2*log(x), Eq(n, -1/3)), (6*a*c**2*n**3*x/(6*n**3 + 11*n**2 + 6*n + 1) + 11*a*c**2*n**2*x/(6*n**3 + 11*n**2 + 6*n + 1) + 6*a*c**2*n*x/(6*n**3 + 11*n**2 + 6*n + 1) + a*c**2*x/(6*n**3 + 11*n**2 + 6*n + 1) + 12*a*c*d*n**2*x*x**n/(6*n**3 + 11*n**2 + 6*n + 1) + 10*a*c*d*n*x*x**n/(6*n**3 + 11*n**2 + 6*n + 1) + 2*a*c*d*x*x**n/(6*n**3 + 11*n**2 + 6*n + 1) + 3*a*d**2*n**2*x*x**(2*n)/(6*n**3 + 11*n**2 + 6*n + 1) + 4*a*d**2*n*x*x**(2*n)/(6*n**3 + 11*n**2 + 6*n + 1) + a*d**2*x*x**(2*n)/(6*n**3 + 11*n**2 + 6*n + 1) + 6*b*c**2*n**2*x*x**n/(6*n**3 + 11*n**2 + 6*n + 1) + 5*b*c**2*n*x*x**n/(6*n**3 + 11*n**2 + 6*n + 1) + b*c**2*x*x**n/(6*n**3 + 11*n**2 + 6*n + 1) + 6*b*c*d*n**2*x*x**(2*n)/(6*n**3 + 11*n**2 + 6*n + 1) + 8*b*c*d*n*x*x**(2*n)/(6*n**3 + 11*n**2 + 6*n + 1) + 2*b*c*d*x*x**(2*n)/(6*n**3 + 11*n**2 + 6*n + 1) + 2*b*d**2*n**2*x*x**(3*n)/(6*n**3 + 11*n**2 + 6*n + 1) + 3*b*d**2*n*x*x**(3*n)/(6*n**3 + 11*n**2 + 6*n + 1) + b*d**2*x*x**(3*n)/(6*n**3 + 11*n**2 + 6*n + 1), True))","A",0
287,1,236,0,0.650444," ","integrate((a+b*x**n)*(c+d*x**n),x)","\begin{cases} a c x + a d \log{\left(x \right)} + b c \log{\left(x \right)} - \frac{b d}{x} & \text{for}\: n = -1 \\a c x + 2 a d \sqrt{x} + 2 b c \sqrt{x} + b d \log{\left(x \right)} & \text{for}\: n = - \frac{1}{2} \\\frac{2 a c n^{2} x}{2 n^{2} + 3 n + 1} + \frac{3 a c n x}{2 n^{2} + 3 n + 1} + \frac{a c x}{2 n^{2} + 3 n + 1} + \frac{2 a d n x x^{n}}{2 n^{2} + 3 n + 1} + \frac{a d x x^{n}}{2 n^{2} + 3 n + 1} + \frac{2 b c n x x^{n}}{2 n^{2} + 3 n + 1} + \frac{b c x x^{n}}{2 n^{2} + 3 n + 1} + \frac{b d n x x^{2 n}}{2 n^{2} + 3 n + 1} + \frac{b d x x^{2 n}}{2 n^{2} + 3 n + 1} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*c*x + a*d*log(x) + b*c*log(x) - b*d/x, Eq(n, -1)), (a*c*x + 2*a*d*sqrt(x) + 2*b*c*sqrt(x) + b*d*log(x), Eq(n, -1/2)), (2*a*c*n**2*x/(2*n**2 + 3*n + 1) + 3*a*c*n*x/(2*n**2 + 3*n + 1) + a*c*x/(2*n**2 + 3*n + 1) + 2*a*d*n*x*x**n/(2*n**2 + 3*n + 1) + a*d*x*x**n/(2*n**2 + 3*n + 1) + 2*b*c*n*x*x**n/(2*n**2 + 3*n + 1) + b*c*x*x**n/(2*n**2 + 3*n + 1) + b*d*n*x*x**(2*n)/(2*n**2 + 3*n + 1) + b*d*x*x**(2*n)/(2*n**2 + 3*n + 1), True))","A",0
288,1,73,0,3.333308," ","integrate((a+b*x**n)/(c+d*x**n),x)","\frac{a x \Phi\left(\frac{d x^{n} e^{i \pi}}{c}, 1, \frac{1}{n}\right) \Gamma\left(\frac{1}{n}\right)}{c n^{2} \Gamma\left(1 + \frac{1}{n}\right)} - \frac{b x \Phi\left(\frac{c x^{- n} e^{i \pi}}{d}, 1, \frac{e^{i \pi}}{n}\right) \Gamma\left(\frac{1}{n}\right)}{d n^{2} \Gamma\left(1 + \frac{1}{n}\right)}"," ",0,"a*x*lerchphi(d*x**n*exp_polar(I*pi)/c, 1, 1/n)*gamma(1/n)/(c*n**2*gamma(1 + 1/n)) - b*x*lerchphi(c*x**(-n)*exp_polar(I*pi)/d, 1, exp_polar(I*pi)/n)*gamma(1/n)/(d*n**2*gamma(1 + 1/n))","C",0
289,1,592,0,8.694235," ","integrate((a+b*x**n)/(c+d*x**n)**2,x)","a \left(\frac{n x \Phi\left(\frac{d x^{n} e^{i \pi}}{c}, 1, \frac{1}{n}\right) \Gamma\left(\frac{1}{n}\right)}{c \left(c n^{3} \Gamma\left(1 + \frac{1}{n}\right) + d n^{3} x^{n} \Gamma\left(1 + \frac{1}{n}\right)\right)} + \frac{n x \Gamma\left(\frac{1}{n}\right)}{c \left(c n^{3} \Gamma\left(1 + \frac{1}{n}\right) + d n^{3} x^{n} \Gamma\left(1 + \frac{1}{n}\right)\right)} - \frac{x \Phi\left(\frac{d x^{n} e^{i \pi}}{c}, 1, \frac{1}{n}\right) \Gamma\left(\frac{1}{n}\right)}{c \left(c n^{3} \Gamma\left(1 + \frac{1}{n}\right) + d n^{3} x^{n} \Gamma\left(1 + \frac{1}{n}\right)\right)} + \frac{d n x x^{n} \Phi\left(\frac{d x^{n} e^{i \pi}}{c}, 1, \frac{1}{n}\right) \Gamma\left(\frac{1}{n}\right)}{c^{2} \left(c n^{3} \Gamma\left(1 + \frac{1}{n}\right) + d n^{3} x^{n} \Gamma\left(1 + \frac{1}{n}\right)\right)} - \frac{d x x^{n} \Phi\left(\frac{d x^{n} e^{i \pi}}{c}, 1, \frac{1}{n}\right) \Gamma\left(\frac{1}{n}\right)}{c^{2} \left(c n^{3} \Gamma\left(1 + \frac{1}{n}\right) + d n^{3} x^{n} \Gamma\left(1 + \frac{1}{n}\right)\right)}\right) + b \left(\frac{n^{2} x x^{n} \Gamma\left(1 + \frac{1}{n}\right)}{c \left(c n^{3} \Gamma\left(2 + \frac{1}{n}\right) + d n^{3} x^{n} \Gamma\left(2 + \frac{1}{n}\right)\right)} - \frac{n x x^{n} \Phi\left(\frac{d x^{n} e^{i \pi}}{c}, 1, 1 + \frac{1}{n}\right) \Gamma\left(1 + \frac{1}{n}\right)}{c \left(c n^{3} \Gamma\left(2 + \frac{1}{n}\right) + d n^{3} x^{n} \Gamma\left(2 + \frac{1}{n}\right)\right)} + \frac{n x x^{n} \Gamma\left(1 + \frac{1}{n}\right)}{c \left(c n^{3} \Gamma\left(2 + \frac{1}{n}\right) + d n^{3} x^{n} \Gamma\left(2 + \frac{1}{n}\right)\right)} - \frac{x x^{n} \Phi\left(\frac{d x^{n} e^{i \pi}}{c}, 1, 1 + \frac{1}{n}\right) \Gamma\left(1 + \frac{1}{n}\right)}{c \left(c n^{3} \Gamma\left(2 + \frac{1}{n}\right) + d n^{3} x^{n} \Gamma\left(2 + \frac{1}{n}\right)\right)} - \frac{d n x x^{2 n} \Phi\left(\frac{d x^{n} e^{i \pi}}{c}, 1, 1 + \frac{1}{n}\right) \Gamma\left(1 + \frac{1}{n}\right)}{c^{2} \left(c n^{3} \Gamma\left(2 + \frac{1}{n}\right) + d n^{3} x^{n} \Gamma\left(2 + \frac{1}{n}\right)\right)} - \frac{d x x^{2 n} \Phi\left(\frac{d x^{n} e^{i \pi}}{c}, 1, 1 + \frac{1}{n}\right) \Gamma\left(1 + \frac{1}{n}\right)}{c^{2} \left(c n^{3} \Gamma\left(2 + \frac{1}{n}\right) + d n^{3} x^{n} \Gamma\left(2 + \frac{1}{n}\right)\right)}\right)"," ",0,"a*(n*x*lerchphi(d*x**n*exp_polar(I*pi)/c, 1, 1/n)*gamma(1/n)/(c*(c*n**3*gamma(1 + 1/n) + d*n**3*x**n*gamma(1 + 1/n))) + n*x*gamma(1/n)/(c*(c*n**3*gamma(1 + 1/n) + d*n**3*x**n*gamma(1 + 1/n))) - x*lerchphi(d*x**n*exp_polar(I*pi)/c, 1, 1/n)*gamma(1/n)/(c*(c*n**3*gamma(1 + 1/n) + d*n**3*x**n*gamma(1 + 1/n))) + d*n*x*x**n*lerchphi(d*x**n*exp_polar(I*pi)/c, 1, 1/n)*gamma(1/n)/(c**2*(c*n**3*gamma(1 + 1/n) + d*n**3*x**n*gamma(1 + 1/n))) - d*x*x**n*lerchphi(d*x**n*exp_polar(I*pi)/c, 1, 1/n)*gamma(1/n)/(c**2*(c*n**3*gamma(1 + 1/n) + d*n**3*x**n*gamma(1 + 1/n)))) + b*(n**2*x*x**n*gamma(1 + 1/n)/(c*(c*n**3*gamma(2 + 1/n) + d*n**3*x**n*gamma(2 + 1/n))) - n*x*x**n*lerchphi(d*x**n*exp_polar(I*pi)/c, 1, 1 + 1/n)*gamma(1 + 1/n)/(c*(c*n**3*gamma(2 + 1/n) + d*n**3*x**n*gamma(2 + 1/n))) + n*x*x**n*gamma(1 + 1/n)/(c*(c*n**3*gamma(2 + 1/n) + d*n**3*x**n*gamma(2 + 1/n))) - x*x**n*lerchphi(d*x**n*exp_polar(I*pi)/c, 1, 1 + 1/n)*gamma(1 + 1/n)/(c*(c*n**3*gamma(2 + 1/n) + d*n**3*x**n*gamma(2 + 1/n))) - d*n*x*x**(2*n)*lerchphi(d*x**n*exp_polar(I*pi)/c, 1, 1 + 1/n)*gamma(1 + 1/n)/(c**2*(c*n**3*gamma(2 + 1/n) + d*n**3*x**n*gamma(2 + 1/n))) - d*x*x**(2*n)*lerchphi(d*x**n*exp_polar(I*pi)/c, 1, 1 + 1/n)*gamma(1 + 1/n)/(c**2*(c*n**3*gamma(2 + 1/n) + d*n**3*x**n*gamma(2 + 1/n))))","C",0
290,1,3706,0,64.993142," ","integrate((a+b*x**n)/(c+d*x**n)**3,x)","a \left(\frac{2 c n^{2} x \Phi\left(\frac{d x^{n} e^{i \pi}}{c}, 1, \frac{1}{n}\right) \Gamma\left(\frac{1}{n}\right)}{2 c^{4} n^{4} \Gamma\left(1 + \frac{1}{n}\right) + 6 c^{3} d n^{4} x^{n} \Gamma\left(1 + \frac{1}{n}\right) + 6 c^{2} d^{2} n^{4} x^{2 n} \Gamma\left(1 + \frac{1}{n}\right) + 2 c d^{3} n^{4} x^{3 n} \Gamma\left(1 + \frac{1}{n}\right)} + \frac{3 c n^{2} x \Gamma\left(\frac{1}{n}\right)}{2 c^{4} n^{4} \Gamma\left(1 + \frac{1}{n}\right) + 6 c^{3} d n^{4} x^{n} \Gamma\left(1 + \frac{1}{n}\right) + 6 c^{2} d^{2} n^{4} x^{2 n} \Gamma\left(1 + \frac{1}{n}\right) + 2 c d^{3} n^{4} x^{3 n} \Gamma\left(1 + \frac{1}{n}\right)} - \frac{3 c n x \Phi\left(\frac{d x^{n} e^{i \pi}}{c}, 1, \frac{1}{n}\right) \Gamma\left(\frac{1}{n}\right)}{2 c^{4} n^{4} \Gamma\left(1 + \frac{1}{n}\right) + 6 c^{3} d n^{4} x^{n} \Gamma\left(1 + \frac{1}{n}\right) + 6 c^{2} d^{2} n^{4} x^{2 n} \Gamma\left(1 + \frac{1}{n}\right) + 2 c d^{3} n^{4} x^{3 n} \Gamma\left(1 + \frac{1}{n}\right)} - \frac{c n x \Gamma\left(\frac{1}{n}\right)}{2 c^{4} n^{4} \Gamma\left(1 + \frac{1}{n}\right) + 6 c^{3} d n^{4} x^{n} \Gamma\left(1 + \frac{1}{n}\right) + 6 c^{2} d^{2} n^{4} x^{2 n} \Gamma\left(1 + \frac{1}{n}\right) + 2 c d^{3} n^{4} x^{3 n} \Gamma\left(1 + \frac{1}{n}\right)} + \frac{c x \Phi\left(\frac{d x^{n} e^{i \pi}}{c}, 1, \frac{1}{n}\right) \Gamma\left(\frac{1}{n}\right)}{2 c^{4} n^{4} \Gamma\left(1 + \frac{1}{n}\right) + 6 c^{3} d n^{4} x^{n} \Gamma\left(1 + \frac{1}{n}\right) + 6 c^{2} d^{2} n^{4} x^{2 n} \Gamma\left(1 + \frac{1}{n}\right) + 2 c d^{3} n^{4} x^{3 n} \Gamma\left(1 + \frac{1}{n}\right)} + \frac{6 d n^{2} x x^{n} \Phi\left(\frac{d x^{n} e^{i \pi}}{c}, 1, \frac{1}{n}\right) \Gamma\left(\frac{1}{n}\right)}{2 c^{4} n^{4} \Gamma\left(1 + \frac{1}{n}\right) + 6 c^{3} d n^{4} x^{n} \Gamma\left(1 + \frac{1}{n}\right) + 6 c^{2} d^{2} n^{4} x^{2 n} \Gamma\left(1 + \frac{1}{n}\right) + 2 c d^{3} n^{4} x^{3 n} \Gamma\left(1 + \frac{1}{n}\right)} + \frac{5 d n^{2} x x^{n} \Gamma\left(\frac{1}{n}\right)}{2 c^{4} n^{4} \Gamma\left(1 + \frac{1}{n}\right) + 6 c^{3} d n^{4} x^{n} \Gamma\left(1 + \frac{1}{n}\right) + 6 c^{2} d^{2} n^{4} x^{2 n} \Gamma\left(1 + \frac{1}{n}\right) + 2 c d^{3} n^{4} x^{3 n} \Gamma\left(1 + \frac{1}{n}\right)} - \frac{9 d n x x^{n} \Phi\left(\frac{d x^{n} e^{i \pi}}{c}, 1, \frac{1}{n}\right) \Gamma\left(\frac{1}{n}\right)}{2 c^{4} n^{4} \Gamma\left(1 + \frac{1}{n}\right) + 6 c^{3} d n^{4} x^{n} \Gamma\left(1 + \frac{1}{n}\right) + 6 c^{2} d^{2} n^{4} x^{2 n} \Gamma\left(1 + \frac{1}{n}\right) + 2 c d^{3} n^{4} x^{3 n} \Gamma\left(1 + \frac{1}{n}\right)} - \frac{2 d n x x^{n} \Gamma\left(\frac{1}{n}\right)}{2 c^{4} n^{4} \Gamma\left(1 + \frac{1}{n}\right) + 6 c^{3} d n^{4} x^{n} \Gamma\left(1 + \frac{1}{n}\right) + 6 c^{2} d^{2} n^{4} x^{2 n} \Gamma\left(1 + \frac{1}{n}\right) + 2 c d^{3} n^{4} x^{3 n} \Gamma\left(1 + \frac{1}{n}\right)} + \frac{3 d x x^{n} \Phi\left(\frac{d x^{n} e^{i \pi}}{c}, 1, \frac{1}{n}\right) \Gamma\left(\frac{1}{n}\right)}{2 c^{4} n^{4} \Gamma\left(1 + \frac{1}{n}\right) + 6 c^{3} d n^{4} x^{n} \Gamma\left(1 + \frac{1}{n}\right) + 6 c^{2} d^{2} n^{4} x^{2 n} \Gamma\left(1 + \frac{1}{n}\right) + 2 c d^{3} n^{4} x^{3 n} \Gamma\left(1 + \frac{1}{n}\right)} + \frac{6 d^{2} n^{2} x x^{2 n} \Phi\left(\frac{d x^{n} e^{i \pi}}{c}, 1, \frac{1}{n}\right) \Gamma\left(\frac{1}{n}\right)}{c \left(2 c^{4} n^{4} \Gamma\left(1 + \frac{1}{n}\right) + 6 c^{3} d n^{4} x^{n} \Gamma\left(1 + \frac{1}{n}\right) + 6 c^{2} d^{2} n^{4} x^{2 n} \Gamma\left(1 + \frac{1}{n}\right) + 2 c d^{3} n^{4} x^{3 n} \Gamma\left(1 + \frac{1}{n}\right)\right)} + \frac{2 d^{2} n^{2} x x^{2 n} \Gamma\left(\frac{1}{n}\right)}{c \left(2 c^{4} n^{4} \Gamma\left(1 + \frac{1}{n}\right) + 6 c^{3} d n^{4} x^{n} \Gamma\left(1 + \frac{1}{n}\right) + 6 c^{2} d^{2} n^{4} x^{2 n} \Gamma\left(1 + \frac{1}{n}\right) + 2 c d^{3} n^{4} x^{3 n} \Gamma\left(1 + \frac{1}{n}\right)\right)} - \frac{9 d^{2} n x x^{2 n} \Phi\left(\frac{d x^{n} e^{i \pi}}{c}, 1, \frac{1}{n}\right) \Gamma\left(\frac{1}{n}\right)}{c \left(2 c^{4} n^{4} \Gamma\left(1 + \frac{1}{n}\right) + 6 c^{3} d n^{4} x^{n} \Gamma\left(1 + \frac{1}{n}\right) + 6 c^{2} d^{2} n^{4} x^{2 n} \Gamma\left(1 + \frac{1}{n}\right) + 2 c d^{3} n^{4} x^{3 n} \Gamma\left(1 + \frac{1}{n}\right)\right)} - \frac{d^{2} n x x^{2 n} \Gamma\left(\frac{1}{n}\right)}{c \left(2 c^{4} n^{4} \Gamma\left(1 + \frac{1}{n}\right) + 6 c^{3} d n^{4} x^{n} \Gamma\left(1 + \frac{1}{n}\right) + 6 c^{2} d^{2} n^{4} x^{2 n} \Gamma\left(1 + \frac{1}{n}\right) + 2 c d^{3} n^{4} x^{3 n} \Gamma\left(1 + \frac{1}{n}\right)\right)} + \frac{3 d^{2} x x^{2 n} \Phi\left(\frac{d x^{n} e^{i \pi}}{c}, 1, \frac{1}{n}\right) \Gamma\left(\frac{1}{n}\right)}{c \left(2 c^{4} n^{4} \Gamma\left(1 + \frac{1}{n}\right) + 6 c^{3} d n^{4} x^{n} \Gamma\left(1 + \frac{1}{n}\right) + 6 c^{2} d^{2} n^{4} x^{2 n} \Gamma\left(1 + \frac{1}{n}\right) + 2 c d^{3} n^{4} x^{3 n} \Gamma\left(1 + \frac{1}{n}\right)\right)} + \frac{2 d^{3} n^{2} x x^{3 n} \Phi\left(\frac{d x^{n} e^{i \pi}}{c}, 1, \frac{1}{n}\right) \Gamma\left(\frac{1}{n}\right)}{c^{2} \left(2 c^{4} n^{4} \Gamma\left(1 + \frac{1}{n}\right) + 6 c^{3} d n^{4} x^{n} \Gamma\left(1 + \frac{1}{n}\right) + 6 c^{2} d^{2} n^{4} x^{2 n} \Gamma\left(1 + \frac{1}{n}\right) + 2 c d^{3} n^{4} x^{3 n} \Gamma\left(1 + \frac{1}{n}\right)\right)} - \frac{3 d^{3} n x x^{3 n} \Phi\left(\frac{d x^{n} e^{i \pi}}{c}, 1, \frac{1}{n}\right) \Gamma\left(\frac{1}{n}\right)}{c^{2} \left(2 c^{4} n^{4} \Gamma\left(1 + \frac{1}{n}\right) + 6 c^{3} d n^{4} x^{n} \Gamma\left(1 + \frac{1}{n}\right) + 6 c^{2} d^{2} n^{4} x^{2 n} \Gamma\left(1 + \frac{1}{n}\right) + 2 c d^{3} n^{4} x^{3 n} \Gamma\left(1 + \frac{1}{n}\right)\right)} + \frac{d^{3} x x^{3 n} \Phi\left(\frac{d x^{n} e^{i \pi}}{c}, 1, \frac{1}{n}\right) \Gamma\left(\frac{1}{n}\right)}{c^{2} \left(2 c^{4} n^{4} \Gamma\left(1 + \frac{1}{n}\right) + 6 c^{3} d n^{4} x^{n} \Gamma\left(1 + \frac{1}{n}\right) + 6 c^{2} d^{2} n^{4} x^{2 n} \Gamma\left(1 + \frac{1}{n}\right) + 2 c d^{3} n^{4} x^{3 n} \Gamma\left(1 + \frac{1}{n}\right)\right)}\right) + b \left(\frac{2 c n^{3} x x^{n} \Gamma\left(1 + \frac{1}{n}\right)}{2 c^{4} n^{4} \Gamma\left(2 + \frac{1}{n}\right) + 6 c^{3} d n^{4} x^{n} \Gamma\left(2 + \frac{1}{n}\right) + 6 c^{2} d^{2} n^{4} x^{2 n} \Gamma\left(2 + \frac{1}{n}\right) + 2 c d^{3} n^{4} x^{3 n} \Gamma\left(2 + \frac{1}{n}\right)} - \frac{c n^{2} x x^{n} \Phi\left(\frac{d x^{n} e^{i \pi}}{c}, 1, 1 + \frac{1}{n}\right) \Gamma\left(1 + \frac{1}{n}\right)}{2 c^{4} n^{4} \Gamma\left(2 + \frac{1}{n}\right) + 6 c^{3} d n^{4} x^{n} \Gamma\left(2 + \frac{1}{n}\right) + 6 c^{2} d^{2} n^{4} x^{2 n} \Gamma\left(2 + \frac{1}{n}\right) + 2 c d^{3} n^{4} x^{3 n} \Gamma\left(2 + \frac{1}{n}\right)} + \frac{c n^{2} x x^{n} \Gamma\left(1 + \frac{1}{n}\right)}{2 c^{4} n^{4} \Gamma\left(2 + \frac{1}{n}\right) + 6 c^{3} d n^{4} x^{n} \Gamma\left(2 + \frac{1}{n}\right) + 6 c^{2} d^{2} n^{4} x^{2 n} \Gamma\left(2 + \frac{1}{n}\right) + 2 c d^{3} n^{4} x^{3 n} \Gamma\left(2 + \frac{1}{n}\right)} - \frac{c n x x^{n} \Gamma\left(1 + \frac{1}{n}\right)}{2 c^{4} n^{4} \Gamma\left(2 + \frac{1}{n}\right) + 6 c^{3} d n^{4} x^{n} \Gamma\left(2 + \frac{1}{n}\right) + 6 c^{2} d^{2} n^{4} x^{2 n} \Gamma\left(2 + \frac{1}{n}\right) + 2 c d^{3} n^{4} x^{3 n} \Gamma\left(2 + \frac{1}{n}\right)} + \frac{c x x^{n} \Phi\left(\frac{d x^{n} e^{i \pi}}{c}, 1, 1 + \frac{1}{n}\right) \Gamma\left(1 + \frac{1}{n}\right)}{2 c^{4} n^{4} \Gamma\left(2 + \frac{1}{n}\right) + 6 c^{3} d n^{4} x^{n} \Gamma\left(2 + \frac{1}{n}\right) + 6 c^{2} d^{2} n^{4} x^{2 n} \Gamma\left(2 + \frac{1}{n}\right) + 2 c d^{3} n^{4} x^{3 n} \Gamma\left(2 + \frac{1}{n}\right)} + \frac{3 d n^{3} x x^{2 n} \Gamma\left(1 + \frac{1}{n}\right)}{2 c^{4} n^{4} \Gamma\left(2 + \frac{1}{n}\right) + 6 c^{3} d n^{4} x^{n} \Gamma\left(2 + \frac{1}{n}\right) + 6 c^{2} d^{2} n^{4} x^{2 n} \Gamma\left(2 + \frac{1}{n}\right) + 2 c d^{3} n^{4} x^{3 n} \Gamma\left(2 + \frac{1}{n}\right)} - \frac{3 d n^{2} x x^{2 n} \Phi\left(\frac{d x^{n} e^{i \pi}}{c}, 1, 1 + \frac{1}{n}\right) \Gamma\left(1 + \frac{1}{n}\right)}{2 c^{4} n^{4} \Gamma\left(2 + \frac{1}{n}\right) + 6 c^{3} d n^{4} x^{n} \Gamma\left(2 + \frac{1}{n}\right) + 6 c^{2} d^{2} n^{4} x^{2 n} \Gamma\left(2 + \frac{1}{n}\right) + 2 c d^{3} n^{4} x^{3 n} \Gamma\left(2 + \frac{1}{n}\right)} + \frac{d n^{2} x x^{2 n} \Gamma\left(1 + \frac{1}{n}\right)}{2 c^{4} n^{4} \Gamma\left(2 + \frac{1}{n}\right) + 6 c^{3} d n^{4} x^{n} \Gamma\left(2 + \frac{1}{n}\right) + 6 c^{2} d^{2} n^{4} x^{2 n} \Gamma\left(2 + \frac{1}{n}\right) + 2 c d^{3} n^{4} x^{3 n} \Gamma\left(2 + \frac{1}{n}\right)} - \frac{2 d n x x^{2 n} \Gamma\left(1 + \frac{1}{n}\right)}{2 c^{4} n^{4} \Gamma\left(2 + \frac{1}{n}\right) + 6 c^{3} d n^{4} x^{n} \Gamma\left(2 + \frac{1}{n}\right) + 6 c^{2} d^{2} n^{4} x^{2 n} \Gamma\left(2 + \frac{1}{n}\right) + 2 c d^{3} n^{4} x^{3 n} \Gamma\left(2 + \frac{1}{n}\right)} + \frac{3 d x x^{2 n} \Phi\left(\frac{d x^{n} e^{i \pi}}{c}, 1, 1 + \frac{1}{n}\right) \Gamma\left(1 + \frac{1}{n}\right)}{2 c^{4} n^{4} \Gamma\left(2 + \frac{1}{n}\right) + 6 c^{3} d n^{4} x^{n} \Gamma\left(2 + \frac{1}{n}\right) + 6 c^{2} d^{2} n^{4} x^{2 n} \Gamma\left(2 + \frac{1}{n}\right) + 2 c d^{3} n^{4} x^{3 n} \Gamma\left(2 + \frac{1}{n}\right)} + \frac{d^{2} n^{3} x x^{3 n} \Gamma\left(1 + \frac{1}{n}\right)}{c \left(2 c^{4} n^{4} \Gamma\left(2 + \frac{1}{n}\right) + 6 c^{3} d n^{4} x^{n} \Gamma\left(2 + \frac{1}{n}\right) + 6 c^{2} d^{2} n^{4} x^{2 n} \Gamma\left(2 + \frac{1}{n}\right) + 2 c d^{3} n^{4} x^{3 n} \Gamma\left(2 + \frac{1}{n}\right)\right)} - \frac{3 d^{2} n^{2} x x^{3 n} \Phi\left(\frac{d x^{n} e^{i \pi}}{c}, 1, 1 + \frac{1}{n}\right) \Gamma\left(1 + \frac{1}{n}\right)}{c \left(2 c^{4} n^{4} \Gamma\left(2 + \frac{1}{n}\right) + 6 c^{3} d n^{4} x^{n} \Gamma\left(2 + \frac{1}{n}\right) + 6 c^{2} d^{2} n^{4} x^{2 n} \Gamma\left(2 + \frac{1}{n}\right) + 2 c d^{3} n^{4} x^{3 n} \Gamma\left(2 + \frac{1}{n}\right)\right)} - \frac{d^{2} n x x^{3 n} \Gamma\left(1 + \frac{1}{n}\right)}{c \left(2 c^{4} n^{4} \Gamma\left(2 + \frac{1}{n}\right) + 6 c^{3} d n^{4} x^{n} \Gamma\left(2 + \frac{1}{n}\right) + 6 c^{2} d^{2} n^{4} x^{2 n} \Gamma\left(2 + \frac{1}{n}\right) + 2 c d^{3} n^{4} x^{3 n} \Gamma\left(2 + \frac{1}{n}\right)\right)} + \frac{3 d^{2} x x^{3 n} \Phi\left(\frac{d x^{n} e^{i \pi}}{c}, 1, 1 + \frac{1}{n}\right) \Gamma\left(1 + \frac{1}{n}\right)}{c \left(2 c^{4} n^{4} \Gamma\left(2 + \frac{1}{n}\right) + 6 c^{3} d n^{4} x^{n} \Gamma\left(2 + \frac{1}{n}\right) + 6 c^{2} d^{2} n^{4} x^{2 n} \Gamma\left(2 + \frac{1}{n}\right) + 2 c d^{3} n^{4} x^{3 n} \Gamma\left(2 + \frac{1}{n}\right)\right)} - \frac{d^{3} n^{2} x x^{4 n} \Phi\left(\frac{d x^{n} e^{i \pi}}{c}, 1, 1 + \frac{1}{n}\right) \Gamma\left(1 + \frac{1}{n}\right)}{c^{2} \left(2 c^{4} n^{4} \Gamma\left(2 + \frac{1}{n}\right) + 6 c^{3} d n^{4} x^{n} \Gamma\left(2 + \frac{1}{n}\right) + 6 c^{2} d^{2} n^{4} x^{2 n} \Gamma\left(2 + \frac{1}{n}\right) + 2 c d^{3} n^{4} x^{3 n} \Gamma\left(2 + \frac{1}{n}\right)\right)} + \frac{d^{3} x x^{4 n} \Phi\left(\frac{d x^{n} e^{i \pi}}{c}, 1, 1 + \frac{1}{n}\right) \Gamma\left(1 + \frac{1}{n}\right)}{c^{2} \left(2 c^{4} n^{4} \Gamma\left(2 + \frac{1}{n}\right) + 6 c^{3} d n^{4} x^{n} \Gamma\left(2 + \frac{1}{n}\right) + 6 c^{2} d^{2} n^{4} x^{2 n} \Gamma\left(2 + \frac{1}{n}\right) + 2 c d^{3} n^{4} x^{3 n} \Gamma\left(2 + \frac{1}{n}\right)\right)}\right)"," ",0,"a*(2*c*n**2*x*lerchphi(d*x**n*exp_polar(I*pi)/c, 1, 1/n)*gamma(1/n)/(2*c**4*n**4*gamma(1 + 1/n) + 6*c**3*d*n**4*x**n*gamma(1 + 1/n) + 6*c**2*d**2*n**4*x**(2*n)*gamma(1 + 1/n) + 2*c*d**3*n**4*x**(3*n)*gamma(1 + 1/n)) + 3*c*n**2*x*gamma(1/n)/(2*c**4*n**4*gamma(1 + 1/n) + 6*c**3*d*n**4*x**n*gamma(1 + 1/n) + 6*c**2*d**2*n**4*x**(2*n)*gamma(1 + 1/n) + 2*c*d**3*n**4*x**(3*n)*gamma(1 + 1/n)) - 3*c*n*x*lerchphi(d*x**n*exp_polar(I*pi)/c, 1, 1/n)*gamma(1/n)/(2*c**4*n**4*gamma(1 + 1/n) + 6*c**3*d*n**4*x**n*gamma(1 + 1/n) + 6*c**2*d**2*n**4*x**(2*n)*gamma(1 + 1/n) + 2*c*d**3*n**4*x**(3*n)*gamma(1 + 1/n)) - c*n*x*gamma(1/n)/(2*c**4*n**4*gamma(1 + 1/n) + 6*c**3*d*n**4*x**n*gamma(1 + 1/n) + 6*c**2*d**2*n**4*x**(2*n)*gamma(1 + 1/n) + 2*c*d**3*n**4*x**(3*n)*gamma(1 + 1/n)) + c*x*lerchphi(d*x**n*exp_polar(I*pi)/c, 1, 1/n)*gamma(1/n)/(2*c**4*n**4*gamma(1 + 1/n) + 6*c**3*d*n**4*x**n*gamma(1 + 1/n) + 6*c**2*d**2*n**4*x**(2*n)*gamma(1 + 1/n) + 2*c*d**3*n**4*x**(3*n)*gamma(1 + 1/n)) + 6*d*n**2*x*x**n*lerchphi(d*x**n*exp_polar(I*pi)/c, 1, 1/n)*gamma(1/n)/(2*c**4*n**4*gamma(1 + 1/n) + 6*c**3*d*n**4*x**n*gamma(1 + 1/n) + 6*c**2*d**2*n**4*x**(2*n)*gamma(1 + 1/n) + 2*c*d**3*n**4*x**(3*n)*gamma(1 + 1/n)) + 5*d*n**2*x*x**n*gamma(1/n)/(2*c**4*n**4*gamma(1 + 1/n) + 6*c**3*d*n**4*x**n*gamma(1 + 1/n) + 6*c**2*d**2*n**4*x**(2*n)*gamma(1 + 1/n) + 2*c*d**3*n**4*x**(3*n)*gamma(1 + 1/n)) - 9*d*n*x*x**n*lerchphi(d*x**n*exp_polar(I*pi)/c, 1, 1/n)*gamma(1/n)/(2*c**4*n**4*gamma(1 + 1/n) + 6*c**3*d*n**4*x**n*gamma(1 + 1/n) + 6*c**2*d**2*n**4*x**(2*n)*gamma(1 + 1/n) + 2*c*d**3*n**4*x**(3*n)*gamma(1 + 1/n)) - 2*d*n*x*x**n*gamma(1/n)/(2*c**4*n**4*gamma(1 + 1/n) + 6*c**3*d*n**4*x**n*gamma(1 + 1/n) + 6*c**2*d**2*n**4*x**(2*n)*gamma(1 + 1/n) + 2*c*d**3*n**4*x**(3*n)*gamma(1 + 1/n)) + 3*d*x*x**n*lerchphi(d*x**n*exp_polar(I*pi)/c, 1, 1/n)*gamma(1/n)/(2*c**4*n**4*gamma(1 + 1/n) + 6*c**3*d*n**4*x**n*gamma(1 + 1/n) + 6*c**2*d**2*n**4*x**(2*n)*gamma(1 + 1/n) + 2*c*d**3*n**4*x**(3*n)*gamma(1 + 1/n)) + 6*d**2*n**2*x*x**(2*n)*lerchphi(d*x**n*exp_polar(I*pi)/c, 1, 1/n)*gamma(1/n)/(c*(2*c**4*n**4*gamma(1 + 1/n) + 6*c**3*d*n**4*x**n*gamma(1 + 1/n) + 6*c**2*d**2*n**4*x**(2*n)*gamma(1 + 1/n) + 2*c*d**3*n**4*x**(3*n)*gamma(1 + 1/n))) + 2*d**2*n**2*x*x**(2*n)*gamma(1/n)/(c*(2*c**4*n**4*gamma(1 + 1/n) + 6*c**3*d*n**4*x**n*gamma(1 + 1/n) + 6*c**2*d**2*n**4*x**(2*n)*gamma(1 + 1/n) + 2*c*d**3*n**4*x**(3*n)*gamma(1 + 1/n))) - 9*d**2*n*x*x**(2*n)*lerchphi(d*x**n*exp_polar(I*pi)/c, 1, 1/n)*gamma(1/n)/(c*(2*c**4*n**4*gamma(1 + 1/n) + 6*c**3*d*n**4*x**n*gamma(1 + 1/n) + 6*c**2*d**2*n**4*x**(2*n)*gamma(1 + 1/n) + 2*c*d**3*n**4*x**(3*n)*gamma(1 + 1/n))) - d**2*n*x*x**(2*n)*gamma(1/n)/(c*(2*c**4*n**4*gamma(1 + 1/n) + 6*c**3*d*n**4*x**n*gamma(1 + 1/n) + 6*c**2*d**2*n**4*x**(2*n)*gamma(1 + 1/n) + 2*c*d**3*n**4*x**(3*n)*gamma(1 + 1/n))) + 3*d**2*x*x**(2*n)*lerchphi(d*x**n*exp_polar(I*pi)/c, 1, 1/n)*gamma(1/n)/(c*(2*c**4*n**4*gamma(1 + 1/n) + 6*c**3*d*n**4*x**n*gamma(1 + 1/n) + 6*c**2*d**2*n**4*x**(2*n)*gamma(1 + 1/n) + 2*c*d**3*n**4*x**(3*n)*gamma(1 + 1/n))) + 2*d**3*n**2*x*x**(3*n)*lerchphi(d*x**n*exp_polar(I*pi)/c, 1, 1/n)*gamma(1/n)/(c**2*(2*c**4*n**4*gamma(1 + 1/n) + 6*c**3*d*n**4*x**n*gamma(1 + 1/n) + 6*c**2*d**2*n**4*x**(2*n)*gamma(1 + 1/n) + 2*c*d**3*n**4*x**(3*n)*gamma(1 + 1/n))) - 3*d**3*n*x*x**(3*n)*lerchphi(d*x**n*exp_polar(I*pi)/c, 1, 1/n)*gamma(1/n)/(c**2*(2*c**4*n**4*gamma(1 + 1/n) + 6*c**3*d*n**4*x**n*gamma(1 + 1/n) + 6*c**2*d**2*n**4*x**(2*n)*gamma(1 + 1/n) + 2*c*d**3*n**4*x**(3*n)*gamma(1 + 1/n))) + d**3*x*x**(3*n)*lerchphi(d*x**n*exp_polar(I*pi)/c, 1, 1/n)*gamma(1/n)/(c**2*(2*c**4*n**4*gamma(1 + 1/n) + 6*c**3*d*n**4*x**n*gamma(1 + 1/n) + 6*c**2*d**2*n**4*x**(2*n)*gamma(1 + 1/n) + 2*c*d**3*n**4*x**(3*n)*gamma(1 + 1/n)))) + b*(2*c*n**3*x*x**n*gamma(1 + 1/n)/(2*c**4*n**4*gamma(2 + 1/n) + 6*c**3*d*n**4*x**n*gamma(2 + 1/n) + 6*c**2*d**2*n**4*x**(2*n)*gamma(2 + 1/n) + 2*c*d**3*n**4*x**(3*n)*gamma(2 + 1/n)) - c*n**2*x*x**n*lerchphi(d*x**n*exp_polar(I*pi)/c, 1, 1 + 1/n)*gamma(1 + 1/n)/(2*c**4*n**4*gamma(2 + 1/n) + 6*c**3*d*n**4*x**n*gamma(2 + 1/n) + 6*c**2*d**2*n**4*x**(2*n)*gamma(2 + 1/n) + 2*c*d**3*n**4*x**(3*n)*gamma(2 + 1/n)) + c*n**2*x*x**n*gamma(1 + 1/n)/(2*c**4*n**4*gamma(2 + 1/n) + 6*c**3*d*n**4*x**n*gamma(2 + 1/n) + 6*c**2*d**2*n**4*x**(2*n)*gamma(2 + 1/n) + 2*c*d**3*n**4*x**(3*n)*gamma(2 + 1/n)) - c*n*x*x**n*gamma(1 + 1/n)/(2*c**4*n**4*gamma(2 + 1/n) + 6*c**3*d*n**4*x**n*gamma(2 + 1/n) + 6*c**2*d**2*n**4*x**(2*n)*gamma(2 + 1/n) + 2*c*d**3*n**4*x**(3*n)*gamma(2 + 1/n)) + c*x*x**n*lerchphi(d*x**n*exp_polar(I*pi)/c, 1, 1 + 1/n)*gamma(1 + 1/n)/(2*c**4*n**4*gamma(2 + 1/n) + 6*c**3*d*n**4*x**n*gamma(2 + 1/n) + 6*c**2*d**2*n**4*x**(2*n)*gamma(2 + 1/n) + 2*c*d**3*n**4*x**(3*n)*gamma(2 + 1/n)) + 3*d*n**3*x*x**(2*n)*gamma(1 + 1/n)/(2*c**4*n**4*gamma(2 + 1/n) + 6*c**3*d*n**4*x**n*gamma(2 + 1/n) + 6*c**2*d**2*n**4*x**(2*n)*gamma(2 + 1/n) + 2*c*d**3*n**4*x**(3*n)*gamma(2 + 1/n)) - 3*d*n**2*x*x**(2*n)*lerchphi(d*x**n*exp_polar(I*pi)/c, 1, 1 + 1/n)*gamma(1 + 1/n)/(2*c**4*n**4*gamma(2 + 1/n) + 6*c**3*d*n**4*x**n*gamma(2 + 1/n) + 6*c**2*d**2*n**4*x**(2*n)*gamma(2 + 1/n) + 2*c*d**3*n**4*x**(3*n)*gamma(2 + 1/n)) + d*n**2*x*x**(2*n)*gamma(1 + 1/n)/(2*c**4*n**4*gamma(2 + 1/n) + 6*c**3*d*n**4*x**n*gamma(2 + 1/n) + 6*c**2*d**2*n**4*x**(2*n)*gamma(2 + 1/n) + 2*c*d**3*n**4*x**(3*n)*gamma(2 + 1/n)) - 2*d*n*x*x**(2*n)*gamma(1 + 1/n)/(2*c**4*n**4*gamma(2 + 1/n) + 6*c**3*d*n**4*x**n*gamma(2 + 1/n) + 6*c**2*d**2*n**4*x**(2*n)*gamma(2 + 1/n) + 2*c*d**3*n**4*x**(3*n)*gamma(2 + 1/n)) + 3*d*x*x**(2*n)*lerchphi(d*x**n*exp_polar(I*pi)/c, 1, 1 + 1/n)*gamma(1 + 1/n)/(2*c**4*n**4*gamma(2 + 1/n) + 6*c**3*d*n**4*x**n*gamma(2 + 1/n) + 6*c**2*d**2*n**4*x**(2*n)*gamma(2 + 1/n) + 2*c*d**3*n**4*x**(3*n)*gamma(2 + 1/n)) + d**2*n**3*x*x**(3*n)*gamma(1 + 1/n)/(c*(2*c**4*n**4*gamma(2 + 1/n) + 6*c**3*d*n**4*x**n*gamma(2 + 1/n) + 6*c**2*d**2*n**4*x**(2*n)*gamma(2 + 1/n) + 2*c*d**3*n**4*x**(3*n)*gamma(2 + 1/n))) - 3*d**2*n**2*x*x**(3*n)*lerchphi(d*x**n*exp_polar(I*pi)/c, 1, 1 + 1/n)*gamma(1 + 1/n)/(c*(2*c**4*n**4*gamma(2 + 1/n) + 6*c**3*d*n**4*x**n*gamma(2 + 1/n) + 6*c**2*d**2*n**4*x**(2*n)*gamma(2 + 1/n) + 2*c*d**3*n**4*x**(3*n)*gamma(2 + 1/n))) - d**2*n*x*x**(3*n)*gamma(1 + 1/n)/(c*(2*c**4*n**4*gamma(2 + 1/n) + 6*c**3*d*n**4*x**n*gamma(2 + 1/n) + 6*c**2*d**2*n**4*x**(2*n)*gamma(2 + 1/n) + 2*c*d**3*n**4*x**(3*n)*gamma(2 + 1/n))) + 3*d**2*x*x**(3*n)*lerchphi(d*x**n*exp_polar(I*pi)/c, 1, 1 + 1/n)*gamma(1 + 1/n)/(c*(2*c**4*n**4*gamma(2 + 1/n) + 6*c**3*d*n**4*x**n*gamma(2 + 1/n) + 6*c**2*d**2*n**4*x**(2*n)*gamma(2 + 1/n) + 2*c*d**3*n**4*x**(3*n)*gamma(2 + 1/n))) - d**3*n**2*x*x**(4*n)*lerchphi(d*x**n*exp_polar(I*pi)/c, 1, 1 + 1/n)*gamma(1 + 1/n)/(c**2*(2*c**4*n**4*gamma(2 + 1/n) + 6*c**3*d*n**4*x**n*gamma(2 + 1/n) + 6*c**2*d**2*n**4*x**(2*n)*gamma(2 + 1/n) + 2*c*d**3*n**4*x**(3*n)*gamma(2 + 1/n))) + d**3*x*x**(4*n)*lerchphi(d*x**n*exp_polar(I*pi)/c, 1, 1 + 1/n)*gamma(1 + 1/n)/(c**2*(2*c**4*n**4*gamma(2 + 1/n) + 6*c**3*d*n**4*x**n*gamma(2 + 1/n) + 6*c**2*d**2*n**4*x**(2*n)*gamma(2 + 1/n) + 2*c*d**3*n**4*x**(3*n)*gamma(2 + 1/n))))","C",0
291,-1,0,0,0.000000," ","integrate((a+b*x**n)/(c+d*x**n)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
292,-1,0,0,0.000000," ","integrate((a+b*x**n)**2*(d+e*x**n)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
293,1,1765,0,77.474078," ","integrate((a+b*x**n)**2*(d+e*x**n)**2,x)","\begin{cases} a^{2} d^{2} x + 2 a^{2} d e \log{\left(x \right)} - \frac{a^{2} e^{2}}{x} + 2 a b d^{2} \log{\left(x \right)} - \frac{4 a b d e}{x} - \frac{a b e^{2}}{x^{2}} - \frac{b^{2} d^{2}}{x} - \frac{b^{2} d e}{x^{2}} - \frac{b^{2} e^{2}}{3 x^{3}} & \text{for}\: n = -1 \\a^{2} d^{2} x + 4 a^{2} d e \sqrt{x} + a^{2} e^{2} \log{\left(x \right)} + 4 a b d^{2} \sqrt{x} + 4 a b d e \log{\left(x \right)} - \frac{4 a b e^{2}}{\sqrt{x}} + b^{2} d^{2} \log{\left(x \right)} - \frac{4 b^{2} d e}{\sqrt{x}} - \frac{b^{2} e^{2}}{x} & \text{for}\: n = - \frac{1}{2} \\a^{2} d^{2} x + 3 a^{2} d e x^{\frac{2}{3}} + 3 a^{2} e^{2} \sqrt[3]{x} + 3 a b d^{2} x^{\frac{2}{3}} + 12 a b d e \sqrt[3]{x} + 2 a b e^{2} \log{\left(x \right)} + 3 b^{2} d^{2} \sqrt[3]{x} + 2 b^{2} d e \log{\left(x \right)} - \frac{3 b^{2} e^{2}}{\sqrt[3]{x}} & \text{for}\: n = - \frac{1}{3} \\a^{2} d^{2} x + \frac{8 a d x^{\frac{3}{4}} \left(a e + b d\right)}{3} - 4 b^{2} e^{2} \log{\left(\frac{1}{\sqrt[4]{x}} \right)} + 8 b e \sqrt[4]{x} \left(a e + b d\right) - \frac{\sqrt{x} \left(- 4 a^{2} e^{2} - 16 a b d e - 4 b^{2} d^{2}\right)}{2} & \text{for}\: n = - \frac{1}{4} \\\frac{24 a^{2} d^{2} n^{4} x}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{50 a^{2} d^{2} n^{3} x}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{35 a^{2} d^{2} n^{2} x}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{10 a^{2} d^{2} n x}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{a^{2} d^{2} x}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{48 a^{2} d e n^{3} x x^{n}}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{52 a^{2} d e n^{2} x x^{n}}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{18 a^{2} d e n x x^{n}}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{2 a^{2} d e x x^{n}}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{12 a^{2} e^{2} n^{3} x x^{2 n}}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{19 a^{2} e^{2} n^{2} x x^{2 n}}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{8 a^{2} e^{2} n x x^{2 n}}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{a^{2} e^{2} x x^{2 n}}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{48 a b d^{2} n^{3} x x^{n}}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{52 a b d^{2} n^{2} x x^{n}}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{18 a b d^{2} n x x^{n}}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{2 a b d^{2} x x^{n}}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{48 a b d e n^{3} x x^{2 n}}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{76 a b d e n^{2} x x^{2 n}}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{32 a b d e n x x^{2 n}}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{4 a b d e x x^{2 n}}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{16 a b e^{2} n^{3} x x^{3 n}}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{28 a b e^{2} n^{2} x x^{3 n}}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{14 a b e^{2} n x x^{3 n}}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{2 a b e^{2} x x^{3 n}}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{12 b^{2} d^{2} n^{3} x x^{2 n}}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{19 b^{2} d^{2} n^{2} x x^{2 n}}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{8 b^{2} d^{2} n x x^{2 n}}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{b^{2} d^{2} x x^{2 n}}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{16 b^{2} d e n^{3} x x^{3 n}}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{28 b^{2} d e n^{2} x x^{3 n}}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{14 b^{2} d e n x x^{3 n}}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{2 b^{2} d e x x^{3 n}}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{6 b^{2} e^{2} n^{3} x x^{4 n}}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{11 b^{2} e^{2} n^{2} x x^{4 n}}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{6 b^{2} e^{2} n x x^{4 n}}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} + \frac{b^{2} e^{2} x x^{4 n}}{24 n^{4} + 50 n^{3} + 35 n^{2} + 10 n + 1} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*d**2*x + 2*a**2*d*e*log(x) - a**2*e**2/x + 2*a*b*d**2*log(x) - 4*a*b*d*e/x - a*b*e**2/x**2 - b**2*d**2/x - b**2*d*e/x**2 - b**2*e**2/(3*x**3), Eq(n, -1)), (a**2*d**2*x + 4*a**2*d*e*sqrt(x) + a**2*e**2*log(x) + 4*a*b*d**2*sqrt(x) + 4*a*b*d*e*log(x) - 4*a*b*e**2/sqrt(x) + b**2*d**2*log(x) - 4*b**2*d*e/sqrt(x) - b**2*e**2/x, Eq(n, -1/2)), (a**2*d**2*x + 3*a**2*d*e*x**(2/3) + 3*a**2*e**2*x**(1/3) + 3*a*b*d**2*x**(2/3) + 12*a*b*d*e*x**(1/3) + 2*a*b*e**2*log(x) + 3*b**2*d**2*x**(1/3) + 2*b**2*d*e*log(x) - 3*b**2*e**2/x**(1/3), Eq(n, -1/3)), (a**2*d**2*x + 8*a*d*x**(3/4)*(a*e + b*d)/3 - 4*b**2*e**2*log(x**(-1/4)) + 8*b*e*x**(1/4)*(a*e + b*d) - sqrt(x)*(-4*a**2*e**2 - 16*a*b*d*e - 4*b**2*d**2)/2, Eq(n, -1/4)), (24*a**2*d**2*n**4*x/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + 50*a**2*d**2*n**3*x/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + 35*a**2*d**2*n**2*x/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + 10*a**2*d**2*n*x/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + a**2*d**2*x/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + 48*a**2*d*e*n**3*x*x**n/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + 52*a**2*d*e*n**2*x*x**n/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + 18*a**2*d*e*n*x*x**n/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + 2*a**2*d*e*x*x**n/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + 12*a**2*e**2*n**3*x*x**(2*n)/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + 19*a**2*e**2*n**2*x*x**(2*n)/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + 8*a**2*e**2*n*x*x**(2*n)/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + a**2*e**2*x*x**(2*n)/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + 48*a*b*d**2*n**3*x*x**n/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + 52*a*b*d**2*n**2*x*x**n/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + 18*a*b*d**2*n*x*x**n/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + 2*a*b*d**2*x*x**n/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + 48*a*b*d*e*n**3*x*x**(2*n)/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + 76*a*b*d*e*n**2*x*x**(2*n)/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + 32*a*b*d*e*n*x*x**(2*n)/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + 4*a*b*d*e*x*x**(2*n)/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + 16*a*b*e**2*n**3*x*x**(3*n)/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + 28*a*b*e**2*n**2*x*x**(3*n)/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + 14*a*b*e**2*n*x*x**(3*n)/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + 2*a*b*e**2*x*x**(3*n)/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + 12*b**2*d**2*n**3*x*x**(2*n)/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + 19*b**2*d**2*n**2*x*x**(2*n)/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + 8*b**2*d**2*n*x*x**(2*n)/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + b**2*d**2*x*x**(2*n)/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + 16*b**2*d*e*n**3*x*x**(3*n)/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + 28*b**2*d*e*n**2*x*x**(3*n)/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + 14*b**2*d*e*n*x*x**(3*n)/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + 2*b**2*d*e*x*x**(3*n)/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + 6*b**2*e**2*n**3*x*x**(4*n)/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + 11*b**2*e**2*n**2*x*x**(4*n)/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + 6*b**2*e**2*n*x*x**(4*n)/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1) + b**2*e**2*x*x**(4*n)/(24*n**4 + 50*n**3 + 35*n**2 + 10*n + 1), True))","A",0
294,1,726,0,2.736839," ","integrate((a+b*x**n)**2*(c+d*x**n),x)","\begin{cases} a^{2} c x + a^{2} d \log{\left(x \right)} + 2 a b c \log{\left(x \right)} - \frac{2 a b d}{x} - \frac{b^{2} c}{x} - \frac{b^{2} d}{2 x^{2}} & \text{for}\: n = -1 \\a^{2} c x + 2 a^{2} d \sqrt{x} + 4 a b c \sqrt{x} + 2 a b d \log{\left(x \right)} + b^{2} c \log{\left(x \right)} - \frac{2 b^{2} d}{\sqrt{x}} & \text{for}\: n = - \frac{1}{2} \\a^{2} c x + \frac{3 a^{2} d x^{\frac{2}{3}}}{2} + 3 a b c x^{\frac{2}{3}} + 6 a b d \sqrt[3]{x} + 3 b^{2} c \sqrt[3]{x} + b^{2} d \log{\left(x \right)} & \text{for}\: n = - \frac{1}{3} \\\frac{6 a^{2} c n^{3} x}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{11 a^{2} c n^{2} x}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{6 a^{2} c n x}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{a^{2} c x}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{6 a^{2} d n^{2} x x^{n}}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{5 a^{2} d n x x^{n}}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{a^{2} d x x^{n}}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{12 a b c n^{2} x x^{n}}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{10 a b c n x x^{n}}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{2 a b c x x^{n}}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{6 a b d n^{2} x x^{2 n}}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{8 a b d n x x^{2 n}}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{2 a b d x x^{2 n}}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{3 b^{2} c n^{2} x x^{2 n}}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{4 b^{2} c n x x^{2 n}}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{b^{2} c x x^{2 n}}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{2 b^{2} d n^{2} x x^{3 n}}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{3 b^{2} d n x x^{3 n}}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{b^{2} d x x^{3 n}}{6 n^{3} + 11 n^{2} + 6 n + 1} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*c*x + a**2*d*log(x) + 2*a*b*c*log(x) - 2*a*b*d/x - b**2*c/x - b**2*d/(2*x**2), Eq(n, -1)), (a**2*c*x + 2*a**2*d*sqrt(x) + 4*a*b*c*sqrt(x) + 2*a*b*d*log(x) + b**2*c*log(x) - 2*b**2*d/sqrt(x), Eq(n, -1/2)), (a**2*c*x + 3*a**2*d*x**(2/3)/2 + 3*a*b*c*x**(2/3) + 6*a*b*d*x**(1/3) + 3*b**2*c*x**(1/3) + b**2*d*log(x), Eq(n, -1/3)), (6*a**2*c*n**3*x/(6*n**3 + 11*n**2 + 6*n + 1) + 11*a**2*c*n**2*x/(6*n**3 + 11*n**2 + 6*n + 1) + 6*a**2*c*n*x/(6*n**3 + 11*n**2 + 6*n + 1) + a**2*c*x/(6*n**3 + 11*n**2 + 6*n + 1) + 6*a**2*d*n**2*x*x**n/(6*n**3 + 11*n**2 + 6*n + 1) + 5*a**2*d*n*x*x**n/(6*n**3 + 11*n**2 + 6*n + 1) + a**2*d*x*x**n/(6*n**3 + 11*n**2 + 6*n + 1) + 12*a*b*c*n**2*x*x**n/(6*n**3 + 11*n**2 + 6*n + 1) + 10*a*b*c*n*x*x**n/(6*n**3 + 11*n**2 + 6*n + 1) + 2*a*b*c*x*x**n/(6*n**3 + 11*n**2 + 6*n + 1) + 6*a*b*d*n**2*x*x**(2*n)/(6*n**3 + 11*n**2 + 6*n + 1) + 8*a*b*d*n*x*x**(2*n)/(6*n**3 + 11*n**2 + 6*n + 1) + 2*a*b*d*x*x**(2*n)/(6*n**3 + 11*n**2 + 6*n + 1) + 3*b**2*c*n**2*x*x**(2*n)/(6*n**3 + 11*n**2 + 6*n + 1) + 4*b**2*c*n*x*x**(2*n)/(6*n**3 + 11*n**2 + 6*n + 1) + b**2*c*x*x**(2*n)/(6*n**3 + 11*n**2 + 6*n + 1) + 2*b**2*d*n**2*x*x**(3*n)/(6*n**3 + 11*n**2 + 6*n + 1) + 3*b**2*d*n*x*x**(3*n)/(6*n**3 + 11*n**2 + 6*n + 1) + b**2*d*x*x**(3*n)/(6*n**3 + 11*n**2 + 6*n + 1), True))","A",0
295,1,170,0,6.831310," ","integrate((a+b*x**n)**2/(c+d*x**n),x)","\frac{a^{2} x \Phi\left(\frac{d x^{n} e^{i \pi}}{c}, 1, \frac{1}{n}\right) \Gamma\left(\frac{1}{n}\right)}{c n^{2} \Gamma\left(1 + \frac{1}{n}\right)} - \frac{2 a b x \Phi\left(\frac{c x^{- n} e^{i \pi}}{d}, 1, \frac{e^{i \pi}}{n}\right) \Gamma\left(\frac{1}{n}\right)}{d n^{2} \Gamma\left(1 + \frac{1}{n}\right)} + \frac{2 b^{2} x x^{2 n} \Phi\left(\frac{d x^{n} e^{i \pi}}{c}, 1, 2 + \frac{1}{n}\right) \Gamma\left(2 + \frac{1}{n}\right)}{c n \Gamma\left(3 + \frac{1}{n}\right)} + \frac{b^{2} x x^{2 n} \Phi\left(\frac{d x^{n} e^{i \pi}}{c}, 1, 2 + \frac{1}{n}\right) \Gamma\left(2 + \frac{1}{n}\right)}{c n^{2} \Gamma\left(3 + \frac{1}{n}\right)}"," ",0,"a**2*x*lerchphi(d*x**n*exp_polar(I*pi)/c, 1, 1/n)*gamma(1/n)/(c*n**2*gamma(1 + 1/n)) - 2*a*b*x*lerchphi(c*x**(-n)*exp_polar(I*pi)/d, 1, exp_polar(I*pi)/n)*gamma(1/n)/(d*n**2*gamma(1 + 1/n)) + 2*b**2*x*x**(2*n)*lerchphi(d*x**n*exp_polar(I*pi)/c, 1, 2 + 1/n)*gamma(2 + 1/n)/(c*n*gamma(3 + 1/n)) + b**2*x*x**(2*n)*lerchphi(d*x**n*exp_polar(I*pi)/c, 1, 2 + 1/n)*gamma(2 + 1/n)/(c*n**2*gamma(3 + 1/n))","C",0
296,0,0,0,0.000000," ","integrate((a+b*x**n)**2/(c+d*x**n)**2,x)","\int \frac{\left(a + b x^{n}\right)^{2}}{\left(c + d x^{n}\right)^{2}}\, dx"," ",0,"Integral((a + b*x**n)**2/(c + d*x**n)**2, x)","F",0
297,-1,0,0,0.000000," ","integrate((a+b*x**n)**2/(c+d*x**n)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
298,1,369,0,9.725038," ","integrate((c+d*x**n)**4/(a+b*x**n),x)","- \frac{4 c^{3} d x \Phi\left(\frac{a x^{- n} e^{i \pi}}{b}, 1, \frac{e^{i \pi}}{n}\right) \Gamma\left(\frac{1}{n}\right)}{b n^{2} \Gamma\left(1 + \frac{1}{n}\right)} + \frac{c^{4} x \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{1}{n}\right) \Gamma\left(\frac{1}{n}\right)}{a n^{2} \Gamma\left(1 + \frac{1}{n}\right)} + \frac{12 c^{2} d^{2} x x^{2 n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, 2 + \frac{1}{n}\right) \Gamma\left(2 + \frac{1}{n}\right)}{a n \Gamma\left(3 + \frac{1}{n}\right)} + \frac{6 c^{2} d^{2} x x^{2 n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, 2 + \frac{1}{n}\right) \Gamma\left(2 + \frac{1}{n}\right)}{a n^{2} \Gamma\left(3 + \frac{1}{n}\right)} + \frac{12 c d^{3} x x^{3 n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, 3 + \frac{1}{n}\right) \Gamma\left(3 + \frac{1}{n}\right)}{a n \Gamma\left(4 + \frac{1}{n}\right)} + \frac{4 c d^{3} x x^{3 n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, 3 + \frac{1}{n}\right) \Gamma\left(3 + \frac{1}{n}\right)}{a n^{2} \Gamma\left(4 + \frac{1}{n}\right)} + \frac{4 d^{4} x x^{4 n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, 4 + \frac{1}{n}\right) \Gamma\left(4 + \frac{1}{n}\right)}{a n \Gamma\left(5 + \frac{1}{n}\right)} + \frac{d^{4} x x^{4 n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, 4 + \frac{1}{n}\right) \Gamma\left(4 + \frac{1}{n}\right)}{a n^{2} \Gamma\left(5 + \frac{1}{n}\right)}"," ",0,"-4*c**3*d*x*lerchphi(a*x**(-n)*exp_polar(I*pi)/b, 1, exp_polar(I*pi)/n)*gamma(1/n)/(b*n**2*gamma(1 + 1/n)) + c**4*x*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 1/n)*gamma(1/n)/(a*n**2*gamma(1 + 1/n)) + 12*c**2*d**2*x*x**(2*n)*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 2 + 1/n)*gamma(2 + 1/n)/(a*n*gamma(3 + 1/n)) + 6*c**2*d**2*x*x**(2*n)*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 2 + 1/n)*gamma(2 + 1/n)/(a*n**2*gamma(3 + 1/n)) + 12*c*d**3*x*x**(3*n)*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 3 + 1/n)*gamma(3 + 1/n)/(a*n*gamma(4 + 1/n)) + 4*c*d**3*x*x**(3*n)*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 3 + 1/n)*gamma(3 + 1/n)/(a*n**2*gamma(4 + 1/n)) + 4*d**4*x*x**(4*n)*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 4 + 1/n)*gamma(4 + 1/n)/(a*n*gamma(5 + 1/n)) + d**4*x*x**(4*n)*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 4 + 1/n)*gamma(4 + 1/n)/(a*n**2*gamma(5 + 1/n))","C",0
299,1,269,0,13.011521," ","integrate((c+d*x**n)**3/(a+b*x**n),x)","- \frac{3 c^{2} d x \Phi\left(\frac{a x^{- n} e^{i \pi}}{b}, 1, \frac{e^{i \pi}}{n}\right) \Gamma\left(\frac{1}{n}\right)}{b n^{2} \Gamma\left(1 + \frac{1}{n}\right)} + \frac{c^{3} x \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{1}{n}\right) \Gamma\left(\frac{1}{n}\right)}{a n^{2} \Gamma\left(1 + \frac{1}{n}\right)} + \frac{6 c d^{2} x x^{2 n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, 2 + \frac{1}{n}\right) \Gamma\left(2 + \frac{1}{n}\right)}{a n \Gamma\left(3 + \frac{1}{n}\right)} + \frac{3 c d^{2} x x^{2 n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, 2 + \frac{1}{n}\right) \Gamma\left(2 + \frac{1}{n}\right)}{a n^{2} \Gamma\left(3 + \frac{1}{n}\right)} + \frac{3 d^{3} x x^{3 n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, 3 + \frac{1}{n}\right) \Gamma\left(3 + \frac{1}{n}\right)}{a n \Gamma\left(4 + \frac{1}{n}\right)} + \frac{d^{3} x x^{3 n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, 3 + \frac{1}{n}\right) \Gamma\left(3 + \frac{1}{n}\right)}{a n^{2} \Gamma\left(4 + \frac{1}{n}\right)}"," ",0,"-3*c**2*d*x*lerchphi(a*x**(-n)*exp_polar(I*pi)/b, 1, exp_polar(I*pi)/n)*gamma(1/n)/(b*n**2*gamma(1 + 1/n)) + c**3*x*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 1/n)*gamma(1/n)/(a*n**2*gamma(1 + 1/n)) + 6*c*d**2*x*x**(2*n)*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 2 + 1/n)*gamma(2 + 1/n)/(a*n*gamma(3 + 1/n)) + 3*c*d**2*x*x**(2*n)*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 2 + 1/n)*gamma(2 + 1/n)/(a*n**2*gamma(3 + 1/n)) + 3*d**3*x*x**(3*n)*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 3 + 1/n)*gamma(3 + 1/n)/(a*n*gamma(4 + 1/n)) + d**3*x*x**(3*n)*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 3 + 1/n)*gamma(3 + 1/n)/(a*n**2*gamma(4 + 1/n))","C",0
300,1,170,0,12.792842," ","integrate((c+d*x**n)**2/(a+b*x**n),x)","- \frac{2 c d x \Phi\left(\frac{a x^{- n} e^{i \pi}}{b}, 1, \frac{e^{i \pi}}{n}\right) \Gamma\left(\frac{1}{n}\right)}{b n^{2} \Gamma\left(1 + \frac{1}{n}\right)} + \frac{c^{2} x \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{1}{n}\right) \Gamma\left(\frac{1}{n}\right)}{a n^{2} \Gamma\left(1 + \frac{1}{n}\right)} + \frac{2 d^{2} x x^{2 n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, 2 + \frac{1}{n}\right) \Gamma\left(2 + \frac{1}{n}\right)}{a n \Gamma\left(3 + \frac{1}{n}\right)} + \frac{d^{2} x x^{2 n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, 2 + \frac{1}{n}\right) \Gamma\left(2 + \frac{1}{n}\right)}{a n^{2} \Gamma\left(3 + \frac{1}{n}\right)}"," ",0,"-2*c*d*x*lerchphi(a*x**(-n)*exp_polar(I*pi)/b, 1, exp_polar(I*pi)/n)*gamma(1/n)/(b*n**2*gamma(1 + 1/n)) + c**2*x*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 1/n)*gamma(1/n)/(a*n**2*gamma(1 + 1/n)) + 2*d**2*x*x**(2*n)*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 2 + 1/n)*gamma(2 + 1/n)/(a*n*gamma(3 + 1/n)) + d**2*x*x**(2*n)*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 2 + 1/n)*gamma(2 + 1/n)/(a*n**2*gamma(3 + 1/n))","C",0
301,1,73,0,4.112011," ","integrate((c+d*x**n)/(a+b*x**n),x)","- \frac{d x \Phi\left(\frac{a x^{- n} e^{i \pi}}{b}, 1, \frac{e^{i \pi}}{n}\right) \Gamma\left(\frac{1}{n}\right)}{b n^{2} \Gamma\left(1 + \frac{1}{n}\right)} + \frac{c x \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{1}{n}\right) \Gamma\left(\frac{1}{n}\right)}{a n^{2} \Gamma\left(1 + \frac{1}{n}\right)}"," ",0,"-d*x*lerchphi(a*x**(-n)*exp_polar(I*pi)/b, 1, exp_polar(I*pi)/n)*gamma(1/n)/(b*n**2*gamma(1 + 1/n)) + c*x*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 1/n)*gamma(1/n)/(a*n**2*gamma(1 + 1/n))","C",0
302,0,0,0,0.000000," ","integrate(1/(a+b*x**n)/(c+d*x**n),x)","\int \frac{1}{\left(a + b x^{n}\right) \left(c + d x^{n}\right)}\, dx"," ",0,"Integral(1/((a + b*x**n)*(c + d*x**n)), x)","F",0
303,-2,0,0,0.000000," ","integrate(1/(a+b*x**n)/(c+d*x**n)**2,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
304,-2,0,0,0.000000," ","integrate(1/(a+b*x**n)/(c+d*x**n)**3,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
305,0,0,0,0.000000," ","integrate((c+d*x**n)**4/(a+b*x**n)**2,x)","\int \frac{\left(c + d x^{n}\right)^{4}}{\left(a + b x^{n}\right)^{2}}\, dx"," ",0,"Integral((c + d*x**n)**4/(a + b*x**n)**2, x)","F",0
306,0,0,0,0.000000," ","integrate((c+d*x**n)**3/(a+b*x**n)**2,x)","\int \frac{\left(c + d x^{n}\right)^{3}}{\left(a + b x^{n}\right)^{2}}\, dx"," ",0,"Integral((c + d*x**n)**3/(a + b*x**n)**2, x)","F",0
307,0,0,0,0.000000," ","integrate((c+d*x**n)**2/(a+b*x**n)**2,x)","\int \frac{\left(c + d x^{n}\right)^{2}}{\left(a + b x^{n}\right)^{2}}\, dx"," ",0,"Integral((c + d*x**n)**2/(a + b*x**n)**2, x)","F",0
308,1,592,0,8.769004," ","integrate((c+d*x**n)/(a+b*x**n)**2,x)","c \left(\frac{n x \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{1}{n}\right) \Gamma\left(\frac{1}{n}\right)}{a \left(a n^{3} \Gamma\left(1 + \frac{1}{n}\right) + b n^{3} x^{n} \Gamma\left(1 + \frac{1}{n}\right)\right)} + \frac{n x \Gamma\left(\frac{1}{n}\right)}{a \left(a n^{3} \Gamma\left(1 + \frac{1}{n}\right) + b n^{3} x^{n} \Gamma\left(1 + \frac{1}{n}\right)\right)} - \frac{x \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{1}{n}\right) \Gamma\left(\frac{1}{n}\right)}{a \left(a n^{3} \Gamma\left(1 + \frac{1}{n}\right) + b n^{3} x^{n} \Gamma\left(1 + \frac{1}{n}\right)\right)} + \frac{b n x x^{n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{1}{n}\right) \Gamma\left(\frac{1}{n}\right)}{a^{2} \left(a n^{3} \Gamma\left(1 + \frac{1}{n}\right) + b n^{3} x^{n} \Gamma\left(1 + \frac{1}{n}\right)\right)} - \frac{b x x^{n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{1}{n}\right) \Gamma\left(\frac{1}{n}\right)}{a^{2} \left(a n^{3} \Gamma\left(1 + \frac{1}{n}\right) + b n^{3} x^{n} \Gamma\left(1 + \frac{1}{n}\right)\right)}\right) + d \left(\frac{n^{2} x x^{n} \Gamma\left(1 + \frac{1}{n}\right)}{a \left(a n^{3} \Gamma\left(2 + \frac{1}{n}\right) + b n^{3} x^{n} \Gamma\left(2 + \frac{1}{n}\right)\right)} - \frac{n x x^{n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, 1 + \frac{1}{n}\right) \Gamma\left(1 + \frac{1}{n}\right)}{a \left(a n^{3} \Gamma\left(2 + \frac{1}{n}\right) + b n^{3} x^{n} \Gamma\left(2 + \frac{1}{n}\right)\right)} + \frac{n x x^{n} \Gamma\left(1 + \frac{1}{n}\right)}{a \left(a n^{3} \Gamma\left(2 + \frac{1}{n}\right) + b n^{3} x^{n} \Gamma\left(2 + \frac{1}{n}\right)\right)} - \frac{x x^{n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, 1 + \frac{1}{n}\right) \Gamma\left(1 + \frac{1}{n}\right)}{a \left(a n^{3} \Gamma\left(2 + \frac{1}{n}\right) + b n^{3} x^{n} \Gamma\left(2 + \frac{1}{n}\right)\right)} - \frac{b n x x^{2 n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, 1 + \frac{1}{n}\right) \Gamma\left(1 + \frac{1}{n}\right)}{a^{2} \left(a n^{3} \Gamma\left(2 + \frac{1}{n}\right) + b n^{3} x^{n} \Gamma\left(2 + \frac{1}{n}\right)\right)} - \frac{b x x^{2 n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, 1 + \frac{1}{n}\right) \Gamma\left(1 + \frac{1}{n}\right)}{a^{2} \left(a n^{3} \Gamma\left(2 + \frac{1}{n}\right) + b n^{3} x^{n} \Gamma\left(2 + \frac{1}{n}\right)\right)}\right)"," ",0,"c*(n*x*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 1/n)*gamma(1/n)/(a*(a*n**3*gamma(1 + 1/n) + b*n**3*x**n*gamma(1 + 1/n))) + n*x*gamma(1/n)/(a*(a*n**3*gamma(1 + 1/n) + b*n**3*x**n*gamma(1 + 1/n))) - x*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 1/n)*gamma(1/n)/(a*(a*n**3*gamma(1 + 1/n) + b*n**3*x**n*gamma(1 + 1/n))) + b*n*x*x**n*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 1/n)*gamma(1/n)/(a**2*(a*n**3*gamma(1 + 1/n) + b*n**3*x**n*gamma(1 + 1/n))) - b*x*x**n*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 1/n)*gamma(1/n)/(a**2*(a*n**3*gamma(1 + 1/n) + b*n**3*x**n*gamma(1 + 1/n)))) + d*(n**2*x*x**n*gamma(1 + 1/n)/(a*(a*n**3*gamma(2 + 1/n) + b*n**3*x**n*gamma(2 + 1/n))) - n*x*x**n*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 1 + 1/n)*gamma(1 + 1/n)/(a*(a*n**3*gamma(2 + 1/n) + b*n**3*x**n*gamma(2 + 1/n))) + n*x*x**n*gamma(1 + 1/n)/(a*(a*n**3*gamma(2 + 1/n) + b*n**3*x**n*gamma(2 + 1/n))) - x*x**n*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 1 + 1/n)*gamma(1 + 1/n)/(a*(a*n**3*gamma(2 + 1/n) + b*n**3*x**n*gamma(2 + 1/n))) - b*n*x*x**(2*n)*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 1 + 1/n)*gamma(1 + 1/n)/(a**2*(a*n**3*gamma(2 + 1/n) + b*n**3*x**n*gamma(2 + 1/n))) - b*x*x**(2*n)*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 1 + 1/n)*gamma(1 + 1/n)/(a**2*(a*n**3*gamma(2 + 1/n) + b*n**3*x**n*gamma(2 + 1/n))))","C",0
309,-2,0,0,0.000000," ","integrate(1/(a+b*x**n)**2/(c+d*x**n),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
310,-2,0,0,0.000000," ","integrate(1/(a+b*x**n)**2/(c+d*x**n)**2,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
311,0,0,0,0.000000," ","integrate(1/(a+b*x**n)**2/(c+d*x**n)**3,x)","\int \frac{1}{\left(a + b x^{n}\right)^{2} \left(c + d x^{n}\right)^{3}}\, dx"," ",0,"Integral(1/((a + b*x**n)**2*(c + d*x**n)**3), x)","F",0
312,-2,0,0,0.000000," ","integrate((a+b*x**n)**p*(c+d*x**n)**q,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
313,1,199,0,93.229067," ","integrate((a+b*x**n)**p*(c+d*x**n)**3,x)","\frac{a^{p} c^{3} x \Gamma\left(\frac{1}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{n}, - p \\ 1 + \frac{1}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{n \Gamma\left(1 + \frac{1}{n}\right)} + \frac{3 a^{p} c^{2} d x x^{n} \Gamma\left(1 + \frac{1}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} - p, 1 + \frac{1}{n} \\ 2 + \frac{1}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{n \Gamma\left(2 + \frac{1}{n}\right)} + \frac{3 a^{p} c d^{2} x x^{2 n} \Gamma\left(2 + \frac{1}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} - p, 2 + \frac{1}{n} \\ 3 + \frac{1}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{n \Gamma\left(3 + \frac{1}{n}\right)} + \frac{a^{p} d^{3} x x^{3 n} \Gamma\left(3 + \frac{1}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} - p, 3 + \frac{1}{n} \\ 4 + \frac{1}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{n \Gamma\left(4 + \frac{1}{n}\right)}"," ",0,"a**p*c**3*x*gamma(1/n)*hyper((1/n, -p), (1 + 1/n,), b*x**n*exp_polar(I*pi)/a)/(n*gamma(1 + 1/n)) + 3*a**p*c**2*d*x*x**n*gamma(1 + 1/n)*hyper((-p, 1 + 1/n), (2 + 1/n,), b*x**n*exp_polar(I*pi)/a)/(n*gamma(2 + 1/n)) + 3*a**p*c*d**2*x*x**(2*n)*gamma(2 + 1/n)*hyper((-p, 2 + 1/n), (3 + 1/n,), b*x**n*exp_polar(I*pi)/a)/(n*gamma(3 + 1/n)) + a**p*d**3*x*x**(3*n)*gamma(3 + 1/n)*hyper((-p, 3 + 1/n), (4 + 1/n,), b*x**n*exp_polar(I*pi)/a)/(n*gamma(4 + 1/n))","C",0
314,1,143,0,42.750598," ","integrate((a+b*x**n)**p*(c+d*x**n)**2,x)","\frac{a^{p} c^{2} x \Gamma\left(\frac{1}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{n}, - p \\ 1 + \frac{1}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{n \Gamma\left(1 + \frac{1}{n}\right)} + \frac{2 a^{p} c d x x^{n} \Gamma\left(1 + \frac{1}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} - p, 1 + \frac{1}{n} \\ 2 + \frac{1}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{n \Gamma\left(2 + \frac{1}{n}\right)} + \frac{a^{p} d^{2} x x^{2 n} \Gamma\left(2 + \frac{1}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} - p, 2 + \frac{1}{n} \\ 3 + \frac{1}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{n \Gamma\left(3 + \frac{1}{n}\right)}"," ",0,"a**p*c**2*x*gamma(1/n)*hyper((1/n, -p), (1 + 1/n,), b*x**n*exp_polar(I*pi)/a)/(n*gamma(1 + 1/n)) + 2*a**p*c*d*x*x**n*gamma(1 + 1/n)*hyper((-p, 1 + 1/n), (2 + 1/n,), b*x**n*exp_polar(I*pi)/a)/(n*gamma(2 + 1/n)) + a**p*d**2*x*x**(2*n)*gamma(2 + 1/n)*hyper((-p, 2 + 1/n), (3 + 1/n,), b*x**n*exp_polar(I*pi)/a)/(n*gamma(3 + 1/n))","C",0
315,1,87,0,6.154292," ","integrate((a+b*x**n)**p*(c+d*x**n),x)","\frac{a^{p} c x \Gamma\left(\frac{1}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{n}, - p \\ 1 + \frac{1}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{n \Gamma\left(1 + \frac{1}{n}\right)} + \frac{a^{p} d x x^{n} \Gamma\left(1 + \frac{1}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} - p, 1 + \frac{1}{n} \\ 2 + \frac{1}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{n \Gamma\left(2 + \frac{1}{n}\right)}"," ",0,"a**p*c*x*gamma(1/n)*hyper((1/n, -p), (1 + 1/n,), b*x**n*exp_polar(I*pi)/a)/(n*gamma(1 + 1/n)) + a**p*d*x*x**n*gamma(1 + 1/n)*hyper((-p, 1 + 1/n), (2 + 1/n,), b*x**n*exp_polar(I*pi)/a)/(n*gamma(2 + 1/n))","C",0
316,1,37,0,1.901955," ","integrate((a+b*x**n)**p,x)","\frac{a^{p} x \Gamma\left(\frac{1}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{n}, - p \\ 1 + \frac{1}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{n \Gamma\left(1 + \frac{1}{n}\right)}"," ",0,"a**p*x*gamma(1/n)*hyper((1/n, -p), (1 + 1/n,), b*x**n*exp_polar(I*pi)/a)/(n*gamma(1 + 1/n))","C",0
317,-2,0,0,0.000000," ","integrate((a+b*x**n)**p/(c+d*x**n),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
318,-2,0,0,0.000000," ","integrate((a+b*x**n)**p/(c+d*x**n)**2,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
319,0,0,0,0.000000," ","integrate((a+b*x**n)**p/(c+d*x**n)**3,x)","\int \frac{\left(a + b x^{n}\right)^{p}}{\left(c + d x^{n}\right)^{3}}\, dx"," ",0,"Integral((a + b*x**n)**p/(c + d*x**n)**3, x)","F",0
320,-1,0,0,0.000000," ","integrate((a+b*x**n)**p*(c+d*x**n)**(-1-1/n-p),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
321,-1,0,0,0.000000," ","integrate((a+b*x**n)**3*(c+d*x**n)**(-4-1/n),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
322,-1,0,0,0.000000," ","integrate((a+b*x**n)**2*(c+d*x**n)**(-3-1/n),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
323,-1,0,0,0.000000," ","integrate((a+b*x**n)*(c+d*x**n)**(-2-1/n),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
324,1,211,0,33.049042," ","integrate((c+d*x**n)**(-1-1/n),x)","\begin{cases} - \frac{d^{- \frac{1}{n}} x x^{- n} \left(x^{n}\right)^{- \frac{1}{n}}}{d n} & \text{for}\: c = 0 \\0^{-1 - \frac{1}{n}} x & \text{for}\: c = - d x^{n} \\x \left(0^{n}\right)^{-1 - \frac{1}{n}} & \text{for}\: c = 0^{n} - d x^{n} \\\frac{c^{2} x}{c^{3} \left(c + d x^{n}\right)^{\frac{1}{n}} + 2 c^{2} d x^{n} \left(c + d x^{n}\right)^{\frac{1}{n}} + c d^{2} x^{2 n} \left(c + d x^{n}\right)^{\frac{1}{n}}} + \frac{c d x x^{n}}{c^{3} \left(c + d x^{n}\right)^{\frac{1}{n}} + 2 c^{2} d x^{n} \left(c + d x^{n}\right)^{\frac{1}{n}} + c d^{2} x^{2 n} \left(c + d x^{n}\right)^{\frac{1}{n}}} + \frac{d x x^{n}}{c^{2} \left(c + d x^{n}\right)^{\frac{1}{n}} + c d x^{n} \left(c + d x^{n}\right)^{\frac{1}{n}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-d**(-1/n)*x*x**(-n)*(x**n)**(-1/n)/(d*n), Eq(c, 0)), (0**(-1 - 1/n)*x, Eq(c, -d*x**n)), (x*(0**n)**(-1 - 1/n), Eq(c, 0**n - d*x**n)), (c**2*x/(c**3*(c + d*x**n)**(1/n) + 2*c**2*d*x**n*(c + d*x**n)**(1/n) + c*d**2*x**(2*n)*(c + d*x**n)**(1/n)) + c*d*x*x**n/(c**3*(c + d*x**n)**(1/n) + 2*c**2*d*x**n*(c + d*x**n)**(1/n) + c*d**2*x**(2*n)*(c + d*x**n)**(1/n)) + d*x*x**n/(c**2*(c + d*x**n)**(1/n) + c*d*x**n*(c + d*x**n)**(1/n)), True))","A",0
325,-2,0,0,0.000000," ","integrate(1/(a+b*x**n)/((c+d*x**n)**(1/n)),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
326,-2,0,0,0.000000," ","integrate((c+d*x**n)**(1-1/n)/(a+b*x**n)**2,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
327,-2,0,0,0.000000," ","integrate((c+d*x**n)**(2-1/n)/(a+b*x**n)**3,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
328,-1,0,0,0.000000," ","integrate((a+b*x**n)**p*(c+d*x**n)**(-2-1/n-p),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
329,-1,0,0,0.000000," ","integrate((a+b*x**n)**((a*d*n-b*c*(1+n))/(-a*d+b*c)/n)*(c+d*x**n)**((a*d*n-b*c*n+a*d)/(-a*d*n+b*c*n)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
330,-1,0,0,0.000000," ","integrate((a+b*x**n)**2*(c+d*x**n)**(-4-1/n),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
331,-1,0,0,0.000000," ","integrate((a+b*x**n)*(c+d*x**n)**(-3-1/n),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
332,-1,0,0,0.000000," ","integrate((c+d*x**n)**(-2-1/n),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
333,-2,0,0,0.000000," ","integrate((c+d*x**n)**(-1-1/n)/(a+b*x**n),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
334,-2,0,0,0.000000," ","integrate(1/(a+b*x**n)**2/((c+d*x**n)**(1/n)),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
335,-1,0,0,0.000000," ","integrate((c+d*x**n)**(1-1/n)/(a+b*x**n)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
336,-2,0,0,0.000000," ","integrate((c+d*x**n)**(2-1/n)/(a+b*x**n)**4,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
337,0,0,0,0.000000," ","integrate(x**5*(b*x**2+a)*(d*x-c)**(1/2)*(d*x+c)**(1/2),x)","\int x^{5} \left(a + b x^{2}\right) \sqrt{- c + d x} \sqrt{c + d x}\, dx"," ",0,"Integral(x**5*(a + b*x**2)*sqrt(-c + d*x)*sqrt(c + d*x), x)","F",0
338,0,0,0,0.000000," ","integrate(x**3*(b*x**2+a)*(d*x-c)**(1/2)*(d*x+c)**(1/2),x)","\int x^{3} \left(a + b x^{2}\right) \sqrt{- c + d x} \sqrt{c + d x}\, dx"," ",0,"Integral(x**3*(a + b*x**2)*sqrt(-c + d*x)*sqrt(c + d*x), x)","F",0
339,0,0,0,0.000000," ","integrate(x*(b*x**2+a)*(d*x-c)**(1/2)*(d*x+c)**(1/2),x)","\int x \left(a + b x^{2}\right) \sqrt{- c + d x} \sqrt{c + d x}\, dx"," ",0,"Integral(x*(a + b*x**2)*sqrt(-c + d*x)*sqrt(c + d*x), x)","F",0
340,0,0,0,0.000000," ","integrate((b*x**2+a)*(d*x-c)**(1/2)*(d*x+c)**(1/2)/x,x)","\int \frac{\left(a + b x^{2}\right) \sqrt{- c + d x} \sqrt{c + d x}}{x}\, dx"," ",0,"Integral((a + b*x**2)*sqrt(-c + d*x)*sqrt(c + d*x)/x, x)","F",0
341,0,0,0,0.000000," ","integrate((b*x**2+a)*(d*x-c)**(1/2)*(d*x+c)**(1/2)/x**3,x)","\int \frac{\left(a + b x^{2}\right) \sqrt{- c + d x} \sqrt{c + d x}}{x^{3}}\, dx"," ",0,"Integral((a + b*x**2)*sqrt(-c + d*x)*sqrt(c + d*x)/x**3, x)","F",0
342,-1,0,0,0.000000," ","integrate((b*x**2+a)*(d*x-c)**(1/2)*(d*x+c)**(1/2)/x**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
343,0,0,0,0.000000," ","integrate(x**4*(b*x**2+a)*(d*x-c)**(1/2)*(d*x+c)**(1/2),x)","\int x^{4} \left(a + b x^{2}\right) \sqrt{- c + d x} \sqrt{c + d x}\, dx"," ",0,"Integral(x**4*(a + b*x**2)*sqrt(-c + d*x)*sqrt(c + d*x), x)","F",0
344,0,0,0,0.000000," ","integrate(x**2*(b*x**2+a)*(d*x-c)**(1/2)*(d*x+c)**(1/2),x)","\int x^{2} \left(a + b x^{2}\right) \sqrt{- c + d x} \sqrt{c + d x}\, dx"," ",0,"Integral(x**2*(a + b*x**2)*sqrt(-c + d*x)*sqrt(c + d*x), x)","F",0
345,0,0,0,0.000000," ","integrate((b*x**2+a)*(d*x-c)**(1/2)*(d*x+c)**(1/2),x)","\int \left(a + b x^{2}\right) \sqrt{- c + d x} \sqrt{c + d x}\, dx"," ",0,"Integral((a + b*x**2)*sqrt(-c + d*x)*sqrt(c + d*x), x)","F",0
346,0,0,0,0.000000," ","integrate((b*x**2+a)*(d*x-c)**(1/2)*(d*x+c)**(1/2)/x**2,x)","\int \frac{\left(a + b x^{2}\right) \sqrt{- c + d x} \sqrt{c + d x}}{x^{2}}\, dx"," ",0,"Integral((a + b*x**2)*sqrt(-c + d*x)*sqrt(c + d*x)/x**2, x)","F",0
347,-1,0,0,0.000000," ","integrate((b*x**2+a)*(d*x-c)**(1/2)*(d*x+c)**(1/2)/x**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
348,-1,0,0,0.000000," ","integrate(x**4*(b*x**2+a)/(c*x-1)**(1/2)/(c*x+1)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
349,1,216,0,62.838553," ","integrate(x**3*(b*x**2+a)/(c*x-1)**(1/2)/(c*x+1)**(1/2),x)","\frac{a {G_{6, 6}^{6, 2}\left(\begin{matrix} - \frac{5}{4}, - \frac{3}{4} & -1, -1, - \frac{1}{2}, 1 \\- \frac{3}{2}, - \frac{5}{4}, -1, - \frac{3}{4}, - \frac{1}{2}, 0 &  \end{matrix} \middle| {\frac{1}{c^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} c^{4}} + \frac{i a {G_{6, 6}^{2, 6}\left(\begin{matrix} -2, - \frac{7}{4}, - \frac{3}{2}, - \frac{5}{4}, -1, 1 &  \\- \frac{7}{4}, - \frac{5}{4} & -2, - \frac{3}{2}, - \frac{3}{2}, 0 \end{matrix} \middle| {\frac{e^{2 i \pi}}{c^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} c^{4}} + \frac{b {G_{6, 6}^{6, 2}\left(\begin{matrix} - \frac{9}{4}, - \frac{7}{4} & -2, -2, - \frac{3}{2}, 1 \\- \frac{5}{2}, - \frac{9}{4}, -2, - \frac{7}{4}, - \frac{3}{2}, 0 &  \end{matrix} \middle| {\frac{1}{c^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} c^{6}} + \frac{i b {G_{6, 6}^{2, 6}\left(\begin{matrix} -3, - \frac{11}{4}, - \frac{5}{2}, - \frac{9}{4}, -2, 1 &  \\- \frac{11}{4}, - \frac{9}{4} & -3, - \frac{5}{2}, - \frac{5}{2}, 0 \end{matrix} \middle| {\frac{e^{2 i \pi}}{c^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} c^{6}}"," ",0,"a*meijerg(((-5/4, -3/4), (-1, -1, -1/2, 1)), ((-3/2, -5/4, -1, -3/4, -1/2, 0), ()), 1/(c**2*x**2))/(4*pi**(3/2)*c**4) + I*a*meijerg(((-2, -7/4, -3/2, -5/4, -1, 1), ()), ((-7/4, -5/4), (-2, -3/2, -3/2, 0)), exp_polar(2*I*pi)/(c**2*x**2))/(4*pi**(3/2)*c**4) + b*meijerg(((-9/4, -7/4), (-2, -2, -3/2, 1)), ((-5/2, -9/4, -2, -7/4, -3/2, 0), ()), 1/(c**2*x**2))/(4*pi**(3/2)*c**6) + I*b*meijerg(((-3, -11/4, -5/2, -9/4, -2, 1), ()), ((-11/4, -9/4), (-3, -5/2, -5/2, 0)), exp_polar(2*I*pi)/(c**2*x**2))/(4*pi**(3/2)*c**6)","C",0
350,-1,0,0,0.000000," ","integrate(x**2*(b*x**2+a)/(c*x-1)**(1/2)/(c*x+1)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
351,1,202,0,41.910120," ","integrate(x*(b*x**2+a)/(c*x-1)**(1/2)/(c*x+1)**(1/2),x)","\frac{a {G_{6, 6}^{6, 2}\left(\begin{matrix} - \frac{1}{4}, \frac{1}{4} & 0, 0, \frac{1}{2}, 1 \\- \frac{1}{2}, - \frac{1}{4}, 0, \frac{1}{4}, \frac{1}{2}, 0 &  \end{matrix} \middle| {\frac{1}{c^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} c^{2}} + \frac{i a {G_{6, 6}^{2, 6}\left(\begin{matrix} -1, - \frac{3}{4}, - \frac{1}{2}, - \frac{1}{4}, 0, 1 &  \\- \frac{3}{4}, - \frac{1}{4} & -1, - \frac{1}{2}, - \frac{1}{2}, 0 \end{matrix} \middle| {\frac{e^{2 i \pi}}{c^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} c^{2}} + \frac{b {G_{6, 6}^{6, 2}\left(\begin{matrix} - \frac{5}{4}, - \frac{3}{4} & -1, -1, - \frac{1}{2}, 1 \\- \frac{3}{2}, - \frac{5}{4}, -1, - \frac{3}{4}, - \frac{1}{2}, 0 &  \end{matrix} \middle| {\frac{1}{c^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} c^{4}} + \frac{i b {G_{6, 6}^{2, 6}\left(\begin{matrix} -2, - \frac{7}{4}, - \frac{3}{2}, - \frac{5}{4}, -1, 1 &  \\- \frac{7}{4}, - \frac{5}{4} & -2, - \frac{3}{2}, - \frac{3}{2}, 0 \end{matrix} \middle| {\frac{e^{2 i \pi}}{c^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} c^{4}}"," ",0,"a*meijerg(((-1/4, 1/4), (0, 0, 1/2, 1)), ((-1/2, -1/4, 0, 1/4, 1/2, 0), ()), 1/(c**2*x**2))/(4*pi**(3/2)*c**2) + I*a*meijerg(((-1, -3/4, -1/2, -1/4, 0, 1), ()), ((-3/4, -1/4), (-1, -1/2, -1/2, 0)), exp_polar(2*I*pi)/(c**2*x**2))/(4*pi**(3/2)*c**2) + b*meijerg(((-5/4, -3/4), (-1, -1, -1/2, 1)), ((-3/2, -5/4, -1, -3/4, -1/2, 0), ()), 1/(c**2*x**2))/(4*pi**(3/2)*c**4) + I*b*meijerg(((-2, -7/4, -3/2, -5/4, -1, 1), ()), ((-7/4, -5/4), (-2, -3/2, -3/2, 0)), exp_polar(2*I*pi)/(c**2*x**2))/(4*pi**(3/2)*c**4)","C",0
352,1,182,0,45.512115," ","integrate((b*x**2+a)/(c*x-1)**(1/2)/(c*x+1)**(1/2),x)","\frac{a {G_{6, 6}^{6, 2}\left(\begin{matrix} \frac{1}{4}, \frac{3}{4} & \frac{1}{2}, \frac{1}{2}, 1, 1 \\0, \frac{1}{4}, \frac{1}{2}, \frac{3}{4}, 1, 0 &  \end{matrix} \middle| {\frac{1}{c^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} c} - \frac{i a {G_{6, 6}^{2, 6}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4}, 0, \frac{1}{4}, \frac{1}{2}, 1 &  \\- \frac{1}{4}, \frac{1}{4} & - \frac{1}{2}, 0, 0, 0 \end{matrix} \middle| {\frac{e^{2 i \pi}}{c^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} c} + \frac{b {G_{6, 6}^{6, 2}\left(\begin{matrix} - \frac{3}{4}, - \frac{1}{4} & - \frac{1}{2}, - \frac{1}{2}, 0, 1 \\-1, - \frac{3}{4}, - \frac{1}{2}, - \frac{1}{4}, 0, 0 &  \end{matrix} \middle| {\frac{1}{c^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} c^{3}} - \frac{i b {G_{6, 6}^{2, 6}\left(\begin{matrix} - \frac{3}{2}, - \frac{5}{4}, -1, - \frac{3}{4}, - \frac{1}{2}, 1 &  \\- \frac{5}{4}, - \frac{3}{4} & - \frac{3}{2}, -1, -1, 0 \end{matrix} \middle| {\frac{e^{2 i \pi}}{c^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} c^{3}}"," ",0,"a*meijerg(((1/4, 3/4), (1/2, 1/2, 1, 1)), ((0, 1/4, 1/2, 3/4, 1, 0), ()), 1/(c**2*x**2))/(4*pi**(3/2)*c) - I*a*meijerg(((-1/2, -1/4, 0, 1/4, 1/2, 1), ()), ((-1/4, 1/4), (-1/2, 0, 0, 0)), exp_polar(2*I*pi)/(c**2*x**2))/(4*pi**(3/2)*c) + b*meijerg(((-3/4, -1/4), (-1/2, -1/2, 0, 1)), ((-1, -3/4, -1/2, -1/4, 0, 0), ()), 1/(c**2*x**2))/(4*pi**(3/2)*c**3) - I*b*meijerg(((-3/2, -5/4, -1, -3/4, -1/2, 1), ()), ((-5/4, -3/4), (-3/2, -1, -1, 0)), exp_polar(2*I*pi)/(c**2*x**2))/(4*pi**(3/2)*c**3)","C",0
353,1,162,0,40.135095," ","integrate((b*x**2+a)/x/(c*x-1)**(1/2)/(c*x+1)**(1/2),x)","- \frac{a {G_{6, 6}^{5, 3}\left(\begin{matrix} \frac{3}{4}, \frac{5}{4}, 1 & 1, 1, \frac{3}{2} \\\frac{1}{2}, \frac{3}{4}, 1, \frac{5}{4}, \frac{3}{2} & 0 \end{matrix} \middle| {\frac{1}{c^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}}} + \frac{i a {G_{6, 6}^{2, 6}\left(\begin{matrix} 0, \frac{1}{4}, \frac{1}{2}, \frac{3}{4}, 1, 1 &  \\\frac{1}{4}, \frac{3}{4} & 0, \frac{1}{2}, \frac{1}{2}, 0 \end{matrix} \middle| {\frac{e^{2 i \pi}}{c^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}}} + \frac{b {G_{6, 6}^{6, 2}\left(\begin{matrix} - \frac{1}{4}, \frac{1}{4} & 0, 0, \frac{1}{2}, 1 \\- \frac{1}{2}, - \frac{1}{4}, 0, \frac{1}{4}, \frac{1}{2}, 0 &  \end{matrix} \middle| {\frac{1}{c^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} c^{2}} + \frac{i b {G_{6, 6}^{2, 6}\left(\begin{matrix} -1, - \frac{3}{4}, - \frac{1}{2}, - \frac{1}{4}, 0, 1 &  \\- \frac{3}{4}, - \frac{1}{4} & -1, - \frac{1}{2}, - \frac{1}{2}, 0 \end{matrix} \middle| {\frac{e^{2 i \pi}}{c^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} c^{2}}"," ",0,"-a*meijerg(((3/4, 5/4, 1), (1, 1, 3/2)), ((1/2, 3/4, 1, 5/4, 3/2), (0,)), 1/(c**2*x**2))/(4*pi**(3/2)) + I*a*meijerg(((0, 1/4, 1/2, 3/4, 1, 1), ()), ((1/4, 3/4), (0, 1/2, 1/2, 0)), exp_polar(2*I*pi)/(c**2*x**2))/(4*pi**(3/2)) + b*meijerg(((-1/4, 1/4), (0, 0, 1/2, 1)), ((-1/2, -1/4, 0, 1/4, 1/2, 0), ()), 1/(c**2*x**2))/(4*pi**(3/2)*c**2) + I*b*meijerg(((-1, -3/4, -1/2, -1/4, 0, 1), ()), ((-3/4, -1/4), (-1, -1/2, -1/2, 0)), exp_polar(2*I*pi)/(c**2*x**2))/(4*pi**(3/2)*c**2)","C",0
354,1,148,0,35.168501," ","integrate((b*x**2+a)/x**2/(c*x-1)**(1/2)/(c*x+1)**(1/2),x)","- \frac{a c {G_{6, 6}^{5, 3}\left(\begin{matrix} \frac{5}{4}, \frac{7}{4}, 1 & \frac{3}{2}, \frac{3}{2}, 2 \\1, \frac{5}{4}, \frac{3}{2}, \frac{7}{4}, 2 & 0 \end{matrix} \middle| {\frac{1}{c^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}}} - \frac{i a c {G_{6, 6}^{2, 6}\left(\begin{matrix} \frac{1}{2}, \frac{3}{4}, 1, \frac{5}{4}, \frac{3}{2}, 1 &  \\\frac{3}{4}, \frac{5}{4} & \frac{1}{2}, 1, 1, 0 \end{matrix} \middle| {\frac{e^{2 i \pi}}{c^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}}} + \frac{b {G_{6, 6}^{6, 2}\left(\begin{matrix} \frac{1}{4}, \frac{3}{4} & \frac{1}{2}, \frac{1}{2}, 1, 1 \\0, \frac{1}{4}, \frac{1}{2}, \frac{3}{4}, 1, 0 &  \end{matrix} \middle| {\frac{1}{c^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} c} - \frac{i b {G_{6, 6}^{2, 6}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4}, 0, \frac{1}{4}, \frac{1}{2}, 1 &  \\- \frac{1}{4}, \frac{1}{4} & - \frac{1}{2}, 0, 0, 0 \end{matrix} \middle| {\frac{e^{2 i \pi}}{c^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} c}"," ",0,"-a*c*meijerg(((5/4, 7/4, 1), (3/2, 3/2, 2)), ((1, 5/4, 3/2, 7/4, 2), (0,)), 1/(c**2*x**2))/(4*pi**(3/2)) - I*a*c*meijerg(((1/2, 3/4, 1, 5/4, 3/2, 1), ()), ((3/4, 5/4), (1/2, 1, 1, 0)), exp_polar(2*I*pi)/(c**2*x**2))/(4*pi**(3/2)) + b*meijerg(((1/4, 3/4), (1/2, 1/2, 1, 1)), ((0, 1/4, 1/2, 3/4, 1, 0), ()), 1/(c**2*x**2))/(4*pi**(3/2)*c) - I*b*meijerg(((-1/2, -1/4, 0, 1/4, 1/2, 1), ()), ((-1/4, 1/4), (-1/2, 0, 0, 0)), exp_polar(2*I*pi)/(c**2*x**2))/(4*pi**(3/2)*c)","C",0
355,1,141,0,63.617766," ","integrate((b*x**2+a)/x**3/(c*x-1)**(1/2)/(c*x+1)**(1/2),x)","- \frac{a c^{2} {G_{6, 6}^{5, 3}\left(\begin{matrix} \frac{7}{4}, \frac{9}{4}, 1 & 2, 2, \frac{5}{2} \\\frac{3}{2}, \frac{7}{4}, 2, \frac{9}{4}, \frac{5}{2} & 0 \end{matrix} \middle| {\frac{1}{c^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}}} + \frac{i a c^{2} {G_{6, 6}^{2, 6}\left(\begin{matrix} 1, \frac{5}{4}, \frac{3}{2}, \frac{7}{4}, 2, 1 &  \\\frac{5}{4}, \frac{7}{4} & 1, \frac{3}{2}, \frac{3}{2}, 0 \end{matrix} \middle| {\frac{e^{2 i \pi}}{c^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}}} - \frac{b {G_{6, 6}^{5, 3}\left(\begin{matrix} \frac{3}{4}, \frac{5}{4}, 1 & 1, 1, \frac{3}{2} \\\frac{1}{2}, \frac{3}{4}, 1, \frac{5}{4}, \frac{3}{2} & 0 \end{matrix} \middle| {\frac{1}{c^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}}} + \frac{i b {G_{6, 6}^{2, 6}\left(\begin{matrix} 0, \frac{1}{4}, \frac{1}{2}, \frac{3}{4}, 1, 1 &  \\\frac{1}{4}, \frac{3}{4} & 0, \frac{1}{2}, \frac{1}{2}, 0 \end{matrix} \middle| {\frac{e^{2 i \pi}}{c^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}}}"," ",0,"-a*c**2*meijerg(((7/4, 9/4, 1), (2, 2, 5/2)), ((3/2, 7/4, 2, 9/4, 5/2), (0,)), 1/(c**2*x**2))/(4*pi**(3/2)) + I*a*c**2*meijerg(((1, 5/4, 3/2, 7/4, 2, 1), ()), ((5/4, 7/4), (1, 3/2, 3/2, 0)), exp_polar(2*I*pi)/(c**2*x**2))/(4*pi**(3/2)) - b*meijerg(((3/4, 5/4, 1), (1, 1, 3/2)), ((1/2, 3/4, 1, 5/4, 3/2), (0,)), 1/(c**2*x**2))/(4*pi**(3/2)) + I*b*meijerg(((0, 1/4, 1/2, 3/4, 1, 1), ()), ((1/4, 3/4), (0, 1/2, 1/2, 0)), exp_polar(2*I*pi)/(c**2*x**2))/(4*pi**(3/2))","C",0
356,1,146,0,61.444454," ","integrate((b*x**2+a)/x**4/(c*x-1)**(1/2)/(c*x+1)**(1/2),x)","- \frac{a c^{3} {G_{6, 6}^{5, 3}\left(\begin{matrix} \frac{9}{4}, \frac{11}{4}, 1 & \frac{5}{2}, \frac{5}{2}, 3 \\2, \frac{9}{4}, \frac{5}{2}, \frac{11}{4}, 3 & 0 \end{matrix} \middle| {\frac{1}{c^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}}} - \frac{i a c^{3} {G_{6, 6}^{2, 6}\left(\begin{matrix} \frac{3}{2}, \frac{7}{4}, 2, \frac{9}{4}, \frac{5}{2}, 1 &  \\\frac{7}{4}, \frac{9}{4} & \frac{3}{2}, 2, 2, 0 \end{matrix} \middle| {\frac{e^{2 i \pi}}{c^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}}} - \frac{b c {G_{6, 6}^{5, 3}\left(\begin{matrix} \frac{5}{4}, \frac{7}{4}, 1 & \frac{3}{2}, \frac{3}{2}, 2 \\1, \frac{5}{4}, \frac{3}{2}, \frac{7}{4}, 2 & 0 \end{matrix} \middle| {\frac{1}{c^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}}} - \frac{i b c {G_{6, 6}^{2, 6}\left(\begin{matrix} \frac{1}{2}, \frac{3}{4}, 1, \frac{5}{4}, \frac{3}{2}, 1 &  \\\frac{3}{4}, \frac{5}{4} & \frac{1}{2}, 1, 1, 0 \end{matrix} \middle| {\frac{e^{2 i \pi}}{c^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}}}"," ",0,"-a*c**3*meijerg(((9/4, 11/4, 1), (5/2, 5/2, 3)), ((2, 9/4, 5/2, 11/4, 3), (0,)), 1/(c**2*x**2))/(4*pi**(3/2)) - I*a*c**3*meijerg(((3/2, 7/4, 2, 9/4, 5/2, 1), ()), ((7/4, 9/4), (3/2, 2, 2, 0)), exp_polar(2*I*pi)/(c**2*x**2))/(4*pi**(3/2)) - b*c*meijerg(((5/4, 7/4, 1), (3/2, 3/2, 2)), ((1, 5/4, 3/2, 7/4, 2), (0,)), 1/(c**2*x**2))/(4*pi**(3/2)) - I*b*c*meijerg(((1/2, 3/4, 1, 5/4, 3/2, 1), ()), ((3/4, 5/4), (1/2, 1, 1, 0)), exp_polar(2*I*pi)/(c**2*x**2))/(4*pi**(3/2))","C",0
357,-1,0,0,0.000000," ","integrate((b*x**2+a)/x**5/(c*x-1)**(1/2)/(c*x+1)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
358,-1,0,0,0.000000," ","integrate(x**4*(b*x**2+a)/(d*x-c)**(1/2)/(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
359,1,240,0,70.842774," ","integrate(x**3*(b*x**2+a)/(d*x-c)**(1/2)/(d*x+c)**(1/2),x)","\frac{a c^{3} {G_{6, 6}^{6, 2}\left(\begin{matrix} - \frac{5}{4}, - \frac{3}{4} & -1, -1, - \frac{1}{2}, 1 \\- \frac{3}{2}, - \frac{5}{4}, -1, - \frac{3}{4}, - \frac{1}{2}, 0 &  \end{matrix} \middle| {\frac{c^{2}}{d^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} d^{4}} + \frac{i a c^{3} {G_{6, 6}^{2, 6}\left(\begin{matrix} -2, - \frac{7}{4}, - \frac{3}{2}, - \frac{5}{4}, -1, 1 &  \\- \frac{7}{4}, - \frac{5}{4} & -2, - \frac{3}{2}, - \frac{3}{2}, 0 \end{matrix} \middle| {\frac{c^{2} e^{2 i \pi}}{d^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} d^{4}} + \frac{b c^{5} {G_{6, 6}^{6, 2}\left(\begin{matrix} - \frac{9}{4}, - \frac{7}{4} & -2, -2, - \frac{3}{2}, 1 \\- \frac{5}{2}, - \frac{9}{4}, -2, - \frac{7}{4}, - \frac{3}{2}, 0 &  \end{matrix} \middle| {\frac{c^{2}}{d^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} d^{6}} + \frac{i b c^{5} {G_{6, 6}^{2, 6}\left(\begin{matrix} -3, - \frac{11}{4}, - \frac{5}{2}, - \frac{9}{4}, -2, 1 &  \\- \frac{11}{4}, - \frac{9}{4} & -3, - \frac{5}{2}, - \frac{5}{2}, 0 \end{matrix} \middle| {\frac{c^{2} e^{2 i \pi}}{d^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} d^{6}}"," ",0,"a*c**3*meijerg(((-5/4, -3/4), (-1, -1, -1/2, 1)), ((-3/2, -5/4, -1, -3/4, -1/2, 0), ()), c**2/(d**2*x**2))/(4*pi**(3/2)*d**4) + I*a*c**3*meijerg(((-2, -7/4, -3/2, -5/4, -1, 1), ()), ((-7/4, -5/4), (-2, -3/2, -3/2, 0)), c**2*exp_polar(2*I*pi)/(d**2*x**2))/(4*pi**(3/2)*d**4) + b*c**5*meijerg(((-9/4, -7/4), (-2, -2, -3/2, 1)), ((-5/2, -9/4, -2, -7/4, -3/2, 0), ()), c**2/(d**2*x**2))/(4*pi**(3/2)*d**6) + I*b*c**5*meijerg(((-3, -11/4, -5/2, -9/4, -2, 1), ()), ((-11/4, -9/4), (-3, -5/2, -5/2, 0)), c**2*exp_polar(2*I*pi)/(d**2*x**2))/(4*pi**(3/2)*d**6)","C",0
360,-1,0,0,0.000000," ","integrate(x**2*(b*x**2+a)/(d*x-c)**(1/2)/(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
361,1,223,0,44.702087," ","integrate(x*(b*x**2+a)/(d*x-c)**(1/2)/(d*x+c)**(1/2),x)","\frac{a c {G_{6, 6}^{6, 2}\left(\begin{matrix} - \frac{1}{4}, \frac{1}{4} & 0, 0, \frac{1}{2}, 1 \\- \frac{1}{2}, - \frac{1}{4}, 0, \frac{1}{4}, \frac{1}{2}, 0 &  \end{matrix} \middle| {\frac{c^{2}}{d^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} d^{2}} + \frac{i a c {G_{6, 6}^{2, 6}\left(\begin{matrix} -1, - \frac{3}{4}, - \frac{1}{2}, - \frac{1}{4}, 0, 1 &  \\- \frac{3}{4}, - \frac{1}{4} & -1, - \frac{1}{2}, - \frac{1}{2}, 0 \end{matrix} \middle| {\frac{c^{2} e^{2 i \pi}}{d^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} d^{2}} + \frac{b c^{3} {G_{6, 6}^{6, 2}\left(\begin{matrix} - \frac{5}{4}, - \frac{3}{4} & -1, -1, - \frac{1}{2}, 1 \\- \frac{3}{2}, - \frac{5}{4}, -1, - \frac{3}{4}, - \frac{1}{2}, 0 &  \end{matrix} \middle| {\frac{c^{2}}{d^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} d^{4}} + \frac{i b c^{3} {G_{6, 6}^{2, 6}\left(\begin{matrix} -2, - \frac{7}{4}, - \frac{3}{2}, - \frac{5}{4}, -1, 1 &  \\- \frac{7}{4}, - \frac{5}{4} & -2, - \frac{3}{2}, - \frac{3}{2}, 0 \end{matrix} \middle| {\frac{c^{2} e^{2 i \pi}}{d^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} d^{4}}"," ",0,"a*c*meijerg(((-1/4, 1/4), (0, 0, 1/2, 1)), ((-1/2, -1/4, 0, 1/4, 1/2, 0), ()), c**2/(d**2*x**2))/(4*pi**(3/2)*d**2) + I*a*c*meijerg(((-1, -3/4, -1/2, -1/4, 0, 1), ()), ((-3/4, -1/4), (-1, -1/2, -1/2, 0)), c**2*exp_polar(2*I*pi)/(d**2*x**2))/(4*pi**(3/2)*d**2) + b*c**3*meijerg(((-5/4, -3/4), (-1, -1, -1/2, 1)), ((-3/2, -5/4, -1, -3/4, -1/2, 0), ()), c**2/(d**2*x**2))/(4*pi**(3/2)*d**4) + I*b*c**3*meijerg(((-2, -7/4, -3/2, -5/4, -1, 1), ()), ((-7/4, -5/4), (-2, -3/2, -3/2, 0)), c**2*exp_polar(2*I*pi)/(d**2*x**2))/(4*pi**(3/2)*d**4)","C",0
362,1,199,0,41.776490," ","integrate((b*x**2+a)/(d*x-c)**(1/2)/(d*x+c)**(1/2),x)","\frac{a {G_{6, 6}^{6, 2}\left(\begin{matrix} \frac{1}{4}, \frac{3}{4} & \frac{1}{2}, \frac{1}{2}, 1, 1 \\0, \frac{1}{4}, \frac{1}{2}, \frac{3}{4}, 1, 0 &  \end{matrix} \middle| {\frac{c^{2}}{d^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} d} - \frac{i a {G_{6, 6}^{2, 6}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4}, 0, \frac{1}{4}, \frac{1}{2}, 1 &  \\- \frac{1}{4}, \frac{1}{4} & - \frac{1}{2}, 0, 0, 0 \end{matrix} \middle| {\frac{c^{2} e^{2 i \pi}}{d^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} d} + \frac{b c^{2} {G_{6, 6}^{6, 2}\left(\begin{matrix} - \frac{3}{4}, - \frac{1}{4} & - \frac{1}{2}, - \frac{1}{2}, 0, 1 \\-1, - \frac{3}{4}, - \frac{1}{2}, - \frac{1}{4}, 0, 0 &  \end{matrix} \middle| {\frac{c^{2}}{d^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} d^{3}} - \frac{i b c^{2} {G_{6, 6}^{2, 6}\left(\begin{matrix} - \frac{3}{2}, - \frac{5}{4}, -1, - \frac{3}{4}, - \frac{1}{2}, 1 &  \\- \frac{5}{4}, - \frac{3}{4} & - \frac{3}{2}, -1, -1, 0 \end{matrix} \middle| {\frac{c^{2} e^{2 i \pi}}{d^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} d^{3}}"," ",0,"a*meijerg(((1/4, 3/4), (1/2, 1/2, 1, 1)), ((0, 1/4, 1/2, 3/4, 1, 0), ()), c**2/(d**2*x**2))/(4*pi**(3/2)*d) - I*a*meijerg(((-1/2, -1/4, 0, 1/4, 1/2, 1), ()), ((-1/4, 1/4), (-1/2, 0, 0, 0)), c**2*exp_polar(2*I*pi)/(d**2*x**2))/(4*pi**(3/2)*d) + b*c**2*meijerg(((-3/4, -1/4), (-1/2, -1/2, 0, 1)), ((-1, -3/4, -1/2, -1/4, 0, 0), ()), c**2/(d**2*x**2))/(4*pi**(3/2)*d**3) - I*b*c**2*meijerg(((-3/2, -5/4, -1, -3/4, -1/2, 1), ()), ((-5/4, -3/4), (-3/2, -1, -1, 0)), c**2*exp_polar(2*I*pi)/(d**2*x**2))/(4*pi**(3/2)*d**3)","C",0
363,1,178,0,39.158079," ","integrate((b*x**2+a)/x/(d*x-c)**(1/2)/(d*x+c)**(1/2),x)","- \frac{a {G_{6, 6}^{5, 3}\left(\begin{matrix} \frac{3}{4}, \frac{5}{4}, 1 & 1, 1, \frac{3}{2} \\\frac{1}{2}, \frac{3}{4}, 1, \frac{5}{4}, \frac{3}{2} & 0 \end{matrix} \middle| {\frac{c^{2}}{d^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} c} + \frac{i a {G_{6, 6}^{2, 6}\left(\begin{matrix} 0, \frac{1}{4}, \frac{1}{2}, \frac{3}{4}, 1, 1 &  \\\frac{1}{4}, \frac{3}{4} & 0, \frac{1}{2}, \frac{1}{2}, 0 \end{matrix} \middle| {\frac{c^{2} e^{2 i \pi}}{d^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} c} + \frac{b c {G_{6, 6}^{6, 2}\left(\begin{matrix} - \frac{1}{4}, \frac{1}{4} & 0, 0, \frac{1}{2}, 1 \\- \frac{1}{2}, - \frac{1}{4}, 0, \frac{1}{4}, \frac{1}{2}, 0 &  \end{matrix} \middle| {\frac{c^{2}}{d^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} d^{2}} + \frac{i b c {G_{6, 6}^{2, 6}\left(\begin{matrix} -1, - \frac{3}{4}, - \frac{1}{2}, - \frac{1}{4}, 0, 1 &  \\- \frac{3}{4}, - \frac{1}{4} & -1, - \frac{1}{2}, - \frac{1}{2}, 0 \end{matrix} \middle| {\frac{c^{2} e^{2 i \pi}}{d^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} d^{2}}"," ",0,"-a*meijerg(((3/4, 5/4, 1), (1, 1, 3/2)), ((1/2, 3/4, 1, 5/4, 3/2), (0,)), c**2/(d**2*x**2))/(4*pi**(3/2)*c) + I*a*meijerg(((0, 1/4, 1/2, 3/4, 1, 1), ()), ((1/4, 3/4), (0, 1/2, 1/2, 0)), c**2*exp_polar(2*I*pi)/(d**2*x**2))/(4*pi**(3/2)*c) + b*c*meijerg(((-1/4, 1/4), (0, 0, 1/2, 1)), ((-1/2, -1/4, 0, 1/4, 1/2, 0), ()), c**2/(d**2*x**2))/(4*pi**(3/2)*d**2) + I*b*c*meijerg(((-1, -3/4, -1/2, -1/4, 0, 1), ()), ((-3/4, -1/4), (-1, -1/2, -1/2, 0)), c**2*exp_polar(2*I*pi)/(d**2*x**2))/(4*pi**(3/2)*d**2)","C",0
364,1,165,0,36.824587," ","integrate((b*x**2+a)/x**2/(d*x-c)**(1/2)/(d*x+c)**(1/2),x)","- \frac{a d {G_{6, 6}^{5, 3}\left(\begin{matrix} \frac{5}{4}, \frac{7}{4}, 1 & \frac{3}{2}, \frac{3}{2}, 2 \\1, \frac{5}{4}, \frac{3}{2}, \frac{7}{4}, 2 & 0 \end{matrix} \middle| {\frac{c^{2}}{d^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} c^{2}} - \frac{i a d {G_{6, 6}^{2, 6}\left(\begin{matrix} \frac{1}{2}, \frac{3}{4}, 1, \frac{5}{4}, \frac{3}{2}, 1 &  \\\frac{3}{4}, \frac{5}{4} & \frac{1}{2}, 1, 1, 0 \end{matrix} \middle| {\frac{c^{2} e^{2 i \pi}}{d^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} c^{2}} + \frac{b {G_{6, 6}^{6, 2}\left(\begin{matrix} \frac{1}{4}, \frac{3}{4} & \frac{1}{2}, \frac{1}{2}, 1, 1 \\0, \frac{1}{4}, \frac{1}{2}, \frac{3}{4}, 1, 0 &  \end{matrix} \middle| {\frac{c^{2}}{d^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} d} - \frac{i b {G_{6, 6}^{2, 6}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4}, 0, \frac{1}{4}, \frac{1}{2}, 1 &  \\- \frac{1}{4}, \frac{1}{4} & - \frac{1}{2}, 0, 0, 0 \end{matrix} \middle| {\frac{c^{2} e^{2 i \pi}}{d^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} d}"," ",0,"-a*d*meijerg(((5/4, 7/4, 1), (3/2, 3/2, 2)), ((1, 5/4, 3/2, 7/4, 2), (0,)), c**2/(d**2*x**2))/(4*pi**(3/2)*c**2) - I*a*d*meijerg(((1/2, 3/4, 1, 5/4, 3/2, 1), ()), ((3/4, 5/4), (1/2, 1, 1, 0)), c**2*exp_polar(2*I*pi)/(d**2*x**2))/(4*pi**(3/2)*c**2) + b*meijerg(((1/4, 3/4), (1/2, 1/2, 1, 1)), ((0, 1/4, 1/2, 3/4, 1, 0), ()), c**2/(d**2*x**2))/(4*pi**(3/2)*d) - I*b*meijerg(((-1/2, -1/4, 0, 1/4, 1/2, 1), ()), ((-1/4, 1/4), (-1/2, 0, 0, 0)), c**2*exp_polar(2*I*pi)/(d**2*x**2))/(4*pi**(3/2)*d)","C",0
365,1,162,0,69.668606," ","integrate((b*x**2+a)/x**3/(d*x-c)**(1/2)/(d*x+c)**(1/2),x)","- \frac{a d^{2} {G_{6, 6}^{5, 3}\left(\begin{matrix} \frac{7}{4}, \frac{9}{4}, 1 & 2, 2, \frac{5}{2} \\\frac{3}{2}, \frac{7}{4}, 2, \frac{9}{4}, \frac{5}{2} & 0 \end{matrix} \middle| {\frac{c^{2}}{d^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} c^{3}} + \frac{i a d^{2} {G_{6, 6}^{2, 6}\left(\begin{matrix} 1, \frac{5}{4}, \frac{3}{2}, \frac{7}{4}, 2, 1 &  \\\frac{5}{4}, \frac{7}{4} & 1, \frac{3}{2}, \frac{3}{2}, 0 \end{matrix} \middle| {\frac{c^{2} e^{2 i \pi}}{d^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} c^{3}} - \frac{b {G_{6, 6}^{5, 3}\left(\begin{matrix} \frac{3}{4}, \frac{5}{4}, 1 & 1, 1, \frac{3}{2} \\\frac{1}{2}, \frac{3}{4}, 1, \frac{5}{4}, \frac{3}{2} & 0 \end{matrix} \middle| {\frac{c^{2}}{d^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} c} + \frac{i b {G_{6, 6}^{2, 6}\left(\begin{matrix} 0, \frac{1}{4}, \frac{1}{2}, \frac{3}{4}, 1, 1 &  \\\frac{1}{4}, \frac{3}{4} & 0, \frac{1}{2}, \frac{1}{2}, 0 \end{matrix} \middle| {\frac{c^{2} e^{2 i \pi}}{d^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} c}"," ",0,"-a*d**2*meijerg(((7/4, 9/4, 1), (2, 2, 5/2)), ((3/2, 7/4, 2, 9/4, 5/2), (0,)), c**2/(d**2*x**2))/(4*pi**(3/2)*c**3) + I*a*d**2*meijerg(((1, 5/4, 3/2, 7/4, 2, 1), ()), ((5/4, 7/4), (1, 3/2, 3/2, 0)), c**2*exp_polar(2*I*pi)/(d**2*x**2))/(4*pi**(3/2)*c**3) - b*meijerg(((3/4, 5/4, 1), (1, 1, 3/2)), ((1/2, 3/4, 1, 5/4, 3/2), (0,)), c**2/(d**2*x**2))/(4*pi**(3/2)*c) + I*b*meijerg(((0, 1/4, 1/2, 3/4, 1, 1), ()), ((1/4, 3/4), (0, 1/2, 1/2, 0)), c**2*exp_polar(2*I*pi)/(d**2*x**2))/(4*pi**(3/2)*c)","C",0
366,1,170,0,70.802382," ","integrate((b*x**2+a)/x**4/(d*x-c)**(1/2)/(d*x+c)**(1/2),x)","- \frac{a d^{3} {G_{6, 6}^{5, 3}\left(\begin{matrix} \frac{9}{4}, \frac{11}{4}, 1 & \frac{5}{2}, \frac{5}{2}, 3 \\2, \frac{9}{4}, \frac{5}{2}, \frac{11}{4}, 3 & 0 \end{matrix} \middle| {\frac{c^{2}}{d^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} c^{4}} - \frac{i a d^{3} {G_{6, 6}^{2, 6}\left(\begin{matrix} \frac{3}{2}, \frac{7}{4}, 2, \frac{9}{4}, \frac{5}{2}, 1 &  \\\frac{7}{4}, \frac{9}{4} & \frac{3}{2}, 2, 2, 0 \end{matrix} \middle| {\frac{c^{2} e^{2 i \pi}}{d^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} c^{4}} - \frac{b d {G_{6, 6}^{5, 3}\left(\begin{matrix} \frac{5}{4}, \frac{7}{4}, 1 & \frac{3}{2}, \frac{3}{2}, 2 \\1, \frac{5}{4}, \frac{3}{2}, \frac{7}{4}, 2 & 0 \end{matrix} \middle| {\frac{c^{2}}{d^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} c^{2}} - \frac{i b d {G_{6, 6}^{2, 6}\left(\begin{matrix} \frac{1}{2}, \frac{3}{4}, 1, \frac{5}{4}, \frac{3}{2}, 1 &  \\\frac{3}{4}, \frac{5}{4} & \frac{1}{2}, 1, 1, 0 \end{matrix} \middle| {\frac{c^{2} e^{2 i \pi}}{d^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} c^{2}}"," ",0,"-a*d**3*meijerg(((9/4, 11/4, 1), (5/2, 5/2, 3)), ((2, 9/4, 5/2, 11/4, 3), (0,)), c**2/(d**2*x**2))/(4*pi**(3/2)*c**4) - I*a*d**3*meijerg(((3/2, 7/4, 2, 9/4, 5/2, 1), ()), ((7/4, 9/4), (3/2, 2, 2, 0)), c**2*exp_polar(2*I*pi)/(d**2*x**2))/(4*pi**(3/2)*c**4) - b*d*meijerg(((5/4, 7/4, 1), (3/2, 3/2, 2)), ((1, 5/4, 3/2, 7/4, 2), (0,)), c**2/(d**2*x**2))/(4*pi**(3/2)*c**2) - I*b*d*meijerg(((1/2, 3/4, 1, 5/4, 3/2, 1), ()), ((3/4, 5/4), (1/2, 1, 1, 0)), c**2*exp_polar(2*I*pi)/(d**2*x**2))/(4*pi**(3/2)*c**2)","C",0
367,-1,0,0,0.000000," ","integrate((b*x**2+a)/x**5/(d*x-c)**(1/2)/(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
368,-1,0,0,0.000000," ","integrate(x**4*(b*x**2+a)/(d*x-c)**(3/2)/(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
369,1,226,0,177.264753," ","integrate(x**3*(b*x**2+a)/(d*x-c)**(3/2)/(d*x+c)**(3/2),x)","a \left(\frac{c {G_{6, 6}^{6, 2}\left(\begin{matrix} - \frac{3}{4}, - \frac{1}{4} & -1, 0, \frac{1}{2}, 1 \\- \frac{3}{4}, - \frac{1}{2}, - \frac{1}{4}, 0, \frac{1}{2}, 0 &  \end{matrix} \middle| {\frac{c^{2}}{d^{2} x^{2}}} \right)}}{2 \pi^{\frac{3}{2}} d^{4}} - \frac{i c {G_{6, 6}^{2, 6}\left(\begin{matrix} -2, - \frac{3}{2}, - \frac{5}{4}, -1, - \frac{3}{4}, 1 &  \\- \frac{5}{4}, - \frac{3}{4} & -2, - \frac{3}{2}, - \frac{1}{2}, 0 \end{matrix} \middle| {\frac{c^{2} e^{2 i \pi}}{d^{2} x^{2}}} \right)}}{2 \pi^{\frac{3}{2}} d^{4}}\right) + b \left(\frac{c^{3} {G_{6, 6}^{6, 2}\left(\begin{matrix} - \frac{7}{4}, - \frac{5}{4} & -2, -1, - \frac{1}{2}, 1 \\- \frac{7}{4}, - \frac{3}{2}, - \frac{5}{4}, -1, - \frac{1}{2}, 0 &  \end{matrix} \middle| {\frac{c^{2}}{d^{2} x^{2}}} \right)}}{2 \pi^{\frac{3}{2}} d^{6}} - \frac{i c^{3} {G_{6, 6}^{2, 6}\left(\begin{matrix} -3, - \frac{5}{2}, - \frac{9}{4}, -2, - \frac{7}{4}, 1 &  \\- \frac{9}{4}, - \frac{7}{4} & -3, - \frac{5}{2}, - \frac{3}{2}, 0 \end{matrix} \middle| {\frac{c^{2} e^{2 i \pi}}{d^{2} x^{2}}} \right)}}{2 \pi^{\frac{3}{2}} d^{6}}\right)"," ",0,"a*(c*meijerg(((-3/4, -1/4), (-1, 0, 1/2, 1)), ((-3/4, -1/2, -1/4, 0, 1/2, 0), ()), c**2/(d**2*x**2))/(2*pi**(3/2)*d**4) - I*c*meijerg(((-2, -3/2, -5/4, -1, -3/4, 1), ()), ((-5/4, -3/4), (-2, -3/2, -1/2, 0)), c**2*exp_polar(2*I*pi)/(d**2*x**2))/(2*pi**(3/2)*d**4)) + b*(c**3*meijerg(((-7/4, -5/4), (-2, -1, -1/2, 1)), ((-7/4, -3/2, -5/4, -1, -1/2, 0), ()), c**2/(d**2*x**2))/(2*pi**(3/2)*d**6) - I*c**3*meijerg(((-3, -5/2, -9/4, -2, -7/4, 1), ()), ((-9/4, -7/4), (-3, -5/2, -3/2, 0)), c**2*exp_polar(2*I*pi)/(d**2*x**2))/(2*pi**(3/2)*d**6))","C",0
370,-1,0,0,0.000000," ","integrate(x**2*(b*x**2+a)/(d*x-c)**(3/2)/(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
371,1,201,0,136.304651," ","integrate(x*(b*x**2+a)/(d*x-c)**(3/2)/(d*x+c)**(3/2),x)","a \left(- \frac{{G_{6, 6}^{5, 3}\left(\begin{matrix} \frac{1}{4}, \frac{3}{4}, 1 & 0, 1, \frac{3}{2} \\\frac{1}{4}, \frac{1}{2}, \frac{3}{4}, 1, \frac{3}{2} & 0 \end{matrix} \middle| {\frac{c^{2}}{d^{2} x^{2}}} \right)}}{2 \pi^{\frac{3}{2}} c d^{2}} - \frac{i {G_{6, 6}^{2, 6}\left(\begin{matrix} -1, - \frac{1}{2}, - \frac{1}{4}, 0, \frac{1}{4}, 1 &  \\- \frac{1}{4}, \frac{1}{4} & -1, - \frac{1}{2}, \frac{1}{2}, 0 \end{matrix} \middle| {\frac{c^{2} e^{2 i \pi}}{d^{2} x^{2}}} \right)}}{2 \pi^{\frac{3}{2}} c d^{2}}\right) + b \left(\frac{c {G_{6, 6}^{6, 2}\left(\begin{matrix} - \frac{3}{4}, - \frac{1}{4} & -1, 0, \frac{1}{2}, 1 \\- \frac{3}{4}, - \frac{1}{2}, - \frac{1}{4}, 0, \frac{1}{2}, 0 &  \end{matrix} \middle| {\frac{c^{2}}{d^{2} x^{2}}} \right)}}{2 \pi^{\frac{3}{2}} d^{4}} - \frac{i c {G_{6, 6}^{2, 6}\left(\begin{matrix} -2, - \frac{3}{2}, - \frac{5}{4}, -1, - \frac{3}{4}, 1 &  \\- \frac{5}{4}, - \frac{3}{4} & -2, - \frac{3}{2}, - \frac{1}{2}, 0 \end{matrix} \middle| {\frac{c^{2} e^{2 i \pi}}{d^{2} x^{2}}} \right)}}{2 \pi^{\frac{3}{2}} d^{4}}\right)"," ",0,"a*(-meijerg(((1/4, 3/4, 1), (0, 1, 3/2)), ((1/4, 1/2, 3/4, 1, 3/2), (0,)), c**2/(d**2*x**2))/(2*pi**(3/2)*c*d**2) - I*meijerg(((-1, -1/2, -1/4, 0, 1/4, 1), ()), ((-1/4, 1/4), (-1, -1/2, 1/2, 0)), c**2*exp_polar(2*I*pi)/(d**2*x**2))/(2*pi**(3/2)*c*d**2)) + b*(c*meijerg(((-3/4, -1/4), (-1, 0, 1/2, 1)), ((-3/4, -1/2, -1/4, 0, 1/2, 0), ()), c**2/(d**2*x**2))/(2*pi**(3/2)*d**4) - I*c*meijerg(((-2, -3/2, -5/4, -1, -3/4, 1), ()), ((-5/4, -3/4), (-2, -3/2, -1/2, 0)), c**2*exp_polar(2*I*pi)/(d**2*x**2))/(2*pi**(3/2)*d**4))","C",0
372,1,182,0,112.360767," ","integrate((b*x**2+a)/(d*x-c)**(3/2)/(d*x+c)**(3/2),x)","a \left(- \frac{{G_{6, 6}^{5, 3}\left(\begin{matrix} \frac{3}{4}, \frac{5}{4}, 1 & \frac{1}{2}, \frac{3}{2}, 2 \\\frac{3}{4}, 1, \frac{5}{4}, \frac{3}{2}, 2 & 0 \end{matrix} \middle| {\frac{c^{2}}{d^{2} x^{2}}} \right)}}{2 \pi^{\frac{3}{2}} c^{2} d} + \frac{i {G_{6, 6}^{2, 6}\left(\begin{matrix} - \frac{1}{2}, 0, \frac{1}{4}, \frac{1}{2}, \frac{3}{4}, 1 &  \\\frac{1}{4}, \frac{3}{4} & - \frac{1}{2}, 0, 1, 0 \end{matrix} \middle| {\frac{c^{2} e^{2 i \pi}}{d^{2} x^{2}}} \right)}}{2 \pi^{\frac{3}{2}} c^{2} d}\right) + b \left(\frac{{G_{6, 6}^{6, 2}\left(\begin{matrix} - \frac{1}{4}, \frac{1}{4} & - \frac{1}{2}, \frac{1}{2}, 1, 1 \\- \frac{1}{4}, 0, \frac{1}{4}, \frac{1}{2}, 1, 0 &  \end{matrix} \middle| {\frac{c^{2}}{d^{2} x^{2}}} \right)}}{2 \pi^{\frac{3}{2}} d^{3}} + \frac{i {G_{6, 6}^{2, 6}\left(\begin{matrix} - \frac{3}{2}, -1, - \frac{3}{4}, - \frac{1}{2}, - \frac{1}{4}, 1 &  \\- \frac{3}{4}, - \frac{1}{4} & - \frac{3}{2}, -1, 0, 0 \end{matrix} \middle| {\frac{c^{2} e^{2 i \pi}}{d^{2} x^{2}}} \right)}}{2 \pi^{\frac{3}{2}} d^{3}}\right)"," ",0,"a*(-meijerg(((3/4, 5/4, 1), (1/2, 3/2, 2)), ((3/4, 1, 5/4, 3/2, 2), (0,)), c**2/(d**2*x**2))/(2*pi**(3/2)*c**2*d) + I*meijerg(((-1/2, 0, 1/4, 1/2, 3/4, 1), ()), ((1/4, 3/4), (-1/2, 0, 1, 0)), c**2*exp_polar(2*I*pi)/(d**2*x**2))/(2*pi**(3/2)*c**2*d)) + b*(meijerg(((-1/4, 1/4), (-1/2, 1/2, 1, 1)), ((-1/4, 0, 1/4, 1/2, 1, 0), ()), c**2/(d**2*x**2))/(2*pi**(3/2)*d**3) + I*meijerg(((-3/2, -1, -3/4, -1/2, -1/4, 1), ()), ((-3/4, -1/4), (-3/2, -1, 0, 0)), c**2*exp_polar(2*I*pi)/(d**2*x**2))/(2*pi**(3/2)*d**3))","C",0
373,1,172,0,136.444931," ","integrate((b*x**2+a)/x/(d*x-c)**(3/2)/(d*x+c)**(3/2),x)","a \left(- \frac{{G_{6, 6}^{5, 3}\left(\begin{matrix} \frac{5}{4}, \frac{7}{4}, 1 & 1, 2, \frac{5}{2} \\\frac{5}{4}, \frac{3}{2}, \frac{7}{4}, 2, \frac{5}{2} & 0 \end{matrix} \middle| {\frac{c^{2}}{d^{2} x^{2}}} \right)}}{2 \pi^{\frac{3}{2}} c^{3}} - \frac{i {G_{6, 6}^{2, 6}\left(\begin{matrix} 0, \frac{1}{2}, \frac{3}{4}, 1, \frac{5}{4}, 1 &  \\\frac{3}{4}, \frac{5}{4} & 0, \frac{1}{2}, \frac{3}{2}, 0 \end{matrix} \middle| {\frac{c^{2} e^{2 i \pi}}{d^{2} x^{2}}} \right)}}{2 \pi^{\frac{3}{2}} c^{3}}\right) + b \left(- \frac{{G_{6, 6}^{5, 3}\left(\begin{matrix} \frac{1}{4}, \frac{3}{4}, 1 & 0, 1, \frac{3}{2} \\\frac{1}{4}, \frac{1}{2}, \frac{3}{4}, 1, \frac{3}{2} & 0 \end{matrix} \middle| {\frac{c^{2}}{d^{2} x^{2}}} \right)}}{2 \pi^{\frac{3}{2}} c d^{2}} - \frac{i {G_{6, 6}^{2, 6}\left(\begin{matrix} -1, - \frac{1}{2}, - \frac{1}{4}, 0, \frac{1}{4}, 1 &  \\- \frac{1}{4}, \frac{1}{4} & -1, - \frac{1}{2}, \frac{1}{2}, 0 \end{matrix} \middle| {\frac{c^{2} e^{2 i \pi}}{d^{2} x^{2}}} \right)}}{2 \pi^{\frac{3}{2}} c d^{2}}\right)"," ",0,"a*(-meijerg(((5/4, 7/4, 1), (1, 2, 5/2)), ((5/4, 3/2, 7/4, 2, 5/2), (0,)), c**2/(d**2*x**2))/(2*pi**(3/2)*c**3) - I*meijerg(((0, 1/2, 3/4, 1, 5/4, 1), ()), ((3/4, 5/4), (0, 1/2, 3/2, 0)), c**2*exp_polar(2*I*pi)/(d**2*x**2))/(2*pi**(3/2)*c**3)) + b*(-meijerg(((1/4, 3/4, 1), (0, 1, 3/2)), ((1/4, 1/2, 3/4, 1, 3/2), (0,)), c**2/(d**2*x**2))/(2*pi**(3/2)*c*d**2) - I*meijerg(((-1, -1/2, -1/4, 0, 1/4, 1), ()), ((-1/4, 1/4), (-1, -1/2, 1/2, 0)), c**2*exp_polar(2*I*pi)/(d**2*x**2))/(2*pi**(3/2)*c*d**2))","C",0
374,1,165,0,136.132616," ","integrate((b*x**2+a)/x**2/(d*x-c)**(3/2)/(d*x+c)**(3/2),x)","a \left(- \frac{d {G_{6, 6}^{5, 3}\left(\begin{matrix} \frac{7}{4}, \frac{9}{4}, 1 & \frac{3}{2}, \frac{5}{2}, 3 \\\frac{7}{4}, 2, \frac{9}{4}, \frac{5}{2}, 3 & 0 \end{matrix} \middle| {\frac{c^{2}}{d^{2} x^{2}}} \right)}}{2 \pi^{\frac{3}{2}} c^{4}} + \frac{i d {G_{6, 6}^{2, 6}\left(\begin{matrix} \frac{1}{2}, 1, \frac{5}{4}, \frac{3}{2}, \frac{7}{4}, 1 &  \\\frac{5}{4}, \frac{7}{4} & \frac{1}{2}, 1, 2, 0 \end{matrix} \middle| {\frac{c^{2} e^{2 i \pi}}{d^{2} x^{2}}} \right)}}{2 \pi^{\frac{3}{2}} c^{4}}\right) + b \left(- \frac{{G_{6, 6}^{5, 3}\left(\begin{matrix} \frac{3}{4}, \frac{5}{4}, 1 & \frac{1}{2}, \frac{3}{2}, 2 \\\frac{3}{4}, 1, \frac{5}{4}, \frac{3}{2}, 2 & 0 \end{matrix} \middle| {\frac{c^{2}}{d^{2} x^{2}}} \right)}}{2 \pi^{\frac{3}{2}} c^{2} d} + \frac{i {G_{6, 6}^{2, 6}\left(\begin{matrix} - \frac{1}{2}, 0, \frac{1}{4}, \frac{1}{2}, \frac{3}{4}, 1 &  \\\frac{1}{4}, \frac{3}{4} & - \frac{1}{2}, 0, 1, 0 \end{matrix} \middle| {\frac{c^{2} e^{2 i \pi}}{d^{2} x^{2}}} \right)}}{2 \pi^{\frac{3}{2}} c^{2} d}\right)"," ",0,"a*(-d*meijerg(((7/4, 9/4, 1), (3/2, 5/2, 3)), ((7/4, 2, 9/4, 5/2, 3), (0,)), c**2/(d**2*x**2))/(2*pi**(3/2)*c**4) + I*d*meijerg(((1/2, 1, 5/4, 3/2, 7/4, 1), ()), ((5/4, 7/4), (1/2, 1, 2, 0)), c**2*exp_polar(2*I*pi)/(d**2*x**2))/(2*pi**(3/2)*c**4)) + b*(-meijerg(((3/4, 5/4, 1), (1/2, 3/2, 2)), ((3/4, 1, 5/4, 3/2, 2), (0,)), c**2/(d**2*x**2))/(2*pi**(3/2)*c**2*d) + I*meijerg(((-1/2, 0, 1/4, 1/2, 3/4, 1), ()), ((1/4, 3/4), (-1/2, 0, 1, 0)), c**2*exp_polar(2*I*pi)/(d**2*x**2))/(2*pi**(3/2)*c**2*d))","C",0
375,-1,0,0,0.000000," ","integrate((b*x**2+a)/x**3/(d*x-c)**(3/2)/(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
376,-1,0,0,0.000000," ","integrate((b*x**2+a)/x**4/(d*x-c)**(3/2)/(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
377,-1,0,0,0.000000," ","integrate((b*x**2+a)/x**5/(d*x-c)**(3/2)/(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
378,1,148,0,30.113529," ","integrate((c**2*x**2+1)/x/(c*x-1)**(1/2)/(c*x+1)**(1/2),x)","\frac{{G_{6, 6}^{6, 2}\left(\begin{matrix} - \frac{1}{4}, \frac{1}{4} & 0, 0, \frac{1}{2}, 1 \\- \frac{1}{2}, - \frac{1}{4}, 0, \frac{1}{4}, \frac{1}{2}, 0 &  \end{matrix} \middle| {\frac{1}{c^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}}} - \frac{{G_{6, 6}^{5, 3}\left(\begin{matrix} \frac{3}{4}, \frac{5}{4}, 1 & 1, 1, \frac{3}{2} \\\frac{1}{2}, \frac{3}{4}, 1, \frac{5}{4}, \frac{3}{2} & 0 \end{matrix} \middle| {\frac{1}{c^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}}} + \frac{i {G_{6, 6}^{2, 6}\left(\begin{matrix} -1, - \frac{3}{4}, - \frac{1}{2}, - \frac{1}{4}, 0, 1 &  \\- \frac{3}{4}, - \frac{1}{4} & -1, - \frac{1}{2}, - \frac{1}{2}, 0 \end{matrix} \middle| {\frac{e^{2 i \pi}}{c^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}}} + \frac{i {G_{6, 6}^{2, 6}\left(\begin{matrix} 0, \frac{1}{4}, \frac{1}{2}, \frac{3}{4}, 1, 1 &  \\\frac{1}{4}, \frac{3}{4} & 0, \frac{1}{2}, \frac{1}{2}, 0 \end{matrix} \middle| {\frac{e^{2 i \pi}}{c^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}}}"," ",0,"meijerg(((-1/4, 1/4), (0, 0, 1/2, 1)), ((-1/2, -1/4, 0, 1/4, 1/2, 0), ()), 1/(c**2*x**2))/(4*pi**(3/2)) - meijerg(((3/4, 5/4, 1), (1, 1, 3/2)), ((1/2, 3/4, 1, 5/4, 3/2), (0,)), 1/(c**2*x**2))/(4*pi**(3/2)) + I*meijerg(((-1, -3/4, -1/2, -1/4, 0, 1), ()), ((-3/4, -1/4), (-1, -1/2, -1/2, 0)), exp_polar(2*I*pi)/(c**2*x**2))/(4*pi**(3/2)) + I*meijerg(((0, 1/4, 1/2, 3/4, 1, 1), ()), ((1/4, 3/4), (0, 1/2, 1/2, 0)), exp_polar(2*I*pi)/(c**2*x**2))/(4*pi**(3/2))","C",0
379,-1,0,0,0.000000," ","integrate((d*x**2+c)/(x**((a**2*d+2*b**2*c)/(a**2*d+b**2*c)))/(b*x-a)**(1/2)/(b*x+a)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
380,0,0,0,0.000000," ","integrate(1/(1+x)**(1/2)/(-1-x**(1/2))**(1/2)/(-1+x**(1/2))**(1/2),x)","\int \frac{1}{\sqrt{- \sqrt{x} - 1} \sqrt{\sqrt{x} - 1} \sqrt{x + 1}}\, dx"," ",0,"Integral(1/(sqrt(-sqrt(x) - 1)*sqrt(sqrt(x) - 1)*sqrt(x + 1)), x)","F",0
381,0,0,0,0.000000," ","integrate(1/(b**2*x+a**2)**(1/2)/(a-b*x**(1/2))**(1/2)/(a+b*x**(1/2))**(1/2),x)","\int \frac{1}{\sqrt{a - b \sqrt{x}} \sqrt{a + b \sqrt{x}} \sqrt{a^{2} + b^{2} x}}\, dx"," ",0,"Integral(1/(sqrt(a - b*sqrt(x))*sqrt(a + b*sqrt(x))*sqrt(a**2 + b**2*x)), x)","F",0
382,-1,0,0,0.000000," ","integrate((a-b*x**n)**p*(a+b*x**n)**p*(c+d*x**(2*n))**q,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
383,-1,0,0,0.000000," ","integrate((a-b*x**n)**p*(a+b*x**n)**p*(a**2+b**2*x**(2*n))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
384,-2,0,0,0.000000," ","integrate((c+d*x**(2*n))**p/(a-b*x**n)/(a+b*x**n),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
385,-1,0,0,0.000000," ","integrate((a-b*x**(1/2*n))**p*(a+b*x**(1/2*n))**p*(a**2*d*(1+p)/b**2/(1+(-n*p-2*n-1)/n)+d*x**n)**((-n*p-2*n-1)/n),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
